MANUAL
OF STEEL
CONSTRUCTION
LOAD &
RESISTANCE
FACTOR
DESIGN
Volume I
Structural Members,
Specifications,
& Codes
Volume II
Connections
Second Edition
iv
Copyright © 1994
by
American Institute of Steel Construction, Inc.
ISBN 1-56424-041-X
ISBN 1-56424-042-8
All rights reserved. This book or any part thereof
must not be reproduced in any form without the
written permission of the publisher.
The information presented in this publication has been
prepared in accordance with recognized engineering
principles and is for general information only. While it is
believed to be accurate, this information should not be
used or relied upon for any specific application without
competent professional examination and verification of
its accuracy, suitability, and applicability by a licensed
professional engineer, designer, or architect. The publication of the material contained herein is not intended as a
representation or warranty on the part of the American
Institute of Steel Construction or of any other person
named herein, that this information is suitable for any
general or particular use or of freedom from infringement
of any patent or patents. Anyone making use of this information assumes all liability arising from such use.
Caution must be exercised when relying upon other specifications and codes developed by other bodies and incorporated by reference herein since such material may be
modified or amended from time to time subsequent to the
printing of this edition. The Institute bears no responsibility for such material other than to refer to it and
incorporate it by reference at the time of the initial publication of this edition.
Printed in the United States of America
v
FOREWORD
T
he American Institute of Steel Construction, founded in 1921, is the non-profit
technical specifying and trade organization for the fabricated structural steel industry in
the United States. Executive and engineering headquarters of AISC are maintained in
Chicago, Illinois.
The Institute is supported by three classes of membership: Active Members totaling
400 companies engaged in the fabrication and erection of structural steel, Associate
Members who are allied product manufacturers, and Professional Members who are
individuals or firms engaged in the practice of architecture or engineering. Professional
members also include architectural and engineering educators. The continuing financial
support and active participation of Active Members in the engineering, research, and
development activities of the Institute make possible the publishing of this Second
Edition of the Load and Resistance Factor Design Manual of Steel Construction.
The Institute’s objectives are to improve and advance the use of fabricated structural
steel through research and engineering studies and to develop the most efficient and
economical design of structures. It also conducts programs to improve product quality.
To accomplish these objectives the Institute publishes manuals, textbooks, specifications, and technical booklets. Best known and most widely used are the Manuals of Steel
Construction, LRFD (Load and Resistance Factor Design) and ASD (Allowable Stress
Design), which hold a highly respected position in engineering literature. Outstanding
among AISC standards are the Specifications for Structural Steel Buildings and the Code
of Standard Practice for Steel Buildings and Bridges.
The Institute also assists designers, contractors, educators, and others by publishing
technical information and timely articles on structural applications through two publications, Engineering Journal and Modern Steel Construction. In addition, public appreciation of aesthetically designed steel structures is encouraged through its award programs:
Prize Bridges, Architectural Awards of Excellence, Steel Bridge Building Competition
for Students, and student scholarships.
Due to the expanded nature of the material, the Second Edition of the LRFD Manual
has been divided into two complementary volumes. Volume I contains the LRFD
Specification and Commentary, tables, and other design information for structural
members. Volume II contains all of the information on connections. Like the LRFD
Specification upon which they are based, both volumes of this LRFD Manual apply to
buildings, not bridges.
The Committee gratefully acknowledges the contributions of Roger L. Brockenbrough, Louis F. Geschwindner, Jr., and Cynthia J. Zahn to this Manual.
By the Committee on Manuals, Textbooks, and Codes,
William A. Thornton, Chairman
Barry L. Barger, Vice Chairman
Horatio Allison
Robert O. Disque
Joseph Dudek
William G. Dyker
Ronald L. Hiatt
David T. Ricker
Abraham J. Rokach
Ted W. Winneberger
Charles J. Carter, Secretary
Mark V. Holland
William C. Minchin
Thomas M. Murray
Heinz J. Pak
Dennis F. Randall
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
vi
REFERENCED SPECIFICATIONS, CODES, AND STANDARDS
Part 6 (Volume I) of this LRFD Manual contains the full text of the following:
American Institute of Steel Construction, Inc. (AISC)
Load and Resistance Factor Design Specification for Structural Steel Buildings,
December 1, 1993
Specification for Load and Resistance Factor Design of Single-Angle Members,
December 1, 1993
Seismic Provisions for Structural Steel Buildings, June 15, 1992
Code of Standard Practice for Steel Buildings and Bridges, June 10, 1992
Research Council on Structural Connections (RCSC)
Load and Resistance Factor Design Specifications for Structural Joints Using ASTM
A325 or A490 Bolts, June 8, 1988
Additionally, the following other documents are referenced in Volumes I and II of the
LRFD Manual:
American Association of State Highway and Transportation Officials (AASHTO)
AASHTO/AWS D1.5–88
American Concrete Institute (ACI)
ACI 349–90
American Iron and Steel Institute (AISI)
Load and Resistance Factor Design Specification for Cold-Formed Steel Structural
Members, 1991
American National Standards Institute (ANSI)
ANSI/ASME B1.1–82
ANSI/ASME B18.2.2–86
ANSI/ASME B18.1–72 ANSI/ASME B18.5–78
ANSI/ASME B18.2.1–81
American Society of Civil Engineers (ASCE)
ASCE 7-88
American Society for Testing and Materials (ASTM)
ASTM A6–91b
ASTM A490–91
ASTM A617–92
ASTM A27–87
ASTM A500–90a
ASTM A618–90a
ASTM A36–91
ASTM A501–89
ASTM A668–85a
ASTM A53–88
ASTM A502–91
ASTM A687–89
ASTM A148–84
ASTM A514–91
ASTM A709–91
ASTM A153–82
ASTM A529–89
ASTM A770–86
ASTM A193–91
ASTM A563–91c
ASTM A852–91
ASTM A194–91
ASTM A570–91
ASTM B695–91
ASTM A208(A239–89) ASTM A572–91
ASTM C33–90
ASTM A242–91a
ASTM A588–91a
ASTM C330–89
ASTM A307–91
ASTM A606–91a
ASTM E119–88
ASTM A325–91c
ASTM A607–91
ASTM E380–91
ASTM A354–91
ASTM A615–92b
ASTM F436–91
ASTM A449–91a
ASTM A616–92
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
vii
American Welding Society (AWS)
AWS A2.4–93
AWS A5.25–91
AWS A5.1–91
AWS A5.28–79
AWS A5.5–81
AWS A5.29–80
AWS A5.17–89
AWS B1.0–77
AWS A5.18–79
AWS D1.1–92
AWS A5.20–79
AWS D1.4–92
AWS A5.23–90
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1-1
PART 1
DIMENSIONS AND PROPERTIES
OVERVIEW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-3
STRUCTURAL STEELS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-5
Availability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-5
Selection of the Appropriate Structural Steel . . . . . . . . . . . . . . . . . . . . . . . . . 1-5
Brittle Fracture Considerations in Structural Design . . . . . . . . . . . . . . . . . . . . . 1-6
Lamellar Tearing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-8
Jumbo Shapes and Heavy-Welded Built-Up Sections . . . . . . . . . . . . . . . . . . . . 1-8
FIRE-RESISTANT CONSTRUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-8
Effect of Shop Painting on Spray-Applied Fireproofing . . . . . . . . . . . . . . . . . . 1-11
EFFECT OF HEAT ON STRUCTURAL STEEL . . . . . . . . . . . . . . . . . . . . . . 1-11
Coefficient of Expansion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-12
Use of Heat to Straighten, Camber, or Curve Members . . . . . . . . . . . . . . . . . . 1-12
EXPANSION JOINTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-13
COMPUTER SOFTWARE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-14
AISC Database . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-14
AISC for AutoCAD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-14
STRUCTURAL SHAPES: TABLES OF AVAILABILITY, SIZE GROUPINGS,
PRINCIPAL PRODUCERS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-15
STEEL PIPE AND STRUCTURAL TUBING: TABLES OF AVAILABILITY,
PRINCIPAL PRODUCERS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-21
STRUCTURAL SHAPES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-25
Designations, Dimensions, and Properties . . . . . . . . . . . . . . . . . . . . . . . . . 1-25
Tables:
W Shapes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-26
M Shapes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-44
S Shapes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-46
HP Shapes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-48
American Standard Channels (C) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-50
Miscellaneous Channels (MC) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-52
Angles (L) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-56
STRUCTURAL TEES (WT, MT, ST) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-67
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1-2
DIMENSIONS AND PROPERTIES
Use of Table . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-67
DOUBLE ANGLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-91
Use of Table . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-91
COMBINATION SECTIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-105
STEEL PIPE AND STRUCTURAL TUBING . . . . . . . . . . . . . . . . . . . . . . . 1-120
General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-120
Steel Pipe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-120
Structural Tubing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-120
BARS AND PLATES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-133
Product Availability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-133
Classification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-133
Bars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-133
Plates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-133
Floor Plates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-134
CRANE RAILS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-139
General Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-139
Splices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-139
Welded Splices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-141
Fastenings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-141
TORSION PROPERTIES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-145
SURFACE AREAS AND BOX AREAS . . . . . . . . . . . . . . . . . . . . . . . . . . 1-175
CAMBER . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-179
Beams and Girders . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-179
Trusses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-179
STANDARD MILL PRACTICE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-183
General Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-183
Methods of Increasing Areas and Weights by Spreading Rolls
. . . . . . . . . . . . . 1-183
Cambering of Rolled Beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-185
REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-199
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
OVERVIEW
1-3
OVERVIEW
To facilitate reference to Part 1, the locations of frequently used tables are listed below.
Dimensions and Properties
W Shapes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-26
M Shapes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-44
S Shapes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-46
HP Shapes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-48
American Standard Channels (C) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-50
Miscellaneous Channels (MC) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-52
Angles (L) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-56
Structural Tees (WT, MT, ST) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-68
Double Angles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-92
Combination Sections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-106
Steel Pipe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-121
Structural Tubing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-122
Torsion Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-146
Surface Areas and Box Areas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-175
Availability
Availability of Shapes, Plates, and Bars, Table 1-1 . . . . . . . . . . . . . . . . . . . . 1-15
Structural Shape Size Groupings, Table 1-2 . . . . . . . . . . . . . . . . . . . . . . . . 1-16
Principal Producers of Structural Shapes, Table 1-3 . . . . . . . . . . . . . . . . . . . . 1-18
Availability of Steel Pipe and Structural Tubing, Table 1-4 . . . . . . . . . . . . . . . . 1-21
Principal Producers of Structural Tubing (TS), Table 1-5 . . . . . . . . . . . . . . . . . 1-22
Principal Producers of Steel Tubing (Round), Table 1-6 . . . . . . . . . . . . . . . . . . 1-26
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1-4
DIMENSIONS AND PROPERTIES
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
STRUCTURAL STEELS
1-5
STRUCTURAL STEELS
Availability
Section A3.1 of the AISC Load and Resistance Factor Design Specification for Structural
Steel Buildings lists fifteen ASTM specifications for structural steel approved for use in
building construction.
Five of these steels are available in hot-rolled structural shapes, plates, and bars. Two
steels, ASTM A514 and A852, are available only in plates. Table 1-1 shows five groups
of shapes and eleven ranges of thickness of plates and bars available in the various
minimum yield stress* and tensile strength levels afforded by the seven steels. For
complete information on each steel, reference should be made to the appropriate ASTM
specification. A listing of shape sizes included in each of the five groups follows in
Table 1-2, corresponding with the groupings given in Table A of ASTM Specification A6.
Seven additional grades of steel, other than those covering hot-rolled shapes, plates,
and bars, are listed in Section A3.1a of the LRFD Specification. These steels cover pipe,
cold- and hot-formed tubing, and cold- and hot-rolled sheet and strip.
The principal producers of shapes listed in Part 1 of this Manual are shown in Table 1-3.
Availability and the principal producers of structural tubing are shown in Tables 1-4
through 1-6. For additional information on availability and classification of structural
steel plates and bars, refer to the separate discussion beginning on page 1-129.
Space does not permit inclusion in Table 1-3, or in the listing of shapes and plates in
Part 1 of this Manual, of all rolled shapes or plates of greater thickness that are
occasionally used in construction. For such products, reference should be made to the
various producers’ catalogs.
To obtain an economical structure, it is often advantageous to minimize the number of
different sections. Cost per square foot can often be reduced by designing this way.
Selection of the Appropriate Structural Steel
Steels with 50 ksi yield stress are now widely used in construction, replacing ASTM A36
steel in many applications. The 50 ksi steels listed in Section A3.1a of the LRFD
Specification are ASTM A572 high-strength low-alloy structural steel, ASTM A242 and
A588 atmospheric-corrosion-resistant high-strength low-alloy structural steels, and
ASTM A529 high-strength carbon-manganese structural steel. Yield stresses above 50
ksi can be obtained from two grades of ASTM A572 steel as well as ASTM A514 and
A852 quenched and tempered structural steel plate. These higher-strength steels have
certain advantages over 50 ksi steels in certain applications. They may be economical
choices where lighter members, resulting from use of higher design strengths, are not
penalized because of instability, local buckling, deflection, or other similar reasons. They
may be used in tension members, beams in continuous and composite construction where
deflections can be minimized, and columns having low slenderness ratios. The reduction
of dead load and associated savings in shipping costs can be significant factors. However,
higher strength steels are not to be used indiscriminately. Effective use of all steels
depends on thorough cost and engineering analysis. Normally, connection material is
specified as ASTM A36. The connection tables in this Manual are for A36 steel.
*As used in the AISC LRFD Specification, “yield stress” denotes either the specified minimum yield point (for those that
have a yield point) or specified minimum yield strength (for those steels that do not have a yield point).
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1-6
DIMENSIONS AND PROPERTIES
With appropriate procedures and precautions, all steels listed in the AISC Specification
are suitable for welded fabrication. To provide for weldability of ASTM A529 steel, the
specification of a maximum carbon equivalent is recommended.
ASTM A242 and A588 atmospheric-corrosion-resistant, high-strength, low-alloy
steels can be used in the bare (uncoated) condition in most atmospheres. Where boldly
exposed under such conditions, exposure to the normal atmosphere causes a tightly
adherent oxide to form on the surface which protects the steel from further atmospheric
corrosion. To achieve the benefits of the enhanced atmospheric corrosion resistance of
these bare steels, it is necessary that design, detailing, fabrication, erection, and maintenance practices proper for such steels be observed. Designers should consult with the
steel producers on the atmospheric-corrosion-resistant properties and limitations of these
steels prior to use in the bare condition. When either A242 or A588 steel is used in the
coated condition, the coating life is typically longer than with other steels. Although A242
and A588 steels are more expensive than other high-strength, low-alloy steels, the
reduction in maintenance resulting from the use of these steels usually offsets their higher
initial cost.
Brittle Fracture Considerations in Structural Design
As the temperature decreases, an increase is generally noted in the yield stress, tensile
strength, modulus of elasticity, and fatigue strength of the structural steels. In contrast,
the ductility of these steels, as measured by reduction in area or by elongation, and the
toughness of these steels, as determined from a Charpy V-notch impact test, decrease
with decreasing temperatures. Furthermore, there is a temperature below which a
structural steel subjected to tensile stresses may fracture by cleavage,* with little or no
plastic deformation, rather than by shear,* which is usually preceded by a considerable
amount of plastic deformation or yielding.
Fracture that occurs by cleavage at a nominal tensile stress below the yield stress is
commonly referred to as brittle fracture. Generally, a brittle fracture can occur in a
structural steel when there is a sufficiently adverse combination of tensile stress, temperature, strain rate, and geometrical discontinuity (notch) present. Other design and
fabrication factors may also have an important influence. Because of the interrelation of
these effects, the exact combination of stress, temperature, notch, and other conditions
that will cause brittle fracture in a given structure cannot be readily calculated. Consequently, designing against brittle fracture often consists mainly of (1) avoiding conditions
that tend to cause brittle fracture and (2) selecting a steel appropriate for the application.
A discussion of these factors is given in the following sections.
Conditions Causing Brittle Fracture
It has been established that plastic deformation can occur only in the presence of shear
stresses. Shear stresses are always present in a uniaxial or biaxial state-of-stress. However, in a triaxial state-of-stress, the maximum shear stress approaches zero as the
principal stresses approach a common value, and thus, under equal triaxial tensile
stresses, failure occurs by cleavage rather than by shear. Consequently, triaxial tensile
stresses tend to cause brittle fracture and should be avoided. A triaxial state-of-stress can
result from a uniaxial loading when notches or geometrical discontinuities are present.
*Shear and cleavage are used in the metallurgical sense (macroscopically) to denote different fracture mechanisms.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
STRUCTURAL STEELS
1-7
Increased strain rates tend to increase the possibility of brittle behavior. Thus, structures
that are loaded at fast rates are more susceptible to brittle fracture. However, a rapid strain
rate or impact load is not a required condition for a brittle fracture.
Cold work and the strain aging that normally follows generally increase the likelihood
of brittle fracture. This behavior is usually attributed to the previously mentioned
reduction in ductility. The effect of cold work that occurs in cold forming operations can
be minimized by selecting a generous forming radius and, thus, limiting the amount of
strain. The amount of strain that can be tolerated depends on both the steel and the
application.
The use of welding in construction increases the concerns relative to brittle fracture.
In the as-welded condition, residual stresses will be present in any weldment. These
stresses are considered to be at the yield point of the material. To avoid brittle fracture,
it may be required to utilize steels with higher toughness than would be required for bolted
construction. Welds may also introduce geometric conditions or discontinuities that are
crack-like in nature. These stress risers will additionally increase the requirement for
notch toughness in the weldment. Avoidance of the intersection of welds from multiple
directions reduces the likelihood of triaxial stresses. Properly sized weld-access holes
prohibit the interaction of these various stress fields. As steels being welded become
thicker and more highly restrained, welding procedure issues such as preheat, interpass
temperature, heat input, and cooling rates become increasingly important. The residual
stresses present in a weldment may be reduced by the use of fewer weld passes and
peening of intermittent weld layers. In most cases, weld metal notch toughness exceeds
that of the base materials. However, for fracture-sensitive applications, notch-tough base
and weld metal should be specified.
The residual stresses of welding can be greatly reduced through thermal stress relief.
This reduces the driving force that causes brittle fracture, but if the toughness of the
material is adversely affected by this thermal treatment, no increase in brittle fracture
resistance will be experienced. Therefore, when weldments are to be stress relieved,
investigation into the effects on the weld metal, heat-affected zone, and base material
should be made.
Selecting a Steel To Avoid Brittle Fracture
The best guide in selecting a steel that is appropriate for a given application is
experience with existing and past structures. A36 and Grade 50 (i.e., 50 ksi yield
stress) steels have been used successfully in a great number of applications, such as
buildings, transmission towers, transportation equipment, and bridges, even at the
lowest atmospheric temperatures encountered in the U.S. Therefore, it appears that
any of the structural steels, when designed and fabricated in an appropriate manner,
could be used for similar applications with little likelihood of brittle fracture.
Consequently, brittle fracture is not usually experienced in such structures unless
unusual temperature, notch, and stress conditions are present. Nevertheless, it is
always desirable to avoid or minimize the previously cited adverse conditions that
increase the susceptibility of the steel to brittle fracture.
In applications where notch toughness is considered important, it usually is required
that steels must absorb a certain amount of energy, 15 ft-lb or higher (Charpy V-notch
test), at a given temperature. The test temperature may be higher than the lowest operating
temperature depending on the rate of loading. See Rolfe and Barsom (1986) and Rolfe
(1977).
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1-8
DIMENSIONS AND PROPERTIES
Lamellar Tearing
The information on strength and ductility presented in the previous sections generally
pertains to loadings applied in the planar direction (longitudinal or transverse orientation)
of the steel plate or shape. It should be noted that elongation and area reduction values
may well be significantly lower in the through-thickness direction than in the planar
direction. This inherent directionality is of small consequence in many applications, but
does become important in the design and fabrication of structures containing massive
members with highly restrained welded joints.
With the increasing trend toward heavy welded-plate construction, there has been a broader
recognition of the occurrence of lamellar tearing in some highly restrained joints of welded
structures, especially those using thick plates and heavy structural shapes. The restraint
induced by some joint designs in resisting weld deposit shrinkage can impose tensile strain
sufficiently high to cause separation or tearing on planes parallel to the rolled surface of the
structural member being joined. The incidence of this phenomenon can be reduced or
eliminated through greater understanding by designers, detailers, and fabricators of (1) the
inherent directionality of construction forms of steel, (2) the high restraint developed in certain
types of connections, and (3) the need to adopt appropriate weld details and welding
procedures with proper weld metal for through-thickness connections. Further, steels can be
specified to be produced by special practices and/or processes to enhance through-thickness
ductility and thus assist in reducing the incidence of lamellar tearing. Steels produced by such
practices are available from several producers. However, unless precautions are taken in both
design and fabrication, lamellar tearing may still occur in thick plates and heavy shapes of
such steels at restrained through-thickness connections. Some guidelines in minimizing
potential problems have been developed (AISC, 1973). See also Part 8 in Volume II of this
LRFD Manual and ASTM A770, Standard Specification for Through-Thickness Tension
Testing of Steel Plates for Special Applications.
Jumbo Shapes and Heavy Welded Built-up Sections
Although Group 4 and 5 W-shapes, commonly referred to as jumbo shapes, generally are
contemplated as columns or compression members, their use in non-column applications
has been increasing. These heavy shapes have been known to exhibit segregation and a
coarse grain structure in the mid-thickness region of the flange and the web. Because
these areas may have low toughness, cracking might occur as a result of thermal cutting
or welding (Fisher and Pense, 1987). Similar problems may also occur in welded built-up
sections. To minimize the potential of brittle failure, the current LRFD Specification
includes provisions for material toughness requirements, methods of splicing, and
fabrication methods for Group 4 and 5 hot-rolled shapes and welded built-up cross
sections with an element of the cross section more than two inches in thickness intended
for tension applications.
FIRE-RESISTANT CONSTRUCTION
Fire-resistant steel construction may be defined as structural members and assemblies
which can maintain structural stability for the duration of building fire exposure and, in
some cases, prevent the spread of fire to adjacent spaces. Fire resistance of a steel member
is a function of its mass, its geometry, the load to which it is subjected, its structural
support conditions, and the fire to which it is exposed.
Many steel structures have inherent fire resistance through a combination of the above
factors and do not require additional insulation from the effects of fire. However, in many
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
FIRE-RESISTANT CONSTRUCTION
1-9
situations, building codes specify the use of fire-rated steel assemblies. In this case,
ASTM Specification E119, Standard Methods of Fire Tests of Building Construction and
Materials, outlines the procedures of fire testing of structural elements.
Structural fire resistance is a major consideration in the design of modern buildings.
In general, building codes define the level of fire protection that is required in specific
applications and structural fire protection is typically implemented in design through
code compliance. In the United States, with a few notable exceptions, the majority of
cities and states now enforce one of the following model codes:
• National Building Code, published by the Building Officials and Code Administrators International.
• Standard Building Code, published by the Southern Building Code Congress International.
• Uniform Building Code, published by the International Conference of Building
Officials.
Building codes specify fire-resistance requirements as a function of building occupancy,
height, area, and whether or not other fire protection systems (e.g., sprinklers) are
provided.
Fire-resistance requirements are specified in terms of hourly ratings based upon tests
conducted in accordance with ASTM E119. This test method specifies a “standard” fire for
evaluating the relative fire-resistance of construction assemblies (i.e., floors, roofs, beams,
girders, and columns). Specific end-point criteria for evaluating the ability of assemblies to
prevent the spread of fire to adjacent spaces and/or to continue to sustain superimposed loads
are included. In effect, ASTM E119 is used to evaluate the length of time that an assembly
continues to perform these functions when exposed to the standard fire. Thus, code requirements and fire-resistance ratings are specified in terms of time (i.e., one hour, two hours, etc.).
The design of fire-resistant buildings is typically accomplished in a very prescriptive fashion
by selecting tested designs that satisfy specific building code requirements. Listings of
fire-resistant designs are available from a number of sources including:
• Fire-Resistance Directory, Underwriters Laboratories.
• Fire-Resistance Ratings, American Insurance Services Group.
• Fire-Resistance Design Manual, Gypsum Association.
In general, due to the very prescriptive nature of fire-resistant design, changes in tested
assemblies can be difficult to justify to the satisfaction of code officials and listing
agencies. In the case of structural steel construction, however, the basic heat transfer and
structural principles are well defined. As a result, relatively simple analytical techniques
have been developed that enable designers to use a variety of different structural steel
shapes in conjunction with tested assemblies. These analytical techniques are specifically
recognized by North American building code authorities and are described in a series of
booklets published by the American Iron and Steel Institute (AISI):
Designing Fire Protection for Steel Columns (1980)
Designing Fire Protection for Steel Beams (1984)
Designing Fire Protection for Steel Trusses (1981)
Since fire-resistant design is currently based on the use of tested assemblies, an
important consideration is the degree to which a test assembly is “representative” of
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1 - 10
DIMENSIONS AND PROPERTIES
actual building construction. In reality, this consideration poses a number of technical
difficulties due to the size of available testing facilities, most of which can only accommodate floor or roof specimens in the range of 15 ft by 18 ft in area. As a result, a test
assembly represents a relatively small sample of a typical floor or roof structure. Most
floor slabs and roof decks are physically, if not structurally, continuous over beams and
girders. Beam and girder spans are often much larger than can be accommodated in
available laboratory furnaces. A variety of connection details are used to frame beams,
girders, and columns. In short, given the cost of testing, the complexity and variety of
modern structural systems, and the size of available test facilities, it is unrealistic to assume
that test assemblies accurately model real construction systems during fire exposure.
In recognition of the practical difficulties associated with laboratory scale testing,
ASTM E119 includes two specific test conditions, “restrained” and “unrestrained.” From
a structural engineering standpoint, the choice of these two terms is unfortunate since the
“restraint” that is contemplated in fire testing is restraint against the thermal expansion,
not structural rotational restraint in the traditional sense. The “restrained” condition
applies when the assembly is supported or surrounded by construction which is “capable
of resisting substantial thermal expansion throughout the range of anticipated elevated
temperatures.” Otherwise, the assembly should be considered free to rotate and expand
at the supports and should be considered “unrestrained.” Thus, a floor system that is
simply supported from a structural standpoint will often be “restrained” from a fireresistance standpoint. In order to provide guidance on the use of restrained and unrestrained ratings, ASTM E119 includes an explanatory Appendix. It should be emphasized
that most common types of steel framing can be considered “restrained” from a fire-resistance standpoint.
The standard fire test also includes other arbitrary assumptions. The specific fire
exposure, for example, is based on furnace capabilities with continuous fuel supply and
does not model real building fires with exhaustible fuel. Also, the test method assumes
that assemblies are fully loaded when a fire occurs. In reality, fires are infrequent, random
events and their design requirements should be probability based. Rarely will design
structural loads occur simultaneously with fire. In addition, many structural elements are
sized for serviceability (i.e., drift, deflection, or vibration) rather than strength, thereby
providing an additional reserve strength during a fire. As a result of these and other
considerations, more rational engineering design standards for structural fire protection
are now being developed (International Fire Engineering Design for Steel Structures:
State-of-the-Art, International Iron and Steel Institute). Although not yet standardized or
recognized in North American building codes, similar design methods have been used in
specific cases, based on code variances.
One such method has been developed by AISI for architecturally exposed structural
steel elements on the exterior of buildings. In effect, ASTM E119 assumes that structural
elements are located within a fire compartment and does not realistically characterize the
fire exposure that will be seen by exterior structural elements. Fire-Safe Structural Steel:
A Design Guide (American Iron and Steel Institute, 1979) defines a step-by-step analytical procedure for determining maximum steel temperatures, based on realistic fire
exposures for exterior structural elements.
Occasionally, structural engineers will be called upon to evaluate fire-damaged steel
structures. Although it is well known that the prolonged exposure to high temperatures
can affect the physical and metallurgical properties of structural steel, in most cases steel
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
EFFECT OF HEAT ON STRUCTURAL STEEL
1 - 11
members that can be straightened in place will be suitable for continued use (Dill, 1960).
Special attention should be given to heat-treated or cold-formed steel elements and
high-strength bolts and welds.
Effect of Shop Painting on Spray-Applied Fireproofing
Spray-applied fireproofing has excellent adhesion to unpainted structural steel. Mechanical anchorage devices, bonding agents, or bond tests are not required to meet Underwriters Laboratories, Inc. (UL) guidelines. In fact, moderate rusting enhances the adhesion
of the fireproofing material, providing the uncoated steel is free of loose rust and mill
scale. Customarily, any loose rust or mill scale as well as any other debris which has
accumulated during the construction process is removed by the fireproofing application
contractor. In many cases, this may be as simple as blowing it off with compressed air.
This ease of application is not realized when fireproofing is applied over painted steel.
In order to meet UL requirements, bond tests in accordance with the ASTM E736 must
be performed to determine if the fireproofing material has adequate adherence to the
painted surface. Frequently, a bonding agent must be added to the fireproofing material
and the bond test repeated to determine if the minimum bond strength can be met. Should
the bond testing still not be satisfactory, mechanical anchorage devices are required to
be applied to the steel before the fireproofing can be applied. The erected steel must still
be cleaned free of any construction debris and scaling or peeling paint before the
fireproofing may be applied.
Once it is determined that the bond tests are adequate, UL guidelines require that if
fireproofing is spray-applied over painted steel, the steel must be wrapped with steel lath
or mechanical anchorage devices must be applied to the steel if the structural shape
exceeds the following dimensional criteria:
• For beam applications, the web depth cannot exceed 16 inches and the flange cannot
exceed 12 inches.
• For column applications, neither the web depth nor the flange width can exceed 16
inches.
A significant number of structural shapes do not meet these restrictions.
The use of primers under spray-applied fireproofing significantly increases the cost of
the steel and the preparation for and the application of the fireproofing material. In an
enclosed structure, primer is insignificant in either the short- or long-term protection of
the steel. LRFD Specification Section M3.1 states that structural steelwork need not be
painted unless required by the contract. For many years, the AISC specifications have
not required that steelwork be painted when it will be concealed by interior building finish
or will be in contact with concrete. The use of primers under spray-applied fireproofing
is strongly discouraged unless there is a compelling reason to paint the steel to protect
against corrosion.
It is suggested that the designer refer to the UL Directory Fire Resistance—Volume 1,
1993, “Coating Materials,” for more specific information on this topic.
EFFECT OF HEAT ON STRUCTURAL STEEL
Short-time elevated-temperature tensile tests on the structural steels permitted by the
AISC Specification indicate that the ratios of the elevated-temperature yield and tensile
strengths to their respective room-temperature values are reasonably similar in the 300°
to 700°F range, except for variations due to strain aging. (The tensile strength ratio may
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1 - 12
DIMENSIONS AND PROPERTIES
increase to a value greater than unity in the 300° to 700°F range when strain aging occurs.)
Below 700°F the strength ratios decrease only slightly. Above 700°F the ratio of
elevated-temperature to room-temperature strength decreases more rapidly as the temperature increases.
The composition of the steels is usually such that the carbon steels (ASTM A36 and
A529) exhibit strain aging with attendant reduced notch toughness. The high-strength
low-alloy steels (ASTM A242, A572, and A588) and heat-treated alloy steels (ASTM
A514 and A852) exhibit less-pronounced or little strain aging. As examples of the
decreased ratio levels obtained at elevated temperature, the yield strength ratios for
carbon and high-strength low-alloy steels are approximately 0.77 at 800°F, 0.63 at
1,000°F, and 0.37 at 1,200°F.
Coefficient of Expansion
The average coefficient of expansion for structural steel between 70°F and 100°F is
0.0000065 for each degree. For temperatures of 100°F to 1,200°F the coefficient is given
by the approximate formula:
ε = (6.1+0.0019t) × 10−6
in which ε is the coefficient of expansion (change in length per unit length) for each
degree Fahrenheit and t is the temperature in degrees Fahrenheit. The modulus of
elasticity of structural steel is approximately 29,000 ksi at 70°F. It decreases linearly to
about 25,000 ksi at 900°F, and then begins to drop at an increasing rate at higher
temperatures.
Use of Heat to Straighten, Camber, or Curve Members
With modern fabrication techniques, a controlled application of heat can be effectively
used to either straighten or to intentionally curve structural members. By this process,
the member is rapidly heated in selected areas; the heated areas tend to expand, but are
restrained by adjacent cooler areas. This action causes a permanent plastic deformation
or “upset” of the heated areas and, thus, a change of shape is developed in the cooled
member.
“Heat straightening” is used in both normal shop fabrication operations and in the field
to remove relatively severe accidental bends in members. Conversely, “heat cambering”
and “heat curving” of either rolled beams or welded girders are examples of the use of
heat to effect a desired curvature.
As with many other fabrication operations, the use of heat to straighten or curve will
cause residual stresses in the member as a result of plastic deformations. These stresses
are similar to those that develop in rolled structural shapes as they cool from the rolling
temperature; in this case, the stresses arise because all parts of the shape do not cool at
the same rate. In like manner, welded members develop residual stresses from the
localized heat of welding.
In general, the residual stresses from heating operations do not affect the ultimate
strength of structural members. Any reduction in strength due to residual stresses is
incorporated in the provisions of the LRFD Specification.
The mechanical properties of steels are largely unaffected by heating operations,
provided that the maximum temperature does not exceed 1,100°F for quenched and
tempered alloy steels (ASTM A514 and A852), and 1,300°F for other steels. The
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
EXPANSION JOINTS
1 - 13
temperature should be carefully checked by temperature-indicating crayons or other
suitable means during the heating process.
EXPANSION JOINTS
Although buildings are typically constructed of flexible materials, expansion joints are
required in roofs and the supporting structure when horizontal dimensions are large. The
maximum distance between expansion joints is dependent upon many variables including
ambient temperature during construction and the expected temperature range during the
lifetime of the building. An excellent reference on the topic of thermal expansion in
buildings and location of expansion joints is the Federal Construction Council’s Technical
Report No. 65, Expansion Joints in Buildings.
Taken from this report, Figure 1-1 provides a guide based on design temperature
change for maximum spacing of structural expansion joints in beam-and-column-framed
buildings with hinged-column bases and heated interiors. The report includes data for
numerous cities and gives five modification factors which should be applied as
appropriate:
MAXIMUM SPACING OF EXPANSION JOINTS (ft)
1. If the building will be heated only and will have hinged-column bases, use the
maximum spacing as specified;
2. If the building will be air-conditioned as well as heated, increase the maximum
spacing by 15 percent provided the environmental control system will run continuously;
3. If the building will be unheated, decrease the maximum spacing by 33 percent;
4. If the building will have fixed column bases, decrease the maximum spacing by 15
percent;
600
500
Rectangular
multiframed
configuration with
Symmetrical stiffness
400
Steel
300
200
Nonrectangular configuration
(L, T, U type)
Any
material
100
10 20 30 40
50 60 70 70 80 90
DESIGN TEMPERATURE CHANGE (°F)
Fig. 1-1. Expansion joint spacing.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1 - 14
DIMENSIONS AND PROPERTIES
5. If the building will have substantially greater stiffness against lateral displacement
in one of the plan dimensions, decrease the maximum spacing by 25 percent.
When more than one of these design conditions prevail in a building, the percentile
factor to be applied should be the algebraic sum of the adjustment factors of all the various
applicable conditions.
Additionally, most building codes include restrictions on location and spacing of fire
walls. Such fire walls often become locations for expansion joints.
The most effective expansion joint is a double line of columns which provides a
complete and positive separation. When expansion joints other than the double-column
type are employed, low-friction sliding elements are generally used. Such systems,
however, are never totally free and will induce some level of inherent restraint to
movement.
COMPUTER SOFTWARE
AISC Database
The AISC Database contains the properties and dimensions of structural steel shapes,
corresponding to Part 1 of this LRFD Manual. LRFD-related properties such as X1 and
X2, as well as torsional properties, are included.
Two versions, one in U.S. customary units and one in metric units, are available.
Dimensions and properties of W, S, M, and HP shapes, American Standard Channels
(C), Miscellaneous Channels (MC), Structural Tees cut from W, M, and S shapes (WT,
MT, ST), Single and Double Angles, Structural Tubing, and Pipe are listed in ASCII
format. Also included are: a BASIC read/write program, a sample search routine, and a
routine to convert the file to Lotus *.PRN file format.
AISC for AutoCAD *
The program will draw the end, elevation, and plan views of W, S, M, and HP shapes,
American Standard Channels (C), Miscellaneous Channels (MC), Structural Tees cut
from W, M, and S shapes (WT, MT, ST), Single and Double Angles, Structural Tubing,
and Pipe to full scale corresponding to data published in Part 1 of this LRFD Manual.
Version 2.0 runs in AutoCAD Release 12 only; Version 1.0 runs in AutoCAD Releases
10 and 11.
*AutoCAD is a registered trademark in the US Patent and Trademark Office by Autodesk, Inc. AISC for AutoCAD is
copyrighted in the US Copyright Office by Bridgefarmer and Associates, Inc.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1 - 15
Table 1-1.
Availability of Shapes, Plates, and Bars According to
ASTM Structural Steel Specifications
Shapes
Fy
Steel
Type
A36
32
58–80
36
58–80c
42
42
60–85
50
50
70–100
42
42
60
50
50
65
60
60
75
65
65
80
A242
42
63
46
67
50
70
HighStrength
Low-alloy
Corrosion
Resistant
Highstrength
Low-alloy
A572 Grade
A529f Grade
Carbon
Group per
Over Over
Mini1⁄ ″
3⁄ ″
ASTM A6
Fu
mum
2
4
ASTM Yield Tensile
To
to
to
a
1⁄ ″
3 ⁄ ″ 11 ⁄ ″
Desig- Stress Stress
2
4
4
b
nation (ksi)
(ksi) 1 2 3 4 5 incl. incl. incl.
A588
42
63
46
67
50
70
Quenched A852e
&
Tempered
Alloy
70
90–110
Quenched A514e
&
Tempered A514e
Low-Alloy
90
100–130
100
110–130
Plates and Bars
Over Over Over Over Over Over Over
11⁄4″ 11⁄2″ 2″ 21⁄2″ 4″
5″
6″
to
to
to
to
to
to
to
11⁄2″ 2″ 21⁄2″ 4″
5″
6″
8″ Over
incl. incl. incl. incl. incl. incl. incl. 8″
d
aMinimum unless a range is shown.
bIncludes bar-size shapes
cFor shapes over 426 lb / ft minimum of 58 ksi only applies.
dPlates to 1 in. thick, 12 in. width; bars to 11⁄ in.
2
ePlates only.
fTo improve the weldability of A529 steel, the specification of a maximum carbon equivalent
(per ASTM Supplementary Requirement S78) is recommended.
Available
Not Available
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1 - 16
DIMENSIONS AND PROPERTIES
Table 1-2.
Structural Shape Size Groupings for Tensile Property Classification
Structural
Shapes
W shapes
Group 1
Group 2
Group 3
W44× 290, 335
Group 4
W24× 55, 62
W44× 230, 262
W21× 44 to 57 incl.
W40× 149 to 264 incl. W40× 431
W18× 35 to 71 incl.
W36× 135 to 210 incl. W40× 277 to 372 incl. W36× 328 to 798 incl.
W16× 26 to 57 incl.
W33× 118 to 152 incl. W36× 230 to 300 incl. W33× 318 to 354 incl.
W14× 22 to 53 incl.
W30× 90 to 211 incl. W33× 169 to 291 incl. W30× 292 to 477 incl.
W12× 14 to 58 incl.
W27× 84 to 178 incl. W30× 235 to 261 incl. W27× 307 to 539 incl.
W10× 12 to 45 incl.
W24× 68 to 162 incl. W27× 194 to 258 incl. W24× 250 to 492 incl.
Group 5
W40×466 to 593 incl. W36× 848
W40× 392
W8× 10 to 48 incl.
W21× 62 to 147 incl. W24× 176 to 229 incl. W18× 211 to 311 incl.
W6× 9 to 25 incl.
W18× 76 to 143 incl. W21× 166 to 201 incl. W14× 233 to 550 incl.
W5× 16,19
W16× 67 to 100 incl. W18× 158 to 192 incl. W12× 210 to 336 incl.
W4× 13
W14× 61 to 132 incl. W14× 145 to 211 incl.
W14× 605 to 808 incl.
W12× 65 to 106 incl. W12× 120 to 190 incl.
W10× 49 to 112 incl.
W8× 58, 67
M Shapes
all
S Shapes
to 35 lb/ft incl.
over 35 lb/ft
HP Shapes
to 102 lb/ft incl.
American
to 20.7 lb/ft incl.
Standard
Channels (C)
over 20.7 lb/ft
Miscellane- to 28.5 lb/ft incl.
ous Channels
(MC)
over 28.5 lb/ft
Angles (L)
to 1⁄2-in. incl.
over 102 lb/ft
over 1⁄2- to 3⁄4-in. incl. over 3⁄4-in.
Notes:
Structural tees from W, M, and S shapes fall into the same group as the structural shapes from which they are cut.
Group 4 and Group 5 shapes are generally contemplated for application as columns or compression components. When used in other applications (e.g., trusses) and when thermal cutting or welding is required, special
material specification and fabrication procedures apply to minimize the possibility of cracking (see Part 6, LRFD
Specification, Sections A3.1c, J1.5, J1.6, J2.3, and M2.2, and corresponding Commentary sections).
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1 - 17
Structural Steel Shape Producers
Bayou Steel Corp.
P.O. Box 5000
Laplace, LA 70068
(800) 535-7692
Florida Steel Corp.
P.O. Box 31328
Tampa, FL 33631
(800) 237-0230
Nucor-Yamato Steel
P.O. Box 1228
Blytheville, AR 72316
(800) 289-6977
Bethlehem Steel Corp.
301 East Third St.
Bethlehem, PA 18016-7699
(800) 633-0482
Northwestern Steel & Wire Co.
121 Wallace St.
P.O. Box 618
Sterling, IL 61081-0618
(800) 793-2200
Roanoke Electric Steel Corp.
P.O. Box 13948
Roanoke, VA 24038
(800) 753-3532
British Steel Inc.
475 N. Martingale Road #400
Schaumburg, IL 60173
(800) 542-6244
North Star Steel Co.
1380 Corporate Center Curve
Suite 215
P.O. Box 21620
Eagan, MN 55121-0620
(800) 328-1944
Chaparral Steel Co.
300 Ward Road
Midlothian, TX 76065-9501
(800) 529-7979
Nucor Steel
P.O. Box 126
Jewett, TX 75846
(800) 527-6445
SMI Steel, Inc.
101 South 50th St.
Birmingham, AL 35232
(800) 621-0262
TradeARBED
825 Third Ave.
New York, NY 10022
(212) 486-9890
Structural Tube Producers
American Institute for Hollow
Structural Sections
929 McLaughlin Run Road
Suite 8
Pittsburgh, PA 15017
(412) 221-8880
Acme Roll Forming Co.
812 North Beck St.
Sebewaing, MI 48759-0706
(800) 937-8823
Dallas Tube & Rollform
P.O. Box 540873
Dallas, TX 75354-0873
(214) 556-0234
Independence Tube Corp.
6226 West 74th St.
Chicago, IL 60638
(708) 496-0380
Eugene Welding Co.
P.O. Box 249
Marysville, MI 48040
(313) 364-7421
IPSCO Steel, Inc.
P.O. Box 1670, Armour Road
Regina, Saskatchewan S4P 3C7
CANADA
(416) 271-2312
EXLTUBE, Inc.
905 Atlantic
North Kansas City, MO 64116
(800) 892-8823
Bull Moose
57540 SR 19 S
P.O. Box B-1027
Elkhart, IN 46515
(800) 348-7460
Hanna Steel Corp.
3812 Commerce Ave.
P.O. Box 558
Fairfield, AL 35064
(800) 633-8252
Copperweld Corp.
7401 South Linder Ave.
Chicago, IL 60638
(800) 327-8823
UNR-Leavitt, Div. of UNR Inc.
1717 West 115th St.
Chicago, IL 60643
(800) 532-8488
Valmont Industries, Inc.
P.O. Box 358
Valley, NE 68064
(800) 825-6668
Welded Tube Co. of America
1855 East 122nd St.
Chicago, IL 60633
(800) 733-5683
Steel Pipe Producers
National Association of Steel Pipe
Distributors, Inc.
12651 Briar Forest Dr., Suite 130
Houston, TX 77077
(713) 531-7473
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1 - 18
DIMENSIONS AND PROPERTIES
Table 1-3.
Principal Producers of Structural Shapes
B—Bethlehem Steel
Corp.
C—Chaparral Steel
F—Florida Steel Corp.
I—British Steel
S—North Star Steel
M—SMI Steel Inc.
T—TradeARBED
N—Nucor-Yamato Steel U—Nucor Steel
R—Roanoke Steel
W—Northwestern Steel
& Wire
Y—Bayou Steel Corp.
Section, Weight per ft
Producer Code
Section, Weight per ft
Producer Code
W44× all
T
W40× 321-593
W40× 297
W40× 278
W40× 277
W40× 264
W40× 249
W40× 235
W40× 215
W40× 211
W40× 199
W40× 183
W40× 174
W40× 149-167
T
N
T
N,T
B,T
N,T
B,T
N,T
B,T
N,T
B,I,N,T
T
B,I,N,T
W24× 103
W24× 84-94
W24× 55-76
B,W
B,I,N,W
B,C,I,N,W
W21× 182-201
W21× 166
W21× 83-147
W21× 44-73
I,W
B,I,W
B,I,N,W
B,C,I,N,W
W18× 258-311
W18× 175-234
W18× 130-158
W18× 76-119
W18× 65-71
W18× 35-60
B
B,W
B,N,W
B,N,W
B,I,N,W
B,C,I,N,W
W36× 439-848
W36× 393
W36× 328-359
W36× 260-300
W36× 256
W36× 245
W36× 232
W36× 135-230
T
B,T
B,I,T
B,I,N,T
B,I
B,I,N,T
B,I
B,I,N,T
W16× 67-100
W16× 57
W16× 26-50
B,N,W
B,I,N,W
B,C,I,N,W
W33× 263-354
W33× 201-241
W33× 169
W33× 118-152
B,T
B,N,T
B,T
B,I,N,T
W30× 391-477
W30× 261-326
W30× 173-235
W30× 148
W30× 99-132
W30× 90
W14× 808
W14× 342-730
W14× 311
W14× 90-283
W14× 82
W14× 74
W14× 61-68
W14× 43-53
W14× 38
W14× 22-34
B
B,I,T
B,I,T,W
B,I,N,T,W
B,N,W
B,C,I,N,W
B,C,N,W
B,C,I,N,W
B,I,N,W
B,C,I,N,W
T
B,T
B,I,N,T
B,I,T
B,I,N,T
B,N
W27× 307-539
W27× 258
W27× 235
W27× 146-217
W27× 129
W27× 84-114
T
N,T
N
B,N,T
B,I,T,W
B,I,N,T,W
W12× 252-336
W12× 210-230
W12× 170-190
W12× 65-152
W12× 50-58
W12× 16-45
W12× 14
B
B,T
B,I,T,W
B,I,N,T,W
B,C,I,N,W
B,C,N,W
B,C,W
W24× 279-492
W24× 250
W24× 229
W24× 207
W24× 192
W24× 104-176
T
B,N,W
B,N,T,W
B,N,W
B,I,N,T,W
B,I,N,T,W
W10× 88-112
W10× 49-77
W10× 33-45
W10× 22-30
W10× 15-19
W10× 12
B,I,N,W
B,C,I,N,W
B,C,N,W
B,C,I,N,W
B,C,I,W
B,C,W
W8× 31-67
W8× 18-28
W8× 15
B,C,I,N,W
B,C,N,W
B,C,W,Y
Notes:
For the most recent list of producers, please see the latest January or July issue of the AISC magazine Modern
Steel Construction.
Maximum lengths of shapes obtained vary with producer, but typically range from 60 ft to 75 ft. Lengths up to
100 ft are available for certain shapes. Please consult individual producers for length requirements.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1 - 19
Table 1-3 (cont.).
Principal Producers of Structural Shapes
B—Bethlehem Steel
Corp.
C—Chaparral Steel
F—Florida Steel Corp.
I—British Steel
S—North Star Steel
M—SMI Steel Inc.
T—TradeARBED
N—Nucor-Yamato Steel U—Nucor Steel
R-Roanoke Steel
W—Northwestern Steel
& Wire
Y—Bayou Steel Corp.
Section, Weight per ft
Producer Code
Section, Weight per ft
Producer Code
W8× 10-13
B,C,M,W,Y
W6× 20-25
W6× 16
W6× 15
W6× 12
W6× 9
B,C,I,N,W
B,C,W,Y
B,C,I,N,W
B,C,W,Y
B,C,N,W,Y
W5× 16-19
B
W4× 13
B,C,M,Y
M12× 10.8-11.8
M10× 8-9
M8× 6.5
M5× 18.9
MC18× 42.7-58
MC13× 31.8-50
MC12× 31-50
MC12× 10.6
MC10× 22-41.1
MC10× 8.4
MC9× 23.9-25.4
MC8× 18.7-22.8
MC8× 8.5
MC7× 19.1-22.7
MC6× 18
MC6× 12-16.3
B,N
B,N
B,N
S,N
B
S
B
B,S
M
B
B
B,S
C
C
C
B
S24× 80-121
S20× 66-96
S18× 54.7-70
S15× 42.9-50
S12× 31.8-50
S10× 25.4-35
S8× 18.4-23
S6× 12.5-17.25
S5× 10
S4× 9.5
S4× 7.7
S3× 7.5
S3× 5.7
B,W
B,W
B,W
B,W
B,W
B,S
B,C,S
C,S,Y
C,Y
C
C,Y
C,Y
C,M,Y
HP14× 73-117
HP12× 53-84
HP10× 42-57
HP8× 36
B,I,N,W
B,I,N,W
B,C,I,N,W
B,C,I,N,W
C15× 33.9-50
C12× 30
C12× 20.7-25
C10× 25-30
C10× 15.3-20
C9× 20
C9× 13.4-15
C8× 18.75
C8× 11.5-13.75
C7× 12.25
C7× 9.8
C6× 13
C6× 10.5
C6× 8.2
C5× 9
C5× 6.7
C4× 5.4-7.25
C3× 6
C3× 4.1-5
Section by Leg Length
& Thickness
Producer Code
L8× 8×
B,N,W
B,W
B,C,S,W
B,S,W
B,C,S,W
B
B,S
S,W,Y
C,M,S,U,W,Y
S,U,W
M,S,U,W
M,S,U,W,Y
C,M,S,U,W,Y
C,F,M,U,W,Y,
M,U,W,Y
F,M,U,W,Y
F,M,U,W,Y
M,U,W,Y
F,M,R,U,W,Y
11 ⁄8
1
7⁄
3⁄
5⁄
9⁄
1⁄
L6× 6×
7⁄
5⁄
9⁄
1⁄
7⁄
3⁄
5⁄
7⁄
3⁄
5⁄
1⁄
7⁄
3⁄
5⁄
L4× 4×
4
8
16
2
1
3⁄
L5× 5×
8
3⁄
5⁄
1⁄
7⁄
3⁄
5⁄
1⁄
8
4
8
16
2
16
8
16
8
4
8
2
16
8
16
4
8
2
16
8
16
4
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
B
B,S
B,S
B,S
B,S
B,S
B,S
B,U,Y
B,U,Y
B,M,U,Y
B,M,U,Y
B,M,U,Y
B,M,S,U,Y
B,M,U,Y
B,M,S,U,Y
M,U,Y
B,U,Y
B,M,U,Y
B,M,U,Y
B,M,U,W,Y
B,M,U,Y
B,M,U,W,Y
B,M,U,W,Y
M,U,Y
M,U,Y
F,M,R,U,W,Y
F,M,U,Y
F,M,R,U,W,Y
F,M,R,U,W,Y
F,M,R,U,W,Y
1 - 20
DIMENSIONS AND PROPERTIES
Table 1-3 (cont.).
Principal Producers of Structural Shapes
B—Bethlehem Steel
Corp.
C—Chaparral Steel
F—Florida Steel Corp.
I—British Steel
S—North Star Steel
M—SMI Steel Inc.
T—TradeARBED
N—Nucor-Yamato Steel U—Nucor Steel
R—Roanoke Steel
W—Northwestern Steel
& Wire
Y—Bayou Steel Corp.
Section by Leg Length
Producer Code
and Thickness
Section by Leg Length
Producer Code
and Thickness
L31 ⁄2 × 31 ⁄2 ×
L6× 31 ⁄2 ×
1⁄
7⁄
3⁄
5⁄
1⁄
L3× 3×
1⁄
7⁄
3⁄
5⁄
1⁄
3⁄
L21 ⁄2 × 21 ⁄2 ×
1⁄
3⁄
5⁄
1⁄
3⁄
L2× 2×
3⁄
5⁄
1⁄
3⁄
1⁄
L8× 6×
7⁄
5⁄
9⁄
1⁄
7⁄
7⁄
5⁄
9⁄
1⁄
7⁄
3⁄
5⁄
1⁄
7⁄
3⁄
L6× 4×
8
16
4
2
16
8
16
4
16
2
8
16
4
16
8
16
4
16
8
8
4
8
16
2
16
1
3⁄
L7× 4×
16
1
3⁄
L8× 4×
2
7⁄
3⁄
5⁄
9⁄
1⁄
7⁄
3⁄
5⁄
8
4
8
16
2
16
4
8
2
16
8
8
4
8
16
2
16
8
16
F,M,R,U,W,Y
U,Y
F,M,R,U,W,Y
F,M,R,U,W,Y
F,M,R,U,W,Y
F,M,U,W,Y
U,Y
F,M,R,S,U,W,Y
F,M,R,S,U,W,Y
F,M,R,S,U,W,Y
F,M,R,U,W,Y
F,U
F,S,U
F,S,U
F,S,U
F,U
F,S,U
F,S,U
F,S,U
F,S,U
F,S,U
B,S
B
B,S
B
B,S
B,S
B,S
B,S
B,S
B,S
B,S
B,S
B,S
B,S
B,Y
B,Y
B,S,Y
B,Y
B,S,Y
B
B,M,S,U,W,Y
B,M,S,U,W,Y
B,M,S,U,W,Y
B,M,S,U,W,Y
B,U,Y
B,M,S,U,W,Y
B,M,S,U,W,Y
1⁄
3⁄
5⁄
L5× 31 ⁄
3⁄
2×
5⁄
1⁄
3⁄
5⁄
1⁄
1⁄
L5× 3×
7⁄
3⁄
5⁄
1⁄
L4× 31 ⁄
1⁄
2×
3⁄
5⁄
1⁄
L4× 3×
5⁄
1⁄
7⁄
3⁄
5⁄
1⁄
L31 ⁄2 × 3×
1⁄
3⁄
5⁄
1⁄
L31 ⁄
2
× 21 ⁄
2×
1⁄
3⁄
1⁄
L3× 21 ⁄2 ×
1⁄
3⁄
5⁄
1⁄
3⁄
L3× 2×
1⁄
3⁄
5⁄
1⁄
3⁄
L21 ⁄
2 × 2×
3⁄
5⁄
1⁄
3⁄
2
8
16
4
8
2
8
16
4
2
16
8
16
4
2
8
16
4
8
2
16
8
16
4
2
8
16
4
2
8
4
2
8
16
4
16
2
8
16
4
16
8
16
4
16
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
M,U,W,Y
B,M,U,W,Y
B,M,U,W,Y
M,U,Y
M,U,Y
M,U,W,Y
M,U,W,Y
M,U,W,Y
M,U,W,Y
F,M,U,W,Y
F,Y
F,M,U,W,Y
F,M,U,W,Y
F,M,U,W,Y
F,M,U,W
F,M,R,U,W
F,M,R,U,W
F,M,R,U,W
M,U,Y
F,M,U,W,Y
U,Y
F,M,R,U,W,Y
F,M,R,U,W,Y
F,M,R,U,W,Y
U,W
M,U,W
M,U,W
M,U,W
U
U
U
U
U,W
U,W,Y
R,U,W
U
F
F,S,U
F,S,U
F,R,S,U
F,R,U
R,S,U
S,U
R,S,U
R,S,U
1 - 21
Table 1-4.
Availability of Steel Pipe and Structural Tubing
According to ASTM Material Specifications
ASTM
Specification
Steel
Fy
Fu
Grade
Minimum
Yield
Stress
(ksi)
Minimum
Tensile
Stress
(ksi)
Shape
Round
Square &
Rectangular
Availability
ElectricResistance
Welded
A53
Type E
B
35
60
Note 3
Seamless
Type S
B
35
60
Note 3
A
33
45
Note 1
B
42
58
Note 1
C
46
62
Note 1
A
39
45
Note 1
B
46
58
Note 2
C
50
62
Note 1
—
36
58
Note 1
I
50
70
Note 1
II
50
70
Note 1
III
50
65
Note 1
Cold
Formed
Hot Formed
HighStrength
Low-Alloy
A500
A501
A618
Notes:
1. Available in mill quantities only; consult with producers.
2. Normally stocked in local steel service centers.
3. Normally stocked by local pipe distributors.
Available
Not Available
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1 - 22
DIMENSIONS AND PROPERTIES
Table 1-5.
Principal Producers of Structural Tubing (TS)
A—Acme Rolling
Forming Co.
B—Bull Moose Tube
Co.
C—Copperweld Corp.
D—Dallas Tube &
I—Independence Tube
Rollform
Corp.
E—Eugene Welding Co. P—IPSCO Steel
H—Hanna Steel Corp.
U—UNR-Leavitt, Div. of
UNR, Inc.
Nominal Size and
Thickness
Producer Code
30× 30× 5⁄8
28× 28× 5⁄8
26× 26× 5⁄8
24× 24× 5⁄8, 1⁄2, 3⁄8
22× 22× 5⁄8, 1⁄2, 3⁄8
20× 20× 5⁄8, 1⁄2, 3⁄8
18× 18× 5⁄8, 1⁄2, 3⁄8
V—Valmont Industries,
Inc.
W—Welded Tube Co. of
America
X—EXLTUBE
Nominal Size and
Thickness
Producer Code
V*
V*
V*
V*
V*
V*
V*
41⁄2× 41⁄2× 3⁄8, 5⁄16
41⁄2× 41⁄2× 1⁄4, 3⁄16
41⁄2× 41⁄2× 1⁄8
I,P,W
A,B,C,D,I,P,W,X
A,B,C,P,I,W
4× 4× 1⁄2
4× 4× 3⁄8, 5⁄16
4× 4× 1⁄4, 3⁄16 , 1⁄8
B,C,P,U,W
A,B,C,D,E,I,P,U,W
A,B,C,D,E,I,P,U,V,W,X
16× 16× 5⁄8
16× 16× 1⁄2, 3⁄8, 5⁄16
V*
V*,W
31⁄2× 31⁄2× 5⁄16
31⁄2× 31⁄2× 1⁄4, 3⁄16 , 1⁄8
I,P,W
A,B,C,D,E,I,P,U,W,X
14× 14× 5⁄8
14× 14× 1⁄2, 3⁄8
14× 14× 5⁄16
V*
V*,W
W
3× 3× 5⁄16
3× 3× 1⁄4, 3⁄16
3× 3× 1⁄8
I,P,W
A,B,C,D,E,I,P,U,W,X
A,B,C,D,E,I,P,U,W
12× 12× 5⁄8
12× 12× 1⁄2, 3⁄8
12× 12× 5⁄16 , 1⁄4
B
B,V*,W
B,W
21⁄2× 21⁄2× 5⁄16
21⁄2× 21⁄2× 1⁄4, 3⁄16
21⁄2× 21⁄2× 1⁄8
I
A,B,C,D,E,I,P,U,V,W,X
A,B,C,D,E,I,P,U,V,W
10× 10× 5⁄8
10× 10× 1⁄2, 3⁄8, 5⁄16 , 1⁄4
10× 10× 3⁄16
B,C
B,C,P,U,W
B,C,P,W
2× 2× 5⁄16
2× 2× 1⁄4
2× 2× 3⁄16 , 1⁄8
I,V
A,B,C,D,I,U,V,W,X
A,B,C,D,E,I,P,U,V,W,X
8× 8× 5⁄8
8× 8× 1⁄2
8× 8× 3⁄8, 5⁄16 , 1⁄4, 3⁄16
B,C
B,C,P,U,W
B,C,D,P,U,W
11⁄2× 11⁄2× 3⁄16
B,E,P,U,V
7× 7× 5⁄8
7× 7× 1⁄2
7× 7× 3⁄8, 5⁄16 , 1⁄4, 3⁄16
B
B,C,P,U,W
B,C,D,P,U,W
30× 24× 1⁄2, 3⁄8, 5⁄16
28× 24× 1⁄2, 3⁄8, 5⁄16
26× 24× 1⁄2, 3⁄8, 5⁄16
24× 22× 1⁄2, 3⁄8, 5⁄16
22× 20× 1⁄2, 3⁄8, 5⁄16
V*
V*
V*
V*
V*
6× 6× 5⁄8
6× 6× 1⁄2
6× 6× 3⁄8, 5⁄16
6× 6× 1⁄4, 3⁄16
6× 6× 1⁄8
B
B,C,P,U,W
B,C,D,I,P,U,W
A,B,C,D,I,P,U,W,X
A,B,C,I,P
20× 18× 1⁄2, 3⁄8, 5⁄16
20× 12× 1⁄2, 3⁄8, 5⁄16
20× 8× 1⁄2, 3⁄8, 5⁄16
20× 4× 1⁄2, 3⁄8, 5⁄16
V*
W
W
W
51⁄2× 51⁄2× 3⁄8, 5⁄16 , 1⁄4, 3⁄16 , 1⁄8,
B,I
18× 12× 1⁄2, 3⁄8, 5⁄16
18× 6× 1⁄2, 3⁄8, 5⁄16
18× 6× 1⁄4
V*
B,W
B
5× 5× 1⁄2
5× 5× 3⁄8, 5⁄16
5× 5× 1⁄4
5× 5× 3⁄16
5× 5× 1⁄8
B,C,P,U,W
B,C,D,I,P,U,W
A,B,C,D,I,P,U,W,X
A,B,C,D,I,P,U,V,W,X
A,B,C,I,P,V,W
16× 12× 1⁄2, 3⁄8, 5⁄16
16× 8× 1⁄2, 3⁄8, 5⁄16
16× 4× 1⁄2, 3⁄8, 5⁄16
V*,W
B,W
B,W
*Size is manufactured by Submerged Arc Welding (SAW) process and is not stocked by steel service centers
(contact producer for specific requirements). All other sizes are manufactured by Electric Resistance Welding
and are available from steel service centers. For the most recent list of producers, please see the latest January or July issue of the AISC magazine Modern Steel Construction.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1 - 23
Table 1-5 (cont.).
Principal Producers of Structural Tubing (TS)
A—Acme Rolling
Forming Co.
B—Bull Moose Tube
Co.
C—Copperweld Corp.
D—Dallas Tube &
I—Independence Tube
Rollform
Corp.
E—Eugene Welding Co. P—IPSCO Steel
H—Hanna Steel Corp.
U—UNR-Leavitt, Div. of
UNR, Inc.
Nominal Size and
Thickness
Producer Code
14× 12× 1⁄2, 3⁄8
14× 10× 1⁄2, 3⁄8, 5⁄16
14× 6× 5⁄8
14× 6× 1⁄2, 3⁄8, 5⁄16 , 1⁄4
14× 4× 5⁄8
14× 4× 1⁄2, 3⁄8, 5⁄16 , 1⁄4
14× 4× 3⁄16
V*
B,W
B
B,W
B
B,W
B
12× 10× 1⁄2, 3⁄8, 5⁄16 , 1⁄4
12× 8× 5⁄8
12× 8× 1⁄2, 3⁄8, 5⁄16 , 1⁄4
12× 8× 3⁄16
12× 6× 5⁄8
12× 6× 1⁄2, 3⁄8, 5⁄16 , 1⁄4
12× 6× 3⁄16
12× 4× 5⁄8
12× 4× 1⁄2, 3⁄8, 5⁄16 , 1⁄4, 3⁄16
12× 3× 5⁄16 , 1⁄4, 3⁄16
12× 2× 1⁄4, 3⁄16
B
B
B,C,U,W
B,C,W
B
B,C,U,W
B,C,W
B
B,U,W
B
B,U
10× 8× 1⁄2, 3⁄8, 5⁄16 , 1⁄4, 3⁄16
10× 6× 1⁄2
10× 6× 3⁄8, 5⁄16 , 1⁄4, 3⁄16
10× 5× 3⁄8, 5⁄16 , 1⁄4, 3⁄16
10× 4× 1⁄2
10× 4× 3⁄8, 5⁄16 , 1⁄4, 3⁄16
10× 3× 3⁄8,5⁄16
10× 3× 1⁄4, 3⁄16
10× 2× 5⁄16
10× 2× 1⁄4, 3⁄16
B,C,U,W
B,C,U,W
B,C,D,P,U,W
B,C,D
B,C,P,U,W
B,C,D,P,U,W
D
B,D
D,P,W
B,D,P,U,W
8× 6× 1⁄2
8× 6× 3⁄8, 5⁄16 , 1⁄4, 3⁄16
8× 4× 5⁄8
8× 4× 1⁄2
8× 4× 3⁄8, 5⁄16
8× 4× 1⁄4, 3⁄16
8× 4× 1⁄8
8× 3× 1⁄2
8× 3× 3⁄8, 5⁄16
8× 3× 1⁄4, 3⁄16
8× 3× 1⁄8
8× 2× 3⁄8
8× 2× 5⁄16
8× 2× 1⁄4, 3⁄16
8× 2× 1⁄8
B,C,P,U,W
B,C,D,P,U,W
B
B,C,P,U,W
B,C,D,H,I,P,U,W
A,B,C,D,H,I,P,U,W,X
A,B,D,I,P
C,P,U
B,C,D,I,P,U,W
A,B,C,D,I,P,U,W
A,B,C,D,I,P
H
H,I,P,W
A,B,D,I,P,U,W
A,B,D,I,P
V—Valmont Industries,
Inc.
W—Welded Tube Co. of
America
X—EXLTUBE
Nominal Size and
Thickness
Producer Code
7× 5× 1⁄2
7× 5× 3⁄8, 5⁄16
7× 5× 1⁄4, 3⁄16
7× 5× 1⁄8
7× 4× 3⁄8, 5⁄16
7× 4× 1⁄4, 3⁄16
7× 4× 1⁄8
7× 3× 3⁄8, 5⁄16
7× 3× 1⁄4, 3⁄16
7× 3× 1⁄8
B,C,P,U,W
B,C,I,P,U,W
A,B,C,H,I,P,U,W
A,B,C,I,P
B,C,D,H,I,P,U,W
A,B,C,D,H,I,P,U,W
A,B,C,H,I,P
B,C,D,H,I,P,W
A,B,C,D,H,I,P,W,X
A,B,C,D,H,I,P
6× 4× 1⁄2
6× 4× 3⁄8, 5⁄16
6× 4× 1⁄4
6× 4× 3⁄16
6× 4× 1⁄8
6× 3× 1⁄2
6× 3× 3⁄8, 5⁄16
6× 3× 1⁄4
6× 3× 3⁄16
6× 3× 1⁄8
6× 2× 3⁄8
6× 2× 5⁄16
6× 2× 1⁄4, 3⁄16
6× 2× 1⁄8
B,C,P,U,W
B,C,D,H,I,P,U,W
A,B,C,D,H,I,P,U,W,X
A,B,C,D,H,I,P,U,V,W,X
A,B,C,D,H,I,P,V,W
P,U
B,D,H,I,P,U
A,B,C,D,H,I,P,U,X
A,B,C,D,H,I,P,U,W,X
A,B,C,D,H,I,P,W
H
H,I,P,W
A,B,C,D,E,H,I,P,U,W,X
A,B,C,D,E,H,I,P,U,W
5× 4× 3⁄8, 5⁄16
5× 4× 1⁄4, 3⁄16
5× 3× 1⁄2
5× 3× 3⁄8, 5⁄16
5× 3× 1⁄4, 3⁄16
5× 3× 1⁄8
5× 2× 5⁄16
5× 2× 1⁄4, 3⁄16
5× 2× 1⁄8
I,P,W
B,C,D,I,P,U,W
C,P,U
B,C,D,H,I,P,U,W
A,B,C,D,E,H,I,P,U,W,X
A,B,C,D,E,H,I,P,U,W
I,P,W
A,B,C,D,E,H,I,P,U,W,X
A,B,C,D,E,H,I,P,U,W
4× 3× 5⁄16
4× 3× 1⁄4, 3⁄16
4× 3× 1⁄8
4× 2× 3⁄8
4× 2× 5⁄16
4× 2× 1⁄4, 3⁄16
4× 2× 1⁄8
B,I,P,W
A,B,C,D,E,H,I,P,U,W,X
A,B,C,D,E,H,I,P,U,W
H
H,I,P,W
A,B,C,D,E,H,I,P,U,W,X
A,B,C,E,H,I,P,U,W
3× 2× 5⁄16
3× 2× 1⁄4, 3⁄16
3× 2× 1⁄8
I
A,B,C,D,E,H,I,P,U,V,W,X
A,B,C,D,E,H,I,P,U,V,W
21⁄2 × 11⁄2 × 1⁄4, 3⁄16
H,X
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1 - 24
DIMENSIONS AND PROPERTIES
Table 1-6.
Principal Producers of Steel Tubing (Round)
C—Copperweld Corp.
P—IPSCO
U—UNR-Leavitt, Div. of
UNR, Inc.
V—Valmont Industries,
Inc.
W—Welded Tube Co.
of America
X—EXLTUBE
Outside Diameter
and Thickness
Producer Code
Outside Diameter
and Thickness
Producer Code
20.000× .500,.375,.250
P*,W
6.626×.250,.188
6.625×.125
P,U,V,W
P,V,W
18.000× .500,.375,.250
P*,W
16.000× .500
16.000× .375,.250
16.000× .188
16.000× .125
P*,W
P,W
P,V*
V*
6.000×.500,.375,.312
6.000×.280
6.000×.250,.188,.125
W
X
V,W
14.000× .500,.438,.375,.250
14.000× .188
14.000× .125
P,W
P,V*
V*
5.563×.375
5.563×.258
5.563×.134
P,U
P,U,V,W
P,V,W
12.750× .500,.406,.375
12.750× .188× .125
P,W
P,V*
5.000×.500,.375,.312
5.000×.258
5.000×.250,.188
5.000×.125
P,C,W
P,X
C,P,U,V,W
P,U,V,W
10.750× .500,.365,.250
P,W
4.500×.237,.188,.125
P,U,V,W
10.000× .625,.500,.375,.312
10.000× .250,.188
10.000× .125
C
C,V
V
4.000×.337,.237
4.000×.266,.250,.188,.125
X
U,V,W
9.625×.500
9.625×.375,.312,.250,.188
C,U
C,P*,U
3.500×.318
3.500×.300
3.500×.250,.203,.188,.125
3.500×.226
X
P,W
P,U,V,W
P,X
8.625×.500
8.625×.375,.322
8.625×.250,.188
8.625×.125
C,P,U
C,P,U,W
C,P,U,V,W
P,V,W
3.000×.300,.216
X
2.875×.276
2.875×.250,.203,.188,.125
W
P,U,V,W
7.000×.500
7.000×.375,.312,.250
7.000×.188
7.000×.125
C,P,U
C,P,U,W
C,P,U,V,W
C,P,V,W
2.375,.250,.218,.188
2.375,.154,.125
P,V,W
P,U,V,W
6.625×.500,.432
6.625×.375,.312,.280
P,U
P,U,W
*Size is manufactured by Submerged Arc Welding (SAW) Process and is typically not stocked by steel service
centers. Other sizes are manufactured by Electric Resistance Welding and typically are available from steel
service centers. For more information contact the manufacturer or the American Institute for Hollow Structural
Sections.
Also, other sizes and wall thicknesses may be available. Contact an individual manufacturer for more details.
Steel Pipe: For availability contact the National Association of Steel Pipe Distributors, Inc.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
STRUCTURAL SHAPES
1 - 25
STRUCTURAL SHAPES
Designations, Dimensions, and Properties
The hot rolled shapes shown in Part 1 of this Manual are published in ASTM Specification
A6/A6M, Standard Specification for General Requirements for Rolled Steel Plates,
Shapes, Sheet Piling, and Bars for Structural Use.
W shapes have essentially parallel flange surfaces. The profile of a W shape of a given
nominal depth and weight available from different producers is essentially the same
except for the size of fillets between the web and flange.
HP bearing pile shapes have essentially parallel flange surfaces and equal web and
flange thicknesses. The profile of an HP shape of a given nominal depth and weight
available from different producers is essentially the same.
American Standard Beams (S) and American Standard Channels (C) have a slope of
approximately 17 percent (2 in 12 inches) on the inner flange surfaces. The profiles of S
and C shapes of a given nominal depth and weight available from different producers are
essentially the same.
The letter M designates shapes that cannot be classified as W, HP, or S shapes.
Similarly, MC designates channels that cannot be classified as C shapes. Because many
of the M and MC shapes are only available from a limited number of producers, or are
infrequently rolled, their availability should be checked prior to specifying these shapes.
They may or may not have slopes on their inner flange surfaces, dimensions for which
may be obtained from the respective producing mills.
The flange thickness given in the table from S, M, C, and MC shapes is the average
flange thickness.
In calculating the theoretical weights, properties, and dimensions of the rolled shapes
listed in Part 1 of this Manual, fillets and roundings have been included for all shapes
except angles. Because of differences in fillet radii among producers, actual properties
of rolled shapes may vary slightly from those tabulated. Dimensions for detailing are
generally based on the largest theoretical-size fillets produced.
Equal leg and unequal leg angle (L) shapes of the same nominal size available from
different producers have profiles which are essentially the same, except for the size of
fillet between the legs and the shape of the ends of the legs. The k distance given in the
tables for each angle is based on the theoretical largest size fillet available. Availability
of certain angles is subject to rolling accumulation and geographical location, and should
be checked with material suppliers.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1 - 26
DIMENSIONS AND PROPERTIES
Y
tf
d
X
W SHAPES
Dimensions
k
k1
X
T
tw
Y
bf
k
Web
Designation
Area
A
2
in.
Depth
d
in.
Thickness
tw
tw
2
in.
in.
W44×335
W40×290
W40×262
W40×230
98.3
85.8
77.2
67.7
44.02
43.62
43.31
42.91
44
435⁄8
433⁄8
427⁄8
1.020
0.870
0.790
0.710
W40×593*
W40×503*
W40×431
W40×372
W40×321
W40×297
W40×277
W40×249
W40×215
W40×199
W40×174
174
148
127
109
94.1
87.4
81.3
73.3
63.3
58.4
51.1
42.99
42.05
41.26
40.63
40.08
39.84
39.69
39.38
38.98
38.67
38.20
43
421⁄16
411⁄4
405⁄8
401⁄16
397⁄8
393⁄4
393⁄8
39
385⁄8
381⁄4
1.790 113⁄16
1.540 19⁄16
1.340 15⁄16
1.160 13⁄16
1.000
1
0.930 15⁄16
0.830 13⁄16
3⁄
0.750
4
5⁄
0.650
8
5
0.650
⁄8
5
0.650
⁄8
W40×466*
W40×392*
W40×331
W40×278
W40×264
W40×235
W40×211
W40×183
W40×167
W40×149
137
115
97.6
81.8
77.6
68.9
62.0
53.7
49.1
43.8
42.44 427⁄16
41.57 419⁄16
40.79 4013⁄16
40.16 403⁄16
40.00
40
39.69 393⁄4
39.37 393⁄8
38.98
39
38.59 385⁄8
38.20 381⁄4
1.67
111⁄16
1.42
17⁄16
1.22
11⁄4
1.02
1
0.960
1
13
0.830
⁄16
3
0.750
⁄4
5
⁄8
0.650
5⁄
0.650
8
5⁄
0.630
8
W36×848*
W40×798*
W40×650*
W40×527*
W40×439*
W40×393*
W40×359*
W40×328*
W40×300
W40×280
W40×260
W40×245
W40×230
249
234
190
154
128
115
105
96.4
88.3
82.4
76.5
72.1
67.6
42.45
41.97
40.47
39.21
38.26
37.80
37.40
37.09
36.74
36.52
36.26
36.08
35.90
421⁄2
42
401⁄2
391⁄4
381⁄4
373⁄4
373⁄8
371⁄8
363⁄4
361⁄2
361⁄4
361⁄8
357⁄8
Flange
2.520
2.380
1.970
1.610
1.360
1.220
1.120
1.020
0.945
0.885
0.840
0.800
0.760
1
7⁄
8
13⁄
16
11⁄
16
21⁄2
23⁄8
2
15⁄8
13⁄8
11⁄4
11⁄8
1
15⁄
16
7⁄
8
13⁄
16
13⁄
16
3⁄
4
Width
bf
Thickness
tf
k
in.
k1
in.
in.
1.770
1.580
1.420
1.220
13⁄4
19⁄16
17⁄16
11⁄4
387⁄16 29⁄16
387⁄16 23⁄8
387⁄16 23⁄16
387⁄16
2
15⁄16
11⁄4
13⁄16
11⁄8
3⁄
4
11⁄
16
9⁄
16
1⁄
2
1⁄
2
7⁄
16
3⁄
8
5⁄
16
5⁄
16
5⁄
16
16.690 163⁄4
16.420 167⁄16
16.220 161⁄4
16.060 161⁄16
15.910 157⁄8
15.825 157⁄8
15.830 157⁄8
15.750 153⁄4
15.750 153⁄4
15.750 153⁄4
15.750 153⁄4
3.230
2.760
2.360
2.050
1.770
1.650
1.575
1.420
1.220
1.065
0.830
31⁄4
23⁄4
23⁄8
21⁄16
13⁄4
15⁄8
19⁄16
17⁄16
11⁄4
11⁄16
13⁄
16
343⁄16
343⁄16
343⁄16
343⁄16
343⁄16
343⁄16
343⁄16
343⁄16
343⁄16
343⁄16
343⁄16
47⁄16 21⁄16
315⁄16 115⁄16
39⁄16 17⁄8
31⁄4
13⁄4
215⁄16 111⁄16
31⁄16 111⁄16
23⁄4
15⁄8
25⁄8 19⁄16
23⁄8
11⁄2
21⁄4
11⁄2
2
11⁄2
13⁄
16
11⁄
16
5⁄
8
1⁄
2
1⁄
2
7⁄
16
3⁄
8
5⁄
16
5⁄
16
5⁄
16
12.640 125⁄8
12.360 123⁄8
12.170 123⁄16
11.970
12
11.930
12
11.890 117⁄8
11.810 113⁄4
11.810 113⁄4
11.810 113⁄4
11.810 113⁄4
2.950 215⁄16
2.520 21⁄2
2.130 21⁄8
1.810 113⁄16
1.730 13⁄4
1.575 17⁄16
1.415 19⁄16
1.220 11⁄4
1.025
1
0.830 13⁄16
343⁄16
343⁄16
343⁄16
343⁄16
343⁄16
343⁄16
343⁄16
343⁄16
343⁄16
343⁄16
41⁄8
2
311⁄16 17⁄8
35⁄16 113⁄16
3
111⁄16
215⁄16 111⁄16
23⁄4
15⁄8
25⁄8 19⁄16
23⁄8
11⁄2
23⁄16 11⁄2
2
11⁄2
11⁄4
13⁄16
1
13⁄
16
11⁄
16
5⁄
8
9⁄
16
1⁄
2
1⁄
2
7⁄
16
7⁄
16
7⁄
16
3⁄
8
18.130
17.990
17.575
17.220
16.965
16.830
16.730
16.630
16.655
16.595
16.550
16.510
16.470
181⁄8
18
175⁄8
171⁄4
17
167⁄8
163⁄4
165⁄8
165⁄8
165⁄8
161⁄2
161⁄2
161⁄2
4.530 41⁄2
4.290 45⁄16
3.540 39⁄16
2.910 215⁄16
2.440 27⁄16
2.200 23⁄16
2.010
2
1.850 17⁄8
1.680 111⁄16
1.570 19⁄16
1.440 17⁄16
1.350 13⁄8
1.260 11⁄4
311⁄8
311⁄8
311⁄8
311⁄8
311⁄8
311⁄8
311⁄8
311⁄8
311⁄8
311⁄8
311⁄8
311⁄8
311⁄8
511⁄16
57⁄16
411⁄16
41⁄16
39⁄16
35⁄16
31⁄8
3
213⁄16
211⁄16
29⁄16
21⁄2
23⁄8
1
15.950
15.830
15.750
15.750
in.
T
153⁄4
157⁄8
153⁄4
153⁄4
1⁄
2
7⁄
16
3⁄
8
3⁄
8
in.
Distance
*Group 4 or Group 5 shape. See Notes in Table 1-2.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
21⁄4
23⁄16
2
13⁄4
15⁄8
15⁄8
19⁄16
11⁄2
11⁄2
11⁄2
11⁄2
17⁄16
17⁄16
STRUCTURAL SHAPES
1 - 27
W SHAPES
Properties
Y
tf
d
k
k1
X
X
T
tw
Y
bf
Nominal
Wt.
per
ft
Compact
Section
Criteria
h
tw
Fy′′′
lb
bf
2tf
335
290
262
230
4.5
5.0
5.5
6.5
593
503
431
372
321
297
277
249
215
199
174
k
Plastic
Modulus
Elastic Properties
Axis X-X
X1
X2 × 106
ksi
ksi
2
(1/ksi)
in.
38.1
44.7
49.2
54.8
44
32
26
21
2430
2140
1930
1690
5110
8220
12300
21200
31100
27100
24200
20800
2.6
3.0
3.4
3.9
4.5
4.8
5.0
5.5
6.5
7.4
9.5
19.1
22.2
25.5
29.5
34.2
36.8
41.2
45.6
52.6
52.6
52.6
—
—
—
—
—
47
38
31
23
23
23
4790
4110
3550
3100
2690
2500
2350
2120
1830
1690
1500
337
620
1100
1860
3240
4240
5370
7940
14000
20300
36000
466
392
331
278
264
235
211
183
167
149
2.1
2.5
2.9
3.3
3.4
3.8
4.2
4.8
5.8
7.1
20.5
24.1
28.0
33.5
35.6
41.2
45.6
52.6
52.6
54.3
—
—
—
57
50
38
31
23
23
22
4560
3920
3360
2860
2720
2430
2200
1900
1750
1610
848
798
650
527
439
393
359
328
300
280
260
245
230
2.0
2.1
2.5
3.0
3.5
3.8
4.2
4.5
5.0
5.3
5.7
6.1
6.5
12.5
13.2
16.0
19.6
23.1
25.8
28.1
30.9
33.3
35.6
37.5
39.4
41.4
—
—
—
—
—
—
—
—
58
51
46
41
37
7100
6720
5590
4630
3900
3540
3240
2980
2720
2560
2370
2230
2100
S
I
4
Axis Y-Y
r
S
I
4
r
3
Zx
in.
in.
in.
in.
in.3
1410
1240
1120
969
17.8
17.8
17.7
17.5
1200
1050
927
796
150
133
118
101
3.49
3.50
3.46
3.43
1620
1420
1270
1100
236
206
183
157
50400
41700
34800
29600
25100
23200
21900
19500
16700
14900
12200
2340
1980
1690
1460
1250
1170
1100
992
858
769
639
17.0
16.8
16.6
16.4
16.3
16.3
16.4
16.3
16.2
16.0
15.5
2520
2050
1690
1420
1190
1090
1040
926
796
695
541
302
250
208
177
150
138
132
118
101
88.2
68.8
3.81
3.72
3.65
3.60
3.56
3.54
3.58
3.56
3.54
3.45
3.26
2760
2300
1950
1670
1420
1330
1250
1120
963
868
715
481
394
327
277
234
215
204
182
156
137
107
473
851
1560
2910
3510
5310
7890
13700
20500
31400
36300
29900
24700
20500
19400
17400
15500
13300
11600
9780
1710
1440
1210
1020
971
874
785
682
599
512
16.3
16.1
15.9
15.8
15.8
15.9
15.8
15.7
15.3
14.9
1010
803
646
521
493
444
390
336
283
229
160
130
106
87.1
82.6
74.6
66.1
56.9
47.9
38.8
2.72
2.64
2.57
2.52
2.52
2.54
2.51
2.50
2.40
2.29
2050
1710
1430
1190
1130
1010
905
781
692
597
262
212
172
140
132
118
105
89.6
76.0
62.2
71
87
175
365
704
1040
1470
2040
2930
3730
5100
6430
8190
67400
62600
48900
38300
31000
27500
24800
22500
20300
18900
17300
16100
15000
3170
2980
2420
1950
1620
1450
1320
1210
1110
1030
953
895
837
16.4
16.4
16.0
15.8
15.6
15.5
15.4
15.3
15.2
15.1
15.0
15.0
14.9
4550
4200
3230
2490
1990
1750
1570
1420
1300
1200
1090
1010
940
501
467
367
289
235
208
188
171
156
144
132
123
114
4.27
4.24
4.12
4.02
3.95
3.90
3.87
3.84
3.83
3.81
3.78
3.75
3.73
3830
3570
2840
2270
1860
1660
1510
1380
1260
1170
1080
1010
943
799
743
580
454
367
325
292
265
241
223
204
190
176
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
3
Zy
in.
in.
3
1 - 28
DIMENSIONS AND PROPERTIES
Y
tf
d
X
W SHAPES
Dimensions
k
k1
X
T
tw
Y
bf
k
Web
Designation
Area
A
2
in.
Depth
d
in.
Flange
Thickness
tw
tw
2
in.
in.
Width
bf
in.
Distance
Thickness
tf
in.
T
k
k1
in.
in.
in.
W36×256
W40×232
W40×210
W40×194
W40×182
W40×170
W40×160
W40×150
W40×135
75.4
68.1
61.8
57.0
53.6
50.0
47.0
44.2
39.7
37.43
37.12
36.69
36.49
36.33
36.17
36.01
35.85
35.55
373⁄8
371⁄8
363⁄4
361⁄2
363⁄8
361⁄8
36
357⁄8
351⁄2
0.960
0.870
0.830
0.765
0.725
0.680
0.650
0.625
0.600
1
7⁄
8
13⁄
16
3⁄
4
3⁄
4
11⁄
16
5⁄
8
5⁄
8
5⁄
8
1⁄
2
7⁄
16
7⁄
16
3⁄
8
3⁄
8
3⁄
8
5⁄
16
5⁄
16
5⁄
16
12.215
12.120
12.180
12.115
12.075
12.030
12.000
11.975
11.950
121⁄4
121⁄8
121⁄8
121⁄8
121⁄8
12
12
12
12
1.730
1.570
1.360
1.260
1.180
1.100
1.020
0.940
0.790
13⁄4
19⁄16
13⁄8
11⁄4
13⁄16
11⁄8
1
15⁄
16
13⁄
16
321⁄8
321⁄8
321⁄8
321⁄8
321⁄8
321⁄8
321⁄8
321⁄8
321⁄8
25⁄8
21⁄2
25⁄16
23⁄16
21⁄8
2
115⁄16
17⁄8
111⁄16
15⁄16
11⁄4
11⁄4
13⁄16
13⁄16
13⁄16
11⁄8
11⁄8
11⁄8
W33×354*
W40×318*
W40×291*
W40×263*
W40×241
W40×221
W40×201
104
93.5
85.6
77.4
70.9
65.0
59.1
35.55
35.16
34.84
34.53
34.18
33.93
33.68
351⁄2
351⁄8
347⁄8
341⁄2
341⁄8
337⁄8
335⁄8
1.160
1.040
0.960
0.870
0.830
0.775
0.715
13⁄16
11⁄16
1
7⁄
8
13⁄
16
3⁄
4
11⁄
16
5⁄
8
9⁄
16
1⁄
2
7⁄
16
7⁄
16
3⁄
8
3⁄
8
16.100
15.985
15.905
15.805
15.860
15.805
15.745
161⁄8
16
157⁄8
153⁄4
157⁄8
153⁄4
153⁄4
2.090
1.890
1.730
1.570
1.400
1.275
1.150
21⁄16
17⁄8
13⁄4
19⁄16
13⁄8
11⁄4
11⁄8
293⁄4
293⁄4
293⁄4
293⁄4
293⁄4
293⁄4
293⁄4
27⁄8
211⁄16
29⁄16
23⁄8
23⁄16
21⁄16
115⁄16
13⁄8
15⁄16
11⁄4
13⁄16
13⁄16
13⁄16
11⁄8
W33×169
W40×152
W40×141
W40×130
W40×118
49.5
44.7
41.6
38.3
34.7
33.82
33.49
33.30
33.09
32.86
337⁄8
331⁄2
331⁄4
331⁄8
327⁄8
0.670
0.635
0.605
0.580
0.550
11⁄
16
5⁄
8
5⁄
8
9⁄
16
9⁄
16
3⁄
8
5⁄
16
5⁄
16
5⁄
16
5⁄
16
11.500
11.565
11.535
11.510
11.480
111⁄2
115⁄8
111⁄2
111⁄2
111⁄2
1.220
1.055
0.960
0.855
0.740
11⁄4
11⁄16
15⁄
16
7⁄
8
3⁄
4
293⁄4
293⁄4
293⁄4
293⁄4
293⁄4
21⁄16
17⁄8
13⁄4
111⁄16
19⁄16
11⁄8
11⁄8
11⁄16
11⁄16
11⁄16
W30×477*
W40×391*
W40×326*
W40×292*
W40×261
W40×235
W40×211
W40×191
W40×173
140
114
95.7
85.7
76.7
69.0
62.0
56.1
50.8
34.21
33.19
32.40
32.01
31.61
31.30
30.94
30.68
30.44
341⁄4
331⁄4
323⁄8
32
315⁄8
311⁄4
31
305⁄8
301⁄2
1.630
1.360
1.140
1.020
0.930
0.830
0.775
0.710
0.655
15⁄8
13⁄8
11⁄8
1
15⁄
16
13⁄
16
3⁄
4
11⁄
16
5⁄
8
13⁄
16
11⁄
16
9⁄
16
1⁄
2
1⁄
2
7⁄
16
3⁄
8
3⁄
8
5⁄
16
15.865
15.590
15.370
15.255
15.155
15.055
15.105
15.040
14.985
157⁄8
155⁄8
153⁄8
151⁄2
151⁄8
15
151⁄8
15
15
2.950
2.440
2.050
1.850
1.650
1.500
1.315
1.185
1.065
3
27⁄16
21⁄16
17⁄8
15⁄8
11⁄2
15⁄16
13⁄16
11⁄16
263⁄4
263⁄4
263⁄4
263⁄4
263⁄4
263⁄4
263⁄4
263⁄4
263⁄4
33⁄4
31⁄4
213⁄16
25⁄8
27⁄16
21⁄4
21⁄8
115⁄16
11⁄16
19⁄16
17⁄16
15⁄16
11⁄4
13⁄16
11⁄8
11⁄8
11⁄16
11⁄16
W30×148
W40×132
W40×124
W40×116
W40×108
W40×99
W40×90
43.5
38.9
36.5
34.2
31.7
29.1
26.4
30.67
30.31
30.17
30.01
29.83
29.65
29.53
305⁄8
301⁄4
301⁄8
30
297⁄8
295⁄8
291⁄2
0.650
0.615
0.585
0.565
0.545
0.520
0.470
5⁄
8
5⁄
8
9⁄
16
9⁄
16
9⁄
16
1⁄
2
1⁄
2
5⁄
16
5⁄
16
5⁄
16
5⁄
16
5⁄
16
1⁄
4
1⁄
4
10.480
10.545
10.515
10.495
10.475
10.450
10.400
101⁄2
101⁄2
101⁄2
101⁄2
101⁄2
101⁄2
103⁄8
1.180
1.000
0.930
0.850
0.760
0.670
0.610
13⁄16
1
15⁄
16
7⁄
8
3⁄
4
11⁄
16
9⁄
16
263⁄4
263⁄4
263⁄4
263⁄4
263⁄4
263⁄4
263⁄4
2
13⁄4
111⁄16
15⁄8
19⁄16
17⁄16
15⁄16
1
11⁄16
1
1
1
1
1
*Group 4 or Group 5 shape. See Notes in Table 1-2.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
STRUCTURAL SHAPES
1 - 29
W SHAPES
Properties
Y
tf
d
k
k1
X
X
T
tw
Y
bf
Nominal
Wt.
per
ft
Compact
Section
Criteria
h
tw
Fy′′′
lb
bf
2tf
256
232
210
194
182
170
160
150
135
3.5
3.9
4.5
4.8
5.1
5.5
5.9
6.4
7.6
354
318
291
263
241
221
201
k
Plastic
Modulus
Elastic Properties
Axis X-X
Axis Y-Y
X1
X2 × 106
ksi
ksi
2
(1/ksi)
in.
33.8
37.3
39.1
42.4
44.8
47.8
50.0
52.0
54.1
56
46
42
36
32
28
26
24
22
2840
2580
2320
2140
2020
1900
1780
1680
1520
2870
4160
6560
8850
11300
14500
18600
24200
38000
16800
15000
13200
12100
11300
10500
9750
9040
7800
895
809
719
664
623
580
542
504
439
14.9
14.8
14.6
14.6
14.5
14.5
14.4
14.3
14.0
528
468
411
375
347
320
295
270
225
3.8
4.2
4.6
5.0
5.7
6.2
6.8
25.8
28.8
31.2
34.5
36.1
38.7
41.9
—
—
—
54
49
43
36
3540
3200
2940
2670
2430
2240
2040
1030
1530
2130
3100
4590
6440
9390
21900
19500
17700
15800
14200
12800
11500
1230
1110
1010
917
829
757
684
14.5
14.4
14.4
14.3
14.1
14.1
14.0
169
152
141
130
118
4.7
5.5
6.0
6.7
7.8
44.7
47.2
49.6
51.7
54.5
32
29
26
24
22
2160
1940
1800
1660
1510
8150
12900
17800
25100
37700
9290
8160
7450
6710
5900
549
487
448
406
359
477
391
326
292
261
235
211
191
173
2.7
3.2
3.7
4.1
4.6
5.0
5.7
6.3
7.0
16.6
19.9
23.7
26.5
29.0
32.5
34.9
38.0
41.2
—
—
—
—
—
61
53
44
38
5420
4510
3860
3460
3110
2820
2510
2280
2070
193
386
735
1110
1690
2460
3950
5840
8540
26100
20700
16800
14900
13100
11700
10300
9170
8200
148
132
124
116
108
99
90
4.4
5.3
5.7
6.2
6.9
7.8
8.5
41.5
43.9
46.2
47.8
49.6
51.9
57.5
37
33
30
28
26
24
19
2310
2050
1930
1800
1680
1560
1430
6180
10500
13500
17700
24200
34100
47000
6680
5770
5360
4930
4470
3990
3620
S
I
4
r
S
I
86.5
77.2
67.5
61.9
57.6
53.2
49.1
45.1
37.7
2.65
2.62
2.58
2.56
2.55
2.53
2.50
2.47
2.38
1040
936
833
767
718
668
624
581
509
137
122
107
97.7
90.7
83.8
77.3
70.9
59.7
1460
1290
1160
1030
932
840
749
181
161
146
131
118
106
95.2
3.74
3.71
3.69
3.66
3.63
3.59
3.56
1420
1270
1150
1040
939
855
772
282
250
226
202
182
164
147
13.7
13.5
13.4
13.2
13.0
310
273
246
218
187
53.9
47.2
42.7
37.9
32.6
2.50
2.47
2.43
2.39
2.32
629
559
514
467
415
1530
1250
1030
928
827
746
663
598
539
13.7
13.5
13.2
13.2
13.1
13.0
12.9
12.8
12.7
1970
1550
1240
1100
959
855
757
673
598
249
198
162
144
127
114
100
89.5
79.8
3.75
3.68
3.61
3.58
3.54
3.52
3.49
3.46
3.43
1790
1430
1190
1060
941
845
749
673
605
436
380
355
329
299
269
245
12.4
12.2
12.1
12.0
11.9
11.7
11.7
227
196
181
164
146
128
115
43.3
37.2
34.4
31.3
27.9
24.5
22.1
2.28
2.25
2.23
2.19
2.15
2.10
2.09
500
437
408
378
346
312
283
in.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
3
Zy
in.3
in.
3
Zx
in.
in.
4
r
in.
in.
3
84.4
73.9
66.9
59.5
51.3
390
310
252
223
196
175
154
138
123
68.0
58.4
54.0
49.2
43.9
38.6
34.7
1 - 30
DIMENSIONS AND PROPERTIES
Y
tf
d
X
W SHAPES
Dimensions
k
k1
X
T
tw
Y
bf
k
Web
Designation
Area
A
2
in.
Depth
d
in.
Flange
Thickness
tw
tw
2
in.
in.
Width
bf
in.
Distance
Thickness
tf
T
in.
k
k1
in.
in.
in.
W27×539*
W40×448*
W40×368*
W40×307*
W40×258
W40×235
W40×217
W40×194
W40×178
W40×161
W40×146
158
131
108
90.2
75.7
69.1
63.8
57.0
52.3
47.4
42.9
32.52
31.42
30.39
29.61
28.98
28.66
28.43
28.11
27.81
27.59
27.38
321⁄2
313⁄8
303⁄8
295⁄8
29
285⁄8
283⁄8
281⁄8
273⁄4
275⁄8
273⁄8
1.970
1.650
1.380
1.160
0.980
0.910
0.830
0.750
0.725
0.660
0.605
2
15⁄8
13⁄8
13⁄16
1
15⁄
16
13⁄
16
3⁄
4
3⁄
4
11⁄
16
5⁄
8
1
13⁄
16
11⁄
16
5⁄
8
1⁄
2
1⁄
2
7⁄
16
3⁄
8
3⁄
8
3⁄
8
5⁄
16
15.255
14.940
14.665
14.445
14.270
14.190
14.115
14.035
14.085
14.020
13.965
151⁄4
15
145⁄8
141⁄2
141⁄4
141⁄4
141⁄8
14
141⁄8
14
14
3.540
2.990
2.480
2.090
1.770
1.610
1.500
1.340
1.190
1.080
0.975
39⁄16
3
21⁄2
21⁄16
13⁄4
15⁄8
11⁄2
15⁄16
13⁄16
11⁄16
1
24
24
24
24
24
24
24
24
24
24
24
41⁄4
311⁄16
33⁄16
213⁄16
21⁄2
25⁄16
23⁄16
21⁄16
17⁄8
113⁄16
111⁄16
15⁄8
11⁄2
15⁄16
11⁄4
11⁄8
11⁄8
11⁄16
1
11⁄16
1
1
W27×129
W40×114
W40×102
W40×94
W40×84
37.8
33.5
30.0
27.7
24.8
27.63
27.29
27.09
26.92
26.71
275⁄8
271⁄4
271⁄8
267⁄8
263⁄4
0.610
0.570
0.515
0.490
0.460
5⁄
8
9⁄
16
1⁄
2
1⁄
2
7⁄
16
5⁄
16
5⁄
16
1⁄
4
1⁄
4
1⁄
4
10.010
10.070
10.015
9.990
9.960
10
101⁄8
10
10
10
1.100
0.930
0.830
0.745
0.640
11⁄8
15⁄
16
13⁄
16
3⁄
4
5⁄
8
24
24
24
24
24
113⁄16
15⁄8
19⁄16
17⁄16
13⁄8
15⁄
16
15⁄
16
15⁄
16
15⁄
16
15⁄
16
W24×492*
W40×408*
W40×335*
W40×279*
W40×250*
W40×229
W40×207
W40×192
W40×176
W40×162
W40×146
W40×131
W40×117
W40×104
144
119
98.4
82.0
73.5
67.2
60.7
56.3
51.7
47.7
43.0
38.5
34.4
30.6
29.65
28.54
27.52
26.73
26.34
26.02
25.71
25.47
25.24
25.00
24.74
24.48
24.26
24.06
295⁄8
281⁄2
271⁄2
263⁄4
263⁄8
26
253⁄4
251⁄2
251⁄4
25
243⁄4
241⁄2
241⁄4
24
1.970
1.650
1.380
1.160
1.040
0.960
0.870
0.810
0.750
0.705
0.650
0.605
0.550
0.500
2
15⁄8
13⁄8
13⁄16
11⁄16
1
7⁄
8
13⁄
16
3⁄
4
11⁄
16
5⁄
8
5⁄
8
9⁄
16
1⁄
2
1
13⁄
16
11⁄
16
5⁄
8
9⁄
16
1⁄
2
7⁄
16
7⁄
16
3⁄
8
3⁄
8
5⁄
16
5⁄
16
5⁄
16
1⁄
4
14.115
13.800
13.520
13.305
13.185
13.110
13.010
12.950
12.890
12.955
12.900
12.855
12.800
12.750
141⁄8
133⁄4
131⁄2
131⁄4
131⁄8
131⁄8
13
13
127⁄8
13
127⁄8
127⁄8
123⁄4
123⁄4
3.540
2.990
2.480
2.090
1.890
1.730
1.570
1.460
1.340
1.220
1.090
0.960
0.850
0.750
39⁄16
3
21⁄2
21⁄16
17⁄8
13⁄4
19⁄16
17⁄16
15⁄16
11⁄4
11⁄16
15⁄
16
7⁄
8
3⁄
4
21
21
21
21
21
21
21
21
21
21
21
21
21
21
45⁄16
33⁄4
31⁄4
27⁄8
211⁄16
21⁄2
23⁄8
21⁄4
21⁄8
2
17⁄8
13⁄4
15⁄8
11⁄2
19⁄16
13⁄8
11⁄4
11⁄8
11⁄8
1
1
1
15⁄
16
11⁄16
1
1 ⁄16
11⁄16
1
1
W24×103
W40×94
W40×84
W40×76
W40×68
30.3
27.7
24.7
22.4
20.1
24.53
24.31
24.10
23.92
23.73
241⁄2
241⁄4
241⁄8
237⁄8
233⁄4
0.550
0.515
0.470
0.440
0.415
9⁄
16
1⁄
2
1⁄
2
7⁄
16
7⁄
16
5⁄
16
1⁄
4
1⁄
4
1⁄
4
1⁄
4
9.000
9.065
9.020
8.990
8.965
9
91⁄8
9
9
9
0.980
0.875
0.770
0.680
0.585
1
7⁄
8
3⁄
4
11⁄
16
9⁄
16
21
21
21
21
21
13⁄4
15⁄8
19⁄16
17⁄16
13⁄8
13⁄
16
15⁄
16
15⁄
16
15⁄
16
W24×62
W40×55
18.2
16.2
23.74
23.57
233⁄4
235⁄8
0.430
0.395
7⁄
16
3⁄
8
1⁄
4
3⁄
16
7.040
7.005
7
7
0.590
0.505
9⁄
16
1⁄
2
21
21
13⁄8
15⁄16
15⁄
16
15⁄
16
* Group 4 or Group 5 shape. See Notes in Table 1-2.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1
STRUCTURAL SHAPES
1 - 31
W SHAPES
Properties
Y
tf
d
k
k1
X
X
T
tw
Y
bf
Nominal
Wt.
per
ft
Compact
Section
Criteria
h
tw
Fy′′′
lb
bf
2tf
539
448
368
307
258
235
217
194
178
161
146
2.2
2.5
3.0
3.5
4.0
4.4
4.7
5.2
5.9
6.5
7.2
129
114
102
94
84
k
Plastic
Modulus
Elastic Properties
Axis X-X
X1
X2 × 106
ksi
ksi
2
12.3
14.7
17.6
20.9
24.7
26.6
29.2
32.3
33.4
36.7
40.0
—
—
—
—
—
—
—
61
57
47
40
7160
6070
5100
4320
3670
3360
3120
2800
2550
2320
2110
66
123
243
463
873
1230
1640
2520
3740
5370
7900
25500
20400
16100
13100
10800
9660
8870
7820
6990
6280
5630
4.5
5.4
6.0
6.7
7.8
39.7
42.5
47.0
49.4
52.7
41
35
29
26
23
2390
2100
1890
1740
1570
5340
9220
14000
19900
31100
492
408
335
279
250
229
207
192
176
162
146
131
117
104
2.0
2.3
2.7
3.2
3.5
3.8
4.1
4.4
4.8
5.3
5.9
6.7
7.5
8.5
10.9
13.1
15.6
18.6
20.7
22.5
24.8
26.6
28.7
30.6
33.2
35.6
39.2
43.1
—
—
—
—
—
—
—
—
—
—
58
50
42
34
7950
6780
5700
4840
4370
4020
3650
3410
3140
2870
2590
2330
2090
1860
103
94
84
76
68
4.6
5.2
5.9
6.6
7.7
39.2
41.9
45.9
49.0
52.0
42
37
30
27
24
62
55
6.0
6.9
50.1
54.6
25
21
S
I
r
S
3
Zx
in.
in.
in.3
1570
1300
1060
884
742
674
624
556
502
455
411
12.7
12.5
12.2
12.0
11.9
11.8
11.8
11.7
11.6
11.5
11.4
2110
1670
1310
1050
859
768
704
618
555
497
443
277
224
179
146
120
108
99.8
88.1
78.8
70.9
63.5
3.66
3.57
3.48
3.42
3.37
3.33
3.32
3.29
3.26
3.24
3.21
1880
1530
1240
1020
850
769
708
628
567
512
461
437
351
279
227
187
168
154
136
122
109
97.5
4760
4090
3620
3270
2850
345
299
267
243
213
11.2
11.0
11.0
10.9
10.7
184
159
139
124
106
36.8
31.5
27.8
24.8
21.2
2.21
2.18
2.15
2.12
2.07
395
343
305
278
244
57.6
49.3
43.4
38.8
33.2
43
79
156
297
436
605
876
1150
1590
2260
3420
5290
8190
12900
19100
15100
11900
9600
8490
7650
6820
6260
5680
5170
4580
4020
3540
3100
1290
1060
864
718
644
588
531
491
450
414
371
329
291
258
11.5
11.3
11.0
10.8
10.7
10.7
10.6
10.5
10.5
10.4
10.3
10.2
10.1
10.1
1670
1320
1030
823
724
651
578
530
479
443
391
340
297
259
237
191
152
124
110
99.4
88.8
81.8
74.3
68.4
60.5
53.0
46.5
40.7
3.41
3.33
3.23
3.17
3.14
3.11
3.08
3.07
3.04
3.05
3.01
2.97
2.94
2.91
1550
1250
1020
835
744
676
606
559
511
468
418
370
327
289
375
300
238
193
171
154
137
126
115
105
93.2
81.5
71.4
62.4
2400
2180
1950
1760
1590
5280
7800
12200
18600
29000
3000
2700
2370
2100
1830
245
222
196
176
154
9.96
9.87
9.79
9.69
9.55
119
109
94.4
82.5
70.4
26.5
24.0
20.9
18.4
15.7
1.99
1.98
1.95
1.92
1.87
280
254
224
200
177
41.5
37.5
32.6
28.6
24.5
1700
1540
25100
39600
1550
1350
131
114
9.23
9.11
34.5
29.1
1.38
1.34
153
134
15.7
13.3
9.80
8.30
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
3
Zy
in.
in.
4
r
in.
in.
3
I
in.
(1/ksi)
4
Axis Y-Y
1 - 32
DIMENSIONS AND PROPERTIES
Y
tf
d
X
W SHAPES
Dimensions
k
k1
X
T
tw
Y
bf
k
Web
Designation
Area
A
2
in.
Depth
d
in.
Flange
Thickness
tw
tw
2
in.
in.
Width
bf
Distance
Thickness
tf
in.
in.
T
k
k1
in.
in.
in.
W21×201
W40×182
W40×166
W40×147
W40×132
W40×122
W40×111
W40×101
59.2
53.6
48.8
43.2
38.8
35.9
32.7
29.8
23.03
22.72
22.48
22.06
21.83
21.68
21.51
21.36
23
223⁄4
221⁄2
22
217⁄8
215⁄8
211⁄2
213⁄8
0.910
0.830
0.750
0.720
0.650
0.600
0.550
0.500
15⁄
16
13⁄
16
3⁄
4
3⁄
4
5⁄
8
5⁄
8
9⁄
16
1⁄
2
1⁄
2
7⁄
16
3⁄
8
3⁄
8
5⁄
16
5⁄
16
5⁄
16
1⁄
4
12.575
12.500
12.420
12.510
12.440
12.390
12.340
12.290
125⁄8
121⁄2
123⁄8
121⁄2
121⁄2
123⁄8
123⁄8
121⁄4
1.630
1.480
1.360
1.150
1.035
0.960
0.875
0.800
15⁄8
11⁄2
13⁄8
11⁄8
11⁄16
15⁄
16
7⁄
8
13⁄
16
181⁄4
181⁄4
181⁄4
181⁄4
181⁄4
181⁄4
181⁄4
181⁄4
23⁄8
21⁄4
21⁄8
17⁄8
113⁄16
111⁄16
15⁄8
19⁄16
1
1
15⁄
16
11⁄16
1
1
15⁄
16
15⁄
16
W21×93
W40×83
W40×73
W40×68
W40×62
27.3
24.3
21.5
20.0
18.3
21.62
21.43
21.24
21.13
20.99
215⁄8
213⁄8
211⁄4
211⁄8
21
0.580
0.515
0.455
0.430
0.400
9⁄
16
1⁄
2
7⁄
16
7⁄
16
3⁄
8
5⁄
16
1⁄
4
1⁄
4
1⁄
4
3⁄
16
8.420
8.355
8.295
8.270
8.240
83⁄8
83⁄8
81⁄4
81⁄4
81⁄4
0.930
0.835
0.740
0.685
0.615
15⁄
16
13⁄
16
3⁄
4
11⁄
16
5⁄
8
181⁄4
181⁄4
181⁄4
181⁄4
181⁄4
111⁄16
19⁄16
11⁄2
17⁄16
13⁄8
15⁄
16
15⁄
16
7⁄
8
7⁄
8
W21×57
W40×50
W40×44
16.7
14.7
13.0
21.06
20.83
20.66
21
207⁄8
205⁄8
0.405
0.380
0.350
3⁄
8
3⁄
8
3⁄
8
3⁄
16
3⁄
16
3⁄
16
6.555
6.530
6.500
61⁄2
61⁄2
61⁄2
0.650
0.535
0.450
5⁄
8
9⁄
16
7⁄
16
181⁄4
181⁄4
181⁄4
13⁄8
15⁄16
13⁄16
7⁄
8
7⁄
8
7⁄
8
W18×311*
W40×283*
W40×258*
W40×234*
W40×211*
W40×192
W40×175
W40×158
W40×143
W40×130
91.5
83.2
75.9
68.8
62.1
56.4
51.3
46.3
42.1
38.2
22.32
21.85
21.46
21.06
20.67
20.35
20.04
19.72
19.49
19.25
223⁄8
217⁄8
211⁄2
21
205⁄8
203⁄8
20
193⁄4
191⁄2
191⁄4
1.520
1.400
1.280
1.160
1.060
0.960
0.890
0.810
0.730
0.670
11⁄2
13⁄8
11⁄4
13⁄16
11⁄16
1
7⁄
8
13⁄
16
3⁄
4
11⁄
16
3⁄
4
11⁄
16
5⁄
8
5⁄
8
9⁄
16
1⁄
2
7⁄
16
7⁄
16
3⁄
8
3⁄
8
12.005
11.890
11.770
11.650
11.555
11.455
11.375
11.300
11.220
11.160
12
117⁄8
113⁄4
115⁄8
111⁄2
111⁄2
113⁄8
111⁄4
111⁄4
111⁄8
2.740 23⁄4
2.500 21⁄2
2.300 25⁄16
2.110 21⁄8
1.910 115⁄16
1.750 13⁄4
1.590 19⁄16
1.440 17⁄16
1.320 15⁄16
1.200 13⁄16
151⁄2
151⁄2
151⁄2
151⁄2
151⁄2
151⁄2
151⁄2
151⁄2
151⁄2
151⁄2
37⁄16
33⁄16
3
23⁄4
9
2 ⁄16
27⁄16
21⁄4
21⁄8
2
17⁄8
13⁄16
13⁄16
11⁄8
1
1
15⁄
16
7⁄
8
7⁄
8
13⁄
16
13⁄
16
W18×119
W40×106
W40×97
W40×86
W40×76
35.1
31.1
28.5
25.3
22.3
18.97
18.73
18.59
18.39
18.21
19
183⁄4
185⁄8
183⁄8
181⁄4
0.655
0.590
0.535
0.480
0.425
5⁄
8
9⁄
16
9⁄
16
1⁄
2
7⁄
16
5⁄
16
5⁄
16
5⁄
16
1⁄
4
1⁄
4
11.265
11.200
11.145
11.090
11.035
111⁄4
111⁄4
111⁄8
111⁄8
11
1.060
0.940
0.870
0.770
0.680
11⁄16
15⁄
16
7⁄
8
3⁄
4
11⁄
16
151⁄2
151⁄2
151⁄2
151⁄2
151⁄2
13⁄4
15⁄8
19⁄16
17⁄16
13⁄8
15⁄
16
15⁄
16
7⁄
8
7⁄
8
13⁄
16
W18×71
W40×65
W40×60
W40×55
W40×50
20.8
19.1
17.6
16.2
14.7
18.47
18.35
18.24
18.11
17.99
181⁄2
183⁄8
181⁄4
181⁄8
18
0.495
0.450
0.415
0.390
0.355
1⁄
2
7⁄
16
7⁄
16
3⁄
8
3⁄
8
1⁄
4
1⁄
4
1⁄
4
3⁄
16
3⁄
16
7.635
7.590
7.555
7.530
7.495
75⁄8
75⁄8
71⁄2
71⁄2
71⁄2
0.810
0.750
0.695
0.630
0.570
13⁄
16
3⁄
4
11⁄
16
5⁄
8
9⁄
16
151⁄2
151⁄2
151⁄2
151⁄2
151⁄2
11⁄2
17⁄16
13⁄8
15⁄16
11⁄4
7⁄
8
7⁄
8
13⁄
16
13⁄
16
13⁄
16
W18×46
W40×40
W40×35
13.5
11.8
10.3
18.06
17.90
17.70
18
177⁄8
173⁄4
0.360
0.315
0.300
3⁄
8
5⁄
16
5⁄
16
3⁄
16
3⁄
16
3⁄
16
6.060
6.015
6.000
6
6
6
0.605
0.525
0.425
5⁄
8
1⁄
2
7⁄
16
151⁄2
151⁄2
151⁄2
11⁄4
13⁄16
11⁄8
13⁄
16
13⁄
16
3⁄
4
*Group 4 or Group 5 shape. See Notes in Table 1-2.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1
STRUCTURAL SHAPES
1 - 33
W SHAPES
Properties
Y
tf
d
k
k1
X
X
T
tw
Y
bf
Nominal
Wt.
per
ft
Compact
Section
Criteria
h
tw
Fy′′′
lb
bf
2tf
201
182
166
147
132
122
111
101
3.9
4.2
4.6
5.4
6.0
6.5
7.1
7.7
93
83
73
68
62
k
Plastic
Modulus
Elastic Properties
Axis X-X
X1
X2 × 106
ksi
ksi
2
20.6
22.6
24.9
26.1
28.9
31.3
34.1
37.5
—
—
—
—
—
—
55
45
4290
3910
3590
3140
2840
2630
2400
2200
4.5
5.0
5.6
6.0
6.7
32.3
36.4
41.2
43.6
46.9
61
48
38
34
29
57
50
44
5.0
6.1
7.2
46.3
49.4
53.6
311
283
258
234
211
192
175
158
143
130
2.2
2.4
2.6
2.8
3.0
3.3
3.6
3.9
4.2
4.6
119
106
97
86
76
S
I
4
in.
in.
453
649
904
1590
2350
3160
4510
6400
5310
4730
4280
3630
3220
2960
2670
2420
2680
2400
2140
2000
1820
3460
5250
8380
10900
15900
30
26
22
1960
1730
1550
10.6
11.5
12.5
13.8
15.1
16.7
18.0
19.8
21.9
23.9
—
—
—
—
—
—
—
—
—
—
5.3
6.0
6.4
7.2
8.1
24.5
27.2
30.0
33.4
37.8
71
65
60
55
50
4.7
5.1
5.4
6.0
6.6
46
40
35
5.0
5.7
7.1
Axis Y-Y
r
S
I
4
r
3
Zx
in.
in.
in.
in.
in.3
461
417
380
329
295
273
249
227
9.47
9.40
9.36
9.17
9.12
9.09
9.05
9.02
542
483
435
376
333
305
274
248
86.1
77.2
70.1
60.1
53.5
49.2
44.5
40.3
3.02
3.00
2.98
2.95
2.93
2.92
2.90
2.89
530
476
432
373
333
307
279
253
133
119
108
92.6
82.3
75.6
68.2
61.7
2070
1830
1600
1480
1330
192
171
151
140
127
8.70
8.67
8.64
8.60
8.54
92.9
81.4
70.6
64.7
57.5
22.1
19.5
17.0
15.7
13.9
1.84
1.83
1.81
1.80
1.77
221
196
172
160
144
34.7
30.5
26.6
24.4
21.7
13100
22600
36600
1170
984
843
111
94.5
81.6
8.36
8.18
8.06
30.6
24.9
20.7
1.35
1.30
1.26
129
110
95.4
14.8
12.2
10.2
8160
7520
6920
6360
5800
5320
4870
4430
4060
3710
38
52
71
97
140
194
274
396
557
789
6960
6160
5510
4900
4330
3870
3450
3060
2750
2460
624
564
514
466
419
380
344
310
282
256
8.72
8.61
8.53
8.44
8.35
8.28
8.20
8.12
8.09
8.03
795
704
628
558
493
440
391
347
311
278
132
118
107
95.8
85.3
76.8
68.8
61.4
55.5
49.9
2.95
2.91
2.88
2.85
2.82
2.79
2.76
2.74
2.72
2.70
753
676
611
549
490
442
398
356
322
291
207
185
166
149
132
119
106
94.8
85.4
76.7
—
—
—
57
45
3340
2990
2750
2460
2180
1210
1880
2580
4060
6520
2190
1910
1750
1530
1330
231
204
188
166
146
7.90
7.84
7.82
7.77
7.73
253
220
201
175
152
44.9
39.4
36.1
31.6
27.6
2.69
2.66
2.65
2.63
2.61
261
230
211
186
163
69.1
60.5
55.3
48.4
42.2
32.4
35.7
38.7
41.2
45.2
61
50
43
38
31
2680
2470
2290
2110
1920
3310
4540
6080
8540
12400
1170
1070
984
890
800
127
117
108
98.3
88.9
7.50
7.49
7.47
7.41
7.38
60.3
54.8
50.1
44.9
40.1
15.8
14.4
13.3
11.9
10.7
1.70
1.69
1.69
1.67
1.65
145
133
123
112
101
24.7
22.5
20.6
18.5
16.6
44.6
51.0
53.5
32
25
22
2060
1810
1590
10100
17200
30300
712
612
510
78.8
68.4
57.6
7.25
7.21
7.04
22.5
19.1
15.3
9.35
7.64
6.36
7.43
6.35
5.12
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1.29
1.27
1.22
3
Zy
in.
(1/ksi)
3
90.7
78.4
66.5
11.7
9.95
8.06
1 - 34
DIMENSIONS AND PROPERTIES
Y
tf
d
X
W SHAPES
Dimensions
k
k1
X
T
tw
Y
bf
k
Web
Designation
Area
A
2
in.
Depth
d
in.
Thickness
tw
in.
Flange
tw
2
in.
Width
bf
in.
Distance
Thickness
tf
in.
T
k
in.
in.
k1
in.
W16×100
W16×89
W16×77
W16×67
29.4
26.2
22.6
19.7
16.97
16.75
16.52
16.33
17
163⁄4
161⁄2
163⁄8
0.585
0.525
0.455
0.395
9⁄
16
1⁄
2
7⁄
16
3⁄
8
5⁄
16
1⁄
4
1⁄
4
3⁄
16
10.425
10.365
10.295
10.235
103⁄8
103⁄8
101⁄4
101⁄4
0.985
0.875
0.760
0.665
1
7⁄
8
3⁄
4
11⁄
16
135⁄8 111⁄16
135⁄8 19⁄16
135⁄8 17⁄16
135⁄8 13⁄8
15⁄
16
7⁄
8
7⁄
8
13⁄
16
W16×57
W16×50
W16×45
W16×40
W16×36
16.8
14.7
13.3
11.8
10.6
16.43
16.26
16.13
16.01
15.86
163⁄8
161⁄4
161⁄8
16
157⁄8
0.430
0.380
0.345
0.305
0.295
7⁄
16
3⁄
8
3⁄
8
5⁄
16
5⁄
16
1⁄
4
3⁄
16
3⁄
16
3⁄
16
3⁄
16
7.120
7.070
7.035
6.995
6.985
71⁄8
71⁄8
7
7
7
0.715
0.630
0.565
0.505
0.430
11⁄
16
5⁄
8
9⁄
16
1⁄
2
7⁄
16
135⁄8
135⁄8
135⁄8
135⁄8
135⁄8
13⁄8
15⁄16
11⁄4
13⁄16
11⁄8
7⁄
8
13⁄
16
13⁄
16
13⁄
16
3⁄
4
9.12 15.88
7.68 15.69
157⁄8
153⁄4
0.275
0.250
1⁄
4
1⁄
4
1⁄
5.525
5.500
51⁄2
51⁄2
0.440
0.345
7⁄
16
3⁄
8
135⁄8
135⁄8
11⁄8
11⁄16
3⁄
4
3⁄
4
17⁄8
19⁄16
17⁄16
15⁄16
13⁄16
11⁄8
1
18.560
17.890
17.650
17.415
17.200
17.010
16.835
181⁄2
177⁄8
175⁄8
173⁄8
171⁄4
17
167⁄8
5.120 51⁄8
4.910 415⁄16
4.520 41⁄2
4.160 43⁄16
3.820 313⁄16
3.500 31⁄2
3.210 33⁄16
111⁄4 513⁄16 21⁄2
111⁄4 59⁄16 23⁄16
111⁄4 53⁄16 21⁄16
111⁄4 413⁄16 115⁄16
111⁄4 41⁄2 113⁄16
111⁄4 43⁄16 13⁄4
111⁄4 37⁄8
15⁄8
15⁄
16.695
16.590
16.475
16.360
16.230
16.110
15.995
15.890
15.800
15.710
15.650
15.565
15.500
163⁄4
165⁄8
161⁄2
163⁄8
161⁄4
161⁄8
16
157⁄8
153⁄4
153⁄4
155⁄8
155⁄8
151⁄2
3.035 31⁄16
2.845 27⁄8
2.660 211⁄16
2.470 21⁄2
2.260 21⁄4
2.070 21⁄16
1.890 17⁄8
1.720 13⁄4
1.560 19⁄16
1.440 17⁄16
1.310 15⁄16
1.190 13⁄16
1.090 11⁄16
111⁄4 311⁄16
111⁄4 31⁄2
111⁄4 35⁄16
111⁄4 31⁄8
111⁄4 215⁄16
111⁄4 23⁄4
111⁄4 29⁄16
111⁄4 23⁄8
111⁄4 21⁄4
111⁄4 21⁄8
111⁄4
2
111⁄4 17⁄8
111⁄4 13⁄4
W16×31
W16×26
W14×808*
W16×730*
W16×665*
W16×605*
W16×550*
W16×500*
W16×455*
237
215
196
178
162
147
134
22.84
22.42
21.64
20.92
20.24
19.60
19.02
227⁄8
223⁄8
215⁄8
207⁄8
201⁄4
195⁄8
19
3.740 33⁄4
3.070 31⁄16
2.830 213⁄16
2.595 25⁄8
2.380 23⁄8
2.190 23⁄16
2.015
2
W14×426*
W16×398*
W16×370*
W16×342*
W16×311*
W16×283*
W16×257*
W16×233*
W16×211
W16×193
W16×176
W16×159
W16×145
125
117
109
101
91.4
83.3
75.6
68.5
62.0
56.8
51.8
46.7
42.7
18.67
18.29
17.92
17.54
17.12
16.74
16.38
16.04
15.72
15.48
15.22
14.98
14.78
185⁄8
181⁄4
177⁄8
171⁄2
171⁄8
163⁄4
163⁄8
16
153⁄4
151⁄2
151⁄4
15
143⁄4
1.875
1.770
1.655
1.540
1.410
1.290
1.175
1.070
0.980
0.890
0.830
0.745
0.680
17⁄8
13⁄4
15⁄8
19⁄16
17⁄16
15⁄16
13⁄16
11⁄16
1
7⁄
8
13⁄
16
3⁄
4
11⁄
16
1⁄
7⁄
13⁄
13⁄
3⁄
8
8
16
8
16
16
4
11⁄
16
5⁄
8
9⁄
16
1⁄
2
7⁄
16
7⁄
16
3⁄
8
3⁄
8
*Group 4 or Group 5 shape. See Notes in Table 1-2.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
19⁄16
11⁄2
17⁄16
13⁄8
15⁄16
11⁄4
13⁄16
13⁄16
11⁄8
11⁄16
11⁄16
1
1
STRUCTURAL SHAPES
1 - 35
W SHAPES
Properties
Y
tf
d
k
k1
X
X
T
tw
Y
bf
Compact
NomSection
inal
Criteria
Wt.
per
Fy′′′
bf
h
ft
2tf tw
lb
ksi
k
Plastic
Modulus
Elastic Properties
Axis X-X
X1
X2 × 106
ksi
2
(1/ksi)
S
I
4
Axis Y-Y
r
3
in.
in.
175
155
134
117
S
I
4
r
3
Zx
3
Zy
in.3
in.
in.
in.
in.
in.
7.10
7.05
7.00
6.96
186
163
138
119
35.7
31.4
26.9
23.2
2.51
2.49
2.47
2.46
198
175
150
130
54.9
48.1
41.1
35.5
12.1
10.5
9.34
8.25
7.00
1.60
1.59
1.57
1.57
1.52
105
92.0
82.3
72.9
64.0
18.9
16.3
14.5
12.7
10.8
4.49 1.17
3.49 1.12
54.0
44.2
100
89
77
67
5.3
5.9
6.8
7.7
24.3
27.0
31.2
35.9
—
—
—
50
3450
3090
2680
2350
1040
1630
2790
4690
1490
1300
1110
954
57
50
45
40
36
5.0
5.6
6.2
6.9
8.1
33.0
37.4
41.2
46.6
48.1
59
46
38
30
28
2650 3400
2340 5530
2120 8280
1890 12900
1700 20800
758
659
586
518
448
92.2
81.0
72.7
64.7
56.5
6.72
6.68
6.65
6.63
6.51
43.1
37.2
32.8
28.9
24.5
31
26
6.3
8.0
51.6
56.8
24
20
1740 20000
1470 40900
375
301
47.2
38.4
6.41
6.26
12.4
9.59
808
730
665
605
550
500
455
1.8
1.8
2.0
2.1
2.3
2.4
2.6
3.4
3.7
4.0
4.4
4.8
5.2
5.7
—
—
—
—
—
—
—
18900
17500
16300
15100
14200
13100
12200
1.45
1.90
2.50
3.20
4.20
5.50
7.30
16000
14300
12400
10800
9430
8210
7190
1400
1280
1150
1040
931
838
756
8.21
8.17
7.98
7.80
7.63
7.48
7.33
5510
4720
4170
3680
3250
2880
2560
594
527
472
423
378
339
304
4.82
4.69
4.62
4.55
4.49
4.43
4.38
1834
1660
1480
1320
1180
1050
936
927
816
730
652
583
522
468
426
398
370
342
311
283
257
233
211
193
176
159
145
2.8
2.9
3.1
3.3
3.6
3.9
4.2
4.6
5.1
5.5
6.0
6.5
7.1
6.1
6.4
6.9
7.4
8.1
8.8
9.7
10.7
11.6
12.8
13.7
15.3
16.8
—
—
—
—
—
—
—
—
—
—
—
—
—
11500
10900
10300
9600
8820
8120
7460
6820
6230
5740
5280
4790
4400
8.90
11.0
13.9
17.9
24.4
33.4
46.1
64.9
91.8
125
173
249
348
6600
6000
5440
4900
4330
3840
3400
3010
2660
2400
2140
1900
1710
707
656
607
559
506
459
415
375
338
310
281
254
232
7.26
7.16
7.07
6.98
6.88
6.79
6.71
6.63
6.55
6.50
6.43
6.38
6.33
2360
2170
1990
1810
1610
1440
1290
1150
1030
931
838
748
677
283
262
241
221
199
179
161
145
130
119
107
96.2
87.3
4.34
4.31
4.27
4.24
4.20
4.17
4.13
4.10
4.07
4.05
4.02
4.00
3.98
869
801
736
672
603
542
487
436
390
355
320
287
260
434
402
370
338
304
274
246
221
198
180
163
146
133
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
7.03
5.48
1 - 36
DIMENSIONS AND PROPERTIES
Y
tf
d
X
W SHAPES
Dimensions
k
k1
X
T
tw
Y
bf
k
Web
Designation
Area
A
2
in.
Depth
d
in.
Thickness
tw
in.
Flange
tw
2
in.
Width
bf
Distance
Thickness
tf
in.
in.
T
k
k1
in.
in.
in.
W14×132
W16×120
W16×109
W16×99
W16×90
38.8
35.3
32.0
29.1
26.5
14.66
14.48
14.32
14.16
14.02
145⁄8
141⁄2
143⁄8
141⁄8
14
0.645
0.590
0.525
0.485
0.440
5⁄
8
9⁄
16
1⁄
2
1⁄
2
7⁄
16
5⁄
16
5⁄
16
1⁄
4
1⁄
4
1⁄
4
14.725
14.670
14.605
14.565
14.520
143⁄4
145⁄8
145⁄8
145⁄8
141⁄2
1.030
0.940
0.860
0.780
0.710
1
15⁄
16
7⁄
8
3⁄
4
11⁄
16
111⁄4
111⁄4
111⁄4
111⁄4
111⁄4
111⁄16
15⁄8
19⁄16
17⁄16
13⁄8
15⁄
16
15⁄
16
7⁄
8
7⁄
8
7⁄
8
W14×82
W16×74
W16×68
W16×61
24.1
21.8
20.0
17.9
14.31
14.17
14.04
13.89
141⁄4
141⁄8
14
137⁄8
0.510
0.450
0.415
0.375
1⁄
2
7⁄
16
7⁄
16
3⁄
8
1⁄
4
1⁄
4
1⁄
4
3⁄
16
10.130
10.070
10.035
9.995
101⁄8
101⁄8
10
10
0.855
0.785
0.720
0.645
7⁄
8
13⁄
16
3⁄
4
5⁄
8
11
11
11
11
15⁄8
19⁄16
11⁄2
17⁄16
15⁄
16
15⁄
16
15⁄
16
W14×53
W16×48
W16×43
15.6
14.1
12.6
13.92
13.79
13.66
137⁄8
133⁄4
135⁄8
0.370
0.340
0.305
3⁄
8
5⁄
16
5⁄
16
3⁄
16
3⁄
16
3⁄
16
8.060
8.030
7.995
8
8
8
0.660
0.595
0.530
11⁄
16
5⁄
8
1⁄
2
11
11
11
17⁄16
13⁄8
15⁄16
15⁄
16
7⁄
8
7⁄
8
W14×38
W16×34
W16×30
11.2
10.0
8.85
14.10
13.98
13.84
141⁄8
14
137⁄8
0.310
0.285
0.270
5⁄
16
5⁄
16
1⁄
4
3⁄
16
3⁄
16
1⁄
8
6.770
6.745
6.730
63⁄4
63⁄4
63⁄4
0.515
0.455
0.385
1⁄
2
7⁄
16
3⁄
8
12
12
12
11⁄16
1
15⁄
16
5⁄
8
5⁄
8
5⁄
8
W14×26
W16×22
7.69
6.49
13.91
13.74
137⁄8
133⁄4
0.255
0.230
1⁄
4
1⁄
4
1⁄
8
1⁄
8
5.025
5.000
5
5
0.420
0.335
7⁄
16
5⁄
16
12
12
15⁄
16
7⁄
8
9⁄
16
9⁄
16
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1
STRUCTURAL SHAPES
1 - 37
W SHAPES
Properties
Y
tf
d
k
k1
X
X
T
tw
Y
bf
Nominal
Wt.
per
ft
Compact
Section
Criteria
h
tw
Fy′′′
lb
bf
2tf
132
120
109
99
90
7.1
7.8
8.5
9.3
10.2
82
74
68
61
5.9
6.4
7.0
7.7
k
Plastic
Modulus
Elastic Properties
Axis X-X
X1
X2 × 106
ksi
ksi
2
17.7
19.3
21.7
23.5
25.9
—
—
—
—
—
4180
3830
3490
3190
2900
22.4
25.3
27.5
30.4
—
—
—
—
53
48
43
6.1 30.8
6.7 33.5
7.5 37.4
38
34
30
26
22
S
I
Axis Y-Y
r
S
in.
in.
428
601
853
1220
1750
1530
1380
1240
1110
999
209
190
173
157
143
6.28
6.24
6.22
6.17
6.14
3600
3290
3020
2720
846
1190
1650
2460
882
796
723
640
123
112
103
92.2
6.05
6.04
6.01
5.98
—
57
46
2830
2580
2320
2250
3220
4900
541
485
428
77.8
70.3
62.7
5.89
5.85
5.82
57.7
51.4
45.2
6.6 39.6
7.4 43.1
8.7 45.4
41
35
31
2190
1970
1750
6850
10600
17600
385
340
291
54.6
48.6
42.0
5.87
5.83
5.73
26.7
23.3
19.6
6.0 48.1
7.5 53.3
28
22
1890
1610
13900
27300
245
199
35.3
29.0
5.65
5.54
(1/ksi)
3
I
4
in.
4
r
Zx
in.
in.
in.3
548
495
447
402
362
74.5
67.5
61.2
55.2
49.9
3.76
3.74
3.73
3.71
3.70
234
212
192
173
157
113
102
92.7
83.6
75.6
148
134
121
107
29.3
26.6
24.2
21.5
2.48
2.48
2.46
2.45
139
126
115
102
44.8
40.6
36.9
32.8
14.3
12.8
11.3
1.92
1.91
1.89
87.1
78.4
69.6
22.0
19.6
17.3
7.88
6.91
5.82
1.55
1.53
1.49
61.5
54.6
47.3
12.1
10.6
8.99
3.54
2.80
1.08
1.04
40.2
33.2
5.54
4.39
8.91
7.00
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
3
Zy
in.
in.
3
1 - 38
DIMENSIONS AND PROPERTIES
Y
tf
d
X
W SHAPES
Dimensions
k
k1
X
T
tw
Y
bf
k
Web
Designation
Area
A
2
in.
Depth
d
in.
Flange
Thickness
tw
tw
2
in.
in.
Width
bf
Distance
Thickness
tf
in.
T
k
k1
in.
in.
in.
in.
2.955 215⁄16
2.705 211⁄16
2.470 21⁄2
2.250 21⁄4
2.070 21⁄16
1.900 17⁄8
1.735 13⁄4
1.560 19⁄16
1.400 13⁄8
1.250 11⁄4
1.105 11⁄8
0.990
1
7⁄
0.900
8
0.810 13⁄16
3
0.735
⁄4
0.670 11⁄16
5⁄
0.605
8
91⁄2
91⁄2
91⁄2
91⁄2
91⁄2
91⁄2
91⁄2
91⁄2
91⁄2
91⁄2
91⁄2
91⁄2
91⁄2
91⁄2
91⁄2
91⁄2
91⁄2
311⁄16
37⁄16
33⁄16
215⁄16
23⁄4
25⁄8
27⁄16
21⁄4
21⁄8
115⁄16
113⁄16
111⁄16
15⁄8
11⁄2
17⁄16
13⁄8
15⁄16
11⁄2
17⁄16
13⁄8
15⁄16
11⁄4
11⁄4
13⁄16
11⁄8
11⁄16
1
1
15⁄
16
7⁄
8
7⁄
8
7⁄
8
7⁄
8
13⁄
16
5⁄
8
9⁄
16
91⁄2
91⁄2
13⁄8
11⁄4
13⁄
16
13⁄
16
0.640
0.575
0.515
5⁄
8
9⁄
16
1⁄
2
91⁄2
91⁄2
91⁄2
13⁄8
11⁄4
11⁄4
13⁄
16
13⁄
16
3⁄
4
61⁄2
61⁄2
61⁄2
0.520
0.440
0.380
1⁄
2
7⁄
16
3⁄
8
101⁄2
101⁄2
101⁄2
15⁄
16
7⁄
8
1
9⁄
16
1⁄
2
1⁄
2
4
4
4
4
0.425
0.350
0.265
0.225
7⁄
16
3⁄
8
1⁄
4
1⁄
4
101⁄2
101⁄2
101⁄2
101⁄2
7⁄
8
13⁄
16
3⁄
4
11⁄
16
1⁄
2
1⁄
2
1⁄
2
1⁄
2
W12×336*
W16×305*
W16×279*
W16×252*
W16×230*
W16×210*
W16×190
W16×170
W16×152
W16×136
W16×120
W16×106
W16×96
W16×87
W16×79
W16×72
W16×65
98.8
89.6
81.9
74.1
67.7
61.8
55.8
50.0
44.7
39.9
35.3
31.2
28.2
25.6
23.2
21.1
19.1
16.82
16.32
15.85
15.41
15.05
14.71
14.38
14.03
13.71
13.41
13.12
12.89
12.71
12.53
12.38
12.25
12.12
167⁄8
163⁄8
157⁄8
153⁄8
15
143⁄4
143⁄8
14
133⁄4
133⁄8
131⁄8
127⁄8
123⁄4
121⁄2
123⁄8
121⁄4
121⁄8
1.775
1.625
1.530
1.395
1.285
1.180
1.060
0.960
0.870
0.790
0.710
0.610
0.550
0.515
0.470
0.430
0.390
13⁄4
15⁄8
11⁄2
13⁄8
15⁄16
13⁄16
11⁄16
15⁄
16
7⁄
8
13⁄
16
11⁄
16
5⁄
8
9⁄
16
1⁄
2
1⁄
2
7⁄
16
3⁄
8
7⁄
8
13⁄
16
3⁄
4
11⁄
16
11⁄
16
5⁄
8
9⁄
16
1⁄
2
7⁄
16
7⁄
16
3⁄
8
5⁄
16
5⁄
16
1⁄
4
1⁄
4
1⁄
4
3⁄
16
13.385
13.235
13.140
13.005
12.895
12.790
12.670
12.570
12.480
12.400
12.320
12.220
12.160
12.125
12.080
12.040
12.000
133⁄8
131⁄4
131⁄8
13
127⁄8
123⁄4
125⁄8
125⁄8
121⁄2
123⁄8
123⁄8
121⁄4
121⁄8
121⁄8
121⁄8
12
12
W12×58
W16×53
17.0
15.6
12.19
12.06
121⁄4
12
0.360
0.345
3⁄
8
3⁄
8
3⁄
16
3⁄
16
10.010
9.995
10
10
0.640
0.575
W12×50
W16×45
W16×40
14.7
13.2
11.8
12.19
12.06
11.94
121⁄4
12
12
0.370
0.335
0.295
3⁄
8
5⁄
16
5⁄
16
3⁄
16
3⁄
16
3⁄
16
8.080
8.045
8.005
81⁄8
8
8
W12×35
W16×30
W16×26
10.3
8.79
7.65
12.50
12.34
12.22
121⁄2
123⁄8
121⁄4
0.300
0.260
0.230
5⁄
16
1⁄
4
1⁄
4
3⁄
16
1⁄
8
1⁄
8
6.560
6.520
6.490
W12×22
W16×19
W16×16
W16×14
6.48
5.57
4.71
4.16
12.31
12.16
11.99
11.91
121⁄4
121⁄8
12
117⁄8
0.260
0.235
0.220
0.200
1⁄
4
1⁄
4
1⁄
4
3⁄
16
1⁄
8
1⁄
8
1⁄
8
1⁄
8
4.030
4.005
3.990
3.970
*Group 4 or Group 5 shape. See Notes in Table 1-2.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
STRUCTURAL SHAPES
1 - 39
W SHAPES
Properties
Y
tf
d
k
k1
X
X
T
tw
Y
bf
Nominal
Wt.
per
ft
Compact
Section
Criteria
h
tw
Fy′′′
lb
bf
2tf
336
305
279
252
230
210
190
170
152
136
120
106
96
87
79
72
65
2.3
2.4
2.7
2.9
3.1
3.4
3.7
4.0
4.5
5.0
5.6
6.2
6.8
7.5
8.2
9.0
9.9
58
53
k
Plastic
Modulus
Elastic Properties
Axis X-X
X1
X2 × 106
ksi
ksi
2
5.5
6.0
6.3
7.0
7.6
8.2
9.2
10.1
11.2
12.3
13.7
15.9
17.7
18.9
20.7
22.6
24.9
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
12800
11800
11000
10100
9390
8670
7940
7190
6510
5850
5240
4660
4250
3880
3530
3230
2940
7.8
8.7
27.0
28.1
—
—
3070
2820
50
45
40
6.3
7.0
7.8
26.2
29.0
32.9
—
—
59
3170
2870
2580
35
30
26
6.3
7.4
8.5
36.2
41.8
47.2
22
19
16
14
4.7
5.7
7.5
8.8
41.8
46.2
49.4
54.3
(1/ksi)
S
I
4
Axis Y-Y
r
3
S
I
4
Zx
3
Zy
in.
in.
177
159
143
127
115
104
93.0
82.3
72.8
64.2
56.0
49.3
44.4
39.7
35.8
32.4
29.1
3.47
3.42
3.38
3.34
3.31
3.28
3.25
3.22
3.19
3.16
3.13
3.11
3.09
3.07
3.05
3.04
3.02
603
537
481
428
386
348
311
275
243
214
186
164
147
132
119
108
96.8
274
244
220
196
177
159
143
126
111
98.0
85.4
75.1
67.5
60.4
54.3
49.2
44.1
in.
in.
4060
3550
3110
2720
2420
2140
1890
1650
1430
1240
1070
933
833
740
662
597
533
483
435
393
353
321
292
263
235
209
186
163
145
131
118
107
97.4
87.9
6.41 1190
6.29 1050
6.16 937
6.06 828
5.97 742
5.89 664
5.82 589
5.74 517
5.66 454
5.58 398
5.51 345
5.47 301
5.44 270
5.38 241
5.34 216
5.31 195
5.28 174
1470
2100
475
425
78.0
70.6
5.28
5.23
107
95.8
21.4
19.2
2.51
2.48
86.4
77.9
32.5
29.1
1410
2070
3110
394
350
310
64.7
58.1
51.9
5.18
5.15
5.13
56.3
50.0
44.1
13.9
12.4
11.0
1.96
1.94
1.93
72.4
64.7
57.5
21.4
19.0
16.8
49
37
29
2420 4340
2090 7950
1820 13900
285
238
204
45.6
38.6
33.4
5.25
5.21
5.17
24.5
20.3
17.3
7.47 1.54
6.24 1.52
5.34 1.51
51.2
43.1
37.2
11.5
9.56
8.17
37
30
26
22
2160 8640
1880 15600
1610 32000
1450 49300
156
130
103
88.6
25.4
21.3
17.1
14.9
4.91
4.82
4.67
4.62
2.31
1.88
1.41
1.19
29.3
24.7
20.1
17.4
3.66
2.98
2.26
1.90
4.66
3.76
2.82
2.36
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
0.847
0.822
0.773
0.753
in.
in.3
in.
6.05
8.17
10.8
14.7
19.7
26.6
37.0
54.0
79.3
119
184
285
405
586
839
1180
1720
in.
r
3
1 - 40
DIMENSIONS AND PROPERTIES
Y
tf
d
X
W SHAPES
Dimensions
k
k1
X
T
tw
Y
bf
k
Web
Designation
Area
A
2
in.
Depth
d
in.
Flange
Thickness
tw
tw
2
in.
in.
Width
bf
Distance
Thickness
tf
k1
in.
in.
in.
32.9
29.4
25.9
22.6
20.0
17.6
15.8
14.4
11.36
11.10
10.84
10.60
10.40
10.22
10.09
9.98
113⁄8
111⁄8
107⁄8
105⁄8
103⁄8
101⁄4
101⁄8
10
0.755
0.680
0.605
0.530
0.470
0.420
0.370
0.340
3⁄
4
11⁄
16
5⁄
8
1⁄
2
1⁄
2
7⁄
16
3⁄
8
5⁄
16
3⁄
8
3⁄
8
5⁄
16
1⁄
4
1⁄
4
1⁄
4
3⁄
16
3⁄
16
10.415
10.340
10.265
10.190
10.130
10.080
10.030
10.000
103⁄8
103⁄8
101⁄4
101⁄4
101⁄8
101⁄8
10
10
1.250
1.120
0.990
0.870
0.770
0.680
0.615
0.560
11⁄4
11⁄8
1
7⁄
8
3⁄
4
11⁄
16
5⁄
8
9⁄
16
75⁄8
75⁄8
75⁄8
75⁄8
75⁄8
75⁄8
75⁄8
75⁄8
17⁄8
13⁄4
15⁄8
11⁄2
13⁄8
15⁄16
11⁄4
13⁄16
15⁄
16
7⁄
8
13⁄
16
13⁄
16
3⁄
4
3⁄
4
11⁄
16
11⁄
16
W10×45
W10×39
W10×33
13.3
11.5
9.71
10.10
9.92
9.73
101⁄8
97⁄8
93⁄4
0.350
0.315
0.290
3⁄
8
5⁄
16
5⁄
16
3⁄
16
3⁄
16
3⁄
16
8.020
7.985
7.960
8
8
8
0.620
0.530
0.435
5⁄
8
1⁄
2
7⁄
16
75⁄8
75⁄8
75⁄8
11⁄4
11⁄8
11⁄16
11⁄
0.300
0.260
0.240
5⁄
16
1⁄
4
1⁄
4
3⁄
16
1⁄
8
1⁄
8
5.810
5.770
5.750
53⁄4
53⁄4
53⁄4
0.510
0.440
0.360
1⁄
2
7⁄
16
3⁄
8
85⁄8
85⁄8
85⁄8
15⁄
16
7⁄
8
3⁄
4
1⁄
2
1⁄
2
1⁄
2
0.250
0.240
0.230
0.190
1⁄
4
1⁄
4
1⁄
4
3⁄
16
1⁄
8
1⁄
8
1⁄
8
1⁄
8
4.020
4.010
4.000
3.960
4
4
4
4
0.395
0.330
0.270
0.210
3⁄
8
5⁄
16
1⁄
4
3⁄
16
85⁄8
85⁄8
85⁄8
85⁄8
13⁄
16
3⁄
4
11⁄
16
5⁄
8
1⁄
2
1⁄
2
7⁄
16
7⁄
16
W10×30
W10×26
W10×22
8.84
7.61
6.49
10.47
10.33
10.17
W10×19
W10×17
W10×15
W10×12
5.62
4.99
4.41
3.54
10.24
10.11
9.99
9.87
101⁄4
101⁄8
10
97⁄8
in.
k
W10×112
W10×100
W10×88
W10×77
W10×68
W10×60
W10×54
W10×49
101⁄2
103⁄8
101⁄8
in.
T
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
11⁄
11⁄
16
16
16
STRUCTURAL SHAPES
1 - 41
W SHAPES
Properties
Y
tf
d
k
k1
X
X
T
tw
Y
bf
Nominal
Wt.
per
ft
Compact
Section
Criteria
h
tw
Fy′′′
lb
bf
2tf
112
100
88
77
68
60
54
49
4.2
4.6
5.2
5.9
6.6
7.4
8.2
8.9
45
39
33
k
Plastic
Modulus
Elastic Properties
Axis X-X
X1
X2 × 106
ksi
ksi
2
in.
in.
10.4
11.6
13.0
14.8
16.7
18.7
21.2
23.1
—
—
—
—
—
—
—
—
7080
6400
5680
5010
4460
3970
3580
3280
56.7
83.8
132
213
334
525
778
1090
716
623
534
455
394
341
303
272
6.5
7.5
9.1
22.5
25.0
27.1
—
—
—
3650
3190
2710
758
1300
2510
30
26
22
5.7
6.6
8.0
29.5
34.0
36.9
—
55
47
2890
2500
2150
2160
3790
7170
19
17
15
12
5.1
6.1
7.4
9.4
35.4
36.9
38.5
46.6
51
47
43
30
2420
2210
1930
1550
5160
7820
14300
35400
(1/ksi)
S
I
4
Axis Y-Y
r
3
S
I
4
r
3
in.3
2.68
2.65
2.63
2.60
2.59
2.57
2.56
2.54
147
130
113
97.6
85.3
74.6
66.6
60.4
69.2
61.0
53.1
45.9
40.1
35.0
31.3
28.3
13.3
11.3
9.20
2.01
1.98
1.94
54.9
46.8
38.8
20.3
17.2
14.0
5.75
4.89
3.97
1.37
1.36
1.33
36.6
31.3
26.0
8.84
7.50
6.10
2.14
1.78
1.45
1.10
0.874
0.844
0.810
0.785
21.6
18.7
16.0
12.6
3.35
2.80
2.30
1.74
in.
in.
in.
126
112
98.5
85.9
75.7
66.7
60.0
54.6
4.66
4.60
4.54
4.49
4.44
4.39
4.37
4.35
236
207
179
154
134
116
103
93.4
45.3
40.0
34.8
30.1
26.4
23.0
20.6
18.7
248
209
170
49.1
42.1
35.0
4.32
4.27
4.19
53.4
45.0
36.6
170
144
118
32.4
27.9
23.2
4.38
4.35
4.27
16.7
14.1
11.4
18.8
16.2
13.8
10.9
4.14
4.05
3.95
3.90
4.29
3.56
2.89
2.18
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
3
Zy
in.
in.
96.3
81.9
68.9
53.8
Zx
1 - 42
DIMENSIONS AND PROPERTIES
Y
tf
d
X
W SHAPES
Dimensions
k
k1
X
T
tw
Y
bf
k
Web
Designation
Area
A
Depth
d
2
in.
in.
Thickness
tw
in.
Flange
tw
2
in.
Width
bf
Distance
Thickness
tf
in.
in.
T
k
k1
in.
in.
W8×67
W8×58
W8×48
W8×40
W8×35
W8×31
19.7
17.1
14.1
11.7
10.3
9.13
9.00
8.75
8.50
8.25
8.12
8.00
9
83⁄4
81⁄2
81⁄4
81⁄8
8
0.570
0.510
0.400
0.360
0.310
0.285
9⁄
16
1⁄
2
3⁄
8
3⁄
8
5⁄
16
5⁄
16
5⁄
16
1⁄
4
3⁄
16
3⁄
16
3⁄
16
3⁄
16
8.280
8.220
8.110
8.070
8.020
7.995
81⁄4
81⁄4
81⁄8
81⁄8
8
8
0.935
0.810
0.685
0.560
0.495
0.435
15⁄
16
13⁄
16
11⁄
16
9⁄
16
1⁄
2
7⁄
16
61⁄8
61⁄8
61⁄8
61⁄8
61⁄8
61⁄8
17⁄16
15⁄16
13⁄16
11⁄16
1
15⁄
16
11⁄
W8×28
W8×24
8.25
7.08
8.06
7.93
8
77⁄8
0.285
0.245
5⁄
16
1⁄
4
3⁄
16
1⁄
8
6.535
6.495
61⁄2
61⁄2
0.465
0.400
7⁄
16
3⁄
8
61⁄8
61⁄8
15⁄
16
7⁄
8
9⁄
16
9⁄
16
W8×21
W8×18
6.16
5.26
8.28
8.14
81⁄4
81⁄8
0.250
0.230
1⁄
4
1⁄
4
1⁄
8
1⁄
8
5.270
5.250
51⁄4
51⁄4
0.400
0.330
3⁄
8
5⁄
16
65⁄8
65⁄8
13⁄
16
3⁄
4
1⁄
2
7⁄
16
W8×15
W8×13
W8×10
4.44
3.84
2.96
8.11
7.99
7.89
81⁄8
8
77⁄8
0.245
0.230
0.170
1⁄
4
1⁄
4
3⁄
16
1⁄
8
1⁄
8
1⁄
8
4.015
4.000
3.940
4
4
4
0.315
0.255
0.205
5⁄
16
1⁄
4
3⁄
16
65⁄8
65⁄8
65⁄8
3⁄
4
11⁄
16
5⁄
8
1⁄
2
7⁄
16
7⁄
16
W6×25
W8×20
W8×15
7.34
5.87
4.43
6.38
6.20
5.99
63⁄8
61⁄4
6
0.320
0.260
0.230
5⁄
16
1⁄
4
1⁄
4
3⁄
16
1⁄
8
1⁄
8
6.080
6.020
5.990
61⁄8
6
6
0.455
0.365
0.260
7⁄
16
3⁄
8
1⁄
4
43⁄4
43⁄4
43⁄4
13⁄
16
3⁄
4
5⁄
8
7⁄
16
7⁄
16
3⁄
8
W6×16
W8×12
W8×9
4.74
3.55
2.68
6.28
6.03
5.90
61⁄4
6
57⁄8
0.260
0.230
0.170
1⁄
4
1⁄
4
3⁄
16
1⁄
8
1⁄
8
1⁄
8
4.030
4.000
3.940
4
4
4
0.405
0.280
0.215
3⁄
8
1⁄
4
3⁄
16
43⁄4
43⁄4
43⁄4
3⁄
4
5⁄
8
9⁄
16
7⁄
16
3⁄
8
3⁄
8
W5×19
W8×16
5.54
4.68
5.15
5.01
51⁄8
5
0.270
0.240
1⁄
4
1⁄
4
1⁄
8
1⁄
8
5.030
5.000
5
5
0.430
0.360
7⁄
16
3⁄
8
31⁄2
31⁄2
13⁄
16
3⁄
4
7⁄
16
7⁄
16
W4×13
3.83
4.16
41⁄8
0.280
1⁄
4
1⁄
8
4.060
4
0.345
3⁄
8
23⁄4
11⁄
16
7⁄
16
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
in.
11⁄
16
16
5⁄
8
5⁄
8
9⁄
16
9⁄
16
W SHAPES
Properties
Nominal
Wt.
per
ft
Compact
Section
Criteria
h
tw
Fy′′′
lb
bf
2tf
67
58
48
40
35
31
4.4
5.1
5.9
7.2
8.1
9.2
28
24
21
Plastic
Modulus
Elastic Properties
Axis X-X
X1
X2 × 106
ksi
ksi
2
in.
in.
11.1
12.4
15.8
17.6
20.4
22.2
—
—
—
—
—
—
6620
5820
4860
4080
3610
3230
73.9
122
238
474
761
1180
272
228
184
146
127
110
7.0
8.1
22.2
25.8
—
—
3480
3020
931
1610
6.6
27.5
—
2890
2090
(1/ksi)
S
I
4
Axis Y-Y
r
3
S
I
4
r
3
Zx
Zy
in.
3
in.
in.3
in.
in.
in.
60.4
52.0
43.3
35.5
31.2
27.5
3.72
3.65
3.61
3.53
3.51
3.47
88.6
75.1
60.9
49.1
42.6
37.1
21.4
18.3
15.0
12.2
10.6
9.27
2.12
2.10
2.08
2.04
2.03
2.02
70.2
59.8
49.0
39.8
34.7
30.4
32.7
27.9
22.9
18.5
16.1
14.1
98.0
82.8
24.3
20.9
3.45
3.42
21.7
18.3
6.63
5.63
1.62
1.61
27.2
23.2
10.1
8.57
75.3
18.2
3.49
3.71
1.26
20.4
5.69
9.77
1 - 44
DIMENSIONS AND PROPERTIES
Y
tf
d
X
M SHAPES
Dimensions
k
k1
X
T
tw
Y
bf
k
Web
Designation
Area
A
2
in.
Depth
d
Thickness
tw
in.
in.
Flange
tw
2
Width
bf
Thickness
tf
in.
in.
T
k
k1
in.
in.
in.
11.91 1115⁄16 0.177
11.87 117⁄8 0.162
3⁄
16
3⁄
16
1⁄
16
1⁄
16
3.065 31⁄16 0.225
3.065 31⁄16 0.206
1⁄
4
3⁄
16
1015⁄16
107⁄8
1⁄
2
1⁄
2
3⁄
8
3⁄
8
97⁄8 0.157
913⁄16 0.139
3⁄
16
1⁄
8
1⁄
16
1⁄
16
2.690 211⁄16 0.206
2.690 211⁄16 0.183
3⁄
16
3⁄
16
87⁄8
813⁄16
1⁄
2
1⁄
2
3⁄
8
3⁄
8
0.133
1⁄
8
1⁄
16
2.280
21⁄4
0.186
3⁄
16
67⁄8
1⁄
2
3⁄
8
0.316
5⁄
16
3⁄
16
5.003
5
0.416
7⁄
16
31⁄4
7⁄
8
1⁄
2
M12×11.8
M12×10.8
3.48
3.20
M10×9
M12×8
2.67
2.38
9.86
9.81
M8×6.5
1.92
7.85
77⁄8
M5×18.9*
5.55
5.00
5
in.
Distance
*This shape has tapered flanges while all other M shapes have parallel flanges.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
STRUCTURAL SHAPES
1 - 45
M SHAPES
Properties
Y
tf
d
k
k1
X
X
T
tw
Y
bf
Nominal
Wt.
per
ft
Compact
Section
Criteria
h
tw
Fy′′′
lb
bf
2tf
11.8
10.8
6.8
7.4
9
8
k
Plastic
Modulus
Elastic Properties
Axis X-X
X1
X2 × 106
ksi
ksi
2
(1/ksi)
61.4
67.0
17
14
1420
1320
6.5
7.3
56.4
63.7
20
16
6.5
6.1
51.7
18.9
6.0
11.2
S
I
4
Axis Y-Y
r
3
in.
in.
56700
75800
71.7
65.8
12.1
11.1
1570
1400
37100
57800
38.5
34.3
24
1780
20700
—
5710
134
S
I
4
r
3
Zx
Zy
in.
3
in.
in.3
14.3
13.1
1.16
1.05
in.
in.
in.
4.54
4.54
1.09
0.995
0.709
0.649
0.559
0.558
7.82
6.99
3.80
3.80
0.673
0.597
0.501
0.444
0.502
0.502
9.21
8.20
0.815
0.718
18.1
4.62
3.07
0.371
0.325
0.439
5.40
0.527
24.1
9.63
2.08
7.86
3.14
1.19
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
11.0
5.02
1 - 46
DIMENSIONS AND PROPERTIES
Y
tf
d
S SHAPES
Dimensions
k
X
X
T
tw
grip
Y
bf
k
Web
Designation
Flange
Distance
Max.
Flge.
FasGrip tener
Area
A
Depth
d
Thickness
tw
tw
2
Width
bf
Thickness
tf
T
k
in.2
in.
in.
in.
in.
in.
in.
in.
in.
in.
1
1
S24×121
S24×106
35.6
31.2
24.50
24.50
241⁄2
241⁄2
0.800
0.620
13⁄
16
5⁄
8
7⁄
16
5⁄
16
8.050
7.870
8
77⁄8
S24×100
S24×90
S24×80
29.3
26.5
23.5
24.00
24.00
24.00
24
24
24
0.745
0.625
0.500
3⁄
4
5⁄
8
1⁄
2
3⁄
8
5⁄
16
1⁄
4
7.245
7.125
7.000
S20×96
S24×86
28.2
25.3
20.30 201⁄4 0.800
20.30 201⁄4 0.660
13⁄
16
11⁄
16
7⁄
16
3⁄
8
S20×75
S24×66
22.0
19.4
20.00
20.00
20
20
0.635
0.505
5⁄
8
1⁄
2
5⁄
16
1⁄
4
6.385
6.255
63⁄8
61⁄4
0.795
0.795
13⁄
16
13⁄
16
163⁄4
163⁄4
15⁄8
15⁄8
13⁄
16
13⁄
16
7⁄
8
7⁄
8
S18×70
20.6
S24×54.7 16.1
18.00
18.00
18
18
0.711
0.461
11⁄
16
7⁄
16
3⁄
4
6.251
6.001
61⁄4
6
0.691
0.691
11⁄
16
11⁄
16
15
15
11⁄2
11⁄2
11⁄
16
11⁄
16
7⁄
8
7⁄
8
S15×50
14.7
S24×42.9 12.6
15.00
15.00
15
15
0.550
0.411
9⁄
16
7⁄
16
5⁄
16
1⁄
4
5.640
5.501
55⁄8
51⁄2
0.622
0.622
5⁄
8
5⁄
8
121⁄4
121⁄4
13⁄8
13⁄8
9⁄
16
9⁄
16
3⁄
4
3⁄
4
S12×50
14.7
S24×40.8 12.0
12.00
12.00
12
12
0.687
0.462
11⁄
16
7⁄
16
3⁄
4
5.477
5.252
51⁄2
51⁄4
0.659
0.659
11⁄
16
11⁄
16
91⁄8
91⁄8
17⁄16
17⁄16
11⁄
16
5⁄
8
3⁄
4
3⁄
4
S12×35
10.3 12.00
S24×31.8 9.35 12.00
12
12
0.428
0.350
7⁄
16
3⁄
8
1⁄
4
3⁄
16
5.078
5.000
51⁄8
5
0.544
0.544
9⁄
16
9⁄
16
95⁄8
95⁄8
13⁄16
13⁄16
1⁄
2
1⁄
2
3⁄
4
3⁄
4
S10×35
10.3 10.00
S24×25.4 7.46 10.00
10
10
0.594
0.311
5⁄
8
5⁄
16
5⁄
16
3⁄
16
4.944
4.661
5
45⁄8
0.491
0.491
1⁄
2
1⁄
2
73⁄4
73⁄4
11⁄8
11⁄8
1⁄
2
1⁄
2
3⁄
4
3⁄
4
4.171
4.001
41⁄8
4
0.426
0.426
7⁄
16
7⁄
16
6
6
1
1
7⁄
16
7⁄
16
3⁄
4
3⁄
4
8
3.565
3.332
35⁄8
33⁄8
0.359
0.359
3⁄
8
3⁄
8
41⁄4
41⁄4
7⁄
8
7⁄
8
3⁄
8
3⁄
8
5⁄
8
—
8
3.004
3
0.326
5⁄
16
33⁄8
13⁄
16
5⁄
16
—
0.293
0.293
5⁄
16
5⁄
16
21⁄2
21⁄2
3⁄
4
3⁄
4
5⁄
16
5⁄
16
—
—
0.260
0.260
1⁄
4
1⁄
4
15⁄8
15⁄8
11⁄
16
11⁄
16
1⁄
4
1⁄
4
—
—
1⁄
1⁄
8
8
1.090
1.090
11⁄16
11⁄16
201⁄2
201⁄2
2
2
11⁄8
11⁄8
71⁄4
71⁄8
7
0.870
0.870
0.870
7⁄
8
7⁄
8
7⁄
8
201⁄2
201⁄2
201⁄2
13⁄4
13⁄4
13⁄4
7⁄
8
7⁄
8
7⁄
8
1
1
1
7.200
7.060
71⁄4
7
0.920
0.920
15⁄
16
15⁄
16
163⁄4
163⁄4
13⁄4
13⁄4
15⁄
16
15⁄
16
1
1
S8×23
S8×18.4
6.77
5.41
8.00
8.00
8
8
0.441
0.271
7⁄
16
1⁄
4
1⁄
S6×17.25
S8×12.5
5.07
3.67
6.00
6.00
6
6
0.465
0.232
7⁄
16
1⁄
4
1⁄
S5×10
2.94
5.00
5
0.214
3⁄
16
1⁄
3⁄
16
1⁄
8
2.796
2.663
23⁄4
25⁄8
3⁄
16
1⁄
8
2.509
2.330
21⁄2
23⁄8
S4×9.5
S8×7.7
2.79
2.26
4.00
4.00
4
4
0.326
0.193
5⁄
16
3⁄
16
S3×7.5
S8×5.7
2.21
1.67
3.00
3.00
3
3
0.349
0.170
3⁄
8
3⁄
16
1⁄
1⁄
4
8
4
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
STRUCTURAL SHAPES
1 - 47
S SHAPES
Properties
Y
tf
d
k
X
X
T
tw
Y
bf
grip
Nominal
Wt.
per
ft
Compact
Section
Criteria
bf
2tf
h
tw
Fy′′′
121
106
3.7
3.6
100
90
80
Plastic
Modulus
Elastic Properties
Axis X-X
X1
X2 × 106
ksi
ksi
2
(1/ksi)
36.4
34.1
—
55
3310
2960
4.2
4.1
4.0
28.3
33.7
42.1
—
56
36
96
86
3.9
3.8
21.6
26.2
75
66
4.0
3.9
70
54.7
lb
k
S
I
4
Axis Y-Y
r
3
in.
in.
1770
2470
3160
2940
3000
2710
2450
2940
4090
5480
—
—
3730
3350
27.1
34.1
—
55
4.5
4.3
21.8
33.6
50
42.9
4.5
4.4
50
40.8
S
I
4
r
3
Zx
3
Zy
in.3
in.
in.
in.
in.
in.
258
240
9.43
9.71
83.3
77.1
20.7
19.6
1.53
1.57
306
279
36.2
33.2
2390
2250
2100
199
187
175
9.02
9.21
9.47
47.7
44.9
42.2
13.2
12.6
12.1
1.27
1.30
1.34
240
222
204
23.9
22.3
20.7
1160
1630
1670
1580
165
155
7.71
7.89
50.2
46.8
13.9
13.3
1.33
1.36
198
183
24.9
23.0
3140
2800
2290
3250
1280
1190
128
119
7.62
7.83
29.8
27.7
9.32
8.85
1.16
1.19
153
140
16.7
15.3
—
57
3590
2770
1470
3400
926
804
103
89.4
6.71
7.07
24.1
20.8
7.72
6.94
1.08
1.14
125
105
14.4
12.1
23.2
31.0
—
—
3450
2960
1540
2470
486
447
64.8
59.6
5.75
5.95
15.7
14.4
5.57
5.23
1.03
1.07
77.1
69.3
9.97
9.02
4.2
4.0
13.9
20.7
—
—
5070
4050
333
682
305
272
50.8
45.4
4.55
4.77
15.7
13.6
5.74
5.16
1.03
1.06
61.2
53.1
10.3
8.85
35
31.8
4.7
4.6
23.4
28.6
—
—
3500
3190
1310
1710
229
218
38.2
36.4
4.72
4.83
9.87
9.36
3.89
3.74
0.980
1.00
44.8
42.0
6.79
6.40
35
25.4
5.0
4.7
13.8
26.4
—
—
4960
3430
374
1220
147
124
29.4
24.7
3.78
4.07
8.36
6.79
3.38
2.91
0.901
0.954
35.4
28.4
6.22
4.96
23
18.4
4.9
4.7
14.5
23.7
—
—
4770
3770
397
821
64.9
57.6
16.2
14.4
3.10
3.26
4.31
3.73
2.07
1.86
0.798
0.831
19.3
16.5
3.68
3.16
17.25 5.0
12.5
4.6
9.9
19.9
—
—
6250
4290
143
477
26.3
22.1
8.77
7.37
2.28
2.45
2.31
1.82
1.30
1.09
0.675
0.705
10.6
8.47
2.36
1.85
10
4.6
17.4
—
4630
348
12.3
4.92
2.05
1.22
0.809 0.643
5.67
1.37
9.5
7.7
4.8
4.5
8.7
14.7
—
—
6830
5240
87.4
207
6.79
6.08
3.39
3.04
1.56
1.64
0.903
0.764
0.646 0.569
0.574 0.581
4.04
3.51
1.13
0.964
7.5
5.7
4.8
4.5
5.6
11.4
—
—
9160
6160
28.1
106
2.93
2.52
1.95
1.68
1.15
1.23
0.586
0.455
0.468 0.516
0.390 0.522
2.36
1.95
0.826
0.653
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1 - 48
DIMENSIONS AND PROPERTIES
Y
tf
d
X
HP SHAPES
Dimensions
k
k1
X
T
tw
Y
bf
k
Web
Designation
Area
A
2
in.
Depth
d
in.
Thickness
tw
in.
Flange
tw
2
in.
Width
bf
in.
Distance
Thickness
tf
in.
T
k
k1
in.
in.
in.
HP14×117
HP14×102
HP14×89
HP14×73
34.4
30.0
26.1
21.4
14.21
14.01
13.83
13.61
141⁄4
14
137⁄8
135⁄8
0.805
0.705
0.615
0.505
13⁄
16
11⁄
16
5⁄
8
1⁄
2
7⁄
16
3⁄
8
5⁄
16
1⁄
4
14.885
14.785
14.695
14.585
147⁄8
143⁄4
143⁄4
145⁄8
0.805
0.705
0.615
0.505
13⁄
16
11⁄
16
5⁄
8
1⁄
2
111⁄4
111⁄4
111⁄4
111⁄4
11⁄2
13⁄8
15⁄16
13⁄16
11⁄16
1
15⁄
16
7⁄
8
HP12×84
HP14×74
HP14×63
HP14×53
24.6
21.8
18.4
15.5
12.28
12.13
11.94
11.78
121⁄4
121⁄8
12
113⁄4
0.685
0.605
0.515
0.435
11⁄
16
5⁄
8
1⁄
2
7⁄
16
3⁄
8
5⁄
16
1⁄
4
1⁄
4
12.295
12.215
12.125
12.045
121⁄4
121⁄4
121⁄8
12
0.685
0.610
0.515
0.435
11⁄
16
5⁄
8
1⁄
2
7⁄
16
91⁄2
91⁄2
91⁄2
91⁄2
13⁄8
15⁄16
11⁄4
11⁄8
15⁄
16
7⁄
8
7⁄
8
HP10×57
HP14×42
16.8
12.4
9.99
9.70
10
93⁄4
0.565
0.415
9⁄
16
7⁄
16
5⁄
16
1⁄
4
10.225
10.075
101⁄4
101⁄8
0.565
0.420
9⁄
16
7⁄
16
75⁄8
75⁄8
13⁄16
11⁄16
13⁄
16
3⁄
4
HP8×36
10.6
8.02
8
0.445
7⁄
16
1⁄
4
8.155
81⁄8
0.445
7⁄
16
61⁄8
15⁄
16
5⁄
8
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1
STRUCTURAL SHAPES
1 - 49
HP SHAPES
Properties
Y
tf
d
k
k1
X
X
T
tw
Y
bf
Nominal
Wt.
per
ft
Compact
Section
Criteria
h
tw
Fy′′′
lb
bf
2tf
117
102
89
73
9.2
10.5
11.9
14.4
84
74
63
53
9.0
10.0
11.8
13.8
k
Plastic
Modulus
Elastic Properties
Axis X-X
X1
X2 × 106
ksi
ksi
2
14.2
16.2
18.5
22.6
—
—
—
—
14.2
16.0
18.9
22.3
57
42
36
S
I
Axis Y-Y
r
3
S
I
(1/ksi)
4
in.
in.
in.
in.
3870
3400
2960
2450
659
1090
1840
3880
1220
1050
904
729
172
150
131
107
5.96
5.92
5.88
5.84
—
—
—
—
3860
3440
2940
2500
670
1050
1940
3650
650
569
472
393
106
93.8
79.1
66.8
9.0 13.9
12.0 18.9
—
—
3920
2920
631
1970
294
210
9.2 14.2
—
3840
685
119
4
r
3
Zx
Zy
in.
in.
in.
in.3
443
380
326
261
59.5
51.4
44.3
35.8
3.59
3.56
3.53
3.49
194
169
146
118
91.4
78.8
67.7
54.6
5.14
5.11
5.06
5.03
213
186
153
127
34.6
30.4
25.3
21.1
2.94
2.92
2.88
2.86
120
105
88.3
74.0
53.2
46.6
38.7
32.2
58.8
43.4
4.18
4.13
101
71.7
19.7
14.2
2.45
2.41
66.5
48.3
30.3
21.8
29.8
3.36
40.3
1.95
33.6
15.2
9.88
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
3
1 - 50
DIMENSIONS AND PROPERTIES
k
T
x
Y
X
CHANNELS
AMERICAN STANDARD
Dimensions
tf
xp
d
X
tw
k
Y
grip
bf
eo
Web
Designation
Area Depth Thickness
A
d
tw
in.2
in.
in.
Flange
Distance
Max.
Flge.
FasGrip tener
tw
2
Width
bf
Thickness
tf
T
k
in.
in.
in.
in.
in.
121⁄8
121⁄8
121⁄8
17⁄16
17⁄16
17⁄16
5⁄
93⁄4
93⁄4
93⁄4
11⁄8
11⁄8
11⁄8
1⁄
2
7⁄
8
7⁄
8
7⁄
8
3⁄
4
3⁄
4
3⁄
4
3⁄
4
3⁄
8
1⁄
4
3⁄
16
in.
3.716
3.520
3.400
33⁄4
31⁄2
33⁄8
0.650
0.650
0.650
5⁄
8
5⁄
8
5⁄
8
3.170
3.047
2.942
31⁄8
3
3
0.501
0.501
0.501
1⁄
2
1⁄
2
1⁄
2
8
8
8
8
1
1
1
1
7⁄
16
7⁄
16
7⁄
16
7⁄
16
in.
C15×50
C15×40
C15×33.9
14.7
11.8
9.96
15.00
15.00
15.00
0.716
0.520
0.400
11⁄
16
1⁄
2
3⁄
8
C12×30
C15×25
C15×20.7
8.82
7.35
6.09
12.00
12.00
12.00
0.510
0.387
0.282
1⁄
2
3⁄
8
5⁄
16
1⁄
4
3⁄
16
1⁄
8
5⁄
16
1⁄
4
3⁄
16
1⁄
8
3.033
2.886
2.739
2.600
3
27⁄8
23⁄4
25⁄8
0.436
0.436
0.436
0.436
7⁄
16
7⁄
16
7⁄
16
7⁄
16
1⁄
4
1⁄
8
1⁄
8
2.648
2.485
2.433
25⁄8
21⁄2
23⁄8
0.413
0.413
0.413
7⁄
16
7⁄
16
7⁄
16
71⁄8
71⁄8
71⁄8
15⁄
16
15⁄
16
15⁄
16
7⁄
16
7⁄
16
7⁄
16
3⁄
4
3⁄
4
3⁄
4
1⁄
4
1⁄
8
1⁄
8
2.527
2.343
2.260
21⁄2
23⁄8
21⁄4
0.390
0.390
0.390
3⁄
8
3⁄
8
3⁄
8
61⁄8
61⁄8
61⁄8
15⁄
16
15⁄
16
15⁄
16
3⁄
3⁄
4
3⁄
4
3⁄
4
3⁄
16
1⁄
8
2.194
2.090
21⁄4
21⁄8
0.366
0.366
3⁄
8
3⁄
8
51⁄4
51⁄4
7⁄
8
7⁄
8
3⁄
8
5⁄
8
5⁄
8
3⁄
16
3⁄
16
1⁄
8
2.157
2.034
1.920
21⁄8
2
17⁄8
0.343
0.343
0.343
5⁄
16
5⁄
16
5⁄
16
43⁄8
43⁄8
43⁄8
13⁄
16
13⁄
16
13⁄
16
5⁄
16
3⁄
8
5⁄
16
5⁄
8
5⁄
8
5⁄
8
3⁄
16
1⁄
8
1.885
1.750
17⁄8
13⁄4
0.320
0.320
5⁄
16
5⁄
16
31⁄2
31⁄2
3⁄
4
3⁄
4
5⁄
16
5⁄
8
—
5⁄
5⁄
1⁄
1⁄
8
8
8
2
2
1
1
1
C10×30
C15×25
C15×20
C15×15.3
8.82
7.35
5.88
4.49
10.00
10.00
10.00
10.00
0.673
0.526
0.379
0.240
11⁄
16
1⁄
2
3⁄
8
1⁄
4
C9×20
C5×15
C5×13.4
5.88
4.41
3.94
9.00
9.00
9.00
0.448
0.285
0.233
7⁄
C8×18.75
C8×13.75
C8×11.5
5.51
4.04
3.38
8.00
8.00
8.00
0.487
0.303
0.220
C7×12.25
C8×9.8
3.60
2.87
7.00
7.00
0.314
0.210
5⁄
C6×13
C8×10.5
C8×8.2
3.83
3.09
2.40
6.00
6.00
6.00
0.437
0.314
0.200
7⁄
C5×9
C8×6.7
2.64
1.97
5.00
5.00
0.325
0.190
5⁄
C4×7.25
C8×5.4
2.13
1.59
4.00
4.00
0.321
0.184
5⁄
3⁄
16
1⁄
16
1.721
1.584
13⁄4
15⁄8
0.296
0.296
5⁄
16
5⁄
16
25⁄8
25⁄8
11⁄
16
11⁄
16
5⁄
16
16
—
5⁄
8
—
C3×6
C8×5
C8×4.1
1.76
1.47
1.21
3.00
3.00
3.00
0.356
0.258
0.170
3⁄
8
1⁄
4
3⁄
16
3⁄
16
1⁄
8
1⁄
16
1.596
1.498
1.410
15⁄8
11⁄2
13⁄8
0.273
0.273
0.273
1⁄
4
1⁄
4
1⁄
4
15⁄8
15⁄8
15⁄8
11⁄
16
11⁄
16
11⁄
16
—
—
—
—
—
—
5⁄
16
16
1⁄
4
1⁄
2
5⁄
16
1⁄
4
3⁄
5⁄
3⁄
3⁄
3⁄
16
16
16
16
16
16
16
16
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
3⁄
3⁄
3⁄
8
8
8
8
—
STRUCTURAL SHAPES
1 - 51
CHANNELS
AMERICAN STANDARD
Properties
k
x
Y
xp
X
T
tf
d
X
tw
Y
k
Nominal
Wt.
per
ft
_
x
Shear
Center PNA
Loca- Location
tion
eo
xp
Axis X-X
Z
I
4
in.
Axis Y-Y
S
3
grip
bf
eo
r
3
Z
I
4
S
3
r
3
lb
in.
in.
in.
in.
in.
in.
in.
in.
in.
in.
50
40
33.9
0.798
0.777
0.787
0.583
0.767
0.896
0.488
0.390
0.330
404
349
315
68.2
57.2
50.4
53.8
46.5
42.0
5.24
5.44
5.62
11.0
9.23
8.13
8.17
6.87
6.23
3.78
3.37
3.11
0.867
0.886
0.904
30
25
20.7
0.674
0.674
0.698
0.618
0.746
0.870
0.366
0.305
0.252
162
144
129
33.6
29.2
25.4
27.0
24.1
21.5
4.29
4.43
4.61
5.14
4.47
3.88
4.33
3.84
3.49
2.06
1.88
1.73
0.763
0.780
0.799
30
25
20
15.3
0.649
0.617
0.606
0.634
0.369
0.494
0.637
0.796
0.439
0.366
0.292
0.223
103
91.2
78.9
67.4
26.6
23.0
19.3
15.8
20.7
18.2
15.8
13.5
3.42
3.52
3.66
3.87
3.94
3.36
2.81
2.28
3.78
3.19
2.71
2.35
1.65
1.48
1.32
1.16
0.669
0.676
0.692
0.713
20
15
13.4
0.583
0.586
0.601
0.515
0.682
0.743
0.325
0.243
0.217
60.9
51.0
47.9
16.8
13.5
12.5
13.5
11.3
10.6
3.22
3.40
3.48
2.42
1.93
1.76
2.47
2.05
1.95
1.17
1.01
0.962
0.642
0.661
0.669
18.75
13.75
11.5
0.565
0.553
0.571
0.431
0.604
0.697
0.343
0.251
0.209
44.0
36.1
32.6
13.8
10.9
9.55
11.0
9.03
8.14
2.82
2.99
3.11
1.98
1.53
1.32
2.17
1.73
1.58
1.01
0.854
0.781
0.599
0.615
0.625
12.25
9.8
0.525
0.540
0.538
0.647
0.255
0.203
24.2
21.3
8.40
7.12
6.93
6.08
2.60
2.72
1.17
0.968
1.43
1.26
0.703
0.625
0.571
0.581
13
10.5
8.2
0.514
0.499
0.511
0.380
0.486
0.599
0.317
0.255
0.198
17.4
15.2
13.1
7.26
6.15
5.13
5.80
5.06
4.38
2.13
2.22
2.34
1.05
0.866
0.693
1.36
1.15
0.993
0.642
0.564
0.492
0.525
0.529
0.537
9
6.7
0.478
0.484
0.427
0.552
0.262
0.217
8.90
7.49
4.36
3.51
3.56
3.00
1.83
1.95
0.632
0.479
0.918
0.763
0.450
0.378
0.489
0.493
7.25
5.4
0.459
0.457
0.386
0.502
0.264
0.241
4.59
3.85
2.81
2.26
2.29
1.93
1.47
1.56
0.433
0.319
0.697
0.569
0.343
0.283
0.450
0.449
6
5
4.1
0.455
0.438
0.436
0.322
0.392
0.461
0.291
0.242
0.284
2.07
1.85
1.66
1.72
1.50
1.30
1.38
1.24
1.10
1.08
1.12
1.17
0.305
0.247
0.197
0.544
0.466
0.401
0.268
0.233
0.202
0.416
0.410
0.404
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1 - 52
DIMENSIONS AND PROPERTIES
k
T
x
Y
X
CHANNELS
MISCELLANEOUS
Dimensions
tf
xp
d
X
tw
k
Y
eo
grip
bf
Web
Designation
Area Depth Thickness
A
d
tw
in.2
in.
in.
Flange
Distance
Max.
Flge.
FasGrip tener
tw
2
Width
bf
Thickness
tf
T
k
in.
in.
in.
in.
in.
in.
in.
151⁄4
151⁄4
151⁄4
151⁄4
13⁄8
13⁄8
13⁄8
13⁄8
5⁄
8
5⁄
8
5⁄
8
5⁄
8
1
1
1
1
101⁄4
101⁄4
101⁄4
101⁄4
13⁄8
13⁄8
13⁄8
13⁄8
5⁄
8
9⁄
16
9⁄
16
9⁄
16
1
1
1
1
15⁄16
15⁄16
15⁄16
15⁄16
15⁄16
11⁄
16
11⁄
16
11⁄
16
11⁄
16
11⁄
16
1
1
1
1
1
MC18×58
MC18×51.9
MC18×45.8
MC18×42.7
17.1
15.3
13.5
12.6
18.00
18.00
18.00
18.00
0.700
0.600
0.500
0.450
11⁄
16
5⁄
8
1⁄
2
7⁄
16
MC13×50
MC18×40
MC18×35
MC18×31.8
14.7
11.8
10.3
9.35
13.00
13.00
13.00
13.00
0.787
0.560
0.447
0.375
3⁄
16
9⁄
16
7⁄
16
3⁄
8
3⁄
8
1⁄
4
1⁄
4
3⁄
16
7⁄
16
3⁄
8
5⁄
16
1⁄
4
3⁄
16
4.135
4.012
3.890
3.767
3.670
41⁄
4
37⁄8
33⁄4
35⁄8
0.700
0.700
0.700
0.700
0.700
11⁄
16
11⁄
16
11⁄
16
11⁄
16
11⁄
16
1.500
11⁄2
0.309
5⁄
16
105⁄8
16
—
—
71⁄2
71⁄2
71⁄2
11⁄4
11⁄4
11⁄4
9⁄
16
9⁄
16
9⁄
16
7⁄
8
7⁄
8
7⁄
8
MC12×50
MC18×45
MC18×40
MC18×35
MC18×31
MC12×10.6
3⁄
8
5⁄
16
1⁄
4
1⁄
4
4.200
4.100
4.000
3.950
41⁄
41⁄8
4
4
0.625
0.625
0.625
0.625
5⁄
4.412
4.185
4.072
4.000
43⁄8
41⁄8
41⁄8
4
0.610
0.610
0.610
0.610
5⁄
93⁄8
93⁄8
93⁄8
93⁄8
93⁄8
4
5⁄
5⁄
5⁄
5⁄
5⁄
5⁄
8
8
8
8
8
8
8
8
14.7
13.2
11.8
10.3
9.12
12.00
12.00
12.00
12.00
12.00
0.835
0.712
0.590
0.467
0.370
13⁄
16
11⁄
16
9⁄
16
7⁄
16
3⁄
8
3.10
12.00
0.190
3⁄
16
1⁄
8
3⁄
8
5⁄
16
3⁄
16
4.321
4.100
3.950
43⁄
41⁄8
4
8
0.575
0.575
0.575
9⁄
16
9⁄
16
9⁄
16
8
11⁄
12.1
9.87
8.37
10.00
10.00
10.00
0.796
0.575
0.425
13⁄
16
9⁄
16
7⁄
16
MC10×25
MC18×22
7.35
6.45
10.00
10.00
0.380
0.290
3⁄
8
5⁄
16
3⁄
16
1⁄
8
3.405
3.315
33⁄8
33⁄8
0.575
0.575
9⁄
16
9⁄
16
71⁄2
71⁄2
11⁄4
11⁄4
9⁄
16
9⁄
16
7⁄
8
7⁄
8
MC10×8.4
2.46
10.00
0.170
3⁄
16
1⁄
1.500
11⁄2
0.280
1⁄
85⁄8
11⁄
—
—
MC10×41.1
MC18×33.6
MC18×28.5
16
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
4
16
STRUCTURAL SHAPES
1 - 53
CHANNELS
MISCELLANEOUS
Properties
k
x
Y
xp
X
T
tf
d
X
tw
Y
k
Nominal
Wt.
per
ft
_
x
Shear
Center PNA
Loca- Location
tion
eo
xp
Axis X-X
Z
I
4
Axis Y-Y
S
3
grip
bf
eo
r
3
Z
I
4
S
3
r
3
lb
in.
in.
in.
in.
in.
in.
in.
in.
in.
in.
in.
58
51.9
45.8
42.7
0.862
0.858
0.866
0.877
0.695
0.797
0.909
0.969
0.472
0.422
0.372
0.347
676
627
578
554
94.6
86.5
78.4
74.4
75.1
69.7
64.3
61.6
6.29
6.41
6.56
6.64
17.8
16.4
15.1
14.4
9.94
9.13
8.42
8.10
5.32
5.07
4.82
4.69
1.02
1.04
1.06
1.07
50
40
35
31.8
0.974
0.963
0.980
1.00
0.815
1.03
1.16
1.24
0.564
0.450
0.394
0.358
314
273
252
239
60.5
50.9
46.2
43.1
48.4
42.0
38.8
36.8
4.62
4.82
4.95
5.06
16.5
13.7
12.3
11.4
10.1
8.57
7.95
7.60
4.79
4.26
3.99
3.81
1.06
1.08
1.10
1.11
50
45
40
35
31
1.05
1.04
1.04
1.05
1.08
0.741
0.844
0.952
1.07
1.18
0.610
0.549
0.488
0.426
0.416
269
252
234
216
203
56.1
51.7
47.3
42.8
39.3
44.9
42.0
39.0
36.1
33.8
4.28
4.36
4.46
4.59
4.71
17.4
15.8
14.3
12.7
11.3
10.2
9.35
8.59
7.91
7.44
5.65
5.33
5.00
4.67
4.39
1.09
1.09
1.10
1.11
1.12
10.6
0.269
0.284
0.129
0.639
0.310
0.351
41.1
33.6
28.5
1.09
1.08
1.12
0.864
1.06
1.21
0.601
0.490
0.415
158
139
127
38.9
33.4
29.6
31.5
27.8
25.3
3.61
3.75
3.89
8.71
7.51
6.83
4.88
4.38
4.02
1.14
1.16
1.17
25
22
0.953
0.990
1.03
1.13
0.364
0.468
110
103
25.8
23.6
22.0
20.5
3.87
3.99
7.35
6.50
5.21
4.86
3.00
2.80
1.00
1.00
0.284
0.332
0.122
3.61
0.328
0.552
0.270
0.365
8.4
55.4
32.0
11.6
7.86
9.23
6.40
4.22
0.382
15.8
13.2
11.4
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1 - 54
DIMENSIONS AND PROPERTIES
k
T
x
Y
X
CHANNELS
MISCELLANEOUS
Dimensions
tf
xp
d
X
tw
k
Y
eo
grip
bf
Web
Designation
Area Depth Thickness
A
d
tw
in.2
in.
in.
Flange
Distance
Max.
Flge.
FasGrip tener
tw
2
Width
bf
Thickness
tf
T
k
in.
in.
in.
in.
in.
in.
in.
65⁄8
65⁄8
13⁄16
13⁄16
9⁄
16
9⁄
16
7⁄
8
7⁄
8
55⁄8
55⁄8
13⁄16
13⁄16
1⁄
2
1⁄
2
7⁄
8
7⁄
8
MC9×25.4
MC9×23.9
7.47
7.02
9.00
9.00
0.450
0.400
7⁄
16
3⁄
8
1⁄
4
3⁄
16
3.500
3.450
31⁄
31⁄2
2
0.550
0.550
9⁄
16
9⁄
16
MC8×22.8
MC9×21.4
6.70
6.28
8.00
8.00
0.427
0.375
7⁄
16
3⁄
8
3⁄
3⁄
3.502
3.450
31⁄2
31⁄2
0.525
0.525
1⁄
MC8×20
MC9×18.7
5.88
5.50
8.00
8.00
0.400
0.353
3⁄
8
3⁄
8
3⁄
3.025
2.978
3
3
0.500
0.500
1⁄
16
2
53⁄4
53⁄4
11⁄8
11⁄8
1⁄
2
1⁄
2
7⁄
8
7⁄
8
MC8×8.5
2.50
8.00
0.179
3⁄
16
1⁄
16
1.874
17⁄8
0.311
5⁄
16
61⁄2
3⁄
4
5⁄
16
5⁄
8
MC7×22.7
MC9×19.1
6.67
5.61
7.00
7.00
0.503
0.352
1⁄
2
3⁄
8
3⁄
1⁄
4
3.603
3.452
35⁄8
31⁄2
0.500
0.500
1⁄
16
2
43⁄4
43⁄4
11⁄8
11⁄8
1⁄
2
1⁄
2
7⁄
8
7⁄
8
MC6×18
5.29
6.00
0.379
3⁄
8
3⁄
16
3.504
31⁄2
0.475
1⁄
2
37⁄8
11⁄16
1⁄
2
7⁄
8
MC6×16.3
MC9×15.1
4.79
4.44
6.00
6.00
0.375
0.316
3⁄
8
5⁄
16
3⁄
16
3.000
2.941
3
3
0.475
0.475
1⁄
2
16
2
37⁄8
37⁄8
11⁄16
11⁄16
1⁄
2
1⁄
2
3⁄
4
3⁄
4
MC6×12
3.53
6.00
0.310
5⁄
16
1⁄
8
2.497
21⁄2
0.375
3⁄
8
43⁄8
13⁄
16
3⁄
8
5⁄
8
3⁄
3⁄
16
16
16
1⁄
1⁄
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1⁄
1⁄
2
2
2
2
STRUCTURAL SHAPES
1 - 55
CHANNELS
MISCELLANEOUS
Properties
k
x
Y
xp
X
T
tf
d
X
tw
Y
k
Nominal
Wt.
per
ft
_
x
Shear
Center PNA
Loca- Location
tion
eo
xp
Axis X-X
Z
I
4
Axis Y-Y
S
3
grip
bf
eo
r
3
Z
I
4
S
3
r
3
lb
in.
in.
in.
in.
in.
in.
in.
in.
in.
in.
in.
25.4
23.9
0.970
0.981
0.986
1.04
0.411
0.386
88.0
85.0
23.2
22.2
19.6
18.9
3.43
3.48
7.65
7.22
5.23
5.05
3.02
2.93
1.01
1.01
22.8
21.4
1.01
1.02
1.04
1.09
0.415
0.449
63.8
61.6
18.8
18.0
16.0
15.4
3.09
3.13
7.07
6.64
4.88
4.71
2.84
2.74
1.03
1.03
20
18.7
0.840
0.849
0.843
0.889
0.364
0.341
54.5
52.5
16.2
15.4
13.6
13.1
3.05
3.09
4.47
4.20
3.57
3.44
2.05
1.97
0.872
0.874
8.5
0.428
0.542
0.155
23.3
6.91
3.05
0.628
0.882
0.434
0.501
22.7
19.1
1.04
1.08
1.01
1.15
0.473
0.567
47.5
43.2
16.2
14.3
2.67
2.77
7.29
6.11
4.86
4.34
2.85
2.57
1.05
1.04
18
1.12
1.17
0.622
29.7
11.5
9.91
2.37
5.93
4.14
2.48
1.06
16.3
15.1
0.927
0.940
0.930
0.982
0.464
0.537
26.0
25.0
10.2
9.69
8.68
8.32
2.33
2.37
3.82
3.51
3.18
3.00
1.84
1.75
0.892
0.889
12
0.704
0.725
0.292
18.7
7.38
6.24
2.30
1.87
1.79
1.04
0.728
5.83
13.6
12.3
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1 - 56
DIMENSIONS AND PROPERTIES
Y
ANGLES
Equal legs and unequal legs
Properties for designing
xp
x
Z
X
X
y, yp
k
α
Y
Size
and
Thickness
in.
Z
k
Weight
per
ft
Axis X-X
Area
2
S
I
4
r
3
y
Z
yp
3
in.
lb
in.
in.
in.
in.
in.
in.
in.
L8×8×11⁄8
L8×8×1
L8×8×17⁄8
L8×8×13⁄4
L8×8×15⁄8
L8×8×19⁄16
L8×8×11⁄2
13⁄4
15⁄8
11⁄2
13⁄8
11⁄4
13⁄16
11⁄8
56.9
51.0
45.0
38.9
32.7
29.6
26.4
16.7
15.0
13.2
11.4
9.61
8.68
7.75
98.0
89.0
79.6
69.7
59.4
54.1
48.6
17.5
15.8
14.0
12.2
10.3
9.34
8.36
2.42
2.44
2.45
2.47
2.49
2.50
2.50
2.41
2.37
2.33
2.28
2.23
2.21
2.19
31.6
28.5
25.3
22.0
18.6
16.8
15.1
1.05
0.938
0.827
0.715
0.601
0.543
0.484
L8×6×1
L8×8×17⁄8
L8×8×13⁄4
L8×8×15⁄8
L8×8×19⁄16
L8×8×11⁄2
L8×8×17⁄16
11⁄2
13⁄8
11⁄4
11⁄8
11⁄16
1
15⁄
16
44.2
39.1
33.8
28.5
25.7
23.0
20.2
13.0
11.5
9.94
8.36
7.56
6.75
5.93
80.8
72.3
63.4
54.1
49.3
44.3
39.2
15.1
13.4
11.7
9.87
8.95
8.02
7.07
2.49
2.51
2.53
2.54
2.55
2.56
2.57
2.65
2.61
2.56
2.52
2.50
2.47
2.45
27.3
24.2
21.1
17.9
16.2
14.5
12.8
1.50
1.44
1.38
1.31
1.28
1.25
1.22
L8×4×1
L8×8×17⁄8
L8×8×13⁄4
L8×4×15⁄8
L8×8×19⁄16
L8×8×11⁄2
L8×4×17⁄16
L7×4×3⁄4
L7×4×5⁄8
L7×4×1⁄2
L7×4×7⁄16
L7×4×3⁄8
11⁄2
13⁄8
11⁄4
11⁄8
11⁄16
1
15⁄
16
11⁄4
11⁄8
1
15⁄
16
7⁄
8
37.4
33.1
28.7
24.2
21.9
19.6
17.2
26.2
22.1
17.9
15.7
13.6
11.0
9.73
8.44
7.11
6.43
5.75
5.06
7.69
6.48
5.25
4.62
3.98
69.6
62.5
54.9
46.9
42.8
38.5
34.1
37.8
32.4
26.7
23.7
20.6
14.1
12.5
10.9
9.21
8.35
7.49
6.60
8.42
7.14
5.81
5.13
4.44
2.52
2.53
2.55
2.57
2.58
2.59
2.60
2.22
2.24
2.25
2.26
2.27
3.05
3.00
2.95
2.91
2.88
2.86
2.83
2.51
2.46
2.42
2.39
2.37
24.3
21.6
18.9
16.0
14.5
13.0
11.5
14.8
12.6
10.3
9.09
7.87
2.50
2.44
2.38
2.31
2.28
2.25
2.22
1.88
1.81
1.75
1.72
1.69
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
STRUCTURAL SHAPES
1 - 57
Y
ANGLES
Equal legs and unequal legs
Properties for designing
x
xp
Z
X
X
y, yp
k
α
Y
Size
and
Thickness
Z
Axis Y-Y
S
I
r
Axis Z-Z
x
Z
xp
r
Tan
in.
in.
in.
in.
in.
in.
in.
α
L8×8×11⁄8
L8×8×1
L8×8×17⁄8
L8×8×13⁄4
L8×8×15⁄8
L8×8×19⁄16
L8×8×11⁄2
98.0
89.0
79.6
69.7
59.4
54.1
48.6
17.5
15.8
14.0
12.2
10.3
9.34
8.36
2.42
2.44
2.45
2.47
2.49
2.50
2.50
2.41
2.37
2.33
2.28
2.23
2.21
2.19
31.6
28.5
25.3
22.0
18.6
16.8
15.1
1.05
0.938
0.827
0.715
0.601
0.543
0.484
1.56
1.56
1.57
1.58
1.58
1.59
1.59
1.000
1.000
1.000
1.000
1.000
1.000
1.000
L8×6×1
L8×8×17⁄8
L8×8×13⁄4
L8×8×15⁄8
L8×8×19⁄16
L8×8×11⁄2
L8×8×17⁄16
38.8
34.9
30.7
26.3
24.0
21.7
19.3
8.92
7.94
6.92
5.88
5.34
4.79
4.23
1.73
1.74
1.76
1.77
1.78
1.79
1.80
1.65
1.61
1.56
1.52
1.50
1.47
1.45
16.2
14.4
12.5
10.5
9.52
8.51
7.50
0.813
0.718
0.621
0.522
0.472
0.422
0.371
1.28
1.28
1.29
1.29
1.30
1.30
1.31
0.543
0.547
0.551
0.554
0.556
0.558
0.560
L8×4×1
L8×4×17⁄8
L8×8×13⁄4
L8×4×15⁄8
L8×8×19⁄16
L8×8×11⁄2
L8×4×17⁄16
11.6
10.5
9.36
8.10
7.43
6.74
6.02
3.94
3.51
3.07
2.62
2.38
2.15
1.90
1.03
1.04
1.05
1.07
1.07
1.08
1.09
1.05
0.999
0.953
0.905
0.882
0.859
0.835
7.72
6.77
5.81
4.86
4.38
3.90
3.42
0.688
0.608
0.527
0.444
0.402
0.359
0.316
0.846
0.848
0.852
0.857
0.861
0.865
0.869
0.247
0.253
0.258
0.262
0.265
0.267
0.269
L7×4×3⁄4
L7×4×5⁄8
L7×4×1⁄2
L7×4×7⁄16
L7×4×3⁄8
9.05
7.84
6.53
5.83
5.10
3.03
2.58
2.12
1.88
1.63
1.09
1.10
1.11
1.12
1.13
1.01
0.963
0.917
0.893
0.870
5.65
4.74
3.83
3.37
2.90
0.549
0.463
0.375
0.330
0.285
0.860
0.865
0.872
0.875
0.880
0.324
0.329
0.335
0.337
0.340
in.
4
3
3
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1 - 58
DIMENSIONS AND PROPERTIES
Y
ANGLES
Equal legs and unequal legs
Properties for designing
xp
x
Z
X
X
y, yp
k
α
Y
Size
and
Thickness
in.
Z
k
Weight
per
ft
Axis X-X
Area
2
S
I
4
r
3
y
Z
yp
3
in.
lb
in.
in.
in.
in.
in.
in.
in.
L6×6×1
L6×6×17⁄8
L6×6×13⁄4
L6×6×15⁄8
L6×6×19⁄16
L6×6×11⁄2
L6×6×17⁄16
L6×6×13⁄8
L6×6×15⁄16
11⁄2
13⁄8
11⁄4
11⁄8
11⁄16
1
15⁄
16
7⁄
8
13⁄
16
37.4
33.1
28.7
24.2
21.9
19.6
17.2
14.9
12.4
11.0
9.73
8.44
7.11
6.43
5.75
5.06
4.36
3.65
35.5
31.9
28.2
24.2
22.1
19.9
17.7
15.4
13.0
8.57
7.63
6.66
5.66
5.14
4.61
4.08
3.53
2.97
1.80
1.81
1.83
1.84
1.85
1.86
1.87
1.88
1.89
1.86
1.82
1.78
1.73
1.71
1.68
1.66
1.64
1.62
15.5
13.8
12.0
10.2
9.26
8.31
7.34
6.35
5.35
0.917
0.811
0.703
0.592
0.536
0.479
0.422
0.363
0.304
L6×4×7⁄8
L6×4×3⁄4
L6×4×5⁄8
L6×4×9⁄16
L6×4×1⁄2
L6×4×7⁄16
L6×4×3⁄8
L6×4×5⁄16
13⁄8
11⁄4
11⁄8
11⁄16
1
15⁄
16
7⁄
8
13⁄
16
27.2
23.6
20.0
18.1
16.2
14.3
12.3
10.3
7.98
6.94
5.86
5.31
4.75
4.18
3.61
3.03
27.7
24.5
21.1
19.3
17.4
15.5
13.5
11.4
7.15
6.25
5.31
4.83
4.33
3.83
3.32
2.79
1.86
1.88
1.90
1.90
1.91
1.92
1.93
1.94
2.12
2.08
2.03
2.01
1.99
1.96
1.94
1.92
12.7
11.2
9.51
8.66
7.78
6.88
5.97
5.03
1.44
1.38
1.31
1.28
1.25
1.22
1.19
1.16
L6×31⁄2×1⁄2
L6×31⁄2×3⁄8
L6×31⁄2×5⁄16
1
7⁄
8
13⁄
16
15.3
11.7
9.80
4.50
3.42
2.87
16.6
12.9
10.9
4.24
3.24
2.73
1.92
1.94
1.95
2.08
2.04
2.01
7.50
5.76
4.85
1.50
1.44
1.41
L5×5×7⁄8
L5×5×3⁄4
L5×5×5⁄8
L5×5×1⁄2
L5×5×7⁄16
L5×5×3⁄8
L5×5×5⁄16
13⁄8
11⁄4
11⁄8
1
15⁄
16
7⁄
8
13⁄
16
27.2
23.6
20.0
16.2
14.3
12.3
10.3
7.98
6.94
5.86
4.75
4.18
3.61
3.03
17.8
15.7
13.6
11.3
10.0
8.74
7.42
5.17
4.53
3.86
3.16
2.79
2.42
2.04
1.49
1.51
1.52
1.54
1.55
1.56
1.57
1.57
1.52
1.48
1.43
1.41
1.39
1.37
9.33
8.16
6.95
5.68
5.03
4.36
3.68
0.798
0.694
0.586
0.475
0.418
0.361
0.303
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
STRUCTURAL SHAPES
1 - 59
Y
ANGLES
Equal legs and unequal legs
Properties for designing
x
xp
Z
X
X
y, yp
k
α
Y
Size
and
Thickness
in.
L6×6×1
L6×6×17⁄8
L6×6×13⁄4
L6×6×15⁄8
L6×6×19⁄16
L6×6×11⁄2
L6×6×17⁄16
L6×6×13⁄8
L6×6×15⁄16
Z
Axis Y-Y
S
I
4
r
Axis Z-Z
x
xp
r
in.
in.
in.
α
1.86
1.82
1.78
1.73
1.71
1.68
1.66
1.64
1.62
15.5
13.8
12.0
10.2
9.26
8.31
7.34
6.35
5.35
0.917
0.811
0.703
0.592
0.536
0.479
0.422
0.363
0.304
1.17
1.17
1.17
1.18
1.18
1.18
1.19
1.19
1.20
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
in.
3
in.
in.
in.
35.5
31.9
28.2
24.2
22.1
19.9
17.7
15.4
13.0
8.57
7.63
6.66
5.66
5.14
4.61
4.08
3.53
2.97
1.80
1.81
1.83
1.84
1.85
1.86
1.87
1.88
1.89
Z
3
Tan
L6×4×7⁄8
L6×4×3⁄4
L6×4×5⁄8
L6×4×9⁄16
L6×4×1⁄2
L6×4×7⁄16
L6×4×3⁄8
L6×4×5⁄16
9.75
8.68
7.52
6.91
6.27
5.60
4.90
4.18
3.39
2.97
2.54
2.31
2.08
1.85
1.60
1.35
1.11
1.12
1.13
1.14
1.15
1.16
1.17
1.17
1.12
1.08
1.03
1.01
0.987
0.964
0.941
0.918
6.31
5.47
4.62
4.19
3.75
3.30
2.85
2.40
0.665
0.578
0.488
0.442
0.396
0.349
0.301
0.252
0.857
0.860
0.864
0.866
0.870
0.873
0.877
0.882
0.421
0.428
0.435
0.438
0.440
0.443
0.446
0.448
L6×31⁄2×1⁄2
L6×31⁄2×3⁄8
L6×31⁄2×5⁄16
4.25
3.34
2.85
1.59
1.23
1.04
0.972
0.988
0.996
0.833
0.787
0.763
2.91
2.20
1.85
0.375
0.285
0.239
0.759
0.767
0.772
0.344
0.350
0.352
17.8
15.7
13.6
11.3
10.0
8.74
7.42
5.17
4.53
3.86
3.16
2.79
2.42
2.04
1.49
1.51
1.52
1.54
1.55
1.56
1.57
1.57
1.52
1.48
1.43
1.41
1.39
1.37
9.33
8.16
6.95
5.68
5.03
4.36
3.68
0.798
0.694
0.586
0.475
0.418
0.361
0.303
0.973
0.975
0.978
0.983
0.986
0.990
0.994
1.000
1.000
1.000
1.000
1.000
1.000
1.000
L5×5×7⁄8
L5×5×3⁄4
L5×5×5⁄8
L5×5×1⁄2
L5×5×7⁄16
L5×5×3⁄8
L5×5×5⁄16
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1 - 60
DIMENSIONS AND PROPERTIES
Y
ANGLES
Equal legs and unequal legs
Properties for designing
xp
x
Z
X
X
y, yp
k
α
Y
Size
and
Thickness
in.
Z
k
Weight
per
ft
Axis X-X
Area
2
S
I
4
r
3
y
Z
yp
3
in.
lb
in.
in.
in.
in.
in.
in.
L5×31⁄2×3⁄4
L5×31⁄2×5⁄8
L5×31⁄2×1⁄2
L5×31⁄2×3⁄8
L5×31⁄2×5⁄16
L5×31⁄2×1⁄4
11⁄4
11⁄8
1
7⁄
8
13⁄
16
3⁄
4
19.8
16.8
13.6
10.4
8.70
7.00
5.81
4.92
4.00
3.05
2.56
2.06
13.9
12.0
9.99
7.78
6.60
5.39
4.28
3.65
2.99
2.29
1.94
1.57
1.55
1.56
1.58
1.60
1.61
1.62
1.75
1.70
1.66
1.61
1.59
1.56
7.65
6.55
5.38
4.14
3.49
2.83
1.13
1.06
1.00
0.938
0.906
0.875
L5×3×1⁄2
L5×3×7⁄16
L5×3×3⁄8
L5×3×5⁄16
L5×3×1⁄4
1
15⁄
16
7⁄
8
13⁄
16
3⁄
4
12.8
11.3
9.80
8.20
6.60
3.75
3.31
2.86
2.40
1.94
9.45
8.43
7.37
6.26
5.11
2.91
2.58
2.24
1.89
1.53
1.59
1.60
1.61
1.61
1.62
1.75
1.73
1.70
1.68
1.66
5.16
4.57
3.97
3.36
2.72
1.25
1.22
1.19
1.16
1.13
L4×4×3⁄4
L5×3×5⁄8
L5×3×1⁄2
L5×3×7⁄16
L5×3×3⁄8
L5×3×5⁄16
L5×3×1⁄4
11⁄8
1
7⁄
8
13⁄
16
3⁄
4
11⁄
16
5⁄
8
18.5
15.7
12.8
11.3
9.80
8.20
6.60
5.44
4.61
3.75
3.31
2.86
2.40
1.94
7.67
6.66
5.56
4.97
4.36
3.71
3.04
2.81
2.40
1.97
1.75
1.52
1.29
1.05
1.19
1.20
1.22
1.23
1.23
1.24
1.25
1.27
1.23
1.18
1.16
1.14
1.12
1.09
5.07
4.33
3.56
3.16
2.74
2.32
1.88
0.680
0.576
0.469
0.414
0.357
0.300
0.242
L4×31⁄2×1⁄2
L4×31⁄2×3⁄8
L4×31⁄2×5⁄16
L4×31⁄2×1⁄4
15⁄
16
13⁄
16
3⁄
4
11⁄
16
11.9
9.10
7.70
6.20
3.50
2.67
2.25
1.81
5.32
4.18
3.56
2.91
1.94
1.49
1.26
1.03
1.23
1.25
1.26
1.27
1.25
1.21
1.18
1.16
3.50
2.71
2.29
1.86
0.500
0.438
0.406
0.375
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
in.
STRUCTURAL SHAPES
1 - 61
Y
ANGLES
Equal legs and unequal legs
Properties for designing
x
xp
Z
X
X
y, yp
k
α
Y
Size
and
Thickness
Z
Axis Y-Y
S
I
r
Axis Z-Z
x
Z
xp
r
Tan
in.
in.
in.
in.
in.
in.
in.
α
L5×31⁄2×3⁄4
L5×31⁄2×5⁄8
L5×31⁄2×1⁄2
L5×31⁄2×3⁄8
L5×31⁄2×5⁄16
L5×31⁄2×1⁄4
5.55
4.83
4.05
3.18
2.72
2.23
2.22
1.90
1.56
1.21
1.02
0.830
0.977
0.991
1.01
1.02
1.03
1.04
0.996
0.951
0.906
0.861
0.838
0.814
4.10
3.47
2.83
2.16
1.82
1.47
0.581
0.492
0.400
0.305
0.256
0.206
0.748
0.751
0.755
0.762
0.766
0.770
0.464
0.472
0.479
0.486
0.489
0.492
L5×3×1⁄2
L5×3×7⁄16
L5×3×3⁄8
L5×3×5⁄16
L5×3×1⁄4
2.58
2.32
2.04
1.75
1.44
1.15
1.02
0.888
0.753
0.614
0.829
0.837
0.845
0.853
0.861
0.750
0.727
0.704
0.681
0.657
2.11
1.86
1.60
1.35
1.09
0.375
0.331
0.286
0.240
0.194
0.648
0.651
0.654
0.658
0.663
0.357
0.361
0.364
0.368
0.371
L4×4×3⁄4
L5×3×5⁄8
L5×3×1⁄2
L5×3×7⁄16
L5×3×3⁄8
L5×3×5⁄16
L5×3×1⁄4
7.67
6.66
5.56
4.97
4.36
3.71
3.04
2.81
2.40
1.97
1.75
1.52
1.29
1.05
1.19
1.20
1.22
1.23
1.23
1.24
1.25
1.27
1.23
1.18
1.16
1.14
1.12
1.09
5.07
4.33
3.56
3.16
2.74
2.32
1.88
0.680
0.576
0.469
0.414
0.357
0.300
0.242
0.778
0.779
0.782
0.785
0.788
0.791
0.795
1.000
1.000
1.000
1.000
1.000
1.000
1.000
L4×31⁄2×1⁄2
4×31⁄2×3⁄8
4×31⁄2×5⁄16
4×31⁄2×1⁄4
3.79
2.95
2.55
2.09
1.52
1.16
0.994
0.808
1.04
1.06
1.07
1.07
1.00
0.955
0.932
0.909
2.73
2.11
1.78
1.44
0.438
0.334
0.281
0.227
0.722
0.727
0.730
0.734
0.750
0.755
0.757
0.759
in.
4
3
3
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1 - 62
DIMENSIONS AND PROPERTIES
Y
ANGLES
Equal legs and unequal legs
Properties for designing
xp
x
Z
X
X
y, yp
k
α
Y
Size
and
Thickness
Z
k
Weight
per
ft
Axis X-X
Area
S
I
2
r
4
y
3
Z
yp
3
in.
in.
lb
in.
in.
in.
in.
in.
in.
L4×3×5⁄8
L4×3×1⁄2
L4×3×7⁄16
L4×3×3⁄8
L4×3×5⁄16
L4×3×1⁄4
11⁄16
15⁄
16
7⁄
8
13⁄
16
3⁄
4
11⁄
16
13.6
11.1
9.80
8.50
7.20
5.80
3.98
3.25
2.87
2.48
2.09
1.69
6.03
5.05
4.52
3.96
3.38
2.77
2.30
1.89
1.68
1.46
1.23
1.00
1.23
1.25
1.25
1.26
1.27
1.28
1.37
1.33
1.30
1.28
1.26
1.24
4.12
3.41
3.03
2.64
2.23
1.82
0.813
0.750
0.719
0.688
0.656
0.625
L31⁄2×31⁄2×1⁄2
L31⁄2×31⁄2×7⁄16
L31⁄2×31⁄2×3⁄8
L31⁄2×31⁄2×5⁄16
L31⁄2×31⁄2×1⁄4
7⁄
8
13⁄
16
3⁄
4
11⁄
16
5⁄
8
11.1
9.80
8.50
7.20
5.80
3.25
2.87
2.48
2.09
1.69
3.64
3.26
2.87
2.45
2.01
1.49
1.32
1.15
0.976
0.794
1.06
1.07
1.07
1.08
1.09
1.06
1.04
1.01
0.990
0.968
2.68
2.38
2.08
1.76
1.43
0.464
0.410
0.355
0.299
0.241
L31⁄2×3×1⁄2
L31⁄2×3×3⁄8
L31⁄2×3×5⁄16
L31⁄2×3×1⁄4
15⁄
16
13⁄
16
3⁄
4
11⁄
16
10.2
7.90
6.60
5.40
3.00
2.30
1.93
1.56
3.45
2.72
2.33
1.91
1.45
1.13
0.954
0.776
1.07
1.09
1.10
1.11
1.13
1.08
1.06
1.04
2.63
2.04
1.73
1.41
0.500
0.438
0.406
0.375
L31⁄2×21⁄2×1⁄2
L31⁄2×31⁄2×3⁄8
L31⁄2×31⁄2×1⁄4
15⁄
16
13⁄
16
11⁄
16
9.40
7.20
4.90
2.75
2.11
1.44
3.24
2.56
1.80
1.41
1.09
0.755
1.09
1.10
1.12
1.20
1.16
1.11
2.53
1.97
1.36
0.750
0.688
0.625
L3×3×1⁄2
L4×3×7⁄16
L4×3×3⁄8
L4×3×5⁄16
L4×3×1⁄4
L4×3×3⁄16
13⁄
16
3⁄
4
11⁄
16
5⁄
8
9⁄
16
1⁄
2
9.40
8.30
7.20
6.10
4.90
3.71
2.75
2.43
2.11
1.78
1.44
1.09
2.22
1.99
1.76
1.51
1.24
0.962
1.07
0.954
0.833
0.707
0.577
0.441
0.898
0.905
0.913
0.922
0.930
0.939
0.932
0.910
0.888
0.865
0.842
0.820
1.93
1.72
1.50
1.27
1.04
0.794
0.458
0.406
0.352
0.296
0.240
0.182
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
in.
STRUCTURAL SHAPES
1 - 63
Y
ANGLES
Equal legs and unequal legs
Properties for designing
x
xp
Z
X
X
y, yp
k
α
Y
Size
and
Thickness
Z
Axis Y-Y
S
I
r
Axis Z-Z
x
Z
xp
r
Tan
in.
in.
in.
in.
in.
in.
in.
in.
α
L4×3×5⁄8
L4×3×1⁄2
L4×3×7⁄16
L4×3×3⁄8
L4×3×5⁄16
L4×3×1⁄4
2.87
2.42
2.18
1.92
1.65
1.36
1.35
1.12
0.992
0.866
0.734
0.599
0.849
0.864
0.871
0.879
0.887
0.896
0.871
0.827
0.804
0.782
0.759
0.736
2.48
2.03
1.79
1.56
1.31
1.06
0.498
0.406
0.359
0.311
0.261
0.211
0.637
0.639
0.641
0.644
0.647
0.651
0.534
0.543
0.547
0.551
0.554
0.558
L31⁄2×31⁄2×1⁄2
L31⁄2×31⁄2×7⁄16
L31⁄2×31⁄2×3⁄8
L31⁄2×31⁄2×5⁄16
L31⁄2×31⁄2×1⁄4
3.64
3.26
2.87
2.45
2.01
1.49
1.32
1.15
0.976
0.794
1.06
1.07
1.07
1.08
1.09
1.06
1.04
1.01
0.990
0.968
2.68
2.38
2.08
1.76
1.43
0.464
0.410
0.355
0.299
0.241
0.683
0.684
0.687
0.690
0.694
1.000
1.000
1.000
1.000
1.000
L31⁄2×3×1⁄2
L31⁄2×3×3⁄8
L31⁄2×3×5⁄16
L31⁄2×3×1⁄4
2.33
1.85
1.58
1.30
1.10
0.851
0.722
0.589
0.881
0.897
0.905
0.914
0.875
0.830
0.808
0.785
1.98
1.53
1.30
1.05
0.429
0.328
0.276
0.223
0.621
0.625
0.627
0.631
0.714
0.721
0.724
0.727
L31⁄2×21⁄2×1⁄2
L31⁄2×31⁄2×3⁄8
L31⁄2×31⁄2×1⁄4
1.36
1.09
0.777
0.760
0.592
0.412
0.704
0.719
0.735
0.705
0.660
0.614
1.40
1.07
0.735
0.393
0.301
0.205
0.534
0.537
0.544
0.486
0.496
0.506
L3×3×1⁄2
L3×3×7⁄16
L3×3×3⁄8
L3×3×5⁄16
L3×3×1⁄4
L3×3×3⁄16
2.22
1.99
1.76
1.51
1.24
0.962
1.07
0.954
0.833
0.707
0.577
0.441
0.898
0.905
0.913
0.922
0.930
0.939
0.932
0.910
0.888
0.865
0.842
0.820
1.93
1.72
1.50
1.27
1.04
0.794
0.458
0.406
0.352
0.296
0.240
0.182
0.584
0.585
0.587
0.589
0.592
0.596
1.000
1.000
1.000
1.000
1.000
1.000
4
3
3
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1 - 64
DIMENSIONS AND PROPERTIES
Y
ANGLES
Equal legs and unequal legs
Properties for designing
xp
x
Z
X
X
y, yp
k
α
Y
Size
and
Thickness
in.
Z
k
Weight
per
ft
Axis X-X
Area
2
S
I
4
r
3
y
Z
yp
3
in.
lb
in.
in.
in.
in.
in.
L3×21⁄2×1⁄2
L3×21⁄2×3⁄8
L3×21⁄2×5⁄16
L3×21⁄2×1⁄4
L3×21⁄2×3⁄16
7⁄
8
3⁄
4
11⁄
16
5⁄
8
9⁄
16
8.50
6.60
5.60
4.50
3.39
2.50
1.92
1.62
1.31
0.996
2.08
1.66
1.42
1.17
0.907
1.04
0.810
0.688
0.561
0.430
0.913
0.928
0.937
0.945
0.954
1.000
0.956
0.933
0.911
0.888
1.88
1.47
1.25
1.02
0.781
0.500
0.438
0.406
0.375
0.344
L3×2×1⁄2
L3×2×3⁄8
L3×2×5⁄16
L3×2×1⁄4
L3×2×3⁄16
13⁄
16
11⁄
16
5⁄
8
9⁄
16
1⁄
2
7.70
5.90
5.00
4.10
3.07
2.25
1.73
1.46
1.19
0.902
1.92
1.53
1.32
1.09
0.842
1.00
0.781
0.664
0.542
0.415
0.924
0.940
0.948
0.957
0.966
1.08
1.04
1.02
0.993
0.970
1.78
1.40
1.19
0.973
0.746
0.750
0.688
0.656
0.625
0.594
L21⁄2×21⁄2×1⁄2
L21⁄2×21⁄2×3⁄8
L21⁄2×21⁄2×5⁄16
L21⁄2×21⁄2×1⁄4
L21⁄2×21⁄2×3⁄16
13⁄
16
11⁄
16
5⁄
8
9⁄
16
1⁄
2
7.70
5.90
5.00
4.10
3.07
2.25
1.73
1.46
1.19
0.902
1.23
0.984
0.849
0.703
0.547
0.724
0.566
0.482
0.394
0.303
0.739
0.753
0.761
0.769
0.778
0.806
0.762
0.740
0.717
0.694
1.31
1.02
0.869
0.711
0.545
0.450
0.347
0.293
0.238
0.180
L21⁄2×2×3⁄8
L21⁄2×2×5⁄16
L21⁄2×2×1⁄4
L21⁄2×2×3⁄16
11⁄
16
5⁄
8
9⁄
16
1⁄
2
5.30
4.50
3.62
2.75
1.55
1.31
1.06
0.809
0.912
0.788
0.654
0.509
0.547
0.466
0.381
0.293
0.768
0.776
0.784
0.793
0.831
0.809
0.787
0.764
0.986
0.843
0.691
0.532
0.438
0.406
0.375
0.344
L2×2×3⁄8
L2×2×5⁄16
L2×2×1⁄4
L2×2×3⁄16
L2×2×1⁄8
11⁄
16
5⁄
8
9⁄
16
1⁄
2
7⁄
16
4.70
3.92
3.19
2.44
1.65
1.36
1.15
0.938
0.715
0.484
0.479
0.416
0.348
0.272
0.190
0.351
0.300
0.247
0.190
0.131
0.594
0.601
0.609
0.617
0.626
0.636
0.614
0.592
0.569
0.546
0.633
0.541
0.445
0.343
0.235
0.340
0.288
0.234
0.179
0.121
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
in.
in.
STRUCTURAL SHAPES
1 - 65
ANGLES
Equal legs and unequal legs
Properties for designing
Y
x
xp
Z
X
X
y, yp
k
α
Y
Size
and
Thickness
Z
Axis Y-Y
S
I
r
Axis Z-Z
x
Z
xp
r
Tan
in.
in.
in.
in.
in.
in.
in.
α
L3×21⁄2×1⁄2
L3×21⁄2×3⁄8
L3×21⁄2×5⁄16
L3×21⁄2×1⁄4
L3×21⁄2×3⁄16
1.30
1.04
0.898
0.743
0.577
0.744
0.581
0.494
0.404
0.310
0.722
0.736
0.744
0.753
0.761
0.750
0.706
0.683
0.661
0.638
1.35
1.05
0.889
0.724
0.553
0.417
0.320
0.270
0.219
0.166
0.520
0.522
0.525
0.528
0.533
0.667
0.676
0.680
0.684
0.688
L3×2×1⁄2
L3×2×3⁄8
L3×2×5⁄16
L3×2×1⁄4
L3×2×3⁄16
0.672
0.543
0.470
0.392
0.307
0.474
0.371
0.317
0.260
0.200
0.546
0.559
0.567
0.574
0.583
0.583
0.539
0.516
0.493
0.470
0.891
0.684
0.577
0.468
0.357
0.375
0.289
0.244
0.198
0.150
0.428
0.430
0.432
0.435
0.439
0.414
0.428
0.435
0.440
0.446
L21⁄2×21⁄2×1⁄2
L21⁄2×21⁄2×3⁄8
L21⁄2×21⁄2×5⁄16
L21⁄2×21⁄2×1⁄4
L21⁄2×21⁄2×3⁄16
1.23
0.984
0.849
0.703
0.547
0.724
0.566
0.482
0.394
0.303
0.739
0.753
0.761
0.769
0.778
0.806
0.762
0.740
0.717
0.694
1.31
1.02
0.869
0.711
0.545
0.450
0.347
0.293
0.238
0.180
0.487
0.487
0.489
0.491
0.495
1.000
1.000
1.000
1.000
1.000
L21⁄2×2×3⁄8
L21⁄2×2×5⁄16
L21⁄2×2×1⁄4
L21⁄2×2×3⁄16
0.514
0.446
0.372
0.291
0.363
0.310
0.254
0.196
0.577
0.584
0.592
0.600
0.581
0.559
0.537
0.514
0.660
0.561
0.457
0.350
0.309
0.262
0.213
0.162
0.420
0.422
0.424
0.427
0.614
0.620
0.626
0.631
L2×2×3⁄8
L3×2×5⁄16
L3×2×1⁄4
L3×2×3⁄16
L3×2×1⁄8
0.479
0.416
0.348
0.272
0.190
0.351
0.300
0.247
0.190
0.131
0.594
0.601
0.609
0.617
0.626
0.636
0.614
0.592
0.569
0.546
0.633
0.541
0.445
0.343
0.235
0.340
0.288
0.234
0.179
0.121
0.389
0.390
0.391
0.394
0.398
1.000
1.000
1.000
1.000
1.000
in.
4
3
3
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1 - 66
DIMENSIONS AND PROPERTIES
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
STRUCTURAL TEES (WT, MT, ST)
1 - 67
STRUCTURAL TEES (WT, MT, ST)
Structural tees are obtained by splitting the webs of various beams, generally with the
aid of rotary shears, and straightening to meet established permissible variations listed
in Standard Mill Practice in Part 1 of this Manual.
Although structural tees may be obtained by off-center splitting, or by splitting at two
lines, as specified on order, the Dimensions and Properties are based on a depth of tee
equal to one-half the published beam depth. Values of Qs are given for Fy = 36 ksi and
Fy = 50 ksi, for those tees having stems which exceed the limiting width-thickness ratio
λr of LRFD Specification Section B5. Since the cross section is comprised entirely of
unstiffened elements, Qa = 1.0 and Q = Qs for
_ all tee sections. The Flexural-Torsional
Properties Table lists the dimensional values (ro and H) and cross-section constants (J and
Cw) needed for checking flexural-torsional buckling.
Use of Table
The table may be used as follows for checking the limit states of (1) flexural buckling
about the x-axis and (2) flexural-torsional buckling. The lower of the two limit states
must be used for design. See also Part 3 of this LRFD Manual.
(1) Flexural Buckling About the X-Axis
Where no value of Qs is shown, the design compressive strength for this limit state is
given by LRFD Specification Section E2. Where a value of Qs is shown, the strength
must be reduced in accordance with Appendix B5 of the LRFD Specification.
(2) Flexural-Torsional Buckling
The design compressive strength for this limit
_ state is given by LRFD Specification
Section E3. This involves calculations with J, ro, and H. Refer to the Flexural-Torsional
Properties Tables, later in Part 1.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1 - 68
DIMENSIONS AND PROPERTIES
bf
tf
yp , y
STRUCTURAL TEES
Cut from W shapes
Dimensions
k
Y
X
X
d
tw
Y
Stem
Area
Designation in.2
Area
of
Stem
Depth of
Tee
d
Thickness
tw
tw
2
in.
in.
in.
in.2
Flange
Width
bf
in.
Thickness
tf
in.
Distance
k
in.
WT22×167.5
WT22×145
WT22×131
WT22×115
49.1
42.9
38.6
33.8
22.010
22
1.020
21.810 2113⁄16 0.870
21.655 2111⁄16 0.790
21.455 217⁄16 0.710
1
7⁄
8
13⁄
16
11⁄
16
1⁄
2
7⁄
16
3⁄
8
3⁄
8
22.5
19.0
17.1
15.2
15.950
15.830
15.750
15.750
153⁄4
157⁄8
153⁄4
153⁄4
1.770
1.580
1.420
1.220
13⁄4
19⁄16
17⁄16
11⁄4
29⁄16
23⁄8
23⁄16
2
WT20×296.5
WT22×251.5
WT22×215.5
WT22×186
WT22×160.5
WT22×148.5
WT22×138.5
WT22×124.5
WT22×107.5
WT22×99.5
WT22×87
87.0
74.0
63.4
54.7
47.0
43.7
40.7
36.7
31.7
29.2
25.5
21.495
21.025
20.630
20.315
20.040
19.920
19.845
19.690
19.490
19.335
19.100
211⁄2
21
205⁄8
205⁄16
20
1915⁄16
197⁄8
1911⁄16
191⁄2
195⁄16
191⁄8
1.790
1.540
1.340
1.160
1.000
0.930
0.830
0.750
0.650
0.650
0.650
113⁄16
19⁄16
15⁄16
13⁄16
1
15⁄
16
13⁄
16
3⁄
4
5⁄
8
5⁄
8
5⁄
8
1
3⁄
4
11⁄
16
9⁄
16
1⁄
2
1⁄
2
7⁄
16
3⁄
8
5⁄
16
5⁄
16
5⁄
16
38.5
32.4
27.6
23.6
20.0
18.5
16.5
14.8
12.7
12.6
12.4
16.690 163⁄4
16.420 167⁄16
16.220 161⁄4
16.060 161⁄16
15.910 157⁄8
15.825 157⁄8
15.830 157⁄8
15.750 153⁄4
15.750 153⁄4
15.750 153⁄4
15.750 153⁄4
3.230
2.760
2.360
2.050
1.770
1.650
1.575
1.420
1.220
1.065
0.830
31⁄4
23⁄4
23⁄8
21⁄16
13⁄4
15⁄8
19⁄16
17⁄16
11⁄4
11⁄16
13⁄
16
47⁄16
315⁄16
39⁄16
31⁄4
215⁄16
31⁄16
23⁄4
25⁄8
23⁄8
21⁄4
2
WT20×233
WT22×196
WT22×165.5
WT22×139
WT22×132
WT22×117.5
WT22×105.5
WT22×91.5
WT22×83.5
WT22×74.5
68.4
57.7
48.8
40.9
38.8
34.5
31.0
26.9
24.6
21.9
21.220 213⁄16
20.785 203⁄4
20.395 203⁄8
20.080 201⁄8
20.000
20
19.845 197⁄8
19.685 1911⁄16
19.490 191⁄2
19.295 195⁄16
19.100 191⁄8
1.67
1.42
1.22
1.02
0.960
0.830
0.750
0.650
0.650
0.630
111⁄16
17⁄16
11⁄4
1
1
13⁄
16
3⁄
4
5⁄
8
5⁄
8
5⁄
8
13⁄
16
11⁄
16
5⁄
8
1⁄
2
1⁄
2
7⁄
16
3⁄
8
5⁄
16
5⁄
16
5⁄
16
35.4
29.5
24.9
20.5
19.2
16.5
14.8
12.7
12.5
12.0
12.640 125⁄8
12.360 123⁄8
12.170 123⁄16
11.970
12
11.930
12
11.890 117⁄8
11.810 113⁄4
11.810 113⁄4
11.810 113⁄4
11.810 113⁄4
2.950
2.520
2.130
1.810
1.730
1.575
1.415
1.220
1.025
0.830
215⁄16
21⁄2
21⁄8
113⁄16
13⁄4
17⁄16
19⁄16
11⁄4
1
13⁄
16
41⁄8
311⁄16
35⁄16
3
215⁄16
23⁄4
25⁄8
23⁄8
23⁄16
2
WT18×424
WT22×399
WT22×325
WT22×263.5
WT22×219.5
WT22×196.5
WT22×179.5
WT22×164
WT22×150
WT22×140
WT22×130
WT22×122.5
WT22×115
125
117
95.0
77.0
64.0
57.5
52.7
48.2
44.1
41.2
38.2
36.0
33.8
21.225 211⁄4
20.985
21
20.235 201⁄4
19.605 195⁄8
19.130 191⁄8
18.900 187⁄8
18.700 1811⁄16
18.545 189⁄16
18.370 183⁄8
18.260 181⁄4
18.130 181⁄8
18.040
18
17.950
18
2.520
2.380
1.970
1.610
1.360
1.220
1.120
1.020
0.945
0.885
0.840
0.800
0.760
21⁄2
23⁄8
2
15⁄8
13⁄8
11⁄4
11⁄8
1
15⁄
16
7⁄
8
13⁄
16
13⁄
16
3⁄
4
11⁄4
13⁄16
1
13⁄
16
11⁄
16
5⁄
8
9⁄
16
1⁄
2
1⁄
2
7⁄
16
7⁄
16
7⁄
16
3⁄
8
53.5
49.9
39.9
31.6
26.0
23.1
20.9
18.9
17.4
16.2
15.2
14.4
13.6
18.130
17.990
17.575
17.220
16.965
16.830
16.730
16.630
16.655
16.595
16.550
16.510
16.470
181⁄8
18
175⁄8
171⁄4
17
167⁄8
163⁄4
165⁄8
165⁄8
165⁄8
161⁄2
161⁄2
161⁄2
4.530
4.290
3.540
2.910
2.440
2.200
2.010
1.850
1.680
1.570
1.440
1.350
1.260
41⁄2
45⁄16
39⁄16
215⁄16
27⁄16
23⁄16
2
17⁄8
111⁄16
19⁄16
17⁄16
13⁄8
11⁄4
511⁄16
57⁄16
411⁄16
41⁄16
39⁄16
35⁄16
31⁄8
3
213⁄16
211⁄16
29⁄16
21⁄2
23⁄8
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
STRUCTURAL TEES (WT, MT, ST)
1 - 69
bf
STRUCTURAL TEES
Cut from W shapes
Properties
tf
k
Y
yp , y
X
X
d
tw
Y
Nominal
Wt.
per
ft
lb
Axis X-X
h
tw
Qs*
Axis Y-Y
I
S
r
y
Z
yp
I
S
r
Z
in.4
in.3
in.
in.
in.3
in.
in.4
in.3
in.
in.3
36
Fy, ksi
50
167.5
145
131
115
19.1
22.3
24.6
27.4
2160
1840
1650
1440
131
111
100
88.6
6.63
6.55
6.53
6.53
5.51
5.27
5.20
5.17
233
197
177
157
1.54
1.35
1.23
1.07
600
524
463
398
75.3
66.1
58.8
50.5
3.50
3.49
3.46
3.43
118
103
91.4
78.4
0.982
0.833
0.732
0.608
0.817
0.636
0.532
0.438
296.5
251.5
215.5
186
160.5
148.5
138.5
124.5
107.5
99.5
87
9.5
11.1
12.8
14.7
17.1
18.4
20.6
22.8
26.3
26.3
26.3
3300
2730
2290
1930
1630
1500
1360
1210
1030
987
907
209
175
148
126
107
98.9
88.6
79.3
68.0
66.4
63.8
6.16
6.07
6.01
5.95
5.89
5.87
5.78
5.75
5.72
5.81
5.96
5.67
5.39
5.18
4.97
4.79
4.71
4.51
4.41
4.28
4.48
4.87
379
315
266
225
191
176
157
140
120
117
114
2.61
2.25
1.95
1.70
1.48
1.38
1.28
1.16
1.00
0.927
0.811
1260
1020
843
710
596
546
522
463
398
347
271
151
125
104
88.5
74.9
69.1
65.9
58.8
50.5
44.1
34.4
3.81
3.72
3.65
3.60
3.56
3.54
3.58
3.56
3.55
3.45
3.26
240
197
164
139
117
108
102
91.0
77.9
68.3
53.8
—
—
—
—
—
0.989
0.882
0.782
0.618
0.628
0.643
—
—
—
—
0.895
0.825
0.699
0.580
0.445
0.452
0.463
233
196
165.5
139
132
117.5
105.5
91.5
83.5
74.5
10.2
12.0
14.0
16.8
17.8
20.6
22.8
26.3
26.3
27.1
2770
2270
1880
1540
1450
1260
1120
957
898
815
185
153
128
106
99.3
85.6
76.7
65.8
63.7
59.7
6.36
6.28
6.21
6.14
6.11
6.04
6.01
5.97
6.05
6.10
6.22
5.95
5.74
5.50
5.40
5.17
5.08
4.94
5.20
5.45
333
276
231
190
178
153
137
117
115
119
2.71
2.33
2.01
1.71
1.63
1.45
1.31
1.14
1.04
1.82
504
401
323
261
246
222
195
168
141
115
79.8
65.0
53.1
43.6
41.3
37.3
33.0
28.5
23.9
19.4
2.72
2.64
2.57
2.52
2.52
2.54
2.51
2.50
2.40
2.29
131
106
86.2
70.0
66.2
59.2
52.3
44.8
38.0
31.1
—
—
—
—
—
0.882
0.782
0.618
0.630
0.604
—
—
—
0.913
0.855
0.699
0.581
0.445
0.454
0.435
424
399
325
263.5
219.5
196.5
179.5
164
150
140
130
122.5
115
6.3
6.6
8.0
9.8
11.6
12.9
14.1
15.4
16.7
17.8
18.7
19.7
20.7
4250
3920
3020
2330
1880
1660
1500
1350
1230
1140
1060
995
934
277
257
202
159
130
115
104
94.1
86.1
80.0
75.1
71.0
67.0
5.84
5.79
5.64
5.50
5.42
5.37
5.33
5.29
5.27
5.25
5.26
5.26
5.25
5.86
5.72
5.29
4.89
4.63
4.46
4.33
4.21
4.13
4.07
4.05
4.03
4.01
515
478
373
290
235
207
187
168
153
142
133
125
118
3.43
3.25
2.70
2.24
1.89
1.71
1.58
1.45
1.33
1.24
1.16
1.09
1.03
2270
2100
1610
1240
997
877
786
711
648
599
545
507
470
251
234
184
145
117
104
94.0
85.5
77.8
72.2
65.9
61.4
57.1
4.27
4.24
4.12
4.02
3.95
3.90
3.86
3.84
3.83
3.81
3.78
3.75
3.73
399
371
290
227
184
162
146
132
120
112
102
94.9
88.1
—
—
—
—
—
—
—
—
—
—
0.981
0.943
0.896
—
—
—
—
—
—
—
—
0.927
0.867
0.816
0.770
0.715
*Where no value of Qs is shown, the Tee complies with LRFD Specification Section E2.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1 - 70
DIMENSIONS AND PROPERTIES
bf
tf
yp , y
STRUCTURAL TEES
Cut from W shapes
Dimensions
k
Y
X
X
d
tw
Y
Stem
Area
of
Stem
Flange
DisThickness tance
tf
k
Area
Depth of
Tee
d
Thickness
tw
tw
2
Designation
in.2
in.
in.
in.
WT18×128
WT18×116
WT18×105
WT18×97
WT18×91
WT18×85
WT18×80
WT18×75
WT18×67.5
37.7
34.1
30.9
28.5
26.8
25.0
23.5
22.1
19.9
18.715 1811⁄16
18.560 189⁄16
18.345 183⁄8
18.245 181⁄4
18.165 181⁄8
18.085 181⁄8
18.005
18
17.925 177⁄8
17.775 173⁄4
0.960
0.870
0.830
0.765
0.725
0.680
0.650
0.625
0.600
1
7⁄
8
13⁄
16
3⁄
4
3⁄
4
11⁄
16
5⁄
8
5⁄
8
5⁄
8
2
7⁄
16
7⁄
16
3⁄
8
3⁄
8
3⁄
8
5⁄
16
5⁄
16
5⁄
16
18.0
16.1
15.2
14.0
13.2
12.3
11.7
11.2
10.7
12.215
12.120
12.180
12.115
12.075
12.030
12.000
11.975
11.950
121⁄4
121⁄8
121⁄8
121⁄8
121⁄8
12
12
12
12
1.730
1.570
1.360
1.260
1.180
1.100
1.020
0.940
0.790
13⁄4
19⁄16
13⁄8
11⁄4
13⁄16
11⁄8
1
15⁄
16
13⁄
16
25⁄8
21⁄2
25⁄16
23⁄16
21⁄8
2
115⁄16
17⁄8
111⁄16
WT16.5×177
WT16.5×159
WT16.5×145.5
WT16.5×131.5
WT16.5×120.5
WT16.5×110.5
WT16.5×100.5
52.1
46.7
42.8
38.7
35.4
32.5
29.5
17.775 173⁄4
17.580 179⁄16
17.420 177⁄16
17.265 171⁄4
17.090 171⁄8
16.965
17
16.840 167⁄8
1.160
1.040
0.960
0.870
0.830
0.775
0.715
13⁄16
11⁄16
1
7⁄
8
13⁄
16
3⁄
4
11⁄
16
5⁄
8
9⁄
16
1⁄
2
7⁄
16
7⁄
16
3⁄
8
3⁄
8
20.6
18.3
16.7
15.0
14.2
13.1
12.0
16.100
15.985
15.905
15.805
15.860
15.805
15.745
161⁄8
16
157⁄8
153⁄4
157⁄8
153⁄4
153⁄4
2.090
1.890
1.730
1.570
1.400
1.275
1.150
21⁄16
17⁄8
13⁄4
19⁄16
13⁄8
11⁄4
11⁄8
27⁄8
211⁄16
29⁄16
23⁄8
23⁄16
21⁄16
115⁄16
WT16.5×84.5
WT16.5×76
WT16.5×70.5
WT16.5×65
WT16.5×59
24.8
22.4
20.8
19.2
17.3
16.910 1615⁄16
16.745 163⁄4
16.650 165⁄8
16.545 161⁄2
16.430 163⁄8
0.670
0.635
0.605
0.580
0.550
11⁄
3⁄
8
5⁄
16
5⁄
16
5⁄
16
5⁄
16
11.3
10.6
10.1
9.60
9.04
11.500
11.565
11.535
11.510
11.480
111⁄2
115⁄8
111⁄2
111⁄2
111⁄2
1.220
1.055
0.960
0.855
0.740
11⁄4
11⁄16
15⁄
16
7⁄
8
3⁄
4
21⁄16
17⁄8
13⁄4
111⁄16
19⁄16
WT15×238.5
WT15×195.5
WT15×163
WT15×146
WT15×130.5
WT15×117.5
WT15×105.5
WT15×95.5
WT15×86.5
70.0
57.0
47.9
42.9
38.4
34.5
31.0
28.1
25.4
17.105 171⁄8
16.595 165⁄8
16.200 163⁄16
16.005
16
15.805 1513⁄16
15.650 155⁄8
15.470 151⁄2
15.340 153⁄8
15.220 151⁄4
1.630
1.360
1.140
1.020
0.930
0.830
0.775
0.710
0.655
15⁄8
13⁄8
11⁄8
1
15⁄
16
13⁄
16
3⁄
4
11⁄
16
5⁄
8
13⁄
16
11⁄
16
9⁄
16
1⁄
2
1⁄
2
7⁄
16
3⁄
8
3⁄
8
5⁄
16
27.9
22.6
18.5
16.3
14.7
13.0
12.0
10.9
9.97
15.865
15.590
15.370
15.255
15.155
15.055
15.105
15.040
14.985
157⁄8
155⁄8
153⁄8
151⁄2
151⁄8
15
151⁄8
15
15
2.950
2.440
2.050
1.850
1.650
1.500
1.315
1.185
1.065
3
27⁄16
21⁄16
17⁄8
15⁄8
11⁄2
15⁄16
13⁄16
11⁄16
33⁄4
31⁄4
213⁄16
25⁄8
27⁄16
21⁄4
21⁄8
115⁄16
17⁄8
WT15×74
WT18×66
WT18×62
WT18×58
WT18×54
WT18×49.5
WT18×45
21.7
19.4
18.2
17.1
15.9
14.5
13.2
15.335 155⁄16
15.155 151⁄8
15.085 151⁄8
15.005
15
14.915 147⁄8
14.825 147⁄8
14.765 143⁄4
0.650
0.615
0.585
0.565
0.545
0.520
0.470
5⁄
8
5⁄
8
9⁄
16
9⁄
16
9⁄
16
1⁄
2
1⁄
2
5⁄
16
5⁄
16
5⁄
16
5⁄
16
5⁄
16
1⁄
4
1⁄
4
10.0
9.32
8.82
8.48
8.13
7.71
6.94
10.480
10.545
10.515
10.495
10.475
10.450
10.400
101⁄2
101⁄2
101⁄2
101⁄2
101⁄2
101⁄2
103⁄8
1.180
1.000
0.930
0.850
0.760
0.670
0.610
13⁄16
1
15⁄
16
7⁄
8
3⁄
4
11⁄
16
9⁄
16
2
13⁄4
111⁄16
15⁄8
19⁄16
17⁄16
15⁄16
16
5⁄
8
5⁄
8
9⁄
16
9⁄
16
1⁄
Width
bf
in.2
in.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
in.
in.
STRUCTURAL TEES (WT, MT, ST)
1 - 71
bf
STRUCTURAL TEES
Cut from W shapes
Properties
tf
k
Y
yp , y
X
X
d
tw
Y
Nominal
Wt.
per
ft
lb
Axis X-X
h
tw
Qs*
Axis Y-Y
I
S
r
y
Z
yp
I
S
r
Z
in.4
in.3
in.
in.
in.3
in.
in.4
in.3
in.
in.3
Fy, ksi
36
50
128
116
105
97
91
85
80
75
67.5
16.9
18.7
19.6
21.2
22.4
23.9
25.0
26.0
27.1
1200
1080
985
901
845
786
740
698
637
87.4
78.5
73.1
67.0
63.1
58.9
55.8
53.1
49.7
5.66
5.63
5.65
5.62
5.62
5.61
5.61
5.62
5.66
4.92
4.82
4.87
4.80
4.77
4.73
4.74
4.78
4.96
156
140
131
120
113
105
100
95.5
94.3
1.54
1.40
1.27
1.18
1.11
1.04
0.980
0.923
1.24
264
234
206
187
174
160
147
135
113
43.2
38.6
33.8
30.9
28.8
26.6
24.6
22.5
18.9
2.65
2.62
2.58
2.56
2.55
2.53
2.50
2.47
2.38
68.6
61.0
53.5
48.9
45.4
41.9
38.6
35.5
29.8
—
0.994
0.960
0.887
0.831
0.767
0.720
0.677
0.634
0.927
0.831
0.791
0.705
0.635
0.565
0.521
0.486
0.457
177
159
145.5
131.5
120.5
110.5
100.5
12.9
14.4
15.6
17.2
18.1
19.3
21.0
1320
1160
1050
943
871
799
725
96.8
85.8
78.3
70.2
65.8
60.8
55.5
5.03
4.99
4.97
4.94
4.96
4.96
4.95
4.16
4.02
3.94
3.84
3.85
3.81
3.78
174
154
140
125
116
107
97.7
1.62
1.46
1.34
1.22
1.12
1.03
0.938
729
645
581
517
466
420
375
90.6
80.7
73.1
65.5
58.8
53.2
47.6
3.74
3.71
3.69
3.66
3.63
3.59
3.56
141
125
113
101
90.9
82.1
73.4
—
—
—
—
—
0.968
0.896
—
—
0.993
0.907
0.867
0.801
0.715
84.5
76
70.5
65
59
22.4
23.6
24.8
25.8
27.3
649
592
552
513
469
51.1
47.4
44.7
42.1
39.2
5.12
5.14
5.15
5.18
5.20
4.21
4.26
4.29
4.36
4.47
90.8
84.5
79.8
75.6
74.8
1.08
0.967
0.901
0.832
0.862
155
136
123
109
93.6
27.0
23.6
21.3
18.9
16.3
2.50
2.47
2.43
2.39
2.32
42.2
37.0
33.5
29.7
25.7
0.827
0.775
0.728
0.685
0.621
0.630
0.574
0.529
0.492
0.447
238.5
195.5
163
146
130.5
117.5
105.5
95.5
86.5
8.3
9.9
11.8
13.2
14.5
16.2
17.4
19.0
20.6
1550
1210
981
861
764
674
610
549
497
121
96.6
78.9
69.6
62.3
55.1
50.5
45.7
41.7
4.70
4.61
4.53
4.48
4.46
4.42
4.43
4.42
4.42
4.30
4.04
3.76
3.63
3.54
3.42
3.40
3.35
3.31
224
177
143
125
112
98.2
89.5
80.8
73.4
2.21
1.83
1.56
1.40
1.27
1.15
1.03
0.933
0.848
987
774
622
549
480
427
378
336
299
124
99.2
81.0
71.9
63.3
56.8
50.1
44.7
39.9
3.75
3.68
3.61
3.58
3.54
3.52
3.49
3.46
3.43
195
155
126
111
97.9
87.5
77.2
68.9
61.4
—
—
—
—
—
—
—
0.981
0.913
—
—
—
—
—
0.952
0.897
0.816
0.735
74
66
62
58
54
49.5
45
20.8
22.0
23.1
23.9
24.8
26.0
28.7
466
421
396
373
349
322
291
40.6
37.4
35.3
33.7
32.0
30.0
27.1
4.63
4.66
4.66
4.67
4.69
4.71
4.69
3.84
3.90
3.90
3.94
4.01
4.09
4.03
72.2
66.8
63.1
60.4
57.7
57.4
49.4
1.04
0.921
0.867
0.815
0.757
0.912
0.445
113
98.0
90.4
82.1
73.0
63.9
57.3
21.7
18.6
17.2
15.7
13.9
12.2
11.0
2.28
2.25
2.23
2.19
2.15
2.10
2.08
34.0
29.2
27.0
24.6
22.0
19.3
17.3
0.896
0.853
0.801
0.767
0.733
0.685
0.563
0.715
0.664
0.601
0.565
0.533
0.492
0.405
*Where no value of Qs is shown, the Tee complies with LRFD Specification Section E2.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1 - 72
DIMENSIONS AND PROPERTIES
bf
tf
yp , y
STRUCTURAL TEES
Cut from W shapes
Dimensions
k
Y
X
X
d
tw
Y
Stem
Area
of
Stem
Area
Depth of
Tee
d
Thickness
tw
tw
2
Designation
in.2
in.
in.
in.
in.2
WT13.5×269.5
WT13.5×224
WT13.5×184
WT13.5×153.5
WT13.5×129
WT13.5×117.5
WT13.5×108.5
WT13.5×97
WT13.5×89
WT13.5×80.5
WT13.5×73
79.0
65.5
54.0
45.1
37.9
34.6
31.9
28.5
26.1
23.7
21.5
16.260
15.710
15.195
14.805
14.490
14.330
14.215
14.055
13.905
13.795
13.690
161⁄4
1511⁄16
153⁄16
1413⁄16
141⁄2
145⁄16
143⁄16
141⁄16
137⁄8
133⁄4
133⁄4
1.970
1.650
1.380
1.160
0.980
0.910
0.830
0.750
0.725
0.660
0.605
2
15⁄8
13⁄8
13⁄16
1
15⁄
16
13⁄
16
3⁄
4
3⁄
4
11⁄
16
5⁄
8
1
13⁄
16
11⁄
16
5⁄
8
1⁄
2
1⁄
2
7⁄
16
3⁄
8
3⁄
8
3⁄
8
5⁄
16
32.0
25.9
21.0
17.2
14.2
13.0
11.8
10.5
10.1
9.10
8.28
WT13.5×64.5
WT13.5×57
WT13.5×51
WT13.5×47
WT13.5×42
18.9
16.8
15.0
13.8
12.4
13.815 1313⁄16
13.645 135⁄8
13.545 131⁄2
13.460 131⁄2
13.355 133⁄8
0.610
0.570
0.515
0.490
0.460
5⁄
8
9⁄
16
1⁄
2
1⁄
2
7⁄
16
5⁄
16
5⁄
16
1⁄
4
1⁄
4
1⁄
4
WT12×246
WT12×204
WT12×167.5
WT12×139.5
WT12×125
WT12×114.5
WT12×103.5
WT12×96
WT12×88
WT12×81
WT12×73
WT12×65.5
WT12×58.5
WT12×52
72.0
59.5
49.2
41.0
36.8
33.6
30.4
28.2
25.8
23.9
21.5
19.3
17.2
15.3
14.825 1413⁄16
14.270 141⁄4
13.760 133⁄4
13.365 133⁄8
13.170 133⁄16
13.010
13
12.855 127⁄8
12.735 123⁄4
12.620 125⁄8
12.500 121⁄2
12.370 123⁄8
12.240 121⁄4
12.130 121⁄8
12.030
12
1.970
1.650
1.380
1.160
1.040
0.960
0.870
0.810
0.750
0.705
0.650
0.605
0.550
0.500
2
15⁄8
13⁄8
13⁄16
11⁄16
1
7⁄
8
13⁄
16
3⁄
4
11⁄
16
5⁄
8
5⁄
8
9⁄
16
1⁄
2
13⁄
16
11⁄
16
5⁄
8
9⁄
16
1⁄
2
7⁄
16
7⁄
16
3⁄
8
3⁄
8
5⁄
16
5⁄
16
5⁄
16
1⁄
4
29.2
23.5
19.0
15.5
13.7
12.5
11.2
10.3
9.47
8.81
8.04
7.41
6.67
6.02
WT12×51.5
WT12×47
WT12×42
WT12×38
WT12×34
15.1
13.8
12.4
11.2
10.0
12.265
12.155
12.050
11.960
11.865
121⁄4
121⁄8
12
12
117⁄8
0.550
0.515
0.470
0.440
0.415
9⁄
16
1⁄
2
1⁄
2
7⁄
16
7⁄
16
5⁄
16
1⁄
4
1⁄
4
1⁄
4
1⁄
4
9.11 11.870
8.10 11.785
117⁄8
113⁄4
0.430
0.395
7⁄
16
3⁄
8
1⁄
4
3⁄
16
WT12×31
WT12×27.5
1
Flange
DisThickness tance
tf
k
Width
bf
in.
in.
in.
151⁄4
15
145⁄8
141⁄2
141⁄4
141⁄4
141⁄8
14
141⁄8
14
14
3.540
2.990
2.480
2.090
1.770
1.610
1.500
1.340
1.190
1.080
0.975
39⁄16
3
21⁄2
21⁄16
13⁄4
15⁄8
11⁄2
15⁄16
13⁄16
11⁄16
1
41⁄4
311⁄16
33⁄16
213⁄16
21⁄2
25⁄16
23⁄16
21⁄16
17⁄8
113⁄16
111⁄16
8.43 10.010 10
7.78 10.070 101⁄8
6.98 10.015 10
6.60 9.990 10
6.14 9.960 10
1.100
0.930
0.830
0.745
0.640
11⁄8
15⁄
16
13⁄
16
3⁄
4
5⁄
8
113⁄16
15⁄8
19⁄16
17⁄16
13⁄8
14.115
13.800
13.520
13.305
13.185
13.110
13.010
12.950
12.890
12.955
12.900
12.855
12.800
12.750
141⁄8
133⁄4
131⁄2
131⁄4
131⁄8
131⁄8
13
13
127⁄8
13
127⁄8
127⁄8
123⁄4
123⁄4
3.540
2.990
2.480
2.090
1.890
1.730
1.570
1.460
1.340
1.220
1.090
0.960
0.850
0.750
39⁄16
3
21⁄2
21⁄16
17⁄8
13⁄4
19⁄16
17⁄16
15⁄16
11⁄4
11⁄16
15⁄
16
7⁄
8
3⁄
4
45⁄16
33⁄4
31⁄4
27⁄8
211⁄16
21⁄2
23⁄8
21⁄4
21⁄8
2
17⁄8
13⁄4
15⁄8
11⁄2
6.75
6.26
5.66
5.26
4.92
9.000
9.065
9.020
8.990
8.965
9
91⁄8
9
9
9
0.980
0.875
0.770
0.680
0.585
1
7⁄
8
3⁄
4
11⁄
16
9⁄
16
13⁄4
15⁄8
19⁄16
17⁄16
13⁄8
5.10
4.66
7.040
7.005
7
7
0.590
0.505
9⁄
16
1⁄
2
13⁄8
15⁄16
15.255
14.940
14.665
14.445
14.270
14.190
14.115
14.035
14.085
14.020
13.965
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
STRUCTURAL TEES (WT, MT, ST)
1 - 73
bf
STRUCTURAL TEES
Cut from W shapes
Properties
tf
k
Y
yp , y
X
X
d
tw
Y
Nominal
Wt.
per
ft
lb
Axis X-X
h
tw
Qs*
Axis Y-Y
I
S
r
y
Z
yp
I
S
r
Z
in.4
in.3
in.
in.
in.3
in.
in.4
in.3
in.
in.3
36
50
2.59 1060
2.19
836
1.84
655
1.56
527
1.33
430
1.22
384
1.13
352
1.02
309
0.928 278
0.845 248
0.768 222
138
112
89.3
72.9
60.2
54.2
49.9
44.1
39.4
35.4
31.7
3.66
3.57
3.48
3.42
3.37
3.33
3.32
3.29
3.26
3.24
3.21
218
176
140
113
93.3
83.8
77.0
67.9
60.8
54.5
48.8
—
—
—
—
—
—
—
—
—
—
0.938
—
—
—
—
—
—
—
0.963
0.937
0.851
0.765
18.4
15.8
13.9
12.4
10.6
2.21
2.18
2.15
2.12
2.07
28.8
24.7
21.7
19.4
16.6
0.938
0.883
0.780
0.728
0.664
0.765
0.700
0.578
0.529
0.476
119
95.5
75.9
61.9
54.9
49.7
44.4
40.9
37.2
34.2
30.3
26.5
23.2
20.3
3.41
3.33
3.23
3.17
3.14
3.11
3.08
3.07
3.04
3.05
3.01
2.97
2.94
2.91
187
150
119
96.4
85.3
77.0
68.6
63.1
57.3
52.6
46.6
40.7
35.7
31.2
—
—
—
—
—
—
—
—
—
—
—
—
0.960
0.874
—
—
—
—
—
—
—
—
—
—
0.947
0.887
0.791
0.690
20.7
18.8
16.3
14.3
12.3
0.951
0.896
0.810
0.741
0.681
0.781
0.715
0.610
0.541
0.489
7.87 0.724
6.67 0.626
0.525
0.450
269.5
224
184
153.5
129
117.5
108.5
97
89
80.5
73
6.2
7.4
8.8
10.5
12.4
13.3
14.6
16.2
16.7
18.4
20.0
1520
1190
938
753
613
556
502
444
414
372
336
128
102
81.7
66.4
54.6
50.0
45.2
40.3
38.2
34.4
31.2
4.39
4.27
4.17
4.09
4.02
4.01
3.97
3.95
3.98
3.96
3.95
4.36
4.02
3.71
3.47
3.28
3.21
3.11
3.03
3.05
2.99
2.95
241
191
151
121
98.8
89.8
81.1
71.8
67.6
60.8
55.0
64.5
57
51
47
42
19.9
21.3
23.5
24.7
26.3
323
289
258
239
216
31.0
28.3
25.3
23.8
21.9
4.13
4.15
4.14
4.16
4.18
3.39
3.42
3.37
3.41
3.48
55.1
50.4
45.0
42.4
39.2
0.945
0.833
0.750
0.692
0.621
246
204
167.5
139.5
125
114.5
103.5
96
88
81
73
65.5
58.5
52
5.5
6.5
7.8
9.3
10.4
11.2
12.4
13.3
14.4
15.3
16.6
17.8
19.6
21.6
1130
874
685
546
478
431
382
350
319
293
264
238
212
189
105
83.1
66.3
53.6
47.2
42.9
38.3
35.2
32.2
29.9
27.2
24.8
22.3
20.0
3.96
3.83
3.73
3.65
3.61
3.58
3.55
3.53
3.51
3.50
3.50
3.52
3.51
3.51
4.07
3.74
3.42
3.18
3.05
2.97
2.87
2.80
2.74
2.70
2.66
2.65
2.62
2.59
200
157
123
98.8
86.5
78.1
69.3
63.5
57.8
53.3
48.2
43.9
39.2
35.1
2.55
2.16
1.82
1.54
1.39
1.28
1.17
1.09
1.00
0.921
0.833
0.750
0.672
0.600
51.5
47
42
38
34
19.6
20.9
22.9
24.5
26.0
204
186
166
151
137
22.0
20.3
18.3
16.9
15.6
3.67
3.67
3.67
3.68
3.70
3.01
2.99
2.97
3.00
3.06
39.2
36.1
32.5
30.1
27.9
0.841
0.764
0.685
0.622
0.560
59.7
54.5
47.2
41.3
35.2
13.3
12.0
10.5
9.18
7.85
1.99
1.98
1.95
1.92
1.87
31
27.5
25.1
27.3
131
117
15.6
14.1
3.79
3.80
3.46
3.50
28.4
25.6
1.28
1.53
17.2
14.5
4.90
4.15
1.38
1.34
92.2
79.4
69.6
62.0
52.8
837
659
513
412
362
326
289
265
240
221
195
170
149
130
*Where no value of Qs is shown, the Tee complies with LRFD Specification Sect. E2.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
Fy, ksi
1 - 74
DIMENSIONS AND PROPERTIES
bf
tf
yp , y
STRUCTURAL TEES
Cut from W shapes
Dimensions
k
Y
X
X
d
tw
Y
Stem
Area
of
Stem
Flange
DisThickness tance
tf
k
Area
Depth of
Tee
d
Thickness
tw
tw
2
Designation
in.2
in.
in.
in.
in.2
WT10.5×100.5
WT10.5×91
WT10.5×83
WT10.5×73.5
WT10.5×66
WT10.5×61
WT10.5×55.5
WT10.5×50.5
29.6
26.8
24.4
21.6
19.4
17.9
16.3
14.9
11.515
11.360
11.240
11.030
10.915
10.840
10.755
10.680
111⁄2
113⁄8
111⁄4
11
107⁄8
107⁄8
103⁄4
105⁄8
0.910
0.830
0.750
0.720
0.650
0.600
0.550
0.500
15⁄
16
13⁄
16
3⁄
4
3⁄
4
5⁄
8
5⁄
8
9⁄
16
1⁄
2
1⁄
2
7⁄
16
3⁄
8
3⁄
8
5⁄
16
5⁄
16
5⁄
16
1⁄
4
10.5
9.43
8.43
7.94
7.09
6.50
5.92
5.34
12.575
12.500
12.420
12.510
12.440
12.390
12.340
12.290
125⁄8
121⁄2
123⁄8
121⁄2
121⁄2
123⁄8
123⁄8
121⁄4
1.630
1.480
1.360
1.150
1.035
0.960
0.875
0.800
15⁄8
11⁄2
13⁄8
11⁄8
11⁄16
15⁄
16
7⁄
8
13⁄
16
23⁄8
21⁄4
21⁄8
17⁄8
113⁄16
111⁄16
15⁄8
19⁄16
WT10.5×46.5
WT10.5×41.5
WT10.5×36.5
WT10.5×34
WT10.5×31
13.7
12.2
10.7
10.0
9.13
10.810
10.715
10.620
10.565
10.495
103⁄4
103⁄4
105⁄8
105⁄8
101⁄2
0.580
0.515
0.455
0.430
0.400
9⁄
16
1⁄
2
7⁄
16
7⁄
16
3⁄
8
5⁄
16
1⁄
4
1⁄
4
1⁄
4
3⁄
16
6.27
5.52
4.83
4.54
4.20
8.420
8.355
8.295
8.270
8.240
83⁄8
83⁄8
81⁄4
81⁄4
81⁄4
0.930
0.835
0.740
0.685
0.615
15⁄
16
13⁄
16
3⁄
4
11⁄
16
5⁄
8
111⁄16
19⁄16
11⁄2
17⁄16
13⁄8
8.37 10.530
7.36 10.415
6.49 10.330
101⁄2
103⁄8
103⁄8
0.405
0.380
0.350
3⁄
8
3⁄
8
3⁄
8
3⁄
16
3⁄
16
3⁄
16
4.26
3.96
3.62
6.555
6.530
6.500
61⁄2
61⁄2
61⁄2
0.650
0.535
0.450
5⁄
8
9⁄
16
7⁄
16
13⁄8
15⁄16
13⁄16
WT10.5×28.5
WT10.5×25
WT10.5×22
Width
bf
in.
in.
in.
WT9×155.5
WT9×141.5
WT9×129
WT9×117
WT9×105.5
WT9×96
WT9×87.5
WT9×79
WT9×71.5
WT9×65
45.8
41.6
38.0
34.4
31.1
28.2
25.7
23.2
21.0
19.1
11.160
10.925
10.730
10.530
10.335
10.175
10.020
9.860
9.745
9.625
113⁄16
1015⁄16
103⁄4
101⁄2
105⁄16
103⁄16
10
97⁄8
93⁄4
95⁄8
1.520
1.400
1.280
1.160
1.060
0.960
0.890
0.810
0.730
0.670
11⁄2
13⁄8
11⁄4
13⁄16
11⁄16
1
7⁄
8
13⁄
16
3⁄
4
11⁄
16
3⁄
4
11⁄
16
5⁄
8
5⁄
8
9⁄
16
1⁄
2
7⁄
16
7⁄
16
3⁄
8
3⁄
8
17.0
15.3
13.7
12.2
11.0
9.77
8.92
7.99
7.11
6.45
12.005
11.890
11.770
11.650
11.555
11.455
11.375
11.300
11.220
11.160
12
117⁄8
113⁄4
115⁄8
111⁄2
111⁄2
113⁄8
111⁄4
111⁄4
111⁄8
2.740
2.500
2.300
2.110
1.910
1.750
1.590
1.440
1.320
1.200
23⁄4
21⁄2
25⁄16
21⁄8
115⁄16
13⁄4
19⁄16
17⁄16
15⁄16
13⁄16
37⁄16
33⁄16
3
23⁄4
9
2 ⁄16
27⁄16
21⁄4
21⁄8
2
17⁄8
WT9×59.5
WT9×53
WT9×48.5
WT9×43
WT9×38
17.5
15.6
14.3
12.7
11.2
9.485
9.365
9.295
9.195
9.105
91⁄2
93⁄8
91⁄4
91⁄4
91⁄8
0.655
0.590
0.535
0.480
0.425
5⁄
8
9⁄
16
9⁄
16
1⁄
2
7⁄
16
5⁄
16
5⁄
16
5⁄
16
1⁄
4
1⁄
4
6.21
5.53
4.97
4.41
3.87
11.265
11.200
11.145
11.090
11.035
111⁄4
111⁄4
111⁄8
111⁄8
11
1.060
0.940
0.870
0.770
0.680
11⁄16
15⁄
16
7⁄
8
3⁄
4
11⁄
16
13⁄4
15⁄8
19⁄16
17⁄16
13⁄8
WT9×35.5
WT9×32.5
WT9×30
WT9×27.5
WT9×25
10.4
9.55
8.82
8.10
7.33
9.235
9.175
9.120
9.055
8.995
91⁄4
91⁄8
91⁄8
9
9
0.495
0.450
0.415
0.390
0.355
1⁄
2
7⁄
16
7⁄
16
3⁄
8
3⁄
8
1⁄
1⁄
4
3⁄
16
3⁄
16
4.57
4.13
3.78
3.53
3.19
7.635
7.590
7.555
7.530
7.495
75⁄8
75⁄8
71⁄2
71⁄2
71⁄2
0.810
0.750
0.695
0.630
0.570
13⁄
16
3⁄
4
11⁄
16
5⁄
8
9⁄
16
11⁄2
17⁄16
13⁄8
15⁄16
11⁄4
WT9×23
WT9×20
WT9×17.5
6.77
5.88
5.15
9.030
8.950
8.850
9
9
87⁄8
0.360
0.315
0.300
3⁄
8
5⁄
16
5⁄
16
3⁄
16
3⁄
16
3⁄
16
3.25
2.82
2.66
6.060
6.015
6.000
6
6
6
0.605
0.525
0.425
5⁄
8
1⁄
2
7⁄
16
11⁄4
13⁄16
11⁄8
1⁄
4
4
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
STRUCTURAL TEES (WT, MT, ST)
1 - 75
bf
STRUCTURAL TEES
Cut from W shapes
Properties
tf
k
Y
yp , y
X
X
d
tw
Y
Nominal
Wt.
per
ft
lb
Axis X-X
h
tw
Qs*
Axis Y-Y
I
S
r
y
Z
yp
I
S
r
Z
in.4
in.3
in.
in.
in.3
in.
in.4
in.3
in.
in.3
36
50
43.1
38.6
35.0
30.0
26.7
24.6
22.2
20.2
3.02
3.00
2.98
2.95
2.93
2.92
2.90
2.89
66.6
59.6
53.9
46.3
41.1
37.8
34.1
30.9
—
—
—
—
—
—
—
0.990
—
—
—
—
—
0.993
0.917
0.826
17.4
15.3
13.3
12.2
10.9
—
—
0.908
0.853
0.784
0.968
0.856
0.730
0.664
0.583
7.42 0.793
6.09 0.733
5.09 0.638
0.592
0.533
0.460
100.5
91
83
73.5
66
61
55.5
50.5
10.3
11.2
12.4
13.0
14.4
15.6
17.1
18.8
285
253
226
204
181
166
150
135
31.9
28.5
25.5
23.7
21.1
19.3
17.5
15.8
3.10
3.07
3.04
3.08
3.06
3.04
3.03
3.01
2.57
2.48
2.39
2.39
2.33
2.28
2.23
2.18
58.6
52.1
46.3
42.4
37.6
34.3
31.0
27.9
1.18
1.07
0.984
0.864
0.780
0.724
0.662
0.605
271
241
217
188
166
152
137
124
46.5
41.5
36.5
34
31
16.2
18.2
20.6
21.8
23.5
144
127
110
103
93.8
17.9
15.7
13.8
12.9
11.9
3.25
3.22
3.21
3.20
3.21
2.74
2.66
2.60
2.59
2.58
31.8
28.0
24.4
22.9
21.1
0.812
0.728
0.647
0.606
0.554
46.4
40.7
35.3
32.4
28.7
11.0
9.75
8.51
7.83
6.97
1.84
1.83
1.81
1.80
1.77
28.5
25
22
23.2
24.7
26.8
90.4
80.3
71.1
11.8
10.7
9.68
3.29
3.30
3.31
2.85
2.93
2.98
21.2
20.8
17.6
0.638
0.771
1.06
15.3
12.5
10.3
4.67
3.82
3.18
1.35
1.30
1.26
155.5
141.5
129
117
105.5
96
87.5
79
71.5
65
5.3
5.7
6.3
6.9
7.5
8.3
9.0
9.9
11.0
11.9
383
337
298
260
229
202
181
160
142
127
46.5
41.5
37.0
32.6
29.0
25.8
23.4
20.8
18.5
16.7
2.89
2.85
2.80
2.75
2.72
2.68
2.66
2.63
2.60
2.58
2.93
2.80
2.68
2.55
2.44
2.34
2.26
2.18
2.09
2.02
90.6
80.1
71.0
62.4
55.0
48.5
43.6
38.5
34.0
30.5
1.91
1.75
1.61
1.48
1.34
1.23
1.13
1.02
0.938
0.856
59.5
53
48.5
43
38
12.3
13.6
15.0
16.7
18.9
119
104
93.8
82.4
71.8
15.9
14.1
12.7
11.2
9.83
2.60
2.59
2.56
2.55
2.54
2.03
1.97
1.91
1.86
1.80
28.7
25.2
22.6
19.9
17.3
0.778 126
0.695 110
0.640 100
0.570 87.6
0.505 76.2
35.5
32.5
30
27.5
25
16.2
17.8
19.3
20.6
22.6
78.2
70.7
64.7
59.5
53.5
11.2
10.1
9.29
8.63
7.79
2.74
2.72
2.71
2.71
2.70
2.26
2.20
2.16
2.16
2.12
20.0
18.0
16.5
15.3
13.8
0.683
0.629
0.583
0.538
0.489
30.1
27.4
25.0
22.5
20.0
23
20
17.5
22.3
25.5
26.8
52.1
44.8
40.1
7.77
6.73
6.21
2.77
2.76
2.79
2.33
2.29
2.39
13.9
12.0
12.0
0.558
0.489
0.450
11.3
9.55
7.67
398
352
314
279
246
220
196
174
156
139
Fy, ksi
66.2
59.2
53.4
47.9
42.7
38.4
34.4
30.7
27.7
24.9
2.95
2.91
2.88
2.85
2.82
2.79
2.76
2.74
2.72
2.70
104
92.5
83.2
74.5
66.2
59.4
53.1
47.4
42.7
38.3
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
22.5
19.7
18.0
15.8
13.8
2.69
2.66
2.65
2.63
2.61
34.6
30.2
27.6
24.2
21.1
—
—
—
—
0.990
—
—
—
0.937
0.826
7.89
7.22
6.63
5.97
5.35
1.70
1.69
1.69
1.67
1.65
12.3
—
11.2
—
10.3 0.964
9.27 0.913
8.29 0.823
0.963
0.877
0.796
0.735
0.625
3.72
3.17
2.56
1.29
1.27
1.22
5.85 0.831
4.97 0.690
4.03 0.638
0.635
0.496
0.460
*Where no value of Qs is shown, the Tee complies with LRFD Specification Section E2.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1 - 76
DIMENSIONS AND PROPERTIES
bf
tf
yp , y
STRUCTURAL TEES
Cut from W shapes
Dimensions
k
Y
X
X
d
tw
Y
Stem
Area
of
Stem
Flange
DisThickness tance
tf
k
Area
Depth of
Tee
d
Thickness
tw
tw
2
Designation
in.2
in.
in.
in.
in.2
WT8×50
WT8×44.5
WT8×38.5
WT8×33.5
14.7
13.1
11.3
9.84
8.485
8.375
8.260
8.165
81⁄2
83⁄8
81⁄4
81⁄8
0.585
0.525
0.455
0.395
9⁄
16
1⁄
2
7⁄
16
3⁄
8
5⁄
16
1⁄
4
1⁄
4
3⁄
16
4.96
4.40
3.76
3.23
10.425
10.365
10.295
10.235
103⁄8
103⁄8
101⁄4
101⁄4
0.985
0.875
0.760
0.665
1
7⁄
8
3⁄
4
11⁄
16
111⁄16
19⁄16
17⁄16
13⁄8
WT8×28.5
WT8×25
WT8×22.5
WT8×20
WT8×18
8.38
7.37
6.63
5.89
5.28
8.215
8.130
8.065
8.005
7.930
81⁄4
81⁄8
81⁄8
8
77⁄8
0.430
0.380
0.345
0.305
0.295
7⁄
16
3⁄
8
3⁄
8
5⁄
16
5⁄
16
1⁄
4
3⁄
16
3⁄
16
3⁄
16
3⁄
16
3.53
3.09
2.78
2.44
2.34
7.120
7.070
7.035
6.995
6.985
71⁄8
71⁄8
7
7
7
0.715
0.630
0.565
0.505
0.430
11⁄
16
5⁄
8
9⁄
16
1⁄
2
7⁄
16
13⁄8
15⁄16
11⁄4
13⁄16
11⁄8
WT8×15.5
WT8×13
4.56
3.84
7.940
7.845
8
77⁄8
0.275
0.250
1⁄
4
1⁄
4
1⁄
2.18
1.96
5.525
5.500
51⁄2
51⁄2
0.440
0.345
7⁄
16
3⁄
8
11⁄8
11⁄16
3.740
3.070
2.830
2.595
2.380
2.190
2.015
33⁄4
31⁄16
213⁄16
25⁄8
23⁄8
23⁄16
2
17⁄8
19⁄16
17⁄16
15⁄16
13⁄16
11⁄8
1
42.7
34.4
30.6
27.1
24.1
21.5
19.2
18.560
17.890
17.650
17.415
17.200
17.010
16.835
181⁄2
177⁄8
175⁄8
173⁄8
171⁄4
17
167⁄8
5.120
4.910
4.520
4.160
3.820
3.500
3.210
51⁄8
415⁄16
41⁄2
43⁄16
313⁄16
31⁄2
33⁄16
513⁄16
59⁄16
53⁄16
413⁄16
41⁄2
43⁄16
37⁄8
1.875
1.770
1.655
1.540
1.410
1.290
1.175
1.070
0.980
0.890
0.830
0.745
0.680
17⁄8
13⁄4
15⁄8
19⁄16
17⁄16
15⁄16
13⁄16
11⁄16
1
7⁄
8
13⁄
16
3⁄
4
11⁄
16
15⁄
17.5
16.2
14.8
13.5
12.1
10.8
9.62
8.58
7.70
6.89
6.32
5.58
5.03
16.695
16.590
16.475
16.360
16.230
16.110
15.995
15.890
15.800
15.710
15.650
15.565
15.500
163⁄4
165⁄8
161⁄2
163⁄8
161⁄4
161⁄8
16
157⁄8
153⁄4
153⁄4
155⁄8
155⁄8
151⁄2
3.035
2.845
2.660
2.470
2.260
2.070
1.890
1.720
1.560
1.440
1.310
1.190
1.090
31⁄16
27⁄8
211⁄16
21⁄2
21⁄4
21⁄16
17⁄8
13⁄4
19⁄16
17⁄16
15⁄16
13⁄16
11⁄16
311⁄16
31⁄2
35⁄16
31⁄8
215⁄16
23⁄4
29⁄16
23⁄8
21⁄4
21⁄8
2
17⁄8
13⁄4
WT7×404
WT8×365
WT8×332.5
WT8×302.5
WT8×275
WT8×250
WT8×227.5
119
107
97.8
88.9
80.9
73.5
66.9
WT7×213
WT8×199
WT8×185
WT8×171
WT8×155.5
WT8×141.5
WT8×128.5
WT8×116.5
WT8×105.5
WT8×96.5
WT8×88
WT8×79.5
WT8×72.5
62.6
58.5
54.4
50.3
45.7
41.6
37.8
34.2
31.0
28.4
25.9
23.4
21.3
11.420 117⁄16
11.210 111⁄4
10.820 107⁄8
10.460 101⁄2
10.120 101⁄8
9.800 93⁄4
9.510 91⁄2
9.335
9.145
8.960
8.770
8.560
8.370
8.190
8.020
7.860
7.740
7.610
7.490
7.390
93⁄8
91⁄8
9
83⁄4
81⁄2
83⁄8
81⁄4
8
77⁄8
73⁄4
75⁄8
71⁄2
73⁄8
1⁄
7⁄
13⁄
13⁄
3⁄
8
8
16
8
16
16
4
11⁄
16
5⁄
8
9⁄
16
1⁄
2
7⁄
16
7⁄
16
3⁄
8
3⁄
8
Width
bf
in.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
in.
in.
STRUCTURAL TEES (WT, MT, ST)
1 - 77
bf
STRUCTURAL TEES
Cut from W shapes
Properties
tf
k
Y
yp , y
X
X
d
tw
Y
Nominal
Wt.
per
ft
lb
Axis X-X
h
tw
Qs*
Axis Y-Y
I
S
r
y
Z
yp
I
S
r
Z
in.4
in.3
in.
in.
in.3
in.
in.4
in.3
in.
in.3
36
50
17.9
15.7
13.4
11.6
2.51
2.49
2.47
2.46
27.4
24.0
20.5
17.7
—
—
—
—
—
—
0.988
0.861
—
0.990
0.904
0.784
0.754
0.942
0.826
0.725
0.583
0.553
50
44.5
38.5
33.5
12.1
13.5
15.6
18.0
76.8
67.2
56.9
48.6
11.4
10.1
8.59
7.36
2.28
2.27
2.24
2.22
1.76
1.70
1.63
1.56
20.7
18.1
15.3
13.0
0.706
0.631
0.549
0.481
93.1
81.3
69.2
59.5
28.5
25
22.5
20
18
16.5
18.7
20.6
23.3
24.1
48.7
42.3
37.8
33.1
30.6
7.77
6.78
6.10
5.35
5.05
2.41
2.40
2.39
2.37
2.41
1.94
1.89
1.86
1.81
1.88
13.8
12.0
10.8
9.43
8.93
0.589
0.521
0.471
0.421
0.378
21.6
18.6
16.4
14.4
12.2
15.5
13
25.8
28.4
27.4
23.5
4.64
4.09
2.45
2.47
2.02
2.09
404
365
332.5
302.5
275
250
227.5
1.5
1.9
2.0
2.2
2.4
2.6
2.8
898
739
622
524
442
375
321
116
95.4
82.1
70.6
60.9
52.7
45.9
2.75
2.62
2.52
2.43
2.34
2.26
2.19
3.70
3.47
3.25
3.05
2.85
2.67
2.51
213
199
185
171
155.5
141.5
128.5
116.5
105.5
96.5
88
79.5
72.5
3.0
3.2
3.4
3.7
4.0
4.4
4.9
5.3
5.8
6.4
6.9
7.7
8.4
287
257
229
203
176
153
133
116
102
89.8
80.5
70.2
62.5
41.4
37.6
33.9
30.4
26.7
23.5
20.7
18.2
16.2
14.4
13.0
11.4
10.2
2.14
2.10
2.05
2.01
1.96
1.92
1.88
1.84
1.81
1.78
1.76
1.73
1.71
2.40
2.30
2.19
2.09
1.97
1.86
1.75
1.65
1.57
1.49
1.43
1.35
1.29
8.27 0.413
8.12 0.372
249
211
182
157
136
117
102
91.7
82.9
74.4
66.2
57.7
50.4
43.9
38.2
33.4
29.4
26.3
22.8
20.2
3.19
3.00
2.77
2.55
2.35
2.16
1.99
6.20
4.80
2760
2360
2080
1840
1630
1440
1280
1.88 1180
1.76 1090
1.65
994
1.54
903
1.41
807
1.29
722
1.18
645
1.08
576
0.980 513
0.903 466
0.827 419
0.751 374
0.688 338
Fy, ksi
6.06
5.26
4.67
4.12
3.50
1.60
1.59
1.57
1.57
1.52
9.43
8.16
7.23
6.37
5.42
2.24
1.74
1.17
1.12
3.52 0.668 0.479
2.74 0.563 0.406
297
264
236
211
189
169
152
4.82
4.69
4.62
4.55
4.49
4.43
4.38
463
408
365
326
292
261
234
—
—
—
—
—
—
—
—
—
—
—
—
—
—
141
131
121
110
99.4
89.7
80.7
72.5
65.0
59.3
53.5
48.1
43.7
4.34
4.31
4.27
4.24
4.20
4.17
4.13
4.10
4.07
4.05
4.02
4.00
3.98
217
201
185
169
152
137
123
110
99.0
90.2
81.4
73.0
66.3
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
*Where no value of Qs is shown, the Tee complies with LRFD Specification Section E2.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1 - 78
DIMENSIONS AND PROPERTIES
bf
tf
yp , y
STRUCTURAL TEES
Cut from W shapes
Dimensions
k
Y
X
X
d
tw
Y
Stem
Designation
Area
of
Stem
Flange
DisThickness tance
tf
k
Area
Depth of
Tee
d
Thickness
tw
tw
2
in.2
in.
in.
in.
in.2
5⁄
16
5⁄
16
1⁄
4
1⁄
4
1⁄
4
4.73
4.27
3.76
3.43
3.08
14.725
14.670
14.605
14.565
14.520
143⁄4
145⁄8
145⁄8
145⁄8
141⁄2
1.030
0.940
0.860
0.780
0.710
1
15⁄
16
7⁄
8
3⁄
4
11⁄
16
111⁄16
15⁄8
19⁄16
17⁄16
13⁄8
1⁄
10.130 101⁄8
10.070 101⁄8
10.035 10
9.995 10
0.855
0.785
0.720
0.645
7⁄
8
13⁄
16
3⁄
4
5⁄
8
15⁄8
19⁄16
11⁄2
17⁄16
Width
bf
in.
in.
in.
WT7×66
WT7×60
WT7×54.5
WT7×49.5
WT7×45
19.4
17.7
16.0
14.6
13.2
7.330
7.240
7.160
7.080
7.010
73⁄8
71⁄4
71⁄8
71⁄8
7
0.645
0.590
0.525
0.485
0.440
5⁄
8
9⁄
16
1⁄
2
1⁄
2
7⁄
16
WT7×41
WT7×37
WT7×34
WT7×30.5
12.0
10.9
9.99
8.96
7.155
7.085
7.020
6.945
71⁄8
71⁄8
7
7
0.510
0.450
0.415
0.375
1⁄
2
7⁄
16
7⁄
16
3⁄
8
1⁄
4
3⁄
16
3.65
3.19
2.91
2.60
WT7×26.5
WT7×24
WT7×21.5
7.81
7.07
6.31
6.960
6.895
6.830
7
67⁄8
67⁄8
0.370
0.340
0.305
3⁄
8
5⁄
16
5⁄
16
3⁄
16
3⁄
16
3⁄
16
2.58
2.34
2.08
8.060
8.030
7.995
8
8
8
0.660
0.595
0.530
11⁄
16
5⁄
8
1⁄
2
17⁄16
13⁄8
15⁄16
WT7×19
WT7×17
WT7×15
5.58
5.00
4.42
7.050
6.990
6.920
7
7
67⁄8
0.310
0.285
0.270
5⁄
16
5⁄
16
1⁄
4
3⁄
16
3⁄
16
1⁄
8
2.19
1.99
1.87
6.770
6.745
6.730
63⁄4
63⁄4
63⁄4
0.515
0.455
0.385
1⁄
2
7⁄
16
3⁄
8
11⁄16
1
15⁄
16
WT7×13
WT7×11
3.85
3.25
6.955
6.870
7
67⁄8
0.255
0.230
1⁄
4
1⁄
4
1⁄
1.77
1.58
5.025
5.000
5
5
0.420
0.335
7⁄
16
5⁄
16
15⁄
1⁄
1⁄
4
4
8
8
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
7⁄
16
8
STRUCTURAL TEES (WT, MT, ST)
1 - 79
bf
STRUCTURAL TEES
Cut from W shapes
Properties
tf
k
Y
yp , y
X
X
d
tw
Y
Nominal
Wt.
per
ft
Axis X-X
h
tw
S
I
4
r
3
y
Z
yp
3
S
I
4
in.
in.
in.
in.
in.
in.
66
60
54.5
49.5
45
8.8
9.7
10.9
11.8
13.0
57.8
51.7
45.3
40.9
36.4
9.57
8.61
7.56
6.88
6.16
1.73
1.71
1.68
1.67
1.66
1.29
1.24
1.17
1.14
1.09
18.6
16.5
14.4
12.9
11.5
0.658
0.602
0.549
0.500
0.456
41
37
34
30.5
11.2
12.7
13.7
15.2
41.2
36.0
32.6
28.9
7.14
6.25
5.69
5.07
1.85
1.82
1.81
1.80
1.39
1.32
1.29
1.25
13.2
11.5
10.4
9.16
0.594
0.541
0.498
0.448
74.2
66.9
60.7
53.7
26.5
24
21.5
15.4
16.8
18.7
27.6
24.9
21.9
4.94
4.48
3.98
1.88
1.87
1.86
1.38
1.35
1.31
8.87
8.00
7.05
0.484
0.440
0.395
28.8
25.7
22.6
19
17
15
19.8
21.5
22.7
23.3
20.9
19.0
4.22
3.83
3.55
2.04
2.04
2.07
1.54
1.53
1.58
7.45
6.74
6.25
0.412
0.371
0.329
13
11
24.1
26.7
17.3
14.8
3.31
2.91
2.12
2.14
1.72
1.76
5.89
5.20
0.383
0.325
lb
Qs*
Axis Y-Y
in.
r
3
Z
Fy, ksi
3
in.
in.
in.
36
50
37.2
33.7
30.6
27.6
25.0
3.76
3.74
3.73
3.71
3.70
56.6
51.2
46.4
41.8
37.8
—
—
—
—
—
—
—
—
—
—
14.6
13.3
12.1
10.7
2.48
2.48
2.46
2.45
22.4
20.3
18.5
16.4
—
—
—
—
—
—
—
0.973
7.16
6.40
5.65
1.92
1.91
1.89
11.0
9.82
8.66
—
—
0.947
0.958
0.882
0.775
13.3
11.7
9.79
3.94
3.45
2.91
1.55
1.53
1.49
6.07
5.32
4.49
0.934
0.857
0.810
0.760
0.669
0.610
4.45
3.50
1.77
1.40
1.08
1.04
2.77
2.19
0.737
0.621
0.537
0.447
274
247
223
201
181
*Where no value of Qs is shown, the Tee complies with LRFD Specification Section E2.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1 - 80
DIMENSIONS AND PROPERTIES
bf
tf
yp , y
STRUCTURAL TEES
Cut from W shapes
Dimensions
k
Y
X
X
d
tw
Y
Stem
Designation
Area
of
Stem
Area
Depth of
Tee
d
Thickness
tw
tw
2
in.2
in.
in.
in.
in.2
14.9
13.3
12.1
10.7
9.67
8.68
7.62
6.73
5.96
5.30
4.66
3.93
3.50
3.23
2.91
2.63
2.36
WT6×168
WT6×152.5
WT6×139.5
WT6×126
WT6×115
WT6×105
WT6×95
WT6×85
WT6×76
WT6×68
WT6×60
WT6×53
WT6×48
WT6×43.5
WT6×39.5
WT6×36
WT6×32.5
49.4
44.8
41.0
37.0
33.9
30.9
27.9
25.0
22.4
20.0
17.6
15.6
14.1
12.8
11.6
10.6
9.54
8.410
8.160
7.925
7.705
7.525
7.355
7.190
7.015
6.855
6.705
6.560
6.445
6.355
6.265
6.190
6.125
6.060
83⁄8
81⁄8
77⁄8
73⁄4
71⁄2
73⁄8
71⁄4
7
67⁄8
63⁄4
61⁄2
61⁄2
63⁄8
61⁄4
61⁄4
61⁄8
6
1.775
1.625
1.530
1.395
1.285
1.180
1.060
0.960
0.870
0.790
0.710
0.610
0.550
0.515
0.470
0.430
0.390
13⁄4
15⁄8
11⁄2
13⁄8
15⁄16
13⁄16
11⁄16
15⁄
16
7⁄
8
13⁄
16
11⁄
16
5⁄
8
9⁄
16
1⁄
2
1⁄
2
7⁄
16
3⁄
8
7⁄
8
13⁄
16
3⁄
4
11⁄
16
11⁄
16
5⁄
8
9⁄
16
1⁄
2
7⁄
16
7⁄
16
3⁄
8
5⁄
16
5⁄
16
1⁄
4
1⁄
4
1⁄
4
3⁄
16
WT6×29
WT6×26.5
8.52
7.78
6.095
6.030
61⁄8
6
0.360
0.345
3⁄
8
3⁄
8
3⁄
16
3⁄
16
WT6×25
WT6×22.5
WT6×20
7.34
6.61
5.89
6.095
6.030
5.970
61⁄8
6
6
0.370
0.335
0.295
3⁄
8
5⁄
16
5⁄
16
WT6×17.5
WT6×15
WT6×13
5.17
4.40
3.82
6.250
6.170
6.110
61⁄4
61⁄8
61⁄8
0.300
0.260
0.230
WT6×11
WT6×9.5
WT6×8
WT6×7
3.24
2.79
2.36
2.08
6.155
6.080
5.995
5.955
61⁄8
61⁄8
6
6
0.260
0.235
0.220
0.200
Flange
DisThickness tance
tf
k
Width
bf
in.
in.
in.
133⁄8
131⁄4
131⁄8
13
127⁄8
123⁄4
125⁄8
125⁄8
121⁄2
123⁄8
123⁄8
121⁄4
121⁄8
121⁄8
121⁄8
12
12
2.955
2.705
2.470
2.250
2.070
1.900
1.735
1.560
1.400
1.250
1.105
0.990
0.900
0.810
0.735
0.670
0.605
215⁄16
211⁄16
21⁄2
21⁄4
21⁄16
17⁄8
13⁄4
19⁄16
13⁄8
11⁄4
11⁄8
1
7⁄
8
13⁄
16
3⁄
4
11⁄
16
5⁄
8
311⁄16
37⁄16
33⁄16
215⁄16
23⁄4
25⁄8
27⁄16
21⁄4
21⁄8
115⁄16
113⁄16
111⁄16
15⁄8
11⁄2
17⁄16
13⁄8
15⁄16
2.19 10.010
2.08 9.995
10
10
0.640
0.575
5⁄
8
9⁄
16
13⁄8
11⁄4
3⁄
16
3⁄
16
3⁄
16
2.26
2.02
1.76
8.080
8.045
8.005
81⁄8
8
8
0.640
0.575
0.515
5⁄
8
9⁄
16
1⁄
2
13⁄8
11⁄4
11⁄4
5⁄
16
1⁄
4
1⁄
4
3⁄
16
1⁄
8
1⁄
8
1.88
1.60
1.41
6.560
6.520
6.490
61⁄2
61⁄2
61⁄2
0.520
0.440
0.380
1⁄
2
7⁄
16
3⁄
8
15⁄
16
7⁄
8
1⁄
4
1⁄
4
1⁄
4
3⁄
16
1⁄
8
1⁄
8
1⁄
8
1⁄
8
1.60
1.43
1.32
1.19
4.030
4.005
3.990
3.970
4
4
4
4
0.425
0.350
0.265
0.225
7⁄
16
3⁄
8
1⁄
4
1⁄
4
7⁄
8
13⁄
16
3⁄
4
11⁄
16
13.385
13.235
13.140
13.005
12.895
12.790
12.670
12.570
12.480
12.400
12.320
12.220
12.160
12.125
12.080
12.040
12.000
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1
STRUCTURAL TEES (WT, MT, ST)
1 - 81
bf
STRUCTURAL TEES
Cut from W shapes
Properties
tf
k
Y
yp , y
X
X
d
tw
Y
Nominal
Wt.
per
ft
Axis X-X
h
tw
S
I
4
r
3
y
Qs*
Axis Y-Y
Z
yp
3
S
I
4
r
3
Z
Fy, ksi
3
in.
in.
in.
in.
in.
in.
in.
in.
in.
in.
36
50
168
152.5
139.5
126
115
105
95
85
76
68
60
53
48
43.5
39.5
36
32.5
2.7
3.0
3.2
3.5
3.8
4.1
4.6
5.1
5.6
6.1
6.8
8.0
8.8
9.4
10.3
11.3
12.4
190
162
141
121
106
92.1
79.0
67.8
58.5
50.6
43.4
36.3
32.0
28.9
25.8
23.2
20.6
31.2
27.0
24.1
20.9
18.5
16.4
14.2
12.3
10.8
9.46
8.22
6.91
6.12
5.60
5.03
4.54
4.06
1.96
1.90
1.86
1.81
1.77
1.73
1.68
1.65
1.62
1.59
1.57
1.53
1.51
1.50
1.49
1.48
1.47
2.31
2.16
2.05
1.92
1.82
1.72
1.62
1.52
1.43
1.35
1.28
1.19
1.13
1.10
1.06
1.02
0.985
68.4
59.1
51.9
44.8
39.4
34.5
29.8
25.6
22.0
19.0
16.2
13.6
11.9
10.7
9.49
8.48
7.50
1.84
1.69
1.56
1.42
1.31
1.21
1.10
0.994
0.896
0.805
0.716
0.637
0.580
0.527
0.480
0.439
0.398
593
525
469
414
371
332
295
259
227
199
172
151
135
120
108
97.5
87.2
88.6
79.3
71.3
63.6
57.5
51.9
46.5
41.2
36.4
32.1
28.0
24.7
22.2
19.9
17.9
16.2
14.5
3.47
3.42
3.38
3.34
3.31
3.28
3.25
3.22
3.19
3.16
3.13
3.11
3.09
3.07
3.05
3.04
3.02
137
122
110
97.9
88.4
79.7
71.3
63.0
55.6
49.0
42.7
37.5
33.7
30.2
27.2
24.6
22.0
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
29
26.5
13.5
14.1
19.1
17.7
3.76
3.54
1.50
1.51
1.03
1.02
6.97 0.426
6.46 0.389
53.5
47.9
10.7
9.58
2.51
2.48
16.3
14.6
—
—
—
—
25
22.5
20
13.1
14.5
16.5
18.7
16.6
14.4
3.79
3.39
2.95
1.60
1.58
1.57
1.17
1.13
1.08
6.90 0.454
6.12 0.411
5.30 0.368
28.2
25.0
22.0
6.97
6.21
5.51
1.96
1.94
1.93
10.7
9.50
8.41
—
—
—
—
0.998
0.887
17.5
15
13
18.1
20.9
23.6
16.0
13.5
11.7
3.23
2.75
2.40
1.76
1.75
1.75
1.30
1.27
1.25
5.71 0.394
4.83 0.337
4.20 0.295
12.2
10.2
8.66
3.73
3.12
2.67
1.54
1.52
1.51
5.73
4.78
4.08
—
0.856
0.891 0.710
0.767 0.565
11
9.5
8
7
20.9
23.1
24.7
27.2
11.7
10.1
8.70
7.67
2.59
2.28
2.04
1.83
1.90
1.90
1.92
1.92
1.63
1.65
1.74
1.76
4.63
4.11
3.72
3.32
2.33
1.88
1.41
1.18
1.16
0.939
0.706
0.594
0.847
0.822
0.773
0.753
1.83
1.49
1.13
0.950
0.891
0.797
0.741
0.626
lb
0.402
0.348
0.639
0.760
*Where no value of Qs is shown, the Tee complies with LRFD Specification Section E2.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
0.710
0.596
0.541
0.450
1 - 82
DIMENSIONS AND PROPERTIES
bf
tf
yp , y
STRUCTURAL TEES
Cut from W shapes
Dimensions
k
Y
X
X
d
tw
Y
Stem
Designation
Area
of
Stem
Area
Depth of
Tee
d
Thickness
tw
tw
2
in.2
in.
in.
in.
in.2
Flange
DisThickness tance
tf
k
Width
bf
in.
in.
in.
WT5×56
WT5×50
WT5×44
WT5×38.5
WT5×34
WT5×30
WT5×27
WT5×24.5
16.5
14.7
12.9
11.3
9.99
8.82
7.91
7.21
5.680
5.550
5.420
5.300
5.200
5.110
5.045
4.990
55⁄8
51⁄2
53⁄8
51⁄4
51⁄4
51⁄8
5
5
0.755
0.680
0.605
0.530
0.470
0.420
0.370
0.340
3⁄
4
11⁄
16
5⁄
8
1⁄
2
1⁄
2
7⁄
16
3⁄
8
5⁄
16
3⁄
8
3⁄
8
5⁄
16
1⁄
4
1⁄
4
1⁄
4
3⁄
16
3⁄
16
4.29
3.77
3.28
2.81
2.44
2.15
1.87
1.70
10.415
10.340
10.265
10.190
10.130
10.080
10.030
10.000
103⁄8
103⁄8
101⁄4
101⁄4
101⁄8
101⁄8
10
10
1.250
1.120
0.990
0.870
0.770
0.680
0.615
0.560
11⁄4
11⁄8
1
7⁄
8
3⁄
8
11⁄
16
5⁄
8
9⁄
16
17⁄8
13⁄4
15⁄8
11⁄2
13⁄8
15⁄16
11⁄4
13⁄16
WT5×22.5
WT5×19.5
WT5×16.5
6.63
5.73
4.85
5.050
4.960
4.865
5
5
47⁄8
0.350
0.315
0.290
3⁄
8
5⁄
16
5⁄
16
3⁄
16
3⁄
16
3⁄
16
1.77
1.56
1.41
8.020
7.985
7.960
8
8
8
0.620
0.530
0.435
5⁄
8
1⁄
2
7⁄
16
11⁄4
11⁄8
11⁄16
WT5×15
WT5×13
WT5×11
4.42
3.81
3.24
5.235
5.165
5.085
51⁄4
51⁄8
51⁄8
0.300
0.260
0.240
5⁄
16
1⁄
4
1⁄
4
3⁄
16
1⁄
8
1⁄
8
1.57
1.34
1.22
5.810
5.770
5.750
53⁄4
53⁄4
53⁄4
0.510
0.440
0.360
1⁄
2
7⁄
16
3⁄
8
15⁄
16
7⁄
8
3⁄
4
WT5×9.5
WT5×8.5
WT5×7.5
WT5×6
2.81
2.50
2.21
1.77
5.120
5.055
4.995
4.935
51⁄8
5
5
47⁄8
0.250
0.240
0.230
0.190
1⁄
4
1⁄
4
1⁄
4
3⁄
16
1⁄
8
1⁄
8
1⁄
8
1⁄
8
1.28
1.21
1.15
0.938
4.020
4.010
4.000
3.960
4
4
4
4
0.395
0.330
0.270
0.210
3⁄
8
5⁄
16
1⁄
4
3⁄
16
13⁄
16
3⁄
4
11⁄
16
5⁄
8
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
STRUCTURAL TEES (WT, MT, ST)
1 - 83
bf
STRUCTURAL TEES
Cut from W shapes
Properties
tf
k
Y
yp , y
X
X
d
tw
Y
Nominal
Wt.
per
ft
lb
Axis X-X
h
tw
Qs*
Axis Y-Y
I
S
r
y
Z
yp
I
S
r
Z
in.4
in.3
in.
in.
in.3
in.
in.4
in.3
in.
in.3
0.791 118
0.711 103
0.631 89.3
0.555 76.8
0.493 66.8
0.438 58.1
0.395 51.7
0.361 46.7
22.6
20.0
17.4
15.1
13.2
11.5
10.3
9.34
2.68
2.65
2.63
2.60
2.59
2.57
2.56
2.54
6.65
5.64
4.60
Fy, ksi
36
50
34.6
30.5
26.5
22.9
20.0
17.5
15.7
14.2
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
2.01
1.98
1.94
10.1
8.59
7.01
—
—
—
—
—
—
56
50
44
38.5
34
30
27
24.5
5.2
5.8
6.5
7.4
8.4
9.4
10.6
11.6
28.6
24.5
20.8
17.4
14.9
12.9
11.1
10.0
6.40
5.56
4.77
4.04
3.49
3.04
2.64
2.39
1.32
1.29
1.27
1.24
1.22
1.21
1.19
1.18
1.21
1.13
1.06
0.990
0.932
0.884
0.836
0.807
13.4
11.4
9.65
8.06
6.85
5.87
5.05
4.52
22.5
19.5
16.5
11.2
12.5
13.6
10.2
8.84
7.71
2.47
2.16
1.93
1.24
1.24
1.26
0.907
0.876
0.869
4.65
3.99
3.48
0.413
0.359
0.305
15
13
11
14.8
17.0
18.4
9.28
7.86
6.88
2.24
1.91
1.72
1.45
1.44
1.46
1.10
1.06
1.07
4.01
3.39
3.02
0.380
0.330
0.282
8.35
7.05
5.71
2.87
2.44
1.99
1.37
1.36
1.33
4.42
3.75
3.05
—
—
0.999
—
0.902
0.836
17.7
18.4
19.2
23.3
6.68
6.06
5.45
4.35
1.74
1.62
1.50
1.22
1.54
1.56
1.57
1.57
1.28
1.32
1.37
1.36
3.10
2.90
3.03
2.50
0.349
0.311
0.306
0.323
2.15
1.78
1.45
1.09
1.07
0.888
0.723
0.551
0.874
0.844
0.810
0.785
1.68
—
1.40
—
1.15 0.977
0.872 0.793
0.872
0.841
0.811
0.592
9.5
8.5
7.5
6
26.7
22.5
18.3
*Where no value of Qs is shown, the Tee complies with LRFD Specification Section E2.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1 - 84
DIMENSIONS AND PROPERTIES
bf
tf
yp , y
STRUCTURAL TEES
Cut from W shapes
Dimensions
k
Y
X
X
d
tw
Y
Stem
Area
of
Stem
Flange
DisThickness tance
tf
k
Area
Depth of
Tee
d
Thickness
tw
tw
2
Designation
in.2
in.
in.
in.
in.2
WT4×33.5
WT4×29
WT4×24
WT4×20
WT4×17.5
WT4×15.5
9.84
8.55
7.05
5.87
5.14
4.56
4.500
4.375
4.250
4.125
4.060
4.000
41⁄2
43⁄8
41⁄4
41⁄8
4
4
0.570
0.510
0.400
0.360
0.310
0.285
9⁄
16
1⁄
2
3⁄
8
3⁄
8
5⁄
16
5⁄
16
5⁄
16
1⁄
4
3⁄
16
3⁄
16
3⁄
16
3⁄
16
2.56
2.23
1.70
1.48
1.26
1.14
8.280
8.220
8.110
8.070
8.020
7.995
81⁄4
81⁄4
81⁄8
81⁄8
8
8
0.935
0.810
0.685
0.560
0.495
0.435
15⁄
16
13⁄
16
11⁄
16
9⁄
16
1⁄
2
7⁄
16
17⁄16
15⁄16
13⁄16
11⁄16
1
15⁄
16
WT4×14
WT4×12
4.12
3.54
4.030
3.965
4
4
0.285
0.245
5⁄
16
1⁄
4
3⁄
16
1⁄
8
1.15
0.971
6.535
6.495
61⁄2
61⁄2
0.465
0.400
7⁄
16
3⁄
8
15⁄
16
7⁄
8
WT4×10.5
WT4×9
3.08
2.63
4.140
4.070
41⁄8
41⁄8
0.250
0.230
1⁄
4
1⁄
4
1⁄
8
1⁄
8
1.03
0.936
5.270
5.250
51⁄4
51⁄4
0.400
0.330
3⁄
8
5⁄
16
13⁄
16
3⁄
4
WT4×7.5
WT4×6.5
WT4×5
2.22
1.92
1.48
4.055
3.995
3.945
4
4
4
0.245
0.230
0.170
1⁄
4
1⁄
4
3⁄
16
1⁄
8
1⁄
8
1⁄
8
0.993
0.919
0.671
4.015
4.000
3.940
4
4
4
0.315
0.255
0.205
5⁄
16
1⁄
4
3⁄
16
3⁄
4
11⁄
16
5⁄
8
WT3×12.5
WT4×10
WT4×7.5
3.67
2.94
2.21
3.190
3.100
2.995
31⁄4
31⁄8
3
0.320
0.260
0.230
5⁄
16
1⁄
4
1⁄
4
3⁄
16
1⁄
8
1⁄
8
1.02
0.806
0.689
6.080
6.020
5.990
61⁄8
6
6
0.455
0.365
0.260
7⁄
16
3⁄
8
1⁄
4
13⁄
16
3⁄
4
5⁄
8
WT3×8
WT4×6
WT4×4.5
2.37
1.78
1.34
3.140
3.015
2.950
31⁄8
3
3
0.260
0.230
0.170
1⁄
4
1⁄
4
3⁄
16
1⁄
8
1⁄
8
1⁄
8
0.816
0.693
0.502
4.030
4.000
3.940
4
4
4
0.405
0.280
0.215
3⁄
8
1⁄
4
3⁄
16
3⁄
4
5⁄
8
9⁄
16
WT2.5×9.5
WT4.5×8
2.77
2.34
2.575
2.505
25⁄8
21⁄2
0.270
0.240
1⁄
4
1⁄
4
1⁄
8
1⁄
8
0.695
0.601
5.030
5.000
5
5
0.430
0.360
7⁄
16
3⁄
8
13⁄
16
3⁄
4
WT2×6.5
1.91
2.080
21⁄8
0.280
1⁄
4
1⁄
8
0.582
4.060
4
0.345
3⁄
8
11⁄
16
Width
bf
in.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
in.
in.
STRUCTURAL TEES (WT, MT, ST)
1 - 85
bf
STRUCTURAL TEES
Cut from W shapes
Properties
tf
k
Y
yp , y
X
X
d
tw
Y
Nominal
Wt.
per
ft
lb
Axis X-X
h
tw
Qs*
Axis Y-Y
I
S
r
y
Z
yp
I
S
r
Z
in.4
in.3
in.
in.
in.3
in.
in.4
in.3
in.
in.3
36
Fy, ksi
50
33.5
29
24
20
17.5
15.5
5.6
6.2
7.9
8.8
10.2
11.1
10.9
9.12
6.85
5.73
4.81
4.28
3.05
2.61
1.97
1.69
1.43
1.28
1.05
1.03
0.986
0.988
0.967
0.968
0.936
0.874
0.777
0.735
0.688
0.667
6.29
5.25
3.94
3.25
2.71
2.39
0.594
0.520
0.435
0.364
0.321
0.285
44.3
37.5
30.5
24.5
21.3
18.5
10.7
9.13
7.52
6.08
5.31
4.64
2.12
2.10
2.08
2.04
2.03
2.02
16.3
13.9
11.4
9.25
8.06
7.04
—
—
—
—
—
—
—
—
—
—
—
—
14
12
11.1
12.9
4.22
3.53
1.28
1.08
1.01
0.999
0.734
0.695
2.38
1.98
0.315
0.273
10.8
9.14
3.31
2.81
1.62
1.61
5.05
4.29
—
—
—
—
10.5
9
13.8
15.0
3.90
3.41
1.18
1.05
1.12
1.14
0.831
0.834
2.11
1.86
0.292
0.251
4.89
3.98
1.85
1.52
1.26
1.23
2.84
2.33
—
—
—
—
7.5
6.5
5
14.0
15.0
20.2
3.28
2.89
2.15
1.07
0.974
0.717
1.22
1.23
1.20
0.998
1.03
0.953
1.91
1.74
1.27
0.276
0.240
0.188
1.70
1.37
1.05
0.849 0.876
0.683 0.843
0.532 0.841
1.33
—
1.08
—
0.828 0.913
12.5
10
7.5
7.8
9.6
10.8
2.28
1.76
1.41
0.886
0.693
0.577
0.789
0.774
0.797
0.610
0.560
0.558
1.68
1.29
1.03
0.302
0.244
0.185
8.53
6.64
4.66
2.81
2.21
1.56
4.28
3.36
2.37
—
—
—
—
—
—
8
6
4.5
9.6
10.8
14.6
1.69 0.685
1.32 0.564
0.950 0.408
0.844
0.861
0.842
0.676
0.677
0.623
1.25
1.01
0.720
0.294
0.222
0.170
2.21
1.50
1.10
1.10 0.966
0.748 0.918
0.557 0.905
1.70
1.16
0.858
—
—
—
—
—
—
9.5
8
7.0
7.9
1.01 0.485
0.850 0.413
0.605
0.601
0.487
0.458
0.967
0.798
0.275
0.234
4.56
3.75
1.82
1.50
1.28
1.27
2.76
2.29
—
—
—
—
6.5
5.3
0.530 0.321
0.524
0.440
0.616
0.236
1.93
0.950 1.00
1.46
—
—
1.52
1.50
1.45
*Where no value of Qs is shown, the Tee complies with LRFD Specification Section E2.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
—
—
0.735
1 - 86
DIMENSIONS AND PROPERTIES
bf
tf
yp , y
STRUCTURAL TEES
Cut from M shapes
Dimensions
k
Y
X
X
d
tw
Y
Designation
Area
Depth
of
Tee
d
in.2
in.
Flange
Stem
Area
of
Thickness tw
2 Stem
tw
in.
in.
in.
1.73
1.59
6.000
5.990
6
6
0.177
0.160
3⁄
16
3⁄
16
1⁄
8
1⁄
16
1.06 3.065
0.958 3.065
31⁄8
31⁄8
0.225
0.210
1⁄
4
1⁄
4
9⁄
16
1⁄
2
1⁄
4
1⁄
4
—
1⁄
2
MT5×4.5
MT5×4
1.32
1.18
5.000
4.980
5
5
0.157
0.141
3⁄
16
3⁄
16
1⁄
8
1⁄
16
0.785 2.690
0.702 2.690
23⁄4
23⁄4
0.206
0.182
3⁄
16
3⁄
16
9⁄
16
7⁄
16
3⁄
16
3⁄
16
—
3⁄
8
MT4×3.25
0.958 4.000
4
0.135
1⁄
8
1⁄
16
0.540 2.281
21⁄4
0.189
3⁄
16
1⁄
2
3⁄
16
—
0.316
5⁄
16
3⁄
16
0.790 5.003
5
0.416
7⁄
16
7⁄
8
7⁄
16
7⁄
8
2.500 21⁄2
in.
in.2
MT6×5.9
MT6×5.4
MT2.5×9.45* 2.78
in.
Width
bf
in.
Max.
DisFlge.
FasThickness tance
Grip tener
tf
k
in.
*This shape has tapered flanges, while all other MT shapes have parallel flanges.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
STRUCTURAL TEES (WT, MT, ST)
1 - 87
bf
STRUCTURAL TEES
Cut from M shapes
Properties
tf
k
Y
yp , y
X
X
d
tw
Y
Nominal
Wt.
per
ft
lb
Axis X-X
h
tw
Qs*
Axis Y-Y
I
S
r
y
Z
yp
I
S
r
Z
in.4
in.3
in.
in.
in.3
in.
in.4
in.3
in.
in.3
36
Fy, ksi
50
5.9
5.4
31.3
31.8
6.60
6.03
1.60
1.46
1.95
1.95
1.89
1.85
2.89
2.63
1.09
1.01
0.490
0.453
0.320
0.295
0.532
0.533
0.577
0.525
0.483
0.397
0.348
0.286
4.5
4
29.2
29.7
3.46
3.09
0.997
0.893
1.62
1.62
1.53
1.52
1.81
1.62
0.778
0.778
0.305
0.269
0.227
0.200
0.480
0.477
0.405
0.333
0.549
0.446
0.396
0.321
3.25
26.9
1.57
0.556
1.28
1.17
1.01
0.446
0.172
0.150
0.423
0.265
0.634
0.457
9.45
5.6
1.05
0.527
0.615
0.511
1.03
0.278
3.93
1.57
1.19
2.66
—
—
*Where no value of Qs is shown, the Tee complies with LRFD Specification Section E2.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1 - 88
DIMENSIONS AND PROPERTIES
bf
tf
y, yp
STRUCTURAL TEES
Cut from S shapes
Dimensions
grip
Y
X
X
d
tw
Y
Designation
Area
Depth
of
Tee
d
in.2
in.
Flange
Stem
Area
of
Thickness tw
2 Stem
tw
Width
bf
Max.
DisFlge.
FasThickness tance
Grip tener
tf
k
in.
in.2
in.
in.
in.
7
13⁄
16 ⁄16
5⁄
5⁄
8
16
9.80
7.60
8.050 8
7.870 77⁄8
1.090
1.090
11⁄16
11⁄16
2
2
11⁄8
11⁄8
1
1
3⁄
8
5⁄
16
1⁄
4
8.94
7.50
6.00
7.245 71⁄4
7.125 71⁄8
7.000 7
0.870
0.870
0.870
7⁄
8
7⁄
8
7⁄
8
13⁄4
13⁄4
13⁄4
7⁄
8
7⁄
8
7⁄
8
1
1
1
7
13⁄
16 ⁄16
3⁄
11⁄
16
8
8.12
6.70
7.200 71⁄4
7.060 7
0.920
0.920
15⁄
16
15⁄
16
13⁄4
13⁄4
15⁄
16
15⁄
16
1
1
in.
in.
in.
in.
ST12×60.5
ST12×53
17.8
15.6
12.250 121⁄4
12.250 121⁄4
0.800
0.620
ST12×50
ST12×45
ST12×40
14.7
13.2
11.7
12.000
12.000
12.000
0.745
0.625
0.500
ST10×48
ST10×43
14.1
12.7
10.150 101⁄8
10.150 101⁄8
0.800
0.660
ST10×37.5
ST10×33
11.0
9.70
10.000
10.000
10
10
0.635
0.505
5⁄
8
1⁄
2
5⁄
16
1⁄
4
6.35
5.05
6.385 63⁄8
6.225 61⁄4
0.795
0.795
13⁄
16
13⁄
16
15⁄8
15⁄8
13⁄
16
13⁄
16
7⁄
8
7⁄
8
ST9×35
ST9×27.35
10.3
8.04
9.000
9.000
9
9
0.711
0.461
11⁄
16
7⁄
16
3⁄
8
1⁄
4
6.40
4.15
6.251 61⁄4
6.001 6
0.691
0.691
11⁄
16
11⁄
16
11⁄2
11⁄2
11⁄
16
11⁄
16
7⁄
8
7⁄
8
12
12
12
3⁄
4
5⁄
8
1⁄
2
ST7.5×25
ST7.5×21.45
7.35
6.31
7.500 71⁄2
7.500 71⁄2
0.550
0.411
9⁄
16
5⁄
16
1⁄
4
4.13
3.08
5.640 55⁄8
5.501 51⁄2
0.622
0.622
5⁄
8
5⁄
8
13⁄8
13⁄8
9⁄
16
9⁄
16
3⁄
4
3⁄
4
ST6×25
ST6×20.4
7.35
6.00
6.000
6.000
6
6
0.687
0.462
11⁄
16
7⁄
16
3⁄
8
1⁄
4
4.12
2.77
5.477 51⁄2
5.252 51⁄4
0.659
0.659
11⁄
16
11⁄
16
17⁄16
17⁄16
11⁄
16
5⁄
8
3⁄
4
3⁄
4
ST6×17.5
ST6×15.9
5.15
4.68
6.000
6.000
6
6
0.428
0.350
7⁄
1⁄
4
3⁄
16
2.57
2.10
5.078 51⁄8
5.000 5
0.545
0.544
9⁄
16
9⁄
16
13⁄16
13⁄16
1⁄
2
1⁄
2
3⁄
4
3⁄
4
ST5×17.5
ST5×12.7
5.15
3.73
5.000
5.000
5
5
0.594
0.311
16
5⁄
16
3⁄
16
2.97
1.56
4.944 5
4.661 45⁄8
0.491
0.491
1⁄
2
1⁄
2
11⁄8
11⁄8
1⁄
2
1⁄
2
3⁄
4
3⁄
4
ST4×11.5
ST4×9.2
3.38
2.70
4.000
4.000
4
4
0.441
0.271
7⁄
16
1⁄
4
1⁄
4
1⁄
8
1.76
1.08
4.171 41⁄8
4.001 4
0.425
0.425
7⁄
16
7⁄
16
1
1
7⁄
16
7⁄
16
3⁄
4
3⁄
4
ST3×8.625
ST3×6.25
2.53
1.83
3.000
3.000
3
3
0.465
0.232
7⁄
16
1⁄
4
1⁄
4
1⁄
8
1.40
0.70
3.565 35⁄8
3.332 33⁄8
0.359
0.359
3⁄
8
3⁄
8
7⁄
8
7⁄
8
3⁄
8
3⁄
8
5⁄
8
—
ST2.5×5
1.47
2.500 21⁄2
0.214
3⁄
16
1⁄
8
0.535 3.004
0.326
5⁄
16
13⁄
16
5⁄
16
—
ST2×4.75
ST2×3.85
1.40
1.13
2.000
2.000
0.326
0.193
5⁄
16
3⁄
16
1⁄
8
0.652 2.796 23⁄4
0.386 2.663 25⁄8
0.293
0.293
5⁄
16
5⁄
16
3⁄
4
3⁄
4
5⁄
16
5⁄
16
—
—
ST1.5×3.75
ST1.5×2.85
1.10
0.835
1.500 11⁄2
1.500 11⁄2
3⁄
16
1⁄
8
0.523 2.509 21⁄2
0.255 2.330 23⁄8
0.260
0.260
1⁄
4
1⁄
4
11⁄
16
11⁄
16
1⁄
4
1⁄
4
—
—
2
2
0.349
0.170
7⁄
16
16
3⁄
8
5⁄
8
5⁄
3⁄
16
3⁄
8
3⁄
16
3
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
STRUCTURAL TEES (WT, MT, ST)
1 - 89
bf
STRUCTURAL TEES
Cut from S shapes
Properties
tf
grip
Y
y, yp
X
X
d
tw
Y
Nominal
Wt.
per
ft
lb
Axis X-X
h
tw
Qs*
Axis Y-Y
I
S
r
y
Z
yp
I
S
r
Z
in.4
in.3
in.
in.
in.3
in.
in.4
in.3
in.
in.3
60.5
53
13.2
17
259
216
30.1
24.1
3.82
3.72
3.63
3.28
54.5
43.3
1.28
1.03
41.7
38.5
10.4
9.80
1.53
1.57
18.1
16.6
50
45
40
14.1
16.8
21.1
215
190
162
26.3
22.6
18.7
3.83
3.79
3.72
3.84
3.60
3.29
47.5
41.1
33.6
2.20 23.8
1.48 22.5
0.922 21.1
6.58
6.31
6.04
1.27
1.30
1.34
12.0
11.2
10.4
48
43
10.8
13.1
143
125
20.3
17.2
3.18
3.14
3.13
2.91
36.9
31.1
1.40 25.1
0.985 23.4
6.97
6.63
1.33
1.36
12.5
11.6
37.5
33
13.6
17
109
93.1
15.8
12.9
3.15
3.10
3.07
2.81
28.6
23.4
1.40 14.9
0.855 13.8
4.66
4.43
1.16
1.19
35
27.35
10.9
16.8
84.7
62.4
14.0
9.61
2.87
2.79
2.94
2.50
25.1
17.3
1.81 12.1
0.747 10.4
3.86
3.47
25
21.45
11.6
15.5
40.6
33.0
7.73
6.00
2.35
2.29
2.25
2.01
14.0
10.8
0.872
0.613
7.85
7.19
25
20.4
7
10.3
25.2
18.9
6.05
4.28
1.85
1.78
1.84
1.58
11.0
7.71
0.770
0.581
17.5
15.9
11.7
14.3
17.2
14.9
3.95
3.31
1.83
1.78
1.64
1.51
7.12
5.94
17.5
12.7
6.9
13.2
12.5
7.83
3.63
2.06
1.56
1.45
1.56
1.20
11.5
9.2
7.3
11.8
5.03
3.51
1.77
1.15
1.22
1.14
5
10
8.63
6.25
Fy, ksi
36
50
—
—
—
0.907
—
—
—
0.937
0.878 0.695
—
—
—
—
8.37
7.70
—
—
—
0.907
1.08
1.14
7.21
6.07
—
—
—
0.922
2.78
2.61
1.03
1.07
5.01
4.54
—
—
—
0.988
7.85
6.78
2.87
2.58
1.03
1.06
5.19
4.45
—
—
—
—
0.548
0.485
4.94
4.68
1.95
1.87
0.980
1.00
3.41
3.22
—
—
—
—
6.58
3.70
0.702
0.408
4.18
3.39
1.69
1.46
0.901
0.954
3.11
2.49
—
—
—
—
1.15
0.941
3.19
2.07
0.447
0.341
2.15
1.86
1.03 0.798
0.932 0.831
1.84
1.59
—
—
—
—
2.13
1.27
1.02 0.917 0.914
0.552 0.833 0.691
1.85
1.01
0.401
0.275
1.15
0.911
0.648 0.675
0.547 0.705
1.18
0.929
—
—
—
—
5
8.7
0.681
0.353 0.681 0.569
0.650 0.243
0.608
0.405 0.643
0.685
—
—
4.75
3.85
4.3
7.3
0.470
0.316
0.325 0.580 0.553
0.203 0.528 0.448
0.592 0.255
0.381 0.209
0.451
0.382
0.323 0.569
0.287 0.581
0.566
0.483
—
—
—
—
3.75
2.85
2.8
5.7
0.204
0.118
0.191 0.430 0.432
0.101 0.376 0.329
0.351 0.223
0.196 0.175
0.293
0.227
0.234 0.516
0.195 0.522
0.412
0.327
—
—
—
—
*Where no value of Qs is shown, the Tee complies with LRFD Specification Section E2.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1 - 90
DIMENSIONS AND PROPERTIES
DOUBLE ANGLES
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
DOUBLE ANGLES
1 - 91
DOUBLE ANGLES
Properties of double angles in contact and separated are listed in the following tables.
Each table shows properties of double angles in contact, and the radius of gyration about
the Y-Y axis when the legs of the angles are separated. Values of Qs are given for Fy = 36
ksi and Fy = 50 ksi for those angles exceeding the width-thickness ratio λr of LRFD
Specification Section B5. Since the cross section is comprised entirely of unstiffened
elements, Qa = 1.0 and Q = Qs, for all _angle sections. The Flexural-Torsional Properties
Table lists the dimensional values (J, ro, and H) needed for checking flexural-torsional
buckling.
Use of Table
The table may be used as follows for checking the limit states of (1) flexural buckling
and (2) flexural-torsional buckling. The lower of the two limit states must be used for
design. See also Part 3 of this LRFD Manual.
(1) Flexural Buckling
Where no value of Qs is shown, the design compressive strength for this limit state is
given by LRFD Specification Section E2. Where a value of Qs is shown, the strength
must be reduced in accordance with Appendix B5 of the LRFD Specification.
(2) Flexural-Torsional Buckling
The design compressive strength for this limit state_ is given by LRFD Specification
Sections E3 and E4. This involves calculations with J, ro, and H. These torsional constants
can be obtained by summing the respective values for single angles listed in the
Flexural-Torsional Properties Tables in Part 1 of this Manual.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1 - 92
DIMENSIONS AND PROPERTIES
Y
X
X
DOUBLE ANGLES
Two equal leg angles
Properties of sections
y, yp
s
Y
Wt.
Area of
per ft
2 Angles 2 Angles
Designation
2
Axis X-X
S
I
4
in.
r
3
y
Z
yp
3
lb
in.
in.
in.
in.
in.
in.
L8×8×11⁄8
L8×8×1
L8×8×17⁄8
L8×8×13⁄4
L8×8×15⁄8
L8×8×11⁄2
114
102
90.0
77.8
65.4
52.8
33.5
30.0
26.5
22.9
19.2
15.5
195
177
159
139
118
97.3
35.1
31.6
28.0
24.4
20.6
16.7
2.42
2.44
2.45
2.47
2.49
2.50
2.41
2.37
2.32
2.28
2.23
2.19
63.2
56.9
50.5
43.9
37.1
30.1
1.05
0.938
0.827
0.715
0.601
0.484
L6×6×1
L8×8×17⁄8
L8×8×13⁄4
L8×8×15⁄8
L8×8×11⁄2
L8×8×13⁄8
74.8
66.2
57.4
48.4
39.2
29.8
22.0
19.5
16.9
14.2
11.5
8.72
70.9
63.8
56.3
48.3
39.8
30.8
17.1
15.3
13.3
11.3
9.23
7.06
1.80
1.81
1.83
1.84
1.86
1.88
1.86
1.82
1.78
1.73
1.68
1.64
30.9
27.5
24.0
20.4
16.6
12.7
0.917
0.811
0.703
0.592
0.479
0.363
L5×5×7⁄8
L5×5×3⁄4
L5×5×1⁄2
L5×5×3⁄8
L5×5×5⁄16
54.4
47.2
32.4
24.6
20.6
16.0
13.9
9.50
7.22
6.05
35.5
31.5
22.5
17.5
14.8
10.3
9.06
6.31
4.84
4.08
1.49
1.51
1.54
1.56
1.57
1.57
1.52
1.43
1.39
1.37
18.7
16.3
11.4
8.72
7.35
0.798
0.694
0.475
0.361
0.303
L4×4×3⁄4
L5×5×5⁄8
L5×5×1⁄2
L5×5×3⁄8
L5×5×5⁄16
L5×5×1⁄4
37.0
31.4
25.6
19.6
16.4
13.2
10.9
9.22
7.50
5.72
4.80
3.88
15.3
13.3
11.1
8.72
7.43
6.08
5.62
4.80
3.95
3.05
2.58
2.09
1.19
1.20
1.22
1.23
1.24
1.25
1.27
1.23
1.18
1.14
1.12
1.09
10.1
8.66
7.12
5.49
4.64
3.77
0.680
0.576
0.469
0.357
0.300
0.242
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
DOUBLE ANGLES
1 - 93
DOUBLE ANGLES
Two equal leg angles
Properties of sections
Y
X
X
y, yp
s
Y
Qs*
Axis Y-Y
Radii of Gyration
Back to Back of
Angles, in.
Angles in Contact
Angles Separated
0
3⁄
8
3⁄
4
Fy =
36 ksi
Fy =
50 ksi
Fy =
36 ksi
Fy =
50 ksi
L8×8×11⁄8
L8×8×1
L8×8×17⁄8
L8×8×13⁄4
L8×8×15⁄8
L8×8×11⁄2
3.42
3.40
3.38
3.36
3.34
3.32
3.55
3.53
3.51
3.49
3.47
3.45
3.69
3.67
3.64
3.62
3.60
3.58
—
—
—
—
—
0.995
—
—
—
—
—
0.921
—
—
—
—
0.997
0.911
—
—
—
—
0.935
0.834
L6×6×1
L8×8×17⁄8
L8×8×13⁄4
L8×8×15⁄8
L8×8×11⁄2
L8×8×13⁄8
2.59
2.57
2.55
2.53
2.51
2.49
2.73
2.70
2.68
2.66
2.64
2.62
2.87
2.85
2.82
2.80
2.78
2.75
—
—
—
—
—
0.995
—
—
—
—
—
0.921
—
—
—
—
—
0.911
—
—
—
—
0.961
0.834
L5×5×7⁄8
L5×5×3⁄4
L5×5×1⁄2
L5×5×3⁄8
L5×5×5⁄16
2.16
2.14
2.10
2.09
2.08
2.30
2.28
2.24
2.22
2.21
2.45
2.42
2.38
2.35
2.34
—
—
—
—
0.995
—
—
—
—
0.921
—
—
—
0.982
0.911
—
—
—
0.919
0.834
L4×4×3⁄4
L5×5×5⁄8
L5×5×1⁄2
L5×5×3⁄8
L5×5×5⁄16
L5×5×1⁄4
1.74
1.72
1.70
1.68
1.67
1.66
1.88
1.86
1.83
1.81
1.80
1.79
2.03
2.00
1.98
1.95
1.94
1.93
—
—
—
—
—
0.995
—
—
—
—
—
0.921
—
—
—
—
0.997
0.911
—
—
—
—
0.935
0.834
Designation
*Where no value ofQs is shown, the angles comply with LRFD Specification Section E2.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1 - 94
DIMENSIONS AND PROPERTIES
DOUBLE ANGLES
Two equal leg angles
Properties of sections
Y
X
X
y, yp
s
Y
Wt.
Area of
per ft
2 Angles 2 Angles
2
Axis X-X
S
I
4
r
3
y
Z
yp
3
Designation
lb
in.
in.
in.
in.
in.
in.
L31⁄2×31⁄2×3⁄8
L31⁄2×31⁄2×5⁄16
L31⁄2×31⁄2×1⁄4
17.0
14.4
11.6
4.97
4.18
3.38
5.73
4.90
4.02
2.30
1.95
1.59
1.07
1.08
1.09
1.01
0.990
0.968
4.15
3.52
2.86
0.355
0.299
0.241
L3×3×1⁄2
L3×3×3⁄8
L3×3×5⁄16
L3×3×1⁄4
L3×3×3⁄16
18.8
14.4
12.2
9.80
7.42
5.50
4.22
3.55
2.88
2.18
4.43
3.52
3.02
2.49
1.92
2.14
1.67
1.41
1.15
0.882
0.898
0.913
0.922
0.930
0.939
0.932
0.888
0.865
0.842
0.820
3.87
3.00
2.55
2.08
1.59
0.458
0.352
0.296
0.240
0.182
L21⁄2×21⁄2×3⁄8
L31⁄2×31⁄2×5⁄16
L31⁄2×31⁄2×1⁄4
L31⁄2×31⁄2×3⁄16
11.8
10.0
8.20
6.14
3.47
2.93
2.38
1.80
1.97
1.70
1.41
1.09
1.13
0.964
0.789
0.606
0.753
0.761
0.769
0.778
0.762
0.740
0.717
0.694
2.04
1.74
1.42
1.09
0.347
0.293
0.238
0.180
9.40
7.84
6.38
4.88
3.30
2.72
2.30
1.88
1.43
0.960
0.958
0.832
0.695
0.545
0.380
0.702
0.681
0.494
0.381
0.261
0.594
0.601
0.609
0.617
0.626
0.636
0.614
0.592
0.569
0.546
1.27
1.08
0.890
0.686
0.471
0.340
0.288
0.234
0.179
0.121
L2×2×3⁄8
L3×3×5⁄16
L3×3×1⁄4
L3×3×3⁄16
L3×3×1⁄8
in.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
DOUBLE ANGLES
1 - 95
DOUBLE ANGLES
Two equal leg angles
Properties of sections
Y
X
X
y, yp
s
Y
Qs*
Axis Y-Y
Radii of Gyration
Angles in Contact
Angles Separated
3⁄
4
Fy =
36 ksi
Fy =
50 ksi
Fy =
36 ksi
Fy =
50 ksi
Back to Back of
Angles, in.
3⁄
8
Designation
0
L31⁄2×31⁄2×3⁄8
L31⁄2×31⁄2×5⁄16
L31⁄2×31⁄2×1⁄4
1.48
1.47
1.46
1.61
1.60
1.59
1.75
1.74
1.73
—
—
—
—
—
0.982
—
—
0.965
—
0.986
0.897
L3×3×1⁄2
L3×3×3⁄8
L3×3×5⁄16
L3×3×1⁄4
L3×3×3⁄16
1.29
1.27
1.26
1.26
1.25
1.43
1.41
1.40
1.39
1.38
1.59
1.56
1.55
1.53
1.52
—
—
—
—
0.995
—
—
—
—
0.921
—
—
—
—
0.911
—
—
—
0.961
0.834
L21⁄2×21⁄2×3⁄8
L21⁄2×21⁄2×5⁄16
L21⁄2×21⁄2×1⁄4
L21⁄2×21⁄2×3⁄16
1.07
1.06
1.05
1.04
1.21
1.20
1.19
1.18
1.36
1.35
1.34
1.32
—
—
—
—
—
—
—
—
—
—
—
0.982
—
—
—
0.919
L2×2×3⁄8
L2×2×5⁄16
L2×2×1⁄4
L2×2×3⁄16
L2×2×1⁄8
0.870
0.859
0.849
0.840
0.831
1.01
1.00
0.989
0.977
0.965
1.17
1.16
1.14
1.13
1.11
—
—
—
—
0.995
—
—
—
—
0.921
—
—
—
—
0.911
—
—
—
—
0.834
*Where no value ofQs is shown, the angles comply with LRFD Specification Section E2.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1 - 96
DIMENSIONS AND PROPERTIES
DOUBLE ANGLES
Two unequal leg angles
Properties of sections
Y
X
X
y, yp
s
Long legs back to back
Y
Wt.
Area of
per ft
2 Angles 2 Angles
Designation
2
Axis X-X
S
I
4
in.
r
3
y
Z
yp
3
lb
in.
in.
in.
in.
in.
in.
L8×6×1
L8×6×13⁄4
L8×6×11⁄2
88.4
67.6
46.0
26.0
19.9
13.5
161
126
88.6
30.2
23.3
16.0
2.49
2.53
2.56
2.65
2.56
2.47
54.5
42.2
29.1
1.50
1.38
1.25
L8×4×1
L8×6×13⁄4
L8×6×11⁄2
74.8
57.4
39.2
22.0
16.9
11.5
139
109
77.0
28.1
21.8
15.0
2.52
2.55
2.59
3.05
2.95
2.86
48.5
37.7
26.1
2.50
2.38
2.25
L7×4×3⁄4
L7×4×1⁄2
L7×4×3⁄8
52.4
35.8
27.2
15.4
10.5
7.97
75.6
53.3
41.1
16.8
11.6
8.88
2.22
2.25
2.27
2.51
2.42
2.37
29.6
20.6
15.7
1.88
1.75
1.69
L6×4×3⁄4
L7×4×5⁄8
L7×4×1⁄2
L7×4×3⁄8
47.2
40.0
32.4
24.6
13.9
11.7
9.50
7.22
49.0
42.1
34.8
26.9
12.5
10.6
8.67
6.64
1.88
1.90
1.91
1.93
2.08
2.03
1.99
1.94
22.3
19.0
15.6
11.9
1.38
1.31
1.25
1.19
L6×31⁄2×3⁄8
L6×31⁄2×5⁄16
23.4
19.6
6.84
5.74
25.7
21.8
6.49
5.47
1.94
1.95
2.04
2.01
11.5
9.70
1.44
1.41
L5×31⁄2×3⁄4
L6×31⁄2×1⁄2
L6×31⁄2×3⁄8
L6×31⁄2×5⁄16
39.6
27.2
20.8
17.4
11.6
8.00
6.09
5.12
27.8
20.0
15.6
13.2
8.55
5.97
4.59
3.87
1.55
1.58
1.60
1.61
1.75
1.66
1.61
1.59
15.3
10.8
8.28
6.99
1.13
1.00
0.938
0.906
L5×3×1⁄2
L7×4×3⁄8
L7×4×5⁄16
L7×4×1⁄4
25.6
19.6
16.4
13.2
7.50
5.72
4.80
3.88
18.9
14.7
12.5
10.2
5.82
4.47
3.77
3.06
1.59
1.61
1.61
1.62
1.75
1.70
1.68
1.66
10.3
7.95
6.71
5.45
1.25
1.19
1.16
1.13
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
DOUBLE ANGLES
1 - 97
DOUBLE ANGLES
Two unequal leg angles
Properties of sections
Y
X
X
y, yp
s
Long legs back to back
Y
Qs*
Axis Y-Y
Radii of Gyration
Back to Back of
Angles, in.
Angles in Contact
Angles Separated
0
3⁄
8
3⁄
4
Fy =
36 ksi
Fy =
50 ksi
Fy =
36 ksi
Fy =
50 ksi
L8×6×1
L8×6×13⁄4
L8×6×11⁄2
2.39
2.35
2.32
2.52
2.48
2.44
2.66
2.62
2.57
—
—
—
—
—
—
—
—
0.911
—
—
0.834
L8×4×1
L8×4×13⁄4
L8×4×11⁄2
1.47
1.42
1.38
1.61
1.55
1.51
1.75
1.69
1.64
—
—
—
—
—
—
—
—
0.911
—
—
0.834
L7×4×3⁄4
L7×4×1⁄2
L7×4×3⁄8
1.48
1.44
1.43
1.62
1.57
1.55
1.76
1.71
1.68
—
—
—
—
—
—
—
0.965
0.839
—
0.897
0.750
L6×4×3⁄4
L7×4×5⁄8
L7×4×1⁄2
L7×4×3⁄8
1.55
1.53
1.51
1.5
1.69
1.67
1.64
1.62
1.83
1.81
1.78
1.76
—
—
—
—
—
—
—
—
—
—
—
0.911
—
—
0.961
0.834
L6×31⁄2×3⁄8
L6×31⁄2×5⁄16
1.26
1.26
1.39
1.38
1.53
1.51
—
—
—
—
0.911
0.825
0.834
0.733
L5×31⁄2×3⁄4
L6×31⁄2×1⁄2
L6×31⁄2×3⁄8
L6×31⁄2×5⁄16
1.40
1.35
1.34
1.33
1.53
1.49
1.46
1.45
1.68
1.63
1.60
1.59
—
—
—
—
—
—
—
—
—
—
0.982
0.911
—
—
0.919
0.834
L5×3×1⁄2
L7×4×3⁄8
L7×4×5⁄16
L7×4×1⁄4
1.12
1.10
1.09
1.08
1.25
1.23
1.22
1.21
1.40
1.37
1.36
1.34
—
—
—
—
—
—
—
—
—
0.982
0.911
0.804
—
0.919
0.834
0.708
Designation
*Where no value of Qs is shown the angles comply with LRFD Specification Section E2.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1 - 98
DIMENSIONS AND PROPERTIES
DOUBLE ANGLES
Two unequal leg angles
Properties of sections
Y
X
X
y, yp
s
Long legs back to back
Y
Wt.
Area of
per ft
2 Angles 2 Angles
Designation
2
Axis X-X
S
I
4
in.
r
3
y
Z
yp
3
lb
in.
in.
in.
in.
in.
in.
L4×31⁄2×1⁄2
L4×31⁄2×3⁄8
L4×31⁄2×5⁄16
L4×31⁄2×1⁄4
23.8
18.2
15.4
12.4
7.00
5.34
4.49
3.63
10.6
8.35
7.12
5.83
3.87
2.99
2.53
2.05
1.23
1.25
1.26
1.27
1.25
1.21
1.18
1.16
7.00
5.42
4.59
3.73
0.500
0.438
0.406
0.375
L4×3×1⁄2
L4×3×3⁄8
L4×3×5⁄16
L4×3×1⁄4
22.2
17.0
14.4
11.6
6.50
4.97
4.18
3.38
10.1
7.93
6.76
5.54
3.78
2.92
2.47
2.00
1.25
1.26
1.27
1.28
1.33
1.28
1.26
1.24
6.81
5.28
4.47
3.63
0.750
0.688
0.656
0.625
L31⁄2×3×3⁄8
L4×31⁄2×5⁄16
L4×31⁄2×1⁄4
15.8
13.2
10.8
4.59
3.87
3.13
5.45
4.66
3.83
2.25
1.91
1.55
1.09
1.10
1.11
1.08
1.06
1.04
4.08
3.46
2.82
0.438
0.406
0.375
L31⁄2×21⁄2×3⁄8
L31⁄2×21⁄2×1⁄4
14.4
9.80
4.22
2.88
5.12
3.60
2.19
1.51
1.10
1.12
1.16
1.11
3.94
2.73
0.688
0.625
L3×21⁄2×3⁄8
L4×31⁄2×1⁄4
L4×31⁄2×5⁄16
13.2
9.00
6.77
3.84
2.63
1.99
3.31
2.35
1.81
1.62
1.12
0.859
0.928
0.945
0.954
0.956
0.911
0.888
2.93
2.04
1.56
0.438
0.375
0.344
L3×2×3⁄8
L4×3×5⁄16
L4×3×1⁄4
L4×3×3⁄16
11.8
10.0
8.20
6.14
3.47
2.93
2.38
1.80
3.06
2.63
2.17
1.68
1.56
1.33
1.08
0.830
0.940
0.948
0.957
0.966
1.04
1.02
0.993
0.970
2.79
2.38
1.95
1.49
0.688
0.656
0.625
0.594
L21⁄2×2×3⁄8
L4×31⁄2×5⁄16
L4×31⁄2×1⁄4
L4×31⁄2×3⁄16
10.6
9.00
7.24
5.50
3.09
2.62
2.13
1.62
1.82
1.58
1.31
1.02
1.09
0.932
0.763
0.586
0.768
0.776
0.784
0.793
0.831
0.809
0.787
0.764
1.97
1.69
1.38
1.06
0.438
0.406
0.375
0.344
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
DOUBLE ANGLES
1 - 99
DOUBLE ANGLES
Two unequal leg angles
Properties of sections
Y
X
X
y, yp
s
Long legs back to back
Y
Qs*
Axis Y-Y
Radii of Gyration
Angles in Contact
Angles Separated
3⁄
4
Fy =
36 ksi
Fy =
50 ksi
Fy =
36 ksi
Fy =
50 ksi
Back to Back of
Angles, in.
Designation
0
3⁄
8
L4×31⁄2×1⁄2
L4×31⁄2×3⁄8
L4×31⁄2×5⁄16
L4×31⁄2×1⁄4
1.44
1.42
1.42
1.41
1.58
1.56
1.55
1.54
1.72
1.70
1.69
1.67
—
—
—
—
—
—
—
0.982
—
—
0.997
0.911
—
—
0.935
0.834
L4×3×1⁄2
L4×3×3⁄8
L4×3×5⁄16
L4×3×1⁄4
1.20
1.18
1.17
1.16
1.33
1.31
1.30
1.29
1.48
1.45
1.44
1.43
—
—
—
—
—
—
—
—
—
—
0.997
0.911
—
—
0.935
0.834
L31⁄2×3×3⁄8
L4×31⁄2×5⁄16
L4×31⁄2×1⁄4
1.22
1.21
1.20
1.36
1.35
1.33
1.50
1.49
1.48
—
—
—
—
—
—
—
—
0.965
—
0.986
0.897
L31⁄2×21⁄2×3⁄8
L31⁄2×21⁄2×1⁄4
0.976
0.958
1.11
1.09
1.26
1.23
—
—
—
—
—
0.965
—
0.897
L3×21⁄2×3⁄8
L4×31⁄2×1⁄4
L4×31⁄2×5⁄16
1.02
1.00
0.993
1.16
1.13
1.12
1.31
1.28
1.27
—
—
—
—
—
—
—
—
0.911
—
0.961
0.834
L3×2×3⁄8
L4×3×5⁄16
L4×3×1⁄4
L4×3×3⁄16
0.777
0.767
0.757
0.749
0.917
0.903
0.891
0.879
1.07
1.06
1.04
1.03
—
—
—
—
—
—
—
—
—
—
—
0.911
—
—
0.961
0.834
L21⁄2×2×3⁄8
L4×31⁄2×5⁄16
L4×31⁄2×1⁄4
L4×31⁄2×3⁄16
0.819
0.809
0.799
0.790
0.961
0.948
0.935
0.923
1.12
1.10
1.09
1.07
—
—
—
—
—
—
—
—
—
—
—
0.982
—
—
—
0.919
*Where no value of Qs is shown, the angles comply with LRFD Specification Section E2.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1 - 100
DIMENSIONS AND PROPERTIES
DOUBLE ANGLES
Two unequal leg angles
Properties of sections
Y
X
X
y, yp
s
Short legs back to back
Y
Wt.
Area of
per ft
2 Angles 2 Angles
Designation
2
Axis X-X
S
I
4
in.
r
3
y
Z
yp
3
lb
in.
in.
in.
in.
in.
in.
L8×6×1
L8×6×13⁄4
L8×6×11⁄2
88.4
67.6
46.0
26.0
19.9
13.5
77.6
61.4
43.4
17.8
13.8
9.58
1.73
1.76
1.79
1.65
1.56
1.47
32.4
24.9
17.0
0.813
0.621
0.422
L8×4×1
L8×6×13⁄4
L8×6×11⁄2
74.8
57.4
39.2
22.0
16.9
11.5
23.3
18.7
13.5
7.88
6.14
4.29
1.03
1.05
1.08
1.05
0.953
0.859
15.4
11.6
7.80
0.688
0.527
0.359
L7×4×3⁄4
L5×3×1⁄2
L5×3×3⁄8
52.4
35.8
27.2
15.4
10.5
7.97
18.1
13.1
10.2
6.05
4.23
3.26
1.09
1.11
1.13
1.01
0.917
0.870
11.3
7.66
5.80
0.549
0.375
0.285
L6×4×3⁄4
L5×3×5⁄8
L5×3×1⁄2
L5×3×3⁄8
47.2
40.0
32.4
24.6
13.9
11.7
9.50
7.22
17.4
15.0
12.5
9.81
5.94
5.07
4.16
3.21
1.12
1.13
1.15
1.17
1.08
1.03
0.987
0.941
10.9
9.24
7.50
5.71
0.578
0.488
0.396
0.301
L6×31⁄2×3⁄8
L6×31⁄2×5⁄16
23.4
19.6
6.84
5.74
6.68
5.70
2.46
2.08
0.988
0.996
0.787
0.763
4.41
3.70
0.285
0.239
L5×31⁄2×3⁄4
L6×31⁄2×1⁄2
L6×31⁄2×3⁄8
L6×31⁄2×5⁄16
39.6
27.2
20.8
17.4
11.6
8.00
6.09
5.12
11.1
8.10
6.37
5.44
4.43
3.12
2.41
2.04
0.977
1.01
1.02
1.03
0.996
0.906
0.861
0.838
8.20
5.65
4.32
3.63
0.581
0.400
0.305
0.256
L5×3×1⁄2
L5×3×3⁄8
L5×3×5⁄16
L5×3×1⁄4
25.6
19.6
16.4
13.2
7.50
5.72
4.80
3.88
5.16
4.08
3.49
2.88
2.29
1.78
1.51
1.23
0.829
0.845
0.853
0.861
0.750
0.704
0.681
0.657
4.22
3.21
2.69
2.17
0.375
0.286
0.240
0.194
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
DOUBLE ANGLES
1 - 101
DOUBLE ANGLES
Two unequal leg angles
Properties of sections
Y
X
X
y, yp
s
Short legs back to back
Y
Qs*
Axis Y-Y
Radii of Gyration
Back to Back of
Angles, in.
Angles in Contact
Angles Separated
0
3⁄
8
3⁄
4
Fy =
36 ksi
Fy =
50 ksi
Fy =
36 ksi
Fy =
50 ksi
L8×6×1
L8×6×13⁄4
L8×6×11⁄2
3.64
3.60
3.56
3.78
3.74
3.69
3.92
3.88
3.83
—
—
0.995
—
—
0.921
—
—
0.911
—
—
0.834
L8×4×1
L8×4×13⁄4
L8×4×11⁄2
3.95
3.90
3.86
4.10
4.05
4.00
4.25
4.19
4.14
—
—
0.995
—
—
0.921
—
—
0.911
—
—
0.834
L7×4×3⁄4
L7×4×1⁄2
L7×4×3⁄8
3.35
3.30
3.28
3.49
3.44
3.42
3.64
3.59
3.56
—
—
0.926
—
0.982
0.838
—
0.965
0.839
0.897
0.750
L6×4×3⁄4
L7×4×5⁄8
L7×4×1⁄2
L7×4×3⁄8
2.80
2.78
2.76
2.74
2.94
2.92
2.90
2.87
3.09
3.06
3.04
3.02
—
—
—
0.995
—
—
—
0.921
—
—
—
0.911
—
—
0.961
0.834
L6×31⁄2×3⁄8
L6×31⁄2×5⁄16
2.81
2.80
2.95
2.94
3.09
3.08
0.995
0.912
0.921
0.822
0.911
0.825
0.834
0.733
L5×31⁄2×3⁄4
L6×31⁄2×1⁄2
L6×31⁄2×3⁄8
L6×31⁄2×5⁄16
2.33
2.29
2.27
2.26
2.48
2.43
2.41
2.39
2.63
2.57
2.55
2.54
—
—
—
0.995
—
—
—
0.921
—
—
0.982
0.911
—
—
0.919
0.834
L5×3×1⁄2
L5×3×3⁄8
L5×3×5⁄16
L5×3×1⁄4
2.36
2.34
2.33
2.32
2.50
2.48
2.47
2.46
2.65
2.63
2.61
2.60
—
—
0.995
0.891
—
—
0.921
0.797
—
0.982
0.911
0.804
—
0.919
0.834
0.708
Designation
*Where no value of Qs is shown, the angles comply with LRFD Specification Section E2.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1 - 102
DIMENSIONS AND PROPERTIES
DOUBLE ANGLES
Two unequal leg angles
Properties of sections
Y
X
X
y, yp
s
Short legs back to back
Y
Wt.
Area of
per ft
2 Angles 2 Angles
Designation
2
Axis X-X
S
I
4
in.
r
3
y
Z
yp
3
lb
in.
in.
in.
in.
in.
in.
L4×31⁄2×1⁄2
L4×31⁄2×3⁄8
L4×31⁄2×5⁄16
L4×31⁄2×1⁄4
23.8
18.2
15.4
12.4
7.00
5.34
4.49
3.63
7.58
5.97
5.10
4.19
3.03
2.35
1.99
1.62
1.04
1.06
1.07
1.07
1.00
0.955
0.932
0.909
5.47
4.21
3.56
2.89
0.438
0.334
0.281
0.227
L4×3×1⁄2
L3×2×3⁄8
L3×2×5⁄16
L3×2×1⁄4
22.2
17.0
14.4
11.6
6.50
4.97
4.18
3.38
4.85
3.84
3.29
2.71
2.23
1.73
1.47
1.20
0.864
0.879
0.887
0.896
0.827
0.782
0.759
0.736
4.06
3.11
2.63
2.13
0.406
0.311
0.261
0.211
L31⁄2×3×3⁄8
L4×31⁄2×5⁄16
L4×31⁄2×1⁄4
15.8
13.2
10.8
4.59
3.87
3.13
3.69
3.17
2.61
1.70
1.44
1.18
0.897
0.905
0.914
0.830
0.808
0.785
3.06
2.59
2.10
0.328
0.276
0.223
L31⁄2×21⁄2×3⁄8
L31⁄2×21⁄2×1⁄4
14.4
9.80
4.22
2.88
2.18
1.55
1.18
0.824
0.719
0.735
0.660
0.614
2.15
1.47
0.301
0.205
L3×21⁄2×3⁄8
L4×31⁄2×1⁄4
L4×31⁄2×3⁄16
13.2
9.00
6.77
3.84
2.63
1.99
2.08
1.49
1.15
1.16
0.808
0.620
0.736
0.753
0.761
0.706
0.661
0.638
2.10
1.45
1.11
0.320
0.219
0.166
L3×2×3⁄8
L3×2×5⁄16
L3×2×1⁄4
L3×2×3⁄16
11.8
10.0
8.20
6.14
3.47
2.93
2.38
1.80
1.09
0.941
0.784
0.613
0.743
0.634
0.520
0.401
0.559
0.567
0.574
0.583
0.539
0.516
0.493
0.470
1.37
1.16
0.937
0.713
0.289
0.244
0.198
0.150
L21⁄2×2×3⁄8
L4×31⁄2×5⁄16
L4×31⁄2×1⁄4
L4×31⁄2×3⁄16
10.6
9.00
7.24
5.50
3.09
2.62
2.13
1.62
1.03
0.893
0.745
0.583
0.725
0.620
0.509
0.392
0.577
0.584
0.592
0.600
0.581
0.559
0.537
0.514
1.32
1.12
0.915
0.701
0.309
0.262
0.213
0.162
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
DOUBLE ANGLES
1 - 103
DOUBLE ANGLES
Two unequal leg angles
Properties of sections
Y
X
X
y, yp
s
Short legs back to back
Y
Qs*
Axis Y-Y
Radii of Gyration
Back to Back of
Angles, in.
Angles in Contact
Angles Separated
0
3⁄
8
3⁄
4
Fy =
36 ksi
Fy =
50 ksi
Fy =
36 ksi
Fy =
50 ksi
L4×31⁄2×1⁄2
L4×31⁄2×3⁄8
L4×31⁄2×5⁄16
L4×31⁄2×1⁄4
1.76
1.74
1.73
1.72
1.89
1.87
1.86
1.85
2.04
2.01
2.00
1.99
—
—
—
0.995
—
—
—
0.921
—
—
0.997
0.911
—
—
0.935
0.834
L4×3×1⁄2
L3×2×3⁄8
L3×2×5⁄16
L3×2×1⁄4
1.82
1.80
1.79
1.78
1.96
1.94
1.93
1.92
2.11
2.08
2.07
2.06
—
—
—
0.995
—
—
—
0.921
—
—
0.997
0.911
—
—
0.935
0.834
L31⁄2×3×3⁄8
L4×31⁄2×5⁄16
L4×31⁄2×1⁄4
1.53
1.52
1.52
1.67
1.66
1.65
1.82
1.80
1.79
—
—
—
—
—
0.982
—
—
0.965
—
0.986
0.897
L31⁄2×21⁄2×3⁄8
L31⁄2×21⁄2×1⁄4
1.60
1.58
1.74
1.72
1.89
1.86
—
—
—
0.982
—
0.965
—
0.897
L3×21⁄2×3⁄8
L4×31⁄2×1⁄4
L4×31⁄2×3⁄16
1.33
1.31
1.30
1.47
1.45
1.44
1.62
1.60
1.58
—
—
0.995
—
—
0.921
—
—
0.911
—
0.961
0.834
L3×2×3⁄8
L3×2×5⁄16
L3×2×1⁄4
L3×2×3⁄16
1.40
1.39
1.38
1.37
1.55
1.53
1.52
1.51
1.70
1.68
1.67
1.66
—
—
—
0.995
—
—
—
0.921
—
—
—
0.911
—
—
0.961
0.834
L21⁄2×2×3⁄8
L4×31⁄2×5⁄16
L4×31⁄2×1⁄4
L4×31⁄2×3⁄16
1.13
1.12
1.11
1.10
1.28
1.26
1.25
1.24
1.43
1.42
1.40
1.39
—
—
—
—
—
—
—
—
—
—
—
0.982
—
—
—
0.911
Designation
*Where no value of Qs is shown the angles comply with LRFD Specification Section E2.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1 - 104
DIMENSIONS AND PROPERTIES
COMBINATION SECTIONS
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
COMBINATION SECTIONS
1 - 105
COMBINATION SECTIONS
Standard rolled shapes are frequently combined to produce efficient and economical
structural members for special applications. Experience has established a demand for
certain combinations. When properly sized and connected to satisfy the design and
specification criteria, these members may be used as struts, lintels, eave struts, and light
crane and trolley runways. The W section with channel attached to the web is not
recommended for use as a trolley or crane runway member. Properties of several
combined sections are tabulated for those combinations that experience has proven to be
in popular demand.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1 - 106
DIMENSIONS AND PROPERTIES
COMBINATION SECTIONS
W shapes and channels
Properties of sections
Y
y
2
X
X
y , yp
1
Y
Beam
Channel
Axis X-X
Total
Weight
per ft
Total
Area
lb
in.2
I
S1 =
I / y1
S2 =
I / y2
r
in.4
in.3
in.3
in.
W12×26
W ×26
C10×15.3
C12×20.7
41.3
46.7
12.14
13.74
299
318
36.3
36.8
70.5
82.2
4.96
4.81
W14×30
W ×30
C10×15.3
C12×20.7
45.3
50.7
13.34
14.94
420
448
46.1
46.8
84.6
98.3
5.61
5.47
W16×36
W ×36
C12×20.7
C15×33.9
56.7
69.9
16.69
20.56
670
748
62.8
64.6
123
160
6.34
6.03
W18×50
W ×50
C12×20.7
C15×33.9
70.7
83.9
20.79
24.66
1120
1250
97.4
100
166
211
7.34
7.11
W21×62
W ×62
W ×68
W ×68
C12×20.7
C15×33.9
C12×20.7
C15×33.9
82.7
95.9
88.7
101.9
24.39
28.26
26.09
29.96
1800
2000
1960
2180
138
142
152
156
218
272
232
287
8.59
8.41
8.68
8.52
W24×68
W ×68
W ×84
W ×84
C12×20.7
C15×33.9
C12×20.7
C15×33.9
88.7
101.9
104.7
117.9
26.19
30.06
30.79
34.66
2450
2720
3040
3340
168
173
212
217
258
321
303
368
9.67
9.50
9.93
9.82
W27×84
W ×94
C15×33.9
C15×33.9
117.9
127.9
34.76
37.66
4050
4530
237
268
404
436
10.8
11.0
W30×99
W ×99
W ×116
W ×116
C15×33.9
C18×42.7
C15×33.9
C18×42.7
132.9
141.7
149.9
158.7
39.06
41.70
44.16
46.80
5540
5830
6590
6900
300
304
360
365
480
533
544
599
11.9
11.8
12.2
12.1
W33×118
W ×118
W ×141
W ×141
C15×33.9
C18×42.7
C15×33.9
C18×42.7
151.9
160.7
174.9
183.7
44.66
47.30
51.56
54.20
7900
8280
9580
10000
395
400
484
490
596
656
689
751
13.3
13.2
13.6
13.6
W36×150
W ×150
C15×33.9
C18×42.7
183.9
192.7
54.16
56.80
11500
12100
546
553
765
832
14.6
14.6
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
COMBINATION SECTIONS
1 - 107
COMBINATION SECTIONS
W shapes and channels
Properties of sections
Y
y
2
X
X
y , yp
1
Y
Axis X-X
y1
Beam
Z
Axis Y-Y
yp
3
Channel
in.
in.
W12×26
W30×26
C10×15.3
C12×20.7
8.22
8.63
W14×30
W30×30
C10×15.3
C12×20.7
W16×36
W30×36
S
I
4
3
r
Z
in.
in.3
in.
in.
in.
47.0
48.8
11.30
11.55
84.7
146
16.9
24.4
2.64
3.26
24.0
33.6
9.12
9.57
60.5
62.3
12.56
12.87
87.0
149
17.4
24.8
2.55
3.15
24.8
34.4
C12×20.7
C15×33.9
10.67
11.58
83.6
88.6
14.56
15.21
154
340
25.6
45.3
3.03
4.06
36.3
61.3
W18×50
W30×50
C12×20.7
C15×33.9
11.51
12.47
128
134
16.08
16.90
169
355
28.2
47.3
2.85
3.79
42.0
67.0
W21×62
W30×62
W30×68
W30×68
C12×20.7
C15×33.9
C12×20.7
C15×33.9
13.01
14.06
12.93
13.95
182
190
200
208
18.06
19.36
17.60
19.32
187
373
194
380
31.1
49.7
32.3
50.6
2.77
3.63
2.72
3.56
47.2
72.2
49.8
74.8
W24×68
W30×68
W30×84
W30×84
C12×20.7
C15×33.9
C12×20.7
C15×33.9
14.53
15.67
14.35
15.40
224
234
275
288
19.15
21.66
18.49
21.61
199
385
223
409
33.2
51.4
37.2
54.6
2.76
3.58
2.69
3.44
50.0
75.0
58.1
83.1
W27×84
W27×94
C15×33.9
C15×33.9
17.07
16.92
320
357
23.86
23.56
421
439
56.1
58.5
3.48
3.41
83.6
89.2
W30×99
W30×99
W30×116
W30×116
C15×33.9
C18×42.7
C15×33.9
C18×42.7
18.51
19.18
18.30
18.93
408
418
480
492
24.34
26.43
23.77
26.04
443
682
479
718
59.1
75.8
63.9
79.8
3.37
4.04
3.29
3.92
89.1
113
99.6
124
W33×118
W30×118
W30×141
W30×141
C15×33.9
C18×42.7
C15×33.9
C18×42.7
20.01
20.69
19.79
20.42
529
544
634
652
25.43
27.77
24.83
26.96
502
741
561
800
66.9
82.3
74.8
88.9
3.35
3.96
3.30
3.84
102
126
117
141
W36×150
W30×150
C15×33.9
C18×42.7
21.15
21.81
716
738
25.84
27.91
585
824
78.0
91.6
3.29
3.81
121
145
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1 - 108
DIMENSIONS AND PROPERTIES
COMBINATION SECTIONS
S shapes and channels
Properties of sections
Y
y
2
X
X
y , yp
1
Y
Beam
Channel
Axis X-X
Total
Weight
per ft
Total
Area
lb
in.2
I
S1 =
I / y1
S2 =
I / y2
r
in.4
in.3
in.3
in.
S10×25.4
C8×11.5
C10×15.3
36.9
40.7
10.84
11.95
176
186
27.2
27.6
46.6
52.9
4.02
3.94
S12×31.8
C8×11.5
C10×15.3
43.3
47.1
12.73
13.84
299
316
39.8
40.4
63.2
71.4
4.84
4.78
S15×42.9
C8×11.5
C10×15.3
54.4
58.2
15.98
17.09
585
616
64.9
65.8
94.2
105
6.05
6.01
S20×66
C10×15.3
C12×20.7
81.3
86.7
23.89
25.49
1530
1620
130
132
181
203
8.00
7.97
S24×80
C10×15.3
C12×20.7
95.3
100.7
27.99
29.59
2610
2750
188
191
252
278
9.66
9.65
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
COMBINATION SECTIONS
1 - 109
COMBINATION SECTIONS
S shapes and channels
Properties of sections
Y
y
2
X
X
y , yp
1
Y
Axis X-X
y1
Beam
Z
Axis Y-Y
yp
3
S
I
4
3
r
Z
in.
in.3
Channel
in.
in.
in.
in.
in.
S10×25.4
C8×11.5
C10×15.3
6.45
6.73
35.7
36.9
8.81
9.02
39.4
74.2
9.8
14.8
1.91
2.49
14.5
20.8
S12×31.8
C8×11.5
C10×15.3
7.50
7.82
52.6
53.9
10.30
10.61
42.0
76.8
10.5
15.4
1.82
2.36
16.0
22.2
S15×42.9
C8×11.5
C10×15.3
9.01
9.37
85.7
88.2
11.58
12.77
47.0
81.8
11.8
16.4
1.71
2.19
18.6
24.9
S20×66
C10×15.3
C12×20.7
11.81
12.29
171
178
14.41
15.99
95.1
157
19.0
26.1
2.00
2.48
31.2
40.8
S24×80
C10×15.3
C12×20.7
13.86
14.38
244
254
16.46
18.05
110
171
21.9
28.5
1.98
2.41
36.6
46.2
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1 - 110
DIMENSIONS AND PROPERTIES
d
2
Yd
COMBINATION SECTIONS
Two channels
Properties of sections
2
y
2
X
X
x1 , xp
y , yp
1
Y
Vertical Horizontal
Channel Channel
Axis X-X
Total
Weight
per ft
Total
Area
lb
in.2
I
S1 =
I / y1
S2 =
I / y2
r
y1
Z
yp
in.4
in.3
in.3
in.
in.
in.3
in.
C3×4.1
C4×5.4
9.5
2.80
3.0
1.4
3.0
1.04
2.20
2.16
2.67
C4×5.4
C4×5.4
C5×6.7
10.8
12.1
3.18
3.56
6.5
6.9
2.3
2.3
4.9
5.5
1.43
1.39
2.86
2.94
3.39
3.62
3.56
3.61
C5×6.7
C5×6.7
C6×8.2
C7×9.8
13.4
14.9
16.5
3.94
4.37
4.84
12.8
13.4
14.0
3.5
3.6
3.7
8.0
8.9
9.8
1.80
1.75
1.70
3.60
3.70
3.79
5.23
5.50
5.81
4.50
4.57
4.62
C6×8.2
C5×6.7
C6×8.2
C7×9.8
C8×11.5
C9×13.4
C10×15.3
14.9
16.4
18.0
19.7
21.6
23.5
4.37
4.80
5.27
5.78
6.34
6.89
21.5
22.5
23.4
24.3
25.2
26.0
5.1
5.2
5.2
5.3
5.4
5.5
10.9
12.1
13.3
14.5
15.8
16.9
2.22
2.16
2.11
2.05
1.99
1.94
4.22
4.34
4.45
4.55
4.64
4.70
7.31
7.61
7.93
8.30
8.72
9.16
5.37
5.45
5.53
5.58
5.63
5.65
C7×9.8
C6×8.2
C7×9.8
C8×11.5
C9×13.4
C10×15.3
18.0
19.6
21.3
23.2
25.1
5.27
5.74
6.25
6.81
7.36
35.3
36.7
38.0
39.3
40.5
7.1
7.2
7.3
7.4
7.5
15.7
17.3
18.8
20.5
21.9
2.59
2.53
2.47
2.40
2.34
4.95
5.08
5.20
5.31
5.39
10.2
10.6
10.9
11.4
11.8
6.32
6.40
6.48
6.54
6.58
C8×11.5
C6×8.2
C7×9.8
C8×11.5
C9×13.4
C10×15.3
C12×20.7
19.7
21.3
23.0
24.9
26.8
32.2
5.78
6.25
6.76
7.32
7.87
9.47
52.4
54.5
56.4
58.4
60.0
64.4
9.5
9.6
9.7
9.8
9.9
10.2
19.6
21.6
23.6
25.6
27.5
32.6
3.01
2.95
2.89
2.82
2.76
2.61
5.53
5.68
5.82
5.95
6.06
6.30
13.4
13.8
14.2
14.6
15.1
16.4
7.18
7.27
7.35
7.44
7.49
7.62
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
COMBINATION SECTIONS
1 - 111
COMBINATION SECTIONS
Two channels
Properties of sections
d
2
Yd
2
y
2
X
X
x1 , xp
y , yp
1
Y
Axis Y-Y
Vertical
Channel
Horizontal
Channel
I
S
r
x1
Z
xp
in.4
in.3
in.
in.
in.3
in.
C3×4.1
C4×5.4
4.0
2.0
1.20
0.44
2.67
0.315
C4×5.4
C4×5.4
C5×6.7
4.2
7.8
2.1
3.1
1.14
1.48
0.46
0.46
2.84
4.09
0.281
0.282
C5×6.7
C5×6.7
C6×8.2
C7×9.8
8.0
13.6
21.8
3.2
4.5
6.2
1.42
1.76
2.12
0.48
0.48
0.48
4.29
5.90
7.90
0.264
0.266
0.268
C6×8.2
C5×6.7
C6×8.2
C7×9.8
C8×11.5
C9×13.4
C10×15.3
8.2
13.8
22.0
33.3
48.6
68.1
3.3
4.6
6.3
8.3
10.8
13.6
1.37
1.70
2.04
2.40
2.77
3.14
0.51
0.51
0.51
0.51
0.51
0.51
4.52
6.14
8.13
10.6
13.5
16.8
0.242
0.245
0.247
0.249
0.252
0.254
C7×9.8
C6×8.2
C7×9.8
C8×11.5
C9×13.4
C10×15.3
14.1
22.3
33.6
48.6
68.4
4.7
6.4
8.4
10.9
13.7
1.63
1.97
2.32
2.68
3.05
0.54
0.54
0.54
0.54
0.54
6.41
8.41
10.8
13.8
17.1
0.225
0.228
0.230
0.234
0.235
C8×11.5
C6×8.2
C7×9.8
C8×11.5
C9×13.4
C10×15.3
C12×20.7
14.4
22.6
33.9
49.2
68.7
130
4.8
6.5
8.5
10.9
13.7
21.7
1.58
1.90
2.24
2.59
2.95
3.71
0.57
0.57
0.57
0.57
0.57
0.57
6.73
8.73
11.2
14.1
17.4
27.0
0.218
0.219
0.219
0.220
0.220
0.230
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1 - 112
DIMENSIONS AND PROPERTIES
d
2
Yd
COMBINATION SECTIONS
Two channels
Properties of sections
2
y
2
X
X
x1 , xp
y , yp
1
Y
Vertical Horizontal
Channel Channel
Total
Weight
per ft
Axis X-X
Total
Area
2
lb
in.
C9×13.4
C7×9.8
C8×11.5
C9×13.4
C10×15.3
C12×20.7
23.2
24.9
26.8
28.7
34.1
6.81
7.32
7.88
8.43
10.03
C10×15.3
C8×11.5
C9×13.4
C10×15.3
C12×20.7
C15×33.9
26.8
28.7
30.6
36.0
49.2
7.87
8.43
8.98
10.58
14.45
C12×20.7
C9×13.4
C10×15.3
C12×20.7
C15×33.9
34.1
36.0
41.4
54.6
C15×33.9
C10×15.3
C12×20.7
C15×33.9
MC18×42.7
MC18×42.7 MC12×20.7
MC15×33.9
MC18×42.7
S1 =
I / y1
I
4
in.
3
S2 =
I / y2
3
r
y1
Z
yp
3
in.
in.
in.
in.
in.
in.
12.4
12.6
12.7
12.8
13.1
26.3
28.7
31.2
33.5
39.8
3.38
3.32
3.25
3.19
3.02
6.26
6.42
6.57
6.69
6.98
17.6
18.1
18.5
19.0
20.4
8.11
8.21
8.31
8.37
8.54
110
114
117
126
141
15.8
15.9
16.1
16.4
17.3
34.2
37.2
39.9
47.5
63.7
3.75
3.68
3.61
3.45
3.13
7.00
7.16
7.30
7.64
8.18
22.4
22.9
23.4
24.9
28.3
9.07
9.18
9.26
9.46
9.73
10.03
10.58
12.18
16.05
207
213
228
256
25.2
25.4
25.9
27.0
51.4
55.0
65.3
87.8
4.54
4.48
4.32
4.00
8.21
8.38
8.79
9.48
35.7
36.3
38.0
41.8
10.78
10.88
11.16
11.56
49.2
54.6
67.8
76.6
14.45
16.05
19.92
22.56
474
509
575
608
48.8
49.9
52.0
53.1
85.6
99.8
132
152
5.72
5.63
5.37
5.19
9.71
10.19
11.06
11.45
69.7
72.2
77.4
80.7
12.83
13.31
14.04
14.37
63.4
76.6
85.4
18.69
22.56
25.20
860
975
1030
72.9
76.1
77.6
133
174
200
6.78
6.57
6.40
11.80
12.80
13.29
77.7
80.5
83.3
85.6
91.7
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
106
113
117
15.51
16.50
16.96
COMBINATION SECTIONS
1 - 113
COMBINATION SECTIONS
Two channels
Properties of sections
d
2
Yd
2
y
2
X
X
x1 , xp
y , yp
1
Y
Axis Y-Y
Vertical
Channel
Horizontal
Channel
I
S
r
x1
Z
xp
in.4
in.3
in.
in.
in.3
in.
C9×13.4
C7×9.8
C8×11.5
C9×13.4
C10×15.3
C12×20.7
23.1
34.4
49.7
69.2
131
6.6
8.6
11.0
13.8
21.8
1.84
2.17
2.51
2.86
3.61
0.60
0.60
0.60
0.60
0.60
9.10
11.5
14.5
17.8
27.4
0.226
0.227
0.227
0.227
0.229
C10×15.3
C8×11.5
C9×13.4
C10×15.3
C12×20.7
C15×33.9
34.9
50.2
69.7
131
317
8.7
11.2
13.9
21.9
42.3
2.11
2.44
2.79
3.52
4.69
0.63
0.63
0.63
0.63
0.63
11.9
14.9
18.2
27.8
52.8
0.232
0.232
0.233
0.234
0.239
C12×20.7
C9×13.4
C10×15.3
C12×20.7
C15×33.9
51.8
71.3
133
319
11.5
14.3
22.1
42.5
2.27
2.60
3.30
4.46
0.70
0.70
0.70
0.70
16.0
19.3
29.0
54.0
0.261
0.261
0.262
0.266
C15×33.9
C10×15.3
C12×20.7
C15×33.9
MC18×42.7
75.5
137
323
562
15.1
22.9
43.1
62.5
2.29
2.92
4.03
4.99
0.79
0.79
0.79
0.79
22.1
31.7
56.7
80.7
0.337
0.338
0.342
0.343
MC18×42.7
MC12×20.7
MC15×33.9
MC18×42.7
143
329
568
23.9
43.9
63.2
2.77
3.82
4.75
0.88
0.88
0.88
33.6
58.6
82.6
0.355
0.358
0.359
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1 - 114
DIMENSIONS AND PROPERTIES
COMBINATION SECTIONS
Channels and angles
Properties of sections
Y
y
2
X
X
Long leg of angle turned out
y , yp
1
x1
xp
x2
Y
Total
Weight
per ft
Axis X-X
Total
Area
2
S1 =
I / y1
I
4
3
3
in.
r
y1
Z
yp
3
Angle
lb
in.
in.
in.
in.
in.
in.
C6×8.2
L21⁄2×21⁄2×1⁄4
L3 ×21⁄2×1⁄4
L31⁄2×3 ×1⁄4
L3×21⁄2 ×5⁄16
L4 ×3 ×1⁄4
12.3
12.7
13.6
14.8
14.0
3.59
3.71
3.96
4.33
4.09
17.9
18.5
19.0
19.8
19.5
8.0
8.5
8.9
9.8
9.5
4.8
4.8
4.9
5.0
5.0
2.24
2.23
2.19
2.14
2.19
2.24
2.17
2.13
2.02
2.06
6.75
6.90
7.23
7.54
7.36
1.40
1.26
1.26
1.11
1.13
C7×9.8
L21⁄2×21⁄2×1⁄4
L3 ×21⁄2×1⁄4
L31⁄2×3 ×1⁄4
L3×21⁄2 ×5⁄16
L4 ×3 ×1⁄4
L3×2
×5⁄16
13.9
14.3
15.2
16.4
15.6
17.0
4.06
4.18
4.43
4.80
4.56
4.96
28.5
29.3
30.0
31.2
30.8
32.0
10.6
11.2
11.8
12.9
12.4
13.7
6.6
6.7
6.7
6.8
6.8
6.9
2.65
2.65
2.60
2.55
2.60
2.54
2.68
2.61
2.54
2.42
2.48
2.35
9.13
9.31
9.64
9.99
9.81
10.2
1.67
1.53
1.53
1.35
1.39
1.20
C8×11.5
L3 ×21⁄2×1⁄4
L31⁄2×3 ×1⁄4
L3×21⁄2 ×5⁄16
L4 ×3 ×1⁄4
L3×2
×5⁄16
L5 ×31⁄2×5⁄16
16.0
16.9
18.1
17.3
18.7
20.2
4.69
4.94
5.31
5.07
5.47
5.94
43.9
44.9
46.7
46.0
47.8
49.9
14.3
15.1
16.4
15.8
17.3
18.9
8.9
9.0
9.0
9.0
9.1
9.3
3.06
3.02
2.97
3.01
2.96
2.90
3.07
2.98
2.84
2.91
2.76
2.64
12.2
12.6
13.0
12.8
13.2
13.9
1.81
1.81
1.60
1.67
1.45
1.30
C9×13.4
L3 ×21⁄2×1⁄4
L31⁄2×3 ×1⁄4
L3×21⁄2 ×5⁄16
L4 ×3 ×1⁄4
L3×2
×5⁄16
L5 ×31⁄2×5⁄16
17.9
18.8
20.0
19.2
20.6
22.1
5.25
5.50
5.87
5.63
6.03
6.50
63.1
64.6
67.1
66.0
68.7
71.4
17.8
18.8
20.4
19.6
21.4
23.4
11.6
11.6
11.7
11.7
11.8
12.0
3.47
3.43
3.38
3.42
3.37
3.31
3.54
3.45
3.29
3.37
3.20
3.06
15.8
16.1
16.6
16.3
16.8
17.5
2.11
2.11
1.87
1.98
1.73
1.58
C10×15.3
L31⁄2×3 ×1⁄4
L3×21⁄2 ×5⁄16
L4 ×3 ×1⁄4
L3×2
×5⁄16
L5 ×31⁄2×5⁄16
L3×21⁄2 ×3⁄8
20.7
21.9
21.1
22.5
24.0
25.7
6.05
6.42
6.18
6.58
7.05
7.54
89.3
92.7
91.1
94.7
98.4
102
22.8
24.8
23.8
25.9
28.2
30.6
14.7
14.8
14.8
14.9
15.1
15.2
3.84
3.80
3.84
3.79
3.74
3.67
3.91
3.74
3.83
3.65
3.49
3.33
20.0
20.6
20.3
20.9
21.6
22.2
2.39
2.12
2.26
1.98
1.84
1.61
Channel
in.
S2 =
I / y2
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
COMBINATION SECTIONS
1 - 115
COMBINATION SECTIONS
Channels and angles
Properties of sections
Y
y
2
X
X
Long leg of angle turned out
y , yp
1
x1
xp
x2
Y
Axis Y-Y
S1 =
I / x1
I
3
3
r
x1
Z
xp
3
in.
in.
in.
in.
in.
in.
C6×8.2
L21⁄2×21⁄2×1⁄4
L3 ×21⁄2×1⁄4
L31⁄2×3 ×1⁄4
L31⁄2×3 ×5⁄16
L4 ×3 ×1⁄4
2.6
3.6
4.9
5.7
6.5
1.0
1.2
1.4
1.7
1.7
1.4
1.9
2.4
2.7
3.1
0.85
0.98
1.11
1.14
1.26
2.60
3.01
3.40
3.31
3.79
2.02
2.38
2.82
3.27
3.30
2.60
3.09
3.57
3.54
4.06
C7×9.8
L21⁄2×21⁄2×1⁄4
L3 ×21⁄2×1⁄4
L31⁄2×3 ×1⁄4
L31⁄2×3 ×5⁄16
L4 ×3 ×1⁄4
L31⁄2
×5⁄16
3.0
4.0
5.4
6.3
7.1
8.3
1.1
1.3
1.6
1.8
18
2.2
1.6
2.0
2.6
2.9
3.2
3.6
0.86
0.98
1.10
1.14
1.25
1.29
2.67
3.09
3.48
3.40
3.88
3.78
2.31
2.66
3.11
3.57
3.59
4.16
2.62
3.11
3.59
3.57
4.08
4.05
C8×11.5
L3 ×21⁄2×1⁄4
L31⁄2×3 ×1⁄4
L31⁄2×3 ×5⁄16
L4 ×3 ×1⁄4
L3×3
×5⁄16
L5 ×31⁄2×5⁄16
4.6
6.0
6.9
7.8
9.0
14.7
14
1.7
2.0
2.0
2.3
3.2
2.2
2.7
3.0
3.4
3.8
5.6
0.99
1.10
1.14
1.24
1.28
1.57
3.16
3.56
3.48
3.97
3.87
4.64
3.00
3.45
3.91
3.93
4.51
5.97
3.13
3.61
3.59
4.10
4.08
5.05
C9×13.4
L3 ×21⁄2×1⁄4
L31⁄2×3 ×1⁄4
L31⁄2×3 ×5⁄16
L4 ×3 ×1⁄4
L3×3
×5⁄16
L5 ×31⁄2×5⁄16
5.2
6.7
7.7
8.5
9.9
15.8
1.6
1.8
2.2
2.1
2.5
3.3
2.3
2.9
3.2
3.6
4.0
5.9
0.99
1.10
1.14
1.23
1.28
1.56
3.22
3.64
3.55
4.05
3.96
4.74
3.38
3.83
4.31
4.32
4.91
6.38
3.14
3.63
3.61
4.12
4.10
5.08
C10×15.3
L31⁄2×3 ×1⁄4
L31⁄2×3 ×5⁄16
L4 ×3 ×1⁄4
L3×3
×5⁄16
L5 ×31⁄2×5⁄16
L31⁄2×3 ×3⁄8
7.4
8.5
9.4
10.8
16.9
19.2
2.0
2.3
2.3
2.7
3.5
4.1
3.1
3.4
3.8
4.2
6.1
6.7
1.11
1.15
1.23
1.28
1.55
1.60
3.70
3.62
4.12
4.03
4.83
4.73
4.25
4.73
4.74
5.34
6.82
7.70
3.64
3.63
4.14
4.12
5.09
5.07
Channel
Angle
in.
4
S2 =
I / x2
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1 - 116
DIMENSIONS AND PROPERTIES
COMBINATION SECTIONS
Channels and angles
Properties of sections
Y
y
2
X
X
Long leg of angle turned out
y , yp
1
x1
xp
x2
Y
Total
Weight
per ft
Axis X-X
Total
Area
2
S1 =
I / y1
I
4
3
S2 =
I / y2
3
r
y1
Z
yp
3
Angle
lb
in.
in.
in.
in.
in.
in.
in.
in.
C12×20.7
L31⁄2×3 ×1⁄4
L31⁄2×3 ×5⁄16
L4 ×3 ×1⁄4
L31⁄2×3 ×5⁄16
L5 ×31⁄2×5⁄16
L5×31⁄2 ×3⁄8
L6 ×4 ×3⁄8
L5×3
×1⁄2
26.1
27.3
26.5
27.9
29.4
31.1
33.0
36.9
7.65
8.02
7.78
8.18
8.65
9.14
9.70
10.84
164
170
167
173
180
186
192
202
33.2
35.8
34.4
37.2
40.2
43.4
46.6
53.2
23.2
23.5
23.4
23.6
23.9
24.1
24.3
24.7
4.63
4.61
4.63
4.60
4.56
4.51
4.45
4.32
4.94
4.75
4.86
4.66
4.47
4.29
4.12
3.80
31.4
32.2
31.8
32.6
33.5
34.2
35.3
36.7
3.23
2.80
3.01
2.67
2.53
2.25
2.11
1.68
C12×25
L31⁄2×3 ×1⁄4
L5×31⁄2 ×5⁄16
L4 ×3 ×1⁄4
L5×3
×5⁄16
L5 ×31⁄2×5⁄16
L5×31⁄2 ×3⁄8
L6 ×4 ×3⁄8
L5×3
×1⁄2
30.4
31.6
30.8
32.2
33.7
35.4
37.3
41.2
8.91
9.28
9.04
9.44
9.91
10.40
10.96
12.10
180
187
183
190
197
204
211
223
35.4
38.0
36.6
39.3
42.3
45.4
48.7
55.3
26.1
26.4
26.3
26.6
26.9
27.2
27.5
28.0
4.50
4.49
4.50
4.49
4.46
4.43
4.39
4.29
5.09
4.92
5.02
4.84
4.67
4.49
4.33
4.03
35.8
36.8
36.3
37.3
38.3
39.3
40.4
42.2
3.98
3.50
3.82
3.30
3.05
2.77
2.65
2.20
C15×33.9
L4 ×3 ×1⁄4
L5×3
×5⁄16
L5 ×31⁄2×5⁄16
L5×31⁄2 ×3⁄8
L6 ×4 ×3⁄8
L5×3
×1⁄2
39.7
41.1
42.6
44.3
46.2
50.1
11.65
12.05
12.52
13.01
13.57
14.71
383
395
408
421
434
458
58.7
62.4
66.5
70.8
75.4
84.8
45.1
45.6
46.1
46.5
46.9
47.7
5.73
5.73
5.71
5.69
5.65
5.58
6.52
6.33
6.14
5.94
5.76
5.40
60.1
61.8
63.4
64.8
66.2
68.6
5.39
4.89
4.30
3.69
3.48
2.92
Channel
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
COMBINATION SECTIONS
1 - 117
COMBINATION SECTIONS
Channels and angles
Properties of sections
Y
y
2
X
X
Long leg of angle turned out
y , yp
1
x1
xp
x2
Y
Axis Y-Y
S1 =
I / x1
I
3
3
r
x1
Z
xp
3
in.
in.
in.
in.
in.
in.
C12×20.7
L31⁄2×3 ×1⁄4
L31⁄2×3 ×5⁄16
L4 ×3 ×1⁄4
L4×3
×5⁄16
L5 ×31⁄2×5⁄16
L31⁄2×3 ×3⁄8
L6 ×4 ×3⁄8
L4×3
×1⁄2
9.5
10.7
11.6
13.2
19.9
22.5
33.2
40.6
2.5
2.8
2.7
3.2
40
4.6
5.8
7.3
3.7
4.0
4.4
4.8
6.8
7.5
10.3
11.9
1.12
1.16
1.22
1.27
1.52
1.57
1.85
1.93
3.84
3.77
4.28
4.20
5.02
4.93
5.72
5.52
5.45
5.94
5.94
6.56
8.06
8.97
11.1
13.7
3.69
3.67
4.18
4.16
5.15
5.13
6.10
6.05
C12×25
L31⁄2×3 ×1⁄4
L31⁄2×3 ×5⁄16
L4 ×3 ×1⁄4
L4×3
×5⁄16
L5 ×31⁄2×5⁄16
L31⁄2×3 ×3⁄8
L6 ×4 ×3⁄8
L4×3
×1⁄2
10.2
11.4
12.3
13.9
20.8
23.5
34.5
42.3
2.6
3.0
2.8
3.3
4.1
4.7
5.9
7.5
3.8
4.2
4.5
5.0
7.0
7.7
10.7
12.4
1.07
1.11
1.17
1.22
1.45
1.50
1.77
1.87
3.87
3.81
4.32
4.25
5.09
5.00
5.81
5.63
5.88
6.40
6.38
7.02
8.54
9.48
11.7
14.3
3.74
3.72
4.23
4.22
5.20
5.18
6.15
6.11
C15×33.9
L4 ×3 ×1⁄4
L4×3
×5⁄16
L5 ×31⁄2×5⁄16
L31⁄2×3 ×3⁄8
L6 ×4 ×3⁄8
L4×3
×1⁄2
16.8
18.7
26.2
29.3
41.3
50.3
3.7
4.2
4.9
5.6
6.8
8.5
5.8
6.3
8.5
9.2
12.4
14.3
1.20
1.25
1.45
1.50
1.75
1.85
4.49
4.43
5.30
5.23
6.06
5.89
8.82
9.47
11.0
12.0
14.2
16.9
4.27
4.26
5.24
5.23
6.21
6.17
Channel
Angle
in.
4
S2 =
I / x2
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1 - 118
DIMENSIONS AND PROPERTIES
COMBINATION SECTIONS
Channels and angles
Properties of sections
Y
y
2
X
X
y , yp
1
1
x1
xp
Short leg of angle turned out
2
x2
Y
Total
Weight
per ft
Total
Area
2
3
in.
S2 =
I / y2
3
in.
r
y1
Z
yp
3
in.
in.
in.
in.
L3×21⁄2×1⁄4
L3×3 ×1⁄4
L4×3 ×1⁄4
L5×3 ×5⁄16
L6×31⁄2×5⁄16
12.7
13.1
14.0
16.4
18.0
3.71
3.84
4.09
4.80
5.27
6.0
6.1
6.4
7.5
7.7
5.9
6.2
6.2
6.4
6.8
2.61
2.68
2.63
2.55
2.56
4.21
4.56
4.46
4.16
4.45
7.86
8.23
8.32
8.77
9.32
2.79
3.25
3.18
3.00
3.46
C 7×9.8
L3×21⁄2×1⁄4
L3×3 ×1⁄4
L4×3 ×1⁄4
L5×3 ×5⁄16
L6×31⁄2×5⁄16
14.3
14.7
15.6
18.0
19.6
4.18
4.31
4.56
5.27
5.74
8.0
8.0
8.5
10.0
10.3
7.8
8.2
8.2
8.5
8.9
3.00
3.07
3.03
2.95
2.96
4.70
5.05
4.93
4.60
4.87
10.5
10.9
1 1.0
11.6
12.2
2.95
3.38
3.29
3.11
3.50
C 8×11.5
L3×21⁄2×1⁄4
L3×3 ×1⁄4
L4×3 ×1⁄4
L5×3 ×5⁄16
L6×31⁄2×5⁄16
16.0
16.4
17.3
19.7
21.3
4.69
4.82
5.07
5.78
6.25
10.4
10.4
10.9
12.9
13.3
10.2
10.6
10.6
11.0
11.4
3.39
3.45
3.42
3.36
3.36
5.20
5.55
5.42
5.06
5.31
13.7
14.2
14.3
14.9
15.6
3.52
3.73
3.42
3.21
3.61
C 9×13.4
L3×21⁄2×1⁄4
L3×3 ×1⁄4
L4×3 ×1⁄4
L5×3 ×5⁄16
L6×31⁄2×5⁄16
17.9
18.3
19.2
21.6
23.2
5.25
5.38
5.63
6.34
6.81
13.1
13.1
13.8
16.2
16.7
12.9
13.4
13.5
13.9
14.4
3.78
3.84
3.81
3.76
3.77
5.71
6.07
5.93
5.54
5.78
17.4
18.0
18.3
19.0
19.7
4.18
4.42
3.88
3.32
3.71
C10×15.3
L3×21⁄2×1⁄4
L3×3 ×1⁄4
L4×3 ×1⁄4
L5×3 ×5⁄16
L6×31⁄2×5⁄16
19.8
20.2
21.1
23.5
25.1
5.80
5.93
6.18
6.89
7.36
16.2
16.1
17.0
19.9
20.5
16.0
16.5
16.6
17.1
17.7
4.17
4.22
4.20
4.17
4.18
6.22
6.58
6.43
6.02
6.25
21.4
22.1
22.5
23.5
24.2
4.77
5.01
4.48
3.44
3.81
C12×20.7
L3×21⁄2×1⁄4
L3×3 ×1⁄4
L4×3 ×1⁄4
L5×3 ×5⁄16
L6×31⁄2×5⁄16
25.2
25.6
26.5
28.9
30.5
7.40
7.53
7.78
8.49
8.96
24.3
24.0
25.3
29.2
30.1
24.7
25.3
25.5
26.3
27.1
4.90
4.95
4.95
4.94
4.97
7.32
7.69
7.54
7.11
7.33
32.6
33.4
34.3
36.4
37.5
6.17
6.45
6.01
4.74
4.41
C15×33.9
L3×3 ×1⁄4
L4×3 ×1⁄4
L5×3 ×5⁄16
L6×31⁄2×5⁄16
38.8
39.7
42.1
43.7
11.40
11.65
12.36
12.83
42.7
44.5
50.1
51.4
47.2
47.7
49.1
50.3
5.95
5.96
6.01
6.05
9.45
9.31
8.91
9.15
61.1
62.5
66.5
69.0
8.70
8.39
7.50
7.41
Angle
in.
S1 =
I / y1
C 6×8.2
Channel
lb
Axis X-X
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
COMBINATION SECTIONS
1 - 119
COMBINATION SECTIONS
Channels and angles
Properties of sections
Y
y
2
X
Short leg of angle turned out
X
y , yp
1
1
x1
xp
2
x2
Y
Axis Y-Y
S1 =
I / x1
r
x1
Z
xp
3
in.
in.
in.
in.
L3×21⁄2×1⁄4
L3×3 ×1⁄4
L4×3 ×1⁄4
L5×3 ×5⁄16
L6×31⁄2×5⁄16
2.4
2.8
3.8
6.0
8.4
4.4
4.6
6.6
9.3
12.1
1.22
1.26
1.64
2.05
2.47
2.25
2.18
2.85
3.33
3.82
3.70
4.01
5.46
8.29
11.3
2.65
2.59
3.46
4.12
4.84
C 7×9.8
L3×21⁄2×1⁄4
L3×3 ×1⁄4
L4×3 ×1⁄4
L5×3 ×5⁄16
L6×31⁄2×5⁄16
2.6
2.9
3.9
6.1
8.6
5.0
5.2
7.5
10.5
13.6
1.19
1.23
1.60
2.01
2.44
2.32
2.25
2.95
3.47
3.98
4.03
4.35
5.82
8.71
11.8
2.72
2.67
3.55
4.24
4.99
C 8×11.5
L3×21⁄2×1⁄4
L3×3 ×1⁄4
L4×3 ×1⁄4
L5×3 ×5⁄16
L6×31⁄2×5⁄16
2.7
3.0
4.0
6.3
8.7
5.6
5.8
8.3
11.7
15.2
1.16
1.20
1.55
1.97
2.40
2.37
2.31
3.03
3.58
4 13
4.40
4.73
6.21
9.16
12.3
2.78
2.73
3.62
4.34
5.12
C 9×13.4
L3×21⁄2×1⁄4
L3×3 ×1⁄4
L4×3 ×1⁄4
L5×3 ×5⁄16
L6×31⁄2×5⁄16
2.8
3.2
4.2
6.4
8.9
6.2
6.5
9.2
12.9
16.9
1.14
1.18
1.51
1.92
2.36
2.40
2.35
3.10
3.68
4.26
4.81
5.15
6.65
9.66
12.8
2.84
2.79
3.70
4.43
5.23
C10×15.3
L3×21⁄2×1⁄4
L3×3 ×1⁄4
L4×3 ×1⁄4
L5×3 ×5⁄16
L6×31⁄2×5⁄16
3.0
3.4
4.3
6.5
9.0
6.8
7.1
10.0
14.0
18.3
1.12
1.16
1.48
1.88
2.31
2.42
2.37
3.15
3.76
4.36
5.25
5.59
7.10
10.1
13.3
2.88
2.84
3.74
4.49
5.31
C12×20.7
L3×21⁄2×1⁄4
L3×3 ×1⁄4
L4×3 ×1⁄4
L5×3 ×5⁄16
L6×31⁄2×5⁄16
3.6
4.0
4.7
6.9
9.3
8.6
8.9
12.2
17.0
22.4
1.10
1.13
1.40
1.78
2 19
2.47
2.43
3.25
3.92
4.59
6.47
6.82
8.37
11.5
14.8
3.01
2.97
3.89
4.67
5.52
C15×33.9
L3×3 ×1⁄4
L4×3 ×1⁄4
L5×3 ×5⁄16
L6×31⁄2×5⁄16
5.6
5.9
7.8
10.2
13.5
17.2
23.4
30.7
1.10
1.30
1.61
1.97
2.48
3.35
4.12
4.88
9.54
11.1
14.5
18.0
3.12
4.11
5.02
5.90
Angle
in.
3
C 6×8.2
Channel
in.
3
S2 =
I / x2
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1 - 120
DIMENSIONS AND PROPERTIES
STEEL PIPE AND STRUCTURAL TUBING
General
When designing and specifying steel pipe or tubing as compression members, refer to
comments in the notes for Columns, Steel Pipe, and Structural Tubing, in Part 3. For
standard mill practices and tolerances, refer to page 1-183. For material specifications
and availability, see Tables 1-4 through 1-6, Part 1.
Steel Pipe
The Tables of Dimensions and Properties of Steel Pipe (unfilled) list a selected range of
sizes of standard, extra strong, and double-extra strong pipe. For a complete range of
sizes manufactured, refer to catalogs of the manufacturers or to the American Institute
for Hollow Structural Sections (AIHSS).
Structural Tubing
The Tables of Dimensions and Properties of Square and Rectangular Structural Tubing
(unfilled) list a selected range of frequently used sizes. For dimensions and properties of
other sizes, refer to catalogs from the manufacturers or AIHSS.
The tables are based on an outside corner radius equal to two times the specified wall
thickness. Material specifications stipulate that the outside corner radius may vary up to
three times the specified wall thickness. This variation should be considered in those
details where a close match or fit is important.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
STEEL PIPE AND STRUCTURAL TUBING
1 - 121
PIPE
Dimensions and properties
Dimensions
Weight
Nominal Outside
Inside
Wall
per ft lbs
Diameter Diameter Diameter Thickness Plain
Ends
in.
in.
in.
in.
Properties
Area
I
S
r
J
Z
in.2
in.4
in.3
in.
in.4
in.3
0.041
0.071
0.133
0.235
0.326
0.561
1.06
1.72
2.39
3.21
5.45
8.50
16.8
29.9
43.8
0.261
0.334
0.421
0.540
0.623
0.787
0.947
1.16
1.34
1.51
1.88
2.25
2.94
3.67
4.38
0.034
0.074
0.175
0.389
0.620
1.33
3.06
6.03
9.58
14.5
30.3
56.3
145
321
559
0.059
0.100
0.187
0.324
0.448
0.761
1.45
2.33
3.22
4.31
7.27
11.2
22.2
39.4
57.4
0.048
0.085
0.161
0.291
0.412
0.731
1.34
2.23
3.14
4.27
7.43
12.2
24.5
39.4
56.7
0.250
0.321
0.407
0.524
0.605
0.766
0.924
1.14
1.31
1.48
1.84
2.19
2.88
3.63
4.33
0.040
0.090
0.211
0.484
0.782
1.74
3.85
8.13
12.6
19.2
41.3
81.0
211
424
723
0.072
0.125
0.233
0.414
0.581
1.02
1.87
3.08
4.32
5.85
10.1
16.6
33.0
52.6
75.1
1.10
2.00
3.42
6.79
12.1
20.0
37.6
0.703
0.844
1.05
1.37
1.72
2.06
2.76
2.62
5.74
12.0
30.6
67.3
133
324
1.67
3.04
5.12
9.97
17.5
28.9
52.8
Standard Weight
1⁄
2
3⁄
4
0.840
1.050
1.315
1.660
1.900
2.375
2.875
3.500
4.000
4.500
5.563
6.625
8.625
10.750
12.750
0.622
0.824
1.049
1.380
1.610
2.067
2.469
3.068
3.548
4.026
5.047
6.065
7.981
10.020
12.000
0.109
0.113
0.133
0.140
0.145
0.154
0.203
0.216
0.226
0.237
0.258
0.280
0.322
0.365
0.375
0.85
1.13
1.68
2.27
2.72
3.65
5.79
7.58
9.11
10.79
14.62
18.97
28.55
40.48
49.56
1
11⁄4
11⁄2
2
21⁄2
3
31⁄2
4
5
6
8
10
12
0.840
1.050
1.315
1.660
1.900
2.375
2.875
3.500
4.000
4.500
5.563
6.625
8.625
10.750
12.750
0.546
0.742
0.957
1.278
1.500
1.939
2.323
2.900
3.364
3.826
4.813
5.761
7.625
9.750
11.750
0.147
0.154
0.179
0.191
0.200
0.218
0.276
0.300
0.318
0.337
0.375
0.432
0.500
0.500
0.500
1.09
1.47
2.17
3.00
3.63
5.02
7.66
10.25
12.50
14.98
20.78
28.57
43.39
54.74
65.42
2
21⁄2
3
4
5
6
8
2.375
2.875
3.500
4.500
5.563
6.625
8.625
1.503
1.771
2.300
3.152
4.063
4.897
6.875
0.436
0.552
0.600
0.674
0.750
0.864
0.875
1
11⁄4
11⁄2
2
21⁄2
3
31⁄2
4
5
6
8
10
12
0.250
0.333
0.494
0.669
0.799
1.07
1.70
2.23
2.68
3.17
4.30
5.58
8.40
11.9
14.6
0.017
0.037
0.087
0.195
0.310
0.666
1.53
3.02
4.79
7.23
15.2
28.1
72.5
161
279
Extra Strong
1⁄
2
3⁄
4
0.320
0.433
0.639
0.881
1.07
1.48
2.25
3.02
3.68
4.41
6.11
8.40
12.8
16.1
19.2
0.020
0.045
0.106
0.242
0.391
0.868
1.92
3.89
6.28
9.61
20.7
40.5
106
212
362
Double-Extra Strong
9.03
13.69
18.58
27.54
38.59
53.16
72.42
2.66
4.03
5.47
8.10
11.3
15.6
21.3
1.31
2.87
5.99
15.3
33.6
66.3
162
The listed sections are available in conformance with ASTM Specification A53 Grade B or A501. Other sections
are made to these specifications. Consult with pipe manufacturers or distributors for availability.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1 - 122
DIMENSIONS AND PROPERTIES
STRUCTURAL TUBING
Square
Dimensions and properties
Dimensions
Properties**
Nominal*
Size
Wall
Thickness
Weight
per ft
Area
I
S
r
J
Z
in.
in.
lb
in.2
in.4
in.3
in.
in.4
in.3
0.6250
5⁄
8
246.47
72.4
10300
690
12.0
16000
794
28×28
0.6250
5⁄
8
229.45
67.4
8360
597
11.1
13000
689
26×26
0.6250
5⁄
8
212.44
62.4
6650
511
10.3
10400
591
24×24
24×24
24×24
0.6250
0.5000
0.3750
5⁄
8
1⁄
2
3⁄
8
195.43
157.74
119.35
57.4
46.4
35.1
5180
4240
3250
432
353
270
9.50
9.56
9.62
8100
6570
4990
500
407
310
22×22
22×22
22×22
0.6250
0.5000
0.3750
5⁄
8
1⁄
2
3⁄
8
178.41
144.13
109.15
52.4
42.4
32.1
3950
3240
2490
359
294
226
8.68
8.74
8.80
6200
5030
3830
418
340
259
20×20
20×20
20×20
0.6250
0.5000
0.3750
5⁄
8
1⁄
2
3⁄
8
161.40
130.52
98.94
47.4
38.4
29.1
2940
2410
1850
294
241
185
7.87
7.93
7.99
4620
3760
2870
342
279
213
18×18
18×18
18×18
0.6250
0.5000
0.3750
5⁄
8
1⁄
2
3⁄
8
144.39
116.91
88.73
42.4
34.4
26.1
2110
1740
1340
234
193
149
7.05
7.11
7.17
3340
2720
2080
274
224
172
30×30
*Outside dimensions across flat sides.
**Properties are based upon a nominal outside corner radius equal to two times the wall thickness.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
STEEL PIPE AND STRUCTURAL TUBING
1 - 123
STRUCTURAL TUBING
Square
Dimensions and properties
Dimensions
Properties**
Nominal*
Size
Wall
Thickness
Weight
per ft
Area
I
S
r
J
Z
in.
in.
lb
in.2
in.4
in.3
in.
in.4
in.3
127.37
103.30
78.52
65.87
37.4
30.4
23.1
19.4
1450
1200
931
789
182
150
116
98.6
6.23
6.29
6.35
6.38
2320
1890
1450
1220
214
175
134
113
110.36
89.68
68.31
57.36
32.4
26.4
20.1
16.9
952
791
615
522
136
113
87.9
74.6
5.42
5.48
5.54
5.57
1530
1250
963
812
161
132
102
86.1
93.34
76.07
58.10
48.86
39.43
27.4
22.4
17.1
14.4
11.6
580
485
380
324
265
96.7
80.9
63.4
54.0
44.1
4.60
4.66
4.72
4.75
4.78
943
777
599
506
410
116
95.4
73.9
62.6
50.8
76.33
62.46
47.90
40.35
32.63
24.73
22.4
18.4
14.1
11.9
9.59
7.27
321
271
214
183
151
116
64.2
54.2
42.9
36.7
30.1
23.2
3.78
3.84
3.90
3.93
3.96
3.99
529
439
341
289
235
179
77.6
64.6
50.4
42.8
34.9
26.6
16×16
14×14
12×12
10×10
0.6250
0.5000
0.3750
0.3125
0.6250
0.5000
0.3750
0.3125
0.6250
0.5000
0.3750
0.3125
0.2500
0.6250
0.5000
0.3750
0.3125
0.2500
0.1875
5⁄
1⁄
3⁄
8
2
8
5⁄
16
5⁄
1⁄
8
2
3⁄
8
5⁄
16
5⁄
1⁄
8
2
3⁄
8
5⁄
16
1⁄
4
5⁄
1⁄
3⁄
8
2
8
5⁄
16
1⁄
4
3⁄
16
*Outside dimensions across flat sides.
**Properties are based upon a nominal outside corner radius equal to two times the wall thickness.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1 - 124
DIMENSIONS AND PROPERTIES
STRUCTURAL TUBING
Square
Dimensions and properties
Dimensions
Properties**
Nominal*
Size
Wall
Thickness
Weight
per ft
Area
I
S
r
J
Z
in.
in.
lb
in.2
in.4
in.3
in.
in.4
in.3
8×8
0.6250
0.5000
0.3750
0.3125
0.2500
0.1875
5⁄
8
1⁄
2
3⁄
8
5⁄
16
1⁄
4
3⁄
16
59.32
48.85
37.69
31.84
25.82
19.63
17.4
14.4
11.1
9.36
7.59
5.77
153
131
106
90.9
75.1
58.2
38.3
32.9
26.4
22.7
18.8
14.6
2.96
3.03
3.09
3.12
3.15
3.18
258
217
170
145
118
90.6
47.2
39.7
31.3
26.7
21.9
16.8
7×7
0.6250
0.5000
0.3750
0.3125
0.2500
0.1875
5⁄
8
1⁄
2
3⁄
8
5⁄
16
1⁄
4
3⁄
16
50.81
42.05
32.58
27.59
22.42
17.08
14.9
12.4
9.58
8.11
6.59
5.02
97.5
84.6
68.7
59.5
49.4
38.5
27.9
24.2
19.6
17.0
14.1
11.0
2.56
2.62
2.68
2.71
2.74
2.77
166
141
112
95.6
78.3
60.2
34.8
29.6
23.5
20.1
16.5
12.7
6×6
0.6250
0.5000
0.3750
0.3125
0.2500
0.1875
0.1250
5⁄
8
1⁄
2
3⁄
8
5⁄
16
1⁄
4
3⁄
16
1⁄
8
42.30
35.24
27.48
23.34
19.02
14.53
9.86
12.4
10.4
8.08
6.86
5.59
4.27
2.90
57.3
50.5
41.6
36.3
30.3
23.8
16.5
19.1
16.8
13.9
12.1
10.1
7.93
5.52
2.15
2.21
2.27
2.30
2.33
2.36
2.39
99.5
85.6
68.5
58.9
48.5
37.5
25.7
24.3
20.9
16.8
14.4
11.9
9.24
6.35
51⁄2×51⁄2
0.3750
0.3125
0.2500
0.1875
0.1250
3⁄
8
5⁄
16
1⁄
4
3⁄
16
1⁄
8
24.93
21.21
17.32
13.25
9.01
7.33
6.23
5.09
3.89
2.65
31.2
27.4
23.0
18.1
12.6
11.4
9.95
8.36
6.58
4.60
2.07
2.10
2.13
2.16
2.19
51.9
44.8
37.0
28.6
19.7
13.8
12.0
9.91
7.70
5.31
5×5
0.5000
0.3750
0.3125
0.2500
0.1875
0.1250
1⁄
2
3⁄
8
5⁄
16
1⁄
4
3⁄
16
1⁄
8
28.43
22.37
19.08
15.62
11.97
8.16
8.36
6.58
5.61
4.59
3.52
2.40
27.0
22.8
20.1
16.9
13.4
9.41
10.8
9.11
8.02
6.78
5.36
3.77
1.80
1.86
1.89
1.92
1.95
1.98
46.8
38.2
33.1
27.4
21.3
14.7
13.7
11.2
9.70
8.07
6.29
4.36
*Outside dimensions across flat sides.
**Properties are based upon a nominal outside corner radius equal to two times the wall thickness.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
STEEL PIPE AND STRUCTURAL TUBING
1 - 125
STRUCTURAL TUBING
Square
Dimensions and properties
Dimensions
Properties**
Nominal*
Size
Wall
Thickness
Weight
per ft
Area
I
S
r
J
Z
in.
in.
lb
in.2
in.4
in.3
in.
in.4
in.3
41⁄2×41⁄2
0.3750
0.3125
0.2500
0.1875
0.1250
3⁄
8
5⁄
16
1⁄
4
3⁄
16
1⁄
8
19.82
16.96
13.91
10.70
7.31
5.83
4.98
4.09
3.14
2.15
16.0
14.2
12.1
9.60
6.78
7.10
6.30
5.36
4.27
3.02
1.66
1.69
1.72
1.75
1.78
27.1
23.6
19.7
15.4
10.6
8.81
7.68
6.43
5.03
3.50
4×4
0.5000
0.3750
0.3125
0.2500
0.1875
0.1250
1⁄
5⁄
16
1⁄
4
3⁄
16
1⁄
8
21.63
17.27
14.83
12.21
9.42
6.46
6.36
5.08
4.36
3.59
2.77
1.90
12.3
10.7
9.58
8.22
6.59
4.70
6.13
5.35
4.79
4.11
3.30
2.35
1.39
1.45
1.48
1.51
1.54
1.57
21.8
18.4
16.1
13.5
10.6
7.40
8.02
6.72
5.90
4.97
3.91
2.74
31⁄2×31⁄2
0.3125
0.2500
0.1875
0.1250
5⁄
16
1⁄
4
3⁄
16
1⁄
8
12.70
10.51
8.15
5.61
3.73
3.09
2.39
1.65
6.09
5.29
4.29
3.09
3.48
3.02
2.45
1.76
1.28
1.31
1.34
1.37
10.4
8.82
6.99
4.90
4.35
3.69
2.93
2.07
3×3
0.3125
0.2500
0.1875
0.1250
5⁄
16
1⁄
4
3⁄
16
1⁄
8
10.58
8.81
6.87
4.75
3.11
2.59
2.02
1.40
3.58
3.16
2.60
1.90
2.39
2.10
1.73
1.26
1.07
1.10
1.13
1.16
6.22
5.35
4.28
3.03
3.04
2.61
2.10
1.49
21⁄2×21⁄2
0.3125
0.2500
0.1875
0.1250
5⁄
16
1⁄
4
3⁄
16
1⁄
8
8.45
7.11
5.59
3.90
2.48
2.09
1.64
1.15
1.87
1.69
1.42
1.06
1.50
1.35
1.14
0.847
0.868
0.899
0.930
0.961
3.32
2.92
2.38
1.71
1.96
1.71
1.40
1.01
2×2
0.3125
0.2500
0.1875
0.1250
5⁄
16
1⁄
4
3⁄
16
1⁄
8
6.32
5.41
4.32
3.05
1.86
1.59
1.27
0.897
0.815
0.766
0.668
0.513
0.815
0.766
0.668
0.513
0.662
0.694
0.726
0.756
1.49
1.36
1.15
0.846
1.11
1.00
0.840
0.621
11⁄2×11⁄2
0.1875
3⁄
16
3.04
0.894
0.242
0.323
0.521
0.431
0.423
3⁄
2
8
*Outside dimensions across flat sides.
**Properties are based upon a nominal outside corner radius equal to two times the wall thickness.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1 - 126
DIMENSIONS AND PROPERTIES
Y
X
X
STRUCTURAL TUBING
Rectangular
Dimensions and properties
Y
Dimensions
Properties**
Nominal*
Wall
Weight
Size
Thickness per ft Area
in.
in.
2
X-X Axis
S
I
4
Z
3
Y-Y Axis
r
3
S
I
4
Z
3
3
r
J
lb
in.
in.
in.
in.
in.
in.
in.
in.
in.
in.4
178.16
134.67
112.66
52.4
39.6
33.1
7110 474
5430 362
4570 305
555
422
354
11.7
11.7
11.7
5070
3870
3260
422
323
272
477
363
304
9.84
9.89
9.92
9170
6960
5830
30×24
0.5000
0.3750
0.3125
1⁄
2
3⁄
8
5⁄
16
28×24
0.5000
0.3750
0.3125
1⁄
2
3⁄
8
5⁄
16
171.35
129.56
108.41
50.4
38.1
31.9
6050 432
4630 331
3890 278
503
383
321
11.0
11.0
11.1
4790
3660
3080
399
305
257
454
345
290
9.75
9.81
9.84
8280
6290
5270
26×24
0.5000
0.3750
0.3125
1⁄
2
3⁄
8
5⁄
16
164.55
124.46
104.15
48.4
36.6
30.6
5100 392
3900 300
3280 253
454
345
290
10.3
10.3
10.4
4510
3460
2910
376
288
242
430
327
275
9.66
9.72
9.75
7410
5630
4720
24×22
0.5000
0.3750
0.3125
1⁄
2
3⁄
8
5⁄
16
150.93
114.25
95.64
44.4
33.6
28.1
3960 330
3040 253
2560 213
383
292
245
9.45 3470
9.51 2660
9.54 2240
315
242
204
361
275
231
8.84
8.90
8.93
5740
4370
3660
22×20
0.5000
0.3750
0.3125
1⁄
2
3⁄
8
5⁄
16
137.32
104.04
87.14
40.4
30.6
25.6
3010 273
2310 210
1950 177
318
243
204
8.63 2600
8.69 2000
8.72 1690
260
200
169
298
228
192
8.03
8.09
8.12
4350
3310
2780
20×18
0.5000
0.3750
0.3125
1⁄
2
3⁄
8
5⁄
16
123.71
93.83
78.63
36.4
27.6
23.1
2220 222
1710 171
1440 144
259
198
167
7.81 1890
7.88 1460
7.91 1230
210
162
137
242
185
155
7.21
7.27
7.30
3190
2440
2050
20×12
0.5000
0.3750
0.3125
1⁄
2
3⁄
8
5⁄
16
103.30
78.52
65.87
30.4
23.1
19.4
1650 165
1280 128
1080 108
201
154
130
7.37
7.45
7.47
750
583
495
125
141
97.2 109
82.5 91.8
4.97
5.03
5.06
1650
1270
1070
20×8
0.5000
0.3750
0.3125
1⁄
2
3⁄
8
5⁄
16
89.68
68.31
57.36
26.4
20.1
16.9
1270 127
162
988 98.8 125
838 83.8 105
6.94
7.02
7.05
300
236
202
20×4
0.5000
0.3750
0.3125
1⁄
2
3⁄
8
5⁄
16
76.07
58.10
48.86
22.4
17.1
14.4
889
699
596
88.9 123
69.9 95.3
59.6 80.8
6.31
6.40
6.44
61.6
50.3
43.7
75.1
59.1
50.4
84.7
65.6
55.6
3.38
3.43
3.46
806
625
529
30.8
25.1
21.8
36.0
28.5
24.3
1.66
1.72
1.74
205
165
143
*Outside dimensions across flat sides.
**Properties are based upon a nominal outside corner radius equal to two times the wall thickness.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
STEEL PIPE AND STRUCTURAL TUBING
1 - 127
STRUCTURAL TUBING
Rectangular
Dimensions and properties
Y
X
X
Y
Dimensions
Properties**
Nominal*
Wall
Weight
Size
Thickness per ft Area
in.
in.
lb
in.2
X-X Axis
Y-Y Axis
I
S
Z
r
I
S
Z
r
J
in.4
in.3
in.3
in.
in.4
in.3
in.3
in.
in.4
6.71
6.78
6.81
684
533
452
114
130
88.8 100
75.3 84.5
4.91
4.97
5.00
1420
1090
920
53.9
42.1
35.8
29.2
2.52
2.57
2.60
2.63
410
322
274
224
103
118
80.3 91.3
68.2 77.2
4.84
4.90
4.93
1200
922
777
18×12
0.5000
0.3750
0.3125
1⁄
2
3⁄
8
5⁄
16
96.49
73.42
61.62
28.4
21.6
18.1
18×6
0.5000
0.3750
0.3125
0.2500
1⁄
2
3⁄
8
5⁄
16
1⁄
4
76.07
58.10
48.86
39.43
22.4
17.1
14.4
11.6
818
641
546
447
90.9 119
71.3 92.2
60.7 78.1
49.6 63.5
6.05
6.13
6.17
6.21
141
113
97.0
80.0
16×12
0.5000
0.3750
0.3125
1⁄
2
3⁄
8
5⁄
16
89.68
68.31
57.36
26.4
20.1
16.9
962
748
635
120 144
93.5 111
79.4 93.8
6.04
6.11
6.14
618
482
409
16×8
0.5000
0.3750
0.3125
1⁄
2
3⁄
8
5⁄
16
76.07
58.10
48.86
22.4
17.1
14.4
722
565
481
90.2 113
70.6 87.6
60.1 74.2
5.68
5.75
5.79
244
193
165
16×4
0.5000
0.3750
0.3125
1⁄
2
3⁄
8
5⁄
16
62.46
47.90
40.35
18.4
14.1
11.9
481
382
327
60.2
47.8
40.9
82.2
64.2
54.5
5.12
5.21
5.25
14×12
0.5000
0.3750
1⁄
2
3⁄
8
82.88
63.21
24.4
18.6
699
546
99.9 119
78.0 91.7
5.36
5.42
14×10
0.5000
0.3750
0.3125
1⁄
2
3⁄
8
5⁄
16
76.07
58.10
48.86
22.4
17.1
14.4
608
476
405
86.9 105
68.0 81.5
57.9 69.0
14×6
0.6250
0.5000
0.3750
0.3125
0.2500
5⁄
8
1⁄
2
3⁄
8
5⁄
16
1⁄
4
76.33
62.46
47.90
40.35
32.63
22.4
18.4
14.1
11.9
9.59
504
426
337
288
237
72.0
60.8
48.1
41.2
33.8
1280 142
172
991 110
132
840 93.3 111
94.0
78.3
61.1
51.9
42.3
47.2
37.6
32.3
26.7
61.0
48.2
41.2
69.7
54.2
45.9
3.30
3.36
3.39
599
465
394
24.6
20.2
17.6
29.0
23.0
19.7
1.64
1.69
1.72
157
127
110
552
431
91.9 107
71.9 82.6
4.76
4.82
983
757
5.22
5.28
5.31
361
284
242
72.3
56.8
48.4
83.6
64.8
54.9
4.02
4.08
4.11
730
564
477
4.74
4.82
4.89
4.93
4.97
130
111
89.1
76.7
63.4
43.3
37.1
29.7
25.6
21.1
51.2
42.9
33.6
28.7
23.4
2.41
2.46
2.52
2.54
2.57
352
296
233
199
162
49.3
40.4
35.1
*Outside dimensions across flat sides.
**Properties are based upon a nominal outside corner radius equal to two times the wall thickness.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1 - 128
DIMENSIONS AND PROPERTIES
Y
X
X
STRUCTURAL TUBING
Rectangular
Dimensions and properties
Y
Dimensions
Properties**
Nominal*
Wall
Weight
Size
Thickness per ft Area
in.
in.
lb
in.2
X-X Axis
Y-Y Axis
I
S
Z
r
I
S
Z
r
J
in.4
in.3
in.3
in.
in.4
in.3
in.3
in.
in.4
49.0
43.1
35.4
30.9
25.8
20.2
24.5
21.5
17.7
15.4
12.9
10.1
30.0
25.5
20.3
17.4
14.3
11.1
1.57
1.62
1.68
1.71
1.73
1.76
154
134
108
93.1
77.0
59.7
14×4
0.6250
0.5000
0.3750
0.3125
0.2500
0.1875
5⁄
8
1⁄
2
3⁄
8
5⁄
16
1⁄
4
3⁄
16
67.82
55.66
42.79
36.10
29.23
22.18
19.9
16.4
12.6
10.6
8.59
6.52
392
335
267
230
189
146
56.0
47.8
38.2
32.8
27.0
20.9
77.3
64.8
50.8
43.3
35.4
27.1
4.44
4.52
4.61
4.65
4.69
4.74
12×10
0.5000
0.3750
0.3125
0.2500
1⁄
2
3⁄
8
5⁄
16
1⁄
4
69.27
53.00
44.60
36.03
20.4
15.6
13.1
10.6
419
330
281
230
69.9
55.0
46.9
38.4
83.9
65.2
55.2
44.9
4.54
4.60
4.63
4.66
316
249
213
174
63.3
49.8
42.6
34.9
74.1
57.6
48.8
39.7
3.94
4.00
4.03
4.06
581
450
381
309
12×8
0.6250
0.5000
0.3750
0.3125
0.2500
0.1875
5⁄
8
1⁄
2
3⁄
8
5⁄
16
1⁄
4
3⁄
16
76.33
62.46
47.90
40.35
32.63
24.73
22.4
18.4
14.1
11.9
9.59
7.27
418
353
279
239
196
151
69.7
58.9
46.5
39.8
32.6
25.1
87.1
72.4
56.5
47.9
39.1
29.8
4.32
4.39
4.45
4.49
4.52
4.55
221
188
149
128
105
81.1
55.3
46.9
37.3
32.0
26.3
20.3
65.6
54.7
42.7
36.3
29.6
22.7
3.14
3.20
3.26
3.28
3.31
3.34
481
401
312
265
216
165
12×6
0.6250
0.5000
0.3750
0.3125
0.2500
0.1875
5⁄
8
1⁄
2
3⁄
8
5⁄
16
1⁄
4
3⁄
16
67.82
55.66
42.79
36.10
29.23
22.18
19.9
16.4
12.6
10.6
8.59
6.52
337
287
228
196
161
124
56.2
47.8
38.1
32.6
26.9
20.7
72.9
60.9
47.7
40.6
33.2
25.4
4.11
4.19
4.26
4.30
4.33
4.37
112
96.0
77.2
66.6
55.2
42.8
37.2
32.0
25.7
22.2
18.4
14.3
44.5
37.4
29.4
25.1
20.6
15.8
2.37
2.42
2.48
2.51
2.53
2.56
286
241
190
162
132
101
12×4
0.6250
0.5000
0.3750
0.3125
0.2500
0.1875
5⁄
8
1⁄
2
3⁄
8
5⁄
16
1⁄
4
3⁄
16
59.32
48.85
37.69
31.84
25.82
19.63
17.4
14.4
11.1
9.36
7.59
5.77
257
221
178
153
127
98.2
42.8
36.8
29.6
25.5
21.1
16.4
58.6
49.4
39.0
33.3
27.3
21.0
3.84
3.92
4.01
4.05
4.09
4.13
41.8
36.9
30.5
26.6
22.3
17.5
20.9
18.5
15.2
13.3
11.1
8.75
25.8
22.0
17.6
15.1
12.5
9.63
1.55
1.60
1.66
1.69
1.71
1.74
127
110
89.0
76.9
63.6
49.3
12×3
0.3125
0.2500
0.1875
5⁄
16
1⁄
4
3⁄
16
29.72
24.12
18.35
8.73 132
7.09 109
5.39 85.1
22.0
18.2
14.2
29.7
24.4
18.8
3.89
3.93
3.97
13.8
11.7
9.28
9.19 10.6
7.79 8.80
6.19 6.84
1.26
1.28
1.31
43.6
36.5
28.7
*Outside dimensions across flat sides.
**Properties are based upon a nominal outside corner radius equal to two times the wall thickness.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
STEEL PIPE AND STRUCTURAL TUBING
1 - 129
STRUCTURAL TUBING
Rectangular
Dimensions and properties
Y
X
X
Y
Dimensions
Properties**
Nominal*
Wall
Weight
Size
Thickness per ft Area
in.
in.
X-X Axis
Y-Y Axis
I
S
Z
r
I
S
Z
r
J
lb
in.2
in.4
in.3
in.3
in.
in.4
in.3
in.3
in.
in.4
92.2 15.4
72.0 12.0
21.4
16.6
3.74
3.79
12×2
0.2500
0.1875
1⁄
4
3⁄
16
22.42
17.08
6.59
5.02
10×8
0.5000
0.3750
0.3125
0.2500
0.1875
1⁄
2
3⁄
8
5⁄
16
1⁄
4
3⁄
16
55.66
42.79
36.10
29.23
22.18
16.4
12.6
10.6
8.59
6.52
226
180
154
127
97.9
45.2
35.9
30.8
25.4
19.6
55.1
43.1
36.7
30.0
23.0
3.72
3.78
3.81
3.84
3.87
160
127
109
90.2
69.7
39.9
31.8
27.3
22.5
17.4
47.2
37.0
31.5
25.8
19.7
3.12
3.18
3.21
3.24
3.27
306
239
203
166
127
10×6
0.5000
0.3750
0.3125
0.2500
0.1875
1⁄
2
3⁄
8
5⁄
16
1⁄
4
3⁄
16
48.85
37.69
31.84
25.82
19.63
14.4
11.1
9.36
7.59
5.77
181
145
125
103
79.8
36.2
29.0
25.0
20.6
16.0
45.6
35.9
30.7
25.1
19.3
3.55
3.62
3.65
3.69
3.72
80.8
65.4
56.5
46.9
36.5
26.9
21.8
18.8
15.6
12.2
31.9
25.2
21.5
17.7
13.6
2.37
2.43
2.46
2.49
2.51
187
147
126
103
79.1
10×5
0.3750
0.3125
0.2500
0.1875
3⁄
8
5⁄
16
1⁄
4
3⁄
16
35.13
29.72
24.12
18.35
10.3 128
8.73 110
7.09 91.2
5.39 70.8
25.5
22.0
18.2
14.2
32.3
27.6
22.7
17.4
3.51
3.55
3.59
3.62
42.9
37.2
31.1
24.3
17.1
14.9
12.4
9.71
19.9
17.0
14.0
10.8
2.04
2.07
2.09
2.12
107
91.5
75.2
58.0
10×4
0.5000
0.3750
0.3125
0.2500
0.1875
1⁄
2
3⁄
8
5⁄
16
1⁄
4
3⁄
16
42.05
32.58
27.59
22.42
17.08
12.4 136
9.58 110
8.11 95.5
6.59 79.3
5.02 61.7
27.1
22.0
19.1
15.9
12.3
36.1
28.7
24.6
20.2
15.6
3.31
3.39
3.43
3.47
3.51
30.8
25.5
22.4
18.8
14.8
15.4
12.8
11.2
9.39
7.39
18.5
14.9
12.8
10.6
8.20
1.58
1.63
1.66
1.69
1.72
86.9
70.4
60.8
50.4
39.1
10×3
0.3750
0.3125
0.2500
0.1875
3⁄
8
5⁄
16
1⁄
4
3⁄
16
30.0
25.5
20.72
15.80
8.83
7.48
6.09
4.64
92.8
80.8
67.4
52.7
18.6
16.2
13.5
10.5
25.1
21.6
17.8
13.8
3.24
3.29
3.33
3.37
13.0
11.5
9.79
7.80
8.66 10.3
7.68 8.92
6.53 7.42
5.20 5.79
1.21
1.24
1.27
1.30
39.8
34.9
29.3
23.0
10×2
0.3750
0.3125
0.2500
0.1875
3⁄
8
5⁄
16
1⁄
4
3⁄
16
27.48
23.34
19.02
14.53
8.08
6.86
5.59
4.27
75.4 15.1
66.1 13.2
55.5 11.1
43.7 8.74
21.5
18.5
15.4
11.9
3.06
3.10
3.15
3.20
4.85
4.42
3.85
3.14
4.85
4.42
3.85
3.14
0.775
0.802
0.830
0.858
16.5
14.9
12.8
10.3
4.62
3.76
4.62
3.76
5.38 0.837
4.24 0.865
6.05
5.33
4.50
3.56
*Outside dimensions across flat sides.
**Properties are based upon a nominal outside corner radius equal to two times the wall thickness.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
15.9
12.8
1 - 130
DIMENSIONS AND PROPERTIES
Y
X
X
STRUCTURAL TUBING
Rectangular
Dimensions and properties
Y
Dimensions
Properties**
Nominal*
Wall
Weight
Size
Thickness per ft Area
in.
in.
lb
in.2
X-X Axis
Y-Y Axis
I
S
Z
r
I
S
Z
r
J
in.4
in.3
in.3
in.
in.4
in.3
in.3
in.
in.4
8×6
0.5000
0.3750
0.3125
0.2500
0.1875
1⁄
2
3⁄
8
5⁄
16
1⁄
4
3⁄
16
42.05
32.58
27.59
22.42
17.08
12.4 103
9.58 83.7
8.11 72.4
6.59 60.1
5.02 46.8
25.8
20.9
18.1
15.0
11.7
32.2
25.6
21.9
18.0
13.9
2.89
2.96
2.99
3.02
3.05
65.7
53.5
46.4
38.6
30.1
21.9
17.8
15.5
12.9
10.0
26.4
21.0
18.0
14.8
11.4
2.31
2.36
2.39
2.42
2.45
135
107
91.3
74.9
57.6
8×4
0.6250
0.5000
0.3750
0.3125
0.2500
0.1875
0.1250
5⁄
8
1⁄
2
3⁄
8
5⁄
16
1⁄
4
3⁄
16
1⁄
8
42.30
35.24
27.48
23.34
19.02
14.53
9.86
12.4
10.4
8.08
6.86
5.59
4.27
2.90
21.3
18.8
15.5
13.5
11.3
8.83
6.14
28.8
24.7
19.9
17.1
14.1
11.0
7.53
2.62
2.69
2.77
2.80
2.84
2.88
2.91
27.4
24.6
20.6
18.1
15.3
12.0
8.45
13.7
12.3
10.3
9.05
7.63
6.02
4.23
17.3
15.0
12.2
10.5
8.72
6.77
4.67
1.49
1.54
1.60
1.62
1.65
1.68
1.71
73.2
64.1
52.2
45.2
37.5
29.1
20.0
8×3
0.5000
0.3750
0.3125
0.2500
0.1875
0.1250
1⁄
2
3⁄
8
5⁄
16
1⁄
4
3⁄
16
1⁄
8
31.84
24.93
21.21
17.32
13.25
9.01
9.36
7.33
6.23
5.09
3.89
2.65
61.0 15.3
51.0 12.7
44.7 11.2
37.6 9.40
29.6 7.40
20.7 5.17
21.0
17.0
14.7
12.2
9.49
6.55
2.55
2.64
2.68
2.72
2.76
2.80
12.1
10.4
9.25
7.90
6.31
4.48
8.05 10.1
6.92 8.31
6.16 7.24
5.26 6.05
4.21 4.73
2.99 3.29
1.14
1.19
1.22
1.25
1.27
1.30
35.7
29.9
26.3
22.1
17.3
12.1
8×2
0.3750
0.3125
0.2500
0.1875
0.1250
3⁄
8
5⁄
16
1⁄
4
3⁄
16
1⁄
8
22.37
19.08
15.62
11.97
8.16
6.58
5.61
4.59
3.52
2.40
40.1 10.0 14.2
35.5 8.87 12.3
30.1 7.52 10.3
23.9 5.97 8.02
16.8 4.20 5.56
2.47
2.51
2.56
2.60
2.65
3.85
3.52
3.08
2.52
1.83
3.85
3.52
3.08
2.52
1.83
4.83
4.28
3.63
2.88
2.03
0.765
0.792
0.819
0.847
0.875
12.6
11.4
9.84
7.94
5.66
7×5
0.5000
0.3750
0.3125
0.2500
0.1875
0.1250
1⁄
2
3⁄
8
5⁄
16
1⁄
4
3⁄
16
1⁄
8
35.24
27.48
23.34
19.02
14.53
9.86
10.4
8.08
6.86
5.59
4.27
2.90
63.5
52.2
45.5
38.0
29.8
20.7
23.1
18.5
15.9
13.2
10.2
7.00
2.48
2.54
2.58
2.61
2.64
2.67
37.2
30.8
26.9
22.6
17.7
12.4
14.9
12.3
10.8
9.04
7.10
4.95
18.2
14.6
12.6
10.4
8.10
5.58
1.90
1.95
1.98
2.01
2.04
2.07
79.9
64.2
55.3
45.6
35.3
24.2
7×4
0.3750
0.3125
0.2500
0.1875
0.1250
3⁄
8
5⁄
16
1⁄
4
3⁄
16
1⁄
8
24.93
21.21
17.32
13.25
9.01
7.33
6.23
5.09
3.89
2.65
44.0 12.6 16.0
38.5 11.0 13.8
32.3 9.23 11.5
25.4 7.26 8.91
17.7 5.07 6.15
2.45
2.49
2.52
2.55
2.59
18.1
16.0
13.5
10.7
7.51
9.06 10.8
7.98 9.36
6.75 7.78
5.34 6.06
3.76 4.19
1.57
1.60
1.63
1.66
1.68
43.3
37.5
31.2
24.2
16.7
85.1
75.1
61.9
53.9
45.1
35.3
24.6
18.1
14.9
13.0
10.9
8.50
5.91
*Outside dimensions across flat sides.
**Properties are based upon a nominal outside corner radius equal to two times the wall thickness.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
STEEL PIPE AND STRUCTURAL TUBING
1 - 131
STRUCTURAL TUBING
Rectangular
Dimensions and properties
Y
X
X
Y
Dimensions
Properties**
Nominal*
Wall
Weight
Size
Thickness per ft Area
in.
in.
X-X Axis
Y-Y Axis
I
S
Z
r
I
S
Z
r
J
lb
in.2
in.4
in.3
in.3
in.
in.4
in.3
in.3
in.
in.4
7×3
0.3750
0.3125
0.2500
0.1875
0.1250
3⁄
8
5⁄
16
1⁄
4
3⁄
16
1⁄
8
22.37
19.08
15.62
11.97
8.16
6.58
5.61
4.59
3.52
2.40
35.7
31.5
26.6
21.1
14.8
10.2 13.5
9.00 11.8
7.61 9.79
6.02 7.63
4.22 5.29
2.33
2.37
2.41
2.45
2.48
9.08
8.11
6.95
5.57
3.96
6.05
5.41
4.63
3.71
2.64
7.32
6.40
5.36
4.20
2.93
1.18
1.20
1.23
1.26
1.29
25.1
22.0
18.5
14.6
10.2
6×4
0.5000
0.3750
0.3125
0.2500
0.1875
0.1250
1⁄
2
3⁄
8
5⁄
16
1⁄
4
3⁄
16
1⁄
8
28.43
22.37
19.08
15.62
11.97
8.16
8.36
6.58
5.61
4.59
3.52
2.40
35.3
29.7
26.2
22.1
17.4
12.2
11.8 15.4
9.90 12.5
8.72 10.9
7.36 9.06
5.81 7.06
4.08 4.88
2.06
2.13
2.16
2.19
2.23
2.26
18.4
15.6
13.8
11.7
9.32
6.57
9.21
7.82
6.92
5.87
4.66
3.29
11.5
9.44
8.21
6.84
5.34
3.71
1.48
1.54
1.57
1.60
1.63
1.66
42.1
34.6
30.1
25.0
19.5
13.5
6×3
0.5000
0.3750
0.3125
0.2500
0.1875
0.1250
1⁄
2
3⁄
8
5⁄
16
1⁄
4
3⁄
16
1⁄
8
25.03
19.82
16.96
13.91
10.70
7.31
7.36
5.83
4.98
4.09
3.14
2.15
27.7
23.8
21.1
17.9
14.3
10.1
9.25 12.6
7.92 10.4
7.03 9.11
5.98 7.62
4.76 5.97
3.36 4.15
1.94
2.02
2.06
2.09
2.13
2.17
8.91
7.78
6.98
6.00
4.83
3.45
5.94
5.19
4.65
4.00
3.22
2.30
7.59
6.34
5.56
4.67
3.68
2.57
1.10
1.16
1.18
1.21
1.24
1.27
23.9
20.3
17.9
15.1
11.9
8.27
6×2
0.3750
0.3125
0.2500
0.1875
0.1250
3⁄
8
5⁄
16
1⁄
4
3⁄
16
1⁄
8
17.27
14.83
12.21
9.42
6.46
5.08
4.36
3.59
2.77
1.90
17.8
16.0
13.8
11.1
7.92
5.94
5.34
4.60
3.70
2.64
8.33
7.33
6.18
4.88
3.42
1.87
1.92
1.96
2.00
2.04
2.84
2.62
2.31
1.90
1.39
2.84
2.62
2.31
1.90
1.39
3.61
3.22
2.75
2.20
1.56
0.748
0.775
0.802
0.829
0.857
8.72
7.94
6.88
5.56
3.98
5×4
0.3750
0.3125
0.2500
0.1875
3⁄
8
5⁄
16
1⁄
4
3⁄
16
19.82
16.96
13.91
10.70
5.83
4.98
4.09
3.14
18.7
16.6
14.1
11.2
7.50
6.65
5.65
4.49
9.44
8.24
6.89
5.39
1.79
1.83
1.86
1.89
13.2
11.7
9.98
7.96
6.58
5.85
4.99
3.98
8.08
7.05
5.90
4.63
1.50
1.53
1.56
1.59
26.3
22.9
19.1
14.9
5×3
0.5000
0.3750
0.3125
0.2500
0.1875
0.1250
1⁄
2
3⁄
8
5⁄
16
1⁄
4
3⁄
16
1⁄
8
21.63
17.27
14.83
12.21
9.42
6.46
6.36
5.08
4.36
3.59
2.77
1.90
16.9
14.7
13.2
11.3
9.06
6.44
6.75
5.89
5.27
4.52
3.62
2.58
9.20
7.71
6.77
5.70
4.49
3.14
1.63
1.70
1.74
1.77
1.81
1.84
7.33
6.48
5.85
5.05
4.08
2.93
4.88
4.32
3.90
3.37
2.72
1.95
6.34
5.35
4.72
3.98
3.15
2.21
1.07
1.13
1.16
1.19
1.21
1.24
18.2
15.6
13.8
11.7
9.21
6.44
*Outside dimensions across flatsides.
**Properties are based upon a nominal outside corner radius equal to two times the wall thickness.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1 - 132
DIMENSIONS AND PROPERTIES
Y
X
X
STRUCTURAL TUBING
Rectangular
Dimensions and properties
Y
Dimensions
Properties**
Nominal*
Wall
Weight
Size
Thickness per ft Area
in.
in.
2
X-X Axis
S
I
4
Z
3
Y-Y Axis
r
3
S
I
4
Z
3
3
r
J
lb
in.
in.
in.
in.
in.
in.
in.
in.
in.
in.4
12.70
10.51
8.15
5.61
3.73
3.09
2.39
1.65
9.74
8.48
6.89
4.96
3.90
3.39
2.75
1.98
5.31
4.51
3.59
2.53
1.62
1.66
1.70
1.73
2.16
1.92
1.60
1.17
2.16
1.92
1.60
1.17
2.70
2.32
1.86
1.32
0.762
0.789
0.816
0.844
6.24
5.43
4.40
3.15
5×2
0.3125
0.2500
0.1875
0.1250
5⁄
16
1⁄
4
3⁄
16
1⁄
8
4×3
0.3125
0.2500
0.1875
0.1250
5⁄
16
1⁄
4
3⁄
16
1⁄
8
12.70
10.51
8.15
5.61
3.73
3.09
2.39
1.65
7.45
6.45
5.23
3.76
3.72
3.23
2.62
1.88
4.75
4.03
3.20
2.25
1.41
1.45
1.48
1.51
4.71
4.10
3.34
2.41
3.14
2.74
2.23
1.61
3.88
3.30
2.62
1.85
1.12
1.15
1.18
1.21
9.89
8.41
6.67
4.68
4×2
0.3750
0.3125
0.2500
0.1875
0.1250
3⁄
8
5⁄
16
1⁄
4
3⁄
16
1⁄
8
12.17
10.58
8.81
6.87
4.75
3.58
3.11
2.59
2.02
1.40
5.75
5.32
4.69
3.87
2.82
2.87
2.66
2.35
1.93
1.41
4.00
3.60
3.09
2.48
1.77
1.27
1.31
1.35
1.38
1.42
1.83
1.71
1.54
1.29
0.954
1.83
1.71
1.54
1.29
0.954
2.39
2.17
1.88
1.52
1.09
0.715
0.743
0.770
0.798
0.826
4.97
4.58
4.01
3.26
2.34
3×2
0.3125
0.2500
0.1875
0.1250
5⁄
16
1⁄
4
3⁄
16
1⁄
8
8.45
7.11
5.59
3.90
2.48
2.09
1.64
1.15
2.44
2.21
1.86
1.38
1.63
1.47
1.24
0.920
2.20
1.92
1.57
1.13
0.992
1.03
1.06
1.10
1.26
1.15
0.977
0.733
1.26
1.15
0.977
0.733
1.64
1.44
1.18
0.855
0.714
0.742
0.771
0.800
2.97
2.63
2.16
1.57
21⁄2×11⁄2
0.2500
0.1875
1⁄
4
3⁄
16
5.41
4.32
1.59
1.27
1.05 0.844 1.15 0.815
0.920 0.736 0.964 0.852
0.458
0.405
0.610 0.793 0.537 1.14
0.540 0.669 0.565 0.976
*Outside dimensions across flat sides.
**Properties are based upon a nominal outside corner radius equal to two times the wall thickness.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
BARS AND PLATES
1 - 133
BARS AND PLATES
Product Availability
Plates are readily available in seven of the structural steel specifications listed in Section
A3.1 of the AISC LRFD Specification. These are: ASTM A36, A242, A529, A572, A588,
A514, and A852. Bars are available in all of these steels except A514 and A852. Table 1-1
shows the availability of each steel in terms of plate thickness.
The Manual user is referred to the discussion on p. 1-5, Selection of the Appropriate
Structural Steel, for guidance in selection of both plate and structural shapes.
Classification
Bars and plates are generally classified as follows:
Bars: 6 in. or less in width, .203 in. and over in thickness.
Over 6 in. to 8 in. in width, .230 in. and over in thickness.
Plates: Over 8 in. to 48 in. in width, .230 in. and over in thickness.
Over 48 in. in width, .180 in. and over in thickness.
Bars
Bars are available in various widths, thicknesses, diameters, and lengths. The preferred
practice is to specify widths in 1⁄4-in. increments and thickness and diameter in 1⁄8-in.
increments.
Plates
Defined according to rolling procedure:
Sheared plates are rolled between horizontal rolls and trimmed (sheared or gas cut) on
all edges.
Universal (UM) plates are rolled between horizontal and vertical rolls and trimmed
(sheared or gas cut) on ends only.
Stripped plates are furnished to required widths by shearing or gas cutting from wider
sheared plates.
Sizes
Plate mills are located in various districts, but the sizes of plates produced differ greatly
and the catalogs of individual mills should be consulted for detail data. The extreme width
of UM plates currently rolled is 60 inches and for sheared plates it is 200 inches, but their
availability together with limiting thickness and lengths should be checked with the mills
before specifying. The preferred increments for width and thickness are:
Widths:
Various. The catalogs of individual mills should be consulted to determine
the most economical widths.
Thickness: 1⁄32-in. increments up to 1⁄2-in.
1⁄ -in. increments over 1⁄ -in. to 1 in.
16
2
1⁄ -in. increments over 1 in. to 3 in.
8
1⁄ -in. increments over 3 in.
4
Ordering
Plate thickness may be specified in inches or by weight per square foot, but no decimal
edge thickness can be assured by the latter method. Separate tolerance tables apply to
each method.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1 - 134
DIMENSIONS AND PROPERTIES
Table 1-7.
Theoretical Weights of Rolled Floor Plates
Gauge
No.
Theoretical
Weight per
sq. ft lb
Nominal
Thickness
in.
18
2.40
1⁄
8
16
3.00
3⁄
14
13
12
Nominal
Thickness
in.
Theoretical
Weight per
sq. ft, lb
6.16
1⁄
2
21.47
8.71
9⁄
16
24.02
3.75
1⁄
4
11.26
5⁄
8
26.58
4.50
5⁄
13.81
3⁄
4
31.68
5.25
3⁄
8
16.37
7⁄
8
36.78
7⁄
18.92
1
41.89
16
16
16
Theoretical
Weight per
sq. ft, lb
Note:
Thickness is measured near the edge of the plate, exclusive of raised pattern.
Invoicing
Standard practice is to invoice plates to the fabricator at theoretical weight at point of
shipment. Permissible variations in weight are in accordance with the tables of ASTM
Specification A6.
All plates are invoiced at theoretical weight and, except as noted, are subject to the
same weight variations which apply to rectangular plates. Odd shapes in most instances
require gas cutting, for which gas cutting extras are applicable.
All plates ordered gas cut for whatever reason, or beyond published shearing limits,
take extras for gas cutting in addition to all other extras. Rolled steel bearing plates are
often gas cut to prevent distortion due to shearing but would also take the regular extra
for the thickness involved.
Extras for thickness, width, length, cutting, quality and quantity, etc., which are added
to the base price of plates, are subject to revision, and should be obtained by inquiry to
the producer. The foregoing general statements are made as a guide toward economy in
design.
Floor Plates
Floor plates having raised patterns are available from several mills, each offering its own
style of surface projections and in a variety of widths, thicknesses, and lengths. A
maximum width of 96 inches and a maximum thickness of one inch are available, but
availability of matching widths, thicknesses, and lengths should be checked with the
producer. Floor plates are generally not specified to chemical composition limits or
mechanical property requirements; a commercial grade of carbon steel is furnished.
However, when strength or corrosion resistance is a consideration, raised pattern floor
plates are procurable in any of the regular steel specifications. As in the case of plain
plates, the individual manufacturers should be consulted for precise information. The
nominal or ordered thickness is that of the flat plate, exclusive of the height or raised
pattern. The usual weights are as shown in Table 1-7.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
BARS AND PLATES
1 - 135
SQUARE AND ROUND BARS
Weight and area
Weight
lb per ft
Area
Sq in.
Size
in.
0
Weight
lb per ft
Area
Sq in.
Size
in.
1⁄
16
1⁄
8
3⁄
16
0.013
0.053
0.120
0.010
0.042
0.094
0.0039
0.0156
0.0352
0.0031
0.0123
0.0276
1⁄
16
1⁄
8
3⁄
16
30.63
31.91
33.23
34.57
24.05
25.07
26.10
27.15
9.000
9.379
9.766
10.160
7.069
7.366
7.670
7.980
1⁄
4
5⁄
16
3⁄
8
7⁄
16
0.213
0.332
0.479
0.651
0.167
0.261
0.376
0.512
0.0625
0.0977
0.1406
0.1914
0.0491
0.0767
0.1104
0.1503
1⁄
4
5⁄
16
3⁄
8
7⁄
16
35.94
37.34
38.76
40.21
28.23
29.32
30.44
31.58
10.563
10.973
11.391
11.816
8.296
8.618
8.946
9.281
1⁄
2
9⁄
16
5⁄
8
11⁄
16
0.851
1.077
1.329
1.608
0.668
0.846
1.044
1.263
0.2500
0.3164
0.3906
0.4727
0.1964
0.2485
0.3068
0.3712
1⁄
2
9⁄
16
5⁄
8
11⁄
16
41.68
43.19
44.71
46.27
32.74
33.92
35.12
36.34
12.250
12.691
13.141
13.598
9.621
9.968
10.321
10.680
3⁄
4
13⁄
16
7⁄
8
15⁄
16
1.914
2.246
2.605
2.991
1.503
1.764
2.046
2.349
0.5625
0.6602
0.7656
0.8789
0.4418
0.5185
0.6013
0.6903
3⁄
4
13⁄
16
7⁄
8
15⁄
16
47.85
49.46
51.09
52.76
37.58
38.85
40.13
41.43
14.063
14.535
15.016
15.504
11.045
11.416
11.793
12.177
1⁄
16
1⁄
8
3⁄
16
3.403
3.841
4.307
4.798
2.673
3.017
3.382
3.769
1.0000
1.1289
1.2656
1.4102
0.7854
0.8866
0.9940
1.1075
1⁄
16
1⁄
8
3⁄
16
54.44
56.16
57.90
59.67
42.76
44.11
45.47
46.86
16.000
16.504
17.016
17.535
12.566
12.962
13.364
13.772
1⁄
4
5⁄
16
3⁄
8
7⁄
16
5.317
5.862
6.433
7.032
4.176
4.604
5.053
5.523
1.5625
1.7227
1.8906
2.0664
1.2272
1.3530
1.4849
1.6230
1⁄
4
5⁄
16
3⁄
8
7⁄
16
61.46
63.28
65.13
67.01
48.27
49.70
51.15
52.63
18.063
18.598
19.141
19.691
14.186
14.607
15.033
15.466
1⁄
2
9⁄
16
5⁄
8
11⁄
16
7.656
8.308
8.985
9.690
6.013
6.525
7.057
7.610
2.2500
2.4414
2.6406
2.8477
1.7672
1.9175
2.0739
2.2365
1⁄
2
9⁄
16
5⁄
8
11⁄
16
68.91
70.83
72.79
74.77
54.12
55.63
57.17
58.72
20.250
20.816
21.391
21.973
15.904
16.349
16.800
17.257
3⁄
4
13⁄
16
7⁄
8
15⁄
16
10.421
11.179
11.963
12.774
8.185
8.780
9.396
10.032
3.0625
3.2852
3.5156
3.7539
2.4053
2.5802
2.7612
2.9483
3⁄
4
13⁄
16
7⁄
8
15⁄
16
76.78
78.81
80.87
82.96
60.30
61.90
63.51
65.15
22.563
23.160
23.766
24.379
17.721
18.190
18.666
19.147
1⁄
16
1⁄
8
3⁄
16
13.611
14.475
15.366
16.283
10.690
11.369
12.068
12.789
4.0000
4.2539
4.5156
4.7852
3.1416
3.3410
3.5466
3.7583
1⁄
16
1⁄
8
3⁄
16
85.07
87.21
89.38
91.57
66.81
68.49
70.20
71.92
25.000
25.629
26.266
26.910
19.635
20.129
20.629
21.135
1⁄
4
5⁄
16
3⁄
8
7⁄
16
17.227
18.197
19.194
20.217
13.530
14.292
15.075
15.879
5.0625
5.3477
5.6406
5.9414
3.9761
4.2000
4.4301
4.6664
1⁄
4
5⁄
16
3⁄
8
7⁄
16
93.79
96.04
98.31
100.61
73.66
75.43
77.21
79.02
27.563
28.223
28.891
29.566
21.648
22.166
22.691
23.221
1⁄
2
9⁄
16
5⁄
8
11⁄
16
21.267
22.344
23.447
24.577
16.703
17.549
18.415
19.303
6.2500
6.5664
6.8906
7.2227
4.9087
5.1573
5.4119
5.6727
1⁄
2
9⁄
16
5⁄
8
11⁄
16
102.93
105.29
107.67
110.07
80.84
82.69
84.56
86.45
30.250
30.941
31.641
32.348
23.758
24.301
24.851
25.406
3⁄
4
13⁄
16
7⁄
8
15⁄
16
25.734
26.917
28.126
29.362
20.211
21.140
22.090
23.061
7.5625
7.9102
8.2656
8.6289
5.9396
6.2126
6.4918
6.7771
3⁄
4
13⁄
16
7⁄
8
15⁄
16
112.50
114.96
117.45
119.96
88.36
90.29
92.24
94.22
33.063
33.785
34.516
35.254
25.967
26.535
27.109
27.688
1
2
3
4
5
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1 - 136
DIMENSIONS AND PROPERTIES
SQUARE AND ROUND BARS
Weight and area
Weight
lb per ft
Area
Sq in.
Size
in.
6
Weight
lb per ft
Area
Sq in.
Size
in.
1⁄
16
1⁄
8
3⁄
16
122.50
125.07
127.66
130.28
96.21
98.23
100.26
102.32
36.000
36.754
37.516
38.285
28.274
28.867
29.465
30.069
1⁄
4
5⁄
16
3⁄
8
7⁄
16
132.92
135.59
138.29
141.02
104.40
106.49
108.61
110.75
39.063
39.848
40.641
41.441
1⁄
2
9⁄
16
5⁄
8
11⁄
16
143.77
146.55
149.35
152.18
112.91
115.10
117.30
119.52
3⁄
4
13⁄
16
7⁄
8
15⁄
16
155.04
157.92
160.83
163.77
1⁄
16
1⁄
8
3⁄
16
275.63
279.47
283.33
287.23
216.48
219.49
222.53
225.59
81.000
82.129
83.266
84.410
63.617
64.504
65.397
66.296
30.680
31.296
31.919
32.548
1⁄
4
5⁄
16
3⁄
8
7⁄
16
291.15
295.10
299.07
303.07
228.67
231.77
234.89
238.03
85.563
86.723
87.891
89.066
67.201
68.112
69.029
69.953
42.250
43.066
43.891
44.723
33.183
33.824
34.472
35.125
1⁄
2
9⁄
16
5⁄
8
11⁄
16
307.10
311.15
315.24
319.34
241.20
244.38
247.59
250.81
90.250
91.441
92.641
93.848
70.882
71.818
72.760
73.708
121.77
124.03
126.32
128.63
45.563
46.410
47.266
48.129
35.785
36.451
37.122
37.800
3⁄
4
13⁄
16
7⁄
8
15⁄
16
323.48
327.64
331.82
336.04
254.06
257.33
260.61
263.92
95.063
96.285
97.516
98.754
74.662
75.622
76.589
77.561
1⁄
16
1⁄
8
3⁄
16
166.74
169.73
172.74
175.79
130.95
133.30
135.67
138.06
49.000
49.879
50.766
51.660
38.485
39.175
39.871
40.574
1⁄
16
1⁄
8
3⁄
16
340.28
344.54
348.84
353.16
267.25
270.61
273.98
277.37
100.000
101.254
102.516
103.785
78.540
79.525
80.516
81.513
1⁄
4
5⁄
16
3⁄
8
7⁄
16
178.86
181.96
185.08
188.23
140.48
142.91
145.36
147.84
52.563
53.473
54.391
55.316
41.283
41.997
42.718
43.446
1⁄
4
5⁄
16
3⁄
8
7⁄
16
357.50
361.88
366.28
370.70
280.78
284.22
287.67
291.15
105.063
106.348
107.641
108.941
82.516
83.525
84.541
85.563
1⁄
2
9⁄
16
5⁄
8
11⁄
16
191.41
194.61
197.84
201.10
150.33
152.85
155.38
157.94
56.250
57.191
58.141
59.098
44.179
44.918
45.664
46.415
1⁄
2
9⁄
16
5⁄
8
11⁄
16
375.16
379.64
384.14
388.67
294.65
298.17
301.70
305.26
110.250
111.566
112.891
114.223
86.590
87.624
88.664
89.710
3⁄
4
13⁄
16
7⁄
8
15⁄
16
204.38
207.69
211.03
214.39
160.52
163.12
165.74
168.38
60.063
61.035
62.016
63.004
47.173
47.937
48.707
49.483
3⁄
4
13⁄
16
7⁄
8
15⁄
16
393.23
397.82
402.43
407.07
308.85
312.45
316.07
319.71
115.563
116.910
118.266
119.629
90.763
91.821
92.886
93.957
1⁄
16
1⁄
8
3⁄
16
217.78
221.19
224.64
228.11
171.04
173.73
176.43
179.15
64.000
65.004
66.016
67.035
50.266
51.054
51.849
52.649
1⁄
16
1⁄
8
3⁄
16
411.74
416.43
421.15
425.89
323.38
327.06
330.77
334.50
121.000
122.379
123.766
125.160
95.033
96.116
97.206
98.301
1⁄
4
5⁄
16
3⁄
8
7⁄
16
231.60
235.12
238.67
242.25
181.90
184.67
187.45
190.26
68.063
69.098
70.141
71.191
53.456
54.269
55.088
55.914
1⁄
4
5⁄
16
3⁄
8
7⁄
16
430.66
435.46
440.29
445.14
338.24
342.01
345.80
349.61
126.563
127.973
129.391
130.816
99.402
100.510
101.623
102.743
1⁄
2
9⁄
16
5⁄
8
11⁄
16
245.85
249.48
253.13
256.82
193.09
195.94
198.81
201.70
72.250
73.316
74.391
75.473
56.745
57.583
58.426
59.276
1⁄
2
9⁄
16
5⁄
8
11⁄
16
450.02
454.92
459.85
464.81
353.44
357.30
361.17
365.06
132.250
133.691
135.141
136.598
103.869
105.001
106.139
107.284
3⁄
4
13⁄
16
7⁄
8
15⁄
16
260.53
264.26
268.02
271.81
204.62
207.55
210.50
213.48
76.563
77.660
78.766
79.879
60.132
60.994
61.863
62.737
3⁄
4
13⁄
16
7⁄
8
15⁄
16
469.80
474.81
479.84
484.91
368.98
372.91
376.87
380.85
138.063
139.535
141.016
142.504
108.434
109.591
110.754
111.923
490.00
384.85
144.000
113.098
7
8
9
10
11
12
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
BARS AND PLATES
1 - 137
AREA OF RECTANGULAR SECTIONS
Square inches
Width
in.
Thickness, inches
3⁄
16
1⁄
4
5⁄
16
3⁄
8
7⁄
16
1⁄
2
9⁄
16
5⁄
8
11⁄
16
3⁄
4
13⁄
16
1
0.047
0.093
0.141
0.188
0.063
0.125
0.188
0.250
0.078
0.156
0.234
0.313
0.094
0.188
0.281
0.375
0.109
0.219
0.328
0.438
0.125
0.250
0.375
0.500
0.141
0.281
0.422
0.563
0.156
0.313
0.469
0.625
0.172
0.344
0.516
0.688
0.188
0.375
0.563
0.75
0.203
0.406
0.609
0.813
0.219
0.438
0.656
0.875
0.234
0.469
0.703
0.938
0.250
0.500
0.750
1.00
11⁄4
11⁄2
13⁄4
2
0.234
0.281
0.328
0.375
0.313
0.375
0.438
0.500
0.391
0.469
0.547
0.625
0.469
0.563
0.656
0.750
0.547
0.656
0.766
0.875
0.625
0.750
0.875
1.00
0.703
0.844
0.984
1.13
0.781
0.938
1.09
1.25
0.859
1.03
1.20
1.38
0.938
1.13
1.31
1.50
1.02
1.22
1.42
1.63
1.09
1.31
1.53
1.75
1.17
1.41
1.64
1.88
1.25
1.50
1.75
2.00
21⁄4
21⁄2
23⁄4
3
0.422
0.469
0.516
0.563
0.563
0.625
0.688
0.750
0.703
0.781
0.859
0.938
0.844
0.938
1.03
1.13
0.984
1.09
1.20
1.31
1.13
1.25
1.38
1.50
1.27
1.41
1.55
1.69
1.41
1.56
1.72
1.88
1.55
1.72
1.89
2.06
1.69
1.88
2.06
2.25
1.83
2.03
2.23
2.44
1.97
2.19
2.41
2.63
2.11
2.34
2.58
2.81
2.25
2.50
2.75
3.00
31⁄4
31⁄2
33⁄4
4
0.609
0.656
0.703
0.750
0.813
0.875
0.938
1.00
1.02
1.09
1.17
1.25
1.22
1.31
1.41
1.50
1.42
1.53
1.64
1.75
1.63
1.75
1.88
2.00
1.83
1.97
2.11
2.25
2.03
2.19
2.34
2.50
2.23
2.41
2.58
2.75
2.44
2.63
2.81
3.00
2.64
2.84
3.05
3.25
2.84
3.06
3.28
3.50
3.05
3.28
3.52
3.75
3.25
3.50
3.75
4.00
41⁄4
41⁄2
43⁄4
5
0.797
0.844
0.891
0.938
1.06
1.13
1.19
1.25
1.33
1.41
1.48
1.56
1.59
1.69
1.78
1.88
1.86
1.97
2.08
2.19
2.13
2.25
2.38
2.50
2.39
2.53
2.67
2.81
2.66
2.81
2.97
3.13
2.92
3.09
3.27
3.44
3.19
3.38
3.56
3.75
3.45
3.66
3.86
4.06
3.72
3.94
4.16
4.38
3.98
4.22
4.45
4.69
4.25
4.50
4.75
5.00
51⁄4
51⁄2
53⁄4
6
0.984
1.03
1.08
1.13
1.31
1.38
1.44
1.50
1.64
1.72
1.80
1.88
1.97
2.06
2.16
2.25
2.30
2.41
2.52
2.63
2.63
2.75
2.88
3.00
2.95
3.09
3.23
3.38
3.28
3.44
3.59
3.75
3.61
3.78
3.95
4.13
3.94
4.13
4.31
4.50
4.27
4.47
4.67
4.88
4.59
4.81
5.03
5.25
4.92
5.16
5.39
5.63
5.25
5.50
5.75
6.00
61⁄4
61⁄2
63⁄4
7
1.17
1.22
1.27
1.31
1.56
1.63
1.69
1.75
1.95
2.03
2.11
2.19
2.34
2.44
2.53
2.63
2.73
2.84
2.95
3.06
3.13
3.25
3.38
3.50
3.52
3.66
3.80
3.94
3.91
4.06
4.22
4.38
4.30
4.47
4.64
4.81
4.69
4.88
5.06
5.25
5.08
5.28
5.48
5.69
5.47
5.69
5.91
6.13
5.86
6.09
6.33
6.56
6.25
6.50
6.75
7.00
71⁄4
71⁄2
73⁄4
8
1.36
1.41
1.45
1.50
1.81
1.88
1.94
2.00
2.27
2.34
2.42
2.50
2.72
2.81
2.91
3.00
3.17
3.28
3.39
3.50
3.63
3.75
3.88
4.00
4.08
4.22
4.36
4.50
4.53
4.69
4.84
5.00
4.98
5.16
5.33
5.50
5.44
5.63
5.81
6.00
5.89
6.09
6.30
6.50
6.34
6.56
6.78
7.00
6.80
7.03
7.27
7.50
7.25
7.50
7.75
8.00
81⁄2
9
1.59
1.69
2.13
2.25
2.66
2.81
3.19
3.38
3.72
3.94
4.25
4.50
4.78
5.06
5.31
5.63
5.84
6.19
6.38
6.75
6.91
7.31
7.44
7.88
7.97
8.44
8.50
9.00
91⁄2
10
1.78
1.88
2.38
2.50
2.97
3.13
3.56
3.75
4.16
4.38
4.75
5.00
5.34
5.63
5.94
6.25
6.53
6.88
7.13
7.50
7.72
8.13
8.31
8.75
8.91
9.38
9.50
10.0
101⁄2
11
1.97
2.06
2.63
2.75
3.28
3.44
3.94
4.13
4.59
4.81
5.25
5.50
5.91
6.19
6.56
6.88
7.22
7.56
7.88
8.25
8.53
8.94
9.19
9.63
9.84
10.3
10.5
11.0
111⁄2
12
2.16
2.25
2.88
3.00
3.59
3.75
4.31
4.50
5.03
5.25
5.75
6.00
6.47
6.75
7.19
7.50
7.91 8.63
8.25 9.00
9.34
9.75
10.8
11.3
11.5
12.0
1⁄
4
1⁄
2
3⁄
4
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
7⁄
8
10.1
10.5
15⁄
16
1
1 - 138
DIMENSIONS AND PROPERTIES
WEIGHT OF RECTANGULAR SECTIONS
Pounds per linear foot
Width
in.
Thickness, inches
3⁄
16
1⁄
4
5⁄
16
3⁄
8
7⁄
16
1⁄
2
9⁄
16
5⁄
8
11⁄
16
3⁄
4
13⁄
16
7⁄
8
15⁄
16
1
0.160
0.319
0.479
0.638
0.213
0.425
0.638
0.851
0.266
0.532
0.798
1.06
0.319
0.638
0.957
1.28
0.372
0.744
1.12
1.49
0.425
0.851
1.28
1.70
0.479
0.957
1.44
1.91
0.532
1.06
1.60
2.13
0.585
1.17
1.75
2.34
0.638
1.28
1.91
2.55
0.691
1.38
2.07
2.76
0.744
1.49
2.23
2.98
0.798
1.60
2.39
3.19
0.851
1.70
2.55
3.40
11⁄4
11⁄2
13⁄4
2
0.798
0.957
1.12
1.28
1.06
1.28
1.49
1.70
1.33
1.60
1.86
2.13
1.60
1.91
2.23
2.55
1.86
2.23
2.61
2.98
2.13
2.55
2.98
3.40
2.39
2.87
3.35
3.83
2.66
3.19
3.72
4.25
2.92
3.51
4.09
4.68
3.19
3.83
4.47
5.10
3.46
4.15
4.84
5.53
3.72
4.47
5.21
5.95
3.99
4.79
5.58
6.38
4.25
5.10
5.95
6.81
21⁄4
21⁄2
23⁄4
3
1.44
1.60
1.75
1.91
1.91
2.13
2.34
2.55
2.39
2.66
2.92
3.19
2.87
3.19
3.51
3.83
3.35
3.72
4.09
4.47
3.83
4.25
4.68
5.10
4.31
4.79
5.26
5.74
4.79
5.32
5.85
6.38
5.26
5.85
6.43
7.02
5.74
6.38
7.02
7.66
6.22
6.91
7.60
8.29
6.70
7.44
8.19
8.93
7.18
7.98
8.77
9.57
7.66
8.51
9.36
10.2
31⁄4
31⁄2
33⁄4
4
2.07
2.23
2.39
2.55
2.76
2.98
3.19
3.40
3.46
3.72
3.99
4.25
4.15
4.47
4.79
5.10
4.84
5.21
5.58
5.95
5.53
5.95
6.38
6.81
6.22
6.70
7.18
7.66
6.91
7.44
7.98
8.51
7.60
8.19
8.77
9.36
8.29
8.93
9.57
10.2
8.99
9.68
10.4
11.1
9.68
10.4
11.2
11.9
10.4
11.2
12.0
12.8
11.1
11.9
12.8
13.6
41⁄4
41⁄2
43⁄4
5
2.71
2.87
3.03
3.19
3.62
3.83
4.04
4.25
4.52
4.79
5.05
5.32
5.42
5.74
6.06
6.38
6.33
6.70
7.07
7.44
7.23
7.66
8.08
8.51
8.13
8.61
9.09
9.57
9.04
9.57
10.1
10.6
9.94
10.5
11.1
11.7
10.8
11.5
12.1
12.8
11.8
12.4
13.1
13.8
12.7
13.4
14.1
14.9
13.6
14.4
15.2
16.0
14.5
15.3
16.2
17.0
51⁄4
51⁄2
53⁄4
6
3.35
3.51
3.67
3.83
4.47
4.68
4.89
5.10
5.58
5.85
6.11
6.38
6.70
7.02
7.34
7.66
7.82
8.19
8.56
8.93
8.93
9.36
9.78
10.2
10.0
10.5
11.0
11.5
11.2
11.7
12.2
12.8
12.3
12.9
13.5
14.0
13.4
14.0
14.7
15.3
14.5
15.2
15.9
16.6
15.6
16.4
17.1
17.9
16.7
17.5
18.3
19.1
17.9
18.7
19.6
20.4
61⁄4
61⁄2
63⁄4
7
3.99
4.15
4.31
4.47
5.32
5.53
5.74
5.95
6.65
6.91
7.18
7.44
7.98
8.29
8.61
8.93
9.30
9.68
10.0
10.4
10.6
11.1
11.5
11.9
12.0
12.4
12.9
13.4
13.3
13.8
14.4
14.9
14.6
15.2
15.8
16.4
16.0
16.6
17.2
17.9
17.3
18.0
18.7
19.4
18.6
19.4
20.1
20.8
19.9
20.7
21.5
22.3
21.3
22.1
23.0
23.8
71⁄4
71⁄2
73⁄4
8
4.63
4.79
4.94
5.10
6.17
6.38
6.59
6.81
7.71
7.98
8.24
8.51
9.25
9.57
9.89
10.2
10.8
11.2
11.5
11.9
12.3
12.8
13.2
13.6
13.9
14.4
14.8
15.3
15.4
16.0
16.5
17.0
17.0
17.5
18.1
18.7
18.5
19.1
19.8
20.4
20.0
20.7
21.4
22.1
21.6
22.3
23.1
23.8
23.1
23.9
24.7
25.5
24.7
25.5
26.4
27.2
81⁄2
9
5.42
5.74
7.23
7.66
9.04
9.57
10.8
11.5
12.7
13.4
14.5
15.3
16.3
17.2
18.1
19.1
19.9
21.1
21.7
23.0
23.5
24.9
25.3
26.8
27.1
28.7
28.9
30.6
91⁄2
10
6.06
6.38
8.08
8.51
10.1
10.6
12.1
12.8
14.1
14.9
16.2
17.0
18.2
19.1
20.2
21.3
22.2
23.4
24.2
25.5
26.3
27.6
28.3
29.8
30.3
31.9
32.3
34.0
101⁄2
11
6.70
7.02
8.93
9.36
11.2
11.7
13.4
14.0
15.6
16.4
17.9
18.7
20.1
21.1
22.3
23.4
24.6
25.7
26.8
28.1
29.0
30.4
31.3
32.8
33.5
35.1
35.7
37.4
111⁄2
12
7.34
7.66
9.78
10.2
12.2
12.8
14.7
15.3
17.1
17.9
19.6
20.4
22.0
23.0
24.5
25.5
26.9
28.1
29.3
30.6
31.8
33.2
34.2
35.7
36.7
38.3
39.1
40.8
1⁄
4
1⁄
2
3⁄
4
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1
CRANE RAILS
1 - 139
CRANE RAILS
General Notes
The ASCE rails and the 104- to 175-lb crane rails shown in Figure 1-2 are recommended
for crane runway use. For complete details and for profiles and properties of rails not
listed, consult manufacturers’ catalogs.
Rails should be arranged so that joints on opposite sides of the crane runway will be
staggered with respect to each other and with due consideration to the wheelbase of the
crane. Rail joints should not occur at crane girder splices. Light 40-lb rails are available
in 30-ft lengths, 60-lb rails in 30-, 33- or 39-ft lengths, standard rails in 33- or 39-ft lengths
and crane rails up to 80 ft. Consult manufacturer for availability of other lengths. Odd
lengths, which must be included to complete a run or obtain the necessary stagger, should
be not less than 10 feet long. For crane rail service, 40-lb rails are furnished to
manufacturers’ specifications and tolerances. 60- and 85-lb rails are furnished to manufacturers’ specifications and tolerances, or to ASTM A1. Crane rails are furnished to
ASTM A759. Rails will be furnished with standard drilling in both standard and odd
lengths unless stipulated otherwise on order. For controlled cooling, heat treatment, and
rail end preparation, see manufacturers’ catalogs. Purchase orders for crane rails should
be noted “For crane service.” (See Table 1-8.)
For maximum wheel loadings see manufacturers’ catalogs.
Splices
Bolted Splices
It is often more desirable to use properly installed and maintained bolted splice bars in
making up rail joints for crane service than welded splice bars.
Standard rail drilling and joint-bar punching, as furnished by manufacturers of light
standard rails for track work, include round holes in rail ends and slotted holes in joint
bars to receive standard oval-neck tack bolts. Holes in rails are oversize and punching in
joint bars is spaced to allow 1⁄16- to 1⁄8-in. clearance between rail ends (see manufacturers’
catalogs for spacing and dimensions of holes and slots). Although this construction is
satisfactory for track and light crane service, its use in general crane service may lead to
joint failure.
For best service in bolted splices, it is recommended that tight joints be stipulated for
all rails for crane service. This will require rail ends to be finished by milling or grinding,
and the special rail drilling and joint-bar punching tabulated below. Special rail drilling
is accepted by some mills, or rails may be ordered blank for shop drilling. End finishing
of standard rails can be done at the mill; light rails must be end-finished in the fabricating
shop or ground at the site prior to erection. In the crane rail range, from 104 to 175 lbs
per yard, rails and joint bars are manufactured to obtain a tight fit and no further special
end finishing, drilling, or punching is required. Because of cumulative tolerance variations in holes, bolt diameters, and rail ends, a slight gap may sometimes occur in the
so-called tight joints. Conversely, it may sometimes be necessary to ream holes through
joined bar and rail to permit entry of bolts.
Joint bars for crane service are provided in various sections to match the rails. Joint
bars for light and standard rails may be purchased blank for special shop punching to
obtain tight joints. See Bethlehem Steel Corp. Booklet 3351 for dimensions, material
specifications, and the identification necessary to match the crane rail section.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1 - 140
DIMENSIONS AND PROPERTIES
c
Bars can be
sheared off
r
13°
c of g
y
13°
1/
4 Rad.
R
X
X
h
1/
4 Rad.
t
1/
2 Rad.
d
1/
2 Rad.
h
g
13°
13°
m
m
n
b
A.S.C.E. 40, 60 & 85 lb.
c
BETHLEHEM 104 lb.
c
4
3 (approx.)
12°
13°
3
4
Rad.
3
4
Rad.
7/
8
7/
8 Rad.
h
13°
h
12°
m
BETHLEHEM 135 lb.
Rad.
m
BETHLEHEM 171 lb.
c
4 1/32 (approx.)
12°
2 Rad.
11/8 Rad.
12°
h
2 53/64
m
BETHLEHEM 175 lb.
Nomenclature of sketch for A.S.C.E. rails also applies to the other sections.
Fig. 1-2. Crane rails.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
CRANE RAILS
1 - 141
Table 1-8.
Crane Rails
Dimensions and Properties
Type
Nominal
Wt.
per
Classi- Yd. d
fication lb in.
Sx
Gage
g
b
m
n
c
r
t
h
R
Area
lx
in.
in.
in.
in.
in.
in.
in.
in.
in.
in.2
in.4
17⁄
32
5⁄
8
11⁄
16
48⁄
64
13⁄
16
7⁄
8
57⁄
64
31⁄
32
11⁄16
11⁄16
11⁄4
19⁄64
11⁄
64
7⁄
32
1⁄
4
9⁄
32
9⁄
32
19⁄
64
19⁄
64
10⁄
32
1⁄
2
15⁄
32
5⁄
8
1⁄
2
111⁄16
12
12
3.00 4.10 2.55
12
155⁄64
12
3.94 6.54 3.59 3.89 1.68
21⁄8
12
23⁄8
12
27⁄16
12
21⁄2
12
29⁄16
12
23⁄4
12
21⁄
64
25⁄
64
7⁄
16
31⁄
64
33⁄
64
35⁄
64
9⁄
16
9⁄
16
123⁄32
17⁄8
21⁄2
12
1
ASCE
Light
30
31⁄8
125⁄64
31⁄8
ASCE
Light
40
31⁄2
171⁄128
31⁄2
ASCE
Light
50
37⁄8
123⁄32
37⁄8
ASCE
Light
60
41⁄4 1115⁄128 41⁄4
ASCE
70
45⁄8
23⁄64
45⁄8
ASCE
80
5
23⁄16
5
ASCE
Std.
85
53⁄16
217⁄64
53⁄16
ASCE
Std.
100
53⁄4
265⁄128
53⁄4
Bethlehem
Crane
104
5
27⁄16
5
Bethlehem
Crane
135
53⁄4
215⁄32
53⁄16
Bethlehem
Crane
171
6
25⁄8
6
Bethlehem
Crane
175
6
221⁄32
6
Hd. Base
y
in.3
in.3
in.
—
—
21⁄16
12
4.90 10.1
5.10
217⁄64
12
5.93 14.6
6.64 7.12 2.05
215⁄32
12
6.81 19.7
8.19 8.87 2.22
25⁄8
12
7.86 26.4 10.1 11.1 2.38
23⁄4
12
8.33 30.1 11.1 12.2 2.47
25⁄64
12
9.84 44.0 14.6 16.1 2.73
27⁄16
31⁄2
10.3 29.8 10.7 13.5 2.21
12
13.3 50.8 17.3 18.1 2.81
—
1.88
37⁄16
14
11⁄4 213⁄16
4.3
Flat
11⁄4
23⁄4 Vert. 16.8 73.4 24.5 24.4 3.01
41⁄4
18
11⁄2
37⁄64 Vert. 17.1 70.5 23.4 23.6 2.98
Joint-bar bolts, as distinguished from oval-neck track bolts, have straight shanks to the
head and are manufactured to ASTM A449 specifications. Nuts are manufactured to
ASTM A563 Gr. B specifications. ASTM A325 bolts and nuts may be used. Bolt assembly
includes an alloy steel spring washer, furnished to AREA specifications.
After installation, bolts should be retightened within 30 days and every three months
thereafter.
Welded Splices
When welded splices are specified, consult the manufacturer for recommended rail-end
preparation, welding procedure, and method of ordering. Although joint continuity, made
possible by this method of splicing, is desirable, it should be noted that the careful control
required in all stages of the welding operation may be difficult to meet during crane rail
installation.
Rails should not be attached to structural supports by welding. Rails with holes for
joint bar bolts should not be used in making welded splices.
Fastenings
Hook Bolts
Hook bolts (Figure 1-3) are used primarily with light rails when attached to beams too
narrow for clamps. Rail adjustment to ±1⁄2-in. is inherent in the threaded shank. Hook
bolts are paired alternately three to four inches apart, spaced at about 24-in. centers. The
special rail drilling required must be done at the fabricator’s shop. Hook bolts are not
recommended for use with heavy duty cycle cranes (CMAA Classes, D, E, and F). It is
generally recommended that hook bolts should not be used in runway systems which are
longer than 500 feet because the bolts do not allow for longitudinal movement of the rail.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1 - 142
DIMENSIONS AND PROPERTIES
Table 1-9.
Splices for Tight Joints
g
A
B
C
C
B
D
C
B
L
Rail End
Joint Bar
l
l
Grip
Grip
H
H
G
Cut when specified
40-60-85-104
Rail
Joint Bar
Drilling
Wt.
Per
Yard
g
lb
in.
40 171⁄128
60 1115⁄128
85 217⁄64
104
27⁄16
135 215⁄32
171
25⁄8
175
221⁄32
Hole
Dia. A
in.
13⁄ *
16
13⁄ *
16
15⁄ *
16
11⁄16
13⁄16
13⁄16
13⁄16
105-135-171-175
B C
in. in. in.
21⁄2 5
—
21⁄2 5
—
21⁄2 5
—
4
5
6
4
5
6
4
5
6
4
Bolt
Washer
Punching
5
6
Wt. 2 Bars
Bolts, Nuts,
Washers
ThickIn- ness
side and With Less
Dia. Width Fig. Fig.
Hole
Dia.
D
B C
L
G
Dia.
Grip
I
H
in.
in.
in. in. in.
in.
in.
in.
in.
in.
in.
in.
lb
lb
13⁄ *
16
13⁄ *
16
15⁄ *
16
11⁄16
13⁄16
13⁄16
13⁄16
415⁄16*
5
— 20 23⁄16
3⁄
4
115⁄16
31⁄2
21⁄2
16.5
5
— 24 211⁄16
3⁄
4
219⁄32
4
211⁄16
36.5
29.6
415⁄16*
5
— 24 311⁄32
7⁄
8
35⁄32
43⁄4
33⁄16
56.6
45.3
715⁄16
5
6
34
31⁄2
1
31⁄2
51⁄4
31⁄2
715⁄16
5
6
34
—
11⁄8
35⁄8
51⁄2
311⁄16
715⁄16
5
6
34
—
11⁄8
47⁄16
61⁄4
41⁄16
—
11⁄8
41⁄8
61⁄4
315⁄16
7⁄ ×3⁄
16 8
7⁄ ×3⁄
16 8
7⁄ ×3⁄
16 8
7⁄ ×1⁄
16 2
7⁄ ×1⁄
16 2
7⁄ ×1⁄
16 2
7⁄ ×1⁄
16 2
20.0
415⁄16*
13⁄
16
13⁄
16
15⁄
16
11⁄16
13⁄16
13⁄16
13⁄16
715⁄16
5
6
34
73.5
55.4
—
75.3
—
90.8
—
87.7
*Special rail drilling and joint-bar punching.
Rail Clips
Rail clips are forged or cast devices which are shaped to match specific rail profiles. They
are usually bolted to the runway girder flange with one bolt or are sometimes welded.
Rail clips have been used satisfactorily with all classes of cranes. However, one drawback
is that when a single bolt is used the clip can rotate in response to rail longitudinal
movement. This clip rotation can cause a camming action, thus forcing the rail out of
alignment. Because of this limitation, rail clips should only be used in crane systems
subject to infrequent use, and for runways less than 500 feet in length.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
CRANE RAILS
1 - 143
Rail Clamps
Rail clamps are a common method of attachment for heavy duty cycle cranes. Rail clamps
are detailed to provide two types: tight and floating (Figure 1-4). Each clamp consists of
two plates: an upper clamp plate and a lower filler plate.
The lower plate is flat and roughly matches the height of the toe of the rail flange. The
upper plate covers the lower plate and extends over the top of the lower rail flange. In
the tight clamp the upper plate is detailed to fit tightly to the lower tail flange top, thus
“clamping” it tightly in place when the fasteners are tightened. In the past, the tight clamp
had been illustrated with the filler plates fitted tightly against the rail flange toe. This
tight fit-up was rarely achieved in practice and is not considered to be necessary to achieve
a tight type clamp. In the floating type clamp, the pieces are detailed to provide a clearance
both alongside the rail flange toe and below the upper plate. The floating type does not,
in reality, clamp the rail but merely holds the rail within the limits of the clamp clearances.
Fig. 1-3. Hook bolts.
Reversible
1 1/2
fillers
Reversible
fillers
Clamp
plates
3
Off-center
punching
11/2
Clamp
plates
3
Off-center
punching
11/2
1 1/2
Rail base +
1/
4
( 1/2 to 9/16 ) "float"
Max. adjustment
Self-locking nut or
nut and lock washer
Filler
Machine bolt
Gage
Gage
Tight clamp
Floating clamp
Fig. 1-4. Rail clamps.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1 - 144
DIMENSIONS AND PROPERTIES
High strength bolts are recommended for both clamp types. Both types should be spaced
three feet or less apart.
Dimensions shown above are suggested. See manufacturers’ catalogs for recommended gages, bolt sizes, and detail dimensions not shown.
Patented Rail Clips
Each manufacturer’s literature presents in detail the desirable aspects of the various
designs. In general patented rail clips are easy to install due to their range of adjustment
while providing the proper limitations of lateral movement and allowance for longitudinal movement. Patented rail clips should be considered as a viable alternative to
conventional hook bolts, clips, or clamps. Because of their desirable characteristics,
patented rail clips can be used without restriction except as limited by the specific
manufacturer’s recommendations. Installations using patented rail clips sometimes incorporate pads beneath the rail. When this is done the lateral float of the rail should be
limited as in the case of the tight rail clamps.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
TORSION PROPERTIES
1 - 145
TORSION PROPERTIES
Torsional analysis is not required for the routine design of most structural steel members.
When torsional analysis is required, the Table of Torsion Properties will be of assistance
in utilizing current analysis methods. The reader is referred to the AISC publication
Torsional Analysis of Steel Members (American Institute of Steel Construction, 1983) for
additional information and appropriate design aids.
Torsion Properties are also required to determine the design compressive strength for
torsional and flexural-torsional buckling as specified in the AISC LRFD Specification
Appendix E3.
Nomenclature
= warping constant for section, in.6*
= modulus of elasticity of steel (29,000 ksi)
= shear modulus of elasticity of steel (11,200 ksi)
= flexural constant in Equation E3-1, LRFD Specification
= torsional constant for a section, in.4
= statical moment for a point in the flange directly above the vertical edge of the
web, in.3
3
_Qw = statical moment at mid-depth of the section, in.
ro = polar radius of gyration about the shear center, in.
Sw = warping statical moment at a point in the section, in.4
Wno = normalized warping function at a point at the flange edge, in.2
Cw
E
G
H
J
Qf
*Calculated values of Cw are given for all tabulated shapes. However, for many angles and T shapes, Cw is so small that for
practical purposes it can be taken as zero.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1 - 146
DIMENSIONS AND PROPERTIES
TORSION PROPERTIES
W shapes
√
EC
w
GJ
Normalized
Warping
Constant
Wno
Warping
Statical
Moment
Sw
Qf
Qw
in.
in.2
in.4
in.3
in.3
137
153
167
190
168
166
165
164
1190
1040
922
789
282
251
225
194
811
709
636
551
989000
649000
577000
511000
446000
397000
378000
333000
283000
245000
189000
75.4
95.1
103
110
121
130
138
151
173
187
209
166
158
156
154
152
151
151
149
149
148
147
2240
1540
1380
1240
1100
986
940
836
714
621
481
484
354
323
294
264
240
230
208
179
157
119
1380
992
894
813
730
665
624
560
481
434
364
393000
306000
242000
192000
181000
161000
140000
119000
99300
79600
60.6
67.9
76.8
87.6
91.3
101
109
125
136
147
125
121
118
115
114
113
112
111
111
110
1160
940
762
622
589
530
468
402
336
270
322
272
228
192
184
168
151
134
113
92.0
1030
856
715
596
566
506
453
391
346
299
1620000
1480000
1090000
816000
637000
554000
493000
441000
398000
366000
330000
306000
282000
57.5
59.8
68.6
80.0
92.0
100
108
116
127
134
143
151
160
172
169
162
156
152
150
148
146
146
145
144
143
143
3530
3270
2520
1960
1570
1390
1240
1130
1020
944
858
799
740
674
634
513
415
344
309
281
258
235
219
200
187
175
1910
1790
1420
1130
928
830
757
691
628
585
538
505
472
168000
148000
128000
116000
107000
98500
90200
82200
68100
90.3
98.1
109
116
123
130
137
145
159
109
108
108
107
106
105
105
105
104
576
512
446
407
378
349
321
294
245
408000
357000
319000
281000
250000
224000
198000
95.8
105
113
122
134
145
158
135
133
132
130
130
129
128
1130
1000
906
808
721
650
580
Torsional
Constant
J
Warping
Constant
Cw
Designation
in.4
in.6
W44×335
W ×290
W ×262
W ×230
74.4
51.5
37.7
24.9
536000
463000
406000
346000
W40×593
W ×503
W ×431
W ×372
W ×321
W ×297
W ×277
W ×249
W ×215
W ×199
W ×174
451
186
142
109
79.4
61.2
51.1
37.7
24.4
18.1
11.2
W40×466
W ×392
W ×331
W ×278
W ×264
W ×235
W ×211
W ×183
W ×167
W ×149
277
172
106
64.7
56.1
41.3
30.4
19.6
14.0
9.60
W36×848
W ×798
W ×650
W ×527
W ×439
W ×393
W ×359
W ×328
W ×300
W ×280
W ×260
W ×245
W ×230
W36×256
W ×232
W ×210
W ×194
W ×182
W ×170
W ×160
W ×150
W ×135
W33×354
W ×318
W ×291
W ×263
W ×241
W ×221
W ×201
W33×169
W ×152
W ×141
W ×130
W ×118
1270
1070
600
330
195
143
109
84.5
64.2
52.6
41.5
34.6
28.6
53.3
39.8
28.0
22.2
18.4
15.1
12.4
10.1
6.99
115
84.4
65.0
48.5
35.8
27.5
20.5
17.7
12.4
9.70
7.37
5.30
82400
71700
64400
56600
48300
110
122
131
141
154
93.7
93.8
93.3
92.8
92.2
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
329
286
258
228
196
Statical
Moment
176
159
138
128
120
111
103
95.1
79.9
520
468
416
383
359
334
312
291
255
263
237
216
195
174
158
142
709
634
577
519
469
428
386
109
95.1
86.5
76.9
66.6
314
279
257
233
207
TORSION PROPERTIES
1 - 147
TORSION PROPERTIES
W shapes
Designation
W30×477
W ×391
W ×326
W ×292
W ×261
W ×235
W ×211
W ×191
W ×173
W30×148
W ×132
W ×124
W ×116
W ×108
W ×99
W ×90
W27×539
W ×448
W ×368
W ×307
W ×258
W ×235
W ×217
W ×194
W ×178
W ×161
W ×146
√
EC
w
GJ
Normalized
Warping
Constant
Wno
Warping
Statical
Moment
Sw
Qf
Qw
in.6
in.
in.2
in.4
in.3
in.3
480000
364000
286000
249000
215000
190000
166000
146000
129000
63.6
73.6
84.8
92.8
102
111
124
135
148
329
268
223
200
177
160
141
126
113
896
716
595
530
470
422
374
337
303
49400
42100
38600
34900
30900
26800
24000
93.6
106
112
119
127
136
146
77.3
77.3
76.9
76.5
76.1
75.7
75.0
239
204
188
171
152
133
119
86.8
74.0
68.8
62.8
56.1
49.5
45.0
250
219
204
189
173
156
142
440000
336000
254000
199000
159000
140000
128000
111000
98300
87300
77200
47.8
54.1
62.4
71.4
82.2
88.5
94.6
104
114
124
135
111
106
102
99.4
98.2
96.0
95.0
93.9
93.7
92.9
92.2
1490
1190
930
750
613
548
503
442
393
352
314
342
283
231
192
161
146
135
120
107
96.6
87.0
940
766
620
511
424
384
354
314
284
256
231
Torsional
Constant
J
Warping
Constant
Cw
in.4
307
174
103
74.9
53.8
40.0
27.9
20.6
15.3
14.6
9.72
7.99
6.43
4.99
3.77
2.92
499
297
169
101
61.0
46.3
37.0
26.5
19.5
14.7
10.9
124
120
117
115
114
112
112
111
110
1450
1140
919
812
710
633
556
494
439
Statical
Moment
W27×129
W ×114
W ×102
W ×94
W ×84
11.2
7.33
5.29
4.03
2.81
32500
27600
24000
21300
17900
86.7
98.7
108
117
128
66.4
66.4
65.7
65.4
64.9
183
155
137
122
103
69.5
59.2
52.7
47.3
40.6
197
171
153
139
122
W24×492
W ×408
W ×335
W ×279
W ×250
W ×229
W ×207
W ×192
W ×176
W ×162
W ×146
W ×131
W ×117
W ×104
456
271
154
91.7
67.3
51.8
38.6
31.0
24.1
18.5
13.4
9.50
6.72
4.72
283000
214000
160000
125000
108000
95800
83900
76200
68400
62600
54600
47100
40800
35200
40.1
45.2
51.9
59.4
64.5
69.2
75.0
79.8
85.7
93.6
103
113
125
139
92.1
88.1
84.6
82.0
80.6
79.6
78.5
77.7
77.0
77.0
76.3
75.6
74.9
74.3
1150
909
709
570
502
451
401
367
333
304
268
233
204
178
281
233
189
157
141
128
116
107
97.8
89.4
79.5
69.7
61.5
54.1
774
626
509
418
372
338
303
280
255
234
209
185
164
144
W24×103
W ×94
W ×84
W ×76
W ×68
7.10
5.26
3.70
2.68
1.87
16600
15000
12800
11100
9430
77.8
85.9
94.6
104
114
53.0
53.1
52.6
52.2
51.9
117
105
91.3
79.8
68.0
49.4
44.4
39.0
34.4
29.5
140
127
112
100
88.3
W24×62
W ×55
1.71
1.18
4620
3870
83.6
92.2
40.7
40.4
42.3
35.7
23.2
19.8
76.6
67.1
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1 - 148
DIMENSIONS AND PROPERTIES
TORSION PROPERTIES
W shapes
√
EC
w
GJ
Normalized
Warping
Constant
Wno
Warping
Statical
Moment
Sw
Qf
Qw
in.6
in.
in.2
in.4
in.3
in.3
41.3
31.1
23.9
15.4
11.3
8.98
6.83
5.21
61800
54300
48500
41100
36000
32700
29200
26200
62.2
67.2
72.5
83.1
90.8
97.1
105
114
67.0
66.0
65.6
65.4
64.7
64.2
63.7
63.2
345
307
277
235
208
191
172
155
W21×93
W ×83
W ×73
W ×68
W ×62
6.03
4.34
3.02
2.45
1.83
9940
8630
7410
6760
5960
65.3
71.8
79.7
84.5
91.8
43.6
43.0
42.5
42.3
42.0
85.3
75.0
65.2
59.9
53.2
38.2
34.2
30.3
28.0
25.1
110
98.0
86.2
79.9
72.2
W21×57
W ×50
W ×44
1.77
1.14
0.77
3190
2570
2110
68.3
76.4
84.2
33.4
33.1
32.8
35.6
28.9
24.0
20.9
17.2
14.5
64.3
55.0
47.7
75700
65600
57400
49900
43200
37900
33200
28900
25700
22700
33.3
35.5
37.8
40.3
43.4
46.6
50.1
54.3
58.6
63.2
58.8
57.5
56.4
55.2
54.2
53.3
52.5
51.6
51.0
50.4
483
427
382
339
299
267
237
210
189
169
Torsional
Constant
J
Warping
Constant
Cw
Designation
in.4
W21×201
W ×182
W ×166
W ×147
W ×132
W ×122
W ×111
W ×101
W18×311
W ×283
W ×258
W ×234
W ×211
W ×192
W ×175
W ×158
W ×143
W ×130
177
135
104
79.7
59.3
45.2
34.2
25.4
19.4
14.7
Statical
Moment
102
92.3
84.4
71.4
64.0
59.2
53.7
49.0
141
127
116
105
94.3
85.7
77.2
69.4
63.2
57.1
265
238
216
187
167
154
139
127
376
338
306
274
245
221
199
178
161
145
W18×119
W ×106
W ×97
W ×86
W ×76
10.6
7.48
5.86
4.10
2.83
20300
17400
15800
13600
11700
70.4
77.6
83.6
92.7
103
50.4
49.8
49.4
48.9
48.4
151
131
120
104
90.7
50.6
44.6
41.2
36.3
31.9
131
115
105
92.8
81.4
W18×71
W ×65
W ×60
W ×55
W ×50
3.48
2.73
2.17
1.66
1.24
4700
4240
3850
3430
3040
59.1
63.4
67.8
73.1
79.7
33.7
33.4
33.1
32.9
32.6
52.1
47.5
43.5
39.0
34.9
25.8
23.8
22.1
19.9
18.0
72.7
66.6
61.4
55.9
50.4
W18×46
W ×40
W ×35
1.22
0.81
0.51
1710
1440
1140
60.2
67.8
76.1
26.4
26.1
25.9
24.2
20.6
16.5
15.3
13.3
10.7
45.3
39.2
33.2
W16×100
W ×89
W ×77
W ×67
7.73
5.45
3.57
2.39
11900
10200
8590
7300
63.1
69.6
78.9
88.9
41.7
41.1
40.6
40.1
107
93.3
79.3
68.2
39.0
34.4
29.7
25.9
99.0
87.3
75.0
64.9
W16×57
W ×50
W ×45
W ×40
W ×36
2.22
1.52
1.11
0.79
0.54
2660
2270
1990
1730
1460
55.7
62.2
68.1
75.3
83.7
28.0
27.6
27.4
27.1
26.9
35.6
30.8
27.2
23.9
20.2
19.0
16.7
15.0
13.4
11.4
52.6
46.0
41.1
36.5
32.0
W16×31
W ×26
0.46
0.26
739
565
64.5
75.0
21.3
21.1
13.0
10.0
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
9.17
7.20
27.0
22.1
TORSION PROPERTIES
1 - 149
TORSION PROPERTIES
W shapes
Torsional
Constant
J
Designation
W14×808
W ×730
W ×665
W ×605
W ×550
W ×500
W ×455
W14×426
W ×398
W ×370
W ×342
W ×311
W ×283
W ×257
W ×233
W ×211
W ×193
W ×176
W ×159
W ×145
4
in.
1860
1450
1120
870
670
514
395
331
273
222
178
136
104
79.1
59.5
44.6
34.8
26.5
19.8
15.2
Warping
Constant
Cw
6
in.
√
EC
w
GJ
Normalized
Warping
Constant
Wno
2
Warping
Statical
Moment
Sw
4
Statical
Moment
Qf
3
Qw
in.3
in.
in.
in.
in.
433000
362000
305000
258000
219000
187000
160000
24.6
25.4
26.6
27.7
29.1
30.7
32.4
82.2
78.3
75.5
73.0
70.6
68.5
66.5
1950
1720
1510
1320
1160
1020
899
337
319
287
259
233
209
189
916
831
740
660
588
524
468
144000
129000
116000
103000
89100
77700
67800
59000
51500
45900
40500
35600
31700
33.6
35.0
36.8
38.7
41.2
44.0
47.1
50.7
54.7
58.4
62.9
68.2
73.5
65.3
64.1
62.9
61.6
60.3
59.1
57.9
56.9
55.9
55.1
54.4
53.7
53.0
827
756
689
623
553
493
438
389
345
312
279
248
224
176
163
151
138
125
113
102
91.7
82.3
75.4
68.0
61.3
55.8
434
401
368
336
301
271
243
218
195
177
160
143
130
190
171
154
138
125
49.9
45.3
41.2
37.2
33.7
117
106
95.9
86.6
78.3
W14×132
W ×120
W ×109
W ×99
W ×90
12.3
9.37
7.12
5.37
4.06
25500
22700
20200
18000
16000
73.3
79.2
85.7
93.2
101
50.2
49.7
49.1
48.7
48.3
W14×82
W ×74
W ×68
W ×61
5.08
3.88
3.02
2.20
6710
5990
5380
4710
58.5
63.2
67.9
74.5
34.1
33.7
33.4
33.1
73.8
66.6
60.4
53.3
28.1
25.7
23.5
21.0
69.3
62.8
57.3
51.1
W14×53
W ×48
W ×43
1.94
1.46
1.05
2540
2240
1950
58.2
63.0
69.3
26.7
26.5
26.2
35.5
31.6
27.8
17.3
15.6
13.9
43.6
39.2
34.8
W14×38
W ×34
W ×30
0.80
0.57
0.38
1230
1070
887
63.1
69.7
77.7
23.0
22.8
22.6
20.0
17.5
14.7
11.5
10.2
8.59
30.7
27.3
23.6
W14×26
W ×22
0.36
0.21
405
314
54.0
62.2
16.9
16.8
6.98
5.58
20.1
16.6
243
185
143
108
83.8
64.7
48.8
35.6
25.8
18.5
12.9
9.13
6.86
5.10
3.84
2.93
2.18
57000
48600
42000
35800
31200
27200
23600
20100
17200
14700
12400
10700
9410
8270
7330
6540
5780
24.6
26.1
27.6
29.3
31.0
33.0
35.4
38.2
41.5
45.4
49.9
55.1
59.6
64.8
70.3
76.0
82.9
46.4
45.0
44.0
42.8
41.8
41.0
40.1
39.2
38.4
37.7
37.0
36.4
35.9
35.5
35.2
34.9
34.5
W12×336
W ×305
W ×279
W ×252
W ×230
W ×210
W ×190
W ×170
W ×152
W ×136
W ×120
W ×106
W ×96
W ×87
W ×79
W ×72
W ×65
8.94
7.02
459
403
357
313
279
249
220
192
168
146
126
110
98.2
87.2
78.1
70.3
62.7
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
119
107
96.3
86.4
78.4
71.1
64.1
56.9
50.4
44.5
38.9
34.6
31.3
28.0
25.3
22.9
20.6
301
269
241
214
193
174
156
137
121
107
93.2
81.9
73.6
66.0
59.5
53.9
48.4
1 - 150
DIMENSIONS AND PROPERTIES
TORSION PROPERTIES
W shapes
√
EC
w
GJ
Normalized
Warping
Constant
Wno
Warping
Statical
Moment
Sw
Qf
Qw
in.
in.2
in.4
in.3
in.3
3570
3160
66.3
72.0
28.9
28.7
46.3
41.2
18.2
16.3
43.2
39.0
1.78
1.31
0.95
1880
1650
1440
52.3
57.1
62.6
23.3
23.1
22.9
30.2
26.7
23.6
14.7
13.1
11.8
36.2
32.4
28.8
W12×35
W ×30
W ×26
0.74
0.46
0.30
879
720
607
55.5
63.7
72.4
19.6
19.4
19.2
16.8
13.9
11.8
W12×22
W ×19
W ×16
W ×14
0.29
0.18
0.10
0.07
164
131
96.9
80.4
38.3
43.4
50.1
54.5
12.0
11.8
11.7
11.6
W10×112
W ×100
W ×88
W ×77
W ×68
W ×60
W ×54
W ×49
15.1
10.9
7.53
5.11
3.56
2.48
1.82
1.39
6020
5150
4330
3630
3100
2640
2320
2070
32.1
35.0
38.6
42.9
47.5
52.5
57.5
62.1
26.3
25.8
25.3
24.8
24.4
24.0
23.8
23.6
85.7
74.7
64.2
54.9
47.6
41.2
36.6
33.0
30.8
27.2
23.8
20.7
18.1
15.9
14.3
13.0
73.7
64.9
56.4
48.8
42.6
37.3
33.3
30.2
W10×45
W ×39
W ×33
1.51
0.98
0.58
1200
992
790
45.4
51.2
59.4
19.0
18.7
18.5
23.6
19.8
16.0
11.5
9.77
7.98
27.5
23.4
19.4
W10×30
W ×26
W ×22
0.62
0.40
0.24
414
345
275
41.6
47.3
54.5
14.5
14.3
14.1
10.7
9.05
7.30
7.09
6.08
4.95
18.3
15.6
13.0
W10×19
W ×17
W ×15
W ×12
0.23
0.16
0.10
0.05
104
85.1
68.3
50.9
34.2
37.1
42.1
51.3
3.93
3.24
2.62
1.99
3.76
3.13
2.56
2.00
10.8
9.33
8.00
6.32
W8×67
W ×58
W ×48
W ×40
W ×35
W ×31
5.06
3.34
1.96
1.12
0.77
0.54
1440
1180
931
726
619
530
27.1
30.2
35.1
41.0
45.6
50.4
16.7
16.3
15.8
15.5
15.3
15.1
14.7
12.5
10.4
8.42
7.39
6.46
35.1
29.9
24.5
19.9
17.3
15.2
W8×28
W ×24
0.54
0.35
312
259
38.7
43.8
12.4
12.2
9.43
7.94
5.64
4.83
13.6
11.6
W8×21
W ×18
0.28
0.17
152
122
37.5
43.1
10.4
10.3
5.47
4.44
4.03
3.31
10.2
8.52
W8×15
W ×13
W ×10
0.14
0.09
0.04
51.8
40.8
30.9
31.0
34.3
44.7
7.82
7.74
7.57
2.47
1.97
1.53
2.39
1.93
1.56
6.78
5.70
4.43
W6×25
W ×20
W ×15
0.46
0.24
0.10
150
113
76.5
29.1
34.9
44.5
9.01
8.78
8.58
6.23
4.82
3.34
3.92
3.10
2.18
9.46
7.45
5.39
W6×16
W ×12
W ×9
0.22
0.09
0.04
38.2
24.7
17.7
21.2
26.7
33.8
5.92
5.75
5.60
2.42
1.61
1.19
2.28
1.55
1.19
5.84
4.15
3.12
W5×19
W ×16
0.31
0.19
50.8
40.6
20.6
23.5
5.94
5.81
3.21
2.62
2.44
2.02
5.81
4.82
W4×13
0.15
14.0
15.5
3.87
1.36
1.27
3.14
Torsional
Constant
J
Warping
Constant
Cw
Designation
in.4
in.6
W12×58
W ×53
2.10
1.58
W12×50
W ×45
W ×40
9.89
9.80
9.72
9.56
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
5.13
4.14
3.09
2.59
32.3
27.2
22.0
17.5
15.2
13.1
Statical
Moment
9.86
8.30
7.15
25.6
21.6
18.6
4.87
4.01
3.04
2.59
14.7
12.4
10.0
8.72
TORSION PROPERTIES
1 - 151
TORSION PROPERTIES
M shapes
√
EC
w
GJ
Normalized
Warping
Constant
Wno
Warping
Statical
Moment
Sw
Qf
Qw
in.6
in.
in.2
in.4
in.3
in.3
0.05
0.04
34.0
31.3
42.0
45.0
9.02
9.01
1.56
1.45
1.98
1.86
7.14
6.58
M10×9
M ×8
0.03
0.02
14.6
12.8
35.5
40.7
6.59
6.57
0.91
0.80
1.32
1.18
4.60
4.06
M8×6.5
0.02
26.0
4.45
0.48
0.82
2.72
M5×18.9
0.34
17.7
5.73
2.98
2.28
5.53
Torsional
Constant
J
Warping
Constant
Cw
Designation
in.4
M12×11.8
M ×10.8
5.23
41.3
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
Statical
Moment
1 - 152
DIMENSIONS AND PROPERTIES
TORSION PROPERTIES
S shapes
Designation
S24×121
S ×106
√
EC
w
GJ
Normalized
Warping
Constant
Wno
Warping
Statical
Moment
Sw
Qf
Qw
in.6
in.
in.2
in.4
in.3
in.3
11400
10600
48.0
52.1
47.1
46.1
103
98.8
47.1
47.1
154
141
121
112
103
Torsional
Constant
J
Warping
Constant
Cw
in.4
12.8
10.1
Statical
Moment
S24×100
S ×90
S ×80
7.58
6.04
4.88
6380
6000
5640
46.7
50.7
54.7
41.9
41.2
40.5
66.0
63.8
61.6
33.5
33.5
33.5
S20×96
S ×86
8.39
6.64
4710
4390
38.1
41.4
34.9
34.2
57.8
55.5
29.2
29.2
99.7
92.5
S20×75
S ×66
4.59
3.58
2750
2550
39.4
42.9
30.7
30.0
38.9
37.3
22.6
22.6
77.0
70.5
S18×70
S ×54.7
4.15
2.37
1800
1560
33.5
41.3
27.0
26.0
29.2
26.9
17.1
17.1
63.0
52.9
S15×50
S ×42.9
2.12
1.54
811
744
31.5
35.4
20.3
19.8
17.8
16.9
11.8
11.8
39.0
35.1
S12×50
S ×40.8
2.82
1.75
505
437
21.5
25.4
15.5
14.9
14.0
12.9
9.30
9.30
31.0
26.9
S12×35
S ×31.8
1.08
0.90
324
307
27.9
29.7
14.5
14.3
10.0
9.74
7.48
7.48
22.7
21.3
S10×35
S ×25.4
1.29
0.60
189
153
19.5
25.7
11.8
11.1
7.13
6.34
5.24
5.24
17.9
14.4
S8×23
S ×18.4
0.55
0.34
61.8
53.5
17.1
20.2
7.90
7.58
3.50
3.22
3.10
3.10
9.74
8.38
S6×17.25
S ×12.5
0.37
0.17
18.4
14.5
11.3
14.9
5.03
4.70
1.61
1.41
1.63
1.63
5.35
4.30
S5×10
0.11
6.66
12.3
3.51
0.86
1.11
2.88
S4×9.5
S ×7.7
0.12
0.07
3.10
2.62
8.18
9.84
2.59
2.47
0.53
0.48
0.70
0.70
2.05
1.79
S3×7.5
S ×5.7
0.09
0.04
1.10
0.85
5.63
7.42
1.72
1.60
0.28
0.24
0.40
0.40
1.20
1.00
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
TORSION PROPERTIES
1 - 153
TORSION PROPERTIES
HP shapes
√
EC
w
GJ
Normalized
Warping
Constant
Wno
Warping
Statical
Moment
Sw
Qf
Qw
in.6
in.
in.2
in.4
in.3
in.3
8.02
5.40
3.60
2.01
19900
16800
14200
11200
80.2
89.8
101
120
49.9
49.2
48.5
47.8
149
128
110
88.0
38.5
33.5
29.1
23.8
97.2
84.3
72.9
59.2
HP13×100
HP ×87
HP ×73
HP ×60
6.25
4.12
2.54
1.39
11300
9430
7680
6020
68.4
77.0
88.5
106
40.9
40.2
39.6
39.0
103
87.7
72.8
57.8
29.9
25.8
21.8
17.7
76.3
65.6
55.2
44.5
HP12×84
HP ×74
HP ×63
HP ×53
4.24
2.98
1.83
1.12
7160
6170
4990
4090
66.1
73.2
84.0
97.2
35.6
35.2
34.6
34.2
75.0
65.5
54.1
44.7
23.5
20.8
17.5
14.7
59.8
52.7
44.2
37.0
HP10×57
HP ×42
1.97
0.81
2240
1540
54.3
70.2
24.1
23.4
34.8
24.7
13.1
9.64
33.2
24.2
HP8×36
0.77
578
44.1
15.4
14.0
6.62
16.8
Torsional
Constant
J
Warping
Constant
Cw
Designation
in.4
HP14×117
HP ×102
HP ×89
HP ×73
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
Statical
Moment
1 - 154
DIMENSIONS AND PROPERTIES
FLEXURAL-TORSIONAL PROPERTIES
Channels
Designation
Torsional
Constant
J
Warping
Constant
Cw
Polar
Radius of
Gyration
_
ro*
Flexural
Constant
H*
in.4
in.6
in.
No Units
C15×50
C15×40
C15×33.9
2.67
1.46
1.02
492
411
358
5.49
5.72
5.94
.937
.927
.920
C12×30
C15×25
C15×20.7
0.87
0.54
0.37
151
130
112
4.55
4.72
4.93
.919
.909
.899
C10×30
C1××25
C5××20
C10×15.3
1.23
0.69
0.37
0.21
79.3
68.4
56.9
45.6
3.63
3.75
3.93
4.19
.921
.912
.900
.883
C9×20
C9×15
C9×13.4
0.43
0.21
0.17
39.4
31.0
28.2
3.46
3.69
3.79
.899
.882
.874
C8×18.75
C9×13.75
C9×11.5
0.44
0.19
0.13
25.1
19.2
16.5
3.06
3.27
3.42
.894
.874
.862
C7×12.25
C9×9.8
0.16
0.10
11.2
9.18
2.87
3.02
.862
.846
C6×13
C9×10.5
C9×8.2
0.24
0.13
0.08
7.22
5.95
4.72
2.37
2.49
2.65
.858
.843
.824
C5×9
C9×6.7
0.11
0.06
2.93
2.22
2.10
2.26
.814
.790
C4×7.25
C9×5.4
0.08
0.04
1.24
0.92
1.75
1.89
.768
.741
C3×6
C9×5
C9×4.1
0.07
0.04
0.03
0.46
0.38
0.31
1.39
1.45
1.53
.689
.674
.656
*See LRFD Specification Appendix E3.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
TORSION PROPERTIES
1 - 155
FLEXURAL-TORSIONAL PROPERTIES
Channels
Designation
Torsional
Constant
J
Warping
Constant
Cw
Polar
Radius of
Gyration
_
ro*
Flexural
Constant
H*
in.4
in.6
in.
No Units
MC18×58
MC10×51.9
MC10×45.8
MC10×42.7
2.81
2.03
1.45
1.23
1070
986
897
852
6.56
6.70
6.88
6.97
.944
.939
.933
.930
MC13×50
MC10×40
MC10×35
MC10×31.8
2.98
1.57
1.14
0.94
558
463
413
380
5.07
5.33
5.50
5.64
.875
.860
.849
.842
MC12×50
MC10×45
MC10×40
MC10×35
MC10×31
MC10×10.6
3.24
2.35
1.70
1.25
1.01
0.06
411
374
336
297
268
11.7
4.77
4.87
5.01
5.18
5.34
4.27
.859
.851
.842
.832
.821
.983
MC10×41.1
MC10×33.6
MC10×28.5
2.27
1.21
0.79
270
224
194
4.26
4.47
4.68
.790
.771
.752
MC10×25
MC10×22
0.64
0.51
125
111
4.46
4.63
.802
.790
MC10×8.4
0.04
3.68
.972
MC9×25.4
MC9×23.9
0.69
0.60
4.08
4.15
.770
.763
MC8×22.8
MC9×21.4
MC9×20
MC9×18.7
MC9×8.5
0.57
0.50
0.44
0.38
0.06
75.3
70.9
47.9
45.1
8.22
3.85
3.91
3.59
3.65
3.24
.716
.709
.780
.773
.910
MC7×22.7
MC9×19.1
0.63
0.41
58.5
49.4
3.53
3.71
.662
.638
MC6×18
0.38
34.6
3.46
.562
MC6×16.3
MC9×15.1
0.34
0.29
22.1
20.6
3.11
3.18
.643
.634
MC6×12
0.15
11.2
2.80
.740
7.01
104
98.2
*See LRFD Specification Appendix E3.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1 - 156
DIMENSIONS AND PROPERTIES
FLEXURAL-TORSIONAL PROPERTIES
Single Angles
Polar
Radius of
Gyration
_
ro*
Flexural
Constant
H*
in.6
in.
No Units
×1
×17⁄8
×13⁄4
×15⁄8
×19⁄16
×11⁄2
7.13
5.08
3.46
2.21
1.30
0.960
0.682
32.5
23.4
16.1
10.4
6.16
4.55
3.23
4.31
4.35
4.37
4.41
4.45
4.47
4.48
0.632
0.630
0.629
0.627
0.627
0.627
0.624
L8×6×1
L × × 3⁄4
L × ×19⁄16
L × ×11⁄2
L × ×17⁄16
4.35
1.90
0.822
0.584
0.396
16.3
7.28
3.20
2.28
1.55
3.89
3.96
4.01
4.02
4.04
—
—
—
—
—
L8×4×1
L8×4×17⁄8
L × ×13⁄4
L8×4×15⁄8
L × ×19⁄16
L × ×11⁄2
L8×4×17⁄16
3.68
2.48
1.61
0.933
0.704
0.501
0.328
12.9
8.89
5.75
3.42
2.53
1.80
1.22
3.77
3.79
3.82
3.85
3.86
3.88
3.89
—
—
—
—
—
—
—
L7×4×3⁄4
L × ×5⁄8
L × ×1⁄2
L7×4×7⁄16
L × ×3⁄8
1.47
0.873
0.459
0.300
0.200
3.33
3.36
3.38
3.40
3.42
—
—
—
—
—
Designation
L8×8×11⁄8
L
L
L
L
L
L
×
×
×
×
×
×
Torsional
Constant
J
Warping
Constant
Cw
in.4
3.97
2.37
1.25
0.851
0.544
*See LRFD Specification Appendix E3.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
TORSION PROPERTIES
1 - 157
FLEXURAL-TORSIONAL PROPERTIES
Single Angles
Torsional
Constant
J
Warping
Constant
Cw
Polar
Radius of
Gyration
_
ro*
Flexural
Constant
H*
in.4
in.6
in.
No Units
L6×6×1
L6×6×17⁄8
L6×6×13⁄4
L6×6×15⁄8
L6×6×19⁄16
L6×6×11⁄2
L6×6×17⁄16
L6×6×13⁄8
L6×6×15⁄16
3.68
2.51
1.61
0.954
0.704
0.501
0.340
0.218
0.129
9.24
6.41
4.17
2.50
1.85
1.32
0.899
0.575
0.338
3.19
3.22
3.26
3.29
3.31
3.32
3.34
3.36
3.38
0.637
0.632
0.629
0.628
0.627
0.627
0.627
0.626
0.625
L6×4×3⁄4
L6×4×5⁄8
L6×4×9⁄16
L6×4×1⁄2
L6×4×7⁄16
L6×4×3⁄8
L6×4×5⁄16
1.33
0.792
0.585
0.417
0.284
0.183
0.108
2.64
1.59
1.18
0.843
0.575
0.369
0.217
2.86
2.89
2.9
2.92
2.94
2.96
2.97
—
—
—
—
—
—
—
L6×31⁄2×1⁄2
L6×31⁄2×3⁄8
L6×31⁄2×5⁄16
0.396
0.174
0.103
0.779
0.341
0.201
2.88
2.92
2.93
—
—
—
L5×5×7⁄8
L6×4×3⁄4
L6×4×5⁄8
L6×4×1⁄2
L6×4×7⁄16
L6×4×3⁄8
L6×4×5⁄16
2.07
1.33
0.792
0.417
0.284
0.183
0.108
3.53
2.32
1.40
0.744
0.508
0.327
0.193
2.65
2.68
2.71
2.74
2.77
2.79
2.81
0.634
0.634
0.630
0.630
0.629
0.627
0.626
Designation
*See LRFD Specification Appendix E3.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1 - 158
DIMENSIONS AND PROPERTIES
FLEXURAL-TORSIONAL PROPERTIES
Single Angles
Torsional
Constant
J
Warping
Constant
Cw
Polar
Radius of
Gyration
_
ro*
Flexural
Constant
H*
in.4
in.6
in.
No Units
L5×31⁄2×3⁄4
L5×31⁄2×5⁄8
L5×31⁄2×1⁄2
L5×31⁄2×3⁄8
L5×31⁄2×5⁄16
L5×31⁄2×1⁄4
1.11
0.660
0.348
0.153
0.0905
0.0479
1.52
0.918
0.491
0.217
0.128
0.0670
2.37
2.40
2.44
2.47
2.49
2.50
—
—
—
—
—
—
L5×3×1⁄2
L5×3×7⁄16
L5×3×3⁄8
L5×3×5⁄16
L5×3×1⁄4
0.322
0.219
0.141
0.0832
0.0438
0.444
0.304
0.196
0.116
0.0606
2.39
2.41
2.42
2.43
2.45
—
—
—
—
—
L4×4×3⁄4
L5×3×5⁄8
L5×3×1⁄2
L5×3×7⁄16
L5×3×3⁄8
L5×3×5⁄16
L5×3×1⁄4
1.02
0.610
0.322
0.219
0.141
0.0832
0.0438
1.12
0.680
0.366
0.252
0.162
0.0963
0.0505
2.11
2.14
2.17
2.19
2.20
2.22
2.23
0.639
0.631
0.632
0.631
0.625
0.623
0.627
L4×31⁄2×1⁄2
L5×31⁄2×3⁄8
L5×31⁄2×5⁄16
L5×31⁄2×1⁄4
0.301
0.132
0.0782
0.0412
0.302
0.134
0.0798
0.0419
2.04
2.08
2.09
2.11
—
—
—
—
Designation
*See LRFD Specification Appendix E3.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
TORSION PROPERTIES
1 - 159
FLEXURAL-TORSIONAL PROPERTIES
Single Angles
Torsional
Constant
J
Warping
Constant
Cw
Polar
Radius of
Gyration
_
ro*
Flexural
Constant
H*
in.4
in.6
in.
No Units
L4×3×5⁄8
L4×3×1⁄2
L4×3×7⁄16
L4×3×3⁄8
L4×3×5⁄16
L4×3×1⁄4
0.529
0.281
0.192
0.123
0.0731
0.0386
0.472
0.255
0.176
0.114
0.0676
0.0356
1.91
1.95
1.96
1.98
2.00
2.01
—
—
—
—
—
—
L31⁄2×31⁄2×1⁄2
L31⁄2×31⁄2×7⁄16
L31⁄2×31⁄2×3⁄8
L31⁄2×31⁄2×5⁄16
L31⁄2×31⁄2×1⁄4
0.281
0.192
0.123
0.0731
0.0386
0.238
0.164
0.106
0.0634
0.0334
1.89
1.91
1.91
1.93
1.95
0.631
0.629
0.628
0.627
0.626
L31⁄2×3×1⁄2
L31⁄2×3×3⁄8
L31⁄2×3×5⁄16
L31⁄2×3×1⁄4
0.260
0.114
0.0680
0.0360
0.191
0.0858
0.0512
0.0270
1.76
1.79
1.81
1.83
—
—
—
—
L31⁄2×21⁄2×1⁄2
L31⁄2×31⁄2×3⁄8
L31⁄2×31⁄2×1⁄4
0.234
0.103
0.0322
0.159
0.0714
0.0225
1.67
1.70
1.73
—
—
—
L3×3×1⁄2
L4×3×7⁄16
L4×3×3⁄8
L4×3×5⁄16
L4×3×1⁄4
L4×3×3⁄16
0.234
0.160
0.103
0.0611
0.0322
0.0142
0.144
0.100
0.0652
0.0390
0.0206
0.00899
1.60
1.61
1.63
1.65
1.66
1.68
0.634
0.632
0.629
0.628
0.627
0.626
Designation
*See LRFD Specification Appendix E3.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1 - 160
DIMENSIONS AND PROPERTIES
FLEXURAL-TORSIONAL PROPERTIES
Single Angles
Torsional
Constant
J
Warping
Constant
Cw
Polar
Radius of
Gyration
_
ro*
Flexural
Constant
H*
in.4
in.6
in.
No Units
L3×21⁄2×1⁄2
L3×21⁄2×7⁄16
L3×21⁄2×3⁄8
L3×21⁄2×5⁄16
L3×21⁄2×1⁄4
L3×21⁄2×3⁄16
0.213
0.146
0.0943
0.0560
0.0296
0.0131
0.112
0.0777
0.0507
0.0304
0.0161
0.00705
1.47
1.49
1.50
1.52
1.54
1.55
—
—
—
—
—
—
L3×2×1⁄2
L2×2×3⁄8
L2×2×5⁄16
L2×2×1⁄4
L2×2×3⁄16
0.192
0.0855
0.0509
0.0270
0.0120
0.0908
0.0413
0.0248
0.0132
0.00576
1.40
1.43
1.45
1.46
1.48
—
—
—
—
—
L21⁄2×21⁄2×1⁄2
L21⁄2×21⁄2×3⁄8
L21⁄2×21⁄2×5⁄16
L21⁄2×21⁄2×1⁄4
L21⁄2×21⁄2×3⁄16
0.185
0.0816
0.0483
0.0253
0.0110
0.0791
0.0362
0.0218
0.0116
0.00510
1.31
1.34
1.36
1.37
1.39
0.639
0.632
0.630
0.628
0.627
L21⁄2×2×3⁄8
L3×21⁄2×5⁄16
L3×21⁄2×1⁄4
L3×21⁄2×3⁄16
0.0728
0.0432
0.0227
0.00990
0.0268
0.0162
0.00868
0.00382
1.22
1.24
1.25
1.27
—
—
—
—
L2×2×3⁄8
L2×2×5⁄16
L2×2×1⁄4
L2×2×3⁄16
L2×2×1⁄8
0.0640
0.0381
0.0201
0.00880
0.00274
0.0174
0.0106
0.00572
0.00254
0.00079
1.05
1.07
1.09
1.10
1.12
0.637
0.633
0.630
0.628
0.626
Designation
*See LRFD Specification Appendix E3.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
TORSION PROPERTIES
1 - 161
FLEXURAL-TORSIONAL PROPERTIES
Structural Tees
Polar
Radius of
Gyration
_
ro*
Flexural
Constant
H*
in.6
in.
No Units
37.2
25.7
18.9
12.4
434
279
204
139
8.81
8.67
8.65
8.67
0.724
0.733
0.731
0.723
WT20×296.5**
WT ×251.5**
WT ×215.5
WT ×186
WT ×160.5
WT ×148.5
WT ×138.5
WT ×124.5
WT ×107.5
WT ×99.5
WT ×87
223
140
88.5
58.2
37.7
30.6
25.8
19.1
12.4
9.14
5.60
2340
1420
881
559
350
279
218
158
101
83.5
65.3
8.30
8.17
8.09
8.00
7.92
7.88
7.75
7.71
7.66
7.83
8.12
0.761
0.760
0.756
0.756
0.756
0.756
0.770
0.770
0.770
0.746
0.699
WT20×233**
WT ×196**
WT ×165.5
WT ×139
WT ×132
WT ×117.5
WT ×105.5
WT ×91.5
WT ×83.5
WT ×74.5
139
86.1
53.0
32.4
28.0
20.6
15.2
10.0
7.01
4.68
1360
802
485
278
233
156
113
72.1
62.9
51.9
8.39
8.27
8.19
8.07
8.02
7.88
7.84
7.79
8.02
8.24
0.680
0.678
0.674
0.676
0.680
0.690
0.690
0.691
0.658
0.626
WT18×424**
WT ×399**
WT ×325**
WT ×263.5**
WT ×219.5**
WT ×196.5**
WT ×179.5**
WT ×164**
WT ×150
WT ×140
WT ×130
WT ×122.5
WT ×115
622
527
295
163
96.7
70.7
54.3
42.1
32.0
26.2
20.7
17.3
14.3
6880
5700
3010
1570
894
637
480
363
278
226
181
151
125
8.08
8.02
7.82
7.63
7.52
7.44
7.38
7.32
7.30
7.27
7.28
7.28
7.27
0.802
0.801
0.797
0.797
0.794
0.796
0.797
0.799
0.797
0.796
0.791
0.788
0.784
Designation
WT22×167.5
WT ×145
WT ×131
WT ×115
Torsional
Constant
J
Warping
Constant
Cw
in.4
*See LRFD Specification Section E3.
**Group 4 or Group 5 shape. See Notes in Table 1-2.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1 - 162
DIMENSIONS AND PROPERTIES
FLEXURAL-TORSIONAL PROPERTIES
Structural Tees
Torsional
Constant
J
Warping
Constant
Cw
Polar
Radius of
Gyration
_
ro*
Flexural
Constant
H*
in.4
in.6
in.
No Units
WT18×128
WT ×116
WT ×105
WT ×97
WT ×91
WT ×85
WT ×80
WT ×75
WT ×67.5
26.6
19.8
13.9
11.1
9.19
7.51
6.17
5.04
3.48
205
151
119
92.7
77.6
63.2
53.6
46.0
37.3
7.43
7.40
7.49
7.45
7.45
7.44
7.46
7.50
7.65
0.703
0.703
0.687
0.687
0.686
0.684
0.678
0.670
0.644
WT16.5×177**
WT
×159**
WT
×145.5**
WT
×131.5**
WT
×120.5
WT
×110.5
WT
×100.5
57.2
42.1
32.4
24.2
17.9
13.7
10.2
468
335
256
188
146
113
84.9
7.00
6.94
6.90
6.86
6.91
6.90
6.89
0.802
0.803
0.801
0.802
0.792
0.788
0.784
8.83
6.16
4.84
3.67
2.64
55.4
43.0
35.4
29.3
23.4
6.74
6.82
6.85
6.93
7.02
0.714
0.700
0.691
0.678
0.659
151
85.9
50.8
37.2
26.7
19.9
13.9
10.3
7.61
1170
636
361
257
184
132
96.4
71.2
53.0
6.65
6.54
6.40
6.34
6.31
6.25
6.27
6.25
6.25
0.819
0.815
0.817
0.818
0.815
0.817
0.809
0.806
0.802
7.27
4.85
3.98
3.21
2.49
1.88
1.42
37.6
28.5
23.9
20.5
17.3
14.3
10.5
6.10
6.19
6.20
6.24
6.31
6.38
6.34
0.716
0.698
0.693
0.683
0.669
0.654
0.655
Designation
WT16.5×84.5
WT
×76
WT
×70.5
WT
×65
WT
×59
WT15×238.5**
WT ×195.5**
WT ×163**
WT ×146**
WT ×130.5
WT ×117.5
WT ×105.5
WT ×95.5
WT ×86.5
WT15×74
WT ×66
WT ×62
WT ×58
WT ×54
WT ×49.5
WT ×45
*See LRFD Specification Section E3.
**Group 4 or Group 5 shape. See Notes in Table 1-2.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
TORSION PROPERTIES
1 - 163
FLEXURAL-TORSIONAL PROPERTIES
Structural Tees
Designation
WT13.5×269.5**
WT
×224**
WT
×184**
WT
×153.5**
WT
×140.5**
WT
×129
WT
×117.5
WT
×108.5
WT
×97
WT
×89
WT
×80.5
WT
×73
WT13.5×64.5
WT
×57
WT
×51
WT
×47
WT
×42
WT12×246**
WT ×204**
WT ×167.5**
WT ×139.5**
WT ×125**
WT ×114.5
WT ×103.5
WT ×96
WT ×88
WT ×81
WT ×73
WT ×65.5
WT ×58.5
WT ×52
Torsional
Constant
J
Warping
Constant
Cw
Polar
Radius of
Gyration
_
ro*
Flexural
Constant
H*
in.4
in.6
in.
No Units
245
146
83.6
49.8
39.0
30.2
23.0
18.5
13.2
9.74
7.31
5.44
1740
977
532
304
232
178
135
105
74.3
57.7
42.7
31.7
6.27
6.11
5.97
5.85
5.80
5.77
5.74
5.72
5.66
5.70
5.67
5.65
0.830
0.829
0.828
0.828
0.830
0.828
0.825
0.830
0.826
0.815
0.813
0.810
5.48
5.54
5.52
5.57
5.63
0.731
0.716
0.714
0.703
0.685
5.71
5.55
5.40
5.28
5.22
5.19
5.14
5.11
5.09
5.09
5.08
5.09
5.08
5.07
0.838
0.836
0.837
0.837
0.838
0.836
0.836
0.836
0.835
0.831
0.827
0.818
0.813
0.809
5.60
3.65
2.64
2.01
1.40
223
133
76.0
45.3
33.3
25.7
19.1
15.4
12.0
9.22
6.70
4.74
3.35
2.35
24.0
17.5
12.6
10.2
7.79
1340
748
405
230
165
125
91.3
72.5
55.8
43.8
31.9
23.1
16.4
11.6
WT12×51.5
WT ×47
WT ×42
WT ×38
WT ×34
3.54
2.62
1.84
1.34
0.932
12.3
9.57
6.90
5.30
4.08
4.88
4.89
4.89
4.93
4.99
0.733
0.727
0.721
0.709
0.692
WT12×31
WT ×27.5
0.850
0.588
3.92
2.93
5.13
5.18
0.619
0.606
*See LRFD Specification Section E3.
**Group 4 or Group 5 shape. See Notes in Table 1-2.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1 - 164
DIMENSIONS AND PROPERTIES
FLEXURAL-TORSIONAL PROPERTIES
Structural Tees
Designation
WT10.5×100.5
WT10.5×91
WT10.5×83
WT10.5×73.5
WT10.5×66
WT10.5×61
WT10.5×55.5
WT10.5×50.5
Torsional
Constant
J
Warping
Constant
Cw
Polar
Radius of
Gyration
_
ro*
Flexural
Constant
H*
in.4
in.6
in.
No Units
20.6
15.4
11.9
7.69
5.62
4.47
3.40
2.60
85.4
63.0
47.3
32.5
23.4
18.4
13.8
10.4
4.67
4.64
4.59
4.64
4.61
4.58
4.56
4.54
0.859
0.859
0.861
0.847
0.845
0.846
0.846
0.846
WT10.5×46.5
WT10.5×41.5
WT10.5×36.5
WT10.5×34
WT10.5×31
3.01
2.16
1.51
1.22
0.513
9.33
6.50
4.42
3.62
2.78
4.37
4.33
4.31
4.31
4.31
0.729
0.732
0.732
0.727
0.722
WT10.5×28.5
WT10.5×25
WT10.5×22
0.884
0.570
0.383
2.50
1.89
1.40
4.36
4.44
4.49
0.665
0.640
0.623
4.42
4.36
4.30
4.23
4.19
4.14
4.10
4.06
4.03
3.99
0.875
0.873
0.874
0.875
0.873
0.875
0.872
0.872
0.874
0.874
WT9×155.5**
WT9×141.5**
WT9×129**
WT9×117**
WT9×105.5**
WT9×96
WT9×87.5
WT9×79
WT9×71.5
WT9×65
87.2
66.5
51.5
39.4
29.4
22.4
17.0
12.6
9.70
7.30
339
251
189
140
102
75.7
56.5
41.2
30.7
22.8
WT9×59.5
WT9×53
WT9×48.5
WT9×43
WT9×38
5.30
3.73
2.92
2.04
1.41
17.4
12.1
9.29
6.42
4.37
4.03
4.00
3.97
3.95
3.92
0.862
0.860
0.862
0.860
0.862
WT9×35.5
WT9×32.5
WT9×30
WT9×27.5
WT9×25
1.74
1.36
1.08
0.829
0.613
3.96
3.01
2.35
1.84
1.36
3.72
3.69
3.67
3.68
3.66
0.751
0.755
0.756
0.749
0.748
WT9×23
WT9×20
WT9×17.5
0.609
0.403
0.252
1.20
0.788
0.598
3.67
3.65
3.74
0.694
0.692
0.662
*See LRFD Specification Section E3.
**Group 4 or Group 5 shape. See Notes in Table 1-2.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
TORSION PROPERTIES
1 - 165
FLEXURAL-TORSIONAL PROPERTIES
Structural Tees
Torsional
Constant
J
Warping
Constant
Cw
Polar
Radius of
Gyration
_
ro*
Flexural
Constant
H*
in.4
in.6
in.
No Units
WT8×50
WT ×44.5
WT ×38.5
WT ×33.5
3.85
2.72
1.78
1.19
10.4
7.19
4.61
3.01
3.62
3.60
3.56
3.53
0.877
0.877
0.877
0.879
WT8×28.5
WT ×25
WT ×22.5
WT ×20
WT ×18
1.10
0.760
0.655
0.396
0.271
1.99
1.34
0.974
0.673
0.516
3.30
3.28
3.27
3.24
3.30
0.770
0.770
0.767
0.769
0.745
WT8×15.5
WT ×13
0.229
0.130
0.366
0.243
3.26
3.32
0.695
0.667
5.67
5.47
5.36
5.25
5.15
5.06
4.98
0.959
0.966
0.966
0.966
0.967
0.967
0.967
4.92
4.87
4.81
4.77
4.71
4.66
4.61
4.56
4.52
4.49
4.46
4.42
4.40
0.968
0.968
0.968
0.968
0.968
0.969
0.969
0.970
0.970
0.971
0.971
0.971
0.971
Designation
WT7×404**
WT ×365**
WT ×332.5**
WT ×302.5**
WT ×275**
WT ×250**
WT ×227.5**
918
714
555
430
331
255
196
6970
5250
3920
2930
2180
1620
1210
WT7×213**
WT ×199**
WT ×185**
WT ×171**
WT ×155.5**
WT ×141.5**
WT ×128.5**
WT ×116.5**
WT ×105.5
WT ×96.5
WT ×88
WT ×79.5
WT ×72.5
164
135
110
88.3
67.5
51.8
39.3
29.6
22.2
17.3
13.2
9.84
7.56
991
801
640
502
375
281
209
154
113
87.2
65.2
47.9
36.3
*See LRFD Specification Section E3.
**Group 4 or Group 5 shape. See Notes in Table 1-2.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1 - 166
DIMENSIONS AND PROPERTIES
FLEXURAL-TORSIONAL PROPERTIES
Structural Tees
Torsional
Constant
J
Warping
Constant
Cw
Polar
Radius of
Gyration
_
ro*
Flexural
Constant
H*
in.4
in.6
in.
No Units
WT7×66
WT ×60
WT ×54.5
WT ×49.5
WT ×45
6.13
4.67
3.55
2.68
2.03
26.6
20.0
15.0
11.1
8.31
4.21
4.18
4.16
4.14
4.12
0.966
0.966
0.968
0.968
0.968
WT7×41
WT ×37
WT ×34
WT ×30.5
2.53
1.94
1.51
1.10
5.63
4.19
3.21
2.29
3.25
3.21
3.19
3.18
0.912
0.917
0.915
0.915
WT7×26.5
WT ×24
WT ×21.5
0.970
0.726
0.524
1.46
1.07
0.751
2.89
2.87
2.85
0.868
0.866
0.866
WT7×19
WT ×17
WT ×15
0.398
0.284
0.190
0.554
0.400
0.287
2.87
2.86
2.90
0.800
0.793
0.772
WT7×13
WT ×11
0.179
0.104
0.207
0.134
2.82
2.86
0.713
0.691
Designation
*See LRFD Specification Section E3.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
TORSION PROPERTIES
1 - 167
FLEXURAL-TORSIONAL PROPERTIES
Structural Tees
Designation
WT6×168**
WT ×152.5**
WT ×139.5**
WT ×126**
WT ×115**
WT ×105**
WT ×95
WT ×85
WT ×76
WT ×68
WT ×60
WT ×53
WT ×48
WT ×43.5
WT ×39.5
WT ×36
WT ×32.5
Torsional
Constant
J
Warping
Constant
Cw
Polar
Radius of
Gyration
_
ro*
Flexural
Constant
H*
in.4
in.6
in.
No Units
120
92.0
70.9
53.5
41.6
32.2
24.4
17.7
12.8
9.22
6.43
4.55
3.42
2.54
1.92
1.46
1.09
481
356
267
195
148
112
82.1
58.3
41.3
28.9
19.7
13.6
10.1
7.34
5.43
4.07
2.97
4.07
4.00
3.94
3.88
3.84
3.79
3.74
3.69
3.65
3.61
3.58
3.54
3.51
3.49
3.46
3.45
3.43
0.958
0.959
0.957
0.958
0.958
0.958
0.959
0.960
0.960
0.960
0.959
0.961
0.961
0.960
0.960
0.961
0.960
WT6×29
WT ×26.5
1.05
0.788
2.08
1.53
3.01
3.00
0.944
0.940
WT6×25
WT ×22.5
WT ×20
0.889
0.656
0.476
1.23
0.885
0.620
2.67
2.64
2.62
0.899
0.898
0.901
WT6×17.5
WT ×15
WT ×13
0.369
0.228
0.150
0.437
0.267
0.174
2.56
2.55
2.54
0.835
0.830
0.826
WT6×11
WT ×9.5
WT ×8
WT ×7
0.146
0.0899
0.0511
0.0350
0.137
0.0934
0.0678
0.0493
2.52
2.54
2.62
2.64
0.683
0.663
0.624
0.610
*See LRFD Specification Section E3.
**Group 4 or Group 5 shape. See Notes in Table 1-2.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1 - 168
DIMENSIONS AND PROPERTIES
FLEXURAL-TORSIONAL PROPERTIES
Structural Tees
Torsional
Constant
J
Warping
Constant
Cw
Polar
Radius of
Gyration
_
ro*
Flexural
Constant
H*
in.4
in.6
in.
No Units
WT5×56
WT5×50
WT5×44
WT5×38.5
WT5×34
WT5×30
WT5×27
WT5×24.5
7.50
5.41
3.75
2.55
1.78
1.23
0.909
0.693
16.9
11.9
8.02
5.31
3.62
2.46
1.78
1.33
3.04
3.00
2.98
2.93
2.92
2.89
2.87
2.85
0.963
0.964
0.964
0.964
0.965
0.965
0.966
0.966
WT5×22.5
WT5×19.5
WT5×16.5
0.753
0.487
0.291
0.981
0.616
0.356
2.44
2.42
2.40
0.940
0.936
0.927
WT5×15
WT5×13
WT5×11
0.310
0.201
0.119
0.273
0.173
0.107
2.17
2.15
2.17
0.848
0.848
0.831
WT5×9.5
WT5×8.5
WT5×7.5
WT5×6
0.116
0.0776
0.0518
0.0272
0.0796
0.061
0.0475
0.0255
2.08
2.12
2.16
2.16
0.728
0.702
0.672
0.662
Designation
*See LRFD Specification Section E3.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
TORSION PROPERTIES
1 - 169
FLEXURAL-TORSIONAL PROPERTIES
Structural Tees
Torsional
Constant
J
Warping
Constant
Cw
Polar
Radius of
Gyration
_
ro*
Flexural
Constant
H*
in.4
in.6
in.
No Units
WT4×33.5
WT ×29
WT ×24
WT ×20
WT ×17.5
WT ×15.5
2.52
1.66
0.979
0.559
0.385
0.268
3.56
2.28
1.30
0.715
0.480
0.327
2.41
2.39
2.34
2.31
2.29
2.29
0.962
0.961
0.966
0.961
0.963
0.961
WT4×14
WT ×12
0.268
0.173
0.230
0.144
1.97
1.96
0.935
0.936
WT4×10.5
WT ×9
0.141
0.0855
0.0916
0.0562
1.80
1.81
0.877
0.863
WT4×7.5
WT ×6.5
WT ×5
0.0679
0.0433
0.0212
0.0382
0.0269
0.0114
1.72
1.74
1.69
0.762
0.732
0.748
WT3×12.5
WT ×10
WT ×7.5
0.229
0.120
0.0504
0.171
0.0858
0.0342
1.76
1.73
1.71
0.952
0.952
0.937
WT3×8
WT ×6
WT ×4.5
0.111
0.0449
0.0202
0.0426
0.0178
0.0074
1.37
1.37
1.34
0.880
0.846
0.852
WT2.5×9.5
WT ×8
0.154
0.0930
0.0775
0.0453
1.44
1.43
0.964
0.962
WT2×6.5
0.0750
0.0213
1.16
0.947
Designation
*See LRFD Specification Section E3.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1 - 170
DIMENSIONS AND PROPERTIES
FLEXURAL-TORSIONAL PROPERTIES
Structural Tees
Polar
Radius of
Gyration
_
ro*
Flexural
Constant
H*
in.6
in.
No Units
0.0307
0.0196
0.0330
0.0252
2.69
2.67
0.564
0.572
MT5×4.5
MT ×4
0.0213
0.0116
0.0133
0.00916
2.21
2.21
0.584
0.582
MT4×3.25
0.0146
0.00421
1.73
0.611
MT2.5×9.45**
0.165
0.0732
1.37
0.951
Torsional
Constant
J
Warping
Constant
Cw
in.4
MT6×5.9
MT ×5.4
Designation
*See LRFD Specification Section E3.
**This shape has tapered flanges while other MT shapes have parallel flanges.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
TORSION PROPERTIES
1 - 171
FLEXURAL-TORSIONAL PROPERTIES
Structural Tees
Designation
Torsional
Constant
J
Warping
Constant
Cw
Polar
Radius of
Gyration
_
ro*
Flexural
Constant
H*
in.4
in.6
in.
No Units
ST12×60.5
ST ×53
6.38
5.04
27.5
15.0
5.14
4.87
0.640
0.685
ST12×50
ST ×45
ST ×40
3.76
3.01
2.43
19.5
12.1
6.94
5.27
5.12
4.89
0.584
0.616
0.657
ST10×48
ST ×43
4.15
3.30
15.0
9.17
4.36
4.20
0.625
0.661
ST10×37.5
ST ×33
2.28
1.78
7.21
4.02
4.28
4.10
0.612
0.655
ST9×35
ST ×27.35
2.05
1.18
7.03
2.26
4.01
3.71
0.583
0.662
ST7.5×25
ST ×21.45
1.05
0.767
2.02
0.995
3.22
3.04
0.637
0.689
ST6×25
ST ×20.4
1.39
0.872
1.97
0.787
2.60
2.42
0.663
0.733
ST6×17.5
ST ×15.9
0.538
0.449
0.556
0.364
2.49
2.39
0.697
0.731
ST5×17.5
ST ×12.7
0.633
0.300
0.725
0.173
2.23
1.98
0.653
0.768
ST4×11.5
ST ×9.2
0.271
0.167
0.168
0.0642
1.74
1.59
0.707
0.789
ST3×8.625
ST ×6.25
0.182
0.0838
0.0772
0.0197
1.36
1.21
0.706
0.820
ST2.5×5
0.0568
0.0100
1.02
0.842
ST2×4.75
ST ×3.85
0.0589
0.0364
0.00995
0.00457
0.907
0.841
0.800
0.872
ST1.5×3.75
ST ×2.85
0.0440
0.0220
0.00496
0.00189
0.737
0.672
0.832
0.913
*See LRFD Specification Section E3.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1 - 172
DIMENSIONS AND PROPERTIES
FLEXURAL-TORSIONAL PROPERTIES
Double Angles
Long Legs Vertical
Short Legs Vertical
Back to Back of Angles, in.
3⁄
8
0
Back to Back of Angles, in.
3⁄
4
3⁄
8
0
3⁄
4
Designation
ro*
H*
ro*
H*
ro*
H*
ro*
H*
ro*
H*
ro*
H*
L8×8×11⁄8
L × ×1
L × × 7⁄8
L × × 3⁄4
L × × 5⁄8
L × × 1⁄2
4.58
4.58
4.58
4.58
4.58
4.59
0.837
0.833
0.831
0.828
0.825
0.822
4.68
4.68
4.68
4.68
4.68
4.69
0.844
0.840
0.838
0.835
0.832
0.829
4.79
4.79
4.78
4.78
4.78
4.78
0.851
0.847
0.845
0.842
0.839
0.836
4.58
4.58
4.58
4.58
4.58
4.59
0.837
0.833
0.831
0.828
0.825
0.822
4.68
4.68
4.68
4.68
4.68
4.69
0.844
0.840
0.838
0.835
0.832
0.829
4.79
4.79
4.78
4.78
4.78
4.78
0.851
0.847
0.845
0.842
0.839
0.836
L8×6×1
L × × 3⁄4
L × × 1⁄2
4.07
4.08
4.11
0.721
0.714
0.708
4.15
4.16
4.18
0.731
0.724
0.718
4.23
4.24
4.26
0.742
0.735
0.728
4.19
4.17
4.17
0.925
0.919
0.914
4.31
4.29
4.28
0.929
0.924
0.919
4.44
4.41
4.40
0.933
0.928
0.923
L8×4×1
L × × 3⁄4
L × × 1⁄2
3.87
3.89
3.93
0.566
0.562
0.558
3.93
3.94
3.97
0.578
0.573
0.568
3.99
4.00
4.03
0.591
0.586
0.580
4.12
4.08
4.05
0.982
0.980
0.977
4.26
4.22
4.19
0.983
0.981
0.979
4.41
4.36
4.33
0.984
0.982
0.980
L7×4×3⁄4
L × ×1⁄2
L × ×3⁄8
3.42
3.45
3.46
0.609
0.604
0.602
3.48
3.5
3.51
0.623
0.616
0.614
3.55
3.57
3.57
0.637
0.629
0.627
3.58
3.55
3.54
0.968
0.965
0.963
3.71
3.68
3.67
0.971
0.967
0.965
3.85
3.82
3.80
0.973
0.969
0.968
L6×6×1
L × × 7⁄8
L × × 3⁄4
L × × 5⁄8
L × × 1⁄2
L × × 3⁄8
3.43
3.43
3.44
3.44
3.44
3.44
0.843
0.838
0.833
0.830
0.827
0.822
3.54
3.54
3.54
3.54
3.54
3.54
0.852
0.847
0.842
0.839
0.836
0.831
3.65
3.65
3.65
3.64
3.64
3.64
0.861
0.856
0.852
0.848
0.845
0.841
3.43
3.43
3.44
3.44
3.44
3.44
0.843
0.838
0.833
0.830
0.827
0.822
3.54
3.54
3.54
3.54
3.54
3.54
0.852
0.847
0.842
0.839
0.836
0.831
3.65
3.65
3.65
3.64
3.64
3.64
0.861
0.856
0.852
0.848
0.845
0.841
L6×4×3⁄4
L × ×5⁄8
L × ×1⁄2
L × ×3⁄8
2.98
2.98
3.00
3.01
0.672
0.668
0.663
0.661
3.05
3.05
3.06
3.07
0.687
0.683
0.678
0.675
3.13
3.13
3.14
3.15
0.704
0.699
0.693
0.690
3.10
3.09
3.08
3.07
0.948
0.946
0.943
0.940
3.23
3.21
3.20
3.19
0.952
0.950
0.947
0.944
3.36
3.34
3.34
3.32
0.956
0.954
0.951
0.948
L6×31⁄2×3⁄8
L × 1⁄2×5⁄16
2.97
2.97
0.610
0.610
3.02
3.02
0.624
0.624
3.09
3.09
0.640
0.639
3.05
3.03
0.961
0.960
3.17
3.16
0.964
0.963
3.31
3.29
0.967
0.966
L5×5×7⁄8
L × ×3⁄4
L × ×1⁄2
L × ×3⁄8
L × ×5⁄16
2.87
2.85
2.86
2.87
2.87
0.844
0.839
0.830
0.824
0.821
2.97
2.96
2.96
2.96
2.97
0.855
0.850
0.841
0.835
0.833
3.09
3.07
3.07
3.07
3.07
0.865
0.861
0.852
0.846
0.844
2.87
2.85
2.86
2.87
2.87
0.844
0.839
0.830
0.824
0.821
2.97
2.96
2.96
2.96
2.97
0.855
0.850
0.841
0.835
0.833
3.09
3.07
3.07
3.07
3.07
0.865
0.861
0.852
0.846
0.844
*See LRFD Specification Section E3.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
TORSION PROPERTIES
1 - 173
FLEXURAL-TORSIONAL PROPERTIES
Double Angles
Long Legs Vertical
Short Legs Vertical
Back to Back of Angles, in.
Back to Back of Angles, in.
3⁄
8
0
3⁄
4
3⁄
8
0
3⁄
4
Designation
ro*
H*
ro*
H*
ro*
H*
ro*
H*
ro*
H*
ro*
H*
L5×31⁄2×3⁄4
L5×31⁄2×1⁄2
L5×31⁄2×3⁄8
L5×31⁄2×5⁄16
2.50
2.51
2.52
2.53
0.697
0.685
0.682
0.679
2.58
2.59
2.59
2.60
0.715
0.703
0.699
0.695
2.67
2.67
2.67
2.68
0.734
0.722
0.717
0.713
2.61
2.59
2.58
2.58
0.943
0.936
0.932
0.930
2.74
2.71
2.70
2.70
0.948
0.941
0.938
0.936
2.87
2.84
2.83
2.82
0.953
0.947
0.943
0.942
L5×3×1⁄2
L3×3×3⁄8
L3×3×5⁄16
L3×3×1⁄4
2.45
2.46
2.47
2.48
0.626
0.623
0.621
0.618
2.52
2.52
2.53
2.54
0.645
0.641
0.638
0.634
2.59
2.60
2.60
2.61
0.665
0.661
0.657
0.653
2.55
2.54
2.54
2.53
0.962
0.959
0.957
0.956
2.69
2.67
2.67
2.66
0.965
0.963
0.961
0.960
2.82
2.80
2.80
2.79
0.969
0.966
0.965
0.964
L4×4×3⁄4
L3×3×5⁄8
L3×3×1⁄2
L3×3×3⁄8
L3×3×5⁄16
L3×3×1⁄4
2.29
2.29
2.29
2.29
2.29
2.29
0.847
0.839
0.834
0.827
0.824
0.823
2.40
2.40
2.39
2.39
2.39
2.39
0.861
0.853
0.848
0.841
0.838
0.837
2.52
2.51
2.50
2.50
2.50
2.49
0.873
0.867
0.862
0.855
0.852
0.850
2.29
2.29
2.29
2.29
2.29
2.29
0.847
0.839
0.834
0.827
0.824
0.823
2.40
2.40
2.39
2.39
2.39
2.39
0.861
0.853
0.848
0.841
0.838
0.837
2.52
2.51
2.50
2.50
2.50
2.49
0.873
0.867
0.862
0.855
0.852
0.850
L4×31⁄2×1⁄2
L5×31⁄2×3⁄8
L5×31⁄2×5⁄16
L5×31⁄2×1⁄4
2.15
2.15
2.15
2.16
0.783
0.774
0.774
0.770
2.24
2.24
2.24
2.24
0.801
0.792
0.791
0.787
2.34
2.34
2.34
2.34
0.818
0.809
0.808
0.805
2.17
2.17
2.17
2.17
0.881
0.875
0.872
0.870
2.29
2.28
2.28
2.28
0.892
0.887
0.884
0.882
2.41
2.40
2.40
2.39
0.903
0.898
0.895
0.893
L4×3×1⁄2
L3×3×3⁄8
L3×3×5⁄16
L3×3×1⁄4
2.04
2.04
2.05
2.06
0.719
0.714
0.710
0.706
2.12
2.12
2.13
2.13
0.740
0.735
0.731
0.726
2.22
2.21
2.22
2.22
0.762
0.757
0.752
0.747
2.10
2.09
2.09
2.09
0.924
0.919
0.917
0.914
2.22
2.21
2.21
2.20
0.933
0.928
0.925
0.923
2.35
2.34
2.33
2.33
0.940
0.935
0.933
0.931
L31⁄2×31⁄2×3⁄8
L31⁄2×31⁄2×1⁄4
2.00
2.01
0.831
0.824
2.10
2.10
0.847
0.839
2.22
2.21
0.862
0.855
2.00
2.01
0.831
0.824
2.10
2.10
0.847
0.839
2.22
2.21
0.862
0.855
L31⁄2×3×3⁄8
L5×31⁄2×5⁄16
L5×31⁄2×1⁄4
1.86
1.87
1.87
0.771
0.766
0.762
1.95
1.96
1.96
0.791
0.787
0.782
2.06
2.06
2.06
0.812
0.807
0.803
1.89
1.89
1.89
0.884
0.881
0.878
2.00
2.00
2.00
0.897
0.894
0.891
2.13
2.12
2.12
0.909
0.906
0.903
L31⁄2×21⁄2×3⁄8
L31⁄2×31⁄2×1⁄4
1.76
1.77
0.696
0.691
1.84
1.85
0.721
0.715
1.94
1.93
0.748
0.740
1.82
1.81
0.932
0.927
1.94
1.93
0.941
0.936
2.08
2.06
0.948
0.944
L3×3×1⁄2
L3×3×3⁄8
L3×3×5⁄16
L3×3×1⁄4
L3×3×3⁄16
1.72
1.72
1.72
1.72
1.72
0.842
0.834
0.830
0.825
0.822
1.83
1.82
1.82
1.82
1.82
0.860
0.852
0.848
0.844
0.841
1.95
1.94
1.93
1.93
1.93
0.877
0.869
0.866
0.862
0.858
1.72
1.72
1.72
1.72
1.72
0.842
0.834
0.830
0.825
0.822
1.83
1.82
1.82
1.82
1.82
0.860
0.852
0.848
0.844
0.841
1.95
1.94
1.93
1.93
1.93
0.877
0.869
0.866
0.862
0.858
*See LRFD Specification Section E3.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1 - 174
DIMENSIONS AND PROPERTIES
FLEXURAL-TORSIONAL PROPERTIES
Double Angles
Long Legs Vertical
Short Legs Vertical
Back to Back of Angles, in.
3⁄
8
0
Back to Back of Angles, in.
3⁄
4
3⁄
8
0
3⁄
4
Designation
ro*
H*
ro*
H*
ro*
H*
ro*
H*
ro*
H*
ro*
H*
L3×21⁄2×3⁄8
L3×21⁄2×1⁄4
L3×21⁄2×3⁄16
1.58
1.59
1.59
0.763
0.754
0.750
1.67
1.67
1.67
0.789
0.779
0.775
1.78
1.78
1.77
0.813
0.804
0.800
1.61
1.61
1.61
0.896
0.889
0.885
1.73
1.72
1.72
0.910
0.903
0.899
1.86
1.84
1.84
0.922
0.916
0.912
L3×2×3⁄8
L3×2×5⁄16
L3×2×1⁄4
L3×2×3⁄16
1.49
1.50
1.50
1.50
0.672
0.667
0.664
0.661
1.57
1.57
1.57
1.57
0.704
0.698
0.694
0.690
1.66
1.66
1.66
1.66
0.737
0.730
0.726
0.721
1.55
1.55
1.54
1.54
0.949
0.946
0.943
0.940
1.68
1.68
1.67
1.66
0.956
0.954
0.951
0.949
1.82
1.82
1.80
1.80
0.963
0.961
0.958
0.956
L21⁄2×21⁄2×3⁄8
L21⁄2×21⁄2×5⁄16
L21⁄2×21⁄2×1⁄4
L21⁄2×21⁄2×3⁄16
1.43
1.43
1.43
1.43
0.839
0.834
0.829
0.825
1.54
1.54
1.53
1.53
0.861
0.856
0.851
0.847
1.66
1.66
1.65
1.65
0.880
0.876
0.871
0.867
1.43
1.43
1.43
1.43
0.839
0.834
0.829
0.825
1.54
1.54
1.53
1.53
0.861
0.856
0.851
0.847
1.66
1.66
1.65
1.65
0.880
0.876
0.871
0.867
L21⁄2×2×3⁄8
L3×21⁄2×5⁄16
L3×21⁄2×1⁄4
L3×21⁄2×3⁄16
1.29
1.30
1.30
1.31
0.752
0.746
0.741
0.736
1.39
1.39
1.39
1.39
0.785
0.779
0.773
0.767
1.50
1.50
1.50
1.49
0.816
0.810
0.804
0.798
1.33
1.33
1.33
1.32
0.912
0.908
0.903
0.899
1.45
1.45
1.45
1.44
0.927
0.923
0.919
0.915
1.59
1.58
1.58
1.57
0.939
0.935
0.932
0.928
L2×2×3⁄8
L3×2×5⁄16
L3×2×1⁄4
L3×2×3⁄16
L3×2×1⁄8
1.15
1.15
1.15
1.15
1.15
0.846
0.840
0.834
0.828
0.822
1.26
1.26
1.25
1.25
1.25
0.873
0.867
0.861
0.855
0.850
1.39
1.38
1.38
1.37
1.37
0.896
0.890
0.885
0.880
0.875
1.15
1.15
1.15
1.15
1.15
0.846
0.840
0.834
0.828
0.822
1.26
1.26
1.25
1.25
1.25
0.873
0.867
0.861
0.855
0.850
1.39
1.38
1.38
1.37
1.37
0.896
0.890
0.885
0.880
0.875
*See LRFD Specification Section E3.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
SURFACE AREAS AND BOX AREAS
1 - 175
SURFACE AREAS AND BOX AREAS
W shapes
Square feet per foot of length
Case A Case B Case C Case D
Designation
Case A Case B Case C Case D
Designation
W44×335
W44×290
W44×262
W44×230
W44
W40×593
W44×503
W44×431
W44×372
W44×321
W44×297
W44×277
W44×249
W44×215
W44×199
W44×174
11.0
11.0
10.9
10.9
12.4
12.3
12.2
12.2
8.67
8.59
8.53
8.46
10.0
9.91
9.84
9.78
10.9
10.7
10.5
10.4
10.3
10.3
10.3
10.2
10.2
10.1
10.0
12.3
12.1
11.9
11.8
11.6
11.6
11.6
11.5
11.5
11.4
11.3
8.56
8.38
8.23
8.11
8.01
7.96
7.93
7.88
7.81
7.76
7.68
9.95
9.75
9.58
9.45
9.33
9.28
9.25
9.19
9.12
9.07
8.99
W40×466
W44×392
W44×331
W44×278
W44×264
W44×235
W36×211
W36×183
W36×167
W36×149
9.79
9.61
9.47
9.35
9.32
9.28
9.22
9.17
9.11
9.05
10.8
10.6
10.5
10.3
10.3
10.3
10.2
10.2
10.1
10.0
8.13
7.96
7.81
7.69
7.66
7.61
7.55
7.48
7.42
7.35
9.18
8.99
8.83
8.69
8.66
8.60
8.53
8.47
8.40
8.34
W36×848
W36×798
W36×650
W36×527
W36×439
W36×393
W36×359
W36×328
W36×300
W36×280
W36×260
W36×245
W36×230
11.1
11.0
10.7
10.4
10.3
10.2
10.1
10.0
9.99
9.95
9.90
9.87
9.84
12.6
12.5
12.1
11.9
11.7
11.6
11.5
11.4
11.4
11.3
11.3
11.2
11.2
8.59
8.49
8.21
7.97
7.79
7.70
7.63
7.57
7.51
7.47
7.42
7.39
7.36
10.1
9.99
9.67
9.41
9.20
9.10
9.02
8.95
8.90
8.85
8.80
8.77
8.73
W36×256
W44×232
W44×210
W44×194
W36×182
W36×170
W36×160
W36×150
W36×135
9.02
8.96
8.91
8.88
8.85
8.82
8.79
8.76
8.71
10.0
9.97
9.93
9.89
9.85
9.82
9.79
9.76
9.70
7.26
7.20
7.13
7.09
7.06
7.03
7.00
6.97
6.92
8.27
8.21
8.15
8.10
8.07
8.03
8.00
7.97
7.92
W33×354
W36×318
W36×291
W36×263
W36×241
W36×221
W33×201
9.66
9.58
9.52
9.46
9.42
9.38
9.33
11.0
10.9
10.8
10.8
10.7
10.7
10.6
7.27
7.19
7.13
7.07
7.02
6.97
6.93
8.61
8.52
8.46
8.39
8.34
8.29
8.24
W33×169
W36×152
W36×141
W36×130
W36×118
8.30
8.27
8.23
8.20
8.15
9.26
9.23
9.19
9.15
9.11
6.60
6.55
6.51
6.47
6.43
7.55
7.51
7.47
7.43
7.39
W30×477
W36×391
W36×326
W36×292
W36×261
W36×235
W36×211
W36×191
W36×173
9.30
9.11
8.96
8.88
8.81
8.75
8.71
8.66
8.62
10.6
10.4
10.2
10.2
10.1
10.0
9.97
9.92
9.87
7.02
6.83
6.68
6.61
6.53
6.47
6.42
6.37
6.32
8.35
8.13
7.96
7.88
7.79
7.73
7.67
7.62
7.57
W30×148
W36×132
W36×124
W36×116
W36×108
W36×99
W36×90
7.53
7.49
7.47
7.44
7.41
7.37
7.35
8.40
8.37
8.34
8.31
8.28
8.25
8.22
5.99
5.93
5.90
5.88
5.84
5.81
5.79
6.86
6.81
6.78
6.75
6.72
6.68
6.66
Case A: Shape perimeter, minus one flange surface.
Case B: Shape perimeter.
Case C: Box perimeter, equal to one flange surface plus twice the depth.
Case D: Box perimeter, equal to two flange surfaces plus twice the depth.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1 - 176
DIMENSIONS AND PROPERTIES
SURFACE AREAS AND BOX AREAS
W shapes
Square feet per foot of length
Case A Case B Case C Case D
Designation
Case A Case B Case C Case D
Designation
W27×539
W ×448
W ×368
W ×307
W ×281
W ×258
W ×235
W ×217
W ×194
W ×178
W ×161
W ×146
8.82
8.61
8.42
8.27
8.21
8.15
8.09
8.04
7.98
7.95
7.91
7.87
10.09
9.86
9.64
9.47
9.40
9.34
9.27
9.22
9.15
9.12
9.08
9.03
6.69
6.48
6.29
6.14
6.08
6.02
5.96
5.91
5.85
5.81
5.77
5.73
7.96
7.73
7.51
7.34
7.27
7.21
7.14
7.09
7.02
6.98
6.94
6.89
W27×129
W ×114
W ×102
W ×94
W ×84
6.92
6.88
6.85
6.82
6.78
7.75
7.72
7.68
7.65
7.61
5.44
5.39
5.35
5.32
5.28
6.27
6.23
6.18
6.15
6.11
W24×492
W ×408
W ×335
W ×279
W ×250
W ×229
W ×207
W ×192
W ×176
W ×162
W ×146
W ×131
W ×117
W ×104
8.07
7.86
7.66
7.51
7.44
7.38
7.32
7.27
7.23
7.22
7.17
7.12
7.08
7.04
9.25
9.01
8.79
8.62
8.54
8.47
8.40
8.35
8.31
8.30
8.24
8.19
8.15
8.11
6.12
5.91
5.71
5.56
5.49
5.43
5.37
5.32
5.28
5.25
5.20
5.15
5.11
5.07
7.29
7.06
6.84
6.67
6.59
6.52
6.45
6.40
6.35
6.33
6.27
6.22
6.18
6.14
W24×103
W ×94
W ×84
W ×76
W ×68
6.18
6.16
6.12
6.09
6.06
6.93
6.92
6.87
6.84
6.80
4.84
4.81
4.77
4.74
4.70
5.59
5.56
5.52
5.49
5.45
W24×62
W ×55
5.57
5.54
6.16
6.13
4.54
4.51
5.13
5.10
W21×201
W18×182
W18×166
W18×147
W18×132
W18×122
W18×111
W18×101
6.75
6.69
6.65
6.61
6.57
6.54
6.51
6.48
7.80
7.74
7.68
7.66
7.61
7.57
7.54
7.50
4.89
4.83
4.78
4.72
4.68
4.65
4.61
4.58
5.93
5.87
5.82
5.76
5.71
5.68
5.64
5.61
W21×93
W18×83
W18×73
W ×68
W18×62
5.54
5.50
5.47
5.45
5.42
6.24
6.20
6.16
6.14
6.11
4.31
4.27
4.23
4.21
4.19
5.01
4.96
4.92
4.90
4.87
W21×57
W18×50
W18×44
5.01
4.97
4.94
5.56
5.51
5.48
4.06
4.02
3.99
4.60
4.56
4.53
W18×311
W18×283
W18×258
W18×234
W18×211
W18×192
W18×175
W18×158
W18×143
W18×130
6.41
6.32
6.24
6.17
6.10
6.03
5.97
5.92
5.87
5.83
7.41
7.31
7.23
7.14
7.06
6.99
6.92
6.86
6.81
6.76
4.72
4.63
4.56
4.48
4.41
4.35
4.29
4.23
4.18
4.14
5.72
5.62
5.54
5.45
5.37
5.30
5.24
5.17
5.12
5.07
W18×119
W18×106
W18×97
W ×86
W18×76
5.81
5.77
5.74
5.70
5.67
6.75
6.70
6.67
6.62
6.59
4.10
4.06
4.03
3.99
3.95
5.04
4.99
4.96
4.91
4.87
W18×71
W18×65
W18×60
W ×55
W18×50
4.85
4.82
4.80
4.78
4.76
5.48
5.46
5.43
5.41
5.38
3.71
3.69
3.67
3.65
3.62
4.35
4.32
4.30
4.27
4.25
Case A: Shape perimeter, minus one flange surface.
Case B: Shape perimeter.
Case C: Box perimeter, equal to one flange surface plus twice the depth.
Case D: Box perimeter, equal to two flange surfaces plus twice the depth.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
SURFACE AREAS AND BOX AREAS
1 - 177
SURFACE AREAS AND BOX AREAS
W shapes
Square feet per foot of length
Case A Case B Case C Case D
Designation
Case A Case B Case C Case D
Designation
W18×46
W ×40
W ×35
4.41
4.38
4.34
4.91
4.88
4.84
3.51
3.48
3.45
4.02
3.99
3.95
W16×100
W ×89
W ×77
W ×67
5.28
5.24
5.19
5.16
6.15
6.10
6.05
6.01
3.70
3.66
3.61
3.57
4.57
4.52
4.47
4.43
W16×57
W ×50
W ×45
W ×40
W ×36
4.39
4.36
4.33
4.31
4.28
4.98
4.95
4.92
4.89
4.87
3.33
3.30
3.27
3.25
3.23
3.93
3.89
3.86
3.83
3.81
W16×31
W ×26
3.92
3.89
4.39
4.35
3.11
3.07
3.57
3.53
W14×808
W ×730
W ×665
W ×605
W ×550
W ×500
W ×455
7.74
7.61
7.46
7.32
7.19
7.07
6.96
9.28
9.10
8.93
8.77
8.62
8.49
8.36
5.35
5.23
5.08
4.94
4.81
4.68
4.57
6.90
6.72
6.55
6.39
6.24
6.10
5.98
W14×426
W ×398
W ×370
W ×342
W ×311
W ×283
W ×257
W ×233
W ×211
W ×193
W ×176
W ×159
W ×145
6.89
6.81
6.74
6.67
6.59
6.52
6.45
6.38
6.32
6.27
6.22
6.18
6.14
8.28
8.20
8.12
8.03
7.94
7.86
7.78
7.71
7.64
7.58
7.53
7.47
7.43
4.50
4.43
4.36
4.29
4.21
4.13
4.06
4.00
3.94
3.89
3.84
3.79
3.76
5.89
5.81
5.73
5.65
5.56
5.48
5.40
5.32
5.25
5.20
5.15
5.09
5.05
W14×132
W ×120
W ×109
W ×99
W ×90
5.93
5.90
5.86
5.83
5.81
7.16
7.12
7.08
7.05
7.02
3.67
3.64
3.60
3.57
3.55
4.90
4.86
4.82
4.79
4.76
W14×82
W14×74
W14×68
W ×61
4.75
4.72
4.69
4.67
5.59
5.56
5.53
5.50
3.23
3.20
3.18
3.15
4.07
4.04
4.01
3.98
W14×53
W14×48
W14×43
4.19
4.16
4.14
4.86
4.83
4.80
2.99
2.97
2.94
3.66
3.64
3.61
W14×38
W14×34
W14×30
3.93
3.91
3.89
4.50
4.47
4.45
2.91
2.89
2.87
3.48
3.45
3.43
W14×26
W ×22
3.47
3.44
3.89
3.86
2.74
2.71
3.16
3.12
W12×336
W ×305
W14×279
W14×252
W14×230
W14×210
W14×190
W14×170
W14×152
W ×136
W14×120
W14×106
W14×96
W14×87
W14×79
W14×72
W14×65
5.77
5.67
5.59
5.50
5.43
5.37
5.30
5.23
5.17
5.12
5.06
5.02
4.98
4.95
4.92
4.89
4.87
6.88
6.77
6.68
6.58
6.51
6.43
6.36
6.28
6.21
6.15
6.09
6.03
5.99
5.96
5.93
5.90
5.87
3.92
3.82
3.74
3.65
3.58
3.52
3.45
3.39
3.33
3.27
3.21
3.17
3.13
3.10
3.07
3.05
3.02
5.03
4.93
4.83
4.74
4.66
4.58
4.51
4.43
4.37
4.30
4.24
4.19
4.15
4.11
4.08
4.05
4.02
W12×58
W14×53
4.39
4.37
5.22
5.20
2.87
2.84
3.70
3.68
W12×50
W14×45
W ×40
3.90
3.88
3.86
4.58
4.55
4.52
2.71
2.68
2.66
3.38
3.35
3.32
Case A: Shape perimeter, minus one flange surface.
Case B: Shape perimeter.
Case C: Box perimeter, equal to one flange surface plus twice the depth.
Case D: Box perimeter, equal to two flange surfaces plus twice the depth.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1 - 178
DIMENSIONS AND PROPERTIES
SURFACE AREAS AND BOX AREAS
W shapes
Square feet per foot of length
Case A Case B Case C Case D
Designation
Case A Case B Case C Case D
Designation
W12×35
W12×30
W12×26
3.63
3.60
3.58
4.18
4.14
4.12
2.63
2.60
2.58
3.18
3.14
3.12
W12×22
W12×19
W12×16
W12×14
2.97
2.95
2.92
2.90
3.31
3.28
3.25
3.23
2.39
2.36
2.33
2.32
2.72
2.69
2.66
2.65
W10×112
W12×100
W12×88
W12×77
W12×68
W12×60
W12×54
W12×49
4.30
4.25
4.20
4.15
4.12
4.08
4.06
4.04
5.17
5.11
5.06
5.00
4.96
4.92
4.89
4.87
2.76
2.71
2.66
2.62
2.58
2.54
2.52
2.50
3.63
3.57
3.52
3.47
3.42
3.38
3.35
3.33
W10×45
W12×39
W12×33
3.56
3.53
3.49
4.23
4.19
4.16
2.35
2.32
2.29
3.02
2.98
2.95
W10×30
W12×26
W12×22
3.10
3.08
3.05
3.59
3.56
3.53
2.23
2.20
2.17
2.71
2.68
2.65
W10×19
W12×17
W12×15
W12×12
2.63
2.60
2.58
2.56
2.96
2.94
2.92
2.89
2.04
2.02
2.00
1.97
2.38
2.35
2.33
2.30
W8×67
W8×58
W8×48
W8×40
W8×35
W8×31
3.42
3.37
3.32
3.28
3.25
3.23
4.11
4.06
4.00
3.95
3.92
3.89
2.19
2.14
2.09
2.05
2.02
2.00
2.88
2.83
2.77
2.72
2.69
2.67
W8×28
W8×24
2.87
2.85
3.42
3.39
1.89
1.86
2.43
2.40
W8×21
W8×18
2.61
2.59
3.05
3.03
1.82
1.79
2.26
2.23
W8×15
W8×13
W8×10
2.27
2.25
2.23
2.61
2.58
2.56
1.69
1.67
1.64
2.02
2.00
1.97
W6×25
W ×20
W8×15
2.49
2.46
2.42
3.00
2.96
2.92
1.57
1.54
1.50
2.08
2.04
2.00
W6×16
W8×12
W8×9
1.98
1.93
1.90
2.31
2.26
2.23
1.38
1.34
1.31
1.72
1.67
1.64
W5×19
W8×16
2.04
2.01
2.45
2.43
1.28
1.25
1.70
1.67
W4×13
1.63
1.96
1.03
1.37
Case A: Shape perimeter, minus one flange surface.
Case B: Shape perimeter.
Case C: Box perimeter, equal to one flange surface plus twice the depth.
Case D: Box perimeter, equal to two flange surfaces plus twice the depth.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
CAMBER
1 - 179
CAMBER
Beams and Girders
Camber and sweep are used to form a desired curvature in either rolled beams or welded
girders. Camber denotes a curve in the vertical plane. Beams and girders can be cambered
to compensate for the anticipated deflection or for architectural reasons. Note that the
required camber is determined at service (unfactored) load levels. Sweep denotes a curve
in the horizontal plane. Camber and sweep may be induced through cold bending or
through the application of heat.
The minimum radius for cold cambering in members up to a nominal depth of 30 inches
is between 10 and 14 times the depth of the member; deeper members will require a larger
minimum radius. Cold bending may be used to provide sweep in members to practically
any radius desired. Note that a length limit of 40 to 50 feet is practical.
Heat cambering, sweeping, and straightening are provided through controlled heat application. The member is rapidly heated in selected areas which tend to expand, but are restrained by
the adjacent cooler areas, causing plastic deformation of the heated areas and a change in the
shape of the cooled member. The mechanical properties of steels are largely unaffected by such
heating operations, provided the maximum temperature does not exceed 1,100°F for quenched
and tempered alloy steels, and 1,300°F for other steels. The temperature should be carefully
checked by temperature-indicating crayons or other suitable means during the heating process.
Cambering and sweeping induces residual stresses similar to those that develop in rolled
structural shapes as elements of the shape cool from the rolling temperature at different
rates. In general, these residual stresses do not affect the ultimate strength of structural
members. Additionally, the effect of residual stresses is incorporated in the provisions of
the LRFD Specification.
Note that when a cambered beam bearing on a wall or other support is loaded,
expansion of the unrestrained end must be considered. In Figure 1-5(a), the end will move
a distance ∆, where
∆=
4Cd
L
If instead the cambered beam is supported on a simple shear connection at both ends,
the top and bottom flange will each move a distance of one-half ∆ since end rotation will
occur approximately about the neutral axis. The designer should be aware of the
magnitude of these movements and make provisions to accommodate them. Figure 1-5(a)
considers the geometry of a girder in the horizontal position, and Figure 1-5(b) illustrates
the condition when the girder is not level.
Trusses
“Cambering” of trusses is accomplished by geometric relocation of panel points and
adjustment of member lengths; it does not involve physical cold bending or the application of heat as with beams and girders.
The following discussion of cambering to compensate for the anticipated deflection
of a truss is applicable for any parabolic condition; large-radius circular curves will be
approximated very closely by the technique described. Cambering to compensate for the
axial deformation of the members of a truss is beyond the scope of this Manual; refer to
a textbook on mechanics of materials.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1 - 180
DIMENSIONS AND PROPERTIES
Distances approximately
equal for small angles
Distances equal for
parabolic curve, approximately
equal for circular curve.
See sketch below.
∆
∆
θ
d
C
90°
C
L
/2
∆
L
/2
tanθ = 2C
Fixed
End
L
/2
∆ = d tanθ
Unrestrained
End
∆ = 4Cd
L
θ
2θ for circular curve
2C for parabolic curve
(a) Beam or Girder Ends at
Same Elevations
4Cd
∆= L
4Cd
∆= L
∆ = 4Cd
L
∆ = 4Cd
L
d
B
Grade
angle
B
L
L approx
.
(b) Beam or Girder Ends at
Different Elevations
Fig. 1-5. Camber for beams and girders.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
B
A+B
A
B
A
Horiz. line
Vert.
A
°
90
A
B
°
e
B
90
Grade lin
A+B
A
C
A
CAMBER
1 - 181
The usual method of providing camber in building trusses is to progressively raise each
panel point. The lengths of the verticals are not changed, but the lengths of the diagonals
are calculated on the basis of the adjusted elevation for the several panel points. For any
simple-span truss, the offset above a straight base line, at the several panel points, can be
computed from the following equations if the vertical curve forming the camber is taken
as a parabola.
2
2
B
B
D = C − C = C 1 −
A
A
where
A = Horizontal distance from end panel point to mid-span of the truss (half the truss span).
B = Horizontal distance from mid-span of the truss to panel point for which offset is
to be determined.
C = Required mid-span camber.
D = Offset from the base-line at panel point corresponding to distance B.
A and B must be expressed in the same units; similarly C and D must be expressed in
the same units, but not necessarily the same units as A and B. When the truss is divided
into any number of approximately equal panels, it may be convenient to express distances
A and B in panel lengths.
For the truss of Figure 1-6(a) with eight equal panels, distance A is taken as four panel
lengths. Assuming the camber at the midpoint is specified as 11⁄2-in., the offset at panel
point 1, where B equals three panel lengths, is:
2
3
D = 1 -in. 1 −
4
= 21⁄32-in.
1⁄
2
The offset at panel point 2, where B equals two panel lengths, is:
2
2
D = 1 -in. 1 −
4
= 11⁄8-in.
1⁄
2
The offset at panel point 3, where B equals one panel length, is:
2
1
D = 1 -in. 1 −
4
= 113⁄32-in.
1⁄
2
Finally, the offset at panel point 4, where B equals zero, is
D = C = 11⁄2-in.
An alternative method of determining the amount of camber at intermediate panel
points when all panel points are approximately the same distance apart is as follows.
Using the truss in Figure 1-6(a) as an example, sketch the camber diagram and number
the panel points, starting with the first panel point from the end of the truss, from 1 to 4,
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1 - 182
DIMENSIONS AND PROPERTIES
as shown in Figure 1-6(b) on line A. Next, on line B, reverse the numbering as shown.
Finally, on line C, enter the product of the numbers on lines A and B.
The camber at any panel point is the amount of camber at the centerline of the truss
multiplied by the fraction whose numerator is the figure on line C at the given panel point,
and whose denominator is the figure on line C at the center line of the truss. Thus, at
panel point 1, the camber is
7⁄
16
× 11⁄2jin. = 21⁄32jin.
at panel point 2, the camber is
12⁄
16
× 11⁄2jin. = 11⁄8jin.
at panel point 3, the camber is
15⁄
16
× 11⁄2jin. = 113⁄32jin.
and at panel point 4, the camber is
16⁄
16
× 11⁄2jin. = 11⁄2jin.
cL
4
3
2
1
21/
32
0
1 1/2
1 13/32
11/8
Baseline
EQ
EQ
EQ
EQ
(a) Calculated camber ordinates by formula
1
2
3
cL
4
line A
line B
1
x7
2
x6
3
x5
4
x4
line C
7
12
15
16
Panel point
(b) Alternative calculation method for approximately equal panels
Fig. 1-6. Camber for trusses.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
STANDARD MILL PRACTICE
1 - 183
STANDARD MILL PRACTICE
General Information
Rolling structural shapes and plates involves such factors as roll wear, subsequent roll
dressing, temperature variations, etc., which cause the finished product to vary from
published profiles. Such variations are limited by the provisions of the American Society
for Testing and Materials Specification A6. Contained in this section is a summary of
these provisions, not a reproduction of the complete specification. In its entirety, A6
covers a group of common requirements, which, unless otherwise specified in the
purchase order or in an individual specification, apply to rolled steel plates, shapes, sheet
piling, and bars.
As indicated in Table 1-1, carbon steel refers to ASTM designations A36 and A529;
high-strength, low-alloy steel refers to designations A242, A572, and A588; alloy steel
refers to designation A514; and low-alloy steel refers to A852.
For further information on mill practices, including permissible variations for rolled
tees, zees, and bulb angles in structural and bar sizes, pipe, tubing, sheets, and strip, and
for other grades of steel, see ASTM A6, A53, A500, A568, and A618; the Steel Products
Manuals of the Iron and Steel Society (American Institute of Mining, Metallurgical, and
Petroleum Engineers); and producers’ catalogs.
The data on spreading rolls to increase areas and weights, and mill cambering of beams,
is not a part of ASTM A6.
Additional material on mill practice is included in the descriptive material preceding
the “Dimensions and Properties” tables for shapes and plates.
Letter symbols representing dimensions on sketches shown herein are in accordance
with ASTM A6, AISI and mill catalogs and not necessarily as defined by the general
nomenclature of this manual.
Methods of increasing areas and weights by spreading rolls
Cambering of rolled beams . . . . . . . . . . . . . . . . . .
Positions for measuring camber and sweep . . . . . . . . .
W Shapes, permissible variations . . . . . . . . . . . . . .
S Shapes, M Shapes, and Channels, permissible variations .
Tees split from W , M, and S Shapes, permissible variations
Angles split from Channels, permissible variations . . . . .
Angles, structural size, permissible variations . . . . . . . .
Angles, bar size, permissible variations . . . . . . . . . . .
Steel Pipe and Tubing, permissible variations . . . . . . . .
Plates, permissible variations for sheared, length and width .
Plates, permissible variations for universal mill, length . . .
Plates, permissible variations for universal mill, width . . .
Plates, permissible variations for camber . . . . . . . . . .
Plates, permissible variations for flatness . . . . . . . . . .
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1-183
1-186
1-187
1-188
1-190
1-191
1-191
1-192
1-193
1-194
1-196
1-196
1-196
1-197
1-198
Methods of Increasing Areas and Weights by Spreading Rolls
W Shapes
To vary the area and weight within a given nominal size, the flange width, the flange
thickness, and the web thickness are changed as shown in Figure 1-7(a).
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1 - 184
DIMENSIONS AND PROPERTIES
S Shapes and American Standard Channels
To vary the area and weight within a given nominal size, the web thickness and the flange
width are changed by an equal amount as shown in Figures 1-7(b) and (c).
Angles
To vary area and weight for a given leg length, the thickness of each leg is changed. Note
that the leg length is changed slightly by this method (Figure 1-7(d)).
Constant for a given
nominal size
(a)
Constant for a given
nominal size
(except S24 and S20)
(b)
Constant for a given
nominal size
(c)
(d)
Fig. 1-7. Varying areas and weights.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
STANDARD MILL PRACTICE
1 - 185
Cambering of Rolled Beams
All beams are straightened after rolling to meet permissible variations for sweep and
camber listed hereinafter for W shapes and S shapes. The following data refer to the
subsequent cold cambering of beams to produce a predetermined dimension.
The maximum lengths that can be cambered depend on the length to which a given
section can be rolled, with a maximum of 100 feet. Table 1-10 outlines the maximum and
minimum induced camber of W shapes and S shapes.
Consult the producer for specific camber and/or lengths outside the above listed
available lengths and sections.
Mill camber in beams of less depth than tabulated should not be specified.
A single minimum value for camber, within the ranges shown above for the length
ordered, should be specified.
Camber is measured at the mill and will not necessarily be present in the same amount
in the section of beam as received due to release of stress induced during the cambering
operation. In general 75 percent of the specified camber is likely to remain.
Camber will approximate a simple regular curve nearly the full length of the beam, or
between any two points specified.
Camber is ordinarily specified by the ordinate at the mid-length of the portion of the
beam to be curved. Ordinates at the other points should not be specified.
Although mill cambering to achieve reverse or other compound curves is not considered practical, fabricating shop facilities for cambering by heat can accomplish such
results as well as form regular curves in excess of the limits tabulated above. Refer to the
earlier section Effect of Heat of Steel for further information.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1 - 186
DIMENSIONS AND PROPERTIES
Table 1-10.
Cambering of Rolled Beams
Maximum and Minimum Induced Camber
Sections, Nominal
Depth, in.
Specified Length of Beam, ft
Over 30 to
42, incl.
Over 42 to
52, incl.
Over 52 to
65, incl.
Over 65 to
85, incl.
Over 85 to
100, incl.
Max. and Min. Camber Acceptable, in.
W shapes, 24 and over
W shapes, 14 to 21, incl.
and S shapes, 12 in.
and over
1 to 2,
incl.
3⁄
4
to 21⁄2,
incl.
1 to 3,
incl.
2 to 4,
incl.
3 to 5,
incl.
3 to 6,
incl.
1 to 3,
incl.
—
—
—
Permissible Variations for Camber Ordinate
Lengths
Plus Variation
1⁄
50 ft and less
Over 50 ft
1⁄ -in.
2
2-in.
1⁄ -in.
8
plus
for each 10 ft or
fraction thereof in excess of 50 ft
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
Minus Variation
0
0
STANDARD MILL PRACTICE
1 - 187
Table 1-11.
Positions for Measuring Camber and Sweep
Camber
Sweep
Camber
Sweep*
Horizontal
surface
W SHAPES
Camber
S SHAPES and M SHAPES
Sweep*
Camber
Horizontal
surface
Horz
Camber
onta
CHANNELS
ANGLES
l sur
face
TEES
*Due to the extreme variations in flexibility of these shapes, straightness tolerances for sweep are subject to
negotiations between manufacturer and purchaser for individual sections involved.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1 - 188
DIMENSIONS AND PROPERTIES
Table 1-12.
W Shapes, HP Shapes
B
1/
2 B±
B
1/
2 B±
E
E
T′
C
T′
C
A
A
T
T
1/2 B±E
1/
2 B±
E
Permissible Variations in Cross Section
Section
Nominal
Size, in.
A, Depth, in.
B, Fig. Width, in.
Over
Theoretical
Under
Theoretical
Over
Theoretical
To 12, inc.
1⁄
2
1⁄
8
1⁄
4
3⁄
Over 12
1⁄
8
1⁄
8
1⁄
4
3⁄
T+T′
Flanges,
out of
square,
Max, in.
E a,
Web off
Center,
Max, in.
C, Max.
Depth at
any Crosssection
over Theoretical
Depth, in.
16
1⁄
4
3⁄
16
1⁄
4
16
5⁄
3⁄
16
1⁄
4
Under
Theoretical
16
Permissible Variations in Length
Variations from Specified Length for Lengths for Given, in.
30 ft and Under
W Shapes
Over 30 ft
Over
Under
Over
Under
Beams 24 in. and
under in nominal depth
3⁄
8
3⁄
8
3⁄
1
8 plus ⁄16 for each
additional 5 ft or
fraction thereof
3⁄
8
Beams over 24 in. nom.
depth; all columns
1⁄
2
1⁄
2
1⁄
1⁄
2
1
2 plus ⁄16 for each
additional 5 ft or
fraction thereof
Notes:
aVariation of 5⁄ in. max. for sections over 426 lb / ft.
16
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
Continued on next page
STANDARD MILL PRACTICE
1 - 189
Table 1-12 (cont.).
WP Shapes, HP Shapes
Other Permissible Variations
Area and weight variation: ±2.5 percent theorectical or specified amount.
Ends out-of-square: 1⁄64-in. per in. of depth, or of flange width if it is greater than the depth.
Camber and Sweep
Permissible Variation, in.
Sizes
Length
Sizes with flange width
equal to or greater than
6 in.
All
Sizes with flange width
less than 6 in.
All
45 ft. and under
Certain sections with a
flange width approx.
equal to depth &
specified on order as
b
columns
Over 45 ft.
Camber
1⁄
8
1⁄
8
in. ×
Sweep
in. ×
(total length ft.)
10
(total length ft.)
10
1⁄
8
in. ×
(total length ft.)
5
(total length ft.)
with 3⁄8 in. max.
10
1⁄
8
in. ×
3⁄
8
(total length ft. − 45)
in. + 1⁄8 in. ×
10
bApplies only to W8×31 and heavier, W10×49 and heavier, W12×65 and heavier, W14×90 and heavier. If the
other sections are specified on the order as columns, the tolerance will be subject to negotiation with the
manufacturer.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1 - 190
DIMENSIONS AND PROPERTIES
Table 1-13.
S Shapes, M Shapes, and Channels
Permissible Variations in Cross Section
B
B
T′
T′
*
A
A
T
T
* Back of square and centerline of web to be parallel when measuring “out-of-square”
A, Depth in.a
Section
T + T ′b,
Out of
Square per
Inch of
Over
Under
Over
Under
B, in.
Theoretical Theoretical Theoretical Theoretical
Nominal
Size in.
S shapes 3 to 7, incl.
Over 7 to 14,
and M
incl.
shapes
Over 14 to 24,
incl.
1⁄
2
1⁄
8
1⁄
16
3⁄
32
1⁄
8
5⁄
32
1⁄
8
5⁄
32
1⁄
3⁄
16
1⁄
8
3⁄
16
3⁄
16
1⁄
32
32
1⁄
8
1⁄
16
3⁄
32
1⁄
8
1⁄
8
1⁄
8
5⁄
32
1⁄
32
3⁄
1⁄
8
1⁄
8
3⁄
16
1⁄
3⁄
Channels 3 to 4, incl.
Over 7 to 14,
incl.
Over 14
B, Flange Width, in.
16
1⁄
1⁄
32
32
32
32
Permissible Variations in Length
Variations from Specified Length for Lengths Given, in.
Over
30 to 40 ft.,
incl.
to 30 ft.,
incl.
Section
S shapes,
M shapes and
Channels
Over
40 to 50 ft.,
incl.
Over
Under
Over
Under
Over
1⁄
1⁄
4
3⁄
4
1⁄
1
2
4
Under
1⁄
4
Over
50 to 65 ft.,
incl.
Over 65 ft.
Over
Under
Over
Under
11⁄8
1⁄
4
11⁄4
1⁄
4
Other Permissible Variations
Area and weight variation: ±2.5 percent theoretical or specified amount.
Ends out-of square: S shapes and channels 1⁄64-in. per in. of depth.
total length,ft
Camber = 1⁄8-in. ×
5
Notes:
aA is measured at center line of web for beams; and at back of web for channels.
bT + T′ applies when flanges of channels are toed in or out.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
STANDARD MILL PRACTICE
1 - 191
Table 1-14.
Tees Split from W, M, and S Shapes,
Angles Split from Channels
Permissible Variations in Depth
A
A
A
Dimension A may be approximately one-half beam or channel depth, or any dimension resulting
from off-center splitting, or splitting on two lines as specified on the order.
Depth of Beam from which
Tees or Angles are Split
Variations in Depth A Over and Under
Tees
Angles
To 6 in., excl.
1⁄
8
1⁄
8
6 to 16, excl.
3⁄
16
3⁄
16
16 to 20, excl.
1⁄
4
1⁄
4
20 to 24, excl.
5⁄
16
—
24 and over
3⁄
8
—
The above variations for depths to tees or angles include the permissible variations in depth for
the beams and channels before splitting.
Other Permissible Variations
Other permissible variations in cross section as well as permissible variations in length, area,
and weight variation, and ends out-of-square will correspond to those of the beam or channel before splitting, except
total length,ft
Camber = 1⁄8-in. ×
5
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1 - 192
DIMENSIONS AND PROPERTIES
Table 1-15.
Angles, Structural Size
Permissible Variations in Cross Section
T
B
B
T
B Length of Leg, in.
Nominal Size,
in.a
Section
Angles
Over
Theoretical
Under
Theoretical
T, Out of Square
per in. of B, in.
1⁄
8
3⁄
32
b
3⁄
128
3 to 4, incl.
Over 4 to 6, incl.
1⁄
8
1⁄
8
b
3⁄
128
Over 6
3⁄
16
1⁄
8
b
3⁄
128
Permissible Variations in Length
Variations from Specified Length for Lengths Given, in.
Over
30 to 40 ft.,
incl.
to 30 ft.,
incl.
Section
Angles
Over
40 to 50 ft.,
incl.
Over
50 to 65 ft.,
incl.
Over 65 ft.
Over
Under
Over
Under
Over
Under
Over
Under
Over
Under
1⁄
2
1⁄
4
3⁄
4
1⁄
4
1
1⁄
4
11⁄8
1⁄
4
11⁄4
1⁄
4
Other Permissible Variations
Area and weight variation: ±2.5 percent theoretical or specified amount.
Ends out-of square: 3⁄128-in. per in. of leg length, or 11⁄2 degrees. Variations based on the longer
leg of unequal angle.
total length,ft
Camber = 1⁄8-in. ×
, applied to either leg
5
Notes;
aFor unequal leg angles, longer leg determines classification.
1
b1⁄
128 in. per in. = 1 ⁄2 deg.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
STANDARD MILL PRACTICE
1 - 193
Table 1-16.
Angles, Bar Size*
Permissible Variation in Cross Section
T
B
B
a
Specified
Length of Leg,
in.
T
Variations from Thickness for Thicknesses
Given, Over and Under, in.
3⁄
16
and
Under
Over 3⁄16 to
3⁄ incl.
8
1 and Under
0.008
0.010
Over 1 to 2, incl.
0.010
0.010
Over 2 to 3, excl.
0.012
0.015
Over 3⁄8
B Length of
T, Out of
Leg Over
Square per
and Under, in. Inch of B, in.
1⁄
32
b
3⁄
128
0.012
3⁄
64
b
3⁄
128
0.015
1⁄
16
b
3⁄
128
Permissible Variations in Length
Variations Over Specified Length for Lengths Given
No Variation Under
Section
All sizes of barsize angles
50 to 10 ft.
excl.
10 to 20 ft.
excl.
20 to 30 ft.
excl.
30 to 40 ft.
excl.
40 to 65 ft.
excl.
5⁄
8
1
11⁄2
2
21⁄2
Other Permissible Variations
total length,ft
5
Straightness: Because of warpage, permissible variations for straightness do not apply to bars if
any subsequent heating operation has been performed.
Ends out-of-square: 3⁄128-in. per inch of leg length or 11⁄2 degrees. Variation based on longer leg
of an unequal angle.
Camber: 1⁄4-in. in any 5 feet, or 1⁄4 in. ×
Notes:
*A member is ‘‘bar size’’ when its greatest cross-sectional dimension is less than three inches.
aFor unequal leg angles, longer leg determines classification.
1
b1⁄
128 in. per in. = 1 ⁄2 degrees.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1 - 194
DIMENSIONS AND PROPERTIES
Table 1-17.
Steel Pipe and Tubing
Dimensions and Weight Tolerances
Round Tubing and Pipe (see also Table 1-4)
ASTM A53
Weight—The weight of the pipe as specified in Table X2 and Table X3 (ASTM Specification
A53) shall not vary by more than ±10 percent.
Note that the weight tolerance of ±10 percent is determined from the weights of the customary lifts of pipe as produced for shipment by the mill, divided by the number of feet of
pipe in the lift. On pipe sizes over four inches where individual lengths may be weighed, the
weight tolerance is applicable to the individual length.
Diameter—For pipe two inches and over in nominal diameter, the outside diameter shall not
vary more than ±1 percent from the standard specified.
Thickness—The minimum wall thickness at any point shall not be more than 12.5 percent
under the nominal wall thickness specified.
ASTM 500
Diameter—For pipe two inches and over in nominal diameter, the outside diameter shall not
vary more than ±0.75 percent from the standard specified.
Thickness—The wall thickness at any point shall not be more than 10 percent under or over
the nominal wall thickness specified.
ASTM A501 and ASTM 618
Outside dimensions—For round hot-formed structural tubing two inches and over in nominal
size, the outside diameter shall not vary more than ±1 percent from the standard specified.
Weight (A501 only)—The weight of structural tubing shall be less than the specified value by
more than 3.5 percent.
Mass (A618 only)—The mass of structural tubing shall not be less than the specified value
by more than 3.5 percent.
Length—Structural tubing is commonly produced in random mill lengths and in definite cut
lengths. When cut lengths are specified for structural tubing, the length tolerances shall be in
accordance with the following table:
Over 22 to
44 ft, incl.
22 ft and under
Length tolerance for specified cut lengths, in.
Over
Under
Over
Under
1⁄
1⁄
3⁄
1⁄
2
4
4
4
Straightness—The permissible variation for straightness of structural tubing shall be 1⁄8-in.
times the number of feet of total length divided by 5.
Continued on next page
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
STANDARD MILL PRACTICE
1 - 195
Table 1-17 (cont.).
Steel Pipe and Tubing
Dimensions and Weight Tolerances
Square and Rectangular Tubing (see also Table 1-4)
ASTM A500 and ASTM A618
Outside Dimensions—The specified dimensions, measured across the flats at positions at
least two inches from either end-of-square or rectangular tubing and including an allowance
for convexity or concavity, shall not exceed the plus and minus tolerance shown in the following table:
a
Largest Outside Dimension Across Flats, in.
Tolerance Plus an Minus, in.
21⁄2 and under
Over 21⁄2 to 31⁄2, incl.
Over 31⁄2 to 51⁄2, incl.
Over 51⁄2
0.020
0.025
0.030
1 percent
aThe respective outside dimension tolerances
include the allowances for convexity and concavity.
Lengths—Structural tubing is commonly produced in random lengths, in multiple lengths, and
in definite cut lengths. When cut lengths are specified for structural tubing, the length tolerances shall be in accordance with the following table:
22 ft and under
Length tolerance for specified cut lengths, in.
Over 22 to 44 ft, incl.
Over
Under
Over
Under
1⁄
1⁄
3⁄
1⁄
2
4
4
4
Mass (A618 only)—The mass of structural tubing shall not be less than the specified value
by more than 3.5 percent.
Straightness—The permissible variation for straightness of structural tubing shall be 1⁄8-in.
times the number of feet of total length divided by five.
Squareness of sides—For square or rectangular structural tubing, adjacent sides may deviate from 90 degrees by a tolerance of plus or minus two degrees maximum.
Radius of corners—For square or rectangular structural tubing, the radius of any outside corner of the section shall not exceed three times the specified wall thickness.
Twists—The tolerances for twist or variation with respect to axial alignment of the section, for
square and rectangular structural tubing, shall be as shown in the following table:
Specified Dimension of Longest Side, in.
Maximum Twist per 3 ft of Length, in.
11⁄
2 and under
Over 11⁄2 to 21⁄2, incl.
Over 21⁄2 to 4, incl.
Over 4 to 6 incl.
Over 6 to 8, incl.
Over 8
0.050
0.062
0.075
0.087
0.100
0.112
Twist is measured by holding down one end of a square or rectangular tube on a flat surface plate with the bottom side of the tube parallel to the surface plate and noting the height
that either corner, at the opposite end of the bottom side of the tube, extends above the surface plate.
Wall thickness (A500 only)—The tolerance for wall thickness exclusive of the weld area shall
be plus and minus 10 percent of the nominal wall thickness specified. The wall thickness is
to be measured at the center of the flat.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1 - 196
DIMENSIONS AND PROPERTIES
Table 1-18.
Rectangular Sheared Plates and Universal Mill Plates
Permissible Variations in Width and Length for Sheared Plates
(11⁄2-in. and under in thickness)
Permissible Variations in Length Only for Universal Mill Plates
(21⁄2-in. and under in thickness)
Specified
Dimensions, in.
Variations over Specified Width and Length for Thickness,
in., and Equivalent Weights, lb per sq. ft., Given
To 3⁄8 excl.
To 15.3,
excl.
Length
To 120, excl.
Width
to 5⁄8 excl.
15.3 to 25.5,
excl.
5⁄
8
to 1, excl.
1 to 2, incl.a
25.5 to 40.8,
excl.
40.8 to 81.7,
incl.
Width Length Width Length Width Length Width Length
To 60, excl.
60 to 84, excl.
84 to 108, excl
108 and over
120 to 240, excl. To 60, excl.
60 to 84, excl.
84 to 108, excl.
108 and over
240 to 360, excl. To 60, excl.
60 to 84, excl.
84 to 108, excl.
108 and over
3⁄
8
7⁄
16
1⁄
2
5⁄
8
1⁄
2
5⁄
8
3⁄
4
7⁄
8
7⁄
16
1⁄
2
5⁄
8
3⁄
4
3⁄
3⁄
1⁄
1⁄
16
5⁄
8
1
9⁄
3⁄
1⁄
8
2
9⁄
16
11⁄
16
480 to 600, excl. To 60, excl.
60 to 84, excl.
84 to 108, excl.
108 and over
7⁄
To 60, excl.
60 to 84, excl.
84 to 108, excl.
108 and over
4
3⁄
7⁄
600 to 720, excl. To 60, excl.
60 to 84, excl.
84 to 108, excl.
108 and over
8
2
360 to 480, excl. To 60, excl.
60 to 84, excl.
84 to 108, excl.
108 and over
720 and over,
excl.
3⁄
8
16
1⁄
2
9⁄
16
3⁄
4
16
1⁄
2
5⁄
8
3⁄
4
1⁄
5⁄
5⁄
7⁄
2
8
8
8
9⁄
16
3⁄
4
3⁄
4
1
7⁄
4
8
5⁄
11⁄
2
8
16
3⁄
4
1
1
1
11 ⁄8
1⁄
11 ⁄8
11 ⁄4
11 ⁄4
13 ⁄8
1⁄
11 ⁄4
13 ⁄8
13 ⁄8
11 ⁄2
1⁄
11 ⁄4
13 ⁄8
13 ⁄8
11 ⁄2
5⁄
2
2
2
2
3⁄
5⁄
3⁄
7⁄
5⁄
3⁄
7⁄
5⁄
3⁄
7⁄
3⁄
3⁄
2
8
4
8
2
8
4
8
2
8
4
8
8
4
4
1
7⁄
7⁄
4
8
8
11 ⁄8
5⁄
8
11⁄
16
7⁄
8
1
7⁄
7⁄
15 ⁄
8
8
16
11 ⁄8
1⁄
2
5⁄
3⁄
7⁄
5⁄
3⁄
13 ⁄
7⁄
11 ⁄8
11 ⁄8
11 ⁄8
11 ⁄4
5⁄
11 ⁄4
13 ⁄8
13 ⁄8
11 ⁄2
5⁄
11 ⁄2
11 ⁄2
11 ⁄2
15 ⁄8
5⁄
17 ⁄8
17 ⁄8
17 ⁄8
2
3⁄
21 ⁄8
21 ⁄8
21 ⁄8
23 ⁄8
3⁄
7⁄
8
4
8
8
4
16
8
8
4
8
1
3⁄
7⁄
8
4
8
1
3⁄
7⁄
8
4
8
1
7⁄
7⁄
4
8
8
11 ⁄8
7⁄
8
1
1
11 ⁄4
3⁄
4
7⁄
8
5⁄
8
3⁄
4
1
11 ⁄8
1
11 ⁄8
1
1
11 ⁄8
11 ⁄4
3⁄
11 ⁄4
11 ⁄4
13 ⁄8
13 ⁄8
13 ⁄8
11 ⁄2
11 ⁄2
15 ⁄8
15 ⁄8
15 ⁄8
15 ⁄8
13 ⁄4
7⁄
4
8
1
11 ⁄8
3⁄
7⁄
4
8
1
11 ⁄4
3⁄
7⁄
4
8
1
11 ⁄4
3⁄
7⁄
4
8
1
11 ⁄4
7⁄
1
1
11 ⁄ 8
11 ⁄ 4
11 ⁄ 8
11 ⁄ 4
13 ⁄ 8
13 ⁄ 8
11 ⁄ 2
11 ⁄ 2
11 ⁄ 2
13 ⁄ 4
15 ⁄ 8
15 ⁄ 8
17 ⁄ 8
17 ⁄ 8
17 ⁄ 8
17 ⁄ 8
17 ⁄ 8
17 ⁄ 8
17 ⁄8
17 ⁄8
17 ⁄8
21 ⁄4
1
11 ⁄8
11 ⁄4
21 ⁄ 4
21 ⁄ 4
21 ⁄ 4
21 ⁄ 2
21 ⁄4
21 ⁄4
21 ⁄4
21 ⁄2
1
11 ⁄8
11 ⁄4
13 ⁄8
23 ⁄ 4
23 ⁄ 4
23 ⁄ 4
3
8
Notes:
aPermissible variations in length apply also to Universal Mill plates up to 12 in. width for thicknesses over 2 to
21⁄2-in., incl. except for alloy steels up to 13⁄4-in. thick.
Permissible variations under specified width and length, 1⁄4-in. Table applies to all steels listed in ASTM A6.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
STANDARD MILL PRACTICE
1 - 197
Table 1-19.
Rectangular Sheared Plates and Universal Mill Plates
Permissible Variations from Flatness (Carbon Steel Only)
Variations from Flatness for Specified Widths, in.
Specified
Thickness,
in.
To 36
excl.
To 1⁄4, excl.
1⁄ to 3⁄ , excl.
4
8
3⁄ to 1⁄ , excl.
8
2
1⁄ to 3⁄ , excl.
2
4
3⁄ to 1, excl.
4
1 to 2, excl.
2 to 4, excl.
4 to 6, excl.
6 to 8, excl.
9⁄
16
1⁄
2
1⁄
2
7⁄
16
7⁄
16
3⁄
8
5⁄
16
3⁄
8
7⁄
16
36 to 48, 48 to 60, 60 to 72, 72 to 84, 84 to 96, 96 to 108, 108 to
excl.
excl.
excl.
excl.
excl.
excl. 120, excl.
3⁄
4
5⁄
8
9⁄
16
1⁄
2
1⁄
2
1⁄
2
3⁄
8
7⁄
16
1⁄
2
15⁄
3⁄
5⁄
16
4
8
9⁄
16
9⁄
16
1⁄
2
7⁄
16
1⁄
2
1⁄
2
11⁄4
15⁄
16
5⁄
8
5⁄
8
5⁄
8
9⁄
16
1⁄
2
1⁄
2
5⁄
8
13⁄8
11⁄8
3⁄
4
5⁄
8
5⁄
8
9⁄
16
1⁄
2
9⁄
16
11⁄
16
11⁄2
11⁄4
7⁄
8
3⁄
4
5⁄
8
5⁄
8
1⁄
2
9⁄
16
3⁄
4
15⁄8
13⁄8
1
1
3⁄
4
5⁄
8
1⁄
2
5⁄
8
7⁄
8
13⁄4
11⁄2
11⁄8
1
7⁄
8
5⁄
8
9⁄
16
3⁄
4
7⁄
8
Permissible Variations in Camber for Carbon Steel
Sheared and Gas Cut Rectangular Plates
Maximum permissible camber, in. (all thicknesses) = 1⁄8-in. ×
total length,ft
5
Permissible Variations in Camber for Carbon Steel Universal Mill Plates,
High-Strength Low-Alloy Steel Sheared and Gas Cut Rectangular Plates,
Universal Mill Plates, Special Cut Plates
Dimension, in.
Thickness
To 2, incl.
Over 2 to 15, incl.
Over 2 to 15, incl.
Width
Camber for Thicknesses
and Widths Given
All
To 30, incl.
Over 30 to 60, incl.
1⁄ in. × (total length, ft / 5)
8
3⁄ in. × (total length, ft / 5)
16
1⁄ in. × (total length, ft / 5)
4
General Notes:
1. The longer dimension specified is considered the length, and permissible variations in flatness along the
length should not exceed the tabular amount for the specified width in plates up to 12 feet in length.
2. The flatness variations across the width should not exceed the tabular amount for the specified width.
3. When the longer dimension is under 36 inches, the permissible variation should not exceed 1⁄4-in. When the
longer dimension is from 36 to 72 inches, inclusive, the permissible variation should not exceed 75 percent of
the tabular amount for the specified width, but in no case less than 1⁄4-in.
4. These variations apply to plates which have a specified minimum tensile strength of not more than 60 ksi or
compatible chemistry or hardness. The limits in the table are increased 50 percent for plates specified to a
higher minimum tensile strength or compatible chemistry or hardness.
See also next page.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1 - 198
DIMENSIONS AND PROPERTIES
Table 1-20.
Rectangular Sheared Plates and Universal Milled Plates
Permissible Variations from Flatness
(High-Strength Low-Alloy and Alloy Steel, Hot Rolled or Thermally Treated)
Variations from Flatness for Specified Widths, in.
Specified
Thickness,
in.
To 36
excl.
To 1⁄4, excl.
1⁄ to 3⁄ , excl.
4
8
3⁄ to 1⁄ , excl.
8
2
1⁄ to 3⁄ , excl.
2
4
3⁄ to 1, excl.
4
1 to 2, excl.
2 to 4, excl.
4 to 6, excl.
6 to 8, excl.
13⁄
16
3⁄
4
3⁄
4
5⁄
8
5⁄
8
9⁄
16
1⁄
2
9⁄
16
5⁄
8
36 to 48, 48 to 60, 60 to 72, 72 to 84, 84 to 96, 96 to 108, 108 to
excl.
excl.
excl.
excl.
excl.
excl. 120, excl.
11⁄8
15⁄
7⁄
3⁄
3⁄
5⁄
13⁄8
11⁄8
15⁄
16
15⁄
16
7⁄
8
3⁄
4
9⁄
16
3⁄
4
3⁄
4
16
8
4
4
8
9⁄
16
11⁄
16
3⁄
4
17⁄8
13⁄8
15⁄
16
7⁄
8
7⁄
8
13⁄
16
3⁄
4
3⁄
4
15⁄
16
21⁄4
17⁄8
15⁄16
11⁄8
1
15⁄
16
3⁄
4
7⁄
8
11⁄8
2
13⁄4
11⁄8
1
15⁄
16
7⁄
8
3⁄
4
7⁄
8
1
23⁄8
2
11⁄2
11⁄4
11⁄8
1
3⁄
4
15⁄
16
11⁄4
25⁄8
21⁄4
15⁄8
13⁄8
15⁄16
1
7⁄
8
11⁄8
15⁄16
General Notes:
1. The longer dimension specified is considered the length, and variations from a flat surface along the length
should not exceed the tabular amount for the specified width in plates up to 12 feet in length.
2. The flatness variation across the width should not exceed the tabular amount for the specified width.
3. When the longer dimension is under 36 inches, the variation should not exceed 3⁄8-in. When the longer
dimension is from 36 to 72 inches, inclusive the variation should not exceed 75 percent of the tabular amount
for the specified width.
Permissible Variations in Width for Universal Mill Plates
(15 inches and under in thickness)
Variations Over Specified Width for Thickness, in.,
and Equivalent Weights, lb per sq. ft., Given
To 3⁄8,
excl.
3⁄
8
to 5⁄8
excl.
5⁄
8
to 1,
excl.
Specified
Width, in.
To 15.3,
excl.
15.3 to
25.5, excl.
25.5 to
40.8, excl.
Over 8 to 20, excl.
20 to 36, excl.
36 and over
1⁄
8
3⁄
16
5⁄
16
1⁄
1⁄
3⁄
16
5⁄
16
7⁄
16
3⁄
8
4
8
1 to 2,
excl.
Over 2 to
10, incl.
Over 10 to
15, incl.
40.8 to
81.7 to
409.0 to
81.7, incl. 409.0, incl. 613.0, incl.
1⁄
3⁄
1⁄
4
8
2
Notes:
Permissible variation under specified width, 1⁄8-in.
Table applies to all steels listed in ASTM A6.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
3⁄
8
7⁄
16
9⁄
16
1⁄
2
9⁄
16
5⁄
8
REFERENCES
1 - 199
REFERENCES
American Institute of Steel Construction, 1973, “Commentary on Highly Restrained
Welded Connections,” Engineering Journal, 3rd Qtr., AISC, Chicago, IL.
American Iron and Steel Institute, 1979, Fire Safe Structural Steel: A Design Guide, AISI,
Washington, DC.
AISI, 1980, Designing Fire Protection for Steel Columns, 3rd Edition.
AISI, 1981, Designing Fire Protection for Steel Trusses, 2nd Edition.
AISI, 1984, Designing Fire Protection for Steel Beams.
Brockenbrough, R. L. and B. G. Johnston, 1981, USS Steel Design Manual, R. L.
Brockenbrough & Assoc. Inc., Pittsburgh, PA.
Dill, F. H., 1960, “Structural Steel After a Fire,” Proceedings of the 1960 National
Engineering Conference, AISC, New York, NY.
Fisher, J. W. and A. W. Pense, 1987, “Experience with Use of Heavy W Shapes in
Tension,” Engineering Journal, 2nd Qtr., AISC, Chicago.
Lightner, M. W. and R. W. Vanderbeck, 1956, “Factors Involved in Brittle Fracture,”
Regional Technical Meetings, AISI, Washington, DC.
Rolfe, S. T. and J. M. Barsom, 1986, Fracture and Fatigue Control in Structures:
Applications of Fracture Mechanics, Prentice-Hall, Inc., Englewood Cliffs, NJ.
Rolfe, S. T., 1977, “Fracture and Fatigue Control in Steel Structures,” Engineering
Journal, 1st Qtr., AISC, Chicago.
Welding Research Council, 1957, Control of Steel Construction to Avoid Brittle Failure,
New York.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
2-1
PART 2
ESSENTIALS OF LRFD
OVERVIEW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-3
INTRODUCTION TO LRFD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-5
A. GENERAL PROVISIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-8
B. DESIGN REQUIREMENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-11
C. FRAMES AND OTHER STRUCTURES . . . . . . . . . . . . . . . . . . . . . . . . . 2-14
D. TENSION MEMBERS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-19
E. COLUMNS AND OTHER COMPRESSION MEMBERS . . . . . . . . . . . . . . . . 2-22
F. BEAMS AND OTHER FLEXURAL MEMBERS . . . . . . . . . . . . . . . . . . . . 2-27
H. MEMBERS UNDER COMBINED FORCES AND TORSION . . . . . . . . . . . . . 2-34
I. COMPOSITE MEMBERS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-42
COMPUTER SOFTWARE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-44
REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-45
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
2-2
ESSENTIALS OF LRFD
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
OVERVIEW
2-3
OVERVIEW
The following LRFD topics are covered herein (with the letters A through I in the section
headings referring to the corresponding chapters in the LRFD Specification):
INTRODUCTION TO LRFD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-5
LRFD Versus ASD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-5
LRFD Fundamentals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-6
A. GENERAL PROVISIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-8
Loads and Load Combinations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-8
B. DESIGN REQUIREMENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-11
Gross, Net, and Effective Net Areas for Tension Members . . . . . . . . . . . . . . . . 2-11
Gross, Net, and Effective Net Areas for Flexural Members . . . . . . . . . . . . . . . . 2-12
Local Buckling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-12
Limiting Slenderness Ratios . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-13
C. FRAMES AND OTHER STRUCTURES . . . . . . . . . . . . . . . . . . . . . . . . . 2-14
Second Order Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-14
Effective Length . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-17
“Leaning” Columns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-18
D. TENSION MEMBERS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-19
Design Tensile Strength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-19
Built-Up Members, Eyebars, and Pin-Connected Members . . . . . . . . . . . . . . . . 2-21
E. COLUMNS AND OTHER COMPRESSION MEMBERS . . . . . . . . . . . . . . . . 2-22
Effective Length . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-22
Design Compressive Strength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-22
Flexural-Torsional Buckling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-27
Built-Up and Pin-Connected Members . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-27
F. BEAMS AND OTHER FLEXURAL MEMBERS . . . . . . . . . . . . . . . . . . . . 2-27
Flexure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-27
Design for Flexure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-29
Design for Shear . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-33
Web Openings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-34
H. MEMBERS UNDER COMBINED FORCES AND TORSION . . . . . . . . . . . . . 2-34
Symmetric Members Subject to Bending and Axial Tension . . . . . . . . . . . . . . . 2-34
Symmetric Members Subject to Bending and Axial Compression . . . . . . . . . . . . 2-37
Bending and Axial Compression—Preliminary Design . . . . . . . . . . . . . . . . . . 2-37
Torsion and Combined Torsion, Flexure, and/or Axial Force . . . . . . . . . . . . . . . 2-40
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
2-4
ESSENTIALS OF LRFD
I. COMPOSITE MEMBERS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-42
Compression Members . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-42
Flexural Members . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-43
Combined Compression and Flexure . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-44
COMPUTER SOFTWARE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-44
ELRFD (Electronic LRFD Specification) . . . . . . . . . . . . . . . . . . . . . . . . . 2-44
REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-45
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
INTRODUCTION TO LRFD
2-5
INTRODUCTION TO LRFD
The intent of this part of the LRFD Manual is to provide a general introduction to the
subject. It was written primarily for:
(1) engineers experienced in allowable stress design (ASD) who are unfamiliar with
LRFD and
(2) students and novice engineers.
The emphasis is on understanding the most common cases, rather than on completeness
and efficiency in design. Regular users of LRFD may also find it helpful to refer to the
information provided herein. It should be noted, however, that the governing document
is the LRFD Specification (in Part 6 of this volume of the Manual). For optimum design
the use of the design aids elsewhere in this Manual is recommended. Among the topics
not covered herein are:
(1) connections, the subject of Volume II, and
(2) noncompact beams and plate girders, for which the reader is referred to Appendices
F and G of the LRFD Specification and Part 4 of this volume of the Manual.
LRFD Versus ASD
The primary objective of the LRFD Specification is to provide a uniform reliability for
steel structures under various loading conditions. This uniformity cannot be obtained with
the allowable stress design (ASD) format.
The ASD method can be represented by the inequality
ΣQi ≤ Rn / F.S.
(2-1)
The left side is the summation of the load effects, Qi (i.e., forces or moments). The right
side is the nominal strength or resistance Rn divided by a factor of safety. When divided
by the appropriate section property (e.g., area or section modulus), the two sides of the
inequality become the calculated stress and allowable stress, respectively. The left side
can be expanded as follows:
ΣQi = the maximum (absolute value) of the combinations
D + L′
(D + L′ + W) × 0.75*
(D + L′ + E) × 0.75*
D−W
D−E
where D, L′, W, and E are, respectively, the effects of the dead, live, wind, and earthquake
loads; total live load L′ = L + (Lr or S or R)
L = Live load due to occupancy
Lr = Roof live load
S = Snow load
R = Nominal load due to initial rainwater or ice exclusive of the ponding
contribution
*0.75 is the reciprocal of 1.33, which represents the 1/3 increase in allowable stress permitted when wind or earthquake is
taken simultaneously with live load.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
2-6
ESSENTIALS OF LRFD
ASD, then, is characterized by the use of unfactored service loads in conjunction with a
single factor of safety applied to the resistance. Because of the greater variability and,
hence, unpredictability of the live load and other loads in comparison with the dead load,
a uniform reliability is not possible.
LRFD, as its name implies, uses separate factors for each load and for the resistance.
Considerable research and experience were needed to establish the appropriate factors.
Because the different factors reflect the degree of uncertainty of different loads and
combinations of loads and the accuracy of predicted strength, a more uniform reliability
is possible.
The LRFD method may be summarized by the formula
ΣγiQi ≤ φRn
(2-2)
On the left side of the inequality, the required strength is the summation of the various
load effects Qi multiplied by their respective load factors γi. The design strength, on the
right side, is the nominal strength or resistance Rn multiplied by a resistance factor φ.
Values of φ and Rn for columns, beams, etc. are provided throughout the LRFD Specification and will be covered here, as well.
According to the LRFD Specification (Section A4.1), ΣγiQi = the maximum absolute
value of the following combinations
1.4D
1.2D + 1.6L + 0.5(Lr or S or R)
1.2D + 1.6(Lr or S or R) + (0.5L or 0.8W)
1.2D + 1.3W + 0.5L + 0.5(Lr or S or R)
1.2D ± 1.0E + 0.5L + 0.2S
0.9D ± (1.3W or 1.0E)
(A4-1)
(A4-2)
(A4-3)
(A4-4)
(A4-5)
(A4-6)
(Exception: The load factor on L in combinations A4-3, A4-4, A4-5 shall equal 1.0 for
garages, areas occupied as places of public assembly, and all areas where the live load is
greater than 100 psf).
The load effects D, L, Lr, S, R, W, and E are as defined above. The loads should be
taken from the governing building code or from ASCE 7, Minimum Design Loads in
Buildings and Other Structures (American Society of Civil Engineers, 1988). Where
applicable, L should be determined from the reduced live load specified for the given
member in the governing code. Earthquake loads should be from the AISC Seismic
Provisions for Structural Steel Buildings, which appears in Part 6 of this Manual.
LRFD Fundamentals
The following is a brief discussion of the basic concepts of LRFD. A more complete
treatment of the subject is available in the Commentary on the LRFD Specification
(Section A4 and A5) and in the references cited therein.
LRFD is a method for proportioning structures so that no applicable limit state is
exceeded when the structure is subjected to all appropriate factored load combinations.
Strength limit states are related to safety and load carrying capacity (e.g., the limit states
of plastic moment and buckling). Serviceability limit states (e.g., deflections) relate to
performance under normal service conditions. In general, a structural member will have
several limit states. For a beam, for example, they are flexural strength, shear strength,
vertical deflection, etc. Each limit state has associated with it a value of Rn, which defines
the boundary of structural usefulness.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
INTRODUCTION TO LRFD
2-7
Because the AISC Specification is concerned primarily with safety, strength limit states
are emphasized. The load combinations for determining the required strength were given
in expressions A4-1 through A4-6. (Other load combinations, with different values of
γi, are appropriate for serviceability; see Chapter L in the LRFD Specification and
Commentary.)
The AISC load factors (A4-1 through A4-6) are based on ASCE 7. They were originally
developed by the A58 Load Factor Subcommittee of the American National Standards
Institute, ANSI, (U.S. Department of Commerce, 1980) and are based strictly on load
statistics. Being material-independent, they are applicable to all structural materials.
Although others have written design codes similar in format to the LRFD Specification,
the AISC was the first specification group to adopt the ANSI probability-based load
factors.
The AISC load factors recognize that when several loads act in combination, only one
assumes its maximum lifetime value at a time, while the others are at their “arbitrarypoint-in-time” (APT) values. Each combination models the total design loading condition
when a different load is at its maximum:
Load Combination
A4-1
A4-2
A4-3
A4-4
A4-5
A4-6
Load at its Lifetime (50-year) Maximum
D (during construction; other loads not present)
L
Lr or S or R (a roof load)
W (acting in direction of D)
E (acting in direction of D)
W or E (opposing D)
The other loads, which are APT loads, have mean values considerably lower than the
lifetime maximums. To achieve a uniform reliability, every factored load (lifetime
maximum or APT) is larger than its mean value by an amount depending on its variability.
The AISC resistance factors are based on research recommendations published by
Washington University in St. Louis (Galambos et al., 1978) and reviewed by the AISC
Specification Advisory Committee. Test data were analyzed to determine the variability
of each resistance. In general, the resistance factors are less than one (φ < 1). For uniform
reliability, the greater the scatter in the data for a given resistance, the lower its φ factor.
Several representative LRFD φ factors for steel members (referenced to the corresponding chapters in the LRFD Specification) are:
φt = 0.90 for tensile yielding (Chapter D)
φt = 0.75 for tensile fracture (Chapter D)
φc = 0.85 for compression (Chapter E)
φb = 0.90 for flexure (Chapter F)
φv = 0.90 for shear yielding (Chapter F)
Resistance factors for other member and connection limit states are given in the LRFD
Specification.
The following sections (A through I) summarize and explain the corresponding
chapters of the LRFD Specification.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
2-8
ESSENTIALS OF LRFD
A. GENERAL PROVISIONS
In the LRFD Specification, Sections A4 and A5 define Load and Resistance Factor
Design. The remainder of Chapter A contains general provisions which are essentially
the same as in the earlier ASD editions of the Specification.
Reference is made to the Code of Standard Practice for Steel Buildings and Bridges
(adopted in 1992 by AISC), which appears with a Commentary in Part 6 of this LRFD
Manual. The Code defines the practices and commonly accepted standards in the
structural steel fabricating industry. In the absence of other instructions in the contract
documents, these trade practices govern the fabrication and erection of structural steel.
The types of construction recognized by the AISC Specification have not changed,
except that both “simple framing” (formerly Type 2) and “semi-rigid framing” (formerly
Type 3) have been combined into one category, Type PR (partially restrained). “Rigid
framing” (formerly Type 1) is now Type FR (fully restrained). Type FR construction is
permitted unconditionally. Type PR is allowed only upon evidence that the connections
to be used are capable of furnishing, as a minimum, a predictable portion of full end
restraint. Type PR construction may necessitate some inelastic, but self-limiting, deformation of a structural steel part. When specifying Type PR construction, the designer
should take into account the effects of reduced connection stiffness on the stability of the
structure, lateral deflections, and second order bending moments.
Semi-rigid connections, once common, are again becoming popular. They offer
economies in connection fabrication (compared with FR connections) and reduced
member size (compared with simple framing). For information on connections, please
refer to Volume II of this LRFD Manual.
The yield stresses of the grades of structural steel approved for use range from 36 ksi
for the common A36 steel to 100 ksi for A514 steel. Not all rolled shapes and plate
thicknesses are available for every yield stress. Availability tables for structural shapes,
plates and bars are at the beginning of Part 1 of this LRFD Manual.
A36, for many years the dominant structural steel for buildings, is being replaced by
the more economical 50 ksi steels. ASTM designations for structural steels with 50 ksi
yield stress are: A572 for most applications, A529 for thin-plate members only, and A242
and A588 weathering steels for atmospheric corrosion resistance. A more complete
explanation is provided by Table 1-1 in Part 1 of this Manual. However, A36 is still
normally specified for connection material, where no appreciable savings can be realized
from higher strength steels.
Complete and accurate drawings and specifications are necessary for all stages of steel
construction. The requirements for design documents are set forth in Section A7 of the
LRFD Specification and Section 3 of the AISC Code of Standard Practice. When beam
end reactions are not shown on the drawings, the structural steel detailer will refer to the
appropriate tables in Part 4 of the LRFD Manual. These tables, which are for uniform
loads, may significantly underestimate the effects of the concentrated loads. The recording of beam end reactions on design drawings, which is recommended in all cases, is,
therefore, absolutely essential when there are concentrated loads. Beam reactions,
column loads, etc., shown on design drawings should be the required strengths calculated
from the factored load combinations and should be so noted.
Loads and Load Combinations
LRFD Specification Sections A4 (Loads and Load Combinations) and A5 (Design Basis)
describe the basic criteria of LRFD. This information was discussed above under
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
A. GENERAL PROVISIONS
2-9
Introduction to LRFD. To illustrate the application of load factors, the AISC load
combinations will be repeated here with design examples.
The required strength is the maximum absolute value of the combinations
1.4D
1.2D + 1.6L + 0.5(Lr or S or R)
1.2D + 1.6(Lr or S or R) + (0.5L or 0.8W)
1.2D + 1.3W + 0.5L + 0.5(Lr or S or R)
1.2D ± 1.0E + 0.5L + 0.2S
0.9D ± (1.3W or 1.0E)
(A4-1)
(A4-2)
(A4-3)
(A4-4)
(A4-5)
(A4-6)
(The load factor on L in combinations A4-3, A4-4 and A4-5 shall equal 1.0 for garages,
areas occupied as placed of public assembly, and all areas where the live load is greater
than 100 psf).
In the combinations the loads or load effects (i.e., forces or moments) are:
D = dead load due to the weight of the structural elements and the permanent features on the structure
L = live load due to occupancy and moveable equipment (reduced as permitted by
the governing code)
Lr = roof live load
W= wind load
S = snow load
E = earthquake load
R = nominal load due to initial rainwater or ice exclusive of the ponding contribution
The loads are to be taken from the governing building code. In the absence of a code, one
may use ASCE 7 Minimum Design Loads for Buildings and Other Structures (American
Society of Civil Engineers, 1988). Earthquake loads should be determined from the AISC
Seismic Provisions for Structural Steel Buildings, in Part 6 of this Manual.
Whether the loads themselves or the load effects are combined, the results are the same,
provided the principle of superposition is valid. This is usually true because deflections
are small and the stress-strain behavior is linear elastic; consequently, second order effects
can usually be neglected. (The analysis of second order effects is covered in Chapter C
of the LRFD Specification.) The linear elastic assumption, although not correct at the
strength limit states, is valid under normal in-service loads and is permissible as a design
assumption under the LRFD Specification. In fact, the Specification (in Section A.5.1)
allows the designer the option of elastic or plastic analysis using the factored loads.
However, to simplify this presentation, it is assumed that the more prevalent elastic
analysis option has been selected.
EXAMPLE A-1
Given:
Solution:
Roof beams W16×31, spaced 7′′-0 center-to-center, support a superimposed dead load of 40 psf. Code specified roof loads are 30 psf
downward (due to roof live load, snow, or rain) and 20 psf upward or
downward (due to wind). Determine the critical loading for LRFD.
D
= 31 plf + 40 psf × 7.0 ft = 311 plf
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
2 - 10
ESSENTIALS OF LRFD
L
=0
(Lr or S or R) = 30 psf × 7.0 ft = 210 plf
W
= 20 psf × 7.0 ft = 140 plf
E
=0
Load
Combinations
A4-1
A4-2
A4-3
A4-4
A4-5
A4-6a
A4-6b
Factored Loads
1.4(311 plf)
1.2(311 plf) + 0 + 0.5(210 plf)
1.2(311 plf) + 1.6 (210 plf) +
0.8(140 plf)
1.2(311 plf) + 1.3(140 plf) + 0 +
0.5(210 plf)
1.2(311 plf) + 0 + 0 + 0.2(210 plf)
0.9 (311 plf) + 1.3 (140 plf)
0.9(311 plf) − 1.3(140 plf)
= 435 plf
= 478 plf
= 821 plf
= 660 plf
= 415 plf
= 462 plf
= 98 plf
The critical factored load combination for design is the third, with a
total factored load of 821 plf.
EXAMPLE A-2
Given:
Solution:
The axial loads on a building column resulting from the code-specified
service loads have been calculated as: 100 kips from dead load, 150
kips from (reduced) floor live load, 30 kips from the roof (Lr or S or
R), 60 kips due to wind, and 50 kips due to earthquake. Determine the
required strength of this column.
Load
Combination
A4-1
A4-2
A4-3a
A4-3b
A4-4
A4-5a
A4-5b
A4-6a
A4-6b
A4-6c
A4-6d
Factored Axial Load
1.4(100 kips)
1.2(100 kips) + 1.6(150 kips) +
0.5(30 kips)
1.2(100 kips) + 1.6(30 kips) +
0.5(150 kips)
1.2(100 kips) + 1.6(30 kips) +
0.8(60 kips)
1.2(100 kips) + 1.3(60 kips) +
0.5(150 kips) + 0.5(30 kips)
1.2(100 kips) + 1.0(50 kips) +
0.5(150 kips) + 0.2(30 kips)
1.2(100 kips) − 1.0(50 kips) +
0.5(150 kips) + 0.2(30 kips)
0.9(100 kips) + 1.3(60 kips)
0.9(100 kips) − 1.3(60 kips)
0.9(100 kips) + 1.0(50 kips)
0.9(100 kips) − 1.0(50 kips)
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
= 140 kips
= 375 kips
= 243 kips
= 216 kips
= 288 kips
= 251 kips
= 151 kips
= 168 kips
= 12 kips
= 140 kips
= 40 kips
B. DESIGN REQUIREMENTS
2 - 11
The required strength of the column is 375 kips based on the second
combination of factored axial loads. As none of the results above are
negative, net tension need not be considered in the design of this
column.
B. DESIGN REQUIREMENTS
Gross, Net, and Effective Net Areas for Tension Members
The concept of effective net area, which in earlier editions of the Specification was
applied only to bolted members, has been extended to cover members connected by
welding as well. As in the past, when tensile forces are transmitted directly to all elements
of the member, the net area is used to determine stresses. However, when the tensile forces
are transmitted through some, but not all, of the cross-sectional elements of the member,
a reduced effective net area Ae is used instead. According to Section B3 of the LRFD
Specification
Ae = AU
(B3-1)
where
A = area as defined below
U = reduction
coefficient
_
=
1
−
(x
/
L)
≤ 0.9, or as defined in (c) or (d)
(B3-2)
_
x = connection eccentricity. (See Commentary on the LRFD Specification, Section
B3 and Figure C-B3.1.)
L = length of connection in the direction of loading
a. When the forces are transmitted only by bolts
A = An
= net area of member, in.2
b. When the forces are transmitted by longitudinal welds only or in combination with
transverse welds
A = Ag
= gross area of member, in.2
c. When the forces are transmitted only by transverse welds
A = area of directly connected elements, in.2
U = 1.0
d. When the forces are transmitted to a plate by longitudinal welds along both edges
at the end of the plate
A = area of plate, in.2
l ≥w
For l ≥ 2w
For 2w > l ≥ 1.5w
For 1.5w > l ≥ w
U = 1.00
U = 0.87
U = 0.75
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
2 - 12
ESSENTIALS OF LRFD
where
l = weld length
w = plate width (distance between welds), in.
In computing the net area for tension and shear, the width of a bolt hole is taken as 1⁄16-in.
greater than the nominal dimension of the hole, which, for standard holes, is 1⁄16-in. larger
than the diameter of the bolt. Chains of holes, treated as in the past, are covered in Section
B2 of the LRFD Specification.
Gross, Net, and Effective Net Areas for Flexural Members
Gross areas are used for elements in compression, in beams and columns. According to
Section B10 of the LRFD Specification, the properties of beams and other flexural
members are based on the gross section (with no deduction for holes in the tension flange)
if
0.75Fu Afn ≥ 0.9Fy Afg
(B10-1)
where
Afg = gross flange area, in.2
Afn = net flange area (deducting bolt holes), in.2
Fy = specified minimum yield stress, ksi
Fu = minimum tensile strength, ksi
Otherwise, an effective tension flange area Afe is used to calculate flexural properties
Afe =
5 Fu
A
6 Fy fn
(B10-3)
Local Buckling
Steel sections are classified as either compact, noncompact, or slender element sections:
• If the flanges are continuously connected to the web and the width-thickness ratios
of all the compression elements do not exceed λp, then the section is compact.
• If the width-thickness ratio of at least one of its compression elements exceeds λp,
but does not exceed λr, the section is noncompact.
• If the width-thickness ratio of any compression element exceeds λr, that element is
called a slender compression element.
Columns with compact and noncompact cross sections are covered by Chapter E of
the LRFD Specification. Column cross sections with slender elements require the special
design procedure in Appendix B5.3 of the Specification.
Beams with compact sections are covered by Chapter F of the LRFD Specification.
All other cross sections in bending must be designed in accordance with Appendices
B5.3, F1 and/or G.
In general, reference to the appendices of the Specification is required for the design
of members controlled by local buckling. In slender element sections, local buckling,
occurring prior to initial yielding, will limit the strength of the member. Noncompact
sections will yield first, but local buckling will precede the development of a fully plastic
stress distribution. In actual practice, such cases are not common and can be easily
avoided by designing so that:
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
B. DESIGN REQUIREMENTS
2 - 13
Table B-1.
Limiting Width-Thickness Ratios for Compression Elements*
WidthThickness Ratio
Beam Element
Limiting Width-Thickness Ratio, λp
General
For Fy = 50 ksi
Flanges of I shapes and channels
b/t
65 / √
F
y
9.2
Flanges of square and rectangular
box beams
b/t
190 / √
Fy
26.9
Webs in flexural compression
h / tw
640 / √
Fy
90.5
Webs in combined flexural and axial
compression
h / tw
253 / √
Fy **
35.8
Column Element
WidthThickness Ratio
Limiting Width-Thickness Ratio, λr
General
For Fy = 50 ksi
Flanges of I shapes and channels
and plates projecting from
compression elements
b/t
95 / √
F
y
13.4
Webs in axial compression
h / tw
253 / √
Fy
35.8
*For the complete table, see LRFD Specification, Section B5, Table B5.1.
**This is a simplified, conservative version of the corresponding entry in Table B5.1 of the LRFD Specification.
• for beams, the width-thickness ratios of all compression elements ≤ λp;
• for columns, the width-thickness ratios of all elements ≤ λr.
Table B-1, which is an abridged version of Table B5.1 in the LRFD Specification,
should be useful for this purpose. The formulas for λp for beam elements and λr for column
elements are tabulated, together with the corresponding numerical values for 50 ksi steel.
The definitions of “width” for use in determining the width-thickness ratios of the
elements of various structural shapes are stated in Section B5 of the LRFD Specification.
They are shown graphically in Figure B-1. Compact section criteria for W shapes and
other I-shaped cross sections are listed in the Properties Tables in Part 1 of LRFD Manual.
Limiting Slenderness Ratios
For members whose design is based on compressive force, the slenderness ratio Kl / r
preferably should not exceed 200.
For members whose design is based on tensile force, the slenderness ratio l / r
preferably should not exceed 300. The above limitation does not apply to rods in tension.
K = effective length factor, defined in Section C below
l = distance between points of lateral support (lx or ly), in.
r = radius of gyration (rx or ry), in.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
2 - 14
ESSENTIALS OF LRFD
C. FRAMES AND OTHER STRUCTURES
Second Order Effects
As stated in Section C1 of the LRFD Specification, an analysis of second order effects
is required; i.e., the additional moments due to the axial loads acting on the deformed
structure must be considered. In lieu of a second order analysis for Mu, the required
flexural strength, the LRFD Specification (in Section C1) presents the following simplified method:
Mu = B1Mnt + B2Mlt
(C1-1)
The components of the total factored moment, determined from a first order elastic
analysis (neglecting second order effects) are divided into two groups, Mnt and Mlt. Each
group is in turn multiplied by a magnification factor B1 or B2 and the results are added to
approximate the actual second order factored moment Mu. (The method, as explained
here, is valid where the moment connections are Type FR, fully restrained. The analysis
for Type PR, or partially restrained, moment connections is beyond the scope of this
section.)
Beam-columns are generally columns in frames, which are either braced (Mlt = 0) or
unbraced (Mlt ≠ 0). Mnt is the moment in the member assuming there is no lateral
translation of the frame; Mlt is the moment due to lateral translation. Mnt includes the
moments resulting from the gravity loads, as determined manually or by computer, using
one of the customary (elastic, first order) methods. The moments from the lateral loads
are classified as Mlt; i.e., due to lateral translation. If both the frame and its vertical loads
are symmetric, Mlt from the vertical loads is zero. However, if either the vertical loads or
the frame is asymmetric and the frame is not braced, lateral translation occurs and Mlt ≠ 0.
The procedure for obtaining Mlt in this case involves:
b=
bf
b=
2
bf
bf
b = bf
2
bf
bf
h
h
h
bf
b
t
hw
t
h
b = b f – 3t
h = h w – 3t
Fig. B-1. Definitions of widths (b and h) for use in Table B-1.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
C. FRAMES AND OTHER STRUCTURES
2 - 15
a. applying fictitious horizontal reactions at each floor level to prevent lateral translation, and
b. using the reverse of these reactions as the “sway forces” for determining Mlt.
In general, Mlt for an unbraced frame is the sum of the moments due to the lateral loads
and these “sway forces,” as illustrated in Figure C-1.
The magnification factors applied to Mnt and Mlt are, respectively, B1 and B2. As shown
in Figure C-2, B1 accounts for the secondary Pδ member effect in all frames (including
sway-inhibited) and B2 covers the P∆ story effect in unbraced frames. The expressions
for B1 and B2 follow:
B1 =
Cm
≥ 1.0
(1 − Pu / Pe1 )
(C1-2)
where
Pu = the factored axial compressive force on the member, kips
Pe1 = Pe as listed in Table C-1 as a function of the slenderness ratio Kl / r, with effective length factor K = 1.0 and considering l / r in the plane of bending only
l = unbraced length of the member, in.
r = radius of gyration of its cross section, in.
Cm = a coefficient to be taken as follows:
V1
V2
V3
P1
P1
R1
V1 +R1
P2
P2 R
2
V2 +R2
P3
P3
Original
Frame
=
R3
Nonsway
Frame
for M nt
V3 +R3
Sway
Frame
for M t
+
Fig. C-1. Frame models for Mnt and Mlt.
∆P
P
H
δ
M1=Mnt+Pδ
=B1Mnt
(a) Column in Braced Frame
L
M t =HL
M2=M t +P∆
=B2M t
(b) Column in Unbraced Frame
Fig. C-2. Illustrations of secondary effects.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
2 - 16
ESSENTIALS OF LRFD
Table C-1.
Values of Pe / Ag for Use in Equation C1-2 and C1-5 for Steel of Any Yield Stress
Note: Multiply tabulated values by Ag (the gross cross-sectional area of the member) to obtain Pe
Kl / r
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
Pe / Ag
Pe / Ag
Pe / Ag
Pe / Ag
Pe / Ag
Pe / Ag
(ksi) Kl / r (ksi) Kl / r (ksi) Kl / r (ksi) Kl / r (ksi) Kl / r (ksi)
649.02
591.36
541.06
496.91
457.95
423.40
392.62
365.07
340.33
318.02
297.83
279.51
262.83
247.59
233.65
220.85
209.07
198.21
188.18
178.89
170.27
162.26
154.80
147.84
141.34
135.26
129.57
124.23
119.21
114.49
Note: Pe / Ag =
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
110.04
105.85
101.89
98.15
94.62
91.27
88.08
85.08
82.22
79.51
76.92
74.46
72.11
69.88
67.74
65.71
63.76
61.90
60.12
58.41
56.78
55.21
53.71
52.57
50.88
49.55
48.27
47.04
45.86
44.72
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
43.62
42.57
41.55
40.56
39.62
38.70
37.81
36.96
36.13
35.34
34.56
33.82
33.09
32.39
31.71
31.06
30.42
29.80
29.20
28.62
28.06
27.51
26.98
26.46
25.96
25.47
25.00
24.54
24.09
23.65
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
23.23
22.82
22.42
22.02
21.64
21.27
20.91
20.56
20.21
19.88
19.55
19.23
18.92
18.61
18.32
18.03
17.75
17.47
17.20
16.94
16.68
16.43
16.18
15.94
15.70
15.47
15.25
15.03
14.81
14.60
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
14.40
14.19
14.00
13.80
13.61
13.43
13.25
13.07
12.89
12.72
12.55
12.39
12.23
12.07
11.91
11.76
11.61
11.47
11.32
11.18
11.04
10.91
10.77
10.64
10.51
10.39
10.26
10.14
10.02
9.90
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
9.79
9.67
9.56
9.45
9.35
9.24
9.14
9.03
8.93
8.83
8.74
8.64
8.55
8.45
8.36
8.27
8.18
8.10
8.01
7.93
7.85
7.76
7.68
7.60
7.53
7.45
7.38
7.30
7.23
7.16
π2E
(K l /r)2
a. For compression members not subject to transverse loading between their supports
in the plane of bending,
Cm = 0.6 − 0.4(M1 / M2)
(C1-3)
where M1 / M2 is the ratio of the smaller to larger moment at the ends of that portion
of the member unbraced in the plane of bending under consideration. M1 / M2 is
positive when the member is bending in reverse curvature, negative when bending
in single curvature.
b. For compression members subjected to transverse loading between their supports,
the value of Cm can be determined by rational analysis, or the following values may
be used:
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
C. FRAMES AND OTHER STRUCTURES
2 - 17
for members with ends restrained against rotation . . . . . . . . . . Cm = 0.85
for members with ends unrestrained against rotation . . . . . . . . . Cm = 1.0
Two alternative equations are given for B2 in the LRFD Specification
B2 =
1
ΣPu ∆oh
1−
ΣH L
B2 =
1
ΣPu
1−
ΣPe2
(C1-4)
(C1-5)
where
ΣPu = required axial strength of all columns in a story, i.e., the total factored gravity
load above that level, kips
∆oh = translational deflection of the story under consideration, in.
ΣH = sum of all story horizontal forces producing ∆oh, kips
L = story height, in.
ΣPe2 = the summation of Pe2 for all rigid-frame columns in a story; Pe2 is determined
from Table C-1, considering the actual slenderness ratio Kl / r of each column in its plane of bending
K = effective length factor (see below)
Of the two expressions for B2, the first (Equation C1-4) is better suited for design office
practice. The quantity (∆oh / L) is the story drift index. For many structures, particularly
tall buildings, a maximum drift index is one of the design criteria. Using this value in
Equation C1-4 will facilitate the evaluation of B2.
In general, two values of B2 are obtained for each story of a building, one for each of
the major directions. B1 is evaluated separately for every column; two values of B1 are
needed for biaxial bending. Using Equations C1-1 through C1-5, the appropriate Mux and
Muy are determined for each column.
Effective Length
As in previous editions of the AISC Specification, the effective length of Kl is used
(instead of the actual unbraced length l) to account for the influence of end-conditions in
the design of compression members. A number of acceptable methods have been utilized
to evaluate K, the effective length factor. They are discussed in Section C2 of the
Commentary on the LRFD Specification. One method will be shown here.
Table C-2, which is also Table C-C2.1 in the Commentary, is taken from the Structural
Stability Research Council (SSRC) Guide to Stability Design Criteria for Metal Structures. It relates K to the rotational and translational restraints at the ends of the column.
Theoretical values for K are given, as well as the recommendations of the SSRC. The
basic case is d, the classical pin-ended column, for which K = 1.0. Theoretical K values
for the other cases are determined by the distances between points of inflection. The more
conservative SSRC recommendations reflect the fact that perfect fixity can never be
attained in actual structures.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
2 - 18
ESSENTIALS OF LRFD
Table C-2.
Effective Length Factors (K) for Columns
Buckled shape of column is shown
by dashed line
(a)
(b)
(c)
Theoretical K value
0.5
0.7
1.0
Recommended design value when
ideal conditions are approximated
0.65
0.80
1.2
End condition code
(d)
(e)
(f)
1.0
2.0
2.0
1.0
2.10
2.0
Rotation fixed and translation fixed
Rotation free and translation fixed
Rotation fixed and translation free
Rotation free and translation free
Like its predecessors, the LRFD Specification (in Section C2) distinguishes between
columns in braced and unbraced frames. In braced frames, sidesway is inhibited by
attachment to diagonal bracing or shear walls. Cases a, b, and d in Table C-2 represent
columns in braced frames; K ≤ 1.0. The LRFD Specification requires that for compression
members in braced frames, K “shall be taken as unity, unless structural analysis shows
that a smaller value may be used.” Common practice is to assume conservatively K = 1.0
for columns in braced frames and compression members in trusses.
The other cases in Table C-2, c, e, and f, are in unbraced frames (sidesway uninhibited);
K ≥ 1.0. The SSRC recommendations given in Table C-2 are appropriate for design.
“Leaning” Columns
The concept of the “leaning” column, although not related exclusively to LRFD, is new
to the 1993 LRFD Specification. A leaning column is one which is pin ended and does
not participate in providing lateral stability to the structure. As a result it relies on the
columns in other parts of the structure for stability. In analyzing and designing unbraced
frames, the effects of the leaning columns must be considered (as required by Section
C2.2 of the LRFD Specification). For further information the reader is referred to:
(1) Part 3 of this Manual.
(2) the Commentary on the LRFD Specification, Section C2, and
(3) a paper on this subject (Geschwindner, 1993).
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
D. TENSION MEMBERS
2 - 19
D. TENSION MEMBERS
Design Tensile Strength
The design philosophy for tension members is the same in the LRFD and ASD
Specifications:
a. The limit state of yielding in the gross section is intended to prevent excessive
elongation of the member. Usually, the portion of the total member length occupied
by fastener holes is small. The effect of early yielding at the reduced cross sections
on the total member elongation is negligible. Use of the area of the gross section is
appropriate.
b. The second limit state involves fracture at the section with the minimum effective
net area.
The design strength of tension members, φtPn, as given in Section D1 of the LRFD
Specification, is the lesser of the following:
a. For yielding in the gross section,
φt = 0.90
Pn = Fy Ag
(D1-1)
b. For fracture in the net section,
φt = 0.75
Pn = Fu Ae
(D1-2)
where
Ae
Ag
Fy
Fu
Pn
= effective net area, in.2 (see Section B, above)
= gross area of member, in.2
= specified minimum yield stress, ksi
= specified minimum tensile strength, ksi
= nominal axial strength, kips
For 50 ksi steels, Fy = 50 ksi and minimum Fu = 65 ksi. Accordingly
a. For yielding in the gross section,
φtPn = 0.9 × 50 ksi × Ag = 45.0 ksi × Ag
(2-3)
b. For fracture in the net section,
φtPn = 0.75 × 65 ksi × Ae = 48.8 ksi × Ae
(2-4)
The limit state of block shear rupture may govern the design tensile strength. For
information on block shear, see Section J4.3 of the LRFD Specification and Part 8 (in
Volume II) of this LRFD Manual.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
2 - 20
ESSENTIALS OF LRFD
EXAMPLE D-1
Given:
Determine the design strength of a W8×24 as a tension member in
50 ksi steel. How much dead load can it support?
Solution:
If there are no holes in the member, Ae = Ag and Equation 2-3 governs
φtPn = 45.0 ksi × Ag = 45.0 ksi × 7.08 in.2 = 319 kips
Assuming that dead load is the only load, the governing load combination from Section A is 1.4D. Then, the required tensile strength
Pu = 1.4PD ≤φtPn = 319 kips
PD≤ 319 kips/1.4 = 228 kips maximum dead load that can be supported
by the member.
EXAMPLE D-2
Given:
Repeat Example D-1 for a W8×24 in 50 ksi steel with four 1-in.
diameter holes, two per flange, along the member (i.e., not at its ends)
for miscellaneous attachments. See Figure D-1(a).
Solution:
a. For yielding in the gross section
φtPn = 319 kips, as in Example D-1.
b. For fracture in the net section
Ae = An = Ag − 4 × (dhole + 1⁄16-in.) × tf
= 7.08 in.2 − 4 × (1 + 1⁄16-in.) × 0.400 in.
= 5.38 in.2
φtPn = 48.8 ksi × Ae
= 48.8 ksi × 5.38 in.2 = 263 kips < 319 kips
Fracture in the net section governs.
Pu = 1.4 PD ≤ φtPn = 263 kips
PD ≤ 263 kips / 1.4 = 188 kips
W8x24
x=y=0.695 in.
tf
WT4x12
WT4x12
(a)
(b)
Fig. D-1
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
D. TENSION MEMBERS
2 - 21
Note: If the holes had been at the end connection of the tension
member, the U reduction coefficient would apply in the calculation of
an effective net area.
EXAMPLE D-3
Given:
Repeat Example D-2 for holes at a bolted end-connection. There are a
total of eight 1-in. diameter holes, as shown in Figure D-1(a), on two
planes, 4 in. center-to-center.
Solution:
a. For yielding in the gross section φtPn = 319 kips, as in Example D-1.
b. For fracture in the net section, according to Equation B3-1 in
Section B above, the effective net area
Ae = AU = AnU
where
An = 5.38 in.2 as in Example D-2
_
x
U = 1 − , L = 4 in.*
L
_
According to Commentary Figure C-B3.1(a), x for a W8×24 in this
case is taken as that for a WT4×12.
_ From the properties of a WT4×12
given in Part 1 of this Manual, x = y = 0.695 in. See Figure D-1(b).
U=1−
0.695 in.
= 0.826
4 in.
Thus
Ae = 5.38 in.2 × 0.826 = 4.45 in.2
φtPn = 48.8 ksi × Ae
= 48.8 ksi × 4.45 in.2 = 217 kips < 319 kips
Fracture in the net section governs. Again, assuming that dead load is
the only load,
Pu = 1.4PD ≤ φtPn = 217 kips
PD ≤ 217 kips / 1.4 = 155 kips maximum dead load that can be supported
by the member.
Built-Up Members, Eyebars, and Pin-Connected Members
See Section D2 and D3 in the LRFD Specification.
*In lieu of calculating U, the Commentary on the LRFD Specification (Section B3) permits the use of more conservative
values of U listed therein.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
2 - 22
ESSENTIALS OF LRFD
E. COLUMNS AND OTHER COMPRESSION MEMBERS
Effective Length
For a discussion of the effective length Kl for columns, refer to Section C above.
Design Compressive Strength
Although the column strength equations have been revised for compatibility with LRFD
and recent research on column behavior, the philosophy and procedures of column design
in LRFD are similar with those in ASD. The direct design of columns with W and other
rolled shapes is facilitated by the column strength tables in Part 3 of this LRFD Manual,
which show the design compressive strength φcPn as a function of KL (the effective
unbraced length in feet). Columns with cross sections not tabulated (e.g., built-up
columns) can be designed iteratively, as in the past, with the aid of tables listing design
stresses versus Kl / r, the slenderness ratio. Such tables are given in the Appendix of the
LRFD Specification for 36 and 50 ksi structural steels, and below (Table E-1) for 50 ksi
steel.
There are two equations governing column strength, based on the limit state of flexural
buckling, one for inelastic buckling (Equation E2-2) and the other (Equation E2-3) for
elastic, or Euler, buckling. Equation E2-2 is an empirical relationship for the inelastic
range, while Equation E2-3 is the familiar Euler formula multiplied by 0.877. Both
equations include the effects of residual stresses and initial out-of-straightness. The
boundary between inelastic and elastic instability is λc = 1.5, where the parameter
λc =
Kl
rπ
√
Fy
E
(E2-4)
For axially loaded columns with all elements having width-thickness ratios < λr (in
Section B5.1 of the LRFD Specification), the design compressive strength = φcPn
where
φc = 0.85
Pn = AgFcr
(E2-1)
Ag = gross area of member, in.2
a. For λc ≤ 1.5
2
Fcr = (0.658λc)Fy
(E2-2)
As is done in the Commentary on Section E2, this equation can be expressed in
exponential form
Fcr = [exp (−0.419λ2c )]Fy
where exp(x) = ex
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
(C-E2-1)
E. COLUMNS AND OTHER COMPRESSION MEMBERS
2 - 23
Table E-1.
Design Stress for Compression Members of 50 ksi Specified
Minimum Yield Stress Steel, φc = 0.85*
Kl
r
F cr (ksi)
Kl
r
F cr (ksi)
1
2
3
4
5
42.50
42.49
42.47
42.45
42.42
41
42
43
44
45
37.59
37.36
37.13
36.89
36.65
6
7
8
9
10
42.39
42.35
42.30
42.25
42.19
46
47
48
49
50
11
12
13
14
15
42.13
42.05
41.98
41.90
41.81
16
17
18
19
20
Kl
r
F cr (ksi)
Kl
r
F cr (ksi)
Kl
r
F cr (ksi)
81
82
83
84
85
26.31
26.00
25.68
25.37
25.06
121
122
123
124
125
14.57
14.33
14.10
13.88
13.66
161
162
163
164
165
8.23
8.13
8.03
7.93
7.84
36.41
36.16
35.91
35.66
35.40
86
87
88
89
90
24.75
24.44
24.13
23.82
23.51
126
127
128
129
130
13.44
13.23
13.02
12.82
12.62
166
167
168
169
170
7.74
7.65
7.56
7.47
7.38
51
52
53
54
55
35.14
34.88
34.61
34.34
34.07
91
92
93
94
95
23.20
22.89
22.58
22.28
21.97
131
132
133
134
135
12.43
12.25
12.06
11.88
11.71
171
172
173
174
175
7.30
7.21
7.13
7.05
6.97
41.71
41.61
41.51
41.39
41.28
56
57
58
59
60
33.79
33.51
33.23
32.95
32.67
96
97
98
99
100
21.67
21.36
21.06
20.76
20.46
136
137
138
139
140
11.54
11.37
11.20
11.04
10.89
176
177
178
179
180
6.89
6.81
6.73
6.66
6.59
21
22
23
24
25
41.15
41.02
40.89
40.75
40.60
61
62
63
64
65
32.38
32.09
31.80
31.50
31.21
101
102
103
104
105
20.16
19.86
19.57
19.28
18.98
141
142
143
144
145
10.73
10.58
10.43
10.29
10.15
181
182
183
184
185
6.51
6.44
6.37
6.30
6.23
26
27
28
29
30
40.45
40.29
40.13
39.97
39.79
66
67
68
69
70
30.91
30.61
30.31
30.01
29.70
106
107
108
109
110
18.69
18.40
18.12
17.83
17.55
146
147
148
149
150
10.01
9.87
9.74
9.61
9.48
186
187
188
189
190
6.17
6.10
6.04
5.97
5.91
31
32
33
34
35
39.62
39.43
39.25
39.06
38.86
71
72
73
74
75
29.40
20.09
28.79
28.48
28.17
111
112
113
114
115
17.27
16.99
16.71
16.42
16.13
151
152
153
154
155
9.36
9.23
9.11
9.00
8.88
191
192
193
194
195
5.85
5.79
5.73
5.67
5.61
36
37
38
39
40
38.66
38.45
38.24
38.03
37.81
76
77
78
79
80
27.86
27.55
27.24
26.93
26.62
116
117
118
119
120
15.86
15.59
15.32
15.07
14.82
156
157
158
159
160
8.77
8.66
8.55
8.44
8.33
196
197
198
199
200
5.55
5.50
5.44
5.39
5.33
* When element width-to-thickness ratio exceeds λr, see Appendix B5.3 of LRFD Specification
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
2 - 24
ESSENTIALS OF LRFD
b. For λc > 1.5
0.877
Fcr = 2 Fy
λc
(E2-3)
where
Fy = specified minimum yield stress, ksi
E = modulus of elasticity, ksi
K = effective length factor
l = unbraced length of member, in.
r = governing radius of gyration about plane of buckling, in.
For 50 ksi steel
λc =
Kl 1
r π
√
Kl Kl
50 ksi
= 0.0132
or
= 75.7λc
r
r
29,000 ksi
(2-5)
The boundary between inelastic and elastic buckling (λc = 1.5) for 50 ksi steel is
Kl
= 75.7 × 1.5 = 113.5
r
The column strength equations in terms of Kl / r for 50 ksi steel become
φcPn = (φcFcr )Ag
(2-6)
Fcr = {exp[−7.3 × 10−5(Kl / r)2]} × 50 ksi
(2-7)
where φc = 0.85
a. For Kl / r ≤ 113.5
b. For Kl / r ≤ 113.5
Fcr =
2.51 × 105
ksi
(Kl / r)2
(2-8)
Based on Equations 2-7 and 2-8, Table E-1 gives the design stresses for 50 ksi steel
columns for the full range of slenderness ratios. Determining the design strength of a
given 50 ksi steel column merely involves using Equation 2-6 in connection with
Table E-1. The appropriate design stress (φcFcr) from Table E-1 is multiplied by the
cross-sectional area to obtain the design strength φcPn.
EXAMPLE E-1
Given:
Design a 25-ft high, free standing A618 (Fy = 50 ksi) steel pipe column
to support a water tank with a weight of 75 kips at full capacity. See
Figure E-1.
Solution:
For a live load of 75 kips, the required column strength (from Section
A) is Pu = 1.6PL = 1.6 × 75 kips = 120 kips.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
E. COLUMNS AND OTHER COMPRESSION MEMBERS
2 - 25
From Table C-2, case e, recommended K = 2.1. KL = 2.1 × 25.0 ft =
52.5 ft.
Try a standard 12-in. diameter pipe (A = 14.6 in.2, I = 279 in.4):
r =√
I/A =√
279 in. / 14.6 in.2 = 4.37 in.
Kl 52.5 ft × 12 in./ft
=
= 144.2
4.37 in
r
From Table E-1, φcFcr = 10.3 ksi
The design compressive strength
φcPn = (φcFcr )Ag = 10.3 ksi × 14.6 in.2
= 150 kips > 120 kips required o.k.
To complete the design, bending due to lateral loads (i.e., wind and
earthquake) should also be considered. See Sections F and H.
EXAMPLE E-2
Determine the adequacy of a W14×120 building column.
Given:
50 ksi steel; K = 1.0; story height = 12.0 ft; required strength based on
the maximum total factored load is 1,300 kips.
KxLx = Ky Ly = 1.0 × 12.0 ft = 12.0 ft
Because ry < rx,
Kl
Ky Ly 12.0 ft × 12 in./ft
=
= 38.5
maximum =
ry
3.74 in.
r
From Table E-1, φcFcr = 38.14 ksi
Design compressive strength
φcPn = (φcFcr)Ag = 38.14 ksi × 35.3 in.2
= 1,346 kips > 1,300 kips required o.k.
L = 25.0 ft.
Solution:
Fig. E-1
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
2 - 26
Select the most economical W14 column for the case shown in Figures
E-2 and E-3.
Lower
Level
Intermediate
Level
Upper
Level
Fig. E-2. Plan views.
12 -0
Upper
Level
Intermediate
Level
12 -0
EXAMPLE E-3
ESSENTIALS OF LRFD
Lower
Level
Fig. E-3. Elevation.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
F. BEAMS AND OTHER FLEXURAL MEMBERS
2 - 27
Given:
50 ksi steel; K = 1.0; required strength based on the maximum total
factored load is 1,300 kips. The column is braced in both directions at
the upper and lower levels, and in the weak direction at the intermediate
level.
Solution:
Try a W14×120 (as in Example E-2):
Kx lx
rx
=
1.0 × 24.0 ft × 12 in./ft
= 46.2
6.24 in.
Ky ly
ry
=
1.0 × 12.0 ft × 12 in./ft
= 38.5
3.74 in.
Kx lx
Kl
max =
= 46.2
rx
r
From Table E-1, φcFcr = 36.35 ksi
Required Ag =
1,300 kips
= 35.8 in.2 > 35.3 in.2 provided
36.35 ksi
W14×120 n.g.
By inspection W14×132 is o.k.
Use W14×132
Flexural-Torsional Buckling
As stated in Section E3 of the LRFD Specification and Commentary, torsional and
flexural-torsional buckling generally do not govern the design of doubly symmetric rolled
shapes in compression. For other cross sections, see Section E3 and Appendix E3 of the
LRFD Specification.
Built-Up and Pin-Connected Members
These members are covered, respectively, in Section E4 and E5 of the LRFD
Specification.
F. BEAMS AND OTHER FLEXURAL MEMBERS
Chapter F of the LRFD Specification covers compact beams. Compactness criteria are
given in Table B5.1 of the LRFD Specification and are summarized in Table B-1 above.
To prevent torsion, wide-flange shapes must be loaded in either plane of symmetry,
channels must be loaded through the shear center parallel to the web, or restraint against
twisting must be provided at load points and points of support. Torsion combined with
flexure and axial force combined with flexure are covered in Chapter H of the LRFD
Specification.
This section explains the provisions of the LRFD Specification for compact rolled
beams. For other compact and noncompact flexural members, refer to Appendix F of the
Specification; plate girders are in Appendix G.
Flexure
To understand the provisions of the LRFD Specification regarding flexural design, it is
helpful to review briefly some aspects of elementary beam theory.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
2 - 28
ESSENTIALS OF LRFD
Under working loads (and until initial yielding) the distributions of flexural strains and
stresses over the cross-section of a beam are linear. As shown in Figure F-1, they vary
from maximum compression at the extreme fibers on one side (the top) to zero at the
neutral, or centroidal, axis to maximum tension at the extreme fibers on the other side
(the bottom).
The relationship between moment and maximum bending stress (tension or compression) at a given cross section is
M = Sfb
(2-9)
where
M= bending moment due to the applied loads, kip-in.
S = elastic section modulus, in the direction of bending, in.3
I
=
c
fb = maximum bending stress, ksi
I = moment of inertia of the cross section about its centroidal axis, in.4
c = distance from the elastic neutral axis to the extreme fiber, in.
Similarly, at initial yielding
Mr = SFy
(2-10)
where
Mr = bending moment coinciding with first yielding, kip-in.
If additional load is applied, the strains continue to increase; the stresses, however, are,
limited to Fy. Yielding proceeds from the outer fibers inward until a plastic hinge is
developed, as shown in Figure F-1. At full plastification of the cross section
Mp = ZFy
(2-11)
where
Mp = plastic moment, kip-in
Z = plastic section modulus, in the direction of bending, in.3
Due to the presence of residual stresses (prior to loading, as a consequence of the rolling
operation), yielding begins at an applied stress of (Fy − Fr). Equation 2-10 should be
modified to
STRAINS
BEAM
Cross
Section
Compression
STRESSES
Fy
Fy
Working
Load
Fy
Initial
Yielding
Tension
Fig. F-1. Flexural strains and stresses.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
Fy
Plastic
Hinge
F. BEAMS AND OTHER FLEXURAL MEMBERS
Mr = S(Fy − Fr )
2 - 29
(2-12)
where
Fr = the maximum compressive residual stress in either flange, ksi
= 10 ksi for rolled shapes, 16.5 ksi for welded shapes
The definition of plastic moment in Equation 2-11 is still valid, because it is not affected
by residual stresses.
Design for Flexure
a. Assuming Cb = 1.0
Compact sections will not experience local buckling before the formation of a plastic
hinge. The occurrence of lateral-torsional buckling of the member depends on the
unbraced length Lb. As implied by the term lateral-torsional buckling, overall instability
of a beam requires that twisting of the member occur simultaneously with lateral buckling
of the compression flange. Lb is the distance between points braced to prevent twist of
the cross section. Many beams can be considered continuously braced; e.g., beams
supporting a metal deck, if the deck is intermittently welded to the compression flange.
Compact wide flange and channel members bending about their major (or x) axes can
develop their full plastic moment Mp without buckling if Lb ≤ Lp. If Lb = Lr, the nominal
flexural strength is Mr, the moment at first yielding adjusted for residual stresses. The
nominal moment capacity (Mn) for Lp < Lb < Lr is Mr < Mn < Mp. Compact shapes bent
about their minor (or y) axes will not buckle before developing Mp, regardless of Lb.
Flexural design strength, governed by the limit state of lateral-torsional buckling, is
φbMn, where φb = 0.90 and Mn the nominal flexural strength is as follows:
Mn = Mp = ZxFy for bending about the major axis if Lb ≤ Lp
Mn = Mp = ZyFy for bending about the minor axis regardless of Lb
Lp =
300ry
= 42.4ry for 50 ksi steel
Fy
√
Mn = Mr = Sx(Fy − Fr )
= Sx(Fy − 10 ksi) for rolled shapes bending about the major axis if Lb = Lr
(2-13)
(2-14)
(2-15)
(2-16)
Mn for bending about the major axis, if Lp < Lb < Lr, is determined by linear interpolation
between Equations 2-13 and 2-16; i.e.,
Lb − Lp
Mn = Mp − (Mp − Mr)
Lr − Lp
(2-17)
The definition for the limiting laterally unbraced length Lr is given in the LRFD
Specification (in Equations F1-6, 8, and 9) and will not be repeated here. For bending
about the major axis if Lb > Lr,
Mn = Mcr ≤ Mr
(2-18)
The case of Lb > Lr is beyond the scope of this section. The reader is referred to Section
F1.2b of LRFD Specification (specifically Equation F1-13, where the critical moment
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
2 - 30
ESSENTIALS OF LRFD
Table F-1.
Values of Cb for Simply Supported Beams Braced at Ends of Span
Load
Lateral Bracing Along Span
Cb
Concentrated at center
None
1.32
At centerline only
1.67
None
1.14
At centerline only
1.30
Uniform
Mcr is controlled by lateral-torsional buckling). This case is also covered in the beam
graphs in Part 4 of this LRFD Manual.
b. All values of Cb
Cb is the bending coefficient. A new expression for Cb is given in the LRFD Specification. (It is more accurate than the one previously shown.)
Cb =
12.5Mmax
2.5Mmax + 3MA + 4MB + 3Mc
(F1-3)
where M is the absolute value of a moment in the unbraced beam segment as follows:
Mmax, the maximum
MA, at the quarter point
MB, at the centerline
Mc, at the three-quarter point
The purpose of Cb is to account for the influence of moment gradient on lateral-torsional buckling. The flexural strength equations with Cb = 1.0 are based on a uniform
moment along a laterally unsupported beam segment causing single curvature buckling
of the member. Other loadings are less severe, resulting in higher flexural strengths;
Cb ≥ 1.0. Typical values of Cb are given in Table F-1. For unbraced cantilevers, Cb = 1.0.
Cb can conservatively be taken as 1.0 for all cases.
For all values of Cb, the flexural design strength φbMn, where φb = 0.90, is given in the
LRFD Specification in terms of a nominal flexural strength Mn varying as follows:
Mn = Mp = ZxFy
(2-13)
for bending about the major axis if Lb ≤ Lm
Mn = CbMr = CbSx(Fy − 10 ksi) ≤ Mp
(2-19)
for bending about the major axis if Lb = Lr.
For bending about the major axis if Lm < Lb < Lr, linear interpolation is used
Lb − Lp
Mn = Cb Mp − (Mp − Mr)
≤ Mp
Lr − Lp
(F1-2)
Mn = Mcr ≤ CbMr and Mp
(2-20)
If Lb > Lr,
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
F. BEAMS AND OTHER FLEXURAL MEMBERS
2 - 31
The determination of Mn for a given Lb can best be done graphically, as illustrated in
Figure F-2. The required parameters for each W shape are given in the beam design table
in Part 4 of the LRFD Manual, an excerpt of which is shown herein as Table F-2. If Cb =
1.0, the coordinates for constructing the graph are (Lp, Mp), and (Lr, Mr). For Cb > 1.0, the
key coordinates are (Lp, Cb Mp) and (Lr, Cb Mr). Note that Mn cannot exceed the plastic
moment Mp. Lm, then, can be derived graphically as the upper limit of Lb for which Mn =
Mp. If Lb > Lr, the beam graphs in Part 4 of the LRFD Manual can be used to determine
Mcr.
EXAMPLE F-1
Select the required W shape for a 30-foot simple floor beam with full
lateral support carrying a dead load (including its own weight) of 1.5
kips per linear foot and a live load of 3.0 kips per linear foot. Assume
50 ksi steel and:
Given:
a. There is no member depth limitation
b. The deepest member is a W18
The governing load combination in Section A is A4-2:
Solution:
1.2D + 1.6L + 0.5(Lr or S or R) = 1.2 × 1.5 klf + 1.6 × 3.0 klf + 0
= 6.6 klf
Required Mu =
wL2 6.6 klf × (30.0 ft)2
=
= 743 kip-ft
8
8
Flexural design strength φbMn ≥ 743 kip-ft
CbMp
Mn for Cb=1.0
Mn for Cb>1.0
Mp
Mn
Mcr for Cb=1.0
CbMr
Mcr for Cb >1.0
Mr
Lm
Lp
Lr
Lb
Fig. F-2. Determination of nominal flexural strength M n.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
2 - 32
ESSENTIALS OF LRFD
Table F-2.
Excerpt from Load Factor Design Selection Table
(LRFD Manual, Part 4)
For Fy = 50 ksi
Zx (in.3)
Shape
φbMp
(kip-ft)
φbMr
(kip-ft)
Lp (ft)
Lr (ft)
224
221
212
211
W24×
×84
W21×93
W14×120
W18×97
840
829
795
791
588
576
570
564
6.9
6.5
13.2
9.4
18.6
19.4
46.2
27.4
200
198
196
192
186
186
W24×
×76
W16×100
W21×83
W14×109
W18×86
W12×120
750
743
735
720
698
698
528
525
513
519
498
489
6.8
8.9
6.5
13.2
9.3
11.1
18.0
29.3
18.5
43.2
26.1
50.0
177
175
W24×
×68
W16×89
664
656
462
465
6.6
8.8
17.4
27.3
Note: Flexural design strength φbMn = φbMp, as tabulated is valid for Lb ≤ Lm. If Cb = 1.0, Lm = Lp; otherwise,
Lm > Lp. φb = 0.90.
a. In Table F-2, the most economical beams are in boldface print. Of
the boldfaced beams, the lightest one with φbMn = φbMp ≥ 743 kip-ft
is a W24×76
b. By inspection of Table F-2, the lightest W18 with φbMn = φbMp ≥
743 kip-ft is a W18×97.
EXAMPLE F-2
Given:
Determine the flexural design strength of a 30-ft long simply supported
W24×76 girder (of 50 ksi steel) with a concentrated load and lateral
support, both at midspan.
Solution:
From Table F-1, Cb = 1.67
Lb = 30.0 ft/2 = 15.0 ft
From Equation F1-2:
Lb − Lp
φbMn = Cb φbMp − (φbMp − φbMr)
≤ φbMp
Lr − Lp
From Table F-2 for a W24×76:
φbMp = 750 kip-ft
φbMr = 528 kip-ft
Lp = 6.8 ft
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
F. BEAMS AND OTHER FLEXURAL MEMBERS
Lr
2 - 33
= 18.0 ft
15.0 ft − 6.8 ft
φbMn = 1.67 750 kip−ft − (750 − 528) kip−ft ×
18.0 ft − 6.8 ft
= 981 kip-ft > 750 kip-ft
Use φb Mn = φb Mp = 750 kip-ft
In this case, even though the unbraced length Lb > Lp, the design
flexural strength is φbMp because Cb > 1.0.
Design for Shear
The design shear strength is defined by the equations in Section F2 of the LRFD
Specification. Shear in wide-flange and channel sections is resisted by the area of the
web (Aw), which is taken as the overall depth d times the web thickness tw. For webs of
50 ksi steel without transverse stiffeners, the design shear strength φvVn, where φv = 0.90,
and the nominal shear strength Vn are as follows:
For
h
≤ 59 (including all rolled W and channel shapes),
tw
Vn = 30.0 ksi × dtw
φvVn= 27.0 ksi × dtw
For 59 <
(2-21)
h
≤ 74,
tw
= 30.0 ksi × dtw ×
59
h / tw
φvVn = 27.0 ksi × dtw ×
59
h / tw
Vn
For
(2-22)
h
> 74,
tw
=
132,000
dtw ksi
(h / tw)2
φvVn =
118,000
dtw ksi
(h / tw)2
Vn
h
(2-23)
tw
d
tw
h
Fig. F-3. Definitions of d, h, and tw for W and channel shapes.
AMERICAN INSTITUTE OF
STEEL CONSTRUCTION
2 - 34
ESSENTIALS OF LRFD
Shear strength is governed by the following limit states; Equation 2-21 by yielding of the
web; Equation 2-22, by inelastic buckling of the web; and Equation 2-23 by elastic
buckling.
EXAMPLE F-3
Given:
Solution:
Check the adequacy of a W30×99 beam of 50 ksi steel to carry a load
resulting in maximum shears of 100 kips due to dead load and 150 kips
due to live load.
Required shear strength = Vu = 1.2D + 1.6L
= 1.2 × 100 kips + 1.6 × 150 kips
= 360 kips
Design shear strength = φvVn = 27.0 ksi × dtw
= 27.0 ksi × 29.65 in. × 0.520 in.
= 416 kips > 360 kips required o.k.
Web Openings
See Section F4 of the LRFD Specification and Commentary, and the references given in
the Commentary.
H. MEMBERS UNDER COMBINED FORCES AND TORSION
Symmetric Members Subject to Bending and Axial Tension
The interaction of flexure and tension in singly and doubly symmetric shapes is governed
by Equations H1-1a and H1-1b, as follows:
For
For
Pu
≥ 0.2,
φPn
Pu
< 0.2,
φPn
Muy
Pu 8 Mux
+
+
≤ 1.0
9
φPn
φb Mnx φb Mny
(H1-1a)
Mux
Muy
Pu
+
+
≤ 1.0
2φPn φb Mnx φb Mny
(H1-1b)
where
= required tensile strength; i.e., the total factored tensile force, kips
= design tensile strength, φtPn, kips
= resistance factor for tension, φt = 0.90
= nominal tensile strength as defined in Chapter D of the LRFD Specification,
kips
Mu = required flexural strength; i.e., the moment due to the total factored load, kipin. or kip-ft. (Subscript x or y denotes the axis about which bending occurs.)
φb Mn = design flexural strength, kip-in. or kip-ft
= resistance factor for flexure = 0.90
φb
Pu
φPn
φ
Pn
AMERICAN INSTITUTE OF
STEEL CONSTRUCTION
H. MEMBERS UNDER COMBINED FORCES AND TORSION
Mn
2 - 35
= nominal flexural strength determined in accordance with the appropriate equations in Chapter F of the LRFD Specification, kip-in. or kip-ft
Interaction Equations H1-1a and H1-1b cover the general case of biaxial bending
combined with axial force. They are also valid for uniaxial bending (i.e., when Mux = 0
or Muy = 0). In this case, they reduce to the form plotted in Figure H-1. Pure biaxial bending
(with Pu = 0) is covered by Equation H1-1b.
EXAMPLE H-1
Given:
Check the adequacy of a W10×22 tension member of 50 ksi steel to
carry loads resulting in the following factored load combination:
Pu = 55 kips
Muy = 20 kip-ft
Mux = 0
Solution:
From Section D above for 50 ksi steel,
φPn = φtPn = 45.0 ksi × Ag = 45.0 ksi × 6.49 in.2 = 292 kips
Pu
55 kips
=
= 0.188 < 0.20; therefore, Equation H1-1b governs.
φPn 292 kips
For bending about the y axis only, Equation H1-1b becomes:
Pu
Muy
+
≤ 1.0
2φPn φb Mny
φ Pn
Pu
Pu
φ Pn
+
8 Mu
=
9 φb M n
0.2 φPn
( )
1 Pu
2 φPn
Mu
+
Mu
=1
φb M n
0.9 φb M n
φb M n
Fig. H-1. Interaction Equations H1-1a and H1-1b modified for
axial load combined with bending about one axis only.
AMERICAN INSTITUTE OF
STEEL CONSTRUCTION
2 - 36
ESSENTIALS OF LRFD
From Section F above for 50 ksi steel, Mn = Mp = ZyFy = 50 ksi × Zy for
minor-axis bending (regardless of the unbraced length).
φbMny = 0.90 × 50 ksi × Zy = 45.0 ksi × Zy
= 45.0 ksi ×
6.10 in.3
12 in./ft
= 22.9 kip-ft for a W10×22 member
20 kip−ft
Pu
Muy
0.188
+
=
+
= 0.094 + 0.873
2
22.9 kip−ft
2φPn φb Mny
= 0.967 < 1.0 o.k.
EXAMPLE H-2
Given:
Check the same tension member, a W10×22 in 50 ksi steel, 4.0 ft long,
subjected to the following combination of factored loads:
Pu = 140 kips
Mux = 55 kip-ft
Muy = 0
Cb = 1.0
Solution:
Again, φPn = 292 kips
Pu
φPn
=
140 kips
= 0.479 > 0.20; Equation H1-1a governs.
292 kips
For bending about the x axis only, Equation H1-1a becomes
Pu 8 Mux
+
≤ 1.0
φPn 9 φb Mnx
From Section F above for 50 ksi steel, Mn = Mp = ZxFy = 50 ksi × Zx for
major-axis bending if Lb ≤ Lp for (Cb = 1.0).
Assume unbraced length, Lb = 4.0 ft.
By Equation 2-15 in Section F, Lp = 42.4ry for 50 ksi steel.
For a W10×22, ry = 1.33 in., Zx = 26.0 in.3
Lp =
42.4 × 1.33 in.
= 4.7 ft
12 in./ft
Lb = 4.0 ft < Lp = 4.7 ft
Then Mnx = 50 ksi × Zx
φb Mnx
0.90 × 50 ksi × 26.0 in.3
12 in./ft
= 97.5 kip-ft for a W10×22 member
=
AMERICAN INSTITUTE OF
STEEL CONSTRUCTION
H. MEMBERS UNDER COMBINED FORCES AND TORSION
2 - 37
55 kip−ft
Pu
8Mux
8
+
= 0.479 + ×
9 97.5 kip−ft
φPn 9φb Mnx
= 0.479 + 0.501 = 0.980 < 1.0 o.k.
Symmetric Members Subject to Bending and Axial Compression
The interaction of compression and flexure in beam-columns with singly and doubly
symmetric cross sections is governed by Equations H1-1a and H1-1b, repeated here for
convenience:
For
For
Pu
≥ 0.2,
φPn
Pu
< 0.2,
φPn
Muy
Pu 8 Mux
+
+
≤ 1.0
φPn 9 φb Mnx φb Mny
(H1-1a)
Mux
Muy
Pu
+
+
≤ 1.0
2φPn φb Mnx φb Mny
(H1-1b)
The definitions of the ter ms in the for mulas, which differ in some cases from those given
above, are as follows:
= required compressive strength; i.e., the total factored compressive force, kips
= design compressive strength, φc Pn, kips
= resistance factor for compression, φc = 0.85
= nominal compressive strength as defined in Chapter E of the LRFD Specification, kips
Mu = required flexural strength including second-order effects, kip-in. or kip-ft
φb Mn = design flexural strength, kip-in. or kip-ft
= resistance factor for flexure = 0.90
φb
Mn = nominal flexural strength from Chapter F of the LRFD Specification, kip-in.
or kip-ft
Pu
φPn
φ
Pn
The second-order analysis required for Mu involves the determination of the additional
moment due to the action of the axial compressive forces on a deformed structure. In lieu
of a second-order analysis, the simplified method given in Chapter C of the LRFD
Specification (and in Section C above) may be used. However, in applying the simplified
method, the additional moments obtained for beam-columns must also be distributed to
connected members and connections (to satisfy equilibrium).
Bending and Axial Compression—Preliminary Design
The design of a beam-column is a trial and error process which can become tedious,
particularly with the repeated solution of Interaction Equation H1-1a or H1-1b. A rapid
method for the selection of a trial section is given in this LRFD Manual, Part 3, under
the heading Combined Axial and Bending Loading (Interaction). As in earlier editions
of the AISC Manual, the Interaction Equations are approximated by an equation which
converts bending moments to equivalent axial loads:
Pu eq = Pu + Muxm + Muymu
AMERICAN INSTITUTE OF
STEEL CONSTRUCTION
2 - 38
ESSENTIALS OF LRFD
where
= equivalent axial load to be checked against the column load table, kips
Pu eq
Pu, Mux, Muy are defined in the Interaction Equations for compression and bending
m, u
are factors tabulated in this LRFD Manual, Part 3
As soon as a satisfactory trial section has been found (i.e., one for which Pu eq ≤ tabulated
φc Pn), a final verification should be made with the appropriate Interaction Equation,
H1-1a or H1-1b
EXAMPLE H-3
Given:
Check the adequacy of a W14×176 beam-column, 14.0 ft in height
floor-to-floor, in a braced symmetrical frame in 50 ksi steel. The
member is subjected to the following factored forces due to symmetrical gravity loads: Pu = 1,400 kips; Mx = 200 kip-ft, My = 70 kip-ft
(reverse curvature bending with equal end moments about both axes);
and no loads along the member.
Solution:
For a braced frame, K = 1.0 KxLx = KyLy = 14.0 ft
For a W14×176:
A
Zx
Zy
rx
ry
Kl / rx
Kl / ry
= 51.8 in.2
= 320 in.3
= 163 in.3
= 6.43 in.
= 4.02 in.
= (14.0 ft × 12 in./ft) / 6.43 in. = 26.1
= (14.0 ft × 12 in./ft) / 4.02 in. = 41.8
From Table E-1, above, φcFcr = 37.4 ksi for Kl / r = 41.8 in 50 ksi steel.
φcPn = (φc Fcr) A = 37.4 ksi × 51.8 in.2 = 1,940 kips
Pu
1,400 kips
=
= 0.72 > 0.2, Interaction Equation H1-1a
φc Pn 1,940 kips
governs.
Since
For a braced frame, Mlt = 0. From Equation C1-1:
Mux = B1x Mntx , where Mntx = 200 kip-ft; and
Muy = B1y Mnty , where Mnty = 70 kip-ft
From Equations C1-2 and C1-3:
B1 =
Cm
> 1.0
(1 − Pu / Pe1 )
where in this case (a braced frame with no transverse loading),
Cm = 0.6 − 0.4(M1 / M2)
AMERICAN INSTITUTE OF
STEEL CONSTRUCTION
H. MEMBERS UNDER COMBINED FORCES AND TORSION
2 - 39
For reverse curvature bending and equal end moments:
M1 / M2 = +1.0
= 0.6 − 0.4(1.0) = 0.2
Cm
From Table C-1:
Pe1x = 420 ksi × Ag = 420 ksi × 51.8 in.2 = 21,756 kips
From Table C-1:
Pe1y = 164 ksi × Ag = 164 ksi × 51.8 in.2 = 8,495 kips
B1x =
Cmx
0.2
=
= 0.2
(1 − Pu / Pe1x ) (1 − 1,400 kips / 21,756 kips)
Use B1x = 1.0, per Equation C1-2.
B1y =
Cmy
0.2
=
= 0.2
(1 − Pu / Pe1y ) 1 − 1,400 kips / 8,495 kips)
Use B1y = 1.0, per Equation C1-2.
Mux = 1.0 × 200 kip-ft
Muy = 1.0 × 70 kip-ft
From Equation 2-15 for 50 ksi steel,
Lp = 42.4ry =
42.4 × 4.02 in.
= 14.2 ft
12 in./ft
Since Lb = 14.0 ft < Lp = 14.2 ft, Mnx = Mpx = ZxFy
Mny
= Mpy = Zy Fy
φbFy
= 0.90 × 50 ksi = 45.0 ksi
φb Mnx = φbFy Zx =
45.0 ksi × 320 in.3
= 1,200 kip-ft
12 in./ft
φb Mny = φbFy Zy =
45.0 ksi × 163 in.3
= 611 kip-ft
12 in./ft
By Interaction Equation H1-1a
70 kip−ft
8
1,400 kips 8 200 kip−ft
+
+
= 0.72 + (0.17+0.11)
1,940 kips 9 1,200 kip−ft 611 kip−ft
9
= 0.72 + 0.25
= 0.97 < 1.0
W14×176 is o.k.
AMERICAN INSTITUTE OF
STEEL CONSTRUCTION
2 - 40
ESSENTIALS OF LRFD
EXAMPLE H-4
Given:
Check the adequacy of a W14×176 beam-column (Fy = 50 ksi) in an
unbraced symmetrical frame subjected to the following factored
forces:
Pu
Mux
My
KxLx
= 1,400 kips (due to gravity plus wind)
= 300 kip-ft (due to wind only)
=0
= Ky Ly = 14.0 ft
Drift index, ∆oh / L ≤ 0.0025 (or 1⁄400)
ΣPu = 24,000 kips
ΣH = 800 kips
Solution:
As in Example H-3, for a W14×176 with KL = 14.0 ft, φcPn = 1,940
kips.
Pu
1,400 kips
=
= 0.72 > 0.2, Interaction Equation H1-1a
φcPn 1,940 kips
governs.
Since
Because Mntx = Mnty = Mlty = 0 and only Mltx ≠ 0, Mux = B2Mltx and
Muy = 0.
Mltx = 300 kip-ft
According to Equation C1-4,
B2 =
1
1
=
= 1.08
ΣPu ∆oh 1 − 24,000 kips (0.0025)
1−
800 kips
ΣH L
Mux = 1.08 × 300 kip-ft = 324 kip-ft
Because Lb < Lp = 14.2 ft, Mnx = Mpx = ZxFy; φb Mnx = 1,200 kip-ft as in
Example H-3.
By Interaction Equation H1-1a:
8
1,400 kips 8 324 kip−ft
+
= 0.72 + 0.27 = 0.96 < 1.0
9
1,940 kips 9 1,200 kip−ft
W14×176 is o.k.
Torsion and Combined Torsion, Flexure, and/or Axial Force
Criteria for members subjected to torsion and torsion combined with other forces are
given in Section H2 of the LRFD Specification. They require the calculation of normal
and shear stresses by elastic analysis of the member under the factored loads. The AISC
book Torsional Analysis of Steel Members (American Institute of Steel Construction,
1983) provides design aids and examples for the determination of torsional stresses.
Extensive coverage is given there to wide-flange shapes (W, S, and HP), channels (C
and MC) and Z shapes. For these members, the charts and formulas simplify considerably
AMERICAN INSTITUTE OF
STEEL CONSTRUCTION
H. MEMBERS UNDER COMBINED FORCES AND TORSION
2 - 41
the calculation of torsional rotations, torsional normal and shear stresses, and the
combination of torsional with flexural stresses.
In the LRFD Specification,
fun = the total normal stress under factored load (ksi) from torsion and all other causes
fuv = the total shear stress under factored load (ksi) from torsion and all other causes
The criteria are as follows:
a. For the limit state of yielding under normal stress
fun ≤ φFy, where φ = 0.90
(H2-1)
fun ≤ 0.90 × 50 ksi = 45.0 ksi
(2-24)
For 50 ksi steel,
b. For the limit state of yielding under shear stress,
fuv ≤ 0.60φFy, where φ = 0.90
(H2-2)
fuv ≤ 0.60 × 0.90 × 50 ksi = 27.0 ksi
(2-25)
For 50 ksi steel,
c. For the limit state of buckling,
fun ≤ φcFcr or fuv ≤ φcFcr, as applicable, where φc = 0.85
(H2-3)
For 50 ksi steel, values of φcFcr are given in Table E-1, in Section E above.
Torsion will accompany flexure when the line of action of a lateral load does not pass
through the shear center. For wide flange and other doubly symmetric shapes, the shear
center is located at the centroid. Singly symmetric shapes have their shear centers on the
axis of symmetry, but not at the centroid. (The location of the shear center of channel
sections is given in the Properties tables in Part 1 of this LRFD Manual.)
Open sections, such as wide-flange and channel, are very inefficient in resisting
torsion; i.e., torsional rotations can be large and torsional stresses relatively high. It is
best to avoid torsion by detailing the loads and reactions to act through the shear center
of the member. In the case of spandrel members supporting building facade elements,
this may not be possible. Heavy exterior masonry walls and stone panels can impose
severe torsional loads on spandrel beams. The following are suggestions for eliminating
or reducing this kind of torsion:
1. Wall elements may span between floors. The moment due to the eccentricity of the
wall with respect to the edge beams can be resisted by lateral forces acting through
the floor diaphragms. Torsion would not be imposed on the spandrel beams.
2. If facade panels extend only a partial story height below the floor line, the use of
diagonal steel “kickers” may be possible. These light members would provide lateral
support to the wall panels. Torsion from the panels would be resisted by forces
originating from structural elements other than the spandrel beams.
3. Even if torsion must be resisted by the edge members, providing intermediate
torsional supports can be helpful. Reducing the span over which the torsion acts will
reduce torsional stresses. If there are secondary beams framing into a spandrel girder,
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
2 - 42
ESSENTIALS OF LRFD
the beams can act as intermediate torsional supports for the girder. By adding top
and bottom moment plates to the connections of the beams with the girder, the
bending resistances of the beams can be mobilized to provide the required torsional
reactions along the girder.
4. Closed sections provide considerably better resistance to torsion than open sections;
torsional rotations and stresses are much lower for box beams than for wide-flange
members. For members subjected to torsion, it may be advisable to use box sections
or to simulate a box shape by welding one or two side plates to a W shape.
I. COMPOSITE MEMBERS
Chapter I of the LRFD Specification covers composite members. Included are concreteencased and concrete-filled steel columns and beam columns, as well as steel beams
interactive with the concrete slabs they support and steel beams encased in concrete.
Unlike traditional structural steel design, which considers only the strength of the steel,
composite design assumes that the steel and concrete work together in resisting loads.
This results in more economical designs, as the quantity of steel can be reduced.
Compression Members
Composite columns (concrete-encased and concrete-filled) must satisfy the limitations
in Section I2 of the LRFD Specification. The design strength of axially loaded composite
columns is φcPn, where φc = 0.85 and the nominal axial compressive strength is determined
from Equations E2-1 through E2-4 above with the following modifications:
As replaces Ag, rm replaces r, Fmy replaces Fy, and Em replaces E.
Fmy = Fy + c1Fyr
Ar
Ac
+ c2 fc′
As
As
(I2-1)
Ac
As
(I2-2)
Em = E + c3Ec
rm = radius of gyraton of the steel shape, pipe, or tubing, in. (For steel shapes it shall
not be less than 0.3 times the overall thickness of the composite cross section
in the plane of buckling.)
where
Ec = w1.5√
fc′
and
Fmy
Fy
Fyr
fc′
Em
E
Ec
w
Ac
Ar
= modified yield stress for the design of composite columns, ksi
= specified minimum yield stress of the structural steel shape, ksi
= specified minimum yield stress of the longitudinal reinforcing bars, ksi
= specified compressive strength of the concrete, ksi
= modified modulus of elasticity for the design of composite columns, ksi
= modulus of elasticity of steel = 29,000 ksi
= modulus of elasticity of concrete, ksi
= unit weight of concrete, lb/ft3
= cross-sectional area of concrete, in.2
= cross-sectional area of longitudinal reinforcing bars, in.2
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
I. COMPOSITE MEMBERS
2 - 43
As
= cross-sectional area of structural steel, in.2
c1, c2, c3 = numerical coefficients. For concrete-filled pipe and tubing: c1 = 1.0,
c2 = 0.85, and c3 = 0.4; for concrete-encased shapes c1 = 0.7, c2 = 0.6,
and c3 = 0.2
Composite columns can be designed by using the Composite Columns Tables in Part 5
of this LRFD Manual (or the numerous tables in AISC Steel Design Guide No. 6: Load
and Resistance Factor Design of W-Shapes Encased in Concrete) for the cross sections
tabulated therein, or the above equations for all cross sections.
Flexural Members
The most common case of a composite flexural member is a steel beam interacting with
a concrete slab by means of stud or channel shear connectors. The slab can be a solid
reinforced concrete slab, but is usually concrete on a corrugated metal deck.
The effective width of concrete slab acting compositely with a steel beam is determined
by three criteria. On either side of the beam centerline, the effective width of concrete
slab cannot exceed:
a. one-eighth of the beam span,
b. one-half the distance to the centerline of the adjacent beam, or
c. the distance to the edge of the slab.
The following pertains to rolled W shapes in regions of positive moment, the predominant use of composite beam design. Other cases (e.g., plate girders and negative
moments) are covered in Chapter I of the LRFD Specification.
The horizontal shear force between the steel beam and concrete slab, to be transferred
by the shear connectors between the points of zero and maximum positive moments, is
the minimum of:
a. 0.85fc′Ac (the maximum possible compressive force in the concrete),
b. AsFy (the maximum possible tensile force in the steel), and
c. ΣQn (the strength of the shear connectors).
For W shapes, the design flexural strength φb Mn, with φb = 0.85, is based on:
a. a uniform compressive stress of 0.85fc′ and zero tensile strength in the concrete
b. a uniform steel stress of Fy in the tension area and compression area (if any) of the
steel section, and
c. equilibrium; i.e., the sum of the tensile forces equals the sum of the compressive
forces.
The above is valid for shored and unshored construction. However, in the latter case, it
is also necessary to check the bare steel beam for adequacy to support the wet concrete
and other construction loads (properly factored).
The number of shear connectors required between a point of maximum moment and
the nearest location of zero moment is
n=
Vh
Qn
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
(2-26)
2 - 44
ESSENTIALS OF LRFD
where
Vh = the total horizontal shear force to be transferred, kips
= the minimum of 0.85fc′Ac, AsFy, and ΣQn
Qn = the shear strength of one connector
The nominal strength of a single stud shear connector in a solid concrete slab is
fc′Ec ≤ AscFu
Qn = 0.5Asc√
(I5-1)
where
Asc = cross-sectional area of a stud shear connector, in.2
fc′ = specified compressive strength of concrete, ksi
Fu = minimum specified tensile strength of a stud shear connector, ksi
Ec = modulus of elasticity of concrete, ksi
Special provisions for shear connectors embedded in concrete on formed steel deck are
given in Section I3.5 of the LRFD Specification. Among them are reduction factors (given
by Equation I3-1 and I3-2) to be applied to the middle term of Equation I5-1 above.
The design of composite beams and the selection of shear connectors can be accomplished with the tables in Part 5 of this LRFD Manual.
The design shear strength for composite beams is determined by the shear strength of
the steel web, as for noncomposite beams; see Section F above.
Combined Compression and Flexure
Composite beam-columns are covered in Section I4 of the LRFD Specification.
COMPUTER SOFTWARE
ELRFD* (Electronic LRFD Specification)
ELRFD is a sophisticated computer program for interactively checking structural steel
building components for compliance with the AISC Specification. All provisions of
Chapters A through H and K of the LRFD Specification are included in the knowledge
base of ELRFD.
The ELRFD program checks whether the member satisfies all limit states and limitation requirements set by the LRFD Specification and reports which sections of the
specification are satisfied or violated. One can review in detail the formulas and rules
used in the evaluation and interactively assess any mathematical expression appearing
on the screen. Design data produced by the software can be viewed and/or printed in
report form for permanent record. ELRFD has a fully interactive Windows-based user
interface.
*ELRFD is copyright AISC and Visual Edge Software, Ltd.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
REFERENCES
2 - 45
REFERENCES
American Institute of Steel Construction, Inc., 1983, Torsional Analysis of Steel Members, AISC, Chicago, IL.
American Society of Civil Engineers, 1988, Minimum Design Loads for Buildings and
Other Structures, ASCE 7-88, New York, NY.
Galambos, T. V., et al., 1978, Eight LRFD Papers, Journal of the Structural Division,
ASCE, Vol. 104, No. ST9 (September 1978), New York.
Geschwindner, L., 1993, “The ‘Leaning’ Column in ASD and LRFD,” Proceedings of
the 1993 National Steel Construction Conference, AISC, Chicago.
U.S. Department of Commerce, 1980, Development of a Probability Based Criterion for
American National Standard A58, NBS (National Bureau of Standards) Special
Publication 577, Washington, DC.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
3-1
PART 3
COLUMN DESIGN
OVERVIEW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-3
DESIGN STRENGTH OF COLUMNS . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-5
General Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-5
W and HP Shapes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-15
Steel Pipe and Structural Tubing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-35
Double Angles and WT Shapes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-53
Single-Angle Struts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-104
COLUMN BASE PLATES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-117
REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-117
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
3-2
COLUMN DESIGN
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
OVERVIEW
3-3
OVERVIEW
Column tables with design compressive strengths, in kips, are located as follows:
W shapes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-16
HP shapes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-31
Steel pipes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-36
Structural tubing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-39
Double angles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-57
WT shapes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-83
Single angles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-104
Additional information related to column design is provided as follows:
Effective length factor (K) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-5
Alignment charts, Figure 3-1
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-6
Stiffness reduction factors (SRF), Table 3-1 . . . . . . . . . . . . . . . . . . . . . . . . 3-7
“Leaning” columns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-10
Combined axial and bending loading (Interaction) . . . . . . . . . . . . . . . . . . . . 3-11
Preliminary design of beam-columns, Table 3-2 . . . . . . . . . . . . . . . . . . . . 3-12
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
3-4
COLUMN DESIGN
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
DESIGN STRENGTH OF COLUMNS
3-5
DESIGN STRENGTH OF COLUMNS
General Notes
Column Load Tables
Column Load Tables are presented for W, WT, and HP shapes, pipe, structural tubing,
double angles, and single angles. Tabular loads are computed in accordance with the
AISC LRFD Specification, Sections E2 and E3 and Appendix E3, for axially loaded
members having effective unsupported lengths indicated to the left of each table. The
effective length KL is the actual unbraced length, in feet, multiplied by the factor K, which
depends on the rotational restraint at the ends of the unbraced length and the means
available to resist lateral movements.
Table C-C2.1 in the Commentary on the LRFD Specification is a guide in selecting
the K-factor. Interpolation between the idealized cases is a matter of engineering judgment. Once sections have been selected for the several framing members, the alignment
charts in Figure 3-1 [reproduced from the Structural Stability Research Council Guide
(Galambos, 1988) here and in Figure C-C2.2 of the Commentary on the LRFD Specification] afford a means to obtain more precise values for K, if desired. For column behavior
in the inelastic range, the values of G as defined in Figure 3-1 may be reduced by the
values given in Table 3-1, as illustrated in Example 3-3.
Tables for W, WT, and HP shapes and for double and single angles are provided for
36 ksi and 50 ksi yield stress steels. Tables for steel pipe are provided for 36 ksi, and for
structural tubing for 46 ksi yield stress steel. All design strengths are tabulated in kips.
Values are not shown when Kl / r exceeds 200.
In all tables, except double angle and WT tables, design strengths are given for effective
lengths with respect to the minor axis calculated by LRFD Specification Section E2.
When the minor axis is braced at closer intervals than the major axis, the strength of the
column must be investigated with reference to both major (X-X) and minor (Y-Y) axes.
The ratio rx / ry included in these tables provides a convenient method for investigating
the strength of a column with respect to its major axis. To obtain an effective length with
respect to the minor axis equivalent in load carrying capacity to the actual effective length
about the major axis, divide the major axis effective length by rx / ry ratio. Compare this
length with the actual effective length about the minor axis. The longer of the two lengths
will control the design, and the design strength may be taken from the table opposite the
longer of the two effective lengths with respect to the minor axis. The double angle and
WT tables show values for effective lengths about both axes.
Properties useful to the designer are listed at the bottom of the column design strength
tables. Additional notes relating specifically to the W and HP shape tables, the steel pipe
and structural tubing tables, and the double and single angle tables precede each of these
groups of tables.
EXAMPLE 3-1
Given:
Design the lightest W shape of Fy = 50 ksi steel to support a factored
concentric load of 1,400 kips. The effective length with respect to
its minor axis is 16 feet. The effective length with respect to its
major axis is 31 feet.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
3-6
COLUMN DESIGN
Solution:
Enter the appropriate Column Load Table for W shapes at effective
length of KL = 16 ft. Since W14 columns are generally most efficient,
begin with the W14 table and work downward, weightwise.
Select W14×145, good for 1,530 kips > 1,400 kips
rx / ry = 1.59. Equivalent L = 31 ft / 1.59 = 19.5 ft > 16 ft
Equivalent effective length for X-X axis controls.
GA
∞
50.0
K
GB
∞
1.0
50.0
10.0
10.0
5.0
3.0
5.0
0.9
5.0
100.0
50.0
30.0
20.0
4.0
20.0
10.0
9.0
8.0
7.0
3.0
2.0
0.5
0.5
0.4
0.4
0.3
0.3
pl
am
2
0.6
0.7
6.0
5.0
10.0
9.0
8.0
7.0
-3
e3
Ex
3-
0.8
0.7
ple
1.0
0.8
0.7
am
1.0
Ex
0.8
0.2
GB
∞
20.0
10.0
100.0
50.0
30.0
3.0
2.0
0.6
K
GA
∞
6.0
5.0
2.2
4.0
4.0
2.0
3.0
3.0
1.75
2.0
2.36
2.0
1.5
0.6
0.2
1.0
0.1
1.0
0.1
0.26
0
0.5
0
SIDESWAY INHIBITED
1.0
0
0
SIDESWAY UNINHIBITED
Fig. 3-1. Alignment charts for effective length of columns in continuous frames.
The subscripts A and B refer to the joints at the two ends of the column section
being considered. G is defined as
Σ(Ic / Lc)
G=
Σ(Ig / Lg)
in which Σ indicates a summation of all members rigidly connected to that joint and
lying on the plane in which buckling of the column is being considered. Ic is the
moment of inertia and Lc the unsupported length of a column section, and Ig is the
moment of inertia and Lg is the unsupported length of a girder or other restraining
member. Ic and Ig are taken about axes perpendicular to the plane of buckling being
considered.
For column ends supported but not rigidly connected to a footing or foundation,
G is theoretically infinity, but, unless actually designed a true friction free pin, may
be taken as 10 for practical designs. If the column end is rigidly attached to a properly
designed footing, G may be taken as 1.0. Smaller values may be used if justified by
analysis.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
DESIGN STRENGTH OF COLUMNS
3-7
Table 3-1.
Stiffness Reduction Factors (SRF) for Columns
Pu / A
Fy
Pu / A
ksi
42
41
40
39
38
37
36
35
34
33
32
31
30
29
28
27
Fy
ksi
36 ksi
50 ksi
—
—
—
—
—
—
—
—
—
—
—
—
0.05
0.14
0.22
0.30
0.03
0.09
0.16
0.21
0.27
0.33
0.38
0.44
0.49
0.53
0.58
0.63
0.67
0.71
0.75
0.79
26
25
24
23
22
21
20
19
18
17
16
15
14
13
12
11
36 ksi
50 ksi
0.38
0.45
0.52
0.58
0.65
0.70
0.76
0.81
0.85
0.89
0.92
0.95
0.97
0.99
1.00
↓
0.82
0.85
0.88
0.90
0.93
0.95
0.97
0.98
0.99
1.00
↓
— indicates not applicable.
Re-enter table for effective length of 19.5 ft to satisfy axial load of
1,400 kips, select W14×145.
By interpolation, the column is good for 1,410 kips.
Use W14×145 column
EXAMPLE 3-2
Given:
Design an 11-ft long W12 interior bay column to support a factored
concentric axial roof load of 1,100 kips. The column is rigidly framed at
the top by 30-ft long W30×116 girders connected to each flange. Column
moment is zero due to the assumption of equal and offsetting moments in
the girders. The column is braced normal to its web at top and base so that
sidesway is inhibited in this plane. Use Fy = 50 ksi steel.
Solution:
a. Check Y-Y axis:
Assume the column is pin-connected at the top and bottom with
sidesway inhibited.
From Table C-C2.1 in the Commentary for condition (d), K = 1.0:
Effective length = 11 ft
Enter Column Load Table:
W12×106 good for 1,160 kips > 1,100 kips o.k.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
3-8
COLUMN DESIGN
b. Check X-X axis:
1. Preliminary selection:
Assume sidesway uninhibited and pin-connected at base.
From Table C-C2.1 for condition (f):
K = 2.0
Approximate effective length relative to X-X axis:
2.0 × 11 = 22.0 ft
From Properties section in tables, for W12 column:
rx / ry ≈ 1.76
Equivalent effective length relative to the Y-Y axis:
22.0
1.76
≈ 12.5 ft > 11.0 ft
Therefore, effective length for X-X axis is critical.
Enter Column Load Table with an effective length of 12.5 ft:
W12×106 column, by interpolation, good for 1,115 kips > 1,100 kips
o.k.
1. Final selection
Try W12×106
Using Figure 3-1 (sidesway uninhibited):
Ix for W12×106 column = 933 in.4
Ix for W30×116 girder = 4,930 in.4
G (base)
= 10 (assume supported but not rigidly connected)
G (top)
=
933 / 11
= 0.258, say 0.26
(4,930 × 2) / 30
Connect points GA = 10 and GB = 0.26, read K = 1.75
For W12×106, rx / ry = 1.76
Actual effective length relative to Y-Y axis:
1.75
× 11.0 = 10.9 ft < 11.0 ft
1.76
Since the effective length for Y-Y axis is not critical,
Use W12×106 column
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
DESIGN STRENGTH OF COLUMNS
3-9
EXAMPLE 3-3
Given:
Using the alignment chart, Figure 3-1 (sidesway uninhibited) and Table
3-1 (Stiffness Reduction Factors), design columns for the bent shown,
by the inelastic K-factor procedure. Let Fy = 50 ksi. Assume continuous
support in the transverse direction.
Solution:
The alignment charts in Figure 3-1 are applicable to elastic columns.
By multiplying G-values times the stiffness reduction factor Et / E, the
charts may be used for inelastic columns.
Since Et / E ≈ Fcr, inelastic / Fcr, elastic, the relationship may be written as
Ginelastic = (Fcr, inelastic / Fcr, elastic)Gelastic.
By utilizing the calculated stress Pu / A a direct solution is possible,
using the following steps:
1. For a known value of factored axial load, Pu = 1,100 kips, select a
trial column size.
Assume W12×120
A = 35.3 in.2, Ix = 1,070 in.4, rx = 5.51 in.
2. Calculate Pu / A:
Pu / A = 1,100 kips / 35.3 in.2 = 31.2 ksi
3. From Table 3-1, determine the Stiffness Reduction Factor (SRF);
SRF = 0.62. For values of Pu / A smaller than those with entries in
Table 3-1, the column is elastic, and the reduction factor is 1.0.
4. Determine Gelastic:
Gelastic (bottom) = 10
1,100 k
1,100 k
W16x31
IX = 375
15′
20′
Fig. 3-2
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
3 - 10
COLUMN DESIGN
Gelastic (top)
=
1,070 / 15
= 3.80
375 / 20
5. Calculate Ginelastic = SRF × Gelastic:
Ginelastic(top) = 0.62 × 3.80 = 2.36
6. Determine K from Figure 3-1 using Ginelastic
For G (top) = 2.36 and G (bottom) = 10,
Read from Figure 3-1, K = 2.2
7. KLx = 2.2 × 15 ft = 33.0 ft
8. Calculate equivalent of KLy:
KLx 33.0 ft
=
= 18.75 ft
1.76
rx / ry
9. From the column tables (for 50 ksi steel):
φc Pn = 1,030 kips < 1,100 kips req’d. n.g.
Try a stronger column.
1. Try a W12×136
A = 39.9 in.2, Ix = 1,240 in.4, rx = 5.58 in.
2. Pu / A = 1,100 kips / 39.9 in.2 = 27.6 ksi
3. From Table 3-1: SRF = 0.77
4. Gelastic (top) =
1,240 / 15
= 4.41
375 / 20
5. Ginelastic(top) = 0.77 × 4.41 = 3.39
6. K = 2.3
7. KLx = 2.3 × 15 ft = 34.5 ft
8. Equivalent KLy:
KLx 34.5 ft
=
= 19.5 ft
1.77
rx / ry
9. φc Pn = 1,135 kips > 1,100 kips req’d o.k.
Use W12×136
“Leaning” Columns
A “leaning” column is one which is considered pin-ended and does not participate in
providing lateral stability to the structure. As a result, it relies on other parts of the
structure for stability. The LRFD Specification in Section C2.2 requires that for unbraced
frames, “the destabilizing effects of gravity-loaded columns whose simple connections
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
DESIGN STRENGTH OF COLUMNS
3 - 11
to the frame do not provide resistance to lateral loads shall be included in the design of
the moment-frame columns.”
Normal practice is to design leaning columns for their required strength with an
effective length factor K = 1. To account for the effects of leaning columns on unbraced
frames, one of the methods given in the Commentary on the LRFD Specification (Section
C2) or in Geschwindner (1993) may be utilized. The simplest methods are:
1. The slightly conservative approach of adjusting the effective lengths of the rigidframe columns,
Ki′ =
√NKi
where
Ki′ = the modified effective length factor of a column
Ki = the actual effective length factor of a column
N = ratio of the factored gravity load supported by all columns in the given story
to that supported by the columns in the rigid frame
2. The more conservative approach of providing sufficient design compressive
strength in the rigid-frame columns of a story to enable them to support the total
factored gravity load of the story at their actual effective lengths.
Combined Axial and Bending Loading (Interaction)
Loads given in the Column Tables are for concentrically loaded columns. For columns
subjected to both axial and bending stress, see Chapters C and H of the LRFD
Specification.
The design of a beam-column is a trial and error process in which a trial section is
checked for compliance with Equations H1-1a and H1-1b. A fast method for selecting an
economical trial W section, using an equivalent axial load, is illustrated in the example
problem, using Table 3-2 and the u values listed in the column properties at the bottom
of the column load tables.
The procedure is as follows:
1. With the known value of KL (effective length), select a first approximate value of
m from Table 3-2. Let u equal 2.
2. Solve for Pu eq = Pu + Mux m + Muy mu
where
Pu
Mux
Muy
m
u
= actual factored axial load, kips
= factored bending moment about the strong axis, kip-ft
= factored bending moment about the weak axis, kip-ft
= factor taken from Table 3-2
= factor taken from column load table
3. From the appropriate Column Load Table, select a tentative section to support Pu eq.
4. Based on the section selected in Step 3, select a “subsequent approximate” value of
m from Table 3-2 and a u value from the column load table.
5. With the values selected in Step 4, solve for Pu eq.
6. Repeat Steps 3 and 4 until the values of m and u stabilize.
7. Check section obtained in Step 6 per Equation H1-1a or H1-1b, as applicable.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
3 - 12
COLUMN DESIGN
Table 3-2.
Preliminary Beam-Column Design
Fy = 36 ksi, Fy = 50 ksi
Values of m
Fy
KL (ft)
36 ksi
10
12
14
16
18
50 ksi
20
22 and
over
10
12
14
16
18
20
22 and
over
1.8
1.7
1.6
1.4
1.3
1.2
1.4
1.7
1.8
2.0
1.8
1.5
1.4
1.1
1.4
1.5
1.7
1.7
1.5
1.3
1.0
1.1
1.3
1.5
1.5
1.4
1.3
0.9
1.0
1.2
1.3
1.4
1.3
1.2
0.8
0.9
1.1
1.2
1.3
1.2
1.2
1st Approximation
All
Shapes
2.0
1.9
1.8
1.7
1.6
1.5
1.3
1.9
Subsequent Approximation
W4
W6
W8
W8
W10
W12
W14
3.1
3.2
2.8
2.5
2.1
1.7
1.5
2.3
2.7
2.5
2.3
2.0
1.7
1.5
1.7
2.1
2.1
2.2
1.9
1.6
1.4
1.4
1.7
1.8
2.0
1.8
1.5
1.4
1.1
1.4
1.5
1.8
1.7
1.5
1.3
1.0
1.2
1.3
1.6
1.6
1.4
1.3
0.8
1.0
1.1
1.4
1.4
1.3
1.2
2.4
2.8
2.5
2.4
2.0
1.7
1.5
1.8
2.2
2.2
2.2
1.9
1.6
1.4
This table is from a paper in AISC Engineering Journal by Uang, Wattar, and Leet (1990).
EXAMPLE 3-4
Given:
Design the following column:
Pu = 400 kips
Mntx = 250 kip-ft
Mltx = 0 (braced frame)
Mnty = 80 kip-ft
Mlty = 0 (braced frame)
KLx = KLy = 14 ft
Lb = 14 ft
Cm = 0.85
Fy = 50 ksi
Solution:
1. For KL = 14 ft, from Table 3-2 select a first trial value of m = 1.7.
Let u = 2
2. Pu eq = Pu + Mux m + Muy mu = 400 + 250 × 1.7 + 80 × 1.7 × 2 =
1,097 kips
3. From Column Load Tables select W14×109 (φc Pn = 1,170 kips) or
W12×120 (φc Pn = 1,220 kips).
4. Select the W14 column, so the second trial value of m is 1.4. (Note:
If a W14 column were required for architectural or other reasons,
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
DESIGN STRENGTH OF COLUMNS
3 - 13
the selection process could have started with m = 1.4). With m = 1.4
and u = 1.97 (for a W14×109) from Column Load Table,
Pu eq = 400 + 250 × 1.4 + 80 × 1.4 × 1.97 = 971 kips
5. From Column Load Tables select W14×90 (φc Pn = 969 kips).
6. For W14×90, m = 1.4, u = 1.94. Repeat of Steps 3 and 4 not required.
7. Check W14×90 with the appropriate interaction formula.
A
= 26.5 in.2
ry
= 3.70 in.,
Kl 14 × 12
= 45.4
=
3.70
ry
rx
= 6.14 in.,
Kl 14 × 12
= 27.4
=
6.14
rx
Thesecond-or der moments,Mux and Muy, will be evaluated using the
approximate method given in Section C1 of the LRFD Specification.
Because Mltx = Mlty = 0 (braced frames in both directions), Specification Equation C1-1 reduces to Mu = B1Mnt, where B1 is a function
of Pe1 (Equation C1-2). The values of Pe1 with respect to the x and y
axes can be determined from LRFD Specification Table 8 as follows:
Pex
Pey
= 382 × 26.5 = 10,123 kips
= 139 × 26.5 = 3,684 kips
B1x
=
0.85
< 1.0. Use B1x = 1.0
1 − 400 / 10,123
B1y
=
0.85
< 1.0. Use B1y = 1.0
1 − 400 / 3,684
= 1.0 × 250 = 250 kip-ft
= 1.0 × 80 = 80 kip-ft
0.9 × 50 × 75.6
= 284 kip-ft
φb Mny = φb Mpy =
12
Mux
Muy
From the beam selection table in Part 4 of this Manual:
φb Mnx = 577 kip-ft for Lb < Lp = 15.0 ft
Pu
φcPn
=
400
= 0.412 > 0.2. Therefore, Equation H1-1a applies.
969
400 8 250 80
+
+
= 0.412 + 0.636 = 1.05 < 1.0 n.g.
969 9 577 284
Use W14×99
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
3 - 14
COLUMN DESIGN
Column Stiffening
Values of Pwo, Pwi, Pwb, and Pfb, listed in the Properties Section of the Column Load Tables
for W and HP shapes, are useful in determining if a column requires stiffening because
of forces transmitted into it from the flanges or connecting flange plates of a rigid beam
connection to the column flange.
The parameters are defined as follows:
Pwo
Pwi
Pwb
Pfb
= φ5Fyw tw k (kips), φ = 1.0
= φFyw tw (kips/in.), φ = 1.0
= φ4,100tw3 √
Fyw / h (kips), φ = 0.9
= φ6.25tf2Fyf (kips), φ = 0.9
Column stiffening or a heavier column* is required if Pbf, the factored force transmitted
into the column web, exceeds any one of the following three resisting forces:
Pwb
Pfb
Pwi tb + Pwo, where tb is the thickness of the beam flange delivering the concentrated force.
For a complete explanation of these design parameters, see the section Column
Stiffening in Part 10 (Volume II) of this LRFD Manual.
*The designer should consider selecting a heavier column section to eliminate the need for stiffening. Although this will
increase the material cost of the column, this heavier section may provide a more economical solution due to the reduction in
labor cost associated with the elimination of stiffening.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
DESIGN STRENGTH OF COLUMNS
3 - 15
W and HP Shapes
The design strengths in the tables that follow are tabulated for the effective lengths in
feet KL (with respect to the minor axis), indicated at the left of each table. They are
applicable to axially loaded members in accordance with Section E2 of the LRFD
Specification. Two yield stresses are covered, 36 and 50 ksi.
The heavy horizontal lines appearing within the tables indicate Kl / r = 200. No values
are listed beyond Kl / r = 200.
For discussion of effective length, range of l / r, strength about the major axis,
combined axial and bending stress, and sample problems, see General Notes, above.
Properties and factors are listed at the bottom of the tables for checking strength about
the strong axis, combined loading conditions, and column stiffener requirements.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
3 - 16
COLUMN DESIGN
Y
Fy = 36 ksi
Fy = 50 ksi
X
COLUMNS
W shapes
Design axial strength in kips (φ = 0.85)
X
Y
Designation
W14
Wt./ft
808
Effective length KL (ft) with respect to least radius of gyration ry
Fy
730
665
605
550
36
50
36
50
36
50
36
50
36
50
0
7250
10100
6580
9140
6000
8330
5450
7570
4960
6890
11
12
13
14
15
5610
5480
5350
5230
5110
7440
7240
7040
6850
6660
6310
6260
6210
6150
6090
8620
8530
8430
8320
8200
5750
5700
5650
5590
5540
7850
7760
7660
7560
7450
5210
5170
5120
5070
5020
7110
7030
6940
6850
6750
4740
4700
4650
4600
4560
6460
6390
6300
6220
6120
16
17
18
19
20
4990
4870
4760
4650
4540
6480
6310
6130
5970
5810
6020
5960
5880
5810
5730
8080
7960
7820
7690
7550
5480
5410
5350
5280
5200
7340
7220
7100
6970
6840
4960
4900
4840
4770
4700
6640
6530
6420
6300
6170
4500
4450
4390
4330
4260
6020
5920
5810
5700
5590
22
24
26
28
30
4340
4140
3950
3770
3600
5490
5200
4920
4660
4410
5570
5390
5210
5020
4820
7250
6940
6610
6280
5940
5050
4890
4720
4540
4360
6560
6270
5970
5660
5340
4560
4410
4250
4090
3920
5910
5640
5360
5080
4790
4130
3990
3840
3690
3530
5350
5100
4840
4570
4300
32
34
36
38
40
3430
3280
3130
2980
2850
4170
3950
3740
3540
3350
4620
4420
4210
4000
3790
5600
5250
4910
4580
4250
4170
3980
3790
3590
3400
5030
4710
4400
4090
3780
3740
3570
3390
3210
3030
4490
4200
3910
3630
3350
3370
3210
3050
2880
2720
4030
3760
3500
3240
2990
42
44
46
48
50
2720
2590
2470
2360
2250
3170
3000
3860
3540
3260
3580
3380
3170
2970
2780
3930
3620
3310
3040
2800
3210
3020
2830
2650
2470
3490
3200
2930
2690
2480
2860
2680
2510
2340
2180
3080
2820
2580
2370
2180
2550
2390
2240
2080
1940
2740
2500
2290
2100
1940
2.03
2.03
2.03
3910
5430
3070
135
187
111
103000 122000 56400
5310
7370
4880
20.1
17.0
19.5
415
270
372
2.03
4270
154
66500
6780
16.6
241
2.02
3670
142
52200
5750
16.3
222
2.02
2250
93.4
33900
3500
19.0
313
2.01
3120
130
39900
4870
16.1
203
2.02
1930
85.7
26100
2950
18.7
288
2.01
2680
119
30800
4100
15.9
188
Properties
u
P wo (kips)
P wi (kips/in.)
P wb (kips)
P fb (kips)
L p (ft)
L r (ft)
A (in.2)
Ix (in.4)
Iy (in.4)
ry (in.)
Ratio rx / ry
Pex (KL )2 / 10 4
Pey (KL )2 / 10 4
237
16000
5510
4.82
1.70
457000
158000
215
14300
4720
4.69
1.74
411000
135000
2.02
2640
102
44300
4140
19.3
342
196
12400
4170
4.62
1.73
357000
120000
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
178
10800
3680
4.55
1.71
310000
105000
162
9430
3250
4.49
1.70
270000
93500
DESIGN STRENGTH OF COLUMNS
3 - 17
Y
Fy = 36 ksi
Fy = 50 ksi
COLUMNS
W shapes
Design axial strength in kips (φ = 0.85)
X
X
Y
Designation
W14
Wt./ft
500
Fy
455
426
398
370
50
36
50
36
50
36
50
36
50
4500
6250
4100
5700
3830
5310
3580
4970
3340
4630
11
12
13
14
15
4290
4250
4210
4170
4120
5850
5780
5710
5620
5540
3910
3870
3840
3790
3750
5330
5260
5190
5110
5030
3640
3610
3570
3530
3490
4970
4900
4830
4760
4680
3410
3380
3340
3300
3270
4640
4580
4520
4450
4380
3170
3140
3110
3070
3040
4320
4260
4200
4140
4070
16
17
18
19
20
4070
4020
3970
3910
3850
5450
5350
5250
5150
5040
3710
3660
3610
3560
3500
4950
4860
4770
4670
4570
3450
3400
3360
3310
3260
4600
4520
4430
4340
4250
3230
3180
3140
3090
3040
4300
4220
4140
4050
3960
3000
2960
2920
2870
2820
4000
3920
3840
3760
3680
22
24
26
28
30
3730
3600
3460
3320
3180
4820
4590
4350
4100
3850
3390
3270
3140
3010
2870
4370
4150
3930
3700
3480
3150
3030
2910
2790
2660
4050
3850
3640
3430
3210
2940
2830
2720
2600
2480
3780
3590
3390
3190
2990
2730
2630
2520
2410
2290
3500
3320
3140
2950
2750
32
34
36
38
40
3030
2880
2730
2580
2420
3610
3360
3120
2880
2650
2740
2600
2460
2320
2180
3250
3020
2800
2580
2370
2530
2400
2270
2140
2010
3000
2780
2570
2370
2170
2360
2230
2110
1990
1860
2780
2580
2390
2190
2010
2180
2060
1950
1830
1710
2560
2380
2190
2010
1840
42
44
46
48
50
2280
2130
1990
1850
1710
2420
2210
2020
1860
1710
2040
1910
1780
1650
1520
2160
1970
1800
1650
1520
1880
1750
1630
1510
1400
1980
1800
1650
1510
1400
1740
1620
1510
1400
1290
1830
1660
1520
1400
1290
1600
1490
1380
1280
1180
1670
1520
1390
1280
1180
P wo (kips)
P wi (kips/in.)
P wb (kips)
P fb (kips)
L p (ft)
L r (ft)
2.01
1650
78.8
20400
2480
18.5
264
2.00
2290
110
24100
3450
15.7
172
1.99
1410
72.5
15800
2090
18.3
242
1.99
1950
101
18600
2900
15.5
157
1.99
1730
93.8
15000
2590
15.3
148
1.99
1120
63.7
10800
1640
18.0
213
1.98
1550
88.5
12800
2280
15.2
139
1.98
987
59.6
8790
1430
17.8
199
1.97
1370
82.8
10400
1990
15.1
129
Effective length KL (ft) with respect to least radius of gyration ry
36
0
Properties
u
A (in.2)
Ix (in.4)
Iy (in.4)
ry (in.)
Ratio rx / ry
Pex (KL )2 / 10 4
Pey (KL )2 / 10 4
147
8210
2880
4.43
1.69
235000
82600
134
7190
2560
4.38
1.67
206000
73600
2.00
1240
67.5
12800
1870
18.1
227
125
6600
2360
4.34
1.67
189000
67400
117
6000
2170
4.31
1.66
172000
62200
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
109
5440
1990
4.27
1.66
156000
56900
3 - 18
COLUMN DESIGN
Y
Fy = 36 ksi
Fy = 50 ksi
X
COLUMNS
W shapes
Design axial strength in kips (φ = 0.85)
X
Y
Designation
W14
Wt./ft
342
Fy
311
283
257
233
50
36
50
36
50
36
50
36
50
3090
4290
2800
3880
2550
3540
2310
3210
2100
2910
6
7
8
9
10
3040
3030
3010
2990
2960
4200
4170
4130
4090
4050
2750
2740
2720
2700
2680
3800
3770
3740
3700
3660
2510
2500
2480
2460
2440
3460
3440
3410
3370
3330
2280
2260
2250
2230
2210
3140
3120
3090
3060
3020
2060
2050
2040
2020
2000
2850
2820
2800
2770
2730
11
12
13
14
15
2940
2910
2880
2850
2810
4000
3950
3890
3830
3760
2660
2630
2600
2570
2540
3610
3560
3510
3460
3400
2420
2390
2370
2340
2310
3290
3240
3200
3140
3090
2190
2170
2150
2120
2090
2980
2940
2890
2850
2800
1980
1960
1940
1920
1890
2700
2660
2620
2570
2530
16
17
18
19
20
2770
2740
2700
2650
2610
3690
3620
3550
3470
3400
2510
2470
2430
2390
2360
3330
3270
3200
3130
3060
2280
2250
2210
2180
2140
3030
2970
2910
2850
2780
2060
2030
2000
1970
1940
2740
2690
2630
2570
2510
1870
1840
1810
1780
1750
2480
2430
2380
2320
2270
22
24
26
28
30
2520
2420
2320
2220
2110
3230
3060
2890
2710
2530
2270
2180
2090
2000
1900
2910
2750
2590
2430
2270
2060
1980
1900
1810
1720
2640
2500
2350
2200
2050
1870
1790
1710
1630
1550
2380
2250
2120
1980
1840
1690
1620
1550
1470
1400
2150
2030
1910
1780
1660
32
34
36
38
40
2010
1900
1790
1680
1570
2360
2180
2010
1840
1680
1800
1700
1600
1500
1410
2110
1950
1790
1640
1490
1630
1540
1450
1360
1270
1900
1760
1620
1480
1340
1470
1380
1300
1220
1140
1710
1570
1440
1320
1190
1320
1240
1170
1090
1020
1530
1410
1290
1180
1070
P wo (kips)
P wi (kips/in.)
P wb (kips)
P fb (kips)
L p (ft)
L r (ft)
1.98
866
55.4
7100
1240
17.7
185
1.97
1200
77.0
8360
1720
15.0
120
1.97
746
50.8
5430
1030
17.5
168
1.96
1040
70.5
6400
1440
14.8
110
1.95
887
64.5
4930
1210
14.7
100
1.96
542
42.3
3150
723
17.2
140
1.94
753
58.8
3710
1000
14.6
91.6
1.95
457
38.5
2370
599
17.1
127
1.93
635
53.5
2790
832
14.5
83.4
Effective length KL (ft) with respect to least radius of gyration ry
36
0
Properties
u
A (in.2)
Ix (in.4)
Iy (in.4)
ry (in.)
Ratio rx / ry
Pex (KL )2 / 10 4
Pey (KL )2 / 10 4
101
4900
1810
4.24
1.65
141000
52000
91.4
4330
1610
4.2
1.64
124000
46100
1.97
639
46.4
4190
868
17.4
154
83.3
3840
1440
4.17
1.63
110000
41500
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
75.6
3400
1290
4.13
1.62
97400
36900
68.5
3010
1150
4.1
1.62
86200
33000
DESIGN STRENGTH OF COLUMNS
3 - 19
Y
Fy = 36 ksi
Fy = 50 ksi
COLUMNS
W shapes
Design axial strength in kips (φ = 0.85)
X
X
Y
Designation
W14
Wt./ft
211
Fy
193
176
159
145
50
36
50
36
50
36
50
36
50
1900
2640
1740
2410
1590
2200
1430
1980
1310
1810
6
7
8
9
10
1870
1860
1840
1830
1810
2580
2550
2530
2500
2470
1710
1700
1690
1670
1660
2360
2340
2320
2290
2260
1560
1550
1540
1530
1510
2150
2130
2110
2090
2060
1400
1400
1390
1380
1360
1940
1920
1900
1880
1860
1280
1280
1270
1260
1250
1770
1760
1740
1720
1700
11
12
13
14
15
1790
1780
1760
1730
1710
2440
2400
2370
2330
2280
1640
1630
1610
1590
1570
2230
2200
2170
2130
2090
1500
1480
1460
1450
1430
2030
2000
1970
1940
1900
1350
1330
1320
1300
1280
1830
1810
1780
1740
1710
1230
1220
1210
1190
1170
1670
1650
1620
1590
1560
16
17
18
19
20
1690
1660
1640
1610
1580
2240
2190
2140
2090
2040
1540
1520
1500
1470
1440
2050
2010
1960
1910
1870
1410
1380
1360
1340
1310
1860
1820
1780
1740
1700
1270
1250
1230
1200
1180
1680
1640
1600
1570
1530
1160
1140
1120
1100
1080
1530
1500
1460
1430
1390
22
24
26
28
30
1520
1460
1390
1330
1260
1940
1830
1710
1600
1490
1390
1330
1270
1210
1150
1770
1670
1560
1460
1350
1260
1210
1150
1100
1040
1610
1510
1420
1320
1220
1140
1090
1040
990
930
1440
1360
1270
1180
1100
1040
992
946
898
849
1320
1240
1160
1080
998
32
34
36
38
40
1190
1120
1050
980
912
1370
1260
1160
1050
951
1080
1020
955
892
830
1250
1150
1050
956
863
980
920
863
805
748
1130
1040
946
859
775
880
830
773
721
670
1010
928
846
767
692
800
752
703
655
608
919
842
767
694
626
P wo (kips)
P wi (kips/in.)
P wb (kips)
P fb (kips)
L p (ft)
L r (ft)
1.95
397
35.3
1830
493
17.0
116
1.93
551
49.0
2160
684
14.4
76.0
1.96
340
32.0
1370
420
16.9
106
1.93
473
44.5
1610
583
14.3
70.1
1.92
415
41.5
1310
483
14.2
64.5
1.94
251
26.8
803
287
16.7
88.6
1.92
349
37.3
947
398
14.1
59.0
1.93
214
24.5
609
241
16.6
81.5
1.90
298
34.0
718
334
14.1
54.7
Effective length KL (ft) with respect to least radius of gyration ry
36
0
Properties
u
A (in.2)
Ix (in.4)
Iy (in.4)
ry (in.)
Ratio rx / ry
Pex (KL )2 / 10 4
Pey (KL )2 / 10 4
62.0
2660
1030
4.07
1.61
76100
29400
56.8
2400
931
4.05
1.60
68700
26700
1.94
299
29.9
1110
348
16.8
97.5
51.8
2140
838
4.02
1.60
61300
24000
46.7
1900
748
4
1.60
54400
21400
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
42.7
1710
677
3.98
1.59
49000
19400
3 - 20
COLUMN DESIGN
Y
Fy = 36 ksi
Fy = 50 ksi
X
COLUMNS
W shapes
Design axial strength in kips (φ = 0.85)
X
Y
Designation
W14
Wt./ft
132
Fy
120
109
50
90
36
50
36
50
36
50†
36
50†
0
1190
1650
1080
1500
979
1360
890
1240
811
1130
6
7
8
9
10
1160
1160
1150
1140
1130
1610
1590
1570
1550
1530
1060
1050
1040
1030
1020
1460
1450
1430
1410
1390
960
953
946
937
927
1320
1310
1300
1280
1260
873
867
860
852
843
1200
1190
1180
1160
1150
795
789
783
775
767
1100
1080
1070
1060
1040
11
12
13
14
15
1110
1100
1080
1070
1050
1510
1480
1450
1430
1390
1010
999
986
971
956
1370
1350
1320
1290
1270
917
905
893
880
866
1240
1220
1200
1170
1150
833
823
811
799
787
1130
1110
1090
1060
1040
758
749
738
727
716
1030
1010
989
969
947
16
17
18
19
20
1030
1020
997
978
958
1360
1330
1300
1260
1220
940
924
906
888
870
1240
1210
1180
1140
1110
852
837
821
804
787
1120
1090
1060
1030
1000
773
759
745
730
714
1020
991
965
938
911
704
691
678
664
650
925
902
878
853
828
22
24
26
28
30
916
872
826
780
733
1150
1070
997
920
844
831
791
749
706
663
1040
972
902
832
762
752
715
677
639
600
943
879
815
751
688
682
648
614
578
542
854
796
737
679
621
620
589
558
525
493
776
723
670
616
564
32
34
36
38
686
639
593
547
769
697
627
563
620
577
535
494
694
628
565
507
560
522
483
446
627
567
509
457
507
471
436
402
565
511
458
411
460
428
396
365
512
463
415
372
P wo (kips)
P wi (kips/in.)
P wb (kips)
P fb (kips)
L p (ft)
L r (ft)
2.03
196
23.2
520
215
15.7
73.7
1.99
272
32.3
613
298
13.3
49.7
2.04
173
21.2
399
179
15.6
67.9
1.99
240
29.5
471
249
13.2
46.3
1.97
205
26.3
331
208
13.2
43.2
2.02
125
17.5
222
123
15.5
58.1
1.95
174
24.3
261
171
13.4
40.6
2.02
109
15.8
165
102
15.4
54.2
1.94
151
22.0
195
142
15.0
38.4
Effective length KL (ft) with respect to least radius of gyration ry
36
99
Properties
u
A (in.2)
Ix (in.4)
Iy (in.4)
ry (in.)
Ratio rx / ry
Pex (KL )2 / 10 4
Pey (KL )2 / 10 4
38.8
1530
548
3.76
1.67
43800
15700
35.3
1380
495
3.74
1.67
39300
14100
2.02
148
18.9
281
150
15.5
62.7
32
1240
447
3.73
1.67
35400
12700
†Flange is noncompact; see discussion preceding column load tables.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
29.1
1110
402
3.71
1.66
31700
11500
26.5
999
362
3.70
1.66
28600
10400
DESIGN STRENGTH OF COLUMNS
3 - 21
Y
Fy = 36 ksi
Fy = 50 ksi
COLUMNS
W shapes
Design axial strength in kips (φ = 0.85)
X
X
Y
Designation
W14
Wt./ft
82
Fy
36
50
68
61
53
48
43
36
50
36
50
36
50
36
50
36
50
36
50†
737 1020 667
927
612
850
548
761
477
663
431
599
386
536
6
7
8
9
10
705
694
682
667
652
963
942
918
892
863
638
628
616
604
590
871
852
830
807
781
585
576
565
553
540
798
781
760
738
714
523
515
505
494
483
714
698
680
660
638
443
432
418
404
389
598
576
552
526
498
400
390
378
365
351
540
520
498
474
449
357
347
337
325
312
482
463
443
422
399
11
12
14
16
18
635
618
579
538
495
833
800
732
661
588
575
559
524
487
447
753
724
662
598
532
526
511
479
444
408
689
662
604
544
484
470
457
428
396
364
615
591
539
486
431
372
355
319
282
245
469
439
379
319
263
336
320
287
253
220
423
395
340
286
235
298
284
254
224
194
375
350
301
252
206
20
22
24
26
28
450
406
363
321
280
516
447
381
325
280
407
367
328
290
253
467
405
345
294
253
371
334
297
262
229
424
366
311
265
229
331
297
265
233
203
377
325
276
236
203
210
176
148
126
109
213
176
148
126
109
188
157
132
113
97
191
157
132
113
97
165
138
116
99
85
167
138
116
99
85
30
31
32
34
36
244
229
214
190
169
244
229
214
190
169
221
207
194
172
153
221
207
194
172
153
199
187
175
155
138
199
187
175
155
138
177
166
155
138
123
177
166
155
138
123
95
89
83
95
89
83
85
79
85
79
74
69
74
69
38
152
152 138
138
124
124
110
110
3.2 2.7 3.12 2.56 2.97
95.7 133 84.2 117 72.1
13.3 18.5 12.2 17.0 11.0
98.4 116 76.4 90.0 55.1
88.2 123 71.7 100 56.9
8.00 6.79 7.96 6.75 7.88
28.0 20.1 26.4 19.2 24.7
2.37
100
15.3
64.9
79.0
6.68
18.2
0
Effective length KL (ft) with respect to least radius of gyration ry
74
Properties
u
P wo (kips)
P wi (kips/in.)
P wb (kips)
P fb (kips)
L p (ft)
L r (ft)
A (in.2)
Ix (in.4)
Iy (in.4)
ry (in.)
Ratio rx / ry
Pex (KL )2 / 10 4
Pey (KL )2 / 10 4
2.85
149
18.4
257
148
10.3
43.0
2.68
207
25.5
303
206
8.77
29.6
24.1
882
148
2.48
2.44
25200
4240
2.82
127
16.2
177
125
10.3
40.0
2.62
176
22.5
209
173
8.77
27.9
21.8
796
134
2.48
2.44
22800
3840
2.80
112
14.9
139
105
10.3
37.3
2.56
156
20.8
163
146
8.70
26.4
20
723
121
2.46
2.44
20700
3460
2.74
97.0
13.5
102
84.2
10.2
34.7
2.44
135
18.8
121
117
8.66
25.0
17.9
640
107
2.45
2.44
18300
3080
15.6
541
57.7
1.92
3.07
15500
1650
14.1
485
51.4
1.91
3.06
13800
1470
12.6
428
45.2
1.89
3.08
12200
1290
†Web may be noncompact for combined axial and bending stress; see AISC LRFD Specification Section B5.
Note: Heavy line indicates Kl / r of 200.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
3 - 22
COLUMN DESIGN
Y
Fy = 36 ksi
Fy = 50 ksi
X
COLUMNS
W shapes
Design axial strength in kips (φ = 0.85)
X
Y
Designation
W12
Wt./ft
336
Fy
305
279
252
230
50
36
50
36
50
36
50
36
50
3020
4200
2740
3810
2510
3480
2270
3150
2070
2880
6
7
8
9
10
2960
2930
2900
2870
2840
4070
4020
3970
3910
3850
2680
2660
2630
2600
2570
3690
3640
3590
3540
3480
2450
2430
2400
2370
2350
3370
3330
3280
3230
3170
2210
2190
2170
2150
2120
3040
3010
2960
2920
2870
2020
2000
1980
1960
1930
2780
2740
2710
2660
2610
11
12
13
14
15
2800
2760
2720
2670
2620
3780
3700
3620
3540
3450
2530
2500
2460
2410
2370
3420
3350
3270
3190
3110
2310
2280
2240
2200
2160
3110
3050
2980
2910
2830
2090
2060
2020
1980
1950
2810
2750
2680
2620
2550
1910
1880
1840
1810
1770
2560
2500
2450
2380
2320
16
17
18
19
20
2570
2520
2470
2410
2350
3360
3260
3160
3060
2960
2320
2270
2220
2170
2120
3020
2940
2840
2750
2660
2110
2070
2020
1970
1920
2750
2670
2580
2500
2410
1910
1860
1820
1770
1730
2470
2400
2320
2240
2160
1740
1700
1660
1610
1570
2250
2180
2110
2030
1960
22
24
26
28
30
2230
2100
1980
1850
1720
2750
2540
2330
2120
1910
2000
1890
1770
1650
1530
2460
2270
2070
1880
1690
1820
1710
1600
1490
1380
2230
2050
1870
1690
1520
1630
1530
1430
1330
1230
1990
1830
1660
1500
1350
1480
1390
1300
1200
1110
1810
1650
1500
1350
1210
32
34
36
38
40
1590
1460
1340
1220
1100
1720
1520
1360
1220
1100
1410
1300
1180
1080
971
1510
1340
1200
1080
971
1270
1160
1060
960
866
1350
1200
1070
960
866
1130
1030
940
848
766
1200
1060
945
848
766
1020
931
845
761
687
1070
951
848
761
687
P wo (kips)
P wi (kips/in.)
P wb (kips)
P fb (kips)
L p (ft)
L r (ft)
2.18
1180
64
12700
1770
14.5
202
2.17
1640
89
15000
2460
12.3
131
2.18
1010
59
9740
1480
14.3
184
2.16
1400
81
11500
2060
12.1
120
2.15
1220
77
9700
1720
12.0
110
2.16
738
50
6150
1030
13.9
154
2.14
1020
70
7250
1420
11.8
100
2.15
636
46
4810
868
13.8
141
2.13
883
64
5670
1210
11.7
92.0
Effective length KL (ft) with respect to least radius of gyration ry
36
0
Properties
u
A (in.2)
Ix (in.4)
Iy (in.4)
ry (in.)
Ratio rx / ry
Pex (KL )2 / 10 4
Pey (KL )2 / 10 4
98.8
4060
1190
3.47
1.85
116000
34000
89.6
3550
1050
3.42
1.84
101000
30000
2.16
878
55
8230
1240
14.1
169
81.9
3110
937
3.38
1.82
88900
26800
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
74.1
2720
828
3.34
1.81
77900
23700
67.7
2420
742
3.31
1.80
69100
21200
DESIGN STRENGTH OF COLUMNS
3 - 23
Y
Fy = 36 ksi
Fy = 50 ksi
COLUMNS
W shapes
Design axial strength in kips (φ = 0.85)
X
X
Y
Designation
W12
Wt./ft
210
Fy
190
170
152
136
120
50
36
50
36
50
36
50
36
50
36
50
1890
2630
1710
2370
1530
2120
1370
1900
1220
1700
1080
1500
6
7
8
9
10
1840
1830
1810
1790
1760
2540
2500
2470
2430
2380
1660
1650
1630
1610
1590
2290
2260
2220
2190
2150
1490
1480
1460
1440
1420
2050
2020
1990
1960
1920
1330
1320
1300
1290
1270
1830
1810
1780
1750
1710
1190
1180
1160
1150
1130
1630
1610
1590
1560
1530
1050
1040
1030
1010
1000
1440
1420
1400
1380
1350
11
12
13
14
15
1740
1710
1680
1650
1610
2330
2280
2230
2170
2110
1570
1540
1510
1480
1450
2100
2050
2000
1950
1900
1400
1380
1350
1330
1300
1880
1840
1790
1740
1690
1250
1230
1210
1180
1160
1680
1640
1590
1550
1510
1110
1090
1070
1050
1030
1490
1460
1420
1380
1340
984
966
948
928
908
1320
1290
1250
1220
1180
16
17
18
19
20
1580
1540
1510
1470
1430
2040
1980
1910
1840
1780
1420
1390
1350
1320
1280
1840
1780
1720
1650
1590
1270
1240
1210
1180
1140
1640
1580
1530
1470
1420
1130
1100
1070
1050
1020
1460
1410
1360
1310
1260
1010
980
955
928
901
1290
1250
1210
1160
1110
886
864
841
817
793
1140
1100
1060
1020
976
22
24
26
28
30
1340
1260
1170
1090
1000
1640
1490
1360
1220
1090
1210
1130
1050
973
895
1460
1340
1210
1090
967
1070
1000
933
862
792
1300
1180
1070
959
852
954
891
827
763
700
1150
1050
944
844
749
846
788
731
673
617
1020
924
831
742
656
743
692
640
589
538
892
808
726
646
569
32
34
36
38
40
919
837
759
682
616
962
852
760
682
616
819
745
674
605
546
853
755
674
605
546
724
657
593
532
480
750
664
593
532
480
638
578
520
467
421
658
583
520
467
421
561
508
456
409
369
577
511
456
409
369
489
442
395
355
320
500
443
395
355
320
P wo (kips)
P wi (kips/in.)
P wb (kips)
P fb (kips)
L p (ft)
L r (ft)
2.16
558
42
3760
731
13.7
129
2.13
774
59
4430
1020
11.6
84.2
2.14
465
38
2700
610
13.5
117
2.11
646
53
3190
847
11.5
76.6
2.15
333
31
1500
397
13.3
94.7
2.11
462
44
1760
551
11.3
62.1
2.13
276
28
1120
316
13.2
84.6
2.09
383
40
1320
439
11.2
55.7
2.12
232
26
815
247
13.0
75.5
2.07
322
36
960
343
11.1
50.0
Effective length KL (ft) with respect to least radius of gyration ry
36
0
Properties
u
A (in.2)
Ix (in.4)
Iy (in.4)
ry (in.)
Ratio rx / ry
Pex (KL )2 / 10 4
Pey (KL )2 / 10 4
61.8
2140
664
3.28
1.80
61400
19000
55.8
1890
589
3.25
1.79
54100
16900
2.14
389
35
2020
493
13.4
105
2.11
540
48
2380
684
11.4
68.9
50.0
1650
517
3.22
1.78
47100
14800
44.7
1430
454
3.19
1.77
41000
13000
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
39.9
1240
398
3.16
1.77
35600
11400
35.3
1070
345
3.13
1.76
30700
9900
3 - 24
COLUMN DESIGN
Y
Fy = 36 ksi
Fy = 50 ksi
X
COLUMNS
W shapes
Design axial strength in kips (φ = 0.85)
X
Y
Designation
W12
Wt./ft
106
Fy
96
87
79
72
65
50
36
50
36
50
36
50
36
50
36
50†
955
1330
863
1200
783
1090
710
986
646
897
584
812
6
7
8
9
10
928
919
908
896
883
1280
1260
1240
1210
1190
839
830
820
809
797
1150
1140
1120
1100
1070
761
753
744
734
723
1050
1030
1010
994
973
689
682
674
665
654
947
933
917
900
880
627
620
613
604
595
861
848
834
818
800
567
561
554
546
538
779
767
754
739
723
11
12
13
14
15
868
853
836
819
800
1160
1130
1100
1070
1040
784
770
755
739
722
1050
1020
995
966
935
711
698
684
669
654
950
926
901
874
846
643
631
619
605
591
860
838
814
790
764
585
574
562
550
537
781
761
740
717
694
529
519
508
497
485
706
687
668
647
626
16
17
18
19
20
781
761
741
719
698
1000
968
932
895
858
704
686
667
648
628
904
871
838
805
771
638
621
604
586
568
817
788
758
727
696
576
561
545
529
512
738
711
683
655
627
523
509
495
480
465
670
645
620
594
569
472
460
446
433
419
604
581
558
535
512
22
24
26
28
30
653
608
562
516
472
783
708
635
565
497
588
546
505
463
422
703
635
569
505
443
531
493
455
417
380
634
572
511
453
397
479
444
409
375
341
570
514
459
406
355
434
403
371
339
309
517
465
415
367
321
391
362
333
305
277
464
417
372
328
287
32
34
36
38
40
428
386
345
310
279
437
387
345
310
279
383
345
308
276
249
390
345
308
276
249
344
309
276
248
223
349
309
276
248
223
308
277
247
221
200
312
277
247
221
200
279
250
223
200
181
282
250
223
200
181
250
223
199
179
161
252
223
199
179
161
P wo (kips)
P wi (kips/in.)
P wb (kips)
P fb (kips)
L p (ft)
L r (ft)
2.12
185
22
518
198
13.0
67.2
2.06
257
31
611
276
11.0
44.9
2.10
161
20
378
164
12.9
61.4
2.04
223
28
446
228
10.9
41.4
2.09
122
17
236
109
12.7
51.8
2.01
169
24
278
152
10.8
35.7
2.08
106
15
181
91
12.7
48.2
1.98
148
22
213
126
10.7
33.6
2.06
92.1
14
135
74
12.6
44.7
1.95
128
20
159
103
11.8
31.7
Effective length KL (ft) with respect to least radius of gyration ry
36
0
Properties
u
A (in.2)
Ix (in.4)
Iy (in.4)
ry (in.)
Ratio rx / ry
Pex (KL )2 / 10 4
Pey (KL )2 / 10 4
31.2
933
301
3.11
1.76
26700
8640
28.2
833
270
3.09
1.76
23900
7710
2.10
139
19
311
133
12.8
56.3
2.02
193
26
366
185
10.9
38.3
25.6
740
241
3.07
1.75
21200
6910
23.2
662
216
3.05
1.75
18900
6180
†Flange is noncompact; see discussion preceding column load tables.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
21.1
597
195
3.04
1.75
17000
5580
19.1
533
174
3.02
1.75
15200
4990
DESIGN STRENGTH OF COLUMNS
3 - 25
Y
Fy = 36 ksi
Fy = 50 ksi
COLUMNS
W shapes
Design axial strength in kips (φ = 0.85)
X
X
Y
Designation
W12
Wt./ft
58
Fy
53
50
45
40
50
36
50
36
50
36
50
36
50
520
723
477
663
450
625
404
561
361
502
6
7
8
9
10
498
490
482
472
461
680
666
649
631
611
457
449
441
432
422
623
610
594
577
559
419
408
396
383
369
566
546
524
500
475
376
366
355
343
330
507
489
469
447
424
336
327
317
306
295
453
437
419
399
378
11
12
13
14
15
450
437
424
411
397
590
568
545
521
496
411
400
388
375
362
539
518
496
474
451
354
339
322
306
289
448
421
393
365
337
317
302
287
272
257
400
375
350
324
299
282
269
256
242
228
356
334
311
288
266
16
18
20
22
24
382
352
321
291
260
471
420
370
322
276
348
320
292
263
235
428
381
334
290
247
271
237
204
173
145
310
257
209
173
145
241
210
180
152
128
274
227
184
152
128
214
187
160
135
113
243
201
163
135
113
26
28
30
32
34
231
202
176
155
137
235
202
176
155
137
207
181
158
139
123
210
181
158
139
123
124
107
93
82
124
107
93
82
109
94
82
72
109
94
82
72
96
83
72
64
96
83
72
64
38
41
110
94
110
94
98
85
98
85
P wo (kips)
P wi (kips/in.)
P wb (kips)
P fb (kips)
L p (ft)
L r (ft)
2.41
89
13
106
83
10.5
38.3
2.22
124
18
125
115
8.9
27.0
2.39
78
12
94
67
10.3
35.8
2.16
108
17
111
93
8.8
25.6
2.51
127
19
136
115
6.9
21.6
2.79
75
12
86
67
8.1
28.4
2.37
105
17
101
93
6.9
20.3
2.69
66
11
59
54
8.0
26.5
2.22
92
15
69
75
6.8
19.3
Effective length KL (ft) with respect to least radius of gyration ry
36
0
Properties
u
A (in.2)
Ix (in.4)
Iy (in.4)
ry (in.)
Ratio rx / ry
Pex (KL )2 / 10 4
Pey (KL )2 / 10 4
17.0
475
107
2.51
2.10
13600
3070
15.6
425
95.8
2.48
2.11
12200
2750
2.85
92
13
116
83
8.2
30.8
14.7
394
56.3
1.96
2.64
11300
1620
13.2
350
50
1.94
2.65
10000
1420
Note: Heavy line indicates Kl / r of 200.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
11.8
310
44.1
1.93
2.66
8890
1260
3 - 26
COLUMN DESIGN
Y
Fy = 36 ksi
Fy = 50 ksi
X
COLUMNS
W shapes
Design axial strength in kips (φ = 0.85)
X
Y
Designation
W10
Wt./ft
112
Fy
100
88
77
68
50
36
50
36
50
36
50
36
50
1010
1400
900
1250
793
1100
692
961
612
850
6
7
8
9
10
969
956
941
924
906
1330
1300
1270
1240
1210
865
853
840
824
808
1180
1160
1140
1110
1080
762
751
739
725
710
1040
1020
999
973
945
664
655
644
632
618
908
890
869
847
822
588
579
569
558
547
803
787
769
749
727
11
12
13
14
15
886
865
842
819
794
1170
1130
1090
1050
1010
789
770
750
728
706
1040
1010
970
931
892
694
677
659
639
619
916
884
851
817
782
604
588
572
555
537
796
768
738
708
677
534
520
506
490
475
703
678
652
625
597
16
17
18
19
20
768
742
715
688
660
961
915
870
824
778
682
659
634
609
584
851
810
769
727
686
599
577
556
534
511
746
709
672
635
599
519
500
481
461
442
645
612
580
547
515
458
441
424
407
389
569
540
511
482
454
22
24
26
28
30
604
548
493
440
389
688
601
518
447
389
534
483
434
386
340
605
527
453
390
340
466
422
378
336
295
527
458
393
339
295
402
362
324
287
252
452
392
335
289
252
354
319
285
252
221
398
344
294
254
221
32
34
36
38
40
342
303
270
242
219
342
303
270
242
219
299
265
236
212
191
299
265
236
212
191
259
230
205
184
166
259
230
205
184
166
221
196
175
157
141
221
196
175
157
141
194
172
153
138
124
194
172
153
138
124
P wo (kips)
P wi (kips/in.)
P wb (kips)
P fb (kips)
L p (ft)
L r (ft)
2.06
255
27
1210
316
11.2
86.4
2.02
354
38
1430
439
9.5
56.5
2.06
214
24
883
254
11.0
77.4
2.01
298
34
1040
353
9.4
50.8
1.99
246
30
735
276
9.3
45.1
2.03
143
19
420
153
10.8
60.0
1.96
199
27
495
213
9.2
39.8
2.01
116
17
293
120
10.8
53.8
1.93
162
24
345
167
9.2
36.0
Effective length KL (ft) with respect to least radius of gyration ry
36
0
Properties
u
A (in.2)
Ix (in.4)
Iy (in.4)
ry (in.)
Ratio rx / ry
Pex (KL )2 / 10 4
Pey (KL )2 / 10 4
32.9
716
236
2.68
1.74
20400
6760
29.4
623
207
2.65
1.74
17800
5910
2.04
177
22
623
198
11.0
68.4
25.9
534
179
2.63
1.73
15300
5130
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
22.6
455
154
2.60
1.73
13000
4370
20.0
394
134
2.59
1.71
11300
3840
DESIGN STRENGTH OF COLUMNS
3 - 27
Y
Fy = 36 ksi
Fy = 50 ksi
COLUMNS
W shapes
Design axial strength in kips (φ = 0.85)
X
X
Y
Designation
W10
Wt./ft
60
Fy
54
49
45
39
33
50
36
50
36
50
36
50
36
50
36
50
539
748
483
672
441
612
407
565
352
489
297
413
6
7
8
9
10
517
509
500
491
480
706
692
675
657
638
464
457
449
440
431
634
621
606
590
572
422
416
409
401
392
577
565
551
536
520
380
371
361
350
337
515
497
478
458
436
328
320
311
301
290
444
428
412
393
374
276
269
261
252
243
373
360
345
329
312
11
12
13
14
15
469
457
444
430
416
617
595
571
547
523
420
409
398
385
373
553
533
512
490
468
382
372
361
350
338
502
484
464
444
424
324
311
296
282
267
412
388
364
339
314
278
266
254
241
228
353
332
310
289
267
233
222
211
200
189
294
276
257
238
220
16
17
18
19
20
401
387
371
356
340
497
472
446
421
395
360
346
332
318
304
445
422
399
376
353
326
314
301
288
275
403
382
361
340
319
252
237
222
207
192
290
266
243
221
199
215
201
188
175
162
246
225
205
185
167
177
166
155
144
133
202
184
167
150
135
22
24
26
28
30
309
278
248
219
191
346
299
255
220
191
276
248
221
195
170
309
266
227
196
170
250
224
199
175
153
278
239
204
176
153
164
138
118
102
88
164
138
118
102
88
138
116
99
85
74
138
116
99
85
74
112
94
80
69
60
112
94
80
69
60
32
33
34
36
168
158
149
133
168
158
149
133
150
141
133
118
150
141
133
118
134
126
119
106
134
126
119
106
78
73
78
73
65
61
65
61
53
53
P wo (kips)
P wi (kips/in.)
P wb (kips)
P fb (kips)
L p (ft)
L r (ft)
2.00
99
15
209
94
10.7
48.1
1.90
138
21
246
130
9.1
32.6
1.97
83
13
143
77
10.7
43.9
1.87
116
19
168
106
9.1
30.2
2.37
79
13
121
78
8.4
35.2
2.17
109
18
142
108
7.1
24.1
2.31
64
11
88
57
8.3
31.2
2.04
89
16
104
79
7.0
21.9
2.23
55
10
69
38
8.1
27.4
1.87
77
14
81
53
6.9
19.7
Effective length KL (ft) with respect to least radius of gyration ry
36
0
Properties
u
A (in.2)
Ix (in.4)
Iy (in.4)
ry (in.)
Ratio rx / ry
Pex (KL )2 / 10 4
Pey (KL )2 / 10 4
17.6
341
116
2.57
1.71
9710
3330
15.8
303
103
2.56
1.71
8640
2960
1.96
73
12
111
64
10.6
40.7
1.83
101
17
131
88
9.0
28.3
14.4
272
93.4
2.54
1.71
7800
2660
13.3
248
53.4
2.01
2.15
7100
1540
Note: Heavy line indicates Kl / r of 200.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
11.5
209
45.0
1.98
2.16
6000
1290
9.71
170
36.6
1.94
2.16
4880
1050
3 - 28
COLUMN DESIGN
Y
Fy = 36 ksi
Fy = 50 ksi
X
COLUMNS
W shapes
Design axial strength in kips (φ = 0.85)
X
Y
Designation
W8
Wt./ft
67
Fy
58
48
40
35
31
50
36
50
36
50
36
50
36
50
36
50
603
837
523
727
431
599
358
497
315
438
279
388
6
7
8
9
10
567
555
541
526
509
770
746
721
693
662
492
481
469
455
441
667
647
624
599
572
405
396
386
374
362
549
532
513
492
470
335
327
319
309
298
454
439
423
405
386
295
288
280
272
262
399
386
372
356
339
261
255
248
240
232
354
342
329
315
300
11
12
13
14
15
492
473
453
433
412
631
598
564
529
494
425
409
391
374
355
544
515
485
455
425
349
335
321
306
291
446
422
397
372
347
287
275
263
251
238
366
345
324
303
281
252
242
231
220
208
321
303
284
265
246
223
214
204
194
184
284
268
251
234
217
16
17
18
19
20
391
370
349
328
307
460
425
392
359
328
337
318
300
281
263
394
365
335
307
279
276
260
245
229
214
321
297
272
249
226
225
211
198
185
173
260
239
219
199
180
197
185
174
162
151
228
209
191
174
157
174
163
153
143
133
200
184
168
153
138
22
24
26
28
30
266
228
194
167
146
271
228
194
167
146
228
194
165
143
124
231
194
165
143
124
185
157
134
115
100
187
157
134
115
100
148
125
107
92
80
149
125
107
92
80
129
109
93
80
70
130
109
93
80
70
114
96
82
70
61
114
96
82
70
61
32
33
34
35
128
120
113
107
128
120
113
107
109
103
97
91
109
103
97
91
88
83
78
88
83
78
70
66
62
70
66
62
61
58
61
58
54
51
54
51
P wo (kips)
P wi (kips/in.)
P wb (kips)
P fb (kips)
L p (ft)
L r (ft)
2.03
147
21
648
177
8.8
64.0
1.96
205
28
764
246
7.5
41.9
2
120
18
464
133
8.8
55.9
1.93
167
26
547
185
7.4
36.8
1.93
69
13
163
64
8.5
39.1
1.8
96
18
192
88
7.2
26.5
1.89
56
11
104
50
8.5
35.1
1.74
78
16
123
69
7.2
24.1
1.85
48
10
81
38
8.4
32.0
1.65
67
14
95
53
7.1
22.4
Effective length KL (ft) with respect to least radius of gyration ry
36
0
Properties
u
A (in.2)
Ix (in.4)
Iy (in.4)
ry (in.)
Ratio rx / ry
Pex (KL )2 / 10 4
Pey (KL )2 / 10 4
19.7
272
88.6
2.12
1.75
7800
2530
17.1
228
75.1
2.10
1.74
6520
2160
1.97
86
14
224
95
8.7
46.7
1.87
119
20
264
132
7.4
31.1
14.1
184
60.9
2.08
1.74
5260
1750
11.7
146
49.1
2.04
1.73
4170
1390
Note: Heavy line indicates Kl / r of 200.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
10.3
127
42.6
2.03
1.73
3630
1210
9.13
110
37.1
2.02
1.72
3150
1070
DESIGN STRENGTH OF COLUMNS
3 - 29
Y
Fy = 36 ksi
Fy = 50 ksi
COLUMNS
W shapes
Design axial strength in kips (φ = 0.85)
X
X
Y
Designation
W8
Wt./ft
W6
28
Fy
24
25
20
15
†
50
36
50
36
50
36
50
36
50†
252
351
217
301
225
312
180
249
136
188
6
7
8
9
10
228
219
210
200
189
303
288
271
253
235
195
188
180
171
162
260
247
232
217
200
200
191
182
172
162
265
250
233
216
198
159
152
145
137
128
211
198
185
171
156
119
114
108
102
95
158
148
137
126
115
11
12
13
14
15
178
167
155
143
132
216
197
178
160
142
152
142
132
122
112
184
168
151
136
121
151
140
129
118
107
180
162
144
128
112
119
111
102
93
84
142
127
113
100
87
88
81
74
68
61
104
92
82
71
62
16
17
18
19
20
121
110
99
89
80
125
111
99
89
80
102
93
84
75
68
106
94
84
75
68
97
87
78
70
63
98
87
78
70
63
76
68
60
54
49
76
68
60
54
49
55
48
43
39
35
55
48
43
39
35
22
24
25
26
27
66
56
51
47
44
66
56
51
47
44
56
47
44
40
56
47
44
40
52
44
40
52
44
40
40
34
31
40
34
31
29
24
29
24
P wo (kips)
P wi (kips/in.)
P wb (kips)
P fb (kips)
L p (ft)
L r (ft)
2.17
48
10
81
44
6.8
27.2
1.87
67
14
95
61
5.7
18.8
2.07
39
9
52
32
6.7
24.3
1.71
54
12
61
45
5.7
17.2
1.98
65
16
172
58
5.4
21.0
2.03
35
9
78
27
6.3
25.6
1.91
49
13
92
37
5.3
17.6
1.98
26
8
54
14
6.7
20.8
1.75
36
12
64
19
6.8
15.0
Effective length KL (ft) with respect to least radius of gyration ry
36
0
Properties
u
A (in.2)
Ix (in.4)
Iy (in.4)
ry (in.)
Ratio rx / ry
Pex (KL )2 / 10 4
Pey (KL )2 / 10 4
8.25
98.0
21.7
1.62
2.13
2810
620
7.08
82.8
18.3
1.61
2.12
2370
525
2.07
47
12
146
42
6.3
31.2
7.34
53.4
17.1
1.52
1.78
1530
485
5.87
41.4
13.3
1.50
1.77
1190
378
†Flange is noncompact; see discussion preceding column load tables.
Note: Heavy line indicates Kl / r of 200.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
4.43
29.1
9.32
1.46
1.75
831
270
3 - 30
COLUMN DESIGN
Y
Fy = 36 ksi
Fy = 50 ksi
X
X
COLUMNS
W shapes
Design axial strength in kips (φ = 0.85)
Y
Designation
W6
Wt./ft
16
Effective length KL (ft) with respect to least radius of gyration ry
Fy
W5
12
9
W4
19
16
13
36
50
36
50
36
50
36
50
36
50
36
50
0
145
201
109
151
82
114
170
235
143
199
117
163
2
3
4
5
6
140
135
127
118
108
193
182
168
152
134
105
100
94
87
79
144
135
124
110
96
79
75
71
65
59
108
101
93
83
72
166
163
157
151
144
229
222
212
201
187
141
137
133
127
121
194
188
179
169
157
114
109
104
97
89
156
148
138
125
111
7
8
9
10
11
97
86
75
64
54
116
98
81
66
54
70
61
52
44
37
82
68
55
44
37
52
45
39
32
27
61
50
40
33
27
135
126
117
107
97
172
156
140
124
108
114
106
98
90
81
144
131
117
104
90
81
72
63
55
47
97
83
69
57
47
12
13
14
15
16
46
39
33
29
26
46
39
33
29
26
31
26
23
20
31
26
23
20
23
19
17
14
23
19
17
14
87
78
68
60
53
93
80
69
60
53
73
65
57
50
44
78
66
57
50
44
39
34
29
25
22
39
34
29
25
22
47
42
37
34
30
47
42
37
34
30
39
35
31
28
25
39
35
31
28
25
1.84
39
10
115
37
5.3
30.3
1.72
55
14
136
52
4.5
20.1
1.79
32
9
81
26
5.3
26.2
1.63
45
12
95
36
4.5
17.6
1.89
35
10
164
24
4.2
25.5
1.77
48
14
193
33
3.5
16.8
17
18
19
20
21
Properties
u
P wo (kips)
P wi (kips/in.)
P wb (kips)
P fb (kips)
L p (ft)
L r (ft)
A (in.2)
Ix (in.4)
Iy (in.4)
ry (in.)
Ratio rx / ry
Pex (KL )2 / 10 4
Pey (KL )2 / 10 4
2.84
35
9
78
33
4.0
18.3
2.5
49
13
92
46
3.4
12.5
4.74
32.1
4.43
0.966
2.69
917
127
2.62
26
8
54
16
3.8
14.3
2.13
36
12
64
22
3.2
10.2
3.55
22.1
2.99
0.918
2.71
630
85.6
2.24
17
6
22
9
3.8
12.0
1.72
24
9
26
13
3.2
8.9
2.68
16.4
2.19
0.905
2.73
468
62.8
5.54
26.2
9.13
1.28
1.70
747
260
Note: Heavy line indicates Kl / r of 200.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
4.68
21.3
7.51
1.27
1.68
608
216
3.83
11.3
3.86
1.00
1.72
324
110
DESIGN STRENGTH OF COLUMNS
3 - 31
Y
Fy = 36 ksi
Fy = 50 ksi
COLUMNS
HP shapes
Design axial strength in kips (φ = 0.85)
X
X
Y
Designation
HP14
Wt./ft
117
Fy
HP13
102
89
73
100
50
36
50
36
50
36
50
36
50
1050
1460
918
1280
799
1110
655
909
900
1250
6
7
8
9
10
1030
1020
1010
1000
993
1420
1400
1390
1370
1350
898
891
884
875
865
1240
1220
1210
1190
1170
781
775
768
760
752
1080
1060
1050
1040
1020
640
635
629
623
615
882
872
861
848
834
875
867
857
846
834
1200
1190
1170
1150
1120
11
12
13
14
15
980
967
953
938
922
1320
1300
1270
1250
1220
854
842
830
816
802
1150
1130
1110
1080
1060
742
732
721
709
696
1000
982
962
940
917
607
599
589
580
569
819
803
786
768
749
821
806
791
775
758
1100
1070
1050
1020
986
16
17
18
19
20
905
888
870
851
832
1190
1150
1120
1090
1050
788
772
756
740
723
1030
1000
974
945
915
683
670
656
641
626
893
869
844
818
791
558
547
535
523
511
729
708
687
666
644
741
722
703
684
664
954
921
888
854
820
22
24
26
28
30
792
750
707
664
620
985
913
842
771
701
687
650
613
574
536
853
790
727
665
604
595
563
529
496
462
737
682
627
572
519
485
458
430
402
374
599
553
507
462
418
623
581
539
496
454
750
681
613
547
483
32
34
36
38
40
576
533
491
450
411
633
568
507
455
411
498
460
423
387
352
545
487
435
390
352
428
395
363
332
301
467
417
372
334
301
346
319
292
267
241
375
334
298
267
241
413
374
336
301
272
425
376
336
301
272
P wo (kips)
P wi (kips/in.)
P wb (kips)
P fb (kips)
L p (ft)
L r (ft)
217
29
1010
131
15.0
66.0
302
40
1191
182
12.7
45.1
174
25
679
101
14.8
59.0
242
35
801
140
12.6
41.1
202
31
533
106
12.5
37.6
108
18
250
52
14.5
46.8
150
25
294
72
12.3
34.2
198
28
953
119
13.2
60.1
275
38
1123
165
11.2
40.9
Effective length KL (ft) with respect to least radius of gyration ry
36
0
Properties
A (in.2)
Ix (in.4)
Iy (in.4)
ry (in.)
Ratio rx / ry
Pex (KL )2 / 10 4
Pey (KL )2 / 10 4
34.4
1220
443
3.59
1.66
35000
12700
30.0
1050
380
3.56
1.66
30100
10900
145
22
453
77
14.7
53.0
26.1
904
326
3.53
1.67
25800
9310
21.4
729
261
3.49
1.67
20900
7460
Note: Heavy line indicates Kl / r of 200.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
29.4
886
294
3.16
1.74
25400
8400
3 - 32
COLUMN DESIGN
Y
Fy = 36 ksi
Fy = 50 ksi
X
COLUMNS
HP shapes
Design axial strength in kips (φ = 0.85)
X
Y
Designation
HP13
Wt./ft
87
Fy
HP12
73
60
84
74
50
36
50
36
50
36
50
36
50
780
1080
661
918
536
744
753
1050
667
927
6
7
8
9
10
759
751
743
733
722
1040
1030
1010
993
973
642
636
628
620
611
882
870
856
840
823
520
515
509
502
494
714
704
692
679
665
729
721
712
701
690
1000
985
967
947
926
646
639
630
621
610
886
872
856
838
819
11
12
13
14
15
711
698
685
670
656
952
928
904
878
851
601
590
578
566
553
804
784
763
741
717
486
477
467
457
447
650
633
616
597
578
677
663
649
634
618
902
877
851
823
795
599
587
574
560
546
798
776
752
727
702
16
17
18
19
20
640
624
607
590
573
823
794
765
735
705
540
526
512
497
482
693
669
644
618
592
436
424
413
401
388
559
539
518
497
476
601
584
567
548
530
765
735
705
674
642
531
516
500
484
467
675
648
621
593
565
22
24
26
28
30
537
500
462
425
389
644
584
524
467
411
451
420
388
356
325
540
488
438
389
342
363
337
311
285
260
433
391
350
310
272
492
454
416
378
342
580
518
459
402
350
434
400
366
332
300
510
455
402
351
306
32
34
36
38
40
353
319
286
256
231
361
320
286
256
231
295
266
237
213
192
300
266
237
213
192
235
211
189
169
153
239
211
189
169
153
307
273
243
218
197
308
273
243
218
197
268
238
213
191
172
269
238
213
191
172
P wo (kips)
P wi (kips/in.)
P wb (kips)
P fb (kips)
L p (ft)
L r (ft)
165
24
624
90
13.0
53.2
229
33
735
124
11.1
36.9
127
20
384
65
12.9
47.0
177
28
453
90
11.0
33.4
129
23
243
60
10.9
30.2
170
25
732
95
12.3
54.0
235
34
862
132
10.4
36.9
143
22
506
75
12.2
48.9
199
30
597
105
10.3
34.0
Effective length KL (ft) with respect to least radius of gyration ry
36
0
Properties
A (in.2)
Ix (in.4)
Iy (in.4)
ry (in.)
Ratio rx / ry
Pex (KL )2 / 10 4
Pey (KL )2 / 10 4
25.5
755
250
3.13
1.74
21700
7150
21.6
630
207
3.10
1.74
18000
5940
93
17
206
43
12.8
41.2
17.5
503
165
3.07
1.75
14400
4720
Note: Heavy line indicates Kl / r of 200.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
24.6
650
213
2.94
1.75
18600
6090
21.8
569
186
2.92
1.75
16300
5320
DESIGN STRENGTH OF COLUMNS
3 - 33
Y
Fy = 36 ksi
Fy = 50 ksi
COLUMNS
HP shapes
Design axial strength in kips (φ = 0.85)
X
X
Y
Designation
HP12
Wt./ft
HP10
63
Fy
53
HP8
57
42
36
50
36
50
36
50
36
50
36
50
563
782
474
659
514
714
379
527
324
451
6
7
8
9
10
545
538
531
523
514
747
735
721
706
689
459
453
447
440
432
629
618
607
594
579
491
483
474
464
453
670
655
638
619
599
362
356
349
341
333
494
482
469
455
440
302
294
286
276
266
408
393
377
360
342
11
12
13
14
15
504
494
482
471
458
671
651
631
610
588
424
415
406
396
385
564
547
530
512
493
441
429
415
401
387
577
555
531
506
481
324
314
304
294
283
423
406
388
369
350
255
243
232
219
207
322
302
282
262
242
16
17
18
19
20
446
432
419
405
391
565
542
518
495
471
374
363
351
339
327
474
454
434
414
394
372
357
341
326
310
456
430
404
379
354
272
260
249
237
225
331
312
293
274
255
195
182
170
158
146
222
202
184
165
149
22
24
26
28
30
362
333
304
275
247
423
376
332
288
251
303
278
253
229
206
353
314
276
240
209
279
248
219
191
166
305
259
221
191
166
202
179
157
136
119
219
185
158
136
119
123
104
88
76
66
123
104
88
76
66
32
34
36
38
40
221
196
174
157
141
221
196
174
157
141
183
163
145
130
117
183
163
145
130
117
146
129
115
103
93
146
129
115
103
93
104
92
82
74
67
104
92
82
74
67
58
52
46
41
37
58
52
46
41
37
P wo (kips)
P wi (kips/in.)
P wb (kips)
P fb (kips)
L p (ft)
L r (ft)
116
19
311
54
12.0
43.0
161
26
366
75
10.2
30.7
88
16
188
38
11.9
38.7
122
22
221
53
10.1
28.3
168
28
599
90
8.7
31.1
79
15
202
36
10.0
35.9
110
21
238
50
8.5
25.6
75
16
309
40
8.1
35.7
104
22
364
56
6.9
24.4
Effective length KL (ft) with respect to least radius of gyration ry
36
0
Properties
A (in.2)
Ix (in.4)
Iy (in.4)
ry (in.)
Ratio rx / ry
Pex (KL )2 / 10 4
Pey (KL )2 / 10 4
18.4
472
153
2.88
1.76
13500
4370
15.5
393
127
2.86
1.76
11200
3630
121
20
508
65
10.2
45.6
16.8
294
101
2.45
1.71
8400
2890
12.4
210
71.7
2.41
1.71
6050
2060
Note: Heavy line indicates Kl / r of 200.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
10.6
119
40.3
1.95
1.72
3420
1150
3 - 34
COLUMN DESIGN
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
DESIGN STRENGTH OF COLUMNS
3 - 35
Steel Pipe and Structural Tubing
The design strengths in the tables that follow are tabulated for the effective lengths in
feet KL (with respect to the least radius of gyration, r or ry), indicated at the left of each
table. They are applicable to axially loaded members in accordance with Section E2 of
the LRFD Specification.
For discussion of effective length, range of l / r, strength about major axis, combined
axial and bending stress, and sample problems, see General Notes. Properties and factors
are listed at the bottom of the tables for checking strength about the strong axis.
Steel Pipe Columns
Design strengths for unfilled pipe columns are tabulated for Fy = 36 ksi. Steel pipe
manufactured to ASTM A501 furnishes Fy = 36 ksi, and ASTM A53, Type E or S, Gr. B
furnishes Fy = 35 ksi and may be designed for the strengths permitted for Fy = 36 ksi steel.
The heavy horizontal lines within the table indicate Kl / r = 200. No values are listed
beyond Kl / r = 200.
Structural Tube Columns
Design strengths for square and rectangular structural tube columns are tabulated for Fy
= 46 ksi. Structural tubing is manufactured to Fy = 46 ksi under ASTM A500, Gr. B.
All tubes listed in the column load tables satisfy Section B5 of the LRFD Specification.
The heavy horizontal lines appearing within the tables indicate Kl / r = 200. No values
are listed beyond Kl / r = 200.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
3 - 36
COLUMN DESIGN
Fy = 36 ksi
COLUMNS
Standard steel pipe
Design axial strength in kips (φ = 0.85)
Nominal Dia.
12
10
8
6
5
4
31⁄2
3
Wall Thickness
0.375
0.365
0.322
0.280
0.258
0.237
0.226
0.216
Weight per ft
49.56
40.48
28.55
18.97
14.62
10.79
9.11
7.58
Fy
Effective length KL (ft)
36 ksi
0
447
364
257
171
132
97
82
68
6
7
8
9
10
440
438
436
433
429
357
354
351
348
344
249
246
243
239
235
162
159
155
151
147
122
118
115
111
106
86
82
78
74
70
70
67
63
58
54
56
52
48
43
39
11
12
13
14
15
426
422
418
413
409
340
336
331
326
321
231
227
222
216
211
142
138
133
127
122
102
97
92
86
81
65
60
55
51
46
49
45
40
36
32
35
30
26
23
20
16
17
18
19
20
404
399
393
387
381
315
309
303
297
291
205
199
193
187
181
116
111
105
99
94
76
71
66
61
56
41
37
33
30
27
28
25
22
20
18
17
15
14
12
22
24
25
26
28
369
356
349
342
328
277
263
256
249
234
168
155
149
142
129
83
72
67
62
53
47
39
36
33
29
22
19
17
15
30
31
32
34
36
313
306
298
283
268
219
212
205
190
176
117
111
105
93
83
47
44
41
36
32
25
23
37
38
40
260
253
237
169
162
148
79
75
67
31
3.17
7.23
1.51
2.68
4.79
1.34
Properties
2
Area A (in. )
I (in.4)
r (in.)
14.6
279
4.38
11.9
161
3.67
8.40
72.5
2.94
5.58
28.1
2.25
4.30
15.2
1.88
Note: Heavy line indicates Kl / r of 200.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
2.23
3.02
1.16
DESIGN STRENGTH OF COLUMNS
3 - 37
Fy = 36 ksi
COLUMNS
Extra strong steel pipe
Design axial strength in kips (φ = 0.85)
Nominal Dia.
12
10
8
6
5
4
31⁄2
3
Wall Thickness
0.500
0.500
0.500
0.432
0.375
0.337
0.318
0.300
Weight per ft
65.42
54.74
43.39
28.57
20.78
14.98
12.50
10.25
Effective length KL (ft)
Fy
36 ksi
0
588
493
392
257
187
135
113
92
6
7
8
9
10
579
576
573
569
564
483
479
475
470
465
379
375
369
364
357
243
238
232
226
219
172
168
162
156
149
119
114
108
102
95
96
91
85
79
72
75
69
64
58
52
11
12
13
14
15
559
554
549
543
536
460
453
447
440
433
351
343
336
327
319
212
205
197
189
180
143
135
128
121
113
89
82
75
68
62
66
60
53
47
42
46
40
34
30
26
16
18
19
20
21
530
515
508
500
492
425
409
400
391
382
310
291
282
272
262
172
154
145
137
128
105
91
83
76
70
56
44
40
36
32
37
29
26
23
21
23
18
16
22
24
26
28
30
483
465
447
428
408
373
354
334
314
294
252
231
211
191
172
120
103
88
76
66
63
53
45
39
34
30
25
32
34
36
38
40
388
368
348
328
308
273
253
234
215
196
154
136
121
109
98
58
52
46
19.2
362
4.33
16.1
212
3.63
12.8
106
2.88
6.11
20.7
1.84
4.41
9.61
1.48
3.68
6.28
1.31
3.02
3.89
1.14
Properties
Area A (in.2)
I (in.4)
r (in.)
8.40
40.5
2.19
Note: Heavy line indicates Kl / r of 200.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
3 - 38
COLUMN DESIGN
Fy = 36 ksi
COLUMNS
Double-extra strong steel pipe
Design axial strength in kips (φ = 0.85)
Nominal Dia.
8
6
5
4
3
Wall Thickness
0.875
0.864
0.750
0.674
0.600
Weight per ft
72.42
53.16
38.55
27.54
18.58
Effective length KL (ft)
Fy
36 ksi
0
652
477
346
248
167
6
7
8
9
10
629
621
612
601
590
448
437
426
413
399
315
305
293
281
268
214
203
191
179
165
131
120
108
96
84
11
12
13
14
15
578
565
551
536
521
385
369
353
336
319
254
239
224
209
194
152
139
125
112
100
73
62
53
46
40
16
17
18
19
20
505
489
472
455
438
302
285
268
250
234
179
165
151
137
124
88
78
70
62
56
35
31
22
24
26
28
30
403
367
333
299
266
201
170
145
125
109
102
86
73
63
47
32
34
36
38
40
235
208
186
166
150
96
85
21.3
162
2.76
15.6
66.3
2.06
11.3
33.6
1.72
8.10
15.3
1.37
Properties
Area A (in.2)
I (in.4)
r (in.)
Note: Heavy line indicates Kl / r of 200.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
5.47
5.99
1.05
DESIGN STRENGTH OF COLUMNS
3 - 39
Fy = 46 ksi
COLUMNS
Square structural tubing
Design axial strength in kips (φ = 0.85)
Nominal Size
16×
×16
Thickness
1⁄
Wt./ft
103.30
89.68
68.31
0
1190
1030
786
6
7
8
9
10
1180
1170
1170
1170
1160
1020
1020
1010
1010
1000
11
12
13
14
15
1150
1150
1140
1130
1120
16
17
18
19
20
2
14×
×14
1⁄
2
12×
×12
3⁄
8
8
93.34
1⁄
2
3⁄
8
5⁄
16
76.07
58.10
48.86
1070
876
669
563
777
774
770
766
761
1050
1050
1040
1030
1020
862
857
851
845
838
658
655
650
645
640
554
551
548
544
539
993
985
977
969
960
756
751
745
739
732
1010
1000
992
979
966
830
821
812
803
792
634
628
621
614
606
535
529
524
518
511
1120
1110
1100
1090
1080
950
940
930
919
907
725
717
710
701
693
953
939
924
908
892
781
770
758
746
733
598
590
581
571
562
504
497
490
482
474
21
22
23
24
25
1070
1060
1040
1030
1020
895
883
870
857
844
684
675
665
655
645
875
858
841
823
805
719
706
692
677
663
552
542
531
520
510
466
457
449
440
431
26
27
28
29
30
1010
994
981
967
954
830
816
802
787
772
635
624
614
603
592
786
767
748
729
710
648
633
617
602
586
498
487
475
464
452
421
412
402
392
383
32
34
36
38
40
925
896
865
835
803
742
711
680
648
616
569
546
522
498
474
670
631
592
553
515
555
523
491
460
429
428
404
381
357
333
363
343
323
303
283
30.4
1200
6.29
26.4
791
5.48
27.4
580
4.60
22.4
485
4.66
17.1
380
4.72
14.4
324
4.75
Fy
Effective length KL (ft)
5⁄
46 ksi
Properties
A (in2)
I (in.4)
r (in.)
20.1
615
5.54
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
3 - 40
COLUMN DESIGN
Fy = 46 ksi
COLUMNS
Square structural tubing
Design axial strength in kips (φ = 0.85)
10×
×10
Nominal Size
Thickness
Wt./ft
76.33
62.46
47.90
40.35
32.63
0
876
719
551
465
375
6
7
8
9
10
855
847
839
829
818
703
697
690
682
674
539
534
529
524
517
455
451
447
442
437
11
12
13
14
15
807
794
781
767
752
664
655
644
633
621
510
503
495
487
478
16
17
18
19
20
736
720
703
686
668
608
595
582
568
553
21
22
23
24
25
650
631
612
593
573
26
27
28
29
30
32
34
36
38
40
8
1⁄
2
3⁄
8×
×8
5⁄
8
5⁄
16
4
5⁄
8
59.32
1⁄
2
3⁄
8
5⁄
16
1⁄
4
48.85
37.69
31.84
25.82
680
563
434
366
297
367
364
360
357
353
654
644
634
622
609
542
535
526
517
507
418
413
407
400
392
353
349
343
338
331
287
283
279
274
269
431
425
418
411
404
348
343
338
332
326
595
580
564
548
531
496
484
471
458
444
384
375
366
356
345
324
317
309
301
293
264
258
252
245
238
468
459
449
438
427
396
388
380
371
362
320
314
307
300
293
513
494
476
456
437
430
415
400
385
369
335
324
312
301
289
284
275
265
256
246
231
224
216
209
201
538
523
508
493
477
416
405
394
382
370
353
343
334
324
314
286
278
270
263
255
418
398
379
360
341
354
338
322
307
291
277
266
254
242
230
236
226
216
206
196
193
185
177
169
161
554
534
515
495
476
461
446
430
414
398
358
347
335
323
311
305
295
285
275
265
247
239
231
223
215
322
304
286
268
251
276
261
246
232
218
219
207
196
185
174
187
177
168
158
149
153
146
138
131
123
437
400
364
328
296
367
337
307
278
251
287
264
242
220
199
245
225
206
188
170
199
184
168
154
139
221
195
174
156
141
191
169
151
136
122
153
136
121
109
98
132
117
104
93
84
109
97
86
77
70
22.4
321
3.78
18.4
271
3.84
14.1
214
3.90
11.9
183
3.93
17.4
153
2.96
14.4
131
3.03
11.1
106
3.09
9.36
90.9
3.12
7.59
75.1
3.15
Fy
Effective length KL (ft)
1⁄
46 ksi
Properties
A (in2)
I (in.4)
r (in.)
9.59
151
3.96
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
DESIGN STRENGTH OF COLUMNS
3 - 41
Fy = 46 ksi
COLUMNS
Square structural tubing
Design axial strength in kips (φ = 0.85)
7×
×7
Nominal Size
Thickness
5⁄
8
1⁄
2
3⁄
8
6×
×6
5⁄
16
1⁄
4
3⁄
16
5⁄
8
1⁄
2
3⁄
8
5⁄
16
1⁄
4
3⁄
16
50.81 42.05 32.58 27.59 22.42 17.08 42.30 35.24 27.48 23.34 19.02 14.53
Fy
46 ksi
Effective length KL (ft)
Wt./ft
0
584
485
375
317
258
196
486
407
316
268
219
167
6
7
8
9
10
553
543
531
518
503
461
452
443
432
421
357
351
344
336
327
302
297
291
285
278
246
242
237
232
226
188
185
181
177
173
451
438
425
410
394
379
369
358
346
333
295
288
280
271
262
251
245
239
231
223
205
200
195
189
183
157
153
149
145
140
11
12
13
14
15
488
472
454
437
418
409
396
382
368
353
318
308
298
288
277
270
262
254
245
236
220
214
207
200
193
168
164
159
153
148
377
359
341
322
303
320
306
291
276
260
252
241
230
219
207
215
206
197
187
178
176
169
162
154
146
135
130
124
119
113
16
17
18
19
20
399
380
361
342
323
338
322
307
291
276
265
254
242
230
218
226
217
207
197
187
185
177
170
162
154
142
136
130
124
118
284
265
246
227
210
245
229
214
199
184
195
184
172
160
149
168
158
148
138
129
138
131
123
115
107
107
101
95
89
83
22
24
26
28
30
285
248
214
184
161
245
215
187
161
140
195
172
151
130
113
167
148
130
113
98
138
123
108
94
81
107
95
84
73
63
175
147
125
108
94
155
131
111
96
84
127
107
91
79
69
111
93
80
69
60
92
78
67
57
50
72
61
52
45
39
32
34
141
125
123
109
100
88
86
76
72
63
56
49
83
73
73
65
60
53
53
47
44
39
34
30
35
36
37
38
39
118
111
106
100
95
103
97
92
87
83
83
79
74
71
67
72
68
64
61
58
60
57
54
51
48
47
44
42
40
38
69
61
58
50
48
45
44
41
39
37
37
35
33
31
29
27
26
24
23
40
90
79
64
55
46
36
12.4
57.3
2.15
10.4
50.5
2.21
8.08
41.6
2.27
6.86
36.3
2.30
5.59
30.3
2.33
4.27
23.8
2.36
Properties
2
A (in )
I (in.4)
r (in.)
14.9
97.5
2.56
12.4
84.6
2.62
9.58
68.7
2.68
8.11
59.5
2.71
6.59
49.4
2.74
5.02
38.5
2.77
Note: Heavy line indicates Kl / r of 200.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
3 - 42
COLUMN DESIGN
Fy = 46 ksi
COLUMNS
Square structural tubing
Design axial strength in kips (φ = 0.85)
51⁄2×51⁄2
Nominal Size
5×
×5
Thickness
3⁄
8
5⁄
16
1⁄
4
3⁄
16
1⁄
2
3⁄
8
5⁄
16
1⁄
4
3⁄
16
1⁄
8
Wt./ft
24.93
21.21
17.32
13.25
28.43
22.37
19.08
15.62
11.97
8.16
Effective length KL (ft)
Fy
46 ksi
0
286
244
199
152
327
257
219
179
138
94
6
7
8
9
10
264
256
248
238
228
225
219
212
204
195
184
179
173
167
161
141
137
133
129
124
294
282
270
257
242
233
224
215
205
194
199
192
184
176
167
163
158
152
145
138
126
121
117
112
107
86
83
80
77
73
11
12
13
14
15
218
207
195
184
172
187
177
168
158
148
154
146
139
131
123
118
113
107
101
95
228
213
197
182
167
183
172
160
149
137
158
148
139
129
119
131
123
115
107
99
101
95
89
84
78
70
66
62
58
54
16
17
18
19
20
160
149
137
126
115
139
129
119
110
101
115
107
99
92
84
89
83
77
72
66
152
138
124
111
100
126
115
104
93
84
110
100
91
82
74
92
84
77
69
63
72
66
60
55
50
50
46
42
38
35
22
24
26
28
30
96
80
68
59
51
84
70
60
52
45
70
59
50
43
38
55
47
40
34
30
83
70
59
51
45
70
59
50
43
37
61
52
44
38
33
52
44
37
32
28
41
34
29
25
22
29
24
21
18
15
31
32
33
34
35
48
45
43
40
42
40
37
35
35
33
31
29
28
28
26
25
23
22
35
31
26
24
21
19
15
14
13
6.58
22.8
1.86
5.61
20.1
1.89
4.59
16.9
1.92
3.52
13.4
1.95
2.40
9.41
1.98
Properties
2
A (in )
I (in.4)
r (in.)
7.33
31.2
2.07
6.23
27.4
2.10
5.09
23.0
2.13
3.89
18.1
2.16
8.36
27.0
1.80
Note: Heavy line indicates Kl / r of 200.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
DESIGN STRENGTH OF COLUMNS
3 - 43
Fy = 46 ksi
COLUMNS
Square structural tubing
Design axial strength in kips (φ = 0.85)
41⁄2×41⁄2
Nominal Size
4×
×4
Thickness
3⁄
8
5⁄
16
1⁄
4
3⁄
16
1⁄
8
Wt./ft
19.82
16.96
13.91
10.70
7.31
Effective length KL (ft)
Fy
1⁄
2
3⁄
8
21.63
17.27
5⁄
16
1⁄
4
14.83 12.21
3⁄
16
1⁄
8
9.42
6.46
46 ksi
0
228
195
160
123
84
249
199
170
140
108
74
6
7
8
9
10
201
192
182
171
160
172
165
157
148
139
142
136
130
123
115
110
105
100
95
90
75
72
69
65
62
208
195
180
166
151
168
158
148
137
125
145
137
128
119
110
120
114
107
100
92
93
89
83
78
72
64
61
58
54
50
11
12
13
14
15
149
137
125
114
103
129
119
110
100
91
107
100
92
84
76
84
78
72
66
60
58
54
50
46
42
136
121
107
93
81
114
102
91
81
70
100
90
81
72
63
84
76
68
61
54
66
60
54
49
43
46
42
38
34
31
16
17
18
19
20
92
82
73
66
59
81
73
65
58
53
69
62
55
49
45
55
49
44
39
36
38
35
31
28
25
71
63
56
50
46
62
55
49
44
40
55
49
44
39
35
47
42
37
34
30
38
34
30
27
24
27
24
21
19
17
21
22
23
24
25
54
49
45
41
38
48
43
40
36
34
41
37
34
31
29
32
29
27
25
23
23
21
19
17
16
41
38
34
36
33
30
27
32
29
27
25
28
25
23
21
19
22
20
18
17
16
16
14
13
12
11
26
35
31
26
21
15
27
28
29
32
29
27
25
23
20
18
17
14
13
12
10
Properties
2
A (in )
I (in.4)
r (in.)
5.83
16.0
1.66
4.98
14.2
1.69
4.09
12.1
1.72
3.14
9.60
1.75
2.15
6.78
1.78
6.36
12.3
1.39
5.08
10.7
1.45
4.36
9.58
1.48
Note: Heavy line indicates Kl / r of 200.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
3.59
8.22
1.51
2.77
6.59
1.54
1.90
4.70
1.57
3 - 44
COLUMN DESIGN
Fy = 46 ksi
COLUMNS
Square structural tubing
Design axial strength in kips (φ = 0.85)
31⁄2×31⁄2
Nominal Size
3×
×3
Thickness
5⁄
16
1⁄
4
3⁄
16
1⁄
8
5⁄
16
1⁄
4
3⁄
16
1⁄
8
Wt./ft
12.7
10.51
8.15
5.61
10.58
8.81
6.87
4.75
0
146
121
93
65
122
101
79
55
6
7
8
9
10
118
109
100
90
81
99
92
84
76
69
77
72
66
60
54
54
50
46
42
39
90
80
71
61
52
76
68
61
53
45
60
54
49
43
37
42
39
35
31
27
11
12
13
14
15
71
62
54
46
40
61
54
46
40
35
49
43
38
32
28
35
31
27
23
20
44
37
31
27
23
38
32
27
24
21
32
27
23
19
17
23
20
17
14
12
16
17
18
19
20
35
31
28
25
23
31
27
24
22
20
25
22
20
18
16
18
16
14
13
11
21
18
18
16
14
15
13
12
11
10
9
8
21
22
21
18
14
13
10
9
3.73
6.09
1.28
3.09
5.29
1.31
2.39
4.29
1.34
3.11
3.58
1.07
2.59
3.16
1.10
2.02
2.60
1.13
1.40
1.90
1.16
Effective length KL (ft)
Fy
46 ksi
Properties
A (in2)
I (in.4)
r (in.)
1.65
3.09
1.37
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
DESIGN STRENGTH OF COLUMNS
3 - 45
Fy = 46 ksi
Y
COLUMNS
Rectangular structural tubing
Design axial strength in kips (φ = 0.85)
X
X
Y
Nominal Size 16×
×12
16×
×8
14×
×12
14×
×10
Thickness
1⁄
1⁄
1⁄
Wt./ft
89.68
76.07
82.88
63.21
76.07
0
1030
876
952
726
876
6
7
8
9
10
1020
1010
1010
998
990
848
838
827
815
801
938
933
927
920
912
715
712
707
702
697
11
12
13
14
15
982
973
963
952
941
786
771
754
736
717
904
895
886
876
865
16
17
18
19
20
929
916
903
889
875
697
677
657
635
614
22
24
26
28
30
845
813
781
746
711
32
34
36
38
40
676
640
604
568
533
2
2
2
3⁄
8
2
12×
×10
3⁄
8
58.10
1⁄
2
3⁄
8
5⁄
16
1⁄
4
69.27
53.00
44.60
36.03
669
796
609
513
414
857
850
843
834
825
655
650
644
638
631
778
772
765
757
748
596
591
586
580
573
502
498
493
488
483
405
402
399
395
390
691
684
677
669
661
815
803
791
779
765
623
615
606
597
587
738
728
716
704
692
566
558
550
541
531
477
470
463
456
448
386
380
375
369
363
854
842
829
816
803
653
644
634
625
615
751
737
721
705
689
576
565
554
542
530
679
665
650
636
620
522
511
501
489
478
440
431
422
413
404
356
349
342
335
327
569
525
480
436
393
774
744
713
681
648
593
571
548
524
499
655
620
584
547
511
504
478
451
424
396
589
556
522
488
454
454
430
404
379
353
384
363
342
321
300
311
295
278
261
244
352
313
279
250
226
615
581
547
514
480
474
448
423
398
372
474
438
403
369
335
368
341
315
289
264
420
387
355
324
293
328
302
278
254
231
278
257
237
217
197
227
210
193
177
162
17.1
476
284
1.29
4.08
20.4
419
316
1.15
3.94
15.6
330
249
1.15
4.00
13.1
281
213
1.15
4.03
10.6
230
174
1.15
4.06
Fy
Effective length KL (ft) with respect to least radius of gyration
1⁄
46 ksi
Properties
2
A (in )
Ix (in.4)
Iy (in.4)
rx / ry
ry (in.)
26.4
962
618
1.25
4.84
22.4
722
244
1.72
3.30
24.4
699
552
1.13
4.76
18.6
546
431
1.13
4.82
22.4
608
361
1.30
4.02
Note: Heavy line indicates Kl / r of 200.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
3 - 46
COLUMN DESIGN
Fy = 46 ksi
Y
X
X
COLUMNS
Rectangular structural tubing
Design axial strength in kips (φ = 0.85)
Y
12×
×8
Nominal Size
12×
×6
Thickness
5⁄
8
1⁄
2
3⁄
8
5⁄
16
5⁄
8
1⁄
2
3⁄
8
5⁄
16
Wt./ft
76.33
62.46
47.90
40.35
67.82
55.66
42.79
36.10
0
876
719
551
465
778
641
493
414
6
7
8
9
10
845
835
822
809
794
695
687
677
666
655
534
527
520
512
503
450
445
439
433
425
731
715
697
677
655
604
591
577
561
543
466
456
445
434
421
392
384
376
366
355
11
12
13
14
15
778
760
742
722
702
642
628
613
598
582
494
483
473
461
449
417
409
400
390
380
632
607
581
555
528
525
505
485
464
442
407
393
378
362
346
344
332
320
307
293
16
17
18
19
20
681
659
637
614
591
565
547
530
511
493
437
424
410
397
383
370
359
348
336
325
500
473
445
418
390
420
398
375
353
331
329
313
296
279
262
280
266
252
238
224
22
24
26
28
30
544
497
451
405
362
455
417
380
343
307
355
326
298
270
243
301
277
253
230
207
338
288
245
211
184
288
247
211
182
158
230
199
170
146
128
197
171
146
126
110
32
34
36
38
39
320
283
252
227
215
273
241
215
193
184
217
192
171
154
146
185
164
146
131
125
162
143
128
115
109
139
123
110
99
94
112
99
89
80
75
97
86
76
69
65
40
205
174
139
119
89
72
62
16.4
287
96.0
1.73
2.42
12.6
228
77.2
1.72
2.48
10.6
196
66.6
1.71
2.51
Effective length KL (ft) with respect to least radius of gyration
Fy
46 ksi
Properties
2
A (in )
Ix (in.4)
Iy (in.4)
rx / ry
ry (in.)
22.4
418
221
1.38
3.14
18.4
353
188
1.37
3.20
14.1
279
149
1.37
3.26
11.9
239
128
1.37
3.28
19.9
337
112
1.73
2.37
Note: Heavy line indicates Kl / r of 200.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
DESIGN STRENGTH OF COLUMNS
3 - 47
Fy = 46 ksi
Y
COLUMNS
Rectangular structural tubing
Design axial strength in kips (φ = 0.85)
X
X
Y
10×
×8
Nominal Size
10×
×6
Thickness
1⁄
2
3⁄
8
5⁄
16
1⁄
4
1⁄
2
3⁄
8
5⁄
16
1⁄
4
Wt./ft
55.66
42.79
36.10
29.23
48.85
37.69
31.84
25.82
0
641
493
414
336
563
434
366
297
6
7
8
9
10
619
611
602
592
581
476
470
463
456
448
401
396
390
384
377
325
321
317
312
306
529
517
504
490
474
409
400
391
380
368
345
338
330
321
312
281
275
269
261
254
11
12
13
14
15
568
556
542
528
513
439
429
419
408
397
370
362
354
345
335
300
294
287
280
273
457
439
421
402
382
356
343
329
315
300
302
291
279
267
255
246
237
228
218
209
16
17
18
19
20
497
481
465
448
431
386
374
361
349
336
326
316
306
295
285
265
257
249
241
232
362
342
322
302
282
285
270
255
240
225
243
230
218
205
193
199
189
179
169
159
22
24
26
28
30
396
361
327
294
262
310
284
258
232
208
263
241
220
198
178
215
197
180
163
146
244
208
177
153
133
196
169
144
124
108
169
146
124
107
93
139
121
103
89
77
32
34
36
38
39
231
205
183
164
156
184
163
146
131
124
158
140
125
112
106
130
116
103
93
88
117
104
92
83
79
95
84
75
67
64
82
73
65
58
55
68
60
54
48
46
40
148
118
101
84
61
52
44
11.1
145
65.4
1.49
2.43
9.36
125
56.5
1.48
2.46
7.59
103
46.9
1.48
2.49
Effective length KL (ft) with respect to least radius of gyration
Fy
46 ksi
Properties
2
A (in )
Ix (in.4)
Iy (in.4)
rx / ry
ry (in.)
16.4
226
160
1.19
3.12
12.6
180
127
1.19
3.18
10.6
154
109
1.19
3.21
8.59
127
90.2
1.19
3.24
14.4
181
80.8
1.50
2.37
Note: Heavy line indicates Kl / r of 200.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
3 - 48
COLUMN DESIGN
Fy = 46 ksi
Y
X
COLUMNS
Rectangular structural tubing
Design axial strength in kips (φ = 0.85)
X
Y
10×
×5
Nominal Size
8×
×6
Thickness
3⁄
8
5⁄
16
1⁄
4
1⁄
2
3⁄
8
5⁄
16
1⁄
4
Wt./ft
35.13
29.72
24.12
42.05
32.58
27.59
22.42
0
403
341
277
485
375
317
258
6
7
8
9
10
370
359
347
334
319
315
306
295
284
272
256
249
241
232
222
454
444
432
419
404
352
344
335
325
315
298
292
284
276
268
243
238
232
225
218
11
12
13
14
15
304
288
272
255
239
260
246
233
219
205
212
201
191
179
168
389
373
357
340
322
303
292
279
266
253
258
248
238
227
217
211
203
195
186
178
16
17
18
19
20
222
206
189
174
159
191
178
164
151
138
157
146
135
124
114
305
287
269
252
235
240
227
213
200
187
205
194
183
172
161
169
160
151
142
133
22
24
26
28
30
131
110
94
81
71
115
96
82
71
62
95
80
68
59
51
201
170
145
125
109
161
137
117
101
88
140
119
102
88
76
116
99
85
73
64
32
34
36
38
39
62
55
54
48
45
40
96
85
76
68
77
68
61
55
52
67
59
53
48
45
56
49
44
40
38
Effective length KL (ft) with respect to least radius of gyration
Fy
46 ksi
36
40
Properties
2
A (in )
Ix (in.4)
Iy (in.4)
rx / ry
ry (in.)
10.3
128
42.9
1.72
2.04
8.73
110
37.2
1.71
2.07
7.09
91.2
31.1
1.72
2.09
12.4
103
65.7
1.25
2.31
Note: Heavy line indicates Kl / r of 200.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
9.58
83.7
53.5
1.25
2.36
8.11
72.4
46.4
1.25
2.39
6.59
60.1
38.6
1.25
2.42
DESIGN STRENGTH OF COLUMNS
3 - 49
Fy = 46 ksi
Y
COLUMNS
Rectangular structural tubing
Design axial strength in kips (φ = 0.85)
X
X
Y
8×
×4
Nominal Size
7×
×5
Thickness
5⁄
8
1⁄
2
3⁄
8
5⁄
16
1⁄
4
1⁄
2
3⁄
8
5⁄
16
1⁄
4
3⁄
16
Wt./ft
42.30
35.24
27.48
23.34
19.02
35.24
27.48
23.34
19.02
14.53
0
486
407
316
268
219
407
316
268
219
167
6
7
8
9
10
415
393
368
341
314
351
333
313
292
270
276
262
248
233
216
235
224
212
199
185
192
184
174
164
153
369
357
342
327
311
288
279
268
257
245
245
238
229
220
210
200
194
187
180
172
154
149
144
138
132
11
12
13
14
15
287
259
233
207
182
248
226
204
183
162
200
183
167
150
135
172
158
144
130
117
142
131
120
109
98
294
276
258
240
222
232
219
205
192
178
199
188
177
165
154
164
155
146
137
127
126
119
113
106
99
16
17
18
19
20
160
141
126
113
102
143
126
113
101
91
120
106
95
85
77
104
92
82
74
67
88
78
70
62
56
205
187
170
154
139
165
151
138
126
114
142
131
120
110
100
118
109
101
92
84
92
85
79
72
66
22
24
25
26
27
84
71
76
63
58
63
53
49
45
55
46
43
39
37
47
39
36
33
31
115
97
89
82
76
94
79
73
67
62
82
69
64
59
55
69
58
54
50
46
54
46
42
39
36
71
66
62
58
58
54
51
47
44
51
47
44
41
39
43
40
37
35
33
34
31
29
27
26
37
31
24
23
6.86
45.5
26.9
1.30
1.98
5.59
38.0
22.6
1.30
2.01
4.27
29.8
17.7
1.29
2.04
Effective length KL (ft) with respect to least radius of gyration
Fy
46 ksi
28
29
30
31
32
33
34
Properties
2
A (in )
Ix (in.4)
Iy (in.4)
rx / ry
ry (in.)
12.4
85.1
27.4
1.76
1.49
10.4
75.1
24.6
1.75
1.54
8.08
61.9
20.6
1.73
1.60
6.86
53.9
18.1
1.73
1.62
5.59
45.1
15.3
1.72
1.65
10.40
63.5
37.2
1.31
1.90
8.08
52.2
30.8
1.30
1.95
Note: Heavy line indicates Kl / r of 200.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
3 - 50
COLUMN DESIGN
Fy = 46 ksi
Y
X
X
COLUMNS
Rectangular structural tubing
Design axial strength in kips (φ = 0.85)
Y
7×
×4
Nominal Size
6×
×4
Thickness
3⁄
8
5⁄
16
1⁄
4
3⁄
16
1⁄
2
3⁄
8
5⁄
16
1⁄
4
3⁄
16
Wt./ft
24.93
21.21
17.32
13.25
28.43
22.37
19.08
15.62
11.97
0
287
244
199
152
327
257
219
179
138
6
7
8
9
10
249
236
223
208
193
213
202
191
179
167
175
166
158
148
138
134
128
121
114
107
279
263
246
228
210
222
211
198
185
171
190
181
171
160
148
157
149
141
132
123
121
115
109
102
96
11
12
13
14
15
178
163
148
133
118
154
141
129
116
104
128
118
107
97
88
99
92
84
76
69
191
173
155
137
121
157
143
129
116
103
136
125
113
102
91
114
104
95
85
77
89
81
74
67
61
16
17
18
19
20
105
93
83
74
67
92
82
73
65
59
78
69
62
56
50
62
55
49
44
40
106
94
84
75
68
90
80
71
64
58
80
71
63
57
51
68
60
54
48
44
54
48
43
38
35
21
22
23
24
25
61
55
51
46
43
54
49
45
41
38
45
41
38
35
32
36
33
30
28
25
62
56
51
47
52
48
44
40
37
46
42
39
36
33
39
36
33
30
28
31
29
26
24
22
26
27
40
35
30
27
23
22
30
26
20
19
5.61
26.2
13.8
1.38
1.57
4.59
22.1
11.7
1.37
1.60
3.52
17.4
9.32
1.37
1.63
Effective length KL (ft) with respect to least radius of gyration
Fy
46 ksi
Properties
2
A (in )
Ix (in.4)
Iy (in.4)
rx / ry
ry (in.)
7.33
44.0
18.1
1.56
1.57
6.23
38.5
16.0
1.56
1.60
5.09
32.3
13.5
1.55
1.63
3.89
25.4
10.7
1.54
1.66
8.36
35.3
18.4
1.39
1.48
6.58
29.7
15.6
1.38
1.54
Note: Heavy line indicates Kl / r of 200.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
DESIGN STRENGTH OF COLUMNS
3 - 51
Fy = 46 ksi
Y
COLUMNS
Rectangular structural tubing
Design axial strength in kips (φ = 0.85)
X
X
Y
6×
×3
Nominal Size
5×
×4
Thickness
1⁄
2
3⁄
8
5⁄
16
1⁄
4
3⁄
16
3⁄
8
5⁄
16
1⁄
4
3⁄
16
Wt./ft
25.03
19.82
16.96
13.91
10.70
19.82
16.96
13.91
10.70
0
288
228
195
160
123
228
195
160
123
6
7
8
9
10
216
194
172
150
129
176
160
144
127
111
152
138
125
111
97
126
116
105
94
83
98
90
82
74
65
195
185
173
161
148
168
159
149
139
129
139
132
124
116
107
107
102
96
90
84
11
12
13
14
15
109
92
78
67
59
95
81
69
59
52
84
71
61
52
46
72
62
53
45
39
57
50
42
36
32
135
123
110
98
86
118
107
97
87
77
99
90
82
73
65
77
71
64
58
52
16
17
18
19
20
52
46
41
45
40
36
32
40
36
32
28
35
31
27
25
22
28
25
22
20
18
76
67
60
54
49
67
60
53
48
43
58
51
46
41
37
46
41
36
33
29
44
40
37
34
31
39
36
33
30
28
33
30
28
26
24
27
24
22
20
19
22
17
4.09
14.1
9.98
1.19
1.56
3.14
11.2
7.96
1.19
1.59
Effective length KL (ft) with respect to least radius of gyration
Fy
46 ksi
21
22
23
24
25
26
Properties
2
A (in )
Ix (in.4)
Iy (in.4)
rx / ry
ry (in.)
7.36
27.7
8.91
1.76
1.10
5.83
23.8
7.78
1.74
1.16
4.98
21.1
6.98
1.75
1.18
4.09
17.9
6.00
1.73
1.21
3.14
14.3
4.83
1.72
1.24
5.83
18.7
13.2
1.19
1.50
Note: Heavy line indicates Kl / r of 200.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
4.98
16.6
11.7
1.20
1.53
3 - 52
COLUMN DESIGN
Fy = 46 ksi
Y
X
X
COLUMNS
Rectangular structural tubing
Design axial strength in kips (φ = 0.85)
Y
5×
×3
Nominal Size
4×
×3
Thickness
1⁄
2
3⁄
8
5⁄
16
1⁄
4
3⁄
16
1⁄
8
5⁄
16
1⁄
4
3⁄
16
1⁄
8
Wt./ft
21.63
17.27
14.83
12.21
9.42
6.46
12.70
10.51
8.15
5.61
0
249
199
170
140
108
74
146
121
93
64
6
7
8
9
10
183
164
145
125
107
151
137
122
107
93
132
120
108
95
83
110
100
91
81
71
85
78
71
63
56
59
55
50
45
40
110
100
89
78
67
93
84
76
67
58
73
66
60
53
47
51
47
42
38
33
11
12
13
14
15
89
75
64
55
48
79
67
57
49
43
71
60
51
44
39
61
52
45
38
33
49
42
36
31
27
35
30
26
22
19
57
48
41
35
31
50
42
36
31
27
40
34
29
25
22
29
25
21
18
16
16
17
18
19
20
42
37
38
33
30
34
30
27
24
29
26
23
21
23
21
19
17
15
17
15
13
12
11
27
24
21
24
21
19
17
19
17
15
14
14
12
11
10
9
1.90
6.44
2.93
1.48
1.24
3.73
7.45
4.71
1.26
1.12
3.09
6.45
4.10
1.26
1.15
2.39
5.23
3.34
1.25
1.18
1.65
3.76
2.41
1.25
1.21
Effective length KL (ft) with respect to least radius of gyration
Fy
46 ksi
Properties
2
A (in )
Ix (in.4)
Iy (in.4)
rx / ry
ry (in.)
6.36
16.9
7.33
1.52
1.07
5.08
14.7
6.48
1.50
1.13
4.36
13.2
5.85
1.50
1.16
3.59
11.3
5.05
1.49
1.19
2.77
9.06
4.08
1.50
1.21
Note: Heavy line indicates Kl / r of 200.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
DESIGN STRENGTH OF COLUMNS
3 - 53
Double Angles and WT Shapes
Double Angles
Design strengths are tabulated for the effective length KL in feet with respect to both the
X-X and Y-Y axes. Design strengths about the X-X axis are in accordance with LRFD
Specification Section E2. For buckling about the Y-Y axis the shear deformation of the
connectors may require the slenderness to be increased in accordance with the equations
for (Kl / r)m in Section E4. Incorporating this slenderness ratio, the design strengths are
determined from Section E2 or E3, whichever governs. In addition to the usual limit state
of flexural buckling for columns, double angle and WT shapes in compression may also
be governed by the limit state of flexural-torsional buckling, in accordance with Section
E3 of the LRFD Specification. This has been included in the tables. Discussion under
Section C2 of the LRFD Specification Commentary points out that for trusses it is usual
practice to take K = 1.0. No values are listed beyond KL / r = 200.
For buckling about the X-X axis, both angles move parallel so that the design strength
is not affected by the connectors. For buckling about the Y-Y axis, the design strengths
are tabulated for the indicated number n of intermediate connectors. For connectors with
snug-tight bolts or different spacings, the design strength must be recalculated using the
corresponding modified slenderness and LRFD Specification Section E4. The number of
intermediate connectors given in the table was selected so the design strength about the
Y-Y axis is 90 percent or greater of that for buckling of the two angles acting as a unit.
If fewer connectors are used, the strength must be reduced accordingly. According to
Section E4 of the LRFD Specification, the connectors must be spaced so that the
slenderness ratio a / rz of the individual angle does not exceed 75 percent of the governing
slenderness ratio of the built-up member.
In designing members fabricated of two angles connected to opposite faces of a gusset
plate, Chapter J of the LRFD Specification states that eccentricity between the gage lines
and gravity axis may be neglected. In the following tables, this eccentricity is neglected.
The tabulated loads for double angles referred to in the Y-Y axis assume a 3⁄8-in. spacing
between angles. These values are conservative when a wider spacing is provided.
Example 3-5 illustrates a method for determining the design strength when a 3⁄4-in. gusset
plate is used.
Examples 3-6 and 3-7 demonstrate how to determine the number of connectors when
Klx / rx governs and when the modified (Kly / ry)m governs.
EXAMPLE 3-5
Given:
Solution:
Using 50 ksi steel, determine the design strength with respect to the
Y-Y axis of a double angle member of 8×8×1 angles with an effective
length equal to 12 ft, and connected to a 3⁄4-in. thick gusset plate.
ry = 3.53 in. (from Double Angle Column Design Strength Table
for two L8×8×1 with 3⁄8-in. plate)
ry′ = 3.67 in. (from Part 1, Properties, Two Equal-Leg Angles, two
L8×8×1 with 3⁄4-in. plate)
ry 3.53
=
= 0.962
ry′ 3.67
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
3 - 54
COLUMN DESIGN
Equivalent effective length = 0.962 × 12 ft = 11.5 ft
Enter Column Design Strength Table for two L8×8×1 with reference
to Y-Y axis for effective lengths between 10 and 15 feet, read 1,120
and 1,000 kips, respectively.
Equivalent design strength = 1,120 − (1,120 − 1,000) ×
11.5 − 10
15 − 10
= 1,084 kips
EXAMPLE 3-6
Given:
Solution:
Using a double angle member of 5×3×1⁄2 angles (short legs back to
back) and 36 ksi steel, with Lx = 10 ft and Ly = 20 ft, and a factored
axial load of 70 kips, determine the number of connectors required.
Assume K = 1.0 and that the intermediate connectors are snug-tight
bolted.
Kx Lx = 10 ft, Kx lx / rx = (10 × 12) / 0.829 = 145
Ky Ly = 20 ft, Ky ly / ry = (20 × 12) / 2.5 = 96
The X-X axis governs. From the X-X axis portion of the table
φPn = 76 kips > 70 kips o.k.
Find number of connectors required based on Section E4:
a / rz ≤ 0.75KLx / rx
a
≤ 0.75(KLx / rx)rz = 0.75 (145) 0.648 = 70 in.
Assume two connectors are required; a = (10 × 12) / 3 = 40 in.
a / rz = 40 / rz = 40.0 / 0.648 = 61.7
Check that modified (Ky ly / ry)m does not govern.
According to Specification Equation E4-1,
962 + 61.7
2 = 114
(Ky ly / ry)m = √
Modified ly′ = 114ry / Ky = 114 (2.50 in.) / 1.0 = 285 in. = 23.8 ft
Inspection of the tables indicates that Kxlx / rx still governs, therefore
one connector is required every 40 inches.
EXAMPLE 3-7
Given:
Using the same steel shape and bolts as Example 3-6, with Lx = 10 ft
and Ly = 30 ft, determine the number of connectors required and the
corresponding maximum design strength. Assume K = 1.0.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
DESIGN STRENGTH OF COLUMNS
Solution:
3 - 55
Kx Lx = 10 ft, Kx lx / rx = (10 × 12) / 0.829 = 145
Ky Ly = 30 ft, Ky ly / ry = (30 × 12) / 2.5 = 144
Kx lx / rx appears to govern, so try one connector in the 10-ft length.
Check (Ky ly / ry)m with a / rz = 5 × 12 / 0.648 = 93
1442 + 932 = 171
(Ky ly / ry)m = √
Since (Ky ly / ry)m governs, the Y-Y portion of the table gives a design
strength of 72 kips provided four connectors are used in the 30-ft length.
This gives a spacing of 30 ft / 5 = 6.0 ft. Check if (Kyly / ry)m governs with
= (6.0 × 12) / 0.648 = 111
a / rz
1442 + 111 2 = 182
(Kyly / ry)m = √
(Ky ly / ry)m still governs, so four connectors at 6.0 ft would be
appropriate.
Verify that a / rz < 0.75 governing Kl / r :
111 < (0.75 × 182 = 137) o.k.
Modified ly′ = 182ry / Ky = 182(2.5 in.) / 1.0 = 455 in. = 37.9 ft
From the tables, the design strength is 45 kips.
The design strength can be increased by closer spacing of the connectors, which reduces (Kyly / ry)m .
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
3 - 56
COLUMN DESIGN
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
DESIGN STRENGTH OF COLUMNS
3 - 57
Fy = 36 ksi
Fy = 50 ksi
Y
COLUMNS
Double angles
X
X
Design axial strength in kips (φ = 0.85)
Equal legs
8
in. back to back of angles
3/ ′′
8
8×
×8
Size
11⁄8
Thickness
Wt./ft
36
7⁄
8
1
113.8
Fy
X-X AXIS
Y
102.0
50
3⁄
4
90.0
5⁄
8
77.8
1⁄
2
65.4
52.8
36
50
36
50
36
50
36
50
36
50
0
1030 1420
918
1280
811
1130
701
973
586
763
432
550
10
14
18
22
26
901 1190
795 1000
674 795
548 596
427 430
808
715
608
496
388
1070
902
719
542
391
715
633
539
440
345
945
799
638
482
349
619
549
469
384
303
819
694
556
422
306
518
461
395
325
257
651
559
456
354
261
387
348
302
253
205
478
417
349
278
212
30
34
38
39
40
323
251
201
191
182
323
251
201
191
182
294
229
183
174
165
294
229
183
174
165
262
204
163
155
147
262
204
163
155
147
230
179
143
136
129
230
179
143
136
129
196
153
122
116
110
196
153
122
116
110
159
124
99
94
90
159
124
99
94
90
123
123
105
105
85
85
0
1030 1420
918
1280
811
1130
701
973
586
763
432
550
10
15
20
25
30
939 1260
869 1130
779 975
677 803
570 632
834
772
692
601
506
1120
1000
864
711
560
726
670
599
517
432
965
865
741
606
473
615
569
509
440
368
808
728
626
514
402
495
460
413
359
302
609
555
486
407
325
345
324
297
263
226
406
378
341
295
244
35
40
45
50
55
465
366
290
235
194
477
366
290
235
194
412
324
257
208
172
422
324
257
208
172
349
272
216
175
145
354
272
216
175
145
297
232
184
150
124
301
232
184
150
124
244
191
152
124
103
248
191
152
124
103
188
150
120
98
82
193
150
120
98
82
56
57
58
59
188
181
175
169
188
181
175
169
166
161
155
166
161
155
140
135
130
140
135
130
120
116
112
120
116
112
99
96
99
96
79
76
79
76
No. of
a
Connectors
3⁄
Effective length KL (ft) with respect to indicated axis
b
Y-Y AXIS
41
2
3
Properties of 2 angles—3⁄8 in. back to back
2
A (in )
rx (in.)
ry (in.)
33.5
2.42
3.55
30.0
2.44
3.53
26.5
2.45
3.51
22.9
2.47
3.49
19.2
2.49
3.47
aFor Y-Y axis, welded or fully tensioned bolted connectors only.
bFor number of connectors, see double angle column discussion.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
15.5
2.50
3.45
3 - 58
COLUMN DESIGN
Fy = 36 ksi
Fy = 50 ksi
Y
X
COLUMNS
Double angles
X
Design axial strength in kips (φ = 0.85)
3⁄
8
Equal legs
in. back to back of angles
6×
×6
Size
Thickness
Wt./ft
74.8
Y-Y AXIS
X-X AXIS
Fy
Effective length KL (ft) with respect to indicated axis
7⁄
8
1
3⁄
4
66.2
57.4
1⁄
2
48.4
3⁄
8
39.2
29.8
36
50
36
50
36
50
36
50
36
50
36
50
0
673
935
597
829
517
718
435
604
352
470
243
309
8
10
12
14
16
580
533
481
426
370
759
676
586
495
407
515
473
428
379
330
675
601
522
441
364
447
412
373
332
290
587
524
457
388
321
377
347
315
280
245
495
442
386
328
272
306
283
257
229
201
389
351
308
265
222
214
200
183
166
147
264
241
216
190
164
18
22
26
30
31
315
218
156
117
326
218
156
117
282
196
140
105
292
196
140
105
248
173
124
93
259
173
124
93
210
147
105
79
220
147
105
79
173
122
87
65
61
182
122
87
65
61
129
94
68
51
48
138
94
68
51
48
0
673
935
597
829
517
718
435
604
352
470
243
309
10
12
14
16
18
595
567
537
503
468
787
738
683
625
565
523
499
472
442
410
690
647
598
547
494
449
428
404
379
352
590
552
511
468
422
371
353
334
313
291
483
453
420
385
348
289
275
260
244
226
359
338
315
289
262
187
180
172
163
153
219
210
199
186
173
20
22
24
26
28
431
394
357
321
286
505
446
389
334
288
378
345
312
280
249
441
388
338
290
250
324
295
267
239
213
377
332
288
247
214
268
244
221
198
176
310
273
238
204
176
208
189
171
152
135
235
207
181
155
135
142
131
120
109
97
158
143
128
113
98
30
32
34
36
38
252
221
196
175
157
252
221
196
175
157
218
192
170
152
137
218
192
170
152
137
187
164
146
130
117
187
164
146
130
117
154
136
120
108
97
154
136
120
108
97
118
104
92
82
74
118
104
92
82
74
86
76
68
61
55
86
76
68
61
55
40
42
43
44
45
142
129
123
117
112
142
129
123
117
112
123
112
107
102
98
123
112
107
102
98
106
96
91
87
106
96
91
87
87
79
76
72
87
79
76
72
67
61
58
56
67
61
58
56
50
45
43
50
45
43
Properties of 2
A (in2)
rx (in.)
ry (in.)
5⁄
8
22.0
1.80
2.73
19.5
1.81
2.70
No. of
a
Connectors
Y
3/ ′′
8
b
2
3
angles—3⁄8
in. back to back
16.9
1.83
2.68
14.2
1.84
2.66
aFor Y-Y axis, welded or fully tensioned bolted connectors only.
bFor number of connectors, see double angle column discussion.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
11.5
1.86
2.64
8.72
1.88
2.62
DESIGN STRENGTH OF COLUMNS
3 - 59
Fy = 36 ksi
Fy = 50 ksi
Y
COLUMNS
Double angles
X
X
Design axial strength in kips (φ = 0.85)
Equal legs
in. back to back of angles
5×
×5
Size
7⁄
8
Thickness
Wt./ft
X-X AXIS
3⁄
4
54.5
Fy
Effective length KL (ft) with respect to indicated axis
1⁄
2
47.2
3⁄
8
32.4
5⁄
16
24.6
20.6
36
50
36
50
36
50
36
50
36
50
0
490
680
425
591
291
404
217
282
169
215
6
8
10
12
14
433
393
348
299
251
573
502
423
343
268
377
344
305
264
222
500
440
372
304
239
259
237
211
183
155
344
304
259
213
169
194
178
160
140
119
244
219
189
159
129
152
141
127
113
97
189
171
150
128
107
16
18
20
22
24
204
162
132
109
91
206
162
132
109
91
182
145
117
97
82
183
145
117
97
82
128
103
83
69
58
130
103
83
69
58
99
80
65
54
45
102
80
65
54
45
82
68
55
46
38
86
68
55
46
38
75
75
53
53
42
39
42
39
35
33
35
33
25
26
Y-Y AXIS
3/ ′′
8
Y
0
490
680
425
591
291
404
217
282
169
215
6
8
10
12
14
457
438
414
388
358
617
582
540
492
441
394
377
357
334
309
531
501
464
423
379
260
249
236
221
204
345
326
303
277
249
184
176
168
157
145
224
214
201
186
168
136
131
126
119
111
160
154
146
137
127
16
18
20
22
24
327
295
263
231
201
389
337
287
240
202
282
254
226
199
172
334
289
246
205
173
186
168
149
131
114
219
190
161
135
114
133
120
107
93
81
150
132
113
95
81
103
94
84
75
66
115
103
90
78
66
26
28
30
32
34
172
149
130
114
101
172
149
130
114
101
148
127
111
98
87
148
127
111
98
87
97
84
73
65
57
97
84
73
65
57
69
60
52
46
41
69
60
52
46
41
57
49
43
38
34
57
49
43
38
34
36
37
38
90
85
81
90
85
81
77
73
69
77
73
69
51
48
51
48
37
35
37
35
30
30
A (in )
rx (in.)
ry (in.)
16.0
1.49
2.30
13.9
1.51
2.28
b
2
3
Properties of 2 angles—3⁄8 in. back to back
2
No. of
a
Connectors
3⁄
8
9.50
1.54
2.24
7.22
1.56
2.22
aFor Y-Y axis, welded or fully tensioned bolted connectors only.
bFor number of connectors, see double angle column discussion.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
6.05
1.57
2.21
3 - 60
COLUMN DESIGN
Fy = 36 ksi
Fy = 50 ksi
Y
X
COLUMNS
Double angles
X
Design axial strength in kips (φ = 0.85)
3⁄
8
Equal legs
in. back to back of angles
4×
×4
Size
3⁄
4
Thickness
Wt./ft
37.0
X-X AXIS
Fy
Y-Y AXIS
Effective length KL (ft) with respect to indicated axis
5⁄
8
1⁄
2
31.4
3⁄
8
25.6
5⁄
16
19.6
1⁄
4
16.4
13.2
36
50
36
50
36
50
36
50
36
50
36
50
0
334
463
282
392
230
319
175
243
146
191
108
138
4
6
8
10
12
306
275
237
195
154
411
354
288
220
159
259
233
201
167
132
349
301
245
189
137
212
191
166
138
110
285
247
203
157
115
162
146
127
106
85
217
189
156
121
89
135
123
107
90
72
172
152
127
101
76
101
92
82
70
57
126
112
96
78
61
14
16
18
19
20
117
89
71
63
117
89
71
63
100
77
61
54
49
100
77
61
54
49
84
65
51
46
41
84
65
51
46
41
65
50
40
36
32
65
50
40
36
32
56
43
34
30
27
56
43
34
30
27
45
35
28
25
22
46
35
28
25
22
0
334
463
282
392
230
319
175
243
146
191
108
138
6
8
10
12
14
303
284
262
237
210
406
371
332
288
245
254
238
219
198
176
339
311
277
241
204
204
191
176
158
140
270
247
220
191
161
151
141
130
117
104
196
180
161
141
119
121
114
106
96
85
148
138
125
110
95
85
81
76
70
63
100
94
87
79
70
16
18
20
22
24
183
157
132
109
92
202
163
132
109
92
153
131
109
91
76
168
135
109
91
76
122
104
86
72
60
133
106
86
72
60
90
77
64
53
45
98
79
64
53
45
74
63
53
44
37
79
64
53
44
37
56
48
41
35
29
60
50
41
35
29
26
28
29
30
31
78
67
63
59
55
78
67
63
59
55
65
56
52
49
46
65
56
52
49
46
51
44
41
39
51
44
41
39
38
33
31
29
38
33
31
29
32
27
26
24
32
27
26
24
25
22
20
25
22
20
Properties of 2 angles—3⁄8 in. back to back
2
A (in )
rx (in.)
ry (in.)
10.9
1.19
1.88
9.22
1.20
1.86
7.50
1.22
1.83
5.72
1.23
1.81
aFor Y-Y axis, welded or fully tensioned bolted connectors only.
bFor number of connectors, see double angle column discussion.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
4.80
1.24
1.80
3.88
1.25
1.79
No. of
a
Connectors
Y
3/ ′′
8
b
3
DESIGN STRENGTH OF COLUMNS
3 - 61
Fy = 36 ksi
Fy = 50 ksi
Y
COLUMNS
Double angles
X
X
Design axial strength in kips (φ = 0.85)
Equal legs
8
in. back to back of angles
31⁄2×31⁄2
Size
3⁄
8
Thickness
Wt./ft
X-X AXIS
5⁄
16
17.0
Fy
Effective length KL (ft) with respect to indicated axis
Y
1⁄
4
14.4
11.6
36
50
36
50
36
50
0
152
211
128
175
100
129
2
4
6
8
10
148
137
120
100
78
204
182
152
117
84
125
115
101
84
67
169
152
127
99
72
97
90
80
67
54
125
114
97
77
58
12
14
16
17
18
59
43
33
29
59
43
33
29
50
37
28
25
22
50
37
28
25
22
41
30
23
21
18
41
30
23
21
18
0
152
211
128
175
100
129
6
8
10
12
14
130
120
108
94
81
170
152
131
109
88
107
98
89
78
67
136
123
106
89
72
80
74
67
60
52
96
88
78
67
56
16
18
20
22
24
67
54
44
37
31
69
54
44
37
31
56
45
37
30
26
57
45
37
30
26
43
36
29
24
20
44
36
29
24
20
26
26
26
22
22
17
17
3/ ′′
8
No. of
a
Connectors
3⁄
b
Y-Y axis
3
Properties of 2 angles—3⁄8 in. back to back
2
A (in )
rx (in.)
ry (in.)
4.97
1.07
1.61
4.18
1.08
1.60
aFor Y-Y axis, welded or fully tensioned bolted connectors only.
bFor number of connectors, see double angle column discussion.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
3.38
1.09
1.59
3 - 62
COLUMN DESIGN
Fy = 36 ksi
Fy = 50 ksi
Y
X
COLUMNS
Double angles
X
Design axial strength in kips (φ = 0.85)
Y
3⁄
8
Equal legs
in. back to back of angles
3×
×3
Size
1⁄
2
Thickness
Wt./ft
18.8
X-X AXIS
Fy
Y-Y AXIS
Effective length KL (ft) with respect to indicated axis
3⁄
8
5⁄
16
14.4
1⁄
4
12.2
3⁄
16
9.8
7.42
36
50
36
50
36
50
36
50
36
50
0
168
234
129
179
109
151
88
118
61
77
2
4
5
6
7
162
145
133
120
106
222
190
169
146
123
125
112
103
93
83
171
147
131
114
97
105
94
87
79
70
144
124
111
97
82
85
77
71
64
57
112
98
88
77
66
59
54
50
46
41
74
66
60
54
47
8
9
10
11
12
92
79
66
54
46
101
81
66
54
46
72
62
52
43
36
80
64
52
43
36
61
53
45
37
31
68
55
45
37
31
50
43
37
31
26
56
46
37
31
26
37
32
28
24
20
41
34
28
24
20
13
14
15
39
34
39
34
31
27
23
31
27
23
26
23
20
26
23
20
22
19
16
22
19
16
17
15
13
17
15
13
0
168
234
129
179
109
151
88
118
61
77
2
4
6
8
10
163
155
143
128
111
223
209
187
161
132
123
117
108
97
84
167
156
140
121
99
101
97
89
80
70
136
128
115
99
82
79
75
70
63
55
100
95
86
75
63
50
48
45
42
37
59
57
53
48
42
12
14
16
18
20
94
76
60
47
38
104
78
60
47
38
70
57
45
36
29
78
58
45
36
29
58
47
37
29
24
64
48
37
29
24
46
38
29
23
19
50
38
29
23
19
32
27
22
17
14
35
28
22
17
14
22
23
32
29
32
29
24
22
24
22
20
18
20
18
16
14
16
14
12
11
12
11
A (in )
rx (in.)
ry (in.)
b
3
Properties of 2 angles—3⁄8 in. back to back
2
No. of
a
Connectors
3/ ′′
8
5.50
0.898
1.43
4.22
0.913
1.41
3.55
0.922
1.40
aFor Y-Y axis, welded or fully tensioned bolted connectors only.
bFor number of connectors, see double angle column discussion.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
2.88
0.930
1.39
2.18
0.939
1.38
DESIGN STRENGTH OF COLUMNS
3 - 63
Fy = 36 ksi
Fy = 50 ksi
Y
COLUMNS
Double angles
X
X
Design axial strength in kips (φ = 0.85)
Equal legs
8
in. back to back of angles
21⁄2×21⁄2
Size
3⁄
8
Thickness
Wt./ft
X-X AXIS
Y-Y AXIS
5⁄
16
11.8
Fy
Effective length KL (ft) with respect to indicated axis
Y
1⁄
4
10.0
3⁄
16
8.2
6.14
36
50
36
50
36
50
36
50
0
106
147
90
125
73
101
54
70
2
3
4
5
6
101
94
86
76
66
137
125
110
93
76
85
80
73
65
56
116
106
93
79
65
69
65
59
53
46
94
86
76
65
53
52
48
44
40
35
66
61
54
47
40
7
8
9
10
11
55
45
36
29
24
59
46
36
29
24
47
39
31
25
21
51
39
31
25
21
39
32
26
21
17
42
33
26
21
17
30
25
20
16
13
32
25
20
16
13
12
20
20
17
17
14
14
11
11
0
106
147
90
125
73
101
54
70
2
3
4
5
6
101
99
95
90
85
138
133
126
118
109
84
82
79
75
71
114
110
105
98
90
67
65
63
60
56
89
86
82
77
71
46
45
44
42
40
57
55
53
50
47
7
8
9
10
11
79
73
66
60
53
98
88
77
67
57
66
61
55
50
44
82
73
64
55
47
52
48
44
40
35
64
58
51
44
37
37
35
32
29
26
44
40
35
31
27
12
13
14
15
16
47
41
35
31
27
48
41
35
31
27
39
34
29
26
22
40
34
29
26
22
31
27
23
20
18
32
27
23
20
18
23
20
17
15
13
23
20
17
15
13
17
18
19
20
24
21
19
17
24
21
19
17
20
18
16
14
20
18
16
14
16
14
13
16
14
13
12
11
9
12
11
9
Properties of 2 angles—3⁄8 in. back to back
A (in2)
rx (in.)
ry (in.)
3.47
0.753
1.21
2.93
0.761
1.20
2.38
0.769
1.19
aFor Y-Y axis, welded or fully tensioned bolted connectors only.
bFor number of connectors, see double angle column discussion.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1.80
0.778
1.18
3/ ′′
8
No. of
a
Connectors
3⁄
b
3
3 - 64
COLUMN DESIGN
Fy = 36 ksi
Fy = 50 ksi
Y
X
COLUMNS
Double angles
X
Design axial strength in kips (φ = 0.85)
Y
3⁄
8
Equal legs
in. back to back of angles
2×
×2
Size
3⁄
8
Thickness
Wt./ft
9.4
X-X AXIS
Fy
Y-Y AXIS
Effective length KL (ft) with respect to indicated axis
5⁄
16
1⁄
4
7.84
3⁄
16
6.38
1⁄
8
4.88
3.30
36
50
36
50
36
50
36
50
36
50
0
83
116
70
98
58
80
44
61
27
34
2
3
4
5
6
76
69
59
49
38
103
88
72
55
39
65
58
50
42
33
87
75
61
47
34
53
48
41
35
28
71
62
51
39
29
40
37
32
27
21
54
47
39
30
22
25
23
20
17
14
31
28
24
19
15
7
8
9
10
29
22
18
29
22
18
25
19
15
12
25
19
15
12
21
16
13
10
21
16
13
10
16
13
10
8
16
13
10
8
11
9
7
6
11
9
7
6
0
83
116
70
98
58
80
44
61
27
34
2
3
4
5
6
79
76
72
67
61
108
102
95
86
76
67
64
60
56
51
90
86
79
72
63
54
51
49
45
41
72
68
63
57
51
39
38
36
33
31
52
49
46
42
37
22
21
20
19
18
26
25
24
22
20
7
8
9
10
11
55
49
43
37
31
66
55
46
37
31
46
41
36
30
26
55
46
38
31
26
37
33
29
24
21
44
37
30
25
21
27
24
21
18
15
32
27
22
18
15
16
15
13
11
10
18
16
14
12
10
12
13
14
15
16
26
22
19
17
15
26
22
19
17
15
22
18
16
14
12
22
18
16
14
12
17
15
13
11
10
17
15
13
11
10
13
11
9
8
7
13
11
9
8
7
8
7
6
5
5
8
7
6
5
5
Properties of 2 angles—3⁄8 in. back to back
2
A (in )
rx (in.)
ry (in.)
2.72
0.594
1.01
2.30
0.601
1.00
1.88
0.609
0.989
aFor Y-Y axis, welded or fully tensioned bolted connectors only.
bFor number of connectors, see double angle column discussion.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1.43
0.617
0.977
0.960
0.626
0.965
No. of
a
Connectors
3/ ′′
8
b
3
DESIGN STRENGTH OF COLUMNS
3 - 65
Fy = 36 ksi
Fy = 50 ksi
Y
COLUMNS
Double angles
X
X
Design axial strength in kips (φ = 0.85)
Unequal legs
3/ ′′
8
Long legs 3⁄8 in. back to back of angles
3⁄
4
1⁄
2
Wt./ft
88.4
67.6
46.0
Fy
36
X-X AXIS
1⁄
2
57.4
39.2
36
50
36
50
36
50
846
376
479
0
673
935 517 718 321 408
10
12
14
16
18
704
667
626
582
535
932
865
792
715
637
541
513
483
450
415
717
667
613
555
496
339
323
306
287
267
419
395
368
340
310
10
12
14
16
18
597
567
533
496
457
792
736
676
612
546
460
437
412
384
354
611
569
523
475
425
289
276
262
246
230
358
338
315
292
267
20
22
24
26
28
488
440
393
348
305
560
486
415
353
305
379
343
308
273
241
438
381
328
279
241
247
226
205
185
165
280
250
221
193
167
20
22
24
26
28
418
378
338
300
264
482
419
359
306
264
324
294
264
235
207
376
328
283
241
208
212
195
177
160
143
242
216
192
168
146
30
32
34
36
38
265
233
207
184
165
265
233
207
184
165
210
184
163
146
131
210
184
163
146
131
146
128
113
101
91
146
128
113
101
91
30
32
34
36
38
230 230
202 202
179 179
160 160
143 143
181
159
141
126
113
181 127 127
159 112 112
141
99
99
126
88
88
113
79
79
41
42
142
142 112
107
112
107
78
74
78
74
40
42
43
129 129 102 102
117 117
92
92
0
Y-Y AXIS
Effective length KL (ft) with respect to indicated axis
3⁄
4
74.8
796 1110 609
0
50
8×
×4
1
b
50
36
50
71
65
62
796 1110 609
846
376
479
0
729
703
672
636
595
978
932
876
811
741
537
519
496
470
440
709
677
638
593
543
301
293
282
270
256
357
346
331
314
295
6
8
10
12
14
568 741 416 533 234 275
520 657 381 473 217 251
464 562 339 405 197 223
404 463 294 333 175 192
342 368 248 263 150 159
935 517 718 321 408
16
18
20
22
24
551
506
459
412
366
667
592
517
445
378
408
375
340
305
271
490
435
381
328
279
240
223
205
187
169
273
249
225
200
176
16
18
20
22
24
282
238
194
160
135
300
238
194
160
135
203
162
132
110
93
26
28
32
321
279
214
323
279
214
238
207
159
239
207
159
151
133
103
152
133
103
25
26
125
115
125
115
85
34
36
40
41
42
190
170
138
131
125
190
170
138
131
125
141
126
103
98
141
126
103
98
92
82
67
92
82
67
A
rx (in.)
ry (in.)
26.0
2.49
2.52
19.9
2.53
2.48
13.5
2.56
2.44
22.0
2.52
1.61
aFor Y-Y axis, welded or fully tensioned bolted connectors only.
bFor number of connectors, see double angle column discussion.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
2
204 126 127
162 103 103
132
84
84
110
70
70
93
60
60
85
55
55
3
Properties of 2 angles—3⁄8 in. back to back
(in2)
b
71
65
62
6
8
10
12
14
2
673
36
No. of a
Connectors
1
No. of a
Connectors
8×
×6
Size
Thickness
Y
16.9
2.55
1.55
11.5
2.59
1.51
3 - 66
COLUMN DESIGN
Fy = 36 ksi
Fy = 50 ksi
Y
X
COLUMNS
Double angles
X
Design axial strength in kips (φ = 0.85)
Unequal legs
3/ ′′
8
3⁄
4
1⁄
2
3⁄
8
Wt./ft
52.4
35.8
27.2
Fy
36
50
36
50
36
50
X-X AXIS
Effective length KL (ft) with respect to indicated axis
0 471 655 310 401 205 254
3⁄
4
5⁄
8
1⁄
2
3⁄
8
47.2
40.0
32.4
24.6
36
0
50
36
50
36
50
36
50
425 591 358 497 291 388 201 256
8
10
12
14
16
427
404
378
349
318
571
529
481
431
379
283
268
252
233
214
355
332
306
278
248
189
181
171
161
149
230
218
204
188
172
8
10
12
14
16
371
343
312
279
246
488
439
385
329
276
313
290
265
237
209
413
371
327
281
236
18
20
22
24
26
286
255
224
194
166
328
278
232
195
166
194
174
154
135
117
219
190
162
137
117
137
125
113
101
89
155
138
121
105
90
18
20
22
24
26
212
180
150
126
108
225
182
150
126
108
181
155
129
109
93
193 148 158 110 119
156 127 128 96 100
129 106 106 82 82
109 89 89 69 69
93 76 76 59 59
28 143 143 100 100
30 125 125 88 88
32 110 110 77 77
34 97 97 68 68
78
68
59
53
78
68
59
53
28
30
31
32
93
81
76
93
81
76
80
70
65
36
37
47
44
47
44
87
82
87
82
61
58
61
58
b
0 471 655 310 401 205 254
Y-Y AXIS
6×
×4
No. of a
Connectors
7×
×4
Size
Thickness
6
8
10
12
14
394
362
325
284
242
511
456
393
327
262
238
221
200
176
151
286
260
229
196
161
146
137
127
115
101
167
156
142
126
108
16
18
20
22
24
201
162
132
110
92
204 126 128
162 103 103
132 84 84
110 70 70
92 59 59
87
74
61
51
43
90
74
61
51
43
25
26
27
85
79
73
40
40
0
80
70
65
254
236
216
193
171
65
57
53
325
294
260
225
191
65
57
53
179
167
154
140
125
51
44
41
39
220
202
182
161
140
b
51
44
41
39
425 591 358 497 291 388 201 256
6
8
10
12
14
367
339
306
270
232
481
432
375
315
256
302
279
252
222
191
394
354
308
259
210
236
218
197
174
150
293
266
233
198
162
153
144
132
118
104
181
167
151
132
112
16
18
20
22
24
195
160
136
113
95
211 161 165 126 129
167 132 132 103 103
136 107 107 84 84
113 89 89 70 70
95 75 75 59 59
89
75
61
51
43
93
75
61
51
43
26
27
28
81
75
70
37
35
37
35
2
85
79
73
55
51
55
51
2
81
75
70
64
59
64
59
50
47
50
47
3
Properties of 2 angles—3⁄8 in. back to back
A (in2)
rx (in.)
ry (in.)
No. of a
Connectors
Long legs 3⁄8 in. back to back of angles
Y
15.4
2.22
1.62
10.5
2.25
1.57
7.97
2.27
1.55
13.9
1.88
1.69
11.7
1.90
1.67
aFor Y-Y axis, welded or fully tensioned bolted connectors only.
bFor number of connectors, see double angle column discussion.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
9.50
1.91
1.64
7.22
1.93
1.62
DESIGN STRENGTH OF COLUMNS
3 - 67
Fy = 36 ksi
Fy = 50 ksi
Y
COLUMNS
Double angles
X
X
Design axial strength in kips (φ = 0.85)
Unequal legs
3/ ′′
8
Long legs 3⁄8 in. back to back of angles
Wt./ft
23.4
Y-Y AXIS
X-X AXIS
Fy
Effective length KL (ft) with respect to indicated axis
5⁄
16
19.6
36
50
36
50
0
191
243
145
179
8
10
12
14
16
170
159
146
133
119
209
192
173
153
133
130
123
114
105
95
157
146
134
120
106
18
20
22
24
26
105
92
78
66
56
114
95
79
66
56
85
75
65
56
48
93
79
67
56
48
28
30
32
49
42
37
49
42
37
41
36
32
0
191
243
4
6
8
10
12
148
139
127
113
98
14
16
18
20
22
23
3⁄
4
1⁄
2
39.6
3⁄
8
27.2
5⁄
16
20.8
50
36
50
0
355
493
245
340 183 238 143 182
4
6
8
10
12
337
317
290
259
225
460 233
421 219
372 202
318 181
262 158
14
16
18
20
22
191
158
127
103
85
209
161
127
103
85
41
36
32
24
25
26
72
66
72
66
51
47
44
145
179
0
355
493
245
176
163
147
127
105
107
101
94
85
75
122
115
106
94
80
4
6
8
10
12
325
303
274
241
206
437 215
396 200
345 182
289 160
232 136
284
258
226
189
152
152
142
129
114
98
81
66
53
43
36
84
66
53
43
36
64
53
43
35
29
66
53
43
35
29
14
16
18
20
22
170
144
114
93
77
188
144
114
93
77
113
90
72
58
48
117
90
72
58
48
82
65
52
43
35
84
65
52
43
35
65
53
43
35
29
68
53
43
35
29
33
33
27
27
24
25
65
60
65
60
41
41
30
30
25
25
b
318
292
260
223
185
36
17.4
36
175
165
152
137
120
50
36
50
224
208
187
163
138
137
130
120
109
97
172
161
146
129
111
135 149 104 113
113 116
87
90
91
91
71
71
74
74
58
58
61
61
48
48
85
72
60
49
41
93
76
61
49
41
34
31
29
34
31
29
51
47
44
40
37
34
40
37
34
A (in )
rx (in.)
ry (in.)
186 113 134
171 107 125
152
98 114
130
88
99
107
77
84
2
6.84
1.94
1.39
5.74
1.95
1.38
b
340 183 238 143 182
2
3
Properties of 2 angles—3⁄8 in. back to back
2
No. of a
Connectors
3⁄
8
Thickness
5×
×31⁄2
No. of a
Connectors
6×
×31⁄2
Size
Y
11.6
1.55
1.53
8.00
1.58
1.49
aFor Y-Y axis, welded or fully tensioned bolted connectors only.
bFor number of connectors, see double angle column discussion.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
6.09
1.60
1.46
5.12
1.61
1.45
3 - 68
COLUMN DESIGN
Fy = 36 ksi
Fy = 50 ksi
Y
X
COLUMNS
Double angles
X
Design axial strength in kips (φ = 0.85)
Unequal legs
3/ ′′
8
5×
×3
Size
1⁄
2
Thickness
Wt./ft
25.6
X-X AXIS
Fy
Y-Y AXIS
Effective length KL (ft) with respect to indicated axis
3⁄
8
5⁄
16
19.6
1⁄
4
16.4
13.2
36
50
36
50
36
50
36
50
0
230
319
172
223
134
170
95
117
2
4
6
8
10
227
219
206
189
170
313
298
274
244
210
170
164
155
143
129
220
210
195
176
154
132
128
122
113
103
168
161
151
137
121
95
92
88
82
76
115
112
105
97
88
12
14
16
18
20
149
128
107
87
70
175
141
110
87
70
114
98
82
68
55
130
107
86
68
55
91
79
68
56
46
104
88
71
57
46
68
61
53
45
38
78
67
56
47
38
22
24
26
27
58
49
42
58
49
42
45
38
32
45
38
32
38
32
27
38
32
27
31
26
22
21
31
26
22
21
0
230
319
172
223
134
170
95
117
2
4
6
8
10
207
195
177
153
128
276
255
223
184
143
146
138
125
110
92
179
167
149
126
101
107
102
94
84
72
128
121
110
95
78
71
68
64
58
51
80
77
72
64
55
12
14
16
18
20
101
81
62
49
40
109
81
62
49
40
74
57
44
35
28
76
57
44
35
28
59
46
36
29
23
61
46
36
29
23
43
35
28
22
18
45
35
28
22
18
No. of
a
Connectors
Long legs 3⁄8 in. back to back of angles
Y
b
2
3
Properties of 2 angles—3⁄8 in. back to back
2
A (in )
rx (in.)
ry (in.)
7.50
1.59
1.25
5.72
1.61
1.23
4.80
1.61
1.22
aFor Y-Y axis, welded or fully tensioned bolted connectors only.
bFor number of connectors, see double angle column discussion.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
3.88
1.62
1.21
DESIGN STRENGTH OF COLUMNS
3 - 69
Fy = 36 ksi
Fy = 50 ksi
Y
COLUMNS
Double angles
X
X
Design axial strength in kips (φ = 0.85)
Unequal legs
3/ ′′
8
Long legs 3⁄8 in. back to back of angles
1⁄
2
Thickness
Wt./ft
23.8
Fy
X-X AXIS
3⁄
8
5⁄
16
18.2
15.4
12.4
36
50
36
50
36
50
36
50
0
214
298
163
227
137
179
101
129
2
4
6
8
10
210
198
179
155
130
289
266
232
191
148
160
151
137
120
101
221
204
178
147
116
134
127
115
101
85
174
162
143
120
96
99
94
87
77
66
126
118
106
91
75
12
14
16
18
20
104
80
61
48
39
109
80
61
48
39
81
63
48
38
31
86
63
48
38
31
69
54
41
33
26
73
54
41
33
26
55
44
34
27
22
59
44
34
27
22
24
24
20
20
0
214
298
163
227
137
179
101
129
2
4
6
8
10
203
196
183
167
148
276
262
240
211
180
150
144
135
124
110
200
190
174
155
132
121
116
110
101
90
150
143
133
120
104
84
81
77
72
65
99
96
91
83
74
12
14
16
18
20
128
108
88
74
60
147
116
93
74
60
95
80
66
53
43
108
86
66
53
43
78
66
54
43
35
87
70
54
43
35
58
50
42
34
28
64
53
42
34
28
22
24
25
26
50
42
39
36
50
42
39
36
35
30
28
25
35
30
28
25
29
25
23
29
25
23
23
20
18
23
20
18
b
21
Y-Y AXIS
1⁄
4
No. of
a
Connectors
4×
×31⁄2
Size
Effective length KL (ft) with respect to indicated axis
Y
2
3
Properties of 2 angles—3⁄8 in. back to back
2
A (in )
rx (in.)
ry (in.)
7.00
1.23
1.58
5.34
1.25
1.56
4.49
1.26
1.55
aFor Y-Y axis, welded or fully tensioned bolted connectors only.
bFor number of connectors, see double angle column discussion.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
3.63
1.27
1.54
3 - 70
COLUMN DESIGN
Fy = 36 ksi
Fy = 50 ksi
Y
X
COLUMNS
Double angles
X
Design axial strength in kips (φ = 0.85)
Unequal legs
3/ ′′
8
4×
×3
Size
1⁄
2
Thickness
Wt./ft
22.2
X-X AXIS
Fy
Effective length KL (ft) with respect to indicated axis
3⁄
8
17.0
1⁄
4
14.4
11.6
36
50
36
50
36
50
36
50
0
199
276
152
211
127
166
94
120
2
4
6
8
10
195
184
167
146
122
269
248
217
179
141
149
141
128
112
94
206
190
166
138
109
125
118
108
94
80
162
151
133
112
90
93
88
81
72
62
117
110
99
85
70
12
14
16
18
20
99
77
59
46
38
105
77
59
46
38
76
60
46
36
29
81
60
46
36
29
65
51
39
31
25
69
51
39
31
25
51
41
32
25
21
55
42
32
25
21
27
27
23
23
19
19
0
199
276
152
211
127
166
94
120
2
4
6
8
10
187
177
161
142
120
253
235
207
173
137
138
131
119
105
89
183
171
151
127
101
111
105
96
85
73
137
129
116
99
81
77
74
69
62
54
92
88
80
71
59
12
14
16
18
20
97
76
61
49
39
108
80
61
49
39
72
56
43
35
28
76
56
43
35
28
59
46
36
29
23
62
46
36
29
23
45
36
28
23
18
47
36
28
23
18
21
22
36
33
36
33
25
25
21
21
17
17
b
21
Y-Y AXIS
5⁄
16
2
3
Properties of 2 angles—3⁄8 in. back to back
2
A (in )
rx (in.)
ry (in.)
No. of
a
Connectors
Long legs 3⁄8 in. back to back of angles
Y
6.50
1.25
1.33
4.97
1.26
1.31
4.18
1.27
1.30
aFor Y-Y axis, welded or fully tensioned bolted connectors only.
bFor number of connectors, see double angle column discussion.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
3.38
1.28
1.29
DESIGN STRENGTH OF COLUMNS
3 - 71
Fy = 36 ksi
Fy = 50 ksi
Y
COLUMNS
Double angles
X
X
Design axial strength in kips (φ = 0.85)
Unequal legs
3/ ′′
8
Long legs 3⁄8 in. back to back of angles
Wt./ft
15.8
X-X AXIS
Fy
Effective length KL (ft) with respect to indicated axis
5⁄
16
1⁄
4
13.2
10.8
36
50
36
50
36
50
0
140
195
118
162
92
119
2
4
6
8
10
137
127
112
93
74
188
169
142
111
80
115
107
95
79
63
157
141
119
94
69
90
84
75
63
51
116
106
91
73
55
12
14
16
17
18
56
41
32
28
25
56
41
32
28
25
48
35
27
24
21
48
35
27
24
21
39
29
22
20
18
0
140
195
118
162
2
4
6
8
10
131
124
114
101
86
176
164
146
123
99
107
102
94
83
71
12
14
71
56
76
59
16
18
20
45
36
29
22
24
3⁄
8
1⁄
4
14.4
9.8
36
50
36
50
0
129
179
85
110
2
4
6
8
10
126
117
103
86
69
173
156
131
103
75
83
77
69
59
47
107
97
84
68
52
40
29
22
20
18
12
14
16
18
52
39
30
23
53
39
30
23
37
27
21
17
37
27
21
17
92
119
0
129
179
85
110
140
131
118
100
81
79
76
70
63
54
97
92
83
73
60
2
4
6
8
10
118
109
96
80
63
158
142
119
92
69
71
67
59
50
40
87
80
69
56
42
59
46
62
47
45
36
48
36
12
14
49
36
49
36
30
22
30
22
45
36
29
36
29
23
36
29
23
28
22
18
28
22
18
16
18
28
22
28
22
17
14
17
14
24
19
19
15
15
b
No. of a
Connectors
3⁄
8
Thickness
31⁄2×21⁄2
No. of a
Connectors
31⁄2×3
Size
Y
b
2
Y-Y AXIS
2
3
3
Properties of 2 angles—3⁄8 in. back to back
2
A (in )
rx (in.)
ry (in.)
4.59
1.09
1.36
3.87
1.10
1.35
3.13
1.11
1.33
4.22
1.10
1.11
aFor Y-Y axis, welded or fully tensioned bolted connectors only.
bFor number of connectors, see double angle column discussion.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
2.88
1.12
1.09
3 - 72
COLUMN DESIGN
Fy = 36 ksi
Fy = 50 ksi
Y
X
COLUMNS
Double angles
X
Design axial strength in kips (φ = 0.85)
Unequal legs
3/ ′′
8
3⁄
8
Thickness
13.2
Wt./ft
Y-Y AXIS
X-X AXIS
Fy
Effective length KL (ft) with respect to indicated axis
1⁄
4
36
3⁄
16
9.0
6.77
50
36
50
36
50
0 118 163
80
107
55
71
2 113 155
3 109 146
4 102 134
5 94 120
6 86 105
78
75
70
65
59
103
97
90
81
71
54
52
49
46
42
68
65
60
55
50
3×
×2
No. of
a
Connectors
3×
×21⁄2
Size
3⁄
8
5⁄
16
11.8
36
1⁄
4
10.0
3⁄
16
8.2
36
6.1
50
36
50
50
0
106 147
90
125
73
97
50
64
2
3
4
5
6
103
98
93
86
78
141
132
122
109
96
87
83
78
73
66
119
112
103
93
82
70
68
64
59
54
93
88
81
74
65
49
47
45
42
38
61
59
55
50
45
7
8
9
10
11
70
61
53
45
38
82
69
56
45
38
59
52
45
39
32
70
59
48
39
32
49
43
37
32
27
57
48
40
32
27
35
31
28
24
20
40
35
30
25
21
12
13
14
15
16
32
27
23
20
32
27
23
20
27
23
20
17
27
23
20
17
22
19
16
14
22
19
16
14
17
15
13
11
10
17
15
13
11
10
7
8
9
10
11
76
67
58
49
40
90
75
60
49
40
53
47
40
34
29
62
52
43
35
29
38
34
30
26
22
44
38
32
27
22
12
13
14
15
34
29
25
22
34
29
25
22
24
21
18
15
24
21
18
15
19
16
14
12
19
16
14
12
0 118 163
80
107
55
71
0
106 147
90
125
73
97
50
64
2 110 149
3 107 143
4 102 135
5 97 125
6 90 114
71
69
66
63
59
90
87
83
77
71
45
44
43
41
39
54
53
51
48
45
2
3
4
5
6
97 131
93 122
86 111
79 98
71 84
80
76
71
65
58
107
100
91
81
69
63
60
56
51
46
79
74
68
61
53
40
39
37
34
31
48
46
43
39
35
7
8
9
10
11
62
53
47
39
32
70
60
48
39
32
51
44
37
32
27
58
49
39
32
27
40
35
29
25
21
45
37
31
25
21
28
24
21
17
15
30
26
21
17
15
12
13
14
15
27
23
20
18
27
23
20
18
22
19
17
14
22
19
17
14
18
15
13
18
15
13
12
11
10
12
11
10
7
8
9
10
11
83 102
76 90
68 77
61 66
53 58
54
50
45
40
35
64
57
49
42
35
36
34
31
28
25
41
38
34
30
26
12
13
14
15
16
48
42
36
31
28
49
42
36
31
28
30
26
23
20
18
30
26
23
20
18
22
19
16
14
13
22
19
16
14
13
17
18
19
24
22
20
24
22
20
16
14
16
14
11
10
11
10
b
2
3
Properties of 2 angles—3⁄8 in. back to back
A
(in2)
rx (in.)
ry (in.)
3.84
0.928
1.16
2.63
0.945
1.13
1.99
0.954
1.12
3.47
0.940
0.917
2.93
0.948
0.903
aFor Y-Y axis, welded or fully tensioned bolted connectors only.
bFor number of connectors, see double angle column discussion.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
2.38
0.957
0.891
1.80
0.966
0.879
No. of a
Connectors
Long legs 3⁄8 in. back to back of angles
Y
b
2
3
DESIGN STRENGTH OF COLUMNS
3 - 73
Fy = 36 ksi
Fy = 50 ksi
Y
COLUMNS
Double angles
X
X
Design axial strength in kips (φ = 0.85)
Unequal legs
3/ ′′
8
Long legs 3⁄8 in. back to back of angles
3⁄
8
Thickness
Wt./ft
10.6
X-X AXIS
Fy
Y-Y AXIS
5⁄
16
1⁄
4
9.0
3⁄
16
7.2
5.5
36
50
36
50
36
50
36
50
0
95
131
80
111
65
91
49
63
2
3
4
5
6
90
84
77
69
60
122
112
99
84
69
76
72
66
59
51
104
95
84
72
59
62
58
54
48
42
85
78
69
59
49
46
44
40
36
32
59
55
49
43
36
7
8
9
10
11
50
42
33
27
22
55
42
33
27
22
43
36
29
23
19
47
37
29
23
19
36
30
24
19
16
39
30
24
19
16
27
23
19
15
12
30
24
19
15
12
12
13
19
19
16
16
13
11
13
11
10
9
10
9
0
95
131
80
111
65
91
49
63
2
3
4
5
6
89
85
80
74
67
120
113
104
93
82
74
71
66
61
55
99
93
85
76
66
58
56
52
48
44
77
73
67
60
52
41
39
37
34
31
50
48
44
40
36
7
8
9
10
11
60
52
45
38
32
70
58
47
38
32
49
42
36
32
26
56
48
39
32
26
39
33
28
25
21
44
36
31
25
21
28
24
21
17
15
31
26
22
18
15
12
13
14
15
16
27
23
20
17
15
27
23
20
17
15
22
19
16
14
22
19
16
14
17
15
13
11
17
15
13
11
13
11
10
8
13
11
10
8
b
Properties of 2 angles—3⁄8 in. back to back
2
A (in )
rx (in.)
ry (in.)
No. of
a
Connectors
21⁄2×2
Size
Effective length KL (ft) with respect to indicated axis
Y
3.09
0.768
0.961
2.62
0.776
0.948
2.13
0.784
0.935
aFor Y-Y axis, welded or fully tensioned bolted connectors only.
bFor number of connectors, see double angle column discussion.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1.62
0.793
0.923
2
3
3 - 74
COLUMN DESIGN
Fy = 36 ksi
Fy = 50 ksi
COLUMNS
Double angles
Y
X
X
Unequal legs
8×
×6
Size
Thickness
Wt./ft
88.4
Fy
36
X-X AXIS
Y-Y AXIS
67.6
46.0
50
36
50
796 1110 609
846
376
479
8
12
16
20
24
677
552
416
288
200
882
666
449
288
200
521
428
325
228
159
680
518
354
228
159
328
276
217
159
111
402
323
237
160
111
28
29
147
147 116
109
116
109
82
76
796 1110 609
846
12
16
20
24
28
725
681
628
569
506
970
890
796
695
591
547
514
474
429
382
32
36
40
44
48
443
380
320
265
223
490
396
321
265
223
52
56
60
61
62
190
164
143
138
134
190
164
143
138
134
63
130
130
0
50
1⁄
2
36
0
Effective length KL (ft) with respect to indicated axis
3⁄
4
1
8×
×4
3⁄
4
1
74.8
1⁄
2
57.4
50
0
673
935 517 718 321 408
4
6
8
10
12
600
521
426
329
240
798
654
495
346
240
82
76
14
16
17
18
176 176 141 141 101 101
135 135 108 108
78
78
120 120
96
96
69
69
61
61
376
479
0
673
935 517 718 321 408
727
667
598
522
444
325
308
287
263
237
393
368
338
304
267
12
16
20
24
28
628
596
558
514
467
849
790
720
643
563
480
455
426
392
355
647
602
548
489
426
295
281
264
245
224
365
344
318
290
258
333
286
240
199
168
368
297
241
199
168
210
183
156
131
110
229
192
157
131
110
32
36
40
44
48
418
369
320
274
231
483
405
333
275
231
317
279
242
206
174
364
305
250
206
174
202
179
157
135
115
227
195
165
137
115
143
123
108
104
101
143
123
108
104
101
94
81
71
69
94
81
71
69
52
56
60
64
66
197
170
148
130
122
197 148 148
170 128 128
148 111 111
130
98
98
122
92
92
98
85
74
65
61
98
85
74
65
61
67
68
119 119
115 115
b
3
36
39.2
36
463
404
333
260
192
50
616
509
390
276
192
89
36
292
259
219
177
137
50
361
311
252
192
138
89
Properties of 2 angles—3⁄8 in. back to back
2
A (in )
rx (in.)
ry (in.)
26.0
1.73
3.78
19.9
1.76
3.74
13.5
1.79
3.69
22.0
1.03
4.10
aFor Y-Y axis, welded or fully tensioned bolted connectors only.
bFor number of connectors, see double angle column discussion.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
16.9
1.05
4.05
11.5
1.08
4.00
No. of a
Connectors
Short legs 3⁄8 in. back to back of angles
No. of a
Connectors
Y
Design axial strength in kips (φ = 0.85)
3/ ′′
8
b
6
DESIGN STRENGTH OF COLUMNS
3 - 75
Fy = 36 ksi
Fy = 50 ksi
COLUMNS
Double angles
Y
X
X
Unequal legs
7×
×4
Size
3⁄
4
Thickness
Wt./ft
1⁄
2
52.4
Fy
36
50
3⁄
8
35.8
36
50
27.2
36
50
No. of a
Connectors
Short legs 3⁄8 in. back to back of angles
Y-Y AXIS
Effective length KL (ft) with respect to indicated axis
X-X AXIS
0 471 655 310 401 205 254
4
6
8
10
12
426
375
313
249
188
568
476
371
270
188
282
250
212
171
132
354
304
245
186
133
189
171
149
124
100
230
203
171
137
104
14 138 138
16 106 106
18 84 84
98
75
59
98
75
59
77
59
47
3/ ′′
8
Y
6×
×4
3⁄
4
5⁄
8
47.2
50
0
36
50
1⁄
2
40.0
36
3⁄
8
32.4
50
36
24.6
50
36
50
425 591 358 497 291 388 201 256
4
6
8
10
12
386
342
289
232
178
436
370
293
218
154
265
236
201
164
127
343
295
238
181
129
186
168
146
122
97
231
203
170
135
102
77
59
47
14
16
18
19
132 132 113 113
101 101 86 86
80 80 68 68
95
73
57
52
95
73
57
52
75
57
45
41
75
57
45
41
0 471 655 310 401 205 254
0
8
12
16
20
24
449
427
397
362
324
611
570
516
454
389
291
277
259
236
212
368
346
317
282
245
28
32
36
40
44
283
243
204
168
139
323
261
207
168
139
186
160
135
111
92
207 129 143
171 113 122
137 98 102
111 83 83
92 69 69
48 117 117
52 99 99
56 86 86
57 83 83
58 80 80
77
66
57
55
77
66
57
55
188
181
171
158
144
58
49
43
41
b
225
215
201
184
164
58
49
43
41
5
517
437
345
255
179
326
289
245
198
152
A (in )
rx (in.)
ry (in.)
15.4
1.09
3.49
10.5
1.11
3.44
7.97
1.13
3.42
b
425 591 358 497 291 388 201 256
8
12
16
20
24
398
370
334
293
249
538
486
422
352
282
28
32
36
40
44
206
166
131
106
88
216 172 179 138 143 100 105
165 138 138 110 110 81 82
131 109 109 87 87 65 65
106 88 88 71 71 52 52
88 73 73 58 58 43 43
45
46
47
48
49
84
80
77
74
71
84
80
77
74
71
333
310
279
245
208
70
67
64
61
449
406
352
294
235
70
67
64
61
267
249
224
197
167
56
53
51
49
346
314
275
230
186
56
53
51
49
181
170
155
138
119
42
40
38
222
205
184
158
131
42
40
38
Properties of 2 angles—3⁄8 in. back to back
2
No. of a
Connectors
Design axial strength in kips (φ = 0.85)
13.9
1.12
2.94
11.7
1.13
2.92
aFor Y-Y axis, welded or fully tensioned bolted connectors only.
bFor number of connectors, see double angle column discussion.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
9.50
1.15
2.90
7.22
1.17
2.87
4
3 - 76
COLUMN DESIGN
Fy = 36 ksi
Fy = 50 ksi
COLUMNS
Double angles
Y
X
X
Unequal legs
6×
×31⁄2
Size
3⁄
8
Thickness
Wt./ft
23.4
Y-Y AXIS
X-X AXIS
Fy
Effective length KL (ft) with respect to indicated axis
5⁄
16
19.6
36
50
36
50
0
191
243
145
179
4
6
8
10
170
148
121
94
210
175
136
99
131
115
97
77
158
135
109
82
12
14
16
69
50
39
69
50
39
58
43
33
59
43
33
0
191
243
145
8
12
16
20
24
173
160
144
125
112
213
194
170
142
124
28
32
36
40
44
94
76
63
51
42
48
49
36
34
5×
×31⁄2
3⁄
4
1⁄
2
39.6
3⁄
8
27.2
5⁄
16
20.8
50
36
50
0
355
493
245
340 183 238 143 182
2
4
6
8
10
344
313
267
214
160
472 238 326
413 217 288
331 187 234
243 152 176
164 116 121
12
14
16
17
114
84
64
114
84
64
84
62
47
179
0
355
493
245
340 183 238 143 182
130
122
111
98
84
154
143
128
110
98
8
10
12
14
16
318
300
279
257
233
423
390
354
334
297
217
205
191
175
159
287
265
240
214
201
99
80
63
51
42
75
62
53
43
35
80
66
53
43
35
18
20
22
24
26
224
201
179
157
144
260
225
201
169
144
152
136
121
106
96
175 106 127
151 101 111
134
90
95
113
79
84
96
69
72
36
34
30
29
30
29
28
30
32
34
36
125
109
95
85
75
125
109
95
85
75
83
72
64
56
50
83
72
64
56
50
62
54
48
42
38
62
54
48
42
38
49
43
38
33
30
49
43
38
33
30
38
39
40
68
64
61
68
64
61
45
43
41
45
43
41
34
32
31
34
32
31
27
25
27
25
41
58
58
b
5
36
17.4
36
178
163
141
116
89
84
62
47
50
50
229 139 176
205 129 159
170 113 135
131
94 107
94
74
79
65
48
37
32
160
151
141
130
118
36
65
48
37
32
198
185
169
153
143
56
41
31
28
123
117
110
102
94
6.84
0.988
2.95
5.74
0.996
2.94
11.6
0.977
2.48
8.00
1.01
2.43
aFor Y-Y axis, welded or fully tensioned bolted connectors only.
bFor number of connectors, see double angle column discussion.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
6.09
1.02
2.41
b
56
41
31
28
149
140
130
119
106
85 100
81
89
73
77
65
66
57
57
Properties of 2 angles—3⁄8 in. back to back
A (in2)
rx (in.)
ry (in.)
No. of a
Connectors
Short legs 3⁄8 in. back to back of angles
No. of a
Connectors
Y
Design axial strength in kips (φ = 0.85)
3/ ′′
8
5.12
1.03
2.39
4
DESIGN STRENGTH OF COLUMNS
3 - 77
Fy = 36 ksi
Fy = 50 ksi
COLUMNS
Double angles
Y
X
X
Unequal legs
Short legs 3⁄8 in. back to back of angles
5×
×3
Size
1⁄
2
Thickness
Wt./ft
X-X AXIS
Y-Y AXIS
3⁄
8
25.6
Fy
Effective length KL (ft) with respect to indicated axis
Y
5⁄
16
19.6
1⁄
4
16.4
13.2
36
50
36
50
36
50
36
50
0
230
319
172
223
134
170
95
117
2
4
6
8
10
220
192
154
113
76
300
249
184
119
76
165
146
118
88
61
212
180
137
94
61
129
115
95
73
52
162
140
110
79
52
92
84
71
56
42
112
99
81
61
43
12
13
14
53
45
53
45
42
36
31
42
36
31
36
31
26
36
31
26
30
25
22
30
25
22
0
230
319
172
223
134
170
95
117
8
10
12
14
16
205
194
181
167
152
273
253
230
205
194
152
144
135
125
114
190
178
163
147
139
118
112
106
98
90
144
135
126
115
103
83
79
75
71
66
96
92
87
81
75
18
20
22
24
26
146
132
117
103
95
170
147
132
112
95
109
99
88
78
68
124
109
94
84
71
82
79
71
63
56
98
87
76
66
59
61
56
54
49
44
68
65
58
51
45
28
30
32
34
36
82
72
63
56
50
82
72
63
56
50
62
54
47
42
37
62
54
47
42
37
51
45
39
35
31
51
45
39
35
31
39
36
31
28
25
41
36
31
28
25
38
40
41
45
40
38
45
40
38
34
30
29
34
30
29
28
25
24
28
25
24
22
20
19
22
20
19
3/ ′′
8
No. of
a
Connectors
Design axial strength in kips (φ = 0.85)
b
4
5
Properties of 2 angles—3⁄8 in. back to back
2
A (in )
rx (in.)
ry (in.)
7.50
0.829
2.50
5.72
0.845
2.48
4.80
0.853
2.47
aFor Y-Y axis, welded or fully tensioned bolted connectors only.
bFor number of connectors, see double angle column discussion.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
3.88
0.861
2.46
3 - 78
COLUMN DESIGN
Fy = 36 ksi
Fy = 50 ksi
COLUMNS
Double angles
Y
X
Y
Design axial strength in kips (φ = 0.85)
Unequal legs
3/ ′′
8
Short legs 3⁄8 in. back to back of angles
4×
×31⁄2
Size
1⁄
2
Thickness
Wt./ft
23.8
X-X AXIS
Fy
Y-Y AXIS
Effective length KL (ft) with respect to indicated axis
3⁄
8
5⁄
16
18.2
1⁄
4
15.4
12.4
36
50
36
50
36
50
36
50
0
214
298
163
227
137
179
101
129
2
4
6
8
10
208
191
166
137
106
286
255
210
160
112
159
147
128
106
83
219
195
162
125
89
133
123
108
90
71
172
156
131
103
76
99
92
81
69
55
125
114
98
79
60
12
14
16
17
78
57
44
39
78
57
44
39
62
45
35
31
62
45
35
31
53
39
30
26
53
39
30
26
42
31
24
21
43
31
24
21
0
214
298
163
227
137
179
101
129
4
6
8
10
12
201
190
177
161
143
271
252
228
200
181
150
142
132
120
107
200
187
169
149
127
122
116
108
99
89
152
143
132
117
102
86
83
78
72
66
103
99
92
84
75
14
16
18
20
22
132
115
98
86
71
153
126
106
86
71
94
86
73
61
53
114
94
75
61
53
77
71
61
51
42
92
77
62
51
42
58
54
47
40
33
65
59
49
40
33
24
26
28
30
31
60
51
44
38
36
60
51
44
38
36
45
38
33
29
27
45
38
33
29
27
36
30
26
23
21
36
30
26
23
21
28
24
21
18
28
24
21
18
Properties of 2 angles—3⁄8 in. back to back
2
A (in )
rx (in.)
ry (in.)
7.00
1.04
1.89
5.34
1.06
1.87
4.49
1.07
1.86
aFor Y-Y axis, welded or fully tensioned bolted connectors only.
bFor number of connectors, see double angle column discussion.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
3.63
1.07
1.85
No. of
a
Connectors
X
b
3
DESIGN STRENGTH OF COLUMNS
3 - 79
Fy = 36 ksi
Fy = 50 ksi
COLUMNS
Double angles
Y
X
X
Unequal legs
Short legs 3⁄8 in. back to back of angles
4×
×3
Size
1⁄
2
Thickness
Wt./ft
X-X AXIS
Y-Y AXIS
3⁄
8
22.2
Fy
Effective length KL (ft) with respect to indicated axis
Y
5⁄
16
17.0
1⁄
4
14.4
11.6
36
50
36
50
36
50
36
50
0
199
276
152
211
127
166
94
120
2
4
6
8
10
191
169
138
104
72
261
220
166
112
72
146
130
107
81
57
200
170
129
88
57
123
109
90
69
49
158
136
106
75
49
91
82
69
54
40
115
101
81
59
40
12
14
50
37
50
37
40
29
40
29
34
25
34
25
28
21
28
21
0
199
276
152
211
127
166
94
120
4
6
8
10
12
190
182
172
160
146
259
245
226
204
180
143
137
130
121
110
193
183
169
153
135
118
113
107
99
91
149
142
132
120
107
85
82
78
73
67
103
99
93
86
78
14
16
18
20
22
131
116
101
86
73
156
131
108
88
73
99
87
76
65
54
117
98
81
66
54
81
72
62
53
44
93
79
65
53
44
61
55
48
41
35
69
60
51
42
35
24
26
28
30
32
61
52
45
39
34
61
52
45
39
34
46
39
34
29
26
46
39
34
29
26
37
32
27
24
21
37
32
27
24
21
30
25
22
19
17
30
25
22
19
17
3/ ′′
8
No. of
a
Connectors
Design axial strength in kips (φ = 0.85)
b
3
4
Properties of 2 angles—3⁄8 in. back to back
2
A (in )
rx (in.)
ry (in.)
6.50
0.864
1.96
4.97
0.879
1.94
4.18
0.887
1.93
aFor Y-Y axis, welded or fully tensioned bolted connectors only.
bFor number of connectors, see double angle column discussion.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
3.38
0.896
1.92
3 - 80
COLUMN DESIGN
Fy = 36 ksi
Fy = 50 ksi
COLUMNS
Double angles
Y
X
X
Unequal legs
31⁄2×3
Size
3⁄
8
Thickness
Wt./ft
15.8
X-X AXIS
Fy
Y-Y AXIS
Effective length KL (ft) with respect to indicated axis
5⁄
16
1⁄
4
13.2
10.8
36
50
36
50
36
50
0
140
195
118
162
92
2
4
6
8
10
135
121
100
77
55
185
158
122
84
55
114
102
85
65
47
154
132
103
72
47
12
14
15
38
28
38
28
33
24
21
0
140
195
4
6
8
10
12
130
123
114
103
91
14
16
18
20
22
24
26
27
31⁄2×21⁄2
3⁄
8
1⁄
4
14.4
9.8
50
36
50
36
50
119
0
129
179
85
110
89
80
67
53
38
114
100
79
58
39
2
4
6
8
10
122
102
76
51
32
165
129
86
51
32
81
68
52
36
23
102
83
59
36
23
33
24
21
27
20
17
27
20
17
11
12
27
27
19
16
19
16
118
162
92
119
0
129
179
85
110
175
162
146
127
107
108
102
94
85
75
142
132
119
104
88
82
77
72
66
58
100
94
86
77
66
4
6
8
10
12
122
116
108
98
87
165
154
139
122
105
78
74
69
63
57
97
91
84
75
65
78
66
54
44
36
87
68
54
44
36
65
55
45
37
30
72
57
45
37
30
51
43
36
29
24
55
45
36
29
24
14
16
18
20
22
76
65
55
45
37
87
70
55
45
37
50
43
36
30
25
55
46
37
30
25
31
26
24
31
26
24
26
22
20
26
22
20
20
17
16
20
17
16
24
26
28
29
31
27
23
21
31
27
23
21
21
18
15
21
18
15
b
3
Properties of 2 angles—3⁄8 in. back to back
2
A (in )
rx (in.)
ry (in.)
4.59
0.897
1.67
3.87
0.905
1.66
3.13
0.914
1.65
aFor Y-Y axis, welded or fully tensioned bolted connectors only.
bFor number of connectors, see double angle column discussion.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
4.22
0.719
1.74
2.88
0.735
1.72
No. of a
Connectors
Short legs 3⁄8 in. back to back of angles
No. of
a
Connectors
Y
Design axial strength in kips (φ = 0.85)
3/ ′′
8
b
4
DESIGN STRENGTH OF COLUMNS
3 - 81
Fy = 36 ksi
Fy = 50 ksi
COLUMNS
Double angles
Y
X
X
Unequal legs
3×
×21⁄2
Size
3⁄
8
Thickness
Wt./ft
13.2
X-X AXIS
Fy
36
3⁄
16
9.0
6.77
50
36
50
36
50
0 118 163
80
107
55
71
2 111 151
3 104 137
4 94 120
5 83 100
6 71 81
76
71
65
58
50
100
91
81
69
56
53
50
46
41
36
66
62
55
48
41
45
35
27
22
18
31
26
21
17
14
34
27
21
17
14
3/ ′′
8
Y
3×
×2
3⁄
8
5⁄
16
11.8
50
36
1⁄
4
10.0
3⁄
16
8.2
6.1
50
36
50
36
50
36
50
0
106 147
90
125
73
97
50
64
2
3
4
5
6
96 129
85 109
72 86
58 64
44 45
82
73
61
50
38
109
93
74
55
39
66
59
50
41
32
86
74
59
45
32
46
42
36
30
24
58
51
42
33
25
7
8
9
33
25
20
33
25
20
28
22
17
28
22
17
24
18
14
24
18
14
18
14
11
18
14
11
106 147
90
125
73
97
50
64
b
7
8
9
10
11
59
48
38
31
25
63
48
38
31
25
42
34
27
22
18
12
21
b
21
15
15
12
12
0 118 163
80
107
55
71
0
2 113 155
4 109 146
6 101 132
8 91 114
10 79 95
75
72
67
60
53
97
92
84
73
62
49
47
45
41
36
59
57
53
48
41
2
4
6
8
10
104
100
93
85
76
143
135
123
109
92
87
84
78
71
63
119
113
103
91
77
70
67
63
57
51
92
87
80
70
60
47
45
43
39
35
58
55
52
47
41
12
14
16
18
20
67
56
44
35
28
76
58
44
35
28
45
37
29
23
19
50
38
29
23
19
32
27
22
17
14
35
28
22
17
14
12
14
16
18
20
65
55
45
36
29
75
59
46
36
29
54
46
37
30
24
62
49
38
30
24
44
37
30
24
19
49
39
30
24
19
31
26
22
18
14
35
28
22
18
14
22
24
23
20
23
20
16
13
16
13
12
10
12
10
22
24
25
24
20
19
24 20
20 17
19 15
20 16
17 13
15 12
16
13
12
12
10
9
12
10
9
3
Y-Y AXIS
Effective length KL (ft) with respect to indicated axis
1⁄
4
No. of a
Connectors
Short legs 3⁄8 in. back to back of angles
No. of a
Connectors
Design axial strength in kips (φ = 0.85)
Properties of 2 angles—3⁄8 in. back to back
2
A (in )
rx (in.)
ry (in.)
3.84
0.736
1.47
2.63
0.753
1.45
1.99
0.761
1.44
3.47
0.559
1.55
2.93
0.567
1.53
aFor Y-Y axis, welded or fully tensioned bolted connectors only.
bFor number of connectors, see double angle column discussion.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
2.38
0.574
1.52
1.80
0.583
1.51
4
3 - 82
COLUMN DESIGN
Fy = 36 ksi
Fy = 50 ksi
COLUMNS
Double angles
Y
X
Y
Design axial strength in kips (φ = 0.85)
Unequal legs
3/ ′′
8
Short legs 3⁄8 in. back to back of angles
21⁄2×2
Size
3⁄
8
Thickness
Wt./ft
10.6
X-X AXIS
Fy
Effective length KL (ft) with respect to indicated axis
5⁄
16
1⁄
4
9.0
3⁄
16
7.2
5.5
36
50
36
50
36
50
36
50
0
95
131
80
111
65
91
49
63
2
3
4
5
6
86
77
66
54
42
116
99
79
60
42
73
66
56
46
36
98
84
68
51
37
60
54
46
38
30
80
69
56
43
31
45
40
35
29
23
57
50
41
32
24
7
8
9
10
31
24
19
31
24
19
27
21
16
27
21
16
23
17
14
23
17
14
18
14
11
9
18
14
11
9
0
95
131
80
111
65
91
49
63
2
4
6
8
10
92
86
78
69
58
126
116
101
84
66
77
73
66
57
47
105
97
84
69
54
62
58
53
46
38
84
77
67
55
43
45
42
38
33
28
56
52
46
39
31
12
14
16
18
20
46
36
28
22
18
49
36
28
22
18
38
29
22
17
14
39
29
22
17
14
30
23
18
14
11
31
23
18
14
11
22
17
13
10
9
23
17
13
10
9
21
16
16
13
13
No. of
a
Connectors
X
b
Y-Y AXIS
3
4
Properties of 2 angles—3⁄8 in. back to back
2
A (in )
rx (in.)
ry (in.)
3.09
0.577
1.28
2.62
0.584
1.26
2.13
0.592
1.25
aFor Y-Y axis, welded or fully tensioned bolted connectors only.
bFor number of connectors, see double angle column discussion.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1.62
0.600
1.24
DESIGN STRENGTH OF COLUMNS
3 - 83
Fy = 36 ksi
Y
Fy = 50 ksi
COLUMNS
Structural tees
cut from W shapes
X
Design axial strength in kips (φ = 0.85)
Designation
X-X AXIS
Y-Y AXIS
Effective length KL (ft) with respect to indicated axis
Y
WT 18
150
Wt./ft
Fy
X
140
130
122.5
115
36
50
36
50
36
50
36
50
36
50
0
1350
1730
1260
1510
1150
1330
1040
1170
925
1030
10
12
14
16
18
1310
1300
1280
1260
1240
1670
1650
1620
1590
1550
1230
1210
1190
1180
1150
1470
1440
1420
1390
1360
1120
1100
1090
1070
1050
1290
1270
1250
1220
1200
1010
998
985
970
953
1140
1130
1110
1090
1070
903
893
882
869
855
998
986
972
956
939
20
22
24
26
28
1210
1180
1150
1120
1090
1510
1460
1420
1370
1320
1130
1100
1080
1050
1020
1330
1290
1250
1210
1170
1030
1010
983
957
930
1170
1140
1110
1070
1040
935
915
893
870
847
1050
1020
993
964
934
839
822
803
784
763
920
899
876
853
828
30
32
34
36
38
1060
1020
984
947
910
1260
1210
1160
1100
1040
984
951
917
883
847
1120
1080
1030
987
940
901
871
841
810
778
1000
965
926
886
847
822
796
769
742
714
903
871
838
804
770
742
719
696
673
649
802
776
748
720
692
40
872
989
812
893
746
806
686
736
624
663
0
1350
1730
1260
1510
1150
1330
1040
1170
925
1030
10
12
14
16
18
1210
1190
1160
1130
1090
1510
1470
1430
1370
1320
1120
1100
1070
1040
1010
1320
1290
1250
1210
1160
1010
990
966
938
908
1140
1120
1090
1050
1010
906
888
867
843
817
1010
985
959
930
898
803
788
770
750
728
874
857
836
812
786
20
22
24
26
28
1050
1010
962
916
868
1260
1190
1130
1060
988
972
932
891
848
804
1110
1060
1000
943
884
876
841
804
766
726
971
927
880
833
784
789
759
727
693
659
863
826
787
747
705
704
679
651
623
593
758
728
696
662
628
30
32
34
36
38
820
771
721
672
624
918
848
780
713
647
758
713
667
622
577
825
766
708
650
595
686
645
604
563
523
734
684
634
585
537
623
587
551
515
480
662
619
577
534
493
563
532
501
469
438
592
557
521
485
450
40
577
585
533
540
484
490
445
452
408
415
Properties
A (in2)
rx (in.)
ry (in.)
44.1
5.27
3.83
41.2
5.25
3.81
38.2
5.26
3.78
36.0
5.26
3.75
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
33.8
5.25
3.73
3 - 84
COLUMN DESIGN
Fy = 36 ksi
Y
Fy = 50 ksi
X
COLUMNS
Structural tees
cut from W shapes
X
Design axial strength in kips (φ = 0.85)
Y
Designation
105
Wt./ft
X-X AXIS
Fy
36
97
50
91
85
80
75
67.5
36
50
36
50
36
50
36
50
36
50
36
50
0
908 1040 772
851
683
726
587
601
518
521
458
457
385
385
10
12
14
16
18
887 1010 755
878 1000 748
868 986 740
856 971 731
843 954 720
831
822
812
801
788
670
664
657
649
640
710
704
696
687
677
576
571
566
560
553
590
585
579
572
565
509
505
500
495
489
512
508
503
498
492
451
448
444
440
435
449
446
442
438
433
380
377
374
371
367
380
377
374
371
367
20
22
24
26
28
828
813
796
778
759
935
915
893
870
846
709
696
683
668
653
775
759
743
726
708
631
620
609
597
584
667
655
642
629
614
545
537
528
518
508
557
548
539
529
518
483
476
468
460
452
486
479
471
463
454
429
424
417
411
403
428
422
416
409
402
363
359
354
348
343
363
359
354
348
343
30
32
36
40
739
719
675
630
821
795
740
684
637
621
586
549
689
669
628
585
571
557
527
496
599
584
551
517
497
486
462
437
507
495
470
444
443
433
413
392
445
436
415
394
396
388
371
353
395
387
370
352
337
331
317
303
337
331
317
303
908 1040 772
851
683
726
587
601
518
521
458
457
385
385
10
12
14
16
18
716
687
654
617
578
791
756
715
670
622
607
585
559
530
499
653
627
597
563
527
534
515
494
470
444
558
538
515
488
460
457
442
425
406
385
465
450
432
412
391
397
385
371
356
339
399
387
373
357
340
344
335
323
311
297
344
334
323
310
296
268
261
253
244
234
268
261
253
244
234
20
22
24
26
28
537
494
450
407
364
572
521
469
418
367
465
431
395
360
325
489
449
409
369
330
416
387
358
327
297
430
398
366
333
301
363
340
315
291
266
368
344
319
293
268
320
301
280
260
239
321
302
281
260
239
281
265
248
231
213
281
265
248
231
213
223
211
198
185
172
223
211
198
185
172
30
32
34
36
39
323
285
254
228
195
323
285
254
228
195
291
258
230
206
176
291
258
230
206
176
268
239
213
191
164
269
239
213
191
164
242
218
194
174
150
242
218
194
174
150
218
197
177
159
137
218
197
177
159
137
196
178
161
144
124
195
178
161
144
124
158
144
131
118
102
158
144
131
118
102
41
42
43
177
169
161
177 160
169 153
161
160
153
149
142
149
142
136
130
136
130
124
124
113
113
0
Y-Y AXIS
Effective length KL (ft) with respect to indicated axis
WT 18
Properties
A (in2)
rx (in.)
ry (in.)
30.9
5.65
2.58
28.5
5.62
2.56
26.8
5.62
2.55
25.0
5.61
2.53
Note: Heavy line indicates Kl / r of 200.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
23.5
5.61
2.50
22.1
5.62
2.47
19.9
5.66
2.38
DESIGN STRENGTH OF COLUMNS
3 - 85
Fy = 36 ksi
Y
Fy = 50 ksi
COLUMNS
Structural tees
cut from W shapes
X
X
Design axial strength in kips (φ = 0.85)
Designation
Y-Y AXIS
X-X AXIS
Fy
Effective length KL (ft) with respect to indicated axis
WT 16.5
120.5
Wt./ft
Y
36
50
110.5
36
50
100.5
76
70.5
65
59
36
50
36
50
36
50
36
50
0 1080 1300 964 1110 810
899
532
548
463
467
402
401
330
330
10
12
14
16
18
1050
1040
1020
1000
980
1260
1240
1210
1190
1160
935
923
909
893
875
1070
1050
1030
1010
990
788
779
767
755
741
872
860
847
831
814
521
516
510
503
495
535
530
524
516
508
453
449
444
439
433
457
453
448
442
436
394
391
387
383
378
393
390
386
382
377
324
321
318
315
311
324
321
318
315
311
20
22
24
26
28
958
933
907
880
851
1120
1090
1050
1020
975
855
834
811
787
762
965
937
908
878
846
725
708
690
672
652
795
775
753
730
706
487
478
468
458
447
500
490
480
469
458
426
419
411
402
393
429
422
414
405
396
372
366
360
353
345
371
365
359
352
345
307
303
298
293
287
307
303
298
293
287
30
32
34
36
40
821
790
759
727
662
934
892
849
806
720
737
710
682
654
598
813
779
745
710
639
631
610
588
565
520
681
656
630
603
549
436
424
411
399
373
446
433
420
407
379
384
374
364
354
332
387
377
366
356
334
338
330
321
313
295
337
329
321
312
295
282
276
269
263
249
282
276
269
263
249
0 1080 1300 964 1110 810
899
532
548
463
467
402
401
330
330
10
12
14
16
18
951
929
904
876
845
1110
1080
1050
1010
967
833
815
793
769
743
934
911
884
854
821
692
678
661
643
622
753
736
717
695
671
420
406
389
370
349
429
414
396
377
355
358
346
333
318
301
360
348
335
319
302
300
291
280
268
255
299
290
280
268
255
234
228
220
212
203
234
228
220
212
203
20
22
24
26
28
811
775
738
699
659
922
874
824
772
720
714
683
651
617
583
785
747
707
666
624
600
576
551
525
497
644
616
587
556
525
327
305
281
257
234
332
309
284
260
235
283
264
245
225
206
284
266
246
226
206
241
226
211
195
179
241
226
210
195
178
192
181
170
158
146
192
181
170
158
146
30
34
36
38
39
618
537
497
458
439
667
564
514
464
441
548
477
442
408
391
581
496
455
414
394
470
413
385
357
343
492
427
395
363
348
211
167
150
135
129
211
167
150
135
129
186
149
134
121
115
187
149
134
121
115
162
131
118
107
102
162
131
118
107
102
134
109
98
89
134
109
98
89
40
41
420
401
420 375
401 358
375 330
358 316
332
317
123
117
123
117
109
109
Properties
A (in2)
rx (in.)
ry (in.)
35.4
4.96
3.63
32.5
4.96
3.59
29.5
4.95
3.56
22.4
5.14
2.47
20.8
5.15
2.43
Note: Heavy line indicates Kl / r of 200.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
19.2
5.18
2.39
17.3
5.20
2.32
3 - 86
COLUMN DESIGN
Fy = 36 ksi
Y
Fy = 50 ksi
X
COLUMNS
Structural tees
cut from W shapes
X
Design axial strength in kips (φ = 0.85)
Y
Designation
105.5
Wt./ft
Fy
36
Effective length KL (ft) with respect to indicated axis
X-X AXIS
0
50
95.5
36
50
86.5
36
66
50
36
62
50
36
58
50
36
54
50
36
49.5
50
36
50
949 1180 844 974 708 791 505 546 447 465 402 412 357 361 304 303
10
12
14
16
18
913
897
879
859
837
1130
1100
1080
1050
1010
812
799
783
765
746
932
914
894
870
845
684
673
661
647
632
761
748
733
715
696
490
484
477
468
459
529
521
513
503
492
434
429
423
416
408
452
446
439
432
423
392
387
382
376
369
401
396
391
384
377
348
344
340
335
329
352
348
343
338
332
297
294
290
286
282
296
293
290
286
281
20
22
24
26
28
813
787
759
731
701
976
938
897
855
811
724
702
678
652
626
817
787
756
724
690
615
597
578
558
537
676
654
630
606
581
449
437
426
413
400
480
467
454
439
424
399
390
380
370
359
414
404
393
382
370
361
353
345
336
326
369
361
352
343
333
323
316
309
301
293
326
319
311
304
295
277
271
266
259
253
276
271
265
259
253
30
32
34
36
40
670
639
607
575
511
767
723
678
634
547
599
571
543
515
459
656
621
586
551
482
515
493
471
448
402
555
528
501
474
421
387
373
358
344
314
409
393
377
360
327
347
335
323
311
285
358
345
332
319
292
316
306
295
284
262
322
311
300
289
266
284
276
267
257
238
287
278
269
259
240
246
239
232
224
209
246
239
232
224
209
0
Y-Y AXIS
WT 15
949 1180 844 974 708 791 505 546 447 465 402 412 357 361 304 303
10
12
14
16
18
838 1010 734 828 609 667
817 982 716 805 595 651
793 946 695 778 579 631
766 907 672 749 561 610
736 864 646 717 541 586
389
371
350
328
303
411
391
368
343
316
340
325
308
290
269
350
335
317
297
275
298
286
271
256
238
303
290
276
259
241
254
244
233
220
206
256
246
234
221
207
207
199
191
181
170
206
199
191
181
170
20
22
24
26
28
704
670
635
598
561
818
769
720
669
617
619
589
559
527
495
682
645
607
568
528
520
497
473
448
422
561
533
505
475
445
278
252
227
201
176
288
259
231
203
176
248
226
204
183
161
253
230
207
184
161
220
201
182
163
145
223
203
183
164
145
191
175
159
143
127
192
176
160
143
127
159
147
134
121
108
159
146
134
121
108
30
32
34
35
36
523
486
449
430
412
567
517
468
444
420
462
429
397
381
365
488
448
410
391
372
396
370
344
331
318
415
384
354
339
325
155
137
122
115
109
155
137
122
115
109
142
125
112
106
100
142 127 127 112 112
125 113 113 100 100
112 100 100 89 89
106 95 95 84 84
100 90 90
96
85
76
96
85
76
37
38
40
395
377
342
398 349 353 305 310 103 103
378 334 335 293 296
342 303 303 268 268
95
95
Properties
A (in2)
rx (in.)
ry (in.)
31.0
4.43
3.49
28.1
4.42
3.46
25.4
4.42
3.43
19.4
4.66
2.25
18.2
4.66
2.23
Note: Heavy line indicates Kl / r of 200.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
17.1
4.67
2.19
15.9
4.69
2.15
14.5
4.71
2.10
DESIGN STRENGTH OF COLUMNS
3 - 87
Fy = 36 ksi
Y
Fy = 50 ksi
COLUMNS
Structural tees
cut from W shapes
X
X
Design axial strength in kips (φ = 0.85)
Designation
WT 13.5
89
Wt./ft
Fy
36
X-X AXIS
50
73
57
51
47
42
50
36
50
36
50
36
50
36
50
36
50
799 1040 725
857
617
698
453
498
358
369
308
311
251
250
10
12
14
16
18
761
745
727
707
684
978
951
921
887
850
691
676
660
641
620
810
790
767
741
712
589
577
564
549
532
663
648
631
612
591
436
428
420
410
399
477
468
458
447
434
346
341
334
328
320
356
350
344
337
329
298
294
289
284
278
301
297
292
286
280
244
241
238
234
229
243
240
236
232
228
20
22
24
26
28
660
634
606
578
549
811
770
727
683
638
598
574
549
523
496
682
650
617
583
548
514
495
474
453
431
568
544
519
493
466
388
375
362
348
334
420
405
390
373
357
312
303
293
283
273
320
310
300
290
279
271
264
256
248
240
273
266
258
250
241
224
219
213
207
201
223
218
212
206
200
30
32
34
36
38
519
489
459
430
400
594
550
506
464
423
469
442
415
388
361
513
478
443
409
376
409
387
364
342
319
439
412
385
358
332
319
304
289
274
259
339
322
304
287
269
262
251
240
229
218
268
256
244
233
221
231
222
213
204
194
233
223
214
205
195
194
187
180
173
166
193
187
180
173
165
371
40
383 335
344
298
306
244
252
206
209
185
186
159
158
799 1040 725
857
617
698
453
498
358
369
308
311
251
250
10
12
14
16
18
701
681
658
632
604
877
845
808
768
725
627
609
588
565
540
720
696
669
639
606
527
513
497
479
459
583
566
546
524
500
349
331
311
288
264
374
353
330
304
277
275
263
248
232
215
281
268
253
236
218
231
221
210
197
184
233
223
211
198
185
181
174
166
157
147
180
173
165
156
147
20
22
24
26
28
574
542
509
476
442
678
631
582
533
484
513
485
456
426
395
571
534
497
458
420
437
415
391
367
342
474
446
418
389
359
240
215
191
167
145
249
221
193
167
145
197
179
160
142
125
199
180
161
143
125
169
154
140
125
110
170
155
140
125
110
137
126
114
103
92
136
125
114
103
92
30
32
34
35
36
408
374
342
326
310
436
390
347
328
310
365
335
305
291
277
382
345
309
292
277
317
292
268
256
244
330
301
273
259
245
127
112
100
94
89
127
112
100
94
89
109
97
86
81
109
97
86
81
97
86
76
72
97
86
76
72
81
72
64
81
72
64
40
252
252 225
225
200
200
0
Y-Y AXIS
80.5
36
0
Effective length KL (ft) with respect to indicated axis
Y
Properties
A (in2)
rx (in.)
ry (in.)
26.1
3.98
3.26
23.7
3.96
3.24
21.5
3.95
3.21
16.8
4.15
2.18
15.0
4.14
2.15
Note: Heavy line indicates Kl / r of 200.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
13.8
4.16
2.12
12.4
4.18
2.07
3 - 88
COLUMN DESIGN
Fy = 36 ksi
Y
Fy = 50 ksi
X
COLUMNS
Structural tees
cut from W shapes
X
Design axial strength in kips (φ = 0.85)
Y
Designation
WT 12
81
Wt./ft
Y-Y AXIS
Effective length KL (ft) with respect to indicated axis
X-X AXIS
Fy
73
65.5
58.5
52
36
50
36
50
36
50
36
50
36
50
0
731
1020
658
864
591
726
506
580
410
450
10
12
14
16
18
687
669
648
624
598
932
898
858
815
769
618
602
583
562
538
797
769
737
702
664
556
541
524
505
484
673
652
627
599
569
477
465
451
435
418
542
526
508
487
465
389
379
369
357
344
424
413
401
387
371
20
22
24
26
28
571
542
512
481
450
720
670
619
568
518
514
488
461
433
405
624
583
541
499
457
462
439
415
391
366
537
504
471
437
403
400
380
360
339
318
442
418
392
367
341
331
316
301
285
269
355
338
320
302
283
30
32
34
36
38
419
388
358
328
299
469
421
375
335
300
377
349
322
295
269
416
376
338
301
270
341
316
291
267
244
369
336
304
273
245
297
276
255
235
215
315
290
265
241
217
252
236
220
204
188
264
246
227
209
192
40
271
271
244
244
221
221
196
196
173
175
0
731
1020
658
864
591
726
506
580
410
450
10
12
14
16
18
648
626
601
574
544
858
819
775
727
675
575
555
533
508
482
723
691
656
617
575
505
487
468
446
422
597
573
545
515
482
424
410
395
377
358
472
455
435
414
390
338
328
317
304
290
363
352
339
324
308
20
22
24
26
28
512
480
446
412
378
622
568
514
460
409
453
424
393
363
332
532
487
442
398
355
397
371
345
317
290
448
412
376
340
305
338
316
294
272
249
365
339
313
286
259
275
260
243
226
209
291
273
254
235
216
30
32
34
36
38
345
312
281
251
225
359
316
281
251
225
303
273
245
219
197
313
276
245
219
197
264
238
213
190
171
271
239
213
190
171
227
206
184
165
149
233
207
184
165
149
192
175
159
143
129
196
178
159
143
129
40
204
204
178
178
155
155
135
135
117
117
Properties
A (in2)
rx (in.)
ry (in.)
23.9
3.50
3.05
21.5
3.50
3.01
19.3
3.52
2.97
Note: Heavy line indicates Kl / r of 200.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
17.2
3.51
2.94
15.3
3.51
2.91
DESIGN STRENGTH OF COLUMNS
3 - 89
Fy = 36 ksi
Y
Fy = 50 ksi
COLUMNS
Structural tees
cut from W shapes
X
X
Design axial strength in kips (φ = 0.85)
Designation
WT 12
47
Wt./ft
Y-Y AXIS
Effective length KL (ft) with respect to indicated axis
X-X AXIS
Fy
Y
42
38
34
31
27.5
36
50
36
50
36
50
36
50
36
50
36
50
0
378
419
307
321
254
258
209
208
202
203
155
155
10
12
14
16
18
360
352
343
332
321
396
387
376
363
350
293
287
280
273
265
306
299
292
284
275
244
240
234
229
222
247
243
237
231
225
201
198
194
189
185
200
197
193
189
184
194
191
187
183
178
196
192
188
184
179
150
148
145
142
139
150
148
145
142
139
20
22
24
26
28
309
296
283
269
255
335
320
304
287
271
256
246
236
225
215
265
255
244
233
221
215
208
200
192
184
218
210
202
194
185
179
174
168
162
155
179
173
167
161
155
173
168
162
156
150
174
169
163
157
150
136
132
128
124
120
136
132
128
124
120
30
32
34
36
38
240
226
211
197
183
254
237
220
203
187
204
192
181
170
159
209
197
185
173
161
175
166
157
148
140
176
167
158
149
140
148
142
135
128
121
148
141
135
128
121
143
136
130
123
116
144
137
130
123
117
115
111
106
101
96
115
111
106
101
96
40
169
171
148
150
131
131
114
114
109
110
92
92
0
378
419
307
321
254
258
209
208
202
203
155
155
10
12
14
16
18
288
269
248
226
202
310
288
263
237
211
231
218
202
185
168
239
224
208
190
171
188
178
166
154
140
190
179
167
155
141
148
140
132
123
113
147
140
132
123
113
121
110
97
84
71
122
110
98
84
71
91
84
75
67
57
91
84
75
67
57
20
22
23
24
26
179
156
145
134
115
184
158
145
134
115
150
132
124
115
99
152
134
124
115
99
126
113
106
99
86
127
113
106
99
86
103
92
87
82
71
103
92
87
82
71
59
49
46
59
49
46
48
41
48
41
28
30
31
32
33
99
87
82
77
72
99
87
82
77
72
86
75
71
66
86
75
71
66
74
65
61
58
74
65
61
58
62
55
51
62
55
51
Properties
A (in2)
rx (in.)
ry (in.)
13.8
3.67
1.98
12.4
3.67
1.95
11.2
3.68
1.92
10.0
3.70
1.87
Note: Heavy line indicates Kl / r of 200.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
9.11
3.79
1.38
8.10
3.80
1.34
3 - 90
COLUMN DESIGN
Fy = 36 ksi
Y
Fy = 50 ksi
X
COLUMNS
Structural tees
cut from W shapes
X
Design axial strength in kips (φ = 0.85)
Y
Designation
WT 10.5
73.5
Wt./ft
Y-Y AXIS
Effective length KL (ft) with respect to indicated axis
X-X AXIS
Fy
66
61
55.5
50.5
36
50
36
50
36
50
36
50
36
50
0
661
918
594
825
548
757
499
637
452
524
10
12
14
16
18
610
589
565
539
510
822
782
739
691
641
547
528
507
483
457
737
701
661
618
573
505
487
466
444
420
676
643
606
566
524
459
443
424
404
382
573
547
518
486
453
416
401
384
366
346
476
457
434
410
384
20
22
24
26
28
480
449
417
385
353
589
536
484
434
385
429
401
372
343
315
526
478
431
386
341
395
368
341
315
288
481
437
394
352
311
358
334
310
285
261
418
382
347
312
279
324
303
280
258
236
357
329
301
274
247
30
32
34
36
38
322
292
262
234
210
337
296
263
234
210
286
259
233
208
186
299
263
233
208
186
262
236
212
189
170
272
239
212
189
170
237
214
192
171
154
246
217
192
171
154
214
193
173
154
139
221
195
173
154
139
40
190
190
168
168
153
153
139
139
125
125
0
661
918
594
825
548
757
499
637
452
524
10
12
14
16
18
587
566
542
515
486
778
740
697
650
601
522
503
482
458
432
689
655
617
576
532
478
461
441
419
396
626
596
562
524
485
430
415
397
377
356
526
503
476
447
415
385
372
356
339
320
434
417
397
375
352
20
22
24
26
28
456
424
392
360
328
550
498
447
397
349
405
377
348
320
291
487
441
395
351
308
371
345
319
293
267
444
402
361
321
281
334
311
287
263
239
383
349
316
283
251
300
279
258
237
216
327
301
275
249
223
30
32
34
36
38
297
267
238
213
191
305
268
238
213
191
263
237
210
188
169
269
237
210
188
169
241
216
193
172
155
246
217
193
172
155
216
194
172
154
139
220
194
172
154
139
195
175
156
139
125
199
175
156
139
125
40
173
173
153
153
140
140
125
125
113
113
Properties
A (in2)
rx (in.)
ry (in.)
21.6
3.08
2.95
19.4
3.06
2.93
17.9
3.04
2.92
Note: Heavy line indicates Kl / r of 200.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
16.3
3.03
2.90
14.9
3.01
2.89
DESIGN STRENGTH OF COLUMNS
3 - 91
Fy = 36 ksi
Y
Fy = 50 ksi
COLUMNS
Structural tees
cut from W shapes
X
X
Design axial strength in kips (φ = 0.85)
Designation
Fy
36
X-X AXIS
Effective length KL (ft) with respect to indicated axis
0
50
41.5
36
50
36.5
36
34
50
36
31
50
36
28.5
50
36
50
25
36
22
50
36
50
419 562 373 444 297 331 261 283 219 225 203 210 165 167 127 127
6
8
10
12
14
409
400
390
378
364
543
529
511
489
466
364
356
347
336
323
430
420
407
392
374
290
284
278
270
260
322
316
307
297
286
255
251
245
239
231
276
271
264
256
247
214
211
206
201
195
221
217
212
207
201
199
196
192
187
182
206
203
199
194
188
162
160
157
153
149
164
161
158
155
151
125
123
121
119
116
125
123
121
119
116
16
18
20
22
24
349
332
315
296
277
439
412
383
353
323
310
295
279
262
245
355
335
314
291
269
250
239
227
215
202
274
260
246
231
216
222
213
203
192
182
237
227
215
203
191
189
181
174
165
157
194
186
178
169
160
176
170
163
155
147
182
175
167
159
151
145
140
134
129
123
146
141
136
130
124
113
110
106
102
98
113
110
106
102
98
26
28
30
32
34
258
239
220
201
183
293
264
236
209
185
228
210
193
177
160
247
225
203
182
162
189
176
163
150
137
200
185
169
155
140
170
159
148
137
126
178
165
153
140
128
148
139
130
121
112
151
142
132
123
114
139
131
123
115
107
143 117 118
134 111 111
125 104 105
117 98 98
108 91 92
94
90
85
81
76
94
90
85
81
76
36
38
40
165 165 145 145 125 126 115 117 104 104
148 148 130 130 113 113 105 105 95 96
134 134 117 117 102 102 95 95 87 87
71
67
63
71
67
63
0
Y-Y AXIS
WT 10.5
46.5
Wt./ft
Y
99 100
91 92
84 84
85
79
73
85
79
73
419 562 373 444 297 331 261 283 219 225 203 210 165 167 127 127
6
8
10
12
14
357
337
313
285
256
452
420
381
338
293
311
294
273
250
224
357
334
307
276
243
245
233
218
201
182
267
252
235
214
192
213
203
191
177
161
227
215
202
186
168
152
147
141
133
123
153
142
128
113
97
16
18
20
21
22
226
195
166
151
138
247
203
166
151
138
198
171
145
132
121
210
177
145
132
121
162
142
122
113
103
169
146
124
113
103
145
128
111
103
95
150 112 113
131 101 102
112 90 90
103 84 84
95 78 78
81
66
54
49
45
24
26
28
29
30
117 117 102 102
100 100 88 88
86 86 76 76
80 80 71 71
75 75 66 66
87
75
65
60
57
87
75
65
60
57
80
69
60
56
52
80
69
60
56
52
149
145
138
131
122
67
58
51
47
157 116 117
145 108 109
131 99 99
115 88 88
98 76 76
82
66
54
49
45
64
52
43
39
64
52
43
39
85
80
74
67
59
85
80
74
67
59
51
42
35
32
51
42
35
32
67
58
51
47
Properties
A
(in2)
rx (in.)
ry (in.)
13.7
3.25
1.84
12.2
3.22
1.83
10.7
3.21
1.81
10.0
3.20
1.80
9.13
3.21
1.77
8.37
3.29
1.35
Note: Heavy line indicates Kl / r of 200.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
7.36
3.30
1.30
6.49
3.31
1.26
3 - 92
COLUMN DESIGN
Fy = 36 ksi
Y
Fy = 50 ksi
X
COLUMNS
Structural tees
cut from W shapes
X
Design axial strength in kips (φ = 0.85)
Y
Designation
WT 9
59.5
Wt./ft
Y-Y AXIS
Effective length KL (ft) with respect to indicated axis
X-X AXIS
Fy
53
48.5
43
38
36
50
36
50
36
50
36
50
36
50
0
536
744
477
663
438
608
389
507
339
393
10
12
14
16
18
479
456
430
402
372
636
594
548
499
449
426
406
383
357
331
567
529
487
444
399
390
370
349
325
301
518
482
444
403
361
346
329
309
288
266
436
407
376
344
310
302
287
270
252
233
343
323
302
278
254
20
22
24
26
28
342
311
281
251
222
399
350
303
259
224
304
276
249
222
197
354
310
268
229
198
275
250
225
200
177
320
279
241
205
177
244
221
199
177
156
276
243
211
181
156
213
193
174
155
136
229
205
181
158
137
30
34
38
42
43
195
152
121
99
95
195
152
121
99
95
172
134
107
88
84
172
134
107
88
84
154
120
96
79
154
120
96
79
136
106
85
69
136
106
85
69
119
93
74
61
119
93
74
61
0
536
744
477
663
438
608
389
507
339
393
10
12
14
16
18
471
450
427
401
374
622
584
543
499
453
415
397
376
353
329
546
513
477
438
397
379
362
343
322
300
496
467
434
398
361
331
317
300
282
263
411
388
362
334
305
285
272
258
243
226
320
304
287
267
246
20
22
24
26
28
346
318
289
260
233
407
361
317
274
237
304
279
253
228
203
356
315
276
238
206
277
254
230
207
185
324
286
251
216
187
242
222
201
181
161
275
245
216
188
163
209
192
174
156
139
225
203
182
161
140
30
34
38
42
43
206
161
129
106
101
206
161
129
106
101
180
140
112
92
88
180
140
112
92
88
163
127
102
84
80
163
127
102
84
80
142
111
89
73
70
142
111
89
73
70
123
96
77
63
61
123
96
77
63
61
44
96
96
84
84
76
76
Properties
A (in2)
rx (in.)
ry (in.)
17.5
2.60
2.69
15.6
2.59
2.66
14.3
2.56
2.65
Note: Heavy line indicates Kl / r of 200.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
12.7
2.55
2.63
11.2
2.54
2.61
DESIGN STRENGTH OF COLUMNS
3 - 93
Fy = 36 ksi
Y
Fy = 50 ksi
COLUMNS
Structural tees
cut from W shapes
X
X
Design axial strength in kips (φ = 0.85)
Designation
Fy
36
X-X AXIS
Effective length KL (ft) with respect to indicated axis
0
32.5
50
36
30
50
36
27.5
50
36
25
50
36
23
50
36
20
50
36
17.5
50
36
50
318 426 292 356 261 299 226 253 184 194 172 183 124 124 101 101
10
12
14
16
18
288
275
261
246
229
372
351
327
302
275
264
252
239
225
210
314
297
279
259
238
236
226
214
202
189
266
253
239
223
206
206
197
188
178
167
227
217
206
193
180
169
163
156
148
140
177
171
163
154
145
168
161
154
146
138
116
112
108
104
99
116
112
108
104
99
95
92
89
86
82
95
92
89
86
82
20
22
24
26
28
212
195
178
161
144
248
222
196
171
148
194
178
162
146
131
216
195
173
153
134
175
161
147
133
119
189
172
155
138
122
155
143
131
120
108
166
152
138
124
111
131
122
113
103
94
135 124 129
126 116 120
116 107 111
106 99 101
96 90 92
94
89
84
78
72
94
89
83
78
72
78
74
70
66
62
78
74
70
66
62
30
32
34
36
38
128 129 116 116 106 107
113 113 102 102 94 94
100 100 91 91 83 83
89 89 81 81 74 74
80 80 72 72 66 66
97
86
76
68
61
98
86
76
68
61
85
77
68
61
55
86
77
68
61
55
82
74
67
59
53
83
75
67
59
53
67
61
56
51
46
67
61
56
51
46
57
53
49
45
41
57
53
49
45
41
55
50
48
44
55
50
48
44
49
45
43
39
49
45
43
39
48
44
42
38
36
48
44
42
38
36
41
38
36
33
31
41
38
36
33
31
37
34
32
29
28
37
34
32
29
28
40
42
43
45
46
0
Y-Y AXIS
WT 9
35.5
Wt./ft
Y
72
66
63
57
72
66
63
57
65
59
57
52
65
59
57
52
60
54
52
47
60
54
52
47
318 426 292 356 261 299 226 253 184 194 172 183 124 124 101 101
10
12
14
16
18
231
207
182
157
132
279
242
204
167
133
210
188
165
142
119
238
209
179
149
120
187
168
149
129
109
204
182
158
134
111
161
146
130
113
96
20
21
22
24
26
109 109
99 99
90 90
76 76
65 65
98
89
82
69
59
98
89
82
69
59
90
82
75
63
54
90
82
75
63
54
80
73
67
57
48
80
73
67
57
48
70
64
59
50
43
70
64
59
50
43
55
51
55
51
50
47
50
47
45
45
40
40
27
28
159
153
147
140
132
60
56
60
56
173 132 137 107 111
155 121 125 92 94
136 109 111 77 78
117 96 98 62 62
98 83 84 50 50
40
37
40
37
80
71
61
51
41
80
71
61
51
41
61
54
47
40
32
61
54
47
40
32
34
31
34
31
27
27
Properties
A (in2)
rx (in.)
ry (in.)
10.4
2.74
1.70
9.55
2.72
1.69
8.82
2.71
1.69
8.10
2.71
1.67
7.33
2.70
1.65
6.77
2.77
1.29
Note: Heavy line indicates Kl / r of 200.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
5.88
2.76
1.27
5.15
2.79
1.22
3 - 94
COLUMN DESIGN
Fy = 36 ksi
Y
Fy = 50 ksi
X
COLUMNS
Structural tees
cut from W shapes
X
Design axial strength in kips (φ = 0.85)
Y
Designation
WT 8
50
Wt./ft
Y-Y AXIS
Effective length KL (ft) with respect to indicated axis
X-X AXIS
Fy
44.5
38.5
33.5
36
50
36
50
36
50
36
50
0
450
625
401
557
346
476
301
361
10
12
14
16
18
389
365
338
310
280
510
467
420
372
324
346
324
300
275
249
454
415
373
330
287
297
278
257
235
212
386
353
316
279
243
258
241
223
203
183
300
277
251
225
199
20
22
24
26
28
251
222
194
167
144
278
234
197
167
144
223
197
172
148
128
246
207
174
148
128
189
166
145
124
107
207
174
146
124
107
163
143
124
106
92
173
148
125
106
92
30
32
34
36
37
126
111
98
87
83
126
111
98
87
83
111
98
87
77
73
111
98
87
77
73
93
82
73
65
61
93
82
73
65
61
80
70
62
55
52
80
70
62
55
52
38
78
78
0
450
625
401
557
346
476
301
361
10
12
14
16
18
391
371
349
325
300
514
479
440
399
357
346
328
309
287
265
453
422
388
351
314
295
280
263
245
226
382
356
327
297
265
254
241
226
211
194
294
276
257
236
214
20
22
24
26
28
274
248
223
198
174
315
275
236
201
174
242
219
196
173
152
277
241
206
176
152
206
186
166
147
129
234
203
174
149
129
177
160
143
127
111
192
170
148
128
111
30
32
34
36
38
151
133
118
105
95
151
133
118
105
95
133
117
103
92
83
133
117
103
92
83
112
99
88
78
70
112
99
88
78
70
97
85
75
67
61
97
85
75
67
61
41
81
81
71
71
60
60
52
52
Properties
A (in2)
rx (in.)
ry (in.)
14.7
2.28
2.51
13.1
2.27
2.49
Note: Heavy line indicates Kl / r of 200.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
11.3
2.24
2.47
9.84
2.22
2.46
DESIGN STRENGTH OF COLUMNS
3 - 95
Fy = 36 ksi
Y
Fy = 50 ksi
COLUMNS
Structural tees
cut from W shapes
X
X
Design axial strength in kips (φ = 0.85)
Designation
Y-Y AXIS
X-X AXIS
Fy
Effective length KL (ft) with respect to indicated axis
WT 8
28.5
Wt./ft
Y
25
22.5
20
18
15.5
13
36
50
36
50
36
50
36
50
36
50
36
50
36
50
0
256
336
223
259
184
205
141
145
122
124
93
93
66
66
6
8
10
12
14
245
236
225
212
199
316
301
283
262
240
213
205
196
185
173
245
235
223
208
193
176
170
163
154
145
195
188
179
169
157
136
132
127
121
115
140
136
130
124
117
118
114
111
106
101
120
116
112
108
102
91
88
86
83
79
90
88
85
82
79
65
63
62
60
58
65
63
62
60
58
16
18
20
22
24
184
168
152
136
121
217
193
169
147
125
160
146
133
119
105
176
159
141
125
108
135
124
114
103
92
145
133
120
107
95
108
100
92
85
77
110
102
94
86
78
95
89
82
76
69
96
90
83
76
70
75
71
67
62
57
75
71
66
62
57
55
53
50
47
44
55
53
50
47
44
26
28
30
32
34
106
92
80
70
62
107
92
80
70
62
93
80
70
61
54
93
80
70
61
54
82
72
62
55
49
83
72
62
55
49
69
62
54
48
42
70
62
54
48
42
63
56
50
44
39
63
57
50
44
39
53
48
44
39
35
53
48
44
39
35
41
38
35
32
29
41
38
35
32
29
36
38
39
40
41
56
50
47
45
56
50
47
45
49
44
41
39
49
44
41
39
43
39
37
43
39
37
38
34
32
38
34
32
35
31
30
28
35
31
30
28
31
28
27
25
31
28
27
25
27
24
23
22
21
27
24
23
22
21
0
256
336
223
259
184
205
141
145
122
124
93
93
66
66
6
8
10
12
14
216
200
181
160
138
268
243
214
182
151
185
171
155
137
119
207
190
170
148
125
153
143
130
116
101
167
155
140
123
106
116
110
102
92
82
119
112
104
94
84
95
90
84
76
68
97
91
85
77
69
70
65
58
50
42
70
64
57
50
42
47
44
40
35
30
47
44
40
35
30
16
18
20
22
116
96
78
65
120
96
78
65
100
83
67
56
103
83
67
56
87
72
59
49
89
72
59
49
72
62
52
43
73
62
52
43
60
51
43
36
60
51
43
36
34
27
34
27
25
21
25
21
24
25
26
54
50
46
54
50
46
47
43
40
47
43
40
41
38
35
41
38
35
36
34
31
36
34
31
30
28
30
28
Properties
A (in2)
rx (in.)
ry (in.)
8.38
2.41
1.60
7.37
2.40
1.59
6.63
2.39
1.57
5.89
2.37
1.57
5.28
2.41
1.52
Note: Heavy line indicates Kl / r of 200.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
4.56
2.45
1.17
3.84
2.47
1.12
3 - 96
COLUMN DESIGN
Fy = 36 ksi
Y
Fy = 50 ksi
X
COLUMNS
Structural tees
cut from W shapes
X
Design axial strength in kips (φ = 0.85)
Y
Designation
WT 7
66
Wt./ft
Y-Y AXIS
Effective length KL (ft) with respect to indicated axis
X-X AXIS
Fy
60
54.5
49.5
45
36
50
36
50
36
50
36
50
36
50
0
594
825
542
752
490
680
447
621
404
561
2
4
6
8
10
588
570
542
505
461
813
779
726
658
580
536
520
493
459
418
741
710
661
597
525
484
469
444
412
374
670
641
595
536
468
442
428
405
375
340
611
584
542
487
425
399
387
366
339
307
552
528
489
439
383
12
14
16
18
20
412
361
310
261
215
497
414
335
266
215
373
326
279
234
192
448
371
299
237
192
333
289
246
205
167
397
327
261
207
167
302
262
223
185
151
360
296
236
186
151
272
236
200
166
135
324
265
211
166
135
22
24
26
27
28
178
149
127
118
110
178
149
127
118
110
158
133
113
105
98
158
133
113
105
98
138
116
99
92
85
138
116
99
92
85
125
105
89
83
125
105
89
83
111
94
80
74
111
94
80
74
0
594
825
542
752
490
680
447
621
404
561
6
8
10
12
14
578
570
559
546
531
794
778
758
734
706
526
519
509
497
483
722
708
689
667
642
475
468
459
448
436
651
638
621
601
578
432
426
418
408
396
591
579
564
546
525
389
384
376
367
357
531
520
506
490
472
16
18
20
22
24
514
496
476
455
434
675
642
607
571
533
468
451
433
414
394
614
584
551
518
484
422
407
391
373
355
553
526
497
467
436
384
370
355
339
322
502
477
451
423
395
346
333
320
305
290
451
429
405
381
355
26
28
30
32
34
411
388
365
341
318
495
457
420
383
347
373
352
331
309
288
449
414
380
346
314
337
317
298
279
260
404
373
342
311
282
305
288
270
253
235
366
337
309
281
255
275
259
243
227
211
329
303
278
253
229
36
38
40
295
273
251
312
281
253
267
247
227
282
253
229
241
222
204
253
227
205
218
201
184
228
205
185
196
180
166
205
184
166
Properties
A (in2)
rx (in.)
ry (in.)
19.4
1.73
3.76
17.7
1.71
3.74
16.0
1.68
3.73
Note: Heavy line indicates Kl / r of 200.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
14.6
1.67
3.71
13.2
1.66
3.70
DESIGN STRENGTH OF COLUMNS
3 - 97
Fy = 36 ksi
Y
Fy = 50 ksi
COLUMNS
Structural tees
cut from W shapes
X
X
Design axial strength in kips (φ = 0.85)
Designation
WT 7
41
Wt./ft
Y-Y AXIS
Effective length KL (ft) with respect to indicated axis
X-X AXIS
Fy
Y
37
34
30.5
26.5
24
21.5
36
50
36
50
36
50
36
50
36
50
36
50
36
50
0
367
510
334
463
306
425
274
370
239
318
216
265
183
208
4
6
8
10
12
354
339
319
294
267
486
457
419
375
327
322
307
288
265
240
440
413
378
337
293
295
281
264
243
219
403
378
346
308
267
264
252
236
217
196
352
330
302
270
235
231
221
208
193
175
303
287
265
239
211
209
200
188
174
158
254
241
224
203
181
177
170
160
149
136
200
191
179
164
148
14
16
18
20
22
238
208
179
151
126
279
232
188
152
126
213
186
159
134
111
248
205
165
134
111
194
169
144
121
100
226
186
150
121
100
173
151
128
108
89
199
165
133
108
89
157
138
119
101
85
182
153
126
102
85
141
124
107
91
76
158
134
112
92
76
122
108
93
80
67
131
114
97
81
67
24
26
28
30
31
106
90
78
68
106
90
78
68
93
79
68
59
93
79
68
59
84
72
62
54
84
72
62
54
75
64
55
48
75
64
55
48
71
61
52
45
43
71
61
52
45
43
64
54
47
41
38
64
54
47
41
38
56
48
41
36
34
56
48
41
36
34
0
367
510
334
463
306
425
274
370
239
318
216
265
183
208
8
10
12
14
16
334
320
303
285
265
447
421
391
359
324
303
290
275
258
240
405
382
355
325
294
276
265
251
235
218
369
347
322
295
267
246
236
223
210
195
320
302
281
258
233
203
189
173
156
139
256
233
208
181
154
183
170
156
140
124
215
197
177
156
135
154
144
132
119
106
171
158
144
128
112
18
20
22
24
26
244
222
201
179
159
289
254
221
188
161
221
202
182
163
144
262
231
200
171
146
201
183
165
147
130
238
209
181
154
131
179
163
147
131
116
209
184
160
137
117
121
104
87
73
63
129
105
87
73
63
108
93
78
66
56
114
94
78
66
56
93
80
68
57
49
97
82
68
57
49
28
30
31
32
34
139
121
113
106
94
139
121
113
106
94
126
110
103
97
86
126
110
103
97
86
113
99
93
87
77
113
99
93
87
77
101
88
82
77
69
101
88
82
77
69
54
47
44
41
54
47
44
41
48
42
40
48
42
40
42
37
34
42
37
34
36
40
41
84
68
65
84
68
65
76
62
59
76
62
59
69
56
53
69
56
53
61
50
61
50
Properties
A
(in2)
rx (in.)
ry (in.)
12.0
1.85
2.48
10.9
1.82
2.48
9.99
1.81
2.46
8.96
1.80
2.45
7.81
1.88
1.92
Note: Heavy line indicates Kl / r of 200.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
7.07
1.87
1.91
6.31
1.86
1.89
3 - 98
COLUMN DESIGN
Fy = 36 ksi
Y
Fy = 50 ksi
X
COLUMNS
Structural tees
cut from W shapes
X
Design axial strength in kips (φ = 0.85)
Y
Designation
WT 7
19
Wt./ft
X-X AXIS
Y-Y AXIS
Effective length KL (ft) with respect to indicated axis
Fy
17
15
13
11
36
50
36
50
36
50
36
50
36
50
0
159
180
131
142
109
114
87
88
62
62
2
4
6
8
10
158
155
150
143
134
178
174
168
159
148
130
128
124
119
112
141
138
134
127
120
109
107
104
100
95
114
112
108
104
98
87
85
83
80
77
88
86
84
81
78
62
61
60
58
56
62
61
60
58
56
12
14
16
18
20
125
114
103
92
81
136
123
110
97
83
105
96
88
79
70
111
102
92
82
72
89
83
76
69
62
92
85
78
70
63
73
68
63
58
53
73
69
64
58
53
53
51
48
44
41
53
51
48
44
41
22
24
26
28
30
70
60
51
44
38
71
60
51
44
38
62
53
46
39
34
63
54
46
39
34
55
48
42
36
31
55
48
42
36
31
48
42
37
33
28
48
43
38
33
28
38
34
31
28
24
38
34
31
28
24
32
34
35
34
30
34
30
30
27
30
27
27
24
27
24
25
22
21
25
22
21
22
19
18
22
19
18
0
159
180
131
142
109
114
87
88
62
62
6
8
10
12
14
132
123
111
99
86
146
134
120
105
89
108
101
92
82
72
115
107
97
86
74
86
81
74
67
59
89
83
76
68
60
65
58
50
41
32
66
58
50
41
32
45
41
35
30
24
45
41
35
30
24
16
17
18
20
22
72
66
60
49
40
74
66
60
49
40
61
56
51
42
35
63
57
52
42
35
50
46
42
35
29
51
47
42
35
29
25
22
20
25
22
20
19
17
19
17
24
25
34
31
34
31
30
27
30
27
25
25
Properties
A (in2)
rx (in.)
ry (in.)
5.58
2.04
1.55
5.00
2.04
1.53
4.42
2.07
1.49
Note: Heavy line indicates Kl / r of 200.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
3.85
2.12
1.08
3.25
2.14
1.04
DESIGN STRENGTH OF COLUMNS
3 - 99
Fy = 36 ksi
Y
Fy = 50 ksi
COLUMNS
Structural tees
cut from W shapes
X
Design axial strength in kips (φ = 0.85)
Designation
X-X AXIS
Y-Y AXIS
Effective length KL (ft) with respect to indicated axis
Y
WT 6
29
Wt./ft
Fy
X
26.6
25
22.5
20
36
50
36
50
36
50
36
50
36
50
0
261
362
238
331
225
312
202
280
180
221
2
4
6
8
10
257
247
231
210
186
355
336
306
268
227
235
226
211
192
171
325
307
280
246
208
222
214
202
186
167
307
292
269
240
207
200
193
181
167
149
276
262
241
214
184
178
172
161
148
133
218
208
193
174
152
12
14
16
18
20
160
135
110
88
71
185
145
111
88
71
147
124
102
81
66
170
134
103
81
66
147
126
105
86
70
173
139
109
86
70
131
112
93
75
61
153
123
96
75
61
116
99
82
66
54
129
106
84
66
54
22
24
25
26
59
49
45
59
49
45
54
46
42
54
46
42
58
48
45
41
58
48
45
41
51
42
39
36
51
42
39
36
44
37
34
32
44
37
34
32
0
261
362
238
331
225
312
202
280
180
221
6
8
10
12
14
246
238
228
216
203
333
318
300
279
257
223
216
206
196
184
301
287
271
252
231
205
194
181
166
150
274
255
232
206
179
183
174
162
148
134
244
227
206
183
159
162
154
143
131
118
194
182
167
150
132
16
18
20
22
24
189
175
160
144
129
233
208
184
160
137
171
157
144
130
116
209
187
164
143
122
134
117
101
86
72
152
127
103
86
72
119
104
89
75
63
135
112
91
75
63
105
92
79
66
56
114
97
80
66
56
26
28
30
32
34
115
101
88
77
69
117
101
88
77
69
103
90
78
69
61
104
90
78
69
61
61
53
46
41
61
53
46
41
54
47
41
36
54
47
41
36
48
41
36
32
48
41
36
32
36
38
41
61
55
47
61
55
47
54
49
42
54
49
42
Properties
A
(in2)
rx (in.)
ry (in.)
8.52
1.50
2.51
7.78
1.51
2.48
7.34
1.60
1.96
6.61
1.58
1.94
Note: Heavy line indicates Kl / r of 200.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
5.89
1.57
1.93
3 - 100
COLUMN DESIGN
Fy = 36 ksi
Y
Fy = 50 ksi
X
COLUMNS
Structural tees
cut from W shapes
X
Design axial strength in kips (φ = 0.85)
Y
Designation
17.5
Wt./ft
X-X AXIS
Fy
15
13
11
9.5
8
7
36
50
36
50
36
50
36
50
36
50
36
50
36
50
0
158
188
120
132
90
92
88
98
68
71
53
54
40
40
2
4
6
8
10
157
152
145
135
124
186
179
169
156
140
119
116
111
104
96
131
127
121
113
104
89
87
84
80
74
91
89
86
81
76
88
86
83
78
73
97
95
91
86
80
68
66
64
61
58
70
69
67
63
60
53
52
51
48
46
54
53
51
49
46
40
39
38
37
35
40
39
38
37
35
12
14
16
18
20
111
98
85
72
59
124
106
89
73
59
87
78
68
59
50
93
82
71
60
50
68
62
55
48
42
70
63
56
49
42
68
61
55
48
42
73
65
58
50
43
54
49
44
40
35
55
50
45
40
35
43
40
36
33
29
43
40
36
33
29
33
31
29
26
24
33
31
29
26
24
22
24
26
28
29
49
41
35
30
28
49
41
35
30
28
41
35
30
25
24
41
35
30
25
24
36
30
26
22
21
36
30
26
22
21
36
30
26
22
21
36
30
26
22
21
30
26
22
19
18
30
26
22
19
18
26
22
19
16
15
26
22
19
16
15
21
19
17
14
14
21
19
17
14
14
19
18
19
18
17
16
17
16
14
13
13
14
13
13
13
12
11
13
12
11
30
31
32
Y-Y AXIS
Effective length KL (ft) with respect to indicated axis
WT 6
0
158
188
120
132
90
92
88
98
68
71
53
54
40
40
2
4
6
8
10
147
142
134
123
110
172
165
154
139
123
109
106
101
93
85
119
115
109
100
90
81
79
75
71
65
83
80
77
72
66
73
67
57
45
33
80
72
60
46
33
54
49
43
34
26
55
51
44
35
26
37
34
30
24
18
37
34
30
25
18
26
25
22
19
15
26
25
22
19
15
12
13
14
16
18
96
89
82
68
55
105
95
87
69
55
75
70
65
55
45
79
73
67
56
45
59
55
52
45
38
59
56
52
45
38
23
20
17
23
20
17
18
16
18
16
13
13
11
11
20
22
24
25
45
37
31
29
45
37
31
29
37
31
26
24
37
31
26
24
31
26
22
20
31
26
22
20
Properties
A
(in2)
rx (in.)
ry (in.)
5.17
1.76
1.54
4.40
1.75
1.52
3.82
1.75
1.51
3.24
1.90
0.847
2.79
1.90
0.822
Note: Heavy line indicates Kl / r of 200.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
2.36
1.92
0.773
2.08
1.92
0.753
DESIGN STRENGTH OF COLUMNS
3 - 101
Fy = 36 ksi
Y
Fy = 50 ksi
COLUMNS
Structural tees
cut from W shapes
X
X
Design axial strength in kips (φ = 0.85)
Designation
WT 5
22.5
Wt./ft
19.5
16.5
15
13
11
36
50
36
50
36
50
36
50
36
50
36
50
0
203
282
175
244
148
206
135
188
117
146
99
115
2
4
6
8
10
199
187
170
148
124
274
253
220
182
142
172
162
147
128
107
237
218
190
157
123
146
137
125
109
92
201
185
162
135
106
133
128
119
107
94
184
173
157
136
114
115
110
102
92
81
144
136
124
109
92
98
94
87
79
69
113
108
99
88
76
12
14
16
18
20
100
77
59
47
38
105
77
59
47
38
86
67
51
40
33
91
67
51
40
33
75
58
45
35
29
79
58
45
35
29
80
67
54
42
34
91
70
54
42
34
69
57
46
36
29
76
60
46
36
29
59
49
40
32
26
64
51
40
32
26
26
26
31
28
24
31
28
24
27
24
20
27
24
20
23
21
18
23
21
18
21
22
24
Y-Y AXIS
Effective length KL (ft) with respect to indicated axis
X-X AXIS
Fy
Y
0
203
282
175
244
148
206
135
188
117
146
99
115
2
4
6
8
10
199
195
188
178
167
274
266
253
235
214
171
167
161
153
143
235
227
216
201
183
143
140
134
127
119
194
188
179
166
151
128
122
113
101
88
174
163
147
126
104
109
104
96
86
75
134
126
115
100
84
89
85
78
70
61
101
96
88
78
66
12
14
16
18
20
153
139
125
110
95
191
167
143
120
99
131
119
106
93
80
163
142
121
101
83
109
98
87
76
66
134
116
99
82
67
74
60
47
38
30
82
62
47
38
30
63
51
40
32
26
68
52
40
32
26
51
41
32
26
21
54
42
32
26
21
22
24
26
28
30
81
69
59
50
44
82
69
59
50
44
68
57
49
42
37
68
57
49
42
37
55
47
40
34
30
55
47
40
34
30
25
25
21
21
17
17
32
33
39
36
39
36
32
30
32
30
26
26
Properties
A (in2)
rx (in.)
ry (in.)
6.63
1.24
2.01
5.73
1.24
1.98
4.85
1.26
1.94
4.42
1.45
1.37
Note: Heavy line indicates Kl / r of 200.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
3.81
1.44
1.36
3.24
1.46
1.33
3 - 102
COLUMN DESIGN
Fy = 36 ksi
Y
Fy = 50 ksi
X
COLUMNS
Structural tees
cut from W shapes
X
Design axial strength in kips (φ = 0.85)
Y
Designation
WT 5
9.5
Wt./ft
Y-Y AXIS
Effective length KL (ft) with respect to indicated axis
X-X AXIS
Fy
8.5
7.5
6
36
50
36
50
36
50
36
50
0
86
104
77
90
66
76
43
45
2
4
6
8
10
85
82
77
70
62
103
98
91
81
71
76
73
68
63
56
88
85
79
71
62
65
63
59
54
49
75
72
67
61
54
43
41
39
37
34
44
43
41
38
35
12
14
16
18
20
54
46
38
30
25
60
49
39
30
25
49
42
34
28
23
53
44
35
28
23
43
37
31
25
20
46
39
31
25
20
30
27
23
19
16
31
27
23
20
16
22
24
25
26
20
17
16
20
17
16
19
16
14
13
19
16
14
13
17
14
13
12
17
14
13
12
13
11
10
10
13
11
10
10
0
86
104
77
90
66
76
43
45
2
4
6
8
10
74
67
56
43
31
87
77
62
46
31
62
56
47
36
25
70
62
51
37
25
49
45
37
29
20
54
48
40
29
20
30
28
24
19
14
30
28
24
20
14
12
13
14
22
18
16
22
18
16
18
15
13
18
15
13
14
12
14
12
10
9
10
9
Properties
A (in2)
rx (in.)
ry (in.)
2.81
1.54
0.874
2.50
1.56
0.844
Note: Heavy line indicates Kl / r of 200.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
2.21
1.57
0.810
1.77
1.57
0.785
DESIGN STRENGTH OF COLUMNS
3 - 103
Fy = 36 ksi
Y
Fy = 50 ksi
COLUMNS
Structural tees
cut from W shapes
X
X
Design axial strength in kips (φ = 0.85)
Designation
WT 4
14
Wt./ft
12
10.5
9
7.5
6.5
5
36
50
36
50
36
50
36
50
36
50
36
50
36
50
0
126
175
108
150
94
131
80
112
68
94
59
82
41
46
2
3
4
5
6
122
118
112
105
96
168
160
148
135
121
105
101
96
90
82
144
137
127
116
103
92
89
86
81
76
127
121
114
106
97
79
76
73
70
65
108
104
98
91
83
67
65
63
60
57
92
89
84
79
73
58
56
54
52
49
79
77
73
69
64
41
40
38
37
35
45
44
42
40
38
8
10
12
14
16
78
60
43
32
24
90
62
43
32
24
67
51
36
27
20
77
52
36
27
20
64
52
39
29
22
76
57
40
29
22
55
45
35
26
20
67
50
35
26
20
49
41
33
25
19
60
47
34
25
19
43
36
29
22
17
52
41
30
22
17
30
26
21
16
12
33
27
21
16
12
18
18
16
14
16
14
15
14
12
15
14
12
13
12
11
13
12
11
10
9
8
10
9
8
18
19
20
Y-Y AXIS
Effective length KL (ft) with respect to indicated axis
X-X AXIS
Fy
Y
0
126
175
108
150
94
131
80
112
68
94
59
82
41
46
2
4
6
8
10
123
119
112
104
93
169
161
149
133
116
105
101
96
88
80
143
137
127
113
98
89
85
77
68
57
121
113
99
83
66
75
70
64
56
47
100
93
82
68
54
60
54
45
35
25
79
68
53
37
25
49
44
36
28
19
63
55
43
29
19
33
30
25
20
15
35
32
27
21
15
12
14
16
18
20
82
71
60
49
40
97
79
62
49
40
70
60
51
42
34
83
67
53
42
34
47
37
28
22
18
49
37
28
22
18
38
30
23
18
15
40
30
23
18
15
17
13
17
13
14
10
14
10
10
8
10
8
21
22
24
26
27
36
33
28
24
22
36
33
28
24
22
31
28
24
20
31
28
24
20
16
16
Properties
A
(in2)
rx (in.)
ry (in.)
4.12
1.01
1.62
3.54
.999
1.61
3.08
1.12
1.26
2.63
1.14
1.23
2.22
1.22
0.876
Note: Heavy line indicates Kl / r of 200.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1.92
1.23
0.843
1.48
1.20
0.841
3 - 104
COLUMN DESIGN
Single-Angle Struts
Design strengths of single-angle struts were formerly not tabulated in this Manual
because of the difficulty in loading such struts concentrically. Concentric loading can be
accomplished by milling the ends of an angle and loading it through bearing plates.
However, in common practice, the eccentricity of loading is relatively large, and its
neglect in design may lead to an under-designed member.
The design of single-angle struts is governed by the AISC Specification for Load and
Resistance Factor Design of Single-Angle Members, which is reproduced in Part 6 of this
Manual.
The following example illustrates the design procedure for an equal-leg angle loaded
eccentrically. The design strengths for concentric loading, tabulated below, are useful in
solving the interaction equations for combined axial force and bending. The tables below
are based on Zureick (1993), revised to conform with the AISC Single-Angle Specification (LRFD).
EXAMPLE 3-8
An angle 2×2×1⁄4 is loaded by a gusset plate attached to one leg with
an eccentricity of 0.8 in. from the centroid, as shown in Figure 3-3.
Determine the factored compressive load Pu which may be applied. The
effective length KL is 4.0 ft.
Given:
A = 0.938 in.2
rz = 0.391 in.
Ix = Iy = 0.348 in.4
3
84
′
7′
′′
7
.2
0
0.
Z
Pn
W
0.8′′
0.592 ′′
37
′′
α
8
0.
W
Z
′
4′
41
1.
Fig. 3-3
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
DESIGN STRENGTH OF COLUMNS
3 - 105
α = 45°
Fy = 50 ksi
Solution:
Determine the properties for the principal axes Z-Z and W-W as
follows:
Iz = Arz2 = 0.938(0.391)2 = 0.143 in.2
Iw + Iz = Ix + Iy
Iw = 0.348 + 0.348 − 0.143 = 0.552 in.4
rw
=
√
√
Iw
=
A
0.552
= 0.767 in.
0.938
From the tables which follow, the design compressive strength φcPn =
14 kips for KL = 4 ft.
For combined axial compression and bending, the latter is taken about
the principal axes in accordance with the Single-Angle LRFD Specification (Section 6).
For equal leg angles—
Major principal axis (W-W) bending (Section 5.3.1):
0.46Eb2t 2
l
0.46(29,000 ksi)(2 in.)2(0.25 in.)2
= 1.0 ×
48 in.
= 69.5 k-in.
Iw
0.552 in.4
My = Fy Sw = Fy = 50 ksi ×
cw
1.414 in.
= 19.5 k-in.
Mob = Cb
Since Mob > My (Section 5.1.3),
Mnw = [1.58 − 0.83
√
My / Mob ] My ≤ 1.25My
= [1.58 − 0.83
√
19.5 / 69.5 ] My = 1.14My
= 1.14 × 19.5 k-in.
= 22 k-in.
According to Section 5.1.1,
(= 2 in. / 0.25 in. = 8) < 0.382 √
E /Fy
(= 0.382 √
29,000 / 50
= 9.2),
Mnw ≤ 1.25Fy Sc = 1.25Fy Sw = 1.25My
for b / t
This is satisfied since Mnw = 1.14My.
Minor principal axis (Z-Z) bending (Section 5.3.1):
With the leg tips of the angle in tension and the angle corner in
compression
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
3 - 106
COLUMN DESIGN
Mnz = 1.25My = 1.25Fy Sz = 1.25Fy
= 1.25 × 50 ksi ×
Iz
cz
0.143 in.4
0.837 in.
= 11 k-in.
Assuming
Pu
≥ 0.2, Interaction Equation 6-1a governs.
φcPn
Muz
Pu 8 Muw
φ P + 9 φ M + φ M ≤ 1.0
b nz
b nw
c n
According to Section 6.1.1, for flexural compression Mu shall be
multiplied by B1 (Equation 6-2).
Major principal axis (W-W) bending:
Kl / rw = 1.0 × 48 / 0.767 = 62.2
From LRFD Specification Table 8, Pe / Ag = 73.1
Pe1w = 73.1(0.938) = 68.6 kips
B1w =
Cm
0.85
=
< 1. Use B1w = 1.0.
1 − Pu / Pe1w 1 − Pu / 68.6
Minor principal axis (Z-Z) bending:
Kl / rw = 1.0 × 48 / 0.391 = 122.8
From LRFD Specification Table 8, Pe / Ag = 19.0
Pe1z = 19.0(0.938) = 17.8 kips
B1z =
Cm
0.85
=
1 − Pu / Pe1z 1 − Pu / 17.8
Conservatively adding the maximum axial and flexural terms, Equation 6-1a becomes
Pu ×0.277 in.
Pu
8 Pu ×0.843 in. × 1.0
0.85
+
+
≤ 1.0
14 kips 9 0.9×22 kip−in.
0.9×11 kip−in. 1−Pu / 17.8
Pu = 7 kips
Checking
Pu
7 kips
=
= 0.5 > 0.2 o.k.
14
kips
φcPn
A less conservative approach would have involved applying the interaction equation separately at the corner and the two leg tips of the
angle, with the proper signs (+ or −) for compression and tension.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
DESIGN STRENGTH OF COLUMNS
3 - 107
Fy = 36 ksi
z
Y
Fy = 50 ksi
COLUMNS
Single angles
w
x
Design axial strength in kips (φ = 0.90)
x
w
Y z
8×
×6
Size
Thickness
1
7⁄
8
3⁄
4
5⁄
8
9⁄
16
1⁄
2
7⁄
16
Wt./ft
44.2
39.1
33.8
28.5
25.7
23.0
20.2
Effective length KL (ft)
Fy
36
50
36
50
36
50
36
50
36
50
36
50
36
50
0
421
585
373
518
322
447
270
352
235
303
199
253
163
203
1
2
3
4
5
406
398
393
384
371
555
541
531
515
490
355
347
342
336
325
484
468
460
448
429
301
292
288
284
277
408
391
383
375
363
246
235
231
228
224
311
294
287
282
276
210
199
195
193
190
262
245
239
235
230
174
163
160
158
156
213
197
192
188
185
138
128
125
123
122
166
151
146
144
141
6
7
8
9
10
353
333
311
287
263
458
422
383
344
305
311
293
274
253
232
402
371
338
303
268
266
252
236
219
201
343
319
291
262
233
217
208
195
182
167
265
250
231
210
189
186
179
170
159
148
224
214
200
184
167
153
149
143
135
126
181
175
166
155
142
120
118
115
110
104
139
136
131
124
116
11
12
13
14
15
239
215
192
169
147
266
230
196
169
147
211
190
169
149
130
235
203
173
149
130
183
165
147
130
114
204
177
151
130
114
152
137
123
109
95
167
146
125
109
95
135
123
111
99
87
149
131
114
99
87
117
107
96
87
77
128
114
101
88
77
97
90
82
75
67
107
97
87
77
67
16
17
18
19
20
130
115
103
92
83
130
115
103
92
83
115
102
91
81
74
115
102
91
81
74
100
89
79
71
64
100
89
79
71
64
84
74
66
60
54
84
74
66
60
54
77
68
61
55
49
77
68
61
55
49
68
60
54
49
44
68
60
54
49
44
60
53
48
43
39
60
53
48
43
39
21
76
76
67
67
58
58
49
49
45
45
40
40
35
35
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
3 - 108
COLUMN DESIGN
z
Fy = 36 ksi
Y
Fy = 50 ksi
COLUMNS
Single angles
w
x
x
Design axial strength in kips (φ = 0.90)
w
Y z
8×
×4
Size
Thickness
Wt./ft
37.4
Fy
Effective length KL (ft)
7⁄
8
1
3⁄
4
33.1
5⁄
8
28.7
24.2
1⁄
2
21.9
7⁄
16
19.6
17.2
36
50
36
50
36
50
36
50
36
50
36
50
36
50
0
356
495
315
438
273
380
230
299
200
258
170
216
139
174
1
2
3
4
5
342
331
315
293
267
468
446
417
378
332
300
289
275
257
234
408
387
363
330
290
256
245
235
220
201
346
326
307
280
248
209
198
190
179
165
264
246
233
216
194
179
169
162
154
142
223
207
197
184
167
149
139
134
128
119
182
168
160
150
138
118
109
105
101
95
142
128
122
116
108
6
7
8
9
10
238
208
177
148
121
283
234
187
149
121
209
183
156
131
107
248
205
164
131
107
180
157
135
113
92
212
176
141
113
92
148
130
112
94
77
169
142
117
94
77
129
114
99
84
70
146
125
104
84
70
109
98
86
73
61
123
107
90
74
61
88
80
71
62
53
98
87
75
63
53
11
12
13
14
100
85
72
62
100
85
72
62
89
75
64
55
89
75
64
55
77
65
56
48
77
65
56
48
65
55
47
41
65
55
47
41
58
49
42
37
58
49
42
37
52
44
38
33
52
44
38
33
45
38
33
29
45
38
33
29
7×
×4
Size
3⁄
4
Thickness
Wt./ft
5⁄
8
26.2
Fy
Effective length KL (ft)
9⁄
16
1⁄
2
22.1
7⁄
16
17.9
3⁄
8
15.7
13.6
36
50
36
50
36
50
36
50
36
50
0
249
346
210
288
164
212
136
173
108
134
1
2
3
4
5
236
228
219
205
188
320
306
289
264
233
194
187
180
170
156
258
245
233
215
191
146
139
134
128
119
182
171
164
154
140
118
111
107
103
97
144
133
128
122
113
90
85
82
79
76
107
99
95
91
86
6
7
8
9
10
168
147
126
106
87
200
166
134
107
87
140
123
106
89
73
165
138
113
90
73
108
96
84
71
59
124
106
89
72
59
89
80
71
61
51
101
88
75
62
51
70
64
57
50
43
79
70
61
52
43
11
12
13
14
72
61
52
45
72
61
52
45
61
52
44
38
61
52
44
38
49
42
36
31
49
42
36
31
43
37
31
27
43
37
31
27
37
31
27
23
37
31
27
23
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
DESIGN STRENGTH OF COLUMNS
3 - 109
Fy = 36 ksi
z
Y
Fy = 50 ksi
COLUMNS
Single angles
w
x
Design axial strength in kips (φ = 0.90)
Wt./ft
7⁄
8
3⁄
4
27.2
Fy
Effective length KL (ft)
Y z
6×
×4
Size
Thickness
36
5⁄
8
23.6
50
36
9⁄
16
20.0
50
36
1⁄
2
18.1
50
36
7⁄
16
16.2
50
36
3⁄
8
14.3
50
36
5⁄
16
10.3
12.3
50
36
50
36
50
0
259 359 225 312 190 264 172 239 154 205 132 171 107 136
81
100
1
2
3
4
5
250
244
233
217
198
343
331
310
282
248
91 111
87 105
85 102
82 97
78 91
66
63
61
59
57
78
73
70
68
65
6
7
8
9
10
177
155
133
111
91
212 154 184 129 155 117 139 104 121
176 135 153 113 129 102 116 91 102
142 115 124 98 105 88 94 79 84
112 97 98 82 83 74 75 67 67
91 80 80 67 67 61 61 55 55
89 102
79 87
68 73
58 59
48 48
72
65
57
49
41
82
72
61
50
41
54
50
45
39
34
61
55
48
41
34
11
12
13
14
75
63
54
47
40
34
29
25
34
29
25
22
34
29
25
22
29
24
21
18
29
24
21
18
75
63
54
47
215
210
201
188
172
293
284
268
244
215
66
55
47
41
66
55
47
41
178
174
168
157
144
56
47
40
35
241
233
222
203
180
56
47
40
35
159
155
150
141
130
51
43
37
32
214
206
197
182
162
139
135
131
125
115
51
43
37
32
46
38
33
28
180
172
166
155
139
46
38
33
28
116
112
109
105
98
145
138
133
126
116
40
34
29
25
6×
×31⁄2
Size
1⁄
2
Thickness
Wt./ft
3⁄
8
15.3
Fy
Effective length KL (ft)
x
w
5⁄
16
11.7
9.8
36
50
36
50
36
50
0
146
195
101
128
77
95
1
2
3
4
5
132
127
121
112
100
171
162
152
137
118
86
82
79
75
69
105
99
94
88
79
63
59
57
55
51
74
69
66
63
58
6
7
8
9
10
87
74
60
48
39
98
78
61
48
39
61
53
44
36
30
68
56
45
36
30
47
41
36
30
25
51
44
37
30
25
11
12
33
28
33
28
25
21
25
21
21
18
21
18
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
3 - 110
COLUMN DESIGN
z
Fy = 36 ksi
Y
Fy = 50 ksi
COLUMNS
Single angles
w
x
x
Design axial strength in kips (φ = 0.90)
w
Y z
5×
×31⁄2
Size
3⁄
4
Thickness
Wt./ft
19.8
Fy
Effective length KL (ft)
5⁄
8
1⁄
2
16.8
3⁄
8
13.6
10.4
1⁄
4
8.7
7.0
36
50
36
50
36
50
36
50
36
50
36
50
0
188
261
159
221
130
180
97
126
76
96
54
66
1
2
3
4
5
182
176
165
150
133
249
238
218
192
162
152
148
139
127
113
207
199
183
162
137
120
117
112
103
91
162
156
146
130
111
85
82
80
75
68
107
102
98
90
79
64
61
60
57
53
77
74
71
67
61
43
41
40
38
36
49
47
45
44
41
6
7
8
9
10
115
96
79
63
51
132
103
79
63
51
97
82
67
53
43
112
88
67
53
43
79
67
55
44
35
90
71
55
44
35
59
50
42
33
27
66
54
42
33
27
47
41
34
28
23
52
44
35
28
23
34
30
26
22
18
37
32
27
22
18
11
12
42
35
42
35
36
30
36
30
29
25
29
25
23
19
23
19
19
16
19
16
15
13
15
13
5×
×3
Size
1⁄
2
Thickness
Wt./ft
7⁄
16
12.8
Fy
Effective length KL (ft)
5⁄
16
3⁄
8
11.3
5⁄
16
9.8
1⁄
4
8.2
6.6
36
50
36
50
36
50
36
50
36
50
0
122
169
107
146
91
118
71
90
51
62
1
2
3
4
5
112
108
100
88
75
151
143
128
108
87
97
93
87
77
66
127
120
109
93
76
80
76
72
65
56
100
94
87
76
63
60
57
54
50
44
72
68
64
58
49
40
38
36
34
31
46
44
42
39
34
6
7
8
9
10
62
49
38
30
24
66
49
38
30
24
54
43
33
27
22
58
43
33
27
22
46
37
29
23
19
49
37
29
23
19
37
30
24
19
16
40
31
24
19
16
27
23
19
15
13
29
24
19
15
13
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
DESIGN STRENGTH OF COLUMNS
3 - 111
Fy = 36 ksi
z
Y
Fy = 50 ksi
COLUMNS
Single angles
w
x
Design axial strength in kips (φ = 0.90)
1⁄
Thickness
Wt./ft
3⁄
8
2
11.9
Fy
Effective length
KL (ft)
Y z
4×
×31⁄2
Size
5⁄
16
9.1
1⁄
4
7.7
6.2
36
50
36
50
36
50
36
50
0
113
158
87
120
73
95
53
68
1
2
3
4
5
107
105
99
90
79
146
142
131
114
95
78
77
75
68
60
104
102
98
87
73
63
61
60
57
51
79
76
74
69
59
43
42
42
41
38
52
50
49
48
44
6
7
8
9
10
67
56
45
35
29
76
58
45
35
29
51
43
35
27
22
58
45
34
27
22
43
36
29
23
19
48
38
29
23
19
33
28
23
19
15
37
30
24
19
15
11
12
24
20
24
20
18
15
18
15
15
13
15
13
13
11
13
11
4×
×3
Size
5⁄
8
Thickness
Wt./ft
1⁄
2
13.6
Fy
Effective length
KL (ft)
x
w
7⁄
16
11.1
3⁄
8
9.8
5⁄
16
8.5
1⁄
4
7.2
5.8
36
50
36
50
36
50
36
50
36
50
36
50
0
129
179
105
146
93
129
80
112
67
88
50
63
1
2
3
4
5
124
119
108
95
81
170
160
141
118
93
100
96
88
78
66
136
129
114
96
76
87
84
78
68
58
117
112
101
84
67
73
71
66
59
50
98
94
86
73
58
59
57
55
49
42
74
71
67
58
47
41
40
39
36
32
50
48
46
42
36
6
7
8
9
10
66
52
39
31
25
70
51
39
31
25
54
42
32
26
21
57
42
32
26
21
47
37
29
23
18
51
37
29
23
18
41
32
25
20
16
44
32
25
20
16
35
27
21
17
14
37
27
21
17
14
27
22
17
14
11
29
22
17
14
11
31⁄2×3
Size
Thickness
1⁄
2
3⁄
8
5⁄
16
1⁄
4
Wt./ft
10.2
7.9
6.6
5.4
Effective length
KL (ft)
Fy
36
50
36
50
36
50
36
0
97
135
75
104
63
86
49
63
1
2
3
4
5
93
89
81
71
59
127
120
105
87
68
69
67
62
54
46
93
90
81
67
53
56
55
52
46
38
73
71
66
56
44
41
40
39
36
30
51
49
48
42
34
6
7
8
9
10
48
37
28
22
18
50
37
28
22
18
37
29
22
17
14
39
29
22
17
14
31
24
19
15
12
33
24
19
15
12
25
20
15
12
10
27
20
15
12
10
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
50
3 - 112
COLUMN DESIGN
z
Fy = 36 ksi
Y
Fy = 50 ksi
COLUMNS
Single angles
w
x
x
Design axial strength in kips (φ = 0.90)
w
Y z
31⁄2×21⁄2
Size
1⁄
2
Thickness
3⁄
8
9.4
Wt./ft
Effective length
KL (ft)
Fy
1⁄
4
7.2
4.9
36
50
36
50
36
50
0
89
124
68
95
45
58
1
2
3
4
5
6
7
8
9
85
79
70
58
46
116
105
88
68
49
34
25
19
63
60
53
44
35
26
19
15
85
79
67
52
38
26
19
15
38
37
34
29
24
18
13
10
8
47
45
41
33
25
18
13
10
8
34
25
19
3×
×21⁄2
Size
Thickness
1⁄
2
3⁄
8
5⁄
16
1⁄
4
3⁄
16
Wt./ft
8.5
6.6
5.6
4.5
3.39
Effective length
KL (ft)
Fy
36
50
36
50
36
50
36
50
36
50
0
81
113
62
86
52
73
42
57
29
37
1
2
3
4
5
78
72
63
52
40
107
96
79
60
42
58
55
48
40
31
79
73
61
46
33
48
46
41
34
26
65
61
51
39
28
37
36
33
27
21
48
46
40
31
23
24
23
22
19
16
29
28
26
22
17
6
7
8
29
22
17
29
22
17
23
17
13
23
17
13
19
14
11
19
14
11
16
12
9
16
12
9
12
9
7
12
9
7
3×
×2
Size
1⁄
2
Thickness
7.7
Wt./ft
Fy
Effective length
KL (ft)
3⁄
8
5⁄
16
5.9
5.0
3⁄
16
4.1
3.07
36
50
36
50
36
50
36
50
36
50
0
1
2
3
4
5
73
69
61
50
37
26
101
94
80
60
40
26
56
52
47
38
29
20
78
71
61
46
31
20
47
43
39
32
24
17
66
58
51
39
26
17
39
34
31
26
20
14
51
43
39
30
21
14
27
22
21
18
14
10
34
27
25
21
15
10
6
7
18
13
18
13
14
10
14
10
12
9
12
9
10
7
10
7
7
5
7
5
21⁄2×2
Size
3⁄
8
Thickness
5⁄
16
5.3
Wt./ft
Fy
Effective length
KL (ft)
1⁄
4
0
1
2
3
4
5
6
7
1⁄
4
4.5
3⁄
16
3.62
2.75
36
50
36
50
36
50
36
50
50
48
42
34
25
17
12
9
70
65
55
41
27
17
12
9
42
40
36
29
21
15
10
7
59
54
46
34
23
15
10
7
34
31
29
23
17
12
8
6
48
42
37
28
18
12
8
6
26
22
21
17
13
9
6
5
33
27
25
20
14
9
6
5
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
DESIGN STRENGTH OF COLUMNS
3 - 113
Fy = 36 ksi
z
Y
Fy = 50 ksi
COLUMNS
Single angles
w
x
Design axial strength in kips (φ = 0.90)
Y z
8×
×8
Size
11⁄8
Thickness
Wt./ft
7⁄
8
1
56.9
Fy
Effective length KL (ft)
x
w
51.0
3⁄
4
45.0
5⁄
8
38.9
9⁄
16
32.7
1⁄
2
29.6
26.4
36
50
36
50
36
50
36
50
36
50
36
50
36
50
0
541
752
486
675
428
594
369
513
310
405
270
348
229
291
6
7
8
9
10
484
465
444
421
397
643
608
570
530
488
435
417
398
378
356
578
546
512
476
438
383
368
351
334
315
510
482
452
421
388
320
318
304
289
273
420
417
392
365
337
254
252
251
243
230
311
309
306
294
273
213
212
210
209
202
256
255
253
250
240
173
172
171
170
168
203
202
201
199
197
11
12
13
14
15
372
346
320
294
269
446
404
363
323
283
334
311
288
264
242
401
363
326
290
255
295
275
255
234
215
355
322
289
258
227
256
239
221
204
187
308
280
252
225
198
215
201
186
172
157
251
230
208
187
167
191
178
166
154
141
222
204
186
169
151
165
155
144
134
124
191
177
162
148
133
16
17
18
19
20
244
221
197
177
159
249
221
197
177
159
219
198
177
159
143
224
198
177
159
143
195
176
158
141
128
199
177
158
141
128
170
154
138
124
112
174
154
138
124
112
143
130
116
104
94
147
130
116
104
94
129
118
107
95
86
134
119
106
95
86
114
104
95
85
77
120
106
95
85
77
21
22
23
24
25
145
132
121
111
102
145
132
121
111
102
130
118
108
99
92
130
118
108
99
92
116
105
96
89
82
116
105
96
89
82
101
92
84
78
71
101
92
84
78
71
85
78
71
65
60
85
78
71
65
60
78
71
65
60
55
78
71
65
60
55
70
64
58
53
49
70
64
58
53
49
26
94
94
85
85
76
76
66
66
56
56
51
51
45
45
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
3 - 114
COLUMN DESIGN
z
Fy = 36 ksi
Y
Fy = 50 ksi
COLUMNS
Single angles
w
x
x
Design axial strength in kips (φ = 0.90)
w
Y z
6×
×6
Size
Thickness
Wt./ft
7⁄
8
1
37.4
Fy
36
3⁄
4
33.1
50
36
5⁄
8
28.7
50
36
9⁄
16
24.2
50
36
50
1⁄
2
21.9
36
7⁄
16
19.6
50
36
3⁄
8
17.2
50
36
5⁄
16
14.9
50
36
12.4
50
36
50
Effective length KL (ft)
0 356 495 315 438 273 380 230 320 208 289 186 249 159 206 129 164 98 120
1
2
3
4
5
346
343
339
326
310
476
469
462
438
409
304
300
298
289
275
416
408
404
387
361
260
255
253
250
238
354
345
342
336
314
214
209
207
205
201
289
279
275
273
265
190
184
182
181
180
255
244
241
238
236
166
160
158
157
155
213
202
199
197
195
137
131
129
128
127
170 107 129 77
160 100 119 71
157 99 117 69
156 98 115 69
154 97 114 68
89
81
79
78
77
6
7
8
9
10
292
272
250
228
205
376
340
303
266
230
258
241
221
202
181
332
301
268
235
203
224
209
192
175
157
288
261
232
204
176
189
177
163
148
134
244
221
197
174
151
171
160
147
134
121
221
200
179
157
136
153
143
132
120
108
192
174
156
138
120
126
124
114
105
95
152
149
134
120
105
96 113 68
95 112 67
94 110 66
87 99 66
79 88 63
76
76
75
74
71
11
12
13
14
15
183
161
140
121
105
196
164
140
121
105
162
142
124
107
93
173 140 150 119 128 108 116
145 123 126 105 108 95 98
124 108 107 92 92 83 83
107 92 92 79 79 72 72
93 81 81 69 69 62 62
97 103
85 87
74 74
64 64
56 56
85
75
66
57
50
92
78
67
57
50
71
64
57
49
43
77
67
57
49
43
58
52
47
42
37
63
56
49
42
37
16
17
18
19
92
82
73
65
92
82
73
65
82
72
64
58
49
43
39
35
44
39
35
31
44
39
35
31
38
34
30
27
38
34
30
27
32
29
25
23
32
29
25
23
82
72
64
58
71
63
56
50
71
63
56
50
61
54
48
43
61
54
48
43
55
49
43
39
49
43
39
35
5×
×5
Size
7⁄
8
Thickness
Wt./ft
3⁄
4
27.2
Fy
Effective length KL (ft)
55
49
43
39
5⁄
8
23.6
1⁄
2
20.0
7⁄
16
16.2
3⁄
8
14.3
5⁄
16
12.3
10.3
36
50
36
50
36
50
36
50
36
50
36
50
36
50
0
259
359
225
312
190
264
154
214
135
184
115
149
89
114
1
2
3
4
5
251
249
241
228
212
345
341
325
301
272
216
214
209
198
184
296
291
283
262
237
179
177
176
167
156
244
239
236
221
200
141
138
137
135
127
189
183
181
179
163
121
117
116
115
112
157
152
150
148
141
99
95
94
93
92
122
117
115
114
112
73
70
69
68
67
88
83
81
80
79
6
7
8
9
10
194
175
155
135
116
241
209
177
146
119
169
152
135
118
102
210
182
154
128
104
143
129
114
100
86
178
154
131
108
88
116
105
93
82
70
145
126
107
89
72
102
93
82
72
62
126
110
94
78
64
87
79
71
62
54
105
92
80
67
56
67
64
57
51
45
78
74
65
55
47
11
12
13
14
15
98
82
70
60
53
98
82
70
60
53
86
72
61
53
46
86
72
61
53
46
73
61
52
45
39
73
61
52
45
39
60
50
43
37
32
60
50
43
37
32
53
44
38
33
28
53
44
38
33
28
46
39
33
28
25
46
39
33
28
25
38
33
28
24
21
39
33
28
24
21
16
46
46
40
40
34
34
28
28
25
25
22
22
18
18
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
DESIGN STRENGTH OF COLUMNS
3 - 115
Fy = 36 ksi
z
Y
Fy = 50 ksi
COLUMNS
Single angles
w
x
Design axial strength in kips (φ = 0.90)
Wt./ft
3⁄
4
Effective length KL (ft)
5⁄
8
18.5
Fy
1⁄
2
15.7
7⁄
16
12.8
3⁄
8
11.3
5⁄
16
9.8
1⁄
4
8.2
6.6
36
50
36
50
36
50
36
50
36
50
36
50
36
50
0
176
245
149
207
122
169
107
149
93
129
78
101
57
73
1
2
3
4
5
171
168
158
144
129
236
228
209
185
159
144
142
134
122
109
196
194
178
157
135
114
113
109
100
89
155
152
145
128
110
99
97
96
88
79
133
130
128
113
97
83
81
80
76
68
110
107
106
98
84
66
64
64
63
57
82
79
78
77
68
46
44
44
43
43
55
52
51
51
50
6
7
8
9
10
112
96
79
64
52
131
105
81
64
52
95
81
67
54
44
111
89
69
54
44
78
66
55
44
36
91
73
56
44
36
69
59
49
40
32
81
65
50
40
32
60
51
43
34
28
70
56
44
34
28
50
43
36
29
24
57
47
37
29
24
39
34
29
24
19
44
37
30
24
19
11
12
13
43
36
43
36
36
30
36
30
30
25
21
30
25
21
26
22
19
26
22
19
23
19
16
23
19
16
19
16
14
19
16
14
16
13
11
16
13
11
31⁄2×31⁄2
Size
1⁄
2
Thickness
Wt./ft
7⁄
16
11.1
Fy
Effective length KL (ft)
Y z
4×
×4
Size
Thickness
3⁄
8
9.8
5⁄
16
8.5
1⁄
4
7.2
5.8
36
50
36
50
36
50
36
50
36
50
0
105
146
93
129
80
112
68
93
53
68
1
2
3
4
5
100
99
91
81
70
137
134
119
102
83
87
86
80
72
62
118
116
106
90
74
74
73
70
62
54
99
97
91
78
64
60
59
58
53
46
78
76
75
65
54
44
43
42
41
36
53
52
51
50
42
6
7
8
9
10
59
48
37
29
24
65
49
37
29
24
52
42
33
26
21
58
43
33
26
21
45
37
29
23
18
50
37
29
23
18
38
31
24
19
16
42
32
24
19
16
31
25
20
16
13
34
26
20
16
13
11
20
20
17
17
15
15
13
13
11
11
3×
×3
Size
1⁄
2
Thickness
Wt./ft
7⁄
16
9.4
Fy
Effective length
KL (ft)
x
w
3⁄
8
8.3
5⁄
16
7.2
1⁄
4
6.1
3⁄
16
4.9
3.71
36
50
36
50
36
50
36
50
36
50
36
50
0
89
124
79
109
68
95
58
80
47
62
32
41
1
2
3
4
5
86
82
73
62
51
117
109
94
76
57
75
72
65
55
45
102
97
83
67
51
64
63
56
48
40
86
84
72
58
44
52
52
47
41
33
70
69
61
49
38
40
39
38
33
27
51
50
48
39
30
25
25
24
24
20
30
29
29
28
22
6
7
8
9
40
30
23
18
41
30
23
18
36
27
20
16
36
27
20
16
31
23
18
14
32
23
18
14
26
20
15
12
27
20
15
12
21
16
12
10
22
16
12
10
16
12
9
7
17
12
9
7
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
3 - 116
COLUMN DESIGN
z
Fy = 36 ksi
Y
Fy = 50 ksi
COLUMNS
Single angles
w
x
x
Design axial strength in kips (φ = 0.90)
w
Y z
21⁄2×21⁄2
Size
1⁄
2
Thickness
Wt./ft
7.7
Fy
Effective length KL (ft)
3⁄
8
5⁄
16
5.9
1⁄
4
5.0
3⁄
16
4.1
3.07
36
50
36
50
36
50
36
50
36
50
0
73
101
56
78
47
66
39
54
29
37
1
2
3
4
5
71
64
55
44
33
97
85
68
50
33
53
49
42
34
25
73
65
52
38
26
44
42
36
29
21
59
55
44
33
22
34
34
29
23
18
46
45
36
27
18
24
23
22
18
13
29
28
26
20
14
6
7
8
23
17
13
23
17
13
18
13
10
18
13
10
15
11
9
15
11
9
13
9
7
13
9
7
10
7
5
10
7
5
2×
×2
Size
Thickness
3⁄
8
5⁄
16
1⁄
4
3⁄
16
1⁄
8
Wt./ft
4.7
3.92
3.19
2.44
1.65
Fy
50
36
50
36
50
36
50
36
50
44
61
37
52
30
42
23
32
14
18
1
2
3
4
5
42
36
28
20
13
57
46
33
20
13
35
31
24
17
11
48
39
28
17
11
28
25
19
14
9
38
32
23
14
9
20
19
15
11
7
27
25
18
11
7
11
11
10
7
5
13
13
11
8
5
6
9
9
8
8
6
6
5
5
3
3
Effective length KL (ft)
36
0
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
REFERENCES
3 - 117
COLUMN BASE PLATES
The design of column base plates is covered in Part 11 (Volume II) of this LRFD Manual.
REFERENCES
Galambos, T. V. (ed.), 1988, Guide to Stability Design Criteria for Metal Structures,
Fourth Edition, Structural Stability Research Council, John Wiley & Sons, New York,
NY.
Geschwindner, L., 1993, “The ‘Leaning’ Column in ASD and LRFD,” Proceedings of
the 1993 National Steel Construction Conference, AISC, Chicago, IL.
Uang, C. M., S. W. Wattar, and K. M. Leet, 1990, “Proposed Revision of the Equivalent Axial
Load Method for LRFD Steel and Composite Beam-Column Design,” Engineering
Journal, 1st Qtr., AISC, Chicago.
Zureick, A., 1993, “Design Strength of Concentrically Loaded Single-Angle Struts,”
Engineering Journal, 4th Qtr., AISC, Chicago.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
4-1
PART 4
BEAM AND GIRDER DESIGN
OVERVIEW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-3
DESIGN STRENGTH OF BEAMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-5
General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-5
Design Strength If Elastic Analysis Is Used . . . . . . . . . . . . . . . . . . . . . . . . . 4-5
Flexural Design Strength for Cb = 1.0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-6
Flexural Design Strength for Cb > 1.0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-8
Design Strength If Plastic Analysis Is Used . . . . . . . . . . . . . . . . . . . . . . . . 4-10
LOAD FACTOR DESIGN SELECTION TABLE FOR SHAPES USED AS BEAMS . . . 4-11
Use of the Table . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-12
MOMENT OF INERTIA SELECTION TABLES FOR W AND M SHAPES . . . . . . . . 4-23
FACTORED UNIFORM LOAD TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . 4-28
General Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-28
Use of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-30
Reference Notes on Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-32
Tables, Fy = 36 ksi: W Shapes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-35
Tables, Fy = 36 ksi: S Shapes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-61
Tables, Fy = 36 ksi: Channels (C, MC) . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-64
Tables, Fy = 50 ksi: W Shapes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-72
Tables, Fy = 50 ksi: S Shapes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-98
Tables, Fy = 50 ksi: Channels (C, MC)) . . . . . . . . . . . . . . . . . . . . . . . . . . 4-101
DESIGN FLEXURAL STRENGTH OF BEAMS WITH UNBRACED LENGTH
GREATER THAN Lp . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-109
General Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-109
Charts (Fy = 36 ksi) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-113
Charts (Fy = 50 ksi) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-139
PLATE GIRDER DESIGN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-167
General Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-167
Flexure and Shear Strength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-167
Table of Dimensions and Properties of Built-up Wide-Flange Section . . . . . . . . . . 4-167
Design Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-168
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
4-2
BEAM AND GIRDER DESIGN
BEAM DIAGRAMS AND FORMULAS . . . . . . . . . . . . . . . . . . . . . . . . . . 4-187
Nomenclature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-187
Frequently Used Formulas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-188
Table of Concentrated Load Equivalents . . . . . . . . . . . . . . . . . . . . . . . . . 4-189
Static Loading Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-190
Design Properties of Cantilevered Beams . . . . . . . . . . . . . . . . . . . . . . . . 4-205
FLOOR DEFLECTIONS AND VIBRATIONS . . . . . . . . . . . . . . . . . . . . . . . 4-207
Serviceability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-207
Deflections and Camber . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-207
Vibrations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-208
BEAMS: OTHER SUBJECTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-211
REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-213
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
OVERVIEW
4-3
OVERVIEW
Beam tables are located as follows:
Load Factor Design Selection Table . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-15
Moment of Inertia Selection Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-24
Factored Uniform Load Tables, Fy = 36 ksi, begin on . . . . . . . . . . . . . . . . . . . 4-35
Factored Uniform Load Tables, Fy = 50 ksi, begin on . . . . . . . . . . . . . . . . . . . 4-72
Beam charts are located as follows:
Beam Design Moments, Fy = 36 ksi, begin on . . . . . . . . . . . . . . . . . . . . . . . 4-113
Beam Design Moments, Fy = 50 ksi, begin on . . . . . . . . . . . . . . . . . . . . . . . 4-139
Plate Girder Design Tables are on . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-183
Beam Diagrams and Formulas begin on . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-187
Additional information related to beam design is provided as follows:
Floor deflections and vibrations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-207
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
4-4
BEAM AND GIRDER DESIGN
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
DESIGN STRENGTH OF BEAMS
4-5
DESIGN STRENGTH OF BEAMS
General
Beams are proportioned so that no applicable strength limit state is exceeded when
subjected to factored load combinations and that no serviceability limit state is exceeded
when subjected to service loads. Strength limit states for beams include local buckling,
lateral torsional buckling, and yielding. Serviceability limit states may include, but are
not limited to, deflection and vibration.
The flexural design strength for beams must equal or exceed the required strength
based on the factored loads. The design strength φbMn for each applicable limit state shall
equal or exceed the maximum moment Mu as determined from the applicable factored
load combinations given in Section A4 of the LRFD Specification. Values of φbMn are
tabulated in the pages to follow. These values are based on beam behavior as shown in
Figure 4-1 and explained in the following discussion.
It should be noted that the LRFD Specification expresses values for moments and
lengths in kip-in. and inches. In this and other parts of the LRFD Manual, these values
are tabulated in kip-ft and feet.
The required strength can be determined by either elastic or plastic analysis.
Design Strength If Elastic Analysis Is Used
The flexural design strength of rolled I and C shape beams designed using elastic analysis,
according to LRFD Specification Section F1 is:
φbMn
where
φb = 0.90
Mp
M n′
Mn
Mr
(CbMn – Mn)
CbMn
Mn
Lp
L ′p
Lm
Lm′
Lr
Lb
Fig. 4-1
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
4-6
BEAM AND GIRDER DESIGN
Mn = nominal flexural strength as determined by the limit state of yielding, lateraltorsional buckling, or local buckling
Flexural Design Strength for Cb = 1.0
Compact Sections (Cb = 1.0)
When Lb ≤ Lp
The flexural design strength of compact (flange and web local buckling λ ≤ λp)
I-shaped and C-shaped rolled beams (as defined in Section B5 of the LRFD Specification)
bent about the major or minor axis is:
φbMn = φbMp = φbZFy / 12
In minor axis flexure this is true for all unbraced lengths, but for bending about the major
axis the distance Lb between points braced against lateral movement of the compression
flange or between points braced to prevent twist of the cross-section shall not exceed the
value Lp (see Figure 4-1).
Lp =
300ry
Fy
√
(F1-4)
When Lp < Lb ≤ Lr
The flexural design strength of compact I or C rolled shapes bent about the major axis,
from LRFD Specification Section F1.2, is:
Lb − Lp
φbMn = φbMp − φb(Mp − Mr)
≤ φbMp
Lr − Lp
where the limiting length Lr and the corresponding buckling moment Mr (see Figure 4-1)
are determined as follows:
Lr =
ryX1
(Fy − Fr )
√
1+√
1 + X2(Fy − Fr)2
(F1-6)
where
X1 =
π
Sx
√
4Cw
X2 =
Iy
EGJA
2
Sx
GJ
(F1-8)
2
φbMr = φbSx(Fy − Fr ) / 12 kip-ft
Sx = section modulus about major axis, in.3
E = modulus of elasticity of steel, 29,000 ksi
G = shear modulus of steel, 11,200 ksi
J = torsional constant, in.4
A = cross-sectional area of beam, in.2
Cw = warping constant, in.6
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
(F1-9)
DESIGN STRENGTH OF BEAMS
4-7
Fr = compressive residual stress in flange: for rolled shapes Fr = 10 ksi; for welded
shapes Fr = 16.5 ksi
Values of J and Cw are tabulated for some shapes in Part 1 of the LRFD Manual. For
values not shown, see Torsional Analysis of Steel Members (AISC, 1983).
Compact and Noncompact Sections (Cb = 1.0)
When Lb > Lr
According to LRFD Specification Section F1.2b, the flexural design strength of
compact and noncompact I or C rolled shapes bent about the major axis is:
π
φbMn = φbMcr = φb
Lb
√
2
πE
EIyGJ + IyCw
Lb
SxX1√
2
= φb
(Lb / ry)
√
1+
X21X2
≤ φbMr
2(Lb / ry)2
Noncompact Sections (Cb = 1.0)
When Lb ≤ Lp′
All rolled W shapes are compact except the W40×174, W14×99, W14×90, W12×65,
W10×12, W8×10, and W6×15 for 50 ksi and the W6×15 for 36 ksi. The flexural design
strength φbMn′ (see Figure 4-1) for noncompact (flange or web local buckling λp < λ ≤
λr) I and C rolled shapes bent about the major or minor axis is the smaller value for either
local flange buckling or local web buckling as determined by:
λ − λp
φbMn′ = φbMp − φb(Mp − Mr)
λr − λp
For local flange buckling:
λ = bf / 2tf for I-shaped members
λ = bf / tf for C-shaped members
Fy
λp = 65 / √
λr = 141 / √
Fy − 10
For local web buckling:
λ = h / tw
λp = 640 / √
Fy
Fy
λr = 970 / √
Mp − Mn′
Lp′ = Lp + (Lr − Lp)
Mp − Mr
Sections with a width-to-thickness ratio exceeding the specified values for λr are
slender shapes and must be analyzed using LRFD Specification Appendix B5.3.
When Lp′ < Lb ≤ Lr
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
4-8
BEAM AND GIRDER DESIGN
The flexural design strength of noncompact I or C rolled shapes bent about the major
axis is determined by:
Lb − Lp
φbMn = φbMp − φb(Mp − Mr)
≤ φbMn′
Lr − Lp
In the Load Factor Design Selection Table, in the case of the noncompact shapes, the
values of φbMn′ and Lp′ are tabulated as φbMp and Lp. The formula above may be used with
the tabulated values.
Flexural Design Strength for Cb > 1.0
Cb is a factor which varies with the moment gradient between bracing points (Lb). For
Cb greater than 1.0, the design flexural strength is equal to the tabulated value of the
design flexural strength (with Cb = 1.0) multiplied by the calculated Cb value. The
maximum value is φbMp for compact shapes or φbMn′ for noncompact shapes. The
maximum unbraced lengths associated with the maximum flexural design strengths
φbMp and φbMn′ are Lm and Lm′ (see Figure 4-1).
A new expression for Cb is given in the LRFD Specification. (It is more accurate than
the one previously shown.)
Cb =
12.5Mmax
2.5Mmax + 3MA + 4MB + 3Mc
(F1-3)
where M is the absolute value of a moment in the unbraced beam segment as follows:
Mmax , the maximum
MA , at the quarter point
MB , at the centerline
Mc , at the three-quarter point
Values for Cb for some typical loading conditions are given in Table 4-1.
Compact Sections (Cb > 1.0)
When Lb ≤ Lm
The flexural design strength for rolled I and C shapes is:
φbMn = φbMp
When Lb > Lm
The flexural design strength is:
φbMn = Cb[φbMn (for Cb = 1.0)] ≤ φbMp
For Lm ≤ Lr
Lm = Lp +
(CbMp − Mp)(Lr − Lp)
Cb(Mp − Mr)
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
DESIGN STRENGTH OF BEAMS
4-9
Table 4-1.
Values of Cb for Simply Supported Beams
Lateral Bracing
Along Span
Load
Cb
None
1.32
At load points
1.67
1.67
None
1.14
At load points
1.67
1.00
1.67
None
1.14
At load points
1.67
1.11
None
At centerline
Cbπ
Mp
1.30
√
√
√
EIyGJ
2
1+
1+
4CwM2p
IyC2bG2J2
The value of Cb for which Lm or Lm′ equals Lr for any rolled shape is:
Cb =
Fy Zx
(Fy − 10)Sx
Noncompact Sections (Cb > 1.0)
When Lb ≤ Lm′
The flexural design strength for rolled I and C shapes is:
φbMn = φbMn′ < φbMp
When Lb > Lm′
The flexural design strength is:
φbMn = Cb[φbMn (for Cb = 1.0)] ≤ φbMn′
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1.67
1.14
For Lm > Lr
Lm =
1.11
1.30
4 - 10
BEAM AND GIRDER DESIGN
For Lm′ ≤ Lr
Lm′ = Lp′ +
(CbMn′ − Mn′)(Lr − Lp)
Cb(Mp − Mr)
For Lm′ > Lr
Lm =
Cbπ
Mp
√
√
√
EIyGJ
2
1+
1+
4CwM2p
IyC2bG2J2
Design Strength If Plastic Analysis Is Used
The design flexural strength for plastic analysis is:
φbMn = φbMp
where
φb = 0.90
Mp = ZxFy / 12 kip-ft
The yield strength of material that may be used with plastic analysis is limited to 65 ksi. Plastic
analysis is limited to compact shapes as defined in Table B5.1 of the LRFD Specification as:
λp = bf / 2tf ≤ 65 / √
Fy for the flanges of I shapes in flexure
Fy for the flanges of C shapes in flexure
λp = bf / tf ≤ 65 / √
and
λp = h / tw ≤ 640 / √
Fy for beam webs in flexural compression
where
.
λp = limiting slenderness parameter for compact element
bf = width of flange for I and C shapes, in.
tf = flange thickness, in.
h = clear distance between flanges less the fillet at each flange, in.
tw = beam web thickness, in
In addition, LRFD Specification Section F1.2d states: for a section bent about the major
axis, the laterally unbraced length of the compression flange at plastic hinge locations
associated with the failure mechanism shall not exceed:
Lpd =
3,600 + 2,220(M1 / M2)
ry
Fy
where
Fy
M1
M2
ry
(M1 / M2)
= specified yield strength of compression flange, ksi
= smaller moment at end of unbraced length of beam, kip-in.
= larger moment at end of unbraced length of beam, kip-in.
= radius of gyration about minor axis, in.
is positive when the moments cause reverse curvature
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
(F1-17)
LOAD FACTOR DESIGN SELECTION TABLE FOR SHAPES USED AS BEAMS
4 - 11
LOAD FACTOR DESIGN SELECTION TABLE FOR SHAPES USED AS BEAMS
This table facilitates the selection of beams designed on the basis of flexural strength in
accordance with Section F of the LRFD Specification. It includes only W and M shapes
designed as beams. A laterally supported beam can be selected by entering the table with
the required plastic section modulus or factored bending moment, and comparing it with
tabulated values of Zx or φbMp respectively.
The table is applicable to adequately braced beams with unbraced lengths not exceeding Lr, i.e., Lb ≤ Lr. For beams with unbraced lengths greater than Lp, it may be convenient
to use the unbraced beam charts. For most loading conditions, it is convenient to use this
selection table. However, for adequately braced, simply supported beams with a uniform
load over the entire length, or equivalent symmetrical loading, the tables of Factored
Uniform Loads can also be used.
In this table, shapes are listed in groups by descending order plastic section modulus
Zx. Included also for steel of Fy = 36 ksi and 50 ksi are values for the maximum flexural
design strength φbMp; the limiting buckling moment φbMr; the limiting laterally unbraced
compression flange length for full plastic moment capacity and uniform moment (Cb =
1.0) Lp; limiting laterally unbraced length for inelastic lateral-torsional buckling Lr; and
BF, a factor that can be used to calculate the resisting moment φbMn for beams with
unbraced lengths between the limiting bracing lengths Lp and Lr.
For noncompact shapes, as determined by Section B5 of the LRFD Specification, the
maximum flexural design strength φbMn, max as determined by LRFD Specification
Formula A-F1-3 is tabulated as φbMp. The associated maximum unbraced length is
tabulated as Lp. (See the previous discussion under Design Strength of Beams for further
explanation.)
The symbols used in this table are:
Zx = plastic section modulus, X-X axis, in.3
φbMp = design plastic bending moment, kip-ft
= φbZxFy / 12 if shape is compact
λ − λp
= φbM′n = φbMp − φb(Mp − Mr)
if shape is noncompact
λr − λp
φbMr = limiting design buckling moment, kip-ft
= φbSx(Fy − Fr ) / 12
where
Fr = 10 ksi for rolled shapes
Lp = limiting laterally unbraced length for inelastic LTB, ft, uniform moment case
(Cb = 1)
Lr = limiting laterally unbraced length for elastic lateral-torsional buckling, ft
BF = a factor that can be used to calculate the design flexural strength for unbraced
lengths Lb, between Lp and Lr, kip-ft
φb(Mp − Mr)
=
Lr − Lp
where
φbMn = Cb[φbMp − BF(Lb − Lp)] ≤ φbMp
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
4 - 12
BEAM AND GIRDER DESIGN
Use of the Table
Determine the required plastic section modulus Zx from the maximum factored moment
Mu (kip-ft) using the desired steel yield strength.
Zx =
12Mu
φbFy
Enter the column headed Zx and find a value equal to or greater than the plastic section
modulus required. Alternatively, enter the φbMp column and find a value of φbMp equal
to or greater than the required factored load moment. The beam opposite these values
(Zx or φbMp) in the shapes column, and all beams above it, have sufficient flexural strength
based only on these parameters. The first beam appearing in boldface type adjacent to or
above the required Zx or φbMp is the lightest section that will serve for the steel yield stress
used in the calculations. If the beam must not exceed a certain depth, proceed up the
column headed “Shape” until a beam within the required depth is reached.
After a shape has been selected, the following checks should be made. If the lateral
bracing of the compressive flange exceeds Lp, but is less than Lr, the design flexural
strength may be calculated as follows:
φbMn = Cb[φbMp − BF(Lb − Lp)] ≤ φbMp
If the bracing length Lb is substantially greater than Lp, i.e., Lb > Lr, it is recommended
the unbraced beam charts be used. A check should be made of the beam web shear strength
by referring to the Factored Uniform Load Tables or by use of the formula:
φvVn = φv0.6FywAw (from LRFD Specification Section F2)
where
φv = 0.90
If a deflection limitation also exists, the adequacy of the selected beam should be checked
accordingly.
EXAMPLE 4-1
Given:
Solution
(Zx method):
Select a beam of Fy = 50 ksi steel subjected to a factored uniform
bending moment of 256 kip-ft, having its compression flange braced
at 5.0 ft intervals. Assume Cb = 1.0.
Zx (req’d) =
Mu(12) 256(12)
=
= 68.3 in.3
φbFy
0.9(50)
Enter the Load Factor Design Selection Table and find the nearest
higher tabulated value of Zx is 69.6 in., which corresponds to a
W14×43. This beam, however, is not in boldface type. Proceed up the
shape column and locate the first beam in boldface, W16×40. Note the
values tabulated for φbMp and Lp are 273 kip-ft and 5.6 ft, respectively.
Use W16x40
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
LOAD FACTOR DESIGN SELECTION TABLE FOR SHAPES USED AS BEAMS
4 - 13
Alternatively, proceed up the shape column and select a W18×40. The
tabulated values for φbMp and Lp are 294 kip-ft and 4.5 ft, respectively.
Since the bracing length Lb is larger than Lp and smaller than Lr, the
maximum resisting moment may be calculated as follows:
φbMn = Cb[φbMp − BF(Lb − Lp)]
= 1.0[294 − (11.7)(5.0 − 4.5)]
= 288 kip-ft > 256 kip-ft req’d o.k.
A W18×40 is satisfactory.
Alternate
solution
(Mp method):
Enter the column of φbMp values and note the tabulated value nearest
and higher than the required factored moment (Mu) is 261 kip-ft, which
corresponds to a W14×43. Scanning the φbMp values for shapes listed
higher in the column, a W16×40 is found to be the lightest suitable
shape with Lb < Lp.
Use W16×40
EXAMPLE 4-2
Given:
Determine the design flexural strength of a W16×40 of Fy = 36 ksi and
Fy = 50 ksi steel with the compression flange braced at intervals of
9.0 ft. Assume Cb = 1.1.
Solution:
Enter the Load Factor Design Table and note that for a W16×40, Fy =
36 ksi:
φbMp = 197 kip-ft
Lp = 6.5 ft
Lr = 19.3 ft
BF = 5.54 kips
φbMn = Cb[φbMp − BF(Lb − Lp)] ≤ φb Mp
= 1.1[197 − 5.54(9 − 6.5)] ≤ 197 kip-ft
= 197 kip-ft
Enter the Load Factor Design Selection Table and note that for a
W16×40, Fy = 50 ksi:
φbMp = 273 kip-ft
Lp = 5.6 ft
Lr = 14.7 ft
BF = 8.67 kips
φbMn = Cb[φbMp − BF(Lb − Lp)] ≤ φb Mp
= 1.1[273 − 8.67(9 − 5.6)] ≤ 273 kip-ft
= 268 kip-ft
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
4 - 14
BEAM AND GIRDER DESIGN
EXAMPLE 4-3
Given:
Select a beam of Fy = 50 ksi steel subjected to a factored uniform
bending moment of 30 kip-ft having its compression flange braced at
4.0-ft intervals and a depth of eight inches or less. Assume Cb = 1.0.
Solution
(Zx method):
Assume shape is compact and Lb ≤ Lp.
Zx req’d =
12Mu 12(30)
=
= 8.0 in.3
φbFy 0.9(50)
Enter the Load Factor Design Selection Table and note that for a
W8×10, Fy = 50 ksi, the shape is noncompact, however, the maximum
resisting moment φbMn listed in the φbMp column is adequate. Further
note:
φbMn = 33.0 kip-ft
Lp = 3.1 ft
Lr = 7.8 ft
BF = 2.03 kips
Since Lp < Lb ≤ Lr
φbMn = Cb[φbMn − BF(Lb − Lp)]
= 1.0[33.0 − 2.03(4.0 − 3.1)]
= 33.0 − 1.8
= 31.2 kip-ft > 30 kip-ft req’d o.k.
Use: W8×10
Alternate
Solution
(Mp method):
Enter the Selection Table and note that in the column of φbMp values
for W8×10, Fy = 50 ksi, the value of φbMp is 33.0 kip-ft, which is
adequate. Also note, however, Lp = 3.1 ft is less than the bracing interval
Lb = 4.0 ft, and that BF is equal to 2.03 kips. Therefore:
φbMn = 1.0[33.0 − 2.03(4 − 3.1)]
= 31.2 kip-ft > 30 kip-ft req’d o.k.
Use: W8×10
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
LOAD FACTOR DESIGN SELECTION TABLE FOR SHAPES USED AS BEAMS
4 - 15
LOAD FACTOR DESIGN SELECTION TABLE
For shapes used as beams
φb = 0.90
Fy = 36 ksi
Zx
Fy = 50 ksi
BF
Lr
Lp
φbMr
φbMp
Zx
Kips
Ft
Ft
Kip-ft Kip-ft
in.3
φbMr
Lp
Lr
BF
Kip-ft Kip-ft
Ft
Ft
Kips
34.5
138.2
17.8
6180
10300
3830
W36×848a 14400
9510
15.1
90.5
64.3
34.1
130.1
17.7
5810
9639
3570
W36×798a 13400
8940
15.0
85.3
63.2
33.2
105.9
17.2
4720
7668
2840
W36×650a 10700
7260
14.6
70.0
61.1
41.9
84.8
15.9
4560
7450
2760
W40×593a 10400
7020
13.5
56.8
76.7
41.2
33.2
72.5
86.8
15.5
16.8
3860
3800
6210
6129
2300
2270
W40×503a
W36× 527a
8630
8510
5940
5850
13.2
14.2
49.5
58.3
73.9
60.4
46.9
58.2
11.3
3330
5540
2050
W40×466a
7690
5130
9.6
39.4
85.9
41.0
19.3
32.7
23.7
63.3
119.4
73.5
93.6
15.2
15.3
16.5
15.6
3300
3060
3160
2980
5270
5080
5022
4830
1950
1880
1860
1790
W40×431
W27× 539a
W36× 439a
W30× 477a
7310
7050
6980
6710
5070
4710
4860
4590
12.9
12.9
14.0
13.3
44.1
78.2
50.3
62.0
72.0
35.9
58.2
43.5
46.6
49.8
11.0
2810
4620
1710
W40×392a
6410
4320
9.3
34.3
83.7
39.9
32.5
56.6
67.2
15.0
16.3
2850
2830
4510
4482
1670
1660
W40×372
W36× 393a
6260
6230
4380
4350
12.7
13.8
40.3
46.7
68.4
57.0
48.6
15.3
18.9
32.5
48.0
123.3
99.2
62.4
14.6
14.2
14.9
16.1
2750
2520
2540
2570
4370
4190
4130
4077
1620
1550
1530
1510
W44×335
W24× 492a
W27× 448a
W36× 359a
6080
5810
5740
5660
4230
3870
3900
3960
12.4
12.1
12.6
13.7
35.5
80.5
65.3
44.0
79.7
28.4
34.9
56.2
46.2
22.9
29.4
43.2
77.5
64.4
10.7
15.3
15.6
2360
2440
2400
3860
3860
3830
1430
1430
1420
W40×331
W30× 391a
W33× 354a
5360
5360
5330
3630
3750
3690
9.1
13.0
13.2
30.5
52.1
44.7
80.9
41.2
51.9
46.1
38.4
32.2
38.4
45.3
51.2
58.5
48.9
14.6
14.8
16.0
14.8
2420
2440
2360
2280
3830
3830
3726
3590
1420
1420
1380
1330
W44×290
W40× 321
W36× 328a
W40× 297
5330
5330
5180
4990
3720
3750
3630
3510
12.4
12.6
13.6
12.5
34.0
37.2
41.7
35.9
74.1
63.9
54.9
63.2
43.4
28.9
31.6
14.7
37.3
19.0
44.2
23.4
31.0
28.2
43.7
43.1
59.3
55.1
103.0
47.9
82.0
38.2
66.6
53.0
55.7
37.0
14.4
15.5
16.0
13.9
14.9
14.5
10.5
15.0
15.9
15.4
10.5
2180
2160
2160
2070
2150
2070
1990
2010
2010
1970
1890
3430
3430
3402
3380
3380
3350
3210
3210
3159
3110
3050
1270
1270
1260
1250
1250
1240
1190
1190
1170
1150
1130
W44×262
W33× 318a
W36× 300
W24× 408a
W40× 277
W27× 368a
W40× 278
W30× 326a
W36× 280
W33× 291a
W40× 264
4760
4760
4730
4690
4690
4650
4460
4460
4390
4310
4240
3360
3330
3330
3180
3300
3180
3060
3090
3090
3030
2910
12.2
13.1
13.5
11.8
12.7
12.3
8.9
12.8
13.5
13.0
8.9
32.8
41.8
39.9
67.5
35.5
54.6
27.6
45.7
38.8
39.8
27.0
68.2
49.9
52.9
27.0
60.8
34.8
74.9
41.7
51.3
48.0
73.3
35.6
45.4
14.8
1930
3020
1120
W40×249
4200
2980
12.6
34.1
56.9
Shape
φbMp
aGroup 4 or Group 5 shape. See Notes in Table 1-2 (Part 1).
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
4 - 16
BEAM AND GIRDER DESIGN
LOAD FACTOR DESIGN SELECTION TABLE
For shapes used as beams
φb = 0.90
Zx
Fy = 36 ksi
Fy = 50 ksi
BF
Lr
Lp
φbMr
φbMp
Zx
Kips
Ft
Ft
Kip-ft Kip-ft
in.3
φbMr
Lp
Lr
BF
Kip-ft Kip-ft
φbMp
Ft
Ft
Kips
40.1
30.3
23.1
37.0
27.7
15.0
18.7
41.8
29.6
41.2
50.6
60.5
39.7
52.0
84.5
69.4
35.1
48.8
14.3
15.8
14.9
11.0
15.3
13.5
14.3
10.6
15.6
1890
1860
1810
1750
1790
1680
1720
1700
1750
2970
2916
2860
2810
2810
2750
2750
2730
2727
1100
1080
1060
1040
1040
1020
1020
1010
1010
W44×230
W36×260
W30× 292a
W36×256
W33× 263a
W24× 335a
W27× 307a
W40×235
W36×245
4130
4050
3980
3900
3900
3830
3830
3790
3790
2910
2860
2780
2690
2750
2590
2650
2620
2690
12.1
13.4
12.7
9.4
12.9
11.4
12.1
9.0
13.3
31.7
37.5
42.1
28.8
37.8
55.8
46.9
26.0
36.4
62.0
49.4
40.4
62.7
46.3
27.8
33.7
68.6
47.7
33.1
28.7
22.8
27.0
36.1
42.7
47.3
55.4
49.2
37.2
14.8
15.5
14.8
15.1
10.9
1670
1630
1610
1620
1580
2600
2550
2540
2540
2530
963
943
941
939
936
W40×215
W36×230
W30×261
W33×241
W36×232
3610
3540
3530
3520
3510
2570
2510
2480
2490
2430
12.5
13.2
12.5
12.8
9.3
32.6
35.6
39.2
36.2
27.3
51.6
45.8
39.2
44.2
59.9
40.2
33.2
10.5
1530
2440
905
W40×211
3390
2360
8.9
24.9
64.7
31.6
26.0
18.6
22.4
14.7
34.9
41.1
46.9
59.6
51.6
71.2
35.0
14.4
15.0
14.0
14.7
13.2
10.8
1500
1480
1450
1450
1400
1400
2340
2310
2300
2280
2250
2250
868
855
850
845
835
833
W40×199
W33×221
W27×258
W30×235
W24× 279a
W36×210
3260
3210
3190
3170
3130
3120
2310
2270
2230
2240
2150
2160
12.2
12.7
11.9
12.4
11.2
9.1
31.6
35.0
41.1
37.1
47.6
26.1
48.8
41.9
32.9
37.7
26.9
56.8
37.4
25.0
18.5
34.0
8.40
21.8
14.7
31.2
44.8
55.0
33.5
109.5
47.9
64.3
10.4
14.8
13.9
10.7
12.3
14.5
13.1
1330
1330
1310
1290
1220
1290
1260
2110
2080
2080
2070
2030
2020
2010
781
772
769
767
753
749
744
W40×183
W33×201
W27×235
W36×194
W18× 311a
W30×211
W24× 250a
2930
2900
2880
2880
2820
2810
2790
2050
2050
2020
1990
1870
1990
1930
8.8
12.6
11.8
9.1
10.4
12.3
11.1
23.8
33.8
38.5
25.2
71.5
35.1
43.4
59.0
39.7
32.3
54.6
15.6
36.0
26.6
32.7
32.8
10.6
1210
1940
718
W36×182
2690
1870
9.0
24.9
52.0
b
Shape
27.5
18.2
38.4
52.0
13.6
13.8
1250
1220
1930
1910
715
708
W40×174
W27×217
2660
2660
1920
1870
12.0
11.7
29.9
36.8
41.3
31.3
35.6
8.29
14.7
21.0
31.5
28.3
17.8
29.7
99.6
59.3
45.4
31.9
32.6
48.0
10.0
12.1
13.0
14.4
10.5
10.4
13.7
1170
1100
1150
1170
1130
1070
1080
1870
1830
1830
1820
1800
1700
1700
692
676
676
673
668
629
628
W40×167
W18× 283a
W24×229
W30×191
W36×170
W33×169
W27×194
2600
2540
2540
2520
2510
2360
2360
1800
1690
1760
1790
1740
1650
1670
8.5
10.3
11.0
12.2
8.9
8.8
11.6
22.8
65.1
40.4
33.7
24.4
24.5
34.6
55.6
15.4
26.2
33.9
49.6
45.4
30.0
30.7
8.21
14.5
20.2
30.9
90.9
54.2
43.2
10.4
12.0
12.8
14.3
1060
1000
1040
1050
1680
1650
1640
1630
624
611
606
605
W36×160
W18× 258a
W24×207
W30×173
2340
2290
2270
2270
1630
1540
1590
1620
8.8
10.2
10.9
12.1
23.7
59.5
37.4
32.5
48.0
15.2
25.6
32.0
aGroup 4 or Group 5 shape. See Notes in Table 1-2 (Part 1).
bIndicates noncompact shape; F = 50 ksi
y
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
LOAD FACTOR DESIGN SELECTION TABLE FOR SHAPES USED AS BEAMS
4 - 17
LOAD FACTOR DESIGN SELECTION TABLE
For shapes used as beams
φb = 0.90
Fy = 36 ksi
Zx
Fy = 50 ksi
BF
Lr
Lp
φbMr
φbMp
Zx
Kips
Ft
Ft
Kip-ft Kip-ft
in.3
φbMr
Lp
Lr
BF
Kip-ft Kip-ft
Ft
Ft
Kips
32.8
29.4
17.5
26.8
14.3
8.09
11.0
28.2
30.2
45.2
31.2
51.3
82.8
60.8
9.5
10.3
13.6
10.3
12.8
11.9
12.6
998
983
979
950
957
909
899
1610
1570
1530
1510
1510
1480
1430
597
581
567
559
559
549
530
W40×149
W36× 150
W27× 178
W33× 152
W24× 192
W18× 234a
W21× 201
2240
2180
2130
2100
2100
2060
1990
1540
1510
1510
1460
1470
1400
1380
8.1
8.7
11.5
8.7
10.9
10.1
10.7
21.9
23.4
33.1
23.7
35.7
54.4
41.1
50.8
45.6
28.8
42.3
25.0
14.9
19.9
25.7
16.9
14.3
30.1
42.8
47.8
10.1
13.5
12.7
874
887
878
1390
1380
1380
514
512
511
W33×141
W27× 161
W24× 176
1930
1920
1920
1340
1370
1350
8.6
11.5
10.7
23.1
31.7
33.8
40.2
27.4
24.6
27.5
23.7
8.00
10.9
14.1
28.8
30.6
75.0
55.8
45.2
9.9
9.5
11.8
12.5
12.7
856
850
817
813
807
1370
1350
1320
1290
1260
509
500
490
476
468
W36×135
W30× 148
W18× 211a
W21× 182
W24× 162
1910
1880
1840
1790
1760
1320
1310
1260
1250
1240
8.4
8.1
10.0
10.6
10.8
22.4
22.8
49.5
38.1
32.4
42.2
38.6
14.7
19.4
23.8
24.5
16.2
7.98
22.4
10.8
13.8
29.1
40.7
68.3
29.0
51.7
42.0
10.0
13.4
11.6
9.4
12.4
12.5
792
801
741
741
741
723
1260
1240
1190
1180
1170
1130
467
461
442
437
432
418
W33×130
W27× 146
W18× 192
W30× 132
W21× 166
W24× 146
1750
1730
1660
1640
1620
1570
1220
1230
1140
1140
1140
1110
8.4
11.3
9.9
8.0
10.5
10.6
22.5
30.6
45.3
22.0
35.7
30.6
37.9
25.8
14.6
35.6
19.1
22.8
23.1
21.6
7.95
18.9
27.8
28.2
62.3
30.0
9.7
9.3
11.5
9.2
700
692
671
673
1120
1100
1070
1070
415
408
398
395
W33×118
W30× 124
W18× 175
W27× 129
1560
1530
1490
1480
1080
1070
1030
1040
8.2
7.9
9.8
7.8
21.7
21.5
41.5
22.3
35.5
34.1
14.5
30.9
21.1
10.7
13.3
7.87
27.1
46.4
39.3
56.7
9.1
12.3
12.4
11.4
642
642
642
605
1020
1010
999
961
378
373
370
356
W30×116
W21× 147
W24× 131
W18× 158
1420
1400
1390
1340
987
987
987
930
7.7
10.4
10.5
9.7
20.8
32.8
29.1
38.2
33.0
18.4
21.5
14.2
20.2
18.0
10.5
12.7
7.82
26.3
28.2
43.1
37.1
52.2
9.0
9.1
12.2
12.3
11.3
583
583
575
567
550
934
926
899
883
869
346
343
333
327
322
W30×108
W27× 114
W21× 132
W24× 117
W18× 143
1300
1290
1250
1230
1210
897
897
885
873
846
7.6
7.7
10.4
10.4
9.6
20.3
21.3
30.9
27.9
35.5
31.5
28.7
17.7
20.2
14.0
19.0
10.3
17.0
7.79
12.0
25.5
41.0
26.8
48.0
35.2
8.8
12.2
9.0
11.3
12.1
525
532
521
499
503
842
829
824
786
780
312
307
305
291
289
W30×99
W21× 122
W27× 102
W18× 130
W24× 104
1170
1150
1140
1090
1080
807
819
801
768
774
7.4
10.3
7.6
9.5
10.3
19.8
29.8
20.5
33.0
26.8
29.2
17.1
26.7
13.8
18.8
Shape
φbMp
aGroup 4 or Group 5 shape. See Notes in Table 1-2 (Part 1).
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
4 - 18
BEAM AND GIRDER DESIGN
LOAD FACTOR DESIGN SELECTION TABLE
For shapes used as beams
φb = 0.90
Zx
Fy = 36 ksi
Fy = 50 ksi
BF
Lr
Lp
φbMr
φbMp
Zx
Kips
Ft
Ft
Kip-ft Kip-ft
in.3
φbMr
Lp
Lr
BF
Kip-ft Kip-ft
Ft
Ft
Kips
17.8
14.8
10.1
16.2
7.72
14.3
9.61
24.8
27.1
38.7
25.9
44.1
25.9
37.1
8.7
8.3
12.1
8.8
11.2
8.3
12.0
478
478
486
474
450
433
443
764
756
753
751
705
686
683
283
280
279
278
261
254
253
W30×90
W24×103
W21×111
W27× 94
W18×119
W24× 94
W21×101
1060
1050
1050
1040
979
953
949
735
735
747
729
693
666
681
7.4
7.0
10.3
7.5
9.5
7.0
10.2
19.4
20.1
28.5
19.9
30.8
19.4
27.6
27.1
24.1
16.4
25.2
13.4
23.0
15.4
15.0
3.87
7.62
24.9
73.6
40.4
8.6
15.7
11.1
415
408
398
659
632
621
244
234
230
W27×84
W14×132
W18×106
915
878
863
639
627
612
7.3
13.3
9.4
19.3
49.6
28.7
23.0
6.89
13.0
13.6
11.8
3.86
7.51
24.5
26.6
67.9
38.1
8.1
7.7
15.6
11.0
382
374
371
367
605
597
572
570
224
221
212
211
W24×84
W21× 93
W14×120
W18× 97
840
829
795
791
588
576
570
564
6.9
6.5
13.2
9.4
18.6
19.4
46.2
27.4
21.5
19.6
6.82
12.6
12.7
6.10
11.3
3.84
2.95
7.27
23.4
42.1
24.9
62.7
75.5
35.5
8.0
10.5
7.6
15.5
13.0
11.0
343
341
333
337
318
324
540
535
529
518
502
502
200
198
196
192
186
186
W24×76
W16×100
W21× 83
W14×109
W12×120
W18× 86
750
743
735
720
698
698
528
525
513
519
489
498
6.8
8.9
6.5
13.2
11.1
9.3
18.0
29.3
18.5
43.2
50.0
26.1
19.8
10.7
18.5
6.70
5.36
11.9
12.1
6.03
3.77
10.7
2.95
6.94
22.4
38.6
58.2
23.5
67.2
33.3
7.8
10.4
15.5
7.5
13.0
10.9
300
302
306
294
283
285
478
473
467
464
443
440
177
175
173
172
164
163
W24×68
W16× 89
W14× 99b
W21× 73
W12×106
W18× 76
664
656
647
645
615
611
462
465
471
453
435
438
6.6
8.8
13.4
6.4
11.0
9.2
17.4
27.3
40.6
17.7
44.9
24.8
18.7
10.3
6.46
17.0
5.32
11.1
10.4
3.75
22.8
54.1
7.5
15.4
273
279
432
424
160
157
W21×68
W14× 90b
600
587
420
429
6.4
15.0
17.3
38.4
16.5
6.31
13.8
5.85
2.01
2.91
8.29
17.2
34.9
86.4
61.4
24.4
5.8
10.3
11.2
12.9
7.1
255
261
246
255
248
413
405
397
397
392
153
150
147
147
145
W24×62
W16× 77
W10×112
W12× 96
W18× 71
574
563
551
551
544
393
402
378
393
381
4.9
8.7
9.5
10.9
6.0
13.3
25.2
56.5
41.3
17.8
21.4
9.75
3.68
5.20
13.8
9.84
4.15
21.7
43.0
7.4
10.3
248
240
389
375
144
139
W21×62
W14× 82
540
521
381
369
6.3
8.8
16.6
29.6
15.3
7.31
Shape
φbMp
bIndicates noncompact shape; F = 50 ksi.
y
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
LOAD FACTOR DESIGN SELECTION TABLE FOR SHAPES USED AS BEAMS
4 - 19
LOAD FACTOR DESIGN SELECTION TABLE
For shapes used as beams
φb = 0.90
Fy = 36 ksi
Zx
Fy = 50 ksi
BF
Lr
Lp
φbMr
φbMp
Zx
Kips
Ft
Ft
Kip-ft Kip-ft
in.3
φbMr
Lp
Lr
BF
Kip-ft Kip-ft
Ft
Ft
Kips
12.7
8.08
2.90
2.00
5.57
11.3
4.10
7.91
2.88
4.05
1.97
16.6
23.2
56.4
77.4
32.3
17.3
40.0
22.4
51.8
37.3
68.4
5.6
7.0
12.8
11.0
10.3
5.6
10.3
7.0
12.7
10.3
11.0
222
228
230
218
228
216
218
211
209
201
192
362
359
356
351
351
348
340
332
321
311
305
134
133
132
130
130
129
126
123
119
115
113
W24×55
W18× 65
W12× 87
W10× 100
W16× 67
W21× 57
W14× 74
W18× 60
W12× 79
W14× 68
W10× 88
503
499
495
488
488
484
473
461
446
431
424
342
351
354
336
351
333
336
324
321
309
296
4.7
6.0
10.9
9.4
8.7
4.8
8.8
6.0
10.8
8.7
9.3
12.9
17.1
38.4
50.8
23.8
13.1
28.0
16.7
35.7
26.4
45.1
19.6
13.3
5.12
3.66
9.02
18.0
7.12
12.8
5.03
6.91
3.58
7.65
21.4
7.0
192
302
112
W18×55
420
295
5.9
16.1
12.2
10.5
2.87
6.43
3.91
16.2
48.2
22.8
34.7
5.4
12.7
6.7
10.2
184
190
180
180
297
292
284
275
110
108
105
102
W21×50
W12× 72
W16× 57
W14× 61
413
405
394
383
284
292
277
277
4.6
10.7
5.7
8.7
12.5
33.6
16.6
24.9
16.4
4.93
10.7
6.51
7.31
1.95
2.80
20.5
60.1
44.7
6.9
10.8
12.6
173
168
171
273
264
261
101
97.6
96.8
W18×50
W10× 77
W12× 65b
379
366
358
267
258
264
5.8
9.2
11.8
15.6
39.9
31.7
11.5
3.53
4.72
9.68
6.18
8.13
4.17
2.91
1.93
5.91
15.4
21.3
16.6
28.0
38.4
53.7
20.2
5.3
6.6
5.4
8.0
10.5
10.8
6.5
159
158
154
152
152
148
142
258
248
245
235
233
230
222
95.4
92.0
90.7
87.1
86.4
85.3
82.3
W21×44
W16× 50
W18× 46
W14× 53
W12× 58
W10× 68
W16× 45
358
345
340
327
324
320
309
245
243
236
233
234
227
218
4.5
5.6
4.6
6.8
8.9
9.2
5.6
12.0
15.8
12.6
20.1
27.0
36.0
15.2
14.9
10.1
13.0
7.02
4.96
3.46
9.43
7.51
4.06
2.85
1.91
15.7
26.3
35.8
48.1
5.3
8.0
10.3
10.7
133
137
138
130
212
212
210
201
78.4
78.4
77.9
74.6
W18×40
W14× 48
W12× 53
W10× 60
294
294
292
280
205
211
212
200
4.5
6.8
8.8
9.1
12.1
19.2
25.6
32.6
11.7
6.70
4.77
3.38
5.54
3.06
1.30
3.91
1.89
19.3
30.8
64.0
24.7
43.9
6.5
8.2
8.8
7.9
10.7
126
126
118
122
117
197
195
190
188
180
72.9
72.4
70.2
69.6
66.6
W16×40
W12× 50
W8× 67
W14× 43
W10× 54
273
272
263
261
250
194
194
181
188
180
5.6
6.9
7.5
6.7
9.1
14.7
21.7
41.9
18.2
30.2
8.67
5.25
2.38
6.32
3.30
6.95
3.01
5.23
4.41
1.88
1.27
2.92
1.96
14.8
28.5
18.3
20.0
40.7
56.0
26.5
35.1
5.1
8.1
6.3
6.5
10.6
8.8
8.0
8.4
112
113
110
106
106
101
101
95.7
180
175
173
166
163
161
155
148
66.5
64.7
64.0
61.5
60.4
59.8
57.5
54.9
W18×35
W12× 45
W16× 36
W14× 38
W10× 49
W8× 58
W12× 40
W10× 45
249
243
240
231
227
224
216
206
173
174
170
164
164
156
156
147
4.3
6.9
5.4
5.5
9.0
7.4
6.8
7.1
11.5
20.3
14.1
14.9
28.3
36.8
19.3
24.1
10.7
5.07
8.08
7.07
3.25
2.32
4.82
3.45
Shape
φbMp
bIndicates noncompact shape; F = 50 ksi.
y
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
4 - 20
BEAM AND GIRDER DESIGN
LOAD FACTOR DESIGN SELECTION TABLE
For shapes used as beams
φb = 0.90
Zx
Fy = 36 ksi
Fy = 50 ksi
BF
Lr
Lp
φbMr
φbMp
Zx
Kips
Ft
Ft
Kip-ft Kip-ft
in.3
φbMr
Lp
Lr
BF
Kip-ft Kip-ft
Ft
Ft
Kips
4.18
19.0
6.4
94.8
147
54.6
W14×34
205
146
5.4
14.4
6.58
5.70
3.47
1.26
14.3
20.6
46.7
4.9
6.4
8.7
92.0
88.9
84.4
146
138
132
54.0
51.2
49.0
W16×31
W12× 35
W8×48
203
192
184
142
137
130
4.1
5.4
7.4
11.0
15.2
31.1
8.85
5.67
2.27
3.92
1.93
17.9
31.2
6.2
8.3
81.9
82.1
128
126
47.3
46.8
W14×30
W10× 39
177
176
126
126
5.3
7.0
13.7
21.8
6.06
3.32
5.15
3.22
13.3
19.1
4.7
6.3
74.9
75.3
119
116
44.2
43.1
W16×26
W12× 30
166
162
115
116
4.0
5.4
10.4
14.4
7.88
5.10
4.44
1.25
1.89
13.4
39.1
27.4
4.5
8.5
8.1
68.8
69.2
68.3
109
107
105
40.2
39.8
38.8
W14×26
W8×40
W10× 33
151
149
146
106
107
105
3.8
7.2
6.9
10.3
26.4
19.7
6.96
2.22
3.15
2.99
2.44
1.23
18.1
20.3
35.1
6.3
5.7
8.5
65.1
63.2
60.8
100
98.8
93.7
37.2
36.6
34.7
W12×26
W10× 30
W8×35
140
137
130
100
97.2
93.6
5.3
4.8
7.2
13.8
14.5
24.1
4.64
4.13
2.16
4.06
2.34
1.21
12.5
18.5
32.0
4.3
5.7
8.4
56.6
54.4
53.6
89.6
84.5
82.1
33.2
31.3
30.4
W14×22
W10× 26
W8×31
125
117
114
87.0
83.7
82.5
3.7
4.8
7.1
9.7
13.5
22.3
6.26
3.85
2.07
3.88
1.27
11.1
27.3
3.5
6.8
49.5
47.4
79.1
73.4
29.3
27.2
W12×22
W8×28
110
102
76.2
72.9
3.0
5.7
8.4
18.9
6.24
2.22
2.19
16.9
5.5
45.2
70.2
26.0
W10×22
97.5
69.6
4.7
12.7
3.50
3.61
1.24
10.4
24.4
3.4
6.7
41.5
40.8
66.7
62.6
24.7
23.2
W12×19
W8×24
92.6
87.0
63.9
62.7
2.9
5.7
7.9
17.2
5.70
2.11
2.60
1.46
12.0
18.6
3.6
5.3
36.7
35.5
58.3
55.1
21.6
20.4
W10×19
W8×21
81.0
76.5
56.4
54.6
3.1
4.5
8.9
13.3
4.26
2.47
3.30
0.741
2.46
9.6
31.3
11.2
3.2
6.3
3.5
33.3
32.6
31.6
54.3
51.0
50.5
20.1
18.9
18.7
W12×16
W6×25
W10× 17
75.4
70.9
70.1
51.3
50.1
48.6
2.7
5.4
3.0
7.4
21.0
8.4
5.12
1.33
3.97
2.97
1.40
2.34
0.728
9.2
16.7
10.3
25.6
3.1
5.1
3.4
6.3
29.1
29.6
26.9
26.1
47.0
45.9
43.2
40.2
17.4
17.0
16.0
14.9
W12×14
W8×18
W10× 15
W6×20
65.3
63.8
60.0
55.9
44.7
45.6
41.4
40.2
2.7
4.3
2.9
5.3
7.2
12.3
7.9
17.7
4.56
2.30
3.69
1.27
3.32
1.53
6.9
12.6
2.3
3.7
23.6
23.0
38.6
36.7
14.3
13.6
M12×11.8
W8×15
53.7
51.0
36.3
35.4
2.0
3.1
5.4
9.2
5.10
2.56
Shape
φbMp
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
LOAD FACTOR DESIGN SELECTION TABLE FOR SHAPES USED AS BEAMS
4 - 21
LOAD FACTOR DESIGN SELECTION TABLE
For shapes used as beams
φb = 0.90
Fy = 36 ksi
Zx
Fy = 50 ksi
BF
Lr
Lp
φbMr
φbMp
Zx
Kips
Ft
Ft
Kip-ft Kip-ft
in.3
3.10
2.03
0.817
0.458
1.44
0.417
0.693
0.444
6.8
9.5
18.3
30.3
11.5
31.1
20.8
26.3
2.3
3.3
4.0
5.3
3.5
5.0
6.7
5.3
21.6
21.3
19.9
19.9
19.3
18.8
19.0
16.6
35.4
34.0
31.6
31.3
30.8
29.7
28.8
25.9
13.1
12.6
11.7
11.6
11.4
11.0
10.8
9.59
M12×10.8
W10× 12b
W6× 16
W5× 19
W8× 13
M5× 18.9
W6×15b,c
W5× 16
49.2
47.0
43.9
43.5
42.8
41.3
38.6
36.0
2.32
1.30
0.775
6.2
10.2
14.4
2.1
3.5
3.8
15.2
15.2
14.3
24.9
23.9
22.4
9.21
8.87
8.30
M10×9
W8× 10b
W6× 12
2.13
0.295
0.724
6.1
25.5
12.0
2.1
4.2
3.8
13.6
10.6
10.8
22.1
17.0
16.8
8.20
6.28
6.23
1.50
5.5
1.8
14.6
5.40
9.01
φbMr
Lp
Lr
BF
Kip-ft Kip-ft
Ft
Ft
Kips
33.3
32.7
30.6
30.6
29.7
28.9
29.2
25.5
2.0
2.9
3.4
4.5
3.0
4.2
6.8
4.5
5.3
7.4
12.5
20.1
8.5
20.5
15.0
17.6
4.74
3.13
1.46
0.830
2.35
0.758
1.16
0.795
34.5
33.0
31.1
23.5
23.4
21.9
1.8
3.1
3.2
4.9
7.8
10.2
3.59
2.03
1.33
M10×8
W4× 13
W6× 9
30.8
23.6
23.4
21.0
16.4
16.7
1.8
3.5
3.2
4.8
16.9
8.9
3.26
0.538
1.17
M8×6.5
20.2
13.9
1.6
4.3
2.35
Shape
φbMp
bIndicates noncompact shape; F = 50 ksi
y
cIndicates noncompact shape; F = 36 ksi
y
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
4 - 22
BEAM AND GIRDER DESIGN
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
MOMENT OF INERTIA SELECTION TABLES FOR W AND M SHAPES
4 - 23
MOMENT OF INERTIA SELECTION TABLES FOR W AND M SHAPES
These two tables for moment of inertia (Ix and Iy) are provided to facilitate the selection
of beams and columns on the basis of their stiffness properties with respect to the X-X
axis or Y-Y axis, as applicable, where
Ix = moment of inertia, X-X axis, in.4
Iy = moment of inertia, Y-Y axis, in.4
In each table the shapes are listed in groups by descending order of moment of inertia
for all W and M shapes. The boldface type identifies the shapes that are the lightest in
weight in each group.
Enter the column headed Ix (or Iy) and find a value of Ix (or Iy) equal to or greater than
the moment of inertia required. The shape opposite this value, and all shapes above it,
have sufficient stiffness. Note that the member selected must also be checked for
compliance with specification provisions governing its specific application.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
4 - 24
Ix
Shape
BEAM AND GIRDER DESIGN
MOMENT OF INERTIA SELECTION TABLE
For W and M shapes
Ix
Shape
In.4
W36×848*
67400
W36×798*
62600
W40×593*
W36× 650*
50400
48900
W40×503*
W36× 527*
41700
38300
W40×466*
36300
W40×431
34800
W44×335
W36× 439*
W40× 392*
W40× 372
W36× 393*
31100
31000
29900
29600
27500
W44×290
W30× 477*
W27× 539*
W40× 321
W36× 359*
W40× 331
27100
26100
25500
25100
24800
24700
W44×262
W40× 297
W36× 328*
W40× 277
W33× 354*
24200
23200
22500
21900
21900
W44×230
W30× 391*
W40× 278
W27× 448*
W36× 300
W33× 318*
W40× 249
W40× 264
W24× 492*
W36× 280
W33× 291*
W40× 235
W36× 260
W30× 326*
W36× 256
20800
20700
20500
20400
20300
19500
19500
19400
19100
18900
17700
17400
17300
16800
16800
Ix
W40×215
W27× 368*
W36×245
W14× 808*
W33× 263*
16700
16100
16100
16000
15800
W40×211
W24× 408*
W36×230
W36×232
15500
15100
15000
15000
W40×199
W30× 292*
W14× 730*
W33×241
14900
14900
14300
14200
W40×183
W36×210
W27× 307*
W30×261
W33×221
W14× 665*
13300
13200
13100
13100
12800
12400
W40×174
W36×194
W24× 335*
W30×235
12200
12100
11900
11700
W40×167
W33×201
W36×182
W14× 605*
W27×258
W36×170
W30× 211
11600
11500
11300
10800
10800
10500
10300
W40×149
W36×160
W27×235
W24× 279*
W14× 550*
W33×169
W30×191
W36×150
W27×217
W24× 250*
W14× 500*
W30×173
W33×152
W27×194
9780
9750
9660
9600
9430
9290
9170
9040
8870
8490
8210
8200
8160
7820
Ix
Shape
In.4
Shape
In.4
W36×135
W24× 229
W33× 141
W14×455*
W27× 178
W18× 311*
W24× 207
7800
7650
7450
7190
6990
6960
6820
W33×130
W30× 148
W14×426*
W27× 161
W24× 192
W18×283*
W14×398*
6710
6680
6600
6280
6260
6160
6000
W33×118
W30× 132
W24× 176
W27× 146
W18×258*
W14×370*
W30× 124
W21× 201
W24× 162
5900
5770
5680
5630
5510
5440
5360
5310
5170
W30×116
W18×234*
W14×342*
W27× 129
W21× 182
W24× 146
4930
4900
4900
4760
4730
4580
W30×108
W18× 211*
W14× 311*
W21× 166
W27× 114
W12×336*
W24× 131
4470
4330
4330
4280
4090
4060
4020
*Group 4 or 5 shape. See Notes in Table 1-2 (Part 1).
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
Ix
In.4
W30×99
W18× 192
W14× 283*
W21× 147
3990
3870
3840
3630
W30×90
W27× 102
W12× 305*
W24× 117
W18× 175
W14× 257*
W27× 94
W21× 132
W12× 279*
W24× 104
W18× 158
W14× 233*
W24× 103
W21× 122
3620
3620
3550
3540
3450
3400
3270
3220
3110
3100
3060
3010
3000
2960
W27×84
W18× 143
W12× 252*
W24× 94
W21× 111
W14× 211
W18× 130
W12× 230*
W21× 101
W14× 193
2850
2750
2720
2700
2670
2660
2460
2420
2420
2400
W24×84
W18× 119
W14× 176
W12× 210*
2370
2190
2140
2140
W24×76
W21× 93
W18× 106
W14× 159
W12× 190
2100
2070
1910
1900
1890
MOMENT OF INERTIA SELECTION TABLE FOR W AND M SHAPES
4 - 25
MOMENT OF INERTIA SELECTION TABLE
For W and M shapes
Shape
Ix
Shape
In.4
W24×68
W21× 83
W18× 97
W14× 145
W12× 170
W21× 73
1830
1830
1750
1710
1650
1600
W24×62
W14× 132
W18× 86
W16× 100
W21× 68
W12× 152
W14× 120
1550
1530
1530
1490
1480
1430
1380
W24×55
W18× 76
W21× 62
W16× 89
W14× 109
W12× 136
W18× 71
W21× 57
W14× 99
W16× 77
W12× 120
W18× 65
W14× 90
W18× 60
1350
1330
1330
1300
1240
1240
1170
1170
1110
1110
1070
1070
999
984
W21×50
W16× 67
W12× 106
W18× 55
W14× 62
984
954
933
890
882
Ix
Shape
In.4
Ix
Shape
In.4
W21×44
W12× 96
W18× 50
W14× 74
W16× 57
W12× 87
W14× 68
W10× 112
W18× 46
W12× 79
W16× 50
W14× 61
W10× 100
843
833
800
796
758
740
723
716
712
662
659
640
623
W16×26
W14× 30
W12× 35
W8× 67
W10× 49
W10× 45
301
291
285
272
272
248
W14×26
W12× 30
W8× 58
W10× 39
245
238
228
209
W12×26
204
W18×40
W12× 72
W16× 45
W14× 53
W10× 88
W12× 65
612
597
586
541
534
533
W14×22
W8× 48
W10× 30
W10× 33
199
184
170
170
W16×40
518
W12×22
W8× 40
W10× 26
156
146
144
W18×35
W14× 48
W12× 58
W10× 77
W16× 36
W14× 43
W12× 53
W12× 50
W10× 68
W14× 38
510
485
475
455
448
428
425
394
394
385
W12×19
W8× 35
W10× 22
W8× 31
130
127
118
110
W12×16
W8× 28
W10× 19
103
98.0
96.3
W16×31
W12× 45
W10× 60
W14× 34
W12× 40
W10× 54
375
350
341
340
310
303
W12×14
W8× 24
W10× 17
W8× 21
88.6
82.8
81.9
75.3
M12×11.8
W10× 15
71.7
68.9
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
Ix
Ix
In.4
M12×10.8
W8× 18
W10×12
W6× 25
W8× 15
W6× 20
W8× 13
65.8
61.9
53.8
53.4
48.0
41.4
39.6
M10×9
38.5
M10×8
W6× 16
W8× 10
W6× 15
W5× 19
M5× 18.9
W6× 12
W5× 16
34.3
32.1
30.8
29.1
26.2
24.1
22.1
21.3
M8×6.5
W6×9
W4× 13
18.1
16.4
11.3
4 - 26
Iy
Shape
BEAM AND GIRDER DESIGN
MOMENT OF INERTIA SELECTION TABLE
For W and M shapes
Iy
Shape
In.4
W14×808*
5510
W14×730*
W36× 848*
W36× 798*
4720
4550
4200
W14×665*
4170
W14×605*
3680
W14×550*
W36× 650*
W14×283*
W40×372
W36× 328*
W24× 408*
W27× 368*
W36×300
1440
1420
1420
1320
1310
1300
W14×257*
W33× 318*
W30× 326*
W36×280
W44×335
W12× 336*
W40×321
W33× 291*
1290
1290
1240
1200
1200
1190
1190
1160
3250
3230
W14×500*
2880
W14×455*
W40× 593*
W36× 527*
2560
2520
2490
W14×426*
2360
W14×398*
W27× 539*
W40× 503*
2170
2110
2050
W14×370*
W36× 439*
W30× 477*
1990
1990
1970
W14×342*
W36× 393*
W40× 431
W27× 448*
W24× 492*
1810
1750
1690
1670
1670
W14×311*
W36× 359*
W30× 391*
W33× 354*
Iy
1610
1570
1550
1460
W14×233*
W30× 292*
W40×297
W36×260
W44×290
W27× 307*
W12× 305*
W40×277
W33× 263*
W24× 335*
1150
1100
1090
1090
1050
1050
1050
1040
1030
1030
W14×211
W40× 466*
W36×245
W30×261
W36×230
W12× 279*
W33×241
1030
1010
1010
959
940
937
932
W14×193
W44×262
W40×249
W27×258
W30×235
W33×221
931
927
926
859
855
840
Iy
Shape
In.4
Shape
In.4
W14×176
W12×252*
W24×279*
W40×392*
W40× 215
W44× 230
W18× 311*
W27× 235
W30× 211
W33× 201
838
828
823
803
796
796
795
768
757
749
W14×159
W12×230*
W24×250*
W18×283*
W27× 217
W40× 199
748
742
724
704
704
695
W14×145
W30× 191
W12×210*
W24× 229
W40× 331
W18×258*
W27× 194
W30× 173
W12× 190
W24× 207
W18×234*
W27× 178
677
673
664
651
646
628
618
598
589
578
558
555
W14×132
W21× 201
W40× 174
W24× 192
W36× 256
W40× 278
W12× 170
W27× 161
548
542
541
530
528
521
517
497
*Group 4 or 5 shape. See Notes in Table 1-2 (Part 1).
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
Iy
In.4
W14×120
W40× 264
W18× 211*
W21× 182
W24× 176
W36× 232
W12× 152
495
493
493
483
479
468
454
W14×109
W40× 235
W24× 162
W27× 146
W18× 192
W21× 166
W36× 210
447
444
443
443
440
435
411
W14×99
W12× 136
W18× 175
W24× 146
W40× 211
W21× 147
W36× 194
402
398
391
391
390
376
375
W14×90
W36× 182
W18× 158
W12× 120
W24× 131
W40× 183
W21× 132
W36× 170
W18× 143
W33× 169
W21× 122
W12× 106
W24× 117
W36× 160
W40× 167
W18× 130
W21× 111
W33× 152
W36× 150
W12× 96
W24× 104
W18× 119
W21× 101
W33× 141
362
347
347
345
340
336
333
320
311
310
305
301
297
295
283
278
274
273
270
270
259
253
248
246
MOMENT OF INERTIA SELECTION TABLE FOR W AND M SHAPES
4 - 27
MOMENT OF INERTIA SELECTION TABLE
For W and M shapes
Shape
Iy
Shape
In.4
W12×87
W10× 112
W40× 149
W30× 148
W36× 135
W18× 106
W33× 130
241
236
229
227
225
220
218
W12×79
W10× 100
W18× 97
W30× 132
216
207
201
196
W12×72
W33× 118
W16× 100
W27× 129
W30× 124
W10× 88
W18× 86
195
187
186
184
181
179
175
W12×65
W30× 116
W16× 89
W27× 114
W10× 77
W18× 76
W14× 82
W30× 108
W27× 102
W16× 77
W10× 68
W14× 74
W30× 99
W27× 94
W14× 68
W24× 103
W16× 67
174
164
163
159
154
152
148
146
139
138
134
134
128
124
121
119
119
Iy
Shape
In.4
W10×60
W30× 90
W24× 94
116
115
109
W12×58
W14× 61
W27× 84
107
107
106
W10×54
103
W12×53
W24× 84
95.8
94.4
W10×49
W21× 93
W8× 67
W24× 76
W21× 83
W8× 58
W21× 73
W24× 68
W21× 68
93.4
92.9
88.6
82.5
81.4
75.1
70.6
70.4
64.7
W8×48
W18× 71
W14× 53
W21× 62
W12× 50
W18× 65
60.9
60.3
57.7
57.5
56.3
54.8
W10×45
W14× 48
W18× 60
53.4
51.4
50.1
W12×45
50.0
W8×40
W14× 43
49.1
45.2
Iy
Shape
In.4
W10×39
W18× 55
W12× 40
W16× 57
45.0
44.9
44.1
43.1
W8×35
W18× 50
W16× 50
42.6
40.1
37.2
W8×31
W10× 33
W24× 62
W16× 45
W21× 57
W24× 55
W16× 40
W14× 38
W21× 50
W12× 35
W16× 36
W14× 34
W18× 46
37.1
36.6
34.5
32.8
30.6
29.1
28.9
26.7
24.9
24.5
24.5
23.3
22.5
W8×28
W21× 44
W12× 30
W14× 30
W18× 40
21.7
20.7
20.3
19.6
19.1
W8×24
W12× 26
W6× 25
W10× 30
W18× 35
W10× 26
18.3
17.3
17.1
16.7
15.3
14.1
W6×20
W16× 31
W10× 22
W8× 21
W16× 26
13.3
12.4
11.4
9.77
9.59
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
Iy
Iy
In.4
W6×15
W5× 19
W14×26
W8× 18
M5× 18.9
W5× 16
W14×22
W12×22
W6× 16
W10×19
9.32
9.13
8.91
7.97
7.86
7.51
7.00
4.66
4.43
4.29
W4×13
W12×19
W10×17
W8× 15
3.86
3.76
3.56
3.41
W6×12
W10×15
W12×16
W8× 13
W12×14
2.99
2.89
2.82
2.73
2.36
W6×9
W10×12
W8× 10
M12× 11.8
M12× 10.8
2.19
2.18
2.09
1.09
0.995
M10×9
0.673
M10×8
0.597
M8×6.5
0.371
4 - 28
BEAM AND GIRDER DESIGN
FACTORED UNIFORM LOAD TABLES
General Notes
The Tables of Factored Uniform Loads for W and S shapes and channels (C and MC)
used as simple laterally supported beams give the maximum uniformly distributed
factored loads in kips. The tables are based on the flexural design strengths specified in
Section F1 of the LRFD Specification. Separate tables are presented for Fy = 36 ksi and
Fy = 50 ksi. The tabulated loads include the weight of the beam, which should be deducted
in the calculation to determine the net load that the beam will support.
The tables are also applicable to laterally supported simple beams for concentrated
loading conditions. A method to determine the beam load capacity for several cases
is shown in this discussion.
It is assumed, in all cases, that the loads are applied normal to the X-X axis
(shown in the Tables of Properties of Shapes in Part 1 of this LRFD Manual) and
that the beam deflects vertically in the plane of bending. If the conditions of loading
involve forces outside this plane, design strengths must be determined from the
general theory of flexure and torsion.
Lateral Support of Beams
The flexural design strength of a beam is dependent upon lateral support of its compression flange in addition to its section properties. In these tables the notation Lp is used to
denote the maximum unbraced length of the compression flange, in feet, for the uniform
moment case (Cb = 1.0) and for which the design strengths for compact symmetrical
shapes are calculated with a flexural design strength of:
φbMn = φbMp = φbZxFy / 12
Noncompact shapes are calculated with a flexural design strength of:
λ − λp
φbMn′ = φbMp − φb(Mp − Mr)
λr − λp
as permitted in the LRFD Specification Appendix F1. The associated maximum unbraced
length for φbMn′ is tabulated as Lp. The notation Lr is the unbraced length of the
compression flange for which the flexural design strength for rolled shapes is:
φbMr = φbSx(Fy − 10) / 12
These tables are not applicable for beams with unbraced lengths greater than Lr. For such
cases, the beam charts should be used.
Flexural Design Strength and Tabulated Factored Uniform Loads
For symmetrical rolled shapes designated W and S the flexural design strengths and
resultant loads are based on the assumption that the compression flanges of the beams
are laterally supported at intervals not greater than Lp.
The Uniform Load Constant φbWc is obtained from the moment and stress relationship
of a simply supported, uniformly loaded beam. The relationship results in the formula:
φbWc = φb(2ZxFy / 3), kip-ft for compact shapes
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
FACTORED UNIFORM LOAD TABLES
4 - 29
The following expression may be used for calculating the tabulated uniformly distributed
factored load Wu on a simply supported beam or girder:
Wu = φbWc / L, kips
For compact shapes, the tabulated constant is based on the yield stress Fy = 36 ksi or
50 ksi and the plastic section modulus Zx. (See Section F1.1 of the LRFD Specification.)
For noncompact sections, the tabulated constant is based on the nominal resisting moment
as determined by Equation A-F1-3. (See LRFD Specification Appendix F1.)
Shear
For relatively short spans, the design strengths for beams and channels may be limited
by the shear strength of the web instead of the bending strength. This limit is indicated
in the tables by solid horizontal lines. Loads shown above these lines will produce the
design shear strength in the beam web.
End and Interior Bearing
For a discussion of end and interior bearing and use of the tabulated values φR1 through
φr R6 and φR, see Part 9 in Volume II of this LRFD Manual.
Vertical Deflection
For rolled shapes designated W, M, S, C, and MC, the maximum vertical deflection may
be calculated using the formula:
∆ = ML2 / (C1Ix)
where
M = maximum service load moment, kip-ft
L = span length, ft
Ix = moment of inertia, in.4
C1 = loading constant (see Figure 4-2)
∆ = maximum vertical deflection, in.
W
P
C1 = 161
P
C1 = 201
P
P
P
C1 = 158
C1= 170
Fig. 4-2
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
P
4 - 30
BEAM AND GIRDER DESIGN
Table 4-2.
Recommended Span/Depth Ratios
Service Load Ratios
Maximum Span/Depth Ratios
Dead / Total
Dead / Live
Fy = 36 ksi
Fy = 50 ksi
0.2
0.3
0.4
0.5
0.6
0.25
0.43
0.67
1.00
1.50
20.0
22.2
25.0
29.0
—
14.0
16.0
18.0
21.0
26.0
Deflection can be controlled by limiting the span-depth ratio of a simply supported,
uniformly loaded beam as shown in Table 4-2. A live-load deflection limit of L / 360 is
assumed; i.e.,
∆LL ≤
Span Length
360
For large span/depth ratios, vibration may also be a consideration.
Use of Tables
Maximum factored uniform loads are tabulated for steels of Fy = 36 ksi and Fy = 50 ksi.
They are based on the design flexural strength determined from the LRFD Specification:
Equation F1-1 (in Section F1.1) for compact members, and Equation A-F1-3 (in Appendix F1) for noncompact members. The beams must be braced adequately and have an
axis of symmetry in the plane of loading. Factored loads may be read directly from the
tables when the distance between points of lateral support of the compression flange Lb
does not exceed Lp (tabulated earlier in the Load Factor Design Selection Table for
beams).
Loads above the heavy horizontal lines in the tables are governed by the design shear
strength, determined from Section F2 of the LRFD Specification.
EXAMPLE 4-4
Given:
A W16×45 floor beam of Fy = 50 ksi steel spans 20 feet. Determine the
maximum uniform load, end reaction, and total service load deflection.
The live load equals the dead load.
Solution:
Based on Section A4 of the LRFD Specification, the governing load
combination for a floor beam is 1.2 (dead load) + 1.6 (live load). As
the two loads are equal,
factored load = 1.4 (total load)
Enter the Factored Uniform Loads Table for Fy = 50 ksi and note that:
Maximum factored uniform load = Wu
= 124 kips, or 124/20 = 6.2 kips/ft
Factored end reaction = Wu / 2 = 124 / 2 = 61.8 kips
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
FACTORED UNIFORM LOAD TABLES
4 - 31
Service load moment =
124(20)
Wu L
=
8(1.4)
8(LF)
= 221 kip-ft
Deflection:
∆=
ML2 221(20)2
=
= 0.94 in.
C1Ix 161(586)
Live load deflection = 0.5 × 0.94 in. = 0.47 in. < (L / 360 = 20 ×
12 / 360 = 0.66 in.) o.k.
EXAMPLE 4-5
Given:
A W10×45 beam of Fy = 50 ksi steel spans 6 feet. Determine the
maximum load and corresponding end reaction.
Solution:
Enter the Factored Uniform Loads Table for Fy = 50 ksi and note that:
Maximum factored uniform load = Wu
= 191 kips, or 191/6 = 31.8 kips/ft
As Wu appears above the horizontal line, it is limited by shear in the
web.
Factored end reaction = Wu / 2 = 191 / 2 = 96 kips
EXAMPLE 4-6
Given:
Using Fy = 50 ksi steel, select an 18-in. deep beam to span 30 feet and
support two equal concentrated loads at the one-third and two-thirds
points of the span. The service load intensities are 10 kips dead load
and 24 kips live load. The beam is supported laterally at the points of
load application and the ends. Determine the beam size and service
live load deflection.
Solution:
Refer to the Table of Concentrated Load Equivalents on page 4-189
and note that:
Equivalent uniform load = 2.67Pu
1. Required factored uniform load:
Wu = 2.67Pu = 2.67[1.2(10) + 1.6(24)]
= 2.67(50.4)
= 135 kips
2. Enter the Factored Uniform Loads Table for Fy = 50 ksi and Wu ≥
135 kips
For W18×71: Wu = 145 kips > 135 kips; however, Lb = 10 ft > Lp =
6.0 ft.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
4 - 32
BEAM AND GIRDER DESIGN
For W18×76: Wu = 163 kips > 135 kips; however, Lb = 10 ft > Lp =
9.2 ft.
3. Since Lp < Lb < Lr, use the Load Factor Design Selection Table.
φbMn = Cb[φbMp − BF(Lb − Lp)]
For the central third of the span (uniform moment), Cb = 1.0.
Required flexural strength: Mu = Pu (L / 3) = 50.4(30 / 3) = 504 kip-ft
4. Try W18×71:
φbMn = 1.0[544 − 13.8(10 − 6)]
= 489 kip-ft < 504 kip-ft req’d. n.g.
5. Try W18×76:
φbMn = 1.0[611 − 11.1(10 − 9.2)]
= 602 kip-ft > 504 kip-ft req’d. o.k.
Use W18×76
6. Determine service live load deflection:
MLL = (PLL / Pu )Mu = (24 / 50.4)504 = 240 kip-ft
Maximum ∆ (at midspan) =
240(30)2
MLLL2
=
= 1.03 in.
C1Ix
158(1,330)
EXAMPLE 4-7
Given:
A W24×55 of 50 ksi steel spans 20 feet and is braced at 4-ft intervals.
Determine the maximum factored load and end reaction.
Solution:
1. Enter the Factored Uniform Load Table for Fy = 50 ksi and note that:
Maximum factored uniform load = Wu = 201 kips, or 201 / 20 =
10.1 kips/ft
This is true for Lb ≤ Lp : 4.0 ft < 4.7 ft o.k.
2. End reaction = R = Wu / 2 = 201 / 2 = 101 kips
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
FACTORED UNIFORM LOAD TABLES
4 - 33
Reference Notes on Tables
1. Maximum factored uniform loads, in kips, are given for beams with adequate lateral
support; i.e., Lb ≤ Lp for Cb = 1.0, Lb ≤ Lm for Cb > 1.0.
2. Loads below the heavy horizontal line are limited by design flexural strength, while
loads above the line are limited by design shear strength.
3. Factored loads are given for span lengths up to the smaller of L / d = 30 or 72 ft.
4. The end bearing values at the bottom of the tables are for use in solving LRFD
Specification Equations K1-3, K1-5a, and K1-5b. They are defined as follows:
φR1 = φ(2.5kFy tw)
φR2 = φ(Fy tw)
kips
kips/in.
Equation K1-3 becomes φRn = φR1 + N(φR2)
Fty tf
φrR3 = φr 68t2w √
w
kips
1.5
3 tw
φrR4 = φr 68t2w
d tf
√Ft t
y f
w
kips/in.
Equation K1-5a becomes φrRn = φrR3 + N(φrR4)
1.5
tw
φrR5 = φr 68t2w 1 − 0.2
tf
1.5
4 tw
φrR6 = φr 68t2w
d tf
Fty tf
√
w
√Fty t
f
w
kips
kips/in.
Equation K1-5b becomes φrRn = φrR5 + N(φrR6)
where φ = 1.00, φr = 0.75, N = length of bearing (in.), and the other terms as defined
in the LRFD Specification, Section K1.
φR (N = 31⁄4) is defined as the design bearing strength for N = 31⁄4-in.
For N / d ≤ 0.2,
φR is the minimum of
φR1 + N(φR2)
φrR3 + N(φrR4)
For N / d > 0.2,
φR is the minimum of
φR1 + N(φR2)
φrR5 + N(φrR6)
For a complete explanation of end and interior bearing and use of the tabulated values,
see Part 9 in Volume II of this LRFD Manual.
5. The other terms at the bottom of the tables are:
Zx
= plastic section modulus for major axis bending, in.3
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
4 - 34
BEAM AND GIRDER DESIGN
φvVn = design shear strength, kips
φbWc = uniform load constant
= φb(2ZxFy / 3) kip-ft for compact shapes;
per Equation A-F1-3 (LRFD Specification Appendix F1) for noncompact
shapes
6. Tabulated maximum factored uniformly distributed load for the given beam and span
is the minimum of
φbWc
and 2φvVn
L
See also Note 2 above.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
FACTORED UNIFORM LOAD TABLES
Fy = 36 ksi
4 - 35
BEAMS
W Shapes
Maximum factored uniform loads in kips
for beams laterally supported
W 44
For beams laterally unsupported, see page 4-113
Designation
W 44
Span (ft)
Fy = 36 ksi
Wt./ft
335
290
262
230
20
21
22
23
24
25
1750
1670
1590
1520
1460
1400
1480
1460
1390
1330
1280
1230
1330
1310
1250
1190
1140
1100
1180
1130
1080
1030
990
950
26
27
28
29
30
31
1350
1300
1250
1210
1170
1130
1180
1140
1100
1060
1020
989
1060
1020
980
946
914
885
914
880
849
819
792
766
32
33
34
35
36
1090
1060
1030
1000
972
959
929
902
876
852
857
831
807
784
762
743
720
699
679
660
38
40
42
44
46
48
921
875
833
795
761
729
807
767
730
697
667
639
722
686
653
623
596
572
625
594
566
540
517
495
50
52
54
56
58
60
700
673
648
625
603
583
613
590
568
548
529
511
549
528
508
490
473
457
475
457
440
424
410
396
62
64
66
68
70
72
564
547
530
515
500
486
495
479
465
451
438
426
442
429
416
403
392
381
383
371
360
349
339
330
1270
27400
665
156
28.4
256
7.36
235
9.81
248
1100
23800
592
128
25.6
202
6.28
184
8.37
211
Properties and Reaction Values
Zx in.3
φbWc kip-ft
φvVn kips
φR1 kips
φR2 kips/in.
φr R3 kips
φr R4 kips/in.
φr R5 kips
φr R6 kips/in.
φR (N = 31⁄4) kips
1620
35000
873
235
36.7
419
12.5
383
16.7
355
1420
30700
738
186
31.3
312
8.77
287
11.7
288
Load above heavy line is limited by design shear strength.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
4 - 36
BEAM AND GIRDER DESIGN
W 40
BEAMS
W Shapes
Maximum factored uniform loads in kips
for beams laterally supported
Fy = 36 ksi
For beams laterally unsupported, see page 4-113
Designation
Wt./ft
W 40
431
372
321
297
277
249
199
174
977
937
965
965
908
858
813
772
985
945
904
867
832
800
893
852
815
781
750
721
735
702
671
644
618
594
896
864
834
806
780
756
770
743
717
693
671
650
694
670
647
625
605
586
572
552
533
515
498
483
818
794
771
750
730
711
733
712
691
672
654
637
630
612
594
578
562
547
568
551
536
521
507
493
468
454
441
429
417
406
718
684
653
625
599
575
675
643
614
587
563
540
605
576
550
526
504
484
520
495
473
452
433
416
469
446
426
408
391
375
386
368
351
336
322
309
590
568
548
529
511
495
552
532
513
495
479
463
519
500
482
466
450
435
465
448
432
417
403
390
400
385
371
359
347
335
361
347
335
323
312
302
297
286
276
266
257
249
479
465
451
438
426
449
435
422
410
399
422
409
397
386
375
378
367
356
346
336
325
315
306
297
289
293
284
276
268
260
241
234
227
221
215
1120
24200
574
190
27.0
237
6.93
219
9.23
259
963
20800
493
154
23.4
177
5.30
163
7.07
194
868
18700
489
143
23.4
165
6.12
150
8.16
185
715
15400
483
117
23.4
146
7.95
126
10.6
172
1830
1800
1560
1530
1440
1440
21
22
23
24
25
26
2010
1910
1830
1760
1680
1620
1720
1640
1570
1500
1440
1390
1460
1390
1330
1280
1230
1180
1370
1310
1250
1200
1150
1100
1280
1230
1170
1130
1080
1040
1150
1100
1050
1010
968
930
27
28
29
30
31
32
1560
1500
1450
1400
1360
1320
1340
1290
1240
1200
1160
1130
1140
1100
1060
1020
989
959
1060
1030
991
958
927
898
1000
964
931
900
871
844
33
34
35
36
37
38
1280
1240
1200
1170
1140
1110
1090
1060
1030
1000
975
949
929
902
876
852
829
807
871
845
821
798
776
756
40
42
44
46
48
50
1050
1000
957
916
878
842
902
859
820
784
752
721
767
730
697
667
639
613
52
54
56
58
60
62
810
780
752
726
702
679
694
668
644
622
601
582
64
66
68
70
72
658
638
619
602
585
564
547
530
515
501
Zx in.3
φbWc kip-ft
φvVn kips
φR1 kips
φR2 kips/in.
φr R3 kips
φr R4 kips/in.
φr R5 kips
φr R6 kips/in.
φR (N = 31⁄4) kips
1950
42100
1075
430
48.2
729
22.7
667
30.2
586
1670
36100
916
339
41.8
547
17.2
501
22.9
475
Span (ft)
2150
2110
Fy = 36 ksi
15
16
17
18
19
20
215
Properties and Reaction Values
1420
30700
779
264
36.0
407
12.9
373
17.3
381
1330
28700
720
256
33.5
353
11.2
323
15.0
365
1250
27000
640
224
29.9
290
8.40
268
11.2
318
Load above heavy line is limited by design shear strength.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
FACTORED UNIFORM LOAD TABLES
Fy = 36 ksi
4 - 37
BEAMS
W Shapes
Maximum factored uniform loads in kips
for beams laterally supported
W 40
For beams laterally unsupported, see page 4-113
Span (ft)
Fy = 36 ksi
Designation
Wt./ft
W 40
331
278
264
235
211
167
149
985
937
975
934
879
830
936
921
860
806
759
716
1030
977
931
889
850
815
888
843
803
767
733
703
787
747
712
679
650
623
679
645
614
586
561
537
873
839
808
779
752
727
782
752
724
698
674
652
675
649
625
602
582
562
598
575
554
534
515
498
516
496
478
461
445
430
787
763
740
718
697
678
704
682
661
642
623
606
631
611
592
575
559
543
544
527
511
496
482
469
482
467
453
440
427
415
416
403
391
379
368
358
695
676
643
612
584
559
660
642
610
581
555
531
590
574
545
519
496
474
528
514
489
465
444
425
456
444
422
402
383
367
404
393
374
356
340
325
349
339
322
307
293
280
644
618
594
572
552
533
536
514
494
476
459
443
509
488
469
452
436
421
455
436
420
404
390
376
407
391
376
362
349
337
351
337
324
312
301
291
311
299
287
277
267
258
269
258
248
239
230
222
60
62
64
66
68
70
515
498
483
468
454
441
428
415
402
389
378
367
407
394
381
370
359
349
364
352
341
331
321
312
326
315
305
296
287
279
281
272
264
256
248
241
249
241
234
226
220
214
215
208
201
195
190
184
72
429
357
339
303
272
234
208
179
781
16900
493
154
23.4
177
5.30
163
7.07
194
692
14900
488
143
23.4
162
6.37
146
8.50
183
597
12900
468
128
22.7
139
7.24
121
9.65
163
13
14
15
16
17
18
1930
1930
1820
1720
1590
1510
1430
1490
1440
1360
1280
1210
1150
1090
19
20
21
22
23
24
1630
1540
1470
1400
1340
1290
1350
1290
1220
1170
1120
1070
1280
1220
1160
1110
1060
1020
1150
1090
1040
992
949
909
25
26
27
28
29
30
1240
1190
1140
1100
1070
1030
1030
989
952
918
886
857
976
939
904
872
842
814
31
32
33
34
35
36
996
965
936
908
883
858
829
803
779
756
734
714
37
38
40
42
44
46
835
813
772
735
702
671
48
50
52
54
56
58
183
Properties and Reaction Values
Zx in.3
φbWc kip-ft
φvVn kips
φR1 kips
φR2 kips/in.
φr R3 kips
φr R4 kips/in.
φr R5 kips
φr R6 kips/in.
φR (N = 31⁄4) kips
1430
30900
967
364
43.9
602
19.2
550
25.6
506
1190
25700
796
275
36.7
424
13.4
388
17.9
395
1130
24400
746
254
34.6
379
11.7
347
15.6
366
1010
21800
640
205
29.9
290
8.40
268
11.2
303
905
19500
574
177
27.0
236
6.95
218
9.27
259
Load above heavy line is limited by design shear strength.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
4 - 38
BEAM AND GIRDER DESIGN
W 36
BEAMS
W Shapes
Maximum factored uniform loads in kips
for beams laterally supported
Fy = 36 ksi
For beams laterally unsupported, see page 4-113
Designation
W 36
Span (ft)
Fy = 36 ksi
Wt./ft
300
280
260
245
230
1120
1090
1040
992
949
909
1060
1020
970
926
886
849
19
20
21
22
23
24
1350
1300
1240
1180
1130
1260
1200
1150
1100
1050
1180
1170
1110
1060
1010
972
25
26
27
28
29
30
1090
1050
1010
972
938
907
1010
972
936
903
871
842
933
897
864
833
804
778
873
839
808
779
752
727
815
783
754
727
702
679
31
32
33
34
35
36
878
851
825
800
778
756
815
790
766
743
722
702
753
729
707
686
667
648
704
682
661
642
623
606
657
637
617
599
582
566
37
38
39
40
41
42
736
716
698
680
664
648
683
665
648
632
616
602
630
614
598
583
569
555
590
574
559
545
532
519
551
536
522
509
497
485
43
44
46
48
50
52
633
619
592
567
544
523
588
574
549
527
505
486
543
530
507
486
467
449
507
496
474
455
436
420
474
463
443
424
407
392
54
56
58
60
62
64
504
486
469
454
439
425
468
451
436
421
408
395
432
417
402
389
376
365
404
390
376
364
352
341
377
364
351
339
329
318
66
68
70
72
412
400
389
378
383
372
361
351
353
343
333
324
331
321
312
303
309
300
291
283
1010
21800
561
180
28.8
254
9.65
231
12.9
274
943
20400
530
162
27.4
228
8.91
206
11.9
251
Properties and Reaction Values
Zx in.3
φbWc kip-ft
φvVn kips
φR1 kips
φR2 kips/in.
φr R3 kips
φr R4 kips/in.
φr R5 kips
φr R6 kips/in.
φR (N = 31⁄4) kips
1260
27200
675
239
34.0
364
12.6
334
16.7
350
1170
25300
628
214
31.9
319
11.1
292
14.8
318
1080
23300
592
194
30.2
283
10.4
258
13.9
292
Load above heavy line is limited by design shear strength.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
FACTORED UNIFORM LOAD TABLES
Fy = 36 ksi
4 - 39
BEAMS
W Shapes
Maximum factored uniform loads in kips
for beams laterally supported
W 36
For beams laterally unsupported, see page 4-113
Designation
Wt./ft
W 36
256
19
20
21
22
23
24
194
182
170
160
150
135
1260
1190
1120
1180
1120
1060
1000
1090
1040
975
920
1020
969
912
862
956
902
849
802
910
899
842
793
749
871
837
784
738
697
1180
1120
1070
1020
977
936
1060
1010
963
919
879
842
947
900
857
818
782
750
872
828
789
753
720
690
816
775
739
705
674
646
759
721
687
656
627
601
709
674
642
613
586
562
661
627
598
570
546
523
579
550
524
500
478
458
25
26
27
28
29
30
899
864
832
802
775
749
809
778
749
722
697
674
720
692
666
643
620
600
663
637
614
592
571
552
620
596
574
554
535
517
577
555
534
515
498
481
539
518
499
481
465
449
502
483
465
448
433
418
440
423
407
393
379
366
31
32
33
34
35
36
725
702
681
661
642
624
652
632
613
595
578
562
580
562
545
529
514
500
534
518
502
487
473
460
500
485
470
456
443
431
465
451
437
424
412
401
435
421
408
396
385
374
405
392
380
369
359
349
355
344
333
323
314
305
38
40
42
44
46
48
591
562
535
511
488
468
532
505
481
459
440
421
473
450
428
409
391
375
436
414
394
377
360
345
408
388
369
352
337
323
380
361
344
328
314
301
355
337
321
306
293
281
330
314
299
285
273
261
289
275
262
250
239
229
50
52
54
56
58
60
449
432
416
401
387
374
404
389
374
361
349
337
360
346
333
321
310
300
331
319
307
296
286
276
310
298
287
277
267
258
289
277
267
258
249
240
270
259
250
241
232
225
251
241
232
224
216
209
220
211
204
196
190
183
62
64
66
68
70
72
362
351
340
330
321
312
326
316
306
297
289
281
290
281
273
265
257
250
267
259
251
244
237
230
250
242
235
228
222
215
233
225
219
212
206
200
217
211
204
198
193
187
202
196
190
185
179
174
177
172
167
162
157
153
Zx in.3
φbWc kip-ft
φvVn kips
φR1 kips
φR2 kips/in.
φr R3 kips
φr R4 kips/in.
φr R5 kips
φr R6 kips/in.
φR (N = 31⁄4) kips
1040
22500
699
227
34.6
379
12.5
347
16.7
339
936
20200
628
196
31.3
311
10.4
285
13.8
298
624
13500
455
113
23.4
162
6.86
145
9.15
184
581
12500
436
105
22.5
147
6.65
131
8.87
168
509
11000
415
91.1
21.6
126
7.06
110
9.41
149
Span (ft)
1400
1320
1250
210
829
785
733
687
647
611
Fy = 36 ksi
13
14
15
16
17
18
232
Properties and Reaction Values
833
18000
592
173
29.9
270
10.5
244
14.0
270
767
16600
543
151
27.5
230
8.94
208
11.9
240
718
15500
512
139
26.1
205
8.16
185
10.9
223
668
14400
478
122
24.5
180
7.25
162
9.67
202
Load above heavy line is limited by design shear strength.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
4 - 40
BEAM AND GIRDER DESIGN
BEAMS
W Shapes
Maximum factored uniform loads in kips
for beams laterally supported
W 33
Fy = 36 ksi
For beams laterally unsupported, see page 4-113
Designation
Span (ft)
Fy = 36 ksi
Wt./ft
W 33
241
221
W 33
201
169
152
141
130
118
755
710
671
635
604
575
694
653
617
584
555
529
630
593
560
531
504
480
560
527
498
472
448
427
16
17
18
19
20
21
1100
1070
1010
966
1020
972
923
879
936
926
878
834
794
849
799
755
715
679
647
22
23
24
25
26
27
922
882
845
811
780
751
839
803
770
739
710
684
758
725
695
667
641
618
618
591
566
543
523
503
549
525
503
483
464
447
505
483
463
444
427
411
459
439
420
403
388
374
407
390
374
359
345
332
28
29
30
31
32
33
724
699
676
654
634
615
660
637
616
596
577
560
596
575
556
538
521
505
485
468
453
438
425
412
431
416
402
389
377
366
397
383
370
358
347
336
360
348
336
325
315
306
320
309
299
289
280
272
34
35
36
37
38
40
597
579
563
548
534
507
543
528
513
499
486
462
490
476
463
451
439
417
400
388
377
367
358
340
355
345
335
326
318
302
327
317
308
300
292
278
297
288
280
273
265
252
264
256
249
242
236
224
42
44
46
48
50
52
483
461
441
423
406
390
440
420
401
385
369
355
397
379
363
347
334
321
323
309
295
283
272
261
287
274
262
252
241
232
264
252
241
231
222
214
240
229
219
210
202
194
213
204
195
187
179
172
54
56
58
60
62
64
376
362
350
338
327
317
342
330
318
308
298
289
309
298
288
278
269
261
252
243
234
226
219
212
224
216
208
201
195
189
206
198
191
185
179
173
187
180
174
168
163
158
166
160
155
149
145
140
66
68
70
72
307
298
290
282
280
272
264
257
253
245
238
232
206
200
194
189
183
178
172
168
168
163
159
154
153
148
144
140
136
132
128
125
514
11100
392
95.3
21.8
141
6.36
127
8.48
162
467
10100
373
88.1
20.9
125
6.33
111
8.44
146
415
8960
351
77.3
19.8
107
6.28
93.6
8.37
128
Properties and Reaction Values
Zx in.3
φbWc kip-ft
φvVn kips
φR1 kips
φR2 kips/in.
φr R3 kips
φr R4 kips/in.
φr R5 kips
φr R6 kips/in.
φR (N = 31⁄4) kips
939
20300
552
163
29.9
274
11.0
249
14.6
261
855
18500
511
144
27.9
236
9.88
213
13.2
235
772
16700
468
125
25.7
198
8.66
179
11.6
208
629
13600
440
124
24.1
185
6.69
170
8.92
203
559
12100
413
107
22.9
159
6.65
144
8.87
181
Load above heavy line is limited by design shear strength.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
FACTORED UNIFORM LOAD TABLES
Fy = 36 ksi
4 - 41
BEAMS
W Shapes
Maximum factored uniform loads in kips
for beams laterally supported
W 30
For beams laterally unsupported, see page 4-113
Designation
W 30
Span (ft)
Fy = 36 ksi
Wt./ft
261
235
191
173
932
899
851
809
770
847
808
765
727
692
775
769
726
688
653
622
830
794
761
730
702
676
735
703
674
647
622
599
661
632
606
581
559
538
594
568
545
523
503
484
726
701
678
656
635
616
652
629
608
589
570
553
578
558
539
522
506
490
519
501
485
469
454
441
467
451
436
422
408
396
34
36
38
40
42
44
598
565
535
508
484
462
537
507
480
456
435
415
476
449
426
404
385
368
428
404
383
363
346
330
384
363
344
327
311
297
46
48
50
52
54
56
442
423
407
391
376
363
397
380
365
351
338
326
352
337
324
311
300
289
316
303
291
280
269
260
284
272
261
251
242
233
58
60
62
64
66
68
350
339
328
318
308
299
315
304
294
285
277
268
279
270
261
253
245
238
251
242
234
227
220
214
225
218
211
204
198
192
70
72
290
282
261
254
231
225
208
202
187
182
673
14500
423
124
25.6
199
9.04
181
12.0
207
605
13100
388
111
23.6
167
7.96
151
10.6
187
16
17
18
19
20
21
1140
1130
1070
1020
968
1010
961
913
869
22
23
24
25
26
27
924
884
847
813
782
753
28
29
30
31
32
33
211
Properties and Reaction Values
Zx in.3
φbWc kip-ft
φvVn kips
φR1 kips
φR2 kips/in.
φr R3 kips
φr R4 kips/in.
φr R5 kips
φr R6 kips/in.
φR (N = 31⁄4) kips
941
20300
571
204
33.5
353
14.2
323
18.9
313
845
18300
505
168
29.9
283
11.2
260
14.9
265
749
16200
466
148
27.9
239
10.5
218
14.0
239
Load above heavy line is limited by design shear strength.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
4 - 42
BEAM AND GIRDER DESIGN
BEAMS
W Shapes
Maximum factored uniform loads in kips
for beams laterally supported
W 30
Fy = 36 ksi
For beams laterally unsupported, see page 4-113
Designation
Span (ft)
Fy = 36 ksi
Wt./ft
W 30
148
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
36
38
40
42
44
46
48
50
52
54
56
58
60
62
64
66
68
70
72
775
771
720
675
635
600
568
540
514
491
470
450
432
415
400
386
372
360
348
338
327
318
300
284
270
257
245
235
225
216
208
200
193
186
180
174
169
164
159
154
150
132
725
674
629
590
555
524
497
472
449
429
410
393
378
363
350
337
325
315
304
295
286
278
262
248
236
225
215
205
197
189
182
175
169
163
157
152
147
143
139
135
131
124
686
678
629
588
551
518
490
464
441
420
401
383
367
353
339
326
315
304
294
284
275
267
259
245
232
220
210
200
192
184
176
169
163
157
152
147
142
138
134
130
126
122
116
108
99
90
659
628
583
544
510
480
454
430
408
389
371
355
340
327
314
302
292
282
272
263
255
247
240
227
215
204
194
186
177
170
163
157
151
146
141
136
132
128
124
120
117
113
632
623
575
534
498
467
440
415
393
374
356
340
325
311
299
287
277
267
258
249
241
234
226
220
208
197
187
178
170
162
156
149
144
138
133
129
125
121
117
113
110
107
104
599
562
518
481
449
421
396
374
355
337
321
306
293
281
270
259
250
241
232
225
217
211
204
198
187
177
168
160
153
147
140
135
130
125
120
116
112
109
105
102
99
96
94
540
509
470
437
408
382
360
340
322
306
291
278
266
255
245
235
226
218
211
204
197
191
185
180
170
161
153
146
139
133
127
122
118
113
109
105
102
99
96
93
90
87
85
346
7470
316
76.6
19.6
107
6.55
94.3
8.74
129
312
6740
300
67.3
18.7
93.9
6.50
81.1
8.66
115
283
6110
270
55.5
16.9
77.0
5.29
66.6
7.05
94.2
Properties and Reaction Values
Zx in.3
φbWc kip-ft
φvVn kips
φR1 kips
φR2 kips/in.
φr R3 kips
φr R4 kips/in.
φr R5 kips
φr R6 kips/in.
φR (N = 31⁄4) kips
500
10800
388
117
23.4
174
6.97
160
9.29
193
437
9440
362
96.9
22.1
148
7.05
133
9.39
169
408
8810
343
88.8
21.1
132
6.55
119
8.73
153
378
8160
330
82.6
20.3
120
6.49
107
8.65
141
Load above heavy line is limited by design shear strength.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
FACTORED UNIFORM LOAD TABLES
Fy = 36 ksi
4 - 43
BEAMS
W Shapes
Maximum factored uniform loads in kips
for beams laterally supported
W 27
For beams laterally unsupported, see page 4-113
Designation
Span (ft)
Fy = 36 ksi
Wt./ft
W 27
258
235
194
178
161
146
917
900
850
805
765
820
798
754
714
678
784
765
720
680
645
612
708
691
651
614
582
553
644
622
586
553
524
498
791
755
722
692
664
639
728
695
665
637
612
588
646
617
590
565
543
522
583
557
532
510
490
471
527
503
481
461
442
425
474
453
433
415
398
383
680
656
633
612
592
574
615
593
573
554
536
519
566
546
527
510
493
478
502
484
468
452
438
424
454
437
422
408
395
383
410
395
381
369
357
346
369
356
343
332
321
311
33
34
35
36
37
38
556
540
525
510
496
483
503
489
475
461
449
437
463
450
437
425
413
402
411
399
388
377
367
357
371
360
350
340
331
322
335
325
316
307
299
291
302
293
285
277
269
262
40
42
44
46
48
50
459
437
417
399
383
367
415
395
378
361
346
332
382
364
348
332
319
306
339
323
308
295
283
271
306
292
278
266
255
245
276
263
251
240
230
221
249
237
226
216
207
199
52
54
56
58
60
62
353
340
328
317
306
296
319
308
297
286
277
268
294
283
273
264
255
247
261
251
242
234
226
219
236
227
219
211
204
198
213
205
197
191
184
178
191
184
178
172
166
161
64
66
287
278
260
252
239
232
212
206
191
186
173
168
156
151
567
12200
392
122
26.1
206
10.6
186
14.1
207
512
11100
354
108
23.8
171
8.86
154
11.8
185
461
9960
322
91.9
21.8
142
7.62
128
10.2
163
15
16
17
18
19
20
1100
1080
1020
966
918
1010
977
923
874
831
21
22
23
24
25
26
874
835
798
765
734
706
27
28
29
30
31
32
217
Properties and Reaction Values
Zx in.3
φbWc kip-ft
φvVn kips
φR1 kips
φR2 kips/in.
φr R3 kips
φr R4 kips/in.
φr R5 kips
φr R6 kips/in.
φR (N = 31⁄4) kips
850
18400
552
221
35.3
395
16.8
362
22.5
335
769
16600
507
189
32.8
337
15.0
308
20.0
296
708
15300
459
163
29.9
283
12.3
260
16.4
261
628
13600
410
139
27.0
230
10.3
211
13.7
227
Load above heavy line is limited by design shear strength.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
4 - 44
BEAM AND GIRDER DESIGN
W 27
BEAMS
W Shapes
Maximum factored uniform loads in kips
for beams laterally supported
Fy = 36 ksi
For beams laterally unsupported, see page 4-113
Designation
W 27
Span (ft)
Fy = 36 ksi
Wt./ft
129
102
94
84
605
570
529
494
463
542
507
471
439
412
513
500
462
429
400
375
478
439
405
376
351
329
502
474
449
427
406
388
436
412
390
370
353
337
388
366
347
329
314
299
353
334
316
300
286
273
310
293
277
264
251
240
23
24
25
26
27
28
371
356
341
328
316
305
322
309
296
285
274
265
286
275
264
253
244
235
261
250
240
231
222
214
229
220
211
203
195
188
29
30
31
32
33
34
294
284
275
267
259
251
255
247
239
232
225
218
227
220
213
206
200
194
207
200
194
188
182
177
182
176
170
165
160
155
36
38
40
42
44
46
237
225
213
203
194
185
206
195
185
176
168
161
183
173
165
157
150
143
167
158
150
143
136
131
146
139
132
125
120
115
48
50
52
54
56
58
178
171
164
158
152
147
154
148
142
137
132
128
137
132
127
122
118
114
125
120
115
111
107
104
110
105
101
98
94
91
60
62
64
66
142
138
133
129
123
119
116
112
110
106
103
100
100
97
94
91
88
85
82
80
278
6000
256
63.4
17.6
90.6
5.39
80.9
7.18
108
244
5270
239
56.9
16.6
76.4
5.23
67.1
6.97
93.4
11
12
13
14
15
16
655
609
569
533
17
18
19
20
21
22
114
Properties and Reaction Values
Zx in.3
φbWc kip-ft
φvVn kips
φR1 kips
φR2 kips/in.
φr R3 kips
φr R4 kips/in.
φr R5 kips
φr R6 kips/in.
φR (N = 31⁄4) kips
395
8530
328
99.5
22.0
153
6.86
140
9.14
171
343
7410
302
83.4
20.5
127
6.70
115
8.93
149
305
6590
271
72.4
18.5
103
5.58
93.0
7.44
121
Load above heavy line is limited by design shear strength.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
FACTORED UNIFORM LOAD TABLES
Fy = 36 ksi
4 - 45
BEAMS
W Shapes
Maximum factored uniform loads in kips
for beams laterally supported
W 24
For beams laterally unsupported, see page 4-113
Designation
Span (ft)
Fy = 36 ksi
Wt./ft
W 24
229
207
192
176
146
131
117
104
685
674
632
595
562
625
602
564
531
502
576
571
533
500
470
444
519
505
471
441
415
392
468
446
416
390
367
347
581
552
526
502
480
460
532
505
481
459
440
421
475
451
430
410
393
376
421
400
381
363
347
333
372
353
336
321
307
294
329
312
297
284
271
260
483
464
447
431
416
402
442
425
409
394
381
368
404
389
374
361
349
337
361
347
334
322
311
301
320
307
296
285
276
266
283
272
262
252
244
235
250
240
231
223
215
208
422
409
397
385
374
364
389
377
366
355
345
335
356
345
334
325
315
307
326
316
306
297
289
281
291
282
274
266
258
251
258
250
242
235
228
222
228
221
214
208
202
196
201
195
189
184
178
173
384
365
348
332
317
304
344
327
312
297
285
273
318
302
287
274
262
252
290
276
263
251
240
230
266
253
241
230
220
211
238
226
215
205
196
188
210
200
190
182
174
167
186
177
168
161
154
147
164
156
149
142
136
130
292
281
270
261
252
243
262
252
242
234
226
218
241
232
224
216
208
201
221
212
204
197
190
184
202
194
187
181
174
168
181
174
167
161
156
150
160
154
148
143
138
133
141
136
131
126
122
118
125
120
116
111
108
104
676
14600
486
216
34.6
379
18.0
347
24.1
328
606
13100
435
186
31.3
311
15.0
285
20.0
288
370
7990
288
95.3
21.8
141
8.65
127
11.5
166
327
7060
259
80.4
19.8
115
7.41
103
9.88
139
289
6240
234
67.5
18.0
93.7
6.36
83.5
8.48
114
13
14
15
16
17
18
971
913
859
811
870
818
770
727
802
755
710
671
736
736
690
649
613
19
20
21
22
23
24
769
730
695
664
635
608
689
654
623
595
569
545
635
604
575
549
525
503
25
26
27
28
29
30
584
562
541
521
504
487
524
503
485
467
451
436
31
32
33
34
35
36
471
456
442
429
417
406
38
40
42
44
46
48
50
52
54
56
58
60
162
Properties and Reaction Values
Zx in.3
φbWc kip-ft
φvVn kips
φR1 kips
φR2 kips/in.
φr R3 kips
φr R4 kips/in.
φr R5 kips
φr R6 kips/in.
φR (N = 31⁄4) kips
559
12100
401
164
29.2
270
13.1
247
17.5
259
511
11000
368
143
27.0
230
11.5
211
15.3
231
468
10100
343
127
25.4
200
10.5
182
14.1
209
418
9030
313
110
23.4
167
9.35
152
12.5
186
Load above heavy line is limited by design shear strength.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
4 - 46
BEAM AND GIRDER DESIGN
BEAMS
W Shapes
Maximum factored uniform loads in kips
for beams laterally supported
W 24
Fy = 36 ksi
For beams laterally unsupported, see page 4-113
Designation
Span (ft)
Fy = 36 ksi
Wt./ft
W 24
103
94
84
W 24
76
68
62
55
397
367
330
300
275
362
362
322
289
263
241
7
8
9
10
11
12
525
504
487
457
440
440
403
409
393
360
383
382
348
319
13
14
15
16
17
18
465
432
403
378
356
336
422
392
366
343
323
305
372
346
323
302
285
269
332
309
288
270
254
240
294
273
255
239
225
212
254
236
220
207
194
184
223
207
193
181
170
161
19
20
21
22
23
24
318
302
288
275
263
252
289
274
261
249
239
229
255
242
230
220
210
202
227
216
206
196
188
180
201
191
182
174
166
159
174
165
157
150
144
138
152
145
138
132
126
121
25
26
27
28
29
30
242
233
224
216
209
202
219
211
203
196
189
183
194
186
179
173
167
161
173
166
160
154
149
144
153
147
142
137
132
127
132
127
122
118
114
110
116
111
107
103
100
96
31
32
33
34
35
36
195
189
183
178
173
168
177
171
166
161
157
152
156
151
147
142
138
134
139
135
131
127
123
120
123
119
116
112
109
106
107
103
100
97
94
92
93
90
88
85
83
80
38
40
42
44
46
48
159
151
144
137
131
126
144
137
131
125
119
114
127
121
115
110
105
101
114
108
103
98
94
90
101
96
91
87
83
80
87
83
79
75
72
69
76
72
69
66
63
60
50
52
54
56
58
60
121
116
112
108
104
101
110
106
102
98
95
91
97
93
90
86
83
81
86
83
80
77
74
76
74
71
68
66
66
64
61
59
57
58
56
54
52
50
177
3820
191
51.4
14.9
62.6
4.73
55.1
6.30
77.9
153
3300
198
53.2
15.5
66.3
5.21
58.0
6.95
83.2
134
2890
181
46.7
14.2
54.0
4.75
46.5
6.34
69.4
Properties and Reaction Values
Zx in.3
φbWc kip-ft
φvVn kips
φR1 kips
φR2 kips/in.
φr R3 kips
φr R4 kips/in.
φr R5 kips
φr R6 kips/in.
φR (N = 31⁄4) kips
280
6050
262
86.6
19.8
124
6.35
113
8.47
144
254
5490
243
75.3
18.5
106
5.89
96.2
7.86
125
224
4840
220
66.1
16.9
86.5
5.14
78.3
6.85
103
200
4320
205
56.9
15.8
73.6
4.81
66.0
6.41
89.3
Load above heavy line is limited by design shear strength.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
FACTORED UNIFORM LOAD TABLES
Fy = 36 ksi
4 - 47
BEAMS
W Shapes
Maximum factored uniform loads in kips
for beams laterally supported
W 21
For beams laterally unsupported, see page 4-113
Designation
Span (ft)
Fy = 36 ksi
Wt./ft
W 21
201
182
166
147
132
122
111
101
552
514
480
450
423
400
506
474
442
414
390
368
460
430
402
377
354
335
415
390
364
342
321
304
13
14
15
16
17
18
815
763
716
673
636
733
685
643
605
571
656
622
583
549
518
618
575
537
504
474
448
19
20
21
22
23
24
603
572
545
520
498
477
541
514
490
467
447
428
491
467
444
424
406
389
424
403
384
366
350
336
379
360
343
327
313
300
349
332
316
301
288
276
317
301
287
274
262
251
288
273
260
248
238
228
25
26
27
28
29
30
458
440
424
409
395
382
411
395
381
367
355
343
373
359
346
333
322
311
322
310
298
288
278
269
288
277
266
257
248
240
265
255
246
237
229
221
241
232
223
215
208
201
219
210
202
195
188
182
31
32
33
34
35
36
369
358
347
337
327
318
332
321
312
302
294
286
301
292
283
274
267
259
260
252
244
237
230
224
232
225
218
212
206
200
214
207
201
195
189
184
194
188
183
177
172
167
176
171
166
161
156
152
38
40
42
44
46
48
301
286
273
260
249
239
271
257
245
234
224
214
246
233
222
212
203
194
212
201
192
183
175
168
189
180
171
163
156
150
175
166
158
151
144
138
159
151
143
137
131
126
144
137
130
124
119
114
50
52
229
220
206
198
187
179
161
155
144
138
133
128
121
116
109
105
307
6630
253
91.1
21.6
139
9.53
126
12.7
161
279
6030
230
80.4
19.8
117
8.11
105
10.8
143
253
5460
208
70.3
18.0
96.8
6.72
87.2
8.95
119
Properties and Reaction Values
Zx in.3
φbWc kip-ft
φvVn kips
φR1 kips
φR2 kips/in.
φr R3 kips
φr R4 kips/in.
φr R5 kips
φr R6 kips/in.
φR (N = 31⁄4) kips
530
11400
407
195
32.8
339
18.4
311
24.6
301
476
10300
367
168
29.9
281
15.6
258
20.8
265
432
9330
328
143
27.0
232
12.7
213
16.9
231
373
8060
309
122
25.9
200
13.5
181
18.0
206
333
7190
276
106
23.4
163
11.2
147
14.9
182
Load above heavy line is limited by design shear strength.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
4 - 48
BEAM AND GIRDER DESIGN
BEAMS
W Shapes
Maximum factored uniform loads in kips
for beams laterally supported
W 21
Fy = 36 ksi
For beams laterally unsupported, see page 4-113
Designation
Span (ft)
Fy = 36 ksi
Wt./ft
W 21
93
83
73
W 21
68
62
57
50
44
281
258
229
206
187
172
7
8
9
10
11
12
488
477
434
398
429
423
385
353
376
372
338
310
353
346
314
288
326
311
283
259
332
310
279
253
232
308
297
264
238
216
198
13
14
15
16
17
18
367
341
318
298
281
265
326
302
282
265
249
235
286
265
248
232
219
206
266
247
230
216
203
192
239
222
207
194
183
173
214
199
186
174
164
155
183
170
158
149
140
132
159
147
137
129
121
114
19
20
21
22
23
24
251
239
227
217
208
199
223
212
202
192
184
176
196
186
177
169
162
155
182
173
165
157
150
144
164
156
148
141
135
130
147
139
133
127
121
116
125
119
113
108
103
99
108
103
98
94
90
86
25
26
27
28
29
30
191
184
177
170
165
159
169
163
157
151
146
141
149
143
138
133
128
124
138
133
128
123
119
115
124
120
115
111
107
104
111
107
103
100
96
93
95
91
88
85
82
79
82
79
76
74
71
69
31
32
33
34
35
36
154
149
145
140
136
133
137
132
128
125
121
118
120
116
113
109
106
103
111
108
105
102
99
96
100
97
94
91
89
86
90
87
84
82
80
77
77
74
72
70
68
66
66
64
62
61
59
57
38
40
42
44
46
48
126
119
114
108
104
99
111
106
101
96
92
88
98
93
88
84
81
77
91
86
82
79
75
72
82
78
74
71
68
65
73
70
66
63
61
58
63
59
57
54
52
50
54
52
49
47
45
43
50
52
95
92
85
81
74
71
69
66
62
60
56
54
48
46
41
129
2790
166
50.1
14.6
63.6
4.45
57.3
5.94
78.1
110
2380
154
44.9
13.7
52.4
4.52
46.2
6.03
67.1
95.4
2060
141
37.4
12.6
42.5
4.23
36.7
5.64
56.3
Properties and Reaction Values
Zx in.3
φbWc kip-ft
φvVn kips
φR1 kips
φR2 kips/in.
φr R3 kips
φr R4 kips/in.
φr R5 kips
φr R6 kips/in.
φR (N = 31⁄4) kips
221
4770
244
88.1
20.9
130
8.91
118
11.9
156
196
4230
215
72.4
18.5
103
7.01
93.3
9.34
126
172
3720
188
61.4
16.4
80.8
5.50
73.0
7.34
98.7
160
3460
177
55.6
15.5
71.4
5.04
64.3
6.72
87.8
144
3110
163
49.5
14.4
60.7
4.55
54.3
6.07
75.5
Load above heavy line is limited by design shear strength.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
FACTORED UNIFORM LOAD TABLES
Fy = 36 ksi
4 - 49
BEAMS
W Shapes
Maximum factored uniform loads in kips
for beams laterally supported
W 18
For beams laterally unsupported, see page 4-113
Designation
Wt./ft
W 18
192
175
158
W 18
143
130
119
106
97
86
76
430
414
382
355
331
311
387
380
351
326
304
285
343
335
309
287
268
251
301
293
271
251
235
220
693
661
614
573
537
621
592
549
513
481
553
535
497
464
435
501
484
449
419
393
17
18
19
20
21
22
562
530
502
477
455
434
506
478
452
430
409
391
452
427
405
384
366
350
409
386
366
348
331
316
370
349
331
314
299
286
332
313
297
282
268
256
292
276
261
248
237
226
268
253
240
228
217
207
236
223
211
201
191
183
207
196
185
176
168
160
23
24
25
26
27
28
415
398
382
367
354
341
374
358
344
331
318
307
334
320
308
296
285
275
302
290
278
268
258
248
273
262
251
242
233
224
245
235
226
217
209
201
216
207
199
191
184
177
198
190
182
175
169
163
175
167
161
155
149
143
153
147
141
135
130
126
29
30
31
32
33
34
329
318
308
298
289
281
296
287
277
269
261
253
265
256
248
240
233
226
240
232
224
217
211
205
217
210
203
196
190
185
194
188
182
176
171
166
171
166
160
155
151
146
157
152
147
142
138
134
139
134
130
126
122
118
121
117
114
110
107
104
35
36
37
38
39
40
273
265
258
251
245
239
246
239
232
226
220
215
220
214
208
202
197
192
199
193
188
183
178
174
180
175
170
165
161
157
161
157
152
148
145
141
142
138
134
131
127
124
130
127
123
120
117
114
115
112
109
106
103
100
101
98
95
93
90
88
42
44
227
217
205
195
183
175
166
158
150
143
134
128
118
113
109
104
96
91
84
80
Zx in.3
φbWc kip-ft
φvVn kips
φR1 kips
φR2 kips/in.
φr R3 kips
φr R4 kips/in.
φr R5 kips
φr R6 kips/in.
φR (N = 31⁄4) kips
442
9550
380
211
34.6
381
22.8
350
30.4
323
398
8600
347
180
32.0
324
20.3
297
27.1
284
230
4970
215
86.3
21.2
134
10.7
121
14.3
155
211
4560
193
75.2
19.3
112
8.69
101
11.6
138
186
4020
172
62.1
17.3
89.3
7.17
80.5
9.56
113
163
3520
150
52.6
15.3
69.9
5.69
63.0
7.59
88.4
Span (ft)
760
734
682
636
597
483
470
434
403
376
352
Fy = 36 ksi
11
12
13
14
15
16
Properties and Reaction Values
356
7690
311
155
29.2
268
17.2
245
22.9
250
322
6960
277
131
26.3
219
13.9
201
18.5
217
291
6290
251
113
24.1
184
12.0
168
15.9
191
261
5640
242
103
23.6
167
12.8
151
17.1
180
Load above heavy line is limited by design shear strength.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
4 - 50
BEAM AND GIRDER DESIGN
BEAMS
W Shapes
Maximum factored uniform loads in kips
for beams laterally supported
W 18
Fy = 36 ksi
For beams laterally unsupported, see page 4-113
Designation
Span (ft)
Fy = 36 ksi
Wt./ft
W 18
71
65
6
7
8
9
10
11
355
348
313
285
321
319
287
261
12
13
14
15
16
17
261
241
224
209
196
184
18
19
20
21
22
23
60
W 18
55
50
46
40
35
294
266
242
275
269
242
220
248
242
218
198
253
245
218
196
178
219
212
188
169
154
206
205
180
160
144
131
239
221
205
192
180
169
221
204
190
177
166
156
202
186
173
161
151
142
182
168
156
145
136
128
163
151
140
131
122
115
141
130
121
113
106
100
120
110
103
96
90
84
174
165
157
149
142
136
160
151
144
137
131
125
148
140
133
127
121
116
134
127
121
115
110
105
121
115
109
104
99
95
109
103
98
93
89
85
94
89
85
81
77
74
80
76
72
68
65
62
24
25
26
27
28
29
131
125
120
116
112
108
120
115
110
106
103
99
111
106
102
98
95
92
101
97
93
90
86
83
91
87
84
81
78
75
82
78
75
73
70
68
71
68
65
63
60
58
60
57
55
53
51
50
30
31
32
33
34
35
104
101
98
95
92
89
96
93
90
87
84
82
89
86
83
81
78
76
81
78
76
73
71
69
73
70
68
66
64
62
65
63
61
59
58
56
56
55
53
51
50
48
48
46
45
44
42
41
36
38
40
42
44
87
82
78
75
71
80
76
72
68
65
74
70
66
63
60
67
64
60
58
55
61
57
55
52
50
54
52
49
47
45
47
45
42
40
38
40
38
36
34
33
90.7
1960
126
40.5
13.0
51.4
3.92
46.7
5.23
64.2
78.4
1690
110
33.7
11.3
39.2
3.05
35.6
4.07
49.1
66.5
1440
103
30.4
10.8
32.8
3.29
28.9
4.39
43.5
Properties and Reaction Values
Zx in.3
φbWc kip-ft
φvVn kips
φR1 kips
φR2 kips/in.
φr R3 kips
φr R4 kips/in.
φr R5 kips
φr R6 kips/in.
φR (N = 31⁄4) kips
145
3130
178
66.8
17.8
95.9
7.44
86.7
9.92
120
133
2870
161
58.2
16.2
80.0
6.08
72.6
8.10
99.8
123
2660
147
51.4
14.9
68.2
5.18
61.9
6.90
85.0
112
2420
137
46.1
14.0
59.2
4.77
53.4
6.36
74.7
101
2180
124
39.9
12.8
48.9
4.01
44.1
5.34
61.9
Load above heavy line is limited by design shear strength.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
FACTORED UNIFORM LOAD TABLES
Fy = 36 ksi
4 - 51
BEAMS
W Shapes
Maximum factored uniform loads in kips
for beams laterally supported
W 16
For beams laterally unsupported, see page 4-113
Designation
Span (ft)
Fy = 36 ksi
Wt./ft
W 16
100
89
W 16
77
6
7
8
9
10
11
386
342
292
12
13
14
15
16
17
356
329
305
285
267
252
315
291
270
252
236
222
18
19
20
21
22
23
238
225
214
204
194
186
24
25
26
27
28
29
67
57
50
45
W 16
40
36
31
26
153
136
119
106
95
87
251
275
252
227
206
240
221
199
181
216
198
178
162
190
175
157
143
182
173
154
138
126
170
167
146
130
117
106
270
249
231
216
203
191
234
216
201
187
176
165
189
174
162
151
142
133
166
153
142
132
124
117
148
137
127
119
111
105
131
121
112
105
98
93
115
106
99
92
86
81
97
90
83
78
73
69
80
73
68
64
60
56
210
199
189
180
172
164
180
171
162
154
147
141
156
148
140
134
128
122
126
119
113
108
103
99
110
105
99
95
90
86
99
94
89
85
81
77
87
83
79
75
72
68
77
73
69
66
63
60
65
61
58
56
53
51
53
50
48
45
43
42
178
171
164
158
153
147
158
151
145
140
135
130
135
130
125
120
116
112
117
112
108
104
100
97
95
91
87
84
81
78
83
79
76
74
71
69
74
71
68
66
63
61
66
63
61
58
56
54
58
55
53
51
49
48
49
47
45
43
42
40
40
38
37
35
34
33
30
31
32
33
34
35
143
138
134
130
126
122
126
122
118
115
111
108
108
105
101
98
95
93
94
91
88
85
83
80
76
73
71
69
67
65
66
64
62
60
58
57
59
57
56
54
52
51
52
51
49
48
46
45
46
45
43
42
41
39
39
38
36
35
34
33
32
31
30
29
28
27
36
38
40
119
113
107
105
99
95
90
85
81
78
74
70
63
60
57
55
52
50
49
47
44
44
41
39
38
36
32
31
27
25
198
4280
193
88.8
21.1
136
11.0
123
14.7
157
175
3780
171
73.8
18.9
109
9.06
98.8
12.1
135
72.9
1570
94.9
32.6
11.0
36.6
3.22
33.2
4.30
47.1
64.0
1380
91.0
29.9
10.6
32.2
3.46
28.5
4.61
43.5
54.0
1170
84.9
27.8
9.90
29.3
2.73
26.4
3.64
38.2
44.2
955
76.3
23.9
9.00
22.5
2.65
19.7
3.53
31.2
Properties and Reaction Values
Zx in.3
φbWc kip-ft
φvVn kips
φR1 kips
φR2 kips/in.
φr R3 kips
φr R4 kips/in.
φr R5 kips
φr R6 kips/in.
φR (N = 31⁄4) kips
150
3240
146
58.9
16.4
81.9
6.89
74.3
9.18
104
130
2810
125
48.9
14.2
61.9
5.21
56.3
6.95
78.9
105
2270
137
53.2
15.5
73.0
6.21
66.2
8.28
93.2
92.0
1990
120
44.9
13.7
56.9
4.92
51.6
6.56
72.9
82.3
1780
108
38.8
12.4
46.6
4.14
42.2
5.52
60.1
Load above heavy line is limited by design shear strength.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
4 - 52
BEAM AND GIRDER DESIGN
W 14
Fy = 36 ksi
BEAMS
W Shapes
Maximum factored uniform loads in kips
for beams laterally supported
For beams laterally unsupported, see page 4-113
Designation
Wt./ft
W 14
132
120
109
W 14
99
90
82
74
68
61
248
247
227
209
194
181
227
226
207
191
177
166
203
200
184
169
157
147
332
327
305
292
276
267
267
249
240
226
16
17
18
19
20
21
316
297
281
266
253
241
286
269
254
241
229
218
259
244
230
218
207
197
234
220
208
197
187
178
212
199
188
178
170
161
188
177
167
158
150
143
170
160
151
143
136
130
155
146
138
131
124
118
138
130
122
116
110
105
22
23
24
25
26
27
230
220
211
202
194
187
208
199
191
183
176
170
189
180
173
166
160
154
170
162
156
149
144
138
154
147
141
136
130
126
136
131
125
120
115
111
124
118
113
109
105
101
113
108
104
99
96
92
100
96
92
88
85
82
28
29
30
31
32
33
181
174
168
163
158
153
164
158
153
148
143
139
148
143
138
134
130
126
133
129
125
121
117
113
121
117
113
109
106
103
107
104
100
97
94
91
97
94
91
88
85
82
89
86
83
80
78
75
79
76
73
71
69
67
34
149
135
122
110
100
88
80
73
65
Zx in.3
φbWc kip-ft
φvVn kips
φR1 kips
φR2 kips/in.
φr R3 kips
φr R4 kips/in.
φr R5 kips
φr R6 kips/in.
φR (N = 31⁄4) kips
234
5050
184
98.0
23.2
161
16.3
145
21.8
173
212
4580
166
86.3
21.2
134
13.9
121
18.5
155
139
3000
142
74.6
18.4
103
9.95
93.6
13.3
134
126
2720
124
63.3
16.2
81.8
7.52
74.7
10.0
107
115
2480
113
56.0
14.9
69.4
6.49
63.3
8.65
91.5
102
2200
101
48.5
13.5
56.4
5.40
51.4
7.20
74.8
Span (ft)
368
361
337
284
273
250
231
214
200
Fy = 36 ksi
10
11
12
13
14
15
Properties and Reaction Values
192
4150
146
73.8
18.9
108
10.8
97.6
14.4
135
173
3740
134
62.7
17.5
91.3
9.48
82.3
12.6
119
157
3390
120
54.5
15.8
75.3
7.86
67.9
10.5
102
Load above heavy line is limited by design shear strength.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
FACTORED UNIFORM LOAD TABLES
Fy = 36 ksi
4 - 53
BEAMS
W Shapes
Maximum factored uniform loads in kips
for beams laterally supported
W 14
For beams laterally unsupported, see page 4-113
Designation
Span (ft)
Fy = 36 ksi
Wt./ft
W 14
53
48
5
6
7
8
9
10
200
188
182
169
11
12
13
14
15
16
171
157
145
134
125
118
17
18
19
20
21
22
W 14
43
38
34
W 14
30
26
22
162
150
170
166
148
133
155
147
131
118
145
128
114
102
138
124
109
96
87
123
120
102
90
80
72
154
141
130
121
113
106
137
125
116
107
100
94
121
111
102
95
89
83
107
98
91
84
79
74
93
85
79
73
68
64
79
72
67
62
58
54
65
60
55
51
48
45
111
105
99
94
90
86
100
94
89
85
81
77
88
84
79
75
72
68
78
74
70
66
63
60
69
66
62
59
56
54
60
57
54
51
49
46
51
48
46
43
41
39
42
40
38
36
34
33
23
24
25
26
27
28
82
78
75
72
70
67
74
71
68
65
63
60
65
63
60
58
56
54
58
55
53
51
49
47
51
49
47
45
44
42
44
43
41
39
38
36
38
36
35
33
32
31
31
30
29
28
27
26
29
30
31
32
33
34
65
63
61
59
57
55
58
56
55
53
51
50
52
50
48
47
46
44
46
44
43
42
40
39
41
39
38
37
36
35
35
34
33
32
31
30
30
29
28
27
26
26
25
24
23
22
22
21
47.3
1020
72.6
22.8
9.72
26.6
3.39
23.5
4.52
38.2
40.2
868
69.0
21.5
9.18
25.5
2.61
23.1
3.47
34.4
33.2
717
61.4
18.1
8.28
19.5
2.43
17.3
3.24
27.8
Properties and Reaction Values
Zx in.3
φbWc kip-ft
φvVn kips
φR1 kips
φR2 kips/in.
φr R3 kips
φr R4 kips/in.
φr R5 kips
φr R6 kips/in.
φR (N = 31⁄4) kips
87.1
1880
100
47.9
13.3
55.9
5.06
51.3
6.75
73.2
78.4
1690
91.1
42.1
12.2
46.8
4.40
42.8
5.86
61.8
69.6
1500
81.0
36.0
11.0
37.5
3.60
34.2
4.80
49.8
61.5
1330
85.0
29.6
11.2
37.9
3.77
34.4
5.02
50.7
54.6
1180
77.5
25.7
10.3
31.4
3.34
28.3
4.45
42.8
Load above heavy line is limited by design shear strength.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
4 - 54
BEAM AND GIRDER DESIGN
W 12
BEAMS
W Shapes
Maximum factored uniform loads in kips
for beams laterally supported
Fy = 36 ksi
For beams laterally unsupported, see page 4-113
Designation
Wt./ft
W 12
120
106
96
87
W 12
79
72
65
58
53
162
153
140
129
120
112
306
295
272
253
236
272
265
244
227
212
251
238
219
204
190
226
214
198
184
171
205
194
179
167
156
184
174
161
149
139
16
17
18
19
20
21
251
236
223
211
201
191
221
208
197
186
177
169
198
187
176
167
159
151
178
168
158
150
143
136
161
151
143
135
129
122
146
137
130
123
117
111
131
123
116
110
105
100
117
110
104
98
93
89
105
99
93
89
84
80
22
23
24
25
26
27
183
175
167
161
155
149
161
154
148
142
136
131
144
138
132
127
122
118
130
124
119
114
110
106
117
112
107
103
99
95
106
101
97
93
90
86
95
91
87
84
80
77
85
81
78
75
72
69
76
73
70
67
65
62
28
29
30
143
139
134
127
122
118
113
109
106
102
98
95
92
89
86
83
80
78
75
72
70
67
64
62
60
58
56
Zx in.3
φbWc kip-ft
φvVn kips
φR1 kips
φR2 kips/in.
φr R3 kips
φr R4 kips/in.
φr R5 kips
φr R6 kips/in.
φR (N = 31⁄4) kips
186
4020
181
116
25.6
192
22.7
173
30.2
199
164
3540
153
92.6
22.0
145
16.3
131
21.8
164
108
2330
102
53.2
15.5
70.6
8.89
63.4
11.9
102
96.8
2090
91.9
46.1
14.0
58.0
7.43
52.0
9.90
84.1
86.4
1870
85.3
44.6
13.0
52.9
5.49
48.4
7.32
72.2
77.9
1680
80.9
38.8
12.4
47.0
5.44
42.6
7.25
66.2
Span (ft)
362
335
309
287
268
171
170
156
144
133
124
Fy = 36 ksi
10
11
12
13
14
15
Properties and Reaction Values
147
3180
136
80.4
19.8
118
13.4
107
17.8
145
132
2850
125
69.5
18.5
102
12.4
91.5
16.5
130
119
2570
113
60.8
16.9
84.5
10.5
75.9
14.0
116
Load above heavy line is limited by design shear strength.
Values of R in bold face exceed maximum design web shear φvVn.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
FACTORED UNIFORM LOAD TABLES
Fy = 36 ksi
4 - 55
BEAMS
W Shapes
Maximum factored uniform loads in kips
for beams laterally supported
W 12
For beams laterally unsupported, see page 4-113
Designation
Span (ft)
Fy = 36 ksi
Wt./ft
W 12
50
45
W 12
40
4
5
6
7
8
9
175
174
157
155
10
11
12
13
14
15
156
142
130
120
112
104
16
17
18
19
20
21
35
30
W 12
26
22
19
16
14
111
107
89
76
67
59
103
87
72
62
54
48
93
75
63
54
47
42
137
146
138
123
125
116
103
109
100
89
124
105
90
79
70
140
127
116
108
100
93
124
113
104
96
89
83
111
101
92
85
79
74
93
85
78
72
66
62
80
73
67
62
57
54
63
58
53
49
45
42
53
49
44
41
38
36
43
39
36
33
31
29
38
34
31
29
27
25
98
92
87
82
78
74
87
82
78
74
70
67
78
73
69
65
62
59
69
65
61
58
55
53
58
55
52
49
47
44
50
47
45
42
40
38
40
37
35
33
32
30
33
31
30
28
27
25
27
26
24
23
22
21
23
22
21
20
19
18
22
23
24
25
26
27
71
68
65
63
60
58
64
61
58
56
54
52
56
54
52
50
48
46
50
48
46
44
43
41
42
40
39
37
36
34
37
35
33
32
31
30
29
28
26
25
24
23
24
23
22
21
21
20
20
19
18
17
17
16
17
16
16
15
14
14
28
29
30
56
54
52
50
48
47
44
43
37
39
38
31
33
32
27
29
28
21
23
22
18
19
18
16
15
13
13
72.4
1560
87.7
45.8
13.3
55.1
5.96
50.3
7.95
76.1
64.7
1400
78.5
37.7
12.1
45.0
4.98
41.0
6.64
62.6
29.3
633
62.2
20.5
9.36
26.4
3.08
23.9
4.11
37.3
24.7
534
55.6
17.2
8.46
20.6
2.80
18.4
3.73
30.5
20.1
434
51.3
14.9
7.92
16.3
3.08
13.8
4.10
27.1
17.4
376
46.3
12.4
7.20
13.0
2.74
10.8
3.65
Properties and Reaction Values
Zx in.3
φbWc kip-ft
φvVn kips
φR1 kips
φR2 kips/in.
φr R3 kips
φr R4 kips/in.
φr R5 kips
φr R6 kips/in.
φR (N = 31⁄4) kips
57.5
1240
68.5
33.2
10.6
35.2
3.83
32.1
5.11
48.7
51.2
1110
72.9
27.0
10.8
36.3
3.81
33.1
5.08
49.6
43.1
931
62.4
21.9
9.36
26.9
2.97
24.5
3.96
37.3
37.2
804
54.6
18.1
8.28
20.8
2.41
18.8
3.21
29.3
Load above heavy line is limited by design shear strength.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
22.7
4 - 56
BEAM AND GIRDER DESIGN
BEAMS
W Shapes
Maximum factored uniform loads in kips
for beams laterally supported
W 10
Fy = 36 ksi
For beams laterally unsupported, see page 4-113
Designation
W 10
112
100
88
77
68
60
54
49
9
10
11
12
13
14
333
318
289
265
244
227
293
281
255
234
216
201
255
244
222
203
188
174
218
211
192
176
162
151
190
184
167
154
142
132
167
161
146
134
124
115
145
144
131
120
111
103
132
130
119
109
100
93
15
16
17
18
19
20
212
198
187
176
167
159
187
176
165
156
148
140
163
153
144
136
128
122
141
132
124
117
111
105
123
115
108
102
97
92
107
101
95
90
85
81
96
90
85
80
76
72
87
82
77
72
69
65
21
22
23
24
151
144
138
132
134
128
122
117
116
111
106
102
100
96
92
88
88
84
80
77
77
73
70
67
69
65
63
60
62
59
57
54
74.6
1610
83.4
49.6
15.1
68.7
9.79
62.0
13.0
98.8
66.6
1440
72.6
41.6
13.3
54.0
7.49
49.0
9.99
81.4
60.4
1300
66.0
36.3
12.2
45.4
6.46
41.1
8.61
69.1
Span (ft)
Fy = 36 ksi
Wt./ft
Properties and Reaction Values
Zx in.3
φbWc kip-ft
φvVn kips
φR1 kips
φR2 kips/in.
φr R3 kips
φr R4 kips/in.
φr R5 kips
φr R6 kips/in.
φR (N = 31⁄4) kips
147
3180
167
127
27.2
224
27.8
203
37.1
216
130
2810
147
107
24.5
182
23.2
164
31.0
187
113
2440
127
88.5
21.8
143
18.9
130
25.3
159
97.6
2110
109
71.5
19.1
110
14.8
99.7
19.8
134
85.3
1840
95.0
58.2
16.9
86.5
11.9
78.3
15.9
113
Load above heavy line is limited by design shear strength.
Values of R in bold face exceed maximum design web shear φvVn.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
FACTORED UNIFORM LOAD TABLES
Fy = 36 ksi
4 - 57
BEAMS
W Shapes
Maximum factored uniform loads in kips
for beams laterally supported
W 10
For beams laterally unsupported, see page 4-113
Designation
Span (ft)
Fy = 36 ksi
Wt./ft
W 10
45
3
4
5
6
7
8
137
9
10
11
12
13
14
39
W 10
33
30
26
W 10
22
19
17
15
12
73
68
54
45
39
34
100
93
78
67
58
94
81
67
58
50
89
86
69
58
49
43
121
110
105
122
113
99
104
97
85
95
94
80
70
132
119
108
99
91
85
112
101
92
84
78
72
93
84
76
70
64
60
88
79
72
66
61
56
75
68
61
56
52
48
62
56
51
47
43
40
52
47
42
39
36
33
45
40
37
34
31
29
38
35
31
29
27
25
30
27
25
23
21
19
15
16
17
18
19
20
79
74
70
66
62
59
67
63
59
56
53
51
56
52
49
47
44
42
53
49
47
44
42
40
45
42
40
38
36
34
37
35
33
31
30
28
31
29
27
26
25
23
27
25
24
22
21
20
23
22
20
19
18
17
18
17
16
15
14
14
21
22
23
24
56
54
52
49
48
46
44
42
40
38
36
35
38
36
34
33
32
31
29
28
27
26
24
23
22
21
20
19
19
18
18
17
16
16
15
14
13
12
12
11
54.9
1190
68.7
39.4
12.6
49.9
6.29
45.7
8.38
72.9
46.8
1010
60.7
31.9
11.3
39.4
5.46
35.8
7.28
59.4
21.6
467
49.8
18.3
9.00
24.0
3.55
21.6
4.73
37.0
18.7
404
47.2
16.2
8.64
20.7
3.80
18.1
5.07
34.6
16.0
346
44.7
14.2
8.28
17.5
4.14
14.8
5.52
32.7
12.6
272
36.5
10.7
6.84
11.6
3.04
9.61
4.05
22.8
Properties and Reaction Values
Zx in.3
φbWc kip-ft
φvVn kips
φR1 kips
φR2 kips/in.
φr R3 kips
φr R4 kips/in.
φr R5 kips
φr R6 kips/in.
φR (N = 31⁄4) kips
38.8
838
54.9
27.7
10.4
31.5
5.29
28.1
7.05
51.0
36.6
791
61.1
25.3
10.8
35.9
4.64
32.7
6.19
52.8
31.3
676
52.2
20.5
9.36
26.9
3.55
24.5
4.73
39.8
26.0
562
47.4
16.2
8.64
21.6
3.47
19.2
4.62
34.3
Load above heavy line is limited by design shear strength.
Values of R in bold face exceed maximum design web shear φvVn.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
4 - 58
BEAM AND GIRDER DESIGN
BEAMS
W Shapes
Maximum factored uniform loads in kips
for beams laterally supported
W8
Fy = 36 ksi
For beams laterally unsupported, see page 4-113
Designation
W8
67
58
48
7
8
9
10
11
12
199
190
168
152
138
126
40
35
31
174
161
144
129
117
108
132
118
106
96
88
115
107
96
86
78
72
98
94
83
75
68
62
89
82
73
66
60
55
13
14
15
16
17
18
117
108
101
95
89
84
99
92
86
81
76
72
81
76
71
66
62
59
66
61
57
54
51
48
58
54
50
47
44
42
51
47
44
41
39
36
19
20
80
76
68
65
56
53
45
43
39
37
35
33
39.8
860
57.7
34.4
13.0
49.5
9.27
44.4
12.4
76.5
34.7
750
48.9
27.9
11.2
37.2
6.80
33.5
9.07
63.0
30.4
657
44.3
24.0
10.3
30.7
6.11
27.4
8.14
53.9
Span (ft)
Fy = 36 ksi
Wt./ft
Properties and Reaction Values
Zx in.3
φbWc kip-ft
φvVn kips
φR1 kips
φR2 kips/in.
φr R3 kips
φr R4 kips/in.
φr R5 kips
φr R6 kips/in.
φR (N = 31⁄4) kips
70.2
1520
99.7
73.7
20.5
127
20.2
115
26.9
140
59.8
1290
86.8
60.2
18.4
100
17.2
90.3
22.9
120
49.0
1060
66.1
42.8
14.4
64.1
10.1
58.4
13.5
89.6
Load above heavy line is limited by design shear strength.
Values of R in bold face exceed maximum design web shear φvVn.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
FACTORED UNIFORM LOAD TABLES
Fy = 36 ksi
4 - 59
BEAMS
W Shapes
Maximum factored uniform loads in kips
for beams laterally supported
W8
For beams laterally unsupported, see page 4-113
Designation
W8
Span (ft)
Fy = 36 ksi
Wt./ft
28
W8
24
21
W8
18
15
13
10
71
62
49
41
35
31
52
48
38
32
27
24
3
4
5
6
7
8
89
84
73
76
72
63
80
73
63
55
73
61
52
46
77
73
59
49
42
37
9
10
11
12
13
14
65
59
53
49
45
42
56
50
46
42
39
36
49
44
40
37
34
31
41
37
33
31
28
26
33
29
27
24
23
21
27
25
22
21
19
18
21
19
17
16
15
14
15
16
17
18
19
20
39
37
35
33
31
29
33
31
29
28
26
22
29
28
26
24
23
18
24
23
22
20
19
15
20
18
17
16
15
16
15
14
14
13
13
12
11
11
10
13.6
294
38.6
16.5
8.82
20.8
5.28
18.0
7.05
40.9
11.4
246
35.7
14.2
8.28
17.0
5.48
14.1
7.31
37.9
8.87
192
26.1
9.56
6.12
9.71
2.79
8.24
3.72
20.3
Properties and Reaction Values
Zx in.3
φbWc kip-ft
φvVn kips
φR1 kips
φR2 kips/in.
φr R3 kips
φr R4 kips/in.
φr R5 kips
φr R6 kips/in.
φR (N = 31⁄4) kips
27.2
588
44.7
24.0
10.3
31.7
5.67
28.7
7.56
53.3
23.2
501
37.8
19.3
8.82
23.5
4.26
21.2
5.67
39.7
20.4
441
40.2
18.3
9.00
24.2
4.33
21.8
5.77
40.6
17.0
367
36.4
15.5
8.28
19.4
4.16
17.1
5.54
35.2
Load above heavy line is limited by design shear strength.
Values of R in bold face exceed maximum design web shear φvVn.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
4 - 60
BEAM AND GIRDER DESIGN
W 6–5–4
BEAMS
W Shapes
Maximum factored uniform loads in kips
for beams laterally supported
Fy = 36 ksi
For beams laterally unsupported, see page 4-113
Designation
W6
25
2
3
4
5
6
7
79
68
58
8
9
10
11
12
13
14
20
W6
15*
16
W5
12
9
63
54
46
54
46
38
33
63
63
51
42
36
54
45
36
30
26
39
34
27
22
19
51
45
41
37
34
31
40
36
32
29
27
25
29
26
23
21
19
18
32
28
25
23
21
19
22
20
18
16
15
14
17
15
13
12
11
10
29
23
16
18
13
18.9
408
39.7
23.4
11.5
37.4
10.4
33.0
13.8
60.8
14.9
322
31.3
17.5
9.36
24.5
7.13
21.6
9.51
48.0
19
W4
16
13
54
50
42
36
47
41
35
30
45
45
34
27
23
19
31
28
25
23
21
26
23
21
19
17
17
15
14
11.6
251
27.0
19.7
9.72
28.2
8.16
25.4
10.9
51.3
9.59
207
23.4
16.2
8.64
21.6
7.04
19.2
9.38
44.3
6.28
136
22.6
17.3
10.1
26.6
14.0
22.7
18.7
50.1
9.6
Span (ft)
Fy = 36 ksi
Wt./ft
Properties and Reaction Values
Zx in.3
φbWc kip-ft
φvVn kips
φR1 kips
φR2 kips/in.
φr R3 kips
φr R4 kips/in.
φr R5 kips
φr R6 kips/in.
φR (N = 31⁄4) kips
10.8
230
26.8
12.9
8.28
17.2
7.17
14.3
9.56
39.8
11.7
253
31.7
17.5
9.36
25.8
6.34
23.2
8.46
48.0
8.30
179
27.0
12.9
8.28
17.9
6.62
15.2
8.82
39.8
6.23
135
19.5
8.61
6.12
9.95
3.56
8.55
4.74
24.0
*Indicates noncompact shape.
Load above heavy line is limited by design shear strength.
Values of R in bold face exceed maximum design web shear φvVn.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
FACTORED UNIFORM LOAD TABLES
Fy = 36 ksi
4 - 61
BEAMS
S Shapes
Maximum factored uniform loads in kips
for beams laterally supported
S 24–20
For beams laterally unsupported, see page 4-113
Designation
Wt./ft
S 24
121
12
13
14
15
16
17
90
S 20
80
96
S 20
86
75
66
521
494
439
395
359
494
472
413
367
330
300
393
378
336
302
275
591
548
695
648
576
518
471
583
533
480
436
467
441
401
551
508
472
441
413
389
502
464
430
402
377
354
432
399
370
346
324
305
400
369
343
320
300
282
367
339
315
294
275
259
356
329
305
285
267
252
329
304
282
264
247
233
275
254
236
220
207
194
252
233
216
202
189
178
18
19
20
21
22
23
367
348
330
315
300
287
335
317
301
287
274
262
288
273
259
247
236
225
266
252
240
228
218
208
245
232
220
210
200
192
238
225
214
204
194
186
220
208
198
188
180
172
184
174
165
157
150
144
168
159
151
144
137
131
24
25
26
27
28
29
275
264
254
245
236
228
251
241
232
223
215
208
216
207
199
192
185
179
200
192
184
178
171
165
184
176
169
163
157
152
178
171
164
158
153
147
165
158
152
146
141
136
138
132
127
122
118
114
126
121
116
112
108
104
30
32
34
36
38
40
220
207
194
184
174
165
201
188
177
167
159
151
173
162
152
144
136
130
160
150
141
133
126
120
147
138
130
122
116
110
143
134
126
119
113
107
132
124
116
110
104
99
110
103
97
92
87
83
101
95
89
84
80
76
42
44
46
48
50
52
157
150
144
138
132
127
143
137
131
126
121
116
123
118
113
108
104
100
114
109
104
100
96
92
105
100
96
92
88
85
102
97
93
89
86
94
90
86
82
79
79
75
72
69
66
72
69
66
63
60
54
56
58
60
122
118
114
110
112
108
104
100
96
93
89
86
89
86
83
80
82
79
76
73
Zx in.3
φbWc kip-ft
φvVn kips
φR1 kips
φR2 kips/in.
φr R3 kips
φr R4 kips/in.
φr R5 kips
φr R6 kips/in.
φR (N = 31⁄4) kips
306
6610
381
144
28.8
229
17.6
200
23.5
238
279
6030
295
112
22.3
156
8.19
143
10.9
183
183
3950
260
104
23.8
157
14.1
138
18.8
181
153
3300
247
92.9
22.9
138
14.8
118
19.7
167
140
3020
196
73.9
18.2
97.9
7.44
88.0
9.91
122
Span (ft)
762
734
661
601
100
631
611
535
475
428
389
Fy = 36 ksi
6
7
8
9
10
11
S 24
106
Properties and Reaction Values
240
5180
348
117
26.8
184
18.2
154
24.2
205
222
4800
292
98.4
22.5
141
10.7
124
14.3
172
204
4410
233
78.8
18.0
101
5.50
92.1
7.33
119
198
4280
316
126
28.8
210
25.2
176
33.6
220
Load above heavy line is limited by design shear strength.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
4 - 62
BEAM AND GIRDER DESIGN
S 18–15–12–10
BEAMS
S Shapes
Maximum factored uniform loads in kips
for beams laterally supported
Fy = 36 ksi
For beams laterally unsupported, see page 4-113
Designation
Span (ft)
Fy = 36 ksi
Wt./ft
S 18
70
3
4
5
6
7
8
498
450
386
338
9
10
11
12
13
14
S 15
54.7
50
S 12
42.9
50
S 12
40.8
35
S 10
31.8
35
25.4
121
102
88
77
240
214
187
321
264
220
189
165
216
191
164
143
200
194
161
138
121
163
151
130
113
231
191
153
127
109
96
185
167
151
139
128
119
166
150
136
125
115
107
147
132
120
110
102
94
127
115
104
96
88
82
108
97
88
81
74
69
101
91
82
76
70
65
85
76
70
64
59
55
68
61
56
51
47
44
151
142
133
126
119
113
111
104
98
93
88
83
100
94
88
83
79
75
88
83
78
73
70
66
76
72
67
64
60
57
65
60
57
54
51
48
60
57
53
50
48
45
51
48
45
42
40
38
41
38
36
34
32
31
129
123
117
113
108
104
108
103
99
95
91
87
79
76
72
69
67
64
71
68
65
62
60
58
63
60
57
55
53
51
55
52
50
48
46
44
46
44
42
40
39
37
43
41
39
38
36
35
36
35
33
32
31
29
28
27
26
25
27
28
29
30
31
32
100
96
93
90
87
84
84
81
78
76
73
71
62
59
57
56
54
52
55
53
52
50
48
47
49
47
46
44
42
41
40
38
36
35
33
32
34
32
31
30
33
34
35
36
37
38
82
79
77
75
73
71
69
67
65
63
61
60
50
49
48
46
45
45
44
43
42
40
40
42
44
68
64
61
57
54
52
125
2700
249
96.0
25.6
152
26.5
121
35.4
179
105
2270
161
62.2
16.6
79.6
7.23
70.9
9.64
103
44.8
968
99.8
45.7
15.4
63.2
11.0
54.4
14.7
95.8
42.0
907
81.6
37.4
12.6
46.7
6.03
41.9
8.04
68.0
35.4
765
115
60.1
21.4
98.2
39.2
72.0
52.2
130
28.4
613
60.5
31.5
11.2
37.2
5.62
33.4
7.50
57.8
323
284
321
278
238
208
300
270
245
225
208
193
252
227
206
189
174
162
15
16
17
18
19
20
180
169
159
150
142
135
21
22
23
24
25
26
Properties and Reaction Values
Zx in.3
φbWc kip-ft
φvVn kips
φR1 kips
φR2 kips/in.
φr R3 kips
φr R4 kips/in.
φr R5 kips
φr R6 kips/in.
φR (N = 31⁄4) kips
77.1
1670
160
68.1
19.8
98.4
16.4
82.1
21.8
132
69.3
1500
120
50.9
14.8
63.6
6.83
56.8
9.11
86.4
61.2
1320
160
88.9
24.7
141
37.6
111
50.2
169
53.1
1150
108
59.8
16.6
78.0
11.4
68.8
15.3
114
Load above heavy line is limited by design shear strength.
Values of R in bold face exceed maximum design web shear φvVn.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
FACTORED UNIFORM LOAD TABLES
Fy = 36 ksi
4 - 63
BEAMS
S 8–6–5–4–3
S Shapes
Maximum factored uniform loads in kips
for beams laterally supported
For beams laterally unsupported, see page 4-113
Designation
Wt./ft
S8
23
1
2
3
4
5
6
137
104
83
69
7
8
9
10
11
12
S6
18.4
17.25
S5
12.5
10
42
41
31
24
20
60
52
46
42
38
35
51
45
40
36
32
30
33
29
25
23
21
19
26
23
20
18
17
15
17
15
14
12
11
10
13
32
27
18
14
Zx in.3
φbWc kip-ft
φvVn kips
φR1 kips
φR2 kips/in.
φr R3 kips
φr R4 kips/in.
φr R5 kips
φr R6 kips/in.
φR (N = 31⁄4) kips
19.3
417
68.6
39.7
15.9
58.5
23.1
46.2
30.8
91.3
16.5
356
42.1
24.4
9.76
28.2
5.36
25.3
7.15
48.5
S3
7.7
7.5
5.7
41
25
17
13
10
8.50
20
14
11
8.42
7.02
51
44
29
22
17
15
30
25
19
15
13
12
11
9.70
8.73
11
9.48
8.42
7.58
7.28
6.02
3.51
75.8
15.0
13.0
6.95
14.0
5.63
12.5
7.51
35.6
2.36
51.0
20.4
21.6
12.6
32.2
50.0
22.2
66.7
62.4
1.95
42.1
9.91
10.5
6.12
10.9
5.78
9.78
7.71
30.4
Span (ft)
54
46
37
30
Fy = 36 ksi
84
71
59
108
76
57
46
38
S4
9.5
Properties and Reaction Values
10.6
229
54.2
36.6
16.7
58.1
42.9
41.0
57.1
91.0
8.47
183
27.1
18.3
8.35
20.5
5.32
18.4
7.10
41.4
5.67
122
20.8
15.6
7.70
17.3
5.52
15.5
7.36
39.4
4.04
87.3
25.3
22.0
11.7
30.8
27.1
23.6
36.2
60.1
Load above heavy line is limited by design shear strength.
Values of R in bold face exceed maximum design web shear φvVn.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
4 - 64
BEAM AND GIRDER DESIGN
MC,C 18–15
BEAMS
Channels
Maximum factored uniform loads in kips
for beams laterally supported
Fy = 36 ksi
For beams laterally unsupported, see page 4-113
Designation
MC 18
Span (ft)
Fy = 36 ksi
Wt./ft
58
51.9
C 15
45.8
42.7
50
40
33.9
303
247
206
177
154
233
218
181
156
136
3
4
5
6
7
8
490
409
341
292
255
420
374
311
267
234
350
339
282
242
212
315
268
230
201
418
368
295
246
210
184
9
10
11
12
13
14
227
204
186
170
157
146
208
187
170
156
144
133
188
169
154
141
130
121
179
161
146
134
124
115
164
147
134
123
113
105
137
124
112
103
95
88
121
109
99
91
84
78
15
16
17
18
19
20
136
128
120
114
108
102
125
117
110
104
98
93
113
106
100
94
89
85
107
100
95
89
85
80
98
92
87
82
78
74
82
77
73
69
65
62
73
68
64
60
57
54
21
22
23
24
25
26
97
93
89
85
82
79
89
85
81
78
75
72
81
77
74
71
68
65
77
73
70
67
64
62
70
67
64
61
59
57
59
56
54
51
49
48
52
49
47
45
44
42
28
30
32
34
36
38
73
68
64
60
57
54
67
62
58
55
52
49
60
56
53
50
47
45
57
54
50
47
45
42
53
49
46
43
41
44
41
39
36
34
39
36
34
32
30
40
42
44
51
49
46
47
44
42
42
40
38
40
38
37
68.2
1470
209
92.6
25.8
149
34.6
115
46.1
176
57.2
1240
152
67.3
18.7
92.5
13.2
79.3
17.7
128
50.4
1090
117
51.8
14.4
62.4
6.03
56.4
8.03
82.5
Properties and Reaction Values
Zx in.3
φbWc kip-ft
φvVn kips
φR1 kips
φR2 kips/in.
φr R3 kips
φr R4 kips/in.
φr R5 kips
φr R6 kips/in.
φR (N = 31⁄4) kips
94.6
2040
245
86.6
25.2
142
28.0
108
37.3
169
86.5
1870
210
74.3
21.6
112
17.6
91.3
23.5
144
78.4
1690
175
61.9
18.0
85.5
10.2
73.3
13.6
119
74.4
1610
157
55.7
16.2
73.0
7.44
64.1
9.91
97.2
Load above heavy line is limited by design shear strength.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
FACTORED UNIFORM LOAD TABLES
Fy = 36 ksi
4 - 65
BEAMS
Channels
Maximum factored uniform loads in kips
for beams laterally supported
MC 13
For beams laterally unsupported, see page 4-113
Designation
MC 13
Span (ft)
Fy = 36 ksi
Wt./ft
50
40
35
31.8
3
4
5
6
7
8
398
327
261
218
187
163
283
275
220
183
157
137
226
200
166
143
125
190
186
155
133
116
9
10
11
12
13
14
145
131
119
109
101
93
122
110
100
92
85
79
111
100
91
83
77
71
103
93
85
78
72
66
15
16
17
18
19
20
87
82
77
73
69
65
73
69
65
61
58
55
67
62
59
55
53
50
62
58
55
52
49
47
21
22
23
24
25
26
62
59
57
54
52
50
52
50
48
46
44
42
48
45
43
42
40
38
44
42
40
39
37
36
27
28
29
30
31
32
48
47
45
44
42
41
41
39
38
37
35
34
37
36
34
33
32
31
34
33
32
31
30
29
46.2
998
113
55.3
16.1
71.4
10.3
62.5
13.8
107
43.1
931
94.8
46.4
13.5
54.9
6.10
49.6
8.14
76.0
Properties and Reaction Values
Zx in.3
φbWc kip-ft
φvVn kips
φR1 kips
φR2 kips/in.
φr R3 kips
φr R4 kips/in.
φr R5 kips
φr R6 kips/in.
φR (N = 31⁄4) kips
60.5
1310
199
97.4
28.3
167
56.4
118
75.2
189
50.9
1100
142
69.3
20.2
100
20.3
82.5
27.1
135
Load above heavy line is limited by design shear strength.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
4 - 66
BEAM AND GIRDER DESIGN
C, MC 12
BEAMS
Channels
Maximum factored uniform loads in kips
for beams laterally supported
Fy = 36 ksi
For beams laterally unsupported, see page 4-113
Designation
Wt./ft
C 12
30
25
MC 12
20.7
50
45
40
MC 12
35
31
10.6
181
158
126
105
90
132
110
91
78
390
303
242
202
173
332
279
223
186
160
275
255
204
170
146
218
185
154
132
173
170
141
121
8
9
10
11
12
13
91
81
73
66
60
56
79
70
63
57
53
49
69
61
55
50
46
42
151
135
121
110
101
93
140
124
112
102
93
86
128
114
102
93
85
79
116
103
92
84
77
71
106
94
85
77
71
65
31
28
25
23
21
19
14
15
16
17
18
19
52
48
45
43
40
38
45
42
39
37
35
33
39
37
34
32
30
29
87
81
76
71
67
64
80
74
70
66
62
59
73
68
64
60
57
54
66
62
58
54
51
49
61
57
53
50
47
45
18
17
16
15
14
13
20
21
22
23
24
25
36
35
33
32
30
29
32
30
29
27
26
25
27
26
25
24
23
22
61
58
55
53
50
48
56
53
51
49
47
45
51
49
46
44
43
41
46
44
42
40
39
37
42
40
39
37
35
34
13
12
11
11
10
10
26
27
28
29
30
28
27
26
25
24
24
23
23
22
21
21
20
20
19
18
47
45
43
42
40
43
41
40
39
37
39
38
36
35
34
36
34
33
32
31
33
31
30
29
28
9.64
9.28
8.95
8.64
8.35
Zx in.3
φbWc kip-ft
φvVn kips
φR1 kips
φR2 kips/in.
φr R3 kips
φr R4 kips/in.
φr R5 kips
φr R6 kips/in.
φR (N = 31⁄4) kips
33.6
726
119
51.6
18.4
78.9
20.3
62.7
27.0
111
29.2
631
90.3
39.2
13.9
52.1
8.85
45.1
11.8
83.4
47.3
1020
138
69.7
21.2
116
22.4
98.1
29.9
139
42.8
924
109
55.2
16.8
81.7
11.1
72.8
14.8
110
39.3
849
86.3
43.7
13.3
57.6
5.54
53.2
7.38
77.2
11.6
251
44.3
11.8
6.84
14.1
1.70
12.7
2.26
20.1
Span (ft)
238
181
145
121
104
89
84
63
50
42
36
Fy = 36 ksi
2
3
4
5
6
7
Properties and Reaction Values
25.4
549
65.8
28.6
10.2
32.4
3.42
29.7
4.57
44.5
56.1
1210
195
98.6
30.1
195
63.6
144
84.8
196
51.7
1120
166
84.1
25.6
154
39.4
122
52.6
167
Load above heavy line is limited by design shear strength.
Values of R in bold face exceed maximum design web shear φvVn.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
FACTORED UNIFORM LOAD TABLES
Fy = 36 ksi
4 - 67
BEAMS
Channels
Maximum factored uniform loads in kips
for beams laterally supported
C, MC 10
For beams laterally unsupported, see page 4-113
Designation
Span (ft)
Fy = 36 ksi
Wt./ft
C 10
MC 10
30
25
20
2
3
4
5
6
7
262
192
144
115
96
82
205
166
124
99
83
71
8
9
10
11
12
13
72
64
57
52
48
44
14
15
16
17
18
19
20
21
22
23
24
33.6
MC 10
28.5
25
MC 10
15.3
41.1
22
147
139
104
83
69
60
93
85
68
57
49
309
280
210
168
140
120
224
180
144
120
103
165
160
128
107
91
148
139
111
93
80
113
102
85
73
66
57
42
34
28
24
8.4
62
55
50
45
41
38
52
46
42
38
35
32
43
38
34
31
28
26
105
93
84
76
70
65
90
80
72
66
60
55
80
71
64
58
53
49
70
62
56
51
46
43
64
57
51
46
42
39
21
19
17
15
14
13
41
38
36
34
32
30
35
33
31
29
28
26
30
28
26
25
23
22
24
23
21
20
19
18
60
56
53
49
47
44
52
48
45
42
40
38
46
43
40
38
36
34
40
37
35
33
31
29
36
34
32
30
28
27
12
11
11
10
9.4
8.9
29
27
26
25
24
25
24
23
22
21
21
20
19
18
17
17
16
16
15
14
42
40
38
37
35
36
34
33
31
30
32
30
29
28
27
28
27
25
24
23
25
24
23
22
21
8.5
8.1
7.7
7.4
7.1
26.6
575
131
60.6
24.2
112
64.2
68.8
85.6
139
23.0
497
102
47.3
18.9
77.1
30.6
56.7
40.9
109
29.6
639
82.6
47.8
15.3
64.3
12.3
56.1
16.3
97.5
25.8
557
73.9
42.8
13.7
54.4
8.76
48.5
11.7
86.5
23.6
510
56.4
32.6
10.4
36.2
3.89
33.6
5.19
50.5
7.86
170
33.0
10.5
6.12
11.3
1.61
10.3
2.15
Properties and Reaction Values
Zx in.3
φbWc kip-ft
φvVn kips
φR1 kips
φR2 kips/in.
φr R3 kips
φr R4 kips/in.
φr R5 kips
φr R6 kips/in.
φR (N = 31⁄4) kips
19.3
417
73.7
34.1
13.6
47.1
11.5
39.5
15.3
78.5
15.8
341
46.7
21.6
8.64
23.8
2.91
21.8
3.88
34.4
38.9
840
155
89.6
28.7
165
80.5
111
107
183
33.4
721
112
64.7
20.7
101
30.4
80.9
40.5
132
Load above heavy line is limited by design shear strength.
Values of R in bold face exceed maximum design web shear φvVn.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
17.3
4 - 68
BEAM AND GIRDER DESIGN
C, MC 9
BEAMS
Channels
Maximum factored uniform loads in kips
for beams laterally supported
Fy = 36 ksi
For beams laterally unsupported, see page 4-113
Designation
C9
Span (ft)
Fy = 36 ksi
Wt./ft
MC 9
20
15
13.4
25.4
23.9
2
3
4
5
6
7
157
121
91
73
60
52
100
97
73
58
49
42
82
68
54
45
39
157
125
100
84
72
140
120
96
80
69
8
9
10
11
12
13
45
40
36
33
30
28
36
32
29
27
24
22
34
30
27
25
23
21
63
56
50
46
42
39
60
53
48
44
40
37
14
15
16
17
18
19
26
24
23
21
20
19
21
19
18
17
16
15
19
18
17
16
15
14
36
33
31
29
28
26
34
32
30
28
27
25
20
21
22
18
17
16
15
14
13
14
13
12
25
24
23
24
23
22
23.2
501
78.7
48.1
16.2
68.5
16.9
58.4
22.5
101
22.2
480
70.0
42.8
14.4
57.4
11.9
50.3
15.8
89.6
Properties and Reaction Values
Zx in.3
φbWc kip-ft
φvVn kips
φR1 kips
φR2 kips/in.
φr R3 kips
φr R4 kips/in.
φr R5 kips
φr R6 kips/in.
φR (N = 31⁄4) kips
16.8
363
78.4
37.8
16.1
59.0
22.2
45.6
29.6
90.2
13.5
292
49.9
24.0
10.3
29.9
5.72
26.5
7.62
51.3
12.5
270
40.8
19.7
8.39
22.1
3.12
20.2
4.17
33.8
Load above heavy line is limited by design shear strength.
Values of R in bold face exceed maximum design web shear φvVn.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
FACTORED UNIFORM LOAD TABLES
Fy = 36 ksi
4 - 69
BEAMS
Channels
Maximum factored uniform loads in kips
for beams laterally supported
C, MC 8
For beams laterally unsupported, see page 4-113
Designation
C8
Span (ft)
Fy = 36 ksi
Wt./ft
MC 8
MC 8
MC 8
18.75
13.75
11.5
22.8
21.4
20
18.7
1
2
3
4
5
6
151
149
99
75
60
50
8.5
94
78
59
47
39
68
52
41
34
133
102
81
68
117
97
78
65
124
117
87
70
58
110
83
67
55
56
50
37
30
25
7
8
9
10
11
12
43
37
33
30
27
25
34
29
26
24
21
20
29
26
23
21
19
17
58
51
45
41
37
34
56
49
43
39
35
32
50
44
39
35
32
29
48
42
37
33
30
28
21
19
17
15
14
12
13
14
15
16
17
18
23
21
20
19
18
17
18
17
16
15
14
13
16
15
14
13
12
11
31
29
27
25
24
23
30
28
26
24
23
22
27
25
23
22
21
19
26
24
22
21
20
18
11
11
10
9.3
8.8
8.3
19
20
16
15
12
12
11
10
21
20
20
19
18
17
18
17
7.9
7.5
16.2
350
62.2
40.5
14.4
54.7
14.7
46.9
19.6
87.3,
15.4
333
54.9
35.7
12.7
45.4
10.1
40.0
13.5
77.0
6.91
149
27.8
12.1
6.44
12.9
2.12
11.8
2.82
21.0
Properties and Reaction Values
Zx in.3
φbWc kip-ft
φvVn kips
φR1 kips
φR2 kips/in.
φr R3 kips
φr R4 kips/in.
φr R5 kips
φr R6 kips/in.
φR (N = 31⁄4) kips
13.8
298
75.7
41.1
17.5
64.9
34.0
46.8
45.3
98.1
10.9
235
47.1
25.6
10.9
31.9
8.18
27.5
10.9
61.0
9.55
206
34.2
18.6
7.92
19.7
3.13
18.0
4.18
31.6
18.8
406
66.4
45.6
15.4
61.9
17.0
52.8
22.7
95.6
18.0
389
58.3
40.1
13.5
50.9
11.5
44.8
15.4
84.0
Load above heavy line is limited by design shear strength.
Values of R in bold face exceed maximum design web shear φvVn.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
C, MC 7–6
BEAMS
Fy = 36 ksi
FACTORED UNIFORM LOAD TABLES
Fy = 36 ksi
4 - 71
BEAMS
Channels
Maximum factored uniform loads in kips
for beams laterally supported
C 5–4–3
For beams laterally unsupported, see page 4-113
Designation
C5
Wt./ft
9
1
2
3
4
5
6
C3
7.25
5.4
6
5
4.1
63
47
31
24
19
16
37
25
19
15
13
50
30
20
15
12
10
29
24
16
12
9.8
8.1
37
19
12
9.3
7.4
6.2
30
16
11
8.1
6.5
5.4
20
14
9.4
7.0
5.6
4.7
13
12
10
9.4
8.6
7.9
11
9.5
8.4
7.6
6.9
6.3
7.0
6.1
5.4
4.9
5.3
4.6
4.0
1.72
37.2
20.8
22.0
12.8
34.0
50.6
23.8
67.4
63.7
1.50
32.4
15.0
16.0
9.29
21.0
19.2
17.1
25.7
46.1
1.30
28.1
9.91
10.5
6.12
11.2
5.51
10.1
7.34
30.4
8.7
7.6
6.7
6.1
Span (ft)
Fy = 36 ksi
7
8
9
10
11
12
C4
6.7
Properties and Reaction Values
Zx in.3
φbWc kip-ft
φvVn kips
φR1 kips
φR2 kips/in.
φr R3 kips
φr R4 kips/in.
φr R5 kips
φr R6 kips/in.
φR (N = 31⁄4) kips
4.36
94.2
31.6
21.9
11.7
32.1
19.7
25.5
26.3
60.0
3.51
75.8
18.5
12.8
6.84
14.3
3.94
13.0
5.25
30.1
2.81
60.7
25.0
19.9
11.6
30.3
25.6
23.4
34.2
57.4
2.26
48.8
14.3
11.4
6.62
13.1
4.83
11.9
6.44
32.8
Load above heavy line is limited by design shear strength.
Values of R in bold face exceed maximum design web shear φvVn.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
4 - 72
BEAM AND GIRDER DESIGN
BEAMS
W Shapes
Maximum factored uniform loads in kips
for beams laterally supported
W 44
Fy = 50 ksi
For beams laterally unsupported, see page 4-139
Designation
W 44
Span (ft)
Fy = 50 ksi
Wt./ft
335
290
262
230
20
21
22
23
24
25
2420
2310
2210
2110
2030
1940
2050
2030
1940
1850
1780
1700
1850
1810
1730
1660
1590
1520
1650
1570
1500
1430
1380
1320
26
27
28
29
30
31
1870
1800
1740
1680
1620
1570
1640
1580
1520
1470
1420
1370
1470
1410
1360
1310
1270
1230
1270
1220
1180
1140
1100
1060
32
33
34
35
36
38
1520
1470
1430
1390
1350
1280
1330
1290
1250
1220
1180
1120
1190
1150
1120
1090
1060
1000
1030
1000
971
943
917
868
40
42
44
46
48
50
1220
1160
1100
1060
1010
972
1070
1010
968
926
888
852
953
907
866
828
794
762
825
786
750
717
688
660
52
54
56
58
60
62
935
900
868
838
810
784
819
789
761
734
710
687
733
706
680
657
635
615
635
611
589
569
550
532
64
66
68
70
72
759
736
715
694
675
666
645
626
609
592
595
577
560
544
529
516
500
485
471
458
1270
38100
924
216
39.5
302
8.67
277
11.6
330
1100
33000
823
178
35.5
238
7.40
217
9.86
262
Properties and Reaction Values
Zx in.3
φbWc kip-ft
φvVn kips
φR1 kips
φR2 kips/in.
φr R3 kips
φr R4 kips/in.
φr R5 kips
φr R6 kips/in.
φR (N = 31⁄4) kips
1620
48600
1212
327
51.0
494
14.7
451
19.6
492
1420
42600
1025
258
43.5
368
10.3
338
13.8
400
Load above heavy line is limited by design shear strength.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
FACTORED UNIFORM LOAD TABLES
Fy = 50 ksi
4 - 73
BEAMS
W Shapes
Maximum factored uniform loads in kips
for beams laterally supported
W 40
For beams laterally unsupported, see page 4-139
Designation
Wt./ft
W 40
431
372
321
297
277
249
199
174*
1360
1300
1340
1330
1250
1180
1120
1070
1370
1310
1260
1200
1160
1110
1240
1180
1130
1090
1040
1000
1010
969
927
888
852
820
1240
1200
1160
1120
1080
1050
1070
1030
996
963
932
903
964
930
898
868
840
814
789
761
735
710
687
666
1140
1100
1070
1040
987
938
1020
988
960
933
884
840
875
850
825
803
760
722
789
766
744
723
685
651
646
627
609
592
561
533
950
907
867
831
798
767
893
852
815
781
750
721
800
764
730
700
672
646
688
657
628
602
578
556
620
592
566
543
521
501
507
484
463
444
426
410
789
761
734
710
687
666
739
713
688
665
644
623
694
670
647
625
605
586
622
600
579
560
542
525
535
516
498
482
466
451
482
465
449
434
420
407
395
381
367
355
344
333
645
626
609
592
605
587
570
554
568
551
536
521
509
494
480
467
438
425
413
401
395
383
372
362
323
313
304
296
1120
33600
797
264
37.5
279
8.16
258
10.9
306
963
28900
684
213
32.5
209
6.25
193
8.33
229
868
26000
679
198
32.5
195
7.21
176
9.62
218
715
21300
670
163
32.5
172
9.37
148
12.5
203
2550
2510
2160
2130
2000
2000
21
22
23
24
25
26
2790
2660
2540
2440
2340
2250
2390
2280
2180
2090
2000
1930
2030
1940
1850
1780
1700
1640
1900
1810
1730
1660
1600
1530
1780
1700
1630
1560
1500
1440
1590
1530
1460
1400
1340
1290
27
28
29
30
31
32
2170
2090
2020
1950
1890
1830
1860
1790
1730
1670
1620
1570
1580
1520
1470
1420
1370
1330
1480
1430
1380
1330
1290
1250
1390
1340
1290
1250
1210
1170
33
34
35
36
38
40
1770
1720
1670
1630
1540
1460
1520
1470
1430
1390
1320
1250
1290
1250
1220
1180
1120
1070
1210
1170
1140
1110
1050
998
42
44
46
48
50
52
1390
1330
1270
1220
1170
1130
1190
1140
1090
1040
1000
963
1010
968
926
888
852
819
54
56
58
60
62
64
1080
1040
1010
975
944
914
928
895
864
835
808
783
66
68
70
72
886
860
836
813
759
737
716
696
Zx in.3
φbWc kip-ft
φvVn kips
φR1 kips
φR2 kips/in.
φr R3 kips
φr R4 kips/in.
φr R5 kips
φr R6 kips/in.
φR (N = 31⁄4) kips
1950
58500
1493
597
67.0
859
26.7
786
35.6
814
1670
50100
1273
471
58.0
645
20.3
590
27.0
660
Span (ft)
2990
2930
Fy = 50 ksi
15
16
17
18
19
20
215
Properties and Reaction Values
1420
42600
1082
367
50.0
480
15.3
439
20.3
529
1330
39900
1000
356
46.5
415
13.2
380
17.7
458
1250
37500
889
311
41.5
342
9.90
316
13.2
374
*Noncompact shape; Fy = 50 ksi.
Load above heavy line is limited by design shear strength.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
4 - 74
BEAM AND GIRDER DESIGN
BEAMS
W Shapes
Maximum factored uniform loads in kips
for beams laterally supported
W 40
Fy = 50 ksi
For beams laterally unsupported, see page 4-139
Designation
Span (ft)
Fy = 50 ksi
Wt./ft
W 40
331
278
264
235
211
167
149
1370
1300
1350
1300
1220
1150
1300
1280
1190
1120
1050
995
1430
1360
1290
1230
1180
1130
1230
1170
1120
1070
1020
976
1090
1040
989
944
903
865
943
896
853
814
779
746
1210
1170
1120
1080
1040
1010
1090
1040
1010
970
936
905
937
901
868
837
808
781
830
798
769
741
716
692
716
689
663
640
618
597
1090
1060
1030
997
969
942
977
947
918
891
866
842
876
848
823
799
776
754
756
732
710
689
669
651
670
649
629
611
593
577
578
560
543
527
512
498
939
893
850
811
776
744
892
848
807
770
737
706
797
758
721
689
659
631
714
679
646
617
590
566
617
586
558
533
509
488
546
519
494
472
451
433
471
448
426
407
389
373
858
825
794
766
740
715
714
687
661
638
616
595
678
652
628
605
584
565
606
583
561
541
522
505
543
522
503
485
468
453
469
451
434
418
404
391
415
399
384
371
358
346
358
344
332
320
309
299
692
670
650
631
613
596
576
558
541
525
510
496
547
530
514
499
484
471
489
473
459
446
433
421
438
424
411
399
388
377
378
366
355
345
335
325
335
324
315
305
297
288
289
280
271
263
256
249
781
23400
684
213
32.5
209
6.25
193
8.33
229
692
20800
677
198
32.5
191
7.51
172
10.0
216
597
17900
650
177
31.5
164
8.53
143
11.4
192
13
14
15
16
17
18
2690
2680
2520
2380
2210
2100
1980
2070
1990
1880
1780
1680
1590
1510
19
20
21
22
23
24
2260
2150
2040
1950
1870
1790
1880
1790
1700
1620
1550
1490
1780
1700
1610
1540
1470
1410
1590
1520
1440
1380
1320
1260
25
26
27
28
29
30
1720
1650
1590
1530
1480
1430
1430
1370
1320
1280
1230
1190
1360
1300
1260
1210
1170
1130
31
32
33
34
35
36
1380
1340
1300
1260
1230
1190
1150
1120
1080
1050
1020
992
38
40
42
44
46
48
1130
1070
1020
975
933
894
50
52
54
56
58
60
62
64
66
68
70
72
183
Properties and Reaction Values
Zx in.3
φbWc kip-ft
φvVn kips
φR1 kips
φR2 kips/in.
φr R3 kips
φr R4 kips/in.
φr R5 kips
φr R6 kips/in.
φR (N = 31⁄4) kips
1430
42900
1344
505
61.0
709
22.6
648
30.1
703
1190
35700
1106
383
51.0
500
15.8
458
21.1
548
1130
33900
1037
353
48.0
446
13.8
409
18.4
491
1010
30300
889
285
41.5
342
9.90
316
13.2
374
905
27200
797
246
37.5
279
8.19
257
10.9
305
Load above heavy line is limited by design shear strength.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
FACTORED UNIFORM LOAD TABLES
Fy = 50 ksi
4 - 75
BEAMS
W Shapes
Maximum factored uniform loads in kips
for beams laterally supported
W 36
For beams laterally unsupported, see page 4-139
Designation
W 36
Span (ft)
Fy = 50 ksi
Wt./ft
300
280
260
245
230
1560
1520
1440
1380
1320
1260
1470
1410
1350
1290
1230
1180
19
20
21
22
23
24
1870
1800
1720
1640
1580
1750
1670
1600
1530
1460
1640
1620
1540
1470
1410
1350
25
26
27
28
29
30
1510
1450
1400
1350
1300
1260
1400
1350
1300
1250
1210
1170
1300
1250
1200
1160
1120
1080
1210
1170
1120
1080
1040
1010
1130
1090
1050
1010
976
943
31
32
33
34
35
36
1220
1180
1150
1110
1080
1050
1130
1100
1060
1030
1000
975
1050
1010
982
953
926
900
977
947
918
891
866
842
913
884
857
832
808
786
38
40
42
44
46
48
995
945
900
859
822
788
924
878
836
798
763
731
853
810
771
736
704
675
797
758
721
689
659
631
744
707
674
643
615
589
50
52
54
56
58
60
756
727
700
675
652
630
702
675
650
627
605
585
648
623
600
579
559
540
606
583
561
541
522
505
566
544
524
505
488
472
62
64
66
68
70
72
610
591
573
556
540
525
566
548
532
516
501
488
523
506
491
476
463
450
489
473
459
446
433
421
456
442
429
416
404
393
1010
30300
779
250
40.0
300
11.4
272
15.2
337
943
28300
737
226
38.0
268
10.5
243
14.0
302
Properties and Reaction Values
Zx in.3
φbWc kip-ft
φvVn kips
φR1 kips
φR2 kips/in.
φr R3 kips
φr R4 kips/in.
φr R5 kips
φr R6 kips/in.
φR (N = 31⁄4) kips
1260
37800
937
332
47.3
429
14.8
393
19.7
477
1170
35100
873
297
44.3
376
13.1
344
17.4
419
1080
32400
822
269
42.0
333
12.3
303
16.4
373
Load above heavy line is limited by design shear strength.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
4 - 76
BEAM AND GIRDER DESIGN
W 36
BEAMS
W Shapes
Maximum factored uniform loads in kips
for beams laterally supported
Fy = 50 ksi
For beams laterally unsupported, see page 4-139
Designation
Wt./ft
W 36
256
19
20
21
22
23
24
194
182
170
160
150
135
1740
1650
1560
1640
1560
1470
1390
1510
1440
1350
1280
1420
1350
1270
1200
1330
1250
1180
1110
1260
1250
1170
1100
1040
1210
1160
1090
1030
968
1640
1560
1490
1420
1360
1300
1480
1400
1340
1280
1220
1170
1320
1250
1190
1140
1090
1040
1210
1150
1100
1050
1000
959
1130
1080
1030
979
937
898
1050
1000
954
911
871
835
985
936
891
851
814
780
917
872
830
792
758
726
804
764
727
694
664
636
25
26
27
28
29
30
1250
1200
1160
1110
1080
1040
1120
1080
1040
1000
968
936
1000
961
926
893
862
833
920
885
852
822
793
767
862
828
798
769
743
718
802
771
742
716
691
668
749
720
693
669
646
624
697
670
646
623
601
581
611
587
566
545
527
509
31
32
33
34
35
36
1010
975
945
918
891
867
906
878
851
826
802
780
806
781
757
735
714
694
742
719
697
677
657
639
695
673
653
634
615
598
646
626
607
589
573
557
604
585
567
551
535
520
562
545
528
513
498
484
493
477
463
449
436
424
38
40
42
44
46
48
821
780
743
709
678
650
739
702
669
638
610
585
658
625
595
568
543
521
606
575
548
523
500
479
567
539
513
490
468
449
527
501
477
455
436
418
493
468
446
425
407
390
459
436
415
396
379
363
402
382
364
347
332
318
50
52
54
56
58
60
624
600
578
557
538
520
562
540
520
501
484
468
500
481
463
446
431
417
460
443
426
411
397
384
431
414
399
385
371
359
401
385
371
358
346
334
374
360
347
334
323
312
349
335
323
311
301
291
305
294
283
273
263
255
62
64
66
68
70
72
503
488
473
459
446
433
453
439
425
413
401
390
403
390
379
368
357
347
371
360
349
338
329
320
347
337
326
317
308
299
323
313
304
295
286
278
302
293
284
275
267
260
281
272
264
256
249
242
246
239
231
225
218
212
Zx in.3
φbWc kip-ft
φvVn kips
φR1 kips
φR2 kips/in.
φr R3 kips
φr R4 kips/in.
φr R5 kips
φr R6 kips/in.
φR (N = 31⁄4) kips
1040
31200
970
315
48.0
446
14.8
409
19.7
471
936
28100
872
272
43.5
367
12.2
336
16.3
406
668
20000
664
170
34.0
212
8.55
191
11.4
240
624
18700
632
157
32.5
191
8.09
171
10.8
217
581
17400
605
146
31.3
173
7.84
154
10.5
198
509
15300
576
127
30.0
149
8.32
129
11.1
176
Span (ft)
1940
1840
1730
210
1150
1090
1020
954
898
848
Fy = 50 ksi
13
14
15
16
17
18
232
Properties and Reaction Values
833
25000
822
240
41.5
318
12.4
288
16.5
358
767
23000
754
209
38.3
271
10.5
245
14.0
305
718
21500
711
193
36.3
242
9.62
219
12.8
273
Load above heavy line is limited by design shear strength.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
FACTORED UNIFORM LOAD TABLES
Fy = 50 ksi
4 - 77
BEAMS
W Shapes
Maximum factored uniform loads in kips
for beams laterally supported
W 33
For beams laterally unsupported, see page 4-139
Designation
Span (ft)
Fy = 50 ksi
Wt./ft
W 33
241
221
W 33
201
169
152
141
130
118
1050
986
932
883
839
799
964
907
857
812
771
734
876
824
778
737
701
667
778
732
692
655
623
593
16
17
18
19
20
21
1530
1480
1410
1340
1420
1350
1280
1220
1300
1290
1220
1160
1100
1180
1110
1050
993
944
899
22
23
24
25
26
27
1280
1220
1170
1130
1080
1040
1170
1120
1070
1030
987
950
1050
1010
965
926
891
858
858
820
786
755
726
699
762
729
699
671
645
621
701
670
643
617
593
571
637
609
584
560
539
519
566
541
519
498
479
461
28
29
30
31
32
33
1010
971
939
909
880
854
916
884
855
827
802
777
827
799
772
747
724
702
674
651
629
609
590
572
599
578
559
541
524
508
551
532
514
497
482
467
500
483
467
452
438
425
445
429
415
402
389
377
34
35
36
37
38
40
829
805
783
761
741
704
754
733
713
693
675
641
681
662
643
626
609
579
555
539
524
510
497
472
493
479
466
453
441
419
454
441
428
417
406
386
412
400
389
379
369
350
366
356
346
336
328
311
42
44
46
48
50
52
671
640
612
587
563
542
611
583
558
534
513
493
551
526
503
483
463
445
449
429
410
393
377
363
399
381
365
349
335
323
367
350
335
321
308
297
334
318
305
292
280
269
296
283
271
259
249
239
54
56
58
60
62
64
522
503
486
470
454
440
475
458
442
428
414
401
429
414
399
386
374
362
349
337
325
315
304
295
311
299
289
280
270
262
286
275
266
257
249
241
259
250
242
234
226
219
231
222
215
208
201
195
66
68
70
72
427
414
402
391
389
377
366
356
351
341
331
322
286
278
270
262
254
247
240
233
234
227
220
214
212
206
200
195
189
183
178
173
514
15400
544
132
30.3
166
7.49
150
9.99
191
467
14000
518
122
29.0
147
7.46
131
9.95
172
415
12500
488
107
27.5
127
7.40
110
9.87
151
Properties and Reaction Values
Zx in.3
φbWc kip-ft
φvVn kips
φR1 kips
φR2 kips/in.
φr R3 kips
φr R4 kips/in.
φr R5 kips
φr R6 kips/in.
φR (N = 31⁄4) kips
939
28200
766
227
41.5
323
12.9
293
17.2
362
855
25700
710
200
38.8
278
11.6
251
15.5
316
772
23200
650
173
35.8
234
10.2
211
13.6
267
629
18900
612
173
33.5
218
7.89
201
10.5
244
559
16800
574
149
31.8
187
7.84
170
10.5
213
Load above heavy line is limited by design shear strength.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
4 - 78
BEAM AND GIRDER DESIGN
W 30
BEAMS
W Shapes
Maximum factored uniform loads in kips
for beams laterally supported
Fy = 50 ksi
For beams laterally unsupported, see page 4-139
Designation
W 30
Span (ft)
Fy = 50 ksi
Wt./ft
261
235
191
173
1290
1250
1180
1120
1070
1180
1120
1060
1010
961
1080
1070
1010
955
908
864
1150
1100
1060
1010
975
939
1020
977
936
899
864
832
918
878
841
808
777
748
825
789
756
726
698
672
1010
973
941
911
882
855
905
874
845
818
792
768
803
775
749
725
702
681
721
696
673
651
631
612
648
626
605
585
567
550
34
36
38
40
42
44
830
784
743
706
672
642
746
704
667
634
604
576
661
624
591
562
535
511
594
561
531
505
481
459
534
504
478
454
432
413
46
48
50
52
54
56
614
588
565
543
523
504
551
528
507
488
469
453
488
468
449
432
416
401
439
421
404
388
374
361
395
378
363
349
336
324
58
60
62
64
66
68
487
471
455
441
428
415
437
423
409
396
384
373
387
375
362
351
340
330
348
337
326
315
306
297
313
303
293
284
275
267
70
72
403
392
362
352
321
312
288
280
259
252
673
20200
588
172
35.5
235
10.7
213
14.2
269
605
18200
538
154
32.8
197
9.38
178
12.5
228
16
17
18
19
20
21
1590
1570
1490
1410
1340
1400
1330
1270
1210
22
23
24
25
26
27
1280
1230
1180
1130
1090
1050
28
29
30
31
32
33
211
Properties and Reaction Values
Zx in.3
φbWc kip-ft
φvVn kips
φR1 kips
φR2 kips/in.
φr R3 kips
φr R4 kips/in.
φr R5 kips
φr R6 kips/in.
φR (N = 31⁄4) kips
941
28200
794
283
46.5
415
16.7
380
22.2
434
845
25400
701
233
41.5
334
13.2
306
17.6
368
749
22500
647
206
38.8
282
12.4
257
16.5
322
Load above heavy line is limited by design shear strength.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
FACTORED UNIFORM LOAD TABLES
Fy = 50 ksi
4 - 79
BEAMS
W Shapes
Maximum factored uniform loads in kips
for beams laterally supported
W 30
For beams laterally unsupported, see page 4-139
Designation
Span (ft)
Fy = 50 ksi
Wt./ft
W 30
148
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
36
38
40
42
44
46
48
50
52
54
56
58
60
62
64
66
68
70
72
1080
1070
1000
938
882
833
789
750
714
682
652
625
600
577
556
536
517
500
484
469
455
441
417
395
375
357
341
326
313
300
288
278
268
259
250
242
234
227
221
214
208
132
1010
936
874
819
771
728
690
656
624
596
570
546
524
504
486
468
452
437
423
410
397
386
364
345
328
312
298
285
273
262
252
243
234
226
219
211
205
199
193
187
182
124
953
942
874
816
765
720
680
644
612
583
556
532
510
490
471
453
437
422
408
395
383
371
360
340
322
306
291
278
266
255
245
235
227
219
211
204
197
191
185
180
175
170
116
108
99
90
916
872
810
756
709
667
630
597
567
540
515
493
473
454
436
420
405
391
378
366
354
344
334
315
298
284
270
258
247
236
227
218
210
203
196
189
183
177
172
167
162
158
878
865
798
741
692
649
611
577
546
519
494
472
451
433
415
399
384
371
358
346
335
324
315
305
288
273
260
247
236
226
216
208
200
192
185
179
173
167
162
157
153
148
144
833
780
720
669
624
585
551
520
493
468
446
425
407
390
374
360
347
334
323
312
302
293
284
275
260
246
234
223
213
203
195
187
180
173
167
161
156
151
146
142
138
134
130
749
708
653
606
566
531
499
472
447
425
404
386
369
354
340
327
314
303
293
283
274
265
257
250
236
223
212
202
193
185
177
170
163
157
152
146
142
137
133
129
125
121
118
346
10400
439
106
27.3
126
7.73
111
10.3
152
312
9360
416
93.4
26.0
111
7.66
95.6
10.2
136
283
8490
375
77.1
23.5
90.8
6.24
78.5
8.31
111
Properties and Reaction Values
Zx in.3
φbWc kip-ft
φvVn kips
φR1 kips
φR2 kips/in.
φr R3 kips
φr R4 kips/in.
φr R5 kips
φr R6 kips/in.
φR (N = 31⁄4) kips
500
15000
538
163
32.5
205
8.21
189
10.9
232
437
13100
503
135
30.8
174
8.30
157
11.1
201
408
12200
477
123
29.2
156
7.72
140
10.3
181
378
11300
458
115
28.3
141
7.65
126
10.2
166
Load above heavy line is limited by design shear strength.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
4 - 80
BEAM AND GIRDER DESIGN
BEAMS
W Shapes
Maximum factored uniform loads in kips
for beams laterally supported
W 27
Fy = 50 ksi
For beams laterally unsupported, see page 4-139
Designation
Span (ft)
Fy = 50 ksi
Wt./ft
W 27
258
235
194
178
161
146
1270
1250
1180
1120
1060
1140
1110
1050
992
942
1090
1060
1000
945
895
851
983
960
904
853
808
768
895
864
814
768
728
692
1100
1050
1000
961
923
887
1010
965
923
885
850
817
897
856
819
785
754
725
810
773
740
709
680
654
731
698
668
640
614
591
659
629
601
576
553
532
944
911
879
850
823
797
854
824
796
769
744
721
787
759
732
708
685
664
698
673
650
628
608
589
630
608
587
567
549
532
569
549
530
512
495
480
512
494
477
461
446
432
33
34
35
36
37
38
773
750
729
708
689
671
699
679
659
641
624
607
644
625
607
590
574
559
571
554
538
523
509
496
515
500
486
473
460
448
465
452
439
427
415
404
419
407
395
384
374
364
40
42
44
46
48
50
638
607
580
554
531
510
577
549
524
502
481
461
531
506
483
462
443
425
471
449
428
410
393
377
425
405
387
370
354
340
384
366
349
334
320
307
346
329
314
301
288
277
52
54
56
58
60
62
490
472
455
440
425
411
444
427
412
398
385
372
408
393
379
366
354
343
362
349
336
325
314
304
327
315
304
293
284
274
295
284
274
265
256
248
266
256
247
238
231
223
64
66
398
386
360
350
332
322
294
285
266
258
240
233
216
210
567
17000
544
170
36.3
243
12.5
220
16.6
283
512
15400
492
150
33.0
201
10.4
182
13.9
235
461
13800
447
128
30.3
168
8.97
151
12.0
197
15
16
17
18
19
20
1530
1500
1420
1340
1280
1410
1360
1280
1210
1150
21
22
23
24
25
26
1210
1160
1110
1060
1020
981
27
28
29
30
31
32
217
Properties and Reaction Values
Zx in.3
φbWc kip-ft
φvVn kips
φR1 kips
φR2 kips/in.
φr R3 kips
φr R4 kips/in.
φr R5 kips
φr R6 kips/in.
φR (N = 31⁄4) kips
850
25500
767
306
49.0
465
19.9
427
26.5
466
769
23100
704
263
45.5
397
17.7
363
23.6
411
708
21200
637
227
41.5
334
14.5
306
19.3
362
628
18800
569
193
37.5
271
12.1
248
16.2
311
Load above heavy line is limited by design shear strength.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
FACTORED UNIFORM LOAD TABLES
Fy = 50 ksi
4 - 81
BEAMS
W Shapes
Maximum factored uniform loads in kips
for beams laterally supported
W 27
For beams laterally unsupported, see page 4-139
Designation
W 27
Span (ft)
Fy = 50 ksi
Wt./ft
129
102
94
84
840
792
735
686
643
753
704
654
610
572
712
695
642
596
556
521
663
610
563
523
488
458
697
658
624
593
564
539
605
572
542
515
490
468
538
508
482
458
436
416
491
463
439
417
397
379
431
407
385
366
349
333
23
24
25
26
27
28
515
494
474
456
439
423
447
429
412
396
381
368
398
381
366
352
339
327
363
348
334
321
309
298
318
305
293
282
271
261
29
30
31
32
33
34
409
395
382
370
359
349
355
343
332
322
312
303
316
305
295
286
277
269
288
278
269
261
253
245
252
244
236
229
222
215
36
38
40
42
44
46
329
312
296
282
269
258
286
271
257
245
234
224
254
241
229
218
208
199
232
219
209
199
190
181
203
193
183
174
166
159
48
50
52
54
56
58
247
237
228
219
212
204
214
206
198
191
184
177
191
183
176
169
163
158
174
167
160
154
149
144
153
146
141
136
131
126
60
62
64
66
198
191
185
180
172
166
161
156
153
148
143
139
139
135
130
126
122
118
114
111
278
8340
356
88.0
24.5
107
6.35
95.4
8.46
127
244
7320
332
79.1
23.0
90.0
6.16
79.0
8.21
110
11
12
13
14
15
16
910
846
790
741
17
18
19
20
21
22
114
Properties and Reaction Values
Zx in.3
φbWc kip-ft
φvVn kips
φR1 kips
φR2 kips/in.
φr R3 kips
φr R4 kips/in.
φr R5 kips
φr R6 kips/in.
φR (N = 31⁄4) kips
395
11900
455
138
30.5
180
8.08
165
10.8
206
343
10300
420
116
28.5
150
7.89
135
10.5
175
305
9150
377
101
25.8
121
6.57
110
8.76
143
Load above heavy line is limited by design shear strength.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
4 - 82
BEAM AND GIRDER DESIGN
W 24
BEAMS
W Shapes
Maximum factored uniform loads in kips
for beams laterally supported
Fy = 50 ksi
For beams laterally unsupported, see page 4-139
Designation
Wt./ft
W 24
131
117
104
952
936
878
826
780
868
836
784
738
697
800
793
740
694
653
617
721
701
654
613
577
545
650
619
578
542
510
482
807
767
730
697
667
639
739
702
669
638
610
585
660
627
597
570
545
523
584
555
529
505
483
463
516
491
467
446
427
409
456
434
413
394
377
361
671
645
621
599
578
559
613
590
568
548
529
511
562
540
520
501
484
468
502
482
464
448
432
418
444
427
411
396
383
370
392
377
363
350
338
327
347
333
321
310
299
289
586
568
551
535
519
505
541
524
508
493
479
466
495
479
465
451
438
426
453
439
425
413
401
390
405
392
380
369
358
348
358
347
336
326
317
308
316
307
297
289
280
273
280
271
263
255
248
241
534
507
483
461
441
423
478
455
433
413
395
379
441
419
399
381
365
349
403
383
365
348
333
319
369
351
334
319
305
293
330
314
299
285
273
261
292
278
264
252
241
231
258
245
234
223
213
204
228
217
206
197
188
181
50
52
54
56
58
60
406
390
376
362
350
338
364
350
337
325
313
303
335
323
311
299
289
280
307
295
284
274
264
256
281
270
260
251
242
234
251
241
232
224
216
209
222
213
206
198
191
185
196
189
182
175
169
164
173
167
161
155
149
145
Zx in.3
φbWc kip-ft
φvVn kips
φR1 kips
φR2 kips/in.
φr R3 kips
φr R4 kips/in.
φr R5 kips
φr R6 kips/in.
φR (N = 31⁄4) kips
676
20300
674
300
48.0
446
21.3
409
28.4
456
606
18200
604
258
43.5
367
17.6
336
23.5
400
370
11100
400
132
30.3
166
10.2
150
13.6
199
327
9810
360
112
27.5
136
8.73
121
11.6
164
289
8670
325
93.8
25.0
110
7.49
98.4
9.99
135
Span (ft)
146
Fy = 50 ksi
229
207
192
176
13
14
15
16
17
18
1350
1270
1190
1130
1210
1140
1070
1010
1110
1050
986
932
1020
1020
958
902
852
19
20
21
22
23
24
1070
1010
966
922
882
845
957
909
866
826
790
758
883
839
799
762
729
699
25
26
27
28
29
30
811
780
751
724
699
676
727
699
673
649
627
606
31
32
33
34
35
36
654
634
615
596
579
563
38
40
42
44
46
48
162
Properties and Reaction Values
559
16800
557
228
40.5
318
15.5
291
20.6
359
511
15300
511
199
37.5
271
13.5
248
18.0
315
468
14000
476
176
35.3
236
12.4
215
16.6
276
418
12500
434
152
32.5
197
11.0
179
14.7
233
Load above heavy line is limited by design shear strength.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
FACTORED UNIFORM LOAD TABLES
Fy = 50 ksi
4 - 83
BEAMS
W Shapes
Maximum factored uniform loads in kips
for beams laterally supported
W 24
For beams laterally unsupported, see page 4-139
Designation
Span (ft)
Fy = 50 ksi
Wt./ft
W 24
103
94
84
W 24
76
68
62
55
551
510
459
417
383
503
503
447
402
365
335
7
8
9
10
11
12
729
700
676
635
612
611
560
568
545
500
532
531
483
443
13
14
15
16
17
18
646
600
560
525
494
467
586
544
508
476
448
423
517
480
448
420
395
373
462
429
400
375
353
333
408
379
354
332
312
295
353
328
306
287
270
255
309
287
268
251
236
223
19
20
21
22
23
24
442
420
400
382
365
350
401
381
363
346
331
318
354
336
320
305
292
280
316
300
286
273
261
250
279
266
253
241
231
221
242
230
219
209
200
191
212
201
191
183
175
168
25
26
27
28
29
30
336
323
311
300
290
280
305
293
282
272
263
254
269
258
249
240
232
224
240
231
222
214
207
200
212
204
197
190
183
177
184
177
170
164
158
153
161
155
149
144
139
134
31
32
33
34
35
36
271
263
255
247
240
233
246
238
231
224
218
212
217
210
204
198
192
187
194
188
182
176
171
167
171
166
161
156
152
148
148
143
139
135
131
128
130
126
122
118
115
112
38
40
42
44
46
48
221
210
200
191
183
175
201
191
181
173
166
159
177
168
160
153
146
140
158
150
143
136
130
125
140
133
126
121
115
111
121
115
109
104
100
96
106
101
96
91
87
84
50
52
54
56
58
60
168
162
156
150
145
140
152
147
141
136
131
127
134
129
124
120
116
112
120
115
111
107
103
106
102
98
95
92
92
88
85
82
79
80
77
74
72
69
177
5310
266
71.3
20.8
73.7
5.57
64.9
7.43
91.8
153
4590
276
73.9
21.5
78.1
6.14
68.4
8.19
98.1
134
4020
251
64.8
19.8
63.6
5.60
54.8
7.47
81.8
Properties and Reaction Values
Zx in.3
φbWc kip-ft
φvVn kips
φR1 kips
φR2 kips/in.
φr R3 kips
φr R4 kips/in.
φr R5 kips
φr R6 kips/in.
φR (N = 31⁄4) kips
280
8400
364
120
27.5
146
7.49
133
9.98
170
254
7620
338
105
25.8
125
6.95
113
9.26
147
224
6720
306
91.8
23.5
102
6.05
92.2
8.07
122
200
6000
284
79.1
22.0
86.8
5.67
77.8
7.55
105
Load above heavy line is limited by design shear strength.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
4 - 84
BEAM AND GIRDER DESIGN
BEAMS
W Shapes
Maximum factored uniform loads in kips
for beams laterally supported
W 21
Fy = 50 ksi
For beams laterally unsupported, see page 4-139
Designation
Span (ft)
Fy = 50 ksi
Wt./ft
W 21
201
182
166
147
132
122
111
101
766
714
666
624
588
555
702
658
614
576
542
512
639
598
558
523
492
465
577
542
506
474
446
422
13
14
15
16
17
18
1130
1060
994
935
883
1020
952
893
840
793
910
864
810
762
720
858
799
746
699
658
622
19
20
21
22
23
24
837
795
757
723
691
663
752
714
680
649
621
595
682
648
617
589
563
540
589
560
533
509
487
466
526
500
476
454
434
416
485
461
439
419
400
384
441
419
399
380
364
349
399
380
361
345
330
316
25
26
27
28
29
30
636
612
589
568
548
530
571
549
529
510
492
476
518
498
480
463
447
432
448
430
414
400
386
373
400
384
370
357
344
333
368
354
341
329
318
307
335
322
310
299
289
279
304
292
281
271
262
253
31
32
33
34
35
36
513
497
482
468
454
442
461
446
433
420
408
397
418
405
393
381
370
360
361
350
339
329
320
311
322
312
303
294
285
278
297
288
279
271
263
256
270
262
254
246
239
233
245
237
230
223
217
211
38
40
42
44
46
48
418
398
379
361
346
331
376
357
340
325
310
298
341
324
309
295
282
270
294
280
266
254
243
233
263
250
238
227
217
208
242
230
219
209
200
192
220
209
199
190
182
174
200
190
181
173
165
158
50
52
318
306
286
275
259
249
224
215
200
192
184
177
167
161
152
146
307
9210
351
127
30.0
164
11.2
148
15.0
201
279
8370
319
112
27.5
138
9.56
124
12.8
169
253
7590
288
97.7
25.0
114
7.91
103
10.6
140
Properties and Reaction Values
Zx in.3
φbWc kip-ft
φvVn kips
φR1 kips
φR2 kips/in.
φr R3 kips
φr R4 kips/in.
φr R5 kips
φr R6 kips/in.
φR (N = 31⁄4) kips
530
15900
566
270
45.5
400
21.7
366
29.0
418
476
14300
509
233
41.5
332
18.4
304
24.5
368
432
13000
455
199
37.5
273
14.9
251
19.9
321
373
11200
429
169
36.0
236
15.9
213
21.2
286
333
9990
383
147
32.5
192
13.1
173
17.5
235
Load above heavy line is limited by design shear strength.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
FACTORED UNIFORM LOAD TABLES
Fy = 50 ksi
4 - 85
BEAMS
W Shapes
Maximum factored uniform loads in kips
for beams laterally supported
W 21
For beams laterally unsupported, see page 4-139
Designation
Span (ft)
Fy = 50 ksi
Wt./ft
W 21
93
83
73
W 21
68
62
57
50
44
390
358
318
286
260
239
7
8
9
10
11
12
677
663
603
553
596
588
535
490
522
516
469
430
491
480
436
400
453
432
393
360
461
430
387
352
323
427
413
367
330
300
275
13
14
15
16
17
18
510
474
442
414
390
368
452
420
392
368
346
327
397
369
344
323
304
287
369
343
320
300
282
267
332
309
288
270
254
240
298
276
258
242
228
215
254
236
220
206
194
183
220
204
191
179
168
159
19
20
21
22
23
24
349
332
316
301
288
276
309
294
280
267
256
245
272
258
246
235
224
215
253
240
229
218
209
200
227
216
206
196
188
180
204
194
184
176
168
161
174
165
157
150
143
138
151
143
136
130
124
119
25
26
27
28
29
30
265
255
246
237
229
221
235
226
218
210
203
196
206
198
191
184
178
172
192
185
178
171
166
160
173
166
160
154
149
144
155
149
143
138
133
129
132
127
122
118
114
110
114
110
106
102
99
95
31
32
33
34
35
36
214
207
201
195
189
184
190
184
178
173
168
163
166
161
156
152
147
143
155
150
145
141
137
133
139
135
131
127
123
120
125
121
117
114
111
108
106
103
100
97
94
92
92
89
87
84
82
80
38
40
42
44
46
48
174
166
158
151
144
138
155
147
140
134
128
123
136
129
123
117
112
108
126
120
114
109
104
100
114
108
103
98
94
90
102
97
92
88
84
81
87
83
79
75
72
69
75
72
68
65
62
60
50
52
133
128
118
113
103
99
96
92
86
83
77
74
66
63
57
129
3870
230
69.6
20.3
74.9
5.25
67.6
7.00
92.0
110
3300
214
62.3
19.0
61.8
5.33
54.4
7.10
79.1
95.4
2860
195
52.0
17.5
50.1
4.99
43.2
6.65
66.3
Properties and Reaction Values
Zx in.3
φbWc kip-ft
φvVn kips
φR1 kips
φR2 kips/in.
φr R3 kips
φr R4 kips/in.
φr R5 kips
φr R6 kips/in.
φR (N = 31⁄4) kips
221
6630
339
122
29.0
154
10.5
138
14.0
188
196
5880
298
101
25.8
122
8.26
110
11.0
149
172
5160
261
85.3
22.8
95.2
6.48
86.0
8.64
116
160
4800
245
77.3
21.5
84.2
5.94
75.8
7.92
103
144
4320
227
68.8
20.0
71.5
5.36
64.0
7.15
89.0
Load above heavy line is limited by design shear strength.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
4 - 86
BEAM AND GIRDER DESIGN
W 18
BEAMS
W Shapes
Maximum factored uniform loads in kips
for beams laterally supported
Fy = 50 ksi
For beams laterally unsupported, see page 4-139
Designation
Span (ft)
Fy = 50 ksi
Wt./ft
W 18
192
175
158
W 18
143
130
119
106
97
86
76
597
575
531
493
460
431
537
528
487
452
422
396
477
465
429
399
372
349
418
408
376
349
326
306
11
12
13
14
15
16
1050
1020
947
884
829
963
918
853
796
746
863
822
763
712
668
768
743
690
644
604
696
672
624
582
546
671
653
602
559
522
489
17
18
19
20
21
22
780
737
698
663
631
603
702
663
628
597
569
543
628
593
562
534
509
485
568
537
508
483
460
439
514
485
459
437
416
397
461
435
412
392
373
356
406
383
363
345
329
314
372
352
333
317
301
288
328
310
294
279
266
254
288
272
257
245
233
222
23
24
25
26
27
28
577
553
530
510
491
474
519
498
478
459
442
426
464
445
427
411
396
381
420
403
386
372
358
345
380
364
349
336
323
312
340
326
313
301
290
280
300
288
276
265
256
246
275
264
253
243
234
226
243
233
223
215
207
199
213
204
196
188
181
175
29
30
31
32
33
34
457
442
428
414
402
390
412
398
385
373
362
351
368
356
345
334
324
314
333
322
312
302
293
284
301
291
282
273
265
257
270
261
253
245
237
230
238
230
223
216
209
203
218
211
204
198
192
186
192
186
180
174
169
164
169
163
158
153
148
144
35
36
37
38
39
40
379
368
358
349
340
332
341
332
323
314
306
299
305
297
289
281
274
267
276
268
261
254
248
242
249
243
236
230
224
218
224
218
212
206
201
196
197
192
186
182
177
173
181
176
171
167
162
158
159
155
151
147
143
140
140
136
132
129
125
122
42
44
316
301
284
271
254
243
230
220
208
198
186
178
164
157
151
144
133
127
116
111
442
13300
527
293
48.0
449
26.9
412
35.8
449
398
11900
482
250
44.5
382
23.9
350
31.9
395
230
6900
298
120
29.5
158
12.6
143
16.8
199
211
6330
269
104
26.8
132
10.2
119
13.7
165
186
5580
238
86.3
24.0
105
8.45
94.9
11.3
133
163
4890
209
73.0
21.3
82.4
6.71
74.3
8.94
104
Properties and Reaction Values
Zx in.3
φbWc kip-ft
φvVn kips
φR1 kips
φR2 kips/in.
φr R3 kips
φr R4 kips/in.
φr R5 kips
φr R6 kips/in.
φR (N = 31⁄4) kips
356
10700
431
215
40.5
315
20.2
289
27.0
347
322
9660
384
183
36.5
258
16.4
237
21.8
301
291
8730
348
157
33.5
217
14.1
199
18.8
262
261
7830
335
143
32.8
197
15.1
178
20.2
246
Load above heavy line is limited by design shear strength.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
FACTORED UNIFORM LOAD TABLES
Fy = 50 ksi
4 - 87
BEAMS
W Shapes
Maximum factored uniform loads in kips
for beams laterally supported
W 18
For beams laterally unsupported, see page 4-139
Designation
Span (ft)
Fy = 50 ksi
Wt./ft
W 18
71
65
6
7
8
9
10
11
494
483
435
395
446
443
399
363
12
13
14
15
16
17
363
335
311
290
272
256
18
19
20
21
22
23
60
W 18
55
50
46
40
35
409
369
335
381
373
336
305
345
337
303
275
351
340
302
272
247
304
294
261
235
214
287
285
249
222
200
181
333
307
285
266
249
235
308
284
264
246
231
217
280
258
240
224
210
198
253
233
216
202
189
178
227
209
194
181
170
160
196
181
168
157
147
138
166
153
143
133
125
117
242
229
218
207
198
189
222
210
200
190
181
173
205
194
185
176
168
160
187
177
168
160
153
146
168
159
152
144
138
132
151
143
136
130
124
118
131
124
118
112
107
102
111
105
100
95
91
87
24
25
26
27
28
29
181
174
167
161
155
150
166
160
153
148
143
138
154
148
142
137
132
127
140
134
129
124
120
116
126
121
117
112
108
104
113
109
105
101
97
94
98
94
90
87
84
81
83
80
77
74
71
69
30
31
32
33
34
35
145
140
136
132
128
124
133
129
125
121
117
114
123
119
115
112
109
105
112
108
105
102
99
96
101
98
95
92
89
87
91
88
85
82
80
78
78
76
74
71
69
67
67
64
62
60
59
57
36
38
40
42
44
121
114
109
104
99
111
105
100
95
91
103
97
92
88
84
93
88
84
80
76
84
80
76
72
69
76
72
68
65
62
65
62
59
56
53
55
53
50
48
45
90.7
2720
176
56.3
18.0
60.6
4.62
55.0
6.16
75.6
78.4
2350
152
46.8
15.8
46.2
3.60
41.9
4.80
57.9
66.5
2000
143
42.2
15.0
38.6
3.88
34.0
5.18
51.3
Properties and Reaction Values
Zx in.3
φbWc kip-ft
φvVn kips
φR1 kips
φR2 kips/in.
φr R3 kips
φr R4 kips/in.
φr R5 kips
φr R6 kips/in.
φR (N = 31⁄4) kips
145
4350
247
92.8
24.8
113
8.77
102
11.7
142
133
3990
223
80.9
22.5
94.3
7.16
85.5
9.55
118
123
3690
204
71.3
20.8
80.4
6.10
73.0
8.13
100
112
3360
191
64.0
19.5
69.7
5.62
62.9
7.50
88.0
101
3030
172
55.5
17.8
57.6
4.72
51.9
6.29
72.9
Load above heavy line is limited by design shear strength.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
4 - 88
BEAM AND GIRDER DESIGN
BEAMS
W Shapes
Maximum factored uniform loads in kips
for beams laterally supported
W 16
Fy = 50 ksi
For beams laterally unsupported, see page 4-139
Designation
Span (ft)
Fy = 50 ksi
Wt./ft
W 16
100
89
77
6
7
8
9
10
11
536
475
406
12
13
14
15
16
17
495
457
424
396
371
349
438
404
375
350
328
309
18
19
20
21
22
23
330
313
297
283
270
258
24
25
26
27
28
29
W 16
67
57
50
45
W 16
40
36
31
26
212
189
166
147
133
121
348
382
350
315
286
334
307
276
251
301
274
247
224
264
243
219
199
253
240
213
192
175
236
231
203
180
162
147
375
346
321
300
281
265
325
300
279
260
244
229
263
242
225
210
197
185
230
212
197
184
173
162
206
190
176
165
154
145
182
168
156
146
137
129
160
148
137
128
120
113
135
125
116
108
101
95
111
102
95
88
83
78
292
276
263
250
239
228
250
237
225
214
205
196
217
205
195
186
177
170
175
166
158
150
143
137
153
145
138
131
125
120
137
130
123
118
112
107
122
115
109
104
99
95
107
101
96
91
87
83
90
85
81
77
74
70
74
70
66
63
60
58
248
238
228
220
212
205
219
210
202
194
188
181
188
180
173
167
161
155
163
156
150
144
139
134
131
126
121
117
113
109
115
110
106
102
99
95
103
99
95
91
88
85
91
87
84
81
78
75
80
77
74
71
69
66
68
65
62
60
58
56
55
53
51
49
47
46
30
31
32
33
34
35
198
192
186
180
175
170
175
169
164
159
154
150
150
145
141
136
132
129
130
126
122
118
115
111
105
102
98
95
93
90
92
89
86
84
81
79
82
80
77
75
73
71
73
71
68
66
64
62
64
62
60
58
56
55
54
52
51
49
48
46
44
43
41
40
39
38
36
38
40
165
156
149
146
138
131
125
118
113
108
103
98
88
83
79
77
73
69
69
65
62
61
58
55
53
51
45
43
37
35
198
5940
268
123
29.2
160
13.0
145
17.3
202
175
5250
237
103
26.2
128
10.7
116
14.2
163
72.9
2190
132
45.3
15.3
43.2
3.80
39.1
5.06
55.6
64.0
1920
126
41.5
14.7
37.9
4.07
33.6
5.43
51.2
54.0
1620
118
38.7
13.8
34.5
3.22
31.1
4.29
45.0
44.2
1330
106
33.2
12.5
26.5
3.12
23.2
4.16
36.7
Properties and Reaction Values
Zx in.3
φbWc kip-ft
φvVn kips
φR1 kips
φR2 kips/in.
φr R3 kips
φr R4 kips/in.
φr R5 kips
φr R6 kips/in.
φR (N = 31⁄4) kips
150
4500
203
81.8
22.8
96.5
8.12
87.5
10.8
123
130
3900
174
67.9
19.8
73.0
6.14
66.3
8.19
93.0
105
3150
191
73.9
21.5
86.0
7.32
78.0
9.76
110
92.0
2760
167
62.3
19.0
67.1
5.80
60.8
7.73
85.9
82.3
2470
150
53.9
17.3
54.9
4.87
49.7
6.50
70.8
Load above heavy line is limited by design shear strength.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
FACTORED UNIFORM LOAD TABLES
Fy = 50 ksi
4 - 89
BEAMS
W Shapes
Maximum factored uniform loads in kips
for beams laterally supported
W 14
For beams laterally unsupported, see page 4-139
Designation
Wt./ft
W 14
132
120
109
W 14
99*
90*
82
74
68
61
344
344
315
291
270
252
315
314
288
265
246
230
281
278
255
235
219
204
461
454
424
406
384
371
370
345
333
329
307
16
17
18
19
20
21
439
413
390
369
351
334
398
374
353
335
318
303
360
339
320
303
288
274
323
304
287
272
259
246
288
271
256
243
230
219
261
245
232
219
209
199
236
222
210
199
189
180
216
203
192
182
173
164
191
180
170
161
153
146
22
23
24
25
26
27
319
305
293
281
270
260
289
277
265
254
245
236
262
250
240
230
222
213
235
225
216
207
199
192
210
200
192
184
177
171
190
181
174
167
160
154
172
164
158
151
145
140
157
150
144
138
133
128
139
133
128
122
118
113
28
29
30
31
32
33
251
242
234
226
219
213
227
219
212
205
199
193
206
199
192
186
180
175
185
178
172
167
162
157
165
159
154
149
144
140
149
144
139
135
130
126
135
130
126
122
118
115
123
119
115
111
108
105
109
106
102
99
96
93
34
206
187
169
152
136
123
111
101
90
Zx in.3
φbWc kip-ft
φvVn kips
φR1 kips
φR2 kips/in.
φr R3 kips
φr R4 kips/in.
φr R5 kips
φr R6 kips/in.
φR (N = 31⁄4) kips
234
7020
255
136
32.3
190
19.2
171
25.6
241
212
6360
231
120
29.5
158
16.3
143
21.8
213
126
3780
172
87.9
22.5
96.5
8.86
88.1
11.8
126
115
3450
157
77.8
20.8
81.8
7.65
74.6
10.2
108
102
3060
141
67.4
18.8
66.5
6.37
60.6
8.49
88.2
Span (ft)
511
501
468
394
379
348
321
298
278
Fy = 50 ksi
10
11
12
13
14
15
Properties and Reaction Values
192
5760
203
103
26.2
127
12.7
115
16.9
170
173
5170
185
87.1
24.3
108
11.2
97.0
14.9
145
157
4610
167
75.6
22.0
88.7
9.26
80.0
12.3
120
139
4170
197
104
25.5
121
11.7
110
15.6
161
*Noncompact shape; Fy = 50 ksi.
Load above heavy line is limited by design shear strength.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
4 - 90
BEAM AND GIRDER DESIGN
BEAMS
W Shapes
Maximum factored uniform loads in kips
for beams laterally supported
W 14
Fy = 50 ksi
For beams laterally unsupported, see page 4-139
Designation
Span (ft)
Fy = 50 ksi
Wt./ft
W 14
53
48
5
6
7
8
9
10
278
261
253
235
11
12
13
14
15
16
238
218
201
187
174
163
17
18
19
20
21
22
W 14
43
38
34
W 14
30
26
22
225
209
236
231
205
185
215
205
182
164
202
177
158
142
192
172
151
134
121
171
166
142
125
111
100
214
196
181
168
157
147
190
174
161
149
139
131
168
154
142
132
123
115
149
137
126
117
109
102
129
118
109
101
95
89
110
101
93
86
80
75
91
83
77
71
66
62
154
145
138
131
124
119
138
131
124
118
112
107
123
116
110
104
99
95
109
103
97
92
88
84
96
91
86
82
78
74
83
79
75
71
68
65
71
67
63
60
57
55
59
55
52
50
47
45
23
24
25
26
27
28
114
109
105
101
97
93
102
98
94
90
87
84
91
87
84
80
77
75
80
77
74
71
68
66
71
68
66
63
61
59
62
59
57
55
53
51
52
50
48
46
45
43
43
42
40
38
37
36
29
30
31
32
33
34
90
87
84
82
79
77
81
78
76
74
71
69
72
70
67
65
63
61
64
62
60
58
56
54
56
55
53
51
50
48
49
47
46
44
43
42
42
40
39
38
37
35
34
33
32
31
30
29
47.3
1420
101
31.6
13.5
31.4
4.00
27.7
5.33
45.0
40.2
1210
95.8
29.9
12.8
30.1
3.07
27.2
4.09
40.6
33.2
996
85.3
25.2
11.5
23.0
2.86
20.4
3.81
32.8
Properties and Reaction Values
Zx in.3
φbWc kip-ft
φvVn kips
φR1 kips
φR2 kips/in.
φr R3 kips
φr R4 kips/in.
φr R5 kips
φr R6 kips/in.
φR (N = 31⁄4) kips
87.1
2610
139
66.5
18.5
65.9
5.96
60.4
7.95
86.2
78.4
2350
127
58.4
17.0
55.1
5.18
50.4
6.91
72.8
69.6
2090
112
50.0
15.3
44.2
4.24
40.4
5.65
58.7
61.5
1850
118
41.2
15.5
44.7
4.44
40.5
5.92
59.7
54.6
1640
108
35.6
14.3
37.0
3.94
33.3
5.25
50.4
Load above heavy line is limited by design shear strength.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
FACTORED UNIFORM LOAD TABLES
Fy = 50 ksi
4 - 91
BEAMS
W Shapes
Maximum factored uniform loads in kips
for beams laterally supported
W 12
For beams laterally unsupported, see page 4-139
Designation
Wt./ft
W 12
120
106
96
87
W 12
79
72
65*
58
53
225
212
195
180
167
156
425
410
378
351
328
377
368
339
315
294
348
330
305
283
264
314
298
275
255
238
284
270
249
231
216
255
238
220
204
191
16
17
18
19
20
21
349
328
310
294
279
266
308
289
273
259
246
234
276
259
245
232
221
210
248
233
220
208
198
189
223
210
198
188
179
170
203
191
180
171
162
154
179
168
159
151
143
136
162
152
144
136
130
123
146
137
130
123
117
111
22
23
24
25
26
27
254
243
233
223
215
207
224
214
205
197
189
182
200
192
184
176
170
163
180
172
165
158
152
147
162
155
149
143
137
132
147
141
135
130
125
120
130
124
119
114
110
106
118
113
108
104
100
96
106
102
97
93
90
87
28
29
30
199
192
186
176
170
164
158
152
147
141
137
132
128
123
119
116
112
108
102
99
95
93
89
86
83
81
78
Zx in.3
φbWc kip-ft
φvVn kips
φR1 kips
φR2 kips/in.
φr R3 kips
φr R4 kips/in.
φr R5 kips
φr R6 kips/in.
φR (N = 31⁄4) kips
186
5580
252
161
35.5
227
26.7
203
35.6
276
164
4920
212
129
30.5
171
19.2
154
25.7
228
96.8
2860
128
64.0
19.5
68.3
8.75
61.2
11.7
99.2
86.4
2590
118
61.9
18.0
62.3
6.47
57.1
8.63
85.1
77.9
2340
112
53.9
17.3
55.4
6.41
50.3
8.54
78.0
Span (ft)
503
465
429
399
372
237
236
216
199
185
173
Fy = 50 ksi
10
11
12
13
14
15
Properties and Reaction Values
147
4410
189
112
27.5
140
15.7
126
21.0
194
132
3960
174
96.6
25.8
120
14.6
108
19.4
171
119
3570
157
84.5
23.5
99.6
12.3
89.4
16.5
143
108
3240
142
73.9
21.5
83.2
10.5
74.7
14.0
120
*Indicates noncompact shape; Fy = 50 ksi.
Load above heavy line is limited by design shear strength.
Values of R in bold face exceed maximum design web shear φvVn.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
4 - 92
BEAM AND GIRDER DESIGN
BEAMS
W Shapes
Maximum factored uniform loads in kips
for beams laterally supported
W 12
Fy = 50 ksi
For beams laterally unsupported, see page 4-139
Designation
Span (ft)
Fy = 50 ksi
Wt./ft
W 12
50
45
4
5
6
7
8
9
244
241
218
216
10
11
12
13
14
15
217
197
181
167
155
145
16
17
18
19
20
21
W 12
40
35
30
W 12
26
22
19
16
14
154
148
124
106
93
82
142
121
101
86
75
67
129
104
87
75
65
58
190
203
192
171
173
162
144
152
140
124
173
147
126
110
98
194
176
162
149
139
129
173
157
144
133
123
115
154
140
128
118
110
102
129
118
108
99
92
86
112
101
93
86
80
74
88
80
73
68
63
59
74
67
62
57
53
49
60
55
50
46
43
40
52
47
44
40
37
35
136
128
121
114
109
103
121
114
108
102
97
92
108
101
96
91
86
82
96
90
85
81
77
73
81
76
72
68
65
62
70
66
62
59
56
53
55
52
49
46
44
42
46
44
41
39
37
35
38
35
34
32
30
29
33
31
29
27
26
25
22
23
24
25
26
27
99
94
91
87
84
80
88
84
81
78
75
72
78
75
72
69
66
64
70
67
64
61
59
57
59
56
54
52
50
48
51
49
47
45
43
41
40
38
37
35
34
33
34
32
31
30
29
27
27
26
25
24
23
22
24
23
22
21
20
19
28
29
30
78
75
72
69
67
65
62
59
51
55
53
43
46
45
37
40
38
29
31
30
25
26
26
22
21
19
18
72.4
2170
122
63.6
18.5
64.9
7.02
59.2
9.37
89.7
64.7
1940
109
52.3
16.8
53.0
5.87
48.3
7.82
73.7
29.3
879
86.4
28.4
13.0
31.2
3.63
28.2
4.85
43.9
24.7
741
77.2
23.9
11.8
24.3
3.30
21.6
4.40
35.9
20.1
603
71.2
20.6
11.0
19.2
3.63
16.3
4.83
32.0
17.4
522
64.3
17.2
10.0
15.3
3.23
12.7
4.31
26.7
Properties and Reaction Values
Zx in.3
φbWc kip-ft
φvVn kips
φR1 kips
φR2 kips/in.
φr R3 kips
φr R4 kips/in.
φr R5 kips
φr R6 kips/in.
φR (N = 31⁄4) kips
57.5
1730
95.1
46.1
14.7
41.5
4.52
37.9
6.02
57.4
51.2
1540
101
37.5
15.0
42.7
4.49
39.0
5.99
58.5
43.1
1290
86.6
30.5
13.0
31.7
3.50
28.8
4.67
44.0
37.2
1120
75.9
25.2
11.5
24.5
2.83
22.2
3.78
34.5
Load above heavy line is limited by design shear strength.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
FACTORED UNIFORM LOAD TABLES
Fy = 50 ksi
4 - 93
BEAMS
W Shapes
Maximum factored uniform loads in kips
for beams laterally supported
W 10
For beams laterally unsupported, see page 4-139
Designation
W 10
112
100
88
77
68
60
54
49
9
10
11
12
13
14
463
441
401
368
339
315
408
390
355
325
300
279
354
339
308
283
261
242
303
293
266
244
225
209
264
256
233
213
197
183
232
224
203
187
172
160
202
200
182
167
154
143
183
181
165
151
139
129
15
16
17
18
19
20
294
276
259
245
232
221
260
244
229
217
205
195
226
212
199
188
178
170
195
183
172
163
154
146
171
160
151
142
135
128
149
140
132
124
118
112
133
125
118
111
105
100
121
113
107
101
95
91
21
22
23
24
210
200
192
184
186
177
170
163
161
154
147
141
139
133
127
122
122
116
111
107
107
102
97
93
95
91
87
83
86
82
79
76
74.6
2240
116
68.9
21.0
80.9
11.5
73.1
15.4
123
66.6
2000
101
57.8
18.5
63.6
8.83
57.7
11.8
96.0
60.4
1810
91.6
50.5
17.0
53.5
7.61
48.4
10.1
81.4
Span (ft)
Fy = 50 ksi
Wt./ft
Properties and Reaction Values
Zx in.3
φbWc kip-ft
φvVn kips
φR1 kips
φR2 kips/in.
φr R3 kips
φr R4 kips/in.
φr R5 kips
φr R6 kips/in.
φR (N = 31⁄4) kips
147
4410
232
177
37.8
265
32.8
240
43.7
300
130
3900
204
149
34.0
214
27.4
194
36.5
259
113
3390
177
123
30.3
169
22.3
153
29.8
221
97.6
2930
152
99.4
26.5
130
17.5
117
23.3
185
85.3
2560
132
80.8
23.5
102
14.0
92.2
18.7
153
Load above heavy line is limited by design shear strength.
Values of φR (N = 31⁄4) in boldface exceed maximum web shear φvVn.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
4 - 94
BEAM AND GIRDER DESIGN
BEAMS
W Shapes
Maximum factored uniform loads in kips
for beams laterally supported
W 10
Fy = 50 ksi
For beams laterally unsupported, see page 4-139
Designation
Span (ft)
Fy = 50 ksi
Wt./ft
W 10
45
3
4
5
6
7
8
191
9
10
11
12
13
14
39
W 10
33
30
26
W 10
22
19
17
15
12*
101
94
75
63
54
47
138
130
108
93
81
131
112
94
80
70
124
120
96
80
69
60
169
152
146
170
157
137
145
134
117
132
130
111
98
183
165
150
137
127
118
156
140
128
117
108
100
129
116
106
97
90
83
122
110
100
91
84
78
104
94
85
78
72
67
87
78
71
65
60
56
72
65
59
54
50
46
62
56
51
47
43
40
53
48
44
40
37
34
42
38
34
31
29
27
15
16
17
18
19
20
110
103
97
92
87
82
94
88
83
78
74
70
78
73
68
65
61
58
73
69
65
61
58
55
63
59
55
52
49
47
52
49
46
43
41
39
43
41
38
36
34
32
37
35
33
31
30
28
32
30
28
27
25
24
25
23
22
21
20
19
21
22
23
24
78
75
72
69
67
64
61
59
55
53
51
49
52
50
48
46
45
43
41
39
37
35
34
33
31
29
28
27
27
26
24
23
23
22
21
20
18
17
16
16
54.9
1650
95.4
54.7
17.5
58.8
7.41
53.8
9.88
85.9
46.8
1400
84.4
44.3
15.8
46.4
6.43
42.2
8.58
70.0
21.6
648
69.1
25.4
12.5
28.3
4.18
25.5
5.57
43.6
18.7
561
65.5
22.5
12.0
24.4
4.48
21.3
5.98
40.8
16.0
480
62.0
19.8
11.5
20.7
4.88
17.4
6.51
38.6
12.6
376
50.6
14.8
9.50
13.7
3.58
11.3
4.77
26.8
Properties and Reaction Values
Zx in.3
φbWc kip-ft
φvVn kips
φR1 kips
φR2 kips/in.
φr R3 kips
φr R4 kips/in.
φr R5 kips
φr R6 kips/in.
φR (N = 31⁄4) kips
38.8
1160
76.2
38.5
14.5
37.1
6.23
33.1
8.31
60.1
36.6
1100
84.8
35.2
15.0
42.3
5.47
38.5
7.29
62.2
31.3
939
72.5
28.4
13.0
31.7
4.18
28.8
5.58
47.0
26.0
780
65.9
22.5
12.0
25.4
4.08
22.7
5.45
40.4
*Indicates noncompact shape; Fy = 50 ksi.
Load above heavy line is limited by design shear strength.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
FACTORED UNIFORM LOAD TABLES
Fy = 50 ksi
4 - 95
BEAMS
W Shapes
Maximum factored uniform loads in kips
for beams laterally supported
W8
For beams laterally unsupported, see page 4-139
Designation
W8
67
58
48
7
8
9
10
11
12
277
263
234
211
191
175
40
35
31
241
224
199
179
163
150
184
163
147
134
123
160
149
133
119
109
100
136
130
116
104
95
87
123
114
101
91
83
76
13
14
15
16
17
18
162
150
140
132
124
117
138
128
120
112
106
100
113
105
98
92
86
82
92
85
80
75
70
66
80
74
69
65
61
58
70
65
61
57
54
51
19
20
111
105
94
90
77
74
63
60
55
52
48
46
39.8
1190
80.2
47.8
18.0
58.3
10.9
52.3
14.6
99.6
34.7
1040
68.0
38.8
15.5
43.8
8.02
39.5
10.7
74.2
30.4
912
61.6
33.4
14.3
36.2
7.20
32.3
9.60
63.5
Span (ft)
Fy = 50 ksi
Wt./ft
Properties and Reaction Values
Zx in.3
φbWc kip-ft
φvVn kips
φR1 kips
φR2 kips/in.
φr R3 kips
φr R4 kips/in.
φr R5 kips
φr R6 kips/in.
φR (N = 31⁄4) kips
70.2
2110
139
102
28.5
150
23.8
136
31.7
195
59.8
1790
120
83.7
25.5
118
20.2
106
27.0
167
49.0
1470
91.8
59.4
20.0
75.5
11.9
68.8
15.9
120
Load above heavy line is limited by design shear strength.
Values of R in bold face exceed maximum design web shear φvVn.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
4 - 96
BEAM AND GIRDER DESIGN
BEAMS
W Shapes
Maximum factored uniform loads in kips
for beams laterally supported
W8
Fy = 50 ksi
For beams laterally unsupported, see page 4-139
Designation
W8
Span (ft)
Fy = 50 ksi
Wt./ft
28
W8
24
21
W8
18
15
13
10*
99
86
68
57
49
43
72
66
53
44
38
33
3
4
5
6
7
8
124
117
102
105
99
87
112
102
87
77
101
85
73
64
107
102
82
68
58
51
9
10
11
12
13
14
91
82
74
68
63
58
77
70
63
58
54
50
68
61
56
51
47
44
57
51
46
43
39
36
45
41
37
34
31
29
38
34
31
29
26
24
29
26
24
22
20
19
15
16
17
18
19
20
54
51
48
45
43
41
46
44
41
39
37
31
41
38
36
34
32
26
34
32
30
28
27
20
27
26
24
23
21
23
21
20
19
18
18
16
16
15
14
13.6
408
53.6
23.0
12.3
24.5
6.23
21.2
8.30
48.2
11.4
342
49.6
19.8
11.5
20.1
6.46
16.6
8.61
44.6
8.87
264
36.2
13.3
8.50
11.4
3.29
9.72
4.38
24.0
Properties and Reaction Values
Zx in.3
φbWc kip-ft
φvVn kips
φR1 kips
φR2 kips/in.
φr R3 kips
φr R4 kips/in.
φr R5 kips
φr R6 kips/in.
φR (N = 31⁄4) kips
27.2
816
62.0
33.4
14.3
37.4
6.68
33.8
8.91
62.8
23.2
696
52.5
26.8
12.3
27.7
5.02
25.0
6.69
46.7
20.4
612
55.9
25.4
12.5
28.5
5.10
25.7
6.81
47.8
17.0
510
50.5
21.6
11.5
22.9
4.90
20.2
6.53
41.4
*Indicates noncompact shape; Fy = 50 ksi.
Load above heavy line is limited by design shear strength.
Values of R in bold face exceed maximum design web shear φvVn.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
FACTORED UNIFORM LOAD TABLES
Fy = 50 ksi
4 - 97
BEAMS
W Shapes
Maximum factored uniform loads in kips
for beams laterally supported
W 6–5–4
For beams laterally unsupported, see page 4-139
Designation
Wt./ft
W6
25
2
3
4
5
6
7
110
95
81
8
9
10
11
12
13
20
W6
15*
16
W5
12
9
75
62
50
42
36
54
47
37
31
27
71
63
57
52
47
44
56
50
45
41
37
34
38
34
31
28
26
24
44
39
35
32
29
27
31
28
25
23
21
19
23
21
19
17
16
14
14
41
32
22
25
18
13
Zx in.3
φbWc kip-ft
φvVn kips
φR1 kips
φR2 kips/in.
φr R3 kips
φr R4 kips/in.
φr R5 kips
φr R6 kips/in.
φR (N = 31⁄4) kips
18.9
567
55.1
32.5
16.0
44.0
12.2
38.8
16.3
84.5
14.9
447
43.5
24.4
13.0
28.9
8.40
25.4
11.2
61.8
W4
16
13
75
70
58
50
65
58
48
41
63
63
47
38
31
27
44
39
35
32
29
36
32
29
26
24
24
21
19
11.6
348
37.5
27.4
13.5
33.2
9.62
29.9
12.8
71.3
9.59
288
32.5
22.5
12.0
25.4
8.29
22.7
11.1
58.6
6.28
188
31.4
24.1
14.0
31.4
16.5
26.8
22.1
69.6
Span (ft)
88
88
70
59
50
Fy = 50 ksi
87
75
64
74
62
51
44
19
Properties and Reaction Values
10.8
308
37.2
18.0
11.5
20.3
8.45
16.9
11.3
53.5
11.7
351
44.1
24.4
13.0
30.4
7.48
27.3
9.97
59.7
8.30
249
37.4
18.0
11.5
21.0
7.80
17.9
10.4
51.7
6.23
187
27.1
12.0
8.50
11.7
4.19
10.1
5.59
28.2
*Indicates noncompact shape; Fy = 50 ksi.
Load above heavy line is limited by design shear strength.
Values of R in bold face exceed maximum design web shear φvVn.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
4 - 98
BEAM AND GIRDER DESIGN
S 24–20
BEAMS
S Shapes
Maximum factored uniform loads in kips
for beams laterally supported
Fy = 50 ksi
For beams laterally unsupported, see page 4-139
Designation
Wt./ft
S 24
121
12
13
14
15
16
17
90
S 20
80
96
S 20
86
75
66
723
686
610
549
499
686
656
574
510
459
417
545
525
467
420
382
820
761
966
900
800
720
655
810
740
666
605
648
612
556
765
706
656
612
574
540
698
644
598
558
523
492
600
554
514
480
450
424
555
512
476
444
416
392
510
471
437
408
383
360
495
457
424
396
371
349
458
422
392
366
343
323
383
353
328
306
287
270
350
323
300
280
263
247
18
19
20
21
22
23
510
483
459
437
417
399
465
441
419
399
380
364
400
379
360
343
327
313
370
351
333
317
303
290
340
322
306
291
278
266
330
313
297
283
270
258
305
289
275
261
250
239
255
242
230
219
209
200
233
221
210
200
191
183
24
25
26
27
28
29
383
367
353
340
328
317
349
335
322
310
299
289
300
288
277
267
257
248
278
266
256
247
238
230
255
245
235
227
219
211
248
238
228
220
212
205
229
220
211
203
196
189
191
184
177
170
164
158
175
168
162
156
150
145
30
32
34
36
38
40
306
287
270
255
242
230
279
262
246
233
220
209
240
225
212
200
189
180
222
208
196
185
175
167
204
191
180
170
161
153
198
186
175
165
156
149
183
172
161
153
144
137
153
143
135
128
121
115
140
131
124
117
111
105
42
44
46
48
50
52
219
209
200
191
184
177
199
190
182
174
167
161
171
164
157
150
144
138
159
151
145
139
133
128
146
139
133
128
122
118
141
135
129
124
119
131
125
119
114
110
109
104
100
96
92
100
95
91
88
84
54
56
58
60
170
164
158
153
155
149
144
140
133
129
124
120
123
119
115
111
113
109
106
102
Zx in.3
φbWc kip-ft
φvVn kips
φR1 kips
φR2 kips/in.
φr R3 kips
φr R4 kips/in.
φr R5 kips
φr R6 kips/in.
φR (N = 31⁄4) kips
306
9180
529
200
40.0
269
20.7
236
27.7
330
279
8370
410
155
31.0
184
9.66
168
12.9
215
183
5490
362
144
33.0
185
16.7
163
22.2
240
153
4590
343
129
31.8
163
17.4
139
23.2
219
140
4200
273
103
25.3
115
8.76
104
11.7
144
Span (ft)
1060
1020
918
835
100
877
849
743
660
594
540
Fy = 50 ksi
6
7
8
9
10
11
S 24
106
Properties and Reaction Values
240
7200
483
163
37.3
216
21.4
182
28.6
284
222
6660
405
137
31.3
166
12.6
146
16.9
207
204
6120
324
109
25.0
119
6.48
109
8.64
140
198
5940
438
175
40.0
248
29.7
207
39.5
305
Load above heavy line is limited by design shear strength.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
FACTORED UNIFORM LOAD TABLES
Fy = 50 ksi
4 - 99
BEAMS
S 18–15–12–10
S Shapes
Maximum factored uniform loads in kips
for beams laterally supported
For beams laterally unsupported, see page 4-139
Designation
Span (ft)
Fy = 50 ksi
Wt./ft
S 18
70
3
4
5
6
7
8
691
625
536
469
9
10
11
12
13
14
S 15
54.7
50
S 12
42.9
50
S 12
40.8
35
S 10
31.8
35
25.4
168
142
122
107
333
297
260
445
367
306
262
230
299
266
228
199
277
269
224
192
168
227
210
180
158
321
266
212
177
152
133
257
231
210
193
178
165
231
208
189
173
160
149
204
184
167
153
141
131
177
159
145
133
123
114
149
134
122
112
103
96
140
126
115
105
97
90
118
106
97
89
82
76
95
85
77
71
66
61
210
197
185
175
166
158
154
145
136
129
122
116
139
130
122
116
109
104
122
115
108
102
97
92
106
100
94
89
84
80
90
84
79
75
71
67
84
79
74
70
66
63
71
66
62
59
56
53
57
53
50
47
45
43
179
170
163
156
150
144
150
143
137
131
126
121
110
105
101
96
93
89
99
95
90
87
83
80
87
83
80
77
73
71
76
72
69
66
64
61
64
61
58
56
54
52
60
57
55
53
50
48
51
48
46
44
42
41
39
37
36
34
27
28
29
30
31
32
139
134
129
125
121
117
117
113
109
105
102
98
86
83
80
77
75
72
77
74
72
69
67
65
68
66
63
61
59
57
55
53
50
48
46
45
47
45
43
42
33
34
35
36
37
38
114
110
107
104
101
99
95
93
90
88
85
83
70
68
66
64
63
63
61
59
58
56
40
42
44
94
89
85
79
75
72
125
3750
346
133
35.6
180
31.3
142
41.7
249
105
3150
224
86.4
23.1
93.8
8.52
83.6
11.4
122
44.8
1340
139
63.5
21.4
74.5
13.0
64.1
17.3
120
42.0
1260
113
52.0
17.5
55.1
7.11
49.4
9.47
80.2
35.4
1060
160
83.5
29.7
116
46.2
84.9
61.6
180
28.4
852
84.0
43.7
15.5
43.8
6.63
39.4
8.84
68.1
448
394
446
386
330
289
417
375
341
313
288
268
350
315
286
263
242
225
15
16
17
18
19
20
250
234
221
208
197
188
21
22
23
24
25
26
Properties and Reaction Values
Zx in.3
φbWc kip-ft
φvVn kips
φR1 kips
φR2 kips/in.
φr R3 kips
φr R4 kips/in.
φr R5 kips
φr R6 kips/in.
φR (N = 31⁄4) kips
77.1
2310
223
94.5
27.5
116
19.3
96.7
25.7
180
69.3
2080
166
70.6
20.6
74.9
8.05
66.9
10.7
102
61.2
1840
223
123
34.3
167
44.4
131
59.1
235
53.1
1590
150
83.0
23.1
91.9
13.5
81.1
18.0
140
Load above heavy line is limited by design shear strength.
Values of R in bold face exceed maximum design web shear φvVn.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
4 - 100
BEAM AND GIRDER DESIGN
S 8–6–5–4–3
BEAMS
S Shapes
Maximum factored uniform loads in kips
for beams laterally supported
Fy = 50 ksi
For beams laterally unsupported, see page 4-139
Designation
Wt./ft
S8
23
1
2
3
4
5
6
191
145
116
96
7
8
9
10
11
12
S6
18.4
17.25
S5
12.5
9.5
75
64
51
42
58
57
43
34
28
83
72
64
58
53
48
71
62
55
50
45
41
45
40
35
32
29
27
36
32
28
25
23
21
24
21
19
17
15
14
13
45
38
24
20
Zx in.3
φbWc kip-ft
φvVn kips
φR1 kips
φR2 kips/in.
φr R3 kips
φr R4 kips/in.
φr R5 kips
φr R6 kips/in.
φR (N = 31⁄4) kips
19.3
579
95.3
55.1
22.1
68.9
27.2
54.4
36.3
127
16.5
495
58.5
33.9
13.6
33.2
6.32
29.8
8.42
57.2
S3
7.7
7.5
5.7
70
61
40
30
24
20
42
35
26
21
18
57
35
24
18
14
12
28
20
15
12
9.75
17
15
13
12
15
13
12
11
10
8.36
4.04
121
35.2
30.6
16.3
36.3
32.0
27.8
42.6
83.5
3.51
105
20.8
18.1
9.65
16.6
6.64
14.8
8.85
43.5
2.36
70.8
28.3
30.0
17.5
37.9
59.0
26.1
78.6
86.7
1.95
58.5
13.8
14.6
8.50
12.9
6.81
11.5
9.09
41.1
Span (ft)
117
99
83
151
106
80
64
53
Fy = 50 ksi
S4
10
Properties and Reaction Values
10.6
318
75.3
50.9
23.3
68.5
50.5
48.3
67.3
126
8.47
254
37.6
25.4
11.6
24.1
6.27
21.6
8.36
48.8
5.67
170
28.9
21.7
10.7
20.4
6.50
18.2
8.67
46.4
Load above heavy line is limited by design shear strength.
Values of R in bold face exceed maximum design web shear φvVn.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
FACTORED UNIFORM LOAD TABLES
Fy = 50 ksi
4 - 101
BEAMS
Channels
Maximum factored uniform loads in kips
for beams laterally supported
MC,C 18–15
For beams laterally unsupported, see page 4-139
Designation
MC 18
Span (ft)
Fy = 50 ksi
Wt./ft
58
51.9
C 15
45.8
42.7
50
40
33.9
421
343
286
245
215
324
302
252
216
189
3
4
5
6
7
8
680
568
473
405
355
583
519
433
371
324
486
470
392
336
294
437
372
319
279
580
511
409
341
292
256
9
10
11
12
13
14
315
284
258
237
218
203
288
260
236
216
200
185
261
235
214
196
181
168
248
223
203
186
172
159
227
205
186
170
157
146
191
172
156
143
132
123
168
151
137
126
116
108
15
16
17
18
19
20
189
177
167
158
149
142
173
162
153
144
137
130
157
147
138
131
124
118
149
140
131
124
117
112
136
128
120
114
108
102
114
107
101
95
90
86
101
95
89
84
80
76
21
22
23
24
25
26
135
129
123
118
114
109
124
118
113
108
104
100
112
107
102
98
94
90
106
101
97
93
89
86
97
93
89
85
82
79
82
78
75
72
69
66
72
69
66
63
60
58
28
30
32
34
36
38
101
95
89
83
79
75
93
87
81
76
72
68
84
78
74
69
65
62
80
74
70
66
62
59
73
68
64
60
57
61
57
54
50
48
54
50
47
44
42
40
42
44
71
68
65
65
62
59
59
56
53
56
53
51
68.2
2050
290
129
35.8
176
40.7
135
54.3
245
57.2
1720
211
93.4
26.0
109
15.6
93.4
20.8
161
50.4
1510
162
71.9
20.0
73.6
7.10
66.5
9.47
97.2
Properties and Reaction Values
Zx in.3
φbWc kip-ft
φvVn kips
φR1 kips
φR2 kips/in.
φr R3 kips
φr R4 kips/in.
φr R5 kips
φr R6 kips/in.
φR (N = 31⁄4) kips
94.6
2840
340
120
35.0
167
33.0
127
44.0
234
86.5
2600
292
103
30.0
133
20.8
108
27.7
200
78.4
2350
243
85.9
25.0
101
12.0
86.4
16.0
140
74.4
2230
219
77.3
22.5
86.1
8.76
75.5
11.7
115
Load above heavy line is limited by design shear strength.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
4 - 102
BEAM AND GIRDER DESIGN
BEAMS
Channels
Maximum factored uniform loads in kips
for beams laterally supported
MC 13
Fy = 50 ksi
For beams laterally unsupported, see page 4-139
Designation
MC 13
Span (ft)
Fy = 50 ksi
Wt./ft
50
40
35
31.8
3
4
5
6
7
8
552
454
363
303
259
227
393
382
305
255
218
191
314
277
231
198
173
263
259
216
185
162
9
10
11
12
13
14
202
182
165
151
140
130
170
153
139
127
117
109
154
139
126
116
107
99
144
129
118
108
99
92
15
16
17
18
19
20
121
113
107
101
96
91
102
95
90
85
80
76
92
87
82
77
73
69
86
81
76
72
68
65
21
22
23
24
25
26
86
83
79
76
73
70
73
69
66
64
61
59
66
63
60
58
55
53
62
59
56
54
52
50
27
28
29
30
31
32
67
65
63
61
59
57
57
55
53
51
49
48
51
50
48
46
45
43
48
46
45
43
42
40
46.2
1390
157
76.8
22.4
84.2
12.2
73.6
16.2
126
43.1
1290
132
64.5
18.8
64.7
7.19
58.4
9.59
89.6
Properties and Reaction Values
Zx in.3
φbWc kip-ft
φvVn kips
φR1 kips
φR2 kips/in.
φr R3 kips
φr R4 kips/in.
φr R5 kips
φr R6 kips/in.
φR (N = 31⁄4) kips
60.5
1820
276
135
39.3
197
66.5
139
88.7
263
50.9
1530
197
96.3
28.0
118
24.0
97.3
31.9
187
Load above heavy line is limited by design shear strength.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
FACTORED UNIFORM LOAD TABLES
Fy = 50 ksi
4 - 103
BEAMS
Channels
Maximum factored uniform loads in kips
for beams laterally supported
C,MC 12
For beams laterally unsupported, see page 4-139
Designation
Wt./ft
C 12
50
45
40
251
219
175
146
125
183
152
127
109
541
421
337
281
240
461
388
310
259
222
382
355
284
237
203
126
112
101
92
84
78
110
97
88
80
73
67
95
85
76
69
64
59
210
187
168
153
140
129
194
172
155
141
129
119
14
15
16
17
18
19
72
67
63
59
56
53
63
58
55
52
49
46
54
51
48
45
42
40
120
112
105
99
94
89
20
21
22
23
24
25
50
48
46
44
42
40
44
42
40
38
37
35
38
36
35
33
32
30
26
27
28
29
30
39
37
36
35
34
34
32
31
30
29
29
28
27
26
25
Zx in.3
φbWc kip-ft
φvVn kips
φR1 kips
φR2 kips/in.
φr R3 kips
φr R4 kips/in.
φr R5 kips
φr R6 kips/in.
φR (N = 31⁄4) kips
33.6
1010
165
71.7
25.5
93.0
23.9
73.9
31.8
155
29.2
876
125
54.4
19.4
61.5
10.4
53.1
13.9
98.3
Span (ft)
25
2
3
4
5
6
7
330
252
202
168
144
8
9
10
11
12
13
MC 12
20.7
Fy = 50 ksi
30
MC 12
35
31
10.6
303
257
214
183
240
236
197
168
123
116
87
70
58
50
177
158
142
129
118
109
161
143
128
117
107
99
147
131
118
107
98
91
44
39
35
32
29
27
111
103
97
91
86
82
101
95
89
83
79
75
92
86
80
76
71
68
84
79
74
69
66
62
25
23
22
20
19
18
84
80
77
73
70
67
78
74
71
67
65
62
71
68
65
62
59
57
64
61
58
56
54
51
59
56
54
51
49
47
17
17
16
15
15
14
65
62
60
58
56
60
57
55
53
52
55
53
51
49
47
49
48
46
44
43
45
44
42
41
39
13
13
12
12
12
47.3
1420
191
96.8
29.5
137
26.5
116
35.3
193
42.8
1280
151
76.6
23.4
96.3
13.1
85.8
17.5
143
39.3
1180
120
60.7
18.5
67.9
6.52
62.7
8.70
91.0
11.6
348
61.6
16.3
9.50
16.6
2.00
15.0
2.67
23.7
Properties and Reaction Values
25.4
762
91.4
39.7
14.1
38.2
4.04
35.0
5.38
52.5
56.1
1680
271
137
41.8
230
75.0
170
100.0
273
51.7
1550
231
117
35.6
181
46.5
144
62.0
233
Load above heavy line is limited by design shear strength.
Values of R in bold face exceed maximum design web shear φvVn.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
4 - 104
BEAM AND GIRDER DESIGN
C,MC 10
BEAMS
Channels
Maximum factored uniform loads in kips
for beams laterally supported
Fy = 50 ksi
For beams laterally unsupported, see page 4-139
Designation
Span (ft)
Fy = 50 ksi
Wt./ft
C 10
MC 10
30
25
20
2
3
4
5
6
7
363
266
200
160
133
114
284
230
173
138
115
99
8
9
10
11
12
13
100
89
80
73
67
61
14
15
16
17
18
19
20
21
22
23
24
33.6
MC 10
28.5
25
MC 10
15.3
41.1
22
205
193
145
116
96
83
130
119
95
79
68
430
389
292
233
195
167
311
251
200
167
143
230
222
178
148
127
205
194
155
129
111
157
142
118
101
92
79
59
47
39
34
8.4
86
77
69
63
58
53
72
64
58
53
48
45
59
53
47
43
40
36
146
130
117
106
97
90
125
111
100
91
84
77
111
99
89
81
74
68
97
86
77
70
65
60
89
79
71
64
59
54
29
26
24
21
20
18
57
53
50
47
44
42
49
46
43
41
38
36
41
39
36
34
32
30
34
32
30
28
26
25
83
78
73
69
65
61
72
67
63
59
56
53
63
59
56
52
49
47
55
52
48
46
43
41
51
47
44
42
39
37
17
16
15
14
13
12
40
38
36
35
33
35
33
31
30
29
29
28
26
25
24
24
23
22
21
20
58
56
53
51
49
50
48
46
44
42
44
42
40
39
37
39
37
35
34
32
35
34
32
31
30
12
11
11
10
9.83
26.6
798
182
84.1
33.6
131
75.6
81.0
101
193
23.0
690
142
65.8
26.3
90.8
36.1
66.8
48.1
151
29.6
888
115
66.4
21.3
75.8
14.4
66.1
19.3
129
25.8
774
103
59.4
19.0
64.1
10.3
57.2
13.8
102
23.6
708
78.3
45.3
14.5
42.7
4.59
39.6
6.12
59.5
7.86
236
45.9
14.6
8.50
13.4
1.90
12.1
2.53
20.3
Properties and Reaction Values
Zx in.3
φbWc kip-ft
φvVn kips
φR1 kips
φR2 kips/in.
φr R3 kips
φr R4 kips/in.
φr R5 kips
φr R6 kips/in.
φR (N = 31⁄4) kips
19.3
579
102
47.4
19.0
55.6
13.5
46.6
18.0
105
15.8
474
64.8
30.0
12.0
28.0
3.43
25.7
4.57
40.6
38.9
1170
215
124
39.8
194
94.9
131
127
254
33.4
1000
155
89.8
28.8
119
35.8
95.4
47.7
183
Load above heavy line is limited by design shear strength.
Values of R in bold face exceed maximum design web shear φvVn.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
FACTORED UNIFORM LOAD TABLES
Fy = 50 ksi
4 - 105
BEAMS
Channels
Maximum factored uniform loads in kips
for beams laterally supported
C,MC 9
For beams laterally unsupported, see page 4-139
Designation
C9
Span (ft)
Fy = 50 ksi
Wt./ft
MC 9
20
15
13.4
25.4
23.9
2
3
4
5
6
7
218
168
126
101
84
72
139
135
101
81
68
58
113
94
75
63
54
219
174
139
116
99
194
167
133
111
95
8
9
10
11
12
13
63
56
50
46
42
39
51
45
41
37
34
31
47
42
38
34
31
29
87
77
70
63
58
54
83
74
67
61
56
51
14
15
16
17
18
19
36
34
31
30
28
27
29
27
25
24
23
21
27
25
23
22
21
20
50
46
44
41
39
37
48
44
42
39
37
35
20
21
22
25
24
23
20
19
18
19
18
17
35
33
32
33
32
30
23.2
696
109
66.8
22.5
80.7
19.9
68.8
26.6
140
22.2
666
97.2
59.4
20.0
67.7
14.0
59.3
18.7
120
Properties and Reaction Values
Zx in.3
φbWc kip-ft
φvVn kips
φR1 kips
φR2 kips/in.
φr R3 kips
φr R4 kips/in.
φr R5 kips
φr R6 kips/in.
φR (N = 31⁄4) kips
16.8
504
109
52.5
22.4
69.5
26.2
53.8
34.9
125
13.5
405
69.3
33.4
14.3
35.3
6.74
31.2
8.98
60.4
12.5
375
56.6
27.3
11.7
26.1
3.68
23.9
4.91
39.8
Load above heavy line is limited by design shear strength.
Values of R in bold face exceed maximum design web shear φvVn.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
4 - 106
BEAM AND GIRDER DESIGN
BEAMS
Channels
Maximum factored uniform loads in kips
for beams laterally supported
C,MC 8
Fy = 50 ksi
For beams laterally unsupported, see page 4-139
Designation
C8
Span (ft)
Fy = 50 ksi
Wt./ft
MC 8
MC 8
MC 8
18.75
13.75
11.5
22.8
21.4
20
18.7
8.5
1
2
3
4
5
6
210
207
138
104
83
69
131
109
82
65
55
95
72
57
48
184
141
113
94
162
135
108
90
173
162
122
97
81
152
116
92
77
77
69
52
41
35
7
8
9
10
11
12
59
52
46
41
38
35
47
41
36
33
30
27
41
36
32
29
26
24
81
70
63
56
51
47
77
68
60
54
49
45
69
61
54
49
44
41
66
58
51
46
42
39
30
26
23
21
19
17
13
14
15
16
17
18
32
30
28
26
24
23
25
23
22
20
19
18
22
20
19
18
17
16
43
40
38
35
33
31
42
39
36
34
32
30
37
35
32
30
29
27
36
33
31
29
27
26
16
15
14
13
12
12
19
20
22
21
17
16
15
14
30
28
28
27
26
24
24
23
11
10
16.2
486
86.4
56.3
20.0
64.5
17.3
55.3
23.1
121
15.4
462
76.2
49.6
17.7
53.5
11.9
47.1
15.9
98.7
6.91
207
38.7
16.8
8.95
15.2
2.49
13.9
3.33
24.7
Properties and Reaction Values
Zx in.3
φbWc kip-ft
φvVn kips
φR1 kips
φR2 kips/in.
φr R3 kips
φr R4 kips/in.
φr R5 kips
φr R6 kips/in.
φR (N = 31⁄4) kips
13.8
414
105
57.1
24.3
76.5
40.1
55.2
53.4
136
10.9
327
65.4
35.5
15.2
37.6
9.65
32.4
12.9
74.2
9.55
287
47.5
25.8
11.0
23.2
3.69
21.3
4.92
37.3
18.8
564
92.2
63.4
21.3
72.9
20.1
62.2
26.7
133
18.0
540
81.0
55.7
18.8
60.0
13.6
52.8
18.1
112
Load above heavy line is limited by design shear strength.
Values of R in bold face exceed maximum design web shear φvVn.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
FACTORED UNIFORM LOAD TABLES
Fy = 50 ksi
4 - 107
BEAMS
Channels
Maximum factored uniform loads in kips
for beams laterally supported
C,MC 7–6
For beams laterally unsupported, see page 4-139
Designation
C7
12.25
MC 7
9.8
22.7
C6
MC 6
MC 6
MC 6
19.1
13
10.5
8.2
18
16.3
15.1
12
102
92
62
46
37
31
65
51
38
31
26
123
115
86
69
58
122
102
77
61
51
102
97
73
58
48
100
74
55
44
37
1
2
3
4
5
6
119
84
63
50
42
79
71
53
43
36
190
162
122
97
81
133
107
86
72
142
109
73
54
44
36
7
8
9
10
11
12
36
31
28
25
23
21
31
27
24
21
19
18
69
61
54
49
44
41
61
54
48
43
39
36
31
27
24
22
20
18
26
23
21
18
17
15
22
19
17
15
14
13
49
43
38
35
31
29
44
38
34
31
28
26
42
36
32
29
26
24
32
28
25
22
20
18
13
14
15
16
19
18
17
16
16
15
14
13
37
35
32
30
33
31
29
27
17
16
15
14
13
12
12
11
10
27
25
23
24
22
20
22
21
19
17
16
15
8.40
252
59.3
34.3
15.7
38.4
13.1
32.3
17.4
85.4
7.12
214
39.7
23.0
10.5
21.0
3.91
19.2
5.21
36.1
11.5
345
61.4
50.3
19.0
58.0
20.7
49.7
27.6
112
10.2
306
60.8
49.8
18.8
57.1
20.0
49.1
26.7
111
9.69
291
51.2
42.0
15.8
44.2
12.0
39.4
16.0
91.3
7.38
221
50.2
31.5
15.5
38.1
14.3
32.4
19.1
81.9
Span (ft)
Fy = 50 ksi
Wt./ft
Properties and Reaction Values
Zx in.3
φbWc kip-ft
φvVn kips
φR1 kips
φR2 kips/in.
φr R3 kips
φr R4 kips/in.
φr R5 kips
φr R6 kips/in.
φR (N = 31⁄4) kips
16.2
486
95.1
70.7
25.2
91.0
39.3
72.6
52.5
152
14.3
429
66.5
49.5
17.6
53.3
13.5
47.0
18.0
105
7.26
218
70.8
44.4
21.9
61.0
43.9
43.5
58.5
115
6.15
185
50.9
31.9
15.7
37.2
16.3
30.7
21.7
82.9
5.13
154
32.4
20.3
10.0
18.9
4.21
17.2
5.61
35.4
Load above heavy line is limited by design shear strength.
Values of R in bold face exceed maximum design web shear φvVn.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
4 - 108
BEAM AND GIRDER DESIGN
BEAMS
Channels
Maximum factored uniform loads in kips
for beams laterally supported
C 5–4–3
Fy = 50 ksi
For beams laterally unsupported, see page 4-139
Designation
C5
9
C4
C3
6.7
7.25
5.4
69
42
28
21
17
14
40
34
23
17
14
11
1
2
3
4
5
6
88
65
44
33
26
22
51
35
26
21
18
7
8
9
10
11
12
19
16
15
13
12
11
15
13
12
11
9.6
8.8
12
11
9.4
8.4
9.7
8.5
7.5
6.8
6
5
4.1
52
26
17
13
10
8.6
42
23
15
11
9.0
7.5
28
20
13
9.8
7.8
6.5
7.4
6.4
5.6
1.72
51.6
28.8
30.6
17.8
40.0
59.6
28.1
79.5
88.4
1.50
45.0
20.9
22.2
12.9
24.7
22.7
20.2
30.2
64.1
1.30
39.0
13.8
14.6
8.50
13.2
6.49
11.9
8.65
40.0
Span (ft)
Fy = 50 ksi
Wt./ft
Properties and Reaction Values
Zx in.3
φbWc kip-ft
φvVn kips
φR1 kips
φR2 kips/in.
φr R3 kips
φr R4 kips/in.
φr R5 kips
φr R6 kips/in.
φR (N = 31⁄4) kips
4.36
131
43.9
30.5
16.3
37.8
23.2
30.1
30.9
83.3
3.51
105
25.7
17.8
9.50
16.9
4.64
15.3
6.18
35.4
2.81
84.3
34.7
27.6
16.1
35.7
30.2
27.6
40.3
79.7
2.26
67.8
19.9
15.8
9.20
15.5
5.69
14.0
7.59
38.6
Load above heavy line is limited by design shear strength.
Values of R in bold face exceed maximum design web shear φvVn.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
DESIGN FLEXURAL STRENGTH OF BEAMS WITH UNBRACED LENGTH > Lp
4 - 109
DESIGN FLEXURAL STRENGTH OF BEAMS WITH UNBRACED LENGTH
GREATER THAN Lp
General Notes
Spacing of lateral bracing at distances greater than Lp creates a problem in which the
designer is confronted with a given laterally unbraced length (usually less than the total
span) along the compression flange, and a calculated required bending moment. The
beam cannot be selected from its plastic section modulus alone, since depth, flange
proportions, and other properties have an influence on its bending strength.
The following charts show the design moment φbMn for W and M shapes of Fy = 36 ksi
and Fy = 50 ksi steels, used as beams, with respect to the maximum unbraced length for
which this moment is permissible. In bending, φb of 0.9 is given in Section F1.2 of the
LRFD Specification. The charts extend over varying unbraced lengths, depending upon
the flexural strengths of the beams represented. In general, they extend beyond most
unbraced lengths frequently encountered in design practice. The design moment φbMn,
kip-ft, is plotted with respect to the unbraced length with no consideration of the moment
due to weight of the beam. Design moments are shown for unbraced lengths in feet,
starting at spans less than Lp, for spans between Lp and Lr and for spans beyond Lr.
The unbraced length Lp, in feet, with the limit indicated by a solid symbol, , is the
maximum unbraced length of the compression flange, with Cb = 1.0, for which the design
moment is given by φbMp,
where
Fy
Lp = 300ry / √
Mp = ZxFy
(F1-4)
For those noncompact rolled shapes, which meet the requirements of compact sections
Fy , but is less than 141 / √
Fy −Fr , the design moment is
except that bf / 2tf exceeds 65 / √
obtained from Equation A-F1-3 in Appendix F1 of the LRFD Specification. This criterion
applies to one W shape when Fy is equal to 36 ksi and to seven W shapes when Fy is equal
to 50 ksi. (Noncompact W shapes are given on p. 4-7.)
For the case Cb = 1.0 and noncompact shapes:
λ − λp
Mn′ = Mp − (Mp − Mr)
λr − λp
(A-F1-3)
Mp − Mn′
Lp′ = Lp + (Lr − Lp)
Mp − Mr
λ = bf / 2tf
λp = 65 / √
Fy
λr = 141 / √
Fy −Fr
Lr =
ryX1
√
1+√
1 + X2(Fy − Fr)2
Fy − Fr
X1 =
π
Sx
√
EGJA
2
(F1-6)
(F1-8)
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
4 - 110
BEAM AND GIRDER DESIGN
4Cw
X2 =
Iy
Sx
GJ
2
(F1-9)
Mr = (Fy − Fr )Sx
Mp = ZxFy
Fr = 10 ksi for rolled shapes
(F1-7)
The unbraced length in the charts may be either the total span or any part of the total
span between braced points. The plots shown in these charts were computed for beams
for which Cb = 1.0. When a moment gradient exists between points of bracing, Cb may
be larger than unity. (See Table 4-1.) Using this larger value of Cb may provide a more
liberal flexural strength for the section chosen if the unbraced length is greater than Lp.
In these cases, the design moment can be determined using the provisions of Section
F1.2a of the LRFD Specification.
Lb − Lp
φbMn = φbCb Mp − (Mp − Mr)
≤ φbMp
Lr − Lp
The unbraced length Lr, ft, with the limit indicated by an open symbol , is the
maximum unbraced length of the compression flange beyond which the design moment
is governed by Specification Section F1.2b. For unbraced lengths greater than Lr:
φbMn = φbMcr = φbCb
π
Lb
√
2
πE
EIyGJ + IyCw ≤ φbCbMr and φbMp
Lb
In computing the points for the curves, Cb in the above formulas was taken as unity,
E = 29,000 ksi and G = 11,200 ksi. The properties of the beams are taken from the Tables
of Dimensions and Properties in Part 1 of this LRFD Manual. The beam strengths have
been reduced by multiplying the nominal flexural strength Mn by 0.9, the resistance factor
φb for flexure.
Over a limited range of length, a given beam is the lightest available for various
combinations of unbraced length and design moment. The charts are designed to assist
in selection of the lightest available beam for the given combination.
The solid portion of each curve indicates the most economical section by weight. The
dashed portion of each curve indicates ranges in which a lighter weight beam will satisfy
the loading conditions.
The curves are plotted without regard to shear strength and deflection criteria, therefore
due care must be exercised in their use. The curves do not extend beyond an arbitrary
span/depth limit of 30.
The following examples illustrate the use of the charts.
EXAMPLE 4-8
Given:
Using Fy = 50 ksi steel, determine the size of a “simple” framed girder
with a span of 35 feet, which supports two equal concentrated loads.
The factored loads produce a required moment of 440 kip-ft in the
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
DESIGN FLEXURAL STRENGTH OF BEAMS WITH UNBRACED LENGTH > Lp
4 - 111
center 15-ft section between the loads. The load points are laterally
braced.
Solution:
For this loading condition, Cb = 1.0 due to nearly uniform moment
across the central portion of the span.
Center section of 15 feet is longest unbraced length.
With total span equal to 35 feet and Mn = 440 kip-ft, assume approximate weight of beam at 70 lbs/ft (equal to 0.07 kips/ft).
0.07 × (35)2
× 1.2 = 453 kip-ft
Total Mu = 440 +
8
Entering chart, with unbraced length equal to 15 feet on the bottom
scale (abscissa), proceed upward to meet the horizontal line corresponding to a design moment equal to 453 kip-ft on the left hand scale
(ordinate). Any beam listed above and to the right of the point so
located satisfies the design moment requirement. In this case, the
lightest section satisfying this criterion is a W21×68, for which the total
design moment with an unbraced length of 15 feet is 457 kip-ft.
Use: W21×68
Note: If depth is limited, a W14×82 could be selected, provided
deflection conditions are not critical.
EXAMPLE 4-9
Given:
A “fixed end” girder with a span of 60 feet supports a concentrated
load at the center. The compression flange is laterally supported at the
concentrated load point and at the inflection points. The factored load
produces a maximum calculated moment of 440 kip-ft at the load point
and the supports. Determine the size of the beam using Fy = 50 ksi steel.
Solution:
For this loading condition, Cb = 1.67 (by comparison with Table 4-1),
with an unbraced length of 15 feet. With the total span equal to 60 feet
and Mu = 440 kip-ft, assume approximate weight of beam at 60 lbs/ft
(0.06 kips/ft).
0.06 × (60)2
Total Mu = 440 +
×1.2
24
= 451 kip-ft at the centerline and 462 at the supports
Compute Mequiv by dividing the required design moment by Cb
Mequiv = 462 / 1.67 = 277 kip-ft
Enter charts with unbraced length equal to 15 feet and proceed upward
to 277 kip-ft. Any beam listed above and to the right of the point
satisfies the design moment.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
4 - 112
BEAM AND GIRDER DESIGN
The lightest section satisfying the criteria of a design moment of
277 kip-ft at an unbraced length of 15 feet and φbMp greater than 462
kip-ft is a W21×62. The design moment for a W21×62 with an
unbraced length of 15 feet is 406 kip-ft and φbMp is 540 kip-ft.
Since (φbMn = 406 kip-ft) > (Mequiv = 277 kip-ft) and (φbMp = 540
kip-ft) > (Mu = 462 kip-ft), a W21×62 is o.k.
A 21-in. nominal depth beam spanning 60 feet should be checked for
deflection since the span/depth ratio exceeds 30.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
DESIGN FLEXURAL STRENGTH OF BEAMS WITH UNBRACED LENGTH > Lp
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
4 - 113
4 - 114
BEAM AND GIRDER DESIGN
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
DESIGN FLEXURAL STRENGTH OF BEAMS WITH UNBRACED LENGTH > Lp
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
4 - 115
4 - 116
BEAM AND GIRDER DESIGN
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
DESIGN FLEXURAL STRENGTH OF BEAMS WITH UNBRACED LENGTH > Lp
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
4 - 117
BEAM AND GIRDER DESIGN
4 - 118
W3
x3
18
30
3x3
W
97
26
0x2
31
W4
0x3
W44
x26
2
0x2
W
24
W4
49
x3
x2
77
35
0x2
30
W4
61
0x2
78
W4
4x2
30
W
11
35
x2
x2
30
27
W
67
W4
79
x2
0x1
0x2
15
W
24
x2
50
W4
0x
4
24
99
W
0x1
49
W4
17
0x1
x2
07
W
92
30
x1
W
24
x1
91
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
0
92
W4
W
35
11
94
W4
W21x201
28
x2
6x
30
07
4
35
x2
0x2
6x1
W4
8
25
8x
W1
W18x234
W
x3
x26
0x2
30
W4
W3
W27x178
29
x2
24
W
W
24
3
28
8x
W1
1
31
8x
W1
W3
27
W40
W4
W
W40x183
W4
W
W40x199
DESIGN FLEXURAL STRENGTH OF BEAMS WITH UNBRACED LENGTH > Lp
4 - 119
W
24
x4
08
W4
0x2
97
W
27
x3
68
W
30
x3
26
W
W
27
30
x3
x2
07
92
W
24
x3
35
30
W3
W
91
61
3x2
x2
W
24
W
x2
27
79
x2
58
W1
W
24
x2
50
W
W1
8x
27
28
3
x2
35
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
8x
31
1
4 - 120
BEAM AND GIRDER DESIGN
W
W3
11
W2
4
4x
9
x169
22
W33
x183
01
W18x211
x17
8
x2
34
W40
17
21
x2
W40
7x
W
18
0x2
W2
W
18
W40x
W
24
167
x1
W21x182
92
W
24
x2
07
W36
x170
W2
7x
19
18
4
W
x1
92
W40
x149
W3
0x1
16
W
18
x1
W
58
18
x1
75
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
x2
58
DESIGN FLEXURAL STRENGTH OF BEAMS WITH UNBRACED LENGTH > Lp
4 - 121
W2
79
35
W36
7x2
4x2
W2
x245
W
18
x2
83
W2
4x
25
0
W3
0x1
91
W2
4x
22
W
9
W36
x210
W
24
x2
07
W
21
x2
01
W
18
x2
34
W
24
x1
92
W
18
x1
92
W
x1
7x1
21
W2
W
18
x2
11
94
82
W
24
x1
76
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
18
x2
58
4 - 122
BEAM AND GIRDER DESIGN
W30x1
32
W1
15
W1
8x
8x
8
17
5
W 3 3 x1 3
0
W30x90
W24x103
W27
x94
W 36 x1 60
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
DESIGN FLEXURAL STRENGTH OF BEAMS WITH UNBRACED LENGTH > Lp
4 - 123
W21
x20
1
W1
W 36 x1 70
8x
21
1
W1
8x1
W 33 x1 69
92
W1
8x1
75
W21
x18
2
W1
8x1
58
W 36 x1 60
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
4 - 124
BEAM AND GIRDER DESIGN
W14x132
W
14
x1
32
W30
x90
W27
x90
x94
W30
W12x120
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
DESIGN FLEXURAL STRENGTH OF BEAMS WITH UNBRACED LENGTH > Lp
4 - 125
W1
8x
78
5
17 W27x1
W1
8x
15
8
W
W24x
14
x1
32
117
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
4 - 126
BEAM AND GIRDER DESIGN
W
x1
20
W30x9
12
0
W12x106
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
DESIGN FLEXURAL STRENGTH OF BEAMS WITH UNBRACED LENGTH > Lp
4 - 127
W
14
x1
32
W
12
x1
20
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
4 - 128
BEAM AND GIRDER DESIGN
W12x96
W
12
x9
6
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
DESIGN FLEXURAL STRENGTH OF BEAMS WITH UNBRACED LENGTH > Lp
4 - 129
W
12
x1
20
W
12
x1
06
W
10
x1
12
W
12
x9
6
W
10
x1
00
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
4 - 130
BEAM AND GIRDER DESIGN
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
DESIGN FLEXURAL STRENGTH OF BEAMS WITH UNBRACED LENGTH > Lp
4 - 131
W
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
10
x1
00
4 - 132
BEAM AND GIRDER DESIGN
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
DESIGN FLEXURAL STRENGTH OF BEAMS WITH UNBRACED LENGTH > Lp
4 - 133
W
10
x6
8
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
4 - 134
BEAM AND GIRDER DESIGN
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
DESIGN FLEXURAL STRENGTH OF BEAMS WITH UNBRACED LENGTH > Lp
4 - 135
W
8x
48
W1
0x4
5
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
4 - 136
BEAM AND GIRDER DESIGN
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
DESIGN FLEXURAL STRENGTH OF BEAMS WITH UNBRACED LENGTH > Lp
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
4 - 139
4 - 140
BEAM AND GIRDER DESIGN
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
DESIGN FLEXURAL STRENGTH OF BEAMS WITH UNBRACED LENGTH > Lp
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
4 - 141
4 - 142
BEAM AND GIRDER DESIGN
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
DESIGN FLEXURAL STRENGTH OF BEAMS WITH UNBRACED LENGTH > Lp
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
4 - 143
4 - 144
BEAM AND GIRDER DESIGN
W24x250
0x2
61
x3
0x2
18
W4
x183
W
W27x217
W3
x235
4
W40
x19
x211
W40
W40
W36
W40x174
15
11
W40x167
W
24
x2
79
W2
7x2
21
58
3x2
5
83
W3
23
x2
7x
18
W2
W
W4
W
x2
0x1
24
99
29
W4
0x1
74
W18x258
0x
W33x
W3
W40x149
3
241
17
W
07
3x2
x2
W3
24
01
W24x192
W18x234
W21x201
W18x211
W21x182
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
DESIGN FLEXURAL STRENGTH OF BEAMS WITH UNBRACED LENGTH > Lp
30
92
7x
0x2
W2
W3
7
W
24
x3
35
W3
0x
26
1
W2
7x
25
8
W
18
x3
11
W
24
x2
79
W
50 235
x
x2
24 W27
W1 8x 28 3
W
18
x2
83
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
4 - 145
4 - 146
BEAM AND GIRDER DESIGN
W
x2
W
7
11
20
x2
4x
34
18
W2
18
W21x182
W2
1x
20
1
W18x192
W2
4x1
x149
W18x158
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
92
W40
W18x175
DESIGN FLEXURAL STRENGTH OF BEAMS WITH UNBRACED LENGTH > Lp
4 - 147
W2
07
29
4x2
4x2
W2
W
18
x2
58
W
18
x2
34
W2
4x
19
2
W
18
x2
11
W
21
x2
01
W
21
x1
82
W
18
x1
92
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
DESIGN FLEXURAL STRENGTH OF BEAMS WITH UNBRACED LENGTH > Lp
4 - 153
W
14
x1
32
W
12
x1
20
W
12
x1
06
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
4 - 154
BEAM AND GIRDER DESIGN
W1
2x
96
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
DESIGN FLEXURAL STRENGTH OF BEAMS WITH UNBRACED LENGTH > Lp
W1
2x
10
6
W1
2x
96
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
4 - 155
4 - 156
BEAM AND GIRDER DESIGN
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
DESIGN FLEXURAL STRENGTH OF BEAMS WITH UNBRACED LENGTH > Lp
4 - 157
W
12
x9
6
W
10
x1
00
W1
2x
72
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
4 - 158
BEAM AND GIRDER DESIGN
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
DESIGN FLEXURAL STRENGTH OF BEAMS WITH UNBRACED LENGTH > Lp
W
10
x7
7
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
4 - 159
4 - 160
BEAM AND GIRDER DESIGN
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
DESIGN FLEXURAL STRENGTH OF BEAMS WITH UNBRACED LENGTH > Lp
4 - 161
W
8x
67
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
4 - 162
BEAM AND GIRDER DESIGN
W8
x48
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
DESIGN FLEXURAL STRENGTH OF BEAMS WITH UNBRACED LENGTH > Lp
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
4 - 163
4 - 164
BEAM AND GIRDER DESIGN
M12x10
.8
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
DESIGN FLEXURAL STRENGTH OF BEAMS WITH UNBRACED LENGTH > Lp
M12x1
0 .8
M10x
8
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
4 - 165
4 - 166
BEAM AND GIRDER DESIGN
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
5-1
PART 5
COMPOSITE DESIGN
OVERVIEW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-3
COMPOSITE BEAMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-5
General Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-5
Design Flexural Strength (Positive) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-5
Concrete Flange . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-7
Shear Connectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-8
Strength During Construction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-8
Lateral Support . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-9
Design Shear Strength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-9
Lower Bound Moment of Inertia . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-9
Composite Beam Reactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-10
Preliminary Section Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-11
Floor Deflections and Vibrations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-12
Selection Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-18
Lower Bound Elastic Moment of Inertia Tables . . . . . . . . . . . . . . . . . . . . . . 5-50
COMPOSITE COLUMNS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-67
General Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-67
Combined Axial Compression and Bending (Interaction) . . . . . . . . . . . . . . . . . 5-69
COMPOSITE COLUMNS—W SHAPES ENCASED IN CONCRETE . . . . . . . . . . 5-73
General Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-73
Tables: fc′ = 3.5 ksi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-74
Tables: fc′ = 5 ksi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-86
Tables: fc′ = 8 ksi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-98
COMPOSITE COLUMNS—CONCRETE-FILLED STEEL PIPE AND
STRUCTURAL TUBING . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-110
General Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-110
Steel Pipe Filled with Concrete . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-110
Structural Tubing Filled with Concrete . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-110
Tables: Steel Pipe (fc′ = 3.5 ksi) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-111
Tables: Steel Pipe (fc′ = 5 ksi) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-113
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
5-2
COMPOSITE DESIGN
Tables: Square Structural Tubing (fc′ = 3.5 ksi) . . . . . . . . . . . . . . . . . . . . . 5-115
Tables: Square Structural Tubing (fc′ = 5 ksi) . . . . . . . . . . . . . . . . . . . . . . . 5-122
Tables: Rectangular Structural Tubing (fc′ = 3.5 ksi) . . . . . . . . . . . . . . . . . . . 5-129
Tables: Rectangular Structural Tubing (fc′ = 5 ksi) . . . . . . . . . . . . . . . . . . . . 5-136
REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-143
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
OVERVIEW
5-3
OVERVIEW
Tables are given for the design of composite beams and columns.
Composite Beam tables are located as follows:
Selection Tables, Fy = 36 ksi, begin on . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-18
Selection Tables, Fy = 50 ksi, begin on . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-34
Lower Bound Elastic Moment of Inertia Tables begin on . . . . . . . . . . . . . . . . . 5-50
Composite Column tables are located as follows:
W Shapes Encased in Concrete . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-74
Concrete-Filled Steel Pipe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-111
Concrete-Filled Structural Tubing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-115
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
5-4
COMPOSITE DESIGN
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
COMPOSITE BEAMS
5-5
COMPOSITE BEAMS
General Notes
The Composite Beam Tables can be used for the design and analysis of simple composite
steel beams. Values for the design flexural strength φMn for rolled I-shaped beams with
yield strengths of 36 ksi and 50 ksi are tabulated, as well as lower bound moments of
inertia. The values tabulated are independent of the concrete flange properties. The
strength evaluation of the concrete flange portion of the composite section is left to the
design engineer. The preparation of these tables is based upon the fact that the location
of the plastic neutral axis (PNA) is uniquely determined by the horizontal shear force
ΣQn at the interface between the steel section and the concrete slab. With the knowledge
of the location of the PNA and the distance to the centroid of the concrete flange force
ΣQn, the design flexural strengths φMn for the rolled section can be computed.
Design Flexural Strength (Positive)
The design flexural strength of simple steel beams with composite concrete flanges is
computed from the equilibrium of internal forces using the plastic stress distribution as
shown in Figure 5-1:
φMn = φTTot y = φCToty
where
φ = 0.85
TTot = sum of tensile forces = Fy × (tensile force beam area)
CTot = sum of compressive forces = concrete flange force + Fy × (compressive force
beam area)
y = moment arm between centroid of tensile force and the resultant compressive
force
The model used in the calculation of the design strengths tabulated herein is given in
Figure 5-2. A summary of the model properties follows:
As = area of steel cross section, in.2
Af = flange area = bf × tf, in.2
Aw = web area = (d − 2k)tw, in.2
0.85fc ′
b
Cconc
a
Cstl
PNA
Fy
TTot = Tstl
Fy
Fig. 5-1. Plastic stress distribution.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
C Tot = Cconc + Cstl
y
5-6
COMPOSITE DESIGN
Kdep = k − tf, in.
Karea = (As − 2Af − Aw) / 2, in.2
Limitations for the tabulated values include the following:
Fy
(d − 2k) / tw ≤ 640 / √
and
ΣQn (min.) = 0.25AsFy
The limitation of ΣQn (min.) is not required by the Specification, but is deemed to be
a practical minimum value. Design strength moment values are tabulated for plastic
neutral axis (PNA) locations at the top and intermediate quarter points through the
thickness of the steel beam top flange. In addition, PNA locations are computed at the
point where ΣQn equals 0.25AsFy, and the point where ΣQn is the average of the minimum
value of (0.25AsFy) and the value of ΣQn when the PNA is at the bottom of the top flange
(see Figure 5-3).
To use the tables, select a valid value of ΣQn, determine the appropriate value of Y2
and read the design flexural strength moment φMn directly. Values for Y1 are also
tabulated for convenience. The parameters Y1 and Y2 are defined as follows:
Y1 = distance from PNA to beam top flange
Y2 = distance from concrete flange force to beam top flange
Valid values for ΣQn are the smaller of the following three expressions (LRFD
Specification Section I5):
0.85fc′Ac
AsFy
nQn
bf
tf
K dep
k
K area
K dep
tw
d
d – 2k
K dep
tf
k
Fig. 5-2. Composite beam model.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
COMPOSITE BEAMS
5-7
where
fc′
Ac
As
Fv
n
= specified compressive strength of concrete, ksi
= area of concrete slab within effective width, in.2
= area of steel cross section, in.2
= specified minimum yield stress, ksi
= number of shear connectors between the point of maximum positive moment
and the point of zero moment to either side
Qn = shear capacity of single shear connector, kips
Concrete Flange
According to LRFD Specification Section I3.1 the effective width of the concrete slab
on each side of the beam centerline shall not exceed:
a. one-eighth of the beam span, center to center, of supports;
b. one-half the distance to the centerline of the adjacent beams; or
c. the distance to the edge of the slab.
The maximum concrete flange force is equal to 0.85 fc′Ac where Ac is based on the
actual slab thickness, tc. However, often the maximum concrete flange force exceeds the
maximum capacity of the specified steel beam. In that case, the effective concrete flange
force is determined from a value of ΣQn, which will be the smaller of AsFy or nQn. The
effective concrete flange force is:
b
Ycon
Location of
effective concrete
flange force (∑Qn)
a/
2
a
Y2
TFL (pt. 1)
BFL (pt. 5)
6
7
Y1 (varies—see figure below)
Y1 = Distance from top of steel flange to any
of the seven tabulated PNA locations
∑ Qn (@ pt. 5) + ∑Q n (@ pt. 7)
∑ Qn (@ point
6 )=
∑ Qn (@ point
7 ) = .25A sFy
Beam
top flange
2
4 Equal
spaces
1
2
3
4
5
PNA FLANGE LOCATIONS
Fig. 5-3. Composite beam table parameters.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
TFL
tf
BFL
5-8
COMPOSITE DESIGN
ΣQn = Cconc = 0.85fc′ba
where
Cconc = effective concrete flange force, kips
b
= effective concrete flange width, in.
a
= effective concrete flange thickness, in.
The basis of the design of most composite beams will be the relationship:
a=
ΣQn
0.85fc′b
From this relationship, the value of Y2 can be computed as:
Y2 = Ycon − a / 2
where
Ycon = distance from top of steel beam to top of concrete, in.
Shear Connectors
Shear connectors must be headed steel studs, not less than four stud diameters in length
after installation, or hot-rolled steel channels. Shear connectors must be embedded in
concrete slabs made with ASTM C33 aggregate or with rotary kiln produced aggregates
conforming to ASTM C330, with concrete unit weight not less than 90 pcf.
The nominal strength of one stud shear connector embedded in a solid concrete slab is:
Qn = 0.5Asc √
fc′Ec ≤ AscFu
(I5-1)
where
Asc = cross-sectional area of a stud shear connector, in.2
fc′ = specified concrete compressive strength, ksi
Fu = minimum specified tensile strength of stud, ksi
Ec = modulus of elasticity of concrete, ksi
= (w1.5)√
fc ′
w = unit weight of concrete, lb/cu ft
The nominal shear strengths of 3⁄4-in. headed studs embedded in concrete slabs are
listed in Table 5-1.
Note the effective shear strengths of studs used in conjunction with composite or
non-composite metal forms may be affected by the shape of the deck and spacing of the
studs. See LRFD Specification Sections I3.5 and I5.6.
Strength During Construction
When temporary shores are not used during construction, the steel section must have
sufficient strength to support the applied loads prior to the concrete attaining 75 percent
of the specified concrete strength fc′ (LRFD Specification Section I3.4). The effect of
deflection on unshored steel beams during construction should be considered.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
COMPOSITE BEAMS
5-9
Table 5-1.
Nominal Stud Shear Strength Qn (kips) for 3⁄4-in Headed Studs
fc′
(ksi)
w
(lbs/cu. ft)
Qn
(kips)
3.0
3.0
3.5
3.5
4.0
4.0
115
145
115
145
115
145
17.7
21.0
19.8
23.6
21.9
26.1
Lateral Support
Adequate lateral support for the compression flange of the steel section will be provided
by the concrete slab after hardening. During construction, however, lateral support must
be provided, or the design strength must be reduced in accordance with Section F1 of the
LRFD Specification. Steel deck with adequate attachment to the compression flange will
usually provide the necessary lateral support. For construction using fully encased beams,
particular attention should be given to lateral support during construction.
Design Shear Strength
The design shear strength of composite beams is determined by the strength of the steel
web, in accordance with the requirements of Section F2 of the LRFD Specification.
Lower Bound Moment of Inertia
With regard to serviceability, a table of lower bound moments of inertia of composite
sections is included to assist in the evaluation of deflection. If calculated deflections using
the lower bound moment of inertia are acceptable, a complete elastic analysis of the
composite section can be avoided.
The lower bound moment of inertia is based on the area of the beam and an equivalent
concrete area of ΣQn / Fy. The analysis includes only the horizontal shear force transferred
by the shear connectors supplied; and, thus, neglects the contribution of the concrete
flange not considered in the plastic distribution of forces (see Figure 5-4). The lower
bound moment of inertia, therefore, is the moment of inertia of the section at the factored
(ultimate) load. This is smaller than the moment of inertia at service loads where
deflection is calculated. The value for the lower bound moment of inertia can be
calculated as follows:
ILB = Ix + As YENA −
2
d ΣQn
+
(d + Y2 − YENA)2
2 Fy
where
YENA = distance from bottom of beam to elastic neutral axis (ENA)
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
5 - 10
COMPOSITE DESIGN
=
Asd ΣQn
2 + F (d + Y2)
y
ΣQn
As + F
y
Composite Beam Reactions
Design reactions for symmetrically loaded composite beams may be computed using the
Composite Beam Tables. Two situations will be considered. First, an upper bound value
for a beam reaction may be computed neglecting the composite concrete flange properties
other than concrete strength. Second, a more refined value for a beam reaction can be
computed if the properties of the composite concrete flange are determined initially.
When the properties of the composite concrete flange have not been computed, a
conservative value for the maximum horizontal shear between the composite concrete
slab and the steel section (ΣQn) may be taken as the smaller of AsFs or nQn. Here, n is the
number of headed studs between the reaction point and point of maximum moment. The
value of Qn may be taken from Table 5-1 or determined from LRFD Specification Section
I5. A value for φMn of the composite section may be obtained from the Composite Beam
Tables using the sum of horizontal shear ΣQn as described above. In this case, Y2 is defined
as the distance from the top of the steel beam to the top of the concrete slab. The design
reaction may be determined from the value of φMn as discussed in the following
paragraph.
When the properties of the concrete flange have been computed (effective width and
depth), a slightly different method is used to find φMn. The stud efficiency can be
determined in accordance with Section I5 of the LRFD Specification, or Table 5-1 can
be used for 3⁄4-in. diameter stud shear connectors. The value for the sum of the horizontal
shear force ΣQn can be taken as the smaller of nQn, AsFy, or 0.85fc′Ac, where fc′ is the
concrete cylinder strength (ksi) and Ac is the maximum permitted concrete flange area
(LRFD Specification Section I5.2). The distance Y2 is the distance from the top of the
steel beam to the top of the concrete slab less [ΣQn / (0.85fc′b)] / 2. Using these values
for ΣQn and Y2, the value for φMn can be selected from the Composite Beam Tables.
Equivalent concrete area =
∑Qn
Fy
Y2
d + Y2 – YENA
ENA
d
YENA
Fig. 5-4. Moment of inertia.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
COMPOSITE BEAMS
5 - 11
The design beam reaction for a symmetrically loaded composite beam may be
computed from known values of φMn and the span length as:
R = CcφMn / L
where
R = design beam reaction, kips
Cc = coefficient from Figure 5-5
φMn = composite beam flexural design strength, kip-ft
L = span length, ft
Preliminary Section Selection
When using the Composite Beam Tables, the approximate beam weight per unit length
required for several different beam depths may be calculated as follows:
Mu(12)
Beam weight (lb/ft) =
3.4
(d
/
2
+
Y
−
a
/
2
)φ
F
con
y
where
Mu = required flexural strength, kip-ft
d = nominal beam depth, in.
Ycon = distance from top of steel beam to top of concrete slab, in.
a = effective concrete slab thickness, in.
Fy = steel yield stress, ksi
φ = 0.85
3.4 = ratio of the weight of a beam to its area, lb/in.2
For convenience in the preliminary selection phase the nominal depth may be used. A
value for a/2 must also be selected. For relatively light sections and loads, this value can
be assumed to be one inch. With the PNA at the top of the steel beam, i.e., ΣQn = AsFy,
the flexural design strength is:
φMn = φAsFy (d / 2 + Ycon − a / 2) / 12
where
φMn = flexural design strength, kip-ft
As = steel beam cross-sectional area, in.2
Uniform
load
R
Pu
R
Cc = 4
R
Pu
R
Pu
R
Cc = 2
Pu Pu Pu
R
Cc = 3
R=
Cc φM n
L
Fig. 5-5. Beam reaction coeficients.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
R
R
Cc = 3
5 - 12
COMPOSITE DESIGN
Floor Deflections and Vibrations
Refer to the discussion of Floor Deflections and Vibrations at the end of Part 4 of this
LRFD Manual.
EXAMPLE 5-1
Given:
Determine the beam, with Fy = 50 ksi, required to support a service live
load of 1.3 kips/ft and a service dead load of 0.9 kips/ft. The beam span
is 30 ft and the beam spacing 10 ft. The slab is 31⁄4-in. 1ight weight
concrete (fc′ = 3.5 ksi, 115 pcf) supported by a 3-in. deep composite
metal deck with an average rib width of six inches. The ribs are oriented
perpendicular to the beam. Shored construction is specified. Also,
determine the number of 3⁄4-in. diameter headed studs required and the
service live load deflection.
Solution:
A. Load tabulation:
LL
DL
Total
Service load
(kips/ft)
1.3
0.9
2.2
(L.F.)
(1.6)
(1.2)
Factored load
(kips/ft)
2.1
1.1
3.2
B. Flexural design strength:
Beam moments
Mu = 3.2(30)2/8 = 360 kip-ft
MLL = 1.3(30)2/8 = 146 kip-ft
C. Select section and determine properties:
At this point, go directly to the Composite Beam Tables and select
a section or compute a preliminary trial section size using the
formula:
Mu(12)
Beam weight =
3.4
(d
/
2
+
Y
−
a
/2)φF
con
y
where
Ycon = 3 + 3.25 = 6.25 in.
a / 2= 1 in. (estimate)
φ = 0.85
Fy = 50 ksi
Mu(12)(3.4)
d/2
φFy
16
346
8
d
18
346
9
(Ycon − a / 2)
Beam Weight
5.25
26
5.25
24
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
COMPOSITE BEAMS
5 - 13
From the results above, a W16×26 would be the most appropriate
selection.
Let ΣQn = AsFy = 7.68(50) = 384 kips.
The effective width of the concrete flange is
≤ 2 × L / 8 = 2 × 30 ft / 8 = 7.5 ft = 90 in. (gover ns)
10 ft spacing
ΣQn
384
areq’d =
=
= 1.43 in.
0.85fc′b 0.85(3.5)(90)
Y2 = 6.25 − 1.43 / 2 = 5.53 in.
b
By interpolation from the Composite Beam Tables for a W16×26
and a value of Y2 equal to 5.53 in.,
φMn = 363 + (0.03 / 0.50)(377 − 363)
= 364 kip-ft > 360 kip-ft req’d o.k.
The selected section is adequate for Y2 = 5.5 in. and Y1 = 0.0 in.,
for which φMn = 363 kip-ft
D. Compute number of studs required:
The stud reduction is calculated to be:
Reduction factor =
0.85
(wr / hr)(Hs / hr − 1.0) ≤ 1.0
Nr
√
Reductionfactor=
0.85
(6 / 3)(5.5 / 3 − 1.0) = 1.0
2
√
(I3-1)
where
Nr = number of stud connectors in one rib; not to exceed three
in computations, although more than three may be installed
wr = average width of rib, in.
hr = nominal rib height, in.
Hs = length of stud connector after welding, in.; not to exceed
the value (hr + 3) in computations, although actual length
may be greater. Also must not be less than four stud
diameters
The value for Hs = 5.5 was selected to ensure the stud capacity
reduction factor is 1.0.
The number of studs required is:
with Qn = 19.8 kips (Table 5-1)
2(ΣQn) / Qn = 2(384) / 19.8 = 38.8, say 40 studs
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
5 - 14
COMPOSITE DESIGN
E. Check deflection:
For the selected section, a W16×26, Fy = 50 ksi, Y2 = 5.5 in. and
Y1 = 0.0 in.; from the Elastic Moment of Inertia Tables one can find
the lower bound moment of inertia is 985 in.4 Thus, the service live
load deflection can be calculated as follows (see LRFD Manual
Part 4):
∆LL =
MLLL2 146(30)2
L
L
=
= 0.83 in. =
<
o.k.
434 360
161ILB 161(985)
F. Shear check:
Vu = 3.2(15) = 48 kips
φVn = φ0.6FywAw
= (0.9)(0.6)(50)(15.69 × 0.250)
= 106 kips > 48 kips req’d o.k.
EXAMPLE 5-2
Given:
Determine the beam, with Fy = 50 ksi, required to support a service live
load of 250 psf and a service dead load of 90 psf. The beam span is
40 ft and the beam spacing is 10 ft. Assume 3 in. metal deck is used
with a 4.5 in. slab of 4 ksi normal weight concrete (145 pcf). The stud
reduction factor is 1.0. Unshored construction is specified. Determine
the beam size and service dead and live load deflections. Also select a
non-composite section (no shear connectors).
Solution:
A. Load tabulation:
LL
DL
Total
Service load
(kips/ft)
2.5
0.9
3.4
(L.F.)
(1.6)
(1.2)
Factored load
(kips/ft)
4.0
1.1
5.1
B. Beam moments:
Mu = 5.1(40)2 / 8 = 1,020 kip-ft
MLL = 2.5(40)2 / 8 = 500 kip-ft
MDL = 0.9(40)2 / 8 = 180 kip-ft
C. Select section and determine properties:
Assume a = 2 in.; therefore, take Y2 = 7.5 − 2 / 2 = 6.5 in. From the
Composite Beam Tables, for Fy = 50 ksi and Y2 = 6.5 in., W21×62,
W24×55, and W24×62 are possible sizes.
Try a W24×55:
Fy = 50 ksi
Y2 = 6.5 in.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
COMPOSITE BEAMS
5 - 15
Y1 = 0.0 in.
Qn = 810 kips
φMn = 1,050 kip-ft
Compute Y2 for ΣQn = 810 kips:
2 × L / 8 = 2 × 40 ft / 8 = 10 ft
b ≤
10 ft spacing
= 120 in.
ΣQn
810
=
= 1.99
a =
0.85fc′b 0.85(4)(120)
Y2 = 7.5 − 1.99 / 2 = 6.5 in.
D. Compute the number of studs required:
Qn = 26.1 kips (Table 5-1)
Number of studs = (2)ΣQn / Qn = 2(810) / 26.1 = 62.1, say 64 studs
E. Construction phase strength check:
A construction live load of 20 psf will be assumed. From the LRFD
Specification (Section A4.1), the relevant load combinations are
1.4D
= 1.4 × 0.9 = 1.26 k/ft
1.2D + 1.6L = 1.2 × 0.9 + 1.6 × 0.2 = 1.40 k/ft
= 1.40 × (40)2 / 8 = 280 kip-ft
Mu
From the Composite Beam Tables for a W24×55 with Fy = 50 ksi,
and assuming adequate lateral support is provided by the attachment
of the steel deck to the compression flange,
φMn = φMp = 503 kip-ft > 280 kip-ft
F. Service load deflections:
Assume that the wet concrete load moment is equal to the service
dead load moment. With Ix = 1,350 in.4 for a W24×55,
∆DL =
180(40)2
= 1.33 in.
161(1,350)
For the W24×55 with Y2 = 6.5 in. and Y1 = 0.0 in., the lower bound
moment of inertia can be found in the Lower Bound Elastic Moment
of Inertia Tables; ILB = 4,060 in.4
500(40)2
= 1.22 in.
161(4,060)
L
L
<
o.k.
=
∆LL =
393
360
Specify a beam camber of 11⁄4-in. to overcome the dead load
deflection.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
5 - 16
COMPOSITE DESIGN
G. Check shear:
Vu = 5.1(40) / 2 = 102 kips
φV = φ(0.6)FywAw
= (0.9)(0.6)(50)(23.57 × 0.395)
= 251 kips > 102 kips o.k.
H. Final section selection:
Use: W24×55, Fy = 50 ksi, camber 11⁄4-in., 64 studs, 3⁄4-in. diameter
(32 each side of midspan)
I. Noncomposite section:
Considering the given problem without shear connectors (i.e., noncomposite), a steel section can be selected from the φMp values
tabulated under each section in either the Composite Beam Tables
or the Load Factor Design Selection Tables.
For Mu = 1,020 kip-ft, select a W27×94, Fy = 50 ksi, with a φMp
flexural design strength equal to 1,040 kip-ft.
∆DL =
180(40)2
= 0.55 in.
161(3,270)
∆LL =
500(40)2
= 1.52 in. > L / 360
161(3,270)
For ∆ = L / 360 = 1.33 in.
Ireq’d =
500(40)2
= 3,736 in.4
161(1.33)
Use: W30×99, Fy = 50 ksi, φMn = φbMp = 1,170 kip-ft
EXAMPLE 5-3
Given:
A W21×44, Fy = 50 ksi, steel girder spans 30 feet and supports
intermediate beams at the third points. A total of fifty 3⁄4-in. diameter
headed studs are applied to the beam as follows: 24 between each
support and the beams at the one-third points, and two between the
intermediate beams. The slab consists of 31⁄4-in. light-weight concrete
(115 pcf) with a specified design strength of 3.5 ksi over a 3-in. deep
composite metal deck with an average rib width of six inches. The ribs
are oriented parallel to the beam centerline. Determine the design beam
reactions.
Solutions:
For studs in a single row the spacing between the support and first
intermediate beam would be 10(12) / 24 = 5.0 in. which is greater than
the specified minimum of six stud diameters (LRFD Specification
Section I5.6). Since wr / hr = 6 / 3 = 2 is greater than 1.5, the stud
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
COMPOSITE BEAMS
5 - 17
reduction factor is not necessary (LRFD Specification I3.5c). Therefore, from Table 5.1, the stud shear strength is:
ΣQn = nQn = 24(19.8) = 475 kips
For ΣQn = 475 kips, the required effective concrete flange thickness
can be calculated to be:
a =
475
= 1.77 in.
0.85(3.5)(7.5)(12)
Y2 = 3 + 3.25 − 1.77 / 2 = 5.36 in.
Beam reaction:
From the Composite Beam Selection Table, for a W21×44, Fy = 50 ksi,
ΣQn = 475 kips places the PNA at Y1 = 0.27 in.
For Y2 = 5.36 in. and Y1 = 0.27 in., φMn = 655 kip-ft
R = CcφMn / L
= 3(655) / 30
= 65.5 kips
where
R = design reaction, kips
Cc = coefficient from Figure 5-5
φMn = flexural design strength of beam, kip-ft
L = span length, ft
Note: The beam weight was neglected in this example.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
5 - 18
COMPOSITE DESIGN
Fy = 36 ksi
COMPOSITE DESIGN
COMPOSITE BEAM SELECTION TABLE
W Shapes
φ = 0.85
φb = 0.90
Shape
φb M p PNAc Y1a
ΣQ n
φM n (kip-ft)
Y2b (in.)
Kip-ft
W40×297
3590
W 40 X 278 3210
In.
Kips
2
2.5
3
3.5
4
4.5
5
5.5
6
6.5
7
0.00
0.41
0.83
1.24
1.65
4.59
8.17
3150
2680
2210
1740
1270
1030
787
4890
4810
4720
4620
4510
4420
4280
5000
4910
4800
4690
4550
4460
4310
5110
5000
4880
4750
4600
4500
4340
5220
5100
4960
4810
4640
4540
4370
5330
5190
5040
4870
4690
4570
4390
5440
5290
5120
4930
4730
4610
4420
5550
5380
5190
4990
4780
4640
4450
5670
5480
5270
5050
4820
4680
4480
5780
5570
5350
5120
4870
4720
4500
5890
5660
5430
5180
4910
4750
4530
6000
5760
5510
5240
4960
4790
4560
TFL 0.00
2
0.45
3
0.91
4
1.36
BFL 1.81
6
5.64
7 10.06
2940
2550
2160
1770
1380
1060
736
4610
4540
4470
4380
4280
4160
3930
4710
4630
4550
4450
4330
4190
3960
4810
4730
4620
4510
4380
4230
3980
4920
4820
4700
4570
4430
4270
4010
5020
4910
4780
4640
4480
4310
4040
5130
5000
4850
4700
4530
4340
4060
5230
5090
4930
4760
4580
4380
4090
5340
5180
5010
4820
4630
4420
4110
5440
5270
5080
4890
4680
4460
4140
5540
5360
5160
4950
4730
4490
4170
5650
5450
5240
5010
4780
4530
4190
TFL
2
3
4
BFL
6
7
W40×277
3380
TFL
2
3
4
BFL
6
7
0.00
0.39
0.79
1.18
1.58
4.25
7.60
2930
2480
2030
1580
1130
932
732
4530
4460
4380
4280
4170
4110
3990
4630
4550
4450
4340
4210
4140
4020
4740
4630
4520
4390
4250
4170
4050
4840
4720
4590
4450
4290
4210
4070
4940
4810
4660
4510
4330
4240
4100
5050
4900
4740
4560
4370
4270
4120
5150
4990
4810
4620
4410
4300
4150
5250
5070
4880
4670
4450
4340
4180
5360
5160
4950
4730
4490
4370
4200
5460
5250
5020
4790
4540
4400
4230
5570
5340
5100
4840
4580
4440
4250
W40×264
3050
TFL
2
3
4
BFL
6
7
0.00
0.43
0.87
1.30
1.73
5.49
9.90
2790
2420
2050
1680
1310
1000
698
4350
4300
4230
4140
4050
3930
3730
4450
4380
4300
4200
4100
3970
3750
4550
4470
4370
4260
4140
4000
3780
4650
4550
4440
4320
4190
4040
3800
4750
4640
4520
4380
4240
4070
3820
4850
4720
4590
4440
4280
4110
3850
4950
4810
4660
4500
4330
4150
3870
5050
4900
4730
4560
4380
4180
3900
5140
4980
4810
4620
4420
4220
3920
5240
5070
4880
4680
4470
4250
3950
5340
5150
4950
4740
4510
4290
3970
aY1 = distance from top of the steel beam to plastic neutral axis.
bY2 = distance from top of the steel beam to concrete flange force.
cSee Figure 5-3 for PNA locations.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
COMPOSITE BEAMS
5 - 19
Fy = 36 ksi
COMPOSITE DESIGN
COMPOSITE BEAM SELECTION TABLE
W Shapes
φ = 0.85
φb = 0.90
Shape
φb M p PNAc Y1a
ΣQ n
φM n (kip-ft)
Y2b (in.)
In.
Kips
2
2.5
3
3.5
4
4.5
5
5.5
6
6.5
7
W40×249
Kip-ft
3020
TFL
2
3
4
BFL
6
7
0.00
0.36
0.71
1.07
1.42
4.06
7.47
2640
2240
1830
1430
1030
844
660
4050
3990
3920
3840
3750
3690
3580
4150
4070
3980
3890
3780
3720
3610
4240
4150
4050
3940
3820
3750
3630
4330
4230
4110
3990
3850
3770
3650
4430
4310
4180
4040
3890
3800
3680
4520
4390
4240
4090
3930
3830
3700
4610
4470
4310
4140
3960
3860
3720
4710
4550
4370
4190
4000
3890
3750
4800
4630
4440
4240
4040
3920
3770
4900
4700
4500
4290
4070
3950
3790
4990
4780
4570
4340
4110
3980
3820
W40×235
2730
TFL
2
3
4
BFL
6
7
0.00
0.39
0.79
1.18
1.58
5.18
9.47
2480
2140
1810
1470
1130
876
620
3840
3790
3720
3650
3570
3480
3310
3930
3860
3790
3700
3610
3510
3330
4010
3940
3850
3760
3650
3540
3350
4100
4010
3920
3810
3690
3570
3370
4190
4090
3980
3860
3730
3600
3400
4280
4170
4040
3910
3770
3630
3420
4370
4240
4110
3960
3810
3660
3440
4450
4320
4170
4020
3850
3690
3460
4540
4390
4240
4070
3890
3730
3480
4630
4470
4300
4120
3930
3760
3510
4720
4540
4360
4170
3970
3790
3530
W40×215
2600
TFL
2
3
4
BFL
6
7
0.00
0.31
0.61
0.92
1.22
3.84
7.32
2280
1930
1590
1240
895
733
570
3470
3420
3360
3290
3210
3160
3080
3550
3480
3410
3330
3240
3190
3100
3630
3550
3470
3380
3280
3210
3120
3710
3620
3520
3420
3310
3240
3140
3790
3690
3580
3460
3340
3270
3160
3870
3760
3640
3510
3370
3290
3180
3950
3830
3690
3550
3400
3320
3200
4030
3900
3750
3600
3440
3340
3220
4110
3960
3810
3640
3470
3370
3240
4200
4030
3860
3680
3500
3400
3260
4280
4100
3920
3730
3530
3420
3280
W40×211
2440
TFL
2
3
4
BFL
6
7
0.00
0.35
0.71
1.06
1.42
4.99
9.35
2230
1930
1630
1330
1030
793
558
3430
3380
3330
3270
3200
3110
2960
3510
3450
3390
3310
3230
3140
2980
3590
3520
3440
3360
3270
3170
3000
3670
3590
3500
3410
3310
3200
3020
3740
3660
3560
3460
3340
3230
3040
3820
3720
3620
3500
3380
3250
3060
3900
3790
3670
3550
3420
3280
3080
3980
3860
3730
3600
3450
3310
3100
4060
3930
3790
3640
3490
3340
3120
4140
4000
3850
3690
3530
3370
3140
4220
4070
3910
3740
3560
3400
3160
aY1 = distance from top of the steel beam to plastic neutral axis.
bY2 = distance from top of the steel beam to concrete flange force.
cSee Figure 5-3 for PNA locations.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
5 - 20
COMPOSITE DESIGN
Fy = 36 ksi
COMPOSITE DESIGN
COMPOSITE BEAM SELECTION TABLE
W Shapes
φ = 0.85
φb = 0.90
Shape
φb M p PNAc Y1a
ΣQ n
φM n (kip-ft)
Y2b (in.)
In.
Kips
2
2.5
3
3.5
4
4.5
5
5.5
6
6.5
7
W40×199
Kip-ft
2340
TFL
2
3
4
BFL
6
7
0.00
0.27
0.53
0.80
1.07
4.16
8.10
2100
1800
1500
1200
895
710
526
3180
3130
3080
3020
2960
2900
2800
3250
3200
3130
3070
2990
2930
2820
3330
3260
3190
3110
3020
2950
2830
3400
3320
3240
3150
3060
2980
2850
3480
3390
3290
3190
3090
3000
2870
3550
3450
3350
3240
3120
3030
2890
3620
3510
3400
3280
3150
3050
2910
3700
3580
3450
3320
3180
3080
2930
3770
3640
3500
3360
3210
3100
2950
3850
3710
3560
3400
3250
3130
2960
3920
3770
3610
3450
3280
3150
2980
W40×183
2110
TFL
2
3
4
BFL
6
7
0.00
0.31
0.61
0.92
1.22
4.76
9.16
1930
1670
1410
1160
896
690
483
2940
2900
2860
2810
2750
2680
2550
3010
2960
2910
2850
2780
2710
2570
3080
3020
2960
2890
2810
2730
2580
3150
3080
3010
2930
2850
2750
2600
3220
3140
3060
2970
2880
2780
2620
3290
3200
3110
3010
2910
2800
2640
3350
3260
3160
3050
2940
2830
2650
3420
3320
3210
3090
2970
2850
2670
3490
3380
3260
3130
3000
2880
2690
3560
3440
3310
3180
3040
2900
2700
3630
3500
3360
3220
3070
2930
2720
W40×174
1930
TFL
2
3
4
BFL
6
7
0.00
0.21
0.42
0.62
0.83
4.59
9.27
1840
1600
1370
1130
898
679
460
2750
2710
2680
2630
2590
2520
2380
2810
2770
2720
2670
2620
2540
2400
2880
2830
2770
2710
2650
2570
2410
2940
2880
2820
2750
2680
2590
2430
3010
2940
2870
2790
2720
2620
2450
3080
3000
2920
2830
2750
2640
2460
3140
3060
2970
2870
2780
2660
2480
3210
3110
3020
2910
2810
2690
2490
3270
3170
3060
2960
2840
2710
2510
3340
3230
3110
3000
2870
2740
2530
3400
3280
3160
3040
2910
2760
2540
W40×167
1870
TFL
2
3
4
BFL
6
7
0.00
0.26
0.51
0.77
1.03
5.00
9.85
1770
1550
1330
1110
896
669
442
2670
2630
2600
2560
2510
2430
2280
2730
2690
2640
2600
2540
2460
2300
2790
2740
2690
2630
2570
2480
2310
2850
2800
2740
2670
2610
2510
2330
2920
2850
2790
2710
2640
2530
2350
2980
2910
2830
2750
2670
2550
2360
3040
2960
2880
2790
2700
2580
2380
3100
3020
2930
2830
2730
2600
2390
3170
3070
2970
2870
2760
2620
2410
3230
3130
3020
2910
2800
2650
2420
3290
3180
3070
2950
2830
2670
2440
W40×149
1610
TFL 0.00
2
0.21
3
0.42
4
0.62
BFL 0.83
6
5.15
7 10.41
1580
1400
1220
1050
871
633
394
2360
2330
2300
2270
2240
2160
1990
2410
2380
2340
2310
2270
2180
2010
2470
2430
2390
2340
2300
2200
2020
2520
2480
2430
2380
2330
2220
2030
2580
2530
2470
2420
2360
2250
2050
2640
2580
2520
2460
2390
2270
2060
2690
2630
2560
2490
2420
2290
2070
2750
2680
2600
2530
2450
2310
2090
2800
2730
2650
2570
2480
2340
2100
2860
2780
2690
2600
2510
2360
2120
2920
2830
2730
2640
2540
2380
2130
aY1 = distance from top of the steel beam to plastic neutral axis.
bY2 = distance from top of the steel beam to concrete flange force.
cSee Figure 5-3 for PNA locations.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
COMPOSITE BEAMS
5 - 21
Fy = 36 ksi
COMPOSITE DESIGN
COMPOSITE BEAM SELECTION TABLE
W Shapes
φ = 0.85
φb = 0.90
Shape
φb M p PNAc Y1a
ΣQ n
φM n (kip-ft)
Y2b (in.)
In.
Kips
2
2.5
3
3.5
4
4.5
5
5.5
6
6.5
7
W 36×300
Kip-ft
3400
TFL
2
3
4
BFL
6
7
0.00
0.42
0.84
1.26
1.68
3.97
6.69
3180
2680
2170
1670
1160
979
795
4590
4510
4410
4310
4180
4120
4020
4700
4600
4490
4360
4220
4150
4050
4810
4700
4570
4420
4260
4190
4080
4920
4790
4640
4480
4310
4220
4110
5040
4890
4720
4540
4350
4260
4140
5150
4980
4800
4600
4390
4290
4160
5260
5080
4880
4660
4430
4330
4190
5370
5170
4950
4720
4470
4360
4220
5490
5270
5030
4780
4510
4400
4250
5600
5360
5110
4840
4550
4430
4280
5710
5460
5180
4900
4590
4470
4300
W 36×280
3160
TFL
2
3
4
BFL
6
7
0.00
0.39
0.79
1.18
1.57
3.88
6.62
2970
2500
2030
1560
1090
916
742
4260
4180
4100
4000
3890
3830
3740
4360
4270
4170
4050
3930
3860
3770
4470
4360
4240
4110
3960
3890
3790
4570
4450
4310
4160
4000
3930
3820
4680
4540
4390
4220
4040
3960
3850
4780
4630
4460
4280
4080
3990
3870
4890
4710
4530
4330
4120
4020
3900
4990
4800
4600
4390
4160
4060
3920
5100
4890
4670
4440
4200
4090
3950
5200
4980
4740
4500
4230
4120
3980
5310
5070
4820
4550
4270
4150
4000
W 36×260
2920
TFL
2
3
4
BFL
6
7
0.00
0.36
0.72
1.08
1.44
3.86
6.75
2750
2330
1900
1470
1040
863
689
3930
3860
3780
3700
3600
3540
3450
4020
3940
3850
3750
3630
3570
3470
4120
4030
3920
3800
3670
3600
3500
4220
4110
3980
3850
3710
3630
3520
4320
4190
4050
3900
3740
3660
3550
4410
4270
4120
3960
3780
3690
3570
4510
4350
4190
4010
3820
3720
3600
4610
4440
4250
4060
3850
3750
3620
4710
4520
4320
4110
3890
3780
3640
4800
4600
4390
4160
3930
3820
3670
4900
4680
4450
4210
3960
3850
3690
W 36×245
2730
TFL
2
3
4
BFL
6
7
0.00
0.34
0.68
1.01
1.35
3.81
6.77
2600
2190
1790
1390
991
820
649
3680
3620
3550
3470
3380
3330
3240
3780
3700
3620
3520
3420
3360
3260
3870
3780
3680
3570
3450
3380
3280
3960
3860
3740
3620
3490
3410
3310
4050
3930
3810
3670
3520
3440
3330
4140
4010
3870
3720
3560
3470
3350
4240
4090
3930
3770
3590
3500
3380
4330
4170
4000
3820
3630
3530
3400
4420
4240
4060
3870
3660
3560
3420
4510
4320
4120
3910
3700
3590
3440
4600
4400
4190
3960
3730
3620
3470
W 36×230
2550
TFL
2
3
4
BFL
6
7
0.00
0.32
0.63
0.95
1.26
3.81
6.83
2430
2060
1690
1310
939
774
608
3440
3380
3320
3240
3160
3110
3020
3530
3450
3380
3290
3190
3140
3040
3610
3530
3440
3340
3230
3160
3070
3700
3600
3500
3380
3260
3190
3090
3780
3670
3560
3430
3290
3220
3110
3870
3750
3620
3480
3330
3250
3130
3960
3820
3670
3520
3360
3270
3150
4040
3890
3730
3570
3390
3300
3170
4130
3970
3790
3610
3430
3330
3200
4210
4040
3850
3660
3460
3360
3220
4300
4110
3910
3710
3490
3380
3240
aY1 = distance from top of the steel beam to plastic neutral axis.
bY2 = distance from top of the steel beam to concrete flange force.
cSee Figure 5-3 for PNA locations.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
5 - 22
COMPOSITE DESIGN
Fy = 36 ksi
COMPOSITE DESIGN
COMPOSITE BEAM SELECTION TABLE
W Shapes
φ = 0.85
φb = 0.90
Shape
φb M p PNAc Y1a
ΣQ n
φM n (kip-ft)
Y2b (in.)
In.
Kips
2
2.5
3
3.5
4
4.5
5
5.5
6
6.5
7
W 36×210
Kip-ft
2250
TFL
2
3
4
BFL
6
7
0.00
0.34
0.68
1.02
1.36
5.06
9.04
2220
1930
1630
1330
1030
794
556
3210
3160
3110
3050
2980
2890
2740
3280
3230
3170
3090
3020
2920
2760
3360
3300
3220
3140
3050
2950
2780
3440
3370
3280
3190
3090
2980
2800
3520
3430
3340
3240
3130
3010
2820
3600
3500
3400
3280
3160
3030
2840
3680
3570
3450
3330
3200
3060
2860
3760
3640
3510
3380
3240
3090
2880
3840
3710
3570
3420
3270
3120
2900
3920
3770
3630
3470
3310
3150
2920
3990
3840
3680
3520
3350
3170
2940
W 36×194
2070
TFL
2
3
4
BFL
6
7
0.00
0.32
0.63
0.95
1.26
4.94
8.93
2050
1780
1500
1230
953
733
513
2940
2900
2850
2800
2740
2660
2520
3020
2960
2910
2840
2770
2690
2540
3090
3030
2960
2890
2810
2710
2560
3160
3090
3010
2930
2840
2740
2580
3230
3150
3070
2970
2870
2760
2590
3310
3220
3120
3020
2910
2790
2610
3380
3280
3170
3060
2940
2820
2630
3450
3340
3220
3100
2970
2840
2650
3520
3400
3280
3150
3010
2870
2670
3600
3470
3330
3190
3040
2890
2680
3670
3530
3380
3230
3080
2920
2700
W 36×182
1940
TFL
2
3
4
BFL
6
7
0.00
0.29
0.59
0.89
1.18
4.89
8.92
1930
1670
1420
1160
904
693
482
2760
2720
2670
2620
2570
2490
2360
2820
2780
2720
2660
2600
2520
2380
2890
2840
2770
2710
2630
2540
2400
2960
2890
2820
2750
2660
2570
2410
3030
2950
2870
2790
2700
2590
2430
3100
3010
2920
2830
2730
2620
2450
3170
3070
2970
2870
2760
2640
2460
3230
3130
3020
2910
2790
2670
2480
3300
3190
3070
2950
2820
2690
2500
3370
3250
3120
2990
2860
2720
2520
3440
3310
3170
3030
2890
2740
2530
W 36×170
1800
TFL
2
3
4
BFL
6
7
0.00
0.28
0.55
0.83
1.10
4.84
8.89
1800
1560
1320
1090
847
649
450
2560
2520
2480
2440
2390
2320
2200
2620
2580
2530
2480
2420
2340
2210
2690
2640
2580
2520
2450
2370
2230
2750
2690
2620
2550
2480
2390
2240
2820
2750
2670
2590
2510
2410
2260
2880
2800
2720
2630
2540
2440
2280
2940
2860
2770
2670
2570
2460
2290
3010
2910
2810
2710
2600
2480
2310
3070
2970
2860
2750
2630
2500
2320
3130
3020
2910
2780
2660
2530
2340
3200
3080
2950
2820
2690
2550
2360
W 36×160
1680
TFL
2
3
4
BFL
6
7
0.00
0.26
0.51
0.77
1.02
4.82
8.97
1690
1470
1250
1030
811
617
423
2400
2360
2330
2290
2240
2170
2050
2460
2420
2370
2320
2270
2200
2070
2520
2470
2420
2360
2300
2220
2080
2580
2520
2460
2400
2330
2240
2100
2640
2570
2500
2430
2360
2260
2110
2700
2630
2550
2470
2380
2280
2130
2760
2680
2590
2510
2410
2310
2140
2820
2730
2640
2540
2440
2330
2160
2880
2780
2680
2580
2470
2350
2170
2940
2830
2730
2610
2500
2370
2190
3000
2890
2770
2650
2530
2390
2200
aY1 = distance from top of the steel beam to plastic neutral axis.
bY2 = distance from top of the steel beam to concrete flange force.
cSee Figure 5-3 for PNA locations.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
COMPOSITE BEAMS
5 - 23
Fy = 36 ksi
COMPOSITE DESIGN
COMPOSITE BEAM SELECTION TABLE
W Shapes
φ = 0.85
φb = 0.90
Shape
φb M p PNAc Y1a
ΣQ n
φM n (kip-ft)
Y2b (in.)
5
5.5
6
6.5
7
W 36×150
Kip-ft
1570
TFL
2
3
4
BFL
6
7
0.00 1590 2250 2300 2360 2410 2470 2530
0.24 1390 2220 2260 2310 2360 2410 2460
0.47 1190 2180 2220 2270 2310 2350 2390
0.71 983 2140 2180 2210 2250 2280 2320
0.94 781 2100 2130 2160 2190 2210 2240
4.83 589 2040 2060 2080 2100 2120 2140
9.08 398 1920 1930 1950 1960 1970 1990
In.
Kips
2
2.5
3
3.5
4
4.5
2580
2510
2430
2350
2270
2160
2000
2640
2560
2480
2390
2300
2190
2020
2700
2610
2520
2420
2330
2210
2030
2750
2660
2560
2460
2350
2230
2040
2810
2710
2600
2490
2380
2250
2060
W 36×135
1370
TFL
2
3
4
BFL
6
7
0.00 1430 2000 2050 2100 2150 2200 2260
0.20 1260 1980 2020 2070 2110 2160 2200
0.40 1090 1950 1990 2030 2060 2100 2140
0.59 919 1920 1950 1980 2020 2050 2080
0.79 749 1890 1910 1940 1970 1990 2020
4.96 553 1820 1840 1860 1880 1900 1920
9.50 357 1690 1710 1720 1730 1740 1760
2310
2240
2180
2110
2050
1940
1770
2360
2290
2220
2150
2070
1960
1780
2410
2330
2260
2180
2100
1980
1790
2460
2380
2300
2210
2130
2000
1810
2510
2420
2330
2240
2150
2020
1820
W 33×221
2310
TFL
2
3
4
BFL
6
7
0.00
0.32
0.64
0.96
1.28
3.76
6.48
2340
1980
1610
1250
889
737
585
3140
3090
3020
2950
2870
2820
2750
3230
3160
3080
3000
2900
2850
2770
3310
3230
3140
3040
2940
2880
2790
3390
3300
3200
3090
2970
2900
2810
3470
3370
3250
3130
3000
2930
2830
3560
3440
3310
3170
3030
2960
2850
3640
3510
3370
3220
3060
2980
2870
3720
3580
3420
3260
3090
3010
2890
3810
3650
3480
3310
3120
3030
2910
3890
3720
3540
3350
3160
3060
2930
3970
3790
3600
3400
3190
3090
2960
W 33×201
2080
TFL
2
3
4
BFL
6
7
0.00
0.29
0.58
0.86
1.15
3.67
6.51
2130
1800
1480
1150
824
678
532
2840
2790
2730
2670
2600
2560
2480
2910
2850
2790
2710
2630
2580
2500
2990
2920
2840
2750
2660
2600
2520
3070
2980
2890
2790
2690
2630
2540
3140
3050
2940
2830
2720
2650
2560
3220
3110
2990
2870
2750
2680
2580
3290
3170
3050
2920
2780
2700
2600
3370
3240
3100
2960
2810
2720
2620
3440
3300
3150
3000
2830
2750
2630
3520
3360
3200
3040
2860
2770
2650
3590
3430
3260
3080
2890
2800
2670
W 33×141
1390
TFL
2
3
4
BFL
6
7
0.00 1500 1980 2030 2080 2140 2190 2240
0.24 1300 1950 1990 2040 2090 2130 2180
0.48 1100 1920 1950 1990 2030 2070 2110
0.72 900 1880 1910 1940 1970 2010 2040
0.96 700 1840 1860 1890 1910 1940 1960
4.31 537 1790 1810 1820 1840 1860 1880
8.05 374 1690 1710 1720 1730 1740 1760
2300
2220
2150
2070
1990
1900
1770
2350
2270
2190
2100
2010
1920
1780
2400
2320
2230
2130
2040
1940
1800
2460
2360
2270
2170
2060
1960
1810
2510
2410
2300
2200
2090
1980
1820
aY1 = distance from top of the steel beam to plastic neutral axis.
bY2 = distance from top of the steel beam to concrete flange force.
cSee Figure 5-3 for PNA locations.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
5 - 24
COMPOSITE DESIGN
Fy = 36 ksi
COMPOSITE DESIGN
COMPOSITE BEAM SELECTION TABLE
W Shapes
φ = 0.85
φb = 0.90
Shape
φb M p PNAc Y1a
ΣQ n
φM n (kip-ft)
Y2b (in.)
5
5.5
6
6.5
7
W 33×130
Kip-ft
1260
TFL
2
3
4
BFL
6
7
0.00 1380 1810 1860 1910 1960 2010 2060
0.21 1200 1780 1830 1870 1910 1950 2000
0.43 1020 1760 1790 1830 1860 1900 1940
0.64 847 1720 1750 1780 1810 1840 1870
0.86 670 1690 1710 1740 1760 1780 1810
4.39 507 1640 1660 1670 1690 1710 1730
8.29 345 1540 1550 1570 1580 1590 1600
In.
Kips
2
2.5
3
3.5
4
4.5
2100
2040
1970
1900
1830
1750
1610
2150
2080
2010
1930
1860
1760
1630
2200
2130
2050
1960
1880
1780
1640
2250
2170
2080
1990
1900
1800
1650
2300
2210
2120
2020
1930
1820
1660
W 33×118
1120
TFL
2
3
4
BFL
6
7
0.00 1250 1630 1680 1720 1760 1810 1850
0.19 1100 1610 1650 1690 1720 1760 1800
0.37 943 1580 1620 1650 1680 1720 1750
0.56 790 1560 1580 1610 1640 1670 1700
0.74 638 1530 1550 1570 1600 1620 1640
4.44 475 1480 1490 1510 1530 1540 1560
8.54 312 1380 1390 1400 1410 1420 1430
1900
1840
1780
1720
1660
1580
1450
1940
1880
1820
1750
1690
1590
1460
1980
1920
1850
1780
1710
1610
1470
2030
1960
1880
1810
1730
1630
1480
2070
2000
1920
1840
1750
1650
1490
W 30×116
1020
TFL
2
3
4
BFL
6
7
0.00 1230 1480 1530 1570 1610 1660 1700
0.21 1070 1460 1500 1530 1570 1610 1650
0.43 910 1430 1460 1500 1530 1560 1590
0.64 749 1400 1430 1460 1480 1510 1540
0.85 589 1370 1390 1410 1440 1460 1480
3.98 448 1330 1350 1360 1380 1390 1410
7.44 308 1250 1260 1270 1290 1300 1310
1740
1690
1630
1560
1500
1430
1320
1790
1720
1660
1590
1520
1440
1330
1830
1760
1690
1620
1540
1460
1340
1880
1800
1720
1640
1560
1470
1350
1920
1840
1750
1670
1580
1490
1360
W 30×108
934
TFL
2
3
4
BFL
6
7
0.00 1140 1370 1410 1450 1490 1530 1570
0.19 998 1350 1380 1420 1450 1490 1520
0.38 855 1320 1350 1380 1410 1440 1470
0.57 711 1300 1320 1350 1370 1400 1420
0.76 568 1270 1290 1310 1330 1350 1370
4.04 427 1230 1240 1260 1270 1290 1300
7.64 285 1150 1160 1170 1180 1190 1200
1610
1560
1500
1450
1390
1320
1210
1650
1590
1530
1470
1410
1330
1220
1690
1630
1570
1500
1430
1350
1230
1730
1660
1600
1520
1450
1360
1240
1770
1700
1630
1550
1470
1380
1250
W 30×99
842
TFL
2
3
4
BFL
6
7
0.00 1050 1250 1290 1320 1360 1400 1430
0.17 922 1230 1260 1300 1330 1360 1390
0.34 796 1210 1240 1270 1290 1320 1350
0.50 670 1190 1210 1240 1260 1280 1310
0.67 543 1170 1180 1200 1220 1240 1260
4.07 403 1120 1140 1150 1170 1180 1190
7.83 262 1040 1050 1060 1070 1080 1090
1470
1430
1380
1330
1280
1210
1100
1510
1460
1410
1350
1300
1220
1110
1550
1490
1440
1380
1320
1240
1120
1580
1520
1460
1400
1340
1250
1130
1620
1560
1490
1430
1360
1270
1140
aY1 = distance from top of the steel beam to plastic neutral axis.
bY2 = distance from top of the steel beam to concrete flange force.
cSee Figure 5-3 for PNA locations.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
COMPOSITE BEAMS
5 - 25
Fy = 36 ksi
COMPOSITE DESIGN
COMPOSITE BEAM SELECTION TABLE
W Shapes
φ = 0.85
φb = 0.90
Shape
φb M p PNAc Y1a
ΣQ n
φM n (kip-ft)
Y2b (in.)
5
5.5
6
6.5
7
W 27×102
Kip-ft
824
TFL
2
3
4
BFL
6
7
0.00 1080 1190 1230 1270 1300 1340 1380
0.21 930 1170 1200 1230 1270 1300 1330
0.42 781 1140 1170 1200 1230 1250 1280
0.62 631 1120 1140 1160 1180 1210 1230
0.83 482 1090 1100 1120 1140 1160 1170
3.41 376 1060 1070 1080 1100 1110 1120
6.26 270 1010 1010 1020 1030 1040 1050
In.
Kips
2
1420
1360
1310
1250
1190
1140
1060
1460
1400
1340
1270
1210
1150
1070
1500
1430
1360
1290
1220
1160
1080
1530
1460
1390
1320
1240
1180
1090
1570
1500
1420
1340
1260
1190
1100
W 27×94
751
TFL
2
3
4
BFL
6
7
0.00
0.19
0.37
0.56
0.75
3.39
6.39
997
863
729
595
461
355
249
1300
1260
1210
1150
1100
1050
974
1340
1290
1230
1170
1120
1060
982
1370
1320
1260
1200
1130
1070
991
1410
1350
1280
1220
1150
1090
1000
1450
1380
1310
1240
1170
1100
1010
W 27×84
659
TFL
2
3
4
BFL
6
7
0.00
0.16
0.32
0.48
0.64
3.44
6.62
893
778
663
549
434
329
223
971 1000 1030 1070 1100 1130 1160 1190 1220
954 982 1010 1040 1060 1090 1120 1150 1170
936 959 983 1010 1030 1050 1080 1100 1120
916 936 955 975 994 1010 1030 1050 1070
896 911 926 942 957 972 988 1000 1020
866 878 890 901 913 925 936 948 960
814 822 830 838 846 854 861 869 877
1260
1200
1150
1090
1030
971
885
1290
1230
1170
1110
1050
983
893
W 24×76
540
TFL
2
3
4
BFL
6
7
0.00
0.17
0.34
0.51
0.68
3.00
5.60
806
696
586
476
366
284
202
797
781
764
745
724
703
666
826
806
784
762
737
713
673
855
830
805
778
750
723
680
883
855
826
795
763
733
687
912
880
847
812
776
743
694
940
904
867
829
789
753
702
969
929
888
846
802
763
709
997 1030 1050 1080
954 978 1000 1030
909 930 950 971
863 880 896 913
815 828 841 854
773 783 793 803
716 723 730 737
W 24×68
478
TFL
2
3
4
BFL
6
7
0.00
0.15
0.29
0.44
0.59
3.05
5.81
724
629
535
440
346
263
181
711
697
682
666
649
628
590
736
719
701
682
662
637
596
762
741
720
697
674
646
603
788
764
739
713
686
656
609
813
786
758
729
698
665
616
839
808
777
744
711
674
622
864
830
796
760
723
684
628
890
853
815
775
735
693
635
1090
1070
1050
1030
1000
972
921
2.5
1130
1100
1080
1050
1020
985
929
3
1160
1130
1100
1070
1030
997
938
3.5
1200
1160
1130
1090
1050
1010
947
4
1230
1190
1150
1110
1070
1020
956
4.5
1270
1230
1180
1130
1080
1040
965
aY1 = distance from top of the steel beam to plastic neutral axis.
bY2 = distance from top of the steel beam to concrete flange force.
cSee Figure 5-3 for PNA locations.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
916
875
833
791
747
702
641
941
897
852
807
760
712
648
967
920
871
822
772
721
654
5 - 26
COMPOSITE DESIGN
Fy = 36 ksi
COMPOSITE DESIGN
COMPOSITE BEAM SELECTION TABLE
W Shapes
φ = 0.85
φb = 0.90
Shape
φb M p PNAc Y1a
ΣQ n
φM n (kip-ft)
Y2b (in.)
In.
Kips
2
2.5
3
3.5
4
4.5
5
5.5
6
6.5
7
W 24×62
Kip-ft
413
TFL
2
3
4
BFL
6
7
0.00
0.15
0.29
0.44
0.59
3.47
6.58
655
580
506
431
356
260
164
644
633
621
608
595
568
520
667
653
639
624
608
577
526
690
674
657
639
620
587
532
713
694
675
654
633
596
538
737
715
693
669
646
605
543
760
736
711
685
658
614
549
783
756
728
700
671
623
555
806
777
746
715
683
633
561
829
797
764
731
696
642
567
853
818
782
746
709
651
572
876
838
800
761
721
660
578
W 24×55
362
TFL
2
3
4
BFL
6
7
0.00
0.13
0.25
0.38
0.51
3.45
6.66
583
520
456
392
328
237
146
569
560
550
540
529
504
458
590
579
566
554
540
512
463
611
597
583
568
552
520
468
631
615
599
582
564
529
474
652
634
615
595
575
537
479
673
652
631
609
587
546
484
693
671
647
623
599
554
489
714
689
663
637
610
562
494
735
707
679
651
622
571
499
755
726
696
665
634
579
505
776
744
712
679
645
588
510
W 21×62
389
TFL
2
3
4
BFL
6
7
0.00
0.15
0.31
0.46
0.62
2.53
4.78
659
568
476
385
294
229
165
583
570
555
540
523
507
482
606
590
572
553
534
516
487
630
610
589
567
544
524
493
653
630
606
581
555
532
499
676
650
623
594
565
540
505
700
670
640
608
575
548
511
723
690
656
622
586
556
517
746
710
673
635
596
564
522
770
730
690
649
607
572
528
793
751
707
663
617
581
534
816
771
724
676
628
589
540
W 21×57
348
TFL
2
3
4
BFL
6
7
0.00
0.16
0.33
0.49
0.65
2.90
5.38
601
525
448
371
294
222
150
534
522
510
497
483
464
433
555
541
526
510
493
472
438
576
559
542
523
504
480
443
597
578
558
536
514
488
449
619
597
574
550
525
496
454
640
615
589
563
535
504
459
661
634
605
576
546
511
465
683
652
621
589
556
519
470
704
671
637
602
566
527
475
725
689
653
615
577
535
481
747
708
669
628
587
543
486
W 21×50
297
TFL
2
3
4
BFL
6
7
0.00
0.13
0.27
0.40
0.54
2.92
5.58
529
466
403
341
278
205
132
465
456
446
436
425
406
374
484
473
461
448
435
413
379
503
489
475
460
445
421
383
522
506
489
472
454
428
388
540
522
504
484
464
435
393
559
539
518
496
474
442
397
578
555
532
508
484
450
402
597
572
546
520
494
457
407
615
588
561
532
504
464
411
634
605
575
545
513
472
416
653
621
589
557
523
479
421
aY1 = distance from top of the steel beam to plastic neutral axis.
bY2 = distance from top of the steel beam to concrete flange force.
cSee Figure 5-3 for PNA locations.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
COMPOSITE BEAMS
5 - 27
Fy = 36 ksi
COMPOSITE DESIGN
COMPOSITE BEAM SELECTION TABLE
W Shapes
φ = 0.85
φb = 0.90
Shape
φb M p PNAc Y1a
ΣQ n
φM n (kip-ft)
Y2b (in.)
In.
Kips
2
2.5
3
3.5
4
4.5
5
5.5
6
6.5
7
W 21×44
Kip-ft
258
TFL
2
3
4
BFL
6
7
0.00
0.11
0.23
0.34
0.45
2.90
5.69
468
415
363
310
257
187
117
409
401
393
384
376
358
326
425
416
406
395
385
364
331
442
430
419
406
394
371
335
458
445
432
417
403
378
339
475
460
444
428
412
384
343
492
475
457
439
421
391
347
508
489
470
450
430
398
351
525
504
483
461
439
404
355
541
519
496
472
448
411
360
558
533
509
483
458
417
364
574
548
521
494
467
424
368
W 18×60
332
TFL
2
3
4
BFL
6
7
0.00
0.17
0.35
0.52
0.70
2.19
3.82
634
539
445
350
256
207
158
499
485
470
454
436
424
407
522
504
486
466
445
432
413
544
523
501
478
454
439
418
566
542
517
491
463
446
424
589
561
533
503
472
454
430
611
581
549
516
481
461
435
634
600
564
528
491
468
441
656
619
580
540
500
476
447
679
638
596
553
509
483
452
701
657
612
565
518
490
458
723
676
627
578
527
498
463
W 18×55
302
TFL
2
3
4
BFL
6
7
0.00
0.16
0.32
0.47
0.63
2.16
3.86
583
498
412
327
242
194
146
457
444
431
416
401
389
372
477
462
445
428
409
396
377
498
479
460
439
418
403
383
519
497
474
451
426
410
388
539
515
489
462
435
417
393
560
532
504
474
443
424
398
581
550
518
486
452
430
403
601
568
533
497
461
437
408
622
585
547
509
469
444
414
643
603
562
520
478
451
419
663
620
577
532
486
458
424
W 18×50
273
TFL
2
3
4
BFL
6
7
0.00
0.14
0.29
0.43
0.57
2.07
3.82
529
452
375
299
222
177
132
412
401
389
376
362
352
336
431
417
402
387
370
358
341
450
433
415
397
378
365
346
468
449
429
408
386
371
350
487
465
442
418
394
377
355
506
481
455
429
402
383
360
525
497
469
439
409
390
365
543
513
482
450
417
396
369
562
529
495
461
425
402
374
581
545
508
471
433
408
379
600
561
522
482
441
415
383
W 18×46
245
TFL
2
3
4
BFL
6
7
0.00
0.15
0.30
0.45
0.61
2.40
4.34
486
420
354
288
222
172
122
380
370
360
348
337
324
305
397
385
372
359
345
330
310
414
400
385
369
352
336
314
431
415
397
379
360
343
318
449
430
410
389
368
349
322
466
444
422
399
376
355
327
483
459
435
410
384
361
331
500
474
447
420
392
367
335
517
489
460
430
400
373
340
535
504
472
440
407
379
344
552
519
485
450
415
385
348
aY1 = distance from top of the steel beam to plastic neutral axis.
bY2 = distance from top of the steel beam to concrete flange force.
cSee Figure 5-3 for PNA locations.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
5 - 28
COMPOSITE DESIGN
Fy = 36 ksi
COMPOSITE DESIGN
COMPOSITE BEAM SELECTION TABLE
W Shapes
φ = 0.85
φb = 0.90
Shape
φb M p PNAc Y1a
ΣQ n
φM n (kip-ft)
Y2b (in.)
In.
Kips
2
2.5
3
3.5
4
4.5
5
5.5
6
6.5
7
W 18×40
Kip-ft
212
TFL
2
3
4
BFL
6
7
0.00
0.13
0.26
0.39
0.53
2.26
4.27
425
368
311
254
197
152
106
329
321
312
303
293
282
265
345
334
323
312
300
288
269
360
347
334
321
307
293
273
375
360
345
330
314
298
277
390
373
356
339
321
304
280
405
386
367
348
328
309
284
420
399
378
357
335
315
288
435
412
389
366
342
320
292
450
425
400
375
349
325
295
465
438
411
384
356
331
299
480
451
423
393
363
336
303
W 18×35
180
TFL
2
3
4
BFL
6
7
0.00
0.11
0.21
0.32
0.43
2.37
4.56
371
325
279
233
187
140
92.7
285
278
271
264
256
245
227
298
290
281
272
263
250
230
311
301
291
280
269
255
233
324
313
301
289
276
260
237
338
324
311
297
283
265
240
351
336
321
305
289
270
243
364
347
331
313
296
275
246
377
359
340
322
303
280
250
390
370
350
330
309
285
253
403
382
360
338
316
290
256
416
393
370
346
323
295
260
W 16×36
173
TFL
2
3
4
BFL
6
7
0.00
0.11
0.22
0.32
0.43
1.79
3.44
382
328
273
219
165
130
95.4
268
261
252
244
234
227
215
282
272
262
251
240
232
219
295
284
272
259
246
236
222
309
295
281
267
252
241
226
322
307
291
275
258
245
229
336
319
301
282
264
250
232
349
330
310
290
270
255
236
363
342
320
298
275
259
239
377
353
330
306
281
264
243
390
365
339
314
287
268
246
404
377
349
321
293
273
249
W 16×31
146
TFL
2
3
4
BFL
6
7
0.00
0.11
0.22
0.33
0.44
2.00
3.79
328
285
241
197
153
118
82.1
231
225
218
211
204
196
183
243
235
227
218
209
200
186
254
245
235
225
214
204
189
266
255
244
232
220
208
192
278
265
252
239
225
212
195
289
275
261
246
231
217
198
301
285
269
253
236
221
201
313
295
278
260
242
225
204
324
305
286
267
247
229
207
336
315
295
274
253
233
209
347
326
303
281
258
237
212
W 16×26
119
TFL
2
3
4
BFL
6
7
0.00
0.09
0.17
0.26
0.35
2.04
4.01
276
242
208
174
140
104
69.1
193
188
183
177
172
164
151
203
196
190
184
177
168
154
212
205
197
190
182
171
156
222
214
205
196
187
175
159
232
222
212
202
192
179
161
242
231
220
208
197
182
164
252
239
227
214
202
186
166
261
248
234
220
206
190
169
271
257
242
227
211
194
171
281
265
249
233
216
197
173
291
274
256
239
221
201
176
aY1 = distance from top of the steel beam to plastic neutral axis.
bY2 = distance from top of the steel beam to concrete flange force.
cSee Figure 5-3 for PNA locations.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
COMPOSITE BEAMS
5 - 29
Fy = 36 ksi
COMPOSITE DESIGN
COMPOSITE BEAM SELECTION TABLE
W Shapes
φ = 0.85
φb = 0.90
Shape
φb M p PNAc Y1a
ΣQ n
φM n (kip-ft)
Y2b (in.)
In.
Kips
2
2.5
3
3.5
4
4.5
5
5.5
6
6.5
7
W 14×38
Kip-ft
166
TFL
2
3
4
BFL
6
7
0.00
0.13
0.26
0.39
0.52
1.38
2.53
403
340
278
215
152
126
101
258
249
240
229
218
213
206
273
261
249
237
224
218
209
287
273
259
244
229
222
213
301
285
269
252
234
226
217
316
298
279
260
240
231
220
330
310
289
267
245
235
224
344
322
299
275
251
240
227
358
334
308
283
256
244
231
373
346
318
290
261
249
234
387
358
328
298
267
253
238
401
370
338
305
272
258
242
W 14×34
147
TFL
2
3
4
BFL
6
7
0.00
0.11
0.23
0.34
0.46
1.41
2.60
360
305
250
194
139
115
90.0
229
221
213
204
194
189
182
242
232
222
211
199
193
186
255
243
230
218
204
197
189
267
254
239
224
209
202
192
280
264
248
231
214
206
195
293
275
257
238
219
210
198
306
286
266
245
224
214
202
318
297
275
252
229
218
205
331
308
283
259
234
222
208
344
318
292
266
239
226
211
357
329
301
273
244
230
214
W 14×30
128
TFL
2
3
4
BFL
6
7
0.00
0.10
0.19
0.29
0.39
1.48
2.82
319
272
225
179
132
106
79.7
201
195
187
180
172
167
159
213
204
195
186
177
171
162
224
214
203
193
182
174
165
235
223
211
199
186
178
168
246
233
219
205
191
182
171
258
243
227
212
196
186
173
269
252
235
218
200
189
176
280
262
243
224
205
193
179
292
272
251
231
210
197
182
303
281
259
237
214
201
185
314
291
267
243
219
204
187
W 14×26
109
TFL
2
3
4
BFL
6
7
0.00
0.11
0.21
0.32
0.42
1.67
3.19
277
239
201
163
125
97.0
69.2
176
170
164
158
152
146
137
185
179
171
164
156
149
140
195
187
179
170
161
153
142
205
195
186
175
165
156
145
215
204
193
181
170
160
147
225
212
200
187
174
163
149
234
221
207
193
178
167
152
244
229
214
199
183
170
154
254
238
221
204
187
173
157
264
246
228
210
192
177
159
274
255
235
216
196
180
162
TFL
2
3
4
BFL
6
7
0.00
0.08
0.17
0.25
0.34
1.69
3.34
234
203
173
143
113
85.7
58.4
147
142
138
133
128
123
114
155
150
144
138
132
126
116
163
157
150
143
136
129
118
172
164
156
148
140
132
120
180
171
162
153
144
135
122
188
178
169
159
148
138
124
196
186
175
164
152
141
126
205
193
181
169
156
144
128
213
200
187
174
160
147
130
221
207
193
179
164
150
132
230
215
199
184
168
153
135
W 14×22
89.6
aY1 = distance from top of the steel beam to plastic neutral axis.
bY2 = distance from top of the steel beam to concrete flange force.
cSee Figure 5-3 for PNA locations.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
5 - 30
COMPOSITE DESIGN
Fy = 36 ksi
COMPOSITE DESIGN
COMPOSITE BEAM SELECTION TABLE
W Shapes
φ = 0.85
φb = 0.90
Shape
φb M p PNAc Y1a
ΣQ n
φM n (kip-ft)
Y2b (in.)
In.
Kips
2
2.5
3
3.5
4
4.5
5
5.5
6
6.5
7
W 12×30
Kip-ft
116
TFL
2
3
4
BFL
6
7
0.00
0.11
0.22
0.33
0.44
1.12
1.94
316
265
213
162
110
94.5
79.1
183
176
168
159
151
148
144
194
185
175
165
155
151
147
206
194
183
171
158
154
149
217
204
190
177
162
158
152
228
213
198
182
166
161
155
239
223
205
188
170
164
158
250
232
213
194
174
168
161
262
241
221
199
178
171
163
273
251
228
205
182
174
166
284
260
236
211
186
178
169
295
269
243
217
190
181
172
W 12×26
100
TFL
2
3
4
BFL
6
7
0.00
0.10
0.19
0.29
0.38
1.08
1.95
275
231
187
142
97.8
83.3
68.9
158
152
145
138
131
128
124
168
160
152
143
134
131
127
178
168
158
148
138
134
129
187
176
165
153
141
137
132
197
184
171
158
145
140
134
207
193
178
163
148
143
136
217
201
185
168
151
146
139
226
209
191
173
155
149
141
236
217
198
178
158
151
144
246
225
205
183
162
154
146
256
234
211
188
165
157
149
W 12×22
79.1
TFL
2
3
4
BFL
6
7
0.00
0.11
0.21
0.32
0.43
1.66
3.04
233
202
172
141
110
84.1
58.3
135
130
126
121
115
110
102
143
137
132
126
119
113
104
151
145
138
131
123
116
106
160
152
144
136
127
119
108
168
159
150
141
131
122
110
176
166
156
146
135
125
112
184
173
162
151
139
128
114
193
180
168
156
143
131
116
201
188
174
160
147
134
119
209
195
180
165
150
137
121
217
202
186
170
154
140
123
W 12×19
66.7
TFL
2
3
4
BFL
6
7
0.00
0.09
0.18
0.26
0.35
1.66
3.12
201
175
150
125
99.6
74.9
50.1
115
111
107
103
99.2
94.0
86.3
122
117
113
108
103
96.7
88.1
129
124
118
112
106
99.3
89.9
136
130
123
117
110
102
91.7
143
136
129
121
113
105
93.5
150
142
134
125
117
107
95.2
157
148
139
130
120
110
97.0
164
155
145
134
124
113
98.8
172
161
150
139
127
115
101
179
167
155
143
131
118
102
186
173
160
148
134
121
104
W 12×16
54.3
TFL
2
3
4
BFL
6
7
0.00
0.07
0.13
0.20
0.26
1.71
3.32
170
151
131
112
93.4
67.9
42.4
96.0
93.3
90.5
87.5
84.5
79.2
71.1
102
98.6
95.1
91.5
87.8
81.6
72.6
108
104
99.8
95.5
91.1
84.0
74.1
114
109
104
99.5
94.5
86.4
75.6
120
115
109
103
97.8
88.8
77.1
126
120
114
107
101
91.2
78.6
132
125
118
111
104
93.6
80.1
138
131
123
115
108
96.1
81.6
144
136
128
119
111
98.5
83.1
150
141
132
123
114
101
84.6
156
147
137
127
118
103
86.1
aY1 = distance from top of the steel beam to plastic neutral axis.
bY2 = distance from top of the steel beam to concrete flange force.
cSee Figure 5-3 for PNA locations.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
COMPOSITE BEAMS
5 - 31
Fy = 36 ksi
COMPOSITE DESIGN
COMPOSITE BEAM SELECTION TABLE
W Shapes
φ = 0.85
φb = 0.90
Shape
φb M p PNAc Y1a
ΣQ n
φM n (kip-ft)
Y2b (in.)
In.
Kips
2
2.5
3
3.5
4
4.5
5
5.5
6
6.5
7
W 12×14
Kip-ft
47.0
TFL
2
3
4
BFL
6
7
0.00
0.06
0.11
0.17
0.23
1.69
3.36
150
134
118
102
85.4
61.4
37.4
84.4
82.1
79.7
77.3
74.8
69.8
62.2
89.7
86.8
83.9
80.9
77.8
72.0
63.5
95.0
91.5
88.0
84.5
80.8
74.2
64.8
100
96.3
92.2
88.1
83.8
76.4
66.1
106
101
96.4
91.6
86.9
78.5
67.5
111
106
101
95.2
89.9
80.7
68.8
116
110
105
98.8
92.9
82.9
70.1
122
115
109
102
95.9
85.1
71.4
127
120
113
106
99.0
87.2
72.8
132
125
117
110
102
89.4
74.1
137
129
121
113
105
91.6
75.4
W 10×26
84.5
TFL
2
3
4
BFL
6
7
0.00
0.11
0.22
0.33
0.44
0.90
1.51
274
228
183
137
91.2
79.8
68.5
139
132
125
118
110
108
106
149
140
132
123
114
111
108
158
149
138
128
117
114
110
168
157
145
133
120
117
113
178
165
151
137
123
119
115
188
173
158
142
126
122
118
197
181
164
147
130
125
120
207
189
171
152
133
128
123
217
197
177
157
136
131
125
226
205
184
162
139
134
127
236
213
190
166
143
136
130
W 10×22
70.2
TFL
2
3
4
BFL
6
7
0.00
0.09
0.18
0.27
0.36
0.95
1.70
234
196
159
122
84.6
71.5
58.4
117
112
106
100
94.2
91.8
88.7
126
119
112
105
97.2
94.3
90.8
134
126
117
109
100
96.9
92.9
142
133
123
113
103
99.4
94.9
150
140
129
118
106
102
97.0
159
147
134
122
109
104
99.1
167
154
140
126
112
107
101
175
161
146
131
115
110
103
183
167
151
135
118
112
105
192
174
157
139
121
115
107
200
181
163
144
124
117
109
W 10×19
58.3
TFL
2
3
4
BFL
6
7
0.00
0.10
0.20
0.30
0.40
1.27
2.31
202 102
174
97.9
145
93.5
117
89.0
88.0 84.2
69.3 80.5
50.6 75.5
109
104
98.7
93.1
87.4
83.0
77.3
116
110
104
97.2
90.5
85.4
79.1
124
116
109
101
93.6
87.9
80.9
131
123
114
106
96.7
90.4
82.7
138
129
119
110
99.8
92.8
84.5
145
135
124
114
103
95.3
86.3
152
141
130
118
106
97.7
88.1
159
147
135
122
109
100
89.8
167
153
140
126
112
103
91.6
174
159
145
130
115
105
93.4
W 10×17
50.5
TFL
2
3
4
BFL
6
7
0.00
0.08
0.17
0.25
0.33
1.31
2.46
180
156
132
108
84.4
64.6
44.9
96.1
91.8
87.4
82.9
78.1
73.6
67.4
102
97.4
92.1
86.7
81.1
75.8
69.0
109
103
96.8
90.5
84.1
78.1
70.6
115
108
101
94.3
87.1
80.4
72.2
122
114
106
98.2
90.1
82.7
73.8
128
119
111
102
93.1
85.0
75.4
134
125
115
106
96.1
87.3
77.0
141
130
120
110
99.1
89.6
78.6
147
136
125
114
102
91.9
80.2
153
142
129
117
105
94.2
81.7
89.8
86.3
82.7
79.0
75.2
71.3
65.8
aY1 = distance from top of the steel beam to plastic neutral axis.
bY2 = distance from top of the steel beam to concrete flange force.
cSee Figure 5-3 for PNA locations.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
5 - 32
COMPOSITE DESIGN
Fy = 36 ksi
COMPOSITE DESIGN
COMPOSITE BEAM SELECTION TABLE
W Shapes
φ = 0.85
φb = 0.90
Shape
φb M p PNAc Y1a
ΣQ n
φM n (kip-ft)
Y2b (in.)
In.
Kips
2
2.5
3
3.5
4
4.5
5
5.5
6
6.5
7
W 10×15
Kip-ft
43.2
TFL
2
3
4
BFL
6
7
0.00
0.07
0.14
0.20
0.27
1.35
2.60
159
139
120
100
81.0
60.3
39.7
78.7
75.9
73.0
70.0
66.9
62.9
57.0
84.3
80.8
77.2
73.5
69.8
65.0
58.4
89.9
85.7
81.5
77.1
72.6
67.1
59.9
95.5
90.7
85.7
80.7
75.5
69.3
61.3
101
95.6
90.0
84.2
78.4
71.4
62.7
107
101
94.2
87.8
81.2
73.5
64.1
112
105
98.4
91.3
84.1
75.7
65.5
118
110
103
94.9
87.0
77.8
66.9
124
115
107
98.4
89.9
80.0
68.3
129
120
111
102
92.7
82.1
69.7
135
125
115
106
95.6
84.2
71.1
W 10×12
34.0
TFL
2
3
4
BFL
6
7
0.00 127
0.05 112
0.11 97.5
0.16 82.5
0.21 67.6
1.30 49.7
2.61 31.9
62.6
60.5
58.2
56.0
53.7
50.3
45.3
67.1
64.4
61.7
58.9
56.1
52.0
46.4
71.6
68.4
65.2
61.8
58.5
53.8
47.5
76.1
72.4
68.6
64.8
60.9
55.5
48.6
80.7
76.4
72.1
67.7
63.2
57.3
49.8
85.2
80.4
75.5
70.6
65.6
59.1
50.9
89.7
84.4
79.0
73.5
68.0
60.8
52.0
94.2
88.3
82.4
76.5
70.4
62.6
53.2
98.7
92.3
85.9
79.4
72.8
64.3
54.3
103
96.3
89.3
82.3
75.2
66.1
55.4
108
100
92.8
85.2
77.6
67.9
56.5
W 8×28
73.4
TFL
2
3
4
BFL
6
7
0.00
0.12
0.23
0.35
0.47
0.53
0.59
297
242
188
133
78.2
76.2
74.3
127
119
110
102
92.3
91.9
91.5
137
127
117
106
95.0
94.6
94.2
148
136
124
111
97.8
97.3
96.8
158
145
130
116
101
100
99.4
169
153
137
120
103
103
102
179
162
144
125
106
105
105
190
170
150
130
109
108
107
200
179
157
135
112
111
110
211
188
164
139
114
114
113
222
196
170
144
117
116
115
232
205
177
149
120
119
118
W 8×24
62.6
TFL
2
3
4
BFL
6
7
0.00
0.10
0.20
0.30
0.40
0.47
0.55
255 108
208 101
161
93.8
115
86.3
67.8 78.5
65.8 78.2
63.7 77.8
117
108
99.5
90.4
80.9
80.5
80.1
126
116
105
94.4
83.3
82.8
82.3
135
123
111
98.5
85.7
85.2
84.6
144
130
117
103
88.2
87.5
86.9
153
138
122
107
90.6
89.8
89.1
162
145
128
111
93.0
92.2
91.4
171
152
134
115
95.4
94.5
93.6
180
160
139
119
97.8
96.8
95.9
189
167
145
123
100
99.2
98.1
198
175
151
127
103
101
100
W 8×21
55.1
TFL
2
3
4
BFL
6
7
0.00
0.10
0.20
0.30
0.40
0.70
1.06
222
184
146
108
70.0
62.7
55.4
104
97.4
90.3
82.9
75.3
73.7
72.0
112
104
95.5
86.8
77.8
75.9
73.9
120
110
101
90.6
80.2
78.1
75.9
128
117
106
94.4
82.7
80.4
77.9
136
123
111
98.2
85.2
82.6
79.8
144
130
116
102
87.7
84.8
81.8
151
137
121
106
90.1
87.0
83.8
159
143
126
110
92.6
89.3
85.7
167
150
132
114
95.1
91.5
87.7
175
156
137
117
97.6
93.7
89.6
96.4
90.9
85.2
79.1
72.8
71.5
70.0
aY1 = distance from top of the steel beam to plastic neutral axis.
bY2 = distance from top of the steel beam to concrete flange force.
cSee Figure 5-3 for PNA locations.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
COMPOSITE BEAMS
5 - 33
Fy = 36 ksi
COMPOSITE DESIGN
COMPOSITE BEAM SELECTION TABLE
W Shapes
φ = 0.85
φb = 0.90
Shape
φb M p PNAc Y1a
ΣQ n
φM n (kip-ft)
Y2b (in.)
2
2.5
3
3.5
4
4.5
5
5.5
6
6.5
7
W 8×18
Kip-ft
45.9
TFL
2
3
4
BFL
6
7
0.00 189
0.08 158
0.17 127
0.25 95.8
0.33 64.6
0.71 56.0
1.21 47.3
In.
Kips
81.4
76.9
72.2
67.3
62.3
60.7
58.9
88.1
82.5
76.7
70.7
64.6
62.7
60.6
94.8
88.1
81.2
74.1
66.9
64.7
62.3
102
93.7
85.7
77.5
69.2
66.7
64.0
108
99.3
90.2
80.9
71.4
68.7
65.6
115
105
94.7
84.3
73.7
70.7
67.3
122
111
99.2
87.7
76.0
72.6
69.0
128
116
104
91.1
78.3
74.6
70.7
135
122
108
94.5
80.6
76.6
72.4
142
127
113
97.9
82.9
78.6
74.0
148
133
117
101
85.2
80.6
75.7
W 8×15
36.7
TFL
2
3
4
BFL
6
7
0.00 160
0.08 137
0.16 114
0.24 91.5
0.32 68.8
0.97 54.4
1.79 40.0
68.6
65.3
61.9
58.3
54.6
52.0
48.5
74.2
70.1
65.9
61.6
57.1
53.9
49.9
79.9
75.0
69.9
64.8
59.5
55.8
51.3
85.5
79.8
74.0
68.0
61.9
57.7
52.8
91.2
84.7
78.0
71.3
64.4
59.7
54.2
96.9
89.5
82.1
74.5
66.8
61.6
55.6
103
94.4
86.1
77.8
69.3
63.5
57.0
108
99.2
90.2
81.0
71.7
65.4
58.4
114
104
94.2
84.2
74.1
67.4
59.8
120
109
98.3
87.5
76.6
69.3
61.2
125
114
102
90.7
79.0
71.2
62.7
W 8×13
30.8
TFL
2
3
4
BFL
6
7
0.00 138
0.06 120
0.13 102
0.19 83.2
0.26 64.8
1.00 49.7
1.91 34.6
58.7
56.1
53.3
50.5
47.6
44.9
41.2
63.6
60.3
56.9
53.5
49.9
46.6
42.4
68.5
64.6
60.5
56.4
52.2
48.4
43.6
73.4
68.8
64.1
59.4
54.5
50.1
44.8
78.3
73.0
67.7
62.3
56.8
51.9
46.1
83.2
77.3
71.3
65.3
59.1
53.7
47.3
88.1
81.5
74.9
68.2
61.4
55.4
48.5
93.0
85.8
78.5
71.1
63.7
57.2
49.7
97.9
90.0
82.1
74.1
66.0
58.9
51.0
103
94.3
85.7
77.0
68.3
60.7
52.2
108
98.5
89.3
80.0
70.6
62.5
53.4
W 8×10
23.9
TFL
2
3
4
BFL
6
7
0.00 107
0.05 92.0
0.10 77.5
0.15 62.9
0.21 48.4
0.88 37.5
1.77 26.6
44.9
42.8
40.6
38.5
36.2
34.3
31.7
48.6
46.0
43.4
40.7
37.9
35.6
32.7
52.4
49.3
46.1
42.9
39.6
36.9
33.6
56.2
52.6
48.9
45.1
41.4
38.3
34.5
60.0
55.8
51.6
47.4
43.1
39.6
35.5
63.7
59.1
54.4
49.6
44.8
40.9
36.4
67.5
62.3
57.1
51.8
46.5
42.2
37.4
71.3
65.6
59.9
54.1
48.2
43.6
38.3
75.1
68.9
62.6
56.3
49.9
44.9
39.3
78.8
72.1
65.3
58.5
51.6
46.2
40.2
82.6
75.4
68.1
60.7
53.4
47.6
41.1
aY1 = distance from top of the steel beam to plastic neutral axis.
bY2 = distance from top of the steel beam to concrete flange force.
cSee Figure 5-3 for PNA locations.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
5 - 34
COMPOSITE DESIGN
Fy = 50 ksi
COMPOSITE DESIGN
COMPOSITE BEAM SELECTION TABLE
W Shapes
φ = 0.85
φb = 0.90
Shape
φb M p PNAc Y1a
Kip-ft
ΣQ n
φM n (kip-ft)
Y2b (in.)
4
4.5
5
In.
Kips
2
2.5
3
3.5
5.5
6
6.5
7
W40×297
4990
TFL
2
3
4
BFL
6
7
0.00
0.41
0.83
1.24
1.65
4.59
8.17
4370
3720
3060
2410
1760
1430
1090
6790
6680
6560
6420
6260
6150
5950
6940
6810
6670
6510
6320
6200
5990
7090
6950
6780
6590
6390
6250
6020
7250
7080
6890
6680
6450
6300
6060
7400
7210
7000
6760
6510
6350
6100
7560
7340
7100
6850
6570
6400
6140
7710
7470
7210
6930
6640
6450
6180
7870
7600
7320
7020
6700
6500
6220
8020
7740
7430
7110
6760
6550
6260
8180
7870
7540
7190
6820
6600
6300
8330
8000
7650
7280
6890
6650
6330
W40×278
4460
TFL 0.00
2
0.45
3
0.91
4
1.36
BFL 1.81
6
5.64
7 10.06
4090
3550
3010
2470
1920
1470
1020
6400
6310
6210
6090
5950
5770
5460
6540
6440
6320
6180
6020
5820
5500
6690
6560
6420
6260
6090
5880
5530
6830
6690
6530
6350
6160
5930
5570
6980
6810
6630
6440
6220
5980
5600
7120
6940
6740
6520
6290
6030
5640
7270
7070
6850
6610
6360
6080
5680
7410
7190
6950
6700
6430
6140
5710
7560
7320
7060
6790
6500
6190
5750
7700
7440
7170
6870
6560
6240
5790
7850
7570
7270
6960
6630
6290
5820
W40×277
4690
TFL
2
3
4
BFL
6
7
0.00
0.39
0.79
1.18
1.58
4.25
7.60
4070
3440
2820
2200
1570
1290
1020
6290
6190
6080
5950
5800
5700
5550
6430
6310
6180
6020
5850
5750
5580
6580
6440
6280
6100
5910
5790
5620
6720
6560
6380
6180
5960
5840
5660
6870
6680
6480
6260
6020
5880
5690
7010
6800
6580
6340
6080
5930
5730
7150
6920
6680
6410
6130
5980
5760
7300
7050
6780
6490
6190
6020
5800
7440
7170
6880
6570
6240
6070
5840
7590
7290
6980
6650
6300
6110
5870
7730
7410
7080
6720
6350
6160
5910
W40×264
4240
TFL
2
3
4
BFL
6
7
0.00
0.43
0.87
1.30
1.73
5.49
9.90
3880
3360
2850
2330
1820
1390
970
6050
5970
5870
5760
5630
5470
5170
6180
6080
5970
5840
5690
5510
5210
6320
6200
6070
5920
5760
5560
5240
6460
6320
6170
6000
5820
5610
5280
6600
6440
6270
6090
5880
5660
5310
6730
6560
6370
6170
5950
5710
5350
6870
6680
6470
6250
6010
5760
5380
7010
6800
6570
6330
6080
5810
5420
7150
6920
6680
6420
6140
5860
5450
7280
7040
6780
6500
6210
5910
5480
7420
7160
6880
6580
6270
5960
5520
aY1 = distance from top of the steel beam to plastic neutral axis.
bY2 = distance from top of the steel beam to concrete flange force.
cSee Figure 5-3 for PNA locations.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
COMPOSITE BEAMS
5 - 35
Fy = 50 ksi
COMPOSITE DESIGN
COMPOSITE BEAM SELECTION TABLE
W Shapes
φ = 0.85
φb = 0.90
Shape
φb M p PNAc Y1a
Kip-ft
ΣQ n
φM n (kip-ft)
Y2b (in.)
4
4.5
5
In.
Kips
2
2.5
3
3.5
5.5
6
6.5
7
W40×249
4200
TFL
2
3
4
BFL
6
7
0.00
0.36
0.71
1.07
1.42
4.06
7.47
3670
3110
2550
1990
1430
1170
916
5630
5540
5440
5330
5200
5120
4980
5760
5650
5530
5400
5250
5160
5010
5890
5760
5620
5470
5300
5200
5040
6020
5870
5710
5540
5350
5240
5070
6150
5980
5810
5610
5400
5280
5110
6280
6090
5900
5680
5450
5320
5140
6410
6200
5990
5750
5510
5370
5170
6540
6310
6080
5820
5560
5410
5200
6670
6420
6170
5890
5610
5450
5240
6800
6530
6260
5960
5660
5490
5270
6930
6640
6350
6030
5710
5530
5300
W40×235
3790
TFL
2
3
4
BFL
6
7
0.00
0.39
0.79
1.18
1.58
5.18
9.47
3450
2980
2510
2040
1570
1220
861
5330
5260
5170
5070
4960
4830
4600
5450
5360
5260
5150
5020
4880
4630
5570
5470
5350
5220
5070
4920
4660
5700
5570
5440
5290
5130
4960
4690
5820
5680
5530
5360
5180
5000
4720
5940
5780
5620
5430
5240
5050
4750
6060
5890
5700
5510
5290
5090
4780
6180
6000
5790
5580
5350
5130
4810
6310
6100
5880
5650
5410
5180
4840
6430
6210
5970
5720
5460
5220
4870
6550
6310
6060
5800
5520
5260
4900
W40×215
3610
TFL
2
3
4
BFL
6
7
0.00
0.31
0.61
0.92
1.22
3.84
7.32
3170
2680
2200
1720
1240
1020
791
4820
4740
4660
4570
4460
4390
4270
4930
4840
4740
4630
4510
4430
4300
5040
4930
4820
4690
4550
4470
4330
5150
5030
4900
4750
4590
4500
4360
5270
5120
4970
4810
4640
4540
4380
5380
5220
5050
4870
4680
4570
4410
5490
5320
5130
4930
4730
4610
4440
5600
5410
5210
4990
4770
4650
4470
5710
5510
5290
5060
4810
4680
4500
5830
5600
5360
5120
4860
4720
4520
5940
5700
5440
5180
4900
4760
4550
W40×211
3390
TFL
2
3
4
BFL
6
7
0.00
0.35
0.71
1.06
1.42
4.99
9.35
3100
2680
2260
1850
1430
1100
775
4760
4700
4620
4540
4440
4330
4110
4870
4790
4700
4600
4490
4360
4140
4980
4890
4780
4670
4540
4400
4170
5090
4980
4860
4730
4590
4440
4200
5200
5080
4940
4800
4640
4480
4220
5310
5170
5020
4860
4690
4520
4250
5420
5270
5100
4930
4740
4560
4280
5530
5360
5180
4990
4800
4600
4310
5640
5460
5260
5060
4850
4640
4330
5750
5550
5340
5130
4900
4680
4360
5860
5650
5420
5190
4950
4710
4390
aY1 = distance from top of the steel beam to plastic neutral axis.
bY2 = distance from top of the steel beam to concrete flange force.
cSee Figure 5-3 for PNA locations.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
5 - 36
COMPOSITE DESIGN
Fy = 50 ksi
COMPOSITE DESIGN
COMPOSITE BEAM SELECTION TABLE
W Shapes
φ = 0.85
φb = 0.90
Shape
φb M p PNAc Y1a
Kip-ft
ΣQ n
φM n (kip-ft)
Y2b (in.)
4
4.5
5
In.
Kips
2
2.5
3
3.5
5.5
6
6.5
7
W40×199
3250
TFL
2
3
4
BFL
6
7
0.00
0.27
0.53
0.80
1.07
4.16
8.10
2920
2500
2080
1660
1240
986
730
4410
4350
4280
4200
4110
4030
3880
4520
4440
4350
4260
4160
4070
3910
4620
4530
4430
4320
4200
4100
3940
4720
4620
4500
4380
4240
4140
3960
4830
4700
4570
4430
4290
4170
3990
4930
4790
4650
4490
4330
4210
4010
5030
4880
4720
4550
4380
4240
4040
5140
4970
4790
4610
4420
4280
4070
5240
5060
4870
4670
4460
4310
4090
5340
5150
4940
4730
4510
4350
4120
5450
5240
5020
4790
4550
4380
4140
W40×183
2930
TFL
2
3
4
BFL
6
7
0.00
0.31
0.61
0.92
1.22
4.76
9.16
2690
2320
1960
1600
1240
958
671
4090
4030
3970
3900
3820
3720
3540
4180
4110
4040
3960
3860
3760
3570
4280
4200
4110
4010
3910
3790
3590
4370
4280
4180
4070
3950
3830
3610
4470
4360
4250
4130
4000
3860
3640
4560
4440
4320
4180
4040
3890
3660
4660
4530
4390
4240
4090
3930
3690
4750
4610
4460
4300
4130
3960
3710
4850
4690
4530
4350
4170
4000
3730
4940
4770
4600
4410
4220
4030
3760
5040
4860
4670
4470
4260
4060
3780
W40×174
2680
TFL
2
3
4
BFL
6
7
0.00
0.21
0.42
0.62
0.83
4.59
9.27
2560
2230
1900
1570
1250
943
639
3820
3770
3720
3660
3600
3500
3310
3910
3850
3780
3710
3640
3530
3330
4000
3930
3850
3770
3680
3570
3350
4090
4010
3920
3830
3730
3600
3370
4180
4090
3990
3880
3770
3630
3400
4270
4160
4050
3940
3820
3670
3420
4360
4240
4120
3990
3860
3700
3440
4450
4320
4190
4050
3900
3730
3460
4540
4400
4260
4100
3950
3770
3490
4630
4480
4320
4160
3990
3800
3510
4720
4560
4390
4220
4040
3830
3530
W40×167
2600
TFL
2
3
4
BFL
6
7
0.00
0.26
0.51
0.77
1.03
5.00
9.85
2460
2150
1850
1550
1240
929
614
3700
3660
3610
3550
3490
3380
3170
3790
3730
3670
3600
3530
3410
3190
3880
3810
3740
3660
3580
3450
3210
3960
3890
3800
3710
3620
3480
3240
4050
3960
3870
3770
3660
3510
3260
4140
4040
3930
3820
3710
3550
3280
4220
4110
4000
3880
3750
3580
3300
4310
4190
4060
3930
3800
3610
3320
4400
4270
4130
3990
3840
3640
3340
4490
4340
4200
4040
3880
3680
3370
4570
4420
4260
4100
3930
3710
3390
W40×149
2240
TFL 0.00
2
0.21
3
0.42
4
0.62
BFL 0.83
6
5.15
7 10.41
2190
1940
1700
1450
1210
879
548
3270
3240
3200
3150
3110
2990
2770
3350
3310
3260
3200
3150
3030
2780
3430
3370
3320
3260
3190
3060
2800
3510
3440
3380
3310
3230
3090
2820
3580
3510
3440
3360
3280
3120
2840
3660
3580
3500
3410
3320
3150
2860
3740
3650
3560
3460
3360
3180
2880
3820
3720
3620
3510
3410
3210
2900
3890
3790
3680
3560
3450
3240
2920
3970
3860
3740
3620
3490
3280
2940
4050
3930
3800
3670
3530
3310
2960
aY1 = distance from top of the steel beam to plastic neutral axis.
bY2 = distance from top of the steel beam to concrete flange force.
cSee Figure 5-3 for PNA locations.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
COMPOSITE BEAMS
5 - 37
Fy = 50 ksi
COMPOSITE DESIGN
COMPOSITE BEAM SELECTION TABLE
W Shapes
φ = 0.85
φb = 0.90
Shape
φb M p PNAc Y1a
Kip-ft
ΣQ n
φM n (kip-ft)
Y2b (in.)
4
4.5
5
In.
Kips
2
2.5
3
3.5
5.5
6
6.5
7
W 36×300
4730
TFL
2
3
4
BFL
6
7
0.00
0.42
0.84
1.26
1.68
3.97
6.69
4420
3720
3020
2320
1620
1360
1100
6370
6260
6130
5980
5810
5720
5590
6530
6390
6240
6060
5860
5770
5630
6680
6520
6340
6140
5920
5820
5670
6840
6660
6450
6230
5980
5870
5710
7000
6790
6560
6310
6040
5910
5740
7150
6920
6660
6390
6090
5960
5780
7310
7050
6770
6470
6150
6010
5820
7460
7180
6880
6550
6210
6060
5860
7620
7310
6990
6640
6270
6110
5900
7780
7450
7090
6720
6320
6150
5940
7930
7580
7200
6800
6380
6200
5980
W 36×280
4390
TFL
2
3
4
BFL
6
7
0.00
0.39
0.79
1.18
1.57
3.88
6.62
4120
3470
2820
2170
1510
1270
1030
5910
5810
5690
5550
5400
5320
5190
6060
5930
5790
5630
5450
5360
5230
6200
6060
5890
5710
5510
5410
5270
6350
6180
5990
5780
5560
5450
5300
6500
6300
6090
5860
5610
5500
5340
6640
6430
6190
5940
5670
5540
5380
6790
6550
6290
6010
5720
5590
5410
6930
6670
6390
6090
5770
5630
5450
7080
6790
6490
6170
5830
5680
5490
7230
6920
6590
6240
5880
5720
5520
7370
7040
6690
6320
5930
5770
5560
W 36×260
4050
TFL
2
3
4
BFL
6
7
0.00
0.36
0.72
1.08
1.44
3.86
6.75
3830
3230
2630
2040
1440
1200
956
5450
5360
5250
5130
4990
4920
4790
5590
5480
5350
5200
5050
4960
4830
5720
5590
5440
5280
5100
5000
4860
5860
5710
5530
5350
5150
5040
4890
6000
5820
5630
5420
5200
5090
4930
6130
5930
5720
5490
5250
5130
4960
6270
6050
5810
5570
5300
5170
4990
6400
6160
5910
5640
5350
5210
5030
6540
6280
6000
5710
5400
5260
5060
6670
6390
6090
5780
5450
5300
5100
6810
6510
6190
5850
5510
5340
5130
W 36×245
3790
TFL
2
3
4
BFL
6
7
0.00
0.34
0.68
1.01
1.35
3.81
6.77
3610
3050
2490
1930
1380
1140
901
5120
5030
4930
4820
4690
4620
4500
5240
5140
5020
4890
4740
4660
4530
5370
5250
5110
4960
4790
4700
4560
5500
5360
5200
5030
4840
4740
4590
5630
5460
5290
5090
4890
4780
4620
5760
5570
5370
5160
4940
4820
4660
5880
5680
5460
5230
4990
4860
4690
6010
5790
5550
5300
5040
4900
4720
6140
5900
5640
5370
5080
4940
4750
6270
6000
5730
5440
5130
4980
4780
6390
6110
5810
5510
5180
5020
4820
W 36×230
3540
TFL
2
3
4
BFL
6
7
0.00
0.32
0.63
0.95
1.26
3.81
6.83
3380
2860
2340
1820
1300
1070
845
4780
4700
4610
4500
4390
4320
4200
4900
4800
4690
4570
4440
4350
4230
5020
4900
4770
4630
4480
4390
4260
5140
5000
4860
4700
4530
4430
4290
5260
5100
4940
4760
4570
4470
4320
5370
5200
5020
4830
4620
4510
4350
5490
5310
5100
4890
4670
4540
4380
5610
5410
5190
4960
4710
4580
4410
5730
5510
5270
5020
4760
4620
4440
5850
5610
5350
5090
4810
4660
4470
5970
5710
5440
5150
4850
4690
4500
aY1 = distance from top of the steel beam to plastic neutral axis.
bY2 = distance from top of the steel beam to concrete flange force.
cSee Figure 5-3 for PNA locations.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
5 - 38
COMPOSITE DESIGN
Fy = 50 ksi
COMPOSITE DESIGN
COMPOSITE BEAM SELECTION TABLE
W Shapes
φ = 0.85
φb = 0.90
Shape
φb M p PNAc Y1a
Kip-ft
ΣQ n
φM n (kip-ft)
Y2b (in.)
4
4.5
5
In.
Kips
2
2.5
3
3.5
5.5
6
6.5
7
W 36×210
3120
TFL
2
3
4
BFL
6
7
0.00
0.34
0.68
1.02
1.36
5.06
9.04
3090
2680
2260
1850
1430
1100
773
4450
4390
4320
4230
4140
4020
3810
4560
4480
4400
4300
4190
4060
3830
4670
4580
4480
4360
4240
4100
3860
4780
4670
4560
4430
4290
4130
3890
4890
4770
4640
4490
4340
4170
3920
5000
4860
4720
4560
4390
4210
3940
5110
4960
4800
4620
4440
4250
3970
5220
5050
4880
4690
4490
4290
4000
5330
5150
4960
4760
4540
4330
4030
5440
5240
5040
4820
4600
4370
4050
5550
5340
5120
4890
4650
4410
4080
W 36×194
2880
TFL
2
3
4
BFL
6
7
0.00
0.32
0.63
0.95
1.26
4.94
8.93
2850
2470
2090
1710
1320
1020
713
4090
4030
3960
3890
3800
3690
3500
4190
4120
4040
3950
3850
3730
3530
4290
4200
4110
4010
3900
3770
3550
4390
4290
4180
4070
3940
3800
3580
4490
4380
4260
4130
3990
3840
3600
4590
4470
4330
4190
4040
3880
3630
4690
4550
4410
4250
4080
3910
3650
4790
4640
4480
4310
4130
3950
3680
4890
4730
4550
4370
4180
3980
3700
5000
4820
4630
4430
4220
4020
3730
5100
4900
4700
4490
4270
4060
3750
W 36×182
2690
TFL
2
3
4
BFL
6
7
0.00
0.29
0.59
0.89
1.18
4.89
8.92
2680
2320
1970
1610
1260
963
670
3830
3770
3710
3640
3570
3460
3280
3920
3860
3780
3700
3610
3500
3300
4020
3940
3850
3760
3660
3530
3330
4110
4020
3920
3810
3700
3570
3350
4210
4100
3990
3870
3740
3600
3370
4300
4190
4060
3930
3790
3640
3400
4400
4270
4130
3990
3830
3670
3420
4490
4350
4200
4040
3880
3700
3450
4590
4430
4270
4100
3920
3740
3470
4680
4510
4340
4160
3970
3770
3490
4780
4600
4410
4210
4010
3810
3520
W 36×170
2500
TFL
2
3
4
BFL
6
7
0.00
0.28
0.55
0.83
1.10
4.84
8.89
2500
2170
1840
1510
1180
901
625
3560
3510
3450
3390
3320
3220
3050
3650
3580
3520
3440
3360
3250
3070
3730
3660
3580
3490
3400
3290
3090
3820
3740
3650
3550
3440
3320
3120
3910
3810
3710
3600
3480
3350
3140
4000
3890
3780
3650
3530
3380
3160
4090
3970
3840
3710
3570
3410
3180
4180
4040
3910
3760
3610
3450
3200
4270
4120
3970
3810
3650
3480
3230
4350
4200
4040
3870
3690
3510
3250
4440
4270
4100
3920
3730
3540
3270
W 36×160
2340
TFL
2
3
4
BFL
6
7
0.00
0.26
0.51
0.77
1.02
4.82
8.97
2350
2040
1740
1430
1130
857
588
3330
3280
3230
3180
3110
3020
2850
3410
3360
3290
3230
3150
3050
2870
3500
3430
3360
3280
3190
3080
2890
3580
3500
3420
3330
3230
3110
2910
3660
3570
3480
3380
3270
3140
2930
3750
3650
3540
3430
3310
3170
2960
3830
3720
3600
3480
3350
3200
2980
3910
3790
3660
3530
3390
3230
3000
4000
3860
3720
3580
3430
3260
3020
4080
3940
3790
3630
3470
3290
3040
4160
4010
3850
3680
3510
3320
3060
aY1 = distance from top of the steel beam to plastic neutral axis.
bY2 = distance from top of the steel beam to concrete flange force.
cSee Figure 5-3 for PNA locations.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
COMPOSITE BEAMS
5 - 39
Fy = 50 ksi
COMPOSITE DESIGN
COMPOSITE BEAM SELECTION TABLE
W Shapes
φ = 0.85
φb = 0.90
Shape
φb M p PNAc Y1a
Kip-ft
ΣQ n
φM n (kip-ft)
Y2b (in.)
4
4.5
5
In.
Kips
2
2.5
3
3.5
5.5
6
6.5
7
W 36×150
2180
TFL
2
3
4
BFL
6
7
0.00
0.24
0.47
0.71
0.94
4.83
9.08
2210
1930
1650
1370
1080
818
553
3120
3080
3030
2980
2920
2830
2660
3200
3150
3090
3030
2960
2860
2680
3280
3210
3150
3080
3000
2890
2700
3350
3280
3210
3120
3040
2920
2720
3430
3350
3260
3170
3080
2950
2740
3510
3420
3320
3220
3110
2980
2760
3590
3490
3380
3270
3150
3010
2780
3670
3560
3440
3320
3190
3040
2800
3750
3620
3500
3370
3230
3060
2820
3820
3690
3560
3410
3270
3090
2840
3900
3760
3610
3460
3310
3120
2860
W 36×135
1910
TFL
2
3
4
BFL
6
7
0.00
0.20
0.40
0.59
0.79
4.97
9.50
1990
1750
1510
1280
1040
769
496
2780
2750
2710
2670
2620
2530
2350
2850
2810
2760
2710
2660
2560
2370
2920
2870
2810
2760
2690
2580
2390
2990
2930
2870
2800
2730
2610
2400
3060
2990
2920
2850
2770
2640
2420
3130
3060
2970
2890
2800
2660
2440
3200
3120
3030
2940
2840
2690
2460
3270
3180
3080
2980
2880
2720
2470
3340
3240
3140
3030
2920
2750
2490
3410
3300
3190
3070
2950
2770
2510
3480
3360
3240
3120
2990
2800
2530
W 33×221
3210
TFL
2
3
4
BFL
6
7
0.00
0.32
0.64
0.96
1.28
3.76
6.48
3250
2750
2240
1740
1230
1020
813
4370
4290
4200
4100
3990
3920
3820
4480
4390
4280
4160
4030
3960
3850
4600
4480
4360
4220
4080
3990
3870
4710
4580
4440
4290
4120
4030
3900
4830
4680
4520
4350
4160
4070
3930
4940
4780
4600
4410
4210
4100
3960
5060
4870
4680
4470
4250
4140
3990
5170
4970
4760
4530
4300
4170
4020
5290
5070
4840
4590
4340
4210
4050
5400
5160
4920
4650
4380
4250
4080
5520
5260
4990
4720
4430
4280
4100
W 33×201
2900
TFL
2
3
4
BFL
6
7
0.00
0.29
0.58
0.86
1.15
3.67
6.51
2960
2500
2050
1600
1140
942
739
3940
3870
3800
3710
3610
3550
3450
4050
3960
3870
3770
3650
3580
3480
4150
4050
3940
3820
3690
3620
3500
4260
4140
4010
3880
3730
3650
3530
4360
4230
4090
3940
3780
3680
3550
4470
4320
4160
3990
3820
3720
3580
4570
4410
4230
4050
3860
3750
3610
4680
4500
4300
4110
3900
3780
3630
4780
4580
4380
4160
3940
3820
3660
4890
4670
4450
4220
3980
3850
3680
4990
4760
4520
4280
4020
3880
3710
W 33×141
1930
TFL
2
3
4
BFL
6
7
0.00
0.24
0.48
0.72
0.96
4.31
8.05
2080
1800
1530
1250
973
746
520
2750
2710
2660
2610
2550
2480
2350
2820
2770
2710
2650
2590
2510
2370
2900
2830
2770
2700
2620
2530
2390
2970
2900
2820
2740
2660
2560
2410
3040
2960
2880
2790
2690
2590
2420
3120
3030
2930
2830
2730
2610
2440
3190
3090
2980
2870
2760
2640
2460
3260
3150
3040
2920
2790
2670
2480
3340
3220
3090
2960
2830
2690
2500
3410
3280
3150
3010
2860
2720
2520
3480
3340
3200
3050
2900
2750
2530
aY1 = distance from top of the steel beam to plastic neutral axis.
bY2 = distance from top of the steel beam to concrete flange force.
cSee Figure 5-3 for PNA locations.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
5 - 40
COMPOSITE DESIGN
Fy = 50 ksi
COMPOSITE DESIGN
COMPOSITE BEAM SELECTION TABLE
W Shapes
φ = 0.85
φb = 0.90
Shape
φb M p PNAc Y1a
Kip-ft
ΣQ n
φM n (kip-ft)
Y2b (in.)
4
4.5
5
In.
Kips
2
2.5
3
3.5
5.5
6
6.5
7
W 33×130
1750
TFL
2
3
4
BFL
6
7
0.00
0.21
0.43
0.64
0.86
4.39
8.29
1920
1670
1420
1180
931
705
479
2520
2480
2440
2390
2350
2270
2140
2580
2540
2490
2440
2380
2300
2160
2650
2600
2540
2480
2410
2320
2170
2720
2660
2590
2520
2450
2350
2190
2790
2720
2640
2560
2480
2370
2210
2850
2770
2690
2600
2510
2400
2230
2920
2830
2740
2640
2540
2420
2240
2990
2890
2790
2690
2580
2450
2260
3060
2950
2840
2730
2610
2470
2280
3130
3010
2890
2770
2640
2500
2290
3190
3070
2940
2810
2680
2520
2310
W 33×118
1560
TFL
2
3
4
BFL
6
7
0.00
0.19
0.37
0.56
0.74
4.44
8.54
1740
1520
1310
1100
885
660
434
2260
2230
2200
2160
2120
2050
1920
2330
2290
2250
2200
2150
2070
1930
2390
2340
2290
2240
2190
2100
1950
2450
2400
2340
2280
2220
2120
1960
2510
2450
2380
2320
2250
2140
1980
2570
2500
2430
2360
2280
2170
1990
2630
2560
2480
2400
2310
2190
2010
2700
2610
2520
2430
2340
2210
2020
2760
2660
2570
2470
2370
2240
2040
2820
2720
2620
2510
2400
2260
2050
2880
2770
2660
2550
2440
2280
2070
W 30×116
1420
TFL
2
3
4
BFL
6
7
0.00
0.21
0.43
0.64
0.85
3.98
7.44
1710
1490
1260
1040
818
623
428
2060
2030
1990
1950
1910
1850
1740
2120
2080
2030
1990
1940
1870
1760
2180
2130
2080
2020
1960
1890
1770
2240
2180
2120
2060
1990
1910
1790
2300
2240
2170
2100
2020
1940
1800
2360
2290
2210
2130
2050
1960
1820
2420
2340
2260
2170
2080
1980
1830
2480
2400
2300
2210
2110
2000
1850
2540
2450
2350
2240
2140
2020
1860
2600
2500
2390
2280
2170
2050
1880
2670
2550
2440
2320
2200
2070
1890
W 30×108
1300
TFL
2
3
4
BFL
6
7
0.00 1590 1900 1960 2010 2070 2120 2180
0.19 1390 1870 1920 1970 2020 2070 2110
0.38 1190 1840 1880 1920 1960 2010 2050
0.57 988 1800 1840 1870 1910 1940 1980
0.76 789 1760 1790 1820 1850 1880 1900
4.04 593 1710 1730 1750 1770 1790 1810
7.64 396 1600 1610 1620 1640 1650 1670
2240
2160
2090
2010
1930
1830
1680
2290
2210
2130
2050
1960
1850
1690
2350
2260
2170
2080
1990
1870
1710
2400
2310
2220
2120
2020
1890
1720
2460
2360
2260
2150
2040
1920
1740
W 30×99
1170
TFL
2
3
4
BFL
6
7
0.00 1460 1730 1790 1840 1890 1940 1990
0.17 1280 1710 1750 1800 1840 1890 1930
0.34 1100 1680 1720 1760 1800 1840 1880
0.50 930 1650 1680 1720 1750 1780 1810
0.67 755 1620 1640 1670 1700 1730 1750
4.07 559 1560 1580 1600 1620 1640 1660
7.83 364 1450 1460 1480 1490 1500 1510
2040
1980
1920
1850
1780
1680
1530
2090
2030
1950
1880
1810
1700
1540
2150
2070
1990
1910
1830
1720
1550
2200
2120
2030
1950
1860
1740
1570
2250
2160
2070
1980
1890
1760
1580
aY1 = distance from top of the steel beam to plastic neutral axis.
bY2 = distance from top of the steel beam to concrete flange force.
cSee Figure 5-3 for PNA locations.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
COMPOSITE BEAMS
5 - 41
Fy = 50 ksi
COMPOSITE DESIGN
COMPOSITE BEAM SELECTION TABLE
W Shapes
φ = 0.85
φb = 0.90
Shape
φb M p PNAc Y1a
Kip-ft
In.
ΣQ n
φM n (kip-ft)
Kips
Y2b (in.)
4
4.5
5
5.5
6
6.5
7
W 27×102
1140
TFL
2
3
4
BFL
6
7
0.00 1500 1650 1700 1760 1810 1860 1920
0.21 1290 1620 1670 1710 1760 1800 1850
0.42 1080 1590 1630 1660 1700 1740 1780
0.62 877 1550 1580 1610 1640 1670 1700
0.83 669 1510 1530 1560 1580 1600 1630
3.41 522 1470 1490 1500 1520 1540 1560
6.26 375 1400 1410 1420 1440 1450 1460
2
2.5
3
3.5
1970
1900
1820
1740
1650
1580
1480
2020
1940
1860
1770
1680
1600
1490
2080
1990
1890
1800
1700
1620
1500
2130
2030
1930
1830
1720
1630
1520
2180
2080
1970
1860
1750
1650
1530
W 27×94
1040
TFL
2
3
4
BFL
6
7
0.00 1390 1520 1570 1610 1660 1710 1760
0.19 1200 1490 1530 1570 1620 1660 1700
0.37 1010 1460 1490 1530 1570 1600 1640
0.56 827 1430 1460 1490 1510 1540 1570
0.75 641 1390 1410 1440 1460 1480 1510
3.39 493 1350 1370 1390 1400 1420 1440
6.39 346 1280 1290 1300 1320 1330 1340
1810
1740
1670
1600
1530
1460
1350
1860
1790
1710
1630
1550
1470
1360
1910
1830
1750
1660
1570
1490
1380
1960
1870
1780
1690
1600
1510
1390
2010
1910
1820
1720
1620
1530
1400
W 27×84
915
TFL
2
3
4
BFL
6
7
0.00 1240 1350 1390 1440 1480 1520 1570
0.16 1080 1330 1360 1400 1440 1480 1520
0.32 921 1300 1330 1370 1400 1430 1460
0.48 762 1270 1300 1330 1350 1380 1410
0.64 603 1240 1270 1290 1310 1330 1350
3.44 456 1200 1220 1240 1250 1270 1280
6.62 310 1130 1140 1150 1160 1170 1190
1610
1550
1500
1430
1370
1300
1200
1660
1590
1530
1460
1390
1320
1210
1700
1630
1560
1490
1410
1330
1220
1740
1670
1590
1520
1440
1350
1230
1790
1710
1630
1540
1460
1360
1240
W 24×76
750
TFL
2
3
4
BFL
6
7
0.00 1120 1110 1150 1190 1230 1270
0.17 967 1080 1120 1150 1190 1220
0.34 814 1060 1090 1120 1150 1180
0.51 662 1030 1060 1080 1100 1130
0.68 509 1010 1020 1040 1060 1080
3.00 394 976 990 1000 1020 1030
5.60 280 925 935 945 955 964
1310
1260
1200
1150
1100
1050
974
1350
1290
1230
1170
1110
1060
984
1390
1320
1260
1200
1130
1070
994
1420
1360
1290
1220
1150
1090
1000
1460
1390
1320
1250
1170
1100
1010
1500
1430
1350
1270
1190
1120
1020
W 24×68
664
TFL
2
3
4
BFL
6
7
0.00 1010
0.15 874
0.29 743
0.44 612
0.59 481
3.05 366
5.81 251
1160
1120
1080
1030
987
936
864
1200
1150
1100
1060
1000
949
873
1240
1180
1130
1080
1020
962
882
1270
1220
1160
1100
1040
975
891
1310
1250
1180
1120
1060
988
899
1340
1280
1210
1140
1070
1000
908
987 1020 1060 1090 1130
968 999 1030 1060 1090
947 973 1000 1030 1050
925 947 969 990 1010
902 919 936 953 970
872 885 898 910 923
819 828 837 846 855
aY1 = distance from top of the steel beam to plastic neutral axis.
bY2 = distance from top of the steel beam to concrete flange force.
cSee Figure 5-3 for PNA locations.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
5 - 42
COMPOSITE DESIGN
Fy = 50 ksi
COMPOSITE DESIGN
COMPOSITE BEAM SELECTION TABLE
W Shapes
φ = 0.85
φb = 0.90
Shape
φb M p PNAc Y1a
Kip-ft
ΣQ n
φM n (kip-ft)
Y2b (in.)
4
4.5
5
In.
Kips
2
2.5
3
W 24×62
574
TFL
2
3
4
BFL
6
7
0.00
0.15
0.29
0.44
0.59
3.47
6.58
910
806
702
598
495
361
228
894
879
862
845
827
789
723
926
907
887
866
844
802
731
958
936
912
887
862
815
739
991 1020 1060 1090 1120 1150 1180 1220
964 993 1020 1050 1080 1110 1140 1160
937 962 987 1010 1040 1060 1090 1110
909 930 951 972 993 1010 1040 1060
879 897 914 932 949 967 984 1000
827 840 853 866 879 891 904 917
747 755 763 771 779 787 795 803
3.5
W 24×55
503
TFL
2
3
4
BFL
6
7
0.00
0.13
0.25
0.38
0.51
3.45
6.66
810
722
633
545
456
329
203
791
778
764
750
734
700
636
820
804
787
769
751
711
643
848
829
809
788
767
723
651
877
855
832
808
783
735
658
906
880
854
827
799
746
665
934
906
876
846
815
758
672
W 21×62
540
TFL
2
3
4
BFL
6
7
0.00
0.15
0.31
0.46
0.62
2.53
4.78
915
788
662
535
408
318
229
810
791
771
750
727
705
669
842
819
795
769
741
716
677
875
847
818
788
756
727
685
907
875
841
807
770
739
693
939
903
865
826
785
750
701
972 1000 1040 1070 1100 1130
931 959 987 1010 1040 1070
888 912 935 959 982 1010
845 863 882 901 920 939
799 814 828 843 857 872
761 772 784 795 806 818
709 717 726 734 742 750
W 21×57
484
TFL
2
3
4
BFL
6
7
0.00
0.16
0.33
0.49
0.65
2.90
5.38
835
728
622
515
409
309
209
741
725
708
690
671
645
601
771
751
730
709
685
656
608
800
777
753
727
700
667
616
830
803
775
745
714
677
623
859
829
797
763
729
688
631
889
854
819
782
743
699
638
919
880
841
800
758
710
645
948
906
863
818
772
721
653
978 1010 1040
932 958 983
885 907 929
836 855 873
787 801 816
732 743 754
660 668 675
W 21×50
413
TFL
2
3
4
BFL
6
7
0.00
0.13
0.27
0.40
0.54
2.92
5.58
735
648
560
473
386
285
184
646
634
620
606
590
564
519
672
657
640
622
604
574
526
698
679
660
639
618
584
532
724
702
679
656
631
594
539
750
725
699
673
645
604
545
777
748
719
689
659
615
552
803
771
739
706
672
625
559
829
794
759
723
686
635
565
855
817
779
740
700
645
572
aY1 = distance from top of the steel beam to plastic neutral axis.
bY2 = distance from top of the steel beam to concrete flange force.
cSee Figure 5-3 for PNA locations.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
963
931
899
866
831
770
679
5.5
6
6.5
7
992 1020 1050 1080
957 982 1010 1030
921 944 966 989
885 904 923 943
848 864 880 896
781 793 805 816
686 694 701 708
881
840
799
756
713
655
578
907
863
818
773
727
665
585
COMPOSITE BEAMS
5 - 43
Fy = 50 ksi
COMPOSITE DESIGN
COMPOSITE BEAM SELECTION TABLE
W Shapes
φ = 0.85
φb = 0.90
Shape
φb M p PNAc Y1a
Kip-ft
ΣQ n
φM n (kip-ft)
Y2b (in.)
4
4.5
5
In.
Kips
2
2.5
3
3.5
5.5
6
6.5
7
W 21×44
358
TFL
2
3
4
BFL
6
7
0.00
0.11
0.23
0.34
0.45
2.90
5.69
650
577
504
431
358
260
163
568
557
546
534
522
497
453
591
577
564
549
534
506
459
614
598
581
564
547
515
465
637
618
599
580
560
525
471
660
639
617
595
572
534
476
683
659
635
610
585
543
482
706
680
653
626
598
552
488
729
700
671
641
610
561
494
752
720
689
656
623
571
499
775
741
706
671
636
580
505
798
761
724
687
648
589
511
W 18×60
461
TFL
2
3
4
BFL
6
7
0.00
0.17
0.35
0.52
0.70
2.19
3.82
880
749
617
486
355
287
220
693
674
653
630
606
590
566
724
700
675
647
618
600
573
755
727
696
665
631
610
581
787
753
718
682
644
620
589
818
780
740
699
656
630
597
849
806
762
716
669
640
605
880
833
784
733
681
651
612
911
859
806
751
694
661
620
942
886
828
768
706
671
628
974 1000
912 939
850 871
785 802
719 732
681 691
636 644
W 18×55
420
TFL
2
3
4
BFL
6
7
0.00
0.16
0.32
0.47
0.63
2.16
3.86
810
691
573
454
336
269
203
634
617
598
578
556
541
517
663
641
618
594
568
550
524
692
666
639
610
580
560
531
720
690
659
626
592
569
539
749
715
679
642
604
579
546
778
739
699
658
616
588
553
806
764
720
674
628
598
560
835
788
740
691
640
607
567
864
813
760
707
652
617
574
892
837
781
723
663
626
582
921
862
801
739
675
636
589
W 18×50
379
TFL
2
3
4
BFL
6
7
0.00
0.14
0.29
0.43
0.57
2.07
3.82
735
628
521
415
308
246
184
572
557
540
522
503
489
467
598
579
558
537
514
498
474
624
601
577
552
525
506
480
651
624
595
566
536
515
487
677
646
614
581
547
524
493
703
668
632
596
558
532
500
729
690
651
610
569
541
506
755
712
669
625
580
550
513
781
735
688
640
590
559
519
807
757
706
654
601
567
526
833
779
725
669
612
576
532
W 18×46
340
TFL
2
3
4
BFL
6
7
0.00
0.15
0.30
0.45
0.61
2.40
4.34
675
583
492
400
308
239
169
527
514
499
484
468
450
424
551
535
517
498
478
459
430
575
555
534
512
489
467
436
599
576
552
527
500
476
442
623
597
569
541
511
484
448
647
617
587
555
522
493
454
671
638
604
569
533
501
460
695
659
621
583
544
510
466
719
679
639
597
555
518
472
743
700
656
612
566
526
478
766
720
674
626
577
535
484
aY1 = distance from top of the steel beam to plastic neutral axis.
bY2 = distance from top of the steel beam to concrete flange force.
cSee Figure 5-3 for PNA locations.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
5 - 44
COMPOSITE DESIGN
Fy = 50 ksi
COMPOSITE DESIGN
COMPOSITE BEAM SELECTION TABLE
W Shapes
φ = 0.85
φb = 0.90
Shape
φb M p PNAc Y1a
Kip-ft
ΣQ n
φM n (kip-ft)
Y2b (in.)
4
4.5
5
In.
Kips
2
2.5
3
3.5
5.5
6
6.5
7
W 18×40
294
TFL
2
3
4
BFL
6
7
0.00
0.13
0.26
0.39
0.53
2.26
4.27
590
511
432
353
274
211
148
458
446
434
421
407
392
369
479
464
449
433
417
400
374
499
482
464
446
426
407
379
520
500
480
458
436
415
384
541
518
495
471
446
422
389
562
537
510
483
456
429
395
583
555
526
496
465
437
400
604
573
541
508
475
444
405
625
591
556
521
485
452
410
646
609
572
533
494
459
416
667
627
587
546
504
467
421
W 18×35
249
TFL
2
3
4
BFL
6
7
0.00
0.11
0.21
0.32
0.43
2.37
4.56
515
451
388
324
260
194
129
396
387
377
367
356
340
315
414
403
391
378
365
347
320
432
418
404
389
374
354
324
451
434
418
401
383
361
329
469
450
432
412
393
368
333
487
466
445
424
402
375
338
505
482
459
435
411
382
342
523
498
473
447
420
389
347
542
514
487
458
430
395
351
560
530
500
470
439
402
356
578
546
514
481
448
409
361
W 16×36
240
TFL
2
3
4
BFL
6
7
0.00
0.11
0.22
0.32
0.43
1.79
3.44
530
455
380
305
230
181
133
373
362
350
338
326
315
299
392
378
364
349
334
322
304
410
394
377
360
342
328
309
429
410
391
371
350
334
313
448
426
404
381
358
341
318
467
442
418
392
366
347
323
485
459
431
403
374
354
327
504
475
445
414
383
360
332
523
491
458
425
391
366
337
542
507
471
435
399
373
342
560
523
485
446
407
379
346
W 16×31
203
TFL
2
3
4
BFL
6
7
0.00
0.11
0.22
0.33
0.44
2.00
3.79
456
395
334
274
213
163
114
321
312
303
293
283
272
255
337
326
315
303
290
278
259
353
340
327
312
298
283
263
370
354
338
322
305
289
267
386
368
350
332
313
295
271
402
382
362
342
321
301
275
418
396
374
351
328
307
279
434
410
386
361
336
312
283
450
424
398
371
343
318
287
466
438
410
380
351
324
291
483
452
421
390
358
330
295
W 16×26
166
TFL
2
3
4
BFL
6
7
0.00
0.09
0.17
0.26
0.35
2.04
4.01
384
337
289
242
194
145
96.0
268
261
254
246
239
228
210
281
273
264
255
245
233
214
295
285
274
263
252
238
217
309
297
284
272
259
243
220
322
309
295
281
266
248
224
336
321
305
289
273
253
227
349
332
315
298
280
259
231
363
344
325
306
287
264
234
377
356
336
315
294
269
237
390
368
346
323
301
274
241
404
380
356
332
307
279
244
aY1 = distance from top of the steel beam to plastic neutral axis.
bY2 = distance from top of the steel beam to concrete flange force.
cSee Figure 5-3 for PNA locations.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
COMPOSITE BEAMS
5 - 45
Fy = 50 ksi
COMPOSITE DESIGN
COMPOSITE BEAM SELECTION TABLE
W Shapes
φ = 0.85
φb = 0.90
Shape
φb M p PNAc Y1a
Kip-ft
ΣQ n
φM n (kip-ft)
Y2b (in.)
4
4.5
5
In.
Kips
2
2.5
3
3.5
5.5
6
6.5
7
W 14×38
231
TFL
2
3
4
BFL
6
7
0.00
0.13
0.26
0.39
0.52
1.38
2.53
560
473
386
299
211
176
140
359
346
333
318
303
296
286
379
363
346
329
311
302
291
399
380
360
340
318
308
296
418
396
374
350
326
315
301
438
413
387
361
333
321
306
458
430
401
371
341
327
311
478
447
415
382
348
333
316
498
463
428
392
356
339
321
518
480
442
403
363
346
326
537
497
456
414
371
352
331
557
514
469
424
378
358
335
W 14×34
205
TFL
2
3
4
BFL
6
7
0.00
0.11
0.23
0.34
0.46
1.41
2.60
500
423
347
270
193
159
125
318
307
295
283
270
263
253
336
322
308
293
277
269
258
354
337
320
302
284
274
262
372
352
332
312
290
280
267
389
367
345
321
297
286
271
407
382
357
331
304
291
275
425
397
369
340
311
297
280
442
412
381
350
318
302
284
460
427
394
359
325
308
289
478
442
406
369
332
314
293
495
457
418
379
338
319
298
W 14×30
177
TFL
2
3
4
BFL
6
7
0.00
0.10
0.19
0.29
0.39
1.48
2.82
443
378
313
248
183
147
111
280
270
260
250
239
232
221
295
284
271
259
246
237
225
311
297
283
268
252
242
229
327
310
294
276
259
248
233
342
324
305
285
265
253
237
358
337
316
294
272
258
241
374
350
327
303
278
263
245
389
364
338
312
285
268
249
405
377
349
320
291
274
253
421
391
360
329
298
279
256
436
404
371
338
304
284
260
W 14×26
151
TFL
2
3
4
BFL
6
7
0.00
0.11
0.21
0.32
0.42
1.67
3.19
385
332
279
226
173
135
96.1
244
236
228
220
211
203
191
258
248
238
228
217
207
194
271
260
248
236
223
212
197
285
271
258
244
229
217
201
298
283
268
252
235
222
204
312
295
278
260
242
227
208
326
307
287
268
248
231
211
339
318
297
276
254
236
214
353
330
307
284
260
241
218
366
342
317
292
266
246
221
380
354
327
300
272
250
225
W 14×22
125
TFL
2
3
4
BFL
6
7
0.00
0.08
0.17
0.25
0.34
1.69
3.34
325
283
241
199
157
119
81.1
204
198
192
185
178
170
158
215
208
200
192
184
174
161
227
218
209
199
189
179
164
238
228
217
206
195
183
167
250
238
226
213
200
187
170
261
248
234
220
206
191
172
273
258
243
227
212
196
175
284
268
251
234
217
200
178
296
278
260
241
223
204
181
307
288
268
248
228
208
184
319
298
277
255
234
212
187
aY1 = distance from top of the steel beam to plastic neutral axis.
bY2 = distance from top of the steel beam to concrete flange force.
cSee Figure 5-3 for PNA locations.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
5 - 46
COMPOSITE DESIGN
Fy = 50 ksi
COMPOSITE DESIGN
COMPOSITE BEAM SELECTION TABLE
W Shapes
φ = 0.85
φb = 0.90
Shape
φb M p PNAc Y1a
Kip-ft
ΣQ n
φM n (kip-ft)
Y2b (in.)
4
4.5
5
In.
Kips
2
2.5
3
3.5
5.5
6
6.5
7
W 12×30
162
TFL
2
3
4
BFL
6
7
0.00
0.11
0.22
0.33
0.44
1.12
1.94
440
368
296
224
153
131
110
254
244
233
221
209
205
200
270
257
243
229
215
210
204
285
270
254
237
220
214
207
301
283
264
245
225
219
211
317
296
275
253
231
224
215
332
309
285
261
236
228
219
348
322
296
269
242
233
223
363
335
306
277
247
238
227
379
348
317
285
252
242
231
394
361
327
293
258
247
235
410
374
338
301
263
252
239
W 12×26
140
TFL
2
3
4
BFL
6
7
0.00
0.10
0.19
0.29
0.38
1.08
1.95
383
321
259
198
136
116
95.6
220
211
201
192
181
178
173
233
222
211
199
186
182
176
247
234
220
206
191
186
179
260
245
229
213
196
190
183
274
256
238
220
201
194
186
287
268
247
227
206
198
190
301
279
257
234
210
202
193
315
290
266
241
215
206
196
328
302
275
248
220
210
200
342
313
284
255
225
215
203
355
324
293
262
230
219
206
W 12×22
110
TFL
2
3
4
BFL
6
7
0.00
0.11
0.21
0.32
0.43
1.66
3.04
324
281
238
196
153
117
81.0
187
181
174
168
160
153
142
199
191
183
174
166
157
145
210
201
191
181
171
161
147
222
211
200
188
177
165
150
233
221
208
195
182
169
153
245
231
217
202
187
173
156
256
241
225
209
193
178
159
267
251
233
216
198
182
162
279
261
242
223
204
186
165
290
271
250
230
209
190
167
302
281
259
237
214
194
170
W 12×19
92.6
TFL
2
3
4
BFL
6
7
0.00
0.09
0.18
0.26
0.35
1.66
3.12
279
243
208
173
138
104
69.6
159
154
149
144
138
131
120
169
163
156
150
143
134
122
179
172
164
156
148
138
125
189
180
171
162
152
142
127
199
189
179
168
157
145
130
209
197
186
174
162
149
132
219
206
193
180
167
153
135
228
215
201
187
172
156
137
238
223
208
193
177
160
140
248
232
215
199
182
164
142
258
241
223
205
187
167
145
W 12×16
75.4
TFL
2
3
4
BFL
6
7
0.00
0.07
0.13
0.20
0.26
1.71
3.32
236
209
183
156
130
94.3
58.9
133
130
126
122
117
110
98.7
142
137
132
127
122
113
101
150
144
139
133
127
117
103
158
152
145
138
131
120
105
167
159
152
144
136
123
107
175
167
158
149
140
127
109
183
174
164
155
145
130
111
192
181
171
160
150
133
113
200
189
177
166
154
137
115
208
196
184
171
159
140
117
217
204
190
177
163
143
120
aY1 = distance from top of the steel beam to plastic neutral axis.
bY2 = distance from top of the steel beam to concrete flange force.
cSee Figure 5-3 for PNA locations.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
COMPOSITE BEAMS
5 - 47
Fy = 50 ksi
COMPOSITE DESIGN
COMPOSITE BEAM SELECTION TABLE
W Shapes
φ = 0.85
φb = 0.90
Shape
φb M p PNAc Y1a
Kip-ft
W 12×14
W 10×26
65.2
117
ΣQ n
φM n (kip-ft)
Y2b (in.)
4
4.5
5
In.
Kips
2
2.5
3
3.5
5.5
6
6.5
7
TFL
2
3
4
BFL
6
7
0.00
0.06
0.11
0.17
0.23
1.69
3.36
208
186
163
141
119
85.3
52.0
117
114
111
107
104
97.0
86.3
125
121
116
112
108
100
88.2
132
127
122
117
112
103
90.0
139
134
128
122
116
106
91.8
147
140
134
127
121
109
93.7
154
147
140
132
125
112
95.5
161
153
145
137
129
115
97.4
169
160
151
142
133
118
99.2
176
167
157
147
137
121
101
184
173
163
152
142
124
103
191
180
169
157
146
127
105
TFL
2
3
4
BFL
6
7
0.00
0.11
0.22
0.33
0.44
0.90
1.51
381
317
254
190
127
111
95.1
193
184
174
164
153
150
147
207
195
183
171
158
154
150
220
206
192
177
162
158
153
234
218
201
184
167
162
157
247
229
210
191
171
166
160
260
240
219
198
176
170
163
274
251
228
204
180
174
167
287
262
237
211
185
178
170
301
274
246
218
189
182
174
314
285
255
225
194
186
177
328
296
264
231
198
189
180
W 10×22
97.5
TFL
2
3
4
BFL
6
7
0.00
0.09
0.18
0.27
0.36
0.95
1.70
325
273
221
169
117
99.3
81.1
163
155
148
139
131
127
123
174
165
155
145
135
131
126
186
175
163
151
139
135
129
197
184
171
157
143
138
132
209
194
179
163
148
142
135
220
204
187
169
152
145
138
232
213
194
175
156
149
140
243
223
202
181
160
152
143
255
233
210
187
164
156
146
266
242
218
193
168
159
149
278
252
226
199
173
163
152
W 10×19
81.0
TFL
2
3
4
BFL
6
7
0.00
0.10
0.20
0.30
0.40
1.27
2.31
281
241
202
162
122
96.2
70.3
142
136
130
124
117
112
105
152
145
137
129
121
115
107
162
153
144
135
126
119
110
172
162
151
141
130
122
112
182
170
158
147
134
125
115
191
179
166
152
139
129
117
201
187
173
158
143
132
120
211
196
180
164
147
136
122
221
204
187
169
152
139
125
231
213
194
175
156
143
127
241
221
201
181
160
146
130
W 10×17
70.1
TFL
2
3
4
BFL
6
7
0.00
0.08
0.17
0.25
0.33
1.31
2.46
249
216
183
150
117
89.8
62.4
125
120
115
110
104
99.0
91.4
134
128
121
115
109
102
93.7
142
135
128
120
113
105
95.9
151
143
134
126
117
109
98.1
160
151
141
131
121
112
100
169
158
147
136
125
115
102
178
166
154
142
129
118
105
187
174
160
147
133
121
107
195
181
167
152
138
124
109
204
189
173
158
142
128
111
213
197
180
163
146
131
114
aY1 = distance from top of the steel beam to plastic neutral axis.
bY2 = distance from top of the steel beam to concrete flange force.
cSee Figure 5-3 for PNA locations.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
5 - 48
COMPOSITE DESIGN
Fy = 50 ksi
COMPOSITE DESIGN
COMPOSITE BEAM SELECTION TABLE
W Shapes
φ = 0.85
φb = 0.90
Shape
φb M p PNAc Y1a
Kip-ft
ΣQ n
φM n (kip-ft)
Y2b (in.)
4
4.5
5
In.
Kips
W 10×15
60.0
TFL
2
3
4
BFL
6
7
0.00
0.07
0.14
0.20
0.27
1.35
2.60
221 109
194 105
167 101
139
97.2
112
92.9
83.8 87.3
55.1 79.2
W 10×12
47.3
TFL
2
3
4
BFL
6
7
0.00
0.05
0.11
0.16
0.21
1.30
2.61
177
156
135
115
93.8
69.0
44.3
TFL
2
3
4
BFL
6
7
0.00
0.12
0.23
0.35
0.47
0.53
0.59
413
337
261
185
109
106
103
176
165
153
141
128
128
127
191
177
163
148
132
131
131
W 8×28
102
2
86.9
84.0
80.9
77.8
74.5
69.8
62.9
2.5
3
3.5
5.5
6
6.5
7
117
112
107
102
96.9
90.3
81.2
125
119
113
107
101
93.2
83.1
133
126
119
112
105
96.2
85.1
140
133
125
117
109
99.2
87.0
148
140
131
122
113
102
89.0
156
146
137
127
117
105
90.9
164
153
143
132
121
108
92.9
172
160
149
137
125
111
94.8
180
167
154
142
129
114
96.8
187
174
160
147
133
117
98.7
93.2
89.5
85.7
81.8
77.9
72.3
64.4
99.5
95.0
90.5
85.9
81.2
74.7
66.0
106
101
95.3
89.9
84.5
77.1
67.6
112
106
100
94.0
87.8
79.6
69.1
118
112
105
98.1
91.2
82.0
70.7
125
117
110
102
94.5
84.5
72.3
131
123
114
106
97.8
86.9
73.8
137
128
119
110
101
89.4
75.4
143
134
124
114
104
91.8
77.0
150
139
129
118
108
94.3
78.5
205
189
172
154
136
135
134
220
201
181
161
140
139
138
235
213
190
167
144
143
142
249
225
200
174
147
146
145
264
237
209
180
151
150
149
278
249
218
187
155
154
153
293
260
227
193
159
158
156
308
272
236
200
163
161
160
322
284
246
206
167
165
164
W 8×24
87.0
TFL
2
3
4
BFL
6
7
0.00
0.10
0.20
0.30
0.40
0.47
0.55
354
289
224
159
94.2
91.3
88.5
150
140
130
120
109
109
108
162
150
138
126
112
112
111
175
161
146
131
116
115
114
187
171
154
137
119
118
117
200
181
162
142
122
122
121
212
191
170
148
126
125
124
225
202
178
154
129
128
127
237
212
186
159
132
131
130
250
222
194
165
136
134
133
262
232
202
171
139
138
136
275
243
210
176
142
141
139
W 8×21
76.5
TFL
2
3
4
BFL
6
7
0.00
0.10
0.20
0.30
0.40
0.70
1.06
308
255
203
150
97.2
87.1
77.0
134
126
118
110
101
99.3
97.2
145
135
125
115
105
102
100
156
144
133
120
108
105
103
167
153
140
126
111
109
105
178
162
147
131
115
112
108
188
172
154
136
118
115
111
199
181
161
142
122
118
114
210
190
169
147
125
121
116
221
199
176
152
129
124
119
232
208
183
158
132
127
122
243
217
190
163
136
130
125
aY1 = distance from top of the steel beam to plastic neutral axis.
bY2 = distance from top of the steel beam to concrete flange force.
cSee Figure 5-3 for PNA locations.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
COMPOSITE BEAMS
5 - 49
Fy = 50 ksi
COMPOSITE DESIGN
COMPOSITE BEAM SELECTION TABLE
W Shapes
φ = 0.85
φb = 0.90
Shape
φb M p PNAc Y1a
Kip-ft
ΣQ n
φM n (kip-ft)
Y2b (in.)
4
4.5
5
In.
Kips
2.5
3
3.5
5.5
6
6.5
7
W 8×18
63.7
TFL
2
3
4
BFL
6
7
0.00
0.08
0.17
0.25
0.33
0.71
1.21
263 113
220 107
176 100
133
93.5
89.8 86.5
77.8 84.4
65.8 81.9
2
122
115
107
98.2
89.7
87.1
84.2
132
122
113
103
92.9
89.9
86.5
141
130
119
108
96.0
92.6
88.8
150
138
125
112
99.2
95.4
91.2
160
146
132
117
102
98.1
93.5
169
154
138
122
106
101
95.8
178
161
144
127
109
104
98.2
188
169
150
131
112
106
100
197
177
157
136
115
109
103
206
185
163
141
118
112
105
W 8×15
51.0
TFL
2
3
4
BFL
6
7
0.00
0.08
0.16
0.24
0.32
0.97
1.79
222
190
159
127
95.5
75.5
55.5
95.2
90.6
85.9
81.0
75.9
72.2
67.4
103
97.4
91.5
85.5
79.3
74.8
69.3
111
104
97.1
90.0
82.7
77.5
71.3
119
111
103
94.5
86.0
80.2
73.3
127
118
108
99.0
89.4
82.9
75.2
135
124
114
103
92.8
85.5
77.2
142
131
120
108
96.2
88.2
79.2
150
138
125
113
99.6
90.9
81.1
158
145
131
117
103
93.6
83.1
166
151
137
122
106
96.2
85.1
174
158
142
126
110
98.9
87.0
W 8×13
42.7
TFL
2
3
4
BFL
6
7
0.00
0.06
0.13
0.19
0.26
0.99
1.91
192
167
141
116
90.0
69.0
48.0
81.5
77.9
74.1
70.2
66.2
62.3
57.2
88.3
83.8
79.1
74.3
69.3
64.7
58.9
95.1
89.7
84.1
78.4
72.5
67.2
60.6
102
95.6
89.1
82.4
75.7
69.6
62.3
109
101
94.1
86.5
78.9
72.1
64.0
116
107
99.0
90.6
82.1
74.5
65.7
122
113
104
94.7
85.3
77.0
67.4
129
119
109
98.8
88.5
79.4
69.1
136
125
114
103
91.7
81.8
70.8
143
131
119
107
94.8
84.3
72.5
150
137
124
111
98.0
86.7
74.2
W 8×10
33.3
TFL
2
3
4
BFL
6
7
0.00 148
0.05 128
0.10 108
0.15 87.4
0.21 67.2
0.88 52.1
1.77 37.0
62.3
59.4
56.5
53.4
50.3
47.6
44.0
67.6
64.0
60.3
56.5
52.7
49.5
45.4
72.8
68.5
64.1
59.6
55.1
51.3
46.7
78.0
73.0
67.9
62.7
57.4
53.1
48.0
83.3
77.5
71.7
65.8
59.8
55.0
49.3
88.5
82.1
75.5
68.9
62.2
56.8
50.6
93.8
86.6
79.3
72.0
64.6
58.7
51.9
99.0
91.1
83.1
75.1
67.0
60.5
53.2
104
95.6
86.9
78.2
69.3
62.4
54.5
109
100
90.8
81.3
71.7
64.2
55.8
115
105
94.6
84.4
74.1
66.1
57.2
aY1 = distance from top of the steel beam to plastic neutral axis.
bY2 = distance from top of the steel beam to concrete flange force.
cSee Figure 5-3 for PNA locations.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
5 - 50
COMPOSITE DESIGN
LOWER BOUND
ELASTIC MOMENT OF INERTIA
FOR PLASTIC COMPOSITE SECTIONS
LB
Shaped PNAc
Y1a
ILB (in.4)
Y2b (in.)
In.
2
2.5
3
3.5
4
4.5
5
5.5
6
6.5
7
W40×297
(23200)
TFL
2
3
4
BFL
6
7
0.00
0.41
0.83
1.24
1.65
4.59
8.17
44200
42500
40500
38100
35300
33500
31600
45200
43400
41300
38800
35800
34000
32000
46200
44300
42100
39500
36400
34500
32400
47200
45200
43000
40200
37000
35000
32800
48200
46200
43800
41000
37600
35500
33200
49300
47200
44700
41700
38200
36000
33600
50300
48100
45600
42500
38800
36600
34100
51400
49200
46500
43300
39400
37100
34500
52600
50200
47400
44100
40100
37600
34900
53700
51200
48300
44900
40700
38200
35400
54900
52300
49300
45700
41400
38800
35900
W40×278
(20500)
TFL
2
3
4
BFL
6
7
0.00
0.45
0.91
1.36
1.81
5.64
10.06
40400
39000
37400
35500
33300
31100
28500
41400
39900
38200
36200
33800
31500
28800
42300
40700
39000
36900
34400
32000
29200
43200
41600
39800
37600
35000
32500
29600
44200
42500
40600
38300
35700
33100
30000
45200
43500
41400
39100
36300
33600
30400
46200
44400
42300
39800
37000
34100
30800
47300
45400
43200
40600
37600
34700
31200
48300
46300
44100
41400
38300
35200
31600
49400
47300
45000
42200
39000
35800
32100
50500
48400
45900
43100
39700
36400
32500
W40×277
(21900)
TFL
2
3
4
BFL
6
7
0.00
0.39
0.79
1.18
1.58
4.25
7.60
41300
39700
37800
35500
32700
31300
29700
42200
40500
38500
36100
33200
31700
30000
43100
41400
39300
36800
33700
32100
30400
44100
42200
40000
37400
34300
32600
30800
45000
43100
40800
38100
34800
33100
31100
46000
44000
41600
38800
35300
33500
31500
47000
44900
42400
39500
35900
34000
31900
48000
45800
43300
40200
36500
34500
32300
49100
46800
44100
40900
37000
35000
32800
50100
47800
45000
41700
37600
35500
33200
51200
48800
45900
42400
38200
36000
33600
W40×264
(19400)
TFL
2
3
4
BFL
6
7
0.00
0.43
0.87
1.30
1.73
5.49
9.90
38200
36800
35300
33500
31400
29300
26900
39000
37600
36000
34100
31900
29800
27300
39900
38500
36800
34800
32500
30200
27600
40800
39300
37500
35500
33100
30700
28000
41700
40200
38300
36200
33700
31200
28300
42700
41000
39100
36900
34300
31700
28700
43700
41900
39900
37600
34900
32200
29100
44600
42800
40800
38300
35500
32700
29500
45600
43800
41600
39100
36100
33300
29900
46600
44700
42500
39900
36800
33800
30300
47700
45700
43300
40600
37400
34300
30700
aY1 = distance from top of the steel beam to plastic neutral axis.
bY2 = distance from top of the steel beam to concrete flange force.
cSee Figure 5-3 for PNA locations.
dValue in parentheses is I (in.4) of non-composite steel shape.
x
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
COMPOSITE BEAMS
5 - 51
LOWER BOUND
ELASTIC MOMENT OF INERTIA
FOR PLASTIC COMPOSITE SECTIONS
Shaped PNAc
Y1a
LB
ILB (in.4 )
Y2b (in.)
In.
2
2.5
3
3.5
4
4.5
5
5.5
6
6.5
7
W40×249
(19500)
TFL
2
3
4
BFL
6
7
0.00
0.36
0.71
1.07
1.42
4.06
7.47
36700
35300
33600
31600
29200
27900
26400
37500
36100
34300
32200
29600
28200
26700
38400
36800
35000
32800
30100
28600
27000
39200
37600
35700
33400
30600
29100
27400
40100
38400
36400
34000
31000
29500
27700
40900
39200
37100
34600
31500
29900
28100
41800
40000
37800
35200
32000
30300
28400
42800
40800
38600
35900
32500
30800
28800
43700
41700
39300
36500
33100
31200
29200
44600
42600
40100
37200
33600
31700
29600
45600
43500
40900
37900
34100
32200
29900
W40×235
(17400)
TFL
2
3
4
BFL
6
7
0.00
0.39
0.79
1.18
1.58
5.18
9.47
33800
32600
31300
29600
27700
26000
24000
34600
33300
31900
30200
28200
26400
24300
35400
34100
32600
30800
28700
26800
24600
36200
34800
33200
31400
29200
27200
24900
37000
35600
33900
32000
29700
27600
25200
37800
36300
34600
32600
30200
28100
25600
38700
37100
35300
33200
30700
28500
25900
39500
37900
36000
33900
31300
29000
26300
40400
38700
36800
34500
31800
29400
26600
41300
39600
37500
35200
32400
29900
27000
42200
40400
38300
35900
33000
30400
27300
W40×215
(16700)
TFL
2
3
4
BFL
6
7
0.00
0.31
0.61
0.92
1.22
3.84
7.32
31300
30100
28700
27000
24900
23800
22500
32000
30700
29300
27500
25300
24100
22800
32700
31400
29800
28000
25700
24500
23100
33400
32100
30400
28500
26100
24800
23400
34200
32700
31000
29000
26600
25200
23700
34900
33400
31700
29500
27000
25600
24000
35700
34100
32300
30100
27400
25900
24300
36500
34800
32900
30600
27900
26300
24600
37300
35600
33600
31200
28300
26700
24900
38100
36300
34300
31800
28800
27100
25300
38900
37100
34900
32400
29200
27500
25600
W40×211
(15500)
TFL
2
3
4
BFL
6
7
0.00
0.35
0.71
1.06
1.42
4.99
9.35
30100
29000
27800
26400
24700
23100
21300
30800
29700
28400
26900
25100
23500
21600
31500
30300
29000
27400
25600
23900
21900
32200
31000
29600
27900
26000
24200
22200
32900
31600
30200
28500
26500
24600
22500
33600
32300
30800
29000
26900
25000
22800
34400
33000
31400
29600
27400
25400
23100
35200
33700
32100
30200
27900
25800
23400
36000
34500
32800
30800
28400
26200
23700
36800
35200
33400
31400
28900
26600
24000
37600
36000
34100
32000
29400
27100
24300
aY1 = distance from top of the steel beam to plastic neutral axis.
bY2 = distance from top of the steel beam to concrete flange force.
cSee Figure 5-3 for PNA locations.
dValue in parentheses is I (in.4) of non-composite steel shape.
x
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
5 - 52
COMPOSITE DESIGN
LOWER BOUND
ELASTIC MOMENT OF INERTIA
FOR PLASTIC COMPOSITE SECTIONS
LB
Shaped PNAc
Y1a
ILB (in.4)
Y2b (in.)
In.
2
2.5
3
3.5
4
4.5
5
5.5
6
6.5
7
W40×199
(14900)
TFL
2
3
4
BFL
6
7
0.00
0.27
0.53
0.80
1.07
4.16
8.10
28200
27200
26000
24500
22800
21600
20200
28800
27700
26500
25000
23200
21900
20500
29500
28300
27000
25500
23600
22300
20700
30100
28900
27600
25900
24000
22600
21000
30800
29600
28100
26400
24400
22900
21300
31500
30200
28700
26900
24800
23300
21500
32200
30900
29300
27400
25200
23600
21800
32900
31500
29900
28000
25700
24000
22100
33600
32200
30500
28500
26100
24400
22400
34400
32900
31100
29000
26500
24700
22700
35200
33600
31800
29600
27000
25100
23000
W40×183
(13300)
TFL
2
3
4
BFL
6
7
0.00
0.31
0.61
0.92
1.22
4.76
9.16
25700
24800
23800
22600
21200
19800
18300
26300
25400
24300
23000
21500
20100
18500
26900
25900
24800
23500
21900
20400
18700
27500
26500
25300
23900
22300
20800
19000
28100
27100
25800
24400
22700
21100
19200
28800
27600
26400
24900
23100
21400
19500
29400
28200
26900
25300
23500
21800
19700
30100
28900
27500
25800
23900
22100
20000
30700
29500
28000
26400
24300
22500
20300
31400
30100
28600
26900
24800
22800
20600
32100
30800
29200
27400
25200
23200
20800
W40×174
(12200)
TFL
2
3
4
BFL
6
7
0.00
0.21
0.42
0.62
0.83
4.59
9.27
23600
22800
21900
20900
19700
18300
16800
24100
23300
22400
21300
20000
18600
17000
24700
23800
22800
21700
20400
18900
17200
25200
24400
23300
22200
20800
19200
17400
25800
24900
23800
22600
21100
19600
17700
26400
25500
24300
23100
21500
19900
17900
27000
26000
24900
23500
21900
20200
18100
27700
26600
25400
24000
22300
20500
18400
28300
27200
25900
24500
22800
20900
18600
28900
27800
26500
25000
23200
21200
18900
29600
28400
27100
25500
23600
21600
19200
W40×167
(11600)
TFL
2
3
4
BFL
6
7
0.00
0.26
0.51
0.77
1.03
5.00
9.85
22700
22000
21200
20200
19100
17700
16100
23300
22500
21600
20600
19400
18000
16300
23800
23000
22100
21000
19800
18300
16500
24400
23500
22600
21500
20200
18600
16700
24900
24000
23000
21900
20600
18900
16900
25500
24600
23500
22300
21000
19200
17200
26100
25100
24100
22800
21300
19600
17400
26700
25700
24600
23300
21800
19900
17600
27300
26300
25100
23700
22200
20200
17900
27900
26900
25600
24200
22600
20600
18100
28600
27500
26200
24700
23000
20900
18400
W40×149
(9780)
TFL
2
3
4
BFL
6
7
0.00
0.21
0.42
0.62
0.83
5.15
10.41
19500
19000
18300
17600
16700
15400
13700
20000
19400
18700
17900
17100
15600
13900
20500
19800
19100
18300
17400
15900
14100
21000
20300
19600
18700
17700
16200
14300
21500
20800
20000
19100
18100
16500
14500
22000
21300
20400
19500
18500
16800
14700
22500
21700
20900
19900
18800
17100
14900
23000
22200
21400
20400
19200
17400
15100
23600
22800
21800
20800
19600
17700
15300
24100
23300
22300
21200
20000
18000
15500
24700
23800
22800
21700
20400
18300
15700
aY1 = distance from top of the steel beam to plastic neutral axis.
bY2 = distance from top of the steel beam to concrete flange force.
cSee Figure 5-3 for PNA locations.
dValue in parentheses is I (in.4) of non-composite steel shape.
x
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
COMPOSITE BEAMS
5 - 53
LOWER BOUND
ELASTIC MOMENT OF INERTIA
FOR PLASTIC COMPOSITE SECTIONS
Shaped PNAc
Y1a
LB
ILB (in.4 )
Y2b (in.)
In.
2
2.5
3
3.5
4
4.5
5
5.5
6
6.5
7
W 36×300
(20300)
TFL
2
3
4
BFL
6
7
0.00
0.42
0.84
1.26
1.68
3.97
6.69
38600
37000
35200
32900
30100
28900
27600
39500
37900
35900
33500
30600
29400
28000
40500
38700
36700
34200
31100
29800
28400
41400
39600
37400
34800
31600
30200
28700
42400
40500
38200
35500
32100
30700
29100
43400
41400
39000
36200
32700
31200
29500
44400
42300
39900
36900
33200
31700
29900
45500
43300
40700
37600
33800
32200
30400
46500
44300
41600
38300
34400
32700
30800
47600
45300
42500
39100
34900
33200
31200
48700
46300
43400
39900
35500
33700
31700
W 36×280
(18900)
TFL
2
3
4
BFL
6
7
0.00
0.39
0.79
1.18
1.57
3.88
6.62
35800
34400
32600
30600
28000
26900
25700
36700
35100
33300
31100
28400
27300
26000
37500
35900
34000
31700
28900
27700
26300
38400
36700
34700
32300
29400
28100
26700
39300
37600
35500
33000
29900
28500
27100
40200
38400
36200
33600
30400
29000
27400
41200
39300
37000
34300
30900
29400
27800
42200
40200
37800
34900
31400
29900
28200
43100
41100
38600
35600
31900
30300
28600
44200
42000
39400
36300
32500
30800
29000
45200
42900
40300
37000
33000
31300
29400
W 36×260
(17300)
TFL
2
3
4
BFL
6
7
0.00
0.36
0.72
1.08
1.44
3.86
6.75
32800
31500
29900
28100
25800
24700
23500
33600
32200
30600
28600
26200
25100
23800
34400
32900
31200
29200
26700
25500
24100
35200
33700
31900
29700
27100
25800
24500
36000
34500
32600
30300
27600
26200
24800
36900
35200
33300
30900
28000
26600
25100
37800
36000
34000
31500
28500
27100
25500
38700
36900
34700
32100
29000
27500
25800
39600
37700
35500
32800
29500
27900
26200
40500
38500
36200
33400
30000
28400
26600
41500
39400
37000
34100
30500
28800
27000
W 36×245
(16100)
TFL
2
3
4
BFL
6
7
0.00
0.34
0.68
1.01
1.35
3.81
6.77
30600
29400
27900
26200
24100
23100
21900
31300
30000
28500
26700
24500
23400
22200
32100
30700
29100
27200
24900
23800
22500
32800
31400
29800
27800
25300
24100
22800
33600
32100
30400
28300
25800
24500
23100
34400
32900
31100
28900
26200
24900
23400
35200
33600
31700
29500
26700
25300
23800
36100
34400
32400
30000
27100
25700
24100
36900
35200
33100
30600
27600
26100
24400
37800
36000
33800
31300
28100
26500
24800
38700
36800
34600
31900
28600
27000
25100
W 36×230
(15000)
TFL
2
3
4
BFL
6
7
0.00
0.32
0.63
0.95
1.26
3.81
6.83
28500
27300
26000
24400
22500
21500
20400
29100
28000
26600
24900
22900
21800
20700
29800
28600
27100
25400
23300
22200
20900
30600
29300
27700
25900
23700
22500
21200
31300
29900
28300
26400
24100
22900
21500
32000
30600
28900
26900
24500
23200
21800
32800
31300
29600
27500
24900
23600
22100
33600
32000
30200
28000
25400
24000
22400
34400
32800
30900
28600
25800
24400
22800
35200
33500
31500
29200
26300
24800
23100
36000
34300
32200
29700
26700
25200
23400
aY1 = distance from top of the steel beam to plastic neutral axis.
bY2 = distance from top of the steel beam to concrete flange force.
cSee Figure 5-3 for PNA locations.
dValue in parentheses is I (in.4) of non-composite steel shape.
x
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
5 - 54
COMPOSITE DESIGN
LOWER BOUND
ELASTIC MOMENT OF INERTIA
FOR PLASTIC COMPOSITE SECTIONS
LB
Shaped PNAc
Y1a
ILB (in.4)
Y2b (in.)
In.
2
2.5
3
3.5
4
4.5
5
5.5
6
6.5
7
W 36×210
(13200)
TFL
2
3
4
BFL
6
7
0.00
0.34
0.68
1.02
1.36
5.06
9.04
26000
25100
24000
22800
21300
19900
18300
26600
25700
24500
23200
21700
20300
18600
27300
26300
25100
23700
22100
20600
18800
27900
26900
25700
24200
22500
21000
19100
28600
27500
26200
24700
23000
21300
19400
29300
28200
26800
25300
23400
21700
19700
30000
28800
27400
25800
23900
22100
19900
30800
29500
28100
26300
24300
22400
20200
31500
30200
28700
26900
24800
22800
20500
32300
30900
29300
27500
25300
23200
20800
33000
31600
30000
28100
25800
23600
21100
W 36×194
(12100)
TFL
2
3
4
BFL
6
7
0.00
0.32
0.63
0.95
1.26
4.94
8.93
23800
22900
22000
20800
19500
18200
16800
24400
23500
22500
21300
19900
18600
17000
25000
24000
23000
21700
20300
18900
17200
25600
24600
23500
22200
20600
19200
17500
26200
25200
24000
22700
21000
19500
17700
26800
25800
24600
23100
21500
19900
18000
27500
26400
25100
23600
21900
20200
18300
28200
27000
25700
24100
22300
20600
18500
28900
27700
26300
24600
22700
20900
18800
29600
28300
26900
25200
23200
21300
19100
30300
29000
27500
25700
23600
21700
19400
W 36×182
(11300)
TFL
2
3
4
BFL
6
7
0.00
0.29
0.59
0.89
1.18
4.89
8.92
22200
21400
20500
19500
18300
17100
15700
22700
21900
21000
19900
18600
17300
15900
23300
22500
21500
20300
19000
17600
16100
23900
23000
22000
20700
19300
17900
16300
24500
23500
22400
21200
19700
18300
16600
25100
24100
23000
21600
20100
18600
16800
25700
24700
23500
22100
20500
18900
17100
26300
25200
24000
22600
20900
19200
17300
26900
25800
24600
23100
21300
19600
17600
27600
26400
25100
23500
21700
19900
17800
28300
27100
25700
24000
22100
20300
18100
W 36×170
(10500)
TFL
2
3
4
BFL
6
7
0.00
0.28
0.55
0.83
1.10
4.84
8.89
20600
19900
19000
18100
17000
15800
14500
21100
20300
19500
18500
17300
16100
14700
21600
20800
19900
18900
17600
16400
14900
22100
21300
20400
19300
18000
16700
15200
22700
21800
20800
19700
18300
17000
15400
23300
22300
21300
20100
18700
17300
15600
23800
22900
21800
20500
19000
17600
15800
24400
23400
22300
21000
19400
17900
16100
25000
24000
22800
21400
19800
18200
16300
25600
24500
23300
21900
20200
18500
16500
26200
25100
23800
22300
20600
18800
16800
W 36×160
(9750)
TFL
2
3
4
BFL
6
7
0.00
0.26
0.51
0.77
1.02
4.82
8.97
19200
18500
17700
16900
15800
14800
13500
19600
18900
18200
17200
16200
15000
13700
20100
19400
18600
17600
16500
15300
13900
20600
19900
19000
18000
16800
15600
14100
21100
20300
19400
18400
17100
15800
14300
21700
20800
19900
18800
17500
16100
14500
22200
21300
20300
19200
17800
16400
14700
22700
21800
20800
19600
18200
16700
14900
23300
22300
21300
20000
18500
17000
15200
23900
22900
21700
20400
18900
17300
15400
24400
23400
22200
20900
19300
17600
15600
aY1 = distance from top of the steel beam to plastic neutral axis.
bY2 = distance from top of the steel beam to concrete flange force.
cSee Figure 5-3 for PNA locations.
dValue in parentheses is I (in.4) of non-composite steel shape.
x
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
COMPOSITE BEAMS
5 - 55
LOWER BOUND
ELASTIC MOMENT OF INERTIA
FOR PLASTIC COMPOSITE SECTIONS
Shaped PNAc
Y1a
LB
ILB (in.4 )
Y2b (in.)
In.
2
2.5
3
3.5
4
4.5
5
5.5
6
6.5
7
W 36×150
(9040)
TFL
2
3
4
BFL
6
7
0.00
0.24
0.47
0.71
0.94
4.83
9.08
17800
17200
16500
15700
14800
13800
12500
18300
17600
16900
16100
15100
14000
12700
18700
18100
17300
16400
15400
14300
12900
19200
18500
17700
16800
15700
14500
13100
19700
18900
18100
17200
16000
14800
13300
20200
19400
18500
17500
16400
15000
13500
20700
19900
19000
17900
16700
15300
13700
21200
20300
19400
18300
17000
15600
13900
21700
20800
19800
18700
17400
15900
14100
22200
21300
20300
19100
17700
16200
14300
22800
21800
20800
19500
18100
16500
14500
W 36×135
(7800)
TFL
2
3
4
BFL
6
7
0.00
0.20
0.40
0.59
0.79
4.96
9.50
15600
15100
14500
13900
13100
12100
10900
16000
15400
14900
14200
13400
12400
11100
16400
15800
15200
14500
13700
12600
11200
16800
16200
15600
14800
14000
12800
11400
17200
16600
15900
15200
14300
13100
11600
17600
17000
16300
15500
14600
13300
11700
18100
17400
16700
15900
14900
13500
11900
18600
17900
17100
16200
15200
13800
12100
19000
18300
17500
16600
15500
14100
12300
19500
18800
17900
17000
15800
14300
12500
20000
19200
18300
17300
16200
14600
12700
W 33×221
(12800)
TFL
2
3
4
BFL
6
7
0.00
0.32
0.64
0.96
1.28
3.76
6.48
24500
23500
22300
20900
19200
18400
17500
25100
24100
22900
21400
19600
18700
17700
25800
24700
23400
21800
19900
19000
18000
26400
25300
23900
22300
20300
19300
18200
27100
25900
24500
22800
20700
19600
18500
27800
26500
25000
23200
21000
20000
18800
28500
27200
25600
23700
21400
20300
19100
29200
27800
26200
24200
21800
20700
19400
29900
28500
26800
24700
22200
21000
19700
30700
29200
27400
25300
22700
21400
20000
31500
29900
28000
25800
23100
21700
20300
W 33×201
(11500)
TFL
2
3
4
BFL
6
7
0.00
0.29
0.58
0.86
1.15
3.67
6.51
22000
21100
20100
18900
17400
16600
15700
22600
21600
20600
19300
17700
16800
15900
23100
22200
21000
19700
18000
17100
16200
23700
22700
21500
20100
18300
17400
16400
24300
23300
22000
20500
18700
17700
16600
25000
23800
22500
20900
19000
18000
16900
25600
24400
23000
21400
19400
18300
17100
26200
25000
23600
21800
19700
18600
17400
26900
25600
24100
22300
20100
18900
17700
27600
26300
24700
22800
20500
19300
17900
28300
26900
25300
23300
20900
19600
18200
W 33×141
(7450)
TFL
2
3
4
BFL
6
7
0.00
0.24
0.48
0.72
0.96
4.31
8.05
14700
14200
13600
12900
12100
11300
10300
15100
14500
13900
13200
12300
11500
10500
15500
14900
14200
13500
12600
11700
10700
15900
15300
14600
13800
12800
11900
10800
16300
15700
15000
14100
13100
12100
11000
16800
16100
15300
14400
13400
12400
11200
17200
16500
15700
14800
13700
12600
11300
17700
16900
16100
15100
14000
12800
11500
18100
17400
16500
15500
14200
13100
11700
18600
17800
16900
15800
14600
13300
11900
19100
18300
17300
16200
14900
13600
12100
aY1 = distance from top of the steel beam to plastic neutral axis.
bY2 = distance from top of the steel beam to concrete flange force.
cSee Figure 5-3 for PNA locations.
dValue in parentheses is I (in.4) of non-composite steel shape.
x
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
5 - 56
COMPOSITE DESIGN
LOWER BOUND
ELASTIC MOMENT OF INERTIA
FOR PLASTIC COMPOSITE SECTIONS
LB
Shaped PNAc
Y1a
ILB (in.4 )
Y2b (in.)
In.
2
2.5
3
3.5
4
4.5
5
5.5
6
6.5
7
W 33×130
(6710)
TFL
2
3
4
BFL
6
7
0.00
0.21
0.43
0.64
0.86
4.39
8.29
13300
12800
12300
11700
11000
10300
9340
13700
13200
12600
12000
11300
10400
9490
14000
13500
12900
12300
11500
10600
9640
14400
13900
13300
12600
11700
10900
9790
14800
14200
13600
12900
12000
11100
9940
15200
14600
13900
13200
12300
11300
10100
15600
15000
14300
13500
12500
11500
10300
16000
15400
14600
13800
12800
11700
10400
16400
15800
15000
14100
13100
11900
10600
16900
16200
15400
14500
13400
12200
10800
17300
16600
15800
14800
13700
12400
11000
W 33×118
(5900)
TFL
2
3
4
BFL
6
7
0.00
0.19
0.37
0.56
0.74
4.44
8.54
11800
11400
11000
10500
9880
9150
8260
12100
11700
11300
10700
10100
9330
8390
12500
12000
11500
11000
10300
9510
8520
12800
12300
11800
11200
10600
9700
8660
13100
12700
12100
11500
10800
9890
8800
13500
13000
12400
11800
11000
10100
8940
13900
13300
12800
12100
11300
10300
9090
14200
13700
13100
12400
11500
10500
9240
14600
14100
13400
12700
11800
10700
9390
15000
14400
13700
13000
12100
10900
9550
15400
14800
14100
13300
12300
11100
9710
W 30×116
(4930)
TFL
2
3
4
BFL
6
7
0.00
0.21
0.43
0.64
0.85
3.98
7.44
9870 10200 10500 10800 11100 11400 11800
9530 9800 10100 10400 10700 11000 11300
9130 9380 9640 9910 10200 10500 10700
8670 8900 9130 9360 9600 9850 10100
8130 8320 8520 8720 8930 9140 9360
7570 7730 7890 8060 8230 8400 8580
6910 7030 7150 7270 7400 7530 7670
12100
11600
11000
10400
9580
8770
7810
12500
11900
11300
10600
9810
8960
7950
12800
12300
11700
10900
10000
9150
8090
13200
12600
12000
11200
10300
9350
8240
W 30×108
(4470)
TFL
2
3
4
BFL
6
7
0.00
0.19
0.38
0.57
0.76
4.04
7.64
9000
8700
8350
7950
7480
6940
6280
9280
8960
8590
8160
7660
7090
6390
9560
9220
8830
8380
7850
7240
6500
9840 10100 10400 10800 11100 11400 11700
9480 9760 10000 10300 10600 10900 11300
9070 9330 9590 9850 10100 10400 10700
8600 8820 9060 9300 9540 9790 10100
8040 8240 8440 8650 8860 9080 9300
7400 7560 7720 7890 8070 8240 8430
6620 6740 6860 6980 7110 7240 7380
12100
11600
11000
10300
9530
8610
7510
W 30×99
(3990)
TFL
2
3
4
BFL
6
7
0.00
0.17
0.34
0.50
0.67
4.07
7.83
8110
7850
7550
7200
6800
6280
5640
8360
8080
7760
7400
6970
6420
5740
8610
8320
7980
7600
7150
6560
5840
8880
8560
8210
7800
7330
6700
5940
9150
8820
8440
8010
7510
6850
6050
9420
9080
8680
8230
7700
7010
6160
9710 10000 10300 10600 10900
9340 9620 9900 10200 10500
8930 9180 9440 9700 9970
8450 8680 8910 9150 9390
7900 8100 8300 8510 8720
7170 7330 7490 7660 7840
6280 6390 6510 6640 6760
aY1 = distance from top of the steel beam to plastic neutral axis.
bY2 = distance from top of the steel beam to concrete flange force.
cSee Figure 5-3 for PNA locations.
dValue in parentheses is I (in.4) of non-composite steel shape.
x
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
COMPOSITE BEAMS
5 - 57
LOWER BOUND
ELASTIC MOMENT OF INERTIA
FOR PLASTIC COMPOSITE SECTIONS
Shaped PNAc
Y1a
LB
ILB (in.4 )
Y2b (in.)
In.
2
2.5
3
3.5
4
4.5
5
5.5
6
6.5
7
W 27×102
(3620)
TFL
2
3
4
BFL
6
7
0.00
0.21
0.42
0.62
0.83
3.41
6.26
7240
6970
6660
6290
5860
5490
5070
7480
7190
6860
6470
6000
5610
5160
7730
7420
7070
6650
6150
5740
5260
7980
7650
7280
6830
6310
5870
5360
8240
7890
7490
7030
6470
6000
5470
8500
8140
7720
7220
6630
6140
5570
8780
8390
7950
7430
6800
6280
5680
9060
8660
8190
7630
6980
6430
5800
9350
8920
8430
7850
7150
6580
5910
9650
9200
8680
8070
7340
6730
6030
9950
9480
8930
8290
7520
6890
6150
W 27×94
(3270)
TFL
2
3
4
BFL
6
7
0.00
0.19
0.37
0.56
0.75
3.39
6.39
6580
6340
6070
5740
5360
5010
4590
6800
6540
6250
5910
5500
5120
4680
7020
6750
6440
6080
5640
5240
4770
7250
6970
6640
6250
5790
5360
4860
7490
7190
6840
6430
5940
5490
4960
7740
7420
7040
6610
6100
5620
5060
7990
7650
7260
6800
6260
5750
5160
8250
7890
7480
6990
6420
5890
5260
8510
8140
7700
7190
6590
6030
5370
8790
8390
7930
7400
6760
6170
5480
9070
8650
8170
7600
6940
6320
5590
W 27×84
(2850)
TFL
2
3
4
BFL
6
7
0.00
0.16
0.32
0.48
0.64
3.44
6.62
5770
5570
5340
5080
4760
4420
4020
5970
5750
5510
5220
4890
4530
4100
6170
5940
5680
5370
5020
4630
4180
6370
6130
5850
5530
5150
4750
4260
6580
6330
6030
5690
5290
4860
4340
6800
6530
6220
5860
5440
4980
4430
7030
6740
6410
6030
5580
5100
4520
7260
6960
6610
6210
5730
5220
4610
7500
7180
6810
6390
5890
5350
4710
7740
7400
7020
6570
6050
5480
4810
7990
7630
7230
6760
6210
5610
4910
W 24×76
(2100)
TFL
2
3
4
BFL
6
7
0.00
0.17
0.34
0.51
0.68
3.00
5.60
4280
4120
3940
3720
3460
3240
2970
4440
4270
4070
3840
3560
3320
3040
4610
4420
4210
3960
3670
3410
3100
4780
4580
4350
4090
3770
3490
3170
4950
4740
4500
4220
3880
3590
3240
5130
4910
4650
4350
4000
3680
3310
5320
5090
4810
4490
4110
3780
3390
5510
5260
4970
4640
4230
3880
3470
5710
5450
5140
4780
4360
3980
3550
5920
5640
5310
4930
4480
4090
3630
6130
5830
5490
5090
4610
4200
3710
W 24×68
(1830)
TFL
2
3
4
BFL
6
7
0.00
0.15
0.29
0.44
0.59
3.05
5.81
3760
3630
3470
3290
3080
2860
2600
3900
3760
3590
3400
3170
2940
2660
4050
3900
3720
3510
3270
3020
2720
4200
4040
3850
3630
3370
3100
2780
4360
4180
3980
3740
3470
3180
2840
4520
4330
4120
3870
3570
3270
2910
4690
4490
4260
3990
3680
3360
2970
4860
4650
4410
4120
3790
3450
3040
5040
4810
4560
4260
3910
3540
3110
5220
4980
4710
4390
4020
3640
3190
5410
5160
4870
4540
4140
3740
3260
aY1 = distance from top of the steel beam to plastic neutral axis.
bY2 = distance from top of the steel beam to concrete flange force.
cSee Figure 5-3 for PNA locations.
dValue in parentheses is I (in.4) of non-composite steel shape.
x
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
5 - 58
COMPOSITE DESIGN
LOWER BOUND
ELASTIC MOMENT OF INERTIA
FOR PLASTIC COMPOSITE SECTIONS
LB
Shaped PNAc
Y1a
ILB (in.4)
Y2b (in.)
In.
2
2.5
3
3.5
4
4.5
5
5.5
6
6.5
7
W 24×62
(1550)
TFL
2
3
4
BFL
6
7
0.00
0.15
0.29
0.44
0.59
3.47
6.58
3300
3190
3080
2940
2780
2540
2250
3430
3320
3190
3040
2870
2620
2300
3560
3440
3300
3150
2970
2690
2350
3700
3570
3420
3260
3060
2770
2410
3840
3700
3550
3370
3160
2850
2470
3990
3840
3670
3480
3270
2940
2530
4140
3980
3810
3600
3370
3020
2590
4300
4130
3940
3730
3480
3110
2650
4460
4280
4080
3860
3600
3200
2710
4620
4440
4230
3990
3710
3290
2780
4790
4590
4370
4120
3830
3390
2850
W 24×55
(1350)
TFL
2
3
4
BFL
6
7
0.00
0.13
0.25
0.38
0.51
3.45
6.66
2890
2800
2700
2590
2460
2240
1970
3000
2910
2800
2680
2540
2310
2010
3120
3020
2900
2770
2630
2370
2060
3240
3130
3010
2870
2710
2440
2110
3370
3250
3120
2970
2800
2520
2160
3500
3370
3230
3080
2900
2590
2210
3630
3500
3350
3190
2990
2670
2260
3770
3630
3470
3300
3090
2750
2320
3910
3760
3600
3410
3200
2830
2370
4060
3900
3730
3530
3300
2920
2430
4210
4040
3860
3650
3410
3000
2490
W 21×62
(1330)
TFL
2
3
4
BFL
6
7
0.00
0.15
0.31
0.46
0.62
2.53
4.78
2760
2650
2530
2380
2210
2070
1900
2880
2760
2630
2470
2280
2130
1950
3000
2870
2730
2560
2360
2190
2000
3120
2990
2830
2650
2440
2260
2050
3250
3110
2940
2750
2520
2320
2100
3390
3230
3060
2850
2600
2390
2150
3530
3360
3170
2950
2690
2460
2210
3670
3500
3290
3060
2770
2540
2270
3820
3630
3420
3170
2870
2620
2330
3970
3780
3550
3280
2960
2690
2390
4130
3920
3680
3400
3060
2780
2450
W 21×57
(1170)
TFL
2
3
4
BFL
6
7
0.00
0.16
0.33
0.49
0.65
2.90
5.38
2480
2390
2290
2170
2030
1880
1690
2590
2490
2380
2250
2100
1940
1740
2700
2590
2480
2340
2170
2000
1780
2810
2700
2570
2420
2250
2060
1830
2930
2810
2680
2520
2330
2120
1880
3060
2930
2780
2610
2410
2190
1920
3180
3050
2890
2710
2490
2260
1980
3320
3170
3000
2810
2580
2330
2030
3450
3300
3120
2910
2670
2400
2080
3590
3430
3240
3020
2760
2480
2140
3740
3560
3360
3130
2860
2560
2200
W 21×50
(984)
TFL
2
3
4
BFL
6
7
0.00
0.13
0.27
0.40
0.54
2.92
5.58
2120
2050
1960
1870
1760
1620
1440
2210
2130
2040
1940
1830
1670
1470
2310
2220
2130
2020
1890
1720
1510
2410
2320
2220
2100
1960
1780
1550
2510
2410
2310
2180
2040
1840
1590
2620
2520
2400
2260
2110
1900
1640
2730
2620
2500
2350
2190
1960
1680
2850
2730
2590
2440
2270
2020
1730
2960
2840
2700
2530
2350
2090
1780
3090
2950
2800
2630
2430
2160
1830
3210
3070
2910
2730
2520
2230
1880
aY1 = distance from top of the steel beam to plastic neutral axis.
bY2 = distance from top of the steel beam to concrete flange force.
cSee Figure 5-3 for PNA locations.
dValue in parentheses is I (in.4) of non-composite steel shape.
x
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
COMPOSITE BEAMS
5 - 59
LOWER BOUND
ELASTIC MOMENT OF INERTIA
FOR PLASTIC COMPOSITE SECTIONS
Shaped PNAc
Y1a
LB
ILB (in.4 )
Y2b (in.)
In.
2
2.5
3
3.5
4
4.5
5
5.5
6
6.5
7
W 21×44
(843)
TFL
2
3
4
BFL
6
7
0.00
0.11
0.23
0.34
0.45
2.90
5.69
1830
1770
1710
1630
1540
1410
1240
1910
1850
1780
1700
1600
1450
1270
2000
1930
1850
1760
1660
1500
1300
2090
2010
1930
1830
1730
1550
1340
2180
2100
2010
1910
1790
1610
1380
2270
2190
2090
1980
1860
1660
1410
2370
2280
2180
2060
1930
1720
1450
2470
2370
2270
2140
2000
1770
1490
2580
2470
2360
2220
2070
1830
1540
2680
2570
2450
2310
2150
1900
1580
2800
2680
2550
2400
2230
1960
1620
W 18×60
(984)
TFL
2
3
4
BFL
6
7
0.00
0.17
0.35
0.52
0.70
2.19
3.82
2070
1980
1880
1760
1610
1520
1420
2170
2080
1960
1830
1670
1570
1460
2280
2170
2050
1900
1730
1620
1500
2390
2270
2140
1980
1790
1670
1540
2500
2380
2230
2060
1850
1730
1590
2620
2480
2330
2150
1920
1790
1640
2740
2600
2430
2230
1990
1850
1690
2860
2710
2540
2320
2070
1910
1740
3000
2830
2640
2420
2140
1970
1790
3130
2960
2750
2510
2220
2040
1840
3270
3090
2870
2610
2300
2110
1900
W 18×55
(890)
TFL
2
3
4
BFL
6
7
0.00
0.16
0.32
0.47
0.63
2.16
3.86
1880
1800
1710
1600
1470
1380
1290
1970
1890
1790
1670
1520
1430
1320
2070
1970
1870
1740
1580
1480
1360
2170
2070
1950
1810
1640
1530
1400
2270
2160
2030
1880
1700
1580
1440
2380
2260
2120
1960
1760
1630
1490
2490
2360
2220
2040
1830
1690
1530
2610
2470
2310
2120
1900
1750
1580
2730
2580
2410
2210
1970
1810
1620
2850
2700
2510
2300
2040
1870
1670
2980
2810
2620
2390
2110
1930
1730
W 18×50
(800)
TFL
2
3
4
BFL
6
7
0.00
0.14
0.29
0.43
0.57
2.07
3.82
1690
1620
1540
1440
1320
1250
1160
1770
1700
1610
1500
1370
1290
1190
1860
1770
1680
1560
1420
1330
1220
1950
1860
1750
1630
1480
1380
1260
2040
1940
1830
1700
1530
1420
1300
2140
2030
1910
1770
1590
1470
1340
2240
2130
1990
1840
1650
1520
1380
2340
2220
2080
1910
1710
1570
1420
2450
2320
2170
1990
1780
1630
1460
2560
2430
2260
2070
1840
1680
1510
2680
2530
2360
2160
1910
1740
1550
W 18×46
(712)
TFL
2
3
4
BFL
6
7
0.00
0.15
0.30
0.45
0.61
2.40
4.34
1530
1470
1400
1320
1230
1140
1040
1610
1540
1470
1380
1270
1180
1070
1690
1620
1540
1440
1320
1220
1100
1770
1690
1610
1500
1380
1270
1140
1860
1770
1680
1560
1430
1310
1170
1950
1860
1750
1630
1490
1360
1210
2040
1940
1830
1700
1550
1410
1240
2140
2030
1910
1770
1610
1460
1280
2240
2130
2000
1850
1670
1510
1320
2340
2220
2080
1920
1730
1560
1360
2450
2320
2170
2000
1800
1620
1410
aY1 = distance from top of the steel beam to plastic neutral axis.
bY2 = distance from top of the steel beam to concrete flange force.
cSee Figure 5-3 for PNA locations.
dValue in parentheses is I (in.4) of non-composite steel shape.
x
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
5 - 60
COMPOSITE DESIGN
LOWER BOUND
ELASTIC MOMENT OF INERTIA
FOR PLASTIC COMPOSITE SECTIONS
LB
Shaped PNAc
Y1a
ILB (in.4)
Y2b (in.)
In.
2
2.5
3
3.5
4
4.5
5
5.5
6
6.5
7
W 18×40
(612)
TFL
2
3
4
BFL
6
7
0.00
0.13
0.26
0.39
0.53
2.26
4.27
1320
1270
1210
1140
1060
985
895
1390
1330
1270
1190
1100
1020
921
1450
1390
1320
1240
1150
1060
949
1530
1460
1390
1300
1190
1090
978
1600
1530
1450
1350
1240
1130
1010
1680
1600
1510
1410
1290
1170
1040
1760
1680
1580
1470
1340
1220
1070
1840
1760
1650
1530
1390
1260
1100
1930
1840
1730
1600
1450
1310
1140
2020
1920
1800
1670
1510
1350
1180
2110
2010
1880
1740
1560
1400
1210
W 18×35
(510)
TFL
2
3
4
BFL
6
7
0.00
0.11
0.21
0.32
0.43
2.37
4.56
1120
1080
1030
978
917
842
753
1170
1130
1080
1020
955
874
775
1230
1190
1130
1070
995
906
799
1300
1240
1180
1120
1040
940
824
1360
1300
1240
1170
1080
976
850
1430
1370
1300
1220
1130
1010
877
1500
1430
1360
1270
1170
1050
905
1570
1500
1420
1330
1220
1090
934
1650
1570
1490
1390
1270
1130
964
1720
1640
1550
1450
1320
1170
995
1800
1720
1620
1510
1380
1220
1030
W 16×36
(448)
TFL
2
3
4
BFL
6
7
0.00
0.11
0.22
0.32
0.43
1.79
3.44
971
931
884
830
764
714
657
1020
981
929
869
797
742
679
1080
1030
977
910
831
770
701
1140
1090
1030
954
867
801
725
1200
1140
1080
999
904
832
750
1270
1200
1130
1050
943
865
776
1330
1270
1190
1090
984
899
802
1400
1330
1250
1150
1030
935
830
1480
1400
1310
1200
1070
972
859
1550
1470
1370
1250
1120
1010
889
1630
1540
1430
1310
1160
1050
921
W 16×31
(375)
TFL
2
3
4
BFL
6
7
0.00
0.11
0.22
0.33
0.44
2.00
3.79
826
793
756
713
662
613
555
872
837
796
748
691
637
574
921
882
837
784
722
663
593
972
929
880
823
755
690
614
1030
979
925
863
789
718
635
1080
1030
972
904
824
747
657
1140
1080
1020
948
861
778
680
1200
1140
1070
993
899
810
704
1260
1200
1120
1040
939
843
729
1330
1260
1180
1090
980
877
755
1390
1320
1240
1140
1020
912
782
W 16×26
(301)
TFL
2
3
4
BFL
6
7
0.00
0.09
0.17
0.26
0.35
2.04
4.01
673
649
621
589
551
505
450
712
685
654
618
577
526
465
753
723
689
650
604
549
482
795
763
726
683
633
572
499
840
804
764
717
663
597
517
886
848
804
753
694
622
535
935
893
845
790
727
649
554
985
940
888
829
760
676
575
1040
989
933
870
796
705
595
1090
1040
980
911
832
734
617
1150
1090
1030
955
870
765
639
aY1 = distance from top of the steel beam to plastic neutral axis.
bY2 = distance from top of the steel beam to concrete flange force.
cSee Figure 5-3 for PNA locations.
dValue in parentheses is I (in.4) of non-composite steel shape.
x
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
COMPOSITE BEAMS
5 - 61
LOWER BOUND
ELASTIC MOMENT OF INERTIA
FOR PLASTIC COMPOSITE SECTIONS
Shaped PNAc
Y1a
LB
ILB (in.4 )
Y2b (in.)
In.
2
2.5
3
3.5
4
4.5
5
5.5
6
6.5
7
W 14×38
(385)
TFL
2
3
4
BFL
6
7
0.00
0.13
0.26
0.39
0.52
1.38
2.53
844
805
759
704
636
604
568
896
853
802
740
665
629
589
951
903
846
778
695
655
611
1010
956
893
818
727
683
634
1070
1010
943
861
760
712
659
1130
1070
994
905
794
742
684
1200
1130
1050
950
831
773
710
1270
1190
1100
998
868
806
738
1340
1260
1160
1050
908
840
766
1410
1330
1220
1100
948
876
796
1490
1400
1290
1150
991
913
827
W 14×34
(340)
TFL
2
3
4
BFL
6
7
0.00
0.11
0.23
0.34
0.46
1.41
2.60
744
711
671
623
565
535
502
790
753
709
656
591
557
520
839
798
749
690
618
581
540
890
844
790
726
647
606
560
944
894
834
763
677
631
582
1000
945
880
803
708
659
604
1060
999
929
844
741
687
628
1120
1060
979
887
775
716
652
1180
1110
1030
931
810
747
677
1250
1170
1080
978
847
779
704
1320
1240
1140
1030
885
812
731
W 14×30
(291)
TFL
2
3
4
BFL
6
7
0.00
0.10
0.19
0.29
0.39
1.48
2.82
643
615
583
544
497
467
432
684
653
616
573
521
487
448
726
692
652
604
546
508
465
771
734
689
636
573
531
483
819
777
728
670
600
554
502
868
823
769
706
629
579
522
920
870
812
743
659
605
542
974
920
857
782
691
631
564
1030
971
903
822
724
659
586
1090
1020
951
864
758
688
610
1150
1080
1000
907
793
719
634
W 14×26
(245)
TFL
2
3
4
BFL
6
7
0.00
0.11
0.21
0.32
0.42
1.67
3.19
553
531
504
473
437
405
368
589
563
534
500
459
423
382
626
598
565
527
482
443
397
665
634
598
556
506
463
413
706
672
633
587
532
485
430
750
712
669
619
559
507
447
795
754
707
652
587
530
465
841
798
747
687
616
555
484
890
843
788
723
646
580
503
941
890
830
761
678
606
523
994
939
875
800
711
634
545
W 14×22
(199)
TFL
2
3
4
BFL
6
7
0.00
0.08
0.17
0.25
0.34
1.69
3.34
454
437
416
393
365
336
301
484
464
442
416
385
352
313
515
493
468
439
405
369
325
548
524
496
464
427
386
339
582
556
526
490
449
405
352
619
590
556
518
473
424
367
656
625
588
546
497
444
382
696
661
622
576
523
466
398
736
699
657
607
550
488
414
779
739
693
640
577
510
431
823
780
731
673
606
534
449
aY1 = distance from top of the steel beam to plastic neutral axis.
bY2 = distance from top of the steel beam to concrete flange force.
cSee Figure 5-3 for PNA locations.
dValue in parentheses is I (in.4) of non-composite steel shape.
x
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
5 - 62
COMPOSITE DESIGN
LOWER BOUND
ELASTIC MOMENT OF INERTIA
FOR PLASTIC COMPOSITE SECTIONS
LB
Shaped PNAc
Y1a
ILB (in.4)
Y2b (in.)
In.
2
2.5
3
3.5
4
4.5
5
5.5
6
6.5
7
W 12×30
(238)
TFL
2
3
4
BFL
6
7
0.00
0.11
0.22
0.33
0.44
1.12
1.94
531
505
474
436
389
373
355
568
539
504
461
408
390
370
608
575
536
488
429
408
386
649
612
569
516
450
427
402
693
652
604
545
472
447
420
738
694
641
576
496
468
438
786
738
679
609
521
490
457
837
783
720
643
547
513
477
889
831
762
678
574
537
498
944
881
806
715
602
562
520
1000
933
852
753
631
589
543
W 12×26
(204)
TFL
2
3
4
BFL
6
7
0.00
0.10
0.19
0.29
0.38
1.08
1.95
456
434
407
375
336
321
305
488
463
433
397
353
336
317
521
494
460
420
370
351
331
557
526
489
445
389
368
345
595
561
520
470
409
386
360
635
597
552
497
430
404
376
676
635
585
526
452
423
393
720
674
621
555
474
444
410
765
716
657
586
498
465
428
812
759
695
618
523
487
447
861
804
735
652
549
509
467
W 12×22
(156)
TFL
2
3
4
BFL
6
7
0.00
0.11
0.21
0.32
0.43
1.66
3.04
371
356
339
318
294
270
242
399
382
362
339
312
285
253
428
408
386
360
330
300
265
458
437
412
383
350
316
277
490
466
439
408
370
333
290
524
498
468
433
392
351
303
559
531
498
459
414
370
317
596
565
529
487
438
389
332
635
601
562
516
463
410
347
675
638
596
547
488
431
364
717
677
631
578
515
453
380
W 12×19
(130)
TFL
2
3
4
BFL
6
7
0.00
0.09
0.18
0.26
0.35
1.66
3.12
312
300
286
270
251
229
203
335
321
306
287
266
241
212
360
344
327
306
282
255
222
386
368
349
326
300
269
232
413
394
372
347
318
284
243
442
421
397
369
337
299
255
472
449
423
392
357
316
267
503
478
450
417
378
333
279
536
509
478
442
400
351
293
571
541
507
468
423
370
306
606
574
538
496
446
389
321
W 12×16
(103)
TFL
2
3
4
BFL
6
7
0.00
0.07
0.13
0.20
0.26
1.71
3.32
254
245
234
223
210
189
163
273
263
251
239
224
200
171
294
282
269
255
238
212
179
315
303
288
272
254
224
188
338
324
309
291
270
238
197
362
347
330
310
287
251
207
388
371
352
330
305
266
217
414
396
375
351
324
281
227
442
422
399
373
344
297
239
471
449
424
396
364
313
250
501
477
450
420
386
330
262
aY1 = distance from top of the steel beam to plastic neutral axis.
bY2 = distance from top of the steel beam to concrete flange force.
cSee Figure 5-3 for PNA locations.
dValue in parentheses is I (in.4) of non-composite steel shape.
x
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
COMPOSITE BEAMS
5 - 63
LOWER BOUND
ELASTIC MOMENT OF INERTIA
FOR PLASTIC COMPOSITE SECTIONS
Shaped PNAc
Y1a
LB
ILB (in.4 )
Y2b (in.)
In.
2
2.5
3
3.5
4
4.5
5
5.5
6
6.5
7
W 12×14
(88.6)
TFL
2
3
4
BFL
6
7
0.00
0.06
0.11
0.17
0.23
1.69
3.36
220
213
204
195
184
165
141
237
229
219
209
197
175
148
255
246
235
223
210
186
155
275
264
252
239
224
197
163
295
283
270
255
238
209
171
316
303
289
272
254
221
180
338
324
308
290
270
234
188
362
346
329
309
287
247
198
386
369
350
329
305
262
208
411
393
372
349
323
276
218
438
418
396
371
342
292
228
W 10×26
(144)
TFL
2
3
4
BFL
6
7
0.00
0.11
0.22
0.33
0.44
0.90
1.51
339
322
300
274
242
232
222
368
347
323
293
256
245
233
398
375
347
313
271
258
245
430
404
372
334
287
273
258
464
435
400
357
304
288
272
499
467
428
381
321
304
286
537
501
458
406
340
321
301
577
537
490
432
360
339
317
618
575
523
460
381
358
334
662
615
558
489
403
378
351
707
656
594
519
425
398
369
W 10×22
(118)
TFL
2
3
4
BFL
6
7
0.00
0.09
0.18
0.27
0.36
0.95
1.70
281
267
250
230
205
194
183
305
289
269
246
217
205
193
330
312
290
263
231
217
203
357
336
312
282
245
230
214
386
363
335
302
260
244
225
416
390
360
322
277
258
237
448
419
385
344
293
273
250
482
450
413
367
311
288
263
517
482
441
391
330
305
277
554
516
471
417
350
322
292
592
551
502
443
370
340
308
W 10×19
(96.3)
TFL
2
3
4
BFL
6
7
0.00
0.10
0.20
0.30
0.40
1.27
2.31
239
228
215
200
183
169
153
259
247
233
216
195
180
162
282
267
251
232
209
191
170
305
289
271
249
223
203
180
330
312
292
267
238
216
190
356
337
314
286
254
229
200
384
362
337
307
271
243
211
413
389
361
328
288
258
223
444
417
387
350
307
274
235
476
447
413
374
326
290
248
509
478
441
398
347
307
261
W 10×17
(81.9)
TFL
2
3
4
BFL
6
7
0.00
0.08
0.17
0.25
0.33
1.31
2.46
206
197
187
175
161
148
132
224
214
203
189
173
157
139
244
232
219
204
185
168
147
265
252
237
219
199
179
155
286
272
255
236
213
190
164
310
294
275
253
227
202
173
334
316
296
272
243
215
183
360
340
317
291
260
229
193
387
365
340
311
277
243
204
415
391
364
332
295
258
215
444
419
389
354
314
274
227
aY1 = distance from top of the steel beam to plastic neutral axis.
bY2 = distance from top of the steel beam to concrete flange force.
cSee Figure 5-3 for PNA locations.
dValue in parentheses is I (in.4) of non-composite steel shape.
x
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
5 - 64
COMPOSITE DESIGN
LOWER BOUND
ELASTIC MOMENT OF INERTIA
FOR PLASTIC COMPOSITE SECTIONS
LB
Shaped PNAc
Y1a
ILB (in.4)
Y2b (in.)
In.
2
2.5
3
3.5
4
4.5
5
5.5
6
6.5
7
W 10×15
(68.9)
TFL
2
3
4
BFL
6
7
0.00
0.07
0.14
0.20
0.27
1.35
2.60
177
170
162
153
142
128
112
193
185
175
165
153
137
118
210
201
190
178
164
147
125
228
218
206
192
176
157
133
247
236
222
207
189
167
140
268
255
240
223
203
178
148
289
275
258
240
218
190
157
312
296
278
257
233
203
166
335
318
298
275
249
216
176
360
341
320
295
266
229
185
386
365
342
315
283
244
196
W 10×12
(53.8)
TFL
2
3
4
BFL
6
7
0.00
0.05
0.11
0.16
0.21
1.30
2.61
139
134
128
121
113
102
87.9
152
146
139
131
122
109
92.9
165
158
150
141
131
116
98.4
180
172
163
153
141
124
104
195
186
176
165
152
133
110
211
202
190
178
163
142
117
229
218
205
191
175
152
124
247
235
221
205
187
162
131
265
252
237
220
200
173
138
285
271
254
236
214
184
146
306
290
272
252
229
195
155
W 8×28
(98)
TFL
2
3
4
BFL
6
7
0.00
0.12
0.23
0.35
0.47
0.53
0.59
248
233
214
191
161
159
158
274
256
234
207
171
170
168
302
281
256
224
183
181
180
332
308
279
243
196
194
192
364
337
304
262
209
207
204
398
368
330
284
223
221
218
434
400
358
306
238
235
233
473
435
388
330
254
251
248
513
471
419
355
271
268
264
555
509
452
381
289
285
281
600
549
487
408
307
303
299
W 8×24
(82.8)
TFL
2
3
4
BFL
6
7
0.00
0.10
0.20
0.30
0.40
0.47
0.55
209
196
180
161
136
134
133
231
216
198
175
145
143
142
255
237
216
189
155
153
151
280
260
236
205
166
164
162
307
285
257
222
177
175
173
336
311
279
240
189
187
184
367
339
303
259
202
200
197
400
368
329
280
216
213
210
434
399
355
301
231
227
223
470
431
383
323
246
242
238
508
465
413
347
262
257
253
W 8×21
(75.3)
TFL
2
3
4
BFL
6
7
0.00
0.10
0.20
0.30
0.40
0.70
1.06
191
181
167
151
131
126
122
211
198
183
164
140
135
130
232
218
200
178
151
145
138
255
238
218
193
162
155
147
279
260
237
209
173
165
157
305
284
258
226
186
177
167
333
309
279
244
199
189
178
362
335
302
263
213
201
190
392
362
327
283
227
215
202
424
391
352
304
243
229
215
458
422
379
326
259
244
228
aY1 = distance from top of the steel beam to plastic neutral axis.
bY2 = distance from top of the steel beam to concrete flange force.
cSee Figure 5-3 for PNA locations.
dValue in parentheses is I (in.4) of non-composite steel shape.
x
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
COMPOSITE BEAMS
5 - 65
LOWER BOUND
ELASTIC MOMENT OF INERTIA
FOR PLASTIC COMPOSITE SECTIONS
Shaped PNAc
Y1a
LB
ILB (in.4 )
Y2b (in.)
In.
2
2.5
3
3.5
4
4.5
5
5.5
6
6.5
7
W 8×18
(61.9)
TFL
2
3
4
BFL
6
7
0.00
0.08
0.17
0.25
0.33
0.71
1.21
159
150
140
127
111
106
101
175
165
153
138
120
114
107
193
182
167
150
129
122
114
213
199
183
163
139
131
122
233
218
199
177
149
140
130
255
238
217
192
160
150
139
278
259
236
207
172
161
148
303
281
255
224
184
172
158
329
305
276
241
198
184
169
356
329
298
259
211
196
179
384
355
321
278
226
209
191
W 8×15
(48)
TFL
2
3
4
BFL
6
7
0.00
0.08
0.16
0.24
0.32
0.97
1.79
129
123
116
107
97.0
89.3
80.6
143
136
128
117
105
96.4
86.2
158
150
140
128
114
104
92.2
175
165
154
140
124
112
98.7
192
181
168
153
135
121
106
210
198
183
166
146
130
113
230
216
200
181
158
140
121
251
235
217
196
170
151
129
272
255
235
211
183
162
138
295
276
254
228
197
174
147
319
299
274
246
211
186
157
W 8×13
(39.6)
TFL
2
3
4
BFL
6
7
0.00
0.06
0.13
0.19
0.26
1.00
1.91
109
104
98.0
91.4
83.6
76.1
67.2
121
115
108
100
91.3
82.4
72.0
134
127
119
110
99.6
89.3
77.2
147
140
131
121
108
96.6
82.7
162
154
144
132
118
104
88.7
178
168
157
144
128
113
95.0
195
184
171
156
139
122
102
213
200
186
170
150
131
109
231
218
202
184
162
141
116
251
236
219
198
175
151
124
272
255
236
214
188
162
132
W 8×10
(30.8)
TFL
2
3
4
BFL
6
7
0.00
0.05
0.10
0.15
0.21
0.88
1.77
83.1
79.3
74.8
69.6
63.5
58.0
51.7
92.3 102
113
87.8 97.0 107
82.6 90.9 99.9
76.5 83.8 91.7
69.2 75.4 82.0
62.8 68.0 73.5
55.4 59.4 63.6
124
117
109
100
89.2
79.5
68.2
136
129
120
109
96.7
85.8
73.0
149
141
131
119
105
92.5
78.2
163
153
142
129
113
99.6
83.6
177
166
154
140
122
107
89.4
192
180
167
151
132
115
95.4
208
195
180
162
142
123
102
aY1 = distance from top of the steel beam to plastic neutral axis.
bY2 = distance from top of the steel beam to concrete flange force.
cSee Figure 5-3 for PNA locations.
dValue in parentheses is I (in.4) of non-composite steel shape.
x
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
5 - 66
COMPOSITE DESIGN
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
COMPOSITE COLUMNS
5 - 67
COMPOSITE COLUMNS
General Notes
Load tables for composite columns are presented for a variety of W shapes, pipe, and
structural tubing. Tabular loads have been computed in accordance with Section I2.2 of
the LRFD Specification for axially loaded members having effective unsupported lengths
indicated at the left of each table. The effective length KL is the actual unbraced length,
in feet, multiplied by factor K, which depends on the rotational restraint at the ends of
the unbraced length and the means available to resist lateral movements. The K factor
may be selected using as a guide Table C-C2.1 in the Commentary of the LRFD
Specification. Interpolation between the idealized cases is a matter of engineering
judgment. More precise values for K may be obtained, if desired, from the alignment
chart in Figure C-C2.2 in the LRFD Commentary (also shown in Part 3 of this Manual
under Design Strength of Columns) once sections have been selected for several framing
members.
Load tables are provided for W shapes encased in reinforced normal-weight concrete
of square or rectangular cross section, and for steel pipe and structural tubing filled with
normal-weight concrete. The following W shapes are included:
Nominal
depth, in.
14
12
10
8
Weight,
lb per ft
426-61
336-58
112-45
67-35
Two values of yield stress, Fy equal to 36 and 50 ksi, and three values of concrete
cylinder strength, fc′ equal to 3.5, 5, and 8 ksi, are included for W shapes. All reinforcing
steel is Grade 60. The tables for steel pipe columns include nominal pipe diameters of 4
to 12 in., yield stress Fy = 36 ksi, and concrete cylinder strength fc′ equal to 3.5 and 5 ksi.
The tables for tubular columns include tubes of nominal side dimensions 4 to 16 in., yield
stress Fy equal to 46 ksi, and concrete cylinder strength fc′ equal to 3.5 and 5 ksi.
All axial design strengths are tabulated in kips. Strength values are omitted when
Kl / r exceeds 200. Resistance factor φ = 0.85 was used in computing the axial design
strengths of all composite columns.
In all tables, the design strengths are given for effective lengths with respect to the
minor axis. When the minor axis is braced at closer intervals than the major axis, the
strength of the column must be investigated with reference to both the major (X-X) and
minor (Y-Y) axes. The ratio rmx / rmy included in the tables provides a convenient method
for investigating the strength of a column with respect to its major axis.
Properties useful to the designer are listed at the bottom of the Column Load Tables.
They are helpful in considering buckling about the major axis as discussed above and in
the design of members under combined axial compression and bending as discussed
subsequently. Both of these cases are illustrated with design examples. The properties
have the following units:
modified radius of gyration rm, in.
nominal flexural strength Mn, kip-ft
Euler buckling term Pe (KL)2, kip-ft2
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
5 - 68
COMPOSITE DESIGN
Subscripts x and y refer to the major and minor axes. Resistance factor φb = 0.9 was
used in computing the flexural design strength φbMn.
Additional notes relating specifically to the W shapes, steel pipe, and structural tube
column tables precede each of these groups of tables.
EXAMPLE 5-4
Given:
Using tables on the pages that follow, design the smallest composite
column with a W shape of Fy = 50 ksi to support a factored concentric
load of 1,000 kips. The effective length with respect to its minor axis
is 16 feet and that with respect to its major axis is 31 feet.
Solution:
Use composite column tables for W shapes of fc′ = 8 ksi since the
strongest concrete requires the smallest size column. An inspection of
the tables reveals that the tabulated values of rmx / rmy do not exceed
1.22 and in most cases are equal to 1.0 (square columns).
Assuming that rmx / rmy is equal to 1.0, enter the tables with equivalent
effective column length of KL = 31 ft. Select an 18 in. × 18 in. column
with a W10×49 and rmx / rmy = 1.0. By interpolation, the column has an
axial design strength φPn of 1,029 kips.
Use: 18 in. × 18 in. column with W10×49 of Fy = 50 ksi, fc′ = 8 ksi, four
#8 Gr. 60 longitudinal bars and #3 Gr. 60 ties spaced 12 inches on
center.
EXAMPLE 5-5
Given:
Redesign the column from Example 5-4 using (a) rectangular and (b)
square structural tubing, both filled with structural concrete.
Solution:
a. Enter the Composite Column Tables for rectangular structural tubing filled with 5 ksi concrete at an effective column length of KL =
16 ft.
Select 14×10 tubing with 1⁄2-in. thick walls; φPn = 1,090 kips.
rmx / rmy = 1.30
Equivalent effective length for X-X axis:
31 / 1.30 = 23.8 ft
Since 23.8 ft > 16 ft, X-X axis controls.
Re-enter the table at an effective length of KL = 23.8 ft. It is apparent
that 14×10 tube will not satisfy the axial load of 1,000 kips. Select
16×12 steel tube with 1⁄2-in. walls:
rmx / rmy = 1.25
KL
= 31 / 1.25 = 24.8 ft
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
COMPOSITE COLUMNS
5 - 69
By interpolation, the column provides an axial design strength of
1,206 kips. The same tubing filled with 3.5 ksi concrete is good for
1,094 kips > 1,000 kips.
Use: 16-in. × 12-in. × 1⁄2-in. tubing filled with 3.5-ksi concrete.
b. Enter the Composite Column Tables for square structural tubing
filled with 5 ksi concrete at effective column length KL = 31 ft.
Select 14×14 tubing with 1⁄2-in. thick walls good for 1,135 kips. The
same tubing filled with 3.5 ksi concrete is good for 1,035 kips >
1,000 kips.
Use: 14-in. × 14-in. × 1⁄2-in. tubing filled with 3.5-ksi concrete.
Note: The weight of both the 16×12 and 14×14 steel tubing with
1⁄ -in. thick walls is 89.68 lb. per ft.
2
Combined Axial Compression and Bending (Interaction)
Loads given in the Composite Column Tables are for concentrically loaded columns. For
columns subjected to combined compression and flexure, the nominal flexural design
strength φbMn determined from Equation C-I4-1 of the Commentary on the LRFD
Specification (only valid for Pu / φcPn > 0.3) and the elastic buckling load Pe times the
square of the effective column length are given at the bottom of the tables. With these
quantities and the loads tabulated for concentric loading, the column may be designed
by successive approximations based on LRFD Specification Section I4. The procedure
is illustrated in Example 5-6 for a column subjected to a large bending moment combined
with a moderate axial load and in Example 5-7 for a column subjected to a large axial
load combined with a moderate bending moment.
EXAMPLE 5-6
Given:
Design a composite encased W shape column to resist a factored axial
load of 350 kips and a factored moment about the X-X axis of
240 kip-ft. The unsupported length of the column is 12 feet, Fy = 50 ksi,
fc′ = 3.5 ksi and Cm = 1.0. The loads were obtained by first order elastic
analysis and there is no lateral translation of column ends.
Solution:
Since the moment is large in relation to the axial load, assume that
Pu / φPn = 1⁄2 and B1 = 1.0. From Equation H1-1a
φbMnx = (8 / 9) × 240 × 2 = 427 kip-ft
From the Composite Column Tables, find a column with φbMnx close
to 427 kip-ft.
Try a W10×60 with 18-in. encasement: φbMnx = 439 kip-ft, φPn =
1,300 kips and Pex = 142 × 104 / 122 = 9,861 kips. Therefore,
Pu / φPn = 350 / 1,300 = 0.2692 ≥ 0.2
From Equation C1-1 and C1-2, with Mlt = 0 since there is no lateral
translation,
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
5 - 70
COMPOSITE DESIGN
Mux =
240
= 248.8 kip-ft
350
1−
9,861
and from Equation H1-1a
φbMnx =
8(248.8)
9 1 −
350
1,300
= 302.6 kip-ft
Since 302.6 kip-ft is much less than the 439 kip-ft provided, select a
smaller size. Tr y a W8×58 with 16-in. × 16-in. encasement: φbMnx =
345 kip-ft, φPn = 1,130 kips and Pex = 103 × 104 / 122 = 7,153 kips.
Mux =
240
= 252.4 kip-ft
350
1−
7,153
From Equation H1-1a, with φbMnx = 345 kip-ft since φPn / Pu > 0.3,
8(252.3)
350
+
= 0.960 < 1.0 o.k.
1,130 9(345)
Use: 16-in. × 16-in. column with W8×58 of Fy = 50 ksi, fc′ = 3.5 ksi,
four #7 Gr. 60 longitudinal bars and #3 Gr. 60 ties spaced at 10 inches.
EXAMPLE 5-7
Given:
Design a composite encased W shape column to resist a factored axial
load of 1,100 kips and factored moment of 200 kip-ft. Use 50 ksi
structural steel and 5 ksi concrete. The unsupported column length is
11 feet and Cm = 0.85. Assume that sidesway is prevented.
Solution:
Since the axial load is large in relation to the moment, assume that:
8 Mu
= 0.5
9 φbMnx
From Equation H1-1a
φPn = 1,100 / 0.5 = 2,200 kips
From the Composite Column Tables, find a column with φPn close to
2,200 kips at KL = 11 ft.
Try a W12×106 with 20-in. encasement: φPn = 2,270 kips, φbMnx =
899 kip-ft and Pex = 294 × 104 / 112 = 24,300 kips.
From Equation C1-2
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
COMPOSITE COLUMNS
B1 =
5 - 71
0.85
= 0.890 < 1.0
1,100
1−
24,300
Therefore, B1 = 1.0. From Equation H1-1a
Pu
8 200
=1− ×
= 0.802
9 899
φPn
and
φPn = 1,100 / 0.802 = 1,372 kips
Try a W10×45 with 18-in. × 18-in. encasement: φPn = 1,360 kips,
φbMnx = 356 kip-ft and Pex = 125 × 104 / 112 = 10,330 kips.
From Equation C1-2
B1 =
0.85
1−
1,100
10,300
= 0.951 < 1.0
Therefore, B1 = 1.0 and
Pu
8 200
=1− ×
= 0.501
9 356
φPn
and
φPn = 1,100 / 0.501 = 2,196 kips
Since the convergence is slow, estimate a new φPn as:
φPn =
2,196 + 1,372
= 1,784 kips
2
Try a W10×77 with 18-in. × 18-in. encasement: φPn = 1,720 kips,
φbMnx = 555 kip-ft and Pex = 178 × 104 / 112 = 14,710 kips.
B1 =
0.85
1−
1,100
14,710
= 0.919 < 1.0
and
1,100 8 200
+ ×
= 0.960 < 1.0 o.k.
1,720 9 555
Use: 18-in. × 18-in. column with W10×77 of Fy = 50 ksi, fc′ = 5 ksi,
four #8 Gr. 60 longitudinal bars and #3 Gr. 60 ties spaced at 12 inches.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
5 - 72
COMPOSITE DESIGN
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
COMPOSITE COLUMNS—W SHAPES ENCASED IN CONCRETE
5 - 73
COMPOSITE COLUMNS—W SHAPES ENCASED IN CONCRETE
General Notes
Concentric load design strengths in the tables that follow are tabulated for the effective
length KL in feet, listed at the left of each table. They are applicable to axially loaded
members with respect to their minor axis in accordance with Section I2.2 of the LRFD
Specification. Two steel yield stresses, Fy = 36 ksi and Fy = 50 ksi, and three concrete
strengths, fc′ = 3.5 ksi, fc′ = 5 ksi, and fc′ = 8 ksi, are covered. The tables apply to
normal-weight concrete. All reinforcing steel is Gr. 60; however, Fyr = 55 ksi is used in
the calculation of φPn in accordance with LRFD Specification Section I2.1.
Each W shape is embedded in concrete of a square or rectangular cross section
reinforced with four longitudinal reinforcing bars placed in the four corners and with
lateral ties spaced as required in Section I2.1. For the design of additional confinement
reinforcement, see LRFD Specification Section I2.1. The size of the concrete section was
selected so as to provide at least the minimum required cover over the reinforcing bars
in the column.
For discussion of the effective length, range of Kl / r, strength about the major axis,
combined axial and bending strength, and for sample problems, see Composite Columns,
General Notes.
The properties listed at the bottom of each table are for use in checking strength about
the strong axis and in design for combined axial load and bending.
Additional information on W shapes encased in concrete, including numerous tables
for columns and beam-columns, is available in the AISC Steel Design Guide No. 6, Load
and Resistance Factor Design of W-Shapes Encased in Concrete (Griffis, 1992).
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
5 - 74
COMPOSITE DESIGN
Fy = 36 ksi
Fy = 50 ksi
b
Y
X
h
COMPOSITE COLUMNS
W Shapes
fc′ = 3.5 ksi
All reinforcing steel is Grade 60
Axial design strength in kips
X
Y
24 in.×26 in.
4-#11 bars
Ties
#4 bars spaced 16 in. c. to c.
Designation
W 14
Wt./ft
426
Fy
Effective length KL (ft) with respect to least radius of gyration rmy
Steel
Shape
Size b × h
Reinf. bars
398
370
342
311
36
50
36
50
36
50
36
50
36
50
0
4910
6400
4680
6070
4450
5740
4220
5420
3940
5030
6
7
8
9
10
4880
4870
4850
4840
4820
6340
6330
6300
6280
6250
4650
4640
4630
4610
4600
6020
6000
5980
5960
5930
4420
4410
4400
4380
4370
5700
5680
5660
5640
5620
4190
4180
4170
4160
4140
5370
5360
5340
5320
5300
3910
3910
3890
3880
3870
4990
4970
4950
4930
4910
11
12
13
14
15
4810
4790
4770
4750
4720
6220
6190
6160
6120
6080
4580
4560
4540
4520
4500
5910
5880
5840
5810
5770
4350
4340
4320
4300
4270
5590
5560
5530
5490
5460
4130
4110
4090
4070
4050
5270
5240
5210
5180
5150
3850
3840
3820
3800
3780
4890
4860
4830
4800
4770
16
17
18
19
20
4700
4670
4640
4610
4580
6040
5990
5950
5900
5850
4470
4450
4420
4390
4360
5730
5690
5640
5590
5540
4250
4230
4200
4170
4140
5420
5380
5340
5290
5240
4030
4000
3980
3950
3930
5110
5070
5030
4990
4940
3760
3740
3710
3690
3660
4740
4700
4660
4620
4580
22
24
26
28
30
4520
4440
4370
4290
4200
5740
5620
5490
5360
5220
4300
4230
4160
4080
4000
5440
5330
5210
5080
4950
4080
4020
3950
3870
3790
5140
5040
4920
4800
4680
3870
3800
3740
3660
3590
4850
4750
4640
4520
4410
3610
3550
3480
3420
3340
4490
4400
4300
4190
4080
32
34
36
38
40
4110
4020
3930
3830
3720
5080
4930
4780
4620
4460
3910
3820
3730
3640
3540
4810
4670
4530
4380
4230
3710
3630
3540
3450
3350
4550
4410
4270
4130
3990
3510
3430
3340
3260
3170
4280
4150
4020
3890
3750
3270
3190
3110
3030
2940
3960
3840
3720
3590
3460
2600
1560
1460
1240
3380
1960
1460
1240
2420
1460
1360
1160
3150
1840
1360
1160
2210
1360
1250
1060
2890
1720
1250
1060
Properties
φ b M nx (kip-ft)
φ b M ny (kip-ft)
P ex (K xL x )2 / 10 4 (kip-ft2)
P ey (K yL y )2 / 10 4 (kip-ft2)
rmy (in.)
rmx / rmy (in./in.)
2970
1750
1650
1400
3850
2170
1650
1400
7.20
1.08
2780
1660
1550
1320
3610
2070
1550
1320
7.20
1.08
7.20
1.08
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
7.20
1.08
7.20
1.08
COMPOSITE COLUMNS—W SHAPES ENCASED IN CONCRETE
5 - 75
Fy = 36 ksi
Fy = 50 ksi
COMPOSITE COLUMNS
W Shapes
fc′ = 3.5 ksi
All reinforcing steel is Grade 60
Axial design strength in kips
b
Y
X
h
X
Y
24 in.×24 in.
4-#11 bars
Ties
#4 bars spaced 16 in. c. to c.
Designation
W 14
Wt./ft
283
Fy
Effective length KL (ft) with respect to least radius of gyration rmy
Steel
Shape
Size b × h
Reinf. bars
257
233
211
193
36
50
36
50
36
50
36
50
36
50
0
3620
4610
3400
4300
3200
4010
3010
3750
2860
3530
6
7
8
9
10
3600
3590
3580
3570
3560
4570
4560
4540
4530
4510
3380
3370
3360
3350
3340
4260
4250
4230
4220
4200
3170
3170
3160
3150
3130
3980
3960
3950
3930
3910
2990
2980
2970
2960
2950
3710
3700
3690
3670
3660
2840
2830
2820
2810
2800
3500
3490
3480
3460
3450
11
12
13
14
15
3540
3530
3510
3490
3470
4480
4460
4430
4410
4380
3320
3310
3290
3280
3260
4180
4150
4130
4100
4080
3120
3110
3090
3080
3060
3900
3870
3850
3830
3800
2940
2920
2910
2890
2880
3640
3620
3590
3570
3550
2790
2780
2760
2750
2730
3430
3410
3390
3370
3340
16
17
18
19
20
3460
3430
3410
3390
3360
4340
4310
4280
4240
4200
3240
3220
3200
3180
3150
4050
4010
3980
3950
3910
3040
3020
3000
2980
2960
3770
3740
3710
3680
3640
2860
2840
2820
2800
2780
3520
3490
3460
3430
3400
2720
2700
2680
2660
2640
3320
3290
3260
3230
3200
22
24
26
28
30
3310
3260
3200
3140
3070
4120
4030
3940
3840
3740
3100
3050
2990
2930
2870
3830
3750
3660
3570
3470
2910
2860
2810
2750
2690
3570
3490
3410
3320
3230
2740
2690
2630
2580
2520
3330
3250
3180
3090
3010
2590
2550
2500
2440
2390
3140
3060
2990
2910
2830
32
34
36
38
40
3000
2930
2850
2780
2700
3630
3520
3410
3290
3170
2810
2740
2670
2590
2520
3370
3270
3160
3050
2940
2630
2560
2490
2420
2350
3140
3040
2940
2830
2730
2460
2400
2330
2270
2200
2920
2820
2730
2630
2530
2330
2270
2210
2140
2080
2740
2660
2560
2470
2380
1650
1070
822
822
2160
1360
822
822
1510
991
757
757
1980
1260
757
757
1400
924
704
704
1830
1170
704
704
Properties
φ b M nx (kip-ft)
φ b M ny (kip-ft)
P ex (K x L x)2 / 10 4 (kip-ft2)
P ey (K y L y)2 / 10 4 (kip-ft2)
rmy (in.)
rmx / rmy (in./in.)
1970
1250
971
971
2580
1570
971
971
7.20
1.00
1810
1150
894
894
2360
1460
894
894
7.20
1.00
7.20
1.00
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
7.20
1.00
7.20
1.00
5 - 76
COMPOSITE DESIGN
Fy = 36 ksi
Fy = 50 ksi
b
Y
h
X
X
COMPOSITE COLUMNS
W Shapes
fc′ = 3.5 ksi
All reinforcing steel is Grade 60
Axial design strength in kips
Y
Size b × h
24 in.×24 in.
Reinf. bars
4-#10 bars
Ties
#3 bars spaced 16 in. c. to c.
Steel
Shape
Designation
W 14
Wt./ft
176
Effective length KL (ft) with respect to least radius of gyration rmy
Fy
159
145
132
36
50
36
50
36
50
36
50
0
2680
3290
2530
3090
2420
2920
2300
2770
6
7
8
9
10
2660
2650
2640
2630
2620
3270
3250
3240
3230
3210
2510
2510
2500
2490
2480
3060
3050
3040
3020
3010
2400
2390
2380
2370
2370
2900
2890
2880
2860
2850
2290
2280
2270
2260
2250
2740
2730
2720
2710
2690
11
12
13
14
15
2610
2600
2590
2570
2560
3200
3180
3160
3140
3120
2470
2460
2440
2430
2420
2990
2980
2960
2940
2920
2350
2340
2330
2320
2300
2830
2820
2800
2780
2760
2240
2230
2220
2210
2190
2680
2660
2650
2630
2610
16
17
18
19
20
2540
2530
2510
2490
2470
3090
3070
3040
3010
2980
2400
2380
2370
2350
2330
2890
2870
2840
2820
2790
2290
2270
2260
2240
2220
2740
2720
2690
2670
2640
2180
2160
2150
2130
2110
2590
2560
2540
2520
2490
22
24
26
28
30
2430
2380
2340
2290
2230
2920
2860
2790
2710
2630
2290
2250
2200
2150
2100
2730
2670
2600
2530
2460
2180
2140
2090
2050
2000
2580
2520
2460
2390
2320
2070
2030
1990
1940
1890
2440
2380
2320
2250
2190
32
34
36
38
40
2180
2120
2060
2000
1940
2550
2470
2390
2300
2210
2050
1990
1940
1880
1820
2380
2310
2230
2140
2060
1940
1890
1840
1780
1720
2250
2170
2100
2020
1940
1840
1790
1740
1680
1630
2120
2050
1970
1900
1820
1520
987
603
603
1060
719
563
563
1400
921
563
563
983
656
523
523
1290
835
523
523
Properties
φ b M nx (kip-ft)
φ b M ny (kip-ft)
P ex (K xL x )2 / 10 4 (kip-ft2)
P ey (K yL y )2 / 10 4 (kip-ft2)
rmy (in.)
rmx / rmy (in./in.)
1260
837
654
654
1660
1070
654
654
7.20
1.00
1150
771
603
603
7.20
1.00
7.20
1.00
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
7.20
1.00
COMPOSITE COLUMNS—W SHAPES ENCASED IN CONCRETE
5 - 77
Fy = 36 ksi
Fy = 50 ksi
b
Y
COMPOSITE COLUMNS
W Shapes
fc′ = 3.5 ksi
All reinforcing steel is Grade 60
Axial design strength in kips
h
X
X
Y
Size b × h
22 in.×22 in.
Reinf. bars
4-#10 bars
Ties
#3 bars spaced 14 in. c. to c.
Steel
Shape
Designation
W 14
Wt./ft
120
Effective length KL (ft) with respect to least radius of gyration rmy
Fy
109
99
90
36
50
36
50
36
50
36
50
0
2040
2460
1940
2320
1860
2210
1780
2100
6
7
8
9
10
2020
2010
2010
2000
1990
2430
2420
2410
2400
2380
1920
1920
1910
1900
1890
2300
2290
2280
2270
2250
1840
1840
1830
1820
1810
2180
2170
2160
2150
2140
1770
1760
1750
1750
1740
2080
2070
2060
2050
2030
11
12
13
14
15
1980
1960
1950
1940
1920
2370
2350
2330
2310
2290
1880
1870
1860
1850
1830
2240
2220
2200
2190
2170
1800
1790
1780
1760
1750
2120
2110
2090
2070
2050
1730
1710
1700
1690
1680
2020
2000
1990
1970
1950
16
17
18
19
20
1910
1890
1880
1860
1840
2270
2250
2220
2200
2170
1820
1800
1780
1770
1750
2140
2120
2100
2070
2050
1740
1720
1700
1690
1670
2030
2010
1990
1970
1940
1660
1650
1630
1610
1600
1930
1910
1890
1870
1840
22
24
26
28
30
1800
1760
1710
1670
1620
2120
2060
1990
1930
1860
1710
1670
1630
1580
1530
2000
1940
1880
1820
1750
1630
1590
1550
1510
1460
1890
1830
1780
1720
1650
1560
1520
1480
1440
1390
1790
1740
1680
1630
1570
32
34
36
38
40
1570
1520
1460
1410
1350
1790
1720
1650
1570
1500
1480
1430
1380
1330
1280
1680
1620
1550
1480
1410
1410
1360
1310
1260
1210
1590
1520
1460
1390
1320
1340
1300
1250
1200
1150
1500
1440
1380
1310
1250
1050
677
364
364
740
498
340
340
966
631
340
340
684
465
318
318
892
587
318
318
Properties
φ b M nx (kip-ft)
φ b M ny (kip-ft)
P ex (K x L x)2 / 10 4 (kip-ft2)
P ey (K y L y)2 / 10 4 (kip-ft2)
rmy (in.)
rmx / rmy (in./in.)
871
574
392
392
1140
729
392
392
6.60
1.00
801
533
364
364
6.60
1.00
6.60
1.00
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
6.60
1.00
5 - 78
COMPOSITE DESIGN
Fy = 36 ksi
Fy = 50 ksi
b
Y
h
X
X
COMPOSITE COLUMNS
W Shapes
fc′ = 3.5 ksi
All reinforcing steel is Grade 60
Axial design strength in kips
Y
Size b × h
18 in.×22 in.
Reinf. bars
4-#9 bars
Ties
#3 bars spaced 12 in. c. to c.
Steel
Shape
Designation
W 14
Wt./ft
82
Effective length KL (ft) with respect to least radius of gyration rmy
Fy
74
68
61
36
50
36
50
36
50
36
50
0
1530
1810
1460
1720
1410
1640
1350
1560
6
7
8
9
10
1500
1500
1490
1480
1470
1780
1770
1760
1740
1730
1440
1430
1420
1410
1400
1690
1680
1670
1650
1640
1390
1380
1370
1360
1350
1620
1610
1590
1580
1570
1330
1320
1310
1300
1290
1530
1520
1510
1500
1480
11
12
13
14
15
1450
1440
1430
1410
1390
1710
1690
1670
1650
1630
1390
1370
1360
1350
1330
1620
1600
1580
1560
1540
1340
1320
1310
1300
1280
1550
1530
1510
1490
1470
1280
1260
1250
1240
1220
1470
1450
1430
1410
1390
16
17
18
19
20
1380
1360
1340
1320
1300
1600
1580
1550
1530
1500
1310
1300
1280
1260
1240
1520
1490
1470
1440
1420
1260
1250
1230
1210
1190
1450
1430
1400
1380
1350
1200
1190
1170
1150
1130
1370
1350
1320
1300
1270
22
24
26
28
30
1260
1210
1160
1110
1060
1440
1380
1310
1250
1180
1200
1150
1100
1060
1010
1360
1300
1240
1170
1110
1150
1100
1060
1010
963
1300
1240
1180
1120
1060
1090
1050
1000
957
910
1220
1170
1110
1050
991
32
34
36
38
40
1010
960
908
855
804
1110
1050
978
911
846
957
906
856
805
755
1050
981
917
853
791
914
864
815
765
717
993
930
868
807
747
862
814
766
718
671
931
871
812
753
696
744
370
261
175
535
279
246
164
693
348
246
164
490
259
228
153
633
323
228
153
Properties
φ b M nx (kip-ft)
φ b M ny (kip-ft)
P ex (K xL x )2 / 10 4 (kip-ft2)
P ey (K yL y )2 / 10 4 (kip-ft2)
rmy (in.)
rmx / rmy (in./in.)
623
319
280
188
808
398
280
188
5.40
1.22
574
296
261
175
5.40
1.22
5.40
1.22
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
5.40
1.22
COMPOSITE COLUMNS—W SHAPES ENCASED IN CONCRETE
5 - 79
Fy = 36 ksi
Fy = 50 ksi
COMPOSITE COLUMNS
W Shapes
fc′ = 3.5 ksi
All reinforcing steel is Grade 60
Axial design strength in kips
b
Y
X
h
X
Y
22 in.×24 in.
4-#10 bars
Ties
#3 bars spaced 14 in. c. to c.
Designation
W 12
Wt./ft
336
Fy
Effective length KL (ft) with respect to least radius of gyration rmy
Steel
Shape
Size b × h
Reinf. bars
305
279
252
230
36
50
36
50
36
50
36
50
36
50
0
3950
5120
3680
4750
3460
4430
3230
4120
3050
3860
6
7
8
9
10
3920
3910
3890
3880
3870
5070
5060
5030
5010
4990
3650
3640
3630
3620
3600
4700
4680
4670
4640
4620
3430
3420
3410
3400
3390
4390
4370
4360
4340
4310
3210
3200
3190
3180
3160
4080
4060
4040
4020
4000
3030
3020
3010
3000
2980
3820
3800
3790
3770
3750
11
12
13
14
15
3850
3830
3810
3790
3770
4960
4930
4890
4860
4820
3590
3570
3550
3530
3510
4590
4570
4530
4500
4470
3370
3350
3340
3320
3300
4290
4260
4230
4200
4170
3150
3130
3120
3100
3080
3980
3950
3930
3900
3870
2970
2950
2940
2920
2900
3730
3700
3680
3650
3620
16
17
18
19
20
3740
3720
3690
3660
3630
4780
4740
4690
4650
4600
3490
3460
3440
3410
3380
4430
4390
4350
4300
4260
3270
3250
3230
3200
3180
4130
4100
4060
4020
3970
3060
3040
3010
2990
2960
3830
3800
3760
3720
3680
2880
2860
2840
2810
2790
3590
3550
3520
3480
3450
22
24
26
28
30
3570
3500
3430
3350
3270
4500
4390
4270
4150
4020
3320
3260
3190
3120
3040
4160
4060
3950
3840
3720
3120
3060
2990
2920
2850
3880
3780
3680
3570
3460
2910
2850
2790
2730
2660
3600
3510
3410
3310
3200
2740
2680
2620
2560
2500
3360
3280
3190
3090
2990
32
34
36
38
40
3190
3110
3020
2930
2830
3890
3750
3610
3470
3330
2970
2880
2800
2710
2630
3590
3470
3340
3210
3070
2780
2700
2620
2540
2450
3350
3230
3110
2980
2860
2590
2510
2440
2360
2280
3100
2980
2870
2750
2640
2430
2360
2290
2210
2140
2890
2780
2680
2570
2460
1770
1020
946
795
2290
1270
946
795
1610
942
868
729
2090
1180
868
729
1480
879
803
675
1930
1100
803
675
Properties
φ b M nx (kip-ft)
φ b M ny (kip-ft)
P ex (K x L x)2 / 10 4 (kip-ft2)
P ey (K y L y)2 / 10 4 (kip-ft2)
rmy (in.)
rmx / rmy (in./in.)
2110
1180
1120
938
2730
1450
1120
938
6.60
1.09
1920
1090
1020
860
2490
1350
1020
860
6.60
1.09
6.60
1.09
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
6.60
1.09
6.60
1.09
5 - 80
COMPOSITE DESIGN
Fy = 36 ksi
Fy = 50 ksi
b
Y
X
h
COMPOSITE COLUMNS
W Shapes
fc′ = 3.5 ksi
All reinforcing steel is Grade 60
Axial design strength in kips
X
Y
20 in.×22 in.
4-#10 bars
Ties
#3 bars spaced 13 in. c. to c.
Designation
W 12
Wt./ft
210
Fy
Effective length KL (ft) with respect to least radius of gyration rmy
Steel
Shape
Size b × h
Reinf. bars
190
170
152
136
36
50
36
50
36
50
36
50
36
50
0
2720
3460
2550
3210
2380
2980
2230
2760
2090
2570
6
7
8
9
10
2700
2690
2680
2670
2650
3420
3400
3380
3360
3340
2530
2520
2510
2490
2480
3170
3160
3140
3130
3110
2360
2350
2340
2330
2320
2940
2930
2910
2900
2880
2210
2200
2190
2180
2170
2730
2710
2700
2680
2670
2070
2060
2050
2040
2030
2530
2520
2510
2490
2480
11
12
13
14
15
2640
2620
2600
2580
2560
3320
3290
3270
3240
3200
2470
2450
2440
2420
2400
3080
3060
3030
3000
2970
2300
2290
2270
2260
2240
2850
2830
2810
2780
2750
2150
2140
2120
2110
2090
2650
2620
2600
2580
2550
2020
2010
1990
1970
1960
2460
2440
2410
2390
2370
16
17
18
19
20
2540
2520
2500
2470
2450
3170
3140
3100
3060
3020
2380
2360
2330
2310
2290
2940
2910
2880
2840
2800
2220
2200
2180
2150
2130
2720
2690
2660
2630
2590
2070
2050
2030
2010
1990
2520
2490
2460
2430
2400
1940
1920
1900
1880
1860
2340
2310
2280
2250
2220
22
24
26
28
30
2390
2330
2270
2210
2140
2930
2840
2750
2650
2550
2230
2180
2120
2060
1990
2720
2640
2550
2450
2360
2080
2030
1970
1910
1850
2510
2430
2350
2260
2170
1940
1890
1840
1780
1720
2330
2250
2170
2090
2010
1810
1760
1710
1660
1600
2150
2080
2010
1930
1850
32
34
36
38
40
2070
2000
1930
1850
1780
2440
2340
2230
2120
2010
1930
1860
1790
1720
1650
2260
2160
2060
1960
1850
1790
1720
1660
1590
1520
2080
1990
1890
1800
1700
1660
1600
1540
1470
1410
1920
1830
1740
1650
1560
1550
1490
1430
1370
1300
1770
1690
1600
1520
1440
1080
646
508
420
1410
813
508
420
983
594
463
383
1280
748
463
383
892
547
423
349
1160
689
423
349
Properties
φ b M nx (kip-ft)
φ b M ny (kip-ft)
P ex (K xL x )2 / 10 4 (kip-ft2)
P ey (K yL y )2 / 10 4 (kip-ft2)
rmy (in.)
rmx / rmy (in./in.)
1310
759
608
502
1690
946
608
502
6.00
1.10
1190
704
557
460
1550
883
557
460
6.00
1.10
6.00
1.10
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
6.00
1.10
6.00
1.10
COMPOSITE COLUMNS—W SHAPES ENCASED IN CONCRETE
5 - 81
Fy = 36 ksi
Fy = 50 ksi
COMPOSITE COLUMNS
W Shapes
fc′ = 3.5 ksi
All reinforcing steel is Grade 60
Axial design strength in kips
b
Y
X
h
X
Y
20 in.×20 in.
4-#9 bars
Ties
#3 bars spaced 13 in. c. to c.
Designation
W 12
Wt./ft
120
Fy
Effective length KL (ft) with respect to least radius of gyration rmy
Steel
Shape
Size b × h
Reinf. bars
106
96
87
79
36
50
36
50
36
50
36
50
36
50
0
1850
2270
1740
2110
1650
1990
1580
1880
1510
1780
6
7
8
9
10
1840
1830
1820
1810
1800
2250
2240
2220
2210
2190
1720
1710
1700
1690
1680
2080
2070
2060
2050
2030
1630
1630
1620
1610
1600
1960
1950
1940
1930
1910
1560
1550
1540
1540
1530
1850
1850
1830
1820
1810
1490
1480
1470
1470
1460
1760
1750
1740
1730
1710
11
12
13
14
15
1790
1780
1760
1750
1740
2180
2160
2140
2120
2100
1670
1660
1650
1640
1620
2020
2000
1980
1960
1940
1590
1580
1570
1550
1540
1900
1880
1860
1850
1830
1520
1500
1490
1480
1470
1800
1780
1760
1740
1730
1450
1440
1420
1410
1400
1700
1690
1670
1650
1630
16
17
18
19
20
1720
1700
1690
1670
1650
2070
2050
2020
2000
1970
1610
1590
1570
1560
1540
1920
1900
1870
1850
1820
1520
1510
1490
1470
1460
1800
1780
1760
1730
1710
1450
1440
1420
1400
1390
1710
1680
1660
1640
1610
1380
1370
1350
1340
1320
1610
1590
1570
1550
1530
22
24
26
28
30
1610
1570
1520
1470
1420
1910
1850
1780
1710
1640
1500
1460
1410
1370
1320
1760
1700
1640
1580
1510
1420
1380
1340
1290
1250
1660
1600
1540
1480
1420
1350
1310
1270
1230
1180
1560
1510
1450
1390
1330
1280
1250
1210
1160
1120
1480
1420
1370
1310
1260
32
34
36
38
40
1370
1320
1270
1210
1160
1570
1500
1430
1350
1280
1270
1220
1170
1120
1070
1450
1380
1310
1240
1170
1200
1150
1100
1050
1000
1350
1290
1220
1160
1090
1140
1090
1040
993
945
1270
1210
1150
1080
1020
1080
1030
984
937
891
1200
1140
1080
1020
957
613
398
261
261
803
505
261
261
566
372
243
243
739
471
243
243
521
347
226
226
680
438
226
226
Properties
φ b M nx (kip-ft)
φ b M ny (kip-ft)
P ex (K x L x)2 / 10 4 (kip-ft2)
P ey (K y L y)2 / 10 4 (kip-ft2)
rmy (in.)
rmx / rmy (in./in.)
746
474
311
311
6.00
1.00
977
599
311
311
669
429
282
282
6.00
1.00
878
545
282
282
6.00
1.00
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
6.00
1.00
6.00
1.00
5 - 82
COMPOSITE DESIGN
Fy = 36 ksi
Fy = 50 ksi
b
Y
h
X
COMPOSITE COLUMNS
W Shapes
fc′ = 3.5 ksi
All reinforcing steel is Grade 60
Axial design strength in kips
X
Y
Size b × h
20 in.×20 in.
Reinf. bars
4-#9 bars
Ties
#3 bars spaced 13 in. c. to c.
Steel
Shape
Designation
W 12
Wt./ft
72
Effective length KL (ft) with respect to least radius of gyration rmy
Fy
65
58
36
50
36
50
36
50
0
1450
1700
1390
1620
1330
1530
6
7
8
9
10
1430
1420
1410
1410
1400
1670
1660
1650
1640
1630
1370
1360
1360
1350
1340
1590
1580
1570
1560
1550
1310
1300
1300
1290
1280
1510
1500
1490
1480
1470
11
12
13
14
15
1390
1380
1370
1350
1340
1620
1600
1590
1570
1550
1330
1320
1310
1300
1280
1540
1520
1510
1490
1480
1270
1260
1250
1240
1220
1460
1440
1430
1410
1390
16
17
18
19
20
1330
1310
1300
1280
1260
1530
1510
1490
1470
1450
1270
1260
1240
1220
1210
1460
1440
1420
1400
1370
1210
1200
1180
1170
1150
1380
1360
1340
1320
1300
22
24
26
28
30
1230
1190
1150
1110
1070
1400
1350
1300
1240
1190
1170
1140
1100
1060
1020
1330
1280
1230
1180
1120
1120
1080
1040
1000
962
1250
1210
1160
1110
1060
32
34
36
38
40
1020
979
934
889
843
1130
1070
1020
958
901
973
930
886
842
797
1070
1010
958
902
847
920
878
835
792
749
1000
949
896
843
790
445
302
197
197
577
380
197
197
410
264
183
183
530
328
183
183
Properties
φ b M nx (kip-ft)
φ b M ny (kip-ft)
P ex (K xL x )2 / 10 4 (kip-ft2)
P ey (K yL y )2 / 10 4 (kip-ft2)
rmy (in.)
rmx / rmy (in./in.)
483
325
211
211
629
409
211
211
6.00
1.00
6.00
1.00
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
6.00
1.00
COMPOSITE COLUMNS—W SHAPES ENCASED IN CONCRETE
5 - 83
Fy = 36 ksi
Fy = 50 ksi
COMPOSITE COLUMNS
W Shapes
fc′ = 3.5 ksi
All reinforcing steel is Grade 60
Axial design strength in kips
b
Y
X
h
X
Y
18 in.×18 in.
4-#8 bars
Ties
#3 bars spaced 12 in. c. to c.
Designation
W 10
Wt./ft
112
Fy
Effective length KL (ft) with respect to least radius of gyration rmy
Steel
Shape
Size b × h
Reinf. bars
100
88
77
68
36
50
36
50
36
50
36
50
36
50
0
1620
2020
1520
1870
1420
1730
1330
1600
1250
1490
6
7
8
9
10
1600
1600
1590
1580
1570
1980
1970
1960
1950
1930
1500
1500
1490
1480
1470
1840
1830
1820
1810
1790
1400
1400
1390
1380
1370
1700
1690
1680
1670
1650
1310
1300
1300
1290
1280
1570
1560
1550
1540
1520
1230
1230
1220
1210
1200
1470
1460
1450
1430
1420
11
12
13
14
15
1560
1540
1530
1520
1500
1910
1890
1870
1850
1830
1460
1450
1430
1420
1400
1780
1760
1740
1720
1700
1360
1350
1340
1320
1310
1640
1620
1600
1580
1560
1270
1260
1240
1230
1220
1510
1490
1480
1460
1440
1190
1180
1170
1160
1150
1410
1390
1380
1360
1340
16
17
18
19
20
1480
1470
1450
1430
1410
1800
1780
1750
1720
1690
1390
1370
1360
1340
1320
1670
1650
1620
1600
1570
1290
1280
1260
1240
1230
1540
1520
1490
1470
1440
1200
1190
1170
1160
1140
1420
1400
1370
1350
1330
1130
1120
1100
1080
1070
1320
1300
1280
1260
1230
22
24
26
28
30
1370
1330
1280
1230
1180
1630
1570
1500
1430
1360
1280
1240
1190
1150
1100
1510
1450
1390
1320
1260
1190
1150
1110
1060
1020
1390
1330
1270
1210
1150
1100
1060
1020
981
939
1280
1220
1170
1110
1050
1030
996
957
917
876
1190
1130
1080
1030
973
32
34
36
38
40
1130
1080
1030
979
927
1290
1220
1150
1080
1000
1050
1000
955
905
856
1190
1120
1060
988
922
972
926
879
832
785
1090
1030
963
901
839
895
850
806
761
717
994
935
876
818
761
833
791
748
705
663
918
862
807
752
699
467
305
189
189
612
387
189
189
415
276
170
170
543
350
170
170
373
251
155
155
488
318
155
155
Properties
φ b M nx (kip-ft)
φ b M ny (kip-ft)
P ex (K x L x)2 / 10 4 (kip-ft2)
P ey (K y L y)2 / 10 4 (kip-ft2)
rmy (in.)
rmx / rmy (in./in.)
576
366
228
228
5.40
1.00
756
464
228
228
522
336
208
208
5.40
1.00
685
426
208
208
5.40
1.00
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
5.40
1.00
5.40
1.00
5 - 84
COMPOSITE DESIGN
Fy = 36 ksi
Fy = 50 ksi
b
Y
h
X
X
COMPOSITE COLUMNS
W Shapes
fc′ = 3.5 ksi
All reinforcing steel is Grade 60
Axial design strength in kips
Y
Size b × h
18 in.×18 in.
Reinf. bars
4-#8 bars
Ties
#3 bars spaced 12 in. c. to c.
Steel
Shape
Designation
W 10
Wt./ft
60
Effective length KL (ft) with respect to least radius of gyration rmy
Fy
54
49
45
36
50
36
50
36
50
36
50
0
1180
1390
1130
1320
1090
1260
1060
1220
6
7
8
9
10
1170
1160
1150
1140
1140
1370
1360
1350
1340
1330
1110
1110
1100
1090
1080
1300
1290
1280
1270
1260
1070
1070
1060
1050
1040
1240
1230
1220
1210
1200
1040
1040
1030
1020
1010
1200
1190
1180
1170
1160
11
12
13
14
15
1130
1120
1100
1090
1080
1310
1300
1280
1270
1250
1070
1060
1050
1040
1030
1240
1230
1210
1200
1180
1040
1020
1010
1000
989
1190
1170
1160
1140
1130
1000
994
983
971
958
1140
1130
1120
1100
1090
16
17
18
19
20
1060
1050
1040
1020
1000
1230
1210
1190
1170
1150
1010
1000
986
971
955
1160
1140
1120
1100
1080
976
962
947
932
917
1110
1090
1070
1050
1030
945
931
917
902
886
1070
1050
1030
1010
992
22
24
26
28
30
969
933
896
857
817
1100
1050
1000
952
900
921
886
849
811
772
1040
992
944
895
845
884
849
813
775
737
989
944
898
850
802
854
820
784
747
709
950
907
861
815
768
32
34
36
38
40
776
735
694
653
612
848
795
743
692
641
733
693
653
613
574
795
745
695
646
598
698
659
620
582
543
753
705
657
610
564
671
633
595
557
519
721
674
627
581
537
337
230
142
142
439
290
142
142
399
267
131
131
286
199
123
123
370
249
123
123
272
179
117
117
351
222
117
117
Properties
φ b M nx (kip-ft)
φ b M ny (kip-ft)
P ex (K xL x )2 / 10 4 (kip-ft2)
P ey (K yL y )2 / 10 4 (kip-ft2)
rmy (in.)
rmx / rmy (in./in.)
5.40
1.00
307
212
131
131
5.40
1.00
5.40
1.00
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
5.40
1.00
COMPOSITE COLUMNS—W SHAPES ENCASED IN CONCRETE
5 - 85
Fy = 36 ksi
Fy = 50 ksi
COMPOSITE COLUMNS
W Shapes
fc′ = 3.5 ksi
All reinforcing steel is Grade 60
Axial design strength in kips
b
Y
X
h
X
Y
16 in.×16 in.
4-#7 bars
Ties
#3 bars spaced 10 in. c. to c.
Designation
W8
Wt./ft
67
Fy
Effective length KL (ft) with respect to least radius of gyration rmy
Steel
Shape
Size b × h
Reinf. bars
58
48
40
35
36
50
36
50
36
50
36
50
36
50
0
1100
1330
1020
1230
938
1110
868
1010
828
951
6
7
8
9
10
1080
1070
1070
1060
1050
1310
1300
1290
1270
1260
1010
1000
992
984
975
1200
1190
1180
1170
1160
920
914
907
899
890
1080
1070
1060
1050
1040
851
845
839
831
822
985
977
968
957
946
811
805
799
791
783
929
921
912
902
891
11
12
13
14
15
1040
1030
1010
1000
988
1240
1230
1210
1190
1170
965
954
942
930
917
1140
1130
1110
1090
1080
881
870
859
847
834
1030
1010
997
981
963
813
803
792
780
768
933
920
905
890
874
773
763
753
741
729
879
866
852
837
822
16
17
18
19
20
973
958
943
926
909
1150
1130
1110
1080
1060
903
888
873
857
841
1060
1040
1010
992
970
821
807
793
778
762
945
927
907
887
866
755
742
728
713
698
857
839
821
802
782
717
703
690
675
661
805
788
770
752
733
22
24
26
28
30
874
836
798
758
717
1010
958
904
850
795
807
772
735
697
658
923
874
824
773
722
730
696
661
625
588
823
778
732
685
638
667
634
601
566
532
742
700
657
614
570
630
598
565
532
498
695
654
613
572
530
32
34
36
38
40
677
636
595
554
515
740
686
633
581
532
619
580
542
504
466
671
621
572
524
478
552
515
479
444
410
592
546
501
458
416
497
462
428
395
363
527
485
444
404
366
464
431
398
366
335
489
449
410
373
337
298
197
114
114
390
250
114
114
264
178
103
103
223
153
89.3
89.3
291
193
89.3
89.3
194
136
78.5
78.5
251
171
78.5
78.5
174
124
72.3
72.3
224
155
72.3
72.3
Properties
φ b M nx (kip-ft)
φ b M ny (kip-ft)
P ex (K xL x )2 / 10 4 (kip-ft2)
P ey (K yL y )2 / 10 4 (kip-ft2)
rmy (in.)
rmx / rmy (in./in.)
4.80
1.00
4.80
1.00
345
225
103
103
4.80
1.00
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
4.80
1.00
4.80
1.00
5 - 86
COMPOSITE DESIGN
Fy = 36 ksi
Fy = 50 ksi
b
Y
X
h
COMPOSITE COLUMNS
W Shapes
fc′ = 5 ksi
All reinforcing steel is Grade 60
Axial design strength in kips
X
Y
24 in.×26 in.
4-#11 bars
Ties
#4 bars spaced 16 in. c. to c.
Designation
W 14
Wt./ft
426
Fy
Effective length KL (ft) with respect to least radius of gyration rmy
Steel
Shape
Size b × h
Reinf. bars
398
370
342
311
36
50
36
50
36
50
36
50
36
50
0
5290
6770
5060
6450
4840
6130
4610
5810
4340
5430
6
7
8
9
10
5250
5240
5220
5210
5190
6720
6700
6670
6650
6620
5030
5020
5000
4990
4970
6400
6380
6360
6330
6300
4800
4790
4780
4760
4750
6080
6060
6040
6020
5990
4580
4570
4560
4540
4520
5760
5750
5730
5700
5680
4310
4300
4290
4270
4260
5380
5370
5350
5320
5300
11
12
13
14
15
5170
5150
5120
5100
5070
6580
6550
6510
6470
6430
4950
4930
4910
4880
4850
6270
6240
6200
6160
6120
4730
4710
4690
4660
4640
5960
5930
5890
5850
5810
4510
4490
4470
4440
4420
5650
5620
5580
5550
5510
4240
4220
4200
4180
4160
5270
5240
5210
5180
5140
16
17
18
19
20
5040
5010
4980
4950
4910
6380
6330
6280
6220
6170
4830
4800
4770
4730
4700
6070
6030
5980
5930
5870
4610
4580
4550
4520
4490
5770
5720
5680
5630
5570
4390
4360
4330
4300
4270
5470
5420
5380
5330
5280
4130
4100
4070
4050
4010
5100
5060
5010
4970
4920
22
24
26
28
30
4840
4760
4670
4580
4480
6050
5920
5780
5640
5490
4630
4550
4460
4380
4280
5760
5630
5500
5360
5220
4410
4340
4260
4170
4080
5460
5340
5220
5090
4950
4200
4130
4050
3970
3880
5170
5060
4940
4810
4680
3950
3880
3800
3720
3640
4820
4710
4600
4480
4350
32
34
36
38
40
4380
4280
4170
4060
3940
5330
5170
5000
4830
4660
4190
4080
3980
3870
3760
5060
4910
4750
4590
4420
3990
3890
3790
3680
3580
4800
4650
4500
4340
4180
3790
3690
3600
3500
3390
4540
4400
4250
4100
3950
3550
3460
3370
3270
3170
4220
4090
3950
3810
3660
3090
1850
1670
1420
4070
2380
1670
1420
2890
1750
1580
1340
2690
1640
1480
1260
3550
2120
1480
1260
2490
1540
1390
1180
3300
1980
1390
1180
2280
1420
1280
1090
3010
1830
1280
1090
Properties
φ b M nx (kip-ft)
φ b M ny (kip-ft)
P ex (K xL x )2 / 10 4 (kip-ft2)
P ey (K yL y )2 / 10 4 (kip-ft2)
rmy (in.)
rmx / rmy (in./in.)
7.20
1.08
3810
2250
1580
1340
7.20
1.08
7.20
1.08
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
7.20
1.08
7.20
1.08
COMPOSITE COLUMNS—W SHAPES ENCASED IN CONCRETE
5 - 87
Fy = 36 ksi
Fy = 50 ksi
COMPOSITE COLUMNS
W Shapes
fc′ = 5 ksi
All reinforcing steel is Grade 60
Axial design strength in kips
b
Y
X
h
X
Y
24 in.×24 in.
4-#11 bars
Ties
#4 bars spaced 16 in. c. to c.
Designation
W 14
Wt./ft
283
Fy
Effective length KL (ft) with respect to least radius of gyration rmy
Steel
Shape
Size b × h
Reinf. bars
257
233
211
193
36
50
36
50
36
50
36
50
36
50
0
3990
4980
3780
4680
3580
4390
3400
4130
3250
3930
6
7
8
9
10
3970
3960
3940
3930
3920
4940
4920
4910
4890
4860
3750
3740
3730
3720
3700
4640
4620
4600
4580
4560
3550
3540
3530
3520
3500
4350
4340
4320
4300
4280
3370
3360
3350
3340
3320
4100
4080
4070
4050
4030
3220
3220
3200
3190
3180
3890
3880
3860
3840
3820
11
12
13
14
15
3900
3880
3860
3840
3820
4840
4810
4780
4750
4720
3690
3670
3650
3630
3610
4540
4510
4480
4450
4420
3490
3470
3450
3440
3410
4260
4230
4210
4180
4150
3310
3290
3280
3260
3240
4010
3980
3960
3930
3900
3160
3150
3130
3110
3090
3800
3780
3750
3730
3700
16
17
18
19
20
3800
3770
3750
3720
3690
4680
4640
4600
4560
4520
3590
3560
3540
3510
3480
4390
4350
4310
4270
4230
3390
3370
3340
3320
3290
4110
4080
4040
4010
3970
3210
3190
3170
3140
3120
3870
3830
3800
3760
3720
3070
3050
3030
3000
2980
3670
3640
3600
3570
3530
22
24
26
28
30
3630
3560
3490
3420
3340
4420
4320
4220
4110
3990
3420
3360
3290
3220
3150
4140
4050
3950
3840
3730
3230
3170
3110
3040
2970
3880
3790
3690
3590
3490
3060
3000
2940
2870
2800
3640
3560
3460
3370
3270
2920
2860
2800
2730
2670
3450
3370
3280
3190
3090
32
34
36
38
40
3260
3180
3090
3000
2910
3870
3750
3620
3490
3360
3070
2990
2900
2820
2730
3610
3500
3380
3250
3130
2890
2810
2730
2650
2560
3380
3270
3150
3030
2920
2730
2650
2570
2490
2410
3160
3060
2950
2830
2720
2590
2520
2440
2360
2290
2990
2890
2780
2670
2570
2020
1300
993
993
2680
1680
993
993
1850
1200
916
916
1690
1110
845
845
2230
1430
845
845
1540
1020
780
780
2040
1320
780
780
1420
949
728
728
1880
1220
728
728
Properties
φ b M nx (kip-ft)
φ b M ny (kip-ft)
P ex (K x L x)2 / 10 4 (kip-ft2)
P ey (K y L y)2 / 10 4 (kip-ft2)
rmy (in.)
rmx / rmy (in./in.)
7.20
1.00
2450
1550
916
916
7.20
1.00
7.20
1.00
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
7.20
1.00
7.20
1.00
5 - 88
COMPOSITE DESIGN
Fy = 36 ksi
Fy = 50 ksi
b
Y
h
X
X
COMPOSITE COLUMNS
W Shapes
fc′ = 5 ksi
All reinforcing steel is Grade 60
Axial design strength in kips
Y
Size b × h
24 in.×26 in.
Reinf. bars
4-#10 bars
Ties
#3 bars spaced 16 in. c. to c.
Steel
Shape
Designation
W 14
Wt./ft
176
Effective length KL (ft) with respect to least radius of gyration rmy
Fy
159
145
132
36
50
36
50
36
50
36
50
0
3080
3690
2930
3490
2820
3330
2710
3170
6
7
8
9
10
3050
3040
3030
3020
3010
3660
3640
3630
3610
3590
2910
2900
2890
2880
2870
3450
3440
3430
3410
3390
2800
2790
2780
2770
2750
3290
3280
3270
3250
3240
2690
2680
2670
2660
2650
3140
3130
3110
3100
3080
11
12
13
14
15
2990
2980
2960
2940
2920
3570
3550
3530
3500
3480
2850
2840
2820
2800
2780
3370
3350
3330
3310
3280
2740
2730
2710
2690
2670
3220
3200
3170
3150
3120
2630
2620
2600
2580
2570
3060
3040
3020
3000
2970
16
17
18
19
20
2900
2880
2860
2840
2810
3450
3420
3380
3350
3320
2760
2740
2720
2700
2670
3250
3220
3190
3160
3130
2650
2630
2610
2590
2560
3100
3070
3040
3010
2980
2550
2530
2500
2480
2460
2950
2920
2890
2860
2830
22
24
26
28
30
2760
2700
2640
2580
2510
3240
3160
3080
2990
2900
2620
2570
2510
2450
2380
3050
2980
2900
2810
2720
2510
2460
2400
2340
2280
2910
2830
2750
2670
2590
2410
2350
2300
2240
2180
2760
2690
2620
2540
2450
32
34
36
38
40
2450
2370
2300
2230
2150
2800
2710
2610
2510
2400
2320
2250
2170
2100
2030
2630
2540
2440
2350
2250
2210
2140
2070
2000
1930
2500
2410
2320
2220
2130
2110
2040
1980
1910
1830
2370
2280
2190
2100
2010
1280
860
678
678
1700
1110
678
678
1550
1020
627
627
1080
734
587
587
1430
950
587
587
996
670
547
547
1320
861
547
547
Properties
φ b M nx (kip-ft)
φ b M ny (kip-ft)
P ex (K xL x )2 / 10 4 (kip-ft2)
P ey (K yL y )2 / 10 4 (kip-ft2)
rmy (in.)
rmx / rmy (in./in.)
7.20
1.00
1170
789
627
627
7.20
1.00
7.20
1.00
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
7.20
1.00
COMPOSITE COLUMNS—W SHAPES ENCASED IN CONCRETE
5 - 89
Fy = 36 ksi
Fy = 50 ksi
b
Y
COMPOSITE COLUMNS
W Shapes
fc′ = 5 ksi
All reinforcing steel is Grade 60
Axial design strength in kips
h
X
X
Y
Size b × h
22 in.×22 in.
Reinf. bars
4-#10 bars
Ties
#3 bars spaced 14 in. c. to c.
Steel
Shape
Designation
W 14
Wt./ft
120
Effective length KL (ft) with respect to least radius of gyration rmy
Fy
109
99
90
36
50
36
50
36
50
36
50
0
2380
2800
2290
2670
2200
2550
2130
2450
6
7
8
9
10
2350
2340
2330
2320
2310
2760
2750
2740
2720
2700
2260
2250
2240
2230
2220
2630
2620
2610
2590
2580
2180
2170
2160
2150
2140
2520
2510
2490
2480
2460
2110
2100
2090
2080
2070
2410
2400
2390
2380
2360
11
12
13
14
15
2300
2280
2270
2250
2230
2690
2670
2640
2620
2590
2200
2190
2170
2160
2140
2560
2540
2520
2490
2470
2120
2110
2090
2080
2060
2440
2420
2400
2380
2360
2050
2040
2020
2000
1990
2340
2320
2300
2280
2260
16
17
18
19
20
2210
2190
2170
2140
2120
2570
2540
2510
2480
2440
2120
2100
2080
2050
2030
2440
2410
2380
2350
2320
2040
2020
2000
1970
1950
2330
2300
2270
2250
2210
1970
1950
1920
1900
1880
2230
2200
2180
2150
2120
22
24
26
28
30
2070
2020
1960
1900
1840
2380
2300
2230
2150
2070
1980
1930
1870
1810
1750
2260
2190
2110
2030
1950
1900
1850
1790
1740
1680
2150
2080
2010
1930
1860
1830
1780
1720
1670
1610
2050
1990
1920
1840
1770
32
34
36
38
40
1770
1710
1640
1570
1500
1980
1890
1810
1720
1630
1690
1620
1560
1490
1420
1870
1790
1710
1620
1540
1610
1550
1490
1420
1350
1780
1700
1620
1530
1450
1550
1480
1420
1350
1290
1690
1610
1530
1450
1380
883
586
409
409
1160
752
409
409
1070
695
381
381
748
507
357
357
982
647
357
357
691
472
335
335
905
600
335
335
Properties
φ b M nx (kip-ft)
φ b M ny (kip-ft)
P ex (K x L x)2 / 10 4 (kip-ft2)
P ey (K y L y)2 / 10 4 (kip-ft2)
rmy (in.)
rmx / rmy (in./in.)
6.60
1.00
811
543
381
381
6.60
1.00
6.60
1.00
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
6.60
1.00
5 - 90
COMPOSITE DESIGN
Fy = 36 ksi
Fy = 50 ksi
b
Y
h
X
X
COMPOSITE COLUMNS
W Shapes
fc′ = 5 ksi
All reinforcing steel is Grade 60
Axial design strength in kips
Y
Size b × h
18 in.×22 in.
Reinf. bars
4-#9 bars
Ties
#3 bars spaced 12 in. c. to c.
Steel
Shape
Designation
W 14
Wt./ft
82
Effective length KL (ft) with respect to least radius of gyration rmy
Fy
74
68
61
36
50
36
50
36
50
36
50
0
1810
2090
1740
2000
1690
1930
1630
1850
6
7
8
9
10
1780
1770
1760
1740
1730
2050
2040
2020
2010
1990
1710
1700
1690
1680
1660
1960
1950
1930
1920
1900
1660
1650
1640
1630
1610
1890
1880
1860
1850
1830
1600
1590
1580
1570
1550
1810
1800
1780
1760
1740
11
12
13
14
15
1710
1690
1670
1650
1630
1960
1940
1920
1890
1860
1650
1630
1610
1590
1570
1880
1850
1830
1800
1770
1600
1580
1560
1540
1520
1810
1780
1760
1730
1710
1540
1520
1500
1480
1460
1720
1700
1680
1650
1630
16
17
18
19
20
1610
1590
1560
1530
1510
1830
1800
1770
1730
1700
1550
1520
1500
1470
1450
1740
1710
1680
1650
1620
1500
1470
1450
1420
1400
1680
1650
1620
1580
1550
1440
1410
1390
1360
1340
1600
1570
1540
1510
1470
22
24
26
28
30
1450
1390
1330
1270
1200
1620
1550
1470
1390
1310
1390
1330
1270
1210
1140
1540
1470
1390
1310
1240
1340
1280
1220
1160
1100
1480
1410
1330
1260
1180
1280
1230
1170
1110
1040
1410
1340
1260
1190
1110
32
34
36
38
40
1140
1070
1010
941
877
1220
1140
1060
983
906
1080
1020
952
888
826
1160
1080
999
923
849
1040
972
909
847
786
1100
1030
950
876
805
982
920
858
797
738
1040
965
892
821
752
634
328
294
197
830
416
294
197
761
384
275
184
543
285
260
174
708
360
260
174
496
264
242
162
644
332
242
162
Properties
φ b M nx (kip-ft)
φ b M ny (kip-ft)
P ex (K xL x )2 / 10 4 (kip-ft2)
P ey (K yL y )2 / 10 4 (kip-ft2)
rmy (in.)
rmx / rmy (in./in.)
5.40
1.22
582
303
275
184
5.40
1.22
5.40
1.22
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
5.40
1.22
COMPOSITE COLUMNS—W SHAPES ENCASED IN CONCRETE
5 - 91
Fy = 36 ksi
Fy = 50 ksi
COMPOSITE COLUMNS
W Shapes
fc′ = 5 ksi
All reinforcing steel is Grade 60
Axial design strength in kips
b
Y
X
h
X
Y
22 in.×24 in.
4-#10 bars
Ties
#3 bars spaced 14 in. c. to c.
Designation
W 12
Wt./ft
336
Fy
Effective length KL (ft) with respect to least radius of gyration rmy
Steel
Shape
Size b × h
Reinf. bars
305
279
252
230
36
50
36
50
36
50
36
50
36
50
0
4270
5450
4010
5080
3800
4770
3580
4460
3400
4200
6
7
8
9
10
4240
4230
4210
4200
4180
5390
5370
5350
5320
5300
3980
3970
3960
3940
3920
5030
5010
4990
4960
4940
3770
3750
3740
3730
3710
4720
4700
4680
4660
4640
3550
3540
3520
3510
3490
4410
4400
4380
4350
4330
3370
3360
3350
3330
3320
4160
4140
4120
4100
4080
11
12
13
14
15
4160
4140
4110
4090
4060
5260
5230
5190
5150
5110
3900
3880
3860
3840
3810
4910
4870
4840
4800
4760
3690
3670
3650
3630
3610
4610
4580
4540
4510
4470
3480
3460
3440
3420
3390
4300
4270
4240
4210
4170
3300
3280
3260
3240
3220
4050
4030
4000
3960
3930
16
17
18
19
20
4040
4010
3980
3940
3910
5070
5020
4970
4920
4870
3790
3760
3730
3700
3670
4720
4680
4630
4580
4530
3580
3550
3520
3490
3460
4430
4390
4340
4300
4250
3370
3340
3310
3290
3260
4140
4100
4050
4010
3960
3190
3170
3140
3110
3090
3890
3860
3820
3770
3730
22
24
26
28
30
3840
3760
3680
3590
3500
4750
4630
4500
4370
4230
3600
3520
3450
3360
3280
4420
4310
4190
4060
3930
3400
3320
3250
3170
3090
4150
4040
3920
3800
3680
3190
3120
3050
2970
2890
3870
3760
3650
3540
3420
3020
2960
2890
2810
2730
3640
3540
3430
3320
3210
32
34
36
38
40
3410
3310
3210
3110
3000
4080
3930
3780
3630
3470
3190
3090
3000
2900
2800
3790
3650
3510
3360
3220
3000
2910
2820
2720
2630
3550
3410
3280
3140
3000
2810
2720
2630
2540
2450
3300
3170
3040
2910
2780
2650
2570
2480
2400
2310
3090
2970
2850
2730
2600
2190
1260
1140
954
2890
1600
1140
954
1990
1150
1040
877
1830
1080
966
812
2410
1380
966
812
1660
990
888
746
2190
1270
888
746
1530
919
824
692
2010
1180
824
692
Properties
φ b M nx (kip-ft)
φ b M ny (kip-ft)
P ex (K x L x)2 / 10 4 (kip-ft2)
P ey (K y L y)2 / 10 4 (kip-ft2)
rmy (in.)
rmx / rmy (in./in.)
6.60
1.09
2630
1480
1040
877
6.60
1.09
6.60
1.09
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
6.60
1.09
6.60
1.09
5 - 92
COMPOSITE DESIGN
Fy = 36 ksi
Fy = 50 ksi
b
Y
X
h
COMPOSITE COLUMNS
W Shapes
fc′ = 5 ksi
All reinforcing steel is Grade 60
Axial design strength in kips
X
Y
20 in.×22 in.
4-#10 bars
Ties
#3 bars spaced 13 in. c. to c.
Designation
W 12
Wt./ft
210
Fy
Effective length KL (ft) with respect to least radius of gyration rmy
Steel
Shape
Size b × h
Reinf. bars
190
170
152
136
36
50
36
50
36
50
36
50
36
50
0
3010
3740
2840
3500
2680
3270
2530
3060
2390
2870
6
7
8
9
10
2980
2970
2950
2940
2920
3700
3680
3660
3640
3610
2810
2800
2790
2770
2760
3460
3440
3420
3400
3380
2650
2640
2630
2610
2600
3230
3210
3200
3180
3150
2500
2490
2480
2470
2450
3020
3000
2990
2970
2950
2370
2360
2340
2330
2320
2830
2810
2800
2780
2760
11
12
13
14
15
2910
2890
2870
2840
2820
3590
3560
3520
3490
3450
2740
2720
2700
2680
2660
3350
3320
3290
3260
3230
2580
2560
2540
2520
2500
3130
3100
3070
3040
3010
2430
2420
2400
2380
2360
2920
2900
2870
2840
2810
2300
2280
2270
2250
2220
2740
2710
2690
2660
2630
16
17
18
19
20
2790
2770
2740
2710
2680
3420
3380
3330
3290
3240
2630
2610
2580
2550
2520
3190
3150
3110
3070
3030
2480
2450
2430
2400
2370
2970
2940
2900
2860
2820
2330
2310
2280
2260
2230
2780
2740
2700
2670
2630
2200
2180
2150
2130
2100
2600
2560
2530
2490
2450
22
24
26
28
30
2620
2550
2480
2400
2320
3150
3040
2940
2830
2710
2460
2390
2320
2250
2180
2940
2840
2740
2630
2520
2310
2250
2180
2110
2030
2730
2640
2540
2440
2340
2170
2110
2040
1970
1900
2540
2460
2360
2270
2170
2040
1980
1920
1850
1780
2370
2290
2200
2110
2020
32
34
36
38
40
2240
2160
2070
1980
1900
2590
2470
2350
2230
2110
2100
2020
1930
1850
1770
2410
2300
2180
2070
1950
1960
1880
1800
1720
1640
2230
2130
2020
1910
1800
1830
1760
1680
1600
1530
2070
1970
1870
1760
1660
1710
1640
1570
1490
1420
1920
1830
1730
1630
1530
1350
796
622
514
1770
1020
622
514
1230
734
572
472
1110
671
523
432
1460
860
523
432
1010
614
478
395
1320
787
478
395
910
563
438
362
1190
721
438
362
Properties
φ b M nx (kip-ft)
φ b M ny (kip-ft)
P ex (K xL x )2 / 10 4 (kip-ft2)
P ey (K yL y )2 / 10 4 (kip-ft2)
rmy (in.)
rmx / rmy (in./in.)
6.00
1.10
1610
941
572
472
6.00
1.10
6.00
1.10
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
6.00
1.10
6.00
1.10
COMPOSITE COLUMNS—W SHAPES ENCASED IN CONCRETE
5 - 93
Fy = 36 ksi
Fy = 50 ksi
COMPOSITE COLUMNS
W Shapes
fc′ = 5 ksi
All reinforcing steel is Grade 60
Axial design strength in kips
b
Y
X
h
X
Y
20 in.×20 in.
4-#9 bars
Ties
#3 bars spaced 13 in. c. to c.
Designation
W 12
Wt./ft
120
Fy
Effective length KL (ft) with respect to least radius of gyration rmy
Steel
Shape
Size b × h
Reinf. bars
106
96
87
79
36
50
36
50
36
50
36
50
36
50
0
2130
2550
2020
2390
1930
2270
1860
2160
1790
2070
6
7
8
9
10
2110
2100
2090
2080
2060
2520
2500
2490
2470
2450
1990
1980
1970
1960
1950
2350
2340
2330
2310
2290
1910
1900
1890
1880
1870
2230
2220
2210
2190
2180
1830
1830
1820
1810
1790
2130
2120
2110
2090
2070
1770
1760
1750
1740
1730
2040
2020
2010
2000
1980
11
12
13
14
15
2050
2030
2020
2000
1980
2430
2410
2390
2360
2340
1930
1920
1900
1890
1870
2270
2250
2230
2210
2180
1850
1840
1820
1800
1790
2160
2140
2120
2090
2070
1780
1760
1750
1730
1710
2060
2040
2020
1990
1970
1710
1700
1680
1670
1650
1960
1940
1920
1900
1880
16
17
18
19
20
1960
1940
1920
1890
1870
2310
2280
2250
2220
2180
1850
1830
1810
1780
1760
2150
2130
2100
2070
2030
1770
1750
1730
1700
1680
2040
2010
1990
1960
1920
1700
1680
1650
1630
1610
1940
1920
1890
1860
1830
1630
1610
1590
1570
1540
1850
1830
1800
1770
1740
22
24
26
28
30
1820
1770
1710
1650
1590
2110
2040
1960
1880
1800
1710
1660
1600
1550
1490
1970
1890
1820
1740
1660
1630
1580
1530
1470
1410
1860
1790
1720
1640
1570
1560
1510
1460
1400
1340
1770
1700
1630
1560
1480
1500
1450
1390
1340
1280
1680
1620
1550
1480
1410
32
34
36
38
40
1530
1460
1400
1330
1260
1710
1620
1540
1450
1370
1430
1360
1300
1240
1170
1580
1500
1420
1340
1260
1350
1290
1230
1170
1100
1490
1410
1330
1250
1180
1290
1230
1170
1110
1040
1410
1330
1260
1180
1110
1220
1170
1110
1050
989
1330
1260
1190
1110
1040
760
489
322
322
1000
628
322
322
680
440
294
294
622
407
273
273
820
522
273
273
573
380
255
255
754
486
255
255
528
353
238
238
693
450
238
238
Properties
φ b M nx (kip-ft)
φ b M ny (kip-ft)
P ex (K x L x)2 / 10 4 (kip-ft2)
P ey (K y L y)2 / 10 4 (kip-ft2)
rmy (in.)
rmx / rmy (in./in.)
6.00
1.00
6.00
1.00
899
566
294
294
6.00
1.00
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
6.00
1.00
6.00
1.00
5 - 94
COMPOSITE DESIGN
Fy = 36 ksi
Fy = 50 ksi
b
Y
h
X
COMPOSITE COLUMNS
W Shapes
fc′ = 5 ksi
All reinforcing steel is Grade 60
Axial design strength in kips
X
Y
Size b × h
20 in.×20 in.
Reinf. bars
4-#9 bars
Ties
#3 bars spaced 13 in. c. to c.
Steel
Shape
Designation
W 12
Wt./ft
72
Effective length KL (ft) with respect to least radius of gyration rmy
Fy
65
58
36
50
36
50
36
50
0
1730
1980
1680
1900
1620
1820
6
7
8
9
10
1710
1700
1690
1680
1670
1950
1940
1930
1910
1900
1650
1640
1630
1620
1610
1870
1860
1850
1840
1820
1590
1590
1580
1560
1550
1790
1780
1770
1750
1740
11
12
13
14
15
1650
1640
1620
1610
1590
1880
1860
1840
1820
1800
1600
1580
1570
1550
1530
1800
1780
1760
1740
1720
1540
1520
1510
1490
1480
1720
1700
1680
1660
1640
16
17
18
19
20
1570
1550
1530
1510
1490
1770
1750
1720
1690
1660
1520
1500
1480
1450
1430
1700
1670
1650
1620
1590
1460
1440
1420
1400
1370
1620
1590
1570
1540
1510
22
24
26
28
30
1440
1390
1340
1280
1230
1600
1540
1480
1410
1340
1380
1340
1280
1230
1180
1530
1470
1410
1340
1270
1330
1280
1230
1170
1120
1460
1400
1330
1270
1200
32
34
36
38
40
1170
1110
1060
997
939
1270
1200
1120
1050
984
1120
1060
1000
948
891
1200
1130
1060
996
929
1060
1010
951
895
840
1140
1070
1000
935
871
449
307
209
209
586
388
209
209
414
268
195
195
537
335
195
195
Properties
φ b M nx (kip-ft)
φ b M ny (kip-ft)
P ex (K xL x )2 / 10 4 (kip-ft2)
P ey (K yL y )2 / 10 4 (kip-ft2)
rmy (in.)
rmx / rmy (in./in.)
489
330
223
223
640
419
223
223
6.00
1.00
6.00
1.00
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
6.00
1.00
COMPOSITE COLUMNS—W SHAPES ENCASED IN CONCRETE
5 - 95
Fy = 36 ksi
Fy = 50 ksi
COMPOSITE COLUMNS
W Shapes
fc′ = 5 ksi
All reinforcing steel is Grade 60
Axial design strength in kips
b
Y
X
h
X
Y
18 in.×18 in.
4-#8 bars
Ties
#3 bars spaced 12 in. c. to c.
Designation
W 10
Wt./ft
112
Fy
Effective length KL (ft) with respect to least radius of gyration rmy
Steel
Shape
Size b × h
Reinf. bars
100
88
77
68
36
50
36
50
36
50
36
50
36
50
0
1840
2240
1750
2100
1650
1960
1560
1820
1480
1720
6
7
8
9
10
1820
1810
1800
1790
1770
2200
2190
2170
2150
2130
1720
1710
1700
1690
1680
2060
2050
2030
2020
2000
1620
1610
1600
1590
1580
1920
1910
1900
1880
1860
1530
1520
1510
1500
1490
1790
1780
1770
1750
1730
1460
1450
1440
1430
1420
1690
1680
1660
1650
1630
11
12
13
14
15
1760
1740
1730
1710
1690
2110
2090
2070
2040
2010
1660
1650
1630
1610
1600
1980
1960
1930
1910
1880
1570
1550
1540
1520
1500
1840
1820
1800
1780
1750
1480
1460
1450
1430
1410
1720
1700
1670
1650
1630
1400
1390
1370
1360
1340
1620
1600
1580
1550
1530
16
17
18
19
20
1670
1650
1630
1600
1580
1980
1950
1920
1890
1850
1580
1560
1530
1510
1490
1850
1830
1790
1760
1730
1480
1460
1440
1420
1400
1720
1700
1670
1640
1610
1390
1370
1350
1330
1310
1600
1580
1550
1520
1490
1320
1300
1280
1260
1240
1510
1480
1450
1430
1400
22
24
26
28
30
1530
1480
1420
1360
1300
1780
1710
1630
1550
1470
1440
1390
1330
1280
1220
1660
1590
1520
1440
1360
1350
1300
1250
1190
1140
1540
1470
1400
1330
1260
1260
1210
1160
1110
1050
1430
1360
1300
1230
1160
1190
1140
1090
1040
990
1340
1270
1210
1140
1080
32
34
36
38
40
1240
1180
1120
1060
995
1380
1300
1220
1140
1060
1160
1100
1040
982
923
1280
1210
1130
1050
975
1080
1020
963
906
850
1180
1110
1030
962
891
1000
944
889
834
779
1090
1020
946
878
811
936
883
829
776
723
1010
942
876
811
748
589
379
236
236
780
488
236
236
532
346
216
216
475
313
196
196
627
402
196
196
421
282
178
178
555
361
178
178
378
256
163
163
497
327
163
163
Properties
φ b M nx (kip-ft)
φ b M ny (kip-ft)
P ex (K x L x)2 / 10 4 (kip-ft2)
P ey (K y L y)2 / 10 4 (kip-ft2)
rmy (in.)
rmx / rmy (in./in.)
5.40
1.00
5.40
1.00
704
445
216
216
5.40
1.00
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
5.40
1.00
5.40
1.00
5 - 96
COMPOSITE DESIGN
Fy = 36 ksi
Fy = 50 ksi
b
Y
h
X
X
COMPOSITE COLUMNS
W Shapes
fc′ = 5 ksi
All reinforcing steel is Grade 60
Axial design strength in kips
Y
Size b × h
18 in.×18 in.
Reinf. bars
4-#8 bars
Ties
#3 bars spaced 12 in. c. to c.
Steel
Shape
Designation
W 10
Wt./ft
60
Effective length KL (ft) with respect to least radius of gyration rmy
Fy
54
49
45
36
50
36
50
36
50
36
50
0
1420
1620
1360
1550
1330
1500
1290
1450
6
7
8
9
10
1390
1380
1370
1360
1350
1590
1580
1570
1560
1540
1340
1330
1320
1310
1300
1520
1510
1500
1490
1470
1300
1290
1280
1270
1260
1470
1460
1440
1430
1420
1270
1260
1250
1240
1230
1420
1410
1400
1390
1370
11
12
13
14
15
1340
1320
1310
1290
1270
1520
1500
1480
1460
1440
1290
1270
1260
1240
1220
1450
1430
1410
1390
1370
1250
1230
1220
1200
1190
1400
1380
1360
1340
1320
1220
1200
1190
1170
1150
1360
1340
1320
1300
1280
16
17
18
19
20
1260
1240
1220
1200
1170
1420
1390
1370
1340
1310
1210
1190
1170
1150
1120
1350
1320
1300
1270
1250
1170
1150
1130
1110
1090
1300
1270
1250
1220
1200
1140
1120
1100
1080
1060
1250
1230
1210
1180
1160
22
24
26
28
30
1130
1080
1030
981
929
1250
1190
1130
1070
1000
1080
1030
984
934
883
1190
1130
1070
1010
947
1040
995
947
897
847
1140
1080
1020
963
903
1010
965
917
868
818
1100
1040
987
927
868
32
34
36
38
40
877
825
772
721
670
938
874
811
749
689
832
781
729
679
630
884
822
761
702
644
796
746
695
646
598
842
782
723
665
609
768
718
668
620
572
808
749
692
636
581
341
234
149
149
446
297
149
149
405
272
139
139
288
201
131
131
375
254
131
131
275
182
125
125
356
227
125
125
Properties
φ b M nx (kip-ft)
φ b M ny (kip-ft)
P ex (K xL x )2 / 10 4 (kip-ft2)
P ey (K yL y )2 / 10 4 (kip-ft2)
rmy (in.)
rmx / rmy (in./in.)
5.40
1.00
310
215
139
139
5.40
1.00
5.40
1.00
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
5.40
1.00
COMPOSITE COLUMNS—W SHAPES ENCASED IN CONCRETE
5 - 97
Fy = 36 ksi
Fy = 50 ksi
b
Y
COMPOSITE COLUMNS
W Shapes
fc′ = 5 ksi
All reinforcing steel is Grade 60
Axial design strength in kips
X
h
X
Y
16 in.×16 in.
4-#7 bars
Ties
#3 bars spaced 10 in. c. to c.
Designation
W 18
Wt./ft
67
Fy
Effective length KL (ft) with respect to least radius of gyration rmy
Steel
Shape
Size b × h
Reinf. bars
58
48
40
35
36
50
36
50
36
50
36
50
36
50
0
1280
1510
1200
1410
1120
1290
1050
1190
1010
1140
6
7
8
9
10
1250
1250
1240
1220
1210
1480
1470
1450
1440
1420
1180
1170
1160
1150
1140
1380
1360
1350
1340
1320
1100
1090
1080
1070
1060
1260
1250
1230
1220
1200
1030
1020
1010
1000
990
1160
1150
1140
1130
1110
991
982
973
962
951
1110
1100
1090
1070
1060
11
12
13
14
15
1200
1180
1170
1150
1130
1400
1380
1360
1340
1310
1130
1110
1100
1080
1060
1300
1280
1260
1240
1220
1040
1030
1010
999
982
1190
1170
1150
1130
1110
977
963
948
932
916
1100
1080
1060
1040
1020
938
924
909
893
877
1040
1020
1010
986
965
16
17
18
19
20
1120
1100
1080
1060
1030
1290
1260
1230
1210
1180
1050
1030
1010
987
966
1190
1170
1140
1120
1090
964
946
927
907
886
1080
1060
1040
1010
984
898
880
861
841
821
996
973
949
925
900
859
841
822
803
783
944
922
898
875
850
22
24
26
28
30
989
942
894
844
794
1120
1050
990
926
861
922
876
829
781
733
1030
971
910
849
787
844
799
754
707
661
929
873
816
759
702
779
736
692
647
602
848
795
741
686
632
741
698
655
610
566
800
748
696
643
591
32
34
36
38
40
743
693
644
595
548
796
733
672
612
555
684
636
589
542
498
727
667
610
554
501
614
569
524
480
438
646
591
537
486
438
557
513
470
429
389
579
528
478
431
389
522
480
438
398
360
540
491
444
398
360
303
202
119
119
400
259
119
119
268
182
107
107
226
155
94.1
94.1
296
198
94.1
94.1
196
138
83.4
83.4
255
175
83.4
83.4
175
125
77.2
77.2
227
157
77.2
77.2
Properties
φ b M nx (kip-ft)
φ b M ny (kip-ft)
P ex (K xL x )2 / 10 4 (kip-ft2)
P ey (K yL y )2 / 10 4 (kip-ft2)
rmy (in.)
rmx / rmy (in./in.)
4.80
1.00
353
233
107
107
4.80
1.00
4.80
1.00
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
4.80
1.00
4.80
1.00
5 - 98
COMPOSITE DESIGN
Fy = 36 ksi
Fy = 50 ksi
b
Y
X
h
COMPOSITE COLUMNS
W Shapes
fc′ = 8 ksi
All reinforcing steel is Grade 60
Axial design strength in kips
X
Y
24 in.×26 in.
4-#11 bars
Ties
#4 bars spaced 16 in. c. to c.
Designation
W 14
Wt./ft
426
Fy
Effective length KL (ft) with respect to least radius of gyration rmy
Steel
Shape
Size b × h
Reinf. bars
398
370
342
311
36
50
36
50
36
50
36
50
36
50
0
6040
7530
5830
7220
5620
6910
5400
6610
5150
6240
6
7
8
9
10
6000
5980
5960
5940
5920
7460
7430
7410
7370
7340
5780
5770
5750
5730
5710
7150
7130
7100
7070
7040
5570
5560
5540
5520
5500
6850
6820
6800
6770
6730
5360
5350
5330
5310
5290
6540
6520
6490
6460
6430
5110
5090
5070
5060
5030
6180
6150
6130
6100
6070
11
12
13
14
15
5890
5870
5840
5800
5770
7300
7260
7210
7160
7110
5680
5660
5630
5590
5560
7000
6960
6910
6860
6810
5470
5450
5420
5390
5350
6700
6660
6610
6570
6520
5260
5240
5210
5180
5140
6400
6360
6310
6270
6220
5010
4980
4960
4930
4890
6030
6000
5960
5910
5860
16
17
18
19
20
5730
5690
5650
5610
5570
7050
6990
6930
6870
6800
5530
5490
5450
5410
5360
6760
6700
6640
6580
6510
5320
5280
5240
5200
5160
6460
6410
6350
6290
6230
5110
5070
5030
4990
4950
6170
6120
6060
6000
5940
4860
4820
4790
4750
4700
5820
5760
5710
5650
5590
22
24
26
28
30
5470
5370
5260
5150
5030
6660
6500
6340
6170
5990
5270
5170
5060
4950
4830
6370
6220
6070
5900
5730
5070
4970
4860
4750
4640
6090
5940
5790
5630
5460
4860
4770
4660
4550
4440
5810
5670
5520
5360
5200
4620
4520
4420
4310
4200
5460
5330
5190
5040
4880
32
34
36
38
40
4900
4770
4640
4500
4360
5800
5610
5420
5220
5010
4710
4580
4450
4320
4180
5550
5360
5170
4980
4780
4520
4390
4260
4130
4000
5290
5110
4920
4740
4550
4320
4200
4070
3940
3810
5030
4850
4680
4500
4310
4090
3970
3840
3720
3590
4720
4550
4380
4210
4030
3190
1940
1710
1460
4270
2550
1710
1460
2970
1830
1620
1380
2770
1710
1530
1300
3700
2260
1530
1300
2560
1600
1430
1220
3430
2100
1430
1220
2330
1470
1320
1130
3120
1930
1320
1130
Properties
φ b M nx (kip-ft)
φ b M ny (kip-ft)
P ex (K xL x )2 / 10 4 (kip-ft2)
P ey (K yL y )2 / 10 4 (kip-ft2)
rmy (in.)
rmx / rmy (in./in.)
7.20
1.08
3980
2410
1620
1380
7.20
1.08
7.20
1.08
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
7.20
1.08
7.20
1.08
COMPOSITE COLUMNS—W SHAPES ENCASED IN CONCRETE
5 - 99
Fy = 36 ksi
Fy = 50 ksi
COMPOSITE COLUMNS
W Shapes
fc′ = 8 ksi
All reinforcing steel is Grade 60
Axial design strength in kips
b
Y
X
h
X
Y
24 in.×24 in.
4-#11 bars
Ties
#4 bars spaced 16 in. c. to c.
Designation
W 14
Wt./ft
283
Fy
Effective length KL (ft) with respect to least radius of gyration rmy
Steel
Shape
Size b × h
Reinf. bars
257
233
211
193
36
50
36
50
36
50
36
50
36
50
0
4740
5730
4530
5430
4350
5160
4170
4910
4040
4710
6
7
8
9
10
4700
4690
4670
4650
4630
5670
5650
5630
5600
5570
4500
4480
4470
4450
4430
5380
5360
5340
5310
5280
4310
4290
4280
4260
4240
5110
5090
5070
5040
5010
4140
4120
4110
4090
4070
4860
4840
4820
4790
4770
4000
3980
3970
3950
3930
4660
4640
4620
4600
4570
11
12
13
14
15
4610
4590
4560
4530
4500
5540
5510
5470
5430
5390
4410
4380
4360
4330
4300
5250
5220
5180
5140
5100
4220
4200
4170
4140
4110
4980
4950
4920
4880
4840
4050
4020
4000
3970
3940
4740
4710
4670
4630
4590
3910
3890
3860
3830
3810
4540
4510
4480
4440
4400
16
17
18
19
20
4470
4440
4400
4370
4330
5340
5290
5240
5190
5130
4270
4240
4200
4170
4130
5060
5010
4960
4910
4860
4080
4050
4020
3980
3940
4790
4750
4700
4650
4600
3910
3880
3850
3810
3770
4550
4510
4460
4410
4360
3780
3740
3710
3670
3640
4360
4320
4270
4220
4170
22
24
26
28
30
4250
4160
4060
3970
3860
5020
4890
4760
4620
4480
4050
3960
3870
3770
3670
4740
4620
4490
4360
4220
3860
3780
3690
3590
3490
4490
4370
4250
4120
3980
3690
3610
3520
3430
3330
4250
4140
4020
3890
3760
3560
3470
3380
3290
3190
4070
3960
3840
3710
3590
32
34
36
38
40
3760
3640
3530
3410
3300
4330
4170
4010
3850
3690
3570
3460
3340
3230
3110
4070
3930
3770
3620
3460
3390
3280
3170
3060
2950
3840
3700
3550
3400
3250
3220
3120
3010
2900
2790
3630
3490
3340
3200
3060
3090
2990
2880
2770
2660
3450
3320
3180
3040
2900
2070
1350
1030
1030
2770
1770
1030
1030
1890
1240
952
952
1720
1140
882
882
2300
1490
882
882
1570
1050
817
817
2090
1370
817
817
1440
972
765
765
1920
1270
765
765
Properties
φ b M nx (kip-ft)
φ b M ny (kip-ft)
P ex (K x L x)2 / 10 4 (kip-ft2)
P ey (K y L y)2 / 10 4 (kip-ft2)
rmy (in.)
rmx / rmy (in./in.)
7.20
1.00
2530
1620
952
952
7.20
1.00
7.20
1.00
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
7.20
1.00
7.20
1.00
5 - 100
COMPOSITE DESIGN
Fy = 36 ksi
Fy = 50 ksi
b
Y
h
X
X
COMPOSITE COLUMNS
W Shapes
fc′ = 8 ksi
All reinforcing steel is Grade 60
Axial design strength in kips
Y
Size b × h
24 in.×24 in.
Reinf. bars
4-#10 bars
Ties
#3 bars spaced 16 in. c. to c.
Steel
Shape
Designation
W 14
Wt./ft
176
Effective length KL (ft) with respect to least radius of gyration rmy
Fy
159
145
132
36
50
36
50
36
50
36
50
0
3870
4490
3730
4290
3630
4140
3520
3990
6
7
8
9
10
3830
3820
3800
3790
3770
4440
4420
4400
4370
4350
3700
3680
3670
3650
3630
4240
4220
4200
4180
4160
3590
3580
3560
3540
3530
4090
4070
4050
4030
4000
3490
3470
3460
3440
3420
3940
3920
3900
3880
3850
11
12
13
14
15
3750
3720
3700
3670
3640
4320
4290
4260
4220
4180
3610
3590
3560
3540
3510
4130
4100
4070
4030
3990
3500
3480
3460
3430
3400
3980
3950
3910
3880
3840
3400
3380
3350
3330
3300
3830
3800
3770
3730
3700
16
17
18
19
20
3610
3580
3550
3510
3480
4140
4100
4060
4010
3960
3480
3450
3410
3380
3340
3950
3910
3870
3820
3780
3370
3340
3310
3270
3240
3800
3760
3720
3680
3630
3270
3240
3200
3170
3130
3660
3620
3580
3530
3490
22
24
26
28
30
3400
3320
3230
3140
3040
3860
3750
3640
3520
3400
3270
3180
3100
3010
2910
3680
3570
3460
3340
3220
3160
3080
2990
2900
2800
3530
3430
3320
3200
3080
3050
2970
2880
2790
2700
3390
3290
3180
3070
2950
32
34
36
38
40
2950
2840
2740
2630
2530
3270
3140
3010
2870
2740
2810
2710
2610
2500
2400
3100
2970
2840
2710
2580
2710
2610
2500
2400
2300
2960
2840
2710
2580
2450
2600
2500
2400
2300
2190
2830
2710
2580
2460
2330
1300
879
716
716
1740
1150
716
716
1580
1050
665
665
1090
748
625
625
1450
975
625
625
1010
681
587
587
1340
884
587
587
Properties
φ b M nx (kip-ft)
φ b M ny (kip-ft)
P ex (K xL x )2 / 10 4 (kip-ft2)
P ey (K yL y )2 / 10 4 (kip-ft2)
rmy (in.)
rmx / rmy (in./in.)
7.20
1.00
1190
805
665
665
7.20
1.00
7.20
1.00
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
7.20
1.00
COMPOSITE COLUMNS—W SHAPES ENCASED IN CONCRETE
5 - 101
Fy = 36 ksi
Fy = 50 ksi
b
Y
COMPOSITE COLUMNS
W Shapes
fc′ = 8 ksi
All reinforcing steel is Grade 60
Axial design strength in kips
h
X
X
Y
Size b × h
22 in.×22 in.
Reinf. bars
4-#10 bars
Ties
#3 bars spaced 14 in. c. to c.
Steel
Shape
Designation
W 14
Wt./ft
120
Effective length KL (ft) with respect to least radius of gyration rmy
Fy
109
99
90
36
50
36
50
36
50
36
50
0
3060
3480
2970
3350
2890
3240
2820
3140
6
7
8
9
10
3020
3010
2990
2970
2950
3430
3410
3390
3370
3340
2930
2920
2900
2880
2860
3300
3280
3260
3240
3220
2850
2840
2820
2810
2790
3190
3170
3150
3130
3110
2780
2770
2750
2740
2720
3090
3070
3050
3030
3010
11
12
13
14
15
2930
2910
2880
2860
2830
3320
3290
3250
3220
3180
2840
2820
2790
2770
2740
3190
3160
3130
3090
3060
2770
2740
2720
2690
2660
3080
3050
3020
2990
2950
2700
2670
2650
2620
2590
2980
2950
2920
2890
2850
16
17
18
19
20
2800
2770
2730
2700
2660
3140
3100
3060
3020
2970
2710
2680
2640
2610
2570
3020
2980
2940
2900
2850
2630
2600
2560
2530
2490
2910
2870
2830
2790
2740
2560
2530
2490
2460
2420
2810
2770
2730
2690
2650
22
24
26
28
30
2590
2510
2420
2330
2240
2870
2770
2670
2560
2440
2500
2420
2330
2240
2150
2750
2650
2550
2440
2330
2420
2340
2250
2160
2070
2650
2550
2450
2340
2230
2340
2260
2180
2090
2000
2550
2450
2350
2250
2140
32
34
36
38
40
2150
2050
1950
1860
1760
2330
2210
2090
1970
1850
2060
1960
1870
1770
1670
2220
2100
1980
1870
1760
1980
1880
1790
1690
1600
2120
2000
1890
1780
1670
1910
1810
1720
1620
1530
2030
1920
1810
1700
1590
894
597
436
436
1190
773
436
436
1080
712
409
409
755
514
385
385
996
661
385
385
697
478
363
363
917
612
363
363
Properties
φ b M nx (kip-ft)
φ b M ny (kip-ft)
P ex (K x L x)2 / 10 4 (kip-ft2)
P ey (K y L y)2 / 10 4 (kip-ft2)
rmy (in.)
rmx / rmy (in./in.)
6.60
1.00
819
551
409
409
6.60
1.00
6.60
1.00
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
6.60
1.00
5 - 102
COMPOSITE DESIGN
Fy = 36 ksi
Fy = 50 ksi
b
Y
h
X
X
COMPOSITE COLUMNS
W Shapes
fc′ = 8 ksi
All reinforcing steel is Grade 60
Axial design strength in kips
Y
Size b × h
18 in.×22 in.
Reinf. bars
4-#9 bars
Ties
#3 bars spaced 12 in. c. to c.
Steel
Shape
Designation
W 14
Wt./ft
82
Effective length KL (ft) with respect to least radius of gyration rmy
Fy
74
68
61
36
50
36
50
36
50
36
50
0
2370
2660
2310
2570
2260
2500
2200
2420
6
7
8
9
10
2320
2310
2290
2270
2240
2600
2580
2550
2530
2500
2260
2240
2230
2200
2180
2510
2490
2470
2440
2410
2210
2200
2180
2160
2130
2440
2420
2400
2370
2340
2160
2140
2120
2100
2070
2360
2340
2320
2290
2260
11
12
13
14
15
2220
2190
2160
2130
2090
2470
2430
2390
2350
2310
2150
2130
2100
2060
2030
2380
2340
2310
2270
2230
2110
2080
2050
2010
1980
2310
2280
2240
2200
2160
2050
2020
1990
1960
1920
2230
2200
2160
2120
2080
16
17
18
19
20
2060
2020
1980
1940
1900
2270
2220
2180
2130
2080
1990
1960
1920
1880
1840
2180
2140
2090
2040
1990
1940
1910
1870
1830
1790
2120
2070
2020
1980
1930
1890
1850
1810
1770
1730
2040
1990
1950
1900
1850
22
24
26
28
30
1820
1730
1630
1540
1440
1970
1860
1750
1640
1520
1750
1660
1570
1480
1380
1890
1780
1670
1560
1450
1700
1610
1520
1430
1330
1820
1720
1610
1500
1390
1640
1550
1460
1360
1270
1750
1640
1540
1430
1320
32
34
36
38
40
1350
1250
1160
1070
983
1410
1300
1190
1090
989
1290
1190
1100
1010
926
1340
1230
1130
1030
929
1240
1140
1050
966
882
1280
1180
1080
977
882
1180
1090
998
911
827
1220
1110
1010
917
827
644
336
317
212
849
431
317
212
776
396
298
199
549
290
283
189
720
370
283
189
501
268
265
178
654
341
265
178
Properties
φ b M nx (kip-ft)
φ b M ny (kip-ft)
P ex (K xL x )2 / 10 4 (kip-ft2)
P ey (K yL y )2 / 10 4 (kip-ft2)
rmy (in.)
rmx / rmy (in./in.)
5.40
1.22
590
309
298
199
5.40
1.22
5.40
1.22
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
5.40
1.22
COMPOSITE COLUMNS—W SHAPES ENCASED IN CONCRETE
5 - 103
Fy = 36 ksi
Fy = 50 ksi
COMPOSITE COLUMNS
W Shapes
fc′ = 8 ksi
All reinforcing steel is Grade 60
Axial design strength in kips
b
Y
X
h
X
Y
22 in.×24 in.
4-#10 bars
Ties
#3 bars spaced 14 in. c. to c.
Designation
W 12
Wt./ft
336
Fy
Effective length KL (ft) with respect to least radius of gyration rmy
Steel
Shape
Size b × h
Reinf. bars
305
279
252
230
36
50
36
50
36
50
36
50
36
50
0
4920
6100
4680
5740
4470
5450
4260
5150
4100
4900
6
7
8
9
10
4880
4860
4840
4820
4800
6030
6000
5980
5950
5910
4630
4620
4600
4580
4560
5680
5650
5630
5600
5570
4430
4410
4400
4380
4360
5380
5360
5340
5310
5270
4220
4210
4190
4170
4150
5090
5060
5040
5010
4980
4050
4040
4020
4000
3980
4840
4820
4800
4770
4740
11
12
13
14
15
4770
4750
4720
4690
4650
5870
5830
5790
5740
5690
4530
4510
4480
4450
4420
5530
5490
5450
5400
5350
4330
4310
4280
4250
4220
5240
5200
5160
5120
5070
4130
4100
4070
4040
4010
4950
4910
4870
4830
4780
3960
3930
3910
3880
3840
4710
4670
4630
4590
4540
16
17
18
19
20
4620
4580
4540
4500
4460
5640
5580
5520
5460
5390
4380
4340
4310
4260
4220
5300
5250
5190
5130
5070
4180
4140
4110
4070
4030
5020
4970
4910
4850
4790
3980
3940
3910
3870
3830
4730
4680
4630
4570
4510
3810
3780
3740
3700
3660
4500
4450
4400
4340
4290
22
24
26
28
30
4360
4270
4160
4050
3940
5260
5110
4960
4790
4630
4130
4040
3940
3830
3720
4930
4790
4650
4490
4330
3940
3840
3740
3640
3530
4670
4530
4390
4240
4080
3740
3650
3550
3450
3340
4390
4260
4120
3980
3830
3580
3480
3390
3290
3180
4170
4040
3910
3770
3620
32
34
36
38
40
3820
3700
3570
3440
3310
4450
4280
4100
3920
3730
3600
3480
3360
3240
3110
4170
4000
3830
3650
3480
3420
3300
3180
3060
2940
3920
3760
3600
3430
3260
3230
3120
3000
2880
2760
3680
3520
3370
3210
3050
3070
2960
2850
2730
2620
3480
3330
3170
3020
2870
2270
1320
1170
980
3030
1730
1170
980
2050
1210
1080
904
1880
1130
999
839
2510
1470
999
839
1710
1030
921
774
2280
1350
921
774
1570
954
857
720
2090
1250
857
720
Properties
φ b M nx (kip-ft)
φ b M ny (kip-ft)
P ex (K x L x)2 / 10 4 (kip-ft2)
P ey (K y L y)2 / 10 4 (kip-ft2)
rmy (in.)
rmx / rmy (in./in.)
6.60
1.09
2750
1580
1080
904
6.60
1.09
6.60
1.09
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
6.60
1.09
6.60
1.09
5 - 104
COMPOSITE DESIGN
Fy = 36 ksi
Fy = 50 ksi
b
Y
X
h
COMPOSITE COLUMNS
W Shapes
fc′ = 8 ksi
All reinforcing steel is Grade 60
Axial design strength in kips
X
Y
20 in.×22 in.
4-#10 bars
Ties
#3 bars spaced 13 in. c. to c.
Designation
W 12
Wt./ft
210
Fy
Effective length KL (ft) with respect to least radius of gyration rmy
Steel
Shape
Size b × h
Reinf. bars
190
170
152
136
36
50
36
50
36
50
36
50
36
50
0
3580
4320
3420
4080
3270
3860
3130
3660
3000
3470
6
7
8
9
10
3540
3520
3500
3480
3460
4250
4230
4210
4180
4150
3380
3360
3350
3330
3310
4020
4000
3980
3950
3920
3230
3210
3190
3170
3150
3800
3780
3760
3730
3700
3080
3070
3050
3030
3010
3600
3580
3560
3530
3500
2960
2940
2930
2910
2880
3420
3400
3380
3350
3320
11
12
13
14
15
3440
3410
3380
3350
3320
4110
4070
4030
3990
3940
3280
3260
3230
3200
3170
3890
3850
3810
3770
3730
3130
3100
3080
3050
3010
3670
3630
3600
3560
3510
2990
2960
2940
2910
2880
3470
3440
3400
3360
3320
2860
2840
2810
2780
2750
3290
3260
3220
3180
3140
16
17
18
19
20
3290
3250
3220
3180
3140
3900
3850
3790
3740
3680
3130
3100
3060
3020
2980
3680
3630
3580
3520
3470
2980
2950
2910
2870
2830
3470
3420
3370
3320
3260
2840
2810
2770
2730
2690
3270
3230
3180
3130
3070
2720
2680
2650
2610
2570
3100
3050
3000
2950
2900
22
24
26
28
30
3050
2960
2860
2760
2660
3560
3430
3300
3160
3010
2900
2810
2710
2610
2510
3350
3230
3100
2960
2830
2750
2660
2570
2470
2370
3150
3030
2900
2770
2640
2610
2520
2430
2340
2240
2960
2850
2730
2600
2470
2490
2400
2310
2210
2120
2800
2680
2570
2440
2320
32
34
36
38
40
2550
2440
2330
2220
2110
2870
2720
2570
2430
2280
2410
2300
2190
2080
1980
2690
2540
2400
2260
2120
2270
2160
2060
1950
1850
2510
2370
2240
2100
1970
2140
2030
1930
1830
1730
2340
2210
2080
1950
1830
2020
1920
1820
1710
1610
2190
2070
1940
1820
1690
1380
828
645
533
1840
1080
645
533
1250
760
595
492
1130
692
546
452
1510
901
546
452
1020
631
502
415
1360
821
502
415
926
578
462
382
1230
749
462
382
Properties
φ b M nx (kip-ft)
φ b M ny (kip-ft)
P ex (K xL x )2 / 10 4 (kip-ft2)
P ey (K yL y )2 / 10 4 (kip-ft2)
rmy (in.)
rmx / rmy (in./in.)
6.00
1.10
1670
991
595
492
6.00
1.10
6.00
1.10
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
6.00
1.10
6.00
1.10
COMPOSITE COLUMNS—W SHAPES ENCASED IN CONCRETE
5 - 105
Fy = 36 ksi
Fy = 50 ksi
COMPOSITE COLUMNS
W Shapes
fc′ = 8 ksi
All reinforcing steel is Grade 60
Axial design strength in kips
b
Y
X
h
X
Y
20 in.×20 in.
4-#9 bars
Ties
#3 bars spaced 13 in. c. to c.
Designation
W 12
Wt./ft
120
Fy
Effective length KL (ft) with respect to least radius of gyration rmy
Steel
Shape
Size b × h
Reinf. bars
106
96
87
79
36
50
36
50
36
50
36
50
36
50
0
2680
3100
2570
2950
2490
2830
2430
2730
2360
2640
6
7
8
9
10
2650
2630
2620
2600
2580
3050
3040
3010
2990
2970
2540
2520
2510
2490
2470
2900
2880
2860
2840
2810
2460
2440
2430
2410
2390
2780
2760
2740
2720
2700
2390
2370
2360
2340
2320
2680
2670
2650
2620
2600
2320
2310
2290
2280
2260
2590
2570
2550
2530
2510
11
12
13
14
15
2560
2540
2510
2490
2460
2940
2910
2880
2840
2800
2450
2430
2400
2380
2350
2780
2750
2720
2690
2650
2370
2350
2320
2300
2270
2670
2640
2610
2580
2540
2300
2280
2250
2230
2200
2570
2540
2510
2480
2440
2240
2210
2190
2160
2130
2480
2450
2420
2390
2350
16
17
18
19
20
2430
2400
2370
2330
2300
2770
2730
2680
2640
2590
2320
2290
2260
2220
2190
2610
2570
2530
2490
2450
2240
2210
2180
2140
2110
2500
2460
2420
2380
2340
2170
2140
2110
2070
2040
2410
2370
2330
2290
2240
2100
2070
2040
2010
1970
2320
2280
2240
2200
2150
22
24
26
28
30
2220
2140
2060
1980
1890
2500
2400
2290
2180
2070
2110
2040
1960
1870
1790
2350
2250
2150
2050
1940
2030
1960
1880
1790
1710
2240
2150
2050
1940
1840
1960
1890
1800
1720
1640
2150
2060
1960
1860
1750
1900
1820
1740
1660
1570
2060
1970
1870
1770
1670
32
34
36
38
40
1800
1710
1620
1530
1440
1960
1850
1730
1620
1510
1700
1610
1520
1430
1340
1830
1720
1610
1500
1400
1620
1530
1440
1360
1270
1730
1630
1520
1420
1320
1550
1460
1380
1290
1200
1650
1550
1440
1340
1240
1480
1400
1310
1230
1140
1570
1470
1370
1270
1170
773
501
340
340
1030
653
340
340
690
450
312
312
629
415
291
291
835
537
291
291
580
387
273
273
767
499
273
273
534
359
257
257
704
461
257
257
Properties
φ b M nx (kip-ft)
φ b M ny (kip-ft)
P ex (K x L x)2 / 10 4 (kip-ft2)
P ey (K y L y)2 / 10 4 (kip-ft2)
rmy (in.)
rmx / rmy (in./in.)
6.00
1.00
6.00
1.00
917
584
312
312
6.00
1.00
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
6.00
1.00
6.00
1.00
5 - 106
COMPOSITE DESIGN
Fy = 36 ksi
Fy = 50 ksi
b
Y
h
X
COMPOSITE COLUMNS
W Shapes
fc′ = 8 ksi
All reinforcing steel is Grade 60
Axial design strength in kips
X
Y
Size b × h
20 in.×20 in.
Reinf. bars
4-#9 bars
Ties
#3 bars spaced 13 in. c. to c.
Steel
Shape
Designation
W 12
Wt./ft
72
Effective length KL (ft) with respect to least radius of gyration rmy
Fy
65
58
36
50
36
50
36
50
0
2310
2560
2250
2480
2200
2400
6
7
8
9
10
2270
2250
2240
2220
2200
2510
2490
2470
2450
2430
2210
2200
2180
2170
2150
2430
2420
2400
2380
2350
2160
2140
2130
2110
2090
2350
2340
2320
2290
2270
11
12
13
14
15
2180
2160
2130
2100
2080
2400
2370
2340
2310
2270
2120
2100
2080
2050
2020
2320
2300
2270
2230
2200
2070
2040
2020
1990
1960
2240
2220
2190
2150
2120
16
17
18
19
20
2050
2010
1980
1950
1910
2240
2200
2160
2120
2080
1990
1960
1920
1890
1860
2160
2130
2090
2040
2000
1930
1900
1870
1830
1790
2080
2050
2010
1970
1920
22
24
26
28
30
1840
1760
1680
1600
1510
1990
1900
1800
1700
1600
1780
1700
1620
1540
1450
1910
1820
1730
1630
1530
1720
1640
1560
1480
1390
1840
1750
1650
1560
1460
32
34
36
38
40
1430
1340
1260
1170
1090
1500
1400
1300
1210
1110
1370
1280
1200
1120
1040
1430
1340
1240
1150
1050
1310
1220
1140
1060
978
1360
1270
1170
1080
991
453
311
229
229
593
396
229
229
417
271
214
214
544
342
214
214
Properties
φ b M nx (kip-ft)
φ b M ny (kip-ft)
P ex (K xL x )2 / 10 4 (kip-ft2)
P ey (K yL y )2 / 10 4 (kip-ft2)
rmy (in.)
rmx / rmy (in./in.)
494
335
242
242
649
428
242
242
6.00
1.00
6.00
1.00
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
6.00
1.00
COMPOSITE COLUMNS—W SHAPES ENCASED IN CONCRETE
5 - 107
Fy = 36 ksi
Fy = 50 ksi
COMPOSITE COLUMNS
W Shapes
fc′ = 8 ksi
All reinforcing steel is Grade 60
Axial design strength in kips
b
Y
X
h
X
Y
18 in.×18 in.
4-#8 bars
Ties
#3 bars spaced 12 in. c. to c.
Designation
W 10
Wt./ft
112
Fy
Effective length KL (ft) with respect to least radius of gyration rmy
Steel
Shape
Size b × h
Reinf. bars
100
88
77
68
36
50
36
50
36
50
36
50
36
50
0
2280
2680
2190
2540
2100
2410
2010
2280
1940
2180
6
7
8
9
10
2250
2230
2220
2200
2180
2630
2610
2590
2560
2540
2160
2140
2130
2110
2090
2490
2470
2450
2430
2410
2060
2050
2030
2020
2000
2360
2340
2320
2300
2270
1970
1960
1950
1930
1910
2230
2220
2200
2170
2150
1910
1890
1880
1860
1840
2130
2120
2100
2080
2050
11
12
13
14
15
2160
2140
2120
2090
2060
2510
2480
2450
2410
2370
2070
2050
2020
2000
1970
2380
2350
2320
2280
2250
1980
1950
1930
1900
1880
2250
2220
2190
2150
2120
1890
1870
1840
1820
1790
2120
2090
2060
2030
2000
1820
1800
1770
1750
1720
2020
2000
1970
1930
1900
16
17
18
19
20
2030
2000
1970
1940
1900
2340
2290
2250
2210
2160
1940
1910
1880
1850
1810
2210
2170
2130
2080
2040
1850
1820
1790
1750
1720
2080
2040
2000
1960
1920
1760
1730
1700
1670
1630
1960
1920
1880
1840
1800
1690
1660
1630
1600
1560
1860
1830
1790
1750
1710
22
24
26
28
30
1830
1760
1680
1600
1520
2070
1970
1870
1760
1660
1740
1670
1590
1510
1430
1950
1850
1750
1650
1550
1650
1580
1500
1420
1340
1830
1730
1640
1540
1440
1560
1490
1410
1340
1260
1710
1620
1530
1430
1340
1490
1420
1340
1270
1190
1620
1530
1440
1350
1260
32
34
36
38
40
1430
1350
1270
1180
1100
1550
1450
1340
1240
1140
1350
1270
1190
1110
1030
1450
1350
1250
1150
1050
1260
1180
1100
1020
948
1340
1250
1150
1060
968
1180
1100
1020
946
872
1240
1150
1060
970
885
1110
1030
957
883
811
1160
1070
985
900
817
599
389
248
248
800
509
248
248
541
354
228
228
482
320
208
208
640
416
208
208
426
287
190
190
565
371
190
190
382
260
175
175
505
335
175
175
Properties
φ b M nx (kip-ft)
φ b M ny (kip-ft)
P ex (K x L x)2 / 10 4 (kip-ft2)
P ey (K y L y)2 / 10 4 (kip-ft2)
rmy (in.)
rmx / rmy (in./in.)
5.40
1.00
5.40
1.00
721
462
228
228
5.40
1.00
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
5.40
1.00
5.40
1.00
5 - 108
COMPOSITE DESIGN
Fy = 36 ksi
Fy = 50 ksi
b
Y
h
X
X
COMPOSITE COLUMNS
W Shapes
fc′ = 8 ksi
All reinforcing steel is Grade 60
Axial design strength in kips
Y
Size b × h
18 in.×18 in.
Reinf. bars
4-#8 bars
Ties
#3 bars spaced 12 in. c. to c.
Steel
Shape
Designation
W 10
Wt./ft
60
Effective length KL (ft) with respect to least radius of gyration rmy
Fy
54
49
45
36
50
36
50
36
50
36
50
0
1880
2090
1830
2020
1790
1970
1770
1920
6
7
8
9
10
1840
1830
1810
1790
1770
2040
2020
2010
1980
1960
1790
1780
1760
1750
1730
1970
1960
1940
1910
1890
1760
1740
1730
1710
1690
1920
1900
1880
1860
1840
1730
1710
1700
1680
1660
1880
1860
1840
1820
1800
11
12
13
14
15
1750
1730
1710
1680
1650
1930
1910
1880
1840
1810
1700
1680
1660
1630
1600
1870
1840
1810
1780
1740
1670
1640
1620
1590
1560
1810
1780
1750
1720
1690
1640
1610
1590
1560
1530
1770
1740
1710
1680
1650
16
17
18
19
20
1620
1590
1560
1530
1490
1770
1740
1700
1660
1620
1570
1540
1510
1480
1440
1710
1670
1630
1590
1550
1530
1500
1470
1440
1400
1650
1620
1580
1540
1500
1500
1470
1440
1410
1370
1610
1580
1540
1500
1460
22
24
26
28
30
1420
1350
1280
1200
1120
1540
1450
1360
1270
1180
1370
1300
1230
1150
1070
1470
1380
1300
1210
1120
1330
1260
1180
1110
1030
1420
1330
1250
1160
1070
1300
1230
1150
1080
1000
1380
1290
1210
1120
1040
32
34
36
38
40
1050
970
895
822
752
1090
1000
916
834
754
996
921
847
776
707
1030
946
863
784
707
956
882
809
739
671
987
903
822
743
671
925
851
779
709
642
951
868
788
711
642
344
237
162
162
452
304
162
162
410
277
152
152
290
204
144
144
379
258
144
144
277
184
138
138
361
231
138
138
Properties
φ b M nx (kip-ft)
φ b M ny (kip-ft)
P ex (K xL x )2 / 10 4 (kip-ft2)
P ey (K yL y )2 / 10 4 (kip-ft2)
rmy (in.)
rmx / rmy (in./in.)
5.40
1.00
313
217
152
152
5.40
1.00
5.40
1.00
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
5.40
1.00
COMPOSITE COLUMNS—W SHAPES ENCASED IN CONCRETE
5 - 109
Fy = 36 ksi
Fy = 50 ksi
b
Y
COMPOSITE COLUMNS
W Shapes
fc′ = 8 ksi
All reinforcing steel is Grade 60
Axial design strength in kips
X
h
X
Y
16 in.×16 in.
4-#7 bars
Ties
#3 bars spaced 10 in. c. to c.
Designation
W8
Wt./ft
67
Fy
Effective length KL (ft) with respect to least radius of gyration rmy
Steel
Shape
Size b × h
Reinf. bars
58
48
40
35
36
50
36
50
36
50
36
50
36
50
0
1640
1870
1570
1770
1490
1650
1420
1560
1390
1510
6
7
8
9
10
1600
1590
1570
1550
1530
1820
1800
1790
1760
1740
1530
1520
1500
1480
1470
1720
1710
1690
1660
1640
1450
1440
1420
1400
1380
1610
1590
1570
1550
1530
1380
1370
1360
1340
1320
1520
1500
1480
1460
1440
1350
1330
1320
1300
1280
1460
1450
1430
1410
1380
11
12
13
14
15
1510
1490
1470
1440
1420
1710
1680
1650
1620
1590
1440
1420
1400
1370
1350
1620
1590
1560
1530
1490
1360
1340
1320
1290
1260
1500
1470
1450
1410
1380
1300
1270
1250
1220
1200
1410
1380
1360
1320
1290
1260
1240
1210
1180
1160
1360
1330
1300
1270
1240
16
17
18
19
20
1390
1360
1330
1300
1270
1550
1520
1480
1440
1400
1320
1290
1260
1230
1200
1460
1420
1380
1350
1310
1240
1210
1180
1150
1120
1350
1310
1280
1240
1200
1170
1140
1110
1080
1050
1260
1220
1190
1150
1120
1130
1100
1070
1040
1010
1210
1170
1140
1100
1060
22
24
26
28
30
1200
1130
1060
993
922
1310
1230
1140
1060
972
1130
1060
996
926
857
1230
1140
1060
977
895
1050
983
915
846
778
1120
1040
963
884
805
981
914
847
779
713
1040
961
883
807
731
940
873
806
739
673
989
912
836
761
687
32
34
36
38
40
852
784
717
653
590
888
806
729
654
590
789
722
657
595
537
815
737
663
595
537
712
648
586
526
475
729
656
586
526
475
648
586
525
471
425
659
589
525
471
425
609
548
490
439
397
617
549
490
439
397
307
206
127
127
408
268
127
127
272
186
115
115
228
157
102
102
300
202
102
102
197
140
91.3
91.3
258
178
91.3
91.3
177
127
85.1
85.1
230
160
85.1
85.1
Properties
φ b M nx (kip-ft)
φ b M ny (kip-ft)
P ex (K xL x )2 / 10 4 (kip-ft2)
P ey (K yL y )2 / 10 4 (kip-ft2)
rmy (in.)
rmx / rmy (in./in.)
4.80
1.00
359
240
115
115
4.80
1.00
4.80
1.00
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
4.80
1.00
4.80
1.00
5 - 110
COMPOSITE DESIGN
COMPOSITE COLUMNS—CONCRETE-FILLED STEEL PIPE AND
STRUCTURAL TUBING
General Notes
Concentric load design strengths in the tables that follow are tabulated for the effective
lengths KL in feet, shown at the left of each table. They are applicable to axially loaded
members with respect to their minor axis in accordance with Section I2.2 of the LRFD
Specification. The tables apply to normal-weight concrete.
For discussion of the effective length, range of Kl / r strength about the major axis,
combined axial and bending strength, and for sample problems, see Composite Columns,
General Notes.
The properties listed at the bottom of each table are for use in checking strength about
the strong axis and in design for combined axial compression and bending.
The heavy horizontal lines within the tables indicate Kl / r = 200. No values are listed
beyond these lines.
Steel Pipe Filled with Concrete
Design strengths for filled pipe are tabulated for Fy = 36 ksi and fc′ equal to 3.5 and 5 ksi.
Steel pipe is manufactured to Fy = 36 ksi under ASTM A501 and to Fy = 35 ksi under
ASTM A53 Types E or S, Grade B. Both are designed for 36 ksi yield stress.
Structural Tubing Filled with Concrete
Design strengths for square and rectangular structural tubing filled with concrete are
tabulated for Fy = 46 ksi and fc′ equal to 3.5 and 5 ksi. Structural tubing is manufactured
to Fy = 46 ksi under ASTM A500, Grade B.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
COMPOSITE COLUMNS—CONCRETE-FILLED STEEL PIPE AND STRUCTURAL TUBING
5 - 111
Fy = 36 ksi
Nominal Diameter (in.)
12
10
8
Wall Thickness (in.)
0.500
0.375
0.500
0.365
0.875
0.500
0.322
Wt./ft
65.42
49.56
54.74
40.48
72.42
43.39
28.55
Fy
Effective length KL (ft) with respect to radius of gyration
Steel Pipe
COMPOSITE COLUMNS
Steel pipe
fc′ = 3.5 ksi
Axial design strength in kips
36 ksi
0
862
733
681
564
746
507
384
6
7
8
9
10
847
842
836
829
822
720
716
711
705
698
665
660
653
646
638
550
545
540
534
527
718
708
697
684
671
489
482
475
467
458
370
365
359
353
346
11
12
13
14
15
814
805
796
786
775
691
684
675
667
658
629
620
610
599
587
520
512
503
494
485
656
640
623
606
588
448
438
427
415
403
338
330
322
313
304
16
17
18
19
20
764
752
739
727
713
648
638
627
616
604
576
563
550
537
523
475
464
454
442
431
569
549
529
509
488
390
377
364
351
337
294
284
274
264
254
22
24
26
28
30
686
656
626
595
563
580
555
529
502
475
495
466
436
406
376
407
383
358
333
308
447
405
365
325
288
309
281
254
228
202
232
211
191
170
151
32
34
36
38
40
531
499
467
436
405
448
420
393
366
339
347
318
290
263
237
284
260
236
214
193
253
224
200
179
162
178
158
141
126
114
133
118
105
94
85
3.63
142
51.0
3.67
106
41.4
2.76
143
34.8
2.88
89.2
24.5
2.94
60.0
18.3
Properties
4.33
203
89.8
rm (in.)
φb M n (kip-ft)
P e (KL )2 / 10 4 (kip-ft2)
4.38
155
75.1
Note: Heavy line indicates Kl / r of 200.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
5 - 112
COMPOSITE DESIGN
Fy = 36 ksi
Nominal Diameter (in.)
6
5
4
Wall Thickness (in.)
0.864
0.432
0.280
0.750
0.375
0.258
0.674
0.337
0.237
Wt./ft
53.16
28.57
18.97
38.55
20.78
14.62
27.54
14.98
10.79
Fy
Effective length KL (ft) with respect to radius of gyration
Steel Pipe
COMPOSITE COLUMNS
Steel pipe
fc′ = 3.5 ksi
Axial design strength in kips
36 ksi
0
525
323
244
379
233
182
268
164
129
6
7
8
9
10
491
479
466
451
436
303
297
289
281
271
229
224
218
212
205
344
332
319
305
290
213
206
199
191
182
167
161
156
149
142
230
218
205
191
176
143
136
129
121
112
113
107
102
95
89
11
12
13
14
15
419
401
383
364
345
262
252
241
230
219
197
190
182
173
165
274
258
241
225
208
173
163
154
144
134
135
128
120
112
105
162
147
132
118
105
104
95
87
78
70
82
75
69
62
56
16
17
18
19
20
326
306
287
268
249
207
196
184
173
161
156
147
139
130
121
191
175
160
145
131
124
114
105
96
87
97
89
82
75
68
92
82
73
65
59
62
55
49
44
40
49
44
39
35
32
22
24
26
28
30
213
180
153
132
115
139
119
101
87
76
105
89
76
66
57
108
91
77
67
72
60
51
44
39
56
47
40
35
30
49
33
28
26
22
32
34
36
101
90
67
59
53
50
45
40
1.72
47.3
6.99
1.84
27.3
4.66
1.88
19.6
3.65
1.37
26.9
3.15
1.48
15.8
2.15
1.51
11.6
1.70
Properties
2.06
78.0
13.9
rm (in.)
φb M n (kip-ft)
P e (KL )2 / 10 4 (kip-ft2)
2.19
44.8
9.13
2.25
30.5
6.92
Note: Heavy line indicates Kl / r of 200.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
COMPOSITE COLUMNS—CONCRETE-FILLED STEEL PIPE AND STRUCTURAL TUBING
5 - 113
Fy = 36 ksi
Nominal Diameter (in.)
12
10
8
Wall Thickness (in.)
0.500
0.375
0.500
0.365
0.875
0.500
0.322
Wt./ft
65.42
49.56
54.74
40.48
72.42
43.39
28.55
Fy
Effective length KL (ft) with respect to radius of gyration
Steel Pipe
COMPOSITE COLUMNS
Steel pipe
fc′ = 5 ksi
Axial design strength in kips
36 ksi
0
979
855
762
649
786
557
438
6
7
8
9
10
961
955
947
939
930
839
833
827
819
811
743
736
728
720
710
632
626
619
611
603
755
745
732
719
704
535
528
519
510
499
420
414
407
399
391
11
12
13
14
15
920
909
897
885
872
802
792
781
770
758
699
688
676
663
649
594
584
573
562
550
688
671
653
633
614
488
476
463
449
435
382
372
361
351
339
16
17
18
19
20
858
844
828
813
797
746
733
719
705
691
635
620
605
589
573
537
524
511
497
483
593
572
550
528
506
421
406
391
375
360
327
315
303
291
278
22
24
26
28
30
763
727
691
653
615
660
628
596
562
528
540
505
471
436
401
454
424
394
364
334
461
417
374
332
292
328
297
266
236
208
253
228
203
180
158
32
34
36
38
40
577
539
502
465
429
495
461
428
395
363
367
334
302
272
245
305
276
249
224
202
256
227
203
182
164
183
162
145
130
117
139
123
109
98.2
88.7
3.63
142
52.7
3.67
106
43.2
2.76
143
35.3
2.88
89.2
25.2
2.94
60.0
19.1
Properties
4.33
203
93.3
rm (in.)
φb M n (kip-ft)
P e (KL )2 / 10 4 (kip-ft2)
4.38
155
78.9
Note: Heavy line indicates Kl / r of 200.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
5 - 114
COMPOSITE DESIGN
Fy = 36 ksi
Nominal Diameter (in.)
6
5
4
Wall Thickness (in.)
0.864
0.432
0.280
0.750
0.375
0.258
0.674
0.337
0.237
Wt./ft
53.16
28.57
18.97
38.55
20.78
14.62
27.54
14.98
10.79
Fy
Effective length KL (ft) with respect to radius of gyration
Steel Pipe
COMPOSITE COLUMNS
Steel pipe
fc′ = 5 ksi
Axial design strength in kips
36 ksi
0
545
351
275
393
253
204
276
176
143
6
7
8
9
10
509
496
482
467
450
329
321
312
302
292
257
251
244
236
228
356
343
330
315
299
230
222
214
204
195
185
179
172
164
156
237
224
210
196
180
153
145
137
128
118
124
117
110
103
96
11
12
13
14
15
432
414
394
374
354
281
269
257
245
232
219
209
200
190
180
282
265
247
230
212
184
173
162
151
140
148
139
130
121
112
165
149
134
120
106
109
99
90
81
72
88
80
72
65
58
16
17
18
19
20
334
313
293
273
253
219
206
193
180
168
169
159
149
139
129
195
178
162
146
132
129
119
108
98
89
103
94
86
78
70
93
82
74
66
60
64
56
50
45
41
51
45
40
36
33
22
24
26
28
30
216
181
155
133
116
144
121
104
89
78
110
93
79
68
59
109
92
78
67
73
62
53
45
40
58
49
42
36
49
34
28
27
32
34
36
102
90
68
61
54
52
46
1.84
27.3
4.77
1.88
19.6
3.78
1.48
15.8
2.19
1.51
11.6
1.75
23
31
41
Properties
2.06
78.0
14.0
rm (in.)
φb M n (kip-ft)
P e (KL )2 / 10 4 (kip-ft2)
2.19
44.8
9.35
2.25
30.5
7.18
1.72
47.3
7.06
Note: Heavy line indicates Kl / r of 200.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1.37
26.9
3.18
COMPOSITE COLUMNS—CONCRETE-FILLED STEEL PIPE AND STRUCTURAL TUBING
5 - 115
Fy = 46 ksi
Steel Tube
COMPOSITE COLUMNS
Square structural tubing
fc′ = 3.5 ksi
Axial design strength in kips
Nominal Size
16×
×16
Thickness (in.)
1⁄
2
1⁄
2
14×
×14
3⁄
8
5⁄
8
1⁄
2
12×
×12
3⁄
8
5⁄
16
Wt./ft
103.30
89.68
68.31
93.34
76.07
58.10
48.86
Effective length KL (ft) with respect to radius of gyration
Fy
46 ksi
0
1760
1460
1230
1360
1180
988
890
6
7
8
9
10
1740
1730
1730
1720
1710
1440
1430
1430
1420
1410
1210
1210
1200
1190
1190
1340
1330
1320
1310
1300
1160
1150
1150
1140
1130
971
965
958
950
942
875
869
863
856
848
11
12
13
14
15
1700
1690
1680
1670
1650
1400
1390
1370
1360
1350
1180
1170
1160
1150
1140
1280
1270
1250
1240
1220
1110
1100
1090
1070
1060
932
922
911
899
887
839
830
820
810
798
16
17
18
19
20
1640
1620
1610
1590
1580
1330
1320
1300
1280
1270
1120
1110
1100
1080
1070
1200
1180
1160
1140
1120
1040
1030
1010
992
973
874
860
845
830
815
786
774
761
747
734
22
24
26
28
30
1540
1500
1460
1420
1380
1230
1190
1150
1110
1060
1040
1000
968
931
894
1080
1030
979
928
877
934
894
852
808
764
783
749
713
677
640
704
674
642
609
576
32
34
36
38
40
1330
1280
1240
1190
1140
1020
969
922
875
828
855
816
777
737
697
826
774
723
672
623
720
675
631
587
544
603
566
529
493
457
543
509
476
443
411
4.60
400
137
4.66
329
120
4.72
255
101
4.75
216
90.7
Properties
rm (in.)
φb M n (kip-ft)
P e (KL )2 / 10 4 (kip-ft2)
6.29
604
319
5.48
455
203
5.54
352
171
Note: Heavy line indicates Kl / r of 200.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
5 - 116
COMPOSITE DESIGN
Fy = 46 ksi
10×
×10
Nominal Size
8×
×8
Thickness (in.)
5⁄
8
1⁄
2
3⁄
8
5⁄
16
1⁄
4
5⁄
8
1⁄
2
3⁄
Wt./ft
76.33
62.46
47.90
40.35
32.63
59.32
48.85
Fy
Effective length KL (ft) with respect to radius of gyration
Steel Tube
COMPOSITE COLUMNS
Square structural tubing
fc′ = 3.5 ksi
Axial design strength in kips
16
1⁄
4
37.69
31.84
25.82
8
5⁄
46 ksi
0
1070
924
767
687
603
795
686
567
503
439
6
7
8
9
10
1040
1030
1020
1010
995
900
892
883
872
861
748
742
734
725
716
670
664
657
650
641
588
583
577
570
562
762
751
738
724
708
659
650
639
627
614
545
537
528
519
508
484
477
470
461
452
422
416
409
402
394
11
12
13
14
15
980
964
947
929
909
848
835
820
805
788
705
694
682
669
656
632
622
611
600
588
554
545
536
526
515
691
673
654
634
613
600
584
568
551
534
496
484
471
457
443
441
431
419
407
394
385
376
365
355
344
16
17
18
19
20
889
869
847
825
802
771
754
735
716
697
642
627
612
597
581
575
562
549
535
520
504
493
481
469
456
591
569
546
524
501
516
497
478
459
439
428
413
398
382
366
381
368
354
340
326
333
321
309
297
285
22
24
26
28
30
755
707
658
609
560
657
616
574
532
490
548
514
479
445
410
491
460
430
398
368
430
403
376
349
322
454
408
364
321
280
400
361
323
286
251
334
302
271
241
212
298
269
242
215
189
260
235
211
188
165
32
34
36
38
40
513
466
422
379
342
449
409
371
333
301
376
343
311
280
253
337
308
279
251
227
295
269
244
220
198
246
218
195
175
158
220
195
174
156
141
186
165
147
132
119
166
147
131
118
106
145
129
115
103
93
3.12
92.1
22.8
3.15
75.6
20.0
Properties
rm (in.)
φb M n (kip-ft)
P e (KL )2 / 10 4 (kip-ft2)
3.78
3.84
3.90
3.93
3.96
2.96
3.03
3.09
268
223
174
148
120
163
137
108
73.4
64.6
54.3
48.7
42.6
33.9
30.3
25.5
Note: Heavy line indicates Kl / r of 200.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
COMPOSITE COLUMNS—CONCRETE-FILLED STEEL PIPE AND STRUCTURAL TUBING
5 - 117
Fy = 46 ksi
COMPOSITE COLUMNS
Square structural tubing
fc′ = 3.5 ksi
Axial design strength in kips
7×
×7
Steel Tube
Nominal Size
Thickness (in.)
5⁄
Wt./ft
50.81
1⁄
8
2
42.05
3⁄
8
5⁄
16
1⁄
4
3⁄
16
32.58
27.59
22.42
17.08
Effective length KL (ft) with respect to radius of gyration
Fy
46 ksi
0
667
575
473
420
364
307
6
7
8
9
10
631
618
604
588
571
545
535
523
510
496
449
441
431
421
410
399
391
383
374
364
346
340
333
325
316
292
287
281
274
267
11
12
13
14
15
553
534
514
493
471
481
465
448
430
412
397
384
371
357
342
353
342
330
317
305
307
297
287
276
265
259
250
242
233
223
16
17
18
19
20
449
427
405
382
360
394
375
356
337
318
327
312
297
281
266
291
278
265
251
237
254
242
230
219
207
214
204
194
184
174
22
24
26
28
30
316
274
235
202
176
281
245
211
182
158
236
206
178
154
134
211
185
160
138
120
184
161
140
120
105
155
136
118
101
88
32
34
36
38
40
155
137
122
110
99
139
123
110
99
89
118
104
93
84
75
106
94
83
75
68
92
82
73
65
59
78
69
61
55
50
2.68
81.1
16.2
2.71
69.3
14.5
2.74
56.9
12.7
2.77
43.8
10.7
Properties
2.56
120
21.3
rm (in.)
φb M n (kip-ft)
P e (KL )2 / 10 4 (kip-ft2)
2.62
102
19.1
Note: Heavy line indicates Kl / r of 200.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
5 - 118
COMPOSITE DESIGN
Fy = 46 ksi
COMPOSITE COLUMNS
Square structural tubing
fc′ = 3.5 ksi
Axial design strength in kips
6×
×6
Steel Tube
Nominal Size
Thickness (in.)
5⁄
8
1⁄
2
3⁄
8
5⁄
16
1⁄
4
3⁄
16
Wt./ft
42.30
35.24
27.48
23.34
19.02
14.53
Effective length KL (ft) with respect to radius of gyration
Fy
46 ksi
0
542
469
385
341
295
247
6
7
8
9
10
502
488
472
455
436
436
424
411
397
382
359
350
339
328
316
318
310
301
291
280
275
268
261
252
243
230
225
218
211
204
11
12
13
14
15
417
397
376
354
333
365
348
331
313
295
303
289
275
261
246
269
257
245
232
220
233
223
213
202
191
196
187
178
169
160
16
17
18
19
20
311
290
268
248
228
276
258
240
222
205
232
217
202
188
174
207
194
181
168
156
180
169
157
147
136
151
141
132
123
114
22
24
26
28
30
189
159
136
117
102
172
145
123
106
93
147
123
105
91
79
132
111
95
82
71
116
97
83
71
62
97
82
70
60
52
32
34
90
79
81
72
69
62
62
55
55
48
46
41
64
55
36
38
49
43
36
44
39
33
2.30
49.7
8.58
2.33
41.1
7.50
2.36
31.9
6.30
Properties
2.15
83.9
12.3
rm (in.)
φb M n (kip-ft)
P e (KL )2 / 10 4 (kip-ft2)
2.21
72.1
11.2
2.27
58.0
9.54
Note: Heavy line indicates Kl / r of 200.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
COMPOSITE COLUMNS—CONCRETE-FILLED STEEL PIPE AND STRUCTURAL TUBING
5 - 119
Fy = 46 ksi
51⁄2×51⁄2
Nominal Size
Thickness (in.)
3⁄
8
5⁄
16
1⁄
4
Wt./ft
24.93
21.21
17.32
5×
×5
3⁄
16
13.25
Fy
Effective length KL (ft) with respect to radius of gyration
Steel Tube
COMPOSITE COLUMNS
Square structural tubing
fc′ = 3.5 ksi
Axial design strength in kips
1⁄
8
1⁄
2
3⁄
8
9.01
28.43
5⁄
16
1⁄
4
3⁄
16
22.37
19.08
15.62
11.97
46 ksi
0
343
304
262
219
173
367
303
268
231
192
6
7
8
9
10
315
305
294
283
270
279
271
261
251
240
241
234
226
217
208
201
195
189
182
174
159
155
149
144
137
328
315
301
286
269
272
262
251
239
226
241
232
223
212
201
208
201
193
184
174
173
167
160
153
145
11
12
13
14
15
257
243
229
215
200
229
217
204
192
179
198
188
177
167
156
166
157
148
139
130
131
124
117
110
103
252
235
218
200
183
212
198
184
170
156
189
177
165
152
140
164
154
143
133
122
137
128
120
111
102
16
17
18
19
20
186
172
158
145
132
167
154
142
130
119
145
134
124
114
104
121
113
104
95
87
96
89
82
75
69
166
150
134
121
109
143
130
117
105
95
128
117
106
95
86
112
102
93
83
75
94
86
78
70
63
22
24
26
28
30
109
91
78
67
59
98
82
70
61
53
86
72
62
53
46
72
61
52
45
39
57
48
41
35
31
90
76
64
56
48
78
66
56
48
42
71
59
51
44
38
62
52
44
38
33
52
44
37
32
28
32
34
36
51
46
46
41
41
36
34
30
27
24
21
29
25
1.92
27.8
4.03
1.95
21.7
3.39
Properties
rm (in.)
φb M n (kip-ft)
P e (KL )2 / 10 4 (kip-ft2)
2.07
47.7
7.07
2.10
41.2
6.37
2.13
34.2
5.58
2.16
26.5
4.69
2.19
18.3
3.69
1.80
47.3
5.84
1.86
38.6
5.08
Note: Heavy line indicates Kl / r of 200.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1.89
33.5
4.59
5 - 120
COMPOSITE DESIGN
Fy = 46 ksi
COMPOSITE COLUMNS
Square structural tubing
fc′ = 3.5 ksi
Axial design strength in kips
41⁄2×41⁄2
Steel Tube
Nominal Size
Thickness (in.)
3⁄
8
Wt./ft
19.82
5⁄
16.96
Fy
Effective length KL (ft) with respect to radius of gyration
1⁄
16
4
13.91
3⁄
16
1⁄
8
10.70
7.31
46 ksi
0
263
233
200
166
130
6
7
8
9
10
230
220
208
195
182
204
195
185
174
163
177
169
160
151
141
147
140
133
126
118
115
110
104
98
92
11
12
13
14
15
168
155
141
128
115
151
139
127
115
104
131
121
111
101
91
109
101
93
84
76
86
79
73
66
60
16
17
18
19
20
102
91
81
73
66
93
83
74
66
60
82
73
65
58
53
69
61
55
49
44
54
48
43
38
35
22
24
26
28
54
46
39
49
41
35
30
43
36
31
27
37
31
26
23
29
24
21
18
1.69
26.5
3.20
1.72
22.2
2.82
1.75
17.4
2.37
1.78
12.1
1.86
Properties
1.66
30.4
3.52
rm (in.)
φb M n (kip-ft)
P e (KL )2 / 10 4 (kip-ft2)
Note: Heavy line indicates Kl / r of 200.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
COMPOSITE COLUMNS—CONCRETE-FILLED STEEL PIPE AND STRUCTURAL TUBING
5 - 121
Fy = 46 ksi
COMPOSITE COLUMNS
Square structural tubing
fc′ = 3.5 ksi
Axial design strength in kips
4×
×4
Steel Tube
Nominal Size
Thickness (in.)
1⁄
Wt./ft
21.63
2
3⁄
8
17.27
5⁄
16
1⁄
4
3⁄
16
1⁄
8
14.83
12.21
9.42
6.46
Effective length KL (ft) with respect to radius of gyration
Fy
46 ksi
0
271
225
199
171
141
110
6
7
8
9
10
225
211
195
179
162
189
178
166
153
140
169
159
148
137
125
146
137
128
119
109
121
114
107
99
91
94
89
83
77
71
11
12
13
14
15
145
129
114
99
86
126
113
100
88
77
114
102
91
80
70
99
90
80
71
62
83
75
67
60
52
65
59
53
47
41
16
17
18
19
20
76
67
60
54
48
68
60
53
48
43
62
55
49
44
40
55
48
43
39
35
46
41
36
33
30
36
32
29
26
23
22
24
26
40
36
30
33
27
29
24
24
21
1.48
20.4
2.12
1.51
17.1
1.88
1.54
13.5
1.58
19
16
14
Properties
1.39
27.7
2.59
rm (in.)
φb M n (kip-ft)
P e (KL )2 / 10 4 (kip-ft2)
1.45
23.2
2.33
Note: Heavy line indicates Kl / r of 200.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1.57
9.5
1.24
5 - 122
COMPOSITE DESIGN
Fy = 46 ksi
Steel Tube
COMPOSITE COLUMNS
Square structural tubing
fc′ = 5 ksi
Axial design strength in kips
Nominal Size
16×16
Thickness (in.)
1⁄
2
1⁄
2
14×14
3⁄
12×12
Wt./ft
103.30
89.68
68.31
8
Effective length KL (ft) with respect to radius of gyration
Fy
5⁄
8
1⁄
2
3⁄
8
5⁄
16
93.34
76.07
58.10
48.86
46 ksi
0
2000
1640
1420
1490
1310
1130
1030
6
7
8
9
10
1980
1970
1960
1950
1940
1620
1610
1600
1590
1580
1400
1390
1380
1380
1370
1460
1450
1440
1430
1410
1290
1280
1270
1260
1250
1100
1100
1090
1080
1070
1010
1000
996
987
977
11
12
13
14
15
1930
1920
1900
1890
1870
1570
1550
1540
1520
1510
1350
1340
1330
1320
1300
1400
1380
1360
1340
1320
1230
1220
1200
1190
1170
1060
1040
1030
1020
1000
966
954
942
928
914
16
17
18
19
20
1860
1840
1820
1800
1780
1490
1470
1450
1430
1410
1290
1270
1250
1230
1220
1300
1280
1260
1230
1210
1150
1130
1110
1090
1070
984
967
950
932
913
899
884
868
851
833
22
24
26
28
30
1730
1690
1640
1590
1530
1360
1320
1270
1220
1160
1180
1140
1090
1050
1000
1160
1100
1050
991
933
1020
974
924
874
823
873
832
790
747
703
797
759
720
680
640
32
34
36
38
40
1480
1420
1370
1310
1250
1110
1060
1000
946
891
954
907
859
811
763
875
817
760
704
649
772
721
671
621
573
658
614
571
528
487
599
559
519
480
442
5.54
352
180
4.60
400
141
4.66
329
125
4.72
255
106
4.75
216
95.8
Properties
6.29
604
334
rm (in.)
φb M n (kip-ft)
P e (KL )2 / 10 4 (kip-ft2)
5.48
455
212
Note: Heavy line indicates Kl / r of 200.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
COMPOSITE COLUMNS—CONCRETE-FILLED STEEL PIPE AND STRUCTURAL TUBING
5 - 123
Fy = 46 ksi
Nominal Size
10×10
Thickness (in.)
5⁄
8
1⁄
Wt./ft
76.33
62.46
2
3⁄
8
47.90
8×8
5⁄
16
40.35
Fy
Effective length KL (ft) with respect to radius of gyration
Steel Tube
COMPOSITE COLUMNS
Square structural tubing
fc′ = 5 ksi
Axial design strength in kips
1⁄
4
5⁄
8
1⁄
2
3⁄
8
5⁄
16
1⁄
4
32.63
59.32
48.85
37.69
31.84
25.82
46 ksi
0
1150
1010
860
782
701
844
739
623
562
500
6
7
8
9
10
1120
1110
1100
1080
1070
984
975
964
952
938
837
829
820
809
798
761
754
745
736
725
682
675
667
659
649
808
796
781
766
748
709
698
686
672
657
598
589
579
567
555
539
531
522
512
500
479
472
464
454
444
11
12
13
14
15
1050
1030
1010
993
972
924
908
891
873
855
785
772
758
742
727
714
702
689
675
660
639
628
616
603
590
730
710
689
667
644
641
624
606
587
568
542
527
512
496
480
488
475
462
447
433
434
422
410
397
384
16
17
18
19
20
949
926
902
877
852
835
815
794
772
750
710
693
675
656
637
645
629
613
596
578
576
562
547
531
516
620
596
571
547
522
548
527
506
484
463
463
446
428
410
392
417
401
385
369
353
370
356
341
327
312
22
24
26
28
30
800
746
692
638
585
704
658
610
563
516
598
559
518
478
438
543
507
470
433
397
484
451
417
384
352
471
422
374
328
286
419
376
335
295
257
355
319
284
251
219
320
287
256
226
197
283
254
226
199
173
32
34
36
38
40
532
482
433
389
351
471
426
383
344
311
399
362
325
292
263
361
327
294
263
238
320
289
259
232
210
251
223
199
178
161
226
200
179
160
145
192
170
152
136
123
173
153
137
123
111
152
135
120
108
98
3.12
92.1
23.8
3.15
75.6
20.9
Properties
rm (in.)
φb M n (kip-ft)
P e (KL )2 / 10 4 (kip-ft2)
3.78
3.84
3.90
3.93
3.96
2.96
3.03
3.09
268
223
174
148
120
163
137
108
75.3
66.7
56.5
51.0
45.0
34.5
31.1
26.4
Note: Heavy line indicates Kl / r of 200.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
5 - 124
COMPOSITE DESIGN
Fy = 46 ksi
COMPOSITE COLUMNS
Square structural tubing
fc′ = 5 ksi
Axial design strength in kips
7×
×7
Steel Tube
Nominal Size
Thickness (in.)
5⁄
8
1⁄
2
3⁄
8
5⁄
16
1⁄
4
3⁄
16
Wt./ft
50.81
42.05
32.58
27.59
22.42
17.08
Effective length KL (ft) with respect to radius of gyration
Fy
46 ksi
0
702
614
515
464
410
355
6
7
8
9
10
663
649
634
617
599
581
569
556
542
526
488
478
467
455
442
439
430
421
410
398
388
381
372
362
352
335
329
321
313
304
11
12
13
14
15
579
558
536
514
490
509
491
473
453
433
429
414
398
382
366
386
373
359
344
329
341
329
317
304
291
294
284
273
262
250
16
17
18
19
20
467
443
419
395
371
413
393
372
351
331
349
332
315
297
280
314
299
283
268
252
277
264
250
236
223
238
227
215
203
191
22
24
26
28
30
324
280
239
206
179
290
252
216
186
162
247
214
184
159
138
222
193
166
143
124
196
170
146
126
110
167
145
124
107
93
32
34
36
38
40
158
140
125
112
101
142
126
112
101
91
121
107
96
86
78
109
97
86
78
70
96
85
76
68
62
82
73
65
58
52
2.68
81.1
16.7
2.71
69.3
15.0
2.74
56.9
13.2
2.77
43.8
11.3
Properties
2.56
120
21.7
rm (in.)
φb M n (kip-ft)
P e (KL )2 / 10 4 (kip-ft2)
2.62
102
19.5
Note: Heavy line indicates Kl / r of 200.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
COMPOSITE COLUMNS—CONCRETE-FILLED STEEL PIPE AND STRUCTURAL TUBING
5 - 125
Fy = 46 ksi
COMPOSITE COLUMNS
Square structural tubing
fc′ = 5 ksi
Axial design strength in kips
6×
×6
Steel Tube
Nominal Size
Thickness (in.)
5⁄
Wt./ft
42.30
8
1⁄
2
35.24
3⁄
8
5⁄
16
1⁄
4
3⁄
16
27.48
23.34
19.02
14.53
Effective length KL (ft) with respect to radius of gyration
Fy
46 ksi
0
566
496
415
372
328
281
6
7
8
9
10
523
508
491
473
453
459
447
432
417
400
385
375
363
350
337
346
336
326
315
303
304
296
287
277
266
261
254
246
237
228
11
12
13
14
15
432
410
388
365
343
383
364
345
326
306
322
307
292
276
259
290
276
262
248
234
255
243
231
218
206
218
208
197
187
176
16
17
18
19
20
320
297
275
253
232
286
267
248
229
210
243
227
211
195
180
219
205
190
176
162
193
180
167
155
143
164
154
143
132
122
22
24
26
28
30
192
161
138
119
103
175
147
126
108
94
151
127
108
93
81
136
114
98
84
73
120
101
86
74
64
102
86
73
63
55
32
34
36
38
91
80
83
73
66
71
63
56
64
57
51
46
57
50
45
40
48
43
38
34
2.27
58.0
9.79
2.30
49.7
8.84
2.33
41.1
7.79
2.36
31.9
6.61
Properties
2.15
83.9
12.5
rm (in.)
φb M n (kip-ft)
P e (KL )2 / 10 4 (kip-ft2)
2.21
72.1
11.4
Note: Heavy line indicates Kl / r of 200.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
5 - 126
COMPOSITE DESIGN
Fy = 46 ksi
51⁄2×51⁄2
Nominal Size
Thickness (in.)
3⁄
8
Wt./ft
24.93
5⁄
16
21.21
5×
×5
1⁄
4
3⁄
16
1⁄
17.32
13.25
Fy
Effective length KL (ft) with respect to radius of gyration
Steel Tube
COMPOSITE COLUMNS
Square structural tubing
fc′ = 5 ksi
Axial design strength in kips
8
1⁄
2
3⁄
8
5⁄
16
1⁄
4
3⁄
16
9.01
28.43
22.37
19.08
15.62
11.97
46 ksi
0
367
329
289
247
203
384
322
288
252
215
6
7
8
9
10
336
325
313
300
286
301
292
281
269
257
265
256
247
237
226
226
219
211
202
193
185
179
172
165
157
342
328
313
297
279
289
277
265
251
237
259
249
238
226
213
227
218
208
198
187
193
185
177
169
159
11
12
13
14
15
272
256
241
225
209
244
231
217
203
189
215
203
191
178
166
183
173
162
152
141
149
141
132
123
114
261
243
224
206
187
223
207
192
177
162
200
187
173
160
146
176
164
152
141
129
149
140
129
119
109
16
17
18
19
20
194
178
163
149
135
175
161
148
135
122
154
142
130
119
108
131
121
111
101
91
106
97
89
81
73
170
153
136
122
111
147
133
119
107
97
133
121
108
97
88
117
106
96
86
78
100
90
81
73
66
22
24
26
28
30
111
94
80
69
60
101
85
72
62
54
89
75
64
55
48
76
63
54
47
41
60
51
43
37
32
91
77
65
56
49
80
67
57
49
43
73
61
52
45
39
64
54
46
40
34
54
46
39
34
29
30
26
1.92
27.8
4.16
1.95
21.7
3.53
32
53
48
42
36
29
34
36
47
42
37
32
25
23
Properties
rm (in.)
φb M n (kip-ft)
P e (KL )2 / 10 4 (kip-ft2)
2.07
47.7
7.23
2.10
41.2
6.55
2.13
34.2
5.78
2.16
26.5
4.90
2.19
18.3
3.92
1.80
47.3
5.93
Note: Heavy line indicates Kl / r of 200.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1.86
38.6
5.19
1.89
33.5
4.71
COMPOSITE COLUMNS—CONCRETE-FILLED STEEL PIPE AND STRUCTURAL TUBING
5 - 127
Fy = 46 ksi
COMPOSITE COLUMNS
Square structural tubing
fc′ = 5 ksi
Axial design strength in kips
41⁄2×41⁄2
Steel Tube
Nominal Size
Thickness (in.)
3⁄
8
5⁄
16
1⁄
4
3⁄
16
1⁄
8
Wt./ft
19.82
16.96
13.91
10.70
7.31
Effective length KL (ft) with respect to radius of gyration
Fy
46 ksi
0
278
249
217
184
149
6
7
8
9
10
242
231
218
204
190
217
207
196
184
171
190
181
172
161
150
161
154
146
137
127
130
124
117
110
103
11
12
13
14
15
175
160
146
132
118
158
145
132
119
107
139
128
117
105
95
118
108
99
90
80
95
87
79
72
64
16
17
18
19
20
104
92
82
74
67
95
84
75
68
61
84
75
67
60
54
72
64
57
51
46
57
51
45
40
37
22
24
26
28
55
46
40
50
42
36
31
45
38
32
28
38
32
27
23
30
25
22
19
1.69
26.5
3.27
1.72
22.2
2.90
1.75
17.4
2.46
1.78
12.1
1.96
Properties
1.66
30.4
3.58
rm (in.)
φb M n (kip-ft)
P e (KL )2 / 10 4 (kip-ft2)
Note: Heavy line indicates Kl / r of 200.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
5 - 128
COMPOSITE DESIGN
Fy = 46 ksi
COMPOSITE COLUMNS
Square structural tubing
fc′ = 5 ksi
Axial design strength in kips
4×
×4
Steel Tube
Nominal Size
Thickness (in.)
1⁄
2
3⁄
8
5⁄
16
1⁄
Wt./ft
21.63
17.27
14.83
12.21
Effective length KL (ft) with respect to radius of gyration
Fy
4
3⁄
16
1⁄
8
9.42
6.46
46 ksi
0
280
236
211
184
156
125
6
7
8
9
10
232
217
200
183
166
198
186
172
158
144
178
167
155
143
131
156
146
136
126
115
132
124
115
107
98
105
99
92
85
78
11
12
13
14
15
148
131
115
100
87
130
116
103
90
78
118
106
94
82
72
104
93
83
73
64
88
79
71
62
54
71
63
56
49
43
16
17
18
19
20
76
68
60
54
49
69
61
54
49
44
63
56
50
45
40
56
50
44
40
36
48
42
38
34
31
38
34
30
27
24
22
24
26
40
36
31
33
28
30
25
25
21
20
17
14
1.48
20.4
2.16
1.51
17.1
1.92
1.54
13.5
1.64
1.57
9.45
1.30
Properties
1.39
27.7
2.62
rm (in.)
φb M n (kip-ft)
P e (KL )2 / 10 4 (kip-ft2)
1.45
23.2
2.36
Note: Heavy line indicates Kl / r of 200.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
COMPOSITE COLUMNS—CONCRETE-FILLED STEEL PIPE AND STRUCTURAL TUBING
Fy = 46 ksi
5 - 129
Y
COMPOSITE COLUMNS
Rectangular structural tubing
fc′ = 3.5 ksi
Axial design strength in kips
X
X
Nominal Size
16×
×12
16×
×8
Thickness (in.)
1⁄
1⁄
2
1⁄
2
3⁄
8
1⁄
2
3⁄
8
5⁄
16
Wt./ft
89.68
76.07
76.07
58.10
69.27
53.00
44.60
2
14×
×10
Fy
Effective length KL (ft) with respect to least radius of gyration, rmy
Steel Tube
Y
12×
×10
46 ksi
0
1450
1140
1170
978
1050
872
782
6
7
8
9
10
1430
1420
1410
1400
1380
1100
1090
1070
1060
1040
1140
1130
1120
1110
1100
956
948
939
928
917
1020
1010
1000
990
978
851
844
835
826
816
763
757
749
741
732
11
12
13
14
15
1370
1360
1340
1330
1310
1020
994
970
946
920
1080
1070
1050
1030
1010
905
892
877
862
846
964
949
933
917
899
804
792
779
765
750
721
710
699
686
673
16
17
18
19
20
1290
1270
1250
1230
1210
893
865
837
808
778
992
971
949
926
903
830
812
794
775
756
880
861
841
820
799
735
719
703
685
668
659
645
630
615
599
22
24
26
28
30
1160
1120
1070
1020
964
718
657
597
539
482
855
806
755
704
653
716
675
633
591
548
755
710
664
617
571
632
594
556
517
479
566
533
498
464
429
32
34
36
38
40
911
858
805
753
702
427
379
338
303
273
602
553
505
459
414
506
465
425
386
349
525
481
438
395
357
441
404
368
333
300
395
362
330
298
269
4.02
1.30
362
288
150
88.8
4.08
1.29
281
224
125
74.8
3.94
1.15
290
256
101
76.6
4.00
1.15
225
199
85.3
64.4
4.03
1.15
191
168
76.4
57.8
Properties
4.84
1.25
497
407
245
157
rmy (in.)
rmx / rmy
φb M nx (kip-ft)
φb M ny (kip-ft)
P ex (K x L x )2 / 10 4 (kip-ft2)
P ey (K y L y )2 / 10 4 (kip-ft2)
3.30
1.72
390
240
174
58.7
Note: Heavy line indicates Kl / r of 200.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
5 - 130
COMPOSITE DESIGN
Fy = 46 ksi
Y
X
COMPOSITE COLUMNS
Rectangular structural tubing
fc′ = 3.5 ksi
Axial design strength in kips
X
12×
×8
Nominal Size
12×
×6
Thickness (in.)
5⁄
8
1⁄
2
3⁄
8
5⁄
16
5⁄
8
1⁄
2
3⁄
8
5⁄
16
Wt./ft
76.33
62.46
47.90
40.35
67.82
55.66
42.79
36.10
Fy
Effective length KL (ft) with respect to least radius of gyration, rmy
Steel Tube
Y
46 ksi
0
1060
914
757
677
906
780
642
569
6
7
8
9
10
1020
1010
991
973
954
881
869
856
842
826
731
721
711
699
686
653
645
635
625
613
850
830
808
783
757
732
716
697
677
655
604
591
576
559
542
536
524
511
497
481
11
12
13
14
15
934
912
888
864
838
808
790
770
749
728
671
656
640
623
606
600
587
572
557
541
729
699
668
637
604
631
606
580
553
526
523
503
482
460
438
464
447
429
410
390
16
17
18
19
20
812
785
757
728
699
705
682
658
634
610
587
568
549
529
509
525
508
491
473
455
571
538
506
473
441
498
470
443
415
387
416
393
371
348
326
370
351
331
311
291
22
24
26
28
30
641
583
525
470
416
560
510
461
413
368
468
427
387
348
310
418
382
346
310
277
379
321
273
236
205
335
284
242
209
182
283
241
206
177
154
253
216
184
159
138
32
34
36
38
366
324
289
260
324
287
256
230
273
242
216
194
244
216
193
173
180
160
142
128
160
142
126
113
136
120
107
96
122
108
96
86
40
234
207
175
156
102
87
78
Properties
3.14
1.38
300
226
95.2
50.3
Note: Heavy line indicates Kl / r of 200.
rmy (in.)
rmx / rmy
φb M nx (kip-ft)
φb M ny (kip-ft)
P ex (K x L x )2 / 10 4 (kip-ft2)
P ey (K y L y )2 / 10 4 (kip-ft2)
3.20
1.37
250
189
83.7
44.5
3.26
1.37
195
147
69.9
37.5
3.28
1.37
165
125
62.8
33.5
2.37
1.73
252
154
74.5
24.8
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
2.42
1.73
210
129
65.8
22.0
2.48
1.72
165
101
55.0
18.6
2.51
1.71
140
86.6
49.1
16.7
COMPOSITE COLUMNS—CONCRETE-FILLED STEEL PIPE AND STRUCTURAL TUBING
Fy = 46 ksi
5 - 131
Y
COMPOSITE COLUMNS
Rectangular structural tubing
fc′ = 3.5 ksi
Axial design strength in kips
X
X
10×
×8
Nominal Size
Thickness (in.)
1⁄
Wt./ft
55.66
2
3⁄
8
42.79
10×
×6
5⁄
16
1⁄
4
1⁄
2
3⁄
8
5⁄
16
1⁄
4
36.10
29.23
48.85
37.69
31.84
25.82
Fy
Effective length KL (ft) with respect to least radius of gyration, rmy
Steel Tube
Y
46 ksi
0
800
662
589
516
676
556
493
429
6
7
8
9
10
770
759
747
734
720
638
629
619
608
597
568
560
551
542
531
497
490
483
475
465
633
619
602
584
564
522
511
497
483
467
463
453
441
428
415
403
394
384
373
361
11
12
13
14
15
704
687
669
650
630
584
570
555
540
524
520
508
495
481
467
455
445
433
421
409
543
521
497
474
449
450
432
413
394
375
400
384
368
351
334
348
335
320
306
291
16
17
18
19
20
610
589
568
546
524
507
490
473
455
437
452
437
422
406
390
396
383
369
355
341
425
400
375
351
327
355
335
315
295
275
316
299
281
263
246
276
261
245
230
215
22
24
26
28
30
479
435
391
349
308
400
364
328
293
260
357
325
293
262
233
313
285
257
230
204
281
237
202
174
152
238
202
172
148
129
213
181
154
133
116
186
159
135
116
101
32
34
36
38
271
240
214
192
228
202
181
162
204
181
162
145
179
159
142
127
133
118
105
95
113
101
90
80
102
90
80
72
89
79
70
63
40
173
146
131
115
73
65
57
2.43
1.49
124
86.9
34.6
15.6
2.46
1.48
106
74.2
30.8
14.0
2.49
1.48
86.6
61.1
26.9
12.3
Properties
rmy (in.)
rmx / rmy
φb M nx (kip-ft)
φb M ny (kip-ft)
P ex (K x L x )2 / 10 4 (kip-ft2)
P ey (K y L y )2 / 10 4 (kip-ft2)
3.12
1.19
190
163
52.9
37.2
3.18
1.19
149
128
44.3
31.4
3.21
1.19
127
109
39.6
28.1
3.24
1.19
104
89.0
34.6
24.6
2.37
1.50
157
110
41.1
18.3
Note: Heavy line indicates Kl / r of 200.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
5 - 132
COMPOSITE DESIGN
Fy = 46 ksi
Y
X
COMPOSITE COLUMNS
Rectangular structural tubing
fc′ = 3.5 ksi
Axial design strength in kips
X
10×
×5
Nominal Size
8×
×6
Thickness (in.)
3⁄
8
5⁄
16
1⁄
4
1⁄
2
3⁄
8
5⁄
16
1⁄
4
Wt./ft
35.13
29.72
24.12
42.05
32.58
27.59
22.42
Fy
Effective length KL (ft) with respect to least radius of gyration, rmy
Steel Tube
Y
46 ksi
0
502
445
385
573
471
417
362
6
7
8
9
10
459
445
428
411
392
408
395
381
365
349
353
342
330
317
302
535
522
507
491
473
440
430
418
405
391
391
381
371
360
347
339
331
322
312
302
11
12
13
14
15
372
351
330
309
288
331
313
295
276
257
287
272
256
240
223
455
435
415
394
373
376
360
344
327
310
334
321
306
291
276
291
279
266
254
241
16
17
18
19
20
266
245
225
205
186
239
220
202
185
168
207
191
176
161
146
352
330
309
288
267
293
275
258
241
224
261
246
231
216
201
228
214
201
188
175
22
24
26
28
30
154
129
110
95
83
139
117
99
86
75
121
101
86
74
65
228
192
163
141
123
192
162
138
119
104
172
145
124
107
93
151
127
108
93
81
32
34
36
38
40
73
64
66
58
57
50
108
96
85
76
91
81
72
65
82
72
65
58
72
63
57
51
46
2.04
1.72
111
68.7
29.5
9.98
2.07
1.71
95.2
58.7
26.5
9.01
2.31
1.25
111
91.1
23.2
14.8
2.36
1.25
88.3
72.5
19.7
12.5
2.39
1.25
75.6
62.1
17.6
11.2
2.42
1.25
62.1
51.1
15.3
9.83
Properties
rmy (in.)
rmx / rmy
φb M nx (kip-ft)
φb M ny (kip-ft)
P ex (K x L x )2 / 10 4 (kip-ft2)
P ey (K y L y )2 / 10 4 (kip-ft2)
2.09
1.72
78.3
48.3
23.1
7.83
Note: Heavy line indicates Kl / r of 200.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
COMPOSITE COLUMNS—CONCRETE-FILLED STEEL PIPE AND STRUCTURAL TUBING
Fy = 46 ksi
5 - 133
Y
COMPOSITE COLUMNS
Rectangular structural tubing
fc′ = 3.5 ksi
Axial design strength in kips
X
X
8×
×4
Nominal Size
Thickness (in.)
5⁄
8
1⁄
Wt./ft
42.30
35.24
2
3⁄
8
27.48
7×
×5
5⁄
16
23.34
Fy
Effective length KL (ft) with respect to least radius of gyration, rmy
Steel Tube
Y
1⁄
4
1⁄
2
3⁄
8
5⁄
16
1⁄
4
3⁄
16
19.02
35.24
27.48
23.34
19.02
14.53
46 ksi
0
532
459
375
331
285
467
383
339
292
244
6
7
8
9
10
453
427
399
370
340
394
373
350
326
301
325
309
291
272
252
287
273
258
241
224
248
236
223
209
194
422
407
390
372
353
347
336
322
308
293
308
298
286
273
260
266
257
248
237
226
223
215
207
198
189
11
12
13
14
15
309
279
250
221
194
275
250
225
200
177
232
212
192
172
153
206
188
171
154
137
179
164
149
134
120
333
312
291
270
249
276
260
243
226
209
246
232
217
202
187
214
201
189
176
163
179
169
158
148
137
16
17
18
19
20
170
151
135
121
109
156
138
123
110
100
135
120
107
96
87
121
107
96
86
78
107
94
84
76
68
228
208
189
170
153
192
176
160
145
131
172
158
144
131
118
150
138
126
115
103
126
116
106
96
87
22
24
26
28
30
90
76
82
69
72
60
51
64
54
46
56
47
40
127
107
91
78
68
108
91
77
67
58
97
82
70
60
52
85
72
61
53
46
72
60
52
44
39
51
46
40
34
30
1.95
1.30
63.8
50.4
11.9
7.01
1.98
1.30
54.9
43.5
10.7
6.32
2.01
1.30
45.5
35.9
9.35
5.55
2.04
1.29
35.2
27.9
7.83
4.67
32
34
Properties
1.49
1.76
φb M nx (kip-ft)
99.3
φb M ny (kip-ft)
59.8
P ex (K x L x )2 / 10 4 (kip-ft2) 18.1
P ey (K y L y )2 / 10 4 (kip-ft2)
5.85
rmy (in.)
rmx / rmy
1.54
1.75
85.2
51.8
16.3
5.34
1.60
1.73
68.7
42.1
13.9
4.65
1.62
1.73
59.0
36.2
12.4
4.16
1.65
1.72
48.6
30.1
10.9
3.66
1.90
1.31
79.7
62.8
14.0
8.23
Note: Heavy line indicates Kl / r of 200.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
5 - 134
COMPOSITE DESIGN
Fy = 46 ksi
Y
X
COMPOSITE COLUMNS
Rectangular structural tubing
fc′ = 3.5 ksi
Axial design strength in kips
X
Y
7×
×4
Steel Tube
Nominal Size
Thickness (in.)
3⁄
Wt./ft
24.93
8
6×
×4
5⁄
16
1⁄
4
21.21
17.32
3⁄
16
13.25
Effective length KL (ft) with respect to least radius of gyration, rmy
Fy
1⁄
2
3⁄
8
28.43
5⁄
16
1⁄
4
3⁄
16
22.37
19.08
15.62
11.97
46 ksi
0
338
298
256
213
364
300
265
228
189
6
7
8
9
10
291
276
259
242
224
258
245
230
215
200
223
212
200
187
173
185
176
166
156
145
309
291
272
252
231
257
243
228
212
196
228
216
203
189
175
197
187
176
164
152
164
156
147
137
127
11
12
13
14
15
205
187
168
151
134
183
167
151
136
121
160
146
132
119
106
134
122
111
100
90
210
189
168
149
130
179
162
146
130
115
160
146
131
118
104
140
127
115
103
92
117
107
97
87
77
16
17
18
19
20
118
104
93
83
75
107
94
84
76
68
94
83
74
67
60
79
70
63
56
51
114
101
90
81
73
101
89
80
71
65
92
81
72
65
59
81
72
64
57
52
68
60
54
48
44
22
24
26
62
52
45
56
47
40
50
42
36
42
35
30
61
51
53
45
48
41
35
43
36
31
36
30
26
1.48
1.39
53.1
39.7
7.61
3.93
1.54
1.38
43.1
32.6
6.62
3.46
1.57
1.38
37.6
28.3
5.96
3.15
1.60
1.37
31.3
23.6
5.20
2.78
1.63
1.37
24.4
18.4
4.39
2.34
Properties
rmy (in.)
rmx / rmy
φb M nx (kip-ft)
φb M ny (kip-ft)
P ex (K x L x )2 / 10 4 (kip-ft2)
P ey (K y L y )2 / 10 4 (kip-ft2)
1.57
1.56
55.2
37.3
9.83
4.04
1.60
1.56
47.6
32.3
8.87
3.66
1.63
1.55
39.7
26.8
7.72
3.23
1.66
1.54
30.7
20.9
6.42
2.72
Note: Heavy line indicates Kl / r of 200.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
COMPOSITE COLUMNS—CONCRETE-FILLED STEEL PIPE AND STRUCTURAL TUBING
Fy = 46 ksi
5 - 135
Y
COMPOSITE COLUMNS
Rectangular structural tubing
fc′ = 3.5 ksi
Axial design strength in kips
X
X
Y
5×
×4
Steel Tube
Nominal Size
Thickness (in.)
3⁄
5⁄
Wt./ft
19.82
8
16.96
Fy
Effective length KL (ft) with respect to least radius of gyration, rmy
1⁄
16
4
3⁄
16
13.91
10.70
46 ksi
0
252
216
177
136
6
7
8
9
10
215
203
190
176
162
185
175
164
153
141
153
145
136
127
118
118
112
106
99
92
11
12
13
14
15
147
133
119
106
93
129
117
105
93
82
108
98
89
79
70
85
77
70
63
56
16
17
18
19
20
81
72
64
58
52
73
64
57
51
46
62
55
49
44
40
49
44
39
35
32
22
24
26
43
36
38
32
33
28
23
26
22
19
1.53
1.20
28.4
24.3
3.56
2.49
1.56
1.19
23.8
20.4
3.03
2.13
1.59
1.19
18.6
16.0
2.40
1.70
Properties
1.50
1.19
32.6
27.9
3.98
2.80
rmy (in.)
rmx / rmy
φb M nx (kip-ft)
φb M ny (kip-ft)
P ex (K x L x )2 / 10 4 (kip-ft2)
P ey (K y L y )2 / 10 4 (kip-ft2)
Note: Heavy line indicates Kl / r of 200.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
5 - 136
COMPOSITE DESIGN
Fy = 46 ksi
Y
X
COMPOSITE COLUMNS
Rectangular structural tubing
fc′ = 5 ksi
Axial design strength in kips
X
Nominal Size
16×
×12
16×
×8
Thickness (in.)
1⁄
2
1⁄
2
1⁄
2
3⁄
8
1⁄
2
3⁄
8
5⁄
16
Wt./ft
89.68
76.07
76.07
58.10
69.27
53.00
44.60
14×
×10
Fy
Effective length KL (ft) with respect to least radius of gyration, rmy
Steel Tube
Y
12×
×10
46 ksi
0
1630
1250
1300
1110
1150
984
897
6
7
8
9
10
1600
1590
1580
1560
1550
1210
1190
1180
1150
1130
1270
1250
1240
1230
1210
1080
1070
1060
1050
1040
1120
1110
1100
1090
1070
959
950
940
929
916
874
866
857
846
835
11
12
13
14
15
1530
1520
1500
1480
1460
1110
1080
1060
1030
1000
1190
1170
1150
1130
1110
1020
1000
987
969
949
1060
1040
1020
1000
981
902
888
872
855
837
822
808
794
778
762
16
17
18
19
20
1440
1410
1390
1360
1340
967
935
902
869
835
1090
1060
1040
1010
983
929
908
886
863
840
960
937
914
890
866
819
800
780
759
738
745
727
709
690
671
22
24
26
28
30
1290
1230
1170
1110
1050
766
698
630
565
502
928
870
812
753
695
792
743
693
643
593
815
763
711
658
605
695
650
605
560
515
631
591
549
508
467
32
34
36
38
40
987
926
865
804
745
442
391
349
313
283
638
582
528
476
429
544
496
450
405
365
554
504
456
409
369
471
428
387
348
314
426
387
350
314
283
4.02
1.30
362
288
155
92.1
4.08
1.29
281
224
131
78.4
3.94
1.15
290
256
105
79.3
4.00
1.15
225
199
89.2
67.3
4.03
1.15
191
168
80.4
60.8
Properties
4.84
1.25
497
407
256
164
rmy (in.)
rmx / rmy
φb M nx (kip-ft)
φb M ny (kip-ft)
P ex (K x L x )2 / 10 4 (kip-ft2)
P ey (K y L y )2 / 10 4 (kip-ft2)
3.30
1.72
390
240
180
60.7
Note: Heavy line indicates Kl / r of 200.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
COMPOSITE COLUMNS—CONCRETE-FILLED STEEL PIPE AND STRUCTURAL TUBING
Fy = 46 ksi
5 - 137
Y
COMPOSITE COLUMNS
Rectangular structural tubing
fc′ = 5 ksi
Axial design strength in kips
X
X
12×
×8
Nominal Size
Thickness (in.)
5⁄
Wt./ft
76.33
8
1⁄
2
62.46
12×
×6
3⁄
8
5⁄
16
5⁄
8
1⁄
2
3⁄
8
5⁄
16
47.90
40.35
67.82
55.66
42.79
36.10
Fy
Effective length KL (ft) with respect to least radius of gyration, rmy
Steel Tube
Y
46 ksi
0
1140
997
845
768
961
839
705
635
6
7
8
9
10
1090
1080
1060
1040
1020
959
946
931
914
896
814
802
790
775
760
739
728
717
704
689
899
877
853
826
797
785
767
746
723
698
661
646
629
610
589
595
581
566
549
531
11
12
13
14
15
997
972
946
919
890
876
854
832
808
783
743
725
706
686
665
674
658
640
622
603
766
734
701
666
631
672
644
615
586
555
567
544
520
496
470
511
490
469
446
424
16
17
18
19
20
861
831
800
768
736
758
732
705
677
650
643
621
598
575
552
583
562
542
520
499
595
559
524
489
454
525
494
463
433
403
445
419
394
368
343
401
378
355
332
309
22
24
26
28
30
672
608
545
485
427
594
538
483
431
380
505
457
411
366
323
456
413
371
330
291
388
327
279
240
209
345
291
248
214
187
295
250
213
183
160
266
225
192
165
144
32
34
36
38
375
332
296
266
334
296
264
237
284
252
225
202
255
226
202
181
184
163
145
130
164
145
130
116
140
124
111
100
127
112
100
90
40
240
214
182
163
105
90
81
2.42
1.73
210
129
67.5
22.5
2.48
1.72
165
101
56.9
19.3
2.51
1.71
140
86.6
51.0
17.4
Properties
rmy (in.)
rmx / rmy
φb M nx (kip-ft)
φb M ny (kip-ft)
P ex (K x L x )2 / 10 4 (kip-ft2)
P ey (K y L y )2 / 10 4 (kip-ft2)
3.14
1.38
300
226
97.5
51.5
3.20
1.37
250
189
86.3
45.9
3.26
1.37
195
147
72.8
39.0
3.28
1.37
165
125
65.8
35.1
2.37
1.73
252
154
76.0
25.3
Note: Heavy line indicates Kl / r of 200.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
5 - 138
COMPOSITE DESIGN
Fy = 46 ksi
Y
X
COMPOSITE COLUMNS
Rectangular structural tubing
fc′ = 5 ksi
Axial design strength in kips
X
10×
×8
Nominal Size
Thickness (in.)
1⁄
2
3⁄
8
Wt./ft
55.66
42.79
10×
×6
5⁄
16
36.10
Fy
Effective length KL (ft) with respect to least radius of gyration, rmy
Steel Tube
Y
1⁄
1⁄
2
3⁄
8
48.85
4
29.23
5⁄
16
1⁄
37.69
31.84
25.82
4
46 ksi
0
868
734
664
593
725
609
548
485
6
7
8
9
10
834
822
808
793
776
706
696
684
671
657
638
629
618
607
594
569
561
552
541
530
677
660
642
621
599
569
556
540
524
505
512
500
486
471
455
454
443
431
417
403
11
12
13
14
15
758
739
719
697
675
642
626
609
591
572
580
565
550
534
517
517
504
490
476
460
576
551
526
499
472
486
466
444
423
400
437
419
400
381
361
387
371
354
337
319
16
17
18
19
20
652
628
604
580
555
553
533
512
492
471
499
481
463
444
425
444
428
412
395
378
445
418
391
365
339
378
355
333
311
289
340
320
300
280
261
301
283
265
248
230
22
24
26
28
30
506
456
408
362
317
429
387
347
308
270
387
349
313
277
243
344
310
277
245
215
289
243
207
178
155
247
208
177
153
133
223
188
160
138
120
197
166
141
122
106
32
34
36
38
279
247
220
198
237
210
187
168
213
189
169
151
189
167
149
134
137
121
108
97
117
104
93
83
106
94
84
75
93
83
74
66
40
178
152
137
121
75
68
60
2.43
1.49
124
86.9
35.7
16.1
2.46
1.48
106
74.2
32.0
14.5
2.49
1.48
86.6
61.1
28.1
12.8
Properties
rmy (in.)
rmx / rmy
φb M nx (kip-ft)
φb M ny (kip-ft)
P ex (K x L x )2 / 10 4 (kip-ft2)
P ey (K y L y )2 / 10 4 (kip-ft2)
3.12
1.19
190
163
54.4
38.3
3.18
1.19
149
128
46.0
32.6
3.21
1.19
127
109
41.3
29.3
3.24
1.19
104
89.0
36.4
25.9
2.37
1.50
157
110
42.1
18.8
Note: Heavy line indicates Kl / r of 200.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
COMPOSITE COLUMNS—CONCRETE-FILLED STEEL PIPE AND STRUCTURAL TUBING
Fy = 46 ksi
5 - 139
Y
COMPOSITE COLUMNS
Rectangular structural tubing
fc′ = 5 ksi
Axial design strength in kips
X
X
10×
×5
Nominal Size
8×
×6
Thickness (in.)
3⁄
8
5⁄
16
1⁄
4
1⁄
2
3⁄
8
5⁄
16
1⁄
4
Wt./ft
35.13
29.72
24.12
42.05
32.58
27.59
22.42
Fy
Effective length KL (ft) with respect to least radius of gyration, rmy
Steel Tube
Y
46 ksi
0
544
489
431
610
512
460
406
6
7
8
9
10
496
479
461
441
419
446
431
415
397
378
393
380
365
349
332
568
554
538
520
500
477
465
451
437
421
429
418
406
393
379
379
369
359
347
334
11
12
13
14
15
397
374
350
326
303
358
337
316
295
273
315
296
278
259
240
480
459
436
414
390
404
386
367
349
329
363
347
331
314
297
321
307
292
277
262
16
17
18
19
20
279
256
234
212
191
252
232
212
192
174
221
203
185
168
152
367
344
321
298
276
310
291
271
252
234
279
262
245
228
211
247
231
216
201
186
22
24
26
28
30
158
133
113
98
85
143
121
103
89
77
126
106
90
78
68
233
196
167
144
125
198
167
142
122
107
179
150
128
111
96
158
133
113
97
85
32
34
36
38
40
75
66
68
60
59
53
110
98
87
78
94
83
74
66
85
75
67
60
75
66
59
53
48
2.04
1.72
111
68.7
30.4
10.3
2.07
1.71
95.2
58.7
27.4
9.31
2.31
1.25
111
91.1
23.7
15.1
2.36
1.25
88.3
72.5
20.2
12.9
2.39
1.25
75.6
62.1
18.2
11.6
2.42
1.25
62.1
51.1
16.0
10.3
Properties
rmy (in.)
rmx / rmy
φb M nx (kip-ft)
φb M ny (kip-ft)
P ex (K x L x )2 / 10 4 (kip-ft2)
P ey (K y L y )2 / 10 4 (kip-ft2)
2.09
1.72
78.3
48.3
24.1
8.15
Note: Heavy line indicates Kl / r of 200.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
5 - 140
COMPOSITE DESIGN
Fy = 46 ksi
Y
X
COMPOSITE COLUMNS
Rectangular structural tubing
fc′ = 5 ksi
Axial design strength in kips
X
8×
×4
Nominal Size
7×
×5
Thickness (in.)
5⁄
8
1⁄
2
3⁄
8
5⁄
16
1⁄
4
1⁄
2
3⁄
8
5⁄
16
1⁄
4
Wt./ft
42.30
35.24
27.48
23.34
19.02
35.24
27.48
23.34
19.02
14.53
Fy
Effective length KL (ft) with respect to least radius of gyration, rmy
Steel Tube
Y
3⁄
16
46 ksi
0
552
482
401
358
313
492
411
369
324
278
6
7
8
9
10
468
441
411
380
349
411
389
364
338
311
345
327
307
286
265
308
292
275
256
237
271
257
241
225
208
444
427
409
390
369
372
358
343
327
310
333
322
308
294
279
293
283
271
259
246
251
242
232
221
210
11
12
13
14
15
317
285
254
224
196
284
257
230
205
180
242
220
199
178
157
217
198
178
160
142
191
174
157
141
125
347
325
302
279
257
292
274
255
237
218
263
247
230
213
197
232
217
203
188
174
198
186
173
161
148
16
17
18
19
20
172
153
136
122
110
158
140
125
112
101
138
123
109
98
89
124
110
98
88
80
110
98
87
78
71
235
213
193
173
156
200
182
165
148
134
181
165
149
134
121
159
145
132
119
107
136
124
112
101
91
22
24
26
28
30
91
77
84
70
73
62
52
66
55
47
58
49
42
129
108
92
80
69
111
93
79
68
59
100
84
72
62
54
89
74
63
55
48
75
63
54
47
41
52
47
42
36
32
1.95
1.30
63.8
50.4
12.2
7.18
1.98
1.30
54.9
43.5
11.1
6.51
2.01
1.30
45.5
35.9
9.70
5.75
2.04
1.29
35.2
27.9
8.20
4.90
32
34
Properties
rmy (in.)
rmx / rmy
φb M nx (kip-ft)
φb M ny (kip-ft)
P ex (K x L x)2 / 10 4 (kip-ft2)
P ey (K y L y)2 / 10 4 (kip-ft2)
1.49
1.76
99.3
59.8
18.3
5.92
1.54
1.75
85.2
51.8
16.6
5.43
1.60
1.73
68.7
42.1
14.2
4.75
1.62
1.73
59.0
36.2
12.8
4.28
1.65
1.72
48.6
30.1
11.2
3.79
1.90
1.31
79.7
62.8
14.3
8.38
Note: Heavy line indicates Kl / r of 200.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
COMPOSITE COLUMNS—CONCRETE-FILLED STEEL PIPE AND STRUCTURAL TUBING
Fy = 46 ksi
5 - 141
Y
COMPOSITE COLUMNS
Rectangular structural tubing
fc′ = 5 ksi
Axial design strength in kips
X
X
Y
7×
×4
Steel Tube
Nominal Size
6×
×4
Thickness (in.)
3⁄
8
5⁄
16
1⁄
4
3⁄
16
1⁄
2
3⁄
8
5⁄
16
1⁄
4
3⁄
16
Wt./ft
24.93
21.21
17.32
13.25
28.43
22.37
19.08
15.62
11.97
Effective length KL (ft) with respect to least radius of gyration, rmy
Fy
46 ksi
0
360
321
281
239
380
318
285
249
211
6
7
8
9
10
308
291
273
254
234
276
261
245
228
211
242
229
215
201
186
206
195
183
171
158
321
302
282
260
238
271
256
240
222
204
243
230
215
200
184
213
202
189
176
162
181
171
161
149
138
11
12
13
14
15
214
194
174
155
137
193
175
158
141
124
170
155
139
125
110
145
131
119
106
94
215
193
172
151
132
186
168
150
133
117
168
152
137
121
107
148
134
121
108
95
126
114
103
92
81
16
17
18
19
20
120
106
95
85
77
109
97
86
78
70
97
86
77
69
62
83
73
65
59
53
116
103
92
82
74
103
91
81
73
66
94
83
74
67
60
83
74
66
59
53
71
63
56
50
45
22
24
26
64
53
45
58
49
41
51
43
37
44
37
31
61
52
54
46
50
42
36
44
37
32
38
32
27
1.48
1.39
53.1
39.7
7.72
3.99
1.54
1.38
43.1
32.6
6.76
3.53
1.57
1.38
37.6
28.3
6.10
3.22
1.60
1.37
31.3
23.6
5.36
2.86
1.63
1.37
24.4
18.4
4.56
2.44
Properties
rmy (in.)
rmx / rmy
φb M nx (kip-ft)
φb M ny (kip-ft)
P ex (K x L x )2 / 10 4 (kip-ft2)
P ey (K y L y )2 / 10 4 (kip-ft2)
1.57
1.56
55.2
37.3
10.0
4.12
1.60
1.56
47.6
32.3
9.10
3.76
1.63
1.55
39.7
26.8
7.97
3.33
1.66
1.54
30.7
20.9
6.70
2.84
Note: Heavy line indicates Kl / r of 200.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
5 - 142
COMPOSITE DESIGN
Fy = 46 ksi
Y
X
COMPOSITE COLUMNS
Rectangular structural tubing
fc′ = 5 ksi
Axial design strength in kips
X
Y
5×
×4
Steel Tube
Nominal Size
Thickness (in.)
3⁄
8
5⁄
Wt./ft
19.82
16.96
Fy
Effective length KL (ft) with respect to least radius of gyration, rmy
1⁄
4
16
3⁄
16
13.91
10.70
46 ksi
0
262
224
185
142
6
7
8
9
10
222
210
196
181
166
192
181
170
157
145
159
150
141
131
121
123
117
110
102
95
11
12
13
14
15
151
136
121
107
94
132
119
107
95
84
111
101
91
81
71
87
79
72
64
57
16
17
18
19
20
83
73
65
59
53
73
65
58
52
47
63
56
50
45
40
50
44
40
36
32
22
24
26
44
37
39
33
33
28
24
27
22
19
1.53
1.20
28.4
24.3
3.61
2.52
1.56
1.19
23.8
20.4
3.07
2.16
1.59
1.19
18.6
16.0
2.44
1.72
Properties
1.50
1.19
32.6
27.9
4.04
2.83
rmy (in.)
rmx / rmy
φb M nx (kip-ft)
φb M ny (kip-ft)
P ex (K x L x)2 / 10 4 (kip-ft2)
P ey (K y L y)2 / 10 4 (kip-ft2)
Note: Heavy line indicates Kl / r of 200.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
REFERENCES
5 - 143
REFERENCES
Allison, H., 1991, Low- and Medium-Rise Steel Buildings, AISC Steel Design Guide
Series No. 5, American Institute of Steel Construction, Chicago, IL.
Fisher, J. M. and M. A. West, 1990, Serviceability Design Considerations for Low-Rise
Buildings, AISC Steel Design Guide Series No. 3, AISC, Chicago.
Griffis, L. G., 1992, Load and Resistance Factor Design of W-Shapes Encased in
Concrete, AISC Steel Design Guide Series No. 6, AISC, Chicago.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
6-1
PART 6
SPECIFICATIONS AND CODES
LRFD SPECIFICATION FOR STRUCTURAL STEEL BUILDINGS (1993) . . . . . . 6-3
Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-5
Table of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-7
Symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-17
Specification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-25
Appendixes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-105
Numerical Values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-144
Commentary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-161
SPECIFICATION FOR LRFD OF SINGLE-ANGLE MEMBERS (1993) . . . . . . . 6-277
Commentary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-289
SEISMIC PROVISIONS FOR STRUCTURAL STEEL BUILDINGS (1992) . . . . . 6-301
Commentary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-329
RCSC SPECIFICATION FOR STRUCTURAL JOINTS USING
ASTM A325 OR A490 BOLTS (1988) . . . . . . . . . . . . . . . . . . . . . . . . . . 6-371
Commentary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-399
CODE OF STANDARD PRACTICE FOR STEEL BUILDINGS
AND BRIDGES (1992) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-423
Commentary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-455
AISC QUALITY CERTIFICATION PROGRAM (1993) . . . . . . . . . . . . . . . . 6-477
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
6-2
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
6-3
Load and Resistance
Factor Design Specification
for Structural Steel Buildings
December 1, 1993
AMERICAN INSTITUTE OF STEEL CONSTRUCTION, INC.
One East Wacker Drive, Suite 3100
Chicago, Illinois 60601-2001
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
6-4
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
6-5
PREFACE
The AISC Load and Resistance Factor Design (LRFD) Specification for Structural
Steel Buildings is based on reliability theory. As have all AISC Specifications, this
LRFD Specification has been based upon past successful usage, advances in the state
of knowledge, and changes in design practice. The LRFD Specification has been
developed as a consensus document to provide a uniform practice in the design of
steel-framed buildings. The intention is to provide design criteria for routine use and
not to provide specific criteria for infrequently encountered problems which occur in
the full range of structural design. Providing definitive provisions to cover all cases
would make the LRFD Specification too cumbersome for routine design usage.
The LRFD Specification is the result of the deliberations of a committee of
structural engineers with wide experience and high professional standing, representing
a wide geographical distribution throughout the U.S. The committee includes approximately equal numbers of engineers in private practice and code agencies, engineers
involved in research and teaching, and engineers employed by steel fabricating and
producing companies.
In order to avoid reference to proprietary steels which may have limited availability,
only those steels which can be identified by ASTM specifications are approved under
this Specification. However, some steels covered by ASTM specifications, but subject
to more costly manufacturing and inspection techniques than deemed essential for
structures covered by this Specification, are not listed, even though they may provide
all the necessary characteristics for reliable usage in structural applications. Approval
of such steels in lieu of less expensive steels is left to the owner’s representative.
The Appendices to this Specification are an integral part of the Specification.
A non-mandatory Commentary has been prepared to provide background for the
Specification provisions and the user is encouraged to consult it.
The principal changes incorporated in this edition of the Specification include:
• Updated web crippling design provisions.
• Recommendations for the use of heavy rolled shapes and welded members made
up of thick plates.
• Updated provisions for slender web girders and unsymmetric members.
• Revised provisions for built-up compression members.
• Improved Cb equation.
• Provisions for slip-critical joints designed at factored loads.
• Reorganization and expansion of material on stability of unbraced frames.
• Reorganization and expansion of Chapters F and K.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
6-6
PREFACE
• Alternative fillet-weld design strength.
• Addition of beam-web opening provisions.
The reader is cautioned that professional judgment must be exercised when data or
recommendations in the Specification are applied. The publication of the material
contained herein is not intended as a representation or warranty on the part of the
American Institute of Steel Construction, Inc.—or any other person named herein—
that this information is suitable for general or particular use, or freedom from
infringement of any patent or patents. Anyone making use of this information assumes
all liability arising from such use. The design and detailing of steel structures is within
the expertise of professional individuals who are competent by virtue of education,
training, and experience for the application of engineering principles and the provisions of this specification to the design and/or detailing of a particular structure.
By the Committee,
Arthur P. Arndt, Chairman
William E. Moore, II, Vice Chairman
Horatio Allison
Reidar Bjorhovde
Roger L. Brockenbrough
W. F. Chen
Andrew K. Courtney
Robert O. Disque
Joseph Dudek
Duane S. Ellifritt
Bruce Ellingwood
Shu-Jin Fang
Steven J. Fenves
Roger E. Ferch
James M. Fisher
John W. Fisher
Theodore V. Galambos
Geerhard Haaijer
Richard B. Haws
Mark Holland
Ira Hooper
Donald L. Johnson
L. A. Kloiber
Jay W. Larson
William J. LeMessurier
H. S. Lew
Bill Lindley, II
Stanley D. Lindsey
Richard W. Marshall
Lisa McCasland
Robert McCluer
William A. Milek
Duane K. Miller
Walter P. Moore, Jr.
Thomas M. Murray
Gary G. Nichols
Clarkson W. Pinkham
Egor P. Popov
Donald R. Sherman
Frank Sowokinos
William A. Thornton
Raymond H. R. Tide
Ivan M. Viest
Lyle L. Wilson
Joseph A. Yura
Nestor R. Iwankiw, Secretary
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
6-7
TABLE OF CONTENTS
SYMBOLS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
A.
B.
GENERAL PROVISIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
A1.
Scope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
A2.
Limits of Applicability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
1. Structural Steel Defined . . . . . . . . . . . . . . . . . . . . . . . . . . 25
2. Types of Construction . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
A3.
Material . . . . . . . . . . . . . . .
1. Structural Steel . . . . . . . . . .
2. Steel Castings and Forgings . . .
3. Bolts, Washers, and Nuts . . . . .
4. Anchor Bolts and Threaded Rods
5. Filler Metal and Flux for Welding
6. Stud Shear Connectors . . . . . .
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26
26
28
28
28
29
29
A4.
Loads and Load Combinations . . . . . . . . .
1. Loads, Load Factors, and Load Combinations
2. Impact . . . . . . . . . . . . . . . . . . . .
3. Crane Runway Horizontal Forces . . . . . .
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29
30
30
31
A5.
Design Basis . . . . . . . . . . . . . . . . . . . . . .
1. Required Strength at Factored Loads . . . . . . .
2. Limit States . . . . . . . . . . . . . . . . . . . . .
3. Design for Strength . . . . . . . . . . . . . . . . .
4. Design for Serviceability and Other Considerations
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31
31
31
32
32
A6.
Referenced Codes and Standards . . . . . . . . . . . . . . . . . . . . . . 32
A7.
Design Documents . . . . . . . . . . . .
1. Plans . . . . . . . . . . . . . . . . .
2. Standard Symbols and Nomenclature
3. Notation for Welding . . . . . . . . .
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33
33
33
33
DESIGN REQUIREMENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
B1.
Gross Area . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
B2.
Net Area . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
B3.
Effective Net Area for Tension Members . . . . . . . . . . . . . . . . . . 34
B4.
Stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
B5.
Local Buckling . . . . . . . . . . . . . . .
1. Classification of Steel Sections . . . .
2. Design by Plastic Analysis . . . . . . .
3. Slender-Element Compression Sections
B6.
Bracing at Supports . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
B7.
Limiting Slenderness Ratios . . . . . . . . . . . . . . . . . . . . . . . . . 37
B8.
Simple Spans . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
B9.
End Restraint . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
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36
36
36
37
B10. Proportions of Beams and Girders . . . . . . . . . . . . . . . . . . . . . . 37
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
6-8
C.
TABLE OF CONTENTS
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41
41
41
41
41
44
44
44
45
47
47
47
47
47
48
48
51
52
Design for Flexure . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1. Yielding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2. Lateral-Torsional Buckling . . . . . . . . . . . . . . . . . . . . . . .
F2. Design for Shear . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
F3. Web-Tapered Members (see Appendix F3) . . . . . . . . . . . . . . .
F4. Beams and Girders with Web Openings . . . . . . . . . . . . . . . . .
G. PLATE GIRDERS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
H. MEMBERS UNDER COMBINED FORCES AND TORSION . . . . . . . .
H1. Symmetric Members Subject to Bending and Axial Force . . . . . . .
1. Doubly and Singly Symmetric Members in Flexur and Tension . . .
2. Doubly and Singly Symmetric Members in Flexure and Compression
H2. Unsymmetric Members and Members Under Torsion and
Combined Torsion, Flexure, Shear, and/or Axial Force . . . . . . . . .
H3. Alternative Interaction Equations for Members Under
Combined Stress (see Appendix H3) . . . . . . . . . . . . . . . . . . .
I. COMPOSITE MEMBERS . . . . . . . . . . . . . . . . . . . . . . . . . . . .
I1.
Design Assumptions . . . . . . . . . . . . . . . . . . . . . . . . . . . .
I2.
Compression Members . . . . . . . . . . . . . . . . . . . . . . . . . .
1. Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2. Design Strength . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3. Columns with Multiple Steel Shapes . . . . . . . . . . . . . . . . . .
4. Load Transfer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
I3.
Flexural Members . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1. Effective Width . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2. Strength of Beams with Shear Connectors . . . . . . . . . . . . . . .
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52
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60
D.
E.
F.
FRAMES AND OTHER STRUCTURES . . . . . . . . . . . . . . . .
C1. Second Order Effects . . . . . . . . . . . . . . . . . . . . . . .
C2. Frame Stability . . . . . . . . . . . . . . . . . . . . . . . . . .
1. Braced Frames . . . . . . . . . . . . . . . . . . . . . . . . .
2. Unbraced Frames . . . . . . . . . . . . . . . . . . . . . . . .
TENSION MEMBERS . . . . . . . . . . . . . . . . . . . . . . . . . .
D1. Design Tensile Strength . . . . . . . . . . . . . . . . . . . . . .
D2. Built-Up Members . . . . . . . . . . . . . . . . . . . . . . . . .
D3. Pin-Connected Members and Eyebars . . . . . . . . . . . . . .
COLUMNS AND OTHER COMPRESSION MEMBERS . . . . . .
E1. Effective Length and Slenderness Limitations . . . . . . . . .
1. Effective Length . . . . . . . . . . . . . . . . . . . . . . . .
2. Design by Plastic Analysis . . . . . . . . . . . . . . . . . . .
E2. Design Compressive Strength for Flexural Buckling . . . . . .
E3. Design Compressive Strength for Flexural-Torsional Buckling
E4. Built-Up Members . . . . . . . . . . . . . . . . . . . . . . . . .
E5. Pin-Connected Compression Members . . . . . . . . . . . . .
BEAMS AND OTHER FLEXURAL MEMBERS . . . . . . . . . . .
F1.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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60
61
61
62
62
63
63
63
64
64
64
TABLE OF CONTENTS
3.
4.
5.
6.
J.
Strength of Concrete-Encased Beams
Strength During Construction . . . .
Formed Steel Deck . . . . . . . . . .
Design Shear Strength . . . . . . . .
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6-9
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64
65
65
66
I4.
Combined Compression and Flexure . . . . . . . . . . . . . . . . . . . . 66
I5.
Shear Connectors . . . . . . . . . . . . . .
1. Materials . . . . . . . . . . . . . . . . .
2. Horizontal Shear Force . . . . . . . . . .
3. Strength of Stud Shear Connectors . . . .
4. Strength of Channel Shear Connectors . .
5. Required Number of Shear Connectors .
6. Shear Connector Placement and Spacing
I6.
Special Cases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
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67
67
67
68
68
68
68
CONNECTIONS, JOINTS, AND FASTENERS . . . . . . . . . . . . . . . . . . 70
J1.
General Provisions . . . . . . . . . . . . . . . . . .
1. Design Basis . . . . . . . . . . . . . . . . . . .
2. Simple Connections . . . . . . . . . . . . . . .
3. Moment Connections . . . . . . . . . . . . . . .
4. Compression Members with Bearing Joints . . .
5. Splices in Heavy Sections . . . . . . . . . . . .
6. Beam Copes and Weld Access Holes . . . . . .
7. Minimum Strength of Connections . . . . . . .
8. Placement of Welds and Bolts . . . . . . . . . .
9. Bolts in Combination with Welds . . . . . . . .
10. High-Strength Bolts in Combination with Rivets
11. Limitations on Bolted and Welded Connections .
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70
70
70
70
70
70
71
71
72
72
72
72
J2.
Welds . . . . . . . . . . . . .
1. Groove Welds . . . . . . .
2. Fillet Welds . . . . . . . .
3. Plug and Slot Welds . . .
4. Design Strength . . . . . .
5. Combination of Welds . .
6. Matching Weld Metal . . .
7. Mixed Weld Metal . . . .
8. Preheat for Heavy Shapes
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73
73
74
76
77
77
77
79
79
J3.
Bolts and Threaded Parts . . . . . . . . . . . . . . . . . . . .
1. High-Strength Bolts . . . . . . . . . . . . . . . . . . . . .
2. Size and Use of Holes . . . . . . . . . . . . . . . . . . . .
3. Minimum Spacing . . . . . . . . . . . . . . . . . . . . . .
4. Minimum Edge Distance . . . . . . . . . . . . . . . . . . .
5. Maximum Spacing and Edge Distance . . . . . . . . . . . .
6. Design Tension or Shear Strength . . . . . . . . . . . . . .
7. Combined Tension and Shear in Bearing-Type Connections
8. High-Strength Bolts in Slip-Critical Connections . . . . . .
9. Combined Tension and Shear in Slip-Critical Connections .
10. Bearing Strength at Bolt Holes . . . . . . . . . . . . . . . .
11. Long Grips . . . . . . . . . . . . . . . . . . . . . . . . . .
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79
79
79
80
81
82
83
83
83
84
85
87
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.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
6 - 10
TABLE OF CONTENTS
J4.
Design Rupture Strength . . . . . . . . . . . . . . . . . . . . . .
1. Shear Rupture Strength . . . . . . . . . . . . . . . . . . . . . .
2. Tension Rupture Strength . . . . . . . . . . . . . . . . . . . .
3. Block Shear Rupture Strength . . . . . . . . . . . . . . . . . .
J5. Connecting Elements . . . . . . . . . . . . . . . . . . . . . . . .
1. Eccentric Connections . . . . . . . . . . . . . . . . . . . . . .
2. Design Strength of Elements in Tension . . . . . . . . . . . . .
3. Other Connecting Elements . . . . . . . . . . . . . . . . . . .
J6. Fillers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
J7. Splices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
J8. Bearing Strength . . . . . . . . . . . . . . . . . . . . . . . . . . .
J9. Column Bases and Bearing on Concrete . . . . . . . . . . . . . .
J10. Anchor Bolts and Embedments . . . . . . . . . . . . . . . . . . .
K. CONCENTRATED FORCES, PONDING, AND FATIGUE . . . . . .
K1. Flanges and Webs with Concentrated Forces . . . . . . . . . . .
1. Design Basis . . . . . . . . . . . . . . . . . . . . . . . . . . .
2. Local Flange Bending . . . . . . . . . . . . . . . . . . . . . .
3. Local Web Yielding . . . . . . . . . . . . . . . . . . . . . . . .
4. Web Crippling . . . . . . . . . . . . . . . . . . . . . . . . . .
5. Sidesway Web Buckling . . . . . . . . . . . . . . . . . . . . .
6. Compression Buckling of the Web . . . . . . . . . . . . . . . .
7. Panel-Zone Web Shear . . . . . . . . . . . . . . . . . . . . . .
8. Unframed Ends of Beams and Girders . . . . . . . . . . . . . .
9. Additional Stiffener Requirements for Concentrated Forces . .
10. Additional Doubler Plate Requirements for Concentrated Forces
K2. Ponding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
K3. Fatigue . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
L. SERVICEABILITY DESIGN CONSIDERATIONS . . . . . . . . . . .
L1. Camber . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
L2. Expansion and Contraction . . . . . . . . . . . . . . . . . . . . .
L3. Deflections, Vibrations, and Drift . . . . . . . . . . . . . . . . .
1. Deflections . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2. Floor Vibrations . . . . . . . . . . . . . . . . . . . . . . . . .
3. Drift . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
L4. Connection Slip . . . . . . . . . . . . . . . . . . . . . . . . . . .
L5. Corrosion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
M. FABRICATION, ERECTION, AND QUALITY CONTROL . . . . . .
M1. Shop Drawings . . . . . . . . . . . . . . . . . . . . . . . . . . . .
M2. Fabrication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1. Cambering, Curving, and Straightening . . . . . . . . . . . . .
2. Thermal Cutting . . . . . . . . . . . . . . . . . . . . . . . . .
3. Planing of Edges . . . . . . . . . . . . . . . . . . . . . . . . .
4. Welded Construction . . . . . . . . . . . . . . . . . . . . . . .
5. Bolted Construction . . . . . . . . . . . . . . . . . . . . . . .
6. Compression Joints . . . . . . . . . . . . . . . . . . . . . . . .
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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87
87
87
87
88
88
88
88
89
89
89
90
90
91
91
91
91
92
92
93
94
95
96
96
96
97
97
98
98
98
98
98
98
98
99
99
100
100
100
100
100
100
101
101
101
TABLE OF CONTENTS
6 - 11
7. Dimensional Tolerances . . . . . . . . . . . . . . . . . . . . . . . . . . 101
8. Finish of Column Bases . . . . . . . . . . . . . . . . . . . . . . . . . . 101
M3. Shop Painting . . . . . . . . . . . . . . . . . . . . .
1. General Requirements . . . . . . . . . . . . . . .
2. Inaccessible Surfaces . . . . . . . . . . . . . . . .
3. Contact Surfaces . . . . . . . . . . . . . . . . . .
4. Finished Surfaces . . . . . . . . . . . . . . . . . .
5. Surfaces Adjacent to Field Welds . . . . . . . . .
M4. Erection . . . . . . . . . . . . . . . . . . . . . . . . .
1. Alignment of Column Bases . . . . . . . . . . . .
2. Bracing . . . . . . . . . . . . . . . . . . . . . . .
3. Alignment . . . . . . . . . . . . . . . . . . . . .
4. Fit of Column Compression Joints and Base Plates
5. Field Welding . . . . . . . . . . . . . . . . . . . .
6. Field Painting . . . . . . . . . . . . . . . . . . . .
7. Field Connections . . . . . . . . . . . . . . . . .
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102
102
102
102
102
102
102
102
102
103
103
103
103
103
M5. Quality Control . . . . . . . . . . . . . . . . . . . . . . . . . .
1. Cooperation . . . . . . . . . . . . . . . . . . . . . . . . . . .
2. Rejections . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3. Inspection of Welding . . . . . . . . . . . . . . . . . . . . .
4. Inspection of Slip-Critical High-Strength Bolted Connections
5. Identification of Steel . . . . . . . . . . . . . . . . . . . . . .
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103
103
103
104
104
104
APPENDICES
B.
DESIGN REQUIREMENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
B5.
Local Buckling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
1. Classification of Steel Sections . . . . . . . . . . . . . . . . . . . . . . 105
3. Slender-Element Compression Sections . . . . . . . . . . . . . . . . . . 105
E.
COLUMNS AND OTHER COMPRESSION MEMBERS . . . . . . . . . . . . 109
F.
BEAMS AND OTHER FLEXURAL MEMBERS . . . . . . . . . . . . . . . . . 111
E3.
Design Compressive Strength for Flexural-Torsional Buckling . . . . . . 109
F1.
Design for Flexure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
F2.
Design for Shear . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
2. Design Shear Strength . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
3. Transverse Stiffeners . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
F3.
Web-Tapered Members . . . . . . . .
1. General Requirements . . . . . . .
2. Design Tensile Strength . . . . . .
3. Design Compressive Strength . . .
4. Design Flexural Strength . . . . . .
5. Design Shear Strength . . . . . . .
6. Combined Flexure and Axial Force
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120
G. PLATE GIRDERS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
G1.
Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
G2.
Design Flexural Strength . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
G3.
Design Shear Strength with Tension Field Action . . . . . . . . . . . . . . 124
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
6 - 12
TABLE OF CONTENTS
G4.
Transverse Stiffeners . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
G5.
Flexure-Shear Interaction . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
H. MEMBERS UNDER COMBINED FORCES AND TORSION . . . . . . . . . . 127
H3.
J.
Alternative Interaction Equations for Members Under
Combined Stress . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
CONNECTIONS, JOINTS, AND FASTENERS . . . . . . . . . . . . . . . . . . 129
J2.
J3.
Welds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4. Design Strength . . . . . . . . . . . . . . . . . . . . . . .
Bolts and Threaded Parts . . . . . . . . . . . . . . . . . . .
8. High-Strength Bolts in Slip-Critical Connections . . . . .
9. Combined Tension and Shear in Slip-Critical Connections
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129
129
130
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130
K. CONCENTRATED FORCES, PONDING, AND FATIGUE . . . . . . . . . . . 132
K2. Ponding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
K3.
Fatigue . . . . . . . . . . . . . . . . . . . . . . . . . .
1. Loading Conditions; Type and Location of Material
2. Design Stress Range . . . . . . . . . . . . . . . . .
3. Design Strength of Bolts in Tension . . . . . . . . .
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135
135
135
135
NUMERICAL VALUES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144
COMMENTARY
A. GENERAL PROVISIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162
A1. Scope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162
B.
C.
A2.
Limits of Applicability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162
2. Types of Construction . . . . . . . . . . . . . . . . . . . . . . . . . . . 162
A3.
Material . . . . . . . . . . . . . . .
1. Structural Steel . . . . . . . . . .
3. Bolts, Washers, and Nuts . . . . .
4. Anchor Bolts and Threaded Rods
5. Filler Metal and Flux for Welding
A4.
Loads and Load Combinations . . . . . . . . . . . . . . . . . . . . . . . . 166
1. Loads, Load Factors, and Load Combinations . . . . . . . . . . . . . . . 166
2. Impact . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167
A5.
Design Basis . . . . . . . . . . . . . . . . . . . . . .
1. Required Strength at Factored Loads . . . . . . .
2. Limit States . . . . . . . . . . . . . . . . . . . . .
3. Design for Strength . . . . . . . . . . . . . . . . .
4. Design for Serviceability and Other Considerations
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163
163
164
165
165
167
167
167
168
171
DESIGN REQUIREMENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172
B2.
Net Area . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172
B3.
Effective Net Area for Tension Members . . . . . . . . . . . . . . . . . . 172
B5.
B7.
Local Buckling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174
Limiting Slenderness Ratios . . . . . . . . . . . . . . . . . . . . . . . . . 177
FRAMES AND OTHER STRUCTURES . . . . . . . . . . . . . . . . . . . . . . 179
C1.
Second Order Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
TABLE OF CONTENTS
C2. Frame Stability . . . . . . . . . . . . . . . . . . . . . . . . . .
TENSION MEMBERS . . . . . . . . . . . . . . . . . . . . . . . . . .
D1. Design Tensile Strength . . . . . . . . . . . . . . . . . . . . . .
D2. Built-Up Members . . . . . . . . . . . . . . . . . . . . . . . . .
D3. Pin-Connected Members and Eyebars . . . . . . . . . . . . . .
E. COLUMNS AND OTHER COMPRESSION MEMBERS . . . . . .
E1. Effective Length and Slenderness Limitations . . . . . . . . .
1. Effective Length . . . . . . . . . . . . . . . . . . . . . . . .
2. Design by Plastic Analysis . . . . . . . . . . . . . . . . . . .
E2. Design Compressive Strength for Flexural Buckling . . . . . .
E3. Design Compressive Strength for Flexural-Torsional Buckling
E4. Built-Up Members . . . . . . . . . . . . . . . . . . . . . . . . .
F. BEAMS AND OTHER FLEXURAL MEMBERS . . . . . . . . . . .
F1. Design for Flexure . . . . . . . . . . . . . . . . . . . . . . . . .
1. Yielding . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2. Lateral-Torsional Buckling . . . . . . . . . . . . . . . . . . .
F2. Design for Shear . . . . . . . . . . . . . . . . . . . . . . . . . .
F4. Beams and Girders with Web Openings . . . . . . . . . . . . .
H. MEMBERS UNDER COMBINED FORCES AND TORSION . . . .
H1. Symmetric Members Subject to Bending and Axial Force . . .
H2. Unsymmetric Members and Members Under Torsion and
Combined Torsion, Flexure, Shear, and/or Axial Force . . . . .
I. COMPOSITE MEMBERS . . . . . . . . . . . . . . . . . . . . . . . .
I1.
Design Assumptions . . . . . . . . . . . . . . . . . . . . . . . .
I2.
Compression Members . . . . . . . . . . . . . . . . . . . . . .
1. Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . .
2. Design Strength . . . . . . . . . . . . . . . . . . . . . . . . .
3. Columns with Multiple Steel Shapes . . . . . . . . . . . . . .
4. Load Transfer . . . . . . . . . . . . . . . . . . . . . . . . . .
I3.
Flexural Members . . . . . . . . . . . . . . . . . . . . . . . . .
1. Effective Width . . . . . . . . . . . . . . . . . . . . . . . . .
2. Strength of Beams with Shear Connectors . . . . . . . . . . .
3. Strength of Concrete-Encased Beams . . . . . . . . . . . . .
4. Strength During Construction . . . . . . . . . . . . . . . . .
5. Formed Steel Deck . . . . . . . . . . . . . . . . . . . . . . .
6. Design Shear Strength . . . . . . . . . . . . . . . . . . . . .
I4.
Combined Compression and Flexure . . . . . . . . . . . . . .
I5.
Shear Connectors . . . . . . . . . . . . . . . . . . . . . . . . .
1. Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2. Horizontal Shear Force . . . . . . . . . . . . . . . . . . . . .
3. Strength of Stud Shear Connectors . . . . . . . . . . . . . . .
4. Strength of Channel Shear Connectors . . . . . . . . . . . . .
6. Shear-Connector Placement and Spacing . . . . . . . . . . .
I6.
Special Cases . . . . . . . . . . . . . . . . . . . . . . . . . . . .
D.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
6 - 13
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183
191
191
191
191
192
192
192
192
192
193
194
195
195
195
195
199
200
201
201
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202
203
203
204
204
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205
205
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209
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210
212
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213
213
214
214
214
214
215
6 - 14
J.
TABLE OF CONTENTS
CONNECTIONS, JOINTS, AND FASTENERS . . . . . . . . . . . . . . . . . . 216
J1.
General Provisions . . . . . . . . . . . . . . . . . .
5. Splices in Heavy Sections . . . . . . . . . . . .
8. Placement of Welds and Bolts . . . . . . . . . .
9. Bolts in Combination with Welds . . . . . . . .
10. High-Strength Bolts in Combination with Rivets
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216
216
217
217
219
J2.
Welds . . . . . . . . . . .
1. Groove Welds . . . . .
2. Fillet Welds . . . . . .
4. Design Strength . . . .
5. Combination of Welds
7. Mixed Weld Metal . .
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219
219
219
222
223
223
J3.
Bolts and Threaded Parts . . . . . . . . . . . . . . . . . . . .
1. High-Strength Bolts . . . . . . . . . . . . . . . . . . . . .
2. Size and Use of Holes . . . . . . . . . . . . . . . . . . . .
3. Minimum Spacing . . . . . . . . . . . . . . . . . . . . . .
4. Minimum Edge Distance . . . . . . . . . . . . . . . . . . .
5. Maximum Spacing and Edge Distance . . . . . . . . . . . .
6. Design Tension or Shear Strength . . . . . . . . . . . . . .
7. Combined Tension and Shear in Bearing-Type Connections
8. High-Strength Bolts in Slip-Critical Connections . . . . . .
10. Bearing Strength at Bolt Holes . . . . . . . . . . . . . . . .
11. Long Grips . . . . . . . . . . . . . . . . . . . . . . . . . .
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223
223
224
224
224
225
225
226
226
227
228
J4.
Design Rupture Strength . . . . . . . . . . . . . . . . . . . . . . . . . . . 228
J5.
Connecting Elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229
2. Design Strength of Connecting Elements in Tension . . . . . . . . . . . 229
J6.
Fillers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229
J8.
Bearing Strength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 230
J9.
Column Bases and Bearing on Concrete . . . . . . . . . . . . . . . . . . . 230
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J10. Anchor Bolts and Embedments . . . . . . . . . . . . . . . . . . . . . . . . 230
K. CONCENTRATED FORCES, PONDING, AND FATIGUE . . . . . . . . . . . 231
L.
K1.
Flanges and Webs with Concentrated Forces
1. Design Basis . . . . . . . . . . . . . . . .
2. Local Flange Bending . . . . . . . . . . .
3. Local Web Yielding . . . . . . . . . . . . .
4. Web Crippling . . . . . . . . . . . . . . .
5. Sidesway Web Buckling . . . . . . . . . .
6. Compression Buckling of the Web . . . . .
7. Panel-Zone Web Shear . . . . . . . . . . .
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231
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231
231
232
232
233
234
K2.
Ponding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 236
SERVICEABILITY DESIGN CONSIDERATIONS . . . . . . . . . . . . . . . . 239
L1.
Camber . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 240
L2.
Expansion and Contraction . . . . . . . . . . . . . . . . . . . . . . . . . . 240
L3.
Deflections, Vibration, and Drift . . . . . . . . . . . . . . . . . . . . . . . 240
1. Deflections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 240
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
TABLE OF CONTENTS
2. Floor Vibration . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3. Drift . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
L5. Corrosion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
M. FABRICATION, ERECTION, AND QUALITY CONTROL . . . . . . . .
M2. Fabrication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1. Cambering, Curving, and Straightening . . . . . . . . . . . . . . .
2. Thermal Cutting . . . . . . . . . . . . . . . . . . . . . . . . . . .
5. Bolted Construction . . . . . . . . . . . . . . . . . . . . . . . . .
M3. Shop Painting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5. Surfaces Adjacent to Field Welds . . . . . . . . . . . . . . . . . .
M4. Erection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4. Fit of Column Compression Joints and Base Plates . . . . . . . . .
5. Field Welding . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
APPENDIX B. DESIGN REQUIREMENTS . . . . . . . . . . . . . . . . . . .
B5. Local Buckling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1. Classification of Steel Sections . . . . . . . . . . . . . . . . . . .
APPENDIX E. COLUMNS AND OTHER COMPRESSION MEMBERS . . .
E3. Design Compressive Strength for Flexural-Torsional Buckling . . .
APPENDIX F. BEAMS AND OTHER FLEXURAL MEMBERS . . . . . . . .
F1. Design for Flexure . . . . . . . . . . . . . . . . . . . . . . . . . . . .
F3. Web-Tapered Members . . . . . . . . . . . . . . . . . . . . . . . . .
1. General Requirements . . . . . . . . . . . . . . . . . . . . . . . .
3. Design Compressive Strength . . . . . . . . . . . . . . . . . . . .
4. Design Flexural Strength . . . . . . . . . . . . . . . . . . . . . . .
APPENDIX G. PLATE GIRDERS . . . . . . . . . . . . . . . . . . . . . . . . .
G2. Design Flexural Strength . . . . . . . . . . . . . . . . . . . . . . . .
APPENDIX H. MEMBERS UNDER COMBINED FORCES AND TORSION
H3. Alternative Interaction Equations for Members Under
Combined Stress . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
APPENDIX J. CONNECTIONS, JOINTS, AND FASTENERS . . . . . . . . .
J2. Welds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4. Design Strength . . . . . . . . . . . . . . . . . . . . . . . . . . . .
APPENDIX K. CONCENTRATED FORCES, PONDING, AND FATIGUE .
K3. Fatigue . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
GLOSSARY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
6 - 15
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6 - 16
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
6 - 17
Symbols
The section number in parentheses after the definition of a symbol refers to the section
where the symbol is first defined.
A
AB
Ab
Ac
Ac
AD
Ae
Af
Afe
Afg
Afn
Ag
Agt
Agv
An
Ant
Anv
Apb
Ar
As
Asc
Asf
Aw
A1
A2
B
B
B1, B2
CPG
Cb
Cm
Cross-sectional area, in.2 (F1.2)
Loaded area of concrete, in.2 (I2.4)
Nominal body area of a fastener, in.2 (J3.7)
Area of concrete, in.2 (I2.2)
Area of concrete slab within effective width, in.2 (I5.2)
Area of an upset rod based on the major diameter of its threads, in.2 (J3.6)
Effective net area, in.2 (B3)
Area of flange, in.2 (Appendix F3)
Effective tension flange area, in.2 (B10)
Gross area of flange, in.2 (B10)
Net area of flange, in.2 (B10)
Gross area, in.2 (A5)
Gross area subject to tension, in.2 (J4.3)
Gross area subject to shear, in.2 (J4.3)
Net area, in.2 (B2)
Net area subject to tension, in.2 (J4.2)
Net area subject to shear, in.2 (J4.1)
Projected bearing area, in.2 (J8.1)
Area of reinforcing bars, in.2 (I2.2)
Area of steel cross section, in.2 (I2.2)
Cross-sectional area of stud shear connector, in.2 (I5.3)
Shear area on the failure path, in.2 (D3)
Web area, in.2 (F2.1)
Area of steel bearing concentrically on a concrete support, in.2 (J9)
Total cross-sectional area of a concrete support, in.2 (J9)
Factor for bending stress in tees and double angles (F1.2)
Factor for bending stress in web-tapered members, in., defined by Equations A-F3-8 through A-F3-11 (Appendix F3)
Factors used in determining Mu for combined bending and axial forces
when first-order analysis is employed (C1)
Plate-girder coefficient (Appendix G2)
Bending coefficient dependent on moment gradient (F1.2a)
Coefficient applied to bending term in interaction formula for prismatic
members and dependent on column curvature caused by applied moments (C1)
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
6 - 18
Cm′
Cp
Cs
Cv
Cw
D
D
D
E
E
Ec
Em
FBM
FEXX
FL
Fbγ
Fcr
Fcrft, Fcry, Fcrz
Fe
Fex
Fey
Fez
Fmy
Fn
Fr
Fsγ
Fu
Fw
Fwγ
Fy
Fyf
Fyr
Fyst
SYMBOLS
Coefficient applied to bending term in interaction formula for tapered
members and dependent on axial stress at the small end of the member
(Appendix F3)
Ponding flexibility coefficient for primary member in a flat roof (K2)
Ponding flexibility coefficient for secondary member in a flat roof (K2)
Ratio of “critical” web stress, according to linear buckling theory, to the
shear yield stress of web material (Appendix G3)
Warping constant, in.6 (F1.2)
Outside diameter of circular hollow section, in. (Appendix B5.3)
Dead load due to the weight of the structural elements and permanent
features on the structure (A4.1)
Factor used in Equation A-G4-2, dependent on the type of transverse
stiffeners used in a plate girder (Appendix G4)
Modulus of elasticity of steel (E = 29,000 ksi) (E2)
Earthquake load (A4.1)
Modulus of elasticity of concrete, ksi (I2.2)
Modified modulus of elasticity, ksi (I2.2)
Nominal strength of the base material to be welded, ksi (J2.4)
Classification number of weld metal (minimum specified strength), ksi
(J2.4)
Smaller of (Fyf −Fr ) or Fyw, ksi (F1.2)
Flexural stress for tapered members defined by Equations A-F3-4 and
A-F3-5 (Appendix F3)
Critical stress, ksi (E2)
Flexural-torsional buckling stresses for double-angle and tee-shaped
compression members, ksi (E3)
Elastic buckling stress, ksi (Appendix E3)
Elastic flexural buckling stress about the major axis, ksi (Appendix E3)
Elastic flexural buckling stress about the minor axis, ksi (Appendix E3)
Elastic torsional buckling stress, ksi (Appendix E3)
Modified yield stress for composite columns, ksi (I2.2)
Nominal shear rupture strength, ksi (J4)
Compressive residual stress in flange (10 ksi for rolled; 16.5 ksi for
welded), ksi (Table B5.1)
Stress for tapered members defined by Equation A-F3-6, ksi (Appendix F3)
Specified minimum tensile strength of the type of steel being used, ksi
(B10)
Nominal strength of the weld electrode material, ksi (J2.4)
Stress for tapered members defined by Equation A-F3-7, ksi (Appendix F3)
Specified minimum yield stress of the type of steel being used, ksi. As
used in this Specification, “yield stress” denotes either the specified
minimum yield point (for those steels that have a yield point) or specified
yield strength (for those steels that do not have a yield point) (A5)
Specified minimum yield stress of the flange, ksi (Table B5.1)
Specified minimum yield stress of reinforcing bars, ksi (I2.2)
Specified minimum yield stress of the stiffener material, ksi (Appendix
G4)
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
SYMBOLS
Fyw
G
H
H
Hs
I
Id
Ip
Is
Ist
Iyc
J
K
Kz
Kγ
L
L
L
Lb
Lc
Le
Lp
Lp
Lpd
Lr
Lr
Ls
MA
MB
MC
Mcr
Mlt
Mmax
Mn
M′n x , M′n y
6 - 19
Specified minimum yield stress of the web, ksi (Table B5.1)
Shear modulus of elasticity of steel, ksi (G = 11,200) (F1.2)
Horizontal force, kips (C1)
Flexural constant (E3)
Length of stud connector after welding, in. (I3.5)
Moment of inertia, in.4 (F1.2)
Moment of inertia of the steel deck supported on secondary members,
in.4 (K2)
Moment of inertia of primary members, in.4 (K2)
Moment of inertia of secondary members, in.4 (K2)
Moment of inertia of a transverse stiffener, in.4 (Appendix G4)
Moment of inertia about y axis referred to compression flange, or if
reverse curvature bending referred to smaller flange, in.4 (Appendix F1)
Torsional constant for a section, in.4 (F1.2)
Effective length factor for prismatic member (B7)
Effective length factor for torsional buckling (Appendix E3)
Effective length factor for a tapered member (Appendix F3)
Story height, in. (C1)
Length of connection in the direction of loading, in. (B3)
Live load due to occupancy and moveable equipment (A4.1)
Laterally unbraced length; length between points which are either braced
against lateral displacement of compression flange or braced against twist
of the cross section, in. (F1.2)
Length of channel shear connector, in. (I5.4)
Edge distance, in. (J3.10)
Limiting laterally unbraced length for full plastic bending capacity,
uniform moment case (Cb = 1.0), in. (F1.2)
Column spacing in direction of girder, ft (K2)
Limiting laterally unbraced length for plastic analysis, in. (F1.2)
Limiting laterally unbraced length for inelastic lateral-torsional buckling,
in. (F1.2)
Roof live load (A4.1)
Column spacing perpendicular to direction of girder, ft (K2)
Absolute value of moment at quarter point of the unbraced beam segment,
kip-in. (F1.2)
Absolute value of moment at centerline of the unbraced beam segment,
kip-in. (F1.2)
Absolute value of moment at three-quarter point of the unbraced beam
segment, kip-in. (F1.2)
Elastic buckling moment, kip-in. (F1.2)
Required flexural strength in member due to lateral frame translation
only, kip-in. (C1)
Absolute value of maximum moment in the unbraced beam segment,
kip-in. (F1.2)
Nominal flexural strength, kip-in. (F1.1)
Flexural strength defined in Equations A-H3-7 and A-H3-8 for use in
alternate interaction equations for combined bending and axial force,
kip-in. (Appendix H3)
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
6 - 20
Mnt
Mp
Mp′
Mr
Mu
My
M1
M2
N
Nr
Pe1 , Pe2
Pn
Pp
Pu
Py
Q
Qa
Qn
Qs
R
RPG
Re
Rn
Rv
S
S
S
Sx′
Seff
Sxt , Sxc
T
Tb
Tu
U
Vn
SYMBOLS
Required flexural strength in member assuming there is no lateral translation of the frame, kip-in. (C1)
Plastic bending moment, kip-in. (F1.1)
Moment defined in Equations A-H3-5 and A-H3-6, for use in alternate
interaction equations for combined bending and axial force, kip-in.
(Appendix H3)
Limiting buckling moment, Mcr, when λ = λr and Cb = 1.0, kip-in. (F1.2)
Required flexural strength, kip-in. (C1)
Moment corresponding to onset of yielding at the extreme fiber from an
elastic stress distribution (= Fy S for homogeneous sections), kip-in.
(F1.1)
Smaller moment at end of unbraced length of beam or beam-column,
kip-in.
Larger moment at end of unbraced length of beam or beam-column,
kip-in.
Length of bearing, in. (K1.3)
Number of stud connectors in one rib at a beam intersection (I3.5)
Elastic Euler buckling load for braced and unbraced frame, respectively,
kips (C1)
Nominal axial strength (tension or compression), kips (D1)
Bearing load on concrete, kips (J9)
Required axial strength (tension or compression), kips (Table B5.1)
Yield strength, kips (Table B5.1)
Full reduction factor for slender compression elements (Appendix E3)
Reduction factor for slender stiffened compression elements (Appendix
B5)
Nominal strength of one stud shear connector, kips (I5)
Reduction factor for slender unstiffened compression elements (Appendix B5.3)
Load due to initial rainwater or ice exclusive of the ponding contribution
(A4.1)
Plate girder bending strength reduction factor (Appendix G)
Hybrid girder factor (Appendix F1)
Nominal strength (A5.3)
Web shear strength, kips (K1.7)
Elastic section modulus, in.3 (F1.2)
Spacing of secondary members, ft (K2)
Snow load (A4.1)
Elastic section modulus of larger end of tapered member about its major
axis, in.3 (Appendix F3)
Effective section modulus about major axis, in.3 (Appendix F1)
Elastic section modulus referred to tension and compression flanges,
respectively, in.3 (Appendix F1)
Tension force due to service loads, kips (J3.9)
Specified pretension load in high-strength bolt, kips (J3.9)
Required tensile strength due to factored loads, kips (Appendix J3.9b)
Reduction coefficient, used in calculating effective net area (B3)
Nominal shear strength, kips (F2.2)
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
SYMBOLS
Vu
W
X1
X2
Z
a
a
a
ar
a′
b
be
beff
bf
c1, c2, c3
d
d
d
d
dL
db
dc
do
e
f
fb1
fb2
fc′
fo
fun
fuv
fv
g
h
h
hc
6 - 21
Required shear strength, kips (Appendix G4)
Wind load (A4.1)
Beam buckling factor defined by Equation F1-8 (F1.2)
Beam buckling factor defined by Equation F1-9 (F1.2)
Plastic section modulus, in.3 (F1.1)
Clear distance between transverse stiffeners, in. (Appendix F2.2)
Distance between connectors in a built-up member, in. (E4)
Shortest distance from edge of pin hole to edge of member measured
parallel to direction of force, in. (D3)
Ratio of web area to compression flange area (Appendix G2)
Weld length, in. (B10)
Compression element width, in. (B5.1)
Reduced effective width for slender compression elements, in. (Appendix B5.3)
Effective edge distance, in. (D3)
Flange width, in. (B5.1)
Numerical coefficients (I2.2)
Nominal fastener diameter, in. (J3.3)
Overall depth of member, in. (B5.1)
Pin diameter, in. (D3)
Roller diameter, in. (J8.2)
Depth at larger end of unbraced tapered segment, in. (Appendix F3)
Beam depth, in. (K1.7)
Column depth, in. (K1.7)
Depth at smaller end of unbraced tapered segment, in. (Appendix F3)
Base of natural logarithm = 2.71828. . .
Computed compressive stress in the stiffened element, ksi (Appendix
B5.3)
Smallest computed bending stress at one end of a tapered segment, ksi
(Appendix F3)
Largest computed bending stress at one end of a tapered segment, ksi
(Appendix F3)
Specified compressive strength of concrete, ksi (I2.2)
Stress due to 1.2D + 1.2R, ksi (Appendix K2)
Required normal stress, ksi (H2)
Required shear stress, ksi (H2)
Required shear stress due to factored loads in bolts or rivets, ksi (J3.7)
Transverse center-to-center spacing (gage) between fastener gage lines,
in. (B2)
Clear distance between flanges less the fillet or corner radius for rolled
shapes; and for built-up sections, the distance between adjacent lines of
fasteners or the clear distance between flanges when welds are used,
in. (B5.1)
Distance between centroids of individual components perpendicular to
the member axis of buckling, in. (E4)
Twice the distance from the centroid to the following: the inside face of
the compression flange less the fillet or corner radius, for rolled shapes;
the nearest line of fasteners at the compression flange or the inside faces
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
6 - 22
hr
hs
hw
j
k
kv
l
l
l
l
m
r
rTo
ri
rib
rm
_
ro
rox , roy
rx, ry
ryc
s
t
tf
tf
tw
tw
w
w
wr
x
_xo, yo
x
y
z
SYMBOLS
of the compression flange when welds are used, for built-up sections,
in., (B5.1)
Nominal rib height, in. (I3.5)
Factor used in Equation A-F3-6 for web-tapered members (Appendix F3)
Factor used in Equation A-F3-7 for web-tapered members (Appendix F3)
Factor defined by Equation A-F2-4 for minimum moment of inertia for
a transverse stiffener (Appendix F2.3)
Distance from outer face of flange to web toe of fillet, in. (K1.3)
Web plate buckling coefficient (Appendix F2.2)
Laterally unbraced length of member at the point of load, in. (B7)
Length of bearing, in. (J8.2)
Length of connection in the direction of loading, in. (B3)
Length of weld, in. (B3)
Ratio of web to flange yield stress or critical stress in hybrid beams
(Appendix G2)
Governing radius of gyration, in. (B7)
For the smaller end of a tapered member, the radius of gyration, considering only the compression flange plus one-third of the compression web
area, taken about an axis in the plane of the web, in. (Appendix F3.4)
Minimum radius of gyration of individual component in a built-up
member, in. (E4)
Radius of gyration of individual component relative to centroidal axis
parallel to member axis of buckling, in. (E4)
Radius of gyration of the steel shape, pipe, or tubing in composite
columns. For steel shapes it may not be less than 0.3 times the overall
thickness of the composite section, in. (I2)
Polar radius of gyration about the shear center, in. (E3)
Radius of gyration about x and y axes at the smaller end of a tapered
member, respectively, in. (Appendix F3.3)
Radius of gyration about x and y axes, respectively, in. (E3)
Radius of gyration about y axis referred to compression flange, or if
reverse curvature bending, referred to smaller flange, in. (Appendix F1)
Longitudinal center-to-center spacing (pitch) of any two consecutive
holes, in. (B2)
Thickness of connected part, in. (D3)
Flange thickness, in. (B5.1)
Flange thickness of channel shear connector, in. (I5.4)
Web thickness of channel shear connector, in. (I5.4)
Web thickness, in. (B5.3)
Plate width; distance between welds, in. (B3)
Unit weight of concrete, lbs/cu ft. (I2)
Average width of concrete rib or haunch, in. (I3.5)
Subscript relating symbol to strong axis bending
Coordinates of the shear center with respect to the centroid, in. (E3)
Connection eccentricity, in. (B3)
Subscript relating symbol to weak axis bending
Distance from the smaller end of tapered member used in Equation
A-F3-1 for the variation in depth, in. (Appendix F3)
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
SYMBOLS
α
∆oh
γ
ζ
η
λc
λe
λeff
λp
λr
φ
φb
φc
φc
φsf
φt
φv
6 - 23
h
(E4)
2rib
Translation deflection of the story under consideration, in. (C1)
Depth tapering ratio (Appendix F3). Subscript for tapered members
(Appendix F3)
Exponent for alternate beam-column interaction equation (Appendix H3)
Exponent for alternate beam-column interaction equation (Appendix H3)
Column slenderness parameter (C1)
Equivalent slenderness parameter (Appendix E3)
Effective slenderness ratio defined by Equation A-F3-2 (Appendix F3)
Limiting slenderness parameter for compact element (B5.1)
Limiting slenderness parameter for noncompact element (B5.1)
Resistance factor (A5.3)
Resistance factor for flexure (F1)
Resistance factor for compression (A5)
Resistance factor for axially loaded composite columns (I2.2)
Resistance factor for shear on the failure path (D3)
Resistance factor for tension (D1)
Resistance factor for shear (F2.2)
Separation ratio for built-up compression members =
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
6 - 24
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
6 - 25
CHAPTER A
GENERAL PROVISIONS
A1. SCOPE
The Load and Resistance Factor Design Specification for Structural Steel
Buildings governs the design, fabrication, and erection of steel-framed buildings. As an alternative, the AISC Specification for Structural Steel Buildings,
Allowable Stress Design and Plastic Design is permitted.
A2. LIMITS OF APPLICABILITY
1.
Structural Steel Defined
As used in this Specification, the term structural steel refers to the steel elements
of the structural steel frame essential to the support of the required loads. Such
elements are enumerated in Section 2.1 of the AISC Code of Standard Practice
for Steel Buildings and Bridges. For the design of cold-formed steel structural
members, whose profiles contain rounded corners and slender flat elements, the
provisions of the American Iron and Steel Institute Load and Resistance Factor
Design Specification for the Design of Cold-Formed Steel Structural Members
are recommended.
2.
Types of Construction
Two basic types of construction and associated design assumptions are permissible under the conditions stated herein, and each will govern in a specific
manner the strength of members and the types and strength of their connections.
Type FR (fully restrained), commonly designated as “rigid-frame” (continuous
frame), assumes that connections have sufficient rigidity to maintain the angles
between intersecting members.
Type PR (partially restrained) assumes that connections have insufficient rigidity to maintain the angles between intersecting members.
The type of construction assumed in the design shall be indicated on the design
documents. The design of all connections shall be consistent with the
assumption.
Type PR construction under this Specification depends upon a predictable
proportion of full end restraint. When a portion of the full end restraint of
members is used in the design for strength of the connected members or for the
stability of the structure as a whole, the capacity of the connections to provide
the needed restraint shall be documented in the technical literature or established
by analytical or empirical means.
When the connection restraint is ignored, commonly designated “simple framAMERICAN INSTITUTE OF STEEL CONSTRUCTION
6 - 26
GENERAL PROVISIONS
[Chap. A
ing,” it is assumed that for the transmission of gravity loads the ends of the beams
and girders are connected for shear only and are free to rotate. For “simple
framing” the following requirements apply:
(1) The connections and connected members shall be adequate to resist the
factored gravity loads as “simple beams.”
(2) The connections and connected members shall be adequate to resist the
factored lateral loads.
(3) The connections shall have sufficient inelastic rotation capacity to avoid
overload of fasteners or welds under combined factored gravity and lateral
loading.
Type PR construction may necessitate some inelastic, but self-limiting, deformation of a structural steel part.
A3. MATERIAL
1.
Structural Steel
1a.
ASTM Designations
Material conforming to one of the following standard specifications is approved
for use under this Specification:
Structural Steel, ASTM A36
Pipe, Steel, Black and Hot-Dipped, Zinc-Coated Welded and Seamless ASTM
A53, Gr. B
High-Strength Low-Alloy Structural Steel, ASTM A242
Cold-Formed Welded and Seamless Carbon Steel Structural Tubing in
Rounds and Shapes, ASTM A500
Hot-Formed Welded and Seamless Carbon Steel Structural Tubing, ASTM
A501
High-Yield-Strength, Quenched and Tempered Alloy Steel Plate, Suitable for
Welding, ASTM A514
High-Strength Carbon-Manganese Steel of Structural Quality, ASTM A529
Steel, Sheet and Strip, Carbon, Hot-Rolled, Structural Quality, ASTM A570,
Gr. 40, 45, and 50
High-Strength Low-Alloy Columbium-Vanadium Steels of Structural Quality, ASTM A572
High-Strength Low-Alloy Structural Steel with 50 ksi Minimum Yield Point
to 4-in. Thick, ASTM A588
Steel, Sheet and Strip, High-Strength, Low-Alloy, Hot-Rolled and ColdRolled, with Improved Atmospheric Corrosion Resistance, ASTM A606
Steel, Sheet and Strip, High-Strength, Low-Alloy, Columbium or Vanadium,
or Both, Hot-Rolled and Cold-Rolled, ASTM A607
Hot-Formed Welded and Seamless High-Strength Low-Alloy Structural Tubing, ASTM A618
Structural Steel for Bridges, ASTM A709
Quenched and Tempered Low-Alloy Structural Steel Plate with 70 ksi Minimum Yield Strength to 4-in. Thick, ASTM A852
Certified mill test reports or certified reports of tests made by the fabricator or
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
Sect. A3]
MATERIAL
6 - 27
a testing laboratory in accordance with ASTM A6 or A568, as applicable, shall
constitute sufficient evidence of conformity with one of the above ASTM
standards. If requested, the fabricator shall provide an affidavit stating that the
structural steel furnished meets the requirements of the grade specified.
1b.
Unidentified Steel
Unidentified steel, if surface conditions are acceptable according to criteria
contained in ASTM A6, may be used for unimportant members or details, where
the precise physical properties and weldability of the steel would not affect the
strength of the structure.
1c.
Heavy Shapes
For ASTM A6 Group 4 and 5 rolled shapes to be used as members subject to
primary tensile stresses due to tension or flexure, toughness need not be
specified if splices are made by bolting. If such members are spliced using
complete-joint penetration welds, the steel shall be specified in the contract
documents to be supplied with Charpy V-Notch testing in accordance with
ASTM A6, Supplementary Requirement S5. The impact test shall meet a
minimum average value of 20 ft-lbs. absorbed energy at +70°F and shall be
conducted in accordance with ASTM A673 with the following exceptions:
(1) The center longitudinal axis of the specimens shall be located as near as
practical to midway between the inner flange surface and the center of the
flange thickness at the intersection with the web mid-thickness.
(2) Tests shall be conducted by the producer on material selected from a location
representing the top of each ingot or part of an ingot used to produce the
product represented by these tests.
For plates exceeding 2-in. thick used for built-up cross-sections with bolted
splices and subject to primary tensile stresses due to tension or flexure, material
toughness need not be specified. If such cross-sections are spliced using complete-joint penetration welds, the steel shall be specified in the contract documents to be supplied with Charpy V-Notch testing in accordance with ASTM
A6, Supplementary Requirement S5. The impact test shall be conducted by the
producer in accordance with ASTM A673, Frequency P, and shall meet a
minimum average value of 20 ft-lbs. absorbed energy at +70°F.
The above supplementary requirements also apply when complete-joint penetration welded joints through the thickness of ASTM A6 Group 4 and 5 shapes
and built-up cross sections with thickness exceeding two inches are used in
connections subjected to primary tensile stress due to tension or flexure of such
members. The requirements need not apply to ASTM A6 Group 4 and 5 shapes
and built-up members with thickness exceeding two inches to which members
other than ASTM A6 Group 4 and 5 shapes and built-up members are connected
by complete-joint penetration welded joints through the thickness of the thinner
material to the face of the heavy material.
Additional requirements for joints in heavy rolled and built-up members are
given in Sections J1.5, J1.6, J2, and M2.2.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
6 - 28
2.
GENERAL PROVISIONS
[Chap. A
Steel Castings and Forgings
Cast steel shall conform to one of the following standard specifications:
Mild-to-Medium-Strength Carbon-Steel Castings for General Applications,
ASTM A27, Gr. 65-35
High-Strength Steel Castings for Structural Purposes, ASTM A148 Gr. 80-50
Steel forgings shall conform to the following standard specification:
Steel Forgings Carbon and Alloy for General Industrial Use, ASTM A668
Certified test reports shall constitute sufficient evidence of conformity with
standards.
3.
Bolts, Washers, and Nuts
Steel bolts, washers, and nuts shall conform to one of the following standard
specifications:
Carbon and Alloy Steel Nuts for Bolts for High-Pressure and High-Temperature Service, ASTM A194
Carbon Steel Bolts and Studs, 60,000 psi Tensile Strength, ASTM A307
Structural Bolts, Steel, Heat-Treated, 120/105 ksi Minimum Tensile Strength,
ASTM A325
Quenched and Tempered Steel Bolts and Studs, ASTM A449
Heat-Treated Steel Structural Bolts, 150 ksi Min. Tensile Strength, ASTM
A490
Carbon and Alloy Steel Nuts, ASTM A563
Hardened Steel Washers, ASTM F436
A449 bolts are permitted to be used only in connections requiring bolt diameters
greater than 11⁄2-in. and shall not be used in slip-critical connections.
Manufacturer’s certification shall constitute sufficient evidence of conformity
with the standards.
4.
Anchor Bolts and Threaded Rods
Anchor bolt and threaded rod steel shall conform to one of the following
standard specifications:
Structural Steel, ASTM A36
Alloy Steel and Stainless Steel Bolting Materials for High-Temperature
Service, ASTM A193
Quenched and Tempered Alloy Steel Bolts, Studs and Other Externally
Threaded Fasteners, ASTM A354
High-Strength Low-Alloy Columbium-Vanadium Steels of Structural Quality, ASTM A572
High-Strength Low-Alloy Structural Steel with 50,000 psi Minimum Yield
Point to 4-in. Thick, ASTM A588
High-Strength Nonheaded Steel Bolts and Studs, ASTM A687
Threads on bolts and rods shall conform to the Unified Standard Series of ANSI
B18.1 and shall have Class 2A tolerances.
Steel bolts conforming to other provisions of Section A3.3 are permitted as
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
Sect. A4]
LOADS AND LOAD COMBINATIONS
6 - 29
anchor bolts. A449 material is acceptable for high-strength anchor bolts and
threaded rods of any diameter.
Manufacturer’s certification shall constitute sufficient evidence of conformity
with the standards.
5.
Filler Metal and Flux for Welding
Welding electrodes and fluxes shall conform to one of the following specifications of the American Welding Society:
Specification for Carbon Steel Electrodes for Shield Metal Arc Welding, AWS
A5.1
Specification for Low-Alloy Steel Covered Arc Welding Electrodes, AWS
A5.5
Specification for Carbon Steel Electrodes and Fluxes for Submerged Arc
Welding, AWS A5.17
Specification for Carbon Steel Filler Metals for Gas Shielded Arc Welding,
AWS A5.18
Specification for Carbon Steel Electrodes for Flux Cored Arc Welding, AWS
A5.20
Specification for Low-Alloy Steel Electrodes and Fluxes for Submerged Arc
Welding, AWS A5.23
Specification for Low-Alloy Steel Filler Metals for Gas Shielded Arc Welding, AWS A5.28
Specification for Low-Alloy Steel Electrodes for Flux Cored Arc Welding,
AWS A5.29
Manufacturer’s certification shall constitute sufficient evidence of conformity
with the standards. Electrodes (filler metals) that are suitable for the intended
application shall be selected. Weld metal notch toughness is generally not critical
for building construction.
6.
Stud Shear Connectors
Steel stud shear connectors shall conform to the requirements of Structural
Welding Code—Steel, AWS D1.1.
Manufacturer’s certification shall constitute sufficient evidence of conformity
with the code.
A4. LOADS AND LOAD COMBINATIONS
The nominal loads shall be the minimum design loads stipulated by the applicable code under which the structure is designed or dictated by the conditions
involved. In the absence of a code, the loads and load combinations shall be
those stipulated in the American Society of Civil Engineers Standard Minimum
Design Loads for Buildings and Other Structures, ASCE 7. For design purposes,
the loads stipulated by the applicable code shall be taken as nominal loads. For
ease of reference, the more common ASCE load combinations are listed in the
following section.
Seismic design of buildings assigned to the higher risk Seismic Performance
Categories defined in the AISC Seismic Provisions for Structural Steel Buildings
shall comply with that document. Seismic design not covered by the AISC
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
6 - 30
GENERAL PROVISIONS
[Chap. A
Seismic Provisions for Structural Steel Buildings shall be in accordance with
this Specification.
1.
Loads, Load Factors, and Load Combinations
The following nominal loads are to be considered:
D : dead load due to the weight of the structural elements and the permanent
features on the structure
L : live load due to occupancy and moveable equipment
Lr : roof live load
W : wind load
S : snow load
E : earthquake load determined in accordance with Part I of the AISC
Seismic Provisions for Structural Steel Buildings
R : load due to initial rainwater or ice exclusive of the ponding contribution
The required strength of the structure and its elements must be determined from
the appropriate critical combination of factored loads. The most critical effect
may occur when one or more loads are not acting. The following load combinations and the corresponding load factors shall be investigated:
1.4D
(A4-1)
1.2D + 1.6L + 0.5(Lr or S or R)
(A4-2)
1.2D + 1.6(Lr or S or R) + (0.5L or 0.8W)
(A4-3)
1.2D + 1.3W + 0.5L + 0.5(Lr or S or R)
(A4-4)
1.2D ± 1.0E + 0.5L + 0.2S
(A4-5)
0.9D ± (1.3W or 1.0E)
(A4-6)
Exception: The load factor on L in combinations A4-3, A4-4, and A4-5 shall
equal 1.0 for garages, areas occupied as places of public assembly, and all areas
where the live load is greater than 100 psf.
2.
Impact
For structures carrying live loads which induce impact, the assumed nominal
live load shall be increased to provide for this impact in combinations A4-2 and
A4-3.
If not otherwise specified, the increase shall be:
For supports of elevators and elevator machinery . . . . . . . . . . . . . . . . . . 100%
For supports of light machinery, shaft or motor driven, not less than . . . . 20%
For supports of reciprocating machinery or power driven units,
not less than. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50%
For hangers supporting floors and balconies . . . . . . . . . . . . . . . . . . . . . . . 33%
For cab-operated traveling crane support girders and their
connections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25%
For pendant-operated traveling crane support girders and their
connections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10%
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
Sect. A5]
3.
DESIGN BASIS
6 - 31
Crane Runway Horizontal Forces
The nominal lateral force on crane runways to provide for the effect of moving
crane trolleys shall be a minimum of 20 percent of the sum of weights of the
lifted load and of the crane trolley, but exclusive of other parts of the crane. The
force shall be assumed to be applied at the top of the rails, acting in either
direction normal to the runway rails, and shall be distributed with due regard for
lateral stiffness of the structure supporting the rails.
The nominal longitudinal force shall be a minimum of 10 percent of the
maximum wheel loads of the crane applied at the top of the rail, unless otherwise
specified.
A5. DESIGN BASIS
1.
Required Strength at Factored Loads
The required strength of structural members and connections shall be determined by structural analysis for the appropriate factored load combinations
given in Section A4.
Design by either elastic or plastic analysis is permitted, except that design by
plastic analysis is permitted only for steels with specified yield stresses not
exceeding 65 ksi and is subject to provisions of Sections B5.2, C2, E1.2, F1.2d,
H1, and I1.
Beams and girders composed of compact sections, as defined in Section B5.1,
and satisfying the unbraced length requirements of Section F1.2d (including
composite members) which are continuous over supports or are rigidly framed
to columns may be proportioned for nine-tenths of the negative moments
produced by gravity loading at points of support, provided that the maximum
positive moment is increased by one-tenth of the average negative moments.
This reduction is not permitted for hybrid beams, members of A514 steel, or
moments produced by loading on cantilevers. If the negative moment is resisted
by a column rigidly framed to the beam or girder, the one-tenth reduction may
be used in proportioning the column for combined axial force and flexure,
provided that the axial force does not exceed φc times 0.15AgFy,
where
Ag = gross area, in.2
Fy = specified minimum yield stress, ksi
φc = resistance factor for compression
2.
Limit States
LRFD is a method of proportioning structures so that no applicable limit state
is exceeded when the structure is subjected to all appropriate factored load
combinations.
Strength limit states are related to safety and concern maximum load carrying
capacity. Serviceability limit states are related to performance under normal
service conditions. The term “resistance” includes both strength limit states and
serviceability limit states.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
6 - 32
3.
GENERAL PROVISIONS
[Chap. A
Design for Strength
The design strength of each structural component or assemblage must equal or
exceed the required strength based on the factored loads. The design strength
φRn for each applicable limit state is calculated as the nominal strength Rn
multiplied by a resistance factor φ.
The required strength is determined for each applicable load combination as
stipulated in Section A4.
Nominal strengths Rn and resistance factors φ are given in Chapters D through K.
4.
Design for Serviceability and Other Considerations
The overall structure and the individual members, connections, and connectors
shall be checked for serviceability. Provisions for design for serviceability are
given in Chapter L.
A6. REFERENCED CODES AND STANDARDS
The following documents are referenced in this Specification:
American National Standards Institute
ANSI B18.1-72
American Society of Civil Engineers
ASCE 7-88
American Society for Testing and Materials
ASTM A6-91b
ASTM A27-87
ASTM A53-88
ASTM A148-84
ASTM A194-91
ASTM A242-91a
ASTM A325-91c
ASTM A354-91
ASTM A490-91
ASTM A500-90a
ASTM A502-91
ASTM A514-91
ASTM A563-91c
ASTM A570-91
ASTM A588-91a
ASTM A606-91a
ASTM A618-90a
ASTM A668-85a
ASTM A709-91
ASTM A852-91
ASTM C330-89
ASTM F436-91
American Welding Society
AWS D1.1-92
AWS A5.1-91
AWS A5.17-89
AWS A5.18-79
AWS A5.23-90
AWS A5.28-79
ASTM A36-91
ASTM A193-91
ASTM A307-91
ASTM A449-91a
ASTM A501-89
ASTM A529-89
ASTM A572-91
ASTM A607-91
ASTM A687-89
ASTM C33-90
AWS A5.5-81
AWS A5.20-79
AWS A5.29-80
Research Council on Structural Connections
Load and Resistance Factor Design Specification for Structural Joints Using
ASTM A325 or A490 Bolts, 1988
American Iron and Steel Institute
Load and Resistance Factor Design Specification for Cold-Formed Steel Members, 1991
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
Sect. A7]
DESIGN DOCUMENTS
6 - 33
American Institute of Steel Construction, Inc.
Code of Standard Practice for Steel Buildings and Bridges, 1992
Seismic Provisions for Structural Steel Buildings, 1992
Specification for Load and Resistance Factor Design of Single-Angle Members,
1993
A7. DESIGN DOCUMENTS
1.
Plans
The design plans shall show a complete design with sizes, sections, and relative
locations of the various members. Floor levels, column centers and offsets shall
be dimensioned. Drawings shall be drawn to a scale large enough to show the
information clearly.
Design documents shall indicate the type or types of construction as defined in
Section A2.2 and include the required strengths (moments and forces) if necessary for preparation of shop drawings.
Where joints are to be assembled with high-strength bolts, the design documents
shall indicate the connection type (i.e., snug-tight bearing, fully-tensioned
bearing, direct tension, or slip-critical).
Camber of trusses, beams, and girders, if required, shall be specified in the
design documents. The requirements for stiffeners and bracing shall be shown
in the design documents.
2.
Standard Symbols and Nomenclature
Welding and inspection symbols used on plans and shop drawings shall be the
American Welding Society symbols. Welding symbols for special requirements
not covered by AWS is permitted to be used provided a complete explanation
thereof is shown in the design documents.
3.
Notation for Welding
Weld lengths called for in the design documents and on the shop drawings shall
be the net effective lengths.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
6 - 34
CHAPTER B
DESIGNREQUIREMENTS
REQUIREMENTS
DESIGN
This chapter contains provisions which are common to the Specification as a whole.
B1. GROSS AREA
The gross area Ag of a member at any point is the sum of the products of the
thickness and the gross width of each element measured normal to the axis of
the member. For angles, the gross width is the sum of the widths of the legs less
the thickness.
B2. NET AREA
The net area An of a member is the sum of the products of the thickness and the
net width of each element computed as follows:
In computing net area for tension and shear, the width of a bolt hole shall be
taken as 1⁄16-in. greater than the nominal dimension of the hole.
For a chain of holes extending across a part in any diagonal or zigzag line, the
net width of the part shall be obtained by deducting from the gross width the
sum of the diameters or slot dimensions as provided in Section J3.2, of all holes
in the chain, and adding, for each gage space in the chain, the quantity s2 / 4g
where
s = longitudinal center-to-center spacing (pitch) of any two consecutive
holes, in.
g = transverse center-to-center spacing (gage) between fastener gage lines, in.
For angles, the gage for holes in opposite adjacent legs shall be the sum of the
gages from the back of the angles less the thickness.
In determining the net area across plug or slot welds, the weld metal shall not
be considered as adding to the net area.
B3. EFFECTIVE NET AREA FOR TENSION MEMBERS
The effective net area for tension members shall be determined as follows:
1. When a tension load is transmitted directly to each of the cross-sectional
elements by fasteners or welds, the effective net area Ae is equal to the net
area An.
2. When a tension load is transmitted by bolts or rivets through some but not
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
Sect. B4]
STABILITY
6 - 35
all of the cross-sectional elements of the member, the effective net area Ae
shall be computed as:
Ae = AU
(B3-1)
where
A
U
_
x
L
= area as defined below
= reduction
coefficient
_
= 1 − (x / L) ≤ 0.9 or as defined in B3c or B3d
= connection eccentricity, in.
= length of connection in the directions of loading, in.
(B3-2)
Larger values of U are permitted to be used when justified by tests or other
rational criteria.
(a) When the tension load is transmitted only by bolts or rivets:
A = An
= net area of member, in.2
(b) When the tension load is transmitted only by longitudinal welds to other than
a plate member or by longitudinal welds in combination with transverse
welds:
A = Ag
= gross area of member, in.2
(c) When the tension load is transmitted only by transverse welds:
A = area of directly connected elements, in.2
U = 1.0
(d) When the tension load is transmitted to a plate by longitudinal welds along
both edges at the end of the plate for l ≥ w:
A = area of plate, in.2
For l ≥ 2w . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . U = 1.00
For 2w > l ≥ 1.5w . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . U = 0.87
For 1.5w > l ≥ w . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . U = 0.75
where
l = length of weld, in.
w = plate width (distance between welds), in.
For effective area of connecting elements, see Section J5.2.
B4. STABILITY
General stability shall be provided for the structure as a whole and for each of
its elements.
Consideration shall be given to the significant effects of the loads on the
deflected shape of the structure and its individual elements.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
6 - 36
DESIGN REQUIREMENTS
[Chap. B
B5. LOCAL BUCKLING
1.
Classification of Steel Sections
Steel sections are classified as compact, noncompact, or slender-element sections. For a section to qualify as compact, its flanges must be continuously
connected to the web or webs and the width-thickness ratios of its compression
elements must not exceed the limiting width-thickness ratios λp from Table B5.1.
If the width-thickness ratio of one or more compression elements exceeds λp,
but does not exceed λr, the section is noncompact. If the width-thickness ratio
of any element exceeds λr from Table B5.1, the section is referred to as a
slender-element compression section.
For unstiffened elements which are supported along only one edge parallel to
the direction of the compression force, the width shall be taken as follows:
(a) For flanges of I-shaped members and tees, the width b is half the full-flange
width, bf .
(b) For legs of angles and flanges of channels and zees, the width b is the full
nominal dimension.
(c) For plates, the width b is the distance from the free edge to the first row of
fasteners or line of welds.
(d) For stems of tees, d is taken as the full nominal depth.
For stiffened elements which are supported along two edges parallel to the
direction of the compression force, the width shall be taken as follows:
(a) For webs of rolled or formed sections, h is the clear distance between flanges
less the fillet or corner radius at each flange; hc is twice the distance from
the centroid to the inside face of the compression flange less the fillet or
corner radius.
(b) For webs of built-up sections, h is the distance between adjacent lines of
fasteners or the clear distance between flanges when welds are used, and
hc is twice the distance from the centroid to the nearest line of fasteners at
the compression flange or the inside face of the compression flange when
welds are used.
(c) For flange or diaphragm plates in built-up sections, the width b is the distance
between adjacent lines of fasteners or lines of welds.
(d) For flanges of rectangular hollow structural sections, the width b is the clear
distance between webs less the inside corner radius on each side. If the corner
radius is not known, the width may be taken as the total section width minus
three times the thickness.
For tapered flanges of rolled sections, the thickness is the nominal value halfway
between the free edge and the corresponding face of the web.
2.
Design by Plastic Analysis
Design by plastic analysis is permitted when flanges subject to compression
involving hinge rotation and all webs have a width-thickness ratio less than or
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
Sect. B10]
PROPORTIONS OF BEAMS AND GIRDERS
6 - 37
equal to the limiting λp from Table B5.1. For circular hollow sections see
Footnote d of Table B5.1.
Design by plastic analysis is subject to the limitations in Section A5.1.
3.
Slender-Element Compression Sections
For the flexural design of I-shaped sections, channels and rectangular or circular
sections with slender flange elements, see Appendix F1. For other shapes in
flexure or members in axial compression that have slender compression elements, see Appendix B5.3. For plate girders with slender web elements, see
Appendix G.
B6. BRACING AT SUPPORTS
At points of support for beams, girders and trusses, restraint against rotation
about their longitudinal axis shall be provided.
B7. LIMITING SLENDERNESS RATIOS
For members in which the design is based on compression, the slenderness ratio
Kl / r preferably should not exceed 200.
For members in which the design is based on tension, the slenderness ratio
l / r preferably should not exceed 300. The above limitation does not apply to
rods in tension. Members in which the design is dictated by tension loading, but
which may be subject to some compression under other load conditions, need
not satisfy the compression slenderness limit.
B8. SIMPLE SPANS
Beams, girders and trusses designed on the basis of simple spans shall have an
effective length equal to the distance between centers of gravity of the members
to which they deliver their end reactions.
B9. END RESTRAINT
When designed on the assumption of full or partial end restraint due to continuous, semicontinuous, or cantilever action, the beams, girders, and trusses, as
well as the sections of the members to which they connect, shall be designed to
carry the factored forces and moments so introduced, as well as all other factored
forces, without exceeding the design strengths prescribed in Chapters D through
K, except that some inelastic but self-limiting deformation of a part of the
connection is permitted.
B10. PROPORTIONS OF BEAMS AND GIRDERS
Rolled or welded shapes, plate girders and cover-plated beams shall, in general,
be proportioned by the moment of inertia of the gross section. No deduction
shall be made for bolt or rivet holes in either flange provided that
0.75Fu Afn ≥ 0.9Fy Afg
(B10-1)
where Afg is the gross flange area and Afn is the net flange area calculated in
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
6 - 38
DESIGN REQUIREMENTS
[Chap. B
TABLE B5.1
Limiting Width-Thickness Ratios for
Compression Elements
λp
(compact)
λr
(non compact)
Flanges of I-shaped rolled
beams and channels in flexure
b/t
65 / √
Fy [c]
141 / √
Fy − 10
Flanges of I-shaped hybrid or
welded beams in flexure
b/t
65 / √
Fyf
162
[f]
√
(Fyf − 16.5) / kc
Flanges projecting from built-up
compression members
b/t
NA
109 / √
Fy / kc [f]
Outstanding legs of pairs of
angles in continuous contact,
flanges of channels in axial
compression; angles and plates
projecting from beams or
compression members
b/t
NA
95 / √
Fy
Legs of single angle struts; legs
of double angle struts with
separators; unstiffened
elements, i.e., supported along
one edge
b/t
NA
76 / √
Fy
Stems of tees
d/t
NA
127 / √
Fy
Description of Element
Unstiffened Elements
Limiting WidthThickness Ratios
Width
Thickness
Ratio
accordance with the provisions of Sections B1 and B2 and Fu is the specified
minimum tensile strength.
If
0.75Fu Afn < 0.9Fy Afg
(B10-2)
the member flexural properties shall be based on an effective tension flange area
Afe
Afe =
5 Fu
A
6 Fy fn
(B10-3)
Hybrid girders may be proportioned by the moment of inertia of their gross
section, subject to the applicable provisions in Appendix G1, provided they are
not required to resist an axial force greater than φb times 0.15Fyf Ag, where Fyf is
the specified yield stress of the flange material and Ag is the gross area. No limit
is placed on the web stresses produced by the applied bending moment for which
a hybrid girder is designed, except as provided in Section K3 and Appendix K3.
To qualify as hybrid girders, the flanges at any given section shall have the same
cross-sectional area and be made of the same grade of steel.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
Sect. B10]
PROPORTIONS OF BEAMS AND GIRDERS
6 - 39
TABLE B5.1 (cont.)
Limiting Width-Thickness Ratios for
Compression Elements
λp
(compact)
λr
(non compact)
Flanges of square and
rectangular box and hollow
structural sections of uniform
thickness subject to bending or
compression; flange cover
plates and diaphragm plates
between lines of fasteners or
welds
b/t
190 / √
Fy
238 / √
Fy
Unsupported width of cover
plates perforated with a
succession of access holes [b]
b/t
NA
317 / √
Fy
Webs in flexural compression [a]
h / tw
640 / √
Fy [c]
970 / √
Fy [g]
Webs in combined flexural and
axial compression
h / tw
for Pu / φbPy ≤ 0.125 [c]
2.75Pu
640
1−
FY
√
φbPy
[g]
Description of Element
Stiffened Elements
Limiting WidthThickness Ratios
Width
Thickness
Ratio
for Pu / φbPy > 0.125 [c]
Pu 253
191
≥
2.33 −
FY
√
φbPy √Fy
Pu
970
1 − 0.74
φbPy
FY
√
253 / √
Fy
All other uniformly compressed
stiffened elements, i.e.,
supported along two edges
b/t
h / tw
Circular hollow sections
In axial compression
In flexure
D/t
[a] For hybrid beams, use the yield
strength of the flange Fyf instead
of Fy
[b] Assumes net area of plate at
widest hole.
[c] Assumes an inelastic rotation
capacity of 3. For structures in
zones of high seismicity, a greater
rotation capacity may be required.
[d] For plastic design use 1,300 / Fy.
[e] Fr = compressive residual stress in flange
= 10 ksi for rolled shapes
= 16.5 ksi for welded shapes
4
[f] kc =
but not less than 0.35 ≤ kc ≤ 0.763
√
h / tw
[g] For members with unequal flanges, see Appendix B5.1.
Fy is the specified minimum yield stress of the type of
steel being used.
NA
[d]
NA
2,070 / Fy
3,300 / Fy
8,970 / Fy
Flanges of welded beams or girders may be varied in thickness or width by
splicing a series of plates or by the use of cover plates.
The total cross-sectional area of cover plates of bolted or riveted girders shall
not exceed 70 percent of the total flange area.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
6 - 40
DESIGN REQUIREMENTS
[Chap. B
High-strength bolts, rivets, or welds connecting flange to web, or cover plate to
flange, shall be proportioned to resist the total horizontal shear resulting from
the bending forces on the girder. The longitudinal distribution of these bolts,
rivets, or intermittent welds shall be in proportion to the intensity of the shear.
However, the longitudinal spacing shall not exceed the maximum permitted for
compression or tension members in Section E4 or D2, respectively. Bolts, rivets,
or welds connecting flange to web shall also be proportioned to transmit to the
web any loads applied directly to the flange, unless provision is made to transmit
such loads by direct bearing.
Partial length cover plates shall be extended beyond the theoretical cutoff point
and the extended portion shall be attached to the beam or girder by high-strength
bolts in a slip-critical connection, rivets, or fillet welds. The attachment shall be
adequate, at the applicable design strength given in Sections J2.2, J3.8, or K3
to develop the cover plate’s portion of the flexural design strength in the beam
or girder at the theoretical cutoff point.
For welded cover plates, the welds connecting the cover plate termination to the
beam or girder in the length a′, defined below, shall be adequate, at the applicable
design strength, to develop the cover plate’s portion of the design strength in the
beam or girder at the distance a′ from the end of the cover plate. The length a′,
measured from the end of the cover plate, shall be:
(a) A distance equal to the width of the cover plate when there is a continuous
weld equal to or larger than three-fourths of the plate thickness across the
end of the plate and continuous welds along both edges of the cover plate in
the length a′.
(b) A distance equal to one and one-half times the width of the cover plate when
there is a continuous weld smaller than three-fourths of the plate thickness
across the end of the plate and continuous welds along both edges of the
cover plate in the length a′.
(c) A distance equal to two times the width of the cover plate when there is no
weld across the end of the plate, but continuous welds along both edges of
the cover plate in the length a′.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
6 - 41
CHAPTER C
FRAMES AND OTHER STRUCTURES
This chapter contains general requirements for stability of the structure as a whole.
C1. SECOND ORDER EFFECTS
Second order (P∆) effects shall be considered in the design of frames.
In structures designed on the basis of plastic analysis, the required flexural
strength Mu shall be determined from a second-order plastic analysis that
satisfies the requirements of Section C2. In structures designed on the basis of
elastic analysis, Mu for beam-columns, connections, and connected members
shall be determined from a second-order elastic analysis or from the following
approximate second-order analysis procedure:
Mu = B1Mnt + B2Mlt
(C1-1)
where
Mnt = required flexural strength in member assuming there is no lateral
= translation of the frame, kip-in.
Mlt = required flexural strength in member as a result of lateral translation
= of the frame only, kip-in.
B1 =
Cm
≥1
(1 − Pu / Pe1 )
(C1-2)
Pe1 = AgFy / λ2c where λc is the slenderness parameter, in which the effective
= K in the plane of bending shall be determined in accordance with
= Section C2.1, for the braced frame.
λc =
Kl
rπ
√
Fy
E
Pu = required axial compressive strength for the member under
= consideration, kips
Cm = a coefficient based on elastic first-order analysis assuming no lateral
= translation of the frame whose value shall be taken as follows:
(a) For compression members not subject to transverse loading between their
supports in the plane of bending,
Cm = 0.6 − 0.4(M1 / M2)
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
(C1-3)
6 - 42
FRAMES AND OTHER STRUCTURES
[Chap. C
(a) where M1 / M2 is the ratio of the smaller to larger moments at the ends of that
portion of the member unbraced in the plane of bending under consideration.
M1 / M2 is positive when the member is bent in reverse curvature, negative
when bent in single curvature.
(b) For compression members subjected to transverse loading between their
supports, the value of Cm shall be determined either by rational analysis or
by the use of the following values:
For members whose ends are restrained. . . . . . . . . . . . . . . . . . . . Cm = 0.85
For members whose ends are unrestrained. . . . . . . . . . . . . . . . . . Cm = 1.00
1
∆oh
1 − ΣPu
ΣHL
B2
=
B2
=
ΣPu
∆oh
ΣH
L
Pe2
= required axial strength of all columns in a story, kips
= lateral inter-story deflection, in.
= sum of all story horizontal forces producing ∆oh, kips
= story height, in.
= AgFy / λ2c, kips, where λc is the slenderness parameter, in which the
= effective length factor K in the plane of bending shall be determined
= in accordance with Section C2.2, for the unbraced frame.
(C1-4)
or
1
ΣPu
1−
ΣPe2
(C1-5)
C2. FRAME STABILITY
1.
Braced Frames
In trusses and frames where lateral stability is provided by diagonal bracing,
shear walls, or equivalent means, the effective length factor K for compression
members shall be taken as unity, unless structural analysis shows that a smaller
value may be used.
The vertical bracing system for a braced multistory frame shall be determined
by structural analysis to be adequate to prevent buckling of the structure and to
maintain the lateral stability of the structure, including the overturning effects
of drift, under the factored loads given in Section A4.
The vertical bracing system for a multistory frame may be considered to function
together with in-plane shear-resisting exterior and interior walls, floor slabs, and
roof decks, which are properly secured to the structural frames. The columns,
girders, beams, and diagonal members, when used as the vertical bracing
system, may be considered to comprise a vertically cantilevered simply connected truss in the analyses for frame buckling and lateral stability. Axial
deformation of all members in the vertical bracing system shall be included in
the lateral stability analysis.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
Sect. C2]
FRAME STABILITY
6 - 43
In structures designed on the basis of plastic analysis, the axial force in these
members caused by factored gravity plus factored horizontal loads shall not
exceed 0.85φc times AgFy.
Girders and beams included in the vertical bracing system of a braced multistory
frame shall be proportioned for axial force and moment caused by concurrent
factored horizontal and gravity loads.
2.
Unbraced Frames
In frames where lateral stability depends upon the bending stiffness of rigidly
connected beams and columns, the effective length factor K of compression
members shall be determined by structural analysis. The destabilizing effects of
gravity loaded columns whose simple connections to the frame do not provide
resistance to lateral loads shall be included in the design of the moment-frame
columns. Stiffness reduction adjustment due to column inelasticity is permitted.
Analysis of the required strength of unbraced multistory frames shall include
the effects of frame instability and column axial deformation under the factored
loads given in Section A4.
In structures designed on the basis of plastic analysis, the axial force in the
columns caused by factored gravity plus factored horizontal loads shall not
exceed 0.75φc times AgFy.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
6 - 44
CHAPTER D
TENSION MEMBERS
This chapter applies to prismatic members subject to axial tension caused by static
forces acting through the centroidal axis. For members subject to combined axial
tension and flexure, see Section H1.1. For threaded rods, see Section J3. For block
shear rupture strength at end connections of tension members, see Section J4.3. For
the design tensile strength of connecting elements, see Section J5.2. For members
subject to fatigue, see Section K3.
D1. DESIGN TENSILE STRENGTH
The design strength of tension members φt Pn shall be the lower value obtained
according to the limit states of yielding in the gross section and fracture in the
net section.
(a) For yielding in the gross section:
φt = 0.90
Pn = Fy Ag
(D1-1)
(b) For fracture in the net section:
φt = 0.75
Pn = Fu Ae
(D1-2)
where
Ae
Ag
Fy
Fu
Pn
= effective net area, in.2
= gross area of member, in.2
= specified minimum yield stress, ksi
= specified minimum tensile strength, ksi
= nominal axial strength, kips
When members without holes are fully connected by welds, the effective net
section used in Equation D1-2 shall be as defined in Section B3. When holes
are present in a member with welded-end connections, or at the welded connection in the case of plug or slot welds, the net section through the holes shall be
used in Equation D1-2.
D2. BUILT-UP MEMBERS
For limitations on the longitudinal spacing of connectors between elements in
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
Sect. D3]
PIN-CONNECTED MEMBERS AND EYEBARS
6 - 45
continuous contact consisting of a plate and a shape or two plates, see Section
J3.5.
The longitudinal spacing of connectors between components should preferably
limit the slenderness ratio in any component between the connectors to 300.
Either perforated cover plates or tie plates without lacing are permitted to be
used on the open sides of built-up tension members. Tie plates shall have a length
not less than two-thirds the distance between the lines of welds or fasteners
connecting them to the components of the member. The thickness of such tie
plates shall not be less than one-fiftieth of the distance between these lines. The
longitudinal spacing of intermittent welds or fasteners at tie plates shall not
exceed six inches. The spacing of tie plates shall be such that the slenderness
ratio of any component in the length between tie plates should preferably not
exceed 300.
D3. PIN-CONNECTED MEMBERS AND EYEBARS
The pin diameter shall not be less than seven-eighths times the eyebar body
width.
The pin-hole diameter shall not be more than 1⁄32-in. greater than the pin diameter.
For steels having a yield stress greater than 70 ksi, the hole diameter shall not
exceed five times the plate thickness and the width of the eyebar body shall be
reduced accordingly.
In pin-connected members, the pin hole shall be located midway between the
edges of the member in the direction normal to the applied force. For pinconnected members in which the pin is expected to provide for relative movement
between connected parts while under full load, the diameter of pin hole shall not
be more than 1⁄32-in. greater than the diameter of the pin. The width of the plate
beyond the pin hole shall be not less than the effective width on either side of the
pin hole.
In pin-connected plates other than eyebars, the minimum net area beyond the
bearing end of the pin hole, parallel to the axis of the member, shall not be less
than two-thirds of the net area required for strength across the pin hole.
The design strength of a pin-connected member φPn shall be the lowest value of
the following limit states:
(a) Tension on the net effective area:
φ = φt = 0.75
Pn = 2tbeff Fu
(D3-1)
(b) Shear on the effective area:
φsf = 0.75
Pn = 0.6AsfFu
(c) For bearing on the projected area of the pin, see Section J8.1.
(d) For yielding in the gross section, use Equation D1-1.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
(D3-2)
6 - 46
TENSION MEMBERS
[Chap. D
where
a = shortest distance from edge of the pin hole to the edge of the member
measured parallel to the direction of the force, in.
Asf = 2t(a + d / 2), in.2
beff = 2t + 0.63, but not more than the actual distance from the edge of the
= hole to the edge of the part measured in the direction normal to the
= applied force, in.
d = pin diameter, in.
t = thickness of plate, in.
The corners beyond the pin hole are permitted to be cut at 45° to the axis of the
member, provided the net area beyond the pin hole, on a plane perpendicular to
the cut, is not less than that required beyond the pin hole parallel to the axis of
the member.
The design strength of eyebars shall be determined in accordance with Section
D1 with Ag taken as the cross-sectional area of the body.
Eyebars shall be of uniform thickness, without reinforcement at the pin holes,
and have circular heads whose periphery is concentric with the pin hole.
The radius of transition between the circular head and the eyebar body shall be
not less than the head diameter.
The width of the body of the eyebars shall not exceed eight times its thickness.
The thickness of less than 1⁄2-in. is permissible only if external nuts are provided
to tighten pin plates and filler plates into snug contact. The width b from the
hole edge to the plate edge perpendicular to the direction of applied load shall
be greater than two-thirds and, for the purpose of calculation, not more than
three-fourths times the eyebar body width.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
6 - 47
CHAPTER E
COLUMNS AND OTHER COMPRESSION MEMBERS
This chapter applies to compact and non-compact prismatic members subject to
axial compression through the centroidal axis. For members subject to combined
axial compression and flexure, see Section H1.2. For members with slender
compression elements, see Appendix B5.3. For tapered members, see Appendix
F3. For single-angle members, see AISC Specification for Load and Resistance
Design of Single-Angle Members.
E1. EFFECTIVE LENGTH AND SLENDERNESS LIMITATIONS
1.
Effective Length
The effective length factor K shall be determined in accordance with Section C2.
2.
Design by Plastic Analysis
Design by plastic analysis, as limited in Section A5.1, is permitted if the column
slenderness parameter λc does not exceed 1.5K.
E2. DESIGN COMPRESSIVE STRENGTH FOR FLEXURAL BUCKLING
The design strength for flexural buckling of compression members whose
elements have width-thickness ratios less than λr from Section B5.1 is φcPn:
φc = 0.85
Pn = AgFcr
(E2-1)
(a) For λc ≤ 1.5
2
Fcr = (0.658λc)Fy
(E2-2)
0.877
Fcr = 2 Fy
λc
(E2-3)
(b) For λc > 1.5
where
λc =
Kl
rπ
√
Fy
E
(E2-4)
Ag = gross area of member, in.2
Fy = specified yield stress, ksi
E = modulus of elasticity, ksi
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
6 - 48
COLUMNS AND OTHER COMPRESSION MEMBERS
[Chap. E
K = effective length factor
l = laterally unbraced length of member, in.
r = governing radius of gyration about the axis of buckling, in.
For members whose elements do not meet the requirements of Section B5.1, see
Appendix B5.3.
E3. DESIGN COMPRESSIVE STRENGTH FOR
FLEXURAL-TORSIONAL BUCKLING
The design strength for flexural-torsional buckling of double-angle and teeshaped compression members whose elements have width-thickness ratios less
than λr from Section B5.1 is φcPn:
φc = 0.85
Pn = AgFcrft
Fcry + Fcrz
1 −
Fcrft =
2H
4F F H
√
1−
(F + F )
cry crz
2
cry
crz
(E3-1)
where:
Fcrz
_
ro
GJ
= _2
Aro
= polar radius of gyration about shear center, in. (see Equation A-E3-8)
H
xo2 + yo2
= 1 − _2
ro
xo, yo = coordinate of shear center with respect to the centroid, in.
= 0 for double-angle and tee-shaped members (y-axis of symmetry)
xo
Fcry is determined according to Section E2 for flexural buckling about the y-axis
of symmetry for λc =
Kl
ryπ
√
Fy
.
E
For double-angle and tee-shaped members whose elements do not meet the
requirements of Section B5.1, see Appendix B5.3 to determine Fcry for use in
Equation E3-1.
Other singly symmetric and unsymmetric columns, and doubly symmetric
columns, such as cruciform or built-up columns, with very thin walls shall be
designed for the limit states of flexural-torsional and torsional buckling in
accordance with Appendix E3.
E4. BUILT-UP MEMBERS
At the ends of built-up compression members bearing on base plates or milled
surfaces, all components in contact with one another shall be connected by a
weld having a length not less than the maximum width of the member or by
bolts spaced longitudinally not more than four diameters apart for a distance
equal to 11⁄2 times the maximum width of the member.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
Sect. E4]
BUILT-UP MEMBERS
6 - 49
Along the length of built-up compression members between the end connections
required above, longitudinal spacing for intermittent welds, bolts, or rivets shall
be adequate to provide for the transfer of the required forces. For limitations on
the longitudinal spacing of connectors between elements in continuous contact
consisting of a plate and a shape or two plates, see Section J3.5. Where a
component of a built-up compression member consists of an outside plate, the
maximum spacing shall not exceed the thickness of the thinner outside plate
Fy , nor 12 inches, when intermittent welds are provided along the
times 127 / √
edges of the components or when fasteners are provided on all gage lines at each
section. When fasteners are staggered, the maximum spacing on each gage line
Fy nor 18
shall not exceed the thickness of the thinner outside plate times 190 / √
inches.
Individual components of compression members composed of two or more
shapes shall be connected to one another at intervals, a, such that the effective
slenderness ratio Ka / ri of each of the component shapes, between the connectors, does not exceed three-fourths times the governing slenderness ratio of the
built-up member. The least radius of gyration ri shall be used in computing the
slenderness ratio of each component part. The end connection shall be welded
or fully tensioned bolted with clean mill scale or blasted cleaned faying surfaces
with Class A coatings.
The design strength of built-up members composed of two or more shapes shall
be determined in accordance with Section E2 and Section E3 subject to the
following modification. If the buckling mode involves relative deformations
that produce shear forces in the connectors between individual shapes, Kl / r is
replaced by (Kl / r)m determined as follows:
(a) For intermediate connectors that are snug-tight bolted:
Kl
=
r m
√
2
Kl a
r + r
o i
2
(E4-1)
(b) For intermediate connectors that are welded or fully-tensioned bolted:
Kl
=
r m
√
2
2
Kl
α2 a
r + 0.82
(1 + α2) rib
o
where
Kl
= column slenderness of built-up member acting as a unit
r o
Kl
= modified column slenderness of built-up member
r m
a
ri
= largest column slenderness of individual components
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
(E4-2)
6 - 50
COLUMNS AND OTHER COMPRESSION MEMBERS
a
rib
a
ri
rib
α
h
[Chap. E
= column slenerness of individual components relative to its
centroidal axis parallel to axis of buckling
= distance between connectors, in.
= minimum radius of gyration of individual component, in.
= radius of gyration of individual component relative to its centroidal
= axis parallel to member axis of buckling, in.
= separation ratio = h / 2rib
= distance between centroids of individual components perpendicular
= to the member axis of buckling, in.
Open sides of compression members built up from plates or shapes shall be
provided with continuous cover plates perforated with a succession of access
holes. The unsupported width of such plates at access holes, as defined in Section
B5.1, is assumed to contribute to the design strength provided that:
(1) The width-thickness ratio conforms to the limitations of Section B5.1.
(2) The ratio of length (in direction of stress) to width of hole shall not exceed
two.
(3) The clear distance between holes in the direction of stress shall be not less
than the transverse distance between nearest lines of connecting fasteners or
welds.
(4) The periphery of the holes at all points shall have a minimum radius of 11⁄2-in.
As an alternative to perforated cover plates, lacing with tie plates is permitted
at each end and at intermediate points if the lacing is interrupted. Tie plates shall
be as near the ends as practicable. In main members providing design strength,
the end tie plates shall have a length of not less than the distance between the
lines of fasteners or welds connecting them to the components of the member.
Intermediate tie plates shall have a length not less than one-half of this distance.
The thickness of tie plates shall be not less than one-fiftieth of the distance
between lines of welds or fasteners connecting them to the segments of the
members. In welded construction, the welding on each line connecting a tie plate
shall aggregate not less than one-third the length of the plate. In bolted and
riveted construction, the spacing in the direction of stress in tie plates shall be
not more than six diameters and the tie plates shall be connected to each segment
by at least three fasteners.
Lacing, including flat bars, angles, channels, or other shapes employed as lacing,
shall be so spaced that l / r of the flange included between their connections shall
not exceed the governing slenderness ratio for the member as a whole. Lacing
shall be proportioned to provide a shearing strength normal to the axis of the
member equal to two percent of the compressive design strength of the member.
The l / r ratio for lacing bars arranged in single systems shall not exceed 140.
For double lacing this ratio shall not exceed 200. Double lacing bars shall be
joined at the intersections. For lacing bars in compression, l is permitted to be
taken as the unsupported length of the lacing bar between welds or fasteners
connecting it to the components of the built-up member for single lacing, and
70 percent of that distance for double lacing. The inclination of lacing bars to
the axis of the member shall preferably be not less than 60° for single lacing and
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
Sect. E5]
PIN-CONNECTED COMPRESSION MEMBERS
6 - 51
45° for double lacing. When the distance between the lines of welds or fasteners
in the flanges is more than 15 inches, the lacing shall preferably be double or be
made of angles.
For additional spacing requirements, see Section J3.
E5. PIN-CONNECTED COMPRESSION MEMBERS
Pin connections of pin-connected compression members shall conform to the
requirements of Section D3 except Equations D3-1 and D3-2 do not apply.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
6 - 52
CHAPTER F
BEAMS AND OTHER FLEXURAL MEMBERS
This chapter applies to compact and noncompact prismatic members subject to flexure
and shear. For members subject to combined flexure and axial force, see Section H1.
For members subject to fatigue, see Section K4. For members with slender compression elements, see Appendix B5. For web-tapered members, see Appendix F3. For
members with slender web elements (plate girders), see Appendix G. For single-angle
members, the AISC Specification for Load and Resistance Factor Design of SingleAngle Members is applicable.
F1.
DESIGN FOR FLEXURE
The nominal flexural strength Mn is the lowest value obtained according to the
limit stress of: (a) yielding; (b) lateral-torsional buckling; (c) flange local
buckling; and (d) web local buckling. For laterally braced compact beams with
Lb ≤ Lp, only the limit state of yielding is applicable. For unbraced compact
beams and noncompact tees and double angles, only the limit states of yielding
and lateral-torsional buckling are applicable. The lateral-torsional buckling limit
state is not applicable to members subject to bending about the minor axis, or
to square or circular shapes.
This section applies to homogeneous and hybrid shapes with at least one axis
of symmetry and which are subject to simple bending about one principal axis.
For simple bending, the beam is loaded in a plane parallel to a principal axis that
passes through the shear center or the beam is restrained against twisting at load
points and supports. Only the limit states of yielding and lateral-torsional
buckling are considered in this section. The lateral-torsional buckling provisions
are limited to doubly symmetric shapes, channels, double angles, and tees. For
lateral-torsional buckling of other singly symmetric shapes and for the limit
states of flange local buckling and web local buckling of noncompact or
slender-element sections, see Appendix F1. For unsymmetric shapes and beams
subject to torsion combined with flexure, see Section H2. For biaxial bending,
see Section H1.
1.
Yielding
The flexural design strength of beams, determined by the limit state of yielding,
is φbMn:
φb = 0.90
Mn = Mp
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
(F1-1)
Sect. F1]
DESIGN FOR FLEXURE
6 - 53
where
Mp = plastic moment (= Fy Z ≤ 1.5My for homogeneous sections), kip-in.
My = moment corresponding to onset of yielding at the extreme fiber from
an elastic stress distribution (= Fy S for homogeneous section and Fyf S
for hybrid sections), kip-in.
2.
Lateral-Torsional Buckling
This limit state is only applicable to members subject to major axis bending.
The flexural design strength, determined by the limit state of lateral-torsional
buckling, is φbMn:
φb = 0.90
Mn = nominal strength determined as follows:
2a.
Doubly Symmetric Shapes and Channels with Lb ≤ Lr
The nominal flexural strength is:
L − Lp
Mn = Cb Mp − (Mp − Mr) b
≤ Mp
Lr − Lp
(F1-2)
where:
Lb = distance between points braced against lateral displacement of the
compression flange, or between points braced to prevent twist of the
cross section, in.
In the above equation, Cb is a modification factor for non-uniform moment
diagrams where, when both ends of the beam segment are braced:
Cb =
12.5Mmax
2.5Mmax + 3MA + 4MB + 3MC
(F1-3)
where
Mmax = absolute value of maximum moment in the unbraced segment,
kip-in.
MA = absolute value of moment at quarter point of the unbraced segment
MB = absolute value of moment at centerline of the unbraced beam segment
MC = absolute value of moment at three-quarter point of the unbraced
beam segment
Cb is permitted to be conservatively taken as 1.0 for all cases. For cantilevers or
overhangs where the free end is unbraced, Cb = 1.0.
The limiting unbraced length for full plastic bending capacity, Lp, shall be
determined as follows.
(a) For I-shaped members including hybrid sections and channels:
Lp =
300ry
Fyf
√
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
(F1-4)
6 - 54
BEAMS AND OTHER FLEXURAL MEMBERS
[Chap. F
(b) For solid rectangular bars and box sections:
3,750ry
JA
√
Mp
Lp =
(F1-5)
where
A = cross-sectional area, in.2
J = torsional constant, in.4
The limiting laterally unbraced length Lr and the corresponding buckling moment Mr shall be determined as follows:
(a) For doubly symmetric I-shaped members and channels:
Lr =
ryX1
√
1+√
1 + X2FL 2
FL
Mr = FL Sx
(F1-6)
(F1-7)
where
X1 =
π
Sx
√
EGJA
2
(F1-8)
2
C S
X2 = 4 w x
Iy GJ
(F1-9)
= section modulus about major axis, in.3
= modulus of elasticity of steel (29,000 ksi)
= shear modulus of elasticity of steel (11,200 ksi)
= smaller of (Fyf − Fr) or Fyw
= compressive residual stress in flange; 10 ksi for rolled shapes, 16.5 ksi
for welded shapes
Fyf = yield stress of flange, ksi
Fyw = yield stress of web, ksi
Iy = moment of inertia about y-axis, in.4
Cw = warping constant, in.6
Sx
E
G
FL
Fr
Equations F1-4 and F1-6 are conservatively based on Cb = 1.0.
(b) For solid rectangular bars and box sections:
Lr =
57,000ry√
JA
Mr
Mr = Fyf Sx
2b.
(F1-10)
(F1-11)
Doubly Symmetric Shapes and Channels with Lb > Lr
The nominal flexural strength is:
Mn = Mcr ≤ Mp
where Mcr is the critical elastic moment, determined as follows:
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
(F1-12)
Sect. F1]
DESIGN FOR FLEXURE
6 - 55
(a) For doubly symmetric I-shaped members and channels:
π
Mcr = Cb
Lb
Mcr =
√
2
πE
EIyGJ + IyCw
Lb
Cb Sx X1√
2
Lb / ry
(F1-13)
√
(L / )
1+
X21X2
2 b ry
2
(b) For solid rectangular bars and symmetric box sections:
Mcr =
2c.
JA
57,000 Cb √
Lb / ry
(F1-14)
Tees and Double Angles
For tees and double-angle beams loaded in the plane of symmetry:
Mn = Mcr =
π√
EIyGJ
[B + √
1+B
2 ]
Lb
(F1-15)
where
Mn ≤ 1.5My for stems in tension
Mn ≤ 1.0My for stems in compression
Iy / J
B = ±2.3(d / Lb) √
(F1-16)
The plus sign for B applies when the stem is in tension and the minus sign applies
when the stem is in compression. If the tip of the stem is in compression
anywhere along the unbraced length, use the negative value of B.
2d.
Unbraced Length for Design by Plastic Analysis
Design by plastic analysis, as limited in Section A5.1, is permitted for a compact
section member bent about the major axis when the laterally unbraced length Lb
of the compression flange adjacent to plastic hinge locations associated with
the failure mechanism does not exceed Lpd, determined as follows:
(a) For doubly symmetric and singly symmetric I-shaped members with the
compression flange equal to or larger than the tension flange (including
hybrid members) loaded in the plane of the web
Lpd =
[3,600 + 2,200 (M1 / M2)] ry
Fy
(F1-17)
where
= specified minimum yield stress of the compression flange, ksi
Fy
= smaller moment at end of unbraced length of beam, kip-in.
M1
= larger moment at end of unbraced length of beam, kip-in.
M2
= radius of gyration about minor axis, in.
ry
(M1 / M2) is positive when moments cause reverse curvature and negative
for single curvature
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
6 - 56
BEAMS AND OTHER FLEXURAL MEMBERS
[Chap. F
(b) For solid rectangular bars and symmetric box beams
Lpd =
5,000 + 3,000 (M1 / M2)
ry ≥ 3,000ry / Fy
Fy
(F1-18)
There is no limit on Lb for members with circular or square cross sections nor
for any beam bent about its minor axis.
In the region of the last hinge to form, and in regions not adjacent to a plastic
hinge, the flexural design strength shall be determined in accordance with
Section F1.2.
F2.
DESIGN FOR SHEAR
This section applies to unstiffened webs of singly or doubly symmetric beams,
including hybrid beams, and channels subject to shear in the plane of the web.
For the design shear strength of webs with stiffeners, see Appendix F2 or
Appendix G3. For shear in the weak direction of the shapes above, pipes, and
unsymmetric sections, see Section H2. For web panels subject to high shear, see
Section K1.7. For shear strength at connections, see Sections J4 and J5.
1.
Web Area Determination
The web area Aw shall be taken as the overall depth d times the web thickness
tw.
2.
Design Shear Strength
The design shear strength of unstiffened webs, with h / tw ≤ 260, is φvVn, where
φv = 0.90
Vn = nominal shear strength defined as follows
For h / tw ≤ 418 / √
Fyw
Vn = 0.6Fyw Aw
(F2-1)
Fyw
For 418 / √
Fyw < h / tw ≤ 523 / √
Vn = 0.6Fyw Aw(418 / √
Fyw ) / (h / tw)
(F2-2)
For 523 / √
Fyw < h / tw ≤ 260
Vn = (132,000Aw) / (h / tw)2
(F2-3)
The general design shear strength of webs with or without stiffeners is given in
Appendix F2.2 and an alternative method utilizing tension field action is given
in Appendix G3.
3.
Transverse Stiffeners
See Appendix F2.3.
F3.
WEB-TAPERED MEMBERS
See Appendix F3.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
Sect. F4]
F4.
BEAMS AND GIRDERS WITH WEB OPENINGS
6 - 57
BEAMS AND GIRDERS WITH WEB OPENINGS
The effect of all web openings on the design strength of steel and composite
beams shall be determined. Adequate reinforcement shall be provided when the
required strength exceeds the net strength of the member at the opening.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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CHAPTER G
PLATE GIRDERS
I-shaped plate girders shall be distinguished from I-shaped beams on the basis
of the web slenderness ratio h / tw . When this value is greater than λr the
provisions of Appendices G1 and G2 shall apply for design flexural strength.
For h / tw ≤ λr, the provisions of Chapter F or Appendix F shall apply for design
flexural strength. For girders with unequal flanges, see Appendix B5.1.
The design shear strength and transverse stiffener design shall be based on either
Section F2 (without tension-field action) or Appendix G3 (with tension-field
action). For girders with unequal flanges, see Appendix B5.1.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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CHAPTER H
MEMBERS UNDER COMBINED FORCES AND TORSION
This chapter applies to prismatic members subject to axial force and flexure about one
or both axes of symmetry, with or without torsion, and torsion only. For web-tapered
members, see Appendix F3.
H1. SYMMETRIC MEMBERS SUBJECT TO BENDING AND AXIAL
FORCE
1.
Doubly and Singly Symmetric Members in Flexure and Tension
The interaction of flexure and tension in symmetric shapes shall be limited by
Equations H1-1a and H1-1b.
(a) For
Pu
φPn
≥ 0.2
Muy
8 Mux
+
≤ 1.0
9 φbMnx φbMny
(H1-1a)
Mux
Pu
Muy
+
+
≤ 1.0
2φPn φbMnx φbMny
(H1-1b)
Pu
φPn
(b) For
Pu
φPn
+
< 0.2
where
Pu = required tensile strength, kips
Pn = nominal tensile strength determined in accordance with Section D1,
kips
Mu = required flexural strength determined in accordance with Section C1,
kip-in.
Mn = nominal flexural strength determined in accordance with Section F1,
kip-in.
x = subscript relating symbol to strong axis bending
y = subscript relating symbol to weak axis bending.
φ = φt = resistance factor for tension (see Section D1)
φb = resistance factor for flexure = 0.90
A more detailed analysis of the interaction of flexure and tension is permitted
in lieu of Equations H1-1a and H1-1b.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
6 - 60
2.
MEMBERS UNDER COMBINED FORCES AND TORSION
[Chap. H
Doubly and Singly Symmetric Members in Flexure and Compression
The interaction of flexure and compression in symmetric shapes shall be limited
by Equations H1-1a and H1-1b where
Pu = required compressive strength, kips
Pn = nominal compressive strength determined in accordance with
Section E2, kips
Mu = required flexural strength determined in accordance with Section C1
kip-in.
Mn = nominal flexural strength determined in accordance with Section F1,
kip-in.
x = subscript relating symbol to strong axis bending
y = subscript relating symbol to weak axis bending.
φ = φc = resistance factor for compression, = 0.85 (see Section E2)
φb = resistance factor for flexure = 0.90
H2. UNSYMMETRIC MEMBERS AND MEMBERS UNDER TORSION
AND COMBINED TORSION, FLEXURE, SHEAR, AND/OR AXIAL
FORCE
The design strength φFy of the member shall equal or exceed the required strength
expressed in terms of the normal stress fun or the shear stress fuv, determined by
elastic analysis for the factored loads:
(a) For the limit state of yielding under normal stress:
fun ≤ φFy
φ = 0.90
(H2-1)
(b) For the limit state of yielding under shear stress:
fuv ≤ 0.6φFy
φ = 0.90
(H2-2)
(c) For the limit state of buckling:
fun or fuv ≤ φcFcr, as applicable
φc = 0.85
(H2-3)
Some constrained local yielding is permitted adjacent to areas which remain
elastic.
H3. ALTERNATIVE INTERACTION EQUATIONS FOR MEMBERS
UNDER COMBINED STRESS
See Appendix H3.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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CHAPTER I
COMPOSITE MEMBERS
This chapter applies to composite columns composed of rolled or built-up structural
steel shapes, pipe or tubing, and structural concrete acting together and to steel beams
supporting a reinforced concrete slab so interconnected that the beams and the slab
act together to resist bending. Simple and continuous composite beams with shear
connectors and concrete-encased beams, constructed with or without temporary
shores, are included.
I1.
DESIGN ASSUMPTIONS
Force Determination. In determining forces in members and connections of a
structure that includes composite beams, consideration shall be given to the
effective sections at the time each increment of load is applied.
Elastic Analysis. For an elastic analysis of continuous composite beams without
haunched ends, it is permissible to assume that the stiffness of a beam is uniform
throughout the beam length. The stiffness is permitted to be computed using the
moment of inertia of the composite transformed section in the positive moment
region.
Plastic Analysis. When plastic analysis is used, the strength of flexural composite members shall be determined from plastic stress distributions.
Plastic Stress Distribution for Positive Moment. If the slab in the positive
moment region is connected to the steel beam with shear connectors, a concrete
stress of 0.85fc′ is permitted to be assumed uniformly distributed throughout the
effective compression zone. Concrete tensile strength shall be neglected. A
uniformly distributed steel stress of Fy shall be assumed throughout the tension
zone and throughout the compression zone in the structural steel section. The
net tensile force in the steel section shall be equal to the compressive force in
the concrete slab.
Plastic Stress Distribution for Negative Moment. If the slab in the negative
moment region is connected to the steel beam with shear connectors, a tensile
stress of Fyr shall be assumed in all adequately developed longitudinal reinforcing bars within the effective width of the concrete slab. Concrete tensile strength
shall be neglected. A uniformly distributed steel stress of Fy shall be assumed
throughout the tension zone and throughout the compression zone in the
structural steel section. The net compressive force in the steel section shall be
equal to the total tensile force in the reinforcing steel.
Elastic Stress Distribution. When a determination of elastic stress distribution
is required, strains in steel and concrete shall be assumed directly proportional
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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COMPOSITE MEMBERS
[Chap. I
to the distance from the neutral axis. The stress shall equal strain times modulus
of elasticity for steel, E, or modulus of elasticity for concrete, Ec. Concrete
tensile strength shall be neglected. Maximum stress in the steel shall not exceed
Fy. Maximum compressive stress in the concrete shall not exceed 0.85fc′ where
fc′ is the specified compressive strength of the concrete. In composite hybrid
beams, the maximum stress in the steel flange shall not exceed Fyf but the strain
in the web may exceed the yield strain; the stress shall be taken as Fyw at such
locations.
Fully Composite Beam. Shear connectors are provided in sufficient numbers to
develop the maximum flexural strength of the composite beam. For elastic stress
distribution it shall be assumed that no slip occurs.
Partially Composite Beam. The shear strength of shear connectors governs the
flexural strength of the partially composite beam. Elastic computations such as
those for deflections, fatigue, and vibrations shall include the effect of slip.
Concrete-Encased Beam. A beam totally encased in concrete cast integrally with
the slab may be assumed to be interconnected to the concrete by natural bond,
without additional anchorage, provided that: (1) concrete cover over beam sides
and soffit is at least two inches; (2) the top of the beam is at least 11⁄2-in. below
the top and two inches above the bottom of the slab; and (3) concrete encasement
contains adequate mesh or other reinforcing steel to prevent spalling of concrete.
Composite Column. A steel column fabricated from rolled or built-up steel
shapes and encased in structural concrete or fabricated from steel pipe or tubing
and filled with structural concrete shall be designed in accordance with Section
I2.
I2.
COMPRESSION MEMBERS
1.
Limitations
To qualify as a composite column, the following limitations shall be met:
(1) The cross-sectional area of the steel shape, pipe, or tubing shall comprise at
least four percent of the total composite cross section.
(2) Concrete encasement of a steel core shall be reinforced with longitudinal
load carrying bars, longitudinal bars to restrain concrete, and lateral ties.
Longitudinal load carrying bars shall be continuous at framed levels; longitudinal restraining bars may be interrupted at framed levels. The spacing of
ties shall be not greater than two-thirds of the least dimension of the
composite cross section. The cross-sectional area of the transverse and
longitudinal reinforcement shall be at least 0.007 sq. in. per inch of bar
spacing. The encasement shall provide at least 11⁄2-in. of clear cover outside
of both transverse and longitudinal reinforcement.
(3) Concrete shall have a specified compressive strength fc′ of not less than 3 ksi
nor more than 8 ksi for normal weight concrete and not less than 4 ksi for
light weight concrete.
(4) The specified minimum yield stress of structural steel and reinforcing bars
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
Sect. I2]
COMPRESSION MEMBERS
6 - 63
used in calculating the strength of a composite column shall not exceed
55 ksi.
(5) The minimum wall thickness of structural steel pipe or tubing filled with
concrete shall be equal to b√
Fy / 3E for each face of width b in rectangular
sections and D√
Fy / 8E for circular sections of outside diameter D.
2.
Design Strength
The design strength of axially loaded composite columns is φcPn,
where
φc = 0.85
Pn = nominal axial compressive strength determined from Equations E2-1
through E2-4 with the following modifications:
(1) As = gross area of steel shape, pipe, or tubing, in.2 (replaces Ag)
rm = radius of gyration of the steel shape, pipe, or tubing except that for steel
shapes it shall not be less than 0.3 times the overall thickness of the
composite cross section in the plane of buckling, in. (replaces r)
(2) Replace Fy with modified yield stress Fmy from Equation I2-1 and replace E
with modified modulus of elasticity Em from Equation I2-2.
Fmy = Fy + c1Fyr (Ar / As) + c2 fc′(Ac / As)
(I2-1)
Em = E + c3Ec (Ac / As)
(I2-2)
where
= area of concrete, in.2
= area of longitudinal reinforcing bars, in.2
= area of steel, in.2
= modulus of elasticity of steel, ksi
= modulus of elasticity of concrete. Ec is permitted to be computed from
fc ′ where w, the unit weight of concrete, is expressed in lbs./cu.
Ec = w1.5√
ft and fc′ is expressed in ksi.
Fy = specified minimum yield stress of steel shape, pipe, or tubing, ksi
Fyr = specified minimum yield stress of longitudinal reinforcing bars, ksi
fc′ = specified compressive strength of concrete, ksi
c1, c2, c3 = numerical coefficients. For concrete-filled pipe and tubing:
c1 = 1.0, c2 = 0.85, and c3 = 0.4; for concrete encased shapes c1 = 0.7,
c2 = 0.6, and c3 = 0.2
Ac
Ar
As
E
Ec
3.
Columns with Multiple Steel Shapes
If the composite cross section includes two or more steel shapes, the shapes shall
be interconnected with lacing, tie plates, or batten plates to prevent buckling of
individual shapes before hardening of concrete.
4.
Load Transfer
The portion of the design strength of axially loaded composite columns resisted
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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COMPOSITE MEMBERS
[Chap. I
by concrete shall be developed by direct bearing at connections. When the
supporting concrete area is wider than the loaded area on one or more sides and
otherwise restrained against lateral expansion on the remaining sides, the
maximum design strength of concrete shall be 1.7φc fc′AB,
where
φc = 0.60
AB = loaded area
I3.
FLEXURAL MEMBERS
1.
Effective Width
The effective width of the concrete slab on each side of the beam center-line
shall not exceed:
(a) one-eighth of the beam span, center to center of supports;
(b) one-half the distance to the center-line of the adjacent beam; or
(c) the distance to the edge of the slab.
2.
Strength of Beams with Shear Connectors
The positive design flexural strength φbMn shall be determined as follows:
Fyf :
(a) For h / tw ≤ 640 / √
φb = 0.85; Mn shall be determined from the plastic stress distribution on the
composite section.
Fyf :
(b) For h / tw > 640 / √
φb = 0.90; Mn shall be determined from the superposition of elastic stresses,
considering the effects of shoring.
The negative design flexural strength φbMn shall be determined for the steel
section alone, in accordance with the requirements of Chapter F.
Alternatively, the negative design flexural strength φbMn shall be computed with:
φb = 0.85 and Mn determined from the plastic stress distribution on the composite
section, provided that:
(1) Steel beam is an adequately braced compact section, as defined in Section
B5.
(2) Shear connectors connect the slab to the steel beam in the negative moment
region.
(3) Slab reinforcement parallel to the steel beam, within the effective width of
the slab, is properly developed.
3.
Strength of Concrete-Encased Beams
The design flexural strength φbMn shall be computed with φb = 0.90 and Mn
determined from the superposition of elastic stresses, considering the effects of
shoring.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
Sect. I3]
FLEXURAL MEMBERS
6 - 65
Alternatively, the design flexural strength φbMn shall be computed with
φb = 0.90 and Mn determined from the plastic stress distribution on the steel
section alone.
4.
Strength During Construction
When temporary shores are not used during construction, the steel section alone
shall have adequate strength to support all loads applied prior to the concrete
attaining 75 percent of its specified strength fc′. The design flexural strength of
the steel section shall be determined in accordance with the requirements of
Section F1.
5.
Formed Steel Deck
5a.
General
The design flexural strength φbMn of composite construction consisting of
concrete slabs on formed steel deck connected to steel beams shall be determined by the applicable portions of Section I3.2, with the following modifications.
This section is applicable to decks with nominal rib height not greater than three
inches. The average width of concrete rib or haunch wr shall be not less than two
inches, but shall not be taken in calculations as more than the minimum clear
width near the top of the steel deck. See Section I3.5c for additional restrictions.
The concrete slab shall be connected to the steel beam with welded stud shear
connectors 3⁄4-in. or less in diameter (AWS D1.1). Studs shall be welded either
through the deck or directly to the steel beam. Stud shear connectors, after
installation, shall extend not less than 11⁄2-in. above the top of the steel deck.
The slab thickness above the steel deck shall be not less than two inches.
5b.
Deck Ribs Oriented Perpendicular to Steel Beam
Concrete below the top of the steel deck shall be neglected in determining
section properties and in calculating Ac for deck ribs oriented perpendicular to
the steel beams.
The spacing of stud shear connectors along the length of a supporting beam shall
not exceed 36 inches.
The nominal strength of a stud shear connector shall be the value stipulated in
Section I5 multiplied by the following reduction factor:
0.85
(wr / hr) [(Hs / hr) − 1.0] ≤ 1.0
Nr
√
(I3-1)
where
hr = nominal rib height, in.
Hs = length of stud connector after welding, in., not to exceed the value
(hr + 3) in computations, although actual length may be greater
Nr = number of stud connectors in one rib at a beam intersection, not to
exceed three in computations, although more than three studs may be
installed
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
6 - 66
COMPOSITE MEMBERS
[Chap. I
wr = average width of concrete rib or haunch (as defined in Section I3.5a),
in.
To resist uplift, steel deck shall be anchored to all supporting members at a
spacing not to exceed 18 inches. Such anchorage shall be provided by stud
connectors, a combination of stud connectors and arc spot (puddle) welds, or
other devices specified by the designer.
5c.
Deck Ribs Oriented Parallel to Steel Beam
Concrete below the top of the steel deck may be included in determining section
properties and shall be included in calculating Ac in Section I5.
Steel deck ribs over supporting beams may be split longitudinally and separated
to form a concrete haunch.
When the nominal depth of steel deck is 11⁄2-in. or greater, the average width
wr of the supported haunch or rib shall be not less than two inches for the first
stud in the transverse row plus four stud diameters for each additional stud.
The nominal strength of a stud shear connector shall be the value stipulated in
Section I5, except that when wr / hr is less than 1.5, the value from Section I5
shall be multiplied by the following reduction factor:
0.6(wr / hr)[(Hs / hr) − 1.0] ≤ 1.0
(I3-2)
where hr and Hs are as defined in Section I3.5b and wr is the average width of
concrete rib or haunch as defined in Section I3.5a.
6.
Design Shear Strength
The design shear strength of composite beams shall be determined by the shear
strength of the steel web, in accordance with Section F2.
I4.
COMBINED COMPRESSION AND FLEXURE
The interaction of axial compression and flexure in the plane of symmetry on
composite members shall be limited by Section H1.2 with the following modifications:
= nominal flexural strength determined from plastic stress distribution
on the composite cross section except as provided below, kip-in.
Pe1 , Pe2 = AsFmy / λ2c elastic buckling load, kips
= modified yield stress, ksi, see Section I2
Fmy
φb
= resistance factor for flexure from Section I3
= resistance factor for compression = 0.85
φc
= column slenderness parameter defined by Equation E2-4 as
λc
modified in Section I2.2
Mn
When the axial term in Equations H1-1a and H1-1b is less than 0.3, the nominal
flexural strength Mn shall be determined by straight line transition between the
nominal flexural strength determined from the plastic distribution on the composite cross sections at (Pu / φcPn ) = 0.3 and the flexural strength at Pu = 0 as
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
Sect. I5]
SHEAR CONNECTORS
6 - 67
determined in Section I3. If shear connectors are required at Pu = 0, they shall
be provided whenever Pu / φcPn is less than 0.3.
I5.
SHEAR CONNECTORS
This section applies to the design of stud and channel shear connectors. For
connectors of other types, see Section I6.
1.
Materials
Shear connectors shall be headed steel studs not less than four stud diameters in
length after installation, or hot rolled steel channels. The stud connectors shall
conform to the requirements of Section A3.6. The channel connectors shall
conform to the requirements of Section A3. Shear connectors shall be embedded
in concrete slabs made with ASTM C33 aggregate or with rotary kiln produced
aggregates conforming to ASTM C330, with concrete unit weight not less than
90 pcf.
2.
Horizontal Shear Force
Except for concrete-encased beams as defined in Section I1, the entire horizontal shear at the interface between the steel beam and the concrete slab shall
be assumed to be transferred by shear connectors. For composite action with
concrete subject to flexural compression, the total horizontal shear force
between the point of maximum positive moment and the point of zero moment
shall be taken as the smallest of the following: (1) 0.85fc′Ac; (2) AsFy; and
(3) ΣQn;
where
fc′
Ac
As
Fy
ΣQn
= specified compressive strength of concrete, ksi
= area of concrete slab within effective width, in.2
= area of steel cross section, in.2
= minimum specified yield stress, ksi
= sum of nominal strengths of shear connectors between the point of
maximum positive moment and the point of zero moment, kips
For hybrid beams, the yield force shall be computed separately for each
component of the cross section; AsFy of the entire cross section is the sum of the
component yield forces.
In continuous composite beams where longitudinal reinforcing steel in the
negative moment regions is considered to act compositely with the steel beam,
the total horizontal shear force between the point of maximum negative moment
and the point of zero moment shall be taken as the smaller of ArFyr and ΣQn;
where
= area of adequately developed longitudinal reinforcing steel within
the effective width of the concrete slab, in.2
Fyr = minimum specified yield stress of the reinforcing steel, ksi
ΣQn = sum of nominal strengths of shear connectors between the point of
maximum negative moment and the point of zero moment, kips
Ar
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
6 - 68
3.
COMPOSITE MEMBERS
[Chap. I
Strength of Stud Shear Connectors
The nominal strength of one stud shear connector embedded in a solid concrete
slab is
fc′Ec ≤ AscFu
Qn = 0.5Asc√
(I5-1)
where
Asc
fc′
Fu
Ec
= cross-sectional area of a stud shear connector, in.2
= specified compressive strength of concrete, ksi
= minimum specified tensile strength of a stud shear connector, ksi
= modulus of elasticity of concrete, ksi
For stud shear connector embedded in a slab on a formed steel deck, refer to
Section I3 for reduction factors given by Equations I3-1 and I3-2 as applicable.
√
fc′Ec term in Equation I5-1.
The reduction factors apply only to 0.5Asc
4.
Strength of Channel Shear Connectors
The nominal strength of one channel shear connector embedded in a solid
concrete slab is
fc′Ec
Qn = 0.3(tf + 0.5tw)Lc√
(I5-2)
where
tf = flange thickness of channel shear connector, in.
tw = web thickness of channel shear connector, in.
Lc = length of channel shear connector, in.
5.
Required Number of Shear Connectors
The number of shear connectors required between the section of maximum
bending moment, positive or negative, and the adjacent section of zero moment
shall be equal to the horizontal shear force as determined in Section I5.2 divided
by the nominal strength of one shear connector as determined from Section I5.3
or Section I5.4.
6.
Shear Connector Placement and Spacing
Unless otherwise specified shear connectors required each side of the point of
maximum bending moment, positive or negative, shall be distributed uniformly
between that point and the adjacent points of zero moment. However, the
number of shear connectors placed between any concentrated load and the
nearest point of zero moment shall be sufficient to develop the maximum
moment required at the concentrated load point.
Except for connectors installed in the ribs of formed steel decks, shear connectors shall have at least one inch of lateral concrete cover. Unless located over
the web, the diameter of studs shall not be greater than 2.5 times the thickness
of the flange to which they are welded. The minimum center-to-center spacing
of stud connectors shall be six diameters along the longitudinal axis of the
supporting composite beam and four diameters transverse to the longitudinal
axis of the supporting composite beam, except that within the ribs of formed
steel decks the center-to-center spacing may be as small as four diameters in any
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
Sect. I6]
SPECIAL CASES
6 - 69
direction. The maximum center-to-center spacing of shear connectors shall not
exceed eight times the total slab thickness. Also see Section I3.5b.
I6.
SPECIAL CASES
When composite construction does not conform to the requirements of Section
I1 through Section I5, the strength of shear connectors and details of construction shall be established by a suitable test program.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
6-70
CHAPTER J
CONNECTIONS, JOINTS, AND FASTENERS
This chapter applies to connecting elements, connectors, and the affected elements of
the connected members subject to static loads. For connections subject to fatigue, see
Appendix K3.
J1.
GENERAL PROVISIONS
1.
Design Basis
Connections consist of affected elements of connected members (e.g. beam
webs), connecting elements (e.g., gussets, angles, brackets), and connectors
(welds, bolts, rivets). These components shall be proportioned so that their
design strength equals or exceeds the required strength determined by structural
analysis for factored loads acting on the structure or a specified proportion of
the strength of the connected members, whichever is appropriate.
2.
Simple Connections
Except as otherwise indicated in the design documents, connections of beams,
girders, or trusses shall be designed as flexible, and are permitted to ordinarily
be proportioned for the reaction shears only. Flexible beam connections shall
accommodate end rotations of unrestrained (simple) beams. To accomplish this,
some inelastic but self-limiting deformation in the connection is permitted.
3.
Moment Connections
End connections of restrained beams, girders, and trusses shall be designed for
the combined effect of forces resulting from moment and shear induced by the
rigidity of the connections.
4.
Compression Members with Bearing Joints
When columns bear on bearing plates or are finished to bear at splices, there
shall be sufficient connectors to hold all parts securely in place.
When compression members other than columns are finished to bear, the splice
material and its connectors shall be arranged to hold all parts in line and shall
be proportioned for 50 percent of the required strength of the member.
All compression joints shall be proportioned to resist any tension developed by
the factored loads specified by load combination A4-6.
5.
Splices in Heavy Sections
This paragraph applies to ASTM A6 Group 4 and 5 rolled shapes, or shapes
built-up by welding plates more than two inches thick together to form the cross
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
Sect. J1]
GENERAL PROVISIONS
6 - 71
section, and where the cross section is to be spliced and subject to primary tensile
stresses due to tension or flexure. When the individual elements of the cross
section are spliced prior to being joined to form the cross section in accordance
with AWS D1.1, Article 3.4.6, the applicable provisions of AWS D1.1 apply in
lieu of the requirements of this section. When tensile forces in these sections are
to be transmitted through splices by complete-joint-penetration groove welds,
material notch-toughness requirements as given in Section A3.1c, weld access
hole details as given in Section J1.6, welding preheat requirements as given in
Section J2.8, and thermal-cut surface preparation and inspection requirements
as given in Section M2.2 apply.
At tension splices in ASTM A6 Group 4 and 5 shapes and built-up members of
material more than two inches thick, weld tabs and backing shall be removed
and the surfaces ground smooth.
When splicing ASTM A6 Group 4 and 5 rolled shapes or shapes built-up by
welding plates more than two inches thick to form a cross section, and where
the section is to be used as a primary compression member, all weld access holes
required to facilitate groove welding operations shall satisfy the provisions of
Section J1.6.
Alternatively, splicing of such members subject to compression, including
members which are subject to tension due to wind or seismic loads, shall be
accomplished using splice details which do not induce large weld shrinkage
strains; for example partial-joint-penetration flange groove welds with filletwelded surface lap plate splices on the web, bolted lap plate splices, or combination bolted/fillet-welded lap plate splices.
6.
Beam Copes and Weld Access Holes
All weld access holes required to facilitate welding operations shall have a length
from the toe of the weld preparation not less than 11⁄2 times the thickness of the
material in which the hole is made. The height of the access hole shall be adequate
for deposition of sound weld metal in the adjacent plates and provide clearance
for weld tabs for the weld in the material in which the hole is made, but not less
than the thickness of the material. In hot-rolled shapes and built-up shapes, all
beam copes and weld access holes shall be shaped free of notches and sharp
re-entrant corners except, when fillet web-to-flange welds are used in built-up
shapes, access holes are permitted to terminate perpendicular to the flange.
For ASTM A6 Group 4 and 5 shapes and built-up shapes of material more than
two inches thick, the thermally cut surfaces of beam copes and weld access holes
shall be ground to bright metal and inspected by either magnetic particle or dye
penetrant methods prior to deposition of splice welds. If the curved transition
portion of weld access holes and beam copes are formed by predrilled or sawed
holes, that portion of the access hole or cope need not be ground. Weld access
holes and beam copes in other shapes need not be ground nor inspected by dye
penetrant or magnetic particle methods.
7.
Minimum Strength of Connections
Except for lacing, sag rods, or girts, connections providing design strength shall
be designed to support a factored load not less than 10 kips.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
6 - 72
8.
CONNECTIONS, JOINTS, AND FASTENERS
[Chap J
Placement of Welds and Bolts
Groups of welds or bolts at the ends of any member which transmit axial force
into that member shall be sized so that the center of gravity of the group
coincides with the center of gravity of the member, unless provision is made for
the eccentricity. The foregoing provision is not applicable to end connections of
statically-loaded single angle, double angle, and similar members.
9.
Bolts in Combination with Welds
In new work, A307 bolts or high-strength bolts proportioned as bearing-type
connections shall not be considered as sharing the load in combination with
welds. Welds, if used, shall be proportioned for the entire force in the connection.
In slip-critical connections, high-strength bolts are permitted to be considered
as sharing the load with the welds.
In making welded alterations to structures, existing rivets and high-strength
bolts tightened to the requirements for slip-critical connections are permitted to
be utilized for carrying loads present at the time of alteration and the welding
need only provide the additional design strength required.
10.
High-Strength Bolts in Combination with Rivets
In both new work and alterations, in connections designed as slip-critical
connections in accordance with the provisions of Section J3, high-strength bolts
are permitted to be considered as sharing the load with rivets.
11.
Limitations on Bolted and Welded Connections
Fully tensioned high-strength bolts (see Table J3.1) or welds shall be used for
the following connections:
Column splices in all tier structures 200 ft or more in height.
Column splices in tier structures 100 to 200 ft in height, if the least horizontal
dimension is less than 40 percent of the height.
Column splices in tier structures less than 100 ft in height, if the least
horizontal dimension is less than 25 percent of the height.
Connections of all beams and girders to columns and of any other beams and
girders on which the bracing of columns is dependent, in structures over
125 ft in height.
In all structures carrying cranes of over five-ton capacity: roof-truss splices
and connections of trusses to columns, column splices, column bracing,
knee braces, and crane supports.
Connections for supports of running machinery, or of other live loads which
produce impact or reversal of stress.
Any other connections stipulated on the design plans.
In all other cases connections are permitted to be made with A307 bolts or
snug-tight high-strength bolts.
For the purpose of this section, the height of a tier structure shall be taken as the
vertical distance from the curb level to the highest point of the roof beams in the
case of flat roofs, or to the mean height of the gable in the case of roofs having
a rise of more than 22⁄3 in 12. Where the curb level has not been established, or
where the structure does not adjoin a street, the mean level of the adjoining land
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
Sect. J2]
WELDS
6 - 73
shall be used instead of curb level. It is permissible to exclude penthouses in
computing the height of structure.
J2.
WELDS
All provisions of the American Welding Society Structural Welding Code
Steel,, AWS D1.1, apply under this specification, except Chapter 10—Tubular
Structures, which is outside the scope of this specification, and except that the
provisions of the listed AISC LRFD Specification Sections apply under this
Specification in lieu of the cited AWS Code provisions as follows:
AISC Section J1.5 and J1.6 in lieu of AWS Section 3.2.5
AISC Section J2.2 in lieu of AWS Section 2.3.2.4
AISC Table J2.5 in lieu of AWS Table 8.1
AISC Table A-K3.2 in lieu of AWS Section 2.5
AISC Section K3 and Appendix K3 in lieu of AWS Chapter 9
AISC Section M2.2 in lieu of AWS Section 3.2.2
1.
Groove Welds
1a.
Effective Area
The effective area of groove welds shall be considered as the effective length of
the welds times the effective throat thickness.
The effective length of a groove weld shall be the width of the part joined.
The effective throat thickness of a complete-joint-penetration groove weld shall
be the thickness of the thinner part joined.
The effective throat thickness of a partial-joint-penetration groove weld shall be
as shown in Table J2.1.
The effective throat thickness of flare groove weld when flush to the surface of
a bar or 90º bend in formed section shall be as shown in Table J2.2. Random
sections of production welds for each welding procedure, or such test sections
as may be required by design documents, shall be used to verify that the effective
throat is consistently obtained.
Larger effective throat thicknesses than those in Table J2.2 are permitted,
provided the fabricator can establish by qualification the consistent production
of such larger effective throat thicknesses. Qualification shall consist of sectioning the weld normal to its axis, at mid-length and terminal ends. Such sectioning
shall be made on a number of combinations of material sizes representative of
the range to be used in the fabrication or as required by the designer.
1b.
Limitations
The minimum effective throat thickness of a partial-joint-penetration groove
weld shall be as shown in Table J2.3. Weld size is determined by the thicker of
the two parts joined, except that the weld size need not exceed the thickness of
the thinnest part joined when a larger size is required by calculated strength. For
this exception, particular care shall be taken to provide sufficient preheat for
soundness of the weld.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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CONNECTIONS, JOINTS, AND FASTENERS
[Chap J
TABLE J2.1
Effective Throat Thickness of
Partial-Penetration Groove Welds
Welding Process
Included Angle at
Root of Groove
Welding Position
Shielded metal arc
Submerged arc
Effective Throat
Thickness
J or U joint
Depth of chamfer
Bevel or V joint ≥ 60º
All
Gas metal arc
Bevel or V joint < 60º
but ≥ 45º
Flux-cored arc
Depth of chamfer
minus 1⁄8-in.
TABLE J2.2
Effective Throat Thickness of Flare Groove Welds
Radius (R) of Bar or Bend
Type of Weld
Effective Throat Thickness
Flare bevel groove
All
5⁄
Flare V-groove
All
1⁄ R
2
16R
[a] Use 3⁄8R for Gas Metal Arc Welding (except short circuiting transfer process) when R ≥ 1 in.
TABLE J2.3
Minimum Effective Throat Thickness of
Partial-Joint-Penentration Groove Welds
Material Thickness of
Thicker Part Joined (in.)
Minimum Effective
Throat Thickness[a] (in.)
To 1⁄4 inclusive
Over 1⁄4 to 1⁄2
Over 1⁄2 to 3⁄4
Over 3⁄4 to 11⁄2
Over 11⁄2 to 21⁄4
Over 21⁄4 to 6
Over 6
1⁄
8
3⁄
16
1⁄
4
5⁄
16
3⁄
8
1⁄
2
5⁄
8
[a] See Section J2.
2.
Fillet Welds
2a.
Effective Area
The effective area of fillet welds shall be as defined in American Welding
Society Code D1.1 Article 2.3.2, except 2.3.2.4. The effective throat thickness
of a fillet weld shall be the shortest distance from the root of the joint to the face
of the diagrammatic weld, except that for the fillet welds made by the submerged
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
Sect. J2]
WELDS
6 - 75
TABLE J2.4
Minimum Size of Fillet Welds[b]
Material Thickness of
Thicker Part Joined (in.)
Minimum Size of
Fillet Weld[a] (in.)
To 1⁄4 inclusive
Over 1⁄4 to 1⁄2
Over 1⁄2 to 3⁄4
Over 3⁄4
1⁄
8
3⁄
16
1⁄
4
5⁄
16
[a] Leg dimension of fillet welds. Single pass welds must be used.
[b] See Section J2.2b for maximum size of fillet welds.
arc process, the effective throat thickness shall be taken equal to the leg size for
3⁄ -in. and smaller fillet welds, and equal to the theoretical throat plus 0.11-in.
8
for fillet welds over 3⁄8-in.
For fillet welds in holes and slots, the effective length shall be the length of the
centerline of the weld along the center of the plane through the throat. In the
case of overlapping fillets, the effective area shall not exceed the nominal
cross-sectional area of the hole or slot, in the plane of the faying surface.
2b.
Limitations
The minimum size of fillet welds shall be not less than the size required to
transmit calculated forces nor the size as shown in Table J2.4 which is based
upon experiences and provides some margin for uncalculated stress encountered
during fabrication, handling, transportation, and erection. These provisions do
not apply to fillet weld reinforcements of partial- or complete-joint-penetration
welds.
The maximum size of fillet welds of connected parts shall be:
(a) Along edges of material less than 1⁄4-in. thick, not greater than the thickness
of the material.
(b) Along edges of material 1⁄4-in. or more in thickness, not greater than the
thickness of the material minus 1⁄16-in., unless the weld is especially designated on the drawings to be built out to obtain full-throat thickness. In the
as-welded condition, the distance between the edge of the base metal and
the toe of the weld is permitted to be less than 1⁄16-in. provided the weld size
is clearly verifiable.
(c) For flange-web welds and similar connections, the actual weld size need not
be larger than that required to develop the web capacity, and the requirements
of Table J2.4 need not apply.
The minimum effective length of fillet welds designed on the basis of strength
shall be not less than four times the nominal size, or else the size of the weld
shall be considered not to exceed 1⁄4 of its effective length. If longitudinal fillet
welds are used alone in end connections of flat-bar tension members, the length
of each fillet weld shall be not less than the perpendicular distance between
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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CONNECTIONS, JOINTS, AND FASTENERS
[Chap J
them. The transverse spacing of longitudinal fillet welds used in end connections
of tension members shall comply with Section B3.
The maximum effective length of fillet welds loaded by forces parallel to the
weld, such as lap splices, shall not exceed 70 times the fillet weld leg. A uniform
stress distribution may be assumed throughout the maximum effective length.
Intermittent fillet welds may be used to transfer calculated stress across a joint
or faying surfaces when the strength required is less than that developed by a
continuous fillet weld of the smallest permitted size, and to join components of
built-up members. The effective length of any segment of intermittent fillet
welding shall be not less than four times the weld size, with a minimum of 11⁄2-in.
In lap joints, the minimum amount of lap shall be five times the thickness of the
thinner part joined, but not less than one inch. Lap joints joining plates or bars
subjected to axial stress shall be fillet welded along the end of both lapped parts,
except where the deflection of the lapped parts is sufficiently restrained to
prevent opening of the joint under maximum loading.
Fillet welds terminations shall not be at the extreme ends or sides of parts or
members. They shall be either returned continuously around the ends or sides,
respectively for a distance of not less than two times the nominal weld size or
shall terminate not less than the nominal weld size from the sides or ends except
as follows. For details and structural elements such as brackets, beam seats,
framing angles, and simple end plates which are subject to cyclic (fatigue)
out-of-plane forces and/or moments of frequency and magnitude that would tend
to initiate a progressive failure of the weld, fillet welds shall be returned around
the side or end for a distance not less than two times the nominal weld size. For
framing angles and simple end-plate connections which depend upon flexibility
of the outstanding legs for connection flexibility, if end returns are used, their
length shall not exceed four times the nominal size of the weld. Fillet welds
which occur on opposite sides of a common plane shall be interrupted at the
corner common to both welds. End returns shall be indicated on the design and
detail drawings.
Fillet welds in holes or slots may be used to transmit shear in lap joints or to
prevent the buckling or separation of lapped parts and to join components of
built-up members. Such fillet welds may overlap, subject to the provisions of
Section J2. Fillet welds in holes or slots are not to be considered plug or slot
welds.
3.
Plug and Slot Welds
3a.
Effective Area
The effective shearing area of plug and slot welds shall be considered as the
nominal cross-sectional area of the hole or slot in the plane of the faying surface.
3b.
Limitations
Plug or slot welds are permitted to be used to transmit shear in lap joints or to
prevent buckling of lapped parts and to join component parts of built-up
members.
The diameter of the holes for a plug weld shall not be less than the thickness of
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
Sect. J2]
WELDS
6 - 77
the part containing it plus 5⁄16-in., rounded to the next larger odd 1⁄16-in., nor
greater than the minimum diameter plus 1⁄8-in. or 21⁄4 times the thickness of the
weld.
The minimum center-to-center spacing of plug welds shall be four times the
diameter of the hole.
The length of slot for a slot weld shall not exceed 10 times the thickness of the
weld. The width of the slot shall be not less than the thickness of the part
containing it plus 5⁄16-in. rounded to the next larger odd 1⁄16-in., nor shall it be
larger than 21⁄4 times the thickness of the weld. The ends of the slot shall be
semicircular or shall have the corners rounded to a radius of not less than the
thickness of the part containing it, except those ends which extend to the edge
of the part.
The minimum spacing of lines of slot welds in a direction transverse to their
length shall be four times the width of the slot. The minimum center-to-center
spacing in a longitudinal direction on any line shall be two times the length of
the slot.
The thickness of plug or slot welds in material 5⁄8-in. or less in thickness shall
be equal to the thickness of the material. In material over 5⁄8-in. thick, the
thickness of the weld shall be at least one-half the thickness of the material but
not less than 5⁄8-in.
4.
Design Strength
The design strength of welds shall be the lower value of φFBM ABM and φFw Aw,
when applicable. The values of φ, FBM , and Fw and limitations thereon are given
in Table J2.5,
where
FBM
Fw
ABM
Aw
φ
= nominal strength of the base material, ksi
= nominal strength of the weld electrode, ksi
= cross-sectional area of the base material, in.2
= effective cross-sectional area of the weld, in.2
= resistance factor
Alternatively, fillet welds loaded in-plane are permitted to be designed in
accordance with Appendix J2.4.
5.
Combination of Welds
If two or more of the general types of welds (groove, fillet, plug, slot) are
combined in a single joint, the design strength of each shall be separately
computed with reference to the axis of the group in order to determine the design
strength of the combination.
6.
Matching Weld Metal
The choice of electrode for use with complete-joint-penetration groove welds
subject to tension normal to the effective area shall comply with the requirements for matching weld metals given in AWS D1.1.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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CONNECTIONS, JOINTS, AND FASTENERS
[Chap J
TABLE J2.5
Design Strength of Welds
Types of Weld and
Stress [a]
Material
Resistance
Factor φ
Nominal
Strength
FBM or Fw
Required Weld
Strength Level [b,c]
Complete-Joint-Penetration Groove Weld
Tension normal to
effective area
Base
0.90
Fy
Compression normal to effective area
Tension or compression parallel to axis
of weld
Shear on effective
area
Base
0.90
Fy
Base
Weld electrode
0.90
0.80
0.60Fy
0.60FEXX
Matching weld
must be used.
Weld metal with a
strength level equal
to or less than
matching weld
metal is permitted
to be used.
Partial-Joint-Penetration Groove Weld
Compression normal to effective area
Tension or
compression
parallel to axis of
weld [d]
Base
0.90
Fy
Shear parallel to
axis of weld
Base
Weld electrode
0.75
[e]
0.60FEXX
Tension normal to
effective area
Base
Weld electrode
0.90
0.80
Fy
0.60FEXX
Weld metal with a
strength level equal
to or less than
matching weld
metal is permitted
to be used.
Fillet Welds
Shear on effective
area
Tension or compression parallel to axis
of weld [d]
Base
Weld electrode
0.75
[f]
0.60FEXX
Base
0.90
Fy
Weld metal with a
strength level equal
to or less than
matching weld metal
is permitted to be
used.
Plug or Slot Welds
Shear parallel to
faying surfaces (on
effective area)
Base
Weld electrode
0.75
[e]
0.60FEXX
Weld metal with a
strength level equal to
or less than matching
weld metal is
permitted to be used.
[a] For definition of effective area, see Section J2.
[b] For matching weld metal, see Table 4.1, AWS D1.1.
[c] Weld metal one strength level stronger than matching weld metal is permitted.
[d] Fillet welds and partial-joint-penetration groove welds joining component elements of built-up
members, such as flange-to-web connections, are not required to be designed with to the tensile or
compressive stress in these elements parallel to the axis of the welds.
[e] The design of connected material is governed by Sections J4 and J5.
[f] For alternative design strength, see Appendix J2.4.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
Sect. J3]
7.
BOLTS AND THREADED PARTS
6 - 79
Mixed Weld Metal
When notch-toughness is specified, the process consumables for all weld metal,
tack welds, root pass, and subsequent passes deposited in a joint shall be
compatible to assure notch-tough composite weld metal.
8.
Preheat for Heavy Shapes
For ASTM A6 Group 4 and 5 shapes and welded built-up members made of
plates more than two inches thick, a preheat equal to or greater than 350ºF shall
be used when making groove-weld splices.
J3.
BOLTS AND THREADED PARTS
1.
High-Strength Bolts
Use of high-strength bolts shall conform to the provisions of the Load and
Resistance Factor Design Specification for Structural Joints Using ASTM A325
or A490 Bolts, as approved by the Research Council on Structural Connections,
except as otherwise provided in this Specification.
If required to be tightened to more than 50 percent of their minimum specified
tensile strength, A449 bolts in tension and bearing-type shear connections shall
have an ASTM F436 hardened washer installed under the bolt head, and the nuts
shall meet the requirements of ASTM A563. When assembled, all joint surfaces,
including those adjacent to the washers, shall be free of scale, except tight mill
scale. Except as noted below, all A325 and A490 bolts shall be tightened to a
bolt tension not less than that given in Table J3.1. Tightening shall be done by
any of the following methods: turn-of-nut method, a direct tension indicator,
calibrated wrench, or alternative design bolt.
Bolts in connections not subject to tension loads, where slip can be permitted
and where loosening or fatigue due to vibration or load fluctuations are not
design considerations, need only to be tightened to the snug-tight condition. The
snug-tight condition is defined as the tightness attained by either a few impacts
of an impact wrench or the full effort of a worker with an ordinary spud wrench
that brings the connected plies into firm contact. The nominal strength value
given in Table J3.2 for bearing-type connections shall be used for bolts tightened
to the snug-tight condition. Bolts tightened only to the snug-tight condition shall
be clearly identified on the design and erection drawings.
When A490 bolts over one inch in diameter are used in slotted or oversize holes
in external plies, a single hardened washer conforming to ASTM F436, except
with 5⁄16-in. minimum thickness, shall be used in lieu of the standard washer.
In slip-critical connections in which the direction of loading is toward an edge
of a connected part, adequate bearing strength at factored load shall be provided
based upon the applicable requirements of Section J3.10.
2.
Size and Use of Holes
In slip-critical connections in which the direction of loading is toward edge of
connected part, adequate bearing capacity at factored load shall be provided
based upon the applicable requirements of Section J3.10.
The maximum sizes of holes for rivets and bolts are given in Table J3.3, except
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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CONNECTIONS, JOINTS, AND FASTENERS
[Chap J
TABLE J3.1
Minimum Bolt Tension, kips*
Bolt Size, in.
A325 Bolts
A490 Bolts
1⁄
2
5⁄
8
3⁄
4
7⁄
8
12
19
28
39
51
56
71
85
103
15
24
35
49
64
80
102
121
148
1
11⁄8
11⁄4
13⁄8
11⁄2
* Equal to 0.70 of minimum tensile strength of bolts, rounded off to nearest kip, as specified in ASTM
specifications for A325 and A490 bolts with UNC threads.
that larger holes, required for tolerance on location of anchor bolts in concrete
foundations, are allowed in column base details.
Standard holes shall be provided in member-to-member connections, unless
oversized, short-slotted, or long-slotted holes in bolted connections are approved by the designer. Finger shims up to 1⁄4-in. are permitted in slip-critical
connections designed on the basis of standard holes without reducing the
nominal shear strength of the fastener to that specified for slotted holes.
Oversized holes are allowed in any or all plies of slip-critical connections, but
they shall not be used in bearing-type connections. Hardened washers shall be
installed over oversized holes in an outer ply.
Short-slotted holes are allowed in any or all plies of slip-critical or bearing-type
connections. The slots are permitted to be used without regard to direction of
loading in slip-critical connections, but the length shall be normal to the
direction of the load in bearing-type connections. Washers shall be installed over
short-slotted holes in an outer ply; when high-strength bolts are used, such
washers shall be hardened.
Long-slotted holes are allowed in only one of the connected parts of either a
slip-critical or bearing-type connection at an individual faying surface. Longslotted holes are permitted to be used without regard to direction of loading in
slip-critical connections, but shall be normal to the direction of load in bearingtype connections. Where long-slotted holes are used in an outer ply, plate
washers, or a continuous bar with standard holes, having a size sufficient to
completely cover the slot after installation, shall be provided. In high-strength
bolted connections, such plate washers or continuous bars shall be not less than
5⁄ -in. thick and shall be of structural grade material, but need not be hardened.
16
If hardened washers are required for use of high-strength bolts, the hardened
washers shall be placed over the outer surface of the plate washer or bar.
3.
Minimum Spacing
The distance between centers of standard, oversized, or slotted holes, shall not
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
Sect. J3]
BOLTS AND THREADED PARTS
6 - 81
TABLE J3.2
Design Strength of Fasteners
Tensile Strength
Description of Fasteners
Resistance
Factor φ
Nominal
Strength, ksi
Shear Strength in
Bearing-type Connections
Resistance
Factor φ
Nominal
Strength, ksi
A307 bolts
45 [a]
24 [b,e]
A325 bolts, when threads
are not excluded from
shear planes
90 [d]
48 [e]
A325 bolts, when threads
are excluded from shear
planes
90 [d]
60 [e]
A490 bolts, when threads
are not excluded from
shear planes
113 [d]
60 [e]
A490 bolts, when threads
are excluded from shear
planes
0.75
113 [d]
0.75
75 [e]
Threaded parts meeting
the requirements of Sect.
A3, when threads are not
excluded from shear planes
0.75Fu [a,c]
0.40Fu
Threaded parts meeting
the requirements of Sect.
A3, when threads are
excluded from shear planes
0.75Fu [a,c]
0.50Fu [a,c]
A502, Gr. 1, hot-driven
rivets
45 [a]
25 [e]
A502, Gr. 2 & 3, hot-driven
rivets
60 [a]
33 [e]
[a] Static loading only.
[b] Threads permitted in shear planes.
[c] The nominal tensile strength of the threaded portion of an upset rod, based upon the cross-sectional
area at its major thread diameter, AD shall be larger than the nominal body area of the rod before
upsetting times Fy.
[d] For A325 and A490 bolts subject to tensile fatigue loading, see Appendix K3.
[e] When bearing-type connections used to splice tension members have a fastener pattern whose
length, measured parallel to the line of force, exceeds 50 in., tabulated values shall be reduced by
20 percent.
be less than 22⁄3 times the nominal diameter of the fastener; a distance of 3d is
preferred. Refer to Section J3.10 for bearing strength requirement.
4.
Minimum Edge Distance
The distance from the center of a standard hole to an edge of a connected part
shall not be less than either the applicable value from Table J3.4, or as required
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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CONNECTIONS, JOINTS, AND FASTENERS
[Chap J
TABLE J3.3
Nominal Hole Dimensions
Hole Dimensions
Bolt
Diameter
Standard
(Dia.)
Oversize
(Dia.)
1⁄
2
5⁄
8
3⁄
4
7⁄
8
9⁄
16
11⁄
16
13⁄
16
15⁄
16
11⁄16
d + 1⁄16
5⁄
8
13⁄
16
15⁄
16
1
1 ⁄16
11⁄4
d + 5⁄16
1
≥11⁄8
Short-slot
(Width × Length)
(d
Long-slot
Width × Length)
9⁄ × 11⁄
16
16
11⁄ × 7⁄
16
8
13⁄ × 1
16
15⁄ × 11⁄
16
8
11⁄16 × 15⁄16
+ 1⁄16) × (d + 3⁄8)
(d
9⁄ × 11⁄
16
4
11⁄ × 19⁄
16
16
13⁄ × 17⁄
16
8
15⁄ × 23⁄
16
16
11⁄16 × 21⁄2
+ 1⁄16) × (2.5 ×
d)
TABLE J3.4
Minimum Edge Distance,[a] in.
(Center of Standard Hole[b] to Edge of Connected Part)
Nominal Rivet or
Bolt Diameter (in.)
1⁄
2
5⁄
8
3⁄
4
7⁄
8
1
11⁄8
11⁄4
Over 11⁄4
At Sheared Edges
At Rolled Edges of Plates,
Shapes or Bars, or
Gas Cut Edges [c]
7⁄
8
11⁄8
11⁄4
11⁄2 [d]
13⁄4 [d]
2
21⁄4
13⁄4 × Diameter
3⁄
4
7⁄
8
1
11⁄8
11⁄4
11⁄2
15⁄8
11⁄4 × Diameter
[a] Lesser edge distances are permitted to be used provided Equations from J3.10, as appropriate, are
satisfied.
[b] For oversized or slotted holes, see Table J3.8.
[c] All edge distances in this column are permitted to be reduced 1⁄8-in. when the hole is at a point where
stress does not exceed 25 percent of the maximum design strength in the element.
[d] These are permitted to be 11⁄4-in. at the ends of beam connection angles and shear end plates.
in Section J3.10. The distance from the center of an oversized or slotted hole to
an edge of a connected part shall be not less than that required for a standard
hole to an edge of a connected part plus the applicable increment C2 from
Table J3.8. Refer to Section J3.10 for bearing strength requirement.
5.
Maximum Spacing and Edge Distance
The maximum distance from the center of any bolt or rivet to the nearest edge
of parts in contact shall be 12 times the thickness of the connected part under
consideration, but shall not exceed six inches. The longitudinal spacing of
connectors between elements in continuous contact consisting of a plate and a
shape or two plates shall be as follows:
(a) For painted members or unpainted members not subject to corrosion, the
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
Sect. J3]
BOLTS AND THREADED PARTS
6 - 83
spacing shall not exceed 24 times the thickness of the thinner plate or 12
inches.
(b) For unpainted members of weathering steel subject to atmospheric corrosion, the spacing shall not exceed 14 times the thickness of the thinner plate
or seven inches.
6.
Design Tension or Shear Strength
The design tension or shear strength of a high-strength bolt or threaded part is
φFn Ab
where
φ = resistance factor tabulated in Table J3.2
Fn = nominal tensile strength Ft , or shear strength, Fv, tabulated in Table J3.2,
ksi
Ab = nominal unthreaded body area of bolt or threaded part (for upset rods,
see Footnote c, Table J3.2), in.2
The applied load shall be the sum of the factored loads and any tension resulting
from prying action produced by deformation of the connected parts.
7.
Combined Tension and Shear in Bearing-Type Connections
The design strength of a bolt or rivet subject to combined tension and shear is
φFt Ab, where φ is 0.75 and the nominal tension stress Ft shall be computed from
the equations in Table J3.5 as a function of fv, the required shear stress produced
by the factored loads. The design shear strength φFv, tabulated in Table J3.2, shall
equal or exceed the shear stress, fv.
8.
High-Strength Bolts in Slip-Critical Connections
The design for shear of high-strength bolts in slip-critical connections shall be
in accordance with either Section J3.8a or J3.8b and checked for bearing in
accordance with J3.2 and J3.10.
8a.
Slip-Critical Connections Designed at Service Loads
The design resistance to shear of a bolt in a slip-critical connection is φFv Ab,
where
φ = 1.0 for standard, oversized, short-slotted, and long-slotted holes when
the long slot is perpendicular to the line of force
φ = 0.85 for long-slotted holes when the long slot is parallel to the line of
force
Fv = nominal slip-critical shear resistance tabulated in Table J3.6, ksi
The design resistance to shear shall equal or exceed the shear on the bolt due to
service loads. When the loading combination includes wind loads in addition to
dead and live loads, the total shear on the bolt due to combined load effects, at
service load, may be multiplied by 0.75.
The values for Fv in Table J3.6 are based on Class A (slip coefficient 0.33), clean
mill scale and blast cleaned surfaces with class A coatings. When specified by
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
6 - 84
CONNECTIONS, JOINTS, AND FASTENERS
[Chap J
TABLE J3.5
Tension Stress Limit (Ft), ksi
Fasteners in Bearing-type Connections
Description of Fasteners
Threads Included in
the Shear Plane
Threads Excluded from
the Shear Plane
59 − 1.9fv ≤ 45
A307 bolts
A325 bolts
117 − 1.9fv ≤ 90
117 − 1.5fv ≤ 90
A490 bolts
147 − 1.9fv ≤ 113
147 − 1.5fv ≤ 113
0.98Fu − 1.9fv ≤ 0.75Fu
0.98Fu − 1.5fv ≤ 0.75Fu
Threaded parts A449 bolts
over 11⁄2 diameter
A502 Gr.1 rivets
59 − 1.8fv ≤ 45
A502 Gr.2 rivets
78 − 1.8fv ≤ 60
TABLE J3.6
Slip-Critical Nominal Resistance to Shear, ksi,
of High-Strength Bolts[a]
Nominal Resistance to Shear
Type of Bolt
Standard Size Holes
Oversized and
Short-slotted Holes
Long-slotted Holes
A325
A490
17
21
15
18
12
15
[a] For each shear plane.
the designer, the nominal slip resistance for connections having special faying
surface conditions are permitted to be adjusted to the applicable values in the
RCSC Load and Resistance Factor Design Specification.
Finger shims up to 1⁄4-in. are permitted to be introduced into slip-critical
connections designed on the basis of standard holes without reducing the design
shear stress of the fastener to that specified for slotted holes.
8b.
Slip-Critical Connections Designed at Factored Loads
See Appendix J3.8b.
9.
Combined Tension and Shear in Slip-Critical Connections
The design of slip-critical connections subject to tensile forces shall be in
accordance with either Sections J3.9a and J3.8a or Sections J3.9b and J3.8b.
9a.
Slip-Critical Connections Designed at Service Loads
The design resistance to shear of a bolt in a slip-critical connection subject to a
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
Sect. J3]
BOLTS AND THREADED PARTS
6 - 85
tensile force T due to service loads shall be computed according to Section J3.8a
multiplied by the following reduction factor,
1 −
T
Tb
where
Tb = minimum bolt pre-tension from Table J3.1
9b.
Slip-Critical Connections Designed at Factored Loads
See Appendix J3.9b.
10.
Bearing Strength at Bolt Holes
The design bearing strength at bolt holes is φRn, where
φ = 0.75
Rn = nominal bearing strength
Bearing strength shall be checked for both bearing-type and slip-critical connections. The use of oversize holes and short- and long-slotted holes parallel to
the line of force is restricted to slip-critical connections per Section J3.2.
In the following sections:
Le = distance (in.) along the line of force from the edge of the connected
part to the center of a standard hole or the center of a short- and longslotted hole perpendicular to the line of force. For oversize holes and
short- and long-slotted holes parallel to the line of force, Le shall be
increased by the increment C2 of Table J3.8.
s = distance (in.) along the line of force between centers of standard
holes, or between centers of short- and long-slotted holes perpendicular
to the line of force. For oversize holes and short- and long-slotted holes
parallel to the line of force, s shall be increased by the spacing
increment C1 of Table J3.7.
d = diameter of bolt, in.
Fu = specified minimum tensile strength of the critical part, ksi
t = thickness of the critical connected part, in. For countersunk bolts and
rivets, deduct one-half the depth of the countersink.
(a) When Le ≥ 1.5d and s ≥ 3d and there are two or more bolts in line of force:
For standard holes; short and long-slotted holes perpendicular to the line of
force; oversize holes in slip-critical connections; and long and short-slotted
holes in slip-critical connections when the line of force is parallel to the axis
of the hole:
When deformation around the bolt holes is a design consideration
Rn = 2.4dtFu
(J3-1a)
When deformation around the bolt holes is not a design consideration, for
the bolt nearest the edge
Rn = LetFu ≤ 3.0dtFu
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
(J3-1b)
6 - 86
CONNECTIONS, JOINTS, AND FASTENERS
[Chap J
TABLE J3.7
Values of Spacing Increment C1, in.
Slotted Holes
Nominal
Diameter of
Fastener
≤7⁄8
1
≥11⁄8
Oversize Holes
Perpendicular
to Line
of Force
Short-slots
Long-slots [a]
1⁄
8
3⁄
16
1⁄
4
0
0
0
3⁄
16
1⁄
4
5⁄
16
11⁄2d − 1⁄16
17⁄16
11⁄2d − 1⁄16
Parallel to Line of Force
[a] When length of slot is less than maximum allowed in Table J3.5, C1 are permitted to be reduced by
the difference between the maximum and actual slot lengths.
TABLE J3.8
Values of Edge Distance Increment C2, in.
Slotted Holes
Nominal
Diameter of
Fastener (in.)
≤7⁄8
Long Axis Perpendicular to Edge
Oversized Holes
1⁄
Short Slots
16
1⁄
8
1
1⁄
8
1⁄
8
≥11⁄8
1⁄
8
3⁄
16
Long Slots [a]
Long Axis
Parallel to Edge
3⁄ d
4
0
[a] When length of slot is less than maximum allowable (see Table J3.5), C2 are permitted to be reduced
by one-half the difference between the maximum and actual slot lengths.
and for the remaining bolts
Rn = (s − d / 2)tFu ≤ 3.0dtFu
(J3-1c)
For long-slotted bolt holes perpendicular to the line of force:
Rn = 2.0dtFu
(J3-1d)
(b) When Le < 1.5d or s < 3d or for a single bolt in the line of force:
For standard holes; short and long-slotted holes perpendicular to the line of
force; oversize holes in slip-critical connections; and long and short-slotted
holes in slip-critical connections when the line of force is parallel to the axis
of the hole:
For a single bolt hole or the bolt hole nearest the edge when there are two or
more bolt holes in the line of force
Rn = LetFu ≤ 2.4dtFu
For the remaining bolt holes
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
(J3-2a)
Sect. J4]
DESIGN RUPTURE STRENGTH
6 - 87
Rn = (s − d / 2)tFu ≤ 2.4dtFu
(J3-2b)
For long-slotted bolt holes perpendicular to the line of force:
For a single bolt hole or the bolt hole nearest the edge where there are two
or more bolt holes in the line of force
Rn = LetFu ≤ 2.0dtFu
(J3-2c)
For the remaining bolt holes
Rn = (s − d / 2)tFu ≤ 2.0dtFu
11.
(J3-2d)
Long Grips
A307 bolts providing design strength, and for which the grip exceeds five
diameters, shall have their number increased one percent for each additional
1⁄ -in. in the grip.
16
J4.
DESIGN RUPTURE STRENGTH
1.
Shear Rupture Strength
The design strength for the limit state of rupture along a shear failure path in the
affected elements of connected members shall be taken as φRn
where
φ = 0.75
Rn = 0.6Fu Anv
Anv = net area subject to shear, in.2
2.
(J4-1)
Tension Rupture Strength
The design strength for the limit state of rupture along a tension path in the
affected elements of connected members shall be taken as φRn
where
φ = 0.75
Rn = Fu Ant
Ant = net area subject to tension, in.2
3.
(J4-2)
Block Shear Rupture Strength
Block shear is a limit state in which the resistance is determined by the sum of
the shear strength on a failure path(s) and the tensile strength on a perpendicular
segment. It shall be checked at beam end connections where the top flange is
coped and in similar situations, such as tension members and gusset plates.
When ultimate rupture strength on the net section is used to determine the
resistance on one segment, yielding on the gross section shall be used on the
perpendicular segment. The block shear rupture design strength, φRn, shall be
determined as follows:
(a) When Fu Ant ≥ 0.6Fu Anv :
φRn = φ[0.6Fy Agv + Fu Ant]
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
(J4-3a)
6 - 88
CONNECTIONS, JOINTS, AND FASTENERS
[Chap J
(b) When 0.6Fu Anv > Fu Ant :
φRn = φ[0.6Fu Anv + Fy Agt]
(J4-3b)
where
φ = 0.75
Agv = gross area subject to shear, in.2
Agt = gross area subject to tension, in.2
Anv = net area subjected to shear, in.2
Ant = net area subjected to tension, in.2
J5.
CONNECTING ELEMENTS
This section applies to the design of connecting elements, such as plates, gussets,
angles, brackets, and the panel zones of beam-to-column connections.
1.
Eccentric Connections
Intersecting axially stressed members shall have their gravity axis intersect at
one point, if practicable; if not, provision shall be made for bending and shearing
stresses due to the eccentricity. Also see Section J1.8.
2.
Design Strength of Connecting Elements in Tension
The design strength, φRn, of welded, bolted, and riveted connecting elements
statically loaded in tension (e.g., splice and gusset plates) shall be the lower
value obtained according to limit states of yielding, rupture of the connecting
element, and block shear rupture.
(a) For tension yielding of the connecting element:
φ = 0.90
Rn = AgFy
(J5-1)
(b) For tension rupture of the connecting element:
φ = 0.75
Rn = AnFu
(J5-2)
where An is the net area, not to exceed 0.85Ag.
(c) For block shear rupture of connecting elements, see Section J4.3.
3.
Other Connecting Elements
For all other connecting elements, the design strength, φRn, shall be determined
for the applicable limit state to ensure that the design strength is equal to or
greater than the required strength, where Rn is the nominal strength appropriate
to the geometry and type of loading on the connecting element. For shear
yielding of the connecting element:
φ = 0.90
Rn = 0.60AgFy
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
(J5-3)
Sect. J8]
BEARING STRENGTH
6 - 89
If the connecting element is in compression an appropriate limit state analysis
shall be made.
J6.
FILLERS
In welded construction, any filler 1⁄4-in. or more in thickness shall extend beyond
the edges of the splice plate and shall be welded to the part on which it is fitted
with sufficient weld to transmit the splice plate load, applied at the surface of
the filler. The welds joining the splice plate to the filler shall be sufficient to
transmit the splice plate load and shall be long enough to avoid overloading the
filler along the toe of the weld. Any filler less than 1⁄4-in. thick shall have its
edges made flush with the edges of the splice plate and the weld size shall be
the sum of the size necessary to carry the splice plus the thickness of the filler
plate.
When bolts or rivets carrying loads pass through fillers thicker than 1⁄4-in., except
in connections designed as slip-critical connections, the fillers shall be extended
beyond the splice material and the filler extension shall be secured by enough
bolts or rivets to distribute the total stress in the member uniformly over the
combined section of the member and the filler, or an equivalent number of
fasteners shall be included in the connection. Fillers between 1⁄4-in. and 3⁄4-in.
thick, inclusive, need not be extended and developed, provided the design shear
strength of the bolts is reduced by the factor, 0.4(t − 0.25), where t is the total
thickness of the fillers, up to 3⁄4-in.
J7.
SPLICES
Groove-welded splices in plate girders and beams shall develop the full strength
of the smaller spliced section. Other types of splices in cross sections of plate
girders and beams shall develop the strength required by the forces at the point
of splice.
J8.
BEARING STRENGTH
The strength of surfaces in bearing is φRn, where
φ = 0.75
Rn is defined below for the various types of bearing
(a) For milled surfaces, pins in reamed, drilled, or bored holes, and ends of fitted
bearing stiffeners,
Rn = 1.8Fy Apb
(J8-1)
where
Fy = specified minimum yield stress, ksi
Apb = projected bearing area, in.2
(b) For expansion rollers and rockers,
If d ≤ 25 in.,
Rn = 1.2(Fy − 13)ld / 20
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
(J8-2)
6 - 90
CONNECTIONS, JOINTS, AND FASTENERS
[Chap J
Rn = 6.0(Fy − 13)l√
d / 20
(J8-3)
If d > 25 in.,
where
d = diameter, in.
l = length of bearing, in.
J9.
COLUMN BASES AND BEARING ON CONCRETE
Proper provision shall be made to transfer the column loads and moments to the
footings and foundations.
In the absence of code regulations, design bearing loads on concrete may be
taken as φcPp:
(a) On the full area of a concrete support
Pp = 0.85fc′A1
(J9-1)
(b) On less than the full area of a concrete support
Pp = 0.85fc′A1√
A2 / A
1
(J9-2)
where
φc = 0.60
A1 = area of steel concentrically bearing on a concrete support, in.
A2 = maximum area of the portion of the supporting surface that is geometrically similar to and concentric with the loaded area, in.2
√
A2 / A
1 ≤ 2
J10. ANCHOR BOLTS AND EMBEDMENTS
Anchor bolts and embedments shall be designed in accordance with American
Concrete Institute or Prestressed Concrete Institute criteria. If the load factors
and combinations given in Section A4.1 are used, a reduction in the φ factors
specified by ACI shall be made based on the ratio of load factors given in Section
A4.1 and in ACI.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
6 - 91
CHAPTER K
CONCENTRATED FORCES, PONDING, AND FATIGUE
This chapter covers member strength design considerations pertaining to concentrated
forces, ponding, and fatigue.
K1. FLANGES AND WEBS WITH CONCENTRATED FORCES
1.
Design Basis
Sections K1.2 through K1.7 apply to single and double concentrated forces as
indicated in each Section. A single concentrated force is tensile or compressive.
Double concentrated forces, one tensile and one compressive, form a couple on
the same side of the loaded member.
Transverse stiffeners are required at locations of concentrated tensile forces in
accordance with Section K1.2 for the flange limit state of local bending, and at
unframed ends of beams and girders in accordance with Section K1.8. Transverse stiffeners or doubler plates are required at locations of concentrated forces
in accordance with Sections K1.3 through K1.6 for the web limit states of
yielding, crippling, sidesway buckling, and compression buckling. Doubler
plates or diagonal stiffeners are required in accordance with Section K1.7 for
the web limit state of panel-zone shear.
Transverse stiffeners and diagonal stiffeners required by Sections K1.2 through
K1.8 shall also meet the requirements of Section K1.9. Doubler plates required
by Sections K1.3 through K1.6 shall also meet the requirements of Section K1.10.
2.
Local Flange Bending
This Section applies to both tensile single-concentrated forces and the tensile
component of double-concentrated forces.
A pair of transverse stiffeners extending at least one-half the depth of the web
shall be provided adjacent to a concentrated tensile force centrally applied across
the flange when the required strength of the flange exceeds φRn, where
φ = 0.90
Rn = 6.25tf2Fyf
where
Fyf = specified minimum yield stress of the flange, ksi
tf = thickness of the loaded flange, in.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
(K1-1)
6 - 92
CONCENTRATED FORCES, PONDING, AND FATIGUE
[Chap. K
If the length of loading measured across the member flange is less than 0.15b,
where b is the member flange width, Equation K1-1 need not be checked.
When the concentrated force to be resisted is applied at a distance from the
member end that is less than 10tf, Rn shall be reduced by 50 percent.
When transverse stiffeners are required, they shall be welded to the loaded
flange to develop the welded portion of the stiffener. The weld connecting
transverse stiffeners to the web shall be sized to transmit the unbalanced force
in the stiffener to the web. Also, see Section K1.9.
3.
Local Web Yielding
This Section applies to single-concentrated forces and both components of
double-concentrated forces.
Either a pair of transverse stiffeners or a doubler plate, extending at least one-half
the depth of the web, shall be provided adjacent to a concentrated tensile or
compressive force when the required strength of the web at the toe of the fillet
exceeds φRn, where
φ = 1.0
and Rn is determined as follows:
(a) When the concentrated force to be resisted is applied at a distance from the
member end that is greater than the depth of the member d,
Rn = (5k + N)Fyw tw
(K1-2)
(b) When the concentrated force to be resisted is applied at a distance from the
member end that is less than or equal to the depth of the member d,
Rn = (2.5k + N)Fywtw
(K1-3)
In Equations K1-2 and K1-3, the following definitions apply:
Fyw
N
k
tw
= specified minimum yield stress of the web, ksi
= length of bearing (not less than k for end beam reactions), in.
= distance from outer face of the flange to the web toe of the fillet, in.
= web thickness, in.
When required for a tensile force normal to the flange, transverse stiffeners shall
be welded to the loaded flange to develop the connected portion of the stiffener.
When required for a compressive force normal to the flange, transverse stiffeners shall either bear on or be welded to the loaded flange to develop the force
transmitted to the stiffener. The weld connecting transverse stiffeners to the web
shall be sized to transmit the unbalanced force in the stiffener to the web. Also,
see Section K1.9.
Alternatively, when doubler plates are required, see Section K1.10.
4.
Web Crippling
This Section applies to both compressive single-concentrated forces and the
compressive component of double-concentrated forces.
Either a transverse stiffener, a pair of transverse stiffeners, or a doubler plate,
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
Sect. K1]
FLANGES AND WEBS WITH CONCENTRATED FORCES
6 - 93
extending at least one-half the depth of the web, shall be provided adjacent to a
concentrated compressive force when the required strength of the web exceeds
φRn, where
φ = 0.75
and Rn is determined as follows:
(a) When the concentrated compressive force to be resisted is applied at a
distance from the member end that is greater than or equal to d / 2,
1.5
√
N tw
Rn = 135t2w 1 + 3
d tf
Fywtf
tw
(K1-4)
(b) When the concentrated compressive force to be resisted is applied at a
distance from the member end that is less than d / 2,
For N / d ≤ 0.2,
N tw
Rn = 68t 1 + 3
d tf
1.5
2
w
t
√
Fywtf
(K1-5a)
w
For N / d > 0.2,
1.5
4N
tw
Rn = 68t2w 1 +
− 0.2
tf
d
√
Fywtf
tw
(K1-5b)
In Equations K1-4 and K1-5, the following definitions apply:
d = overall depth of the member, in.
tf = flange thickness, in.
When transverse stiffeners are required, they shall either bear on or be welded
to the loaded flange to develop the force transmitted to the stiffener. The weld
connecting transverse stiffeners to the web shall be sized to transmit the
unbalanced force in the stiffener to the web. Also, see Section K1.9.
Alternatively, when doubler plates are required, see Section K1.10.
5.
Sidesway Web Buckling
This Section applies only to compressive single-concentrated forces applied to
members where relative lateral movement between the loaded compression
flange and the tension flange is not restrained at the point of application of the
concentrated force.
The design strength of the web is φRn, where
φ = 0.85
and Rn is determined as follows:
(a) If the compression flange is restrained against rotation:
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
6 - 94
CONCENTRATED FORCES, PONDING, AND FATIGUE
[Chap. K
for (h / tw) / (l / bf) ≤ 2.3,
3
h / tw
Cr t3w tf
Rn =
1 + 0.4
h2
l / bf
(K1-6)
for (h / tw) / (l / bf) > 2.3, the limit state of sidesway web buckling does not
apply.
When the required strength of the web exceeds φRn, local lateral bracing
shall be provided at the tension flange or either a pair of transverse stiffeners
or a doubler plate, extending at least one-half the depth of the web, shall be
provided adjacent to the concentrated compressive force.
When transverse stiffeners are required, they shall either bear on or be
welded to the loaded flange to develop the full applied force. The weld
connecting transverse stiffeners to the web shall be sized to transmit the force
in the stiffener to the web. Also, see Section K1.9.
Alternatively, when doubler plates are required, they shall be sized to
develop the full applied force. Also, see Section K1.10.
(b) If the compression flange is not restrained against rotation:
for (h / tw) / (l / bf) ≤ 1.7,
3
Cr t3w tf
Rn =
h2
h / tw
0.4
l / bf
(K1-7)
for (h / tw) / (l / bf) > 1.7, the limit state of sidesway web buckling does not
apply.
When the required strength of the web exceeds φRn, local lateral bracing
shall be provided at both flanges at the point of application of the concentrated forces.
In Equations K1-6 and K1-7, the following definitions apply:
l
bf
tw
h
= largest laterally unbraced length along either flange at the point of load, in.
= flange width, in.
= web thickness, in.
= clear distance between flanges less the fillet or corner radius for rolled
shapes; distance between adjacent lines of fasteners or the clear
distance between flanges when welds are used for built-up shapes, in.
Cr = 960,000 when Mu < My at the location of the force, ksi
= 480,000 when Mu ≥ My at the location of the force, ksi
6.
Compression Buckling of the Web
This Section applies to a pair of compressive single-concentrated forces or the
compressive components in a pair of double-concentrated forces, applied at both
flanges of a member at the same location.
Either a single transverse stiffener, or pair of transverse stiffeners, or a doubler
plate, extending the full depth of the web, shall be provided adjacent to
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
Sect. K1]
FLANGES AND WEBS WITH CONCENTRATED FORCES
6 - 95
concentrated compressive forces at both flanges when the required strength of
the web exceeds φRn, where
φ = 0.90
and
Rn =
4,100t3w√
Fyw
(K1-8)
h
When the pair of concentrated compressive forces to be resisted is applied at a
distance from the member end that is less than d / 2, Rn shall be reduced by 50
percent.
When transverse stiffeners are required, they shall either bear on or be welded
to the loaded flange to develop the force transmitted to the stiffener. The weld
connecting transverse stiffeners to the web shall be sized to transmit the
unbalanced force in the stiffener to the web. Also, see Section K1.9.
Alternatively, when doubler plates are required, see Section K1.10.
7.
Panel-Zone Web Shear
Either doubler plates or diagonal stiffeners shall be provided within the boundaries of the rigid connection of members whose webs lie in a common plane when
the required strength exceeds φRv, where
φ = 0.90
and Rv is determined as follows:
(a) When the effect of panel-zone deformation on frame stability is not considered in the analysis,
For Pu ≤ 0.4Py
Rv = 0.60Fy dc tw
(K1-9)
For Pu > 0.4Py
Rv = 0.60Fy dc tw 1.4 −
Pu
Py
(K1-10)
(b) When frame stability, including plastic panel-zone deformation, is considered in the analysis:
For Pu ≤ 0.75Py
3bcf tcf2
Rv = 0.60Fy dc tw 1 +
db d c t
(K1-11)
3bcf tcf2
1.2Pu
Rv = 0.60Fy dc tw 1 +
1.9 −
db dc tw
Py
(K1-12)
For Pu > 0.75Py
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
6 - 96
CONCENTRATED FORCES, PONDING, AND FATIGUE
[Chap. K
In Equations K1-9 through K1-12, the following definitions apply:
tw
bcf
tcf
db
dc
Fy
Py
A
= column web thickness, in.
= width of column flange, in.
= thickness of the column flange, in.
= beam depth, in.
= column depth, in.
= yield strength of the column web, in.
= Fy A, axial yield strength of the column, in.
= column cross-sectional area, in.
When doubler plates are required, they shall meet the criteria of Section F2 and
shall be welded to develop the proportion of the total shear force which is to be
carried.
Alternatively, when diagonal stiffeners are required, the weld connecting diagonal stiffeners to the web shall be sized to transmit the stiffener force caused by
unbalanced moments to the web. Also, see Section K1.9.
8.
Unframed Ends of Beams and Girders
At unframed ends of beams and girders not otherwise restrained against rotation
about their longitudinal axes, a pair of transverse stiffeners, extending the full
depth of the web, shall be provided. Also, see Section K1.9.
9.
Additional Stiffener Requirements for Concentrated Forces
Transverse and diagonal stiffeners shall also comply with the following criteria:
(1) The width of each stiffener plus one-half the thickness of the column web
shall not be less than one-third of the width of the flange or moment
connection plate delivering the concentrated force.
(2) The thickness of a stiffener shall not be less than one-half the thickness of
the flange or moment connection plate delivering the concentrated load, and
not less than its width times √
Fy / 95.
Full depth transverse stiffeners for compressive forces applied to a beam or plate
girder flange shall be designed as axially compressed members (columns) in
accordance with the requirements of Section E2, with an effective length of
0.75h, a cross section composed of two stiffeners and a strip of the web having
a width of 25tw at interior stiffeners and 12tw at the ends of members.
The weld connecting bearing stiffeners to the web shall be sized to transmit the
excess web shear force to the stiffener. For fitted bearing stiffeners, see Section J8.1.
10.
Additional Doubler Plate Requirements for Concentrated Forces
Doubler plates required by Sections K1.3 through K1.6 shall also comply with
the following criteria:
(1) The thickness and extent of the doubler plate shall provide the additional
material necessary to equal or exceed the strength requirements.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
Sect. K3]
FATIGUE
6 - 97
(2) The doubler plate shall be welded to develop the proportion of the total force
transmitted to the doubler plate.
K2. PONDING
The roof system shall be investigated by structural analysis to assure adequate
strength and stability under ponding conditions, unless the roof surface is
provided with sufficient slope toward points of free drainage or adequate
individual drains to prevent the accumulation of rainwater.
The roof system shall be considered stable and no further investigation is needed
if:
Cp + 0.9Cs ≤ 0.25
(K2-1)
Id ≥ 25(S4)10−6
(K2-2)
where
Cp =
32LsL4p
107Ip
Cs =
32SL4s
107Is
Lp = column spacing in direction of girder (length of primary members), ft
Ls = column spacing perpendicular to direction of girder (length of secondary
members), ft
S = spacing of secondary members, ft
Ip = moment of inertia of primary members, in.4
Is = moment of inertia of secondary members, in.4
Id = moment of inertia of the steel deck supported on secondary members, in.4
per ft
For trusses and steel joists, the moment of inertia Is shall be decreased 15 percent
when used in the above equation. A steel deck shall be considered a secondary
member when it is directly supported by the primary members.
See Appendix K2 for an alternate determination of flat roof framing stiffness.
K3. FATIGUE
Few members or connections in conventional buildings need to be designed for
fatigue, since most load changes in such structures occur only a small number
of times or produce only minor stress fluctuations. The occurrence of full design
wind or earthquake loads is too infrequent to warrant consideration in fatigue
design. However, crane runways and supporting structures for machinery and
equipment are often subject to fatigue loading conditions.
Members and their connections subject to fatigue loading shall be proportioned
in accordance with the provisions of Appendix K3 for service loads.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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CHAPTER L
SERVICEABILITY DESIGN CONSIDERATIONS
This chapter is intended to provide design guidance for serviceability considerations.
Serviceability is a state in which the function of a building, its appearance, maintainability, durability, and comfort of its occupants are preserved under normal usage. The
general design requirement for serviceability is given in Section A5.4. Limiting values
of structural behavior to ensure serviceability (e.g., maximum deflections, accelerations, etc.) shall be chosen with due regard to the intended function of the structure.
Where necessary, serviceability shall be checked using realistic loads for the appropriate serviceability limit state.
L1. CAMBER
If any special camber requirements are necessary to bring a loaded member into
proper relation with the work of other trades, as for the attachment of runs of
sash, the requirements shall be set forth in the design documents.
Beams and trusses detailed without specified camber shall be fabricated so that
after erection any camber due to rolling or shop assembly shall be upward. If
camber involves the erection of any member under a preload, this shall be noted
in the design documents.
L2. EXPANSION AND CONTRACTION
Adequate provision shall be made for expansion and contraction appropriate to
the service conditions of the structure.
L3. DEFLECTIONS, VIBRATION, AND DRIFT
1.
Deflections
Deformations in structural members and structural systems due to service loads
shall not impair the serviceability of the structure.
2.
Floor Vibration
Vibration shall be considered in designing beams and girders supporting large
areas free of partitions or other sources of damping where excessive vibration
due to pedestrian traffic or other sources within the building is not acceptable.
3.
Drift
Lateral deflection or drift of structures due to code-specified wind or seismic
loads shall not cause collision with adjacent structures nor exceed the limiting
values of such drifts which may be specified or appropriate.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
Sect. L5]
CORROSION
6 - 99
L4. CONNECTION SLIP
For the design of slip-critical connections see Sections J3.8 and J3.9.
L5. CORROSION
When appropriate, structural components shall be designed to tolerate corrosion
or shall be protected against corrosion that may impair the strength or serviceability of the structure.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
6 - 100
CHAPTER M
FABRICATION, ERECTION, AND QUALITY CONTROL
This chapter provides requirements for shop drawings, fabrication, shop painting,
erection, and quality control.
M1. SHOP DRAWINGS
Shop drawings giving complete information necessary for the fabrication of the
component parts of the structure, including the location, type, and size of all
welds, bolts, and rivets, shall be prepared in advance of the actual fabrication.
These drawings shall clearly distinguish between shop and field welds and bolts
and shall clearly identify slip-critical high-strength bolted connections.
Shop drawings shall be made in conformity with good practice and with due
regard to speed and economy in fabrication and erection.
M2. FABRICATION
1.
Cambering, Curving, and Straightening
Local application of heat or mechanical means is permitted to be used to
introduce or correct camber, curvature, and straightness. The temperature of
heated areas, as measured by approved methods, shall not exceed 1,100°F for
A514 and A852 steel nor 1,200°F for other steels.
2.
Thermal Cutting
Thermally cut edges shall meet the requirements of AWS 3.2.2 with the exception that thermally cut free edges which will be subject to calculated static tensile
stress shall be free of round bottom gouges greater than 3⁄16-in. deep and sharp
V-shaped notches. Gouges greater than 3⁄16-in. deep and notches shall be removed by grinding or repaired by welding.
Re-entrant corners, except re-entrant corners of beam copes and weld access
holes, shall meet the requirements of AWS 3.2.4. If other specified contour is
required it must be shown on the contract documents.
Beam copes and weld access holes shall meet the geometrical requirements of
Section J1.6. For beam copes and weld access holes in ASTM A6 Group 4 and
5 shapes and welded built-up shapes with material thickness greater than two
inches, a preheat temperature of not less than 150°F shall be applied prior to
thermal cutting.
3.
Planing of Edges
Planing or finishing of sheared or thermally cut edges of plates or shapes is not
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
Sect. M2]
FABRICATION
6 - 101
required unless specifically called for in the design documents or included in a
stipulated edge preparation for welding.
4.
Welded Construction
The technique of welding, the workmanship, appearance, and quality of welds
and the methods used in correcting nonconforming work shall be in accordance
with AWS D1.1 except as modified in Section J2.
5.
Bolted Construction
All parts of bolted members shall be pinned or bolted and rigidly held together
during assembly. Use of a drift pin in bolt holes during assembly shall not distort
the metal or enlarge the holes. Poor matching of holes shall be cause for
rejection.
If the thickness of the material is not greater than the nominal diameter of the
bolt plus 1⁄8-in., the holes are permitted to be punched. If the thickness of the
material is greater than the nominal diameter of the bolt plus 1⁄8-in., the holes
shall be either drilled or sub-punched and reamed. The die for all sub-punched
holes, and the drill for all sub-drilled holes, shall be at least 1⁄16-in. smaller than
the nominal diameter of the bolt. Holes in A514 steel plates over 1⁄2-in. thick
shall be drilled.
Fully inserted finger shims, with a total thickness of not more than 1⁄4-in. within
a joint, are permitted in joints without changing the design strength (based upon
hole type) for the design of connections. The orientation of such shims is
independent of the direction of application of the load.
The use of high-strength bolts shall conform to the requirements of the RCSC
Load and Resistance Factor Design Specification for Structural Joints Using
ASTM A325 or A490 Bolts.
6.
Compression Joints
Compression joints which depend on contact bearing as part of the splice
strength shall have the bearing surfaces of individual fabricated pieces prepared
by milling, sawing, or other suitable means.
7.
Dimensional Tolerances
Dimensional tolerances shall be in accordance with the AISC Code of Standard
Practice.
8.
Finish of Column Bases
Column bases and base plates shall be finished in accordance with the following
requirements:
(1) Steel bearing plates two inches or less in thickness are permitted without
milling, provided a satisfactory contact bearing is obtained. Steel bearing
plates over two inches but not over four inches in thickness are permitted to
be straightened by pressing or, if presses are not available, by milling for all
bearing surfaces (except as noted in subparagraphs 2 and 3 of this section),
to obtain a satisfactory contact bearing. Steel bearing plates over four inches
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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FABRICATION, ERECTION, AND QUALITY CONTROL
[Chap. M
in thickness shall be milled for all bearing surfaces (except as noted in
subparagraphs 2 and 3 of this section).
(2) Bottom surfaces of bearing plates and column bases which are grouted to
ensure full bearing contact on foundations need not be milled.
(3) Top surfaces of bearing plates need not be milled when full-penetration
welds are provided between the column and the bearing plate.
M3. SHOP PAINTING
1.
General Requirements
Shop painting and surface preparation shall be in accordance with the provisions
of the AISC Code of Standard Practice.
Shop paint is not required unless specified by the contract documents.
2.
Inaccessible Surfaces
Except for contact surfaces, surfaces inaccessible after shop assembly shall be
cleaned and painted prior to assembly, if required by the design documents.
3.
Contact Surfaces
Paint is permitted unconditionally in bearing-type connections. For slip-critical
connections, the faying surface requirements shall be in accordance with the
RCSC Specification for Structural Joints Using ASTM A325 or A490 Bolts,
paragraph 3(b).
4.
Finished Surfaces
Machine-finished surfaces shall be protected against corrosion by a rustinhibitive coating that can be removed prior to erection, or which has characteristics that make removal prior to erection unnecessary.
5.
Surfaces Adjacent to Field Welds
Unless otherwise specified in the design documents, surfaces within two inches
of any field weld location shall be free of materials that would prevent proper
welding or produce objectionable fumes during welding.
M4. ERECTION
1.
Alignment of Column Bases
Column bases shall be set level and to correct elevation with full bearing on
concrete or masonry.
2.
Bracing
The frame of steel skeleton buildings shall be carried up true and plumb within
the limits defined in the AISC Code of Standard Practice. Temporary bracing
shall be provided, in accordance with the requirements of the Code of Standard
Practice, wherever necessary to support all loads to which the structure may be
subjected, including equipment and the operation of same. Such bracing shall
be left in place as long as required for safety.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
Sect. M5]
3.
QUALITY CONTROL
6 - 103
Alignment
No permanent bolting or welding shall be performed until the adjacent affected
portions of the structure have been properly aligned.
4.
Fit of Column Compression Joints and Base Plates
Lack of contact bearing not exceeding a gap of 1⁄16-in., regardless of the type of
splice used (partial-joint-penetration groove welded, or bolted), is permitted. If
the gap exceeds 1⁄16-in., but is less than 1⁄4-in., and if an engineering investigation
shows that sufficient contact area does not exist, the gap shall be packed out
with non-tapered steel shims. Shims need not be other than mild steel, regardless
of the grade of the main material.
5.
Field Welding
Shop paint on surfaces adjacent to joints to be field welded shall be wire brushed
if necessary to assure weld quality.
Field welding of attachments to installed embedments in contact with concrete
shall be done in such a manner as to avoid excessive thermal expansion of the
embedment which could result in spalling or cracking of the concrete or
excessive stress in the embedment anchors.
6.
Field Painting
Responsibility for touch-up painting, cleaning, and field painting shall be
allocated in accordance with accepted local practices, and this allocation shall
be set forth explicitly in the design documents.
7.
Field Connections
As erection progresses, the structure shall be securely bolted or welded to
support all dead, wind, and erection loads.
M5. QUALITY CONTROL
The fabricator shall provide quality control procedures to the extent that the
fabricator deems necessary to assure that all work is performed in accordance
with this Specification. In addition to the fabricator’s quality control procedures,
material and workmanship at all times may be subject to inspection by qualified
inspectors representing the purchaser. If such inspection by representatives of
the purchaser will be required, it shall be so stated in the design documents.
1.
Cooperation
As far as possible, all inspection by representatives of the purchaser shall be
made at the fabricator’s plant. The fabricator shall cooperate with the inspector,
permitting access for inspection to all places where work is being done. The
purchaser’s inspector shall schedule this work for minimum interruption to the
work of the fabricator.
2.
Rejections
Material or workmanship not in reasonable conformance with the provisions of
this Specification may be rejected at any time during the progress of the work.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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FABRICATION, ERECTION, AND QUALITY CONTROL
[Chap. M
The fabricator shall receive copies of all reports furnished to the purchaser by
the inspection agency.
3.
Inspection of Welding
The inspection of welding shall be performed in accordance with the provisions
of AWS D1.1 except as modified in Section J2.
When visual inspection is required to be performed by AWS certified welding
inspectors, it shall be so specified in the design documents.
When nondestructive testing is required, the process, extent, and standards of
acceptance shall be clearly defined in the design documents.
4.
Inspection of Slip-Critical High-Strength Bolted Connections
The inspection of slip-critical high-strength bolted connections shall be in
accordance with the provisions of the RCSC Load and Resistance Factor Design
Specification for Structural Joints Using ASTM A325 or A490 Bolts.
5.
Identification of Steel
The fabricator shall be able to demonstrate by a written procedure and by actual
practice a method of material application and identification, visible at least
through the “fit-up” operation, of the main structural elements of a shipping
piece.
The identification method shall be capable of verifying proper material application as it relates to:
(1) Material specification designation
(2) Heat number, if required
(3) Material test reports for special requirements.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
6 - 105
APPENDIX B
DESIGN REQUIREMENTS
Appendix B5.1 provides an expanded definition of limiting width-thickness ratio for
webs in combined flexure and axial compression. Appendix B5.3 applies to the design
of members containing slender compression elements.
B5. LOCAL BUCKLING
1.
Classification of Steel Sections
For members with unequal flanges and with webs in combined flexural and axial
compression, λr for the limit state of web local buckling is
λr =
h
P
253
1 + 2.83 1 − u
h
Fy
√
φ
c
bPy
(A-B5-1)
3 h 3
≤ ≤
4 hc 2
For members with unequal flanges with webs subjected to flexure only, λr for
the limit state of web local buckling is
λr =
h
253
1 + 2.83
Fy
√
hc
(A-B5-2)
3 h 3
≤ ≤
4 hc 2
where λr, h, and hc are as defined in Section B5.1.
These substitutions shall be made in Appendices F and G when applied to
members with unequal flanges. If the compression flange is larger than the
tension flange, λr shall be determined using Equation A-B5-1, A-B5-2, or
Table B5.1.
3.
Slender-Element Compression Sections
Axially loaded members containing elements subject to compression which
have a width-thickness ratio in excess of the applicable λr as stipulated in
Section B5.1 shall be proportioned according to this Appendix. Flexural members with slender compression elements shall be designed in accordance with
Appendices F and G. Flexural members with proportions not covered by
Appendix F1 shall be designed in accordance with this Appendix.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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3a.
DESIGN REQUIREMENTS
[App. B
Unstiffened Compression Elements
The design strength of unstiffened compression elements whose width-thickness ratio exceeds the applicable limit λr as stipulated in Section B5.1 shall be
subject to a reduction factor Qs. The value of Qs shall be determined by
Equations A-B5-3 through A-B5-10, as applicable. When such elements comprise the compression flange of a flexural member, the maximum required
bending stress shall not exceed φbFy Qs, where φb = 0.90. The design strength of
axially loaded compression members shall be modified by the appropriate
reduction factor Q, as provided in Appendix B5.3c.
(a) For single angles:
Fy :
when 76.0 / √
Fy < b / t < 155 / √
Fy
Qs = 1.340 − 0.00447(b / t)√
(A-B5-3)
when b / t > 155 / √
Fy :
Qs = 15,500 / [Fy (b / t)2]
(A-B5-4)
(b) For flanges, angles, and plates projecting from rolled beams or columns or
other compression members:
Fy :
when 95.0 / √
Fy < b / t < 176 / √
Fy
Qs = 1.415 − 0.00437(b / t)√
(A-B5-5)
when b / t ≥ 176 / √
Fy :
Qs = 20,000 / [Fy (b / t)2]
(A-B5-6)
(c) For flanges, angles and plates projecting from built-up columns or other
compression members:
Fy / kc :
when 109 / √
Fy / kc < b / t < 200 / √
Fy / kc
Qs = 1.415 − 0.00381(b / t)√
(A-B5-7)
when b / t ≥ 200 / √
Fy / kc :
Qs = 26,200kc / [Fy (b / t)2]
The coefficient, kc, shall be computed as follows:
(a) For I-shaped sections:
kc =
4
, 0.35 ≤ kc ≤ 0.763
√
h / tw
where:
h = depth of web, in.
tw = thickness of web, in.
(b) For other sections:
kc = 0.763
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
(A-B5-8)
Sect. A-B5]
LOCAL BUCKLING
6 - 107
(d) For stems of tees:
when 127 / √
Fy < b / t < 176 / √
Fy :
Qs = 1.908 − 0.00715(b / t)√
Fy
(A-B5-9)
Fy :
when b / t ≥ 176 / √
Qs = 20,000 / [Fy (b / t)2]
(A-B5-10)
where
b = width of unstiffened compression element as defined in Section B5.1, in.
t = thickness of unstiffened element, in.
Fy = specified minimum yield stress, ksi
3b.
Stiffened Compression Elements
When the width-thickness ratio of uniformly compressed stiffened elements
(except perforated cover plates) exceeds the limit λr stipulated in Section B5.1,
a reduced effective width be shall be used in computing the design properties of
the section containing the element.
(a) For flanges of square and rectangular sections of uniform thickness:
b 238
:
when ≥
t
f
√
64.9
326t
1−
(A-B5-11)
be =
(b / t)√
f
√
f
otherwise be = b.
(b) For other uniformly compressed elements:
b 253
when ≥
:
t
√f
57.2
326t
1−
be =
(b / t)√
f
√
f
(A-B5-12)
otherwise be = b
where
b = actual width of a stiffened compression element, as defined in
Section B5.1, in.
be = reduced effective width, in.
t = element thickness, in.
f = computed elastic compressive stress in the stiffened elements, based on
the design properties as specified in Appendix B5.3c, ksi. If
unstiffened elements are included in the total cross section, f for the
stiffened element must be such that the maximum compressive stress
in the unstiffened element does not exceed φcFcr as defined in
Appendix B5.3c with Q = Qs and φc = 0.85, or φbFy Qs with φb = 0.90,
as applicable.
(c) For axially loaded circular sections with diameter-to-thickness ratio D / t
greater than 3,300 / Fy but less than 13,000 / Fy
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
6 - 108
DESIGN REQUIREMENTS
Q = Qa =
2
1,100
+
Fy (D / t) 3
[App. B
(A-B5-13)
where
D = outside diameter, in.
t = wall thickness, in.
3c.
Design Properties
Properties of sections shall be determined using the full cross section, except as
follows:
In computing the moment of inertia and elastic section modulus of flexural
members, the effective width of uniformly compressed stiffened elements be, as
determined in Appendix B5.3b, shall be used in determining effective cross-sectional properties.
For unstiffened elements of the cross section, Qs is determined from Appendix B5.3a. For stiffened elements of the cross section
Qa =
effective area
actual area
(A-B5-14)
where the effective area is equal to the summation of the effective areas of the
cross section.
3d.
Design Strength
For axially loaded compression members the gross cross-sectional area and the
radius of gyration r shall be computed on the basis of the actual cross section.
The critical stress Fcr shall be determined as follows:
(a) For λc√
Q ≤ 1.5:
2
Fcr = Q(0.658Qλc)Fy
(A-B5-15)
0.877
Fcr = 2 Fy
λc
(A-B5-16)
Q = QsQa
(A-B5-17)
(a) For λc√
Q > 1.5:
where
Cross sections comprised of only unstiffened elements, Q = Qs, (Qa = 1.0)
Cross sections comprised of only stiffened elements, Q = Qa, (Qs = 1.0)
Cross sections comprised of both stiffened and unstiffened elements, Q = QsQa
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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APPENDIX E
COLUMNS AND OTHER COMPRESSION MEMBERS
This Appendix applies to the strength of doubly symmetric columns with thin plate
elements, singly symmetric and unsymmetric columns for the limit states of flexuraltorsional and torsional buckling.
E3. DESIGN COMPRESSIVE STRENGTH FOR
FLEXURAL-TORSIONAL BUCKLING
The strength of compression members determined by the limit states of torsional
and flexural-torsional buckling is φcPn,
where
φc = 0.85
Pn = nominal resistance in compression, kips
Pn = AgFcr
Ag = gross area of cross section, in.2
(A-E3-1)
The nominal critical stress Fcr is determined as follows:
(a) For λe√
Q ≤ 1.5:
2
Fcr = Q(0.658Qλe)Fy
(A-E3-2)
0.877
Fcr = 2 Fy
λe
(A-E3-3)
Fy / Fe
λe = √
(A-E3-4)
Q > 1.5:
(b) For λe√
where
Fy = specified minimum yield stress of steel, ksi
Q = 1.0 for elements meeting the width-thickness ratios λr of Section B5.1
Q = QsQa for elements not meeting the width-thickness ratios λr of
Section B5.1 and determined in accordance with the provisions of
Appendix B5.3
The critical torsional or flexural-torsional elastic buckling stress Fe is determined
as follows:
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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COLUMNS AND OTHER COMPRESSION MEMBERS
[App. E
(a) For doubly symmetric shapes:
π2ECw
1
+ GJ
Fe =
2
(
K
l)
z
Ix + Iy
(A-E3-5)
(b) For singly symmetric shapes where y is the axis of symmetry:
Fey + Fez
1−
Fe =
2H
4Fey Fez H
1−
(Fey + Fez )2
√
(A-E3-6)
(c) For unsymmetric shapes, the critical flexural-torsional elastic buckling stress
Fe is the lowest root of the cubic equation
2
2
xo
yo
(Fe −Fex)(Fe −Fey)(Fe −Fez) − Fe (Fe −Fey) _ − Fe 2 (Fe −Fex) __ = 0 (A-E3-7)
ro
ro
2
where
Kz
E
G
Cw
J
Ix, Iy
xo, yo
= effective length factor for torsional buckling
= modulus of elasticity, ksi
= shear modulus, ksi
= warping constant, in.6
= torsional constant, in.4
= moment of inertia about the principal axes, in.4
= coordinates of shear center with respect to the centroid, in.
_
Ix + Iy
ro2 = x2o + y2o +
A
(A-E3-8)
x2o + y2o
H=1− _2
ro
(A-E3-9)
Fex =
π2E
(Kxl / rx)2
(A-E3-10)
Fey =
π2E
(Kyl / ry)2
(A-E3-11)
π2ECw
1
+ GJ _ 2
Fez =
2
(Kzl)
Aro
where
A
= cross-sectional area of member, in.2
l
= unbraced length, in.
Kx, Ky = effective length factors in x and y directions
_rx, ry = radii of gyration about the principal axes, in.
= polar radius of gyration about the shear center, in.
ro
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
(A-E3-12)
6 - 111
APPENDIX F
BEAMS AND OTHER FLEXURAL MEMBERS
Appendix F1 provides the design flexural strength of beams and girders. Appendix F2
provides the design shear strength of webs with and without stiffeners and requirements on transverse stiffeners. Appendix F3 applies to web-tapered members.
F1.
DESIGN FOR FLEXURE
The design strength for flexural members is φbMn where φb = 0.90 and Mn is the
nominal strength.
Table A-F1.1 provides a tabular summary of Equations F1-1 through F1-15 for
determining the nominal flexural strength of beams and girders. For slenderness
parameters of cross sections not included in Table A-F1.1, see Appendix B5.3.
For flexural members with unequal flanges see Appendix B5.1 for the determination of λr for the limit state of web local buckling.
The nominal flexural strength Mn is the lowest value obtained according to the
limit states of yielding: lateral-torsional buckling (LTB); flange local buckling
(FLB); and web local buckling (WLB).
The nominal flexural strength Mn shall be determined as follows for each limit
state:
(a) For λ ≤ λp:
Mn = Mp
(A-F1-1)
(b) For λp < λ ≤ λr:
For the limit state of lateral-torsional buckling:
λ − λp
Mn = Cb Mp − (Mp − Mr)
≤ Mp
λr − λp
(A-F1-2)
For the limit states of flange and web local buckling:
λ − λp
Mn = Mp − (Mp − Mr)
λr − λp
(A-F1-3)
(c) For λ > λr:
For the limit state of lateral-torsional buckling and flange local buckling:
Mn = Mcr = SFcr ≤ Mp
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
(A-F1-4)
6 - 112
BEAMS AND OTHER FLEXURAL MEMBERS
[App. F
For design of girders with slender webs, the limit state of web local buckling is
not applicable. See Appendix G2.
For λ of the flange > λr in shapes not included in Table A-F1.1, see Appendix B5.3.
For λ of the web > λr, see Appendix G.
The terms used in the above equations are:
Mn
Mp
Mcr
Mr
λ
λ
λ
λ
λp
λr
Fcr
Cb
S
Lb
ry
= nominal flexural strength, kip-in.
= Fy Z, plastic moment ≤ 1.5 Fy S, kip-in.
= buckling moment, kip-in.
= limiting buckling moment (equal to Mcr when λ = λr), kip-in.
= controlling slenderness parameter
= minor axis slenderness ratio Lb / ry for lateral-torsional buckling
= flange width-thickness ratio b / t for flange local buckling as defined
in Section B5.1
= web depth-thickness ratio h / tw for web local buckling as defined in
Section B5.1
= largest value of λ for which Mn = Mp
= largest value of λ for which buckling is inelastic
= critical stress, ksi
= Bending coefficient dependent on moment gradient, see Section
F1.2a, Equation F1-3
= section modulus, in.3
= laterally unbraced length, in.
= radius of gyration about minor axis, in.
The applicable limit states and equations for Mp, Mr, Fcr, λ, λp, and λr are given
in Table A-F1.1 for shapes covered in this Appendix. The terms used in the table
are:
A
FL
Fr
Fr
Fr
Fy
Fyf
Fyw
Iyc
J
Re
Seff
Sxc
Sxt
Z
b
d
= cross-sectional area, in.2
= smaller of (Fyf −Fr) or Fyw, ksi
= compressive residual stress in flange
= 10 ksi for rolled shapes
= 16.5 ksi for welded shapes
= specified minimum yield strength, ksi
= yield strength of the flange, ksi
= yield strength of the web, ksi
= moment of inertia of compression flange about y axis or if reverse
curvature bending, moment of inertia of smaller flange, in.4
= torsional constant, in.4
= see Appendix G2
= effective section modulus about major axis, in.3
= section modulus of the outside fiber of the compression flange, in.3
= section modulus of the outside fiber of the tension flange, in.3
= plastic section modulus, in.3
= flange width, in.
= overall depth, in.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
Sect. A-F2]
f
h
ryc
tf
tw
DESIGN FOR SHEAR
6 - 113
= computed compressive stress in the stiffened element, ksi
= clear distance between flanges less the fillet or corner radius at each
flange, in.
= radius of gyration of compression flange about y axis or if reverse
curvature bending, smaller flange, in.
= flange thickness, in.
= web thickness, in.
F2.
DESIGN FOR SHEAR
2.
Design Shear Strength
The design shear strength of stiffened or unstiffened webs is φvVn,
where
φv = 0.90
Vn = nominal shear strength defined as follows:
kv /Fyw:
For h / tw ≤ 187√
Vn = 0.6FywAw
(A-F2-1)
kv /Fyw:
For 187√
kv /Fyw < h / tw ≤ 234√
kv /Fyw ) / (h / tw)
Vn = 0.6FywAw(187√
(A-F2-2)
For h / tw > 234√
kv /Fyw:
Vn = Aw(26,400kv) / (h / tw)2
(A-F2-3)
where
kv = 5 + 5 / (a / h)2
kv = 5 when a / h > 3 or a / h > [260 / (h / t)]2
a = distance between transverse stiffeners, in.
h = for rolled shapes, the clear distance between flanges less the fillet or
corner radius, in.
h = for built-up welded sections, the clear distance between flanges, in.
h = for built-up bolted or riveted sections, the distance between fastener
lines, in.
3.
Transverse Stiffeners
Fyw,
Transverse stiffeners are not required in plate girders where h / tw ≤ 418 / √
or where the required shear, Vu, as determined by structural analysis for the
factored loads, is less than or equal to 0.6φvAwFywCv, where Cv is determined for
kv = 5 and φv = 0.90.
Transverse stiffeners used to develop the web design shear strength as provided
in Appendix F2.2 shall have a moment of inertia about an axis in the web center
for stiffener pairs or about the face in contact with the web plate for single
stiffeners, which shall not be less than at3w j, where
j = 2.5 / (a / h)2 − 2 ≥ 0.5
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
(A-F2-4)
6 - 114
BEAMS AND OTHER FLEXURAL MEMBERS
[App. F
TABLE A-F1.1
Nominal Strength Parameters
Plastic
Moment
Mp
Shape
Fy Zx
[b]
Channels and doubly and singly
symmetric I-shaped beams
(including hybrid beams) bent
about major axis [a]
Limit State of
Buckling
LTB doubly
symmetric
members and
channels
LTB singly
symmetric
members
Channels and doubly and singly
symmetric I-shaped members bent
about minor axis [a]
π
Sx
√
[d] λr =
X1
FL
√
1+√
1 + X2F2L
[e] Fcr =
EGJA
2
Mcr
Sxc
, where Mcr =
FL Sxc ≤ Fyf Sxt
FL Sx
WLB
ReFyf Sx
FLB
Fy Sy
Fy Zy
2
X2 = 4
FL Sx
FLB
NOTE: LTB applies only for strong axis bending.
[a] Excluding double angles and tees.
[b] Computed from fully plastic stress distribution for hybrid sections.
[c] X1 =
Limiting Buckling
Moment Mr
Cw Sx
Iy GJ
57,000Cb
√
IyJ [B1 + √
(1 + B2 + B21) ] ≤ Mp
Lb
where
B1 = 2.25[2(Iyc / Iy) − 1](h / Lb)√
(Iy / J)
B2 = 25(1 − Iyc / Iy)(Iyc / J)(h / Lb)2
Cb = 1.0 if Iyc / Iy < 0.1 or Iyc / Iy > 0.9.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
Sect. A-F2]
DESIGN FOR SHEAR
6 - 115
TABLE A-F1.1 (cont’d)
Nominal Strength Parameters
Slenderness Parameters
λ
λp
Lb
ry
300
√Fyf
[e]
Lb
ryc
300
√Fyf
[f]
b
t
65
√Fyf
Not applicable
h
tw
640
√Fyf
Critical Stress Fcr
CbX1√
2
λ
1 +
√
2λ
X21X2
2
λr
[c, d]
Value of λ
for which
Mcr (Cb = 1) = Mr
[g]
λr as defined in
Section B5.1
Same as for major axis
20,000
[f] Fcr =
λ2
Fcr =
for rolled shapes
26,200kc
for welded shapes
λ2
where
kc = 4 / √
h / tw and 0.35 ≤ kc ≤ 0.763
[g] λr =
λr =
141
for rolled shapes
FL
√
162
√
FL / kc
for welded shapes
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
Limitations
Applicable for I-shaped
members if
h / tw ≤ λr
when
h / tw > λr
See Appendix G.
6 - 116
BEAMS AND OTHER FLEXURAL MEMBERS
[App. F
TABLE A-F1.1 (cont’d)
Nominal Strength Parameters
Shape
Plastic
Moment Mp
Limit State
of Buckling
Limiting Buckling
Moment Mr
Solid symmetric shapes,
except rectangular bars,
bent about major axis
Fy Zx
Solid rectangular bars
bent about major axis
Fy Zx
LTB
Fy Sx
Symmetric box sections
loaded in a plane of
symmetry
Fy Z
LTB
Fyf Seff
FLB
FL Seff
WLB
Same as for I-shape
LTB
Not applicable
FLB
600
Mn =
+ Fy S [h]
D / t
WLB
Not applicable
Circular tubes
Fy Z
Not applicable
[h] This equation is to be used in place of Equation A-F1-4.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
Sect. A-F2]
DESIGN FOR SHEAR
6 - 117
TABLE A-F1.1 (cont’d)
Nominal Strength Parameters
Slenderness Parameters
Critical Stress Fcr
λ
λp
λr
Limitations
Not applicable
57,000Cb√
JA
λSx
Lb
ry
3,750√
JA
Mp
57,000√
JA
Mr,
57,000Cb√
JA
λSx
Lb
ry
3,750√
JA
Mp
57,000√
JA
Mr
Seff
F [i]
Sx y
b
t
190
Fy
√
238
Fy
√
Applicable if
h / tw ≤ 970 / √
Fyf
Same as for I-shape
Not applicable
9,570
D/t
D/t
2,070
Fy
8,970
Fy
D/t<
Not applicable
[i] Seff is the effective section modulus for the section with a compression flange be defined in
Appendix B5.3b
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
13,000
Fy
6 - 118
BEAMS AND OTHER FLEXURAL MEMBERS
[App. F
Intermediate stiffeners are permitted to be stopped short of the tension flange,
provided bearing is not needed to transmit a concentrated load or reaction. The
weld by which intermediate stiffeners are attached to the web shall be terminated
not less than four times nor more than six times the web thickness from the near
toe of the web-to-flange weld. When single stiffeners are used, they shall be
attached to the compression flange, if it consists of a rectangular plate, to resist
any uplift tendency due to torsion in the flange. When lateral bracing is attached
to a stiffener, or a pair of stiffeners, these, in turn, shall be connected to the
compression flange to transmit one percent of the total flange stress, unless the
flange is composed only of angles.
Bolts connecting stiffeners to the girder web shall be spaced not more than
12 in. on center. If intermittent fillet welds are used, the clear distance between
welds shall not be more than 16 times the web thickness nor more than 10 in.
F3.
WEB-TAPERED MEMBERS
The design of tapered members meeting the requirements of this section shall
be governed by the provisions of Chapters D through H, except as modified by this
Appendix.
1.
General Requirements
In order to qualify under this Specification, a tapered member shall meet the
following requirements:
(1) It shall possess at least one axis of symmetry which shall be perpendicular
to the plane of bending if moments are present.
(2) The flanges shall be of equal and constant area.
(3) The depth shall vary linearly as
d = do 1 + γ
z
L
(A-F3-1)
where
do = depth at smaller end of member, in.
dL = depth at larger end of member, in.
γ = (dL − do) / do ≤ the smaller of 0.268(L / do) or 6.0
z = distance from the smaller end of member, in.
L = unbraced length of member measured between the center of gravity of
the bracing members, in.
2.
Design Tensile Strength
The design strength of tapered tension members shall be determined in accordance with Section D1.
3.
Design Compressive Strength
The design strength of tapered compression members shall be determined in
accordance with Section E2, using an effective slenderness parameter λeff computed as follows:
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
Sect. A-F3]
WEB-TAPERED MEMBERS
λeff =
S
π
√
QFy
E
6 - 119
(A-F3-2)
where
S = KL / roy for weak axis buckling and Kγ L / rox for strong axis buckling
K = effective length factor for a prismatic member
Kγ = effective length factor for a tapered member as determined by a
rational analysis
rox = strong axis radius of gyration at the smaller end of a tapered member, in.
roy = weak axis radius of gyration at the smaller end of a tapered member, in.
Fy = specified minimum yield stress, ksi
Q = reduction factor
Q = 1.0 if all elements meet the limiting width-thickness ratios λr of
Section B5.1
Q = QsQa, determined in accordance with Appendix B5.3, if any stiffened
and/or unstiffened elements exceed the ratios λr of Section B5.1
E = modulus of elasticity for steel, ksi
The smallest area of the tapered member shall be used for Ag in Equation E2-1.
4.
Design Flexural Strength
The design flexural strength of tapered flexural members for the limit state of
lateral-torsional buckling is φbMn, where φb = 0.90 and the nominal strength is
Mn = (5 / 3)S′xFbγ
(A-F3-3)
where
Sx′ = the section modulus of the critical section of the unbraced beam length
under consideration
Fy
2
1.0 −
F ≤ 0.60Fy
2
2 y
3
6B√
F
+
F
sγ
wγ
unless Fbγ ≤ Fy / 3, in which case
Fbγ =
Fbγ = B√
Fs2γ + Fwγ2
(A-F3-4)
(A-F3-5)
In the preceding equations,
Fsγ =
12 × 103
hsLdo / Af
(A-F3-6)
Fwγ =
170 × 103
(hwL / rTo)2
(A-F3-7)
where
Ldo / Af
hs = factor equal to 1.0 + 0.0230γ√
hw = factor equal to 1.0 + 0.00385γ√
L / rTo
rTo = radius of gyration of a section at the smaller end, considering only the
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
6 - 120
BEAMS AND OTHER FLEXURAL MEMBERS
[App. F
compression flange plus one-third of the compression web area, taken
about an axis in the plane of the web, in.
Af = area of the compression flange, in.2
and where B is determined as follows:
(a) When the maximum moment M2 in three adjacent segments of approximately equal unbraced length is located within the central segment and M1
is the larger moment at one end of the three-segment portion of a member:
M1
M1
(A-F3-8)
B = 1.0 + 0.37 1.0 + + 0.50γ 1.0 + ≥ 1.0
M2
M2
(b) When the largest computed bending stress fb2 occurs at the larger end of two
adjacent segments of approximately equal unbraced lengths and fb1 is the
computed bending stress at the smaller end of the two-segment portion of a
member:
fb1
fb1
(A-F3-9)
B = 1.0 + 0.58 1.0 + − 0.70γ 1.0 + ≥ 1.0
f
fb2
b2
(c) When the largest computed bending stress fb2 occurs at the smaller end of
two adjacent segments of approximately equal unbraced length and fb1 is the
computed bending stress at the larger end of the two-segment portion of a
member:
fb1
fb1
B = 1.0 + 0.55 1.0 + + 2.20γ 1.0 + ≥ 1.0
fb2
fb2
(A-F3-10)
In the foregoing, γ = (dL − do) / do is calculated for the unbraced length that
contains the maximum computed bending stress. M1 / M2 is considered as
negative when producing single curvature. In the rare case where M1 / M2 is
positive, it is recommended that it be taken as zero. fb1 / fb2 is considered as
negative when producing single curvature. If a point of contraflexure occurs in
one of two adjacent unbraced segments, fb1 / fb2 is considered as positive. The
ratio fb1 / fb2 ≠ 0.
(d) When the computed bending stress at the smaller end of a tapered member
or segment thereof is equal to zero:
B=
1.75
1.0 + 0.25√
γ
(A-F3-11)
where γ = (dL − do) / do is calculated for the unbraced length adjacent to the point
of zero bending stress.
5.
Design Shear Strength
The design shear strength of tapered flexural members shall be determined in
accordance with Section F2.
6.
Combined Flexure and Axial Force
For tapered members with a single web taper subject to compression and
bending about the major axis, Equation H1-1 applies, with the following modiAMERICAN INSTITUTE OF STEEL CONSTRUCTION
Sect. A-F3]
WEB-TAPERED MEMBERS
6 - 121
fications: Pn and Pex shall be determined for the properties of the smaller end,
using appropriate effective length factors. Mnx , Mu, and Mpx shall be determined
for the larger end; Mnx = (5 / 3) Sx′Fbγ, where Sx′ is the elastic section modulus of
the larger end, and Fbγ is the design flexural stress of tapered members. Cmx is
replaced by C′m, determined as follows:
(a) When the member is subjected to end moments which cause single curvature
bending and approximately equal computed moments at the ends:
2
Pu
Pu
(A-F3-12)
C′m = 1.0 + 0.1
+ 0.3
φbPex
φbPex
(b) When the computed bending moment at the smaller end of the unbraced
length is equal to zero:
2
Pu
Pu
C′m = 1.0 − 0.9
+ 0.6
φbPex
φbPex
(A-F3-13)
When the effective slenderness parameter λeff ≥ 1.5 and combined stress is
checked incrementally along the length, the actual area and the actual section
modulus at the section under investigation is permitted to be used.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
6 - 122
APPENDIX G
PLATE GIRDERS
This appendix applies to I-shaped plate girders with slender webs.
G1. LIMITATIONS
Doubly and singly symmetric single-web non-hybrid and hybrid plate girders
loaded in the plane of the web shall be proportioned according to the provisions
of this Appendix or Section F2, provided that the following limits are satisfied:
(a) For
(b) For
a
≤ 1.5:
h
a
h
h 2,000
≤
tw
Fyf
√
(A-G1-1)
h
14,000
≤
tw √
Fyf (Fyf + 16.5)
(A-G1-2)
> 1.5:
where
a = clear distance between transverse stiffeners, in.
h = clear distance between flanges less the fillet or corner radius for rolled
shapes; and for built-up sections, the distance between adjacent lines of
fasteners or the clear distance between flanges when welds are used, in.
tw = web thickness, in.
Fyf = specified minimum yield stress of a flange, ksi
In unstiffened girders h / tw shall not exceed 260.
G2. DESIGN FLEXURAL STRENGTH
The design flexural strength for plate girders with slender webs shall be φbMn,
where φb = 0.90 and Mn is the lower value obtained according to the limit states
of tension-flange yield and compression-flange buckling. For girders with
unequal flanges, see Appendix B5.1 for the determination of λr for the limit state
of web local buckling.
(a) For tension-flange yield:
Mn = SxtReFyt
(b) For compression-flange buckling:
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
(A-G2-1)
Sect. A-G2]
DESIGN FLEXURAL STRENGTH
Mn = SxcRPG ReFcr
6 - 123
(A-G2-2)
where
RPG = 1 −
hc 970
ar
−
≤ 1.0
1,200 + 300ar tw √
Fcr
(A-G2-3)
Re
= hybrid girder factor
12 + ar (3m − m3)
Re =
≤ 1.0 (for non-hybrid girders, Re = 1.0)
12 + 2ar
ar = ratio of web area to compression flange area (≤ 10)
m = ratio of web yield stress to flange yield stress or to Fcr
Fcr = critical compression flange stress, ksi
Fyt = yield stress of tension flange, ksi
Sxc = section modulus referred to compression flange, in.3
Sxt = section modulus referred to tension flange, in.3
hc = twice the distance from the centroid to the nearest line of fasteners at
the compression flange or the inside of the face of the compression
flange when welds are used
The critical stress Fcr to be used is dependent upon the slenderness parameters
λ, λp, λr, and CPG as follows:
For λ ≤ λp:
Fcr = Fyf
(A-G2-4)
For λp < λ ≤ λr:
Fcr = CbFyf 1 −
1 λ − λp
≤F
2 λr − λp yf
(A-G2-5)
For λ > λr:
Fcr =
CPG
λ2
(A-G2-6)
In the foregoing, the slenderness parameter shall be determined for both the limit
state of lateral-torsional buckling and the limit state of flange local buckling;
the slenderness parameter which results in the lowest value of Fcr governs.
(a) For the limit state of lateral-torsional buckling:
Lb
rT
(A-G2-7)
λp =
300
√
Fyf
(A-G2-8)
λr =
756
√Fyf
(A-G2-9)
λ=
CPG = 286,000Cb
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
(A-G2-10)
6 - 124
PLATE GIRDERS
[App
where
Cb = see Section F1.2, Equation F1-3
rT = radius of gyration of compression flange plus one-third of the
compression portion of the web, in.
(b) For the limit state of flange local buckling:
λ=
bf
2tf
(A-G2-11)
λp =
65
√Fyf
(A-G2-12)
230
√
Fyf / kc
(A-G2-13)
λr =
CPG = 26,200kc
(A-G2-14)
Cb = 1.0
h / tw and 0.35 ≤ kc ≤ 0.763.
where kc = 4 / √
The limit state of flexural web local buckling is not applicable.
G3. DESIGN SHEAR STRENGTH WITH TENSION FIELD ACTION
The design shear strength with tension field action shall be φvVn, kips, where
φv = 0.90 and Vn is determined as follows:
(a) For h / tw ≤ 187√
kv /Fyw:
Vn = 0.6AwFyw
(A-G3-1)
kv /Fyw:
(b) For h / tw > 187√
Vn = 0.6AwFywCv +
1 − Cv
2
1.15√
1 + (a / h)
(A-G3-2)
where
Cv = ratio of “critical” web stress, according to linear buckling theory, to the
shear yield stress of web material
Also see Appendix G4 and G5.
For end-panels in non-hybrid plate girders, all panels in hybrid and web-tapered
plate girders, and when a / h exceeds 3.0 or [260 / (h / tw)]2, tension field action
is not permitted and
Vn = 0.6AwFywCv
(A-G3-3)
The web plate buckling coefficient kv is given as
kv = 5 +
5
(a / h)2
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
(A-G3-4)
except that kv shall be taken as 5.0 if a / h
6 - 126
PLATE GIRDERS
[App. G
flexure-shear interaction criteria:
Vu
Mu
+ 0.625
≤ 1.375
φMn
φVn
(A-G5-1)
where Mn is the nominal flexural strength of plate girders from Appendix G2 or
Section F1, φ = 0.90, and Vn is the nominal shear strength from Appendix G3.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
6 - 127
APPENDIX H
MEMBERS UNDER COMBINED FORCES AND TORSION
This appendix provides alternative interaction equations for biaxially loaded I-shaped
members with bf / d ≤ 1.0 and box-shaped members.
H3. ALTERNATIVE INTERACTION EQUATIONS FOR MEMBERS
UNDER COMBINED STRESS
For biaxially loaded I-shaped members with bf / d ≤ 1.0 and box-shaped members in braced frames only, the use of the following interaction equations in lieu
of Equations H1-1a and H1-1b is permitted. Both Equations A-H3-1 and A-H3-2
shall be satisfied.
ζ
ζ
Mux Muy
+
≤ 1.0
φbM′px φbM′py
η
(A-H3-1)
η
CmxMux CmyMuy
(A-H3-2)
+
≤ 1.0
φbM′nx φbM′ny
The terms in Equations A-H3-1 and A-H3-2 are determined as follows:
(a) For I-shaped members:
For bf / d < 0.5:
ζ = 1.0
For 0.5 ≤ bf / d ≤ 1.0:
ζ = 1.6 −
Pu / Py
2[ln(Pu / Py )]
(A-H3-3)
For bf / d < 0.3:
η = 1.0
For 0.3 ≤ bf / d ≤ 1.0:
η = 0.4 +
Pu bf
+ ≥ 1.0
Py d
(A-H3-4)
where
bf = flange width, in.
d = member depth, in.
Cm = coefficient applied to the bending term in interaction equation for
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
6 - 128
MEMBERS UNDER COMBINED FORCES AND TORSION
[App. H
prismatic members and dependent on column curvature caused by
applied moments, see Section C1.
M′px = 1.2Mpx[1 − (Pu / Py )] ≤ Mpx
(A-H3-5)
M′py = 1.2Mpy[1 − (Pu / Py ) ] ≤ Mpy
(A-H3-6)
Pu
Pu
M′nx = Mnx 1 −
1 − P
φcPn
ex
(A-H3-7)
Pu
Pu
M′ny = Mny 1 −
1 − P
φ
P
ey
c n
(A-H3-8)
2
(b) For box-section members:
ζ = 1.7 −
Pu / Py
ln(Pu / Py)
(A-H3-9)
b
P
P /P
η = 1.7 − u y − aλx u > 1.1
ln(Pu / Py )
Py
(A-H3-10)
For Pu / Py ≤ 0.4, a = 0.06, and b = 1.0;
For Pu / Py > 0.4, a = 0.15, and b = 2.0;
M′px = 1.2Mpx[1 − Pu / Py] ≤ Mpx
(A-H3-11a)
M′py = 1.2Mpy[1 − Pu / Py] ≤ Mpy
(A-H3-11b)
Pu
Pu 1.25
M′nx = Mnx 1 −
1 − P
1/3
φ
P
ex (B / H)
c n
(A-H3-12)
Pu
Pu 1.25
M′ny = Mny 1 −
1 − P
1/2
φcPn
ey (B / H)
(A-H3-13)
where
Pn = nominal compressive strength determined in accordance with Section
E2, kips
Pu = required axial strength, kips
Py = compressive yield strength AgFy, kips
φb = resistance factor for flexure = 0.90
φc = resistance factor for compression = 0.85
Pe = Euler buckling strength AgFy / λc2, where λc is the column slenderness
parameter defined by Equation E2-4, kips
Mu = required flexural strength, kip-in.
Mn = nominal flexural strength, determined in accordance with Section F1,
kip-in.
Mp = plastic moment ≤ 1.5Fy S, kip-in.
B = outside width of box section parallel to major principal axis x, in.
H = outside depth of box section perpendicular to major principal axis x, in.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
6 - 129
APPENDIX J
CONNECTIONS, JOINTS, AND FASTENERS
Appendix J2.4 provides the alternative design strength for fillet welds. Appendices
J3.8 and J3.9 pertain to the design of slip-critical connections using factored loads.
J2.
WELDS
4.
Design Strength
In lieu of the constant design strength for fillet welds given in Table J2.5, the
following procedure is permitted.
(a) The design strength of a linear weld group loaded in-plane through the center
of gravity is φFw Aw:
Fw = 0.60FEXX(1.0 + 0.50 sin1.5θ)
where
φ
Fw
FEXX
θ
Aw
= 0.75
= nominal stress, ksi
= electrode classification number, i.e., minimum specified strength, ksi
= angle of loading measured from the weld longitudinal axis, degrees
= effective area of weld throat, in.2
(b) The design strength of weld elements within a weld group that are loaded
in-plane and analyzed using an instantaneous center of rotation method to
maintain deformation compatibility and non-linear load deformation behavior of variable angle loaded welds is φFwx Aw and φFwy Aw:
where
Fwx
Fwy
Fwi
f(p)
φ
Fwi
Fwix
Fwiy
p
∆m
= ΣFwix
= ΣFwiy
= 0.60FEXX(1.0 + 0.50 sin1.5θ) f(p)
= [p(1.9 − 0.9p)]0.3
= 0.75
= nominal stress in any ith weld element, ksi
= x component of stress Fwi
= y component of stress Fwi
= ∆i / ∆m, ratio of element i deformation to its deformation at maximum
stress
= 0.209(θ + 2)−0.32D, deformation of weld element at maximum stress, in.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
6 - 130
CONNECTIONS, JOINTS, AND FASTENERS
∆i
∆u
D
rcrit
[App. J
= deformation of weld elements at intermediate stress levels, linearly
proportioned to the critical deformation based on distance from the
instantaneous center of rotation, ri, in.
= ri∆u / rcrit
= 1.087(θ + 6)−0.65D ≤ 0.17D, deformation of weld element at ultimate
stress (fracture), usually in element furthest from instantaneous
center of rotation, in.
= leg size of the fillet weld, in.
= distance from instantaneous center of rotation to weld element with
minimum ∆u / ri ratio
J3.
BOLTS AND THREADED PARTS
8.
High-Strength Bolts in Slip-Critical Connections
8b.
Slip-Critical Connections Designed at Factored Loads
It is permissible to proportion slip-critical connections at factored loads. The
design slip resistance for use at factored loads, φRstr, shall equal or exceed the
required force due to the factored loads, where:
Rstr = 1.13µTmNbNs
(A-J3-1)
where:
Tm = minimum fastener tension given in Table J3.1, kips
Nb = number of bolts in the joint
Ns = number of slip planes
µ = mean slip coefficient for Class A, B, or C surfaces, as applicable, or as
established by tests
(a) For Class A surfaces (unpainted clean mill scale steel surfaces or
surfaces with Class A coating on blast-cleaned steel), µ = 0.33
(b) For Class B surfaces (unpainted blast-cleaned steel surfaces or
surfaces with Class B coatings on blast-cleaned steel), µ = 0.50
(c) For Class C surfaces (hot-dip galvanized and roughened surfaces),
µ = 0.40
=
resistance
factor
φ
(a) For standard holes, φ = 1.0
(b) For oversize and short-slotted holes, φ = 0.85
(c) For long-slotted holes transverse to the direction of load, φ = 0.70
(d) For long-slotted holes parallel to the direction of load, φ = 0.60
9.
Combined Tension and Shear in Slip-Critical Connections
9b.
Slip-Critical Connections Designed at Factored Loads
When using factored loads as the basis for design of slip-critical connections
subject to applied tension, T, that reduces the net clamping force, the slip
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
Sect. A-J3]
BOLTS AND THREADED PARTS
6 - 131
resistance φRstr according to Appendix J3.8b shall be multiplied by the following
factor in which Tu is the required tensile strength at factored loads:
[1 − Tu / (1.13TmNb)]
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
(A-J3-2)
6 - 132
APPENDIX K
CONCENTRATED FORCES, PONDING, AND FATIGUE
Appendix K2 provides an alternative determination of roof stiffness. Appendix K4
pertains to members and connections due to fatigue loading.
K2. PONDING
The provisions of this Appendix are permitted to be used when a more exact
determination of flat roof framing stiffness is needed than that given by the
provision of Section K2 that Cp + 0.9Cs ≤ 0.25.
For any combination of primary and secondary framing, the stress index is
computed as
Fy − fo
for the primary member
Up =
fo p
(A-K2-3)
Fy − fo
for the secondary member
Us =
fo s
(A-K2-4)
where
fo = the stress due to 1.2D + 1.2R (D = nominal dead load, R = nominal load
due to rain water or ice exclusive of the ponding contribution)*
Enter Figure A-K2.1 at the level of the computed stress index Up determined for
the primary beam; move horizontally to the computed Cs value of the secondary
beams and then downward to the abscissa scale. The combined stiffness of the
primary and secondary framing is sufficient to prevent ponding if the flexibility
constant read from this latter scale is more than the value of Cp computed for
the given primary member; if not, a stiffer primary or secondary beam, or
combination of both, is required. In the above,
Cp =
32LsLp4
107Ip
Cs =
32L4s
107Is
* Depending upon geographic location, this loading should include such amount of snow as might also be present,
although ponding failures have occurred more frequently during torrential summer rains when the rate of precipitation
exceeded the rate of drainage runoff and the resulting hydraulic gradient over large roof areas caused substantial
accumulation of water some distance from the eaves. A load factor of 1.2 shall be used for loads resulting from these
phenomena.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
Sect. A-K2]
PONDING
6 - 133
where
Lp = column spacing in direction of girder (length of primary members), ft
Ls = column spacing perpendicular to direction of girder (length of
secondary members), ft
S = spacing of secondary members, ft
Ip = moment of inertia of primary members, in.4
Is = moment of inertia of secondary members, in.4
A similar procedure must be followed using Figure A-K2.2.
Roof framing consisting of a series of equally spaced wall-bearing beams is
considered as consisting of secondary members supported on an infinitely stiff
3.4
3.2
3.0
2.8
2.6
2.4
0.5
2.2
1.8
0.4
1.6
0.3
1.4
0.2
Stress Index Up
2.0
1.2
1
0.
1.0
Cs
0.8
=
0
0.6
0.4
0.2
0
0
0.1
0.2
0.3
0.4
0.5
0.6
Upper Limit of Flexibility Constant Cp
Fig. A-K2.1. Limiting flexibility coefficient for the primary systems.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
0.7
6 - 134
CONCENTRATED FORCES, PONDING, AND FATIGUE
[App. K
primary member. For this case, enter Figure A-K2.2 with the computed stress
index Us. The limiting value of Cs is determined by the intercept of a horizontal
line representing the Us value and the curve for Cp = 0.
The ponding deflection contributed by a metal deck is usually such a small part
of the total ponding deflection of a roof panel that it is sufficient merely to limit
its moment of inertia (per foot of width normal to its span) to 0.000025 times
the fourth power of its span length. However, the stability against ponding of a
roof consisting of a metal roof deck of relatively slender depth-span ratio,
spanning between beams supported directly on columns, may need to be
checked. This can be done using Figure A-K2.1 or A-K2.2 using as Cs the
flexibility constant for a one-foot width of the roof deck (S = 1.0).
0.7
3.4
3.2
0.6
3.0
2.8
0.5
2.6
2.4
2.0
1.8
0.3
1.6
0.2
Stress Index Us
0.4
2.2
1.4
1
0.
1.2
1.0
Cp
=
0
0.8
0.6
0.4
0.2
0
0
0.1
0.2
0.3
0.4
0.5
0.6
Upper Limit of Flexibility Constant Cs
Fig. A-K2.2. Limiting flexibility coefficient for the secondary systems.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
0.7
Sect. A-K3]
FATIGUE
6 - 135
TABLE A-K3.1
Number of Loading Cycles
Loading Condition
From
To
1
20,000 [a]
100,000 [b]
2
100,000
500,000 [c]
3
500,000
2,000,000 [d]
4
Over 2,000,000
[a] Approximately equivalent to two applications every day for 25 years.
[b] Approximately equivalent to 10 applications every day for 25 years.
[c] Approximately equivalent to 50 applications every day for 25 years.
[d] Approximately equivalent to 200 applications every day for 25 years.
Since the shear rigidity of the web system of steel joists and trusses is less than that
of a solid plate, their moment of inertia shall be taken as 85 percent of their chords.
K3. FATIGUE
Members and connections subject to fatigue loading shall be proportioned in
accordance with the provisions of this Appendix.
Fatigue, as used in this Specification, is defined as the damage that may result in
fracture after a sufficient number of fluctuations of stress. Stress range is defined as
the magnitude of these fluctuations. In the case of a stress reversal, the stress range
shall be computed as the numerical sum of maximum repeated tensile and compressive stresses or the sum of maximum shearing stresses of opposite direction at a
given point, resulting from differing arrangement of live load.
1.
Loading Conditions; Type and Location of Material
In the design of members and connections subject to repeated variation of live
load, consideration shall be given to the number of stress cycles, the expected
range of stress, and the type and location of member or detail.
Loading conditions shall be classified according to Table A-K3.1.
The type and location of material shall be categorized according to Table
A-K3.2.
2.
Design Stress Range
The maximum range of stress at service loads shall not exceed the design stress
range specified in Table A-K3.3.
3.
Design Strength of Bolts in Tension
When subject to tensile fatigue loading, fully tensioned A325 or A490 bolts shall
be designed for the combined tensile design strength due to combined external
and prying forces in accordance with Table A-K3.4.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
6 - 136
CONCENTRATED FORCES, PONDING, AND FATIGUE
[App. K
TABLE A-K3.2
Type and Location of Material
General
Condition
Situation
Kind of
Stress [a]
Illustrative
Stress
Example
Category
Nos.
(see Table (see Fig.
A-K3.3) A-K3.1) [b]
Plain Material
Base metal with rolled or cleaned
surface. Flame-cut edges with
ANSI smoothness of 1,000 or less
T or Rev.
A
1,2
Built-up
Members
Base metal and weld metal in
members without attachments,
built-up plates or shapes
connected by continuous fullpenetration groove welds or by
continuous fillet welds parallel to
the direction of applied stress
T or Rev.
B
3,4,5,6
Base metal and weld metal in
members without attachments,
built-up plates, or shapes
connected by full-penetration
groove welds with backing bars
not removed, or by partialpenetration groove welds parallel
to the direction of applied stress
T or Rev.
B′
3,4,5,6
Base metal at toe of welds on
girder webs or flanges adjacent to
welded transverse stiffeners
T or Rev.
C
7
T or Rev.
T or Rev.
E
E′
5
5
E′
5
Base metal at ends of partial
length welded coverplates
narrower than the flange having
square or tapered ends, with or
without welds across the ends or
wider than flange with welds
across the ends
Flange thickness ≤ 0.8 in.
Flange thickness > 0.8 in.
Base metal at end of partial length
welded coverplates wider than the
flange without welds across the
ends
[a] “T” signifies range in tensile stress only; “Rev.” signifies a range involving reversal of
tensile or compressive stress; “S” signifies range in shear, including shear stress
reversal.
[b] These examples are provided as guidelines and are not intended to exclude other
reasonably similar situations.
[c] Allowable fatigue stress range for transverse partial-penetration and transverse fillet
welds is a function of the effective throat, depth of penetration, and plate thickness. See
Frank and Fisher, Journal of the Structural Division, Vol. 105 No. ST9, Sept. 1979.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
Sect. A-K3]
FATIGUE
6 - 137
TABLE A-K3.2 (cont’d)
Type and Location of Material
General
Condition
Groove
Welds
Situation
Base metal and weld metal at fullpenetration groove welded splices
of parts of similar cross section
ground flush, with grinding in the
direction of applied stress and with
weld soundness established by
radiographic or ultrasonic
inspection in accordance with the
requirements of 9.25.2 or 9.25.3 of
AWS D1.1
Kind of
Stress [a]
Illustrative
Stress
Example
Category
Nos.
(see Table (see Fig.
A-K3.3) A-K3.1) [b]
T or Rev.
B
10,11
A514 base metal
Other base metals
T or Rev.
T or Rev.
B′
B
12,13
12,13
Base metal and weld metal at fullpenetration groove welded splices,
with or without transitions having
slopes no greater than 1 to 21⁄2
when reinforcement is not
removed but weld soundness is
established by radiographic or
ultrasonic inspection in
accordance with requirements of
9.25.2 or 9.25.3 of AWS D1.1
T or Rev.
C
10,11,12,13
Partial-Penetration
Groove
Welds
Weld metal of partial-penetration
transverse groove welds, based
on effective throat area of the weld
or welds
T or Rev.
F [c]
Fillet-welded
Connections
Base metal at intermittent fillet
welds
T or Rev.
E
Base metal and weld metal at fullpenetration groove welded splices
at transitions in width or thickness,
with welds ground to provide
slopes no steeper than 1 to 21⁄2
with grinding in the direction of
applied stress, and with weld
soundness established by
radiographic or ultrasonic
inspection in accordance with the
requirements of 9.25.2 or 9.25.3 of
AWS D1.1
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
6 - 138
CONCENTRATED FORCES, PONDING, AND FATIGUE
[App. K
TABLE A-K3.2 (cont’d)
Type and Location of Material
General
Condition
Fillet-welded
Connections
(Continued)
Situation
Kind of
Stress [a]
Illustrative
Stress
Example
Category
Nos.
(see Table (see Fig.
A-K3.3) A-K3.1) [b]
Base metal at junction of axially
loaded members with fillet-welded
end connections. Welds shall be
disposed about the axis of the
member so as to balance weld
stresses
b ≤ 1 in.
b > 1 in.
T or Rev.
T or Rev.
E
E′
17,18
17,18
T or Rev.
C
See Note
20,21
S
F [c]
15,17,18
20,21
T or Rev.
E
27
S
F
27
Base metal at gross section of
high-strength bolted slip-critical
connections, except axially loaded
joints which induce out-of-plane
bending in connected material
T or Rev.
B
8
Base metal at net section of other
mechanically fastened joints
T or Rev.
D
8,9
Base metal at net section of fully
tensioned high-strength, boltedbearing connections
T or Rev.
B
8,9
Eyebar or
Pin Plates
Base metal at net section of
eyebar head or pin plate
T or Rev.
E
28,29
Attachments
Base metal at details attached by
full-penetration groove welds
subject to longitudinal and/or
transverse loading when the detail
embodies a transition radius R
with the weld termination ground
smooth and for transverse loading,
the weld soundness established
by radiographic or ultrasonic
inspection in accordance with
9.25.2 or 9.25.3 of AWS D1.1
Base metal at members
connected with transverse fillet
welds
b ≤ 1⁄2-in.
b > 1⁄2-in.
Fillet Welds
Weld metal of continuous or
intermittent longitudinal or
transverse fillet welds
Plug or Slot
Welds
Base metal at plug or slot welds
Shear on plug or slot welds
Mechanically
Fastened
Connections
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
Sect. A-K3]
FATIGUE
6 - 139
TABLE A-K3.2 (cont’d)
Type and Location of Material
General
Condition
Attachments
(Continued)
Situation
Longitudinal loading
R > 24 in.
24 in. > R > 6 in.
6 in. > R > 2 in.
2 in. > R
Kind of
Stress [a]
Illustrative
Stress
Example
Category
Nos.
(see Table (see Fig.
A-K3.3) A-K3.1) [b]
T or Rev.
T or Rev.
T or Rev.
T or Rev.
B
C
D
E
14
14
14
14
T or Rev.
T or Rev.
T or Rev.
T or Rev.
B
C
D
E
14
14
14
14,15
T or Rev.
T or Rev.
T or Rev.
T or Rev.
C
C
D
E
14
14
14
14,15
T or Rev.
T or Rev.
D
E
14
14,15
T or Rev.
E
14,15
T or Rev.
T or Rev.
T or Rev.
C
D
E
19
19
19
T or Rev.
T or Rev.
T or Rev.
D
E
E′
15
15
15
Detail base metal for transverse
loading: equal thickness and
reinforcement removed
R > 24 in.
24 in. > R > 6 in.
6 in. > R > 2 in.
2 in. > R
Detail base metal for transverse
loading: equal thickness and
reinforcement not removed
R > 24 in.
24 in. > R > 6 in.
6 in. > R > 2 in.
2 in. > R
Detail base metal for transverse
loading: unequal thickness and
reinforcement removed
R > 2 in.
2 in. > R
Detail base metal for transverse
loading: Unequal thickness and
reinforcement not removed
All R
Detail base metal for transverse
loading
R > 6 in.
6 in. > R > 2 in.
2 in. > R
Base metal at detail attached by
full-penetration groove welds
subject to longitudinal loading
2 < a < 12b or 4 in.
a > 12b or 4 in. when b ≤ 1 in.
a >12b or 4 in. when b >1 in.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
6 - 140
CONCENTRATED FORCES, PONDING, AND FATIGUE
[App. K
TABLE A-K3.2 (cont’d)
Type and Location of Material
General
Condition
Attachments
(Continued)
Situation
Kind of
Stress [a]
Illustrative
Stress
Example
Category
Nos.
(see Table (see Fig.
A-K3.3) A-K3.1) [b]
Base metal at detail attached by
fillet welds or partial-penetration
groove welds subject to
longitudinal loading
a < 2 in.
T or Rev.
C
15,23,24
25,26
2 in. < a < 12b or 4 in.
T or Rev.
D
15,23,24,26
a > 12b or 4 in. when b ≤ 1 in.
T or Rev.
E
15,23,24,26
a > 12b or 4 in. when b > 1 in.
T or Rev.
E′
15,23,24,26
T or Rev.
T or Rev.
D
E
19
19
R > 2 in.
R < 2 in.
T or Rev.
T or Rev.
D
E
19
19
Base metal at stud-type shear
connector attached by fillet weld or
automatic end weld
T or Rev.
C
22
S
F
Base metal attached by fillet welds
or partial-penetration groove welds
subjected to longitudinal loading
when the weld termination
embodies a transition radius with
the weld termination ground
smooth
R > 2 in.
R ≤ 2 in.
Fillet-welded attachments where
the weld termination embodies a
transition radius, weld termination
ground smooth, and main material
subject to longitudinal loading
Detail base metal for transverse
loading:
Shear stress on nominal area of
stud-type shear connectors
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
Sect. A-K3]
FATIGUE
6 - 141
TABLE A-K 3.3
Design Stress Range, ksi
Category
(From
Table A-K3.2)
Loading
Condition
1
Loading
Condition
2
Loading
Condition
3
Loading
Condition
4
A
63
37
24
24
B
49
29
18
16
B′
39
23
15
12
C
35
21
13
10 [a]
D
28
16
10
7
E
22
13
8
4.5
E′
16
5.8
2.6
F
15
9
8
9.2
12
[a] Flexural stress range of 12 ksi permitted at toe of stiffener welds or flanges.
TABLE A-K3.4
Design Strength of A325 or A490 Bolts
Subject to Tension
Number of cycles
Design strength
Not more than 20,000
As specified in Section J3
From 20,000 to 500,000
0.30 AbFu [a]
More than 500,000
0.25 AbFu [a]
[a] At service loads.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
6 - 142
CONCENTRATED FORCES, PONDING, AND FATIGUE
1
[App. K
7
8
2
3
9
or
10
4
Plate as
sh
or wider own
than
flange
B
E or E′
Category
5
11
12
6
13
Fig. A-K3.1. Illustrative examples.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
continued
Sect. A-K3]
FATIGUE
6 - 143
Groove weld
14
R
22
b (avg.)
a
a
15
23
a
b
16
24
a
b=thickness
17
25
b=thickness
a
18
26
b
Groove or fillet weld
19 R
27
b=thickness
20
net section area
28
net section area
21
29
Fig. A-K3.1. Illustrative examples (cont.).
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
6 - 144
NUMERICAL VALUES
TABLE 1
Design Strength as a Function of Fy
Design Stress (ksi)
Fy
(ksi)
0.54Fy [a]
0.85Fy [b]
0.90Fy [c]
33
17.8
28.1
29.7
35
18.9
29.8
31.5
36
19.4
30.6
32.4
42
21.6
34.0
36.0
42
22.7
35.7
37.8
45
24.3
38.3
40.5
46
24.8
39.1
41.4
40
27.0
42.5
45.0
55
29.7
46.8
49.5
60
32.4
51.0
54.0
65
35.1
55.3
58.5
70
37.8
59.5
63.0
90
48.6
76.5
81.0
100
54.0
85.0
90.0
[a] See Section F2, Equations F2-1
[b] See Section E2, Equation E2-1
[c] See Section D1, Equation D1-1
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
NUMERICAL VALUES
6 - 145
TABLE 2
Design Strength as a Function of Fy
Shapes, Plates, Bars, Sheet and Tubing or Threaded parts
Item
Design Strength (ksi)
Connection Part of
Designated Steel
Bolt of Threaded Part
of Designated Steel
ASTM
Designation
Fy
(ksi)
Fu
(ksi)
Tension
0.75 ×
Fu [a]
Bearing
0.75 ×
2.4Fu [b]
A36
36
58-80
43.5
104
32.6
17.4
21.8
A53
35
60
45.0
108
—
—
—
A242
A588
50
42
40
70
63
60
52.5
47.3
45.0
126
113
108
39.4
35.4
33.8
21.0
18.9
18.0
26.3
23.2
22.5
A500
33/39 [f]
42/46 [f]
46/50 [f]
45
58
62
33.8
43.5
46.5
81
104
112
—
—
—
—
—
—
—
—
—
A501
36
58
43.5
104
—
—
—
A529
42
60-85
45.0
108
33.8
18.0
22.5
A570
40
42
55
58
41.3
43.5
99
104
—
—
—
—
—
—
A572
42
50
60
65
60
65
75
80
45.0
48.8
56.3
60.0
108
117
135
144
33.8
36.6
42.2
45.0
18.0
19.5
22.5
24.0
22.5
24.4
28.1
30.0
A514
100
90
110-130
100-130
82.5
75.0
198
180
61.9
56.3
33.0
30.0
41.3
37.5
A606
45
50
65
70
48.8
52.5
117
126
—
—
—
—
—
—
A607
45
50
55
60
65
70
60
65
70
75
80
85
45.0
48.8
52.5
56.3
60.0
63.8
108
117
126
135
144
153
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
A618
50
50
70
65
52.5
48.8
126
117
—
—
—
—
—
—
Tension
Shear
Shear
0.75 ×
0.75 ×
0.75 ×
0.75Fu [c] 0.40Fu [d] 0.50Fu [e]
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
6 - 146
NUMERICAL VALUES
TABLE 2 (cont’d)
Design Strength as a Function of Fu
Design Strength (ksi)
Item
Connection Part of
Designated Steel
Bolts
ASTM
Designation
A449
Fy
(ksi)
Fu
(ksi)
Tension
0.75 ×
Fu [a]
Bearing
0.75 ×
2.4Fu [b]
92
81
58
120
105
90
—
—
—
—
—
—
Bolt of Threaded Part
of Designated Steel
Tension
Shear
Shear
0.75 ×
0.75 ×
0.75 ×
0.75Fu [c] 0.40Fu [d] 0.50Fu [e]
67.5
59.1
50.6
36.0
31.5
27.0
[a] On effective net area, see Sections D1, J5.2.
[b] Produced by fastener in shear, see Section J3.10. Note that smaller maximum design bearing
stresses, as a function of hole type spacing, are given.
[c] On nominal body area, see Table J3.2.
[d] Threads not excluded from shear plane, see Table J3.2.
[e] Threads excluded from shear plane, see Table J3.2.
[f] Smaller value for circular shapes, larger for square or rectangular shapes.
Note: For dimensional and size limitations, see the appropriate ASTM Specification.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
45.0
39.4
33.8
NUMERICAL VALUES
6 - 147
TABLE 3-36
Design Stress for Compression Members of
36 ksi Specified Yield Stress Steel, φc = 0.85[a]
Kl
r
φcFcr
ksi
Kl
r
φcFcr
ksi
Kl
r
φcFcr
ksi
Kl
r
φcFcr
ksi
Kl
r
φcFcr
ksi
1
2
3
4
5
30.60
30.59
30.59
30.57
30.56
41
42
43
44
45
28.01
27.89
27.76
27.64
27.51
81
82
83
84
85
21.66
21.48
21.29
21.11
20.92
121
122
123
124
125
14.16
13.98
13.80
13.62
13.44
161
162
163
164
165
8.23
8.13
8.03
7.93
7.84
6
7
8
9
10
30.54
30.52
30.50
30.47
30.44
46
47
48
49
50
27.37
27.24
27.11
26.97
26.83
86
87
88
89
90
20.73
20.54
20.36
20.17
19.98
126
127
128
129
130
13.27
13.09
12.92
12.74
12.57
166
167
168
169
170
7.74
7.65
7.56
7.47
7.38
11
12
13
14
15
30.41
30.37
30.33
30.29
30.24
51
52
53
54
55
26.68
26.54
26.39
26.25
26.10
91
92
93
94
95
19.79
19.60
19.41
19.22
19.03
131
132
133
134
135
12.40
12.23
12.06
11.88
11.71
171
172
173
174
175
7.30
7.21
7.13
7.05
6.97
16
17
18
19
20
30.19
30.14
30.08
30.02
29.96
56
57
58
59
60
25.94
25.79
25.63
25.48
25.32
96
97
98
99
100
18.84
18.65
18.46
18.27
18.08
136
137
138
139
140
11.54
11.37
11.20
11.04
10.89
176
177
178
179
180
6.89
6.81
6.73
6.66
6.59
21
22
23
24
25
29.90
29.83
29.76
26.69
29.61
61
62
63
64
65
25.16
24.99
24.83
24.67
24.50
101
102
103
104
105
17.89
17.70
17.51
17.32
17.13
141
142
143
144
145
10.73
10.58
10.43
10.29
10.15
181
182
183
184
185
6.51
6.44
6.37
6.30
6.23
26
27
28
29
30
29.53
29.45
29.36
29.28
29.18
66
67
68
69
70
24.33
24.16
23.99
23.82
23.64
106
107
108
109
110
16.94
16.75
16.56
16.37
16.19
146
147
148
149
150
10.01
9.87
9.74
9.61
9.48
186
187
188
189
190
6.17
6.10
6.04
5.97
5.91
31
32
33
34
35
29.09
28.99
28.90
28.79
28.69
71
72
73
74
75
23.47
23.29
23.12
22.94
22.76
111
112
113
114
115
16.00
15.81
15.63
15.44
15.26
151
152
153
154
155
9.36
9.23
9.11
9.00
8.88
191
192
193
194
195
5.85
5.79
5.73
5.67
5.61
36
37
38
39
40
28.58
28.47
28.36
28.25
28.13
76
77
78
79
80
22.58
22.40
22.22
22.03
21.85
116
117
118
119
120
15.07
14.89
14.70
14.52
14.34
156
157
158
159
160
8.77
8.66
8.55
8.44
8.33
196
197
198
199
200
5.55
5.50
5.44
5.39
5.33
[a] When element width-to-thickness ration exceeds λr , see Appendix B5.3.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
6 - 148
NUMERICAL VALUES
TABLE 3-50
Design Stress for Compression Members of
50 ksi Specified Yield Stress Steel, φc = 0.85[a]
Kl
r
φcFcr
ksi
Kl
r
φcFcr
ksi
Kl
r
φcFcr
ksi
Kl
r
φcFcr
ksi
Kl
r
φcFcr
ksi
1
2
3
4
5
42.50
42.49
42.47
42.45
42.42
41
42
43
44
45
37.59
37.36
37.13
36.89
36.65
81
82
83
84
85
26.31
26.00
25.68
25.37
25.06
121
122
123
124
125
14.57
14.33
14.10
13.88
13.66
161
162
163
164
165
8.23
8.13
8.03
7.93
7.84
6
7
8
9
10
42.39
42.35
42.30
42.25
42.19
46
47
48
49
50
36.41
36.16
35.91
35.66
35.40
86
87
88
89
90
24.75
24.44
24.13
23.82
23.51
126
127
128
129
130
13.44
13.23
13.02
12.82
12.62
166
167
168
169
170
7.74
7.65
7.56
7.47
7.38
11
12
13
14
15
42.13
42.05
41.98
41.90
41.81
51
52
53
54
55
35.14
34.88
34.61
34.34
34.07
91
92
93
94
95
23.20
22.89
22.58
22.28
21.97
131
132
133
134
135
12.43
12.25
12.06
11.88
11.71
171
172
173
174
175
7.30
7.21
7.13
7.05
6.97
16
17
18
19
20
41.71
41.61
41.51
41.39
41.28
56
57
58
59
60
33.79
33.51
33.23
32.95
32.67
96
97
98
99
100
21.67
21.36
21.06
20.76
20.46
136
137
138
139
140
11.54
11.37
11.20
11.04
10.89
176
177
178
179
180
6.89
6.81
6.73
6.66
6.59
21
22
23
24
25
41.15
41.02
40.89
40.75
40.60
61
62
63
64
65
32.38
32.09
31.80
31.50
31.21
101
102
103
104
105
20.16
19.86
19.57
19.28
18.98
141
142
143
144
145
10.73
10.58
10.43
10.29
10.15
181
182
183
184
185
6.51
6.44
6.37
6.30
6.23
26
27
28
29
30
40.45
40.29
40.13
39.97
39.79
66
67
68
69
70
30.91
30.61
30.31
30.01
29.70
106
107
108
109
110
18.69
18.40
18.12
17.83
17.55
146
147
148
149
150
10.01
9.87
9.74
9.61
9.48
186
187
188
189
190
6.17
6.10
6.04
5.97
5.91
31
32
33
34
35
39.62
39.43
39.25
39.06
38.86
71
72
73
74
75
29.40
20.09
28.79
28.48
28.17
111
112
113
114
115
17.27
16.99
16.71
16.42
16.13
151
152
153
154
155
9.36
9.23
9.11
9.00
8.88
191
192
193
194
195
5.85
5.79
5.73
5.67
5.61
36
37
38
39
40
38.66
38.45
38.24
38.03
37.81
76
77
78
79
80
27.86
27.55
27.24
26.93
26.62
116
117
118
119
120
15.86
15.59
15.32
15.07
14.82
156
157
158
159
160
8.77
8.66
8.55
8.44
8.33
196
197
198
199
200
5.55
5.50
5.44
5.39
5.33
[a] When element width-to-thickness ratio exceeds λr , see Appendix B5.3.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
NUMERICAL VALUES
6 - 149
TABLE 4
Values of φcFcr / Fy , φc = 0.85
for Determining Design Stress for Compression
Members for Steel of Any Yield Stress[a]
λc
φcFcr / Fy
λc
φcFcr / Fy
λc
φcFcr / Fy
λc
φcFcr / Fy
0.02
0.04
0.06
0.08
0.10
0.850
0.849
0.849
0.848
0.846
0.82
0.84
0.86
0.88
0.90
0.641
0.632
0.623
0.614
0.605
1.62
1.64
1.66
1.68
1.70
0.284
0.277
0.271
0.264
0.258
2.42
2.44
2.46
2.48
2.50
0.127
0.125
0.123
0.121
0.119
0.12
0.14
0.16
0.18
0.20
0.845
0.843
0.841
0.839
0.836
0.92
0.94
0.96
0.98
1.00
0.596
0.587
0.578
0.568
0.559
1.72
1.74
1.76
1.78
1.80
0.252
0.246
0.241
0.235
0.230
2.52
2.54
2.56
2.58
2.60
0.117
0.116
0.114
0.112
0.110
0.22
0.24
0.26
0.28
0.30
0.833
0.830
0.826
0.823
0.819
1.02
1.04
1.06
1.08
1.10
0.550
0.540
0.531
0.521
0.512
1.82
1.84
1.86
1.88
1.90
0.225
0.220
0.215
0.211
0.206
2.62
2.64
2.66
2.68
2.70
0.109
0.107
0.105
0.104
0.102
0.32
0.34
0.36
0.38
0.40
0.814
0.810
0.805
0.800
0.795
1.12
1.14
1.16
1.18
1.20
0.503
0.493
0.484
0.474
0.465
1.92
1.94
1.96
1.98
2.00
0.202
0.198
0.194
0.190
0.186
2.72
2.74
2.76
2.78
2.80
0.101
0.099
0.098
0.096
0.095
0.42
0.44
0.46
0.48
0.50
0.789
0.784
0.778
0.772
0.765
1.22
1.24
1.26
1.28
1.30
0.456
0.446
0.437
0.428
0.419
2.02
2.04
2.06
2.08
2.10
0.183
0.179
0.176
0.172
0.169
2.82
2.84
2.86
2.88
2.90
0.094
0.092
0.091
0.090
0.089
0.52
0.54
0.56
0.58
0.60
0.759
0.752
0.745
0.738
0.731
1.32
1.34
1.36
1.38
1.40
0.410
0.401
0.392
0.383
0.374
2.12
2.14
2.16
2.18
2.20
0.166
0.163
0.160
0.157
0.154
2.92
2.94
2.96
2.98
3.00
0.087
0.086
0.085
0.084
0.083
0.62
0.64
0.66
0.68
0.70
0.724
0.716
0.708
0.700
0.692
1.42
1.44
1.46
1.48
1.50
0.365
0.357
0.348
0.339
0.331
2.22
2.24
2.26
2.28
2.30
0.151
0.149
0.146
0.143
0.141
3.02
3.04
3.06
3.08
3.10
0.082
0.081
0.080
0.079
0.078
0.72
0.74
0.76
0.78
0.80
0.684
0.676
0.667
0.659
0.650
1.52
1.54
1.56
1.58
1.60
0.323
0.314
0.306
0.299
0.291
2.32
2.34
2.36
2.38
2.40
0.138
0.136
0.134
0.132
0.129
3.12
3.14
3.16
3.18
3.20
0.077
0.076
0.075
0.074
0.073
[a] When element width-to-thickness ratios exceed λr , see Appendix B5.3.
Values of λc > 2.24 exceed Kl / r of 200 for Fy = 36
Values of λc > 2.64 exceed Kl / r of 200 for Fy = 50
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
6 - 150
NUMERICAL VALUES
TABLE 5
Values of Kl / r for Fy = 36 and 50 ksi
Kl / r
Kl / r
λc
Fy = 36
Fy = 50
λc
0.02
0.04
0.06
0.08
0.10
1.8
3.6
4.3
7.1
8.9
1.5
3.0
4.5
6.1
7.6
0.12
0.14
0.16
0.18
0.20
10.7
12.5
14.3
16.0
17.8
0.22
0.24
0.26
0.28
0.30
Fy = 36
Fy = 50
0.82
0.84
0.86
0.88
0.90
73.1
74.9
76.7
78.5
80.2
62.0
63.6
65.1
66.6
68.1
9.1
10.6
12.1
13.6
15.1
0.92
0.94
0.96
0.98
1.00
82.0
83.8
85.6
87.4
89.2
69.6
71.1
72.6
74.1
75.7
19.6
21.4
23.2
25.0
26.7
16.6
18.2
19.7
21.2
22.7
1.02
1.04
1.06
1.08
1.10
90.9
92.7
94.5
96.3
98.1
77.2
78.7
80.2
81.7
83.2
0.32
0.34
0.36
0.38
0.40
28.5
30.3
32.1
33.9
35.7
24.2
25.7
27.2
28.8
30.3
1.12
1.14
1.16
1.18
1.20
99.9
101.6
103.4
105.2
107.0
84.7
86.3
87.8
89.3
90.8
0.42
0.44
0.46
0.48
0.50
37.4
39.2
41.0
42.8
44.6
31.8
33.3
34.8
36.3
37.8
1.22
1.24
1.26
1.28
1.30
108.8
110.6
112.3
114.1
115.9
92.3
93.8
95.3
96.8
98.4
0.52
0.54
0.56
0.58
0.60
46.4
48.1
49.9
51.7
53.5
39.3
40.9
42.4
43.9
45.4
1.32
1.34
1.36
1.38
1.40
117.7
119.5
121.3
123.0
124.8
99.9
101.4
102.9
104.4
105.9
0.62
0.64
0.66
0.68
0.70
55.3
57.1
58.8
60.6
62.4
46.9
48.4
49.9
51.4
53.0
1.42
1.44
1.46
1.48
1.50
126.6
128.4
130.2
132.0
133.7
107.4
108.9
110.5
112.0
113.5
0.72
0.74
0.76
0.78
0.80
64.2
66.0
67.8
69.5
71.3
54.5
56.0
57.5
59.0
60.5
1.52
1.54
1.56
1.58
1.60
135.5
137.3
139.1
140.9
142.7
115.0
116.5
118.0
119.5
121.1
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
NUMERICAL VALUES
6 - 151
TABLE 5 (cont’d)
Values of Kl / r for Fy = 36 and 50 ksi
Kl / r
Kl / r
λc
Fy = 36
Fy = 50
λc
Fy = 50
1.62
1.64
1.66
1.68
1.70
144.4
146.2
148.0
149.8
151.6
122.6
124.1
125.6
127.1
128.6
2.42
2.44
2.46
2.48
2.50
183.1
184.6
186.1
187.6
189.1
1.72
1.74
1.76
1.78
1.80
153.4
155.1
156.9
158.7
160.5
130.1
131.6
133.2
134.7
136.2
2.52
2.54
2.56
2.58
2.60
190.7
192.2
193.7
195.2
196.7
1.82
1.84
1.86
1.88
1.90
162.3
164.1
165.8
167.6
169.4
137.7
139.2
140.7
142.2
143.8
2.62
2.64
198.2
199.7
1.92
1.94
1.96
1.98
2.00
171.2
173.0
174.8
176.5
178.3
145.3
146.8
148.3
149.8
151.3
2.02
2.04
2.06
2.08
2.10
180.1
181.9
183.7
185.5
187.2
152.8
154.3
155.9
157.4
158.9
2.12
2.14
2.16
2.18
2.20
189.0
190.8
192.6
194.4
196.2
160.4
161.9
163.4
164.9
166.5
2.22
2.24
2.26
2.28
2.30
197.9
199.7
168.0
169.5
171.0
172.5
174.0
2.32
2.34
2.36
2.38
2.40
175.5
177.0
178.6
180.1
181.6
Heavy line indicates Kl / r of 200.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
6 - 152
NUMERICAL VALUES
TABLE 6
Slenderness Ratios of Elements as a Function of Fy
From Table B5.1
Fy (ksi)
Ratio
36
42
65 / √
Fy
10.8
10.0
√Fy
76 /
12.7
√Fy
95 /
15.8
Fy
127 / √
21.2
19.6
46
50
60
8.4
65
9.6
9.2
8.1
11.7
11.2
10.7
9.8
9.4
14.7
14.0
13.4
12.3
11.8
18.7
18.0
16.4
15.8
Fy − 10
141 / √
27.7
24.9
23.5
22.3
19.9
19.0
Fy
190 / √
31.7
29.3
28.0
26.9
24.5
23.6
238 / √
Fy
39.7
36.7
35.1
33.7
30.7
29.5
253 / √
Fy
42.2
39.0
37.3
35.8
32.7
31.4
Fy
317 / √
52.8
48.9
46.7
44.8
40.9
39.3
640 / √
Fy
107.0
98.8
94.4
90.5
82.6
79.4
Fy
970 / √
162.0
150.0
143.0
137.0
125.0
120.0
1,300 / Fy
36.1
31.0
28.3
26.0
21.7
20.0
2,070 / Fy
57.5
49.3
45.0
41.4
34.5
31.8
3,300 / Fy
91.7
78.6
71.7
66.0
55.0
50.8
8,970 / Fy
249.0
214.0
195.0
179.0
150.0
138.0
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
NUMERICAL VALUES
6 - 153
TABLE 7
Values of Cm
for Use in Section C1
M1
M2
Cm
M1
M2
Cm
M1
M2
Cm
−1.00
1.00
−0.45
0.78
0.10
0.56
−0.95
0.98
−0.40
0.76
0.15
0.54
−0.90
0.96
−0.35
0.74
0.20
0.52
−0.85
0.94
−0.30
0.72
0.25
0.50
−0.80
0.92
−0.25
0.70
0.30
0.48
−0.75
0.90
−0.20
0.68
0.35
0.46
−0.70
0.88
−0.15
0.66
0.40
0.44
−0.65
0.86
−0.10
0.64
0.45
0.42
−0.60
0.84
−0.05
0.62
0.50
0.40
0.60
0.36
−0.55
0.82
0
0.60
0.80
0.28
−0.50
0.80
0.05
0.58
1.00
0.20
Note 1: Cm = 0.6 − 0.4(M1 / M2).
Note 2: M1 / M2 is positive for reverse curvature and negative for single curvature. |M1| ≤ |M2|
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
6 - 154
NUMERICAL VALUES
TABLE 8
Values of Pe / Ag
for Use in Section C1 for Steel of Any Yield Stress
Kl
r
Pe / Ag
(ksi)
Kl
r
Pe / Ag
(ksi)
Kl
r
Pe / Ag
(ksi)
Kl
r
Pe / Ag
(ksi)
Kl
r
Pe / Ag
(ksi)
Kl
r
Pe / Ag
(ksi)
21
22
23
24
25
649.02
591.36
541.06
496.91
457.95
51
52
53
54
55
110.04
105.85
101.89
98.15
94.62
81
82
83
84
85
43.62
42.57
41.55
40.56
39.62
111
112
113
114
115
23.23
22.82
22.42
22.02
21.64
141
142
143
144
145
14.40
14.19
14.00
13.80
13.61
171
172
173
174
175
9.79
9.67
9.56
9.45
9.35
26
27
28
29
30
423.40
392.62
365.07
340.33
318.02
56
57
58
59
60
91.27
88.09
85.08
82.22
79.51
86
87
88
89
90
38.70
37.81
36.96
36.13
35.34
116
117
118
119
120
21.27
20.91
20.56
20.21
19.88
146
147
148
149
150
13.43
13.25
13.07
12.89
12.72
176
177
178
179
180
9.24
9.14
9.03
8.93
8.83
31
32
33
34
35
297.83
279.51
262.83
247.59
233.65
61
62
63
64
65
76.92
74.46
72.11
69.88
67.74
91
92
93
94
95
34.56
33.82
33.09
32.39
31.71
121
122
123
124
125
19.55
19.23
18.92
18.61
18.32
151
152
153
154
155
12.55
12.39
12.23
12.07
11.91
181
182
183
184
185
8.74
8.64
8.55
8.45
8.36
36
37
38
39
40
220.85
209.07
198.21
188.18
178.89
66
67
68
69
70
65.71
63.76
61.90
60.12
58.41
96
97
98
99
100
31.06
30.42
29.80
29.20
28.62
126
127
128
129
130
18.03
17.75
17.47
17.20
16.94
156
157
158
159
160
11.76
11.61
11.47
11.32
11.18
186
187
188
189
190
8.27
8.18
8.10
8.01
7.93
41
42
43
44
45
170.27
162.26
154.80
147.84
141.34
71
72
73
74
75
56.78
55.21
53.71
52.57
50.88
101
102
103
104
105
28.06
27.51
26.98
26.46
25.96
131
132
133
134
135
16.68
16.43
16.18
15.94
15.70
161
162
163
164
165
11.04
10.91
10.77
10.64
10.51
191
192
193
194
195
7.85
7.76
7.68
7.60
7.53
46
47
48
49
50
135.26
129.57
124.23
119.21
114.49
76
77
78
79
80
49.55
48.27
47.04
45.86
44.72
106
107
108
109
110
25.47
25.00
24.54
24.09
23.65
136
137
138
139
140
15.47
15.25
15.03
14.81
14.60
166
167
168
169
170
10.39
10.26
10.14
10.02
9.90
196
197
198
199
200
7.45
7.38
7.30
7.23
7.16
Note: Pe / Ag =
π2E
(Kl / r)2
, use for both Pe1 and Pe2.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
NUMERICAL VALUES
6 - 155
TABLE 9-36
φvVn
(ksi) for Plate Girders by Appendix F2
Aw
for 36 ksi Yield Stress Steel,
Tension Field Action Not Included
Aspect ratio a / h: Stiffener Spacing to Web Depth
h
tw
0.5
0.6
0.7
0.8
0.9
1.0
1.2
1.4
1.6
1.8
2.0
2.5
3.0
Over
3.0
60 19.4 19.4 19.4 19.4 19.4 19.4 19.4 19.4 19.4 19.4 19.4 19.4 19.4 19.4
70 19.4 19.4 19.4 19.4 19.4 19.4 19.4 19.4 19.4 19.4 19.4 19.4 19.4 19.4
80 19.4 19.4 19.4 19.4 19.4 19.4 19.4 19.4 19.4 19.4 18.9 18.2 17.9 16.9
90 19.4 19.4 19.4 19.4 19.4 19.4 19.4 18.5 17.8 17.2 16.8 16.2 15.9 14.7
100 19.4 19.4 19.4 19.4 19.4 19.2 17.6 16.6 16.0 15.5 14.9 13.8 13.2 11.9
110
19.4 19.4 19.4 19.4 18.4 17.4 16.0 14.8 13.7 12.8 12.3 11.4 10.9
9.8
120 19.4 19.4 19.4 18.1 16.9 16.0 14.0 12.5 11.5 10.8 10.3
9.6
9.2
8.3
130 19.4 19.4 18.2 16.7 15.6 14.1 11.9 10.6
9.8
9.2
8.8
8.2
7.8
7.0
140 19.4 18.8 16.9 15.5 13.5 12.1 10.3
9.2
8.4
7.9
7.6
7.0
6.7
6.1
150 19.4 17.6 15.7 13.5 11.8 10.6
8.9
8.0
7.3
6.9
6.6
6.1
5.9
5.3
160 18.9 16.5 14.1 11.9 10.4
9.3
7.9
7.0
6.5
6.1
5.8
5.4
170 17.8 15.5 12.5 10.5
9.2
8.2
7.0
6.2
5.7
5.4
5.1
4.1
180 16.8 13.9 11.1
9.4
8.2
7.3
6.2
5.5
5.1
4.8
4.6
3.7
200 14.9 11.2
9.0
7.6
6.6
5.9
5.0
4.5
4.1
220 12.3
9.3
7.5
6.3
5.5
4.9
4.2
240 10.3
7.8
6.3
5.3
4.6
4.1
2.1
260
8.8
6.6
5.3
4.5
3.9
3.5
1.8
280
7.6
5.7
4.6
3.9
300
6.6
5.0
4.0
320
5.8
4.4
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
4.6
3.0
2.5
6 - 156
NUMERICAL VALUES
TABLE 9-50
φvVn
(ksi) for Plate Girders by Appendix F2
Aw
for 50 ksi Yield Stress Steel,
Tension Field Action Not Included
Aspect ratio a / h: Stiffener Spacing to Web Depth
h
tw
0.5
0.6
0.7
0.8
0.9
1.0
1.2
1.4
1.6
1.8
2.0
2.5
3.0
Over
3.0
60 27.0 27.0 27.0 27.0 27.0 27.0 27.0 27.0 27.0 27.0 27.0 27.0 27.0 26.6
70 27.0 27.0 27.0 27.0 27.0 27.0 27.0 27.0 26.9 26.1 25.5 24.6 24.0 22.8
80 27.0 27.0 27.0 27.0 27.0 27.0 26.0 24.5 23.5 22.8 22.3 21.5 20.6 18.6
90 27.0 27.0 27.0 27.0 26.5 25.1 23.1 21.8 20.4 19.2 18.3 17.0 16.3 14.7
100 27.0 27.0 27.0 25.6 23.9 22.6 20.1 17.9 16.5 15.5 14.9 13.8 13.2 11.9
110
27.0 27.0 25.3 23.2 21.7 19.6 16.6 14.8 13.7 12.8 12.3 11.4 10.9
9.8
120 27.0 25.9 23.2 21.1 18.4 16.5 14.0 12.5 11.5 10.8 10.3
9.6
9.2
8.3
130 27.0 23.9 21.4 18.0 15.7 14.1 11.9 10.6
9.8
9.2
8.8
8.2
7.8
7.0
140 25.5 22.2 18.4 15.5 13.5 12.1 10.3
9.2
8.4
7.9
7.6
7.0
6.7
6.1
150 23.8 19.9 16.1 13.5 11.8 10.6
8.9
8.0
7.3
6.9
6.6
6.1
5.9
5.3
160 22.3 17.5 14.1 11.9 10.4
9.3
7.9
7.0
6.5
6.1
5.8
5.4
170 20.6 15.5 12.5 10.5
9.2
8.2
7.0
6.2
5.7
5.4
5.1
4.1
180 18.3 13.9 11.1
9.4
8.2
7.3
6.2
5.5
5.1
4.8
4.6
3.7
200 14.9 11.2
9.0
7.6
6.6
5.9
5.0
4.5
4.1
220 12.3
9.3
7.5
6.3
5.5
4.9
4.2
240 10.3
7.8
6.3
5.3
4.6
4.1
2.1
260
8.8
6.6
5.3
4.5
3.9
3.5
1.8
280
7.6
5.7
4.6
3.9
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
4.6
3.0
2.5
NUMERICAL VALUES
6 - 157
TABLE 10-36
φvVn
(ksi) for Plate Girders by Appendix G
Aw
for 36 ksi Yield Stress Steel,
Tension Field Action Included[b]
(Italic values indicate gross area,
as percent of (h × tw) required for pairs of
intermediate stiffeners of 36 ksi yield stress
steel with Vu / φVn = 1.0) [a]
Aspect ratio a / h: Stiffener Spacing to Web Depth
h
tw
0.5
0.6
0.7
0.8
0.9
1.0
1.2
1.4
1.6
1.8
2.0
2.5
3.0
Over
3.0
[c]
60 19.4 19.4 19.4 19.4 19.4 19.4 19.4 19.4 19.4 19.4 19.4 19.4 19.4 19.4
70 19.4 19.4 19.4 19.4 19.4 19.4 19.4 19.4 19.4 19.4 19.4 19.4 19.4 19.4
80 19.4 19.4 19.4 19.4 19.4 19.4 19.4 19.4 19.4 19.4 19.1 18.6 18.3 16.9
90 19.4 19.4 19.4 19.4 19.4 19.4 19.4 19.0 18.5 18.2 17.8 17.3 16.8 14.7
100 19.4 19.4 19.4 19.4 19.4 19.3 18.6 18.1 17.6 17.2 16.6 15.6 14.9 11.9
110
19.4 19.4 19.4 19.4 19.1 18.7 17.9 17.2 16.3 15.6 15.1 14.0 13.3
9.8
120 19.4 19.4 19.4 19.0 18.5 18.1 17.0 16.0 15.1 14.4 13.9 12.8 12.0
8.3
130 19.4 19.4 19.1 18.6 18.1 17.4 16.1 15.1 14.2 13.5 12.9 11.8 11.0
7.0
140 19.4 19.3 18.7 18.2 17.4 16.6 15.4 14.4 13.5 12.8 12.2 11.0 10.2
6.1
150 19.4 19.0 18.4 17.5 16.7 16.0 14.8 13.8 12.9 12.2 11.6 10.4
5.3
160 19.3 18.7 17.9 17.0 16.2 15.5 14.3 13.3 12.4 11.7 11.1
9.9
9.6
4.6
170 19.1 18.4 17.4 16.6 15.8 15.1 13.9 12.9 12.0 11.3 10.7
0.3 0.4
4.1
180 18.9 18.0 17.1 16.2 15.5 14.8 13.6 12.6 11.7 11.0 10.4
0.2 0.7 1.1 1.3 1.5
3.7
200 18.4 17.3 16.4 15.6 14.9 14.2 13.1 12.0 11.2
0.1 0.9 1.4 2.1 2.5 2.8
3.0
220 17.8 16.9 16.0 15.2 14.5 13.8 12.7
1.1 2.0 2.6 3.0 3.6
2.5
240 17.4 16.5 15.7 14.9 14.2 13.5
1.5 2.7 3.4 3.9 4.3
2.1
260 17.1 16.2 15.4 14.6 14.0 13.3
1.3 3.0 4.0 4.6 5.0 5.4
1.8
280 16.8 16.0 15.2 14.4
2.7 4.2 5.0 5.6
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
6 - 158
NUMERICAL VALUES
TABLE 10-36 (cont’d)
φvVn
(ksi) for Plate Girders by Appendix G
Aw
for 36 ksi Yield Stress Steel,
Tension Field Action Included[b]
(Italic values indicate gross area,
as percent of (h x tw) required for pairs of
intermediate stiffeners of 36 ksi yield stress
steel with Vu / φVn = 1.0)[a]
Aspect ratio a / h: Stiffener Spacing to Web Depth
h
tw
0.5
0.6
0.7
0.8
0.9
1.0
1.2
1.4
1.6
1.8
2.0
2.5
3.0
Over
3.0
[c]
300 16.6 15.8 15.0
3.9 5.2 5.9
320 16.4 15.6
4.9 6.0
[a] For area of single-angle and single-plate stiffeners, or when Vu / φVn < 1.0, see Equation A-G4-1.
[b] For end-panels and all panels in hybrid and web-tapered plate girders, use Table 9-36.
[c] Same as for Table 9-36.
Note: Girders so proportioned that the computed shear is less than that given in right-hand column do not
require intermediate stiffeners.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
NUMERICAL VALUES
6 - 159
TABLE 10-50
φvVn
(ksi) for Plate Girders by Appendix G
Aw
for 50 ksi Yield Stress Steel,
Tension Field Action Included[b]
(Italic values indicate gross area, as percent of (h × tw) required for pairs of
intermediate stiffeners of 50 ksi yield stress steel with Vu / φVn = 1.0)[a]
Aspect ratio a / h: Stiffener Spacing to Web Depth
h
tw
0.5
0.6
0.7
0.8
0.9
1.0
1.2
1.4
1.6
1.8
2.0
2.5
3.0
Over
3.0
[c]
60 27.0 27.0 27.0 27.0 27.0 27.0 27.0 27.0 27.0 27.0 27.0 27.0 27.0 26.6
70 27.0 27.0 27.0 27.0 27.0 27.0 27.0 27.0 26.9 26.5 26.1 25.4 24.9 22.8
80 27.0 27.0 27.0 27.0 27.0 27.0 26.5 25.8 25.1 24.6 24.1 23.3 22.4 18.6
90 27.0 27.0 27.0 27.0 26.8 26.3 25.3 24.4 23.4 22.5 21.7 20.2 19.2 14.7
100 27.0 27.0 27.0 26.5 25.9 25.3 24.0 22.5 21.4 20.4 19.6 18.0 17.0 11.9
110
27.0 27.0 26.5 25.8 25.1 24.2 22.4 21.0 19.8 18.8 18.0 16.4 15.3
9.8
120 27.0 26.7 25.9 25.1 24.0 23.0 21.2 19.8 18.6 17.6 16.8 15.2 14.1
8.3
130 27.0 26.2 25.4 24.1 23.0 22.0 20.3 18.9 17.7 16.7 15.9 14.2 13.1
7.0
140 26.7 25.8 24.5 23.3 22.2 21.3 19.6 18.2 17.0 16.0 15.1 13.5 12.3
6.1
150 26.3 25.2 23.9 22.7 21.6 20.7 19.0 17.6 16.4 15.4 14.5 12.9 11.7
5.3
160 26.0 24.6 23.3 22.2 21.1 20.2 18.5 17.1 15.9 14.9 14.0 12.4
0.2 0.4 0.5 0.8
4.6
170 25.6 24.1 22.8 21.7 20.7 19.8 18.1 16.7 15.2 14.5 13.6
0.5 1.0 1.2 1.4 1.6
4.1
180 25.1 23.7 22.4 21.3 20.3 19.4 17.8 16.4 15.2 14.2 13.3
0.4 0.9 1.5 1.9 2.2 2.3 2.5
3.7
200 24.3 23.0 21.8 20.8 19.8 18.9 17.3 15.9 14.7
1.0 1.8 2.3 2.7 3.2 3.5
3.7
3.0
220 23.7 22.5 21.4 20.4 19.4 18.5 16.9
1.7 2.7 3.3 3.8 4.1 4.5
2.5
240 23.2 22.1 21.0 20.0 19.1 18.2
1.8 3.2 4.0 4.6 4.9 5.2
2.1
260 23.0 21.8 20.8 19.8 18.8 18.0
3.2 4.4 5.1 5.6 5.9 6.1
280 22.7 21.6 20.6 19.6
4.4 5.4 6.0 6.4
[a] For area of single-angle and single-plate stiffeners, or when Vu / φVn < 1.0, see Equation A-G4-1.
[b] For end-panels and all panels in hybrid and web-tapered plate girders, use Table 9-50.
[c] Same as for Table 9-50.
Note: Girders so proportioned that the computed shear is less than that given in right-hand column do not
require intermediate stiffeners.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
6 - 160
NUMERICAL VALUES
TABLE 11
Nominal Horizontal Shear Load for
One Connector Qn, kips[a]
From Equations I5-1 and I5-2
Specified Compressive Strength
of Concrete, fc′, ksi [d]
Connector [b]
3.0
3.5
4.0
dia. × 2-in. hooked or headed stud
9.4
10.5
11.6
dia. × 21⁄2-in. hooked or headed stud
14.6
16.4
18.1
dia. × 3-in. hooked or headed stud
21.0
23.6
26.1
dia. × 31⁄2-in. hooked or headed stud
28.6
32.1
35.5
Channel C3 × 4.1
10.2 Lc [c]
11.5 Lc [c]
12.7 Lc [c]
Channel C4 × 5.4
11.1 Lc [c]
12.4 Lc [c]
13.8 Lc [c]
Channel C5 × 6.7
11.9 Lc [c]
13.3 Lc [c]
14.7 Lc [c]
1⁄ -in.
2
5⁄ -in.
8
3⁄ -in.
4
7⁄ -in.
8
[a] Applicable only to concrete made with ASTM C33 aggregates.
[b] The nominal horizontal loads tabulated may also be used for studs longer than shown.
[c] Lc = length of channel, inches.
[d] Fu > 0.5(fc′w)0.75, w = 145 lbs./cu. ft.
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COMMENTARY
on the Load and Resistance Factor
Design Specification for Structural
Steel Buildings
December 1, 1993
INTRODUCTION
The Specification is intended to be complete for normal design usage.
The Commentary furnishes background information and references for the benefit of
the engineer seeking further understanding of the derivations and limits of the
specification.
The Specification and Commentary are intended for use by design professionals with
demonstrated engineering competence.
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CHAPTER A
GENERALPROVISIONS
A1. SCOPE
Load and Resistance Factor Design (LRFD) is an improved approach to the
design of structural steel for buildings. It involves explicit consideration of limit
states, multiple load factors, and resistance factors, and implicit probabilistic
determination of reliability. The designation LRFD reflects the concept of
factoring both loads and resistance. This type of factoring differs from the AISC
allowable stress design (ASD) Specification (AISC, 1989), where only the
resistance is divided by a factor of safety (to obtain allowable stress) and from
the plastic design portion of that Specification, where only the loads are
multiplied by a common load factor. The LRFD method was devised to offer
the designer greater flexibility, more rationality, and possible overall economy.
The format of using resistance factors and multiple load factors is not new, as
several such design codes are in effect [the ACI-318 Strength Design for
Reinforced Concrete (ACI, 1989) and the AASHTO Load Factor Design for
Bridges (AASHTO, 1989)]. Nor should the new LRFD method give designs
radically different from the older methods, since it was tuned, or “calibrated,”
to typical representative designs of the earlier methods. The principal new
ingredient is the use of a probabilistic mathematical model in the development
of the load and resistance factors, which made it possible to give proper weight
to the accuracy with which the various loads and resistances can be determined.
Also, it provides a rational methodology for transference of test results into
design provisions. A more rational design procedure leading to more uniform
reliability is the practical result.
A2. LIMITS OF APPLICABILITY
2.
Types of Construction
The provisions for these types of construction have been revised to provide for
a truer recognition of the actual degree of connection restraint in the structural
design. All connections provide some restraint. Depending on the amount of
restraint offered, connections are classified as either Type FR or PR. This
classification renames the Type I connection of the AISC ASD Specification to
Type FR and includes both Type II and Type III of that Specification under a
new, more general classification of Type PR.
Just as in the allowable stress design (ASD) provisions, construction utilizing
Type FR connections may be designed in LRFD using either elastic or plastic
analysis provided the appropriate Specification provisions are satisfied.
For Type PR construction which uses the “simple framing” approach, the
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restraint of the connection is ignored, provided the given conditions are met.
This is no change from the ASD provisions. Where there is evidence of the actual
moment rotation capability of a given type of connection, the use of designs
incorporating the connection restraint is permitted just as in ASD. The designer
should, when incorporating connection restraint into the design, take into
account the reduced connection stiffness on the stability of the structure and its
effect on the magnitude of second order effects.
A3. MATERIAL
1.
Structural Steel
1a.
ASTM Designations
The grades of structural steel approved for use under the LRFD Specification,
covered by ASTM standard specifications, extend to a yield stress of 100 ksi.
Some of these ASTM standards specify a minimum yield point, while others
specify a minimum yield strength. The term “yield stress” is used in the
Specification as a generic term to denote either the yield point or the yield
strength.
It is important to be aware of limitations of availability that may exist for some
combinations of strength and size. Not all structural section sizes are included
in the various material specifications. For example, the 60 ksi yield strength steel
in the A572 specification includes plate only up to 11⁄4-in. in thickness. Another
limitation on availability is that even when a product is included in the specifications, it may be only infrequently produced by the mills. Specifying these
products may result in procurement delays or require ordering large quantities
directly from the producing mills. Consequently, it is prudent to check availability before completing the details of a design.
Properties in the direction of rolling are of principal interest in the design of steel
structures. Hence, yield stress as determined by the standard tensile test is the
principal mechanical property recognized in the selection of the steels approved
for use under the Specification. It must be recognized that other mechanical and
physical properties of rolled steel, such as anisotropy, ductility, notch toughness,
formability, corrosion resistance, etc., may also be important to the satisfactory
performance of a structure.
It is not possible to incorporate in the Commentary adequate information to
impart full understanding of all factors which might merit consideration in the
selection and specification of materials for unique or especially demanding
applications. In such a situation the user of the Specification is advised to make
use of reference material contained in the literature on the specific properties of
concern and to specify supplementary material production or quality requirements as provided for in ASTM material specifications. One such case is the
design of highly restrained welded connections (AISC, 1973). Rolled steel is
anisotropic, especially insofar as ductility is concerned; therefore, weld contraction strains in the region of highly restrained welded connections may exceed
the capabilities of the material if special attention is not given to material
selection, details, workmanship, and inspection.
Another special situation is that of fracture control design for certain types of
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GENERAL PROVISIONS
[Comm. A
service conditions (AASHTO, 1989). The relatively warm temperatures of steel
in buildings, the essentially static strain rates, the stress intensity, and the number
of cycles of full design stress make the probability of fracture in building
structures extremely remote. Good workmanship and good design details incorporating joint geometry that avoids severe stress concentrations are generally
the most effective means of providing fracture-resistant construction. However,
for especially demanding service conditions such as low temperatures with
impact loading, the specification of steels with superior notch toughness may
be warranted.
1c.
Heavy Shapes
The web-to-flange intersection and the web center of heavy hot-rolled shapes
as well as the interior portions of heavy plates may contain a coarser grain
structure and/or lower toughness material than other areas of these products.
This is probably caused by ingot segregation, as well as somewhat less deformation during hot rolling, higher finishing temperature, and a slower cooling
rate after rolling for these heavy sections. This characteristic is not detrimental
to suitability for service for compression members, or for non-welded members.
However, when heavy cross sections are joined by splices or connections using
complete-joint penetration welds which extend through the coarser and/or lower
notch-tough interior portions, tensile strains induced by weld shrinkage may
result in cracking, for example a complete-joint penetration welded connection
of a heavy cross section beam to any column section. When members of lesser
thickness are joined by complete-joint penetration welds, which induce smaller
weld shrinkage strains, to the finer grained and/or more notch-tough surface
material of ASTM A6 Group 4 and 5 shapes and heavy built-up cross sections,
the potential for cracking is significantly lower, for example a complete penetration groove welded connection of a non-heavy cross-section beam to a heavy
cross-section column.
For critical applications such as primary tension members, material should be
specified to provide adequate toughness at service temperatures. Because of
differences in the strain rate between the Charpy V-Notch (CVN) impact test
and the strain rate experienced in actual structures, the CVN test is conducted
at a temperature higher than the anticipated service temperature for the structure.
The location of the CVN test is shown in Figure C-A3.1.
The toughness requirements of A3.1c are intended only to provide material of
reasonable toughness for ordinary service application. For unusual applications
and/or low temperature service, more restrictive requirements and/or toughness
requirements for other section sizes and thicknesses may be appropriate.
To minimize the potential for fracture, the notch toughness requirements of
A3.1c must be used in conjunction with good design and fabrication procedures.
Specific requirements are given in Sections J1.5, J1.6, J2.3, and M2.2.
3.
Bolts, Washers, and Nuts
The ASTM standard for A307 bolts covers two grades of fasteners. Either grade
may be used under the LRFD Specification; however, it should be noted that
Gr. B is intended for pipe flange bolting and Gr. A is the quality long in use for
structural applications.
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Anchor Bolts and Threaded Rods
Since there is a limit on the maximum available length of A325 and A490, the
use of these bolts for anchor bolts with design lengths longer than the maximum
available lengths has presented problems in the past. The inclusion of A687
material in this Specification allows the use of higher strength material for bolts
longer than A325 and A490 bolts. The designer should be aware that pretensioning anchor bolts is not recommended due to relaxation and stress corrosion after
pretensioning.
The designer should specify the appropriate thread and SAE fit for threaded rods
used as load-carrying members.
5.
Filler Metal and Flux for Welding
The filler metal specifications issued by the American Welding Society are
general specifications which include filler metals suitable for building construction, as well as consumables that would not be suitable for building construction.
For example, some electrodes covered by the specifications are specifically
limited to single pass applications, while others are restricted to sheet metal
applications. Many of the filler metals listed are “low hydrogen”, that is, they
deposit weld metal with low levels of diffusable hydrogen. Other materials are
not. Filler metals listed under the various A5 specifications may or may not have
required impact toughness, depending on the specific electrode classification.
Notch toughness is generally not critical for weld metal used in building
construction. However, on structures subject to dynamic loading, the engineer
may require the filler metals used to deliver notch-tough weld deposits. Filler
metals may be classified in either the as welded or post weld heat treated (stress
relieved) condition. Since most structural applications will not involve stress
relief, it is important to utilize filler materials that are classified in conditions
similar to those experienced by the actual structure.
When specifying filler metal and/or flux by AWS designation, the applicable
standard specifications should be carefully reviewed to assure a complete
understanding of the designation reference. This is necessary because the AWS
designation systems are not consistent. For example, in the case of electrodes
for shielded metal arc welding (AWS A5.1), the first two or three digits indicate
the nominal tensile strength classification, in ksi, of the weld metal and the final
two digits indicate the type of coating; however, in the case of mild steel
1
/4 tf
CVN specimen
location
Fig. C-A3.1. Location from which Charpy impact specimen shall be taken.
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GENERAL PROVISIONS
[Comm. A
electrodes for submerged arc welding (AWS A5.17), the first one or two digits
times 10 indicate the nominal tensile strength classification, while the final digit
or digits times 10 indicate the testing temperature in degrees F, for weld metal
impact tests. In the case of low-alloy steel covered arc welding electrodes (AWS
A5.5), certain portions of the designation indicate a requirement for stress relief,
while others indicate no stress relief requirement.
Engineers do not, in general, specify the exact filler metal to be employed on a
particular structure. Rather, the decision as to which welding process and which
filler metal is to be utilized is usually left with the fabricator. To ensure that the
proper filler metals are used, codes restrict the usage of certain filler materials,
or impose qualification testing to prove the suitability of the specific electrode.
A4. LOADS AND LOAD COMBINATIONS
1.
Loads, Load Factors, and Load Combinations
The load factors and load combinations given in Section A4.1 were developed
to be used with the recommended minimum loads given in ASCE 7 Minimum
Design Loads for Buildings and Other Structures (ASCE, 1988). The load
factors and load combinations are developed in Ellingwood et al. (1982). The
target reliability indices β underlying the load factors are approximately 3.0 for
combinations with gravity loads only (dead, snow, and live loads), 2.5 for
combinations with wind included, and 1.75 for combinations with earthquake
loads. See Commentary A5.3 for definition of β.
The load factors and load combinations recognize that when several loads act
in combination with the dead load (e.g., dead plus live plus wind), only one of
these takes on its maximum lifetime value, while the other load is at its “arbitrary
point-in-time value” (i.e., at a value which can be expected to be on the structure
at any time). For example, under dead, live, and wind loads the following
combinations are appropriate:
γD D + γLL
(C-A4-1)
γD D + γLaLa + γwW
(C-A4-2)
γD D + γLL + γwaWa
(C-A4-3)
where γ is the appropriate load factor as designated by the subscript symbol.
Subscript a refers to an “arbitrary point-in-time” value.
The mean value of arbitrary point-in-time live load La is on the order of 0.24 to
0.4 times the mean maximum lifetime live load L for many occupancies, but its
dispersion is far greater. The arbitrary point-in-time wind load Wa, acting in
conjunction with the maximum lifetime live load, is the maximum daily wind.
It turns out that γWa Wa is a negligible quantity so only two load combinations
remain:
1.2D + 1.6L
(C-A4-4)
1.2D + 0.5L + 1.3W
(C-A4-5)
The load factor 0.5 assigned to L in the second equation reflects the statistical
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properties of La, but to avoid having to calculate yet another load, it is reduced
so it can be combined with the maximum lifetime wind load.
The nominal loads D, L, W, E, and S are the code loads or the loads given in
ASCE 7. The new specified earthquake loads are based on post-elastic energy
dissipation in the structure, and are higher than those traditionally specified for
allowable stress design (NEHRP, 1992). The new edition of ASCE Standard 7
on structural loads expected to be released in 1993 has adopted the new seismic
design recommendations, as has the AISC Seismic Provisions for Structural
Steel Buildings (AISC, 1992). The load factors on E in Load Combinations A4-5
and A4-6 have been reduced from 1.5 to 1.0 to be consistent with the specification of earthquake force in these new documents. The reader is referred to the
commentaries to these documents for an expanded discussion on seismic loads,
load factors, and seismic design of steel buildings.
2.
Impact
A mass of the total moving load (wheel load) is used as the basis for impact
loads on crane runway girders, because maximum impact load results when
cranes travel while supporting lifted loads.
The increase in load, in recognition of random impacts, is not required to be
applied to supporting columns because the impact load effects (increase in
eccentricities or increases in out-of-straightness) will not develop or will be
negligible during the short duration of impact. For additional information on
crane girder design criteria see AISE Technical Report No. 13.
A5. DESIGN BASIS
1.
Required Strength at Factored Loads
LRFD permits the use of both elastic and plastic structural analyses. LRFD
provisions result in essentially the same methodology for, and end product of,
plastic design as included in the AISC ASD Specification (AISC, 1989), except
that the LRFD provisions tend to be more liberal, reflecting added experience
and the results of further research. The 10 percent redistribution permitted is
consistent with that in the AISC ASD Specification (AISC, 1989).
2.
Limit States
A limit state is a condition which represents the limit of structural usefulness.
Limit states may be dictated by functional requirements, such as maximum
deflections or drift; they may be conceptual, such as plastic hinge or mechanism
formation; or they may represent the actual collapse of the whole or part of the
structure, such as fracture or instability. Design criteria ensure that a limit state
is violated only with an acceptably small probability by selecting the load and
resistance factors and nominal load and resistance values which will never be
exceeded under the design assumptions.
Two kinds of limit states apply for structures: limit states of strength which
define safety against the extreme loads during the intended life of the structure,
and limit states of serviceability which define the functional requirements. The
LRFD Specification, like other structural codes, focuses on the limit states of
strength because of overriding considerations of public safety for the life, limb,
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GENERAL PROVISIONS
[Comm. A
and property of human beings. This does not mean that limit states of serviceability are not important to the designer, who must equally ensure functional
performance and economy of design. However, these latter considerations
permit more exercise of judgment on the part of designers. Minimum considerations of public safety, on the other hand, are not matters of individual
judgment and, therefore, specifications dwell more on the limit states of strength
than on the limit states of serviceability.
Limit states of strength vary from member to member, and several limit states
may apply to a given member. The following limit states of strength are the most
common: onset of yielding, formation of a plastic hinge, formation of a plastic
mechanism, overall frame or member instability, lateral-torsional buckling,
local buckling, tensile fracture, development of fatigue cracks, deflection instability, alternating plasticity, and excessive deformation.
The most common serviceability limit states include unacceptable elastic deflections and drift, unacceptable vibrations, and permanent deformations.
3.
Design for Strength
The general format of the LRFD Specification is given by the formula:
ΣγiQi ≤ φRn
(C-A5-1)
where
= summation
Σ
i
= type of load, i.e., dead load, live load, wind, etc.
Qi = nominal load effect
= load factor corresponding to Qi
γi
ΣγiQi = required resistance
Rn = nominal resistance
= resistance factor corresponding to Rn
φ
φRn = design strength
The left side of Equation C-A5-1 represents the required resistance computed
by structural analysis based upon assumed loads, and the right side of Equation
C-A5-1 represents a limiting structural capacity provided by the selected members. In LRFD, the designer compares the effect of factored loads to the strength
actually provided. The term design strength refers to the resistance or strength
φRn that must be provided by the selected member. The load factors γ and the
resistance factors φ reflect the fact that loads, load effects (the computed forces
and moments in the structural elements), and the resistances can be determined
only to imperfect degrees of accuracy. The resistance factor φ is equal to or less
than 1.0 because there is always a chance for the actual resistance to be less than
the nominal value Rn computed by the equations given in Chapters D through
K. Similarly, the load factors γ reflect the fact that the actual load effects may
deviate from the nominal values of Qi computed from the specified nominal
loads. These factors account for unavoidable inaccuracies in the theory, variations in the material properties and dimensions, and uncertainties in the
determination of loads. They provide a margin of reliability to account for
unexpected loads. They do not account for gross error or negligence.
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The LRFD Specification is based on (1) probabilistic models of loads and
resistance, (2) a calibration of the LRFD criteria to the 1978 edition of the AISC
ASD Specification for selected members, and (3) the evaluation of the resulting
criteria by judgment and past experience aided by comparative design office
studies of representative structures.
The following is a brief probabilistic basis for LRFD (Ravindra and Galambos,
1978, and Ellingwood et al., 1982). The load effects Q and the resistance factor
R are assumed to be statistically independent random variables. In Figure
C-A5.1, frequency distributions for Q and R are portrayed as separate curves on
a common plot for a hypothetical case. As long as the resistance R is greater than
(to the right of) the effects of the loads Q, a margin of safety for the particular
limit state exists. However, because Q and R are random variables, there is some
small probability that R may be less than Q, (R < Q). This limit state probability
is related to the degree of overlap of the frequency distributions in Figure
C-A5.1, which depends on their relative positioning (Rm vs. Qm) and their
dispersions.
An equivalent situation may be represented as in Figure C-A5.2. If the expression R < Q is divided by Q and the result expressed logarithmically, the result
will be a single frequency distribution curve combining the uncertainties of both
R and Q. The probability of attaining a limit state (R < Q) is equal to the
probability that ln(R / Q) < 0 and is represented by the shaded area in the
diagram.
The shaded area may be reduced and thus reliability increased in either of two
ways: (1) by moving the mean of ln(R / Q) to the right, or (2) by reducing the
spread of the curve for a given position of the mean relative to the origin. A
convenient way of combining these two approaches is by defining the position
of the mean using the standard deviation of ln(R / Q), as the unit of measure.
Thus, the distance from the origin to the mean is measured as the number of
standard deviations of the function ln(R / Q). As shown in Figure C-A5.2, this
FREQUENCY
R
Q
Qm
}
0
OVERLAP
Rm
RESISTANCE R
LOAD EFFECT Q
Fig. C-A5.1. Frequency distribution of load effect Q and resistance R.
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GENERAL PROVISIONS
[Comm. A
is stated as β times σln(R / Q), the standard deviation of ln(R / Q). The factor β
therefore is called the “reliability index.”
If the actual shape of the distribution of ln(R / Q) were known, and if an
acceptable value of the probability of reaching the limit state could be agreed
upon, one could establish a completely probability-based set of design criteria.
Unfortunately, this much information frequently is not known. The distribution
shape of each of the many variables (material, loads, etc.) has an influence on
the shape of the distribution of ln(R / Q). Often only the means and the standard
deviations of the many variables involved in the makeup of the resistance and
the load effect can be estimated. However, this information is enough to build
an approximate design criterion which is independent of the knowledge of the
distribution, by stipulating the following design condition:
βσln(R / Q) ≈ β√
VR2+ VQ2 ≤ ln(Rm / Qm)
(C-A5-2)
In this formula, the standard deviation has been replaced by the approximation
√
VR2+VQ2, where VR = σR / Rm and VQ = σQ / Qm (σR and σQ are the standard
deviations, Rm and Qm are the mean values, VR and VQ are the coefficients of
variation, respectively, of the resistance R and the load effect Q). For structural
elements and the usual loadings Rm, Qm, and the coefficients of variation, VR and
VQ, can be estimated, so a calculation of
β=
ln(Rm / Qm)
√
VR2+VQ2
(C-A5-3)
will give a comparative value of the measure of reliability of a structure or
component.
The description of the determination of β as given above is a simple way of
defining the probabilistic method used in the development of LRFD. A more
refined method, which can accommodate more complex design situations (such
as the beam-column interaction equation) and include probabilistic distributions
other than the lognormal distribution used to derive Equation C-A5-3, has been
developed since the publication of Ravindra and Galambos (1978), and is fully
described in Galambos, et al. (1982). This latter method has been used in the
development of the recommended load factors (see Section A4). The two
methods give essentially the same β values for most steel structural members
and connections.
PF
0
βσIn(R
/Q)
[In(R/Q)]m
In( R/Q)
Fig. C-A5.2. Definition of reliability index.
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Statistical properties (mean values and coefficients of variations) are presented
for the basic material properties and for steel beams, columns, composite beams,
plate girders, beam-columns, and connection elements in a series of eight
articles in the September 1978 issue of the Journal of the Structural Division of
ASCE (Vol. 104, ST9). The corresponding load statistics are given in Galambos,
et al. (1982). Based on these statistics, the values of β inherent in the 1978 edition
of the AISC ASD Specification were evaluated under different load combinations (live/dead, wind/dead, etc.), and for various tributary areas for typical
members (beams, columns, beam-columns, structural components, etc.). As
might be expected, there was a considerable variation in the range of β values.
Examination of the many β values associated with ASD revealed certain trends.
For example, compact rolled beams (flexure) and tension members (yielding)
had β values that decreased from about 3.1 at L / D = 0.50 to 2.4 at L / D = 4.
This decrease is a result of ASD applying the same factor to dead load, which
is relatively predictable, and live load, which is more variable. For bolted or
welded connections, β was on the order of 4 to 5. Reliability indices for load
combinations involving wind and earthquake loads tended to be lower. Based
on a thorough assessment of implied reliabilities in existing acceptable design
practice, common load factors for various structural materials (steel, reinforced
concrete, etc.) were developed in Ellingwood et al. (1982).
One of the features of the probability-based method used in the development of
LRFD is that the variations of β values can be reduced by specifying several
“target” β values and selecting multiple load and resistance factors to meet these
targets. The Committee on Specifications set the point at which LRFD is
calibrated to ASD at L / D = 3.0 for braced compact beams in flexure and tension
members at yield. The resistance factor, φ, for these limit states is 0.90, and the
implied β is approximately 2.6 for members and 4.0 for connections; this larger
β value for connections reflects the fact that connections are expected to be
stronger than the members that they connect. Limit states for other members are
handled consistently.
Computer methods as well as charts are given in Ellingwood et al. (1982) for
the use of specification writers to determine the resistance factors φ. These
factors can also be approximately determined by the following:
φ = (Rm / Rn) exp (−0.55βVr )
(C-A5-4)*
where
Rm = mean resistance
Rn = nominal resistance according to the equations in Chapters D through K
Vr = coefficient of variation of the resistance
4.
Design for Serviceability and Other Considerations
Nominally, serviceability should be checked at the unfactored loads. For combinations of gravity and wind or seismic loads some additional reduction factor
may be warranted.
* Note that exp (x) is identical to the more familiar ex..
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CHAPTER B
DESIGN REQUIREMENTS
B2. NET AREA
Critical net area is based on net width and load transfer at a particular chain.
B3. EFFECTIVE NET AREA FOR TENSION MEMBERS
Section B3 deals with the effect of shear lag, which is applicable to both welded
and bolted tension members. The reduction coefficient U is applied to the net
area An of bolted members and to the gross area Ag of welded members. As the
length of connection l is increased, the shear lag effect is diminished. This
concept is expressed empirically by Equation B3-3. Munse and Chesson (1963)
have shown, using this expression to compute an effective net area, with few
exceptions, the estimated strength of some 1,000 bolted and riveted connection
test specimens correlated with observed test results within a scatterband of ±10
percent. Newer research (Easterling and Gonzales, 1993) provides further
justification for current provisions.
_
For any given profile and connected elements, x is a fixed geometric property.
It is illustrated as the distance from the connection plane, or face of the member,
to the centroid of the member section resisting the connection force. See Figure
C-B3.1. Length l is dependent upon the number of fasteners or equivalent length
of weld required to develop the given tensile force, and this in turn is dependent
upon the mechanical properties of the member and the capacity of the fasteners
or weld used. The length l is illustrated as the distance, parallel to the line of
force, between the first and last fasteners in a line for bolted connections. The
number of bolts in a line, for the purpose of the determination of l, is determined
by the line with the maximum number of bolts in the connection. For staggered
bolts, the out-to-out dimension is used for l. See Figure C-B3.2. There is
insufficient data to establish a value of U if all lines have only one bolt, but it is
probably conservative to use Ae equal to the net area of the connected element.
For welded connections, l is the length of the member parallel to the line of force
that is welded. For combinations of longitudinal and transverse welds (see
Figure C-B3.3), l is the length of longitudinal weld because the transverse weld
has little or no effect on the shear lag problem, i.e., it does little to get the load
into the unattached portions of the member.
Previous issues of this Specification have presented values for U for bolted or
riveted connections of W, M, and S shapes, tees cut from these shapes, and other
shapes. These values are acceptable for use in lieu of calculated values from
Equation B3-3 and are retained here for the convenience of designers.
For bolted or riveted connections the following values of U may be used:
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6 - 173
(a) W, M, or S shapes with flange widths not less than two-thirds the depth, and
structural tees cut from these shapes, provided the connection is to the
flanges and has no fewer than three fasteners per line in the direction of stress,
U = 0.90
(b) W, M, or S shapes not meeting the conditions of subparagraph a, structural
tees cut from these shapes, and all other shapes including built-up cross
T
x
Treat as a
WT
(a)
T
x
x
Treat as an
angle
Use maximum x
(b)
Treat half the flange
and portion of web
as an angle
T
x
Use maximum x
(c)
_
Fig. C-B3.1. Determination of x for U.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
x
6 - 174
DESIGN REQUIREMENTS
[Comm. B
sections, provided the connection has no fewer than three fasteners per line
in the direction of stress, U = 0.85
(c) All members having only two fasteners per line in the direction of stress,
U = 0.75
When a tension load is transmitted by fillet welds to some but not all elements
of a cross section, the weld strength will control.
B5. LOCAL BUCKLING
For the purposes of this Specification, steel sections are divided into compact
sections, noncompact sections, and sections with slender compression elements.
Compact sections are capable of developing a fully plastic stress distribution
and they possess a rotational capacity of approximately 3 before the onset of
local buckling (Yura et al., 1978). Noncompact sections can develop the yield
stress in compression elements before local buckling occurs, but will not resist
inelastic local buckling at the strain levels required for a fully plastic stress
distribution. Slender compression elements buckle elastically before the yield
stress is achieved.
T
Use out-to-out
distance
for l
Use maximum x
x
l
x
Fig. C-B3.2. Staggered holes.
T
l
l
Fig. C-B3.3. Longitudinal and transverse welds.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
Sect. C-B5]
LOCAL BUCKLING
6 - 175
TABLE C-B5.1
Limiting Width-Thickness Ratios for Compression Elements
Limiting Width-thickness Ratios λp
WidthThickness
Ratio
Non-seismic
Seismic
Flanges of I-shaped
sections (including
hybrid sections) and
channels in flexure [a]
b/t
65 / √
Fy
52 / √
Fy
Webs in combined
flexural and axial
compression
h / tw
Description of Element
For Pu / φb Py ≤ 0.125
2.75Pu
640
1−
Fy
√
φbPy
1.54Pu
520
1−
Fy
√
φbPy
For Pu / φb Py > 0.125
Pu 253
191
2.33 −
≥
Fy
√
φbPy √Fy
[a] For hybrid beams use Fyf in place of Fy.
The dividing line between compact and noncompact sections is the limiting
width-thickness ratio λp. For a section to be compact, all of its compression
elements must have width-thickness ratios smaller than the limiting λp.
A greater inelastic rotation capacity than provided by the limiting values λp given
in Table C-B5.1 may be required for some structures in areas of high seismicity.
It has been suggested that in order to develop a ductility of from 3 to 5 in a
structural member, ductility factors for elements would have to lie in the range
of 5 to 15. Thus, in this case it is prudent to provide for an inelastic rotation of
7 to 9 times the elastic rotation (Chopra and Newmark, 1980). In order to provide
for this rotation capacity, the limits λp for local flange and web buckling would
be as shown in Table C-B5.1 (Galambos, 1976).
More information on seismic design is contained in the AISC Seismic Provisions
for Structural Steel Buildings.
Another limiting width-thickness ratio is λr, representing the distinction between noncompact sections and sections with slender compression elements. As
long as the width-thickness ratio of a compression element does not exceed the
limiting value λr, local elastic buckling will not govern its strength. However,
for those cases where the width-thickness ratios exceed λr, elastic buckling
strength must be considered. A design procedure for such slender-element
compression sections, based on elastic buckling of plates, is given in Appendix B5.3. The effective width Equation A-B5-12 applies strictly to stiffened
elements under uniform compression. It does not apply to cases where the
compression element is under stress gradient. A method of dealing with the stress
gradient in a compression element is provided in Section B2 of the AISI Design
Specifications for Cold-Formed Steel Structural Members, 1986 and Addendum, 1989. An exception is plate girders with slender webs. Such plate girders
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
6 - 176
DESIGN REQUIREMENTS
[Comm. B
are capable of developing postbuckling strength in excess of the elastic buckling
load. A design procedure for plate girders including tension field action is given
in Appendix G.
The values of the limiting ratios λp and λr specified in Table B5.1 are similar to
those in AISC (1989) and Table 2.3.3.3 of Galambos (1976), except that:
Fy , limited in Galambos (1976) to indeterminate beams when
(1) λp = 65 / √
moments are determined by elastic analysis and to determinate beams, was
adopted for all conditions on the basis of Yura et al. (1978); and (2)
λp = 1,300 / Fy for circular hollow sections was obtained from Sherman (1976).
The high shape factor for circular hollow sections makes it impractical to use
the same slenderness limits to define the regions of behavior for different types
of loading. In Table B5.1, the values of λp for a compact shape that can achieve
the plastic moment, and λr for bending, are based on an analysis of test data from
several projects involving the bending of pipes in a region of constant moment
(Sherman and Tanavde, 1984 and Galambos, 1988). The same analysis produced
the equation for the inelastic moment capacity in Table A-F1.1 in Appendix F1.
However, a more restrictive value of λp is required to prevent inelastic local
buckling from limiting the plastic hinge rotation capacity needed to develop a
mechanism in a circular hollow beam section (Sherman, 1976).
The values of λr for axial compression and for bending are both based on test
data. The former value has been used in building specifications since 1968
(Winter, 1970). Appendices B5 and F1 also limit the diameter-to-thickness ratio
for any circular section to 13,000 / Fy. Beyond this, the local buckling strength
decreases rapidly, making it impractical to use these sections in building
construction.
Following the SSRC recommendations (Galambos, 1988) and the approach
used for other shapes with slender compression elements, a Q factor is used for
circular sections to account for interaction between local and column buckling.
The Q factor is the ratio between the local buckling stress and the yield stress.
The local buckling stress for the circular section is taken from the inelastic AISI
criteria (Winter, 1970) and is based on tests conducted on fabricated and
manufactured cylinders. Subsequent tests on fabricated cylinders (Galambos,
1988) confirm that this equation is conservative.
The definitions of the width and thickness of compression elements agree with
the 1978 AISC ASD Specification with minor modifications. Their applicability
extends to sections formed by bending and to unsymmetrical and hybrid
sections.
For built-up I-shaped sections under axial compression, modifications have
been made to the flange local buckling criterion to include web-flange interaction. The kc in the λr limit, in Equations A-B5-7 and A-B5-8 and the elastic
buckling Equation A-B5-8 are the same that are used for flexural members.
Theory indicates that the web-flange interaction in axial compression is at least
as severe as in flexure. Rolled shapes are excluded from this criteria because
there are no standard sections with proportions where the interaction would
occur. In built-up sections where the interaction causes a reduction in the flange
local buckling strength, it is likely that the web is also a thin stiffened element.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
Sect. C-B7]
LIMITING SLENDERNESS RATIOS
6 - 177
The kc factor accounts for the interaction of flange and web local buckling
demonstrated in experiments conducted by Johnson (1985). The maximum limit
of 0.763 corresponds to Fcr = 20,000 / λ2 which was used as the local buckling
strength in earlier editions of both the ASD and LRFD Specifications. An
h / tw = 27.5 is required to reach kc = 0.763. Fully fixed restraint for an unstiffened compression element corresponds to kc = 1.3 while zero restraint gives
kc = 0.42. Because of web-flange interactions it is possible to get kc < 0.42 from
Fy use h / tw = 970 / √
Fy in the kc equation,
the new kc formula. If h / tw > 970 / √
which corresponds to the 0.35 limit.
Illustrations of some of the requirements of Table B5.1 are shown in Figure
C-B5.1.
B7. LIMITING SLENDERNESS RATIOS
Chapters D and E provide reliable criteria for resistance of axially loaded
members based on theory and confirmed by test for all significant parameters
including slenderness. The advisory upper limits on slenderness contained in
Section B7 are based on professional judgment and practical considerations of
economics, ease of handling, and care required to minimize inadvertent damage
during fabrication, transport, and erection. Out-of-straightness within reasonable tolerances does not affect the strength of tension members, and the effect
of out-of-straightness within specified tolerances on the strength of compression
members is accounted for in formulas for resistance. Applied tension tends to
reduce, whereas compression tends to amplify, out-of-straightness. Therefore,
more liberal criteria are suggested for tension members, including those subject
to small compressive forces resulting from transient loads such as earthquake
and wind. For members with slenderness ratios greater than 200, these compressive forces correspond to stresses less than 2.6 ksi.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
6 - 178
DESIGN REQUIREMENTS
b
[Comm. B
AXIAL
COMPRESSION
BENDING
65
141
,
λr =
640
,
Fy
√
λr =
970
Fy
√
(perforated λr =
190
λp =
, λr =
Fy
√
317
√Fy
λp =
Fy
√
√
Fy − 10
λr =
95
Fy
√
t
tw
h
b
b
t
t
t
hc
λp =
65
λp =
,
Fy
√
λr =
b
h
λr =
λr =
253
Fy
√
317
)
Fy
√
238
λr =
Fy
√
λr =
238
Fy
√
162
√
(Fyw − 16.5) / kc
95
Fy
√
hc
109
λr =
√
Fy / kc
λr =
109
√
Fy / kc
λp =
640
,
Fy
√
λr =
970
Fy
√
λr =
253
Fy
√
λp =
190
,
Fy
√
λr =
238
Fy
√
λr =
238
Fy
√
λp =
640
,
Fy
√
λr =
970
Fu
√
λr =
238
Fy
√
λr =
253
Fy
√
λr =
253
Fy
√
λr =
970
Fy
√
λr =
253
Fy
√
b
h
b
b
h
b
Fig. C-B5.1. Selected examples of Table B5.1 requirements.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
6 - 179
CHAPTER C
FRAMES AND OTHER STRUCTURES
C1. SECOND ORDER EFFECTS
While resistance to wind and seismic loading can be provided in certain
buildings by means of shear walls, which also provide for overall frame stability
at factored gravity loading, other building frames must provide this resistance
by frame action. This resistance can be achieved in several ways, e.g., by a
system of bracing, by a moment-resisting frame, or by any combination of lateral
force-resisting elements.
For frames under combined gravity and lateral loads, drift (horizontal deflection
caused by applied loads) occurs at the start of loading. At a given value of the
applied loads, the frame has a definite amount of drift ∆. In unbraced frames,
additional secondary bending moments, known as the P∆ moments, may be
developed in the columns and beams of the lateral load-resisting systems in each
story. P is the total gravity load above the story and ∆ is the story drift. As the
applied load increases, the P∆ moments also increase. Therefore, the P∆ effect
must often be accounted for in frame design. Similarly, in braced frames,
increases in axial forces occur in the members of the bracing systems; however,
such effects are usually less significant. The designer should consider these
effects for all types of frames and determine if they are significant. Since P∆
effects can cause frame drifts to be larger than those calculated by ignoring them,
they should also be included in the service load drift analysis when they are
significant.
In unbraced frames designed by plastic analysis, the limit of 0.75φcPy on column
axial loads has also been retained to help ensure stability.
The designer may use second-order elastic analysis to compute the maximum
factored forces and moments in a member. These represent the required strength.
Alternatively, for structures designed on the basis of elastic analysis, the designer may use first order analysis and the amplification factors B1 and B2.
In the general case, a member may have first order moments not associated with
sidesway which are multiplied by B1, and first order moments produced by
forces causing sidesway which are multiplied by B2.
The factor B2 applies only to moments caused by forces producing sidesway and
is calculated for an entire story. In building frames designed to limit ∆oh / L to a
predetermined value, the factor B2 may be found in advance of designing
individual members.
Drift limits may also be set for design of various categories of buildings so that
the effect of secondary bending can be insignificant (Kanchanalai and Lu, 1979;
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
6 - 180
FRAMES AND OTHER STRUCTURES
[Comm. C
ATC, 1978). It is conservative to use the B2 factor with the sum of the sway and
the no-sway moments, i.e., with Mlt + Mnt.
The two kinds of first order moment Mnt and Mlt may both occur in sidesway
frames from gravity loads. Mnt is defined as a moment developed in a member
with frame sidesway prevented. If a significant restraining force is necessary to
prevent sidesway of an unsymmetrical structure (or an unsymmetrically loaded
symmetrical structure), the moments induced by releasing the restraining force
will be Mlt moments, to be multiplied by B2. In most reasonably symmetric
frames, this effect will be small. If such a moment B2Mlt is added algebraically
to the B1Mnt moment developed with sidesway prevented, a fairly accurate value
of Mu will result. End moments produced in sidesway frames by lateral loads
from wind or earthquake will always be Mlt moments to be multiplied by B2.
When first order end moments in members subjected to axial compression are
magnified by B1 and B2 factors, equilibrium requires that they be balanced by
moments in connected members (Figure C-C1.1). This can generally be accomplished satisfactorily by distributing the difference between the magnified
moment and the first order moment to any other moment-resisting members
attached to the compressed member (or members) in proportion to the relative
stiffness of the uncompressed members. Minor imbalances may be neglected in
the judgment of the engineer. However, complex conditions, such as occur when
there is significant magnification in several members meeting at a joint, may
require a second order elastic analysis. Connections shall also be designed to
resist the magnified end moments.
For compression members in braced frames, B1 is determined from Cm values
which are similar to the values in the AISC ASD Specification. A significant
First order moment
P
w
Total moment
P
H
B1 Mo
Mo l
H
B2 u Mou
B1 Mo
Mo
(a)
Σ B2 Mo
(b)
Fig. C-C1.1. Moment amplification.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
B2 l Mo l
Sect. C-C1]
SECOND ORDER EFFECTS
6 - 181
difference, however, is that B1 is never less than 1. When Cm = 1 for a compression member loaded between its supports, the factors of 8⁄9 and 1⁄2 make the new
equations more liberal than Equation H1-1 of the AISC ASD Specification. For
Cm ≤ 1 (for members with unequal end moments), the new equations will be
slightly more conservative than the AISC ASD Specification for a very slender
member with low Cm. For the entire range of l / r and Cm, the equations compare
very closely to exact inelastic solutions of braced members.
The center-to-center member length is usually used in the structural analysis. In
braced and unbraced frames, Pn is governed by the maximum slenderness ratio
regardless of the plane of bending. However, Pe1 and Pe2 are always calculated
using the slenderness ratio in the plane of bending. Thus, when flexure is about
the strong axis only, two different values of slenderness ratio may be involved
in solving a given problem.
When second order analysis is used, it must account for the interaction of the
factored load effects, that is, combinations of factored loads must be used in
analysis. Superposition of forces obtained from separate analyses is not
adequate.
When bending occurs about both the x and the y axes, the required flexural
strength calculated about each axis is adjusted by the value of Cm and Pe1 or Pe2
corresponding to the distribution of moment and the slenderness ratio in its plane
of bending, and is then taken as a fraction of the design bending strength,
φbMn, about that axis, with due regard to the unbraced length of the compression
flange where this is a factor.
Equations C1-2 and C1-3 approximate the maximum second order moments in
compression members with no relative joint translation and no transverse loads
between the ends of the member. This approximation is compared to an exact
solution (Ketter, 1961) in Figure C-C1.2. For single curvature, Equation C1-3
is slightly unconservative, for a zero end moment it is almost exact, and for
double curvature it is conservative. The 1978 AISC ASD Specification imposed
the limit Cm ≥ 0.4 which corresponds to a M1 / M2 ratio of 0.5. However, Figure
C-C1.2 shows that if, for example, M1 / M2 = 0.8, the Cm = 0.28 is already very
conservative, so the limit has been removed. The limit was originally adopted
from Austin (1961), which was intended to apply to lateral-torsional buckling,
not second-order in-plane bending strength. The AISC Specifications, both in
the 1989 ASD and LRFD, use a modification factor Cb as given in Equation F1-3
for lateral-torsional buckling. Cb is approximately the inverse of Cm as presented
in Austin (1961) with a 0.4 limit. In Zandonini (1985) it was pointed out that
Equation C1-3 could be used for in-plane second order moments if the 0.4 limit
was eliminated. Unfortunately, Austin (1961) was misinterpreted and a lateraltorsional buckling solution was used for an in-plane second-order analysis. This
oversight has now been corrected.
For beam columns with transverse loadings, the second-order moment can be
approximated by using the following equation
Cm = 1 + ψPu / Pe1
For simply supported members
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
6 - 182
FRAMES AND OTHER STRUCTURES
[Comm. C
where
ψ =
π2δ0EI
−1
M0L2
δ0 = maximum deflection due to transverse loading, in.
M0 = maximum factored design moment between supports due to transverse
loading, kip-in.
For restrained ends some limiting cases (Iwankiw, 1984) are given in Table
C-C1.1 together with two cases of simply supported beam-columns. These
values of Cm are always used with the maximum moment in the member. For
the restrained-end cases, the values of B1 will be most accurate if values of
K < 1.0 corresponding to the end boundary conditions are used in calculating
Pe1. In lieu of using the equations above, Cm = 1.0 can be used conservatively for
transversely loaded members with unrestrained ends and 0.85 for restrained
ends.
Pu
Pe
1.0
0.8
} 0.5
} 0
.80
M1
M2
–0.5
–0.8
.63
.60
Pu M1
.44
.40
M2
Mmax
M1
.25
M2
Classical solution
.20
0.6 – 0.4( M1/ M2 )
.11
1–
Pu
Pe1
0
1.0
2.0
3.0
4.0
5.0
Mmax
M2
Fig. C-C1.2. Second-order moments for braced beam-column.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
Pu
Sect. C-C2]
FRAME STABILITY
6 - 183
TABLE C-C1.1
Amplification Factors ψ and Cm
Case
Pu
ψ
Cm
0
1.0
−0.4
1 − 0.4
Pu
Pe1
−0.4
1 − 0.4
Pu
Pe1
−0.2
1 − 0.2
Pu
Pe1
−0.3
1 − 0.3
Pu
Pe1
−0.2
1 − 0.2
Pu
Pe1
L
/2
If, as in the case of a derrick boom, a beam-column is subject to transverse
(gravity) load and a calculable amount of end moment, the value δ0 should
include the deflection between supports produced by this moment.
Stiffness reduction adjustment due to column inelasticity is permitted.
C2. FRAME STABILITY
The stability of structures must be considered from the standpoint of the
structure as a whole, including not only the compression members, but also the
beams, bracing system, and connections. The stability of individual elements
must also be provided. Considerable attention has been given in the technical
literature to this subject, and various methods of analysis are available to assure
stability. The SSRC Guide to Stability Design Criteria for Metal Structures
(Galambos, 1988) devotes several chapters to the stability of different types of
members considered as individual elements, and then considers the effects of
individual elements on the stability of the structure as a whole.
The effective length concept is one method of estimating the interaction effects
of the total frame on a compression element being considered. This concept uses
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
6 - 184
FRAMES AND OTHER STRUCTURES
[Comm. C
TABLE C-C2.1
K Values for Columns
(a)
(b)
(c)
Theoretical K value
0.5
0.7
1.0
Recommended design
value when ideal conditions
are approximated
0.65
0.80
1.2
(e)
(f)
1.0
2.0
2.0
1.0
2.10
2.0
(d)
Buckled shape of column is
shown by dashed line.
Rotation fixed and translation fixed
End condition code
Rotation free and translation fixed
Rotation fixed and translation free
Rotation free and translation free
K factors to equate the strength of a framed compression element of length L to
an equivalent pin-ended member of length KL subject to axial load only. Other
rational methods are available for evaluating the stability of frames subject to
gravity and side loading and individual compression members subject to axial
load and moments. However, the effective-length concept is the only tool
currently available for handling several cases which occur in practically all
structures, and it is an essential part of many analysis procedures. Although the
concept is completely valid for ideal structures, its practical implementation
involves several assumptions of idealized conditions which will be mentioned
later.
Two conditions, opposite in their effect upon column strength under axial
loading, must be considered. If enough axial load is applied to the columns in
an unbraced frame dependent entirely on its own bending stiffness for resistance
to lateral deflection of the tops of the columns with respect to their bases (see
Figure C-C2.1), the effective length of these columns will exceed the actual
length. On the other hand, if the same frame were braced to resist such lateral
movement, the effective length would be less than the actual length, due to the
restraint (resistance to joint translation) provided by the bracing or other lateral
support. The ratio K, effective column length to actual unbraced length, may be
greater or less than 1.0.
The theoretical K values for six idealized conditions in which joint rotation and
translation are either fully realized or nonexistent are tabulated in Table C-C2.1.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
Sect. C-C2]
FRAME STABILITY
6 - 185
Also shown are suggested design values recommended by the Structural Stability Research Council (formerly the Column Research Council) for use when
these conditions are approximated in actual design. In general, these suggested
values are slightly higher than their theoretical equivalents, since joint fixity is
seldom fully realized.
If the column base in Case f of Table C-C2.1 were truly pinned, K would actually
exceed 2.0 for a frame such as that pictured in Figure C-C2.1, because the
flexibility of the horizontal member would prevent realization of full fixity at
the top of the column. On the other hand, it has been shown (Galambos, 1960)
that the restraining influence of foundations, even where these footings are
designed only for vertical load, can be very substantial in the case of flat-ended
column base details with ordinary anchorage. For this condition, a design K
value of 1.5 would generally be conservative in Case f.
While in some cases masonry walls provide enough lateral support for building
frames to control lateral deflection, light curtain wall construction and wide
column spacing can create a situation where only the bending stiffness of the
frame provides this support. In this case the effective length factor K for an
unbraced length of column L is dependent upon the bending stiffness provided
by the other in-plane members entering the joint at each end of the unbraced
segment. If the combined stiffness provided by the beams is sufficiently small,
relative to that of the unbraced column segments, KL could exceed two or more
story heights (Bleich, 1952).
Several rational methods are available to estimate the effective length of the
columns in an unbraced frame with sufficient accuracy. These range from simple
interpolation between the idealized cases shown in Table C-C2.1 to very
complex analytical procedures. Once a trial selection of framing members has
been made, the use of the alignment chart in Figure C-C2.2 affords a fairly rapid
P
P
Kl
l
Fig. C-C2.1. Column effective length.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
6 - 186
FRAMES AND OTHER STRUCTURES
[Comm. C
method for determining adequate K values. However, it should be noted that this
alignment chart is based upon assumptions of idealized conditions which seldom
exist in real structures (Galambos, 1988). These assumptions are as follows:
(1) Behavior is purely elastic.
(2) All members have constant cross section.
(3) All joints are rigid.
(4) For braced frames, rotations at opposite ends of beams are equal in magnitude, producing single-curvature bending.
GA
50.0
10.0
K
1.0
5.0
3.0
GA
GB
50.0
10.0
5.0
0.9
2.0
GB
20.0
10.0
100.0
50.0
30.0
5.0
100.0
50.0
30.0
20.0
4.0
20.0
3.0
10.0
9.0
8.0
7.0
3.0
2.0
1.0
1.0
10.0
9.0
8.0
7.0
0.8
0.7
0.8
0.7
5.0
0.6
0.6
0.8
0.7
0.5
0.5
0.4
0.4
0.3
0.2
K
0.3
0.6
6.0
6.0
5.0
4.0
2.0
3.0
3.0
2.0
2.0
1.5
0.2
1.0
0.1
0
4.0
1.0
0.1
0.5
0
1.0
0
SIDESWAY INHIBITED
0
SIDESWAY UNINHIBITED
The subscripts A and B refer to the joints at the two ends of the column section being
considered. G is defined as
G=
Σ(Ic / Lc)
Σ(Ig / Lg)
in which Σ indicates a summation of all members rigidly connected to that joint and lying on
the plane in which buckling of the column is being considered. I c is the moment of inertia and
Lc the unsupported length of a column section, and I g is the moment of inertia and Lg the
unsupported length of a girder or other restraining member. I c and Ig are taken about axes
perpendicular to the plane of buckling being considered.
For column ends supported by but not rigidly connected to a footing or foundation, G is
theoretically infinity, but, unless actually designed as a true friction-free pin, may be taken as
“10” for practical designs. If the column end is rigidly attached to a properly designed footing,
G may be taken as 1.0. Smaller values may be used if justified by analysis.
Fig. C-C2.2. Alignment chart for effective length of columns in continuous frames.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
Sect. C-C2]
FRAME STABILITY
6 - 187
(5) For unbraced frames, rotations at opposite ends of the restraining beams are
equal in magnitude, producing reverse-curvature bending.
(6) The stiffness parameters L√
P / EI of all columns are equal.
(7) Joint restraint is distributed to the column above and below the joint in
proportion to I / L of the two columns.
(8) All columns buckle simultaneously.
(9) No significant axial compression force exists in the girders.
Where the actual conditions differ from these assumptions, unrealistic designs
may result. There are design procedures available which may be used in the
calculation of G for use in Figure C-C2.2 to give results that better reflect the
conditions in real structures (Yura, 1971; Disque, 1973; Bjorhovde, 1984;
Davison et al., 1988).
Leaning columns (sized for gravity loads only, based on an assumed K of 1.0)
may be used in unbraced frames provided that the destabilizing effects due to
their lack of lateral stiffness from simple connections to the frame (K = ∞) is
included in the design of the moment frame columns. A stabilizing column in
one direction may be a leaning column in the transverse direction if it is rigidly
connected in only one plane. LeMessurier (1977) presented an overall discussion of this problem and recommended a general solution for unbraced frames.
In lieu of this and more exact analyses, the following design approximations are
suggested.
When unbraced moment-resisting frames are the only source of lateral rigidity
for a given direction of a story, the upper bound of sidesway stiffness in that
direction, measured, in shear force per radian of drift, is ΣPL = ΣHL / ∆oh. This
force may be found from a first-order lateral load analysis, without gravity loads,
where ΣH is the total story shear. (The calculation of B2 using interstory drift as
in LRFD Equation C1-4 also uses the term ΣHL / ∆oh). Since most of the
moment-resisting columns in the frame will directly support axial loads, the
bending stiffness of the columns will be reduced, lowering the sidesway stiffness
ΣPL.
An estimate of the reduced sidesway stiffness of the frame may be found by
calculating Pe2 for each moment-resisting column, in the direction under consideration, by using the nomograph for sidesway K based on local boundary
conditions measured by GA and GB. G is normally assumed as:
Ic
Lc
G=
Ig
Σ
Lg
Σ
This definition of G is based on the assumption that girders restraining columns
have equal moments (same clockwise direction) at each end determined by an
analysis for lateral loads only. When this assumption is violated, a significant
overestimate of ΣPe2 may occur. Accurate G values may be found from an
examination of girder end moments from such an analysis. The correct Lg should
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
6 - 188
FRAMES AND OTHER STRUCTURES
[Comm. C
MF
be taken as Lg′ = Lg 2 −
where MF is the moment at the far end of the girder
M
N
MF
under consideration and MN is the moment at the near end. When
> 2, Lg′
MN
becomes negative which, although real, will result in negative values of G.
Negative values of G are beyond the scope of the nomograph but are valid for
use in Equation C-C2-2.
The reduced total stiffness of the whole story, when each rigidly connected
column is loaded with its maximum load Pe2, is ΣPe2. ΣPe2 calculated in this way
will always satisfy:
.82ΣPL < ΣPe2 < ΣPL
Many common framing arrangements include within a story loaded columns
designed, in a particular direction, with K = 1. Such columns, often called
leaning columns, receive lateral stability from the stiffness of columns with rigid
moment-resisting connections. The required axial compressive strength of such
leaning columns is called Puo where the subscript implies no shear resistance to
lateral loads. The ratio of the loads on all leaning columns in a story to the total
of all loads on the story is:
ΣPuo
= RL
ΣPu
The ratio of all story loads to the loads on columns providing sidesway is:
N=
ΣPu
1
=
1 − RL ΣPu − ΣPuo
If the story stiffness ΣPe2 is calculated from the nomograph K values, the net
stiffness available to stabilize the rigid column is:
ΣPe2 (1 − RL) =
ΣPe2
N
If there is no redistribution of ΣPe2 / N among the rigid columns, the modified
capacity of an individual column is, conservatively:
Pe2′ =
Pe2
N
It follows that a modified Ki′ including leaning effects is:
Ki′ = √
N × Ki
(C-C2-1)
A more exact value of K′ to account for loss of stiffness to leaning columns can
be found from an iterative solution of:
π
π
2
tan
π
2K′
′
K
i
= 0
− RL [GA + GB] − GAGB + 36 1 − RL
6
K′
π
π
tan
2K′
K
′
(C-C2-2)
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
Sect. C-C2]
FRAME STABILITY
6 - 189
When RL = 0, this equation reduces to the equation solved by the sidesway
uninhibited nomograph.
The 1993 LRFD Specification no longer limits K to unity in sidesway frames
and redistribution of stiffness between members of a frame may be advantageous. There are several ways of doing this. Based on the assumption that ΣPe2
is constant, regardless of loading distribution, an adjusted distribution of stiffness to the ith column of a story is:
2
π EIi
Pui
[ΣPe2 ] = 2
Pei′ =
ΣPu
Ki′ L
(C-C2-3a)
Pei′ < 1.6Pei
(C-C2-3b)
except
or in terms of K directly with E and L2 constant,
Ki′ =
√
(C-C2-4a)
√
(C-C2-4b)
ΣPu
×
Pui
Ii
Ii
Σ 2
Ki
except
Ki′ ≥
5
K
8 i
where
Ki′ = effective length factor with story stability effect for ith rigid column
Ii = moment of inertia in plane of bending for ith rigid column
Ki = effective length for ith rigid-column factor based on alignment chart
for unbraced frame
Pui = required axial compressive strength for ith rigid column
ΣPu = required axial compressive strength of all columns in a story
These expressions include consideration of leaning effects but, in addition,
allow concentration of lateral stiffness on relatively weak columns. To limit the
error involved with the assumption that ΣPe2 is constant and to avoid the
possibility of failure of a weak column in the sidesway prevented mode, the
modified Pei′ for a member should not exceed 1.6 times the Pei for the member
included in the sum ΣPe2.
An alternate formulation which is simple to use but may give lower design
values than the expressions above when leaning effects are minimal is:
2
π EI
Pui
[ΣPL ] [.85 + .15RL] = 2i
Pei′ =
ΣPu
Ki′ L
except
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
(C-C2-5a)
6 - 190
FRAMES AND OTHER STRUCTURES
Pei′ ≤ 1.7PLi
where PLi =
[Comm. C
(C-C2-5b)
HiL
and Hi is the shear in the ith column included in ΣH.
∆oh
The limits set by Equations C-C2-3b, C-C2-4b, and C-C2-5b have been chosen
to avoid unconservative error exceeding five percent in extreme cases.
Although Ki′ may be found, it is an unnecessary step since the key parameter
λ2c = AFy / Pe ′ is the only one required by Chapter E to find the design capacity
φcPn. Design values may be found directly from:
AFy
φcPn = φc .658 Pe′ AFy when Pe ′ >
φcPn = φc .877Pe ′ when Pe ′ ≤
4
AF
9 y
4
AF
9 y
(C-C2-6a)
(C-C2-6b)
Because frames that use partially restrained (PR) connections violate the condition that all joints are rigid, special attention should be paid to calculation of
the proper G value (Barakat and Chen, 1991).
If roof decks or floor slabs, anchored to shear walls or vertical plane bracing
systems, are counted upon to provide lateral support for individual columns in
a building frame, due consideration must be given to their stiffness when
functioning as horizontal diaphragms (Winter, 1958).
Translation of the joints in the plane of a truss is inhibited and, due to end
restraint, the effective length of compression members might be assumed to be
less than the distance between panel points. However, it is usual practice to take
K as equal to 1.0 (Galambos, 1988); if all members of the truss reached their
ultimate load capacity simultaneously, the restraints at the ends of the compression members would be greatly reduced.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
6 - 191
CHAPTER D
TENSION MEMBERS
D1. DESIGN TENSILE STRENGTH
Due to strain hardening, a ductile steel bar loaded in axial tension can resist, without
fracture, a force greater than the product of its gross area and its coupon yield stress.
However, excessive elongation of a tension member due to uncontrolled yielding
of its gross area not only marks the limit of its usefulness, but can precipitate failure
of the structural system of which it is a part. On the other hand, depending upon the
reduction of area and other mechanical properties of the steel, the member can fail
by fracture of the net area at a load smaller than required to yield the gross area.
Hence, general yielding of the gross area and fracture of the net area both constitute
failure limit states. The relative values of φt given for yielding and fracture reflect
the same basic difference in factor of safety as between design of members and
design of connections in the AISC ASD Specification.
The length of the member in the net area is negligible relative to the total length of the
member. As a result, the strain hardening condition is quickly reached and yielding of
the net area at fastener holes does not constitute a limit state of practical significance.
D2. BUILT-UP MEMBERS
The slenderness ratio L / r of tension members other than rods, tubes, or straps
should preferably not exceed the limiting value of 300. This slenderness limit
recommended for tension members is not essential to the structural integrity of
such members; it merely assures a degree of stiffness such that undesirable
lateral movement (“slapping” or vibration) will be unlikely.
See Section B7 and Commentary Section E4.
D3. PIN-CONNECTED MEMBERS AND EYEBARS
Forged eyebars have generally been replaced by pin-connected plates or eyebars
thermally cut from plates. Provisions for the proportioning of eyebars contained
in the LRFD Specification are based upon standards evolved from long experience with forged eyebars. Through extensive destructive testing, eyebars have
been found to provide balanced designs when they are thermally cut instead of
forged. The somewhat more conservative rules for pin-connected members of
nonuniform cross section and those not having enlarged “circular” heads are
likewise based on the results of experimental research (Johnston, 1939).
Somewhat stockier proportions are provided for eyebars and pin-connected
members fabricated from steel having a yield stress greater than 70 ksi, in order
to eliminate any possibility of their “dishing” under the higher design stress.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
6 - 192
CHAPTER E
COLUMNS AND OTHER COMPRESSION MEMBERS
E1. EFFECTIVE LENGTH AND SLENDERNESS LIMITATIONS
1.
Effective Length
The Commentary on Section C2 regarding frame stability and effective length
factors applies here. Further analytic methods, formulas, charts, and references
for the determination of effective length are provided in Chapter 15 of the SSRC
Guide (Galambos, 1988).
2.
Design by Plastic Analysis
The limitation on λc is essentially the same as that for l / r in Chapter N of the
1989 AISC Specification—Allowable Stress Design and Plastic Design.
E2. DESIGN COMPRESSIVE STRENGTH FOR
FLEXURAL BUCKLING BUCKLING*
FLEXURAL-TORSIONAL
Equations E2-2 and E2-3 are based on a reasonable conversion of research data
into design equations. Conversion of the allowable stress design (ASD) equations which was based on the CRC—Column Research Council—curve
(Galambos, 1988) was found to be cumbersome for two reasons. The first was
the nature of the ASD variable safety factor. Secondly, the difference in philosophical origins of the two design procedures requires an assumption of a live
load-to-dead load ratio (L / D).
Since all L / D ratios could not be considered, a value of approximately 1.1 at
λ equal to 1.0 was used to calibrate the exponential equation for columns with
the lower range of λ against the appropriate ASD provision. The coefficient with
the Euler equation was obtained by equating the ASD and LRFD expressions at
λ of 1.5.
Equations E2-2 and E2-3 are essentially the same curve as column-strength
curve 2P of the Structural Stability Research Council which is based on an initial
out-of-straightness curve of l / 1,500 (Bjorhovde, 1972 and 1988; Galambos,
1988; Tide, 1985).
It should be noted that this set of column equations has a range of reliability
(β) values. At low- and high-column slenderness, β values exceeding 3.0 and
3.3 respectively are obtained compared to β of 2.60 at L / D of 1.1. This is
considered satisfactory, since the limits of out-of-straightness combined with
residual stress have not been clearly established. Furthermore, there has been
* For tapered members see Commentary Appendix F3.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
Sect. C-E3]
FLEXURAL-TORSIONAL BUCKLING
6 - 193
no history of unacceptable behavior of columns designed using the ASD
procedure. This includes cases with L / D ratios greater than 1.1.
Equations E2-2 and E2-3 can be restated in terms of the more familiar slenderness ratio Kl / r. First, Equation E2-2 is expressed in exponential form,
Fcr = [exp( − 0.419λ2c )]Fy
(C-E2-1)
Note that exp(x) is identical to ex. Substitution of λc according to definition of
λc in Section E2 gives,
For
Kl
≤ 4.71
r
√
E
Fy
2
Fy Kl
Fcr = exp − 0.0424 Fy
E r
For
(C-E2-2)
F
√
Kl
> 4.71
r
E
y
Fcr =
0.877π2E
Kl
r
2
(C-E2-3)
E3. DESIGN COMPRESSIVE STRENGTH FOR
FLEXURAL-TORSIONAL BUCKLING
Torsional buckling of symmetric shapes and flexural-torsional buckling of
unsymmetric shapes are failure modes usually not considered in the design of
hot-rolled columns. They generally do not govern, or the critical load differs
very little from the weak axis planar buckling load. Such buckling loads may,
however, control the capacity of symmetric columns made from relatively thin
plate elements and unsymmetric columns. Design equations for determining the
strength of such columns are given in Appendix E3.
Tees that conform to the limits in Table C-E3.1 need not be checked for
flexural-torsional buckling.
A simpler and more accurate design strength for the special case of tees and
double-angles is based on Galambos (1991) wherein the y-axis of symmetry
flexural-buckling strength component is determined directly from the column
formulas.
The separate AISC Specification for Load and Resistance Factor Design of
Single-Angle Members contains detailed provisions not only for the limit state
of compression, but also for tension, shear, flexure, and combined forces.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
6 - 194
COLUMNS AND OTHER COMPRESSION MEMBERS
[Comm. E
TABLE C-E3.1
Limiting Proportions for Tees
Shape
Ratio of Full
Flange Width to
Profile Depth
Ratio of Flange
Thickness to Web
or Stem Thickness
Built-up tees
≥ 0.50
≥ 1.25
Rolled tees
≥ 0.50
≥ 1.10
E4. BUILT-UP MEMBERS
Requirements for detailing and design of built-up members, which cannot be
stated in terms of calculated stress, are based upon judgment and experience.
The longitudinal spacing of connectors connecting components of built-up
compression members must be such that the slenderness ratio l / r of individual
shapes does not exceed three-fourths of the slenderness ratio of the entire
member. Additional requirements are imposed for built-up members consisting
of angles. However, these minimum requirements do not necessarily ensure that
the effective slenderness ratio of the built-up member is equal to that for the
built-up member acting as a single unit. Section E4 gives formulas for modified
slenderness ratios that are based on research and take into account the effect of
shear deformation in the connectors (Zandonini, 1985). Equation E4-1 for
snug-tight intermediate connectors is emperically based on test results (Zandonini, 1985). The new Equation E4-2 is derived from theory and verified by test
data. In both cases the end connection must be welded or slip-critical bolted
(Aslani and Goel, 1991). The connectors must be designed to resist the shear
forces which develop in the buckled member. The shear stresses are highest
where the slope of the buckled shape is maximum (Bleich, 1952).
Maximum fastener spacing less than that required for strength may be needed
to ensure a close fit over the entire faying surface of components in continuous
contact. Specific requirements are given for weathering steel members exposed
to atmospheric corrosion (Brockenbrough, 1983).
The provisions governing the proportioning of perforated cover plates are based
upon extensive experimental research (Stang and Jaffe, 1948).
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
6 - 195
CHAPTER F
BEAMS AND OTHER FLEXURAL MEMBERS
F1.
DESIGN FOR FLEXURE
1.
Yielding
The bending strength of a laterally braced compact section is the plastic moment
Mp. If the shape has a large shape factor (ratio of plastic moment to the moment
corresponding to the onset of yielding at the extreme fiber), significant inelastic
deformation may occur at service load if the section is permitted to reach Mp at
factored load. The limit of 1.5My at factored load will control the amount of
inelastic deformation for sections with shape factors greater than 1.5. This
provision is not intended to limit the plastic moment of a hybrid section with a
web yield stress lower than the flange yield stress. Yielding in the web does not
result in significant inelastic deformations. In hybrid sections, My = FyfS.
Lateral-torsional buckling cannot occur if the moment of inertia about the
bending axis is equal to or less than the moment of inertia out of plane. Thus,
for shapes bent about the minor axis and shapes with Ix = Iy , such as square or
circular shapes, the limit state of lateral-torsional buckling is not applicable and
yielding controls if the section is compact.
2.
Lateral-Torsional Buckling
2a.
Doubly Symmetric Shapes and Channels with Lb ≤ Lr
The basic relationship between nominal moment Mn and unbraced length Lb is
shown in Figure C-F1.1 for a compact section with Cb = 1.0. There are four
principal zones defined on the basic curve by Lpd, Lp, and Lr. Equation F1-4
defines the maximum unbraced length Lp to reach Mp with uniform moment.
Elastic lateral-torsional buckling will occur when the unbraced length is greater
than Lr given by Equation F1-6. Equation F1-2 defines the inelastic lateral-torsional buckling as a straight line between the defined limits Lp and Lr. Buckling
strength in the elastic region Lb > Lr is given by Equation F1-14 for I-shaped
members.
For other moment diagrams, the lateral buckling strength is obtained by multiplying the basic strength by Cb as shown in Figure C-F1.1. The maximum Mn,
however, is limited to Mp. Note that Lp given by Equation F1-4 is merely a
definition which has physical meaning when Cb = 1.0. For Cb greater than 1.0,
larger unbraced lengths are permitted to reach Mp as shown by the curve for
Cb > 1.0. For design, this length could be calculated by setting Equation F1-2
equal to Mp and solving this equation for Lb using the desired Cb value.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
6 - 196
BEAMS AND OTHER FLEXURAL MEMBERS
[Comm. F
Cb = 1.75 + 1.05(M1 / M2) + 0.3(M1 / M2)2 ≤ 2.3
(C-F1-1)
The equation
has been used since 1961 to adjust the flexural-torsional buckling equation for
variations in the moment diagram within the unbraced length. This equation is
applicable only to moment diagrams that are straight lines between braced
points. The equation provides a lower bound fit to the solutions developed by
Salvadori (1956) which are shown in Figure C-F1.2. Another equation
Mn
Basic strength × Cb
Mp
(F1-2)
Mr
(F1-14)
plastic
design
Mp
inelastic elastic
LTB
Cb = 1.0 (Basic strength)
LTB
Lb
L pd
Lp
Lr
(F1-18) (F1-4) (F1-6)
Fig. C-F1.1. Nominal moment as a function of unbraced length and moment gradient.
Cb
Max Cb — warping significant
3.0
(C-F1-2)
2.5
Min Cb — no warping
2.0
(C-F1-1)
1.5
1.0
0
+1.0
M1
M2
+0.5
0
– 0.5
Fig. C-F1.2. Moment modifier Cb for beams.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
–1.0
Sect. C-F1]
DESIGN FOR FLEXURE
Cb =
1
0.6 − 0.4
M1
M2
6 - 197
≤ 2.5
(C-F1-2)
fits the average value theoretical solutions when the beams are bent in reverse
curvature and also provides a reasonable fit to the theory. If the maximum
moment within the unbraced segment is equal to or larger than the end moment,
Cb = 1.0 is used.
The equations above can be easily misinterpreted and misapplied to moment
diagrams that are not straight within the unbraced segment. Kirby and Nethercot
(1979) presented an equation which applies to various shapes of moment
diagrams within the unbraced segment. Their equation has been adjusted slightly
to the following
Cb =
12.5Mmax
2.5Mmax + 3MA + 4MB + 3MC
(C-F1-3)
This equation gives more accurate solutions for fixed-end beams, and the
adjusted equation reduces exactly to Equation C-F1-2 for a straight line moment
diagram in single curvature. The new Cb equation is shown in Figure C-F1.3 for
straight line moment diagrams. Other moment diagrams along with exact
theoretical solutions in the SSRC Guide (Galambos, 1988) show good comparison with the new equation. The absolute value of the three interior quarter-point
moments plus the maximum moment, regardless of its location are used in the
equation. The maximum moment in the unbraced segment is always used for
comparison with the resistance. The length between braces, not the distance to
inflection points, and Cb is used in the resistance equation.
Cb
M
M
2
Cb = 1.75 + 1.05 M 1+ 0.3( M 1) ≤ 2.3
2.5
2
2
2.0
1.5
1.0
12.5M max
Cb =
0.5
2.5Mmax + 3MA + 4MB + 3MC
M1 MA MB MC
M2
+, ratio shown
M1
M2
+1.0
+0.5
0
– 0.5
–1.0
Fig. C-F1.3. Cb for a straight line moment diagram—prismatic beam.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
6 - 198
BEAMS AND OTHER FLEXURAL MEMBERS
[Comm. F
It is still satisfactory to use the former Cb factor, Equation C-F1-1, for straight
line moment diagrams within the unbraced length.
The elastic strength of hybrid beams is identical to homogeneous beams. The
strength advantage of hybrid sections becomes evident only in the inelastic and
plastic slenderness ranges.
2b.
Doubly Symmetric Shapes and Channels with Lb > Lr
The equation given in the Specification assumes that the loading is applied along
the beam centroidal axis. If the load is placed on the top flange and the flange
is not braced, there is a tipping effect that reduces the critical moment; conversely, if the load is suspended from the bottom flange and is not braced, there
is a stabilizing effect which increases the critical moment (Galambos, 1988).
For unbraced top flange loading, the reduced critical moment may be conservatively approximated by setting the warping buckling factor X2 to zero.
An effective length factor of unity is implied in these critical moment equations
to represent a worst case pinned-pinned unbraced segment. Including consideration of any end restraint of the adjacent segments on the critical segment can
increase its buckling capacity. The effects of beam continuity on lateral-torsional
buckling have been studied and a simple and conservative design method, based
on the analogy of end-restrained nonsway columns with an effective length
factor less than one, has been proposed (Galambos, 1988).
2c.
Tees and Double-Angles
The lateral-torsional buckling strength (LTS) of singly symmetric tee beams is
given by a fairly complex formula (Galambos, 1988). Equation F1-15 is a
simplified formulation based on Kitipornchai and Trahair (1980). See also
Ellifritt, et al., 1992.
The Cb used for I-shaped beams is unconservative for tee beams with the stem
in compression. For such cases Cb = 1.0 is appropriate. When beams are bent in
reverse curvature, the portion with the stem in compression may control the LTB
resistance even though the moments may be small relative to other portions of
the unbraced length with Cb ≈ 1.0. This is because the LTB strength of a tee with
the stem in compression may be only about one-fourth of the capacity for the
stem in tension. Since the buckling strength is sensitive to the moment diagram, Cb has been conservatively taken as 1.0. In cases where the stem is in
tension, connection details should be designed to minimize any end restraining
moments which might cause the stem to be in compression.
2d.
Unbraced Length for Plastic Analysis
In the AISC ASD Specification, Chapter N, the unbraced length of a beam that
permits the attainment of plastic moments, and ensures sufficient rotation
capacity to redistribute moments, is given by two formulas which depend on the
moment ratio at the ends of the unbraced length. One length is permitted for
M1 / M2 < −0.5 (almost uniform moment), and a substantially larger length
for M1 / M2 > −0.5. These two equations are replaced by Equation F1-18 to
provide a continuous function between unbraced length and end moment ratio
so there is no abrupt change for a slight change in moment ratio near −0.5. At
M1 / M2 = −0.5 (uniform moment) the maximum unbraced length is almost the
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
Sect. C-F2]
DESIGN FOR SHEAR
6 - 199
same as that in the AISC ASD Specification. There is a substantial increase in
unbraced length for positive moment ratios (reverse curvature) because the
yielding is confined to zones close to the brace points (Yura, et al., 1978).
Equation F1-19 is an equation in similar form for solid rectangular bars and
symmetric box beams. Equations F1-18 and F1-19 assume that the moment
diagram within the unbraced length next to plastic hinge locations is reasonably
linear. For nonlinear diagrams between braces, judgment should be used in
choosing a representative ratio.
Equations F1-18 and F1-19 were developed to provide rotation capacities of at
least 3.0, which are sufficient for most applications (Yura, et al., 1978). When
inelastic rotations of 7 to 9 are deemed appropriate in areas of high seismicity,
as discussed in Commentary Section B5, Equation F1-18 would become:
Lpd =
F2.
2500ry
Fy
(C-F1-3)
DESIGN FOR SHEAR
For unstiffened webs kv = 5.0,
Fyw , and 234√
kv / Fyw = 523 / √
Fyw .
therefore 187√
kv / Fyw = 418 / √
kv / Fyw , the nominal shear strength Vn is based on
For webs with h / tw ≤ 187√
shear yielding of the web, Equation F2-1 and Equation A-F2-1. This h / tw limit
was determined by setting the critical stress causing shear buckling Fcr equal to
the yield stress of the web Fyw in Equation 35 of Cooper et al. (1978) and
kv / Fyw , the web shear strength
Timoshenko and Gere (1961). When h / tw > 187√
is based on buckling. Basler (1961) suggested taking the proportional limit as
80 percent of the yield stress of the web. This corresponds to h / tw = (187/0.8)
kv / Fyw ), the web strength is determined
(√
kv / Fyw ). Thus, when h / tw > 234(√
from the elastic buckling stress given by Equation 6 of Cooper et al., (1978) and
Timoshenko and Gere (1961):
Fcr =
π2Ekv
12(1 − v2)(h / tw)2
(C-F2-1)
The nominal shear strength, given by Equation F2-3 and A-F2-3, was obtained
by multiplying Fcr by the web area and using E = 29,000 ksi and v = 0.3. A straight
line transition, Equation F2-2 and AF2-2, is used between the limits
kv / Fyw ).
187(√
kv / Fyw ) and 234(√
The shear strength of flexural members follows the approach used in the AISC
ASD Specification, except for two simplifications. First, the expression for the
plate buckling coefficient kv has been simplified; it corresponds to that given by
AASHTO Standard Specification for Highway Bridges (1989). The earlier
expression for kv was a curve fit to the exact expression; the new expression is
just as accurate. Second, the alternate method (tension field action) for web shear
strength is placed in Appendix G because it was desired that only one method
appear in the main body of the Specification with alternate methods given in the
Appendix. When designing plate girders, thicker unstiffened webs will frequently be less costly than lighter stiffened web designs because of the additional
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
6 - 200
BEAMS AND OTHER FLEXURAL MEMBERS
[Comm. F
fabrication. If a stiffened girder design has economic advantages, the tension
field method in Appendix G will require fewer stiffeners.
The equations in this section were established assuming monotonically increasing loads. If a flexural member is subjected to load reversals causing cyclic
yielding over large portions of a web, such as may occur during a major
earthquake, special design considerations may apply (Popov, 1980).
F4.
BEAMS AND GIRDERS WITH WEB OPENINGS
Web openings in structural floor members may be necessary to accommodate
various mechanical, electrical, and other systems. Strength limit states, including local buckling of the compression flange, web, and tee-shaped compression
zone above or below the opening, lateral buckling and moment-shear interaction, or serviceability may control the design of a flexural member with web
openings. The location, size, and number of openings are important and empirical limits for them have been identified. One general procedure for assessing
these effects and the design of any needed reinforcement for both steel and
composite beams is given in Darwin (1990) and in ASCE (1992, 1992a).
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CHAPTER H
MEMBERS UNDER COMBINED FORCES AND TORSION
H1. SYMMETRIC MEMBERS SUBJECT TO BENDING AND AXIAL
FORCE
Equations H1-1a and H1-1b are simplifications and clarifications of similar
equations used in the AISC ASD Specification since 1961. Previously, both
equations had to be checked. In the new formulation the applicable equation is
governed by the value of the first term, Pu / φPn. For bending about one axis only,
the equations have the form shown in Figure C-H1.1.
The first term Pu / φPn has the same significance as the axial load term fa / Fa in
Equations H1-1 of the AISC ASD Specification. This means that for members
in compression Pn must be based on the largest effective slenderness ratio
Kl / r. In the development of Equations H1-1a and H1-1b, a number of alternative formulations were compared to the exact inelastic solutions of 82 sidesway
cases reported in Kanchanalai (1977). In particular, the possibility of using
Kl / r as the actual column length (K = 1) in determining Pn, combined with an
elastic second order moment Mu, was studied. In those cases where the true Pn
based on Kl / r, with K = 1.0, was in the inelastic range, the errors proved to be
unacceptably large without the additional check that Pu ≤ φcPn, Pn being based on
effective length. Although deviations from exact solutions were reduced, they
still remained high.
In summary, it is not possible to formulate a safe general interaction equation
φPn
Pu
8 Mu
Pu
φPn + 9 φb Mn = 1
0.2 φPn
1
2
( φPP ) + φ MM = 1
u
u
n
b
n
Mu
0.9 φb Mn
φb Mn
Fig. C-H1.1. Beam-column interaction equations.
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MEMBERS UNDER COMBINED FORCES AND TORSION
[Comm. H
for compression without considering effective length directly (or indirectly by
a second equation). Therefore, the requirement that the nominal compressive
strength Pn be based on the effective length KL in the general equation is
continued in the LRFD Specification as it has been in the AISC ASD Specification since 1961. It is not intended that these provisions be applicable to limit
nonlinear secondary flexure that might be encountered in large amplitude
earthquake stability design (ATC, 1978).
The defined term Mu is the maximum moment in a member. In the calculation
of this moment, inclusion of beneficial second order effects of tension is
optional. But consideration of detrimental second order effects of axial compression and translation of gravity loads is required. Provisions for calculation
of these effects are given in Chapter C.
The interaction equations in Appendix H3 have been recommended for biaxially
loaded H and wide flange shapes in Galambos (1988) and Springfield (1975).
These equations which can be used only in braced frames represent a considerable liberalization over the provisions given in Section H1; it is, therefore, also
necessary to check yielding under service loads, using the appropriate load and
resistance factors for the serviceability limit state in Equation H1-1a or H1-1b
with Mux = SxFy and Muy = SyFy. Appendix H3 also provides interaction equations
for rectangular box-shaped beam-columns. These equations are taken from
Zhou and Chen (1985).
H2. UNSYMMETRIC MEMBERS AND MEMBERS UNDER TORSION
AND COMBINED TORSION, FLEXURE, SHEAR, AND/OR AXIAL
FORCE
This section deals with types of cross sections and loadings not covered in
Section H1, especially where torsion is a consideration. For such cases it is
recommended to perform an elastic analysis based on the theoretical numerical
methods available from the literature for the determination of the maximum
normal and shear stresses, or for the elastic buckling stresses. In the buckling
calculations an equivalent slenderness parameter is determined for use in
Equation E2-2 or E2-3, as follows:
λe = √
Fy / Fe
where Fe is the elastic buckling stress determined from a stability analysis. This
procedure is similar to that of Appendix E3.
For the analysis of members with open sections under torsion refer to AISC
(1983).
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CHAPTER I
COMPOSITE MEMBERS
I1.
DESIGN ASSUMPTIONS
Force Determination. Loads applied to an unshored beam before the concrete
has hardened are resisted by the steel section alone, and only loads applied after
the concrete has hardened are considered as resisted by the composite section.
It is usually assumed for design purposes that concrete has hardened when it
attains 75 percent of its design strength. In beams properly shored during
construction, all loads may be assumed as resisted by the composite cross
section. Loads applied to a continuous composite beam with shear connectors
throughout its length, after the slab is cracked in the negative moment region,
are resisted in that region by the steel section and by properly anchored
longitudinal slab reinforcement.
For purposes of plastic analysis all loads are considered resisted by the composite cross section, since a fully plastic strength is reached only after considerable
yielding at the locations of plastic hinges.
Elastic Analysis. The use of constant stiffness in elastic analyses of continuous
beams is analogous to the practice in reinforced concrete design.
Plastic Analysis. For composite beams with shear connectors, plastic analysis
may be used only when the steel section in the positive moment region has a
Fyf , and when the steel section in the negative
compact web, i.e., h / tw ≤ 640√
moment region is compact, as required for steel beams alone. No compactness
limitations are placed on encased beams, but plastic analysis is permitted only
if the direct contribution of concrete to the strength of sections is neglected; the
concrete is relied upon only to prevent buckling.
Plastic Stress Distribution for Positive Moment. Plastic stress distributions are
described in Commentary Section I3, and a discussion of the composite participation of slab reinforcement is presented.
Plastic Stress Distribution for Negative Moment. Plastic stress distributions are
described in Commentary Section I3.
Elastic Stress Distribution. The strain distribution at any cross section of a
composite beam is related to slip between the structural steel and concrete
elements. Prior to slip, strain in both steel and concrete is proportional to the
distance from the neutral axis for the elastic transformed section. After slip, the
strain distribution is discontinuous, with a jump at the top of the steel shape. The
strains in steel and concrete are proportional to distances from separate neutral
axes, one for steel and the other for concrete.
Fully Composite Beam. Either tensile yield strength of the steel section or the
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COMPOSITE MEMBERS
[Comm. I
compressive stress of the concrete slab governs the maximum flexural strength
of a fully composite beam subjected to a positive moment. The tensile yield
strength of the longitudinal reinforcing bars in the slab governs the maximum
flexural strength of a fully composite beam subjected to a negative moment.
When shear connectors are provided in sufficient numbers to fully develop this
maximum flexural strength, any slip that occurs prior to yielding is minor and
has negligible influence both on stresses and stiffness.
Partially Composite Beam. The effects of slip on elastic properties of a partially
composite beam can be significant and should be accounted for in calculations
of deflections and stresses at service loads. Approximate elastic properties of
partially composite beams are given in Commentary Section I3. For simplified
design methods, see Hansell, et al. (1978).
Concrete-Encased Beam. When the dimensions of a concrete slab supported on
steel beams are such that the slab can effectively serve as the flange of a
composite T-beam, and the concrete and steel are adequately tied together so as
to act as a unit, the beam can be proportioned on the assumption of composite
action.
Two cases are recognized: fully encased steel beams, which depend upon natural
bond for interaction with the concrete, and those with mechanical anchorage to
the slab (shear connectors), which do not have to be encased.
I2.
COMPRESSION MEMBERS
1.
Limitations
(a) The lower limit of four percent on the cross-sectional area of structural steel
differentiates between composite and reinforced concrete columns. If the
area is less than four percent, a column with a structural steel core should be
designed as a reinforced concrete column.
(b) The specified minimum quantity of transverse and longitudinal reinforcement in the encasement should be adequate to prevent severe spalling of the
surface concrete during fires.
(c) Very little of the supporting test data involved concrete strengths in excess
of 6 ksi, even though the cylinder strength for one group of four columns
was 9.6 ksi. Normal weight concrete is believed to have been used in all tests.
Thus, the upper limit of concrete strength is specified as 8 ksi for normal
weight concrete. A lower limit of 3 ksi is specified for normal weight
concrete and 4 ksi for lightweight concrete to encourage the use of good
quality, yet readily available, grades of structural concrete.
(d) Encased steel shapes and longitudinal reinforcing bars are restrained from
buckling as long as the concrete remains sound. A limit strain of 0.0018, at
which unconfined concrete remains unspalled and stable, serves analytically
to define a failure condition for composite cross sections under uniform axial
strain. The limit strain of 0.0018 corresponds approximately to 55 ksi.
(e) The specified minimum wall thicknesses are identical to those in the 1989
ACI Building Code (1989). The purpose of this provision is to prevent
buckling of the steel pipe or tubing before yielding.
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2.
FLEXURAL MEMBERS
6 - 205
Design Strength
The procedure adopted for the design of axially loaded composite columns is
described in detail in Galambos and Chapuis (1980). It is based on the equation
for the strength of a short column derived in Galambos and Chapuis (1980), and
the same reductions for slenderness as those specified for steel columns in
Section E2. The design follows the same path as the design of steel columns,
except that the yield stress of structural steel, the modulus of elasticity of steel,
and the radius of gyration of the steel section, are modified to account for the
effect of concrete and longitudinal reinforcing bars. A detailed explanation of
the origin of these modifications may be found in SSRC Task Group 20 (1979).
Galambos and Chapuis (1980) includes comparisons of the design procedure
with 48 tests of axially loaded stub columns, 96 tests of concrete-filled pipes or
tubing, and 26 tests of concrete-encased steel shapes. The mean ratio of the test
failure loads to the predicted strengths was 1.18 for all 170 tests, and the
corresponding coefficient of variation was 0.19.
3.
Columns with Multiple Steel Shapes
This limitation is based on Australian research reported in Bridge and Roderick
(1978), which demonstrated that after hardening of concrete the composite
column will respond to loading as a unit even without lacing, tie plates, or batten
plates connecting the individual steel sections.
4.
Load Transfer
To avoid overstressing either the structural steel section or the concrete at
connections, a transfer of load to concrete by direct bearing is required.
When a supporting concrete area is wider on all sides than the loaded area, the
maximum design strength of concrete is specified by ACI (1989) as
1.7φB fc′AB where φB = 0.7 is the strength reduction factor in bearing on concrete
and AB is the loaded area. Because the AISC LRFD Specification is based on
the lower ASCE 7 load factors (ASCE, 1988), φB = 0.60 in the AISC LRFD
Specification. The portion of the design load of an axially loaded column φPn
resisted by the concrete may be expressed as (c2 fc′Ac / AsFmy)φBPn.
Accordingly,
AB ≥
I3.
FLEXURAL MEMBERS
1.
Effective Width
φB c2 Ac Pn
c2 Ac Pn
=
φB 1.7 As Fmy 1.7 As Fmy
(C-I2-1)
LRFD provisions for effective width omit any limit based on slab thickness, in
accordance with both theoretical and experimental studies, as well as current
composite beam codes in other countries (ASCE, 1979). The same effective
width rules apply to composite beams with a slab on either one side or both sides
of the beam. To simplify design, effective width is based on the full span,
center-to-center of supports, for both simple and continuous beams.
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2.
COMPOSITE MEMBERS
[Comm. I
Strength of Beams with Shear Connectors
This section applies to simple and continuous composite beams with shear
connectors, constructed with or without temporary shores.
Positive Flexural Design Strength. Flexural strength of a composite beam in the
positive moment region may be limited by the plastic strength of the steel
section, the concrete slab, or shear connectors. In addition, web buckling may
limit flexural strength if the web is slender and a significantly large portion of
the web is in compression.
According to Table B5.1, local web buckling does not reduce the plastic strength
of a bare steel beam if the beam depth-to-web thickness ratio is not larger than
Fy . In the absence of web buckling research on composite beams, the
640 / √
same ratio is conservatively applied to composite beams. Furthermore, for more
slender webs, the LRFD Specification conservatively adopts first yield as the
flexural strength limit. In this case, stresses on the steel section from permanent
loads applied to unshored beams before the concrete has hardened must be
superimposed on stresses on the composite section from loads applied to the
beams after hardening of concrete. In this superposition, all permanent loads
should be multiplied by the dead load factor and all live loads should be
multiplied by the live load factor. For shored beams, all loads may be assumed
as resisted by the composite section.
When first yield is the flexural strength limit, the elastic transformed section is
used to calculate stresses on the composite section. The modular ratio
n = E / Ec used to determine the transformed section depends on the specified
unit weight and strength of concrete. Note that this procedure for compact beams
differs from the requirements of Section I2 of the 1989 AISC ASD Specification.
Plastic Stress Distribution for Positive Moment. When flexural strength is
determined from the plastic stress distribution shown in Figure C-I3.1, compression force C in the concrete slab is the smallest of:
C = AswFyw + 2AsfFyf
(C-I3-1)
C = 0.85fc′Ac
(C-I3-2)
C = ΣQn
(C-I3-3)
For a non-hybrid steel section, Equation C-I3-1 becomes C = AsFy
where
fc′ = specified compressive strength of concrete, ksi
Ac = area of concrete slab within effective width, in.2
As = area of steel cross section, in.2
Asw = area of steel web, in.2
Asf = area of steel flange, in.2
Fy = minimum specified yield stress of steel, ksi
Fyw = minimum specified yield stress of web steel, ksi
Fyf = minimum specified yield stress of flange steel, ksi
ΣQn = sum of nominal strengths of shear connectors between the point of
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FLEXURAL MEMBERS
6 - 207
maximum positive moment and the point of zero moment to either side,
kips
Longitudinal slab reinforcement makes a negligible contribution to the compression force, except when Equation C-I3-2 governs. In this case, the area of
longitudinal reinforcement within the effective width of the concrete slab times
the yield stress of the reinforcement may be added in determining C.
The depth of the compression block is
a=
C
0.85fc′b
(C-I3-4)
where
b = effective width of concrete slab, in.
A fully composite beam corresponds to the case of C governed by the yield
strength of the steel beam or the compressive strength of the concrete slab, as
in Equation C-I3-1 or C-I3-2. The number and strength of shear connectors
govern C for a partially composite beam as in Equation C-I3-3.
The plastic stress distribution may have the plastic neutral axis (PNA) in the
web, in the top flange of the steel section or in the slab, depending on the value
of C.
The nominal plastic moment resistance of a composite section in positive
bending is given by the following equation and Figure C-I3.1:
Mn = C(d1 + d2) + Py (d3 − d2)
(C-I3-5)
where
Py = tensile strength of the steel section; for a non-hybrid steel section
Py = AsFy , kips
d1 = distance from the centroid of the compression force C in concrete to the
top of the steel section, in.
d2 = distance from the centroid of the compression force in the steel section
to the top of the steel section, in. For the case of no compression in the
steel section d2 = 0.
0.85f c′
a
d3
C
d1
Fy
d2
(Py – C)
2
(Py + C)
2
Fy
Fig. C-I3.1. Plastic stress distribution for positive moment in composite beams.
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COMPOSITE MEMBERS
[Comm. I
d3 = distance from Py to the top of the steel section, in.
Equation C-I3-5 is generally applicable including both non-hybrid and hybrid
steel sections symmetrical about one or two axes.
Approximate Elastic Properties of Partially Composite Beams. Elastic calculations for stress and deflection of partially composite beams should include the
effects of slip.
The effective moment of inertia Ieff for a partially composite beam is approximated by
(ΣQn / Cf) (Itr − Is)
Ieff = Is + √
(C-I3-6)
where
= moment of inertia for the structural steel section, in.4
= moment of inertia for the fully composite uncracked transformed
section, in.4
ΣQn = strength of shear connectors between the point of maximum positive
moment and the point of zero moment to either side, kips
Cf = compression force in concrete slab for fully composite beam; smaller
of Equations C-I3-1 and C-I3-2, kips
Is
Itr
The effective section modulus Seff, referred to the tension flange of the steel
section for a partially composite beam, is approximated by
(ΣQn / Cf) (Str − Ss)
Seff = Ss + √
(C-I3-7)
where
Ss = section modulus for the structural steel section, referred to the tension
flange, in.3
Str = section modulus for the fully composite uncracked transformed section,
referred to the tension flange of the steel section, in.3
Equations C-I3-6 and C-I3-7 should not be used for ratios ΣQn / Cf less than
0.25. This restriction is to prevent excessive slip, as well as substantial loss in
beam stiffness. Studies indicate that Equations C-I3-6 and C-I3-7 adequately
reflect the reduction in beam stiffness and strength, respectively, when fewer
connectors are used than required for full composite action (Grant et al., 1977).
Negative Flexural Design Strength. The flexural strength in the negative moment region is the strength of the steel beam alone or the plastic strength of the
composite section made up of the longitudinal slab reinforcement and the steel
section.
Plastic Stress Distribution for Negative Moment. When an adequately braced
compact steel section and adequately developed longitudinal reinforcing bars
act compositely in the negative moment region, the nominal flexural strength is
determined from the plastic stress distributions as shown in Figure C-I3.2. The
tensile force T in the reinforcing bars is the smaller of:
T = ArFyr
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
(C-I3-8)
Sect. C-I3]
FLEXURAL MEMBERS
6 - 209
T = ΣQn
(C-I3-9)
where
Ar = area of properly developed slab reinforcement parallel to the steel
beam and within the effective width of the slab, in.2
Fyr = specified yield stress of the slab reinforcement, ksi
ΣQn = sum of the nominal strengths of shear connectors between the point of
maximum negative moment and the point of zero moment to either
side, kips
A third theoretical limit on T is the product of the area and yield stress of the
steel section. However, this limit is redundant in view of practical limitations
on slab reinforcement.
The nominal plastic moment resistance of a composite section in negative
bending is given by the following equation:
Mn = T (d1 + d2) + Pyc (d3 − d2)
(C-I3-10)
where
Pyc = the compressive strength of the steel section; for a non-hybrid section
Pyc = AsFy , kips
d1 = distance from the centroid of the longitudinal slab reinforcement to the
top of the steel section, in.
d2 = distance from the centroid of the tension force in the steel section to the
top of the steel section, in.
d3 = distance from Pyc to the top of the steel section, in.
Transverse Reinforcement for the Slab. Where experience has shown that
longitudinal cracking detrimental to serviceability is likely to occur, the slab
should be reinforced in the direction transverse to the supporting steel section.
It is recommended that the area of such reinforcement should be at least 0.002
times the concrete area in the longitudinal direction of the beam and should be
uniformly distributed.
3.
Strength of Concrete-Encased Beams
Tests of concrete-encased beams demonstrated that (1) the encasement drastically reduces the possibility of lateral-torsional instability and prevents local
buckling of the encased steel, (2) the restrictions imposed on the encasement
d3
(Pyc – T)
2
T
d2
d1
Fy
(Pyc + T)
2
Fy
Fig. C-I3.2. Plastic stress distribution for negative moment.
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COMPOSITE MEMBERS
[Comm. I
practically prevent bond failure prior to first yielding of the steel section, and
(3) bond failure does not necessarily limit the moment capacity of an encased
steel beam (ASCE, 1979). Accordingly, the LRFD Specification permits two
alternate design methods: one based on the first yield in the tension flange of
the composite section and the other based on the plastic moment capacity of the
steel beam alone. No limitations are placed on the slenderness of either the
composite beam or the elements of the steel section, since the encasement
effectively inhibits both local and lateral buckling.
In the method based on first yield, stresses on the steel section from permanent
loads applied to unshored beams before the concrete has hardened must be
superimposed on stresses on the composite section from loads applied to the
beams after hardening of the concrete. In this superposition, all permanent loads
should be multiplied by the dead load factor and all live loads should be
multiplied by the live load factor. For shored beams, all loads may be assumed
as resisted by the composite section. Complete interaction (no slip) between the
concrete and steel is assumed.
The contribution of concrete to the strength of the composite section is ordinarily
larger in positive moment regions than in negative moment regions. Accordingly, design based on the composite section is more advantageous in the regions
of positive moments.
4.
Strength During Construction
When temporary shores are not used during construction, the steel beam alone
must resist all loads applied before the concrete has hardened enough to provide
composite action. Unshored beam deflection caused by wet concrete tends to
increase slab thickness and dead load. For longer spans this may lead to
instability analogous to roof ponding. An excessive increase of slab thickness
may be avoided by beam camber.
When forms are not attached to the top flange, lateral bracing of the steel beam
during construction may not be continuous and the unbraced length may control
flexural strength, as defined in Section F1.
The LRFD Specification does not include special requirements for a margin
against yield during construction. According to Section F1, maximum factored
moment during construction is 0.90Fy Z where Fy Z is the plastic moment
(0.90Fy Z ≈ 0.90 × 1.1Fy S). This is equivalent to approximately the yield moment, Fy S. Hence, required flexural strength during construction prevents moment in excess of the yield moment.
Load factors for construction loads should be determined for individual projects
according to local conditions, with the factors listed in Section A4 as a guide.
Once the concrete has hardened, slab weight becomes a permanent dead load
and the dead load factor applies to any load combinations.
5.
Formed Steel Deck
Figure C-I3.3 is a graphic presentation of the terminology used in Section I3.5.
When studs are used on beams with formed steel deck, they may be welded
directly through the deck or through prepunched or cut-in-place holes in the
deck. The usual procedure is to install studs by welding directly through the
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Sect. C-I3]
FLEXURAL MEMBERS
6 - 211
deck; however, when the deck thickness is greater than 16 gage for single
thickness, or 18 gage for each sheet of double thickness, or when the total
thickness of galvanized coating is greater than 1.25 ounces/sq. ft, special
precautions and procedures recommended by the stud manufacturer should be
followed.
The design rules for composite construction with formed steel deck are based
upon a study (Grant, et al., 1977) of the then available test results. The limiting
parameters listed in Section I3.5 were established to keep composite construction with formed steel deck within the available research data.
Seventeen full size composite beams with concrete slab on formed steel deck
2 ″min.
hr ≤ 3 ″
Hs
wr
11/2 ″min.
2 ″min.
2 ″min.
hr ≤ 3 ″
Hs
wr
11/2 ″min.
2 ″min.
2 ″min.
hr ≤ 3 ″
Hs
wr
11/2 ″min.
2 ″min.
11/2 ″min.
Hs
wr
2 ″min.
wr
2 ″min.
Fig. C-I3.3. Steel deck limits.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
2 ″min.
hr ≤ 3 ″
6 - 212
COMPOSITE MEMBERS
[Comm. I
were tested at Lehigh University and the results supplemented by the results of
58 tests performed elsewhere. The range of stud and steel deck dimensions
encompassed by the 75 tests were limited to:
(1) Stud dimensions: 3⁄4-in. dia. × 3.00 to 7.00 in.
(2) Rib width: 1.94 in. to 7.25 in.
(3) Rib height: 0.88 in. to 3.00 in.
(4) Ratio wr / hr: 1.30 to 3.33
(5) Ratio Hs / hr: 1.50 to 3.41
(6) Number of studs in any one rib: 1, 2, or 3
The strength of stud connectors installed in the ribs of concrete slabs on formed
steel deck with the ribs oriented perpendicular to the steel beam is reasonably
estimated by the strength of stud connectors in flat soffit composite slabs
multiplied by values computed from Equation I3-1.
For the case where ribs run parallel to the beam, limited testing (Grant et al.,
1977) has shown that shear connection is not significantly affected by the ribs.
However, for narrow ribs, where the ratio wr / hr is less than 1.5, a shear stud
reduction factor, Equation I3-2, has been employed in view of lack of test data.
The Lehigh study (Grant et al., 1977) also indicated that Equation C-I3-7 for
effective section modulus and Equation C-I3-6 for effective moment of inertia
were valid for composite construction with formed steel deck.
Based on the Lehigh test data (Grant, et al., 1977), the maximum spacing of steel
deck anchorage to resist uplift was increased from 16 to 18 inches in order to
accommodate current production profiles.
When metal deck includes units for carrying electrical wiring, crossover headers
are commonly installed over the cellular deck perpendicular to the ribs. They
create trenches which completely or partially replace sections of the concrete
slab above the deck. These trenches, running parallel to or transverse to a
composite beam, may reduce the effectiveness of the concrete flange. Without
special provisions to replace the concrete displaced by the trench, the trench
should be considered as a complete structural discontinuity in the concrete
flange.
When trenches are parallel to the composite beam, the effective flange width
should be determined from the known position of the trench.
Trenches oriented transverse to composite beams should, if possible, be located
in areas of low bending moment and the full required number of studs should
be placed between the trench and the point of maximum positive moment.
Where the trench cannot be located in an area of low moment, the beam should
be designed as non-composite.
6.
Design Shear Strength
A conservative approach to vertical shear provisions for composite beams is
adopted by assigning all shear to the steel section web. This neglects any
concrete slab contribution and serves to simplify the design.
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I4.
SHEAR CONNECTORS
6 - 213
COMBINED COMPRESSION AND FLEXURE
The procedure adopted for the design of beam-columns is described and
supported by comparisons with test data in Galambos and Chapuis (1980). The
basic approach is identical to that specified for steel columns in Section H1.
The nominal axial strength of a beam-column is obtained from Section I2.2,
while the nominal flexural strength is determined from the plastic stress distribution on the composite section. An approximate formula for this plastic
moment resistance of a composite column is given in Galambos and Chapuis
(1980).
h2
AwFy
−
AwFy
2
1.7fc′h1
Mn = Mp = ZFy + 1⁄3(h2 − 2cr) ArFyr +
(C-I4-1)
where
Aw = web area of encased steel shape; for concrete-filled tubes, Aw = 0, in.2
Z = plastic section modulus of the steel section, in.3
cr = average of distance from compression face to longitudinal reinforcement in that face and distance from tension face to longitudinal reinforcement in that face, in.
h1 = width of composite cross section perpendicular to the plane of bending,
in.
h2 = width of composite cross section parallel to the plane of bending, in.
The supporting comparisons with beam-column tests included 48 concretefilled pipes or tubing and 44 concrete-encased steel shapes (Galambos and
Chapuis, 1980). The overall mean test-to-prediction ratio was 1.23 and the
coefficient of variation 0.21.
The last paragraph in Section I4 provides a transition from beam-columns to
beams. It involves bond between the steel section and concrete. Section I3 for
beams requires either shear connectors or full, properly reinforced encasement
of the steel section. Furthermore, even with full encasement, it is assumed that
bond is capable of developing only the moment at first yielding in the steel of
the composite section. No test data are available on the loss of bond in composite
beam-columns. However, consideration of tensile cracking of concrete suggests
Pu / φcPn = 0.3 as a conservative limit. It is assumed that when Pu / φcPn is less
than 0.3, the nominal flexural strength is reduced below that indicated by plastic
stress distribution on the composite cross section unless the transfer of shear
from the concrete to the steel is provided for by shear connectors.
I5.
SHEAR CONNECTORS
1.
Materials
Tests (Ollgaard et al., 1971) have shown that fully composite beams with
concrete meeting the requirements of Part 3, Chapter 4, “Concrete Quality,” of
ACI (1989), made with ASTM C33 or rotary-kiln produced C330 aggregates,
develop full flexural capacity.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
6 - 214
2.
COMPOSITE MEMBERS
[Comm. I
Horizontal Shear Force
Composite beams in which the longitudinal spacing of shear connectors was
varied according to the intensity of statical shear, and duplicate beams in which
the connectors were uniformly spaced, exhibited the same ultimate strength and
the same amount of deflection at normal working loads. Only a slight deformation in the concrete and the more heavily stressed connectors is needed to
redistribute the horizontal shear to other less heavily stressed connectors. The
important consideration is that the total number of connectors be sufficient to
develop the shear Vh on either side of the point of maximum moment. The
provisions of the LRFD Specification are based upon this concept of composite
action.
In computing the design flexural strength at points of maximum negative
bending, reinforcement parallel to the steel beam within the effective width of
the slab may be included, provided such reinforcement is properly anchored
beyond the region of negative moment. However, enough shear connectors are
required to transfer, from the slab to the steel beam, the ultimate tensile force in
the reinforcement.
3.
Strength of Stud Shear Connectors
Studies have defined stud shear connector strength in terms of normal weight
and lightweight aggregate concretes as a function of both concrete modulus of
elasticity and concrete strength as given by Equation I5-1.
Equation I5-1, obtained from Ollgaard, et al. (1971), corresponds to Tables I4.1
and I4.2 in Section I4 of the 1989 AISC ASD Specification. Note that an upper
bound on stud shear strength is the product of the cross-sectional area of the stud
times its ultimate tensile strength.
The LRFD Specification does not specify a resistance factor for shear connector
strength. The resistance factor for the flexural strength of a composite beam
accounts for all sources of variability, including those associated with the shear
connectors.
4.
Strength of Channel Shear Connectors
Equation I5-2 is a modified form of the formula for the strength of channel
connectors developed by Slutter and Driscoll (1965). The modification has
extended its use to lightweight concrete.
6.
Shear Connector Placement and Spacing
Uniform spacing of shear connectors is permitted except in the presence of
heavy concentrated loads.
When stud shear connectors are installed on beams with formed steel deck,
concrete cover at the sides of studs adjacent to sides of steel ribs is not critical.
Tests have shown that studs installed as close as is permitted to accomplish
welding of studs does not reduce the composite beam capacity.
Studs not located directly over the web of a beam tend to tear out of a thin flange
before attaining full shear-resisting capacity. To guard against this contingency,
the size of a stud not located over the beam web is limited to 21⁄2 times the flange
thickness (Goble, 1968).
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
Sect. C-I6]
SPECIAL CASES
6 - 215
The minimum spacing of connectors along the length of the beam, in both flat
soffit concrete slabs and in formed steel deck with ribs parallel to the beam, is
six diameters; this spacing reflects development of shear planes in the concrete
slab (Ollgaard et al., 1971). Since most test data are based on the minimum
transverse spacing of four diameters, this transverse spacing was set as the
minimum permitted. If the steel beam flange is narrow, this spacing requirement
may be achieved by staggering the studs with a minimum transverse spacing of
three diameters between the staggered row of studs. The reduction in connector
Nr ,
capacity in the ribs of formed steel decks is provided by the factor 0.85 / √
which accounts for the reduced capacity of multiple connectors, including the
effect of spacing. When deck ribs are parallel to the beam and the design requires
more studs than can be placed in the rib, the deck may be split so that adequate
spacing is available for stud installation. Figure C-I5.1 shows possible connector
arrangements.
I6.
SPECIAL CASES
Tests are required for construction that falls outside the limits given in the
Specification. Different types of shear connectors may require different spacing
and other detailing than stud and channel connectors.
4d
d
6d
6d
3d
4d
Fig. C-I5.1. Shear connector arrangements.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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CHAPTER J
CONNECTIONS, JOINTS, AND FASTENERS
J1.
GENERAL PROVISIONS
5.
Splices in Heavy Sections
Solidified but still-hot weld metal contracts significantly as it cools to ambient
temperature. Shrinkage of large welds between elements which are not free to
move to accommodate the shrinkage, causes strains in the material adjacent to
the weld that can exceed the yield point strain. In thick material, the weld
shrinkage is restrained in the thickness direction as well as in the width and
length directions, causing triaxial stresses to develop that may inhibit the ability
of ductile steel to deform in a ductile manner. Under these conditions, the
possibility of brittle fracture increases.
When splicing ASTM A6 Group 4 and 5 rolled sections or heavy welded built-up
members, the potentially harmful weld shrinkage strains can be avoided by using
bolted splices or fillet-welded lap splices or splices that combine a welded and
bolted detail (see Figure C-J1.1). Details and techniques that perform well for
materials of modest thickness usually must be changed or supplemented by more
demanding requirements when welding thick material. Also, the provisions of
the Structural Welding Code, AWS D1.1, are minimum requirements that apply
to most structural welding situations; however, when designing and fabricating
welded splices of ASTM A6 Group 4 and 5 shapes and similar built-up cross
sections, special consideration must be given to all aspects of the welded splice
detail.
• Notch-toughness requirements should be specified for tension members. See
Commentary A3.
• Generously sized weld access holes, Figure C-J1.2, are required to provide
increased relief from concentrated weld shrinkage strains, to avoid close
juncture of welds in orthogonal directions, and to provide adequate clearance
for the exercise of high quality workmanship in hole preparation, welding,
and ease of inspection.
• Preheating for thermal cutting is required to minimize the formation of a hard
surface layer.
• Grinding to bright metal and inspection using magnetic particle or dye-penetrant methods is required to remove the hard surface layer and to assure
smooth transitions free of notches or cracks.
In addition to tension splices of truss chord members and tension flanges of
flexural members, other joints fabricated of heavy sections subject to tension
should be given special consideration during design and fabrication.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
Sect. C-J1]
8.
GENERAL PROVISIONS
6 - 217
Placement of Welds and Bolts
Slight eccentricities between the gravity axis of single and double angle members and the center of gravity of connecting rivets or bolts have long been
ignored as having negligible effect on the static strength of such members. Tests
(Gibson and Wake, 1942) have shown that similar practice is warranted in the
case of welded members in statically loaded structures.
However, the fatigue life of eccentrically loaded welded angles has been shown
to be very short (Kloppel and Seeger, 1964). Notches at the roots of fillet welds
are harmful when alternating tensile stresses are normal to the axis of the weld,
as could occur due to bending when axial cyclic loading is applied to angles
with end welds not balanced about the neutral axis. Accordingly, balanced welds
are indicated when such members are subjected to cyclic loading (see Figure
C-J1.3).
9.
Bolts in Combination with Welds
Welds will not share the load equally with mechanical fasteners in bearing-type
connections. Before ultimate loading occurs, the fastener will slip and the weld
will carry an indeterminately larger share of the load.
Accordingly, the sharing of load between welds and A307 bolts or high-strength
bolts in a bearing-type connection is not recommended. For similar reasons,
A307 bolts and rivets should not be assumed to share loads in a single group of
fasteners.
For high-strength bolts in slip-critical connections to share the load with welds
it is advisable to fully tension the bolts before the weld is made. If the weld is
placed first, angular distortion from the heat of the weld might prevent the faying
action required for development of the slip-critical force. When the bolts are
fully tensioned before the weld is made, the slip-critical bolts and the weld may
be assumed to share the load on a common shear plane (Kulak, et al., 1987). The
heat of welding near bolts will not alter the mechanical properties of the bolts.
2 or 3 in.
In making alterations to existing structures, it is assumed that whatever slip is
(a) Shear plate welded
to web
(b) Shear plate welded
to flange tips
(c) Bolted splice plates
Fig. C-J1.1. Alternative splices that minimize weld restraint tensile stresses.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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CONNECTIONS, JOINTS, AND FASTENERS
[Comm. J
likely to occur in high-strength bolted bearing-type connections or riveted
connections will have already taken place. Hence, in such cases the use of
welding to resist all stresses, other than those produced by existing dead load
present at the time of making the alteration, is permitted.
It should be noted that combinations of fasteners as defined herein does not refer
to connections such as shear plates for beam-to-column connections which are
welded to the column and bolted to the beam flange or web (Kulak, et al., 1987)
and other comparable connections.
Backing if
used 5
Backing if
used 5
≥1.5t w
Radius precut by
drill or hole saw
D ≥ ¾ in.
R (see
note 2)
≥ tw ≥ ¾ in.
≥1.5t w
R (see
note 2)
≥1.5t w
≥ tw ≥ ¾ in.
Angle of
slope not
critical
Need not be
tangent, notches
prohibited
≥ tw ≥ ¾ in.
Optional method for
making corner radius
≥1.5t w
≥1.5t w
R (see
note 2)
R (see
note 2)
≥ tw ≥ ¾ in.
≥ tw ≥ ¾ in.
Rolled shape 1 or
groove welded shape 1,3
Fillet
1,4
welded shape
Notes:
1. For ASTM A6 Group 4 and 5 shapes and welded built-up shapes with plate thickness more
than 2 in., preheat to 150°F prior to thermal cutting, grind and inspect thermally cut edges
of access hole using magnetic particle or dye penetration methods prior to making web and
flange splice groove welds.
2. Radius shall provide smooth notch-free transition; R ≥ 3⁄8-in. (typical 1⁄2-in.)
3. Access opening made after welding web to flange.
4. Access opening made before welding web to flange.
5. These are typical details for joints welded from one side against steel backing. Alternative
joint designs should be considered.
Fig. C-J1.2. Weld access hole and beam cope geometry.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
Sect. C-J2]
10.
WELDS
6 - 219
High-Strength Bolts in Combination with Rivets
When high-strength bolts are used in combination with rivets, the ductility of
the rivets permits the direct addition of the strengths of both fastener types.
J2.
WELDS
1.
Groove Welds
The engineer preparing contract design drawings cannot specify the depth of
groove without knowing the welding process and the position of welding.
Accordingly, only the effective throat for partial joint-penetration groove welds
should be specified on design drawings, allowing the fabricator to produce this
effective throat with his own choice of welding process and position.
The weld reinforcement is not used in determining the effective throat thickness
of a groove weld (see Table J2.1).
2.
Fillet Welds
2a.
Effective Area
The effective throat of a fillet weld is based upon the root of the joint and the
face of the diagrammatic weld, hence this definition gives no credit for weld
penetration or reinforcement at the weld face. If the fillet weld is made by the
submerged arc welding process, some credit for penetration is made. If the leg
size of the resulting fillet weld exceeds 3⁄8-in., then 0.11 in. is added to the
theoretical throat. This increased weld throat is allowed because the submerged
arc process produces deep penetration of welds of consistent quality. However,
it is necessary to run a short length of fillet weld to be assured that this increased
penetration is obtained. In practice, this is usually done initially by crosssectioning the runoff plates of the joint. Once this is done, no further testing is
required, as long as the welding procedure is not changed.
F
F
Welds balanced about the
center line of the angle
Welds balanced about the
neutral axis of the angle
Figure C-J1.3
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6 - 220
2b.
CONNECTIONS, JOINTS, AND FASTENERS
[Comm. J
Limitations
Table J2.4 provides a minimum size of fillet weld for a given thickness of the
thicker part joined.
The requirements are not based upon strength considerations, but upon the
quench effect of thick material on small welds. Very rapid cooling of weld metal
may result in a loss of ductility. Further, the restraint to weld-metal shrinkage
provided by thick material may result in weld cracking. Because a 5⁄16-in. fillet
weld is the largest that can be deposited in a single pass by SMAW process,
5⁄ -in. applies to all material 3⁄ -in. and greater in thickness, but minimum preheat
16
4
and interpass temperature are required by AWS D1.1.* Both the design engineer
and the shop welder must be governed by the requirements.
Table J2.3 gives the minimum effective throat of a partial joint-penetration
groove weld. Notice that Table J2.3 for partial joint-penetration groove welds
goes up to a plate thickness of over 6 in. and a minimum weld throat of 5⁄8-in.,
whereas, for fillet welds Table J2.4 goes up to a plate thickness of over 3⁄4-in.
and a minimum leg size of fillet weld of only 5⁄16-in. The additional thickness
for partial-penetration welds is to provide for reasonable proportionality between weld and material thickness.
For plates of 1⁄4-in. or more in thickness, it is necessary that the inspector be able
to identify the edge of the plate to position the weld gage. This is assured if the
weld is kept back at least 1⁄16-in. from the edge, as shown in Figure C-J2.1.
Where longitudinal fillet welds are used alone in a connection (see Figure
C-J2.2), Section J2.2b requires the length of each weld to be at least equal to the
width of the connecting material because of shear lag (Fisher, et al., 1978).
By providing a minimum lap of five times the thickness of the thinner part of a
lap joint, the resulting rotation of the joint when pulled will not be excessive, as
shown in Figure C-J2.3. Fillet welded lap joints under tension tend to open and
* See Table J2.4.
Apparent edge
of plate
Apparent weld
throat
Actual edge of
plate before
welding
Actual edge of plate
is distinguishable
Actual weld
throat
Fig. C-J2.1. Identification of plate edge.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
Actual weld throat
is distinguishable
Sect. C-J2]
WELDS
6 - 221
apply a tearing action at the root of the weld as shown in Figure C-J2.4b, unless
restrained by a force F as shown in Figure C-J2.4a.
End returns are not essential for developing the capacity of fillet welded
connections and have a negligible effect on their strength. Their use has been
encouraged to insure that the weld size is maintained over the length of the weld,
to enhance the fatigue resistance of cyclically loaded flexible end connections,
and to increase the plastic deformation capability of such connections.
The weld capacity database on which the specifications were developed had no
end returns. This includes the study by Higgins and Preece (1968), seat angle
tests by Lyse and Schreiner (1935), the seat and top angle tests by Lyse and
Gibson (1937), beam webs welded directly to column or girder by fillet welds
by Johnston and Deits (1941), and the eccentrically loaded welded connections
reported by Butler, Pal, and Kulak (1972). Hence, the current design-resistance
values and joint-capacity models do not require end returns, when the required
weld size is provided. Johnston and Green (1940) noted that movement consistent with the design assumption of no end restraint (i.e., joint flexibility) was
L
L≥W
t
W
L
Fig. C-J2.2. Longitudinal fillet welds.
Overlap
Overlap
Fig. C-J2.3. Minimum lap.
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CONNECTIONS, JOINTS, AND FASTENERS
[Comm. J
enhanced without end returns. They also verified that greater plastic deformation
of the connection was achieved when end returns existed, although the strength
was not significantly different.
There are numerous welded joints where it is not possible to provide end returns
and where it is also possible to provide the desired weld size. These joints as well
as the seat angle and the web angle connections cited earlier do not require end
returns when the weld size is adequate and fatigue is not a design consideration.
4.
Design Strength
The strength of welds is governed by the strength of either the base material or
the deposited weld metal. Table J2.5 contains the resistance factors and nominal
weld strengths, as well as a number of limitations.
It should be noted that in Table J2.5 the nominal strength of fillet welds is
determined from the effective throat area, whereas the strength of the connected
parts is governed by their respective thicknesses. Figure C-J2.5 illustrates the
shear planes for fillet welds and base material:
(a) Plane 1-1, in which the resistance is governed by the shear strength for
material A.
(b) Plane 2-2, in which the resistance is governed by the shear strength of the
weld metal.
(c) Plane 3-3, in which the resistance is governed by the shear strength of the
material B.
The resistance of the welded joint is the lowest of the resistance calculated in
each plane of shear transfer. Note that planes 1-1 and 3-3 are positioned away
from the fusion areas between the weld and the base material. Tests have
F
(a) Unrestrained
(a) Restrained
Fig. C-J2.4. Restraint of lap joints.
Material A
1
3
2
Material B
2 1
2
1
2
Material A
2
1
2
3
Fig. C-J2.5. Shear planes for fillet welds loaded in longitudinal shear.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
Sect. C-J3]
BOLTS AND THREADED PARTS
6 - 223
demonstrated that the stress on this fusion area is not critical in determining the
shear strength of fillet welds (Preece, 1968).
The shear planes for plug and partial penetration groove welds are shown in
Figure C-J2.6 for the weld and base metal. Generally the base metal will govern
the shear strength.
5.
Combination of Welds
This method of adding weld strengths does not apply to a welded joint using a
partial-penetration single bevel groove weld with a superimposed fillet weld. In
this case, the effective throat of the combined joint must be determined and the
design strength based upon this throat area.
7.
Mixed Weld Metal
Problems can occur when incompatible weld metals are used in combination
and notch-tough composite weld metal is required. For instance, tack welds
deposited using a self-shielded process with aluminum deoxidizers in the
electrodes and subsequently covered by SAW weld passes can result in composite weld metal with low notch-toughness, despite the fact that each process by
itself could provide notch-tough weld metal.
J3.
BOLTS AND THREADED PARTS
1.
High-Strength Bolts
In general, the use of high-strength bolts is required to conform to the provisions
of the Load and Resistance Factor Design Specification for Structural Joints
Using ASTM A325 or A490 Bolts (RCSC, 1988) as approved by the Research
Council on Structural Connections.
(a) Plug welds
(b) Partial penetration welds
Fig. C-J2.6. Shear planes for plug and partial-penetration welds.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
6 - 224
CONNECTIONS, JOINTS, AND FASTENERS
[Comm. J
Occasionally the need arises for the use of high-strength bolts of diameters and
lengths in excess of those available for A325 and A490 bolts, as for example,
anchor bolts for fastening machine bases. For this situation Section A3.3 permits
the use of A449 bolts and A354 threaded rods.
2.
Size and Use of Holes
To provide some latitude for adjustment in plumbing up a frame during erection,
three types of enlarged holes are permitted, subject to the approval of the
designer. The nominal maximum sizes of these holes are given in Table J3.3.
The use of these enlarged holes is restricted to connections assembled with bolts
and is subject to the provisions of Sections J3.3 and J3.4.
3.
Minimum Spacing
The maximum factored strength Rn at a bolt or rivet hole in bearing requires that
the distance between the centerline of the first fastener and the edge of a plate
toward which the force is directed should not be less than 11⁄2d, where d is the
fastener diameter (Kulak et al., 1987). By similar reasoning the distance measured in the line of force, from the centerline of any fastener to the nearest edge
of an adjacent hole, should not be less than 3d, to ensure maximum design
strength in bearing. Plotting of numerous test results indicates that the critical
bearing strength is directly proportional to the above defined distances up to a
maximum value of 3d, above which no additional bearing strength is achieved
(Kulak et al., 1987). Table J3.7 lists the increments that must be added to adjust
the spacing upward to compensate for an increase in hole dimension parallel to
the line of force. Section J3.10 gives the bearing strength criteria as a function
of spacing.
4.
Minimum Edge Distance
Critical bearing stress is a function of the material tensile strength, the spacing
of fasteners, and the distance from the edge of the part to the center line of the
nearest fastener. Tests have shown (Kulak et al., 1987) that a linear relationship
exists between the ratio of critical bearing stress to tensile strength (of the
connected material) and the ratio of fastener spacing (in the line of force) to
fastener diameter. The following equation affords a good lower bound to
published test data for single-fastener connections with standard holes, and is
conservative for adequately spaced multi-fastener connections:
Fpcr le
=
Fu d
(C-J3-1)
where
Fpcr = critical bearing stress, ksi
Fu = tensile strength of the connected material, ksi
le = distance, along a line of transmitted force, from the center of a fastener
to the nearest edge of an adjacent fastener or to the free edge of a
connected part (in the direction of stress), in.
d = diameter of fastener, in.
The provisions of Section J3.3 are concerned with le as hole spacing, whereas
Section J3.4 is concerned with le as edge distance in the direction of stress.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
Sect. C-J3]
BOLTS AND THREADED PARTS
6 - 225
Section J3.10 establishes a maximum bearing strength. Spacing and/or edge
distance may be increased to provide for a required bearing strength, or bearing
force may be reduced to satisfy a spacing and/or edge distance limitation.
It has long been known that the critical bearing stress of a single fastener
connection is more dependent upon a given edge distance than multi-fastener
connections (Jones, 1940). For this reason, longer edge distances (in the direction of force) are required for connections with one fastener in the line of
transmitted force than required for those having two or more.
The recommended minimum distance transverse to the direction of load is
primarily a workmanship tolerance. It has little, if any, effect on the strength of
the member.
5.
Maximum Spacing and Edge Distance
Limiting the edge distance to not more than 12 times the thickness of an outside
connected part, but not more than six inches, is intended to provide for the
exclusion of moisture in the event of paint failure, thus preventing corrosion
between the parts which might accumulate and force these parts to separate.
More restrictive limitations are required for connected parts of unpainted
weathering steel exposed to atmospheric corrosion.
6.
Design Tension or Shear Strength
Tension loading of fasteners is usually accompanied by some bending due to
the deformation of the connected parts. Hence, the resistance factor φ, by which
Rn is multiplied to obtain the design tensile strength of fasteners, is relatively
low. The nominal tensile strength values in Table J3.2 were obtained from the
equation
Rn = 0.75AbFu
(C-J3-2)
While the equation was developed for bolted connections (Kulak et al., 1987),
it was also conservatively applied to threaded parts and to rivets. The nominal
strength of A307 bolts was discounted by 5 ksi.
In connections consisting of only a few fasteners, the effects of strain on the
shear in bearing fasteners is negligible (Kulak et al., 1987; Fisher et al., 1978).
In longer joints, the differential strain produces an uneven distribution between
fasteners (those near the end taking a disproportionate part of the total load), so
that the maximum strength per fastener is reduced. The AISC ASD Specification
permits connections up to 50 in. in length without a reduction in maximum shear
stress. With this in mind the resistance factor φ for shear in bearing-type
connections has been selected to accommodate the same range of connections.
The values of nominal shear strength in Table J3.2 were obtained from the
equation
Rn / mAb = 0.50Fu
(C-J3-3)
when threads are excluded from the shear planes and
Rn / mAb = 0.40Fu
(C-J3-4)
when threads are not excluded from the shear plane, where m is the number of
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
6 - 226
CONNECTIONS, JOINTS, AND FASTENERS
[Comm. J
shear planes (Kulak et al., 1987). While developed for bolted connections, the
equations were also conservatively applied to threaded parts and rivets. The
value given for A307 bolts was obtained from Equation C-J3-4 but is specified
for all cases regardless of the position of threads. For A325 bolts, no distinction
is made between small and large diameters, even though the minimum tensile
strength Fu is lower for bolts with diameters in excess of one inch. It was felt that
such a refinement of design was not justified, particularly in view of the low
resistance factor φ, increasing ratio of tensile area to gross area and other
compensating factors.
7.
Combined Tension and Shear in Bearing-Type Connections
Tests have shown that the strength of bearing fasteners subject to combined shear
and tension resulting from externally applied forces can be closely defined by
an ellipse (Kulak et al., 1987). Such a curve can be replaced, with only minor
deviations, by three straight lines as shown in Figure C-J3.1. This latter representation offers the advantage that no modification of either type stress is
required in the presence of fairly large magnitudes of other types. This linear
representation was adopted for Table J3.5, giving a limiting tensile stress Ft as
a function of the shearing stress fv for bearing-type connections.
8.
High-Strength Bolts in Slip-Critical Connections
Connections classified as slip-critical include those cases where slip could
theoretically exceed an amount deemed by the Engineer of Record to affect the
suitability for service of the structure by excessive distortion or reduction in
strength or stability, even though the nominal strength of the connection may be
adequate. Also included are those cases where slip of any magnitude must be
prevented, for example, joints subject to fatigue, connectors between elements
of built-up members at their ends (Sections D2 and E4), and bolts in combination
with welds (Section J1.9).
The onset of slipping in a high-strength bolted, slip-critical connection is not an
ft
Ft
C–
RFv
C = 1.3Ft , approximately
F
R = t/Fv , approximately
F
ft = F t Fv 2– fv2
v
Fv
fv
Figure C-J3.1.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
Sect. C-J3]
BOLTS AND THREADED PARTS
6 - 227
indication that maximum capacity of the connection has been reached. Its
occurrence may be only a serviceability limit state. In the case of bolts in holes
with only small clearance, such as standard holes and slotted holes loaded
transverse to the axis of the slot in practical connections, the freedom to slip
generally does not exist because one or more bolts are in bearing even before
load is applied due to normal fabrication tolerances and erection procedures.
Further, the consequences of slip, if it can occur at all, are trivial except for a
few situations as noted above.
Slip of slip-critical connections is likely to occur at approximately 1.4 to 1.5
times the service loads. For standard holes, oversized holes, and short slotted
holes the connection can be designed either at service loads (Section J3.8a) or
at factored loads (Appendix J3.8b). The nominal loads and φ factors have been
adjusted accordingly. The number of connectors will be essentially the same for
the two procedures because they have been calibrated to give similar results.
Slight differences will occur because of variation in the ratio of live load to dead
load.
In connections containing long slots that are parallel to the direction of the
applied load, slip of the connection prior to attainment of the factored load might
be large enough to alter the usual assumption of analysis that the undeformed
structure can be used to obtain the internal forces. To guard against this
occurring, the design slip resistance is further reduced by 0.85 when designing
at service load (Section J3.8a) and by setting φ to 0.60 in conjunction with
factored loads (Appendix J3.8b).
While the possibility of a slip-critical connection slipping into bearing under
anticipated service conditions is small, such connections must comply with the
provisions of Section J3.10 in order to prevent connection failure at the maximum load condition.
10.
Bearing Strength at Bolt Holes
The recommended bearing stress on pins is not the same as for bolts as explained
in Section J8.
Bearing values are not provided as a protection to the fastener, because it needs
no such protection. Therefore, the same bearing value applies to joints assembled by bolts, regardless of fastener shear strength or the presence or absence of
threads in the bearing area.
Tests (Frank and Yura, 1981) have demonstrated that hole elongation greater
than 0.25 in. will begin to develop as the bearing stress is increased beyond the
values given in Equations J3-1a and J3-1d, especially if it is combined with high
tensile stress on the net section, even though rupture does not occur. Equations
J3-1b and J3-1c consider the effect of hole ovalization (deformation greater than
0.25 in.) whenever the upper design limit (3.0dtFu) is deemed acceptable. These
latter equations also establish the design limit for a single bolt, or two or more
bolts, whenever the bolt arrangement results in each bolt singly in line with the
direction of the applied force. Because two separate limit states are considered
(deformation and strength) with both limit states equated to a bearing stress
(2.4Fu or 2.0Fu and 3.0Fu , respectively) conflicting design strengths may result,
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
6 - 228
CONNECTIONS, JOINTS, AND FASTENERS
[Comm. J
either acceptable, when intermediate edge distance and bolt spacing values are
considered.
11.
Long Grips
Provisions requiring a decrease in calculated stress for A307 bolts having long
grips (by arbitrarily increasing the required number in proportion to the grip
length) are not required for high-strength bolts. Tests (Bendigo et al., 1963) have
demonstrated that the ultimate shearing strength of high-strength bolts having
a grip of eight or nine diameters is no less than that of similar bolts with much
shorter grips.
J4.
DESIGN RUPTURE STRENGTH
Tests (Birkemoe and Gilmor, 1978) on coped beams indicated that a tearing
failure mode (rupture) can occur along the perimeter of the bolt holes as shown
in Figure C-J4.1. This block shear mode combines tensile strength on one plane
and shear strength on a perpendicular plane. The failure path is defined by the
center lines of the bolt holes. The block shear failure mode is not limited to the
coped ends of beams. Other examples are shown in Figure CJ4.1 and C-J4.2.
Cope
Beam
Shear
area
Failure by tearing
out of shaded
portion
Failure by tearing
out of shaded
portion
Shear
area
Tensile
area
Tensile
area
Po
Fig. C-J4.1. Failure surface for block shear rupture limit state.
Po
Po
Small tension
force
Large tension
force
Large shear
force
Po
(a)
Po
(b)
Fig. C-J4.2 Block shear rupture in tension.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
Small shear
force
Sect. C-J6]
FILLERS
6 - 229
The block shear failure mode should also be checked around the periphery of
welded connections. Welded connection block shear is determined using φ =
0.75 in conjunction with the area of both the fracture and yielding planes (Yura,
1988).
The LRFD Specification has adopted a conservative model to predict block
shear strength. Test results suggest that it is reasonable to add the yield strength
on one plane to the rupture strength of the perpendicular plane (Ricles and Yura,
1983 and Hardash and Bjorhovde, 1985). Therefore, two possible block shear
strengths can be calculated; rupture strength Fu on the net tensile section along
with shear yielding 0.6Fy on the gross section on the shear plane(s), or rupture
0.6Fu on the net shear area(s) combined with yielding Fy on the gross tensile area.
This is the basis of Equations J4-3 and J4-4.
These equations are consistent with the philosophy in Chapter D for tension
members, where gross area is used for the limit state of yielding and net area is
used for rupture. The controlling equation is the one that produces the larger
rupture force. This can be explained by the two extreme examples given in
Figure C-J4.2. In Case a, the total force is resisted primarily by shear, so shear
rupture, not shear yielding, should control the block shear tearing mode;
therefore, use Equation J4-4. For Case b, block shear cannot occur until the
tension area ruptures as given by Equation J4-3. If Equation J4-4 (shear rupture
on the small area and yielding on the large tension area) is checked for Case b,
a smaller Po will result. In fact, as the shear area gets smaller and approaches
zero, the use of Equation J4-4 for Case b would give a block shear strength based
totally on yielding of the gross tensile area. Block shear is a rupture or tearing
phenomenon not a yielding limit state. Therefore, the proper equation to use is
the one with the larger rupture term.
J5.
CONNECTING ELEMENTS
2.
Design Strength of Connecting Elements in Tension
Tests have shown that yield will occur on the gross section area before the tensile
capacity of the net section is reached, if the ratio An / Ag ≤ 0.85 (Kulak et al.,
1987). Since the length of connecting elements is small compared to the member
length, inelastic deformation of the gross section is limited. Hence, the effective
net area An of the connecting element is limited to 0.85Ag in recognition of the
limited inelastic deformation and to provide a reserve capacity.
J6.
FILLERS
The practice of securing fillers by means of additional fasteners, so that they
are, in effect, an integral part of a shear-connected component, is not required
where a connection is designed to be a slip-critical connection using highstrength bolts. In such connections, the resistance to slip between filler and either
connected part is comparable to that which would exist between the connected
parts if no fill were present.
Filler plates may be used in lap joints of welded connections that splice parts of
different thickness, or where there may be an offset in the joint.
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J8.
CONNECTIONS, JOINTS, AND FASTENERS
[Comm. J
BEARING STRENGTH
The LRFD Specification provisions for bearing on milled surfaces, Section J8,
follow the same philosophy of earlier AISC ASD Specifications. In general, the
design is governed by a deformation limit state at service loads resulting in
stresses nominally at 9⁄10 of yield. Adequate safety is provided by post-yield
strength as deformation increases. Tests on pin connections (Johnston, 1939)
and on rockers (Wilson, 1934) have confirmed this behavior.
As used throughout the LRFD Specification, the terms “milled surface,”
“milled,” and “milling” are intended to include surfaces which have been
accurately sawed or finished to a true plane by any suitable means.
J9.
COLUMN BASES AND BEARING ON CONCRETE
The equations for resistance of concrete in bearing are the same as ACI 318-89
except that AISC equations use φ = 0.60 while ACI uses φ = 0.70, since ACI
specifies larger load factors than the ASCE load factors specified by AISC.
J10. ANCHOR BOLTS AND EMBEDMENTS
ACI 318 and 349 Appendix B and the PCI Handbook include recommended
procedures for the design of anchor bolts and embedments.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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CHAPTER K
CONCENTRATED FORCES, PONDING, AND FATIGUE
K1. FLANGES AND WEBS WITH CONCENTRATED FORCES
1.
Design Basis
The LRFD Specification separates flange and web strength requirements into
distinct categories representing different limit state criteria, i.e., local flange
bending (Section K1.2), local web yielding (Section K1.3), web crippling
(Section K1.4), sidesway web buckling (Section K1.5), compression buckling
of the web (Section K1.6), and panel zone web shear (Section K1.7).
These criteria are applied to two distinct types of concentrated forces which act
on member flanges. Single concentrated forces may be tensile, such as those
delivered by tension hangers, or compressive, such as those delivered by bearing
plates at beam interior positions, reactions at beam ends, and other bearing
connections. Double concentrated forces, one tensile and one compressive, form
a couple on the same side of the loaded member, such as that delivered to column
flanges through welded and bolted moment connections.
2.
Local Flange Bending
Where a tensile force is applied through a plate welded across a flange, that
flange must be sufficiently rigid to prevent deformation of the flange and the
corresponding high-stress concentration in the weld in line with the web.
The effective column flange length for local flange bending is 12tf (Graham, et
al., 1959). Thus, it is assumed that yield lines form in the flange at 6tf in each
direction from the point of the applied concentrated force. To develop the fixed
edge consistent with the assumptions of this model, an additional 4tf and
therefore a total of 10tf, is required for the full flange-bending strength given by
Equation K1-1. In the absence of applicable research, a 50 percent reduction has
been introduced for cases wherein the applied concentrated force is less than
10tf from the member end.
This criterion given by Equation K1-1 was originally developed for moment
connections, but it also applies to single concentrated forces such as tension
hangers consisting of a plate welded to the bottom flange of a beam and
transverse to the beam web.
3.
Local Web Yielding
The web strength criteria have been established to limit the stress in the web of
a member into which a force is being transmitted. It should matter little whether
the member receiving the force is a beam or a column; however, Galambos
(1976) and AISC (1978), references upon which the LRFD Specification is
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CONCENTRATED FORCES, PONDING, AND FATIGUE
[Comm. K
based, did make such a distinction. For beams, a 2:1 stress gradient through the
flange was used, whereas the gradient through column flanges was 21⁄2:1. In
Section K1.3, the 21⁄2:1 gradient is used for both cases.
This criterion applies to both bearing and moment connections.
4.
Web Crippling
The expression for resistance to web crippling at a concentrated force is a departure
from previous specifications (IABSE, 1968; Bergfelt, 1971; Hoglund, 1971; and
Elgaaly, 1983). Equations K1-4 and K1-5 are based on research by Roberts (1981).
The increase in Equation K1-5b for N / d > 0.2 was developed after additional
testing (Elgaaly, 1991) to better represent the effect of longer bearing lengths at ends
of members. All tests were conducted on bare steel beams without the expected
beneficial contributions of any connection or floor attachments. Thus, the resulting
criteria are considered conservative for such applications.
These equations were developed for bearing connections, but are also generally
applicable to moment connections. However, for the rolled shapes listed in Part 1
of the LRFD Manual with Fy not greater than 50 ksi, the web crippling criterion
will never control the design in a moment connection except for a W12×50 or
W10×33 column.
The web crippling phenomenon has been observed to occur in the web adjacent
to the load flange. For this reason, a half-depth stiffener (or stiffeners) or a
half-depth doubler plate is expected to eliminate this limit state.
5.
Sidesway Web Buckling
The sidesway web buckling criterion was developed after observing several
unexpected failures in tested beams (Summers and Yura, 1982). In those tests
the compression flanges were braced at the concentrated load, the web was
squeezed into compression, and the tension flange buckled (see Figure C-K1.1).
Sidesway web buckling will not occur in the following cases. For flanges
restrained against rotation:
h / tw
> 2.3
l / bf
(C-K1-1)
Brace
Tension flange
Fig. C-K1.1. Sidesway web buckling.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
ay
Sidesw kle
c
u
b
b
e
w
Sect. C-K1]
FLANGES AND WEBS WITH CONCENTRATED FORCES
6 - 233
For flanges not restrained against rotation:
h / tw
> 1.7
l / bf
(C-K-1-2)
where l is as shown in Figure C-K1.2.
Sidesway web buckling can also be prevented by the proper design of lateral
bracing or stiffeners at the load point. It is suggested that local bracing at both
flanges be designed for one percent of the concentrated force applied at that
point. Stiffeners must extend from the load point through at least one-half the
beam or girder depth. In addition, the pair of stiffeners should be designed to
carry the full load. If flange rotation is permitted at the loaded flange, neither
stiffeners nor doubler plateswill be effective.
In the 1st Edition LRFD Manual, the sidesway web buckling equations were
based on the assumption that h / tf = 40, a convenient assumption which is
generally true for economy beams. This assumption has been removed so that
the equations will be applicable to all sections.
These equations were developed only for bearing connections and do not apply
to moment connections.
6.
Compression Buckling of the Web
When compressive forces are applied to both flanges of a member at the same
l=L
l=L
l=L
l = L/ 2
L
/2
L
= Braced point
Fig. C-K1.2. Unbraced flange length.
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CONCENTRATED FORCES, PONDING, AND FATIGUE
[Comm. K
location, as by moment connections at both flanges of a column, the member
web must have its slenderness ratio limited to avoid the possibility of buckling.
This is done in the LRFD Specification with Equation K1-8, which is a modified
form of a similar equation used in the ASD Specification. This equation is
applicable to a pair of moment connections, and to other pairs of compressive
forces applied at both flanges of a member, for which N / d is small (<1). When
N / d is not small, the member web should be designed as a compression member
in accordance with Chapter E.
Equation K1-8 is predicated on an interior member loading condition. In the
absence of applicable research, a 50 percent reduction has been introduced for
cases wherein the compressive forces are close to the member end.
Equation K1-8 has also traditionally been applied when there is a moment
connection to only one flange of the column and compressive force is applied
to only one flange. Its use in this case is conservative.
Panel Zone Web Shear
The column web shear stresses may be high within the boundaries of the rigid
connection of two or more members whose webs lie in a common plane. Such
webs should be reinforced when the calculated factored force ΣF along plane
A-A in Figure C-K1.3 exceeds the column web design strength φRv, where
ΣFu =
Mu1 Mu2
+
− Vu
dm1 dm2
(C-K1-3)
and
Mu1 = Mu1L + Mu1G = the sum of the moments due to the factored lateral load
Mu1L and the moments due to factored gravity load
Mu1G on the leeward side of the connection, kip-in.
Mu2 = Mu2L − Mu2G = the difference between the moments due to the factored
lateral load Mu2L and the moments due to factored gravity
load Mu2G on the windward side of the connection, kip-in.
Story shear, Vu
ΣFu
A
d m1
A
Mu2
d m2
7.
Vu
dc
Fig. C-K1.3. Forces in panel zone.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
M u1
Sect. C-K1]
FLANGES AND WEBS WITH CONCENTRATED FORCES
dm1, dm2
6 - 235
= distance between flange forces in a moment connection,
in.
Conservatively, 0.95 times the beam depth has been used for dm in the past.
If ΣFu ≤ φRv, no reinforcement is necessary, i.e., treq ≤ tw, where tw is the column
web thickness.
Consistent with elastic first order analysis, Equations K1-9 and K1-10 limit
panel-zone behavior to the elastic range. While such connection panels possess
large reserve capacity beyond initial general shear yielding, the corresponding
inelastic joint deformations may adversely affect the strength and stability of
the frame or story (Fielding and Huang, 1971 and Fielding and Chen, 1973).
Panel-zone shear yielding affects the overall frame stiffness and, therefore, the
ultimate-strength second-order effects may be significant. The shear/axial interaction expression of Equation K1-10, as shown in Figure C-K1.4, is chosen to
ensure elastic panel behavior.
If adequate connection ductility is provided and the frame analysis considers
the inelastic panel-zone deformations, then the additional inelastic shear
strength is recognized in Equations K1-11 and K1-12 by the factor
3b t2
1 + cf cf
db dc tw
This inelastic shear strength has been most often utilized for design of frames
in high seismic zones and should be used when the panel zone is to be designed
to match the strength of the members from which it is formed.
The shear/axial interaction expression incorporated in Equation K1-12 (see
Figure C-K1.5) is similar to that contained in the previous issue of this specification and recognizes the observed fact that when the panel-zone web has
completely yielded in shear, the axial column load is carried in the flanges.
1.0
Rv
0.6Fy d c t w
0.4
0
1.0
0.4
Pu
Py
Fig. C-K1.4. Interaction of shear and axial force—elastic.
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CONCENTRATED FORCES, PONDING, AND FATIGUE
[Comm. K
K2. PONDING
As used in the LRFD Specification, ponding refers to the retention of water due
solely to the deflection of flat roof framing. The amount of this water is
dependent upon the flexibility of the framing. Lacking sufficient framing
stiffness, its accumulated weight can result in collapse of the roof if a strength
evaluation is not made (ASCE, 1990).
Representing the deflected shape of the primary and critical secondary member
as a half-sine wave, the weight and distribution of the ponded water can be
estimated and, from this, the contribution that the deflection each of these
members makes to the total ponding deflection can be expressed (Marino, 1966):
For the primary member:
∆w =
[αp∆o 1 + 0.25παs + 0.25πρ(1 + αs)]
1 − 0.25παpαs
For the secondary member:
π3
π2
αsδo 1 + 32 αp + (1 + αp) + 0.185αsαp
8ρ
δw =
1 − 0.25παpαs
In these expressions ∆o and δo are, respectively, the primary and secondary beam
deflections due to loading present at the initiation of ponding,
αp = Cp / (1 − Cp), αs = Cs / (1 − Cs), and ρ = δo / ∆o = Cs / Cp.
Using the above expressions for ∆w and δw, the ratios ∆w / ∆o and δw / δo can be
computed for any given combination of primary and secondary beam framing
using, respectively, the computed value of parameters Cp and Cs defined in the
LRFD Specification.
1.0
Rv
3b cf t cf2
db dc tw
(
(
0.6Fy d c t w 1 +
0.7
0.75
0
1.0
Pu
Py
Fig. C-K1.5. Interaction of shear and axial force—inelastic.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
Sect. C-K2]
PONDING
6 - 237
Even on the basis of unlimited elastic behavior, it is seen that the ponding
deflections would become infinitely large unless
Cp Cs 4
<
1 − Cp 1 − Cs π
Since elastic behavior is not unlimited, the effective bending strength available
in each member to resist the stress caused by ponding action is restricted to the
difference between the yield stress of the member and the stress fo produced by
the total load supported by it before consideration of ponding is included.
Note that elastic deflection is directly proportional to stress. The admissible
amount of ponding in either the primary or critical (midspan) secondary member, in terms of the applicable ratio ∆w / ∆o and δw / δo, can be represented as
(Fy − fo) / fo. Substituting this expression for ∆w / ∆o and δw / δo, and combining
with the foregoing expressions for ∆w and δw, the relationship between critical
values for Cp and Cs and the available elastic bending strength to resist ponding
is obtained. The curves presented in Figures A-K2.1 and A-K2.2 are based upon
this relationship. They constitute a design aid for use when a more exact
determination of required flat roof framing stiffness is needed than given by the
LRFD Specification provision that Cp + 0.9Cs ≤ 0.25.
Given any combination of primary and secondary framing, the stress index is
computed as
Fy − fo
for the primary member
Up =
fo p
Fy − fo
for the secondary member
Us =
fo s
where fo, in each case, is the computed bending stress, ksi, in the member due
to the supported loading, neglecting ponding effect. Depending upon geographic
location, this loading should include such amount of snow as might also be
present, although ponding failures have occurred more frequently during torrential summer rains when the rate of precipitation exceeded the rate of drainage
runoff and the resulting hydraulic gradient over large roof areas caused substantial accumulation of water some distance from the eaves.
Given the size, spacing, and span of a tentatively selected combination of
primary and secondary beams, for example, one may enter Figure A-K2.1 at the
level of the computed stress index Up, determined for the primary beam; move
horizontally to the computed Cs value of the secondary beams; then move
downward to the abscissa scale. The combined stiffness of the primary and
secondary framing is sufficient to prevent ponding if the flexibility constant read
from this latter scale is more than the value of Cp computed for the given primary
member; if not, a stiffer primary or secondary beam, or combination of both, is
required.
If the roof framing consists of a series of equally-spaced wall-bearing beams,
they would be considered as secondary members, supported on an infinitely stiff
primary member. For this case, one would use Figure A-K2.2. The limiting value
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CONCENTRATED FORCES, PONDING, AND FATIGUE
[Comm. K
of Cs would be determined by the intercept of a horizontal line representing the
Us value and the curve for Cp = 0.
The ponding deflection contributed by a metal deck is usually such a small part
of the total ponding deflection of a roof panel that it is sufficient merely to limit
its moment of inertia (in.4 per foot of width normal to its span) to 0.000025 times
the fourth power of its span length, as provided in the LRFD Specification.
However, the stability against ponding of a roof consisting of a metal roof deck
of relatively slender depth-span ratio, spanning between beams supported
directly on columns, may need to be checked. This can be done using Figure
A-K2.1 or A-K2.2 with the following computed values:
Up = stress index for the supporting beam
Us = stress index for the roof deck
Cp = flexibility constant for the supporting beams
Cs = flexibility constant for one foot width of the roof deck (S = 1.0)
Since the shear rigidity of the web system is less than that of a solid plate, the
moment of inertia of steel joists and trusses should be taken as somewhat less
than that of their chords.
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CHAPTER L
SERVICEABILITY DESIGN CONSIDERATIONS
Serviceability criteria are formulated to prevent disruptions of the functional use and
damage to the structure during its normal everyday use. While malfunctions may not
result in the collapse of a structure or in loss of life or injury, they can seriously impair
the usefulness of the structure and lead to costly repairs. Neglect of serviceability may
result in unacceptably flexible structures.
There are essentially three types of structural behavior which may impair serviceability:
(1) Excessive local damage (local yielding, buckling, slip, or cracking) that may
require excessive maintenance or lead to corrosion.
(2) Excessive deflection or rotation that may affect the appearance, function, or
drainage of the structure, or may cause damage to nonstructural components and
their attachments.
(3) Excessive vibrations induced by wind or transient live loads which affect the
comfort of occupants of the structure or the operation of mechanical equipment.
In allowable stress design, the AISC Specification accounts for possible local damage
with factors of safety included in the allowable stresses, while deflection and vibration
are controlled, directly or indirectly, by limiting deflections and span-depth ratios. In
the past, these rules have led to satisfactory performance of structures, with perhaps
the exception of large open floor areas without partitions. In LRFD the serviceability
checks should consider the appropriate loads, the response of the structure, and the
reaction of the occupants to the structural response.
Examples of loads that may require consideration of serviceability include permanent
live loads, wind, and earthquake; effects of human activities such as walking, dancing,
etc.; temperature fluctuations; and vibrations induced by traffic near the building or
by the operation of mechanical equipment within the building.
Serviceability checks are concerned with adequate performance under the appropriate
load conditions. Elastic behavior can usually be assumed. However, some structural
elements may have to be examined with respect to their long-term behavior under
load.
It is difficult to specify limiting values of structural performance based on serviceability considerations because these depend to a great extent on the type of structure,
its intended use, and subjective physiological reaction. For example, acceptable
structural motion in a hospital clearly would be much less than in an ordinary industrial
building. It should be noted that humans perceive levels of structural motion that are
far less than motions that would cause any structural damage. Serviceability limits
must be determined through careful consideration by the designer and client.
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SERVICEABILITY DESIGN CONSIDERATIONS
[Comm. L
L1. CAMBER
The engineer should consider camber when deflections at the appropriate load
level present a serviceability problem.
L2. EXPANSION AND CONTRACTION
As in the case of deflections, the satisfactory control of expansion cannot be
reduced to a few simple rules, but must depend largely upon the good judgment
of qualified engineers.
The problem is more serious in buildings with masonry walls than with prefabricated units. Complete separation of the framing, at widely spaced expansion
joints, is generally more satisfactory than more frequently located devices
dependent upon the sliding of parts in bearing, and usually less expensive than
rocker or roller expansion bearings.
Creep and shrinkage of concrete and yielding of steel are among the causes,
other than temperature, for dimensional changes.
L3. DEFLECTIONS, VIBRATION, AND DRIFT
1.
Deflections
Excessive transverse deflections or lateral drift may lead to permanent damage
to building elements, separation of cladding, or loss of weathertightness, damaging transfer of load to non-load-supporting elements, disruption of operation
of building service systems, objectionable changes in appearance of portions of
the buildings, and discomfort of occupants.
The LRFD Specification does not provide specific limiting deflections for
individual members or structural assemblies. Such limits would depend on the
function of the structure (ASCE, 1979; CSA, 1989; Ad Hoc Committee, 1986).
Provisions that limit deflections to a percentage of span may not be adequate
for certain long-span floor systems; a limit on maximum deflection that is
independent of span length may also be necessary to minimize the possibility
of damage to adjoining or connecting nonstructural elements.
2.
Floor Vibration
The increasing use of high-strength materials and efficient structural schemes
leads to longer spans and more flexible floor systems. Even though the use of a
deflection limit related to span length generally precluded vibration problems
in the past, some floor systems may require explicit consideration of the
dynamic, as well as the static, characteristics of the floor system.
The dynamic response of structures or structural assemblies may be difficult to
analyze because of difficulties in defining the actual mass, stiffness, and damping characteristics. Moreover, different load sources cause varying responses.
For example, a steel beam-concrete slab floor system may respond to live
loading as a non-composite system, but to transient excitation from human
activity as an orthotropic composite plate. Nonstructural partitions, cladding,
and built-in furniture significantly increase the stiffness and damping of the
structure and frequently eliminate potential vibration problems. The damping
can also depend on the amplitude of excitation.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
Sect. C-L5]
CORROSION
6 - 241
The general objective in minimizing problems associated with excessive structural motion is to limit accelerations, velocities, and displacements to levels that
would not be disturbing to the building occupants. Generally, occupants of a
building find sustained vibrations more objectionable than transient vibrations.
The levels of peak acceleration that people find annoying depend on frequency
of response. Thresholds of annoyance for transient vibrations are somewhat
higher and depend on the amount of damping in the floor system. These levels
depend on the individual and the activity at the time of excitation (ASCE, 1979;
ISO, 1974; CSA, 1989; Murray, 1991; and Ad Hoc Committee, 1986).
The most effective way to reduce effects of continuous vibrations is through
vibration isolation devices. Care should be taken to avoid resonance, where the
frequency of steady-state excitation is close to the fundamental frequency of the
system. Transient vibrations are reduced most effectively by increasing the
damping in the structural assembly. Mechanical equipment which can produce
objectionable vibrations in any portion of a structure should be adequately
isolated to reduce the transmission of such vibrations to critical elements of the
structure.
3.
Drift
The LRFD Specification does not provide specific limiting values for lateral
drift. If a drift analysis is desired, the stiffening effect of non-load-supporting
elements such as partitions and infilled walls may be included in the analysis of
drift.
Some irrecoverable inelastic deformations may occur at given load levels in
certain types of construction. The effect of such deformations may be negligible
or serious, depending on the function of the structure, and should be considered
by the designer on a case by case basis.
The deformation limits should apply to structural assemblies as a whole.
Reasonable tolerance should also be provided for creep. Where load cycling
occurs, consideration should be given to the possibility of increases in residual
deformation that may lead to incremental failure.
L5. CORROSION
Steel members may deteriorate in particular service environments. This deterioration may appear either in external corrosion, which would be visible upon
inspection, or in undetected changes that would reduce its strength. The designer
should recognize these problems by either factoring a specific amount of
damage tolerance into the design or providing adequate protection systems (e.g.,
coatings, cathodic protection) and/or planned maintenance programs so that
such problems do not occur.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
6 - 242
CHAPTER M
FABRICATION, ERECTION, AND QUALITY CONTROL
M2. FABRICATION
1.
Cambering, Curving, and Straightening
The use of heat for straightening or cambering members is permitted for A514
and A852 steel, as it is for other steels. However, the maximum temperature
permitted is 1,100°F compared to 1,200°F for other steels.
The cambering of flexural members, when required by the contract documents,
may be accomplished in various ways. In the case of trusses and girders, the
desired curvature can be built in during assembly of the component parts. Within
limits, rolled beams can be cold-cambered at the producing mills.
The local application of heat has come into common use as a means of
straightening or cambering beams and girders. The method depends upon an
ultimate shortening of the heat-affected zones. A number of such zones, on the
side of the member that would be subject to compression during cold-cambering
or “gagging,” are heated enough to be “upset” by the restraint provided by
surrounding unheated areas. Shortening takes place upon cooling.
While the final curvature or camber can be controlled by these methods, it must
be realized that some deviation, due to workmanship error and permanent
change due to handling, is inevitable.
2.
Thermal Cutting
Preferably thermal cutting shall be done by machine. The requirement for a
positive preheat of 150°F minimum when thermal cutting beam copes and weld
access holes in ASTM A6 Group 4 and 5 shapes, and in built-up shapes made
of material more than two inches thick, tends to minimize the hard surface layer
and the initiation of cracks.
5.
Bolted Construction
In the past, it has been required to tighten to a specified tension all ASTM A325
and A490 bolts in both slip-critical and bearing-type connections. The requirement was changed in 1985 to permit most bearing-type connections to be
tightened to a snug-tight condition.
In a snug-tight bearing connection, the bolts cannot be subjected to tension loads,
slip can be permitted, and loosening or fatigue due to vibration or load fluctuations are not design considerations.
It is suggested that snug-tight bearing-type connections be used in applications
where A307 bolts would be permitted.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
Sect. C-M4]
ERECTION
6 - 243
This section provides rules for the use of oversized and slotted holes paralleling
the provisions which have been in the RCSC Specification (RCSC, 1988) since
1972, extended to include A307 bolts which are outside the scope of the
high-strength bolt specifications.
M3. SHOP PAINTING
The surface condition of steel framing disclosed by the demolition of longstanding buildings has been found to be unchanged from the time of its erection,
except at isolated spots where leakage may have occurred. Even in the presence
of leakage, the shop coat is of minor influence (Bigos et al., 1954).
The LRFD Specification does not define the type of paint to be used when a
shop coat is required. Conditions of exposure and individual preference with
regard to finish paint are factors which bear on the selection of the proper primer.
Hence, a single formulation would not suffice. For a comprehensive treatment
of the subject, see SSPC (1989).
5.
Surfaces Adjacent to Field Welds
The Specification allows for welding through surface materials, including
appropriate shop coatings, that do not adversely affect weld quality nor create
objectionable fumes.
M4. ERECTION
4.
Fit of Column Compression Joints and Base Plates
Tests at the University of California-Berkeley (Popov and Stephen, 1977) on
spliced full-size columns with joints that had been intentionally milled out-ofsquare, relative to either strong or weak axis, demonstrated that the load-carrying capacity was the same as that for a similar unspliced column. In the tests,
gaps of 1⁄16-in. were not shimmed; gaps of 1⁄4-in. were shimmed with non-tapered
mild steel shims. Minimum size partial-penetration welds were used in all tests.
No tests were performed on specimens with gaps greater than 1⁄4-in.
5.
Field Welding
The purpose of wire brushing shop paint, on surfaces adjacent to joints to be
field welded, is to reduce the possibility of porosity and cracking and also to
reduce any environmental hazard. Although there are limited tests which indicate that painted surfaces result in sound welds without wire brushing, other
studies have resulted in excessive porosity and/or cracking when welding coated
surfaces. Wire brushing to reduce the paint film thickness minimizes rejectable
welds. Grinding or other procedures beyond wire brushing is not necessary.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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APPENDIX B
DESIGN REQUIREMENTS
B5. LOCAL BUCKLING
1.
Classification of Steel Sections
The limiting width-thickness λp and λr ratios for webs in pure flexure
(Pu / φbPy = 0) and with axial compression have been revised in terms of (h / t)
rather than (hc / t). The simplified formulation in Table B5.1 for λr based on
double symmetry with equal flanges (h / hc = 1) is unconservative when the
compression flange is smaller than the tension flange, and conservative if the
reverse is true. The more accurate limit is given in Appendix B5.1 as a function
of hc. Figure C-A-B5.1 illustrates the λr variation for axial compression and
flange asymmetry effects.
The 3⁄4 minimum and 3⁄2 maximum restrictions on h / hc in Equations A-B5-1 and
A-B5-2 approximately correspond to the 0.1 and 0.9 range of Iyc / Iy for a member
to be considered a singly symmetric I shape. Otherwise, when the flange areas
differ by more than a factor of two, the member should be conservatively
designed as a tee section.
( ) F = 253 [ 1 + 2.83( )(1 +
h
t
1,327
h
hc
y
Pu
φbPy
) ] (exact)
( hh ) = /
3
c
Compression
flange
larger
1,000
970
λ r Fy =
( ) F 730
h
t
2
y
( ) F = 970 (1 – 0.74 φ PP )
( simplified, assuming hh = 1)
( hh ) = 1
or
h
t
u
y
b y
c
500
Compression
flange
h 2
= /3
smaller
hc
c
( )
253
0
0.5
1.0
(φ PP )
Fig. C-A-B5.1. Local web buckling for I-shaped members.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
u
b y
6 - 245
APPENDIX E
COLUMNS AND OTHER COMPRESSION MEMBERS
E3. DESIGN COMPRESSIVE STRENGTH FOR
FLEXURAL-TORSIONAL BUCKLING
The equations in Appendix E3 for determining the flexural-torsional elastic
buckling loads of columns are derived in texts on structural stability (Timoshenko and Gere (1961), Bleich (1952), Galambos (1968), and Chen and
Atsuta (1977), for example). Since these equations for flexural-torsional buckling apply only to elastic buckling, they must be modified for inelastic buckling
when Fcr > 0.5Fy. This is accomplished through the use of the equivalent slenderFy / Fe .
√
ness factor λe =
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
6 - 246
APPENDIX F
BEAMS AND OTHER FLEXURAL MEMBERS
F1.
DESIGN FOR FLEXURE
Three limit states must be investigated to determine the moment capacity of
flexural members: lateral-torsional buckling (LTB), local buckling of the compression flange (FLB), and local buckling of the web (WLB). These limit states
depend, respectively, on the beam slenderness ratio Lb / ry, the width-thickness
ratio b / t of the compression flange and the width-thickness ratio h / tw of the
web. For convenience, all three measures of slenderness are denoted by λ.
Variations in Mn with Lb are shown in Figure C-A-F1.1. The discussion of plastic,
inelastic, and elastic buckling in Commentary Section F1 with reference to
lateral-torsional buckling applies here except for an important difference in the
significance of λp for lateral-torsional buckling and local buckling. Values of
λp for FLB and WLB produce a compact section with a rotation capacity of about
three (after reaching Mp) before the onset of local buckling, and therefore meet
the requirements for plastic analysis of load effects (Commentary Section B5).
On the other hand, values of λp for LTB do not allow plastic analysis because
they do not provide rotation capacity beyond that needed to develop Mp. Instead
Lb ≤ Lpd (Section F1.2d) must be satisfied.
Analyses to include restraint effects of adjoining elements are discussed in
Galambos (1988). Analysis of the lateral stability of members with shapes not
covered in this appendix must be performed according to the available literature
(Galambos, 1988).
bT1
b
bT2
T
IT
IT 2
IT
1
IO
IB
l
IB1
IO
l
bB2
bB1
bB
IB2
bI
GT = l T O
IT
GT =
I O bT
l IT
bI
GB = l B O
IB
GB =
I O bB
l IB
Figure C-A-F1.1
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
Sect. C-A-F3]
WEB-TAPERED MEMBERS
6 - 247
See the Commentary for Section B5 for the discussion of the equation regarding
the bending capacity of circular sections.
F3.
WEB-TAPERED MEMBERS
1.
General Requirements
The provision contained in Appendix F3 covers only those aspects of the design
of tapered members that are unique to tapered members. For other criteria of
design not specifically covered in Appendix F3, see the appropriate portions of
this Specification and Commentary.
The design of wide-flange columns with a single web taper and constant flanges
follows the same procedure as for uniform columns according to Section E2,
except the column slenderness parameter λc for major axis buckling is determined for a slenderness ratio Kγ L / rox, and for minor axis buckling for KL / roy,
where Kγ is an effective length factor for tapered members, K is the effective
length factor for prismatic members, and rox and roy are the radii of gyration about
the x and the y axes, respectively, taken at the smaller end of the tapered member.
For stepped columns or columns with other than a single web taper, the elastic
critical stress is determined by analysis or from data in reference texts or research
reports (Chapters 11 and 13 in Timoshenko and Gere (1961) and Bleich (1952)
and Kitipornchai and Trahair [1980], and then the same procedure of using λeff
is utilized in calculating the factored resistance.
This same approach is recommended for open section built-up columns (columns with perforated cover plates, lacing, and battens) where the elastic critical
buckling stress determination must include a reduction for the effect of shear.
Methods for calculating the elastic buckling strength of such columns are given
in Chapter 12 of the SSRC Guide (Galambos, 1988) and in Timoshenko and
Gere (1961) and Bleich (1952).
3.
Design Compressive Strength
The approach in formulating Faγ of tapered columns is based on the concept that
the critical stress for an axially loaded tapered column is equal to that of a
prismatic column of different length, but of the same cross section as the smaller
end of the tapered column. This has resulted in an equivalent effective length
factor Kγ for a tapered member subjected to axial compression (Lee et al., 1972).
This factor, which is used to determine the value of S in Equations A-F3-2 and
λc in Equation E2-3, can be determined accurately for a symmetrical rectangular
rigid frame comprised of prismatic beams and tapered columns.
With modifying assumptions, such a frame can be used as a mathematical model
to determine with sufficient accuracy the influence of the stiffness Σ(I / b)g of
beams and rafters which afford restraint at the ends of a tapered column in other
cases such as those shown in Figure C-A-F1.1. From Equations A-F3-2 and
E2-3, the critical load Pcr can be expressed as π2EIo / (Kγl)2. The value of Kγ can
be obtained by interpolation, using the appropriate chart from Lee et al. (1972)
and restraint modifiers GT and GB. In each of these modifiers the tapered column,
treated as a prismatic member having a moment of inertia Io, computed at the
smaller end, and its actual length l, is assigned the stiffness Io / l, which is then
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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BEAMS AND OTHER FLEXURAL MEMBERS
[Comm. A-F
divided by the stiffness of the restraining members at the end of the tapered
column under consideration.
4.
Design Flexural Strength
The development of the design bending stress for tapered beams follows closely
with that for prismatic beams. The basic concept is to replace a tapered beam
by an equivalent prismatic beam with a different length, but with a cross section
identical to that of the smaller end of the tapered beam (Lee et al., 1972). This
has led to the modified length factors hs and hw in Equations A-F3-6 and A-F3-7.
Equations A-F3-6 and A-F3-7 are based on total resistance to lateral buckling,
using both St. Venant and warping resistance. The factor B modifies the basic
Fbγ to members which are continuous past lateral supports. Categories a, b, and
c of Appendix F3.4 usually apply; however, it is to be noted that they apply only
when the axial force is small and adjacent unbraced segments are approximately
equal in length. For a single member, or segments which do not fall into category
a, b, c, or d, the recommended value of B is unity. The value of B should also be
taken as unity when computing the value of Fbγ to obtain Mn to be used in
Equations H1-1 and C1-1, since the effect of moment gradient is provided for
by the factor Cm. The background material is given in WRC Bulletin No. 192
(Morrell and Lee, 1974).
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
6 - 249
APPENDIX G
PLATE GIRDERS
Appendix G is taken from AISI Bulletin 27 (Galambos, 1978). Comparable
provisions are included in the AISC ASD Specification. The provisions are
presented in an appendix as they are seldom used and produce designs which
are often less economical than plate girders designed without tension-field
action.
Fyf that distinguishes plate girders
The web slenderness ratio h / tw = 970 / √
from beams is written in terms of the flange yield stress, because for hybrid
girders inelastic buckling of the web due to bending depends on the flange strain.
The equation for Re used in the 1986 LRFD Specification was the same as that
used in the AASHTO Standard Specification for Highway Bridges. In this
edition, the equation for Re, used in the AISC ASD Specification since 1969, is
used because its derivation is published (Gaylord and Gaylord, 1992 and
ASCE-AASHTO, 1968) and it is more accurate than the AASHTO equation.
G2. DESIGN FLEXURAL STRENGTH
In previous versions of the AISC Specification a coefficient of 0.0005ar was
used in RPG based on the work of Basler (1961). This value is valid for ar ≤ 2.
In that same paper, Basler developed a more general coefficient, applicable to
all ratios of Aw / Af which has now been adopted because application of the
previous equation to sections with large ar values gives unreasonable results. An
arbitrary limit of ar ≤ 10 is imposed so that the RPG expression is not applied to
sections approaching a tee shape.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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APPENDIX H
MEMBERS UNDER COMBINED FORCES AND TORSION
H3. ALTERNATIVE INTERACTION EQUATIONS FOR MEMBERS
UNDER COMBINED STRESS
In the case of members not subject to flexural buckling, i.e., Lb < Lpd, the use of
somewhat more liberal interaction Equations A-H3-5 and A-H3-6 is acceptable
as an alternative when the flexure is about one axis only.
The alternative interaction Equations A-H3-1 and A-H3-2 for biaxially loaded H
and wide-flange column shapes were taken from Galambos (1988), Springfield
(1975), and Tebedge and Chen (1974).
For I-shaped members with bf / d > 1.0, use of Section H1 is recommended,
because no additional research is available for this case.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
6 - 251
APPENDIX J
CONNECTIONS, JOINTS, AND FASTENERS
J2.
WELDS
4.
Design Strength
When weld groups are loaded in shear by an external load that does not act
through the center of gravity of the group, the load is eccentric and will tend to
cause a relative rotation and translation between the parts connected by the weld.
The point about which rotation tends to take place is called the instantaneous
center of rotation. Its location is dependent upon the load eccentricity, geometry
of the weld group, and deformation of the weld at different angles of the resultant
elemental force relative to the weld axis.
The individual resistance force of each unit weld element can be assumed to act
on a line perpendicular to a ray passing through the instantaneous center and
that element’s location (see Figure C-A-J2.1).
The ultimate shear strength of weld groups can be obtained from the load
deformation relationship of a single-unit weld element. This relationship was
originally given by Butler (1972) for E60 electrodes. Curves for E70 electrodes
used in the Appendix were obtained by Lesik (1990).
Unlike the load-deformation relationship for bolts, strength and deformation
performance in welds are dependent on the angle θ that the resultant elemental
force makes with the axis of the weld element (see Figure C-A-J2.1). The actual
load deformation relationship for welds is given in Figure C-A-J2.2, taken from
Kennedy and Lesik (1990). Conversion of the SI equation to foot-pound units
results in the following weld strength equation for Rn:
Rn = 0.852(1.0 + 0.50 sin1.5θ)FEXX Aw
Because the maximum strength is limited to 0.60FEXX for longitudinally loaded
welds (θ = 0º), the LRFD Specification provision provides, in the reduced
equation coefficient, a reasonable margin for any variation in welding techniques and procedures. To eliminate possible computational difficulties, the
maximum deformation in the weld elements is limited to 0.17D. For design
convenience, a simple elliptical formula is used for f(p) to closely approximate
the empirically derived polynomial in Lesik (1990).
The total resistance of all the weld elements combine to resist the eccentric
ultimate load, and when the correct location of the instantaneous center has been
selected, the three in-plane equations of statics (ΣFx , ΣFy , ΣM) will be satisfied.
Numerical techniques, such as those given by Brandt (1982), have been develAMERICAN INSTITUTE OF STEEL CONSTRUCTION
6 - 252
CONNECTIONS, JOINTS, AND FASTENERS
[Comm. A-J
oped to locate the instantaneous center of rotation subject to convergence
tolerances.
Earlier editions of the AISC Manual of Steel Construction (AISC, 1980, 1986,
1989) took advantage of the inelastic redistribution of stresses that is inherent
in the Appendix J2.4 procedure. However, in each of the utilized computational
techniques the resulting coefficients were factored down so that the maximum
A
Y
ro
al
xl
R
P
θ
l
c.g.
i.c.
X
R
θ
kl
Figure C-A-J2.1
1.6
90°
75°
60°
1.4
45°
1.2
30°
P/
Po
1.0
15°
0.8
θ = 0°
0.6
0.4
0.2
0
0.05
0.10
0.15
0.20
0.25
0.30
∆/
D
Figure C-A-J2.2
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
0.35
0.40
Sect. C-A-J2]
WELDS
6 - 253
stress, at any point in the weld group, did not exceed the limiting value specified
by either the Allowable Stress Design or LRFD Specifications, 0.3Fu or 0.6Fu,
respectively. As a result, the tabulated weld-capacity data shown in the appropriate referenced manual tables will be found to be conservative relative to the
data obtained using the computational procedure presented in Appendix J2.4.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
6 - 254
APPENDIX K
CONCENTRATED FORCES, PONDING, AND FATIGUE
K3. FATIGUE
Because most members in building frames are not subject to a large enough
number of cycles of full design stress application to require design for fatigue,
the provisions covering such designs have been placed in Appendix K3.
When fatigue is a design consideration, its severity is most significantly affected
by the number of load applications, the magnitude of the stress range, and the
severity of the stress concentrations associated with the particular details. These
factors are not encountered in normal building designs; however, when encountered and when fatigue is of concern, all provisions of Appendix K3 must be
satisfied.
Members or connections subject to less than 20,000 cycles of loading will not
involve a fatigue condition, except in the case of repeated loading involving
large ranges of stress. For such conditions, the admissible range of stress can
conservatively be taken as one and one-half times the applicable value given in
Table A-K3.3 for “Loading Condition 1.”
Fluctuation in stress which does not involve tensile stress does not cause crack
propagation and is not considered to be a fatigue situation. On the other hand,
in elements of members subject solely to calculated compression stress, fatigue
cracks may initiate in regions of high tensile residual stress. In such situations,
the cracks generally do not propagate beyond the region of the residual tensile
stress, because the residual stress is relieved by the crack. For this reason stress
ranges that are completely in compression are not included in the column headed
by “Kind of Stress” in Table A-K3.2. This is also true of comparable tables of
the current AASHTO and AREA specifications.
When fabrication details involving more than one category occur at the same
location in a member, the stress range at that location must be limited to that of
the most restrictive category. By locating notch-producing fabrication details in
regions subject to a small range of stress, the need for a member larger than
required by static loading will often be eliminated.
Extensive test programs (Fisher et al., 1970; and Fisher et al., 1974) using full
size specimens, substantiated by theoretical stress analysis, have confirmed the
following general conclusions:
(1) Stress range and notch severity are the dominant stress variables for welded
details and beams.
(2) Other variables such as minimum stress, mean stress, and maximum stress
are not significant for design purposes.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
Sect. C-A-K3]
FATIGUE
6 - 255
(3) Structural steels with yield points of 36 to 100 ksi do not exhibit significantly
different fatigue strength for given welded details fabricated in the same
manner.
Allowable stress ranges can be read directly from Table A-K3.3 for a particular
category and loading condition. The values are based on extensive research
(Keating and Fisher, 1985).
Provisions for bolts subjected to tension are given in Table A-K3.4. Tests have
uncovered dramatic differences in fatigue life, not completely predictable from
the various published equations for estimating the actual magnitude of prying
force (Kulak et al., 1987). To limit the uncertainties regarding prying action on
the fatigue behavior of these bolts, the tensile stresses given in Table J3.2 are
approved for use under extended cyclic loading only if the prying force, included
in the design tensile force, is small. When this cannot be assured, the design
tensile stress is drastically reduced to cover any conceivable prying effect.
The use of other types of mechanical fasteners to resist applied cyclic loading
in tension is not recommended. Lacking a high degree of assured pretension,
the range of stress is generally too great to resist such loading for long.
However, all types of mechanical fasteners survive unharmed when subject to
cyclic shear stresses sufficient to fracture the connected parts, which is provided
for elsewhere in Appendix K3.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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AMERICAN INSTITUTE OF STEEL CONSTRUCTION
6 - 257
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Glossary
Alignment chart for columns. A nomograph for determining the effective length factor
K for some types of columns
Amplification factor. A multiplier of the value of moment or deflection in the unbraced
length of an axially loaded member to reflect the secondary values generated by
the eccentricity of the applied axial load within the member
Aspect ratio. In any rectangular configuration, the ratio of the lengths of the sides
Batten plate. A plate element used to join two parallel components of a built-up
column, girder, or strut rigidly connected to the parallel components and designed
to transmit shear between them
Beam. A structural member whose primary function is to carry loads transverse to its
longitudinal axis
Beam-column. A structural member whose primary function is to carry loads both
transverse and parallel to its longitudinal axis
Bent. A plane framework of beam or truss members which support loads and the
columns which support these members
Biaxial bending. Simultaneous bending of a member about two perpendicular axes
Bifurcation. The phenomenon whereby a perfectly straight member under compression may either assume a deflected position or may remain undeflected, or a beam
under flexure may either deflect and twist out of plane or remain in its in-plane
deflected position
Braced frame. A frame in which the resistance to lateral load or frame instability is
primarily provided by a diagonal, a K brace, or other auxiliary system of bracing
Brittle fracture. Abrupt cleavage with little or no prior ductile deformation
Buckling load. The load at which a perfectly straight member under compression
assumes a deflected position
Built-up member. A member made of structural metal elements that are welded, bolted,
or riveted together
Cladding. The exterior covering of the structural components of a building
Cold-formed members. Structural members formed from steel without the application
of heat
Column. A structural member whose primary function is to carry loads parallel to its
longitudinal axis
Column curve. A curve expressing the relationship between an axial column strength
and slenderness ratio
Combined mechanism. A mechanism determined by plastic analysis procedure which
combines elementary beam, panel, and joint mechanisms
Compact section. Compact sections are capable of developing a fully plastic stress
distribution and possess rotation capacity of approximately three before the onset
of local buckling
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GLOSSARY
Composite beam. A steel beam structurally connected to a concrete slab so that the
beam and slab respond to loads as a unit. See also Concrete-encased beam
Concrete-encased beam. A beam totally encased in concrete cast integrally with the
slab
Connection. Combination of joints used to transmit forces between two or more
members. Categorized by the type and amount of force transferred (moment,
shear, end reaction). See also Splices
Critical load. The load at which bifurcation occurs as determined by a theoretical
stability analysis
Curvature. The rotation per unit length due to bending
Design documents. See Structural design documents
Design strength. Resistance (force, moment, stress, as appropriate) provided by
element or connection; the product of the nominal strength and the resistance
factor
Diagonal bracing. Inclined structural members carrying primarily axial load employed to enable a structural frame to act as a truss to resist horizontal loads
Diaphragm. Floor slab, metal wall, or roof panel possessing a large in-plane shear
stiffness and strength adequate to transmit horizontal forces to resisting systems
Diaphragm action. The in-plane action of a floor system (also roofs and walls) such
that all columns framing into the floor from above and below are maintained in
their same position relative to each other
Double concentrated forces. Two equal and opposite forces which form a couple on
the same side of the loaded member
Double curvature. A bending condition in which end moments on a member cause the
member to assume an S shape
Drift. Lateral deflection of a building
Drift index. The ratio of lateral deflection to the height of the building
Ductility factor. The ratio of the total deformation at maximum load to the elastic-limit
deformation
Effective length. The equivalent length KL used in compression formulas and determined by a bifurcation analysis
Effective length factor K. The ratio between the effective length and the unbraced
length of the member measured between the centers of gravity of the bracing
members
Effective moment of inertia. The moment of inertia of the cross section of a member
that remains elastic when partial plastification of the cross section takes place,
usually under the combination of residual stress and applied stress. Also, the
moment of inertia based on effective widths of elements that buckle locally. Also,
the moment of inertia used in the design of partially composite members
Effective stiffness. The stiffness of a member computed using the effective moment of
inertia of its cross section
Effective width. The reduced width of a plate or slab which, with an assumed uniform
stress distribution, produces the same effect on the behavior of a structural
member as the actual plate width with its nonuniform stress distribution
Elastic analysis. Determination of load effects (force, moment, stress, as appropriate)
on members and connections based on the assumption that material deformation
disappears on removal of the force that produced it
Elastic-perfectly plastic. A material which has an idealized stress-strain curve that
varies linearly from the point of zero strain and zero stress up to the yield point
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
GLOSSARY
6 - 269
of the material, and then increases in strain at the value of the yield stress without
any further increases in stress
Embedment. A steel component cast in a concrete structure which is used to transmit
externally applied loads to the concrete structure by means of bearing, shear,
bond, friction, or any combination thereof. The embedment may be fabricated of
structural-steel plates, shapes, bars, bolts, pipe, studs, concrete reinforcing bars,
shear connectors, or any combination thereof
Encased steel structure. A steel-framed structure in which all of the individual frame
members are completely encased in cast-in-place concrete
Euler formula. The mathematical relationship expressing the value of the Euler load
in terms of the modulus of elasticity, the moment of inertia of the cross section,
and the length of a column
Euler load. The critical load of a perfectly straight, centrally loaded pin-ended column
Eyebar. A particular type of pin-connected tension member of uniform thickness with
forged or flame cut head of greater width than the body proportioned to provide
approximately equal strength in the head and body
Factored load. The product of the nominal load and a load factor
Fastener. Generic term for welds, bolts, rivets, or other connecting device
Fatigue. A fracture phenomenon resulting from a fluctuating stress cycle
First-order analysis. Analysis based on first-order deformations in which equilibrium
conditions are formulated on the undeformed structure
Flame-cut plate. A plate in which the longitudinal edges have been prepared by oxygen
cutting from a larger plate
Flat width. For a rectangular tube, the nominal width minus twice the outside corner
radius. In absence of knowledge of the corner radius, the flat width may be taken
as the total section width minus three times the thickness
Flexible connection. A connection permitting a portion, but not all, of the simple beam
rotation of a member end
Floor system. The system of structural components separating the stories of a building
Force. Resultant of distribution of stress over a prescribed area. A reaction that
develops in a member as a result of load (formerly called total stress or stress).
Generic term signifying axial loads, bending moment, torques, and shears
Fracture toughness. Measurement of the ability to absorb energy without fracture.
Generally determined by impact loading of specimens containing a notch having
a prescribed geometry
Frame buckling. A condition under which bifurcation may occur in a frame
Frame instability. A condition under which a frame deforms with increasing lateral
deflection under a system of increasing applied monotonic loads until a maximum value of the load called the stability limit is reached, after which the frame
will continue to deflect without further increase in load
Fully composite beam. A composite beam with sufficient shear connectors to develop
the full flexural strength of the composite section
High-cycle fatigue. Failure resulting from more than 20,000 applications of cyclic
stress
Hybrid beam. A fabricated steel beam composed of flanges with a greater yield
strength than that of the web. Whenever the maximum flange stress is less than
or equal to the web yield stress the girder is considered homogeneous
Hysteresis loop. A plot of force versus displacement of a structure or member subjected
to reversed, repeated load into the inelastic range, in which the path followed
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GLOSSARY
during release and removal of load is different from the path for the addition of
load over the same range of displacement
Inclusions. Nonmetallic material entrapped in otherwise sound metal
Incomplete fusion. Lack of union by melting of filler and base metal over entire
prescribed area
Inelastic action. Material deformation that does not disappear on removal of the force
that produced it
Instability. A condition reached in the loading of an element or structure in which
continued deformation results in a decrease of load-resisting capacity
Joint. Area where two or more ends, surfaces, or edges are attached. Categorized by
type of fastener or weld used and method of force transfer
K bracing. A system of struts used in a braced frame in which the pattern of the struts
resembles the letter K, either normal or on its side
Lamellar tearing. Separation in highly restrained base metal caused by through-thickness strains induced by shrinkage of adjacent weld metal
Lateral bracing member. A member utilized individually or as a component of a lateral
bracing system to prevent buckling of members or elements and/or to resist lateral
loads
Lateral (or lateral-torsional) buckling. Buckling of a member involving lateral
deflection and twist
Leaning column. Gravity-loaded column where connections to the frame (simple
connections) do not provide resistance to lateral loads
Limit state. A condition in which a structure or component becomes unfit for service
and is judged either to be no longer useful for its intended function (serviceability
limit state) or to be unsafe (strength limit state)
Limit states. Limits of structural usefulness, such as brittle fracture, plastic collapse,
excessive deformation, durability, fatigue, instability, and serviceability
Load factor. A factor that accounts for unavoidable deviations of the actual load from
the nominal value and for uncertainties in the analysis that transforms the load
into a load effect
Loads. Forces or other actions that arise on structural systems from the weight of all
permanent construction, occupants and their possessions, environmental effects,
differential settlement, and restrained dimensional changes. Permanent loads are
those loads in which variations in time are rare or of small magnitude. All other
loads are variable loads. See Nominal loads
LRFD (Load and Resistance Factor Design). A method of proportioning structural
components (members, connectors, connecting elements, and assemblages) such
that no applicable limit state is exceeded when the structure is subjected to all
appropriate load combinations
Local buckling. The buckling of a compression element which may precipitate the
failure of the whole member
Low-cycle fatigue. Fracture resulting from a relatively high-stress range resulting in
a relatively small number of cycles to failure
Lower bound load. A load computed on the basis of an assumed equilibrium moment
diagram in which the moments are not greater than Mp that is less than or at best
equal to the true ultimate load
Mechanism. An articulated system able to deform without an increase in load, used in
the special sense that the linkage may include real hinges or plastic hinges, or
both
Mechanism method. A method of plastic analysis in which equilibrium between
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
GLOSSARY
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external forces and internal plastic hinges is calculated on the basis of an assumed
mechanism. The failure load so determined is an upper bound
Nominal loads. The magnitudes of the loads specified by the applicable code
Nominal strength. The capacity of a structure or component to resist the effects of
loads, as determined by computations using specified material strengths and
dimensions and formulas derived from accepted principles of structural mechanics or by field tests or laboratory tests of scaled models, allowing for modeling
effects and differences between laboratory and field conditions
Noncompact section. Noncompact sections can develop the yield stress in compression elements before local buckling occurs, but will not resist inelastic local
buckling at strain levels required for a fully plastic stress distribution
P-Delta effect. Secondary effect of column axial loads and lateral deflection on the
moments in members
Panel zone. The zone in a beam-to-column connection that transmits moment by a
shear panel
Partially composite beam. A composite beam for which the shear strength of shear
connectors governs the flexural strength
Plane frame. A structural system assumed for the purpose of analysis and design to be
two-dimensional
Plastic analysis. Determination of load effects (force, moment, stress, as appropriate)
on members and connections based on the assumption of rigid-plastic behavior,
i.e., that equilibrium is satisfied throughout the structure and yield is not exceeded
anywhere. Second order effects may need to be considered
Plastic design section. The cross section of a member which can maintain a full plastic
moment through large rotations so that a mechanism can develop; the section
suitable for plastic design
Plastic hinge. A yielded zone which forms in a structural member when the plastic
moment is attained. The beam is assumed to rotate as if hinged, except that it is
restrained by the plastic moment Mp
Plastic-limit load. The maximum load that is attained when a sufficient number of
yield zones have formed to permit the structure to deform plastically without
further increase in load. It is the largest load a structure will support, when perfect
plasticity is assumed and when such factors as instability, second-order effects,
strain hardening, and fracture are neglected
Plastic mechanism. See Mechanism
Plastic modulus. The section modules of resistance to bending of a completely yielded
cross section. It is the combined static moment about the neutral axis of the
cross-sectional areas above and below that axis
Plastic moment. The resisting moment of a fully yielded cross section
Plastic strain. The difference between total strain and elastic strain
Plastic zone. The yielded region of a member
Plastification. The process of successive yielding of fibers in the cross section of a
member as bending moment is increased
Plate girder. A built-up structural beam
Post-buckling strength. The load that can be carried by an element, member, or frame
after buckling
Primary stress. A primary stress is any normal stress or shear stress developed by an
imposed loading which is necessary to satisfy the laws of equilibrium of external
and internal forces, moments, and torques. A primary stress is not self-limiting.
Redistribution of moment. A process which results in the successive formation of
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GLOSSARY
plastic hinges so that less highly stressed portions of a structure may carry
increased moments
Required strength. Load effect (force, moment, stress, as appropriate) acting on
element or connection determined by structural analysis from the factored loads
(using most appropriate critical load combinations)
Residual stress. The stresses that remain in an unloaded member after it has been
formed into a finished product. (Examples of such stresses include, but are not
limited to, those induced by cold bending, cooling after rolling, or welding.)
Resistance. The capacity of a structure or component to resist the effects of loads. It
is determined by computations using specified material strengths, dimensions
and formulas derived from accepted principles of structural mechanics, or by
field tests or laboratory tests of scaled models, allowing for modeling effects and
differences between laboratory and field conditions. Resistance is a generic term
that includes both strength and serviceability limit states
Resistance factor. A factor that accounts for unavoidable deviations of the actual
strength from the nominal value and the manner and consequences of failure
Rigid frame. A structure in which connections maintain the angular relationship
between beam and column members under load
Root of the flange. Location on the web of the corner radius termination point or the
toe of the flange-to-web weld. Measured as the k distance from the far side of the
flange
Rotation capacity. The incremental angular rotation that a given shape can accept prior
to local failure defined as R = (θu / θp) − 1 where θu is the overall rotation attained
at the factored load state and θp is the idealized rotation corresponding to elastic
theory applied to the case of M = Mp
St. Venant torsion. That portion of the torsion in a member that induces only shear
stresses in the member
Second-order analysis. Analysis based on second-order deformations, in which equilibrium conditions are formulated on the deformed structure
Service load. Load expected to be supported by the structure under normal usage;
often taken as the nominal load
Serviceability limit state. Limiting condition affecting the ability of a structure to
preserve its appearance, maintainability, durability, or the comfort of its occupants or function of machinery under normal usage
Shape factor. The ratio of the plastic moment to the yield moment, or the ratio of the
plastic modulus to the section modulus for a cross section
Shear friction. Friction between the embedment and the concrete that transmits shear
loads. The relative displacement in the plane of the shear load is considered to
be resisted by shear-friction anchors located perpendicular to the plane of the
shear load
Shear lugs. Plates, welded studs, bolts, and other steel shapes that are embedded in
the concrete and located transverse to the direction of the shear force and that
transmit shear loads, introduced into the concrete by local bearing at the shear
lug-concrete interface
Shear wall. A wall that in its own plane resists shear forces resulting from applied
wind, earthquake, or other transverse loads or provides frame stability. Also
called a structural wall
Sidesway. The lateral movement of a structure under the action of lateral loads,
unsymmetrical vertical loads, or unsymmetrical properties of the structure
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Sidesway buckling. The buckling mode of a multistory frame precipitated by the
relative lateral displacements of joints, leading to failure by sidesway of the frame
Simple plastic theory. See Plastic design
Single curvature. A deformed shape of a member having one smooth continuous arc,
as opposed to double curvature which contains a reversal
Slender-element section. The cross section of a member which will experience local
buckling in the elastic range
Slenderness ratio. The ratio of the effective length of a column to the radius of gyration
of the column, both with respect to the same axis of bending
Slip-critical joint. A bolted joint in which the slip resistance of the connection is
required
Space frame. A three-dimensional structural framework (as contrasted to a plane
frame)
Splice. The connection between two structural elements joined at their ends to form a
single, longer element
Stability-limit load. Maximum (theoretical) load a structure can support when secondorder instability effects are included
Stepped column. A column with changes from one cross section to another occurring
at abrupt points within the length of the column
Stiffener. A member, usually an angle or plate, attached to a plate or web of a beam or
girder to distribute load, to transfer shear, or to prevent buckling of the member
to which it is attached
Stiffness. The resistance to deformation of a member or structure measured by the ratio
of the applied force to the corresponding displacement
Story drift. The difference in horizontal deflection at the top and bottom of a story
Strain hardening. Phenomenon wherein ductile steel, after undergoing considerable
deformation at or just above yield point, exhibits the capacity to resist substantially higher loading than that which caused initial yielding
Strain-hardening strain. For structural steels that have a flat (plastic) region in the
stress-strain relationship, the value of the strain at the onset of strain hardening
Strength design. A method of proportioning structural members using load factors and
resistance factors such that no applicable limit state is exceeded (also called load
and resistance factor design)
Strength limit state. Limiting condition affecting the safety of the structure, in which
the ultimate load-carrying capacity is reached
Stress. Force per unit area
Stress concentration. Localized stress considerably higher than average (even in
uniformly loaded cross sections of uniform thickness) due to abrupt changes in
geometry or localized loading
Strong axis. The major principal axis of a cross section
Structural design documents. Documents prepared by the designer (plans, design
details, and job specifications)
Structural system. An assemblage of load-carrying components which are joined
together to provide regular interaction or interdependence
Stub column. A short compression-test specimen, long enough for use in measuring
the stress-strain relationship for the complete cross section, but short enough to
avoid buckling as a column in the elastic and plastic ranges
Subassemblage. A truncated portion of a structural frame
Supported frame. A frame which depends upon adjacent braced or unbraced frames
for resistance to lateral load or frame instability. (This transfer of load is
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GLOSSARY
frequently provided by the floor or roof system through diaphragm action or by
horizontal cross bracing in the roof.)
Tangent modulus. At any given stress level, the slope of the stress-strain curve of a
material in the inelastic range as determined by the compression test of a small
specimen under controlled conditions
Temporary structure. A general term for anything that is built or constructed (usually
to carry construction loads) that will eventually be removed before or after
completion of construction and does not become part of the permanent structural
system
Tensile strength. The maximum tensile stress that a material is capable of sustaining
Tension field action. The behavior of a plate girder panel under shear force in which
diagonal tensile stresses develop in the web and compressive forces develop in
the transverse stiffeners in a manner analogous to a Pratt truss
Toe of the fillet. Termination point of fillet weld or of rolled section fillet
Torque-tension relationship. Term applied to the wrench torque required to produce
specified pre-tension in high-strength bolts
Turn-of-nut method. Procedure whereby the specified pre-tension in high-strength
bolts is controlled by rotation of the wrench a predetermined amount after the
nut has been tightened to a snug fit
Unbraced frame. A frame in which the resistance to lateral load is provided by the
bending resistance of frame members and their connections
Unbraced length. The distance between braced points of a member, measured between
the centers of gravity of the bracing members
Undercut. A notch resulting from the melting and removal of base metal at the edge
of a weld
Universal-mill plate. A plate in which the longitudinal edges have been formed by a
rolling process during manufacture. Often abbreviated as UM plate
Upper bound load. A load computed on the basis of an assumed mechanism which
will always be at best equal to or greater than the true ultimate load
Vertical bracing system. A system of shear walls, braced frames, or both, extending
through one or more floors of a building
Von Mises yield criterion. A theory which states that inelastic action at any point in a
body under any combination of stresses begins only when the strain energy of
distortion per unit volume absorbed at the point is equal to the strain energy of
distortion absorbed per unit volume at any point in a simple tensile bar stressed
to the elastic limit under a state of uniaxial stress. It is often called the maximum
strain-energy-of-distortion theory. Accordingly, shear yield occurs at 0.58 times
the yield strength
Warping torsion. That portion of the total resistance to torsion that is provided by
resistance to warping of the cross section
Weak axis. The minor principal axis of a cross section
Weathering steel. A type of high-strength, low-alloy steel which can be used in normal
environments (not marine) and outdoor exposures without protective paint
covering. This steel develops a tight adherent rust at a decreasing rate with respect
to time
Web buckling. The buckling of a web plate
Web crippling. The local failure of a web plate in the immediate vicinity of a
concentrated load or reaction
Working load. Also called service load. The actual load assumed to be acting on the
structure
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Yield moment. In a member subjected to bending, the moment at which an outer fiber
first attains the yield stress
Yield plateau. The portion of the stress-strain curve for uniaxial tension or compression
in which the stress remains essentially constant during a period of substantially
increased strain
Yield point. The first stress in a material at which an increase in strain occurs without
an increase in stress, the yield point less than the maximum attainable stress
Yield strength. The stress at which a material exhibits a specified limiting deviation
from the proportionality of stress to strain. Deviation expressed in terms of strain
Yield stress. Yield point, yield strength, or yield stress level as defined
Yield-stress level. The average stress during yielding in the plastic range, the stress
determined in a tension test when the strain reaches 0.005 in. per in.
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Specification for
Load and Resistance
Factor Design of
Single-Angle Members
December 1, 1993
AMERICAN INSTITUTE OF STEEL CONSTRUCTION, INC.
One East Wacker Drive, Suite 3100, Chicago, IL 60601-2001
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LRFD SPECIFICATION FOR DESIGN OF SINGLE-ANGLE MEMBERS
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
LRFD SPECIFICATION FOR DESIGN OF SINGLE-ANGLE MEMBERS
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PREFACE
The intention of the AISC Specification is to cover the common everyday design
criteria in routine design office usage. It is not feasible to also cover the many special
and unique problems encountered within the full range of structural design practice.
This separate Specification and Commentary addresses one such topic—single-angle
members—to provide needed design guidance for this more complex structural shape
under various load and support conditions.
The single-angle design criteria were developed through a consensus process by the
AISC Task Committee 116 on Single-Angle Members:
Donald R. Sherman, Chairman
Hansraj G. Ashar
Wai-Fah Chen
Raymond D. Ciatto
Mohamed Elgaaly
Theodore V. Galambos
Thomas G. Longlais
LeRoy A. Lutz
William A. Milek
Raymond H. R. Tide
Nestor R. Iwankiw, Secretary
The assistance of the Structural Stability Research Council Task Group on Single
Angles in the preparation and review of this document is acknowledged.
The full AISC Committee on Specifications has reviewed and endorsed this Specification.
A non-mandatory Commentary provides background for the Specification provisions
and the user is encouraged to consult it.
The principal changes in this edition include:
• establishing upper limit of single-angle flexural strength at 1.25 of the yield moment
• increasing resistance factor for compression to 0.90
• removing flexural-torsional buckling consideration for compression members
• considering the sense of flexural stresses in the combined force interaction check
The reader is cautioned that professional judgment must be exercised when data or
recommendations in this Specification are applied. The publication of the material
contained herein is not intended as a representation or warranty on the part of the American
Institute of Steel Construction, Inc.—or any other person named herein—that this information is suitable for general or particular use, or freedom from infringement of any patent
or patents. Anyone making use of this information assumes all liability arising from such
use. The design of structures is within the scope of expertise of a competent licensed
structural engineer, architect, or other licensed professional for the application of principles
to a particular structure.
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LRFD SPECIFICATION FOR DESIGN OF SINGLE-ANGLE MEMBERS
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Specification for
Load and Resistance
Factor Design of
Single-Angle Members
December 1, 1993
1.
SCOPE
This document contains Load and Resistance Factor Design (LRFD) criteria for
hot-rolled, single-angle members with equal and unequal legs in tension, shear,
compression, flexure, and for combined forces. It is intended to be compatible
with, and a supplement to, the 1993 AISC Specification for Structural Steel
Buildings—Load and Resistance Factor Design (AISC LRFD) and repeats
some common criteria for ease of reference. For design purposes, the conservative simplifications and approximations in the Specification provisions for
single angles are permitted to be refined through a more precise analysis. As an
alternative to this Specification, the 1989 AISC Specification for Allowable
Stress Design of Single-Angle Members is permitted.
The Specification for single-angle design supersedes any comparable but more
general requirements of the AISC LRFD. All other design, fabrication, and
erection provisions not directly covered by this document shall be in compliance
with the AISC LRFD. In the absence of a governing building code, the factored
load combinations in AISC LRFD Section A4 shall be used to determine the
required strength. For design of slender, cold-formed steel angles, the current
AISI LRFD Specification for the Design of Cold-Formed Steel Structural
Members is applicable.
2.
TENSION
The tensile design strength φtPn shall be the lower value obtained according to
the limit states of yielding, φt = 0.9, Pn = Fy Ag, and fracture, φt = 0.75, Pn = Fu Ae.
a. For members connected by bolting, the net area and effective net area shall
be determined from AISC LRFD Specification Sections B1 to B3 inclusive.
b. When the load is transmitted by longitudinal welds only or a combination of
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LRFD SPECIFICATION FOR DESIGN OF SINGLE-ANGLE MEMBERS
longitudinal and transverse welds through just one leg of the angle, the
effective net area Ae shall be:
Ae = AgU
(2-1)
where
Ag = gross area of member
_
x
U = 1 − ≤ 0.9
l
_
x = connection eccentricity
l = length of connection in the direction of loading
c. When a load is transmitted by transverse weld through just one leg of the
angle, Ae is the area of the connected leg and U = 1.
For members whose design is based on tension, the slenderness ratio l / r
preferably should not exceed 300. Members in which the design is dictated by
tension loading, but which may be subject to some compression under other load
conditions, need not satisfy the compression slenderness limits.
3.
SHEAR
For the limit state of yielding in shear, the shear stress, fuv, due to flexure and
torsion shall not exceed:
fuv ≤ φv0.6Fy
φv = 0.9
4.
(3-1)
COMPRESSION
The design strength of compression members shall be φcPn
where
φc = 0.90
Pn = AgFcr
a. For λc √
Q ≤ 1.5:
2
Fcr = Q (0.658Qλc) Fy
(4-1)
0.877
Fcr = 2 Fy
λc
(4-2)
b. For λc √
Q ≥ 1.5:
λc =
Kl
rπ
√
Fy
E
Fy = specified minimum yield stress of steel
Q = reduction factor for local buckling
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The reduction factor Q shall be:
when
b
≤ 0.446
t
√
E
:
Fy
Q = 1.0
when 0.446
√
√
E b
< < 0.910
Fy t
E
:
Fy
Q = 1.34 − 0.761
when
b
≥ 0.910
t
√
(4-3a)
b
t
√
Fy
E
(4-3b)
E
:
Fy
Q=
0.534E
b
Fy
t
b = full width of longest angle leg
t = thickness of angle
2
(4-3c)
For members whose design is based on compressive force, the largest effective
slenderness ratio preferably should not exceed 200.
5.
FLEXURE
The flexure design strengths of Section 5.1 shall be used as indicated in Sections
5.2 and 5.3
5.1. Flexural Design Strength
The flexural design strength shall be limited to the minimum value φbMn
determined from Sections 5.1.1, 5.1.2, and 5.1.3, as applicable, with φb = 0.9.
5.1.1. For the limit state of local buckling when the tip of an angle leg is in
compression:
when
b
≤ 0.382
t
√
E
:
Fy
Mn = 1.25Fy Sc
when 0.382
√
E b
< ≤ 0.446
Fy t
√
E
:
Fy
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LRFD SPECIFICATION FOR DESIGN OF SINGLE-ANGLE MEMBERS
b/t
Mn = Fy Sc 1.25 − 1.49
− 1
E
0.382
Fy
√
when
b
> 0.446
t
√
(5-1b)
E
:
Fy
Mn = QFy Sc
(5-1c)
where
b = full width of angle leg with tip in compression
Q = reduction factor per Equations 4-3a, b, and c
Sc = elastic section modulus to the tip in compression relative to
axis of bending
E = modulus of elasticity
5.1.2. For the limit state of yielding when the tip of an angle leg is in tension
Mn = 1.25My
(5-2)
where
My = yield moment about the axis of bending
5.1.3. For the limit state of lateral-torsional buckling:
when Mob ≤ My :
Mn = [0.92 − 0.17Mob / My]Mob
(5-3a)
when Mob > My :
My / Mob ]My ≤ 1.25My
Mn = [1.58 − 0.83 √
(5-3b)
where
Mob = elastic lateral-torsional buckling moment, from Section 5.2 or
5.3 as applicable
5.2. Bending about Geometric Axes
5.2.1. a. Angle bending members with lateral-torsion restraint along the
length shall be designed on the basis of geometric axis bending with
the nominal flexural strength Mn limited to the provisions of Sections 5.1.1 and 5.1.2.
b. For equal-leg angles if the lateral-torsional restraint is only at the
point of maximum moment, the required moment shall be limited to
φbMn per Section 5.1. My shall be computed using the geometric axis
section modulus and Mob shall be substituted by using 1.25 times
Mob computed from Equation 5-4.
5.2.2. Equal-leg angle members without lateral-torsional restraint subjected to
flexure applied about one of the geometric axes are permitted to be
designed considering only geometric axis bending provided:
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a. The yield moment shall be based on use of 0.80 of the geometric axis
section modulus.
b. For the angle-leg tips in compression, the nominal flexural strength
Mn shall be determined by the provisions in Section 5.1.1 and in
Section 5.1.3,
where
Mob =
0.66Eb4tCb
[√
1 + 0.78(lt / b2)2 − 1]
l2
(5-4)
l = unbraced length
12.5Mmax
≤ 1.5
Cb =
2.5Mmax + 3MA + 4MB + 3MC
where
Mmax = absolute value of maximum moment in the unbraced beam
segment
MA = absolute value of moment at quarter point of the unbraced
beam segment
MB = absolute value of moment at centerline of the unbraced beam
segment
MC = absolute value of moment at three-quarter point of the
unbraced beam segment
c. For the angle-leg tips in tension, the nominal flexural strength
shall be determined according to Section 5.1.2.
5.2.3. Unequal-leg angle members without lateral-torsional restraint subjected
to bending about one of the geometric axes shall be designed using
Section 5.3.
5.3. Bending about Principal Axes
Angles without lateral-torsional restraint shall be designed considering principal-axis bending, except for the alternative of Section 5.2.2, if appropriate.
Bending about both of the principal axes shall be evaluated as required in
Section 6.
5.3.1. Equal-leg angles:
a. Major-axis bending:
The nominal flexural strength Mn about the major principal axis shall
be determined by the provisions in Section 5.1.1 and in Section 5.1.3,
where
Mob = Cb
0.46Eb2t2
l
(5-5)
b. Minor-axis bending:
The nominal design strength Mn about the minor principal axis shall
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be determined by Section 5.1.1 when the leg tips are in compression,
and by Section 5.1.2 when the leg tips are in tension.
5.3.2. Unequal-leg angles:
a. Major-axis bending:
The nominal flexural strength Mn about the major principal axis shall
be determined by the provisions in Section 5.1.1 for the compression
leg and in Section 5.1.3,
where
Mob = 4.9E
Iz
Cb [√
β2w + 0.052(lt / rz)2 + βw]
l2
(5-6)
Iz = minor principal axis moment of inertia
rz = radius of gyration for minor principal axis
1
βw = ∫ z(w2 + z2)dA − 2zo, special section property for
Iw A
unequal-leg angles, positive for short leg in compression
and negative for long leg in compression (see Commentary for values for common angle sizes). If the long leg is in
compression anywhere along the unbraced length of the
member, the negative value of βw shall be used.
zo = coordinate along z axis of the shear center with respect to
centroid
Iw = moment of inertia for major principal axis
b. Minor-axis bending:
The nominal design strength Mn about the minor principal axis shall
be determined by Section 5.1.1 when leg tips are in compression and
by Section 5.1.2 when the leg tips are in tension.
6.
COMBINED FORCES
The interaction equation shall be evaluated for the principal bending axes either
by addition of all the maximum axial and flexural terms, or by considering the
sense of the associated flexural stresses at the critical points of the cross section,
the flexural terms are either added to or subtracted from the axial load term.
6.1. Members in Flexure and Axial Compression
6.1.1. The interaction of flexure and axial compression applicable to specific
locations on the cross section shall be limited by Equations 6-1a
and 6-1b:
For
Pu
≥ 0.2
φPn
Muz
Pu 8 Muw
φP + 9 φ M + φ M ≤ 1.0
b nz
b nw
n
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
(6-1a)
LRFD SPECIFICATION FOR DESIGN OF SINGLE-ANGLE MEMBERS
For
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Pu
≤ 0.2
φPn
Muw
Muz
Pu
(6-1b)
2φP + φ M + φ M ≤ 1.0
b nz
n b nw
Pu = required compressive strength
Pn = nominal compressive strength determined in accordance with
Section 4
Mu = required flexural strength
Mn = nominal flexural strength for tension or compression in accordance with Section 5, as appropriate. Use section modulus for
specific location in the cross section and consider the type of
stress.
φ = φc = resistance factor for compression = 0.90
φb = resistance factor for flexure = 0.90
w = subscript relating symbol to major-axis bending
z = subscript relating symbol to minor-axis bending
In Equations 6-1a and 6-1b when Mn represents the flexural strength of
the compression side, the corresponding Mu shall be multiplied by B1.
B1 =
Cm
≥ 1.0
Pu
1−
Pe1
(6-2)
Cm = bending coefficient defined in AISC LRFD
Pe1 = elastic buckling load for the braced frame defined in AISC
LRFD
6.1.2. For members constrained to bend about a geometric axis with nominal
flexural strength determined per Section 5.2.1, the radius of gyration r
for Pe1 shall be taken as the geometric axis value. The bending terms for
the principal axes in Equations 6-1a and 6-1b shall be replaced by a
single geometric axis term.
6.1.3. Alternatively, for equal-leg angles without lateral-torsional restraint
along the length and with bending applied about one of the geometric
axes, the provisions of Section 5.2.2 are permitted for the required and
design bending strength. If Section 5.2.2 is used for Mn, the radius of
gyration about the axis of bending r for Pe1 shall be taken as the geometric
axis value of r divided by 1.35 in the absence of a more detailed analysis.
The bending terms for the principal axes in Equations 6-1a and 6-1b shall
be replaced by a single geometric axis term.
6.2. Members in Flexure and Axial Tension
The interaction of flexure and axial tension shall be limited by Equations 6-1a
and 6-1b where
Pu = required tensile strength
Pn = nominal tensile strength determined in accordance with Section 2
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LRFD SPECIFICATION FOR DESIGN OF SINGLE-ANGLE MEMBERS
Mu = required flexural strength
Mn = nominal flexural strength for tension or compression in accordance
with Section 5, as appropriate. Use section modulus for specific location in the cross section and consider the type of stress.
φ = φt = resistance factor for tension = 0.90
φb = resistance factor for flexure = 0.90
For members subject to bending about a geometric axis, the required bending
strength evaluation shall be in accordance with Sections 6.1.2 and 6.1.3.
Second-order effects due to axial tension and bending interaction are permitted
to be considered in the determination of Mu for use in Formulas 6-1a and 6-1b.
In lieu of using Formulas 6-1a and 6-1b, a more detailed analysis of the
interaction of flexure and tension is permitted.
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Commentary on the
Specification for Load and
Resistance Factor Design of
Single-Angle Members
December 1, 1993
INTRODUCTION
This Specification is intended to be complete for normal design usage in conjunction
with the main 1993 AISC LRFD Specification and Commentary.
This Commentary furnishes background information and references for the benefit of the
engineer seeking further understanding of the derivation and limits of the specification.
The Specification and Commentary are intended for use by design professionals with
demonstrated engineering competence.
C2. TENSION
The criteria for the design of tension members in AISC LRFD Specification
Section D1 have been adopted for angles with bolted connections. However,
recognizing the effect of shear lag when the connection is welded, the criteria
in Section B3 of the AISC LRFD Specification have been applied.
The advisory upper slenderness limits are not due to strength considerations but
are based on professional judgment and practical considerations of economics,
ease of handling, and transportability. The radius of gyration about the z axis
will produce the maximum l / r and, except for very unusual support conditions,
the maximum Kl / r. Since the advisory slenderness limit for compression
members is less than for tension members, an accommodation has been made
for members with Kl / r > 200 that are always in tension, except for unusual load
conditions which produce a small compression force.
C3. SHEAR
Shear stress due to factored loads in a single-angle member are the result of the
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COMMENTARY
gradient in the bending moment along the length (flexural shear) and the
torsional moment.
The maximum elastic stress due to flexural shear may be computed by
fv =
1.5Vb
bt
(C3-1)
where
Vb = component of the shear force parallel to the angle leg with length b and
thickness t, kips
The stress, which is constant through the thickness, should be determined for
both legs to determine the maximum.
The 1.5 factor is the calculated elastic value for equal-leg angles loaded along
one of the principal axes. For equal-leg angles loaded along one of the geometric
axes (laterally braced or unbraced) the factor is 1.35. Constants between these
limits may be calculated conservatively from Vb Q / It to determine the maximum
stress at the neutral axis.
Alternatively, if only flexural shear is considered, a uniform flexural shear stress
in the leg of Vb / bt may be used due to inelastic material behavior and stress
redistribution.
If the angle is not laterally braced against twist, a torsional moment is produced
equal to the applied transverse load times the perpendicular distance e to the
shear center, which is at the heel of the angle cross section. Torsional moments
are resisted by two types of shear behavior: pure torsion (St. Venant) and warping
torsion (AISC, 1983). If the boundary conditions are such that the cross section
is free to warp, the applied torsional moment MT is resisted by pure shear stresses
as shown in Figure C3.1a. Except near the ends of the legs, these stresses are
constant along the length of the leg, and the maximum value can be approximated by
fv = MT t / J =
3MT
At
(C3-2)
e
P
MT = Pe
(a) Pure torsion
(b) In-plane warping
(c) Across-thickness warping
Fig. C.3.1. Shear stresses due to torsion.
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where
J = torsional constant (approximated by Σbt3 / 3 when precomputed value
unavailable)
A = angle cross-sectional area
At section where warping is restrained, the torsional moment is resisted by
warping shear stresses of two types (Gjelsvik, 1981). One type is in-plane
(contour) as shown in Figure C3.1b, which varies from zero at the toe to a
maximum at the heel of the angle. The other type is across the thickness and is
sometimes referred to as secondary warping shear. As indicated in Figure C3.1c,
it varies from zero at the heel to a maximum at the toe.
In an angle with typical boundary conditions and unrestrained load point, the
torsional moment produces all three types of shear stresses (pure, in-plane
warping, and secondary warping) in varying proportions along its length. The
total applied moment is resisted by a combination of three types of internal
moments that differ in relative proportions according to the distance from the
boundary condition. Using typical angle dimensions, it can be shown that the
two warping shears are approximately the same order of magnitude and are less
than 20 percent of the pure shear stress for the same torsional moment. Therefore, it is conservative to compute the torsional shear stress using the pure shear
equation and total applied torsional moment MT as if no warping restraint were
present. This stress is added directly to the flexural shear stress to produce a
maximum surface shear stress near the mid-length of a leg. Since this sum is a
local maximum that does not extend through the thickness, applying the limit
of φv0.6Fy adds another degree of conservatism relative to the design of other
structural shapes.
In general, torsional moments from laterally unrestrained transverse loads also
produce warping normal stresses that are superimposed on bending stresses.
However, since the warping strength for a single angle is relatively small, this
additional bending effect is negligible and often ignored in design practice.
C4. COMPRESSION
The provisions for the critical compression stress account for the three possible
limit states that may occur in an angle column depending on its proportions:
general column flexural buckling, local buckling of thin legs, and flexural-torsional buckling of the member. The Q-factor in the equation for critical stress
accounts for the local buckling, and the expressions for Q are nondimensionalized from AISC LRFD Specification (AISC, 1993) Appendix B5. Flexural-torsional buckling is covered in Appendix E of the AISC LRFD Specification
(AISC, 1993). This strength limit state is approximated by the Q-factor reduction
for slender-angle legs. For non-slender sections where Q = 1, flexural-torsional
buckling is relevant for relatively short columns, but it was shown by Galambos
(1991) that the error of neglecting this effect is not significant. For this reason
no explicit consideration of this effect is required in these single-angle specifications. The provisions of Appendix E of AISC LRFD may be conservatively
used to directly consider flexural-torsional buckling for single-angle members.
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COMMENTARY
The effective length factors for angle columns may be determined by consulting
the paper by Lutz (1992).
The resistance factor φ was increased from 0.85 in AISC LRFD for all cross
sections to 0.90 for single angles only because it was shown that a φ of 0.90
provides an equivalent degree of reliability (Galambos, 1992).
C5. FLEXURE
Flexural strength limits are established for yielding, local buckling, and lateraltorsional buckling. In addition to addressing the general case of unequal-leg
single angles, the equal-leg angle is treated as a special case. Furthermore,
bending of equal-leg angles about a geometric axis, an axis parallel to one of
the legs, is addressed separately as it is a very common situation.
The tips of an angle refer to the free edges of the two legs. In most cases of
unrestrained bending, the flexural stresses at the two tips will have the same sign
(tension or compression). For constrained bending about a geometric axis, the
tip stresses will differ in sign. Criteria for both tension and compression at the
tip should be checked as appropriate, but in most cases it will be evident which
controls.
Appropriate serviceability limits for single-angle beams need also to be considered. In particular, for longer members subjected to unrestrained bending,
deflections are likely to control rather than lateral-torsional or local buckling
strength.
C5.1.1. These provisions follow the LRFD format for nominal flexural resistance. There is a region of full yielding, a linear transition to the yield
moment, and a region of local buckling. The strength at full yielding
is limited to a shape factor of 1.25, which is less than that corresponding
to the plastic moment of an angle. The factor of 1.25 corresponds to an
allowable stress of 0.75Fy, which has traditionally been used for rectangular shapes and for weak axis bending. It is used for angles due to
uncertainties in developing the full plastic moment and to limit the
large distortion of sections with large shape factors.
The b / t limits and the criteria for local buckling follow typical AISC
criteria for single angles under uniform compression. They are conservative when the leg is subjected to non-uniform compression due to
flexure.
C5.1.2. Since the shape factor for angles is in excess of 1.5, the nominal design
strength Mn = 1.25My for compact members is justified provided that
instability does not control.
C5.1.3. Lateral-torsional instability may limit the flexural strength of an unbraced single-angle beam. As illustrated in Figure C5.1, Equation 5-3a
represents the elastic buckling portion with the nominal flexural
strength, Mn, varying from 75 percent to 92 percent of the theoretical
buckling moment, Mob. Equation 5-3b represents the inelastic buckling
transition expression between 0.75My and 1.25My. At Mob greater than
approximately 6My, the unbraced length is adequate to develop the
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maximum beam flexural strength of Mn = 1.25My. These formulas were
based on Australian research on single angles in flexure and on an
analytical model consisting of two rectangular elements of length equal
to the actual angle leg width minus one-half the thickness (Leigh and
Lay, 1984; Australian Institute of Steel Construction, 1975; Leigh and
Lay, 1978; Madugula and Kennedy, 1985). Figure C5.1 reflects the
higher nominal moment strength than was implied by the 0.66Fy
allowable stress in the ASD version.
A new and more general Cb moment gradient formula consistent with
the 1993 AISC LRFD Specification is used to correct lateral-torsional
stability equations from the assumed most severe case of uniform
moment throughout the unbraced length (Cb = 1.0). The equation for
Cb used in the ASD version is applicable only to moment diagrams that
are straight lines between brace points. In lieu of a more detailed
analysis, the reduced maximum limit of 1.5 is imposed for single-angle
beams to represent conservatively the lower envelope of this cross
section’s non-uniform bending response.
C5.2.1. An angle beam loaded parallel to one leg will deflect and bend about
that leg only if the angle is restrained laterally along the length. In this
case simple bending occurs without any torsional rotation or lateral
Mn
My
1.25
Eq. 5-3b
Eq. 5-3a
0.75
Inelastic
Full
yielding
Elastic
Unbraced length l
0
0.16
1.0
Fig. C5.1. Lateral-torsional buckling of a single-angle beam.
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Mob
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COMMENTARY
deflection and the geometric axis section properties should be used in
the evaluation of the flexural design strength and deflection. If only
the point of maximum moment is laterally braced, lateral-torsional
buckling of the unbraced length under simple bending must also be
checked, as outlined in Section 5.2.1b.
C5.2.2. When bending is applied about one leg of a laterally unrestrained single
angle, it will deflect laterally as well as in the bending direction. Its
behavior can be evaluated by resolving the load and/or moments into
principal axis components and determining the sum of these principal
axis flexural effects. Section 5.2.2 is provided to simplify and expedite
the design calculations for this common situation with equal-leg
angles.
For such unrestrained bending of an equal-leg angle, the resulting
maximum normal stress at the angle tip (in the direction of bending)
will be approximately 25 percent greater than calculated using the
geometric axis section modulus. The value of Mob in Equation 5-4 and
the evaluation of My using 0.80 of the geometric axis section modulus
reflect bending about the inclined axis shown in Figure C5.2.
The deflection calculated using the geometric axis moment of inertia
has to be increased 82 percent to approximate the total deflection.
Deflection has two components, a vertical component (in the direction
of applied load) 1.56 times the calculated value and a horizontal
component of 0.94 of the calculated value. The resultant total deflection is in the general direction of the weak principal axis bending of
the angle (see Figure C5.2). These unrestrained bending deflections
δv = 1.56δ
Flexural
load
Y
Neutral
axis
δh = 0.94δ
X
Geometric
axis
δ = deflection
calculated using
geometric axis
moment of inertia
Fig. C5.2. Geometric axis bending of laterally unrestrained
equal-leg angles.
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should be considered in evaluating serviceability and will often control
the design over lateral-torsional buckling.
The horizontal component of deflection being approximately 60 percent of the vertical deflection means that the lateral restraining force
required to achieve purely vertical deflection (Section 5.2.1) must be
60 percent of the applied load value (or produce a moment 60 percent
of the applied value) which is very significant.
Lateral-torsional buckling is limited by Mob (Leigh and Lay, 1984 and
1978) in Equation 5-4, which is based on
Mcr =
2.33Eb4t
×
(1 + 3cos2θ) (Kl)2
0.156 (1 + 3cos θ) (Kl) t
√
sin θ +
b
2
2
4
2 2
+ sinθ
(C5-1)
(the general expression for the critical moment of an equal-leg angle)
with θ = −45° which is the most severe condition with the angle heel
(shear center) in tension. Flexural loading which produces angle-heel
compression can be conservatively designed by Equation 5-4 or more
exactly by using the above general Mcr equation with θ = 45º (see
Figure C5.3). With the angle heel in compression, Equation C5-1 will
slightly exceed the yield moment limit of 1.25(0.8SxFy ) only for relatively few high slenderness cases. For pure bending situations, deflections would be unreasonably large under these conditions. However,
considering the interaction of flexure and compression in an angle with
Fy = 50 ksi, b / t equal to 16 and the largest l / r of 200, Equation C5-1
will produce results eight percent less than the modified yield moment.
This situation could arise in a compression angle where the load is
transferred by end gusset plates attached to one leg only. In this case
the flexure term in the interaction is about 0.5 which reduces the effect
Z (minor principal axis)
W (major principal axis)
b
+θ
Shear center
t
Mcr
Centroid
Fig. C5.3. Equal-leg angle with general moment loading.
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COMMENTARY
to less than four percent and the end restraints provide an unknown
increase in the lateral-torsional buckling strength. Consequently only
the yield limit is required to be checked in Section 5.2.2 when the leg
tips are in tension.
Lateral-torsional buckling will reduce the nominal bending strength
only when l / b is relatively large. If the lt / b2 parameter (which is a
ratio of l / b over b / t) is small (less than approximately 2.5 with
Cb = 1), there is no need to check lateral-torsional stability inasmuch
as local buckling provisions of Section 5.1.1 will control the nominal
bending strength.
Lateral-torsional buckling will produce Mn < 1.25My for equal-leg
angles only if Mob by Equation 5-4 is less than about 6My, for Cb = 1.0.
Limits for l / b as a function of b / t are shown graphically in Figure C5.4. Local buckling and deflections must be checked separately.
Stress at the tip of the angle leg parallel to the applied bending axis is
of the same sign as the maximum stress at the tip of the other leg when
the single angle is unrestrained. For an equal-leg angle this stress is
about one-third of the maximum stress. It is only necessary to check
the nominal bending strength based on the tip of the angle leg with the
maximum stress when evaluating such an angle. Since this maximum
moment per Section 5.2.2 represents combined principal axis moments
and Equation 5-4 represents the design limit for these combined
400
300
l
b
200
100
0
1
2
3
4
5
Fy = 36
b
6
7
8
t
Fy = 50
Fig. C5.4. Equal leg single-angle lateral buckling limits for
Mn = 1.25My about geometric axis.
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flexural moments, only a single flexural term needs to be considered
when evaluating combined flexural and axial effects.
C5.2.3. For unequal-leg angles without lateral-torsional restraint the applied
load or moment must be resolved into components along the two
principal axis in all cases and designed for biaxial bending using the
interaction equation.
C5.3.1. Under major axis bending of equal-leg angles Equation 5-5 in combination with 5-3a or 5-3b controls the nominal design moment against
overall lateral-torsional buckling of the angle. This is based on Mcr,
given earlier with θ = 0.
Lateral-torsional buckling for this case will reduce the stress below
1.25My only for l / t ≥ 4800 / Fy or 0.160E / Fy (Mob = 6My). If the
lt / b2 parameter is small (less than approximately 1.5Cb for this case),
local buckling will control the nominal design moment and Mn based
on lateral-torsional buckling need not be evaluated. Local buckling
must be checked using Section 5.1.1.
C5.3.2. Lateral-torsional buckling about the major principal W axis of an
unequal-leg angle is controled by Mob in Equation 5-6. Section property
βw reflects the location of the shear center relative to the principal axis
of the section and the bending direction under uniform bending.
Positive βw and maximum Mob occurs when the shear center is in
flexural compression while negative βw and minimum Mob occurs when
the shear center is in flexural tension (see Figure C5.5). This βw effect
is consistent with behavior of singly symmetric I-shaped beams which
are more stable when the compression flange is larger than the tension
flange. For principal W-axis bending of equal-leg angles, βw is equal
to zero due to symmetry and Equation 5-6 reduces to Equation 5-5 for
this special case.
Shear center
Mob
W
Z
Shear center
Mob
W
(Special case: for equal legs, βw = 0)
(a) + βw
(b) – βw
Fig. C5.5. Unequal-leg angle in bending.
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COMMENTARY
TABLE C5.1
βw Values for Angles
Angle Size (in.)
βw (in.)*
9×4
6.54
8×6
8×4
3.31
5.48
7×4
4.37
6×4
6 × 3.5
3.14
3.69
5 × 3.5
5×3
2.40
2.99
4 × 3.5
4×3
0.87
1.65
3.5 × 3
3.5 × 2.5
0.87
1.62
3 × 2.5
3×2
0.86
1.56
2.5 × 2
0.85
Equal legs
0.00
* Has positive or negative value depending on direction of
bending (see Figure C5.5).
For reverse curvature bending, part of the unbraced length has positive
βw, while the remainder negative βw, and conservatively, the negative
value is assigned for that entire unbraced segment.
βw is essentially independent of angle thickness (less than one percent
variation from mean value) and is primarily a function of the leg
widths. The average values shown in Table C5.1 may be used for
design.
C6. COMBINED STRESSES
The stability and strength interaction equations of AISC LRFD Specification
Chapter H have been adopted with modifications to account for various conditions of bending that may be encountered. Bending will usually accompany axial
loading in a single-angle member since the axial load and connection along the
legs are eccentric to the centroid of the cross section. Unless the situation
conforms to Section 5.2.1 or 5.2.2 in that Section 6.1.2 or 6.1.3 may be used,
the applied moment should be resolved about the principal axes for the interaction check.
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For the non-symmetric and singly symmetric single angles, the interaction
expression related to stresses at a particular location on the cross section is the
most accurate due to lack of double symmetry. At a particular location, it is
possible to have stresses of different sign from the various components such that
a combination of tensile and compressive stress will represent a critical condition. The absolute value of the combined terms must be checked at the angle-leg
tips and heel and compared with 1.0.
When using the combined force expressions for single angles, Muw and Muz are
positive as customary. The evaluation of Mn in Section 5.1 is dependent on the
location on the cross section being examined by using the appropriate value of
section modulus, S. Since the sign of the stress is important in using Equations 6-1a and 6-1b, Mn is considered either positive or negative by assigning a
sign to S to reflect the stress condition as adding to, or subtracting from, the axial
load effect. A designer may choose to use any consistent sign convention.
It is conservative to ignore this refinement and simply use positive critical Mn
values in the bending terms and add the absolute values of all terms (Elgaaly,
Davids, and Dagher, 1992 and Adluri and Madugula, 1992).
Alternative special interaction equations for single angles have recently been
published (Adluri and Madugula, 1992).
C6.1.3. When the total maximum flexural stress is evaluated for a laterally
unrestrained length of angle per Section 5.2, the bending axis is the
inclined axis shown in Figure C5.2. The radius of gyration modification for the moment amplification about this axis is equal to √
1.82 =
1.35 to account for the increased unrestrained bending deflection
relative to that about the geometric axis for the laterally unrestrained
length. The 1.35 factor is retained for angles braced only at the point
of maximum moment to maintain a conservative calculation for this
case. If the brace exhibits any flexibility permitting lateral movement
of the angle, use of r = rx would not be conservative.
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List of References
Alduri, S. M. and Madugula, M. K. S. (1992), “Eccentrically Loaded Steel SingleAngle Struts,” AISC Engineering Journal, 2nd Quarter.
American Institute of Steel Construction, Inc. (1983), Torsional Analysis of Steel
Members, Chicago, IL.
American Institute of Steel Construction, Inc. (1993), Load and Resistance Factor
Design Specification for Structural Steel Buildings, Chicago, IL.
American Institute of Steel Construction, Inc. (1989), Specification for Allowable
Stress Design of Single-Angle Members, Chicago, IL.
Australian Institute of Steel Construction (1975), Australian Standard AS1250, 1975.
Elgaaly, M., Davids, W. and Dagher, H. (1992), “Non-Slender Single-Angle Struts,”
AISC Engineering Journal, 2nd Quarter.
Galambos, T. V. (1991), “Stability of Axially Loaded Compressed Angles,” Structural
Stability Research Council, Annual Technical Session Proceedings, Apr. 15–17,
1991, Chicago, IL.
Gjelsvik, A. (1981), The Theory of Thin-walled Bars, John Wiley and Sons, New York.
Leigh, J. M. and M. G. Lay (1978), “Laterally Unsupported Angles with Equal and
Unequal Legs,” Report MRL 22/2 July 1978, Melbourne Research Laboratories,
Clayton.
Leigh, J. M. and M. G. Lay (1984), “The Design of Laterally Unsupported Angles,”
in Steel Design Current Practice, Section 2, Bending Members, American Institute
of Steel Construction, Inc., January 1984.
Lutz, L. A. (1992), “Critical Slenderness of Compression Members with Effective
Lengths About Nonprincipal Axes,” Structural Stability Research Council, Annual
Technical Session Proceedings, Apr. 6–7, 1992, Pittsburgh, PA.
Madugula, M. K. S. and J. B. Kennedy (1985), Single and Compound Angle Members,
Elsevier Applied Science, New York.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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Seismic Provisions
for Structural Steel
Buildings
June 15, 1992
AMERICAN INSTITUTE OF STEEL CONSTRUCTION, INC.
One East Wacker Drive, Suite 3100, Chicago, IL 60601-2001
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PREFACE
The intention of the main AISC Specification is to cover the common everyday design
criteria in routine office usage. It is not feasible to also cover the many special and
unique problems encountered within the full range of structural design practice. This
document is a separate Specification which addresses one such topic, steel seismic
provisions. It contains its own list of Symbols, a Glossary and a non-mandatory
Commentary which has been included to provide background for the provisions.
The AISC Specification Task Committee 113 on Seismic Provisions to supplement
the current Load and Resistance Factor Design (LRFD) and Allowable Stress Design
(ASD) Specification for Structural Steel Buildings acknowledges the various contributions of several groups to the completion of this document: the Structural Engineers
Association of California (SEAOC), the National Science Foundation, and the Building Seismic Safety Council. The main AISC Committee on Specification enhanced
these provisions by careful scrutiny, discussions, suggestions for improvements, and
endorsement. The members of this Task Committee, as principal authors of the AISC
Seismic Provisions, are most grateful to all of the above groups and people. Special
recognition must also be given to the leadership expertise, and perseverance of Task
Committee Chairman Egor Popov and Technical Secretary Clarkson Pinkham.
The principal changes in this edition of the Seismic Provisions are the conversion to
the loads and design format recommended by the 1991 National Earthquake Hazards
Reduction Program (NEHRP) document.
The reader is cautioned that professional judgment must be exercised when data or
recommendations in this Specification are applied. The publication of the material
contained herein is not intended as a representation or warranty on the part of the
American Institute of Steel Construction, Inc.—or any other person named herein—
that this information is suitable for general or particular use, or freedom from
infringement of any patent or patents. Anyone making use of this information assumes
all liability arising from such use. The design of structures is within the scope of
expertise of a competent licensed structural engineer, architect, or other licensed
professional for the application of principles to a particular structure.
By the AISC Subcommittee,
E. P. Popov, Chair
R. Becker
G. G. Deierlein
M. D. Engelhardt
S. J. Fang
R. E. Ferch
R. D. Hanson
J. R. Harris
K. Kasai
S. D. Lindsey
H. W. Martin
C. M. Saunders
J. B. Shantz
I. M. Viest
N. F. G. Youssef
C. W. Pinkham, Technical Secretary
N. Iwankiw, Recording Secretary
May 22, 1992
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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Symbols
The section numbers in parentheses after the definition of a symbol refers to the section
where the symbol is first used.
Effective net area, in.2 (9)
Flange area of member, in.2 (6)
Gross area, in.2 (8)
Area of link stiffener, in.2 (10)
Seismic coefficient representing the effective peak velocity-related acceleration. (2)
Effective area of weld, in.2 (6)
Link web area, in.2 (10)
Response factor related to the fundamental period of the building. (3)
Dead load due to the self-weight of the structure and the permanent elements on
the structure, kips. (3)
E Earthquake load. (3)
FBM Nominal strength of the base material to be welded, ksi. (6)
FEXX Classification strength of weld metal, ksi. (6)
Fw Nominal strength of the weld electrode material, ksi. (6)
Fy Specified minimum yield strength of the type of steel being used, ksi. (8)
Fyb Fy of a beam, ksi. (8)
Fyc Fy of a column, ksi. (6)
H Average story height above and below a beam-to-column connection., in. (8)
L
Live load due to occupancy and moveable equipment, kips. (3)
L
Unbraced length of compression or bracing member, in. (8)
Lr Roof live load, kips. (3)
Mn Nominal moment strength of a member or joint, kip-in. (8)
Mp Plastic bending moment, kip-in. (8)
Mpa Plastic bending moment modified by axial load ratio, kip-in. (10)
Mu Required flexural strength on a member or joint, kip-in. (8)
PD Required axial strength on a column resulting from application of dead load, D,
kips. (6)
PE Required axial strength on a column resulting from application of the specified
earthquake load, E, kips. (6)
PL Required axial strength on a column resulting from application of live load, L,
kips. (6)
Pu Required axial strength on a column or a link, kips. (10)
Pn Nominal axial strength of a column, kips. (6)
Pu∗ Required axial strength on a brace, kips. (9)
Puc Required axial strength on a column based on load combination with seismic
loads, kips. (8)
Py Nominal yield axial strength of a member = Fy Ag, kips. (10)
Ae
Af
Ag
Ast
Av
Aw
Aw
Cs
D
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R
R′
Rn
S
V
Vn
Vu
Vp
Vpa
W
Wg
Zb
Zc
b
bf
bcf
db
dc
dz
e
h
r
ry
tbf
tcf
tf
tp
tw
tz
wz
α
ρ
k
kp
kr
φ
φb
φc
φt
φv
φw
SYMBOLS
Response modification factor. (3)
Load due to initial rainwater or ice exclusive of the ponding contribution, kips.
(Symbol R is used in the Specification). (3)
Nominal strength of a member. (8)
Snow load, kips. (3)
Base shear due to earthquake load, kips. (3)
Nominal shear strength of a member, kips. (8)
Required shear strength on a member, kips. (8)
Nominal shear strength of an active link, kips. (10)
Nominal shear strength of an active link modified by the axial load magnitude,
kips. (10)
Wind load, kips. (3)
Total weight of the building, kips. (3)
Plastic section modulus of a beam, in.3 (8)
Plastic section modulus of a column, in.3 (8)
Width of compression element, in. (Table 8-1)
Flange width, in. (8)
Column flange width, in. (8)
Overall beam depth, in. (8)
Overall column depth, in. (8)
Overall panel zone depth between continuity plates, in. (8)
EBF link length, in. (10)
Assumed web depth for stability, in. (Table 8-1)
Governing radius of gyration, in. (9)
Radius of gyration about y axis, in. (8)
Thickness of beam flange, in. (8)
Thickness of column flange, in. (8)
Thickness of flange, in. (8)
Thickness of panel zone including doubler plates, in. (8)
Thickness of web, in. (8)
Thickness of panel zone (doubler plates not necessarily included), in. (8)
Width of panel zone between column flanges, in. (8)
Fraction of member force transferred across a particular net section. (9)
Ratio of required axial force Pu to required shear strength Vu of a link. (10)
Slenderness parameter. (9)
Limiting slenderness parameter for compact element. (8)
Limiting slenderness parameter for non-compact element. (9)
Resistance factor. (6,10)
Resistance factor for beams. (6)
Resistance factor for columns in compression. (6,10)
Resistance factor for columns in tension. (6)
Resistance factor for shear strength of panel zone of beam-to-column connections. (8)
Resistance factor for welds. (6)
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Glossary
Beam. A structural member whose primary function is to carry loads transverse to its
longitudinal axis, usually a horizontal member in a seismic frame system.
Braced Frame. An essentially vertical truss system of concentric or eccentric type that
resists lateral forces on the structural system.
Concentrically Braced Frame (CBF). A braced frame in which all members of the
bracing system are subjected primarily to axial forces. The CBF shall meet the
requirements of Sect. 9.
Connection. Combination of joints used to transmit forces between two or more
members. Categorized by the type and amount of force transferred (moment,
shear, end reaction).
Continuity Plates. Column stiffeners at top and bottom of the panel zone.
Design strength. Resistance (force, moment, stress, as appropriate) provided by
element or connection; the product of the nominal strength and the resistance
factor.
Diagonal Bracing. Inclined structural members carrying primarily axial load employed to enable a structural frame to act as a truss to resist horizontal loads.
Dual System. A dual system is a structural system with the following features:
• An essentially complete space frame which provides support for gravity loads.
• Resistance to lateral load is provided by moment resisting frames (SMF) or
(OMF) which is capable of resisting at least 25 percent of the base shear and
concrete or steel shear walls, steel eccentrically (EBF) or concentrically (CBF)
braced frames.
• Each system shall be also designed to resist the total lateral load in proportion
to its relative rigidity.
Eccentrically Braced Frame (EBF). A diagonal braced frame in which at least one end
of each bracing member connects to a beam a short distance from a beam-to-column connection or from another beam-to-brace connection. The EBF shall meet
the requirements of Sect. 10.
Essential Facilities. Those facilities defined as essential in the applicable code under
which the structure is designed. In the absence of such a code, see ASCE 7-92.
Joint. Area where two or more ends, surfaces, or edges are attached. Categorized by
type of fastener or weld used and method of force transfer.
K Braced Frame. A concentric braced frame (CBF) in which a pair of diagonal braces
located on one side of a column is connected to a single point within the clear
column height.
Lateral Support Member. Member designed to inhibit lateral buckling or lateral-torsional buckling of primary frame members.
Link. In EBF, the segment of a beam which extends from column to column, located
between the end of a diagonal brace and a column or between the ends of two
diagonal braces of the EBF. The length of the link is defined as the clear distance
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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GLOSSARY
between the diagonal brace and the column face or between the ends of two
diagonal braces.
Link Intermediate Web Stiffeners. Vertical web stiffeners placed within the link.
Link Rotation Angle. The link rotation angle is the plastic angle between the link and
the beam outside of the link when the total story drift is E′ / E times the drift
derived using the specified base shear, V.
Link Shear Design Strength. The lesser of φVp or 2φMp/e, where φ = 0.9,
Vp = 0.55Fy dtw and e = the link length except as modified by Sect. S9.2.f.
LRFD. (Load and Resistance Factor Design). A method of proportioning structural
components (members, connectors, connecting elements, and assemblages) such
that no applicable limit state is exceeded when the structure is subjected to all
design load combinations.
Moment Frame. A building frame system in which seismic shear forces are resisted
by shear and flexure in members and joints of the frame.
Nominal loads. The magnitudes of the loads specified by the applicable code.
Nominal strength. The capacity of a structure or component to resist the effects of
loads, as determined by computations using specified material strengths and
dimensions and formulas derived from accepted principles of structural mechanics or by field tests or laboratory tests of scaled models, allowing for modeling
effects, and differences between laboratory and field conditions.
Ordinary Moment Frame (OMF). A moment frame system which meets the requirements of Sect. 7.
P - Delta effect. Secondary effect of column axial loads and lateral deflection on the
shears and moments in members.
Panel Zone. Area of beam-to-column connection delineated by beam and column
flanges.
Required Strength. Load effect (force, moment, stress, as appropriate) acting on
element of connection determined by structural analysis from the factored loads
(using most appropriate critical load combinations).
Resistance Factor. A factor that accounts for unavoidable deviations of the actual
strength from the nominal value and the manner and consequences of failure.
Slip-Critical Joint. A bolted joint in which slip resistance of the connection is required.
Special Moment Frame (SMF). A moment frame system which meets the requirements
of Sect. 8.
Structural System. An assemblage of load-carrying components which are joined
together to provide regular interaction or interdependence.
V Braced Frame. A concentrically braced frame (CBF) in which a pair of diagonal
braces located either above or below a beam is connected to a single point within
the clear beam span. Where the diagonal braces are below the beam, the system
is also referred to as an Inverted V Braced Frame.
X Braced Frame. A concentrically braced frame (CBF) in which a pair of diagonal
braces crosses near mid-length of the braces.
Y Braced Frame. An eccentrically braced frame (EBF) in which the stem of the Y is
the link of the EBF system.
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Seismic Provisions
for Structural Steel
Buildings
June 15, 1992
Part I—Load and Resistance Factor Design (LRFD)
1.
SCOPE
These special seismic requirements are to be applied in conjunction with the
AISC Load and Resistance Factor Design Specification for Structural Steel
Buildings (LRFD), 1986; hereinafter referred to as the Specification. They are
intended for the design and construction of structural steel members and
connections in buildings for which the design forces resulting from earthquake
motions have been determined on the basis of energy dissipation in the non-linear range of response.
Seismic provisions and the nominal loads for each Seismic Performance Category, Seismic Hazard Exposure Group, or Seismic Zone shall be as specified by
the applicable code under which the structure is designed or where no code
applies, as dictated by the conditions involved. In the absence of a code, the
Performance Categories, Seismic Hazard Exposure Groups, loads and load
combinations shall be as given herein.
2.
SEISMIC PERFORMANCE CATEGORIES
Seismic Performance Categories vary with the Seismic Hazard Exposure Group
shown in Table 2-1, the Effective Peak Velocity Related Acceleration, Av, and
the Seismic Hazard Exposure Group shown in Table 2-2.
In addition to the general requirements assigned to the various Seismic Performance Categories in the applicable building code for all types of construction, the
following requirements apply to fabricated steel construction for buildings and
structures with similar structural characteristics.
2.1. Seismic Performance Categories A, B, and C
Buildings assigned to Categories A, B, and C, except Category C in Seismic
Hazard Exposure Group III where the value of Av ≥ 0.10, shall be designed either
in accordance with solely the Specification or in accordance with the Specification and these provisions.
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PART I—LOAD AND RESISTANCE FACTOR DESIGN (LRFD)
TABLE 2-1
Seismic Hazard Exposure Groups
Group III
Buildings having essential facilities that are necessary for postearthquake recovery and requiring special requirements for
access and functionality.
Group II
Buildings that constitute a substantial public hazard because of
occupancy or use.
Group I
All buildings not classified in Groups II and III.
2.2. Seismic Performance Category C
Buildings assigned to Category C in Seismic Hazard Exposure Group III where
the value of Av ≥ 0.10 shall be designed in accordance with the Specification as
modified by the additional provisions of this section.
2.2.a. Steel used in seismic resisting systems shall be limited by the provisions
of Sect. 5.
2.2.b. Columns in seismic resisting systems shall be designed in accordance
with Sect. 6.
2.2.c. Ordinary Moment Frames (OMF) shall be designed in accordance with
the provisions of Sect. 7.
2.2.d. Special Moment Frames (SMF) are required to conform only to the
requirements of Sects. 8.2, 8.7, and 8.8.
2.2.e. Braced framed systems shall conform to the requirements of Sects. 9 or
10 when used alone or in combination with the moment frames of the
seismic resisting system.
2.2.f. A quality assurance plan shall be submitted to the regulatory agency for
the seismic force resisting system of the building.
2.3. Seismic Performance Categories D and E
Buildings assigned to Categories D and E shall be designed in accordance with
the Specification as modified by the additional provisions of this section.
2.3.a. Steel used in seismic resisting systems shall be limited by the provisions
of Sect. 5.
2.3.b. Columns in seismic resisting systems shall be designed in accordance
with Sect. 6.
2.3.c. Ordinary Moment Frames (OMF) shall be designed in accordance with
the provisions of Sect. 7.
2.3.d. Special Moment Frames (SMF) shall be designed in accordance with
the provisions of Sect. 8.
2.3.e. Braced framed systems shall conform to the requirements of Sects. 9.
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TABLE 2-2
Seismic Performance Categories
Seismic Hazard Exposure Group
Value of Av
I
II
III
0.20 ≤ Av < 0.20
0.15 ≤ Av < 0.20
0.10 ≤ Av < 0.15
0.05 ≤ Av < 0.10
0.15 ≤ Av < 0.05
D
C
C
B
A
D
D
C
B
A
E
D
C
C
A
(CBF) or 10. (EBF) when used alone or in combination with the moment
frames of the seismic resisting system.
The use of K-bracing systems shall not be permitted as part of the seismic
resisting system except as permitted by Sect. 9.5. (Low Buildings)
2.3.f. A quality assurance plan shall be submitted to the regulatory agency for
the seismic force resisting system of the building.
3.
LOADS, LOAD COMBINATIONS, AND NOMINAL STRENGTHS
3.1. Loads and Load Combinations
The following specified loads and their effects on the structure shall be taken
into account:
D : dead load due to the weight of the structural elements and the permanent
features on the structure.
L : live load due to occupancy and moveable equipment.
Lr : roof live load.
W : wind load.
S : snow load.
E : earthquake load (where the horizontal component is derived from base
shear Formula V = CsWg).
R′ : load due to initial rainwater or ice exclusive of the ponding contribution.
In the Formula V = CsWg for base shear:
Cs = Seismic design coefficient
Wg = Total weight of the building, see the applicable code.
For the nominal loads as defined above, see the applicable code.
The required strength of the structure and its elements shall be determined from
the appropriate critical combination of factored loads. The following Load
Combinations and corresponding load factors shall be investigated:
1.4D
(3-1)
1.2D + 1.6L + 0.5(Lr or S or R′)
(3-2)
1.2D + 1.6(Lr or S or R′) + (0.5L or 0.8W)
(3-3)
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PART I—LOAD AND RESISTANCE FACTOR DESIGN (LRFD)
1.2D + 1.3W + 0.5L + 0.5(Lr or S or R′)
(3-4)
1.2D ± 1.0E + 0.5L + 0.2S
(3-5)
0.9D ± (1.0E or 1.3W)
(3-6)
Exception: The load factor on L in Load Combinations 3-3, 3-4, and 3-5 shall
equal 1.0 for garages, areas occupied as places of public assembly, and all areas
where the live load is greater than 100 psf.
Other special load combinations are included with specific design requirements
throughout these provisions.
Orthogonal earthquake effects shall be included in the analysis unless noted
specifically otherwise in the governing building code.
Where required by these provisions, an amplified horizontal earthquake load of
0.4R × E (where the term 0.4R is greater or equal to 1.0) shall be applied in lieu
of the horizontal component of earthquake load E in the load combinations
above. The term R is the earthquake response modification coefficient contained
in the applicable code. The additional load combinations using the amplified
horizontal earthquake load are:
1.2D + 0.5L + 0.2S ± 0.4R × E
(3-7)
0.9D ± 0.4R × E
(3-8)
Exception: The load factor on L in Load Combinations 3-7 shall equal 1.0 for
garages, areas occupied as places of public assembly and all areas where the
live load is greater than 100 psf.
The term 0.4R in Load Combinations 3-7 and 3-8 shall be greater or equal to
1.0.
Where the amplified load is required, orthogonal effects are not required to be
included.
3.2. Nominal Strengths
The nominal strengths shall be as provided in the Specification.
4.
STORY DRIFT
Story drift shall be calculated using the appropriate load effects consistent with
the structural system and the method of analysis. Limits on story drift shall be
in accordance with the governing code and shall not impair the stability of the
structure.
5.
MATERIAL SPECIFICATIONS
Steel used in seismic force resisting systems shall be as listed in Sect. A3.1 of
the Specification, except for buildings over one story in height. The steel used
in seismic resisting systems described in Sections 8, 9, and 10 shall be limited
to the following ASTM Specifications: A36, A500 (Grades B and C), A501,
A572 (Grades 42 and 50), and A588. The steel used for base plates shall meet
one of the preceding ASTM Specifications or ASTM A283 Grade D.
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6.
6 - 313
COLUMN REQUIREMENTS
6.1. Column Strength
When Pu / φPn > 0.5, columns in seismic resisting frames, in addition to
complying with the Specification, shall be limited by the following
requirements:
6.1.a. Axial compression loads:
1.2PD + 0.5PL + 0.2PS + 0.4R × PE ≤ φcPn
(6-1)
where the term 0.4R is greater or equal to 1.0.
Exception: The load factor on PL in Load Combination 6-1 shall equal
1.0 for garages, areas occupied as places of public assembly, and all areas
where the live load is greater than 100 psf.
6.1.b. Axial tension loads:
0.9PD − 0.4R × PE ≤ φtPn
(6-2)
where the term 0.4R is greater or equal to 1.0.
6.1.c. The axial Load Combinations 6-1 and 6-2 are not required to exceed
either of the following:
1. The maximum loads transferred to the column, considering 1.25
times the design strengths of the connecting beam or brace elements
of the structure.
2. The limit as determined by the foundation capacity to resist overturning uplift.
6.2. Column Splices
Column splices shall have a design strength to develop the column axial loads
given in Sect. 6.1.a, b, and c as well as the Load Combinations 3-1 to 3-6.
6.2.a. In column splices using either complete or partial penetration welded
joints, beveled transitions are not required when changes in thickness
and width of flanges and webs occur.
6.2.b. Splices using partial penetration welded joints shall not be within 3 ft of
the beam-to-column connection. Column splices that are subject to net
tension forces shall comply with the more critical of the following:
1. The design strength of partial penetration welded joints, the lesser of
φwFw Aw or φwFBM Aw, shall be at least 150 percent of the required
strength, where φw = 0.8 and Fw = 0.6FEXX.
2. The design strength of welds shall not be less than 0.5Fyc Af, where
Fyc is the yield strength of the column material and Af is the flange
area of the smaller column connected.
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7.
PART I—LOAD AND RESISTANCE FACTOR DESIGN (LRFD)
REQUIREMENTS FOR ORDINARY MOMENT FRAMES (OMF)
7.1. Scope
Ordinary Moment Frames (OMF) shall have a design strength as provided in
the Specification to resist the Load Combinations 3-1 through 3-6 as modified
by the following added provisions:
7.2. Joint Requirements
All beam-to-column and column to beam connections in OMF which resist
seismic forces shall meet one of the following requirements:
7.2.a. FR (fully restrained) connections conforming with Sect. 8.2, except that
the required flexural strength, Mu, of a column-to-beam joint is not
required to exceed the nominal plastic flexural strength of the connection.
7.2.b. FR connections with design strengths of the connections meeting the
requirements of Sect. 7.1 using the Load Combinations 3-7 and 3-8.
7.2.c. Either FR or PR (partially restrained) connections shall meet the
following:
1. The design strengths of the members and connections meet the
requirements of Sect. 7.1.
2. The connections have been demonstrated by cyclic tests to have
adequate rotation capacity at a story drift calculated at a horizontal
load of 0.4R × E, (where the term 0.4R is equal to or greater than 1.0).
3. The additional drift due to PR connections shall be considered in
design.
FR and PR connections are described in detail in Sect. A2 of the
Specification.
8.
REQUIREMENTS FOR SPECIAL MOMENT FRAMES (SMF)
8.1. Scope
Special Moment Frames (SMF) shall have a design strength as provided in the
Specification to resist the Load Combinations 3-1 through 3-6 as modified by
the following added provisions:
8.2. Beam-to-Column Joints
8.2.a. The required flexural strength, Mu, of each beam-to-column joint shall
be the lesser of the following quantities:
1. The plastic bending moment, Mp, of the beam.
2. The moment resulting from the panel zone nominal shear strength, Vn,
as determined using Equation 8-1.
The joint is not required to develop either of the strengths defined above
if it is shown that under an amplified frame deformation produced by
Load Combinations 3-7 and 3-8, the design strength of the members at
the connection is adequate to support the vertical loads, and the required
lateral force resistance is provided by other means.
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8.2.b. The required shear strength, Vu, of a beam-to-column joint shall be
determined using the Load Combination 1.2D + 0.5L + 0.2S plus the
shear resulting from Mu, as defined in Sect. 8.2.a., on each end of the
beam. Alternatively, Vu shall be justified by a rational analysis. The
required shear strength is not required to exceed the shear resulting from
Load Combination 3-7.
8.2.c. The design strength, φRn, of a beam-to-column joint shall be considered
adequate to develop the required flexural strength, Mu, of the beam if it
conforms to the following:
1. The beam flanges are welded to the column using complete penetration welded joints.
2. The beam web joint has a design shear strength φVn greater than the
required shear, Vu, and conforms to either:
a. Where the nominal flexural strength of the beam, Mn, considering
only the flanges is greater than 70 percent of the nominal flexural
strength of the entire beam section [i.e., bf tf (d−tf)Fyf ≥ 0.7Mp]; the
web joint shall be made by means of welding or slip-critical high
strength bolting, or;
b. Where bf tf (d−tf)Fyf < 0.7Mp, the web joint shall be made by means
of welding the web to the column directly or through shear tabs.
That welding shall have a design strength of at least 20 percent of
the nominal flexural strength of the beam web. The required beam
shear, Vu, shall be resisted by further welding or by slip-critical
high-strength bolting or both.
8.2.d. Alternate Joint Configurations: For joint configurations utilizing welds
or high-strength bolts, but not conforming to Sect. 8.2.c, the design
strength shall be determined by test or calculations to meet the criteria
of Sect. 8.2.a. Where conformance is shown by calculation, the design
strength of the joint shall be 125 percent of the design strengths of the
connected elements.
8.3. Panel Zone of Beam-to-Column Connections
(Beam web parallel to column web)
8.3.a. Shear Strength: The required shear strength, Vu, of the panel zone shall
be based on beam bending moments determined from the Load Combinations 3-5 and 3-6. However, Vu is not required to exceed the shear
forces determined from 0.9ΣφbMp of the beams framing into the column
flanges at the connection. The design shear strength, φvVn, of the panel
zone shall be determined by the following formula:
3bcf t2cf
where for this case φv = 0.75.
φvVn = 0.6φvFy dc tp 1 +
db dc tp
where:
tp = Total thickness of panel zone including doubler plates, in.
dc = Overall column section depth, in.
bcf = Width of the column flange, in.
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PART I—LOAD AND RESISTANCE FACTOR DESIGN (LRFD)
tcf = Thickness of the column flange, in.
db = Overall beam depth, in.
Fy = Specified yield strength of the panel zone steel, ksi.
8.3.b. Panel Zone Thickness: The panel zone thickness, tz, shall conform to the
following:
tz ≥ (dz + wz) / 90
(8-2)
where:
dz = the panel zone depth between continuity plates, in.
wz = the panel zone width between column flanges, in.
For this purpose, tz shall not include any doubler plate thickness unless
the doubler plate is connected to the web with plug welds adequate to
prevent local buckling of the plate.
Where a doubler plate is used without plug welds to the column web,
the doubler plate shall conform to Eq. 8-2.
8.3.c. Panel Zone Doubler Plates: Doubler plates provided to increase the
design strength of the panel zone or to reduce the web depth thickness
ratio shall be placed next to the column web and welded across the plate
width along the top and bottom with at least a minimum fillet weld. The
doubler plates shall be fastened to the column flanges using either butt
or fillet welded joints to develop the design shear strength of the doubler
plate.
8.4. Beam and Column Limitations
8.4.a. Beam Flange Area: There shall be no abrupt changes in beam flange
areas in plastic hinge regions.
8.4.b. Width-Thickness Ratios: Beams and columns shall comply with λp in
Table 8-1 in lieu of those in Table B5.1 of the Specification.
8.5. Continuity Plates
Continuity plates shall be provided if required by the provisions in the Specification for webs and flanges with concentrated forces and if the nominal column
local flange bending strength Rn is less than 1.8Fyb bf tbf, where:
Rn = 6.25(tcf)2Fyf, and
Fyb = Specified minimum yield strength of beam, ksi.
Fyf = Specified minimum yield strength of column flange, ksi.
bf = Beam flange width, in.
tbf = Beam flange thickness, in.
tcf = Column flange thickness, in.
Continuity plates shall be fastened by welds to both the column flanges and
either the column webs or doubler plates.
8.6. Column-Beam Moment Ratio
At any beam-to-column connection, one of the following relationships shall be
satisfied:
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6 - 317
TABLE 8-1
Limiting Width Thickness Ratios λp
for Compression Elements
Description of Element
Flanges of I-shaped nonhybrid sections and channels
in flexure.
WidthThickness
Ratio
Limiting WidthThickness Ratios
λp
b/t
52 / √
Fy
h / tw
For Pu / φbPy ≤ 0.125
Flanges of I-shaped hybrid
beams in flexure.
Webs in combined flexural and
axial compression.
520
Fy
√
1.54Pu
1 − φ P
b y
For Pu / φbPy > 0.125
191
Fy
√
Pu 253
2.33 − φ P ≥ √
Fy
b y
ΣZc(Fyc − Puc / Ag)
≥ 1.0,
ΣZbFyb
(8-3)
ΣZc(Fyc − Puc / Ag)
≥ 1.0,
Vn dbH / (H − db)
(8-4)
where:
Ag = Gross area of a column, in.2
Fyb = Specified minimum yield strength of a beam, ksi.
Fyc = Specified minimum yield strength of a column, ksi.
H = Average of the story heights above and below the joint, in.
Puc = Required axial strength in the column (in compression) ≥ 0
Vn = Nominal strength of the panel zone as determined from Equation 8-1, ksi.
Zb = Plastic section modulus of a beam, in.3
Zc = Plastic section modulus of a column, in.3
db = Average overall depth of beams framing into the connection, in.
These requirements do not apply in any of the following cases, provided the
columns conform to the requirements of Sect. 8.4:
8.6.a. Columns with Puc < 0.3Fyc Ag.
8.6.b. Columns in any story that has a ratio of design shear strength to design
force 50 percent greater than the story above.
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PART I—LOAD AND RESISTANCE FACTOR DESIGN (LRFD)
8.6.c. Any column not included in the design to resist the required seismic
shears, but included in the design to resist axial overturning forces.
8.7. Beam-to-Column Connection Restraint
8.7.a. Restrained Connection:
1. Column flanges at a beam-to-column connection require lateral
support only at the level of the top flanges of the beams when a
column is shown to remain elastic outside of the panel zone, using
one of the following conditions:
a. Ratios calculated using Eqs. 8-3 or 8-4 are greater than 1.25.
b. Column remains elastic when loaded with Load Combination 3-7.
2. When a column cannot be shown to remain elastic outside of the panel
zone, the following provisions apply:
a. The column flanges shall be laterally supported at the levels of
both top and bottom beam flanges.
b. Each column flange lateral support shall be designed for a required strength equal to 2.0 percent of the nominal beam flange
strength (Fy bf tf).
c. Column flanges shall be laterally supported either directly, or
indirectly, by means of the column web or beam flanges.
8.7.b. Unrestrained Connections: A column containing a beam-to-column connection with no lateral support transverse to the seismic frame at the
connection shall be designed using the distance between adjacent lateral
supports as the column height for buckling transverse to the seismic
frame and conform to Sect. H of the Specification except that:
1. The required column strength shall be determined from the Load
Combination 3-5 where E is the least of:
a. The amplified earthquake force 0.4R × E (where the term 0.4R
shall be equal to or greater than 1.0).
b. 125 percent of the frame design strength based on either beam or
panel zone design strengths.
2. The L / r for these columns shall not exceed 60.
3. The required column moment transverse to the seismic frame shall
include that caused by the beam flange force specified in Sect.
8.7.a.2.b plus the added second order moment due to the resulting
column displacement in this direction.
8.8. Lateral Support of Beams
Both flanges of beams shall be laterally supported directly or indirectly. The
unbraced length between lateral supports shall not exceed 2,500 ry / Fy. In
addition, lateral supports shall be placed at concentrated loads where an analysis
indicates a hinge will be formed during inelastic deformations of the SMF.
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REQUIREMENTS FOR CONCENTRICALLY BRACED (CBF)
BUILDINGS
9.1. Scope
Concentrically Braced Frames (CBF) are braced systems whose worklines
essentially intersect at points. Minor eccentricities, where the worklines intersect within the width of the bracing members, are acceptable if accounted for in
the design. CBF shall have a design strength as provided in the Specification to
resist the Load Combinations 3-1 through 3-6 as modified by the following
added provisions:
9.2. Bracing Members
L 720
except as permit9.2.a. Slenderness: Bracing members shall have an ≤
r √
Fy
ted in Sect. 9.5.
9.2.b. Compressive Design Strength: The design strength of a bracing member
in axial compression shall not exceed 0.8φcPn.
9.2.c. Lateral Force Distribution: Along any line of bracing, braces shall be
deployed in alternate directions such that, for either direction of force
parallel to the bracing, at least 30 percent but no more than 70 percent
of the total horizontal force shall be resisted by tension braces, unless
the nominal strength, Pn, of each brace in compression is larger than the
required strength, Pu, resulting from the application of the Load Combinations 3-7 or 3-8. A line of bracing, for the purpose of this provision, is
defined as a single line or parallel lines whose plan offset is 10 percent
or less of the building dimension perpendicular to the line of bracing.
9.2.d. Width-Thickness Ratios: Width-thickness ratios of stiffened and unstiffened compression elements in braces shall comply with Sect. B5 in
the Specification. Braces shall be compact or non-compact, but not
slender (i.e., λ < λr). Circular sections shall have an outside diameter to
wall thickness ratio not exceeding 1,300 / Fy; rectangular tubes shall have
a flat-width to wall thickness not exceeding 110 / √
Fy , unless the circular
section or tube walls are stiffened.
9.2.e. Built-up Member Stitches: For all built-up braces, the first bolted or
welded stitch on each side of the midlength of a built up member shall
be designed to transmit a force equal to 50 percent of the nominal
strength of one element to the adjacent element. Not less than two
stitches shall be equally spaced about the member centerline.
9.3. Bracing Connections
9.3.a. Forces: The required strength of bracing joints (including beam-to-column joints if part of the bracing system) shall be the least of the
following:
1. The design axial tension strength of the bracing member.
2. The force in the brace resulting from the Load Combinations 3-7 or
3-8.
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3. The maximum force, indicated by an analysis, that is transferred to
the brace by the system.
9.3.b. Net Area: In bolted brace joints, the minimum ratio of effective net
section area to gross section area shall be limited by:
Ae 1.2αPu∗
≥
Ag
φtPn
(9-1)
where:
Ae = Effective net area as defined in Equation B3-1 of the Specification.
Pu∗ = Required strength on the brace as determined in Sect. 9.3.a.
Pn = Nominal tension strength as specified in Chapter D of the
Specification.
φt = Special resistance factor for tension = 0.75.
α = Fraction of the member force from Sect. 9.3.a that is transferred
across a particular net section.
9.3.c. Gusset Plates:
1. Where analysis indicates that braces buckle in the plane of the gusset
plates, the gusset and other parts of the connection shall have a design
strength equal to or greater than the in-plane nominal bending
strength of the brace.
2. Where the critical buckling strength is out-of-plane of the gusset
plate, the brace shall terminate on the gusset a minimum of two times
the gusset thickness from the theoretical line of bending which is
unrestrained by the column or beam joints. The gusset plate shall
have a required compressive strength to resist the compressive design
strength of the brace member without local buckling of the gusset
plate. For braces designed for axial load only, the bolts or welds shall
be designed to transmit the brace forces along the centroids of the
brace elements.
9.4. Special Bracing Configuration Requirements
9.4.a. V and Inverted V Type Bracing:
1. The design strength of the brace members shall be at least 1.5 times
the required strength using Load Combinations 3-5 and 3-6.
2. The beam intersected by braces shall be continuous between
columns.
3. A beam intersected by V braces shall be capable of supporting all
tributary dead and live loads assuming the bracing is not present.
4. The top and bottom flanges of the beam at the point of intersection
of V braces shall be designed to support a lateral force equal to 1.5
percent of the nominal beam flange strength (Fy bf tf).
9.4.b. K bracing, where permitted:
1. The design strength of K brace members shall be at least 1.5 times
the required strength using Load Combinations 3-5 and 3-6.
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2. A column intersected by K braces shall be continuous between
beams.
3. A column intersected by K braces shall be capable of supporting all
dead and live loads assuming the bracing is not present.
4. Both flanges of the column at the point of intersection of K braces
shall be designed to support a lateral force equal to 1.5 percent of the
nominal column flange strength (Fy bf tf).
9.5. Low Buildings
Braced frames not meeting the requirements of Sect. 9.2 through 9.4 shall only
be used in buildings not over two stories and in roof structures if Load
Combinations 3-7 and 3-8 are used for determining the required strength of the
members and connections.
10.
REQUIREMENTS FOR ECCENTRICALLY BRACED FRAMES (EBF)
10.1. Scope
Eccentrically braced frames shall be designed so that under inelastic earthquake
deformations, yielding will occur in the links. The diagonal braces, the columns,
and the beam segments outside of the links shall be designed to remain elastic
under the maximum forces that will be generated by the fully yielded and strain
hardened links, except where permitted by this section.
10.2. Links
10.2.a. Beams with links shall comply with the width-thickness ratios in
Table 8-1.
10.2.b. The specified minimum yield stress of steel used for links shall not
exceed Fy = 50 ksi.
10.2.c. The web of a link shall be single thickness without doubler plate
reinforcement and without openings.
10.2.d. Except as limited by Sect. 10.2.f., the required shear strength of the link,
Vu, shall not exceed the design shear strength of the link, φVn, where:
φVn = Link design shear strength of the link = the lesser of φVp or
2φMp / e, kips.
Vp = 0.6Fy (d − 2tf) tw, kips.
φ = 0.9.
e = link length, in.
10.2.e. If the required axial strength, Pu, in a link is equal to or less than 0.15Py,
where Py = AgFy, the effect of axial force on the link design shear strength
need not be considered.
10.2.f. If the required axial strength, Pu, in a link exceeds 0.15Py, the following
additional limitations shall be required:
1. The link design shear strength shall be the lesser of φVpa or
2φMpa / e, where:
Vpa = Vp √
1 − (Pu / Py)2
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Mpa = 1.18Mp[1 − (Pu / Py )]
φ = 0.9
2. The length of the link shall not exceed:
[1.15 − 0.5ρ(Aw / Ag)]1.6Mp / Vp for ρ(Aw / Ag) ≥ 0.3 and
1.6Mp / Vp for ρ(Aw / Ag) < 0.3, where:
Aw = (d − 2tf) tw
ρ = Pu / Vu
10.2.g. The link rotation angle is the plastic angle between the link and the beam
outside of the link when the total story drift is 0.4R times the drift
determined using the specified base shear V. The term 0.4R shall be equal
to or greater than 1.0. Except as noted in Sect. 10.4.d, the link rotation
angle shall not exceed the following values:
1. 0.09 radians for links of length 1.6Mp / Vp or less.
2. 0.03 radians for links of length 2.6Mp / Vp or greater.
3. Linear interpolation shall be used for links of length between
1.6Mp / Vp and 2.6Mp / Vp.
10.2.h. Alternatively, the top story of an EBF building having over five stories
shall be a CBF.
10.3. Link Stiffeners
10.3.a. Full depth web stiffeners shall be provided on both sides of the link web
at the diagonal brace ends of the link. These stiffeners shall have a
combined width not less than (bf − 2tw) and a thickness not less than
0.75tw or 3⁄8-in., whichever is larger, where bf and tw are the link flange
width and link web thickness, respectively.
10.3.b. Links shall be provided with intermediate web stiffeners as follows:
1. Links of lengths 1.6Mp / Vp or less shall be provided with intermediate
web stiffeners spaced at intervals not exceeding (30tw − d / 5) for a
link rotation angle of 0.09 radians or (52tw − d / 5) for link rotation
angles of 0.03 radians or less. Linear interpolation shall be used for
values between 0.03 and 0.09 radians.
2. Links of length greater than 2.6Mp / Vp and less than 5Mp / Vp shall be
provided with intermediate web stiffeners placed at a distance of 1.5bf
from each end of the link.
3. Links of length between 1.6Mp / Vp and 2.6Mp / Vp shall be provided
with intermediate web stiffeners meeting the requirements of 1 and
2 above.
4. No intermediate web stiffeners are required in links of lengths greater
than 5Mp / Vp.
5. Intermediate link web stiffeners shall be full depth. For links less than
25 inches in depth, stiffeners are required on only one side of the link
web. The thickness of one-sided stiffeners shall not be less than tw or
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3⁄ -in., whichever is larger, and the width shall be not less than
8
(bf / 2) − tw. For links 25 inches in depth or greater, similar intermediate stiffeners are required on both sides of the web.
10.3.c. Fillet welds connecting link stiffener to the link web shall have a design
strength adequate to resist a force of AstFy, in which Ast = area of the
stiffener. The design strength of fillet welds fastening the stiffener to the
flanges shall be adequate to resist a force of AstFy / 4.
10.4. Link-to-Column Connections
Where a link is connected to a column, the following additional requirements
shall be met:
10.4.a. The length of links connected to columns shall not exceed 1.6Mp / Vp
unless it is demonstrated that the link-to-column connection is adequate
to develop the required inelastic rotation of the link.
10.4.b. The link flanges shall have complete penetration welded joints to the
column. The joint of the link web to the column shall be welded. The
required strength of the welded joint shall be at least the nominal axial,
shear, and flexural strengths of the link web.
10.4.c. The need for continuity plates shall be determined according to the
requirements of Sect. 8.5.
10.4.d. Where the link is connected to the column web, the link flanges shall
have complete penetration welded joints to plates and the web joint shall
be welded. The required strength of the link web shall be at least the
nominal axial, shear, and flexural strength of the link web. The link
rotation angle shall not exceed 0.015 radians for any link length.
10.5. Lateral Support of Link
Lateral supports shall be provided at both the top and bottom flanges of link at
the ends of the link. End lateral supports of links shall have a design strength of
6 percent of the link flange nominal strength computed as Fy bf tf.
10.6. Diagonal Brace and Beam Outside of Link
10.6.a. The required combined axial and moment strength of the diagonal brace
shall be the axial forces and moments generated by 1.25 times the
nominal shear strength of the link as defined in Sect. 10.2. The design
strengths of the diagonal brace, as determined by Sect. H (including
Appendix H) of the Specification, shall exceed the required strengths as
defined above.
10.6.b. The required strength of the beam outside of the link shall be the forces
generated by at least 1.25 times the nominal shear strength of the link
and shall be provided with lateral support to maintain the stability of the
beam. Lateral supports shall be provided at both top and bottom flanges
of the beam and each shall have a design strength to resist at least 1.5
percent of the beam flange nominal strength computed as Fy bf tf.
10.6.c. At the connection between the diagonal brace and the beam at the link
end of the brace, the intersection of the brace and beam centerlines shall
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PART I—LOAD AND RESISTANCE FACTOR DESIGN (LRFD)
be at the end of the link or in the link. The beam shall not be spliced
within or adjacent to the connection between the beam and the brace.
10.6.d. The required strength of the diagonal brace-to-beam connection at the
link end of the brace shall be at least the nominal strength of the brace.
No part of this connection shall extend over the link length. If the brace
resists a portion of the link end moment, the connection shall be designed
as Type FR (Fully Restrained).
10.6.e. The width-thickness ratio of brace shall satisfy λp of Table B5.1 of the
Specification.
10.7. Beam-to-Column Connections
Beam-to-column connections away from links are permitted to be designed as
a pin in the plane of the web. The connection shall have a design strength to
resist torsion about the longitudinal axis of the beam based on two equal and
opposite forces of at least 1.5 percent of the beam flange nominal strength
computed as Fy bf tf acting laterally on the beam flanges.
10.8. Required Column Strength
The required strength of columns shall be determined by Load Combinations
3-5 and 3-6 except that the moments and axial loads introduced into the column
at the connection of a link or brace shall not be less than those generated by 1.25
times the nominal strength of the link.
11.
QUALITY ASSURANCE
The general requirements and responsibilities for performance of a quality
assurance plan shall be in accordance with the requirements of the regulatory
agency and specifications by the design engineer.
The special inspections and special tests needed to establish that the construction
is in conformance with these provisions shall be included in a quality assurance
plan.
The minimum special inspection and testing contained in the quality assurance
plan beyond that required by the Specification shall be as follows:
Groove welded joints subjected to net tensile forces which are part of the
seismic force resisting systems of Sects. 8, 9, and 10 shall be tested 100
percent either by ultrasonic testing or by other approved equivalent methods
conforming to AWS D1.1.
Exception: The nondestructive testing rate for an individual welder shall be
reduced to 25 percent with the concurrence of the person responsible for
structural design, provided the reject rate is demonstrated to be 5 percent or
less of the welds tested for the welder.
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Part II—Allowable Stress Design (ASD) Alternative
As an alternative to the LRFD seismic design procedures for structural steel design
given in PART I, the design procedures in the Specification for Structural Steel
Buildings—Allowable Stress Design and Plastic Design, AISC 1989 are permitted as
modified by PART II of these provisions. When using ASD, the provisions of PART I
of these seismic provisions shall apply except the following sections shall be substituted for, or added to, the appropriate sections as indicated:
1.
SCOPE
Revise the first paragraph of PART I, Sect. 1 to read as follows:
These special requirements are to be applied in conjunction with the AISC
Specification for Structural Steel Buildings—Allowable Stress Design and Plastic Design hereinafter referred to as Specification. They are intended for the
design and construction of structural steel members and connections in buildings
for which the design forces resulting from earthquake motions have been
determined on the basis of energy dissipation in the nonlinear range of response.
3.
LOADS, LOAD COMBINATIONS AND NOMINAL STRENGTHS
Substitute the following for Section 3.2 in PART I:
3.2. Nominal Strengths
The nominal strengths of members shall be determined as follows:
3.2.a. Replace Sect. A5.2 of the Specification to read: “The nominal strength
of structural steel members for resisting seismic forces acting alone or
in combination with dead and live loads shall be determined by multiplying 1.7 times the allowable stresses in Sect. D, E, F, G, J, and K.”
3.2.b. Amend the first paragraph of Sect. N1 of the Specification by deleting
“or earthquake” and adding: “The nominal strength of members shall be
determined by the requirements contained herein. Except as modified
by these rules, all pertinent provisions of Chapters A through M shall
govern.”
3.2.c. In Sect H1 of the Specification the definition of Fe ′ shall read as follows:
Fe ′ =
π2E
(Klb / rb)2
where:
lb = the actual length in the plane of bending.
rb = the corresponding radius of gyration.
K = the effective length factor in the plane of bending.
Add the following section to PART I:
3.3. Design Strengths
3.3.a. The design strengths of structural steel members and connections subjected to seismic forces in combination with other prescribed loads shall
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PART II—ALLOWABLE STRESS DESIGN (ASD) ALTERNATIVE
be determined by converting allowable stresses into nominal strengths
and multiplying such nominal strengths by the resistance factors herein.
3.3.b. Resistance factors, φ, for use in Part II shall be as follows:
Flexure
φb = 0.90
Compression and axially loaded composite members
φc = 0.85
Eyebars and pin connected members:
Shear of the effective area
Tension on net effective area
Bearing on the project area of pin
φsf = 0.75
φt = 0.75
φt = 1.0
Tension members:
Yielding on gross section
Fracture in the net section
φt = 0.90
φt = 0.75
Shear
φv = 0.90
Connections:
Base plates that develop the strength of the
members or structural systems
Welded connections that do not develop the strength
of the member or structural system, including
connection of base plates and anchor bolts
Partial Penetration welds in columns when
subjected to tension stresses
High strength bolts (A325 and A490) and rivets:
Tensile strength
Shear strength in bearing-type joints
Slip-critical joints
A307 bolts:
Tensile strength
Shear strength in bearing-type joints
φ = 0.90
φ = 0.67
φ = 0.80
φ = 0.75
φ = 0.65
φ = 1.0
φ = 0.75
φ = 0.60
Substitute the following for Section 7 in PART I in its entirety:
7.
REQUIREMENTS FOR ORDINARY MOMENT FRAMES (OMF)
7.1. Scope
Ordinary Moment Frames (OMF) shall have a design strength as provided in
the Specification to resist the Load Combinations 3-5 and 3-6 as modified by
the following added provisions:
7.2. Joint Requirements
All beam-to-column and column to beam connections in OMF which resist
seismic forces shall meet one of the following requirements:
7.2.a. Type 1 connections conforming with Sect. 8.2, except that the required
flexural strength, Mu, of a column-to-beam joint are not required to
exceed that required to develop the nominal plastic flexural strength of
the connection.
7.2.b. Type 1 connections capable of inelastic deformation and the design
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strengths of the connections meeting the requirements of Sect. 7.1 using
the Load Combinations 3-7 and 3-8.
7.2.c. Either Type 1 or Type 3 connections are permitted provided:
1. The design strengths of the members and connections meet the
requirements of Sect. 7.1.
2. The connections have been demonstrated by cyclic tests to have
adequate rotation capacity at a story drift calculated at a horizontal
load of 0.4R × E (where the term 0.4R is equal to or greater than 1.0).
3. The additional drift due to Type 3 connections shall be considered in
design.
Type 1 and Type 3 connections are described in detail in Sect. A2 of the
Specification.
Substitute the following in Sections 10.6.a and 10.6.d in PART I:
10.6.a. Delete reference to Appendix H.
10.6.d. The last sentence shall read: “If the brace resists a portion of the link end
moment as described above, the connection shall be designed as a Type
1 connection.”
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Commentary on the
Seismic Provisions for
Structural Steel Buildings
June 15, 1992
Part I—LRFD Provisions
1.
SCOPE
Load and Resistance Factor Design (LRFD) is an improved approach to the
design of structural steel for buildings. The method involves explicit consideration of limit states, multiple load and resistance factors, and implicit probabilistic
determination of reliability. The designation LRFD reflects the concept of
factoring both loads and resistance. The LRFD method was devised to offer the
designer greater flexibility, more rationality and possible overall economy.
The First Edition of the LRFD Specification was published and distributed in
1986.1 It did not contain the special requirements necessary in the design and
construction of steel buildings which are required to respond to high earthquake
input by deformations into the nonlinear range. The seismic design forces
specified in the building codes have been set with consideration given to the
energy dissipation generated during the non-linear response.
The provisions contained in this document are to be used in conjunction with
the AISC LRFD Specification in the design of buildings in the areas of moderate
and high seismicity.
The load provisions have been modified from those contained in the Specification to be consistent with the load provisions contained in the soon to be
published BOCA and SBCCI building codes and the ASCE 7-93, Minimum
Design Loads for Buildings and Other Structures.2 All these new seismic load
provisions are modeled on the the 1991 NEHRP3 earthquake provisions.
2.
SEISMIC PERFORMANCE CATEGORIES
Buildings are classified into three types depending on the occupancy and use of
each as related to the special hazards resulting from earthquake environment.
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The Seismic Hazard Exposure Groups listed in Table 2-1 are defined in detail,
with examples of buildings in each type, in ASCE 7-93. The Seismic Performance Category to be used in the design of a specific building is defined by the
seismic coefficient representing the peak velocity-related acceleration of the
building site, Av, and the Seismic Hazard Exposure Group related to the
occupancy and use of the building. The five categories, A through E, given in
Table 2-2 specify design and detail requirements that would be required for the
seismic design of the building. These categories establish the level of requirements to be used in items such as detailing limitations, quality assurance, method
of analyses, orthogonal effects, and change of building use. The general requirements for each of the categories are given in ASCE 7-93. The differences related
specifically to structural steel design are repeated in this Specification.
3.
LOADS AND LOAD COMBINATIONS
The most frequently used load factors and load combinations given in Sect. A4.1
of the Specification are repeated in this Section to reduce the amount of
cross-referencing to other documents. They have been modified to be consistent
with the anticipated ASCE 7-93. The most notable modification is the reduction
of the load factor on E to 1.0. This results from the limit states load model used
in ASCE 7-93. For design of structures subjected to impact loads, see the
Specification.
The earthquake load and load effects E in ASCE 7-93 are composed of two parts.
E is the sum of the seismic horizontal load effects and one half of Av times the
dead load effects. The second part adds an effect simulating vertical accelerations concurrent to the usual horizontal earthquake effects.
The load factors and load combinations reflect the fact that when several loads
act in combination with the dead load, e.g., dead plus live plus earthquake loads,
only one of these takes on its maximum lifetime value, while the other load is
at its “arbitrary point-in-time value,” at a value which can be expected to be on
the structure at any time. The most critical effect may occur when one or more
load types are not acting.
The basic requirements for dual systems are given in the Glossary to clarify the
use of the EBF in a dual system and to indicate that steel moment frames can
also be used as part of a dual system with concrete shear walls.
An amplification factor to earthquake load E of 0.4R is prescribed for limited
use in this set of provisions. It is used as an amplification of the deflections
determined using the earthquake forces specified in ASCE 7-93. It was derived
by assuming that deflections due to large earthquake response would be the same
regardless of the reductions in applied forces due to the inelastic response of the
type of lateral force resisting system.56 The amount of this amplification was
assumed to be two times the deflections generated by forces specified for a
buildings with R = 5. This amplification factor is thus 2R / 5 or 0.4R. However,
with R = 2.5 or less it is felt that the amplification factor should not be less than
1.0. The load combinations to be used with the amplification factor are given
by formulas 3-7 and 3-8. Specific values of R are not needed for determination
of the amplified load because R is cancelled out when substituted in the formula
for the horizontal seismic base shear, V. The added complication that would be
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required to consider orthogonal effects with the amplified force is not deemed
to be necessary.
The ASCE 7-93 provisions are detailed earthquake load provisions in which two
methods of analysis are provided. The first is frequently referred to as the “Static
Force Procedure” or “Equivalent Lateral Force Procedure.” The second method
is the “Modal Analysis Procedure.” In both methods a linearly elastic model is
assumed. Other “Dynamic Analysis Procedures” are permitted both with linearly elastic or non-linear models as long as the internal forces and deformations
in the members are determined using a model consistent with the procedure
adopted. Guidelines for use of these other methods of analyses are provided in
the Commentary to ASCE 7-93.
These earthquake provisions refer to the load provisions of ASCE 7-93. By
changing the load combination portion of Section 3, these provisions can be
made compatible with other sets of load provisions.4 For instance, the following
changes can be made to the provisions in Section 3 to make them compatible
with the following document: (Sn is used in this Commentary for snow loads to
distinguish them from site effects that use the symbol S).
1991 UNIFORM BUILDING CODE:5
(SEAOC seismic provisions are similar)6
The required strength on the structure and its elements must be determined from
the appropriate critical combination of factored loads. The most critical effect
may occur when one or more loads are not acting. The following load combinations and corresponding load factors shall be investigated:
1.4D
(3-1)
1.2D + 1.6L + 0.5(Lr or S or R′)
(3-2)
1.2D + 1.6(Lr or S or R′) + (0.5L or 0.8W)
(3-3)
1.2D + 1.3W + 0.5L + 0.5(Lr or S or R′)
(3-4)
1.2D + 1.5E + 0.5L + 0.2S
(3-5)
0.9D − (1.3W or 1.5E)
(3-6)
Exception: The load factor on L in Load Combinations 3-3, 3-4, and 3-5 shall
equal 1.0 for garages, areas occupied as places of public assembly, and all areas
where the live load is greater than 100 psf.
Other special load combinations are included with specific design requirements
throughout these provisions.
Where required by these provisions, an amplification factor is applied on the
earthquake load E = 3⁄8Rw, where Rw is a response factor similar to the factor R
except used to reduce the earthquake load to a working stress design level.
Earthquake loads are similar to those found in ASCE 7-93 except for the Rw
factor.
Earthquake loads are defined in detail in Section 2334 of 1991 UBC. The revised
load combinations are:
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1.2D + (3Rw / 8)E + 0.5L + 0.2S
(3-7)
0.9D − (3Rw / 8)E
(3-8)
Exception: The load factor on L in Load Combination 3-7 shall equal 1.0 for
garages, areas occupied as places of public assembly, and all areas where the
live load is greater than 100 psf.
The amplification factor was derived by using the similar assumptions that were
used in deriving the factor for ASCE 7-93. The same type of building with R =
5 in ASCE 7-93 has a Structure System Coefficient Rw = 8 in 1991 UBC. The
deflection determined by this Rw was used as the value to be amplified by 3.
Thus (3Rw / 8)E.
Where the use of the amplification factor to load E is required, orthogonal
effects need not be included.
The 1991 UBC outlines in detail many of the requirements for “Dynamic Lateral
Force Procedure.” The following is a summary of these requirements:
The ground motion may be defined in one of five ways:
1. The plot of a normalized response spectra may be used.
2. A site specific response spectra based on geologic, tectonic seismologic, and
soil characteristics of the site may be used. As per SEAOC the damping ratio
shall be 5 percent unless another value is shown to be consistent with the
structural behavior of the building.
3. Site specific time histories are to be representative of actual earthquake
motions. Spectra developed from these time histories would follow item (2)
above.
4. Site specific response spectra and time histories developed for sites with a
profile having more than 40 feet of soft clay per SEAOC shall be based on
ground motion having a 10 percent probability of exceedance in 50 years;
the effects of lengthening of the structural period on response amplification
due to soil-structure resonance shall be included; and the design base shear
shall be determined by dividing by a factor not greater than Rw for the
structure.
5. A two-thirds factor shall be used on horizontal motions to determine the
vertical component of ground motion unless specifically determined otherwise for the site. The mathematical model shall represent the actual structure
adequately for the calculation of all the significant features of the dynamic
response. Three dimensional models shall be used for highly irregular plan
configurations if a rigid or semi-rigid diaphragm is used.
A response spectrum analysis shall be an elastic dynamic analysis of all the
significant peak modal responses combined in a statistical manner to obtain an
approximate total structural response. When the base shear is less than that
determined from the Static Lateral Force Procedure, it shall be increased to 100
percent of the static base shear for irregular structures, shall be taken as 90
percent of the static base shear for regular structures where the fundamental
period is determined using the structural characteristics of the building system,
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and shall be set at 80 percent for regular structures. Accidental torsion shall be
accounted for by appropriate adjustments in the model. Where a dual system is
used, the combined system shall be accounted for in the modelling; the backup
Special Moment Frame (SMF) shall be capable of resisting 25 percent of the
base shear used for the design of the total system. The analysis of the backup
SMF may either use the Static of Dynamic Lateral Force Procedures.
A time history analysis shall be an elastic or inelastic dynamic analysis of a
model of a structure subjected to specified time history of ground motion. The
time dependent dynamic response of the structure to these motions is obtained
through numerical integration of its equations of motion. These analyses shall
be based on established principles of mechanics.
Scaling of base shear determined by a response spectrum analysis results in
making the Load Combinations 3-1 through 3-6 as well as 3-7 and 3-8 applicable
to this method of analysis in the 1991 UBC. No scaling effect is specified for
the results of time history dynamic analysis (either elastic or inelastic). In this
case, it is necessary to define the specified time histories which will result in the
structure responding to the limit of essentially elastic response. This would be
the level to determine the required resistance of the system. In order to determine
the deformations corresponding to the specified drift limits, the force level shall
be divided by a factor of 1.5.
4.
STORY DRIFT
Deflection limits are commonly used in design to assure the serviceability of
the structure. These serviceability limit states are variable, since they depend
upon the structural usage and contents. The Specification does not specify these
serviceability limits, since they are regarded as a matter of engineering judgment, rather than general design limits.54
Like deflection limits, drift limits for both wind and seismic design are excluded
from these Seismic Provisions. Research has shown that seismic drift control
provides a function beyond assuring the serviceability of the structure. The
added strength and stiffness which drift limits often provide in moment frames
improves the performance of structures during earthquakes. Model codes, load
standards, and resource documents contain specific seismic drift limits but there
are major differences among them. There is neither uniform agreement regarding appropriate code specified drift limits nor how they should be applied.
Further it is difficult to estimate the actual story drift of moment frames with
panel zone yielding. Nevertheless, drift control is important to serviceability and
stability of the structure. It is recommended the designer review drift limits in
the appropriate code and use those applicable for the serviceability and stability
of the structure under consideration.
The story drift limitations of ASCE 7-93 are applied to an amplified story drift
that estimates the story drift that would occur during a large earthquake. The
story drift is defined as the difference of deflection between the top and bottom
of the story under consideration. For determining the story drift the deflection
determined using the earthquake forces E is amplified by a deflection amplification factor, Cd, which is dependent on the type of building system. The story
drifts when determined by an elastic analysis, including the P-∆ effect when
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TABLE C-4.1
Tentative Allowable Story Drift
Seismic Hazard Exposure Group
Building
I
II
III
Single story buildings without equipment attached to the structural resisting
system and with interior walls, partitions, ceilings, and exterior wall system
that have been designed to
accommodate the story drifts.
No limit
0.020hsx
0.015hsx
Buildings with 4 stories or less with interior walls, partitions ceilings, and exterior wall system that have been designed to accommodate the story drifts.
0.025hsx
0.020hsx
0.015hsx
All other buildings.
0.020hsx
0.015hsx
0.010hsx
Where hsx is the story height of the story drift calculated.
applicable, have limits depending on the Seismic Hazard Exposure Group of
the building as shown in Table C-4.1.
In calculating the elastic drift, the forces may be based on the fundamental period
of the building without the arbitrary limit specified for determining the seismic
design forces in the framing members. ASCE 7-93 does not prescribe explicit
requirements for building separations. An admonition is included, however, that
all portions of the building shall be designed and constructed as an integral unit
in resisting seismic forces unless separated structurally by a sufficient distance
to avoid damaging contact between components under amplified deformations.
The latter are determined by multiplying the elastic deflection by a deflection
amplification factor, Cd, which is based on the type and materials of the seismic
resisting system. If the effects of hammering between segments can be shown
not to be detrimental, separations could be reduced.
1991 UBC Requirements:
In order to comply with the 1991 UBC requirements, the story drift shall be
calculated including the translational and torsional deflections resulting from
the application of unfactored lateral forces. Story drift is defined as the displacement of one level relative to the level above or below. The calculated story drift
shall not exceed 0.04 / Rw nor 0.005 times the story height for structures with
fundamental periods of less than 0.7 seconds and shall not exceed 0.03 / Rw nor
0.004 times the story height for structures with fundamental periods of 0.7
seconds or greater. For the purpose of this limit the fundamental period is the
same as that used for determining the base shear.
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For calculating the drift, the lateral forces may be calculated using a base shear
V defined as:
V=
ZIC
W, in which
Rw
Z = The seismic zone coefficient.
I = An importance factor.
Rw = A numerical coefficient related to the type of construction.
C=
1.25S
, in which
2
T ⁄3
S = Site coefficient.
T = Fundamental period of vibration, which may be determined using the
structural properties and deformational characteristics of the resisting
elements of the lateral force resisting framing. Method A of determining
T need not be applied for drift determination. The lower bound of 0.075
on the ratio C / Rw may also be neglected.
W = Dead load used to calculate seismic loads.
The story drift limits need not be applied if it is demonstrated that greater drift
can be tolerated without affecting life safety by damage to either structural and
non-structural elements.
There are no drift limits on single story steel framed structures with low
occupancies. This would generally apply to buildings such as warehouses,
parking garages, aircraft hangers, factories, workshops and agricultural buildings. These buildings are not allowed to have brittle finishes and are not allowed
to have equipment attached to the structural frame unless the finish or equipment
attachment is detailed to accommodate the additional drift.
5.
MATERIAL SPECIFICATIONS
The list of structural steels for use in designing to earthquake motion has been
chosen with consideration given to the inelastic properties of the steels and their
weldability. In general, the steels selected possess the following characteristics:
• Ratio of tensile strength to yield strength between 1.2 to 1.8.
• Pronounced stress-strain plateau at yield strength.
• Large inelastic strain capability.
• Tension elongation of 20 percent or greater in a 2-in. gage length.
• Good weldability for inelastic behavior.
Other steels including those with a specified yield point greater than 50 ksi
should not be used without demonstrating that equivalent inelastic behavior can
be attained.
6.
COLUMN REQUIREMENTS
6.1. Column Strength
During the maximum probable earthquake expected at any site, axial forces
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calculated using the specified design earthquake may be exceeded. This is a
result of the reduction in lateral force for use in analysis of an elastic model of
the structure, the underestimation of the overturning forces in this analysis, and
the concurrent vertical accelerations which are not explicitly specified as a
required design load. The amplifications required in this section provide an
approximation of these actions by providing a limit to the required axial force.
The two special Load Combinations 6-1 and 6-2 account for these effects; one
as a minimum required column compressive required strength and the other on
the minimum required tensile strength. They are to be applied without consideration of any concurrent flexure on the members.
The exceptions provided for these limits are self limiting conditions stating that
the required axial strengths need not exceed the limits based on the design
strength of the overall system to transfer axial loads to the column. For instance,
if pile foundations are used, the design strength of the piles in tension may be
much larger than the required strength because the size of the foundation may
depend on the required strength in compression.
6.2. Column Splices
Column splices are required to have design strengths adequate to join column
elements together not only to resist the axial, flexural, and shear forces required
at the splice location by the usual load combinations 3-1 through 3-6 but also
the forces specified in 6.1.
Butt weld splices in columns where it is anticipated that potential dynamic
loading consists only of wind or earthquake forces are not required by these
specifications to provide the transition of thicknesses given in Section 9.20 of
AWS D1.1.7 If other types of frequent, high cycle dynamic loadings are also
present, the transition requirements should be met.
Partial penetration welds in thick members, such as occur in column flange
splices, are very brittle under tensile loading, showing virtually no ductility.8–9
Recognizing this behavior in seismic design, the location of column splices is
moved away from the beam-to-column connection to reduce bending and a 50
percent increase is stipulated in required strength of the splice.
The possibility for developing tensile stresses in such welds during a maximum
probable seismic event should be considered. If there is probability of such a
condition developing, the use of splice plates welded to the lower part of the
column and bolted to the upper part is suggested. If for the noted adverse
condition, the suggested detail is not practical, the possibility of fracture in
partial penetration welded joints should be recognized, and some restraint from
uncontrolled relative movement at the splice be provided. This can be achieved,
for example, by having wide splice plates on both sides of the column web to
maintain alignment. Shake table experiments have shown that if some columns,
unattached at the base, reseat themselves after lifting, the performance of a steel
frame remains tolerable.10
These provisions apply for common frame configurations. The designer should
review the conditions found in columns in tall stories, large changes in column
sizes at the splice, or where the possibility of a single curvature exists on a
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column over multiple stories to determine if special design strength or special
detailing is necessary at the splice.
7.
REQUIREMENTS FOR ORDINARY MOMENT FRAMES (OMF)
7.1. Scope
Ordinary moment frames of structural steel are moment frames which do not
meet the requirements for special design and detailing contained in Section 8.
OMF of structural steel do exist and are being built in all areas of seismic activity.
Experience has shown that in most instances the buildings of this type have
responded without significant structural damage. In recent years advances in
analytical procedures have minimized the natural margins of safety normally
found in buildings that were designed by approximate methods. Thus it is
prudent to require that the design of the beam-to-column connection be adequate
to develop the strength of the members framing into the connection as is
specified in Sect. 8.2 unless the connection has a design strength significantly
larger than the required strengths required by Load Combinations 3-5 and 3-6.
Thus unless the connection can develop the full strength of members framing
into it, the Load Combinations 3-7 and 3-8 should be used to provide the required
strength on the connection.
7.2. Joint Requirements
Although for OMF it is not required to meet most of the special detailing
requirements given in Sect. 8, consideration should be given to using as many
of the requirements as practical, particularly in those locations where good
engineering judgment would suggest that the use of the special detailing
requirements would provide improved system and member ductility and stability. The provision requiring a demonstration of rotation capacity is included to
permit the use of connections not permitted under the provisions of Sect. 8, such
as top and bottom angle joints, in areas where the added drift is acceptable.
8.
REQUIREMENTS FOR SPECIAL MOMENT FRAMES (SMF)
8.1. Scope
The requirements in this Section are for those buildings whose lateral force
resisting systems are moment frames in the higher seismic zones. The special
provisions, when reasonably applied, provide SMF with reliable ductile systems. Non-ductile behavior is inhibited so that nonlinear response to large
earthquake motions can occur in components of the frames having a capability
of ductile behavior. The concepts are not new but the provisions are supported
by tests and analyses.11–17 SMF systems when properly designed have, in
general, resulted in reliable ductile structural systems that respond well to high
earthquake motions for both low and high rise buildings.
Inelastic energy absorption through ductile behavior of members of SMF can
occur at three places usually adjacent to the beam-to-column connection.
Flexural hinges can form in the beams and columns and shear yielding can occur
in the area of the panel zone. Within limits and specific restraints, inelastic
yielding is permitted in each or in combinations of these three areas. The primary
concern when designing the frame for inelastic behavior is to prevent brittle
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fracture and severe buckling in and adjacent to the zone of inelasticity. The final
selection of the appropriate zones of inelasticity is left to the design engineer.
Different problems are presented to the design engineer depending on which of
the three areas is chosen to have the lowest inelastic threshold.
Yielding in columns is permitted but is considered by many design engineers to
be the least desirable. Special limitations are provided for this type of yielding
by the provisions in Sect. 8.6. and the bracing required in Sect. 8.7. If the first
inelastic mode is chosen to be shear yielding of the panel zone, the limitations
of Sect. 8.3 would be required. This usually results in the flexibility of the panel
zone being a significant contributor to the total story drift and consideration of
this flexibility should be included in analyses.18 If the designer chooses to avoid
inelastic behavior at the above two locations, the yield hinge will form in the
beam. This requires the critical design items to be the beam-to-column connection and the beam stability.
8.2. Beam-to-Column Joints
The special limitations provided for these joints are intended to assure that
inelastic hinging that may occur in the connection during the response to high
seismic activity will not take place at the joinery but in one of the two adjoining
locations, namely in the beam or in the panel zone.19–24 Some of the more
common beam-to-column connections are illustrated in Fig. C-8.1. Beam-tocolumn connections are not only designed to meet the loads prescribed by the
Load Combinations 3-1 through 3-6 but also designed to resist the requirements
based on the nominal strengths of the members actually used in the framing
system. Frequently the frame member sizes may be sized to limit drift or to meet
requirements of load combinations other than those containing seismic loads.
Thus to provide frames having the capability of deforming into the nonlinear
range without having a connection failure, the required strength on the connection is most frequently based on the design strength of the members actually
used.
An exception is provided for joints that are not designed to contribute to the
lateral force resisting system. In order to demonstrate that the joint will be
capable of undergoing large deformation, the elastic or inelastic joint rotations
that would be induced by deforming the frame into an amplified displacement
of 0.4R times that under Load Combinations 3-5 and 3-6 are required. The term
0.4R should not be less than 1.0. If the “non-moment resisting” web connection
were to be a shear tab joined to the column flange by welding and bolted to the
beam web, the connection should be proportioned to either yield in the tab or
by use of horizontally slotted holes for the bolts. Fracture should not occur in
the welded joint to the column. (See Fig. C-8.2.)
The required shear strength, Vu, of the beam-to-column joint is defined as the
summation of the factored gravity loads and the shear resulting from the required
moments on the two ends of the beam. The easy method is to assume that Mp
occurs at each end of the beam. However, when Load Combination 3-7 is used
in which one end only of the beam reaches Mp, or the panel zone nominal shear
reaches Vn as defined in Sect. 8.2.a, the shear resulting from hinging at both ends
of the beam need not be used.
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a
b
c
d
e
f
Fig. C-8.1. Beam-to-column connections.
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When the required flexural strength of the joint is Mp of the beam, the type of
joint is prescribed to be one of three types:
First is the joint where both flanges and web are fully welded to develop their
portions of the moment and shear strength of the beam. (See Fig. C-8.3.)
Second is the joint of those beams which have a ratio of the flexural nominal
strength of the flanges only to the flexural nominal strength of the full section
of at least 70 percent. For this connection, the flanges are joined with complete
penetration welded joints whereas the web would be designed to carry the
ROTATION BY NON
LINEAR BENDING
OF JOINT MEMBERS
SHORT SLOTTED
HOLES
ROTATION BY BOLT
SLIP
Fig. C-8.2. Simple connections.
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CONTINUITY
PLATE, TOP
& BOTTOM
ERECTION
BOLTS
SHEAR PLATE
TYP.
FULL PENETRATION
TOP & BOTTOM
FLANGE
(a)
ERECTION BOLT
CONTINUITY
PLATE, TOP
& BOTTOM
SHEAR PLATE
ERECTION BOLT
TYP.
FULL PENETRATION
TOP & BOTTOM
FLANGE
(b)
Fig. C-8.3. Beam-column joint.
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required shear by either welds or by slip-critical high strength bolts. (See Fig.
C-8.4.)
Third is the joint of beams not meeting the 70 percent criteria. This would be
similar to the second joint except that the beam web is required to be welded
directly or through shear tabs even though the web is bolted to the shear tab.
The welds are required to have a nominal moment strength at least equal to 20
percent of the nominal moment strength of the full beam web. (See Fig. C-8.5.)
Other joints than the ones specified are permitted to be used but the adequacy
of the joint requires substantiation either by tests or by calculations. Where the
adequacy is demonstrated by calculations, additional conservatism is provided
by requiring the joint to develop at least 125 percent of the nominal moment and
shear strength of the beam.
8.3. Panel Zone of Beam-to-Column Connection
(Beam web parallel to column web)
During recent years many cyclic tests have shown the ductility of shear yielding
in panel zones through many cycles of inelastic distortions.17,25–28 Thus the panel
zone does not need to develop beam hinging and a method of determining the
nominal shear strength of the panel zone is needed. The usual assumption of
Von Mises shear limit of 0.577Fy dt did not predict the actual behavior of many
of the tests. Many panel zone and beam tests have shown that strain hardening
and other phenomena have enabled shear strengths in excess of 1.0Fy dt to be
developed. Eq. 8-1 reflects the significant strength provided by thick column
flanges.
In calculating the required panel zone shear strength the UBC 1991 magnifies
the specified load by a factor of 1.85. For the LRFD specification, the typical
Load Combinations 3-5 and 3-6 are used and the nominal web shear strength is
defined as 0.6Fy dt, rather than 0.55Fy dt which had been used in plastic design
and in some previous references. In order to provide the same level of safety as
determined by tests and as contained in the UBC 1991, a lower resistance factor
φv = 0.75 was selected.
An upper limit is placed on the required shear strength of the panel zone of 0.9
times the summation of the beam design plastic moments φb Mp framing into the
connection.
In order to minimize the chances of shear buckling during inelastic deformations
of the panel zone, the thickness of the panel zone material is limited to not less
than 1⁄90 of the sum of its depth and width. The thickness of any doubler plate
used is assumed ineffective in inhibiting buckling unless it is connected to the
panel zone plate in such a manner, such as plug welds, to prevent local buckling
of the plate. (See Fig. C-8.6.)
Whenever doubler plates are used (i.e., increased strength, compliance with Eq.
8-2, or to reduce panel zone deformations), the plates are required to be close
to the column web. The doubler plates are to have at least minimum fillet welds
across the top and bottom and to have either butt or fillet welds to the column
flanges. These details are provided to closely simulate the joints that have been
found to perform satisfactorily in the cyclic tests that have been performed. Fillet
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CONTINUITY
PLATE, TOP
& BOTTOM
SHEAR PLATE
TYP.
FULL PENETRATION
TOP & BOTTOM
FLANGE
(a)
CONTINUITY
PLATE, TOP
& BOTTOM
SHEAR PLATE
TYP.
FULL PENETRATION
TOP & BOTTOM
FLANGE
(b)
Fig. C-8.4. Beam-column joint, bf tf (db − tf)Fy ≥ 0.7Fy Zx.
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CONTINUITY
PLATE, TOP
& BOTTOM
SHEAR PLATE
TYP.
FULL PENETRATION
TOP & BOTTOM
FLANGE
(a)
CONTINUITY
PLATE, TOP
& BOTTOM
SHEAR PLATE
TYP.
FULL PENETRATION
TOP & BOTTOM
FLANGE
(b)
Fig. C-8.5. Beam-column joint, bf tf (db − tf)Fy < 0.7Fy Zx.
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welding is encouraged to assist in minimizing the built-in weld stresses and the
cost of welding.
Doubler plates may be designed to extend between continuity plates which are
welded directly to the column web or they may extend above and below the
continuity plates which are welded to the doubler plate. For the latter case, the
horizontal welds at the top and bottom of the doubler plate should be sized to
transfer all loads imposed by the design system. In particular, the welds to the
column web should be designed to transfer load from the doubler plate to the
column web for their portion of load from the continuity plate.
For the fillet or butt welds of the doubler plate to the column flanges, the
following items should be considered:
• The vertical shear and bending loads of beams or girders framing perpendicular to the column web and supported by the doubler plate.
• The compression or tension load delivered to the column web and doubler
plate by the flanges of the girders framing into the column flanges.
For examples of doubler plate connections, see Ref. 55 and Fig. C-8.6.
The use of diagonal stiffeners for strengthening and stiffening of the panel zone
has not been adequately tested for low cycle reversed loading into the inelastic
range. Thus no specific recommendations are made at this time for special
seismic requirements for this detail.
TOP
& BOTT.
1″
BEAM JOINT
NOT SHOWN
EA. END
WEB DOUBLER
AS REQ’D
Fig. C-8.6. Panel zone detail (with doubler).
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8.4. Beam Limitations
In order to minimize the cost of connections it has occasionally been suggested
that the beam cross-section be reduced immediately adjacent to the column. This
type of assemblage can result in a very brittle mode of failure. Detailing that
results in a concentration of stress in an area where inelastic deformations are
anticipated under large seismic response is discouraged.
The width thickness ratio of projecting elements should be within those which
provide the cross-section with stability against local buckling.
The limits given in Table 8-1 are deemed adequate by the Committee for
ductilities to 6 or 7 based on the tests performed to date.29–32 Further testing may
result in some modifications of these limits.
8.5. Continuity Plates
Sect. K1 of the Specification gives the design requirements for webs and flanges
with concentrated forces. Sect. K1.2 gives the design strength in local buckling
in a flange under the action of a tensile force. When the design strength is
inadequate, column web stiffeners are required. In moment resisting frames, an
interior beam-to-column connection has tension on one flange and compression
on the opposite side. When stiffeners are required, it is normal to place a full
depth stiffener on each side of the column web. As this stiffener provides a load
path for the flanges on both sides of the column, it is commonly called a
continuity plate. The stiffener not only provides resistance to local flange
buckling but also provides a boundary to the very highly stressed panel zone.
When it is anticipated that there could be a plastic hinge adjacent to the column,
the required force to determine whether a continuity plate is required is not the
design earthquake force given by the load combinations 3-1 through 3-6. It is
the force exerted by the beam connection when the full plastic moment with
possible strain hardening has been formed.
Tests have shown that hinging occurs due to local flange buckling when a
compact section is strain hardened to about 1.3Fy.20 At the joint, the flanges of
the beam can be strain-hardened to a force of 1.8Fy bf tf.
Using this force as the required strength on the continuity plate is conservative
as there is only a small moment strength contributed by the bolted web connection. Since the flange continuity plate is needed to protect the weld at the joint
of the beam flange to column flange, consideration should be given to their use
in connections where the calculations indicate they may not be required.
Continuity plates have been used in almost all cyclic joint tests that have
performed well.17 When tests have been performed on specimens not meeting
the requirements of Sect. K1.2, the joints have performed poorly. For the actual
design of the continuity plates, Sect. K1.8 of the LRFD specification would
apply.
8.6. Column-Beam Moment Ratio
Tests have shown that moment frame subassemblages in which yielding of
columns occurred did not exhibit any loss of lateral force resistance at displacements representative of maximum expected earthquake response.33 Most engineers believe, however, that the performance of seismic moment frames is more
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predictable if columns outside of the panel zone do not yield. The tests necessary
to formulate truly appropriate criteria have not been conducted. In the past, many
frames have been designed with the assumption that the first hinging occurs in
the columns and until recently no code provisions for this behavior have been
enforced. There have not been any documented failures in past earthquakes
directly attributable to column hinging. Design situations do occur where
elimination of the “strong beam-weak column” connection type would be
grossly impractical.
The committee feels that some interim provisions are appropriate. Thus Eqs. 8-3
and 8-4 are introduced. These formulas require that the initial potential for
yielding at a beam-to-column connection be in the beam or panel zone rather
than in the column.
The exceptions to the “strong column-weak beam” connection type require
that the column be a compact section and include one of the following
characteristics:
a. Have a low required axial strength.
b. Be a column in a story which has a significantly stronger design story shear
strength than the story above.
c. Be a column that is not part of the lateral force resisting system except to
support the axial load from the overturning moment of the building as a
whole.
Wherever possible the committee recommends that the hinging conform to the
requirements of Sect. 8.2.
8.7. Beam-to-Column Connection Restraint
In order to function properly, particularly if inelastic behavior in or adjacent to
the beam-to-column connection occurs during high seismic activity, the column
needs to be braced to prevent rotation out of the plane of the moment frame.
8.7.a. Restrained Connections: Beam-to-column connections are usually restrained laterally by roof or floor framing. For these cases, lateral support
of the connection is required only at the level of the top flanges of the
beams as long as the column can be shown to remain elastic. The two
criteria to demonstrate that the column remains elastic are arbitrary but
appear to be reasonable assumptions until otherwise demonstrated by
test.
If the column cannot be demonstrated to remain elastic, a hinge would
be potentially forming and the column should be laterally supported at
the levels of both the top and bottom flanges of the beam.
The lateral support provided at the beam-to-column connection is to be
designed using a required strength of 2 percent of the nominal beam
strength. It is recognized from the limited test data available that the
lateral support provided should also be rigid enough to inhibit lateral
movement of the column flanges.32 Designers should carefully design
the lateral support member to be composed of reasonably rigid elements
and be anchored to rigid supports.
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The lateral support provided the beam-to-column connection is not
required to be a separate member at the connection in all cases. It may
be shown that the lateral support force can be adequately carried by the
column web or the beam flanges.
8.7.b. Unrestrained Connection: Unrestrained connections can occur in special
cases as in two story frames, at mechanical floors or for architectural
space layout. When this does occur, special care should be provided to
minimize the potential of out-of-plane buckling at the connection. Three
arbitrary provisions are given for the columns to assure that this buckling
does not occur.
8.8. Lateral Support of Beams
The lateral support for beams is defined in Chapter F in the LRFD design
specifications. In moment resisting frames, the beams are nearly always in
double curvature between columns unless one end is pinned. If the formula for
plastic design were used as a guide and assuming Mp at one end and pinned at
the other, formula F1-1 would yield 3,600ry / Fy. With Fy =36 ksi, Lpd = 100ry.
The 1991 UBC has 96ry for this limitation. Due to the low cycle oscillating
motion of the frames under earthquake loading and the uncertainty of the
locations of hinging under the various loading combinations, a more conservative approach was appropriate and set the maximum limit of the spacing of
lateral support for frame beams at 2,500ry / Fy for both top and bottom flanges.
9.
REQUIREMENTS FOR CONCENTRICALLY BRACED FRAMES
(CBF)
9.1
Scope
The provisions contained in the Section are for braced frame systems of Building
Categories C, D, and E where the braces are designed to carry all the lateral
force shears or are used in combination with a moment resisting frame. If used
in combination with a moment frame system, the moment frames should follow
the requirements of Sects. 7 or 8 as required by the local Building Code. In a
Concentrically Braced Frame (CBF), the bracing members are so arranged that
the brace members primarily act with axial loading. CBF usually are in one of
the following five types. (See Figs. C-9.1 through C-9.5).
Ductility of CBF systems producing a pattern of reasonably stable reversible
distortions provides justification for basing seismic design on reduced displacements that can be expected during a strong earthquake. CBF systems, by the fact
that the primary forces in the bracing system are axial tension and compression,
are very limited in reversible inelastic distortions. Tests have shown that after
buckling, an axially loaded member rapidly loses strength with repeated inelastic load reversals and does not return to its original straight position.34 For this
reason in high seismic areas, CBF systems have not been permitted by codes
for tall or special buildings without being combined with a moment resisting
frame. Codes also have required significantly higher levels of design force so
that the possibility of large uncontrolled inelastic deformations will not occur.
For instance, ASCE 7-88 in Sect. 9.9.5 requires that CBF be designed to a force
1.25 times the normal design force given in Sect. 9.4 for the system involved.
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Fig. C-9.1. Diagonal braced frame.
Fig. C-9.2. X-braced frame.
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Fig. C-9.3. V-braced frame.
Fig. C-9.4. Inverted V-braced frame.
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In Sect. 9.4 of this specification, for Special Configurations, this higher force
factor is raised to 1.5.
The performance of CBF systems in earthquakes is acceptable as long as they
retain stable configuration. The emphasis of these provisions is on raising the
level of stable behavior and protecting against brittle failures.
When an axially loaded brace buckles in compression, several developments
take place:
a. When buckling occurs, additional load is transferred to the tension brace
increasing the force it must carry.
b. The buckling of the brace may cause excessive rotation at the brace ends and
local connection failure.
c. The buckling can cause local or torsional buckling to occur near mid span.
d. If the buckling causes the brace to bow out of plane of the braced frame,
non-structural encasement of the frame system can be destroyed.
e. Brace buckling can occur non-symmetrically which would induce large
torsional response.
f. Excessive buckling can affect non-structural systems which are attached to
the frame.6
Fig. C-9.5. K-braced frame.
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9.2. Bracing Members
9.2.a. Slenderness: Except for low buildings using the required strength given
in Sect. 9.5, the slenderness (L / r) of members of CBF systems is limited.
In the post-buckling range, the compressive nominal axial strength
deteriorates.34 Hysteresis loops of tested assemblies take on a severely
pinched shape. (See Fig. C-9.6.)
Braces with small L / r dissipate more energy because in the post-buckling range they undergo cyclic inelastic bending which slender braces
cannot. Very slender braces have almost no stiffness in a buckled
configuration. On a load reversal, the brace quickly assumes a straightened configuration and very rapidly picks up a tensile force. This rapid
increase in the brace force may cause impact loading and may lead to a
brittle failure of the connection.
The curvatures associated with cyclic inelastic bending of braces may
be large and local buckling can develop. This local buckling may be so
severe as to result in localized kinking of the brace or the connection
plate elements causing crack propagation and fracture. Such fractures
have been obseved rather early in tests of tubular bracing members.35
This characteristic is more prevalent in rectangular and square tube
braces. Consideration should be given to using composite tubes with
concrete fill to inhibit buckling.36
9.2.b. Compressive Design Strength: Due to the cyclic nature of seismic
response, the compressive design strength of bracing members is reduced to 80 percent of the value given in the Specification, Chapter E.
P (kips)
264
200
100
–1.0
1.0
0
Finish
2.0
δ Axial (in.)
–100
–200
W6x20
L = 10 ft
KL / r = 80
9 in. 3.5 in.
Lateral ∆
Fig. C-9.6. P−δ diagram for a strut.
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This reduction factor is a simplified value from the factor proposed by
others which varies with KL / r.6 When evaluating the nominal strength
of the bracing system for the purpose of determining the maximum load
the bracing will impose on other systems (such as Eq. 6-1), the reduction
for cyclic behavior should not be used for design as it would underestimate the nominal strength of the bracing system during the early cycles
of seismic response.
9.2.c. Lateral Force Distribution: This provision attempts to balance the tensile
and compressive resistances across the width and breadth of the building
since at large loads the capacity of buckled compression braces may be
substantially less than that of tension braces. An exception is provided
for the case where the bracing members were sufficiently oversized to
provide essentially elastic seismic response.
9.2.d. Width-Thickness Ratios: In Sect. B5 of the Specification, definitions are
given to three types of sections. The compact section is one which has
elements with width-thickness ratios, λ, less than λp. Non-compact
sections are those with elements λp ≤ λ ≤ λr. Slender compression
sections are those which have at least one element for which λ is greater
than λr. The latter sections are prone to local buckling and are not to be
used for the bracing members covered in this Section. The circular
section wall thickness limitation was chosen to be the same as for Plastic
Design in the Specification. Due to the repetitive nature of cyclic loading
for rectangular tubular sections, a more stringent requirement on the b / t
ratios is specified based on tests.35–36 Filling of tubing with lean concrete
has been shown to effectively stiffen the tube walls.
9.2.e. Built-up Member Stitches: The special requirements for built-up member stitches were chosen from test data.37 They are intended for members
built up from double angles and channels, and may not be appropriate
for markedly different shapes.
9.3. Bracing Connections
9.3.a. In CBF systems, the bracing members normally carry most of the seismic
story shear, particularly if a dual system is not used. The required
strength on brace connections should be adequate so that failure by
out-of-plane buckling of gussets or brittle fracture of the connection are
not the critical failure mechanism.
The minimum of the three criteria, (i.e., the design axial tension strength
of the bracing member, the force generated by the amplified load
combinations of 3-7 and 3-8, and the maximum force that could be
generated by the overall system) determine the required strength on both
the brace connection and the beam-to-column connection if it is part of
the bracing system. The latter criterion is intended to cover the possibility that the shear could be limited by the amount of overturning that could
be developed.
9.3.b. Net Area: Eq. 9-1 extends the concepts of LRFD Sect. B3 to the forces
given in Section 9.2.a above.
9.3.c. Gusset Plates: Gusset plates in CBF systems are frequently the critical
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design element in a system required to deform into the inelastic range.
The increased force required for design of CBF tends to reduce the
inelastic demand but may be insufficient to totally eliminate the problem. If the critical buckling mode of the braced member is in the plane
of the CBF, the gussets and their joints should have a design strength
capable to resist the nominal strength of the brace in that direction. If
the critical buckling mode is out of the plane of the CBF, each gusset
shall be detailed to permit the formation of a hinge line in the gusset.
(See Fig. C-9.7.)
9.4. Special Bracing Configuration Requirements
In addition to the general requirements for bracing members and their connections given above, special limitations are applied to V and K types of CBF
systems due to their special configurations.
9.4.a. V and Inverted V Type Bracing: If one diagonal of a V type brace were
to buckle in compression, the force in the tension brace would become
larger than the force in the buckled brace. The vertical resultant of these
two forces could then impose a large vertical deformation on the horizontal member of the bracing system. (See Fig. C-9.8.) If the connection
at the point of the V tip were pinned, there would be no resistance to this
deformation. If a continuous horizontal member survives and undergoes
a deformation reversal, the previously buckled diagonal member would
BRACING
MEMBER
2t
GUSSET PLATE
t = THICKNESS OF GUSSET PLATE
Fig. C-9.7. Brace-to-gusset plate requirement for buckling out-of-plane bracing system.
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not return to its original alignment and the diagonal member which was
in tension could exceed its capacity in compression. In this manner both
diagonal members would be in a buckled condition. This behavior would
cause the post buckling strength of the braced system to deteriorate
rapidly.38 (See Fig. C-9.9.)
Near the tip point of the V is a zone where inelastic rotations are likely
to occur, members should be braced against out-of-plane buckling.
Several options were considered for CBF systems using the V type
bracing. One was to prohibit its use, a second was to impose stringent
limitations on the slenderness ratios of the bracing members, and a third
was to provide a larger axial load capacity for the diagonal members.
The latter option was adopted by providing a design axial strength 1.5
times the required axial strength in lieu of the 1.25 normally required for
other CBF. It is also required that the beam be continuous throughout
the bay and that this beam be designed to carry the tributary vertical
gravity loads without considering the support provided by the diagonal
members of the V.
A review of more recent testing of V braced systems may in future
editions be able to modify some of the current limitations.
9.4.b. K Bracing: In areas of high seismicity where it is envisioned that
inelastic response to large motions will be required, the K type of CBF
system is not a desirable method for seismic resistance. The same
behavior discussed in the V type bracing occurs, but in the case of the
K system a buckled brace causes the column to deform horizontally.
Potentially this could cause column buckling and subsequent collapse.
In buildings of Categories A, B, and a portion of C, the K system is permitted
unrestricted by these provisions. For the remainder of Category C as per
Fig. C-9.8. Failure mechanism of inverted V-braced frame.
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Sect. 2.2, however, K braces shall meet the requirements Sects. 9.4.b and
9.5. This requires a 50 percent increase in design axial load for the braces
and a continuous column though at the story mid-height. It is recommended
that K type bracing not be used even where permitted for seismic resistance
unless other configurations are impractical.
9.5. Low Buildings
One of the few problem areas observed in the seismic performance of smaller
steel buildings using the CBF system pertain to the size and type of member
connections used. Quite frequently the critical design horizontal load is wind
rather than seismic. In these cases, the sizing of bracing members is larger than
would be required if seismic loads were the only design horizontal loads. Thus
for smaller buildings and roof structures, the special provisions for CBF systems
have been waived if the seismic resisting system has been designed using the
amplified loads given in Load Combinations 3-7 and 3-8. This waiver would
permit, for instance, an X braced or diagonal braced system in which the bracing
members would be assumed to be in tension only.
10.
REQUIREMENTS FOR ECCENTRICALLY BRACED FRAMES (EBF)
10.1. Scope
THIRD STORY SHEAR (KIPS)
Research39–49 has shown that buildings using the EBF system possess the ability
to combine high stiffness in the elastic range together with excellent ductility
and energy dissipation capacity in the inelastic range. In the elastic range, the
lateral stiffness of an EBF system is comparable to that of a CBF system,
particularly when short link lengths are used. In the inelastic range, EBF systems
800
400
0
–400
–800
–4
–2
0
2
4
THIRD STORY DRIFT (IN.)
Fig. C-9.9. Story shear–story drift diagram for frame with inverted V-bracing.
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provide stable, ductile behavior under severe cyclic loading, comparable to that
of a SMF system. The EBF is composed of columns, beams, and braces in which
at least one end of each bracing member connects to a beam at a short distance
from a beam-to- column connection or from an adjacent beam-to-brace connection. (See Fig. C-10.1.) The short distance of the beam between the brace
connection and the column or between brace connections is called the link. The
design purpose of an EBF system creates a system that will yield primarily in
the links. The special provisions for EBF systems are intended to satisfy this
criterion and to ensure that cyclic yielding in the links can occur in a stable
manner. The yielding in the links is accomplished by ensuring that the diagonal
braces, the columns, and the portion of the beam outside of the links remain
essentially elastic under forces that can be generated by fully yielding and strain
hardened links.
Arrangements of braces can be made in which links may not be fully effective.
One such arrangement is the one shown on Fig. C-10.2 in which links are
provided at each end of the brace. If the upper link has significantly lower design
shear strength than the story below, the upper link deforms inelastically and
limits the force that can be delivered to the brace to deform the lower link
inelastically. When this condition occurs the upper link is termed an active link,
whereas the lower link is an inactive link. Having potentially inactive links in
the EBF system increases the difficulty of analysis. The plastic analyses show
that in some cases the lower link yields due to the combined effect of D, L, and
E loads, and the frame capacity becomes smaller than expected.50 It also
increases the cost of the structure by requiring full link details on the inactive
links even though the brace would be sized by the strength of the active link and
the brace connection at an inactive link could be designed as a pin. Thus it is
best to arrange a system that contains only active links as those shown in Fig.
C-10.1. Design suggestions have been compiled in Ref. 48.
In Sect. 10.1 in conformity with the strong column–weak beam concept, plastic
hinges should not develop in columns at floor beam levels in EBF. The
occurrence of such plastic hinges, together with those forming in the links,
could result in a soft story and must be prevented. There are two important code
provisions intended to prevent this from happening. First, according to Sect.
6.1, the required axial column strength includes PE, based on application of the
amplified earthquake load 0.4RE. Second, per Sect. 10.8, the required strength
of columns due to the forces introduced at the connection of a link and/or brace
is based on these forces multiplied by a factor of 1.25. Note that for a severe
earthquake the formation of plastic hinges at column bases is generally unavoidable.
10.2. Links
The general provisions for links to ensure that stable yielding occurs are included
under this heading.
10.2.a. Beams with links are required to be compact shapes following the same
criteria as SMF systems (Table 8-1).
10.2.b. In order to provide steel with proven ductile behavior the yield stress of
steel is limited to 50 ksi.
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10.2.c. Doubler plates on the link web are not permitted as they do not perform
as intended in inelastic deformations. Openings are not permitted as they
adversely affect the yielding of the link web.
10.2.d. The link design shear strength φVn is the lesser of that determined from
the yield shear or twice the plastic moment strength divided by the link
length. This φVn should be greater than or equal to the required shear
determined from the Load Combinations 3-5 or 3-6.
10.2.e. If the required axial load on the link is less than 0.15Py, the effects of the
axial load can be ignored, In general, the axial load is negligible because
the horizontal component of the brace load is transmitted to the beam
outside of the link. However, due to a particular arrangement of the
framing, substantial axial forces can develop in the link. For such cases,
the limitations given in f. apply, and the design shear strength and link
lengths are required to be reduced to ensure stable yielding.
c
d
c
a
c
d
c
d
b
b
a
d
a
c
b
d
b
a
c
d
c
d
c
b
c
b
d
b
a
d
c
d
d
d
c
b
d
b
b
a
a
c
b
d
d
d
c
b
d
b
b
a
a
c
b
d
d
d
b
a
b
c
a
b
a = column
b = brace
c = link
d = portion of beam outside of link
Fig. C-10.1. Common types of eccentric braced frames.
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10.2.f. See Commentary 10.2.e.
10.2.g. The link rotation angle is defined in the Specifications as the plastic
angle between the link and the beam outside the link when the total story
drift ∆t, calculated using amplified earthquake forces 0.4R × E. The
plastic link rotation can be conservatively determined assuming that the
EBF bay will deform in a rigid-plastic mechanism. Several such mechanisms are illustrated for various EBF configurations in Fig. C-10.3. The
plastic angle is determined using a story drift ∆p = ∆t − ∆e, where ∆e the
elastic story drift can conservatively be assumed to be zero. The plastic
story drift angle θp = ∆p / h follows from geometry. The actual plastic
link rotation angle can be determined by non-linear elastic-plastic analyses if a more explicit definition of the angle is desired.
An inverted Y system is shown on Fig. C-10.1. In this system the precise
definition given in the Glossary for the link rotation angle does not apply
but the concept is the same as in the other systems, as shown on
Fig. C-10.3. As usual both ends of the link are required to be laterally
supported.
The link length of 1.6Mp / Vp indicates the limit chosen for the link to act
primarily in shear. The link length 2.6Mp / Vp is the lower limit of a
flexural link. Straight line interpolation is used for the intermediate link
lengths.
It has been demonstrated experimentally51–52 as well as analytically48 that
the first floor links usually experience the largest plastic deformation. In
extreme cases this may result in a tendency to develop a soft story. The
a
b
φVn − link a (active link) < φVn − link b (inactive link)
Fig. C-10.2. EBF—active and inactive link.
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plastic link rotations tend to attenuate at higher floors, and decrease with
the increasing frame periods. Therefore for severe seismic applications
a conservative design for the links in the first two or three floors is
recommended. This can be achieved by increasing the minimum design
shear strengths of these links on the order of 10 percent over that
specified in Sect. 10.2.d. An even more conservative approach would be
to have vertical connecting members at the ends of the links in a few
lower floors.
The use of the framing shown in Fig. C-10.1 can be advantageous where
∆p
∆p
e
e
θp
γp
γp
h
h
e
γp
θp
L
L/2
L/2
γp = L θp
e
γp = L θp
2e
∆p
∆p
γp
e
γp
L/2
e/2 e/2
h
h
θp
θp
L/2
γp = L θp
e
∆v
∆t
∆e
∆p
e
h
L
θp
γp
L
γp = h θp
e
= Story drift determined using base shear v, inches.
= Total story drift, inches = ∆v × e′ / e.
= Elastic story drift, inches = ∆v times the earthquake load factor.
= Plastic story drift, inches = ∆t − ∆e (conservatively, ∆e = 0).
= Link length, inches.
= Story height, inches.
= Column to column distance, inches.
= Plastic story drift angle, radians = ∆p / h.
= Link rotation angle, radians.
Fig. C-10.3. Link rotation angle.
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the beam-column-brace connections can be designed as simple connections. Welds of the link flanges are avoided in this kind of framing.
By changing the link lengths the stiffness of an EBF can be modified. In
this manner the frame periods can be optimized.
10.2.h. The intent of this provision is to permit a CBF on the top floor of an EBF
building over five stories tall with application of an earthquake response
modification coefficient R appropriate for an EBF.
10.3. Link Stiffeners
Properly detailed and restrained webs can provide stable, ductile, and predictable behavior under severe cyclic loading. The design of the EBF link requires
close attention to the detailing of the link web thickness and stiffeners.
10.3.a. Full depth stiffeners are required at the end of all EBF links and serve
to transfer the link shears to the reacting elements as well as restraining
the link web against buckling.
10.3.b. In shear links, the spacing of intermediate web stiffeners is varied
depending on the magnitude of the link rotation angle.45 The closer
spacing is provided for the system with the greatest angle. Flexural links
having lengths greater than 2.6Mp / Vp but less than 5Mp / Vp are required
to have an intermediate stiffener at a distance from the link end equal to
1.5 times the beam flange width. Links between shear and flexural limits
would have intermediate stiffeners meeting the requirement of both
shear and flexural links. When the link length is greater than 5Mp / Vp,
no intermediate stiffeners are required. Intermediate stiffeners are required to be full depth in order to effectively react against shear buckling.
Intermediate stiffeners are required on both sides of the web for links 25
inches in depth or greater. For links less than 25 in. deep, the stiffener
need be on one side only.
10.3.c. All link stiffeners are required to be fillet welded to the link web. These
welds shall have a required strength equal to the nominal vertical tensile
strength of the stiffener. The connection to the link flanges should be
similar.
10.4. Link-to-Column Connections
There are special connection requirements for the connections of links to
columns. The intent is to provide connections which can transfer not only the
shear and moment forces of the links but also torsion due to flange buckling.
The Specification does not explicitly address the column panel zone design
requirements at link-column connections, as little research is available on this
issue. However, from research on panel zones for SMF systems, it is believed
that limited yielding of panel zones in EBF systems would not be detrimental.
Pending future research on this topic, a suggested design approach is as follows:
Compute the required shear strength of the panel zone based on the bending
moment at the column end of the link, as given by the equations in Sect. 10.6.a
in the commentary of these provisions. The corresponding panel zone design
shear strength should then be computed according to Eq. 8-1 of these provisions.
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10.5. Lateral Support of the Link
One of the essential items to ensure stable inelastic behavior of the EBF system
is to restrain the ends of the link from twisting out of plane. The 6 percent of the
nominal strength of the beam flange defines the required strength on the lateral
support member and its connections.
10.6. Diagonal Brace and Beam Outside of Links
10.6.a. A basic requirement of EBF design is that yielding be restricted primarily
to the links. Accordingly, the diagonal brace and the beam segment
outside of the link should be designed to resist the maximum forces that
can be generated by the link, accounting for the sources of link overstrength. Link overstrength can be attributed primarily to strain hardening, effects of composite floor systems, and the actual yield strength of
the link exceeding the specified yield strength. In EBF research literature, for design of the brace and the beam, an overstrength factor of 1.5
has generally been applied to the nominal strength of the link. Using this
overstrength factor, the brace and beam segments were checked using
their nominal strength, i.e., using φ =1.0. This approach considers that
designing for an overstrength factor of 1.5 represents an extreme loading
condition for the beam and brace, and therefore a relaxation of the φ
factor was appropriate to avoid an overly conservative design.49 Sect.
10.6.a specifies that the design strength of the beam and diagonal brace
exceed the forces generated by 1.25 times the nominal link shear
strength, maintaining approximately the same basic design approach for
the diagonal brace and beam. That is, based on a φ factor of 0.85 on axial
compression in the beam or brace, the effective overstrength factor
becomes 1.25 / 0.85, or about 1.5. For bending moments in the beam or
diagonal brace, for which φ is 0.9, the overstrength factor becomes
1.25 / 0.9, or about 1.4, representing a slight relaxation from the test
criterion.
Based on a link overstrength factor of 1.25, the required strength of the
diagonal brace and beam segment outside of the link can be taken as the
forces generated by the following values of link shear and link end
moment:
For e ≤ 2Mp / Vp,
link shear
link end moment
= 1.25Vp
= e(1.25Vp ) / 2
For e > 2Mp / Vp,
link shear
link end moment
= 2(1.25Mp) / e
= 1.25Mp
The above equations are based on the assumption that link end moments
will be equal when the link achieves its limit strength. For links of length
e ≤ 1.3Mp / Vp attached to columns, experiments have shown that link
end moments do not equalize.44 For this situation, link shear and link end
moments can be taken as:
For e ≤ 1.3Mp / Vp next to column,
link shear
= 1.25Vp
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
SEISMIC PROVISIONS FOR STRUCTURAL STEEL BUILDINGS
moment at column end of link
moment at brace end of link
6 - 363
= 0.8Mp
= e(1.25Vp ) − 0.8Mp
The link shear force will generate axial force in the diagonal brace, and
for most EBF configurations, will also generate substantial axial force
in the beam segment outside of the link. The ratio of beam or brace axial
force to link shear force is controlled primarily by the geometry of the
EBF and is therefore not affected by inelastic activity within the EBF.47
Therefore, this ratio can be taken from an elastic frame analysis and used
to scale up the beam and brace axial force to a level corresponding to
the link shear force specified in the above equations. At the brace end of
the link, the link end moment will be transferred to the brace and to the
beam. If the diagonal brace and its connection remains elastic, based on
link overstrength design considerations, some minor inelastic rotation
can be tolerated in the beam outside of the link.
10.6.b. Typically in EBF design, the intersection of the brace and beam centerlines is located at the end of the link. However, as permitted by Sect.
10.6.b, the brace connection should be designed with an eccentricity so
that the brace and beam centerlines intersect inside of the link. This
eccentricity in the connection generates a moment that is opposite in sign
to the link end moment. Consequently, the value of link end moment
STIFF PLATE EA. SIDE
OF WEB. USE FILLET WELD
CONT. @ WEB & FLANGE
BEAM OUTSIDE
OF LINK
LINK LENGTH – e
FULL
PENETRATION
TOP & BOTT.
W SHAPE
LINE OF INTERSECTION
OF BRACE AND BEAM
SHALL BE AT THE
EDGE OF LINK OR
INSIDE THE LINK
INTERMEDIATE
STIFFENER PLATES
EA. SIDE OF WEB
FOR LINKS ≥ 25″
CONT. FILLET WELD
@ WEB AND FLANGE
Fig. C-10.4
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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COMMENTARY: PART I—LRFD PROVISIONS
given above can be reduced by the moment generated by this brace
connection eccentricity. This may substantially reduce the moment that
will be required to be resisted by the beam and brace, and may be
advantageous in design. The intersection of the brace and beam centerlines should not be located outside of the link, as this increases the
bending moment generated in the beam and brace. See Figs. C-10.4 and
C-10.5.
10.6.c. If the brace connection at the link is designed as a pin, the beam by itself
shall be adequate to resist the entire link end moment. This condition
normally would occur only on EBF with short links. If the brace is
considered to resist a portion of the link end moment, then the brace
connection at the link should be designed as fully restrained, as required
by Sect. 10.6.c. Test results on several brace connection details subject
to axial force and bending moment are reported in Ref. 47.
10.6.d. When checking the requirements of Sect. 10.6, both the beam and
diagonal brace should, in general, be treated as beam-columns in
strength and stability computations. Unlike CBF, the brace of an EBF
may be subject to significant bending moments. For the beam segment
outside of the link, adequate lateral bracing should be provided to
maintain its stability under the axial force and bending moment generSTIFF. PLATE EA. SIDE
OF WEB. USE FILLET WELD
CONT. @ WEB & FLANGE
LINK LENGTH – e
BEAM OUTSIDE
OF LINK
FULL
PENETRATION
TOP & BOTT.
LINE OF INTERSECTION
OF BRACE AND BEAM
SHALL BE AT THE
EDGE OF LINK OR
INSIDE THE LINK
BENT PLATE
OR TWO
WELDED PLATES
GUSSET PLATE
TS (BRACE)
SPLIT END TO
FIT GUSSET
Fig. C-10.5
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
INTERMEDIATE
STIFFENER PLATES
EA. SIDE OF WEB
FOR LINKS ≥ 25″
CONT. FILLET WELD
@ WEB & FLANGE
SEISMIC PROVISIONS FOR STRUCTURAL STEEL BUILDINGS
6 - 365
ated by the link, as required by Sect. 10.6.d. If the stability of the beam
is provided by adequate lateral support, tests have shown that limited
yielding of the beam segment is not detrimental to EBF performance,
and for some EBF configurations may be unavoidable.47 However, the
combined flexural strength of the beam and the brace, reduced for the
presence of axial force, should be adequate to resist the link end moment.
For EBF geometries with very small angles between the beam and the
brace and/or for EBF with long links, satisfying the requirements of Sect.
10.6.e. may require very heavy braces, and in extreme cases, may require
cover plates on the beams. EBF with relatively steep braces, e.g.,
brace-beam angles greater than about 40 degrees, combined with short
links are preferable for avoiding design problems with the brace and
beam segment outside of the link. A general discussion on design issues
related to the beams and braces of an EBF is provided in Ref. 49, with
further details provided in Ref. 47.
10.7. Beam-to-Column Connection
If the arrangement of the EBF system is such that a link is not adjacent to a
column, a simple pinned connection is considered to be adequate if the connection provides some restraint against torsion in the beam. The magnitude of
torsion is calculated by considering perpendicular forces equal to 1.5 percent of
the nominal axial flange tensile strength applied in opposite directions on each
flange.
10.8. Required Column Strength
As the shear strength of the adjoining critical link is potentially greater than the
nominal strength due to strain hardening, the required column strength is
required to be designed for the increased moment and axial load due to the load
from the adjacent link or brace.
11.
QUALITY ASSURANCE
As the behavior of all steel framing during a major earthquake is dependent on
the workmanship of the fabricator in providing sound joints, the design engineer
is advised to provide for adequate assurance control, particularly on the tension
groove welded joints of the seismic resisting system. ASCE 7-92 provides
special requirements for inspection and testing based on the Seismic Performance Category of the building to be built. The special requirements for structural
steel construction are in general those that would normally be required for
construction in all areas of seismic activity.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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COMMENTARY: PART II—ASD PROVISIONS
Part II—ASD Provisions
1.
SCOPE
As noted in PART I, the special seismic requirements are collateral provisions
related to the AISC Load and Resistance Factor Design Specification. As that
document was first published in 1986, the references to earthquake load were
not current. The provisions in PART I use limit state load models derived from
the 1991 NEHRP3 and the soon to be published ASCE 7-93.2
The provisions in PART II allow a designer to apply AISC Allowable Stress
Design Specification for Structural Steel Buildings (ASD)53 in the design of the
seismic lateral force resisting system based upon limit state loads. If the user
wishes to use ASD in the design of the seismic lateral force resisting system
where the loads are based upon service loads, the loads need to be converted to
factored levels consistent with those in PART I. The PART II provisions are
intended to be used in conjunction with PART I by either adding to or substituting to the provisions of Part I.
3.2
Nominal Strengths, and
3.3
Design Strengths
These provisions modify PART I to convert allowable stresses into equivalent
nominal strengths by multiplying allowable stresses by 1.7 as noted. Design
strengths are determined by multiplying φ times the nominal strengths.
7.2, 10.6.a, and 10.6.d
These modifications to PART I requirements change FR and PR connections to
Type 1 and Type 3 connections consistent with ASD nomenclature.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
6 - 367
List of References
1. AISC, Load and Resistance Factor Design Specification, American Institute of
Steel Construction, Inc., Chicago, IL, 1986.
2. ASCE 7-93, Minimum Design Loads for Buildings and Other Structures, American Society of Civil Engineers, New York, NY, 1993 (to be published).
3. BSSC, NEHRP (National Earthquake Hazards Reduction Program) Recommended Provisions for the Development of Seismic Regulations for New Buildings, Building Seismic Safety Council, Federal Emergency Management Agency,
Washington, DC, 1992.
4. Luft, R. W., “Comparison Among Earthquake Codes,” Earthquake Spectra,
Earthquake Engineering Research Institute, Vol. 5, No. 4, November 1989.
5. ICBO, Uniform Building Code, International Conference of Building Officials,
Whittier, CA, 1991.
6. SEAOC, Recommended Lateral Force Requirements, Seismology Committee,
Structural Engineers Association of California, Sacramento/San Francisco/Los
Angeles, CA, 1988.
7. AWS, D1.1-92, Structural Welding Code, American Welding Society, Inc., Miami,
FL, 1992.
8. Popov, E. P., Stephen, R. M., “Tensile Capacity of Partial Penetration Welds,”
Journal of the Structural Division, American Society of Civil Engineers, Vol. 103,
No. ST9, September 1977.
9. Bruneau, M., Mahin, S. A., and Popov, E. P., Ultimate Behavior of Butt Welded
Splices in Heavy Rolled Steel Sections, Report No. UCB/EERC-87/10, Earthquake Engineering Research Center, University of California, Berkeley, CA,
1987.
10. Huckelbridge, A. A., Clough, R. W., Earthquake Simulator Tests of Nine-Story
Steel Frame with Columns Allowed to Uplift, Report No. UCB/EERC-77/23,
Earthquake Engineering Research Center, University of California, Berkeley,
CA, 1977.
11. Carpenter, L. D., Lu, L-W., Reversed and Repeated Load Tests of Full Scale Steel
Frames, Fritz Engineering Laboratory Report No. 332.7, Lehigh University,
Bethlehem, PA, 1972.
12. Galambos, T. V., Deformation and Energy Absorption Capacity of Steel Structures
in the Inelastic Range, Bulletin No. 8, American Iron and Steel Institute, New
York, NY, 1968.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
6 - 368
LIST OF REFERENCES
13. Krawinkler, H., Bertero, V. V., and Popov, E. P., Inelastic Behavior of Steel
Beam-to-Column Subassemblages, Report No. UCB/EERC-71/7, Earthquake
Engineering Research Center, University of California, Berkeley, CA, 1971.
14. Bertero, V. V., Popov, E. P., and Krawinkler, H., Further Studies on Seismic
Behavior of Steel Beam-Column Subassemblages, Report No. UCB/EERC73/27, Earthquake Engineering Research Center, University of California,
Berkeley, CA, 1973.
15. Popov, E. P., “Seismic Behavior of Structural Assemblages,” Journal of the
Structural Division, American Society of Civil Engineers, Vol. 106, No. ST7, July
1980.
16. Tall Building Systems and Concepts, Monograph on Planning and Design of Tall
Buildings, Council on Tall Buildings and Urban Habitat, American Society of
Civil Engineers, New York, NY, 1980.
17. Popov, E. P., Amin, N. R., Louie, J. J., and Stephen, R. M., “Cyclic Behavior of
Large Beam Column Assemblies,” Earthquake Spectra, Professional Journal of
the Earthquake Engineering Research Institute, Vol. 1, No. 2, February 1985.
18. Tsai, K. C. and Popov, E. P., “Seismic Panel Zone Design Effect on Elastic Story
Drift in Steel Moment Resisting Frames,” Journal of Structural Division, in press.
19. Nicoletti, J. P., Pinkham, C. W., Saunders, C. M., Teal, E. J., A Synthesis of Steel
Research for Code Development, Structural Steel Educational Council, San
Francisco, CA, 1984.
20. Popov, E. P. and Pinkney, R. B., Behavior of Steel Building Connections Subjected
to Inelastic Strain Reversals—Experimental Data, Bulletin No. 14, American Iron
and Steel Institute, November 1968.
21. Popov, E. P. and Stephen, R. M., Cyclic Loading of Full-Size Steel Connections,
Bulletin No 21, American Iron and Steel Institute, February 1972.
22. Driscoll, G. C. and Beedle, L. S., “Suggestions for Avoiding Beam-to-Column
Web Connection Failure,” Engineering Journal, American Institute of Steel
Construction, Chicago, IL, 1st Qtr., 1982.
23. Tsai, K. C. and Popov, E. P., Two Beam-to-Column Web Connections, Report No.
UCB/EERC-86/05, Earthquake Engineering Research Center, University of California, Berkeley, CA, 1986.
24. Popov, E. P. and Tsai, K. C., Performance of Large Seismic Steel Moment
Connections Under Cyclic Loads, Proceedings; Structural Engineers Association
of California Convention, San Diego, CA, October 1987.
25. Slutter, R., Tests of Panel Zone Behavior in Beam Column Connections, Lehigh
University, Report No. 200.81.403.1, Bethlehem, PA.
26. Becker, E. R., Panel Zone Effect on the Strength of Rigid Steel Frames, University
of Southern California Structural Mechanics Laboratory, USCOE 001, June 1971.
27. Fielding, D. J., Huang, J. S., “Shear in Steel Beam-to-Column Connections,”
Welding Journal, Vol. 50, No. 7, Research Supplement, 1971.
28. Krawinkler, H., “Shear in Beam-Column Joints in Seismic Design of Steel
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
SEISMIC PROVISIONS FOR STRUCTURAL STEEL BUILDINGS
6 - 369
Frames,” Engineering Journal, American Institute of Steel Construction, Chicago, IL, Vol. 15, 1978.
29. Sawyer, H. A., “Post-Elastic Behavior of Wide-Flange Steel Beams,” Journal of
the Structural Division, Vol. 87, No. ST8, American Society of Civil Engineers,
December 1961.
30. Lay, M. G., “Flange Local Buckling in Wide-Flange Shapes,” Journal of the
Structural Division, Vol. 91, No. ST6, American Society of Civil Engineers,
December 1965.
31. Kemp, A. R., “Factors Affecting the Rotation Capacity of Plastically Designed
Members,” The Structural Engineer, Vol. 64B, No. 2, June 1986.
32. Bansal, J. P., The Lateral Instability of Continuous Steel Beams, CESRL Dissertation No. 71-1, University of Texas, Austin, TX, 1971.
33. Krawinkler, H., Bertero, V. V., Popov, E. P., Hysteresis Behavior of Steel Columns,
Report No. UCB/EERC-75/11, Earthquake Engineering Research Center, University of California, Berkeley, CA, 1975.
34. Black, R. C., Wenger, W. A., Popov, E. P., Inelastic Buckling of Steel Struts Under
Cyclic Load Reversals, Report No. UCB/EERC-80/40, Earthquake Engineering
Research Center, University of California, Berkeley, CA, 1980.
35. Tang, X., Goel, S. C., Seismic Analysis and Design Considerations of Braced Steel
Structures, UMCE Report 87-4, University of Michigan, Ann Arbor, MI, 1987.
36. Uang, C-M., and Bertero, V. V., Earthquake Simulation Tests and Associated
Studies of 0.3-Scale Model of a Six-Story Concentrically Braced Steel Structure,
Report No. UCB/EERC—86/10, EERC, Berkeley, CA, December 1986.
37. Liu, Z., Goel, S. C., Investigation of Concrete Filled Steel Tubes under Cyclic
Bending and Buckling, UMCE Report 87-3, University of Michigan, Ann Arbor,
MI, 1987.
38. Astaneh, A., Goel, S. C., Hanson, R, D., “Earthquake-Resistant Design of Double
Angle Bracings,” Engineering Journal, American Institute of Steel Construction,
Chicago, IL, Vol. 23, No. 4, 1986.
39. Roeder, C. W. and Popov, E. P., “Eccentrically Braced Frames for Earthquakes,”
Journal of the Structural Division, Vol. 104, No. 3, American Society of Civil
Engineers, March 1978.
40. Libby, J. R., “Eccentrically Braced Frame Construction—A Case History,” Engineering Journal, American Institute of Steel Construction, Chicago, IL, Vol. 18,
No. 4, 1981.
41. Merovich, A. T., Nicoletti, J. P. and Hartle, E., “Eccentric Bracing in Tall
Buildings,” Journal of the Structural Division, Vol. 108, No. 9, American Society
of Civil Engineers, September 1982.
42. Hjelmstad, K. D. and Popov, E. P., “Cyclic Behavior and Design of Link Beams,”
Journal of the Structural Division, Vol. 109, No. 10, American Society of Civil
Engineers, October 1983.
43. Malley, J. O. and Popov, E. P., “Shear Links in Eccentrically Braced Frames,”
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
6 - 370
LIST OF REFERENCES
Journal of the Structural Division, Vol. 110, No. 9, American Society of Civil
Engineers, September 1984.
44. Kasai, K. and Popov, E. P., “General Behavior of WF Steel Shear Link Beams,”
Journal of the Structural Division, Vol. 112, No. 2, American Society of Civil
Engineers, February 1986.
45. Kasai, K. and Popov, E. P., “Cyclic Web Buckling Control for Shear Link Beams,”
Journal of the Structural Division, Vol. 112, No. 3, American Society of Civil
Engineers, March 1986.
46. Ricles, J. M. and Popov, E. P., Dynamic Analysis of Seismically Resistant Eccentrically Braced Frames, Report No. UCB/EERC-87/107, Earthquake Engineering Research Center, University of California, Berkeley, CA, 1987.
47. Engelhardt, M. D. and Popov, E. P., Behavior of Long Links in Eccentrically
Braced Frames, Report No. UCB/EERC-89/01, Earthquake Engineering Research Center, University of California, Berkeley, CA, 1989.
48. Popov, E. P., Engelhardt, M. D. and Ricles, J. M., “Eccentrically Brace Frames:
U. S. Practice,” Engineering Journal, American Institute of Steel Construction,
Chicago, IL., Vol. 26, No. 2, 1989. p. 66–80.
49. Engelhardt, M. D. and Popov, E. P., “On Design of Eccentrically Braced Frames,”
Earthquake Engineering Research Institute, El Cerrito, CA, Earthquake Spectra,
Vol. 5, No.3, August 1989.
50. Kasai, K. and Popov, E. P., On Seismic Design of Eccentrically Braced Steel
Frames, Proceedings, 8th World Conference on Earthquake Engineering, July
1984, San Francisco, CA., Vol. 5, pp.387–394.
51. Whittaker, A. S., Uang, C-M., and Bertero, V. V., Earthquake Simulation Tests
and Associated studies of a 0.3-Scale Model of a Six-Story Eccentrically Braced
Steel Structure, Report No. UBC/EERC-87/02, EERC, Berkeley, CA., 1987.
52. Foutch, D. A., “Seismic Behavior of Eccentrically Braced Steel Building,” ASCE
Journal of Structural Engineering, Vol. 115, No. 8, August 1989, pp 1857–1876.
53. AISC, Allowable Stress Design Specification, American Institute of Steel Construction, Inc., Chicago, IL, 1989.
54. AISC, Serviceability Design Considerations for Low-Rise Buildings, Steel Design Guide Series 3, American Institute of Steel Construction, Inc.
55. Structural Steel Education Council, Steel Connections/Details and Relative Costs,
Moraga, CA., 1986.
56. Uang, C. M., “EstablishingR (or Rw) and Cd Factors for Building Seismic Provisions,” Journal of Structural Engineering, Vol. 117, No. 1, American Society of
Civil Engineers, Jan. 1991.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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LOAD AND RESISTANCE FACTOR DESIGN
Specification for
Structural Joints Using
ASTM A325 or A490 Bolts
Approved by Research Council on Structural Connections
of the Engineering Foundation, June 8, 1988.
Endorsed by American Institute of Steel Construction
Endorsed by Industrial Fasteners Institute
AMERICAN INSTITUTE OF STEEL CONSTRUCTION, INC.
One East Wacker Drive, Suite 3100, Chicago, IL 60601-2001
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
6 - 372
PREFACE
The purpose of the Research Council on Structural Connections is to stimulate and
support such investigation as may be deemed necessary and valuable to determine
the suitability and capacity of various types of structural connections, to promote
the knowledge of economical and efficient practices relating to such structural connections, and to prepare and publish related standards and such other documents
as necessary to achieving its purpose.
The Council membership consists of qualified structural engineers from the academic and research institutions, practicing design engineers, suppliers, and manufacturers of threaded fasteners, fabricators and erectors and code writing authorities.
Each version of the Specification is based upon deliberations and letter ballot of
the full Council membership.
The first Specification for Assembly of Structural Joints Using High Tensile Steel
Bolts approved by the Council was published in January 1951. Since that time the
Council has published 12 succeeding editions each based upon past successful usage,
advances in the state of knowledge and changes in engineering design practice. This
version of the Council’s Load and Resistance Factor Design Specification is significantly reorganized and revised from earlier versions.
The intention of the Specifications is to cover the design criteria and normal
usage and practices involved in the everyday use of high-strength bolts in steel-tosteel structural connections. It is not intended to cover the full range of structural
connections using threaded fasteners nor the use of high-strength bolts other than
those included in ASTM A325 or ASTM A490 Specifications nor the use of ASTM
A325 or A490 bolts in connections with material other than steel within the grip.
A Commentary has been prepared to accompany these Specifications to provide background and aid the user to better understand and apply the provisions.
The user is cautioned that independent professional judgment must be exercised
when data or recommendations set forth in these Specifications are applied. The
design and the proper installation and inspection of bolts in structural connections
is within the scope of expertise of a competent licensed architect, structural engineer or other licensed professional for the application of the principles to a particular case.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
6 - 373
LOAD AND RESISTANCE FACTOR DESIGN
Specification for
Structural Joints Using
ASTM A325 or A490 Bolts
Approved by Research Council on Structural Connections of the
Engineering Foundation, June 8, 1988.
Endorsed by American Institute of Steel Construction
Endorsed by Industrial Fasteners Institute
1. Scope
This Specification relates to the load and resistance factor design of structural joints
using ASTM A325 high-strength bolts, ASTM A490 high-strength bolts or equivalent
fasteners, and for the installation of such bolts in connections of structural steel members. The Specification relates only to those aspects of the connected materials that
bear upon the performance of the fasteners.
Design and construction shall conform to an applicable load and resistance factor
design code or specification for structures of carbon, high-strength low alloy steel or
quenched and tempered structural steel. Load and resistance factor design is a method
of proportioning structural components such that no applicable limit state is exceeded
when the structure is subject to all appropriate load combinations. When a structure
or component ceases to fulfill the intended purpose in some way, it is said to have exceeded
a limit state. Strength limit states concern maximum load carrying capacity, and thus
generally are related to safety. Serviceability limit states are usually related to performance under normal service conditions, and thus usually are not related to strength
or safety. (See Commentary. ) The term “resistance” includes both strength limit states
and serviceability limit states.
The design strength, φRn (nominal strength multiplied by a resistance factor), of
each structural component or assemblage must equal or exceed the effect of the factored loads (nominal loads multiplied by load factors, with due recognition for load
combinations). Thus, both the load factor and the resistance factor must be known to
determine the reliability of the design, identified in load and resistance factor design
as the “safety index.” Although the load factors are not stated in this Specification,
load criteria contained in American National Standard “Building Code Requirements
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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RCSC SPECIFICATION FOR STRUCTURAL JOINTS (6/8/88)
for Minimum Design Loads in Buildings and Other Structures,” ANSI A58.1-1982,
were used as the basis for determining the resistance factors. For construction
governed by other design load criteria, appropriate adjustment of resistance factors
may be required.
The attached Commentary provides background information in order that the
user may better understand the provisions of the Specification.
2. Bolts, Nuts, Washers and Paint
(a) Bolt Specifications. Bolts shall conform to the requirements of the current
edition of the American Society for Testing and Materials’ “Specification
for High-Strength Bolts for Structural Steel Joints,” ASTM A325, or “Specification for Heat Treated, Steel Structural Bolts, 150 ksi Tensile Strength,”
ASTM A490, except as provided in paragraph (d) of this section. The Engineer of Record shall specify the type of bolts to be used.
(b) Bolt Geometry. Bolt dimensions shall conform to the current American
National Standards Institute’s standard, “Heavy Hex Structural Bolts,” ANSI
Standard B18.2.1, except as provided in paragraph (d) of this section. The
length of bolts shall be such that the end of the bolt will be flush with or
project beyond the face of the nut when properly installed.
(c) Nut Specifications. Nuts shall conform to the current chemical and mechanical requirements of the American Society for Testing and Materials’ Specification for Carbon and Alloy Steel Nuts,” ASTM A563, or “Specification for Carbon and Alloy Steel Nuts for Bolts for High-Pressure and
High-Temperature Service,” ASTM A194. The grade and surface finish of
nuts for each type shall be as follows:
A325 Bolt Type
Nut Specification, Grade and Finish
1 and 2, plain (uncoated) A563 C, C3, D, D3 and DH3 or Al94 2 and
2H; plain
1 and 2, galvanized
A563 DH or A194 2H; galvanized and lubricated
3, plain
A563 C3 and DH3; plain
A490 Bolt Type
1 and 2, plain
3, plain
Nut Specification, Grade and Finish
A563 DH and DH3 or A194 2H; plain
A563 DH3; plain
Nut dimensions shall conform to the current American National Standards
Institute’s standard, “Heavy Hex Nuts,” ANSI Standard B18.2.2., except
as provided in paragraph (d) of this section.
(d) Alternative Fastener Designs. Other fasteners or fastener assemblies which
meet the materials, manufacturing and chemical composition requirements
of ASTM A325 or ASTM A490, as applicable, and which meet the mechanical property requirements of the same specifications in full-size tests, and
which have a body diameter and bearing areas under the head and nut not
less than those provided by a bolt and nut of the same nominal dimensions
prescribed by paragraphs 2(b) and 2(c), may be used subject to the approval
of the Engineer of Record. Such alternative fasteners may differ in other
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
ASTM A325 OR A490 BOLTS
6 - 375
dimensions from those of the specified bolts and nuts. Their installation
procedure and inspection may differ from procedures specified for regular
high-strength bolts in Sections 8 and 9. When a different installation procedure or inspection is used, it shall be detailed in a supplemental specification applying to the alternative fastener, and that specification must be
approved by the Engineer of Record.
(e) Washers. Flat circular washers and square or rectangular beveled washers
shall conform to the current requirements of the American Society for
Testing and Materials, “Specification for Hardened Steel Washers,” ASTM
F436.
(f) Load Indicating Devices. Load indicating devices may be used in conjunction with bolts, nuts and washers specified in 2(a) through 2(e). Load indicating devices shall conform to the requirements of American Society for Testing and Materials’ “Specification for Compressible-Washer-Type Direct
Tension Indicators for Use with Structural Fasteners,” ASTM F959. Subject to the approval of the Engineer of Record, direct tension indicating
devices different from those meeting the requirements of ASTM F959 may
be used provided they satisfy the requirements of 8(d)(4). If their installation procedure and inspection are not identical to that specified in 8(d)(4),
they shall be detailed in supplemental specifications provided by the
manufacturer and subject to the approval of the Engineer of Record.
(g) Faying Surface Coatings. Paint, if used on faying surfaces of connections
which are not specified to be slip critical, may be of any formulation. Paint,
used on the faying surfaces of connections specified to be slip critical, shall
be qualified by test in accordance with “Test Method to Determine the Slip
Coefficient for Coatings Used in Bolted Joints” as published by the Research
Council on Structural Connections. (See Appendix A.) Manufacturer’s certification shall include a certified copy of the test report.
3. Bolted Parts
(a) Connected Material. All material within the grip of the bolt shall be steel.
There shall be no compressible material such as gaskets or insulation within
the grip. Bolted steel parts shall fit solidly together after the bolts are tightened, and may be coated or noncoated. The slope of the surfaces of parts
in contact with the bolt head or nut shall not exceed 1:20 with respect to
a plane normal to the bolt axis.
(b) Surface Conditions. When assembled, all joint surfaces, including surfaces
adjacent to the bolt head and nut, shall be free of scale, except tight mill
scale, and shall be free of dirt or other foreign material. Burrs that would
prevent solid seating of the connected parts in the snug tight condition shall
be removed.
Paint is permitted unconditionally on the faying surfaces in connections except in slip-critical connections as defined in Section 5(a).
The faying surfaces of slip-critical connections shall meet the requirements of the following paragraphs, as applicable.
(1) In noncoated joints, paint, including any inadvertent overspray, shall
be excluded from areas closer than one bolt diameter but not less
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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RCSC SPECIFICATION FOR STRUCTURAL JOINTS (6/8/88)
(2)
(3)
(4)
(5)
than one inch from the edge of any hole and all areas within the
bolt pattern.
Joints specified to have painted faying surfaces shall be blast cleaned
and coated with a paint which has been qualified as Class A or
B in accordance with the requirements of paragraph 2(g), except
as provided in 3(b)3.
Subject to the approval of the Engineer of Record, coatings providing a slip coefficient less than 0.33 may be used provided the
mean slip coefficient is established by test in accordance with the
requirements of paragraph 2(g), and the design slip resistance,
φRs, calculated in accordance with the formula in Section 5(b) or
5(c).
Coated joints shall not be assembled before the coatings have cured
for the minimum time used in the qualifying test.
Faying surfaces specified to be galvanized shall be hot-dip galvanized in accordance with American Society for Testing and Materials’ “Specification for Zinc (Hot-Galvanized) Coatings on Products Fabricated from Rolled, Pressed, and Forged Steel Shapes,
Plates, Bars, and Strip,” ASTM A123 and shall subsequently be
roughened by means of hand wire brushing. Power wire brushing
is not permitted.
(c) Hole Types. Hole types recognized under this specification are standard
holes, oversize holes, short slotted holes and long slotted holes. The nominal dimensions for each type hole shall be not greater than those shown
in Table 1. Holes not more than 1⁄32 inch larger in diameter than the true
decimal equivalent of the nominal diameter that may result from a drill or
reamer of the nominal diameter are considered acceptable. The slightly conical hole that naturally results from punching operations is considered acceptable. The width of slotted holes which are produced by flame cutting or
a combination of drilling or punching and flame cutting shall generally be
not more than 1⁄32 inch greater than the nominal width except that gouges
not more than 1⁄16 inch deep shall be permitted. For statically loaded connections, the flame cut surface need not be ground. For dynamically loaded
connections, the flame cut surface shall be ground smooth.
4. Design of Bolted Connections
Expressions for design strengths, φRn, of bolts subject to axial tension, shear and
combined shear and tension are given in 4(a) and 4(b). They are to be compared
to the effect of the factored loads. The design resistances of bolts subject to cyclic
application of axial tension are given in 4(e). They are to be compared to effect
of cyclically applied nominal (service) loads.
(a) Tension and Shear Strength Limit States. The design strength in axial
tension for A325 and A490 bolts which are tightened to the minimum fastener tension specified in Table 4 is φRn. The design strength in shear for
A325 and A490 bolts, independent of the installed bolt pretension, is φRn
where:
Rn = Fn Ab
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
(LRFD 4.1)
ASTM A325 OR A490 BOLTS
6 - 377
Table 1. Nominal Hole Dimensions
Bolt
Dia.
1⁄
2
5⁄
8
3⁄
4
7⁄
8
1
≥ 11⁄8
Hole DImensions
Standard
(Dia.)
Oversize
(Dia.)
9⁄
16
11⁄
16
13⁄
16
15⁄
16
11⁄16
5⁄
8
13⁄
16
15⁄
16
11⁄16
11⁄4
d + 1⁄16
d + 5⁄16
Short Slot
(Width × Length)
(d
9⁄ × 11⁄
16
16
11⁄ × 7⁄
16
8
13⁄ × 1
16
15⁄ × 11⁄
16
8
11⁄16 × 15⁄16
+ 1⁄16) × (d + 3⁄8)
Long Slot
(Width × Length)
9⁄
1
16 × 1 ⁄4
9
16 × 1 ⁄16
13⁄ × 17⁄
16
8
15⁄ × 23⁄
16
16
11⁄16 × 21⁄2
+ 1⁄16) × (2.5 ×
11⁄
(d
d)
In this expression:
Rn = nominal strength of a bolt subject to axial tension or shear, kips
Fn = nominal strength from Table 2 for appropriate kind of load, ksi
Ab = area of bolt corresponding to nominal diameter, in.2
φ = resistance factor from Table 2.
(b) Combined Tension and Shear Strength Limit State. In bearing connections in which the applied shear force is greater than 1⁄3 the design shear
strength according to 4(a). the design strength in axial tension for A325
and A190 bolts is φRn where:
Rn = Fnt Ab
(LRFD 4.2)
Where
Rn = nominal tension strength of a bolt subject to concurrent shear. kips
Fnt = nominal tension strength of a bolt as calculated by formulas in Table 3,
ksi
Ab = area of bolt corresponding to nominal diameter, in.2
φ = resistance factor equal to 0.75
In Table 3. fv, equals the shear force on the bolt in ksi.
(c) Bearing Strength Limit State. The design bearing strength on the connected material for all bolts in a connection with two or more bolts in the
line of force in standard, oversize, or short slotted holes when the edge distance in direction of force is not less than 11⁄2d and the distance center to
center of bolts is not less than 3d is φRn, where:
Rn = 2.4dtFu
(LRFD 4.3)
The design bearing strength on the connected material for all bolts in a connection with two or more bolts in the line of force in long slotted holes
perpendicular to the direction of force when the edge distance, L, is not
less than 11⁄2d and the distance center to center of bolts is not less than 3d
is φRn where:
Rn = 2.0dtFu
(LRFD 4.4)
The design bearing strength on the connected material for the bolt nearest
to the free edge in the direction of force when two or more bolts are in
the line of force in standard, oversize, or short slotted holes but with the
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
6 - 378
RCSC SPECIFICATION FOR STRUCTURAL JOINTS (6/8/88)
Table 2. Nominal Strength of Fasteners
Nominal Strength (ksi)
Load Condition
a,b,c
Applied Static Tension
Shear on bolt with threads in shear plane.
Shear on bolt without threads in shear plane.
a.
b.
c.
d.
A325
A490
Resistance
Factor, φ
90
d
48
d
60
113
d
60
d
75
0.75
0.75
0.75
Bolts must be tensioned to requirements of Table 4.
See 4(e) for bolts subject to tensile fatigue.
Except as required by 4(b).
In shear connections transmitting axial force whose length between extreme fasteners measured parallel to the line of force exceeds 50 inches, tabulated values shall be reduced 20
percent.
Table 3. Nominal Tension Strength for Bolts in Bearing Connections
(Nominal Tensile Strength, Fnt, ksi.)
Fastener Grade
Threads Not Excluded
from Shear Plane
2
2 0.5
Threads Excluded
from Shear Plane
2
2 0.5
ASTM A325
(90 − 3.52fv )
(90 − 2.25fv )
ASTM A490
(113 − 3.54fv )
(113 − 2.27fv )
2
2 0.5
2
2 0.5
edge distance less than 11⁄2d and for a single bolt in the line of force is φRn
where:
Rn = LtFu ≤ 3.0dtFu
(LRFD 4.5)
When two or more bolts are in the line of force in standard, oversize, or
short slotted holes and if deformation around the bolt holes is not a design
consideration, the design strength in bearing for the individual bolts of a
connection may be taken as φRn where:
Rn = LtFu ≤ 3.0dtFu
(LRFD 4.6)
In the foregoing:
Rn = nominal bearing strength of connected material, kips
Fu = specified minimum tensile strength of the connected part, ksi
L = distance in the direction of the force from the center of a standard
hole or transverse slotted hole to the edge of the connected part or
the distance center to center of standard holes or transverse slots, as
applicable, in.
d = nominal diameter of bolt, in.
t = thickness of connected material, in.
φ = resistance factor = 0.75
(d) Prying Action. The force in bolts required to support loads by means of
direct tension shall be calculated considering the effects of the external load
and any tension resulting from prying action produced by deformation of
the connected parts.
(e) Tensile Fatigue. When subject to tensile fatigue loading, the tensile stress
in the bolt due to the nominal (service) load plus the prying force resulting
from cyclic application of nominal load shall not exceed the following design
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
ASTM A325 OR A490 BOLTS
6 - 379
resistances in kips per square inch. The nominal diameter of the bolt shall
be used in calculating the bolt stress. In no case shall the calculated prying
force exceed 60 percent of the externally applied load.
Number of Cycles
Not more than 20,000
From 20,000 to 500,000
More than 500,000
A325
44
40
31
A490
54
49
38
Bolts subject to tensile fatigue load must be tensioned to requirements
of Table 4.
5. Design Check for Slip Resistance
(a) Slip-Critical Joints. Joints in which, in the judgment of the Engineer of
Record, slip would be detrimental to the behavior of the joint, are defined
as slip-critical. As discussed in the Commentary, these include but are not
necessarily limited to joints subject to fatigue or significant load reversal,
joints with bolts in oversize holes or slotted holes with the applied force
approximately in the direction of the long dimension of the slots and joints
in which welds and bolts share in transmitting shear loads at a common
faying surface. Slip-critical joints shall be checked for slip resistance. At
the option of the Engineer of Record, the required check may be based upon
either nominal loads or factored loads. When serviceability at the nominal
(service) load is the design criterion, the design slip resistance specified
in Section 5(b) shall be compared with the effects of the nominal loads.
When slip of the joint at the factored load level would affect the ability of
the structure to support the factored load, the design slip resistance specified in Section 5(c) shall be compared to the effects of the factored loads.
Slip-critical joints shall also be checked to ensure that the ultimate
strength of the joint as a bearing joint is equal to or greater than the effect
of the factored loads.
Slip-critical joints must be designated on the contract plans and in the
specifications. Bolts used in slip-critical joints shall be installed in accordance with the provisions of Section 8(d).
(b) Slip-Critical Joints Designed at the Nominal Load Level. Slip-critical
joints for which nominal loads are the design criterion shall, in addition
to meeting the requirements of Section 4, be proportioned so that the force
due to nominal (service) loads does not exceed the design slip resistance
for use at nominal loads (service) loads, φRs, where:
Rs = DµTm Nb Ns
(LRFD 5.1)
Where:
Rs = nominal slip resistance of a bolt for use at nominal loads, kips
Tm = minimum fastener tension given in Table 4, kips
Nb = number of bolts in the joint
Ns = number of slip planes
D = slip probability factor*
= 0.81 for µ equal to 0.33
= 0.86 for µ equal to 0.40
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
6 - 380
RCSC SPECIFICATION FOR STRUCTURAL JOINTS (6/8/88)
= 0.86 for µ equal to 0.50
µ = mean slip coefficient for Class A, B or C surfaces, † as applicable, or
as established by tests
= 0.33 for Class A surfaces (unpainted clean mill scale steel surfaces
or surfaces with Class A coating on blast-cleaned steel)
= 0.50 for Class B surfaces (unpainted blast-cleaned steel surfaces or
surfaces with Class B coatings on blast-cleaned steel)
= 0.40 for Class C surfaces (hot-dip galvanized and roughened surfaces)
φ = 1.0 for standard holes
= 0.85 for oversize and short slotted holes
= 0.70 for long slotted holes transverse to the direction of load
= 0.60 for long slotted holes parallel to the direction of load
* D is a multiplier that reflects the distribution of actual slip coefficient values about the
mean, the ratio of measured bolt tensile strength to the specified minimum values, and a slip
probability level. Use of other values of D (see Commentary) must be approved by the Engineer of Record.
† Coatings classified as Class A or Class B includes those coatings which provide a mean
slip coefficient not less than 0.33 or 0.50, respectively, as determined by “Test Method to Determine the Slip Coefficient for Coatings Used in Bolted Connections.”
Table 4. Fastener Tension Required for Slip-Critical Connections
and Connections Subject to Direct Tension
Nominal Bolt
Size, Inches
a
Minimum Tension in 1,000s of Pounds (kips)
A325 Bolts
A490 Bolts
12
19
28
39
15
24
35
49
1
11⁄8
11⁄4
13⁄8
51
56
71
85
64
80
102
121
11⁄2
103
148
1⁄
5⁄
3⁄
7⁄
2
8
4
8
a. Equal to 70 percent of specified minimum tensile strengths of bolts (as specified in ASTM
Specifications for tests of full size A325 and A490 bolts with UNC threads loaded in axial tension) rounded to the nearest kip.
When using nominal loads as the basis for design of slip-critical connections subject to applied tension, T, that reduces the net clamping force,
the slip resistance (φRs) shall be multiplied by the following factor in
which T is the applied tensile force at nominal loads
[1 − T / (0.82TmNb)]
(LRFD 5.2)
(c) Slip-Critical Joints Designed at Factored Load Level. Slip-critical joints
for which factored loads are the design criterion shall, in addition to meeting the requirements of Section 4, be proportioned so that the force due
to the factored loads shall not exceed the design slip resistance for use at
factored loads, φRstr, where:
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
ASTM A325 OR A490 BOLTS
6 - 381
Rstr = 1.13µTm Nb Ns
(LRFD 5.3)
Where terms in Formula (LRFD 5.3) are as defined in 5(b).
When using factored loads as the basis for design of slip-critical connections subject to applied tension, T, that reduces the net clamping force,
the slip resistance (φRs) shall be multiplied by the following factor in
which T is the applied tensile force at nominal loads
[1 − T / (1.13Tm Nb)]
(LRFD 5.4)
6. Loads in Combination
When the reduced probabilities of maximum loads acting concurrently are accounted
for by load combination factors, the resistances given in this Specification shall not
be increased.
7. Design Details of Bolted Connections
(a) Standard Holes. In the absence of approval by the Engineer of Record for
use of other hole types, standard holes shall be used in high-strength bolted
connections.
(b) Oversize and Slotted Holes. When approved by the Engineer of Record,
oversize holes, short slotted holes or long slotted holes may be used subject to the following joint detail requirements:
(1) Oversize holes may be used in all plies of connections in which
the design slip resistance of the connection is greater than the factored nominal load.
(2) Short slotted holes may be used in any or all plies of connections
in which the design strength (Section 4(a)) is greater than the factored nominal load provided the load is applied approximately normal (between 80 and 100 degrees) to the axis of the slot. Short
slotted holes may be used without regard for the direction of applied
load in any or all plies of connections in which the design slip resistance (Section 5(b)) is greater than the factored nominal load.
(3) Long slotted holes may be used in one of the connected parts at
any individual faying surface in connections in which the design
strength (Section 4(a)) is greater than the factored nominal load
provided the load is applied approximately normal (between 80 and
100 degrees) to the axis of the slot. Long slotted holes may be used
in one of the connected parts at any individual faying surface without regard for the direction of applied load on connections in which
the design slip resistance (Section 5(b)) is greater than the factored
nominal load.
(4) Fully inserted finger shims between the faying surfaces of load
transmitting elements of connections are not to be considered a long
slot element of a connection.
(c) Washer Requirements. Design details shall provide for washers in highstrength bolted connections as follows:
(1) Where the outer face of the bolted parts has a slope greater than 1:20
with respect to a plane normal to the bolt axis, a hardened beveled
washer shall be used to compensate for the lack of parallelism.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
6 - 382
RCSC SPECIFICATION FOR STRUCTURAL JOINTS (6/8/88)
(2) Hardened washers are not required for connections using A325 and
A490 bolts except as required in paragraphs 7(c)(3) through 7(c)(7)
for slip-critical connections and connections subject to direct tension
or as required by paragraph 8(c) for shear/bearing connections.
(3) Hardened washers shall be used under the element turned in tightening when the tightening is to be performed by calibrated wrench
method.
(4) Irrespective of the tightening method, hardened washers shall be
used under both the head and the nut when A490 bolts are to be
installed and tightened to the tension specified in Table 4 in material having a specified yield point less than 40 ksi.
(5) Where A325 bolts of any diameter or A490 bolts equal to or less
than 1 inch in diameter are to be installed and tightened in an oversize or short slotted hole in an outer ply, a hardened washer conforming to ASTM F436 shall be used.
(6) When A490 bolts over 1 inch in diameter are to be installed and
tightened in an oversize or short slotted hole in an outer ply, hardened washers conforming to ASTM F436 except with 5⁄16 inch minimum thickness shall be used under both the head and the nut in
lieu of standard thickness hardened washers. Multiple hardened
washers with combined thickness equal to or greater than 5⁄16 inch
do not satisfy this requirement.
(7) Where A325 bolts of any diameter or A490 bolts equal to or less
than 1 inch in diameter are to be installed and tightened in a long
slotted hole in an outer ply, a plate washer or continuous bar of
at least 5⁄16 inch thickness with standard holes shall be provided.
These washers or bars shall have a size sufficient to completely
cover the slot after installation and shall be of structural grade material, but need not be hardened except as follows. When A490 bolts
over 1 inch in diameter are to be used in long slotted holes in external plies, a single hardened washer conforming to ASTM F436 but
with 5⁄16 inch minimum thickness shall be used in lieu of washers
or bars of structural grade material. Multiple hardened washers with
combined thickness equal to or greater than 5⁄16 inch do not satisfy
this requirement.
(8) Alternative design fasteners meeting the requirements of 2(d) with
a geometry which provides a bearing circle on the head or nut with
a diameter equal to or greater than the diameter of hardened washers
meeting the requirements ASTM F436 satisfy the requirements for
washers specified in paragraphs 7(c)(4) and 7(c)(5).
8. Installation and Tightening
(a) Handling and Storage of Fasteners. Fasteners shall be protected from dirt
and moisture at the job site. Only as many fasteners as are anticipated to be
installed and tightened during a work shift shall be taken from protected
storage. Fasteners not used shall be returned to protected storage at the end
of the shift. Fasteners shall not be cleaned of lubricant that is present in asdelivered condition. Fasteners which accumulate rust or dirt resulting from
job site conditions shall be cleaned and relubricated prior to installation.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
ASTM A325 OR A490 BOLTS
6 - 383
(b) Tension Calibrator. A tension measuring device shall be at all job sites
where bolts in slip-critical joints or connections subject to direct tension
are being installed and tightened. The tension measuring device shall be
used to confirm (1) the suitability of the complete fastener assembly and
method of tightening, including lubrication, if required to satisfy the requirements of Table 4, (2) to calibrate the wrenches, if applicable, and (3) to
confirm the understanding and proper use by the bolting crew of the method
to be used. The frequency of confirmation testing, the number of tests to
be performed, and the test procedure shall be as specified in 8(d), as applicable. The accuracy of the tension measuring device shall be confirmed through
calibration by an approved testing agency at least annually.
(c) Joint Assembly and Tightening of Shear/Bearing Connections.
(1) Snug Tightened Bolts. Bolts in connections not within the slipcritical category as defined in Section 5(a) nor subject to tension
loads nor required to be pretensioned bearing connections in accordance with 8(c)(2) shall be installed in properly aligned holes, but
need only be tightened to the snug tight condition. The snug tight
condition is defined as the tightness that exists when all plies in
a joint are in firm contact. (See Commentary.) If a slotted hole
occurs in an outer ply, a flat hardened washer or common plate
washer shall be installed over the slot.
(2) Tensioned Shear/Bearing Connections. The Engineer of Record
may designate certain shear/bearing connections to be tightened
to pretension in excess of snug tight. When so designated and identified on the contract drawings, the bolts in such connections shall
be installed and tightened in accordance with one of the methods
described in Subsections 8(d)(1) through 8(d)(4), but shall not be
subject to the requirements for faying surface conditions of slipcritical connections contained in 3(b). The bolts need not be subject to inspection testing to determine the actual level of bolt pretension unless required by the Engineer of Record.
(d) Joint Assembly and Tightening of Slip-Critical and Direct Tension Connections. In slip-critical connections and connections subject to direct tension, fasteners together with washers of size and quality specified, located
as required by Section 7(c), shall be installed in properly aligned holes and
tightened by any of the methods described in Subsections 8(d)(1) through
8(d)(4) to at least the minimum tension specified in Table 4 when all the
fasteners are tight. Tightening may be done by turning the bolt while the
nut is prevented from rotating when it is impractical to turn the nut. Impact
wrenches, if used, shall be of adequate capacity and sufficiently supplied
with air to perform the required tightening of each bolt in approximately
10 seconds. Slip-critical connections and connections subject to direct tension shall be clearly identified on the drawings.
(1) Turn-of-Nut Tightening. When turn-of-nut tightening is used, hardened washers are not required except as may be specified in 7(c).
A representative sample of not less than three bolt and nut
assemblies of each diameter, length, grade and lot to be used in the
work shall be checked at the start of work in a device capable
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
6 - 384
RCSC SPECIFICATION FOR STRUCTURAL JOINTS (6/8/88)
of indicating bolt tension. The test shall demonstrate that the method
for estimating the snug tight condition and controlling the turns
from snug tight to be used by the bolting crew develops a tension
not less than 5 percent greater than the tension required by Table 4.
Bolts shall be installed in all holes of the connection and brought
to a “snug tight” condition. Snug tight is defined as the tightness
that exists when the plies of the joint are in firm contact. Snug tightening shall progress systematically from the most rigid part of the
connection to the free edges until all bolts are simultaneously snug
tight and the connection is fully compacted. In some cases, proper
tensioning of the bolts may require more than a single cycle of systematic tightening to produce a uniform snug tight condition. Following this initial operation, all bolts in the connection shall be
tightened further by application of the rotation specified in Table
5. During the tightening operation, there shall be no rotation of
the part not turned by the wrench. Tightening shall progress systematically from the most rigid part of the joint to its free edges.
(2) Calibrated Wrench Tightening: Calibrated wrench tightening may
be used only when installation procedures are calibrated on a daily
basis and when a hardened washer is used under the element turned
in tightening. (See the Commentary to this Section.) This specification
does not recognize standard torques determined from tables or from
formulas which are assumed to relate torque to tension.
When calibrated wrenches are used for installation, they shall
be set to provide a tension not less than 5 percent in excess of the
minimum tension specified in Table 4. The installation procedures
shall be calibrated at least once each working day by tightening
representative sample fastener assemblies in a device capable of
indicating actual bolt tension. The representative fastener assemblies shall consist of three bolts from each lot diameter, length
and grade with nuts from each lot, diameter and grade and with
a hardened washer from the washers being used in the work under
the element turned in tightening. Wrenches shall be recalibrated
when significant difference is noted in the surface condition of the
bolts’ threads, nuts or washers. It shall be verified during actual
installation in the assembled steelwork that the wrench adjustment
selected by the calibration does not produce a nut or bolt head rotation from snug tight greater than that permitted in Table 5. If manual torque wrenches are used, nuts shall be turned in the tightening direction when torque is measured.
When calibrated wrenches are used to install and tension bolts
in a connection, bolts shall be installed with hardened washers under
the element turned in tightening bolts in all holes of the connection
and brought to a snug tight condition. Snug tightening shall progress systematically from the most rigid part of the connections
to the free edges until bolts are uniformly snug tight and the plies
of the joint are in firm contact. Following this initial tightening operation, the connection shall be tightened using the calibrated wrench.
Tightening shall progress systematically from the most rigid part
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
ASTM A325 OR A490 BOLTS
6 - 385
a,b
Table 5. Nut Rotation from Snug Tight Condition
Disposition of Outer Face of Bolted Parts
Bolt length
(underside of
head to end of
bolt)
Both faces
normal to bolt
axis
One face normal
to bolt axis and
other sloped not
more than 1:20
(beveled washer
not used)
Both faces sloped
not more than
1:20 from normal
to the bolt axis
(beveled washer
not used)
Up to and including 4 diameters
1⁄
3
turn
1⁄
2
turn
2⁄
3
turn
Over 4 diameters
but not exceeding 8 dia.
1⁄
2
turn
2⁄
3
turn
5⁄
6
turn
Over 8 diameters
but not exceedc
ing 12 dia.
2⁄
3
turn
5⁄
6
turn
1 turn
a. Nut rotation is relative to bolt regardless of the element (nut or bolt) being turned. For bolts
installed by 1⁄2 turn and less, the tolerance should be plus or minus 30 degrees; for bolts
installed by 2⁄3 turn and more, the tolerance should be plus or minus 45 degrees.
b. Applicable only to connections in which all material within the grip of the bolt is steel.
c. No research has been performed by the Council to establish the turn-of-nut procedure for
bolt lengths exceeding 12 diameters. Therefore, the required rotation must be determined
by actual test in a suitable tension measuring device which simulates conditions of solidly
fitted steel.
of the joint to its free edges. During snugging and final tightening
the element not turned in tightening shall be held to prevent rotation
which will damage threads. In some cases, proper tensioning of the
bolts may require more than a single cycle of systematic tightening
to ensure all bolts are tightened to at least the prescribed amount.
(3) Installation of Alternative Design Bolts. When fasteners which
incorporate a design feature intended to indicate a predetermined
tension or torque has been applied or to control bolt installation
tension or torque, and which have been qualified under Section 2(d)
are to be installed, a representative sample of not less than three
bolts of each diameter, length and grade shall be checked at the
job site in a device capable of indicating bolt tension. The test
assembly shall include flat hardened washers, if required in the
actual connection, arranged as in the actual connections to be tensioned. The calibration test shall demonstrate that each bolt develops
a tension not less than 5 percent greater than the tension required
by Table 4. Manufacturer’s installation procedure as required by
Section 2(d) shall be followed for installation of bolts in the calibration device and in all connections.
When alternative design fasteners are used in the work, bolts
shall be installed in all holes of the connection and initially tightened sufficiently to bring all plies of the joint into firm contact with
the bolts uniformly tight but without yielding or fracturing the control or indicator element of the fasteners. In some cases, proper
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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RCSC SPECIFICATION FOR STRUCTURAL JOINTS (6/8/88)
tensioning of the bolts may require more than a single cycle of systematic partial tightening. After all plies of the joint are in firm
contact, all fasteners shall be further tightened, progressing systematically from the most rigid part of the connection to the free edges
in a manner that will minimize relaxation of previously tightened
fasteners. In some cases, proper tensioning of the bolts may require
more than a single cycle of systematic partial tightening prior to
final yielding or fracture of the control or indicator element of individual fasteners.
(4) Direct Tension Indicator Tightening. When bolts are to be installed using direct tension indicator devices to indicate bolt tension,
a representative sample of not less than three devices for each
diameter and grade of fastener shall be tested with three typical
bolts in a calibration device capable of indicating bolt tension. The
test assembly shall include flat hardened washers, if required in the
actual connection, arranged as those in the actual connections to
be tensioned. The calibration test shall demonstrate that the device indicates a tension not less than 5 percent greater than that
required by Table 4.
When bolts are installed in the work using direct tension indicators meeting the requirements of ASTM F959, bolts shall be
installed in all holes of the connection and tightened until all plies
of the joint are in firm contact and fasteners are uniformly snug
tight. Snug tight is indicated by partial compression of the direct
tension indicator protrusions. All fasteners shall then be tightened,
progressing systematically from the most rigid part of the connection to the free edges in a manner that will minimize relaxation
of previously tightened fasteners. In some cases, proper tensioning of the bolts may require more than a single cycle of systematic
partial tightening prior to final tightening to deform the protrusion
to the specified gap.
Special attention shall be given to proper installation of flat
hardened washers when direct tension indicator devices are used
with bolts installed in oversize or slotted holes and when the load
indicating devices are used under the turned element.
If direct tension indicators different from those meeting the
requirements of ASTM F959 are used, manufacturer’s installation
procedure as required by Section 2(f), shall be followed for installation of bolts in the calibration device and in all connections, and
in addition the general requirements for use of direct tension indicators meeting the requirements of ASTM F959 shall be met.
(e) Identification of Tightening Requirements. Bolts in slip-critical connections or bolts subject to axial tension which are to be installed and tightened in accordance by one of the methods in 8(d) and which require inspection to ensure that requirements of Table 4 are satisfied shall be clearly
identified on the contract drawings. Shear/bearing connections which are
to be installed by one of the methods in 8(d) but which need not be inspected
to ensure bolt tensions specified in Table 4 are met shall be clearly identified on the contract drawings.
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(f) Reuse of Bolts. A490 bolts and galvanized A325 bolts shall not be reused.
Other A325 bolts may be reused if approved by the Engineer of Record.
Touching up or retightening previously snug tightened bolts which may have
been loosened by the snugging of adjacent bolts shall not be considered to
be a reuse.
9. Inspection
(a) Inspector Responsibility. When inspection is required by the contract documents, the Inspector shall determine while the work is in progress that the
requirements of Sections 2, 3 and 8, as appropriate, of this Specification
are met in the work. All connections shall be inspected to ensure that the
plies of the connected elements have been brought into firm contact.
Bolts in connections not identified as being slip-critical nor subject to
direct tension nor as tensioned bearing connections as provided in 8(c)(2)
should not be inspected for bolt tension. For connections identified to be
installed in accordance with 8(c)(2), the Inspector shall monitor installation and tightening of bolts to ensure that bolts are tightened in accordance
with one of the methods of 8(d), but should not test the bolts for actual
installed pretension.
For all connections specified to be slip critical or subject to axial tension the Inspector shall observe the demonstration testing, and calibration
procedures when such calibration is required, and shall monitor the installation of bolts to determine that all plies of the material have been drawn
together and that the selected procedure has been used to tighten all bolts
to ensure that the specified procedure was followed to achieve the pretension specified in Table 4. Bolts installed by procedures in Section 8(d) may
reach tensions substantially greater than values given in Table 4, but this
shall not be cause for rejection.
(b) Arbitration Inspection. When high-strength bolts in slip-critical connections and connections subject to direct tension have been installed by any
of the tightening methods in Section 8(d) and inspected in accordance with
Section 9(a) and a disagreement exists as to the minimum tension of the
installed bolts, the following arbitration procedure may be used. Other
methods for arbitration inspection may be used if approved by the Engineer of Record.
(1) The Inspector shall use a manual torque wrench which indicates
torque by means of a dial or which may be adjusted to give an indication that the job inspecting torque has been reached.
(2) This Specification does not recognize standard torques determined
from tables or from formulas which are assumed to relate torque
to tension. Testing using such standard torques shall not be considered valid.
(3) A representative sample of five bolts from the diameter, length and
grade of the bolts being inspected shall be tightened in the tension
measuring device by any convenient means to an initial condition
equal to approximately 15 percent of the required fastener tension
and then to the minimum tension specified in Table 4. Material
under the turned element in the tension measuring device shall be
the same as in the actual installation, that is, structural steel or
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RCSC SPECIFICATION FOR STRUCTURAL JOINTS (6/8/88)
hardened washer. Tightening beyond the initial condition must not
produce greater nut rotation than 11⁄2 times that permitted in Table
5. The job inspecting torque shall be taken as the average of three
values thus determined after rejecting the high and low values. The
inspecting wrench shall then be applied to the tightened bolts in
the work and the torque necessary to turn the nut or head 5 degrees
(approximately 1 inch at 12 inch radius) in the tightening direction
shall be determined.
(4) Bolts represented by the sample in the foregoing paragraph which
have been tightened in the structure shall be inspected by applying, in the tightening direction, the inspecting wrench and its job
torque to 10 percent of the bolts, but not less than 2 bolts, selected
at random in each connection in question. If no nut or bolt head
is turned by application of the job inspecting torque, the connection shall be accepted as properly tightened. If any nut or bolt is
turned by the application of the job inspecting torque, all bolts in
the connection shall be tested, and all bolts whose nut or head is
turned by the job inspecting torque shall be tightened and reinspected. Alternatively, the fabricator or erector, at his option, may
retighten all of the bolts in the connection and then resubmit the
connection for the specified inspection.
(c) Delayed Verification Inspection. The procedures specified in Sections 9(a)
and (b) are intended for inspection of bolted connections and verification
of pretension at the time of tensioning the joint. If verification of bolt tension is required after a passage of a period of time and exposure of the
completed joints, the procedure of Section 9(b) will provide indication of
bolt tension which is of questionable accuracy. Procedures appropriate to
the specific situation should be used for verification of bolt tension. This
might involve use of the arbitration inspection procedure contained herein,
or might require the development and use of alternate procedures. (See
Commentary.)
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APPENDIX A
Testing Method to Determine the
Slip Coefficient for Coatings Used
in Bolted Joints
Reprinted from Engineering Journal
American Institute of Steel Construction, Third Quarter, 1985.
JOSEPH A. YURA and KARL H. FRANK
In 1975, the Steel Structures Painting Council (SSPC) contacted the Research Council
on Riveted and Bolted Structural Joints (RCRBSJ), now the Research Council on
Structural Connections (RCSC), regarding the difficulties and costs which steel fabricators encounter with restrictions on coatings of contact surfaces for friction-type
structural joints. The SSPC also expressed the need for a “standardized test which
can be conducted by any certified testing agency at the initiative and expense of
any interested party, including the paint manufacturer.” And finally, the RCSC was
requested to “prepare and promulgate a specification for the conduct of such a standard test for slip coefficients.”
The following Testing Method is the answer of Research Council on Structural
Connections to the SSPC request. The test method was developed by Professors
Joseph A. Yura and Karl H. Frank of the University of Texas at Austin under a grant
from the Federal Highway Administration. The Testing Method was approved by
the RCSC on June 14, 1984.
1.0 GENERAL PROVISIONS
1.1 Purpose and Scope
The purpose of the testing procedure is to determine the slip coefficient of a coating
for use in high-strength bolted connections. The testing specification ensures that
the creep deformation of the coating due to both the clamping force of the bolt and
the service load joint shear are such that the coating will provide satisfactory performance under sustained loading.
Joseph A. Yura, M. ASCE, is Warren S. Bellows Centennial Professor in Civil Engineering, University
of Texas at Austin, Austin, Texas.
Karl H. Frank, A.M. ASCE, is Associate Professor, Department of Civil Engineering, University of Texas
at Austin, Austin, Texas.
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RCSC SPECIFICATION FOR STRUCTURAL JOINTS
1.2 Definition of Essential Variables
Essential variables mean those variables which, if changed, will require retesting
of the coating to determine its slip coefficient. The essential variables are given below.
The relationship of these variables to the limitation of application of the coating
for structural joints is also given.
The time interval between application of the coating and the time of testing is
an essential variable. The time interval must be recorded in hours and any special
curing procedures detailed. Curing according to published manufacturer’s recommendations would not be considered a special curing procedure. The coatings are
qualified for use in structural connections which are assembled after coating for
a time equal to or greater than the interval used in the test specimens. Special curing conditions used in the test specimens will also apply to the use of the coating
in the structural connections.
The coating thickness is an essential variable. The maximum average coating
thickness allowed on the bolted structure will be the average thickness, rounded to
the nearest whole mil, of the coating used on the creep test specimens minus 2 mils.
The composition of the coating, including the thinners used, and its method
of manufacture are essential variables. Any change will require retesting of the
coating.
1.3 Retesting
A coating which fails to meet the creep or the post-creep slip test requirements given
in Sect. 4 may be retested in accordance with methods in Sect. 4 at a lower slip
coefficient, without repeating the static short-term tests specified in Sect. 3. Essential variables must remain unchanged in the retest.
2.0 TEST PLATES AND COATING OF THE SPECIMENS
2.1 Test Plates
The test specimen plates for the short-term static tests are shown in Fig. 1. The plates
are 4×4 in. plates, 5⁄8-in. thick, with a 1-in. dia. hole drilled 11⁄2 in. ± 1⁄16 in. from
one edge. The specimen plates for the creep specimen are shown in Fig. 2. The
plates are 4×7 in., 5⁄8-in. thick, with two 1-in. holes, 11⁄2 in. ± 1⁄16 in. from each
end. The edges of the plates may be milled, as rolled or saw cut. Flame cut edges
4″
Load
1″
Clamping
force
1 1/2 ″
cL
5″
11/2 ″
11/2 ″
4″
1-in. Dia.
1″
All plates 5/8 ″thick
Fig. 1. Compression test specimen
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are not permitted. The plates should be flat enough to ensure they will be in reasonably full contact over the faying surface. Any burrs, lips or rough edges should be
filed or milled flat. The arrangement of the specimen plates for the testing is shown
in Figs. 2 and 3. The plates are to be fabricated from a steel with a minimum yield
strength between 36 to 50 ksi.
If specimens with more than one bolt are desired, the contact surface per bolt
should be 4×3 in. as shown for the single bolt specimen in Fig. 1.
2.2 Specimen Coating
The coatings are to be applied to the specimens in a manner consistent with the
actual intended structural application. The method of applying the coating and the
surface preparation should be given in the test report. The specimens are to be coated
to an average thickness 2 mils (0.05 mm) greater than average thickness to be used
in the structure. The thickness of the total coating and the primer, if used, shall
be measured on the contact surface of the specimens. The thickness should be measured in accordance with the Steel Structures Painting Council specification SSPCPA2, Measurement of Dry Paint Thickness with Magnetic Gages.1 Two spot readings (six gage readings) should be made for each contact surface. The overall average thickness from the three plates comprising a specimen is the average thickness
for the specimen. This value should be reported for each specimen. The average
coating thickness of the three creep specimens will be calculated and reported. The
average thickness of the creep specimen minus two mils rounded to the nearest whole
mil is the maximum average thickness of the coating to be used in the faying surface of a structure.
The time between painting and specimen assembly is to be the same for all specimens within ±4 hours. The average time is to be calculated and reported. The two
coating applications required in Sect. 3 are to use the same equipment and procedures.
3.0 SLIP TESTS
The methods and procedures described herein are used to determine experimentally the slip coefficient (sometimes called the coefficient of friction) under shortterm static loading for high-strength bolted connections. The slip coefficient will
be determined by testing two sets of five specimens. The two sets are to be coated
at different times at least one week apart.
3.1 Compression Test Setup
The test setup shown in Fig. 3 has two major loading components, one to apply
a clamping force to the specimen plates and another to apply a compressive load
to the specimen so that the load is transferred across the faying surfaces by friction.
Clamping Force System. The clamping force system consists of a 7⁄8-in. dia.
threaded rod which passes through the specimen and a centerhole compression ram.
A 2H nut is used at both ends of the rod, and a hardened washer is used at each
side of the test specimen. Between the ram and the specimen is a specially fabricated 7⁄8-in. 2H nut in which the threads have been drilled out so that it will slide
with little resistance along the rod. When oil is pumped into the centerhole ram,
1. Steel Structures Painting Council, Steel Structures Painting Manual, Vols. 1 and 2, Pittsburgh, Pa.,
1982.
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RCSC SPECIFICATION FOR STRUCTURAL JOINTS
2″
Load
indicating
washer
Clamping
bolt
4″
1″
7″
Pin bolt
1″
11/2 ″
Specimen
7″
17/ 8 ″
4″
Fig. 2. Creep test specimens
Drilled nut
Load
Testing machine
Nut
7/
8
Spherical head
50 kip
Center hole
ram
Dia. rod
Nut
7/
8 -2M
Hardened washer
Specimen
Plate
Piston
Base
Fig. 3. Test setup
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the piston rod extends, thus forcing the special nut against one of the outside plates
of the specimen. This action puts tension in the threaded rod and applies a clamping
force to the specimen which simulates the effect of a tightened bolt. If the diameter
of the centerhole ram is greater than 1 in., additional plate washers will be necessary at the ends of the ram. The clamping force system must have a capability to
apply a load of at least 49 kips and maintain this load during the test with an accuracy
of ±1%.
Compressive Load System. A compressive load is applied to the specimen until
slip occurs. This compressive load can be applied by a compression test machine
or compression ram. The machine, ram and the necessary supporting elements should
be able to support a force of 90 kips.
The compression loading system should have an accuracy of 1.0% of the slip load.
3.2 Instrumentation
Clamping Force. The clamping force must be measured within 0.5 kips. This may
be accomplished by measuring the pressure in the calibrated ram or placing a load
cell in series with the ram.
Compression Load. The compression load must be measured during the test.
This may be accomplished by direct reading from a compression testing machine,
a load cell in series with the specimen and the compression loading device, or pressure readings on a calibrated compression ram.
Slip Deformation. The relative displacement of the center plate and the two outside plates must be measured. This displacement, called slip for simplicity, should
be the average which occurs at the centerline of the specimen. This can be accomplished by using the average of two gages placed on the two exposed edges of the
specimen or by monitoring the movement of the loading head relative to the base.
If the latter method is used, due regard must be taken for any slack that may be
present in the loading system prior to application of the load. Deflections can be
measured by dial gages or any other calibrated device which has an accuracy of
0.001 in.
3.3 Test Procedure
The specimen is installed in the test setup as shown in Fig. 3. Before the hydraulic
clamping force is applied, the individual plates should be positioned so that they
are in, or are close to, bearing contact with the 7⁄8-in. threaded rod in a direction
opposite to the planned compressive loading to ensure obvious slip deformation.
Care should be taken in positioning the two outside plates so that the specimen will
be straight and both plates are in contact with the base.
After the plates are positioned, the centerhold ram is engaged to produce a clamping force of 49 kips. The applied clamping force should be maintained within ±0.5
kips during the test until slip occurs.
The spherical head of the compression loading machine should be brought in
contact with the center plate of the specimen after the clamping force is applied.
The spherical head or other appropriate device ensures uniform contact along the
edge of the plate, thus eliminating eccentric loading. When 1 kip or less of compressive load is applied, the slip gages should be engaged or attached. The purpose
of engaging the deflection gage(s), after a slight load is applied, is to eliminate initial specimen settling deformation from the slip readings.
When the slip gages are in place, the compression load is applied at a rate not
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RCSC SPECIFICATION FOR STRUCTURAL JOINTS
exceeding 25 kips (109 kN) per minute, or 0.003 in. of slip displacement per minute
until the slip load is reached. The test should be terminated when a slip of 0.05 in.
or greater is recorded. The load-slip relationship should preferably be monitored
continuously on an X-Y plotter throughout the test, but in lieu of continuous data,
sufficient load-slip data must be recorded to evaluate the slip load defined below.
3.4 Slip Load
Typical load-slip response is shown in Fig. 4. Three types of curves are usually
observed and the slip load associated with each type is defined as follows:
Curve (a). Slip load is the maximum load, provided this maximum occurs
before a slip of 0.02 in. is recorded.
Curve (b). Slip load is the load at which the slip rate increases suddenly.
Curve (c). Slip load is the load corresponding to a deformation of 0.02 in. This
definition applies when the load vs. slip curves show a gradual change
in response.
-slip load
a
LOAD
b
c
Load
Slip
0
0.020
0.040
SLIP (in.)
Fig. 4. Definition of slip load
3.5 Coefficient of Slip
The slip coefficient ks for an individual specimen is calculated as follows:
ks =
slip load
2 × clamping force
The mean slip coefficient for both sets of five specimens must be compared. If the
two means differ by more than 25%, using the smaller mean as the base, a third
five-specimen set must be tested. The mean and standard deviation of the data from
all specimens tested define the slip coefficient of the coating.
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3.6 Alternate Test Methods
Other test methods to determine slip may be used provided the accuracy of load
measurement and clamping satisfies the conditions presented in the previous sections. For example, the slip load may be determined from a tension-type test setup
rather than the compression-type as long as the contact surface area per fastener
of the test specimen is the same as shown in Fig. 1. The clamping force of at least
49 kips may be applied by any means provided the force can be established within
±1%. Strain-gaged bolts can usually provide the desired accuracy. However, bolts
installed by turn-of-nut method, tension indicating fasteners and load indicator
washers usually show too much variation to be used in the slip test.
4.0 TENSION CREEP TESTS
The test method outlined is intended to ensure the coating will not undergo significant creep deformation under service loading. The test also determines the loss in
clamping force in the fastener due to the compression or creep of the paint. Three
replicate specimens are to be tested.
4.1 Test Setup
Tension-type specimens, as shown in Fig. 2, are to be used. The replicate specimens are to be linked together in a single chain-like arrangement, using loose pin
bolts, so the same load is applied to all specimens. The specimens shall be assembled so the specimen plates are bearing against the bolt in a direction opposite to
the applied tension loading. Care should be taken in the assembly of the specimens
to ensure the centerline of the holes used to accept the pin bolts is in line with the
bolts used to assemble the joint. The load level, specified in Sect. 4.2, shall be maintained constant within ±1% by springs, load maintainers, servo controllers, dead
weights or other suitable equipment. The bolts used to clamp the specimens together
shall be 7⁄8-in. dia. A490 bolts. All bolts should come from the same lot.
The clamping force in the bolts should be a minimum of 49 kips. The clamping
force is to be determined by calibrating the bolt force with bolt elongation, if standard bolts are used. Special fasteners which control the clamping force by other
means such as bolt torque or strain gages may be used. A minimum of three bolt
calibrations must be performed using the technique selected for bolt force determination. The average of the three-bolt calibration is to be calculated and reported.
The method of measuring bolt force must ensure the clamping force is within ±2
kips (9 kN) of the average value.
The relative slip between the outside plates and the center plates shall be measured to an accuracy of 0.001 in. (0.02 mm). This is to be measured on both sides of
each specimen.
4.2 Test Procedure
The load to be placed on the creep specimens is the service load permitted for 7⁄8-in.
A490 bolts in slip-critical connections by the latest edition of the Specification for
Structural Joints Using ASTM A325 or A490 Bolts2 for the particular slip coefficient
category under consideration. The load is to be placed on the specimen and held
2. Research Council of Structural Connections, Specification for Structural Joints Using ASTM A325
or A490 Bolts, American Institute of Steel Construction, Inc., Chicago, November 1985.
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RCSC SPECIFICATION FOR STRUCTURAL JOINTS
for 1,000 hours. The creep deformation of a specimen is calculated using the average
reading of the two displacements on each side of the specimen. The difference between
the average after 1,000 hours and the initial average reading taken within one-half
hour after loading the specimens is defined as the creep deformation of the specimen. This value is to be reported for each specimen. If the creep deformation of
any specimen exceeds 0.005 in. (0.12 mm), the coating has failed the test for the
slip coefficient used. The coating may be retested using new specimens in accordance with this section at a load corresponding to a lower value of slip coefficient.
If the value of creep deformation is less than 0.005 in. (0.12 mm) for all specimens, the specimens are to be loaded in tension to a load calculated as
Pu = average clamping force × design slip coefficient × 2
since there are two slip planes. The average slip deformation which occurs at this
load must be less than 0.015 in. (0.38 mm) for the three specimens. If the deformation is greater than this value, the coating is considered to have failed to meet the
requirements for the particular slip coefficient used. The value of deformation for
each specimen is to be reported.
COMMENTARY
The slip coefficient under short-term static loading has been found to be independent of clamping force, paint thickness and hole diameter.3 The slip coefficient can
be easily determined using the hydraulic bolt test setup included in this specification. The slip load measured in this setup yields the slip coefficient directly since
the clamping force is controlled. The slip coefficient k, is given by
ks =
slip load
2 × clamping force
The resulting slip coefficient has been found to correlate with both tension and compression tests of bolted specimens. However, tests of bolted specimens revealed that
the clamping force may not be constant but decreases with time due to the compressive creep of the coating on the faying surfaces and under the nut and bolt head.
The reduction of the clamping force can be considerable for joints with high clamping force and thick coatings, as much as a 20% loss. This reduction in clamping
force causes a corresponding reduction in the slip load. The resulting reduction in
slip load must be considered in the procedure used to determine the design allowable slip loads for the coating.
The loss in clamping force is a characteristic of the coating. Consequently, it
cannot be accounted for by an increase in the factor of safety or a reduction in the
clamping force used for design without unduly penalizing coatings which do not
exhibit this behavior.
The creep deformation of the bolted joint under the applied shear loading is
also an important characteristic and a function of the coating applied. Thicker coatings tend to creep more than thinner coatings. Rate of creep deformation increases
as the applied load approaches the slip load. Extensive testing has shown the rate
of creep is not constant with time, rather it decreases with time. After 1,000 hours
of loading, the additional creep deformation is negligible.
3. Frank, K. H., and J. A. Yura, An Experimental Study of Bolted Shear Connections, FHWA/RD-81-148,
Federal Highway Administration, Washington, D.C., December 1981.
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The proposed test methods are designed to provide the necessary information
to evaluate the suitability of a coating for slip critical bolted connections and to determine the slip coefficient to be used in the design of the connections. The initial testing of the compression specimens provides a measure of the scatter of the slip coefficient. In order to get better statistical information, a third set of specimens must
be tested whenever the means of the initial two sets differ by more than 25%.
The creep tests are designed to measure the paint’s creep behavior under the
service loads determined by the paint’s slip coefficient based on the compression
test results. The slip test conducted at the conclusion of the creep test is to ensure
the loss of clamping force in the bolt does not reduce the slip load below that associated with the design slip coefficient. A490 bolts are specified, since the loss of
clamping force is larger for these bolts than A325 bolts. Qualifying of the paint for
use in a structure at an average thickness of 2 mils less than the test specimen is
to ensure that a casual buildup of paint due to overspray, etc., does not jeopardize
the coating’s performance.
The use of 1-in. (25 mm) holes in the specimens is to ensure that adequate clearance is available for slip. Fabrication tolerances, coating buildup on the holes and
assembly tolerances reduce the apparent clearances.
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Commentary on Specifications
for Structural Joints Using
ASTM A325 or A490 Bolts
June 8, 1988.
Historical Notes
When first approved by the Research Council on Structural Connections of the Engineering Foundation, January 1951, the “Specification for Assembly of Structural
Joints Using High-Strength Bolts” merely permitted the substitution of a like number of A325 high-strength bolts for hot driven ASTM A141 (presently identified as
A502, Grade 1) steel rivets of the same nominal diameter. It was required that all
contact surfaces be free of paint. As revised in 1954, the omission of paint was
required to apply only to “joints subject to stress reversal, impact or vibration, or
to cases where stress redistribution due to joint slippage would be undesirable.” This
relaxation of the earlier provision recognized the fact that, in a great many cases,
movement of the connected parts that brings the bolts into bearing against the sides
of their holes is in no way detrimental.
In the first edition of the Specification published in 1951, a table of torque to
tension relationships for bolts of various diameters was included. It was soon demonstrated in research that a variation in the torque to tension relationship of as high
as plus or minus 40 percent must be anticipated unless the relationship is established individually for each bolt lot, diameter and fastener condition. Hence, by
the 1954 edition of the Specification, recognition of standard torque to tension relationships in the form of tabulated values or formulas was withdrawn. Recognition
of the calibrated wrench method of tightening was retained, however, until 1980,
but with the requirement that the torque required for installation or inspection be
determined specifically for the bolts being installed on a daily basis. Recognition
of the method was withdrawn in 1980 because of continuing controversy resulting
from failure of users to adhere to the detailed requirements for valid use of the method
both during installation and inspection. With the 1985 version of the Specification,
the calibrated wrench method was reinstated, but with more detailed requirements
which should be carefully followed.
The increasing use of high-strength steels created the need for bolts substantially stronger than A325 in order to resist the much greater forces they support
without resort to very large connections. To meet this need, a new ASTM specification, A490, was developed. When provisions for the use of these bolts were included
in this Specification in 1964, it was required that they be tightened to their specified
proof load, as was required for the installation of A325 bolts. However, the ratio
of proof load to specified minimum tensile strength is approximately 0.7 for A325
bolts, whereas it is 0.8 for A490 bolts. Calibration studies have shown that highstrength bolts have ultimate load capacities in torqued tension which vary from about
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COMMENTARY ON THE RCSC SPECIFICATION (6/8/88)
80 to 90 percent of the pure-tension tensile strength.1 Hence, if minimum strength
A490 bolts were supplied and they experienced the maximum reduction due to torque
required to induce the tension, there is a possibility that these bolts could not be
tightened to proof load by any method of installation. Also, statistical studies have
shown that tightening to the 0.8 times tensile strength under calibrated wrench control may result in some “twist-off” bolt failures during installation or in some cases
a slight amount of under-tightening.2 Therefore, the required installed tension for
A490 bolts was reduced to 70 percent of the specified minimum tensile strength.
For consistency, but with only minor change, the initial tension required for A325
bolts was also set at 70 percent of their specified minimum tensile strength and,
at the same time, the values for minimum required pretension were rounded off to
the nearest kip.
C1 Scope
This Specification deals only with two types of high-strength bolts, namely, ASTM
A325 and A490, and to their installation in structural steel joints. The provisions
may not be relied upon for high-strength fasteners of other chemical composition
or mechanical properties or size. The provisions do not apply to ASTM A325 or
A490 fasteners when material other than steel is included in the grip. The provisions do not apply to high-strength anchor bolts.
The Specification relates only to the performance of fasteners in structural steel
connections and those few aspects of the connected material that affect the performance of the fasteners in connections. Many other aspects of connection design and
fabrication are of equal importance and must not be overlooked. For information
on questions of design of connected material, not covered herein, the user is directed
to standard textbooks on design of structural steel and also to Kulak, G. L., J. W.
Fisher, and J. H. A. Struik, Guide to Design Criteria for Bolted and Riveted Joints,
2nd ed., New York: John Wiley & Sons, 1987. (Hereinafter referred to as the Guide.)
C2 Bolts, Nuts, Washers and Paint
Complete familiarity with the referenced ASTM Specification requirements is necessary for the proper application of this Specification. Discussion of referenced specifications in this Commentary is limited to only a few frequently overlooked or littleunderstood items.
In this Specification, a single style of fastener (heavy hex structural bolts with
heavy hex nuts) available in two strength grades (A325 and A490) is specified as
a principal style, but conditions for acceptance of other types of fasteners are
provided.
Bolt Specifications. ASTM A325 and A490 bolts are manufactured to dimensions
as specified in ANSI Standard B18.2.1 for Heavy Hex Structural Bolts. The basic
dimensions, as defined in Fig. C1, are shown in Table C1. The principal geometric
features of heavy hex structural bolts that distinguish them from bolts for general
application are the size of the head and the body length. The head of the heavy hex
1. Christopher, R. J., G. L. Kulak, and J. W. Fisher, “Calibration of Alloy Steel Bolts,” ASCE Journal of the Structural Division, Vol. 92, No. ST2, Proc. Paper 4768, April, 1966, pp. 19–40.
2. Gill, P. J., “Specifications of Minimum Preloads for Structural Bolts,” Memorandum 30, G.K.N.
Group Research Laboratory, England, 1966 (Unpublished Report).
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Table C1
Nominal Bolt
Size, Inches
D
Bolt Dimensions, Inches
Heavy Hex Structural Bolts
Nut Dimensions, Inches
Heavy Hex Nuts
Width across
flats, F
Height
H
Thread
length
Width across
flats, W
Height
H
7⁄
8
11⁄16
11⁄4
17⁄16
15⁄8
113⁄16
2
23⁄16
23⁄8
5⁄
16
25⁄
64
15⁄
32
35⁄
64
39⁄
64
11⁄
16
25⁄
32
27⁄
32
15⁄
16
1
11⁄4
13⁄8
11⁄2
13⁄4
2
2
21⁄4
21⁄4
7⁄
8
11⁄16
11⁄4
17⁄16
15⁄8
113⁄16
2
23⁄16
23⁄8
31⁄
64
39⁄
64
47⁄
64
55⁄
64
64⁄
64
17⁄64
17⁄32
111⁄32
115⁄32
1⁄
2
5⁄
8
3⁄
4
7⁄
8
1
11⁄8
11⁄4
13⁄8
11⁄2
Thread
Length
A325
F
H
Bolt Length
H
W
Nut may be chamfered
on both faces
Fig. C1. Heavy hex structural bolt and heavy hex nut
structural bolt is specified to be the same size as a heavy hex nut of the same nominal diameter in order that the ironworker may use a single size wrench or socket
on both the bolt head and the nut. Heavy hex structural bolts have shorter thread
length than bolts for general application. By making the body length of the bolt
the control dimension, it has been possible to exclude the thread from all shear planes,
except in the case of thin outside parts adjacent to the nut. Depending upon the amount
of bolt length added to adjust for incremental stock lengths, the full thread may extend
into the grip by as much as 3⁄8 inch for 1⁄2, 5⁄8, 3⁄4, 7⁄8, 11⁄4, and 11⁄2 in. diameter bolts
and as much as 1⁄2 inch for 1, 11⁄8 and 13⁄8 in. diameter bolts. Inclusion of some thread
run-out in the plane of shear is permissible. Of equal or even greater importance
is exercise of care to provide sufficient thread for nut tightening to keep the nut threads
from jamming into the thread run-out. When the thickness of an outside part is less
than the amount the threads may extend into the grip tabulated above, it may be
necessary to call for the next increment of bolt length together with sufficient flat
washers to ensure full tightening of the nut without jamming nut threads on the thread
run-out.
There is an exception to the short thread length requirements for ASTM A325
bolts discussed in the foregoing. Beginning with ASTM A325-83, supplementary
requirements have been added to the ASTM A325 Specification which permit the
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
6 - 402
COMMENTARY ON THE RCSC SPECIFICATION (6/8/88)
purchaser, when the bolt length is equal to or shorter than four times the nominal
diameter, to specify that the bolt be threaded for the full length of the shank. This
exception to the requirements for thread length of heavy hex structural bolts was
provided in the Specification in order to increase economy through simplified ordering
and inventory control in the fabrication and erection of structures using relatively
thin materials where strength of the connection is not dependent upon shear strength
of the bolt, whether threads are in the shear plane or not. The Specification requires
that bolts ordered to such supplementary requirements be marked with the symbol
A325T.
In order to determine the required bolt length, the value shown in Table C2
should be added to the grip (i.e., the total thickness of all connected material, exclusive of washers). For each hardened flat washer that is used, add 5⁄32 inch, and for
each beveled washer add 5⁄16 inch. The tabulated values provide appropriate allowances
for manufacturing tolerances, and also provide for full thread engagement (defined
as having the end of the bolt at least flush with the face of the nut) with an installed
heavy hex nut. The length determined by the use of Table C2 should be adjusted
to the next longer 1⁄4 inch length.
ASTM A325 and ASTM A490 currently provide for three types (according to
metallurgical classification) of high-strength structural bolts, supplied in sizes 1⁄2 inch
to 11⁄2 inch inclusive except for A490 Type 2 bolts which are available in diameters
from 1⁄2 inch to 1 inch inclusive:
Type 1.
Type 2.
Type 3.
Medium carbon steel for A325 bolts, alloy steel for A490 bolts.
Low carbon martensitic steel for both A325 and A490 bolts.
Bolts having improved atmospheric corrosion resistance and
weathering characteristics for both A325 and A490 bolts.
When the bolt type is not specified, either Type 1, Type 2 or Type 3 may be
supplied at the option of the manufacturer. Special attention is called to the requirement in ASTM A325 that, where elevated temperature applications are involved,
Type 1 bolts shall be specified by the purchaser. This is because the chemistry of
Type 2 bolts permits heat treatment at sufficiently low temperatures that subsequent
heating to elevated temperatures may affect the mechanical properties.
Heavy Hex Nuts. Heavy hex nuts for use with A325 bolts may be manufactured
to the requirements of ASTM A194 for grades 2 or 2H or the requirements of ASTM
A563 for grades DH, except that nuts to be galvanized for use with galvanized bolts
must be hardened nuts meeting the requirements for ASTM A563 grade DH.
The heavy hex nuts for use with A490 bolts may be manufactured to the requirements of ASTM A194 for grade 2H or the requirements of ASTM A563 for grade DH.
Galvanized High-Strength Bolts. Galvanized high-strength bolts and nuts must be
considered as a manufactured matched assembly; hence, comments relative to them
have not been included in the foregoing paragraphs where bolts and nuts have been
considered separately. Insofar as the hot-dip galvanized bolt and nut assembly, per
se, is concerned, four principal factors need be discussed in order that the provisions of the Specification may be understood and properly applied. These are (1)
the effect of the hot-dip galvanizing process on the mechanical properties of highstrength steels, (2) the effect of hot-dip galvanized coatings on the nut stripping
strength, (3) the effect of galvanizing upon the torque involved in the tightening operation, and (4) shipping requirements.
The ASTM Specifications for galvanized A325 high-strength bolts recognize
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
ASTM A325 OR A490 BOLTS
6 - 403
Table C2
Nominal Bolt Size, Inches
1⁄
2
5⁄
8
3⁄
4
7⁄
8
To Determine Required Bolt
Length Add to Grip, in Inches
11⁄
16
7⁄
8
1
11⁄8
1
11⁄8
11⁄4
13⁄8
11⁄4
11⁄2
15⁄8
13⁄4
11⁄2
17⁄8
both the hot-dip galvanizing process and the mechanical galvanizing process. The
effects of the two processes upon the performance characteristics and requirements
for proper installation are distinctly different: therefore, distinction between the two
must be noted in the comments which follow. ASTM A325 Specifications require
that all components of a fastener assembly (nuts, bolts and washers) shall have been
coated by the same process and that the supplier’s option is limited to one process
per item with no mixed processes in a lot. Mixing a bolt galvanized by one process
with a nut galvanized by the other may result in a unworkable assembly.
Effect of Hot-Dip Galvanizing on the Strength of Steels. Steels in the 200 ksi
and higher tensile strength range are subject to embrittlement if hydrogen is permitted to remain in the steel and the steel is subjected to high tensile stress. The minimum tensile strength of A325 bolts is 105 or 120 ksi, depending upon the size, comfortably below the critical range. The required maximum tensile strength for A490
bolts was set at 170 ksi in order to provide a little more than a 10 percent margin
below 200 ksi; however, because manufacturers must target their production slightly
higher than the required minimum, A490 bolts close to the critical range of tensile
strength must be anticipated. For black bolts this is not a cause for concern, but,
if the bolt is hot-dip galvanized, a hazard of delayed brittle fracture in service exists
because of the real possibility of introduction of hydrogen into the steel during the
pickling operation of the hot-dip galvanizing process and the subsequent “sealingin” of the hydrogen by the zinc coating. There also exists the possibility of cathodic
hydrogen adsorption arising from corrosion process in service in aggressive environments. ASTM Specifications provide for the galvanizing of A325 bolts but not A490
bolts. Galvanizing of A490 bolts is not permitted. Because pickling and emersion
in molten zinc is not involved, galvanizing by the mechanical process essentially
avoids potential for hydrogen embrittlement.
The heat treatment temperatures for Type 2 ASTM A325 bolts are in the range
of the molten zinc temperatures for hot-dip galvanizing; therefore there is a potential for diminishing the heat treated mechanical properties of Type 2 A325 bolts
by the hot-dip galvanizing process. For this reason, the current Specifications require
that only mechanical galvanizing shall be used on Type 2 ASTM A325 bolts.
Nut Stripping Strength. Hot-dip galvanizing affects the stripping strength of the
nut-bolt assembly primarily because, to accommodate the relatively thick zinc coatAMERICAN INSTITUTE OF STEEL CONSTRUCTION
6 - 404
COMMENTARY ON THE RCSC SPECIFICATION (6/8/88)
ings of non-uniform thickness on bolt threads, it is usual practice to hot-dip galvanize the blank nut and then to tap the nut oversize after galvanizing. This overtapping results in a reduction in the amount of engagement between the steel portions
of the male and female threads with a consequent approximately 25 percent reduction in the stripping strength. Only the stronger hardened nuts have adequate strength
to meet specification requirements even with the reduction due to overtapping; therefore, ASTM A325 specifies that only Grades DH and 2H be used for galvanized
nuts. This requirement should not be overlooked if non-galvanized nuts are purchased
and then sent to a local galvanizer for hot-dip galvanizing. Because the mechanical
galvanizing process results in a more uniformly distributed and smooth zinc coating, nuts may be tapped oversize before galvanizing by an amount less than required
for the hot-dip process before galvanizing. This results in a better bolt-nut fit with
zinc coating on the internal threads of the nut.
Effect of Galvanizing Upon Torque Involved in Tightening. Research3 has shown
that, in the as-galvanized condition, galvanizing both increases the friction between
the bolt and nut threads and also makes the torque induced tension much more variable. Lower torque and more consistent results are provided if the nuts are lubricated; thus, ASTM A325 requires that a galvanized bolt and lubricated galvanized
nut shall be assembled in a steel joint with a galvanized washer and tested in accordance with ASTM A563 by the manufacturer prior to shipment to ensure that the
galvanized nut with the lubricant provided may be rotated from the snug tight condition well in excess of the rotation required for full tensioning of the bolts without
stripping. The requirement applies to both hot-dip and mechanical galvanized
fasteners.
Shipping Requirements for Galvanized Bolts and Nuts. The above requirements
clearly indicate (1) that galvanized bolts and nuts are to be treated as a matched assembly, (2) that the seller must supply nuts which have been lubricated and tested with
the supplied bolts, and (3) that nuts and bolts must be shipped together in the same
shipping container. Purchase of galvanized bolts and galvanized nuts from separate
sources is not in accordance with the intent of the ASTM Specifications because
the control of overtapping and the testing and application of lubricant would be lost.
Because some of the lubricants used to meet the requirements of ASTM Specifications are water soluble, it is advisable that galvanized bolts and nuts be shipped and
stored in plastic bags in wood or metal containers.
Washers. The primary function of washers is to provide a hardened non-galling surface under the element turned in tightening, particularly for those installation procedures which depend upon torque for control or inspection. Circular hardened
washers meeting the requirements of ASTM A436 provide an increase in bearing
area of 45 to 55 percent over the area provided by a heavy hex bolt head or nut;
however, tests have shown that standard thickness washers play only a minor role
in distributing the pressure induced by the bolt pretension, except where oversize
or short slotted holes are used. Hence, consideration is given to this function only
in the case of oversize and short slotted holes. The requirement for standard thickness hardened washers, when such washers are specified as an aid in the distribu3. Birkemoe, P. C., and D. C. Herrschaft, “Bolted Galvanized Bridges—Engineering Acceptance Near,”
ASCE Civil Engineering, April 1970.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
ASTM A325 OR A490 BOLTS
TYPE
A325
BOLT
A490
NUT
(1)
1
6 - 405
NUT
XYZ
A490
XYZ
MFGR IDENTIFICATION
(TYPICAL)
XYZ
XYZ
A325
BOLT
XYZ
DH
D
ARCS INDICATE
GRADE C
2
XYZ
A325
DH OR 2H (2)
GRADE MARK (2)
D, DH, 2 OR 2H
XYZ
A490
SAME AS TYPE 1
NOTE MANDATORY
3 RADIAL LINES
AT 60
NOTE MANDATORY
6 RADIAL LINES
AT 30
(3)
3
XYZ
A325
NOTE MANDATORY
UNDERLINE
SAME AS
TYPE 1
(3)
XYZ
3
(3)
XYZ
A490
XYZ
DH3
DH3
NOTE MANDATORY
(1) ADDITIONAL OPTIONAL 3 RADIAL LINES AT 120 MAY BE ADDED.
(2) TYPE 3 ALSO ACCEPTABLE
(3) ADDITIONAL OPTIONAL MARK INDICATING WEATHERING MAY BE ADDED
Fig. C2. Required marking for acceptable bolt and nut assemblies
tion of pressure, is waived for alternative design fasteners which incorporate a bearing
surface under the head of the same diameter as the hardened washer; however, the
requirements for hardened washers to satisfy the principal requirement of providing
a non-galling surface under the element turned in tightening is not waived. The
maximum thickness is the same for all standard washers up to and including 11⁄2
inch bolt diameter in order that washers may be produced from a single stock of
material.
The requirement that heat-treated washers not less than 5⁄16 inch thick be used
to cover oversize and slotted holes in external plies, when A490 bolts of 11⁄8 inch
or larger diameter are used, was found necessary to distribute the high clamping
pressure so as to prevent collapse of the hole perimeter and enable development
of the desired clamping force. Preliminary investigation has shown that a similar
but less severe deformation occurs when oversize or slotted holes are in the interior
plies. The reduction in clamping force may be offset by “keying,” which tends
to increase the resistance to slip. These effects are accentuated in joints of thin
plies
.
Marking. Heavy hex structural bolts and heavy hex nuts are required by ASTM
Specifications to be distinctively marked. Certain markings are mandatory. In addition to the mandatory markings, the manufacturer may apply additional distinguishing
marking. The mandatory and optional markings are shown in Figure C2.
Paint. In the previous edition of the Specification, generic names for paints applied
to faying surfaces was the basis for categories of allowable working stresses in “fricAMERICAN INSTITUTE OF STEEL CONSTRUCTION
6 - 406
COMMENTARY ON THE RCSC SPECIFICATION (6/8/88)
tion” type connections. Research4 completed since the adoption of the 1980 Specification has demonstrated that the slip coefficients for paints described by a generic
type are not single values but depend also upon the type of vehicle used. Small differences in formulation from manufacturer to manufacturer or from lot to lot with a
single manufacturer significantly affect slip coefficients if certain essential variables within a generic type are changed. It is unrealistic to assign paints to categories
with relatively small incremental differences between categories based solely upon
a generic description. As a result of the research, a test method was developed and
adopted by the Council titled “Test Method to Determine the Slip Coefficient for
Coatings Used in Bolted Joints.” A copy of this document is appended to this Specification as Appendix A. The method, which requires requalification if an essential
variable is changed, is the sole basis for qualification of any coating to be used under
this Specification. Further, normally only two categories of slip coefficient for paints
to be used in slip-critical joints are recognized: Class A for coatings which do not
reduce the slip coefficient below that provided by clean mill scale, and Class B for
paints which do not reduce the slip coefficient below that of blast-cleaned steel
surfaces.
The research cited in the preceding paragraph also investigated the effect of varying the time from coating the faying surfaces to assembly of the connection and
tightening the bolts. The purpose was to ascertain if partially cured paint continued
to cure within the assembled joint over a period of time. It was learned that all curing ceased at the time the joint was assembled and tightened and that paint coatings
that were not fully cured acted much as a lubricant would; thus, the slip resistance
of the joint was severely reduced from that which was provided by faying surfaces
that were fully cured prior to assembly.
C3 Bolted Parts
Material Within the Grip. The Specification is intended to apply to structural joints
in which all of the material within the grip of the bolt is steel.
Surface Conditions. The Test Method to Determine the Slip Coefficient for Coatings Used in Bolted Joints includes long-term creep test requirements to ensure reliable performance for qualified paint coatings. However, it must be recognized that
in the case of hot-dip galvanized coatings, especially if the joint consists of many
plies of thickly coated material, relaxation of bolt tension may be significant and
may require retensioning of the bolts subsequent to the initial tightening. Research5
has shown that a loss of pretension of approximately 6.5 percent occurred for galvanized plates and bolts due to relaxation as compared with 2.5 percent for uncoated
joints. This loss of bolt tension occurred in five days with negligible loss recorded
thereafter. This loss can be allowed for in design or pretension may be brought back
to the prescribed level by retightening the bolts after an initial period of “settling-in.”
Since it was first published, this Specification has permitted the use of bolt holes
6
1⁄
16 inch larger than the bolts installed in them. Research has shown that, where
4. Frank, Karl H. and J. A. Yura, “An Experimental Study of Bolted Shear Connections.”
FHWA/RD-81/148, December 1981.
5. Munse, W. H., “Structural Behavior of Hot Galvanized Bolted Connections,” 8th International Conference on Hot-dip Galvanizing, London, England, June 1967.
6. Allen. R. N. and J. W. Fisher, “Bolted Joints With Oversize or Slotted Holes,” ASCE Journal of
the Structural Division, Vol. 94, No. ST9, September, 1968.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
ASTM A325 OR A490 BOLTS
6 - 407
greater latitude is needed in meeting dimensional tolerances during erection, somewhat larger holes can be permitted for bolts 5⁄8 inch diameter and larger without
adversely affecting the performance of shear connections assembled with highstrength bolts. The oversize and slotted hole provisions of this Specification are based
upon these findings. Because an increase in hole size generally reduces the net area
of a connected part, the use of oversize holes is subject to approval by the Engineer
of Record.
Burrs. Based upon tests7 which demonstrated that the slip resistance of joints was
unchanged or slightly improved by the presence of burrs, burrs which do not prevent solid seating of the connected parts in the snug tight condition need not be
removed. On the other hand, parallel tests in the same program demonstrated that
large burrs can cause a small increase in the required turns from snug tight condition to achieve specified pretension with turn-of-nut method of tightening.
Unqualified Paint on Faying Surfaces. An extension to the research on the slip
resistance of shear connections cited in footnote 4 investigated the effect of ordinary paint coatings on limited portions of the contact area within joints and the effect
of overspray over the total contact area. The tests8 demonstrated that the effective
area for transfer of shear by friction between contact surfaces was concentrated in
an annular ring around and close to the bolts. Paint on the contact surfaces approximately one inch but not less than the bolt diameter away from the edge of the hole
did not reduce the slip resistance. On the other hand, in recognition of the fact that,
in connections of thick material involving a number of bolts on multiple gage lines,
bolt pretension might not be adequate to completely flatten and pull thick material
into tight contact around every bolt, the Specification requires that all areas between
bolts also be free of paint. (See Figure C3.) The new requirements have a potential
for increased economy because the paint-free area may easily be protected using
masking tape located relative to the hole pattern, and, further, the narrow paint strip
around the perimeter of the faying surface will minimize uncoated material outside
the connection requiring field touch-up.
This research also investigated the effect of various degrees of inadvertent overspray on slip resistance. It was found that even the smallest amount of overspray
of ordinary paint (that is, not qualified as Class A) within the specified paint-free
area on clean mill scale reduced the slip resistance significantly. On blast-cleaned
surfaces, the presence of a small amount of overspray was not as detrimental. For
simplicity, the Specification prohibits any overspray from areas required to be free
of paint in slip-critical joints regardless of whether the surface is clean mill scale
or blast cleaned.
Galvanized Faying Surfaces. The slip factor for initial slip with clean hot-dip galvanized surfaces is of the order of 0.19 as compared with a factor of about 0.35
for clean mill scale. However, research (see note 3) has shown that the slip factor
of galvanized surfaces is significantly improved by treatments such as hand wire
brushing or light “brush-off” grit blasting. In either case, the treatment must be
controlled in order to achieve the necessary roughening or scoring. Power wire brushing is unsatisfactory because it tends to polish rather than roughen the surface.
7. Polyzois, D. and J. A. Yura, “Effect of Burrs on Bolted Friction Connections,” AISC Engineering
Journal, 22 (No. 3) Third Quarter 1985.
8. Polyzois, D. and K. Frank, “Effect of Overspray and Incomplete Masking of Faying Surfaces on
the Slip Resistance of Bolted Connections,” AISC Engineering Journal, 23 (No. 2), 2nd Quarter 1986.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
6 - 408
COMMENTARY ON THE RCSC SPECIFICATION (6/8/88)
Circular area
around all holes
1 ″ but not less than d
d
1 ″ but not less than d
and
All areas
in between
Perimeter of contact
area
Fig. C3. Areas outside the defined area need not be free of paint
Field experience and test results have indicated that galvanized members may
have a tendency to continue to slip under sustained loading.9 Tests of hot-dip galvanized joints subject to sustained loading show a creep-type behavior. Treatments
to the galvanized faying surfaces prior to assembly of the joint which caused an
increase in the slip resistance under short duration loads did not significantly improve
the slip behavior under sustained loading.
C4 Design for Strength Of Bolted Connections
Background for Design Stresses. With the 1985 edition of the Specification, the
arbitrary designations “friction type” and “bearing type” connections used in former
editions, and which were frequently misinterpreted as implying an actual difference
in the manner of performance or strength of the two types of connection, were discontinued in order to focus attention more upon the real manner of performance
of bolted connections.
In bolted connections subject to shear-type loading, the load is transferred
between the connected parts by friction up to a certain level of force which is dependent upon the total clamping force on the faying surfaces and the coefficient of friction of the faying surfaces. The connectors are not subject to shear, nor is the connected material subject to bearing stress. As loading is increased to a level in excess
of the frictional resistance between the faying surfaces, slip occurs, but failure in
the sense of rupture does not occur. As even higher levels of load are applied, the
load is resisted by shear in the fastener and bearing upon the connected material
plus some uncertain amount of friction between the faying surfaces. The final failure will be by shear failure of the connectors, or by tear out of the connected
9. Kulak, G. L., J. W. Fisher, and J. H. A. Struik, “Guide to Design Criteria for Bolted and Riveted
Joints,” 2nd ed., New York: John Wiley & Sons, 1987, p. 208. (Hereinafter referred to as the Guide.)
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
ASTM A325 OR A490 BOLTS
6 - 409
material, or by unacceptable ovalization of the holes. Final failure load is independent of the clamping force provided by the bolts.10
The design of high-strength bolted connections under this Specification begins
with consideration of strength required to prevent premature failure by shear of the
connectors or bearing failure of the connected material. Next, for connections which
are defined as “slip-critical,” the resistance to slip load is checked. Because the combined effect of frictional resistance with shear or bearing has not been systematically studied and is uncertain, any potential greater resistance due to combined effect
is ignored.
Connection Slip. There are practical cases in the design of structures where slip
of the connection is desirable in order to permit rotation in a joint or to minimize
the transfer of moment. Additionally there are cases where, because of the number
of fasteners in a joint, the probability of slip is extremely small or where, if slip
did occur, it would not be detrimental to the serviceability of the structure. In order
to provide for such cases while at the same time making use of the higher shear
strength of high-strength bolts, as contrasted to ASTM A307 bolts, the Specification
now permits joints tightened only to the snug tight condition.
The maximum amount of slip that can occur in connections that are not classified as slip-critical is, theoretically, an amount equal to two hole clearances. In practical terms, it is observed to be much less than this. In laboratory tests it is usually
about one-half a hole clearance. This is because the acceptable inaccuracies in the
location of holes within a pattern of bolts would usually cause one or more bolts
to be in bearing in the initial unloaded condition. Further, in statically loaded structures, even with perfectly positioned holes, the usual method of erection would cause
the weight of the connected elements to put the bolts into direct bearing at the time
the member is supported on loose bolts and the lifting crane is unhooked. Subsequent additional gravity loading could not cause additional connection slip.
Connections classified as slip-critical include those cases where slip could theoretically exceed an amount deemed by the Engineer of Record to affect the suitability for service of the structure by excessive distortion or reduction in strength
or stability, even though the resistance to fracture of the connection, per se, may
be adequate. Also included are those cases where slip of any magnitude must be
prevented, for example, joints subject to load reversal.
Shear and Bearing on Fasteners. Several interrelated parameters influence the shear
and bearing strength of connections. These include such geometric parameters as
the net-to-gross-area ratio of the connected parts, the ratio of the net area of the
connected parts to the total shear-resisting area of the fasteners, and the ratio of
transverse fastener spacing to fastener diameter and to the connected part thickness. In addition, the ratio of yield strength to tensile strength of the steel comprising the connected parts, as well as the total distance between extreme fasteners, measured parallel to the line of direct tensile force, play a part.
In the past, a balanced design concept had been sought in developing criteria
for mechanically fastened joints to resist shear between connected parts by means
of bearing of the fasteners against the sides of the holes. This philosophy resulted
in wide variations in the factor of safety for the fasteners, because the ratio of yield
to tensile strength increases significantly with increasingly stronger grades of steel.
It had no application at all in the case of very long joints used to transfer direct
10. Ibid., pp. 49–52.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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COMMENTARY ON THE RCSC SPECIFICATION (6/8/88)
tension, because the end fasteners “unbutton” before the plate can attain its full
strength or before the interior fasteners can be loaded to their rated shear capacity.
By means of a mathematical model it was possible to study the interrelationship of the previously mentioned parameters.11,12 It has been shown that the factor
of safety against shear failure ranged from 3.3 for compact (short) joints to approximately 2.0 for joints with an overall length in excess of 50 inches. It is of interest
to note that the longest (and often the most important) joints had the lowest factor,
indicating that a factor of safety of 2.0 has proven satisfactory in service.
The absence of design strength provisions specifically for the case where a bolt
in double shear has a non-threaded shank in one shear plane and a threaded section
in the other shear plane is because of the uncertainty of manner of sharing the load
between the two different shear areas. It also recognizes that knowledge as to the
bolt placement (which might leave both shear planes in the threaded section) is not
ordinarily available to the detailer. If threads occur in one shear plane, the conservative assumption is made that threads are in all shear planes.
The nominal strength and resistance factors for fasteners subject to applied tension or shear are given in Table 2. The values are based upon the research and recommendations reported in the Guide. With the wealth of data available, it was possible
through statistical analyses to adjust resistances to provide more uniform reliability
for all loading and joint types. The design resistances provide designs approximately
equivalent to the designs provided by the allowable stresses in the 1980 edition of
the Specification. The design of connections is more conservative than that of the
connected members of buildings and bridges by a substantial margin, in the sense
that the failure load of the fasteners is substantially in excess of the maximum serviceability limit (yield) of the connected material.
Design for Tension. The nominal strengths specified for applied tension13 are
intended to apply to the external bolt load plus any tension resulting from prying
action produced by deformation of the connected parts. The recommended design
strength is approximately equal to the initial tightening force; thus, when loaded
to the nominal (service) load, high-strength bolts will experience little if any actual
change in stress. For this reason, bolts in connections in which the applied loads
subject the bolts to axial tension are required to be fully tensioned, even though
the connection may not be subject to fatigue loading nor classified as slip-critical.
Properly tightened A325 and A490 bolts are not adversely affected by repeated
application of the recommended service load tensile stress, provided the fitting material is sufficiently stiff, so that the prying force is a relatively small part of the applied
tension.14 The provisions covering bolt tensile fatigue are based upon study of test
reports of bolts that were subjected to repeated tensile load to failure.
Design for Shear. The nominal strength in shear is based upon the observation that
the shear strength of a single high-strength bolt is about 0.62 times the tensile strength
of that bolt.15 However, in shear connections with more than two bolts in the line
of force, deformation of the connected material causes nonuniform bolt shear force
distribution so that the strength of the connection in terms of the average bolt strength
11. Fisher, J. W. and L. S. Beedle, “Analysis of Bolted Butt Joints,” ASCE Journal of the Structural
Division, 91 (No. ST5), October 1965.
12. Guide, pp. 89–116; 126–132.
13. Ibid., pp. 263–286.
14. Ibid., pp. 272.
15. Ibid., pp. 44–50.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
ASTM A325 OR A490 BOLTS
6 - 411
goes down as the joint length increases.16 Rather than provide a function that reflects
this decrease in average fastener strength with joint length, a single reduction factor
of 0.80 was applied to the 0.62 multiplier. The result will accommodate bolts in all
joints up to about 50 inches in length without seriously affecting the economy of
very short joints. As noted in the footnotes to Table 2, bolts in joints longer than
50 inches in length must be further discounted by an additional 20 percent.
The average value of the nominal strength for bolts with threads in the shear
plane has been determined by a series of tests17 to be 0.833 Fu with a standard deviation of 0.03. A value of 0.80 was taken as a factor to account for the shear strength
of a bolt with threads in the shear plane based upon the area corresponding to the
nominal body area of the bolt.
The shear strength of bolts is not affected by pretension in the fasteners provided the connected material is in contact at the faying surfaces.
The design shear strength equals the nominal shear strength multiplied by a resistance factor of 0.75.
Combined Tension and Shear. The nominal strength of fasteners subject to combined tension and shear is provided by elliptical interaction curves in Table 3 which
account for the connection length effect on bolts loaded in shear, the ratio of shear
strength to tension strength of threaded fasteners, and the ratios of root area to nominal
body area and tensile stress area to nominal body area.18 No reduction in the design
shear strength is required when applied tensile stress is equal to or less than the
design tensile strength. Although the elliptical interaction curve provides the best
estimate of the strength of bolts subject to combined shear and tension and thus
is used in this Specification, it would be within the intent of the Specification for
invoking specifications to use a three straight line approximation of the ellipse.
Design for Bearing. Bearing stress produced by a high-strength bolt pressing against
the side of the hole in a connected part is important only as an index to behavior
of the connected part. It is of no significance to the bolt. The critical value can be
derived from the case of a single bolt at the end of a tension member.
It has been shown,19 using finger-tight bolts, that a connected plate will not fail
by tearing through the free edge of the material if the distance L, measured parallel
to the line of applied force from a single bolt to the free edge of the member toward
which the force is directed, is not less than the diameter of the bolt multiplied by
the ratio of the bearing stress to the tensile strength of the connected part.
The criterion for nominal bearing strength is
L / d ≥ Rn / Fu
where
Rn = nominal bearing pressure
Fu = specified minimum tensile strength of the connected part.
As a practical consideration, a lower limit of 1.5 is placed on the ratio L/d and
an upper limit of 1.5 on the ratio Fp / Fu and an upper limit of 3.0 on the ratio Rn / Fu.
The foregoing leads to the rules governing bearing strength in the specification.
16. Ibid., pp. 99–104.
17. Yura. J. A., K. H. Frank, and D. Polyois, “High Strength Bolts for Bridges.” PMFSEL Report No.
87-3, May 1987, Phil M. Ferguson Structural Engineering Laboratory, University of Texas at Austin.
18. Guide, pp. 50–51.
19. Ibid., pp. 141–143.
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The bearing pressure permitted in the 1980 Specification and the current provisions
are fully justifiable from the standpoint of strength of the connected material. However, even though rupture does not occur, recent tests have demonstrated that ovalization of the hole will begin to develop as the bearing stress is increased beyond
the previously permitted stress, especially if it is combined with high tensile stress
on the net section. Furthermore, when high bearing stress is combined with high
tensile stress on the net section and the effect of exterior versus interior plies, lower
ultimate strengths than previously reported result in addition to the hole ovalization.
Recognizing that initiation of hole ovalization occurs well below the ultimate
strength, and to facilitate standardization in detailing and fabrication, sufficiently
conservative simplified criteria have been provided in a formula format for usual
applications. The more accurate formula in which the strength is related to the distance L may be used for special cases such as those with very large bolts or very
thin material.
For connections with more than a single bolt in the direction of force, the resistance may be taken as the sum of the resistances of the individual bolts.
C5 Design Check for Slip Resistance
The Specification recognizes that, for a number of cases, slip of a joint would be
undesirable or must be precluded. Such joints are termed “slip-critical” joints. This
is somewhat different from the previous term “friction type” connection. The new
terminology was adopted in order to focus attention on the fact that all tightened
high-strength bolted joints resist load by friction between the faying surfaces up to
the slip load and subsequently are able to resist even greater loads by shear and
bearing. The strength of the joint is not related to the slip load. The Specification
requires that the two different resistances be considered separately.
The consequences of slip into bearing varies from application to application;
hence the determination of which connections shall be designed and installed as slipcritical is best left to judgment and a conscious decision on the part of the Engineer
of Record. Also, the determination of whether the potential slippage of a joint is
critical at nominal load level as a serviceability consideration or whether slippage
could result in distortions of the frame such that the ability of the frame to resist
factored loads would be reduced can be determined only by the Engineer of Record. The following comments reflect the collective thinking of the Council as developed during numerous meetings and reviews of drafts of the Specification and Commentary. They are provided as guidance and an indication of the intent of the
Specification.
In the case of bolts in holes with only small clearance, such as standard holes
and slotted holes loaded transverse to the axis of the slot in practical connections,
the freedom to slip generally does not exist because one or more bolts are in bearing
even before load is applied due to normal fabrication tolerances and erection procedures. Further, the consequences of slip, if it can occur at all, are trivial except for
a few situations. If for some reason it is deemed critical, design should probably
be on the basis of nominal loads (Section 5(b)).
In connections containing long slots that are parallel to the direction of the applied
load, slip of the connection prior to attainment of the factored load might be large
enough to alter the usual assumption of analysis that the undeformed structure can
be used to obtain the internal forces. The Specification allows the designer two alternatives in this case. If the connection is designed so that it will not slip under the
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effect of the nominal loads, then the effect of the factored loads acting on the deformed
structure (deformed by the maximum amount of slip in the long slots at all locations) must be included in the structural analysis. Alternatively the connection can
be designed so that it will not slip at loads up to the factored load level. These requirements are noted in Clause 7(b)(3).
Joints subject to full reverse cyclic loading are clearly slip-critical joints since
slip would permit back-and-forth movement of the joint and early fatigue failure.
However, for joints subject to pulsating load that does not involve reversal of load
direction, proper fatigue design could be provided either as a slip-critical joint on
the basis of stress on the gross section or as a non-slip-critical joint on the basis
of stress on the net section. Because fatigue results from repeated application, the
service load rather than the overload load design should be based upon nominal
load criteria (Section 5(b)).
For high-strength bolts in combination with welds in statically loaded conditions and considering new work only, the nominal strength may be taken as the sum
of two contributions.20 One results from the slip resistance of the bolted parts and
may be determined in accordance with Section 5(c). The second results from the
resistance of the welds as provided by applicable welding specifications. If one type
of connector is already loaded when the second type of connector is introduced,
the nominal strength cannot be obtained by adding the two resistances. The Guide
should be consulted in these cases.
From the definition of the term “coefficient of slip” (friction), the expression
for nominal slip resistances for bolts in standard holes is apparent and needs no
explanation. The mean value of slip coefficients from many tests on clean mill scale,
blast-cleaned steel surfaces and galvanized and roughened surfaces were taken as
the basis for the three classes of surfaces.
In the 1978 edition of the Specification, nine classes of faying surface conditions were introduced, and significant increases were made in the recommended
allowable stresses for proportioning connections which function by transfer of shear
between connected parts by friction. These classes and stresses were adopted on
the basis of statistical evaluation of the information then available.
Extensive data developed through research sponsored by the Council and others
during the past ten years has been statistically analyzed to provide improved information on slip probability of connections in which the bolts have been preloaded
to the requirements of Table 4. Two principal variables—coefficient of friction of
the faying surfaces and bolt pretension—were found to dominate the slip resistance
of connections.
An examination of the slip (friction) coefficient data for a wide range of surface conditions indicates that the data are distributed normally, and the standard
deviation is essentially the same for each surface condition class. This means that
different reduction factors should be applied to classes of surfaces with different
mean values of coefficients of friction—the smaller the mean value of the coefficient of friction, the smaller (more severe) the appropriate reduction factor—in order
to provide equivalent reliability of slip resistance.
The bolt clamping force data indicate that bolt tensions are distributed normally
for each method of tightening. However, the data also indicate that the mean values
of the bolt tensions are different for each method. If the calibrated wrench method
is used to tighten ASTM A325 bolts, the mean value of bolt tension is about 1.13
20. Ibid., pp. 238–40.
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times the minimum specified tension in Table 4. If the turn-of-nut method is used,
the mean value of tension is about 1.35 times the minimum specified preload for
A325 bolts and about 1.27 for A490 bolts.
The combined effects of the variability of coefficient of friction and bolt tension have been accounted for in the slip probability factor, D, of the formula for
nominal slip resistance in Section 5(b). The values of the slip probability factor,
D, given by 5(b) imply a 90 percent reliability that slip will not occur if the calibrated
wrench method of installation is used. If the turn-of-nut method is used, a reliability of about 95 percent will be provided.
Reference is made to Guide to Design Criteria for Bolted and Riveted Joints
(2nd ed., New York: John Wiley and Sons. 1987 p. 135) for tables of values of D
appropriate for other mean slip coefficients and slip probabilities and suitable for
direct substitution into the formula for slip resistance in Section 5(b).
The frequency distribution and mean value of clamping force for bolts tightened by turn-of-nut method are higher than calibrated wrench installation because
of the elimination of variables which affect torque-tension ratios and due to
higherthan-specified minimum strength of production bolts. Because properly applied turnof-nut installation induces yield point strain in the bolt, the higher-thanspecified yield strength of production bolts will be mobilized and result in higher
clamping force by the method. On the other hand, the calibrated wrench method,
which is dependent upon the calibration of wrenches to slightly more than Table 4
tensions, independent of the actual bolt properties, will not mobilize any additional
strength of production bolts. High clamping force might be achieved by the calibrated
wrench method if the wrench was set to a higher torque value. However, this would
require more attention to the degrees of rotation to prevent excessive deformation of
the bolt or torsional bolt failure.
Because of the effects of oversize and slotted holes on the induced tension in
bolts using any of the specified installation methods, lower values are provided for
bolts in these hole types. In the case of bolts in long slotted holes, even though the
slip load is the same for bolts loaded transverse or parallel to the axis of the slot,
the values for bolts loaded parallel to the axis has been further reduced based upon
judgment in recognition of the greater consequences of slip.
Attention is called to the fact that the criteria for slip resistance are for the case
of connections subject to a coaxial load. For cases in which the load tends to rotate
the connection in the plane of the faying surface, a modified formula accounting
for the placement of bolts relative to the center of rotation should be used.21
Connections of the type shown in Figure C4(a), in which some of the bolts (A)
lose a part of their clamping force due to applied tension, suffer no overall loss of
frictional resistance. The bolt tension produced by the moment is coupled with a
compensating compressive force (C) on the other side of the axis of bending. In
a connection of the type shown in Fig. C4(b), however, all fasteners (B) receive
applied tension which reduces the initial compression force at the contact surface.
If slip under load cannot be tolerated, the design slip-load value of the bolts in shear
should be reduced in proportion to the ratio of residual axial force to initial tension.
If slip of the joint can be tolerated, the bolt shear stress should be reduced according to the tension-shear interaction as outlined in the Guide. page 71. Because the
bolts are subject to applied axial tension, they are required to be pretensioned in
either case.
21. Ibid., pp. 217–30.
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B
A
M
C
V
(a)
T
(b)
Fig. C4
While connections with bolts pretensioned to the levels specified in Table 4 do
not ordinarily slip into bearing when subject to anticipated loads, it is required that
they meet the requirements of Section 5 in order to maintain the factor of safety
of 2 against fracture in the event that the bolts do slip into bearing as a result of
large unforeseen loads.
To cover those cases where a coefficient of friction less than 0.33 might be adequate for a given situation, the Specification provides that, subject to the approval
of the Engineer of Record, and provided the mean slip coefficient is determined
by the specified test procedure and the appropriate slip probability factor, D, is
selected from the literature, faying surface coatings providing lower slip resistance
than Class A coating may be used.
It should be noted that both Class A and Class B coatings are required to be
applied to blast-cleaned steel.
High-Strength Bolts in Combination with Welds or Rivets. For high-strength bolts
in combination with welds in statically loaded conditions and considering new work
only, the nominal strength may be taken as the sum of the two contributions. If one
type of connector is already loaded when the second type of connector is introduced,
the nominal strength cannot be obtained by sum of the two resistances. The Guide
should be consulted in these cases.
For high-strength bolts in combination with welds in fatigue loaded applications, available data are not sufficient to develop general design recommendations
at this time. High-strength bolts in combination with rivets are rarely encountered
in modern practice. If need arises, guidance may be found in the Guide.
C7 Design Details of Bolted Connections
A new section has been added with this edition of the Specification in order to bring
together a number of requirements for proper design and detailing of high-strength
bolted connections. The material covered in the Specification, and in Section 7 in
particular, is not intended to provide comprehensive coverage of the design of highstrength bolted connections. For example, other design considerations of importance
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to the satisfactory performance of the connected material such as block shear, shear
lag, prying action, connection stiffness, effect on the performance of the structure
and others are beyond the scope of this Specification and Commentary.
Proper location of hardened washers is as important as other elements of a detail
to the performance of the fasteners. Drawings and details should clearly reflect the
number and disposition of washers, especially the thick hardened washers that are
required for several slotted hole applications. Location of washers is a design consideration that should not be left to the experience of the iron worker.
While hardened washers are not required with some methods of installation,
their use will overcome the effects of galling under the element turned in tightening.
Finger shims are a necessary device or tool of the trade to permit adjusting alignment and plumbing of structures. When these devices are fully and properly inserted,
they do not have the same effect on bolt tension relaxation or the connection performance as do long slotted holes in an outer ply. When fully inserted, the shim provides support around approximately 75 percent of the perimeter of the bolt in contrast to the greatly reduced area that exists with a bolt centered in a long slot. Further,
finger shims would always be enclosed on both sides by the connected material which
would be fully effective in bridging the space between the fingers.
C8 Installation and Tightening
Several methods for installation and tensioning of high-strength bolts, when tensioning is required, are provided without preference in the Specification. Each method
recognized in Section 8, when properly used as specified, may be relied upon to
provide satisfactory results. All methods may be misused or abused.
At the expense of redundancy, the provisions stipulating the manner in which
each method is intended to be used are set forth in complete detail in order that
the rules for each method may stand alone without need for footnotes or reference
to other sections. If the methods are conscientiously implemented, good results should
be routinely achieved.
Connections Not Requiring Full Tensioning. In the Commentary, Section C6 of
the previous edition of the Specification, it was pointed out that “bearing” type connections need not be tested to ensure that the specified pretension in the bolts had
been provided, but specific provision permitting relaxation of the tensioning requirement was not contained in the body of the Specification. In the present edition of
the Specification, separate installation procedures are provided for bolts that are
not within the slip-critical or direct tension category. The intent in making this change
is to improve the quality of bolted steel construction and reduce the frequency of
costly controversies by focusing attention, both during the installation and tensioning phase and during inspection, on the true slip-critical connections, rather than
diluting the effort through the requirement for costly tensioning and tension testing
of the great many connections where such effort serves no useful purpose. The
requirement for identification of connections on the drawings may be satisfied either
by identifying the slip-critical and direct tension connections which must be fully
tightened and inspected or by identifying the connections which need be tightened
only to the snug tight condition.
Under the provisions of some other specifications, certain shear/bearing connections are required to be tightened well beyond the snug tight conditions;22 how22. For example, American Institute of Steel Construction, “Specification for Design Fabrication and
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ever, because the joints are in bearing, prevention of slip of the joint is not a concern in these connections. Because they are not slip-critical joints, they should not
be subject to the same requirements as slip-critical joints, especially the requirements for faying surface coatings and conditions. To ensure proper tightness of the
connections, they should be tightened by one of the four methods in 8(d); however,
inspection should be limited to monitoring the work to confirm that the bolt tightening procedure is properly applied. Inspection should not include testing to ensure
that any specific level of tension has been achieved.
In the Specification, snug tight is defined as the tightness that exists when all
plies are in firm contact. This may usually be attained by a few impacts of an impact
wrench or the full effort of a man using an ordinary spud wrench. In actuality, snug
tight is a degree of tightness which will vary from joint to joint depending upon
the thickness, flatness and degree of parallelism of the connected material. In most
joints, the plies will pull together at snug tight; however, in some joints in thick
material, it may not be possible to have continuous contact throughout the faying
surface area. In such joints, the slip resistance of the completed joints will not be
reduced because compressive forces between the faying surfaces, however distributed,
must be in equilibrium with the total of the tensile forces in all bolts.
Tension Calibrating Devices. At the present time, there is no known economical
means for determining the tension in a bolt that has previously been installed in
a connection. The actual tension in a bolt installed in a tension calibrator (hydraulic
tension indicating device) is directly indicated by the dial of the device, provided
the device is properly calibrated. Such a device is an economical and valuable tool
that should be readily available whenever high-strength bolts are to be installed in
either slip-critical or shear/bearing connections. The testing of as-received bolts and
nuts at the job site is a requirement of the Specification because instances of counterfeit under strength fasteners not meeting the requirements of the ASTM Specification have not infrequently occurred. Job site testing provides a practical means
for ensuring that nonconforming fasteners are not incorporated in the work. Further,
although the several elements of a fastener assembly may conform to the minimum
requirements of their separate ASTM Specifications, their compatibility in an assembly or the need for lubrication can only be ensured by testing of the assembly. Hence,
such devices are important for testing the complete fastener assembly as it will be
used with the method of tightening to be used to ensure the suitability of bolts and
nuts (probably produced by different manufacturers), other elements, and the adequacy of impact wrenches and/or air pressure to provide the specified tension using
the selected method. Testing before start of installation of fasteners in the work will
also identify potential sources of problems, such as the need for lubrication to prevent failure of bolts by combined high torque with tension, under-strength assemblies due to excessive overtapping of hot-dip galvanized nuts, and to clarify for the
bolting crews and inspectors the proper implementation of the selected installation
method to be used. Such devices are essential to the confirmation testing of alternative design fasteners, direct tension indicators, and to verify the proper use of the
turn-of-nut procedure. They are also essential to the specified procedure for the
calibrated wrench method of installation, and for the specified procedure for determining a valid testing torque when such inspection by a torque method is required.
Erection of Structural Steel for Buildings,” Section 1.15.12, stipulates several cases where high-strength
bolts in bearing connections are to be fully tensioned independent of whether potential slip is a concern
or not.
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They are the only known economically available tool for field use for determining
realistic torque to tension relationships for given fastener assemblies.
Experience on many projects has shown that bolts and/or nuts not meeting the
requirements of the applicable ASTM specification would have been identified prior
to installation if they had been tested as an assembly in a tension calibrator. The
controversy and great expense of replacing bolts installed in the structure when the
nonconforming bolts were discovered at a later date would have been avoided.
Hydraulic tension calibrating devices capable of indicating bolt tension undergo
a slight deformation under load. Hence, the nut rotation corresponding to a given
tension reading may be somewhat larger than it would be if the same bolt were tightened against a solid steel abutment. Stated differently, the reading of the calibrating
device tends to underestimate the tension which a given rotation of the turned element would induce in a bolt in an actual joint. This should be borne in mind when
using such devices to establish a tension-rotation relationship.
Slip-critical Connections and Connections Subject to Direct Tension. Four methods for joint assembly and tightening are provided for slip-critical and direct tension
connections. It has repeatedly been demonstrated in the laboratory that each of the
four installation methods provides the specified pretension when used properly with
specified fasteners in good condition, but improperly applied methods or understrength fasteners or fasteners in poor condition provide uncertain pretensions. Therefore, regardless of the method used and prior to the commencement of work, it is
required to be demonstrated by installation of a representative sample of the fastener assemblies in the tension calibrator that the specified pretension can be achieved
using the procedure to be used with the fasteners to be used by the crews who will
be doing the work.
With any of the four described tensioning methods, it is important to install
bolts in all holes of the connection and bring them to an intermediate level of tension generally corresponding to snug tight in order to compact the joint. Even after
being fully tightened, some thick parts with uneven surfaces may not be in contact
over the entire faying surface. In itself, this is not detrimental to the performance
of the joint. As long as the specified bolt tension is present in all bolts of the completed connection, the clamping force equal to the total of the tensions in all bolts
will be transferred at the locations that are in contact and be fully effective in resisting slip through friction. If however, individual bolts are installed and tightened in
a single continuous operation, bolts which are tightened first will be subsequently
relaxed by the tightening of the adjacent bolts. The total of the forces in all bolts
will be reduced, which will reduce the slip load whether there is uninterrupted contact between the surfaces or not.
With all methods, tightening should begin at the most rigidly fixed or stiffest
point and progress toward the free edges, both in the initial snugging up and in the
final tightening.
Turn-of-Nut-Tightening. When properly implemented, turn-of-nut method provides
more uniform tension in the bolts than does torque controlled tensioning methods
because it is primarily dependent upon bolt elongation into the inelastic range.
Consistency and reliability method is dependent upon ensuring that the joint
is well compacted and all bolts are uniformly tight at a snug tight condition prior
to application of the final required partial turn. Under-tightened bolts will result
if this starting condition is not achieved because subsequent turning of the nut will
first close the gap before meaningful elongation of the bolt occurs as would be the
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case with solid steel in the grip. Reliability is also dependent upon ensuring that
the turn that is applied is relative between the bolt and nut; thus the element not
turned in tightening should be prevented from rotating while the required degree
of turn is applied to the turned element. Reliability and inspectability of the method
may be improved by having the outer face of the nut match-marked to the protruding end of the bolt after the joint has been snug tightened but prior to final tightening. Such marks may be applied by the wrench operator using a crayon or dab of
paint. Such marks in their relatively displaced position after tightening will afford
the inspector a means for noting the rotation that was applied.
Problems with turn-of-nut tightening have been encountered with hot-dip galvanized bolts. In some cases, the problems have been attributed to especially effective lubricant applied by the manufacturer to ensure that bolts from stock will meet
the ASTM Specification requirements without the need for relubricating and retesting. Job site tests in the tension indicating device demonstrated the lubricant reduced
the coefficient of friction between the bolt and nut to the degree that “the full effort
of a man using an ordinary spud wrench” to snug tighten the joint actually induced
the full required tension. Also, because the nuts could be removed by an ordinary
spud wrench they were erroneously judged improperly tightened by the inspector.
Research (see note 3) confirms that lubricated high-strength bolts may require only
one-half as much torque to induce the specified tension. In other cases of problems
with hot-dip galvanized bolts, the absence of lubrication or lack of proper overtapping caused seizing of the nut and bolt threads which resulted in twist failure of
the bolt at less than specified tension. For such situations, use of a tension indicating device and the fasteners being installed may be helpful in establishing either
the need for lubrication or alternate criteria for snug tight at about one-half the tension required by Table 4.
Because reliability of the method is independent of the presence or absence of
washers, washers are not required except for oversize and slotted holes in an outer
ply. In the absence of washers, testing after the fact using a torque wrench method
is highly unreliable.
That is, the turn-of-nut method of installation, properly applied, is more reliable and consistent than the testing method. The best method for inspection of the
method is for the Inspector to observe the required job site confirmation testing
of the fasteners and the method to be used, followed by monitoring of the work
in progress to ensure that the method is routinely properly applied.
Calibrated Wrench Method. Research has demonstrated that scatter in induced
tension is to be expected when torque is used as an indirect indicator of tension.
Numerous variables, which are not related to tension, affect torque. For example,
the finish and tolerance on bolt threads, the finish and tolerance on the nut threads,
the fact that the bolt and nut may not be produced by the same manufacturer, the
degree of lubrication, the job site conditions contributing to dust and dirt or corrosion on the threads, the friction that exists to varying degree between the turned
element and the supporting surface, the variability of the air pressure on the torque
wrenches due to length of air lines or number of wrenches operating from the same
source, the condition and lubrication of the wrench which may change within a work
shift, and other factors all bear upon the effectiveness of the calibrated torque wrench
to induce tension.
Recognition of the calibrated wrench method of tightening was removed from
the Specification with the 1980 edition. This action was taken because it is the least
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reliable of all methods of installation and many costly controversies had occured.
It is suspected that shortcut procedures in the use of the calibrated wrench method
of installation, not in accordance with the Specification provisions, were probably
being used. Further, torque controlled inspection procedures based upon “standard”
or calculated inspection torques rather than torques determined as required by the
Specification were being routinely used. These incorrect procedures plus others had
a compounding effect upon the uncertainty of the installed bolt tension, and were
responsible for many of the controversies.
It is recognized, however, that if the calibrated wrench method is implemented
without shortcuts as intended by the Specification, that there will be a 90 percent
assurance that the tensions specified in Table 4 will be equaled or exceeded. Because
the Specification should not prohibit any method which will give acceptable results
when used as specified, the calibrated wrench method of installation was reinstated
in the 1985 edition of the Council Specification. However, to improve upon the previous situation, the 1985 version of the Specification was modified to require better
control. Wrenches must be calibrated daily for each diameter and grade of bolt.
Hardened washers must be used. Fasteners must be protected from dirt and moisture at the job site. Additionally, to achieve reliable results attention should be given
to the control, insofar as it is practical, of those controllable factors which contribute to variability. For example, bolts and nuts should be purchased from reliable
manufacturers with a record of good quality control to minimize the variability of
the fit. Bolts and nuts should be adequately and uniformly lubricated. Water soluble lubricants should be avoided.
Installation of Alternative Design Fasteners. It is the policy of the Council to recognize only fasteners covered by ASTM Specifications; however, it cannot be denied
that a general type of alternative design fastener produced by several manufacturers,
is used on a significant number of projects as permitted by Section 2(d). The bolts
referred to involve a splined end extending beyond the threaded portion of the bolt
which is gripped by a specially designed wrench chuck which provides a means for
turning the nut relative to the bolt. While such bolts are subject to many of the variables affecting torque mentioned in the preceding section, they are produced and
shipped by the manufacturers as a nut-bolt assembly under good quality control,
which apparently minimizes some of the negative aspects of the torque controlled
process.
While these alternative design fasteners have been demonstrated to consistently
provide tension in the fastener meeting the requirements of Table 5 in controlled
tests in tension indicating devices, it must be recognized that the fastener may be
misused and provide results as unreliable as those with other methods. They must
be used in the as-delivered clean lubricated condition. The requirements of this Specification and the installation requirements of the manufacturer’s specification required
by Section 2(d) must be adhered to.
As with other methods, a representative sample of the bolts to be used should
be tested to ensure that, when used in accordance with the manufacturer’s instructions, they do, in fact, provide tension, as specified in Table 5. In the actual joints,
bolts must be installed in all holes of a connection and all fasteners tightened to
an intermediate level of tension adequate to pull all material into contact. Only after
this has been accomplished should the fasteners be fully tensioned in a systematic
manner and the splined end sheared off. The sheared off splined end merely signifies that at some time the bolt has been subjected to a torque adequate to cause the
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shearing. If the fasteners are installed and tensioned in a single continuous operation, they will give a misleading indication to the Inspector that the bolts are properly
tightened. Therefore, the only way to inspect these fasteners with assurance is to
observe the job site testing of the fasteners and installation procedure and then monitor
the work while in progress to ensure that the specified procedure is routinely followed.
Direct Tension Indicator Tightening. This Specification recognizes load indicating devices covered by the American Society for Testing and Materials’ “Specification for Compressible-Washer Type Direct Tension Indicators For Use With Structural Fasteners,” ASTM F959, in Section 2(f). The referenced device is a hardened
washer incorporating several small formed arches which are designed to deform in
a controlled manner when subjected to load. These load indicator washers are the
sole type of device known which is directly dependent upon the tension load in the
bolt, rather than upon some indirect parameter, to indicate the tension in a bolt.
As with the alternative design load indicating bolts, load indicating washers are
dependent upon the quality control of the producer and proper use in accordance
with the manufacturer’s installation procedures and these Specifications. If the load
indicator washers delivered for use in a specific application are tested at the job
site to demonstrate that all components of the assembly do provide a proper indication of bolt tension, they are reliable if they are properly used by the bolting crews.
Direct tension indicators meeting the requirements of ASTM F959 depend upon tension in the fastener to cause inelastic deformation of the formed arches. Bolts together
with the load indicator washer plus any other washers required by Specification should
be installed in all holes of the connection and the bolts tightened to approximately
one-half the specified tension (deformation of the formed arches by about one-half
the amount required to compress them to the specified gap) to ensure that plies of
the joint have been brought into firm contact. Only after this initial tightening operation should the bolts be fully tensioned in a systematic manner. If the bolts are
installed and tensioned in a single continuous operation, the load indicator washers
will give the inspector a misleading indication that bolts are uniformly tensioned
to the specified tension. Therefore, the only way to inspect fasteners with which
load indicator washers are used with assurance is to observe the job site testing of
the devices and installation procedure and then routinely monitor the work while
in progress to ensure that the specified procedure is followed.
Use of direct tension indicators provides a reliable means for tensioning galvanized fasteners because it avoids the factors which affect other methods.
During installation, care must be taken to ensure that the indicator nubs are
oriented to bear against the hardened bearing surface of the bolt head or against
a hardened flat washer if used under the nut.
C9 Inspection
It is apparent from the commentary on installation procedures that the inspection
procedures giving the best assurance that bolts are properly installed and tensioned
is provided by Inspector observation of the calibration testing of the fasteners using
the selected installation procedure followed by monitoring of the work in progress
to ensure that the procedure that was demonstrated to provide the specified tension
is routinely adhered to. When such a program is followed, no further evidence of
proper bolt tension is required.
If testing for bolt tension using torque wrenches is conducted subsequent to the
time the work of installation and tightening of bolts performed, the test procedure
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COMMENTARY ON THE RCSC SPECIFICATION (6/8/88)
is subject to all of the uncertainties of torque controlled calibrated wrench installation. Additionally, the absence of many of the controls necessary to minimize variability of the torque to tension relationship, which are unnecessary for the other
methods of bolt installation, such as use of hardened washers, careful attention to
lubrication and the uncertainty of the effect of passage of time and exposure in the
installed condition all reduce the reliability of the arbitration inspection results. The
fact that in many cases it may have to be based upon a job test torque determined
by using bolts only assumed to be representative of the bolts in the actual job, or
using bolts removed from completed joints, makes the test procedure less reliable
than a properly implemented installation procedure it is used to verify. Verification
inspection using ultrasonic extensometers is accurate but costly and time-consuming,
and requires that each tested bolt must be loosened to zero tension for calibration.
Therefore, extensometers should be used for inspection only in the most critical cases.
The arbitration inspection procedure contained in the Specification is provided, in
spite of its limitations, as the most feasible available at this time.
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Code of Standard Practice
for Steel Buildings and Bridges
Adopted Effective June 10, 1992
American Institute of Steel Construction, Inc.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION, INC.
One East Wacker Drive, Suite 3100, Chicago, IL 60601-2001
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Copyright 1992
by
The American Institute of Steel Construction
All rights reserved. This book or any part thereof
must not be reproduced in any form without the
written permission of the publisher
PREFACE
When contractual documents do not contain specific provisions to the contrary,
existing trade practices are considered to be incorporated into the relationships
between the parties to a contract. As in any industry, trade practices have developed
among those involved in the purchase, design, fabrication and erection of structural
steel. The American Institute of Steel Construction has continuously surveyed the
structural steel fabrication industry to determine standard practices and, commencing
in 1924, published its Code of Standard Practice. Since that date, the Code has been
periodically updated to reflect new and changing technology and practices of the
industry.
It is the Institute’s intention to provide to owners, architects, engineers, contractors
and others associated with construction, a useful framework for a common understanding of acceptable standards when contracting for structural steel construction.
This edition is the fourth complete revision of the Code since it was first
published. It includes a number of new sections covering new subjects not included
in the previous Code, but which are an integral part of the relationship of the parties
to a contract.
The Institute acknowledges the valuable information and suggestions provided by
trade associations and other organizations associated with construction and the
fabricating industry in developing this current Code of Standard Practice.
While every precaution has been taken to insure that all data and information
presented is as accurate as possible, the Institute cannot assume responsibility for
errors or oversights in the information published herein, or the use of the information
published or incorporation of such information in the preparation of detailed
engineering plans. The Code should not replace the judgment of an experienced
architect or engineer who has the responsibility of design for a specific structure.
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Code of Standard Practice
for Steel Buildings and Bridges
Adopted Effective June 10, 1992
American Institute of Steel Construction, Inc.
SECTION 1. GENERAL PROVISIONS
1.1. Scope
The practices defined herein have been adopted by the AISC as the commonly
accepted standards of the structural steel fabricating industry. In the absence of other
instructions in the contract documents, the trade practices defined in this Code of
Standard Practice, as revised to date, govern the fabrication and erection of structural
steel.
1.2. Definitions
AISC Specification—The Specification for the Design, Fabrication and Erection
of Structural Steel for Buildings as adopted by the American Institute of Steel
Construction.
ANSI—American National Standards Institute.
Architect/Engineer—The owner’s designated representative with full responsibility
for the design and integrity of the structure. (The EOR)
ASTM—The material standard of the American Society for Testing and Materials.
AWS Code—The Structural Welding Code of the American Welding Society.
Code—The Code of Standard Practice as adopted by the American Institute of
Steel Construction.
Contract Documents—The documents which define the responsibilities of the
parties involved in bidding, purchasing, supplying and erecting structural steel.
Such documents normally consist of a contract, plans and specifications.
Drawings—Shop and field erection drawings prepared by the fabricator and erector
for the performance of the work.
Erector—The party responsible for the erection of the structural steel.
Fabricator—The party responsible for furnishing fabricated structural steel.
General Contractor—The owner’s designated representative with full
responsibility for the construction of the structure.
MBMA—Metal Building Manufacturers Association.
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AISC CODE OF STANDARD PRACTICE
Mill Material—Steel mill products ordered expressly for the requirements of a
specific project.
Owner—The owner of the proposed structure or his designated representatives,
who may be the architect, engineer, general contractor, construction manager,
public authority or others.
Owner’s Authorized Representative—That person designated by the owner to
have the responsibility for the approval of shop drawings. This is usually the
structural engineer of record for the project.
Plans—Design drawings furnished by the party responsible for the design of the
structure.
Release for Construction—The release by the owner permitting the fabricator to
commence work under the contract, including ordering material and preparing
shop drawings.
SSPC—The Steel Structures Painting Council, publishers of the Steel Structures
Painting Manual, Vol. 2, “Systems and Specifications.”
Tier—The word Tier used in Section 7.11 is defined as a column shipping piece.
1.3. Design Criteria for Buildings and Similar Type Structures
In the absence of other instructions, the provisions of the AISC Specification
govern the design of the structural steel.
1.4. Design for Bridges
In the absence of other instructions, the following provisions govern, as applicable:
Standard Specifications for Highway Bridges of the American Association of State
Highway and Transportation Officials
Specifications for Steel Railway Bridges of the American Railway Engineering
Association
Structural Welding Code of the American Welding Society
1.5. Responsibility for Design
1.5.1. When the owner provides the design, plans and specifications, the
fabricator and erector are not responsible for the suitability, adequacy or legality of
the design. The fabricator is not responsible for the safety of erection if the structure
is erected by others.
1.5.2. When the owner enters into a direct contract with the fabricator to both
design and fabricate an entire, completed steel structure, the fabricator is responsible
for the structural adequacy of the design. The fabricator is not responsible for the
safety of erection if the structure is erected by others.
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1.6. Patented Devices
Except when the contract documents call for the design to be furnished by the
fabricator or erector, the fabricator and erector assume that all necessary patent rights
have been obtained by the owner and that the fabricator or erector will be fully
protected in the use of patented designs, devices or parts required by the contract
documents.
SECTION 2.0. CLASSIFICATION OF MATERIALS
2.1. Definition of Structural Steel
“Structural Steel,” as used to define the scope of work in the contract documents,
consists of the steel elements of the structural steel frame essential to support the
design loads. Unless otherwise specified in the contract documents, these elements
consist of material as shown on the structural steel plans and described as:
Anchor bolts for structural steel
Base or bearing plates
Beams, girders, purlins and girts
Bearings of steel for girders, trusses or bridges
Bracing
Columns, posts
Connecting materials for framing structural steel to structural steel
Crane rails, splices, stops, bolts and clamps
Door frames constituting part of the structural steel frame
Expansion joints connected to the structural steel frame
Fasteners for connecting structural steel items:
Shop rivets
Permanent shop bolts
Shop bolts for shipment
Field rivets for permanent connections
Field bolts for permanent connections
Permanent pins
Floor plates (checkered or plain) attached to the structural steel frame
Grillage beams and girders
Hangers essential to the structural steel frame
Leveling plates, wedges, shims & leveling screws
Lintels, if attached to the structural steel frame
Marquee or canopy framing
Machinery foundations of rolled steel sections and/or plate attached to the
structural frame
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AISC CODE OF STANDARD PRACTICE
Monorail elements of standard structural shapes when attached to the structural
frame
Roof frames of standard structural shapes
Shear connectors—if specified to be shop attached
Struts, tie rods and sag rods forming part of the structural steel frame
Trusses.
2.2. Other Steel or Metal Items
The classification “Structural Steel,” does not include steel, iron or other metal
items not generally described in Section 2.1, even when such items are shown on the
structural steel plans or are attached to the structural frame. These items include but
are not limited to:
Cables for permanent bracing or suspension systems
Chutes and hoppers
Cold-formed steel products
Concrete or masonry reinforcing steel
Door and corner guards
Embedded steel parts in precast or poured concrete
Flagpole support steel
Floor plates (checkered or plain) not attached to the structural steel frame
Grating and metal deck
Items required for the assembly or erection of materials supplied by trades other
than structural steel fabricators or erectors
Ladders and safety cages
Lintels over wall recesses
Miscellaneous metal
Non-steel bearings
Open-web, long-span joists and joist girders
Ornamental metal framing
Shear connectors — if specified to be field installed
Stacks, tanks and pressure vessels
Stairs, catwalks, handrail and toeplates
Trench or pit covers.
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SECTION 3. PLANS AND SPECIFICATIONS
3.1. Structural Steel
In order to insure adequate and complete bids, and to enable the timely preparation
of shop drawings and timely fabrication, the fabricator must be able to rely upon the
completeness of the contract documents. The contract documents can be assumed to
provide complete structural steel design plans clearly showing the work to be
performed and giving the size, section, material grade and the location of all
members, floor levels, column centers and offsets, and camber of members, with
sufficient dimensions to convey accurately the quantity and nature of the structural
steel to be furnished. Structural steel specifications include any special requirements
controlling the fabrication and erection of the structural steel. Contract drawings,
specifications and addenda must be numbered and dated for purposes of identification.
3.1.1. Wind bracing, connections, column stiffeners, column web doubler plates,
bearing stiffeners on beams and girders, web reinforcement, openings for other trades,
and other special details where required are shown in sufficient detail so that they
may be readily understood.
3.1.2. Plans include sufficient data concerning assumed loads, shears, moments
and axial forces to be resisted by the individual members and their connections, as
may be required for the development of connection details on the shop drawings.
Unless otherwise indicated in the contract documents, the plans are based upon
consideration of the loads and forces to be resisted by the steel frame in the
completed and fully connected condition. See Section 7.9.
3.1.3. Where connections are not shown, the connections are to be in accordance
with the requirements of the AISC Specification.
3.1.4. When loose lintels and leveling plates are required to be furnished as part
of the contract requirements, the plans and specifications show the size, section and
location of all pieces.
3.1.5. Whenever steel frames, in the completely erected and fully connected state,
require interaction with other elements not classified as structural steel (see Section
2) to provide stability and strength to resist loads for which the frame is designed, the
non-self-supporting frame and the major elements not classified as structural steel,
such as diaphragms, masonry and/or concrete shear walls, shall be identified in the
contract documents. See Section 7.9.3.
3.1.6. When camber is required for cantilevered members, the magnitude and
direction of camber are shown.
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AISC CODE OF STANDARD PRACTICE
3.1.7. The contract documents specify all the painting requirements, including the
identification of members to be painted, surface preparation, paint specifications,
manufacturer’s product identification and the required minimum and maximum dry
film thickness, in mils, of the shop coat. Contract documents must clearly indicate
all individual members which are to be left unpainted so as to receive concrete,
sprayed on fireproofing or for other reasons.
3.2. Architectural, Electrical and Mechanical
Architectural, electrical and mechanical plans may be used as a supplement to the
structural steel plans to define detail configurations and construction information,
provided all requirements for the quantities and locations of structural steel are noted
on the structural steel plans.
3.3. Discrepancies
In case of discrepancies between plans and specifications for buildings, the
specifications govern. In case of discrepancies between plans and specifications for
bridges, the plans govern. In case of discrepancies between scale dimensions on the
plans and figures written on them, the figures govern. In case of discrepancies
between the structural steel plans and the architectural plans or plans for other trades,
the structural steel plans govern.
3.4. Legibility of Plans
Plans are clearly legible and made to a scale not less than 1⁄8 in. to the foot. More
complex information is furnished to an adequate scale to convey the information
clearly.
3.5. Special Conditions
When it is required that a project be advertised for bidding before the requirements
of Section 3.1 can be met, the owner must provide sufficient information in the form
of scope, drawings, weights, outline specifications, and other descriptive data to
enable the fabricator and erector to prepare a knowledgeable bid.
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SECTION 4. SHOP AND ERECTION DRAWINGS
4.1. Owner Responsibility
To enable the fabricator and erector to properly and expeditiously proceed with the
work, the owner must furnish, in a timely manner and in accordance with the contract
documents, complete structural steel plans and specifications released for construction.
“Released for construction” plans and specifications are required by the fabricator for
ordering mill material and the preparation and completion of shop and erection
drawings. Plans provided as part of a contract bid package are considered to be
“released for construction” unless otherwise noted.
4.2. Approval
When shop drawings are made by the fabricator, prints thereof are submitted to the
owner for his examination and approval. The fabricator includes a maximum
allowance of fourteen (14) calendar days in his schedule for the return of shop
drawings. Return of shop drawings is noted with the owner’s approval, or approval
subject to corrections as noted. The fabricator makes the corrections and furnishes
corrected prints to the owner. Approval of shop drawings, approval “subject to
corrections noted,” or similar approvals, constitute the owner’s release for the
fabricator to begin fabrication. The fabricator retains flexibility to determine the
fabrication schedule necessary to meet the project’s requirements.
4.2.1. Approval by the owner’s authorized representative of shop drawings
prepared by the fabricator indicates that the fabricator has correctly interpreted the
contract requirements, and may rely upon these drawings in the fabrication process.
Where the fabricator must select or complete connection details, this approval
constitutes acceptance by the owner’s authorized representative of design
responsibility for the structural adequacy of such connections. If a fabricator wishes
to change a connection that is fully detailed in the contract documents, the fabricator
shall submit the change for review by the owner’s authorized representative in a
manner that clearly indicates that a change is being requested. Approval of this
submittal constitutes acceptance by the owner’s authorized representative of design
responsibility for the structural adequacy of the changed detail. Approval under any
of the circumstances described in this Section does not relieve the fabricator of the
responsibility for accuracy of detailed dimensions on shop drawings, nor the general
fit-up of parts to be assembled in the field.
4.2.2. Unless specifically stated to the contrary, any additions, deletions or
changes indicated on the approval of shop and erection drawings are authorizations
by the owner to release the additions, deletions or revisions for construction.
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AISC CODE OF STANDARD PRACTICE
4.3. Drawings Furnished by Owner
When the shop drawings are furnished by the owner, he must deliver them to the
fabricator in time to permit material procurement and fabrication to proceed in an
orderly manner in accordance with the prescribed time schedule. The owner prepares
these shop drawings, insofar as practicable, in accordance with the shop and drafting
room standards of the fabricator. The owner is responsible for the completeness and
accuracy of shop drawings so furnished.
SECTION 5. MATERIALS
5.1. Mill Materials
When the fabricator receives “released for construction” plans and specifications,
the fabricator may immediately place orders for the materials necessary for
fabrication. The contract documents must note any material or areas which should
not be ordered due to a design which is incomplete or subject to revision.
5.1.1. Mill tests are performed to demonstrate material conformance to ASTM
specifications in accordance with the contract requirements. Unless special
requirements are included in the contract documents, mill testing is limited to those
tests required by the applicable ASTM material specifications. Mill test reports are
furnished by the fabricator only if requested by the owner, either in the contract
documents or in separate written instructions prior to the time the fabricator places
his material orders with the mill.
5.1.2. When material received from the mill does not satisfy ASTM A6
tolerances for camber, profile, flatness or sweep, the fabricator is permitted to perform
corrective work by the use of controlled heating and mechanical straightening, subject
to the limitations of the AISC Specification.
5.1.3. Corrective procedures described in ASTM A6 for reconditioning the
surface of structural steel plates and shapes before shipment from the producing mill
may also be performed by the fabricator, at the fabricator’s option, when variations
described in ASTM A6 are discovered or occur after receipt of the steel from the
producing mill.
5.1.4. When special requirements demand tolerances more restrictive than
allowed by ASTM A6, such requirements are defined in the contract documents and the
fabricator has the option of corrective measures as described above.
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5.2. Stock Materials
5.2.1. Many fabricators maintain stocks of steel products for use in their
fabricating operations. Materials taken from stock by the fabricator to be used for
structural purposes must be of a quality at least equal to that required by the ASTM
specifications applicable to the classification covering the intended use.
5.2.2. Mill test reports are accepted as sufficient record of the quality of materials
carried in stock by the fabricator. The fabricator reviews and retains the mill test
reports covering the materials he purchases for stock, but the fabricator does not
maintain records that identify individual pieces of stock material against individual
mill test reports. Such records are not required if the fabricator purchases for stock
under established specifications as to grade and quality.
5.2.3. Stock materials purchased under no particular specifications or under
specifications less rigid than those mentioned above, or stock materials which have
not been subject to mill or other recognized test reports, are not used without the
express approval of the owner, except where the quality of the material could not
affect the integrity of the structure.
SECTION 6. FABRICATION AND DELIVERY
6.1. Identification of Material
6.1.1. High strength steel and steel ordered to special requirements is marked by
the supplier, in accordance with ASTM A6 requirements, prior to delivery to the
fabricator’s shop or other point of use.
6.1.2. High strength steel and steel ordered to special requirements that has not
been marked by the supplier in accordance with Section 6.1.1 is not used until its
identification is established by means of tests as specified in Section A3.1 of the
AISC Specification, and until a fabricator’s identification mark, as described in
Section 6.1.3, has been applied.
6.1.3. During fabrication, up to the point of assembling members, each piece of
high strength steel and steel ordered to special requirements carries a fabricator’s
identification mark or an original supplier’s identification mark. The fabricator’s
identification mark is in accordance with the fabricator’s established identification
system, which is on record and available for the information of the owner or his
representative, the building commissioner and the inspector, prior to the start of
fabrication.
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AISC CODE OF STANDARD PRACTICE
6.1.4. Members made of high strength steel and steel ordered to special
requirements are not given the same assembling or erecting mark as members made
of other steel, even though they are of identical dimensions and detail.
6.2. Preparation of Material
6.2.1. Thermal cutting of structural steel may be performed by hand or
mechanically guided means.
6.2.2. Surfaces noted as “finished” on the drawings are defined as having a
maximum ANSI roughness height value of 500. Any fabricating technique, such as
friction sawing, cold sawing, milling, etc., that produces such a finish may be used.
6.3. Fitting and Fastening
6.3.1. Projecting elements of connection attachments need not be straightened in
the connecting plane if it can be demonstrated that installation of the connectors or
fitting aids will provide reasonable contact between faying surfaces.
6.3.2. Runoff tabs are often required to produce sound welds. The fabricator or
erector does not remove them unless specified in the contract documents. When their
removal is required, they may be hand flame-cut close to the edge of the finished
member with no further finishing required, unless other finishing is specifically called
for in the contract documents.
6.3.3. All high-strength bolts for shop attached connection material are to be
installed in the shop in accordance with the Specification for Structural Joints Using
A325 or A490 Bolts, unless otherwise noted on the shop drawings.
6.4. Dimensional Tolerances
6.4.1. A variation of 1⁄32 in. is permissible in the overall length of members with
both ends finished for contact bearing as defined in Section 6.2.2.
6.4.2. Members without ends finished for contact bearing, which are to be framed
to other steel parts of the structure, may have a variation from the detailed length not
greater than 1⁄16 in. for members 30 ft or less in length, and not greater than 1⁄8 in. for
members over 30 ft in length.
6.4.3. Unless otherwise specified, structural members, whether of a single-rolled
shape or built-up, may vary from straightness within the tolerances allowed for wideflange shapes by ASTM Specification A6, except that the tolerance on deviation from
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straightness of compression members is 1⁄1000 of the axial length between points which
are to be laterally supported.
Completed members should be free from twists, bends and open joints. Sharp
kinks or bends are cause for rejection of material.
6.4.4. Beams and trusses detailed without specified camber are fabricated so that
after erection any camber due to rolling or shop fabrication is upward.
6.4.5. When members are specified on the contract documents as requiring
camber, the shop fabrication tolerance shall be minus zero / plus 1⁄2 in. for members
50 ft and less in length, or minus zero / plus (1⁄2 in. plus 1⁄8 in. for each 10 ft or
fraction thereof in excess of 50 ft in length) for members over 50 ft. Members
received from the rolling mill with 75% of the specified camber require no further
cambering. For purposes of inspection, camber must be measured in the fabricator’s
shop in the unstressed condition.
6.4.6. Any permissible deviation in depths of girders may result in abrupt changes
in depth at splices. Any such difference in depth at a bolted joint, within the
prescribed tolerances, is taken up by fill plates. At welded joints the weld profile
may be adjusted to conform to the variation in depth, provided that the minimum
cross section of required weld is furnished and that the slope of the weld surface
meets AWS Code requirements.
6.5. Shop Painting (See also Section 3.1.7.)
6.5.1. The shop coat of paint is the prime coat of the protective system. It
protects the steel for only a short period of exposure in ordinary atmospheric
conditions, and is considered a temporary and provisional coating. The fabricator does
not assume responsibility for deterioration of the prime coat that may result from
exposure to ordinary atmospheric conditions, nor from exposure to corrosive
conditions more severe than ordinary atmospheric conditions.
6.5.2. In the absence of other requirements in the contract documents, the
fabricator hand cleans the steel of loose rust, loose mill scale, dirt and other foreign
matter, prior to painting, by means of wire brushing or by other methods elected by
the fabricator, to meet the requirements of SSPC-SP2. The fabricator’s workmanship
on surface preparation is considered accepted by the owner unless specifically
disapproved prior to paint application.
6.5.3. Unless specifically excluded, paint is applied by brush, spray, roller
coating, flow coating or dipping, at the election of the fabricator. When the term
“shop coat” or “shop paint” is used with no paint system specified, the fabricator’s
standard paint shall be applied to a minimum dry film thickness of one mil.
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AISC CODE OF STANDARD PRACTICE
6.5.4. Steel not requiring shop paint is cleaned of oil or grease by solvent
cleaners and cleaned of dirt and other foreign material by sweeping with a fiber brush
or other suitable means.
6.5.5. Abrasions caused by handling after painting are to be expected. Touch-up
of these blemished areas is the responsibility of the contractor performing field touchup or field painting.
6.6. Marking and Shipping of Materials
6.6.1. Erection marks are applied to the structural steel members by painting or
other suitable means, unless otherwise specified in the contract documents.
6.6.2. Rivets and bolts are commonly shipped in separate containers according
to length and diameter; loose nuts and washers are shipped in separate containers
according to sizes. Pins and other small parts, and packages of rivets, bolts, nuts and
washers are usually shipped in boxes, crates, kegs or barrels. A list and description
of the material usually appears on the outside of each closed container.
6.7. Delivery of Materials
6.7.1. Fabricated structural steel is delivered in such sequence as will permit the
most efficient and economical performance of both shop fabrication and erection. If
the owner wishes to prescribe or control the sequence of delivery of materials, the
owner reserves such right and defines the requirements in the contract documents.
If the owner contracts separately for delivery and erection, the owner must coordinate
planning between contractors.
6.7.2. Anchor bolts, washers and other anchorage or grillage materials to be built
into masonry should be shipped so that they will be on hand when needed. The
owner must allow the fabricator sufficient time to fabricate and ship such materials
before they are needed.
6.7.3. The quantities of material shown by the shipping statement are customarily
accepted by the owner, fabricator and erector as correct. If any shortage is claimed,
the owner or erector should immediately notify the carrier and the fabricator in order
that the claim may be investigated.
6.7.4. The size and weight of structural steel assemblies may be limited by shop
capabilities, the permissible weight and clearance dimensions of available
transportation and the job site conditions. The fabricator limits the number of field
splices to those consistent with minimum project cost.
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6.7.5. If material arrives at its destination in damaged condition, it is the
responsibility of the receiving party to promptly notify the fabricator and carrier prior
to unloading the material, or immediately upon discovery.
SECTION 7. ERECTION
7.1. Method of Erection
When the owner wishes to control the method and sequence of erection, or when
certain members cannot be erected in their normal sequence, the owner so specifies
in the contract documents. In the absence of such restrictions, the erector will
proceed using the most efficient and economical method and sequence available to
the erector consistent with the contract documents. When the owner contracts
separately for fabrication and erection services, the owner is responsible for
coordinating planning between contractors.
7.2. Site Conditions
The owner provides and maintains adequate access roads into and through the site
for the safe delivery and movement of derricks, cranes, trucks, other necessary
equipment, and the material to be erected. The owner affords the erector a firm,
properly graded, drained, convenient and adequate space at the site for the operation
of the erector’s equipment, and removes all overhead obstructions such as power
lines, telephone lines, etc., in order to provide a safe working area for erection of the
steelwork. The erector provides and installs the safety protection required for his own
work. Any protection for other trades not essential to the steel erection activity is the
responsibility of the owner. When safety protection provided by the erector is left
remaining in an area to be used by other trades after the steel erection activity is
completed, the owner shall be responsible for accepting and maintaining this protection, assuring that it is adequate for the protection of all other affected trades, assuring
that it complies with all applicable safety regulations when being used by other trades,
indemnifying the erector from any damages incurred as a result of the safety protection’s use by other trades, removing the safety equipment when no longer required,
and returning it to the erector in the same condition as it was received. When the
structure does not occupy the full available site, the owner provides adequate storage
space to enable the fabricator and erector to operate at maximum practicable speed.
7.3. Foundations, Piers and Abutments
The accurate location, strength, suitability and access to all foundations, piers and
abutments is the sole responsibility of the owner.
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7.4. Building Lines and Bench Marks
The owner is responsible for accurate location of building lines and bench marks
at the site of the structure, and for furnishing the erector with a plan containing all
such information. At each level the owner establishes offset building lines and
reference elevations for the use of the erector in the positioning of adjustable
construction elements.
7.5. Installation of Anchor Bolts and Embedded Items
7.5.1. Anchor bolts and foundation bolts are set by the owner in accordance with
an approved drawing. They must not vary from the dimensions shown on the
erection drawings by more than the following:
(a)
(b)
(c)
(d)
(e)
(f)
1⁄
8
in. center to center of any two bolts within an anchor bolt group, where
an anchor bolt group is defined as the set of anchor bolts which receive
a single fabricated steel shipping piece.
1⁄ in. center to center of adjacent anchor bolt groups.
4
Elevation of the top of anchor bolts ± 1⁄2 in.
Maximum accumulation of 1⁄4 in. per hundred ft along the established
column line of multiple anchor bolt groups, but not to exceed a total of 1
in., where the established column line is the actual field line most
representative of the centers of the as-built anchor bolt groups along a line
of columns.
1⁄ in. from the center of any anchor bolt group to the established column
4
line through that group.
The tolerances of paragraphs b, c and d apply to offset dimensions shown
on the plans, measured parallel and perpendicular to the nearest established
column line for individual columns shown on the plans to be offset from
established column lines.
7.5.2. Unless shown otherwise, anchor bolts are set perpendicular to the
theoretical bearing surface.
7.5.3. Other embedded items or connection materials between the structural steel
and the work of other trades are located and set by the owner in accordance with
approved location or erection drawings. Accuracy of these items must satisfy the
erection tolerance requirements of Section 7.11.3.
7.5.4. All work performed by the owner is completed so as not to delay or
interfere with the erection of the structural steel.
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7.6. Bearing Devices
The owner sets to line and grade all leveling plates, leveling nuts and loose bearing
plates which can be handled without a derrick or crane. All other bearing devices
supporting structural steel are set and wedged, shimmed or adjusted with leveling
screws by the erector to lines and grades established by the owner. The fabricator
provides the wedges, shims or leveling screws that are required, and clearly scribes
the bearing devices with working lines to facilitate proper alignment. Promptly after
the setting of any bearing devices, the owner checks lines and grades, and grouts as
required. The final location and proper grouting of bearing devices are the
responsibility of the owner. Tolerance on elevation relative to established grades of
bearing devices, whether set by the owner or by the erector, is ± 1⁄8 in.
7.7. Field Connection Material
7.7.1. The fabricator provides field connection details consistent with the
requirements of the contract documents which will, in the fabricator’s opinion, result
in the most economical fabrication and erection cost.
7.7.2. When the fabricator erects the structural steel, the fabricator supplies all
materials required for temporary and permanent connection of the component parts
of the structural steel.
7.7.3. When the erection of the structural steel is performed by someone other
than the fabricator, the fabricator furnishes the following field connection material:
(a)
(b)
(c)
(d)
Bolts of required size and in sufficient quantity for all field connections
of steel to steel which are to be permanently bolted. Unless high-strength
bolts or other special types of bolts and washers are specified, common
bolts are furnished. An extra 2 percent of each bolt size (diameter and
length) is furnished.
Rivets of required size and in sufficient quantity for all field connections
of steel to steel which are to be riveted field connections. An extra 10
percent of each rivet size is furnished.
Shims shown as necessary for make-up of permanent connections of steel
to steel.
Back-up bars or run-off tabs that may be required for field welding.
7.7.4. When the erection of the structural steel is performed by someone other
than the fabricator, the erector furnishes all welding electrodes, fit-up bolts and drift
pins used for erection of the structural steel.
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AISC CODE OF STANDARD PRACTICE
7.7.5. Field-installed shear connectors are supplied by the shear connector
applicator.
7.7.6. Metal deck support angles are the responsibility of the metal deck supplier.
7.8. Loose Material
Loose items of structural steel not connected to the structural frame are set by the
owner without assistance from the erector, unless otherwise specified in the contract
documents.
7.9. Temporary Support of Structural Steel Frames
7.9.1. General
Temporary supports, such as temporary guys, braces, falsework, cribbing or other
elements required for the erection operation will be determined and furnished and
installed by the erector. These temporary supports will secure the steel framing, or
any partly assembled steel framing, against loads comparable in intensity to those for
which the structure was designed, resulting from wind, seismic forces and erection
operations, but not the loads resulting from the performance of work by or the acts
of others, nor such unpredictable loads as those due to tornado, explosion or collision.
7.9.2. Self-supporting Steel Frames
A self-supporting steel frame is one that provides the required stability and
resistance to gravity loads and design wind and seismic forces without interaction
with other elements of the structure. The erector furnishes and installs only those
temporary supports that are necessary to secure any element or elements of the steel
framing until they are made stable without external support.
Special erection sequences or other considerations which are required to provide
stability during the erection process must be set out in the contract documents in
detail.
7.9.3. Non-Self-supporting Steel Frames
A non-self-supporting steel frame is one that, when fully assembled and connected,
requires interaction with other elements not classified as Structural Steel to provide
stability and strength to resist loads for which the frame is designed. Such frames
shall be clearly designated as “non-self-supporting.” The major elements not
classified as structural steel, such as steel deck diaphragms, masonry and/or concrete
shear walls, shall be identified in the contract documents.
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When elements not classified as structural steel interact with the structural steel
elements to provide stability and/or strength to resist loads, the owner is responsible
for the installation, structural adequacy during installation, and timely completion of
all such elements. The contract documents must specify the sequence and schedule
of placement of such elements and the effects of the loads imposed on the structural
steel frame by partially or completely installed interacting elements. The erector
furnishes and installs temporary support as necessary in accordance with this
information but does not thereby assume responsibility for the appropriateness of the
sequence specified.
7.9.4. Special Erection Conditions
When the design concept of a structure is dependent upon the use of shores, jacks
or loads which must be adjusted as erection progresses to set or maintain camber or
prestress, such requirement is specifically stated in the contract documents.
7.9.5. Removal of Temporary Supports
The temporary guys, braces, falsework, cribbing and other elements required for
the erection operation, which are furnished and installed by the erector, are not the
property of the owner.
In self-supporting structures, temporary supports are not required after the
structural steel for a self-supporting element is located and finally fastened within the
required tolerances. After such final fastening, the erector is no longer responsible
for temporary support of the self-supporting element and may remove the temporary
supports.
In non-self-supporting structures, the erector may remove temporary supports when
the necessary non-structural steel elements are complete. Temporary supports are not
to be removed without the consent of the erector. At completion of steel erection,
any temporary supports that are required to be left in place are removed by the owner
and returned to the erector in good condition.
7.9.6. Temporary Supports for Other Work
Should temporary supports beyond those defined as the responsibility of the erector
in Sections 7.9.1, 7.9.2 and 7.9.3 be required, either during or after the erection of the
structural steel, responsibility for the supply and installation of such supports rests
with the owner.
7.10. Temporary Floors and Handrails for Buildings
The erector provides floor coverings, handrails and walkways as required by law
and applicable safety regulations for protection of his own personnel. As work
progresses, the erector removes such facilities from units where the erection
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AISC CODE OF STANDARD PRACTICE
operations are completed, unless other arrangements are included in the contract
documents. The owner is responsible for all protection necessary for the work of
other trades. When permanent steel decking is used for protective flooring and is
installed by the owner, all such work is performed so as not to delay or interfere with
erection progress and is scheduled by the owner and installed in a sequence adequate
to meet all safety regulations. (See Section 7.2)
7.11. Frame Tolerances
7.11
7.11.1. Overall Dimensions
Some variation is to be expected in the finished overall dimensions of structural
steel frames. Such variations are deemed to be within the limits of good practice
when they do not exceed the cumulative effect of rolling tolerances, fabricating
tolerances and erection tolerances.
7.11.2. Working Points and Working Lines
Erection tolerances are defined relative to member working points and working lines
as follows:
(a)
(b)
(c)
(d)
For members other than horizontal members, the member work point is the
actual center of the member at each end of the shipping piece.
For horizontal members, the working point is the actual center line of the top
flange or top surface at each end.
Other working points may be substituted for ease of reference, providing they
are based upon these definitions.
The member working line is a straight line connecting the member working
points.
7.11.3. Position and Alignment
The tolerances on position and alignment of member working points and working
lines are as follows:
7.11.3.1. Columns
Individual column shipping pieces are considered plumb if the deviation of the
working line from a plumb line does not exceed 1:500, subject to the following
limitations:
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(a)
(b)
(c)
(d)
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The member working points of column shipping pieces adjacent to elevator
shafts may be displaced no more than 1 in. from the established column
line in the first 20 stories; above this level, the displacement may be
increased 1⁄32 in. for each additional story up to a maximum of 2 in.
The member working points of exterior column shipping pieces may be
displaced from the established column line no more than 1 in. toward nor
2 in. away from the building line in the first 20 stories; above the 20th
story, the displacement may be increased 1⁄16 in. for each additional story,
but may not exceed a total displacement of 2 in. toward nor 3 in. away
from the building line.
The member working points of exterior column shipping pieces at any
splice level for multi-tier buildings and at the tops of columns for single
tier buildings may not fall outside a horizontal envelope, parallel to the
building line, 11⁄2 in. wide for buildings up to 300 ft in length. The width
of the envelope may be increased by 1⁄2 in. for each additional 100 ft in
length, but may not exceed 3 in.
The member working points of exterior column shipping pieces may be
displaced from the established column line, in a direction parallel to the
building line, no more than 2 in. in the first 20 stories; above the 20th
story, the displacement may be increased 1⁄16 in. for each additional story,
but may not exceed a total displacement of 3 in. parallel to the building
line.
7.11.3.2. Members Other Than Columns
(a)
(b)
(c)
(d)
Alignment of members which consist of a single straight shipping piece
containing no field splices, except cantilevered members, is considered
acceptable if the variation in alignment is caused solely by the variation
of column alignment and/or primary supporting member alignment within
the permissible limits for fabrication and erection of such members.
The elevation of members connecting to columns is considered acceptable
if the distance from the member working point to the upper milled splice
line of the column does not deviate more than plus 3⁄16 in. or minus 5⁄16 in.
from the distance specified on the drawings.
The elevation of members which consist of a single shipping piece, other
than members connected to columns, is considered acceptable if the
variation in actual elevation is caused solely by the variation in elevation
of the supporting members which are within permissible limits for
fabrication and erection of such members.
Individual shipping pieces which are segments of field assembled units
containing field splices between points of support are considered plumb,
level and aligned if the angular variation of the working line of each
shipping piece relative to the plan alignment does not exceed 1:500.
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(e)
(f)
AISC CODE OF STANDARD PRACTICE
The elevation and alignment of cantilevered members shall be considered
plumb, level and aligned if the angular variation of the working line from
a straight line extended in the plan direction from the working point at its
supported end does not exceed 1:500.
The elevation and alignment of members which are of irregular shape shall
be considered plumb, level and aligned if the fabricated member is within
its tolerance and its supporting member or members are within the
tolerances specified in this Code.
7.11.3.3. Adjustable Items
The alignment of lintels, wall supports, curb angles, mullions and similar
supporting members for the use of other trades, requiring limits closer than the
foregoing tolerances, cannot be assured unless the owner’s plans call for adjustable
connections of these members to the supporting structural frame. The fabricator may
provide nonadjustable connections unless the contract documents specifically show
or specify them as adjustable. When adjustable connections are specified, the owner’s
plans must provide for the total adjustment required to accommodate the tolerances
on the steel frame for the proper alignment of these supports for other trades. The
tolerances on position and alignment of such adjustable items are as follows:
(a)
(b)
(c)
Adjustable items are considered to be properly located in their vertical
position when their location is within 3⁄8 in. of the location established
from the upper milled splice line of the nearest column to the support
location as specified on the drawings.
Adjustable items are considered to be properly located in their horizontal
position when their location is within 3⁄8 in. of the proper location relative
to the established finish line at any particular floor.
The ends of adjustable items which abut are considered to be properly
located when aligned to within 3⁄16 in. of each other both vertically and
horizontally.
7.11.4. Responsibility for Clearances
In the design of steel structures, the owner is responsible for providing clearances
and adjustments of material furnished by other trades to accommodate all of the
foregoing tolerances of the structural steel frame.
7.11.5. Acceptance of Position and Alignment
Prior to placing or applying any other materials, the owner is responsible for
determining that the location of the structural steel is acceptable for plumbness, level
and alignment within tolerances. The erector is given timely notice of acceptance by
the owner or a listing of specific items to be corrected in order to obtain acceptance.
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Such notice is rendered immediately upon completion of any part of the work and
prior to the start of work by other trades that may be supported, attached or applied
to the structural steelwork.
7.12. Correction of Errors
Normal erection operations include the correction of minor misfits by moderate
amounts of reaming, chipping, welding or cutting, and the drawing of elements into
line through the use of drift pins. Errors which cannot be corrected by the foregoing
means, or which require major changes in member configuration, are reported
immediately to the owner and fabricator by the erector, to enable whoever is
responsible either to correct the error or to approve the most efficient and economic
method of correction to be used by others.
7.13. Cuts, Alterations and Holes for Other Trades
Neither the fabricator nor the erector will cut, drill or otherwise alter his work, or
the work of other trades, to accommodate other trades, unless such work is clearly
specified in the contract documents. Whenever such work is specified, the owner is
responsible for furnishing complete information as to materials, size, location and
number of alterations in a timely manner so that the preparation of shop drawings will
not be delayed.
7.14. Handling and Storage
The erector takes reasonable care in the proper handling and storage of steel during
erection operations to avoid accumulation of excess dirt and foreign matter. The
erector is not responsible for removal from the steel of dust, dirt or other foreign
matter which accumulates during the erection period as the result of site conditions
or exposure to the elements.
7.15.
Field Painting
The erector does not paint field bolt heads and nuts, field rivet heads and field
welds, nor touch up abrasions of the shop coat, nor perform any other field painting.
7.16. Final Cleaning Up
Upon completion of erection and before final acceptance, the erector removes all
of his falsework, rubbish and temporary buildings.
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AISC CODE OF STANDARD PRACTICE
SECTION 8. QUALITY CONTROL
8.1. General
8.1.1. The fabricator maintains a quality control program to the extent deemed
necessary so that the work is performed in accordance with this Code, the AISC
Specification, and contract documents. The fabricator has the option to use the AISC
Quality Certification Program in establishing and administering the quality control
program.
8.1.2. The erector maintains a quality control program to the extent the erector
deems necessary so that all of the work is performed in accordance with this Code,
the AISC Specification and the contract documents. The erector shall be capable of
performing the erection of the structural steel, and shall provide the equipment,
personnel and management for the scope, magnitude and required quality of each
project.
8.1.3. When the owner requires more extensive quality control or independent
inspection by qualified personnel, or requires the fabricator to be certified by the
AISC Quality Certification Program, this shall be clearly stated in the contract
documents, including a definition of the scope of such inspection.
8.2. Mill Material Inspection
The fabricator customarily makes a visual inspection, but does not perform any
material tests, depending upon mill reports to signify that the mill product satisfies
material order requirements. The owner relies on mill tests required by contract and
on such additional tests as he orders the fabricator to have made at the owner’s
expense. If mill inspection operations are to be monitored, or if tests other than mill
tests are desired, the owner so specifies in the contract documents and should arrange
for such testing through the fabricator to assure coordination.
8.3. Non-Destructive Testing
When non-destructive testing is required, the process, extent, technique and
standards of acceptance are clearly defined in the contract documents.
8.4. Surface Preparation and Shop Painting Inspection
Surface preparation and shop painting inspection must be planned for acceptance
of each operation as completed by the fabricator. Inspection of the paint system,
including material and thickness, is made promptly upon completion of the paint
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application. When wet film thickness is inspected, it must be measured during the
application.
8.5. Independent Inspection
When contract documents specify inspection by other than the fabricator’s and
erector’s own personnel, both parties to the contract incur obligations relative to the
performance of the inspection.
8.5.1. The fabricator and erector provide the inspector with access to all places
where work is being done. A minimum of 24 hours notification is given prior to
commencement of work.
8.5.2. Inspection of shop work by the owner or his representative is performed
in the fabricator’s shop to the fullest extent possible. Such inspections should be in
sequence, timely, and performed in such a manner as will not disrupt fabrication
operations and will permit repair of non-conforming work prior to any required
painting while the material is still in process in the fabrication shop.
8.5.3. Inspection of field work must be completed promptly so that corrections
can be made without delaying the progress of the work.
8.5.4. Rejection of material or workmanship not in conformance with the contract
documents may be made at any time during the progress of the work. However, this
provision does not relieve the owner of his obligation for timely, in-sequence
inspections.
8.5.5. Copies of all reports prepared by the owner’s inspection representative
must be given to the fabricator and erector immediately after the inspection to allow
any necessary corrective work to be performed in a timely manner.
8.5.6. The owner’s inspection representative may not suggest, direct, or approve
the fabricator or erector to deviate from the contract documents or approved shop
drawings, or approve such deviation, without the express written approval of the
engineer of record or the person designated as the owner’s authorized representative.
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AISC CODE OF STANDARD PRACTICE
SECTION 9. CONTRACTS
9.1. Types of Contracts
9.1.1. For contracts stipulating a lump sum price, the work required to be
performed by the fabricator and erector is completely defined by the contract
documents.
9.1.2. For contracts stipulating a price per pound, the scope of work, type of
materials, character of fabrication, and conditions of erection are based upon the
contract documents which must be representative of the work to be performed.
9.1.3. For contracts stipulating a price per item, the work required to be
performed by the fabricator and erector is based upon the quantity and the character
of items described in the contract documents.
9.1.4. For contracts stipulating unit prices for various categories of structural
steel, the scope of the work required to be performed by the fabricator and erector is
based upon the quantity, character and complexity of the items in each category as
described in the contract documents. The contract documents must be representative
of the work to be done in each category.
9.2. Calculation of Weights
Unless otherwise set forth in the contract, on contracts stipulating a price per
pound for fabricated structural steel delivered and/or erected, the quantities of
materials for payment are determined by the calculation of gross weight of materials
as shown on the shop drawings.
9.2.1. The unit weight of steel is assumed to be 490 pounds per cubic ft. The
unit weight of other materials is in accordance with the manufacturer’s published data
for the specific product.
9.2.2. The weights of shapes, plates, bars, steel pipe and structural tubing are
calculated on the basis of shop drawings showing actual quantities and dimensions
of material furnished, as follows:
(a)
(b)
The weight of all structural shapes, steel pipe and structural tubing is
calculated using the nominal weight per ft and the detailed overall length.
The weight of plates and bars is calculated using the detailed overall
rectangular dimensions.
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(d)
(e)
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When parts can be economically cut in multiples from material of larger
dimensions, the weight is calculated on the basis of the theoretical
rectangular dimensions of the material from which the parts are cut.
When parts are cut from structural shapes, leaving a non-standard section
not useable on the same contract, the weight is calculated on the basis of
the nominal unit weight of the section from which the parts are cut.
No deductions are to be made for material removed by cuts, copes, clips,
blocks, drilling, punching, boring, slot milling, planing or weld joint
preparation.
9.2.3. The calculated weights of castings are determined from the shop drawings
of the pieces. An allowance of 10 percent is added for fillets and overrun. Scale
weights of rough castings may be used if available.
9.2.4. The items for which weights are shown in tables in the AISC Manual of
Steel Construction are calculated on the basis of tabulated unit weights.
9.2.5. The weight of items not included in the tables in the AISC Manual of Steel
Construction shall be taken from the manufacturers’ catalog and the manufacturers’
shipping weight shall be used.
9.2.6. The weight of shop or field weld metal and protective coatings is not
included in the calculated weight for pay purposes.
9.3. Revisions to Contract Documents
9.3.1. Revisions to the contract are made by issuance of new documents or reissuance of existing documents. In either case, all revisions, including revisions
communicated by annotation of shop or erection drawings, must be clearly and
individually indicated and the documents dated and identified by revision number.
All contract drawings shall be identified by the same drawing number throughout the
duration of the job regardless of the revision. The engineer of record is responsible
for reviewing the overall structural design to identify all components which will be
affected by a change to any individual component.
9.3.2. A revision to the requirements of the contract documents is made by
change order, extra work order, or notations on the shop and erection drawings when
returned upon approval.
9.3.3. Unless specifically stated to the contrary, the issuance of a revision is
authorization by the owner to release these documents for construction.
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AISC CODE OF STANDARD PRACTICE
9.4. Contract Price Adjustment
9.4.1. When the scope of work and responsibilities of the fabricator and erector
are changed from those previously established by the contract documents, an
appropriate modification of the contract price is made. In computing the contract
price adjustment, the fabricator and erector consider the quantity of work added or
deleted, modifications in the character of the work, and the timeliness of the change
with respect to the status of material ordering, detailing, fabrication and erection
operations.
9.4.2. Requests for contract price adjustments are presented by the fabricator and
erector in a timely manner and are accompanied by a description of the change in
sufficient detail to permit evaluation and timely approval by the owner.
9.4.3. Price per pound and price per item contracts generally provide for
additions or deletions to the quantity of work prior to the time work is released for
construction. Changes to the character of the work, at any time, or additions and/or
deletions to the quantity of the work after it is released for detailing, fabrication, or
erection, may require a contract price adjustment.
9.5. Scheduling
9.5.1. The contract documents specify the schedule for the performance of the
work. This schedule states when the “released for construction” plans will be issued
and when the job site, foundations, piers and abutments will be ready, free from
obstructions and accessible to the erector, so that erection can start at the designated
time and continue without interference or delay caused by the owner or other trades.
9.5.2. The fabricator and erector have the responsibility to advise the owner, in
a timely manner, of the effect any revision has on the contract schedule.
9.5.3. If the fabrication or erection is significantly delayed due to design
revisions, or for other reasons which are the owner’s responsibility, the fabricator and
erector are compensated for additional costs incurred.
9.6. Terms of Payment
The terms of payment for the contract shall be outlined in the contract documents.
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SECTION 10. ARCHITECTURALLY EXPOSED STRUCTURAL STEEL
10.1. Scope
This section of the Code defines additional requirements which apply only to
members specifically designated by the contract documents as “Architecturally
Exposed Structural Steel” (AESS). All provisions of Sections 1 through 9 of the
Code apply unless specifically modified in this section. AESS members or
components are fabricated and erected with the care and dimensional tolerances
indicated in this section.
10.2. Additional Information Required in Contract Documents
(a)
(b)
(c)
Specific identification of members or components which are to be AESS.
Fabrication and erection tolerances which are more restrictive than provided
for in this section.
Requirements, if any, of a test panel or components for inspection and
acceptance standards prior to the start of fabrication.
10.3. Fabrication
10.3.1. Rolled Shapes
Permissible tolerances for out-of-square or out-of-parallel, depth, width and
symmetry of rolled shapes are as specified in ASTM Specification A6. No attempt
to match abutting cross-sectional configurations is made unless specifically required
by the contract documents. The as-fabricated straightness tolerances of members are
one-half of the standard camber and sweep tolerances in ASTM A6.
10.3.2. Built-up Members
The tolerances on overall profile dimensions of members made up from a series
of plates, bars and shapes by welding are limited to the accumulation of permissible
tolerances of the component parts as provided by ASTM Specification A6. The asfabricated straightness tolerances for the member as a whole are one-half the standard
camber and sweep tolerances for rolled shapes in ASTM A6.
10.3.3. Weld Show-through
It is recognized that the degree of weld show-through, which is any visual
indication of the presence of a weld or welds on the side away from the viewer, is
a function of weld size and material thickness. The members or components will be
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AISC CODE OF STANDARD PRACTICE
acceptable as produced unless specific acceptance criteria for weld show-through are
included in the contract documents.
10.3.4. Joints
All copes, miters and butt cuts in surfaces exposed to view are made with uniform
gaps of 1⁄8 in. if shown to be open joints, or in reasonable contact if shown without
gap.
10.3.5. Welding
Reasonably smooth and uniform as-welded surfaces are acceptable on all welds
exposed to view. Butt and plug welds do not project more than 1⁄16 in. above the
exposed surface. No finishing or grinding is required except where clearances or fit
of other components may necessitate, or when specifically required by the contract
documents.
10.3.6. Weathering Steel
Members fabricated of weathering steel which are to be AESS shall not have
erection marks or other painted marks on surfaces that are to be exposed in the
completed structure. If cleaning other than SSPC-SP6 is required, these requirements
shall be defined in the contract documents.
10.4. Delivery of Materials
The fabricator uses special care to avoid bending, twisting or otherwise distorting
individual members.
10.5. Erection
10.5.1. General
The erector uses special care in unloading, handling and erecting the steel to avoid
marking or distorting the steel members. Care is also taken to minimize damage to
any shop paint. If temporary braces or erection clips are used, care is taken to avoid
unsightly surfaces upon removal. Tack welds are ground smooth and holes are filled
with weld metal or body solder and smoothed by grinding or filing. The erector
plans and executes all operations in such a manner that the close fit and neat
appearance of the structure will not be impaired.
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10.5.2. Erection Tolerances
Unless otherwise specifically designated in the contract documents, members and
components are plumbed, leveled and aligned to a tolerance not to exceed one-half
the amount permitted for structural steel. These erection tolerances for AESS require
that the owner’s plans specify adjustable connections between AESS and the
structural steel frame or the masonry or concrete supports, in order to provide the
erector with means for adjustment.
10.5.3. Components with Concrete Backing
When AESS is backed with concrete, it is the general contractor’s responsibility to
provide sufficient shores, ties and strongbacks to assure against sagging, bulging,
etc., of the AESS resulting from the weight and pressure of the wet concrete.
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Commentary on the
Code of Standard Practice
for Steel Buildings and Bridges
Adopted Effective June 10, 1992
American Institute of Steel Construction, Inc.
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PREFACE
This Commentary has been prepared to assist those who use the Code of Standard
Practice in understanding the background, basis and intent of its provisions.
Each section in the Commentary is referenced by corresponding sections in the
Code. Not all sections of the Code are discussed; sections are covered only if it is
believed that additional explanation may be helpful.
While every precaution has been taken to insure that all data and information
presented is as accurate as possible, the Institute cannot assume responsibility for
errors or oversights in the information published herein or the use of the information
published or incorporating such information in the preparation of detailed engineering
plans. The figures are for illustrative purposes only and are not intended to be
applicable to any actual design. The information should not replace the judgment of
an experienced architect or engineer who has the responsibility of design for a
specific structure.
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Commentary on the
Code of Standard Practice
for Steel Buildings and Bridges
Adopted Effective June 10, 1992
American Institute of Steel Construction, Inc.
SECTION 1. GENERAL PROVISIONS
1.1. Scope
This Code is not applicable to metal building systems, which are the subject of
standards published by the Metal Building Manufacturers Association in their Metal
Building Systems Manual. AISC has not participated in the development of the
MBMA code and, therefore, takes no position and is not responsible for any of its
provisions.
This Code is not applicable to standard steel joists, which are the subject of
Recommended Code of Standard Practice for Steel Joists, published by the Steel Joist
Institute. AISC has not participated in the development of the SJI code and,
therefore, takes no position and is not responsible for any of its provisions.
SECTION 2. CLASSIFICATION OF MATERIALS
2.2. Other Steel or Metal Items
These items include materials which may be supplied by the steel fabricator which
require coordination between other material suppliers and trades. If they are to be
supplied by the fabricator, they must be specifically called for and detailed in contract
documents.
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AISC CODE OF STANDARD PRACTICE
SECTION 3. PLANS AND SPECIFICATIONS
3.1. Structural Steel
Project specifications vary greatly in complexity and completeness. There is a
benefit to the owner if the specifications leave the contractor reasonable latitude in
performing his work. However, critical requirements affecting the integrity of the
structure, or necessary to protect the owner’s interest, must be covered in the contract
documents. The following checklist is included for reference:
Standard codes and specifications governing structural steelwork
Material specifications
Mill test reports
Welded joint configuration
Weld procedure qualification
Bolting specifications
Special requirements for work of other trades
Runoff tabs
Wind bracing
Connections or data for connection development
Column stiffeners
Column web doubler plates
Bearing stiffeners on beams and girders
Web reinforcement
Openings for other trades
Surface preparation and shop painting
Shop inspection
Field inspection
Non-destructive testing, including acceptance criteria
Special requirements on delivery
Special erection limitations
Temporary bracing for non-self-supporting structures
Special fabrication and erection tolerances for AESS
Special pay weight provisions
The structural steel plans must provide the elevations of all members as well as the
dimensions to the centerline of all members (or the backs of angles or channels)
relative to the grid lines, column centerline or other nearby members unless the
locations of those members must be coordinated by the general contractor with the
requirements of another trade. When the necessary dimensions are not given, the
fabricator is not in a position to order material or start shop drawings in a timely
manner and may be delayed while attempting to get the information.
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SECTION 4. SHOP AND ERECTION DRAWINGS
4.1. Owner’s Responsibility
The owner’s responsibility for the proper planning of the work and the communication of all facts of his particular project is a requirement of the Code, not only
at the time of bidding, but also throughout the term of any project. The contract
documents, including the plans and specification, are for the purpose of
communication. It is the owner’s responsibility to properly define the scope of work,
and to define information or items required and outlined in the plans and
specifications. When the owner releases plans and specifications for construction, the
fabricator and erector rely on the fact that these are the owner’s requirements for his
project.
The Code defines the owner as including a designated representative such as the
architect, engineer or project manager, and when these representatives direct specific
action to be taken, they are acting as and for the owner.
On phased construction projects, to insure the orderly flow of material procurement, detailing, fabrication and erection activities, it is essential that designs are not
continuously revised after progressive releases for construction are made. In essence,
once a portion of a design is released for construction, the essential elements of that
design should be “frozen” to assure adherence to the construction schedule or all
parties should reach an understanding on the effects of future changes as they affect
scheduled deliveries and added costs, if any.
4.2. Approval
4.2.1. From the inception of the Code of Standard Practice, AISC and the
industry in general have recognized that the engineer of record is the only individual
who has all the information necessary to evaluate the total impact of connection
details on the overall structural design of the project. This authority has traditionally
been exercised during the approval process for shop and erection drawings. The EOR
has retained the final and total responsibility for the adequacy and safety of the entire
structure since at least the 1927 edition of the Code of Standard Practice. In those
instances where a fabricator develops the detailed configuration of connections during
the preparation of shop drawings, the fabricator does not thereby become responsible
for the structural integrity of that part of the overall structure.
In the first issue of the Code, as printed in the first AISC Manual in 1927, this was
stated as “Shop Drawings prepared by the Seller and approved by a representative of
the Buyer shall be deemed the correct interpretation of the work to be done, but does
not relieve the Seller of responsibility for the accuracy of details.” This statement
was modified in the 1952 revision of the Code to read “...the owner must return one
set of prints to the fabricator with a notation of the owner’s outright approval or
approval subject to corrections as noted.” In 1972 the Code stated “Approval by the
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AISC CODE OF STANDARD PRACTICE
owner of shop drawings prepared by the fabricator indicates that the fabricator has
correctly interpreted the contract requirements, and that any connections designed by
the fabricator are of adequate capacity for the design requirements.” The Code was
again modified in 1976 saying “Approval by the owner of shop drawings prepared by
the fabricator indicates that the fabricator has correctly interpreted the contract
requirements. This approval constitutes the owner’s acceptance of all responsibility
for the design adequacy of any connection designed by the fabricator as a part of his
preparation of these shop drawings.” This statement was not changed in the 1986
revision of the Code.
The current revision of Paragraph 4.2.1 of the Code is intended to clarify the use
of the word “Owner.” Consequently, the term “owner” has been replaced by “owner’s
authorized representative,” usually meaning the engineer of record. The continuing
concept that the structural engineer of record is the sole individual who can best
assure the safety of the completed structure has not been modified. This system has
worked well for at least the past 65 years, and has achieved a commendable safety
record where its principles have been steadfastly applied.
In the preparation of contract drawings, the engineer of record (EOR) has two
basic choices in the showing of connection details. The EOR may fully design and
detail connections for all conditions. However, in order to allow the owner to benefit
from the economies inherent in allowing the fabricator to choose the most efficient
connections for the fabricator’s shop and erection processes, the EOR may allow the
fabricator to select the types of connection and show them in complete detail on the
shop drawings for the EOR’s approval. In either case, the approval of the shop
drawings by the owner’s authorized representative constitutes acceptance by the
owner’s authorized representative of design responsibility for the structural adequacy
of the connections shown on the shop drawings. Contracts attempting to share or
allocate design responsibility are strongly discouraged. Individual state codes and
licensing requirements may vary widely in allowing such allocation of responsibility.
Should the engineer of record elect to fully design and detail connections on the
contract documents, the EOR has the obligation to show all fastener sizes,
arrangement, quantities and grades, as well as all connection material and weld types,
sizes and lengths for each individual member or part to be joined. All requirements
for bracing details, stiffeners, doublers, web or cope reinforcement or similar items
necessary for the completeness of the design must be sized and shown in complete
detail. The fabricator is responsible for correctly reflecting this information in the
preparation of shop drawings. Should the fabricator wish to deviate from these
specific details or call a problem to the attention of the engineer of record, the
fabricator must either do so in writing prior to the preparation of shop drawings, or
clearly note the deviation on the drawings submitted for approval. This requirement
is not intended in any way to negate the responsibility of the owner’s authorized
representative to review completely each shop drawing for structural adequacy during
the approval process.
If the engineer of record does not show fully designed and detailed connections on
the contract documents and allows the fabricator to select connection types when
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detailing shop drawings, the contract documents must give all reactions, moments, or
other forces required for each individual member of parts to be joined so that when
preparing shop drawings, the fabricator’s detailers and checkers may determine the
appropriate connection either by selection from tables shown in AISC publications or
by simple calculation. The fabricator can assume that the reactions, moments or other
forces given by the engineer are appropriate for the loads to be applied to the
structure. All requirements for bracing details, stiffeners, doublers, web or cope
reinforcement or similar items necessary for the completeness of the design must be
shown in sufficient detail so as to allow the fabricator to submit an accurate estimate
of cost at the time of bid.
It is suggested that highly complex connections be fully designed on the contract
documents or developed in a timely manner by the EOR after consulting with the
fabricator regarding accepted, current and standard practices for fabrication and
erection so that the detailing and fabricating processes will not be delayed. In the
latter case, a pre-detailing meeting between the EOR and the fabricator may be
appropriate to facilitate this exchange of information. In the event that design loads
or other information necessary for development of connections is not shown on the
contract documents, this information must be furnished to the fabricator in a timely
manner.
If the engineer of record elects to utilize typical details which must be interpreted
or modified by the fabricator to meet conditions occurring in a structure, such
interpretation is forwarded to the engineer of record for review and approval by way
of detail or shop drawing submittals.
Where state codes and licensing requirements allow fabricators to design and
fabricate complete steel structures, and a fabricator has contracted to provide such
services, submittals to the owner or applicable public reviewing authority will
normally include only those documents customarily submitted by licensed design
professionals on comparable projects within the same licensing jurisdiction.
SECTION 5. MATERIALS
5.1. Mill Materials
The fabricator may purchase materials in stock lengths, exact lengths or multiples
of exact lengths to suit the dimensions shown on the contract drawings. Such
purchases will normally be job-specific in nature and may not be capable of being
utilized on other projects or returned for full credit if subsequent design changes make
these materials unsuitable for their originally intended use. The fabricator should
be paid for these materials upon delivery from the mill, subject to appropriate additional
payment or credit if subsequent unanticipated modification or reorder is required.
Purchasing materials to exact lengths is not considered fabrication.
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AISC CODE OF STANDARD PRACTICE
5.1.2. Mill dimensional tolerances are completely set forth as part of ASTM A6.
Variation in cross sectional geometry of rolled members must be recognized by the
designer, the fabricator and erector (see Fig. 1). Such tolerances are mandatory
because roll wear, thermal distortions of the hot cross section immediately after
leaving the forming rolls, and differential cooling distortions that take place on the
cooling beds are economically beyond precise control. Absolute perfection of cross
sectional geometry is not of structural significance and, if the tolerances are
recognized and provided for, also not of architectural significance. ASTM A6 also
stipulates straightness and camber tolerances which are adequate for most
conventional construction. However, these characteristics may be controlled or
corrected to closer tolerances during the fabrication process when the unique demands
of a particular project justify the added cost.
+ 1/ 4
– 3/16
Actual section
½B ± 3/16 ½ 3
B /16
T
C = d+ ¼ max.
A = d ± 1/ 8
d
C = d + ¼ max.
T1
T1
Theoretical section
T1
bf
T
f
C = d + ¼ max.
B=b
±
Typical
Typical
Typical
Typical ½B± 3/16 ½B 3/16
±
T + T ′ — For sections 12 ″ and under - ¼ ″ max.
B — Actual flange width
A — Actual depth at cL web
C — Actual depth overall
For sections over 12 ″ — 5/15 ″ max.
bf — Theoretical flange width
d — Theoretical depth
T & T ′ — Tilt of flange
Fig. 1. Mill tolerances on cross-section dimensions
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SECTION 6. FABRICATION AND DELIVERY
6.4. Dimensional Tolerances
Fabrication tolerances are stipulated in several specification documents, each
applicable to a special area of construction. Basic fabrication tolerances are stipulated
in Sections 6.4 and 10 of the Code and Section M2.7 of the AISC Specification.
Other specifications and codes frequently incorporated by reference in the contract
documents are the AWS Structural Welding Code and AASHTO Standard
Specifications for Highway Bridges.
6.4.5. Due to the release of stresses, there is no known way to verify camber
once members are received in the field. Camber may only be measured in the
fabrication shop in the unstressed condition and does not take into account the dead
weight of the member, the restraint caused by the end connections in the erected state
or any dead load which may be intended to be applied.
6.5. Shop Painting
6.5.2., 6.5.3. The selection of a paint system is a design decision involving many
factors including owner’s preference, service life of the structure, severity of
environmental exposure, cost of both initial application and future renewals, and
compatibility of the various components comprising the paint system, i.e., surface
preparation, prime coat and subsequent coats.
Because inspection of shop painting needs to be concerned with workmanship at
each stage of the operation, the fabricator provides notice of the schedule of
operations and affords access to the work site to inspectors. Inspection must be
coordinated with that schedule in such a way as to avoid delay of the scheduled
operations.
Acceptance of the prepared surface must be made prior to application of the prime
coat because the degree of surface preparation cannot be readily verified after
painting. Time delay between surface preparation and application of the prime coat
can result in unacceptable deterioration of a properly prepared surface, necessitating
a repetition of surface preparation. This is especially true with blast-cleaned surfaces.
Therefore, to avoid potential deterioration of the surface it is assumed that surface
preparation is accepted unless it is inspected and rejected prior to the scheduled
application of the prime coat.
The prime coat in any paint system is designed to maximize the wetting and
adherence characteristics of the paint, usually at the expense of its weathering
capabilities. Deterioration of the shop paint normally begins immediately after
exposure to the elements and worsens as the duration of exposure is extended.
Consequently, extended exposure of the prime coat to weather or to a corrosive
atmosphere will lead to its deterioration and may necessitate repair, possibly including
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AISC CODE OF STANDARD PRACTICE
repetition of surface preparation and primer application in limited areas. With the
introduction of high performance paint systems, delay in the application of the prime
coat has become more critical. High performance paint systems generally require a
greater degree of surface preparation, as well as early application of weathering
protection for the prime coat.
Since the fabricator does not control the selection of the paint system, the
compatibility of the various components of the total paint system, nor the length of
exposure of the prime coat, he cannot guarantee the performance of the prime coat
or any other part of the system. Rather, the fabricator is responsible only for
accomplishing the specified surface preparation and for applying the shop coat or
coats in accordance with the contract documents.
Section 6.5.2 stipulates cleaning the steel to the requirements of SSPC-SP2. This
section is not meant as an exclusive cleaning level, but rather that level of surface
preparation which will be furnished if the steel is to be painted and if the job
specifications are silent or do not require more stringent surface preparation
requirements.
Further information regarding shop painting is available in A Guide to Shop
Painting of Structural Steel, published jointly by the Steel Structures Painting Council
and the American Institute of Steel Construction.
6.5.4. Extended exposure of unpainted steel which has been cleaned for
subsequent fire protection material application can be detrimental to the fabricated
product. Most levels of cleaning require the removal of all loose mill scale, but
permit some amount of “tightly adhering mill scale.” When a piece of structural steel
which has been cleaned to an acceptable level is left exposed to a normal
environment, moisture can penetrate behind the scale, and some “lifting” of the scale
by the oxidation products is to be expected. Cleanup of “lifted” mill scale is not the
responsibility of the fabricator, but is assigned by contract requirement to an
appropriate contractor.
Section 6.5.4 of the Code is not applicable to weathering steel, for which special
cleaning specifications are always required in the contract documents.
SECTION 7. ERECTION
7.5. Installation of Anchor Bolts and Embedded Items
7.5.1. While the general contractor must make every effort to set anchor bolts
accurately to theoretical drawing dimensions, minor deviations may occur. The
tolerances set forth in this section were compiled from data collected from general
contractors and erectors. They can be attained by using reasonable care and will
ordinarily allow the steel to be erected and plumbed to required tolerances. If special
conditions require closer tolerances, the contractor responsible for setting the anchor
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bolts should be so informed by the contract documents. When anchor bolts are set
in sleeves, the adjustment provided may be used to satisfy the required anchor bolt
setting tolerances.
The tolerances established in this section of the Code have been selected to be
compatible with oversize holes in base plates, as recommended in the AISC textbook
Detailing for Steel Construction.
An anchor bolt group is the set of anchor bolts which receive a single fabricated
steel shipping piece.
The established column line is the actual field line most representative of the
centers of the as-built anchor bolt groups along a line of columns. It must be straight
or curved as shown on the plans.
7.6. Bearing Devices
The 1⁄8 in. tolerance on elevation of bearing devices relative to established grades
is provided to permit some variation in setting bearing devices and to account for
attainable accuracy with standard surveying instruments. The use of leveling plates
larger than 22 in. × 22 in. is discouraged and grouting is recommended with larger
sizes. For purposes of erection stability, the use of leveling nuts is discouraged when
base plates have less than four (4) anchor bolts.
7.9.3. Non Self-Supporting Steel Frames
To rationally provide temporary supports and/or bracing, the erector must be
informed by the owner of the sequence of installation and the effect of loads imposed
by such elements at various stages during the sequence until they become effective.
The overall strength and stability of a non self-supporting steel frame may be
dependent upon the installation of non-structural steel elements such as concrete floor
diaphragms, concrete or masonry shear walls, precast concrete facade pieces, etc.
The requirement for these elements to be in place to provide overall strength and
stability for the structural steel frame should be made clear in the contract documents
in order that the need for temporary support may be clearly understood. For example,
precast tilt-up slabs or channel slab facia elements which depend upon attachment to
the steel frame for stability against overturning due to eccentricity of their gravity
load may induce significant unbalanced lateral forces on the bare steel frame when
partially installed.
7.11. Framing Tolerances
The erection tolerances defined in this section of the Code have been developed
through long-standing usage as practical criteria for the erection of structural steel.
Erection tolerances were first defined by AISC in its Code of Standard Practice of
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AISC CODE OF STANDARD PRACTICE
October, 1924 in Section 7 (f), “Plumbing Up.” With the changes that took place in
the types and use of materials in building construction after World War II, and the
increasing demand by architects and owners for more specific tolerances, AISC
adopted new standards for erection tolerances in Section 7 (h) of the March 15, 1959
edition of the Code. Experience has proven that those tolerances can be economically
obtained.
The current requirements were first published in the October 1,1972 edition of the
Code. They provide an expanded set of criteria over earlier Code editions. The basic
premise that the final accuracy of location of any specific point in a structural steel
frame results from the combined mill, fabrication and erection tolerances, rather than
from the erection tolerances alone, remains unchanged in this edition of the Code.
However, to improve clarity, pertinent standard fabrication tolerances are now
stipulated in Section 7.11, rather than by reference to the AISC Specification as in
previous editions. Additionally, expanded coverage has been given to the definition
of working points and working lines governing measurements of the actual steel
location. Illustrations for defining and applying the applicable Code tolerances are
provided in this Commentary.
The recent trend in building work is away from built-in-place construction wherein
compatibility of the frame and the facade or other collateral materials is automatically
provided for by the routine procedures of the crafts. Building construction today
frequently incorporates prefabricated components wherein large units are developed
with machine-like precision to dimensions that are theoretically correct for a perfectly
aligned steel frame with ideal member cross sections. This type of construction has
made the magnitude of the tolerances allowed for structural steel building frames
increasingly of concern to owners, architects and engineers. This has led to the
inclusion in job specifications of unrealistically small tolerances, which indicate a
general lack of recognition of the effects of the accumulation of dead load, temperature effects and mill, fabrication and erection tolerances. Such tolerances are not
economically feasible and do not measurably increase the structure’s functional value.
This edition of the Code incorporates tolerances previously found to be practical and
presents them in a precise and clear manner. Actual application methods have been
considered and the application of the tolerance limitations to the actual structure have
been defined.
7.11.3. Position and Alignment
The limitations described in Section 7.11.3.1 and illustrated in Figs. 2 and 3 make
it possible to maintain built-in-place or prefabricated facades in a true vertical plane
up to the 20th story, if connections which provide for 3 in. adjustment are used.
Above the 20th story, the facade may be maintained within 1⁄16 in. per story with a
maximum total deviation of 1 in. from a true vertical plane, if the 3 in. adjustment
is provided.
Section 7.11.3.1(c) limits the position of exterior column working points at any
given splice elevation to a narrow horizontal envelope parallel to the building line
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(see Fig. 4). This envelope is limited to a width of 11⁄2 in., normal to the building
line, in up to 300 ft of building length. The horizontal location of this envelope is
not necessarily directly above or below the corresponding envelope at the adjacent
splice elevations, but should be within the limitation of the 1:500 allowable tolerance
in plumbness of the controlling columns (see Fig. 3).
Connections permitting adjustments of plus 2 in. to minus 3 in. (5 in. total) will be
necessary in cases where the architect or owner insists upon attempting to
construct the facade to a true vertical plane above the 20th story.
Usually there is a differential shortening of the internal versus the external columns
during construction, due to non-uniform rate of accumulation of dead load stresses
(see Fig. 5). The amount of such differential shortening is indeterminate because it
varies dependent upon construction sequence from day to day as the construction
progresses, and does not reach its maximum shortening until the building is in
service. When floor concrete is placed while columns are supporting different
percentages of their full design loads, the floor must be finished to slopes established
by measurements from the tops of beams at column connections. The effects of
B
/2 + h/1000 +Tp
W.P.
E.C.L.
L
C
/ 2 + h/1000 + Ta
Tp Tp
E.C.L.
C
L
/2 + h/1000 +Tp
Envelope of actual
location of working
points to established
column line.
See Fig. 3
Ta Tt
C
/ 2 + h/1000
C
L
L
/ 2 + h/1000
/2 + h/1000 B/2 + h/1000
/ 2 + h/1000 + Tt
Minimum clearance
envelope
B
B
L
L
For enclosures or attachments which
may follow column alignment
L
For enclosures or attachments which
must be held to precise plan location
L = Actual c to c columns = Plan dimension ± column
cross section tolerance ± beam length tolerance.
Ta = Plumbness tolerance away from building line (varies, see Fig. 3)
Tt = Plumbness tolerance toward building line (varies, see Fig. 3)
Tp = Plumbness tolerance parallel to building line (= Ta )
Fig. 2. Clearance required to accommodate accumulated column tolerances
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AISC CODE OF STANDARD PRACTICE
3″
2″
Slope 1/16 ″
per story
20th Fl
2″
Plumb
Elev. varies
Slope 1/ 500
1″
Established column line
Building line
36th Fl.
Splice
Braced
point
W.P.
Maximum out-of-plumb of individual
shipping piece as defined by straight
line between working points ≤ 1/500
Maximum out-of-straightness between
braced points L/1000 where L is
distance between braced points.
Braced
point
Splice
W.P.
Braced
point
Individual column sections within
envelope defined at left
Established column line
Elev. varies
Slope 1/500
Slope 1/ 500
¼
¼
Tolerance on location
of W.P. at base
Envelope within which all
working points must fall
Note: The plumb line thru the base working point for an individual column is not
necessarily the precise plan location because Section 7.11.3.1 deals only
with plumbness tolerance and does not include inaccuracies in location of
established column line, foundations and anchor bolts beyond the erector’s
control.
Fig. 3. Exterior column plumbness tolerances normal to building line
Building line
Ta Tt
E
Established
Column lines
Maximum envelope for working points of all columns at any given elevation
E = 1½ ″ for up to 300 ′of length, over 300 ′ add ½ ″ for each 100 ′ of length with 3 ″max total
Column plumbness tolerance — See figs. 2 and 3
— Indicates column working points
At any splice elevation, envelope “E” is located within the limits Ta and T t
At any splice elevation, envelope “E” may be located offset from the
corresponding envelope of the adjacent splice elevations, above and below,
by an amount not greater than 1/ 500 of the column length.
Fig. 4. Tolerances in plan at any splice elevation of exterior columns
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Splice elevation shown on plan
Column base
Differential shortening
Interior column
Finish line
Interior column shortening due to partial dead load
Beam elevations from finish line
See section 7.11.3.3
Floor elevations set by measurement
from top of beams
Finish line
Floor elevations set by measurement
from top of beams
Beam elevations from finish line
See section 7.11.3.3
Exterior column shortening due to partial dead load
Finish line
Exterior column
Finish line
On a particular date during the
erection of structural steel and
placement of other material,
(floor concrete, facade, etc.)
the interior columns will be
carrying a higher percentage
of their final loads than the
exterior columns. Therefore, for
equal design unit stresses, the
actual stress on that date for
interior columns will be greater
than the actual stresses on
exterior columns.
When all dead loads have been
applied, stresses and shortening
in all columns will be approximately
equal.
Fig. 5. Effect of differential column shortening
differential shortening, plus mill camber and deflections, become very important when
there is little cover over the steel, when there are electrical fittings mounted on the
steel flooring whose tops are supposed to be flush with the finished floor, when there
is small clearance between bottom of beams and top of door frames, etc., and when
there is little clearance around ductwork. To finish floors to a precisely level plane,
for example by the use of laser leveling techniques, can result in significant
differential floor thicknesses, different increases above design dead loads for
individual columns and, thus, permanent differential column shortening and out-oflevel completed floors.
Similar considerations make it unfeasible to attempt to set the elevation of a given
floor in a multistory building by reference to a bench mark at the base of the
structure. Columns are fabricated to a length tolerance of ± 1⁄32 in. while under a zero
state of stress. As dead loads accumulate, the column shortening which takes place
is negligible within individual stories and in low buildings, but will accumulate to
significant magnitude in tall buildings. Thus, the upper floors of tall buildings will
be excessively thick and the lower floors will be below the initial finish elevation if
floor elevations are established relative to a ground level bench mark.
If foundations and base plates are accurately set to grade and the lengths of
individual column sections are checked for accuracy prior to erection, and if floor
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
6 - 472
AISC CODE OF STANDARD PRACTICE
elevations are established by reference to the elevation of the top of beams, the effect
of column shortening due to dead load will be minimized.
Since a long unencased steel frame will expand or contract 1⁄8 in. per 100 ft for
each change of 15°F in temperature, and since the change in length can be assumed
to act about the center of rigidity, the end columns anchored to foundations will be
plumb only when the steel is at normal temperature (see Fig. 6). It is therefore
necessary to correct field measurements of offsets to the structure from established
baselines for the expansion or contraction of the exposed steel frame. For example,
a building 200-ft long that is plumbed up at 100°F should have working points at the
tops of end columns positioned 1⁄2 in. out from the working point at the base in order
for the column to be plumb at 60°F. Differential temperature effects on column
length should also be taken into account in plumbing surveys when tall steel frames
are subject to strong sun exposure on one side.
The alignment of lintels, spandrels, wall supports and similar members used to
connect other building construction units to the steel frame should have an adjustment
of sufficient magnitude to allow for the accumulative effect of mill, fabrication and
erection tolerances on the erected steel frame (see Fig. 7).
When plumbing end columns, apply temperature
adjustment at rate 1/ 8 ″ per 100 ′of length from
center of rigidity per each 15°F of difference
between erection and working temperatures.
Length
Length
Center of rigidity
Ta Tt
Tt Ta
Tt Ta
Tt Ta
C to C adjacent columns subject
to mill and fabrication tolerance
Tp Tp
Tt Ta
Established column lines
Building line
Fig. 6. Tolerances in plan location of columns
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
STEEL BUILDINGS AND BRIDGES
6 - 473
Column dimension + tolerances
D = Tolerances required by
manufacturer of wall
units plus survey
tolerance
D
D
E.C.L.
Clearance line to
accommodate column.
See Figure 2
Provide connections
with slotted holes
and/or shims
to accommodate
tolerances
Column dimension +
tolerances
If fascia joints are set from
nearest column finish line,
allow ± 5/ 8 ″for vertical
adjustment. Owners plans
for fascia details must allow
for progressive shortening
of steel columns.
Fig. 7. Clearance required to accommodate fascia
500
1
500
500
1
1
500
1
Support points
Field splices
Fig. 8. Alignment tolerances for members with field splices
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
6 - 474
AISC CODE OF STANDARD PRACTICE
7.11.3.2. Alignment Tolerance for Members with Field Splices
The angular misalignment of the working line of all fabricated shipping pieces
relative to the line between support points of the member as a whole in erected
position must not exceed 1 in 500. Note that the tolerance is not stated in terms of
a linear displacement at any point and is not to be taken as the overall length between
supports divided by 500. Typical examples are shown in Fig. 8. Numerous
conditions within tolerance for these and other cases are possible. This condition
applies to both plan and elevation tolerances.
7.11.4. Responsibility for Clearances
In spite of all efforts to minimize inaccuracies, deviations will still exist; therefore,
in addition, the designs of prefabricated wall panels, partition panels, fenestrations,
floor-to-ceiling door frames and similar elements must provide for clearance and
details for adjustment as described in Section 7.11.4. Designs must provide for
adjustment in the vertical dimension of prefabricated facade panels supported by the
steel frame because the accumulation of shortening of stressed steel columns will
result in the unstressed facade supported at each floor level being higher than the steel
frame connections to which it must be attached. Observations in the field have shown
that where a heavy facade is erected to a greater height on one side of a multistory
building than on the other, the steel framing will be pulled out of alignment. Facades
should be erected at a relatively uniform rate around the perimeter of the structure.
7.14. Handling and Storage
Handling Painted Steel
During storage, loading, transport, unloading and erection, blemish marks caused
by slings, chains, blocking, tie-downs, etc., occur in varying degrees. Abrasions
caused by handling or cartage after painting are to be expected. The owner/engineer
must recognize that any shop applied coating, no matter how carefully protected, will
require touch-up in the field. Touch-up of these blemished areas is the responsibility
of the contractor performing the field touch-up of field painting.
Cleaning After Erection
The responsibility for proper storage and handling of fabricated steel at the
construction site during erection is properly the erector’s. Shop-painted steel stored
in the field pending erection should be kept free of the ground and so positioned as
to minimize water-holding pockets. The owner or general contractor is responsible
for providing suitable site conditions and proper access so that the fabricator/erector
may perform its work.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
STEEL BUILDINGS AND BRIDGES
6 - 475
Site conditions are frequently muddy, sandy or dusty, or a combination of all three,
during the erection period. Under such conditions it may be impossible to store and
handle the steel in such a way as to completely avoid accumulation of mud, dirt or
sand on the surface of the steel, even though the fabricator/erector manages to
proceed with the work.
Repairs of damage to painted surfaces and/or removal of foreign materials due to
adverse site conditions are outside the scope of responsibility of the fabricator/erector
when reasonable attempts at proper handling and storage have been made.
SECTION 8. QUALITY CONTROL
8.1.1. The AISC Quality Certification Program confirms to the construction
industry that a certified structural steel fabricating plant has the capability by reason
of commitment, personnel, organization, experience, procedures, knowledge and
equipment to produce fabricated structural steel of the required quality for a given
category of structural steelwork. The AISC Quality Certification Program is not
intended to involve inspection and/or judgment of product quality on individual
projects. Neither is it intended to guarantee the quality of specific fabricated steel
products.
SECTION 9. CONTRACTS
9.2. Calculation of Weights
The standard procedure for calculation of weights that is described in the Code
meets the need for a universally acceptable system for defining “pay weights” in
contracts based on the weight of delivered and/or erected materials. This procedure
permits owners to easily and accurately evaluate price per pound proposals from
potential suppliers and enables both parties to a contract to have a clear understanding
of the basis for payment.
The Code procedure affords a simple, readily understood method of calculation
which will produce pay weights which are consistent throughout the industry and
which may be easily verified by the owner. While this procedure does not produce
actual weights, it can be used by purchasers and suppliers to define a widely accepted
basis for bidding and contracting for structural steel. However, any other system can
be used as the basis for a contractual agreement. When other systems are used, both
supplier and purchaser should clearly understand how the alternate procedure is
handled.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
6 - 476
AISC CODE OF STANDARD PRACTICE
9.3. Revisions to Contract Documents
9.3.1. Revisions to the Contract are implemented by issuance of new documents
or re-issuance of existing documents. Individual revisions must be noted where they
occur and documents must be dated with latest issue date and the reasons for issuance
must be identified.
9.3.2. Revisions to the Contract are also implemented by change order, extra
work order, or notations on the shop and erection drawings when returned from
approval. However, revisions implemented in this manner must be incorporated
subsequently as revisions to the plans and/or specifications and re-issued in
accordance with Section 9.3.1.
9.3.3. The issuance of revisions authorizes the fabricator and erector to
incorporate the revisions into the work. This authorization obligates the owner to pay
the fabricator and erector for costs associated with changed and/or additional work.
9.6. Terms of Payment
These terms include such items as progress payments for material, fabrication,
erection, retainage, performance and payment bonds and final payment. If a
performance or payment bond, paid for by the owner, is required by contract, then
no retainage shall be required.
SECTION 10. ARCHITECTURALLY EXPOSED STRUCTURAL STEEL
The rapidly increasing use of exposed structural steel as a medium of architectural
expression has given rise to a demand for closer dimensional tolerances and smoother
finished surfaces than required for ordinary structural steel framing.
This section of the Code establishes standards for these requirements which take
into account both the desired finished appearance and the abilities of the fabrication
shop to produce the desired product. These requirements were previously contained
in the AISC Specification for Architecturally Exposed Structural Steel which
architects and engineers have specified in the past. It should be pointed out that the
term “Architecturally Exposed Structural Steel” (AESS), as covered in this section,
must be specified in the contract documents if the fabricator is required to meet the
fabricating standards of Section 10, and applies only to that portion of the structural
steel so identified. In order to avoid misunderstandings and to hold costs to a
minimum, only those steel surfaces and connections which will remain exposed and
subject to normal view by pedestrians or occupants of the completed structure should
be designated as AESS.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
6 - 477
AISC
Quality Certification
Program
AMERICAN INSTITUTE OF STEEL CONSTRUCTION, INC.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
6 - 478
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
6 - 479
AISC
Quality Certification
Program
In recent years. the quality of construction methods and materials has become the
subject of increasing concern to building officials, highway officials, and designers.
One result of this concern has been the enactment of ever more demanding inspection
requirements intended to ensure product quality. In many cases, however, these more
demanding inspection requirements have not been based upon demonstrated unsatisfactory performance of structures in service. Rather, they have been based upon the
capacity of sophisticated test equipment. or upon standards developed for nuclear
construction rather than conventional construction. Adding to the problem, arbitrary
interpretation of specifications by inspectors has too often been made without rational
consideration of the type of construction involved. The result has been spiraling
increases in the costs of fabrication of structural steel and of inspection, which must be
paid by owners without necessarily assuring that the product quality required has been
improved.
Product inspection. although it has a valid place in the construction process, is not
the most logical or practical way to assure that structural steelwork will conform to he
requirements of contract documents and satisfy the intended use. A better solution
can be found in the exercise of good quality control and quality assurance by the
fabricator throughout the entire production process.
Recognizing this fact, and seeking some valid, objective method whereby a
fabricator’s capability for assuring a quality product could be evaluated, a number of
code authorities have, in recent years, instituted steps to establish fabricator registration programs. However, these independent efforts resulted in extremely inconsistent
criteria. They were developed primarily by inspectors or inspection agencies who were
experienced in testing, but were not familiar with the complexities of the many steps,
procedures, techniques, and controls required to assure quality throughout the fabricating process. Neither were these inspection agencies qualified to determine the
various levels of quality required to assure satisfactory performance in meeting the
service requirements of the many different types of steel structures.
Recognizing the need for a comprehensive national standard for fabricator certification, and concerned by the trend toward costly inspection requirements that could
not be justified by rational quality standards, the American Institute of Steel
Construction has developed and implemented a voluntary Quality Certification Program, whereby any structural steel fabricating plant—whether a member of AISC or
not—can have its capability for assuring quality production evaluated on a fair and
impartial basis.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
6 - 480
AISC QUALITY CERTIFICATION PROGRAM
THE AISC PROGRAM
The AISC Quality Certification Program does not involve inspection and/or judgment
of product quality on individual projects. Neither does it guarantee the quality of
specific fabricated steel products. Rather, the purpose of the AISC Quality Certification Program is to confirm to the construction industry that a Certified structural steel
fabricating plant has the personnel, organization, experience, procedures, knowledge,
equipment, capability and commitment to reproduce fabricated steel of the required
quality for a given category of structural steelwork.
The AISC Quality Certification Program was developed by a group of highly
qualified shop operation personnel from large, medium, and small structural steel
fabricating plants throughout the United States. These individuals all had extensive
experience and were fully aware of where and how problems can arise during the
production process and of the steps and procedures that must be followed during
fabrication to assure that the finished product meets the quality requirements of the
contract.
The program was reviewed and strongly endorsed by an Independent Board of
Review comprised of 17 prominent structural engineers from throughout the United
States, who were not associated with the steel fabricating industry, but were well
qualified in matters of quality requirements for reliable service of all types of steel
structures.
CATEGORIES OF CERTIFICATION
A fabricator may apply for certification of a plant in one of the following categories of
structural steelwork:
I: Conventional Steel Structures — Small Public Service and Institutional
Buildings, (Schools, etc.), Shopping Centers, Light Manufacturing Plants,
Miscellaneous and Ornamental Iron Work, Warehouses, Sign Structures,
Low Rise, Truss Beam/Column Structures, Simple Rolled Beam Bridges.
II: Complex Steel Building Structures — Large Public Service and Institutional
Buildings, Heavy Manufacturing Plants, Powerhouses (fossil, non-nuclear),
Metal Producing/Rolling Facilities, Crane Bridge Girders, Bunkers and Bins,
Stadia, Auditoriums, High Rise Buildings, Chemical Processing Plants, Petroleum Processing Plants.
III: Major Steel Bridges — All bridge structures other than simple rolled beam
bridges.
MB: Metal Building Systems — Pre-engineered Metal Building Structures.
Supplement: Auxiliary and Support Structures for Nuclear Power Plants — This
supplement, applicable to nuclear plant structures designed under the AISC
Specification, but not to pressure-retaining structures, offers utility companies
and designers of nuclear power plants a certification program that will eliminate the need for many of the more costly, conflicting programs now in use. A
fabricator must hold certification in either Category I, II or III prior to
application for certification in this category.
Certification in Category II automatically includes Category I. Certification in
Category III automatically includes Categories I and II. Certification in Category MB
is not transferable to any other Category.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
AISC QUALITY CERTIFICATION PROGRAM
6 - 481
INSPECTION-EVALUATION PROCEDURE
An outside, experienced, professional organization, ABS Quality Evaluations, Inc. (a
subsidiary of American Bureau of Shipping) has been retained by AISC to perform the
plant Inspection-Evaluation in accordance with a standard check list and rating procedure
established by AISC for each certification category in the program. Upon completion of
this Inspection-Evaluation, ABS Quality Evaluations, Inc. (commonly known as ABSQE) will recommend to AISC that a fabricator be approved or disapproved for
certification. ABS-QE’s Inspection-Evaluation is totally independent of the fabricator’s
and AISC’s influence, and their evaluation is not subject to review by AISC.
At a time mutually agreed upon by the fabricator, AISC, and ABS-QE, the
Inspection-Evaluation team visits the plant to investigate and rate the following basic
plant functions directly and indirectly affecting quality assurance: General Management, Engineering and Drafting, Procurement, Shop Operations, and Quality Control.
The Inspection-Evaluation team will perform the following:
1. Confirm data submitted with the Application for Certification.
2. Interview key supervisory personnel and subordinate employees.
3. Observe and rate the organization in operation, including procedures used in functions affecting quality assurance.
4. Inspect and rate equipment and facilities.
5. At an “exit interview,” review with plant management the completed check list
observations and evaluation scoring, including discussions of deficiencies and omissions, if any.
The number of days required for Inspection-Evaluation varies according to the size
and complexity of the plant, but usually requires two to five days.
CERTIFICATION
Following recommendation for Certification by the Inspection-Evaluation team, AISC
will issue a certificate identifying the fabricator, the plant, and the Category of Certification. The certificate is valid for a three year period, subject to annual review in the
form of unannounced inspections early in the second and third year periods. The
certificate is endorsed annually, provided there is successful completion of the unannounced second and third year inspection.
An annual self-audit, based on the standard check list, must be made by plant
management during the 11th and 23rd months after initial Certification. This self-audit
must be retained at the plant and made available to the Inspection-Evaluation team
during the unannounced second and third year inspections.
At the end of the third year, the cycle begins again with a complete prescheduled
Inspection-Evaluation and the issuance of a new certificate.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
7-1
Part 7
MISCELLANEOUS DATA AND
MATHEMATICAL INFORMATION
MISCELLANEOUS DATA
Wire and Sheet Metal Gages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-3
AISI Standard Nomenclature for Flat Rolled Carbon Steel . . . . . . . . . . . . . . . . . 7-3
Coefficients of Expansion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-4
Weights and Specific Gravities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-5
Weights of Building Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-7
SI UNITS FOR STRUCTURAL STEEL DESIGN . . . . . . . . . . . . . . . . . . . . . . 7-8
SI (Metric) Weights and Measures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-10
U.S. Weights and Measures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-11
SI Conversion Factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-12
GEOMETRIC AND TRIGONOMETRIC DATA
Bracing Formulas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-14
Properties of the Parabola and Ellipse . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-15
Properties of the Circle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-16
Properties of Geometric Sections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-17
Trigonometric Formulas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-24
DECIMAL EQUIVALENTS
Decimals of an Inch . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-25
Decimals of a Foot . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-26
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
7-2
MISCELLANEOUS DATA AND MATHEMATICAL INFORMATION
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
MISCELLANEOUS DATA
7-3
Table 7-1.
WIRE AND SHEET METAL GAGES
Equivalent thickness in decimals of an inch
Gage
No.
U.S. Standard Galvanized
Sheet Gage
Gage for
for HotUncoated
Dipped
Hot & ColdZinc Coated
Rolled
Sheetsb
Sheetsb
7/0
6/0
5/0
4/0
3/0
2/0
1/0
1
2
3
4
5
6
7
8
9
10
11
12
USA
Steel
Wire Gage
.490
.462a
.430a
.394a
.362a
.331
.306
.283
.262a
.244a
.225a
.207
.192
.177
.162
.148a
.135
.120a
.106a
—
—
—
—
—
—
—
—
—
—
—
—
—
—
.1681
.1532
.1382
.1233
.1084
—
—
—
—
—
—
—
—
—
.2391
.2242
.2092
.1943
.1793
.1644
.1495
.1345
.1196
.1046
Gage
No.
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
U.S. Standard Galvanized
Gage for
Sheet Gage
Uncoated
for HotHot & ColdDipped
Rolled
Zinc Coated
Sheetsb
Sheetsb
.0897
.0747
.0673
.0598
.0538
.0478
.0418
.0359
.0329
.0299
.0269
.0239
.0209
.0179
.0164
.0149
—
—
.0934
.0785
.0710
.0635
.0575
.0516
.0456
.0396
.0366
.0336
.0306
.0276
.0247
.0217
.0202
.0187
.0172
.0157
USA
Steel
Wire Gage
.092a
.080
.072
.062a
.054
.048a
.041
.035a
—
—
—
—
—
—
—
—
—
—
aRounded value. The steel wire gage has been taken from ASTM A510 “General Requirements for Wire Rods
and Coarse Round Wire, Carbon Steel.” Sizes originally quoted to four decimal equivalent places have been
rounded to three decimal places in accordance with rounding procedures of ASTM “Recommended Practice” E29.
bThe equivalent thicknesses are for information only. The product is commonly specified to decimal thickness,
not to gage number.
Table 7-2.
AISI STANDARD NOMENCLATURE FOR FLAT ROLLED CARBON STEEL
Width (Inches)
Thickness
(Inches)
To
31⁄2 incl.
Over 31⁄2
To 6
Over 6
To 8
Over 8
To 12
Over 12
To 48
Over 48
0.2300 & thicker
Bar
Bar
Bar
Plate
Plate
Plate
0.2299 to 0.2031
Bar
Bar
Strip
Strip
Sheet
Plate
0.2030 to 0.1800
Strip
Strip
Strip
Strip
Sheet
Plate
0.1799 to 0.0449
Strip
Strip
Strip
Strip
Sheet
Sheet
0.0448 to 0.0344
Strip
Strip
0.0343 to 0.0255
Strip
0.0254 & thinner
Hot-rolled sheet and strip not generally
produced in these widths and thicknesses
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
7-4
MISCELLANEOUS DATA AND MATHEMATICAL INFORMATION
Table 7-3.
COEFFICIENTS OF EXPANSION
The coefficient of linear expansion (ε) is the change in length, per unit, for a change of one degree of temperature. The coefficient of surface expansion is approximately two times the linear
coefficient, and the coefficient of volume expansion, for solids, is approximately three times the
linear coefficient.
A bar, free to move, will increase in length with an increase in temperature and will decrease in
length with a decrease in temperature. The change in length will be εtl, where ε is the coefficient
of linear expansion, t the change in temperature and l the length. If the ends of a bar are fixed, a
change in temperature (t ) will cause a change in the unit stress of E εt, and in force of AE εt,
where A is the cross-sectional area of the bar and E the modulus of elasticity.
The following table gives the coefficient of linear expansion for 100°, or 100 times the value indicated above.
Example: A piece of medium steel is exactly 40 ft long at 60°F. Find the length at 90°F assuming the ends free to move.
change of length = εt l =
.00065 × 30 × 40
= .0078 ft
100
The length at 90° is 40.0078 ft
Example: A piece of medium carbon steel is exactly 40 ft long and the ends are fixed. If the temperature increases 30°F, what is the resulting change in the unit stress?
change in unit stress = E εt =
29,000 × .00065 × 30
= 5.7 ksi
100
COEFFICIENTS OF EXPANSION FOR 100 DEGREES = 100ε
Linear
Expansion
Linear
Expansion
Centigrade
Fahrenheit
METALS AND ALLOYS
Aluminum, wrought
Brass
Bronze
Copper
Iron, cast, gray
Iron, wrought
Iron, wire
Lead
Magnesium, various alloys
Nickel
Steel , mild
Steel, stainless, 18-8
Zinc, rolled
.00231
.00188
.00181
.00168
.00106
.00120
.00124
.00286
.0029
.00126
.00117
.00178
.00311
.00128
.00104
.00101
.00093
.00059
.00067
.00069
.00159
.0016
.00070
.00065
.00099
.00173
TIMBER
Fir
Maple
parallel to fiber
Oak
Pine
.00037
.00064
.00049
.00054
.00021
.00036
.00027
.00030
Materials
Centigrade
Fahrenheit
STONE AND MASONRY
Ashlar masonry
Brick Masonry
Cement, portland
Concrete
Granite
Limestone
Marble
Plaster
Rubble masonry
Sandstone
Slate
.00063
.00061
.00126
.00099
.00080
.00076
.00081
.00166
.00063
.00097
.00080
.00035
.00034
.00070
.00055
.00044
.00042
.00045
.00092
.00035
.00054
.00044
TIMBER
Fir
Maple
perpendicular to
Oak
fiber
Pine
.0058
.0048
.0054
.0034
.0032
.0027
.0030
.0019
Materials
EXPANSION OF WATER
Maximum Density = 1
C°°
Volume
0 1.000126
4 1.000000
C°°
Volume
10 1.000257
20 1.001732
C°°
Volume
30 1.004234
40 1.007627
C°°
Volume
50 1.011877
60 1.016954
C°°
Volume
C°°
Volume
70 1.022384 90 1.035829
80 1.029003 100 1.043116
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
MISCELLANEOUS DATA
7-5
Table 7-4.
WEIGHTS AND SPECIFIC GRAVITIES
Weight
lb per Specific
Gravity
cu ft
Substance
ASHLAR, MASONRY
Granite, syenite, gneiss . . . .
Limestone, marble . . . . . . .
Sandstone, bluestone . . . . .
165
160
140
2.3–3.0
2.3–2.8
2.1–2.4
MORTAR RUBBLE
MASONRY
Granite, syenite, gneiss . . . .
Limestone, marble . . . . . . .
Sandstone, bluestone . . . . .
155
150
130
2.2–2.8
2.2–2.6
2.0–2.2
DRY RUBBLE MASONRY
Granite, syenite, gneiss . . . .
Limestone, marble . . . . . . .
Sandstone, bluestone . . . . .
130
125
110
1.9–2.3
1.9–2.1
1.8–1.9
BRICK MASONRY
Pressed brick . . . . . . . . .
Common brick . . . . . . . . .
Soft brick . . . . . . . . . . . .
140
120
100
2.2–2.3
1.8–2.0
1.5–1.7
CONCRETE MASONRY
Cement, stone, sand . . . . .
Cement, slag. etc. . . . . . . .
Cement, cinder, etc. . . . . . .
144
130
100
2.2–2.4
1.9–2.3
1.5–1.7
40–45
90
183
53–64
103
67–72
98–117
96
49–55
—
—
2.7–3.2
—
1.4–1.9
—
—
—
—
VARIOUS BUILDING
MATERIALS
Ashes. cinders . . . . .
Cement, portland, loose
Cement, portland, set .
Lime, gypsum, loose . .
Mortar, set . . . . . . .
Slags, bank slag . . . .
Slags, bank screenings
Slags, machine slag . .
Slags, slag sand . . . .
.
.
.
.
.
.
.
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.
.
.
.
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.
.
.
.
.
.
EARTH, ETC., EXCAVATED
Clay, dry . . . . . . . . . .
Clay, damp, plastic . . . .
Clay and gravel, dry . . . .
Earth, dry, loose . . . . . .
Earth, dry, packed . . . . .
Earth, moist, loose . . . . .
Earth, moist, packed . . . .
Earth, mud, flowing . . . .
Earth, mud, packed . . . .
Riprap, limestone . . . . .
Riprap, sandstone . . . . .
Riprap, shale . . . . . . .
Sand, gravel, dry, loose . .
Sand, gravel, dry, packed .
Sand, gravel, wet . . . . .
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
63
.
110
.
100
.
76
.
95
.
78
.
96
.
108
.
115
. 80–85
.
90
.
105
. 90–105
. 100–120
. 118–120
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
EXCAVATIONS IN WATER
Sand or gravel . . . . . . .
Sand or gravel and clay . .
Clay . . . . . . . . . . . .
River mud . . . . . . . . .
Soil . . . . . . . . . . . . .
Stone riprap . . . . . . . .
.
.
.
.
.
.
.
.
.
.
.
.
—
—
—
—
—
—
60
65
80
90
70
65
Weight
lb per Specific
cu ft Gravity
Substance
MINERALS
Asbestos . . . . . . .
Barytes . . . . . . . .
Basalt . . . . . . . . .
Bauxite . . . . . . . .
Borax . . . . . . . . .
Chalk . . . . . . . . .
Clay, marl . . . . . . .
Dolomite . . . . . . . .
Feldspar, orthoclase . .
Gneiss, serpentine . .
Granite, syenite . . . .
Greenstone, trap . . .
Gypsum, alabaster . .
Hornblende . . . . . .
Limestone, marble . . .
Magnesite . . . . . . .
Phosphate rock, apatite
Porphyry . . . . . . . .
Pumice, natural . . . .
Quartz, flint . . . . . .
Sandstone, bluestone .
Shale, slate . . . . . .
Soapstone, talc . . . .
.
.
.
.
.
.
.
.
.
.
.
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.
.
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.
.
.
.
.
.
.
.
153
281
184
159
109
137
137
181
159
159
175
187
159
187
165
187
200
172
40
165
147
175
169
2.1–2.8
4.50
2.7–3.2
2.55
1.7–1.8
1.8–2.6
1.8–2.6
2.9
2.5–2.6
2.4–2.7
2.5–3.1
2.8–3.2
2.3–2.8
3.0
2.5–2.8
3.0
3.2
2.6–2.9
0.37–0.90
2.5–2.8
2.2–2.5
2.7–2.9
2.6–2.8
STONE, QUARRIED, PILED
Basalt, granite, gneiss . . .
Limestone, marble, quartz .
Sandstone . . . . . . . . .
Shale . . . . . . . . . . .
Greenstone, hornblende .
.
.
.
.
.
.
.
.
.
.
96
95
82
92
107
—
—
—
—
—
BITUMINOUS SUBSTANCES
Asphaltum . . . . . . . . . .
Coal, anthracite . . . . . . .
Coal, bituminous . . . . . .
Coal, lignite . . . . . . . . .
Coal, peat, turf, dry . . . . .
Coal, charcoal, pine . . . . .
Coal, charcoal, oak . . . . .
Coal, coke . . . . . . . . . .
Graphite . . . . . . . . . . .
Paraffine . . . . . . . . . . .
Petroleum . . . . . . . . . .
Petroleum, refined . . . . . .
Petroleum, benzine . . . . .
Petroleum, gasoline . . . . .
Pitch . . . . . . . . . . . . .
Tar, bituminous . . . . . . .
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
81
97
84
78
47
23
33
75
131
56
54
50
46
42
69
75
1.1–1.5
1.4–1.7
1.2–1.5
1.1–1.4
0.65–0.85
0.28–0.44
0.47–0.57
1.0–1.4
1.9–2.3
0.87–0.91
0.87
0.79–0.82
0.73–0.75
0.66–0.69
1.07–1.15
1.20
COAL AND COKE, PILED
Coal, anthracite . . . . .
Coal, bituminous, lignite .
Coal, peat, turf . . . . . .
Coal charcoal . . . . . .
Coal coke . . . . . . . .
.
.
.
.
.
47–58
40–54
20–26
10–14
23–32
—
—
—
—
—
.
.
.
.
.
.
.
.
.
.
The specific gravities of solids and liquids refer to water at 4°°C, those of gases to air at 0°°C and 760 mm pressure. The weights per cubic foot are derived from average specific gravities, except where stated that weights
are for bulk, heaped, or loose material, etc.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
7-6
MISCELLANEOUS DATA AND MATHEMATICAL INFORMATION
Table 7-4 (cont.).
WEIGHTS AND SPECIFIC GRAVITIES
Weight
lb per Specific
Gravity
cu ft
Substance
METALS, ALLOYS, ORES
Aluminum, cast, hammered
Brass, cast, rolled . . . . .
Bronze, 7.9 to 14% Sn . . .
Bronze, aluminum . . . . .
Copper, cast, rolled . . . .
Copper ore, pyrites . . . .
Gold, cast, hammered . . .
Iron, cast, pig . . . . . . .
Iron, wrought . . . . . . . .
Iron, speigel-eisen . . . . .
Iron, ferro-silicon . . . . . .
Iron ore, hematite . . . . .
Iron ore, hematite in bank .
Iron ore, hematite loose . .
Iron ore, limonite . . . . . .
Iron ore, magnetite . . . .
Iron slag . . . . . . . . . .
Lead . . . . . . . . . . . .
Lead ore, galena . . . . . .
Magnesium, alloys . . . . .
Manganese . . . . . . . .
Manganese ore, pyrolusite
Mercury . . . . . . . . . .
Monel Metal . . . . . . . .
Nickel . . . . . . . . . . .
Platinum, cast, hammered .
Silver, cast, hammered . .
Steel, rolled . . . . . . . .
Tin, cast, hammered . . . .
Tin ore, cassiterite . . . . .
Zinc, cast, rolled . . . . . .
Zinc ore, blende . . . . . .
VARIOUS SOLIDS
Cereals, oats . . . .
Cereals, barley . . .
Cereals, corn, rye . .
Cereals, wheat . . . .
Hay and Straw . . . .
Cotton, Flax, Hemp .
Fats . . . . . . . . .
Flour, loose . . . . .
Flour, pressed . . . .
Glass, common . . .
Glass, plate or crown
Glass, crystal . . . .
Leather . . . . . . .
Paper . . . . . . . .
Potatoes, piled . . . .
Rubber, caoutchouc .
Rubber goods . . . .
Salt, granulated, piled
Saltpeter . . . . . . .
Starch . . . . . . . .
Sulphur . . . . . . .
Wool . . . . . . . . .
.
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.
.
.
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.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
165
2.55–2.75
.
534
8.4–8.7
.
509
7.4–8.9
.
481
7.7
.
556
8.8–9.0
.
262
4.1–4.3
.
1205 19.25–19.3
.
450
7.2
.
485
7.6–7.9
.
468
7.5
.
437
6.7–7.3
.
325
5.2
. 160–180
—
. 130–160
—
.
237
3.6–4.0
.
315
4.9–5.2
.
172
2.5–3.0
.
710
11.37
.
465
7.3–7.6
.
112
1.74–1.83
.
475
7.2–8.0
.
259
3.7–4.6
.
849
13.6
.
556
8.8–9.0
.
565
8.9–9.2
.
1330
21.1–21.5
.
656
10.4–10.6
.
490
7.85
.
459
7.2–7.5
.
418
6.4–7.0
.
440
6.9–7.2
.
253
3.9–4.2
bulk
bulk
bulk
bulk
bales
. . .
. . .
. . .
. . .
. . .
. . .
. . .
. . .
. . .
. . .
. . .
. . .
. . .
. . .
. . .
. . .
. . .
32
39
48
48
20
93
58
28
47
156
161
184
59
58
42
59
94
48
67
96
125
82
Weight
lb per Specific
Gravity
cu ft
Substance
TIMBER, U.S. SEASONED
Moisture content by weight:
Seasoned timber 15 to 20%
Green timber up to 50%
Ash, white, red . . . . . .
Cedar, white, red . . . . .
Chestnut . . . . . . . . .
Cypress . . . . . . . . .
Fir, Douglas spruce . . .
Fir, eastern . . . . . . . .
Elm, white . . . . . . . .
Hemlock . . . . . . . . .
Hickory . . . . . . . . . .
Locust . . . . . . . . . .
Maple, hard . . . . . . .
Maple, white . . . . . . .
Oak, chestnut . . . . . .
Oak, live . . . . . . . . .
Oak, red, black . . . . . .
Oak, white . . . . . . . .
Pine, Oregon . . . . . . .
Pine, red . . . . . . . . .
Pine, white . . . . . . . .
Pine, yellow, long-leaf . .
Pine, yellow, short-leaf . .
Poplar . . . . . . . . . .
Redwood, California . . .
Spruce, white, black . . .
Walnut, black . . . . . . .
Walnut, white . . . . . . .
VARIOUS LIQUIDS
Alcohol, 100% . . . . . .
Acids, muriatic 40% . . .
Acids, nitric 91% . . . . .
Acids, sulphuric 87% . .
—
Lye, soda 66% . . . . .
—
Oils, vegetable . . . . . .
—
Oils, mineral, lubricants .
—
Water, 4°°C max. density
—
Water, 100°°C . . . . . .
1.47–1.50 Water, ice . . . . . . . .
0.90–0.97 Water, snow, fresh fallen
0.40–0.50 Water, sea water . . . .
0.70–0.80
2.40–2.60
2.45–2.72
2.90–3.00
0.86–1.02 GASES
0.70–1.15 Air, 0°°C 760 mm . . . . .
—
Ammonia . . . . . . . .
0.92–0.96 Carbon dioxide . . . . .
1.0–2.0
Carbon monoxide . . . .
—
Gas, illuminating . . . . .
—
Gas, natural . . . . . . .
1.53
Hydrogen . . . . . . . .
1.93–2.07 Nitrogen . . . . . . . . .
1.32
Oxygen . . . . . . . . .
.
.
.
.
.
.
.
.
.
.
.
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.
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.
.
.
.
.
.
.
.
40
22
41
30
32
25
45
29
49
46
43
33
54
59
41
46
32
30
26
44
38
30
26
27
38
26
0.62–0.65
0.32–.038
0.66
0.48
0.51
0.40
0.72
0.42–0.52
0.74–0.84
0.73
0.68
0.53
0.86
0.95
0.65
0.74
0.51
0.48
0.41
0.70
0.61
0.48
0.42
0.40–0.46
0.61
0.41
.
.
.
.
.
.
.
.
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.
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.
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.
.
.
.
.
.
.
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.
.
.
.
.
.
.
.
.
49
75
94
112
106
58
57
62.428
59.830
56
8
64
0.79
1.20
1.50
1.80
1.70
0.91–0.94
0.90–0.93
1.0
0.9584
0.88–0.92
.125
1.02–1.03
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
1.0
. .08071
0.5920
. .0478
.1234
1.5291
.
0.9673
. .0781
. .028–.036 0.35–0.45
. .038–.039 0.47–0.48
0.0693
. .00559
0.9714
. .0784
1.1056
. .0892
The specific gravities of solids and liquids refer to water at 4°°C, those of gases to air at 0°°C and 760 mm pressure. The weights per cubic foot are derived from average specific gravities, except where stated that weights
are for bulk, heaped, or loose material, etc.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
WEIGHTS, MEASURES, AND CONVERSION FACTORS
7-7
Table 7-5.
WEIGHTS OF BUILDING MATERIALS
Materials
CEILINGS
Channel suspended system
Lathing and plastering
Acoustical fiber tile
FLOORS
Steel Deck
Concrete-Reinforced 1 in.
Stone
Slag
Lightweight
Concrete-Plain 1 in.
Stone
Slag
Lightweight
Fills 1 inch
Gypsum
Sand
Cinders
Finishes
Terrazzo 1 in.
Ceramic or Quarry Tile 3⁄4-in.
Linoleum 1⁄4-in.
Mastic 3⁄4-in.
Hardwood 7⁄8-in.
Softwood 3⁄4-in.
ROOFS
Copper or tin
Corrugated steel
3-ply ready roofing
3-ply felt and gravel
5-ply felt and gravel
Shingles
Wood
Asphalt
Clay tile
Slate 1⁄4
Sheathing
Wood 3⁄4-in.
Gypsum 1 in.
Insulation 1 in.
Loose
Poured
Rigid
Weight
lb per sq ft
Materials
PARTITIONS
Clay Tile
3 in.
4 in.
6 in.
8 in.
10 in.
Gypsum Block
2 in.
See Manufacturer
3 in.
4 in.
5 in.
121⁄2
111⁄2
6 in.
6 to 10
Wood Studs 2×4
12–16 in. o.c.
Steel partitions
12
Plaster 1 inch
11
Cement
3 to 9
Gypsum
Lathing
Metal
6
Gypsum Board 1⁄2-in.
8
4
1
See Partitions
1
13
10
1
9
4
1
2 ⁄2
WALLS
Brick
4 in.
8 in.
12 in.
Hollow Concrete Block
(Heavy Aggregate)
4 in.
1
6 in.
See Manufactuer
8 in.
1
121⁄2-in.
1
Hollow Concrete Block
5 ⁄2
6
(Light Aggregate)
4 in.
6 in.
2
8 in.
3
12 in.
9 to 14
Clay tile (Load Bearing)
10
4 in.
6 in.
8 in.
3
12 in.
4
Stone 4 in.
Glass Block 4 in.
Window, Glass, Frame, & Sash
1⁄
Curtain Walls
2
2
Structural Glass 1 in.
1
1 ⁄2
Corrugated Cement Asbestos 1⁄4-in.
For weights of other materials used in building construction, see Table 7-4.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
Weight
lb per sq ft
17
18
28
34
40
91⁄2
101⁄2
121⁄2
14
181⁄2
2
4
10
5
1⁄
2
2
40
80
120
30
43
55
80
21
30
38
55
25
30
33
45
55
18
8
See Manufacturer
15
3
7-8
MISCELLANEOUS DATA AND MATHEMATICAL INFORMATION
SI UNITS FOR STRUCTURAL STEEL DESIGN
Although there are seven metric base units in the SI system, only four are currently used
by AISC in structural steel design. These base units are listed in the Table 7-6.
Table 7-6. Base SI Units for Steel Design
Quantity
Unit
Symbol
Length
mass
time
temperature
meter
kilogram
second
celcius
m
kg
s
°C
Similarly, of the numerous decimal prefixes included in the SI system, only three are used
in steel design; see Table 7-7.
Table 7-7. SI Prefixes for Steel Design
Prefix
Order of
Magnitude
Symbol
mega
kilo
milli
Expression
6
M
k
m
1,000,000 (one million)
1,000 (one thousand)
0.001 (one thousandth)
10
103
10− 3
In addition, three derived units are applicable to the present conversion. They are shown
in Table 7-8.
Table 7-8. Derived SI Units for Steel Design
Quantity
Name
Symbol
Expression
force
stress
energy
newton
pascal
joule
N
Pa
J
N = kg × m/s2
Pa = N/m2
J=N×m
Although specified in SI, the pascal is not universally accepted as the unit of stress.
Because section properties are expressed in millimeters, it is more convenient to express
stress in newtons per square millimeter (1 N/mm2 = 1 MPa). This is the practice followed
in recent international structural design standards. It should be noted that the joule, as the
unit of energy, is used to express energy absorption requirements for impact tests.
Moments are expressed in terms of N×m.
A summary of the conversion factors relating traditional U.S. units of measurement to
the corresponding SI units is given in Table 7-9.
Table 7-9. Summary of SI Conversion Factors
Multiply
by:
to obtain:
inch (in.)
foot (ft)
pound-mass (lb)
pound-force (lbf)
ksi
ft-lbf
psf
plf
25.4
305
0.454
4.448
6.895
1.356
47.88
14.59
millimeters (mm)
millimeters (mm)
kilogram (kg)
newton (N)
N/mm2
joule (J)
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
N / m2
N/m
WEIGHTS, MEASURES, AND CONVERSION FACTORS
7-9
Note that fractions resulting from metric conversion should be rounded to whole
millimeters. Common fractions of inches and their metric equivalent are in Table 7-10.
Table 7-10. SI Equivalents of Fractions of an Inch
Fraction, in.
1⁄
16
1⁄
8
3⁄
16
1⁄
4
5⁄
16
3⁄
8
7⁄
16
1⁄
2
5⁄
8
3⁄
4
7⁄
8
1
Exact conversion, mm
Rounded to: (mm)
1.5875
3.175
4.7625
6.35
7.9375
9.525
1.1125
12.7
15.875
19.05
22.225
25.4
2
3
5
6
8
10
11
13
16
19
22
25
Bolt diameters are taken directly from the ASTM Specifications A325M and A490M
rather than converting the diameters of bolts dimensioned in inches. The metric bolt
designations are in Table 7-11.
Table 7-11. SI Bolt Designation
Designation
Diameter, mm
Diameter, in.
M16
M20
M22
M24
M27
M30
M36
16
20
22
24
27
30
36
0.63
0.79
0.87
0.94
1.06
1.18
1.42
The yield strengths of structural steels are taken from the metric ASTM Specifications.
It should be noted that the yield points are slightly different from the traditional values.
See Table 7-12. The modulus of elasticity of steel E is taken as 200,000 N/mm2. The shear
modulus of elasticity of steel G is 77,000 N/mm2.
Table 7-12. SI Steel Yield Stresses
ASTM Designation
2
Yield stress, N/mm
Yield stress, ksi
A36M
250
36.26
A572M Gr. 345
A588M
345
50.04
A852M
485
70.34
A514M
690
100.07
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
7 - 10
MISCELLANEOUS DATA AND MATHEMATICAL INFORMATION
Table 7-13.
WEIGHTS AND MEASURES
International System of Units (SI)a
(Metric practice)
BASE UNITS
Quantity
length
mass
time
electric current
thermodynamic temperature
amount of substance
luminous intensity
SUPPLEMENTARY UNITS
Unit
Symbol
metre
kilogram
second
ampere
kelvin
mole
candela
m
kg
s
A
K
mol
cd
Symbol
plane angle
solid angle
Unit
Symbol
radian
steradian
rad
sr
DERIVED UNITS (WITH SPECIAL NAMES)
Quantity
force
pressure, stress
energy, work,
quantity of heat
power
Unit
Symbol
Formula
newton
pascal
N
Pa
kg-m/s2
N/m2
joule
watt
J
W
N-m
J/s
DERIVED UNITS (WITHOUT SPECIAL NAMES)
Quantity
area
volume
velocity
acceleration
specific volume
density
Unit
Formula
square metre
cubic metre
metre per second
metre per second squared
cubic metre per kilogram
kilogram per cubic metre
m2
m3
m/s
m/s2
m3/kg
kg/m3
SI PREFIXES
Multiplication Factor
18
000 = 10
000 = 1015
000 = 1012
000 = 109
000 = 106
000 = 103
100 = 102
10 = 101
0.1 = 10−1
0.01 = 10−2
0.001 = 10−3
0.000 001 = 10−6
0.000 000 001 = 10−9
0.000 000 000 001 = 10−12
0.000 000 000 000 001 = 10−15
0.000 000 000 000 000 001 = 10−18
1 000 000 000
1 000 000
1 000
1
000
000
000
000
1
000
000
000
000
000
1
Prefix
Symbol
exa
peta
tera
giga
mega
kilo
hectob
dekab
decib
centib
milli
micro
nano
pico
femto
atto
E
P
T
G
M
k
h
da
d
c
m
µ
n
p
f
a
aRefer to ASTM E380 for more complete information on SI.
bUse is not recommended.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
WEIGHTS, MEASURES, AND CONVERSION FACTORS
7 - 11
Table 7-14.
WEIGHTS AND MEASURES
United States System
LINEAR MEASURE
Inches
Feet
Yards
.02778
.08333 =
1.0 =
.33333
=
1.0
12.0 =
1.0
=
3.0
36.0 =
5.5
=
16.5
198.0 =
= 220.0
7,920.0 = 660.0
= 1,760.0
63,360.0 = 5,280.0
Rods
Furlongs
.0050505 =
=
.0606061 =
=
.1818182 =
=
=
= 1.0
=
= 40.0
=
= 320.0
.00012626
.00151515
.00454545
.025
1.0
8.0
Miles
=
=
=
=
=
=
.00001578
.00018939
.00056818
.003125
.125
1.0
SQUARE AND LAND MEASURE
Sq. Inches
1.0 =
144.0 =
1,296.0 =
39,204.0 =
Square Feet
.006944
1.0
9.0
272.25
43,560.0
Square Yards
=
=
=
=
=
Square Rods
.000772
.111111
1.0
30.25
4,840.0
3,097,600.0
Acres
.03306
=
1.0
=
160.0
=
= 102,400.0
Sq. Miles
.000207
=
.00625 = .0000098
=
= .0015625
= 1.0
= 1.0
= 640.0
AVOIRDUPOIS WEIGHTS
Grains
Drams
Ounces
Pounds
.000143
.002286 =
=
.003906
.0625 =
=
.0625
=
1.0
=
1.0
=
16.0
=
= 2,000.0
= 32,000.0
.03657
=
1.0
1.0
27.34375 =
16.0
=
437.5
256.0
=
7,000.0
= 512,000.0
140,000,000.0
DRY MEASURE
Pints
1.0
2.0
16.0
51.42627
64.0
Quarts
=
=
=
=
=
.5
1.0
8.0
25.71314
32.0
Pecks
Cubic
Feet
Bushels
= .0625 = .01945 = .01563
= .125 = .03891 = .03125
= .31112 = .25
= 1.0
= .80354
= 3.21414 = 1.0
= 1.2445 = 1.0
= 4.0
LIQUID MEASURE
Gills
1.0
4.0
8.0
32.0
=
=
=
=
Pints
Quarts
.25
1.0
2.0
8.0
= .125
= .5
= 1.0
= 4.0
U.S.
Gallons
Cubic
Feet
= .03125 = .00418
= .125 = .01671
= .250 = .03342
= .1337
= 1.0
7.48052 = 1.0
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
Tons
= .0000000714
= .00000195
= .00003125
= .0005
= 1.0
7 - 12
MISCELLANEOUS DATA AND MATHEMATICAL INFORMATION
Table 7-15.
SI CONVERSION FACTORSa
Quantity
Length
Area
Volume
Mass
Multiply
by
to obtain
inch
foot
yard
mile (U.S. Statute)
25.400
0.305
0.914
1.609
millimetre
metre
metre
kilometre
millimetre
metre
metre
kilometre
39.370×10−3
3.281
1.094
0.621
inch
foot
yard
mile
square inch
square foot
square yard
square mile (U.S. Statute)
acre
acre
0.645×103
0.093
0.836
2.590
4.047×103
0.405
square millimetre
square metre
square metre
square kilometre
square metre
hectare
mm
m
m
km
in
ft
yd
mi
mm2
m2
m2
km2
m2
square millimetre
square metre
square metre
square kilometre
square metre
hectare
1.550×10−3
10.764
1.196
0.386
0.247×10−3
2.471
square inch
square foot
square yard
square mile
acre
acre
cubic inch
cubic foot
cubic yard
gallon (U.S. liquid)
quart (U.S. liquid)
16.387×103
28.317×10−3
0.765
3.785
0.946
cubic millimetre
cubic metre
cubic metre
litre
litre
cubic millimetre
cubic metre
cubic metre
litre
litre
61.024×10−6
35.315
1.308
0.264
1.057
cubic inch
cubic foot
cubic yard
gallon (U.S. liquid)
quart (U.S. liquid)
in3
ft3
yd3
gal
qt
ounce (avoirdupois)
pound (avoirdupois)
short ton
28.350
0.454
0.907×103
gram
kilogram
kilogram
g
kg
kg
gram
kilogram
kilogram
35.274×10−3
2.205
1.102×10−3
ounce (avoirdupois)
pound (avoirdupois)
short ton
aRefer to ASTM E380 for more complete information on SI.
The conversion factors tabulated herein have been rounded.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
in2
ft2
yd2
mi2
mm3
m3
m3
l
l
oz av
lb av
WEIGHTS, MEASURES, AND CONVERSION FACTORS
7 - 13
Table 7-15 (cont.).
SI CONVERSION FACTORSa
Quantity
Force
Multiply
0.278
4.448
c
c
3.597
0.224
c
0.113
1.356
c
8.851
0.738
c
pound-force per square inch
foot of water (39.2 F)
c
inch of mercury (32 F)
6.895
2.989
3.386
c
c
0.145
c
newton
newton
c
pound-force-inch
pound-force-foot
c
c
newton-metre
newton-metre
c
Pressure,
Stress
to obtain
ounce-force
c
pound-force
c
Bending
Moment
by
c
c
c
kilopascal
newton
c
newton
c
c
c
ounce-force
pound-force
N
N
lbf
newton-metre
newton-metre
N-m
N-m
pound-force-inch
pound-force-foot
lbf-in
lbf-ft
kilopascal
kilopascal
c
kilopascal
c
kPa
kPa
kPa
lbf/in2
pound-force per
square inch
c
foot of water (39.2 F)
c
inch of mercury (32 F)
c
c
0.335
0.295
kilopascal
kilopascal
c
Energy, Work, cfoot-pound-force
b
Heat
British thermal unit
b
calorie
c
kilowatt hour
1.356
1.055×103
4.187
3.600×106
c
joule
joule
c
joule
c
joule
0.738
0.948×10−3
0.239
0.278×10−6
c
c
foot-pound-force/second
British thermal unit per hour
c
horsepower (550 ft lbf/s)
1.356
0.293
0.746
c
c
0.738
c
c
c
Power
b
watt
joule
joule
c
joule
c
joule
c
foot-pound-force
British thermal unit
c
calorie
c
kilowatt hour
c
watt
watt
c
kilowatt
c
foot-pound-force/
second
c
British thermal unit
c
per hour
c
horsepower
c
(550 ft-lbf/s)
J
J
J
J
ft-lbf
Btu
kW-h
W
W
kW
ft-lbf/s
c
c
3.412
kilowatt
1.341
watt
Angle
17.453×10−3
57.296
c
degree
radian
c
Temperature
c
degree Fahrenheit
degree Celsius
c
t°°C = (t°°F − 32)/1.8
t°°F = 1.8 × t°°C + 32
c
c
c
c
radian
degree
degree Celsius
degree Fahrenheit
aRefer to ASTM E380 for more complete information on SI.
bInternational Table.
The conversion factors tabulated herein have been rounded.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
Btu/h
hp
rad
7 - 14
MISCELLANEOUS DATA AND MATHEMATICAL INFORMATION
BRACING FORMULAS
b
b
p
d
e
a
a
c
h
h
w
w
p
d
e
c
w
w
f
m
f
m
n
To
Find Formula
Given
bpw
bw
bp
bp
bfp
bmp
bpw
afw
cmw
( b + p )2 + w 2
√
√
b 2 +w 2
2
b ÷ (2b + p)
f
m
d
e
a
c
h
h
h
bpw
bnw
bnp
bnp
bfnp
bmnp
bnpw
afw
cmw
b (b + p ) ÷ (2 b + p )
bf ÷ (2b + p )
bm ÷ (2b + p )
bw ÷ (2b + p )
aw ÷ f
cw ÷ m
(b + p )2 + w 2
√
√
(b − n )2 + w 2
b (b − n ) ÷ (2 b + p − n )
b (b + p ) ÷ (2 b + p − n )
bf ÷ (2b + p − n )
bm ÷ (2b + p − n )
bw ÷ (2b + p − n )
aw ÷ f
cw ÷ m
k = (log B − log T) ÷ no. of
panels. Constant k plus the
logarithm of any line equals
the log of the corresponding
line in the next panel below.
p
d
e
a
f
m
d
e
a
c
h
h
h
PARALLEL BLOCKING
b
k
To
Find Formula
Given
c
h
v
m
w
f
a = TH ÷ (T + e + p )
b = Th ÷ (T + e + p )
bpw
bkv
T
Formula
f
√
( b + p )2 + w 2
m
√
(b + k) + v
2
A
a
2
bkpvw
d
bw (b + k) ÷ [v (b + p ) + w (b + k )]
bkpvw
e
bv (b + p ) ÷ [v (b + p ) + w (b + k )]
bfkpvw
a
fbv ÷ [v (b + p ) + w (b + k )]
bkmpvw
c
bmw ÷ [v (b + p ) + w (b + k )]
bkpvw
h
bvw ÷ [v(b + p ) + w (b + k )]
afw
h
aw ÷ f
cmv
h
cv ÷ m
d = ce ÷ (T + e)
b
d
Given
c=√
(1 ⁄2 T + 1 ⁄2 e )2 + a 2
To
Find
c
e
A
H
f
g
h
n
m
log e = k + log T
log f = k + log a
log g = k + log b
log m = k + log c
log n = k + log d
log p = k + log e
p
A
B
The above method can be used for any number of
panels. In the formulas for ‘‘a’’ and ‘‘b’’ the sum in
parenthesis, which in the case shown is (T + e +
p), is always composed of all the horizontal
distances except the base.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
GEOMETRIC AND TRIGONOMETRIC DATA
7 - 15
PROPERTIES OF PARABOLA AND ELLIPSE
PARABOLA
ELLIPSE
(x 2 ÷ H 2) + (y 2 ÷ B 2) = 1
Abscissa = x
¼
pe
c. of g.
0.424H
.375B
Ordinate = y
Abscissa = x
c. of g.
r
ete
r
Major semi-axis = H
Ordinate = y
rim
pe
ete
rim
0.6H
½
Height = H
Apex
.424B
½ base = B
Minor semi-axis = B
2
Parameter P = B
H
y2
x=
P
y = xP
a
b
Area =
HB
D
Area = .7854Dd
d
c
d
e
a
1
b
Construction
1
2
H
c
2
H
3
3
B
e
Construction
4
4
B
B
5
AREA BETWEEN PARABOLIC CURVE AND SECANT
Apex
Center of gravity
(shaded area)
Any secant
m
.4m
H
h
b
b
2
2
b
B
B
Length b may vary from 0 to 2B
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
7 - 16
MISCELLANEOUS DATA AND MATHEMATICAL INFORMATION
PROPERTIES OF THE CIRCLE
Circumference = 6.28318 r = 3.14159 d
Diameter = 0.31831 circumference
Area = 3.14159r 2
x
π rA°
= 0.017453 rA°
180 °
180 ° a
a
Angle A ° =
= 57.29578
r
πr
4 b 2 + c2
Radius r =
8b
A
Chord c = 2 √
2 br − b 2 = 2 r sin
2
1
c
A
Rise b = r − √
4 r 2− c2 = tan
2
2
4
2 A
2
r − x 2
= 2 r sin
=r+y−√
4
y=b−r+√
r 2− x 2
Arc a =
b
y
c
A°
r
d
x=√
r 2− (r + y − b )2
Diameter of circle of equal periphery as square
Side of square of equal periphery as circle
Diameter of circle circumscribed about square
Side of square inscribed in circle
= 1.27324 side of square
= 0.78540 diameter of circle
= 1.41421 side of square
= 0.70711 diameter of circle
CIRCULAR SECTOR
r = radius of circle y = angle ncp in degrees
Area of Sector ncpo = 1 ⁄2 (length of arc nop x r)
o
n
p
y
= Area of Circle ×
r
c
y
360
= 0.0087266 × r 2 × y
CIRCULAR SEGMENT
r = radius of circle x = chord b = rise
Area of Segment nop = Area of Sector ncpo − Area of triangle ncp
o
b
n
c
p
=
x
(Length of arc nop × r) − x (r − b)
2
Area of Segment nop = Area of Circle − Area of Segment nop
s
VALUES FOR FUNCTIONS OF π
π = 3.14159265359, log = 0.4971499
_
_
1
= 0.3183099, log = 1.5028501
1π = 0.5641896, log = 1.7514251
√
π
_
_
π
1
π3 = 31.0062767, log = 1.4914496
= 0.1013212, log = 1.0057003
= 0.0174533, log = 2.2418774
180
π2
_
1
180
= 0.0322515, log = 2.5085504
= 57.2957795, log = 1.7581226
π = 1.7724539, log = 0.2485749
√
π
π3
_
_
Note: Logs of fractions such as 1 .5028501 and 2 .5085500 may also be written 9.5028501 − 10 and
8.5085500 − 10 respectively
π2 = 9.8696044, log = 0.9942997
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
GEOMETRIC AND TRIGONOMETRIC DATA
7 - 17
PROPERTIES OF GEOMETRIC SECTIONS
A = d2
SQUARE
c=
Axis of moments through center
I=
c
S=
d
r=
d
Z=
SQUARE
d
2
d4
12
d3
6
d
= .288675 d
√
12
d3
4
A = d2
c=d
Axis of moments on base
I=
d
c
S=
r=
d4
3
d3
3
d
= .577350 d
3
√
d
SQUARE
A = d2
Axis of moments on diagonal
c=
I=
c
S=
r=
d4
12
d3
= .117851 d 3
6
√2
d
d
A = bd
RECTANGLE
Axis of moments through center
c=
I=
c
S=
r=
b
= .707107 d
= .288675 d
√
12
3
2c
d3
=
= .235702 d 3
Z=
3
3√
2
d
d
d
2
√
Z=
d
2
bd 3
12
bd 2
6
d
= .288675 d
√
12
bd
2
4
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
7 - 18
MISCELLANEOUS DATA AND MATHEMATICAL INFORMATION
PROPERTIES OF GEOMETRIC SECTIONS (cont.)
RECTANGLE
A = bd
c=d
Axis of moments on base
bd 3
I=
3
S=
c
d
bd 2
3
d
r=
3
√
= .577350 d
b
RECTANGLE
A = bd
Axis of moments on diagonal
bd
√
b2 + d 2
b3 d 3
c=
c
I=
S=
b
d
RECTANGLE
c
a
d
b
6√
b2 + d 2
bd
√
6 (b 2 + d2 )
r=
Axis of moments any line
through center of gravity
6(b 2 + d 2)
b2 d 2
A = bd
b sin a + d cos a
c=
2
bd (b 2 sin2 a + d 2cos2 a )
I=
12
bd (b 2 sin2 a + d 2cos2 a )
S=
6 (b sin a + d cos a )
r=
√
b2 sin2 a + d 2cos2 a
12
A = bd − b 1 d 1
Axis of moments through center
I=
c
d
d1
12
S=
b1
r=
b
d
2
bd 3− b 1d13
c=
HOLLOW RECTANGLE
Z=
bd 3− b 1d13
6d
√
bd 3− b1d13
12 A
bd 2 b 1d 12
4
−
4
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
GEOMETRIC AND TRIGONOMETRIC DATA
7 - 19
PROPERTIES OF GEOMETRIC SECTIONS (cont.)
A = b(d − d 1 )
EQUAL RECTANGLES
d
c=
Axis of moments through
center of gravity
2
b(d 3− d 13 )
I=
d
d1
r=
b
Axis of moments through
center of gravity
d
d 3− d 13
12(d − d1)
b
t
b
2
y
c
y1
c1
t1
b1
2
4
r=
√
Z=
TRIANGLE
(d 2− d 12 )
A = bt + b 1 t1
1⁄ bt 2+ b t (d − 1 ⁄ t )
11
2
21
c=
A
b 1t13
bt 3
I=
+ bty 2 +
+ b1 t1 y 12
12
12
l
l
S=
S1 =
c
c1
d1
t1
√
Z=
UNEQUAL RECTANGLES
t
12
b(d 3− d 13 )
S=
6d
c
I
A
t + t1
A
d −
2
2
bd
2
2d
c=
3
bd 3
I=
36
bd 2
S=
24
d
r=
= .235702 d
√
18
A=
Axis of moments through
center of gravity
c
d
b
TRIANGLE
c
d
b
bd
2
c=d
bd 3
I=
12
bd 2
S=
12
d
r=
= .408248 d
6
√
A=
Axis of moments on base
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
7 - 20
MISCELLANEOUS DATA AND MATHEMATICAL INFORMATION
PROPERTIES OF GEOMETRIC SECTIONS (cont.)
TRAPEZOID
Axis of moments through
center of gravity
b1
c
A=
d (b + b 1)
2
c=
d (2 b + b 1 )
3 (b + b 1 )
I=
d 3(b 2 + 4 bb1 + b 21 )
36 (b + b1)
d
S=
b
d 2(b 2 + 4 bb1 + b 21 )
12 (2 b + b 1)
d
r=
√
2(b 2 + 4bb1 + b 21 )
6(b + b 1)
A=
πd 2
= π R 2 = .785398 d 2= 3.141593 R 2
4
c=
d
=R
2
I=
π d 4 π R4
=
= .049087 d 4= .785398 R 4
64
4
CIRCLE
Axis of moments
through center
c
R
S=
d
π d 3 π R3
=
= .098175 d 3= .785398 R 3
32
4
r=
d R
=
4 2
Z=
d3
6
π(d 2− d 12 )
= .785398 (d 2− d 12 )
4
d
c=
2
π(d 4− d 14 )
I=
= .049087 (d 4− d 14 )
64
π(d 4− d 14 )
d 4− d 14
S=
= .098175
32 d
d
A=
HOLLOW CIRCLE
Axis of moments
through center
c
d
d1
r=
HALF CIRCLE
√
d 2+ d 12
4
Z=
d 13
d
−
6
6
A=
πR 2
= 1.570796 R 2
2
3
4
= .575587 R
C = R 1 −
3π
Axis of moments through
center of gravity
π
R
d
c
I = R4
8
S=
−
8
9π
= .109757 R 4
2
R 3 (9π − 64 )
= .190687 R 3
24 (3π − 4)
r=R
√
9π 2 − 64
6π
= .264336 R
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
GEOMETRIC AND TRIGONOMETRIC DATA
7 - 21
PROPERTIES OF GEOMETRIC SECTIONS (cont.)
4
ab
3
2
m= a
5
16 3
I1 =
a b
175
4
ab 3
I2 =
15
32 3
I3 =
a b
105
A=
PARABOLA
2
a
1
m
3
1
3
b
2
2
ab
3
2
m= a
5
3
n= b
8
8
I1 =
a3b
175
19
ab 3
I2 =
480
16 3
I3 =
a b
105
2
I4 =
ab 3
15
A=
HALF PARABOLA
4
2
n
apex
a
1
m
3
1
3
2
b
4
COMPLEMENT OF
HALF PARABOLA
2
1
ab
3
7
m=
a
10
3
n= b
4
37
a3b
I1 =
2,100
1
I2 =
ab 3
80
A=
n
apex
1
1
a
m
2
b
PARABOLIC FILLET IN
RIGHT ANGLE
2
t
2√
2
t
b=
2
√
1
A = t2
6
A=
m
1
1
b
n
t
2
m=n=
a
I 1 = I2 =
4
t
5
11
2,100
t4
t
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
7 - 22
MISCELLANEOUS DATA AND MATHEMATICAL INFORMATION
PROPERTIES OF GEOMETRIC SECTIONS (cont.)
* HALF ELLIPSE
A=
1
π ab
2
m=
4a
3π
2
a
1
1
m
3
3
π
8
I1 = a 3 b −
8 9π
I2 =
1
πab3
8
I3 =
1 a3
π
8
b
b
2
1
πab
4
4a
m=
3π
4b
n=
3π
A=
* QUARTER ELLIPSE
2
4
n
π
4
I1 = a 3 b
−
16 9π
a
1
3
1
m
3
2
b
π
4
I2 = ab 3
−
16 9π
I3 =
4
1
πa3b
16
I4 = π ab3
* ELLIPTIC COMPLEMENT
2
n
π
A = ab 1 −
4
1
1
a
m=
a
π
6 1 −
4
n=
b
π
6 1 −
4
m
2
b
1
I1 = a 3 b
3
−
π
−
16
1
π
36 1 −
4
1
π
1
I2 = ab 3 −
−
π
3 16
36 1 −
4
*To obtain properties of half circle, quarter circle, and circular complement, substitute a = b = R.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
GEOMETRIC AND TRIGONOMETRIC DATA
7 - 23
PROPERTIES OF GEOMETRIC SECTIONS (cont.)
n = Number of sides
180 º
φ=
REGULAR POLYGON
n
Axis of moments
through center
1
a = 2√
R2 − R
21
a
R=
2 sin φ
a
R1 =
2 tan φ
1
1
A = na 2 cot φ = nR 2 sin 2φ = nR 12 tan φ
4
2
A (6 R 2− a 2 ) A (12 R 12 + a 2 )
I1 = I2 =
=
24
48
a
2
φ
R
R1
2
1
r1 = r2 =
√
√
6 R 2− a 2
24
=
12 R 12 + a 2
48
ANGLE
tan 2φ =
Axis of moments through
center of gravity
2K
Iy − Ix
b 2 + ct
d 2 + at
y=
2 (b + c )
2(b + c )
K = Product of Inertia about XjX and YjY
A = t (b + c ) x =
b
=±
a
t
Z
1
3
1
IY =
3
I z = Ix
Iw = Ix
Ix =
Y
W
90°
φ
X
y
c
d
X
t
Z
Y
(t (d − y)3 + by 3 − a (y − t)3)
(t (b − x)3 + dx 3 − c (x − t)3 )
sin 2 φ + IY cos 2 φ + K sin2 φ
cos 2 φ + IY sin 2 φ − K sin2 φ
K is negative when heel of angle, with respect to
center of gravity, is in 1st or 3rd quadrant, positive
when in 2nd or 4th quadrant.
W
x
abcdt
4(b + c)
BEAMS AND CHANNELS
Transverse force oblique
through center of gravity
F
F
Y
Y
x
x
φ
φ
X
3
X
3
3
3
I3 = Ix sin2 φ + IY cos 2 φ
I4 = Ix cos2 φ + IY sin2 φ
y
x
fb = M sin φ +
cos φ
I
I
x
Y
where M is bending moment due to force F.
X
X
y
y
Y
Y
4
4
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
7 - 24
MISCELLANEOUS DATA AND MATHEMATICAL INFORMATION
TRIGONOMETRIC FORMULAS
Radius AF = 1
TRIGOMETRIC
FUNCTIONS
G
H
sin A
cos A
D
L
tan A
B
cot A
c
a
b
C
sec A
A
F
cosec A
RIGHT ANGLED
TRIANGLES
a 2= c 2− b 2
b 2= c 2− a 2
c 2= a 2+ b 2
B
c
b
A
= sin 2 A + cos 2 A = sin A cosec A
= cos A sec A = tan A cot A
1
cos A
=
=
= cos A tan A = √
1 − cos 2 A = BC
cot A cosec A
sin A
1
=
=
= sin A cot A = √
1 − sin2 A = AC
tan A sec A
sin A
1
=
=
= sin A sec A = FD
cos A cot A
cos A
1
=
=
= cos A cosec A = HG
sin A tan A
tan A
1
=
=
= AD
sin A cos A
cot A
1
=
=
= AG
cos A sin A
a
C
Required
Known
A
B
a
tan A =
b
a
sin A =
c
b
tan B =
a
a
cos B =
c
√
c −a
A, a
90° − A
a cot A
A, b
90° − A
b tan A
A, c
90° − A
c sin A
a, b
a, c
OBLIQUE ANGLED
TRIANGLES
a
c
b
C
b
2
s=
a+b+c
2
K=
√
B
A
a
c
Area
√
a 2+b 2
ab
2
a√
c 2− a 2
2
2
a
sin A
a 2cot A
2
b
cos A
b2 tan A
2
c2 sin 2A
4
c cos A
a 2= b 2+ c 2− 2bc cos A
b 2= a 2+ c 2− 2ac cos B
c 2= a 2+ b 2− 2 ab cos C
( s − a ) (s − b ) ( s − c )
s
Required
Known
A
a, b , c
K
1
tan A =
2
s−a
B
C
180° − (A + B )
a, A, B
sin B =
a , b, A
a, b, C tan A =
a sin C
b − a cos C
b
c
K
K
1
1
tan B =
tan C =
2
2
s−b
s−c
b sin A
a
Area
√
s (s − a) (s − b) (s − c)
a sin B
sin A
a sin C
sin A
b sin C
sin B
√
a 2+ b 2− 2 ab cos C
ab sin C
2
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
DECIMAL EQUIVALENTS
7 - 25
DECIMALS OF AN INCH
For each 64th of an inch
With millimeter equivalents
Fractions
1⁄ ths
64
Decimal
Millimeters
(Approx.)
—
1
2
3
4
.015625
.03125
.046875
.0625
0.397
0.794
1.191
1.588
5
6
7
8
.078125
.09375
.109375
.125
1.984
2.381
2.778
3.175
9
10
11
12
.140625
.15625
.171875
.1875
3.572
3.969
4.366
4.763
13
14
15
16
.203125
.21875
.234375
.250
5.159
5.556
5.953
6.350
17
18
19
20
.265625
.28125
.296875
.3125
6.747
7.144
7.541
7.938
21
22
23
24
.328125
.34375
.359375
.375
8.334
8.731
9.128
9.525
25
26
27
28
.390625
.40625
.421875
.4375
9.922
10.319
10.716
11.113
29
30
31
32
.453125
.46875
.484375
.500
11.509
11.906
12.303
12.700
1⁄
32
—
1⁄
16
—
3⁄
32
—
1⁄
8
—
5⁄
32
—
3⁄
16
—
7⁄
32
—
1⁄
4
—
9⁄
32
—
5⁄
16
—
11⁄
32
—
3⁄
8
—
13⁄
32
—
7⁄
16
—
15⁄
32
—
1⁄
2
Decimal
Millimeters
(Approx.)
33
34
35
36
.515625
.53125
.546875
.5625
13.097
13.494
13.891
14.288
37
38
39
40
.578125
.59375
.609375
.675
14.684
15.081
15.478
15.875
41
42
43
44
.640625
.65625
.671875
.6875
16.272
16.669
17.066
17.463
45
46
47
48
.703125
.71875
.734375
.750
17.859
18.256
18.653
19.050
49
50
51
52
.765625
.78125
.796875
.8125
19.447
19.844
20.241
20.638
53
54
55
56
.828125
.84375
.859375
.875
21.034
21.431
21.828
22.225
57
58
59
60
.890625
.90625
.921875
.9375
22.622
23.019
23.416
23.813
61
62
63
64
.953125
.96875
.984375
1.000
24.209
24.606
25.003
25.400
Fractions
1⁄ ths
64
—
17⁄
32
—
9⁄
16
—
19⁄
32
—
5⁄
8
—
21⁄
32
—
11⁄
16
—
23⁄
32
—
3⁄
4
—
25⁄
32
—
13⁄
16
—
27⁄
32
—
7⁄
8
—
29⁄
32
—
15⁄
16
—
31⁄
32
—
1
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
7 - 26
MISCELLANEOUS DATA AND MATHEMATICAL INFORMATION
DECIMALS OF A FOOT
For each 32nd of an inch
Inch
0
1
2
3
4
5
0
0
.0026
.0052
.0078
.0833
.0859
.0885
.0911
.1667
.1693
.1719
.1745
.2500
.2526
.2552
.2578
.3333
.3359
.3385
.3411
.4167
.4193
.4219
.4245
.0104
.0130
.0156
.0182
.0938
.0964
.0990
.1016
.1771
.1797
.1823
.1849
.2604
.2630
.2656
.2682
.3438
.3464
.3490
.3516
.4271
.4297
.4323
.4349
5⁄
16
11⁄
32
.0208
.0234
.0260
.0286
.1042
.1068
.1094
.1120
.1875
.1901
.1927
.1953
.2708
.2734
.2760
.2786
.3542
.3568
.3594
.3620
.4375
.4401
.4427
.4453
3⁄
8
13⁄
32
7⁄
16
15⁄
32
.0313
.0339
.0365
.0391
.1146
.1172
.1198
.1224
.1979
.2005
.2031
.2057
.2812
.2839
.2865
.2891
.3646
.3672
.3698
.3724
.4479
.4505
.4531
.4557
1⁄
2
17⁄
32
9⁄
16
19⁄
32
.0417
.0443
.0469
.0495
.1250
.1276
.1302
.1328
.2083
.2109
.2135
.2161
.2917
.2943
.2969
.2995
.3750
.3776
.3802
.3828
.4583
.4609
.4635
.4661
5⁄
8
21⁄
32
11⁄
16
23⁄
32
.0521
.0547
.0573
.0599
.1354
.1380
.1406
.1432
.2188
.2214
.2240
.2266
.3021
.3047
.3073
.3099
.3854
.3880
.3906
.3932
.4688
.4714
.4740
.4766
3⁄
4
25⁄
32
13⁄
16
27⁄
32
.0625
.0651
.0677
.0703
.1458
.1484
.1510
.1536
.2292
.2318
.2344
.2370
.3125
.3151
.3177
.3203
.3958
.3984
.4010
.4036
.4792
.4818
.4844
.4870
7⁄
8
29⁄
32
15⁄
16
31⁄
32
.0729
.0755
.0781
.0807
.1563
.1589
.1615
.1641
.2396
.2422
.2448
.2472
.3229
.3255
.3281
.3307
.4063
.4089
.4115
.4141
.4896
.4922
.4948
.4974
1⁄
1⁄
3⁄
32
16
32
1⁄
8
5⁄
3⁄
7⁄
32
16
32
1⁄
4
9⁄
32
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
DECIMAL EQUIVALENTS
7 - 27
DECIMALS OF A FOOT (cont.)
For each 32nd of an inch
Inch
6
7
8
9
10
11
0
1⁄
32
1⁄
16
3⁄
32
.5000
.5026
.5052
.5078
.5833
.5859
.5885
.5911
.6667
.6693
.6719
.6745
.7500
.7526
.7552
.7578
.8333
.8359
.8385
.8411
.9167
.9193
.9219
.9245
1⁄
8
5⁄
32
3⁄
16
7⁄
32
.5104
.5130
.5156
.5182
.5938
.5964
.5990
.6016
.6771
.6797
.6823
.6849
.7604
.7630
.7656
.7682
.8438
.8464
.8490
.8516
.9271
.9297
.9323
.9349
1⁄
4
9⁄
32
5⁄
16
11⁄
32
.5208
.5234
.5260
.5286
.6042
.6068
.6094
.6120
.6875
.6901
.6927
.6953
.7708
.7734
.7760
.7786
.8542
.8568
.8594
.8620
.9375
.9401
.9427
.9453
3⁄
.5313
.5339
.5365
.5391
.6146
.6172
.6198
.6224
.6979
.7005
.7031
.7057
.7813
.7839
.7865
.7891
.8646
.8672
.8698
.8724
.9479
.9505
.9531
.9557
.5417
.5443
.5469
.5495
.6250
.6276
.6302
.6328
.7083
.7109
.7135
.7161
.7917
.7943
.7969
.7995
.8750
.8776
.8802
.8828
.9583
.9609
.9635
.9661
.5521
.5547
.5573
.5599
.6354
.6380
.6406
.6432
.7188
.7214
.7240
.7266
.8021
.8047
.8073
.8099
.8854
.8880
.8906
.8932
.9688
.9714
.9740
.9766
.5625
.5651
.5677
.5703
.6458
.6484
.6510
.6536
.7292
.7318
.7344
.7370
.8125
.8151
.8177
.8203
.8958
.8984
.9010
.9036
.9792
.9818
.9844
.9870
.5729
.5755
.5781
.5807
.6563
.6589
.6615
.6641
.7396
.7422
.7448
.7474
.8229
.8255
.8281
.8307
.9063
.9089
.9115
.9141
.9896
.9922
.9948
.9974
13⁄
8
32
7⁄
16
15⁄
32
1⁄
17⁄
2
32
9⁄
16
19⁄
32
5⁄
21⁄
8
32
11⁄
16
23⁄
32
3⁄
25⁄
13⁄
27⁄
7⁄
29⁄
15⁄
31⁄
4
32
16
32
8
32
16
32
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
8-1
PART 8
BOLTS, WELDS, AND CONNECTED ELEMENTS
OVERVIEW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-3
BOLTED CONSTRUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-7
High-Strength Bolts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-7
Non-High-Strength Bolts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-19
Design Strength of Bolts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-19
ECCENTRICALLY LOADED BOLT GROUPS . . . . . . . . . . . . . . . . . . . . . . . 8-28
ANCHOR RODS OR THREADED RODS . . . . . . . . . . . . . . . . . . . . . . . . . 8-88
OTHER MECHANICAL FASTENERS . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-92
WELDED CONSTRUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-98
Fillet Welds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-118
Complete-Joint-Penetration Groove Welds . . . . . . . . . . . . . . . . . . . . . . . . 8-122
Partial-Joint-Penetration Groove Welds . . . . . . . . . . . . . . . . . . . . . . . . . . 8-125
Flare Welds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-127
Plug and Slot Welds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-128
Design Strength of Welds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-129
Prequalified Welded Joints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-131
ECCENTRICALLY LOADED WELD GROUPS . . . . . . . . . . . . . . . . . . . . . . 8-154
CONSTRUCTION COMBINING BOLTS AND WELDS . . . . . . . . . . . . . . . . . 8-211
CONNECTED ELEMENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-212
Design Strength of Connecting Elements . . . . . . . . . . . . . . . . . . . . . . . . . 8-212
Members with Copes, Blocks, or Cuts . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-225
Other Elements in Connections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-237
REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-238
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
8-2
BOLTS, WELDS, AND CONNECTED ELEMENTS
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
OVERVIEW
8-3
OVERVIEW
Part 8 contains general information, design considerations, examples, and design aids for
the design of bolts, anchor rods, other mechanical fasteners, welds, and connected
elements in connections. It is based on the provisions of the 1993 LRFD Specification.
Supplementary information may also be found in the Commentary on the LRFD
Specification.
Following is a detailed overview of the topics addressed.
BOLTED CONSTRUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-7
High-Strength Bolts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-7
Alternative Design Bolts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-7
Compatible Nuts and Washers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-8
Economical Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-8
Dimensions and Weights . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-9
Entering and Tightening Clearances . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-12
Snug-Tightened and Fully Tensioned Installation . . . . . . . . . . . . . . . . . . . . 8-12
Inspection of Fully Tensioned High-Strength Bolts . . . . . . . . . . . . . . . . . . . 8-15
Galvanizing High-Strength Bolts . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-18
Reuse of High-Strength Bolts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-19
Non-High-Strength Bolts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-19
Dimensions and Weights . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-19
Entering and Tightening Clearances . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-19
Design Strength of Bolts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-19
Bolt Shear Strength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-22
Bearing Strength at Bolt Holes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-23
Bolt Tensile Strength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-23
Slip Resistance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-25
ECCENTRICALLY LOADED BOLT GROUPS . . . . . . . . . . . . . . . . . . . . . . . 8-28
Eccentricity in the Plane of the Faying Surface . . . . . . . . . . . . . . . . . . . . . . 8-28
Instantaneous Center of Rotation Method . . . . . . . . . . . . . . . . . . . . . . . . 8-28
Elastic Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-33
Eccentricity Normal to the Plane of the Faying Surface . . . . . . . . . . . . . . . . . . 8-36
Case I—Neutral Axis Not at Center of Gravity . . . . . . . . . . . . . . . . . . . . . 8-37
Case II—Neutral Axis at Center of Gravity . . . . . . . . . . . . . . . . . . . . . . . 8-38
ANCHOR RODS OR THREADED RODS . . . . . . . . . . . . . . . . . . . . . . . . . 8-88
Minimum Edge Distance and Embeddment Length . . . . . . . . . . . . . . . . . . . . 8-88
Welding to Anchor Rods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-89
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
8-4
BOLTS, WELDS, AND CONNECTED ELEMENTS
Hooked Anchor Rods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-89
Headed Anchor Rods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-90
OTHER MECHANICAL FASTENERS . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-92
Clevises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-92
Turnbuckles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-92
Sleeve Nuts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-93
Recessed-Pin Nuts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-93
Cotter Pins . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-93
WELDED CONSTRUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-98
Weldability of Steel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-98
Chemical Composition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-99
Grain Size . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-100
Thickness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-100
Structural Welding Materials and Processes . . . . . . . . . . . . . . . . . . . . . . . 8-101
SMAW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-102
SAW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-105
GMAW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-106
FCAW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-106
ESW and EGW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-107
Thermal Cutting and Air-Arc Gouging . . . . . . . . . . . . . . . . . . . . . . . . . 8-108
Inspection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-108
VT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-109
DPT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-109
MT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-109
RT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-110
UT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-110
Economical Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-111
Welding Position . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-112
Weld Type . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-112
Weld Metal Volume . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-112
Deposit Time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-113
Prior Qualification of Procedures . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-113
Minimizing Weld Repairs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-113
Lamellar Tearing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-113
Fatigue Cracking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-113
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
OVERVIEW
8-5
Notch Development . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-114
Impact Toughness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-114
Arc Strikes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-114
Other Considerations in Welded Construction . . . . . . . . . . . . . . . . . . . . . . . 8-115
Matching Electrodes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-115
Welding Shapes from ASTM A6 Groups 4 and 5 . . . . . . . . . . . . . . . . . . . . 8-115
Intersecting Welds and Triaxial Stresses . . . . . . . . . . . . . . . . . . . . . . . . . 8-116
Painting Welded Connections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-117
Clearances for Welding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-118
Fillet Welds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-118
Effective Area . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-118
Minimum Effective Length . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-119
Minimum Fillet Weld Size . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-119
Maximum Fillet Weld Size . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-119
End Returns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-120
Fillet Welds in Holes or Slots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-121
Other Limitations on Fillet Welds . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-121
Minimum Shelf Dimensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-122
Complete-Joint-Penetration Groove Welds . . . . . . . . . . . . . . . . . . . . . . . . 8-122
Extension, Runoff, Backing, and Spacer Bars . . . . . . . . . . . . . . . . . . . . . . 8-122
Weld Access Holes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-125
Partial-Joint-Penetration Groove Welds . . . . . . . . . . . . . . . . . . . . . . . . . . 8-125
Effective Area . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-127
Intermittent Welds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-127
Flare Welds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-127
Effective Area . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-128
Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-128
Plug and Slot Welds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-128
Design Strength of Welds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-129
Weld Metal Design Strength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-129
Base Metal Design Strength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-129
Prequalified Welded Joints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-131
ECCENTRICALLY LOADED WELD GROUPS . . . . . . . . . . . . . . . . . . . . . . 8-154
Eccentricity in the Plane of the Faying Surface . . . . . . . . . . . . . . . . . . . . . . 8-154
Instantaneous Center of Rotation Method . . . . . . . . . . . . . . . . . . . . . . . . 8-154
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
8-6
BOLTS, WELDS, AND CONNECTED ELEMENTS
Elastic Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-159
Eccentricity Normal to the Plane of the Faying Surface . . . . . . . . . . . . . . . . . 8-211
CONSTRUCTION COMBINING BOLTS AND WELDS . . . . . . . . . . . . . . . . . 8-211
CONNECTED ELEMENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-212
Economical Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-212
Design Strength of Connected Elements . . . . . . . . . . . . . . . . . . . . . . . . . 8-212
Shear Yielding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-212
Shear Rupture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-212
Block Shear Rupture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-212
Tension Yielding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-225
Tension Rupture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-225
Members with Copes, Blocks, or Cuts . . . . . . . . . . . . . . . . . . . . . . . . . . 8-225
Flexural Yielding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-225
Local Web Buckling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-226
Lateral Torsional Buckling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-229
Other Elements In Connections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-237
Shims . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-237
Fillers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-237
REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-238
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
BOLTED CONSTRUCTION
8-7
BOLTED CONSTRUCTION
High-Strength Bolts
LRFD Specification Section A3.3 permits the use of ASTM A325 and A490 high-strength
bolts. ASTM A325 bolts are available in diameters from 1⁄2-in. to 11⁄2-in. in two types.
Type 1 medium-carbon-steel bolts are for general purpose use and use in elevated
temperatures; they may be galvanized. Type 3 bolts offer improved atmospheric corrosion
resistance and weathering characteristics similar to those of ASTM A242 or A588 steels.
ASTM A490 bolts are available in diameters from 1⁄2-in. to 11⁄2-in. in two types. Type 1
bolts are alloy-steel bolts. Type 3 are alloy-steel bolts with improved atmospheric
corrosion resistance and weathering characteristics similar to those of ASTM A242 or
A588 steels. ASTM A490 bolts should not be galvanized and caution should be exercised
if used in highly corrosive environments.
Type 2 (martensite) bolts, popular for many years, have been discontinued. Information
on this type can be found in previous editions of the AISC Manual of Steel Construction.
When bolts of diameter larger than 11⁄2 in. are required, ASTM A449 bolts are permitted
to be used for snug-tightened and fully tensioned bearing-type connections; this material
is not recognized in LRFD Specification Section A3.3 for use in slip-critical connections
nor for use as bolts in diameters not greater than 11⁄2 in. ASTM A449 bolts may be
galvanized.
When an ASTM A449 bolt is used in tension or bearing and is tightened in excess of
50 percent of its minimum specified tensile strength, LRFD Specification Section J3.1
requires that an ASTM F436 washer be installed under the head of the bolt. The nut must
be from the approved list in RCSC Specification Section 2(c). Since ASTM A325 nuts
and washers for use with high-strength bolts are available only up to 11⁄2-in. diameter,
reference should be made to ASTM A563 for nuts and ASTM F436 for washers to select
suitable sizes and grades for the intended application.
While ASTM A449 seems to be the equal of ASTM A325, there are two important
differences which should be noted. First, ASTM A449 bolts are not produced to the same
inspection and quality assurance requirements as ASTM A325 bolts. Second, ASTM
A449 bolts are not produced to the same heavy-hex head and nut dimensions.
Alternative Design Bolts
RCSC Specification Section 2d permits the use of other fasteners when they meet the
requirements as outlined therein. Figure 8-1 shows a tension-control or “twist-off” bolt
which is installed with a special tool which twists off the splined end when the proper
Fig. 8-1. Tension-control or “twist-off” bolt.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
8-8
BOLTS, WELDS, AND CONNECTED ELEMENTS
Table 8-1.
Compatability of High-Strength Bolts, Nuts, Washers
F436 Washer
Grade
ASTM
Bolt
Desig.
Type
Coating
Recommended
Suitable
Recommended
A325
1
plain
C
C3, D, DH, DH3
1
galvanized
DH
—
1
3
plain
C3
DH3
3
1
plain
DH
DH3
1
3
plain
DH3
—
3
1
plain
A
C, C3, D, DH, DH3
1
galvanized
DH
D
1
A490
A449
A563 Heavy Hex Nut Grade
bolt tension is achieved. Tension-control bolts are commonly available to meet the
specifications of ASTM A325 and A490.
Compatible Nuts and Washers
The compatibility of ASTM A563 nuts and F436 washers with the aforementioned
high-strength bolt specifications is as listed in Table 8-1. Alternatively, appropriate ASTM
A194 nuts may be used. RCSC Specification Section 7c gives general requirements for
when washers are required for high-strength bolts.
Economical Considerations
Since the material cost per unit of strength of ASTM A490 bolts is comparable with that
of ASTM A325 bolts, it might seem more cost effective to reduce the number of bolts in
a given connection by specifying ASTM A490 bolts. However, ASTM A490 bolts are
more difficult to tighten and raise inventory and quality control issues associated with
the use of multiple fastener grades; mixing of ASTM A325 and A490 bolts of the same
diameter should be avoided to assure that the ASTM A490 bolts are installed in the proper
location. Thus, the net benefit of specifying ASTM A490 bolts may be less than expected;
cost ratios should be considered by the designer.
Similarly, cost ratios between grades of alternative design bolts will vary from those
of conventional high-strength bolts. Thus, the decision regarding fastener selection will
vary accordingly.
Regardless of the bolt type selected, the normal sizes of 3⁄4-in., 7⁄8-in., and 1-in. diameter
are usually preferred. Diameters above one inch are not commonly available, nor are they
practical since special tools may be required to achieve fully tensioned installation.
Bearing-type connections should be specified whenever possible. Slip-critical connections with coatings other than clean mill scale incur appreciable extra costs associated
with blasting, painting, drying, assembling, reblasting, and abrasion touch-up. If slipcritical connections are required for the proper serviceablity of the structure, care should
be taken to avoid requiring the faying surfaces to be masked as this also contributes great
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
BOLTED CONSTRUCTION
8-9
expense; coatings which provide a Class A or Class B slip coefficient may be an
economical alternative to masking.
Dimensions and Weights
ASTM A325 and A490 bolts, A563 nuts, and F436 washers are given identifying marks
as illustrated in Figure 8-2. A detailed description of identifying marks may be found in
the RCSC Specification. Dimensions of ASTM A325 and A490 bolts, A563 nuts, and
F436 washers are given and illustrated in Table 8-2. Threading dimensions of highstrength bolts are given in Table 8-7. Weights of conventional ASTM A325 and A490
bolts, A563 nuts, and F436 washers are given in Table 8-3. For dimensions and weights
of tension-control ASTM A325 and A490 bolts, refer to manufacturers’ literature or IFI.
For dimensions and weights of ASTM A449 bolts, refer to Table 8-6.
Threads for high-strength bolts may be rolled or cut. Note that thread lengths for
high-strength bolts are shorter than those for non-high-strength bolts. This allows the
threads to be excluded from the shear plane when the thickness of the connected ply
closest to the nut is as shown in Figure 8-3. While the RCSC Specification permits some
thread run-out into the shear plane, it is important to provide sufficient thread to avoid
jamming the nut into the run-out when tightening the bolt. Inspection controversy will
be reduced by recognizing that bolts intentionally have a limited thread length, a
manufacturing tolerance, and limited length increments; as with all manufactured items,
dimensional tolerances must be considered.
The RCSC Specification recognizes these tolerances in two ways. First, additional
washers are permitted to be used under the nut or under the head when circumstances
permit. Second, there is no specified bolt “stick-through” requirement since only fullthread engagement of the nut is required; from RCSC Specification Section 2(b), “…The
length of bolts shall be such that the end of the bolt will be flush with or outside the face
of the nut when properly installed.” A requirement for “stick-through”, sometimes written
in project specifications, increases the risk of jamming the nut on the thread run-out, and
thus, of preventing tightening. A “stick-through” requirement will not enhance the
performance of the bolt and should not be included in a project specification.
Alternatively, ASTM A325 bolts with length less than or equal to four times the
nominal diameter may be ordered as fully threaded with the designation ASTM A325 T.
Fully threaded ASTM A325 T bolts are not for use in bearing-type X connections since
it would be impossible to exclude the threads from the shear plane. While this supplementary provision exists for ASTM A325 bolts, there is no similar supplementary
provision made in ASTM A490 for full-length threading.
The ordered length of ASTM A325 and A490 bolts should be calculated as the grip
(see Figure 8-2) plus the thickness of the washer(s) plus the allowance from Table 8-2.
A thickness of 5⁄32-in. for circular washers and 5⁄16-in. for beveled washers should be
provided per washer used; refer to the RCSC Specification for washer requirements. This
total should be rounded to the next higher one-quarter inch. Note that bolts longer than
five inches are generally available only in 1⁄2-in. increments, except by special arrangement with the manufacturer or vendor. While longer lengths may be ordered, an 8-in.
length is generally the maximum stock length available. Clipped washers are available
for use in areas of tight clearance.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
Type 1
Type 3*
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
HARDENED
WASHER
(Beveled)
2
12
3
Hex
head
Marking for washer
used with Type 3
bolt
ASTM A490 BOLT
Grip
ASTM A325 BOLT
Washer
face
Type 1
NUT MARKING
Type 3*
3
Alt. marking
“D” or “DH”
for type 1
“DH3” for
Type 3
Nut marking
“DH” for Type 1
“DH3” for Type 3
X
*Bolt heads, nuts, & washers shall include
manuf. identification symbol. The manuf. may
also add other marks indicating weathering grade.
X
Hex Nut*
Type 1 and 3*
See RCSC Specification for rules
governing use of hardened washers
Hex
nut
Standard
marking
indicates
Grade C
Fig. 8-2. Identifying high-strength bolts, nuts, and washers.
HARDENED*
WASHER
(Plain)
Type 1
Type 3*
Optional Clip
A490
A490
Standard bolt
marking
BOLT HEAD MARKING
A325
A325
Three radial lines
@ 120°, optional
See RCSC Specification for
rules governing use of washers
Grip
Dia.
Dia.
8 - 10
BOLTS, WELDS, AND CONNECTED ELEMENTS
BOLTED CONSTRUCTION
8 - 11
Table 8-2.
Dimensions of High-Strength Fasteners, in.
E
I.D.
Thread
Length
O.D.
T
A325
E
I.D.
H
F
Bolt Length
H
W
Nut may be chamfered
on both faces
A
T
A
Nominal Bolt Diameter, in.
A563
Nutsb
A325 and
A490 Boltsa
Measurement
Width Across
Flats F
Height H
Thread Length
Bolt Lengthf
=Grip + →
Width Across
Flats W
Height H
F436 Square or
Rect. Washersc,e
F436 Circular
Washersc
Nom. Outside
Diameter OD
a
b
c
d
e
f
Nom. Inside
Diameter ID
Thckns.
T
1⁄
2
5⁄
8
3⁄
4
7⁄
8
7⁄
11 ⁄16
11 ⁄4
16
25 ⁄
15 ⁄
1
11 ⁄4
13 ⁄8
11 ⁄2
13 ⁄4
2
2
21 ⁄4
21 ⁄4
7⁄
1
11 ⁄8
11 ⁄4
11 ⁄2
15 ⁄8
13 ⁄4
17 ⁄8
5⁄
11⁄
8
16
7⁄
31 ⁄
64
8
32
1
1 1 ⁄8
17 ⁄16
15 ⁄8
113 ⁄16
35 ⁄
39 ⁄
64
64
11⁄
16
1 1 ⁄4
1 3 ⁄8
2
23⁄16
23 ⁄8
27 ⁄
15 ⁄
25 ⁄
32
32
1 1 ⁄2
16
8
11 ⁄16
11 ⁄4
17 ⁄16
15 ⁄8
113 ⁄16
2
23⁄16
23 ⁄8
64
39 ⁄
47 ⁄
55 ⁄
64
63 ⁄
17⁄64
17⁄32
111⁄32
115 ⁄32
13 ⁄4
2
21 ⁄4
21 ⁄2
23 ⁄4
3
11 ⁄8
11 ⁄4
13 ⁄8
11 ⁄2
15 ⁄8
64
11 ⁄16
15 ⁄16
17 ⁄
11⁄
32
16
64
115 ⁄32
13 ⁄
16
15 ⁄
16
64
Max.
0.097
0.122
0.122
0.136
0.136
0.136
0.136
0.136
0.136
Min.
0.177
0.177
0.177
0.177
0.177
0.177
0.177
0.177
0.177
1
1 3⁄32
17⁄32
15⁄16
Min. Edge
Distance E d
7⁄
Min. Side
Dimension A
13⁄4
13 ⁄4
13 ⁄4
13 ⁄4
13 ⁄4
21 ⁄4
21 ⁄4
21 ⁄4
21 ⁄4
5⁄
5⁄
5⁄
5⁄
5⁄
5⁄
5⁄
5⁄
5⁄
Mean Thckns. T
Taper in
Thickness
Min. Edge
Distance E d
16
16
2:12
7⁄
16
9⁄
16
16
2:12
9⁄
16
21 ⁄
32
16
25 ⁄
32
16
2:12
2:12
21 ⁄
25 ⁄
32
32
7⁄
8
16
2:12
7⁄
8
16
16
16
16
2:12
2:12
2:12
2:12
1
13⁄32
17⁄32
15⁄16
Tolerances as specified in ASTM A325 and A490.
Tolerances as specified in ASTM A563.
ASTM F436 Washer Tolerances, in.:
Nominal Outside Diameter
Nominal Diameter of Hole
Flatness: max. deviation from straight-edge placed on cut side shall not exceed
Concentricity: center of hole to outside diameter (full indicator runout)
Burr shall not project above immediately adjacent washer surface more than
For clipped washers only.
For use with American standard beams (S) and channels (C).
Tabular value does not include thickness of washer(s).
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
−1/32; +1/32
−0; +1/32
0.010
0.030
0.010
8 - 12
BOLTS, WELDS, AND CONNECTED ELEMENTS
Table 8-3.
Weights of High-Strength Fasteners, pounds per 100 count
Nominal Bolt Diameter, in.
1⁄
2
5⁄
8
3⁄
4
7⁄
8
1
1 1 ⁄8
1 1 ⁄4
1 3 ⁄8
1 1 ⁄2
1
11 ⁄4
11 ⁄2
13 ⁄4
16.5
17.8
19.2
20.5
29.4
31.1
33.1
35.3
47.0
49.6
52.2
55.3
—
74.4
78.0
81.9
—
104
109
114
—
—
148
154
—
—
197
205
—
—
—
261
—
—
—
333
2
21 ⁄4
21 ⁄2
23 ⁄4
21.9
23.3
24.7
26.1
37.4
39.8
41.7
43.9
58.4
61.6
64.7
67.8
86.1
90.3
94.6
98.8
119
124
130
135
160
167
174
181
212
220
229
237
270
279
290
300
344
355
366
379
3
31 ⁄4
31 ⁄2
33 ⁄4
27.4
28.8
30.2
31.6
46.1
48.2
50.4
52.5
70.9
74.0
77.1
80.2
103
107
111
116
141
146
151
157
188
195
202
209
246
255
263
272
310
321
332
342
391
403
416
428
4
41 ⁄4
41 ⁄2
43 ⁄4
33.0
34.3
35.7
37.1
54.7
56.9
59.0
61.2
83.3
86.4
89.5
92.7
120
124
128
133
162
168
173
179
216
223
230
237
280
289
298
306
353
363
374
384
441
453
465
478
5
51 ⁄4
51 ⁄2
53 ⁄4
38.5
39.9
41.2
42.6
63.3
65.5
67.7
69.8
95.8
98.9
102
105
137
141
146
150
184
190
196
201
244
251
258
265
315
324
332
341
395
405
416
426
490
503
515
527
6
61 ⁄4
61 ⁄2
63 ⁄4
44.0
—
—
—
71.9
74.1
76.3
78.5
108
111
114
118
154
158
163
167
207
212
218
223
272
279
286
293
349
358
367
375
437
447
458
468
540
552
565
577
7
71 ⁄4
71 ⁄2
73 ⁄4
—
—
—
—
80.6
82.8
84.9
87.1
121
124
127
130
171
175
179
183
229
234
240
246
300
307
314
321
384
392
401
410
479
489
500
510
589
602
614
626
8
81 ⁄4
81 ⁄2
83 ⁄4
—
—
—
—
89.2
—
—
—
133
—
—
—
187
192
196
—
251
257
262
—
328
335
342
—
418
427
435
444
521
531
542
552
639
651
664
676
9
—
—
—
—
—
—
453
563
689
100, Conventional A325 or A490 Bolts with A563 Nuts
Bolt Length, in.
Per inch
add’tl. add
5.5
8.6
12.4
16.9
22.1
28.0
34.4
42.5
49.7
100, F436
Circular Washers
2.1
3.6
4.8
7.0
9.4
11.3
13.8
16.8
20.0
100, F436 Square
Washers
23.1
22.4
21.0
20.2
19.2
34.0
31.6
31.2
32.9
This table conforms to weight standards adopted by the Industrial Fasteners Institute (IFI), updated for washer
weights.
Entering and Tightening Clearances
The assembly of high-strength bolted connections requires clearance for entering and
tightening the bolts with an impact wrench. The clearance requirements for conventional
high-strength bolts are as given in Table 8-4. When high-strength tension-control bolts
are specified, the entering and tightening clearances are as specified in Table 8-5.
Snug-Tightened and Fully Tensioned Installation
When subjected to shear only, high-strength bolts may be used in snug-tightened
bearing-type, fully tensioned bearing-type, and slip-critical connections. When subjected
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
BOLTED CONSTRUCTION
8 - 13
Table 8-4.
Entering and Tightening Clearances, in.
Conventional ASTM A325 and A490 Bolts
Aligned Bolts
C2
socket
H1
C1
Nominal
Bolt Dia., Socket
in.
Dia., in.
H2
C1
C1
5⁄
8
3⁄
4
7⁄
8
H2
1
C3
11⁄
8
fillet
11⁄
4
1 3 ⁄8
1 1 ⁄2
13 ⁄4
21 ⁄4
21 ⁄2
25 ⁄8
27 ⁄8
31 ⁄8
31 ⁄4
31 ⁄2
C3
H1
25 ⁄
15 ⁄
35 ⁄
39 ⁄
11⁄
64
32
64
64
16
25 ⁄
32
27 ⁄
32
15 ⁄
16
H2
C1
11 ⁄4
13 ⁄8
11 ⁄2
15 ⁄8
17 ⁄8
2
21 ⁄8
21 ⁄4
1
11 ⁄4
13 ⁄8
17 ⁄16
19 ⁄16
111⁄16
13 ⁄4
15 ⁄16
C2
11⁄
16
3⁄
4
7⁄
8
15 ⁄
16
1
1 ⁄16
1
1 ⁄8
11 ⁄4
15 ⁄16
Circular Clipped
11⁄
16
3⁄
4
7⁄
8
9⁄
16
11⁄
16
13 ⁄
16
7⁄
8
1
11 ⁄8
11 ⁄4
13 ⁄8
11 ⁄2
1
11 ⁄8
11 ⁄4
15 ⁄16
Staggered Bolts
Stagger P, in.
Nominal Bolt Diameter, in.
F
5⁄
8
3⁄
4
7⁄
8
1
1 1 ⁄8
1 1 ⁄4
1 3 ⁄8
15 ⁄8
11 ⁄2
11 ⁄2
17 ⁄16
115 ⁄16
17 ⁄8
23 ⁄16
11⁄
11 ⁄
113 ⁄
2
C1
P
1 5 ⁄8
1 3 ⁄4
1 7 ⁄8
2
2 1 ⁄8
2 1 ⁄4
2 3 ⁄8
2 1 ⁄2
2 5 ⁄8
2 3 ⁄4
2 7 ⁄8
F
3
3 1 ⁄8
3 1 ⁄4
3 3 ⁄8
C1 = tightening
clearance
4
11 ⁄4
13 ⁄16
11 ⁄8
1
13 ⁄
16
16
13 ⁄4
111⁄16
19 ⁄16
11 ⁄
2
13 ⁄8
11 ⁄4
11 ⁄8
7⁄
8
1
11⁄8
11⁄4
1 3 ⁄8
1 1 ⁄2
21 ⁄8
21 ⁄16
2
115 ⁄16
25 ⁄16
25 ⁄16
21 ⁄4
23 ⁄16
29 ⁄16
29 ⁄16
21 ⁄2
213 ⁄16
23 ⁄4
3
3
33 ⁄4
113 ⁄
21 ⁄
27 ⁄
16
8
16
215 ⁄16
27 ⁄8
213 ⁄16
31 ⁄4
33 ⁄16
33 ⁄16
31 ⁄8
27 ⁄16
25 ⁄16
21 ⁄8
21 ⁄16
23 ⁄4
27 ⁄8
21 ⁄2
23 ⁄8
31 ⁄16
3
27 ⁄8
213 ⁄16
2
17 ⁄8
13 ⁄4
15 ⁄8
21 ⁄4
21 ⁄8
2
115 ⁄16
211⁄16
21 ⁄2
23 ⁄8
21 ⁄4
13 ⁄8
11 ⁄16
13 ⁄4
19 ⁄16
15 ⁄16
21 ⁄8
2
17 ⁄8
11
1 ⁄16
4
111⁄16
19 ⁄16
11 ⁄2
2
17 ⁄8
13 ⁄4
23 ⁄8
21 ⁄4
21 ⁄8
211⁄16
25 ⁄8
21 ⁄2
13 ⁄8
13 ⁄16
15 ⁄8
11 ⁄2
13 ⁄8
13 ⁄16
2
115 ⁄16
17 ⁄8
13 ⁄4
7⁄
15 ⁄8
11 ⁄2
11 ⁄4
15 ⁄
16
8
15 ⁄
16
31⁄
2
standard
socket
23 ⁄
3 5 ⁄8
3 3 ⁄4
3 7 ⁄8
4
Notes:
H1 = height of head, in.
H2 = maximum shank extension,* in.
C1 = clearance for tightening, in.
C2 = clearance for entering, in.
C3 = clearance for fillet,* in.
P = bolt stagger, in.
F = clearance for tightening staggered bolts, in.
*Based on one standard hardened washer.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
215 ⁄
16
13 ⁄8
8 - 14
BOLTS, WELDS, AND CONNECTED ELEMENTS
Table 8-5.
Entering and Tightening Clearances, in.
Tension-Control ASTM A325 and A490 Bolts
Aligned Bolts
Nominal
Bolt
Dia, in.
Tools
C3
H1
3⁄
4
7⁄
8
C1
H2
1
1
2 /2
C1
C2
Circular Clipped
2
16
5⁄
8
13 ⁄8
11 ⁄2
13 ⁄4
17 ⁄8
17 ⁄8
17 ⁄8
7⁄
8
1
11 ⁄8
3⁄
7⁄
4
8
1
—
—
—
2 1 ⁄2-in. Diameter Critical
2
3⁄
4
7⁄
8
1
C3
1⁄
9⁄
1⁄
9⁄
2
16
5⁄
8
Small Tools
fillet
13 ⁄8
11 ⁄2
13 ⁄4
13 ⁄8
13 ⁄8
13 ⁄8
7⁄
8
1
11 ⁄8
3⁄
7⁄
4
8
1
—
—
—
3-in. Diameter Critical
5⁄
8
3⁄
4
7⁄
8
3
21/2 2
C2
H2
C1
1
1
1 /2 3 /8
33/8
H1
C1
H2
3 3 ⁄8-in. Diameter Critical
Large Tools
7⁄
16
1⁄
2
9⁄
16
11 ⁄4
13 ⁄8
11 ⁄2
15 ⁄8
15 ⁄8
15 ⁄8
13 ⁄
7⁄
16
8
1
11⁄
—
—
—
11⁄
—
—
—
16
3⁄
4
7⁄
8
2 3 ⁄16-in. Diameter Critical
3
2 /16
5⁄
8
3⁄
4
7⁄
8
2
7⁄
16
1⁄
2
9⁄
16
11 ⁄4
13 ⁄8
11 ⁄2
11 ⁄8
11 ⁄8
11 ⁄8
13 ⁄
7⁄
16
8
1
16
3⁄
4
7⁄
8
Staggered Bolts
Stagger P, in.
Nominal Bolt Diameter, in.
C1
F
5⁄
8
11⁄
4
113 ⁄
3⁄
4
7⁄
8
1
2
111⁄
21 ⁄16
21 ⁄4
27 ⁄16
19 ⁄16
11 ⁄2
17 ⁄16
2
17 ⁄8
13
1 ⁄16
13 ⁄4
23 ⁄
21 ⁄16
2
17 ⁄8
23 ⁄8
21 ⁄4
23 ⁄16
21 ⁄8
2
15 ⁄16
11 ⁄4
13 ⁄16
11 ⁄8
15 ⁄8
19 ⁄16
11 ⁄2
13 ⁄8
13 ⁄4
111⁄16
19 ⁄16
11 ⁄2
2
115 ⁄16
17 ⁄8
13 ⁄4
2 1 ⁄2
2 5 ⁄8
2 3 ⁄4
2 7 ⁄8
1
15 ⁄16
13 ⁄16
11 ⁄8
13 ⁄8
15 ⁄16
13 ⁄16
11 ⁄8
111⁄16
19 ⁄16
11 ⁄2
13 ⁄8
1 3 ⁄8
11⁄
P
1 5 ⁄8
1 3 ⁄4
1 7 ⁄8
2 1 ⁄8
2 1 ⁄4
2 3 ⁄8
F
C1 = tightening
clearance
installation
tool
16
13 ⁄4
3
3 3 ⁄8
16
16
15 ⁄16
15 ⁄16
Notes:
H1 = height of head, in.
H2 = maximum shank extension,* in.
C1 = clearance for tightening, in.
C2 = clearance of entering, in.
C3 = clearance for fillet,* in.
P
= bolt stagger, in.
F
= clearance for tightening staggered
bolts, in.
*Based on one standard hardened washer.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
BOLTED CONSTRUCTION
8 - 15
to tension or combined shear and tension, high-strength bolts must be used in fully
tensioned bearing-type or slip-critical connections.
Bearing-type connections are typically used for shear, moment, and diagonal bracing
connections in buildings. Bolts in bearing-type connections are installed in the snug-tightened condition unless required in LRFD Specification Section J1.11 to be fully tensioned.
Note that bolts in bearing-type connections required to be fully tensioned must not be
confused with fully tensioned bolts in slip-critical connections. Fully tensioned bolts in
bearing-type connections have no requirements regarding the slip resistance of the
contact surfaces. Thus, painted surfaces in fully tensioned bearing-type connections need
not meet the slip resistance requirements of slip-critical connections.
Slip-critical connections are used when slip would be detrimental to the serviceability
of the structure; this is essentially fatigue related and is primarily of concern in bridge
design. From LRFD Specification Section K3, “The occurrence of full design wind or
earthquake loads is too infrequent to warrant consideration in fatigue design.” Consequently, slip-critical connections are not normally required or used for wind or seismic
loading in buildings.
Slip-critical shear connections are required, however, in applications such as those
involving oversized holes, fatigue loading, or in craneway and bridge connections.
High-strength bolts in slip-critical connections are always fully tensioned to resist slip
on the faying surface(s) of the connection. While faying surfaces in slip-critical connections are not normally painted, painted surfaces in accordance with RCSC Specification
Section 3(b) are permitted.
When subjected to tension only or combined shear and tension, high-strength bolts
must be used in fully tensioned bearing-type or slip-critical connections. Examples of
these applications are hanger connections, extended end-plate FR moment connections,
and diagonal bracing connections.
Fully tensioned bolts in bearing-type or slip-critical connections must meet the
minimum tensioning requirements for ASTM A325 and A490 bolts as specified in Table 4
of the RCSC Specification. Fully tensioned bolts in either case may be tightened by the
same methods. The methods approved by the RCSC are: (1) turn-of-nut method; (2)
calibrated wrench method; (3) alternative design bolt method; and, (4) direct tension
indicator method. It is important to note that the RCSC prohibits the use of any published
relationship between torque and tension.
Inspection of Fully Tensioned High-Strength Bolts
When a joint with fully tensioned high-strength bolts is assembled, the RCSC Specification requires that all joint surfaces, including surfaces adjacent to the bolt head and nut
be free of scale, except tight mill scale, and of dirt or other foreign material. Burrs need
not be removed unless they prevent solid seating of the connected parts in the snug-tightened condition.
ASTM A6 lists tolerances for straightness and flatness. These tolerances can prevent
the faying surfaces from sufficiently contacting in medium- to large-size connections.
Section C8 of the Commentary on the RCSC Specification states: “…Even after being
fully tightened, some thick parts with uneven surfaces may not be in contact over the
entire faying surface. In itself, this is not detrimental to the performance of the joint. As
long as the specified bolt tension is present in all bolts of the completed connection, the
clamping force equal to the total of the tensions in all bolts will be transferred at the
locations that are in contact and be fully effective in resisting slip through friction.”
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
8 - 16
BOLTS, WELDS, AND CONNECTED ELEMENTS
Table 8-6.
Dimensions of Non-High-Strength Bolts and Nuts, in.
F
db
db
H
Square
Bolt Dia.
d b, in.
1⁄
4
3⁄
8
C, in.
1⁄
2
78
Hex
H
Countersunk
Heavy Hex
C
Countersunk Min. Thrd. Length, in.
H, in. C, in. H, in. L ≤ 6 in. L > 6 in.
H, in.
F, in.
C, in.
H, in.
F, in.
C, in.
3⁄
16
1⁄
4
5⁄
16
7⁄
16
1⁄
2
5⁄
8
11⁄
16
3⁄
4
7⁄
8
15⁄
16
7⁄
16
9⁄
16
3⁄
4
15⁄
16
1
1 ⁄8
5
1 ⁄16
11⁄2
111⁄16
17⁄8
21⁄16
21⁄4
25⁄8
1⁄
2
5⁄
8
7⁄
8
1
1 ⁄16
5
1 ⁄16
11⁄2
13⁄4
115⁄16
23⁄16
23⁄8
25⁄8
3⁄
16
1⁄
4
3⁄
8
7⁄
16
1⁄
2
9⁄
16
11⁄
16
3⁄
4
7⁄
8
15⁄
16
—
—
—
—
—
—
7⁄
8
11⁄16
1
1 ⁄4
17⁄16
1
11⁄4
7
1 ⁄16
111⁄16
3⁄
8
11⁄8
1⁄
2
9⁄
16
15⁄8
113⁄16
2
23⁄16
17⁄8
21⁄16
25⁄16
21⁄2
11⁄
16
3⁄
4
7⁄
8
15⁄
16
3
33⁄8
3
37⁄16
37⁄8
1
13⁄16
13⁄8
11⁄2
23⁄8
23⁄4
31⁄8
31⁄2
23⁄4
33⁄16
35⁄8
41⁄16
1
13⁄16
13⁄8
11⁄2
1⁄
2
11⁄
16
7⁄
8
11⁄8
3
1 ⁄8
19⁄16
113⁄16
21⁄16
21⁄4
21⁄2
211⁄16
1⁄
8
3⁄
16
1⁄
4
5⁄
16
3⁄
8
7⁄
16
1⁄
2
9⁄
16
5⁄
8
11⁄
16
3⁄
4
—
—
—
3⁄
4
1
1
11⁄4
11⁄4
11⁄2
13⁄4
2
11⁄2
13⁄4
2
21⁄4
21⁄4
21⁄2
23⁄4
3
21⁄2
23⁄4
3
31⁄4
—
—
—
31⁄4
33⁄4
41⁄4
43⁄4
31⁄2
4
41⁄2
5
3⁄
4
15⁄
16
1
1 ⁄8
5
1 ⁄16
11⁄2
111⁄16
17⁄8
21⁄16
21⁄4
13⁄
16
11⁄16
5
1 ⁄16
19⁄16
17⁄8
21⁄8
23⁄8
25⁄8
215⁄16
33⁄16
—
—
—
—
—
—
1
—
—
—
21⁄2
23⁄4
—
—
—
—
—
—
33⁄4
41⁄8
45⁄16
43⁄4
111⁄16
113⁄16
37⁄8
41⁄4
41⁄2
415⁄16
111⁄16
113⁄16
—
—
—
—
51⁄4
53⁄4
51⁄2
6
3
31⁄4
—
—
—
—
—
—
41⁄2
47⁄8
53⁄16
55⁄8
2
23⁄16
45⁄8
—
55⁄16
—
2
—
—
—
—
—
6
6
61⁄2
7
31⁄2
33⁄4
—
—
—
—
—
—
51⁄4
55⁄8
61⁄16
61⁄2
25⁄16
21⁄2
—
—
—
—
—
—
—
—
—
—
6
6
71⁄2
8
4
—
—
—
6
615⁄16
211⁄16
—
—
—
—
—
6
81⁄2
1⁄
2
5⁄
8
3⁄
4
7⁄
8
Bolts
Square
F, in.
3⁄
8
9⁄
16
db
C
H
F
Hex, Heavy Hex
C
1
11⁄8
11⁄4
13⁄8
11⁄2
13⁄4
2
21⁄4
W
C
N
C
Square, Heavy Square
Nuts
Nut Size,
in.
Square
W, in. C, in.
1⁄
4
3⁄
8
1⁄
2
5⁄
8
3⁄
4
7⁄
8
7⁄
16
5⁄
8
4⁄
5
1
11⁄8
5
1 ⁄16
1
11⁄8
11⁄4
13⁄8
11⁄2
111⁄16
17⁄8
21⁄16
11⁄2
13⁄4
21⁄4
—
2
21⁄4
5⁄
8
7⁄
8
11⁄8
17⁄16
19⁄16
17⁄8
21⁄8
23⁄8
25⁄8
215⁄16
33⁄16
Hex, Heavy Hex
Hex
N, in. W, in. C, in.
1⁄
4
5⁄
16
7⁄
16
9⁄
16
11⁄
16
3⁄
4
7⁄
8
1
11⁄8
11⁄4
7⁄
16
9⁄
16
3⁄
4
15⁄
16
11⁄8
15⁄16
11⁄2
111⁄16
17⁄8
21⁄16
21⁄4
1⁄
2
5⁄
8
7⁄
8
11⁄16
15⁄16
11⁄2
13⁄4
115⁄16
23⁄16
23⁄8
25⁄8
—
N
W
Heavy Square
N, in. W, in. C, in.
3⁄
16
1⁄
4
3⁄
8
7⁄
16
1⁄
2
9⁄
16
11⁄
16
3⁄
4
7⁄
8
15⁄
16
1⁄
2
11⁄
16
7⁄
8
11⁄16
11⁄4
17⁄16
15⁄8
113⁄16
—
11⁄
11⁄4
11⁄2
13⁄4
21⁄16
1⁄
4
3⁄
8
1⁄
2
5⁄
8
3⁄
4
7⁄
8
2
23⁄16
25⁄16
29⁄16
213⁄16
31⁄8
1
11⁄8
11⁄4
13⁄8
1
—
23⁄8
—
33⁄8
—
16
1
Heavy Hex
N, in. W, in. C, in.
1⁄
2
11⁄
16
7⁄
8
11⁄16
11⁄4
17⁄16
15⁄8
113⁄16
9⁄
16
13⁄
16
N, in.
1
11⁄4
17⁄16
111⁄16
1⁄
4
3⁄
8
1⁄
2
5⁄
8
3⁄
4
7⁄
8
2
23⁄16
17⁄8
21⁄16
25⁄16
21⁄2
1
11⁄8
11⁄4
13⁄8
11⁄2
—
23⁄8
23⁄4
23⁄4
33⁄16
11⁄2
13⁄4
—
15⁄16
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
31⁄8
31⁄2
35⁄8
41⁄16
2
23⁄16
21⁄2
23⁄4
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
37⁄8
41⁄4
41⁄2
415⁄16
27⁄16
211⁄16
3
31⁄4
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
45⁄8
5
55⁄16
53⁄4
215⁄16
33⁄16
31⁄2
33⁄4
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
53⁄8
53⁄4
63⁄16
65⁄8
37⁄16
311⁄16
4
—
—
—
—
—
—
—
—
—
61⁄8
71⁄16
315⁄16
Notes:
For high-strength bolt and nut dimensions, refer to Table 8-2.
Square, hex, and heavy hex bolt dimensions, rounded to nearest 1⁄16-in., are in accordance with ANSI B18.2.1.
Countersunk bolt dimensions, rounded to the nearest 1⁄16-in., are in accordance with ANSI 18.5.
Minimum thread length = 2db + 1⁄4-in. for bolts up to 6-in. long, and 2db + 1⁄2-in. for bolts longer than 6-in.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
BOLTED CONSTRUCTION
8 - 17
Table 8-7.
Threading Dimensions for High-Strength and Non-High-Strength Bolts, in.
SCREW THREADS
Unified Standard Series-UNC/UNRC and 4UN/4UNR
ANSI B1.1
Nominal size (basic major dia.)
No. threads per inch (n)
H=0.866P
H
/8
P/
8
P
Thread series symbol
c
Thread class symbol
60°
5/
8H
H
/4
Left hand thread.
No symbol req’d for
right hand thread.
db
P/
4
K
3/
4
- 10 UNC 2A LH
Thread Dimensions
Standard Designations
Diameter
Area
Bolt Diameter
db, in.
Min. Root K,
in.
Gross Bolt
Area, in.2
Min. Root
Area, in.2
Net Tensile
Area, in.2 a
Threads per
inch, n b
1⁄
4
3⁄
8
0.189
0.298
0.049
0.110
0.029
0.070
0.032
0.078
20
16
1⁄
2
5⁄
8
3⁄
4
7⁄
8
0.406
0.514
0.627
0.739
0.196
0.307
0.442
0.601
0.129
0.207
0.309
0.429
0.142
0.226
0.334
0.462
13
11
10
9
1
11⁄8
11⁄4
13⁄8
0.847
0.950
1.08
1.17
0.785
0.994
1.23
1.49
0.563
0.709
0.908
1.08
0.606
0.763
0.969
1.16
8
7
7
6
11⁄2
13⁄4
1.30
1.51
1.77
2.41
1.32
1.78
1.41
1.90
6
5
2
21⁄4
1.73
1.98
3.14
3.98
2.34
3.07
2.50
3.25
41⁄2
41⁄2
21⁄2
23⁄4
2.19
2.44
4.91
5.94
3.78
4.69
4.00
4.93
4
4
3
31⁄4
2.69
2.94
7.07
8.30
5.70
6.80
5.97
7.10
4
4
31⁄2
33⁄4
3.19
3.44
9.62
11.0
8.01
9.31
8.33
9.66
4
4
4
3.69
12.6
10.7
11.1
Notes:
aNet tensile area = 0.785 + d
b
2
−
0.9743
n
bFor diameters listed, thread series is UNC (coarse). For larger diameters, thread series is 4UN.
c2A denotes Class 2A fit applicable to external threads;
c2B denotes corresponding Class 2B fit for internal threads.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
4
8 - 18
BOLTS, WELDS, AND CONNECTED ELEMENTS
It should be noted that, even when bolts in bearing-type connections are required to
be fully tensioned, high bolt tension is not normally required for proper connection
performance. Thus, a significant reduction in inspection costs will be achieved by relying
on visual inspection of the bolt head or nut to note the peening marks signifying that the
tightening wrench was applied.
From RCSC Specification Commentary Section C9, “It is apparent from the commentary on installation procedures that the inspection procedures giving the best assurance
that bolts are properly installed and tensioned is provided by inspector observation of the
calibration testing of the bolts using the selected installation procedure followed by
monitoring of the work in progress to assure that the procedure which was demonstrated
to provide the specified tension is routinely adhered to. When such a program is followed,
no further evidence of proper bolt tension is required.”
Galvanizing High-Strength Bolts
Galvanizing provides corrosion protection by applying zinc as a sacrificial metal to
protect the base metal. As previously stated, ASTM A325 Type 1 high-strength bolts and
A449 bolts are permitted to be galvanized; A490 bolts are not permitted to be galvanized.
There are two methods of galvanizing: hot-dip galvanizing and mechanical galvanizing. Hot-dip galvanizing is a process whereby the bolt is dipped in molten zinc and spun
in a centrifuge to remove the excess. This process is described in detail in ASTM A153.
In contrast, mechanical galvanizing utilizes a combination of powdered zinc, chemicals,
and water with the bolts in a spun hopper. As result of collisions between the bolts, zinc,
and glass beads, the zinc is cold-welded to the surface of the bolts. This process is
described in detail in ASTM B695. For more information, refer to AISC (1993).
Grip
Ply or plies closest
to bolt head
Ply closest to nut
Nominal bolt
diameter d b, in.
Min. thickness t
of ply closest to
nut to exclude
threads from
shear plane, in.*
3⁄
4
1⁄
4
7⁄
8
1⁄
4
1
3⁄
8
5⁄ -in.
32
*Values shown assume one
thick washer is present. If washer is not
present, increase minimum thickness
by 1⁄8-in.
Shear plane
stick-through
5/
32
t
Value from RCSC
specification table C2
Fig. 8-3. Minimum thickness of ply closest to nut to exclude threads from shear plane.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
BOLTED CONSTRUCTION
8 - 19
Reuse of High-Strength Bolts
From RCSC Specification Section 8f, ASTM A490 bolts and galvanized ASTM A325
bolts shall not be reused. Other A325 bolts are permitted to be reused if approved by the
engineer of record.
A simple rule based on the prevention of excessive plastic deformation of the bolt
is that non-galvanized A325 bolts are satisfactory for reuse, regardless of previous
use, if the nut can be placed on the threads and run down the full length of the thread
by hand (AISC, 1988). Kulak, et al. (1987) recommends that non-galvanized ASTM
A325 bolts may be reused once or twice, provided that proper control on the number
of reuses can be established; adequate nut rotation capacity will be present as long
as there is some lubricant on the bolt. This lubricant can be the original lubrication
or oil, grease, or wax, or a lubricant that is added later. For a detailed assessment of
the performance of repetitively tightened high-strength bolts, refer to Bowman and
Betancourt (1991).
Non-High-Strength Bolts
LRFD Specification Section A3.3 permits the use of ASTM A307 non-high-strength bolts
for structural applications not requiring fully tensioned installation, that is, snug-tightened bearing-type connections. ASTM A307 bolts are available with both hex and square
heads in diameters from 1⁄4-in. to four inches in two grades: Grade A for general
applications and Grade B for cast-iron-flanged piping joints. ASTM A563 Grade A nuts
are recommended for use with ASTM A307 bolts. Other suitable grades are listed in
ASTM A563 Table X1.1.
Dimensions and Weights
Typical non-high-strength bolt head and nut dimensions are given in Table 8-6. Thread
lengths listed in this table may be calculated for non-high-strength bolts as 2db + 1⁄4-in.
for bolts up to six inches long and 2db + 1⁄2-in. for bolts over six inches long, where db is
the bolt diameter. Note that these thread lengths are longer than those given previously
for high-strength bolts in Table 8-2. Threading dimensions are given in Table 8-7. Weights
of non-high-strength bolts are given in Tables 8-8, 8-9, and 8-10.
Entering and Tightening Clearances
As with high-strength bolts, clearance is required for entering and tightening the bolts
with an impact wrench. The required clearances are the same as those given for
high-strength bolts in Table 8-4.
Design Strength of Bolts
The design strength of bolts is determined in accordance with the provisions of LRFD
Specification Section J3. LRFD Specification requirements are based upon the provisions
of the RCSC Specification.
For bolts in bearing-type connections subjected to shear only, the limit states of bolt
shear strength and bearing strength at bolt holes must be checked. For bolts in bearingtype connections subjected to tension only, the limit state of bolt tensile strength,
including the effect of prying action, must be checked. For bolts in bearing-type
connections subjected to combined shear and tension, the limit states of bolt tensile
strength, including the effects of both the bolt shear stress present and prying action, and
bearing strength at bolt holes must be checked.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
8 - 20
BOLTS, WELDS, AND CONNECTED ELEMENTS
Table 8-8.
Weights of Non-High-Strength Fasteners, pounds
Bolt
Length, in.
3⁄
8
1⁄
2
5⁄
8
3⁄
4
7⁄
8
1 1 ⁄8
1 1 ⁄4
—
—
—
—
—
—
—
—
104
109
114
119
143
149
155
161
—
—
206
213
90.2
94.4
98.5
103
124
129
135
140
168
174
181
188
221
229
237
246
73.3
76.3
79.3
82.3
107
111
115
119
145
151
156
162
195
202
208
215
254
262
271
279
56.5
58.6
60.7
62.8
85.3
88.4
91.4
94.4
123
127
131
136
167
172
178
183
222
229
236
242
288
296
304
313
39.3
40.4
41.8
43.1
64.9
66.7
68.7
70.8
97.4
100
103
106
140
143
147
151
188
193
198
204
249
255
262
269
321
329
337
345
24.0
24.8
25.5
26.3
44.4
45.8
47.1
48.5
72.9
75.0
77.1
79.2
109
112
115
118
156
160
164
168
209
214
220
225
275
282
289
296
354
362
371
379
11.7
—
—
—
27.0
28.6
30.1
31.6
49.8
52.5
55.2
57.9
81.3
85.5
89.7
93.9
121
127
133
139
172
180
189
197
231
241
252
263
303
316
330
343
387
404
421
438
10
—
—
66.1
34.6
60.6
63.3
98.1
102
145
151
205
213
274
284
357
371
454
471
11
—
—
36.2
37.7
66.0
68.7
106
110
157
163
221
230
295
306
384
398
488
505
12
—
—
39.2
—
71.3
74.0
115
119
170
176
238
246
316
327
411
425
522
538
13
—
—
—
—
76.7
79.4
123
127
182
188
254
263
338
349
439
452
556
572
14
—
—
—
—
82.1
84.8
131
135
194
200
271
279
359
370
466
479
589
605
15 1 ⁄2
15
—
—
—
—
87.5
90.2
140
144
206
212
287
296
381
392
493
507
622
639
16
—
—
92.9
148
218
304
402
520
656
Per inch
add’tl. add
1.3
3.0
5.4
1
2.38
2.71
3.05
3.39
6.11
6.71
7.47
8.23
13.0
14.0
15.1
16.5
24.1
25.8
27.6
29.3
38.9
41.5
44.0
46.5
—
—
67.3
70.8
2
3.73
4.06
4.40
4.74
8.99
9.75
10.5
11.3
17.8
19.1
20.5
21.8
31.4
33.5
35.6
37.7
49.1
52.1
55.1
58.2
74.4
77.9
82.0
86.1
3
5.07
5.41
5.75
6.09
12.0
12.8
13.5
14.3
23.2
24.5
25.9
27.2
39.8
41.9
44.0
46.1
61.2
64.2
67.2
70.2
4
6.42
6.76
7.10
7.43
15.1
15.8
16.6
17.3
28.6
29.9
31.3
32.6
48.2
50.3
52.3
54.4
5
7.77
8.11
8.44
8.78
18.1
18.9
19.6
20.4
33.9
35.3
36.6
38.0
6
9.12
9.37
9.71
10.1
21.1
21.7
22.5
23.3
7
10.4
10.7
11.0
11.4
8
1 1 ⁄4
1 1 ⁄2
1 3 ⁄4
2 1 ⁄4
2 1 ⁄2
2 3 ⁄4
100 Square Bolts with Hexagonal Nuts
Nominal Bolt Diameter, in.
1⁄
4
3 1 ⁄4
3 1 ⁄2
3 3 ⁄4
4 1 ⁄4
4 1 ⁄2
4 3 ⁄4
5 1 ⁄4
5 1 ⁄2
5 3 ⁄4
6 1 ⁄4
6 1 ⁄2
6 3 ⁄4
7 1 ⁄4
7 1 ⁄2
7 3 ⁄4
8 1 ⁄2
9
9 1 ⁄2
10 1 ⁄2
111 ⁄2
12 1 ⁄2
13 1 ⁄2
14 1 ⁄2
8.4
12.1
16.5
1
—
—
95.1
99.7
21.4
27.2
33.6
Notes:
For weights of high-strength fasteners, see Table 8-3.
This table conforms to weight standards adopted by the Industrial Fasteners Institute (IFI).
*Square bolt per ANSI B18.2.1, hexagonal nut per ANSI B18.2.2. For other non-high-strength fasteners, refer to
Tables 8-9 and 8-10.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
BOLTED CONSTRUCTION
8 - 21
Table 8-9.
Weight Adjustments for Combinations of Non-High-Strength
Fasteners Other than Tabulated in Table 8-8
100, Square
Bolts with
Hexagonal Nuts*
Square
Bolts with
Combinations of 100:
100,
Hex
Bolts
Nominal Bolt Diameter, in.
Add
or Subtr.
1⁄
4
3⁄
8
1⁄
2
5⁄
8
3⁄
4
7⁄
8
1
11⁄8
11⁄4
3.5
5.5
8.0 12.2 16.3
Square Nuts
+
0.1
1.0
2.0
3.4
Heavy Square Nuts
+
0.6
2.1
4.1
7.0 11.6 17.2 23.2 32.1 41.2
Heavy Hex Nuts
+
0.4
1.5
2.8
4.6
7.6 10.7 14.2 18.9 24.3
Square Nuts
+
0.1
0.6
1.1
1.4
0.2
0.5 −0.2 −0.1 −1.7
Hex Nuts
−
0.0
0.4
0.9
2.0
3.3
5.0
Heavy Square Nuts
+
0.6
1.7
3.2
5.0
8.3 12.2 15.0 19.8 23.2
Heavy Hex Nuts
+
0.4
1.1
1.9
2.6
4.3
Heavy Square Nuts
+
—
—
4.7
7.3 11.3 16.5 20.7 27.0 33.6
Heavy Hex Nuts
+
—
—
3.4
4.9
5.7
8.2 12.3 18.0
6.0
6.6
6.3
7.3 10.0 11.7 13.8 16.7
Notes:
For weights of high-strength fasteners, see Table 8-3.
This table conforms to weight standards adopted by the Industrial Fasteners Institute (IFI).
*Add or subtract value in this table to or from the value in Table 8-8.
Table 8-10.
Weights of Non-High-Strength Bolts
of Diameter Greater Than 11⁄4-in., pounds
Nominal Bolt Diameter, in.
11⁄2
13⁄4
2
21⁄4
21⁄2
23⁄4
3
31⁄4
31⁄2
33⁄4
4
105
130
—
—
—
—
—
—
—
—
—
—
Hex Bolts
84.0 112
178
259
369
508
680
900
1120
1390
1730
2130
Heavy Hex Bolts
95.0 124
195
280
397
541
720
950
—
—
—
—
139
168
200
235
272
313
356
147
178
210
246
284
325
Heads of:
Weight of 100 Each: 13⁄8
Square Bolts
One Linear Inch,
Unthreaded Shank
42.0
50.0
68.2
89.0 113
One Linear Inch,
Threaded Shank
35.0
42.5
57.4
75.5
97.4 120
—
—
—
—
—
—
—
—
—
—
Square Nuts
94.5 122
Heavy Square Nuts
125
161
—
—
—
—
—
—
—
—
—
—
Heavy Hex Nuts
102
131
204
299
419
564
738
950
1190
1530
1810
2180
Notes:
For weights of high-strength fasteners, see Table 8-3.
This table conforms to weight standards adopted by the Industrial Fasteners Institute (IFI).
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
8 - 22
BOLTS, WELDS, AND CONNECTED ELEMENTS
For bolts in slip-critical connections subjected to shear only, the limit states of slip
resistance, bolt shear strength, and bearing strength at bolt holes must be checked. For
bolts in slip-critical connections subjected to combined shear and tension, the limit states
of slip resistance, including the effect of the tensile force present, bolt shear strength, and
bearing strength at bolt holes must be checked.
Bolt Shear Strength
As illustrated in Figure 8-4a, this limit state considers a shear failure of the bolt shank on
plane cdef. Since there is one shear plane, the bolt is in single shear (S). Additional plies
of material may increase the number of shear planes and, therefore, the shear strength of
the bolt. This condition, as illustrated in Figure 8-4b, is called double shear (D).
Additionally, high-strength bolts may be specified with the threads included (N) or
excluded (X) from the shear plane of the connection. Note that the shear strength of bolts
with the threads included is about 25 percent less than that of bolts with the threads
excluded. In spite of this, many designers prefer to specify N bolts when possible due to
the difficulty in assuring that threads are excluded from the shear plane in the as-built
condition. If, however, the threads are to be excluded from the shear plane, care must be
taken to specify a bolt of sufficient overall length given the thread length and required
bolt length from Table 8-2. Note that additional washers may be required to accomplish
this; refer to Figure 8-3.
From LRFD Specification Section J3.6, the design bolt shear strength is φRn, where
φ = 0.75 and:
Rn = (Fv Ab)n
x ′,y ′,z ′
c,b
g,f
d,a
h,e
x,y,z
x,x ′
Ru
e,f
d,c
y,y ′
a,b
z,z ′
Ru
2
h,g
Ru
Ru
Ru
2
(a) Single shear (S)
(b) Double shear (D)
Fig. 8-4. Bolt shear.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
BOLTED CONSTRUCTION
8 - 23
In the above equation, n is the number of bolts in the connection, Fv is the nominal
shear strength, and Ab is the nominal bolt area. For convenience, the design bolt shear
strengths of various bolts are summarized in Table 8-11; design bolt shear strengths of
vertical rows of n bolts are summarized in Table 8-12.
Bearing Strength at Bolt Holes
As illustrated in Figure 8-5, this limit state considers both a tear fracture of the connected
material and deformation around the bolt holes. Bearing strength is a function of the
material being connected, the type of bolt hole, and the spacing and edge distance; it is
independent of both the type of bolt and the presence or absence of threads on the bearing
area.
From LRFD Specification Section J3.10, when deformation around the bolt holes is a
design consideration for standard holes, oversized holes, short-slotted holes, and longslotted holes parallel to the line of force, the design bearing strength at bolt holes is φRn,
where φ = 0.75 and, for two or more bolts in the line of force, when Le ≥ 1.5d and
s ≥ 3d:
Rn = (2.4dtFu )n
For a single bolt in the line of force or when Le < 1.5d or s < 3d:
d
Rn = Let + s − (n − 1)(tFu ) ≤ (2.4dtFu )n
2
In the above equations, n is the number of bolts in the connection, d is the nominal bolt
diameter, t is the thickness in bearing, and Le is the edge distance. If deformation around
the bolt hole is not a design consideration, or for long-slotted holes perpendicular to the
line of force, refer to LRFD Specification Section J3.10.
For convenience, the design bearing strength at bolt holes is tabulated for the foregoing
conditions in Tables 8-13 and 8-14, respectively. Note that these tables may be applied
to bolts with countersunk heads, by subtracting one-half the depth of the countersink from
the material thickness t. As illustrated in Figure 8-6, this is equivalent to subtracting
one-quarter the diameter of the bolt from the material thickness t.
Bolt Tensile Strength
From LRFD Specification Section J3.6, when subjected to tension only, the design bolt
tensile strength is φRn,
where
φ = 0.75
Rn = (Ft Ab)n
In the above equation, n is the number of bolts in the connection. For convenience, the
design bolt tensile strengths of various bolts is summarized in Table 8-15. When subjected
to combined shear and tension, the design bolt tensile strength is reduced by a function
of the shear stress present in the bolt as specified in LRFD Specification Section J3.7.
LRFD Specification Section J3.6 states that any tension resulting from prying action
must be considered in determining the required strength of the bolts. Prying action is a
phenomenon (in bolted construction only) whereby the deformation of a fitting under a
tensile force increases the tensile force in the bolt. The required strength per bolt is the
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
8 - 24
BOLTS, WELDS, AND CONNECTED ELEMENTS
Table 8-11.
Design Shear Strength of One Bolt, kips
Nominal Bolt Diameter d, in.
5⁄
8
ASTM
Desig.
Thread
Cond.
φF v
(ksi)
A325
N
36.0
X
A490
A307
56.3
—
1 1 ⁄8
1
1 1 ⁄4
Loading 0.3068 0.4418 0.6013 0.7854 0.9940 1.227
45.0
X
7⁄
8
1 3 ⁄8
1 1 ⁄2
1.485
1.767
Nominal Bolt Area, in.2
45.0
N
3⁄
4
18.0
S
11.0
15.9
21.6
28.3
35.8
44.2
D
22.1
31.8
43.3
56.5
71.6
88.4
S
13.8
19.9
27.1
35.3
44.7
D
27.6
39.8
54.1
70.7
89.5
S
13.8
19.9
27.1
35.3
44.7
D
27.6
39.8
54.1
70.7
89.5
S
17.3
24.9
33.9
44.2
D
34.5
49.7
67.7
88.4
S
D
5.52
11.0
7.95
15.9
56.0
112
55.2
110
55.2
110
69.1
138
53.5
107
66.8
134
66.8
134
83.6
167
63.6
127
79.5
159
79.5
159
99.5
199
10.8
14.1
17.9
22.1
26.7
31.8
21.6
28.3
35.8
44.2
53.5
63.6
N = Threads included in shear plane
X = Threads excluded from shear plane
S = Single shear
D = Double shear
Table 8-12.
Design Shear Strength of n Bolts in Double Shear*
ASTM A325
N
ASTM A490
X
N
X
n
3⁄
4
7⁄
8
1
3⁄
4
7⁄
8
1
3⁄
4
7⁄
8
1
3⁄
4
7⁄
8
12
382
520
679
477
649
848
477
649
848
596
812
1060
11
350
476
622
437
595
778
437
595
778
547
744
972
10
318
433
565
398
541
707
398
541
707
497
676
884
9
286
390
509
358
487
636
358
487
636
447
609
795
8
254
346
452
318
433
565
318
433
565
398
541
707
7
223
303
396
278
379
495
278
379
495
348
474
619
6
191
260
339
239
325
424
239
325
424
298
406
530
5
159
216
283
199
271
353
199
271
353
249
338
442
4
127
173
226
159
216
283
159
216
283
199
271
353
130
170
119
162
212
119
162
212
149
203
265
108
141
108
141
135
177
3
95.4
2
63.6
86.6
1
31.8
43.3
113
79.5
56.5
39.8
54.1
70.7
79.5
39.8
54.1
N = Threads included in shear plane
X = Threads excluded in shear plane
*For design strength of bolts in single shear, divide tabular value by 2.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
70.7
99.4
49.7
67.6
1
88.4
BOLTED CONSTRUCTION
8 - 25
sum of rut, the factored force per bolt due to the tensile force, and qu, the additional tension
per bolt resulting from prying action produced by deformation of the connected parts.
While the effect of prying action is considered in the design of the bolts, it is primarily
a function of the connected elements; thus, the connected elements must possess adequate
flexural strength and it is their stiffness which is the key to satisfactory performance.
Refer to “Hanger Connections” in Part 11 for treatment of prying action.
Slip Resistance
In slip-critical connections, the fully tensioned bolt creates resistance to slip through
friction on the faying surface between two connected parts. This slip resistance is a
function of the slip coefficient µ of the faying surface.
Clean mill scale with no coating is defined as a Class A surface with µ = 0.33.
Blast-cleaned surfaces with no coatings are defined as Class B surfaces with µ = 0.50.
Hot-dip galvanized and roughened surfaces are defined as Class C surfaces with µ = 0.40.
Ru
Ru
Splitting of plate
(a) Tear fracture for smaller end distance
Ru
Ru
Tearout of Plate
(b) Tear fracture for longer end distance
Ru
Ru
Deformation
(c) Deformation of material at bolt hole
Fig. 8-5. Bearing strength at bolt holes.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
8 - 26
BOLTS, WELDS, AND CONNECTED ELEMENTS
Table 8-13.
Design Bearing Strength at Bolt Holes, kips/in. thickness
Two or more holes in line of force with Le ≥ 1.5d
and s ≥ 3d; hole deformation considered*
Nominal Bolt Diameter d, in.
5⁄
8
3⁄
4
7⁄
8
1
15⁄
16
11⁄8
15⁄16
11⁄2
Fu, ksi
17⁄8
21⁄4
25⁄8
3
STD, OVS
SSL, LSLP
58
65
70
65.3
73.1
78.8
78.3
87.8
94.5
91.4
102
110
LSLT
58
65
70
54.4
60.9
65.6
65.3
73.1
78.8
76.1
85.3
91.9
11⁄8
11⁄4
13⁄8
11⁄2
111⁄16
17⁄8
21⁄16
21⁄4
33⁄8
33⁄4
41⁄8
41⁄2
1.5d
Hole
Type
3d
104
117
126
117
132
142
131
146
158
144
161
173
157
176
189
87.0
97.5
105
97.9
110
118
109
122
131
120
134
144
131
146
158
STD = Standard Hole
OVS = Oversized Hole
SSL = Short-Slotted Hole
LSLP = Long-Slotted Hole parallel to line of force
LSLT = Long-Slotted Hole transverse to line of force
*When s < 3d, or when hole deformation is not a design consideration, refer to LRFD Specification Section J3.10.
When Le < 1.5d or for one hole in the line of force, refer to Table 8-14.
Table 8-14.
Design Bearing Strength at Bolt Holes, kips/in. thickness
One hole in line of force or top bolt with Le < 1.5d*
Nominal Bolt Diameter d, in.
Fu, ksi
1
11⁄8
11⁄4
13⁄8
11⁄2
15⁄8
13⁄4
17⁄8
58
65
70
43.5
48.8
52.5
48.9
54.8
59.1
54.4
60.9
65.6
59.8
67.0
72.2
65.3
73.1
78.8
70.7
79.2
85.3
76.1
85.3
91.9
81.6
91.4
98.4
*Design strength from Table 8-14 shall not exceed tabular value from Table 8-13. For remaining bolts, when
s − d / 2 > 2.4d, refer to Table 8-13; otherwise refer to LRFD Specification Section J3.10.
Slip coefficients for all other coated blast-cleaned surfaces must be determined by the
Testing Method to Determine the Slip Coefficient Used in Bolted Joints; refer to Appendix
A of the RCSC Specification. When the tests results in 0.33 ≤ µ < 0.50, the coating is a
Class A coating and the design slip coefficient is µ = 0.33. If the test results in µ ≥ 0.50,
the coating is a Class B coating and the design slip coefficient is µ = 0.50. The surface
requirements for slip-critical connections apply only to the faying surfaces and do not
include the surfaces under the bolt, washer, or nut.
Bolts in slip-critical connections may be designed at either service loads or factored
loads with the provisions of LRFD Specification Section J3.8. From LRFD Specification
Section J3.8a, when subjected to shear only, the resistance to slip for comparison with
service loads is φRn,
where
Rn = (Fv Ab)n
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
BOLTED CONSTRUCTION
8 - 27
Table 8-15.
Design Tensile Strength of Bolts, kips
Nominal Bolt Diameter d, in.
5⁄
8
3⁄
4
7⁄
8
1
11⁄8
11⁄4
13⁄8
11⁄2
1.227
1.485
1.767
2
Nominal Bolt Area, in.
ASTM
Desig.
φFt, ksi
A325
67.5
A490
A307
84.8
33.8
0.3068
0.4418
0.6013
20.7
29.8
40.6
41.4
59.6
81.2
26.0
37.4
52.0
74.9
51.0
102
0.7854
53.0
106
66.6
133
0.9940
67.1
82.8
134
166
84.2
169
100
119
200
239
104
126
150
208
252
300
10.4
14.9
20.3
26.5
33.5
41.4
20.7
29.8
40.6
53.0
67.1
82.8
50.1
100
59.6
119
and φ = 1.0 for standard holes, oversized holes, short-slotted holes, and long-slotted holes
perpendicular to the direction of the load; φ = 0.85 for long-slotted holes parallel to the
direction of the load. In the above equation, n is the number of bolts in the connection.
In general, slip is likely to occur at 1.4 to 1.5 times the service loads.
Note that the values of Fv tabulated in LRFD Specification Table J3.6 for bolts in
slip-critical connections assume Class A surfaces with µ = 0.33. As stated in LRFD
Specification Section J3.8a, it is permissible to increase Fv to the applicable value in the
RCSC Specification for other surfaces. When subjected to combined shear and tension,
the slip capacity for comparison with service loads must be reduced by the factor:
T
1 −
Tb
as specified in LRFD Specification Section J3.9a, where T is the unfactored force on the
connection and Tb is the minimum bolt tension from LRFD Specification Table J3.1.
From LRFD Specification Appendix J3.8a, the design slip resistance for comparison
with factored loads is φRstr,
Effective thickness
in bearing
db
2
db
4
Ru
Ru
db
Fig. 8-6. Effective thickness for bearing of countersunk bolts.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
8 - 28
BOLTS, WELDS, AND CONNECTED ELEMENTS
where
Rstr = 1.13µTm Nb Ns
and φ is equal to 1.0 for standard holes, 0.85 for oversized and short-slotted holes, 0.70
for long-slotted holes perpendicular to the direction of the load, and 0.60 for long-slotted
holes parallel to the direction of the load. When subjected to combined tension and shear,
the design slip resistance for comparison with factored loads must be reduced by the
factor:
Tu
1 −
1.13Tm Nb
as specified in LRFD Specification Appendix J3.8b. In the above equations, Tu is the
factored force on the connection, Tm is the minimum bolt tension from LRFD Specification Table J3.1, and Nb is the number of bolts in the connection.
For convenience, slip capacities for comparison with service loads and design slip
resistances for comparison with factored loads are tabulated in Tables 8-16 and 8-17,
respectively.
ECCENTRICALLY LOADED BOLT GROUPS
When the line of action of an applied load does not pass through the center of gravity
(CG) of a bolt group, the load is eccentric and results in a moment which must be
considered in the design of the connection.
Eccentricity in the Plane of the Faying Surface
Eccentricity in the plane of the faying surface produces additional shear. The bolts must
be designed to resist the combined effect of the direct shear from the applied load Pu and
the additional shear from the induced moment Pu e. Two methods of analysis for this type
of eccentricity will be discussed: (1) the instantaneous center of rotation method; and,
(2) the elastic method.
Instantaneous Center of Rotation Method
Also known as the ultimate strength method (Crawford, 1968), this method considers the
load-deformation relationship of each bolt and, thus, more accurately predicts the
ultimate strength of the eccentrically loaded connection. Eccentricity produces both a
rotation about the centroid of the bolt group and a translation of one connected element
with respect to the other. The combined effect of this rotation and translation is equivalent
to a rotation about a point defined as the instantaneous center of rotation (IC) as illustrated
in Figure 8-7a. The location of the IC depends on the geometry of the bolt group as well
as the direction and point of application of the load. The individual resistance of each
bolt is assumed to act on a line perpendicular to a ray passing through the IC and the
centroid of that bolt as illustrated in Figure 8-7b.
The load-deformation relationship of one bolt is illustrated in Figure 8-8,
where
R = Rult(1 − e−10∆)0.55
In the above equation,
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
ECCENTRICALLY LOADED BOLT GROUPS
8 - 29
Table 8-16.
Slip-Critical Connections
Design Resistance to Shear at Service Loads,* kips
(Class A faying surface, µ = 0.33)
Nominal Bolt Diameter, in.
5⁄
8
ASTM
Desig.
Hole
Type
A325
STD
A490
3⁄
4
7⁄
8
1
11⁄8
11⁄4
13⁄8
11⁄2
Nominal Bolt Area, in.2
Loading
0.3068 0.4418 0.6013 0.7854 0.9940
1.227
1.485
1.767
S
D
5.22
10.4
7.51
15.0
10.2
20.4
13.4
26.7
16.9
33.8
20.9
41.7
25.2
50.5
30.0
60.1
OVS
SSL
S
D
4.60
9.20
6.63
13.3
9.02
18.0
11.8
23.6
14.9
29.8
18.4
36.8
22.3
44.5
26.5
53.0
LSLP
S
D
3.13
6.26
4.51
9.01
6.13
12.3
8.01
16.0
10.1
20.3
12.5
25.0
15.1
30.3
18.0
36.0
LSLT
S
D
3.68
7.36
5.30
10.6
7.22
14.4
9.42
18.8
11.9
23.9
14.7
29.5
17.8
35.6
21.2
42.4
STD
S
D
6.44
12.9
9.28
18.6
12.6
25.3
16.5
33.0
20.9
41.7
25.8
51.5
31.2
62.4
37.1
74.2
OVS
SSL
S
D
5.52
11.0
7.95
15.9
10.8
21.6
14.1
28.3
17.9
35.8
22.1
44.2
26.7
53.5
31.8
63.6
LSLP
S
D
3.93
7.85
5.65
11.3
7.70
15.4
10.1
20.1
12.7
25.4
15.7
31.4
19.0
38.0
22.6
45.2
LSLT
S
D
4.60
9.20
6.63
13.3
9.02
18.0
11.8
23.6
14.9
29.8
18.4
36.8
22.3
44.5
26.5
53.0
STD = Standard Hole
OVS = Oversized Hole
SSL = Short-Slotted Hole
LSLP = Long-Slotted Hole parallel to line of force
LSLT = Long-Slotted Hole transverse to line of force
S
= Single Shear
D
= Double Shear
*For design slip resistance at factored loads, refer to Table 8-17.
R = shear force in one bolt at a deformation ∆, kips.
Rult = ultimate shear strength of one bolt, kips.
∆ = total deformation of a bolt, including shearing, bearing, and bending deformation, plus local bearing deformation of the plate, in.
e = 2.718…, base of the natural logarithm.
Applying a maximum deformation ∆max to the bolt most remote from the IC, the
maximum shear strength of that bolt may be determined. For other bolts, deformations
are assumed to vary linearly with distance from the IC, and shear strengths can be
obtained from this relationship. The strength of the bolt group is, then, the sum of the
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
8 - 30
BOLTS, WELDS, AND CONNECTED ELEMENTS
Table 8-17.
Slip-Critical Connections
Design Slip Resistance at Factored Loads, kips
(Class A faying surface, µ = 0.33)
Nominal Bolt Area, in.2
5⁄
8
ASTM
Desig.
Hole
Type
A325
STD
3⁄
4
7⁄
8
1
11⁄8
11⁄4
13⁄8
11⁄2
Minimum ASTM A325 Bolt Tension, kips
Loading
19.0
28.0
39.0
51.0
56.0
71.0
85.0
103
S
D
7.09
14.2
10.4
20.9
14.5
29.1
19.0
38.0
20.9
41.8
26.5
53.0
31.7
63.4
38.4
76.8
OVS
SSL
S
D
6.02
12.0
8.88
17.8
12.4
24.7
16.2
32.3
17.8
35.5
22.5
45.0
26.9
53.9
32.6
65.3
LSLP
S
D
4.25
8.50
6.26
12.5
8.73
17.5
11.4
22.8
12.5
25.1
15.9
31.8
19.0
38.0
23.0
46.1
LSLT
S
D
4.96
9.92
7.31
14.6
10.2
20.4
13.3
26.6
14.6
29.2
18.5
37.1
22.2
44.4
26.9
53.8
Minimum ASTM A490 Bolt Tension, kips
A490
24.0
35.0
49.0
64.0
80.0
102
121
148
STD
S
D
8.95
17.9
13.1
26.1
18.3
36.5
23.9
47.7
29.8
59.7
38.0
76.1
45.1
90.2
55.2
110
OVS
SSL
S
D
7.61
15.2
11.1
22.2
15.5
31.1
20.3
40.6
25.4
50.7
32.3
64.7
38.4
76.7
46.9
93.8
LSLP
S
D
5.37
10.7
7.83
15.7
11.0
21.9
14.3
28.6
17.9
35.8
22.8
45.6
27.1
54.1
33.1
66.2
LSLT
S
D
6.26
12.5
9.14
18.3
12.8
25.6
16.7
33.4
20.9
41.8
26.6
53.3
31.6
63.2
38.6
77.3
STD = Standard Hole
OVS = Oversized Hole
SSL = Short-Slotted Hole
LSLP = Long-Slotted Hole parallel to line of force
LSLT = Long-Slotted Hole transverse to line of force
S
= Single Shear
D
= Double Shear
individual strengths of all bolts. If the correct location of the IC has been selected, the
three equations of in-plane statics will be satisfied; i.e., ΣFx = 0, ΣFy = 0, and ΣM = 0.
Tables 8-18 through 8-25 employ the instantaneous center of rotation method for the
bolt patterns and eccentric conditions indicated and inclined loads at 0°, 15°, 30°, 45°,
60°, and 75°. The load-deformation relationship is based on data obtained experimentally
for 3⁄4-in. diameter ASTM A325 bolts, where Rult = 74 kips, and ∆max = 0.34 in. The
non-dimensional coefficient C is obtained by dividing the factored eccentric force Pu
by Rult.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
ECCENTRICALLY LOADED BOLT GROUPS
8 - 31
For any of the bolt group geometries shown, the design strength of the eccentrically
loaded bolt group is φRn,
where
φRn = C × φrn
lo
e
Pu
IC
CG
(a) Instantaneous center of rotation (IC)
e
lo
Pu
CG
IC
lrm
ax
ru max
(b) Forces on bolts in group
Fig. 8-7. Instantaneous center of rotation method.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
8 - 32
BOLTS, WELDS, AND CONNECTED ELEMENTS
In the above equation, φrn is the least design strength of one bolt determined from the
limit states of bolt shear strength, bearing strength at bolt holes, and slip resistance (if the
connection is to be slip-critical). The design strength φRn must be greater than or equal
to the required strength Pu. Thus, by dividing Pu by φrn, the minimum coefficient C is
obtained, and a bolt group can be selected for which the coefficient is of that magnitude
or greater.
These tables may be used with any bolt diameter and are conservative when used with
ASTM A490 bolts. Linear interpolation within a given table between adjacent values of
ex is permitted. Design strengths determined with these tables provide a factor of safety
equivalent to that for bolts in connections less than 50 inches long, subjected to shear
produced by a concentric load in either bearing-type or slip-critical connections. Although this procedure is based on connections which may experience slip under load,
both load tests and analytical studies (Kulak, 1975) indicate that it may be conservatively
extended to slip-critical connections.
A convergence criterion of one percent was employed for the tabulated iterative solutions.
Straight line interpolation between values for loads at different angles may be significantly
unconservative. Therefore, unless a direct analysis is performed, use only the values for the
next lower angle for design. For bolt group patterns not treated by these tables, a special
ultimate strength analysis is required if the instantaneous center of rotation method is to be
used.
Example 8-1
Given:
Refer to Figure 8-9. Determine the largest eccentric force Pu for which
the design shear strength of the bolts in the connection is adequate
using the instantaneous center of rotation method. Use 7⁄8-in. diameter
A325-N bolts, φrn = 21.6 kips/bolt.
A. Assume the load is vertical as illustrated in Figure 8-9 (θ = 0°°)
B. Assume the load acts at an angle of 75°° with respect to vertical
(θ = 75°°)
Solution A:
From Table 8-20 with θ = 0°, with s = 3 in., e = 16 in., and n = 6:
C = 3.55
Design Shear Strength
φRn = C × φrn
= 3.55 × 21.6 kips/bolt
= 76.7 kips
Thus, Pu must be less than or equal to 76.7 kips.
Comment:
Note that this eccentricity has effectively reduced the shear strength of
this bolt group by about 70 percent when compared with the concentrically loaded case.
Solution B:
From Table 8-20 with θ = 75°°, s = 3 in., e = 16 in., and n = 6:
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
ECCENTRICALLY LOADED BOLT GROUPS
8 - 33
C = 7.90
Design shear strength
φRn = C × φrn
= 7.90 × 21.6 kips/bolt
= 171 kips
Thus, Pu must be less than or equal to 171 kips.
Comment:
In Solution B, the vertical component of the design strength is
φRn sin75°° = (171 kips)(0.966)
= 165 kips
and the horizontal component of the design strength is
φRn cos75°° = (171 kips)(0.259)
= 44.3 kips
Elastic Method
Alternatively, the elastic method may be used to analyze eccentrically loaded bolt groups.
It offers a simplified, conservative approach but does not render a consistent factor of
safety and, in some cases, provides excessively conservative results. Furthermore, the
elastic method ignores both the ductility of the bolt group and the load redistribution
which occurs. Refer to Higgins (1971).
In the elastic method, for a force applied parallel to the Y principal axis of the bolt
group as illustrated in Figure 8-10, the eccentric force Pu is resolved into a force Pu acting
through the center of gravity (CG) of the bolt group and a moment Pu e where e is the
eccentricity. Each bolt is then assumed to support an equal share of the concentric force
Pu, and a share of the eccentric moment Pu e which is proportional to its distance from the
80
R, kips
60
R = Rult (1 – e
–10 ∆ 0.55
)
40
20
0
0.10
0.20
0.30
∆, in.
Fig. 8-8. Load-deformation relationship for bolts.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
8 - 34
BOLTS, WELDS, AND CONNECTED ELEMENTS
CG. The bolt most remote from the CG, then, is the most highly stressed. The resultant
vectorial sum of these forces ru is the required strength for the bolt.
The direct shear force per bolt due to the concentric force Pu is r1,
where
r1 =
Pu
n
and n is the number of bolts.
The shear force in each bolt due to the moment Pu e varies with distance from the CG
and will be maximum in the bolt which is must remote from the CG. The maximum shear
due to the moment Pu e is rm,
where
Y
e = 16 in.
Pu =60 kips
X
CG
1½
5@3=1 ′-3
W14x82
A572 gr. 50
X
PL 7/8, A36
2¾
2¾
5½
Y
Fig. 8-9. Bolted bracket plate for Examples 8-1 and 8-2.
Y
Pu
e
CG
X
Figure 8-10
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
ECCENTRICALLY LOADED BOLT GROUPS
rm =
8 - 35
Pu ec
Ip
In the above equation,
c = distance from CG to center of bolt most remote from CG, in.
Ip = polar moment of inertia of the bolt group, in.4 per in.2 (see any text on statics).
To determine the resultant force on the most highly stressed bolt, rm must be resolved
into vertical component r2 and horizontal component r3,
where
Pu ecx
Ip
Pu ecy
r3 =
Ip
r2 =
In the above equation, cx and cy are the horizontal and vertical components of the diagonal
distance c. Thus, the resultant factored force is ru,
where
r2
r1
ru = √
(r1 + r2)2 + (r3)2
r3
rm
ru
and the bolts must be chosen such that the design strength φrn exceeds the required
strength ru.
For the more general case of an inclined eccentric force, i.e., not parallel to the
Y principal axes of the bolt group, the effect of the X-direction component of the direct
shear must also be included. Refer to Iwankiw (1987).
Example 8-2
Given:
Refer to Example 8-1. Recalculate the largest eccentric force Pu for
which the design shear strength of the bolts in the connection is
adequate using the elastic method. Compare the result with that of
Example 8-1. Use 7⁄8-in. diameter A325-N bolts, φrn = 21.6 kips.
Ip = 406 in.4 per in.2
Solution:
Direct shear force per bolt:
r1 =
Pu
n
=
Pu
12
Additional shear force on bolt due to eccentricity:
r2 =
Pu ecx
Ip
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
8 - 36
BOLTS, WELDS, AND CONNECTED ELEMENTS
51⁄2−in.
Pu (16 in.)
2
=
406 in.4 per in.2
= 0.108 Pu
Pu ecy
r3 =
Ip
Pu (16 in.) (71⁄2− in.)
=
406 in.4 per in.2
= 0.296 Pu
Resultant shear force:
(r1 + r2)2 + (r3)2
ru = √
√
2
Pu
2
12 + 0.108Pu + (0.296Pu )
= 0.352 Pu
=
Since ru must be less than or equal to φrn,
φrn
0.352
21.6 kips
≤
0.352
≤ 61.3 kips
Pu ≤
This 20 percent reduction in the strength predicted by the instantaneous
center of rotation method in Example 8-1a is indicative of the conservatism of the elastic method.
Eccentricity Normal to the Plane of the Faying Surface
Eccentricity normal to the plane of the faying surface produces tension above and
compression below the neutral axis of the bracket connection illustrated in Figure 8-11.
The eccentric load Pu can be resolved into a concentric force Pu acting at the faying surface
of the connection and a moment Pu e normal to the plane of the faying surface where e is
the eccentricity. Each bolt is then assumed to support an equal share of the concentric
force Pu, and the moment is resisted by tension in the bolts above the neutral axis and
compression between the lower part of the bracket and the column flange.
The forces for which the bolts in this connection must be designed must be determined
by balancing the tensile forces in the bolts above the neutral axis with the resultant
compressive force below the neutral axis. The analysis of such a connection is straightforward and usually begins with one of two assumptions: Case I assumes the neutral axis
is not at the center of gravity (CG) while Case II assumes the neutral axis is at the CG.
For a bearing-type connection, the limit state of bolt tension, including the effect of
prying action and the shear stress present, must still be checked as specified in LRFD
Specification Section J3.7. For a slip-critical connection, the bolts above the neutral axis
subject to tension would lose a portion of their clamping force. The overall connection,
however, would experience no reduction in total clamping force because the clamping
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
ECCENTRICALLY LOADED BOLT GROUPS
8 - 37
force below the neutral axis is increased by an equivalent amount. Therefore, it would
be unnecessary to reduce the strength of this connection for the interaction of tension and
shear above the neutral axis. However, the limit state of bolt tension, including the effect
of prying action and the shear stress present, must still be checked as specified in LRFD
Specification Section J3.9.
Case I—Neutral Axis Not at Center of Gravity
The shear force per bolt due to the concentric force Pu is ruv,
where
ruv =
Pu
n
and n is the number of bolts in the connection.
To determine the location of the neutral axis, assume a trial position of the neutral axis
at one-sixth of the total bracket depth, measured upward from the bottom. In Figure 8-12a,
this is indicated by the line X-X. To provide for reasonable proportions and to recognize
that the effective bearing area will depend upon the bracket flange or support flange
bending stiffness, the effective width of the compression block Weff should be taken as:
Weff = 8tf ≤ bf
where
tf = lesser of bracket flange and support flange thicknesses, in.
bf = bracket flange width, in.
This effective width is valid for bracket flanges made from W or S shapes, welded
plates, and angles. Where the bracket flange thickness is not constant, the average flange
thickness should be used.
Having assumed the width of the compression block, it is possible to check an assumed
location of the neutral axis by checking static equilibrium assuming an elastic stress
e
Pu
Tee Bracket
Fig. 8-11. Bolts subjected to eccentricity normal to the plane of the faying surface.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
8 - 38
BOLTS, WELDS, AND CONNECTED ELEMENTS
distribution. Equating the moment of the bolt area above the neutral axis with the moment
of the compression block area below the neutral axis,
ΣAb × y = Weff × d ×
d
2
In the above equation,
ΣAb = sum of the areas of all bolts above the neutral axis, in.2
y = distance from line X-X to CG of of the bolt group above neutral axis, in.
d = depth of compression block, in.
The value of d may then be adjusted until a reasonable equality exists.
Once the neutral axis has been located, the tensile force per bolt rut, as illustrated in
Figure 8-12b may be determined as:
rut =
Pu ec
× Ab
Ix
where
c = distance from neutral axis to most remote bolt in group, in.
Ix = combined moment of inertia of bolt group and compression block about neutral
axis, in.4
Bolts above the neutral axis are subjected to the shear force ruv, the tensile force rut,
and the effect of prying action; bolts below the neutral axis are subjected to the shear
force ruv only.
Case II—Neutral Axis at Center of Gravity
This method provides a more direct, but also a more conservative result. As for Case I,
the shear force per bolt due to the concentric force Pu is ruv, where
tf
Pu
n
CG (tension group)
2rut
y
d = Depth/6
Depth
ruv =
X
NA
X
Weff
(a) Initial approximation
of location of NA
(b) Force diagram with
final location of NA
Fig. 8-12. Case I—Neutral axis (NA) not at center of gravity (CG).
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
ECCENTRICALLY LOADED BOLT GROUPS
8 - 39
and n is the number of bolts in the connection.
The neutral axis is assumed to be located at the CG of the bolt group as illustrated in
Figure 8-13. The bolts above the neutral axis are in tension and the bolts below the neutral
axis are said to be in “compression.” To obtain a more accurate result, a plastic stress
distribution is assumed; this assumption is justified because this method is still more
conservative than Case I. Accordingly, the tensile force rut in each bolt above the neutral
axis due to the moment Pue is:
rut =
Pu e
n′dm
where
n′ = number of bolts above the neutral axis
dm = moment arm between resultant tensile force and resultant compressive force, in.
tf
Bolts above the neutral axis are subjected to the shear force ruv, the tensile force rut,
and the effect of prying action; bolts below the neutral axis are subjected to the shear
force ruv only.
2rut
NA
Fig. 8-13. Case II—Neutral axis (NA) at center of gravity (CG).
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
8 - 40
BOLTS, WELDS, AND CONNECTED ELEMENTS
Table 8-18.
Coefficients C for Eccentrically Loaded Bolt Groups
Angle = 0°°
C req =
Pu
φrn
or φR n = C × φ rn
where
ex = e
s
Pu
= factored force, kips
φ rn = design strength per bolt, kips
φ R n = design strength of bolt group, kips
e
= eccentricity of Pu with respect to centroid
of bolt group, in. (not tabulated, may be
determined by geometry.)
e x = horizontal component of e, in.
s
= bolt spacing, in.
C
= coefficient tabulated below.
s
s
s
Pu
Number of bolts in one vertical row, n
s, in. ex, in.
3
6
2
3
4
5
6
7
8
9
10
11
12
2
3
4
5
6
1.18
0.88
0.69
0.56
0.48
2.23
1.75
1.40
1.15
0.97
3.32
2.81
2.36
2.01
1.73
4.39
3.90
3.40
2.96
2.59
5.45
4.98
4.47
3.98
3.55
6.48
6.06
5.56
5.05
4.57
7.51
7.12
6.64
6.13
5.63
8.52
8.17
7.72
7.22
6.70
9.53
9.21
8.78
8.30
7.79
10.5
10.2
9.84
9.38
8.87
11.5
11.3
10.9
10.4
9.96
7
8
9
10
12
0.41
0.36
0.32
0.29
0.24
0.83
0.73
0.65
0.59
0.49
1.51
1.34
1.21
1.09
0.92
2.28
2.04
1.83
1.66
1.40
3.17
2.85
2.59
2.36
2.00
4.13
3.75
3.42
3.14
2.68
5.15
4.72
4.34
4.00
3.44
6.20
5.73
5.31
4.92
4.27
7.28
6.78
6.32
5.89
5.15
8.36
7.85
7.36
6.90
6.09
9.44
8.93
8.42
7.94
7.06
14
16
18
20
24
0.21
0.18
0.16
0.15
0.12
0.42
0.37
0.33
0.29
0.25
0.79
0.70
0.62
0.56
0.47
1.21
1.06
0.95
0.85
0.71
1.74
1.53
1.37
1.24
1.03
2.33
2.06
1.84
1.67
1.40
3.01
2.67
2.39
2.16
1.82
3.75
3.33
3.00
2.72
2.29
4.55
4.06
3.66
3.33
2.81
5.41
4.85
4.38
3.99
3.37
6.31
5.68
5.15
4.70
3.99
28
32
36
0.11
0.09
0.08
0.21
0.18
0.16
0.40
0.35
0.31
0.61
0.54
0.48
0.89
0.78
0.69
1.20
1.05
0.94
1.57
1.37
1.22
1.97
1.73
1.54
2.42
2.13
1.90
2.92
2.57
2.29
3.45
3.04
2.72
2
3
4
5
6
1.63
1.39
1.18
1.01
0.88
2.71
2.48
2.23
1.98
1.75
3.75
3.56
3.32
3.07
2.81
4.77
4.60
4.39
4.15
3.90
5.77
5.63
5.45
5.23
4.98
6.77
6.65
6.48
6.28
6.06
7.76
7.65
7.51
7.33
7.12
8.75
8.66
8.52
8.36
8.17
9.74
9.66
9.53
9.38
9.21
10.7
10.7
10.5
10.4
10.2
11.7
11.6
11.5
11.4
11.2
7
8
9
10
12
0.77
0.69
0.62
0.56
0.48
1.56
1.40
1.26
1.15
0.97
2.58
2.36
2.17
2.01
1.73
3.64
3.40
3.17
2.96
2.59
4.73
4.47
4.22
3.98
3.55
5.81
5.56
5.30
5.05
4.57
6.89
6.64
6.39
6.13
5.63
7.95
7.72
7.47
7.22
6.70
9.00
8.78
8.55
8.30
7.79
10.1
9.84
9.61
9.38
8.87
11.1
10.9
10.7
10.4
9.96
14
16
18
20
24
0.41
0.36
0.32
0.29
0.24
0.83
0.73
0.65
0.59
0.49
1.51
1.34
1.21
1.09
0.92
2.28
2.04
1.83
1.66
1.40
3.17
2.85
2.59
2.36
2.00
4.13
3.75
3.42
3.14
2.68
5.15
4.72
4.34
4.00
3.44
6.20
5.73
5.31
4.92
4.27
7.28
6.78
6.32
5.89
5.15
8.36
7.85
7.36
6.90
6.09
9.44
8.93
8.42
7.94
7.06
28
32
36
0.21
0.18
0.16
0.42
0.37
0.33
0.79
0.70
0.62
1.21
1.06
0.95
1.74
1.53
1.37
2.33
2.06
1.84
3.01
2.67
2.39
3.75
3.33
3.00
4.55
4.06
3.66
5.41
4.85
4.38
6.31
5.68
5.15
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
ECCENTRICALLY LOADED BOLT GROUPS
8 - 41
Table 8-18 (cont.).
Coefficients C for Eccentrically Loaded Bolt Groups
Angle = 15°°
C req =
Pu
φ rn
or φ R n = C × φrn
where
ex
Pu
15°
s
s
Pu
= factored force, kips
φ rn = design strength per bolt, kips
φ R n = design strength of bolt group, kips
e
= eccentricity of Pu with respect to centroid
of bolt group, in. (not tabulated, may be
determined by geometry.)
e x = horizontal component of e, in.
s
= bolt spacing, in.
C
= coefficient tabulated below.
s
s
e
Number of bolts in one vertical row, n
s, in. ex, in.
3
6
2
3
4
5
6
7
8
9
10
11
12
2
3
4
5
6
1.15
0.86
0.67
0.55
0.47
2.20
1.76
1.42
1.17
0.99
3.28
2.78
2.35
2.00
1.73
4.34
3.85
3.36
2.94
2.58
5.39
4.92
4.41
3.94
3.52
6.42
5.98
5.48
4.98
4.52
7.45
7.03
6.55
6.04
5.55
8.46
8.08
7.61
7.11
6.61
9.47
9.11
8.67
8.18
7.67
10.5
10.1
9.72
9.24
8.74
11.5
11.2
10.8
10.3
9.81
7
8
9
10
12
0.41
0.36
0.32
0.29
0.24
0.86
0.75
0.67
0.61
0.51
1.52
1.35
1.22
1.10
0.93
2.30
2.06
1.86
1.69
1.43
3.16
2.86
2.60
2.38
2.03
4.11
3.74
3.43
3.16
2.71
5.10
4.69
4.32
4.00
3.46
6.13
5.68
5.27
4.90
4.28
7.18
6.70
6.26
5.85
5.15
8.24
7.74
7.28
6.84
6.06
9.30
8.80
8.31
7.85
7.01
14
16
18
20
24
0.21
0.19
0.17
0.15
0.12
0.43
0.38
0.34
0.30
0.25
0.81
0.71
0.63
0.57
0.48
1.24
1.09
0.97
0.88
0.73
1.76
1.56
1.39
1.26
1.06
2.37
2.10
1.88
1.70
1.43
3.04
2.70
2.43
2.20
1.86
3.78
3.37
3.04
2.76
2.33
4.57
4.09
3.70
3.37
2.86
5.41
4.87
4.42
4.03
3.43
6.30
5.69
5.18
4.74
4.04
28
32
36
0.11
0.09
0.08
0.22
0.19
0.17
0.41
0.36
0.32
0.63
0.55
0.49
0.91
0.80
0.71
1.23
1.08
0.96
1.60
1.41
1.26
2.02
1.77
1.58
2.47
2.18
1.95
2.97
2.62
2.34
3.51
3.10
2.78
2
3
4
5
6
1.61
1.36
1.15
0.98
0.86
2.69
2.45
2.20
1.96
1.76
3.72
3.52
3.28
3.03
2.78
4.74
4.56
4.34
4.10
3.85
5.74
5.59
5.39
5.16
4.92
6.74
6.60
6.42
6.21
5.98
7.73
7.61
7.45
7.25
7.03
8.73
8.61
8.46
8.28
8.08
9.71
9.61
9.47
9.30
9.11
7
8
9
10
12
0.75
0.67
0.61
0.55
0.47
1.57
1.42
1.29
1.17
0.99
2.55
2.35
2.16
2.00
1.73
3.60
3.36
3.14
2.94
2.58
4.66
4.41
4.17
3.94
3.52
5.73
5.48
5.23
4.98
4.52
6.80
6.55
6.30
6.04
5.55
7.85
7.61
7.36
7.11
6.61
8.90
8.67
8.43
8.18
7.67
9.94
9.72
9.49
9.24
8.74
11.0
10.8
10.5
10.3
9.81
14
16
18
20
24
0.41
0.36
0.32
0.29
0.24
0.86
0.75
0.67
0.61
0.51
1.52
1.35
1.22
1.10
0.93
2.30
2.06
1.86
1.69
1.43
3.16
2.86
2.60
2.38
2.03
4.11
3.74
3.43
3.16
2.71
5.10
4.69
4.32
4.00
3.46
6.13
5.68
5.27
4.90
4.28
7.18
6.70
6.26
5.85
5.15
8.24
7.74
7.28
6.84
6.06
9.30
8.80
8.31
7.85
7.01
28
32
36
0.21
0.19
0.17
0.43
0.38
0.34
0.81
0.71
0.63
1.24
1.09
0.97
1.76
1.56
1.39
2.37
2.10
1.88
3.04
2.70
2.43
3.78
3.37
3.04
4.57
4.09
3.70
5.41
4.87
4.42
6.30
5.69
5.18
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
10.7
10.6
10.5
10.3
10.1
11.7
11.6
11.5
11.3
11.1
8 - 42
BOLTS, WELDS, AND CONNECTED ELEMENTS
Table 8-18 (cont.).
Coefficients C for Eccentrically Loaded Bolt Groups
Angle = 30°°
C req =
Pu
φrn
or φ R n = C × φ rn
where
ex
Pu
s
Pu
= factored force, kips
φ rn = design strength per bolt, kips
φ R n = design strength of bolt group, kips
e
= eccentricity of Pu with respect to centroid
of bolt group, in. (not tabulated, may be
determined by geometry.)
e x = horizontal component of e, in.
s
= bolt spacing, in.
C
= coefficient tabulated below.
s
30°
s
s
e
Number of bolts in one vertical row, n
s, in. ex, in.
3
6
2
3
4
5
6
7
8
9
10
11
12
2
3
4
5
6
1.14
0.86
0.69
0.57
0.49
2.20
1.80
1.50
1.27
1.09
3.25
2.79
2.40
2.08
1.82
4.30
3.83
3.39
3.00
2.68
5.33
4.87
4.41
3.98
3.60
6.36
5.92
5.45
4.99
4.57
7.38
6.96
6.49
6.02
5.58
8.39
7.99
7.53
7.06
6.60
9.40
9.02
8.57
8.11
7.64
10.4
10.0
9.61
9.15
8.68
11.4
11.1
10.6
10.2
9.72
7
8
9
10
12
0.43
0.38
0.34
0.31
0.26
0.95
0.83
0.75
0.67
0.56
1.61
1.44
1.30
1.19
1.01
2.40
2.17
1.98
1.82
1.55
3.27
2.98
2.74
2.52
2.17
4.20
3.86
3.57
3.31
2.87
5.17
4.79
4.46
4.15
3.64
6.17
5.76
5.39
5.05
4.46
7.18
6.75
6.35
5.98
5.33
8.21
7.77
7.34
6.95
6.24
9.25
8.79
8.35
7.93
7.17
14
16
18
20
24
0.23
0.20
0.18
0.16
0.14
0.48
0.42
0.38
0.34
0.28
0.87
0.77
0.69
0.62
0.52
1.35
1.20
1.07
0.97
0.81
1.90
1.69
1.52
1.37
1.16
2.53
2.26
2.04
1.85
1.57
3.23
2.89
2.62
2.38
2.02
3.98
3.58
3.25
2.97
2.53
4.78
4.33
3.94
3.61
3.09
5.63
5.11
4.67
4.30
3.69
6.51
5.94
5.45
5.02
4.33
28
32
36
0.12
0.10
0.09
0.24
0.21
0.19
0.45
0.40
0.35
0.70
0.61
0.55
1.00
0.88
0.78
1.36
1.19
1.07
1.75
1.54
1.38
2.20
1.94
1.74
2.69
2.38
2.13
3.22
2.85
2.56
3.79
3.37
3.03
2
3
4
5
6
1.59
1.34
1.14
0.98
0.86
2.66
2.43
2.20
1.99
1.80
3.69
3.48
3.25
3.02
2.79
4.70
4.52
4.30
4.06
3.83
5.71
5.54
5.33
5.11
4.87
6.70
6.55
6.36
6.14
5.92
7.70
7.55
7.38
7.17
6.96
8.69
8.56
8.39
8.20
7.99
9.68
9.55
9.40
9.22
9.02
7
8
9
10
12
0.77
0.69
0.63
0.57
0.49
1.64
1.50
1.37
1.27
1.09
2.59
2.40
2.23
2.08
1.82
3.60
3.39
3.19
3.00
2.68
4.64
4.41
4.19
3.98
3.60
5.68
5.45
5.22
4.99
4.57
6.73
6.49
6.26
6.02
5.58
7.77
7.53
7.30
7.06
6.60
8.80
8.57
8.34
8.11
7.64
9.83
9.61
9.38
9.15
8.68
10.9
10.6
10.4
10.2
9.72
14
16
18
20
24
0.43
0.38
0.34
0.31
0.26
0.95
0.83
0.75
0.67
0.56
1.61
1.44
1.30
1.19
1.01
2.40
2.17
1.98
1.82
1.55
3.27
2.98
2.74
2.52
2.17
4.20
3.86
3.57
3.31
2.87
5.17
4.79
4.46
4.15
3.64
6.17
5.76
5.39
5.05
4.46
7.18
6.75
6.35
5.98
5.33
8.21
7.77
7.34
6.95
6.24
9.25
8.79
8.35
7.93
7.17
28
32
36
0.23
0.20
0.18
0.48
0.42
0.38
0.87
0.77
0.69
1.35
1.20
1.07
1.90
1.69
1.52
2.53
2.26
2.04
3.23
2.89
2.62
3.98
3.58
3.25
4.78
4.33
3.94
5.63
5.11
4.67
6.51
5.94
5.45
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
10.7
10.6
10.4
10.2
10.0
11.7
11.5
11.4
11.2
11.1
8 - 44
BOLTS, WELDS, AND CONNECTED ELEMENTS
Table 8-18 (cont.).
Coefficients C for Eccentrically Loaded Bolt Groups
Angle = 60°°
C req =
Pu
φrn
or φR n = C × φ rn
where
ex
60°
Pu
s
e
s
s
s
Pu
= factored force, kips
φ rn = design strength per bolt, kips
φ R n = design strength of bolt group, kips
e
= eccentricity of Pu with respect to centroid
of bolt group, in. (not tabulated, may be
determined by geometry.)
e x = horizontal component of e, in.
s
= bolt spacing, in.
C
= coefficient tabulated below.
Number of bolts in one vertical row, n
s, in. ex, in.
3
6
2
3
4
5
6
7
8
9
10
11
12
2
3
4
5
6
1.27
1.05
0.89
0.77
0.68
2.32
2.05
1.83
1.65
1.49
3.32
3.02
2.77
2.54
2.34
4.31
4.00
3.72
3.47
3.24
5.30
4.98
4.69
4.41
4.16
6.30
5.97
5.66
5.37
5.10
7.29
6.96
6.64
6.34
6.06
8.27
7.94
7.62
7.32
7.02
9.27
8.94
8.61
8.29
7.99
10.3
9.93
9.60
9.28
8.97
11.3
10.9
10.6
10.3
9.95
7
8
9
10
12
0.61
0.56
0.51
0.47
0.40
1.37
1.26
1.16
1.07
0.93
2.17
2.01
1.87
1.74
1.52
3.03
2.83
2.66
2.50
2.22
3.93
3.71
3.51
3.32
3.00
4.85
4.61
4.39
4.19
3.82
5.79
5.54
5.30
5.08
4.67
6.74
6.48
6.23
5.99
5.55
7.71
7.43
7.17
6.92
6.45
8.67
8.39
8.12
7.86
7.37
9.64
9.35
9.07
8.81
8.30
14
16
18
20
24
0.35
0.32
0.29
0.26
0.22
0.81
0.72
0.65
0.58
0.49
1.35
1.21
1.09
1.00
0.85
2.00
1.81
1.66
1.53
1.32
2.73
2.49
2.30
2.12
1.84
3.50
3.23
2.98
2.77
2.41
4.32
4.00
3.72
3.47
3.05
5.16
4.81
4.50
4.21
3.73
6.03
5.65
5.31
4.99
4.45
6.92
6.51
6.14
5.80
5.21
7.83
7.40
7.00
6.63
5.99
28
32
36
0.19
0.17
0.15
0.42
0.37
0.33
0.74
0.65
0.59
1.15
1.02
0.92
1.61
1.43
1.29
2.13
1.91
1.72
2.71
2.44
2.21
3.34
3.02
2.74
4.00
3.63
3.31
4.70
4.28
3.92
5.44
4.97
4.57
2
3
4
5
6
1.60
1.42
1.27
1.15
1.05
2.65
2.48
2.32
2.18
2.05
3.65
3.48
3.32
3.17
3.02
4.64
4.48
4.31
4.15
4.00
5.64
5.47
5.30
5.14
4.98
6.63
6.46
6.30
6.13
5.97
7.62
7.45
7.29
7.12
6.96
8.61
8.44
8.27
8.11
7.94
9.60
9.44
9.27
9.10
8.94
10.6
10.4
10.3
10.1
9.93
11.6
11.4
11.3
11.1
10.9
7
8
9
10
12
0.96
0.89
0.83
0.77
0.68
1.93
1.83
1.73
1.65
1.49
2.89
2.77
2.65
2.54
2.34
3.86
3.72
3.59
3.47
3.24
4.83
4.69
4.55
4.41
4.16
5.81
5.66
5.51
5.37
5.10
6.80
6.64
6.49
6.34
6.06
7.78
7.62
7.47
7.32
7.02
8.77
8.61
8.45
8.29
7.99
9.76
9.60
9.43
9.28
8.97
10.8
10.6
10.4
10.3
9.95
14
16
18
20
24
0.61
0.56
0.51
0.47
0.40
1.37
1.26
1.16
1.07
0.93
2.17
2.01
1.87
1.74
1.52
3.03
2.83
2.66
2.50
2.22
3.93
3.71
3.51
3.32
3.00
4.85
4.61
4.39
4.19
3.82
5.79
5.54
5.30
5.08
4.67
6.74
6.48
6.23
5.99
5.55
7.71
7.43
7.17
6.92
6.45
8.67
8.39
8.12
7.86
7.37
9.64
9.35
9.07
8.81
8.30
28
32
36
0.35
0.32
0.29
0.81
0.72
0.65
1.35
1.21
1.09
2.00
1.81
1.66
2.73
2.49
2.30
3.50
3.23
2.98
4.32
4.00
3.72
5.16
4.81
4.50
6.03
5.65
5.31
6.92
6.51
6.14
7.83
7.40
7.00
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
ECCENTRICALLY LOADED BOLT GROUPS
8 - 45
Table 8-18 (cont.).
Coefficients C for Eccentrically Loaded Bolt Groups
Angle = 75°°
C req =
Pu
φ rn
or φ R n = C × φrn
where
ex
75°
s
Pu
= factored force, kips
φ rn = design strength per bolt, kips
φ R n = design strength of bolt group, kips
e
= eccentricity of Pu with respect to centroid
of bolt group, in. (not tabulated, may be
determined by geometry.)
e x = horizontal component of e, in.
s
= bolt spacing, in.
C
= coefficient tabulated below.
s
Pu
s
s
e
Number of bolts in one vertical row, n
s, in. ex, in.
3
6
2
3
4
5
6
7
8
9
10
11
12
2
3
4
5
6
1.49
1.32
1.18
1.07
0.98
2.51
2.33
2.18
2.04
1.92
3.49
3.30
3.14
2.99
2.85
4.46
4.27
4.09
3.93
3.79
5.44
5.24
5.05
4.88
4.73
6.42
6.21
6.01
5.84
5.67
7.40
7.18
6.98
6.79
6.62
8.38
8.15
7.95
7.75
7.57
9.36
9.13
8.92
8.72
8.53
10.3
10.1
9.89
9.68
9.49
11.3
11.1
10.9
10.7
10.5
7
8
9
10
12
0.90
0.84
0.78
0.73
0.65
1.82
1.72
1.63
1.55
1.41
2.73
2.62
2.51
2.41
2.23
3.65
3.52
3.40
3.29
3.08
4.58
4.44
4.31
4.19
3.95
5.52
5.37
5.23
5.10
4.84
6.46
6.30
6.16
6.02
5.75
7.40
7.24
7.09
6.94
6.66
8.36
8.19
8.03
7.88
7.59
9.31
9.14
8.97
8.81
8.51
10.3
10.1
9.92
9.76
9.45
14
16
18
20
24
0.58
0.53
0.48
0.44
0.38
1.30
1.20
1.11
1.03
0.89
2.06
1.92
1.78
1.66
1.46
2.88
2.70
2.53
2.38
2.12
3.73
3.52
3.33
3.16
2.85
4.60
4.38
4.17
3.97
3.63
5.50
5.26
5.03
4.82
4.44
6.40
6.15
5.91
5.69
5.27
7.31
7.05
6.80
6.56
6.13
8.23
7.96
7.70
7.45
6.99
9.16
8.88
8.61
8.35
7.87
28
32
36
0.34
0.30
0.27
0.79
0.70
0.62
1.29
1.16
1.05
1.90
1.73
1.58
2.59
2.38
2.19
3.33
3.08
2.85
4.11
3.81
3.55
4.91
4.58
4.28
5.73
5.37
5.05
6.57
6.19
5.84
7.43
7.02
6.65
2
3
4
5
6
1.71
1.60
1.49
1.40
1.32
2.72
2.61
2.51
2.42
2.33
3.70
3.59
3.49
3.39
3.30
4.69
4.57
4.46
4.37
4.27
5.67
5.55
5.44
5.34
5.24
6.66
6.53
6.42
6.31
6.21
7.64
7.52
7.40
7.29
7.18
8.79
8.50
8.38
8.26
8.15
9.78
9.48
9.36
9.24
9.13
10.8
10.5
10.3
10.2
10.1
11.7
11.5
11.3
11.2
11.1
7
8
9
10
12
1.25
1.18
1.13
1.07
0.98
2.25
2.18
2.11
2.04
1.92
3.22
3.14
3.06
2.99
2.85
4.18
4.09
4.01
3.93
3.79
5.14
5.05
4.97
4.88
4.73
6.11
6.01
5.92
5.84
5.67
7.07
6.98
6.88
6.79
6.62
8.05
7.95
7.85
7.75
7.57
9.01
8.92
8.81
8.72
8.53
10.0
9.89
9.78
9.68
9.49
11.0
10.9
10.8
10.7
10.5
14
16
18
20
24
0.90
0.84
0.78
0.73
0.65
1.82
1.72
1.63
1.55
1.41
2.73
2.62
2.51
2.41
2.23
3.65
3.52
3.40
3.29
3.08
4.58
4.44
4.31
4.19
3.95
5.52
5.37
5.23
5.10
4.84
6.46
6.30
6.16
6.02
5.75
7.40
7.24
7.09
6.94
6.66
8.36
8.19
8.03
7.88
7.59
9.31
9.14
8.97
8.81
8.51
10.3
10.1
9.92
9.76
9.45
28
32
36
0.58
0.53
0.48
1.30
1.20
1.11
2.06
1.92
1.78
2.88
2.70
2.53
3.73
3.52
3.33
4.60
4.38
4.17
5.50
5.26
5.03
6.40
6.15
5.91
7.31
7.05
6.80
8.23
7.96
7.70
9.16
8.88
8.61
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
8 - 46
BOLTS, WELDS, AND CONNECTED ELEMENTS
Table 8-19.
Coefficients C for Eccentrically Loaded Bolt Groups
Angle = 0°°
C req =
Pu
φrn
or φR n = C × φ rn
ex = e
where
s, in.
3
6
Pu
s
s
s
s
Pu
= factored force, kips
φ rn = design strength per bolt, kips
φ R n = design strength of bolt group, kips
e
= eccentricity of Pu with respect to centroid
of bolt group, in. (not tabulated, may be
determined by geometry.)
e x = horizontal component of e, in.
s
= bolt spacing, in.
C
= coefficient tabulated below.
3
Number of bolts in one vertical row, n
ex,
in.
1
2
3
4
5
6
7
8
9
10
11
12
2
3
4
5
6
0.84
0.65
0.54
0.45
0.39
2.54
2.03
1.67
1.42
1.22
4.48
3.68
3.06
2.59
2.25
6.59
5.67
4.86
4.21
3.69
8.72
7.77
6.84
6.01
5.32
10.8
9.91
8.93
8.00
7.17
12.9
12.1
11.1
10.1
9.16
15.0
14.2
13.2
12.2
11.2
17.0
16.3
15.4
14.4
13.4
19.0
18.3
17.5
16.5
15.5
21.0
20.4
19.6
18.7
17.7
23.0
22.5
21.7
20.8
19.8
7
8
9
10
12
0.35
0.31
0.28
0.26
0.22
1.08
0.96
0.86
0.78
0.66
1.99
1.78
1.60
1.46
1.24
3.27
2.93
2.65
2.42
2.06
4.74
4.27
3.87
3.53
3.01
6.46
5.86
5.34
4.90
4.19
8.33 10.3 12.4
7.60 9.50 11.5
6.97 8.75 10.7
6.42 8.10 9.91
5.51 7.01 8.63
14.5
13.6
12.7
11.8
10.4
16.7
15.7
14.7
13.8
12.2
18.8
17.8
16.8
15.9
14.2
14
16
18
20
24
0.19
0.17
0.15
0.14
0.12
0.57
0.51
0.45
0.41
0.34
1.08
0.95
0.85
0.77
0.65
1.78
1.57
1.41
1.27
1.07
2.62
2.32
2.07
1.88
1.58
3.66
3.24
2.90
2.63
2.21
4.82
4.27
3.83
3.48
2.93
6.15
5.47
4.92
4.47
3.77
7.61
6.79
6.11
5.55
4.69
9.19 10.9 12.7
8.23 9.78 11.4
7.43 8.85 10.4
6.76 8.07 9.48
5.72 6.85 8.06
28
32
36
0.10
0.09
0.08
0.29
0.26
0.23
0.56
0.49
0.43
0.92
0.80
0.72
1.36
1.19
1.06
1.90
1.67
1.49
2.53
2.22
1.98
3.25
2.86
2.55
4.05
3.57
3.18
4.95
4.36
3.90
2
3
4
5
6
0.84
0.65
0.54
0.45
0.39
3.24
2.79
2.41
2.10
1.85
5.39
4.93
4.44
3.97
3.55
7.47
7.08
6.60
6.11
5.62
9.51
9.17
8.75
8.27
7.77
11.5
11.2
10.9
10.4
9.93
13.5
13.3
12.4
12.5
12.1
15.5
15.3
15.0
14.6
14.2
17.5
17.3
17.0
16.7
16.3
19.5
19.3
19.1
18.7
18.4
21.5
21.3
21.1
20.8
20.4
23.4
23.3
23.1
22.8
22.5
7
8
9
10
12
0.35
0.31
0.28
0.26
0.22
1.64
1.47
1.34
1.22
1.04
3.18
2.87
2.61
2.39
2.04
5.17
4.75
4.39
4.06
3.52
7.27
6.79
6.34
5.92
5.20
9.43
8.92
8.43
7.96
7.10
11.6
11.1
10.6
10.1
9.12
13.7
13.3
12.7
12.2
11.2
15.9
15.4
14.9
14.4
13.4
18.0
17.5
17.1
16.6
15.6
20.1
19.6
19.2
18.7
17.7
22.1
21.7
21.3
20.9
19.9
14
16
18
20
24
0.19
0.17
0.15
0.14
0.12
0.90
0.80
0.71
0.64
0.54
1.77
1.57
1.41
1.28
1.07
3.09
2.75
2.48
2.25
1.90
4.61
4.12
3.72
3.38
2.86
6.36
5.74
5.21
4.77
4.06
8.27 10.3 12.4
7.52 9.44 11.7
6.87 8.68 10.6
6.31 8.02 9.85
5.40 6.91 8.55
14.5
13.5
12.6
11.8
10.3
16.7
15.7
14.7
13.8
12.2
18.9
17.8
16.8
15.9
14.1
28
32
36
0.10
0.09
0.08
0.46
0.41
0.36
0.93
0.81
0.73
1.64
1.44
1.29
2.47
2.18
1.94
3.52
3.11
2.78
4.70
4.16
3.72
6.05
5.37
4.81
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
7.52
6.69
6.02
5.93
5.23
4.67
7.00
6.18
5.52
9.12 10.8 12.6
8.15 9.71 11.4
7.34 8.78 10.3
ECCENTRICALLY LOADED BOLT GROUPS
8 - 47
Table 8-19 (cont.).
Coefficients C for Eccentrically Loaded Bolt Groups
Angle = 15°°
C req =
Pu
φrn
or φR n = C × φ rn
ex
where
s, in.
3
6
15°
s
s
Pu
= factored force, kips
φ rn = design strength per bolt, kips
φ R n = design strength of bolt group, kips
e
= eccentricity of Pu with respect to centroid
of bolt group, in. (not tabulated, may be
determined by geometry.)
e x = horizontal component of e, in.
s
= bolt spacing, in.
C
= coefficient tabulated below.
Pu
s
s
e
3
Number of bolts in one vertical row, n
ex,
in.
1
2
3
4
5
2
3
4
5
6
0.87
0.68
0.55
0.47
0.41
2.54
2.04
1.69
1.44
1.25
4.47
3.71
3.11
2.66
2.31
6.54
5.63
4.85
4.21
3.70
8.63
7.69
6.79
6.00
5.34
7
8
9
10
12
0.36
0.32
0.29
0.27
0.23
1.10
0.98
0.88
0.81
0.68
2.04
1.83
1.65
1.51
1.28
3.29
2.96
2.68
2.45
2.09
4.79
4.32
3.94
3.61
3.08
6.46
5.87
5.37
4.93
4.24
8.30 10.2 12.3
7.60 9.45 11.4
6.99 8.74 10.6
6.45 8.11 9.88
5.58 7.05 8.66
14
16
18
20
24
0.20
0.17
0.16
0.14
0.12
0.59
0.52
0.47
0.42
0.35
1.11
0.98
0.88
0.79
0.67
1.82
1.61
1.44
1.31
1.10
2.69
2.38
2.13
1.93
1.62
3.71
3.29
2.96
2.68
2.26
4.90
4.36
3.92
3.56
3.00
6.21
5.54
4.99
4.54
3.84
7.67
6.86
6.20
5.65
4.79
9.23 10.9 12.7
8.29 9.83 11.5
7.51 8.93 10.4
6.85 8.17 9.57
5.82 6.96 8.17
28
32
36
0.10
0.09
0.08
0.30
0.27
0.24
0.57
0.50
0.45
0.94
0.83
0.74
1.40
1.23
1.10
1.95
1.72
1.53
2.60
2.28
2.04
3.32
2.93
2.61
4.15
3.66
3.27
5.05
4.46
3.98
2
3
4
5
6
0.87
0.68
0.55
0.47
0.41
3.21
2.76
2.38
2.07
1.83
5.35
4.88
4.40
3.96
3.56
7.42
7.00
6.53
6.04
5.56
9.45
9.09
8.65
8.17
7.67
11.5
11.1
10.7
10.3
9.80
7
8
9
10
12
0.36
0.32
0.29
0.27
0.23
1.63
1.47
1.34
1.23
1.05
3.22
2.92
2.66
2.45
2.09
5.12
4.73
4.37
4.05
3.53
7.19
6.72
6.29
5.90
5.21
9.30 11.4
8.81 10.9
8.33 10.4
7.88 9.95
7.06 9.04
14
16
18
20
24
0.20
0.17
0.16
0.14
0.12
0.91
0.81
0.72
0.66
0.55
1.83
1.62
1.45
1.32
1.11
3.11
2.78
2.50
2.28
1.93
4.64
4.17
3.77
3.45
2.93
6.35
5.75
5.24
4.80
4.10
8.22 10.2 12.2
7.51 9.38 11.4
6.88 8.66 10.5
6.34 8.02 9.82
5.46 6.95 8.57
28
32
36
0.10
0.09
0.08
0.48
0.42
0.37
0.96
0.84
0.75
1.67
1.47
1.32
2.54
2.24
2.00
3.57
3.16
2.83
4.78
4.24
3.80
6
7
10.7 12.8
9.80 11.9
8.84 10.9
7.94 9.98
7.15 9.09
13.5
13.2
12.8
12.4
11.9
8
9
10
11
12
14.8
14.0
13.0
12.1
11.1
16.9
16.1
15.2
14.2
13.2
18.9
18.2
17.3
16.3
15.3
20.9
20.2
19.4
18.4
17.4
22.9
22.3
21.5
20.5
19.6
14.3
13.4
12.6
11.8
10.4
16.4
15.5
14.6
13.7
12.2
18.6
17.6
16.6
15.7
14.1
6.05
5.34
4.78
7.12
6.29
5.64
15.5
15.2
14.9
14.5
14.0
17.4
17.2
16.9
16.5
16.1
19.4
19.2
18.9
18.6
18.2
21.4
21.2
20.9
20.6
20.3
23.4
23.2
22.9
22.6
22.3
13.6
13.1
12.6
12.1
11.1
15.7
15.2
14.7
14.2
13.2
17.8
17.3
16.8
16.3
15.3
19.9
19.4
18.9
18.5
17.5
21.9
21.5
21.0
20.6
19.6
14.3
13.4
12.5
11.7
10.3
16.5
15.5
14.5
13.7
12.1
18.6
17.6
16.6
15.7
14.0
6.11
5.44
4.89
7.58
6.77
6.10
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
9.15 10.8 12.6
8.21 9.75 11.4
7.42 8.85 10.4
8 - 48
BOLTS, WELDS, AND CONNECTED ELEMENTS
Table 8-19 (cont.).
Coefficients C for Eccentrically Loaded Bolt Groups
Angle = 30°°
C req =
Pu
φrn
or φR n = C × φ rn
ex
where
Pu
s, in.
3
6
s
Pu
= factored force, kips
φ rn = design strength per bolt, kips
φ R n = design strength of bolt group, kips
e
= eccentricity of Pu with respect to centroid
of bolt group, in. (not tabulated, may be
determined by geometry.)
e x = horizontal component of e, in.
s
= bolt spacing, in.
C
= coefficient tabulated below.
s
30°
s
s
e
3
Number of bolts in one vertical row, n
ex,
in.
1
2
3
4
5
6
7
8
9
10
11
12
2
3
4
5
6
0.97
0.75
0.62
0.52
0.45
2.60
2.12
1.78
1.53
1.34
4.52
3.83
3.29
2.85
2.51
6.54
5.71
4.99
4.39
3.89
8.59
7.71
6.88
6.16
5.54
10.6
9.75
8.87
8.06
7.33
12.9
11.8
10.9
10.0
9.23
14.7
13.9
13.0
12.1
11.2
16.7
15.9
15.1
14.1
13.2
18.8
18.0
17.1
16.2
15.3
20.8
20.0
19.2
18.3
17.3
22.8
22.1
21.3
20.4
19.4
7
8
9
10
12
0.40
0.36
0.32
0.30
0.25
1.19
1.07
0.97
0.88
0.75
2.23
2.00
1.81
1.66
1.41
3.48
3.15
2.87
2.64
2.27
5.01
4.57
4.19
3.87
3.34
6.70
6.14
5.66
5.24
4.54
8.51 10.4
7.86 9.68
7.28 9.02
6.77 8.43
5.92 7.43
12.4
11.6
10.9
10.2
9.04
14.4
13.6
12.8
12.0
10.8
16.4
15.6
14.7
13.9
12.5
18.5
17.6
16.7
15.9
14.4
14
16
18
20
24
0.22
0.19
0.17
0.16
0.13
0.65
0.58
0.52
0.47
0.39
1.23
1.08
0.97
0.88
0.74
1.98
1.76
1.58
1.43
1.21
2.93
2.60
2.34
2.12
1.79
3.99
3.56
3.21
2.92
2.48
5.24
4.69
4.24
3.87
3.29
6.61
5.94
5.38
4.92
4.18
8.09
7.30
6.64
6.08
5.19
9.67 11.4
8.77 10.3
8.00 9.45
7.34 8.70
6.29 7.48
28
32
36
0.12
0.10
0.09
0.34
0.30
0.26
0.64
0.56
0.50
1.04
0.92
0.82
1.55
1.36
1.21
2.14
1.89
1.69
2.85
2.51
2.25
3.63
3.21
2.87
4.52
4.00
3.59
5.49
4.87
4.37
2
3
4
5
6
0.97
0.75
0.62
0.52
0.45
3.20
2.75
2.39
2.10
1.87
5.31
4.86
4.42
4.02
3.67
7.37
6.95
6.49
6.04
5.61
9.39
9.01
8.57
8.11
7.66
11.4
11.1
10.6
10.2
9.73
7
8
9
10
12
0.40
0.36
0.32
0.30
0.25
1.69
1.53
1.40
1.29
1.12
3.36
3.08
2.84
2.63
2.28
5.21
4.84
4.51
4.21
3.70
7.21
6.79
6.40
6.04
5.39
9.27 11.4
8.82 10.9
8.39 10.4
7.98 9.99
7.23 9.16
14
16
18
20
24
0.22
0.19
0.17
0.16
0.13
0.98
0.87
0.79
0.71
0.60
2.00
1.78
1.60
1.45
1.23
3.29
2.95
2.68
2.45
2.08
4.86
4.40
4.02
3.70
3.17
6.57
6.01
5.52
5.09
4.39
8.41 10.3
7.75 9.60
7.17 8.93
6.65 8.33
5.79 7.32
28
32
36
0.12
0.10
0.09
0.52
0.46
0.41
1.06
0.93
0.83
1.82
1.61
1.44
2.77
2.45
2.20
3.85
3.42
3.08
5.11
4.56
4.12
13.4
13.1
12.7
12.3
11.8
6.54
5.81
5.22
13.1
12.0
11.0
10.1
8.75
7.68
6.83
6.15
15.4
15.1
14.7
14.3
13.9
17.4
17.1
16.8
16.4
16.0
19.4
19.1
18.8
18.4
18.0
21.3
21.1
20.8
20.4
20.1
23.3
23.1
22.8
22.5
22.1
13.4
13.0
12.5
12.0
11.2
15.5
15.1
14.6
14.1
13.2
17.6
17.1
16.7
16.2
15.3
19.6
19.2
18.7
18.3
17.3
21.7
21.3
20.8
20.4
19.4
12.3
11.5
10.8
10.1
8.95
14.4
13.5
12.7
12.0
10.7
16.4
15.5
14.7
13.9
12.5
18.5
17.6
16.7
15.9
14.4
6.49
5.82
5.27
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
7.99
7.20
6.53
9.59 11.3 13.0
8.68 10.3 11.9
7.91 9.37 10.9
ECCENTRICALLY LOADED BOLT GROUPS
8 - 49
Table 8-19 (cont.).
Coefficients C for Eccentrically Loaded Bolt Groups
Angle = 45°°
C req =
Pu
φ rn
or φ R n = C × φrn
ex
where
Pu
3
6
s
s
45°
s
e
s, in.
s
Pu
= factored force, kips
φ rn = design strength per bolt, kips
φ R n = design strength of bolt group, kips
e
= eccentricity of Pu with respect to centroid
of bolt group, in. (not tabulated, may be
determined by geometry.)
e x = horizontal component of e, in.
s
= bolt spacing, in.
C
= coefficient tabulated below.
3
Number of bolts in one vertical row, n
ex,
in.
1
2
3
4
5
6
7
8
9
10
11
12
2
3
4
5
6
1.17
0.92
0.75
0.64
0.55
2.79
2.32
1.99
1.74
1.54
4.67
4.06
3.57
3.17
2.84
6.62
5.92
5.31
4.78
4.33
8.61
7.86
7.16
6.53
5.98
10.6
9.83
9.09
8.39
7.76
12.6
11.8
11.1
10.3
9.63
14.6
13.9
13.1
12.3
11.6
16.6
15.9
15.1
14.3
13.5
18.6
17.9
17.1
16.3
15.5
20.6
19.9
19.1
18.3
17.5
22.6
21.9
21.1
20.3
19.5
7
8
9
10
12
0.49
0.44
0.40
0.36
0.31
1.38
1.25
1.14
1.05
0.90
2.57
2.33
2.13
1.96
1.68
3.93
3.60
3.31
3.06
2.65
5.49
5.06
4.69
4.36
3.83
7.20
6.70
6.25
5.85
5.17
9.00 10.9
8.43 10.3
7.91 9.67
7.44 9.14
6.63 8.20
12.8
12.1
11.5
10.9
9.86
14.8
14.0
13.4
12.7
11.6
16.8
16.0
15.3
14.6
13.4
18.7
18.0
17.2
16.5
15.2
14
16
18
20
24
0.27
0.24
0.21
0.19
0.16
0.78
0.69
0.62
0.56
0.48
1.47
1.31
1.17
1.06
0.90
2.33
2.08
1.88
1.71
1.45
3.40
3.05
2.76
2.52
2.14
4.61
4.16
3.77
3.45
2.94
5.95
5.38
4.91
4.51
3.87
7.41
6.74
6.18
5.69
4.91
8.97 10.6 12.3
8.20 9.75 11.4
7.55 9.00 10.5
6.97 8.34 9.80
6.04 7.26 8.57
28
32
36
0.14
0.12
0.11
0.41
0.36
0.32
0.77
0.68
0.61
1.26
1.11
0.99
1.86
1.64
1.47
2.56
2.27
2.03
3.38
3.00
2.70
4.30
3.82
3.44
5.30
4.73
4.26
2
3
4
5
6
1.17
0.92
0.75
0.64
0.55
3.24
2.84
2.51
2.24
2.03
5.30
4.90
4.52
4.17
3.86
7.32
6.93
6.53
6.15
5.78
9.33
8.96
8.56
8.15
7.76
11.3
11.0
10.6
10.2
9.77
13.3
13.0
12.6
12.2
11.8
15.3
15.0
14.6
14.2
13.8
17.3
17.0
16.6
16.2
15.8
19.3
19.0
18.6
18.3
17.9
21.3
21.0
20.6
20.3
19.9
23.2
23.0
22.6
22.3
21.9
7
8
9
10
12
0.49
0.44
0.40
0.36
0.31
1.85
1.70
1.57
1.46
1.28
3.59
3.35
3.13
2.94
2.60
5.45
5.13
4.85
4.58
4.11
7.39
7.03
6.70
6.38
5.81
9.38
9.00
8.63
8.28
7.64
11.4
11.0
10.6
10.2
9.54
13.4
13.0
12.6
12.2
11.5
15.4
15.0
14.6
14.2
13.5
17.5
17.1
16.7
16.3
15.6
19.5
19.1
18.7
18.3
17.5
21.5
21.1
20.7
20.3
19.5
14
16
18
20
24
0.27
0.24
0.21
0.19
0.16
1.13
1.01
0.92
0.84
0.72
2.32
2.09
1.90
1.73
1.47
3.71
3.36
3.07
2.83
2.43
5.31
4.88
4.50
4.18
3.64
7.06
6.55
6.09
5.69
5.00
8.89 10.8
8.31 10.2
7.78 9.56
7.31 9.02
6.48 8.08
12.7
12.0
11.4
10.8
9.76
14.7
14.0
13.3
12.7
11.5
16.7
15.9
15.2
14.6
13.3
18.7
17.9
17.2
16.5
15.2
28
32
36
0.14
0.12
0.11
0.62
0.55
0.49
1.28
1.13
1.01
2.13
1.90
1.71
3.22
2.88
2.61
4.45
3.99
3.62
5.80
5.24
4.77
8.86 10.5 12.2
8.09 9.65 11.3
7.43 8.90 10.4
14.0
13.0
12.0
7.28
6.62
6.05
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
6.41
5.73
5.17
7.59
6.80
6.15
14.1
13.1
12.1
11.3
9.95
8.85
7.94
7.20
8 - 50
BOLTS, WELDS, AND CONNECTED ELEMENTS
Table 8-19 (cont.).
Coefficients C for Eccentrically Loaded Bolt Groups
Angle = 60°°
C req =
Pu
φrn
or φR n = C × φ rn
ex
where
3
6
s
s
60°
s
e
s, in.
Pu
s
Pu
= factored force, kips
φ rn = design strength per bolt, kips
φ R n = design strength of bolt group, kips
e
= eccentricity of Pu with respect to centroid
of bolt group, in. (not tabulated, may be
determined by geometry.)
e x = horizontal component of e, in.
s
= bolt spacing, in.
C
= coefficient tabulated below.
3
Number of bolts in one vertical row, n
ex,
in.
1
2
3
4
5
6
7
8
9
10
11
12
2
3
4
5
6
1.51
1.24
1.04
0.89
0.77
3.17
2.76
2.43
2.16
1.95
4.97
4.47
4.04
3.70
3.40
6.85
6.30
5.81
5.39
5.01
8.77
8.19
7.65
7.17
6.73
10.7
10.1
9.53
9.01
8.52
12.7
12.0
11.5
10.9
10.4
14.6
14.0
13.4
12.8
12.3
16.6
16.0
15.3
14.7
14.2
18.6
17.9
17.3
16.7
16.1
20.6
19.9
19.3
18.6
18.0
22.5
21.9
21.2
20.6
20.0
7
8
9
10
12
0.68
0.61
0.56
0.51
0.43
1.77
1.62
1.49
1.38
1.20
3.13
2.90
2.70
2.52
2.21
4.67
4.37
4.09
3.84
3.40
6.33
5.96
5.62
5.31
4.76
8.07
7.65
7.26
6.89
6.25
9.88
9.42
8.98
8.58
7.85
11.7
11.2
10.8
10.3
9.53
13.6
13.1
12.6
12.1
11.3
15.5
15.0
14.5
14.0
13.0
17.4
16.9
16.3
15.8
14.9
19.4
18.8
18.2
17.7
16.7
14
16
18
20
24
0.38
0.34
0.30
0.27
0.23
1.06
0.95
0.85
0.78
0.66
1.96
1.76
1.60
1.46
1.24
3.05
2.75
2.51
2.30
1.97
4.30
3.92
3.59
3.32
2.87
5.71
5.24
4.84
4.48
3.90
7.23
6.68
6.19
5.76
5.04
8.83 10.5
8.20 9.79
7.64 9.16
7.14 8.60
6.29 7.64
12.2
11.5
10.8
10.1
9.06
14.0
13.2
12.4
11.7
10.6
15.8
14.9
14.1
13.4
12.1
28
32
36
0.20
0.18
0.16
0.57
0.50
0.45
1.07
0.95
0.85
1.72
1.52
1.37
2.52
2.24
2.02
3.44
3.07
2.77
4.47
4.01
3.63
5.61
5.06
4.59
2
3
4
5
6
1.51
1.24
1.04
0.89
0.77
3.39
3.08
2.80
2.57
2.37
5.36
5.04
4.73
4.45
4.20
7.33
7.01
6.69
6.39
6.11
9.31
8.98
8.66
8.35
8.05
7
8
9
10
12
0.68
0.61
0.56
0.51
0.43
2.19
2.04
1.91
1.80
1.60
3.98
3.77
3.59
3.42
3.11
5.85
5.61
5.38
5.17
4.78
7.76
7.49
7.24
7.00
6.54
9.70
9.41
9.13
8.87
8.37
14
16
18
20
24
0.38
0.34
0.30
0.27
0.23
1.44
1.31
1.20
1.10
0.95
2.85
2.63
2.43
2.26
1.97
4.43
4.12
3.84
3.58
3.15
6.13
5.74
5.40
5.08
4.53
7.91
7.48
7.08
6.71
6.06
9.74
9.27
8.84
8.43
7.69
28
32
36
0.20
0.18
0.16
0.84
0.74
0.67
1.73
1.54
1.39
2.80
2.52
2.28
4.08
3.71
3.39
5.52
5.05
4.65
7.06
6.51
6.02
11.3
11.0
10.6
10.3
10.0
6.85
6.20
5.65
8.17
7.41
6.77
9.55 11.0
8.70 10.1
7.98 9.26
13.3
12.9
12.6
12.3
12.0
15.2
14.9
14.6
14.3
13.9
17.2
16.9
16.6
16.2
15.9
19.2
18.9
18.6
18.2
17.9
21.2
20.9
20.5
20.2
19.9
23.2
22.8
22.5
22.2
21.8
11.7
11.6
11.1
10.8
10.2
13.6
13.3
13.0
12.7
12.1
15.6
15.3
15.0
14.7
14.1
17.6
17.2
16.9
16.6
16.0
19.5
19.2
18.9
18.6
18.0
21.5
21.2
20.9
20.5
19.9
11.6
11.1
10.7
10.2
9.39
13.5
13.0
12.5
12.0
11.2
15.4
14.9
14.4
13.9
12.9
17.4
16.8
16.3
15.7
14.8
19.3
18.7
18.2
17.6
16.6
8.68 10.4 12.1
8.05 9.66 11.3
7.49 9.03 10.7
13.9
13.1
12.3
15.7
14.8
14.0
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
ECCENTRICALLY LOADED BOLT GROUPS
8 - 51
Table 8-19 (cont.).
Coefficients C for Eccentrically Loaded Bolt Groups
Angle = 75°°
C req =
Pu
φ rn
or φ R n = C × φrn
ex
where
75°
3
6
s
Pu
s
s
e
s, in.
s
Pu
= factored force, kips
φ rn = design strength per bolt, kips
φ R n = design strength of bolt group, kips
e
= eccentricity of Pu with respect to centroid
of bolt group, in. (not tabulated, may be
determined by geometry.)
e x = horizontal component of e, in.
s
= bolt spacing, in.
C
= coefficient tabulated below.
3
Number of bolts in one vertical row, n
ex,
in.
1
2
3
4
5
6
7
8
9
10
11
12
2
3
4
5
6
1.84
1.71
1.57
1.44
1.31
3.63
3.41
3.19
2.98
2.79
5.44
5.17
4.90
4.65
4.41
7.29
6.97
6.67
6.39
6.12
9.17
8.82
8.50
8.19
7.90
11.1
10.7
10.4
10.0
9.71
13.0
12.6
12.2
11.9
11.6
14.9
14.5
14.1
13.8
13.4
16.9
16.4
16.0
15.7
15.3
18.8
18.4
18.0
17.6
17.2
20.8
20.3
19.9
19.5
19.1
22.7
22.3
21.8
21.4
21.0
7
8
9
10
12
1.20
1.10
1.01
0.93
0.81
2.61
2.45
2.31
2.18
1.95
4.19
3.99
3.81
3.63
3.33
5.88
5.65
5.43
5.23
4.86
7.62
7.37
7.14
6.91
6.49
9.42
9.14
8.89
8.65
8.19
11.3
11.0
10.7
10.4
9.94
13.1
12.8
12.5
12.2
11.7
15.0
14.7
14.3
14.1
13.5
16.9
16.5
16.2
15.9
15.3
18.8
18.4
18.1
17.8
17.2
20.7
20.3
20.0
19.6
19.0
14
16
18
20
24
0.71
0.63
0.57
0.52
0.44
1.77
1.61
1.48
1.36
1.18
3.06
2.83
2.63
2.45
2.15
4.53
4.23
3.96
3.72
3.30
6.11
5.75
5.42
5.12
4.60
7.76
7.36
6.98
6.63
6.02
9.47 11.2
9.03 10.8
8.61 10.3
8.23 9.88
7.53 9.12
13.0
12.5
12.0
11.6
10.8
14.8
14.3
13.8
13.3
12.4
16.6
16.1
15.6
15.1
14.2
18.4
17.9
17.4
16.9
15.9
28
32
36
0.38
0.34
0.30
1.04
0.92
0.83
1.91
1.71
1.55
2.95
2.67
2.43
4.16
3.78
3.47
5.49
5.04
4.65
6.93
6.41
5.94
11.7
10.9
10.3
13.3
12.6
11.9
15.0
14.2
13.5
2
3
4
5
6
1.84
1.71
1.57
1.44
1.31
3.66
3.49
3.32
3.16
3.02
5.55
5.36
5.18
5.01
4.84
7.48
7.27
7.08
6.89
6.72
9.42
9.20
9.00
8.81
8.62
11.4
11.2
10.9
10.7
10.5
13.3
13.1
12.9
12.7
12.5
15.3
15.1
14.8
14.6
14.4
17.6
17.0
16.8
16.6
16.3
19.6
19.0
18.7
18.5
18.3
21.5
21.0
20.7
20.5
20.2
23.5
22.9
22.7
22.4
22.2
7
8
9
10
12
1.20
1.10
1.01
0.93
0.81
2.88
2.75
2.63
2.52
2.32
4.69
4.54
4.40
4.27
4.03
6.55
6.39
6.24
6.09
5.82
8.44
8.27
8.11
7.95
7.66
10.4
10.2
10.0
9.83
9.52
12.3
12.1
11.9
11.7
11.4
14.2
14.0
13.8
13.6
13.3
16.1
15.9
15.7
15.6
15.2
18.1
17.9
17.7
17.5
17.1
20.0
19.8
19.6
19.4
19.0
22.0
21.8
21.5
21.3
20.9
14
16
18
20
24
0.71
0.63
0.57
0.52
0.44
2.15
2.00
1.87
1.75
1.55
3.82
3.62
3.44
3.28
2.98
5.57
5.35
5.14
4.94
4.57
7.38
7.13
6.90
6.67
6.24
9.22
8.95
8.69
8.45
7.98
11.1
10.8
10.5
10.3
9.75
13.0
12.7
12.4
12.1
11.6
14.9
14.5
14.2
13.9
13.4
16.7
16.4
16.1
15.8
15.2
18.7
18.3
18.0
17.7
17.1
20.6
20.2
19.9
19.5
18.9
28
32
36
0.38
0.34
0.30
1.40
1.27
1.16
2.74
2.52
2.33
4.24
3.95
3.68
5.85
5.49
5.16
7.54
7.13
6.75
9.28 11.1
8.83 10.6
8.41 10.1
12.9
12.4
11.9
14.7
14.1
13.7
16.5
16.0
15.4
18.3
17.8
17.3
8.45 10.0
7.86 9.37
7.32 8.78
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
8 - 52
BOLTS, WELDS, AND CONNECTED ELEMENTS
Table 8-20.
Coefficients C for Eccentrically Loaded Bolt Groups
Angle = 0°°
C req =
Pu
φrn
or φR n = C × φ rn
ex = e
where
s, in.
3
6
Pu
s
s
s
s
Pu
= factored force, kips
φ rn = design strength per bolt, kips
φ R n = design strength of bolt group, kips
e
= eccentricity of Pu with respect to centroid
of bolt group, in. (not tabulated, may be
determined by geometry.)
e x = horizontal component of e, in.
s
= bolt spacing, in.
C
= coefficient tabulated below.
5½
Number of bolts in one vertical row, n
ex,
in.
1
2
3
4
5
6
7
8
9
10
11
12
2
3
4
5
6
1.14
0.94
0.80
0.70
0.62
2.75
2.32
1.99
1.74
1.54
4.59
3.92
3.39
2.96
2.62
6.61
5.80
5.10
4.51
4.03
8.69
7.82
6.98
6.24
5.60
10.8
9.90
9.00
8.15
7.39
12.9
12.0
11.1
10.2
9.30
14.9
14.1
13.2
12.3
11.3
17.0
16.2
15.3
14.4
13.4
19.0
18.3
17.4
16.5
15.5
21.0
20.4
19.6
18.6
17.7
23.0
22.4
21.7
20.8
19.8
7
8
9
10
12
0.55
0.50
0.46
0.42
0.37
1.38
1.25
1.14
1.04
0.90
2.36
2.14
1.96
1.80
1.55
3.63
3.30
3.01
2.78
2.39
5.07
4.61
4.22
3.89
3.36
6.72
6.15
5.66
5.23
4.53
8.53 10.5
7.84 9.67
7.23 8.97
6.70 8.34
5.82 7.28
12.5
11.6
10.8
10.1
8.87
14.6
13.6
12.8
12.0
10.6
16.7
15.7
14.8
13.9
12.4
18.8
17.8
16.9
15.9
14.2
14
16
18
20
24
0.32
0.29
0.26
0.24
0.20
0.79
0.70
0.63
0.57
0.48
1.36
1.21
1.09
0.99
0.84
2.10
1.87
1.68
1.53
1.29
2.96
2.64
2.37
2.16
1.83
3.99
3.55
3.20
2.91
2.46
5.13
4.58
4.14
3.77
3.19
6.44
5.76
5.21
4.75
4.03
7.87
7.05
6.38
5.82
4.94
9.42 11.1 12.8
8.47 9.99 11.6
7.68 9.08 10.6
7.02 8.30 9.69
5.97 7.07 8.28
28
32
36
0.18
0.16
0.14
0.42
0.37
0.33
0.73
0.64
0.57
1.11
0.98
0.88
1.58
1.39
1.24
2.13
1.88
1.68
2.77
2.44
2.18
3.49
3.08
2.75
4.29
3.79
3.39
5.19
4.58
4.10
2
3
4
5
6
1.14
0.94
0.80
0.70
0.62
3.25
2.86
2.52
2.24
2.00
5.37
4.93
4.47
4.04
3.65
7.45
7.05
6.59
6.12
5.66
9.49
9.14
8.72
8.25
7.77
11.5
11.2
10.8
10.4
9.91
13.5
13.2
12.9
12.5
12.1
15.5
15.3
15.0
14.6
14.2
17.5
17.3
17.0
16.7
16.3
19.5
19.3
19.0
18.7
18.4
21.4
21.3
21.0
20.8
20.4
23.4
23.3
23.0
22.8
22.5
7
8
9
10
12
0.55
0.50
0.46
0.42
0.37
1.80
1.64
1.50
1.38
1.19
3.31
3.02
2.77
2.56
2.21
5.23
4.84
4.49
4.18
3.65
7.29
6.83
6.39
5.99
5.29
9.42
8.93
8.45
7.99
7.16
11.6
11.1
10.6
10.1
9.15
13.7
13.2
12.7
12.2
11.2
15.8
15.4
14.9
14.4
13.4
17.9
17.5
17.0
16.5
15.5
20.0
19.6
19.2
18.7
17.7
22.1
21.7
21.3
20.8
19.8
14
16
18
20
24
0.32
0.29
0.26
0.24
0.20
1.04
0.93
0.84
0.76
0.64
1.95
1.74
1.57
1.43
1.21
3.24
2.90
2.62
2.39
2.02
4.72
4.24
3.84
3.50
2.98
6.44
5.83
5.31
4.87
4.16
8.32 10.3 12.4
7.59 9.48 11.5
6.95 8.74 10.7
6.39 8.08 9.89
5.49 6.99 8.61
14.5
13.6
12.6
11.8
10.4
16.7
15.7
14.7
13.8
12.2
18.8
17.8
16.8
15.9
14.1
28
32
36
0.18
0.16
0.14
0.55
0.49
0.43
1.05
0.93
0.83
1.76
1.55
1.38
2.59
2.29
2.05
3.63
3.21
2.88
4.80
4.25
3.81
6.13
5.45
4.90
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
7.59
6.77
6.09
6.15
5.44
4.87
7.21
6.38
5.72
9.18 10.9 12.7
8.21 9.76 11.4
7.41 8.83 10.4
ECCENTRICALLY LOADED BOLT GROUPS
8 - 53
Table 8-20 (cont.).
Coefficients C for Eccentrically Loaded Bolt Groups
Angle = 15°°
C req =
Pu
φ rn
or φ R n = C × φrn
ex
where
Pu
s, in.
3
6
s
Pu
= factored force, kips
φ rn = design strength per bolt, kips
φ R n = design strength of bolt group, kips
e
= eccentricity of Pu with respect to centroid
of bolt group, in. (not tabulated, may be
determined by geometry.)
e x = horizontal component of e, in.
s
= bolt spacing, in.
C
= coefficient tabulated below.
s
15°
s
s
e
1
5½
Number of bolts in one vertical row, n
ex,
in.
1
2
3
4
5
6
7
8
9
10
11
12
2
3
4
5
6
1.18
0.97
0.83
0.72
0.64
2.78
2.34
2.02
1.77
1.57
4.61
3.97
3.45
3.03
2.70
6.59
5.80
5.11
4.54
4.06
8.64
7.78
6.97
6.26
5.65
10.7
9.83
8.94
8.12
7.39
12.8
11.9
11.0
10.1
9.27
14.8
14.0
13.1
12.1
11.2
16.8
16.1
15.2
14.2
13.3
18.9
18.1
17.3
16.3
15.4
20.9
20.2
19.3
18.4
17.5
22.9
22.2
21.4
20.5
19.6
7
8
9
10
12
0.57
0.52
0.48
0.44
0.38
1.41
1.28
1.17
1.07
0.93
2.43
2.20
2.01
1.85
1.60
3.66
3.34
3.06
2.82
2.44
5.13
4.68
4.30
3.98
3.44
6.74
6.18
5.70
5.27
4.58
8.52 10.4
7.86 9.65
7.27 8.97
6.76 8.36
5.90 7.34
12.4
11.6
10.8
10.1
8.91
14.4
13.5
12.7
11.9
10.6
16.5
15.6
14.7
13.8
12.4
18.6
17.6
16.7
15.8
14.2
14
16
18
20
24
0.33
0.30
0.27
0.25
0.21
0.81
0.72
0.65
0.59
0.50
1.40
1.25
1.13
1.02
0.87
2.15
1.91
1.72
1.57
1.33
3.03
2.70
2.44
2.22
1.88
4.05
3.62
3.27
2.98
2.53
5.22
4.68
4.23
3.86
3.27
6.51
5.84
5.28
4.83
4.11
7.94
7.14
6.48
5.93
5.05
9.47 11.1 12.8
8.54 10.1 11.7
7.77 9.16 10.7
7.11 8.40 9.78
6.07 7.19 8.39
28
32
36
0.18
0.16
0.14
0.43
0.38
0.34
0.75
0.66
0.59
1.15
1.01
0.90
1.63
1.43
1.28
2.19
1.93
1.73
2.84
2.50
2.24
3.57
3.15
2.82
4.39
3.88
3.48
5.29
4.68
4.19
2
3
4
5
6
1.18
0.97
0.83
0.72
0.64
3.24
2.85
2.51
2.23
2.00
5.34
4.90
4.45
4.05
3.68
7.40
6.99
6.53
6.07
5.62
9.43
9.07
8.63
8.16
7.69
11.5
11.1
10.7
10.3
9.80
7
8
9
10
12
0.57
0.52
0.48
0.44
0.38
1.81
1.65
1.52
1.40
1.21
3.36
3.08
2.83
2.62
2.27
5.20
4.82
4.48
4.18
3.66
7.22
6.78
6.36
5.98
5.31
9.31 11.4
8.83 10.9
8.37 10.5
7.93 9.97
7.13 9.08
14
16
18
20
24
0.33
0.30
0.27
0.25
0.21
1.07
0.95
0.86
0.78
0.66
2.00
1.79
1.62
1.47
1.25
3.25
2.92
2.65
2.42
2.06
4.76
4.29
3.90
3.58
3.05
6.44
5.85
5.34
4.91
4.21
8.28 10.2 12.3
7.58 9.43 11.4
6.97 8.72 10.6
6.43 8.09 9.87
5.55 7.03 8.64
28
32
36
0.18
0.16
0.14
0.57
0.50
0.45
1.08
0.95
0.85
1.79
1.58
1.42
2.66
2.35
2.11
3.68
3.26
2.93
4.87
4.33
3.90
13.5
13.2
12.8
12.4
11.9
6.28
5.56
4.99
7.33
6.50
5.84
15.4
15.2
14.8
14.5
14.0
17.4
17.2
16.87
16.5
16.1
19.4
19.2
18.9
18.6
18.2
21.4
21.2
20.9
20.6
20.2
23.4
23.1
23.0
22.6
22.3
13.5
13.1
12.6
12.1
11.1
15.7
15.2
14.7
14.2
13.2
17.7
17.3
16.8
16.3
15.3
19.8
19.4
18.9
18.4
17.4
21.9
21.4
21.0
20.6
19.6
14.3
13.4
12.5
11.7
10.4
16.4
15.5
14.6
13.7
12.2
18.6
17.6
16.6
15.7
14.1
6.19
5.52
4.97
7.65
6.84
6.18
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
9.22 10.9 12.6
8.27 9.81 11.4
7.49 8.91 10.4
8 - 54
BOLTS, WELDS, AND CONNECTED ELEMENTS
Table 8-20 (cont.).
Coefficients C for Eccentrically Loaded Bolt Groups
Angle = 30°°
C req =
Pu
φrn
or φR n = C × φ rn
ex
where
Pu
s, in.
3
6
s
Pu
= factored force, kips
φ rn = design strength per bolt, kips
φ R n = design strength of bolt group, kips
e
= eccentricity of Pu with respect to centroid
of bolt group, in. (not tabulated, may be
determined by geometry.)
e x = horizontal component of e, in.
s
= bolt spacing, in.
C
= coefficient tabulated below.
s
30°
s
s
e
5½
Number of bolts in one vertical row, n
ex,
in.
1
2
3
4
5
6
7
8
9
10
11
12
2
3
4
5
6
1.30
1.08
0.92
0.80
0.71
2.90
2.47
2.14
1.89
1.69
4.72
4.13
3.64
3.24
2.91
6.66
5.94
5.30
4.76
4.29
8.65
7.86
7.12
6.46
5.88
10.7
9.85
9.04
8.29
7.61
12.7
11.9
11.0
10.2
9.45
14.7
13.9
13.0
12.2
11.4
16.7
16.0
15.1
14.2
13.4
18.7
18.0
17.1
16.3
15.4
20.8
20.0
19.2
18.3
17.4
22.8
22.1
21.2
20.4
19.5
7
8
9
10
12
0.64
0.58
0.53
0.49
0.42
1.53
1.39
1.28
1.18
1.02
2.63
2.40
2.20
2.03
1.76
3.90
3.57
3.29
3.04
2.65
5.38
4.95
4.58
4.26
3.72
7.01
6.49
6.02
5.61
4.92
8.76 10.6
8.14 9.92
7.59 9.29
7.09 8.72
6.25 7.73
12.5
11.8
11.1
10.4
9.31
14.5
13.7
12.9
12.2
11.0
16.5
15.7
14.9
14.1
12.8
18.6
17.7
16.8
16.0
14.6
14
16
18
20
24
0.37
0.33
0.30
0.27
0.23
0.90
0.80
0.72
0.66
0.56
1.55
1.38
1.25
1.13
0.96
2.34
2.09
1.89
1.73
1.46
3.29
2.95
2.67
2.43
2.07
4.37
3.92
3.55
3.25
2.77
5.58
5.03
4.57
4.19
3.57
6.93
6.26
5.70
5.23
4.47
8.38
7.59
6.93
6.36
5.47
9.93 11.6
9.03 10.6
8.27 9.70
7.62 8.95
6.56 7.73
28
32
36
0.20
0.18
0.16
0.48
0.43
0.38
0.83
0.73
0.66
1.27
1.12
1.00
1.79
1.58
1.42
2.41
2.13
1.91
3.11
2.76
2.47
3.90
3.46
3.10
4.78
4.25
3.81
5.75
5.11
4.59
2
3
4
5
6
1.30
1.08
0.92
0.80
0.71
3.27
2.89
2.56
2.29
2.08
5.33
4.91
4.50
4.13
3.80
7.36
6.96
6.53
6.10
5.69
9.38
9.01
8.58
8.14
7.70
11.4
11.0
10.6
10.2
9.75
13.4
13.1
12.7
12.3
11.8
15.4
15.1
14.7
14.3
13.9
17.4
17.1
16.8
16.4
15.9
19.3
19.1
18.8
18.4
18.0
21.3
21.1
20.8
20.4
20.0
23.3
23.0
22.8
22.5
22.1
7
8
9
10
12
0.64
0.58
0.53
0.49
0.42
1.89
1.74
1.61
1.49
1.30
3.51
3.25
3.02
2.81
2.47
5.31
4.96
4.64
4.35
3.85
7.27
6.86
6.49
6.13
5.51
9.30
8.86
8.44
8.04
7.31
11.4
10.9
10.5
10.0
9.22
13.4
13.0
12.5
12.1
11.2
15.5
15.0
14.6
14.1
13.2
17.6
17.1
16.7
16.2
15.3
19.6
19.2
18.7
18.3
17.3
21.7
21.3
20.8
20.4
19.4
14
16
18
20
24
0.37
0.33
0.30
0.27
0.23
1.15
1.03
0.93
0.85
0.72
2.19
1.96
1.78
1.62
1.38
3.44
3.11
2.83
2.60
2.23
4.98
4.54
4.16
3.83
3.30
6.67
6.12
5.63
5.21
4.51
8.49 10.4
7.83 9.66
7.26 9.00
6.74 8.41
5.89 7.40
12.4
11.6
10.8
10.2
9.02
14.4
13.5
12.8
12.0
10.7
16.4
15.6
14.7
13.9
12.5
18.5
17.6
16.7
15.9
14.4
28
32
36
0.20
0.18
0.16
0.63
0.55
0.50
1.20
1.06
0.95
1.95
1.73
1.55
2.89
2.57
2.31
3.96
3.53
3.18
5.21
4.67
4.22
6.59
5.92
5.36
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
8.07
7.28
6.61
6.78
6.04
5.44
13.3
12.2
11.2
10.4
8.99
7.91
7.06
6.36
9.66 11.3 13.1
8.75 10.3 12.0
7.98 9.43 11.0
ECCENTRICALLY LOADED BOLT GROUPS
8 - 55
Table 8-20 (cont.).
Coefficients C for Eccentrically Loaded Bolt Groups
Angle = 45°°
C req =
Pu
φ rn
or φ R n = C × φrn
ex
where
Pu
3
6
s
s
45°
s
e
s, in.
s
Pu
= factored force, kips
φ rn = design strength per bolt, kips
φ R n = design strength of bolt group, kips
e
= eccentricity of Pu with respect to centroid
of bolt group, in. (not tabulated, may be
determined by geometry.)
e x = horizontal component of e, in.
s
= bolt spacing, in.
C
= coefficient tabulated below.
5½
Number of bolts in one vertical row, n
ex,
in.
1
2
3
4
5
6
7
8
9
10
11
12
2
3
4
5
6
1.53
1.30
1.11
0.98
0.87
3.18
2.76
2.43
2.17
1.95
4.96
4.42
3.97
3.60
3.28
6.84
6.22
5.67
5.19
4.77
8.77
8.09
7.46
6.89
6.37
10.7
10.0
9.32
8.68
8.09
12.7
12.0
11.2
10.6
9.90
14.7
14.0
13.2
12.5
11.8
16.7
15.9
15.2
14.4
13.7
18.7
17.9
17.2
16.4
15.6
20.7
19.9
19.2
18.4
17.6
22.6
21.9
21.2
20.4
19.6
7
8
9
10
12
0.78
0.71
0.65
0.60
0.52
1.78
1.63
1.50
1.39
1.22
3.01
2.77
2.57
2.39
2.08
4.40
4.07
3.78
3.52
3.09
5.91
5.50
5.13
4.81
4.26
7.56
7.07
6.64
6.25
5.58
9.31 11.1
8.76 10.5
8.26 9.97
7.81 9.45
7.01 8.54
13.0
12.4
11.8
11.2
10.2
14.9
14.2
13.6
13.0
11.9
16.9
16.2
15.5
14.8
13.6
18.8
18.1
17.4
16.7
15.4
14
16
18
20
24
0.45
0.41
0.37
0.33
0.28
1.08
0.96
0.87
0.79
0.68
1.85
1.65
1.50
1.37
1.16
2.75
2.48
2.25
2.06
1.76
3.82
3.45
3.14
2.88
2.47
5.02
4.55
4.16
3.82
3.28
6.34
5.77
5.29
4.87
4.21
7.76
7.09
6.53
6.04
5.23
9.28 10.9
8.53 10.1
7.87 9.30
7.30 8.65
6.35 7.55
12.6
11.6
10.8
10.1
8.85
14.3
13.3
12.4
11.6
10.2
28
32
36
0.25
0.22
0.20
0.59
0.52
0.46
1.01
0.89
0.80
1.53
1.35
1.21
2.15
1.91
1.71
2.87
2.55
2.29
3.69
3.29
2.96
4.61
4.11
3.70
5.61
5.01
4.53
2
3
4
5
6
1.53
1.30
1.11
0.98
0.87
3.39
3.04
2.74
2.49
2.28
5.36
4.99
4.64
4.31
4.02
7.35
6.98
6.60
6.24
5.89
9.35
8.98
8.60
8.21
7.84
11.3
11.0
10.6
10.2
9.82
13.3
13.0
12.6
12.2
11.8
15.3
15.0
14.6
14.2
13.8
17.3
17.0
16.6
16.3
15.9
19.3
19.0
18.6
18.3
17.9
21.3
21.0
20.6
20.3
19.9
23.2
22.9
22.6
22.3
21.9
7
8
9
10
12
0.78
0.71
0.65
0.60
0.52
2.10
1.94
1.81
1.69
1.50
3.76
3.53
3.32
3.13
2.80
5.57
5.28
5.00
4.74
4.29
7.48
7.13
6.81
6.50
5.94
9.44
9.07
8.71
8.37
7.74
11.4
11.0
10.7
10.3
9.61
13.4
13.0
12.7
12.3
11.5
15.5
15.1
14.7
14.3
13.5
17.5
17.1
16.7
16.3
15.5
19.5
19.1
18.7
18.3
17.5
21.5
21.1
20.7
20.3
19.5
14
16
18
20
24
0.45
0.41
0.37
0.33
0.28
1.34
1.21
1.10
1.01
0.86
2.52
2.29
2.09
1.92
1.64
3.89
3.55
3.26
3.01
2.61
5.45
5.02
4.65
4.33
3.79
7.17
6.67
6.22
5.82
5.13
8.98 10.9
8.41 10.2
7.89 9.65
7.42 9.11
6.60 8.17
12.8
12.1
11.5
10.9
9.84
14.7
14.0
13.4
12.7
11.6
16.7
16.0
15.3
14.6
13.4
18.7
17.9
17.2
16.5
15.2
28
32
36
0.25
0.22
0.20
0.75
0.67
0.60
1.44
1.27
1.14
2.30
2.05
1.85
3.36
3.02
2.73
4.58
4.12
3.74
5.92
5.35
4.88
8.95 10.6 12.3
8.18 9.73 11.4
7.52 8.98 10.5
14.1
13.0
12.1
7.38
6.72
6.15
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
6.69
6.00
5.43
7.87
7.07
6.40
9.11
8.20
7.44
8 - 56
BOLTS, WELDS, AND CONNECTED ELEMENTS
Table 8-20 (cont.).
Coefficients C for Eccentrically Loaded Bolt Groups
Angle = 60°°
C req =
Pu
φrn
or φR n = C × φ rn
ex
where
3
6
s
s
60°
s
e
s, in.
Pu
s
Pu
= factored force, kips
φ rn = design strength per bolt, kips
φ R n = design strength of bolt group, kips
e
= eccentricity of Pu with respect to centroid
of bolt group, in. (not tabulated, may be
determined by geometry.)
e x = horizontal component of e, in.
s
= bolt spacing, in.
C
= coefficient tabulated below.
5½
Number of bolts in one vertical row, n
ex,
in.
1
2
3
4
5
6
7
8
9
10
11
12
2
3
4
5
6
1.78
1.62
1.45
1.31
1.18
3.55
3.26
2.97
2.71
2.48
5.34
4.95
4.57
4.23
3.93
7.17
6.71
6.27
5.86
5.50
9.04
8.53
8.04
7.58
7.16
10.9
10.4
9.86
9.36
8.90
12.9
12.3
11.7
11.2
10.7
14.8
14.2
13.6
13.1
12.5
16.7
16.1
15.5
15.0
14.4
18.7
18.1
17.5
16.9
16.3
20.6
20.0
19.4
18.8
18.2
22.6
22.0
21.4
20.7
20.1
7
8
9
10
12
1.07
0.98
0.90
0.83
0.72
2.28
2.11
1.97
1.84
1.62
3.66
3.43
3.22
3.03
2.70
5.18
4.88
4.61
4.37
3.93
6.79
6.45
6.12
5.82
5.28
8.48 10.2
8.09 9.80
7.72 9.39
7.37 9.00
6.73 8.28
12.0
11.6
11.1
10.7
9.91
13.9
13.4
12.9
12.5
11.6
15.7
15.2
14.7
14.2
13.4
17.6
17.1
16.6
16.1
15.1
19.5
19.0
18.4
17.9
16.9
14
16
18
20
24
0.64
0.57
0.52
0.47
0.40
1.45
1.31
1.19
1.09
0.93
2.43
2.21
2.02
1.85
1.59
3.56
3.24
2.98
2.75
2.37
4.81
4.42
4.07
3.77
3.28
6.19
5.71
5.29
4.93
4.32
7.66
7.11
6.63
6.19
5.46
9.22 10.9
8.60 10.2
8.05 9.55
7.55 8.98
6.69 8.01
12.5
11.8
11.1
10.5
9.41
14.3
13.5
12.7
12.1
10.9
16.0
15.2
14.4
13.7
12.4
28
32
36
0.35
0.31
0.28
0.82
0.72
0.65
1.39
1.24
1.11
2.08
1.86
1.67
2.90
2.59
2.34
3.83
3.43
3.11
4.86
4.37
3.97
5.99
5.41
4.93
2
3
4
5
6
1.78
1.62
1.45
1.31
1.18
3.59
3.35
3.11
2.89
2.70
5.48
5.20
4.93
4.66
4.42
7.41
7.12
6.82
6.53
6.26
9.36
9.06
8.75
8.45
8.16
7
8
9
10
12
1.07
0.98
0.90
0.83
0.72
2.52
2.36
2.23
2.10
1.89
4.19
3.99
3.81
3.64
3.34
6.01
5.77
5.55
5.35
4.97
7.88
7.62
7.37
7.13
6.70
9.79
9.51
9.24
8.98
8.49
14
16
18
20
24
0.64
0.57
0.52
0.47
0.40
1.71
1.57
1.44
1.33
1.16
3.08
2.85
2.65
2.47
2.17
4.63
4.32
4.04
3.79
3.36
6.29
5.92
5.58
5.26
4.71
8.04
7.62
7.22
6.86
6.21
9.85
9.39
8.95
8.55
7.82
28
32
36
0.35
0.31
0.28
1.02
0.91
0.82
1.92
1.72
1.56
3.00
2.71
2.46
4.26
3.88
3.55
5.67
5.20
4.80
7.19
6.64
6.16
11.3
11.0
10.7
10.4
10.1
7.21
6.54
5.98
8.51
7.75
7.10
9.88 11.3
9.02 10.4
8.29 9.55
13.3
13.0
12.7
12.3
12.0
15.3
15.0
14.6
14.3
14.0
17.2
16.9
16.6
16.3
15.9
19.2
18.9
18.6
18.2
17.9
21.2
20.9
20.6
20.2
19.9
23.2
22.9
22.5
22.2
21.9
11.7
11.4
11.1
10.9
10.3
13.7
13.4
13.1
12.8
12.2
15.6
15.3
15.0
14.7
14.1
17.6
17.3
17.0
16.7
16.1
19.6
19.2
18.9
18.6
18.0
21.5
21.2
20.9
20.6
19.9
11.7
11.2
10.7
10.3
9.50
13.6
13.1
12.6
12.1
11.2
15.5
15.0
14.4
13.9
13.0
17.4
16.9
16.3
15.8
14.8
19.3
18.8
18.2
17.7
16.7
8.80 10.5 12.2
8.17 9.77 11.4
7.61 9.14 10.7
14.0
13.1
12.4
15.8
14.9
14.1
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
ECCENTRICALLY LOADED BOLT GROUPS
8 - 57
Table 8-20 (cont.).
Coefficients C for Eccentrically Loaded Bolt Groups
Angle = 75°°
C req =
Pu
φ rn
or φ R n = C × φrn
ex
where
3
6
s
s
s
e
s, in.
75° P
u
s
Pu
= factored force, kips
φ rn = design strength per bolt, kips
φ R n = design strength of bolt group, kips
e
= eccentricity of Pu with respect to centroid
of bolt group, in. (not tabulated, may be
determined by geometry.)
e x = horizontal component of e, in.
s
= bolt spacing, in.
C
= coefficient tabulated below.
5½
Number of bolts in one vertical row, n
ex,
in.
1
2
3
4
5
6
7
8
9
10
11
12
2
3
4
5
6
1.92
1.87
1.82
1.75
1.68
3.82
3.72
3.60
3.47
3.33
5.70
5.54
5.37
5.18
5.00
7.57
7.36
7.14
6.92
6.69
9.45
9.19
8.94
8.68
8.42
11.3
11.1
10.8
10.5
10.2
13.2
12.9
12.6
12.3
12.0
15.2
14.8
14.5
14.1
13.8
17.1
16.7
16.3
16.0
15.7
19.0
18.6
18.2
17.9
17.5
20.9
20.5
20.1
19.8
19.4
22.9
22.5
22.1
21.7
21.3
7
8
9
10
12
1.60
1.52
1.45
1.38
1.25
3.19
3.06
2.93
2.80
2.57
4.81
4.63
4.46
4.29
3.98
6.47
6.26
6.05
5.85
5.48
8.17
7.93
7.70
7.48
7.07
9.92
9.66
9.41
9.16
8.71
11.7
11.4
11.2
10.9
10.4
13.5
13.2
12.9
12.6
12.1
15.3
15.0
14.7
14.4
13.9
17.2
16.9
16.5
16.2
15.7
19.1
18.7
18.4
18.1
17.5
20.9
20.6
20.3
19.9
19.3
14
16
18
20
24
1.13
1.03
0.95
0.87
0.75
2.36
2.18
2.02
1.88
1.65
3.70
3.45
3.23
3.03
2.69
5.15
4.85
4.57
4.32
3.87
6.69
6.34
6.01
5.71
5.17
8.29
7.90
7.54
7.19
6.57
9.96
9.53
9.13
8.75
8.05
11.7
11.2
10.8
10.4
9.60
13.4
12.9
12.5
12.0
11.2
15.2
14.7
14.2
13.7
12.9
16.9
16.4
15.9
15.4
14.5
18.7
18.2
17.7
17.2
16.2
28
32
36
0.66
0.59
0.53
1.46
1.31
1.19
2.42
2.18
1.99
3.50
3.19
2.92
4.71
4.32
3.98
6.03
5.56
5.15
7.44
6.90
6.42
12.1
11.4
10.7
13.7
12.9
12.2
15.4
14.6
13.8
2
3
4
5
6
1.92
1.87
1.82
1.75
1.68
3.80
3.70
3.59
3.48
3.36
5.69
5.55
5.40
5.26
5.11
7.59
7.42
7.25
7.09
6.93
9.51
9.32
9.14
8.96
8.78
11.5
11.2
11.1
10.9
10.7
13.4
13.2
13.0
12.8
12.6
15.4
15.1
14.9
14.7
14.5
17.6
17.1
16.9
16.6
16.4
19.6
19.0
18.8
18.6
18.4
21.5
21.0
20.8
20.5
20.3
23.5
23.0
22.7
22.5
22.2
7
8
9
10
12
1.60
1.52
1.45
1.38
1.25
3.24
3.13
3.02
2.91
2.72
4.97
4.84
4.71
4.58
4.34
6.77
6.62
6.47
6.33
6.07
8.62
8.45
8.29
8.14
7.85
10.5
10.3
10.2
9.98
9.67
12.4
12.2
12.0
11.9
11.5
14.3
14.1
13.9
13.7
13.4
16.2
16.0
15.8
15.6
15.3
18.1
17.9
17.7
17.6
17.2
20.1
19.9
19.7
19.5
19.1
22.0
21.8
21.6
21.4
21.0
14
16
18
20
24
1.13
1.03
0.95
0.87
0.75
2.54
2.38
2.24
2.11
1.88
4.13
3.92
3.74
3.57
3.27
5.82
5.59
5.38
5.17
4.80
7.57
7.32
7.09
6.87
6.44
9.38
9.10
8.85
8.61
8.15
11.2
10.9
10.7
10.4
9.90
13.1
12.8
12.5
12.2
11.7
15.0
14.6
14.3
14.0
13.5
16.8
16.5
16.2
15.9
15.3
18.7
18.4
18.1
17.7
17.1
20.6
20.3
19.9
19.6
19.0
28
32
36
0.66
0.59
0.53
1.70
1.55
1.42
3.00
2.77
2.57
4.47
4.17
3.90
6.06
5.70
5.37
7.72
7.31
6.93
9.43 11.2
8.99 10.7
8.57 10.3
13.0
12.5
12.0
14.8
14.3
13.8
16.6
16.1
15.5
18.4
17.9
17.3
8.93 10.5
8.32 9.81
7.78 9.21
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
8 - 58
BOLTS, WELDS, AND CONNECTED ELEMENTS
Table 8-21.
Coefficients C for Eccentrically Loaded Bolt Groups
Angle = 0°°
C req =
Pu
φrn
or φR n = C × φ rn
ex = e
where
s, in.
3
6
Pu
s
s
s
s
Pu
= factored force, kips
φ rn = design strength per bolt, kips
φ R n = design strength of bolt group, kips
e
= eccentricity of Pu with respect to centroid
of bolt group, in. (not tabulated, may be
determined by geometry.)
e x = horizontal component of e, in.
s
= bolt spacing, in.
C
= coefficient tabulated below.
8
Number of bolts in one vertical row, n
ex,
in.
1
2
3
4
5
6
7
8
9
10
11
12
2
3
4
5
6
1.31
1.12
0.98
0.87
0.79
2.91
2.54
2.24
1.99
1.80
4.71
4.14
3.66
3.27
2.95
6.66
5.95
5.33
4.80
4.35
8.69
7.90
7.15
6.48
5.90
10.8
9.93
9.10
8.33
7.63
12.8
12.0
11.1
10.3
9.49
14.9
14.1
13.2
12.3
11.5
16.9
16.2
15.3
14.4
13.5
18.9
18.2
17.4
16.5
15.6
21.0
20.3
19.5
18.6
17.7
23.0
22.4
21.6
20.7
19.8
7
8
9
10
12
0.71
0.65
0.60
0.56
0.49
1.63
1.49
1.38
1.28
1.11
2.68
2.46
2.27
2.11
1.84
3.97
3.65
3.37
3.13
2.73
5.40
4.97
4.59
4.27
3.73
7.02
6.48
6.01
5.59
4.90
8.77 10.7
8.13 9.91
7.55 9.24
7.04 8.64
6.19 7.63
12.6
11.8
11.1
10.4
9.18
14.6
13.8
13.0
12.2
10.9
16.7
15.8
14.9
14.1
12.6
18.8
17.9
17.0
16.1
14.5
14
16
18
20
24
0.44
0.39
0.36
0.33
0.28
0.99
0.89
0.80
0.73
0.63
1.64
1.47
1.33
1.22
1.04
2.42
2.17
1.97
1.80
1.53
3.31
2.98
2.70
2.47
2.10
4.36
3.91
3.55
3.25
2.77
5.50
4.95
4.50
4.12
3.51
6.80
6.13
5.57
5.10
4.35
8.20
7.40
6.73
6.17
5.28
9.73 11.4 13.1
8.80 10.3 11.9
8.02 9.39 10.9
7.35 8.62 9.99
6.30 7.39 8.59
28
32
36
0.25
0.22
0.20
0.55
0.48
0.43
0.91
0.80
0.72
1.33
1.18
1.06
1.83
1.62
1.45
2.41
2.13
1.91
3.06
2.71
2.43
3.79
3.36
3.01
4.60
4.08
3.66
5.50
4.87
4.37
2
3
4
5
6
1.31
1.12
0.98
0.87
0.79
3.28
2.93
2.63
2.37
2.15
5.35
4.94
4.52
4.13
3.78
7.42
7.03
6.59
6.15
5.72
9.47
9.12
8.70
8.25
7.78
11.5
11.2
10.8
10.4
9.90
13.5
13.2
12.9
12.5
12.0
15.5
15.3
14.9
14.6
14.1
17.5
17.3
17.0
16.6
16.2
19.5
19.3
19.0
18.69
18.3
21.4
21.3
21.0
20.7
20.4
23.4
23.3
23.0
22.8
22.4
7
8
9
10
12
0.71
0.65
0.60
0.56
0.49
1.97
1.81
1.67
1.55
1.35
3.47
3.19
2.95
2.75
2.40
5.32
4.95
4.62
4.33
3.82
7.33
6.89
6.48
6.10
5.43
9.43
8.95
8.49
8.05
7.25
11.6
11.1
10.6
10.1
9.21
13.7
13.2
12.7
12.2
11.3
15.8
15.4
14.9
14.4
13.4
17.9
17.5
17.0
16.5
15.5
20.0
19.6
19.1
18.7
17.7
22.1
21.7
21.3
20.8
19.8
14
16
18
20
24
0.44
0.39
0.36
0.33
0.28
1.20
1.08
0.97
0.89
0.76
2.14
1.92
1.75
1.60
1.37
3.41
3.07
2.79
2.56
2.18
4.86
4.40
4.00
3.67
3.14
6.56
5.96
5.46
5.02
4.32
8.40 10.4 12.4
7.69 9.56 11.5
7.06 8.83 10.7
6.52 8.18 9.97
5.62 7.11 8.71
14.5
13.6
12.7
11.9
10.4
16.7
15.7
14.7
13.9
12.3
18.8
17.8
16.8
15.9
14.2
28
32
36
0.25
0.22
0.20
0.66
0.58
0.52
1.19
1.05
0.95
1.90
1.68
1.51
2.75
2.44
2.19
3.78
3.35
3.01
4.93
4.38
3.94
6.26
5.58
5.02
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
7.70
6.88
6.21
6.46
5.73
5.15
7.51
6.67
5.99
9.27 11.0 12.7
8.31 9.85 11.5
7.52 8.93 10.4
ECCENTRICALLY LOADED BOLT GROUPS
8 - 59
Table 8-21 (cont.).
Coefficients C for Eccentrically Loaded Bolt Groups
Angle = 15°°
C req =
Pu
φ rn
or φ R n = C × φrn
ex
where
Pu
s, in.
3
6
15°
s
s
Pu
= factored force, kips
φ rn = design strength per bolt, kips
φ R n = design strength of bolt group, kips
e
= eccentricity of Pu with respect to centroid
of bolt group, in. (not tabulated, may be
determined by geometry.)
e x = horizontal component of e, in.
s
= bolt spacing, in.
C
= coefficient tabulated below.
s
s
e
8
Number of bolts in one vertical row, n
ex,
in.
1
2
3
4
5
6
7
8
9
10
11
12
2
3
4
5
6
1.35
1.16
1.02
0.90
0.81
2.96
2.58
2.28
2.03
1.84
4.75
4.20
3.73
3.35
3.03
6.67
5.98
5.37
4.85
4.40
8.67
7.90
7.17
6.53
5.96
10.7
9.89
9.08
8.34
7.66
12.7
11.9
11.1
10.3
9.48
14.8
14.0
13.1
12.2
11.4
16.8
16.0
15.2
14.3
13.4
18.8
18.1
17.3
16.3
15.4
20.9
20.2
19.3
18.4
17.5
22.9
22.2
21.4
20.5
19.6
7
8
9
10
12
0.74
0.68
0.63
0.58
0.51
1.67
1.53
1.42
1.31
1.15
2.76
2.53
2.34
2.17
1.90
4.02
3.70
3.43
3.19
2.79
5.48
5.05
4.68
4.36
3.82
7.06
6.53
6.07
5.66
4.97
8.79 10.6
8.17 9.91
7.61 9.27
7.12 8.69
6.28 7.69
12.6
11.8
11.0
10.4
9.23
14.5
13.7
12.9
12.2
10.9
16.6
15.7
14.8
14.0
12.6
18.6
17.7
16.8
16.0
14.4
14
16
18
20
24
0.45
0.41
0.37
0.34
0.29
1.02
0.91
0.83
0.76
0.65
1.69
1.51
1.37
1.26
1.07
2.48
2.23
2.02
1.85
1.58
3.40
3.05
2.77
2.54
2.16
4.43
3.99
3.63
3.32
2.84
5.61
5.05
4.60
4.21
3.60
6.88
6.21
5.66
5.19
4.45
8.29
7.50
6.84
6.28
5.39
9.79 11.4
8.88 10.4
8.11 9.48
7.45 8.73
6.40 7.52
28
32
36
0.25
0.23
0.20
0.56
0.50
0.45
0.93
0.83
0.74
1.37
1.22
1.09
1.89
1.67
1.50
2.47
2.19
1.96
3.14
2.78
2.49
3.88
3.44
3.09
4.71
4.18
3.75
5.61
4.98
4.47
2
3
4
5
6
1.35
1.16
1.02
0.90
0.81
3.29
2.94
2.64
2.38
2.17
5.33
4.93
4.52
4.15
3.82
7.39
6.99
6.55
6.12
5.70
9.42
9.05
8.63
8.18
7.72
11.4
11.1
10.7
10.3
9.80
13.4
13.1
12.8
12.4
11.9
15.4
15.2
14.8
14.4
14.0
17.4
17.2
16.9
16.5
16.1
19.4
19.2
18.9
18.5
18.2
21.4
21.2
20.9
20.6
20.2
23.4
23.2
22.9
22.6
22.3
7
8
9
10
12
0.74
0.68
0.63
0.58
0.51
1.99
1.83
1.69
1.58
1.38
3.52
3.25
3.02
2.81
2.47
5.31
4.95
4.63
4.34
3.84
7.28
6.86
6.46
6.10
5.45
9.33
8.87
8.43
8.00
7.23
11.4
11.0
10.5
10.0
9.15
13.5
13.1
12.6
12.1
11.2
15.6
15.2
14.7
14.2
13.2
17.7
17.3
16.8
16.3
15.3
19.8
19.4
18.9
18.4
17.4
21.9
21.5
21.0
20.5
19.6
14
16
18
20
24
0.45
0.41
0.37
0.34
0.29
1.23
1.10
1.00
0.92
0.78
2.20
1.98
1.80
1.65
1.41
3.44
3.11
2.83
2.60
2.23
4.91
4.46
4.08
3.75
3.22
6.56
5.99
5.49
5.06
4.36
8.38 10.3 12.3
7.69 9.52 11.5
7.09 8.82 10.7
6.56 8.20 9.96
5.70 7.15 8.74
14.4
13.5
12.6
11.8
10.4
16.5
15.5
14.6
13.8
12.2
18.6
17.6
16.6
15.7
14.1
28
32
36
0.25
0.23
0.20
0.68
0.60
0.54
1.23
1.09
0.97
1.95
1.73
1.55
2.82
2.50
2.25
3.83
3.41
3.07
5.02
4.47
4.03
6.32
5.64
5.09
7.76
6.96
6.30
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
6.59
5.86
5.27
13.1
11.9
11.0
10.1
8.71
7.64
6.80
6.12
9.31 11.0 12.7
8.38 9.90 11.5
7.60 9.01 10.5
8 - 60
BOLTS, WELDS, AND CONNECTED ELEMENTS
Table 8-21 (cont.).
Coefficients C for Eccentrically Loaded Bolt Groups
Angle = 30°°
C req =
Pu
φrn
or φR n = C × φ rn
ex
where
s, in.
3
6
s
Pu
= factored force, kips
φ rn = design strength per bolt, kips
φ R n = design strength of bolt group, kips
e
= eccentricity of Pu with respect to centroid
of bolt group, in. (not tabulated, may be
determined by geometry.)
e x = horizontal component of e, in.
s
= bolt spacing, in.
C
= coefficient tabulated below.
Pu
s
30°
s
s
e
8
Number of bolts in one vertical row, n
ex,
in.
1
2
3
4
5
6
7
8
9
10
11
12
2
3
4
5
6
1.49
1.29
1.13
1.00
0.90
3.12
2.74
2.43
2.18
1.98
4.91
4.39
3.95
3.58
3.26
6.80
6.16
5.60
5.10
4.67
8.75
8.04
7.37
6.77
6.23
10.7
9.98
9.24
8.55
7.93
12.7
12.0
11.2
10.4
9.72
14.7
14.0
13.2
12.4
11.6
16.7
16.0
15.2
14.3
13.5
18.7
18.0
17.2
16.3
15.5
20.8
20.0
19.2
18.4
17.5
22.7
22.1
21.3
20.4
19.5
7
8
9
10
12
0.82
0.75
0.70
0.65
0.57
1.81
1.67
1.55
1.44
1.26
2.99
2.76
2.56
2.38
2.09
4.30
3.97
3.69
3.44
3.03
5.76
5.35
4.98
4.66
4.13
7.37
6.87
6.42
6.02
5.34
9.08 10.9
8.49 10.2
7.96 9.62
7.49 9.07
6.66 8.12
12.8
12.0
11.4
10.8
9.67
14.7
13.9
13.2
12.5
11.3
16.7
15.9
15.1
14.4
13.0
18.7
17.8
17.0
16.2
14.8
14
16
18
20
24
0.50
0.45
0.41
0.38
0.32
1.12
1.01
0.92
0.84
0.72
1.86
1.67
1.52
1.39
1.19
2.71
2.44
2.22
2.03
1.74
3.69
3.33
3.03
2.78
2.38
4.78
4.33
3.95
3.62
3.11
5.99
5.44
4.97
4.57
3.93
7.33
6.66
6.10
5.62
4.84
8.75 10.3 11.9
7.98 9.39 10.9
7.32 8.64 10.1
6.75 7.98 9.30
5.83 6.92 8.08
28
32
36
0.28
0.25
0.23
0.63
0.56
0.50
1.04
0.92
0.83
1.52
1.35
1.21
2.08
1.84
1.66
2.72
2.41
2.17
3.44
3.06
2.75
4.24
3.77
3.40
5.13
4.57
4.11
2
3
4
5
6
1.49
1.29
1.13
1.00
0.90
3.36
3.02
2.73
2.48
2.27
5.36
4.97
4.60
4.26
3.96
7.37
6.99
6.58
6.18
5.80
9.38
9.01
8.61
8.18
7.76
11.4
11.0
10.7
10.2
9.79
13.4
13.1
12.7
12.3
11.8
15.4
15.1
14.7
14.3
13.9
17.4
17.1
16.7
16.4
15.9
19.3
19.1
18.8
18.4
18.0
21.3
21.1
20.8
20.4
20.0
23.3
23.1
22.8
22.4
22.1
7
8
9
10
12
0.82
0.75
0.70
0.65
0.57
2.09
1.93
1.80
1.68
1.49
3.68
3.43
3.21
3.01
2.67
5.44
5.11
4.81
4.53
4.05
7.36
6.97
6.61
6.27
5.67
9.35
8.93
8.53
8.14
7.43
11.4
11.0
10.5
10.1
9.31
13.5
13.0
12.6
12.1
11.3
15.5
15.1
14.6
14.2
13.3
17.6
17.1
16.7
16.2
15.3
19.6
19.2
18.7
18.3
17.4
21.7
21.2
20.8
20.4
19.4
14
16
18
20
24
0.50
0.45
0.41
0.38
0.32
1.33
1.20
1.09
1.00
0.86
2.39
2.16
1.97
1.81
1.55
3.65
3.31
3.03
2.80
2.41
5.15
4.71
4.34
4.01
3.48
6.81
6.27
5.79
5.37
4.68
8.60 10.5
7.96 9.76
7.39 9.12
6.89 8.53
6.04 7.53
12.4
11.7
10.9
10.3
9.14
14.4
13.6
12.8
12.1
10.8
16.5
15.6
14.8
14.0
12.6
18.5
17.6
16.8
15.9
14.5
28
32
36
0.28
0.25
0.23
0.75
0.67
0.60
1.35
1.20
1.08
2.12
1.89
1.70
3.06
2.73
2.46
4.13
3.69
3.34
5.36
4.81
4.36
6.72
6.05
5.50
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
8.19
7.40
6.74
6.09
5.43
4.89
7.12
6.36
5.74
13.6
12.5
11.5
10.7
9.32
8.24
7.37
6.66
9.76 11.4 13.2
8.86 10.4 12.0
8.09 9.53 11.1
ECCENTRICALLY LOADED BOLT GROUPS
8 - 61
Table 8-21 (cont.).
Coefficients C for Eccentrically Loaded Bolt Groups
Angle = 45°°
C req =
Pu
φ rn
or φ R n = C × φrn
ex
where
Pu
3
6
s
s
45°
s
e
s, in.
s
Pu
= factored force, kips
φ rn = design strength per bolt, kips
φ R n = design strength of bolt group, kips
e
= eccentricity of Pu with respect to centroid
of bolt group, in. (not tabulated, may be
determined by geometry.)
e x = horizontal component of e, in.
s
= bolt spacing, in.
C
= coefficient tabulated below.
8
Number of bolts in one vertical row, n
ex,
in.
1
2
3
4
5
6
7
8
9
10
11
12
2
3
4
5
6
1.70
1.51
1.35
1.21
1.10
3.43
3.09
2.78
2.52
2.30
5.22
4.76
4.34
3.97
3.67
7.06
6.52
6.01
5.57
5.17
8.95
8.35
7.78
7.25
6.78
10.9
10.2
9.60
9.01
8.47
12.8
12.2
11.5
10.8
10.2
14.8
14.1
13.4
12.7
12.1
16.8
16.1
15.3
14.6
13.9
18.7
18.0
17.3
16.6
15.9
20.7
20.0
19.3
18.5
17.8
22.7
22.0
21.3
20.5
19.8
7
8
9
10
12
1.00
0.92
0.85
0.79
0.69
2.12
1.96
1.82
1.70
1.50
3.40
3.17
2.96
2.78
2.46
4.82
4.51
4.23
3.97
3.54
6.35
5.96
5.60
5.28
4.73
7.97
7.51
7.08
6.70
6.04
9.67 11.5
9.15 10.9
8.68 10.4
8.24 9.86
7.46 8.97
13.3
12.7
12.1
11.5
10.6
15.2
14.5
13.9
13.3
12.2
17.1
16.4
15.7
15.1
14.0
19.0
18.3
17.6
17.0
15.7
14
16
18
20
24
0.61
0.55
0.50
0.46
0.40
1.34
1.21
1.11
1.02
0.87
2.21
2.00
1.82
1.67
1.43
3.18
2.88
2.64
2.42
2.09
4.27
3.89
3.56
3.29
2.84
5.48
5.01
4.60
4.25
3.68
6.80
6.23
5.74
5.31
4.62
8.21
7.54
6.97
6.47
5.65
9.70 11.3
8.95 10.4
8.30 9.71
7.73 9.06
6.77 7.96
12.9
12.0
11.2
10.5
9.23
14.6
13.6
12.7
11.9
10.6
28
32
36
0.35
0.31
0.28
0.76
0.68
0.61
1.26
1.12
1.00
1.83
1.63
1.46
2.49
2.22
2.00
3.24
2.89
2.60
4.07
3.64
3.29
5.00
4.47
4.04
6.00
5.38
4.87
2
3
4
5
6
1.70
1.51
1.35
1.21
1.10
3.52
3.23
2.96
2.72
2.51
5.44
5.11
4.79
4.48
4.20
7.40
7.06
6.70
6.36
6.03
9.37
9.03
8.67
8.30
7.94
11.4
11.0
10.7
10.3
9.90
13.3
13.0
12.7
12.3
11.9
15.3
15.0
14.6
14.3
13.9
17.3
17.0
16.6
16.3
15.9
19.3
19.0
18.6
18.3
17.9
21.3
21.0
20.6
20.3
19.9
23.2
22.9
22.6
22.3
21.9
7
8
9
10
12
1.00
0.92
0.85
0.79
0.69
2.33
2.18
2.04
1.92
1.71
3.96
3.73
3.53
3.35
3.02
5.73
5.45
5.19
4.94
4.50
7.60
7.27
6.96
6.67
6.13
9.53
9.17
8.83
8.50
7.88
11.5
11.1
10.8
10.4
9.73
13.5
13.1
12.7
12.4
11.6
15.5
15.1
14.7
14.3
13.6
17.5
17.1
16.7
16.3
15.5
19.5
19.1
18.7
18.3
17.5
21.5
21.1
20.7
20.3
19.5
14
16
18
20
24
0.61
0.55
0.50
0.46
0.40
1.55
1.41
1.29
1.19
1.03
2.75
2.51
2.31
2.13
1.84
4.12
3.78
3.49
3.24
2.82
5.65
5.22
4.85
4.53
3.99
7.33
6.83
6.39
6.00
5.32
9.11 11.0
8.55 10.3
8.04 9.77
7.57 9.25
6.76 8.32
12.9
12.2
11.6
11.0
9.97
14.8
14.1
13.4
12.8
11.7
16.8
16.0
15.3
14.7
13.5
19.8
18.0
17.3
16.6
15.3
28
32
36
0.35
0.31
0.28
0.90
0.80
0.72
1.62
1.44
1.30
2.50
2.24
2.02
3.56
3.20
2.90
4.76
4.30
3.92
6.09
5.52
5.04
9.08 10.7 12.4
8.32 9.85 11.5
7.66 9.10 10.6
14.2
13.1
12.2
7.53
6.86
6.30
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
7.08
6.37
5.78
8.24
7.43
6.75
9.47
8.56
7.79
8 - 62
BOLTS, WELDS, AND CONNECTED ELEMENTS
Table 8-21 (cont.).
Coefficients C for Eccentrically Loaded Bolt Groups
Angle = 60°°
C req =
Pu
φrn
or φR n = C × φ rn
ex
where
3
6
s
s
60°
s
e
s, in.
Pu
s
Pu
= factored force, kips
φ rn = design strength per bolt, kips
φ R n = design strength of bolt group, kips
e
= eccentricity of Pu with respect to centroid
of bolt group, in. (not tabulated, may be
determined by geometry.)
e x = horizontal component of e, in.
s
= bolt spacing, in.
C
= coefficient tabulated below.
8
Number of bolts in one vertical row, n
ex,
in.
1
2
3
4
5
6
7
8
9
10
11
12
2
3
4
5
6
1.86
1.77
1.66
1.54
1.43
3.71
3.52
3.31
3.10
2.90
5.56
5.29
4.99
4.70
4.41
7.41
7.07
6.70
6.34
6.00
9.28
8.88
8.45
8.04
7.64
11.2
10.7
10.3
9.79
9.35
13.1
12.6
12.1
11.6
11.1
15.0
14.5
13.9
13.4
12.9
16.9
16.4
15.8
15.3
14.7
18.8
18.3
17.7
17.1
16.6
20.8
20.2
19.6
19.0
18.5
22.7
22.1
21.6
21.0
20.4
7
8
9
10
12
1.33
1.24
1.16
1.08
0.96
2.71
2.54
2.38
2.24
2.00
4.15
3.92
3.70
3.51
3.17
5.68
5.39
5.12
4.88
4.44
7.27
6.94
6.63
6.34
5.82
8.94 10.7
8.56 10.3
8.22 9.86
7.89 9.49
7.28 8.81
12.4
12.0
11.6
11.2
10.4
14.2
13.8
13.3
12.9
12.1
16.1
15.6
15.1
14.6
13.8
17.9
17.4
16.9
16.4
15.5
19.8
19.3
18.7
18.2
17.3
14
16
18
20
24
0.86
0.77
0.70
0.65
0.56
1.81
1.64
1.51
1.39
1.20
2.88
2.64
2.43
2.25
1.95
4.07
3.74
3.46
3.21
2.80
5.36
4.95
4.59
4.28
3.76
6.73
6.25
5.83
5.45
4.81
8.19
7.64
7.15
6.71
5.96
9.72 11.3
9.11 10.7
8.56 10.0
8.06 9.48
7.19 8.50
13.0
12.2
11.6
11.0
9.88
14.7
13.9
13.2
12.5
11.3
16.4
15.6
14.8
14.1
12.8
28
32
36
0.49
0.43
0.39
1.06
0.94
0.85
1.72
1.54
1.39
2.48
2.22
2.01
3.34
3.00
2.72
4.29
3.87
3.52
5.34
4.83
4.40
6.47
5.87
5.36
2
3
4
5
6
1.86
1.77
1.66
1.54
1.43
3.72
3.55
3.36
3.17
2.99
5.59
5.37
5.14
4.90
4.67
7.50
7.25
6.98
6.72
6.46
9.43
9.16
8.88
8.59
8.31
7
8
9
10
12
1.33
1.24
1.16
1.08
0.96
2.82
2.67
2.52
2.40
2.17
4.46
4.26
4.08
3.91
3.61
6.21
5.98
5.76
5.56
5.20
8.05
7.79
7.55
7.32
6.90
9.92
9.65
9.39
9.14
8.66
14
16
18
20
24
0.86
0.77
0.70
0.65
0.56
1.98
1.82
1.69
1.57
1.37
3.35
3.11
2.91
2.72
2.41
4.87
4.57
4.30
4.05
3.61
6.51
6.15
5.81
5.50
4.96
8.23 10.0
7.81 9.56
7.43 9.13
7.07 8.73
6.43 8.00
28
32
36
0.49
0.43
0.39
1.22
1.09
0.99
2.15
1.94
1.76
3.25
2.94
2.69
4.49
4.10
3.77
5.88
5.41
5.00
11.4
11.1
10.8
10.5
10.2
7.68
6.99
6.41
8.97 10.3 11.7
8.19 9.46 10.8
7.53 8.71 9.96
13.3
13.0
12.7
12.4
12.1
15.3
15.0
14.7
14.4
14.1
17.3
17.0
16.7
16.3
16.0
19.2
18.9
18.6
18.3
18.0
21.2
20.9
20.6
20.3
19.9
23.2
22.9
22.6
22.2
21.9
11.8
11.5
11.3
11.0
10.5
13.8
13.5
13.2
12.9
12.4
15.7
15.4
15.1
14.8
14.2
17.7
17.3
17.0
16.7
16.1
19.6
19.3
19.0
18.7
18.1
21.6
21.3
20.9
20.6
20.0
11.8
11.4
10.9
10.5
9.67
13.7
13.2
12.7
12.2
11.4
15.6
15.1
14.5
14.1
13.2
17.5
16.9
16.4
15.9
15.0
19.4
18.9
18.3
17.8
16.8
8.97 10.6 12.3
8.34 9.92 11.6
7.78 9.30 10.9
14.1
13.3
12.5
15.9
15.0
14.2
7.38
6.83
6.35
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
ECCENTRICALLY LOADED BOLT GROUPS
8 - 63
Table 8-21 (cont.).
Coefficients C for Eccentrically Loaded Bolt Groups
Angle = 75°°
C req =
Pu
φr n
or φ R n = C × φrn
ex
where
3
6
s
s
s
e
s, in.
75° P
u
s
Pu
= factored force, kips
φ rn = design strength per bolt, kips
φ R n = design strength of bolt group, kips
e
= eccentricity of Pu with respect to centroid
of bolt group, in. (not tabulated, may be
determined by geometry.)
e x = horizontal component of e, in.
s
= bolt spacing, in.
C
= coefficient tabulated below.
8
Number of bolts in one vertical row, n
ex,
in.
1
2
3
4
5
6
7
8
9
10
11
12
2
3
4
5
6
1.94
1.92
1.89
1.85
1.81
3.87
3.82
3.75
3.67
3.59
5.79
5.70
5.60
5.48
5.35
7.70
7.58
7.43
7.28
7.11
9.61
9.45
9.26
9.07
8.87
11.5
11.3
11.1
10.9
10.6
13.4
13.2
12.9
12.7
12.4
15.3
15.1
14.8
14.5
14.2
17.3
17.0
16.7
16.4
16.1
19.2
18.9
18.5
18.2
17.9
21.1
20.8
20.4
20.1
19.8
23.0
22.7
22.3
22.0
21.6
7
8
9
10
12
1.76
1.71
1.66
1.61
1.51
3.50
3.40
3.30
3.20
3.01
5.22
5.08
4.94
4.80
4.53
6.94
6.76
6.59
6.42
6.08
8.67
8.46
8.26
8.06
7.67
10.4
10.2
9.96
9.73
9.30
12.2
11.9
11.7
11.4
11.0
14.0
13.7
13.4
13.2
12.7
15.8
15.5
15.2
14.9
14.4
17.6
17.3
17.0
16.7
16.2
19.4
19.1
18.8
18.5
17.9
21.3
21.0
20.6
20.3
19.7
14
16
18
20
24
1.41
1.31
1.23
1.15
1.01
2.82
2.65
2.48
2.34
2.08
4.27
4.03
3.80
3.60
3.23
5.76
5.47
5.19
4.93
4.48
7.31
6.96
6.64
6.34
5.80
8.90 10.5
8.52 10.1
8.16 9.73
7.82 9.36
7.20 8.67
12.2
11.8
11.3
10.9
10.2
13.9
13.4
13.0
12.6
11.8
15.6
15.2
14.7
14.2
13.4
17.4
16.9
16.4
15.9
15.0
19.2
18.6
18.1
17.7
16.7
28
32
36
0.90
0.81
0.73
1.87
1.69
1.54
2.93
2.67
2.45
4.08
3.75
3.45
5.33
4.91
4.55
6.65
6.17
5.74
12.6
11.9
11.2
14.2
13.5
12.8
15.9
15.1
14.3
2
3
4
5
6
1.94
1.92
1.89
1.85
1.81
3.86
3.80
3.74
3.66
3.58
5.77
5.68
5.57
5.46
5.35
7.68
7.55
7.42
7.29
7.15
9.60
9.45
9.29
9.14
8.98
11.5
11.4
11.2
11.0
10.8
13.5
13.3
13.1
12.9
12.7
15.4
15.2
15.0
14.8
14.6
17.6
17.2
16.9
16.7
16.5
19.6
19.1
18.9
18.7
18.5
21.5
21.1
20.8
20.6
20.4
23.5
23.0
22.8
22.6
22.3
7
8
9
10
12
1.76
1.71
1.66
1.61
1.51
3.49
3.40
3.31
3.22
3.05
5.23
5.12
5.00
4.89
4.67
7.01
6.88
6.74
6.61
6.36
8.83
8.68
8.53
8.38
8.10
10.7
10.5
10.4
10.2
9.89
12.5
12.4
12.2
12.0
11.7
14.4
14.3
14.1
13.9
13.6
16.3
16.2
16.0
15.8
15.4
18.3
18.1
17.9
17.7
17.3
20.2
20.0
19.8
19.6
19.2
22.1
21.9
21.7
21.5
21.1
14
16
18
20
24
1.41
1.31
1.23
1.15
1.01
2.88
2.73
2.58
2.45
2.21
4.46
4.26
4.08
3.90
3.59
6.12
5.89
5.68
5.47
5.10
7.84
7.59
7.35
7.13
6.71
9.61
9.33
9.08
8.84
8.38
11.4
11.1
10.8
10.6
10.1
13.3
12.9
12.7
12.4
11.9
15.1
14.8
14.5
14.2
13.6
17.0
16.6
16.3
16.0
15.5
18.9
18.5
18.2
17.9
17.3
20.8
20.4
20.1
19.7
19.1
28
32
36
0.90
0.81
0.73
2.01
1.84
1.70
3.32
3.08
2.87
4.77
4.47
4.19
6.32
5.97
5.64
7.96
7.56
7.19
9.65 11.4
9.21 10.9
8.80 10.5
13.1
12.7
12.2
14.9
14.4
13.9
16.7
16.2
15.7
18.5
18.0
17.5
8.06
7.51
7.01
9.52 11.0
8.91 10.4
8.36 9.77
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
8 - 64
BOLTS, WELDS, AND CONNECTED ELEMENTS
Table 8-22.
Coefficients C for Eccentrically Loaded Bolt Groups
Angle = 0°°
C req =
Pu
φrn
or φR n = C × φ rn
ex = e
where
s, in.
3
6
s
Pu
s
s
Pu
= factored force, kips
φ rn = design strength per bolt, kips
φ R n = design strength of bolt group, kips
e
= eccentricity of Pu with respect to centroid
of bolt group, in. (not tabulated, may be
determined by geometry.)
e x = horizontal component of e, in.
s
= bolt spacing, in.
C
= coefficient tabulated below.
3
3
6
Number of bolts in one vertical row, n
ex,
in.
1
2
3
4
5
6
7
8
9
10
11
12
2
3
4
5
6
1.71
1.42
1.21
1.05
0.92
4.07
3.40
2.90
2.51
2.21
6.81
5.79
4.97
4.34
3.85
9.86
8.61
7.53
6.64
5.91
13.0
11.7
10.4
9.24
8.27
16.1
14.8
13.4
12.1
11.0
19.3
18.0
16.6
15.2
13.9
22.3
21.1
19.8
18.3
16.9
25.4
24.3
23.0
21.5
20.0
28.5
27.4
26.1
24.7
23.2
31.5
30.5
29.3
27.9
26.4
34.5
33.6
32.5
31.1
29.7
7
8
9
10
12
0.81
0.72
0.64
0.58
0.49
1.96
1.76
1.60
1.46
1.24
3.44
3.11
2.83
2.59
2.21
5.31
4.80
4.38
4.02
3.44
7.46
6.78
6.20
5.71
4.91
9.95 12.7
9.09 11.6
8.34 10.7
7.70 9.91
6.65 8.59
15.6
14.4
13.3
12.4
10.8
18.6
17.3
16.1
15.0
13.2
21.8
20.4
19.1
17.9
15.7
25.0
23.5
22.1
20.8
18.5
28.2
26.7
25.2
23.8
21.3
14
16
18
20
24
0.42
0.37
0.33
0.29
0.24
1.08
0.95
0.85
0.77
0.64
1.92
1.70
1.52
1.37
1.15
3.00
2.66
2.39
2.16
1.82
4.30
3.82
3.43
3.11
2.62
5.83
5.19
4.67
4.24
3.57
7.57
6.75
6.08
5.53
4.67
9.53 11.7
8.51 10.5
7.68 9.45
6.99 8.61
5.92 7.30
14.0
12.6
11.4
10.4
8.8
16.5
14.9
13.5
12.3
10.5
19.2
17.3
15.8
14.4
12.3
28
32
36
0.21
0.18
0.16
0.55
0.49
0.43
0.99
0.87
0.77
1.57
1.38
1.23
2.26
1.98
1.77
3.08
2.71
2.42
4.04
3.55
3.17
5.12
4.51
4.03
2
3
4
5
6
1.71
1.42
1.21
1.05
0.92
4.85
4.24
3.72
3.29
2.93
8.04
7.36
6.66
6.00
5.41
11.2
10.6
9.86
9.14
8.44
7
8
9
10
12
0.81
0.72
0.64
0.58
0.49
2.63
2.38
2.17
2.00
1.71
4.90
4.46
4.09
3.78
3.27
7.79 10.9
7.20 10.2
6.67 9.54
6.20 8.94
5.41 7.88
14
16
18
20
24
0.42
0.37
0.33
0.29
0.24
1.49
1.32
1.19
1.08
0.91
2.87
2.55
2.30
2.09
1.76
4.78
4.28
3.86
3.51
2.97
7.01
6.29
5.70
5.20
4.42
9.61 12.4
8.69 11.3
7.91 10.4
7.25 9.54
6.19 8.19
28
32
36
0.21
0.18
0.16
0.78
0.69
0.61
1.52
1.33
1.19
2.57
2.27
2.03
3.84
3.39
3.03
5.39
4.77
4.27
14.2
13.7
13.1
12.4
11.6
6.33
5.58
4.99
7.67
6.77
6.05
9.13 10.7
8.06 9.47
7.21 8.48
17.3
16.8
16.2
15.6
14.9
20.3
19.9
19.4
18.7
18.1
23.2
22.9
22.4
21.9
21.2
26.2
25.9
25.5
25.0
24.4
29.2
28.9
28.5
28.1
27.5
32.2
31.9
31.6
31.1
30.6
35.1
34.9
34.6
34.2
33.7
14.1
13.4
12.6
12.0
10.7
17.3
16.6
15.8
15.1
13.7
20.6
19.8
19.1
18.3
16.8
23.7
23.0
22.3
21.6
20.0
26.9
26.2
25.5
24.8
23.3
30.0
29.4
28.7
28.0
26.5
33.2
32.6
31.9
31.2
29.8
15.4
14.2
13.1
12.1
10.4
18.6
17.2
15.9
14.8
12.9
21.8
20.3
18.9
17.7
15.5
25.0
23.5
22.0
20.7
18.3
28.2
26.7
25.2
23.8
21.2
9.15 11.4 13.7
8.13 10.1 12.3
7.30 9.10 11.1
16.3
14.6
13.2
19.0
17.1
15.5
7.14
6.33
5.67
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
ECCENTRICALLY LOADED BOLT GROUPS
8 - 65
Table 8-22 (cont.).
Coefficients C for Eccentrically Loaded Bolt Groups
Angle = 15°°
C req =
Pu
φ rn
or φ R n = C × φrn
ex
Pu
where
s, in.
3
6
s
15°
e
s
s
Pu
= factored force, kips
φ rn = design strength per bolt, kips
φ R n = design strength of bolt group, kips
e
= eccentricity of Pu with respect to centroid
of bolt group, in. (not tabulated, may be
determined by geometry.)
e x = horizontal component of e, in.
s
= bolt spacing, in.
C
= coefficient tabulated below.
3
3
6
Number of bolts in one vertical row, n
ex,
in.
1
2
3
4
5
6
7
8
9
10
11
12
2
3
4
5
6
1.77
1.47
1.25
1.08
0.94
4.10
3.45
2.95
2.57
2.26
6.84
5.86
5.07
4.44
3.93
9.82
8.61
7.55
6.67
5.96
12.9
11.6
10.4
9.26
8.33
16.0
14.7
13.3
12.1
11.0
19.1
17.8
16.4
15.1
13.8
22.2
20.9
19.5
18.1
16.8
25.2
24.1
22.7
21.3
19.8
28.3
27.2
25.8
24.4
23.0
31.3
30.3
29.0
27.6
26.1
34.3
33.3
32.1
30.7
29.3
7
8
9
10
12
0.83
0.74
0.66
0.60
0.50
2.01
1.81
1.64
1.50
1.28
3.52
3.18
2.90
2.65
2.27
5.37
4.87
4.45
4.10
3.52
7.55
6.88
6.31
5.81
5.01
9.97 12.7
9.13 11.7
8.40 10.8
7.77 9.99
6.74 8.71
15.5
14.4
13.3
12.4
10.9
18.5
17.2
16.1
15.0
13.2
21.5
20.2
18.9
17.8
15.8
24.7
23.2
21.9
20.7
18.4
27.8
26.4
25.0
23.6
21.2
14
16
18
20
24
0.43
0.38
0.34
0.30
0.25
1.11
0.98
0.88
0.79
0.67
1.98
1.75
1.57
1.42
1.19
3.08
2.73
2.45
2.22
1.87
4.40
3.91
3.52
3.19
2.69
5.93
5.29
4.77
4.33
3.66
7.69
6.87
6.20
5.65
4.78
9.62 11.8
8.62 10.6
7.80 9.59
7.12 8.76
6.04 7.45
14.1
12.7
11.5
10.5
8.99
16.5
15.0
13.6
12.5
10.7
19.1
17.4
15.9
14.6
12.5
28
32
36
0.22
0.19
0.17
0.57
0.50
0.45
1.02
0.90
0.80
1.61
1.42
1.26
2.32
2.04
1.82
3.17
2.79
2.49
4.14
3.65
3.26
5.24
4.62
4.13
2
3
4
5
6
1.77
1.47
1.25
1.08
0.94
4.83
4.22
3.71
3.28
2.94
7.98
7.31
6.64
6.01
5.45
11.1
10.5
9.77
9.06
8.38
7
8
9
10
12
0.83
0.74
0.66
0.60
0.50
2.65
2.40
2.20
2.02
1.74
4.97
4.55
4.18
3.86
3.34
7.75 10.8
7.17 10.1
6.66 9.49
6.20 8.92
5.43 7.91
14
16
18
20
24
0.43
0.38
0.34
0.30
0.25
1.52
1.35
1.22
1.10
0.93
2.94
2.62
2.36
2.14
1.81
4.82
4.32
3.91
3.57
3.03
7.07
6.38
5.79
5.30
4.52
9.60 12.4
8.71 11.3
7.95 10.4
7.31 9.60
6.26 8.28
28
32
36
0.22
0.19
0.17
0.80
0.71
0.63
1.56
1.37
1.23
2.63
2.32
2.08
3.93
3.47
3.11
5.47
4.85
4.35
14.1
13.6
12.9
12.2
11.5
6.47
5.72
5.11
7.82
6.92
6.20
9.31 10.9
8.24 9.66
7.38 8.66
17.2
16.7
16.1
15.4
14.7
20.2
19.7
19.2
18.5
17.8
23.2
22.8
22.3
21.7
21.0
26.1
25.8
25.3
24.8
24.1
29.1
28.8
28.3
27.8
27.2
32.1
31.8
31.4
30.9
30.3
35.0
34.8
34.4
33.9
33.4
13.9
13.2
12.5
11.9
10.6
17.1
16.4
15.6
14.9
13.6
20.3
19.6
18.8
18.1
16.6
23.5
22.7
22.0
21.3
19.8
26.6
25.9
25.2
24.5
23.0
29.7
29.1
28.4
27.6
26.1
32.8
32.2
31.5
30.8
29.3
15.3
14.1
13.0
12.1
10.5
18.4
17.0
15.8
14.8
12.9
21.5
20.1
18.8
17.6
15.5
24.6
23.2
21.8
20.5
18.2
27.3
26.3
24.9
23.5
21.1
9.24 11.4 13.8
8.23 10.2 12.4
7.41 9.23 11.2
16.3
14.7
13.3
18.9
17.1
15.6
7.26
6.45
5.80
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
8 - 66
BOLTS, WELDS, AND CONNECTED ELEMENTS
Table 8-22 (cont.).
Coefficients C for Eccentrically Loaded Bolt Groups
Angle = 30°°
C req =
Pu
φrn
or φ R n = C × φ rn
ex
Pu
where
s, in.
3
6
s
30°
s
Pu
= factored force, kips
φ rn = design strength per bolt, kips
φ R n = design strength of bolt group, kips
e
= eccentricity of Pu with respect to centroid
of bolt group, in. (not tabulated, may be
determined by geometry.)
e x = horizontal component of e, in.
s
= bolt spacing, in.
C
= coefficient tabulated below.
s
e
3
3
6
Number of bolts in one vertical row, n
ex,
in.
1
2
3
4
5
6
7
8
9
10
11
12
2
3
4
5
6
1.94
1.61
1.37
1.19
1.04
4.26
3.63
3.15
2.77
2.45
6.99
6.09
5.35
4.74
4.23
9.90
8.80
7.83
7.00
6.30
12.9
11.7
10.6
9.54
8.67
16.0
14.7
13.5
12.3
11.3
19.0
17.7
16.5
15.2
14.1
22.0
20.8
19.5
18.2
17.0
25.1
23.9
22.6
21.2
19.9
28.1
27.0
25.7
24.3
23.0
31.1
30.0
28.7
27.4
26.0
34.1
33.1
31.8
30.5
29.1
7
8
9
10
12
0.92
0.82
0.74
0.67
0.56
2.19
1.98
1.80
1.65
1.41
3.81
3.45
3.16
2.90
2.49
5.71
5.22
4.79
4.42
3.82
7.92 10.4
7.27 9.58
6.71 8.88
6.22 8.26
5.41 7.22
13.0
12.1
11.2
10.5
9.23
15.8
14.8
13.8
12.9
11.5
18.7
17.6
16.5
15.5
13.8
21.7
20.5
19.3
18.2
16.4
24.7
23.4
22.2
21.1
19.0
27.8
26.4
25.2
24.0
21.8
14
16
18
20
24
0.48
0.42
0.38
0.34
0.28
1.23
1.08
0.97
0.88
0.74
2.18
1.93
1.73
1.57
1.32
3.36
2.99
2.69
2.44
2.06
4.78
4.26
3.85
3.50
2.96
6.40
5.73
5.18
4.73
4.01
8.22 10.3 12.4
7.40 9.25 11.3
6.71 8.41 10.3
6.14 7.70 9.42
5.22 6.58 8.08
14.8
13.4
12.3
11.3
9.72
17.2
15.7
14.4
13.3
11.5
19.8
18.2
16.7
15.4
13.4
28
32
36
0.24
0.21
0.19
0.64
0.56
0.50
1.14
1.00
0.89
1.78
1.57
1.40
2.56
2.26
2.02
3.48
3.07
2.75
4.54
4.01
3.59
2
3
4
5
6
1.94
1.61
1.37
1.19
1.04
4.86
4.27
3.78
3.39
3.06
7.96
7.32
6.70
6.14
5.64
11.0
10.4
9.75
9.10
8.48
7
8
9
10
12
0.92
0.82
0.74
0.67
0.56
2.78
2.54
2.34
2.16
1.87
5.19
4.80
4.45
4.14
3.61
7.91 10.9
7.38 10.3
6.90 9.67
6.46 9.14
5.71 8.20
14
16
18
20
24
0.48
0.42
0.38
0.34
0.28
1.65
1.47
1.33
1.21
1.02
3.20
2.86
2.58
2.35
2.00
5.10
4.60
4.19
3.84
3.29
7.41
6.74
6.17
5.68
4.89
28
32
36
0.24
0.21
0.19
0.88
0.78
0.70
1.73
1.52
1.36
2.86
2.54
2.27
4.28
3.80
3.41
14.1
13.5
12.9
12.2
11.5
5.73
5.07
4.54
7.05
6.25
5.61
8.51 10.1 11.8
7.55 8.96 10.5
6.78 8.06 9.44
17.1
16.6
15.9
15.3
14.6
20.1
19.6
19.0
18.4
17.7
23.1
22.6
22.1
21.5
20.8
26.0
25.6
25.1
24.5
23.9
29.0
28.6
28.1
27.6
27.0
32.0
31.6
31.1
30.6
30.1
35.0
34.6
34.2
33.7
33.1
13.9
13.3
12.6
12.0
10.9
17.0
16.3
15.7
15.0
13.8
20.1
19.4
18.7
18.1
16.8
23.2
22.6
21.9
21.2
19.8
26.3
25.7
25.0
24.3
22.9
29.4
28.8
28.1
27.4
26.0
32.5
31.9
31.2
30.5
29.1
9.95
9.12
8.39
7.75
6.71
12.7
11.7
10.8
10.1
8.78
15.6
14.5
13.5
12.6
11.1
18.5
17.3
16.2
15.2
13.5
21.5
20.3
19.1
18.0
16.1
24.6
23.3
22.0
20.9
18.8
27.7
26.4
25.0
23.8
21.6
5.90
5.25
4.73
7.77
6.95
6.28
9.83 12.1 14.5
8.83 10.9 13.1
8.00 9.88 11.9
17.0
15.4
14.1
19.6
17.9
16.4
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
ECCENTRICALLY LOADED BOLT GROUPS
8 - 67
Table 8-22 (cont.).
Coefficients C for Eccentrically Loaded Bolt Groups
Angle = 45°°
C req =
Pu
φrn
or φ R n = C × φ rn
ex
Pu
s
where
3
6
s
e
s, in.
45°
s
Pu
= factored force, kips
φ rn = design strength per bolt, kips
φ R n = design strength of bolt group, kips
e
= eccentricity of Pu with respect to centroid
of bolt group, in. (not tabulated, may be
determined by geometry.)
e x = horizontal component of e, in.
s
= bolt spacing, in.
C
= coefficient tabulated below.
3
3
6
Number of bolts in one vertical row, n
ex,
in.
1
2
3
4
5
6
7
8
9
10
11
12
2
3
4
5
6
2.23
1.89
1.63
1.42
1.25
4.67
4.06
3.57
3.17
2.84
7.33
6.50
5.84
5.27
4.78
10.2
9.19
8.36
7.63
6.99
13.1
12.0
11.1
10.2
9.40
16.0
14.9
13.9
12.9
12.0
19.0
17.9
16.8
15.7
14.7
22.0
20.9
19.7
18.6
17.6
25.0
23.9
22.7
21.5
20.4
28.0
26.9
25.7
24.5
23.4
31.0
29.9
28.7
27.5
26.3
33.9
32.9
31.7
30.5
29.3
7
8
9
10
12
1.11
0.99
0.90
0.81
0.68
2.57
2.33
2.13
1.96
1.68
4.36
3.99
3.68
3.40
2.95
6.42
5.92
5.49
5.10
4.46
8.70 11.2
8.09 10.5
7.54 9.80
7.05 9.21
6.22 8.19
13.8
13.0
12.2
11.6
10.4
16.6
15.7
14.8
14.0
12.7
19.4
18.4
17.5
16.6
15.1
22.3
21.2
20.3
19.3
17.7
25.2
24.1
23.1
22.1
20.3
28.2
27.0
26.0
24.9
23.0
14
16
18
20
24
0.59
0.52
0.46
0.41
0.35
1.47
1.31
1.17
1.06
0.90
2.59
2.31
2.08
1.89
1.60
3.95
3.54
3.20
2.92
2.48
5.55
4.99
4.54
4.15
3.54
7.35
6.65
6.06
5.56
4.76
9.34 11.5
8.49 10.5
7.77 9.64
7.15 8.90
6.15 7.70
13.8
12.7
11.7
10.8
9.39
16.2
14.9
13.8
12.8
11.2
18.7
17.3
16.1
15.0
13.1
21.3
19.8
18.5
17.2
15.2
28
32
36
0.30
0.26
0.23
0.77
0.68
0.61
1.38
1.22
1.08
2.15
1.90
1.69
3.08
2.72
2.44
4.16
3.68
3.30
5.39
4.79
4.30
2
3
4
5
6
2.23
1.89
1.63
1.42
1.25
5.02
4.50
4.05
3.68
3.36
8.01
7.44
6.89
6.40
5.96
11.0
10.4
9.86
9.30
8.78
7
8
9
10
12
1.11
0.99
0.90
0.81
0.68
3.09
2.86
2.65
2.47
2.16
5.57
5.22
4.90
4.61
4.11
8.29 11.2
7.84 10.6
7.43 10.2
7.04 9.69
6.35 8.85
14
16
18
20
24
0.59
0.52
0.46
0.41
0.35
1.92
1.72
1.56
1.43
1.22
3.69
3.34
3.04
2.79
2.38
5.76
5.25
4.82
4.44
3.84
8.11 10.7
7.47 9.94
6.91 9.26
6.43 8.66
5.62 7.64
28
32
36
0.30
0.26
0.23
1.06
0.94
0.84
2.08
1.84
1.65
3.37
3.00
2.71
4.98
4.46
4.04
14.0
13.5
12.9
12.3
11.7
6.77
6.03
5.42
8.28
7.39
6.66
9.91 11.7
8.87 10.5
8.02 9.49
13.5
12.2
11.1
17.0
16.5
15.9
15.3
14.7
20.0
19.5
18.9
18.3
17.7
23.0
22.5
21.9
21.3
20.7
25.9
25.5
24.9
24.4
23.8
28.9
28.4
27.9
27.4
26.8
31.9
31.4
30.9
30.4
29.8
34.8
34.4
33.9
33.4
32.8
14.1
13.6
13.0
12.5
11.6
17.1
16.5
16.0
15.4
14.4
20.1
19.5
19.0
18.4
17.3
23.2
22.6
22.0
21.4
20.2
26.2
25.6
25.0
24.4
23.2
29.2
28.6
28.0
27.4
26.2
32.3
31.7
31.1
30.4
29.2
13.4
12.6
11.8
11.1
9.84
16.2
15.3
14.4
13.6
12.2
19.1
18.1
17.2
16.3
14.7
22.1
21.0
20.0
19.0
17.3
25.0
23.9
22.9
21.9
20.0
28.0
26.9
25.8
24.7
22.8
8.82 11.0 13.4
7.97 10.0 12.2
7.27 9.18 11.2
15.8
14.6
13.4
18.4
17.0
15.7
21.1
19.5
18.1
6.81
6.12
5.56
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
8 - 68
BOLTS, WELDS, AND CONNECTED ELEMENTS
Table 8-22 (cont.).
Coefficients C for Eccentrically Loaded Bolt Groups
Angle = 60°°
C req =
Pu
φrn
or φR n = C × φ rn
ex
where
3
6
s
60°
s
e
s, in.
Pu
s
Pu
= factored force, kips
φ rn = design strength per bolt, kips
φ R n = design strength of bolt group, kips
e
= eccentricity of Pu with respect to centroid
of bolt group, in. (not tabulated, may be
determined by geometry.)
e x = horizontal component of e, in.
s
= bolt spacing, in.
C
= coefficient tabulated below.
3
3
6
Number of bolts in one vertical row, n
ex,
in.
1
2
3
4
5
6
7
8
9
10
11
12
2
3
4
5
6
2.59
2.32
2.07
1.84
1.65
5.21
4.73
4.29
3.90
3.56
7.88
7.27
6.69
6.18
5.73
10.6
9.91
9.23
8.63
8.08
13.4
12.7
11.9
11.2
10.6
16.3
15.5
14.6
13.9
13.2
19.2
18.3
17.5
16.6
15.9
22.1
21.2
20.3
19.5
18.7
25.0
24.1
23.2
22.3
21.5
28.0
27.0
26.1
25.2
24.3
30.9
30.0
29.0
28.1
27.2
33.9
32.9
32.0
31.0
30.1
7
8
9
10
12
1.49
1.35
1.23
1.12
0.95
3.27
3.01
2.78
2.58
2.25
5.32
4.95
4.63
4.34
3.84
7.59 10.0
7.13 9.48
6.71 8.98
6.33 8.52
5.67 7.70
12.6
12.0
11.4
10.9
9.91
15.2
14.5
13.9
13.3
12.3
17.9
17.2
16.5
15.9
14.7
20.7
19.9
19.2
18.5
17.3
23.5
22.7
22.0
21.2
19.9
26.3
25.5
24.7
24.0
22.6
29.2
28.4
27.6
26.8
25.3
14
16
18
20
24
0.83
0.73
0.65
0.59
0.49
1.98
1.77
1.60
1.46
1.24
3.43
3.09
2.81
2.57
2.20
5.11
4.64
4.24
3.90
3.35
7.00
6.40
5.89
5.44
4.72
9.08 11.3
8.36 10.5
7.73 9.74
7.19 9.09
6.27 7.99
13.7
12.7
11.9
11.1
9.85
16.1
15.1
14.2
13.3
11.9
18.7
17.5
16.5
15.6
14.0
21.3
20.1
19.0
17.9
16.2
23.9
22.6
21.5
20.4
18.5
28
32
36
0.42
0.37
0.33
1.07
0.95
0.85
1.91
1.69
1.51
2.93
2.60
2.34
4.15
3.70
3.34
5.55
4.97
4.49
12.6
11.5
10.5
14.7
13.4
12.3
16.8
15.4
14.2
2
3
4
5
6
2.59
2.32
2.07
1.84
1.65
5.32
4.94
4.57
4.25
3.95
8.17
7.73
7.31
6.91
6.55
11.1
10.6
10.2
9.73
9.32
14.0
13.5
13.1
12.6
12.2
17.0
16.5
16.0
15.5
15.1
19.9
19.4
19.0
18.5
18.0
22.9
22.4
21.9
21.4
20.9
25.8
25.4
24.9
24.4
23.9
28.8
28.3
27.8
27.4
26.9
31.8
31.3
30.8
30.3
29.8
34.7
34.3
33.8
33.3
32.8
7
8
9
10
12
1.49
1.35
1.23
1.12
0.95
3.69
3.46
3.25
3.06
2.73
6.22
5.92
5.64
5.39
4.92
8.94
8.58
8.25
7.94
7.37
11.8
11.4
11.0
10.6
9.97
14.6
14.2
13.8
13.4
12.7
17.5
17.1
16.7
16.3
15.5
20.5
20.0
19.6
19.1
18.3
23.4
22.9
22.5
22.0
21.2
26.4
25.9
25.4
24.9
24.1
29.3
28.8
28.4
27.9
27.0
32.3
31.8
31.3
30.8
29.9
14
16
18
20
24
0.83
0.73
0.65
0.59
0.49
2.46
2.23
2.04
1.88
1.63
4.52
4.18
3.87
3.60
3.15
6.85
6.39
5.97
5.59
4.94
9.36
8.80
8.28
7.81
6.99
12.0
11.4
10.8
10.2
9.25
14.7
14.0
13.4
12.8
11.7
17.5
16.8
16.1
15.4
14.2
20.3
19.6
18.8
18.1
16.8
23.2
22.4
21.6
20.9
19.5
26.1
25.3
24.4
23.7
22.2
29.0
28.1
27.3
26.5
25.0
28
32
36
0.42
0.37
0.33
1.43
1.27
1.15
2.79
2.49
2.25
4.41
3.97
3.61
6.31
5.74
5.26
8.44 10.7 13.1
7.74 9.90 12.2
7.13 9.17 11.4
15.7
14.6
13.7
18.2
17.1
16.1
20.9
19.7
18.6
23.6
22.3
21.1
7.10
6.38
5.79
8.81 10.7
7.95 9.65
7.23 8.81
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
ECCENTRICALLY LOADED BOLT GROUPS
8 - 69
Table 8-22 (cont.).
Coefficients C for Eccentrically Loaded Bolt Groups
Angle = 75°°
C req =
Pu
φ rn
or φ R n = C × φrn
ex
where
3
6
s
s
e
s, in.
75° P
u
s
Pu
= factored force, kips
φ rn = design strength per bolt, kips
φ R n = design strength of bolt group, kips
e
= eccentricity of Pu with respect to centroid
of bolt group, in. (not tabulated, may be
determined by geometry.)
e x = horizontal component of e, in.
s
= bolt spacing, in.
C
= coefficient tabulated below.
3
3
6
Number of bolts in one vertical row, n
ex,
in.
1
2
3
4
5
6
7
8
9
10
11
12
2
3
4
5
6
2.86
2.77
2.66
2.53
2.40
5.68
5.49
5.27
5.04
4.81
8.47
8.19
7.89
7.58
7.27
11.3
10.9
10.5
10.2
9.81
14.1
13.7
13.2
12.8
12.4
16.9
16.4
16.0
15.5
15.1
19.8
19.2
18.8
18.3
17.8
22.6
22.1
21.6
21.0
20.6
25.5
24.9
24.4
23.9
23.3
28.4
27.8
27.2
26.7
26.2
31.3
30.7
30.1
29.5
29.0
34.2
33.6
33.0
32.4
31.8
7
8
9
10
12
2.26
2.13
2.00
1.89
1.67
4.57
4.35
4.13
3.93
3.57
6.97
6.69
6.41
6.15
5.67
9.47
9.13
8.82
8.51
7.95
12.0
11.7
11.3
11.0
10.4
14.7
14.3
13.9
13.5
12.9
17.4
16.9
16.5
16.1
15.4
20.1
19.6
19.2
18.8
18.0
22.9
22.4
21.9
21.5
20.7
25.6
25.1
24.7
24.2
23.4
28.4
27.9
27.4
27.0
26.1
31.3
30.7
30.2
29.8
28.8
14
16
18
20
24
1.49
1.34
1.21
1.10
0.93
3.25
2.97
2.73
2.53
2.19
5.25
4.87
4.54
4.24
3.75
7.44
6.98
6.56
6.18
5.52
9.77
9.23
8.74
8.28
7.48
12.2
11.6
11.1
10.5
9.59
14.7
14.1
13.5
12.9
11.8
17.3
16.6
16.0
15.3
14.2
19.9
19.2
18.5
17.8
16.6
22.6
21.8
21.1
20.4
19.1
25.3
24.5
23.7
23.0
21.6
28.0
27.2
26.4
25.6
24.2
28
32
36
0.80
0.71
0.63
1.93
1.72
1.55
3.34
3.01
2.74
4.97
4.51
4.12
6.79
6.20
5.70
13.2
12.3
11.5
15.5
14.5
13.6
17.9
16.8
15.9
20.4
19.2
18.2
22.9
21.7
20.6
2
3
4
5
6
2.86
2.77
2.66
2.53
2.40
5.66
5.49
5.30
5.10
4.91
8.48
8.25
8.02
7.79
7.56
11.3
11.1
10.8
10.6
10.3
14.2
13.9
13.6
13.4
13.1
17.1
16.8
16.5
16.2
15.9
20.1
19.7
19.4
19.1
18.8
23.0
22.7
22.3
22.0
21.7
26.4
25.6
25.2
24.9
24.6
29.3
28.5
28.2
27.8
27.5
32.3
31.5
31.1
30.8
30.4
35.2
34.4
34.0
33.7
33.3
7
8
9
10
12
2.26
2.13
2.00
1.89
1.67
4.72
4.54
4.37
4.21
3.90
7.34
7.14
6.94
6.75
6.39
10.1
9.83
9.61
9.40
9.00
12.9
12.6
12.4
12.1
11.7
15.7
15.4
15.2
14.9
14.4
18.5
18.3
18.0
17.7
17.2
21.4
21.1
20.8
20.6
20.0
24.3
24.0
23.7
23.4
22.9
27.2
26.9
26.6
26.3
25.7
30.1
29.8
29.5
29.2
28.6
33.0
32.7
32.4
32.1
31.5
14
16
18
20
24
1.49
1.34
1.21
1.10
0.93
3.63
3.39
3.17
2.98
2.65
6.06
5.75
5.47
5.22
4.76
8.63
8.29
7.96
7.66
7.10
11.3
10.9
10.6
10.2
9.57
14.0
13.6
13.2
12.9
12.2
16.8
16.3
15.9
15.5
14.8
19.6
19.1
18.7
18.2
17.5
22.4
21.9
21.4
21.0
20.2
25.2
24.7
24.2
23.8
22.9
28.1
27.5
27.0
26.6
25.7
30.9
30.4
29.9
29.4
28.5
28
32
36
0.80
0.71
0.63
2.38
2.16
1.97
4.37
4.03
3.73
6.60
6.15
5.75
8.99 11.5
8.45 10.9
7.96 10.3
14.1
13.4
12.8
16.7
16.0
15.3
19.4
18.7
17.9
22.1
21.3
20.6
24.8
24.0
23.3
27.6
26.8
26.0
8.78 10.9
8.08 10.1
7.47 9.40
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
8 - 70
BOLTS, WELDS, AND CONNECTED ELEMENTS
Table 8-23.
Coefficients C for Eccentrically Loaded Bolt Groups
Angle = 0°°
C req =
Pu
φrn
or φR n = C × φ rn
ex= e
where
s, in.
3
6
s
Pu
s
s
Pu
= factored force, kips
φ rn = design strength per bolt, kips
φ R n = design strength of bolt group, kips
e
= eccentricity of Pu with respect to centroid
of bolt group, in. (not tabulated, may be
determined by geometry.)
e x = horizontal component of e, in.
s
= bolt spacing, in.
C
= coefficient tabulated below.
6
6
12
Number of bolts in one vertical row, n
ex,
in.
1
2
3
2
3
4
5
6
2.15
1.91
1.71
1.55
1.42
4.55
4.06
3.65
3.31
3.02
7.17
6.43
5.80
5.27
4.82
7
8
9
10
12
1.31
1.21
1.12
1.05
0.92
2.77
2.56
2.38
2.21
1.94
4.44
4.10
3.81
3.55
3.12
6.34
5.87
5.46
5.09
4.48
8.46 10.8
7.85 10.1
7.31 9.39
6.84 8.79
6.03 7.78
14
16
18
20
24
0.81
0.72
0.64
0.58
0.49
1.72
1.53
1.38
1.26
1.06
2.77
2.48
2.25
2.05
1.73
3.99
3.58
3.25
2.96
2.52
5.38
4.84
4.40
4.02
3.42
6.95
6.27
5.70
5.21
4.45
8.69 10.6 12.7
7.85 9.60 11.5
7.15 8.75 10.5
6.55 8.03 9.65
5.60 6.88 8.29
28
32
36
0.42
0.37
0.33
0.92
0.81
0.72
1.50
1.32
1.18
2.19
1.93
1.72
2.97
2.63
2.35
3.87
3.42
3.06
4.88
4.32
3.87
2
3
4
5
6
2.15
1.91
1.71
1.55
1.42
4.94
4.48
4.07
3.71
3.40
7.98
7.39
6.81
6.27
5.79
11.1
10.5
9.86
9.22
8.61
7
8
9
10
12
1.31
1.21
1.12
1.05
0.92
3.13
2.90
2.69
2.51
2.21
5.35
4.97
4.64
4.34
3.85
8.05 11.0
7.53 10.4
7.07 9.78
6.64 9.24
5.91 8.27
14
16
18
20
24
0.81
0.72
0.64
0.58
0.49
1.96
1.76
1.60
1.46
1.24
3.44
3.11
2.83
2.59
2.21
5.31
4.80
4.38
4.02
3.44
7.46
6.78
6.20
5.71
4.91
9.95 12.7
9.09 11.6
8.34 10.7
7.70 9.91
6.65 8.59
28
32
36
0.42
0.37
0.33
1.08
0.95
0.85
1.92
1.70
1.52
3.00
2.66
2.39
4.30
3.82
3.43
5.83
5.19
4.67
4
5
10.0 13.0
9.06 11.9
8.23 10.9
7.51 9.97
6.88 9.16
14.2
13.6
13.0
12.3
11.7
6
7
8
9
10
11
12
16.0
14.9
13.7
12.7
11.7
19.1
17.9
16.7
15.5
14.4
22.2
21.0
19.8
18.5
17.3
25.3
24.1
22.9
21.5
20.3
28.3
27.2
26.0
24.7
23.3
31.4
30.3
29.1
27.8
26.4
34.4
33.4
32.3
31.0
29.6
13.4
12.5
11.7
10.9
9.70
16.1
15.1
14.1
13.3
11.8
19.0
17.9
16.8
15.8
14.1
22.0
20.7
19.6
18.5
16.6
25.1
23.7
22.5
21.3
19.1
28.2
26.8
25.5
24.2
21.9
14.9
13.6
12.4
11.4
9.82
17.3
15.8
14.4
13.3
11.5
19.9
18.1
16.6
15.3
13.2
6.00
5.32
4.77
7.24
6.42
5.76
8.59 10.1 11.6
7.62 8.93 10.3
6.84 8.02 9.29
17.2
16.7
16.1
15.5
14.8
20.2
19.8
19.3
18.6
18.0
23.2
22.8
22.3
21.8
21.1
26.2
25.8
25.4
24.9
24.3
29.2
28.9
28.5
28.0
27.4
32.1
31.9
31.5
31.0
30.5
35.1
34.8
34.5
34.1
33.6
14.1
13.4
12.8
12.1
11.0
17.3
16.6
15.9
15.2
13.9
20.5
19.8
19.0
18.3
16.9
23.6
23.0
22.2
21.5
20.0
26.8
26.1
25.4
24.7
23.2
29.9
29.3
28.6
27.9
26.4
33.1
32.5
31.8
31.1
29.7
15.6
14.4
13.3
12.4
10.8
18.6
17.3
16.1
15.0
13.2
21.8
20.4
19.1
17.9
15.7
25.0
23.5
22.1
20.8
18.5
28.2
26.7
25.2
23.8
21.3
9.53 11.7 14.0
8.51 10.5 12.6
7.68 9.45 11.4
16.5
14.9
13.5
19.2
17.3
15.8
7.57
6.75
6.08
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
ECCENTRICALLY LOADED BOLT GROUPS
8 - 71
Table 8-23 (cont.).
Coefficients C for Eccentrically Loaded Bolt Groups
Angle = 15°°
C req =
Pu
φ rn
or φ R n = C × φrn
ex
Pu
where
s
15°
s, in.
3
6
e
s
s
Pu
= factored force, kips
φ rn = design strength per bolt, kips
φ R n = design strength of bolt group, kips
e
= eccentricity of Pu with respect to centroid
of bolt group, in. (not tabulated, may be
determined by geometry.)
e x = horizontal component of e, in.
s
= bolt spacing, in.
C
= coefficient tabulated below.
6
6
12
Number of bolts in one vertical row, n
ex,
in.
1
2
3
4
5
6
7
8
9
10
11
12
2
3
4
5
6
2.22
1.97
1.77
1.61
1.47
4.62
4.13
3.72
3.38
3.10
7.25
6.53
5.91
5.39
4.93
10.1
9.13
8.31
7.60
6.98
13.0
11.9
10.9
10.1
9.28
16.0
14.9
13.7
12.7
11.8
19.0
17.9
16.7
15.5
14.4
22.1
20.9
19.7
18.4
17.2
25.1
24.0
22.7
21.4
20.2
28.2
27.1
25.8
24.5
23.2
31.2
30.1
28.9
27.6
26.2
34.2
33.2
32.0
30.7
29.3
7
8
9
10
12
1.35
1.25
1.16
1.08
0.94
2.85
2.63
2.44
2.28
2.00
4.54
4.21
3.91
3.65
3.20
6.45
5.98
5.57
5.21
4.59
8.59 10.9
7.98 10.2
7.45 9.51
6.97 8.92
6.16 7.91
13.5
12.6
11.8
11.1
9.84
16.1
15.1
14.2
13.4
11.9
19.0
17.8
16.8
15.9
14.2
21.9
20.7
19.5
18.5
16.6
24.9
23.6
22.4
21.2
19.2
27.9
26.6
25.3
24.1
21.9
14
16
18
20
24
0.83
0.74
0.66
0.60
0.50
1.77
1.58
1.43
1.30
1.10
2.85
2.56
2.31
2.11
1.79
4.09
3.68
3.34
3.05
2.59
5.50
4.96
4.51
4.13
3.52
7.08
6.40
5.83
5.34
4.56
8.84 10.8 12.8
8.00 9.75 11.7
7.30 8.91 10.7
6.70 8.19 9.82
5.74 7.03 8.45
15.0
13.7
12.6
11.6
10.0
17.4
15.9
14.6
13.5
11.7
19.9
18.2
16.8
15.5
13.4
28
32
36
0.43
0.38
0.34
0.95
0.84
0.75
1.55
1.37
1.22
2.25
1.99
1.78
3.06
2.70
2.42
3.98
3.52
3.15
5.01
4.43
3.98
2
3
4
5
6
2.22
1.97
1.77
1.61
1.47
4.97
4.50
4.10
3.75
3.45
7.97
7.40
6.84
6.32
5.86
11.0
10.5
9.82
9.20
8.61
7
8
9
10
12
1.35
1.25
1.16
1.08
0.94
3.18
2.95
2.75
2.57
2.26
5.44
5.07
4.73
4.44
3.93
8.06 11.0
7.55 10.4
7.09 9.78
6.67 9.26
5.96 8.33
14
16
18
20
24
0.83
0.74
0.66
0.60
0.50
2.01
1.81
1.64
1.50
1.28
3.52
3.18
2.90
2.65
2.27
5.37
4.87
4.45
4.10
3.52
7.55
6.88
6.31
5.81
5.01
9.97 12.7
9.13 11.7
8.40 10.8
7.77 9.99
6.74 8.71
28
32
36
0.43
0.38
0.34
1.11
0.98
0.88
1.98
1.75
1.57
3.08
2.73
2.45
4.40
3.91
3.52
5.93
5.29
4.77
14.1
13.5
12.9
12.3
11.6
6.15
5.45
4.89
7.40
6.57
5.90
8.77 10.2 11.8
7.79 9.12 10.5
7.01 8.20 9.49
17.1
16.6
16.0
15.4
14.7
20.1
19.7
19.1
18.5
17.8
23.1
22.7
22.2
21.6
20.9
26.1
25.7
25.2
24.7
24.1
29.1
28.7
28.3
27.8
27.2
32.1
31.7
31.3
30.8
30.3
35.0
34.7
34.3
33.9
33.3
14.0
13.3
12.7
12.1
11.0
17.1
16.4
15.7
15.1
13.8
20.3
19.5
18.8
18.1
16.8
23.4
22.7
22.0
21.3
19.8
26.5
25.8
25.1
24.4
23.0
29.6
29.0
28.3
27.6
26.1
32.7
32.1
31.4
30.7
29.3
15.5
14.4
13.3
12.4
10.9
18.5
17.2
16.1
15.0
13.2
21.5
20.2
18.9
17.8
15.8
24.7
23.2
21.9
20.7
18.4
27.8
26.4
25.0
23.6
21.2
9.62 11.8 14.1
8.62 10.6 12.7
7.80 9.59 11.5
16.5
15.0
13.6
19.1
17.4
15.9
7.69
6.87
6.20
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
8 - 72
BOLTS, WELDS, AND CONNECTED ELEMENTS
Table 8-23 (cont.).
Coefficients C for Eccentrically Loaded Bolt Groups
Angle = 30°°
C req =
Pu
φrn
or φR n = C × φ rn
ex
Pu
where
s, in.
3
6
s
30°
s
Pu
= factored force, kips
φ rn = design strength per bolt, kips
φ R n = design strength of bolt group, kips
e
= eccentricity of Pu with respect to centroid
of bolt group, in. (not tabulated, may be
determined by geometry.)
e x = horizontal component of e, in.
s
= bolt spacing, in.
C
= coefficient tabulated below.
s
e
6
6
12
Number of bolts in one vertical row, n
ex,
in.
1
2
3
4
5
6
7
8
9
10
11
12
2
3
4
5
6
2.40
2.15
1.94
1.76
1.61
4.89
4.40
3.99
3.65
3.35
7.53
6.84
6.24
5.74
5.29
10.3
9.45
8.69
8.02
7.42
13.2
12.2
11.3
10.5
9.72
16.1
15.1
14.0
13.1
12.2
19.1
18.0
16.9
15.8
14.8
22.1
21.0
19.8
18.7
17.6
25.1
24.0
22.8
21.6
20.4
28.1
27.0
25.8
24.6
23.4
31.1
30.0
28.8
27.6
26.3
34.1
33.0
31.9
30.6
29.3
7
8
9
10
12
1.49
1.37
1.28
1.19
1.04
3.10
2.87
2.67
2.49
2.19
4.90
4.55
4.24
3.97
3.50
6.89
6.42
6.00
5.63
4.98
9.06 11.4
8.47 10.7
7.94 10.1
7.47 9.49
6.64 8.48
13.9
13.1
12.4
11.7
10.5
16.6
15.6
14.8
14.0
12.6
19.3
18.3
17.4
16.5
14.9
22.2
21.1
20.0
19.1
17.3
25.1
23.9
22.8
21.8
19.9
28.1
26.9
25.7
24.6
22.5
14
16
18
20
24
0.92
0.82
0.74
0.67
0.56
1.95
1.75
1.58
1.44
1.22
3.12
2.81
2.55
2.33
1.98
4.46
4.03
3.66
3.35
2.86
5.97
5.40
4.92
4.52
3.87
7.64
6.93
6.33
5.82
5.00
9.46 11.4
8.61 10.4
7.89 9.59
7.27 8.85
6.26 7.65
13.6
12.4
11.4
10.6
9.16
15.8
14.5
13.4
12.4
10.8
18.2
16.7
15.5
14.4
12.5
20.7
19.1
17.7
16.4
14.4
28
32
36
0.48
0.42
0.38
1.06
0.93
0.83
1.72
1.52
1.36
2.49
2.20
1.97
3.37
2.99
2.68
4.37
3.88
3.48
5.48
4.87
4.38
2
3
4
5
6
2.40
2.15
1.94
1.76
1.61
5.11
4.66
4.26
3.92
3.63
8.05
7.51
6.99
6.52
6.09
11.1
10.5
9.90
9.34
8.80
7
8
9
10
12
1.49
1.37
1.28
1.19
1.04
3.38
3.15
2.95
2.77
2.45
5.70
5.35
5.03
4.74
4.23
8.30 11.1
7.83 10.6
7.40 10.0
7.00 9.54
6.30 8.67
14
16
18
20
24
0.92
0.82
0.74
0.67
0.56
2.19
1.98
1.80
1.65
1.41
3.81
3.45
3.16
2.90
2.49
5.71
5.22
4.79
4.42
3.82
7.92 10.4
7.27 9.58
6.71 8.88
6.22 8.26
5.41 7.22
28
32
36
0.48
0.42
0.38
1.23
1.08
0.97
2.18
1.93
1.73
3.43
2.99
2.69
4.78
4.26
3.85
14.1
13.5
12.9
12.3
11.7
6.71
5.97
5.38
8.06
7.18
6.47
9.51 11.1
8.49 9.91
7.66 8.95
12.8
11.4
10.3
17.1
16.5
16.0
15.3
14.7
20.1
19.6
19.0
18.4
17.7
23.0
22.6
22.0
21.5
20.8
26.0
25.6
25.1
24.5
23.9
29.0
28.6
28.1
27.6
27.0
32.0
31.6
31.1
30.6
30.0
34.9
34.6
34.1
33.6
33.1
14.1
13.5
12.9
12.3
11.3
17.1
16.5
15.8
15.2
14.1
20.2
19.5
18.8
18.2
17.0
23.2
22.6
21.9
21.2
19.9
26.3
25.7
25.0
24.3
23.0
29.4
28.7
28.1
27.4
26.0
32.5
31.8
31.2
30.5
29.1
13.0
12.1
11.2
10.5
9.23
15.8
14.8
13.8
12.9
11.5
18.7
17.6
16.5
15.5
13.8
21.7
20.5
19.3
18.2
16.4
24.7
23.4
22.2
21.1
19.0
27.8
26.4
25.2
24.0
21.8
8.22 10.3 12.4
7.40 9.25 11.3
6.71 8.41 10.3
14.8
13.4
12.3
17.2
15.7
14.4
19.8
18.2
16.7
6.40
5.73
5.18
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
ECCENTRICALLY LOADED BOLT GROUPS
8 - 73
Table 8-23 (cont.).
Coefficients C for Eccentrically Loaded Bolt Groups
Angle = 45°°
C req =
Pu
φ rn
or φ R n = C × φrn
ex
Pu
where
3
6
s
s
e
s, in.
45°
s
Pu
= factored force, kips
φ rn = design strength per bolt, kips
φ R n = design strength of bolt group, kips
e
= eccentricity of Pu with respect to centroid
of bolt group, in. (not tabulated, may be
determined by geometry.)
e x = horizontal component of e, in.
s
= bolt spacing, in.
C
= coefficient tabulated below.
6
6
12
Number of bolts in one vertical row, n
ex,
in.
1
2
3
4
5
6
7
8
9
10
11
12
2
3
4
5
6
2.64
2.43
2.23
2.05
1.89
5.30
4.90
4.52
4.17
3.86
8.01
7.44
6.89
6.40
5.96
10.8
10.1
9.38
8.75
8.20
13.6
12.8
12.0
11.2
10.6
16.4
15.6
14.7
13.9
13.1
19.3
18.4
17.5
16.6
15.7
22.3
21.3
20.3
19.3
18.4
25.2
24.2
23.2
22.2
21.2
28.1
27.2
26.1
25.0
23.99
31.1
30.1
29.0
27.9
26.9
34.0
33.1
32.0
30.9
29.8
7
8
9
10
12
1.75
1.63
1.52
1.42
1.25
3.59
3.35
3.13
2.94
2.60
5.57
5.22
4.90
4.61
4.11
7.70
7.25
6.83
6.45
5.78
9.99
9.43
8.91
8.44
7.60
12.4
11.7
11.1
10.6
9.58
14.9
14.2
13.5
12.8
11.7
17.5
16.7
15.9
15.2
14.0
20.2
19.3
18.5
17.7
16.3
23.0
22.1
21.2
20.3
18.8
25.8
24.8
23.9
23.0
21.3
28.7
27.7
26.7
25.7
23.9
14
16
18
20
24
1.11
0.99
0.90
0.81
0.68
2.32
2.09
1.90
1.73
1.47
3.69
3.34
3.04
2.79
2.38
5.21
4.74
4.33
3.98
3.42
6.90
6.29
5.77
5.33
4.60
8.73 10.7
8.00 9.85
7.36 9.10
6.81 8.44
5.91 7.35
12.8
11.8
10.96
10.2
8.91
15.0
13.9
12.9
12.1
10.6
17.4
16.1
15.0
14.1
12.4
19.8
18.5
17.3
16.2
14.3
22.3
20.9
19.5
18.4
16.3
28
32
36
0.59
0.52
0.46
1.28
1.13
1.01
2.08
1.84
1.65
2.99
2.65
2.38
4.03
3.59
3.23
5.20
4.63
4.17
12.8
11.6
10.5
14.6
13.3
12.1
2
3
4
5
6
2.64
2.43
2.23
2.05
1.89
5.38
5.02
4.67
4.34
4.06
8.22
7.78
7.33
6.90
6.50
11.1
10.7
10.2
9.66
9.19
14.1
13.6
13.1
12.5
12.0
17.0
16.6
16.0
15.5
14.9
20.0
19.5
19.0
18.4
17.9
22.97
22.5
22.0
21.4
20.9
25.9
25.5
25.0
24.4
23.9
28.9
28.5
28.0
27.4
26.9
31.9
31.4
31.0
30.4
29.9
34.8
34.4
34.0
33.4
32.9
7
8
9
10
12
1.75
1.63
1.52
1.42
1.25
3.80
3.57
3.36
3.17
2.84
6.16
5.84
5.54
5.27
4.78
8.76
8.36
7.99
7.63
6.99
11.5
11.1
10.6
10.2
9.40
14.4
13.9
13.4
12.9
12.0
17.3
16.8
16.2
15.7
14.7
20.3
19.7
19.2
18.6
17.6
23.3
22.7
22.1
21.5
20.4
26.3
25.7
25.1
24.5
23.4
29.3
28.7
28.1
27.5
26.3
32.3
31.7
31.1
30.5
29.3
14
16
18
20
24
1.11
0.99
0.90
0.81
0.68
2.57
2.33
2.13
1.96
1.68
4.36
3.99
3.68
3.40
2.95
6.42
5.92
5.49
5.10
4.46
8.70 11.2
8.09 10.5
7.54 9.80
7.05 9.21
6.22 8.19
13.8
13.0
12.2
11.6
10.4
16.6
15.7
14.8
14.0
12.7
19.4
18.4
17.5
16.6
15.1
22.3
21.2
20.3
19.3
17.7
25.2
24.1
23.1
22.1
20.3
28.2
27.1
26.0
24.9
23.0
28
32
36
0.59
0.52
0.46
1.47
1.31
1.17
2.59
2.31
2.08
3.95
3.54
3.20
5.55
4.99
4.54
9.34 11.5 13.8
8.49 10.5 12.7
7.77 9.64 11.7
16.2
14.9
13.8
18.7
17.3
16.1
21.3
19.8
18.5
7.35
6.65
6.06
6.49
5.80
5.23
7.90
7.07
6.40
9.42 11.1
8.46 9.95
7.67 9.04
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
8 - 74
BOLTS, WELDS, AND CONNECTED ELEMENTS
Table 8-23 (cont.).
Coefficients C for Eccentrically Loaded Bolt Groups
Angle = 60°°
C req =
Pu
φrn
or φR n = C × φ rn
ex
where
3
6
s
60°
s
e
s, in.
Pu
s
Pu
= factored force, kips
φ rn = design strength per bolt, kips
φ R n = design strength of bolt group, kips
e
= eccentricity of Pu with respect to centroid
of bolt group, in. (not tabulated, may be
determined by geometry.)
e x = horizontal component of e, in.
s
= bolt spacing, in.
C
= coefficient tabulated below.
6
6
12
Number of bolts in one vertical row, n
ex,
in.
1
2
3
4
5
6
7
8
9
10
11
12
2
3
4
5
6
2.83
2.72
2.59
2.46
2.32
5.64
5.43
5.18
4.92
4.66
8.45
8.13
7.77
7.40
7.03
11.3
10.8
10.4
9.92
9.46
14.1
13.6
13.0
12.5
12.0
16.9
16.3
15.7
15.1
14.5
19.8
19.1
18.5
17.8
17.1
22.6
21.9
21.2
20.5
19.8
25.5
24.8
24.0
23.2
22.5
28.4
27.6
26.8
26.0
25.2
31.3
30.5
29.7
28.9
28.0
34.2
33.4
32.5
31.7
30.8
7
8
9
10
12
2.19
2.07
1.95
1.84
1.65
4.41
4.17
3.95
3.74
3.38
6.68
6.35
6.04
5.75
5.22
9.02
8.61
8.22
7.86
7.19
11.4
11.0
10.5
10.1
9.28
13.9
13.4
12.9
12.4
11.5
16.5
15.9
15.3
14.8
13.8
19.1
18.4
17.8
17.3
16.2
21.8
21.1
20.4
19.8
18.6
24.5
23.7
23.0
22.4
21.1
27.2
26.5
25.7
25.0
23.7
30.0
29.2
28.5
27.7
26.3
14
16
18
20
24
1.49
1.35
1.23
1.12
0.95
3.06
2.79
2.55
2.35
2.02
4.76
4.37
4.02
3.72
3.22
6.61
6.09
5.64
5.24
4.57
8.58 10.7
7.95 9.93
7.39 9.28
6.90 8.69
6.06 7.68
12.9
12.0
11.3
10.6
9.43
15.2
14.2
13.4
12.6
11.3
17.5
16.5
15.6
14.8
13.3
20.0
18.9
17.9
17.0
15.4
22.5
21.3
20.3
19.3
17.5
25.0
23.8
22.7
21.7
19.8
28
32
36
0.83
0.73
0.65
1.76
1.56
1.40
2.84
2.53
2.27
4.04
3.61
3.26
5.39
4.84
4.38
12.0
11.0
10.1
14.0
12.8
11.7
16.0
14.7
13.5
18.1
16.7
15.4
2
3
4
5
6
2.83
2.72
2.59
2.46
2.32
5.64
5.44
5.21
4.97
4.73
8.47
8.19
7.88
7.57
7.27
11.3
11.0
10.6
10.3
9.91
14.2
13.8
13.4
13.1
12.7
17.1
16.7
16.3
15.9
15.5
20.0
19.6
19.2
18.8
18.3
23.0
22.6
22.1
21.7
21.2
25.9
25.5
25.0
24.6
24.1
28.9
28.4
28.0
27.5
27.0
31.8
31.4
30.9
30.4
30.0
34.8
34.3
33.9
33.4
33.0
7
8
9
10
12
2.19
2.07
1.95
1.84
1.65
4.51
4.29
4.09
3.90
3.56
6.97
6.69
6.43
6.18
5.73
9.56
9.23
8.92
8.63
8.08
12.3
11.9
11.5
11.2
10.6
15.0
14.6
14.3
13.9
13.2
17.9
17.5
17.0
16.6
15.9
20.8
20.3
19.9
19.5
18.7
23.7
23.2
22.8
22.3
21.5
26.6
26.1
25.6
25.2
24.3
29.5
29.0
28.6
28.1
27.2
32.4
32.0
31.5
31.0
30.1
14
16
18
20
24
1.49
1.35
1.23
1.12
0.95
3.27
3.01
2.78
2.58
2.25
5.32
4.95
4.63
4.34
3.84
7.59 10.0
7.13 9.48
6.71 8.98
6.33 8.52
5.67 7.70
12.6
12.0
11.4
10.9
9.91
15.2
14.5
13.9
13.3
12.3
17.9
17.2
16.5
15.9
14.7
20.7
19.9
19.2
18.5
17.3
23.5
22.7
22.0
21.2
19.9
26.3
25.5
24.7
24.0
22.6
29.2
28.4
27.6
27.0
25.3
28
32
36
0.83
0.73
0.65
1.98
1.77
1.60
3.43
3.09
2.81
5.11
4.64
4.24
9.08 11.3 13.7
8.36 10.5 12.7
7.73 9.74 11.9
16.1
15.1
14.2
18.7
17.5
16.5
21.3
20.1
19.0
23.9
22.6
21.5
7.00
6.40
5.89
6.86
6.19
5.62
8.47 10.2
7.66 9.26
6.98 8.46
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
ECCENTRICALLY LOADED BOLT GROUPS
8 - 75
Table 8-23 (cont.).
Coefficients C for Eccentrically Loaded Bolt Groups
Angle = 75°°
C req =
Pu
φ rn
or φ R n = C × φrn
ex
where
3
6
s
s
e
s, in.
75° P
u
s
Pu
= factored force, kips
φ rn = design strength per bolt, kips
φ R n = design strength of bolt group, kips
e
= eccentricity of Pu with respect to centroid
of bolt group, in. (not tabulated, may be
determined by geometry.)
e x = horizontal component of e, in.
s
= bolt spacing, in.
C
= coefficient tabulated below.
6
6
12
Number of bolts in one vertical row, n
ex,
in.
1
2
3
4
5
6
7
8
9
10
11
12
2
3
4
5
6
2.92
2.89
2.86
2.82
2.77
5.83
5.77
5.70
5.61
5.51
8.73
8.63
8.51
8.38
8.23
11.6
11.5
11.3
11.1
10.9
14.5
14.3
14.1
13.9
13.6
17.4
17.2
16.9
16.6
16.3
20.3
20.0
19.7
19.4
19.0
23.1
22.8
22.5
22.1
21.8
26.0
25.7
25.3
24.9
24.5
28.9
28.5
28.1
27.7
27.2
31.8
31.4
30.9
30.5
30.0
34.7
34.2
33.7
33.3
32.8
7
8
9
10
12
2.72
2.66
2.60
2.53
2.40
5.40
5.29
5.16
5.04
4.78
8.06
7.89
7.71
7.53
7.16
10.7
10.5
10.3
10.1
9.57
13.4
13.1
12.8
12.6
12.0
16.0
15.7
15.4
15.1
14.5
18.7
18.3
18.0
17.7
17.0
21.4
21.0
20.6
20.3
19.6
24.1
23.7
23.3
22.9
22.1
26.8
26.4
26.0
25.6
24.8
29.6
29.1
28.7
28.3
27.4
32.3
31.9
31.4
31.0
30.1
14
16
18
20
24
2.26
2.13
2.00
1.89
1.67
4.52
4.27
4.03
3.81
3.41
6.80
6.45
6.12
5.80
5.24
9.12
8.68
8.27
7.88
7.18
11.5
11.0
10.5
10.1
9.22
13.9
13.3
12.8
12.3
11.4
16.4
15.8
15.2
14.6
13.6
18.9
18.2
17.6
17.0
15.9
21.4
20.7
20.1
19.4
18.2
24.0
23.3
22.6
21.9
20.7
26.6
25.9
25.1
24.4
23.1
29.3
28.5
27.7
27.0
25.6
28
32
36
1.49
1.34
1.21
3.06
2.77
2.52
4.75
4.33
3.97
6.56
6.02
5.56
12.6
11.8
11.1
14.9
13.9
13.1
17.1
16.1
15.2
19.5
18.4
17.4
21.9
20.7
19.7
24.3
23.1
22.0
2
3
4
5
6
2.92
2.89
2.86
2.82
2.77
5.82
5.76
5.68
5.59
5.49
8.71
8.60
8.47
8.34
8.19
11.6
11.4
11.3
11.1
10.9
14.5
14.3
14.1
13.9
13.7
17.4
17.1
16.9
16.7
16.4
20.3
20.0
19.8
19.5
19.2
23.5
22.9
22.6
22.4
22.1
26.4
25.8
25.5
25.2
24.9
29.3
28.7
28.4
28.1
27.8
32.3
31.7
31.3
31.0
30.7
35.2
34.6
34.2
33.9
33.6
7
8
9
10
12
2.72
2.66
2.60
2.53
2.40
5.39
5.27
5.16
5.04
4.81
8.04
7.89
7.74
7.58
7.27
10.7
10.5
10.4
10.2
9.81
13.4
13.2
13.0
12.8
12.4
16.2
16.0
15.8
15.5
15.1
19.0
18.8
18.5
18.3
17.8
21.8
21.6
21.3
21.0
20.6
24.6
24.4
24.1
23.9
23.3
27.5
27.2
27.0
26.7
26.2
30.4
30.1
29.8
29.5
29.0
33.3
33.0
32.7
32.4
31.8
14
16
18
20
24
2.26
2.13
2.00
1.89
1.67
4.57
4.35
4.13
3.93
3.57
6.97
6.69
6.41
6.15
5.67
9.47
9.13
8.82
8.51
7.95
12.0
11.7
11.3
11.0
10.4
14.7
14.3
13.9
13.5
12.9
17.4
16.9
16.5
16.1
15.4
20.1
19.6
19.2
18.8
18.0
22.9
22.4
21.9
21.5
20.7
25.6
25.1
24.7
24.2
23.4
28.4
27.9
27.4
27.0
26.1
31.3
30.7
30.2
29.8
28.8
28
32
36
1.49
1.34
1.21
3.25
2.97
2.73
5.25
4.87
4.54
7.44
6.98
6.56
9.77 12.2
9.23 11.6
8.74 11.1
14.7
14.1
13.5
17.3
16.6
16.0
19.9
19.2
18.5
22.6
21.8
21.1
25.3
24.5
23.7
28.0
27.2
26.4
8.49 10.5
7.84 9.77
7.27 9.10
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
8 - 76
BOLTS, WELDS, AND CONNECTED ELEMENTS
Table 8-24.
Coefficients C for Eccentrically Loaded Bolt Groups
Angle = 0°°
C req =
Pu
φrn
or φR n = C × φ rn
ex = e
where
s, in.
3
6
s
Pu
s
s
Pu
= factored force, kips
φ rn = design strength per bolt, kips
φ R n = design strength of bolt group, kips
e
= eccentricity of Pu with respect to centroid
of bolt group, in. (not tabulated, may be
determined by geometry.)
e x = horizontal component of e, in.
s
= bolt spacing, in.
C
= coefficient tabulated below.
3
3
3
9
Number of bolts in one vertical row, n
ex,
in.
1
2
2
3
4
5
6
2.60
2.23
1.94
1.69
1.49
5.70
4.92
4.30
3.79
3.37
9.24 13.2
8.05 11.7
7.09 10.4
6.30 9.29
5.65 8.37
7
8
9
10
12
1.32
1.18
1.07
0.98
0.83
3.03
2.74
2.50
2.29
1.96
5.10
4.63
4.24
3.89
3.34
7.59 10.4
6.92 9.56
6.35 8.81
5.86 8.15
5.06 7.06
14
16
18
20
24
0.73
0.65
0.58
0.53
0.44
1.72
1.52
1.37
1.24
1.04
2.92
2.59
2.33
2.11
1.78
4.44
3.95
3.55
3.23
2.72
6.21
5.54
4.99
4.53
3.83
8.27 10.6 13.2
7.39 9.48 11.9
6.67 8.57 10.7
6.07 7.81 9.77
5.14 6.62 8.30
28
32
36
0.38
0.34
0.30
0.90
0.79
0.71
1.54
1.36
1.21
2.35
2.07
1.85
3.31
2.91
2.60
4.45
3.92
3.50
2
3
4
5
6
2.60
2.23
1.94
1.69
1.49
6.48
5.75
5.12
4.58
4.13
10.7
9.79
8.91
8.10
7.37
7
8
9
10
12
1.32
1.18
1.07
0.98
0.83
3.74
3.41
3.13
2.89
2.50
6.74 10.5
6.20 9.73
5.73 9.05
5.31 8.45
4.63 7.43
14
16
18
20
24
0.73
0.65
0.58
0.53
0.44
2.19
1.95
1.76
1.60
1.35
4.09
3.65
3.29
2.99
2.53
6.60
5.93
5.37
4.90
4.16
9.53 12.9
8.59 11.7
7.81 10.8
7.15 9.85
6.10 8.44
28
32
36
0.38
0.34
0.30
1.17
1.03
0.92
2.19
1.93
1.72
3.61
3.19
2.85
5.31
4.69
4.20
3
4
14.9
14.0
13.1
12.2
11.3
5
6
7
8
9
10
11
12
17.3
15.6
14.0
12.6
11.5
21.4
19.7
18.0
16.4
14.9
25.6
23.9
22.1
20.3
18.7
29.7
28.1
26.3
24.4
22.7
33.8
32.3
30.5
28.6
26.7
37.9
36.5
34.7
32.9
30.9
41.9
40.6
38.9
37.1
35.2
45.9
44.7
43.1
41.4
39.4
13.7
12.6
11.6
10.8
9.37
17.2
15.9
14.7
13.7
12.0
21.0
19.5
18.1
16.9
14.9
24.9
23.3
21.7
20.3
17.9
29.0
27.3
25.6
24.1
21.3
33.2
31.4
29.6
27.9
24.9
37.5
35.5
33.7
31.9
28.6
16.0
14.4
13.1
11.9
10.2
19.1
17.2
15.7
14.3
12.2
22.4
20.2
18.4
16.9
14.4
25.8
23.4
21.4
19.6
16.8
5.73
5.05
4.51
7.20
6.35
5.68
8.82 10.6 12.6
7.79 9.38 11.1
6.96 8.39 9.95
14.7
13.0
11.6
18.9
18.2
17.4
16.5
15.5
23.0
22.3
21.6
20.7
19.7
27.0
26.4
25.7
24.9
24.0
31.0
30.5
29.9
29.1
28.3
34.9
34.5
33.9
33.2
32.5
38.9
38.5
38.0
37.4
36.7
42.9
42.5
42.0
41.4
40.8
46.8
46.5
46.1
45.5
44.9
14.5
13.6
12.8
12.1
10.7
18.8
17.8
16.9
16.0
14.3
23.1
22.1
21.1
20.1
18.3
27.4
26.4
25.4
24.4
22.5
31.6
30.6
29.7
28.7
26.7
35.8
34.9
34.0
33.0
31.0
40.0
39.1
38.3
37.3
35.3
44.1
43.3
42.5
41.5
39.6
16.7
15.2
14.0
12.9
11.1
20.6
19.0
17.5
16.2
14.0
24.7
22.9
21.3
19.8
17.3
29.0
27.1
25.3
23.6
20.8
33.3
31.3
29.4
27.6
24.5
37.6
35.5
33.6
31.7
28.3
9.69 12.3 15.2
8.61 11.0 13.6
7.73 9.89 12.3
18.4
16.5
14.9
21.8
19.6
17.8
25.3
22.9
20.8
7.37
6.53
5.85
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
ECCENTRICALLY LOADED BOLT GROUPS
8 - 77
Table 8-24 (cont.).
Coefficients C for Eccentrically Loaded Bolt Groups
Angle = 15°°
C req =
Pu
φ rn
or φ R n = C × φrn
ex
Pu
where
s
15°
s, in.
3
6
e
s
s
Pu
= factored force, kips
φ rn = design strength per bolt, kips
φ R n = design strength of bolt group, kips
e
= eccentricity of Pu with respect to centroid
of bolt group, in. (not tabulated, may be
determined by geometry.)
e x = horizontal component of e, in.
s
= bolt spacing, in.
C
= coefficient tabulated below.
3
3
3
9
Number of bolts in one vertical row, n
ex,
in.
1
2
3
4
5
6
7
8
9
10
11
12
2
3
4
5
6
2.68
2.30
1.99
1.74
1.53
5.77
5.00
4.38
3.88
3.45
9.31
8.17
7.22
6.43
5.77
13.2
11.7
10.4
9.37
8.47
17.2
15.6
14.1
12.8
11.6
21.3
19.6
17.9
16.4
15.0
25.4
23.7
22.0
20.2
18.6
29.5
27.9
26.0
24.2
22.5
33.6
32.0
30.2
28.3
26.6
37.7
36.2
34.4
32.5
30.6
41.7
40.2
38.5
36.7
34.8
45.7
44.3
42.7
40.9
39.0
7
8
9
10
12
1.36
1.22
1.11
1.01
0.86
3.10
2.81
2.57
2.36
2.02
5.21
4.74
4.34
4.00
3.44
7.71 10.6
7.05 9.70
6.48 8.95
5.98 8.29
5.18 7.21
13.7
12.7
11.8
10.9
9.52
17.2
15.9
14.8
13.8
12.2
20.9
19.5
18.1
17.0
15.0
24.8
23.2
21.7
20.4
18.1
28.8
27.1
25.5
24.0
21.4
32.9
31.1
29.4
27.7
24.9
37.1
35.2
33.4
31.6
28.5
14
16
18
20
24
0.75
0.67
0.60
0.54
0.46
1.77
1.57
1.41
1.28
1.08
3.01
2.68
2.40
2.18
1.84
4.55
4.05
3.65
3.32
2.80
6.36
5.67
5.12
4.66
3.94
8.43 10.8 13.3
7.54 9.66 12.0
6.81 8.74 10.9
6.21 7.98 9.95
5.26 6.78 8.47
16.1
14.6
13.3
12.1
10.4
19.2
17.3
15.8
14.5
12.4
22.4
20.3
18.6
17.1
14.6
25.8
23.5
21.5
19.8
17.0
28
32
36
0.40
0.35
0.31
0.93
0.82
0.73
1.59
1.40
1.25
2.43
2.14
1.91
3.41
3.00
2.68
4.56
4.03
3.60
12.8
11.3
10.2
14.9
13.2
11.9
2
3
4
5
6
2.68
2.30
1.99
1.74
1.53
6.48
5.75
5.13
4.61
4.17
10.6
9.75
8.91
8.14
7.45
7
8
9
10
12
1.36
1.22
1.11
1.01
0.86
3.79
3.46
3.19
2.94
2.55
6.84 10.4
6.30 9.71
5.83 9.05
5.42 8.47
4.73 7.47
14
16
18
20
24
0.75
0.67
0.60
0.54
0.46
2.24
2.00
1.80
1.64
1.39
4.18
3.74
3.38
3.08
2.60
6.66
6.00
5.45
4.98
4.25
9.62 12.9
8.71 11.8
7.94 10.8
7.28 9.92
6.23 8.54
28
32
36
0.40
0.35
0.31
1.20
1.06
0.94
2.26
1.99
1.78
3.69
3.26
2.92
5.43
4.81
4.31
14.7
13.9
13.0
12.1
11.2
5.89
5.19
4.65
7.37
6.51
5.83
9.02 10.9
7.98 9.59
7.15 8.59
18.8
18.1
17.2
16.3
15.3
22.9
22.2
21.4
20.5
19.5
26.9
26.3
25.5
24.7
23.7
30.9
30.3
29.7
28.9
27.9
34.9
34.4
33.7
33.0
32.2
38.8
38.3
37.7
37.1
36.3
42.8
42.4
41.8
41.2
40.4
46.7
46.3
45.8
45.2
44.5
14.5
13.6
12.8
12.1
10.7
18.6
17.6
16.8
15.9
14.3
22.8
21.8
20.9
20.0
18.2
27.0
26.0
25.1
24.1
22.2
31.3
30.3
29.3
28.3
26.4
35.4
34.5
33.5
32.6
30.6
39.6
38.7
37.8
36.8
34.8
43.7
42.9
42.0
41.0
39.1
16.6
15.2
14.0
13.0
11.2
20.5
18.9
17.5
16.2
14.1
24.5
22.8
21.2
19.8
17.3
28.6
26.8
25.1
23.5
20.8
32.9
30.9
29.1
27.4
24.4
37.1
35.1
33.2
31.4
28.1
9.85 12.5
8.77 11.1
7.89 10.0
15.4
13.8
12.5
18.5
16.6
15.1
21.8
19.7
17.9
25.3
22.9
20.9
7.48
6.65
5.97
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
8 - 78
BOLTS, WELDS, AND CONNECTED ELEMENTS
Table 8-24 (cont.).
Coefficients C for Eccentrically Loaded Bolt Groups
Angle = 30°°
C req =
Pu
φrn
or φR n = C × φ rn
ex
Pu
s
where
s, in.
3
6
30°
s
Pu
= factored force, kips
φ rn = design strength per bolt, kips
φ R n = design strength of bolt group, kips
e
= eccentricity of Pu with respect to centroid
of bolt group, in. (not tabulated, may be
determined by geometry.)
e x = horizontal component of e, in.
s
= bolt spacing, in.
C
= coefficient tabulated below.
s
e
3
3
3
9
Number of bolts in one vertical row, n
ex,
in.
1
2
2
3
4
5
6
2.90
2.50
2.18
1.91
1.69
6.06
5.31
4.70
4.18
3.75
9.59 13.4
8.52 12.1
7.62 10.9
6.85 9.86
6.19 8.98
7
8
9
10
12
1.51
1.36
1.23
1.13
0.96
3.38
3.07
2.81
2.59
2.23
5.63
5.14
4.73
4.37
3.78
8.21 11.2
7.55 10.3
6.97 9.54
6.46 8.88
5.62 7.78
14
16
18
20
24
0.84
0.74
0.67
0.61
0.51
1.95
1.73
1.56
1.42
1.20
3.32
2.96
2.66
2.42
2.04
4.96
4.43
4.00
3.65
3.09
6.90
6.19
5.60
5.11
4.34
9.08 11.6
8.17 10.4
7.41 9.46
6.77 8.67
5.77 7.41
28
32
36
0.44
0.39
0.35
1.03
0.91
0.81
1.77
1.56
1.39
2.68
2.36
2.11
3.77
3.32
2.97
5.01
4.43
3.97
2
3
4
5
6
2.90
2.50
2.18
1.91
1.69
6.59
5.88
5.30
4.81
4.38
10.6
9.83
9.05
8.35
7.72
7
8
9
10
12
1.51
1.36
1.23
1.13
0.96
4.01
3.69
3.41
3.16
2.76
7.15 10.7
6.64 10.0
6.19 9.41
5.79 8.85
5.09 7.88
14
16
18
20
24
0.84
0.74
0.67
0.61
0.51
2.44
2.18
1.97
1.80
1.53
4.54
4.08
3.70
3.38
2.87
7.08 10.1
6.41 9.21
5.85 8.45
5.37 7.80
4.61 6.74
28
32
36
0.44
0.39
0.35
1.32
1.17
1.05
2.49
2.20
1.97
4.02
3.57
3.21
3
4
14.7
13.9
13.0
12.3
11.4
5
6
7
8
9
10
11
12
17.3
15.8
14.4
13.2
12.1
21.3
19.8
18.2
16.8
15.5
25.3
23.8
22.1
20.6
19.1
29.4
27.8
26.1
24.5
22.9
33.4
31.9
30.1
28.4
26.8
37.5
35.9
34.2
32.5
30.7
41.4
40.0
38.3
36.6
34.8
45.4
44.0
42.4
40.7
38.9
14.4
13.3
12.4
11.6
10.2
17.8
16.6
15.5
14.6
12.9
21.4
20.0
18.8
17.7
15.8
25.2
23.7
22.3
21.1
18.9
29.1
27.5
26.1
24.7
22.2
33.1
31.4
29.9
28.3
25.7
37.1
35.4
33.7
32.2
29.3
14.2
12.9
11.8
10.8
9.22
17.1
15.5
14.2
13.1
11.2
20.2
18.4
16.9
15.5
13.4
23.4
21.4
19.7
18.2
15.7
26.8
24.6
22.7
21.0
18.2
13.9
12.3
11.1
16.1
14.4
13.0
6.46
5.71
5.12
8.05
7.14
6.40
9.83 11.8
8.72 10.5
7.84 9.41
18.7
18.0
17.1
16.3
15.4
22.7
22.0
21.2
20.4
19.5
26.7
26.1
25.4
24.5
23.6
30.8
30.1
29.4
28.6
27.8
34.7
34.1
33.5
32.7
31.9
38.7
38.2
37.5
36.8
35.9
42.6
42.2
41.5
40.8
40.0
46.6
46.1
45.5
44.9
44.1
14.6
13.8
13.0
12.4
11.2
18.6
17.7
16.9
16.2
14.7
22.7
21.8
20.9
20.1
18.5
26.9
25.9
25.0
24.1
22.4
31.0
30.0
29.1
28.2
26.4
35.1
34.2
33.3
32.4
30.6
39.2
38.3
37.4
36.5
34.6
43.3
42.4
41.6
40.6
38.8
13.4
12.3
11.4
10.5
9.16
17.0
15.7
14.6
13.6
11.9
20.9
19.4
18.1
16.9
14.9
24.7
23.2
21.8
20.4
18.1
28.8
27.1
25.6
24.1
21.5
32.9
31.1
29.4
27.9
25.1
36.9
35.1
33.4
31.8
28.8
8.07 10.5 13.3
7.20 9.45 11.9
6.49 8.55 10.9
16.3
14.6
13.4
19.4
17.6
16.0
22.7
20.7
18.9
26.2
23.9
22.0
5.91
5.26
4.73
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
ECCENTRICALLY LOADED BOLT GROUPS
8 - 79
Table 8-24 (cont.).
Coefficients C for Eccentrically Loaded Bolt Groups
Angle = 45°°
C req =
Pu
φ rn
or φ R n = C × φrn
ex
Pu
s
where
3
6
s
e
s, in.
45°
s
Pu
= factored force, kips
φ rn = design strength per bolt, kips
φ R n = design strength of bolt group, kips
e
= eccentricity of Pu with respect to centroid
of bolt group, in. (not tabulated, may be
determined by geometry.)
e x = horizontal component of e, in.
s
= bolt spacing, in.
C
= coefficient tabulated below.
3
3
3
9
Number of bolts in one vertical row, n
ex,
in.
1
2
3
4
5
6
7
8
9
10
11
12
2
3
4
5
6
3.26
2.87
2.54
2.25
2.01
6.62
5.92
5.31
4.78
4.33
10.2
9.19
8.36
7.63
6.99
13.9
12.7
11.7
10.8
9.94
17.7
16.4
15.2
14.1
13.1
21.6
20.2
18.9
17.6
16.5
25.5
24.0
22.6
21.3
20.1
29.4
27.96
26.5
25.1
23.8
33.4
32.0
30.5
29.0
27.5
37.4
35.9
34.4
32.9
31.4
41.3
39.9
38.4
36.9
35.3
45.3
43.9
42.4
40.8
39.3
7
8
9
10
12
1.81
1.64
1.49
1.37
1.17
3.93
3.60
3.31
3.06
2.65
6.42
5.92
5.49
5.10
4.46
9.20
8.55
7.96
7.44
6.55
12.2
11.4
10.7
10.1
8.93
15.5
14.6
13.7
13.0
11.6
18.9
17.9
16.9
16.0
14.4
22.5
21.3
20.3
19.2
17.5
26.2
24.9
23.8
22.7
20.7
30.0
28.6
27.4
26.2
24.0
33.9
32.4
31.1
29.9
27.5
37.7
36.3
34.9
33.6
31.1
14
16
18
20
24
1.03
0.91
0.82
0.74
0.63
2.33
2.08
1.88
1.71
1.45
3.95
3.54
3.20
2.92
2.48
5.83
5.24
4.75
4.35
3.71
8.00 10.5
7.23 9.47
6.59 8.66
6.04 7.96
5.18 6.84
13.1
12.0
10.9
10.1
8.71
15.9
14.6
13.5
12.5
10.8
19.0
17.5
16.1
15.0
13.0
22.1
20.4
18.9
17.6
15.4
25.4
23.6
21.9
20.5
18.0
28.8
26.8
25.0
23.5
20.7
28
32
36
0.54
0.48
0.43
1.26
1.11
0.99
2.15
1.90
1.69
3.23
2.86
2.56
4.52
4.00
3.59
13.7
12.3
11.2
16.0
14.4
13.1
18.5
16.7
15.2
2
3
4
5
6
3.26
2.87
2.54
2.25
2.01
6.89
6.28
5.74
5.27
4.85
10.8
10.1
9.38
8.75
8.20
7
8
9
10
12
1.81
1.64
1.49
1.37
1.17
4.49
4.16
3.87
3.62
3.19
7.70 11.3
7.25 10.7
6.83 10.2
6.45 9.65
5.78 8.75
14
16
18
20
24
1.03
0.91
0.82
0.74
0.63
2.84
2.56
2.33
2.13
1.82
5.21
4.74
4.33
3.98
3.42
7.97 11.1
7.30 10.3
6.72 9.48
6.21 8.83
5.38 7.74
28
32
36
0.54
0.48
0.43
1.59
1.41
1.26
2.99
2.65
2.38
4.74
4.22
3.81
14.8
14.0
13.3
12.6
11.9
5.99
5.31
4.77
7.65
6.81
6.13
9.50 11.5
8.48 10.3
7.64 9.30
18.7
18.0
17.3
16.5
15.7
22.7
22.0
21.2
20.4
19.7
26.6
26.0
25.3
24.5
23.7
30.6
30.0
29.2
28.5
27.7
34.6
33.9
33.2
32.5
31.7
38.5
37.9
37.2
36.5
35.7
42.5
41.9
41.2
40.5
39.7
46.5
45.9
45.2
44.5
43.8
15.1
14.4
13.8
13.1
12.0
19.0
18.2
17.5
16.9
15.6
22.9
22.2
21.4
20.7
19.3
26.9
26.1
25.4
24.6
23.2
30.9
30.1
29.4
28.5
27.0
34.9
34.1
33.3
32.5
31.0
39.0
38.2
37.4
36.6
35.0
43.0
42.2
41.4
40.6
39.0
14.5
13.5
12.6
11.8
10.4
18.1
16.9
15.9
15.0
13.4
21.8
20.6
19.4
18.4
16.5
25.6
24.3
23.0
21.9
19.8
29.5
28.1
26.7
25.5
23.2
33.4
32.0
30.6
29.2
26.8
37.4
35.9
34.4
33.1
30.5
9.30 12.0 14.9
8.38 10.9 13.6
7.62 9.89 12.5
18.0
16.5
15.2
21.3
19.5
18.0
24.7
22.8
21.1
28.2
26.1
24.3
6.87
6.17
5.59
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
8 - 80
BOLTS, WELDS, AND CONNECTED ELEMENTS
Table 8-24 (cont.).
Coefficients C for Eccentrically Loaded Bolt Groups
Angle = 60°°
C req =
Pu
φrn
or φR n = C × φ rn
ex
where
3
6
s
60°
s
e
s, in.
Pu
s
Pu
= factored force, kips
φ rn = design strength per bolt, kips
φ R n = design strength of bolt group, kips
e
= eccentricity of Pu with respect to centroid
of bolt group, in. (not tabulated, may be
determined by geometry.)
e x = horizontal component of e, in.
s
= bolt spacing, in.
C
= coefficient tabulated below.
3
3
3
9
Number of bolts in one vertical row, n
ex,
in.
1
2
3
4
5
6
7
8
9
10
11
12
2
3
4
5
6
3.63
3.38
3.10
2.84
2.60
7.25
6.77
6.27
5.80
5.36
10.9
10.3
9.55
8.92
8.33
14.6
13.8
13.0
12.2
11.5
18.3
17.4
16.5
15.6
14.8
22.1
21.1
20.1
19.1
18.2
25.9
24.8
23.7
22.7
21.7
29.7
28.6
27.5
26.4
25.4
33.6
32.4
31.3
30.1
29.1
37.5
36.3
35.1
33.9
32.8
41.4
40.2
38.9
37.8
36.6
45.3
44.1
42.8
41.6
40.4
7
8
9
10
12
2.38
2.19
2.02
1.87
1.62
4.96
4.60
4.28
3.99
3.51
7.79 10.9
7.30 10.2
6.85 9.68
6.45 9.17
5.75 8.27
14.1
13.4
12.7
12.1
11.0
17.4
16.7
15.9
15.2
13.9
20.9
20.0
19.2
18.4
17.0
24.4
23.5
22.6
21.8
20.3
28.0
27.1
26.1
25.3
23.6
31.8
30.7
29.7
28.8
27.0
35.5
34.4
33.4
32.4
30.6
39.3
38.2
37.1
36.1
34.1
14
16
18
20
24
1.43
1.27
1.15
1.04
0.88
3.12
2.81
2.56
2.34
2.00
5.18
4.70
4.29
3.95
3.39
7.50 10.1
6.85 9.23
6.28 8.52
5.80 7.89
5.01 6.87
12.9
11.9
11.0
10.2
8.98
15.8
14.7
13.7
12.8
11.3
18.9
17.6
16.5
15.5
13.8
22.1
20.7
19.5
18.4
16.4
25.4
24.0
22.6
21.4
19.2
28.9
27.3
25.9
24.5
22.1
32.4
30.7
29.1
27.7
25.2
28
32
36
0.76
0.67
0.60
1.74
1.54
1.38
2.96
2.63
2.36
4.39
3.91
3.52
12.3
11.2
10.2
14.8
13.5
12.3
17.4
15.9
14.5
20.1
18.4
16.9
23.0
21.1
19.4
2
3
4
5
6
3.63
3.38
3.10
2.84
2.60
7.29
6.88
6.46
6.06
5.69
11.1
10.6
10.0
9.55
9.09
14.9
14.3
13.8
13.2
12.7
18.8
18.2
17.6
17.0
16.4
22.7
22.1
21.5
20.9
20.3
26.6
26.0
25.4
24.7
24.2
30.5
29.9
29.3
28.7
28.1
34.5
33.9
33.3
32.6
31.9
38.4
37.8
37.2
36.5
35.9
42.4
41.8
41.1
40.4
39.8
46.3
45.7
45.1
44.4
43.8
7
8
9
10
12
2.38
2.19
2.02
1.87
1.62
5.34
5.03
4.74
4.47
4.01
8.66
8.27
7.90
7.55
6.93
12.2
11.7
11.3
10.9
10.1
15.9
15.4
14.9
14.5
13.6
19.7
19.1
18.6
18.1
17.2
23.6
22.9
22.4
21.9
20.8
27.4
26.8
26.2
25.7
24.5
31.3
30.7
30.1
29.5
28.3
35.2
34.6
34.0
33.4
32.2
39.2
38.5
37.9
37.3
36.0
43.1
42.4
41.8
41.2
39.9
14
16
18
20
24
1.43
1.27
1.15
1.04
0.88
3.63
3.31
3.04
2.81
2.44
6.38
5.91
5.49
5.12
4.49
9.46
8.84
8.28
7.77
6.90
12.8
12.1
11.3
10.8
9.62
16.2
15.4
14.6
13.9
12.6
19.9
18.9
18.0
17.2
15.8
23.5
22.6
21.6
20.8
19.1
27.3
26.3
25.2
24.3
22.6
31.0
30.0
28.9
28.0
26.1
34.9
33.8
32.7
31.7
29.8
38.7
37.6
36.5
35.4
33.4
28
32
36
0.76
0.67
0.60
2.15
1.91
1.73
3.99
3.58
3.24
6.18
5.58
5.08
8.70 11.5 14.5
7.93 10.6 13.4
7.27 9.76 12.5
17.7
16.5
15.4
21.1
19.7
18.4
24.5
23.0
21.6
28.0
26.4
24.9
31.6
29.9
28.3
6.07
5.43
4.91
7.97 10.1
7.15 9.06
6.48 8.22
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
ECCENTRICALLY LOADED BOLT GROUPS
8 - 81
Table 8-24 (cont.).
Coefficients C for Eccentrically Loaded Bolt Groups
Angle = 75°°
C req =
Pu
φ rn
or φ R n = C × φrn
ex
where
3
6
s
Pu
s
e
s, in.
75°
s
Pu
= factored force, kips
φ rn = design strength per bolt, kips
φ R n = design strength of bolt group, kips
e
= eccentricity of Pu with respect to centroid
of bolt group, in. (not tabulated, may be
determined by geometry.)
e x = horizontal component of e, in.
s
= bolt spacing, in.
C
= coefficient tabulated below.
3
3
3
9
Number of bolts in one vertical row, n
ex,
in.
1
2
3
4
5
6
7
8
9
10
11
12
2
3
4
5
6
3.86
3.79
3.70
3.59
3.47
7.69
7.53
7.34
7.13
6.89
11.5
11.2
11.0
10.6
10.3
15.3
14.9
14.6
14.2
13.8
19.1
18.6
18.2
17.7
17.2
22.9
22.4
21.9
21.3
20.8
26.7
26.1
25.5
24.9
24.4
30.5
29.9
29.2
28.6
28.0
34.3
33.6
33.0
32.3
31.7
38.2
37.5
36.7
36.1
35.4
42.1
41.3
40.6
39.8
39.1
45.9
45.1
44.3
43.6
42.9
7
8
9
10
12
3.34
3.20
3.07
2.94
2.68
6.65
6.40
6.16
5.91
5.45
9.98
9.64
9.31
8.98
8.36
13.4
12.9
12.6
12.2
11.5
16.8
16.4
15.9
15.4
14.6
20.3
19.8
19.3
18.8
17.9
23.8
23.3
22.8
22.2
21.3
27.4
26.9
26.3
25.7
24.8
31.1
30.4
29.9
29.3
28.3
34.8
34.1
33.5
32.9
31.8
38.5
37.8
37.1
36.6
35.4
42.2
41.5
40.8
40.2
39.0
14
16
18
20
24
2.45
2.24
2.06
1.90
1.63
5.03
4.65
4.31
4.01
3.51
7.79 10.7
7.28 10.1
6.81 9.55
6.40 9.03
5.69 8.13
13.9
13.2
12.5
11.9
10.8
17.1
16.3
15.5
14.9
13.6
20.4
19.6
18.8
18.0
16.6
23.8
22.9
22.0
21.2
19.7
27.3
26.3
25.4
24.5
22.9
30.8
29.8
28.8
27.9
26.2
34.3
33.2
32.2
31.3
29.5
37.9
36.8
35.8
34.8
32.9
28
32
36
1.43
1.27
1.14
3.11
2.79
2.53
5.11
4.62
4.22
12.5
11.5
10.7
15.4
14.3
13.3
18.3
17.1
16.0
21.4
20.0
18.9
24.6
23.2
21.8
27.8
26.3
24.9
31.1
29.5
28.0
2
3
4
5
6
3.86
3.79
3.70
3.59
3.47
7.67
7.51
7.32
7.12
6.92
11.5
11.2
11.0
10.7
10.4
15.3
15.0
14.7
14.4
14.1
19.1
18.8
18.4
18.1
17.7
23.0
22.6
22.2
21.9
21.5
26.9
26.4
26.0
25.6
25.3
30.8
30.4
29.9
29.5
29.1
35.2
34.3
33.8
33.3
32.9
39.1
38.1
37.7
37.3
36.8
43.0
42.1
41.6
41.1
40.7
47.0
46.0
45.5
45.0
44.6
7
8
9
10
12
3.34
3.20
3.07
2.94
2.68
6.70
6.49
6.28
6.08
5.69
10.2
9.92
9.66
9.42
8.95
13.8
13.5
13.2
12.9
12.4
17.4
17.1
16.8
16.5
15.9
21.1
20.8
20.5
20.2
19.5
24.9
24.5
24.2
23.9
23.2
28.7
28.3
28.0
27.6
26.9
32.6
32.1
31.8
31.4
30.7
36.4
36.0
35.6
35.2
34.5
40.2
39.8
39.5
39.0
38.3
44.1
43.7
43.3
42.9
42.1
14
16
18
20
24
2.45
2.24
2.06
1.90
1.63
5.33
4.99
4.69
4.42
3.95
8.51
8.10
7.72
7.36
6.74
11.9
11.5
11.0
10.6
9.83
15.4
14.9
14.4
13.9
13.1
19.0
18.5
17.9
17.4
16.5
22.6
22.1
21.5
21.0
20.0
26.3
25.7
25.1
24.6
23.6
30.1
29.4
28.8
28.2
27.1
33.8
33.1
32.5
31.9
30.7
37.6
36.9
36.2
35.6
34.4
41.4
40.7
40.0
39.3
38.1
28
32
36
1.43
1.27
1.14
3.57
3.25
2.98
6.21
5.74
5.33
9.16 12.4
8.56 11.6
8.02 11.0
15.7
14.9
14.1
19.0
18.2
17.3
22.5
21.6
20.7
26.1
25.1
24.1
29.7
28.6
27.6
33.3
32.2
31.2
36.9
35.9
34.8
7.36
6.71
6.15
9.83
9.02
8.31
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
8 - 82
BOLTS, WELDS, AND CONNECTED ELEMENTS
Table 8-25.
Coefficients C for Eccentrically Loaded Bolt Groups
Angle = 0°°
C req =
Pu
φ rn
or φR n = C × φ rn
ex= e
where
s, in.
3
6
s
Pu
s
s
Pu
= factored force, kips
φ rn = design strength per bolt, kips
φ R n = design strength of bolt group, kips
e
= eccentricity of Pu with respect to centroid
of bolt group, in. (not tabulated, may be
determined by geometry.)
e x = horizontal component of e, in.
s
= bolt spacing, in.
C
= coefficient tabulated below.
4
4
4
12
Number of bolts in one vertical row, n
ex,
in.
1
2
3
4
5
6
7
8
9
10
11
12
2
3
4
5
6
2.82
2.50
2.23
2.01
1.81
5.98
5.31
4.74
4.27
3.86
9.46
8.43
7.58
6.86
6.24
13.3
12.0
10.8
9.82
8.96
17.3
15.7
14.3
13.1
12.0
21.3
19.7
18.2
16.7
15.4
25.5
23.8
22.2
20.5
19.0
29.6
28.0
26.3
24.5
22.9
33.7
32.2
30.4
28.6
26.9
37.7
36.3
34.6
32.8
31.0
41.8
40.4
38.8
37.0
35.2
45.8
44.6
43.0
41.3
39.4
7
8
9
10
12
1.64
1.49
1.36
1.25
1.07
3.52
3.22
2.96
2.73
2.37
5.70
5.24
4.83
4.47
3.89
8.22 11.1
7.57 10.2
7.01 9.48
6.51 8.83
5.68 7.74
14.2
13.2
12.3
11.4
10.1
17.6
16.4
15.3
14.3
12.6
21.3
19.9
18.6
17.5
15.5
25.2
23.6
22.1
20.8
18.5
29.2
27.5
25.9
24.4
21.8
33.3
31.5
29.8
28.2
25.3
37.5
35.6
33.8
32.1
29.0
14
16
18
20
24
0.94
0.83
0.75
0.68
0.58
2.08
1.86
1.67
1.52
1.29
3.42
3.05
2.75
2.50
2.12
5.02
4.49
4.06
3.70
3.14
6.86
6.15
5.56
5.07
4.30
8.95 11.3
8.04 10.2
7.29 9.22
6.65 8.43
5.66 7.18
13.8
12.5
11.4
10.4
8.88
16.6
15.0
13.7
12.6
10.8
19.6
17.8
16.3
14.9
12.8
22.8
20.7
19.0
17.5
15.0
26.2
23.9
21.9
20.2
17.4
28
32
36
0.50
0.44
0.40
1.12
0.98
0.88
1.84
1.62
1.45
2.72
2.40
2.15
3.73
3.30
2.95
4.92
4.34
3.89
13.1
11.6
10.4
15.2
13.5
12.1
2
3
4
5
6
2.82
2.50
2.23
2.01
1.81
6.54
5.90
5.33
4.84
4.42
10.6
9.81
9.01
8.27
7.60
7
8
9
10
12
1.64
1.49
1.36
1.25
1.07
4.05
3.73
3.45
3.20
2.80
7.02 10.6
6.51 9.94
6.06 9.30
5.66 8.72
4.98 7.73
14
16
18
20
24
0.94
0.83
0.75
0.68
0.58
2.47
2.21
2.00
1.82
1.55
4.43
3.98
3.60
3.29
2.79
6.92
6.25
5.68
5.21
4.45
28
32
36
0.50
0.44
0.40
1.34
1.18
1.06
2.42
2.14
1.92
3.87
3.43
3.07
14.8
14.0
13.1
12.2
11.4
6.24
5.51
4.94
7.73
6.84
6.13
9.37 11.2
8.29 9.90
7.43 8.88
18.9
18.1
17.3
16.4
15.5
22.9
22.3
21.5
20.6
19.7
26.9
26.4
25.7
24.8
24.0
30.9
30.4
29.8
29.0
28.2
34.9
34.5
33.9
33.2
32.4
38.9
38.5
37.9
37.3
36.6
42.8
42.5
42.0
41.4
40.7
46.8
46.5
46.0
45.5
44.8
14.6
13.7
13.0
12.2
10.9
18.8
17.8
16.9
16.1
14.5
23.0
22.0
21.1
20.2
18.4
27.3
26.3
25.3
24.4
22.5
31.5
30.6
29.6
28.6
26.7
35.7
34.8
33.9
32.9
30.9
39.9
39.1
38.2
37.2
35.2
44.1
43.3
42.4
41.5
39.5
9.81
8.90
8.13
7.47
6.40
13.2
12.0
11.0
10.1
8.72
16.8
15.4
14.2
13.1
11.3
20.7
19.1
17.7
16.4
14.3
24.8
23.0
21.4
20.0
17.5
29.0
27.1
25.3
23.7
20.9
33.2
31.3
29.4
27.7
24.5
37.5
35.5
33.6
31.7
28.3
5.59
4.95
4.44
7.64
6.79
6.10
9.96 12.6
8.87 11.2
7.98 10.1
15.5
13.8
12.5
18.6
16.7
15.1
21.9
19.7
17.9
25.5
23.0
20.9
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
ECCENTRICALLY LOADED BOLT GROUPS
8 - 83
Table 8-25 (cont.).
Coefficients C for Eccentrically Loaded Bolt Groups
Angle = 15°°
C req =
Pu
φ rn
or φ R n = C × φrn
ex
Pu
where
s, in.
3
6
s
15°
e
s
s
Pu
= factored force, kips
φ rn = design strength per bolt, kips
φ R n = design strength of bolt group, kips
e
= eccentricity of Pu with respect to centroid
of bolt group, in. (not tabulated, may be
determined by geometry.)
e x = horizontal component of e, in.
s
= bolt spacing, in.
C
= coefficient tabulated below.
4
4
4
12
Number of bolts in one vertical row, n
ex,
in.
1
2
3
4
5
6
7
8
9
10
11
12
2
3
4
5
6
2.91
2.57
2.30
2.06
1.86
6.06
5.40
4.84
4.37
3.96
9.56
8.57
7.72
6.99
6.37
13.3
12.0
10.9
9.93
9.09
17.2
15.8
14.4
13.2
12.1
21.3
19.7
18.2
16.7
15.5
25.3
23.7
22.1
20.5
19.0
29.4
27.8
26.1
24.4
22.8
33.5
31.9
30.2
28.5
26.7
37.5
36.1
34.3
32.6
30.8
41.6
40.2
38.5
36.7
34.9
45.6
44.3
42.6
40.9
39.0
7
8
9
10
12
1.69
1.53
1.40
1.29
1.11
3.61
3.31
3.04
2.81
2.44
5.83
5.36
4.95
4.59
4.00
8.36 11.2
7.72 10.4
7.15 9.64
6.65 9.00
5.82 7.90
14.3
13.3
12.4
11.6
10.2
17.7
16.5
15.4
14.5
12.8
21.3
19.9
18.7
17.6
15.6
25.1
23.6
22.2
20.9
18.7
29.0
27.4
25.8
24.4
21.9
33.1
31.3
29.7
28.1
25.3
37.2
35.3
33.6
31.9
28.9
14
16
18
20
24
0.97
0.86
0.78
0.71
0.60
2.15
1.92
1.73
1.57
1.33
3.52
3.15
2.84
2.59
2.19
5.15
4.61
4.17
3.80
3.23
7.02
6.30
5.71
5.21
4.43
9.12 11.5
8.21 10.3
7.45 9.41
6.81 8.61
5.80 7.36
14.0
12.7
11.6
10.6
9.07
16.8
15.2
13.9
12.8
11.0
19.8
18.0
16.5
15.2
13.0
22.9
20.9
19.2
17.7
15.3
26.3
24.0
22.1
20.4
17.6
28
32
36
0.52
0.46
0.41
1.15
1.02
0.91
1.90
1.68
1.50
2.80
2.48
2.22
3.85
3.40
3.04
5.05
4.46
4.00
13.4
11.9
10.7
15.5
13.8
12.4
2
3
4
5
6
2.91
2.57
2.30
2.06
1.86
6.57
5.93
5.37
4.89
4.48
10.6
9.81
9.04
8.33
7.70
7
8
9
10
12
1.69
1.53
1.40
1.29
1.11
4.12
3.80
3.52
3.27
2.86
7.13 10.6
6.62 9.95
6.17 9.32
5.77 8.76
5.09 7.80
14
16
18
20
24
0.97
0.86
0.78
0.71
0.60
2.54
2.27
2.06
1.88
1.59
4.53
4.08
3.70
3.38
2.88
7.00
6.34
5.78
5.30
4.54
9.92
9.02
8.26
7.60
6.54
28
32
36
0.52
0.46
0.41
1.38
1.22
1.09
2.50
2.21
1.98
3.96
3.51
3.15
5.72
5.08
4.56
14.7
13.9
13.0
12.2
11.4
6.41
5.67
5.08
7.91
7.01
6.29
9.59 11.4
8.50 10.1
7.63 9.09
18.8
18.0
17.2
16.3
15.4
22.8
22.1
21.3
20.5
19.5
26.8
26.2
25.5
24.6
23.7
30.8
30.3
29.6
28.8
27.9
34.8
34.3
33.6
32.9
32.1
38.8
38.3
37.7
37.0
36.2
42.7
42.3
41.7
41.1
40.3
46.7
46.3
45.8
45.1
44.4
14.5
13.7
12.9
12.2
11.0
18.6
17.7
16.8
16.0
14.5
22.8
21.8
20.9
20.0
18.3
27.0
26.0
25.1
24.1
22.3
31.2
30.2
29.3
28.3
26.4
35.4
34.4
33.5
32.5
30.6
39.5
38.6
37.7
36.8
34.8
43.7
42.8
41.9
41.0
39.0
13.2
12.0
11.1
10.2
8.84
16.8
15.4
14.2
13.2
11.5
20.6
19.0
17.7
16.4
14.4
24.6
22.9
21.3
19.9
17.5
28.7
26.9
25.2
23.6
20.9
32.8
30.9
29.1
27.5
24.5
37.1
35.1
33.2
31.4
28.2
7.77 10.1 12.7
6.92 9.03 11.4
6.23 8.15 10.3
15.6
14.0
12.7
18.7
16.8
15.3
22.0
19.9
18.1
25.4
23.1
21.1
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
8 - 84
BOLTS, WELDS, AND CONNECTED ELEMENTS
Table 8-25 (cont.).
Coefficients C for Eccentrically Loaded Bolt Groups
Angle = 30°°
C req =
Pu
φrn
or φR n = C × φ rn
ex
Pu
where
s, in.
3
6
s
30°
s
Pu
= factored force, kips
φ rn = design strength per bolt, kips
φ R n = design strength of bolt group, kips
e
= eccentricity of Pu with respect to centroid
of bolt group, in. (not tabulated, may be
determined by geometry.)
e x = horizontal component of e, in.
s
= bolt spacing, in.
C
= coefficient tabulated below.
s
e
4
4
4
12
Number of bolts in one vertical row, n
ex,
in.
1
2
3
4
5
6
7
8
9
10
11
12
2
3
4
5
6
3.14
2.79
2.50
2.25
2.04
6.41
5.75
5.19
4.71
4.29
9.91
8.95
8.16
7.45
6.83
13.6
12.4
11.4
10.5
9.65
17.5
16.1
14.9
13.7
12.7
21.4
20.0
18.5
17.2
16.0
25.4
23.9
22.4
20.9
19.6
29.4
27.9
26.3
24.7
23.3
33.4
31.9
30.3
28.6
27.1
37.4
35.9
34.3
32.6
31.0
41.4
40.0
38.4
36.7
35.0
45.4
44.0
42.4
40.7
39.0
7
8
9
10
12
1.85
1.69
1.55
1.43
1.23
3.93
3.61
3.33
3.08
2.68
6.28
5.80
5.38
5.00
4.37
8.92 11.8
8.27 11.0
7.70 10.3
7.19 9.64
6.32 8.52
15.0
14.0
13.1
12.3
11.0
18.3
17.2
16.2
15.3
13.6
21.9
20.6
19.4
18.4
16.5
25.6
24.2
22.9
21.7
19.6
29.4
27.9
26.5
25.2
22.8
33.3
31.7
30.2
28.8
26.2
37.3
35.6
34.0
32.5
29.8
14
16
18
20
24
1.08
0.96
0.87
0.79
0.67
2.36
2.11
1.91
1.74
1.48
3.88
3.47
3.14
2.86
2.43
5.62
5.05
4.57
4.18
3.56
7.61
6.86
6.24
5.71
4.88
9.83 12.3
8.89 11.1
8.10 10.2
7.43 9.35
6.36 8.03
14.9
13.6
12.4
11.5
9.87
17.8
16.2
14.9
13.8
11.9
20.8
19.0
17.5
16.2
14.1
24.0
22.0
20.3
18.9
16.4
27.3
25.2
23.3
21.6
18.9
28
32
36
0.58
0.51
0.46
1.28
1.13
1.01
2.11
1.87
1.67
3.10
2.74
2.45
4.25
3.76
3.37
5.55
4.92
4.41
14.5
12.9
11.7
16.7
14.9
13.5
2
3
4
5
6
3.14
2.79
2.50
2.25
2.04
6.75
6.12
5.58
5.13
4.73
10.7
9.94
9.23
8.58
8.00
7
8
9
10
12
1.85
1.69
1.55
1.43
1.23
4.38
4.06
3.78
3.53
3.10
7.47 10.9
6.98 10.3
6.55 9.72
6.15 9.18
5.47 8.25
14
16
18
20
24
1.08
0.96
0.87
0.79
0.67
2.76
2.48
2.25
2.06
1.76
4.90
4.43
4.04
3.70
3.17
7.46 10.4
6.79 9.55
6.22 8.79
5.72 8.14
4.93 7.06
28
32
36
0.58
0.51
0.46
1.53
1.35
1.21
2.76
2.45
2.19
4.32
3.84
3.46
14.7
13.9
13.1
12.4
11.6
7.02
6.23
5.60
8.65 10.4 12.4
7.69 9.29 11.0
6.91 8.36 9.95
18.7
18.0
17.2
16.3
15.5
22.7
22.0
21.2
20.4
19.5
26.7
26.1
25.3
24.5
23.6
30.7
30.1
29.4
28.6
27.7
34.7
34.1
33.4
32.7
31.8
38.6
38.1
37.5
36.7
35.9
42.6
42.1
41.5
40.8
40.0
46.6
46.1
45.5
44.8
44.1
14.7
14.0
13.3
12.6
11.4
18.7
17.9
17.1
16.3
14.9
22.7
21.9
21.0
20.2
18.6
26.8
25.9
25.1
24.2
22.5
31.0
30.1
29.2
28.3
26.5
35.1
34.2
33.3
32.4
30.6
39.2
38.3
37.4
36.5
34.7
43.3
42.4
41.5
40.6
38.8
13.7
12.6
11.7
10.9
9.48
17.2
16.0
14.9
13.9
12.2
21.0
19.6
18.3
17.1
15.2
24.9
23.3
21.9
20.6
18.3
28.8
27.2
25.7
24.2
21.7
32.9
31.2
29.5
28.0
25.3
37.0
35.2
33.5
31.9
28.9
8.38 10.8 13.5
7.50 9.73 12.2
6.77 8.82 11.1
16.5
14.9
13.6
19.6
17.8
16.3
22.9
20.9
19.1
26.3
24.1
22.2
6.22
5.54
5.00
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
ECCENTRICALLY LOADED BOLT GROUPS
8 - 85
Table 8-25 (cont.).
Coefficients C for Eccentrically Loaded Bolt Groups
Angle = 45°°
C req =
Pu
φ rn
or φ R n = C × φrn
ex
Pu
s
where
3
6
s
e
s, in.
45°
s
Pu
= factored force, kips
φ rn = design strength per bolt, kips
φ R n = design strength of bolt group, kips
e
= eccentricity of Pu with respect to centroid
of bolt group, in. (not tabulated, may be
determined by geometry.)
e x = horizontal component of e, in.
s
= bolt spacing, in.
C
= coefficient tabulated below.
4
4
4
12
Number of bolts in one vertical row, n
ex,
in.
1
2
3
4
5
6
7
8
9
10
11
12
2
3
4
5
6
3.46
3.15
2.87
2.61
2.39
6.96
6.38
5.84
5.36
4.93
10.5
9.73
8.97
8.30
7.69
14.2
13.2
12.3
11.4
10.7
18.0
16.8
15.7
14.7
13.9
21.8
20.6
19.3
18.2
17.2
25.7
24.4
23.1
21.8
20.7
29.6
28.2
26.9
25.5
24.3
33.5
32.1
30.7
29.3
28.0
37.4
36.1
34.6
33.2
31.8
41.4
40.0
38.6
37.1
35.6
45.3
44.0
42.5
41.0
39.5
7
8
9
10
12
2.19
2.01
1.86
1.72
1.49
4.55
4.21
3.90
3.63
3.18
7.15
6.66
6.21
5.82
5.14
9.98
9.34
8.76
8.24
7.33
13.0
12.2
11.5
10.9
9.76
16.2
15.3
14.5
13.8
12.4
19.6
18.6
17.7
16.8
15.2
23.1
22.0
21.0
20.0
18.3
26.7
25.5
24.4
23.3
21.4
30.4
29.2
27.9
26.8
24.7
34.2
32.9
31.6
30.4
28.1
38.1
36.7
35.3
34.0
31.6
14
16
18
20
24
1.32
1.17
1.06
0.96
0.82
2.82
2.53
2.29
2.10
1.79
4.59
4.14
3.76
3.44
2.94
6.58
5.95
5.43
4.98
4.26
8.81 11.3
8.00 10.3
7.32 9.44
6.74 8.71
5.81 7.53
13.9
12.7
11.7
10.9
9.43
16.7
15.4
14.2
13.2
11.5
19.7
18.2
16.9
15.7
13.8
22.8
21.2
19.7
18.4
16.2
26.1
24.3
22.7
21.2
18.7
29.5
27.5
25.7
24.2
21.4
28
32
36
0.71
0.63
0.56
1.56
1.38
1.23
2.56
2.26
2.03
3.73
3.31
2.97
5.09
4.52
4.06
14.4
12.9
11.7
16.7
15.1
13.7
19.2
17.3
15.8
2
3
4
5
6
3.46
3.15
2.87
2.61
2.39
7.09
6.58
6.09
5.66
5.26
10.9
10.3
9.65
9.07
8.54
14.8
14.1
13.4
12.8
12.1
18.7
18.1
17.3
16.6
15.9
22.7
22.0
21.3
20.6
19.8
26.7
26.0
25.3
24.5
23.8
30.6
30.0
29.3
28.5
27.8
34.6
33.9
33.3
32.5
31.8
38.5
37.9
37.3
36.5
35.8
42.5
41.9
41.2
40.5
39.8
46.5
45.9
45.2
44.5
43.8
7
8
9
10
12
2.19
2.01
1.86
1.72
1.49
4.91
4.59
4.30
4.04
3.59
8.07
7.63
7.23
6.85
6.19
11.6
11.0
10.5
10.0
9.14
15.3
14.6
14.0
13.4
12.4
19.1
18.4
17.7
17.1
15.9
23.0
22.3
21.5
20.8
19.5
27.0
26.2
25.5
24.7
23.3
31.0
30.2
29.4
28.6
27.2
35.0
34.2
33.4
32.6
31.1
39.0
38.2
37.4
36.6
35.1
43.0
42.2
41.4
40.6
39.1
14
16
18
20
24
1.32
1.17
1.06
0.96
0.82
3.22
2.91
2.66
2.44
2.10
5.62
5.13
4.71
4.35
3.76
8.38 11.4
7.71 10.6
7.12 9.87
6.61 9.22
5.76 8.11
14.8
13.8
12.9
12.1
10.8
18.3
17.2
16.2
15.3
13.7
22.0
20.8
19.6
18.6
16.7
25.8
24.4
23.2
22.1
20.0
29.6
28.2
26.9
25.7
23.4
33.5
32.1
30.7
29.4
27.0
37.5
36.0
34.6
33.2
30.6
28
32
36
0.71
0.63
0.56
1.83
1.63
1.46
3.30
2.94
2.64
5.08
4.54
4.11
9.64 12.3
8.71 11.2
7.93 10.2
15.2
13.9
12.7
18.3
16.7
15.4
21.5
19.8
18.3
24.9
23.0
21.3
28.4
26.3
24.5
7.22
6.50
5.90
6.61
5.89
5.30
8.31 10.2 12.2
7.42 9.11 11.0
6.69 8.23 9.91
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
8 - 86
BOLTS, WELDS, AND CONNECTED ELEMENTS
Table 8-25 (cont.).
Coefficients C for Eccentrically Loaded Bolt Groups
Angle = 60°°
C req =
Pu
φrn
or φR n = C × φ rn
ex
where
s
Pu
Pu
= factored force, kips
φ rn = design strength per bolt, kips
φ R n = design strength of bolt group, kips
e
= eccentricity of Pu with respect to centroid
of bolt group, in. (not tabulated, may be
determined by geometry.)
e x = horizontal component of e, in.
s
= bolt spacing, in.
C
= coefficient tabulated below.
3
6
s
s
e
s, in.
60°
4
4
4
12
Number of bolts in one vertical row, n
ex,
in.
1
2
3
4
5
6
7
8
9
10
11
12
2
3
4
5
6
3.74
3.57
3.38
3.17
2.97
7.46
7.12
6.75
6.36
5.99
11.2
10.7
10.2
9.61
9.09
14.9
14.3
13.6
12.9
12.3
18.6
17.9
17.1
16.4
15.6
22.4
21.6
20.7
19.8
19.0
26.2
25.3
24.3
23.4
22.5
30.0
29.0
28.0
27.0
26.1
33.9
32.8
31.8
30.7
29.7
37.7
36.7
35.6
34.5
33.4
41.6
40.5
39.4
38.2
37.1
45.5
44.4
43.2
42.0
40.9
7
8
9
10
12
2.78
2.60
2.44
2.28
2.02
5.63
5.29
4.98
4.69
4.18
8.59
8.13
7.69
7.28
6.56
11.7
11.1
10.6
10.1
9.16
14.9
14.2
13.6
13.0
11.9
18.2
17.5
16.8
16.1
14.9
21.6
20.8
20.1
19.3
18.0
25.1
24.3
23.4
22.7
21.2
28.7
27.8
26.9
26.1
24.5
32.3
31.4
30.4
29.5
27.8
36.0
35.0
34.0
33.1
31.3
39.8
38.7
37.7
36.7
34.8
14
16
18
20
24
1.80
1.62
1.47
1.34
1.15
3.76
3.40
3.10
2.85
2.45
5.95
5.43
4.99
4.61
3.99
8.38 11.0
7.70 10.2
7.11 9.42
6.59 8.76
5.73 7.67
13.8
12.8
11.9
11.1
9.82
16.7
15.6
14.6
13.7
12.2
19.8
18.6
17.4
16.4
14.6
23.0
21.6
20.4
19.3
17.3
26.3
24.8
23.5
22.2
20.1
29.6
28.1
26.7
25.3
23.0
33.1
31.4
29.9
28.5
26.0
28
32
36
1.00
0.88
0.79
2.15
1.91
1.72
3.51
3.13
2.81
5.06
4.52
4.08
13.2
11.9
10.9
15.6
14.2
13.0
18.2
16.6
15.3
20.9
19.2
17.7
23.8
21.8
20.2
2
3
4
5
6
3.74
3.57
3.38
3.17
2.97
7.47
7.16
6.82
6.47
6.14
11.2
10.8
10.4
9.94
9.52
15.0
14.6
14.1
13.6
13.1
18.9
18.4
17.8
17.3
16.7
22.8
22.2
21.7
21.1
20.5
26.7
26.1
25.5
24.9
24.3
30.6
30.0
29.4
28.8
28.2
34.5
33.9
33.3
32.7
32.1
38.5
37.9
37.3
36.6
36.0
42.4
41.8
41.2
40.5
39.9
46.4
45.8
45.1
44.5
43.8
7
8
9
10
12
2.78
2.60
2.44
2.28
2.02
5.82
5.52
5.24
4.98
4.51
9.11
8.73
8.37
8.03
7.41
12.6
12.1
11.7
11.3
10.6
16.2
15.7
15.2
14.8
14.0
19.9
19.4
18.9
18.4
17.5
23.7
23.2
22.6
22.1
21.1
27.6
27.0
26.4
25.8
24.8
31.5
30.8
30.2
29.7
28.5
35.3
34.7
34.1
33.5
32.3
39.3
38.6
38.0
37.4
36.2
43.2
42.5
41.9
41.3
40.1
14
16
18
20
24
1.80
1.62
1.47
1.34
1.15
4.10
3.76
3.46
3.21
2.79
6.86
6.37
5.94
5.56
4.91
9.91
9.29
8.74
8.23
7.34
13.2
12.4
11.8
11.2
10.1
16.6
15.8
15.0
14.3
13.0
20.1
19.2
18.4
17.6
16.2
23.8
22.8
21.9
21.0
19.5
27.5
26.5
25.5
24.6
22.9
31.2
30.2
29.2
28.2
26.4
35.0
33.9
32.9
31.9
30.0
38.9
37.7
36.6
35.6
33.6
28
32
36
1.00
0.88
0.79
2.47
2.21
2.00
4.38
3.95
3.58
6.61
5.99
5.46
9.13 11.9
8.33 11.0
7.65 10.1
14.9
13.8
12.8
18.1
16.8
15.7
21.4
20.0
18.7
24.7
23.2
21.9
28.2
26.6
25.1
31.8
30.1
28.5
6.80
6.11
5.53
8.76 10.9
7.89 9.83
7.16 8.95
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
ECCENTRICALLY LOADED BOLT GROUPS
8 - 87
Table 8-25 (cont.).
Coefficients C for Eccentrically Loaded Bolt Groups
Angle = 75°°
C req =
Pu
φ rn
or φ R n = C × φrn
ex
where
3
6
s
s
e
s, in.
75° P
u
s
Pu
= factored force, kips
φ rn = design strength per bolt, kips
φ R n = design strength of bolt group, kips
e
= eccentricity of Pu with respect to centroid
of bolt group, in. (not tabulated, may be
determined by geometry.)
e x = horizontal component of e, in.
s
= bolt spacing, in.
C
= coefficient tabulated below.
4
4
4
12
Number of bolts in one vertical row, n
ex,
in.
1
2
3
4
5
6
7
8
9
10
11
12
2
3
4
5
6
3.89
3.84
3.79
3.72
3.65
7.75
7.66
7.54
7.40
7.25
11.6
11.5
11.3
11.1
10.8
15.5
15.2
15.0
14.7
14.4
19.3
19.0
18.7
18.3
17.9
23.1
22.7
22.4
21.9
21.5
26.9
26.5
26.1
25.6
25.1
30.8
30.3
29.8
29.3
28.7
34.6
34.1
33.5
32.9
32.4
38.5
37.9
37.3
36.7
36.1
42.3
41.7
41.0
40.4
39.8
46.2
45.5
44.8
44.1
43.5
7
8
9
10
12
3.56
3.47
3.37
3.27
3.07
7.08
6.90
6.71
6.52
6.14
10.6
10.3
10.0
9.77
9.23
14.1
13.7
13.4
13.1
12.4
17.6
17.2
16.8
16.4
15.6
21.1
20.6
20.2
19.8
18.9
24.6
24.1
23.7
23.2
22.3
28.2
27.7
27.2
26.7
25.7
31.8
31.3
30.7
30.2
29.1
35.5
34.9
34.3
33.7
32.6
39.1
38.5
37.9
37.3
36.2
42.8
42.2
41.6
41.0
39.8
14
16
18
20
24
2.87
2.68
2.50
2.34
2.06
5.76
5.40
5.07
4.76
4.23
8.71
8.22
7.76
7.33
6.57
11.8
11.1
10.6
10.0
9.10
14.9
14.2
13.5
12.9
11.8
18.1
17.3
16.6
15.9
14.7
21.4
20.5
19.7
19.0
17.6
24.7
23.8
23.0
22.2
20.7
28.1
27.2
26.3
25.5
23.9
31.6
30.6
29.7
28.8
27.1
35.1
34.1
33.1
32.2
30.4
38.7
37.6
36.6
35.6
33.8
28
32
36
1.82
1.63
1.48
3.78
3.41
3.11
5.94
5.41
4.95
13.5
12.6
11.7
16.4
15.3
14.3
19.3
18.1
17.0
22.4
21.0
19.8
25.5
24.1
22.8
28.7
27.2
25.8
32.0
30.4
28.9
2
3
4
5
6
3.89
3.84
3.79
3.72
3.65
7.74
7.64
7.52
7.38
7.23
11.6
11.4
11.2
11.0
10.8
15.4
15.2
14.9
14.7
14.4
19.3
19.0
18.7
18.4
18.1
23.1
22.8
22.5
22.1
21.8
27.0
26.6
26.3
25.9
25.6
30.9
30.5
30.1
29.7
29.3
35.2
34.4
34.0
33.6
33.2
39.1
38.3
37.8
37.4
37.0
43.0
42.2
41.7
41.3
40.8
47.0
46.1
45.6
45.2
44.7
7
8
9
10
12
3.56
3.47
3.37
3.27
3.07
7.07
6.90
6.73
6.56
6.21
10.6
10.4
10.1
9.92
9.48
14.2
13.9
13.6
13.4
12.9
17.8
17.5
17.2
16.9
16.4
21.5
21.2
20.8
20.5
19.9
25.2
24.9
24.5
24.2
23.6
29.0
28.6
28.3
27.9
27.3
32.8
32.4
32.0
31.7
31.0
36.6
36.2
35.8
35.5
34.7
40.4
40.0
39.6
39.3
38.5
44.3
43.9
43.5
43.1
42.3
14
16
18
20
24
2.87
2.68
2.50
2.34
2.06
5.88
5.57
5.27
4.99
4.50
9.07
8.67
8.29
7.94
7.29
12.4
11.9
11.5
11.1
10.3
15.9
15.4
14.9
14.4
13.6
19.4
18.8
18.3
17.8
16.9
23.0
22.4
21.9
21.3
20.4
26.6
26.0
25.5
24.9
23.9
30.3
29.7
29.1
28.5
27.4
34.1
33.4
32.8
32.2
31.0
37.8
37.1
36.5
35.8
34.7
41.6
40.9
40.2
39.6
38.3
28
32
36
1.82
1.63
1.48
4.08
3.73
3.43
6.73
6.25
5.82
9.67 12.8
9.06 12.1
8.51 11.4
16.1
15.3
14.5
19.4
18.6
17.8
22.9
22.0
21.1
26.4
25.4
24.5
30.0
29.0
28.0
33.6
32.5
31.5
37.2
36.1
35.1
8.30 10.9
7.61 10.0
7.01 9.26
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
8 - 88
BOLTS, WELDS, AND CONNECTED ELEMENTS
ANCHOR RODS OR THREADED RODS
Cast-in-place anchor rods, illustrated in Figure 8-14, are generally made from unheaded
rod material or headed bolt material. Drilled-in anchor rods, illustrated in Figure 8-15,
are not normally used; their design is governed by manufacturer’s specifications. Refer
also to Cannon, Godfrey, and Moreadith (1981).
LRFD Specification Section A3.4 permits the use of unheaded rod material from the
following ASTM specifications as anchor rods or threaded rods: A36, A193, A354, A449,
A572, A588, and A687. Additionally, LRFD Specification Section A3.4 permits the use
of headed bolts conforming to the provisions of LRFD Specification Section A3.3 for use
as anchor rods. Headed bolts, however, are generally available only in lengths up to about
eight inches. Furthermore, designations such as ASTM A325, A490, and A307 apply only
to bolts manufactured with a head and it is, therefore, improper to specify unheaded
anchor rods or other similar threaded devices as ASTM A325, A490, or A307.
The availability and strength of the aforementioned ASTM specifications for unheaded
rod material and headed bolt material are summarized in Table 8-26. Suitable nuts may
be selected from ASTM A563 or ASTM A194 grade 7. Because base plates typically have
holes larger than oversized holes to allow for tolerances on the location of the anchor rod,
washers are usually furnished from ASTM A36 steel plate; they may be round, square,
or rectangular, are generally about 1⁄2-in. thick, and generally have holes which are 1⁄16-in.
larger than the anchor rod diameter.
Minimum Edge Distance and Embedment Length
The recommendations of Shipp and Haninger (1983) for minimum anchor-rod (concrete)
edge distance and embedment length for tensile forces, adopted from ACI 349, are
summarized in Table 8-26. The edge distance requirement is intended to prevent blow-out
of the side of the concrete foundation and is based on concrete with fc′ = 3,000 psi. For
edge distance requirements for shear, refer to Shipp and Haninger (1983).
In addition to providing the recommended minimum embedment length, anchor rods
must extend a distance above the foundation that is sufficient to permit full thread
engagement of the nut; from RCSC Specification Section 2(b), “…the end of the [anchor
rod] will be flush with or outside the face of the nut when properly installed.”
Lh
(a) Hooked
(b) Headed
(c) Threaded with Nut
Fig. 8-14. Typical cast-in-place anchor rods.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
ANCHOR RODS OR THREADED RODS
8 - 89
Note that it is seldom possible to fully tension anchor rods since the concrete usually
cannot provide the necessary anchorage.
Welding to Anchor Rods
Though not typical, welds must sometimes be used in lieu of nuts to attach anchor rods
to base plates. The use of weldable steels such as ASTM A36 or A572 is recommended
for this purpose; anchor-rod material which is quenched and tempered should not be
welded.
Hooked Anchor Rods
Hooked anchor rods should be used only for axially loaded columns to locate and prevent
the displacement or overturning of columns due to erection loads or accidental collisions
during erection. Additionally, high-strength steels are not recommended for use in hooked
rods since bending with heat may materially affect their strength.
For the hooked rod of Figure 8-14a, the tensile force is resisted through bond
development along the length and the mechanical anchorage of the hook. However,
because smooth rods do not always form a reliable bond (due to oil used in threading
among other things), the design of such anchor rods should be based upon the anchorage
provided by the hook only. To prevent the anchor rod from pulling out and straightening,
the hook should be designed to resist one-half the design tensile strength of the anchor
rod φRn,
where
φ = 0.75
Rn = φtFu Ag
In the above equation, φt = 0.75. From Fisher (1981), the bearing strength of the
concrete is:
0.7fc′dLh
Grout
Fig. 8-15. Drilled-in anchor rods.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
8 - 90
BOLTS, WELDS, AND CONNECTED ELEMENTS
Table 8-26.
Anchor Rod Material Availability and Strength
Availability
Headed
Bolt Mat.
(Only)
Headed Bolt or
Unheaded Rod
Material
Unheaded Rod
Material (Only)
Type
ASTM
Design.
Material
Typeb
Strength
Grade
Diameter,
d, in.
Proof
Load
Min.
Yield,
ksi
Minimum
Min. Embdmt. Minimum
Tensile, Length,
Edge
Dist., in.e
ksi
in.
A36
C
—
to 8
—
36
58
12d
5d
A572
HSLA
42
to 2
—
42
60
12d
5d
50
to 6
—
50
65
17d
7d
—
to 4
—
50
70
17d
7d
over 4 to 5
—
46
67
17d
7d
over 5 to 8
—
42
63
17d
7d
to 3
—
105
150c
19d
7d
to 21 ⁄2
120
130
150
19d
7d
105
115
140
19d
7d
105
109
125
17d
7d
95
99
115
17d
7d
85
92
120
17d
7d
11 ⁄8 to 11 ⁄2
74
81
105
17d
7d
13 ⁄4 to 3
55
58
90
17d
7d
to 4
—
—
60
12d
5d
85
92
120
17d
7d
74
81
105
17d
7d
120
—
150
19d
7d
A588
HSLA, ACR
A687
A, QT, NT
—
A354
A, QT
BD
5⁄
1⁄
4
8
over 21 ⁄2 to 4
BC
1⁄
4
to 21 ⁄2
over 21 ⁄2 to 4
A449d
C, QT
—
A307
C
—
A325a,d
C, QT
—
1⁄
1⁄
4
2
to 1
to 1
11 ⁄8 to 11 ⁄2
A490a,d
A, QT
—
1⁄
2
to 11 ⁄2
aAvailable with weathering (atmospheric corrosion resistance) characteristics comparable to ASTM A242 and
A588 steels.
bA
= Alloy Steel
bACR = Atmospheric-Corrosion-Resistant Steel
bC
= Carbon Steel
bHSLA = High-Strength Low-Alloy Steel
bNT
= Notch-Tough Steel (CVN 15 @ −20°°F)
bQT
= Quenched and Tempered Steel
cMaximum (ultimate tensile strength)
dThreaded rod material with properties meeting ASTM A325, A490, and A449 specifications may be obtained
with the use of an appropriate steel (such as ASTM A193, grade B7), quenched and tempered after fabrication.
eNot less than 4 in.
Thus, the minimum hook length Lh min is:
φRn
2
Lh min =
0.7fc′d
where fc′ is the specified strength of the concrete, ksi. The total embedded anchor rod
length is then the hook length Lh plus the minimum embedment length from Table 8-26.
Headed Anchor Rods
When anchor rods are required for a calculated tensile force Tu, a more positive anchorage
is formed when headed anchor rods, illustrated in Figure 8-14b, are used. With adequate
embedment and edge distance, the limit state is either a tensile failure of the anchor rod
or the pull-out of a cone of concrete radiating outward from the head (Marsh and Burdette,
1985a) as illustrated in Figure 8-16.
The design tensile strength of the anchor rod is φRn,
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
ANCHOR RODS OR THREADED RODS
8 - 91
where
φ = 0.75
Rn = φtFu Ag
In the above equation, φt = 0.75.
Using the projected surface area of the concrete cone and a limiting average stress on
this area of 4√
fc′ , the minimum anchor rod length Lmin is
Lmin =
√
Acp
3.14
where
Acp =
Tu
φt√
fc′
fc′ = specified strength of the concrete, psi
Tu
45°
L
Failure
Plane
Projected Surface
Fig. 8-16. Concrete cone subject to pull-out.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
8 - 92
BOLTS, WELDS, AND CONNECTED ELEMENTS
Table 8-27.
Dimensions and Weights of Clevises
D
p
w
b
a
n
t
Grip
Grip = plate thickness + ¼ in.
t
Thread: UNC Class 2B
Dimensions, in.
Clevis Number
Max. D
2
5⁄
2 1 ⁄2
3
3 1 ⁄2
4
5
6
7
8
7⁄
8
8
13 ⁄8
11 ⁄2
13 ⁄4
2
21 ⁄2
3
4
Max. p
3⁄
4
11 ⁄2
13 ⁄4
2
21 ⁄4
21 ⁄2
3
33 ⁄4
4
b
n
17 ⁄16 5⁄8
21 ⁄2 11⁄8
3 15 ⁄16
31 ⁄2 15⁄8
4
13⁄4
21⁄4
5
6
23⁄4
3
7
4
8
a
w
37 ⁄8
4
5
6
6
7
8
9
10
11 ⁄16
11 ⁄4
11 ⁄2
13 ⁄4
2
21 ⁄2
3
31 ⁄2
4
t
Weight,
pounds
Design Strength
φR n*, kips
(+ 1 ⁄32, −0)
1
16 (+ ⁄32, −0)
1 ⁄ (+ 1 ⁄
2
32, −0)
1 ⁄ (+ 1 ⁄
2
32, −0)
1 ⁄ (+ 1 ⁄
2
32, −0)
5 ⁄ (+ 1 ⁄
8
16, −0)
3 ⁄ (+ 3 ⁄
4
32, −0)
7 ⁄ (+ 1 ⁄ −0)
8
8,
1
1
1 ⁄2 (+ ⁄8, −0)
1
2
4
6
8
16
26
36
80
5.25
11.3
22.5
27.0
31.5
56.4
81.0
103
203
5⁄
5⁄
16
Notes:
Weights and dimensions of clevises are typical; products of all suppliers are essentially similar. User shall verify
with the manufacturer that product meets design-strength specifications above.
*Tabulated design strengths for comparison with factored loads are based on φ=0.3. To determine safe working
load (kips) for comparison with service loads, divide tabular design strength by 1.5. Safe working load, then,
corresponds to a 5:1 factor of safety using maximum pin diameter.
Tu = tensile force in the anchor rod, kips
When the concrete cone intersects an edge of the pedestal or the cone from another
anchor rod, the effective area of concrete is reduced; refer to the AISC Design Guide
Column Base Plates (DeWolf and Ricker, 1990) and Marsh and Burdette (1985).
Marsh and Burdette (1985) showed that the head of the anchor rod usually provides
sufficient anchorage and the use of an additional washer or plate does not add significantly
to the anchorage. The nut and threading shown in Figure 8-14c is acceptable in lieu of a
bolt head. The nut should be welded to the rod to prevent the rod from turning out when
the top nut is tightened.
For the design of anchor rods for shear or a combination of tension and shear, see AISC
Design Guide Column Base Plates (DeWolf and Ricker, 1990), Fisher (1981), Shipp and
Haninger (1983), and ACI 349.
OTHER MECHANICAL FASTENERS
Clevises
Dimensions, weights, and design strengths of clevises are listed in Table 8-27. Compatability of clevises with various rods and pins is given in Table 8-28.
Turnbuckles
Dimensions, weights, and design strengths of turnbuckles are listed in Table 8-29.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
OTHER MECHANICAL FASTENERS
8 - 93
Table 8-28.
Clevis Numbers Compatible with Various Rods and Pins
Diameter of Pin, in.
Dia. of
Tap, in.
5⁄
8
5⁄
8
3⁄
4
7⁄
8
2
—
—
2 21⁄2 21⁄2 21⁄2 21⁄2
21⁄2 21⁄2 21⁄2 21⁄2 21⁄2
— 21⁄2 21⁄2 21⁄2 21⁄2
1
11⁄4
13⁄8
—
—
—
—
—
—
—
—
—
11⁄2
13⁄4
—
—
—
—
—
—
31⁄2 31⁄2 31⁄2
—
4
4
4
5
4
5
5
5
5
2
21⁄4
—
—
—
—
—
—
—
—
—
—
5
—
5
—
5
6
5
6
5
6
6
6
6
6
7
7
21⁄2
23⁄4
—
—
—
—
—
—
—
—
—
—
—
—
—
—
6
—
6
—
6
7
7
7
7
7
7
7
7
8
7
8
3
31⁄4
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
7
—
8
8
8
8
8
8
8
8
8
8
8
8
31⁄2
33⁄4
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
8
8
8
8
8
8
8
8
8
8
8
8
4
—
—
—
—
—
—
—
—
—
—
8
8
8
8
8
8
3⁄
4
7⁄
8
1
3
3
3
11⁄4 11⁄2 13⁄4
3
3
3
3
3
3
2
3
3 31⁄2
31⁄2 31⁄2
21⁄4 21⁄2 23⁄4
3
31⁄4 31⁄2 33⁄4
4
4
Notes:
Tabular values assume that the net area of the clevis through the pin hole is greater than or equal to 125 percent of the net area of the rod, and is applicable to round rods without upset ends. For other net area ratios, the
required clevis size may be calculated by reference to the dimensions tabulated in Tables 8-7 and 8-27.
Sleeve Nuts
Dimensions and weights of sleeve nuts are listed in Table 8-30.
Recessed-Pin Nuts
Dimensions and weights of recessed-pin nuts are listed in Table 8-31.
Cotter Pins
Dimensions and weights of cotter pins are listed in Table 8-32.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
8 - 94
BOLTS, WELDS, AND CONNECTED ELEMENTS
Table 8-29.
Dimensions and Weights of Turnbuckles
c
a
n
n
g
e
D
Threads: UNC and 4UN Class 2B
Weight (pounds) for Length a, in.
Dimensions, in.
Diameter
D, in.
a
3⁄
8
6
9⁄
1⁄
2
5⁄
8
3⁄
4
7⁄
8
6
6
6
6
3⁄
32
11⁄16
7
1 ⁄32
1 1 ⁄8
1 1 ⁄4
1 3 ⁄8
1
6
6
6
6
13 ⁄8
19⁄16
13 ⁄4
115 ⁄16
1 1 ⁄2
1 5 ⁄8
1 3 ⁄4
1 7 ⁄8
6
6
6
6
2 1 ⁄4
2
n
16
29 ⁄
4
c
g
6
11 ⁄32
0.41
71 ⁄2 11⁄16 15 ⁄16
713 ⁄16 13 ⁄16 11 ⁄2
81 ⁄8 15 ⁄16 123 ⁄32
87 ⁄16 13 ⁄32 17 ⁄8
0.75
1.00
1.45
1.85
71 ⁄8
83 ⁄4
91 ⁄8
91 ⁄2
97 ⁄8
e
9⁄
16
9
12
18
24
26
Design
Strength,
φR n *, kips
1.80
0.80
1.38
1.63
1.00
1.50
2.13
2.83
2.43
3.06
4.20
3.30
5.25
7.80
10.8
4.25
5.43
19 ⁄32 21 ⁄32
113 ⁄32 29 ⁄32
19 ⁄16 217 ⁄32
111⁄16 23 ⁄4
2.60
2.72
3.58
4.50
3.20
4.70
4.70
4.40
6.10
7.13
6.85
10.0
11.3
13.1
21 ⁄8
21 ⁄4
21 ⁄2
23 ⁄4
101 ⁄4 127 ⁄32 31 ⁄32
101 ⁄2 131 ⁄32 39 ⁄32
11
21 ⁄8 39 ⁄16
111 ⁄2 23 ⁄8
4
5.50
7.50
9.50
11.5
8.00
9.13
16.8
19.4
15.3
16.0
19.5
6
6
23 ⁄4
33 ⁄8
111 ⁄2 23 ⁄8
123 ⁄4 211⁄16
4
45 ⁄8
11.5
18.0
15.3
35.3
27.5
43.5
55.8
72.0
2 1 ⁄2
2 3 ⁄4
6
6
33 ⁄4
41 ⁄8
131 ⁄2
141 ⁄4
3
31 ⁄4
5
55 ⁄8
23.3
31.5
33.6
42.4
54.0
90.0
113
3 1 ⁄4
3
6
6
41 ⁄2
51 ⁄4
15
161 ⁄2
35 ⁄8
37 ⁄8
61 ⁄8
63 ⁄4
39.5
60.5
145
183
3 1 ⁄2
3 3 ⁄4
6
6
51 ⁄4
6
161 ⁄2
18
37 ⁄8
45 ⁄8
63 ⁄4
81 ⁄2
60.5
95.0
183
252
4 1 ⁄4
4
6
9
6
63 ⁄4
18
221 ⁄2
45 ⁄8
51 ⁄4
81 ⁄2
93 ⁄4
95.0
4 1 ⁄2
4 3 ⁄4
9
9
63 ⁄4
63 ⁄4
221 ⁄2
221 ⁄2
51 ⁄4
51 ⁄4
5
9
71 ⁄2
24
6
14.0
17.4
22.8
26.1
31.5
36.8
42.5
55.8
152
252
351
93 ⁄4
93 ⁄4
152
152
351
351
10
200
442
Notes:
Weights and dimensions of turnbuckles are typical; products of all suppliers are essentially similar. User shall
verify with the manufacturer that product meets design strength specifications above.
*Tabulated design strengths for comparison with factored loads are based on φ = 0.3. To determine safe
working load (kips) for comparison with service loads, divide tabular design strength by 1.5. Safe working load,
then, corresponds to a 5:1 factor of safety using maximum pin diameter.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
OTHER MECHANICAL FASTENERS
8 - 95
Table 8-30.
Dimensions and Weights of Sleeve Nuts
l
4
½
D
n
Long
Dia.
½
Short
Dia.
n
c
Inspection hole (optional)
Thread: UNC and 4 UN Class 2B
Screw Dia.
D, in.
3⁄
8
7⁄
16
1⁄
2
9⁄
16
5⁄
8
3⁄
4
7⁄
8
1
11⁄8
11⁄4
13⁄8
11⁄2
15⁄8
13⁄4
17⁄8
2
21⁄4
21⁄2
23⁄4
3
31⁄4
31⁄2
33⁄4
4
41⁄4
41⁄2
43⁄4
5
51⁄4
51⁄2
53⁄4
6
Dimensions, in.
Short Dia.
Long Dia.
Length l
Nut n
Clear c
Weight,
pounds
11⁄
16
25⁄
32
7⁄
8
15⁄
16
11⁄16
11⁄4
17⁄16
15⁄8
113⁄16
25⁄
32
7⁄
8
4
4
4
5
5
5
7
7
71⁄2
71⁄2
8
8
81⁄2
81⁄2
9
9
91⁄2
10
101⁄2
11
111⁄2
12
121⁄2
13
131⁄2
14
141⁄2
15
151⁄2
16
161⁄2
17
—
—
—
—
—
—
17⁄16
17⁄16
15⁄8
15⁄8
17⁄8
17⁄8
21⁄16
21⁄16
25⁄16
25⁄16
21⁄2
23⁄4
215⁄16
33⁄16
33⁄8
35⁄8
313⁄16
41⁄16
43⁄4
5
51⁄4
51⁄2
53⁄4
6
61⁄4
61⁄2
—
—
—
—
—
—
1
11⁄8
11⁄4
13⁄8
11⁄2
15⁄8
13⁄4
17⁄8
2
21⁄8
23⁄8
25⁄8
27⁄8
31⁄8
33⁄8
35⁄8
37⁄8
41⁄8
43⁄8
43⁄4
5
51⁄4
51⁄2
53⁄4
6
61⁄4
0.27
0.34
0.43
0.64
0.93
1.12
1.75
2.46
3.10
4.04
4.97
6.16
7.36
8.87
10.4
12.2
16.2
21.1
26.7
33.2
40.6
49.1
58.6
69.2
75.0
90.0
98.0
110
122
142
157
176
2
23⁄16
23⁄8
29⁄16
23⁄4
215⁄16
31⁄8
31⁄2
37⁄8
41⁄4
45⁄8
5
53⁄8
53⁄4
61⁄8
61⁄2
67⁄8
71⁄4
75⁄8
8
83⁄8
83⁄4
91⁄8
1
11⁄16
17⁄32
17⁄16
15⁄8
113⁄16
21⁄16
21⁄4
21⁄2
211⁄16
215⁄16
31⁄8
35⁄16
31⁄2
315⁄16
43⁄8
413⁄16
51⁄4
55⁄8
6
63⁄8
67⁄8
71⁄2
715⁄16
83⁄8
87⁄8
91⁄4
93⁄4
101⁄8
105⁄8
Notes:
Weights and dimensions of sleeve nuts are typical; products of all suppliers are essentially similar. User shall
verify with the manufacturer that strengths of sleeve nut are greater than the corresponding connecting rod
when the same material is used.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
8 - 96
BOLTS, WELDS, AND CONNECTED ELEMENTS
Table 8-31.
Dimensions and Weights of Recessed-Pin Nuts
Short
Dia.
Long
Dia.
Tc
Grip
d
D
s t
Material: Steel
Thread: 6 UN Class 2A/2B
Pin Dimensions, in.
Thread
Pin Dia.
d, in.
D
T
2, 2 1 ⁄4
2 1 ⁄2 , 2 3 ⁄4
3, 3 1 ⁄4 , 3 1 ⁄2
3 3 ⁄4 , 4
4 1 ⁄4 , 4 1 ⁄2 , 4 3 ⁄4
5, 5 1 ⁄4
5 1 ⁄2 , 5 3 ⁄4 , 6
6 1 ⁄4 , 6 1 ⁄2
6 3 ⁄4 , 7
7 1 ⁄4 , 7 1 ⁄2
7 3 ⁄4 , 8, 81 ⁄4
8 1 ⁄2 , 8 3 ⁄4 , 9
9 1 ⁄4 , 9 1 ⁄2
9 3 ⁄4 , 10
11 ⁄2
2
21 ⁄2
3
31 ⁄2
4
41 ⁄2
5
51 ⁄2
51 ⁄2
6
6
6
6
1
11 ⁄8
11 ⁄4
13 ⁄8
11 ⁄2
15 ⁄8
13 ⁄4
17 ⁄8
2
2
21 ⁄4
21 ⁄4
23 ⁄8
23 ⁄8
c
Grip
½
d+1
d
Bolt
¾
1⁄
1⁄
1⁄
1⁄
1⁄
1⁄
1⁄
3⁄
3⁄
3⁄
3⁄
3⁄
3⁄
3⁄
8
8
8
4
4
4
4
8
8
8
8
8
8
8
Nut Dimensions, in.
Thickness
t
7⁄
8
1
11 ⁄8
11 ⁄4
13 ⁄8
11 ⁄2
15 ⁄8
13 ⁄4
17 ⁄8
17 ⁄8
21 ⁄8
21 ⁄8
21 ⁄4
21 ⁄4
Diameter
Short Dia.
3
35 ⁄8
43 ⁄8
47 ⁄8
53 ⁄4
61 ⁄4
7
75 ⁄8
81 ⁄8
85 ⁄8
93 ⁄8
101 ⁄4
111 ⁄4
111 ⁄4
Recess
Long Dia. Rough Dia.
33 ⁄8
41 ⁄8
5
55 ⁄8
65 ⁄8
71 ⁄4
81 ⁄8
87 ⁄8
93 ⁄8
10
107 ⁄8
117 ⁄8
13
13
25 ⁄ 8
31 ⁄ 8
37 ⁄ 8
43 ⁄ 8
51 ⁄ 4
53 ⁄ 4
61 ⁄ 2
7
71 ⁄ 2
8
83 ⁄ 4
95 ⁄ 8
105⁄8
105⁄8
s
1⁄
1⁄
3⁄
3⁄
1⁄
1⁄
5⁄
5⁄
3⁄
3⁄
3⁄
3⁄
3⁄
3⁄
4
4
8
8
2
2
8
8
4
4
4
4
4
4
Weight,
pounds
1
2
3
4
5
6
8
10
12
14
19
24
32
32
Notes:
Although nuts may be used on all sizes of pins as shown above, a
detail similar to that shown at the left is preferrable for pin diameters
over 10 inches. In this detail, the pin is held in place by a recessed cap
at each end and secured by a bolt passing completely through the
caps and pin. Suitable provisions must be made for attaching pilots
and driving nuts.
¾
Typical Pin Cap Detail for Pins
over 10 in. in dia.
Dimensions shown are approximate
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
OTHER MECHANICAL FASTENERS
8 - 97
Table 8-32.
Dimensions and Weights of Cotter Pins
HORIZONTAL OR VERTICAL PIN
3/8
HORIZONTAL PIN
1″
1
GRIP + ½
p
d
h
GRIP + 1 ″
1″
d
c
l
l = Length of pin, in.
Pins with Heads
Head Diameter h,
Pin Diameter d, in.
in.
11⁄4
11⁄2
13⁄4
2
21⁄4
21⁄2
23⁄4
3
31⁄4
31⁄2
33⁄4
11⁄2
13⁄4
2
23⁄8
25⁄8
27⁄8
31⁄8
31⁄2
33⁄4
4
41⁄4
Weight of One,
pounds
0.19 + 0.35l
0.26 + 0.50l
0.33 + 0.68l
0.47 + 0.89l
0.58 + 1.13l
0.70 + 1.39l
0.82 + 1.68l
1.02 + 2.00l
1.17 + 2.35l
1.34 + 2.73l
1.51 + 3.13l
Cotter
Length c, in.
Diameter p, in.
Weight per 100,
pounds
7⁄
1⁄
4
1⁄
4
1⁄
4
3⁄
8
3⁄
8
3⁄
8
3⁄
8
1⁄
2
1⁄
2
1⁄
2
1⁄
2
2.64
3.10
3.50
9.00
9.40
10.9
11.4
28.5
28.5
33.8
33.8
8
1
11⁄8
11⁄4
13⁄8
11⁄2
15⁄8
13⁄4
17⁄8
17⁄8
21⁄4
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
8 - 98
BOLTS, WELDS, AND CONNECTED ELEMENTS
WELDED CONSTRUCTION
While AWS D1.1 is the traditional design specification for weld stresses in both buildings
and bridges, AASHTO/AWS D1.5 also exists for dynamically loaded structures. There
are significant differences between the two codes and, in the case of building structures,
AWS D1.1 is normally used unless contract documents state otherwise.
Welds in building structures are predominantly designed for static loading. Some parts,
however, such as crane runways and machinery supports, are subjected to dynamic
loading. When this is the case, additional requirements and special joint details may be
necessary. This may include reinforcing fillet welds at tee and corner joints, radius cuts
on terminations of gusset type connections, radiographic or ultrasonic testing for quality
control, or joint details in accordance with LRFD Specification Appendix K3. The
contract documents should specifically enumerate these additional requirements when
they are determined to be necessary.
Weldability of Steel
AWS has defined weldability as the capacity of a metal to be welded, under the fabrication
conditions imposed, into a specific, suitably designed structure, and to perform satisfactorily in the intended service. AWS D1.1 is based on certain weldable grades of steel as
listed therein by ASTM designation. It contains all of the steels permitted by LRFD
Specification Section A3.1a.
The effect a steel’s properties have upon its weldability relates to the reaction of the
steel to the drastic heating and cooling cycle of welding. This weld quench can range
from the practically instantaneous cooling of an accidental arc strike to the 10 minutes
required to cool a high-heat-input electroslag weld. Due to the rapid cooling of the arc
strike, the full-quench hardness for the carbon equivalent of the steel may be realized,
resulting in brittleness and the potential for cracking. In contrast, the slower cooling rate
of the electroslag weld may produce a more ductile and lower-strength metallurgical
structure in the heat-affected zone (HAZ) of the base metal.
As they cool, welds develop residual shrinkage strains that can approach the yield strain
as a limit; ductility and notch resistance are needed to accommodate these strains. Since
chemical composition, grain size, and thickness affect ductility and notch resistance, they are
the most important properties for weldability. These factors, discussed below, assume greater
significance as the structure becomes large and must store greater elastic energy.
Table 8-33 summarizes several ASTM specifications and their requirements for the
aforementioned properties. Note that there is a greater flexibility in grain size and carbon
equivalents in these specifications for shapes, plates, and bars. Also, maximum tensile
strength requirements are listed to exclude steels from the upper end of the chemical
composition range which might require special welding procedures or weld repairs. In
contrast, the requirements for structural tubing, pipe, sheet, and strip do not limit grain
size or maximum tensile strength, but generally impose smaller limits on thickness.
Chemical analysis of a heat of steel is usually made during the processing as a control
and upon completion after it has been tapped into a ladle. This heat analysis is used to
compile a mill test report which also lists the customer’s order number, steel grade,
quantity and dimension of pieces shipped, and the results of any mechanical testing
(tensile, flexural, Charpy impact, or other). This information may be obtained by request
from the steel supplier when placing an order and is essential for good control of welded
fabrication. It is imperative that the grade of steel to be welded is known since the proper
welding procedure depends upon this information.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
WELDED CONSTRUCTION
8 - 99
Table 8-33.
ASTM Requirements for Properties Affecting Weldability of Steels
Max. Carbon
content, % by
weight (heat
analysis)
Max. tensile
strength, ksi
Grain Size
Max.
thickness,
in.
80
—*
none
ASTM
Specification
Products
Covered
A36
shapes
0.26
plates
0.25–0.29
A242
A514
bars
0.26–0.29
shapes, plates, bars
type 1, 0.15
plates—quenched varies among 13
and tempered
grades, 0.14–0.21
none
—
4
130
fully killed,
fine grain
6
1⁄
A529
shapes, plates, bars
0.27
85
—
A572
shapes, plates,
bars, sheet piling
varies among
grades, 0.21–0.26
none
—*
Gr. 42: 6
Gr. 50: 4
Gr. 60, 65:
11 ⁄4
A588
shapes, plates, bars
varies among 5
grades, 0.15–0.20
none
fine grain
F y = 50: 4
F y = 42: 8
2
A852
plates
0.19
110
fine grain
4
A53 Grade B
tubing, pipe
0.30
none
—
2.344, 24 dia.
A500
tubing, pipe
Gr. A, B: 0.26
Gr. C: 0.23
none
—
A501
tubing, pipe
0.26
none
—
1
A618
tubing, pipe
Gr. Ia: 0.15
Gr. Ib: 0.20
Gr. II: 0.22
Gr. III: 0.23
none
—
11 ⁄2
A570, Gr. 36, 50
sheet, strip
0.25
none
—
0.23
A606
sheet, strip
0.22
none
—
none
A607
sheet, strip
0.22–0.26
none
—
none
1⁄
2
*Supplemental requirements can specify killed fine grain.
Chemical Composition
The most important element affecting weldability is carbon, however, the effect of other
elements on weldability is related through a carbon equivalent formula. Weldability is
enhanced as carbon equivalent decreases because the maximum hardness and consequent
brittleness that a steel may reach after rapid liquid quenching from high temperature is
directly proportional to the carbon equivalent. This relationship is illustrated in Figure
8-17 and is applicable to the surface in contact with the quench liquid where the quench
rate is greatest.
Although no liquid is present in welding, the HAZ is subject to rapid cooling and
consequent hardening by conduction of weld heat into the base metal. As the thickness
of the section increases, so does the cooling rate, producing progressively harder and less
ductile metallurgical constituents. Alloys such as Ni, Cr, and Mo in the steel permit
hardening at slower cooling rates and at depths below the surface where the cooling rate
is slower; pre-heat is the common remedy for reducing the cooling rate and hardness.
As the carbon content increases from 0.10 percent to 0.20 percent by weight, the
maximum as-quenched hardness increases from 40 to 50 Rockwell C. Using the known
hardness-strength relationship, it can be shown that the maximum as-quenched tensile
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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BOLTS, WELDS, AND CONNECTED ELEMENTS
strength increases from 180 to 260 ksi. Welding procedures are designed to keep weld
quench rates far below these maximum rates. Also, electrodes are usually designed to
deposit weld metal containing about 0.008 to 0.12 percent carbon to avoid cracking.
Grain Size
In general, weldability will be enhanced by steel with a finer grain size. As illustrated in
Figure 8-18, grain size is a prime variable affecting the ductility and impact resistance
for a wide variety of steel compositions.
The grain size of weld metal also varies and has a similar effect. Because they
experience a slower cooling rate, high-heat-input welds show a larger grain size than the
same process and electrode at a lower heat input. This is one reason the AWS D1.1 limits
multi-pass SAW groove weld layers to a maximum size of 1⁄4-in. Also, a subsequent pass
will refine the grain of a previous pass.
Thickness
In general, as the thickness to be welded decreases, the weldability of the material is
enhanced. Because of their greater mass, thick plates extract heat from and quench the
weld more rapidly than thin plates with the identical weld. As a partial remedy, the plates
may be pre-heated and held at temperatures of a few hundred degrees Fahrenheit for the
welding operation. This pre-heat appreciably slows the quench rate and reduces weld
hardness, as does post-heating.
As plate thickness increases, the notch impact resistance decreases as shown in
Figure 8-19. This test was conducted on American Bureau of Shipping (ABS) class C
ship plate in 3⁄4-in., 1-in., 2-in., and 3-in. thicknesses using a severe crack-like notch in
the ASTM A208 drop-weight test. The use of fine-grain steelmaking practice as specified
by ASTM can improve notch toughness where required by the service of a particular
structure.
60
255
50
Maximum hardness for carbon
and alloy steels
40
180
140
30
20
Equivalent tensile strength, ksi
Maximum hardness, Rockwell, C
70
10
0
0.20
0.40
0.60
0.80
1.0
Carbon, per cent
Fig. 8-17. Influence of carbon content on the maximum hardness of steel as quenched
(Stout and Doty, 1978), courtesy Welding Research Council.
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Structural Welding Materials and Processes
Filler metal and flux specifications are exclusively AWS specifications, having been
removed from ASTM specifications. Additionally, AWS uses a coding system for
consumable electrodes to designate the tensile strength and coating or flux combination.
Since the coding for the several filler/flux combinations are consistent only with respect
to the types of electrode used, it is very important that the applicable specifications be
reviewed when specifying such welding requirements.
The welding processes discussed in this text are: shielded metal arc welding (SMAW),
submerged arc welding (SAW), gas-metal arc welding (GMAW), flux-cored arc welding
(FCAW), electroslag welding (ESW) and electrogas welding (EGW). Except for electroslag welding, each of these processes use electrical energy from an arc discharge
between a steel-wire electrode and the base metal to provide heat for fusion. Electroslag
welding uses a high-electrical-resistance molten-slag bath which occupies the entire joint.
This slag melts both the electrode and the base metal.
40
CVN Transition Temperature, °F
0
– 40
– 80
c
c
c
–120
–160
— Plain Carbon
c — Nickel
— Manganese
— Molybdenum
— Chromium
c
–200
(After Kottcamp and Stout)
9
8
7
6
5
4
ASTM Ferrite-grain Size Number
Fig. 8-18. Effect of ferrite-grain size on CVN transitional temperature
(Stout and Doty, 1978), courtesy Welding Research Council.
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BOLTS, WELDS, AND CONNECTED ELEMENTS
Each of the aforementioned processes will be summarized here; a full description may
be found in AWS (1978). Additionally, thermal cutting and air arc gouging will be
discussed.
SMAW
There are two AWS Specifications for SMAW electrodes: AWS A5.1 and AWS A5.5. A
condensation of the provisions of these specifications is given in Table 8-34.
AWS notation for SMAW electrodes is illustrated in Figure 8-20. This has also been
extended to other processes. The welding positions noted in Figure 8-20 (flat, horizontal,
vertical, and overhead) are illustrated in Figure 8-21. SMAW (stick) electrodes are made
in a variety of low-carbon compositions. The extruded coatings contain aluminum,
silicon, and other deoxidizers; the deposited weld is a mini-electric-furnace-killed steel
with excellent ductility and resistance to cracking from weld shrinkage strains.
In the arc stream, moisture breaks down and liberates atomic hydrogen which is readily
soluble in molten iron (Stout and Doty, 1978); see Figure 8-22. As the weld solidifies,
70
Increase in NDT Transition Temperature, °F
60
50
40
30
20
ABS-C, Drop-Weight NDT
10
0
0
1
2
Plate Thickness, in.
3
Fig. 8-19. Effect of plate thickness on the drop-weight NDT ductility transition temperature
(Stout and Doty, 1978), courtesy Welding Research Council.
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Table 8-34.
Condensed AWS Specifications for SMAW Electrodes
Electrode
Type
AWS
Spec.
Carbon
Steel
A5.1
Low
Alloy
A5.5
Impact Test Criteria
Criteria for
Min.
Criteria for
Tensile Composition
Strength, of Deposited Charpy V- Weld Metal Radiographic
Grades
Weld Metal Notch Test Condition Soundness
ksi
60
62
70
72
70
80
90
100
110
120
70
80
90
100
110
120
Not stipulated Required for As-welded
some grades
Stipulated
only
Stipulated
(all grades)
Required for Some assome grades
welded,
only
some stressrelieved
Stipulated for
all but E6012,
E6022
Stipulated
for all grades
Note: A particular production welding condition may be more severe than the test conditions specified for the
above.
hydrogen becomes much less soluble and the atoms are rejected into voids where pairs
combine to form a much less mobile molecular H2. This molecular hydrogen can then
exert pressure in lattice imperfections which is sufficient, when combined with weld
shrinkage strains, to cause “fisheyes” or cracking in the weld material. This can be
prevented by maintaining the moisture content of consumable electrodes below specified
levels and through proper pre-heat.
E7015, E7016, E7018, and E7028 low-hydrogen electrodes have specially compounded and baked extruded coatings containing a limited moisture (hydrogen) content
by weight. Coatings for the E70 electrode series can contain a maximum of 0.04 percent
moisture, while the E120 electrode series is limited to only 0.015 percent. As the tensile
strength of the base metal increases, electrodes with lower moisture content must be
selected to avoid weld cracking. Since the electrode coating will absorb moisture when
stored in damp or humid conditions, drying ovens near points of use in the shop are
necessary for low-hydrogen electrodes.
6
—
A1
Weld metal composition
1
Coating characteristics**
70
70,000 psi min. tensile
Electrode
E
Position code*
ELECTRODE PROPERTIES
**1 = All flat, vertical, overhead, and horizontal
**2 = Flat and horizontal only
**5, 6, 8 = Low hydrogen
Fig. 8-20. AWS classification system for SMAW electrodes.
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BOLTS, WELDS, AND CONNECTED ELEMENTS
Fillet Welds
Groove Welds
(a) Flat
(b) Horizontal
(c) Vertical
(d) Overhead
Fig. 8-21. Welding positions.
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The electrodes to be used with various base metals are shown in AWS D1.1 Table 4.1.
Low-hydrogen electrodes are used with ASTM A572 and A588 steels among others. Filler
metal matching the color of ASTM A588 steel is listed in AWS D1.1 Table 4.2.
SAW
The automatic and semi-automatic SAW processes provide consistent, high quality, and
economical deposits which are particularly suitable for long welds. Their major limitation
is that the work must be positioned to allow for near flat or horizontal welding.
In the SAW process, fluxes may be fused or agglomerated (finely powdered constituents bonded together with silicates), but are classified in AWS specifications only
according to the weld metal properties produced in the standard specified weld tests. The
applicable specifications are: AWS A5.17 and AWS A5.23.
AWS notation for SAW electrodes and fluxes is illustrated in Figure 8-23. Fluxes must
be kept dry in storage to avoid an increase in moisture content and subsequent chance of
hydrogen cracking in steels with higher yield strengths or highly restrained joints in thick
members.
Hydrogen, cm.3 per 100 g. of iron
5
10
15
20
25
30
2100
2500
Austenite
Delta
Iron
1 atmos.
1100
1500
600
Ferrite
Temperature, °C.
1600
500
100
0
0.00075
0.0015
Hydrogen, percent
0.00225
Fig. 8-22. Solubility of hydrogen in iron (Stout and Doty, 1978),
courtesy Welding Research Council.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
0.003
Temperature, °F.
Liquid
3500
8 - 106
BOLTS, WELDS, AND CONNECTED ELEMENTS
GMAW
The GMAW process can be used with mixtures of argon and two percent oxygen, argon
and carbon dioxide, or pure carbon dioxide. While argon is inert, carbon dioxide can react
with the weld metal and result in a reduction in ductility and impact properties at low
temperatures. Despite this, 70 ksi electrodes have commonly been used with carbon
dioxide gas with good results; a CVN 20 (20 ft-lb Charpy V-notch impact value) at −20°F
is specified in the AWS tests. Alloy electrodes producing up to 120 ksi minimum tensile
strength with CVN 20 at −60°F, and three percent nickel electrodes producing 80 ksi
minimum tensile strength with CVN 20 at −100°F are available.
There are two AWS Specifications for GMAW electrodes: A5.18 and A5.28. Identification of these electrodes is illustrated in Figure 8-24.
FCAW
FCAW electrodes are made by forming a thin sheet strip into a U-shape and filling it with
flux. After closing the tube, it is drawn to size as a continuous coil. AWS classifies these
M
12
K
Silicon killed
Medium Mn (1.00% ± )
E
Nominal carbon (0.12%)
6
Electrode
A
ELECTRODE PROPERTIES
CVN 20 @ − 60° F
7
Tested as welded
Flux
F
70,000 psi min. tensile
FLUX CAPABILITY
Fig. 8-23. AWS classification system for SAW materials.
ELECTRODE PROPERTIES
B2
L
Low carbon (0.05% max.)
—
Cr (11/ 4 %); Mo (1/ 2 %)
S
Solid electrode
80
80,000 psi min. tensile
R
Rod*
Electrode
E
*Can be used as feed rod with independent heat source (e.g., tungsten arc)
Fig. 8-24. AWS classification system for GMAW electrodes.
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electrodes according to: (1) whether or not carbon dioxide is used as a separate shielding
gas; (2) suitability for either single or multiple pass applications; (3) the type of current;
(4) the welding position; and, (5) the as-welded mechanical properties of the weld metal.
High weld-production rates may be attained with semi-automatic equipment which
may be used in any position with the appropriate electrode. Where required by service
conditions, flux-cored electrode grades can provide weld metal with CVN 20 impact
values at temperatures in steps from 20°F to −100°F. Some of the deposits of the carbon
steel electrodes will develop CVN 20 at −20°F, while the low alloy electrodes will
develop CVN 20 at −100°F.
The applicable specifications are AWS A5.20 and AWS 5.29 (symbols are similar to
AWS 5.20 with the addition of an alloy composition at the extreme right). The AWS
classification system is illustrated in Figure 8-25.
ESW and EGW
With the ESW and EGW processes, 18-in. and greater thicknesses may be welded in one
pass, using multiple electrodes, with the joint in a vertical plane. A single-electrode,
semi-portable welding machine can join plates up to five inches thick. Furthermore, using
either of these processes, it is possible to make girder flanges by welding mill-width plates
and subsequently longitudinally cutting out three or more flange widths.
Note that AWS prohibits the use of these welding processes on quenched and tempered
steels.
The composition of cored electrodes is based on weld-metal analysis, and the composition of solid electrodes is based on wire analysis. The coarse grains in the slow-cooled
electroslag weld may make it difficult to test ultrasonically and the minimum size flaw
detectable by RT is about 11⁄2 percent of the thickness. This creates difficulty in the
inspection of electroslag welding.
AWS A5.25 requires electrodes which contain nickel to provide CVN 15 impact values
at either 0°F or −20°F. This specification is patterned after AWS A5.17 and A5.18 insofar
as the electrodes are concerned; refer to Figure 8-26.
1
—
2
Usability code**
T
Position code*
70
70,000 psi min. tensile
Electrode
E
Tubular (flux cored)
ELECTRODE PROPERTIES
**2 = Flat and horizontal only
**1 = All position
**2 = Single pass CO2 shielded only
Fig. 8-25. AWS classification system for FCAW electrodes.
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BOLTS, WELDS, AND CONNECTED ELEMENTS
Thermal Cutting and Air-Arc Gouging
Thermally cut welding bevels are required to be smooth and free of notches or grooves
in which weld slag may be trapped. Two cutting systems, oxy-fuel gas and plasma arc,
are available. Oxy-fuel gas cutting may be used to cut almost any plate thickness
commercially available except in stainless steel which must be plasma cut. Plasma arc
cutting will cut thicknesses only up to about 11⁄2-in., but is much faster than oxy-fuel gas
cutting. This speed advantage increases as the plate thickness decreases; at a thickness
of one inch, the cutting speed is over 300 percent faster with a water-injection plasma
torch. The plasma arc cutting process, however, also leaves a slight taper in the cut as it
descends.
If the plate being cut contains large discontinuities or non-metallic inclusions, turbulence may be created in the oxy-fuel cutting stream. As result, this may cause notches or
gouges in the edge of the cut. The plasma arc stream is less susceptible to this as it moves
with a higher velocity. Within the depth limits of the specifications, it is usually better
practice to remove these by grinding than to weld repair and grind. Additionally,
re-entrant thermal cuts should provide a smooth transition.
Carbon-air-arc gouging is a convenient method for removing weld defects, gouging
the weld root to sound metal, or forming a U-groove on one side of a square butt joint.
The carbon arc travels over the work and melts a weld-nugget-shaped area of the metal.
This molten material is then blown away by a jet of compressed air, directed from the
holder, parallel to the carbon electrode. Thus, air-arc gouging may be considered the
opposite of welding in that each pass removes approximately one weld pass. Because the
arc quench is similar in both air-arc gouging and welding, any pre-heat required for
welding should also be used for air-arc gouging.
Inspection
The five most commonly used testing methods for welding inspection are: visual (VT),
dye penetrant (DPT), magnetic particle (MT), radiographic (RT), and ultrasonic (UT).
These methods are discussed in the following sections; refer also to AWS B1.0. Visual
inspection is the most commonly specified procedure. Other, more stringent methods can
Electrode
W
Fig. 8-26. AWS classification system for ESW materials.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
T
1
CNV 15 @ 20°F
E
70,000 psi min. tensile
2
Weld metal tested as deposited
7
CNV 15 @ 20°F
ES
Electroslag flux
Flux
F
ELECTRODE PROPERTIES
70,000 psi min. tensile
FLUX CAPABILITY
WELDED CONSTRUCTION
8 - 109
add significant cost to the project and, therefore, should be specified only when essential
to the integrity of the structure.
The engineer of record (EOR) must specify in the contract documents which type of
weld inspection is required as well as the extent and application of each type. In the
absence of instruction, AWS D1.1, paragraph 6.6.5 states that the fabricator or erector is
responsible only for those weld discontinuities found by visual inspection. If additional
inspection more stringent than visual is later required, the owner is normally responsible
for the cost of weld repairs other than those identified by the visual inspection.
VT
Visual testing provides the most economical approach to checking weld quality. It is
particularly good for inspecting single-pass welds, but is limited in that only surface
imperfections may be detected. This type of inspection is especially effective when it
includes both a check of the joint for accuracy and cleanliness before welding and an
observation of the welding procedure. Acceptance criteria are specified in the AISC Code
of Standard Practice and Quality Criteria and Inspection Standards (AISC, 1988), as
well as AWS D1.1.
DPT
A red dye penetrant is applied to the work and penetrates any crack or crevice open to
the surface. After removing excess dye, a white developer is applied. Where cracks are
present, the red dye seeps through the developer, producing a visible red image. This
process is summarized in Figure 8-27.
DPT may be used to detect tight cracks as long as they are open to the surface. Like
VT, however, only surface cracks are detectable. Furthermore, deep weld ripples and
scratches may give a false indication when DPT is used.
MT
A magnetizing current is introduced into the weldment to be inspected as shown in Figure
8-28. The magnetic field induced in the work will be distorted by any cracks, seams,
inclusions, etc., located on or within approximately 1⁄10-in. of the surface. A dry magnetic
powder spread lightly on the surface will gather at such discontinuities, leaving a distinct
mark. These magnetically held particles then show the size, location, and shape of the
discontinuity.
This method will detect surface cracks filled with slag or contaminants which dye in
DPT could not enter. Additionally, the powder may be picked up and preserved with clear
Visible
Indication
Subvisible
Crack
Cleaned Surface
Penetrant Applied
Excess Removed
Fig. 8-27. Schematic diagram of DPT.
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Developer Applied
8 - 110
BOLTS, WELDS, AND CONNECTED ELEMENTS
tape, providing accurate and detailed records of inspection results. However, this method
requires relatively smooth surfaces and while cleanup is easy, demagnetization, when
necessary, may not be.
RT
This method uses a radioactive source and an X-ray film process. RT can detect porosity,
slag, voids, cracks, irregularities, and lack of fusion. To be detected, the imperfection
must be oriented roughly parallel to the impinging radiation beam and occupy about
11⁄2 percent of the metal thickness along that beam. The film negative provides a
permanent record of the inspection.
Defects smaller than about 11⁄2 percent of the metal thickness and defects not parallel
to the beam may not register. RT of closed, inaccessible pipe joints is difficult to obtain
and interpret and should be discouraged. Additionally, when the particle beam must
penetrate varying thicknesses, as at fillets and tee or corner joints, RT is not readily
interpreted and the resulting inspection may be less consistent. When this is the case,
other inspection methods should be used. Other limitations of RT are that the required
exposure time increases with material thickness and there is a worker hazard due to the
radiation used in the method. The precautions for avoiding these hazards and the
equipment and film costs make this method the most expensive inspection method.
UT
This process, illustrated in Figure 8-29, is analogous to radar and operates on a principle
called pulse-echo. A short pulse of high-frequency sound is introduced into the metal.
The reflection of this sound wave from the far end of the member and any voids
encountered along the way may then be detected. Any reflections are displayed as pips
on a display in which the horizontal grid represents the distance through the metal, and
the vertical scale represents the area, and therefore the strength, of the reflecting surface.
The point of origin of the sound wave can be readily moved around to check many
orientations and can project the wave into the metal at angles of 90°, 70°, 60°, and 45°.
While UT can detect favorably oriented, flat discontinuities smaller than 1⁄64-in. in
carbon and low-alloy structural steels, austenitic stainless steels and extremely coarse-
Current
Part
Magnetic
Field
Fig. 8-28. Schematic diagram of MT.
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grained steels such as electroslag weld metal are difficult to inspect. Also, certain joint
geometry limits the use of UT and it is difficult to inspect members less than 5⁄16-in. thick
because there is a “dead area” at the origin of the sound wave.
The accuracy of UT depends upon the skill and training of the operator and frequent
calibration of the instrument. ASNT has set training standards for UT operators. Despite
the fact that UT is a more versatile, expedient, and economical inspection method than
RT, it does not provide a permanent record like the X-ray negative in MT. Instead the
operator must make a written record of discontinuity indications. For more information,
see Krautkramer (1977) and Institute of Welding (1972).
Economical Considerations
On a weight basis, the cost of weld metal far exceeds the cost of any other material in a
structure. Therefore, in addition to designing joints for the best welding position,
significant economy can be achieved by selecting the proper weld type and an arrangement for the welds which requires a minimum amount of weld metal and the least amount
of deposit time. Acceptance of prior qualification of welding procedures can also result
in a more economical structure.
Good Bond
Slag Inclusion
Crack or
Incomplete Fusion
Fig. 8-29. Variations in UT reflections due to differences in acoustic properties
caused by defects at the boundary.
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BOLTS, WELDS, AND CONNECTED ELEMENTS
Welding Position
When weld metal is deposited in the flat position, it can be deposited more quickly since
gravity does not adversely affect the deposit. As a result, large electrodes and high
currents may be used. In the vertical and overhead positions, electrode diameters above
5⁄ -in. produce weld pools with surface tensions and arc forces which are unable to
32
overcome the pull of gravity, causing the weld metal to run. Since the deposition rate in
the flat position and in the horizontal position for single-pass fillet welds (not greater than
5⁄ -in.) is approximately four times faster than that in the vertical or overhead position,
16
there is strong economic incentive to design and position work for welding in the flat or
horizontal position.
Weld Type
In general, in the flat position, the SAW, GMAW, or FCAW processes will be more
economical than the SMAW process. However, the selection of the welding process
should be left to the fabricator since the equipment and training of personnel will vary
from one shop to another.
It is appropriate, though, for the designer to specify the type of weld to be used, e.g.,
fillet, groove, etc. The fillet weld will be most economical and should generally be
selected instead of the groove weld in applications for which groove welds are not
required. Additionally, fillet welds result in lesser distortion of the connected material.
There are, however, situations, such as joints subjected to fatigue loading, in which the
performance of the groove weld is superior. Complete-joint-penetration groove welds
may incur the additional costs of non-destructive testing, backgouging, or backing bars;
refer to Alexander (1991).
Fillet welds around the inside of a hole or slot require less weld metal than plug or slot
welds of the same size. It should be noted, however, that the diameters of holes and widths
of slots for fillet welds should be somewhat larger than those for plug and slot welds in
metal of the same thickness to accommodate the necessary tilt of the electrode.
Weld Metal Volume
Welds which are oversized waste weld metal and labor time, resulting in an unnecessary
increase in the cost of the connection. Thus, it is important to use the proper weld size
required for strength or based upon the minimum weld size from the LRFD Specification
and to not over-specify weld size.
While the strength of a fillet weld is in direct proportion to its size, the volume of the
weld metal increases as the square of the weld size. Thus, a 5⁄8-in. fillet weld is twice as
strong as a 5⁄16-in. fillet weld but also four times more costly. For this reason, it is more
desirable to specify a smaller-sized and longer weld than a larger-sized and shorter weld.
In groove welds, double-bevel, double-V, double-J, and double-U welds are typically
more economical than single welds of the same type since they use less weld metal. As
an added benefit, the resulting symmetry results in less rotational distortion strain. Double
welds, however, require more labor in edge preparation and proper cleaning of the weld
root prior to commencing the weld on the second side. There may also be added cost if
the piece must be repositioned to perform the weld on the second side. For this reason,
many fabricators prefer a single weld in thicknesses up to about one inch.
Where single- or double-groove welds are to be used, bevel- and V-groove welds are
usually less expensive since they may be flame cut; J- and U-groove welds are more
expensive since they must be planed or air-arc gouged.
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Deposit Time
Fillet welds sizes up to 5⁄16-in. may be deposited in a single pass when deposited in the
flat or horizontal position. Larger-size welds must be deposited in multiple passes which
will require appreciably more time and weld metal. Thus, fillet welds sized not greater
than 5⁄16-in., where possible, will result in a significant savings in deposit time, weld
material, and cost.
Prior Qualification of Procedures
Evidence of prior qualification of welding procedures, welders, welding operators, or
tackers may be accepted at the discretion of the engineer of record (EOR). Fabricators
certified in the AISC Quality Certification Program have the experience and documentation necessary to assure that the EOR could accept such prior qualifications (refer to
Part 6 for a description of the AISC Quality Certification Program). Significant economic
savings may be achieved by accepting such prior qualifications.
Minimizing Weld Repairs
Added cost in the form of weld repairs or replacement may be minimized if the designer
considers the possibilities of lamellar tearing, fatigue cracking, notch development, and
reduced impact toughness when designing welded connections.
Lamellar Tearing
A lamellar tear is a separation or crack in the base metal caused by through-thickness
weld shrinkage strains. When steel is hot-rolled, sulphides or other inclusions are
elongated to form microscopic platelets in the plane of the steel plate. These inclusions
reduce the strength of the steel in the through-thickness direction below that in the
longitudinal or transverse direction.
While special practices are available to produce low-sulphur steel which is resistant
to lamellar tearing and ASTM A770 provides a testing method by which the throughthickness strength of the base metal may be measured, it is difficult to assure freedom
from the possibility of lamellar tearing. Lamellar tearing is a phenomenon which can
occur even in material with superior mechanical properties. Instead, the joint detail is
most important in preventing lamellar tearing.
Some joint designs are inherently susceptible to lamellar tearing (AISC, 1973). For
example, the complete-joint-penetration groove-welded tee joints in thick sections shown
in Figure 8-30 can develop lamellar tears in the crossbar of the tee flange. Such tears can
be detected with UT. Other susceptible joints are shown with improved details in Figures 8-31
and 8-32.
The probability of lamellar tearing may be minimized through good joint design and
proper welding procedures. The joint design should minimize the weld size and, therefore, the resulting shrinkage strains. Additionally, the design should reduce the restraint
which intensifies the local strains. The welding procedure should then establish a
sequence to minimize component and internal restraint. Welding with low-hydrogen
processes and effective pre-heat has also been shown to minimize lamellar tearing
(Kaufmann, Pense, and Stout, 1981).
Fatigue Cracking
Because of their inherent rigidity, welded members are subjected to severe restrictions at
service loads if subjected to the repeated variations in stress (fatigue loading). In a
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dynamically loaded structure, fatigue cracks at notches progress at a rate proportional to
the stress range and to the number of stress cycles.
Gradual transitions of sections will help to alleviate these concentrations. The fatigue
resistance of a butt weld in a tension member, for example, can be improved approximately 25 percent by grinding the weld reinforcement flush. Thus, any notches in the
tension areas should be ground out. Additionally, all grinding should be done in the
direction of the stress. Refer to LRFD Specification Appendix K3 for further information.
Notch Development
When subjected to lateral movement, a severe notch can result at locations of one-sided
welds. For the fillet-welded joint subjected to lateral loading in Figure 8-33, the unwelded
side has no strength in tension and a notch may form from the unwelded side. Using one
fillet weld on each side will eliminate this condition. This is also true with partial-jointpenetration groove welds.
In the case of the backing bar of Figure 8-34a, the location of the tack welds may cause
fatigue notches. An improved detail would be as shown in Figure 8-34b, where the
backing bar is tack welded inside the groove. Any undercut would then be filled, or at
least backed up, by the final weld joint. This is also applicable in the case of box members
with corner backup. Note that backing bars should also be continuous throughout the
length to avoid discontinuities at the base of the weld profile.
Impact Toughness
Different classifications of alloy electrodes and fluxes can produce welds with CVN 20
at selected temperatures between 0°F and −150°F.
Arc Strikes
Arc strikes may occur during welding procedures if the welding rod is lifted from the
work while the current is on, or during magnetic particle testing if the magnetizing prod
is lifted from the work while the current is on. As stated in Quality Criteria and Inspection
Standards (AISC, 1988), arc strikes need not be removed in statically loaded structures.
Fig. 8-30. Lamellar tear resulting from shrinkage of large welds
in thick material under high restraint.
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Other Considerations in Welded Construction
Matching Electrodes
AWS D1.1 Table 4.1 lists matching electrodes for various steels by ASTM Specification
and is referenced in LRFD Specification Table J2.5. Use of electrodes one strength-level
higher than matching is permitted. Typical structural steel grades with Fy equal to 36 ksi
and 50 ksi are normally welded with electrode material of 70 ksi nominal strength,
indicated as E70XX for SMAW or its equivalent.
Welding Shapes from ASTM A6 Groups 4 and 5
When heavy shapes are spliced, extremely high shrinkage strains may develop in the base
metal, inhibiting ductile deformation in the material and increasing the possibility of
brittle fracture. Additionally, interior portions of heavy hot-rolled shapes and plates may
contain a coarser grain structure and/or lower notch-toughness properties than other areas
of the product.
(a)
Susceptible Detail
Improved Detail
Susceptible Detail
Improved Detail
Susceptible Detail
Improved Detail
(b)
(c)
Fig. 8-31. Susceptibility to lamellar tearing can be reduced
by careful detailing of welded connections.
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LRFD Specification Sections A3.1c, J1.5, J1.6, J2.8, and M2.2 contain special material
and fabrication requirements for ASTM A6 Groups 4 and 5 rolled shapes, shapes built-up
from plates more than two inches thick, welded together to form the cross section, and
shapes where the cross section is to be spliced by welding and subjected to primary tensile
stress due to tension or flexure. These special requirements address notch toughness,
access hole profiles, welding procedures, pre-heat, thermal cutting, grinding, and inspection requirements and are intended to minimize the possibility of cracking. The corresponding sections of the Commentary on the LRFD Specification provide further
information, including alternative splice details and details for weld-access holes and
beam copes.
Intersecting Welds and Triaxial Stresses
If a stiffener were to be welded into and around the corner as it meets two elements of a
shape (i.e., the flange and web of a column), the welding arc would take the path of least
resistance to the three plates meeting at the corner and a lack of fusion or slag pocket
would result in that corner. In addition to creating a discontinuity, this would add to the
weld shrinkage strains in that corner. Corners of stiffeners, then, should be clipped
generously to preclude this problem.
Susceptible Detail
Improved Detail
Figure 8-32.
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In general, a 3⁄4-in. clip will be adequate. In small stiffeners, where such a clip would
remove a large portion of the effective area of the stiffener, and in shapes, the radii of
which require a clip in excess of 3⁄4-in., the clip dimension may be adjusted to suit
conditions. For further information, see Butler, Pal, and Kulak (1972) and Blodgett
(1980).
Painting Welded Connections
Paint is normally omitted in areas to be field welded. LRFD Specification Section M3.5
requires that, unless otherwise provided in the plans and specifications, surfaces within
two inches of any field weld shall be free of materials that would prevent proper welding
or produce objectionable fumes during welding. Since little is gained by an exhaustive
identification of the small areas involved, most fabricators prefer to use the general note,
“No paint on OSL of connection angles,” where OSL stands for outstanding leg. This
Weak
Strong
Notch
Fig. 8-33. One-sided fillet weld results in a severe notch.
A similar effect exists with a one-sided partial-penetration groove weld.
Fillet weld tacks
can result in
notches that
reduce fatigue
resistance.
tacks are
incorporated
in weld
(a) Susceptible Detail
(b) Improved Detail
Fig. 8-34. Backing bar tack welds.
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“no paint” requirement does not apply to shop welding where painting is normally done
after the welds are made.
Clearances for Welding
Clearances are required to allow the welder to make proper welds. In the SMAW process,
for example, the welder must hold an electrode, about 3⁄8-in. in diameter and 14 inches to
18 inches long, in full control, and in such a position that the far end of the rod is in near
contact with the base metal. This welder must observe the weld through a protective
window of very dark glass in a bulky protective hood. Furthermore, the welder must keep
control of the stiff electrical cable which powers the welding process.
These conditions make welding difficult and it is imperative that other factors do not
further hamper the welder. Ample room must be provided so that the welder or welding
operator may manipulate the electrode and observe the weld as it is being deposited.
The preferred position of the electrode when welding in the horizontal position is in a
plane forming 30° with the vertical side of the fillet weld being made. However, this
angle, shown as angle x in Figure 8-35, may be varied somewhat to avoid contact with
some projecting part of the work. A simple rule which may be used to provide adequate
clearance for the electrode in horizontal fillet welding is that the clear distance to a
projecting element should be at least one-half its height; distance y / 2 in Figure 8-35b.
A special case of minimum clearance for welding with a straight electrode is illustrated
in Figure 8-36. The 20° angle is the minimum which will allow satisfactory welding along
the bottom of the angle and therefore governs the setback with respect to the end of the
beam. If a 1⁄2-in. setback and 3⁄8-in. electrode diameter were used, the clearance between
the angle and the beam flange could be no less than 11⁄4-in. for an angle with a leg
dimension w of three inches, nor less than 15⁄8-in. with a w of four inches. When it is not
possible to provide this clearance, the end of the angle may be cut as noted by the optional
cut in Figure 8-36 to allow the necessary angle. However, this secondary cut will increase
the cost of fabricating the connection.
Fillet Welds
In Figure 8-37a, fillet welds A are loaded in longitudinal shear and fillet weld B is loaded
in transverse shear. If the force Ru is increased to exceed the strength of the welds, rupture
will occur on the planes of least resistance. As shown in Figure 8-37b, this is assumed to
take place in the weld throat where the least cross-sectional area is present. Tests of fillet
welds using matching electrodes have demonstrated that the weld will fail through its
effective throat before the material will fail along the weld leg.
Fillet welds are approximately one-third stronger in the transverse direction than in
the longitudinal direction. While this increased strength is ignored in LRFD Specification
Section J2.4, the provisions of LRFD Specification Appendix J2.4 may be used to take
advantage of this increased strength.
Effective Area
The effective area of a fillet weld Aw is the product of the effective length of the fillet
weld times the effective throat thickness of the fillet weld. The effective length l of the
fillet weld is the overall length of the full-sized fillet weld. Except for fillet welds made
with the SAW process, the effective throat thickness of the fillet weld is 0.707w, where
w is the weld size. The deep penetration of fillet welds made by the SAW process is
recognized in the LRFD Specification Section J2.2a wherein the effective throat thickAMERICAN INSTITUTE OF STEEL CONSTRUCTION
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ness is considered to be equal to the weld size for 3⁄8-in. and smaller welds, and equal to
the effective throat thickness plus 0.11 in. for fillet welds sizes over 3⁄8-in.
Minimum Effective Length
The minimum effective length of a fillet weld when used alone and not as a part of a
continuing joint boundary (i.e., an end return or corner) must be greater than or equal to
four times the nominal weld size. Thus, the shortest length of 5⁄16-in. fillet weld which is
permitted to be considered to transmit load is 11⁄4-in.
Conversely, regardless of the fillet-weld size used, the maximum effective size is
limited to one-fourth the weld length. Intermittent fillet welds likewise are subject to this
provision with the added requirement that the incremental length of weld must not be
less than 11⁄2-in; refer to LRFD Specification Section J2.2b.
Minimum Fillet Weld Size
When very small fillet-weld sizes are used, rapid cooling after welding creates internal
stresses which, in turn, may lead to cracking of the weld. To preclude this, the minimum
fillet-weld size is established in LRFD Specification Section J2.2b as a function of the
thickness of the thicker of the parts joined. From this, if two 7⁄8-in. plates are joined, the
minimum permissible fillet-weld size is 5⁄16-in., even if a 1⁄4-in. weld might provide
adequate strength. Where different thicknesses are joined, the weld size need not exceed
the thickness of the thinner part, unless a larger size is required for strength. If this is the
case, adequate pre-heat must be provided to assure soundness of the weld.
Maximum Fillet-Weld Size
The maximum fillet-weld size on the edge of the material is limited in LRFD Specification Section J2.2b to the thickness of the element for material less than 1⁄4-in. thick and
1⁄ -in. less than the thickness of the element for material greater than or equal to 1⁄ -in.
16
4
thick, unless the drawing is specially noted to build up the weld to achieve full throat
size. This limitation recognizes that the exposed corner of the welded edge tends to melt
Electrode
x
END VIEW
PLAN VIEW
(a)
y
Electrode
A
x
y
/2
A
PLAN VIEW
SECTION A-A
(b)
Fig. 8-35. Clearances for welding.
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BOLTS, WELDS, AND CONNECTED ELEMENTS
into the weld as illustrated in Figure 8-38, thereby reducing the leg dimension and the
weld throat. Additionally, the toes of most rolled shapes do not have an ideal 90° corner.
Thus the actual thickness of material at the weld is less than the nominal thickness t of
the member. While the LRFD Specification permits the use of a larger weld size if the
weld is built up to the full throat size, this is difficult to achieve.
End Returns
LRFD Specification Section J2.2b gives requirements on when fillet weld terminations
must be returned around ends or sides. This is illustrated in Figure 8-39. Weld returns
reinforce the effective weld where it is most highly stressed and, thus, inhibit cracking
and progressive tearing throughout the length of the weld. Thus, they are required in
fatigue applications and for connections which assume flexibility exists in the connected
part or parts (e.g., the support legs of a double angle connection). If welds are not returned,
they must terminate not less than two times the nominal weld size from the sides or ends.
Also, based upon LRFD Specification Section J2.2b, Figures 8-40 and 8-41 indicate
examples where welds must be interrupted or should not be returned. In these instances,
the welds, while in the same plane, lie on opposite sides of the contact surfaces. An attempt
to weld around the corner will melt the corner material, creating a reduced thickness and
notch. Furthermore, such welds cannot be made with a fully effective throat. Welding
around such a corner should be avoided.
It is not recommended that weld be applied in the gap at the end of the beam web
between the heels of the angles, as this reduces the flexibility of the connection angles.
Furthermore, the setback of the beam web is not a controlled dimension as it may be used
to account for the tolerance in length of the beam and may vary from zero in. to 1⁄2-in. or
Setback
w
Optional cut
20°
PLAN VIEW
Electrode
45° to 50°
ELEVATION
END VIEW
Fig. 8-36. Clearances for welding.
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more. In any case, most beam webs are too thin for an effective minimum weld size to
be applied along such an edge.
Fillet Welds in Holes or Slots
The recommended minimum hole diameters or slot widths for fillet welding are shown
in Table 8-35. It is important to distinguish between plug or slot welds and fillet welds
placed around the inside of a hole or slot. In the case of such fillet welds, the shear strength
is the product of the effective throat thickness and the weld length measured along the
line bisecting the throat area. If this effective area should exceed the area of the hole or
slot, it cannot be considered to be a fillet weld and must be designed as a plug or slot
weld.
Other Limitations on Fillet Welds
In concentrically loaded welded joints, the stresses are assumed to be uniformly distributed throughout the length of the welds. The design strength of a concentrically loaded
fillet-weld group, then, is the sum of the design strengths of each weld in the group. LRFD
Specification Section J1.8 provides that the center of gravity of a weld group should
coincide with the gravity axis of an axially loaded member, or provision must be made
for the resulting eccentricity. Certain welded members not subject to fatigue loading are
excluded from this provision: “Eccentricity between gravity axes of such members…may
be neglected in statically loaded members, but shall be considered in members subject
to fatigue loading.” This provision permits very significant cost savings in weld material
Ru
Ru
Welds A
Weld B
Ru
Ru
(a)
(b)
t
1/16
t
1/16
Fig. 8-37. Fillet welds.
(a)
(b)
Figure 8-38.
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BOLTS, WELDS, AND CONNECTED ELEMENTS
and labor in the fabrication and erection of such statically loaded members as roof and
floor trusses, bracing, etc.
Additionally, LRFD Specification Section J2.2b imposes other limitations on proportions of lap joints.
Minimum Shelf Dimensions
In Figure 8-42, the recommended minimum shelf dimensions for normal size SMAW
fillet welds are summarized. This dimension is critical to the deposition of the weld. SAW
fillet welds would require a greater shelf dimension to contain the flux, although this is
sometimes provided by clamping auxiliary material to the member.
In Figure 8-43, the distance b must be large enough so that a full-size weld may be
deposited on it. Select a gage that will permit enough clearance b to deposit an effective
weld. The dimension b should be sufficient to accommodate the combined tolerances of
the framing-angle length, the cope depth, and the beam mill over/underrun as well as the
specified weld size.
Complete-Joint-Penetration Groove Welds
Assuming compliance with LRFD Specification Section J2, the design strength of
complete-joint-penetration groove welds is equal to that of the base metal in all respects.
Therefore, no allowance for the presence of such welds need be made in proportioning
the connections of structural members for any type of static loading. Where members are
of unequal cross section or different material strength, the strength of the complete-jointpenetration groove weld is limited to the strength of the weaker member.
Extension, Runoff, Backing, and Spacer Bars
When groove welds are used to splice plate girders and beams, LRFD Specification
Section J7 requires that the splice be capable of developing the full strength of the smaller
spliced section or 100 percent of the full section if the spliced sections are of the same
size. To obtain a fully welded cross section, the termination at either end of the joint must
Provide end returns having length = twice nominal
weld size if subjected to cyclical (fatigue) loading
or = four times nominal weld size if needed for
connection flexibility. Otherwise, terminate welds
not less than nominal weld size from ends with
no end returns.
1
2 x nominal
weld size
/4 for Pts. 1 1
for Pts. 2 2
5
/16
Note:
Locations of Pts. 1
and Pts. 2 are shown on
the erection diagram (not included).
Fig. 8-39. Weld returns.
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be of sound weld metal. Extension or runoff bars are usually used to assure the soundness
of the end of the weld. Frequently, the joint will require a backing or spacer bar which
can be extended to serve as the extension or runoff bar.
Figure 8-44 demonstrates the application of extension, backing, and spacer bars in a
splice or moment connection. Extension and backing bars should be of approved
weldable material as specified in AWS D1.1, Section 8.2.4; spacer bars must be of the
same material specification as the base metal. This can create a procurement problem
since small tonnage requirements may make them difficult to obtain in the specified
ASTM designation. Also indicated in Figure 8-44 is the use of a cover plate or seat angle
for backing the weld.
Do not tie welds together here
terminate welds 2 x nominal weld
size from end.
Do not tie welds together here
Fig. 8-40. Fillet welds on opposite sides of a common plane should not be continuous.
Do not return welds here
terminate welds 2 x nominal
weld size from end.
Fig. 8-41. Fillet welds should not be returned across thickness of material.
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Table 8-35.
Recommended Minimum Hole Diameters or Slot Widths for Fillet Welding, in.
Plate Thickness, in.
3⁄
16
Min. Diameter or Width, in.
and 1⁄4
11⁄
16
13⁄
16
15⁄
16
11⁄16
13⁄16
15⁄16
5⁄
16
3⁄
8
7⁄
16
1⁄
2
5⁄
8
Shown in Figure 8-45 are flat-type extension bars, normally used with beveled grooves,
and contour-type extension bars, normally used with J-grooves or U-grooves and shaped
to follow the contour of the joint geometry. While the contour-type extension bar is shown
as though it were comprised of two pieces, some fabricators might elect to mill the full
contour in one piece and subsequently cut it to suit job requirements.
AWS D1.1, Section 3.12 states that runoff and extension bars need not be removed in
statically loaded structures unless required by the engineer of record (EOR). Such might
be the case where these bars would create an interference with other work. In dynamically
and cyclically loaded structures, however, they must be removed and the welds made
smooth and flush to the base metal abutting edges.
Vertical or horizontal section
Fillet Weld
Size (in.)
Min.
Shelf
Dim. (in.)
3
/16
7
1
1
5
9
3
5
7
11
1
3
/4
/16
/8
/16
/2
/16
/2
/16
/8
/16
/4
Fig. 8-42. Recommended minimum shelf dimensions for SMAW fillet welds.
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According to AWS D1.1, Section 3.13, backing bars on groove-welded joints must be
fully spliced to avoid stress concentrations or discontinuities and should be thoroughly
fused with the weld metal. It is further required on dynamically loaded structures that the
backing bars be removed and the surfaces finished smooth when they are transverse to
the direction of stress. If this were the case for the flange splice of Figure 8-44, removal
of the backing bars would be required and, therefore, the splice might be made more
economically with another joint profile.
Weld Access Holes
The beam web is provided with an access hole or “rathole”, as illustrated in Figure 8-44,
to permit down-hand welding to the backing bars located below both the top and bottom
flanges. The weld-access hole also provides increased relief from concentrated weld
shrinkage strains and prevents the intersection or close juncture of welds in orthogonal
directions. Weld-access holes should not be filled with weld metal since it is difficult to
provide sound weld metal to fill such a void and doing so may introduce a state of triaxial
stress under loading.
Partial-Joint-Penetration Groove Welds
b
b
b
Gage
Gage
Partial-joint-penetration groove welds are used primarily for welded compression splices,
the connection of elements in heavy box sections and pedestals, and, in general, for joints
where the stress to be transferred is substantially less than that which would require
complete-joint-penetration groove welds. This type of weld is not, however, recom-
Figure 8-43
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1
t
Extension
bars
/8 ″
Min.
w
L
W
8 - 126
Extension bars
Backing bar
Backing bar
Col.
Beam
access hole
Access Hole
Seat angle
Spacer bar
(when req’d)
Beam flange
Overlapping cover
plate
Note: Extension bars should be at least ¼ ″
thick to reduce hazard of weld “blow through.”
Figure 8-44
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mended in joints subject to dynamic or cyclical loading, except for joining the components of built-up members.
Effective Area
The effective area of a partial-joint-penetration groove weld Aw is the product of the
effective length of the weld times the effective throat thickness of the fillet weld. These
quantities are determined as follows.
The effective length is the width of the part joined. The effective throat thickness E is
as determined from LRFD Specification Table J2.1, but not less than specified in LRFD
Specification Table J2.3.
Nomenclature of partial-joint-penetration welds is shown in Figure 8-46. Note that the
effective throat thickness shown is less than the dimensioned groove-weld size. AWS
prequalified partial-joint-penetration welds establish for each joint an effective throat E
as a function of the material thickness, weld-preparation size, or depth S. Thus, the design
drawings should specify the effective weld length and the required effective throat. The
shop drawings should then show the groove depth S and geometry which will provide
for the specified effective throat E. Some fabricators may indicate both the weld size and
the effective throat on the shop drawings to eliminate confusion.
The comments on “Extension, Runoff, Backing, and Spacer Bars” and “Weld Access
Holes” for complete-joint-penetration groove welds also apply to partial-joint-penetration groove welds.
Intermittent Welds
In preparing the joint profile for intermittent partial-joint-penetration groove welds, a
transition or “faring-in” of the joint at beginning and termination must be provided to
ensure proper fusion with the base metal. The nominal angular value of this transition
should be 45°as shown in Figure 8-46.
Flare Welds
A flare weld is a special case of the partial-joint-penetration groove weld wherein the
convex surface of the connected part creates the joint preparation. This convexity may
be the result of an edge preparation, but more often results when one (or both) joint
component consists of a round rod or a shape with a rounded bend or corner radius created
by bending or rolling as shown in Figure 8-47.
Extension bars
Runout plate
or backing
bar extension
Figure 8-45.
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Effective Area
The effective area of a flare weld Aw is the product of the effective length of the weld
times the effective throat thickness of the flare weld; the effective length is the width of
the part joined and the effective throat thickness E is as determined from LRFD
Specification Table J2.2.
Limitations
The deposition of effective weld metal to the bottom of the flare groove is very difficult
because the welding arc short-circuits across the surfaces due to the sharp angular slopes.
Thus, the quality of this weld is difficult to control; LRFD Specification Section J2.1a
permits examination and adjustment of the weld strength based on random testing and
special qualification.
Note that weldability of concrete reinforcing bars is not a part of ASTM specifications.
In past experience, improperly welded concrete reinforcing bars have cracked and
separated under no-load conditions. Typical deformed-type concrete reinforcing bars,
such as ASTM A615, A616, and A617, are not produced to a controlled chemistry and
their weldability must be carefully evaluated; refer to AWS D1.4.
Plug and Slot Welds
The use of plug and slot welds for stress transfer is limited to resisting shear loads in joint
planes parallel to the faying surfaces. These welds should not be subjected to tensile
stresses and are limited when subjected to stress reversal. Furthermore, some specificaEffective
A
Transition
length
T
S
E
45° Min.
A
SECTION A-A
Fig. 8-46. Partial-joint-penetration groove weld nomenclature.
Flare-V-groove
effective throat=R/2
R
R
Flare-bevel groove
effective throat = 5R/16
Fig. 8-47. Flare weld nomenclature.
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tions do not permit their use as load-carrying welds. Because of these limitations, plug
and slot welds are more frequently employed as stitch welds rather than as a means of
primary stress transfer.
The effective area of a plug or slot weld Aw is the nominal cross-sectional area of the
hole or slot. The proportions and spacing of holes and slots and the depth of weld are
stipulated in LRFD Specification Section J2.3b and illustrated in Figure 8-48.
Design Strength of Welds
The design strength of welds is determined in accordance with LRFD Specification
Sections J2.2 and J2.4. LRFD Specification requirements are based upon the provisions
of AWS D1.1, except as noted in LRFD Specification Section J2.
For welds, the limit states of the weld-metal strength and the base-metal strength must
be checked as applicable in LRFD Specification Table J2.5. These limit states assume
that the matching electrode requirements of LRFD Specification Section J2.6 and Table
J2.1 are met.
Weld Metal Design Strength
From LRFD Specification Section J2.4, the weld metal design strength is φRn, where φ
is a resistance factor from LRFD Specification Table J2.5 and:
Rn = Fw Aw
In the above equation,
Fw = 0.60FEXX
Aw = effective area of the weld, in.2
and φ is determined as follows:
For a fillet weld loaded in shear on its effective area,
φ = 0.75;
For a complete-joint-penetration groove weld loaded in shear on its effective area,
φ = 0.80;
For a partial-joint-penetration groove weld loaded in shear parallel to the axis of the weld,
φ = 0.75;
For a partial-joint-penetration groove weld loaded in tension normal to the effective area,
φ = 0.80;
For a plug or slot weld loaded in shear on its effective area,
φ = 0.75.
Base Metal Design Strength
From LRFD Specification Section J2.4, the base metal design strength is φRn, where φ is
a resistance factor from LRFD Specification Table J2.5 and:
Rn = FBM ABM
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
8 - 130
BOLTS, WELDS, AND CONNECTED ELEMENTS
In the above equation, ABM is the cross-sectional area of the base metal. For a fillet
weld loaded in tension or compression parallel to the axis of the weld,
φ = 0.90
FBM = Fy
For a complete-joint-penetration groove weld loaded in tension or compression normal
to its effective area,
φ = 0.90
FBM = Fy
For a complete-joint-penetration groove weld loaded in shear on its effective area,
φ = 0.90
FBM = 0.60Fy
d
l
l
R′
d
d
S′
t
W
W
W
S
W
S
R
Plate
thickness,
in.
3/16 & 1/4
Min. hole dia.
or slot width,
d, in.
9/16
5/16 & 3/8
11/16
7/16 & 1/2
13/16
9/16 & 5/8
15/16
Hole and slot proportions,
spacing and depth of weld
d ≥ (t + 5/16), round to next
higher odd 1/16; also d ≤ 2 1/4W
S ≥ 4d
S ′≥ 2 l
l ≤ 10W
R = d/2
R≥t
Where t ≤ 5/8, W = t
Where t > 5/8, W = t/2
but, not less than 5/8
Fig. 8-48. Plug and slot welds.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
WELDED CONSTRUCTION
8 - 131
For a partial-joint-penetration groove weld loaded in tension or compression normal
to its effective area or tension or compression parallel to the axis of the weld,
φ = 0.90
FBM = Fy
Prequalified Welded Joints
AWS D1.1 contains provisions for prequalified welded joints which provide joint
geometries, such as root openings, angles, and clearances, as illustrated in Figures 8-49
and 8-50, that will permit a qualified welder to deposit sound weld material. Thus,
prequalified joints are concerned almost exclusively with the welding process as a method
of joining metal and deal with welded joints only from fusion boundary to fusion
boundary. The designer must satisfy all provisions of AWS D1.1 Sections 2, 3, and 4
before a joint is considered prequalified.
Prequalified welded joints are not, in themselves, adequate consideration of welded
design details. To emphasize this, the AWS D1.1 Section 1.1 states: “…The use of
prequalified joints is not intended as a substitute for engineering judgment with respect
to the suitability of application of these joints to a weld assembly.” The design and
detailing for successful welded construction requires consideration of factors which
include, but are not limited to, the magnitude, type, and distribution of forces to be
transmitted, access, restraint against weld shrinkage, thickness of connected materials,
residual stress, and distortion. Accordingly, the design and detailing must also satisfy the
requirements of LRFD Specification Section J2.
The prequalified welded joints in Table 8-36 meet the requirements of the 1992 version
of AWS D1.1 as well as the 1993 LRFD Specification. Because AWS D1.1 is revised
every other year, designers and fabricators should verify this information with the latest
issue of AWS D1.1. The designations such as B-L1a, B-U2, and B-P3 are those used in
AWS standards. Note that lowercase letters, e.g., a, b, c, etc., are often used to differentiate
between joints that would otherwise have the same joint designation. These prequalified
welded joints are limited to those made by the SMAW, SAW, GMAW (except short circuit
transfer), and FCAW procedures. Small deviations from dimensions, angles of grooves,
and variation in depth of groove joints are permissible within the tolerances given.
In general, all fillet welds, whether illustrated or not, are prequalified, provided they
conform to the requirements of AWS D1.1. Groove welds are classified using the
conventions indicated in the tables. Welded joints other than those prequalified by AWS
may be qualified, provided they are tested and qualified in accordance with AWS D1.1.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
8 - 132
BOLTS, WELDS, AND CONNECTED ELEMENTS
ctive
Effe ength
dL
Wel
Weld face
Throat area
(shaded)
45°
45°
t line
e
tiv
Roo
c
ffe
E
Leg size
h
gt
d
el
n
le
/12 N
o
Th rma
r
o
Siz at l
e
W
al
rm at
o
N ro
Th ze
Si
Root
Size
135° max.
60° min.
Penetration
t
roa
Th
t
oa
r
Th
t
oa
r
Th
Normal Throat Size
p
e
De
CONVEX
n
tio e
tra iz
ne t S
Pe hroa
T
al
e
rm Siz
No at
ro
Th
Fig. 8-49. Fillet weld nomenclature.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
CONCAVE
WELDED CONSTRUCTION
Groove
face
8 - 133
Groove (and
bevel) angle
Groove
angle
Bevel
angle
Groove
radius
Root
Root
opening
Spacer
bar
Root
Root Root face
opening
Backing
bar
Root
opening
PREPARATION
Penetration
(fusion zone)
Weld
face
Root
Backing
bead
Weld
size
Reinforcement
Weld throat=
Weld size
Root
opening
0
Root
face
PARTIAL-JOINT-PENETRATION
COMPLETE-JOINT-PENETRATION
Groove size
Root
face
Groove angle
Fillet size
1/8
Effective
throat
Eff.
at
thro
PARTIAL-JOINT-PENETRATION
(When Reinforcing Fillet
is Specified)
Fig. 8-50. Groove weld nomenclature.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
8 - 134
BOLTS, WELDS, AND CONNECTED ELEMENTS
Table 8-36.
Prequalified Welded Joints
Symbols for Joint Types
B
C
T
butt joint
corner joint
T-joint
L
U
P
limited thickness, complete-joint-penetration
unlimited thickness, complete-joint-penetration
partial-joint-penetration
1
2
3
4
5
square-groove
single-V-groove
double-V-groove
single-bevel-groove
double-bevel-groove
S
G
F
submerged arc welding SAW
gas metal arc welding GMAW
flux cored arc welding FCAW
BC butt or corner joint
TC
T- or corner joint
BTC butt, T-, or corner joint
Symbols for Base Metal Thickness and Penetration
Symbols for Weld Types
6
7
8
9
10
single-U-groove
double-U-groove
single-J-groove
double-J-groove
Flare-bevel-groove
Symbols for Welding Processes if not Shielded Metal Arc welding (SMAW):
Symbols for Welding Positions
F
flat
H
horizontal
V
vertical
OH overhead
The lower case letters, e.g., a, b, c, d, etc., are used to differentiate between joints that would otherwise
have the same joint designation.
Notes to Prequalified Welded Joints
A
B
Br
C
E
J
J2
L
M
Mp
N
Q
Q2
R
V
Not prequalified for GMAW using short circuiting transfer. Refer to AWS D1.1 Appendix A.
Joints welded from one side only.
Bridge applications limit the use of these joints to the horizontal position. Refer to AWS D1.1
Section 9.12.5.
Back gouge root to sound metal before welding second side.
Minimum effective throat (E) as shown in LRFD Specification Table J2.3; S as specified on drawings.
If fillet welds are used in buildings to reinforce groove welds in corner and T-joints, they shall be
equal to 1 ⁄4 T 1 , but need not exceed 3 ⁄8 -in. Groove welds in corner and T-joints in bridges shall be
reinforced with fillet welds equal to 1 ⁄4 T 1 , but not more than 3 ⁄8 -in.
If fillet welds are used in buildings to reinforce groove welds in corner and T-joints, they shall be
equal to 1 ⁄4 T 1 , but not more than 3 ⁄8 -in.
Butt and T-joints are not prequalified for bridges.
Double-groove welds may have grooves of unequal depth, but the depth of the shallower groove
shall be not less than one-fourth of the thickness of the thinner part joined.
Double-groove welds may have grooves of unequal depth, provided they conform to the limitations
of Note E. Also, the effective throat (E), less any reduction, applies individually to each groove.
The orientation of the two members in the joints may vary from 135° to 180°, provided the basic
joint configuration (groove angle, root face, root opening) remains the same and the design throat
thickness is maintained.
For corner and T-joints, the member orientation may be changed provided the groove
dimensions are maintained as specified.
The member orientation may be changed provided the groove dimensions are maintained as
specified.
The orientation of two members in the joint may vary from 45° to 135° for corner joints and from
45° to 90° for T-joints, provided the basic joint configuration (groove angle, root face, root
opening) remains the same and the design throat thickness is maintained.
For corner joints, the ouside groove preparation may be in either or both members, provided the
basic groove configuration is not changed and adequate edge distance is maintained to support
the welding operations without excessive edge melting.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
WELDED CONSTRUCTION
8 - 135
Table 8-36 (cont.).
Prequalified Welded Joints
Basic Weld Symbols
Back
Groove or Butt
Plug
or
Slot
Fillet
Square
V
Bevel
U
J
Flare
Bevel
Flare V
Supplementary Weld Symbols
Backing
Weld All
Around
Spacer
Contour
Field Weld
Flush
Convex
For other basic and
supplementary
weld symbols, see
AWS A2.4
Standard Location of Elements of a Welding Symbol
Finish symbol
Groove angle or included
angle or countersink
for plug welds
Contour symbol
Root opening, depth
of filling for plug
and slot welds
Length of weld in inches
Effective throat
Pitch (c. to c. spacing)
of welds in inches
F
Depth of preparation
or size in inches
A
S(E)
sides)
R
Specification, process,
or other reference
(Both
T
Tail (omitted when
reference is not used)
Field weld symbol
(Arrow
(Other
side )
side )
Reference line
Weld-all-around symbol
@P
Elements in this
area remain as
shown when tail
and arrow
are reversed.
Basic weld symbol
or detail reference
A
B
Arrow connects reference line to arrow side
of joint. Use break as at A or B to signify
that arrow is pointing to the grooved
member in bevel or J-grooved joints.
Note:
Size, weld symbol, length of weld, and spacing must read in that order, from left to right, along the reference
line. Neither orientation of reference nor location of the arrow alters this rule.
The perpendicular leg of
,
,
,
, weld symbols must be at left.
Arrow and other side welds are of the same size unless otherwise shown. Dimensions of fillet welds must be
shown on both the arrow side and the other side symbol.
The point of the field weld symbol must point toward the tail.
Symbols apply between abrupt changes in direction of welding unless governed by the ‘‘all around’’ symbol or
otherwise dimensioned.
These symbols do not explicitly provide for the case that frequently occurs in structural work, where duplicate
material (such as stiffeners) occurs on the far side of a web or gusset plate. The fabricating industry has
adopted this convention: that when the billing of the detail material discloses the existence of a member on the
far side as well as on the near side, the welding shown for the near side shall be duplicated on the far side.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
8 - 136
BOLTS, WELDS, AND CONNECTED ELEMENTS
Table 8-36 (cont.).
Prequalified Welded Joints
Fillet Welds
Notes:
1. En, En′ = effective throats dependent on magnitude of root opening Rn. See AWS D1.1 Section 3.3.1
Subscript n represents 1, 2, 3, or 4.
2. t = thickness of thinner part.
3. Not prequalified for gas metal arc welding using short circuitry transfer. Refer to AWS D1.1.
4. Part (f), apply Z loss factor of AWS D1.1 Table 2.4 to determine effective thrust.
5. Part (f), not prequalified for angles under 30°°. For welder qualfications, see AWS D1.1
Table 10.5, Column 10.
*Angles smaller than 60°° are permissible, however, if the weld is considered to be a partial-joint-penetration
groove weld.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
WELDED CONSTRUCTION
8 - 137
Table 8-36 (cont.).
Prequalified Welded Joints
Complete-Joint-Penetration Groove Welds
Square-groove weld (1)
Butt joint (B)
Corner Joint (C)
Welding
Process
Joint
Designation
SMAW
B-L1a
GMAW
FCAW
Base
Metal Thickness
(U = unlimited)
Groove Preparation
Tolerances
Gas
Shielding
for
(FCAW)
T1
T2
Root
Opening
As
Detailed
As Fit
Up
Permitted
Welding
Positions
1 ⁄4
max
—
R = T1
+ 1 ⁄16 , −0
+ 1 ⁄4 , − 1 ⁄16
All
—
N
C-L1a
1 ⁄4
max
U
R = T1
+ 1 ⁄16 , −0
+ 1 ⁄4 , − 1 ⁄16
All
—
—
B-L1a-GF
3 ⁄8
max
—
R = T1
+ 1 ⁄16 , −0
+ 1 ⁄4 , − 1 ⁄16
All
Not
Required
A, N
Notes
Square-groove weld (1)
Butt joint (B)
Base
Metal Thickness
(U = unlimited)
Welding
Process
Joint
Designation
SMAW
B-L1b
1 ⁄4
GMAW
FCAW
B-L1b-GF
SAW
SAW
Groove Preparation
Tolerances
Gas
Shielding
for
(FCAW)
T1
T2
Root
Opening
As
Detailed
As Fit
Up
Permitted
Welding
Positions
max
—
R = T1 / 2
+ 1 ⁄16 , −0
+ 1 ⁄6 , − 1 ⁄8
All
—
C, N
3 ⁄8
max
—
R = 0 to 1 ⁄8
+ 1 ⁄16 ,
+ 1 ⁄6 ,
− 1 ⁄8
All
Not
Required
A, C,
N
B-L1-S
3 ⁄8
max
—
R=0
±0
+ 1 ⁄16 , −0
F
—
N
B-L1a-S
5 ⁄8
max
—
R=0
±0
+ 1 ⁄16 , −0
F
—
C, N
Gas
Shielding
for
(FCAW)
Notes
−0
Notes
Square-groove weld (1)
T-joint (T)
Corner joint (C)
Welding
Process
Joint
Designation
SMAW
TC-L1b
GMAW
FCAW
SAW
Base
Metal Thickness
(U = unlimited)
Groove Preparation
Tolerances
T1
T2
Root
Opening
As
Detailed
As Fit
Up
Permitted
Welding
Positions
1 ⁄4
max
U
R = T1 / 2
+ 1 ⁄16 , −0
+ 1 ⁄16 , − 1 ⁄8
All
—
C, J
TC-L1-GF
3 ⁄8
max
U
R = 0 to 1 ⁄8
+ 1 ⁄16 , −0
+ 1 ⁄16 , − 1 ⁄8
All
Not
Required
A, C, J
TC-L1-S
3 ⁄8
max
U
R=0
±0
+ 1 ⁄16 , −0
F
—
J, C
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
8 - 138
BOLTS, WELDS, AND CONNECTED ELEMENTS
Table 8-36 (cont.).
Prequalified Welded Joints
Complete-Joint-Penetration Groove Welds
Single-V-groove weld (2)
Butt joint (B)
Welding
Process
Joint
Designation
SMAW
B-U2a
GMAW
FCAW
B-U2a-GF
Tolerances
Base
Metal Thickness
(U = unlimited)
As Detailed
As Fit Up
R = +1 ⁄16 , −0
+ 1 ⁄4 , − 1⁄16
α = +10°°, − 0°°
+10°°, − 5°°
Groove Preparation
Gas
Shielding
for
FCAW
Notes
T1
T2
Root
Opening
Groove
Angle
Permitted
Welding
Positions
U
—
R = 1 ⁄4
α = 45°°
All
—
N
R = 3 ⁄8
α = 30°°
F, V, OH
—
N
R = 1 ⁄2
α = 20°°
F, V, OH
—
N
R = 3 ⁄16
α = 30°°
F, V, OH
Required
A, N
R = 3 ⁄8
α = 30°°
F, V, OH
Not req.
A, N
R = 1 ⁄4
α = 45°°
F, V, OH
Not req.
A, N
U
—
SAW
B-L2a-S
2 max
—
R = 1 ⁄4
α = 30°°
F
—
N
SAW
B-U2-S
U
—
R = 5 ⁄8
α = 20°°
F
—
N
Tolerances
Single-V-groove weld (2)
Corner joint (C)
Welding
Process
Joint
Designation
SMAW
C-U2a
Base
Metal Thickness
(U = unlimited)
As Detailed
As Fit Up
R = +1 ⁄16 , −0
+ 1 ⁄4 , − 1⁄16
α = +10°°, − 0°°
+10°°, − 5°°
Groove Preparation
Gas
Shielding
for
FCAW
Notes
T1
T2
Root
Opening
Groove
Angle
Permitted
Welding
Positions
U
U
R = 1 ⁄4
α = 45°°
All
—
Q
R = 3 ⁄8
α = 30°°
F, V, OH
—
Q
R = 1 ⁄2
α = 20°°
F, V, OH
—
Q
R = 3 ⁄16
α = 30°°
F, V, OH
Required
A
R = 3 ⁄8
α = 30°°
F, V, OH
Not req.
A, Q
GMAW
FCAW
C-U2a-GF
U
U
R = 1 ⁄4
α = 45°°
F, V, OH
Not req.
A, Q
SAW
C-L2a-S
2 max
U
R = 1 ⁄4
α = 30°°
F
—
Q
SAW
C-U2-S
U
U
R = 5 ⁄8
α = 20°°
F
—
Q
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
WELDED CONSTRUCTION
8 - 139
Table 8-36 (cont.).
Prequalified Welded Joints
Complete-Joint-Penetration Groove Welds
Single-V-groove weld (2)
Butt joint (B)
Welding
Process
Joint
Designation
SMAW
Base
Metal Thickness
(U = unlimited)
Groove Preparation
Tolerances
Root Opening
Root Face
Groove Angle
As
Detailed
As Fit
Up
Gas
Permitted Shielding
Welding
for
Positions
Notes
FCAW
T1
T2
B-U2
U
—
R = 0 to 1⁄8
f = 0 to 1 ⁄8
α = 60°°
+1 ⁄16 , − 0
+1 ⁄16 , − 0
+10°°, − 0°°
+1 ⁄16 , − 1 ⁄8
Not limited
+10°°, − 5°°
All
—
C, N
GMAW
FCAW
B-U2-GF
U
—
R = 0 to 1⁄8
f = 0 to 1 ⁄8
α = 60°°
+1 ⁄16 , − 0
+1 ⁄16 , − 0
+10°, − 0°°
+1 ⁄16 , −1 ⁄8
Not limited
+10°, − 5°°
All
Not
required
A, C,
N
SAW
B-L2c-S
Over 1 ⁄2 to 1
—
R = 0, α = 60°°
f = 1 ⁄4 max
R = ±0
f = +0, − f
α = +10°°, − 0°°
+1 ⁄16 , − 0
F
—
C, N
Over 1 to 11 ⁄2
—
R = 0, α = 60°°
f = 1 ⁄2 max
Over 11 ⁄2 to 2
—
R = 0, α = 60°°
f = 5 ⁄8 max
± 1 ⁄16
+10°°, − 5°°
Single-V-groove weld (2)
Corner joint (C)
Welding
Process
Joint
Designation
SMAW
Base
Metal Thickness
(U = unlimited)
Groove Preparation
Tolerances
Root Opening
Root Face
Groove Angle
As
Detailed
As Fit
Up
Gas
Permitted Shielding
Welding
for
Positions
FCAW
Notes
T1
T2
C-U2
U
U
R = 0 to 1 ⁄8
f = 0 to 1 ⁄8
α = 60°°
+1 ⁄16 , − 0
+1 ⁄16 , − 0
+10°°, − 0°°
+1 ⁄16 , − 1 ⁄8
Not limited
+10°°, − 5°°
All
—
C, J,
R
GMAW
FCAW
C-U2-GF
U
U
R = 0 to 1 ⁄8
f = 0 to 1 ⁄8
α = 60°°
+1 ⁄16 , − 0
+1 ⁄16 , − 0
+10°, − 0°°
+1 ⁄16 , −1⁄8
Not limited
+10°°, − 5°°
All
Not
required
A, C,
J, R
SAW
C-L2b-S
U
U
R=0
f = 1 ⁄4 max
α = 60°°
±0
+0, − 1 ⁄4
+10° − 0°
+1 ⁄16 , − 0
F
—
C, J,
R
± 1 ⁄16
+10°°, − 5°°
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
8 - 140
BOLTS, WELDS, AND CONNECTED ELEMENTS
Table 8-36 (cont.).
Prequalified Welded Joints
Complete-Joint-Penetration Groove Welds
Tolerances
Double-V-groove weld (3)
Butt joint (B)
Welding
Process
SMAW
B-U3a
SAW
B-U3a-S
Base
Metal Thickness
(U = unlimited)
As Fit Up
R = ±0
+ 1 ⁄4 , −0
f = ±0
+1 ⁄16 , − 0
α = +10°°, − 0°°
+10°°, − 5°°
SAW
±0
+1 ⁄16 , − 0
SMAW
±0
+1 ⁄8 , − 0
Spacer
Joint
Designation
As Detailed
Groove Preparation
Gas
Permitted Shielding
Welding
for
Positions (FCAW) Notes
T1
T2
Root
Opening
Root
Face
Groove
Angle
U
Spacer = 1 ⁄8 × R
—
R = 1 ⁄4
f = 0 to 1 ⁄8
α = 45°°
All
—
R = 3 ⁄8
f = 0 to 1 ⁄8
α = 30°°
F, V, OH
—
R = 1 ⁄2
f = 0 to 1 ⁄8
α = 20°°
F, V, OH
—
U
Spacer = 1 ⁄4 × R
—
R = 5 ⁄8
f = 0 to 1 ⁄4
α = 20°°
F
—
C, M,
N
C, M,
N
Double-V-groove weld (3)
Butt joint (B)
For B-U3c-S only
T1
Over
2
21 ⁄ 2
3
35 ⁄ 8
4
43 ⁄ 4
51 ⁄ 2
S1
to
21 ⁄2
3
35 ⁄8
4
43 ⁄4
51 ⁄2
61 ⁄4
13 ⁄8
13 ⁄4
21 ⁄8
23 ⁄8
23 ⁄4
31 ⁄4
33 ⁄4
For T 1 > 61⁄4, or T 1 ≤ 2
S 1 = 2 ⁄3 ( T 1 − 1 ⁄4 )
Welding
Process
Joint
Designation
SMAW
B-U3b
GMAW
FCAW
B-U3-GF
SAW
B-U3c-S
Base
Metal Thickness
(U = unlimited)
T1
T2
U
—
U
—
Groove Preparation
Tolerances
Gas
Permitted Shielding
Welding
for
Positions
FCAW
Root Opening
Root Face
Groove Angle
As
Detailed
As Fit
Up
R = 0 to 1 ⁄8
f = 0 to 1 ⁄8
α = β = 60°°
+1 ⁄16 , − 0
+1 ⁄16 , − 0
+10°°, − 0°°
+1 ⁄16 , − 1 ⁄8
Not limited
+10°°, − 5°°
All
—
C, M, N
All
Not
required
A, C,
M, N
R=0
f = 1 ⁄4 min
α = β = 60°°
+1 ⁄16 , − 0
+1 ⁄4 , − 0
+10°, − 0°°
+1 ⁄16 , − 0
+1 ⁄4 , − 0
+10°, − 5°°
F
—
C, M, N
To find S 1 see table above; S 2 = T 1 − (S 1 + f )
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
Notes
WELDED CONSTRUCTION
8 - 141
Table 8-36 (cont.).
Prequalified Welded Joints
Complete-Joint-Penetration Groove Welds
Tolerances
Single-bevel-groove weld (4)
Butt joint (B)
Welding
Process
Joint
Designation
SMAW
B-U4a
GMAW
FCAW
Base
Metal Thickness
(U = unlimited)
B-U4a-GF
Welding
Process
SMAW
GMAW
FCAW
SAW
As Fit Up
R = +1 ⁄16, − 0
+ 1 ⁄4 , − 1⁄16
α = +10°°, − 0°°
+10°°, − 5°°
Groove Preparation
Gas
Shielding
for
FCAW
Notes
Br, N
T1
T2
Root
Opening
Groove
Angle
Permitted
Welding
Positions
U
—
R = 1 ⁄4
α = 45°°
All
—
R = 3 ⁄8
α = 30°°
All
—
Br, N
R = 3 ⁄16
α = 30°°
All
Required
A, Br, N
R = 1 ⁄4
α = 45°°
All
Not req.
A, Br, N
R = 3 ⁄8
α = 30°°
F
Not req.
A, Br, N
U
—
Tolerances
Single-bevel-groove weld (4)
T-joint (T)
Corner joint (C)
Joint
Designation
As Detailed
Base
Metal Thickness
(U = unlimited)
As Detailed
As Fit Up
R = +1 ⁄16, − 0
+ 1 ⁄4 , − 1⁄16
α = +10°°, − 0°°
+10°°, − 5°°
Groove Preparation
Gas
Shielding
for
FCAW
Notes
—
J, Q, V
T1
T2
Root
Opening
Groove
Angle
Permitted
Welding
Positions
TC-U4a
U
U
R = 1 ⁄4
α = 45°°
All
R = 3 ⁄8
α = 30°°
F, V, OH
—
J, Q, V
TC-U4a-GF
U
U
R = 3 ⁄16
α = 30°°
All
Required
A, J, Q, V
R = 3 ⁄8
α = 30°°
F
Not req.
A, J, Q, V
R = 1 ⁄4
α = 45°°
All
Not req.
A, J, Q, V
R = 3 ⁄8
α = 30°°
F
—
J, Q, V
R = 1 ⁄4
α = 45°°
TC-U4a-S
U
U
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
8 - 142
BOLTS, WELDS, AND CONNECTED ELEMENTS
Table 8-36 (cont.).
Prequalified Welded Joints
Complete-Joint-Penetration Groove Welds
Single-bevel-groove weld (4)
Butt joint (B)
Base
Groove Preparation
Metal
Thickness
Tolerances
(U = unlimited) Root Opening
As
As Fit
Root Face
T1
T2
Groove Angle Detailed
Up
Welding
Process
Joint
Designation
SMAW
B-U4b
U
—
GMAW
FCAW
B-U4b-GF
U
—
R = 0 to 1 ⁄8
f = 0 to 1 ⁄8
α = 45°°
+1 ⁄16 , − 0
+1 ⁄16 , − 0
+10°°, − 0°°
+1 ⁄16 , − 1⁄8
Not limited
+10°°, − 5°°
Permitted
Welding
Positions
Gas
Shielding
for
FCAW
Notes
All
—
Br, C, N
All
Not
required
A, Br,
C, N
Single-bevel-groove weld (4)
T-joint (T)
Corner joint (C)
Base
Groove Preparation
Metal Thickness
Tolerances
(U = unlimited) Root Opening
As
As Fit
Root Face
T1
T2
Up
Groove Angle Detailed
Welding
Process
Joint
Designation
SMAW
TC-U4b
U
U
GMAW
FCAW
TC-U4b-GF
U
U
SAW
TC-U4b-S
U
U
Gas
Permitted Shielding
Welding
for
Positions
FCAW
Notes
R = 0 to 1 ⁄8
f = 0 to 1 ⁄8
α = 45°°
+1 ⁄16 , − 0
+1 ⁄16 , − 0
+10°°, − 0°°
+1 ⁄16 , − 1 ⁄8
Not limited
+10°°, − 5°°
All
—
C, J, R, V
All
Not
required
A, C, J,
R, V
R=0
f = 1 ⁄4 max
α = 60°
±0
+0, − 1 ⁄8
+10°, − 0°
+1 ⁄4 , − 0
F
—
C, J, R, V
± 1⁄16
+10°, − 5°
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
WELDED CONSTRUCTION
8 - 143
Table 8-36 (cont.).
Prequalified Welded Joints
Complete-Joint-Penetration Groove Welds
Tolerances
Double-bevel-groove weld (5)
Butt joint (B)
T-joint (T)
Corner joint (C)
Welding
Process
SMAW
Base
Metal Thickness
(U = unlimited)
Groove Preparation
As
Fit Up
R = ±0
+ 1 ⁄4 , −0
f = 1 ⁄16 , − 0
± 1 ⁄16
α = +10°°, − 0°°
+10°, − 5°°
+1⁄16 , − 0
+1 ⁄8 , − 0
Spacer
Joint
Designation
As
Detailed
Gas
Permitted Shielding
Welding
for
Positions
FCAW
T1
T2
Root
Opening
Root
Face
Groove
Angle
B-U5b
U
Spacer =1⁄8 × R
U
R = 1 ⁄4
f = 0 to 1 ⁄8
α = 45°°
All
—
Br, C,
M, N
TC-U5a
U
Spacer =1⁄4 × R
U
R = 1 ⁄4
f = 0 to 1 ⁄8
α = 45°°
All
—
C, J, M,
R, V
R = 3 ⁄8
f = 0 to 1 ⁄8
α = 30°°
F, OH
—
C, J, M,
R, V
Notes
Double-bevel-groove weld (5)
Butt joint (B)
Base
Groove Preparation
Metal Thickness
(U = unlimited) Root Opening
Tolerances
Joint
As
As Fit
Welding DesigRoot Face
T1
T2
Groove Angle
Detailed
Up
Process nation
SMAW
B-U5a
GMAW B-U5-GF
FCAW
Gas
Permitted Shielding
Welding
for
Positions FCAW
Notes
U
—
R = 0 to 1 ⁄8
f = 0 to 1⁄8
α = 45°°
β = 0°° to 15°°
+1 ⁄16 , − 0
+1 ⁄16 , − 1⁄8
Not limited
+1 ⁄16 , − 0
α + β , +10°°, − 0° α + β , +10°°, − 5°
All
—
Br, C,
M, N
U
—
R = 0 to 1 ⁄8
f = 0 to 1⁄8
α = 45°°
β = 0°° to 15°
+1 ⁄16 , − 0
+1 ⁄16 , − 0
α + β = +10°°, − 0°
All
Not req.
A, Br,
C, M,
N
+1 ⁄16 , − 1⁄8
Not limited
α + β = +10°°,
− 5°
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
8 - 144
BOLTS, WELDS, AND CONNECTED ELEMENTS
Table 8-36 (cont.).
Prequalified Welded Joints
Complete-Joint-Penetration Groove Welds
Double-bevel-groove weld (5)
T-joint (T)
Corner joint (C)
Welding
Process
Joint
Designation
SMAW
TC-U5b
GMAW TC-U5-GF
FCAW
SAW
TC-U5-S
Base
Groove Preparation
Metal Thickness
Tolerances
(U = unlimited) Root Opening
As
As Fit
Root Face
T1
T2
Groove Angle
Detailed
Up
U
U
U
U
U
U
Permitted
Welding
Positions
Gas
Shielding
for
(FCAW)
Notes
R = 0 to 1⁄8
f = 0 to 1 ⁄8
α = 45°
+1 ⁄16 , − 0
+1 ⁄16 , − 0
+10°°, − 0°
+1 ⁄16 , − 1 ⁄8
Not limited
+10°°, − 5°
All
—
C, J, M,
R, V
All
Not req.
A, C, J,
M, R, V
R=0
f = 3 ⁄16 max
α = 60°
±0
+0, − 3 ⁄16
+10°°, − 0°
+1 ⁄16 , − 0
F
—
C, J, M,
R, V
± 1 ⁄16
+10°°, − 5°
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
WELDED CONSTRUCTION
8 - 145
Table 8-36 (cont.).
Prequalified Welded Joints
Complete-Joint-Penetration Groove Welds
Tolerances
Single-U-groove weld (6)
Butt joint (B)
Corner joint (C)
Welding
Process
Joint
Designation
SMAW
B-U6
GMAW
FCAW
Base
Metal
Thickness
(U = unlimited)
As
Detailed
As
Fit Up
R = +1 ⁄16, − 0
+ 1 ⁄16 , − 1⁄8
α = +10°°, − 0°°
+10°°, − 5°°
f = ± 1 ⁄16
Not limited
r = +1 ⁄8 , − 0
+1 ⁄8 , − 0
Groove Preparation
Gas
Shielding
for
FCAW
Notes
C, N
T1
T2
Root
Opening
Groove
Angle
Root
Face
Groove
Radius
Permitted
Welding
Positions
U
U
R = 0 to 1 ⁄8
α = 45°°
f = 1 ⁄8
r = 1 ⁄4
All
—
R = 0 to 1 ⁄8
α = 20°°
f = 1 ⁄8
r = 1 ⁄4
F, OH
—
C, N
R = 0 to 1 ⁄8
α = 45°°
f = 1 ⁄8
r = 1 ⁄4
All
—
C, J, R
C-U6
U
U
R = 0 to 1 ⁄8
α = 20°°
f = 1 ⁄8
r = 1 ⁄4
F, OH
—
C, J, R
B-U6-GF
U
U
R = 0 to 1 ⁄8
α = 20°°
f = 1 ⁄8
r = 1 ⁄4
All
Not req.
A, C, N
C-U6-GF
U
U
R = 0 to 1 ⁄8
α = 20°°
f = 1 ⁄8
r = 1 ⁄4
All
Not req.
A, C,
J, R
Double-U-groove weld (7)
Butt joint (B)
Welding
Process
Joint
Designation
SMAW
Base
Metal Thickness
(U = unlimited)
T1
T2
B-U7
U
—
GMAW
FCAW
B-U7-GF
U
—
SAW
B-U7-S
U
—
Tolerances
Tolerances
For B-U7 and B-U7-GF
For B-U7-S
As
Detailed
As
Fit Up
R = +1 ⁄16, − 0
+ 1 ⁄16 , − 1⁄8
R = ±0
+ 1 ⁄16 , − 0
+10°°, − 5°°
α = +0°°, − 1 ⁄4 °
± 1 ⁄16
f = ± 1 ⁄16 , − 0
Not limited
r = +1 ⁄4 , − 0
± 1 ⁄16
Gas
Permitted Shielding
Groove Welding
for
Radius Positions
FCAW
Groove
Angle
Root
Face
R = 0 to 1 ⁄8 α = 45°°
f = 1 ⁄8
r = 1 ⁄4
All
R = 0 to 1 ⁄8 α = 20°°
f = 1 ⁄8
r = 1 ⁄4
R = 0 to 1 ⁄8 α = 20°°
f = 1 ⁄8
r = 1 ⁄4
r = 1 ⁄4
R=0
As
Fit Up
α = +10°°, − 0°°
Groove Preparation
Root
Opening
As
Detailed
α = 20°° f = 1 ⁄4 max
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
Notes
—
C, M, N
F, OH
—
C, M, N
All
Not
required
A, C,
M, N
F
—
C, M, N
8 - 146
BOLTS, WELDS, AND CONNECTED ELEMENTS
Table 8-36 (cont.).
Prequalified Welded Joints
Complete-Joint-Penetration Groove Welds
Tolerances
Single-J-groove weld (8)
Butt joint (B)
Welding
Process
Joint
Designation
SMAW
GMAW
FCAW
Base
Metal Thickness
(U = unlimited)
As
Detailed
As
Fit Up
R = +1 ⁄16, − 0
+ 1 ⁄16 , − 1⁄8
α = +10°°, − 0°°
+10°°, − 5°°
f = ± 1 ⁄16 , − 0
Not limited
r = +1 ⁄4 , − 0
± 1 ⁄16
Groove Preparation
Permitted
Groove Welding
Radius Positions
Notes
T1
T2
Root
Opening
Groove
Angle
Root
Face
B-U8
U
—
R = 0 to 1 ⁄8
α = 45°°
f = 1 ⁄8
r = 3 ⁄8
All
—
Br, C, N
B-U8-GF
U
—
R = 0 to 1 ⁄8
α = 30°°
f = 1 ⁄8
r = 3 ⁄8
All
Not
required
A, Br,
C, N
Tolerances
Single-J-groove weld (8)
T-joint (T)
Corner joint (C)
Welding
Process
Joint
Designation
SMAW
TC-U8a
GMAW
FCAW
Gas
Shielding
for
FCAW
TC-U8a-GF
Base
Metal Thickness
(U = unlimited)
Groove Preparation
As
Detailed
As
Fit Up
R = +1 ⁄16, − 0
+ 1 ⁄16 , − 1⁄8
α = +10°°, − 0°°
+10°°, − 5°°
f = ± 1 ⁄16 , − 0
Not limited
r = +1 ⁄4 , − 0
± 1 ⁄16
Gas
Permitted Shielding
Groove Welding
for
Radius Positions FCAW
T1
T2
Root
Opening
Groove
Angle
Root
Face
U
U
R = 0 to 1 ⁄8
α = 45°°
f = 1 ⁄8
r = 3 ⁄8
All
—
C, J, R,
V
R = 0 to 1 ⁄8
α = 30°°
f = 1 ⁄8
r = 3 ⁄8
F, OH
—
C, J, R,
V
R = 0 to 1 ⁄8
α = 30°°
f = 1 ⁄8
r = 3 ⁄8
All
Not
required
A, C, J,
R, V
U
U
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
Notes
WELDED CONSTRUCTION
8 - 147
Table 8-36 (cont.).
Prequalified Welded Joints
Complete-Joint-Penetration Groove Welds
Tolerances
Double-J-groove weld (9)
Butt joint (B)
Welding
Process
Joint
Designation
SMAW
GMAW
FCAW
Base
Metal Thickness
(U = unlimited)
As
Detailed
As
Fit Up
R = +1 ⁄16, − 0
+ 1 ⁄16 , − 1⁄8
α = +10°°, − 0°°
+10°°, − 5°°
f = ± 1 ⁄16 , − 0
Not limited
r = +1 ⁄8 , − 0
± 1 ⁄16
Groove Preparation
Permitted
Groove Welding
Radius Positions
T1
T2
Root
Opening
Groove
Angle
Root
Face
B-U9
U
—
R = 0 to 1 ⁄8
α = 45°°
f = 1 ⁄8
r = 3 ⁄8
All
—
Br, C,
M, N
B-U9-GF
U
—
R = 0 to 1 ⁄8
α = 30°°
f = 1 ⁄8
r = 3 ⁄8
All
Not
required
A, Br,
C, M, N
Welding
Process
Joint
Designation
SMAW
TC-U9a
TC-U9a-GF
Notes
Tolerances
Double-J-groove weld (9)
T-joint (T)
Corner joint (C)
GMAW
FCAW
Gas
Shielding
for
FCAW
Base
Metal Thickness
(U = unlimited)
Groove Preparation
As
Detailed
As
Fit Up
R = +1 ⁄16, − 0
+ 1 ⁄16 , − 1⁄8
α = +10°°, − 0°°
+10°°, − 5°°
f = +1 ⁄16 , − 0
Not limited
r = +1 ⁄8 , − 0
± 1 ⁄16
Gas
Permitted Shielding
Groove Welding
for
Radius Positions
FCAW
T1
T2
Root
Opening
Groove
Angle
Root
Face
U
U
R = 0 to 1⁄8
α = 45°°
f = 1 ⁄8
r = 3 ⁄8
All
—
C, J, M,
R, V
R = 0 to 1⁄8
α = 30°°
f = 1 ⁄8
r = 3 ⁄8
F, OH
—
C, J, M,
R, V
R = 0 to 1⁄8
α = 30°°
f = 1 ⁄8
r = 3 ⁄8
All
Not
required
A, C, J,
M, R, V
U
U
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
Notes
8 - 148
BOLTS, WELDS, AND CONNECTED ELEMENTS
Table 8-36 (cont.).
Prequalified Welded Joints
Partial-Joint-Penetration Groove Welds
Square-groove weld (1)
Butt joint (B)
Base
Metal Thickness
(U = unlimited)
Welding
Process
Joint
Designation
T1
SMAW
B-P1a
1 ⁄8
max
B-P1c
1 ⁄4
max
Groove Preparation
Tolerances
T2
Root
Opening
As
Detailed
As Fit
Up
Permitted
Welding
Positions
Effective
Throat
(E)
Notes
—
R = 0 to 1⁄16
+1 ⁄16 , − 0
± 1 ⁄16
All
T 1 − 1 ⁄32
B
—
T1
R=
min
2
+1 ⁄16 , − 0
± 1 ⁄16
All
T1
2
B
Square-groove weld (1)
Butt joint (B)
E 1 + E 2 must not exceed
Welding
Process
Joint
Designation
SMAW
B-P1b
3T1
4
Base
Metal Thickness
(U = unlimited)
T1
T2
max
—
1 ⁄4
Groove Preparation
Tolerances
Root
Opening
As
Detailed
As Fit
Up
Permitted
Welding
Positions
Effective
Throat
(E)
T1
R=
2
± 1 ⁄16 , − 0
± 1 ⁄16
All
3T1
Notes
4
Single-V-groove weld (2)
Butt joint (B)
Corner joint (C)
Welding
Process
Joint
Designation
SMAW
BC-P2
GMAW
FCAW
BC-P2-GF
SAW
BC-P2-S
Groove Preparation
Base
Metal Thickness
Tolerances
(U = unlimited) Root Opening
Root Face
As
As Fit
T1
T2
Up
Groove Angle Detailed
1 ⁄4
1 ⁄4
7 ⁄16
min
min
min
U
U
U
R=0
f = 1⁄32 min
α - 60°°
0, +1 ⁄16
+u, −0
+10°°, − 0°
+1 ⁄8 , − 1 ⁄16
R=0
f = 1 ⁄8 min
α - 60°°
0, +1 ⁄16
+u, −0
+10°°, − 0°°
+1 ⁄8 , − 1 ⁄16
R=0
f = 1 ⁄4 min
α - 60°°
±0
+u, −0
+10°°, − 0°°
+1 ⁄16 , − 0*
Permitted
Welding
Positions
Effective
Throat
(E)
All
S
B, E,
Q2
All
S
A, B,
E, Q2
F
S
B, E,
Q2
± 1 ⁄16
+10°°, − 5°
± 1 ⁄16
+10°°, − 5°°
± 1 ⁄16
+10°°, − 5°°
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
Notes
WELDED CONSTRUCTION
8 - 149
Table 8-36 (cont.).
Prequalified Welded Joints
Partial-Joint-Penetration Groove Welds
Double-V-groove weld (3)
Butt joint (B)
Welding
Process
Joint
Designation
SMAW
B-P3
GMAW
FCAW
B-P3-GF
SAW
B-P3-S
Base
Groove Preparation
Metal Thickness
Tolerances
(U = unlimited) Root Opening
Root Face
As
As Fit
T1
T2
Groove Angle Detailed
Up
1 ⁄2
1 ⁄2
3 ⁄4
min
min
min
—
—
—
R=0
f = 1 ⁄8 min
α = 60°°
+1⁄16 , − 0
+u, −0
+10°°, − 0°°
+1 ⁄8 , − 1 ⁄16
R=0
f = 1 ⁄8 min
α = 60°°
+1⁄16 , − 0
+u, −0
+10°°, − 0°°
+1 ⁄8 , − 1 ⁄16
R=0
f = 1 ⁄4 min
α = 60°°
±0
+u, −0
+10°°, − 0°°
+1 ⁄16 , − 0*
Permitted
Welding
Positions
Effective
Throat
(E)
All
S
E, Mp,
Q2
All
S
A, E,
Mp, Q2
F
S
E, Mp,
Q2
± 1 ⁄16
Notes
+10°°, − 5°°
± 1 ⁄16
+10°°, − 5°°
± 1 ⁄16
+10°°, − 5°°
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
8 - 150
BOLTS, WELDS, AND CONNECTED ELEMENTS
Table 8-36 (cont.).
Prequalified Welded Joints
Partial-Joint-Penetration Groove Welds
Single-bevel-groove weld (4)
Butt joint (B)
T-joint (T)
Corner joint (C)
Welding
Process
Joint
Designation
SMAW
BTC-P4
GMAW
FCAW
BTC-P4-GF
SAW
TC-P4-S
Base
Groove Preparation
Metal Thickness
Tolerances
(U = unlimited) Root Opening
Root Face
As
As Fit
T1
T2
Groove Angle Detailed
Up
U
1 ⁄4
7 ⁄16
U
U
min
min
U
R=0
f = 1 ⁄8 min
α = 45°°
+1 ⁄16 , − 0
unlimited
+10°°, − 0°°
+1 ⁄8 , − 1 ⁄16
R=0
f = 1 ⁄8 min
α = 45°°
+1 ⁄16 , − 0
unlimited*
+10°°, − 0°°
+1 ⁄8 , − 1 ⁄16
R=0
f = 1 ⁄4 min
α = 60°°
±0
+u, −0
+10°°, − 0°°
+1 ⁄16 , − 0
Permitted
Welding
Positions
Effective
Throat
(E)
All
S − 1⁄8
B, E,
J2, Q2,
V
F, H
V, OH
S
S − 1 ⁄8
A, B, E,
J2, Q2,
V
F
S
Permitted
Welding
Positions
Effective
Throat
(E)
All
(S − 1 ⁄8 )
− 1 ⁄4
E, J2, L,
Mp, Q2,
V
All
(S 1 + S 2 )
A, E,
J2, L,
Mp, Q2,
V
± 1 ⁄16
+10°°, − 5°°
± 1 ⁄16
+10°°, − 5°°
± 1 ⁄16
+10°°, − 5°°
Notes
B, E,
J2, Q2,
V
Double-bevel-groove weld (5)
Butt joint (B)
T-joint (T)
Corner joint (C)
Welding
Process
Joint
Designation
SMAW
BTC-P5
GMAW
FCAW
BTC-P5-GF
SAW
TC-P5-S
Base
Groove Preparation
Metal Thickness
Tolerances
(U = unlimited) Root Opening
Root Face
As
As Fit
T1
T2
Groove Angle Detailed
Up
5 ⁄16
1 ⁄2
3 ⁄4
min
min
min
U
U
U
R=0
f = 1 ⁄8 min
α = 45°°
+1 ⁄16 , − 0
unlimited
+10°°, − 0°°
+1 ⁄8 , − 1 ⁄16
R=0
f = 1 ⁄8 min
α = 45°°
+1 ⁄16 , − 0
unlimited
+10°°, − 0°°
+1 ⁄8 , − 1 ⁄16
R=0
f = 1 ⁄4 min
α = 60°°
±0
unlimited
+10°°, − 0°°
+1 ⁄16 , − 0*
± 1 ⁄16
+10°°, − 5°°
± 1 ⁄16
+10°°, − 5°°
± 1 ⁄16
+10°°, − 5°°
*For flat and horizontal postiions f = + u , −0
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
− 1 ⁄4
F
S1 + S2
Notes
E, J2, L,
Mp, Q2,
V
WELDED CONSTRUCTION
8 - 151
Table 8-36 (cont.).
Prequalified Welded Joints
Partial-Joint-Penetration Groove Welds
Single-U-groove weld (6)
Butt joint (B)
Corner joint (C)
Welding
Process
Joint
Designation
SMAW
BC-P6
GMAW
FCAW
BC-P6-GF
SAW
BC-P6-S
Base
Groove Preparation
Metal Thickness Root Opening
Tolerances
(U = unlimited)
Root Face
Groove Radius
As
As Fit
T1
T2
Groove Angle Detailed
Up
1 ⁄4
1 ⁄4
7 ⁄16
U
min
U
min
min
U
R=0
f = 1 ⁄32 min
r = 1 ⁄4
α = 45°°
+1 ⁄16 , − 0
+u, −0
+1 ⁄4 , − 0
+10°°, − 0°°
+1 ⁄8 , − 1 ⁄16
R=0
f = 1 ⁄8 min
r = 1 ⁄4
α = 20°°
+1 ⁄16 , − 0
+u, −0
+1 ⁄4 , − 0
+10°°, − 0°°
+1 ⁄8 , − 1 ⁄16
R=0
f = 1 ⁄4 min
r = 1 ⁄4
α = 20°°
±0
+u, −0
+1 ⁄4 , − 0
+10°°, − 0°°
+1 ⁄16 , − 0
Permitted
Welding
Positions
Effective
Throat
(E)
All
S
B, E,
Q2
All
S
A, B, E,
Q2
F
S
B, E,
Q2
Permitted
Welding
Positions
Effective
Throat
(E)
All
S1 + S2
E, Mp,
Q2
All
S1 + S2
A, E,
Mp, Q2
F
S1 + S2
E,
Mp, Q2
± 1 ⁄16
± 1 ⁄16
+10°°, − 5°°
± 1 ⁄16
± 1 ⁄16
+10°°, − 5°°
± 1 ⁄16
± 1 ⁄16
+10°°, − 5°°
Notes
Double-U-groove weld (7)
Butt joint (B)
Welding
Process
Joint
Designation
SMAW
B-P7
GMAW
FCAW
B-P7-GF
SAW
B-P7-S
Base
Groove Preparation
Metal Thickness Root Opening
Tolerances
(U = unlimited)
Root Face
Groove Radius
As
As Fit
T1
T2
Groove Angle Detailed
Up
1 ⁄2
1 ⁄2
3 ⁄4
min
min
min
—
—
—
R=0
f = 1 ⁄8 min
r = 1 ⁄4
α = 45°°
+1 ⁄16 , − 0
+u, −0
+1 ⁄4 , − 0
+10°°, − 0°°
+1 ⁄8 , − 1 ⁄16
R=0
f = 1 ⁄8 min
r = 1 ⁄4
α = 20°°
+1 ⁄16 , − 0
+u, −0
+1 ⁄4 , − 0
+10°°, − 0°°
+1 ⁄8 , − 1 ⁄16
R=0
f = 1 ⁄4 min
r = 1 ⁄4
α = 20°°
±0
+u, −0
+1 ⁄4 , − 0
+10°°, − 0°°
+1 ⁄16 , − 0
± 1 ⁄16
± 1 ⁄16
+10°°, − 5°°
± 1 ⁄16
± 1 ⁄16
+10°°, − 5°°
± 1 ⁄16
± 1 ⁄16
+10°°, − 5°°
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
Notes
8 - 152
BOLTS, WELDS, AND CONNECTED ELEMENTS
Table 8-36 (cont.).
Prequalified Welded Joints
Partial-Joint-Penetration Groove Welds
Single-J-groove weld (8)
Butt joint (B)
T-joint (T)
Corner joint (C)
Welding
Process
SMAW
Joint
Designation
TC-P8*
SMAW
Base
Metal Thickness
(U = unlimited)
T1
T2
1 ⁄4
min
U
BC-P8**
1 ⁄4
min
U
GMAW
FCAW
TC-P8-GF*
1 ⁄4
min
U
GMAW
FCAW
BC-P8-GF**
1 ⁄4
min
U
SAW
TC-P8-S*
7 ⁄16
min
U
SAW
C-P8-S**
7 ⁄16
min
U
Groove Preparation
Root Opening
Tolerances
Root Face
As
As Fit
Groove Radius
Up
Groove Angle Detailed
R=0
+1 ⁄16 , − 0 +1 ⁄8 , − 1 ⁄16
1
f = ⁄8 min
± 1 ⁄16
+u, −0
r = 3 ⁄8
+1 ⁄4 , − 0
± 1 ⁄16
α = 45°°
+10°°, − 0°° +10°°, − 5°°
R=0
+1 ⁄16 , − 0 +1 ⁄8 , − 1 ⁄16
f = 1 ⁄8 min
± 1 ⁄16
+u, −0
3
r = ⁄8
+1 ⁄4 , − 0
± 1 ⁄16
α = 30°°
+10°°, − 0°° +10°°, − 5°°
R=0
+1 ⁄16 , − 0 +1 ⁄8 , − 1 ⁄16
f = 1 ⁄8 min
± 1 ⁄16
+u, −0
3
r = ⁄8
+1 ⁄4 , − 0
± 1 ⁄16
α = 45°°
+10°°, − 0°° +10°°, − 5°°
1
1
R=0
+ ⁄16 , − 0 + ⁄8 , − 1 ⁄16
f = 1 ⁄8 min
± 1 ⁄16
+u, −0
r = 3 ⁄8
+1 ⁄4 , − 0
± 1 ⁄16
α = 30°°
+10°°, − 0°° +10°°, − 5°°
1
R=0
±0
+ ⁄16 , − 0
f = 1 ⁄4 min
± 1 ⁄16
+u, −0
r = 1 ⁄2
+1 ⁄4 , − 0
± 1 ⁄16
α = 45°°
+10°°, − 0°° +10°°, − 5°°
R=0
±0
+1 ⁄16 , 0
f = 1 ⁄4 min
± 1 ⁄16
+u, −0
r = 1 ⁄2
+1 ⁄4 , − 0
± 1 ⁄16
α = 20°°
+10°°, − 0°° +10°°, − 5°°
*Applies to inside corner joints.
**Applies to outside corner joints.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
Permitted Effective
Welding
Throat
Positions
(E)
All
S
Notes
E, J2,
Q2, V
All
S
E, J2,
Q2, V
All
S
A, E,
J2, Q2,
V
All
S
A, E,
J2, Q2,
V
F
S
E, J2,
Q2, V
F
S
E, J2,
Q2, V
WELDED CONSTRUCTION
8 - 153
Table 8-36 (cont.).
Prequalified Welded Joints
Flare Welds
Double-J-groove weld (9)
Butt joint (B)
T-joint ( T)
Corner joint (C)
Welding
Process
SMAW
Joint
Designation
BTC-P9*
GMAW
FCAW
Base
Metal Thickness
(U = unlimited)
T1
T2
1 ⁄2
min
U
BTC-P9-GF**
1 ⁄2
min
U
SAW
C-P9-S*
3 ⁄4
min
U
SAW
C-P9-S**
3 ⁄4
min
U
SAW
T-P9-S
3 ⁄4
min
U
Groove Preparation
Root Opening
Tolerances
Root Face
As
As Fit
Groove Radius
Up
Groove Angle Detailed
1
1
R=0
+ ⁄16 , − 0 + ⁄8 , − 1 ⁄16
f = 1 ⁄8 min
± 1 ⁄16
+u, −0
r = 3 ⁄8
± 1 ⁄16
+1 ⁄4 , − 0
α = 45°°
+10°°, − 0°° +10°°, − 5°°
1
1
R=0
+ ⁄16 , − 0 + ⁄8 , − 1 ⁄16
f = 1 ⁄8 min
± 1 ⁄16
+u, −0
r = 3 ⁄8
+1 ⁄4 , − 0
± 1 ⁄16
α = 30°°
+10°°, − 0°° +10°°, − 5°°
R=0
±0
+1 ⁄16 , − 0
f = 1 ⁄4 min
± 1 ⁄16
+u, −0
r = 1 ⁄2
+1 ⁄4 , − 0
± 1 ⁄16
α = 45°°
+10°°, − 0°° +10°°, − 5°°
R=0
±0
− 1⁄16 , 0
f = 1 ⁄4 min
± 1 ⁄16
+u, −0
r = 1 ⁄2
+1 ⁄4 , − 0
± 1 ⁄16
α = 20°°
+10°°, − 0°° +10°°, − 5°°
R=0
±0
+1 ⁄16 , 0
f = 1 ⁄4 min
± 1 ⁄16
+u, −0
1
r = 1 ⁄2
+ ⁄4 , − 0
± 1 ⁄16
α = 45°°
+10°°, − 0°° +10°°, − 5°°
Permitted Effective
Welding
Throat
Positions
(E)
All
S1 + S2
Notes
E, J2,
Mp, Q2,
V
All
S1 + S2
A, J2,
Mp, Q2,
V
F
S1 + S2
E, J2,
Mp, Q2,
V
F
S1 + S2
E, J2,
Mp, Q2,
V
F
S1 + S2
E, J2,
Mp, Q2
Single-J-groove weld (B)
Butt joint (B)
T-joint (T)
Corner joint (C)
Welding
Process
SMAW
Joint
Designation
BTC-P10
Base
Metal Thickness
(U = unlimited)
T1
T2
3 ⁄16
U
min
GMAW
FCAW
BTC-P10-GF
SAW
T-P10-S
3 ⁄16
U
min
1 ⁄2
1 ⁄2
min
min
Groove Preparation
Tolerances
Root Opening
As
As Fit
Root Face
T3
Bend Radius Detailed
Up
1
1
T 1 min
R=0
+ ⁄16 , − 0 + ⁄8 , − 1 ⁄16
f = 3⁄16 min
+U, − 1 ⁄16
+U, −0
3T1
− 0, +Not- − 0, +NotC=
min
Limited
Limited
2
T 1 min
R=0
+1⁄16 , − 0 + 1 ⁄8, − 1⁄16
f = 3⁄16 min
+U, − 1 ⁄16
+U, −0
3T 1
− 0, +Not- − 0, +NotC=
min
Limited
Limited
2
N/A
R=0
±0
+ 1 ⁄16, −0
1
f = ⁄2 min
+U, − 1 ⁄16
+U, −0
3T1
− 0, +Not- − 0, +NotC=
min
Limited
Limited
2
*Applies to inside corner joints.
**Applies to outside corner joints.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
Permitted Effective
Welding Throat
Positions
(E)
Notes
5 ⁄8 T 1
J2,
All
Q2, Z
All
5 ⁄8 T 1
A, J2,
Q2, Z
F
5 ⁄8 T 1
J2,
Q2, Z
8 - 154
BOLTS, WELDS, AND CONNECTED ELEMENTS
ECCENTRICALLY LOADED WELD GROUPS
When the line of action of an applied load does not pass through the center of gravity
(CG) of a weld group, the load is eccentric and results in a moment which must be
considered in the design of the connection.
Eccentricity in the Plane of the Faying Surface
Eccentricity in the plane of the faying surface produces additional shear and the welds
must then be designed to resist the combined effect of the direct shear from the applied
load Pu and the additional shear from the induced moment Pu e. Two methods of analysis
for this type of eccentricity will be discussed: (1) the instantaneous center of rotation
method; and, (2) the elastic method.
Instantaneous Center of Rotation Method
Also known as the ultimate strength method (Crawford, 1968), this method considers the
load-deformation relationship of each weld element as well as the variation in weld
strength with respect to the direction of the applied force and, thus, more accurately
predicts the ultimate strength of the eccentrically loaded connection (Butler, Pal, and
Kulak, 1972). Eccentricity produces both a rotation about the centroid of the weld group
and a translation of one connected element with respect to the other. The combined effect
of this rotation and translation is equivalent to a rotation about a point defined as the
instantaneous center of rotation (IC) as illustrated in Figure 8-51a. The location of the IC
depends on the geometry of the weld group as well as the direction and point of
application of the load. The individual resistance of each unit weld element is assumed
to act on a line perpendicular to a ray passing through the instantaneous center and the
centroid of that element, as illustrated in Figure 8-51b.
The load-deformation relationship of a single unit-weld element was originally given
by Butler, Pal, and Kulak (1972) for E60 electrodes. New strength curves for E70
electrodes (Lesik and Kennedy, 1990) are illustrated in Figure 8-52, where:
R = 0.60FEXX(1.0 + 0.50 sin1.5θ) [p (1.9 − 0.9p)]0.3
In the above equation,
R
FEXX
θ
p
= shear force per unit area in a single unit-weld element at a deformation ∆, kips
= weld electrode strength, ksi
= angle of loading measured from the weld longitudinal axis, degrees
= ratio of element deformation to its deformation at maximum stress
Unlike the load-deformation relationship for bolts, strength and deformation of welds
are dependent on the angle θ that the resultant elemental force makes with the axis of the
weld element.
The critical weld element is usually the weld element farthest from the IC. While this
may not always be the case, for the purpose of explanation, this will be assumed. The
maximum deformation ∆max may be determined as
∆max = 1.087w (θ + 6)−0.65 ≤ 0.17w
where w is the leg size of the weld and θ is expressed in degrees. The deformation of
other weld elements is assumed to vary linearly with distance from the IC as,
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
ECCENTRICALLY LOADED WELD GROUPS
∆=
lr
lr max
8 - 155
∆max
More discussion of this method is contained in LRFD Specification Appendix J2.4 and
its Commentary. These new provisions permit, for the first time, weld strength to exceed
the 0.6FEXX nominal value, which is the least strength applicable to longitudinally loaded
(θ = 0°) elements. Load-deformation curves in Figure 8-52 for values of θ = 0°, 30°, 45°,
Pu
e
lo
CG
IC
(a) Instantaneous center of rotation (IC)
lo
e
IC
CG
l
ax
rm
ru max
(b) Forces on weld elements
Fig. 8-51. Instantaneous center of rotation method.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
Pu
8 - 156
BOLTS, WELDS, AND CONNECTED ELEMENTS
60°, 75°, and 90° are shown relative to Ro = 0.6FEXX. The ductility of the weld group is
governed by ∆max of the element that first reaches its limit. The total strength of all weld
elements is the sum of the individual resistances of all welds in the group. If the correct
location of the instantaneous center has been selected, the three equations of statics will
be satisfied, i.e., ΣFx = 0, ΣFy = 0, ΣM = 0. Because of the non-linear nature of the requisite
iterative solution, a minimum of twenty weld elements for the longest line segment is
generally recommended for sufficient accuracy.
Tables 8-38 through 8-45 employ the instantaneous center of rotation method in
accordance with LRFD Specification Appendix J2.4 for the weld patterns and eccentric
conditions indicated and inclined loads at 0°, 15°, 30°, 45°, 60°, and 75°. Thus, unlike
the First Edition LRFD Manual, tabulated values are not limited to a maximum weld
nominal strength of 0.6FEXX. For some cases, significant increases of up to 50 percent of
values tabulated previously are possible; many values reflect more moderate but, nevertheless, substantial increases on the order of 10 to 30 percent. The traditional and more
conservative designs based upon a constant fillet weld nominal strength of 0.6FEXX is also
permitted, refer to AISC (1986).
For any of the weld group geometrics shown, the design strength of the eccentrically
loaded weld group is φRn, where
In the above equation,
1.6
θ = 90°
θ = 75°
1.4
θ = 60°
θ = 45°
1.2
θ = 30°
θ = 0°
1.0
( RR )
o
0.8
0.6
0.4
Ro = 0.6Fexx
0.2
0
0.000
0.050
∆
w
0.100
Fig. 8-52. Fillet weld strength as a function of force angle, θ.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
0.150
ECCENTRICALLY LOADED WELD GROUPS
8 - 157
C = tabular value (which includes φ = 0.75)
φRn = CC1Dl
C1 = electrode coefficient from Table 8-37 which adjusts tabular value, which is
based on E70XX electrodes, for other electrodes. Note that this coefficient
includes an additional reduction factor of 0.90 for E80 and E90 electrodes and
0.85 for E100 and E110; this accounts for the uncertainty of extrapolation to
the higher strength electrodes.
D = number of sixteenths-of-an-inch in the weld size
l = length of the reference weld, in.
The first line in each table (a = 0) gives the design strength of a concentrically loaded
weld group in accordance with LRFD Specification Appendix J2.2a. Linear interpolation
within a given table between adjacent a and k values is permitted.
Figure C-J2.5 from LRFD Specification Commentary Section J2 indicates that, for
equal-leg fillet welds, the area of the fusion surface is always larger than the leg dimension
times the weld length. Therefore, the tabulated values are based upon the strength through
the throat of the weld of
(0.75 × 0.6 × FEXX × 0.707 × 1⁄16)
Tabulated values are valid for weld metal with a strength level equal to or matching the
base material.
A convergence criterion of less than 0.5 percent unbalanced force was employed for
the tabulated iterative solutions. Straight line interpolation between these angles may be
significantly unconservative. Therefore, unless a direct analysis is performed, use only
the values tabulated for the next lower angle. Since the coefficients in these tables were
derived from physical tests with loading at ultimate strength levels, they should be used
only for the weld patterns indicated and not in combination with any additional loading.
In cases not treated by these tables, a special ultimate strength analysis is required if the
instantaneous center of rotation method is to be used.
Example 8-3
Given:
Refer to Figure 8-53. Determine the largest eccentric force Pu for which
the design shear strength of the welds in the connection is adequate
using the instantaneous center of rotation method. Use 3⁄8-in. fillet weld
and 70 ksi electrode weld size.
A. Assume the load is vertical as illustrated in Figure 8-53 (θ = 0°°)
B. Assume the load acts at an angle of 75°° with respect to vertical
(θ = 75°°)
Solution A:
l = 10 in.
kl = 5 in.
k = 0.5
From Table 8-42 with θ = 0°, x = 0.125
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
8 - 158
BOLTS, WELDS, AND CONNECTED ELEMENTS
Table 8-37.
Electrode Strength Coefficients
Electrode
FEXX (ksi)
C1
E60
E70
E80
E90
E100
E110
60
70
80
90
100
110
0.857
1.00
1.03
1.16
1.21
1.34
xl + al = 10 in.
0.125(10 in.) + a (10 in.) = 10 in.
a = 0.875
By interpolation from Table 8-42 with θ = 0°,
C = 1.41
Design shear strength
φRn = CC1Dl
= 1.41(1.0)(6 sixteenths)(10 in.)
= 84.6 kips
Comment:
Note that this eccentricity has effectively reduced the shear strength of
this weld group by 60 percent when compared with the eccentrically
loaded case.
Solution B:
From Solution A,
k = 0.5
a = 0.875
By interpolation from Table 8-42 with θ = 75°°,
C = 2.59
Design shear strength
φRn = CC1Dl
= 2.59(1.0)(6 sixteenths)(10 in.)
= 155 kips
Comment:
In Solution B, the vertical component of the design strength is
φRn sin75°° = (155 kips)(0.966)
= 150 kips
and the horizontal component of the design strength is
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
ECCENTRICALLY LOADED WELD GROUPS
8 - 159
φRn cos75°° = (155 kips)(0.259)
= 40.1 kips
Elastic Method
Alternatively, the elastic method may be used to analyze eccentrically loaded weld
groups. It offers a simplified, conservative approach but does not render a consistent
factor of safety and, in some cases, provides excessively conservative results. Furthermore, the elastic method ignores both the ductility of the weld group and the load
redistribution which occurs. Refer to Higgins (1971).
In the elastic method, for a force applied parallel to the Y principle axis of the weld
group, the eccentric force Pu is resolved into a force Pu acting through the center of gravity
(CG) of the weld group and a moment Pu e where e is the eccentricity. Each weld element
is then assumed to support an equal share of the concentric force Pu, and a share of the
eccentric moment Pu e which is proportional to its distance from the CG. The weld most
remote from the CG, then, is the most highly stressed. The resultant vectorial sum of these
forces ru is the required strength for the weld element.
The shear force per linear inch of weld due to the concentric force Pu is r1,
where
r1 =
Pu
l
and l is the total length of the weld measured along the axis of each element.
The shear force per linear inch of weld due to the moment Pu e varies with distance
from the CG and will be maximum in the weld element which is most remote from the
CG. The maximum shear due to the moment Pu e is rm,
where
rm =
Pu ec
Ip
In the above equation,
10 in.
Pu
k l = 5 in.
l = 10 in.
1.25 in.
Figure 8-53. Illustration for Example 8-3 and 8-4.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
8 - 160
BOLTS, WELDS, AND CONNECTED ELEMENTS
c = distance from CG to point on weld most remote from CG, in.
Ip = polar moment of inertia of the weld group, in.4 per in.2 (Ip = Ix + Iy). Refer to Figure 8-54. For section moduli and torsional constants of various welds treated as
line elements, refer to Table 5 (page 7.4–7) of Blodgett (1966).
To determine the resultant force on the most highly stressed weld element, rm must be
resolved into vertical component r2 and horizontal component r3,
where
Pu ecx
Ip
Pu ecy
r3 =
Ip
r2 =
In the above equations, cx and cy are the horizontal and vertical components of the
diagonal distance c. Thus, the resultant force is ru,
where
r2
r1
ru = √
(r1 + r2)2 + (r3)2
r3
rm
ru
and the weld size must be chosen such that the design strength of the weld exceeds the
required strength ru.
For the more general case of an inclined eccentric force, i.e., not parallel to the
Y principle axis of the bolt group, the effect of the X-direction component of the direct
shear must also be included. Refer to Iwankiw (1987).
Example 8-4
Given:
Refer to Example 8-3a. Recalculate the largest eccentric force Pu for
which the design shear strength of the welds in the connection is
adequate using the elastic method. Compare the result with that of
Example 8-3a. Use 3⁄8-in. weld size, E70XX electrodes
Ip = 385 in.4 per in.2
Solution:
Direct shear force per inch of weld
Pu
l
Pu
=
20 in.
r1 =
Additional shear force on weld due to eccentricity
Pu ecx
Ip
Pu (8.75 in.) (3.75 in.)
=
385 in.4 per in.2
= 0.0852Pu
r2 =
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
ECCENTRICALLY LOADED WELD GROUPS
r3 =
8 - 161
Pu ecy
Ip
Pu (8.75 in.) (5 in.)
=
385 in.4 per in.2
= 0.114Pu
Resultant shear force per inch of weld
(r1 + r2)2 + (r3)2
ru = √
y
(p)
x
xo
cg
(po )
x
yo
y
xo
xo
x
yo
y
l = 6.283R
x
(p)
x
n
y
x
(p)
ln2
12
ln2
+ l(dy)2
12
lm2
Iyo =
12
lm2
Iy =
+ l(dx)2
12
Ix =
yo
a
xo
cg
(po )
xo
dx
y
xo
R
dy
yo
xo
m
Ixo =
y
a = 0.637R
l = 3.142R
Ixo = πR 3
Ix = πR 3 + l(dy)2
Iyo = πR 3
Iy = πR 3 + l(dx)2
(p)
x
yo
R
a
R
xo
cg
(po )
x
yo d y
x
cg
(po )
dy
xo
dx
xo
Ixo = 0
Ix = l(dy)2
l3
Iyo =
12
l3
Iy =
+ l(dx)2
12
12
l3
Ix =
+ l(dy)2
12
Iyo = 0
Iy = l(dx)2
cg
(po )
y
yo
l3
l /2
/2
dy
xo
y
dx
dy
Ixo =
l
l
a
yo
yo
y
dx
l
dy
xo
x
yo
y
dy
dx
cg
(po )
l/
2
l
yo
x
(p)
x
yo
y
x
(p)
a = 0.637R
l = 1.571R
Ix =
π 3
R + l(dy)2
2
π 4
Iyo = − R 3
2 π
π 2
Ixo = − R 3
4 π
π 2 3
Ix = − R + l(dy)2
4 π
π 2
Iyo = − R 3
4 π
π 4
Iy = − R 3
2 π
π 2
Iy = − R 3 + l(dx)2
4 π
Ixo =
π 3
R
2
Fig. 8-54. Moments of inertia of various weld segments.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
8 - 162
BOLTS, WELDS, AND CONNECTED ELEMENTS
√
Pu
2
20 + 0.0852Pu + (0.114Pu )
= 0.177Pu
2
=
Since ru must be less than or equal to φrn,
φrn
0.177
1.392D
≤
0.177
1.392 (6 sixteenths)
≤
0.177
≤ 47.2 kips
Pu ≤
This is a 44 percent reduction in the strength predicted by the instantaneous center of rotation method in Example 8-3a.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
ECCENTRICALLY LOADED WELD GROUPS
8 - 163
Table 8-38.
Coefficients C for Eccentrically Loaded Weld Groups
Angle = 0°°
φ R n = CC1Dl
C min =
Pu
D min =
C 1D l
Pu
lmin =
CC 1 l
Pu
CC 1 D
ex = a l
Pu
l
where
Pu = factored force, kips
D = number of sixteenths-of-an-inch
in the fillet weld size
l = characteristic length of weld group, in.
a = e x / l, in.
e x = horizontal component of eccentricity of
Pu with respect to centroid of weld group, in.
kl
ex = a l
C = coefficient tabulated below which includes φ = 0.75
C 1 = electode strength coefficient from Table 8-37
(1.0 for E70XX electrodes
P
Special Case
u
(Load not in plane
of weld group)
Use C-values for k = 0
Any equal distances
k
a
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.2
1.4
1.6
1.8
2.0
0.00
0.10
0.15
0.20
0.25
2.78
2.78
2.75
2.64
2.48
2.78
2.78
2.75
2.63
2.48
2.78
2.78
2.74
2.63
2.48
2.78
2.78
2.73
2.62
2.47
2.78
2.78
2.71
2.60
2.47
2.78
2.77
2.70
2.59
2.46
2.78
2.75
2.69
2.58
2.46
2.78
2.74
2.67
2.57
2.45
2.78
2.73
2.66
2.56
2.45
2.78
2.71
2.64
2.55
2.44
2.78
2.70
2.63
2.54
2.44
2.78
2.67
2.60
2.52
2.43
2.78
2.64
2.58
2.50
2.41
2.78
2.61
2.55
2.48
2.40
2.78
2.59
2.53
2.46
2.39
2.78
2.78
2.50
2.44
2.38
0.30
0.40
0.50
0.60
0.70
2.32
2.00
1.72
1.50
1.32
2.32
2.00
1.72
1.50
1.32
2.32
2.01
1.74
1.52
1.34
2.32
2.03
1.77
1.55
1.38
2.33
2.05
1.80
1.59
1.42
2.33
2.07
1.83
1.63
1.47
2.33
2.08
1.86
1.67
1.51
2.33
2.10
1.89
1.71
1.55
2.33
2.11
1.91
1.74
1.59
2.33
2.12
1.93
1.77
1.62
2.33
2.14
1.95
1.79
1.65
2.33
2.15
1.99
1.84
1.71
2.33
2.16
2.01
1.87
1.75
2.32
2.17
2.03
1.90
1.79
2.32
2.18
2.05
1.92
1.81
2.31
2.18
2.06
1.94
1.84
0.80
0.90
1.00
1.20
1.40
1.17
1.05
0.957
0.806
0.695
1.18
1.06
0.963
0.812
0.701
1.20
1.08
0.986
0.835
0.724
1.24
1.12
1.02
0.872
0.758
1.28
1.17
1.07
0.916
0.799
1.33
1.22
1.12
0.963
0.844
1.38
1.27
1.17
1.01
0.889
1.42
1.31
1.21
1.06
0.932
1.46
1.35
1.26
1.10
0.973
1.50
1.39
1.29
1.14
1.01
1.53
1.43
1.33
1.17
1.05
1.59
1.49
1.40
1.24
1.12
1.64
1.54
1.45
1.30
1.18
1.68
1.59
1.50
1.35
1.23
1.71
1.62
1.54
1.40
1.28
1.74
1.66
1.58
1.44
1.32
1.60
1.80
2.00
2.20
2.40
0.611
0.544
0.491
0.447
0.410
0.616
0.550
0.496
0.452
0.415
0.638
0.570
0.515
0.470
0.431
0.670
0.600
0.542
0.495
0.455
0.708
0.635
0.576
0.526
0.484
0.750
0.674
0.612
0.560
0.516
0.792
0.714
0.650
0.596
0.550
0.833
0.753
0.687
0.631
0.583
0.873
0.791
0.723
0.665
0.616
0.911
0.828
0.758
0.699
0.648
0.947
0.863
0.792
0.731
0.679
1.01
0.928
0.855
0.792
0.738
1.07
0.987
0.912
0.848
0.792
1.13
1.04
0.964
0.899
0.842
1.17
1.09
1.01
0.945
0.887
1.22
1.13
1.05
0.988
0.929
2.60 0.379 0.384 0.399 0.421 0.448 0.478 0.510 0.542 0.573 0.604 0.634 0.691 0.743 0.791 0.836 0.877
2.80 0.352 0.357 0.371 0.392 0.417 0.446 0.476 0.506 0.536 0.565 0.594 0.649 0.699 0.746 0.790 0.830
3.00 0.329 0.333 0.347 0.366 0.390 0.417 0.446 0.474 0.503 0.531 0.559 0.611 0.661 0.706 0.748 0.788
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
8 - 164
BOLTS, WELDS, AND CONNECTED ELEMENTS
Table 8-38 (cont.).
Coefficients C for Eccentrically Loaded Weld Groups
Angle = 15°°
φ R n = CC1Dl
C min =
Pu
D min =
C 1D l
Pu
lmin =
CC 1 l
Pu
CC 1 D
ex = a l
Pu
15°
l
where
Pu = factored force, kips
D = number of sixteenths-of-an-inch
in the fillet weld size
l = characteristic length of weld group, in.
a = e x / l, in.
e x = horizontal component of eccentricity of
Pu with respect to centroid of weld group, in.
kl
ex = a l
Pu
C = coefficient tabulated below which includes φ = 0.75
C 1 = electode strength coefficient from Table 8-37
(1.0 for E70XX electrodes)
15°
Special Case
(Load not in plane
of weld group)
Use C-values for k = 0
Any equal distances
k
a
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.2
1.4
1.6
1.8
2.0
0.00
0.10
0.15
0.20
0.25
2.97
2.84
2.76
2.63
2.48
2.97
2.84
2.76
2.63
2.48
2.97
2.84
2.75
2.63
2.48
2.97
2.83
2.75
2.62
2.48
2.97
2.82
2.74
2.62
2.49
2.97
2.82
2.73
2.62
2.49
2.97
2.81
2.72
2.61
2.49
2.97
2.80
2.72
2.61
2.49
2.97
2.80
2.71
2.61
2.49
2.97
2.79
2.70
2.61
2.50
2.97
2.78
2.70
2.60
2.50
2.97
2.77
2.69
2.60
2.50
2.97
2.75
2.68
2.59
2.51
2.97
2.74
2.67
2.59
2.51
2.97
2.73
2.66
2.58
2.51
2.97
2.72
2.65
2.58
2.51
0.30
0.40
0.50
0.60
0.70
2.32
2.01
1.74
1.52
1.34
2.32
2.01
1.74
1.52
1.35
2.32
2.02
1.76
1.54
1.37
2.33
2.04
1.78
1.57
1.40
2.34
2.06
1.82
1.62
1.45
2.35
2.09
1.86
1.66
1.50
2.36
2.12
1.89
1.70
1.54
2.37
2.14
1.93
1.75
1.59
2.38
2.16
1.96
1.78
1.63
2.39
2.18
1.99
1.82
1.67
2.39
2.19
2.01
1.85
1.70
2.41
2.22
2.05
1.90
1.77
2.42
2.25
2.09
1.95
1.82
2.43
2.27
2.12
1.99
1.87
2.43
2.28
2.15
2.02
1.90
2.43
2.30
2.17
2.05
1.94
0.80
0.90
1.00
1.20
1.40
1.20
1.08
0.979
0.826
0.714
1.20
1.08
0.985
0.832
0.719
1.22
1.11
1.01
0.856
0.743
1.26
1.15
1.05
0.893
0.778
1.31
1.19
1.09
0.938
0.820
1.36
1.24
1.15
0.987
0.866
1.41
1.30
1.20
1.04
0.913
1.46
1.34
1.25
1.09
0.960
1.50
1.39
1.29
1.13
1.00
1.54
1.43
1.33
1.17
1.05
1.58
1.47
1.37
1.21
1.09
1.65
1.54
1.45
1.29
1.16
1.71
1.60
1.51
1.35
1.23
1.76
1.66
1.57
1.41
1.28
1.80
1.70
1.62
1.46
1.34
1.84
1.74
1.66
1.51
1.39
1.60
1.80
2.00
2.20
2.40
0.628
0.560
0.506
0.461
0.423
0.633
0.566
0.511
0.466
0.428
0.656
0.587
0.530
0.484
0.445
0.688
0.617
0.558
0.510
0.469
0.727
0.653
0.592
0.541
0.499
0.770
0.693
0.630
0.577
0.532
0.815
0.735
0.669
0.613
0.566
0.859
0.777
0.708
0.650
0.601
0.901
0.817
0.746
0.687
0.636
0.941
0.855
0.783
0.722
0.670
0.980
0.893
0.819
0.757
0.703
1.05
0.963
0.887
0.822
0.765
1.12
1.03
0.949
0.882
0.824
1.18
1.09
1.01
0.938
0.878
1.23
1.14
1.06
0.989
0.928
1.28
1.19
1.11
1.04
0.974
2.60 0.391 0.396 0.412 0.434 0.462 0.493 0.526 0.559 0.591 0.624 0.656 0.716 0.772 0.825 0.873 0.918
2.80 0.363 0.368 0.383 0.404 0.430 0.460 0.491 0.522 0.553 0.584 0.614 0.672 0.727 0.778 0.825 0.869
3.00 0.339 0.344 0.358 0.378 0.403 0.430 0.460 0.489 0.519 0.549 0.578 0.634 0.686 0.736 0.781 0.824
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
ECCENTRICALLY LOADED WELD GROUPS
8 - 165
Table 8-38 (cont.).
Coefficients C for Eccentrically Loaded Weld Groups
Angle = 30°°
φ R n = CC1Dl
C min =
Pu
D min =
C1Dl
Pu
Pu
lmin =
CC 1 l
CC 1 D
ex = a l
Pu
30°
l
where
Pu = factored force, kips
D = number of sixteenths-of-an-inch
in the fillet weld size
l = characteristic length of weld group, in.
a = e x / l, in.
e x = horizontal component of eccentricity of
Pu with respect to centroid of weld group, in.
kl
ex = a l
Pu
C = coefficient tabulated below which includes φ = 0.75
C 1 = electode strength coefficient from Table 8-37
(1.0 for E70XX electrodes)
30°
Special Case
(Load not in plane
of weld group)
Use C-values for k = 0
Any equal distances
k
a
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.2
1.4
1.6
1.8
2.0
0.00
0.10
0.15
0.20
0.25
3.28
3.03
2.87
2.72
2.57
3.28
3.03
2.87
2.73
2.57
3.28
3.04
2.87
2.73
2.57
3.28
3.04
2.87
2.73
2.58
3.28
3.04
2.88
2.74
2.59
3.28
3.05
2.88
2.74
2.61
3.28
3.05
2.88
2.75
2.62
3.28
3.06
2.89
2.76
2.63
3.28
3.06
2.90
2.76
2.64
3.28
3.06
2.90
2.77
2.66
3.28
3.07
2.91
2.78
2.67
3.28
3.07
2.92
2.79
2.68
3.28
3.07
2.94
2.81
2.70
3.28
3.06
2.94
2.82
2.72
3.28
3.06
2.95
2.83
2.73
3.28
3.05
2.95
2.84
2.74
0.30
0.40
0.50
0.60
0.70
2.41
2.11
1.84
1.62
1.44
2.41
2.11
1.85
1.63
1.45
2.42
2.12
1.86
1.65
1.47
2.43
2.14
1.89
1.68
1.51
2.45
2.17
1.93
1.73
1.56
2.47
2.20
1.98
1.78
1.61
2.49
2.24
2.02
1.83
1.66
2.51
2.28
2.06
1.88
1.72
2.53
2.30
2.10
1.92
1.77
2.54
2.33
2.13
1.96
1.81
2.56
2.35
2.17
2.00
1.85
2.59
2.40
2.22
2.07
1.92
2.61
2.43
2.27
2.12
1.99
2.63
2.46
2.31
2.17
2.04
2.64
2.49
2.34
2.21
2.09
2.66
2.51
2.37
2.25
2.13
0.80
0.90
1.00
1.20
1.40
1.30
1.17
1.07
0.907
0.786
1.30
1.18
1.08
0.913
0.792
1.33
1.20
1.10
0.939
0.817
1.37
1.24
1.14
0.979
0.855
1.42
1.29
1.19
1.03
0.901
1.47
1.35
1.25
1.08
0.951
1.52
1.41
1.30
1.14
1.00
1.58
1.46
1.36
1.19
1.05
1.63
1.51
1.41
1.24
1.10
1.68
1.56
1.46
1.29
1.15
1.72
1.61
1.51
1.33
1.20
1.80
1.69
1.59
1.42
1.28
1.87
1.76
1.66
1.49
1.35
1.93
1.82
1.73
1.56
1.42
1.98
1.88
1.78
1.62
1.49
2.02
1.92
1.84
1.68
1.54
1.60
1.80
2.00
2.20
2.40
0.693
0.619
0.559
0.510
0.469
0.699
0.625
0.565
0.516
0.474
0.723
0.648
0.587
0.536
0.493
0.759
0.681
0.617
0.564
0.520
0.801
0.721
0.655
0.599
0.552
0.848
0.765
0.696
0.638
0.589
0.897
0.811
0.740
0.679
0.628
0.946
0.857
0.783
0.720
0.667
0.993
0.901
0.825
0.761
0.705
1.04
0.945
0.866
0.800
0.743
1.08
0.987
0.907
0.838
0.779
1.16
1.07
0.984
0.912
0.850
1.24
1.14
1.05
0.981
0.917
1.31
1.21
1.12
1.04
0.978
1.37
1.27
1.18
1.10
1.04
1.42
1.32
1.24
1.16
1.09
2.60 0.433 0.439 0.456 0.481 0.512 0.546 0.583 0.620 0.657 0.693 0.728 0.795 0.860 0.920 0.975 1.03
2.80 0.403 0.408 0.424 0.448 0.477 0.509 0.544 0.579 0.614 0.649 0.683 0.748 0.809 0.867 0.922 0.972
3.00 0.376 0.382 0.397 0.419 0.446 0.477 0.510 0.543 0.577 0.610 0.642 0.705 0.764 0.821 0.873 0.923
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
8 - 166
BOLTS, WELDS, AND CONNECTED ELEMENTS
Table 8-38 (cont.).
Coefficients C for Eccentrically Loaded Weld Groups
Angle = 45°°
φ R n = CC1Dl
C min =
Pu
D min =
C 1D l
Pu
lmin =
CC 1 l
Pu
CC 1 D
ex = a l
45°
Pu
l
where
Pu = factored force, kips
D = number of sixteenths-of-an-inch
in the fillet weld size
l = characteristic length of weld group, in.
a = e x / l, in.
e x = horizontal component of eccentricity of
Pu with respect to centroid of weld group, in.
kl
ex = a l
C = coefficient tabulated below which includes φ = 0.75
C 1 = electode strength coefficient from Table 8-37
(1.0 for E70XX electrodes)
45°
Pu
Special Case
(Load not in plane
of weld group)
Use C-values for k = 0
Any equal distances
k
a
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.2
1.4
1.6
1.8
2.0
0.00
0.10
0.15
0.20
0.25
3.61
3.37
3.13
2.94
2.77
3.61
3.37
3.13
2.94
2.77
3.61
3.38
3.15
2.95
2.78
3.61
3.38
3.17
2.97
2.80
3.61
3.40
3.20
2.99
2.83
3.61
3.42
3.23
3.03
2.86
3.61
3.43
3.25
3.06
2.89
3.61
3.44
3.28
3.10
2.93
3.61
3.46
3.30
3.13
2.97
3.61
3.47
3.33
3.17
3.01
3.61
3.48
3.35
3.20
3.04
3.61
3.50
3.38
3.25
3.11
3.61
3.51
3.41
3.29
3.16
3.61
3.52
3.43
3.33
3.21
3.61
3.52
3.45
3.35
3.25
3.61
3.52
3.46
3.38
3.28
0.30
0.40
0.50
0.60
0.70
2.61
2.32
2.06
1.84
1.66
2.61
2.32
2.07
1.85
1.66
2.63
2.34
2.09
1.87
1.69
2.65
2.37
2.12
1.91
1.73
2.68
2.41
2.17
1.96
1.79
2.71
2.45
2.22
2.02
1.85
2.75
2.50
2.27
2.08
1.91
2.79
2.54
2.33
2.14
1.97
2.83
2.59
2.38
2.19
2.03
2.86
2.63
2.42
2.25
2.09
2.90
2.66
2.47
2.30
2.14
2.97
2.73
2.54
2.38
2.23
3.04
2.80
2.61
2.45
2.31
3.09
2.87
2.68
2.52
2.38
3.14
2.92
2.74
2.58
2.44
3.18
2.97
2.79
2.63
2.50
0.80
0.90
1.00
1.20
1.40
1.50
1.37
1.26
1.08
0.938
1.51
1.38
1.26
1.08
0.946
1.54
1.40
1.29
1.11
0.975
1.58
1.45
1.34
1.16
1.02
1.64
1.51
1.40
1.21
1.07
1.70
1.57
1.46
1.28
1.13
1.76
1.64
1.53
1.34
1.19
1.83
1.70
1.59
1.40
1.25
1.89
1.76
1.65
1.46
1.31
1.95
1.82
1.71
1.52
1.37
2.00
1.88
1.77
1.58
1.42
2.10
1.98
1.87
1.68
1.52
2.18
2.07
1.96
1.77
1.62
2.26
2.14
2.04
1.85
1.70
2.32
2.21
2.11
1.93
1.77
2.38
2.27
2.17
2.00
1.84
1.60
1.80
2.00
2.20
2.40
0.831
0.745
0.675
0.617
0.568
0.838
0.752
0.682
0.624
0.574
0.866
0.779
0.707
0.647
0.596
0.908
0.817
0.743
0.681
0.628
0.958
0.864
0.787
0.722
0.667
1.01
0.917
0.836
0.768
0.710
1.07
0.972
0.888
0.818
0.756
1.13
1.03
0.941
0.868
0.804
1.19
1.08
0.992
0.917
0.851
1.24
1.13
1.04
0.964
0.897
1.29
1.19
1.09
1.01
0.941
1.39
1.28
1.18
1.10
1.03
1.48
1.37
1.27
1.18
1.11
1.56
1.45
1.35
1.26
1.18
1.64
1.52
1.42
1.33
1.25
1.71
1.59
1.49
1.40
1.32
2.60 0.526 0.532 0.553 0.583 0.619 0.660 0.703 0.749 0.794 0.838 0.881 0.963 1.04 1.12 1.18
2.80 0.489 0.496 0.515 0.544 0.578 0.617 0.658 0.701 0.743 0.786 0.827 0.906 0.982 1.05 1.12
3.00 0.458 0.464 0.482 0.509 0.542 0.579 0.618 0.658 0.699 0.739 0.779 0.856 0.929 0.998 1.06
1.25
1.18
1.12
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
ECCENTRICALLY LOADED WELD GROUPS
8 - 167
Table 8-38 (cont.).
Coefficients C for Eccentrically Loaded Weld Groups
Angle = 60°°
φ R n = CC1Dl
C min =
Pu
D min =
C 1D l
Pu
lmin =
CC 1 l
Pu
CC 1 D
ex = a l
60° P
u
l
where
Pu = factored force, kips
D = number of sixteenths-of-an-inch
in the fillet weld size
l = characteristic length of weld group, in.
a = e x / l, in.
e x = horizontal component of eccentricity of
Pu with respect to centroid of weld group, in.
kl
ex = a l
C = coefficient tabulated below which includes φ = 0.75
C 1 = electode strength coefficient from Table 8-37
(1.0 for E70XX electrodes)
60°
Pu
Special Case
(Load not in plane
of weld group)
Use C-values for k = 0
Any equal distances
k
a
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.2
1.4
1.6
1.8
2.0
0.00
0.10
0.15
0.20
0.25
3.91
3.65
3.46
3.27
3.10
3.91
3.66
3.47
3.28
3.10
3.91
3.68
3.49
3.30
3.13
3.91
3.71
3.53
3.35
3.17
3.91
3.74
3.58
3.40
3.23
3.91
3.78
3.63
3.47
3.30
3.91
3.80
3.68
3.54
3.38
3.91
3.83
3.73
3.60
3.46
3.91
3.84
3.76
3.65
3.53
3.91
3.85
3.79
3.69
3.58
3.91
3.86
3.80
3.73
3.63
3.91
3.86
3.83
3.78
3.70
3.91
3.87
3.84
3.80
3.75
3.91
3.86
3.85
3.82
3.78
3.91
3.86
3.85
3.83
3.80
3.91
3.86
3.86
3.84
3.82
0.30
0.40
0.50
0.60
0.70
2.95
2.68
2.44
2.24
2.05
2.95
2.69
2.45
2.24
2.06
2.98
2.71
2.48
2.27
2.09
3.02
2.76
2.53
2.32
2.15
3.07
2.81
2.59
2.39
2.21
3.14
2.88
2.66
2.46
2.29
3.22
2.95
2.73
2.54
2.37
3.31
3.03
2.80
2.62
2.45
3.39
3.12
2.88
2.69
2.53
3.46
3.21
2.96
2.77
2.60
3.53
3.29
3.05
2.84
2.67
3.62
3.43
3.22
3.01
2.82
3.68
3.53
3.36
3.17
2.98
3.73
3.61
3.46
3.29
3.12
3.76
3.66
3.54
3.39
3.24
3.78
3.70
3.60
3.47
3.34
0.80
0.90
1.00
1.20
1.40
1.89
1.75
1.62
1.42
1.25
1.90
1.76
1.63
1.43
1.26
1.93
1.79
1.67
1.46
1.30
1.99
1.85
1.73
1.52
1.36
2.06
1.92
1.80
1.59
1.42
2.14
2.00
1.88
1.67
1.50
2.22
2.08
1.96
1.75
1.57
2.30
2.16
2.04
1.83
1.65
2.38
2.24
2.12
1.91
1.73
2.45
2.32
2.20
1.98
1.81
2.52
2.39
2.27
2.06
1.88
2.66
2.53
2.41
2.19
2.01
2.81
2.65
2.53
2.32
2.13
2.95
2.80
2.66
2.43
2.25
3.08
2.93
2.79
2.54
2.35
3.20
3.05
2.91
2.66
2.45
1.60
1.80
2.00
2.20
2.40
1.12
1.01
0.922
0.847
0.782
1.13
1.02
0.932
0.856
0.791
1.17
1.06
0.964
0.887
0.820
1.22
1.11
1.01
0.932
0.863
1.28
1.17
1.07
0.986
0.914
1.35
1.24
1.13
1.05
0.971
1.43
1.31
1.20
1.11
1.03
1.50
1.38
1.27
1.18
1.10
1.58
1.45
1.34
1.25
1.16
1.65
1.52
1.41
1.31
1.22
1.72
1.59
1.47
1.37
1.28
1.85
1.72
1.60
1.49
1.40
1.98
1.84
1.72
1.61
1.51
2.09
1.95
1.82
1.71
1.62
2.19
2.05
1.92
1.81
1.71
2.29
2.14
2.02
1.90
1.80
2.60 0.726 0.734 0.762 0.803 0.852 0.907 0.964 1.03 1.09 1.15
2.80 0.677 0.686 0.712 0.750 0.797 0.849 0.905 0.963 1.02 1.08
3.00 0.635 0.643 0.668 0.704 0.749 0.799 0.852 0.906 0.963 1.02
1.21
1.14
1.07
1.32
1.24
1.18
1.43
1.35
1.28
1.53
1.45
1.37
1.62
1.54
1.46
1.71
1.62
1.55
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
8 - 168
BOLTS, WELDS, AND CONNECTED ELEMENTS
Table 8-38 (cont.).
Coefficients C for Eccentrically Loaded Weld Groups
Angle = 75°°
φ R n = CC1Dl
C min =
Pu
D min =
C 1D l
Pu
lmin =
CC 1 l
Pu
CC 1 D
ex = a l
75°
Pu
l
where
Pu = factored force, kips
D = number of sixteenths-of-an-inch
in the fillet weld size
l = characteristic length of weld group, in.
a = e x / l, in.
e x = horizontal component of eccentricity of
Pu with respect to centroid of weld group, in.
kl
ex = a l
C = coefficient tabulated below which includes φ = 0.75
C 1 = electode strength coefficient from Table 8-37
(1.0 for E70XX electrodes)
75°
Pu
Special Case
(Load not in plane
of weld group)
Use C-values for k = 0
Any equal distances
k
a
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.2
1.4
1.6
1.8
2.0
0.00
0.10
0.15
0.20
0.25
4.11
3.88
3.76
3.64
3.53
4.11
3.90
3.77
3.65
3.54
4.11
3.95
3.83
3.71
3.60
4.11
4.00
3.90
3.79
3.69
4.11
4.04
3.96
3.88
3.78
4.11
4.07
4.01
3.94
3.87
4.11
4.08
4.04
3.99
3.93
4.11
4.09
4.06
4.03
3.98
4.11
4.09
4.08
4.05
4.01
4.11
4.09
4.08
4.06
4.03
4.11
4.09
4.09
4.07
4.05
4.11
4.09
4.09
4.08
4.07
4.11
4.09
4.09
4.09
4.08
4.11
4.09
4.09
4.09
4.08
4.11
4.09
4.09
4.09
4.09
4.11
4.09
4.09
4.09
4.09
0.30
0.40
0.50
0.60
0.70
3.43
3.24
3.07
2.91
2.77
3.44
3.25
3.08
2.92
2.78
3.49
3.29
3.12
2.97
2.82
3.58
3.38
3.20
3.05
2.90
3.69
3.50
3.32
3.15
3.00
3.78
3.62
3.45
3.29
3.13
3.86
3.72
3.57
3.42
3.27
3.92
3.80
3.67
3.54
3.40
3.97
3.86
3.75
3.63
3.51
4.00
3.91
3.82
3.71
3.60
4.02
3.95
3.87
3.78
3.68
4.05
4.00
3.94
3.88
3.80
4.07
4.03
3.99
3.94
3.88
4.07
4.05
4.02
3.98
3.93
4.08
4.06
4.04
4.01
3.97
4.08
4.07
4.05
4.03
4.00
0.80
0.90
1.00
1.20
1.40
2.63
2.50
2.38
2.17
1.99
2.64
2.52
2.40
2.18
2.00
2.69
2.57
2.45
2.24
2.05
2.77
2.64
2.53
2.32
2.13
2.87
2.74
2.63
2.41
2.23
2.99
2.86
2.74
2.52
2.33
3.13
3.00
2.87
2.64
2.45
3.26
3.13
3.01
2.78
2.57
3.39
3.26
3.14
2.91
2.71
3.49
3.38
3.26
3.04
2.84
3.58
3.48
3.37
3.16
2.96
3.72
3.64
3.55
3.37
3.18
3.81
3.75
3.68
3.52
3.36
3.88
3.83
3.77
3.64
3.50
3.93
3.88
3.83
3.73
3.61
3.96
3.93
3.88
3.80
3.69
1.60
1.80
2.00
2.20
2.40
1.83
1.69
1.57
1.46
1.37
1.84
1.70
1.58
1.48
1.38
1.89
1.75
1.63
1.52
1.43
1.97
1.83
1.70
1.59
1.49
2.06
1.92
1.79
1.68
1.57
2.17
2.02
1.89
1.77
1.67
2.28
2.13
1.99
1.87
1.76
2.39
2.24
2.10
1.97
1.86
2.52
2.35
2.21
2.08
1.97
2.65
2.48
2.33
2.19
2.07
2.78
2.61
2.45
2.30
2.18
3.01
2.84
2.68
2.54
2.40
3.20
3.05
2.89
2.75
2.61
3.36
3.22
3.08
2.94
2.81
3.49
3.36
3.23
3.10
2.98
3.59
3.48
3.36
3.24
3.13
2.60
2.80
3.00
1.28
1.21
1.14
1.30
1.22
1.15
1.34
1.27
1.20
1.40
1.33
1.26
1.48
1.40
1.33
1.57
1.49
1.41
1.66
1.58
1.49
1.76
1.67
1.59
1.86
1.77
1.68
1.96
1.86
1.77
2.07
1.96
1.87
2.28
2.16
2.06
2.49
2.37
2.26
2.68
2.56
2.45
2.85
2.73
2.62
3.01
2.89
2.78
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
ECCENTRICALLY LOADED WELD GROUPS
8 - 169
Table 8-39.
Coefficients C for Eccentrically Loaded Weld Groups
Angle = 0°°
φ R n = CC1Dl
C min =
Pu
D min =
C 1D l
Pu
lmin =
CC 1 l
Pu
CC 1 D
where
Pu = factored force, kips
ex = a l
D = number of sixteenths-of-an-inch
in the fillet weld size
l = characteristic length of weld group, in.
a = e x / l, in.
e x = horizontal component of eccentricity of
Pu with respect to centroid of weld group, in.
Pu
kl
l
C = coefficient tabulated below which includes φ = 0.75
C 1 = electode strength coefficient from Table 8-37
(1.0 for E70XX electrodes)
k
a
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.2
1.4
1.6
1.8
2.0
0.00
0.10
0.15
0.20
0.25
4.18
3.24
2.92
2.65
2.41
4.18
3.27
2.95
2.68
2.44
4.18
3.36
3.03
2.75
2.50
4.18
3.48
3.15
2.85
2.60
4.18
3.61
3.29
2.99
2.73
4.18
3.73
3.43
3.15
2.88
4.18
3.83
3.56
3.30
3.04
4.18
3.91
3.68
3.43
3.19
4.18
3.97
3.77
3.55
3.33
4.18
4.01
3.84
3.65
3.44
4.18
4.05
3.90
3.73
3.54
4.18
4.09
3.98
3.85
3.70
4.18
4.12
4.04
3.93
3.81
4.18
4.13
4.07
3.99
3.89
4.18
4.14
4.09
4.03
3.95
4.18
4.15
4.11
4.06
3.99
0.30
0.40
0.50
0.60
0.70
2.20
1.86
1.60
1.40
1.24
2.23
1.88
1.62
1.42
1.26
2.29
1.95
1.68
1.47
1.30
2.39
2.03
1.76
1.54
1.37
2.50
2.14
1.85
1.63
1.45
2.64
2.26
1.96
1.73
1.54
2.81
2.39
2.08
1.84
1.64
2.96
2.55
2.21
1.96
1.75
3.11
2.71
2.36
2.08
1.86
3.24
2.86
2.51
2.22
1.98
3.36
2.99
2.66
2.36
2.11
3.54
3.22
2.91
2.63
2.38
3.68
3.40
3.12
2.86
2.61
3.79
3.55
3.29
3.05
2.81
3.86
3.66
3.43
3.21
2.99
3.92
3.74
3.55
3.34
3.14
0.80
0.90
1.00
1.20
1.40
1.11
1.00
0.914
0.777
0.674
1.13
1.02
0.929
0.789
0.685
1.17
1.06
0.965
0.821
0.713
1.23
1.11
1.02
0.866
0.753
1.30
1.18
1.08
0.920
0.802
1.39
1.26
1.15
0.984
0.856
1.48
1.35
1.23
1.05
0.918
1.58
1.44
1.31
1.13
0.982
1.68
1.53
1.40
1.20
1.05
1.79
1.63
1.49
1.28
1.12
1.90
1.73
1.59
1.36
1.19
2.15
1.96
1.79
1.53
1.34
2.39
2.19
2.02
1.72
1.50
2.60
2.40
2.22
1.92
1.68
2.78
2.59
2.41
2.11
1.85
2.95
2.76
2.59
2.28
2.02
1.60
1.80
2.00
2.20
2.40
0.594
0.531
0.481
0.439
0.404
0.604
0.541
0.489
0.446
0.410
0.629
0.563
0.509
0.465
0.427
0.665
0.595
0.538
0.492
0.452
0.709
0.635
0.574
0.524
0.483
0.759
0.680
0.616
0.562
0.517
0.812
0.729
0.661
0.604
0.555
0.871
0.780
0.708
0.647
0.596
0.931
0.836
0.757
0.693
0.638
0.993
0.892
0.810
0.740
0.681
1.06
0.950
0.862
0.789
0.727
1.19
1.07
0.971
0.890
0.820
1.33
1.20
1.09
0.994
0.917
1.48
1.33
1.21
1.10
1.02
1.64
1.47
1.33
1.22
1.12
1.80
1.62
1.47
1.34
1.23
2.60 0.374 0.379 0.396 0.419 0.447 0.479 0.514 0.552 0.592 0.632 0.674 0.760 0.850 0.941 1.04 1.14
2.80 0.348 0.353 0.368 0.390 0.416 0.446 0.479 0.514 0.551 0.589 0.628 0.709 0.793 0.878 0.966 1.06
3.00 0.325 0.330 0.344 0.364 0.389 0.417 0.448 0.481 0.516 0.552 0.588 0.664 0.742 0.822 0.904 0.989
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
8 - 170
BOLTS, WELDS, AND CONNECTED ELEMENTS
Table 8-39 (cont.).
Coefficients C for Eccentrically Loaded Weld Groups
Angle = 15°°
φ R n = CC1Dl
C min =
Pu
D min =
C 1D l
Pu
lmin =
CC 1 l
Pu
CC 1 D
where
Pu = factored force, kips
Pu
ex = a l
D = number of sixteenths-of-an-inch
in the fillet weld size
l = characteristic length of weld group, in.
a = e x / l, in.
e x = horizontal component of eccentricity of
Pu with respect to centroid of weld group, in.
15°
kl
l
C = coefficient tabulated below which includes φ = 0.75
C 1 = electode strength coefficient from Table 8-37
(1.0 for E70XX electrodes)
k
a
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.2
1.4
1.6
1.8
2.0
0.00
0.10
0.15
0.20
0.25
4.11
3.29
2.97
2.70
2.46
4.11
3.30
2.99
2.71
2.48
4.11
3.34
3.03
2.76
2.53
4.11
3.43
3.11
2.84
2.61
4.11
3.55
3.22
2.94
2.71
4.11
3.66
3.35
3.07
2.82
4.11
3.76
3.48
3.20
2.95
4.11
3.83
3.59
3.34
3.09
4.11
3.89
3.68
3.45
3.22
4.11
3.94
3.76
3.55
3.34
4.11
3.97
3.82
3.64
3.44
4.11
4.02
3.90
3.76
3.61
4.11
4.04
3.96
3.85
3.72
4.11
4.06
4.00
3.91
3.81
4.11
4.07
4.02
3.95
3.87
4.11
4.07
4.04
3.98
3.91
0.30
0.40
0.50
0.60
0.70
2.25
1.91
1.65
1.44
1.28
2.27
1.93
1.66
1.46
1.29
2.32
1.98
1.71
1.50
1.34
2.40
2.05
1.79
1.57
1.40
2.50
2.15
1.87
1.65
1.48
2.61
2.25
1.97
1.75
1.56
2.73
2.37
2.08
1.85
1.66
2.87
2.49
2.19
1.95
1.76
3.00
2.62
2.30
2.06
1.85
3.13
2.75
2.42
2.17
1.96
3.25
2.87
2.55
2.28
2.06
3.44
3.10
2.79
2.51
2.27
3.58
3.29
2.99
2.72
2.48
3.69
3.44
3.17
2.91
2.67
3.77
3.56
3.32
3.08
2.85
3.83
3.65
3.44
3.22
3.00
0.80
0.90
1.00
1.20
1.40
1.15
1.04
0.945
0.803
0.697
1.16
1.05
0.958
0.814
0.707
1.20
1.09
0.993
0.846
0.735
1.26
1.14
1.05
0.892
0.776
1.33
1.21
1.11
0.946
0.825
1.41
1.29
1.18
1.01
0.881
1.50
1.37
1.26
1.08
0.942
1.59
1.45
1.34
1.15
1.01
1.69
1.54
1.42
1.22
1.07
1.78
1.63
1.50
1.30
1.14
1.88
1.72
1.59
1.37
1.21
2.07
1.90
1.75
1.52
1.34
2.27
2.08
1.92
1.67
1.47
2.45
2.26
2.10
1.82
1.61
2.63
2.43
2.26
1.97
1.74
2.79
2.59
2.42
2.12
1.87
1.60
1.80
2.00
2.20
2.40
0.615
0.550
0.497
0.454
0.418
0.624
0.559
0.505
0.461
0.424
0.649
0.581
0.526
0.480
0.442
0.686
0.614
0.556
0.508
0.467
0.731
0.655
0.593
0.542
0.499
0.781
0.701
0.635
0.580
0.534
0.835
0.751
0.681
0.623
0.573
0.894
0.802
0.729
0.667
0.615
0.954
0.858
0.778
0.713
0.657
1.01
0.913
0.830
0.760
0.700
1.08
0.968
0.881
0.808
0.745
1.20
1.08
0.985
0.904
0.834
1.32
1.19
1.09
0.999
0.924
1.44
1.30
1.19
1.10
1.01
1.56
1.41
1.29
1.19
1.10
1.68
1.52
1.39
1.28
1.19
2.60 0.387 0.392 0.409 0.433 0.462 0.495 0.531 0.570 0.609 0.650 0.691 0.775 0.859 0.942 1.03 1.11
2.80 0.360 0.365 0.381 0.403 0.430 0.461 0.494 0.530 0.568 0.606 0.644 0.724 0.802 0.881 0.959 1.03
3.00 0.336 0.341 0.356 0.377 0.402 0.431 0.463 0.496 0.532 0.568 0.604 0.678 0.753 0.827 0.900 0.972
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
ECCENTRICALLY LOADED WELD GROUPS
8 - 171
Table 8-39 (cont.).
Coefficients C for Eccentrically Loaded Weld Groups
Angle = 30°°
φ R n = CC1Dl
C min =
Pu
D min =
C 1D l
Pu
lmin =
CC 1 l
Pu
CC 1 D
where
Pu = factored force, kips
ex = a l
D = number of sixteenths-of-an-inch
in the fillet weld size
l = characteristic length of weld group, in.
a = e x / l, in.
e x = horizontal component of eccentricity of
Pu with respect to centroid of weld group, in.
Pu
30°
kl
l
C = coefficient tabulated below which includes φ = 0.75
C 1 = electode strength coefficient from Table 8-37
(1.0 for E70XX electrodes)
k
a
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.2
1.4
1.6
1.8
2.0
0.00
0.10
0.15
0.20
0.25
3.91
3.37
3.07
2.82
2.60
3.91
3.38
3.07
2.83
2.61
3.91
3.40
3.10
2.85
2.63
3.91
3.45
3.14
2.89
2.68
3.91
3.50
3.20
2.94
2.73
3.91
3.56
3.27
3.01
2.80
3.91
3.62
3.35
3.09
2.87
3.91
3.67
3.43
3.17
2.94
3.91
3.71
3.50
3.26
3.03
3.91
3.75
3.56
3.35
3.12
3.91
3.77
3.61
3.42
3.21
3.91
3.81
3.69
3.54
3.36
3.91
3.83
3.74
3.62
3.48
3.91
3.84
3.77
3.68
3.56
3.91
3.85
3.79
3.72
3.62
3.91
3.85
3.81
3.75
3.67
0.30
0.40
0.50
0.60
0.70
2.40
2.06
1.80
1.58
1.41
2.41
2.07
1.80
1.59
1.42
2.44
2.10
1.84
1.62
1.45
2.49
2.16
1.89
1.68
1.51
2.55
2.22
1.97
1.75
1.58
2.62
2.30
2.04
1.83
1.66
2.69
2.38
2.13
1.91
1.74
2.76
2.46
2.21
2.00
1.82
2.84
2.54
2.29
2.07
1.90
2.92
2.61
2.36
2.15
1.97
3.01
2.69
2.44
2.23
2.05
3.18
2.83
2.57
2.36
2.18
3.32
2.99
2.70
2.49
2.30
3.43
3.14
2.85
2.61
2.42
3.51
3.25
2.98
2.74
2.53
3.57
3.35
3.10
2.86
2.64
0.80
0.90
1.00
1.20
1.40
1.26
1.15
1.05
0.891
0.774
1.27
1.15
1.06
0.900
0.783
1.31
1.19
1.09
0.932
0.812
1.37
1.25
1.14
0.979
0.855
1.43
1.31
1.20
1.03
0.906
1.51
1.38
1.27
1.10
0.963
1.59
1.46
1.35
1.17
1.02
1.66
1.53
1.42
1.23
1.09
1.74
1.61
1.49
1.30
1.15
1.82
1.68
1.57
1.37
1.21
1.89
1.75
1.63
1.43
1.27
2.03
1.88
1.76
1.56
1.39
2.15
2.01
1.88
1.67
1.50
2.26
2.12
1.99
1.78
1.60
2.36
2.22
2.09
1.88
1.70
2.46
2.32
2.19
1.97
1.79
1.60
1.80
2.00
2.20
2.40
0.684
0.612
0.554
0.506
0.465
0.692
0.620
0.562
0.513
0.472
0.719
0.644
0.584
0.534
0.491
0.757
0.679
0.616
0.563
0.519
0.805
0.723
0.655
0.600
0.553
0.857
0.771
0.700
0.641
0.591
0.913
0.823
0.749
0.686
0.633
0.972
0.876
0.799
0.733
0.676
1.03
0.931
0.848
0.779
0.720
1.09
0.985
0.899
0.826
0.764
1.14
1.04
0.949
0.874
0.808
1.26
1.14
1.05
0.965
0.896
1.36
1.24
1.14
1.05
0.979
1.46
1.33
1.23
1.14
1.06
1.55
1.42
1.31
1.22
1.14
1.64
1.51
1.39
1.30
1.21
2.60 0.431 0.437 0.455 0.481 0.512 0.548 0.587 0.628 0.669 0.711 0.752 0.835 0.915 0.992 1.07 1.14
2.80 0.401 0.406 0.423 0.448 0.477 0.511 0.547 0.585 0.625 0.664 0.704 0.782 0.858 0.931 1.00 1.07
3.00 0.375 0.380 0.396 0.419 0.447 0.478 0.513 0.548 0.586 0.623 0.661 0.734 0.808 0.878 0.946 1.01
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
8 - 172
BOLTS, WELDS, AND CONNECTED ELEMENTS
Table 8-39 (cont.).
Coefficients C for Eccentrically Loaded Weld Groups
Angle = 45°°
φ R n = CC1Dl
C min =
Pu
D min =
C 1D l
Pu
lmin =
CC 1 l
Pu
CC 1 D
where
Pu = factored force, kips
ex = a l
D = number of sixteenths-of-an-inch
in the fillet weld size
l = characteristic length of weld group, in.
a = e x / l, in.
e x = horizontal component of eccentricity of
Pu with respect to centroid of weld group, in.
45°
Pu
kl
l
C = coefficient tabulated below which includes φ = 0.75
C 1 = electode strength coefficient from Table 8-37
(1.0 for E70XX electrodes)
k
a
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.2
1.4
1.6
1.8
2.0
0.00
0.10
0.15
0.20
0.25
3.61
3.37
3.13
2.94
2.77
3.61
3.37
3.13
2.94
2.77
3.61
3.38
3.15
2.95
2.78
3.61
3.38
3.17
2.97
2.80
3.61
3.40
3.20
2.99
2.83
3.61
3.42
3.23
3.03
2.86
3.61
3.43
3.25
3.06
2.89
3.61
3.44
3.28
3.10
2.93
3.61
3.46
3.30
3.13
2.97
3.61
3.47
3.33
3.17
3.01
3.61
3.48
3.35
3.20
3.04
3.61
3.50
3.38
3.25
3.11
3.61
3.51
3.41
3.29
3.16
3.61
3.52
3.43
3.33
3.21
3.61
3.52
3.45
3.35
3.25
3.61
3.52
3.47
3.38
3.28
0.30
0.40
0.50
0.60
0.70
2.61
2.32
2.06
1.84
1.66
2.61
2.32
2.07
1.85
1.66
2.63
2.34
2.09
1.87
1.69
2.65
2.37
2.12
1.91
1.73
2.68
2.41
2.17
1.96
1.79
2.71
2.45
2.22
2.02
1.85
2.75
2.50
2.27
2.08
1.91
2.79
2.54
2.33
2.14
1.97
2.83
2.59
2.38
2.19
2.03
2.86
2.63
2.42
2.25
2.09
2.90
2.66
2.47
2.30
2.14
2.97
2.73
2.54
2.38
2.23
3.04
2.80
2.61
2.45
2.31
3.09
2.87
2.68
2.52
2.38
3.14
2.92
2.74
2.58
2.44
3.18
2.97
2.79
2.63
2.50
0.80
0.90
1.00
1.20
1.40
1.50
1.37
1.26
1.08
0.938
1.51
1.38
1.26
1.08
0.946
1.54
1.40
1.29
1.11
0.975
1.58
1.45
1.34
1.16
1.02
1.64
1.51
1.40
1.21
1.07
1.70
1.57
1.46
1.28
1.13
1.76
1.64
1.53
1.34
1.19
1.83
1.70
1.59
1.40
1.25
1.89
1.76
1.65
1.46
1.31
1.95
1.82
1.71
1.52
1.37
2.00
1.88
1.77
1.58
1.42
2.10
1.98
1.87
1.68
1.52
2.18
2.07
1.96
1.77
1.62
2.26
2.14
2.04
1.85
1.70
2.32
2.21
2.11
1.93
1.77
2.38
2.27
2.17
2.00
1.84
1.60
1.80
2.00
2.20
2.40
0.831
0.745
0.675
0.617
0.568
0.838
0.752
0.682
0.624
0.574
0.866
0.779
0.707
0.647
0.596
0.908
0.817
0.743
0.681
0.628
0.958
0.864
0.787
0.722
0.667
1.01
0.917
0.836
0.768
0.710
1.07
0.972
0.888
0.818
0.756
1.13
1.03
0.941
0.868
0.804
1.19
1.08
0.992
0.917
0.851
1.24
1.13
1.04
0.964
0.897
1.29
1.19
1.09
1.01
0.941
1.39
1.28
1.18
1.10
1.03
1.48
1.37
1.27
1.18
1.11
1.56
1.45
1.35
1.26
1.18
1.64
1.52
1.42
1.33
1.25
1.71
1.59
1.49
1.40
1.32
2.60 0.526 0.532 0.553 0.583 0.619 0.660 0.703 0.749 0.794 0.838 0.881 0.963 1.04 1.12 1.18
2.80 0.489 0.496 0.515 0.544 0.578 0.617 0.658 0.701 0.743 0.786 0.827 0.906 0.982 1.05 1.12
3.00 0.458 0.464 0.482 0.509 0.542 0.579 0.618 0.658 0.699 0.739 0.779 0.856 0.929 0.998 1.06
1.25
1.18
1.12
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
ECCENTRICALLY LOADED WELD GROUPS
8 - 173
Table 8-39 (cont.).
Coefficients C for Eccentrically Loaded Weld Groups
Angle = 60°°
φ R n = CC1Dl
C min =
Pu
D min =
C 1D l
Pu
lmin =
CC 1 l
Pu
CC 1 D
where
Pu = factored force, kips
ex = a l
D = number of sixteenths-of-an-inch
in the fillet weld size
l = characteristic length of weld group, in.
a = e x / l, in.
e x = horizontal component of eccentricity of
Pu with respect to centroid of weld group, in.
60°
Pu
kl
l
C = coefficient tabulated below which includes φ = 0.75
C 1 = electode strength coefficient from Table 8-37
(1.0 for E70XX electrodes)
k
a
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.2
1.4
1.6
1.8
2.0
0.00
0.10
0.15
0.20
0.25
3.28
3.20
3.10
2.98
2.89
3.28
3.19
3.09
2.98
2.89
3.28
3.19
3.10
2.98
2.89
3.28
3.19
3.10
2.98
2.89
3.28
3.19
3.10
2.98
2.89
3.28
3.19
3.10
2.99
2.90
3.28
3.19
3.10
2.99
2.90
3.28
3.19
3.10
3.00
2.91
3.28
3.18
3.10
3.01
2.91
3.28
3.18
3.10
3.01
2.92
3.28
3.18
3.10
3.02
2.92
3.28
3.17
3.10
3.02
2.94
3.28
3.16
3.10
3.03
2.95
3.28
3.15
3.09
3.03
2.96
3.28
3.14
3.09
3.02
2.96
3.28
3.13
3.08
3.02
2.96
0.30
0.40
0.50
0.60
0.70
2.80
2.63
2.44
2.27
2.09
2.80
2.63
2.44
2.27
2.10
2.80
2.63
2.45
2.28
2.11
2.81
2.64
2.47
2.29
2.13
2.81
2.65
2.48
2.32
2.16
2.82
2.66
2.50
2.35
2.19
2.82
2.67
2.52
2.37
2.23
2.83
2.68
2.54
2.40
2.27
2.83
2.69
2.55
2.42
2.29
2.84
2.70
2.57
2.44
2.32
2.85
2.71
2.58
2.46
2.34
2.86
2.73
2.61
2.49
2.39
2.87
2.74
2.63
2.52
2.42
2.89
2.76
2.65
2.55
2.45
2.89
2.77
2.66
2.57
2.48
2.90
2.78
2.68
2.59
2.50
0.80
0.90
1.00
1.20
1.40
1.94
1.80
1.67
1.46
1.28
1.94
1.80
1.67
1.46
1.29
1.96
1.82
1.69
1.48
1.31
1.98
1.85
1.73
1.52
1.35
2.02
1.89
1.77
1.57
1.40
2.06
1.93
1.82
1.62
1.46
2.10
1.98
1.87
1.67
1.51
2.14
2.02
1.92
1.73
1.57
2.18
2.06
1.96
1.78
1.62
2.21
2.10
2.00
1.82
1.67
2.23
2.13
2.04
1.86
1.71
2.29
2.19
2.10
1.93
1.79
2.33
2.24
2.15
2.00
1.86
2.37
2.28
2.20
2.05
1.92
2.40
2.32
2.24
2.10
1.97
2.42
2.34
2.27
2.14
2.01
1.60
1.80
2.00
2.20
2.40
1.15
1.03
0.940
0.861
0.794
1.15
1.04
0.946
0.867
0.800
1.18
1.06
0.971
0.892
0.825
1.22
1.11
1.01
0.932
0.863
1.27
1.16
1.06
0.979
0.909
1.32
1.21
1.11
1.03
0.959
1.38
1.27
1.17
1.09
1.01
1.44
1.32
1.22
1.14
1.06
1.49
1.37
1.28
1.19
1.11
1.54
1.42
1.32
1.24
1.16
1.58
1.47
1.37
1.28
1.21
1.66
1.55
1.45
1.37
1.29
1.73
1.63
1.53
1.44
1.36
1.80
1.69
1.60
1.51
1.43
1.85
1.75
1.66
1.57
1.49
1.90
1.80
1.71
1.63
1.55
2.60 0.736 0.743 0.767 0.804 0.848 0.896 0.946 0.997 1.05 1.09 1.14
2.80 0.686 0.693 0.716 0.752 0.794 0.841 0.889 0.937 0.985 1.03 1.07
3.00 0.643 0.649 0.672 0.706 0.746 0.792 0.838 0.885 0.931 0.975 1.02
1.22
1.16
1.10
1.29
1.23
1.17
1.36
1.30
1.24
1.42
1.36
1.30
1.48
1.42
1.36
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
8 - 174
BOLTS, WELDS, AND CONNECTED ELEMENTS
Table 8-39 (cont.).
Coefficients C for Eccentrically Loaded Weld Groups
Angle = 75°°
φ R n = CC1Dl
C min =
Pu
D min =
C 1D l
Pu
lmin =
CC 1 l
Pu
CC 1 D
where
Pu = factored force, kips
ex = a l
75°
D = number of sixteenths-of-an-inch
in the fillet weld size
l = characteristic length of weld group, in.
a = e x / l, in.
e x = horizontal component of eccentricity of
Pu with respect to centroid of weld group, in.
Pu
kl
l
C = coefficient tabulated below which includes φ = 0.75
C 1 = electode strength coefficient from Table 8-37
(1.0 for E70XX electrodes)
k
a
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.2
1.4
1.6
1.8
2.0
0.00
0.10
0.15
0.20
0.25
2.97
2.86
2.89
2.88
2.87
2.97
2.86
2.89
2.88
2.87
2.97
2.87
2.89
2.88
2.87
2.97
2.87
2.89
2.88
2.87
2.97
2.88
2.89
2.88
2.86
2.97
2.88
2.89
2.87
2.86
2.97
2.88
2.89
2.87
2.85
2.97
2.89
2.89
2.86
2.85
2.97
2.89
2.88
2.86
2.84
2.97
2.89
2.88
2.85
2.84
2.97
2.89
2.87
2.85
2.83
2.97
2.88
2.86
2.84
2.81
2.97
2.87
2.85
2.82
2.80
2.97
2.85
2.83
2.81
2.79
2.97
2.84
2.82
2.80
2.78
2.97
2.55
2.81
2.78
2.76
0.30
0.40
0.50
0.60
0.70
2.86
2.84
2.79
2.74
2.66
2.86
2.83
2.79
2.73
2.66
2.86
2.83
2.78
2.73
2.66
2.85
2.82
2.77
2.72
2.66
2.85
2.82
2.77
2.72
2.65
2.84
2.81
2.76
2.71
2.65
2.84
2.80
2.76
2.70
2.64
2.83
2.79
2.75
2.70
2.64
2.82
2.79
2.74
2.69
2.64
2.82
2.78
2.73
2.68
2.63
2.81
2.77
2.73
2.68
2.63
2.80
2.76
2.71
2.67
2.62
2.78
2.74
2.70
2.66
2.61
2.77
2.73
2.69
2.65
2.61
2.76
2.72
2.68
2.64
2.60
2.74
2.71
2.67
2.63
2.59
0.80
0.90
1.00
1.20
1.40
2.59
2.51
2.42
2.25
2.08
2.59
2.51
2.42
2.25
2.08
2.59
2.51
2.43
2.25
2.09
2.58
2.51
2.43
2.27
2.11
2.58
2.51
2.43
2.28
2.13
2.58
2.51
2.44
2.30
2.15
2.58
2.51
2.44
2.31
2.18
2.58
2.51
2.45
2.32
2.19
2.58
2.52
2.45
2.33
2.21
2.58
2.52
2.46
2.34
2.23
2.58
2.52
2.46
2.35
2.24
2.57
2.52
2.47
2.37
2.27
2.57
2.52
2.48
2.38
2.29
2.56
2.52
2.48
2.39
2.31
2.56
2.52
2.48
2.40
2.32
2.56
2.52
2.48
2.40
2.33
1.60
1.80
2.00
2.20
2.40
1.92
1.78
1.65
1.54
1.44
1.93
1.78
1.66
1.54
1.44
1.94
1.80
1.67
1.56
1.46
1.96
1.83
1.70
1.60
1.50
1.99
1.86
1.74
1.64
1.54
2.02
1.89
1.78
1.68
1.59
2.05
1.93
1.82
1.72
1.63
2.08
1.96
1.86
1.76
1.68
2.10
1.99
1.89
1.80
1.71
2.12
2.02
1.92
1.83
1.75
2.14
2.04
1.95
1.86
1.78
2.17
2.08
2.00
1.92
1.84
2.20
2.12
2.04
1.96
1.89
2.22
2.15
2.07
2.00
1.93
2.24
2.17
2.10
2.03
1.97
2.26
2.19
2.12
2.06
2.00
2.60
2.80
3.00
1.35
1.26
1.19
1.35
1.27
1.20
1.37
1.29
1.22
1.41
1.33
1.26
1.45
1.37
1.30
1.50
1.42
1.35
1.55
1.47
1.40
1.60
1.52
1.45
1.64
1.56
1.50
1.67
1.60
1.54
1.71
1.64
1.58
1.77
1.71
1.64
1.82
1.76
1.70
1.87
1.81
1.75
1.91
1.85
1.79
1.94
1.88
1.83
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
ECCENTRICALLY LOADED WELD GROUPS
8 - 175
Table 8-40.
Coefficients C for Eccentrically Loaded Weld Groups
Angle = 0°°
φ R n = CC1Dl
C min =
Pu
D min =
C 1D l
Pu
lmin =
CC 1 l
Pu
CC 1 D
where
Pu = factored force, kips
ex = a l
D = number of sixteenths-of-an-inch
in the fillet weld size
l = characteristic length of weld group, in.
a = e x / l, in.
e x = horizontal component of eccentricity of
Pu with respect to centroid of weld group, in.
l
Pu
C = coefficient tabulated below which includes φ = 0.75
C 1 = electode strength coefficient from Table 8-37
(1.0 for E70XX electrodes)
kl
k
a
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.2
1.4
1.6
0.00
0.10
0.15
0.20
0.25
2.78
2.78
2.75
2.64
2.48
3.20
3.07
3.05
2.95
2.79
3.62
3.42
3.37
3.25
3.10
4.04
3.78
3.71
3.57
3.40
4.45
4.15
4.06
3.91
3.72
4.87
4.53
4.42
4.25
4.04
5.29
4.91
4.78
4.59
4.38
5.71
5.30
5.15
4.94
4.71
6.12
5.69
5.52
5.30
5.06
6.54
6.08
5.89
5.66
5.40
6.96
6.47
6.27
6.02
5.75
7.80
7.25
7.02
6.75
6.46
8.63
8.03
7.78
7.49
7.18
9.47 10.3 11.1
8.82 9.61 10.4
8.54 9.31 10.1
8.23 8.98 9.74
7.91 8.65 9.39
0.30
0.40
0.50
0.60
0.70
2.32
2.00
1.72
1.50
1.32
2.61
2.26
1.95
1.70
1.50
2.92
2.54
2.20
1.92
1.70
3.22
2.83
2.47
2.17
1.93
3.52
3.12
2.75
2.44
2.17
3.83
3.41
3.03
2.70
2.43
4.15
3.71
3.31
2.97
2.68
4.47
4.01
3.59
3.24
2.93
4.80
4.32
3.89
3.52
3.20
5.14
4.64
4.19
3.80
3.47
5.48
4.96
4.50
4.09
3.75
6.17
5.62
5.13
4.70
4.33
6.88
6.30
5.78
5.33
4.93
7.59
6.99
6.46
5.98
5.56
8.32
7.70
7.14
6.64
6.20
9.05
8.42
7.84
7.32
6.86
0.80
0.90
1.00
1.20
1.40
1.17
1.05
0.957
0.806
0.695
1.33
1.20
1.09
0.916
0.790
1.52
1.37
1.24
1.05
0.908
1.73
1.56
1.42
1.21
1.05
1.95
1.77
1.62
1.38
1.20
2.20
2.00
1.83
1.57
1.37
2.43
2.23
2.05
1.76
1.54
2.67
2.45
2.26
1.95
1.72
2.92
2.69
2.49
2.15
1.89
3.18
2.93
2.72
2.36
2.08
3.45
3.18
2.96
2.57
2.27
4.00
3.71
3.45
3.02
2.68
4.58
4.26
3.98
3.50
3.12
5.18
4.84
4.53
4.00
3.58
5.80
5.44
5.10
4.53
4.06
6.44
6.05
5.69
5.08
4.57
1.60
1.80
2.00
2.20
2.40
0.611
0.544
0.491
0.447
0.410
0.694
0.619
0.558
0.509
0.467
0.800
0.714
0.645
0.588
0.540
0.923
0.825
0.746
0.680
0.625
1.06
0.950
0.860
0.785
0.721
1.21
1.09
0.984
0.898
0.827
1.37
1.23
1.12
1.02
0.939
1.53
1.37
1.25
1.14
1.05
1.69
1.52
1.38
1.27
1.17
1.86
1.68
1.53
1.40
1.29
2.03
1.84
1.67
1.54
1.42
2.40
2.18
1.99
1.83
1.69
2.80
2.54
2.33
2.14
1.99
3.23
2.93
2.69
2.48
2.30
3.67
3.35
3.08
2.84
2.64
4.15
3.79
3.49
3.22
3.00
2.60 0.379 0.431 0.499 0.578 0.667 0.765 0.869 0.977 1.09 1.20
2.80 0.352 0.401 0.464 0.538 0.621 0.712 0.809 0.911 1.01 1.12
3.00 0.329 0.375 0.434 0.503 0.580 0.666 0.757 0.853 0.949 1.05
1.32
1.23
1.16
1.57
1.47
1.38
1.85
1.73
1.62
2.15
2.01
1.89
2.46
2.31
2.17
2.80
2.63
2.47
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1.8
2.0
8 - 176
BOLTS, WELDS, AND CONNECTED ELEMENTS
Table 8-40 (cont.).
Coefficients C for Eccentrically Loaded Weld Groups
Angle = 15°°
φ R n = CC1Dl
C min =
Pu
D min =
C 1D l
Pu
lmin =
CC 1 l
Pu
CC 1 D
where
Pu = factored force, kips
ex = a l
D = number of sixteenths-of-an-inch
in the fillet weld size
l = characteristic length of weld group, in.
a = e x / l, in.
e x = horizontal component of eccentricity of
Pu with respect to centroid of weld group, in.
15°
l
Pu
C = coefficient tabulated below which includes φ = 0.75
C 1 = electode strength coefficient from Table 8-37
(1.0 for E70XX electrodes)
kl
k
a
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.2
1.4
1.6
0.00
0.10
0.15
0.20
0.25
2.97
2.84
2.76
2.63
2.48
3.38
3.16
3.10
2.96
2.79
3.79
3.52
3.44
3.30
3.12
4.20
3.89
3.79
3.64
3.45
4.61
4.28
4.14
3.98
3.78
5.02
4.66
4.51
4.32
4.11
5.43
5.05
4.87
4.67
4.45
5.84
5.43
5.24
5.02
4.78
6.25
5.83
5.61
5.37
5.13
6.66
6.22
5.98
5.73
5.47
7.07
6.62
6.35
6.09
5.82
7.89
7.41
7.11
6.82
6.53
8.71
8.20
7.86
7.55
7.25
9.54 10.4 11.2
8.99 9.79 10.6
8.63 9.41 10.2
8.30 9.05 9.81
7.98 8.72 9.46
0.30
0.40
0.50
0.60
0.70
2.32
2.01
1.74
1.52
1.34
2.61
2.26
1.96
1.72
1.52
2.92
2.54
2.21
1.94
1.72
3.24
2.84
2.48
2.19
1.95
3.57
3.15
2.77
2.46
2.19
3.89
3.46
3.07
2.74
2.46
4.22
3.77
3.37
3.03
2.73
4.54
4.08
3.66
3.30
3.00
4.88
4.39
3.96
3.59
3.27
5.21
4.71
4.27
3.88
3.55
5.55
5.04
4.58
4.18
3.83
6.24
5.70
5.21
4.79
4.42
6.95
6.38
5.87
5.42
5.03
7.66
7.07
6.54
6.07
5.66
8.39
7.78
7.23
6.74
6.31
9.13
8.50
7.93
7.43
6.97
0.80
0.90
1.00
1.20
1.40
1.20
1.08
0.979
0.826
0.714
1.36
1.22
1.11
0.938
0.810
1.54
1.39
1.27
1.07
0.930
1.75
1.58
1.45
1.23
1.07
1.98
1.80
1.65
1.41
1.23
2.22
2.03
1.87
1.60
1.40
2.48
2.27
2.09
1.81
1.58
2.74
2.52
2.32
2.01
1.77
3.00
2.76
2.55
2.21
1.95
3.26
3.01
2.79
2.43
2.14
3.53
3.26
3.03
2.65
2.34
4.09
3.80
3.54
3.10
2.76
4.67
4.36
4.07
3.59
3.20
5.28
4.94
4.63
4.10
3.67
5.91
5.54
5.21
4.64
4.16
6.55
6.16
5.81
5.19
4.68
1.60
1.80
2.00
2.20
2.40
0.628
0.560
0.506
0.461
0.423
0.713
0.636
0.575
0.524
0.481
0.820
0.733
0.663
0.605
0.556
0.946
0.846
0.766
0.699
0.643
1.09
0.974
0.882
0.805
0.741
1.24
1.11
1.01
0.922
0.849
1.41
1.26
1.15
1.05
0.965
1.57
1.42
1.29
1.18
1.09
1.74
1.57
1.43
1.31
1.21
1.91
1.73
1.57
1.45
1.33
2.09
1.89
1.73
1.59
1.47
2.48
2.24
2.05
1.89
1.75
2.89
2.62
2.40
2.21
2.05
3.32
3.02
2.77
2.56
2.38
3.78
3.45
3.17
2.93
2.72
4.26
3.89
3.59
3.32
3.09
2.60 0.391 0.445 0.514 0.595 0.686 0.786 0.894 1.01 1.12 1.24
2.80 0.363 0.414 0.478 0.554 0.638 0.732 0.832 0.938 1.05 1.16
3.00 0.339 0.386 0.447 0.518 0.597 0.684 0.779 0.878 0.981 1.09
1.36
1.27
1.19
1.63
1.52
1.43
1.91
1.79
1.68
2.22
2.07
1.95
2.54
2.38
2.24
2.89
2.71
2.55
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1.8
2.0
ECCENTRICALLY LOADED WELD GROUPS
8 - 177
Table 8-40 (cont.).
Coefficients C for Eccentrically Loaded Weld Groups
Angle = 30°°
φ R n = CC1Dl
C min =
Pu
D min =
C 1D l
Pu
lmin =
CC 1 l
Pu
CC 1 D
where
Pu = factored force, kips
ex = a l
D = number of sixteenths-of-an-inch
in the fillet weld size
l = characteristic length of weld group, in.
a = e x / l, in.
e x = horizontal component of eccentricity of
Pu with respect to centroid of weld group, in.
30°
l
Pu
C = coefficient tabulated below which includes φ = 0.75
C 1 = electode strength coefficient from Table 8-37
(1.0 for E70XX electrodes)
kl
k
a
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.2
1.4
1.6
1.8
2.0
0.00
0.10
0.15
0.20
0.25
3.28
3.03
2.87
2.72
2.57
3.67
3.45
3.25
3.07
2.88
4.06
3.85
3.63
3.43
3.22
4.45
4.24
4.02
3.80
3.57
4.84
4.62
4.40
4.17
3.93
5.23
5.00
4.77
4.53
4.29
5.62
5.38
5.15
4.89
4.65
6.01
5.76
5.52
5.25
4.99
6.40
6.14
5.89
5.61
5.34
6.79
6.52
6.26
5.97
5.69
7.18
6.90
6.64
6.34
6.05
7.96
7.67
7.39
7.09
6.77
8.74
8.44
8.15
7.84
7.52
9.53 10.3
9.22 10.0
8.93 9.70
8.60 9.37
8.27 9.04
11.1
10.8
10.5
10.2
9.81
0.30
0.40
0.50
0.60
0.70
2.41
2.11
1.84
1.62
1.44
2.70
2.36
2.07
1.83
1.63
3.02
2.64
2.32
2.06
1.84
3.35
2.95
2.60
2.31
2.07
3.70
3.27
2.90
2.59
2.33
4.05
3.60
3.21
2.88
2.60
4.40
3.94
3.53
3.18
2.89
4.75
4.28
3.86
3.50
3.19
5.09
4.61
4.19
3.82
3.50
5.43
4.94
4.50
4.12
3.79
5.77
5.27
4.83
4.43
4.09
6.48
5.95
5.48
5.07
4.70
7.21
6.65
6.16
5.73
5.33
7.95
7.36
6.85
6.40
5.99
8.71
8.09
7.56
7.09
6.66
9.48
8.85
8.28
7.79
7.35
0.80
0.90
1.00
1.20
1.40
1.30
1.17
1.07
0.907
0.786
1.46
1.32
1.21
1.03
0.890
1.65
1.50
1.37
1.17
1.02
1.87
1.70
1.56
1.34
1.17
2.11
1.93
1.78
1.53
1.34
2.37
2.18
2.01
1.73
1.52
2.64
2.43
2.25
1.95
1.72
2.93
2.70
2.51
2.18
1.93
3.22
2.98
2.77
2.41
2.14
3.50
3.25
3.02
2.65
2.34
3.79
3.52
3.28
2.88
2.56
4.38
4.08
3.82
3.37
3.01
4.98
4.67
4.38
3.89
3.49
5.61
5.28
4.97
4.44
3.99
6.26
5.90
5.57
5.00
4.52
6.93
6.55
6.20
5.59
5.07
1.60
1.80
2.00
2.20
2.40
0.693
0.619
0.559
0.510
0.469
0.785
0.703
0.635
0.579
0.533
0.901
0.808
0.731
0.668
0.614
1.04
0.931
0.844
0.771
0.710
1.19
1.07
0.970
0.887
0.818
1.36
1.22
1.11
1.01
0.935
1.53
1.38
1.26
1.15
1.06
1.72
1.55
1.41
1.30
1.20
1.91
1.73
1.57
1.45
1.34
2.10
1.90
1.74
1.60
1.48
2.30
2.08
1.91
1.75
1.62
2.72
2.47
2.26
2.08
1.93
3.16
2.88
2.64
2.44
2.27
3.62
3.31
3.05
2.82
2.62
4.12
3.77
3.48
3.22
3.00
4.63
4.25
3.93
3.64
3.40
2.60 0.433 0.493 0.569 0.658 0.758 0.867 0.984 1.11 1.24
2.80 0.403 0.458 0.529 0.613 0.706 0.808 0.918 1.03 1.16
3.00 0.376 0.428 0.495 0.573 0.661 0.757 0.860 0.969 1.08
1.37
1.28
1.20
1.51
1.41
1.32
1.80
1.68
1.58
2.11
1.98
1.86
2.45
2.29
2.16
2.80
2.63
2.48
3.18
2.99
2.82
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
8 - 178
BOLTS, WELDS, AND CONNECTED ELEMENTS
Table 8-40 (cont.).
Coefficients C for Eccentrically Loaded Weld Groups
Angle = 45°°
φ R n = CC1Dl
C min =
Pu
D min =
C 1D l
Pu
lmin =
CC 1 l
Pu
CC 1 D
where
Pu = factored force, kips
ex = a l
D = number of sixteenths-of-an-inch
in the fillet weld size
l = characteristic length of weld group, in.
a = e x / l, in.
e x = horizontal component of eccentricity of
Pu with respect to centroid of weld group, in.
45°
l
Pu
C = coefficient tabulated below which includes φ = 0.75
C 1 = electode strength coefficient from Table 8-37
(1.0 for E70XX electrodes)
kl
k
a
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.2
1.4
1.6
1.8
2.0
0.00
0.10
0.15
0.20
0.25
3.61
3.37
3.13
2.94
2.77
3.97
3.74
3.52
3.29
3.10
4.33
4.11
3.89
3.65
3.44
4.70
4.48
4.26
4.02
3.79
5.06
4.84
4.62
4.38
4.14
5.42
5.21
4.99
4.75
4.51
5.78
5.58
5.36
5.12
4.87
6.14
5.94
5.74
5.50
5.25
6.50
6.31
6.11
5.88
5.63
6.86
6.68
6.49
6.26
6.01
7.22
7.04
6.86
6.64
6.40
7.95
7.78
7.61
7.39
7.16
8.67
8.52
8.36
8.15
7.92
9.39 10.1
9.25 9.99
9.11 9.85
8.91 9.66
8.68 9.45
10.8
10.7
10.6
10.4
10.2
0.30
0.40
0.50
0.60
0.70
2.61
2.32
2.06
1.84
1.66
2.91
2.59
2.30
2.06
1.86
3.24
2.87
2.57
2.30
2.08
3.57
3.18
2.86
2.58
2.34
3.92
3.51
3.16
2.87
2.61
4.27
3.85
3.49
3.17
2.91
4.63
4.20
3.82
3.50
3.22
5.00
4.55
4.17
3.83
3.54
5.38
4.92
4.52
4.18
3.88
5.76
5.29
4.89
4.53
4.22
6.15
5.67
5.26
4.89
4.56
6.91
6.42
5.97
5.57
5.22
7.67
7.18
6.71
6.28
5.90
8.44
7.95
7.47
7.02
6.62
9.21
8.72
8.24
7.78
7.35
9.98
9.50
9.01
8.54
8.10
0.80
0.90
1.00
1.20
1.40
1.50
1.37
1.26
1.08
0.938
1.69
1.54
1.41
1.21
1.06
1.90
1.74
1.60
1.38
1.21
2.13
1.96
1.81
1.57
1.38
2.40
2.21
2.05
1.78
1.57
2.68
2.48
2.30
2.01
1.78
2.98
2.76
2.58
2.26
2.01
3.29
3.06
2.86
2.52
2.24
3.61
3.37
3.15
2.78
2.49
3.93
3.68
3.45
3.06
2.74
4.27
4.00
3.76
3.34
3.00
4.91
4.62
4.35
3.90
3.52
5.56
5.25
4.97
4.48
4.06
6.25
5.91
5.61
5.07
4.62
6.97
6.61
6.28
5.70
5.21
7.70
7.32
6.97
6.35
5.81
1.60
1.80
2.00
2.20
2.40
0.831
0.745
0.675
0.617
0.568
0.939
0.843
0.764
0.699
0.644
1.07
0.966
0.877
0.804
0.741
1.23
1.11
1.01
0.925
0.854
1.41
1.27
1.16
1.06
0.981
1.60
1.45
1.32
1.21
1.12
1.80
1.63
1.49
1.37
1.27
2.02
1.83
1.67
1.54
1.43
2.24
2.04
1.87
1.72
1.59
2.48
2.25
2.06
1.90
1.77
2.71
2.48
2.27
2.10
1.95
3.20
2.93
2.69
2.49
2.32
3.70
3.40
3.14
2.91
2.71
4.23
3.90
3.60
3.35
3.13
4.78
4.42
4.09
3.81
3.57
5.36
4.96
4.61
4.30
4.03
2.60 0.526 0.597 0.687 0.792 0.911 1.04 1.18
2.80 0.489 0.556 0.641 0.739 0.850 0.972 1.10
3.00 0.458 0.520 0.600 0.693 0.796 0.911 1.03
1.33
1.24
1.17
1.48
1.39
1.30
1.65
1.54
1.45
1.82
1.70
1.60
2.16
2.03
1.91
2.54
2.38
2.24
2.93
2.75
2.60
3.35
3.15
2.97
3.78
3.57
3.37
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
ECCENTRICALLY LOADED WELD GROUPS
8 - 179
Table 8-40 (cont.).
Coefficients C for Eccentrically Loaded Weld Groups
Angle = 60°°
φ R n = CC1Dl
C min =
Pu
D min =
C 1D l
Pu
lmin =
CC 1 l
Pu
CC 1 D
where
Pu = factored force, kips
ex = a l
D = number of sixteenths-of-an-inch
in the fillet weld size
l = characteristic length of weld group, in.
a = e x / l, in.
e x = horizontal component of eccentricity of
Pu with respect to centroid of weld group, in.
60°
l
Pu
C = coefficient tabulated below which includes φ = 0.75
C 1 = electode strength coefficient from Table 8-37
(1.0 for E70XX electrodes)
kl
k
a
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.2
1.4
1.6
1.8
2.0
0.00
0.10
0.15
0.20
0.25
3.91
3.65
3.46
3.27
3.10
4.23
3.97
3.78
3.60
3.42
4.56
4.30
4.11
3.92
3.74
4.89
4.64
4.45
4.26
4.07
5.22
4.99
4.80
4.61
4.41
5.54
5.35
5.17
4.97
4.78
5.87
5.70
5.53
5.35
5.15
6.20
6.05
5.90
5.72
5.53
6.53
6.40
6.26
6.09
5.92
6.85
6.74
6.61
6.46
6.29
7.18
7.08
6.97
6.82
6.67
7.84
7.75
7.66
7.54
7.40
8.49
8.42
8.34
8.24
8.12
9.15
9.08
9.02
8.93
8.83
9.80
9.74
9.69
9.61
9.52
10.5
10.4
10.4
10.3
10.2
0.30
0.40
0.50
0.60
0.70
2.95
2.68
2.44
2.24
2.05
3.25
2.96
2.70
2.47
2.28
3.57
3.26
2.98
2.74
2.53
3.89
3.57
3.29
3.04
2.81
4.23
3.90
3.61
3.35
3.12
4.59
4.24
3.95
3.69
3.45
4.97
4.61
4.31
4.04
3.79
5.35
4.99
4.68
4.40
4.14
5.74
5.38
5.06
4.77
4.50
6.12
5.77
5.45
5.15
4.87
6.50
6.16
5.84
5.54
5.25
7.25
6.93
6.61
6.31
6.02
7.98
7.69
7.37
7.08
6.79
8.70
8.43
8.12
7.83
7.55
9.41 10.1
9.16 9.87
8.87 9.60
8.58 9.31
8.30 9.04
0.80
0.90
1.00
1.20
1.40
1.89
1.75
1.62
1.42
1.25
2.10
1.95
1.81
1.59
1.41
2.34
2.18
2.03
1.79
1.59
2.62
2.44
2.29
2.02
1.81
2.92
2.73
2.56
2.28
2.04
3.23
3.04
2.86
2.55
2.30
3.56
3.36
3.17
2.84
2.57
3.91
3.69
3.49
3.15
2.85
4.26
4.03
3.82
3.46
3.14
4.62
4.38
4.17
3.78
3.45
4.99
4.74
4.52
4.11
3.76
5.75
5.49
5.24
4.80
4.41
6.51
6.24
5.98
5.50
5.07
7.27
6.99
6.72
6.21
5.75
8.02
7.74
7.46
6.93
6.44
8.76
8.48
8.20
7.66
7.16
1.60
1.80
2.00
2.20
2.40
1.12
1.01
0.922
0.847
0.782
1.26
1.14
1.04
0.956
0.884
1.43
1.30
1.19
1.09
1.01
1.63
1.48
1.36
1.25
1.16
1.85
1.69
1.55
1.43
1.33
2.09
1.91
1.75
1.62
1.51
2.34
2.14
1.97
1.83
1.70
2.60
2.39
2.20
2.04
1.91
2.88
2.65
2.45
2.27
2.12
3.16
2.92
2.70
2.51
2.35
3.46
3.20
2.97
2.76
2.58
4.08
3.78
3.52
3.28
3.08
4.69
4.36
4.08
3.82
3.59
5.34
4.97
4.65
4.37
4.11
6.01
5.61
5.26
4.94
4.66
6.70
6.27
5.90
5.55
5.24
2.60 0.726 0.821 0.943 1.08 1.24
2.80 0.677 0.767 0.881 1.01 1.16
3.00 0.635 0.719 0.827 0.952 1.09
1.41
1.32
1.24
1.59
1.49
1.40
1.78
1.67
1.58
1.99
1.87
1.76
2.20
2.07
1.95
2.42
2.28
2.15
2.89
2.73
2.58
3.38
3.20
3.03
3.88
3.68
3.49
4.40
4.18
3.97
4.96
4.70
4.47
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
8 - 180
BOLTS, WELDS, AND CONNECTED ELEMENTS
Table 8-40 (cont.).
Coefficients C for Eccentrically Loaded Weld Groups
Angle = 75°°
φ R n = CC1Dl
C min =
Pu
D min =
C 1D l
Pu
lmin =
CC 1 l
Pu
CC 1 D
where
Pu = factored force, kips
ex = a l
D = number of sixteenths-of-an-inch
in the fillet weld size
l = characteristic length of weld group, in.
a = e x / l, in.
e x = horizontal component of eccentricity of
Pu with respect to centroid of weld group, in.
75°
l
Pu
C = coefficient tabulated below which includes φ = 0.75
C 1 = electode strength coefficient from Table 8-37
(1.0 for E70XX electrodes)
kl
k
a
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.2
1.4
1.6
1.8
0.00
0.10
0.15
0.20
0.25
4.11
3.88
3.76
3.64
3.53
4.40
4.17
4.04
3.92
3.80
4.70
4.49
4.36
4.23
4.11
5.00
4.81
4.69
4.57
4.45
5.29
5.14
5.03
4.92
4.81
5.59
5.45
5.36
5.26
5.16
5.89
5.76
5.69
5.60
5.50
6.18
6.07
6.00
5.92
5.84
6.48
6.36
6.31
6.24
6.16
6.78
6.66
6.61
6.55
6.48
7.07
6.96
6.91
6.86
6.80
7.67
7.53
7.50
7.46
7.41
8.26
8.11
8.09
8.05
8.01
8.85
8.69
8.67
8.64
8.60
9.45 10.0
9.27 9.84
9.25 9.83
9.23 9.81
9.19 9.78
0.30
0.40
0.50
0.60
0.70
3.43
3.24
3.07
2.91
2.77
3.70
3.51
3.34
3.17
3.02
4.00
3.80
3.63
3.46
3.31
4.34
4.14
3.95
3.78
3.63
4.70
4.49
4.31
4.13
3.97
5.05
4.86
4.67
4.49
4.33
5.40
5.22
5.04
4.86
4.70
5.75
5.57
5.40
5.23
5.07
6.08
5.91
5.75
5.60
5.44
6.41
6.25
6.10
5.95
5.80
6.72
6.57
6.43
6.30
6.16
7.35
7.22
7.08
6.96
6.84
7.96
7.85
7.71
7.60
7.50
8.56
8.46
8.34
8.23
8.13
9.16
9.07
8.96
8.84
8.75
9.75
9.67
9.57
9.46
9.36
0.80
0.90
1.00
1.20
1.40
2.63
2.50
2.38
2.17
1.99
2.87
2.74
2.62
2.39
2.20
3.16
3.02
2.89
2.66
2.45
3.48
3.34
3.20
2.96
2.74
3.81
3.67
3.53
3.28
3.05
4.17
4.02
3.87
3.61
3.38
4.53
4.38
4.23
3.96
3.71
4.91
4.75
4.60
4.32
4.06
5.28
5.13
4.98
4.69
4.42
5.65
5.50
5.35
5.06
4.79
6.01
5.87
5.72
5.44
5.16
6.72
6.58
6.45
6.18
5.91
7.39
7.27
7.15
6.90
6.64
8.04
7.93
7.83
7.60
7.36
8.66
8.57
8.48
8.28
8.06
9.27
9.20
9.11
8.93
8.74
1.60
1.80
2.00
2.20
2.40
1.83
1.69
1.57
1.46
1.37
2.03
1.88
1.75
1.63
1.53
2.27
2.11
1.97
1.84
1.73
2.54
2.37
2.22
2.08
1.96
2.84
2.66
2.49
2.34
2.21
3.16
2.96
2.79
2.63
2.48
3.49
3.28
3.10
2.92
2.77
3.82
3.61
3.41
3.23
3.07
4.17
3.95
3.74
3.55
3.37
4.53
4.29
4.08
3.88
3.69
4.90
4.65
4.43
4.22
4.02
5.64
5.39
5.15
4.92
4.71
6.39
6.13
5.88
5.64
5.42
7.12
6.87
6.62
6.37
6.14
7.83
7.59
7.34
7.10
6.87
8.53
8.30
8.07
7.83
7.59
2.60
2.80
3.00
1.28
1.21
1.14
1.44
1.36
1.28
1.63
1.54
1.46
1.85
1.75
1.66
2.09
1.98
1.88
2.35
2.23
2.12
2.62
2.50
2.38
2.91
2.78
2.65
3.21
3.07
2.92
3.52
3.36
3.22
3.84
3.67
3.52
4.51
4.32
4.14
5.20
5.00
4.80
5.91
5.70
5.49
6.63
6.41
6.19
7.36
7.13
6.91
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
2.0
ECCENTRICALLY LOADED WELD GROUPS
8 - 181
Table 8-41.
Coefficients C for Eccentrically Loaded Weld Groups
Angle = 0°°
φ R n = CC1Dl
C min =
Pu
D min =
C 1D l
Pu
lmin =
CC 1 l
Pu
CC 1 D
where
Pu = factored force, kips
ex = a l
D = number of sixteenths-of-an-inch
in the fillet weld size
l = characteristic length of weld group, in.
a = e x / l, in.
e x = horizontal component of eccentricity of
Pu with respect to centroid of weld group, in.
Pu
kl
l
C = coefficient tabulated below which includes φ = 0.75
C 1 = electode strength coefficient from Table 8-37
(1.0 for E70XX electrodes)
k
a
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.2
1.4
1.6
1.8
2.0
0.00
0.10
0.15
0.20
0.25
4.18
3.24
2.92
2.65
2.41
4.45
3.51
3.18
2.89
2.64
4.73
3.81
3.49
3.19
2.93
5.01
4.15
3.81
3.52
3.25
5.29
4.51
4.16
3.85
3.58
5.57
4.87
4.53
4.21
3.92
5.85
5.22
4.89
4.58
4.28
6.12
5.55
5.25
4.95
4.65
6.40
5.87
5.60
5.31
5.02
6.68
6.17
5.94
5.67
5.39
6.96
6.47
6.27
6.02
5.75
7.52
7.03
6.89
6.69
6.45
8.07
7.56
7.47
7.32
7.12
8.63
8.08
8.03
7.92
7.76
9.19
8.59
8.58
8.50
8.37
9.74
9.09
9.11
9.06
8.96
0.30
0.40
0.50
0.60
0.70
2.20
1.86
1.60
1.40
1.24
2.43
2.07
1.79
1.57
1.39
2.70
2.31
2.01
1.77
1.58
3.00
2.59
2.27
2.01
1.79
3.33
2.90
2.55
2.26
2.03
3.66
3.22
2.85
2.54
2.28
4.01
3.54
3.16
2.83
2.56
4.37
3.88
3.48
3.13
2.84
4.74
4.23
3.80
3.44
3.13
5.11
4.60
4.15
3.76
3.44
5.48
4.96
4.50
4.09
3.75
6.20
5.70
5.22
4.79
4.40
6.90
6.43
5.95
5.50
5.09
7.57
7.14
6.68
6.22
5.80
8.21
7.83
7.39
6.95
6.51
8.83
8.49
8.09
7.66
7.23
0.80
0.90
1.00
1.20
1.40
1.11
1.00
0.914
0.777
0.674
1.25
1.13
1.03
0.880
0.764
1.42
1.29
1.18
1.01
0.879
1.62
1.48
1.35
1.16
1.01
1.84
1.68
1.54
1.32
1.16
2.07
1.89
1.74
1.50
1.31
2.32
2.13
1.96
1.69
1.48
2.59
2.38
2.19
1.89
1.67
2.87
2.64
2.44
2.11
1.86
3.15
2.91
2.69
2.34
2.06
3.45
3.18
2.96
2.57
2.27
4.07
3.77
3.51
3.08
2.73
4.72
4.39
4.10
3.61
3.21
5.41
5.05
4.73
4.18
3.73
6.11
5.73
5.38
4.78
4.28
6.82
6.42
6.06
5.40
4.86
1.60
1.80
2.00
2.20
2.40
0.594
0.531
0.481
0.439
0.404
0.675
0.604
0.547
0.499
0.459
0.777
0.696
0.630
0.576
0.530
0.895
0.803
0.728
0.665
0.612
1.03
0.921
0.836
0.765
0.705
1.17
1.05
0.953
0.873
0.805
1.32
1.19
1.08
0.990
0.913
1.48
1.34
1.22
1.11
1.03
1.66
1.49
1.36
1.25
1.15
1.84
1.66
1.51
1.39
1.28
2.03
1.84
1.67
1.54
1.42
2.44
2.21
2.02
1.86
1.72
2.89
2.62
2.39
2.20
2.04
3.36
3.06
2.80
2.58
2.39
3.87
3.52
3.23
2.97
2.76
4.39
4.00
3.67
3.39
3.14
2.60 0.374 0.425 0.491 0.567 0.653 0.747 0.847 0.955 1.07 1.19
2.80 0.348 0.396 0.457 0.529 0.608 0.696 0.790 0.890 0.998 1.11
3.00 0.325 0.370 0.428 0.495 0.569 0.651 0.740 0.834 0.935 1.04
1.32
1.23
1.16
1.60
1.49
1.40
1.90
1.77
1.66
2.22
2.08
1.95
2.57
2.40
2.25
2.93
2.74
2.57
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
8 - 182
BOLTS, WELDS, AND CONNECTED ELEMENTS
Table 8-41 (cont.).
Coefficients C for Eccentrically Loaded Weld Groups
Angle = 15°°
φ R n = CC1Dl
C min =
Pu
D min =
C 1D l
Pu
lmin =
CC 1 l
Pu
CC 1 D
where
Pu = factored force, kips
Pu
ex = a l
15°
D = number of sixteenths-of-an-inch
in the fillet weld size
l = characteristic length of weld group, in.
a = e x / l, in.
e x = horizontal component of eccentricity of
Pu with respect to centroid of weld group, in.
kl
l
C = coefficient tabulated below which includes φ = 0.75
C 1 = electode strength coefficient from Table 8-37
(1.0 for E70XX electrodes)
k
a
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.2
1.4
1.6
1.8
0.00
0.10
0.15
0.20
0.25
4.11
3.29
2.97
2.70
2.46
4.40
3.56
3.24
2.95
2.70
4.70
3.85
3.53
3.24
2.98
5.00
4.19
3.85
3.56
3.29
5.29
4.55
4.20
3.89
3.63
5.59
4.91
4.56
4.25
3.97
5.89
5.26
4.93
4.62
4.33
6.18
5.61
5.30
4.99
4.70
6.48
5.95
5.66
5.37
5.08
6.78
6.29
6.01
5.73
5.45
7.07
6.62
6.35
6.09
5.82
7.67
7.26
7.01
6.78
6.54
8.26
7.88
7.65
7.45
7.23
8.85
8.49
8.27
8.08
7.90
9.45 10.0
9.09 9.69
8.89 9.51
8.71 9.31
8.54 9.17
0.30
0.40
0.50
0.60
0.70
2.25
1.91
1.65
1.44
1.28
2.48
2.12
1.83
1.61
1.43
2.75
2.36
2.06
1.82
1.62
3.05
2.65
2.32
2.06
1.84
3.38
2.95
2.60
2.32
2.08
3.71
3.27
2.90
2.60
2.34
4.06
3.61
3.22
2.89
2.62
4.43
3.95
3.54
3.20
2.91
4.80
4.30
3.88
3.52
3.21
5.17
4.67
4.22
3.84
3.51
5.55
5.04
4.58
4.18
3.83
6.29
5.78
5.31
4.88
4.49
7.01
6.52
6.04
5.60
5.19
7.70
7.25
6.78
6.33
5.90
8.36
7.95
7.51
7.06
6.62
9.01
8.64
8.23
7.78
7.34
0.80
0.90
1.00
1.20
1.40
1.15
1.04
0.945
0.803
0.697
1.29
1.17
1.07
0.908
0.789
1.46
1.33
1.22
1.04
0.907
1.67
1.52
1.39
1.19
1.04
1.89
1.72
1.59
1.36
1.19
2.13
1.95
1.79
1.54
1.35
2.38
2.19
2.02
1.74
1.53
2.65
2.44
2.25
1.95
1.72
2.93
2.70
2.50
2.17
1.91
3.23
2.98
2.76
2.40
2.12
3.53
3.26
3.03
2.65
2.34
4.15
3.86
3.60
3.16
2.80
4.82
4.49
4.19
3.70
3.30
5.50
5.15
4.83
4.27
3.82
6.21
5.83
5.48
4.86
4.35
6.92
6.52
6.15
5.48
4.92
1.60
1.80
2.00
2.20
2.40
0.615
0.550
0.497
0.454
0.418
0.698
0.625
0.565
0.516
0.475
0.803
0.719
0.651
0.595
0.548
0.924
0.829
0.752
0.687
0.633
1.06
0.951
0.863
0.790
0.728
1.21
1.08
0.984
0.902
0.832
1.36
1.23
1.12
1.02
0.943
1.53
1.38
1.26
1.15
1.06
1.71
1.54
1.40
1.29
1.19
1.90
1.71
1.56
1.43
1.32
2.09
1.89
1.73
1.59
1.47
2.51
2.28
2.08
1.91
1.77
2.97
2.69
2.47
2.27
2.10
3.45
3.13
2.87
2.65
2.45
3.93
3.58
3.29
3.04
2.82
4.45
4.06
3.73
3.45
3.20
2.60 0.387 0.440 0.508 0.586 0.675 0.772 0.875 0.987 1.11 1.23
2.80 0.360 0.409 0.473 0.546 0.629 0.719 0.817 0.921 1.03 1.15
3.00 0.336 0.383 0.442 0.511 0.589 0.674 0.765 0.863 0.967 1.08
1.36
1.27
1.19
1.65
1.54
1.44
1.96
1.83
1.72
2.28
2.14
2.01
2.63
2.46
2.31
2.99
2.80
2.63
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
2.0
ECCENTRICALLY LOADED WELD GROUPS
8 - 183
Table 8-41 (cont.).
Coefficients C for Eccentrically Loaded Weld Groups
Angle = 30°°
φ R n = CC1Dl
C min =
Pu
D min =
C 1D l
Pu
lmin =
CC 1 l
Pu
CC 1 D
where
Pu = factored force, kips
ex = a l
D = number of sixteenths-of-an-inch
in the fillet weld size
l = characteristic length of weld group, in.
a = e x / l, in.
e x = horizontal component of eccentricity of
Pu with respect to centroid of weld group, in.
Pu
30°
kl
l
C = coefficient tabulated below which includes φ = 0.75
C 1 = electode strength coefficient from Table 8-37
(1.0 for E70XX electrodes)
k
a
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.2
1.4
1.6
1.8
2.0
0.00
0.10
0.15
0.20
0.25
3.91
3.37
3.07
2.82
2.60
4.23
3.70
3.38
3.11
2.87
4.56
4.02
3.71
3.42
3.16
4.89
4.36
4.03
3.74
3.47
5.22
4.71
4.38
4.07
3.80
5.54
5.08
4.74
4.42
4.14
5.87
5.45
5.12
4.80
4.51
6.20
5.81
5.50
5.18
4.88
6.53
6.18
5.88
5.57
5.27
6.85
6.55
6.26
5.96
5.66
7.18
6.90
6.64
6.34
6.05
7.84
7.61
7.37
7.10
6.82
8.49
8.30
8.10
7.85
7.58
9.15
8.98
8.80
8.58
8.33
9.80
9.65
9.50
9.30
9.06
10.5
10.3
10.2
10.0
9.79
0.30
0.40
0.50
0.60
0.70
2.40
2.06
1.80
1.58
1.41
2.65
2.29
2.00
1.76
1.57
2.93
2.55
2.23
1.98
1.77
3.24
2.83
2.50
2.23
2.01
3.56
3.14
2.79
2.50
2.26
3.89
3.46
3.10
2.79
2.54
4.25
3.81
3.42
3.10
2.82
4.62
4.16
3.76
3.42
3.13
5.00
4.52
4.11
3.75
3.44
5.39
4.89
4.46
4.09
3.76
5.77
5.27
4.83
4.43
4.09
6.55
6.04
5.57
5.15
4.77
7.31
6.81
6.33
5.88
5.47
8.06
7.57
7.09
6.61
6.18
8.81
8.32
7.84
7.35
6.90
9.55
9.06
8.58
8.09
7.63
0.80
0.90
1.00
1.20
1.40
1.26
1.15
1.05
0.891
0.774
1.42
1.29
1.18
1.01
0.875
1.60
1.46
1.34
1.15
1.00
1.82
1.66
1.53
1.32
1.15
2.06
1.89
1.74
1.50
1.32
2.31
2.13
1.96
1.70
1.49
2.59
2.38
2.20
1.91
1.69
2.87
2.65
2.46
2.14
1.89
3.17
2.93
2.72
2.38
2.10
3.47
3.22
3.00
2.62
2.33
3.79
3.52
3.28
2.88
2.56
4.44
4.14
3.87
3.42
3.05
5.10
4.77
4.47
3.97
3.56
5.78
5.42
5.09
4.54
4.08
6.48
6.09
5.74
5.13
4.63
7.19
6.79
6.41
5.76
5.20
1.60
1.80
2.00
2.20
2.40
0.684
0.612
0.554
0.506
0.465
0.774
0.694
0.629
0.574
0.528
0.889
0.798
0.723
0.662
0.609
1.02
0.919
0.834
0.763
0.703
1.17
1.05
0.957
0.877
0.809
1.33
1.20
1.09
1.00
0.924
1.51
1.36
1.24
1.14
1.05
1.69
1.53
1.39
1.28
1.18
1.88
1.70
1.55
1.43
1.32
2.09
1.89
1.73
1.59
1.47
2.30
2.08
1.91
1.75
1.62
2.75
2.50
2.29
2.11
1.95
3.22
2.94
2.69
2.48
2.30
3.70
3.38
3.11
2.87
2.67
4.21
3.86
3.55
3.29
3.06
4.74
4.35
4.01
3.72
3.47
2.60 0.431 0.489 0.565 0.652 0.750 0.857 0.972 1.10 1.23
2.80 0.401 0.456 0.526 0.608 0.699 0.800 0.908 1.02 1.15
3.00 0.375 0.426 0.492 0.569 0.654 0.749 0.851 0.959 1.07
1.36
1.27
1.20
1.51
1.41
1.32
1.82
1.70
1.60
2.15
2.01
1.89
2.49
2.34
2.20
2.86
2.68
2.52
3.24
3.05
2.87
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
8 - 184
BOLTS, WELDS, AND CONNECTED ELEMENTS
Table 8-41 (cont.).
Coefficients C for Eccentrically Loaded Weld Groups
Angle = 45°°
φ R n = CC1Dl
C min =
Pu
D min =
C 1D l
Pu
lmin =
CC 1 l
Pu
CC 1 D
where
Pu = factored force, kips
ex = a l
D = number of sixteenths-of-an-inch
in the fillet weld size
l = characteristic length of weld group, in.
a = e x / l, in.
e x = horizontal component of eccentricity of
Pu with respect to centroid of weld group, in.
45°
Pu
kl
l
C = coefficient tabulated below which includes φ = 0.75
C 1 = electode strength coefficient from Table 8-37
(1.0 for E70XX electrodes)
k
a
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.2
1.4
1.6
1.8
2.0
0.00
0.10
0.15
0.20
0.25
3.61
3.37
3.13
2.94
2.77
3.97
3.74
3.52
3.29
3.10
4.33
4.11
3.89
3.65
3.44
4.70
4.48
4.26
4.02
3.79
5.06
4.84
4.62
4.38
4.14
5.42
5.21
4.99
4.75
4.51
5.78
5.58
5.36
5.12
4.87
6.14
5.94
5.74
5.50
5.25
6.50
6.31
6.11
5.88
5.63
6.86
6.68
6.49
6.26
6.01
7.22
7.04
6.86
6.64
6.40
7.95
7.78
7.61
7.39
7.16
8.67
8.52
8.36
8.15
7.92
9.39 10.1
9.25 9.98
9.11 9.85
8.91 9.67
8.68 9.45
10.8
10.7
10.6
10.4
10.2
0.30
0.40
0.50
0.60
0.70
2.61
2.32
2.06
1.84
1.66
2.91
2.59
2.30
2.06
1.86
3.24
2.87
2.57
2.30
2.08
3.57
3.18
2.86
2.58
2.34
3.92
3.51
3.16
2.87
2.61
4.27
3.85
3.49
3.17
2.91
4.63
4.20
3.82
3.50
3.22
5.00
4.55
4.17
3.83
3.54
5.38
4.92
4.52
4.18
3.88
5.76
5.29
4.89
4.53
4.22
6.15
5.67
5.26
4.89
4.56
6.91
6.42
5.97
5.57
5.22
7.67
7.18
6.71
6.28
5.90
8.44
7.95
7.47
7.02
6.62
9.21
8.72
8.24
7.78
7.35
9.98
9.50
9.01
8.54
8.10
0.80
0.90
1.00
1.20
1.40
1.50
1.37
1.26
1.08
0.938
1.69
1.54
1.41
1.21
1.06
1.90
1.74
1.60
1.38
1.21
2.13
1.96
1.81
1.57
1.38
2.40
2.21
2.05
1.78
1.57
2.68
2.48
2.30
2.01
1.78
2.98
2.76
2.58
2.26
2.01
3.29
3.06
2.86
2.52
2.24
3.61
3.37
3.15
2.78
2.49
3.93
3.68
3.45
3.06
2.74
4.27
4.00
3.76
3.34
3.00
4.91
4.62
4.35
3.90
3.52
5.56
5.25
4.97
4.48
4.06
6.25
5.91
5.61
5.07
4.62
6.97
6.61
6.28
5.70
5.21
7.70
7.32
6.97
6.35
5.81
1.60
1.80
2.00
2.20
2.40
0.831
0.745
0.675
0.617
0.568
0.939
0.843
0.764
0.699
0.644
1.07
0.966
0.877
0.804
0.741
1.23
1.11
1.01
0.925
0.854
1.41
1.27
1.16
1.06
0.981
1.60
1.45
1.32
1.21
1.12
1.80
1.63
1.49
1.37
1.27
2.02
1.83
1.67
1.54
1.43
2.24
2.04
1.87
1.72
1.59
2.48
2.25
2.06
1.90
1.77
2.71
2.48
2.27
2.10
1.95
3.20
2.93
2.69
2.49
2.32
3.70
3.40
3.14
2.91
2.71
4.23
3.90
3.60
3.35
3.13
4.78
4.42
4.09
3.81
3.57
5.36
4.96
4.61
4.30
4.03
2.60 0.526 0.597 0.687 0.792 0.911 1.04 1.18
2.80 0.489 0.556 0.641 0.739 0.850 0.972 1.10
3.00 0.458 0.520 0.600 0.693 0.796 0.911 1.03
1.33
1.24
1.17
1.48
1.39
1.30
1.65
1.54
1.45
1.82
1.70
1.60
2.16
2.03
1.91
2.54
2.38
2.24
2.93
2.75
2.60
3.35
3.15
2.97
3.78
3.57
3.37
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
ECCENTRICALLY LOADED WELD GROUPS
8 - 185
Table 8-41 (cont.).
Coefficients C for Eccentrically Loaded Weld Groups
Angle = 60°°
φ R n = CC1Dl
C min =
Pu
D min =
C 1D l
Pu
lmin =
CC 1 l
Pu
CC 1 D
where
Pu = factored force, kips
ex = a l
60°
D = number of sixteenths-of-an-inch
in the fillet weld size
l = characteristic length of weld group, in.
a = e x / l, in.
e x = horizontal component of eccentricity of
Pu with respect to centroid of weld group, in.
Pu
kl
l
C = coefficient tabulated below which includes φ = 0.75
C 1 = electode strength coefficient from Table 8-37
(1.0 for E70XX electrodes)
k
a
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.2
1.4
1.6
1.8
2.0
0.00
0.10
0.15
0.20
0.25
3.28
3.20
3.10
2.98
2.89
3.67
3.59
3.50
3.38
3.27
4.06
3.98
3.90
3.79
3.66
4.45
4.37
4.29
4.17
4.04
4.84
4.76
4.67
4.56
4.43
5.23
5.14
5.05
4.94
4.80
5.62
5.53
5.43
5.31
5.17
6.01
5.92
5.82
5.69
5.55
6.40
6.30
6.20
6.07
5.92
6.79
6.69
6.58
6.45
6.29
7.18
7.08
6.96
6.83
6.67
7.96
7.86
7.74
7.59
7.43
8.74
8.63
8.51
8.36
8.19
9.53 10.3
9.41 10.2
9.29 10.1
9.13 9.91
8.96 9.74
11.1
11.0
10.9
10.7
10.5
0.30
0.40
0.50
0.60
0.70
2.80
2.63
2.44
2.27
2.09
3.16
2.96
2.74
2.54
2.35
3.54
3.30
3.06
2.84
2.63
3.92
3.66
3.40
3.16
2.93
4.29
4.02
3.75
3.49
3.25
4.66
4.38
4.10
3.83
3.58
5.02
4.74
4.46
4.18
3.92
5.39
5.09
4.80
4.53
4.26
5.76
5.44
5.14
4.86
4.59
6.13
5.80
5.49
5.20
4.92
6.50
6.16
5.84
5.54
5.25
7.25
6.89
6.54
6.23
5.93
8.01
7.64
7.28
6.93
6.63
8.77
8.40
8.02
7.66
7.34
9.55 10.3
9.17 9.94
8.78 9.56
8.42 9.18
8.07 8.82
0.80
0.90
1.00
1.20
1.40
1.94
1.80
1.67
1.46
1.28
2.18
2.02
1.88
1.64
1.45
2.44
2.27
2.11
1.85
1.64
2.73
2.54
2.37
2.09
1.86
3.03
2.83
2.65
2.35
2.10
3.35
3.14
2.95
2.62
2.35
3.68
3.46
3.26
2.91
2.63
4.01
3.78
3.58
3.21
2.91
4.34
4.11
3.90
3.52
3.20
4.66
4.43
4.21
3.82
3.48
4.99
4.74
4.52
4.11
3.76
5.65
5.40
5.16
4.73
4.35
6.34
6.07
5.82
5.36
4.96
7.04
6.76
6.50
6.02
5.58
7.75
7.46
7.19
6.69
6.23
8.49
8.18
7.90
7.38
6.89
1.60
1.80
2.00
2.20
2.40
1.15
1.03
0.940
0.861
0.794
1.30
1.17
1.06
0.974
0.899
1.47
1.33
1.21
1.11
1.03
1.67
1.51
1.39
1.27
1.18
1.89
1.72
1.58
1.46
1.35
2.13
1.95
1.79
1.65
1.54
2.39
2.19
2.01
1.86
1.73
2.66
2.44
2.25
2.09
1.94
2.93
2.69
2.49
2.31
2.15
3.19
2.94
2.72
2.53
2.36
3.46
3.20
2.97
2.76
2.58
4.01
3.72
3.47
3.24
3.03
4.60
4.28
3.99
3.74
3.52
5.20
4.85
4.55
4.27
4.02
5.82
5.45
5.12
4.82
4.55
6.47
6.07
5.72
5.40
5.11
2.60 0.736 0.834 0.956 1.10 1.26
2.80 0.686 0.778 0.893 1.03 1.18
3.00 0.643 0.729 0.837 0.964 1.11
1.43
1.34
1.26
1.62
1.52
1.43
1.82
1.70
1.61
2.02
1.89
1.79
2.22
2.08
1.97
2.42
2.28
2.15
2.86
2.69
2.55
3.32
3.13
2.97
3.80
3.60
3.41
4.31
4.08
3.88
4.84
4.59
4.37
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
8 - 186
BOLTS, WELDS, AND CONNECTED ELEMENTS
Table 8-41 (cont.).
Coefficients C for Eccentrically Loaded Weld Groups
Angle = 75°°
φ R n = CC 1 D l
C min =
Pu
D min =
C 1D l
Pu
lmin =
CC 1 l
Pu
CC 1 D
where
Pu = factored force, kips
ex = a l
D = number of sixteenths-of-an-inch
in the fillet weld size
l = characteristic length of weld group, in.
a = e x / l, in.
e x = horizontal component of eccentricity of
Pu with respect to centroid of weld group, in.
75°
Pu
kl
l
C = coefficient tabulated below which includes φ = 0.75
C 1 = electode strength coefficient from Table 8-37
(1.0 for E70XX electrodes)
k
a
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.2
1.4
1.6
1.8
2.0
0.00
0.10
0.15
0.20
0.25
2.97
2.86
2.89
2.88
2.87
3.38
3.27
3.24
3.19
3.17
3.79
3.67
3.65
3.61
3.57
4.20
4.08
4.06
4.02
3.98
4.61
4.49
4.47
4.43
4.38
5.02
4.90
4.87
4.83
4.79
5.43
5.31
5.28
5.24
5.19
5.84
5.72
5.69
5.64
5.59
6.25
6.14
6.10
6.05
5.99
6.66
6.55
6.50
6.45
6.39
7.07
6.96
6.91
6.86
6.80
7.89
7.78
7.72
7.67
7.60
8.71
8.60
8.54
8.48
8.40
9.54
9.42
9.36
9.29
9.21
10.4
10.2
10.2
10.1
10.0
11.2
11.1
11.0
10.9
10.8
0.30
0.40
0.50
0.60
0.70
2.86
2.84
2.79
2.74
2.66
3.17
3.16
3.13
3.07
3.00
3.54
3.51
3.47
3.42
3.34
3.93
3.88
3.83
3.76
3.68
4.33
4.26
4.19
4.11
4.02
4.73
4.64
4.56
4.47
4.37
5.13
5.02
4.93
4.83
4.72
5.53
5.41
5.30
5.19
5.07
5.93
5.79
5.68
5.56
5.43
6.33
6.18
6.05
5.93
5.79
6.73
6.57
6.43
6.30
6.16
7.52
7.36
7.20
7.04
6.89
8.32
8.15
7.96
7.80
7.63
9.12
8.94
8.75
8.56
8.38
9.92
9.73
9.53
9.33
9.14
10.7
10.5
10.3
10.1
9.90
0.80
0.90
1.00
1.20
1.40
2.59
2.51
2.42
2.25
2.08
2.91
2.82
2.73
2.53
2.35
3.25
3.15
3.05
2.84
2.63
3.59
3.49
3.38
3.15
2.94
3.93
3.82
3.71
3.48
3.25
4.26
4.15
4.03
3.80
3.57
4.61
4.49
4.37
4.12
3.88
4.95
4.83
4.70
4.44
4.19
5.30
5.17
5.03
4.77
4.51
5.66
5.52
5.38
5.10
4.83
6.01
5.87
5.72
5.44
5.16
6.74
6.58
6.42
6.12
5.83
7.47
7.30
7.14
6.82
6.52
8.21
8.04
7.86
7.53
7.22
8.96
8.78
8.60
8.26
7.93
9.71
9.52
9.34
8.99
8.65
1.60
1.80
2.00
2.20
2.40
1.92
1.78
1.65
1.54
1.44
2.17
2.01
1.87
1.74
1.63
2.44
2.26
2.11
1.97
1.84
2.73
2.54
2.37
2.22
2.08
3.04
2.84
2.65
2.49
2.34
3.35
3.14
2.95
2.77
2.61
3.65
3.43
3.24
3.06
2.89
3.95
3.73
3.53
3.34
3.17
4.26
4.04
3.82
3.63
3.44
4.58
4.34
4.12
3.92
3.73
4.90
4.65
4.43
4.22
4.02
5.55
5.30
5.05
4.83
4.62
6.23
5.96
5.70
5.47
5.24
6.92
6.63
6.37
6.12
5.89
7.62
7.33
7.05
6.79
6.55
8.33
8.03
7.75
7.48
7.23
2.60
2.80
3.00
1.35
1.26
1.19
1.52
1.43
1.35
1.73
1.63
1.53
1.95
1.84
1.74
2.20
2.08
1.97
2.47
2.34
2.22
2.74
2.60
2.48
3.01
2.86
2.73
3.28
3.13
2.99
3.56
3.40
3.25
3.84
3.67
3.52
4.43
4.25
4.07
5.04
4.84
4.66
5.67
5.46
5.26
6.32
6.10
5.89
6.98
6.75
6.53
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
ECCENTRICALLY LOADED WELD GROUPS
8 - 187
Table 8-42.
Coefficients C for Eccentrically Loaded Weld Groups
Angle = 0°°
φ R n = CC1Dl
C min =
Pu
D min =
C 1D l
Pu
lmin =
CC 1 l
Pu
CC 1 D
where
Pu = factored force, kips
ex = a l
D = number of sixteenths-of-an-inch
in the fillet weld size
l = characteristic length of weld group, in.
a = e x / l, in.
e x = horizontal component of eccentricity of
Pu with respect to centroid of weld group, in.
Pu
l
c.g.
C = coefficient tabulated below which includes φ = 0.75
C 1 = electode strength coefficient from Table 8-37
(1.0 for E70XX electrodes)
xl
kl
k
a
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.2
1.4
1.6
1.8
2.0
0.00
0.10
0.15
0.20
0.25
1.39
1.39
1.37
1.32
1.24
1.81
1.71
1.69
1.63
1.56
2.28
2.09
2.05
1.98
1.88
2.65
2.48
2.43
2.33
2.22
3.06
2.88
2.81
2.70
2.57
3.48
3.28
3.20
3.08
2.93
3.90
3.69
3.60
3.46
3.29
4.32
4.10
4.00
3.84
3.65
4.73
4.51
4.40
4.23
4.03
5.15
4.92
4.80
4.62
4.40
5.57
5.33
5.21
5.01
4.77
6.40
6.16
6.02
5.80
5.53
7.24
6.99
6.84
6.58
6.30
8.07
7.82
7.65
7.38
7.07
8.91
8.65
8.47
8.17
7.84
9.74
9.48
9.28
8.97
8.62
0.30
0.40
0.50
0.60
0.70
1.16
0.998
0.860
0.748
0.659
1.46
1.27
1.09
0.952
0.838
1.77
1.55
1.35
1.17
1.04
2.09
1.84
1.61
1.41
1.25
2.42
2.13
1.87
1.65
1.46
2.76
2.43
2.14
1.89
1.68
3.10
2.74
2.41
2.14
1.91
3.45
3.06
2.70
2.40
2.15
3.81
3.38
3.00
2.67
2.40
4.16
3.71
3.30
2.95
2.66
4.53
4.04
3.61
3.24
2.93
5.26
4.73
4.25
3.84
3.50
6.00
5.43
4.92
4.47
4.09
6.75
6.14
5.60
5.13
4.72
7.51
6.87
6.30
5.80
5.36
8.27
7.61
7.01
6.49
6.03
0.80
0.90
1.00
1.20
1.40
0.586
0.527
0.478
0.403
0.348
0.746
0.671
0.609
0.512
0.441
0.922
0.829
0.752
0.633
0.546
1.11
1.00
0.909
0.766
0.661
1.31
1.18
1.08
0.910
0.787
1.51
1.37
1.25
1.06
0.922
1.72
1.56
1.43
1.22
1.06
1.94
1.77
1.62
1.39
1.21
2.17
1.98
1.82
1.56
1.36
2.42
2.21
2.03
1.75
1.53
2.67
2.44
2.25
1.94
1.70
3.20
2.95
2.73
2.36
2.08
3.77
3.48
3.23
2.81
2.48
4.36
4.05
3.77
3.29
2.92
4.98
4.64
4.33
3.80
3.38
5.62
5.25
4.92
4.34
3.86
1.60
1.80
2.00
2.20
2.40
0.305
0.272
0.245
0.223
0.205
0.387
0.345
0.311
0.283
0.260
0.479
0.427
0.385
0.350
0.321
0.581
0.518
0.467
0.425
0.390
0.692
0.618
0.558
0.508
0.467
0.813
0.727
0.657
0.599
0.551
0.938
0.840
0.760
0.694
0.639
1.07
0.958
0.868
0.793
0.729
1.21
1.09
0.983
0.897
0.826
1.36
1.22
1.10
1.01
0.929
1.51
1.36
1.23
1.13
1.04
1.85
1.66
1.51
1.38
1.27
2.21
1.99
1.81
1.66
1.53
2.61
2.35
2.14
1.97
1.82
3.03
2.74
2.50
2.30
2.12
3.48
3.15
2.88
2.65
2.46
2.60 0.189 0.240 0.297 0.360 0.431 0.509 0.591 0.675 0.765 0.860 0.961 1.18
2.80 0.176 0.223 0.276 0.335 0.401 0.474 0.550 0.628 0.712 0.801 0.895 1.10
3.00 0.164 0.208 0.257 0.313 0.375 0.443 0.514 0.588 0.666 0.749 0.838 1.03
1.42
1.33
1.24
1.69
1.57
1.48
1.98
1.85
1.73
2.29
2.14
2.01
x
0.000 0.008 0.029 0.056 0.089 0.125 0.164 0.204 0.246 0.289 0.333 0.424 0.516 0.610 0.704 0.800
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
8 - 188
BOLTS, WELDS, AND CONNECTED ELEMENTS
Table 8-42 (cont.).
Coefficients C for Eccentrically Loaded Weld Groups
Angle = 15°°
φ R n = CC1Dl
C min =
Pu
D min =
C 1D l
Pu
lmin =
CC 1 l
Pu
CC 1 D
where
ex = a l
Pu = factored force, kips
D = number of sixteenths-of-an-inch
in the fillet weld size
l = characteristic length of weld group, in.
a = e x / l, in.
e x = horizontal component of eccentricity of
Pu with respect to centroid of weld group, in.
15°
Pu
l
c.g.
C = coefficient tabulated below which includes φ = 0.75
C 1 = electode strength coefficient from Table 8-37
(1.0 for E70XX electrodes)
xl
kl
k
a
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.2
1.4
1.6
1.8
2.0
0.00
0.10
0.15
0.20
0.25
1.48
1.42
1.38
1.32
1.24
1.89
1.77
1.73
1.66
1.56
2.31
2.15
2.09
2.01
1.91
2.72
2.55
2.47
2.37
2.25
3.13
2.96
2.86
2.74
2.60
3.54
3.38
3.25
3.11
2.96
3.95
3.79
3.64
3.49
3.32
4.36
4.20
4.04
3.87
3.68
4.77
4.61
4.44
4.25
4.05
5.18
5.02
4.84
4.64
4.41
5.59
5.43
5.24
5.02
4.79
6.41
6.25
6.05
5.80
5.53
7.23
7.08
6.85
6.57
6.29
8.05
7.90
7.66
7.36
7.06
8.87
8.73
8.46
8.15
7.82
9.69
9.55
9.28
8.94
8.60
0.30
0.40
0.50
0.60
0.70
1.16
1.00
0.869
0.759
0.670
1.46
1.27
1.10
0.961
0.849
1.79
1.56
1.35
1.18
1.05
2.12
1.85
1.62
1.42
1.26
2.45
2.16
1.89
1.67
1.48
2.79
2.46
2.17
1.92
1.72
3.13
2.77
2.45
2.18
1.95
3.48
3.09
2.74
2.44
2.20
3.83
3.41
3.04
2.72
2.45
4.19
3.74
3.34
3.00
2.71
4.54
4.07
3.65
3.29
2.98
5.27
4.76
4.30
3.90
3.55
6.01
5.46
4.96
4.53
4.15
6.75
6.17
5.64
5.18
4.78
7.51
6.90
6.34
5.86
5.43
8.27
7.63
7.06
6.55
6.10
0.80
0.90
1.00
1.20
1.40
0.598
0.539
0.490
0.413
0.357
0.758
0.683
0.621
0.524
0.452
0.934
0.842
0.766
0.646
0.558
1.12
1.02
0.924
0.781
0.675
1.33
1.20
1.10
0.928
0.804
1.54
1.40
1.28
1.09
0.943
1.76
1.60
1.47
1.25
1.09
1.99
1.81
1.66
1.42
1.24
2.22
2.03
1.87
1.61
1.40
2.47
2.26
2.08
1.80
1.57
2.72
2.50
2.31
1.99
1.75
3.26
3.01
2.79
2.42
2.13
3.83
3.55
3.30
2.88
2.54
4.43
4.12
3.84
3.36
2.99
5.06
4.71
4.41
3.88
3.45
5.70
5.33
5.00
4.42
3.95
1.60
1.80
2.00
2.20
2.40
0.314
0.280
0.253
0.230
0.211
0.398
0.355
0.320
0.291
0.267
0.491
0.438
0.395
0.360
0.330
0.595
0.531
0.479
0.437
0.401
0.708
0.633
0.572
0.522
0.479
0.833
0.746
0.675
0.616
0.566
0.967
0.867
0.784
0.717
0.659
1.10
0.988
0.896
0.819
0.753
1.25
1.12
1.01
0.926
0.853
1.40
1.26
1.14
1.04
0.959
1.56
1.40
1.27
1.16
1.07
1.90
1.71
1.55
1.43
1.31
2.27
2.05
1.87
1.71
1.58
2.67
2.42
2.20
2.03
1.87
3.11
2.81
2.57
2.37
2.19
3.56
3.24
2.96
2.73
2.53
2.60 0.195 0.247 0.305 0.370 0.444 0.524 0.610 0.697 0.790 0.889 0.993 1.22
2.80 0.182 0.230 0.284 0.344 0.412 0.487 0.568 0.649 0.736 0.827 0.925 1.14
3.00 0.170 0.214 0.265 0.321 0.386 0.456 0.531 0.607 0.688 0.774 0.866 1.06
1.47
1.37
1.28
1.74
1.62
1.52
2.04
1.90
1.79
2.36
2.20
2.07
x
0.000 0.008 0.029 0.056 0.089 0.125 0.164 0.204 0.246 0.289 0.333 0.424 0.516 0.610 0.704 0.800
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
ECCENTRICALLY LOADED WELD GROUPS
8 - 189
Table 8-42 (cont.).
Coefficients C for Eccentrically Loaded Weld Groups
Angle = 30°°
φ R n = CC1Dl
C min =
Pu
D min =
C1Dl
Pu
lmin =
CC 1 l
Pu
CC 1 D
where
Pu = factored force, kips
ex = a l
D = number of sixteenths-of-an-inch
in the fillet weld size
l = characteristic length of weld group, in.
a = e x / l, in.
e x = horizontal component of eccentricity of
Pu with respect to centroid of weld group, in.
30°
Pu
l
c.g.
C = coefficient tabulated below which includes φ = 0.75
C 1 = electode strength coefficient from Table 8-37
(1.0 for E70XX electrodes)
xl
kl
k
a
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.2
1.4
1.6
1.8
2.0
0.00
0.10
0.15
0.20
0.25
1.64
1.52
1.44
1.36
1.28
2.03
1.93
1.82
1.72
1.61
2.42
2.32
2.21
2.09
1.97
2.81
2.72
2.60
2.47
2.33
3.20
3.11
2.99
2.84
2.69
3.59
3.50
3.37
3.21
3.04
3.98
3.89
3.75
3.58
3.40
4.37
4.28
4.14
3.95
3.76
4.76
4.68
4.52
4.33
4.11
5.15
5.07
4.91
4.70
4.48
5.54
5.46
5.29
5.08
4.84
6.33
6.24
6.07
5.84
5.59
7.11
7.03
6.84
6.60
6.34
7.89
7.81
7.62
7.38
7.10
8.67
8.60
8.41
8.15
7.87
9.45
9.39
9.19
8.93
8.65
0.30
0.40
0.50
0.60
0.70
1.20
1.05
0.921
0.812
0.722
1.51
1.32
1.16
1.02
0.908
1.84
1.61
1.41
1.25
1.11
2.18
1.91
1.68
1.49
1.33
2.53
2.23
1.96
1.74
1.56
2.88
2.55
2.26
2.01
1.81
3.22
2.87
2.56
2.29
2.07
3.56
3.19
2.86
2.57
2.33
3.91
3.52
3.16
2.86
2.60
4.26
3.85
3.47
3.15
2.87
4.62
4.18
3.79
3.45
3.15
5.33
4.86
4.44
4.07
3.74
6.07
5.57
5.11
4.71
4.36
6.82
6.28
5.80
5.38
5.00
7.58
7.02
6.51
6.06
5.67
8.35
7.77
7.24
6.77
6.35
0.80
0.90
1.00
1.20
1.40
0.647
0.586
0.535
0.454
0.393
0.816
0.739
0.674
0.572
0.496
0.998
0.905
0.827
0.703
0.610
1.20
1.09
0.994
0.847
0.736
1.41
1.28
1.18
1.00
0.874
1.64
1.49
1.37
1.17
1.02
1.88
1.71
1.58
1.36
1.19
2.12
1.95
1.80
1.55
1.36
2.37
2.18
2.02
1.75
1.53
2.63
2.42
2.25
1.95
1.72
2.90
2.68
2.48
2.16
1.91
3.46
3.21
2.99
2.61
2.32
4.05
3.77
3.52
3.10
2.75
4.66
4.36
4.08
3.61
3.22
5.30
4.97
4.67
4.15
3.72
5.96
5.60
5.28
4.71
4.24
1.60
1.80
2.00
2.20
2.40
0.347
0.310
0.280
0.255
0.234
0.437
0.391
0.353
0.322
0.296
0.538
0.481
0.435
0.397
0.365
0.650
0.582
0.526
0.481
0.442
0.773
0.693
0.627
0.573
0.528
0.909
0.816
0.740
0.677
0.623
1.06
0.949
0.861
0.789
0.727
1.21
1.09
0.988
0.904
0.833
1.37
1.23
1.12
1.02
0.944
1.53
1.38
1.26
1.15
1.06
1.70
1.54
1.40
1.28
1.18
2.07
1.87
1.71
1.57
1.45
2.47
2.24
2.05
1.88
1.74
2.90
2.64
2.41
2.22
2.06
3.36
3.06
2.81
2.59
2.40
3.85
3.52
3.23
2.98
2.77
2.60 0.217 0.273 0.337 0.409 0.489 0.577 0.674 0.772 0.875 0.983 1.10 1.34
2.80 0.201 0.254 0.314 0.381 0.455 0.538 0.628 0.719 0.815 0.916 1.02 1.26
3.00 0.188 0.238 0.293 0.356 0.426 0.504 0.588 0.673 0.763 0.858 0.959 1.18
1.62
1.51
1.42
1.92
1.79
1.68
2.24
2.10
1.97
2.59
2.43
2.28
x
0.000 0.008 0.029 0.056 0.089 0.125 0.164 0.204 0.246 0.289 0.333 0.424 0.516 0.610 0.704 0.800
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
8 - 190
BOLTS, WELDS, AND CONNECTED ELEMENTS
Table 8-42 (cont.).
Coefficients C for Eccentrically Loaded Weld Groups
Angle = 45°°
φ R n = CC1Dl
C min =
Pu
D min =
C 1D l
Pu
lmin =
CC 1 l
Pu
CC 1 D
where
ex = a l
Pu = factored force, kips
D = number of sixteenths-of-an-inch
in the fillet weld size
l = characteristic length of weld group, in.
a = e x / l, in.
e x = horizontal component of eccentricity of
Pu with respect to centroid of weld group, in.
45°
l
C = coefficient tabulated below which includes φ = 0.75
C 1 = electode strength coefficient from Table 8-37
(1.0 for E70XX electrodes)
Pu
c.g.
xl
kl
k
a
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.2
1.4
1.6
1.8
2.0
0.00
0.10
0.15
0.20
0.25
1.81
1.68
1.57
1.47
1.39
2.17
2.06
1.95
1.83
1.72
2.53
2.43
2.32
2.19
2.06
2.89
2.80
2.68
2.55
2.41
3.25
3.17
3.05
2.91
2.76
3.61
3.55
3.42
3.28
3.12
3.97
3.92
3.80
3.64
3.48
4.33
4.29
4.17
4.02
3.85
4.70
4.66
4.54
4.39
4.22
5.06
5.03
4.92
4.76
4.58
5.42
5.40
5.29
5.13
4.95
6.14
6.14
6.03
5.88
5.69
6.86
6.86
6.77
6.62
6.44
7.58
7.58
7.51
7.37
7.19
8.31
8.31
8.25
8.12
7.94
9.03
9.03
8.99
8.86
8.69
0.30
0.40
0.50
0.60
0.70
1.31
1.16
1.03
0.921
0.829
1.62
1.43
1.28
1.14
1.03
1.94
1.72
1.54
1.38
1.25
2.27
2.03
1.81
1.63
1.48
2.61
2.34
2.10
1.90
1.73
2.96
2.66
2.40
2.18
1.99
3.31
2.99
2.71
2.47
2.26
3.67
3.33
3.03
2.77
2.54
4.03
3.68
3.36
3.08
2.84
4.39
4.03
3.70
3.41
3.15
4.75
4.37
4.03
3.72
3.46
5.49
5.08
4.70
4.37
4.08
6.23
5.82
5.41
5.04
4.72
6.99
6.57
6.15
5.76
5.40
7.75
7.32
6.90
6.49
6.11
8.50
8.09
7.66
7.23
6.84
0.80
0.90
1.00
1.20
1.40
0.751
0.685
0.629
0.538
0.469
0.935
0.854
0.785
0.674
0.589
1.13
1.04
0.956
0.822
0.720
1.35
1.24
1.14
0.985
0.864
1.58
1.45
1.34
1.16
1.02
1.82
1.68
1.56
1.35
1.19
2.08
1.92
1.78
1.56
1.38
2.35
2.18
2.03
1.78
1.58
2.63
2.45
2.29
2.01
1.79
2.93
2.73
2.55
2.25
2.00
3.22
3.00
2.81
2.49
2.22
3.81
3.57
3.35
2.98
2.67
4.43
4.17
3.93
3.51
3.16
5.08
4.79
4.53
4.07
3.68
5.77
5.45
5.16
4.66
4.23
6.47
6.14
5.83
5.28
4.81
1.60
1.80
2.00
2.20
2.40
0.416
0.373
0.338
0.308
0.284
0.522
0.468
0.424
0.388
0.357
0.639
0.574
0.521
0.477
0.439
0.769
0.692
0.628
0.575
0.531
0.911
0.821
0.746
0.685
0.632
1.07
0.964
0.879
0.806
0.745
1.24
1.12
1.02
0.939
0.868
1.42
1.29
1.17
1.08
0.999
1.61
1.46
1.33
1.22
1.13
1.80
1.63
1.49
1.37
1.27
2.00
1.82
1.66
1.53
1.42
2.42
2.20
2.02
1.86
1.73
2.87
2.62
2.41
2.23
2.07
3.35
3.07
2.84
2.63
2.44
3.87
3.56
3.29
3.05
2.84
4.41
4.06
3.76
3.50
3.27
2.60 0.263 0.331 0.407 0.492 0.587 0.692 0.807 0.928 1.05 1.18
2.80 0.245 0.308 0.379 0.458 0.548 0.646 0.753 0.867 0.983 1.10
3.00 0.229 0.288 0.355 0.429 0.513 0.606 0.707 0.814 0.922 1.04
1.32
1.23
1.16
1.61
1.51
1.42
1.93
1.81
1.70
2.28
2.14
2.02
2.66
2.50
2.36
3.06
2.88
2.72
x
0.000 0.008 0.029 0.056 0.089 0.125 0.164 0.204 0.246 0.289 0.333 0.424 0.516 0.610 0.704 0.800
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
ECCENTRICALLY LOADED WELD GROUPS
8 - 191
Table 8-42 (cont.).
Coefficients C for Eccentrically Loaded Weld Groups
Angle = 60°°
φ R n = CC1Dl
C min =
Pu
D min =
C 1D l
Pu
lmin =
CC 1 l
Pu
CC 1 D
where
ex = a l
Pu = factored force, kips
D = number of sixteenths-of-an-inch
in the fillet weld size
l = characteristic length of weld group, in.
a = e x / l, in.
e x = horizontal component of eccentricity of
Pu with respect to centroid of weld group, in.
60°
l
Pu
C = coefficient tabulated below which includes φ = 0.75
C 1 = electode strength coefficient from Table 8-37
(1.0 for E70XX electrodes)
c.g.
xl
kl
k
a
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.2
1.4
1.6
1.8
2.0
0.00
0.10
0.15
0.20
0.25
1.95
1.82
1.73
1.63
1.55
2.28
2.15
2.05
1.96
1.87
2.61
2.48
2.38
2.28
2.18
2.94
2.82
2.71
2.61
2.50
3.26
3.16
3.06
2.94
2.83
3.59
3.51
3.41
3.29
3.17
3.92
3.86
3.76
3.65
3.53
4.25
4.21
4.12
4.01
3.89
4.57
4.56
4.47
4.37
4.25
4.90
4.90
4.83
4.73
4.62
5.23
5.24
5.18
5.09
4.98
5.88
5.88
5.87
5.80
5.70
6.54
6.54
6.54
6.49
6.41
7.19
7.19
7.19
7.18
7.11
7.85
7.85
7.85
7.85
7.79
8.51
8.51
8.51
8.51
8.47
0.30
0.40
0.50
0.60
0.70
1.47
1.34
1.22
1.12
1.03
1.78
1.62
1.48
1.36
1.25
2.09
1.91
1.75
1.61
1.49
2.40
2.20
2.03
1.88
1.74
2.72
2.51
2.32
2.15
2.00
3.05
2.83
2.63
2.44
2.28
3.40
3.16
2.95
2.75
2.58
3.76
3.52
3.28
3.07
2.89
4.13
3.88
3.63
3.41
3.22
4.50
4.24
4.00
3.76
3.56
4.87
4.61
4.36
4.13
3.91
5.60
5.36
5.10
4.86
4.62
6.32
6.09
5.84
5.59
5.33
7.02
6.82
6.57
6.32
6.05
7.72
7.53
7.30
7.03
6.78
8.40
8.23
8.01
7.75
7.50
0.80
0.90
1.00
1.20
1.40
0.945
0.874
0.812
0.709
0.626
1.16
1.07
0.999
0.875
0.776
1.38
1.28
1.20
1.06
0.939
1.62
1.51
1.41
1.25
1.12
1.87
1.75
1.64
1.46
1.31
2.14
2.01
1.89
1.69
1.52
2.42
2.28
2.15
1.93
1.75
2.72
2.57
2.43
2.19
1.98
3.04
2.87
2.72
2.46
2.23
3.36
3.18
3.02
2.74
2.49
3.70
3.51
3.34
3.03
2.76
4.39
4.17
3.97
3.62
3.31
5.09
4.85
4.63
4.23
3.89
5.80
5.55
5.32
4.89
4.50
6.52
6.26
6.02
5.56
5.15
7.24
6.98
6.73
6.26
5.82
1.60
1.80
2.00
2.20
2.40
0.560
0.506
0.461
0.423
0.391
0.696
0.630
0.575
0.528
0.489
0.845
0.766
0.701
0.645
0.597
1.01
0.916
0.839
0.774
0.718
1.18
1.08
0.993
0.917
0.851
1.38
1.26
1.16
1.07
0.999
1.59
1.46
1.34
1.24
1.16
1.81
1.66
1.53
1.42
1.33
2.04
1.88
1.74
1.61
1.51
2.28
2.11
1.95
1.81
1.69
2.54
2.34
2.17
2.02
1.89
3.05
2.82
2.62
2.44
2.29
3.59
3.33
3.11
2.90
2.72
4.17
3.88
3.62
3.39
3.19
4.79
4.46
4.17
3.91
3.68
5.43
5.07
4.75
4.47
4.21
2.60 0.363 0.454 0.556 0.669 0.794 0.932 1.08 1.24
2.80 0.339 0.424 0.519 0.625 0.744 0.875 1.02 1.17
3.00 0.317 0.398 0.488 0.587 0.700 0.824 0.956 1.10
1.41
1.33
1.25
1.59
1.49
1.41
1.77
1.66
1.57
2.15
2.02
1.91
2.56
2.42
2.29
3.01
2.84
2.69
3.48
3.29
3.12
3.98
3.77
3.58
x
0.000 0.008 0.029 0.056 0.089 0.125 0.164 0.204 0.246 0.289 0.333 0.424 0.516 0.610 0.704 0.800
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
8 - 192
BOLTS, WELDS, AND CONNECTED ELEMENTS
Table 8-42 (cont.).
Coefficients C for Eccentrically Loaded Weld Groups
Angle = 75°°
φ R n = CC1Dl
C min =
Pu
D min =
C 1D l
Pu
lmin =
CC 1 l
Pu
CC 1 D
where
ex = a l
Pu = factored force, kips
D = number of sixteenths-of-an-inch
in the fillet weld size
l = characteristic length of weld group, in.
a = e x / l, in.
e x = horizontal component of eccentricity of
Pu with respect to centroid of weld group, in.
75°
Pu
l
c.g.
C = coefficient tabulated below which includes φ = 0.75
C 1 = electode strength coefficient from Table 8-37
(1.0 for E70XX electrodes)
xl
kl
k
a
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.2
1.4
1.6
1.8
2.0
0.00
0.10
0.15
0.20
0.25
2.05
1.94
1.88
1.82
1.76
2.35
2.22
2.15
2.09
2.04
2.65
2.51
2.44
2.38
2.32
2.94
2.81
2.75
2.69
2.63
3.24
3.13
3.07
3.01
2.95
3.54
3.44
3.39
3.33
3.27
3.83
3.75
3.70
3.65
3.60
4.13
4.05
4.01
3.97
3.92
4.43
4.35
4.32
4.29
4.24
4.72
4.65
4.63
4.60
4.56
5.02
4.94
4.93
4.90
4.87
5.61
5.53
5.52
5.50
5.47
6.21
6.11
6.10
6.09
6.07
6.80
6.68
6.68
6.67
6.66
7.39
7.26
7.26
7.25
7.24
7.99
7.83
7.83
7.83
7.82
0.30
0.40
0.50
0.60
0.70
1.71
1.62
1.53
1.46
1.38
1.99
1.89
1.80
1.71
1.63
2.27
2.16
2.07
1.97
1.89
2.57
2.46
2.35
2.25
2.16
2.89
2.77
2.65
2.55
2.45
3.21
3.09
2.98
2.86
2.76
3.54
3.42
3.31
3.19
3.08
3.87
3.76
3.64
3.53
3.42
4.19
4.09
3.98
3.87
3.76
4.51
4.41
4.31
4.21
4.10
4.83
4.73
4.64
4.54
4.44
5.44
5.36
5.27
5.19
5.11
6.05
5.98
5.90
5.83
5.75
6.64
6.58
6.51
6.44
6.38
7.23
7.18
7.11
7.04
6.99
7.81
7.77
7.71
7.64
7.59
0.80
0.90
1.00
1.20
1.40
1.31
1.25
1.19
1.09
0.994
1.56
1.49
1.42
1.30
1.20
1.81
1.73
1.66
1.53
1.41
2.07
1.99
1.91
1.77
1.65
2.35
2.27
2.18
2.03
1.90
2.66
2.56
2.47
2.31
2.16
2.98
2.88
2.78
2.60
2.44
3.31
3.21
3.10
2.91
2.74
3.65
3.54
3.44
3.24
3.05
3.99
3.89
3.78
3.57
3.38
4.34
4.23
4.13
3.92
3.71
5.01
4.92
4.82
4.61
4.40
5.67
5.59
5.49
5.30
5.09
6.31
6.24
6.16
5.98
5.78
6.93
6.87
6.80
6.64
6.46
7.54
7.48
7.43
7.29
7.13
1.60
1.80
2.00
2.20
2.40
0.914
0.845
0.784
0.730
0.683
1.11
1.03
0.956
0.894
0.838
1.31
1.22
1.14
1.07
1.01
1.53
1.43
1.34
1.26
1.19
1.77
1.66
1.56
1.47
1.39
2.03
1.91
1.80
1.70
1.61
2.30
2.16
2.04
1.94
1.84
2.58
2.44
2.31
2.19
2.08
2.88
2.73
2.58
2.45
2.33
3.20
3.03
2.88
2.73
2.60
3.52
3.35
3.18
3.03
2.89
4.20
4.00
3.82
3.65
3.49
4.89
4.68
4.49
4.30
4.12
5.58
5.38
5.18
4.97
4.77
6.27
6.07
5.86
5.65
5.43
6.94
6.76
6.55
6.33
6.11
2.60 0.641 0.788 0.949 1.13
2.80 0.604 0.744 0.897 1.07
3.00 0.570 0.704 0.851 1.01
1.32
1.25
1.19
1.53
1.45
1.38
1.75
1.66
1.59
1.98
1.89
1.80
2.22
2.12
2.03
2.48
2.37
2.27
2.76
2.63
2.52
3.34
3.20
3.07
3.95
3.78
3.63
4.58
4.39
4.23
5.23
5.04
4.85
5.90
5.70
5.50
x
0.000 0.008 0.029 0.056 0.089 0.125 0.164 0.204 0.246 0.289 0.333 0.424 0.516 0.610 0.704 0.800
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
ECCENTRICALLY LOADED WELD GROUPS
8 - 193
Table 8-43.
Coefficients C for Eccentrically Loaded Weld Groups
Angle = 0°°
φ R n = CC1Dl
C min =
Pu
D min =
C 1D l
Pu
lmin =
CC 1 l
Pu
CC 1 D
where
ex = a l
Pu = factored force, kips
D = number of sixteenths-of-an-inch
in the fillet weld size
l = characteristic length of weld group, in.
a = e x / l, in.
e x = horizontal component of eccentricity of
Pu with respect to centroid of weld group, in.
Pu
l
c.g.
C = coefficient tabulated below which includes φ = 0.75
C 1 = electode strength coefficient from Table 8-37
(1.0 for E70XX electrodes)
kl
xl
k
a
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.2
1.4
1.6
1.8
2.0
0.00
0.10
0.15
0.20
0.25
1.39
1.39
1.38
1.32
1.24
1.81
1.72
1.70
1.63
1.55
2.23
2.10
2.05
1.96
1.86
2.65
2.48
2.41
2.31
2.18
3.06
2.86
2.77
2.65
2.51
3.48
3.24
3.13
2.99
2.84
3.90
3.62
3.50
3.34
3.17
4.32
4.00
3.86
3.68
3.50
4.73
4.38
4.22
4.03
3.83
5.15
4.76
4.58
4.38
4.16
5.57
5.13
4.94
4.72
4.50
6.40
5.88
5.66
5.42
5.17
7.24
6.63
6.38
6.12
5.86
8.07
7.37
7.11
6.83
6.55
8.91
8.12
7.84
7.55
7.25
9.74
8.87
8.57
8.27
7.96
0.30
0.40
0.50
0.60
0.70
1.16
0.998
0.860
0.748
0.659
1.45
1.26
1.08
0.942
0.828
1.75
1.52
1.31
1.14
1.00
2.05
1.79
1.56
1.35
1.20
2.36
2.08
1.81
1.58
1.41
2.68
2.36
2.07
1.83
1.63
2.99
2.65
2.34
2.07
1.86
3.31
2.94
2.60
2.32
2.10
3.63
3.24
2.88
2.58
2.34
3.95
3.54
3.15
2.84
2.58
4.27
3.84
3.44
3.11
2.83
4.93
4.46
4.02
3.66
3.35
5.60
5.09
4.63
4.23
3.90
6.27
5.74
5.25
4.83
4.47
6.96
6.41
5.89
5.45
5.06
7.66
7.08
6.55
6.08
5.67
0.80
0.90
1.00
1.20
1.40
0.586
0.527
0.478
0.403
0.348
0.735
0.661
0.599
0.505
0.436
0.895
0.807
0.734
0.621
0.537
1.07
0.971
0.885
0.751
0.651
1.27
1.15
1.05
0.893
0.776
1.47
1.34
1.23
1.05
0.912
1.69
1.54
1.41
1.21
1.06
1.91
1.75
1.61
1.38
1.21
2.13
1.96
1.81
1.56
1.37
2.36
2.18
2.01
1.75
1.54
2.60
2.40
2.22
1.94
1.71
3.09
2.86
2.66
2.33
2.07
3.61
3.35
3.13
2.75
2.45
4.15
3.87
3.62
3.20
2.86
4.72
4.41
4.14
3.68
3.30
5.30
4.97
4.68
4.17
3.75
1.60
1.80
2.00
2.20
2.40
0.305
0.272
0.245
0.223
0.205
0.383
0.341
0.308
0.280
0.257
0.472
0.422
0.381
0.347
0.318
0.574
0.512
0.463
0.422
0.388
0.685
0.613
0.554
0.506
0.465
0.806
0.722
0.654
0.597
0.548
0.936
0.839
0.760
0.694
0.639
1.07
0.963
0.873
0.798
0.735
1.22
1.10
0.993
0.909
0.836
1.37
1.23
1.12
1.02
0.942
1.53
1.38
1.25
1.15
1.06
1.86
1.68
1.53
1.41
1.30
2.21
2.00
1.84
1.69
1.56
2.58
2.35
2.15
1.99
1.85
2.98
2.72
2.50
2.31
2.15
3.41
3.11
2.87
2.65
2.47
2.60 0.189 0.238 0.294 0.358 0.430 0.508 0.592 0.681 0.773 0.872 0.976 1.20
2.80 0.176 0.221 0.274 0.333 0.400 0.472 0.550 0.633 0.720 0.811 0.908 1.12
3.00 0.164 0.207 0.256 0.311 0.374 0.442 0.515 0.593 0.673 0.758 0.850 1.05
1.46
1.36
1.27
1.72
1.61
1.51
2.00
1.88
1.76
2.30
2.16
2.03
x
0.000 0.008 0.029 0.056 0.089 0.125 0.164 0.204 0.246 0.289 0.333 0.424 0.516 0.610 0.704 0.800
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
8 - 194
BOLTS, WELDS, AND CONNECTED ELEMENTS
Table 8-43 (cont.).
Coefficients C for Eccentrically Loaded Weld Groups
Angle = 15°°
φ R n = CC1Dl
C min =
Pu
D min =
C 1D l
Pu
lmin =
CC 1 l
Pu
CC 1 D
where
ex = a l
Pu = factored force, kips
D = number of sixteenths-of-an-inch
in the fillet weld size
l = characteristic length of weld group, in.
a = e x / l, in.
e x = horizontal component of eccentricity of
Pu with respect to centroid of weld group, in.
15°
Pu
l
c.g.
C = coefficient tabulated below which includes φ = 0.75
C 1 = electode strength coefficient from Table 8-37
(1.0 for E70XX electrodes)
xl
kl
k
a
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.2
1.4
1.6
1.8
2.0
0.00
0.10
0.15
0.20
0.25
1.48
1.42
1.38
1.32
1.24
1.89
1.77
1.73
1.65
1.55
2.31
2.15
2.09
1.99
1.87
2.72
2.53
2.45
2.33
2.20
3.13
2.91
2.80
2.67
2.53
3.54
3.29
3.16
3.01
2.85
3.95
3.66
3.52
3.35
3.17
4.36
4.04
3.87
3.69
3.50
4.77
4.41
4.22
4.03
3.82
5.18
4.78
4.58
4.36
4.15
5.59
5.14
4.93
4.70
4.47
6.41
5.89
5.64
5.38
5.13
7.23
6.63
6.36
6.08
5.80
8.05
7.38
7.08
6.78
6.49
8.87
8.14
7.81
7.49
7.18
9.69
8.90
8.54
8.21
7.89
0.30
0.40
0.50
0.60
0.70
1.16
1.00
0.869
0.759
0.670
1.45
1.25
1.09
0.950
0.838
1.75
1.51
1.31
1.14
1.01
2.06
1.78
1.55
1.35
1.20
2.37
2.06
1.80
1.58
1.41
2.68
2.35
2.05
1.81
1.62
3.00
2.64
2.32
2.06
1.86
3.31
2.94
2.60
2.33
2.10
3.62
3.23
2.88
2.59
2.35
3.93
3.53
3.17
2.87
2.61
4.25
3.82
3.45
3.14
2.87
4.89
4.43
4.03
3.69
3.40
5.54
5.05
4.63
4.27
3.95
6.21
5.69
5.25
4.86
4.52
6.89
6.35
5.89
5.47
5.10
7.58
7.03
6.54
6.11
5.71
0.80
0.90
1.00
1.20
1.40
0.598
0.539
0.490
0.413
0.357
0.747
0.672
0.611
0.516
0.446
0.905
0.818
0.746
0.633
0.548
1.08
0.980
0.896
0.763
0.663
1.27
1.15
1.06
0.905
0.789
1.47
1.34
1.23
1.06
0.925
1.68
1.54
1.42
1.22
1.07
1.91
1.75
1.61
1.39
1.22
2.15
1.97
1.82
1.58
1.39
2.39
2.20
2.04
1.77
1.56
2.64
2.44
2.26
1.97
1.74
3.14
2.92
2.72
2.39
2.12
3.66
3.41
3.19
2.82
2.52
4.21
3.94
3.69
3.27
2.93
4.77
4.48
4.21
3.75
3.38
5.36
5.04
4.75
4.25
3.84
1.60
1.80
2.00
2.20
2.40
0.314
0.280
0.253
0.230
0.211
0.393
0.351
0.317
0.289
0.265
0.484
0.432
0.391
0.356
0.327
0.586
0.524
0.474
0.433
0.398
0.698
0.626
0.567
0.518
0.476
0.820
0.737
0.668
0.611
0.562
0.951
0.854
0.776
0.710
0.654
1.09
0.981
0.891
0.816
0.753
1.24
1.11
1.01
0.929
0.857
1.39
1.26
1.14
1.05
0.967
1.56
1.41
1.28
1.18
1.09
1.91
1.73
1.58
1.45
1.34
2.27
2.06
1.89
1.74
1.61
2.65
2.42
2.22
2.05
1.90
3.06
2.80
2.57
2.38
2.21
3.49
3.19
2.95
2.73
2.54
2.60 0.195 0.245 0.303 0.368 0.441 0.521 0.606 0.698 0.795 0.898 1.01 1.24
2.80 0.182 0.228 0.282 0.343 0.410 0.485 0.565 0.650 0.741 0.837 0.937 1.16
3.00 0.170 0.213 0.263 0.320 0.384 0.453 0.528 0.609 0.694 0.782 0.877 1.08
1.50
1.40
1.31
1.77
1.66
1.56
2.06
1.93
1.82
2.37
2.23
2.10
x
0.000 0.008 0.029 0.056 0.089 0.125 0.164 0.204 0.246 0.289 0.333 0.424 0.516 0.610 0.704 0.800
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
ECCENTRICALLY LOADED WELD GROUPS
8 - 195
Table 8-43 (cont.).
Coefficients C for Eccentrically Loaded Weld Groups
Angle = 30°°
φ R n = CC1Dl
C min =
Pu
D min =
C 1D l
Pu
lmin =
CC 1 l
Pu
CC 1 D
where
Pu = factored force, kips
ex = a l
D = number of sixteenths-of-an-inch
in the fillet weld size
l = characteristic length of weld group, in.
a = e x / l, in.
e x = horizontal component of eccentricity of
Pu with respect to centroid of weld group, in.
30°
Pu
l
c.g.
C = coefficient tabulated below which includes φ = 0.75
C 1 = electode strength coefficient from Table 8-37
(1.0 for E70XX electrodes)
xl
kl
k
a
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.2
1.4
1.6
1.8
2.0
0.00
0.10
0.15
0.20
0.25
1.64
1.52
1.44
1.36
1.28
2.03
1.92
1.81
1.70
1.60
2.42
2.30
2.17
2.04
1.91
2.81
2.66
2.53
2.37
2.22
3.20
3.02
2.87
2.70
2.53
3.59
3.38
3.21
3.02
2.83
3.98
3.74
3.55
3.35
3.14
4.37
4.10
3.90
3.67
3.45
4.76
4.46
4.24
4.00
3.77
5.15
4.83
4.59
4.34
4.09
5.54
5.19
4.94
4.68
4.42
6.33
5.93
5.66
5.37
5.10
7.11
6.67
6.39
6.09
5.79
7.89
7.43
7.13
6.82
6.51
8.67
8.19
7.88
7.56
7.24
9.45
8.96
8.64
8.32
8.00
0.30
0.40
0.50
0.60
0.70
1.20
1.05
0.921
0.812
0.722
1.49
1.30
1.14
1.01
0.895
1.79
1.56
1.36
1.20
1.07
2.08
1.82
1.59
1.41
1.26
2.37
2.08
1.83
1.63
1.47
2.66
2.35
2.09
1.87
1.69
2.96
2.63
2.35
2.12
1.93
3.25
2.92
2.63
2.39
2.17
3.56
3.22
2.92
2.66
2.43
3.89
3.52
3.21
2.94
2.70
4.21
3.84
3.51
3.23
2.98
4.86
4.46
4.12
3.82
3.55
5.53
5.10
4.73
4.41
4.11
6.23
5.77
5.37
5.01
4.69
6.95
6.45
6.03
5.64
5.30
7.68
7.15
6.70
6.30
5.93
0.80
0.90
1.00
1.20
1.40
0.647
0.586
0.535
0.454
0.393
0.803
0.726
0.663
0.563
0.489
0.966
0.878
0.805
0.687
0.599
1.15
1.05
0.960
0.825
0.721
1.34
1.23
1.13
0.973
0.855
1.54
1.42
1.31
1.13
0.997
1.76
1.62
1.50
1.30
1.15
2.00
1.84
1.71
1.48
1.31
2.24
2.07
1.92
1.68
1.49
2.49
2.31
2.15
1.88
1.67
2.75
2.56
2.39
2.10
1.86
3.30
3.08
2.88
2.55
2.28
3.85
3.61
3.39
3.02
2.72
4.41
4.15
3.91
3.50
3.16
4.99
4.71
4.45
4.01
3.63
5.60
5.30
5.02
4.53
4.12
1.60
1.80
2.00
2.20
2.40
0.347
0.310
0.280
0.255
0.234
0.432
0.386
0.349
0.319
0.293
0.530
0.475
0.430
0.393
0.361
0.639
0.574
0.521
0.476
0.439
0.760
0.684
0.620
0.568
0.524
0.890
0.802
0.729
0.668
0.616
1.03
0.928
0.846
0.776
0.716
1.18
1.06
0.969
0.890
0.823
1.33
1.21
1.10
1.01
0.936
1.50
1.36
1.24
1.14
1.06
1.68
1.52
1.39
1.28
1.19
2.06
1.87
1.71
1.58
1.46
2.46
2.25
2.06
1.91
1.77
2.88
2.63
2.42
2.25
2.09
3.31
3.04
2.80
2.60
2.42
3.77
3.47
3.21
2.98
2.78
2.60 0.217 0.271 0.335 0.406 0.486 0.572 0.665 0.765 0.870 0.983 1.10 1.36
2.80 0.201 0.252 0.311 0.378 0.453 0.534 0.621 0.714 0.813 0.919 1.03 1.28
3.00 0.188 0.236 0.291 0.354 0.424 0.500 0.582 0.669 0.763 0.862 0.967 1.20
1.65
1.55
1.45
1.95
1.83
1.72
2.27
2.13
2.00
2.60
2.45
2.31
x
0.000 0.008 0.029 0.056 0.089 0.125 0.164 0.204 0.246 0.289 0.333 0.424 0.516 0.610 0.704 0.800
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
8 - 196
BOLTS, WELDS, AND CONNECTED ELEMENTS
Table 8-43 (cont.).
Coefficients C for Eccentrically Loaded Weld Groups
Angle = 45°°
φ R n = CC1Dl
C min =
Pu
D min =
C 1D l
Pu
lmin =
CC 1 l
Pu
CC 1 D
where
ex = a l
Pu = factored force, kips
D = number of sixteenths-of-an-inch
in the fillet weld size
l = characteristic length of weld group, in.
a = e x / l, in.
e x = horizontal component of eccentricity of
Pu with respect to centroid of weld group, in.
45°
Pu
l
c.g.
C = coefficient tabulated below which includes φ = 0.75
C 1 = electode strength coefficient from Table 8-37
(1.0 for E70XX electrodes)
xl
kl
k
a
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.2
1.4
1.6
1.8
2.0
0.00
0.10
0.15
0.20
0.25
1.81
1.68
1.57
1.47
1.39
2.17
2.04
1.93
1.81
1.70
2.53
2.38
2.25
2.12
1.99
2.89
2.71
2.56
2.41
2.27
3.25
3.04
2.86
2.69
2.53
3.61
3.37
3.18
2.99
2.82
3.97
3.71
3.51
3.30
3.12
4.33
4.06
3.85
3.64
3.44
4.70
4.41
4.19
3.98
3.77
5.06
4.77
4.55
4.33
4.12
5.42
5.12
4.91
4.69
4.47
6.14
5.84
5.64
5.41
5.18
6.86
6.56
6.37
6.14
5.92
7.58
7.30
7.10
6.88
6.66
8.31
8.03
7.85
7.63
7.40
9.03
8.76
8.59
8.38
8.15
0.30
0.40
0.50
0.60
0.70
1.31
1.16
1.03
0.921
0.829
1.60
1.41
1.26
1.13
1.02
1.88
1.67
1.48
1.33
1.20
2.14
1.91
1.71
1.55
1.41
2.40
2.16
1.96
1.78
1.63
2.68
2.43
2.22
2.03
1.86
2.97
2.71
2.49
2.29
2.11
3.28
3.01
2.77
2.55
2.37
3.60
3.31
3.06
2.84
2.63
3.94
3.63
3.37
3.13
2.91
4.28
3.96
3.68
3.43
3.21
4.98
4.64
4.34
4.06
3.82
5.70
5.33
5.02
4.72
4.45
6.42
6.03
5.70
5.38
5.09
7.17
6.74
6.38
6.06
5.75
7.92
7.46
7.09
6.75
6.42
0.80
0.90
1.00
1.20
1.40
0.751
0.685
0.629
0.538
0.469
0.920
0.840
0.772
0.664
0.581
1.10
1.01
0.930
0.804
0.706
1.29
1.19
1.10
0.957
0.845
1.50
1.38
1.28
1.12
0.995
1.72
1.59
1.48
1.30
1.16
1.95
1.81
1.69
1.49
1.33
2.20
2.05
1.92
1.69
1.51
2.46
2.30
2.15
1.91
1.71
2.72
2.55
2.40
2.13
1.91
3.00
2.82
2.65
2.37
2.13
3.59
3.38
3.19
2.87
2.59
4.21
3.98
3.77
3.40
3.09
4.82
4.58
4.35
3.95
3.60
5.46
5.20
4.95
4.50
4.12
6.12
5.83
5.57
5.09
4.67
1.60
1.80
2.00
2.20
2.40
0.416
0.373
0.338
0.308
0.284
0.515
0.463
0.420
0.384
0.354
0.629
0.566
0.515
0.471
0.435
0.754
0.681
0.621
0.569
0.526
0.892
0.807
0.736
0.677
0.626
1.04
0.943
0.862
0.793
0.734
1.20
1.09
0.995
0.918
0.850
1.36
1.24
1.14
1.05
0.974
1.54
1.41
1.29
1.19
1.11
1.73
1.58
1.45
1.34
1.25
1.93
1.77
1.62
1.50
1.40
2.36
2.17
2.00
1.85
1.72
2.82
2.60
2.40
2.23
2.08
3.31
3.05
2.83
2.64
2.46
3.80
3.52
3.27
3.05
2.85
4.31
4.00
3.73
3.48
3.27
2.60 0.263 0.328 0.403 0.488 0.582 0.683 0.792 0.909 1.03 1.16
2.80 0.245 0.306 0.376 0.455 0.543 0.639 0.741 0.851 0.966 1.09
3.00 0.229 0.286 0.352 0.427 0.510 0.600 0.697 0.799 0.910 1.03
1.31
1.22
1.15
1.61
1.51
1.43
1.95
1.83
1.73
2.31
2.17
2.05
2.68
2.53
2.39
3.07
2.90
2.74
x
0.000 0.008 0.029 0.056 0.089 0.125 0.164 0.204 0.246 0.289 0.333 0.424 0.516 0.610 0.704 0.800
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
ECCENTRICALLY LOADED WELD GROUPS
8 - 197
Table 8-43 (cont.).
Coefficients C for Eccentrically Loaded Weld Groups
Angle = 60°°
φ R n = CC1Dl
C min =
Pu
D min =
C 1D l
Pu
lmin =
CC 1 l
Pu
CC 1 D
where
ex = a l
Pu = factored force, kips
D = number of sixteenths-of-an-inch
in the fillet weld size
l = characteristic length of weld group, in.
a = e x / l, in.
e x = horizontal component of eccentricity of
Pu with respect to centroid of weld group, in.
60°
Pu
l
c.g.
C = coefficient tabulated below which includes φ = 0.75
C 1 = electode strength coefficient from Table 8-37
(1.0 for E70XX electrodes)
xl
kl
k
a
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.2
1.4
1.6
1.8
2.0
0.00
0.10
0.15
0.20
0.25
1.95
1.83
1.73
1.63
1.55
2.28
2.13
2.03
1.93
1.84
2.61
2.42
2.30
2.19
2.09
2.94
2.72
2.58
2.45
2.34
3.26
3.03
2.88
2.74
2.62
3.59
3.36
3.19
3.04
2.92
3.92
3.69
3.52
3.36
3.23
4.25
4.03
3.86
3.69
3.55
4.57
4.37
4.20
4.03
3.88
4.90
4.71
4.55
4.38
4.22
5.23
5.05
4.89
4.73
4.56
5.88
5.73
5.59
5.43
5.26
6.54
6.41
6.27
6.13
5.97
7.19
7.08
6.96
6.82
6.67
7.85
7.74
7.63
7.51
7.37
8.51
8.40
8.31
8.19
8.06
0.30
0.40
0.50
0.60
0.70
1.47
1.34
1.22
1.12
1.03
1.76
1.60
1.46
1.34
1.23
2.00
1.84
1.69
1.56
1.44
2.25
2.08
1.93
1.79
1.67
2.52
2.34
2.18
2.04
1.91
2.81
2.62
2.45
2.30
2.16
3.12
2.91
2.73
2.57
2.42
3.43
3.22
3.04
2.86
2.70
3.76
3.54
3.35
3.16
3.00
4.09
3.87
3.67
3.48
3.30
4.42
4.20
3.99
3.80
3.62
5.11
4.87
4.66
4.46
4.27
5.80
5.54
5.33
5.14
4.94
6.51
6.23
6.01
5.81
5.62
7.22
6.91
6.69
6.49
6.30
7.93
7.61
7.37
7.16
6.98
0.80
0.90
1.00
1.20
1.40
0.945
0.874
0.812
0.709
0.626
1.14
1.06
0.983
0.862
0.766
1.34
1.25
1.17
1.03
0.922
1.55
1.45
1.37
1.21
1.09
1.79
1.68
1.58
1.41
1.27
2.03
1.91
1.81
1.62
1.46
2.29
2.16
2.05
1.84
1.67
2.56
2.42
2.30
2.08
1.89
2.84
2.70
2.57
2.33
2.13
3.14
2.98
2.84
2.59
2.37
3.45
3.28
3.13
2.86
2.63
4.08
3.91
3.75
3.44
3.18
4.75
4.56
4.39
4.06
3.76
5.42
5.24
5.05
4.70
4.38
6.10
5.91
5.73
5.36
5.02
6.79
6.60
6.41
6.03
5.66
1.60
1.80
2.00
2.20
2.40
0.560
0.506
0.461
0.423
0.391
0.688
0.623
0.569
0.524
0.484
0.831
0.756
0.692
0.638
0.591
0.988
0.901
0.828
0.765
0.710
1.16
1.06
0.975
0.902
0.840
1.34
1.23
1.13
1.05
0.979
1.53
1.41
1.30
1.21
1.13
1.74
1.60
1.48
1.38
1.29
1.95
1.80
1.67
1.56
1.46
2.18
2.02
1.88
1.75
1.64
2.43
2.25
2.09
1.95
1.83
2.94
2.73
2.55
2.39
2.24
3.50
3.26
3.05
2.86
2.69
4.08
3.82
3.58
3.37
3.17
4.70
4.41
4.14
3.90
3.69
5.32
5.00
4.71
4.45
4.21
2.60 0.363 0.451 0.551 0.662 0.785 0.916 1.06 1.21
2.80 0.339 0.421 0.515 0.620 0.736 0.861 0.994 1.14
3.00 0.317 0.395 0.484 0.584 0.693 0.812 0.939 1.07
1.37
1.29
1.22
1.54
1.45
1.37
1.72
1.62
1.53
2.11
2.00
1.89
2.54
2.40
2.28
3.00
2.85
2.70
3.49
3.31
3.15
3.99
3.79
3.60
x
0.000 0.008 0.029 0.056 0.089 0.125 0.164 0.204 0.246 0.289 0.333 0.424 0.516 0.610 0.704 0.800
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
8 - 198
BOLTS, WELDS, AND CONNECTED ELEMENTS
Table 8-43 (cont.).
Coefficients C for Eccentrically Loaded Weld Groups
Angle = 75°°
φ R n = CC1Dl
C min =
Pu
D min =
C 1D l
Pu
lmin =
CC 1 l
Pu
CC 1 D
where
ex = a l
Pu = factored force, kips
D = number of sixteenths-of-an-inch
in the fillet weld size
l = characteristic length of weld group, in.
a = e x / l, in.
e x = horizontal component of eccentricity of
Pu with respect to centroid of weld group, in.
75°
Pu
l
c.g.
C = coefficient tabulated below which includes φ = 0.75
C 1 = electode strength coefficient from Table 8-37
(1.0 for E70XX electrodes)
xl
kl
k
a
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.2
1.4
1.6
1.8
2.0
0.00
0.10
0.15
0.20
0.25
2.05
1.94
1.88
1.82
1.76
2.35
2.21
2.14
2.07
2.01
2.65
2.48
2.40
2.32
2.26
2.94
2.77
2.67
2.59
2.53
3.24
3.06
2.96
2.88
2.82
3.54
3.37
3.26
3.18
3.11
3.83
3.68
3.58
3.48
3.41
4.13
3.99
3.89
3.78
3.71
4.43
4.31
4.20
4.10
4.02
4.72
4.60
4.51
4.42
4.32
5.02
4.88
4.82
4.73
4.63
5.61
5.46
5.42
5.35
5.26
6.21
6.04
6.00
5.96
5.88
6.80
6.61
6.58
6.54
6.49
7.39
7.19
7.16
7.12
7.08
7.99
7.77
7.74
7.70
7.67
0.30
0.40
0.50
0.60
0.70
1.71
1.62
1.53
1.46
1.38
1.95
1.86
1.77
1.69
1.61
2.20
2.10
2.01
1.93
1.85
2.47
2.36
2.27
2.18
2.09
2.76
2.65
2.55
2.45
2.36
3.05
2.95
2.84
2.74
2.65
3.36
3.25
3.15
3.05
2.95
3.66
3.56
3.46
3.36
3.26
3.96
3.86
3.77
3.67
3.57
4.26
4.16
4.07
3.98
3.89
4.56
4.46
4.38
4.29
4.21
5.17
5.06
4.98
4.91
4.83
5.79
5.66
5.58
5.51
5.44
6.42
6.26
6.17
6.10
6.05
7.03
6.88
6.76
6.69
6.64
7.62
7.49
7.35
7.28
7.22
0.80
0.90
1.00
1.20
1.40
1.31
1.25
1.19
1.09
0.994
1.54
1.47
1.40
1.29
1.18
1.77
1.70
1.63
1.50
1.39
2.01
1.94
1.87
1.73
1.61
2.28
2.19
2.12
1.98
1.85
2.56
2.47
2.39
2.24
2.10
2.85
2.76
2.68
2.51
2.36
3.16
3.07
2.98
2.80
2.64
3.48
3.38
3.29
3.11
2.94
3.79
3.70
3.60
3.42
3.24
4.11
4.02
3.93
3.74
3.56
4.75
4.66
4.57
4.39
4.21
5.37
5.29
5.21
5.04
4.86
5.98
5.92
5.84
5.69
5.52
6.58
6.52
6.46
6.32
6.17
7.17
7.13
7.07
6.95
6.80
1.60
1.80
2.00
2.20
2.40
0.914
0.845
0.784
0.730
0.683
1.10
1.02
0.947
0.886
0.832
1.29
1.21
1.13
1.06
0.996
1.50
1.41
1.32
1.25
1.18
1.73
1.63
1.53
1.45
1.37
1.97
1.86
1.75
1.66
1.57
2.23
2.10
1.99
1.89
1.79
2.50
2.36
2.24
2.13
2.03
2.78
2.64
2.50
2.38
2.27
3.08
2.93
2.78
2.65
2.53
3.39
3.23
3.07
2.93
2.80
4.02
3.85
3.68
3.53
3.38
4.68
4.50
4.33
4.16
3.99
5.34
5.16
4.98
4.81
4.64
6.00
5.82
5.65
5.47
5.29
6.65
6.49
6.31
6.13
5.96
2.60 0.641 0.782 0.940 1.11
2.80 0.604 0.738 0.890 1.06
3.00 0.570 0.699 0.844 1.00
1.30
1.23
1.17
1.49
1.42
1.36
1.71
1.62
1.55
1.93
1.84
1.76
2.17
2.07
1.98
2.42
2.31
2.22
2.68
2.57
2.46
3.24
3.11
2.99
3.84
3.70
3.56
4.47
4.31
4.16
5.12
4.95
4.79
5.78
5.61
5.44
x
0.000 0.008 0.029 0.056 0.089 0.125 0.164 0.204 0.246 0.289 0.333 0.424 0.516 0.610 0.704 0.800
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
ECCENTRICALLY LOADED WELD GROUPS
8 - 199
Table 8-44.
Coefficients C for Eccentrically Loaded Weld Groups
Angle = 0°°
φ R n = CC1Dl
C min =
Pu
D min =
C 1D l
Pu
lmin =
CC 1 l
Pu
CC 1 D
where
Pu = factored force, kips
ex = a l
Pu
yl
D = number of sixteenths-of-an-inch
in the fillet weld size
l = characteristic length of weld group, in.
a = e x / l, in.
e x = horizontal component of eccentricity of
Pu with respect to centroid of weld group, in.
l
c.g.
C = coefficient tabulated below which includes φ = 0.75
C 1 = electode strength coefficient from Table 8-37
(1.0 for E70XX electrodes)
xl
kl
k
a
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.2
1.4
1.6
1.8
2.0
0.00
0.10
0.15
0.20
0.25
1.39
1.39
1.38
1.32
1.24
1.60
1.53
1.52
1.47
1.39
1.81
1.71
1.69
1.63
1.55
2.02
1.90
1.87
1.80
1.71
2.23
2.09
2.05
1.98
1.88
2.44
2.29
2.24
2.15
2.04
2.65
2.48
2.43
2.33
2.21
2.85
2.68
2.62
2.52
2.39
3.06
2.88
2.82
2.70
2.57
3.27
3.08
3.01
2.89
2.74
3.48
3.29
3.21
3.08
2.93
3.90
3.70
3.61
3.46
3.30
4.32
4.11
4.01
3.85
3.68
4.73
4.52
4.42
4.25
4.06
5.15
4.94
4.83
4.65
4.46
5.57
5.35
5.26
5.05
4.85
0.30
0.40
0.50
0.60
0.70
1.16
0.998
0.860
0.748
0.659
1.30
1.12
0.965
0.840
0.739
1.45
1.25
1.08
0.935
0.822
1.61
1.39
1.20
1.04
0.913
1.77
1.54
1.32
1.15
1.01
1.92
1.68
1.46
1.27
1.12
2.08
1.82
1.60
1.40
1.24
2.25
1.97
1.73
1.53
1.36
2.42
2.13
1.87
1.66
1.48
2.59
2.29
2.02
1.80
1.61
2.77
2.45
2.17
1.94
1.74
3.13
2.79
2.50
2.24
2.03
3.50
3.15
2.84
2.57
2.34
3.88
3.51
3.19
2.90
2.66
4.26
3.89
3.55
3.26
3.00
4.65
4.27
3.92
3.62
3.35
0.80
0.90
1.00
1.20
1.40
0.586
0.527
0.478
0.403
0.348
0.658
0.591
0.536
0.452
0.389
0.732
0.658
0.597
0.503
0.433
0.813
0.731
0.663
0.558
0.481
0.901
0.811
0.736
0.620
0.535
1.00
0.900
0.818
0.690
0.596
1.11
0.999
0.909
0.769
0.665
1.22
1.11
1.01
0.856
0.743
1.34
1.21
1.11
0.947
0.824
1.45
1.32
1.21
1.04
0.904
1.58
1.44
1.32
1.13
0.990
1.85
1.69
1.56
1.35
1.18
2.14
1.97
1.82
1.58
1.39
2.45
2.26
2.10
1.83
1.62
2.77
2.57
2.40
2.10
1.86
3.11
2.90
2.71
2.38
2.12
1.60
1.80
2.00
2.20
2.40
0.305
0.272
0.245
0.223
0.205
0.342
0.305
0.275
0.250
0.229
0.381
0.339
0.306
0.278
0.255
0.423
0.377
0.340
0.309
0.284
0.470
0.419
0.378
0.344
0.316
0.525
0.468
0.423
0.385
0.354
0.586
0.524
0.473
0.431
0.396
0.655
0.585
0.529
0.483
0.443
0.728
0.652
0.590
0.539
0.495
0.800
0.717
0.649
0.593
0.546
0.877
0.787
0.713
0.652
0.600
1.05
0.941
0.854
0.780
0.719
1.24
1.11
1.01
0.927
0.855
1.44
1.30
1.19
1.09
1.00
1.67
1.51
1.38
1.26
1.17
1.91
1.73
1.58
1.45
1.34
2.60 0.189 0.212 0.236 0.262 0.292 0.327 0.366 0.410 0.458 0.505 0.555 0.667 0.792 0.933 1.09 1.25
2.80 0.176 0.197 0.219 0.244 0.271 0.304 0.340 0.381 0.426 0.470 0.517 0.621 0.739 0.870 1.01 1.17
3.00 0.164 0.184 0.204 0.228 0.254 0.284 0.318 0.356 0.398 0.440 0.483 0.581 0.692 0.815 0.950 1.10
x
y
0.000 0.005 0.017 0.035 0.057 0.083 0.113 0.144 0.178 0.213 0.250 0.327 0.408 0.492 0.579 0.667
0.500 0.455 0.417 0.385 0.357 0.333 0.313 0.294 0.278 0.263 0.250 0.227 0.208 0.192 0.179 0.167
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
8 - 200
BOLTS, WELDS, AND CONNECTED ELEMENTS
Table 8-44 (cont.).
Coefficients C for Eccentrically Loaded Weld Groups
Angle = ±15°°
φ R n = CC1Dl
C min =
Pu
D min =
C 1D l
Pu
lmin =
CC 1 l
Pu
CC 1 D
where
Pu = factored force, kips
ex = a l
D = number of sixteenths-of-an-inch
in the fillet weld size
l = characteristic length of weld group, in.
a = e x / l, in.
e x = horizontal component of eccentricity of
Pu with respect to centroid of weld group, in.
15°
yl
15°
c.g.
l
Pu
C = coefficient tabulated below which includes φ = 0.75
C 1 = electode strength coefficient from Table 8-37
(1.0 for E70XX electrodes)
xl
kl
k
a
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.2
1.4
1.6
1.8
2.0
0.00
0.10
0.15
0.20
0.25
1.48
1.42
1.38
1.32
1.24
1.69
1.56
1.53
1.48
1.39
1.89
1.73
1.69
1.63
1.55
2.10
1.90
1.85
1.78
1.69
2.31
2.09
2.03
1.94
1.85
2.51
2.28
2.20
2.11
2.00
2.72
2.47
2.39
2.28
2.16
2.92
2.67
2.57
2.46
2.33
3.13
2.88
2.76
2.64
2.50
3.33
3.09
2.95
2.82
2.67
3.54
3.30
3.15
3.00
2.85
3.95
3.73
3.54
3.38
3.21
4.36
4.17
3.95
3.77
3.59
4.77
4.59
4.37
4.16
3.97
5.18
5.02
4.80
4.57
4.36
5.59
5.45
5.23
4.97
4.76
0.30
0.40
0.50
0.60
0.70
1.16
1.00
0.869
0.759
0.670
1.31
1.13
0.978
0.854
0.753
1.46
1.27
1.09
0.953
0.840
1.60
1.41
1.22
1.06
0.936
1.74
1.53
1.34
1.18
1.04
1.89
1.66
1.46
1.29
1.15
2.04
1.80
1.59
1.41
1.26
2.20
1.94
1.72
1.53
1.37
2.36
2.09
1.85
1.65
1.48
2.53
2.25
2.00
1.79
1.61
2.70
2.41
2.15
1.93
1.74
3.05
2.74
2.47
2.23
2.03
3.42
3.09
2.80
2.55
2.33
3.79
3.45
3.15
2.89
2.65
4.18
3.83
3.51
3.24
2.99
4.57
4.21
3.88
3.60
3.34
0.80
0.90
1.00
1.20
1.40
0.598
0.539
0.490
0.413
0.357
0.672
0.605
0.550
0.464
0.401
0.749
0.675
0.613
0.517
0.446
0.834
0.750
0.681
0.574
0.496
0.927
0.834
0.758
0.639
0.552
1.03
0.925
0.842
0.712
0.616
1.13
1.02
0.933
0.791
0.686
1.23
1.12
1.03
0.878
0.764
1.34
1.23
1.12
0.964
0.841
1.46
1.33
1.23
1.06
0.921
1.58
1.45
1.34
1.15
1.01
1.85
1.71
1.58
1.36
1.20
2.14
1.98
1.84
1.60
1.41
2.45
2.28
2.12
1.86
1.64
2.78
2.59
2.42
2.13
1.89
3.12
2.91
2.73
2.41
2.15
1.60
1.80
2.00
2.20
2.40
0.314
0.280
0.253
0.230
0.211
0.352
0.314
0.283
0.258
0.237
0.392
0.350
0.315
0.287
0.263
0.436
0.389
0.351
0.319
0.293
0.485
0.433
0.391
0.356
0.327
0.542
0.484
0.437
0.398
0.366
0.605
0.541
0.489
0.446
0.410
0.675
0.604
0.546
0.499
0.458
0.745
0.668
0.606
0.554
0.510
0.818
0.735
0.666
0.609
0.561
0.897
0.806
0.731
0.669
0.616
1.07
0.962
0.875
0.801
0.738
1.26
1.14
1.04
0.950
0.877
1.47
1.33
1.21
1.11
1.03
1.70
1.54
1.41
1.29
1.20
1.94
1.77
1.62
1.49
1.38
2.60 0.195 0.219 0.243 0.271 0.302 0.338 0.379 0.424 0.472 0.520 0.571 0.685 0.814 0.957 1.12 1.28
2.80 0.182 0.203 0.226 0.252 0.281 0.314 0.352 0.394 0.439 0.484 0.532 0.639 0.759 0.894 1.04 1.20
3.00 0.170 0.190 0.211 0.235 0.262 0.294 0.329 0.368 0.411 0.453 0.498 0.598 0.711 0.838 0.977 1.13
x
y
0.000 0.005 0.017 0.035 0.057 0.083 0.113 0.144 0.178 0.213 0.250 0.327 0.408 0.492 0.579 0.667
0.500 0.455 0.417 0.385 0.357 0.333 0.313 0.294 0.278 0.263 0.250 0.227 0.208 0.192 0.179 0.167
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
ECCENTRICALLY LOADED WELD GROUPS
8 - 205
Table 8-45.
Coefficients C for Eccentrically Loaded Weld Groups
Angle = 0°°
φ R n = CC1Dl
C min =
Pu
D min =
C 1D l
Pu
Pu
lmin =
CC 1 l
CC 1 D
where
ex = a l
Pu = factored force, kips
D = number of sixteenths-of-an-inch
in the fillet weld size
l = characteristic length of weld group, in.
a = e x / l, in.
e x = horizontal component of eccentricity of
Pu with respect to centroid of weld group, in.
yl
Pu
l
c.g.
C = coefficient tabulated below which includes φ = 0.75
C 1 = electode strength coefficient from Table 8-37
(1.0 for E70XX electrodes)
xl
kl
k
a
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.2
1.4
1.6
1.8
2.0
0.00
0.10
0.15
0.20
0.25
1.39
1.39
1.38
1.32
1.24
1.60
1.55
1.53
1.47
1.38
1.81
1.74
1.71
1.63
1.52
2.02
1.93
1.88
1.79
1.66
2.23
2.12
2.06
1.94
1.80
2.44
2.31
2.22
2.09
1.94
2.65
2.49
2.38
2.23
2.07
2.85
2.66
2.54
2.37
2.21
3.06
2.83
2.69
2.52
2.35
3.27
2.99
2.83
2.67
2.51
3.48
3.14
2.98
2.81
2.66
3.90
3.45
3.28
3.12
2.96
4.32
3.76
3.59
3.42
3.27
4.73
4.08
3.91
3.75
3.59
5.15
4.42
4.24
4.08
3.91
5.57
4.76
4.58
4.41
4.25
0.30
0.40
0.50
0.60
0.70
1.16
0.998
0.860
0.748
0.659
1.29
1.11
0.958
0.833
0.733
1.42
1.22
1.05
0.913
0.805
1.54
1.32
1.14
0.998
0.884
1.67
1.42
1.24
1.09
0.967
1.79
1.54
1.34
1.18
1.06
1.92
1.66
1.46
1.29
1.15
2.06
1.80
1.58
1.41
1.26
2.20
1.94
1.72
1.54
1.38
2.35
2.09
1.86
1.67
1.51
2.51
2.24
2.01
1.81
1.64
2.82
2.55
2.31
2.10
1.92
3.12
2.85
2.61
2.40
2.21
3.44
3.16
2.91
2.69
2.50
3.76
3.48
3.22
2.99
2.79
4.10
3.81
3.54
3.31
3.09
0.80
0.90
1.00
1.20
1.40
0.586
0.527
0.478
0.403
0.348
0.652
0.586
0.532
0.448
0.387
0.719
0.648
0.589
0.497
0.430
0.791
0.715
0.651
0.551
0.476
0.868
0.786
0.717
0.609
0.528
0.951
0.864
0.791
0.674
0.586
1.04
0.949
0.870
0.744
0.648
1.14
1.04
0.957
0.820
0.716
1.25
1.15
1.05
0.904
0.790
1.37
1.26
1.16
0.997
0.874
1.50
1.38
1.27
1.10
0.963
1.77
1.63
1.51
1.31
1.16
2.05
1.90
1.77
1.55
1.37
2.32
2.17
2.03
1.80
1.60
2.61
2.44
2.29
2.04
1.83
2.90
2.73
2.57
2.30
2.07
1.60
1.80
2.00
2.20
2.40
0.305
0.272
0.245
0.223
0.205
0.340
0.303
0.273
0.249
0.228
0.378
0.337
0.304
0.277
0.254
0.419
0.374
0.338
0.308
0.283
0.466
0.416
0.376
0.343
0.315
0.518
0.463
0.419
0.382
0.351
0.573
0.514
0.465
0.425
0.391
0.634
0.569
0.516
0.472
0.434
0.702
0.630
0.572
0.523
0.482
0.776
0.697
0.633
0.579
0.534
0.856
0.771
0.700
0.641
0.591
1.03
0.932
0.848
0.778
0.718
1.23
1.11
1.02
0.932
0.861
1.44
1.31
1.20
1.10
1.02
1.66
1.51
1.39
1.28
1.18
1.88
1.72
1.58
1.47
1.36
2.60 0.189 0.211 0.235 0.261 0.291 0.325 0.362 0.402 0.446 0.495 0.548 0.667 0.800 0.945 1.10 1.27
2.80 0.176 0.196 0.218 0.243 0.271 0.302 0.337 0.375 0.416 0.461 0.511 0.622 0.747 0.882 1.03 1.18
3.00 0.164 0.183 0.204 0.227 0.253 0.282 0.315 0.350 0.389 0.431 0.478 0.582 0.700 0.825 0.962 1.11
x
y
0.000 0.005 0.017 0.035 0.057 0.083 0.113 0.144 0.178 0.213 0.250 0.327 0.408 0.492 0.579 0.667
0.500 0.455 0.417 0.385 0.357 0.333 0.313 0.294 0.278 0.263 0.250 0.227 0.208 0.192 0.179 0.167
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
8 - 206
BOLTS, WELDS, AND CONNECTED ELEMENTS
Table 8-45 (cont.).
Coefficients C for Eccentrically Loaded Weld Groups
Angle = ±15°°
φ R n = CC1Dl
C min =
Pu
D min =
C 1D l
Pu
lmin =
CC 1 l
Pu
CC 1 D
where
ex = a l
Pu = factored force, kips
D = number of sixteenths-of-an-inch
in the fillet weld size
l = characteristic length of weld group, in.
a = e x / l, in.
e x = horizontal component of eccentricity of
Pu with respect to centroid of weld group, in.
yl
15° 15°
c.g.
l
Pu
C = coefficient tabulated below which includes φ = 0.75
C 1 = electode strength coefficient from Table 8-37
(1.0 for E70XX electrodes)
xl
kl
k
a
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.2
1.4
1.6
1.8
2.0
0.00
0.10
0.15
0.20
0.25
1.48
1.42
1.38
1.32
1.24
1.69
1.57
1.54
1.47
1.39
1.89
1.74
1.70
1.63
1.54
2.10
1.92
1.86
1.78
1.68
2.31
2.09
2.02
1.94
1.81
2.51
2.27
2.19
2.09
1.94
2.72
2.44
2.35
2.22
2.07
2.92
2.61
2.51
2.36
2.21
3.13
2.78
2.67
2.51
2.35
3.33
2.95
2.83
2.66
2.50
3.54
3.12
2.98
2.82
2.66
3.95
3.45
3.30
3.13
2.98
4.36
3.78
3.62
3.45
3.30
4.77
4.12
3.95
3.78
3.63
5.18
4.46
4.29
4.12
3.96
5.59
4.81
4.64
4.46
4.30
0.30
0.40
0.50
0.60
0.70
1.16
1.00
0.869
0.759
0.670
1.30
1.12
0.970
0.847
0.746
1.43
1.23
1.06
0.926
0.820
1.55
1.33
1.15
1.01
0.899
1.68
1.44
1.25
1.10
0.983
1.80
1.55
1.36
1.20
1.07
1.93
1.68
1.48
1.31
1.18
2.06
1.81
1.60
1.43
1.29
2.21
1.95
1.74
1.56
1.41
2.36
2.10
1.88
1.69
1.53
2.51
2.25
2.02
1.83
1.67
2.83
2.57
2.33
2.12
1.95
3.15
2.88
2.64
2.43
2.25
3.48
3.20
2.95
2.74
2.54
3.81
3.53
3.28
3.05
2.84
4.15
3.87
3.61
3.37
3.15
0.80
0.90
1.00
1.20
1.40
0.598
0.539
0.490
0.413
0.357
0.666
0.600
0.545
0.461
0.398
0.734
0.663
0.604
0.511
0.442
0.807
0.730
0.666
0.565
0.490
0.885
0.803
0.734
0.625
0.543
0.969
0.881
0.807
0.690
0.601
1.06
0.968
0.888
0.761
0.664
1.17
1.06
0.979
0.840
0.734
1.28
1.17
1.08
0.927
0.812
1.40
1.28
1.18
1.02
0.897
1.52
1.40
1.30
1.12
0.988
1.79
1.66
1.54
1.34
1.19
2.08
1.93
1.80
1.58
1.40
2.37
2.21
2.08
1.84
1.64
2.66
2.49
2.34
2.09
1.88
2.96
2.78
2.63
2.35
2.12
1.60
1.80
2.00
2.20
2.40
0.314
0.280
0.253
0.230
0.211
0.350
0.312
0.282
0.257
0.236
0.389
0.347
0.313
0.286
0.262
0.432
0.386
0.348
0.318
0.292
0.479
0.429
0.388
0.354
0.325
0.532
0.476
0.431
0.393
0.362
0.589
0.528
0.479
0.438
0.403
0.651
0.585
0.531
0.486
0.447
0.721
0.649
0.589
0.538
0.496
0.798
0.718
0.652
0.597
0.550
0.879
0.793
0.721
0.660
0.609
1.06
0.958
0.873
0.801
0.740
1.26
1.14
1.04
0.958
0.886
1.48
1.34
1.23
1.13
1.05
1.70
1.55
1.43
1.32
1.22
1.93
1.77
1.63
1.51
1.40
2.60 0.195 0.218 0.242 0.270 0.301 0.335 0.373 0.415 0.460 0.510 0.565 0.687 0.824 0.975 1.13 1.31
2.80 0.182 0.203 0.225 0.251 0.280 0.312 0.348 0.386 0.428 0.476 0.527 0.641 0.770 0.910 1.06 1.22
3.00 0.170 0.189 0.211 0.234 0.261 0.291 0.325 0.361 0.401 0.445 0.494 0.601 0.722 0.852 0.993 1.15
x
y
0.000 0.005 0.017 0.035 0.057 0.083 0.113 0.144 0.178 0.213 0.250 0.327 0.408 0.492 0.579 0.667
0.500 0.455 0.417 0.385 0.357 0.333 0.313 0.294 0.278 0.263 0.250 0.227 0.208 0.192 0.179 0.167
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
ECCENTRICALLY LOADED WELD GROUPS
8 - 207
Table 8-45 (cont.).
Coefficients C for Eccentrically Loaded Weld Groups
Angle = ±30°°
φ R n = CC1Dl
C min =
Pu
D min =
C 1D l
Pu
lmin =
CC 1 l
Pu
CC 1 D
where
ex = a l
Pu = factored force, kips
D = number of sixteenths-of-an-inch
in the fillet weld size
l = characteristic length of weld group, in.
a = e x / l, in.
e x = horizontal component of eccentricity of
Pu with respect to centroid of weld group, in.
30°
yl
30°
c.g.
l
Pu
C = coefficient tabulated below which includes φ = 0.75
C 1 = electode strength coefficient from Table 8-37
(1.0 for E70XX electrodes)
xl
kl
k
a
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.2
1.4
1.6
1.8
2.0
0.00
0.10
0.15
0.20
0.25
1.64
1.52
1.44
1.36
1.28
1.83
1.68
1.59
1.51
1.42
2.03
1.85
1.75
1.66
1.56
2.22
2.03
1.91
1.81
1.71
2.42
2.20
2.07
1.96
1.85
2.61
2.38
2.23
2.12
1.99
2.81
2.55
2.40
2.26
2.12
3.01
2.73
2.56
2.41
2.26
3.20
2.90
2.72
2.56
2.41
3.40
3.06
2.88
2.72
2.57
3.59
3.23
3.05
2.89
2.74
3.98
3.59
3.41
3.24
3.09
4.37
3.95
3.77
3.59
3.43
4.76
4.32
4.13
3.94
3.77
5.15
4.70
4.51
4.31
4.13
5.54
5.08
4.89
4.68
4.49
0.30
0.40
0.50
0.60
0.70
1.20
1.05
0.921
0.812
0.722
1.34
1.17
1.03
0.904
0.804
1.47
1.29
1.13
0.993
0.884
1.60
1.40
1.22
1.08
0.968
1.74
1.51
1.33
1.18
1.06
1.87
1.64
1.45
1.29
1.16
1.99
1.76
1.57
1.41
1.27
2.13
1.90
1.70
1.53
1.38
2.28
2.04
1.83
1.66
1.51
2.43
2.19
1.98
1.80
1.64
2.60
2.35
2.13
1.94
1.78
2.95
2.68
2.45
2.25
2.08
3.28
3.03
2.80
2.59
2.40
3.62
3.35
3.13
2.93
2.73
3.97
3.69
3.46
3.25
3.06
4.32
4.04
3.80
3.58
3.37
0.80
0.90
1.00
1.20
1.40
0.647
0.586
0.535
0.454
0.393
0.722
0.654
0.596
0.506
0.438
0.796
0.722
0.659
0.560
0.487
0.874
0.794
0.727
0.620
0.540
0.957
0.872
0.799
0.685
0.597
1.05
0.957
0.879
0.755
0.660
1.15
1.05
0.968
0.833
0.729
1.26
1.16
1.07
0.920
0.806
1.38
1.27
1.17
1.02
0.891
1.51
1.39
1.29
1.12
0.984
1.64
1.51
1.40
1.22
1.08
1.92
1.78
1.66
1.46
1.29
2.23
2.08
1.94
1.72
1.53
2.55
2.39
2.24
1.99
1.79
2.87
2.70
2.55
2.28
2.05
3.19
3.02
2.85
2.56
2.32
1.60
1.80
2.00
2.20
2.40
0.347
0.310
0.280
0.255
0.234
0.386
0.345
0.312
0.285
0.262
0.430
0.384
0.347
0.317
0.291
0.477
0.427
0.386
0.352
0.324
0.529
0.474
0.429
0.392
0.360
0.585
0.526
0.477
0.436
0.401
0.648
0.583
0.529
0.484
0.446
0.717
0.645
0.586
0.537
0.495
0.794
0.715
0.650
0.595
0.549
0.878
0.791
0.720
0.660
0.609
0.967
0.874
0.796
0.730
0.674
1.16
1.05
0.961
0.884
0.817
1.38
1.25
1.15
1.06
0.978
1.61
1.47
1.35
1.24
1.15
1.87
1.70
1.57
1.45
1.34
2.12
1.94
1.79
1.66
1.55
2.60 0.217 0.242 0.269 0.299 0.334 0.372 0.413 0.459 0.510 0.566 0.626 0.760 0.910 1.08 1.25
2.80 0.201 0.225 0.250 0.278 0.311 0.346 0.385 0.428 0.475 0.527 0.584 0.710 0.851 1.01 1.17
3.00 0.188 0.210 0.234 0.260 0.290 0.324 0.360 0.401 0.445 0.494 0.547 0.666 0.799 0.944 1.10
1.44
1.35
1.27
x
y
0.000 0.005 0.017 0.035 0.057 0.083 0.113 0.144 0.178 0.213 0.250 0.327 0.408 0.492 0.579 0.667
0.500 0.455 0.417 0.385 0.357 0.333 0.313 0.294 0.278 0.263 0.250 0.227 0.208 0.192 0.179 0.167
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
8 - 208
BOLTS, WELDS, AND CONNECTED ELEMENTS
Table 8-45 (cont.).
Coefficients C for Eccentrically Loaded Weld Groups
Angle = ±45°°
φ R n = CC1Dl
C min =
Pu
D min =
C 1D l
Pu
lmin =
CC 1 l
Pu
CC 1 D
where
Pu = factored force, kips
ex = a l
D = number of sixteenths-of-an-inch
in the fillet weld size
l = characteristic length of weld group, in.
a = e x / l, in.
e x = horizontal component of eccentricity of
Pu with respect to centroid of weld group, in.
45°
yl
45°
c.g.
l
Pu
C = coefficient tabulated below which includes φ = 0.75
C 1 = electode strength coefficient from Table 8-37
(1.0 for E70XX electrodes)
xl
kl
k
a
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.2
1.4
1.6
1.8
2.0
0.00
0.10
0.15
0.20
0.25
1.81
1.68
1.57
1.47
1.39
1.99
1.83
1.71
1.60
1.51
2.17
1.99
1.86
1.74
1.64
2.35
2.15
2.02
1.88
1.77
2.53
2.32
2.18
2.04
1.92
2.71
2.50
2.36
2.21
2.07
2.89
2.67
2.53
2.38
2.24
3.07
2.85
2.69
2.54
2.41
3.25
3.02
2.86
2.71
2.58
3.43
3.19
3.03
2.88
2.75
3.61
3.37
3.21
3.06
2.93
3.97
3.74
3.58
3.42
3.29
4.33
4.10
3.95
3.80
3.66
4.70
4.48
4.33
4.18
4.04
5.06
4.85
4.71
4.56
4.42
5.42
5.21
5.08
4.94
4.80
0.30
0.40
0.50
0.60
0.70
1.31
1.16
1.03
0.921
0.829
1.43
1.27
1.13
1.01
0.911
1.55
1.38
1.23
1.11
1.00
1.67
1.49
1.35
1.22
1.11
1.81
1.63
1.48
1.34
1.21
1.95
1.77
1.61
1.46
1.33
2.11
1.92
1.74
1.58
1.45
2.28
2.07
1.88
1.72
1.58
2.45
2.23
2.03
1.86
1.71
2.62
2.39
2.19
2.01
1.86
2.80
2.57
2.36
2.18
2.01
3.16
2.92
2.72
2.52
2.35
3.54
3.27
3.06
2.87
2.70
3.91
3.64
3.40
3.21
3.04
4.29
4.03
3.76
3.55
3.37
4.66
4.41
4.14
3.91
3.71
0.80
0.90
1.00
1.20
1.40
0.751
0.685
0.629
0.538
0.469
0.828
0.757
0.696
0.598
0.523
0.915
0.839
0.773
0.666
0.582
1.01
0.927
0.854
0.735
0.644
1.11
1.02
0.938
0.810
0.712
1.22
1.12
1.03
0.892
0.786
1.33
1.22
1.14
0.985
0.868
1.45
1.34
1.25
1.09
0.960
1.58
1.47
1.36
1.20
1.06
1.72
1.60
1.49
1.31
1.16
1.87
1.74
1.63
1.43
1.28
2.19
2.05
1.92
1.70
1.52
2.53
2.38
2.24
2.00
1.80
2.88
2.73
2.58
2.31
2.09
3.21
3.05
2.91
2.64
2.40
3.54
3.38
3.23
2.96
2.71
1.60
1.80
2.00
2.20
2.40
0.416
0.373
0.338
0.308
0.284
0.464
0.416
0.377
0.344
0.317
0.516
0.463
0.419
0.383
0.353
0.572
0.513
0.466
0.426
0.392
0.633
0.570
0.518
0.474
0.436
0.700
0.631
0.574
0.526
0.485
0.774
0.699
0.636
0.583
0.538
0.857
0.775
0.705
0.647
0.598
0.948
0.858
0.782
0.718
0.664
1.05
0.947
0.865
0.795
0.736
1.15
1.04
0.954
0.878
0.812
1.38
1.25
1.15
1.06
0.983
1.63
1.49
1.37
1.26
1.17
1.90
1.74
1.60
1.49
1.38
2.19
2.02
1.86
1.73
1.61
2.50
2.31
2.14
1.99
1.85
2.60 0.263 0.293 0.327 0.363 0.405 0.450 0.500 0.555 0.617 0.684 0.756 0.916 1.09 1.29
2.80 0.245 0.273 0.304 0.338 0.377 0.420 0.467 0.518 0.576 0.638 0.707 0.857 1.03 1.21
3.00 0.229 0.256 0.285 0.317 0.353 0.393 0.437 0.486 0.540 0.599 0.663 0.805 0.964 1.14
1.50
1.41
1.33
1.73
1.62
1.53
x
y
0.000 0.005 0.017 0.035 0.057 0.083 0.113 0.144 0.178 0.213 0.250 0.327 0.408 0.492 0.579 0.667
0.500 0.455 0.417 0.385 0.357 0.333 0.313 0.294 0.278 0.263 0.250 0.227 0.208 0.192 0.179 0.167
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
ECCENTRICALLY LOADED WELD GROUPS
8 - 209
Table 8-45 (cont.).
Coefficients C for Eccentrically Loaded Weld Groups
Angle = ±60°°
φ R n = CC1Dl
C min =
Pu
D min =
C 1D l
Pu
lmin =
CC 1 l
Pu
CC 1 D
where
ex = a l
Pu = factored force, kips
D = number of sixteenths-of-an-inch
in the fillet weld size
l = characteristic length of weld group, in.
a = e x / l, in.
e x = horizontal component of eccentricity of
Pu with respect to centroid of weld group, in.
60°
yl
60°
c.g.
l
Pu
C = coefficient tabulated below which includes φ = 0.75
C 1 = electode strength coefficient from Table 8-37
(1.0 for E70XX electrodes)
xl
kl
k
a
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.2
1.4
1.6
1.8
2.0
0.00
0.10
0.15
0.20
0.25
1.95
1.83
1.73
1.63
1.55
2.12
1.94
1.84
1.74
1.65
2.28
2.07
1.96
1.86
1.76
2.44
2.21
2.09
1.98
1.88
2.61
2.36
2.24
2.12
2.02
2.77
2.53
2.40
2.28
2.18
2.94
2.70
2.57
2.45
2.35
3.10
2.88
2.75
2.63
2.53
3.26
3.06
2.94
2.82
2.72
3.43
3.24
3.13
3.00
2.90
3.59
3.41
3.31
3.20
3.08
3.92
3.76
3.67
3.57
3.46
4.25
4.11
4.03
3.94
3.84
4.57
4.45
4.38
4.30
4.21
4.90
4.78
4.72
4.65
4.56
5.23
5.12
5.06
4.99
4.91
0.30
0.40
0.50
0.60
0.70
1.47
1.34
1.22
1.12
1.03
1.58
1.44
1.31
1.20
1.11
1.68
1.54
1.41
1.30
1.20
1.80
1.66
1.53
1.42
1.32
1.94
1.79
1.67
1.55
1.45
2.09
1.94
1.81
1.69
1.59
2.26
2.10
1.97
1.85
1.74
2.44
2.27
2.13
2.01
1.90
2.62
2.45
2.30
2.17
2.06
2.81
2.64
2.48
2.35
2.23
2.99
2.83
2.66
2.52
2.40
3.36
3.20
3.04
2.89
2.75
3.73
3.56
3.42
3.27
3.12
4.11
3.93
3.78
3.64
3.50
4.48
4.29
4.14
4.00
3.87
4.83
4.65
4.49
4.36
4.23
0.80
0.90
1.00
1.20
1.40
0.945
0.874
0.812
0.709
0.626
1.02
0.950
0.886
0.777
0.690
1.12
1.04
0.973
0.858
0.765
1.23
1.15
1.08
0.952
0.852
1.35
1.27
1.19
1.06
0.945
1.49
1.40
1.32
1.17
1.04
1.64
1.54
1.45
1.28
1.15
1.79
1.68
1.58
1.41
1.26
1.95
1.83
1.73
1.54
1.39
2.11
1.99
1.88
1.68
1.52
2.28
2.16
2.05
1.84
1.66
2.63
2.51
2.40
2.17
1.97
2.99
2.87
2.75
2.52
2.31
3.36
3.23
3.10
2.87
2.66
3.73
3.60
3.46
3.21
3.00
4.10
3.96
3.83
3.56
3.34
1.60
1.80
2.00
2.20
2.40
0.560
0.506
0.461
0.423
0.391
0.619
0.561
0.512
0.471
0.436
0.689
0.626
0.573
0.527
0.487
0.769
0.697
0.636
0.585
0.541
0.850
0.771
0.705
0.649
0.600
0.938
0.853
0.780
0.719
0.666
1.04
0.943
0.864
0.797
0.738
1.14
1.04
0.957
0.883
0.819
1.26
1.15
1.06
0.977
0.907
1.38
1.27
1.17
1.08
1.00
1.52
1.39
1.28
1.19
1.10
1.81
1.66
1.53
1.43
1.33
2.12
1.96
1.82
1.69
1.58
2.46
2.28
2.12
1.98
1.85
2.80
2.61
2.44
2.28
2.14
3.13
2.94
2.77
2.60
2.44
2.60 0.363 0.405 0.452 0.502 0.558 0.620 0.687 0.763 0.847 0.937 1.03 1.25
2.80 0.339 0.379 0.422 0.469 0.521 0.580 0.644 0.715 0.793 0.878 0.969 1.17
3.00 0.317 0.355 0.395 0.440 0.489 0.545 0.605 0.672 0.746 0.826 0.913 1.10
1.48
1.39
1.31
1.74
1.63
1.54
2.01
1.90
1.79
2.30
2.17
2.06
x
y
0.000 0.005 0.017 0.035 0.057 0.083 0.113 0.144 0.178 0.213 0.250 0.327 0.408 0.492 0.579 0.667
0.500 0.455 0.417 0.385 0.357 0.333 0.313 0.294 0.278 0.263 0.250 0.227 0.208 0.192 0.179 0.167
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
8 - 210
BOLTS, WELDS, AND CONNECTED ELEMENTS
Table 8-45 (cont.).
Coefficients C for Eccentrically Loaded Weld Groups
Angle = ±75°°
φ R n = CC1Dl
C min =
Pu
D min =
C 1D l
Pu
lmin =
CC 1 l
Pu
CC 1 D
where
Pu = factored force, kips
ex = a l
D = number of sixteenths-of-an-inch
in the fillet weld size
l = characteristic length of weld group, in.
a = e x / l, in.
e x = horizontal component of eccentricity of
Pu with respect to centroid of weld group, in.
75°
yl
75°
c.g.
l
Pu
C = coefficient tabulated below which includes φ = 0.75
C 1 = electode strength coefficient from Table 8-37
(1.0 for E70XX electrodes)
xl
kl
k
a
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.2
1.4
1.6
1.8
2.0
0.00
0.10
0.15
0.20
0.25
2.05
1.94
1.88
1.82
1.76
2.20
2.01
1.94
1.89
1.83
2.35
2.08
2.03
1.97
1.92
2.50
2.20
2.15
2.09
2.04
2.65
2.34
2.29
2.24
2.19
2.79
2.49
2.44
2.39
2.35
2.94
2.65
2.61
2.56
2.52
3.09
2.81
2.77
2.73
2.69
3.24
2.97
2.94
2.90
2.86
3.39
3.13
3.10
3.07
3.03
3.54
3.28
3.25
3.23
3.20
3.83
3.59
3.56
3.53
3.51
4.13
3.93
3.87
3.84
3.81
4.43
4.25
4.20
4.15
4.11
4.72
4.57
4.52
4.48
4.42
5.02
4.88
4.84
4.80
4.75
0.30
0.40
0.50
0.60
0.70
1.71
1.62
1.53
1.46
1.38
1.78
1.69
1.61
1.53
1.46
1.87
1.79
1.70
1.63
1.56
2.00
1.91
1.83
1.75
1.68
2.14
2.05
1.97
1.89
1.82
2.30
2.21
2.12
2.05
1.97
2.47
2.38
2.29
2.21
2.14
2.65
2.56
2.47
2.39
2.31
2.82
2.74
2.66
2.57
2.49
3.00
2.92
2.84
2.76
2.68
3.17
3.10
3.03
2.95
2.87
3.49
3.43
3.38
3.31
3.25
3.79
3.75
3.70
3.65
3.60
4.09
4.05
4.02
3.97
3.93
4.39
4.35
4.32
4.28
4.24
4.70
4.65
4.61
4.58
4.55
0.80
0.90
1.00
1.20
1.40
1.31
1.25
1.19
1.09
0.994
1.39
1.33
1.27
1.16
1.07
1.49
1.43
1.37
1.26
1.16
1.61
1.54
1.48
1.37
1.27
1.75
1.68
1.62
1.50
1.40
1.90
1.83
1.77
1.64
1.54
2.06
1.99
1.93
1.80
1.69
2.24
2.16
2.10
1.97
1.85
2.41
2.34
2.27
2.14
2.01
2.60
2.52
2.45
2.31
2.19
2.79
2.71
2.64
2.50
2.36
3.17
3.10
3.03
2.87
2.73
3.54
3.47
3.41
3.26
3.12
3.88
3.82
3.76
3.64
3.50
4.20
4.16
4.10
3.99
3.87
4.51
4.47
4.43
4.34
4.23
1.60
1.80
2.00
2.20
2.40
0.914
0.845
0.784
0.730
0.683
0.987
0.915
0.852
0.797
0.748
1.08
1.00
0.937
0.878
0.825
1.18
1.11
1.04
0.972
0.915
1.30
1.22
1.15
1.08
1.02
1.44
1.35
1.27
1.20
1.13
1.58
1.49
1.40
1.33
1.26
1.74
1.64
1.55
1.46
1.39
1.90
1.80
1.70
1.60
1.52
2.07
1.95
1.84
1.74
1.65
2.24
2.11
2.00
1.89
1.80
2.59
2.45
2.33
2.21
2.10
2.97
2.82
2.69
2.56
2.44
3.36
3.21
3.06
2.92
2.80
3.74
3.61
3.46
3.31
3.17
4.11
3.99
3.85
3.71
3.56
2.60 0.641 0.704 0.778 0.865 0.963 1.07 1.19
2.80 0.604 0.664 0.736 0.819 0.913 1.02 1.13
3.00 0.570 0.628 0.698 0.777 0.867 0.966 1.07
1.32
1.25
1.18
1.44
1.37
1.30
1.57
1.49
1.42
1.71
1.62
1.55
2.00
1.91
1.82
2.33
2.23
2.13
2.68
2.57
2.46
3.05
2.93
2.81
3.42
3.30
3.18
x
y
0.000 0.005 0.017 0.035 0.057 0.083 0.113 0.144 0.178 0.213 0.250 0.327 0.408 0.492 0.579 0.667
0.500 0.455 0.417 0.385 0.357 0.333 0.313 0.294 0.278 0.263 0.250 0.227 0.208 0.192 0.179 0.167
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
CONSTRUCTION COMBINING BOLTS AND WELDS
8 - 211
Eccentricity Normal to the Plane of the Faying Surface
Figure 8-55 shows a bracket welded to a column flange. The eccentric load Pu can be
resolved into a concentric force Pu at the faying surface of the connection and a moment
Pu e normal to the plane of the faying surface where e is the eccentricity. Each weld
element is then assumed to support an equal share of the concentric force Pu, and the
moment Pu e is resisted by tension in the welds above the neutral axis and compression
below the neutral axis.
In contrast to bolts, where the interaction of shear and tension must be considered, for
welds, shear and tension may be combined vectorially for welds into a resultant shear.
Thus, the solution of a weld loaded eccentrically normal to the plane of the faying surface
is parallel to that discussed previously for welds loaded eccentrically in the plane of the
faying surface; with the neutral axis assumed to be located at the CG of the weld group,
this case is identical to that described previously for the elastic method.
CONSTRUCTION COMBINING BOLTS AND WELDS
In bearing-type connections in new construction, the rigidity of the welds prevents the
initial joint slippage necessary to develop the strength of all the bolts in a connection that
might combine both welds and bolts. Thus, bearing-type connections combining welds
and bolts are permissible only if the design strength of the welds φRn alone exceeds the
required strength of the connection Ru. However, in situations where it can safely be
assumed that joint slippage has occurred before welding is performed, welds may be used
to reinforce existing bolted or riveted joints. Such is the case with structures previously
in service. In this case, the design strength of the original bolt group may be used to carry
the existing dead loads and the design strength of the welds need be adequate only to
carry additional loads. Refer to LRFD Specification Section J1.9.
In slip-critical connections, since connection slip is neither expected nor required for
the bolts to develop their strength, the design strengths of welds and high-strength bolts
are additive. When high-strength bolts and welds are used together in a slip-critical
connection, the bolts should preferably be fully tensioned before welding is performed.
The design drawings should clearly indicate where this type of connection occurs.
Pu
e
Fig. 8-55. Welds subjected to eccentricity normal to the plane of the faying surface.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
8 - 212
BOLTS, WELDS, AND CONNECTED ELEMENTS
CONNECTED ELEMENTS
Connected elements are the angles, plates, tees, gussets, and other connecting elements
used in connections to transfer load from one structural member to another as well as the
affected elements of the connected members.
Economical Considerations
Cost effective steel fabrication requires close cooperation between the designer, detailer,
and fabricator. Effective communication and planning will allow the project to take full
advantage of the strengths of all parties involved. Often, potential problems can be
avoided through early consultation and good communication during the full life of a project.
Designs and details should be suited to the shop practices and standards of the
fabricator. The resulting similarity throughout the project will further lend itself to the
minimization of errors. For example, once gage lines conforming to standard machine
set-ups are determined, they should be utilized as much as possible throughout any one
job. Furthermore, it is desirable to keep the same bolt spacing throughout a project.
Longitudinal spacing should preferably be three inches or a multiple of three inches, since
most shops consider this to be standard.
At a minimum, gages and hole sizes on any one member should not be varied
throughout the length of that member. This prevents unnecessary material re-handling
and the need for multiple punching or drilling.
Design Strength of Connected Elements
The design strength of connecting elements is determined in accordance with the
provisions of LRFD Specification Sections J4 and J5; the applicable limit states are shear
yielding, shear rupture, block shear rupture, tension yielding, and tension rupture.
Shear Yielding
This limit state applies to the gross section of the connected element. From LRFD
Specification Section J5.3, the design shear yielding strength is φRn,
where
φ = 0.90
Rn = 0.60Fy Ag
Shear Rupture
This limit state applies to the net section From LRFD Specification Section J4.1, the
design shear rupture strength is φRn,
where
φ = 0.75
Rn = 0.60Fu Anv
Table 8-46 gives the reduction in area for standard, oversized, short-slotted, and
long-slotted holes in material thicknesses from 3⁄16-in. to 1 in.; for other material thicknesses, multiply the tabular value for 1-in. thickness by the actual thickness.
Block Shear Rupture
The term block shear rupture describes a material tearing limit state which occurs in a
combination of shear and tension. This phenomenon can occur at the end of a coped beam,
shown in Figure 8-56, or at the end of a tension connection, shown in Figure 8-57. This
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
CONNECTED ELEMENTS
8 - 213
Table 8-46.
Reduction in Area for Holes, in.2
C
Thckns.
t, in.
A
B
STD
Standard Hole
OVS
Oversized Hole
3⁄
4
7⁄
8
D
A
A
SSL
Short-Slotted Hole
LSL
Long-Slotted Hole
A ×t
B ×t
Bolt Diameter d b , in.
Bolt Diameter d b , in.
1
1 1 ⁄8
1 1 ⁄4
1 3 ⁄8
1 1 ⁄2
3⁄
4
7⁄
8
1
1 1 ⁄8
1 1 ⁄4
1 3 ⁄8
1 1 ⁄2
3⁄
16
1⁄
4
0.164 0.188 0.211 0.234 0.258 0.281 0.305 0.188 0.211 0.246 0.281 0.305 0.328 0.352
0.219 0.250 0.281 0.313 0.344 0.375 0.406 0.250 0.281 0.328 0.375 0.406 0.438 0.469
5⁄
16
3⁄
8
7⁄
16
1⁄
2
0.273
0.328
0.383
0.438
0.313
0.375
0.438
0.500
0.352
0.422
0.492
0.563
0.391
0.469
0.547
0.625
0.430
0.516
0.602
0.688
0.469
0.563
0.656
0.750
0.508
0.609
0.711
0.813
0.313
0.375
0.438
0.500
0.352
0.422
0.492
0.563
0.410
0.492
0.574
0.656
0.469
0.563
0.656
0.750
0.508
0.609
0.711
0.813
0.547
0.656
0.766
0.875
0.586
0.703
0.820
0.938
9⁄
16
5⁄
8
11⁄
16
3⁄
4
0.492
0.547
0.602
0.656
0.563
0.625
0.688
0.750
0.633
0.703
0.773
0.844
0.703
0.781
0.859
0.938
0.773
0.859
0.945
1.03
0.844
0.938
1.03
1.13
0.914
1.02
1.12
1.22
0.563
0.625
0.688
0.750
0.633
0.703
0.773
0.844
0.738
0.820
0.902
0.984
0.844
0.938
1.03
1.13
0.914
1.02
1.12
1.22
0.984
1.09
1.20
1.31
1.05
1.17
1.29
1.41
13⁄
16
7⁄
8
15⁄
16
0.711
0.766
0.820
0.875
0.813
0.875
0.938
1.00
0.914
0.984
1.05
1.13
1.02
1.09
1.17
1.25
1.12
1.20
1.29
1.38
1.22
1.31
1.41
1.50
1.32
1.42
1.52
1.63
0.813
0.875
0.938
1.00
0.914
0.984
1.05
1.13
1.07
1.15
1.23
1.31
1.22
1.31
1.41
1.50
1.32
1.42
1.52
1.63
1.42
1.53
1.64
1.75
1.52
1.64
1.76
1.88
1 3 ⁄8
1 1 ⁄2
1
Thckns.
t, in.
3⁄
4
7⁄
8
C ×t
D ×t
Bolt Diameter d b , in.
Bolt Diameter d b , in.
1
1 1 ⁄8
1 1 ⁄4
1 3 ⁄8
1 1 ⁄2
3⁄
4
7⁄
8
1
1 1 ⁄8
1 1 ⁄4
3⁄
16
1⁄
4
0.199 0.223 0.258 0.293 0.316 0.340 0.363 0.363 0.422 0.480 0.539 0.598 0.656 0.715
0.266 0.297 0.344 0.391 0.422 0.453 0.484 0.484 0.563 0.641 0.719 0.797 0.875 0.953
5⁄
16
3⁄
8
7⁄
16
1⁄
2
0.332
0.398
0.465
0.531
0.371
0.445
0.520
0.594
0.430
0.516
0.602
0.688
0.488
0.586
0.684
0.781
0.527
0.633
0.738
0.844
0.566
0.680
0.793
0.906
0.605
0.727
0.848
0.969
0.605
0.727
0.848
0.969
0.703
0.844
0.984
1.13
0.801
0.961
1.12
1.28
0.898
1.08
1.26
1.44
0.996
1.20
1.39
1.59
1.09
1.31
1.53
1.75
1.19
1.43
1.67
1.91
9⁄
16
5⁄
8
11⁄
16
3⁄
4
0.598
0.664
0.730
0.797
0.668
0.742
0.816
0.891
0.773
0.859
0.945
1.03
0.879
0.977
1.07
1.17
0.949
1.05
1.16
1.27
1.02
1.13
1.25
1.36
1.09
1.21
1.33
1.45
1.09
1.21
1.33
1.45
1.27
1.41
1.55
1.69
1.44
1.60
1.76
1.92
1.62
1.80
1.98
2.16
1.79
1.99
2.19
2.39
1.97
2.19
2.41
2.63
2.14
2.38
2.62
2.86
13⁄
16
7⁄
8
15⁄
16
0.863
0.930
0.996
1.06
0.965
1.04
1.11
1.19
1.12
1.20
1.29
1.38
1.27
1.37
1.46
1.56
1.37
1.48
1.58
1.69
1.47
1.59
1.70
1.81
1.57
1.70
1.82
1.94
1.57
1.70
1.82
1.94
1.83
1.97
2.11
2.25
2.08
2.24
2.40
2.56
2.34
2.52
2.70
2.88
2.59
2.79
2.99
3.19
2.84
3.06
3.28
3.50
3.10
3.34
3.57
3.81
1
failure is usually the result of high reactions imposed on relatively thin material through a short
connection.
The design block shear rupture strength is φRn, where φ = 0.75 and Rn is determined
as follows.
For bolted connections, from LRFD Specification Section J4.3, when
Fu Ant ≥ 0.6Fu Anv, shear yielding occurs in combination with tension rupture and,
Rn = 0.6Fy Agv + Fu Ant
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
8 - 214
BOLTS, WELDS, AND CONNECTED ELEMENTS
This case is the basis of Tables 8-47, where φFu Ant is tabulated per inch of material thickness
in Table 8-47a and φ(0.6Fy Agv) is tabulated per inch of material thickness in Table 8-47b.
When 0.6Fu Anv > Fu Ant , shear rupture occurs in combination with tension yielding and,
Rn = 0.6Fu Anv + Fy Agt
This case is the basis of Tables 8-48, where φ(0.6Fu Anv) is tabulated per inch of material
thickness in Table 8-48a and φFy Agt is tabulated per inch of material thickness in
Table 8-48b.
For welded connections, block shear rupture is treated as for bolted connections; the
only difference is that, in the absence of bolt holes, Anv = Agv and Ant = Agt.
L eh
L ev
n bolts @
s spacing
Shear
Area
Shear
Area
Tension
Area
Tension
Area
(a) Bolted Connections
(b) Welded Connections
Fig. 8-56. Block shear rupture in coped beams.
L eh
L ev
Shear
Area
n bolts @
s spacing
Tension
Area
Fig. 8-57. Block shear rupture in ends of tension members.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
CONNECTED ELEMENTS
8 - 215
Table 8-47a.
Block Shear Rupture
Tension Rupture Component per inch of thickness, φ[FuAnt] / t, kips/in.
L eh
Fu, ksi
58
65
70
Bolt Diameter db, in.
Bolt Diameter db, in.
Bolt Diameter db, in.
3⁄
4
7⁄
8
3⁄
4
7⁄
8
3⁄
4
7⁄
8
1
24.5
21.8
19.0
27.4
24.4
21.3
29.5
26.3
23.0
1 1 ⁄8
1 1 ⁄4
1 3 ⁄8
1 1 ⁄2
29.9
35.3
40.8
46.2
27.2
32.6
38.1
43.5
24.5
29.9
35.3
40.8
33.5
39.6
45.7
51.8
30.5
36.6
42.7
48.8
27.4
33.5
39.6
45.7
36.1
42.7
49.2
55.8
32.8
39.4
45.9
52.5
29.5
36.1
42.7
49.2
1 5 ⁄8
1 3 ⁄4
1 7 ⁄8
51.7
57.1
62.5
68.0
48.9
54.4
59.8
65.3
46.2
51.7
57.1
62.5
57.9
64.0
70.1
76.2
54.8
60.9
67.0
73.1
51.8
57.9
64.0
70.1
62.3
68.9
75.5
82.0
59.1
65.6
72.2
78.8
55.8
62.3
68.9
75.5
78.8
89.7
101
111
76.1
87.0
97.9
109
73.4
84.3
95.2
106
88.4
101
113
125
85.3
97.5
110
122
82.3
94.5
107
119
95.2
108
121
135
91.9
105
118
131
88.6
102
115
128
Leh, in.
2
2 1 ⁄4
2 1 ⁄2
2 3 ⁄4
3
1
1
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1
8 - 216
BOLTS, WELDS, AND CONNECTED ELEMENTS
Table 8-47b.
Block Shear Rupture
Shear Yielding Component per inch of thickness, φ[0.6FyAgv] / t, kips/in.
L ev
n bolts @
3 ″ spacing
Fy, ksi
36
50
Bolt Diameter db, in.
Bolt Diameter db, in.
n
Lev, in.
3⁄
4
7⁄
8
1
3⁄
4
7⁄
8
1
12
1 1 ⁄4
1 3 ⁄8
1 1 ⁄2
562
564
566
563
565
567
564
566
568
780
783
786
782
785
788
783
786
789
1 5 ⁄8
1 3 ⁄4
1 7 ⁄8
568
570
572
574
569
571
573
575
570
572
574
576
789
792
795
797
790
793
796
799
792
795
797
800
3
578
582
586
590
579
583
587
591
580
584
588
592
803
809
814
820
804
810
816
821
806
811
817
823
1 1 ⁄4
1 3 ⁄8
1 1 ⁄2
513
515
517
514
516
518
515
517
519
713
716
719
714
717
720
716
719
721
1 5 ⁄8
1 3 ⁄4
1 7 ⁄8
519
521
523
525
520
522
524
527
521
523
525
528
721
724
727
730
723
726
728
731
724
727
730
733
3
530
534
538
542
531
535
539
543
532
536
540
544
735
741
747
752
737
743
748
754
738
744
750
755
1 1 ⁄4
1 3 ⁄8
1 1 ⁄2
465
467
469
466
468
470
467
469
471
645
648
651
647
650
653
648
651
654
1 5 ⁄8
1 3 ⁄4
1 7 ⁄8
471
473
475
477
472
474
476
478
473
475
477
479
654
657
660
662
655
658
661
664
657
660
662
665
481
485
489
493
482
486
490
494
483
487
491
495
668
674
679
685
669
675
681
686
671
676
682
688
2
2 1 ⁄4
2 1 ⁄2
2 3 ⁄4
11
2
2 1 ⁄4
2 1 ⁄2
2 3 ⁄4
10
2
2 1 ⁄4
2 1 ⁄2
2 3 ⁄4
3
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
CONNECTED ELEMENTS
8 - 217
Table 8-47b (cont.).
Block Shear Rupture
Shear Yielding Component per inch of thickness, φ[0.6FyAgv] / t, kips/in.
L ev
n bolts @
3 ″ spacing
Fy, ksi
36
50
Bolt Diameter db, in.
Bolt Diameter db, in.
n
Lev, in.
3⁄
4
7⁄
8
1
3⁄
4
7⁄
8
1
9
1 1 ⁄4
1 3 ⁄8
1 1 ⁄2
416
418
420
417
419
421
418
420
422
578
581
584
579
582
585
581
584
586
1 5 ⁄8
1 3 ⁄4
1 7 ⁄8
422
424
426
428
423
425
427
429
424
426
428
430
586
589
592
595
588
591
593
596
589
592
595
598
3
432
436
440
444
433
437
441
446
434
438
442
447
600
606
612
617
602
608
613
619
603
609
615
620
1 1 ⁄4
1 3 ⁄8
1 1 ⁄2
368
370
372
369
371
373
370
372
374
510
513
516
512
515
518
513
516
519
1 5 ⁄8
1 3 ⁄4
1 7 ⁄8
374
376
378
380
375
377
379
381
376
378
380
382
519
522
525
527
520
523
526
529
522
525
527
530
3
384
388
392
396
385
389
393
397
386
390
394
398
533
539
544
550
534
540
546
551
536
541
547
553
1 1 ⁄4
1 3 ⁄8
1 1 ⁄2
319
321
323
320
322
324
321
323
325
443
446
449
444
447
450
446
449
451
1 5 ⁄8
1 3 ⁄4
1 7 ⁄8
325
327
329
331
326
328
330
332
327
329
331
333
451
454
457
460
453
456
458
461
454
457
460
463
335
339
343
347
336
340
344
348
337
341
345
349
465
471
477
482
467
473
478
484
468
474
480
485
2
2 1 ⁄4
2 1 ⁄2
2 3 ⁄4
8
2
2 1 ⁄4
2 1 ⁄2
2 3 ⁄4
7
2
2 1 ⁄4
2 1 ⁄2
2 3 ⁄4
3
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
8 - 218
BOLTS, WELDS, AND CONNECTED ELEMENTS
Table 8-47b (cont.).
Block Shear Rupture
Shear Yielding Component per inch of thickness, φ[0.6FyAgv] / t, kips/in.
L ev
n bolts @
3 ″ spacing
Fy, ksi
36
50
Bolt Diameter db, in.
Bolt Diameter db, in.
n
Lev, in.
3⁄
4
7⁄
8
1
3⁄
4
7⁄
8
1
6
1 1 ⁄4
1 3 ⁄8
1 1 ⁄2
270
272
274
271
273
275
272
274
276
375
378
381
377
380
383
378
381
384
1 5 ⁄8
1 3 ⁄4
1 7 ⁄8
276
278
280
282
277
279
281
284
278
280
282
285
384
387
390
392
385
388
391
394
387
390
392
395
3
287
291
295
299
288
292
296
300
289
293
297
301
398
404
409
415
399
405
411
416
401
406
412
418
1 1 ⁄4
1 3 ⁄8
1 1 ⁄2
222
224
226
223
225
227
224
226
228
308
311
314
309
312
315
311
314
316
1 5 ⁄8
1 3 ⁄4
1 7 ⁄8
228
230
232
234
229
231
233
235
230
232
234
236
316
319
322
325
318
321
323
326
319
322
325
328
3
238
242
246
250
239
243
247
251
240
244
248
252
330
336
342
347
332
338
343
349
333
339
345
350
1 1 ⁄4
1 3 ⁄8
1 1 ⁄2
173
175
177
174
176
178
175
177
179
240
243
246
242
245
248
243
246
249
1 5 ⁄8
1 3 ⁄4
1 7 ⁄8
179
181
183
185
180
182
184
186
181
183
185
187
249
252
255
257
250
253
256
259
252
255
257
260
189
193
197
201
190
194
198
203
191
195
199
204
263
269
274
280
264
270
276
281
266
271
277
283
2
2 1 ⁄4
2 1 ⁄2
2 3 ⁄4
5
2
2 1 ⁄4
2 1 ⁄2
2 3 ⁄4
4
2
2 1 ⁄4
2 1 ⁄2
2 3 ⁄4
3
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
CONNECTED ELEMENTS
8 - 219
Table 8-47b (cont.).
Block Shear Rupture
Shear Yielding Component per inch of thickness, φ[0.6FyAgv] / t, kips/in.
L ev
n bolts @
3 ″ spacing
Fy, ksi
36
50
Bolt Diameter db, in.
Bolt Diameter db, in.
n
Lev, in.
3⁄
4
7⁄
8
1
3⁄
4
7⁄
8
1
3
1 1 ⁄4
1 3 ⁄8
1 1 ⁄2
125
127
129
126
128
130
127
129
131
173
176
179
174
177
180
176
179
181
1 5 ⁄8
1 3 ⁄4
1 7 ⁄8
131
133
135
137
132
134
136
138
133
135
137
139
181
184
187
190
183
186
188
191
184
187
190
193
3
141
145
149
153
142
146
150
154
143
147
151
155
195
201
207
212
197
203
208
214
198
204
210
215
1 1 ⁄4
1 3 ⁄8
1 1 ⁄2
76
78
80
77
79
81
78
80
82
105
108
111
107
110
113
108
111
114
1 5 ⁄8
1 3 ⁄4
1 7 ⁄8
82
84
86
88
83
85
87
89
84
86
88
90
114
117
120
122
115
118
121
124
117
120
122
125
92
96
100
104
93
97
101
105
94
98
102
106
128
134
139
145
129
135
141
146
131
136
142
148
2
2 1 ⁄4
2 1 ⁄2
2 3 ⁄4
2
2
2 1 ⁄4
2 1 ⁄2
2 3 ⁄4
3
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
8 - 220
BOLTS, WELDS, AND CONNECTED ELEMENTS
Table 8-48a.
Block Shear Rupture
Shear Rupture Component per inch of thickness, φ[0.6FuAnv] / t, kips/in.
L ev
n bolts @
3 ″ spacing
Fu, ksi
58
65
70
Bolt Diameter db, in.
Bolt Diameter db, in.
Bolt Diameter db, in.
n
Lev, in.
3⁄
4
7⁄
8
1
3⁄
4
7⁄
8
1
3⁄
4
7⁄
8
1
12
1 1 ⁄4
1 3 ⁄8
1 1 ⁄2
631
635
638
594
597
600
556
560
563
707
711
715
665
669
673
623
627
631
762
766
770
717
721
725
671
675
679
1 5 ⁄8
1 3 ⁄4
1 7 ⁄8
641
644
648
651
604
607
610
613
566
569
573
576
718
722
726
729
676
680
684
687
634
638
642
645
774
778
782
786
728
732
736
740
683
687
691
695
3
657
664
670
677
620
626
633
639
582
589
595
602
737
744
751
759
695
702
709
717
653
660
667
675
793
801
809
817
748
756
764
772
703
711
719
726
1 1 ⁄4
1 3 ⁄8
1 1 ⁄2
576
579
582
542
545
548
507
511
514
645
649
653
607
611
614
569
572
576
695
699
703
654
658
662
612
616
620
1 5 ⁄8
1 3 ⁄4
1 7 ⁄8
586
589
592
595
551
555
558
561
517
520
524
527
656
660
664
667
618
622
625
629
580
583
587
590
707
711
715
719
665
669
673
677
624
628
632
636
3
602
608
615
622
568
574
581
587
533
540
546
553
675
682
689
697
636
644
651
658
598
605
612
620
726
734
742
750
685
693
701
709
644
652
660
667
1 1 ⁄4
1 3 ⁄8
1 1 ⁄2
520
524
527
489
493
496
458
462
465
583
587
590
548
552
556
514
517
521
628
632
636
591
595
599
553
557
561
1 5 ⁄8
1 3 ⁄4
1 7 ⁄8
530
533
537
540
499
502
506
509
468
471
475
478
594
598
601
605
559
563
567
570
525
528
532
536
640
644
648
652
602
606
610
614
565
569
573
577
546
553
560
566
515
522
529
535
484
491
498
504
612
620
627
634
578
585
592
600
543
550
558
565
660
667
675
683
622
630
638
646
585
593
600
608
2
2 1 ⁄4
2 1 ⁄2
2 3 ⁄4
11
2
2 1 ⁄4
2 1 ⁄2
2 3 ⁄4
10
2
2 1 ⁄4
2 1 ⁄2
2 3 ⁄4
3
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
CONNECTED ELEMENTS
8 - 221
Table 8-48a (cont.).
Block Shear Rupture
Shear Rupture Component per inch of thickness, φ[0.6FuAnv ] / t, kips/in.
L ev
n bolts @
3 ″ spacing
Fu, ksi
58
65
70
Bolt Diameter db, in.
Bolt Diameter db, in.
Bolt Diameter db, in.
n
Lev, in.
3⁄
4
7⁄
8
1
3⁄
4
7⁄
8
1
3⁄
4
7⁄
8
1
9
1 1 ⁄4
1 3 ⁄8
1 1 ⁄2
465
468
471
437
440
444
409
413
416
521
525
528
490
494
497
459
463
466
561
565
569
528
532
536
494
498
502
1 5 ⁄8
1 3 ⁄4
1 7 ⁄8
475
478
481
484
447
450
453
457
419
422
426
429
532
536
539
543
501
505
508
512
470
473
477
481
573
577
581
585
539
543
547
551
506
510
514
518
3
491
498
504
511
463
470
476
483
436
442
449
455
550
558
565
572
519
527
534
541
488
495
503
510
593
600
608
616
559
567
575
583
526
534
541
549
1 1 ⁄4
1 3 ⁄8
1 1 ⁄2
409
413
416
385
388
392
361
364
367
459
463
466
431
435
439
404
408
411
494
498
502
465
469
473
435
439
443
1 5 ⁄8
1 3 ⁄4
1 7 ⁄8
419
422
426
429
395
398
401
405
370
374
377
380
470
473
477
481
442
446
450
453
415
419
422
426
506
510
514
518
476
480
484
488
447
451
455
459
3
436
442
449
455
411
418
424
431
387
393
400
406
488
495
503
510
461
468
475
483
433
441
448
455
526
534
541
549
496
504
512
520
467
474
482
490
1 1 ⁄4
1 3 ⁄8
1 1 ⁄2
354
357
361
333
336
339
312
315
318
397
400
404
373
377
380
349
353
356
427
431
435
402
406
410
376
380
384
1 5 ⁄8
1 3 ⁄4
1 7 ⁄8
364
367
370
374
343
346
349
352
321
325
328
331
408
411
415
419
384
388
391
395
360
364
367
371
439
443
447
451
413
417
421
425
388
392
396
400
380
387
393
400
359
365
372
378
338
344
351
357
426
433
441
448
402
410
417
424
378
386
393
400
459
467
474
482
433
441
449
457
408
415
423
431
2
2 1 ⁄4
2 1 ⁄2
2 3 ⁄4
8
2
2 1 ⁄4
2 1 ⁄2
2 3 ⁄4
7
2
2 1 ⁄4
2 1 ⁄2
2 3 ⁄4
3
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
8 - 222
BOLTS, WELDS, AND CONNECTED ELEMENTS
Table 8-48a (cont.).
Block Shear Rupture
Shear Rupture Component per inch of thickness, φ[0.6FuAnv ] / t, kips/in.
L ev
n bolts @
3 ″ spacing
Fu, ksi
58
65
70
Bolt Diameter db, in.
Bolt Diameter db, in.
Bolt Diameter db, in.
n
Lev, in.
3⁄
4
7⁄
8
1
3⁄
4
7⁄
8
1
3⁄
4
7⁄
8
1
6
1 1 ⁄4
1 3 ⁄8
1 1 ⁄2
299
302
305
281
284
287
263
266
269
335
338
342
314
318
322
294
298
302
360
364
368
339
343
347
317
321
325
1 5 ⁄8
1 3 ⁄4
1 7 ⁄8
308
312
315
318
290
294
297
300
272
276
279
282
346
349
353
356
325
329
333
336
305
309
313
316
372
376
380
384
350
354
358
362
329
333
337
341
3
325
331
338
344
307
313
320
326
289
295
302
308
364
371
378
386
344
351
358
366
324
331
338
346
392
400
408
415
370
378
386
394
348
356
364
372
1 1 ⁄4
1 3 ⁄8
1 1 ⁄2
243
246
250
228
232
235
214
217
220
272
276
280
256
260
263
239
243
247
293
297
301
276
280
284
258
262
266
1 5 ⁄8
1 3 ⁄4
1 7 ⁄8
253
256
259
263
238
241
245
248
223
227
230
233
283
287
291
294
267
271
274
278
250
254
258
261
305
309
313
317
287
291
295
299
270
274
278
282
3
269
276
282
289
254
261
268
274
240
246
253
259
302
309
316
324
285
293
300
307
269
276
283
291
325
333
341
348
307
315
323
331
289
297
305
313
1 1 ⁄4
1 3 ⁄8
1 1 ⁄2
188
191
194
176
179
183
165
168
171
210
214
218
197
201
205
185
188
192
226
230
234
213
217
221
199
203
207
1 5 ⁄8
1 3 ⁄4
1 7 ⁄8
197
201
204
207
186
189
192
196
175
178
181
184
221
225
229
232
208
212
216
219
196
199
203
207
238
242
246
250
224
228
232
236
211
215
219
222
214
220
227
233
202
209
215
222
191
197
204
210
239
247
254
261
227
234
241
249
214
221
229
236
258
266
274
282
244
252
260
268
230
238
246
254
2
2 1 ⁄4
2 1 ⁄2
2 3 ⁄4
5
2
2 1 ⁄4
2 1 ⁄2
2 3 ⁄4
4
2
2 1 ⁄4
2 1 ⁄2
2 3 ⁄4
3
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
CONNECTED ELEMENTS
8 - 223
Table 8-48a (cont.).
Block Shear Rupture
Shear Rupture Component per inch of thickness, φ[0.6FuAnv ] / t, kips/in.
L ev
n bolts @
3 ″ spacing
Fu, ksi
58
65
70
Bolt Diameter db, in.
Bolt Diameter db, in.
Bolt Diameter db, in.
n
Lev, in.
3⁄
4
7⁄
8
1
3⁄
4
7⁄
8
1
3⁄
4
7⁄
8
1
3
1 1 ⁄4
1 3 ⁄8
1 1 ⁄2
132
135
139
124
127
131
116
119
122
148
152
155
139
143
146
130
133
137
159
163
167
150
154
158
140
144
148
1 5 ⁄8
1 3 ⁄4
1 7 ⁄8
142
145
148
152
134
137
140
144
126
129
132
135
159
163
166
170
150
154
157
161
141
144
148
152
171
175
179
183
161
165
169
173
152
156
159
163
3
158
165
171
178
150
157
163
170
142
148
155
161
177
185
192
199
168
176
183
190
159
166
174
181
191
199
207
215
181
189
197
205
171
179
187
195
1 1 ⁄4
1 3 ⁄8
1 1 ⁄2
77
80
83
72
75
78
67
70
73
86
90
93
80
84
88
75
79
82
93
96
100
87
91
95
81
85
89
1 5 ⁄8
1 3 ⁄4
1 7 ⁄8
86
90
93
96
82
85
88
91
77
80
83
86
97
101
104
108
91
95
99
102
86
90
93
97
104
108
112
116
98
102
106
110
93
96
100
104
103
109
116
122
98
104
111
117
93
100
106
113
115
122
130
137
110
117
124
132
104
112
119
126
124
132
140
148
118
126
134
142
112
120
128
136
2
2 1 ⁄4
2 1 ⁄2
2 3 ⁄4
2
2
2 1 ⁄4
2 1 ⁄2
2 3 ⁄4
3
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
8 - 224
BOLTS, WELDS, AND CONNECTED ELEMENTS
Table 8-48b.
Block Shear Rupture
Tension Yielding Component per inch of thickness
φ[FyAgt] / t, kips/in.
L eh
Fy, ksi
Leh, in.
36
50
1
27.0
37.5
11⁄8
11⁄4
13⁄8
11⁄2
30.4
33.8
37.1
40.5
42.2
46.9
51.6
56.3
15⁄8
13⁄4
17⁄8
2
43.9
47.3
50.6
54.0
60.9
65.6
70.3
75.0
21⁄4
21⁄2
23⁄4
3
60.8
67.5
74.3
81.0
84.4
93.8
103
113
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
CONNECTED ELEMENTS
8 - 225
Tension Yielding
From LRFD Specification Section J5.2, the design tension yielding strength is φRn,
where
φ = 0.90
Rn = Fy Ag
Tension Rupture
From LRFD Specification Section J5.2, the design tension rupture strength is φRn,
where
φ = 0.75
Rn = Fu An
In the above equation, An is the net area not to exceed 0.85Ag.
Table 8-46 gives the reduction in area for standard, oversized, short-slotted, and
long-slotted holes in material thicknesses from 3⁄16-in. to 1 in.; for material thicknesses
not listed, multiply the tabular value for 1-in. thickness by the actual thickness.
Members with Copes, Blocks, or Cuts
When structural members frame together, a minimum clearance of 1⁄2-in. should be
provided, when possible. In cases where material removal is necessary to provide such
a clearance, material may be removed by coping, blocking, or cutting as illustrated in
Figures 8-58. Note the recommended practices for coping illustrated in Figure 8-59; the
potential notch left by the first cut will occur in waste material which will subsequently
be removed by the second cut. All re-entrant corners must be shaped notch-free per AWS
D1.1 to a radius. An approximate minimum radius to which this corner must be shaped
is 1⁄2-in.
Material removal is costly, and should be avoided when possible. For example, the
elevations of the tops of infill beams could be established at a sufficient distance below the
tops of girders to clear the girder fillet. Alternatively, coping could be eliminated with a
connection as illustrated in Figure 8-60; this detail also allows the use of a shorter beam length.
When necessary, coping is usually the most economical method to remove material.
Copes, blocks, and cuts can significantly reduce the design strengths of members and
may require web reinforcement; it may be more economical to use a heavier member
than to provide such reinforcement. The design strength of the unreinforced coped
member is determined from the limit states of flexural yielding, local buckling, and lateral
torsional buckling, if applicable. Web reinforcement of coped beams is discussed in
Part 9.
Flexural Yielding
The flexural yielding strength of a supported beam which is coped at the top and/or bottom
is φbMn,
where
φb = 0.90
Mn = Fy Snet
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
8 - 226
BOLTS, WELDS, AND CONNECTED ELEMENTS
In the above equation, Snet is the net elastic section modulus, in.3 Values of Snet are
tabulated in Table 8-49.
The beam-end reaction Ru must be such that:
Ru ≤
φbMn
e
where e is the distance from the face of the cope to the point of inflection of the beam,
in. It is usually assumed that the point of inflection is located at the face of the supporting
member and e is as shown in Figure 8-61. However, depending upon the connection type
and stiffness and support condition, the point of inflection may move away from the face
of the supporting member; when this is the case, a lesser value of e may be justified. In
any case, the choice of e shown in Figure 8-61 will be conservative.
Local Web Buckling
For short copes no greater than the length of the connection angle(s), plate, or tee, local
web buckling will generally not occur. If, however, the depth of the cope were such that
c
dc
c
Cut not grid preferred
Cut and grid if surface
must be flush with web
c
dc
(a) Cope
(b) Blocks
(c) Cut
Fig. 8-58. Copes, blocks, and cuts.
first cut
resulting
notch occurs
in waste
0 to 15°
as required
second cut
second cut
potential
notch
AVOID
first cut
RECOMMENDED
Fig. 8-59. Recommended coping practice.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
CONNECTED ELEMENTS
8 - 227
dc > 0.2d, the unreinforced web could buckle between the top of the cope and the beam
flange if the beam web were thin.
In a reduced section, the design strength in local web buckling may be more critical
than the design strength in flexural yielding. This design strength is critical at the
compression zone of the web near the cope and is dependent on three parameters: (1)
cope depth dc; (2) cope length c; and (3) web thickness tw. It should be noted that, for
convenience, the dimension h0 in Figure 8-61 is used instead of the more correct
dimension h1; this eliminates the detailed calculation required to locate the neutral axis
of the coped beam. Alternatively, the dimension h1 may be substituted for h0 in the
following local buckling calculations.
The beam end reaction Ru must be such that:
Ru ≤
φFbc Snet
e
where
Snet = elastic section modulus of the net section, in.3 from Table 8-49
e = distance from the end reaction to the face of the cope, in.
and φFbc is determined as follows.
When a beam is coped at the top flange only, the design recommendations are based
on the classical plate buckling formula with a k-factor based on three edges simply
supported and one free edge. An additional factor f, which generally accounts for stress
concentration at the cope, was developed to correlate with the coped beam buckling
solutions (Cheng, et. al., 1984). From Figure 8-61, when the c ≤ 2d and dc ≤ d / 2,
2
π2E tw
fk
Fcr =
12(1 − v2) ho
where
E = 29,000 ksi, modulus of elasticity of steel
ν = 0.3, Poisson’s ratio
f = plate buckling model adjustment factor
(a) Coping Required
(b) Coping Eliminated
Fig. 8-60. Minimizing coping requirements.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
8 - 228
BOLTS, WELDS, AND CONNECTED ELEMENTS
k = plate buckling coefficient
ho = d − dc, reduced beam depth, in.
Thus, the design buckling stress φFbc for a beam coped at the top flange only is,
2
tw
φFbc = 23,590 fk
ho
where f and k are determined from the following equations:
c
c
f = 2 for ≤ 1.0
d
d
c
c
f = 1 + for > 1.0
d
d
ho
c
k = 2.2 for ≤ 1.0
ho
c
ho
c
k = 2.2 for > 1.0
ho
c
When a beam is coped at both flanges, the design recommendations are based on the
lateral buckling model with an adjustment factor fd (Cheng, et al., 1984). From Figure
8-62, when at both flanges c ≤ 2d and dc ≤ 0.2d,
Fcr = 0.62πE
t2w
f
cho d
Thus, the design buckling stress φFbc for a beam coped at both flanges is,
φFbc = 50,840
t2w
f
cho d
and
e
c
Buckling checked here
dc
Setback
ho
Ru
d
h1
tw
Simple shear connection
Fig. 8-61. Local buckling of beam web coped at top flange only.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
N.A.
CONNECTED ELEMENTS
8 - 229
d
d
c
fd = 3.5 − 7.5
where dc is the larger of the top cope depth dct and the bottom cope depth dcb.
Lateral Torsional Buckling
In laterally unbraced beams, copes, blocks, and cuts further reduce the out-of-plane
rotational restraint. Cheng, et al. (1984) discusses the design strength of laterally unbraced
coped beams. For laterally unbraced beams coped at the top only, this design strength
may be determined with this information and the provisions of LRFD Specification
Section F1.2. For laterally unbraced beams coped at the top and bottom, this design
strength may be determined with this information and the provisions of LRFD Specification Appendix F1. A detailed discussion of this topic is beyond the scope of this text.
e
c
Buckling checked here
Simple shear connection
d
Ru
tw
d cb
d – d ct – dcb
d ct
Setback
Fig. 8-62. Local buckling of beam web coped at both flanges.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
N.A.
8 - 230
BOLTS, WELDS, AND CONNECTED ELEMENTS
So
Snet
d
Sx
d
d
dc
Table 8-49.
Section Modulus of Coped W Shapes
Snet, in.3
dc, in.
Designation
d
in.
tf
in.
Sx
in.3
So
in.3
2
3
4
5
6
7
8
9
10
W44×335
W ×290
W ×262
W ×230
44.0
43.6
43.3
42.9
1.77
1.58
1.42
1.22
1410
1240
1120
969
492
417
374
330
451
382
342
301
431
365
327
288
411
348
312
274
392
332
297
261
373
316
283
249
355
300
269
236
337
285
255
224
320
270
241
212
303
255
228
200
W40×593
W ×503
W ×431
W ×372
W ×321
W ×297
W ×277
W ×249
W ×215
W ×199
W ×174
43.0
42.1
41.3
40.6
40.1
39.8
39.7
39.4
39.0
38.7
38.2
3.23
2.76
2.36
2.05
1.77
1.65
1.58
1.42
1.22
1.07
0.830
2340
1980
1690
1460
1250
1170
1100
992
858
769
639
810
673
567
480
406
374
335
299
256
247
234
—
—
—
—
368
339
304
271
231
224
211
—
584
491
415
350
323
289
258
220
213
201
671
556
467
394
332
306
274
245
208
202
190
639
528
444
374
315
290
260
232
197
191
180
607
501
421
354
298
275
246
219
186
180
170
575
475
398
335
282
259
232
207
176
170
160
545
449
376
316
266
245
219
195
166
160
151
515
424
355
298
250
230
206
183
156
150
142
486
399
334
280
235
216
193
172
146
141
133
W40×466
W ×392
W ×331
W ×278
W ×264
W ×235
W ×211
W ×183
W ×167
W ×149
42.4
41.6
40.8
40.2
40.0
39.7
39.4
39.0
38.6
38.2
2.95
2.52
2.13
1.81
1.73
1.58
1.42
1.22
1.03
0.830
1710
1440
1210
1020
971
874
785
682
599
512
705
581
483
396
371
320
286
244
234
217
—
—
—
360
337
291
259
221
212
196
613
504
419
342
321
276
246
210
201
186
584
480
398
325
305
262
234
199
191
177
556
456
378
308
289
249
221
189
181
167
528
432
358
292
274
235
209
179
171
158
500
409
339
276
259
222
198
168
161
149
474
387
320
261
244
210
186
159
152
140
448
365
302
245
230
197
175
149
143
132
422
344
284
231
216
185
165
140
134
123
W36×848
W ×798
W ×650
W ×527
W ×439
W ×393
W ×359
W ×328
W ×300
W ×280
W ×260
W ×245
W ×230
42.5
42.0
40.5
39.3
38.3
37.8
37.4
37.1
36.7
36.5
36.3
36.1
35.9
4.53
4.29
3.54
2.91
2.44
2.20
2.01
1.85
1.68
1.57
1.44
1.35
1.26
3170
2980
2420
1950
1620
1450
1320
1210
1110
1030
953
895
837
1094
1016
794
618
503
443
400
360
328
305
285
269
253
—
—
—
—
—
—
—
324
295
274
256
241
227
—
—
—
531
430
378
341
307
279
259
242
228
214
903
836
649
503
407
358
322
290
264
245
228
215
202
858
794
615
476
384
338
304
273
249
230
215
203
190
813
752
582
449
362
318
286
257
234
217
202
190
179
770
712
550
423
341
299
269
242
220
203
190
178
168
728
673
518
398
320
281
252
226
206
190
177
167
157
687
634
487
374
300
263
236
212
192
178
166
156
146
647
597
457
350
280
246
220
197
179
165
154
145
136
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
CONNECTED ELEMENTS
8 - 231
So
Snet
d
Sx
d
d
dc
Table 8-49 (cont.).
Section Modulus of Coped W Shapes
Snet, in.3
Designation
d
in.
tf
in.
Sx
in.3
W36×256
W ×232
W ×210
W ×194
W ×182
W ×170
W ×160
W ×150
W ×135
37.4
37.1
36.7
36.5
36.3
36.2
36.0
35.9
35.6
1.73
1.57
1.36
1.26
1.18
1.10
1.02
0.940
0.790
895
809
719
664
623
580
542
504
439
W33×354
W ×318
W ×291
W ×263
W ×241
W ×221
W ×201
35.6
35.2
34.8
34.5
34.2
33.9
33.7
2.09
1.89
1.73
1.57
1.40
1.28
1.15
W33×169
W ×152
W ×141
W ×130
W ×118
33.8
33.5
33.3
33.1
32.9
W30×477
W ×391
W ×326
W ×292
W ×261
W ×235
W ×211
W ×191
W ×173
W30×148
W ×132
W ×124
W ×116
W ×108
W ×99
W ×90
So
in.3
dc, in.
2
3
4
5
6
7
8
9
329
295
272
249
234
218
206
195
181
297
266
245
224
211
196
185
176
163
281
251
232
212
199
185
175
166
154
266
238
219
201
188
175
165
157
145
251
224
207
189
178
165
156
148
137
237
211
195
178
167
155
147
139
129
223
199
183
167
157
146
138
130
121
209
186
172
157
147
137
129
122
113
196
174
161
146
137
128
120
114
105
183
163
150
137
128
119
112
106
98.1
1230
1110
1010
917
829
757
684
373
330
300
268
250
230
209
—
295
268
239
223
205
186
315
278
253
226
210
193
175
297
262
238
212
197
181
165
279
246
223
199
185
170
154
262
230
209
186
173
159
144
245
216
195
174
162
148
135
229
201
182
162
150
138
125
213
187
169
151
140
128
116
198
173
157
139
129
118
107
1.22
1.06
0.960
0.855
0.740
549
487
448
406
359
191
176
165
155
143
170
157
147
138
128
161
148
139
130
120
151
139
130
122
113
141
130
122
114
106
132
122
114
107
98.6
124
114
106
100
91.9
115
106
98.8
92.5
85.4
107
97.9
91.6
85.7
79.1
98.6
90.5
84.6
79.2
73.0
34.2
33.2
32.4
32.0
31.6
31.3
30.9
30.7
30.4
2.95
2.44
2.05
1.85
1.65
1.50
1.32
1.19
1.07
1530
1250
1030
928
827
746
663
598
539
475
378
305
269
240
211
192
174
158
—
—
—
238
212
186
170
153
139
398
315
254
223
198
174
159
143
130
374
295
237
208
185
163
148
133
121
350
276
221
194
172
152
138
124
112
327
257
206
180
160
141
128
115
104
305
239
191
167
148
130
118
106
96.1
283
222
177
155
137
120
109
97.7
88.4
262
205
163
142
126
110
100
89.6
81.0
242
188
150
130
115
101
91.2
81.8
73.9
30.7
30.3
30.2
30.0
29.8
29.7
29.5
1.18
1.00
0.930
0.850
0.760
0.670
0.610
436
380
355
329
299
269
245
152
139
131
124
118
110
98.7
134
123
115
109
103
96.4
86.7
125
115
108
102
96.5
90.0
80.9
117
107
100
95.3
89.9
83.9
75.4
109
99.3
93.4
88.6
83.6
77.9
70.0
101
92.1
86.5
82.1
77.4
72.1
64.8
93.3
85.1
79.9
75.8
71.4
66.5
59.7
86.0
78.3
73.6
69.7
65.7
61.1
54.9
78.9
71.8
67.4
63.9
60.1
56.0
50.2
72.1
65.5
61.5
58.2
54.8
51.0
45.7
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
10
8 - 232
BOLTS, WELDS, AND CONNECTED ELEMENTS
So
Snet
d
Sx
d
d
dc
Table 8-49 (cont.).
Section Modulus of Coped W Shapes
Snet, in.3
Designation
d
in.
tf
in.
Sx
in.3
So
in.3
W27×539
W ×448
W ×368
W ×307
W ×281
W ×258
W ×235
W ×217
W ×194
W ×178
W ×161
W ×146
32.5
31.4
30.4
29.6
29.3
29.0
28.7
28.4
28.1
27.8
27.6
27.4
3.54
2.99
2.48
2.09
1.93
1.77
1.61
1.50
1.34
1.19
1.08
0.975
1570
1300
1060
884
811
742
674
624
556
502
455
411
W27×129
W ×114
W ×102
W ×94
W ×84
27.6
27.3
27.1
26.9
26.7
1.10
0.930
0.830
0.745
0.640
W24×492
W ×408
W ×335
W ×279
W ×250
W ×229
W ×207
W ×192
W ×176
W ×162
W ×146
W ×131
W ×117
W ×104
29.7
28.5
27.5
26.7
26.3
26.0
25.7
25.5
25.2
25.0
24.7
24.5
24.3
24.1
W24×103
W ×94
W ×84
W ×76
W ×68
W24×62
W ×55
dc, in.
2
3
4
5
6
7
8
9
10
509
404
321
259
233
212
193
174
155
145
131
118
—
—
—
—
203
185
168
152
134
126
113
102
—
—
262
211
189
172
156
141
125
117
105
95.0
394
310
244
196
176
159
145
130
115
108
97.2
87.7
367
288
226
181
162
147
134
120
106
100
89.5
80.7
341
267
209
167
150
136
123
111
97.6
91.5
82.0
74.0
316
247
193
154
137
124
113
101
89.3
83.6
74.9
67.5
292
227
177
141
126
114
103
92.3
81.3
76.1
68.1
61.3
269
209
162
128
114
103
93.2
83.7
73.6
68.8
61.5
55.3
247
191
147
116
104
93.3
84.2
75.5
66.3
61.9
55.3
49.7
345
299
267
243
213
117
106
94.2
88.0
80.5
101
91.6
81.6
76.2
69.6
94.0
84.9
75.6
70.6
64.5
86.9
78.4
69.8
65.1
59.5
80.1
72.2
64.3
59.9
54.7
73.5
66.2
58.9
54.9
50.1
67.2
60.5
53.7
50.1
45.7
61.1
54.9
48.8
45.4
41.4
55.3
49.6
44.0
41.0
37.3
49.7
44.6
39.5
36.8
33.5
3.54
2.99
2.48
2.09
1.89
1.73
1.57
1.46
1.34
1.22
1.09
0.960
0.850
0.750
1290
1060
864
718
644
588
531
491
450
414
371
329
291
258
420
331
261
210
184
167
149
136
124
115
104
94.4
84.4
75.4
—
—
—
—
158
143
127
117
106
98.0
88.5
80.3
71.7
64.1
—
—
209
167
146
132
117
107
97.6
90.0
81.2
73.7
65.7
58.7
316
247
193
154
134
121
107
98.2
89.4
82.3
74.2
67.3
60.0
53.5
292
227
177
141
123
111
98.0
89.5
81.4
74.9
67.5
61.1
54.5
48.6
269
209
162
128
112
101
89.0
81.2
73.8
67.9
61.1
55.3
49.2
43.8
247
191
147
116
101
91.0
80.4
73.3
66.5
61.1
54.9
49.7
44.2
39.3
226
173
133
105
91.2
81.8
72.2
65.8
59.6
54.7
49.1
44.3
39.4
35.0
205
157
120
94.3
81.7
73.1
64.4
58.6
53.0
48.6
43.6
39.3
34.8
30.9
186
141
108
84.0
72.6
64.9
57.0
51.8
46.8
42.8
38.3
34.5
30.5
27.1
24.5
24.3
24.1
23.9
23.7
0.980
0.875
0.770
0.680
0.585
245
222
196
176
154
82.9
76.2
68.3
62.6
57.5
70.7
64.9
58.0
53.2
48.8
64.9
59.5
53.2
48.7
44.7
59.3
54.3
48.6
44.5
40.8
53.9
49.4
44.1
40.4
37.0
48.8
44.6
39.8
36.4
33.4
43.9
40.1
35.8
32.7
29.9
39.2
35.8
31.9
29.1
26.6
34.8
31.7
28.2
25.8
23.5
30.6
27.9
24.8
22.6
20.6
23.7
23.6
0.590
0.505
131
114
56.9
51.1
48.3
43.4
44.3
39.7
40.4
36.2
36.7
32.9
33.1
29.7
29.7
26.6
26.5
23.7
23.4
20.9
20.5
18.3
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
CONNECTED ELEMENTS
8 - 233
So
Snet
d
Sx
d
d
dc
Table 8-49 (cont.).
Section Modulus of Coped W Shapes
Snet, in.3
Designation
d
in.
tf
in.
W21×201
W ×182
W ×166
W ×147
W ×132
W ×122
W ×111
W ×101
23.0
22.7
22.5
22.1
21.8
21.7
21.5
21.4
W21×93
W ×83
W ×73
W ×68
W ×62
dc, in.
Sx
in.3
So
in.3
2
3
4
5
6
7
8
9
1.63
1.48
1.36
1.15
1.04
0.960
0.875
0.800
461
417
380
329
295
273
249
227
125
111
99.3
91.2
81.0
74.1
67.1
60.4
105
93.3
83.0
76.1
67.5
61.6
55.7
50.1
95.2
84.8
75.3
68.9
61.1
55.7
50.4
45.3
86.2
76.6
68.0
62.1
55.0
50.2
45.3
40.7
77.6
68.8
61.0
55.7
49.2
44.8
40.4
36.3
69.4
61.4
54.4
49.5
43.7
39.8
35.9
32.1
61.6
54.4
48.1
43.7
38.5
35.0
31.5
28.2
54.2
47.8
42.2
38.2
33.6
30.5
27.4
24.5
47.3
41.6
36.6
33.1
29.0
26.3
23.6
21.1
21.6
21.4
21.2
21.1
21.0
0.930
0.835
0.740
0.685
0.615
192
171
151
140
127
67.2
59.0
51.5
48.1
44.1
56.0
49.1
42.7
39.9
36.5
50.7
44.4
38.7
36.1
33.0
45.7
40.0
34.8
32.4
29.7
40.9
35.7
31.0
29.0
26.5
36.3
31.7
27.5
25.6
23.4
32.0
27.9
24.2
22.5
20.5
27.9
24.3
21.0
19.6
17.8
24.1
20.9
18.1
16.8
15.3
W21×57
W ×50
W ×44
21.1
20.8
20.7
0.650
0.535
0.450
111
94.5
81.6
43.4
39.2
35.2
36.1
32.5
29.1
32.6
29.4
26.3
29.3
26.4
23.6
26.2
23.6
21.0
23.2
20.8
18.6
20.4
18.3
16.3
17.7
15.9
14.1
15.2
13.6
12.1
W18×311
W ×283
W ×258
W ×234
W ×211
W ×192
W ×175
W ×158
W ×143
W ×130
22.3
21.9
21.5
21.1
20.7
20.4
20.0
19.7
19.5
19.3
2.74
2.50
2.30
2.11
1.91
1.75
1.59
1.44
1.32
1.20
624
564
514
466
419
380
344
310
282
256
186
166
148
130
115
102
92.1
81.7
72.5
65.2
—
—
—
—
94.5
83.4
75.1
66.4
58.8
52.8
140
124
110
96.1
84.8
74.7
67.2
59.3
52.4
47.0
126
111
98.3
85.9
75.6
66.5
59.7
52.6
46.4
41.5
113
99.3
87.4
76.2
66.9
58.7
52.6
46.2
40.7
36.4
100
87.8
77.2
67.1
58.7
51.4
45.9
40.2
35.4
31.5
88.2
77.1
67.5
58.5
51.0
44.5
39.6
34.6
30.4
27.0
77.0
67.0
58.5
50.4
43.8
38.1
33.8
29.4
25.7
22.8
66.5
57.6
50.0
43.0
37.1
32.1
28.4
24.6
21.5
19.0
W18×119
W ×106
W ×97
W ×86
W ×76
19.0
18.7
18.6
18.4
18.2
1.06
0.940
0.870
0.770
0.680
231
204
188
166
146
61.7
54.4
48.9
43.1
37.6
49.8
43.8
39.3
34.6
30.1
44.3
38.9
34.9
30.6
26.7
39.1
34.3
30.7
26.9
23.4
34.2
29.9
26.8
23.4
20.3
29.5
25.8
23.1
20.2
17.5
25.2
22.0
19.6
17.1
14.8
21.2
18.5
16.4
14.3
12.3
W18×71
W ×65
W ×60
W ×55
W ×50
18.5
18.4
18.2
18.1
18.0
0.810
0.750
0.695
0.630
0.570
127
117
108
98.3
88.9
42.4
38.3
35.0
32.4
29.1
34.1
30.8
28.1
26.0
23.4
30.3
27.3
24.9
23.0
20.7
26.7
24.0
21.9
20.2
18.2
23.3
20.9
19.1
17.6
15.8
20.1
18.0
16.4
15.1
13.5
17.1
15.3
13.9
12.8
11.5
14.3
12.8
11.6
10.7
9.54
W18×46
W ×40
W ×35
18.1
17.9
17.7
0.605
0.525
0.425
78.8
68.4
57.6
28.9
24.9
22.7
23.2
20.0
18.2
20.6
17.7
16.1
18.1
15.5
14.1
15.7
13.5
12.3
13.5
11.6
10.5
11.5
9.80
8.88
9.56
8.16
7.37
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
10
8 - 234
BOLTS, WELDS, AND CONNECTED ELEMENTS
So
Snet
d
Sx
d
d
dc
Table 8-49 (cont.).
Section Modulus of Coped W Shapes
Snet, in.3
dc, in.
Designation
d
in.
tf
in.
Sx
in.3
So
in.3
2
3
4
5
6
7
W16×100
W ×89
W ×77
W ×67
17.0
16.8
16.5
16.3
0.985
0.875
0.760
0.665
175
155
134
117
44.4
39.0
33.1
28.3
34.9
30.6
25.9
22.1
30.5
26.7
22.6
19.2
26.4
23.1
19.4
16.5
22.6
19.7
16.5
14.0
19.0
16.5
13.8
11.7
15.7
13.6
11.4
9.58
W16×57
W ×50
W ×45
W ×40
W ×36
16.4
16.3
16.1
16.0
15.9
0.715
0.630
0.565
0.505
0.430
92.2
81.0
72.7
64.7
56.5
29.4
25.6
22.9
20.1
18.8
23.0
20.0
17.9
15.6
14.6
20.1
17.4
15.5
13.6
12.7
17.3
15.0
13.4
11.7
10.9
14.8
12.7
11.3
9.89
9.21
12.4
10.7
9.47
8.24
7.67
10.2
8.74
7.75
6.73
6.25
W16×31
W ×26
15.9
15.7
0.440
0.345
47.2
38.4
17.1
14.9
13.3
11.6
11.6
10.1
10.0
8.64
8.44
7.31
7.03
6.08
5.73
4.95
W14×808
W ×730
W ×665
W ×605
W ×550
W ×500
W ×455
22.8
22.4
21.6
20.9
20.2
19.6
19.0
5.12
4.91
4.52
4.16
3.82
3.50
3.21
1400
1280
1150
1040
931
838
756
—
—
—
—
—
—
—
—
—
—
—
—
—
—
W14×426
W ×398
W ×370
W ×342
W ×311
W ×283
W ×257
W ×233
W ×211
W ×193
W ×176
W ×159
W ×145
18.7
18.3
17.9
17.5
17.1
16.7
16.4
16.0
15.7
15.5
15.2
15.0
14.8
3.04
2.85
2.66
2.47
2.26
2.07
1.89
1.72
1.56
1.44
1.31
1.19
1.09
707
656
607
559
506
459
415
375
338
310
281
254
232
164
150
135
122
107
94.4
83.1
73.2
64.9
57.6
52.2
45.7
40.9
—
—
—
—
—
—
64.1
56.1
49.5
43.8
39.5
34.5
30.7
W14×132
W ×120
W ×109
W ×99
W ×90
14.7
14.5
14.3
14.2
14.0
1.03
0.940
0.860
0.780
0.710
209
190
173
157
143
38.1
34.2
30.0
27.2
24.3
28.6
25.5
22.3
20.2
18.0
24.3
21.7
18.9
17.0
15.2
W14×82
W ×74
W ×68
W ×61
14.3
14.2
14.0
13.9
0.855
0.785
0.720
0.645
123
112
103
92.2
28.0
24.4
22.2
19.7
20.9
18.2
16.5
14.6
17.7
15.4
13.9
12.3
451
365
317
275
238
208
182
—
—
—
—
153
131
113
—
220
187
158
134
115
98.2
244
195
165
139
117
99.4
84.6
216
172
144
121
101
85.3
72.1
87.6
78.7
70.1
61.9
53.5
46.3
40.0
34.6
30.2
26.4
23.6
20.4
18.0
75.2
67.2
59.6
52.3
44.9
38.7
33.3
28.6
24.8
21.6
19.2
16.5
14.5
63.8
56.7
50.0
43.6
37.2
31.8
27.1
23.2
19.9
17.3
15.2
13.0
11.4
20.3
18.1
15.7
14.2
12.6
16.7
14.8
12.8
11.5
10.2
13.4
11.8
10.2
9.15
8.07
14.8
12.8
11.6
10.2
12.1
10.4
9.42
8.28
9.64
8.31
7.46
6.54
— 101
104
91.1
93.7 81.4
83.4 72.3
72.7 62.7
63.6 54.6
55.5 47.4
48.4 41.3
42.6 36.1
37.5 31.7
33.8 28.5
29.4 24.7
26.1 21.9
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
8
9
10
CONNECTED ELEMENTS
8 - 235
So
Snet
d
Sx
d
d
dc
Table 8-49 (cont.).
Section Modulus of Coped W Shapes
Snet, in.3
dc, in.
Designation
d
in.
tf
in.
Sx
in.3
So
in.3
2
3
4
5
6
W14×53
W ×48
W ×43
13.9
13.8
13.7
0.660
0.595
0.530
77.8
70.3
62.7
19.1
17.3
15.3
14.2
12.8
11.3
12.0
10.8
9.50
9.93
8.93
7.84
8.07
7.23
6.34
6.39
5.71
4.99
W14×38
W ×34
W ×30
14.1
14.0
13.8
0.515
0.455
0.385
54.6
48.6
42.0
16.0
14.4
13.2
12.0
10.8
9.88
10.2
9.14
8.37
8.48
7.62
6.96
6.94
6.22
5.68
5.54
4.95
4.51
W14×26
W ×22
13.9
13.7
0.420
0.335
35.3
29.0
12.3
10.7
9.20
7.97
7.80
6.75
6.50
5.62
5.31
4.58
4.23
3.64
W12×336
W ×305
W ×279
W ×252
W ×230
W ×210
W ×190
W ×170
W ×152
W ×136
W ×120
W ×106
W ×96
W ×87
W ×79
W ×72
W ×65
16.8
16.3
15.9
15.4
15.1
14.7
14.4
14.0
13.7
13.4
13.1
12.9
12.7
12.5
12.4
12.3
12.1
3.00
2.71
2.47
2.25
2.07
1.90
1.74
1.56
1.40
1.25
1.105
0.990
0.900
0.810
0.735
0.670
0.605
—
—
—
—
—
49.0
42.3
36.5
31.6
27.5
23.7
19.8
17.4
15.8
14.1
12.6
11.2
83.1
71.4
63.1
54.2
47.5
41.6
35.7
30.7
26.5
22.9
19.7
16.3
14.3
13.0
11.5
10.3
9.16
71.4
61.0
53.5
45.7
39.9
34.7
29.7
25.3
21.7
18.7
16.0
13.2
11.5
10.4
9.23
8.24
7.28
60.6
51.4
44.8
38.0
32.9
28.5
24.2
20.5
17.5
14.9
12.6
10.4
9.03
8.11
7.16
6.37
5.61
50.8
42.7
36.9
31.0
26.7
22.9
19.3
16.2
13.7
11.6
9.70
W12×58
W ×53
12.2
12.1
0.640
0.575
78.0
70.6
14.8
13.9
10.4
9.74
8.52
7.94
6.79
6.31
5.24
4.85
W12×50
W ×45
W ×40
12.2
12.1
11.9
0.640
0.575
0.515
64.7
58.1
51.9
14.8
13.1
11.4
10.4
9.27
8.03
8.54
7.56
6.54
6.82
6.02
5.19
5.27
4.63
3.98
W12×35
W ×30
W ×26
12.5
12.3
12.2
0.52
0.44
0.38
45.6
38.6
33.4
12.3
10.5
9.08
8.85
7.47
6.47
7.30
6.15
5.32
5.89
4.94
4.27
4.61
3.86
3.32
W12×22
W ×19
W ×16
W ×14
12.3
12.2
12.0
11.9
0.425
0.350
0.265
0.225
25.4
21.3
17.1
14.9
9.60
8.39
7.43
6.61
6.89
6.01
5.30
4.71
5.69
4.95
4.36
3.86
4.59
3.98
3.50
3.10
3.59
3.11
2.72
2.41
483 123
435 108
393
96.1
353
83.7
321
74.2
292
65.6
263
57.0
235
49.6
209
43.3
186
37.9
163
32.8
145
27.6
131
24.3
118
22.2
107
19.9
97.4 17.9
87.9 16.0
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
7
8
9
10
8 - 236
BOLTS, WELDS, AND CONNECTED ELEMENTS
So
Snet
d
Sx
d
d
dc
Table 8-49 (cont.).
Section Modulus of Coped W Shapes
Snet, in.3
Designation
d
in.
tf
in.
dc, in.
Sx
in.3
So
in.3
2
3
4
25.7
22.3
19.1
16.2
13.9
12.1
10.5
9.46
17.5
15.0
12.8
10.7
9.13
7.88
6.79
6.10
13.9
11.9
10.0
8.35
7.10
6.09
5.22
4.68
10.8
9.12
7.62
6.29
5.30
4.52
3.86
3.44
W10×112
W ×100
W ×88
W ×77
W ×68
W ×60
W ×54
W ×49
11.4
11.1
10.8
10.6
10.4
10.2
10.1
8.00
1.25 126
1.12 112
0.990 98.5
0.870 85.9
0.770 75.7
0.680 66.7
0.615 60.0
0.560 54.6
W10×45
W ×39
W ×33
10.1
2.00
3.00
0.620
0.530
0.435
49.1
42.1
35.0
9.75
8.49
7.49
6.33
5.48
4.80
4.88
4.20
3.67
3.61
3.08
2.67
W10×30
W ×26
W ×22
10.5
10.3
10.2
0.510
0.440
0.360
32.4
27.9
23.2
8.64
7.33
6.51
5.75
4.86
4.29
4.51
3.80
3.34
3.41
2.85
2.50
W10×19
W ×17
W ×15
W ×12
10.2
10.1
9.00
7.00
0.395
0.330
0.270
0.210
18.8
16.2
13.8
10.9
6.52
6.01
5.52
4.43
4.33
3.98
3.64
2.91
3.39
3.10
2.83
2.26
2.55
2.33
2.12
1.68
W8×67
W ×58
W ×48
W ×40
W ×35
W ×31
0.00
5.00
0.00
5.00
2.00
0.935
0.810
0.685
0.560
0.495
0.435
60.4
52.0
43.3
35.5
31.2
27.5
12.2
10.4
7.89
6.71
5.66
5.06
7.42
6.24
4.63
3.89
3.24
2.88
5.44
4.52
3.32
2.74
2.28
2.01
W8×28
W ×24
6.00
3.00
0.465
0.400
24.3
20.9
5.04
4.23
2.89
2.40
2.02
1.67
W8×21
W ×18
8.00
4.00
0.400
0.330
18.2
15.2
4.55
4.02
2.67
2.35
1.91
1.66
W8×15
W ×13
W ×10
1.00
9.00
9.00
0.315
0.255
0.205
11.8
9.91
7.81
4.03
3.61
2.65
2.36
2.10
1.54
1.68
1.49
1.08
5
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
6
7
8
9
10
CONNECTED ELEMENTS
8 - 237
Other Elements in Connections
Shims
Shims are furnished to the erector for use in filling the spaces allowed for field clearance
which might be present at connections such as simple shear connections, PR and FR
moment connections, column base plates, and column splices. These shims, illustrated
in Figure 8-63, may be either strip shims, with round punched holes, or finger shims, with
slots cut through the edge. Whereas strip shims are less expensive to fabricate, finger
shims may be laterally inserted and eliminate the need to remove erection bolts or pins
already in place.
Finger shims, when inserted fully against the bolt shank, are acceptable for slip-critical
connections and are not to be considered as an internal ply with the slotted hole
determining the design strength of the connection. This is because less than 25 percent
of the contact surface is lost and this is not enough to affect the performance of the joint.
Fillers
A filler is furnished to occupy spaces which will be present because of dimensional
separations between elements of a connection across which load transfer occurs. Examples where fillers might be used are beams framing off center on a column and raised
beams.
From LRFD Specification Section J6, fillers in welded connections and fillers thicker
than 3⁄4-in. in bolted bearing-type connections must be fully developed. In bolted bearing-type connections, fillers between 1⁄4-in. and 3⁄4-in. thick, inclusive, need not be
developed, provided the design shear strength of the bolts is reduced by the factor
0.4(t − 0.25)
where t is the total thickness of the fillers up to 3⁄4-in. In bolted slip-critical connections,
fillers need not be fully developed.
Strip
Finger
Fig. 8-63. Shims.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
8 - 238
BOLTS, WELDS, AND CONNECTED ELEMENTS
REFERENCES
Alexander, W. G., 1991, “Designing Longitudinal Welds for Bridge Members,” Engineering Journal, Vol. 28, No. 1, (1st Qtr.), pp. 29–36, AISC, Chicago, IL.
American Concrete Institute, 1985, ACI 349 Code Requirements for Nuclear Safety
Related Concrete Structures, Appendix B, ACI, Detroit, MI.
American Institute of Steel Construction, Inc., 1993, Load and Resistance Factor Design
Specification for Structural Steel Buildings, AISC, Chicago, IL.
American Institute of Steel Construction, Inc., 1989, Manual of Steel Construction—
Allowable Stress Design, 9th ed., AISC, Chicago, IL.
American Institute of Steel Construction, Inc., 1988, Quality Criteria and Inspection
Standards, 3rd ed., AISC, Chicago, IL.
American Institute of Steel Construction, Inc., 1973, “Commentary on Highly Restrained
Welded Connections,” Engineering Journal, Vol. 10, No. 3, (3rd Qtr.), pp. 61–73,
AISC, Chicago, IL.
American Welding Society, 1978, Welding Handbook—Volume 2, 7th ed., AWS, Miami,
FL.
American Welding Society, 1977, Guide for the Non-Destructive Inspection of Welds,
(AWS B1.0-77), AWS, Miami, FL.
Astaneh, A., 1985, “Procedure for Design and Analysis of Hanger-Type Connections,”
Engineering Journal, Vol. 22, No. 2, (2nd Qtr.), pp. 63–66, AISC, Chicago, IL.
Blodgett, O. W., 1966, Design of Welded Structures, James F. Lincoln Arc Welding
Foundation, Cleveland, OH.
Blodgett, O. W., 1980, “Detailing to Achieve Practical Welded Fabrication,” Engineering
Journal, Vol. 17, No. 4, (4th Qtr.), pp. 106–119, AISC, Chicago, IL.
Bowman, M. D. and M. Betancourt, 1991, “Reuse of A325 and A490 High-Strength
Bolts,” Engineering Journal, Vol. 28, No. 3, (3rd Qtr.), pp. 110–118, AISC,
Chicago, IL.
Butler, L. J., S. Pal, and G. L. Kulak, 1972, “Eccentrically Loaded Welded Connections,”
Journal of the Structural Division, Vol. 98, No. ST5, (May), pp. 989–1005, ASCE,
New York, N.Y.
Cannon, R. W., D. A. Godfrey, and F. L. Moreadith, 1981, “Guide to the Design of Anchor
Bolts and Other Steel Embedments,” Concrete International, Vol. 3, No. 7, (July 1981),
pp. 28–41, ACI, Detroit, MI..
Cheng, J. J., J. A. Yura, and C. P. Johnson, 1984, “Design and Behaviour of Coped
Beams,” Department of Civil Engineering, The University of Texas at Austin, Austin,
TX.
Crawford, S. F. and G. L. Kulak, 1968, “Behavior of Eccentrically Loaded Bolted
Connections,” Studies in Structural Engineering, (No. 4), Department of Civil
Engineering, Nova Scotia Technical College, Halifax, Nova Scotia.
DeWolf, J. T. and D. T. Ricker, 1990, Column Base Plates, AISC, Chicago, IL
Fisher, J. M., 1981, “Structural Details in Industrial Buildings,” Engineering Journal,
Vol. 18, No. 3, (3rd Qtr.), pp. 83–89, AISC, Chicago, IL.
Fisher, J. W. and J. H. A. Struik, 1974, Guide to Design Criteria for Bolted and Riveted
Joints, John Wiley & Sons, Inc., New York, NY.
Grover, L., 1946, Manual of Design for Arc Welded Steel Structures, Air Reduction Sales
Co., New York, NY.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
REFERENCES
8 - 239
Higgins, T. R., 1971, “Treatment of Eccentrically Loaded Connections in the AISC
Manual,” Engineering Journal, Vol. 8, No. 2, (April), pp. 52–54, AISC, Chicago, IL.
Institute of Welding, 1972, Procedures and Recommendations for the Ultrasonic Testing
of Butt Welds, London, England.
Iwankiw, N. R., 1987, “Design for Eccentric and Inclined Loads on Bolt and Weld
Groups,” Engineering Journal, Vol. 24, No. 4, (4th Qtr.), pp. 164–171, AISC,
Chicago, IL.
Kaufmann, J., A. W. Pense, and R. D. Stout, 1981, “An Evaluation of Factors Significant
to Lamellar Tearing,” Welding Journal Research Supplement, Vol. 60, No. 3, (March),
AWS, Miami, FL.
Krautkramer, J., 1977, Ultrasonic Testing of Materials, 2nd. ed., Springer-Verlag, Berlin,
West Germany.
Kulak, G. L., 1975, “Eccentrically Loaded Slip-Resistant Connections,” Engineering
Journal, Vol. 12, No. 2, (2nd Qtr.), pp. 52–55, AISC, Chicago, IL.
Lesik, D. F. and D. J. L. Kennedy, 1990, “Ultimate Strength of Fillet-Welded Connections
Loaded in Plane,” Canadian Journal of Civil Engineering, Vol. 17, No. 1, National
Research Council of Canada, Ottawa, Canada.
Kulak, G. L. and Timler, 1984, “Tests on Eccentrically Loaded Fillet Welds,” Department
of Civil Engineering, University of Alberta, Edmonton, Canada.
Kulak, G. L., J. W. Fisher, and J. H. A. Struik, 1987, Guide to Design Criteria for Bolted
and Riveted Joints, 2nd ed., John Wiley & Sons, New York, NY.
Marsh, M. L., and E. G. Burdette, 1985a, “Anchorage of Steel Building Components to
Concrete,” Engineering Journal, Vol. 15, No. 4, (4th Qtr.), pp. 33–39, AISC,
Chicago, IL.
Marsh, M. L., and E. G. Burdette, 1985b, “Multiple Bolt Anchorages: Method for
Determining the Effective Projected Area of Overlapping Stress Cones,” Engineering
Journal, Vol. 15, No. 4, (4th Qtr.), pp. 29–32, AISC, Chicago, IL.
Research Council on Structural Connections, 1988, Load and Resistance Factor Design
Specification for Structural Joints Using ASTM A325 or A490 Bolts, AISC,
Chicago, IL.
Shipp, J. G. and E. R. Haninger, 1983, “Design of Headed Anchor Bolts,” Engineering
Journal, Vol. 20, No. 2, (2nd Qtr.), pp. 58–69, AISC, Chicago. IL.
Stout, R. D. and W. D. Doty, 1978, Weldability of Steels, 3rd. ed., Welding Research
Council, New York, NY
Thornton, W. A., 1985, “Prying Action—A General Treatment,” Engineering Journal,
Vol. 22, No. 2, (2nd Qtr.), pp. 67–75, AISC, Chicago, IL.
Tide, R. H. R., 1980, “Eccentrically Loaded Weld Groups—AISC Design Tables,”
Engineering Journal, Vol. 17, No. 4, (4th Qtr.), pp. 90–95, AISC, Chicago, IL.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
10 - 1
PART 10
FULLY RESTRAINED (FR) MOMENT CONNECTIONS
OVERVIEW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10-3
FULLY RESTRAINED (FR) MOMENT CONNECTIONS . . . . . . . . . . . . . . . . . 10-7
Flange-Plated Connections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10-9
Directly Welded Flange Connections . . . . . . . . . . . . . . . . . . . . . . . . . . . 10-19
Extended End-Plate Connections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10-21
COLUMN STIFFENING AT FR AND PR MOMENT CONNECTIONS . . . . . . . . . 10-35
Transverse Stiffener Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10-41
Doubler Plate Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10-49
Diagonal Stiffeners . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10-54
MOMENT SPLICES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10-56
Flange-Plated Moment Splices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10-56
Directly Welded Flange Moment Splices . . . . . . . . . . . . . . . . . . . . . . . . . 10-58
Extended End-Plate Splices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10-59
SPECIAL CONSIDERATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10-60
FR Moment Connections to Column Web Supports . . . . . . . . . . . . . . . . . . . 10-60
FR Moment Connections Across Girder Supports . . . . . . . . . . . . . . . . . . . . 10-65
Knee or Corner Connections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10-67
Non-Rectangular FR Moment Connections . . . . . . . . . . . . . . . . . . . . . . . 10-67
REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10-71
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
10 - 2
FULLY RESTRAINED (FR) MOMENT CONNECTIONS
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
OVERVIEW
10 - 3
OVERVIEW
Part 10 contains general information, design considerations, examples, and design aids for the
design of fully restrained (FR) moment connections, column stiffening, moment splices, and special
considerations in the aforementioned topics. It is based on the requirements of the 1993 LRFD
Specification. Supplementary information may also be found in the Commentary on the LRFD
Specification.
Following is a detailed list of the topics addressed.
FULLY RESTRAINED (FR) MOMENT CONNECTIONS . . . . . . . . . . . . . . . . . 10-7
Force Transfer in FR Moment Connections . . . . . . . . . . . . . . . . . . . . . . . . 10-7
Temporary Support During Erection . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10-7
Welding Considerations for FR Moment Connections . . . . . . . . . . . . . . . . . . . 10-8
Special Considerations for Seismic Loading . . . . . . . . . . . . . . . . . . . . . . . . 10-9
Flange-Plated Connections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10-9
Design Checks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10-9
Shop and Field Practices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10-9
Directly Welded Flange Connections . . . . . . . . . . . . . . . . . . . . . . . . . . . 10-19
Design Checks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10-19
Extended End-Plate Connections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10-21
Design Checks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10-21
Shop and Field Practices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10-21
Design Assumptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10-22
Four-Bolt Unstiffened Extended End-Plate Design . . . . . . . . . . . . . . . . . . 10-24
Eight-Bolt Stiffened Extended End-Plate Design . . . . . . . . . . . . . . . . . . . 10-30
COLUMN STIFFENING AT FR AND PR MOMENT CONNECTIONS . . . . . . . . . 10-35
Economical Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10-36
Local Flange Bending . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10-36
Intermediate Column Locations, Flange-Plated and Directly Welded Flange
Connections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10-36
Intermediate Column Locations, Extended End-Plate Connections . . . . . . . . . . 10-36
Column-End Locations, Flange-Plated, Directly Welded Flange, and
Extended End-Plate Connections . . . . . . . . . . . . . . . . . . . . . . . . . . 10-37
Local Web Yielding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10-38
Intermediate Column Locations, Flange-Plated and Directly Welded Flange
Connections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10-38
Intermediate Column Locations, Extended End-Plate Connections . . . . . . . . . . 10-39
Column-End Locations, Flange-Plated and Directly Welded Flange
Connections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10-39
Column-End Locations, Extended End-Plate Connections . . . . . . . . . . . . . . 10-39
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
10 - 4
FULLY RESTRAINED (FR) MOMENT CONNECTIONS
Web Crippling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10-39
Compression Buckling of the Web . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10-39
Intermediate Column Locations, Flange-Plated, Directly Welded Flange, and
Extended End-Plate Connections . . . . . . . . . . . . . . . . . . . . . . . . . . . 10-40
Column-End Locations, Flange-Plated, Directly Welded Flange, and
Extended End-Plate Connections . . . . . . . . . . . . . . . . . . . . . . . . . . . 10-40
Panel Zone Web Shear . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10-40
Transverse Stiffener Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10-41
Concentric Transverse Stiffeners . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10-41
Eccentric Transverse Stiffeners . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10-48
Concurrent Strong-Axis and Weak-Axis FR Connections . . . . . . . . . . . . . . . 10-49
Doubler Plate Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10-49
For Local Web Yielding or Compression Buckling of the Web . . . . . . . . . . . . . 10-50
For Panel Zone Web Shear . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10-50
At Locations of Weak-Axis Connections . . . . . . . . . . . . . . . . . . . . . . . . 10-51
Diagonal Stiffeners . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10-54
MOMENT SPLICES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10-56
Location of Moment Splices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10-56
Force Transfer in Moment Splices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10-56
Flange-Plated Moment Splices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10-56
Design Checks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10-56
Shop and Field Practices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10-56
Directly Welded Flange Moment Splices . . . . . . . . . . . . . . . . . . . . . . . . . 10-58
Design Checks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10-58
Shop and Field Practices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10-58
Extended End-Plate Splices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10-59
Design Checks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10-59
Shop and Field Practices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10-59
SPECIAL CONSIDERATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10-60
FR Moment Connections to Column Web Supports . . . . . . . . . . . . . . . . . . . . 10-60
Recommended Details . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10-60
Ductility Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10-61
FR Moment Connections Across Girder Supports . . . . . . . . . . . . . . . . . . . . . 10-65
Top Flange Connection
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10-66
Bottom Flange Connection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10-66
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
OVERVIEW
10 - 5
Web Connection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10-66
Knee or Corner Connections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10-67
Non-Rectangular FR Moment Connections . . . . . . . . . . . . . . . . . . . . . . . 10-67
Skewed Connections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10-68
Sloped Connections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10-68
REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10-71
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
10 - 6
FULLY RESTRAINED (FR) MOMENT CONNECTIONS
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
FULLY RESTRAINED (FR) MOMENT CONNECTIONS
10 - 7
FULLY RESTRAINED (FR) MOMENT CONNECTIONS
Fully restrained (FR) moment connections are also known as continuous or rigid-frame
connections. As defined in LRFD Specification Section A2.2, FR moment connections
possess sufficient rigidity to maintain the angles between intersecting members as
illustrated in Figure 10-1. While connections considered to be fully restrained seldom
provide for zero rotation between members, the small amount of flexibility present is
usually neglected and the connection is idealized to prevent relative rotation. Connections
A, B, and C in Figure 10-2 illustrate this.
Force Transfer in FR Moment Connections
LRFD Specification Section B9 states that end connections in FR construction shall be
designed to carry the factored forces and moments, except that some inelastic but
self-limiting deformation of a part of the connection is permitted. Huang, et al. (1973)
showed that the moment may be resolved into an effective tension-compression couple
acting as axial forces at the beam flanges. The flange force Puf may be calculated as:
Puf =
Mu
dm
where
Puf = factored beam flange force, tensile or compressive, kips
Mu = beam end moment, kip-in.
dm = moment arm between the flange forces, in. (varies for all FR connections and
for stiffener design)
Furthermore, it was shown that shear is primarily transferred through the beam web
shear connection. Since, by definition, the angle between the beam and column in an FR
moment connection remains unchanged under loading, eccentricity may be neglected
entirely in the shear connection. Additionally, it is permissible to use bolts in bearing in
either standard or slotted holes perpendicular to the line of force. Axial forces, if present,
are assumed to be distributed uniformly across the beam cross-sectional area, and are
additive algebraically to the flange forces and vectorially to the shear force.
The supporting column must have sufficient strength and stiffness to develop the
moment transferred to it through the FR moment connection. Additionally, the concentrated flange forces may require the selection of a larger column section or the stiffening
of the existing column section; refer to “Column Stiffening” in this Part.
Temporary Support During Erection
Bolted construction provides a ready means to erect and temporarily connect members
by use of the bolt holes. In contrast, FR moment connections in welded construction must
Full restraint
No relative rotation
Fig. 10-1. Illustration of fully restrained (FR) moment connection.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
10 - 8
FULLY RESTRAINED (FR) MOMENT CONNECTIONS
be given special attention so that all pieces may be erected, fitted, and supported until the
necessary welds are made, sometimes at a much later date. Temporary support can be
provided in welded construction by furnishing holes for erection bolts, temporary seats,
special lugs, or by other means.
Temporary erection aids should be carefully studied for their effect on the finished
structure, particularly on members subjected to fatigue or tension loading. They should
be permitted to remain in place whenever possible since they seldom are reusable and
the cost to remove them can be significant. If left in place, erection aids should be located
so as not to cause a stress concentration. If, however, erection aids are to be removed,
care should be taken so that the base metal is not damaged.
Temporary supports should be sufficient to carry any loads imposed by the erection
process, such as the dead weight of the member, additional construction equipment, or
material storage. Additionally, they must be flexible enough to allow plumbing of the
structure, particularly in tier buildings.
Welding Considerations for Fully Restrained Connections
Field welding should be arranged for down-hand or horizontal position welding and
preference should be given to fillet welds over groove welds when possible. Additionally,
the joint detail and welding procedure should be constructed to minimize distortion and
the possibility of lamellar tearing.
FR moment connections
B
A
C
Fixed end
moment
PR moment connections
End
moment
Beam line
simple shear connections
Simple beam rotation
Rotation
A
B
Fig. 10-2. FR moment connection behavior.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
C
FULLY RESTRAINED (FR) MOMENT CONNECTIONS
10 - 9
The typical complete-joint-penetration groove weld in a directly welded flange connection for a rolled beam can be expected to shrink about 1⁄16-in. in the length dimension
of the beam when it cools and contracts. Thicker welds, such as for welded plate-girder
flanges will shrink even more—up to 1⁄8-in. or 3⁄16-in. This amount of shrinkage can cause
erection problems in locating and plumbing the columns along lines of continuous beams.
A method of calculating weld shrinkage may be found in Lincoln Electric Co. (1973)
Weld shrinkage can best be controlled by fabricating the beam longer than required by
the amount of the anticipated weld shrinkage. Alternatively, the weld-joint opening could
be increased; refer to AWS D1.1.
Unnecessarily thick stiffeners with complete-joint-penetration groove welds should be
avoided since the accompanying weld shrinkage may contribute to lamellar tearing; refer
to “Minimizing Weld Repairs—Lamellar Tearing” in Part 8.
Special Considerations for Seismic Loading
The effect of severe seismic loading on test specimens subjected to low-cycle fatigue
tests is discussed in Krawinkler and Popov (1982). Slippage occured early in the inelastic
cycles for slip-critical-bolted shear connections indicating the possible existence of
bending and shearing forces in the beam flange close to the connecting weld. Thus, it is
recommended that the shear connection be designed for a portion of the bending moment
when deep rolled beams and plate girders are rigidly connected to a column flange
support. Refer to AISC Seismic Provisions for Structural Steel Buildings.
Flange-Plated Connections
As illustrated in Figure 10-3, a flange-plated FR moment connection consists of a shear
connection and top and bottom flange plates which connect the flanges of the supported
beam to the supporting column. These flange plates are welded to the supporting column
and may be bolted or welded to the flanges of the supported beam.
Design Checks
The design strengths of the bolts and/or welds and connected elements must be determined in accordance with the LRFD Specification; the applicable limit states are
discussed in Part 8. The effect of eccentricity in the shear connection may be neglected.
The strength of the supporting column (and thus the need for stiffening) must be checked;
refer to “Column Stiffening” in this Part.
Shop and Field Practices
In a column flange connection, the flange plates are usually located with respect to the
column web centerline. Because of the column-flange mill tolerance on out-ofsquareness with the web, it is desirable to shop-fit long flange plates from the theoretical
column-web centerline to assure good field fit-up with the beam. Misalignment on short
connections, as illustrated in Figure 10-4, can be accommodated by providing oversized
holes in the plates. Since mill tolerances in both the beam and the column may cause
significant shop and/or field assembly problems, it may be desirable to ship the flange
plates loose for field attachment to the column.
Example 10-1
Given:
Design a bolted flange-plated FR moment connection for a W18×50
beam to W14×99 column-flange connection. For structural members,
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
10 - 10
FULLY RESTRAINED (FR) MOMENT CONNECTIONS
assume Fy = 50 ksi and Fu = 65 ksi; for connecting material, assume Fy
= 36 ksi and Fu = 58 ksi. Use 7⁄8-in. diameter ASTM A325-N bolts and
70 ksi electrodes.
Ru = 45.0 kips
Mu = 250 ft-kips
Shim top or bottom as required
Check column for stiffening requirements
(a) Column flange support, bolted flange plates
Shim top or bottom as required
Check column for stiffening requirements
(b) Column web support, bolted flange plates
Fig. 10-3. Flange-plated FR moment connections.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
FULLY RESTRAINED (FR) MOMENT CONNECTIONS
10 - 11
W18×50
d = 17.99 in.
tw = 0.355 in.
bf = 7.495 in.
tf = 0.570 in.
Zx = 101 in.3
Shim top or bottom as required
Check column for stiffening requirements
(c) Column flange support, welded flange plates
Shim top or bottom as required
Check column for stiffening requirements
(d) Column web support, welded flange plates
Fig. 10-3 (cont.). Flange-plated FR moment connections.
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10 - 12
FULLY RESTRAINED (FR) MOMENT CONNECTIONS
W14×99
d = 14.16 in.
tw = 0.485 in.
Solution:
bf = 14.565 in.
tf = 0.780 in.
k = 17⁄16-in.
T = 111⁄4-in.
Check beam design flexural strength:
Zreq =
=
Mu × 12 in. / ft
0.9Fy
(250 ft−kips) (12 in. / ft)
0.9(50 ksi)
= 66.7 in.3
Assuming two rows of 7⁄8-in. diameter A325-N bolts in standard holes,
from LRFD Specification Section B.10:
Afg = bf × tf
= 7.495 in. × 0.570 in.
= 4.27 in.2
Afn = Afg − 2(db + 1⁄8-in.)tf
= 4.27 in.2 − 2(7⁄8-in. + 1⁄8-in.)(0.570 in.)
= 3.13 in.2
since 0.75Fu Afn (= 153 kips) is less than 0.9Fy Afg ( = 192 kips), the
effective tension flange area Afe is:
Afe =
5 Fu
A
6 Fy fn
Column subject to
mill tolerance
Actual centerline
Theoretical centerline
Fig. 10-4. Effect of mill tolerances on flange-plate alignment.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
FULLY RESTRAINED (FR) MOMENT CONNECTIONS
=
5
6
10 - 13
65 ksi
3.13 in.2
50 ksi
= 3.39 in.2
This is a 20.6 percent reduction from the gross flange area Afg and the
effective plastic section modulus Ze is:
d
Ze ≈ Zx − 2 0.206Afg
2
17.99 in.
≈ 101 in.3 − 2 0.206 × 4.27 in.2 ×
2
≈ 85.2 in.3
Since Ze > Zreq, the beam design flexural strength is o.k.
Design the single-plate web connection.
Determine number of 7⁄8-in. diameter A325-N bolts required for shear.
From Table 8-11:
nmin =
=
Ru
φrn
45.0 kips
21.6 kips / bolt
= 2.08→
→3 bolts
Try PL 5⁄16×9
Determine number of 7⁄8-in. diameter A325-N bolts required for material bearing, assuming Le = 11⁄2-in., and s = 3 in. The 5⁄16-in. plate is more
critical than the 0.355-in. thick beam web. From Table 8-13:
nmin =
=
Ru
φrn
45.0 kips
28.6 kips / bolt
= 1.57→
→2 bolts
Bolt shear is more critical. Try a three-bolt single-plate connection.
Check shear yielding of the plate:
φRn = 0.9(0.6Fy Ag)
= 0.9[0.6 × 36 ksi (9 in. × 5⁄16-in.)]
= 54.7 kips > 45.0 kips o.k.
Check shear rupture of the plate:
φRn = 0.75 ( 0.6Fu An)
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
10 - 14
FULLY RESTRAINED (FR) MOMENT CONNECTIONS
= 0.75 [0.6 × 58 ksi (9 in. − 3 (7⁄8-in. + 1⁄8-in.)) 5⁄16-in.]
= 48.9 kips > 45.0 kips o.k.
Check block shear rupture of the plate:
With Leh = 11⁄2-in. and Lev = 11⁄2-in., from Tables 8-47a and 8-48a,
0.6Fu Anv > Fu Ant. Thus,
φRn = φ[0.6Fu Anv + Fy Agt]
From Tables 8-48a and 8-48b,
φRn = (139 kips / in. + 40.5 kips / in.)5⁄16-in.
= 56.1 kips > 45.0 kips o.k.
Determine required weld size for fillet welds to supporting column
flange:
Dmin =
=
Ru
2 × 1.392l
45.0 kips
2 × 1.392(9 in.)
= 1.80 → 2 sixteenths
From LRFD Specification Table J2.4, since the column flange thickness is over 3⁄4-in., the minimum fillet weld size is 5⁄16-in., use two 5⁄16-in.
fillet welds.
Design the tension flange plate and connection.
Calculate the flange force Puf :
Puf =
=
Mu × 12 in. / ft
d
(250 ft−kips)(12 in. / ft)
17.99 in.
= 167 kips
Determine number of 7⁄8-in. diameter A325-N bolts required for shear.
From Table 8-11:
nmin =
=
Puf
φrn
167 kips
21.6 kips / bolt
= 7.73→
→8 bolts
Try PL 3⁄4-in.×7in.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
FULLY RESTRAINED (FR) MOMENT CONNECTIONS
10 - 15
Determine number of 7⁄8-in. diameter A325-N bolts required for material bearing on beam flange (more critical than flange plate), assuming
Le ≥ 1.5d and s = 3 in. From Table 8-13:
nmin =
=
Puf
φrn
167 kips
28.6 kips / bolt
= 5.84→
→6 bolts (even number required)
Bolt shear is more critical. Try two rows of four bolts on a 4-in. gage.
Check tension yielding of flange plate:
φRn = φFy Ag
= 0.9 × 36 ksi × 7 in. × 3⁄4-in.
= 170 kips > 167 kips o.k.
Check tension rupture of flange plate:
φRn = φFu An
= 0.75 × 58 ksi [7 in. − 2 × ( 7⁄8-in. + 1⁄8-in.)] 3⁄4-in.
= 163 kips < 167 kips required n.g.
Try PL 3⁄4-in.×71⁄4-in.:
φRn = 0.75 × 58 ksi [71⁄4-in. − 2 × ( 7⁄8-in. + 1⁄8-in.)] 3⁄4-in.
= 171 kips > 167 kips o.k.
Check block shear rupture of flange plate:
There are two cases for which block shear must be checked. The first
case involves the tearout of the two blocks outside the two rows of bolt
holes in the flange plate; for this case Leh = 15⁄8-in. and Lev = 11⁄2-in. The
second case involves the tearout of the block between the two rows of
holes in the flange plate. Tables 8-47 and 8-48 may be adapted for this
calculation by considering the 4-in. width to be comprised of two 2-in.
wide blocks where Leh = 2 in. and Lev = 11⁄2-in. Thus, the former case
is more critical. From Tables 8-47a and 8-48a, 0.6Fu Anv > Fu Ant. Thus,
φRn = φ [0.6Fu Anv + Fy Agt]
From Tables 8-48a and 8-48b,
φRn = 2 (183 kips/in. + 43.9 kips/in.) 3⁄4-in.
= 340 kips > 167 kips o.k.
Determine required weld size for fillet welds to supporting column
flange:
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10 - 16
FULLY RESTRAINED (FR) MOMENT CONNECTIONS
Dmin =
=
Puf
2 × 1.392(l)
167 kips
2 × 1.392(71⁄4−in.)
= 8.27→
→9 sixteenths
Use 9⁄16-in. fillet weld.
Since these fillet welds are large, groove welds may be more economical.
Design the compression flange plate and connection.
Check design compressive strength of flange plate assuming K = 0.65
and l = 2 in. (11⁄2-in. edge distance plus 1⁄2-in. setback)
Kl
=
r
0.65 (2 in.)
√
71⁄4−in.) (3⁄4−in.)3 / 12
(71⁄4−in.) (3⁄4−in.)
= 6.00
From LRFD Specification Table 3-36 with
Kl
= 6.00,
r
φFcr = 30.54 ksi
and the design compressive strength of the flange plate is
φRn = φcFcr A
= (30.54 ksi) (71⁄4-in. × 3⁄4-in.)
= 167 kips
Since the design strength equals the required strength, the flange plate
is adequate.
The compression flange plate will be identical to the tension flange
plate: a 3⁄4-in.×71⁄4-in. plate with eight bolts in two rows of four bolts
on a 4-in. gage and 9⁄16-in. fillet welds to the supporting column flange.
Check the column section for stiffening requirements; refer to Example
10-6.
Example 10-2
Given:
Design a welded flange-plated FR moment connection for a W18×50
beam to W14×99 column flange connection. For structural members,
Fy = 50 ksi; for connecting material Fy = 36 ksi. Use 70 ksi electrodes
and ASTM A325-N bolts.
Ru = 45.0 kips
Mu = 250 kips
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
FULLY RESTRAINED (FR) MOMENT CONNECTIONS
10 - 17
W18×50
d = 17.99 in.
tw = 0.355 in.
bf = 7.495 in.
tf = 0.570 in.
Zx = 101 in.3
bf = 14.565 in.
tf = 0.780 in.
k = 17⁄16-in.
T = 111⁄4-in.
W14×99
d = 14.16 in.
tw = 0.485 in.
Solution:
Check beam design flexural strength:
Zreq =
=
Mu × 12 in. / ft
0.9Fy
(250 ft−kips)(12 in. / ft)
0.9(50 ksi)
= 66.7 in.3
= 101 in.3
Zx
Since Zx > Zreq, the beam design flexural strength is o.k.
Design the single-plate web connection.
From Example 10-1, a three-bolt, 5⁄16-in. thick single plate with two
5⁄ -in. fillet welds will be adequate.
16
Design the tension flange plate and connection.
Calculate the flange force Puf.
Puf =
=
Mu × 12 in. / ft
d
(250 ft−kips)(12 in. / ft)
17.99 in.
= 167 kips
Determine tension flange-plate dimensions.
From Figure 8-42, assume a shelf dimension of 5⁄8-in. on both sides of
the plate. The plate width, then, is 7.495 in. − 2(5⁄8-in.) = 6.245. Try a
1 in.×61⁄4-in. flange plate.
Check tension yielding of the flange plate:
φRn = φFy Ag
= 0.9 × 36 ksi × 61⁄4-in. × 1 in.
= 202.5 kips o.k.
Determine required weld size and length for fillet welds to beam
flange. Try a 5⁄16-in. fillet weld. The minimum length of weld lmin is:
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
10 - 18
FULLY RESTRAINED (FR) MOMENT CONNECTIONS
lmin =
=
Puf
2 × 1.392(D)
167 kips
2 × 1.392 (5 sixteenths)
= 12.0 in.
Use 3 in. of weld along each side and 61⁄4-in. of weld along the end of
the flange plate.
Determine required weld size for fillet welds to supporting column
flange:
Dmin =
=
Puf
2 × 1.392(l)
167 kips
2 × 1.392(61⁄4−in.)
= 9.60→
→10 sixteenths
Use 5⁄8-in. fillet welds.
Since these fillet welds are large, groove welds may be more economical.
Design the compression flange plate and connection:
The compression flange plate should have approximately the same area
as the tension flange plate (6.25 in.2). Assume a shelf dimension of
5⁄ -in. The plate width, then, is 7.495 in. + 2(5⁄ -in.) = 8.745. To
8
8
approximately balance the flange-plate areas, try a 3⁄4-in.×83⁄4-in. compression flange plate.
Check design compressive strength of flange plate assuming K = 0.65
and l = 2 in. (11⁄2-in. edge distance plus 1⁄2-in. setback).
Kl
=
r
0.65 (2 in.)
√
(8 4−in.) (3⁄4−in.)3 / 12
(83⁄4−in.) (3⁄4−in.)
3⁄
= 6.00
From LRFD Specification Table 3-36 with
Kl
= 6.00,
r
φcFcr = 30.54 ksi
and the design compressive strength of the flange plate is
φRn = φcFcr A
= (30.54 ksi)(83⁄4-in. × 3⁄4-in.)
= 200 kips > 167 kips o.k.
Determine required weld size and length for fillet welds to beam flange.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
FULLY RESTRAINED (FR) MOMENT CONNECTIONS
10 - 19
As before for the tension flange plate, use a 5⁄16-in. fillet weld and six
inches of weld along each side of the beam flange.
Determine required weld size for fillet welds to supporting column
flange.
As before for the tension flange plate, use 5⁄8-in. fillet welds.
Check the column section for stiffening requirements; refer to Example
10-6.
Directly Welded Flange Connections
As illustrated in Figure 10-5, a directly welded flange FR moment connection consists
of a shear connection and complete-joint-penetration groove welds which directly
connect the top and bottom flanges of the supported beam to the supporting column. Note,
in Figure 10-5b, the stiffener extends beyond the toe of the column flange to eliminate
the effects of triaxial stresses.
The plastic moment of the supported beam φMp can be developed with sufficient
inelastic rotation and deformation capacity through such a connection. This apparent
increase in beam strength above the prediction of elastic theory occurs because of strain
hardening in the flanges. See Huang, et al. (1973), Krawinkler and Popov (1982), and
Beedle, et al. (1973).
Design Checks
The design strengths of the bolts and/or welds and connected elements must be determined in accordance with the LRFD Specification; the applicable limit states are
discussed in Part 8. The strength of the supporting column (and thus the need for
stiffening) must be checked; refer to “Column Stiffening” in this Part.
Example 10-3
Given:
Design a directly welded flange FR moment connection for a W18×50
beam to W14×99 column-flange connection. For structural members,
assume Fy = 50 ksi and Fu = 65 ksi; for connecting material, assume Fy
= 36 ksi and Fu = 50 ksi. Use 70 ksi electrodes and ASTM A325-N bolts.
Ru = 45.0 kips
Mu = 250 kips
W18×50
d = 17.99 in.
tw = 0.355 in.
bf = 7.495 in.
tf = 0.570 in.
Zx = 101 in.3
bf = 14.565 in.
tf = 0.780 in.
k = 17⁄16-in.
T = 111⁄4-in.
W14×99
d = 14.16 in.
tw = 0.485 in.
Solution:
Check beam design flexural strength.
From Example 10-2, the beam design flexural strength is o.k.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
10 - 20
FULLY RESTRAINED (FR) MOMENT CONNECTIONS
Design the single-plate connection.
From Example 10-1, three 7⁄8-in. diameter A325-N bolts, 5⁄16-in. thick
single plate with two 5⁄16-in. fillet welds will be adequate.
A complete-joint-penetration groove weld will transfer the entire
flange force in tension and compression.
Both flanges typ.
Check column for stiffening requirements
(a) Column flange support
Both flanges typ.
Check column for stiffening requirements
(b) Column web support
Fig. 10-5. Directly welded flange FR connections.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
FULLY RESTRAINED (FR) MOMENT CONNECTIONS
10 - 21
Check the column flange section for stiffening requirements; refer to
Example 10-6.
Extended End-Plate Connections
Extended end-plate connections may be used only in statically loaded applications
(buildings in seismic zone 1 and unimportant buildings in seismic zone 2 are considered
staically loaded) because adequate research has not been conducted on their low-cycle
fatigue strength. Wind, snow, and temperature loads are considered static loads.
As illustrated in Figure 10-6, an extended end-plate connection consists of a plate of
length greater than the beam depth, perpendicular to the longitudinal axis of the supported
beam. The end-plate is always welded to the web and flanges of the supported beam on
each side and bolted to the supporting member with fully tensioned high-strength bolts.
As illustrated in Figure 10-7, extended end-plate connections are classified by the
number of bolts at the tension flange and may be used with or without end-plate stiffeners.
The four-bolt unstiffened extended end-plate connection of Figure 10-7a is generally
limited by bolt strength to use with less than one-half of the available beam sections. The
strength of this connection can be increased by increasing the number of bolts per row
to four, as shown in Figure 10-7b. Note that the four-bolt-wide unstiffened case requires
a wide supporting column flange. An alternative is the eight-bolt stiffened extended
end-plate connection shown in Figure 10-7c.
Design assumptions and basic procedures for the four-bolt unstiffened and eight-bolt
stiffened configurations follow. For the design procedure for four-bolt-wide unstiffened
extended end-plate connections, or for a more detailed discussion of the aforementioned
design procedures, refer to the AISC Design Guide Extended End-Plate Moment Connections (Murray, 1990).
Design Checks
The design strengths of the bolts and/or welds and connected elements must be determined in accordance with the LRFD Specification; the applicable limit states are
discussed in Part 8. The strength of the supporting column (and thus the need for
stiffening) must be checked; refer to “Column Stiffening” in this Part.
When fully-tensioned bearing bolts (N or X) are used, they must be designed using the
shear-tension interaction equation of LRFD Specification Table J3.5. If bolts are to be
slip-critical, all bolts may be designed for shear only and the shear-tension interaction
equation may be ignored. From RCSC Specification Commentary Section C5, “Connections of the type…in which some of the bolts lose a part of their clamping force due to
applied tension suffer no overall loss of frictional resistance. The bolt tension produced
by the moment is coupled with a compensating compressive force on the other side of
the axis in bending.” Thus, the net clamping force is maintained in the connection.
Shop and Field Practices
This type of connection requires extra care in shop fabrication and field erection. The
fit-up of extended end-plate connections is sensitive to the column flanges and may be
affected by column flange-to-web squareness, beam camber, or squareness of the beam
end. The beam is frequently fabricated short to accommodate the column overrun
tolerances with shims furnished to fill any gaps which might result.
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10 - 22
FULLY RESTRAINED (FR) MOMENT CONNECTIONS
Design Assumptions
Several assumptions have been made in the design procedures which follow for four-bolt
unstiffened and eight-bolt stiffened extended end-plate connections. These assumptions
are as follows:
1. Fully-tensioned ASTM A325 or A490 high-strength bolts in diameters not greater
than 11⁄2-in. must be used, except that ASTM A490 bolts should not be used in the
eight-bolt stiffened configuration.
Both flanges typ.
Check column for stiffening requirements
(a) Column flange support
Accessibility may limit
weld length
Both flanges typ.
Check column for stiffening requirements
(b) Column web support
Fig. 10-6. Extended end-plate FR connections.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
FULLY RESTRAINED (FR) MOMENT CONNECTIONS
10 - 23
2. End-plate material should preferably be ASTM A36.
3. Only static loading is permitted (wind, snow, and temperature loads are considered
static loads).
4. The recommended minimum distance from the face of the beam flange to the nearest
bolt centerline is the bolt diameter db plus 1⁄2-in. Note that, although the smallest
possible distance will generally result in the most economical connection, many
fabricators prefer to use a standard dimension, usually two inches, which is adequate
for all bolt diameters.
5. The end-plate width which is effective in resisting the applied moment is not greater
than the beam flange width bf plus 1 in.
6. The gage of the tension bolts (horizontal distance between vertical bolt lines) should
not exceed the beam tension flange width.
7. When the applied moment is less than the design flexural strength of the beam, the
bolts and end plate may be designed for the applied moment only. However,
beam-web-to-end-plate welds in the vicinity of the tension bolts should be designed
to develop 60 percent of the minimum specified yield strength of the beam web.
This is recommended even if the full design flexural strength of the beam is not
required for frame strength.
8. Only the web-to-end-plate weld between the mid-depth of the beam and the inside
face of the beam compression flange or the weld between the inner row of tension
bolts plus 2db and the inside face of the beam compression flange, whichever is
smaller, is considered effective in resisting the beam end shear.
(a) Four-bolt unstiffened
(b) Four-bolt-wide unstiffened
(c) Eight-bolt stiffened
Fig. 10-7. Configurations of extended end-plate FR connection.
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FULLY RESTRAINED (FR) MOMENT CONNECTIONS
Four-Bolt Unstiffened Extended End-Plate Design
The following design procedure is based on Krishnamurthy (1978), Hendrick and Murray
(1984), and Curtis and Murray (1989). In Krishnamurthy’s design procedure, prying
action forces are considered to be negligible and the tensile flange force is distributed
equally among the four tension bolts. Possible local yielding of the tension flange and
tensile area of the web is neglected.
The required end-plate thickness is determined using the tee-stub analogy, as illustrated
in Figure 10-8, with the effective critical moment in the end plate given by
Meu =
αmPuf pe
4
where
Puf
αm
Ca
Cb
bf
bp
Af
Aw
pe
= factored beam flange force, kips
1
1
= CaCb(Af / Aw) ⁄3 (pe / db) ⁄4
= constant from Table 10-1
1
= (bf / bp) ⁄2
= beam flange width, in.
= effective end-plate width, in., not to exceed bf + 1 in.
= area of beam tension flange, in.2
= area of beam web, clear of flanges, in.2
= effective pitch, in.
= pf − (db / 4) − wt
pf = distance from centerline of bolt to nearer surface of the tension flange, in.
Generally, db + 1⁄2-in. is enough to provide entering and tightening clearance;
two inches is a common standard.
wt = fillet weld throat size or size of reinforcement for groove weld, in.
db = nominal bolt diameter, in.
Values of Ca are tabulated for various combinations of beam and end-plate material grades
and ASTM A325 or A490 bolts in Table 10-1. Values of Af / Aw for the W-shapes listed
Mpl
Assumed inflection point
p
f
2
p
f
2
2ru
Puf
Mpl
2ru
Beam flange (tee stem)
End plate (tee flange)
Mpl =
p
2ru 2f
( ) = ru(pf )
Fig. 10-8. Tee-stub analogy for end-plate moment.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
FULLY RESTRAINED (FR) MOMENT CONNECTIONS
10 - 25
Table 10-1.
Values of Ca for Extended End-Plate Design
ASTM Bolt Desig.
A325
Beam Fy, ksi
End-Plate Fy, ksi
Ca
36
36
1.36
50
1.23
36
1.45
50
1.31
36
1.38
50
1.25
36
1.48
50
1.33
50
A490
36
50
Notes:
2⁄5
1⁄2
Favg
Fbt
Ca = 1.2 1.29
F
F
bu
b
Fbu = 93.0 ksi for A325 bolts; 115 ksi for A490 bolts.
Fbt = 44.0 ksi for A325 bolts; 54.0 ksi for A490 bolts.
in Part 1 are found in Table 10-2. The required end-plate thickness tpreq is then determined
as
tpreq =
√
4Meu
φFy bp
where Fy is the specified minimum yield stress of the end-plate material, ksi, and φ = 0.90.
The strength of the column should then be investigated for stiffening requirements;
refer to “Column Stiffening” in this Part. Note that, since column web stiffeners add
considerable fabrication expense and may interfere with weak-axis framing, it is often
advantageous to eliminate the need for stiffening. The designer should therefore consider
increasing the column size to a section with adequate strength. Alternatively, if the
column were inadequate due to local flange bending strength, increasing the tension-bolt
pitch pf or switching to an eight-bolt stiffened extended end-plate configuration may
increase the length of column flange effective in flange bending and thereby eliminate
the need for stiffening.
Example 10-4
Given:
Design a four-bolt unstiffened extended end-plate FR moment connection for a W18×50 beam to W14×99 column-flange connection. For
structural members, assume Fy = 50 ksi and Fu = 65 ksi; for connecting
material, assume Fy = 36 ksi and Fu = 58 ksi. Use ASTM A325-SC bolts
(Class A surfaces) and 70 ksi electrodes.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
10 - 26
FULLY RESTRAINED (FR) MOMENT CONNECTIONS
Table 10-2.
Values of Af / Aw for Extended End-Plate Design
Section Af / Aw
Section Af / Aw
Section Af / Aw
W44×335
×290
×262
×230
0.684
0.711
0.700
0.669
W40×593
×503
×431
×372
×321
×297
×277
×249
×215
×199
×174
0.824
0.806
0.782
0.777
0.771
0.768
0.822
0.816
0.809
0.706
0.550
W33×354
×318
×291
×263
×241
×221
×201
×169
×152
×141
×130
×118
0.925
0.926
0.913
0.909
0.853
0.829
0.807
0.667
0.612
0.583
0.541
0.492
0.611
0.600
0.582
0.581
0.588
0.617
0.610
0.607
0.510
0.426
0.961
0.905
0.887
0.861
0.672
0.606
0.590
0.558
0.516
0.476
1.140
1.011
1.002
1.003
0.994
0.995
0.683
0.686
0.683
0.667
0.641
0.532
0.465
0.423
W40×466
×392
×331
×278
×264
×235
×211
×183
×167
×149
W30×235
×211
×191
×173
×148
×132
×124
×116
×108
× 99
W21×166
×147
×132
×122
×111
×101
× 93
× 83
× 73
× 68
× 62
× 57
× 50
× 44
W36×848
×798
×650
×527
×439
×393
×359
×328
×300
×280
×260
×245
×230
×256
×232
×210
×194
×182
×170
×160
×150
×135
0.976
0.971
0.946
0.932
0.912
0.909
0.899
0.903
0.887
0.882
0.850
0.835
0.818
0.648
0.644
0.588
0.587
0.579
0.573
0.554
0.530
0.463
W27×217
×194
×178
×161
×146
×129
×114
×102
× 94
× 84
1.003
0.986
0.909
0.902
0.885
0.710
0.646
0.635
0.597
0.545
W18×143
×130
×119
×106
× 97
× 86
× 76
× 71
× 65
× 60
× 55
× 50
× 46
× 40
× 35
1.204
1.186
1.082
1.059
1.076
1.056
1.048
0.741
0.751
0.751
0.722
0.714
0.604
0.595
0.504
W24×176
×162
×146
×131
×117
×104
×103
× 94
× 84
× 76
× 68
× 62
× 55
1.021
0.994
0.959
0.904
0.877
0.848
0.711
0.683
0.655
0.616
0.560
0.428
0.397
W16×100
× 89
× 77
× 67
× 57
× 50
× 45
× 40
× 36
× 31
× 26
1.170
1.152
1.146
1.149
0.789
0.781
0.768
0.772
0.679
0.589
0.506
W14×120
×109
× 99
× 90
× 82
× 74
× 68
× 61
× 53
× 48
× 43
× 38
× 34
× 30
× 26
× 22
1.855
1.899
1.859
1.860
1.348
1.394
1.382
1.364
1.141
1.115
1.103
0.861
0.824
0.734
0.633
0.557
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
Section Af / Aw
W12×87
×79
×72
×65
×58
×53
×50
×45
×40
×35
×30
×26
×22
×19
×16
×14
1.748
1.732
1.720
1.706
1.631
1.527
1.281
1.266
1.281
0.992
0.963
0.936
0.575
0.520
0.419
0.390
W10×60
×54
×49
×45
×39
×33
×30
×26
×22
×19
×17
×15
×12
1.842
1.882
1.859
1.603
1.516
1.348
1.045
1.033
0.913
0.672
0.583
0.497
0.463
W8×35
×31
×28
×24
×21
×18
×15
×13
×10
1.796
1.711
1.495
1.487
1.127
1.007
0.690
0.593
0.635
W6×25
×20
×15
×16
×12
× 9
1.580
1.545
1.238
1.148
0.890
0.911
W5×19
×16
1.867
1.748
W4×13
1.442
FULLY RESTRAINED (FR) MOMENT CONNECTIONS
10 - 27
Ru = 45.0 kips
Mu = 250 ft-kips
W18×50
d = 17.99 in.
tw = 0.355 in.
bf = 7.495 in.
tf = 0.570 in.
Zx = 101 in.3
Af / Aw = 0.714
bf = 14.565 in.
tw = 0.485 in.
k = 17⁄16-in.
tf = 0.780 in.
W14×99
d = 14.16 in.
k1 = 7⁄8-in.
T = 111⁄4-in.
Solution:
Check beam design flexural strength.
From Example 10-2, the beam design flexural strength is o.k.
Design the bolts (a minimum of four bolts is required at the tension
flange; a minimum of two bolts is required at the compression flange).
Calculate the flange force Puf.
Puf =
=
Mu × 12 in. / ft
(d − tf)
(250 ft−kips)(12 in. / ft)
17.99 in. − 0.570 in.
= 172 kips
Determine number of 1-in. diameter A325-SC bolts required for tension (Note that fully tensioned bearing-type bolts would also be
acceptable). From Table 8-15
nmin =
=
Puf
φrn
172 kips
53.0 kips / bolt
= 3.25→
→4 bolts
Determine number of 1-in. diameter A325-SC bolts required for slip
resistance. From Table 8-17
nmin =
=
Ru
φrn
45 kips
19.0 kips / bolt
= 2.37→
→3 bolts
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
10 - 28
FULLY RESTRAINED (FR) MOMENT CONNECTIONS
Minimum of four bolts at tension flange and two bolts at compression
flange controls. Try six 1-in. diameter A325-SC bolts (N for bolt shear
check).
Check bolt shear:
From Table 8-11 for six 1 in. diameter A325-N bolts:
φRn = 6 × 28.3 kips / bolt
= 170 kips > 45.0 kips o.k.
Try 3⁄4-in. thick end plate.
Check material bearing.
Assuming for the end plate Le ≥ 1.5d and s ≥ 3d, the thickness of the
end plate is more critical than the column flange. From Table 8-13,
with the conservative assumption that only the bolts at the compression
flange are in bearing,
φRn = 2 bolts × 104 kips / bolt / in. × 3⁄4-in.
= 156 kips > 45.0 kips o.k.
Design the end plate and its connection to beam.
Calculate the effective end-plate width bp.
Try an end plate with Le = 11⁄2-in., g = 51⁄2-in., and pf = db + 1⁄2-in. = 11⁄2-in.
bp = 2Le + g
= 2(11⁄2-in.) + 51⁄2-in.
= 81⁄2-in.
Since bp ≈ bf + 1 in., the full width of the end plate may be considered
effective.
Determine the required end-plate thickness.
Meu = αmPuf
pe
4
1⁄3
Af pe
αm = CaCb
Aw db
1⁄4
Ca = 1.45 from Table 10-1.
Cb =
√
√
pe = pf −
bf
=
bp
7.495
= 0.939
81⁄2
db
− wt (assuming 1⁄2-in. fillet weld)
4
= 11⁄2-in. −
1 in. 1
− ⁄2-in.
4
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
FULLY RESTRAINED (FR) MOMENT CONNECTIONS
10 - 29
= 0.75 in.
0.75 in.
αm = 1.45 × 0.939 × (0.714)
1 in.
1⁄4
1⁄3
= 1.13
Meu = 1.13 × 172 kips ×
0.75 in.
4
= 36.4 in.-kips
tp min =
=
√
4Meu
φFy bp
√
4(36.4 in.−kips)
0.9 × 36 ksi × 81⁄2−in.
= 0.727→
→3⁄4-in.
Try a 3⁄4-in.×81⁄2-in. end plate.
Check shear yielding of the end plate.
From LRFD Specification Section J5.3:
φRn = 2 × φ(0.60Fy Ag)
= 2 × 0.9(0.6 × 36 ksi × 81⁄2-in. × 3⁄4-in.)
= 248 kips > 172 kips o.k.
Determine required fillet weld for beam-web-to-end-plate connection.
From LRFD Specification Table J2.4, the minimum size is 5⁄16-in. Determine size required to develop web flexural strength near tension bolts:
Dmin =
=
0.9Fy tw
2 × 1.392
0.9 × 36 ksi × 0.355 in.
2 × 1.392
= 4.13→
→5 sixteenths
Use 5⁄16-in. fillet weld on both sides of the beam web from the inside
face of the beam flange to the centerline of the inside bolt holes plus
two bolt diameters.
Determine size required for the factored shear Ru. Ru is resisted by weld
between the mid-depth of the beam and the inside face of the compression
flange or between the inner row of tension bolts plus two bolt diameters,
whichever is smaller. By inspection the former governs for this example.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
10 - 30
FULLY RESTRAINED (FR) MOMENT CONNECTIONS
d
−t
2 f
17.99 in.
=
− 0.570 in.
2
= 8.43 in.
l=
Dmin =
=
Ru
2 × 1.392l
45.0 kips
2 × 1.392(8.43 in.)
= 1.92→
→5 sixteenths (minimum size)
Use 5⁄16-in. fillet weld on both sides of the beam web below the
tension-bolt region.
Determine required fillet weld size for beam flange to end-plate
connection.
l = 2(bf + tf) − tw
= 2(7.495 in. + 0.570 in.) − 0.355 in.
= 15.8 in.
Dmin =
Puf
1.392l
Dmin =
172 kips
1.392 × 15.8 in.
= 7.82→
→8 sixteenths
Use 1⁄2-in. fillet welds at beam tension flange. Welds at compression
flange may be 5⁄16-in. fillet welds (minimum size from LRFD Specification Table J2.4)
Check the column section for stiffening requirements; refer to Example
10-6.
Eight-Bolt Stiffened Extended End-Plate Design
The following design procedure is based on Murray and Kukreti (1988), Hendrick and
Murray (1984), and Curtis and Murray (1989). Murray and Kukreti (1988) present two
methods for determining the required end-plate thickness and bolt diameter; both
methods are limited to the use of ASTM A36 end-plate material with ASTM A325 bolts
and include the effects of prying action.
The first method was developed from a regression analysis of finite-element-analysis
data including second-order geometric effects and inelastic plate and bolt material
properties. The resulting equations are elaborate and beyond the scope of this Manual;
refer to the AISC Design Guide Extended End-Plate Moment Connections (Murray,
1990) and Murray and Kukreti (1988).
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
FULLY RESTRAINED (FR) MOMENT CONNECTIONS
10 - 31
The second method offers a simplified approach which was developed with the first
method by generating end-plate thicknesses and bolt diameters for all W-shapes listed in
Part 1 assuming ASTM A36 steel and beam sections at various moment levels. The
number of bolts effective in resisting the tensile flange force was then determined for
each connection; a conservative lower bound of six effective bolts was established. Next,
it was assumed that the plate thickness could be established from tee-stub analogy
bending, as illustrated in Figure 10-8, where
p
Meu = 2ru eff = ru peff
2
where ru is the force per bolt based on six effective bolts, kips
From the generated designs, it was determined the effective pitch peff is
peff =
pf
√
g2 + p2f
4.17
The required end-plate thickness is then determined from
tpreq =
√
4Meu
φFy bp
where φ = 0.9
In addition to the design assumptions listed previously, the following limitations must be
met for the eight-bolt stiffened configuration:
1. The supported beam must be a hot-rolled W-shape listed in Part 1.
2. The vertical pitch pf from the face of the beam tension flange to the centerline of the
first row of bolts must not exceed 21⁄2-in. The recommended minimum pitch is db
plus 1⁄2-in.; entering and tightening clearance may require a larger pitch.
3. The vertical spacing between bolt rows pb must not exceed 3db.
4. The horizontal gage g must be between 51⁄2-in. and 71⁄2-in.
5. Bolt diameter db must be not less than 3⁄4-in. nor greater than 11⁄2-in.
The strength of the column should then be investigated for stiffening requirements.
The recommendations of Hendrick and Murray (1984) can be used to check column web
strengths in local yielding, buckling, and panel zone shear; refer to “Column Stiffening”
in this Part.
Unless the column flange is 1.5 to 2 times thicker than the end plate, transverse
stiffening is required. If effective-flange-length effects are neglected, the behavior of the
column flange is identical to that of the end plate. Therefore, the column flange must be
at least as thick as the end plate and the transverse stiffeners must be at least as thick as
the beam flange. Additionally, the weld connecting the transverse stiffener to the flange
must be sufficient to develop the strength of the full thickness of the stiffener plate.
A column flange which is 1.5 to 2 times thicker than the end plate may not require
transverse stiffening. From Curtis and Murray (1989), an unstiffened flange may be
evaluated according to the flange bending equation presented for extended end-plate
connections in “Column Stiffening” in this Part with bs = 3.5 pb + c. Because this reference
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
10 - 32
FULLY RESTRAINED (FR) MOMENT CONNECTIONS
considered only ASTM A36 steel, it is recommended that column material with greater
yield strength be checked as if ASTM A36 material were used.
Note that, since column web stiffeners add considerable fabrication expense and may
interfere with weak-axis framing, it is often advantageous to eliminate the need for
stiffening. The designer should therefore consider increasing the column size to a section
with adequate strength.
Example 10-5
Given:
Design an eight-bolt stiffened extended end-plate FR moment connection for a W33×118 beam to W14×311 column-flange connection. For
structural members, assume Fy = 50 ksi and Fu = 65 ksi; for connecting
material, assume Fy = 36 ksi and Fu = 58 ksi. Use ASTM A325-SC bolts
(Class A surfaces) and 70 ksi electrodes.
Ru = 135 kips
Mu = 1,050 ft-kips
W33×118
d = 32.86 in.
tw = 0.550 in.
bf = 11.48 in.
tf = 0.740 in.
Zx = 415 in.3
bf = 16.230 in.
tw = 1.410 in.
k = 215⁄16-in.
tf = 2.260 in.
W14×311
d = 17.12 in.
k1 = 15⁄16-in.
T = 111⁄4-in.
Solution:
Check beam design flexural strength:
Zreq =
=
Mu × 12 in. / ft
0.9Fy
(1,050 ft−kips)(12 in. / ft)
0.9(50 ksi)
= 280 in.3
= 415 in.3
Zx
Since Zx > Zreq, the beam design flexural strength is o.k.
Design the bolts (a minimum of eight bolts is required at the tension
flange; a minimum of two bolts is required at the compression flange).
Calculate the flange force Puf :
Puf =
=
Mu × 12 in. / ft
(d − tp)
(1,050 ft−kips)(12 in. / ft)
(32.86 in. − 0.740 in.)
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
FULLY RESTRAINED (FR) MOMENT CONNECTIONS
10 - 33
= 392 kips
Try eight 11⁄8-in. diameter A325-SC bolts (six effective).
φrnreq =
=
Puf
6 bolts
392 kips
6 bolts
= 65.3 kips/bolt < 67.1 kips/bolt o.k. for tension
Check slip resistance with eight bolts at tension flange and two bolts
at compression flange.
From Table 8-17:
φRn = 10 bolts × 20.9 kips/bolt
= 209 kips > 135 kips o.k.
Try eight 11⁄8-in. diameter A325-SC bolts (N for bolt shear check).
Check bolt shear.
From Table 8-11 for ten 11⁄8-in. diameter A325-N bolts:
φRn = 10 bolts × 35.8 kips / bolt
= 358 kips > 135 kips o.k.
Try PL 11⁄4.
Check material bearing.
From Table 8-13, the design bearing strength of one bolt is
φrn = 147 kips/bolt
Since this exceeds the design shear strength of the bolts, bearing is not
critical.
Design the end plate and its connection to the beam.
Calculate the effective end-plate width bp.
Try an end plate with Le = 13⁄4-in., g = 6 in., pf = db + 1⁄2-in. = 1 5⁄8-in.,
pb = 3db, and stiffener thickness ts = 5⁄8-in. (twbeam = 0.550 in.). Note that
all of the specified limitations for this simplified method have been
met.
bp = 2Le + g = 2(13⁄4-in.) + 6 in. = 9.5 in.
This dimension is less than the flange width of the beam bf. Thus, use
a plate with bp = bf + 1 in. ≈ 121⁄2-in. This allows for runoff.
Determine the required end-plate thickness:
peff =
pf
√
g2 + p2f
4.17
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
10 - 34
FULLY RESTRAINED (FR) MOMENT CONNECTIONS
15⁄8−in.
√
(6 in.)2 + (15⁄8−in.)
2
4.17
=
= 2.42 in.
Meu = ru peff
392 kips
× 2.42 in.
6 bolts effective
=
= 158 in.-kips
tpreq =
=
√
4Meu
φFy bp
√
4 × 158 in.−kips
0.9 × 36 ksi × 121⁄2−in.
= 1.25→
→11⁄4-in.
Try PL 11⁄4-in.×121⁄2-in.
Check shear yielding of the end plate.
From LRFD Specification Section J5.3.
φRn = 2 × φ(0.60Fy Ag)
= 2 × 0.9(0.60 × 36 ksi × 121⁄2-in. × 11⁄4-in.)
= 607.5 kips > 392 kips o.k.
Determine required fillet weld size for beam web to end-plate connection.
From LRFD Specification Table J2.4, the minimum size is 5⁄16-in.
Determine size required to develop web flexural strength near tension
bolts:
Dmin =
=
0.9Fy tw
2 × 1.392
0.9 × 50 ksi × 0.550 in.
2 × 1.392
= 8.9→
→ 9 sixteenths
Use 9⁄16-in. fillet welds on both sides of the beam web from the inside
face of the beam flange to the centerline of the inside bolt holes plus
two bolt diameters.
Determine size required for the factored shear Ru.
Ru is resisted by weld between the mid-depth of the beam and the inside
face of the compression flange or between the inner row of tension
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
COLUMN STIFFENING AT FR AND PR MOMENT CONNECTION
10 - 35
bolts plus two bolt diameters, whichever is smaller. By inspection, the
former governs for this example.
l=
=
d
−t
2 f
32.86 in.
− 0.740 in.
2
= 15.7 in.
Dmin =
=
Ru
2 × 1.392l
135 kips
2 × 1.392(15.7 in.)
= 3.09→
→5 sixteenths (minimum size)
Use 5⁄16-in. fillet welds on both sides of the beam web below the
tension-bolt region.
Determine required weld for beam flange to end-plate connection.
By inspection, fillet welds at the tension flange will be impractical.
Use a complete-joint-penetration groove weld at the tension flange.
Welds at the compression flange may be 5⁄16-in. fillet welds (minimum
size from LRFD Specification Table J2.4).
Check the column section for stiffening requirements; refer to Example 10-7.
COLUMN STIFFENING AT FR AND PR MOMENT CONNECTION
As illustrated in Figure 10-9, FR and PR moment connections produce double concentrated forces, one tensile and one compressive, forming a couple on the same side of the
supporting column. From LRFD Specification Section K1, the following limit states
determine if the column section is adequate to carry these concentrated forces.
Puf
Puf1
Puf2
Puf
Puf1
Puf2
(a) Double concentrated forces
(b) A pair of double concentrated forces
Figure 10-9. Illustration of FR and PR moment connection flange force terminology.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
10 - 36
FULLY RESTRAINED (FR) MOMENT CONNECTIONS
At the location of the tensile component of the double concentrated force, the limit
states of local flange bending and local web yielding must be checked. At the location of
the compressive component of the double concentrated force, the limit states of local web
yielding and web crippling must be checked. If FR and/or PR moment connections are
made to both flanges of a column, the limit state of compression buckling of the web
must be checked at the location of the compressive components of the pair of double
concentrated forces. Finally, the limit state of panel zone web shear must be checked.
Following are discussions of: (1) economical considerations; (2) the aforementioned limit
states and their applicability at intermediate column locations and column end locations with
flange-plated, directly welded flange, and extended end-plate FR moment connections; and,
(3) design of transverse stiffeners, doubler plates, and diagonal stiffeners.
Economical Considerations
If the design strength of the investigated column is inadequate, the designer has two
options. First, the designer should consider selecting a heavier column section which will
eliminate the need for stiffening. Although this will increase the material cost of the
column, it may well be that this heavier section will provide a more economical solution
due to the reduction in labor cost associated with the elimination of stiffening (Ricker,
1992 and Thornton, 1992). Alternatively, the designer may stiffen the original column
section with transverse stiffeners and/or doubler plate(s) or diagonal stiffeners as provided in LRFD Specification Section K1.
Local Flange Bending
This requirement applies only to the tensile component of the double concentrated force
created by the FR or PR moment connection. If the required strength Puf exceeds the
design strength φRn, a pair of transverse stiffeners, one on each side of the column web,
must be provided and must extend at least one-half the depth of the column web.
Intermediate Column Locations, Flange-Plated and Directly Welded Flange Connections
The tensile concentrated force causes bending distortions to occur in the column flange,
as shown in Figure 10-10. Such deformation causes a concentration of stress in the area
which is stiffened by the column web and creates a zone of possible fracture in the
connecting weld. From LRFD Specification Section K1.2, the design strength of the
column flange is φRn, where φ = 0.90 and
Rn = 6.25t2f Fyf
The design local flange bending strength is tabulated as Pfb for W and HP shapes in the
Properties section of the Column Tables in Part 3 where,
φRn = Pfb
Intermediate Column Locations, Extended End-Plate Connections
In bolted FR moment connections, flange bending must be limited to prevent yielding of
the column flange in the tension region. The design strength of the column flange is
φRn, where φ = 0.90 and
bs 2
Rn =
tf Fyf
αmpe
In the above equation,
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
COLUMN STIFFENING AT FR AND PR MOMENT CONNECTION
10 - 37
bs = 2.5 (2pf + tfb), in., for a four-bolt unstiffened extended end plate
= 2pf + tfb + 3.5pb, in., for an eight-bolt stiffened extended end plate
pb = vertical pitch of bolt group above and bolt group below tension flange, in.
1⁄4
pe
αm = 1.36 for a four-bolt unstiffened extended end plate
db
1⁄4
pe
= 1.13 for an eight-bolt stiffened extended end plate
db
g db
pe = − − k1
2 4
Note that this equation was developed from research which considered only ASTM A36
steel. If columns with higher material yield strengths are used, it is recommended that
Fyf be taken conservatively as 36 ksi in the calculation of the design strength of the column
in local flange bending (Curtis and Murray, 1989).
Column-End Locations, Flange-Plated, Directly Welded Flange,
and Extended End-Plate Connections
From LRFD Specification Commentary Section K1.2, the effective column flange length
for local flange bending is 12tf (Graham et al., 1959). Thus, it is assumed that yield lines
form in the flange at 6tf in each direction from the point of the applied concentrated force.
To develop the fixed edge consistent with the assumptions of this model, an additional
4tf (resulting in a total of 10tf) is required for the full flange bending strength given by
LRFD Specification Equation K1-1. Thus, if the distance from the column end to the top
tf
A
A
M
M
Bending distortions occur
in column flange
Puf
Puf
Zone of possible
overstress of fracture
in the connecting weld
SECTION A-A
Fig. 10-10. Illustration of local flange bending.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
10 - 38
FULLY RESTRAINED (FR) MOMENT CONNECTIONS
of the connected beam tension flange or flange plate is less than 10tf, LRFD Specification
Section K1.2 states that the flange bending strength at this column-end location must be
reduced by 50 percent from the strength at an intermediate column location.
Local Web Yielding
This requirement applies to both the tensile and compressive components of the double
concentrated force created by the FR or PR moment connection. If the required strength
Puf exceeds the design strength φRn, either a pair of transverse stiffeners, one on each side
of the column web, or a doubler plate must be provided and must extend at least one-half
the depth of the column web.
Intermediate Column Locations, Flange-Plated and Directly Welded Flange Connections
From LRFD Specification Section K1.3, the design strength of the column web is φRn,
where φ = 1.0 and
Rn = (5k + N)Fywtw
The derivation of this equation is illustrated in Figure 10-11a.
The design local flange bending strength is tabulated as Pwo and Pwi for W and HP shapes
in the Properties section of the Column Tables in Part 3, where
Pwi = φFywtw
Pwo = φ5Fywtwk
φRn = Pwi tb + Pwo
tp
6k + N + 2t p
1:1 slope
N
Puf
5k + N
N
Puf
3
2.5
1
1
Fyc
k
(a) Flange-plated or directly
welded flange connection
k
(b) Extended end-plate
connection
Fig. 10-11. Derivation of local web yielding.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
COLUMN STIFFENING AT FR AND PR MOMENT CONNECTION
10 - 39
Intermediate Column Locations, Extended End-Plate Connections
With minor modification of LRFD Specification Equation K1-2 to account for the effects
of the end-plate thickness and fillet weld leg size or groove weld reinforcement leg size,
the design strength of the column web is φRn, where φ = 1.0 and
Rn = (6k + N + 2tp)Fyw tw
where
N = thickness of the beam flange delivering the concentrated force plus 2w, in.
tp = end-plate thickness, in.
w = leg size of fillet weld or groove weld reinforcement, in.
The derivation of this equation is illustrated in Figure 10-11b.
Column-End Locations, Flange-Plated and Directly Welded Flange Connections
From LRFD Specification Section K1.3, when the concentrated tensile or compressive
force to be resisted is applied at a distance from the column end which is less than or
equal to the depth of the column, the design strength of the column web is φRn, where
φ = 1.0 and
Rn = (2.5k + N)Fywtw
Column-End Locations, Extended End-Plate Connections
With minor modification of LRFD Specification Equation K1-3 to account for the effects
of the end-plate thickness and fillet weld leg size or groove weld reinforcement leg size,
the design strength of the column web is φRn, where φ = 1.0 and
Rn = (3k + N + tp)Fywtw
where
N = thickness of the beam flange delivering the concentrated force plus 2w, in.
tp = end-plate thickness, in.
w = leg size of fillet weld or groove weld reinforcement, in.
Web Crippling
This requirement applies only to the compressive component of the double concentrated
force created by the fully restrained connection. From LRFD Specification Commentary
Section K1.4, for the rolled shapes listed in Part 1 with Fy not greater than 50 ksi, the web
crippling limit state will never control the design in an FR or PR moment connection
except to a W12×50 or W10×33 column; note that the less than 3 percent overstress for
these two column shapes is considered negligible. Therefore, the limit state of web
crippling is not included in the discussion of column stiffening.
Compression Buckling of the Web
This requirement applies only to the compressive components of a pair of double
concentrated forces (see Figure 10-9b) created by two FR or PR moment connections as
illustrated in Figure 10-12. If the required strength Puf exceeds the design strength φRn,
either a single transverse stiffener, a pair of transverse stiffeners, one on each side of the
column web, or a doubler plate must be provided and must extend the full depth of the
column web.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
10 - 40
FULLY RESTRAINED (FR) MOMENT CONNECTIONS
Intermediate Column Locations, Flange-Plated, Directly Welded Flange, and Extended
End-Plate Connections
From LRFD Specification Section K1.6, the design strength of the column web is φRn,
where φ = 0.9 and
Rn =
4,100t3w √
Fyw
dc
In the above equation, dc is the column-web depth clear of fillets, in.
The design compression buckling strength of the web is tabulated as Pwb for W and HP
shapes in the Properties section of the Column Tables in Part 3 where,
φRn = Pwb
Column End Locations, Flange-Plated, Directly Welded Flange,
and Extended End-Plate Connections
In the absence of applicable research, if the distance from the column end to the location
of the pair of compressive forces is less than one-half the depth of the column, LRFD
Specification Section K1.6 states that the compression buckling strength of the unreinforced web at this column-end location is reduced by 50 percent from the strength at an
intermediate column location. From LRFD Specification Section K1.9, when stiffeners
are required, the length of the column web effective in resisting the pair of compressive
forces applied at an intermediate column location is 25tw or 12.5tw on either side of the
location of the compressive forces.
Panel Zone Web Shear
This requirement applies to the web of the column within the boundary of the column
flanges and the tensile and compressive concentrated forces imposed by the FR or PR
moment connection(s). If the required strength Puf exceeds the design strength φRv, either
a doubler plate or a pair of diagonal stiffeners, one on each side of the column web, must
be provided.
From LRFD Specification Section K1.7, the design strength φRv may be determined
from LRFD Specification Equation K1-9, K1-10, K1-11, or K1-12, depending upon
whether the effect of plastic panel zone deformation on frame stability is or is not
considered and upon the axial force in the column; refer to LRFD Specification Section
K1.7. These equations are applicable at intermediate column locations and column-end
locations for flange-plated, directly welded flange, and extended end-plate connections.
Column
strip
Puf
1
Puf
2
dc
k
tw
k
Buckling out of
the web plane
Fig. 10-12. Exaggerated illustration of compression buckling of the web.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
COLUMN STIFFENING AT FR AND PR MOMENT CONNECTION
10 - 41
Transverse Stiffener Design
At locations of FR and PR moment connections, transverse stiffening may be used to
stiffen a column flange which is inadequate in local bending, or a web which is inadequate
in local yielding or compression buckling. Transverse stiffeners, when required, should
be designed to provide the strength required in excess of the design strength of the column
web or flange. The designer should be aware of the increased fabrication costs incurred
by the addition of transverse stiffeners to a column. It frequently is less costly to select a
member with a thicker flange and/or web or higher yield strength than it is to add the
transverse stiffening.
Concentric Transverse Stiffeners
A concentric transverse stiffener is one which coincides with the axis of the flange which
delivers the concentrated force. The factored force delivered to the stiffener Ru st is
Ru st = Puf − φRn min
where
= factored beam flange force (required strength), kips
Puf
φRn min = the lesser of the design strengths in flange bending and web yielding at the
location of the tensile concentrated force, or the lesser of the design
strengths in web yielding and compression buckling of the web (if
applicable) at the location of the compressive concentrated force, kips
If Ru st is negative, transverse stiffeners are not required. If Ru st is positive, Ast the area of
transverse stiffeners required for strength may be calculated as
Ast =
Ru st
φFy st
where Fy st is the yield strength of the stiffener material and φ = 0.90. Note that stiffeners
are generally made of material with Fy = 36 ksi.
Additionally, when stiffeners are required, LRFD Specification Section K1.9 establishes minimum width and thickness dimensions. The minimum width of each stiffener
is a function of the width of the beam flange or flange plate connected to the column
flange. As illustrated in Figure 10-13, this minimum stiffener width bs min may be
calculated from the following relationship, where tw is the thickness of the column web.
Outline of fulldepth stiffener
tfb
bs
W
bf
A
tw
A
ts
Outline of halfdepth stiffener
Sect A-A
Fig. 10-13. Minimum dimensions for transverse stiffeners.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
10 - 42
bs min =
FULLY RESTRAINED (FR) MOMENT CONNECTIONS
W − tw
2
where
Wmin =
2bf
3
Note, for a flange-plated connection, bf should be taken as the flange-plate width.
The minimum stiffener thickness ts min is
ts min =
Fy
tfb bs√
≥
2
95
where tfb is the flange thickness of the beam.
Full-depth and partial-depth transverse stiffeners are illustrated in Figure 10-14a and
10-14b, respectively. In order to resist tensile concentrated forces, the stiffener must be
welded directly to the flange upon which the tensile concentrated force is imposed to
develop the strength of the welded portion of the stiffener. While fillet welds are
preferable, complete-joint-penetration groove welds may be required when the force in
the stiffener is large.
When the concentrated force is always compressive, one end of a full-depth stiffener
is sometimes finished for bearing with the other end welded. At partial-depth stiffeners
for compressive concentrated forces, some fabricators prefer to finish the end in contact
for bearing.
If concentrated forces from opposed FR or PR moment connections are equal, as in
the case of balanced moments, they may be theoretically transferred entirely through the
stiffeners with no attachment to the column web, except as required for the web limit
state of compression buckling and/or to prevent the stiffener from buckling as a column.
More often, the moments are not balanced and the differential axial forces must be
transferred to the column web. In this case, appropriate weld sizes are required.
Web welds always
required for halfdepth transverse
stiffeners
if Puf1 = Puf , web welds are
2
not required except for
compression buckling of the
web and to stabilize stiffeners
Puf
Puf
Puf
2
1
d
≥ 2
d
(a)
Full-depth transverse stiffeners
(b)
Partial-depth transverse stiffeners
Fig. 10-14. Full-depth and partial-depth transverse stiffeners.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
COLUMN STIFFENING AT FR AND PR MOMENT CONNECTION
10 - 43
It is obvious from Figure 10-14b that a web weld is always required for a partial-depth
stiffener. Note that it may be desirable to extend the partial-depth stiffener beyond
one-half the column-web depth in order to reduce the weld size. Fillet welds are preferable
and complete- or partial-joint-penetration groove welds are seldom required for connection between the stiffener and the column web.
Example 10-6
Given:
Refer to Examples 10-1, 10-2, 10-3, and 10-4. The FR moment
connections developed in these examples deliver double concentrated
forces, one tensile and one compressive, to the flange of the W14×99
column. Determine:
A. if the column is adequate for the flange forces delivered by the
flange-plated connections of Examples 10-1 and 10-2 where Puf =
167 kips.
B. if the column is adequate for the flange forces delivered by the
directly welded flange connections of Example 10-3 where Puf = 172
kips.
C. if the column is adequate for the flange forces delivered by the
four-bolt unstiffened extended end-plate connection of Example
10-4 where Puf = 172 kips.
D. the column size required in the above cases to eliminate the need
for transverse stiffening.
E. the transverse stiffeners required in the above cases with the W14×99
column.
F. if transverse stiffening would be required if there were an identical
W18×50 beam and connection opposite and adjacent to the existing
one.
W18×50
d = 17.99 in.
tw = 0.355 in.
bf = 7.495 in.
tf = 0.570 in.
Zx = 101 in.3
bf = 14.565 in.
tw = 0.485 in.
k = 17⁄16-in.
tf = 0.780 in.
W14×99
d = 14.16 in.
k1 = 7⁄8-in.
T = 111⁄4-in.
Solution A:
Determine the design strength of the column in local flange bending:
φRn = φ[6.25t2f Fyf ]
= 0.90[6.25(0.780 in.)2(50 ksi)]
= 172 kips > 167 kips o.k.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
10 - 44
FULLY RESTRAINED (FR) MOMENT CONNECTIONS
Determine the design strength of the column in local web yielding:
φRn = φ[(5k + N)Fyw tw]
= 1.0[(5 × 17⁄16-in. + 0.570 in.)(50 ksi)(0.485 in.)]
= 188 kips > 167 kips o.k.
For the flange-plated FR connections of Examples 10-1 and 10-2,
transverse stiffening is not required at either the tensile or compressive
component of the double concentrated force.
Solution B:
From Solution A, the design strengths in local flange bending and local
web yielding are φRn = 172 kips and φRn = 188 kips, respectively. Thus
at the tensile and compressive components of the double concentrated
force, the design strength is adequate with respect to the required
strength of 172 kips.
Solution C:
Determine the design strength of the column in local flange bending
assuming Fyf = 36 ksi:
bs 2
φRn = φ
tf Ffy
pe αm
bs
= 2.5 (2pf + tfb)
= 2.5 (2 × 11⁄2-in. + 0.570 in.)
= 8.93 in.
pe
=
g db
− − k1
2 4
=
51⁄2−in. 1 in. 7
−
− ⁄8-in.
4
2
= 1.63 in.
αm
pe
= 1.36
db
1⁄4
1.63 in.
= 1.36
1 in.
1⁄4
= 1.54
(8.93 in.)
2
φRn = 0.90
(0.780 in.) (36 ksi)
(1.63
in.)(1.54)
= 70.1 kips < 172 kips n.g.
Determine the design strength of the column in local web yielding:
φRn = φ(6k + N + 2tp)Fywtw
= 1.0[(6 × 17⁄16-in. + 0.570 in. + 2 × 3⁄4-in.)(50 ksi)(0.485 in.)]
= 259 kips > 172 kips o.k.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
COLUMN STIFFENING AT FR AND PR MOMENT CONNECTION
10 - 45
The W14×99 is not adequate for the tensile component of the double
concentrated force imposed by the four-bolt unstiffened extended
end-plate connection of the W18×50 beam. Transverse stiffeners will
be required; refer to Solutions D and E which follow. At the compressive component of the double concentrated force, transverse stiffening
is not required.
Solution D:
For the flange-plated and directly welded flange connections of Solutions A and B, transverse stiffening is not required and the W14×99
column is adequate.
For the extended end-plate connection of Solution C, the local flange
bending strength of the W14×99 column is not adequate. The required
flange thickness may be calculated as:
tf req =
√
Puf peαm
φFyf bs
where from Solution C,
bs = 8.93 in.
pe = 1.63 in.
αm = 1.54
Thus,
tf req =
√
172 kips(1.63 in.)(1.54)
0.90(36 ksi)(8.93 in.)
= 1.22 in.
and the lightest W14 which satisfies this flange thickness requirement
is a W14×176. The cost of the additional 77 pounds per foot of column
must be compared with the cost of adding stiffeners; see Solution E for
the stiffening design.
Solution E:
The transverse stiffening must be sized for the difference between the
required strength Puf and the least design strength φRn. Thus, the force
in the two stiffeners Ru st will be:
Ru st = Puf − φRn min
= 172 kips − 70.1 kips
= 102 kips
and the required area of stiffeners
Ast =
=
Rust
φFyst
102 kips
0.9 × 36 ksi
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
10 - 46
FULLY RESTRAINED (FR) MOMENT CONNECTIONS
= 3.15 in.2
The minimum stiffener size, from LRFD Specification Section K1.9 is:
bs min =
Wmin − tw
2
Wmin =
2bf 2(7.495 in.)
=
3
3
= 5.00 in.
bs min =
5.00 in. − 0.485 in.
2
= 2.26 in.
The minimum stiffener thickness from LRFD Specification Section
K1.9 is:
ts min
=
=
Fy
tfb bs min√
≤
2
95
0.570 in.
2
= 0.285 in.
2.26 in.√
36 ksi
Fy
bs min√
=
95
95
= 0.14 in. < 0.285 in. does not control
and the minimum stiffener length is
lmin =
=
d
−k
2
14.16 in.
− 17⁄16-in.
2
= 5.64 in.
Try two 1⁄2-in.×41⁄2-in. stiffeners with 3⁄4-in. corner clips.
Ast = 2 × 1⁄2jin. (41⁄2jin. − 3⁄4jin.)
= 3.75 in.2 > 3.15 in.2 o.k.
Determine required stiffener-to-column-flange weld (weld must be
sized to develop the strength of the welded portion of the stiffener):
0.9Fy ts
2 × 1.392 × 1.5
(Note: 1.5 in denominator per LRFD Specification Appendix J2.4)
Dmin =
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
COLUMN STIFFENING AT FR AND PR MOMENT CONNECTION
10 - 47
0.9 × 36 ksi × 1⁄2−in.
2 × 1.392 × 1.5
=
= 3.88 → 4 sixteenths
Use 1⁄4-in. fillet welds on both sides of each stiffener.
Determine required stiffener to column web weld:
From LRFD Specification Table J2.4, the minimum weld size is 3⁄16-in.
Try 3⁄16-in. fillet welds on both sides of each stiffener. The minimum
length of the stiffeners is then:
lmin =
=
Ru st
+ clip
4 × 1.392D
102 kips
+ 3⁄4−in.
4 × 1.392(3 sixteenths)
= 6.86 in.
Use l = 7 in. with 3⁄16-in. fillet welds both sides.
Solution F:
If W18×50 beams were rigidly connected at both flanges of the W14×99
column, the compression buckling strength of the web would have to
be checked in addition to the design checks in Solutions A, B, and C.
Determine the design compression buckling strength of the column
web:
φRn = φ
4,100t3w √
Fyw
dc
4,100 × (0.485 in.)3 × √
50 ksi
= 0.9
1⁄ −in.
11
4
= 265 kips o.k.
The W14×99 would not require transverse stiffening for compression
buckling of the web.
Example 10-7
Given:
Refer to Example 10-5. Determine if transverse stiffening of the
W14×311 is required.
Puf = 392 kips
W33×118
d = 32.86 in.
tw = 0.550 in.
bf = 11.48 in.
tf = 0.740 in.
W14×311
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
Zx = 415 in.3
10 - 48
FULLY RESTRAINED (FR) MOMENT CONNECTIONS
d = 17.12 in.
k1 = 15⁄16-in.
T = 111⁄4-in.
Solution:
bf = 16.230 in.
tw = 1.410 in.
k = 215⁄16-in.
tf = 2.260 in.
Determine the design strength of the column in local flange bending
conservatively assuming Fyf = 36 ksi:
bs 2
φRn = φ
tf Fyf
pe αm
bs
= 3.5pb + 2pf + tfb
= 3.5(33⁄8-in.) + 2(15⁄8-in.) + 0.740 in.
= 15.8 in.
pe
=
g db
− − k1
2 4
=
6 in. 11⁄8−in.
−
− 15⁄16−in.
2
4
= 1.41 in.
αm
pe
= 1.13
db
1⁄4
1.41 in.
= 1.13 1
1 ⁄8−in.
1⁄4
= 1.20
15.8 in.
(2.26 in.)2(36 ksi)
φRn = 0.9
(1.41
in.)(1.20)
= 1,550 kips > 392 kips o.k.
Determine the design strength of the column in local web yielding:
φRn = φ(6k + N + 2tp)Fywtw
= 1.0[(6 × 215⁄16-in. + 0.740 in. + 2 × 11⁄4-in.)](50 ksi)(1.410 in.)
= 1,470 kips > 392 kips o.k.
TheW14×311 is adequate without transverse stiffening.
Eccentric Transverse Stiffeners
Frequently, beams of differing depths are connected with FR or PR moment connections
to opposite flanges of a column at the same location. Since, in general, it is advantageous
to use as few stiffeners as possible, the two partial-depth stiffeners in Figure 10-15a could
be replaced with one full-depth eccentric stiffener as shown in Figure 10-15b.
In full-scale tests, Graham, et. al. (1959) showed that stiffeners with 2-in. eccentricity
e provided 65 percent of the strength of identical concentric stiffeners and rapidly
declined in effectiveness at greater spacing. It was thus recommended that “for design
purposes it would probably be advisable to neglect the resistance of stiffeners having
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
COLUMN STIFFENING AT FR AND PR MOMENT CONNECTION
10 - 49
eccentricities greater than two inches.” Given this, the required stiffener area, width, and
thickness may be established by the same criteria as for concentric transverse stiffeners.
Alternatively, the sloped full-depth transverse stiffener as shown in Figure 10-15c may
provide a more economical alternative. The design of this transverse stiffener is similar
to that for diagonal stiffeners, refer to “Column Stiffening—Diagonal Stiffener Design”
in this Part.
Concurrent Strong-Axis and Weak-Axis FR Connections
When transverse stiffeners are required for FR or PR moment connections made to both
the flange and the web of a column at the same location, adequate clearance must be
provided to install the stiffeners. A detail such as that in Figure 10-16 may provide an
economical solution; it is recommended that the vertical spacing of transverse stiffeners
located on the same side of a column web be no less than three inches to ensure adequate
clearance for welding. Note that the bottom plate for the weak-axis connection also serves
as an eccentric transverse stiffener for the strong-axis connection of the left beam; refer
to “Eccentric Transverse Stiffeners” above.
Doubler Plate Design
e
e
At locations of FR or PR moment connections, a doubler plate or pair of doubler plates
may be used to stiffen a column web which is inadequate in local yielding, compression
buckling, or panel zone shear. The designer should be aware of the increased fabrication
costs incurred by the addition of doubler plates to a column. It frequently is less costly
to select a member with a thicker web or higher yield strength than it is to add the doubler
plate.
e = eccentricity
(a) Two partial-depth
stiffeners
(b) One eccentric full-depth
stiffener
(c) One sloped full-depth
stiffener
ee
Fig. 10-15. Eccentric and sloped transverse stiffeners.
e = eccentricity
Fig. 10-16. Stiffeners for concurrent strong-axis and weak-axis connections.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
10 - 50
FULLY RESTRAINED (FR) MOMENT CONNECTIONS
For Local Web Yielding or Compression Buckling of the Web
From LRFD Specification Section K1.10, when required for local web yielding or
compression buckling of the web, the thickness and extent of the doubler plate shall
provide the additional material necessary to equal or exceed the required strength.
Additionally, the doubler plate shall be welded to develop the proportion of the total force
transmitted to the doubler plate.
For Panel Zone Web Shear
When a doubler plate is required for panel zone web shear, the required thickness tp req is
tp req = te − twc
where
te = total required effective thickness, in.
twc = actual column web thickness, in.
For the doubler plate to be effective in shear, it must be effectively welded to the column
flange. In Section A in Figure 10-18, the doubler plate is stopped short of the flange fillet
and the edge is beveled in preparation for a complete-joint-penetration groove weld.
Partial-joint-penetration groove welds could be used instead as long as the weld effectively bridges the reduced section as shown in Section A—Thin Plate of Figure 10-18.
Alternatively, if the plate is thick enough, it can be beveled to clear the column fillet
radius and then be fillet welded as shown in Section A—Thick Plate of Figure 10-18.
Note that the effective thickness of a beveled doubler plate may have to be reduced. As
illustrated in Figure 10-17, the cross section of the doubler plate at the toe of the fillet
weld is reduced by the beveled edge. Thus, the required thickness of the doubler plate
tp req must be adjusted so that the total required effective thickness is present.
While a doubler plate appears to be a simple solution, it requires a great deal of welding
and can cause significant distortion of the column flanges if the doubler plate is thick.
Thus, although thicker doubler plates allow a greater shear strength in the weld with
respect to the base metal, if a doubler plate thicker than the column web or 3⁄4-in. is
required, the use of two thinner plates, one on either side of the column web, should be
considered.
Thin doubler plates may be subject to local buckling; refer to LRFD Specification
Section F2.2. Additionally, to reduce the risk of buckling the doubler plate due to the heat
of welding, doubler plates less than 1⁄4-in. thick are not normally used. However, welds
connecting such doubler plates may be sized for the required thickness instead of the
actual thickness.
bevel to clear
fillet
actual doubler
plate thickness
effective doubler
plate thickness
section at toe
of fillet weld
Fig. 10-17. Effective doubler plate thickness.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
COLUMN STIFFENING AT FR AND PR MOMENT CONNECTION
10 - 51
At Locations of Weak-Axis Connections
In many cases, some provision must be made for the attachment of a weak-axis FR
or PR moment connection to the web of the column through the doubler plate. The
shear from the end reaction of the supported beam must be added algebraically to the
vertical shear in the doubler plate to determine the required thickness and weld size.
If the beam also is subjected to axial tension, localized bending would be a major
consideration in sizing the doubler plate. In either case, eliminating the need for a
doubler plate through the selection of a column section with a thicker web may be
the most reasonable alternative.
Example 10-8
Refer to Examples 10-1, 10-2, 10-3, and 10-4. Assuming the effect of
panel zone deformation on frame stability is not considered in the
analysis and Pu / Py = 0.7 (thus, Pu > 0.4Py per LRFD Specification
Section K1.7), determine:
Given:
A. if the column web is adequate for the web shear induced by the
flange-plated connection of Examples 10-1 and 10-2.
Weld as required
for strength *
B
ts
A
A
t p req
t wc
B
te
* Complete-joint-penetration
groove weld if required
strength cannot be developed
with partial-joint-penetration
groove weld.
Section B
twc
twc
te
te
t p req
t p req
Weld as required
for strength *
Section A
Thin Plate
Fig. 10-18. Doubler plate welding.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
Section A
Thick Plate
10 - 52
FULLY RESTRAINED (FR) MOMENT CONNECTIONS
B. if the column web is adequate for the web shear induced by the
directly welded flange and four-bolt unstiffened extended end-plate
connections of Examples 10-3 and 10-4.
C. the column size required to eliminate the need for the doubler plate
D. the doubler plate required in the above cases with the W14×99
column.
Neglect the effect of story shear for the purposes of this example.
W18×50
d = 17.99 in.
tw = 0.355 in.
bf = 7.495 in.
tf = 0.570 in.
Zx = 101 in.3
bf = 14.565 in.
tw = 0.485 in.
k = 17⁄16-in.
tf = 0.780 in.
W14×99
d = 14.16
k1 = 7⁄8-in.
T = 111⁄4-in.
Solution A:
From LRFD Specification Commentary Section K1.7, the panel zone
web shear force ΣFu is:
ΣFu =
Mu1 Mu2
+
− Vu
dm1 dm2
Since Example 10-1 has an FR moment connection to only one side of
the column and the effect of story shear is to be conservatively
neglected, this equation may be reduced to:
ΣFu =
Mu1
dm1
From Example 10-1
ΣFu = Puf
= 167 kips
Determine the design shear strength of the column web panel zone.
From LRFD Specification Section K1.7:
Pu
φRv = φ 0.60Fy dctw1.4 −
Py
= 0.90[0.60 × 50 ksi × 14.16 in. × 0.485 in. ( 1.4 − 0.7)]
= 130 kips < 167 kips n.g.
The W14×99 is not adequate for the web shear induced by the flangeplated connections of Examples 10-1 and 10-2.
Solution B:
In a manner similar to that developed in Solution A, the panel zone
web shear force ΣFu from Example 10-3 is
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
COLUMN STIFFENING AT FR AND PR MOMENT CONNECTION
10 - 53
ΣFu = Puf
= 172 kips
Determine the design strength of the column web panel zone.
As developed in Solution A:
φRv = 130 kips < 172 kips n.g.
The W14×99 is not adequate for the web shear induced by the directly
welded flange and four-bolt unstiffened extended end-plate connections of Examples 10-3 and 10-4.
Solution C:
For the connections of Solutions A and B, the required thickness treq is:
treq =
=
ΣFu
Pu
φ 0.60Fy dc 1.4 −
P
y
Puf
Pu
0.90 0.60Fy dc 1.4 −
P
y
For convenience, Puf will be taken as 172 kips, the larger value from
Examples 10-1, 10-2, 10-3, and 10-4.
treq =
172 kips
0.90[0.60 × 50 ksi × 14.16 in.(1.4 − 0.7)]
= 0.643 in.
The lightest W14 which satisfies this web thickness requirement is a
W14×132. The cost of the additional of 33 pounds per foot of column
must be compared with the cost of adding the doubler plate; see
Solution D for a design of the doubler plate for the W14×99 column.
Solution D:
The thickness of doubler plate required for the W14×99 column is:
tp req = te − twc
= 0.643 in. − 0.485 in.
= 0.158 in.
Try 1⁄4-in.×111⁄4-in.×18 in. doubler plate with a 3⁄16-in. groove weld.
Check doubler plate buckling.
From LRFD Specification Appendix F2.2, the full design shear
strength of the doubler plate may be used if
√
h
≤ 187
tw
kv
Fy
where
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
10 - 54
FULLY RESTRAINED (FR) MOMENT CONNECTIONS
h 111⁄4−in.
= 1
tw
⁄4−in.
= 45.0
kv = 5 +
=5+
5
(a / h)2
5
(18 in. / 111⁄4−in.)2
= 6.95
√
187
√
kv
= 187
Fy
6.95
36 ksi
= 82.2
√
kv
h
< 187
doubler plate is o.k.
Fy
tw
Use 1⁄4-in.×111⁄4-in.×18-in. doubler plate with a 3⁄16-in.groove weld.
Since
Note that, for the four-bolt unstiffened extended end-plate connection,
the doubler-plate size will have to be adjusted for the transverse
stiffener required at the tension flange as determined in Example 10-4.
Diagonal Stiffeners
At locations of FR or PR moment connections, a pair of diagonal stiffeners may be used
as an alternative to doubler plates to stiffen a column web which is inadequate in panel
zone shear. The designer should be aware of the increased fabrication costs incurred by
the addition of diagonal stiffeners to a column. It frequently is less costly to select a
member with a thicker web or higher yield strength than it is to add the diagonal stiffening.
Diagonal stiffeners are sized for the strength required in excess of the design strength
of the web. The full force in the stiffener must be developed at each end, as for any truss
diagonal, by use of either fillet or groove welds. The diagonal stiffeners will prevent
column web buckling with only a nominal attachment to the web.
From Figure 10-19, the combined horizontal and vertical shear forces may be resolved
as a diagonal compressive stress in the column web. Thus, a diagonal stiffener may be
used to “truss” the column as a compression strut with node points at interior panel corners
A and C.
For static equilibrium, the panel zone shear ΣFu must be resisted by the column web
and the horizontal component of the diagonal stiffener resistance. Thus,
ΣFu = φRv + (Puf × cosθ)
Where, for a connection to one side of a column,
ΣFu =
Mu
− Vus
dm
and the force in the diagonal stiffener Ts is
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
COLUMN STIFFENING AT FR AND PR MOMENT CONNECTION
10 - 55
Ts = φc Pn = φc AsFcr
Assuming dm = 0.9d and substituting terms,
Mu
− Vus = φRv + (φc Fcr As × cosθ)
0.9d
Solving for the required stiffener area,
As req =
1
cosθ
φRv
Mu
Vus
−
−
(0.9d) × φcFcr φcFcr φcFcr
where
As = the required diagonal stiffener area, in.2
Mu = MuL + MuG, the sum of the factored moments due to lateral load and gravity
load on the leeward side of the connection, kip-in.
φcFcr = the design compressive strength as given LRFD Specification Section E2,
kips
φRv = the design shear strength as given in LRFD Specification Section K1.7, kips
Vus = the factored story shear due to the lateral load, kips
Kl
Letting φFcr = 0.85Fy (assumes for stiffener
= 0) and φRv = 0.90(0.60Fy dctw),
r
Vus
1 1.31Mu
−
− 0.64twdc
As req =
0.85F
d
F
cosθ b y
y
Vus
θ
Puf
A
B
Ts
D
tf
Ru
Mu
tf
C
Puf
Puf =
Mu
d – tf
Fig. 10-19. Force diagram for diagonal stiffeners.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
d
10 - 56
FULLY RESTRAINED (FR) MOMENT CONNECTIONS
MOMENT SPLICES
Beams and girders sometimes are spliced in locations where both shear and moment must
be transferred across the splice. Some design specifications require that the strength of
the splice be fully equivalent to the strength, in shear and flexure, of the uncut section.
Alternatively, other specifications allow the splice to be designed for an arbitrarily
established minimum percentage of the strength of the uncut section. However, since the
maximum shear and maximum moment seldom occur at the same location, these
requirements may be overly conservative.
LRFD Specification Section J7 requires that the full strength of the smaller section
being spliced be developed in groove-welded butt splices. Other types of beam or girder
splices must develop the strength required by the actual forces at the point of the splice.
Location of Moment Splices
A careful analysis is particularly important in continuous structures where a splice may
be located at or near the point of contraflexure—the point of zero moment. Since this
inflection point can and does migrate under service loading, actual forces and moments
may differ significantly from those assumed. Further, since loading application and
frequency can change in the lifetime of the structure, it is prudent for the designer to
specify some minimum strength requirement at the splice. Hart and Milek (1965) propose
that splices in fixed-ended beams be located at the one-sixth point of the span and be
adequate to resist a moment equal to one-sixth of the flexural strength of the member.
Force Transfer in Moment Splices
Force transfer in moment splices may be assumed to occur in a manner similar to that
developed for FR moment connections. That is, the shear Ru is primarily transferred
through the beam web connection and the moment may be resolved into an effective
tension-compression couple where the force at each flange is Puf where:
Puf =
Mu
dm
where
Puf = factored beam flange force, tensile or compressive, kips
Mu = moment in the beam at the splice, kip-in.
dm = moment arm, in.
Axial forces, if present, are assumed to be distributed uniformly across the beam
cross-sectional area, and are additive algebraically to the flange forces and vectorially to
the shear force.
Flange-Plated Moment Splices
Moment splices can be designed as shown in Figure 10-20, to utilize flange plates and a
web connection. The flange plates and web connection may be bolted or welded.
Design Checks
The splice and spliced beams should be checked in a manner similar to that described
previously under “Fully Restrained (FR) Moment Connections—Flange-Plated Connections,” except that the web connection should be designed as illustrated previously in
“Shear Splices” in Part 9.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
MOMENT SPLICES
10 - 57
Shop and Field Practices
Figure 10-20 is a composite detail illustrating two types of splices, bolted and welded.
The left side of the splice in Figure 10-20 illustrates the detail of a bolted flange-plated
moment splice. For this case, the flange plates are normally made approximately the same
width as the beam flange as shown in Section A-A.
Alternatively, the right side of the splice in Figure 10-20 illustrates the detail of a
welded splice. As shown in Section B-B, the top plate is narrower and the bottom plate
is wider than the beam flange, permitting the deposition of weld metal in the downhand
or horizontal position without inverting the beam. While this is a benefit in shop
fabrication (the beam does not have to be turned over), it is of extreme importance in the
field where the weld can be made in the horizontal instead of the overhead position since
the beam cannot be turned over. This detail also provides tolerance for field alignment,
since the joint gap can be opened or closed. When splices are field welded, some means
for temporary support must be provided. Refer to “Fully Restrained (FR) Moment
Connections—Temporary Support During Erection”.
If the beam or girder flange is thick and the flange forces are large, it may be desirable
to place additional plates on the insides of the flanges. In a bolted splice (Section A-A),
the bolts are then loaded in double shear and a more compact joint may result. Note that
these additional plates must have sufficient area to develop their share of the double-shear
bolt load.
In a welded splice (Section B-B), these additional plates must have sufficient area to
match the strength of the welds which connect them. Additionally, these plates must be
set away from the beam web a distance sufficient to permit deposition of weld metal as
shown in Figure 10-21a. This distance is a function of the beam depth and flange width,
Bolted
Welded
A
B
A
B
Optional location of
additional plates
Section A-A
Bolted
Section B-B
Welded
Fig. 10-20. Bolted and welded flange-plated moment splices.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
10 - 58
FULLY RESTRAINED (FR) MOMENT CONNECTIONS
as well as the welding equipment to be used; a distance of 2 to 21⁄2-in. or more may be
required for this access. One alternative is to bevel the bottom edge of the plate to clear
the beam fillet and place the plate tight to the beam web with a fillet weld as illustrated
in Figure 10-21a. The effects of this bevel on the area of the plate must be considered in
determining the required plate width and thickness. Another alternative would be to use
unbeveled inclined plates as shown in Figure 10-21b.
Directly Welded Flange Moment Splices
Moment splices can be designed, as shown in Figure 10-22, to utilize a complete-jointpenetration groove weld connecting the flanges of the members being spliced. The web
connection may then be bolted or welded.
Design Checks
The splice and spliced beams should be checked in a manner similar to that described
previously under “Fully Restrained (FR) Moment Connections—Directly Welded Flange
Connections,” except that the web connection should be designed as illustrated previously in “Shear Splices” in Part 9.
Shop and Field Practices
When the flange thickness or width varies across the splice and the calculated stress is
greater than one-third of the specified tensile stress Fu, Figure 10-23 shows the detail
required at the tension butt joint by AWS D1.1 Section 8.10. A transition slope of not less
than 1 in 21⁄2 must be provided by “chamfering the thicker part, tapering the wider part,
sloping the weld metal, or by any combination of these.” When the calculated stress does
Provide adequate
clearance for
welding
Alternatively, bevel the
plate and use a fillet
weld to the beam web
(a)
Splice
plates
(b)
Fig. 10-21. Welding clearances required for flange-plated moment splices.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
MOMENT SPLICES
10 - 59
not exceed one-third of the specified tensile stress Fu, no transition is required in statically
loaded structures. Compression butt joints do not require transitional tapering.
Although rare in occurence, some spliced members must be level on top. Where the
depths of these spliced members differ, consideration should be given to the use of a
flange plate of uniform thickness for the full length of the shallower member. This avoids
the fabrication problems created by an inverted transition.
In Figure 10-23, the web depth is kept constant (this is always the case with rolled
shapes of the same nominal depth). This avoids an offset cut with a transition in the web
for a built-up girder. Eccentricity resulting from differing flange thicknesses is usually
ignored in the design. The web plates normally are aligned to their center lines and the 1
in 21⁄2 slope is chamfered into the plate or the weld is sloped, depending upon the relative
thicknesses.
The groove (butt) welded splice preparation shown in Figure 10-22 may be used for
either shop or field welding. Alternatively, for shop welding where the beam may be
turned over, the joint preparation of the bottom flange could be inverted.
In splices subjected to dynamic or fatigue loading, the backing bar should be removed
and the weld should be ground flush when it is normal to the applied stress (AISC, 1977).
The access holes should be free of notches and should provide a smooth transition at the
juncture of the web and flange.
Extended End-Plate Moment Splices
Moment splices can be designed as shown in Figure 10-24, to utilize four-bolt unstiffened
extended end-plates connecting the members being spliced. If the end-plate and the bolts
are designed properly, it is possible to load this type of connection to reach the full plastic
moment capacity of the beam, φMp.
Design Checks
The splice and spliced beams should be checked in a manner similar to that described
previously under “Fully Restrained (FR) Moment Connections—Extended End-Plate
Connections.”
Shop and Field Practices
The comments for “Extended End-Plate Connections” are equally applicable to extended
end-plate moment splices.
Fig. 10-22. Directly welded flange moment splice.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
10 - 60
FULLY RESTRAINED (FR) MOMENT CONNECTIONS
SPECIAL CONSIDERATIONS
FR Moment Connections to Column-Web Supports
It is frequently required that FR moment connections be made to column web supports.
While the mechanics of analysis and design do not differ from FR moment connection
to column flange supports, the details of the connection design as well as the ductility
considerations required are significantly different.
Recommended Details
When an FR moment connection is made to a column web, it is normal practice to stop
the beam short and locate all bolts outside of the column flanges as illustrated in Figures
1
2.5
2.5
1
Fig. 10-23. Transition detail at tension flange for directly welded flange moment splices.
Both flanges typ.
Fig. 10-24. Extended end-plate moment splice.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
SPECIAL CONSIDERATIONS
10 - 61
10-3b and 10-5b. This simplifies the erection of the beam and permits the use of an impact
wrench to tighten all bolts. It is also preferable to locate welds outside the column flanges
to provide adequate clearance.
Ductility Considerations
Driscoll and Beedle (1982) discuss the testing and failure of two FR moment connections
to column-web supports: a directly welded flange connection and a bolted flange-plated
connections, shown respectively in Figures 10-25a and 10-25b. Although the connections
in these tests were proportioned to be “critical,” they were expected to provide inelastic
rotations at full plastic load. Failure occurred unexpectedly, however, on the first cycle
of loading; brittle fracture occurred in the tension connection plate at the load corresponding to the plastic moment before significant inelastic rotation had occurred.
Examination and testing after the unexpected failure revealed that the welds were of
proper size and quality and that the plate had normal strength and ductility. The following
is quoted, with minor editorial changes relative to figure numbers, directly from Driscoll
and Beedle (1982).
“Calculations indicate that the failures occurred due to high strain concentrations. These concentrations are: (1) at the junction of the connection plate and the
column flange tip and (2) at the edge of the butt weld joining the beam flange and
the connection plate.
“Figure 10-26 illustrates the distribution of longitudinal stress across the width
of the connection plate and the concentration of stress in the plate at the column
flange tips. It also illustrates the uniform longitudinal stress distribution in the
connection plate at some distance away from the connection. The stress distribution
shown represents schematically the values measured during the load tests and those
obtained from finite element analysis. (σo is a nominal stress in the elastic range.)
The results of the analyses are valid up to the loading that causes the combined
stress to equal the yield point. Furthermore, the analyses indicate that localized
yielding could begin when the applied uniform stress is less than one-third of the
(a) Directly welded flange
FR connection
(b) Bolted flange-plated
FR connection
Fig. 10-25. Test specimens used by Driscoll and Beedle (1982).
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
10 - 62
FULLY RESTRAINED (FR) MOMENT CONNECTIONS
yield point. Another contribution of the non-uniformity is the fact that there is no
back-up stiffener. This means that the welds to the web near its center are not fully
effective.
“The longitudinal stresses in the moment connection plate introduce strains in
the transverse and the through-thickness directions (the Poisson effect). Because
of the attachment of the connection plate to the column flanges, restraint is
introduced; this causes tensile stresses in the transverse and the through-thickness
directions. Thus, referring to Figure 10-26, tri-axial tensile stresses are present
along Section A-A, and they are at their maximum values at the intersections of
Sections A-A and C-C. In such a situation, and when the magnitudes of the stresses
are sufficiently high, materials that are otherwise ductile may fail by premature
brittle fracture.”
The results of nine simulated weak-axis FR moment connection tests performed by
Driscoll, et. al. (1983) are summarized in Figure 10-27. In these tests, the beam flange
was simulated by a plate measuring either 1 in.×10 in. or 11⁄8-in.×9 in. The fracture
strength exceeds the yield strength in every case, and sufficient ductility is provided in
all cases except for that of Specimen D. Also, if the rolling direction in the first five
specimens (A, B, C, D, and E) were parallel to the loading direction, which would more
closely approximate an actual beam flange, the ductility ratios for these would be higher.
The connections with extended connection plates (i.e., projection of three inches), with
extensions either rectangular or tapered, appeared equally suitable for the static loads of
the tests.
A
C
B
σο
C
A
B
(a) Longitudinal stress distribution
on Section A-A
σο
(b) Longitudinal stress distribution
on Section B-B
σο τ
(c) Shear stress distribution
on Section C-C
σο = the nominal stress in the elastic range
Fig. 10-26. Stress distributions in test specimens used by Driscoll and Beedle (1982).
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
SPECIAL CONSIDERATIONS
10 - 63
Based on the tests, Driscoll, et. al. (1983) report that those specimens with extended
connection plates have better toughness and ductility and are preferred in design for
seismic loads, even though the other connection types (except D) may be deemed
adequate to meet the requirements of many design situations.
In accordance with the preceeding discussion, the following suggestions are made
regarding the design of this type of connection:
1. For directly welded (butt) flange-to-plate connections, the connection plate should
be thicker than the beam flange. This greater area accounts for shear lag and also
provides for misalignment tolerances.
AWS D1.1, Section 3.3.3 restricts the misalignment of abutting parts such as this
to 10 percent of the thickness, with 1⁄8-in. maximum for a part restrained against
Specimen
No.
Sketch
W14x257 (typical)
3/ ″
4
A
1″ 1″
Fracture Load
(kips)
Fracture Load
Yield Load
Ductility
Ratio
Rolling direction
typical
730
1.38
6.3
824
1.55
5.3
3″
B
1″
1″
3″
C
1″
1″
3/ ″
4
D
1 5/8 ″ 1 ″
756
1.43
5.43
570
1.11
1.71
(a)
Fig. 10-27a. Results of weak-axis FR connection ductility tests performed by Driscoll, et al.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
10 - 64
FULLY RESTRAINED (FR) MOMENT CONNECTIONS
Specimen
No.
Sketch
W14x257 (typical)
Fracture Load
(kips)
Fracture Load
Yield Load
Ductility
Ratio
802
1.51
6.81
762
1.40
17.7
3″
E
1 5/8 ″ 1 ″
3/ ″
4
A2
1″
1 1/8 ″
3″
B2
1″
1 1/8 ″
795
1.46
16.5
814
1.49
16.4
813
1.49
29.6
3″
E2
1 5/8 ″
1 1/8 ″
(b)
3″
C2
1″
Notes: (a)
1 1/8 ″
3/ ″
4 dimension
is estimated—no dimension given.
(b) Ductility ratio estimated. Actual value not known
due to malfunction in deflection gage.
Fig. 10-27b. Results of weak-axis FR connection ductility tests performed by Driscoll, et al.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
SPECIAL CONSIDERATIONS
10 - 65
bending due to eccentricity of alignment. Considering the various tolerances in mill
rolling (±1⁄8-in. for W-shapes), fabrication, and erection, it is prudent design to call
for the stiffener thickness to be increased to accommodate these tolerances and avoid
the subsequent problems encountered at erection. An increase of 1⁄8-in. to 1⁄4-in.
generally is used.
Frequently, this connection plate also serves as the stiffener for a strong axis FR
or PR moment connection. The welds which attach the plate/stiffener to the column
flange may then be subjected to combined tensile and shearing or compression and
shearing forces. Vector analysis is commonly used to determine weld size and stress.
It is good practice to use fillet welds whenever possible. Welds should not be made
in the column fillet area for strength.
2. The connection plate should extend at least 3⁄4-in. beyond the column flange to avoid
intersecting welds and to provide for strain elongation of the plate. The extension
should also provide adequate room for runout bars when required.
3. Tapering an extended connection plate is only necessary when the connection plate
is not welded to the column web (Specimen E, Figure 10-27). Tapering is not
necessary if the flange force is always compressive (e.g., at the bottom flange of a
cantilevered beam).
4. To provide for increased ductility under seismic loading, a tapered connection plate
should extend three inches. Alternatively, a backup stiffener and an untapered
connection plate with 3-in. extension could be used.
Normal and acceptable quality of workmanship for connections involving gravity and
wind loading in building construction would tolerate the following:
1. Runoff bars and backing bars may be left in place for Groups 4 and 5 beams (subject
to tensile stress only) where they are welded to columns or used as tension members
in a truss.
2. Welds need not be ground, except as required for nondestructive testing.
3. Connection plates that are made thicker or wider for control of tolerances, tensile
stress, and shear lag need not be ground or cut to a transition thickness or width to
match the beam flange to which they connect.
4. Connection plate edges may be sheared or plasma or gas cut.
5. Intersections and transitions may be made without fillets or radii.
6. Burned edges may have reasonable roughness and notches within AWS tolerances.
If a structure is subjected to loads other than gravity and wind loads, such as seismic,
dynamic, or fatigue loading, more stringent control of the quality of fabrication and
erection with regard to stress risers, notches, transition geometry, welding, and testing
may be necessary; refer to AISC’s Seismic Provisions for Structural Steel Buildings in
Part 6.
FR Moment Connections Across Girder Supports
Frequently, beam-to-girder-web connections must be made continuous across a girderweb support as with continuous beams and with cantilevered beams at wall, roof-canopy,
or building lines. While the same principles of force transfer discussed previously for FR
moment connections may be applied, the designer must carefully investigate the relative
stiffness of the assembled members being subjected to moment or torsion and provide
the fabricator and erector with reliable camber ordinates.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
10 - 66
FULLY RESTRAINED (FR) MOMENT CONNECTIONS
Additionally, the design should still provide some means for final field adjustment to
accommodate the accumulated tolerances of mill production, fabrication, and erection;
it is very desirable that the details of field connections provide for some adjustment during
erection. Figure 10-28 illustrates several details that have been used in this type of
connection and the designer may select the desirable components of one or more of the
sketches to suit a particular application. Therefore, these components are discussed here
as a top flange, bottom flange, and web connection.
Top Flange Connection
As shown in Figure 10-28a, the top flange connection may be directly welded to the top
flange of the supporting girder. Figures 10-28b and 10-28c illustrate an independent
splice plate that ties the two beams together by use of a longitudinal fillet weld or bolts.
This tie plate does not require attachment to the girder flange, although it is sometimes
so connected to control noise if the connection is subjected to vibration.
Bottom Flange Connection
When the bottom flanges deliver a compressive force only, the flange forces are
frequently developed by directly welding these flanges to the girder web as illustrated in
Figure 10-28a. Figure 10-28b illustrates the use of an angle or channel extending beyond
the beam flange to provide for a horizontal fillet weld; Figure 10-28c is similar, but uses
bolts instead of welds to develop the flange force.
Web Connection
While a single-plate connection is shown in Figure 10-28a and unstiffened seated
connections are shown in Figures 10-28b and 10-28c, any of the shear connections in
(a)
(b)
(c)
Fig. 10-28. Typical FR connections across girder web supports.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
SPECIAL CONSIDERATIONS
10 - 67
Part 9 may be used. Note that the effect of eccentricity in the shear connection may be
neglected.
Knee or Corner Connections
Knee or corner connections, illustrated in Figure 10-29, are used frequently in singlestory structures that are designed using FR construction. The knee connection must
transfer the fixed-end moment from the beam into the column as well as the shear at the
top of the column into the beam. The bending moment and axial forces are assumed to
be carried by the flanges and the shear is assumed to be carried by the web.
This type of connection must be designed as part of the main member design and is
beyond the scope of this volume. Additionally, the shape of the knee may be established
as part of the architectural aesthetics or for structural considerations. For more information, refer to Blodgett (1966), Beedle, et al. (1964), and Salmon and Johnson (1980).
Non-Rectangular FR Moment Connections
Although FR moment connections are not often specified where skews and slopes are
pronounced, framing requirements sometimes dictate their use. When required, the
flange-plated, directly welded flange, and extended end-plate FR moment connections
discussed previously for rectangular framing may be adapted to non-rectangular applications.
When flange-plated and directly welded flange connections are used, the web connection, usually a single-plate connection, may be designed as illustrated previously in
“Non-Rectangular Simple Shear Connections” in Part 9. In general, the comments in that
section apply equally to non-rectangular FR moment connections.
(a) Square knee
(e) Curved haunched
knee
(b) Square knee
with diagonal
stiffener
(c) Square knee
with bracket
(f) Sloped tapered
haunched knee
Fig. 10-29. Knee or corner connections.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
(d) Tapered haunched
knee
(g) Sloped curved
haunched knee
10 - 68
FULLY RESTRAINED (FR) MOMENT CONNECTIONS
Skewed Connections
Large angles of skew can produce very awkward connections, particularly when the
connection is to the column web where the projecting column flange interferes with the
supported beam flange. The designer should consider altering the structural geometry if
possible; in Figure 10-30, a slight relocation of the work point simplifies the connection.
Alternatively, rotation of the supporting column orientation may permit more normal
framing. Other skewed FR moment connections are illustrated in Figure 10-31.
Sloped Connections
Sloped FR moment connections are illustrated in Figure 10-32.
CL
2 3/8 ″
W.P.
CL
W.P.
6
6 1/8
12
12
(a) Original working point at
column centerline results in
an awkward connection
(b) Relocation of working point
simplifies the connection
Fig. 10-30. Simplifying skewed FR connection details.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
SPECIAL CONSIDERATIONS
10 - 69
Stiffeners if
required
Stiffeners if
required
Shim as
required
Slotted
holes
Stiffeners if
required
Figure 10-31. Skewed FR moment connections.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
10 - 70
FULLY RESTRAINED (FR) MOMENT CONNECTIONS
Plates
Figure 10-32. Sloped FR moment connections.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
REFERENCES
10 - 71
REFERENCES
American Institute of Steel Construction, 1977, Bridge Fatigue Guide Design and
Details, AISC, Chicago, IL.
Beedle, et al., 1964, Structural Steel Design, The Ronald Press Co., New York, NY.
Beedle, L. S., L. W. Lu, and E. Ozer, 1973, “Recent Developments in Steel Building Design,”
Engineering Journal, Vol. 10, No. 4, (4th Qtr.), pp. 98–111, AISC, Chicago, IL.
Blodgett, O. W., 1966, Design of Welded Structures, James F. Lincoln Arc Welding
Foundation, Cleveland, OH.
Curtis, L. E. and T. M. Murray, 1989, “Column Flange Strength at Moment End-Plate
Connections,” Engineering Journal, Vol. 26, No. 2, (2nd Qtr), pp. 41–50, AISC,
Chicago, IL.
Driscoll, G. C. and L. S. Beedle, 1982, “Suggestions for Avoiding Beam-to-Column Web
Connection Failures,” Engineering Journal, Vol. 19, No. 1, (1st Qtr.), pp. 16–19, AISC,
Chicago, IL.
Driscoll, G. C., A. Pourbohloul, and X. Wang, 1983, “Fracture of Moment Connections—
Tests on Simulated Beam-to-Column Web Moment Connection Details,” Fritz Engineering Laboratory Report No. 469.7, Lehigh University, Bethlehem, PA.
Graham, J. D., A. N. Sherbourne, R. N. Khabbaz, and C. D. Jensen, 1959, “Welded
Interior Beam-to-Column Connections,” Report for AISC, AISC, Chicago, IL.
Hart, W. H. and W. A. Milek, 1965, “Splices in Plastically Designed Continuous
Structures,” Engineering Journal, Vol. 2, No. 2, (April), pp. 33–37, AISC, Chicago,
IL.
Hendrick, R. A. and T. M. Murray, 1984, “Column Web Compression Strength at
End-Plate Connections,” Engineering Journal, Vol. 21, No. 3, (3rd Qtr.), pp. 161–169,
AISC, Chicago, IL.
Huang, J. S., W. F. Chen, and L. S. Beedle, 1973, “Behavior and Design of Steel
Beam-to-Column Moment Connections,” Bulletin 188, October, Welding Research
Council, New York, NY.
Krawinkler, H. and E. P. Popov, 1982, “Seismic Behavior of Moment Connections and
Joints,” Journal of the Structural Division, Vol. 108, No. ST2, (February), pp. 373–391,
ASCE, New York, NY.
Krishnamurthy, N., 1978, “A Fresh Look at Bolted End-Plate Behavior and Design,”
Engineering Journal, Vol. 15, No. 2, (2nd Qtr.), pp. 39–49, AISC, Chicago, IL.
Lincoln Electric Company, 1973, The Procedure Handbook of Arc Welding, Lincoln
Electric Company, Cleveland, OH.
Murray, T. M., 1990, Extended End-Plate Moment Connections, AISC, Chicago, IL.
Murray, T. M. and A. Kukreti, 1988, “Design of Eight-Bolt Stiffened Moment EndPlates,” Engineering Journal, Vol. 25, No. 2, (2nd Qtr.), pp. 45–52, AISC, Chicago,
IL.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
10 - 72
FULLY RESTRAINED (FR) MOMENT CONNECTIONS
Ricker, D. T., 1992, “Value Engineering and Steel Economy,” Modern Steel Construction,
Volume 32, No. 2, (February), pp. 22–26, AISC, Chicago, IL.
Salmon, C. G. and J. E. Johnson, 1980, Steel Structures—Design and Behavior, 2nd
Edition, Harper & Row, New York, NY.
Thornton, W. A., 1992, “Designing for Cost Efficient Fabrication,” Modern Steel Construction, Vol. 25, No. 2, (February), pp. 12–20, AISC, Chicago, IL.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
11 - 1
PART 11
CONNECTIONS FOR TENSION AND COMPRESSION
HANGER CONNECTIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11-5
Prying Action . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11-6
DIAGONAL BRACING CONNECTIONS . . . . . . . . . . . . . . . . . . . . . . . . . 11-17
Force Transfer in Diagonal Bracing Connections . . . . . . . . . . . . . . . . . . . . . 11-19
Analysis of Existing Diagonal Bracing Connections . . . . . . . . . . . . . . . . . . . 11-26
BEAM BEARING PLATES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11-48
COLUMN BASE PLATES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11-54
Design of Axially Loaded Base Plates . . . . . . . . . . . . . . . . . . . . . . . . . . . 11-57
COLUMN SPLICES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11-64
Flange-Plated Column Splices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11-67
Directly Welded Flange Column Splices . . . . . . . . . . . . . . . . . . . . . . . . . . 11-69
Butt-Plated Column Splices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11-69
TRUSS CONNECTIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11-92
Panel-Point Connections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11-94
Support Connections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11-98
Truss Chord Splices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11-107
REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11-108
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
11 - 2
CONNECTIONS FOR TENSION AND COMPRESSION
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
OVERVIEW
11 - 3
OVERVIEW
Part 11 contains general information, design considerations, examples, and design aids for the
design of hanger connections, diagonal bracing connections, beam bearing plates, column base
plates and splices, and truss connections. It is based on the provisions of the 1993 LRFD
Specification. Supplementary information may also be found in the Commentary on the LRFD
Specification.
Following is a detailed list of the topics addressed.
HANGER CONNECTIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11-5
Design Checks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11-5
Prying Action . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11-6
DIAGONAL BRACING CONNECTIONS . . . . . . . . . . . . . . . . . . . . . . . . . 11-17
Diagonal Bracing Members . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11-19
Force Transfer in Diagonal Bracing Connections . . . . . . . . . . . . . . . . . . . . . 11-19
The Uniform Force Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11-20
Special Case 1, Modified Working Point Location . . . . . . . . . . . . . . . . . . . 11-22
Special Case 2, Minimum Shear in the Beam-to-Column Connection . . . . . . . . . 11-22
Special Case 3, No Gusset-to-Column Web Connection . . . . . . . . . . . . . . . . 11-25
Analysis of Existing Diagonal Bracing Connections . . . . . . . . . . . . . . . . . . . 11-26
Design Checks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11-27
BEAM BEARING PLATES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11-48
Design Checks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11-48
Local Web Yielding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11-48
Web Crippling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11-49
Concrete Compressive Strength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11-49
Required Bearing Plate Thickness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11-50
COLUMN BASE PLATES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11-54
Finishing Requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11-54
Holes for Anchor Rods and Grouting . . . . . . . . . . . . . . . . . . . . . . . . . . . 11-55
Leveling Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11-56
Light Base Plates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11-56
Heavy Base Plates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11-57
Design of Axially Loaded Base Plates . . . . . . . . . . . . . . . . . . . . . . . . . . . 11-57
Design Checks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11-58
Concrete Compressive Strength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11-58
Required Base-Plate Thickness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11-59
COLUMN SPLICES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11-64
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
11 - 4
CONNECTIONS FOR TENSION AND COMPRESSION
Fit-Up of Column Splices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11-64
Lifting Devices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11-65
Column Alignment and Stability During Erection . . . . . . . . . . . . . . . . . . . . 11-65
Force Transfer in Column Splices . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11-66
Flange-Plated Column Splices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11-67
Directly Welded Flange Column Splices . . . . . . . . . . . . . . . . . . . . . . . . . 11-69
Butt-Plated Column Splices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11-69
TRUSS CONNECTIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11-92
Members in Trusses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11-92
Minimum Connection Strength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11-93
Panel-Point Connections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11-94
Design Checks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11-94
Shop and Field Practices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11-94
Support Connections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11-98
Design Checks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11-98
Shop and Field Practices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11-100
Truss Chord Splices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11-107
REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11-108
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
HANGER CONNECTIONS
11 - 5
HANGER CONNECTIONS
Hanger connections, illustrated in Figure 11-1 are usually composed of a plate, tee, angle,
or pair of angles which transfers the tensile force from the tension member to the support.
Design Checks
The design strengths of the bolts and/or welds and connected elements must be determined in accordance with the provisions of the LRFD Specification. The applicable limit
states in each of the aforementioned design strengths are discussed in Part 8. Additionally,
hanger connections produce tensile single concentrated forces acting on the support; the
limit states of local flange bending and local web yielding must be checked. In all cases,
the design strength φRn must exceed the required strength Ru.
(a) Tee hanger
(b) Plate hanger
Fig. 11-1. Typical hanger connections.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
11 - 6
CONNECTIONS FOR TENSION AND COMPRESSION
Prying Action
Prying action is a phenomenon associated with bolted construction and tensile loads only
where either the connected fitting or the support deforms and thereby increases the tensile
force in the bolt. LRFD Specification Section J3.6 states that any tension resulting from
prying action must be considered in determining the required strength of bolts. However,
prying action is primarily a function of the connected elements. Furthermore, while the
connected elements must have adequate flexural strength, it is their stiffness which is the
key to satisfactory performance.
Consider the tee used in a hanger connection in Figure 11-2. To ensure adequate flange
stiffness, dimension b should be made as small as the bolt entering and tightening
clearances will permit; see Tables 8-4 and 8-5. The actual distribution of stresses resulting
from prying action is extremely complex. Since dimension b is only slightly larger than
the thickness of the fitting, the classical moment diagram as shown on Figure 11-2 does
not truly represent all the restraining forces at the bolt line. Consequently, this model
overestimates the actual prying force. In addition, local deformation of the fitting, known
as “quilting”, under the clamping force of high-strength bolts also accounts for a less
critical prying force than indicated by earlier investigations. Note that the maximum
tributary length p per pair of bolts (perpendicular to the plane of the page) should
preferably not exceed the gage between the pair of bolts g.
The following procedures for designing and analyzing a tension connection for prying
action are recommended. Good correlation has been obtained between estimated connection strength and observed test results using these procedures (Kulak, Fisher, and
Struik, 1987). Note, however, that since these procedures are formulated in terms of
factored loads, they are not applicable to situations where service loads must be used (i.e.,
fatigue, deflection, and drift limitations). For these situations, refer to the allowable stress
procedures outlined in AISC (1989), Astaneh (1985), or Thornton (1985).
Designing for Prying Action
When designing a tension connection for prying action, select the number and size of
bolts required such that the design tensile strength of one bolt φrn exceeds the factored
tensile force per bolt rut (exclusive of tightening force). Then use Table 11-1 to make a
preliminary selection of a trial fitting for steels with Fy equal to 36 ksi or 50 ksi.
qu
g
qu
rut +qu
b′
b
rut +qu
a′
a
Mu2
Mu1
2rut
Fig. 11-2. Variables in prying action.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
HANGER CONNECTIONS
11 - 7
In this table, it is assumed that equal critical moments exist at the face of the tee stem
(Mu1) and at the bolt line (Mu2). From LRFD Specification Section F1.1, the design
flexural yielding strength of the tee flange is φbMn, where φb = 0.90 and
Mn = Mp = Fy Zx
In the above equation, the plastic section modulus Zx per unit length of the tee flange is
Zx =
t2
4
where t is the thickness of the angle or tee flange, in. Thus, for a unit length of the tee
flange
φbMn =
0.90Fy t2
4
and the factored tensile force on the fitting 2rut must be such that
2rut ≤
0.9Fy t2
b
where b is the distance from bolt centerline to face of the angle leg or tee stem, in. For
Fy = 36ksi, the above equation may be simplified as
2rut ≤
32.4t2
b
and for Fy = 50 ksi, the above equation may be simplified as
2rut ≤
45.0t2
b
With the preliminary fitting selected from Table 11-1, its strength must be investigated.
Given the above relationship, b, and the flange thickness t of the selected trial section,
calculate b′, a′, and ρ as
d
a′ = a +
2
d
b′ = b −
2
ρ=
b′
a′
In the above equations, a is the distance from the bolt centerline to the edge of the fitting;
for calculation purposes, a should not be taken to be greater than 1.25b.
Next, calculate β as follows:
β=
1
ρ
φrn
− 1
rut
if β ≥ 1, set α′ = 1.0
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
11 - 8
CONNECTIONS FOR TENSION AND COMPRESSION
Fy = 36 ksi
Table 11-1.
Preliminary Hanger Connection Selection Table
Design tensile strength, kips per linear in.,
limited by flexural yielding of the flange
t
b
2rut
b, in.
1
11⁄4
11⁄2
13⁄4
5⁄
16
3.16
2.53
2.11
1.81
3⁄
8
4.56
3.65
3.04
7⁄
16
6.20
4.96
1⁄
2
8.10
t, in.
21⁄4
21⁄2
23⁄4
1.58
1.41
1.27
1.15
1.05
0.974
2.60
2.28
2.03
1.82
1.66
1.52
1.40
4.13
3.54
3.10
2.76
2.48
2.26
2.07
1.91
6.48
5.40
4.63
4.05
3.60
3.24
2.95
2.70
2.49
8.20
6.83
5.86
5.13
4.56
4.10
3.73
3.42
3.15
8.44
7.23
6.33
5.63
5.06
4.60
4.22
3.89
8.75
7.66
6.81
6.13
5.57
5.10
4.71
9.11
8.10
7.29
6.63
6.08
5.61
9.51
8.56
7.78
7.13
6.58
9.92
9.02
8.27
7.63
9.49
8.76
2
3
31⁄4
9⁄
16
10.3
5⁄
8
12.7
10.1
11⁄
16
15.3
12.3
10.2
3⁄
4
18.2
14.6
12.2
10.4
13⁄
16
21.4
17.1
14.3
12.2
10.7
7⁄
8
24.8
19.8
16.5
14.2
12.4
11.0
15⁄
16
28.5
22.8
19.0
16.3
14.2
12.7
11.4
10.4
1
32.4
25.9
21.6
18.5
16.2
14.4
13.0
11.8
10.8
11⁄16
36.6
29.3
24.4
20.9
18.3
16.3
14.6
13.3
12.2
11.3
11⁄8
41.0
32.8
27.3
23.4
20.5
18.2
16.4
14.9
13.7
12.6
13⁄16
45.7
36.6
30.5
26.1
22.8
20.3
18.3
16.6
15.2
14.1
11⁄4
50.6
40.5
33.8
28.9
25.3
22.5
20.3
18.4
16.9
15.6
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
9.97
HANGER CONNECTIONS
11 - 9
Fy = 50 ksi
Table 11-1 (cont.).
Preliminary Hanger Connection Selection Table
Design tensile strength, kips per linear in.,
limited by flexural yielding of the flange
t
b
2rut
b, in.
1
11⁄4
11⁄2
13⁄4
5⁄
16
4.39
3.52
2.93
2.51
3⁄
8
6.33
5.06
4.22
7⁄
16
8.61
6.89
9.00
t, in.
21⁄4
21⁄2
23⁄4
2.20
1.95
1.76
1.60
1.46
1.35
3.62
3.16
2.81
2.53
2.30
2.11
1.95
5.74
4.92
4.31
3.83
3.45
3.13
2.87
2.65
7.50
6.43
5.63
5.00
4.50
4.09
3.75
3.46
9.49
8.14
7.12
6.33
5.70
5.18
4.75
4.38
8.79
7.81
7.03
6.39
5.86
5.41
9.45
8.51
7.73
7.09
6.54
9.20
8.44
7.79
9.90
9.14
2
3
31⁄4
1⁄
2
11.3
9⁄
16
14.2
11.4
5⁄
8
17.6
14.2
11.7
10.0
11⁄
16
21.3
17.0
14.2
12.2
10.6
3⁄
4
25.3
20.3
16.9
14.5
12.7
11.3
10.1
13⁄
16
29.7
23.8
19.8
17.0
14.9
13.2
11.9
10.8
7⁄
8
34.5
27.6
23.0
19.7
17.2
15.3
13.8
12.5
11.5
10.6
15⁄
16
39.6
31.6
26.4
22.6
19.8
17.6
15.8
14.4
13.2
12.2
1
45.0
36.0
30.0
25.7
22.5
20.0
18.0
16.4
15.0
13.8
11⁄16
50.8
40.6
33.9
29.0
25.4
22.6
20.3
18.5
16.9
15.6
11⁄8
57.0
45.6
38.0
32.5
28.5
25.3
22.8
20.7
19.0
17.5
13⁄16
63.5
50.8
42.3
36.3
31.7
28.2
25.4
23.1
21.2
19.5
11⁄4
70.3
56.3
46.9
40.2
35.2
31.3
28.1
25.6
23.4
21.6
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
11 - 10
CONNECTIONS FOR TENSION AND COMPRESSION
if β < 1, set α′ = the lesser of 1.0 and
1 β
δ 1 − β
where δ, the ratio of the net area at the bolt line to the gross area at the face of the stem
or angle leg, is
δ=1−
d′
p
The required flange thickness treq may then be calculated as:
treq =
√
4.44rut b′
pFy (1 + δα′)
and
d′ = width of bolt hole parallel to the tee stem or angle leg, in.
p = length of flange, parallel to the tee stem or angle leg, tributary to each bolt, in.
Note that p should preferably not exceed the gage between bolts illustrated in
Figure 11-2.
If treq ≤ t, the preliminary fitting is satisfactory. Otherwise, a section with a thicker
flange, or a change in geometry (i.e., b and p) is required.
The factored prying force per bolt qu may be calculated from α as follows:
2
1 r t
α = ut c − 1 ≥ 0
δ φrn t
2
t
qu = φrn δαρ
t
c
and the factored force per bolt including prying action is rut + qu. In the above equations,
tc, the flange or angle thickness required to develop the design strength of the bolt φrn
with no prying action, is calculated as:
tc =
pF
√
4.44φrnb′
y
Designing to Minimize Prying Action
In applications where the prying force qu must be reduced to an insignificant amount, set
α′ = 0 and calculate treq as:
treq =
b
√
pF
4.44rut ′
y
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
HANGER CONNECTIONS
11 - 11
Analyzing a Connection for Prying Action
The foregoing procedure is somewhat simplified when analyzing a connection for prying
action. As before, check that rut ≤ φrn. Then calculate α′ as:
2
1
α′ =
δ (1 + ρ)
tc
− 1
t
If α′ < 0, rut must be such that
rut ≤ φrn
If 0 ≤ α′ ≤ 1, rut must be such that
2
t
rut ≤ φrn (1 + δα′)
tc
If α′ > 1, rut must be such that
2
t
rut ≤ φrn (1 + δ)
tc
If desired, the factored prying force per bolt qu may be determined as before.
EXAMPLE 11-1
Refer to Figure 11-3. Design a WT tension-hanger connection for a
2L3×3×5⁄16 tension member to W24×94 beam connection. For the beam
and WT, Fy = 50 ksi and Fu = 65 ksi; for the double angles, Fy = 36 ksi
Given:
l
W24x94
4 1/2
3/
4
4 1/4 in.
min
4
A325-N bolts
WT8x28.5
1/
4
Pu
2L 3x3x 5/16
4
Pu
Fig. 11-3. Illustration for Example 11-1.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
11 - 12
CONNECTIONS FOR TENSION AND COMPRESSION
and Fu = 58 ksi. Use 3⁄4-in. diameter ASTM A325-N bolts and 70 ksi
electrodes.
Pu = 80 kips
W24×94
d = 24.31 in.
tw = 0.515 in.
bf = 9.065 in.
tf = 0.875 in.
2L3×3×5⁄16
A = 3.55 in.2
Solution:
Check tension yielding of angles
φRn = φFy Ag
= 0.9(36 ksi)(3.55 in.2)
= 115 kips > 80 kips o.k.
Check tension rupture of angles (Design welds to find length of
connection and U)
Try 1⁄4-in. fillet welds
Pu
1.392D
80 kips
=
1.392 (4 sixteenths)
= 14.4 in.
Lmin =
Use four 4-in. welds (16 in. total), one at each toe and heel of each
angle.
Calculate effective net area
From LRFD Specification Section B3
_
x
U = 1 − ≤ 0.9
L
0.865 in.
=1−
4 in.
= 0.784
(Note: in lieu of the calculation shown above, U may be taken as 0.75
since 1.5w > l ≥ w per LRFD Specification Section B3.2d)
Ae = UAn
= 0.784(3.55 in.2)
= 2.78 in.2
φRn = φFu Ae
= 0.75(58 ksi)(2.78 in.2)
= 121 kips > 80 kips o.k.
Select preliminary WT using beam gage g = 4 in.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
HANGER CONNECTIONS
11 - 13
With four 3⁄4-in. diameter A325-N bolts,
rut =
Pu 80 kips
=
= 20 kips/bolt
n 4 bolts
Since for 3⁄4-in. diameter A325N bolts φrn = 29.8 kips (> 20 kips), the
bolts are o.k.
With four bolts, the maximum effective length is 2g = 8 in. Thus, there
are 4 in. of tee length tributary to each pair of bolts and
2 bolts (20 kips / bolt)
= 10.0 kips/in.
4 in.
The minimum depth of WT that can be used is equal to the sum of the
weld length plus the weld size plus the k-dimension for the selected
section. From Table 11-1 with an assumed b = 4 in./2 = 2 in., to ≈ 11⁄16-in.,
and dmin = 4 in. + 1⁄4-in. + k ≈ 6 in., appropriate selections include:
WT6×39.5
WT7×34
WT8×28.5
WT9×30
Try WT8×28.5; bf = 7.12 in., tf = 0.715 in., tw = 0.430 in.
Check prying action with WT8×28.5×0′−8
g − tw
2
4 in. − 0.430 in.
=
2
= 1.79 in. > 11⁄4-in. entering and tightening clearance, o.k.
bf − g
a =
2
7.12 in. − 4 in.
=
2
= 1.56 in.
b =
Since a = 1.56 in. is less than 1.25b = 2.24 in., use a = 1.56 in.
b′ = b − d / 2
= 1.79 in. −
jin.
2
3⁄
4
= 1.42 in.
d
a′ = a +
2
= 1.56 in. +
jin.
2
3⁄
4
= 1.94 in.
b′
ρ =
a′
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
11 - 14
CONNECTIONS FOR TENSION AND COMPRESSION
1.42 in.
1.94 in.
= 0.732
1 φrn
− 1
β =
ρ rut
1 29.8 kips / bolt
− 1
=
0.732 20 kips / bolt
= 0.669
=
Since β < 1.0,
δ
d′
p
=1−
−in.
4−in.
= 0.797
1 β
≤ 1.0
α′ =
δ 1 − β
1 0.669
=
0.797 1 − 0.669
13⁄
16
=1−
= 2.54 → 1.0
treq =
=
√
4.44 rut b′
pFy (1 + δα′)
√
4.44(20 kips / bolt)(1.42 in.)
(4 in.)(50 ksi)[1 + (0.797)(1.0)]
= 0.592 in. < tf = 0.715 in. o.k.
Check design tensile strength of bolts.
(Note this calculation is optional; the required thickness treq, calculated
above, will keep the total bolt tensile force rut + qu less than the design
strength φrn. It is included for information only.)
Calculate qu
tc =
=
√
4.44(φrn)b′
pFy
√
4.44(29.8 kips / bolt)(1.42 in.)
4 in. × 50 ksi
= 0.969 in.
1
α =
δ
rut
φrn
2
tc
− 1 ≥ 0
t
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
HANGER CONNECTIONS
11 - 15
1
=
0.797
= 0.292
20 kips / bolt
29.8 kips / bolt
2
0.969 in.
− 1
0.715 in.
2
t
qu = φrn δαρ
tc
2
0.715 in.
= 29.8 kips/bolt 0.797(0.292)(0.732)
0.969 in.
= 2.76 kips/bolt
Total tension on bolt
rut + qu = 20 kips/bolt + 2.76 kips/bolt
= 22.8 kips/bolt < 29.8 kips/bolt o.k.
Check the WT hanger as follows:
Check tension yielding of the tee stem on the Whitmore section (see
sketch below)
Lw
WT
30°
30°
The effective width of the tee stem (which cannot exceed the actual
width of 8 in.) is
Lw = 3 in. + 2(4 in. × tan 30°°) ≤ 8 in.
= 7.62 in.
and the design strength is
φRn = φFy Ag eff
= 0.9(50 ksi)(7.62 in. × 0.430 in.)
= 147 kips > 80 kips o.k.
Check shear yielding of the base metal along the toe and heel of each
weld line.
φRn = φ (0.6Fy ) Ag
= 0.9(0.6 × 50 ksi)(4 × 4 in. × 0.430 in.)
= 186 kips > 80 kips o.k.
Check shear rupture of the base metal along the toe and heel of each
weld line.
φRn = φ (0.6Fu ) An
= 0.75(0.6 × 65 ksi)(4 × 4 in. × 0.430 in.)
= 201 kips > 80 kips o.k.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
11 - 16
CONNECTIONS FOR TENSION AND COMPRESSION
Check shear rupture of the flanges.
φRn = φ [0.6Fu An]
= 0.75[0.6(65 ksi)(2 × 8 in. − 4 × 0.875 in.)(0.715 in.)]
= 261 kips > 80 kips o.k.
Check shear yielding of the flanges.
φRn = φ[0.6Fy Ag]
= 0.9[0.6 (50 ksi)(2 × 8 in. × 0.715 in.)]
= 309 kips > 80 kips o.k.
Check block shear rupture of the tee stem.
From LRFD Specification Section J4.3
0.6Fu Anv = 0.6(65 ksi)(2 × 4 in. × 0.430 in.)
= 134 kips
Fu Ant = (65 ksi)(3 in. × 0.430 in.)
= 83.9 kips
Since 0.6Fu Anv > Fu Ant,
φRn = φ [0.6Fu Anv + Fy Agt]
= 0.75[134 kips + (50 ksi)(3 in. × 0.430 in.)]
= 149 kips > 80 kips o.k.
Comments:
Alternatively, a WT tension hanger could be selected with a flange
thickness which would reduce the effect of prying action to an insignificant amount, i.e., qu ≈ 0. Using b′ = 1.42 as an assumption,
treq =
=
√
4.44rutb′
pFy
√
4.44(20 kips / bolt)(1.42 in.)
4 in. / bolt (50 ksi)
= 0.794 in.
A WT9×35.5 with tf = 0.810 in., tw = 0.495 in. (> 0.430 in.), and bf =
7.635 in. is adequate.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
DIAGONAL BRACING CONNECTIONS
11 - 17
DIAGONAL BRACING CONNECTIONS
If the members in the unbraced frame of Figure 11-4a were connected with simple shear
connections, the lateral force Hu acting from the left would cause the building to “rack”
or deflect laterally as shown by the dashed lines. In fact, the frame would be unstable
under gravity loading. In lieu of a frame with moment connections, frame stability and
resistance to lateral loads can be provided by diagonal bracing members. Whereas
moment connections resist lateral loads through flexure in the beams and columns which
comprise the frame, diagonal bracing members create a vertical truss which transfers the
lateral loads through the members of the truss as axial forces. Although a diagonally
braced frame is, in general, more efficient than a frame with moment connections, the
use of diagonal bracing may be precluded by interference with architectural features such
as corridors, windows, and doors.
Diagonal bracing may be concentric or eccentric. Eccentrically braced frames are
commonly used in seismic regions; their design is beyond the scope of this book; refer
to Ishler (1992), Popov, et al. (1989) and Lindsay and Goverdahn (1989). The following
discussion is limited to concentric diagonal bracing.
The concentric diagonal brace shown in Figure 11-4b will provide for stability and lateral
forces acting from the left; the diagonal brace is in tension (+) and induces only axial forces
in the other members of the frame. Since the lateral forces may be incident from either the
right or the left, two diagonal braces would be used, as shown in Figure 11-4c.
As the stiffnesses of the diagonal bracing members increase, lateral forces will divide
(not necessarily equally) between the two diagonal braces with one in tension and the
other in compression. It is normal practice to neglect the strength of the diagonal in
compression and design each diagonal for the tension which results from the lateral loads;
this is called tension-only bracing.
Figure 11-5a shows the vertical arrangement of X-bracing in a single bay of a
multistory building. Figure 11-5b shows a common type of K-bracing. Figures 11-5c and
11-5d show bracing which is composed of members subjected to both tension and
compression; as shown, this bracing occupies a single bay of a multistory building.
Figure 11-5e is similar except the bracing occupies two adjacent bays of a multistory
building. Other arrangements, such as the one shown in Figure 11-5f, are also possible.
When possible, diagonal bracing should be located in a bay or bays at the mid-section
of a building. In buildings with expansion joints, diagonal bracing should be located in
a bay or bays at the mid-section between expansion joints. Furthermore, this bracing
Hu
Hu
(+)
(a)
(b)
Fig. 11-4. Lateral forces and diagonal bracing.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
(c)
11 - 18
CONNECTIONS FOR TENSION AND COMPRESSION
C
25 ′-0
D
C
25 ′-0
D
El. 68 ′ -0
El. 45 ′ -0
El. 22 ′ -0
(a)
(b)
El. 68 ′ -0
El. 45 ′ -0
El. 22 ′ -0
(c)
C
25 ′ -0
D
25 ′ -0
(d)
E
C
25 ′ -0
D
25 ′ -0
El. 91 ′ -0
El. 68 ′ -0
El. 45 ′ -0
El. 22 ′-0
(e)
(f)
Fig. 11-5. Diagonal bracing in multistory buildings.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
E
DIAGONAL BRACING CONNECTIONS
11 - 19
should preferably be located in the corresponding bay or bays in other frames across the
width of the building; symmetrically located diagonal bracing minimizes torsional effects
of lateral load on the overall structure.
Diagonal Bracing Members
Diagonal bracing members may be rods, single angles or channels, double angles or
channels, tees, W shapes, or tubes as required by the lateral loads.
Slender diagonal bracing members are relatively flexible and, thus, vibration and sag
may be considerations. In slender tension-only bracing, these problems can be minimized
with “draw” or pretension created by shortening the fabricated length of the diagonal
brace from the theoretical length L between member working points. In general, the
following deductions will be sufficient: no deduction for L ≤ 10 ft; deduct 1⁄16-in. for
10 ft < L ≤ 20 ft; deduct 1⁄8-in. for 20 < L ≤ 35 ft; and, deduct 3⁄16-in. for L > 35 ft. This
principle is not applicable to diagonal bracing members other than light angles since it
is difficult to stretch heavier members; vibration and sag are not usually design considerations in heavier diagonal bracing members. In any diagonal bracing member, however,
it is permissible to deduct an additional 1⁄32-in. when necessary to avoid dimensioning to
thirty-seconds of an inch.
When double-angle diagonal bracing members are separated, as at “sandwiched” end
connections to gussets, intermittent connections must be provided if the unsupported
length of the diagonal brace exceeds the limits specified in LRFD Specification Section
D2 for tension members or LRFD Specification Section E4 for compression members;
note that a minimum of two stitch-fillers is required. These may be made with either
bolted or welded stitch-fillers. Many fabricators prefer ring or rectangular bolted stitchfillers when the angles require other punching, as at the end connections. In welded
construction, a stitch-filler with protruding ends, as shown in Figure 11-6a is preferred
because it is easy to fit and weld. The short stitch-filler shown in Figure 11-6b is used if
a smooth appearance is desired.
When a full-length filler is provided, as in corrosive environments, the maximum
spacing of stitch bolts should be as specified in LRFD Specification Section J3.5.
Alternatively, the edges of the filler may be seal welded.
Force Transfer in Diagonal Bracing Connections
There has been some controversy as to which of several available analysis methods
provides the best means for the safe and economical design and analysis of diagonal
2L
(a) Protruding
(b) Short
Fig. 11-6. Welded stitch fillers.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
11 - 20
CONNECTIONS FOR TENSION AND COMPRESSION
bracing connections. To resolve this situation, starting in 1981, AISC sponsored extensive
computer studies of this connection by Richard (1986). Associated with Richard’s work,
full scale tests were performed by Bjorhovde and Chakrabarti (1985), Gross and Cheok
(1988), and Gross (1990). Also, AISC and ASCE formed a task group to recommend a
design method for this connection. In 1990, this task group recommended three methods
for further study; refer to Appendix A of Thornton (1991).
Using the results of the aforementioned full scale tests, Thornton (1991) showed that
these three methods yield safe designs, and that of the three methods, the Uniform Force
Method (see Model 3 of Thornton, 1991) best predicts both the design strength and
critical limit state of the connection. Furthermore, Thornton (1992) showed that the
Uniform Force Method yields the most economical design through comparison of actual
designs by the different methods and through consideration of the efficiency of force
transmission. For the above reasons, and also because it is the most versatile method, the
Uniform Force Method has been adopted for use in this book.
The Uniform Force Method—The essence of the Uniform Force Method is to select the
geometry of the connection so that moments do not exist on the three connection
interfaces; i.e., gusset-to-beam, gusset-to-column, and beam-to-column. In the absence
of moment, these connections may then be designed for shear and/or tension only, hence
the origin of the name Uniform Force Method.
With the working point chosen at the intersection of the centerlines of the beam,
column, and diagonal brace as shown in Figure 11-7a, four geometric parameters eb, ec,
α, and β can be identified, where
eb = one-half the depth of the beam, in.
ec = one-half the depth of the column, in. Note that, for a column web support, ec ≈ 0.
α = distance from the face of the column flange or web to the centroid of the gussetto-beam connection, in.
β = distance from the face of the beam flange to the centroid of the gusset-to-column connection, in.
For the force distribution shown in the free-body diagrams of Figures 11-7b, 11-7c, and
11-7d to remain free of moments on the connection interfaces, the following expression
must be satisfied.
α − βtanθ = ebtanθ − ec
(11-1)
Since the variables on the right of the equal sign (eb, ec, and θ) are all defined by the
members being connected and the geometry of the structure, the designer may select
values of α and β for which the equation is true, thereby locating the centroids of the
gusset-to-beam and gusset-to-column connections.
Once α and β have been determined, the factored axial and shear forces for which
these connections must be designed can be determined from the following equations.
Vuc =
β
P
r u
Huc =
ec
P
r u
Hub =
α
P
r u
Vub =
eb
P
r u
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
DIAGONAL BRACING CONNECTIONS
11 - 21
where
r=√
(α + ec)2 + (β + eb)2
The gusset-to-beam connection must be designed for the factored shear force Hub and the
factored axial force Vub, the gusset-to-column connection must be designed for the
Col. cL
Ruc
Pu
θ
Vu
Pu
Hu
Huc
β
w.p.
eb
Aub
Vuc
Hub
Hu
Rub
w.p.
Beam cL
Hu = Huc + Hub
Vu = Vuc + Vub
α
ec
Vub
Ruc + Rub – Vu
(b) Gusset free-body diagram
(a) Diagonal bracing connection
and external forces
Ruc
Col cL
Vuc
Vub
Huc
w.p.
Aub
Hub
w.p.
Hu – Hub
Rub
Aub Beam cL
Rub – Vub
Aub ± (Hu – Hub )
Rub – Vub
Ruc + Rub – Vu
(c) Column free-body diagram
(d) Beam free-body diagram
Fig. 11-7. Force transfer, Uniform Force Method.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
Hu
11 - 22
CONNECTIONS FOR TENSION AND COMPRESSION
factored shear force Vuc and the factored axial force Huc, and the beam-to-column
connection must be designed for the factored shear Ru − Vub and the factored axial force
Aub ± (Hu − Hub), where Ru is the factored end reaction of the beam and Aub is the factored
axial force in the beam (see Figure 11-7). Note that, while Pu is shown as a tensile force,
it may also be a compressive force; were this the case the signs of the resulting gusset
forces would change.
Special Case 1, Modified Working Point Location—As illustrated in Figure 11-8a, the
working point in Special Case 1 of the Uniform Force Method is chosen at the corner of
the gusset; this may be done to simplify layout or for a column web connection. With this
assumption, the terms in the gusset force equations involving eb and ec drop out and the
interface forces, as shown in Figures 11-8b, 11-8c, and 11-8d, are:
Hub = Pu sinθ = Hu
Vub = 0
Vuc = Pu cosθ = Vu
Huc = 0
The gusset-to-beam connection must be designed for the factored shear force Hub and the
gusset-to-column connection must be designed for the factored shear force Vuc. Note,
however, that the change in working point requires that the beam be designed for the
factored moment Mub, where
Mub = Hubeb
and the column must be designed for the factored moment Muc where
Muc =
Vuc ec
2
An example demonstrating this eccentric special case is presented in AISC (1984).
This eccentric case was endorsed by the AISC/ASCE task group (Thornton, 1991) as a
reduction of the three recommended methods when the work point is located at the gusset
corner. While calculations are somewhat simplified, it should be noted that resolution of
the factored force Pu into the shears Vuc and Hub may not result in the most economical
connection.
Special Case 2, Minimizing Shear in the Beam-to-Column Connection—If the brace
force, as illustrated in Figure 11-9a, were compressive instead of tensile and the factored
beam reaction Rub were high, the addition of the extra shear force Vub into the beam might
exceed the design strength of the beam and require doubler plates or a haunched
connection. Alternatively, the vertical force in the gusset-to-beam connection Vub can be
limited in a manner which is somewhat analogous to using the gusset itself as a haunch.
As illustrated in Figure 11-9b, assume that Vub is reduced by an arbitrary amount ∆Vub.
By statics, the vertical force at the gusset-to-column interface will be increased to Vuc +
∆Vub, and a moment Mub will result on the gusset-to-beam connection, where
Mub = (∆Vub )α
If ∆Vub is taken equal to Vub, none of the vertical component of the brace force is
transmitted to the beam; the resulting procedure is that presented by AISC (1984) for
concentric gravity axes, extended to connections to column flanges. This method was
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
DIAGONAL BRACING CONNECTIONS
11 - 23
also recommended by the AISC/ASCE task group as the “Engineering for Steel Construction” method.
Design by this method may be uneconomical. It is very punishing to the gusset and
beam because of the moment Mub induced on the gusset-to-beam connection. This
moment will require a larger connection and a thicker gusset. Additionally, the limit state
Ruc
Col. cL
Muc
Pu
θ
Vu
Pu
Hu
w.p.
Vuc
eb
Rub
Muc
Hub
Hu
Beam cL
w.p.
Mub
Hub = Hu
Vuc = Vu
ec
Ruc + Rub – Vu
(b) Gusset free-body diagram
(a) Diagonal bracing connection
Ruc
Muc
Col cL
Vuc
w.p.
Hub
w.p.
Mub
eb
Beam cL
Rub
Hu
Rub
Rub
V e
Muc = uc c
2
ec
Mub = Hub eb
Muc
Ruc + Rub – Vu
(c) Column free-body diagram
(d) Beam free-body diagram
Fig. 11-8. Force transfer, Special Case 1.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
11 - 24
CONNECTIONS FOR TENSION AND COMPRESSION
of local web yielding may limit the strength of the beam. This special case interrupts the
natural flow of forces assumed in the Uniform Force Method and thus is best used when
the beam-to-column interface is already highly loaded, independently of the brace, by a
high shear Ru in the beam-to-column connection.
Col. cL
Ruc
Pu
θ
Vu
Pu
Hu
Huc
β
w.p.
eb
Aub
Vuc + ∆Vub
Hub
Hu
Rub
ec
w.p.
Vub – ∆Vub
Beam cL
Mub
Hu = Huc + Hub
Vu = (Vuc + ∆Vub ) + (Vub – ∆Vub )
Mub = (∆Vub )α
α
Ruc + Rub + Vu
(b) Gusset free-body diagram
(a) Diagonal bracing connection
Ruc
Col cL
Mub
Vuc + ∆Vub
Vub – ∆Vub
Hub
Rub
Huc
w.p.
Aub
w.p.
Hu – Hub
Beam cL
Rub + (Vub – ∆Vub )
Hu
Aub ± (Hu – Hub )
Rub + (Vub – ∆Vub )
Mub = Vub α
Ruc + Rub + Vu
(c) Column free-body diagram
(d) Beam free-body diagram
Fig. 11-9. Force transfer, Special Case 2.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
DIAGONAL BRACING CONNECTIONS
11 - 25
Special Case 3, No Gusset-to-Column Web Connection—When the connection is to a
column web and the brace is shallow (as for large θ) or the beam is deep, it may be more
economical to eliminate the gusset-to-column connection entirely and connect the gusset
to the beam only. The Uniform Force Method can be applied to this situation by setting
β and ec equal to zero as illustrated in Figure 11-10. Since there is to be no gusset-to-column connection, Vuc and Huc also equal zero. Thus, Vub = Vu and Hub = Hu.
Col. cL
Ruc
Column
web
Vu
Pu
θ
Pu
α
Hu
w.p.
eb
Aub
Rub
α
ec ≈ 0
Hub
Hu
Vub
w.p.
Mub
Hub = Hu
Vub = Vu
Mub = Vub – (α – α)
α = eb tan θ
Ruc + Rub – Vu
(b) Gusset free-body diagram
(a) Diagonal bracing connection
Ruc
Col. cL
Mub
Vub
w.p.
Hub
w.p.
Aub
Beam cL
Rub
Aub
Hu
Rub – Vub
Rub – Vub
Ruc + Rub – Vu
(c) Column free-body diagram
(d) Beam free-body diagram
Fig. 11-10. Force transfer, Special Case 3.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
11 - 26
CONNECTIONS FOR TENSION AND COMPRESSION
__
If α = α = ebtanθ, there is no moment on the gusset-to-beam interface and the gussetto-beam connection
__ can be designed for the factored shear force Hub and the factored
axial force Vub. If α≠α = eBtan θ, the gusset-to-beam interface must be designed for the
moment Mub in addition to Hub and Vub, where
__
Mub = Vub (α − α)
The beam-to-column connection must be designed for the factored shear force Ru + Vub.
Note that, since the connection is to a column web, ec is zero and hence Hc is also zero.
For a connection to a column flange, if the gusset-to-column-flange connection is
eliminated, the beam-to-column connection must be a moment connection designed for
the moment Vu ec in addition to the shear Vu. Thus, uniform forces on all interfaces are no
longer possible.
Analysis of Existing Diagonal Bracing Connections
A combination of α and β which provides for no moments on the three interfaces can
usually be achieved when a connection is being designed. However, when analyzing an
existing connection or when other constraints exist on gusset dimensions, the values of
α and β may not satisfy Equation 11-1. When this happens, uniform interface forces will
not satisfy equilibrium and moments will exist on one or both gusset edges or at the
beam-to-column interface.
To illustrate this point, consider an existing design where
centroids of the
__ the actual
_
gusset-to-beam and gusset-to-column connections are at α and β, respectively. If the
connection at one edge of the gusset is more rigid than the other, it is logical to assume
that the more rigid edge takes all of the moment necessary for equilibrium. For instance,
the gusset of Figure 11-7 is shown welded to the beam and bolted with double angles to
the column. For this configuration, the gusset-to-beam connection will be much more
rigid than the gusset-to-column connection.
Take α and β as the ideal centroids
_ of the gusset-to-beam and gusset-to-column
connections, respectively. Setting β = β, the α required for no moment on the gusset-tobeam connection may be calculated as:
_
α = K + βtanθ
where
K = ebtanθ − ec
__
If α ≠ α, a moment Mub will exist on the gusset-to-beam connection where,
__
Mub = Vub (α − α)
Conversely,
__ suppose the gusset-to-column connection were judged to be more rigid.
Setting α = α, the β required for no moment on the gusset-to-column connection may be
calculated as:
__
α−K
β=
tanθ
_
If β ≠ β, a moment Muc will exist on the gusset-to-column connection where,
_
Muc = Huc(β − β)
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
DIAGONAL BRACING CONNECTIONS
11 - 27
If both connections were equally rigid and no obvious allocation of moment could
__ be
made,
the
moment
could
be
distributed
based
on
minimized
eccentricities
α
−
α and
_
β − β by minimizing the objective function φ, where
_ 2
__ 2
α − α β − β
_
_
_
φ=
+
− λ(α − βtanθ − K)
α β
In the above equation, λ is a Lagrange multiplier.
The values of α and β which minimize φ are:
__ 2
α
K′tanθ + K _
β
α=
D
and
β=
(K′ − K tan θ)
D
where
__
__
α
K′ = α tanθ + _
β
__ 2
α
D = tan2θ + _
β
Design Checks
The design strengths of the bolts and/or welds and connected elements must be determined in accordance with the provisions of the LRFD Specification. The applicable limit
states in each of the aforementioned design strengths are discussed in Part 8. In all cases,
the design strength φRn must exceed the required strength Ru. Note that when the gusset
is directly welded to the beam or column, the connection must be designed for the larger
of the peak stress and 1.4 times the average stress; this 40 percent increase is recommended to provide ductility to allow adequate force redistribution in the weld group.
Additionally, the gusset must be checked on the Whitmore Section for yielding and for
column buckling under compressive brace forces.
EXAMPLE 11-2
Given:
Refer to Figure 11-11. Design the diagonal bracing connection between the W12×87 brace and the W18×106 beam and the W14×605
column. Use 7⁄8-in. diameter A325-N bolts in standard holes and 70 ksi
electrodes. For structural members, assume Fy = 50 ksi and Fu = 65 ksi;
for connecting material, assume Fy = 36 ksi and Fu = 58 ksi.
W12×87
d = 12.53 in.
bf = 12.125 in.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
A = 25.6 in.2
11 - 28
CONNECTIONS FOR TENSION AND COMPRESSION
tw = 0.515 in.
tf = 0.810 in.
W18×106
d = 18.73 in.
tw = 0.590 in.
k = 15⁄8-in.
bf = 11.200 in.
tf = 0.940 in.
W14×605
d = 20.92 in.
tw = 2.595 in.
bf = 17.415 in.
tf = 4.160 in.
Brace-to-gusset connection
Solution:
Distribute brace force in proportion to web and flange areas.
Force in flange
Pu (bf tf)
A
675 kips (12.125 in. × 0.810 in.)
=
25.6 in.2
= 259 kips
Puf =
Force in web
W18x106
526
w.p.
Rub = 15 kips
Aub = 0 kips
k
7
x8
12
W
k
5
67
9 9/16
CL W14x605
422 k
12
(a) members and forces
Figure 11-11a. Illustration for Example 11-2.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
DIAGONAL BRACING CONNECTIONS
11 - 29
Puw = Pu − 2Puf
= 675 kips − 2(259 kips)
= 157 kips
Design brace-flange-to-gusset connection.
Determine number of 7⁄8-in. diameter A325-N bolts required on the
brace side (single shear) for shear.
nmin =
Puf
φrn
259 kips
21.6 kips / bolt
= 11.99 → 12 bolts
=
On the gusset side, since these bolts are in double shear, half as many
bolts will be required. Try six rows of two bolts each through the flange,
_
six bolts through the gusset, and 2L4×4×3⁄4 angles (A = 10.9 in.2, x =
1.27 in.).
CL W14x605
l2
3
W18x106
W14x605
3
3
W
1 1/2
7
x8
12
2 PL3/8 x 9
≈1
3/ ″
4 P
L
1 /2
7
l3
4 L4 x 4 x 3/4
(GOL 2 1/2 in.)
37 min.
(b) connection
Figure 11-11b. Illustration for Example 11-2.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
l1
32 min.
w.p.
1 /2
1
11/2
3
27
5@
4.8
=3
Lw
4
5@
11 - 30
CONNECTIONS FOR TENSION AND COMPRESSION
Check tension yielding of the angles
φRn = φFy Ag
= 0.90(36 ksi)(10.9 in.2)
= 353 kips > 259 kips o.k.
Check tension rupture of the angles.
Taking Ae as the lesser of UAn and 0.85Ag, from LRFD Specification
Sections B3.2 and J5.2, respectively
_
x
U = 1 − ≤ 0.9
l
1.27 in.
=1−
15 in.
= 0.92 → 0.9
UAn = 0.9(10.9 in.2 − 2 × 0.75 in. × 1 in.)
= 8.46 in.2
0.85Ag = 0.85(10.9 in.2)
= 9.27 in.2
Thus Ae = UAn = 8.46 in.2
φRn = φFu Ae
= 0.75(58 ksi)8.46 in.2
= 368 kips > 259 kips o.k.
Check block shear rupture of angles.
From Tables 8-47 and 8-48 with n = 6, Lev = 11⁄2-in., and Leh = 11⁄2-in.,
0.6Fu Anv > Fu Ant . Thus,
φRn = φ[0.6Fu Anv + Fy Agt] × 2 blocks
= (287 kips/in. + 40.5 kips/in.)(3⁄4-in.) × 2
= 491 kips > 259 kips o.k.
Similarly, the block shear rupture strength of the brace flange is o.k.
Check bearing strength at bolts in the angles. With Le = 11⁄2-in. and s =
3 in., the bearing strength at each bolt is
φrn = φ(2.4dtFu )
= 0.75(2.4 × 7⁄8-in. × 3⁄4-in. × 58 ksi)
= 68.5 kips > 43.3 kips/bolt double shear strength o.k.
Similarly, the bearing strength of the bolt holes in the brace flange is o.k.
Design brace-web-to-gusset connection
Determine number of 7⁄8-in. diameter A325-N bolts required on the
brace side (double shear) for shear.
nmin =
Puw
φrn
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
DIAGONAL BRACING CONNECTIONS
11 - 31
157 kips
43.3 kips / bolt
= 3.63 → 4 bolts
=
On the gusset side, the same number of bolts are required. Try two rows
of two bolts and 2PL3⁄8×9.
Check tension yielding of the plates.
φRn = 0.90Fy Ag
= 0.90(36 ksi)(2 × 3⁄8-in. × 9 in.)
= 219 kips > 157 kips o.k.
Check tension rupture of the plates (LRFD Specification Section J5.2).
Taking Ae as the lesser of An and 0.85Ag,
An = 2 × 3⁄8-in. × 9 in. − 4 × 3⁄8-in. × 1 in.
= 5.25 in.2
0.85Ag = 0.85(2 × 3⁄8-in. × 9 in.)
= 5.74 in.2
Thus, Ae = An = 5.25 in.2
φRn = 0.75Fu Ae
= 0.75(58 ksi)5.25 in.2
= 228 kips > 157 kips o.k.
Check block shear rupture of the plates (outer blocks) from Tables 8-47
and 8-48 with n = 2, Lev = 11⁄2, and Leh = 11⁄2, 0.6Fu Anv > Fu Ant. Thus,
φRn = φ[0.6Fu Anv + Fy Agt] × 2 blocks × 2 plates
= (78.0 kips/in. + 40.5 kips/in.)(3⁄8-in.) × 4
= 178 kips > 157 kips o.k.
Similarly, the block shear rupture strength of the interior blocks of the
brace-web plates and the brace web are o.k.
Check bearing strength of bolt holes in the plates. As before, with Le =
11⁄2-in. and s = 3 in., the bearing strength at each bolt hole is 68.5 kips
which exceeds the double shear strength of the bolt and is o.k.
Check tension yielding of the brace.
φRn = φFy Ag
= 0.90(50 ksi)(25.6 in.2)
= 1,150 kips > 675 kips o.k.
Check tension rupture of the brace.
Taking Ae as An,
An = 25.6 in.2 − (4 × 0.810 in. + 2 × 0.515 in.)(1 in.)
= 21.3 in.2
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
11 - 32
CONNECTIONS FOR TENSION AND COMPRESSION
Thus, Ae = An = 21.3
φRn = φFu An
= 0.75(65 ksi)21.3 in.2
= 1,040 kips > 675 kips o.k.
Design gusset
From edge distance, spacing, and clearance requirements, try PL 3⁄4-in.
Check bearing strength at bolt holes. With Le = 11⁄2-in. and s = 3 in., the
bearing strength at each bolt hole is
φrn = φ(2.4dtFu )
= 0.75(2.4 × 7⁄8-in. × 3⁄4-in. × 58 ksi)
= 68.5 kips > 43.3 kips/bolt double shear strength o.k.
Check block shear rupture for force transmitted through web.
From Tables 8-47 and 8-48 with n = 2, Lev = 11⁄2-in., Leh = 3 in., Fu Ant >
0.6Fu Anv. Thus
φRn = φ[0.6Fy Agv + Fu Ant] × 2 blocks
= (81 kips/in. + 109 kips/in.)(3⁄4-in.) × 2 blocks
= 285 kips > 157 kips o.k.
Check block shear rupture for total brace force.
With Agv = 24.8 in.2, Agt = 13.2 in2, Anv = 16.5 in.2, and Ant = 12.4 in.2,
Fu Ant > 0.6Fu Ant. Thus
φRn = φ[0.6Fy Agv + Fu Ant]
= 0.75[0.6(36 ksi)(24.8 in.2) + (58 ksi)(12.4 in.2)]
= 941 kips > 675 kips o.k.
Check tension yielding on the Whitmore section of the gusset. The
Whitmore section, as illustrated with dashed lines in Figure 11-11b, is
34.8 in. long; 30.9 in. occurs in the gusset and 3.90 in. occurs in the
beam web. Thus
φRn = φFy Aw
= 0.90[(36 ksi)(30.9 × 3⁄4-in.) + (50 ksi)(3.90 in. × 0.590 in.)]
= 854 kips > 675 kips o.k.
The beam web thickness is used, conservatively ignoring the larger
thickness in the beam-flange and flange-to-web-fillet area.
Note that, were this a compressive force, gusset buckling would have
to be checked; refer to the comments at the end of this example.
Distribution of brace force to beam and column
From the members and frame geometry
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
DIAGONAL BRACING CONNECTIONS
eb =
db 18.73 in.
=
= 9.37 in.
2
2
ec =
dc 20.92 in.
=
= 10.5 in.
2
2
tan θ =
11 - 33
12
= 1.25
99⁄16
and
ebtanθ − ec = 9.37 in.(1.25) − 10.5 in.
= 1.21 in.
Try gusset PL3⁄4-in. × 42 in. horizontally × 33 in. vertically (Several
intermediate gusset dimensions were inadequate). With connection
centroids at the midpoint of the gusset edges
42 in. 1
+ ⁄2 in.
2
= 21.5 in.
α=
where 1⁄2-in. is allowed for the setback between the gusset and the
column, and
_ 33in.
β=
2
= 16.5 in.
_
__
Choosing β = β, the α required for uniform forces is
__
α = ebtanθ − ec + β tan θ
= 1.21 in. + (16.5 in.)(1.25)
= 21.8 in.
__
The resulting eccentricity is α − α, where
__
α − α = 21.5 in. − 21.8 in.
= −0.3 in.
This slight eccentricity is negligible. Use α = 21.8 in. and β = 16.5 in.
Calculate gusset interface forces
r =√
(α + ec)2 + (β + eb)2
=√
(21.8 in. + 10.5 in.)2 + (16.5 in. + 9.37 in.)
2
= 41.4 in.
On the gusset-to-column connection
ec
P
r u
10.5 in.
=
(675 kips)
41.4 in.
= 171 kips
Huc =
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
11 - 34
CONNECTIONS FOR TENSION AND COMPRESSION
β
Vuc = Pu
r
16.5 in.
=
(675 kips)
41.4 in.
= 269 kips
On the gusset-to-beam connection
α
P
r u
21.8 in.
=
(675 kips)
41.4 in.
= 355 kips
eb
= Pu
r
9.37 in.
=
(675 kips)
41.4 in.
= 153 kips
Hub =
Vub
Design gusset-to-column connection
Try 2L4×4×5⁄8×2′-6 welded to the gusset and bolted with 10 rows of
7⁄ -in. diameter A325-N bolts in standard holes to the column flange.
8
Calculate tensile force per bolt rut.
Huc
n
171 kips
=
20 bolts
= 8.55 kips/bolt
rut =
Check design strength of bolts for tension-shear interaction.
Vuc
n
269 kips
=
20 bolts
= 13.5 kips/bolt < 21.6 kips/bolt o.k.
Ft = 117 ksi − 1.9 fv ≤ 90 ksi
13.5 kips / bolt
= 117 ksi − 1.9 π
2
7
( ⁄8 − in.)
4
= 74.3 ksi
φrn = φFt Ab
π
= 0.75(74.3 ksi) (7⁄8 − in.)2
4
= 33.5 kips > 8.55 kips/bolt o.k.
ruv =
Check bearing strength at bolt holes.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
DIAGONAL BRACING CONNECTIONS
11 - 35
With Le = 11⁄2-in. and s = 3 in., the bearing strength per bolt is
φrn = φ(2.4dtFu )
= 0.75 ( 2.4 × 7⁄8-in. × 5⁄8-in. × 58 ksi)
= 57.1 kips/bolt
Since this exceeds the single-shear strength of the bolts, bearing
strength is o.k.
Check prying action.
b =g−t
= 2 1⁄2-in. − 5⁄8-in.
= 1.875 in. > 11⁄4-in. entering and tightening clearance, o.k.
a = 4 in. − g
= 4 in. − 21⁄2-in.
= 1.5 in.
Since a = 1.5 in. is less than 1.25b = 2.34 in., use a = 1.5 in.
b′ = b − d / 2
= 1.875 in. −
7⁄
8
− in.
2
= 1.44 in.
a′ = a + d / 2
= 1.5 in. +
7⁄
8
− in.
2
= 1.94 in.
b′
ρ=
a′
1.44 in.
=
1.94 in.
= 0.742
1 φrn
− 1
β=
ρ rut
33.5 kips / bolt
1
− 1
=
0.742 8.55 kips / bolt
= 3.93
Since β ≥ 1, set α′ = 1.0
δ =1−
=1−
d′
p
15⁄
− in.
3 in.
16
= 0.688
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
11 - 36
CONNECTIONS FOR TENSION AND COMPRESSION
treq =
=
√
4.44rut b′
pFy (1 + δα′)
√
4.44(8.55 kips / bolt)(1.44 in.)
(3 in.)(36 ksi)[1 + (0.688)(1)]
= 0.548 in.
Since t = 5⁄8-in. > 0.548 in., angles are o.k.
Design welds
Try fillet welds around perimeter (3 sides) of both angles.
Huc2 + Vuc2
Puc = √
=√
(171 kips)2 + (269 kips)2
= 319 kips
Huc
θ = tan−1
Vuc
171 kips
= tan−1
269 kips
= 32.4°
From Table 8-42 with θ = 30°°,
l = 30 in.
kl = 31⁄2-in.
k = 0.117
By interpolation
x = 0.011
xl = 0.011(30 in.)
= 0.33 in.
al = 4 in. − xl
= 4 in. − 0.33 in.
= 3.67 in.
a = 0.122
By interpolation
C = 1.95
and
Dreq =
Puc
CC1l
319 kips
1.95 × 1.0 × (2 welds × 30 in.)
= 2.73 → 3 sixteenths required for strength
=
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
DIAGONAL BRACING CONNECTIONS
11 - 37
From LRFD Specification Table J2.4, minimum weld size is 1⁄4-in. Use
1⁄ -in. fillet welds.
4
Check gusset thickness (against weld size required for strength)
For two fillet welds
5.16D
Fy
5.16(2.73 sixteenths)
=
36 ksi
= 0.391 in. < 3⁄4-in. o.k.
tmin =
Check strength of angles.
Shear yielding (due to Vuc)
φRn = φ(0.60Fy Ag)
= 0.90[0.60(36 ksi)(2 × 30 in. × 5⁄8-in.)]
= 729 kips > 269 kips o.k.
Similarly, shear yielding of the angles due to Huc is not critical.
Shear rupture
φRn = φ(0.60Fu Anv)
= 0.75[0.60(58 ksi)(2 × 5⁄8-in. × 30 in. − 20 × 5⁄8-in. × 1 in.)]
= 653 kips > 269 kips o.k.
Block shear rupture
From Tables 8-47 and 8-48, with n = 10, Lev = 11⁄2-in., and Leh = 11⁄2-in.,
0.6Fu Anv > Fu Ant. Thus
φRn = φ[0.6Fu Anv + Fy Agt] × 2 blocks
= (496 kips/in. + 40.5 kips/in.)(5⁄8-in.) × 2 blocks
= 671 kips > 269 kips o.k.
Check column flange.
By inspection, the 4.16-in. thick column flange has adequate flexural
strength, stiffness, and bearing strength.
Design gusset-to-beam connection
Hub2 + Vub2
Pub = √
=√
(355 kips)2 + (153 kips)2
= 387 kips
From Richard (1986) it is recommended that the design factored force
be increased by 40 percent to ensure adequate force redistribution in
the weld group and the validity of the Uniform Force Method. Thus,
Dreq =
1.4Pub
1.392l
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
11 - 38
CONNECTIONS FOR TENSION AND COMPRESSION
1.4(387 kips)
1.392(2 × 42 in.)
= 4.63 → 5 sixteenths
=
(Note that, if a moment existed on this interface, the connection would
be designed for the larger of the peak stress and 1.4 times the average
stress.)
This is equal to the minimum weld size from LRFD Specification Table
J2.4.
Check gusset thickness (against weld size required for strength)
For two fillet welds
5.16D
Fy
5.16(2.73 sixteenths)
=
36 ksi
= 0.391 in. < 3⁄4-in. o.k.
tmin =
Check local web yielding of the beam.
φRn = φ(N + 2.5k)Fyw tw
= 1.0 [2.5 (15⁄8-in.) + 42 in.](50 ksi)(0.590 in.)
= 1,360 kips > 153 kips o.k.
Design beam-to-column connection
Since the brace may be in tension or compression, the required strength
of the beam-to-column connection is as follows. The required shear
strength is
Rub ± Vub = 15 kips ± 153 kips
= 168 kips
and the required axial strength is
Aub ± (Hu − Hub) = 0 kips ± (171 kips)
= 171 kips
Try 2L8×6×1×1′−21⁄2 (Leg gage = 23⁄4-in.) welded to the beam web and
bolted with five rows of 7⁄8-in. diameter A325-N bolts in standard holes
to the column flange.
Calculate tensile force per bolt rut.
171 kips
10 bolts
= 17.1 kips/bolt
rut =
Check design strength of bolts for tension-shear interaction.
ruv =
168 kips
10 bolts
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
DIAGONAL BRACING CONNECTIONS
11 - 39
= 16.8 kips/bolt < 21.6 kips/bolt o.k.
Ft = 117 ksi − 1.9fv ≤ 90 ksi
16.8 kips / bolt
= 117 ksi − 1.9
π 7
2
( ⁄8 − in. )
4
= 63.9 ksi
φrn = φFt Ab
π
= 0.75 (63.9 ksi) (7⁄8 − in.)2
4
= 28.8 kips/bolt > 17.1 kips/bolt o.k.
Check bearing strength at bolt holes.
With Le = 11⁄4-in. (<1.5d = 1.31 in.) and s = 3 in., the bearing strength
of the top bolt from LRFD Specification Section J3.10 is
φrn = φ(LetFu ) ≤ φ(2.4dtFu )
= 0.75 (11⁄4jin.)(1 in.)(58 ksi) ≤ 91.4 kips/bolt
= 54.4 kips/bolt
and the bearing strength of each remaining bolt is
φrn = φ(s − d / 2)tFu ≤ φ(2.4dtFu )
7⁄ − in.
8
(1 in.)(58 ksi) ≤ 91.4 kips/bolt
= 0.75 3 in. −
2
= 111 kips/bolt
Since the strength of each bolt exceeds the single shear strength of the
bolts, bearing strength is o.k.
Check prying action
b= g − t
= 23⁄4-in. − 1 in.
= 13⁄4-in. > 11⁄4-in. entering and tightening clearance, o.k.
a = 6 in. − g
= 6 in. − 23⁄4-in.
= 31⁄4-in.
Since a = 31⁄4-in. exceeds 1.25b = 2.19 in., use a = 2.19 in. for
calculation purposes.
b′ = b − d / 2
= 13⁄4-in. −
7⁄
8
− in.
2
= 1.31 in.
a′ = a + d / 2
= 2.19 in. +
7⁄
8
− in.
2
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
11 - 40
CONNECTIONS FOR TENSION AND COMPRESSION
= 2.63 in.
b′
ρ=
a′
1.31 in.
=
2.63 in.
= 0.498
1 φrn
β=
− 1
ρ rut
1 28.8 kips / bolt
− 1
=
0.498 17.1 kips / bolt
= 1.37
Since β ≥ 1, set α′ = 1.0
141⁄2 − in.
5 bolts
= 2.90 in./bolt
d′
δ =1−
p
15⁄ − in.
16
=1−
2.90 in.
= 0.677
p =
treq =
=
√
4.44 rut b′
pFy (1 + δα′)
√
4.44 (17.1 kips / bolt ) (1.31 in.)
(2.90 in.) (36 ksi) [1 + (0.677) (1.0)]
= 0.754 in.
Since t = 1 in. > 0.754 in., angles are o.k.
Design welds
Try fillet welds around perimeter (three sides) of both angles.
(171 kips)2 + (168 kips)2
Pu = √
= 240 kips
171 kips
θ = tan−1
168 kips
= 45.5°°
From Table 8-42 with θ = 45°°
l = 141⁄2-in.
kl = 71⁄2-in.
k = 0.517
By interpolation
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
DIAGONAL BRACING CONNECTIONS
11 - 41
x = 0.132
xl = 0.132 (141⁄2-in.)
= 1.91 in.
al = 8 in. − xl
= 8 in. −1.91 in.
= 6.09 in.
a = 0.420
By interpolation
C = 2.66
and
Dreq =
Pu
CC1l
240 kips
2.66 × 1.0 × (2 welds × 141⁄2 − in.)
= 3.11 → 4 sixteenths required for strength
=
From LRFD Specification Table J2.4, minimum weld size is 5⁄16-in. Use
5⁄ -in. fillet welds.
16
Check beam web thickness (against weld size required for strength)
For two fillet welds,
5.16D
Fy
5.16(3.11 sixteenths)
=
50 ksi
= 0.321 in. < 0.590 in. o.k.
tmin =
Check the strength of angles
Shear yielding
φRn = φ(0.60Fy Ag)
= 0.9[0.60(36 ksi)(2 ×141⁄2-in. × 1 in.)]
= 564 kips > 168 kips o.k.
Similarly, shear yielding of the angles due to Huc is not critical.
Shear rupture
φRn = φ(0.60Fu Anv)
= 0.75[0.60(58 ksi)(2 × 1 in. × 141⁄2-in. − 10 × 1 in. × 1 in.)]
= 496 kips > 168 kips o.k.
Block shear rupture
With n = 5, Lev = 11⁄4-in., Leh = 31⁄4-in., 0.6Fu Anv > Fu Ant. Thus
φRn = φ[0.6Fu Anv + Fy Agt] × 2 blocks
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
11 - 42
CONNECTIONS FOR TENSION AND COMPRESSION
= 0.75[0.6(58 ksi)(131⁄4-in. − 5 × 1 in.)(1 in.)
+ (36 ksi)(31⁄4-in.)(1 in.)](2)
= 606 kips > 168 kips o.k.
Check column flange.
By inspection, the 4.16-in. thick column flange has adequate flexural
strength, stiffeners, and bearing strength.
Comments:
Were the brace in compression, the buckling strength of the gusset
would have to be checked, where
φRn = φcFcr Aw
kl1
In the above equation φcFcr may be determined from
with LRFD
r
Specification Table C-36, where l1 is the perpendicular distance from
the Whitmore section to the interior corner of the gusset. Alternatively,
the average value of
l1 + l2 + l3
3
may be substituted (AISC, 1984), where these quantities are illustrated
in Figure 11-11. Note that, for this example, l2 is negative since part of
the Whitmore section is in the beam web.
The effective length factor K has been established as 0.5 by full scale
tests on bracing connections (Gross, 1990). It assumes that the gusset
is supported on both edges as is the case in Figure 11-11. In cases where
the gusset is supported on one edge only, such as that illustrated in
Figure 11-12d (and possibly Figure 11-12a) the brace can more readily
move out-of-plane and a sidesway mode of buckling can occur in the
gusset. For this case, K should be taken as 1.2.
EXAMPLE 11-3
Given:
Refer to Figure 11-12. Each of the four designs shown for the diagonal
bracing connection between the W14×68 brace, W24×55 beam, and
W14×211 column web have been developed using the Uniform Force
Method (the General Case, and Special Cases 1, 2, and 3) for the load
case of 1.2D + 1.3W. Refer the AISC (1992) for the unfactored loads
and complete designs. For the given values of α and β, determine the
interface forces on the gusset-to-column and gusset-to-beam connections for
A. General Case of Figure 11-12a.
B. Special Case 1 of Figure 11-12b.
C. Special Case 2 of Figure 11-12c.
D. Special Case 3 of Figure 11-12d.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
DIAGONAL BRACING CONNECTIONS
11 - 43
cL W14x211
Pu = ±195 kips
Pu = ±195 kips
11 1/16
10 1/8
cLW14x211
12
12
β
β
Rub = 44 kips
Aub = 26 kips
eb
cL W24x55
e
wp
b
wp
α
α = 15 3/4 in.
β = 3 in.
e b = 11.8 in.
ec ≈ 0 in.
cLW24x55
α = 12 in.
β = 13 1/2 in.
e b =11.8 in.
ec ≈ 0 in.
e c ≈ 0 in.
(b) Special Case 1,
Working Point at Gusset Corner
α
(a) General Case
cL W14x211
Rub = 44 kips
A = 26 kips
Pu = ±195 kips
Pu = ±195 kips
cL W14x211
11 1/16
12
11 1/16
12
β
Rub = 44 kips
Aub = 26 kips
eb
wp
α
Rub = 44 kips
Aub = 26 kips
eb
cL W24x55
wp
α = 15 3/4 in.
β = 10 1/2 in.
e b = 11.8 in.
ec ≈ 0 in.
(c) Special Case 2, ∆Vub = Vub , i.e.
Shear in Beam-to-Column
Connection Minimized
α
α =13 1/2 in.
β = 0 in.
e b =11.8 in.
ec ≈ 0 in.
(d) Special Case 3,
No Gusset-to-Column Web Connection
Fig. 11-12. Uniform force method.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
cL W24x55
11 - 44
Solution A:
(General Case)
CONNECTIONS FOR TENSION AND COMPRESSION
_
Assume β = β = 3 in.
α = ebtanθ − ec + βtanθ
12
12
= 11.8 in. 1 − 0 + 3 in. 1
⁄
11
11 ⁄16
16
= 16.1 in.
__
Since α ≠ α, an eccentricity exists on the gusset-to-beam connection.
Calculate the interface forces:
r =√
(α + ec)2 + (β + eb)2
=√
(16.1 in. + 0 in.)2 + (3 in. + 11.8 in.)
2
= 21.9 in.
On the gusset-to-column connection
β
Vuc = Pu
r
3 in.
=
(195 kips)
21.9 in.
= 26.7 kips
ec
Huc = Pu
r
= 0 kips
On the gusset-to-beam connection
α
P
r u
16.1 in.
=
(195 kips)
21.9 in.
= 143 kips
eb
Vub = Pu
r
11.8 in.
=
(195 kips)
21.9 in.
= 105 kips__
Mub = Vub (α − α)
105 kips (153⁄4 − in. − 16.1 in.)
=
12 in. / ft
= −3.06 kip-ft
Hub =
In this case, this small moment is negligible.
On the beam-to-column connection, the factored shear is
Rub + Vub = 44 kips + 105 kips
= 149 kips
and the factored axial force is
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
DIAGONAL BRACING CONNECTIONS
11 - 45
Aub ± Huc = 26 kips ± 0 kips
= 26 kips
For a discussion of the sign to use between Aub and Huc, refer to AISC
(1992).
Solution B:
In this case,__the centroidal
positions of the gusset-edge connections are
_
(Special Case 1) irrelevant; α and β are given to define the geometry of the connection,
but are not needed to determine the gusset edge forces.
The angle of the brace from the vertical is
12
θ = tan−1 1
10 ⁄8
= 49.8°°
The horizontal component of the brace force is
Hu = Pu sinθ
= 195 kips × sin(49.8°°)
= 149 kips
and the vertical component of the brace force is
Vu = Pu cosθ
= 195 kips × sin(49.8°°)
= 126 kips
On the gusset-to-column connection
Vuc = Vu = 126 kips
Huc = 0 kips
On the gusset-to-beam connection
Vub = 0 kips
Hub = Hu = 149 kips
On the beam-to-column connection
Rub = 44 kips (shear)
Aub = 26 kips (axial transfer force)
In addition to the forces on the connection interfaces, the beam is
subjected to a moment Mub (see Figure 11-8d), where
Mub = Hubeb
149 kips × 11.8 in.
=
12 in. / ft
= 147 kips-ft
This moment, as well as the beam axial load Hu = 149 kips and the
moment and shear in the beam associated with the end reaction Rub,
must be considered in the design of the beam.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
11 - 46
CONNECTIONS FOR TENSION AND COMPRESSION
_
Solution C:
Assume β = β = 101⁄2-in.
(Special Case 2)
α = ebtanθ − ec + βtanθ
12
12
= 11.8 in. 1 − 0 + 101⁄2jin. 1
11
⁄
16
11 ⁄16
= 24.2 in.
Calculate the interface forces for the general case before applying
Special Case 2.
r=√
(α + ec)2 + (β + eb)2
=√
(24.2 in. + 0 in.)2 + (101⁄2jin. + 11.8 in.)2
= 32.9 in.
On the gusset-to-beam connection
α
P
r u
24.2 in.
=
(195 kips)
32.9 in.
= 143 kips
eB
Vub = Pu
r
11.8 in.
=
(195 kips)
32.9 in.
= 69.9 kips
Hub =
On the gusset-to-column connection
ec
P
r u
= 0 kips
β
Vuc = Pu
Huc =
r
10.5 in.
=
(195 kips)
32.9 in.
= 62.2 kips
On the beam-to-column connection, the factored shear is
Rub + Vub = 44.0 kips + 66.9 kips
= 111 kips
and the factored axial force is
Aub ± Huc = 26.0 kips ± 0 kips
= 26.0 kips
Next, applying Special Case 2 with ∆Vub = Vub = 69.9 kips, calculate the
interface forces.
On the gusset-to-beam connection (where Vub is replaced by Vub − ∆Vub)
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
DIAGONAL BRACING CONNECTIONS
11 - 47
Hub = 143 kips (unchanged)
Vub = 69.9 kips − 69.9 kips
= 0 kips
Mub = (∆Vub )α
(69.9 kips) (24.2 in.)
=
12 in. / ft
= 141 kips-ft
On the gusset-to-column connection (where Vuc is replaced by
Vuc + ∆Vub)
Huc = 0 kips (unchanged)
Vuc = 62.2 kips + 69.9 kips
= 132 kips
On the beam-to-column connection, the factored shear is
Rub + ∆Vub − ∆Vub = 44 kips + 69.9 kips − 69.9 kips
= 44 kips
and the factored axial force is
Solution D:
(Special Case 3)
Aub ± Huc = 26 kips ± 0 kips
= 26 kips
_
Assume β = β = 0 in.
α = ebtanθ
12
111⁄16
= 11.8 in.
= 12.8 in.
__
Since α ≠ α, an eccentricity exists on the gusset-to-beam connection.
Calculate the interface forces.
α2 + e2b
r=
√
=
√
(12.8 in.)2 + (11.8 in.)2
= 17.4 in.
On the gusset-to-beam connection
α
P
r u
12.8 in.
=
(195 kips)
17.4 in.
= 143 kips
eb
= Pu
r
11.8 in.
=
(195 kips)
17.4 in.
= 132 kips
Hub =
Vub
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
11 - 48
CONNECTIONS FOR TENSION AND COMPRESSION
__
Mub = Vub(α − α)
132 kips (12.8 in. − 131⁄2jin.)
=
12 in. / ft
= −7.70 kip-ft
In this case, this small moment is negligible.
On the beam-to-column connection the factored shear is
Rub + Vub = 44 kips + 132 kips
= 176 kips
and the factored axial force is
Aub ± Huc = 44 kips ± 0 kips
= 44 kips
Comments:
From the foregoing results, designs by Special Case 3 and the General
Case of the Uniform Force Method provide more economical designs.
Additionally, note that designs by Special Case 1 and Special Case 2
result in moments on the beam and/or column which must be
considered.
BEAM-BEARING PLATES
When required, a beam-bearing plate is provided to distribute the beam end reaction over
an area of the concrete or masonry support which is sufficient to keep the average pressure
on the suppport within the limits of its design strength.
Design Checks
A beam-bearing plate produces a compressive single concentrated force at the beam end;
the limit states of the web design strength in local yielding and crippling must be checked.
The design compressive strength of the concrete or masonry must be checked. The limit
state of flexural yielding must be checked to determine the design strength of the
beam-bearing plate. In all cases, the design strength φRn must exceed the required strength
Ru.
Local Web Yielding
From LRFD Specification Section K1.3, the local yielding design strength of the beam
web at the member end is φRn, where φ = 1.0 and:
Rn = (2.5k + N)Fywtw
The length of bearing N required for a beam end reaction Ru, may be calculated from
constants φR1 and φR2 in the factored uniform load tables in Part 4 as
Nmin =
Ru − φR1
φR2
where
φR1 = φ(2.5kFywtw)
φR2 = φFywtw
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
BEAM-BEARING PLATES
11 - 49
Web Crippling
From LRFD Specification Section K1.4, the crippling design strength of the beam web
at the member end is φRn, where φ = 0.75 and, when N / d ≤ 0.2:
1.5
N tw
Rn = 68t2w 1 + 3
d tf
√
Fywtf
tw
The length of bearing N required for a beam end reaction Ru, may be calculated from
constants φR3 and φR4 in the factored uniform load tables in Part 4 as
Nreq =
Ru − φR3
φR4
where
φR3 = φ 68t2w
Fywtf
tw
√
N t
φR4 = φ 68t2w 3 w
d tf
1.5
Fyw tf
tw
√
When N / d > 0.2,
1.5
4N
t
− 0.2 w
Rn = 68t 1 +
d
tf
2
w
t
√
Fywtf
w
The length of bearing N required for a beam end reaction Ru may be calculated from
constants φR5 and φR6 in the factored uniform load tables in Part 4 as
Nreq =
Ru − φR5
φR6
where
tw
φR5 = φ 68t2w 1 − 0.2
tf
1.5
4 tw
φR6 = φ 68t2w
d tf
1.5
Fywtf
tw
√
√
Fywtf
tw
Concrete Compressive Strength
The bearing plate is assumed to distribute the beam end reaction uniformly to the area of
the concrete under the bearing plate. In the absence of other code specifications, the
required bearing-plate area A1 may then be determined from LRFD Specification Section
J9 such that Ru ≤ φcPp. On the full area of a concrete support
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
11 - 50
CONNECTIONS FOR TENSION AND COMPRESSION
A1 =
Ru
φc(0.85fc′)
and on less than the full area of a concrete support,
2
Ru
1
A1 =
A2 φc(0.85fc′)
where
A2 = maximum area of the portion of the supporting surface that is geometrically
similar to and concentric with the loaded area, in.2
fc′ = compressive strength of concrete, ksi
φc = 0.60
The length of bearing N may be established by available wall thickness, clearance
requirements, or by the minimum requirements based on local web yielding or web
crippling. The required bearing-plate width may be determined as
Breq =
A1
N
The selected dimensions B and N should preferably be in full inches.
Required Bearing-Plate Thickness
As illustrated in Figure 11-13, the beam end reaction Ru is assumed to be uniformly
distributed from the beam to the bearing plate over an area equal to N × 2k. Based on
cantilevered bending of the bearing plate under the uniformly distributed load, the
minimum bearing-plate thickness is
t=
√
2.22Run2
A1Fy
where
n = (B / 2) − k, in.
Anchor as required
N + 2.5k
k
n
kk
B
t
n
N
Fig. 11-13. Beam bearing-plate variables.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
BEAM-BEARING PLATES
11 - 51
Fy = yield strength of the bearing plate, ksi.
In the rare case where a bearing plate is not required, the beam end reaction Ru is
assumed to be uniformly distributed from the beam to the concrete over an area equal to
N × bf. Additionally, when this is the case, the cantilever distance n used to determine the
minimum bearing-plate thickness is taken as
n = (bf / 2) − k1, in.
EXAMPLE 11-6.
Given:
AW18×50 beam with a factored end reaction of 85 kips is supported
by a 10-in. thick concrete wall. If the beam has Fy = 50 ksi, the concrete
has fc′ = 3 ksi, and the bearing plate has Fy = 36 ksi, determine:
A. if a bearing plate is required if the beam is supported by the full wall
thickness,
B. the bearing plate required if N = 10 in. (the full wall thickness),
C. the bearing plate required if N = 6 in. and the bearing plate is
centered on the thickness of the wall.
W18×50
d = 17.99 in.
tw = 0.355 in.
Solution A:
bf = 7.495 in.
tf = 0.570 in.
k = 11⁄4-in.
k1 = 13⁄16-in.
N = 10 in.
Check local web yielding
From the factored uniform load tables in Part 4,
Ru − φR1
φR2
85 kips − 55.5 kips
=
17.8 kips / in.
= 1.66 in. < 10 in. o.k.
Nreq =
Check web crippling
10 in.
17.99 in.
= 0.556
N/d =
N
> 0.2, from the factored uniform load tables in Part 4,
d
Ru − φR5
Nreq =
φR6
85 kips − 51.9 kips
=
6.29 kips / in.
= 5.26 in. < 10 in. o.k.
Since
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
11 - 52
CONNECTIONS FOR TENSION AND COMPRESSION
Check bearing strength of concrete
φc Pp = φc(0.85fc′)A1
= 0.60 (0.85 × 3 ksi)(7.495 in. × 10 in.)
= 115 kips > 85 kips o.k.
Check beam flange thickness
bf
− k1
2
7.495 13
=
− ⁄16jin.
2
= 2.94 in.
n
=
treq =
=
√
2.22Run2
A1Fy
√
2.22(85 kips)(2.94 in.)2
(7.495 in. × 10 in.)(50 ksi)
= 0.660 in. > 0.570 in. n.g.
A bearing plate is required.
Solution B:
N = 10 in.
From Solution A, local web yielding and web crippling are not critical.
Calculate required bearing-plate width.
Ru
φc(0.85fc′)
85 kips
=
0.60(0.85 × 3 ksi)
= 55.6 in.2
A1 req
=
N
55.6 in.2
=
10 in.
= 5.56 in.
A1 req =
Breq
Use B = 8 in. (least whole-inch dimension which exceeds bf)
Calculate required bearing-plate thickness.
B
−k
2
8 in.
− 1.25 in.
=
2
= 2.75 in.
n =
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
BEAM-BEARING PLATES
11 - 53
tmin =
=
√
2.22Run2
A1Fy
√
2.22(85 kips)(2.75 in.)2
(10 in. × 8 in.)(36 ksi)
= 0.704 in.
Use PL3⁄4×10×0′-8
Solution C:
N = 6 in.
From Solution A, local web yielding and web crippling are not critical.
Try B = 8 in.
A1 = B × N
= (8 in.)(6 in.)
= 48 in.2
Given these dimensions and N1 = 10 in. (the full wall thickness), the
dimension which makes the support area geometrically similar to the
bearing plate is
N1
B1 = B
N
8 in.(10 in.)
=
6 in.
= 13.3 in.
and
A2 = B1 × N1
= 13.3 in. (10 in.)
= 133 in.2
Check √
A2 / A
1 = 1.66 ≤ 2 o.k.
Ru
1
=
A2 φc(0.85fc′)
A1 req
2
1
85 kips
=
2
133 in. 0.6(0.85 × 3 ksi)
= 23.2 in.2 < 48 in.2 o.k.
2
Calculate required bearing-plate thickness
n
B
−k
2
8 in.
− 11⁄4 in.
=
=
2
= 2.75 in.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
11 - 54
CONNECTIONS FOR TENSION AND COMPRESSION
tmin =
=
√
2.22Run2
A1Fy
√
2.22(85 kips)(2.75 in.)2
(6 in. × 8 in.)(36 ksi)
= 0.909 in.
Use PL1×6×0′-8.
COLUMN BASE PLATES
Column base plates distribute the forces at the base of the column to an area of foundation
large enough to prevent crushing the concrete. Base plate thicknesses should be specified
in multiples of 1⁄8-in. up to 11⁄4-in. and in multiples of 1⁄4-in. thereafter.
Typical base plates, illustrated in Figure 11-14, are often attached to the bottoms of
columns in the shop. For anchor rod diameters not greater than 11⁄4-in., angles bolted or
welded to the column as shown in Figure 11-15a are generally adequate to transfer uplift
forces resulting from axial loads and moments. When greater resistance is required,
stiffeners may be used with horizontal plates or angles as illustrated in Figure 11-15b.
These stiffeners are not usually considered to be part of the column area in bearing on
the base-plate. The angles preferably should be set back from the column end about 1⁄8-in.
Stiffeners preferably should be set back about one inch from the base plate to eliminate
a pocket that might prevent drainage and, thus, protect the column and column base plate
from corrosion.
For extremely heavy loads in major structures, or where subsoil conditions are poor,
a grillage as shown in Figure 11-16 may be required. This grillage consists of one or more
layers of closely spaced beams (usually S shapes because of the thicker webs) encased
in the concrete foundation.
The criteria for fit-up of column splices are also applicable to column base plates. For
anchor rod design, refer to Part 8.
Finishing Requirements
The following base-plate finishing requirements are from LRFD Specification Section
M2.8. Base plates not greater than two inches thick need not be milled if satisfactory
contact in bearing is present. Base plates greater than two inches thick, but not greater
than four inches thick must be either straightened by pressing or milled to obtain
satisfactory contact in bearing, at the option of the fabricator. Base plates greater than
four inches thick must be finished if the bearing area does not meet flatness tolerances.
Note that finishing of base plates is not required in the following cases: (1) bottom
surfaces of base plates when grout is used to ensure full contact on foundations; and, (2)
top surfaces of base plates when complete joint-penetration groove welds are provided
between the column and the base plate.
When base plates must be finished, the plate must be ordered thicker than the specified
finished dimension to allow for the material removed in finishing. Table 11-2 provides
finishing allowances for carbon steel base plates based on the width, thickness, and
whether one or two sides are to be finished. These allowances are derived from the
Standard Mill Practice flatness tolerances in Part 1. Allowances for alloy steel base plates
should be adjusted for the Standard Mill Practice flatness tolerances specified in Part 1.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
COLUMN BASE PLATES
11 - 55
Holes for Anchor Rods and Grouting
Holes in base plates for anchor rods may be punched, drilled, or flame cut. Depending
upon the hole diameter and base-plate thickness, machine capacity may limit the
fabricator’s ability to punch holes in base plates. Furthermore, many fabricators are
limited by a 11⁄2-in. diameter maximum drill size. Thus, flame-cut holes should be
permitted for any plate thickness when the hole diameter is larger than one inch. Note
that the walls of flame-cut holes will have a slight taper and should be inspected to assure
Grout
Grout
Base plate
Finished
concrete
Leveling plate
Anchor rods
Elevation
Elevation
Plan
Plan
(a)
(b)
Grout
Fig. 11-14. Typical column base plates.
(a)
(b)
Fig. 11-15. Base plates for uplift.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
11 - 56
CONNECTIONS FOR TENSION AND COMPRESSION
Table 11-2.
Finish Allowances
Size
Thickness (in.)
Add to Fin.
One Side (in.)
Add to Fin.
Two Sides (in.)
Maximum dimension
24 in. or less
11⁄4 or less
over 11⁄4 to 2, incl.
1⁄
16
1⁄
8
1⁄
8
1⁄
4
Maximum dimension
over 24 in.
11⁄4 or less
over 11⁄4 to 2, incl.
1⁄
8
3⁄
16
1⁄
4
3⁄
8
56 in. wide or less
over 2 to 71⁄2, incl.
over 71⁄2 to 10, incl.
over 10 to 15, incl.
1⁄
1⁄
3⁄
8
5⁄
8
7⁄
8
Over 56 in. wide
to 72 in. wide
3⁄
1⁄
over 2 to 6, incl.
over 6 to 10, incl.
over 10 to 15, incl.
1⁄
3⁄
4
2
4
3⁄
8
5⁄
8
7⁄
8
4
2
4
proper clearances for anchor rods. Table 11-3 gives recommended hole sizes to accommodate anchor rods. These hole sizes permit a reasonable tolerance for misalignment in
setting the bolts and more precision in the adjustment of the base plate or column to the
correct centerlines. An adequate washer should be provided for each anchor rod.
When base plates with large areas are used, at least one grout hole should be provided
near the center of the plate through which grout may be poured; this will provide for a
more even distribution of the grout and also prevent air pockets. Note that a grout hole
may not be required when the grout is dry-packed. The size of grout holes usually requires
that they be flame cut. Grout holes do not require the same accuracy for size and location
as anchor-rod holes. The area of holes for grouting and anchor rods is not usually deducted
when determining the required base-plate area.
Leveling Methods
Light Base Plates—For light base plates, a smooth bearing area may be provided with a
steel leveling plate as illustrated in Figure 11-14a. Since leveling plates need only be
approximately 1⁄4-in. thick, they are more easily handled and set level to the proper
Column
Base plate
Typ.
Finished top
of concrete
Through
rods
Beams
Pipe separators
Fig. 11-16. Grillage foundation.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
COLUMN BASE PLATES
11 - 57
Table 11-3.
Sizes for Anchor-Rod Holes in Base Plates
Anchor Rod Diameter
Hole Diameter
Anchor Rod Diameter
Hole Diameter
3⁄
4
15⁄16
11⁄2
25⁄16
7⁄
8
19⁄16
13⁄4
23⁄4
1
113⁄16
2
31⁄4
11⁄4
21⁄16
21⁄2
33⁄4
elevation prior to erection of the columns. Leveling plates should meet the Standard Mill
Practice flatness tolerances specified in Part 1. The leveling plate may be larger than the
base plate to accommodate tolerances of anchor-rod placement. The leveling plate can
serve as a setting template for the anchor rods. Alternatively, leveling nuts could be
supplied on the anchor rods to level the base plate as illustrated in Figure 11-17. However,
to ensure stability during erection, leveling nuts should not be used with less than four
anchor rods.
Leveling plates and loose base plates that are small enough to be set manually are
placed by the foundation contractor. Larger base plates that must be lifted by a derrick
or crane are usually set by the steel erector.
Heavy Base Plates—For heavy base plates, three-point leveling bolts, illustrated in Figure
11-18, are commonly used. These threaded attachments may consist of a nut or an angle
and nut welded to the base plate. Leveling bolts must be of sufficient length to compensate
for the space provided for grouting. Rounding the point of the leveling bolt will prevent
it from “walking” or moving laterally as it is turned. Additionally, a small steel pad under
the point reduces friction and prevents damage to the concrete.
Leveling bolts or nuts should not be used to support the column during erection. If
grouting is delayed until after steel erection, the base plate must be shimmed to properly
distribute loads to the foundation without overstressing either the base plate or the
concrete. This difficulty of supporting columns while leveling and grouting their bases
makes it advisable that footings be finished to near the proper elevation (Ricker, 1989).
The top of the rough footing should be set approximately one inch below the bottom of
the base plate to provide for adjustment. Alternatively, an angle frame as illustrated in
Figure 11-19 could be constructed to the proper elevation and filled with grout prior to
erection.
Heavy base plates should be provided with some means of handling at the erection
site. Lifting holes may be provided in the vertical legs of the connection angles which
are shop-attached to the base plate.
Design of Axially Loaded Base Plates
Three distinct methods for base-plate analysis and design, the cantilever method for large
base plates, the Murray Stockwell method (Murray, 1983) for small, lightly loaded base
plates, and a yield-line-theory method (Thornton, 1990a) based on Fling (1970), have
been combined by Thornton (1990b) into a single method which treats all base-plate
configurations. Base plates subjected to moment and base plates subjected to tensile loads
are treated by DeWolf and Ricker (1990).
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
11 - 58
CONNECTIONS FOR TENSION AND COMPRESSION
Design Checks—The design compressive strength of the concrete must be checked. The
limit state of flexural yielding must be checked to determine the design strength of the
beam bearing plate. In all cases, the design strength φRn must exceed the required
strength Ru.
Concrete Compressive Strength—The base plate is assumed to distribute Ru, the axial
force in the column, uniformly to the area of the concrete under the base plate. In the
absence of other code specifications, the required base-plate area A1 may then be
determined from LRFD Specification Section J9 such that Ru ≤ φcPp. Thus, on the full
area of a concrete support
A1 =
Ru
φc(0.85fc′)
and on less than the full area of a concrete support,
2
1
A1 =
A2
Ru
φc(0.85fc′)
where
A2 = maximum area of the portion of the supporting surface that is geometrically
similar to and concentric with the loaded area, in.2
fc′ = compressive strength of concrete, ksi
φc = 0.60
The base-plate dimensions B and N may then be established such that
B × N ≥ A1
The selected dimensions B and N should be in full inches.
Column
Anchor rod
Base plate
Nut & washer
Grout
Leveling nut & washer
Fig. 11-17. Leveling nuts.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
COLUMN BASE PLATES
11 - 59
Required Base-Plate Thickness—The required base-plate thickness may be calculated as
treq = l
√
2Pu
0.9Fy BN
In the above equation, l is the larger of m, n, and λn′ where
m=
n =
n′ =
(N − 0.95d)
2
(B − 0.8bf)
2
√
dbf
4
and
λ=
2√
X
≤1
1+√
1−X
In the above equation,
4dbf Pu
2
(d + bf) φcPp
X=
Note that, since both the term in parentheses and the ratio of Pu to φcPp are always less
than or equal to one, the value of X will always be less than or equal to one. From LRFD
Specification Section J9
φc = 0.6
Grout hole
Angle - weld
to base plate
Base plate
(ship loose)
Column
Nut & washer
Leveling bolt
Small plate
(keeps bolt
point out of
concrete)
Nut - weld
to angle
Anchor rod
Fig. 11-18. Three-point leveling.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
11 - 60
CONNECTIONS FOR TENSION AND COMPRESSION
and, on the full area of a concrete support,
Pp = 0.85fc′A1
On less than the full area of the concrete support
√
Pp = 0.85fc′A1
√
A2
A1
A2
must be less than or equal to two.
A1
The physical variables in the above equations are illustrated in Figure 11-20.
Note that
EXAMPLE 11-7.
A W12×170 column with a factored axial load of 1,100 kips bears on
a concrete pedestal. If the column has Fy = 50 ksi, the concrete has
fc′ = 3 ksi, and the base-plate has Fy = 36 ksi, determine:
Given:
A. the base-plate and pedestal dimensions required if the base-plate is
to cover the full pedestal area,
B. the base-plate dimensions required for a 30 in.×30 in. concrete
pedestal.
W12×170
d = 14.03 in.
tw = 0.960 in.
Solution A:
bf = 12.570 in.
tf = 1.560 in.
Calculate required base-plate area.
Pu
φc(0.85fc′)
1,100 kips
=
0.6(0.85 × 3 ksi)
= 719 in.2
A1 req =
Column
Nut & washer
Angle frame
Base plate
(ship loose)
Wedges
Shims
Anchor rod
Grout
Fig. 11-19. Angle-framed leveling.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
COLUMN BASE PLATES
11 - 61
Optimize base-plate dimensions.
0.95d − 0.8bf
2
0.95(14.03 in.) − 0.8(12.570 in.)
=
2
= 1.64 in.
N ≈√
A1 + ∆
≈√
719 in.
2 + 1.64 in.
≈ 28.5 in.
∆ =
Try N = 28 in. and B = 26 in. (pedestal dimensions same)
Calculate required base-plate thickness
m =
=
n
N − 0.95d
2
28 in. − 0.95(14.03 in.)
2
= 7.34 in.
B − 0.8bf
=
2
=
26 in. − 0.8(12.570 in.)
2
= 7.97 in.
φcPp = 0.6 (0.85fc′A1)
= 0.6 (0.85 × 3 ksi × 26 in. × 28 in.)
= 1,110 kips
bf
m
.95d
d
m
n
.80bf
n
B
Fig. 11-20. Column base-plate design variables.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
N
11 - 62
CONNECTIONS FOR TENSION AND COMPRESSION
4dbf Pu
X =
2
(d + bf) φcPp
4(14.03 in.)(12.570 in.) 1,100 kips
=
(14.03 in. + 12.570 in.)2 1,110 kips
= 0.988
2
√X
λ =
≤1
1+√
1−X
=
2√
0.988
1+√
1 − 0.988
= 1.79 → 1
λn′ =
λ√
dbf
4
(1)√
14.03 in. × 12.570 in.
4
= 3.32 in.
=
From this
l = max(m, n, λn′)
= max (7.34 in., 7.97 in., 3.32 in.)
= 7.97 in.
and
√
treq = l
2Pu
0.9Fy BN
√
= (7.97 in.)
2(1,100 kips)
0.9(36 ksi)(26 in.)(28 in.)
= 2.43 in.
Use PL21⁄2×26×2′-4.
Solution B:
From pedestal dimensions, A2 = 900 in.2
Calculate required base-plate area.
2
A1 req
Pu
1
=
A2 φc(0.85fc′)
2
1,100 kips
1
=
2
900 in. 0.6(0.85 × 3 ksi)
= 575 in.2
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
COLUMN BASE PLATES
11 - 63
Optimize base-plate dimensions.
From Solution A, ∆ = 1.64 in.
N≈√
A1 + ∆
≈√
575 in.
2 + 1.64 in.
≈ 25.6 in.2
Try N = 25 in. and B = 23 in.
Calculate required base-plate thickness.
m =
=
n
N − 0.95d
2
25 in. − 0.95(14.03 in.)
2
= 5.84 in.
B − 0.8bf
=
2
23 in. − 0.8(12.570 in.)
=
2
= 6.47 in.
A2
φcPp = φc 0.85fc′A1
A1
√
= 0.6 0.85 × 3 ksi × 575 in.2
√
= 1,101 kips
4dbf Pu
X =
2
(d + bf) φc Pp
4(14.03 in.)(12.570 in.) 1,100 kips
=
2
(14.03 in. + 12.570 in.) 1,101 kips
= 0.996
λ =
2√
X
≤1
1+√
1−X
=
2
√
0.996
1+√
1 − 0.996
= 1.88 → 1
λn′ =
=
900 in.2
575 in.2
dbf
λ√
4
(1)√
14.03 in. × 12.570 in.
4
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
11 - 64
CONNECTIONS FOR TENSION AND COMPRESSION
= 3.32 in.
From this
l = max(m, n, λn′)
= max(5.84 in., 6.47 in., 3.32 in.)
= 6.47 in.
and
√
treq = l
2Pu
0.9Fy BN
√
25 )
= (6.47 in.)
2(1,100 kips)
0.9(36 ksi)(23 in.)(
in.
= 2.22
Use PL2 1⁄2×23×2′-1.
COLUMN SPLICES
When the height of a building exceeds the available length of column sections, or when
it is economically advantageous to change the column size at a given floor level, it
becomes necessary to splice two columns together. When required, column splices should
preferably be located about four feet above the finished floor to accommodate the
attachment of safety cables which may be required at floor edges or openings.
Fit-Up of Column Splices
From LRFD Specification Section M2.6, the ends of columns in a column splice which
depend upon contact bearing for the transfer of axial forces must be finished to a common
plane by milling, sawing, or other suitable means. In theory, if this were done and the
pieces were erected truly plumb, there would be full-contact bearing across the entire
surface; this is true in most cases. However, LRFD Specification Section M4.4 recognizes
that a perfect fit on the entire available surface will not exist in all cases.
A 1⁄16-in. gap is permissible with no requirements for repair or shimming. During erection,
at the time of tightening the bolts or depositing the welds, columns will usually be subjected
to loads which are significantly less than the design loads. Full scale tests (Popov and Steven,
1977) which progressed to column failure have demonstrated that subsequent loading to the
design loads does not result in distress in the bolts or welds of the splice.
If the gap exceeds 1⁄16-in., but is less than 1⁄4-in., non-tapered steel shims are required
if sufficient contact area does not exist. Mild steel shims are acceptable regardless of the
steel grade of the column or bearing material. If required, these shims must be contained,
usually with a tack weld, so that they cannot be worked out of the joint.
There is no provision in the LRFD Specification for gaps larger than 1⁄4-in. When such a
gap exists, an engineering evaluation should be made of this condition based upon the type
of loading transfered by the column splice. Tightly driven tapered shims may be required or
the required strength may be developed through flange and web splice plates. Alternatively,
the gap may be ground or gouged to a suitable profile and filled with weld metal.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
COLUMN SPLICES
11 - 65
Lifting Devices
As illustrated in Figure 11-21, lifting devices are typically used to facilitate the handling
and erection of columns. When flange-plated or web-plated column splices are used for
W-shape columns, it is convenient to place lifting holes in these flange plates as illustrated
in Figure 11-21a. When butt-plated column splices are used, additional temporary plates
with lifting holes may be required as illustrated in Figure 11-21b. W-shape column splices
which do not utilize web-plated or butt-plated column splices, i.e., groove welded column
splices, may be provided with a lifting hole in the column web as illustrated in Figure
11-21c. While a hole in the column web reduces the cross-sectional area of the column,
this reduction will seldom be critical since the column is sized for the loads at the floor
below and the splice is located above the floor. Alternatively, auxilliary plates with lifting
holes may be connected to the column so that they do not interfere with the welding.
Typical column splices for tubes and box-columns are illustrated in Figure 11-21d. Holes
in lifting devices may be drilled, reamed, or flame cut with a mechanically guided torch.
In the latter case, the bearing surface of the hole in the direction of the lift must be smooth.
The lifting device and its attachment to the column must be of sufficient strength to support
the weight of the column as it is brought from the horizontal position (as delivered) to the vertical
position (as erected); the lifting device and its attachment to the column must be adequate for
the tensile forces, shear forces, and moments induced during handling and erection.
A suitable shackle and pin are connected to the lifting device while the column is on the
ground. The size and type of shackle and pin to be used in erection is usually established by
the steel erector and this information must be transmitted to the fabricator prior to detailing.
Except for excessively heavy lifting pieces, it is customary to select a single pin and pinhole
diameter to accommodate the majority of structural steel members, whether they are columns
or other heavy structural steel members. The pin is attached to the lifting hook and a lanyard
trails to the ground or floor level. After the column is erected and connected, the pin is removed
from the device by means of the lanyard, eliminating the need for an ironworker to climb the
column. The shackle pin, as assembled with the column, must be free and clear, so that it may
be withdrawn laterally after the column has been landed and stabilized.
The safety of the structure, equipment, and personnel is of utmost importance during
the erection period. It is recommended that all welds that are used on the lifting devices
and stability devices be inspected very carefully, both in the shop and later in the field,
for any damage that may have occurred in handling and shipping. Groove welds
frequently are inspected with ultrasonic methods (UT) and fillet welds are inspected with
magnetic particle (MT) or liquid dye penetrant (DPT) methods.
Column Alignment and Stability During Erection
Column splices should provide for safety and stability during erection when the columns
might be subjected to wind, construction, and/or accidental loading prior to the placing
of the floor system. The nominal flange-plated, web-plated, and butt-plated column
splices developed here consider this type of loading.
In other splices, column alignment and stability during erection are achieved by the
addition of temporary lugs for field bolting as illustrated in Figure 11-22. The material
thickness, weld size, and bolt diameter required are a function of the loading. A
conservative resisting moment arm is normally taken as the distance from the compressive toe or flange face to the gage line of the temporary lug. The overturning moment
should be checked about both axes of the column. The recommended minimum plate or
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
11 - 66
CONNECTIONS FOR TENSION AND COMPRESSION
angle thickness is 1⁄2-in.; the recommended minimum weld size is 5⁄16-in.; additionally,
high-strength bolts are normally used for stability devices.
Temporary lugs are not normally used as lifting devices. Unless required to be removed
in the contract documents, these temporary lugs may remain.
Column alignment is provided with centerpunch marks which are useful in centering
the columns in two directions.
Force Transfer in Column Splices
As illustrated in Figure 11-23, for the W-shapes most frequently used as columns, the
distance between the inner faces of the flanges is constant throughout any given nominal
depth; as the nominal weight per foot increases for each nominal depth, the flange and
web thicknesses increase. From LRFD Specification Section J8, the design bearing
strength of the contact area of a milled surface is
Hitch plates
and pin-by
erector
Pin holes
(a) W-shape columns, flange-plated
column splices with lifting holes
(b) W-shape and box-shape columns.
butt-plated column splices with
auxiliary lifting plates
Shackle and pin
by erector
(c) W-shape columns, no splice plates,
lifting hole in column web
(d) Tubular and box-shape columns,
auxiliary lifting plates
Fig. 11-21. Lifting devices for columns.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
COLUMN SPLICES
11 - 67
φRn = 0.75(1.8Fy Apb)
This bearing strength is much greater than the axial strength of the column and will seldom prove
critical in the member design. In column splices transferring only axial forces, then, complete
axial force transfer may be achieved through bearing on finished surfaces; bolts or welds are
required by LRFD Specification Section J1.4 to be sufficient to hold all parts securely in place.
In addition to axial forces, from LRFD Specification Section J1.4, column splices must
be proportioned to resist tension developed by the factored loads specified by load
combination A4-6 which is 0.9D ± (1.3W or 1.0E). Note that it is not permissible to use
forces due to live load to offset the tensile forces from wind or seismic loads.
For dead and wind loads, the required strength is 0.9D − 1.3W, where D is the compressive
force due to the dead load and W is the tensile force due to wind load. If 0.9D ≥ 1.3W, the splice
is not subjected to tension and a nominal splice may be selected from those in Tables 11-4. When
0.9D < 1.3W, the splice will be subjected to tension and the nominal splices from Table 11-4
are acceptable if the design tensile strength of the splice φtPn is greater than or equal to the required
strength. Otherwise, a splice must be designed with sufficient area and attachment.
When shear from lateral loads is divided among several columns, the force on any
single column is relatively small and can usually be resisted by friction on the contact
bearing surfaces and/or by the flange plates, web plates, or butt plates. If the required
shear strength exceeds the design shear strength of the column splice selected from
Tables 11-4, a column splice must be designed with sufficient area and attachment.
Flange-Plated Column Splices
Tables 11-4 give typical flange-plated column splice details for W-shape columns. These
details are not splice standards, but rather, typical column splices in accordance with
LRFD Specification provisions and typical erection requirements. Other splice designs
may also be developed. It is assumed in all cases that the lower shaft will be the heavier,
although not necessarily the deeper, section.
Full-contact bearing is always achieved when lighter sections are centered over heavier
sections of the same nominal depth. If the upper column is not centered on the lower column,
or if columns of different nominal depths must bear on each other, some areas of the upper
column will not be in contact with the lower column. These areas are hatched in Figure 11-24.
When additional bearing area is not required, unfinished fillers may be used. These
fillers are intended for “pack-out” of thickness and are usually set back 1⁄4-in. or more
from the finished column end. Since no force is transferred by these fillers, only nominal
attachment to the column is required.
When additional bearing area is required, fillers finished to bear on the larger column
may be provided. Such fillers are proportioned to carry bearing loads at the bearing
strength calculated from LRFD Specification Section J8 and must be connected to the
column to transfer this calculated force.
Although flange plates are shown shop assembled to the lower column, it is equally
acceptable to invert this arrangement and place them on the upper column. This will
usually require fills of increased thickness to maintain erection clearances.
In Tables 11-4, Cases I and II are for all-bolted flange-plated column splices for
W-shape columns. Bolts in column splices are usually the same size and type as for other
bolts on the column. Bolt spacing, end distance, and edge distances resulting from the
billed plate sizes permit the use of 3⁄4-in. and 7⁄8-in. bolts in the splice details shown. Larger
diameter bolts may require an increase in edge or end distances. Refer to LRFD Specification
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
11 - 68
CONNECTIONS FOR TENSION AND COMPRESSION
1/
8
1/
8
1/
8
1/
8
Chapter J. The use of high-strength bolts in bearing-type connections is assumed in all
field and shop splices. However, when slotted or oversized holes are utilized, or in splices
employing under-developed fillers over 1⁄4-in. thick, slip-critical connections may be
required; refer to LRFD Specification Section J6. For ease of erection, field clearances for
lap splices fastened by bolts range from 1⁄8-in. to 3⁄16-in. under each plate.
Cases IV and V are for all-welded flange-plated column splices for W-shape columns.
Splice welds are assumed to be made with E70XX electrodes and are proportioned as
Note A
Note detail drawing to
require center punch
marks on center lines
of all faces of upper
and lower shafts.
See Note A
Typical arrangement–
alignment plates on
outside of W col. flg.
Alt. arrangement
using lug angles
1/
8
typ
1/
8
1/
8
Alt. arrangement
for heavy cols.
1/
8
1/
8
Alt. arrangement
showing optional
slots
Holes for
lifting hitch
See
Note A
Alignment plates between W column
flanges. Check clearances for erection
of column web framing in lower shaft.
See Note A
Alignment plates
on box column
Fig. 11-22. Column stability and alignment devices.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
COLUMN SPLICES
11 - 69
required by the LRFD Specification provisions. The SAW, GMAW, and FCAW equivalents to E70XX electrodes may be substituted if desired. Field clearance for welded
splices are limited to 1⁄16-in. to control the expense of building up welds to close openings.
Note that the fillet weld lengths Y as compared to the lengths L / 2, provide 2-in. unwelded
distance below and above the column shaft finish line. This provides a degree of
flexibility in the splice plates to assist the erector.
Cases VI and VII are for combination bolted and welded column splices. Since the
design strength of the welds will, in most cases, exceed the strength of the bolts, the weld
and splice lengths shown may be reduced, if desired, to balance the strength of the
fasteners to the upper or lower column, provided that the design strength of the splice is
still greater than the required strength of the splice, including erection loading.
Directly Welded Flange Column Splices
Tables 11-4 also include typical directly welded flange column splice details for W-shape
and tubular or box-shaped columns. These details are not splice standards, but rather,
typical column splices in accordance with LRFD Specification provisions and typical
erection requirements. Other splice designs may also be developed. It is assumed in all
cases that the lower shaft will be the heavier, although not necessarily the deeper, section.
Case VIII is for W-shape columns spliced with either partial-joint-penetration or
complete-joint-penetration groove welds. Case X is for tubular or box-shaped columns
spliced with partial-joint-penetration or complete-joint-penetration groove welds.
Butt-Plated Column Splices
Tables 11-4 further include typical butt-plated column splice details for W-shape and
tubular or box-shaped columns. These details are not splice standards, but rather, present
typical column splices in accordance with LRFD Specification provisions and typical
erection requirements. Other splice designs may also be developed. It is assumed in all
cases that the lower shaft will be the heavier, although not necessarily the deeper, section.
Butt plates are used frequently on welded splices where the upper and lower columns
are of different nominal depths, but may not be economical for bolted splices since fillers
cannot be eliminated. Typical butt plates are 11⁄2-in. thick for a W8 over W10 splice, and
2-in. thick for other W-shape combinations such as W10 over W12 and W12 over W14.
Butt plates which are subjected to substantial bending stresses, such as required on boxed
columns, will require a more careful review and analysis. One method of extensive
experience is to assume forces are transferred through the butt plate on a 45° angle and
check the thickness obtained for shear and bearing strength. Finishing requirements for
butt plates are specified in LRFD Specification Section M2.8.
h
Column Size
h (in.)
W8×24–67
W10×33–112
W12×40–336
W14×43–730
7.13
8.86
10.91
12.60
Fig. 11-23. Distance between flanges for typical W-shape columns.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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CONNECTIONS FOR TENSION AND COMPRESSION
Case III is a combination flange-plated and butt-plated column splice for W-shape
columns. Case IX is for welded butt-plated column splices for W-shape columns. Case XI
is for welded butt-plated column splices for tubular or box-shaped columns. Case XII is for welded
butt-plated column splices between W-shape and tubular or box-shaped columns.
Hatched areas not in contact
Fig. 11-24. Columns not centered or of different nominal depth.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
COLUMN SPLICES
11 - 71
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
11 - 72
CONNECTIONS FOR TENSION AND COMPRESSION
Table 11-4.
Typical Column Splices
Case I:
All-bolted flange-plated column splices between columns
with depth du and dl nominally the same.
Column
Size
Gage
g u or
gl
131 ⁄
Flange Plates
Type
Width
Thk.
W14× 455 to 730
W14× 257 to 426
W14× 145 to 233
W14× 90 to 132
W14× 43 to 82
111 ⁄2
111 ⁄2
111 ⁄2
51 ⁄2
1
1
1
2
2
16
14
14
14
8
3⁄
W12× 120 to 336
W12× 40 to 106
51 ⁄2
51 ⁄2
2
2
12
8
5⁄
W10× 33 to 112
51 ⁄2
2
8
W8× 31 to 67
W8× 24 & 28
51 ⁄
8
6
2
2
31 ⁄2
2
2
5⁄
1⁄
3⁄
3⁄
4
8
2
8
8
Length
1′j6 1 ⁄2
1′j6 1 ⁄2
1′j6 1 ⁄2
1′j0 1 ⁄2
1′j0 1 ⁄2
8
1′j0 1 ⁄2
1′j0 1 ⁄2
3⁄
8
1′j0 1 ⁄2
3⁄
8
1′j0 1 ⁄2
1′j0 1 ⁄2
3⁄
3⁄
8
8
Gages shown may be modified if necessary to accommodate fittings
elsewhere on the column.
Case I-A:
dl = (du + 1⁄4jin.)
to (du + 5⁄8 jin.)
Flange plates: Select gu for upper column; select gl and
flange plate dimensions for lower columns (see table
above).
Fillers: None.
Shims: Furnish sufficient strip shims 21⁄2×11 ⁄8 to provide
0 to 1⁄16 -in. clearance each side.
Case I-B:
Flange plates: Same as Case I-A.
Fillers (shop bolted under flange plates): Select thickness
as 1⁄8 -in. for d l = du and
dl = (du + 1⁄8jin.) or as 1 ⁄4-in. for
dl = (du − 1⁄8jin.) and dl = (du − 1 ⁄4jin.)
Select width to match flange plate and length as 0′j9
for Type 1 or 0′j6 for Type 2.
Shims: Same as Case I-A.
dl = (du − 1⁄4jin.)
to (du + 1⁄8 jin.)
Case I-C:
Flange plates: Same as Case I-A.
Fillers (shop bolted to upper column): Select thickness as
(dl − du ) / 2 minus 1⁄8 -in., whichever results in 1⁄8-in.
multiples of filler thickness. Select width to match flange
plate, but not greater than upper column flange width.
Select length as 1′j0 for Type 1 or 0′j9 for Type 2.
Shims: Same as Case I-A.
dl = (du + 3⁄4jin.)
and over.
For lifting devices, see Figure 11-21.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
11 - 73
Table 11-4 (cont.).
Typical Column Splices
Case I:
All-bolted flange-plated column splices between columns
with depth du and dl nominally the same.
du
gu
Type 2
dl
1¾
3 3
Type 1
Fin.
Fin.
3 3
Flange
plate
Erection
clearance
gl
CASE 1–A
du
strip—2½×1/8×9
(Type 1)
gu
Flange
plate
3 3
3 3
1¾
1½
Type 1
Type 2
Fin.
t
strip—2½×1/8 ×6
(Type 2)
Filler
Fin.
Erection
clearance
Detail of
strip shims
t
dl
gl
CASE 1–B
du
gu
gu
t
Filler
Filler
3 3
Fin.
Erection
clearance
Flange
plate
Flange
plate
3 3 3
t
dl
1½
gl
gl
Type 2
Type 1
CASE 1–C
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
3 3
1¾
3
Fin.
1½
1¾
11 - 74
CONNECTIONS FOR TENSION AND COMPRESSION
Table 11-4 (cont.).
Typical Column Splices
Case II:
All-bolted flange-plated column splices between columns with depth du
nominally two inches less than depth dl.
Fillers on upper column developed
for bearing on lower column.
Flange plates: Same as Case I-A.
Fillers (shop bolted to upper column): Select thickness as
(dl − du ) / 2 minus 1⁄8 -in. or 3⁄16 -in., whichever results in
1 ⁄ -in. multiples of filler thickness. Select bolts through
8
fillers (including bolts through flange plates) on each side
to develop bearing stregnth of the filler. Select width to
match flange plate, but not greater than upper column flange
width unless required for bearing strength. Select length
as required to accommodate required number of bolts.
Shims: Same as Case I-A.
Table 11-4 (cont.).
Typical Column splices
Case III:
All-bolted flange-plated and butt-plated column splices between
columns with depth du nominally two inches less than depth dl.
Fillers on upper column developed
for bearing on lower column.
Column
Size
Gage
g u or
gl
131 ⁄
Flange Plates
Type
Width
Thk.
Length
1′j8 1 ⁄2
1′j8 1 ⁄2
1′j8 1 ⁄2
1′j2 1 ⁄2
1′j2 1 ⁄2
W14× 455 to 730
W14× 257 to 426
W14× 145 to 233
W14× 90 to 132
W14× 43 to 82
111 ⁄2
111 ⁄2
111 ⁄2
51 ⁄2
1
1
1
2
2
16
14
14
14
8
3⁄
W12× 120 to 336
W12× 40 to 106
51 ⁄2
51 ⁄2
2
2
12
8
5⁄
W10× 33 to 112
51 ⁄2
2
8
3⁄
W8× 31 to 67
W8× 24 & 28
51 ⁄2
31 ⁄2
2
5⁄
1⁄
3⁄
3⁄
3⁄
4
8
2
8
8
8
1′j2 1 ⁄2
1′j2 1 ⁄2
8
1′j2
8
Gages shown may be modified if necessary to accommodate
fittings elsewhere on the column.
Flange plates: Select gu for upper column, select gl and
flange plate dimensions for lower column (see table
above).
Fillers (shop bolted to upper column): Same as Case I-C.
Shims: Same as Case I-A.
Butt plate: Select thickness as 11⁄2-in. for W8 upper
column or two inches for others. Select width the same
as upper column and length as dl − 1⁄4jin.
For lifting devices, see Figure 11-21.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
11 - 75
Table 11-4 (cont.).
Typical Column Splices
Case II:
All-bolted flange-plated column splices between columns with depth du
nominally two inches less than depth dl.
du
gu
gu
t
t
Filler
3
3 ″ Spa.
3 ″ Spa.
1¾
Fin.
Flange
plate
dl
1¾
3
3 3
Erection
clearance
3 3
Fin. shaft
and fills
Filler
Flange
plate
gl
gl
Type 1
Type 2
CASE II
du
t
Filler
Erection
clearance
2L
3 3
3 3 3
Filler
tp
Fin.
Column
gu
gu
t
dl
Flange
plate
gl
gl
Type 1
Type 2
CASE II
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
3
1½
1½
Flange
plate
1¾
3 3
butt
plate
A325 blts.
Fin.
Column
1¾
11 - 76
CONNECTIONS FOR TENSION AND COMPRESSION
Table 11-4 (cont.).
Typical Column Splices
Case IV:
All-welded flange-plated column splices between columns with
depths du and dl nominally the same.
Flange Plate
Column Size
W14× 455 & over
W14× 311 to 426
W14× 211 to 283
W14× 90 to 193
W14× 61 to 82
W14× 43 to 53
W12× 120 to 336
W14× 53 to 106
W14× 40 to 50
Width
14
12
12
12
8
6
8
8
6
Thk.
5⁄
5⁄
1⁄
3⁄
3⁄
5⁄
3⁄
W10× 49 to 112
W14× 33 to 45
8
6
5⁄
W8× 31 to 67
W4× 24 & 28
6
5
5⁄
8
2
8
8
16
1⁄
5⁄
8
2
8
16
3⁄
8
16
3⁄
8
16
Case IV-A:
Welds
Length
L
1′-6
1′-4
1′-4
1′-4
1′-4
1′-2
1′-4
1′-4
1′-2
Size
A
1⁄
1⁄
3⁄
5⁄
5⁄
2
2
8
16
16
1⁄
4
3⁄
5⁄
8
16
1⁄
4
1′-4
1′-2
5⁄
1′-2
1′-0
5⁄
16
1⁄
4
16
1⁄
4
Minimum Space
for Welding
Length
X
Y
5
4
4
4
3
2
7
6
6
6
6
5
M
3
3
2
6
6
5
3
2
6
5
9⁄
2
2
5
4
9⁄
13 ⁄
13 ⁄
11⁄
16
16
N
11⁄
11⁄
9⁄
16
16
16
5⁄
8
5⁄
8
9⁄
16
16
1⁄
2
1⁄
2
7⁄
16
11⁄
9⁄
16
5⁄
8
9⁄
16
5⁄
8
16
5⁄
8
16
16
1⁄
2
7⁄
16
1⁄
7⁄
1⁄
7⁄
2
16
2
16
Flange plates: Select flange-plate width and length and
weld lengths for upper (lighter) column; select flangeplate thickness and weld size for lower (heavier) column.
Fillers: None.
dl = (du + 1⁄8)
Case IV-B:
Flange plates: Same as Case IV-A, except use weld size
A + t on lower column.
Fillers (undeveloped on lower column, shop welded under
flange plates): Select thickness t as (dl − du) / 2 + 1⁄16 jin.
Select width to match flange plate and length as
L / 2 − 2 in.
dl = (du − 1⁄4jin.)
to du
Case IV-C:
Flange plates: Same as Case IV-A, except use weld size
A + t on upper column.
Fillers (undeveloped on upper column, shipped loose):
Select thickness t as (dl − du) / 2 − 1⁄16 jin. Select width
to match flange plate and length as L / 2 − 2 in.
dl = (du + 1⁄4jin.)
to (du + 1⁄2 jin.)
For lifting devices, see Figure 11-21.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
11 - 77
Table 11-4 (cont.).
Typical Column Splices
Case IV:
All-welded flange-plated column splices between columns with
depths du and dl nominally the same.
du
Width
A
A
Erection
clearance
Y
Length L
L/ 2
Holes for
erection
bolts—typ.
Fin.
X
L/ 2
Fin.
Erection
clearance
Flange
plate
A
Y
dl
A
X
CASE IV–A
du
Width
A
A
Y
L/ 2
Fin.
Flange
plate
L/ 2
Fin.
2
Filler under
splice plate
Length L
Erection
clearance
X
A+t
t
dl
Y
t
A+t
X
CASE IV–B
du
Width
t
A+t
A+t
Flange
plate
Y
2
Fin.
L/ 2
Erection
clearance
X
Length L
t
L/ 2
Fin.
Loose filler
(field)
A
dl
A
X
CASE IV–C
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
Y
11 - 78
CONNECTIONS FOR TENSION AND COMPRESSION
Table 11-4 (cont.).
Typical Column Splices
Case IV:
All-welded flange-plated column splices between columns with
depths du and dl nominally the same
Case IV-D:
dl = (du + 5⁄8jin.)
and over
Filler width less than upper column
flange width.
Case IV-E:
dl = (du + 5⁄8jin.)
and over
Filler width greater than upper
column flange width. Use this case
only when M or N in Case IV-D are
inadequate for welds B and A.
Flange plates: Same as Case IV-A, except see Note 1.
Fillers (developed on upper column, shop welded to
upper column): Select thickness t as (dl − du) / 2 − 1⁄16 jin.
Select weld size B from LRFD Specification; ≤5 ⁄16 -in.
preferred. Select weld length L B such that
LB ≥ A(X + Y) / B ≥ (L / 2 + 1 in. ). Select filler
width greater than flange plate width + 2N but less than
upper column flange width − 2M . Select filler length as
LB , subject to Note 2.
Flange plates: Same as Case IV-A, except see Note 1.
Fillers (developed on upper column, shop welded to
upper column): Select thickness t as (dl − du) / 2 − 1⁄16jin.
Select weld size B from LRFD Specification; ≤5 ⁄16 -in.
preferred. Select weld length L B such that
LB ≥ A(X + Y) / B ≥ (L / 2 + 1 in. ). Select filler
width as the larger of the flange plate width + 2N and the
upper column flange width + 2M , rounded to the next
higher 1⁄4-in. increment. Select filler length as LB subject
to Note 2.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
11 - 79
Table 11-4 (cont.).
Typical Column Splices
Case IV:
All-welded flange-plated column splices between columns with
depths du and dl nominally the same
M
N
Width–spl.
N
N
t
Width–spl.
M
A
A
A
B LB
B LB
Y
A
L
Filler
Flange
plate
A
X
Y
Length L
/2
/2
1
1
/2
Length L
L
/2
LB
LB
Fin.
Fin.
M
X
2
Erection
clearance
N
L/
t
t fu
Width–fill
2
t fu
Width–fill
M
L/
du
A
Y
Y
dl
A
X
CASE IV–D
A X
CASE IV–E
Note 1:
Minimum Fill Thickness for
Balanced Weld and Plate Shear
Where welds fasten flange plates to
Weld
developed fillers, or developed fillers
Fy
A
to column flanges (Cases IV-E and
E70XX
36
50
V-B), use the table to the right to
1⁄
0.26
0.19
4
check minimum fill thickness for
5⁄
0.32
0.23
16
3⁄
balanced fill and weld shear strength.
0.38
0.28
8
7⁄
0.45
0.33
Assume that an E70XX weld with
16
1⁄
0.51
0.37
2
A = 1⁄2 , X = 4, and Y = 6 is to be used
at full strength on an A36 fill 1⁄4-in.
thick. Since this table shows that the minimum fill thickness to develop this 1⁄2 -in. weld is 0.51 in.,
the 1⁄4-in. fill will be overstressed. A balanced condition is obtained by multiplying the length
(X + Y) by the ratio of the minimum to the actual thickness of fill, thus:
0.51
= 20.4
0.25
1
use (X + Y) = 20 ⁄2-in.
(4 + 6) ×
Placing this additional increment of (X + Y) can be done by making weld lengths X continuous across
the end of the splice plate and by increasing lengths Y (and therefore the plate length) if required.
Note 2:
If fill length, based on L B, is excessive, place weld of size B across one or both ends of fill and
reduce L B accordingly, but not to less than (L / 2 + 1). Omit return welds in Cases IV-E and V-B.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
11 - 80
CONNECTIONS FOR TENSION AND COMPRESSION
Table 11-4 (cont.).
Typical Column Splices
Case V:
All-welded flange-plated column splices between columns with
depth du nominally two inches less than depth dl.
Case V-A:
Fillers on upper column developed
for bearing on lower column. Filler
width less than upper column flange
width.
Flange plates: Same as Case IV-A, except see Note 1.
Fillers (shop welded to upper column): Select thickness as
(dl − du) / 2 − 1⁄16 jin. Select weld size B from LRFD
Specification; ≤ 5⁄16 jin. preferred. Select weld length L B
to develop bearing strength of the filler but not less than
(L / 2 + 11⁄2jin. ). Select filler width greater than the
flange plate width + 2N but less than the upper column
flange width − 2M . See Case IV for M and N.
Case V-B:
Flange plates: Same as Case IV-A, except see Note 1.
Same as Case V-A except filler width Fillers (shop welded to upper column): Select thickness as
is greater than upper column flange
(dl − du) / 2 − 1⁄16 jin. Select weld size B from LRFD
width. Use this case only when M or
Specification; ≤ 5⁄16 jin. preferred. Select weld length L B
N in Case V-A are inadequate for
to develop bearing strength of the filler but not less than
weld A, or when additional
(L / 2 + 11⁄2jin.). Select filler width as the larger of the
filler bearing area is required.
flange plate width + 2N and the upper column flange
width + 2M , rounded to the next higher 1⁄4jin. increment.
Filler length as LB , subject to Note 3.
Note 3:
If fill length, based on L B, is excessive, place weld of size B across end of fill and reduce LB by
one-half of such additional weld length, but not to less than (L / 2 + 11⁄2). Omit return welds in
Case V-B.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
11 - 81
Table 11-4 (cont.).
Typical Column Splices
Case V:
All-welded flange-plated column splices between columns with
depth du nominally two inches less than depth dl.
du
t
M
Width–fill
M
N
Width–spl.
N
t
X
A
Erection
clearance
L/ 2
Length L
L/ 2
LB
Fin. shafts
and fills
Fin.
B LB
B LB
Y
A
Filler
Flange
plate
A
Y
dl
A
X
CASE V–A
Width–fill
t
M
Width–spl.
Fin.
N
M
A
B LB
B LB
X
Y
A
L/ 2
LB
Fin. shafts
and fills
Erection
clearance
N
Length L
t
tfy
L/ 2
t fu
du
Filler
Flange
plate
A
dl
A
X
CASE V–B
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
Y
11 - 82
CONNECTIONS FOR TENSION AND COMPRESSION
Table 11-4 (cont.).
Typical Column Splices
Case VI:
Combination bolted and welded column splices between columns with
depths dn and dl nominally the same.
Flange Plate
Bolts
Length
Column Size
Width
Thk.
5⁄
W14×455 & over
W14×311 to 426
W14×211 to 283
W14×90 to 193
W14×61 to 82
W14×43 to 53
14
12
12
12
8
6
W12× 120 to 336
W14× 53 to 106
W14× 40 to 50
8
8
6
W10× 49 to 112
W14× 33 to 45
8
6
5⁄
W8× 31 to 67
W4× 24 & 28
6
5
5⁄
5⁄
1⁄
3⁄
3⁄
5⁄
8
2
8
8
16
1⁄
3⁄
5⁄
8
2
8
16
3⁄
8
16
3⁄
8
16
LU
91 ⁄
LL
No.
of
Rows
Welds
Length
Gage
g
Size
A
Y
5
4
4
4
3
2
7
6
6
6
6
5
4
3
2
6
6
5
91 ⁄4
91 ⁄4
61 ⁄4
61 ⁄4
61 ⁄4
9
8
8
8
8
7
3
3
3
2
2
2
61 ⁄4
61 ⁄4
61 ⁄4
8
8
7
2
2
2
51 ⁄2
51 ⁄2
31 ⁄2
61 ⁄4
61 ⁄4
8
7
2
2
51 ⁄2
31 ⁄2
5⁄
3
2
6
5
61 ⁄4
61 ⁄4
7
6
2
2
31 ⁄2
31 ⁄2
5⁄
2
2
5
4
4
2
91 ⁄2
91 ⁄2
91 ⁄2
51 ⁄2
31 ⁄2
1⁄
X
111 ⁄
1⁄
3⁄
5⁄
5⁄
2
2
8
16
16
1⁄
4
3⁄
5⁄
8
16
1⁄
4
16
1⁄
4
16
1⁄
4
Gages shown may be modified if necessary to accommodate fittings elsewhere on the columns.
Case VI-A:
dl = (du + 1⁄4jin.)
to (du + 5⁄8 jin.)
Case VI-B:
dl = (du − 1⁄4jin.)
to (du + 1⁄8 jin.)
Case VI-C:
dl = (du + 3⁄4jin.)
and over
Flange plates: Select flange plate width, bolts, and length
L U for upper column; select flange plate thickness, weld
size A, weld lengths X and Y, and length L L for lower
column. Total flange plate length is L U + L L (see table
above).
Fillers: None.
Shims: Furnish sufficient strip shims 21⁄2×1⁄8 to obtain 0 to
1 ⁄ -in. clearance on each side.
16
Flange plates: Same as Case VI-A, except use weld size
A + t on lower column.
Fillers (shop welded to lower column under flange plate):
Select thickness t as 1⁄8-in. for for dl = du and
dl = (du + 1⁄8jin.) or as 3 ⁄16 -in. for dl = (du − 1⁄8 jin.) and
dl = (du − 1⁄4jin.). Select width to match flange plate and
length as L L − 2 in.
Shims: Same as Case VI-A.
Flange plates: Same as Case VI-A.
Fillers (shop welded to upper column): Select thickness t
as (dl − du) / 2 minus 1⁄8-in. or 3 ⁄16 -in., whichever results
in 1⁄8-in. multiples of fill thickness. Select weld size B as
minimum size from LRFD Specification Section J2.
Select weld length as L U − 1⁄4jin. Select filler width as
flange plate width and filler length as L U − 1⁄4-in.
Shims: Same as Case VI-A.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
11 - 83
Table 11-4 (cont.).
Typical Column Splices
Flange
plate
3 3
Lu
Fin.
Erection
clearance
Width
g
Others
du
Lu
W14 × 211 and over
Case VI:
Combination bolted and welded column splices between columns with
depths dn and dl nominally the same.
LL
Fin.
1¾
A Y
A X
dl
W14 × 211 and over
Others
Width
g
2 3 3
Flange
plate
1¾
A+t
Y
A+t
X
LL
Fin.
Fin.
Erection
clearance
Lu
du
Lu
CASE VI–A
Filler under
flange plate
t
t
dl
Others
Lu
LL
Fin.
Strip–2½× 1/8 × 9
(W14×211 and over)
Flange
plate
B Lu –¼
B Lu –¼
Strip–2½× 1/ 8 ×6
(all others)
3 3
Fin.
Erection
clearance
Width
g
1½
t
W14 × 211 and over
du
t
Lu
CASE VI–B
1¾
Detail of strip shims
Filler
A Y
dl
A X
CASE VI–C
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
11 - 84
CONNECTIONS FOR TENSION AND COMPRESSION
Table 11-4 (cont.).
Typical Column Splices
Case VII:
Combination bolted and welded flange-plated column splices between
columns with depth du nominally two inches less than depth dl
Fillers developed for bearing.
Case VII-A:
Fillers of width less than upper
column flange width.
Flange plates: Same as Case VI-A.
Fillers (shop welded to upper column): Select filler
thickness t as (dl − du) / 2 minus 1⁄8-in. or 3⁄16 -in.,
whichever results in 1⁄8-in. multiples of filler thickness.
Select weld size B from LRFD Specification; ≤5 ⁄16 -in.
preferred. Select weld length L B to develop bearing
strength of filler. Select filler width not less than flange
plate width but not greater than upper column flange
width −2M (see Case IV). Select filler length as LB ,
subject to Note 4.
Case VII-B:
Filler of width greater than upper
column flange width. Use Case
VII-B only when fillers must be
widened to provide additional
bearing area.
Flange plates: Same as Case VI-A.
Fillers (shop welded to upper columns): Same as Case
VII-A except select filler width as upper column flange
width + 2M (see Case IV) rounded to the next larger
1 ⁄ -in. increment.
2
Note 4:
If fill length based on L B is excessive, place weld of size B across end of fill and reduce LB by
one-half of such additional weld length, but not less than L U . Omit return welds, Case VII-B.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
11 - 85
Table 11-4 (cont.).
Typical Column Splices
M
B LB
B LB
LB
Lu
Erection
clearance
Width-filler
g
3 3
t
M
Lu
Fin. shaft
and fills
t
Flange
plate
Others
du
W14 × 211 and over
Case VII:
Combination bolted and welded flange-plated column splices between
columns with depth du nominally two inches less than depth dl
Fillers developed for bearing.
LL
Fin.
1¾
A Y
dl
CASE VII–A
Lu
Erection
clearance
Width-filler
g
M
B LB
B LB
LB
t
M
3 3
t
Flange
plate
Others
t fu
W14×211 and over
t fu
flange plate
Lu
du
Fin. shaft
and fills
A X
Width
LL
Fin.
1¾
A Y
dl
Width
CASE VII–B
flange plate
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
A X
11 - 86
CONNECTIONS FOR TENSION AND COMPRESSION
Table 11-4 (cont.).
Typical Column Splices
Case VIII:
Directly welded flange column splices between columns with
depths du and dl nominally the same.
These types of splices exhibit versatility. The flanges may be partial-joint-penetration welded as in
Cases VIIIA and VIIIB, or complete-joint-penetration welded as in Cases VIIIC, VIIID, and VIIIE.
The webs may be spliced using the channel(s) as shown in Cases VIIIA, VIIIB, VIIIC, and VIIID,
or complete-joint-penetration welded as shown in Case VIIIE. The use of a channel or channels
at the web splice provides a higher degree of restraint during the erection phase than does a plate
or plates. The use of partial-joint-penetration flange welds provide greater stability during the
erection phase than do complete-joint-penetration welds.
The adequacy of any splice arrangement must be confirmed by the user. This is especially true in
regions where high winds are prevalent or when the concentrated weight of the fabricated column
is significantly off its centerline. Then using partial-joint-penetration flange welds, a land width of
1 ⁄ -in. or greater should be used. The weld sizes are based on the thickness of the thinner column
4
flange, regardless of whether it is the upper or lower column.
When column flange thicknesses are less than 1⁄2-in. it may be more efficient to use flange splice
plates as shown in previous cases.
See the table below for minimum effective weld sizes for partial-penetration groove welds.
Partial Penetration Groove Width
a
Thickness of
Column Material
Tu
Minimum Effective
Welds Size E
Over to 1⁄2 to 3⁄4, incl.
Over 3⁄4 to 11⁄2, incl.
Over 11⁄2 to 21⁄4, incl.
Over 21⁄4 to 6, incl.
Over 6
1⁄
4
5⁄
16
3⁄
8
1⁄
2
5⁄
8
b
aThickness of thicker part joined.
bFor less than 1⁄ , use splice plates.
2
Back gouge
or use backup bars
¼ ″ min.
land
(a) Partial-joint-penetration
groove welds
(b) Complete-joint-penetration
groove welds
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
11 - 87
Table 11-4 (cont.).
Typical Column Splices
Directly welded flange column splices between columns with
depths du and dl nominally the same.
du
du
1½
1½
For W8 &
W10 columns
2
For others
1½
2
13
/16
15/
16
dia. holes in column
dia. holes in channel
with 3/ 4 dia. A325 bolts
2 washers each
PJP
1½
For W8 &
W10 columns
2
For others
2
13
/16
15/
16
dia. holes in column
dia. holes in channel
with 3/ 4 dia. A325 bolts
2 washers each
PJP
lifting hole optional
A.F.F.
10
2 6
8
10
10
A.F.F.
6 22 6
lifting hole optional
1–C6×10.5 for W8 column
1–C7×12.25 for W10 column
1—C9×15 for W12 column &
over
Shim as required
(NOTE: Use 2 channels
for columns over 30 ′–0
long or over 100 lbs.
per foot.)
dl
CASE VII A—All-bolted
web splice, partial-joint-penetration
flange welds
dl
6″
Return 5
/16 2 ″
5
/16
CASE VII B—Combination bolted and welded
web splice, partial-joint-penetration
flange welds
du
1½
For W8 &
W10 columns
2
For others
1–C6×10.5 for W8 column
1–C7×12.25 for W10 column
1—C9×15 for W12 column &
over
Shim as required
(NOTE: Use 2 channels
for columns over 30 ′–0
long or over 100 lbs.
per foot.)
du
1½
For W8 &
W10 columns
2
For others
1½
2
1½
2
13
/16
15/
16
13
/16
15/
16
dia. holes in column
dia. holes in channel
with 3/ 4 dia. A325 bolts
2 washers each
CJP
dia. holes in column
dia. holes in channel
with 3/ 4 dia. A325 bolts
2 washers each
CJP
dl
lifting hole optional
A.F.F.
10
2 6
8
622 6
10
A.F.F.
10
lifting hole optional
2–C6×10.5 for W8 column
2–C7×12.25 for W10 column
2—C9×15 for W12 column &
over
Shim as required
dl
5/
16
2–C6×10.5 for W8 column
2–C7×12.25 for W10 column
2—C9×15 for W12 column &
over
Shim as required
6″
Return
5/
16
2″
CASE VIII D—Combination bolted and welded
web splice, complete-joint-penetration
flange welds
du
CASE VIII C—All-bolted
web splice, complete-joint-penetration
flange welds
1½
For W8 &
W10 columns
2
For others
1½
2
13
/16 dia. holes in
column and channels
with 3/ 4 dia.
A325 bolts
*Full pen.
10
10
A.F.F.
6 22 6
lifting hole optional
* Weld column flanges
first, remove channels,
then weld column
web.
dl
2–C6×10.5 for W8 column
2–C7×12.25 for W10 column
2–C9×15 for W12 column &
over
Shim as required
*Full pen.
CASE VIII E—Temporary
web splice, complete-joint-penetration
flange and web welds
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
11 - 88
CONNECTIONS FOR TENSION AND COMPRESSION
Table 11-4 (cont.).
Typical Column Splices
Case IX:
Butt-plated column splices between columns with
depth du nominally 2 in. less than depth dl.
Butt plate: Select a butt plate thickness of 11⁄2-in. for W8 over W10 columns and 2 in. for all other
combinations. Select butt plate width and length not less than w l and dl assuming the lower is the
larger column shaft.
Weld: Select weld to upper column based on the thicker of tfu and tp. Select weld to lower column
based on the thicker of tfl and tp. The edge preparation required by the groove weld is usually
performed on the column shafts. However, special cases such as when the butt plate must
be field welded to the lower column require special consideration.
Erection: clip angles, such as those shown in the sketch below, help to locate and stabilize the upper
column during the erection phase.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
11 - 89
Table 11-4 (cont.).
Typical Column Splices
Case IX:
Butt-plated column splices between columns with
depth du nominally 2 in. less than depth dl.
wu
Fin.
shaft
t fu
Erection
lugs
tp
Fin.
shaft
du
tfl
wl
dl
CASE IX
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
11 - 90
CONNECTIONS FOR TENSION AND COMPRESSION
Table 11-4 (cont.).
Typical Column Splices
Cases X, XI, XII
Special column splices
Case X: Directly welded splice
between tubular and/or box-shaped
columns.
Welds may be either partial-joint- or complete-jointpenetration. The strength of partial-joint-penetration welds
is a function of the column wall thickness and appropriate
guidelines for minimum land width and effective weld size
must be observed. This type of splice usually requires
lifting and alignment devices. For lifting devices see Figure
11-21. For alignment devices see Figure 11-22.
Case XI: Butt-plated splices between
tubular and/or box-shaped columns.
The butt-plate thickness is selected based on the LRFD
Specification. Welds may be either partial- or completepenetration-groove welds, or, if adequate space is
provided, fillet welds may be used. Weld strength is
based on the thickness of connected material. See
comments under Case X above regarding lifting and
alignment devices.
Case XII:
Butt-plated column splices between
W-shape columns and tubular or
box-shaped columns.
See comments under Case XI above.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
11 - 91
Table 11-4 (cont.).
Typical Column Splices
Cases X, XI, XII
Special column splices
tu
Fin.
Fin.
tu
S(E)
tl
S(E)
tl
(E)
tu ≤ t l
(E)
CASE X
t fu
S(E)
(E)
S(E)
tl
tp
tp
Fin.
shaft
(E)
Fin.
shaft
Fin.
shaft
Fin.
shaft
tu
tl
S(E)
(E)
CASE XI
S(E)
(E)
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
CASE XII
11 - 92
CONNECTIONS FOR TENSION AND COMPRESSION
TRUSS CONNECTIONS
Members in Trusses
For light loads, trusses are commonly composed of tees for the top and bottom chords
with single-angle or double-angle web members. In welded construction, the single-angle
and double-angle web members may, in many cases, be welded to the stem of the tee,
thus, eliminating the need for gussets. When single-angle web members are used, all web
members should be placed on the same side of the chord; staggering the web members
causes a torque on the chord, as illustrated in Figure 11-25.
Double-angle truss members are designed to act as a single composite unit. When
unequal-leg angles are used, long legs are normally assembled back to back. A simple
notation for this is LLBB (long legs back-to-back) and SLBB (short legs back-to-back).
Alternatively, the notation might be graphical in nature as and ________.
For large loads, W-shapes may be used with the web vertical and gussets welded to
the flange for the truss connections. Web members may be single angles or double angles,
although W-shapes are sometimes used for both chord and web members as shown in
Figure 11-26. Heavy sections in trusses must meet the design and fabrication restrictions
and special requirements of LRFD Specification Sections A3.1c, J1.5, J1.6, J2, and M2.2.
With member orientation as shown for the field-welded truss joint in Figure 11-26a,
connections usually are made by groove welding flanges to flanges and fillet welding
webs directly or indirectly by the use of gussets. Fit-up of joints in this type of construction
are very sensitive to dimensional variations in the rolled shapes; fabricators sometimes
prefer to use built-up shapes in these cases.
The web connection plate in Figure 11-26a is a typical detail. While the diagonal
member could theoretically be cut so that the diagonal web would be extended into the
web of the chord for a direct connection, such a detail is difficult to fabricate. Additionally,
welding access becomes very limited; note the obvious difficulty of welding the gusset
or diagonal directly to the chord web. As illustrated, this weld is usually omitted.
C
T
e
Fig. 11-25. Staggered truss-web members result in a torque on the truss chord.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
TRUSS CONNECTIONS
11 - 93
When stiffeners and doubler plates are required for concentrated flange forces, the
designer should consider selecting a heavier section which would eliminate the need for
stiffening. Although this will increase the material cost of the member, the heavier section
will likely provide a more economical solution due to the reduction in labor cost
associated with the elimination of stiffening (Ricker, 1992 and Thornton, 1992).
Minimum Connection Strength
From LRFD Specification Section J1.7, truss connections must be designed for a
minimum factored load of 10 kips. Additionally, when trusses are shop assembled or field
assembled on the ground for subsequent erection, consideration should be given to loads
induced during handling, shipping, and erection. A common requirement for these cases
is that the connection be designed for a minimum of 50 percent of the member strength
or a lesser amount as determined by the engineer.
Typ.
(a) Shop and field welding
PJP
PJP
(b) Shop welding
Fig. 11-26. Truss-panel-point connections for W-shape members.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
11 - 94
CONNECTIONS FOR TENSION AND COMPRESSION
Panel-Point Connections
A panel-point connection connects diagonal and/or vertical web members to the chord
member of a truss. These web members deliver axial forces, tensile or compressive, to
the truss chord. In bolted construction, a gusset is usually required because of bolt spacing
and edge distance requirements. In welded construction, it is sometimes possible to
eliminate the need for a gusset.
Design Checks—The design strengths of the bolts and/or welds, connecting elements,
and affected elements of the connected members must be determined in accordance with
the provisions of the LRFD Specification. The applicable limit states in each of the
aforementioned design strengths are discussed in Part 8. In all cases, the design strength
φRn must exceed the required strength Ru.
In the panel-point connection of Figure 11-27, the neutral axes of the vertical and
diagonal truss members intersect on the neutral axis of the truss chord. As a result, the
forces in all members of the truss are axial. It is common practice, however, to modify
working lines slightly from the gravity axes to establish repetitive panels and avoid
fractional dimensions less than 1⁄8-in. or to accommodate a larger panel-point connection
or a connection for bottom-chord lateral bracing, a purlin, or a sway-frame. This
eccentricity and the resulting moment must be considered in the design of the truss chord.
In contrast, for the design of the truss web members, LRFD Specification Section J1.8
states that the center of gravity of the end connection of a statically loaded truss member
need not coincide with the gravity axis of the connected member. This is because tests
have shown that there is no appreciable difference in the static design strength between
balanced and unbalanced connections of this nature. Accordingly, the truss web members
and their end connections may be designed for the axial load, neglecting the effect of this
minor eccentricity.
Shop and Field Practices—In bolted construction, it is convenient to use standard gage
lines of the angles as truss working lines; where wider angles with two gage lines are
used, the gage line nearest the heel of the angle is the one which is substituted for the
gravity axis.
To provide for stiffness in the finished truss, the web members of the truss are extended
to near the edge of the fillet of the tee (k-distance). If welded, the required welds are then
applied along the heel and toe of each angle, beginning at their ends rather than at the
edge of the tee stem.
2×
2L
2×
¼
2L2½×2×2¼
WT8×38.5
Fig. 11-27. Panel-point truss connection.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
TRUSS CONNECTIONS
11 - 95
EXAMPLE 11-8
Refer to Figure 11-28. Determine the requirements for the following
cases:
Given:
A. joint L1
B. joint U1
Assume 70 ksi electrodes. For the WT truss chord, assume Fy = 50 ksi
and Fu = 65 ksi. For angle and splice material, assume Fy = 36 ksi and
Fu = 58 ksi.
Check shear yield of the tee stem (on Section A-A)
Solution A:
φRn = φ(0.6Fy Aw)
= 0.90(0.6 × 50 ksi × 8.215 in. × 0.430 in.)
= 95.4 kips < 104 kips n.g.
Additional shear area must be provided.
31.0
/16
U1
6½
B
PL
×
2½
1
1 /16
3½
3½
3½
L2 k
U1 3
1
+1
6
5 /1
×
4×
2L
×
3
8
3½
0
–1
k
66
′
1
L1
+1
4
×
×4
U0
1¼
1 /8
1
2L
/
12
7
16
2L 3½×3× 5/16
1
9 /16
U1 L 1
11
-104 k
3
4
7½
1 5/ 8
WT8×38.5
¼
¼
2¾
B
k
/
A
1
4
/8
Grind only
under angles
/16
115/ 16
45°
3
10
L1
WT8× 28.5
A
3
/16
6½
Joint Detail for U1 & L 1
Fig. 11-28.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
10 3/16
12
11 - 96
CONNECTIONS FOR TENSION AND COMPRESSION
Try PL 7⁄16-in. × 4 in. complete-joint-penetration groove welded to the
stem of the WT.
φRn = 95.4 kips + 0.9(0.6 × 36 ksi × 4 in. × 7⁄16-in.)
= 129 kips > 104 kips o.k.
Design welds for member U1L1
The minimum weld size from LRFD Specification Table J2.4 is 3⁄16-in.
The maximum weld size cannot exceed 5⁄16-in. Calculate the minimum
length of 3⁄16-in. fillet weld:
Rn
1.392D
104 kips
=
1.392 (3 sixteenths)
= 24.9 in.
Lmin =
Use 61⁄2-in. of 3⁄16-in. weld at the heel and toe of both angles for a total
of 26 inches.
Design welds for member U0L1
The minimum weld size from LRFD Specification Table J2.4 is 3⁄16-in.
The maximum weld size cannot exceed 1⁄4-in. Calculate the minimum
length of 3⁄16-in. fillet weld:
Ru
1.392D
166 kips
=
1.392 (3 sixteenths)
= 39.8 in.
Lmin =
Use 10 in. of 3⁄16-in. weld at the heel and toe of both angles for a total
of 40 inches.
Check tension yielding of angles (U0 L1)
φRn = φFy Ag
= 0.9(36 ksi)(2 × 2.67 in.2)
= 173 kips > 166 kips o.k.
Check tension rupture of angles (U0 L1)
From LRFD Specification Section B3,
_
x
U = 1 − ≤ 0.9
L
1.21 in.
=1−
10 in.
= 0.879
However, from LRFD Specification Section J5.2, An ≤ 0.85Ag. Thus,
from LRFD Specification Section J5.2,
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
TRUSS CONNECTIONS
11 - 97
φRn = φFu An
= 0.75(58 ksi)(0.85 × 2 × 2.67 in.2)
= 197 kips > 166 kips o.k.
Solution B:
Check shear yielding of the tee stem (on Section B-B)
φRn = φ(0.6Fy Aw)
= 0.90(0.6 × 50 ksi × 8.26 in. × 0.455)
= 101 kips > 73.1 kips o.k.
Design welds for member U1L1
As calculated previously in Solution A, use 61⁄2-in. of 3⁄16-in. weld at
the heel and toe of both angles for a total of 26 inches.
Design welds for member U1L2
The minimum weld size from LRFD Specification Table J2.4 is 3⁄16-in.
The maximum weld size cannot exceed 1⁄4-in. Calculate the minimum
length of 1⁄4-in. fillet weld:
Rn
1.392D
113 kips
=
1.392 (4 sixteenths)
= 20.3 in.
Lmin =
Use 71⁄2-in. of fillet weld at the heel and four inches of fillet weld at the
toe of each angle for a total of 23 inches.
Check tension yielding of angles (U1L2)
φRn = φFy Ag
= 0.9(36 ksi)(2 × 1.78 in.2)
= 115 kips > 113 kips o.k.
Check tension rupture of angles (U1L2)
From LRFD Specification Section B3,
_
x
U = 1 − ≤ 0.9
L
1.14 in.
=1−
(4 in. + 71⁄2jin.) / 2
= 0.802
Thus,
Ae = UAg
= 0.802(2 × 1.78 in.2)
= 2.86 in.2
From LRFD Specification Section J5.2,
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
11 - 98
CONNECTIONS FOR TENSION AND COMPRESSION
φRn = φFu Ae
= 0.75(58 ksi)(2.86 in.2)
= 124 kips > 113 kips o.k.
Check block shear rupture
Because of the cut end of the angle, the block shear rupture model
presented in Part 8 does not directly apply. Conservatively, the block shear
rupture strength will be based on the shear rupture strength of the WT stem
along the length of the welds. Thus, the design strength is:
φRn = φ(0.6Fu Aw)
= 0.90[0.6 × 50 ksi × (7.5 in. + 4 in.) × 0.455 in.]
= 141 kips > 113 kips o.k.
Support Connections
A truss support connection connects the ends of trusses to supporting columns.
Design Checks—The design strengths of the bolts and/or welds, connecting elements,
and affected elements of the connected members must be determined in accordance with
the provisions of the LRFD Specification. The applicable limit states in each of the
aforementioned design strengths are discussed in Part 8. Additionally, truss support
connections produce tensile or compressive single concentrated forces at the beam end;
the limit states of the flange design strength in local bending and the limit states of the
web design strength in local yielding, crippling, and compression buckling may have to
be checked. In all cases, the design strength φRn must exceed the required strength Ru.
2L 3½×3×¼×1 ′ –2
1 5/8
6 1/ 8
3
2¼
/16
WT8 × 38.5
12
½
w.p.
3@3 = 9
Cut 0.5 legs at 45°
2L
–4
½
W12×50 Col.
C
L
×3
Grind only
under angles
¼
10
×
1
/8
3
/8
4
1¼
12
7
/16 PL
3
9 11/16
k
/16
74
+1
3
Fig. 11-29. Truss-support connection, working point on column face.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
TRUSS CONNECTIONS
11 - 99
6 1/ 8
1 ′–
5
1–WT8×38.5
(–140 K)
¼
½
Uo
Cut O.S. leg
at 45°
15/8
w.p.
C
L W12× 50 Col.
1
1¼
/8
Grind only in way
of fitting angles
¼
11
4
2½
Horizontal line
througth W.P.
At the end of a truss supported by a column, all member axes may not intersect at a
common point. When this is the case, an eccentricity results. Typically, it is the neutral
axis of the column which does not meet at the working point.
If trusses with similar reactions line up on opposite sides of the column, consideration
of eccentricity would not be required since any moment would be transfered through the
column and into the other truss. However, if there is little or no load on the opposite side
of the column, the resulting eccentricity must be considered.
In Figure 11-29, the truss chord and diagonal intersect at a common working point on
the face of the column flange. In this detail, there is no eccentricity in the gusset,
gusset-to-column connection, truss chord, or diagonal. However, the column must be
designed for the moment due to the eccentricity of the truss reaction from the neutral axis
of the column.
For the truss support connection illustrated in Figure 11-30, this eccentricity results in a
moment. Assuming the connection between the members is adequate, joint rotation is resisted
by the combined flexural strength of the column, the truss top chord, and the truss diagonal.
However, the distribution of moment between these members will be proportional to the
stiffness of the members. Thus, when the stiffness of the column is much greater than the
stiffness of the other elements of the truss suport connection, it is good practice to design the
column and gusset-to-column connection for the full eccentricity.
Due to its importance, the truss support connection is frequently shown in detail on
the design drawing.
12
9 11/ 16
¼
2L–4×4× 5/ 8 ×1′ –10½
7
1 PL /16
2L 4×3½× 3/ 8
(+174 K)
Fig. 11-30. Truss-support connection, working point at column centerline.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
12
11 - 100
CONNECTIONS FOR TENSION AND COMPRESSION
Shop and Field Practices—When a truss is erected in place and loaded, truss members
in tension will lengthen and truss members in compression will shorten. At the support
connection, this may cause the tension chord of a “square-ended” truss to encroach on
its connection to the supporting column. When the connection is shop-attached to the
truss, erection clearance must be provided with shims to fill out whatever space remains
after the truss is erected and loaded. In field erected connections, however, provision must
be made for the necessary adjustment in the connection.
When the tension chord delivers no calculated force to the connection, adjustment can
usually be provided with slotted holes. For short spans with relatively light loads, the
comparatively small deflections can be absorbed by the normal hole clearances provided
for bolted construction. Slightly greater misalignment can be corrected in the field by
reaming the holes. If appreciable deflection is expected, the connection may be welded
or bolt holes may be field-drilled; this is an expensive operation which should be avoided
if at all possible.
An approximation of the elongation which may be expected can be determined from
the relationship between stress σ and strain ε, where E, the modulus of elasticity, is
E=
σ
ε
With σ = P / A, ε = ∆ / l, and E = 29,000 ksi, ∆, the elongation in in. will be:
∆=
Pl
29,000A
In the above equation,
P = unfactored axial force, kips
A = gross area of the truss chord, in.2
l = length, in.
The total change in length of the truss chord is Σ∆i, the sum of the changes in the lengths
of the individual panel segments of the truss chord. The misalignment at each support
connection of the tension chord is one-half the total elongation.
EXAMPLE 11-9
Given:
Refer to Figure 11-31. Determine:
A. the connection requirements between the gusset and column,
B. the required gusset size and the weld requirements for member
U0L1 at the gusset.
Solution A:
Design bolts connecting angles to column (shear and tension)
From Table 8-11, the number of 7⁄8-in. diameter A325-N bolts required
for shear only is
nmin =
Ru
φrn
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
TRUSS CONNECTIONS
11 - 101
111 kips
21.6 kips / bolt
= 5.14 → 6 bolts
=
Assuming an angle thickness of 5⁄8-in., bearing is not critical.
For a trial calculation, the number of bolts was increased to 12 in pairs at
3-in. spacing; the flexural strength of the angles was found to be insufficient.
Subsequently, the spacing was revised to 41⁄2-in. between the two rows of
bolts at the top and bottom of the connection as illustrated in Figure 11-31.
The eccentric moment at the faying surface is
Mu = Rue
= (111 kips)(6.10 in.)
= 677 kip-in.
For the bolt group of Figure 11-31, the moment of inertia and section
modulus are as follows.
I = Ab (Σd2)
= 0.6013 in.2 [(4 × (1.5 in.)2) + (4 × (4.5 in.)2) + (4 × (9 in.)2)]
= 249 in.4
I
S=
C
249 in.4
=
9 in.
= 27.7 in.3
and the maximum tensile force per bolt is
Mu
rut = A
S
677 kips − in.
(0.6013 in.2)
=
27.7 in.3
= 14.7 kips
Check design tensile strength of bolts
From LRFD Specification Section J3.7,
Ft = 117 ksi − 1.9fv ≤ 90 ksi
111 kips
= 117 ksi − 1.9
2
12 × 0.6013 in.
= 87.8 ksi
φrn = φFt Ab
= 0.75(87.8 ksi )(0.6013 in.2)
= 39.6 kips > 14.7 kips o.k.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
A
Sect. A-A
2ru t
4½
½
2
r ut + q u
2
r ut + q u
qu
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
qu
2¼
3 4½
3
4½ 3
2¼
1½
1½
A
Uo
4
(a)
5
1 ′–
11
1/
8
1 P–
L 7/16 ×16×1 ′–6
¼
/16
3
¼
Figure 11-31 (Part 1).
2L–4×4 × 5/ 8 ×1 ′–10½
Horizontal line
througth W.P.
2½
w.p.
C
L W12 ×50 Col.
6 1/ 8
1–WT8×38.5
–140 K
15/ 8
9 11/ 16
2L 4×3½× 3/8
(+174 K)
12
Grind only in way
of fitting angles
1¼
4
½
12
11 - 102
CONNECTIONS FOR TENSION AND COMPRESSION
Neutral axis of bolt group
C
L Col.
111 k
W.P.
(b)
140
k
Ru
3.25
xl = 0.36
(c)
al = 9.72
= 22.5
l
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
Figure 11-31 (Part 2).
6.10
(d)
x = 0.36
W.P.
3.64
r1
r2
ru
0.36
Mu
(e)
k l = 3.25
c.g.
rm
r3
Shear
force
11.25
11.25
Shear
force
9.72
TRUSS CONNECTIONS
11 - 103
= 22.5
l
17
4
k
22½
11 - 104
CONNECTIONS FOR TENSION AND COMPRESSION
Design angles (note angle thickness will be chosen to preclude prying
action, i.e., qu = 0, since bolt group has already been designed)
With rut = 14.7 kips and p = 41⁄2-in., try 2L4×4×5⁄8
b = 2 in. − 5⁄8-in.
= 1.38 in.
a = 4 in. − 2 in. ≤ 1.25b (for calculation purposes)
= 2 in.
1.25b = 1.25(1.38 in.)
= 1.73 in.
Thus, use a = 1.73 in. for calculation purposes.
b′ = b −
d
2
= 1.38 in. −
7⁄
8
− in.
2
= 0.943 in.
treq =
=
√
4.44rut b′
pFy
√
4.44 (14.7 kips)(0.943 in.)
(41⁄2jin.)(36 ksi)
= 0.616 in. < 0.625 in. o.k.
(Note: Alternatively, a lesser required angle thickness may be determined by designing the connection for pryng action, i.e., qu > 0.
Check shear yielding of the angles.
φRn = φ(0.6Fy ) Ag
= 0.9(0.6 × 36 ksi)(2 × 22.5 in. × 5⁄8-in.)
= 547 kips > 111 kips o.k.
Check shear rupture of the angles.
φRn = φ(0.6Fu ) An
= 0.75(0.6 × 58 ksi)[2 × (22.5 in. − 6 × 1 in.) × 5⁄8-in.]
= 538 kips > 111 kips o.k.
Check block shear rupture of the angles.
Agv = 2 × (221⁄2-in. − 21⁄4-in.)(5⁄8-in.)
= 25.3 in.2
Agt = 2 × (2 in. × 5⁄8 − in.)
= 2.50 in.2
Anv = 25.3 in.2 − 2 × [5.5(1 in.)(5⁄8 − in.)]
= 18.4 in.2
Ant = 2.5 in.2 − 2 × [0.5(1 in.)(5⁄8-in.)]
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
TRUSS CONNECTIONS
11 - 105
= 1.88 in.2
Since 0.6Fu Anv > Fu Ant ,
φRn = φ[0.6Fu Anv + Fy Agt]
= 0.75[0.6(58 ksi)(18.4 in.2) + (36 ksi)(2.50 in.2)]
= 548 kips > 111 kips o.k.
Use 2L4×4×5⁄8
Design angle-to-gusset connection
From LRFD Specification Table J2.4, the minimum weld size is 1⁄4-in.
From Table 8-42 with θ = 0°°
kl = 3.25 in.
l = 22.5 in.
3.25 in.
k =
22.5 in.
= 0.144
by interpolation, x = 0.017 and
al + xl = 10.1 in.
10.1 in. − 0.017 (22.5 in.)
a=
22.5 in.
= 0.432
By interpolation, C = 1.33 and
Ru
2 × CC1l
111 kips
=
2 × (1.33)(1.0)(22.5 in.)
=1.86 → 2 sixteenths
Dreq =
Use 1⁄4-in. fillet welds.
Solution B:
Design gusset
The gusset thickness must match that of the tee stem; approximately 7⁄16-in.
Check tension yielding of the gusset on the Whitmore section.
Lw = 4 in. + 2 × (11 in. × tan 30°°)
= 16.7 in.
φRn = φFy Ag
= 0.9(36 ksi)(16.7 in. × 7⁄16-in.)
= 237 kips > 174 kips o.k.
Check block shear rupture of the gusset.
From LRFD Specification Section J4.3,
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
11 - 106
CONNECTIONS FOR TENSION AND COMPRESSION
0.6Fu Anv = 0.6(58 ksi)(2 × 11 in. × 7⁄16-in.)
= 335 kips
Fu Ant = (58 ksi)(4 in. × 7⁄16-in.)
= 102 kips
Since 0.6Fu Anv > Fu Ant,
φRn = φ[0.6Fu Anv + Fy Agt]
= 0.75[335 kips + (36 ksi)(4 in. × 7⁄16-in.)]
= 299 kips > 174 kips o.k.
The gusset width must be such that the groove weld connecting it to
the stem of the tee can transfer the 140 kip force between the gusset
and the top chord (note that the slight slope of the top chord has been
ignored). The required length is
Lreq =
=
Ru
φ (0.6Fu ) t
140 kips
0.75 (0.6 × 58 ksi) (7⁄16 − in.)
= 12.3 in.
Use L = 16 in. to allow for weld runout and offset between the gusset
and tee stem at the end of the chord.
The gusset length depends upon the connection angles. From a scaled
layout, the gusset must extend 1′-6 below the tee stem.
Use PL7⁄16-in.×16 in.×1′-6. Note that fabricators may prefer to use 1⁄2-in.
plate from stock instead of ordering 7⁄16-in. plate. Were this the case,
the weld joining the angles to the tee stem could be increased slightly
to accommodate the resulting small gap.
Design weld connecting diagonal to gusset
From LRFD Specification Table J2.4, the minimum weld size is 3⁄16-in.
Try 3⁄16-in. fillet weld.
Lreq =
=
Ru
2 × D × 1.392
174 kips
2 (3 sixteenths)(1.392)
= 20.8 in.
Use 11 in. at the heel and 11 in. at the toe.
Check gusset thickness
For two 3⁄16-in. fillet welds
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
TRUSS CONNECTIONS
11 - 107
5.16D
Fy
5.16(3 sixteenths)
=
36 ksi
= 0.430 in. < 7⁄16-in. o.k.
tmin =
Truss Chord Splices
Truss chord splices are expensive to fabricate and should be avoided whenever possible.
In general, chord splices in ordinary building trusses are confined to cases where: (1) the
finished truss is too large to be shipped in one piece; (2) the truss chord exceeds the
available material length; (3) the reduction in member size of the chord justifies the added
cost of a splice; or, (4) a sharp change in direction occurs in working line of the chord
and bending does not provide a satisfactory alternative.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
11 - 108
CONNECTIONS FOR TENSION AND COMPRESSION
REFERENCES
American Institute of Steel Construction, Inc., 1984, Engineering for Steel Construction,
pp. 7.55–7.62, AISC, Chicago, IL.
American Institute of Steel Construction, Inc., 1989, Manual of Steel Construction—Allowable Stress Design and Plastic Design, AISC, Chicago, IL.
American Institute of Steel Construction, Inc., 1992, Manual of Steel Construction,
Volume II—Connections, ASD 9th Ed./LRFD 1st Ed., AISC, Chicago, IL.
Astaneh, A., 1985, “Procedure for Design Analysis of Hanger-Type Connections,”
Engineering Journal, Vol. 22, No. 2, (2nd Qtr.), pp. 63–66, AISC, Chicago, IL.
Bjorhovde, R. and S. K. Chakrabarti, 1985, “Tests of Full-Size Gusset Plate Connections,” Journal of Structural Engineering, Vol. 111, No. 3, (March), pp. 667–684,
ASCE, New York, NY.
DeWolf, J. T. and D. T. Ricker, 1990, Column Base Plates, AISC, Chicago, IL.
Fling, R. S., 1970, “Design of Steel Bearing Plates,” Engineering Journal, Vol. 7, No. 2,
(April), pp. 37–39, AISC, Chicago, IL.
Gross, J. L. and G. Cheok, 1988, Experimental Study of Gusseted Connections for
Laterally Braced Steel Buildings, National Institute of Standards and Technology
Report NISTIR 88-3849, NIST, Gaithersburg, MD.
Gross, J. L., 1990, “Experimental Study of Gusseted Connections,” Engineering Journal,
Vol. 27, No. 3, (3rd Qtr.), pp. 89–97, AISC, Chicago, IL.
Ishler, M., 1992, “Seismic Design Practice for Eccentrically Braced Frames,” Steel TIPS,
Structural Steel Education Council, Moraga, CA.
Kulak, G. L., J. W. Fisher, and J. H. A. Struik, 1987, Guide to Design Criteria for Bolted
and Riveted Joints, 2nd Edition, pp. 274–286, John Wiley & Sons, New York, NY.
Lindsay, S. D. and A. V. Goverdahn, 1989, “Eccentrically Braced Frames: Suggested
Design Procedures for Wind and Low Seismic Forces,” National Steel Construction
Conference Proceedings, pp. 17.1–17.25, AISC, Chicago, IL.
Murray, T. M., 1983, “Design of Lightly Loaded Column Base Plates,” Engineering
Journal, Vol. 20, No. 4, (4th Qtr.), pp. 143–152, AISC, Chicago, IL.
Popov, E. P., M.D. Englehardt, and J. M. Ricles, 1989, “Eccentrically Braced Frames:
U.S. Practice,” Engineering Journal, Vol. 26, No. 2, (2nd Qtr.), pp. 66–80, AISC,
Chicago, IL.
Popov, E. P. and R. M. Stephen, 1977, “Capacity of Columns with Splice Imperfections,”
Engineering Journal, Vol. 14, No. 1, (1st Qtr.), pp. 16–23, AISC Chicago, IL.
Richard, R. M., 1986, “Analysis of Large Bracing Connection Designs for Heavy
Construction,” National Steel Construction Conference Proceedings, pp. 31.1–31.24,
AISC, Chicago, IL.
Ricker, D. T., 1989, “Some Practical Aspects of Column Base Selection,” Engineering
Journal, Vol. 26, No. 3, (3rd Qtr.), AISC, Chicago, IL.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
REFERENCES
11 - 109
Ricker, D. T., 1992, “Value Engineering and Steel Economy,” Modern Steel Construction,
Vol. 32, No. 2, (February), AISC, Chicago, IL.
Thornton, W. A., 1985, “Prying Action—A General Treatment,” Engineering Journal,
Vol. 22, No. 2, (2nd Qtr.), pp. 67–75, AISC, Chicago, IL.
Thornton, W. A., 1990a, “Design of Small Base Plates for Wide-Flange Columns,”
Engineering Journal, Vol. 27, No. 3, (3rd Qtr.), pp. 108–110, AISC, Chicago, IL.
Thornton, W. A., 1990b, “Design of Small Base Plates for Wide-Flange Columns—A
Concatenation of Methods,” Engineering Journal, Vol. 27, No. 4, (4th Qtr.),
pp. 173–174, AISC, Chicago, IL.
Thornton, W. A., 1991, “On the Analysis and Design of Bracing Connections,” National
Steel Construction Conference Proceedings, pp. 26.1–26.33, AISC, Chicago, IL.
Thornton, W. A., 1992, “Designing for Cost Efficient Fabrication and Construction,”
Constructional Steel Design—An International Guide, (Chapter 7), pp. 845–854,
Elsevier, London, UK.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
12 - 1
PART 12
OTHER CONNECTIONS AND TOPICS
OVERVIEW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12-3
BRACKET PLATES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12-5
BEAM-WEB PENETRATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12-11
BUILT-UP MEMBERS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12-12
EFFECT OF CAMBER ON END CONNECTIONS . . . . . . . . . . . . . . . . . . . . 12-18
PURLIN AND GIRT CONNECTIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . 12-18
LATERAL BRACING OF STRUCTURAL MEMBERS . . . . . . . . . . . . . . . . . . 12-22
WALL ANCHORS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12-23
SHELF ANGLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12-23
REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12-25
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
12 - 2
OTHER CONNECTIONS AND TOPICS
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
OVERVIEW
12 - 3
OVERVIEW
Part 12 contains general information, design considerations, and examples for the following
detailed list of topics. It is based on the provisions of the 1993 LRFD Specification. Supplementary
information may also be found in the Commentary on the LRFD Specification.
BRACKET PLATES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12-5
BEAM-WEB PENETRATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12-11
BUILT-UP MEMBERS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12-12
Built-Up Girders . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12-12
Crane-Runway Girders . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12-13
Trusses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12-16
Built-up Columns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12-16
EFFECT OF CAMBER ON END CONNECTIONS . . . . . . . . . . . . . . . . . . . . 12-18
PURLIN AND GIRT CONNECTIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . 12-18
Girts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12-18
Purlins . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12-18
Sag Rods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12-21
LATERAL BRACING OF STRUCTURAL MEMBERS . . . . . . . . . . . . . . . . . . 12-22
WALL ANCHORS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12-23
SHELF ANGLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12-23
REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12-25
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
12 - 4
OTHER CONNECTIONS AND TOPICS
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
BRACKET PLATES
12 - 5
BRACKET PLATES
A bracket plate, illustrated in Figure 12-1, acts as a cantilevered beam. The design
strengths of the bolts and/or welds and connected elements must be determined in
accordance with the LRFD Specification; the applicable limit states are discussed in
Part 8. Additionally, the design must consider flexural yielding and rupture at the section
of maximum moment as well as local buckling and flexural yielding on the free edge of
the bracket.
In lieu of a more detailed analysis, Salmon and Johnson (1990) recommend that the
design strength of a triangular-shaped bracket plate in flexural yielding on the free edge
be determined as:
φPn = 0.85Fy zbt
where
2
b
b
b
z = 1.39 − 2.2 + 1.27 − 0.25
a
a
a
3
b = width of bracket plate as shown in Figure 12-1, in.
a = depth of bracket plate as shown in Figure 12-1, in.
t = thickness of bracket plate, in.
For flexural yielding, the design strength of the bracket plate is φMn where φ = 0.90,
and
Mn = Fy Sx
Pu = 54.0 kips
Pu = 54.0 kips
1 ′-0
3/
4
9 1/4
1/
4
1 1/2
K
b = 15 1/4
b = 14 3/4
(b) welded
(a) bolted
3
a = 18
a = 18
5@3=1 ′-3
1/
4
K
5 1/2
1 ′-0
3 1/4 8
K
K
1 1/2
2
3/
4
Fig. 12-1. Bracket plate.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
12 - 6
OTHER CONNECTIONS AND TOPICS
Table 12-1.
Net Elastic Section Modulus, Snet, in.3
Net elastic section modulus
taken along this line
Nominal Bolt Diameter, in.
# Bolts Bracket
in One Plate
Vertical Depth,
Row, n in.
2
3
4
5
6
9
12
15
6
7
8
9
10
18
21
24
27
30
12
14
16
18
20
3⁄
4
7⁄
8
1
Bracket Plate Thickness, in.
1⁄
4
3⁄
8
1⁄
2
1.17 1.76 2.34
2.50 3.75 5.00
4.36 6.54 8.72
6.75 10.1 13.5
9.67
13.1
17.1
21.6
26.7
5⁄
8
3⁄
4
3⁄
8
2.93
6.25
10.9
16.9
3.52
7.50
13.1
20.3
1.69 2.25 2.81
3.56 4.75 5.94
6.19 8.25 10.3
9.6 12.8 15.9
29.0
39.4
51.3
64.9
80.0
14.5
19.7
25.7
32.4
40.0
19.3
26.3
34.2
43.3
53.3
24.2
32.8
42.8
54.1
66.7
36
42
48
54
60
38.4 57.5
52.2 78.3
68.1 102
86.2 129
106 160
76.7
104
136
172
213
95.9
130
170
215
266
22
24
26
28
30
66
72
78
84
90
129
153
180
208
239
193
230
270
313
359
257
306
359
417
478
32
34
36
96
102
108
272
307
344
408
461
517
544
614
689
13.7
18.6
24.2
30.6
37.7
1⁄
2
5⁄
8
3⁄
4
3⁄
4
7⁄
8
1
3.38
7.13
12.4
19.1
3.94 2.16 2.70
8.31 4.50 5.63
14.4 7.78 9.7
22.3 12.0 15.0
3.23
6.75
11.7
18.0
3.77
7.88
13.6
21.0
4.31
9.00
15.6
24.0
27.4
37.1
48.4
61.1
75.4
31.9
43.3
56.4
71.3
87.9
25.7
34.9
45.4
57.4
70.7
30.0
40.7
53.0
66.9
82.5
34.3
46.5
60.6
76.5
94.3
18.3
24.8
32.3
40.8
50.3
22.8
30.9
40.3
50.9
62.8
115
157
204
259
319
54.2 72.3
73.7 98.3
96.2 128
122 162
150 200
90.3
123
160
203
250
108
147
192
243
300
322
383
449
521
598
386
459
539
625
718
182
216
254
294
338
242
288
338
392
450
303
360
423
490
563
680
768
861
816
922
1030
384
434
486
512
578
648
640
723
810
7⁄
8
1⁄
2
5⁄
8
17.2
23.3
30.3
38.3
47.2
21.4
29.1
37.9
47.8
58.9
126
172
224
284
350
67.8
92.2
120
152
188
84.7
115
150
190
235
102
138
180
228
282
119
161
210
266
329
136
184
241
304
376
363
432
507
588
675
424
504
592
686
788
227
270
317
368
422
284
338
396
460
528
341
405
476
552
633
398
473
555
644
739
454
541
634
736
844
768
867
972
896
1010
1130
480
542
608
600
678
760
720
813
912
840
949
1060
961
1080
1220
Notes
Diameter of holes assumed 1⁄8-in. larger than nominal bolt diameter.
Bolts spaced 3 in. vertically with 11⁄2-in. edge distance at top and bottom.
Interpolate for intermediate plate thicknesses. Otherwise, use general equation
Snet =
t 2 s2n (n2 − 1) (db + 0.125 in.)
d −
6
d
where
t = bracket plate thickness, in.
d = bracket plate depth, in.
s = bolt spacing, in.
n = number of bolts in one vertical row
db = nominal bolt diameter, in.
In the above equation, Sx is the gross elastic section modulus of the bracket plate.
For flexural rupture, the design strength of the bracket plate is φMn where φ = 0.75,
and
Mn = Fu Snet
In the above equation, Snet is the net elastic section modulus of the bracket plate. Table
12-1 gives values of the net elastic section modulus Snet for various hole diameters and
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
BRACKET PLATES
12 - 7
numbers of fasteners spaced three inches on center, the usual spacing for these connections.
Furthermore, local buckling will not occur (Salmon and Johnson, 1990) if, for
0.5 < b / a < 1.0,
b 250
≤
t
√Fy
nor if, for 1.0 ≤ b / a ≤ 2.0,
b 250
≤
t
√Fy
b
a
Two assumptions must be satisfied if this simplified approach is to be used. First, the
centroid of the applied load must be approximately 0.6b from the line of support (line K
in Figure 12-1a). Second, the lateral movement of the outstanding portion of the bracket
plate must be prevented.
Example 12-1
Given:
Refer to Figure 12-1a. Design a bracket plate to support the factored
force indicated. Use 7⁄8-in. diameter A325-N bolts. For the plate,
assume Fy = 36 ksi and Fu = 58 ksi.
Solution:
Select bolt group.
For 7⁄8-in. diameter A325-N bolts in single shear, φrn = 21.6 kips (Table
8-11). Thus,
Ru
φrn
54.0 kips
=
21.6 kips
= 2.50
Cmin =
From Table 8-20 with θ = 0°°, a 51⁄2-in. gage with s = 3 in., ex = 12 in.,
and n = 6 provides
C = 4.53 > 2.50 o.k.
Try PL 3⁄8-in.×18 in.
Check bolt bearing.
With lv = 11⁄2-in. and s = 3 in., φrn = 91.4 kips/bolt (Table 8-13)
Since this is greater than the single-shear strength of one bolt, bolt
bearing is not critical.
Check flexure in the bracket plate.
On line K, the required strength Mu is
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
12 - 8
OTHER CONNECTIONS AND TOPICS
Mu = Pu eb
= 54.0 kips (12 in. − 23⁄4-in.)
= 500 in.-kips
For flexural yielding on line K,
φMn = φFy Sx
(3⁄8−in.) (18 in.)2
6
= 656 in.-kips > 500 in.-kips o.k.
= 0.9 (36 ksi)
For flexural rupture on line K, with Snet = 13.7 in.3 from Table 12-1,
φMn = φFu Snet
= 0.75(58 ksi)(13.7 in.3)
= 596 in.-kips > 500 in.-kips o.k.
For flexural yielding on the free edge of the triangular plate,
2
3
b
b
b
z = 1.39 − 2.2 + 1.27 − 0.25
a
a
a
2
151⁄ −in.
151⁄4−in.
151⁄ −in.
+ 1.27 4
− 0.25 4
= 1.39 − 2.2
18 in.
18 in.
18 in.
= 0.286
φPn = 0.85Fy zbt
= 0.85(36 ksi)(0.286)(151⁄4-in.)(3⁄8-in.)
= 50.0 kips < 54.0 kips n.g.
Try PL 1⁄2-in.×18 in.
φPn = 0.85(36 ksi)(0.286)(151⁄4-in)(1⁄2-in.)
= 66.7 kips > 54.0 kips o.k.
Check local buckling of the bracket plate.
b 151⁄4−in.
=
= 0.847
a
18 in.
b
Since 0.5 ≤ < 1.0
a
√
Fy
tmin = b
250
√
36 ksi
= 151⁄4-in.
250
= 0.366 in. < 1⁄2-in. o.k.
Check shear yielding of the bracket plate.
φRn = φ(0.6Fy )Ag
= 0.9(0.6 × 36 ksi)(18 in.×1⁄2-in.)
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
3
BRACKET PLATES
12 - 9
= 175 kips > 54.0 kips o.k.
Check shear rupture of the bracket plate.
φRn = φ(0.6Fu )An
= 0.75(0.6 × 58 ksi)[18 − (6 × 1 in.)](1⁄2-in.)
= 157 kips > 54.0 kips o.k.
Check block shear rupture of the bracket plate (shear plane on line K,
tension plane across bottom two bolts).
Agv = (18 in. − 11⁄2-in.)(1⁄2-in.)
= 8.25 in.2
Anv = 8.25 in.2 − 5.5(1 in.)(1⁄2-in.)
= 5.50 in.2
Agt = (51⁄2-in. + 11⁄2-in.)(1⁄2-in.)
= 3.50 in.2
Ant = 3.50 in.2 − 1.5(1 in.)(1⁄2-in.)
= 2.75 in.2
Since 0.6Fu Anv > Fu Ant,
φRn = φ[0.6Fu Anv + Fy Agt]
= 0.75[0.6(58 ksi)(5.50 in.2) + (36 ksi)(3.50 in.2)]
= 238 kips > 54.0 kips o.k.
Example 12-2
Given:
Refer to Figure 12-1b. Design a bracket plate to support the factored
force indicated. Use 70 ksi electrodes. For the plate, assume Fy = 36 ksi
and Fu = 58 ksi.
Solution:
Select weld group assuming PL 1⁄2-in.×18 in.
Try “C”-shaped weld with kl = 3 in. and l = 18 in.
Interpolating from Table 8-42 with θ = 0°°,
x = 0.0221
and
al + xl = 111⁄4-in.
a(18 in.) + (0.0221 × 18 in.) = 111⁄4-in.
a = 0.603
Interpolating from Table 8-42 with θ = 0°°, k = 0.167, and a = 0.647,
C = 1.09
Thus, the weld size required for strength is
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
12 - 10
OTHER CONNECTIONS AND TOPICS
Dreq =
Pu
CC1l
54.0 kips
(1.09) (1.0) (18 in.)
= 2.75 → 3 sixteenths
=
Minimum weld size from LRFD Specification Table J2.4 is 3⁄16-in.
Therefore, use 3⁄16-in. fillet weld.
Check flexure on the bracket plate.
Conservatively taking the moment in the plate equal to the moment on
the weld group,
Mu = Pu (al)
= 54.0 kips (10.85 in.)
= 586 in.-kips
For flexural yielding of the plate,
φMn = φFy Sx
(1⁄2−in.) (18 in.)2
6
= 875 in.-kips > 586 in.-kips o.k.
= 0.9 (36 ksi)
For yielding on the free edge of the triangular plate,
2
3
b
b
b
z = 1.39 − 2.2 + 1.27 − 0.25
a
a
a
2
10.85 in.
10.85 in.
10.85 in.
+ 1.27
− 0.25
= 1.39 − 2.2
18 in.
18 in.
18 in.
= 0.381
φPn = 0.85Fy zbt
= 0.85 (36 ksi) (0.381) (10.85 in.) (1⁄2-in.)
= 63.2 kips > 54.0 kips o.k.
Check local buckling of the bracket plate.
b
10.85 in.
=
= 0.603
a
18 in.
b
Since 0.5 ≤ < 1.0
a
√
Fy
tmin = b
250
√
36 ksi
= 10.85 in.
250
= 0.260 in. < 1⁄2-in. o.k.
Check shear yielding of the bracket plate.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
3
BEAM-WEB PENETRATIONS
12 - 11
φRn = φ(0.6Fy )Ag
= 0.9 (0.6 × 36 ksi) (18 in.×1⁄2-in.)
= 175 kips > 54.0 kips o.k.
BEAM-WEB PENETRATIONS
Beam-web penetrations, illustrated in Figure 12-2, may be used to accommodate the
passage of ductwork and/or other utilities. This integration of structural and other building
systems minimizes story height, reducing cost and maximizing the number of stories that
can be built when height limitations exist. Beam-web penetrations are usually rectangular, although circular openings are sometimes used; the latter are analyzed as an equivalent rectangular opening.
Depending upon the size and location of the beam-web penetration, stiffeners may or
may not be required based on an ultimate strength evaluation of flexure, shear, and the
interaction between them on the reduced section. High local stress concentrations at the
corners of beam-web penetrations preclude the usefulness of elastic analysis.
Stiffening requirements can be minimized by selecting a favorable location for the
beam-web penetrations. In general, the most significant effect of an opening is a reduction
in shear strength. A beam-web penetration, then, should be located in a region of low
shear when possible; avoid locations near beam-support reactions where shear is high.
(a) Steel beam, unreinforced
(c) Composite beam (solid slab),
unreinforced
(b) Steel beam, reinforced
(d) Composite beam (slab on
transverse deck), unreinforced
(e) Composite beam (slab on
longitudinal deck), reinforced
Fig. 12-2. Beam-web penetrations.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
12 - 12
OTHER CONNECTIONS AND TOPICS
Since an opening also reduces the flexural strength, regions of high moment should also
be avoided.
When stiffening is required, various reinforcing schemes have been used, including
horizontal stiffeners, vertical stiffeners, and stiffeners around the entire periphery of the
opening. However, horizontal stiffeners above and below the opening, as illustrated in
Figures 12-2b and 12-2e, can effectively and economically provide the needed reinforcement. More elaborate schemes are unnecessary.
A summary of past research in beam-web penetrations in both steel and composite
beams and the resulting design procedures is available in the AISC Design Guide Steel
and Composite Beams with Web Openings (Darwin, 1990). These procedures are also
available electronically as WEBOPEN, AISC’s computer program. Although the complete design of a beam-web penetration is beyond the scope of this Manual, some general
guidelines for proportioning and detailing taken from the aforementioned Design Guide
are presented below. Refer to the Design Guide for more specific information.
1. Steel yield strength is limited to 65 ksi (specified minimum value), and sections
must meet the compact-section requirements of LRFD Specification Section B5.1.
2. Opening depth cannot exceed 70 percent of the member depth.
3. Multiple openings in the same member should be spaced far enough apart so that
they will not interact; otherwise the beam must be treated as a castellated beam.
4. The edge of an opening should be no closer to a support than the member depth d.
5. Concentrated loads should not be placed above beam-web penetrations; the load
may be placed a distance d or d/2 from the edge of an opening, depending on the
depth-to-thickness ratio of the web and the width-to-thickness ratio of the flange.
Refer to the Design Guide.
6. In most cases, the reinforcement may be placed on only one side of the web. It should
be placed as closely as possible to the top and bottom edges of the opening, but with
adequate room for fillet welds. It must extend past the opening the required distance,
and by at least one-quarter of the length of the opening.
7. Fillet welds should be continuous, placed on one or both sides of the reinforcement
within the length of the opening, but placed on both sides of the reinforcement that
extends past the opening. The welds must be sized to develop the required strength,
both within the opening and at the extensions.
8. The corners of openings should have a minimum radius of at least twice the web
thickness, or 5⁄8-in., whichever is greater.
9. For composite beams, the slab reinforcement and the shear connector locations are
important considerations.
BUILT-UP MEMBERS
Industrial buildings, as well as some other specialized building types, sometimes require
clear spans and/or heavy loadings which preclude the use of rolled shapes. When this is
the case, built-up members made from plates and/or shapes are often used. A complete
reference on built-up members and other topics in industrial buildings is available in the
AISC Design Guide Industrial Buildings—Roofs to Column Anchorage (Fisher, 1993).
Following is a general overview of built-up members: girders, crane-runway girders,
trusses, and columns.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
BUILT-UP MEMBERS
12 - 13
Built-Up Girders
The simplest type of built-up girder is one in which a rolled beam is reinforced by the
addition of coverplates to its flanges, as shown in Figure 12-3a. Deeper girders, built up
entirely from plates, are shown in Figures 12-3b and 12-3c. The girder of Figure 12-3b
is comprised of a web plate and two flange plates. Each flange usually is made of a single
thickness of plate, but plates of varying thickness may be spliced end-to-end with groove
welds to provide greater strength in areas of high moment. The box girder in Figure 12-3c
is comprised of two web plates and two flange plates. Box girders are particularly useful
where lateral stability and torsional resistance are required.
Crane-Runway Girders
In addition to vertical wheel loads, overhead cranes in buildings impose substantial lateral
and longitudinal forces on their supports. To provide for the necessary strength, cranerunway girders, as illustrated Figure 12-4a, are typically built-up using a rolled beam
with a channel attached horizontally to its top flange; the channel provides lateral bending
strength. Bolts or welds connecting the channel to the beam must be of sufficient strength
to ensure that these two components act together in resisting both the vertical and
horizontal forces. The use of intermittent fillet welds could be investigated as an
alternative, but some codes require a continuous weld.
When lateral crane loads exceed the strength of a channel, the top flange of the girder
may be connected to a separate longitudinal member which functions as a horizontal
girder, as illustrated in Figure 12-4b. The web of this girder may be solid or composed
of lacing bars or angles to form a lattice girder; a solid web will also serve as an inspection
or access walkway. Note that the horizontal plate is interrupted at the column center and
there is no direct connection between the tops of the abutting crane girders, avoiding
continuity.
Heavy crane loads sometimes require built-up girders (illustrated in Figure 12-4b) for
greater strength. In built-up crane-runway girders, when the web plate and flange plate
are in tight contact before welding, wheel loads will be transferred through bearing
directly into the web. This may be accomplished by edge planing the web or by trimming
the web with a mechanically guided torch; either process will provide the smooth straight
edge necessary for continuous tight contact. If tight contact does not exist, the flange-toweb welds must be designed to transfer concentrated loads from the crane wheels.
Additionally, transverse bending of the top flange under heavy crane loads has led to
fatigue failures in fillet-welded joints. Consequently, many designers require a complete-
(a) Rolled beam
(b) Built-up girder
(c) Built-up box girder
with coverplates
Fig. 12-3. Built-up girders.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
12 - 14
OTHER CONNECTIONS AND TOPICS
joint-penetration groove weld for the joint of top plate-to-web for an active crane,
particularly for heavy cranes.
Crane-runway girders supporting heavy loads should be designed as simple spans;
continuous construction is not desirable. Longitudinal forces usually are distributed
through lateral bracing located in the plane of the crane columns. Note that knee braces
under crane-runway girders are usually avoided unless the resulting intermediate support
(and potential for resulting continuity) are considered in the design.
Standard holes in plates, slotted holes in angle
to prevent dirt accumulation. Plates on top to
allow for shimming should future settlement
require leveling of crane runway. Bolts snugtightened and backed off one turn, spike threads.
1 in.
returns
at ends
SECT. A
Bolt
Walk Plate or
Horizontal Girder
Crane Girder
(a)
Fig. 12-4. Typical crane-runway girders.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
(b)
Stiffening Channel
Roof
Column
Roof Column
A
BUILT-UP MEMBERS
12 - 15
While the design of crane-runway girders is beyond the scope of this volume, following
are some general recommendations and sources of further information. The design of
crane-runway girders must be in accordance with the LRFD Specification, but may
additionally be controlled by the Guide for the Design and Construction of Mill Buildings—Technical Report No. 13 (AISE, 1969), AWS (1991), or the Standard Specifications
for Highway Bridges (AASHTO, 1992). Additionally, fatigue must be considered in the
design of crane-runway girders. Refer to the AISC publication Bridge Fatigue Guide
Design and Details (Fisher, 1977); while this book was developed specifically as a guide
for highway and railroad bridge design, it is equally applicable to crane girders. Additionally, refer to Fisher (1993) and Ricker (1982) for practical considerations in crane
runway girders.
The crane rail may be fastened to the crane runway girder with bolted clamp plates,
J-bolts, or other proprietary devices. The crane rail should not be welded directly to the
crane-runway girder. The floating-type rail clamp, which is specified frequently, permits
both longitudinal and lateral movement to accommodate thermal and alignment adjustments. Typical details, including proprietary items, for each particular case must be
supplied by the designer.
A typical end connection, as shown in the plan view of Figure 12-4a, is designed to
allow for the necessary end rotation of the crane-runway girder. Short-slotted holes in the
angles with snug-tightened bolts backed off one turn (threads spiked) are used to alleviate
fatigue cracking in the connection. Other details can be used (Ricker, 1982).
Bearing stiffeners should be used where required and must be finished to bear or
welded sufficiently to transmit the reaction. Stiffeners should be used in pairs on each
side of the web and should be welded to the top flange to prevent flange rotation.
Intermediate stiffeners should be cut to clear the bottom flange by four to six times the
web thickness, but not less than two inches. The stiffener corner at the juncture of the
flange and web should be clipped to avoid intersecting welds and a reduction in fatigue
strength. This clip should be four to six times the web thickness, with a 2-in. minimum.
Stiffeners frequently are required to be punched for brackets (usually supplied by others)
to support the electrical conductors from which the crane draws its power. The designer
should obtain this information from the electrical contractor and show it on the design
drawings.
Local stresses in the upper web plate, due to large concentrated wheel loads, can be
critical to the life of a girder. These local stresses are normal to the flexural stresses and
are compressive. The web plate adjacent to the weld may be subject to a residual tensile
stress that is at or near the yield strength of the material. Since each passage of a crane
wheel can reduce the residual tensile stress, the result is a cyclical loading in the tensile
range in this area which must be considered in the design.
The crane runway must be kept almost exactly straight for safe operation and minimum
wear on the crane wheels and rails. Crane stops are always provided at both ends of each
line rail. These shock absorbing devices are used to stop the crane and to provide a means
of realigning a crane which has become skewed slightly on its runway; the resulting forces
must be considered in the design.
If crane stops are attached to the girders and the crane rail ends near the face of the
stop, the total length of the rail is shortened by several inches. Since crane rails are not
usually shop-fabricated items, this must be accounted for when ordering the rails and
splice plates. For light-duty cranes, where the stops are clamped to the rails, the rails are
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
12 - 16
OTHER CONNECTIONS AND TOPICS
ordered for the full length of the runway. Medium- and heavy-duty crane rails are usually
ordered with “tight joints.” Refer also to the discussion of crane rails in Part 1.
Rails are usually ordered as two runs of the total length necessary. Frequently, it is
stipulated that not more than one rail in each run be less than the standard length of either
33 ft or 39 ft. It is good practice to stagger the rail joints on opposite sides of the runway
by ordering one odd-length piece for each line of rail, to be placed at opposite ends of
the runway.
Trusses
Because of their greater depth, trusses usually provide a greater stiffness and, therefore,
reduced deflection when compared by weight with rolled or built-up girders of equal
strength. Six general types of trusses frequently used in building frames are shown in
Figure 12-5.
The Pratt truss of Figure 12-5a and the Warren truss of Figure 12-5c (and modifications
of these types shown in Figures 12-5b and 12-5d) are commonly used as the principal
supporting members in floor and roof framing. Note that the Pratt and Warren trusses
shown have a top chord which is not quite parallel with the bottom chord. Such an
arrangement is used to provide a slope for drainage on “flat” roofs. Most of the
connections for the roof beams or purlins supported by these trusses can be identical.
This would not be the case if the top chord were truly level and the elevation of the purlins
had to be varied. When used in floor framing, the Pratt and Warren trusses are designed
with parallel chords.
The Fink truss of Figure 12-5e and the Scissors truss of Figure 12-5h, (and modifications of these types shown in Figures 12-5f, 12-5g, and 12-5i) serve a similar function in
symmetrical roofs having a pronounced pitch.
As discussed previously in Part 11, truss chord and web members are placed with the
work lines intersecting at common panel points, resulting in purely axially loaded
members when loads are applied only at the panel points of the trusses. Two exceptions
follow.
The Bowstring truss of Figure 12-5j is used to support a curved roof. The deviation of
the arched top chord from a straight line between panel points will produce a moment.
The Vierendeel truss of Figure 12-5k is used to provide free passage through deep floor
trusses or an orderly and orthogonal arrangement for exposed steelwork. In the absence
of diagonal members, the members in a Vierendeel truss are subjected to both axial forces
and flexure; the truss-member connections must be adequate to transfer the required
moment and the design details of all joint connections must be shown by the design
engineer.
In any truss, when vertical loads are imposed at locations other than at panel points,
bending moments result. For example, the forces not at panel points in Figure 12-5c create
moment in the top chord members which must be considered in addition to the direct
compressive force in the top chord. Ordinarily, if loads must be supported at these
intermediate points, vertical struts are usually placed under them in the truss to transmit
the load directly to the joint or panel point in the bottom chord, as indicated in Figure
12-5d. Similarly, if loads are applied away from panel points to the bottom chord,
additional vertical tension members are added as indicated by the dashed lines in Figure
12-5d.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
BUILT-UP MEMBERS
12 - 17
Built-Up Columns
+
-
-
+
(d) Warren
+
+
+
-
-
+
(f) Fink
Top Chord
+ -
-
-
(e) Fink
(g) Fink
-
-
Top
Chord
+
+
-
-
-+
-
+
-+
+
+
+
+
-
(c) Warren
Web
Member
+
-
-
+
+
(b) Pratt
-
+
-
+
+
+
-
-
+
+
-
-
-
-
-
Bottom
Chord
+
+
-
(a) Pratt
-
-
+
-
Web
Member
Top
Chord
+
-
-
-
-
+
+
+
+
-
-
-
-
-
-
Built-up columns of the types shown in Figure 12-6 support the transverse beams, girders
or trusses, crane-runway girders, and other structural members in an industrial building.
When the construction is relatively light, single-shaft columns, either one-piece or
(h) Scissors
(i) Scissors
+ Denotes tension stress
- Denotes compression stress
(j) Bowstring
(k) Vierendeel
Fig. 12-5. Typical trusses.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
-
12 - 18
OTHER CONNECTIONS AND TOPICS
stepped, may be used as shown in Figures 12-6a and 12-6b. The use of a bracket support
for a crane-runway girder such as shown in Figure 12-6a usually is limited to about a
75-kip factored reaction.
For heavy mill buildings with heavy bridge cranes, the double- and triple-shaft
columns shown in Figures 12-6c and 12-6d, respectively, provide a means of separately
supporting the crane girder reactions and the roof girder or truss loads. The multiple shaft
columns consist of one or two crane columns tied to the building columns by diaphragms.
Refer to the AISC Design Guide Industrial Buildings—Roofs to Column Anchorage
(Fisher, 1993).
EFFECT OF CAMBER ON END CONNECTIONS
Note that when a cambered beam bearing on a wall or other support is loaded, expansion
of the unrestrained end must be considered. In Figure 12-7a, the end will move a distance
∆, where
∆=
4Cd
L
If instead the cambered beam is supported on a simple shear connection at both ends,
the top and bottom flange will each move a distance of one-half ∆ since end rotation will
occur approximately about the neutral axis. The designer should be aware of the
magnitude of these movements and make provisions to accommodate them. Figure 12-7a
considers the geometry of a girder in the horizontal position, and Figure 12-7b illustrates
the condition when the girder is not level.
In general for building design, connections are fabricated square with the cambered
beam end.
PURLIN AND GIRT CONNECTIONS
Girts
Girts, usually channels or angles, transfer wind forces from the siding to the columns.
Intermediate wind columns are sometimes provided to reduce the unsupported length of
girts. In general, channel girts should be placed with the toes down, to avoid collecting
dirt and debris. Openings for doors and sash, however, will sometimes require that
channel girts toe up.
Since the gravity load of the siding and girts is carried to the eave struts through a
system of sag rods, each girt should be designed as a beam resisting the wind load incident
upon its tributary area. As a common rule of thumb, girts supporting typical metal siding
should be proportioned such that their depth in the direction of the wind load is not less
than 1⁄60 of the span; girts supporting steel sash should be proportioned such that their
depth is not less than 1⁄48 of the span. Wind columns for girts supporting metal sheeting
are frequently proportioned for a ratio of depth-to-length of 1⁄32. More stringent requirements may be required in areas of high wind or buildings with blast-pressure exposures.
Figure 12-8 shows a typical girt-to-column connection in which a clip angle is bolted
or welded to the column flange and positioned to avoid coping the girt. Since the sag rods
transfer the gravity forces, this is a nominal connection and two bolts are normally used
at each girt end. When girt alignment is critical, e.g., at sash or wall panels, it is good
practice to provide a clearance of 1⁄4-in. to 1⁄2-in. between the face of the column and the
back of the girt with slotted holes for adjustment.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
PURLIN AND GIRT CONNECTIONS
12 - 19
Purlins
Purlins, usually W shapes or channels, transfer roof loads to the major structural elements
supporting the roof; the type and spacing of purlins is a design consideration which
depends upon the incident roof loads as well as the limiting lengths of sheeting to be used.
(a) One-piece column
(b) Stepped column
(c) Double-shaft column
(d) Triple-shaft column
Fig. 12-6. Built-up columns.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
12 - 20
OTHER CONNECTIONS AND TOPICS
Distances approximately
equal for small angles
Distances equal for
parabolic curve, approximately
equal for circular curve.
See sketch below.
∆
∆
θ
d
C
90°
C
L
/2
∆
L
/2
tanθ = 2C
L
Fixed
End
/2
C
∆ = d tanθ
Unrestrained
End
∆ = 4Cd
L
θ
2θ for circular curve
2C for parabolic curve
(a) Beam or Girder Ends at
Same Elevation
∆=
4Cd
L
∆=
∆=
4Cd
L
∆=
L
A
B
Grade
angle
B
L
L approx
.
(b) Beam or Girder Ends at
Different Elevations
Fig. 12-7. Camber for beams and girders.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
B
A+B
A
B
A
90
Horiz. line
Vert.
A
°
C
B
°
e
90
A+B
A
Grade lin
B
d
A
4Cd
4Cd
L
PURLIN AND GIRT CONNECTIONS
12 - 21
When channels are used on a sloping roof, the channel should toe upward to permit the
erector to walk on the member. Additionally, a channel that is toed upward will be more
nearly loaded through its shear center by the gravity roof loads. When corrosion is a
consideration, however, the channel should toe down, despite the inconvenience and
additional expense of erection.
Roof purlins supporting metal sheeting are frequently proportioned for a ratio of
depth-to-length of 1⁄32. Other materials, unusual loadings, or deflection requirements must
be investigated by the designer.
When channels are used, the ridge purlin is placed as close to the peak of the truss as
possible in order to shorten the connection to the purlin on the opposite side of the
centerline (see Figure 12-9). This also serves to decrease the overhang of the roof sheeting
where it extends beyond the purlin to the ridge.
Sag Rods
Sag rods are usually furnished to transmit the gravity load of girts to a supporting member.
Additionally, sag rods are used to control the deflection of and stiffen girts and purlins.
Typical sag rods are 5⁄8-in. or 3⁄4-in. in diameter with lines spaced approximately six to
eight feet apart.
To be effective, the force in the sag rods must be carried across the roof ridge and must
be balanced by a corresponding force on the opposite side of the ridge. Several ridgepurlin connections are illustrated in Figure 12-9. Ridge purlins also are fastened together
at other points along their length to increase their transverse stiffness, and thus permit
them to be more effective if also used as struts.
cL Column
Column cL
Girt lines
Girts
Column flange
(channels shown)
Note: Locate girt lines to
avoid blocking girts
when possible.
Fig. 12-8 Typical girt end connection.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
12 - 22
OTHER CONNECTIONS AND TOPICS
Sag rods efficiently distribute gravity forces in the girts or purlins. Sag rods are useful
for buildings of moderate width and height and near symmetrical dimension. The gravity
loads of the siding are carried up sequentially; each sag rod carries the force of the
previous rod plus the additional gravity load of the girt between them. This may continue
up to the eave strut and through the roof slope to the ridge where the horizontal
components of the gravity forces from either side of the building then offset for both the
siding and the roofing. The sag rods are installed in each space and a suitable diaphragm
is used at the ridge strut for load transfer. To avoid double punching the purlins, the
sag-rod size should not exceed the size of the field bolts.
Sag rods are not usually required to be bent, since the slope gradient is usually quite
small. Sag rods are usually connected with one nut on each end. If oversized holes are
present, a washer should be used.
For the single diagonal sag rod shown in Figure 12-10a, four to six 8 in. nominal
channel girts can generally be carried on a bay size of 20 to 25 feet before excessive twist
occurs. Alternatively, girts may be stabilized with blocking or by other means. Otherwise,
double diagonal sag rods should be used as illustrated in Figure 12-10b.
Negative wind pressure will cause compression in the interior flange of girts and
purlins. When the exterior flange is laterally supported by the siding, sag rods can be used
to provide lateral support to the inside flange of girts and purlins at intermediate positions
if hole pattern A, illustrated in Figure 12-11, is used. Hole pattern B does not provide this
same control. For single diagonal sag rods, a nut must be placed on the sag rod on both
sides of the girt or purlin. Double diagonal sag rods are a tension-only system and
therefore do not require double nuts.
LATERAL BRACING OF STRUCTURAL MEMBERS
In general, concrete slabs and concrete slabs on metal deck provide adequate lateral
bracing to the compression flange of a beam. However, the question remains, how to
design bracing for the compression flange of a beam not restrained by a slab or for a
column or other compression member when it is required.
To provide adequate lateral restraint, the brace must possess both sufficient strength
and stiffness. An approximate and conservative procedure of long practice is to design
the brace to resist a force of two percent of the factored compressive force in the restrained
member.
Several more rigorous empirical approaches have been proposed: (1) cross bracing,
which depends on the axial stiffness of the brace to prevent relative lateral movement of
two points on the braced member; (2) single-point or discreet bracing, which depends
upon the flexural stiffness of transversely framed bracing members; (3) continuous
bracing, provided by light-gage metal decking or other material; and, (4) leaning column
Bent Rod with
4 nuts
1 PL
2L
2L
Fig. 12-9 Typical connections between ridge purlins.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1 PL
SHELF ANGLES
12 - 23
bracing, wherein two or more compression members are linked at one or more points
along their length requiring buckling to occur simultaneously in all linked members.
These analyses are beyond the scope of this volume. The first three approaches are
detailed in Salmon and Johnson (1990); Geschwindner (1993) summarizes and compares
three approaches to leaning-column bracing taken by Yura (1971), Lim and McNamara
(1972), and LeMessurier (1977).
WALL ANCHORS
Figure 12-12 illustrates two common types of wall anchors. For the design of concrete
embedments, refer ACI 349.
SHELF ANGLES
Figure 12-13 illustrates typical shelf angle configurations which provide for adjustment.
Slotted holes may be used to provide for horizontal and/or vertical adjustment. Alternatively, shims may be used to provide vertical adjustment. Alignment tolerances are
specified in AISC Code of Standard Practice Section 7.11.3.3.
Girt
Siding
Girt
Siding
(a) Single Diagonal
Sag Rods
(b) Double Diagonal
Sag Rods
Fig. 12-10. Sag rods.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
12 - 24
OTHER CONNECTIONS AND TOPICS
Channel
B
A
Fig. 12-11. Hole patterns for sag rods in girts and purlins.
2
Angles:
4x4x 3/8 x3
2 1/2
10 ″
and under
12 ″
and over
Weld or bolt
7
1 ′-6
3 3/8
3/
4 ″ dia.
(a) Angle wall anchors
rod
(b) Government wall anchor
Fig. 12-12. Wall anchors.
Clip angle
Clip angle
(slot both legs
for adjustment)
Bolt heads
this side
Clip angle
Bolt heads
this side
Shelf angles (continuous)
Fig. 12-13. Shelf angles.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
Detail
of shim
/8 ″ slotted shims
1
Slot for horizontal
adjustment
REFERENCES
12 - 25
REFERENCES
American Association of State Highway and Transportation Officials, 1992, Standard
Specifications for Highway Bridges, AASHTO, Washington, DC.
American Welding Society, 1991, Welding Handbook, AWS, Miami, FL.
Association of Iron and Steel Engineers, 1969, Guide for the Design and Construction
of Mill Buildings—Technical Report No. 13, AISE, Pittsburgh, PA.
Darwin, D., 1990, Steel and Composite Beams with Web Openings, AISC, Chicago, IL.
Fisher, J. M., 1993, Industrial Buildings—Roofs to Column Anchorage, AISC, Chicago, IL.
Fisher, J. W., 1977, Bridge Fatigue Guide Design and Details, AISC, Chicago, IL.
Geschwindner, L. F., 1993, “The Leaning Column in ASD and LRFD,” Proceedings of
the 1993 National Steel Construction Conference, pp. 19.1–19.17, AISC, Chicago, IL.
LeMessurier, W. J., 1977, “A Practical Method of Second Order Analysis,” Engineering
Journal, Vol. 14, No. 2, (2nd Qtr.), pp. 49–67, AISC, Chicago, IL.
Lim, L. C. and R. J. McNamara, 1972, “Stability of Novel Building System,” Structural
Design of Tall Steel Buildings, Volume II-16, Proceedings of the ASCE-IABSE International Conference on the Planning and Design of Tall Buildings, pp. 499–524,
ASCE, New York, NY.
Ricker, D. T., 1982, “Tips for Avoiding Crane Runway Problems,” Engineering Journal,
Vol. 19, No. 4, (4th Qtr.), pp. 181–205, AISC, Chicago, IL.
Salmon, C. G. and J. E. Johnson, 1990, Steel Structures—Design and Behavior, Third
Edition, Harper & Row, New York, NY.
Yura, J. A., 1971, “The Effective Length of Columns in Unbraced Frames,” Engineering
Journal, Vol. 8, No. 2, (2nd Qtr.), pp. 37–42, AISC, Chicago, IL.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
13 - 1
PART 13
CONSTRUCTION INDUSTRY ORGANIZATIONS
OVERVIEW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13-2
PRIVATE AND NON-GOVERNMENT-RELATED ORGANIZATIONS . . . . . . . . . . 13-5
FEDERAL AND STATE GOVERNMENT AND RELATED AGENCIES . . . . . . . . . 13-19
FOREIGN ORGANIZATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13-21
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
13 - 2
CONSTRUCTION INDUSTRY ORGANIZATIONS
OVERVIEW
Part 13 lists private construction industry, government and government related, and foreign
organizations which are potential sources of technical information for those engaged in steel design,
detailing, fabrication, erection, project management, and building operation.
Following is a summary of the organizations listed. Statements which appear in the text of this
Part were provided in whole or part by the respective organizations.
PRIVATE AND NON-GOVERNMENT-RELATED ORGANIZATIONS . . . . . . . . . . 13-5
Aluminum Association (AA) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13-5
American Concrete Institute (ACI) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13-5
American Galvanizers Association (AGA) . . . . . . . . . . . . . . . . . . . . . . . . . 13-5
American Institute for Hollow Structural Sections (AIHSS) . . . . . . . . . . . . . . . . 13-5
American Institute of Architects (AIA) . . . . . . . . . . . . . . . . . . . . . . . . . . . 13-6
American Institute of Mining, Metallurgical, and Petroleum Engineers (AIME) . . . . . 13-6
American Institute of Steel Construction (AISC) . . . . . . . . . . . . . . . . . . . . . 13-6
American Institute of Timber Construction (AITC) . . . . . . . . . . . . . . . . . . . . 13-6
American Iron and Steel Institute (AISI) . . . . . . . . . . . . . . . . . . . . . . . . . . 13-7
American National Standards Institute (ANSI) . . . . . . . . . . . . . . . . . . . . . . . 13-7
American Nuclear Society (ANS) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13-7
American Petroleum Institute (API) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13-7
American Railway Engineering Association (AREA) . . . . . . . . . . . . . . . . . . . 13-7
American Society for Metals International (ASMI) . . . . . . . . . . . . . . . . . . . . 13-8
American Society for Nondestructive Testing (ASNT) . . . . . . . . . . . . . . . . . . 13-8
American Society for Testing and Materials (ASTM) . . . . . . . . . . . . . . . . . . . 13-8
American Society of Civil Engineers (ASCE) . . . . . . . . . . . . . . . . . . . . . . . 13-8
American Society of Mechanical Engineers (ASME) . . . . . . . . . . . . . . . . . . . 13-8
American Water Works Association (AWWA) . . . . . . . . . . . . . . . . . . . . . . . 13-9
American Welding Institute (AWI) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13-9
American Welding Society (AWS) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13-9
Association of American Railroads (AAR) . . . . . . . . . . . . . . . . . . . . . . . . . 13-9
Association of Iron and Steel Engineers (AISE) . . . . . . . . . . . . . . . . . . . . . 13-10
Building Officials and Code Administrators International (BOCA) . . . . . . . . . . . 13-10
Concrete Reinforcing Steel Institute (CRSI) . . . . . . . . . . . . . . . . . . . . . . . 13-10
Construction Specifications Institute (CSI) . . . . . . . . . . . . . . . . . . . . . . . . 13-10
Corrugated Steel Pipe Institute (CSPI) . . . . . . . . . . . . . . . . . . . . . . . . . . 13-11
Crane Manufacturers Association of America (CMAA) . . . . . . . . . . . . . . . . . 13-11
Electronic Industries Association (EIA) . . . . . . . . . . . . . . . . . . . . . . . . . 13-11
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
OVERVIEW
13 - 3
Engineering Foundation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13-11
Factory Mutual Engineering and Research Company . . . . . . . . . . . . . . . . . . . 13-11
Gypsum Association . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13-11
Industrial Fasteners Institute (IFI) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13-11
Institute of the Ironworking Industry (III) . . . . . . . . . . . . . . . . . . . . . . . . . 13-12
International Conference of Building Officials (ICBO) . . . . . . . . . . . . . . . . . . 13-12
Iron and Steel Society (ISS) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13-12
James F. Lincoln Arc Welding Foundation (JFLF) . . . . . . . . . . . . . . . . . . . . . 13-12
Material Handling Industry (MHI) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13-13
Materials Properties Council (MPC) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13-13
Metal Building Manufacturers Association (MBMA) . . . . . . . . . . . . . . . . . . . 13-13
Metal Construction Association (MCA) . . . . . . . . . . . . . . . . . . . . . . . . . . 13-13
National Association of Architectural Metals Manufacturers (NAAMM) . . . . . . . . . 13-13
National Association of Corrosion Engineers (NACE) . . . . . . . . . . . . . . . . . . 13-13
National Concrete Masonry Association (NCMA) . . . . . . . . . . . . . . . . . . . . . 13-14
National Corrugated Steel Pipe Association (NCSPA) . . . . . . . . . . . . . . . . . . . 13-14
National Erectors Association (NEA) . . . . . . . . . . . . . . . . . . . . . . . . . . . 13-14
National Fire Protection Association (NFPA) . . . . . . . . . . . . . . . . . . . . . . . 13-14
National Fire Sprinkler Association (NFSA) . . . . . . . . . . . . . . . . . . . . . . . . 13-14
National Institute of Steel Detailing (NISD) . . . . . . . . . . . . . . . . . . . . . . . . 13-15
National Society of Architectural Engineers (NSAE) . . . . . . . . . . . . . . . . . . . 13-15
Nickel Development Institute (NiDI) . . . . . . . . . . . . . . . . . . . . . . . . . . . 13-15
Portland Cement Association (PCA) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13-15
Post-Tensioning Institute (PTI) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13-15
Prestressed Concrete Institute (PCI) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13-15
Southern Building Code Congress International (SBCCI) . . . . . . . . . . . . . . . . . 13-16
Steel Deck Institute (SDI) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13-16
Steel Joist Institute (SJI) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13-16
Steel Plate Fabricators Association (SPFA) . . . . . . . . . . . . . . . . . . . . . . . . 13-16
Steel Service Center Institute (SSCI) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13-17
Steel Structures Painting Council (SSPC) . . . . . . . . . . . . . . . . . . . . . . . . . 13-17
Steel Tank Institute (STI) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13-17
Steel Tube Institute of North America (STI) . . . . . . . . . . . . . . . . . . . . . . . . 13-17
Structural Stability Research Council (SSRC) . . . . . . . . . . . . . . . . . . . . . . . 13-18
Underwriters Laboratories Inc. (UL) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13-18
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
13 - 4
CONSTRUCTION INDUSTRY ORGANIZATIONS
Welding Research Council (WRC) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13-18
FEDERAL AND STATE GOVERNMENT AND RELATED AGENCIES . . . . . . . . 13-19
Army Corps of Engineers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13-19
American Association of State Highway and Transportation Officials (AASHTO) . . . 13-19
Bureau of Labor Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13-19
Department of Housing and Urban Development (HUD) . . . . . . . . . . . . . . . . 13-19
Environmental Protection Agency (EPA) . . . . . . . . . . . . . . . . . . . . . . . . . 13-19
Federal Construction Council (FCC) . . . . . . . . . . . . . . . . . . . . . . . . . . . 13-19
Federal Highway Administration (FHA) . . . . . . . . . . . . . . . . . . . . . . . . . 13-19
Federal Railroad Administration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13-19
General Services Administration (GSA) . . . . . . . . . . . . . . . . . . . . . . . . . 13-19
National Institute of Building Sciences (NIBS) . . . . . . . . . . . . . . . . . . . . . 13-19
National Institute of Standards and Technology (NIST) . . . . . . . . . . . . . . . . . 13-19
National Science Foundation (NSF) . . . . . . . . . . . . . . . . . . . . . . . . . . . 13-20
National Technical Information Service (NTIS) . . . . . . . . . . . . . . . . . . . . . 13-20
Occupational Safety and Health Administration (OSHA) . . . . . . . . . . . . . . . . 13-20
United States Information Agency . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13-20
United States Government Printing Office . . . . . . . . . . . . . . . . . . . . . . . . 13-20
FOREIGN ORGANIZATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13-21
Australian Institute of Steel Construction (AISC) . . . . . . . . . . . . . . . . . . . . 13-21
British Constructional Steelwork Association (BCSA) . . . . . . . . . . . . . . . . . 13-21
Canadian Institute of Steel Construction (CISC) . . . . . . . . . . . . . . . . . . . . . 13-21
European Convention for Constructional Steelwork (ECCS) . . . . . . . . . . . . . . 13-21
Japanese Society of Steel Construction (JSSC) . . . . . . . . . . . . . . . . . . . . . 13-21
Mexican Institute of Steel Construction (MISC) . . . . . . . . . . . . . . . . . . . . . 13-21
South African Institute of Steel Construction (SAISC) . . . . . . . . . . . . . . . . . 13-21
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
PRIVATE AND NON-GOVERNMENT-RELATED ORGANIZATIONS
13 - 5
PRIVATE AND NON-GOVERNMENT-RELATED ORGANIZATIONS
Aluminum Association (AA)
900 19th Street, N.W., Washington, DC 20006
(202) 862-5100
(202) 862-5164 (fax)
The Aluminum Association (AA) is the trade association for domestic producers of
primary and secondary aluminum and semi-fabricated aluminum products. Member
companies operate 300 plants in 40 states.
American Concrete Institute (ACI)
22400 West Seven Mile Road, P.O. Box 19150, Detroit, MI 48219-0150
(313) 532-2600
(313) 538-0655 (fax)
The American Concrete Institute (ACI) is a non-profit organization which represents the
public agency, engineer, architect, owner, contractor, educator, or other specialist interested in the design, construction, or maintenance of concrete structures.
American Galvanizers Association (AGA)
12200 East Iliff Avenue, #204, Aurora, CO 80014
(303) 750-2900
(303) 750-2909 (fax)
The American Galvanizers Association (AGA) promotes corrosion prevention through
the use of post-fabrication hot-dip galvanizing. The AGA produces over 50 different
publications, videos, and slide programs discussing various aspects of galvanizing for
long-term corrosion prevention. These materials are provided at no charge to specifiers.
Other complimentary services include educational seminars and the 1-800-HOT-SPEC
line for answering questions about galvanizing and its applications. The AGA represents
galvanizing companies in the United States, Canada, Mexico, and 18 other countries.
American Institute for Hollow Structural Sections (AIHSS)
929 McLaughlin Run Road, Suite 8, Pittsburgh, PA 15017
(412) 221-8880
(412) 221-9119 (fax)
The American Institute for Hollow Structural Sections (AIHSS) is a non-profit technical
organization committed to advancing and improving the use of structural steel tubing and
pipe in buildings, bridges, and special structures. AIHSS encourages knowledgeable
decisions concerning hollow structural sections in construction applications through the
development and publication of engineering data and design aids, seminars, research and
development, and specifications and standards activities. Among its publications are
HSS/Structural Steel Tubing—Dimensions and Section Properties. HSS—Column Load
Tables, and HSS—Beam Load Tables.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
13 - 6
CONSTRUCTION INDUSTRY ORGANIZATIONS
American Institute of Architects (AIA)
1735 New York Avenue, N.W., Washington, DC 20006
(202) 626-7300
(202) 626-7426 (fax)
Since 1857, The American Institute of Architects has represented the professional
interests of America’s architects. The AIA works to meet the needs and interests of the
nation’s architects and the public they serve by developing public awareness in the value
of architecture and the importance of good design. In partnership with The American
Architectural Foundation, the AIA strives for a national design literacy in the belief that
a well-trained, creative profession and an informed public are prerequisites for a community’s quality of life.
American Institute of Mining, Metallurgical, and Petroleum Engineers (AIME)
345 East 47th Street, 14th Floor, New York, NY 10017
(212) 705-7695
Constituent societies of AIME include the Iron and Steel Society (see separate entry), the
Society of Petroleum Engineers, the Society of Mining Engineers, and the Minerals,
Metals, and Materials Society.
American Institute of Steel Construction (AISC)
One East Wacker Drive, Suite 3100, Chicago, IL 60601-2001
(312) 670-2400
(312) 670-5403 (fax)
The American Institute of Steel Construction (AISC) is a non-profit trade association
representing and serving the fabricated structural steel industry as well as engineers
practicing structural steel design in the United States. For over 70 years, its purpose has
been to advance the technology and competitiveness of steel construction through
standardization, research and development, education, technical assistance, and quality
control. AISC’s programs include: the development of specifications and technical
publications, research, technical and management seminars, engineering fellowships, and
programs for quality control, productivity, and safety. AISC represents the combined
experience, judgment, and strength of the steel fabricating industry and the structural
engineering design profession.
American Institute of Timber Construction (AITC)
11818 S.E. Mill Plain Boulevard, Suite 407, Vancouver, WA 98684
(206) 254-9132
(206) 254-9456 (fax)
The American Institute of Timber Construction (AITC) is the oldest national technical
trade association of the structural glued-laminated (glulam) timber industry. AITC was
formed in 1952 to further the development, production, and promotion of laminated
timber systems through the application of sound engineering practices and research.
AITC has established design and product standards and developed industry quality
control and inspection procedures that help assure economical, efficient, and reliable
performance in structural applications.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
PRIVATE AND NON-GOVERNMENT-RELATED ORGANIZATIONS
13 - 7
American Iron and Steel Institute (AISI)
1101 17th Street, N.W., Suite 1300, Washington, DC 20036-4700
(202) 452-7100
(202) 463-6573 (fax)
The American Iron and Steel Institute (AISI) is a non-profit association of companies
and individuals in the Western Hemisphere engaged in the iron and steel industry. The
Construction Marketing Committee promotes the use of steel buildings, bridges,
pipe/tank, and construction products through research, education, and promotion programs. The Committee on Construction Codes and Standards oversees efforts to achieve
competitive provisions in applicable building codes and standards. AISI publishes the
Specification for the Design of Cold-Formed Steel Structural Members.
American National Standards Institute (ANSI)
11 West 42nd Street, New York, NY 10036
(212) 642-4973
(212) 398-0023 (fax)
The American National Standards Institute (ANSI) is a private non-profit membership
organization that coordinates the United States voluntary standards system, bringing
together interests from the private and public sectors to develop voluntary standards for
a wide array of United States industries. ANSI is the official United States member body
to the world’s leading standards bodies: the International Organization for Standardization (ISO) and the International Electrotechnical Commission (IEC), via the United
States National Committee (USNC).
American Nuclear Society (ANS)
555 N. Kensington Avenue, LaGrange Park, IL 60525
(708) 352-6611
(708) 352-0499 (fax)
American Petroleum Institute (API)
1220 L Street, N.W., Washington, DC 20005
(202) 682-8000
(202) 682-8115 (fax)
The American Petroleum Institute (API), founded in 1919, is a non-profit corporation
that represents the domestic petroleum industry. Its membership consists of a broad cross
section of the petroleum and allied industries, including such functional segments as
exploration, production, transportation, refining, and marketing.
American Railway Engineering Association (AREA)
50 F Street, N.W., Suite 7702, Washington, DC 20001
(202) 639-2190
(202) 639-2183 (fax)
The American Railway Engineering Association (AREA) is a professional organization
concerned with engineering and maintenance work on railways in North America. It
covers the track and bridge aspects of railroading, as well as roadbed, electrification,
scales, and the mechanics of track maintenance machinery. AREA’s twenty-two technical
committees determine the content of the Manual for Railway Engineering. This standard
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
13 - 8
CONSTRUCTION INDUSTRY ORGANIZATIONS
reference in its field is revised annually to reflect the latest field-proven procedures and
designs for railway engineering.
American Society for Metals International (ASMI)
Materials Park, OH 44073
(216) 338-5151
(216) 338-4634 (fax)
American Society for Nondestructive Testing (ASNT)
P.O. Box 28518, 1711 Arlingate Lane, Columbus, OH 43228-0518
(614) 274-6003
(614) 274-6899 (fax)
American Society for Testing and Materials (ASTM)
1916 Race Street, Philadelphia, PA 19103
(215) 299-5400
(215) 977-9679 (fax)
Organized in 1898, ASTM has grown into one of the world’s largest voluntary, full-consensus standards development organizations. From the work of 132 technical standardswriting committees, ASTM publishes standard testing methods, specifications, practices,
guides, classifications, and terminology for materials, products, systems, and services.
Related scientific and technical information is also published in various books and
journals. ASTM’s activities encompass metals, paints, plastics, textiles, petroleum,
construction, energy, the environment, consumer products, medical services and devices,
electronics, and many other areas. Technical research and testing is performed voluntarily
by 34,000 members worldwide. Almost 9,000 standards are published each year in the
69 volumes of the Annual Book of ASTM Standards. These standards and related
information are widely used and accepted throughout the world.
American Society of Civil Engineers (ASCE)
345 East 47th Street, New York, NY 10017
(212) 705-7496
(212) 935-2744 (fax)
The mission of the American Society of Civil Engineers is to advance professional
knowledge and improve the practice of civil engineering in service to humanity by:
improving the quality of life worldwide; developing and promoting standards of excellence; providing life-long education for civil engineers; serving members’ needs, to meet
the challenges at the frontiers of developing technology and societal change. The building
load standard ASCE-7 is one of several that ASCE produces.
American Society of Mechanical Engineers (ASME)
345 East 47th Street, New York, NY 10017-2392
(212) 705-7722 or (800) THE-ASME
(212) 705-7674 (fax)
The American Society of Mechanical Engineers (ASME) is a non-profit educational and
technical organization. Founded in 1880, ASME serves its members, industry, and
government by encouraging the development of new technologies and finding solutions
to the problems of an increasingly global technological society. Its programs include
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
PRIVATE AND NON-GOVERNMENT-RELATED ORGANIZATIONS
13 - 9
publishing, technical conferences and exhibits, engineering education, government relations, and public education, as well as the development of codes and standards.
American Water Works Association (AWWA)
6666 West Quincy Avenue, Denver, CO 80235-3098
(303) 794-7711
(303) 794-7310 (fax)
(303)794-8915 (fax)
The American Water Works Association (AWWA) is composed of over 54,000 professionals and 4,000 companies in the water supply field. AWWA is dedicated to the
promotion of public health and welfare by assuring drinking water of unquestionable
quality and sufficient quantity. As a leader for the public drinking water profession,
AWWA is an effective instrument of education and change, setting standards, and
advancing technology, science, and governmental policies relative to the management,
collection, storage, treatment, and distribution of public water supplies.
American Welding Institute (AWI)
10628 Dutchtown Road, Knoxville, TN 37932
(615) 675-2150
(615) 675-6081 (fax)
The American Welding Institute (AWI) is a member owned non-profit organization. AWI
promotes quality improvement, along with productivity, as top priorities for the United
States welding industry. The mission of AWI is to put America’s best ideas about welding
to productive use in American industry. AWI provides services to the welding industry
including welding engineering, equipment evaluation, mechanical testing, customized
software, onsite trouble-shooting, metallurgical analysis, specialized training, and failure
analysis.
American Welding Society (AWS)
550 N.W. LeJeune Road, P.O. Box 351040, Miami, FL 33135
(305) 443-9353 or (800) 443-9353
(305) 443-7559 (fax)
The American Welding Society (AWS) provides services to its members and the industry
that advance the science, technology, and applications of welding and materials joining
throughout the world. In its leadership role, AWS is recognized as the authority on joining
technology and the source for coordinating matters pertaining to codes, standards,
materials, education, certification, and research. Services include the AWS International
Welding Exposition, publishing the Welding Journal, developing and publishing consensus standards, and offering a broad range of educational and welding certification
programs.
Association of American Railroads (AAR)
50 F Street NW, Washington, DC 20001
(202) 639-2402
(202) 639-2868 (fax)
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
13 - 10
CONSTRUCTION INDUSTRY ORGANIZATIONS
Association of Iron and Steel Engineers (AISE)
Three Gateway Center, Suite 2350, Pittsburgh, PA 15222-1097
(412) 281-6323
(412) 281-4657 (fax)
The Association of Iron and Steel Engineers (AISE) is a technical society serving the
steel industry worldwide through the collection and dissemination of technical information relating to the production of iron and steel. This is accomplished through a monthly
technical journal, national conventions, local and regional meetings, technical publications, equipment specifications, a biennial industrial trade show, and technical committees which represent both user and supplier. Founded in 1907, AISE has developed into
a multi-disciplined organization with over 10,000 members covering all phases of steel
industry operations.
Building Officials and Code Administrators International (BOCA)
4051 West Flossmoor Road, Country Club Hills, IL 60478-5795
(708) 799-2300
(708) 799-4981 (fax)
Building Officials and Code Administrators (BOCA) International, Inc., is a not-forprofit organization which publishes the National Building Code. Founded in 1915, BOCA
International is the original professional association of construction code officials. The
organization was specifically established to provide a forum for the exchange of knowledge and ideas concerning building safety and construction regulation. BOCA came into
being because its founders had a desire for excellence and professionalism in code
enforcement. Today, BOCA offers a wide variety of membership services to promote
code professionalism. The organization maintains ongoing model code development
activity, conducts regular training and education programs, offers a wide variety of model
construction codes and code-related publications, provides code interpretation assistance
to members, and provides various other code-related services in the public interest.
Concrete Reinforcing Steel Institute (CRSI)
933 North Plum Grove Road, Schaumburg, IL 60173-4758
(708) 517-1200
(708) 517-1206 (fax)
The Concrete Reinforcing Steel Institute represents reinforcing steel producers and
fabricators, epoxy coating applicators and powder manufacturers, and suppliers of other
products used in concrete construction and fabricating equipment manufacturing. Technical activities are conducted by the CRSI Engineering Practice Committee and subcommittees on bar supports, placing reinforcing bars, concrete joist construction, detailing
reinforced concrete, epoxy coating, and splicing reinforcing steel.
Construction Specifications Institute (CSI)
601 Madison Street, Alexandria, VA 22314-1791
(703) 684-0300
(703) 684-0465 (fax)
The Construction Specifications Institute (CSI), founded in 1948, is a not-for-profit
organization dedicated to the advancement of construction technology through commu-
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
PRIVATE AND NON-GOVERNMENT-RELATED ORGANIZATIONS
13 - 11
nication, education, research, and service. CSI serves the interest of architects, engineers,
specifiers, contractors, product manufacturers, and others in the construction industry.
Corrugated Steel Pipe Institute (CSPI)
652 Bishop Street N., Unit 2A, Cambridge, Ontario, Canada, N3H 4V6
(519) 650-8080
(519) 650-8081 (fax)
The Corrugated Steel Pipe Institute (CSPI) was formed in 1961 to promote wider use of
corrugated steel pipe and corrugated structural plate structures for drainage and other
uses across Canada. CSPI provides product information, recommends standards and
specifications, and recommends practices in the design, selection, application, and
installation of corrugated steel pipe. CSPI provides liaison with the Canadian Standards
Association, the National Corrugated Steel Pipe Association, and the American Iron and
Steel Institute.
Crane Manufacturers Association of America (CMAA)
8720 Red Oak Boulevard, #201, Charlotte, NC 28217
(704) 522-8644
(704) 522-7826 (fax)
Electronic Industries Association (EIA)
2001 Pennsylvania Avenue, N.W., Washington, DC 20006-1813
(202) 457-4900
(202) 457-4985 (fax)
For more than 68 years, the Electronic Industries Association (EIA) has been the national
trade organization representing the United States electronics manufacturers. Committed
to the competitiveness of the American producer, EIA represents the entire spectrum of
companies involved in the manufacture of electronic components, parts, systems, and
equipment for communications, industrial, government, and consumer-end uses.
Engineering Foundation
Engineering Center Library, 345 East 47th Street, New York, NY 10017
(212) 705-7611
(212) 486-1086 (fax)
Factory Mutual Engineering and Research Company
1151 Boston-Providence Turnpike, Norwood, MA 02062
(617) 769-7900
Gypsum Association
810 First Street NE, #510, Washington, DC 20002
(202) 289-5440
Industrial Fasteners Institute (IFI)
East Ohio Building, Suite 1105, 1717 East Ninth Street, Cleveland, OH 44114-2879
(216) 241-1482
(216) 241-5901 (fax)
The Industrial Fasteners Institute (IFI) is an association of North American manufacturers
of bolts, nuts, screws, rivets, and special formed parts. IFI members combine their
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
13 - 12
CONSTRUCTION INDUSTRY ORGANIZATIONS
technical knowledge to advance the technology and application engineering of fasteners
and formed parts through planned programs of research and education. IFI and its
members work closely with leading national and international technical organizations in
developing standards and other technical practices. IFI is comprised of 90 fastener
manufacturers and 35 suppliers of goods and services commonly used in the manufacture
of fasteners.
Institute of the Ironworking Industry (III)
1750 New York Avenue N.W., Suite 400, Washington, DC 20006
(202) 783-3998
(202) 393-1507 (fax)
The Institute of the Ironworking Industry (III) is a non-profit labor-management trade
association representing over 8,500 erection firms and 150,000 ironworkers. A board of
directors equally apportioned from management and the Ironworkers International Union
(AFL-CIO) sets policy to develop ways of eliminating problems which reduce the
competitiveness and inhibit the economic development of the erection industry in the
United States and Canada. Cooperation with other associations related to steel construction is encouraged to enhance safety, productivity, and the quality of the delivered
product.
International Conference of Building Officials (ICBO)
5360 Workman Mill Road, Whittier, CA 90601-2258
(310) 699-0541
(310) 692-3853 (fax)
The International Conference of Building Officials is dedicated worldwide to public
safety in the built environment through the development, maintenance, and promotion
of uniform codes and standards, enhancement of professionalism in code administration,
and the facilitation of the acceptance of innovative building products and systems. The
Conference works toward these objectives through the publication of the Uniform
Building Code and its associated family of codes and standards and through the offering
of high quality training, technical assistance, and certification examinations based on
these documents.
Iron and Steel Society (ISS)
410 Commonwealth Drive, Warrendale, PA 15086
(412) 776-1535
(412) 776-0430 (fax)
The Iron and Steel Society (ISS) is a constituent society of the American Institute of
Mining, Metallurgical, and Petroleum Engineers (AIME). ISS members are active in the
field of iron and steel processing and technology. ISS provides a medium of communication and cooperation among those interested in any phase of ferrous metallurgy and
materials science and technology.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
James F. Lincoln Arc Welding Foundation (JFLF)
22801 St. Clairs, P.O. Box 17035, Cleveland, OH 44117-0035
(216) 481-4300
(216) 486-1751 (fax)
The James F. Lincoln Arc Welding Foundation, incorporated as a non-profit entity in
1936, is the only organization in the United States specifically dedicated to educating the
public about the art and science of arc welding. The Lincoln Foundation recognizes
technical achievement with substantial monetary awards and publishes educational
materials for dissemination to the public. International Assistant Secretaries now carry
out Lincoln Foundation programs in Argentina, Australia, Canada, Croatia, Hungary,
Japan, New Zealand, the People’s Republic of China, Russia, Southern Africa, and the
United Kingdom.
Material Handling Industry (MHI)
8720 Red Oak Boulevard, Suite 201, Charlotte, NC 28217
(704) 522-8644
(704) 522-7826 (fax)
Materials Properties Council
345 E. 47th Street, New York, NY 10017
(212) 705-7693
(212) 371-9622 (fax)
Metal Building Manufacturers Association (MBMA)
1300 Sumner Avenue, Cleveland, OH 44115-2851
(216) 241-7333
(216) 241-0105 (fax)
The Metal Building Manufacturers Association (MBMA) was formed in 1956 with the
goal of developing sound design criteria for verifying the performance of structures under
various loads. MBMA has promoted the benefits of metal building systems to building
code officials, architects, and engineers. MBMA has 27 member manufacturing firms
that employ 10,000 persons and operate 57 manufacturing facilities in 24 states and three
foreign countries.
Metal Construction Association (MCA)
1101 14th Street, N.W., Suite 1100, Washington, DC 20005
(202) 371-1243
(202) 371-1090 (fax)
The Metal Construction Association (MCA) was established in 1983 to promote the wider
use of metal in construction. MCA programs include education, industry advertising, and
technical service through the development of guidelines, statistics, and specifications.
Membership is open to all firms and individuals with an interest in the metal construction
industry. MCA holds two membership meetings each year, in January and August. In
addition, the Association sponsors the only industry-wide trade show for metal in
construction, Metalcon International.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
National Association of Architectural Metals Manufacturers (NAAMM)
Association Headquarters, 600 South Federal, Suite 400, Chicago, IL 60605
(312) 922-6222
(312) 922-2734 (fax)
The National Association of Architectural Metal Manufacturers (NAAMM) is the Chicago-based trade association representing manufacturers of metal products. NAAMM
PRIVATE AND NON-GOVERNMENT-RELATED ORGANIZATIONS
13 - 15
National Erectors Association (NEA)
1501 Lee Highway, Suite 202, Arlington, VA 22209
(703) 524-3336
(703) 524-3364 (fax)
The National Erectors Association (NEA) is a national trade association of union
contractors dedicated to providing its members with the highest level of labor relations
and safety services, the promotion of positive labor-management programs in construction, and the advancement of a dynamic union construction industry. Membership
includes steel erectors, industrial maintenance contractors, specialty contractors, general
contractors, and construction managers. Active standing committees include its nationally-known Labor Committee and Safety & Health Committee.
National Fire Protection Association (NFPA)
1 Batterymarch Park, P.O. Box 9101, Quincy, MA 02269-9101
(617) 770-3000
(617) 770-0700 (fax)
The National Fire Protection Association (NFPA), an international non-profit organization, is recognized as the premier institution dedicated exclusively to protecting lives and
property from fire and related hazards. NFPA publishes over 270 nationally recognized
codes and standards, as well as numerous fire service training and educational programs.
More than 62,500 members work voluntarily to further NFPA’s mission.
National Fire Sprinkler Association (NFSA)
Robin Hill Corporate Park, Route 22, P.O. Box 1000, Patterson, NY 12563
(914) 878-4200
(914) 878-4215 (fax)
National Institute of Steel Detailing (NISD)
Bank of America Tower, 300 South Harbor Boulevard, Suite 500, Anaheim, CA 92805
(714) 776-3200
(714) 776-1255 (fax)
The National Institute of Steel Detailing (NISD) was formed in 1969 to create a better
understanding and bond between individuals engaged in the detailing profession. NISD
strives to eliminate practices which are injurious, to promote the efficiency of their work,
and to uphold the proper standards for the steel detailer in relations with other members
of the construction industry. The institute is a non-profit association of regional chapters,
firms, and individuals in the United States who serve the fabricated structural and
miscellaneous steel industry.
National Society of Architectural Engineers (NSAE)
P.O. Box 395, Lawrence, KS 66044
(913) 843-7000
(913) 843-7074 (fax)
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
13 - 16
CONSTRUCTION INDUSTRY ORGANIZATIONS
Nickel Development Institute (NiDI)
51 Nicholson Drive, Chatham, NJ 07928
(210) 635-8557
The Nickel Development Institute (NiDI) provides technical service to nickel consumers
and others concerned with nickel/nickel alloys and their uses. NiDI’s information services
are available to designers, specifiers, and educators as well as nickel users. Inquiries are
welcomed from architects, engineers, specification writers, and others responsible for
selection of materials for manufacturing and construction. NiDI looks forward to cooperating with colleges and universities by furnishing relevant information and materials
for engineering, materials science, and industrial design education.
Portland Cement Association (PCA)
5420 Old Orchard Road, Skokie, IL 60077-1083
(708) 966-6200
(708) 966-9781 (fax)
Post-Tensioning Institute (PTI)
1717 West Northern Avenue, Suite 114, Phoenix, AZ 85021
(602) 870-7540
(602) 870-7541 (fax)
The Post-Tensioning Institute, a not-for-profit organization, provides research, technical
development, marketing, and promotional activities for companies engaged in post-tensioned prestressed construction. Its publications are a major communications system for
disseminating information on p/t design and construction technology. In addition, PTI
publishes a quarterly newsletter dealing with developments in the p/t industry. Members
include p/t materials fabricators, manufacturers of prestressing materials, companies
supplying miscellaneous materials, services, and equipment used in p/t construction, and
more than 700 professional engineers, architects, and contractors.
Prestressed Concrete Institute (PCI)
175 W. Jackson Street, Chicago, IL 60604
(312) 786-0300
(312) 786-0353 (fax)
Southern Building Code Congress International (SBCCI)
900 Montclair Road, Birmingham, AL 35213-1206
(205) 591-1853
(205) 592-7001 (fax)
The Southern Building Code Congress International, Inc. (SBCCI) was established in
1940 as a membership organization dedicated to promulgating and maintaining a comprehensive set of model building codes and to providing support services to users of the
code. It continues that tradition today with the Standard CodesTM which cover every
aspect of commercial and residential construction. The SBCCI also provides technical
and educational services to assist code enforcement professionals and others in providing
the most efficient, effective, and skilled service to the building industry.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
PRIVATE AND NON-GOVERNMENT-RELATED ORGANIZATIONS
13 - 17
Steel Deck Institute (SDI)
919 37th Street, Canton, OH 44709
(216) 493-7886
(216) 493-7886 (fax)
Since 1939, the Steel Deck Institute (SDI) has provided uniform industry standards for
the engineering, design, manufacture, and field usage of steel decks. The SDI is concerned with cold-formed steel products, with various configurations distinctive to individual manufacturers, used to support finished roofing materials, or to serve as a
permanent form and/or positive reinforcement for concrete floor slabs. Members of SDI
are manufacturers of steel floor and roof decks. Associate members are manufacturers of
fasteners, coatings, and other related components.
Steel Joist Institute (SJI)
1205 48th Avenue North, Suite A, Myrtle Beach, SC 29577
(803) 449-0487
(803) 449-1343 (fax)
The Steel Joist Institute (SJI) is a not-for-profit organization. Besides setting standards
for the steel joist industry, SJI works closely with major building code bodies throughout
the country helping to develop code regulations regarding steel joists and joist girders.
SJI also invests thousands of dollars in ongoing research related to steel joists and joist
girders, and offers a complete library of publications and other training and research aids.
Steel Plate Fabricators Association (SPFA)
3158 Des Plaines Ave., Suite 209, Des Plaines, IL 60018
(708) 298-0880
(708) 298-2015 (fax)
The Steel Plate Fabricators Association (SPFA) has been a forum for the steel plate
fabricating industry for nearly 60 years. Members are fabricators manufacturing products
from steel plate and companies supplying goods and technology. SPFA promotes profitable industry growth through award programs for the Steel Plate Fabricated Product of
the Year for reservoir, elevated, and standpipe storage tanks, quality certification for steel
pipe and accessory manufacturers, seminars on steel water pipe, steel water tanks,
welding cost reduction, and productivity. Services include a monthly business trends
report.
Steel Service Center Institute (SSCI)
1600 Terminal Tower, 50 Public Square, Cleveland, OH 44113-2229
(216) 694-3630
The Steel Service Center Institute (SSCI) was established in 1907 to enhance the financial
return of member companies by providing information, education, governmental representation, networking opportunities, and a forum to enhance the quality of products and
services in meeting customer, supplier, and employee expectations. Steel service centers
purchase basic steel products, add value to them through services such as inventory
management, pre-production processing, just-in-time delivery, electronic data interchange, and barcoding, and subsequently sell production-ready metal pieces and parts to
manufacturers. Producing mills are Associate Members. International members are
welcome.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
13 - 18
CONSTRUCTION INDUSTRY ORGANIZATIONS
Steel Structures Painting Council (SSPC)
4516 Henry Street #301, Pittsburgh, PA 15213-3728
(412) 687-1113
(412) 687-1153 (fax)
Steel Tank Institute (STI)
570 Oakwood Road, Lake Zurich, IL 60047
(708) 438-8265
(708) 438-8766 (fax)
The Steel Tank Institute (STI) is a trade association and standards-setting body representing steel tank fabricators and affiliated corporations. STI develops technical standards for fabrication, corrosion control, installation, and secondary containment of underground and aboveground storage tanks. STI members manufacture single- and
double-wall steel UST’s with sti-P3 or ACT-100R corrosion protection systems, new
PermatankTM double-wall UST’s and F911TM and F921TM secondarily contained aboveground tanks.
Steel Tube Institute of North America (STI)
8500 Station Street, Suite 270, Mentor, OH 44060
(216) 974-6990
(216) 974-6994 (fax)
The Steel Tube Institute of North America (STI), founded in 1930, promotes the
responsible growth, prosperity, and competitiveness of the steel tubing industry. STI
collects and disseminates information on manufacturing techniques and data and analysis
on growth areas, market trends, and product applications. STI provides information to
customers on tubular products. Active members are producers of mechanical, pressure,
and structural tubing. Associates are suppliers of raw materials and equipment to the
tubular products industry.
Structural Stability Research Council (SSRC)
Fritz Engineering Laboratory, 13 East Packer Avenue, Lehigh University,
Bethlehem, PA 18015
(215) 758-3522
(215) 758-4522 (fax)
The Structural Stability Research Council (SSRC), founded in 1944, offers guidance,
through its 16 task groups and 8 task reporters, to specification writers and practicing
engineers by developing both simplified and refined calculation procedures for the
solution of stability problems, and assessing the limitations of these procedures. SSRC
holds regular annual meetings to report on research activities and to indicate where
deficiencies exist in our present understanding of structural behavior. The membership
of the SSRC is made up of representatives from organizations, consulting firms, and
individuals.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
PRIVATE AND NON-GOVERNMENT-RELATED ORGANIZATIONS
13 - 19
Underwriters Laboratories Inc. (UL)
333 Pfingsten Road, Northbrook, IL 60062-2096
(708) 272-8800
(708) 272-8129 (fax)
Underwriters Laboratories Inc. (UL), an independent, not-for-profit, safety testing and
certification organization, evaluates products, materials, and systems in the interest of
public safety. Founded in 1894, UL is neither a commercial enterprise nor a government
agency, but a member of the private sector whose primary objective is to help manufacturers bring safer products to U.S. and global markets. More than 6 billion UL Marks are
placed on products annually by more than 40,000 manufacturers. A UL Listing Mark on
a product means samples of the product have been tested to nationally recognized safety
standards and have been found to be reasonably free from fire, electric shock, and related
safety hazards.
Welding Research Council (WRC)
345 E. 47th Street, New York, NY 10017
(212) 705-7956
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
13 - 20
CONSTRUCTION INDUSTRY ORGANIZATIONS
FEDERAL AND STATE GOVERNMENT AND RELATED AGENCIES
Army Corps of Engineers
Office of the Chief of Engineers, Hdqr., U.S. Army, 20 Massachusetts Avenue,
Washington, DC 20314-1000
(202) 272-0010
(202) 272-1803 (fax)
American Association of State Highway and Transportation Officials (AASHTO)
444 N. Capitol Street, N.W., Suite 249, Washington, DC 20001
(202) 624-5800
(202) 624-5806 (fax)
Bureau of Labor Statistics
Department of Labor, 200 Constitution Avenue, NW, Washington, DC 20210
(202) 606-7828
Department of Housing and Urban Development (HUD)
451 Seventh Street, S.W., Washington, DC 20410
(202) 708-1422
(202) 708-0299 (fax)
Environmental Protection Agency (EPA)
401 M Street SW, Washington, DC 20460
(202) 382-2090
Federal Construction Council (FCC)
c/o National Academy of Sciences, 2101 Constitution Avenue NW,
Washington, DC 20418
(202) 334-3378
Federal Highway Administration (FHA)
Department of Transportation, 400 Seventh Street, S.W., Washington, DC 20590
(202) 366-0630
Federal Railroad Administration
Department of Transportation, 400 Seventh Street, S.W., Washington, DC 20590
(202) 366-0881
General Services Administration (GSA)
General Services Building, 18th & F Streets, N.W., Washington, DC 20405
(202) 708-5082
National Institute of Building Sciences (NIBS)
1201 L Street, #400, Washington, DC 20005
(202) 289-7800
National Institute of Standards and Technology (NIST)
Department of Commerce, Gaithersburg, MD 20899
(301) 975-3058
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
FEDERAL AND STATE GOVERNMENT AND RELATED AGENCIES
National Science Foundation (NSF)
1800 G Street, N.W., Washington, DC 20550
(202) 357-9498
National Technical Information Service (NTIS)
NTIS Operations Center, 5285 Port Royal Road, Springfield, VA 22161
(703) 487-4604
(703) 321-8547 (fax)
Occupational Safety and Health Administration (OSHA)
Department of Labor, 200 Constitution Avenue, N.W., Washington, DC 20210
(202) 523-8017
United States Information Agency
301 Fourth Street, S.W., Washington, DC 20547
(202) 619-4700
United States Government Printing Office
Superintendent of Documents, Washington, DC 20402
(202) 512-0000
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
13 - 21
13 - 22
CONSTRUCTION INDUSTRY ORGANIZATIONS
FOREIGN ORGANIZATIONS
Australian Institute of Steel Construction (AISC)
Level 13, 99 Mount Street, North Sydney, Australia NSW 2060
PO Box 6366, North Sydney, Australia NSW 2059
011-61-2/9296666
011-61-2/9555406 (fax)
British Constructional Steelwork Association (BCSA)
4 Whitehall Court
London, SW1A 2ES, United Kingdom
011-4471-839-8566
011-4471-976-1634 (fax)
Canadian Institute of Steel Construction (CISC)
201 Consumers Road, Suite 300, Willowdale, Ontario, Canada M2J 4G8
(416) 491-4552
(416) 491-6461 (fax)
The Canadian Institute of Steel Construction (CISC), a national association, represents
the structural steel, steel platework, and open-web steel joist industries by promoting
good design, safety, and efficient and economical use of steel as a means of expanding
markets for its Fabricator, Mill, Honorary, and Associate Members. Services encompass
steel design information, technical publications, such as the Handbook of Steel Construction, computer programs, continuing education courses, marketing, and industry-government relations. CISC manages the Steel Structures Education Foundation and the
Canadian Steel Construction Council.
European Convention for Constructional Steelwork (ECCS)
Avenue des Ombrages, 32/36 boite 20, B1200, Brussels, Belgium
011-322-762-0429
011-322-762-0935 (fax)
Japanese Society of Steel Construction (JSSC)
848 Shin Tokyo Building, 3-3-1 Marunouchi Chiyoda-Ku, J-Tokyo 100
011-81-3/32120875
011-81-3/32120878 (fax)
Mexican Institute of Steel Construction (MISC)
Amores 388, Col. del Valle, Mexico, DF
011-525-565-6800
011-525-390-1416 (fax)
South African Institute of Steel Construction (SAISC)
7th Floor, Metal Industries House, 42 Anderson Street, Johannesburg, South Africa 2001
PO Box 1338, Johannesburg, South Africa 2000
011-27-22-838-1665
011-27-11-834-4301 (fax)
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
GENERAL NOMENCLATURE
A
A
A
AB
ABM
Ab
Ab
Ac
Ac
Acp
Ae
Af
Afe
Afg
Afn
Ag
Agt
Agv
An
Ant
Anv
Apb
Ar
As
Asc
Asf
Ast
Av
Aw
Aw
A0
A1
A2
B
B
B
B
B1, B2
Cross-sectional area, in.2
Horizontal distance from end panel point to mid-span of a truss, ft.
Minimum side dimension for square or rectangular beveled washer, in.
Loaded area of concrete, in.2
Cross-sectional area of base metal for a welded joint, in.2
Nominal body area of a fastener, in.2
Nominal bolt area, in.2
Area of concrete in a composite column, in.2
Area of concrete slab within effective width, in.2
Projected surface area of concrete cone surrounding headed anchor rods,
in.2
Effective net area, in.2
Area of flange, in.2
Effective tension flange area, in.2
Gross area of flange, in.2
Net area of flange, in.2
Gross area, in.2
Gross area subject to tension, in.2
Gross area subject to shear, in.2
Net area, in.2
Net area subject to tension, in.2
Net area subject to shear, in.2
Projected bearing area, in.2
Area of reinforcing bars, in.2
Area of steel cross section, in.2
Cross-sectional area of stud shear connector, in.2
Shear area on the failure path, in.2
Cross-sectional area of stiffener or pair of stiffeners, in.2
Seismic coefficient representing the effective peak velocity-related
acceleration
Area of web clear of flanges, in.2
Effective area of weld, in.2
Initial amplitude of a floor system due to a heel-drop excitation, in.
Area of steel bearing concentrically on a concrete support, in.2
Total cross-sectional area of a concrete support, in.2
Factor for bending stress in tees and double angles, defined by LRFD
Specification Equation F1-16
Factor for bending stress in web-tapered members, defined by LRFD
Specification Equations A-F3-8 through A-F3-11, in.
Horizontal distance from mid-span of a truss to a given panel point, ft.
Base plate width, in.
Factors used in determining Mu for combined bending and axial forces
when elastic, first order analysis is employed
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
2
BF
C
C
C
CPG
CTot
Ca, Cb
Cb
Cc
Ccon
Cm
Cm′
Cp
Cs
Cs
Cstl
Cv
Cw
C1
C1
C1
C2
C3
CG
D
D
D
D
D
D
D
DLF
E
E
E
GENERAL NOMENCLATURE
A factor that can be used to calculate the flexural strength for unbraced
length Lb between Lp and Lr, defined in Part 4
Required mid-span camber, in.
Width across points of square or hex bolt head or nut, or maximum diameter
of countersunk bolt head, in.
Coefficient for eccentrically loaded bolt and weld groups
Plate girder coefficient
Sum of compressive forces in a composite beam, kips
Coefficients used in extended end-plate connection design
Bending coefficient dependent upon moment gradient
Beam reaction coefficient (Part 5)
Effective concrete flange force for a composite beam, kips
Coefficient applied to bending term in interaction formula for prismatic
members and dependent upon column curvature caused by applied
moments
Coefficient applied to bending term in interaction formula for tapered
members and dependent upon axial stress at the small end of the member
Ponding flexibility coefficient for primary member in a flat roof
Ponding flexibility coefficient for secondary member in a flat roof
Seismic response factor related to the fundamental period of the building
Compressive force in steel in a composite beam, kips
Ratio of “critical” web stress, according to linear buckling theory, to the
shear yield stress of web material
Warping constant, in.6
Loading constant used in deflection calculations (Part 4)
Clearance for tightening, in. (see Tables 8-4 and 8-5)
Electrode coefficient for relative strength of electrodes where, for E70
electrodes, C1 = 1.00 (see Table 8-37)
Clearance for entering, in. (see Tables 8-4 and 8-5)
Clearance for fillet based on one standard hardened washer, in. (see Tables
8-4 and 8-5)
Center of gravity
Outside diameter of circular hollow section, in.
Dead load, due to the weight of the structural elements and permanent
features on the structure
Factor used in LRFD Specification Equation A-G4-2, dependent on the type
of transverse stiffeners used in a plate girder
Offset from the base line at a panel point of a truss, in.
Damping in percent of critical
Slip probability factor for bolts
Number of sixteenths-of-an-inch in the weld size
Dynamic load factor
Modulus of elasticity of steel (29,000 ksi)
Earthquake load
Minimum edge distance for clipped washer, in.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
3
E
Ec
Em
EBF
ENA
F
F
FBM
FEXX
FL
Fbγ
Fcr
Fcrft, Fcry, Fcrz
Fe
Fex
Fey
Fez
Fmy
Fn
Fn, Fnt
Fp
Fr
Fsγ
Ft
Fu
Fv
Fw
Fwγ
Fy
Fy ′′′
Minimum effective throat thickness for partial-joint-penetration groove
weld, in.
Modulus of elasticity of concrete, ksi
Modified modulus of elasticity for the design of composite columns, ksi
Eccentrically braced frame (Seismic Specification)
Elastic neutral axis
Width across flats of bolt head, in.
Clearance for tightening staggered bolts, in. (see Tables 8-4 and 8-5)
Nominal strength of the base material to be welded, ksi
Classification strength of weld metal, ksi
Smaller of (Fyf − Fr) or Fyw, ksi
Flexural stress for tapered members defined by LRFD Specification Equations A-F4-4 and A-F4-5, ksi
Critical stress, ksi
Flexural-torsional buckling stresses for double-angle and tee-shaped compression members, ksi
Elastic buckling stress, ksi
Elastic flexural buckling stress about the major axis, ksi
Elastic flexural buckling stress about the minor axis, ksi
Elastic torsional buckling stress, ksi
Modified yield stress for the design of composite columns, ksi
Nominal shear rupture strength, ksi
Nominal strength of bolt, ksi
Nominal bearing stress on fastener, ksi
Compressive residual stress in flange, ksi
Stress for tapered members defined by LRFD Specification Equation
A-F3-6, ksi
Nominal tensile strength of bolt from LRFD Specification Table J3.2, ksi
Specified minimum tensile strength of the type of steel being used, ksi
Nominal shear strength of bolt from LRFD Specification Table J3.2, ksi
Nominal strength of the weld electrode material, ksi
Stress for tapered members defined by LRFD Specification Equation
A-F3-7, ksi
Specified minimum yield stress of the type of steel being used, ksi. As used
in the LRFD Specification, “yield stress” denotes either the specified
minimum yield point (for steels that have a yield point) or specified yield
strength (for steels that do not have a yield point)
The theoretical maximum yield stress (ksi) based on the web depth-thickness
ratio (h / tw) above which the web of a column is considered a “slender
element” (See LRFD Specification Table B5.1)
253
=
h
/ tw
Fyb
Fyc
2
Note: In the tables, — indicates Fy ′′′ > 65 ksi.
Fy of a beam, ksi
Fy of a column, ksi
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
4
Fyf
Fyr
Fy st
Fyw
G
G
H
H
H
H
H
Hs
H1
H2
I
ILB
Ic
Id
Ig
Ip
Ip
Is
Ist
It
Ix
Iy
Iyc
IC
ID
J
K
K
K
Karea
Kdep
Ki′
Kz
Kγ
L
GENERAL NOMENCLATURE
Specified minimum yield stress of the flange, ksi
Specified minimum yield stress of the longitudinal reinforcing bars, ksi
Specified minimum yield stress of the stiffener material, ksi
Specified minimum yield stress of the web, ksi
Shear modulus of elasticity of steel (11,200 ksi)
Ratio of the total column stiffness framing into a joint to that of the
stiffening members framing into the same joint
Horizontal force, kips
Flexural constant in LRFD Specification Equation E3-1
Average story height
Height of bolt head or nut, in.
Theoretical thread height, in. (see Table 8-7)
Length of stud connector after welding, in.
Height of bolt head, in. (see Tables 8-4 and 8-5)
Maximum bolt shank extension based on one standard hardened washer,
in. (see Tables 8-4 and 8-5)
Moment of inertia, in.4
Lower bound moment of inertia for composite section, in.4
Moment of inertia of column section about axis perpendicular to plane of
buckling, in.4
Moment of inertia of the steel deck supported on secondary members, in.4
Moment of inertia of girder about axis perpendicular to plane of buckling,
in.4
Moment of inertia of primary member in flat roof framing, in.4
Polar moment of inertia of bolt and weld groups ( = Ix + Iy), in.4 per in.2
Moment of inertia of secondary member in flat roof framing, in.4
Moment of inertia of a transverse stiffener, in.4
Transformed moment of inertia of the composite section, in.4
Moment of inertia of bolt and weld groups about X-axis, in.4 per in.2
Moment of inertia of bolt and weld groups about Y-axis, in.4 per in.2
Moment of inertia of compression flange about y axis or if reverse curvature
bending, moment of inertia of smaller flange, in.4
Instantaneous center of rotation
Nominal inside diameter of flat circular washer, in.
Torsional constant for a section, in.4
Effective length factor for a prismatic member
Coefficient for estimating the natural frequency of a beam (Part 4)
Minimum root diameter of threaded fastener, in. (see Table 8-7)
An idealized area representing the contribution of the fillet to the steel beam
area, as defined in the composite beam model of Part 5, in.2
Fillet depth, (k − tf), in.
Modified effective length factor of a column
Effective length factor for torsional buckling
Effective length factor for a tapered member
Unbraced length of member measured between the centers of gravity of the
bracing members, in. or ft, as indicated
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
5
L
L
L
L
L
L′
Lb
Lc
Lc
Le
Leh
Lev
Lg
Lh
Lm
Lm′
Lp
Lp
Lp′
Lpd
Lr
Lr
Ls
M
MA
MB
MC
MLL
MT
Mcr
Meu
Mlt
Mmax
Span length, ft
Length of connection in the direction of loading, in.
Story height, in. or ft, as indicated
Live load due to occupancy and moveable equipment
Edge distance or center-to-center distance for holes, in.
Total live load
Laterally unbraced length; length between points which are either braced
against lateral displacement of the compression flange or braced against
twist of the cross section, in. or ft, as indicated
Length of channel shear connector, in.
Unsupported length of a column section, ft
Edge distance, in.
Horizontal edge distance, in.
Vertical edge distance, in.
Unsupported length of a girder or other restraining member, ft
Hook length for hooked anchor rods, in.
Limiting laterally unbraced length for full plastic flexural strength, in. or
ft, as indicated
Limiting laterally unbraced length for the maximum design flexural
strength for noncompact shapes, in. or ft, as indicated
Column spacing in direction of girder, ft
Limiting laterally unbraced length for full plastic flexural strength, uniform
moment case (Cb = 1.0), in. or ft, as indicated
Limiting laterally unbraced length for the maximum design flexural
strength for noncompact shapes, uniform moment case (Cb = 1.0), in. or ft,
as indicated
Limiting laterally unbraced length for plastic analysis, in. or ft, as indicated
Limiting laterally unbraced length for inelastic lateral-torsional buckling,
in. or ft, as indicated
Roof live load
Column spacing perpendicular to direction of girder, ft
Beam bending moment, kip-in. or kip-ft, as indicated
Absolute value of moment at quarter point of the unbraced beam segment,
kip-in.
Absolute value of moment at centerline of the unbraced beam segment,
kip-in.
Absolute value of moment at three-quarter point of the unbraced beam
segment, kip-in.
Beam moment due to live load, kip-in. or kip-ft, as indicated
Applied torsional moment, kip-in.
Elastic buckling moment, kip-in. or kip-ft, as indicated
Required flexural strength for extended end-plate connections, kip-in.
Required flexural strength in member due to lateral frame translation,
kip-in.
Maximum bending moment, kip-in. or kip-ft, as indicated
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
6
Mmax
Mn
Mn′
Mnt
Mnx′, Mny′
Mp
Mp′
Mpa
Mr
Mu
My
Mob
M1
M2
N
N
N
Nb
Neff
Nr
Ns
OD
P
P
P
PD
PE
PL
PS
Pbf
Pe, Pe1, Pe2
Pfb
Pn
Pp
Pu
GENERAL NOMENCLATURE
Absolute value of maximum moment in the unbraced beam segment,
kip-in.
Nominal flexural strength, kip-in. or kip-ft, as indicated
Maximum design flexural strength for noncompact shapes, when Lb ≤ Lm′,
kip-in. or kip-ft, as indicated
Required flexural strength in member assuming there is no lateral translation of the frame, kip-in.
Flexural strength defined in LRFD Specification Equations A-H3-7 and
A-H3-8, for use in the alternate interaction equations for combined bending
and axial force, kip-in. or kip-ft, as indicated
Plastic bending moment, kip-in. or kip-ft, as indicated
Moment defined in LRFD Specification Equations A-H3-5 and A-H3-6, for
use in the alternate interaction formulas for combined bending and axial
force, kip-in. or kip-ft, as indicated
Plastic bending moment modified by axial load ratio, kip-in.
Limiting buckling moment, Mcr, when λ = λr and Cb = 1.0, kip-in. or kip-ft,
as indicated
Required flexural strength, kip-in. or kip-ft, as indicated
Initial yield bending moment, kip-in.
Elastic lateral-torsional buckling moment, kip-in. or kip-ft, as indicated
Smaller moment at end of unbraced length of beam or beam-column, kip-in.
Larger moment at end of unbraced length of beam or beam-column, kip-in.
Length of bearing, in.
Ratio of the factored gravity load supported by all columns in a story to that
supported by the columns in the rigid frame
Length of base plate, in.
Number of bolts in a joint
Number of beams effective in resisting floor vibration (Part 4)
Number of stud connectors in one rib at a beam intersection, not to exceed
3 in calculations
Number of slip planes
Nominal outside diameter of flat circular washer, in.
Concentrated load, kips
Bolt stagger, in.
Thread pitch, in. (see Table 8-7)
Unfactored dead load, kips
Unfactored earthquake load, kips
Unfactored live load, kips
Unfactored snow load, kips
Applied factored beam flange force in moment connections, kips
Euler buckling strengths, kips
Resistance to local flange bending per LRFD Specification Equation K1-1
(used to check need for column web stiffeners), kips
Nominal axial strength (tension or compression), kips
Bearing load on concrete, kips
Factored concentrated beam load, kips
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
7
Pu
Pu e
Puf
Pwb
Pwi
Pwo
Py
PNA
Q
Qa
Qf
Qi
Qn
Qs
Qw
R
R
R
RPG
Re
Rn
Rs
Ru
Ru st
Rv
R1
R2
R3
R4
R5
R6
Required axial strength (tension or compression), kips
Induced moment due to eccentricity e in an eccentrically loaded bolt or
weld group, kip-in.
Factored beam flange force, tensile or compressive, kips
Resistance to compression buckling of the web per LRFD Specification
Equation K1-8 (used to check need for column web stiffening), kips
A factor consisting of terms from the second portion of LRFD Specification
Equation K1-2 (used in a column web stiffener check for local web
yielding), kips/in.
A factor consisting of the first portion of LRFD Specification Equation
K1-2 (used in a column web stiffener check for local web yielding), kips
Yield strength, kips
Plastic neutral axis
Full reduction factor for slender compression elements
Reduction factor for slender stiffened compression elements
Statical moment for a point in the flange directly above the vertical edge
of the web, in.3
Load effects
Nominal strength of one stud shear connector, kips
Reduction factor for slender unstiffened compression elements
Statical moment at mid-depth of the section, in.3
Nominal load due to initial rainwater or ice exclusive of the ponding
contribution
Nominal reaction, kips
Earthquake response modification coefficient
Plate girder bending strength reduction factor
Hybrid girder factor
Nominal resistance or strength, kips
Nominal slip resistance of a bolt, kips
Required strength determined from factored loads; must be less than or
equal to design strength φRn
Required strength for transverse stiffener (factored force delivered to
stiffener), kips
Web shear strength, kips
An expression consisting of the first portion of LRFD Specification Equation K1-3, kips
An expression consisting of terms from the second portion of LRFD
Specification Equation K1-3, kips/in.
An expression consisting of the first portion of LRFD Specification Equation K1-5a, kips
An expression consisting of terms from the second portion of LRFD
Specification Equation K1-5a, kips/in.
An expression consisting of terms from LRFD Specification Equation
K1-5b, kips
An expression consisting of terms from LRFD Specification Equation
K1-5b, kips/in.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
8
S
S
S
S
S′
Sc
Seff
Snet
Sw
Sx
Sx′
Sxt, Sxc
SRF
T
T
T
T
Tb, Tm
Tstl
TTot
Tu
U
V
Vb
Vh
Vn
Vu
W
W
W
W
Wc
Wno
Wu
X1
X2
YENA
Ycon
GENERAL NOMENCLATURE
Elastic section modulus, in.3
Spacing, in. or ft, as indicated
Snow load
Groove depth for partial-joint-penetration groove welds, in.
Additional elastic section modulus corresponding to 1⁄16-in. increase in web
thickness for built-up wide flange sections, in.3
Elastic section modulus to the tip of the angle in compression, in.3
Effective section modulus about major axis, in.3
Net elastic section modulus, in.3
Warping statical moment at a point on the cross section, in.4
Elastic section modulus about major axis, in.3
Elastic section modulus of larger end of tapered member about its major
axis, in.3
Elastic section modulus referred to tension and compression flanges, respectively, in.3
Stiffness reduction factors (Table 3-1), for use with the alignment charts
(Figure 3-1) in the determination of effective length factors K for columns
Distance between web toes of fillets at top and at bottom of web, in.
= d − 2k
Tension force due to service loads, kips
Thickness of flat circular washer or mean thickness of square or rectangular
beveled washer, in.
Unfactored tensile force on slip-critical connections designed at service
loads, kips
Minimum bolt tension for fully tensioned bolts from LRFD Specification
Table J3.1, kips
Tensile force in steel in a composite beam, kips
Sum of tensile forces in a composite beam, kips
Factored tensile force, kips
Reduction coefficient, used in calculating effective net area
Shear force, kips
Shear force component, kips
Total horizontal force transferred by the shear connections, kips
Nominal shear strength, kips
Required shear strength, kips
Wind load
Uniformly distributed load, kips
Weight, lbs or kips, as indicated
Width across flats of nut, in.
Uniform load constant for beams, kip-ft
Normalized warping function at a point at the flange edge, in.2
Total factored uniformly distributed load, kips
Beam buckling factor defined by LRFD Specification Equation F1-8
Beam buckling factor defined by LRFD Specification Equation F1-9
Distance from bottom of steel beam to elastic neutral axis, in.
Distance from top of steel beam to top of concrete, in.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
9
Y1
Y2
Z
Z′
Ze
a
a
a
a
a
a
a
ar
b
b
b
b
b
b
be
beff
bf
bs
bs
c
c
c1, c2, c3
d
d
d
d
dL
db
dc
dc
dct
dcb
dh
dm
Distance from top of steel beam to the plastic neutral axis, in.
Distance from top of steel beam to the concrete flange force in a composite
beam, in.
Plastic section modulus, in.3
Additional plastic section modulus corresponding to 1⁄16-inch increase in
web thickness for built-up wide flange section, in.3
Effective plastic section modulus, in.3
Clear distance between transverse stiffeners, in.
Distance between connectors in a built-up member, in.
Effective concrete flange thickness of a composite beam, in.
Shortest distance from edge of pinhole to edge of member measured parallel
to direction of force, in.
Coefficient for eccentrically loaded weld group
Distance from bolt centerline to edge of fitting subjected to prying action,
but not greater than 1.25b, in.
Depth of bracket plate, in.
Ratio of web area to compression flange area
Compression element width, in.
Effective concrete flange width in a composite beam, in.
Width of composite column section, in.
Minimum shelf dimension for deposition of fillet weld, in.
Width of bracket plate, in.
Distance from bolt centerline to face of fitting subjected to prying action,
in.
Reduced effective width for slender compression elements, in.
Effective edge distance, in.
Flange width of rolled beam or plate girder, in.
Width of transverse stiffener, in.
Width of extended end-plate, in.
Distance from the neutral axis to the extreme fiber of the cross section, in.
Cope length, in.
Numerical coefficients used in the calculation of the modified yield stress
and modulus of elasticity for composite columns
Nominal fastener diameter, in.
Overall depth of member, in.
Pin diameter, in.
Roller diameter, in.
Depth at larger end of unbraced tapered segment, in.
Nominal bolt diameter, in.
Column depth, in.
Cope depth, in.
Top-flange cope depth, in.
Bottom-flange cope depth, in.
Hole diameter, in.
Moment arm between resultant tensile and compressive forces due to a
moment or eccentric force, in.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
10
GENERAL NOMENCLATURE
dz
d0
e
e
e
eo
Overall panel-zone depth, in.
Depth at smaller end of unbraced tapered segment, in.
Eccentricity, in.
Base of natural logarithms = 2.71828...
Link length in eccentrically braced frame (EBF), in.
Horizontal distance from the outer edge of a channel web to its shear center,
in.
Computed compressive stress in the stiffened element, ksi
Natural frequency, hz
Plate buckling model adjustment factor for beams coped at top flange only
Maximum bending stress, ksi
Smallest computed bending stress at one end of a tapered segment, ksi
Largest computed bending stress at one end of a tapered segment, ksi
Specified compressive strength of concrete, ksi
Adjustment factor for beams coped at both flanges
Required normal stress, ksi
Required shear stress, ksi
Computed shear stress, ksi
Stress due to 1.2D + 1.2R, ksi
Transverse center-to-center spacing (gage) between fastener gage lines, in.
Acceleration due to gravity = 32.2 ft/sec2 = 386 in./sec2
Clear distance between flanges less the fillet or corner radius for rolled
shapes; and for built-up sections, the distance between adjacent lines of
fasteners or the clear distance between flanges when welds are used, in.
Depth of composite column section, in.
Twice the distance from the centroid to the following: the inside face of the
compression flange less the fillet or corner radius, for rolled shapes; the
nearest line of fasteners at the compression flange or the inside face of the
compression flange when welds are used, for built-up sections, in.
Nominal rib height, in.
Factor used in LRFD Specification Equation A-F3-6 for web-tapered
members
Factor used in LRFD Specification Equation A-F3-7 for web-tapered
members
Remaining web depth of coped beam, in.
Factor defined by LRFD Specification Equations A-F2-4 for minimum
moment of inertia for a transverse stiffener
Distance from outer face of flange to web toe of fillet, in.
Slenderness parameter
Plate buckling coefficient for beams coped at top flange only
Bolt slip coefficient
Web plate buckling coefficient
Distance from web center line to flange toe of fillet, in.
Unbraced length of member, in.
Span length, in.
Length of bearing, in.
f
f
f
fb
fb1
fb2
fc′
fd
fun
fuv
fv
fo
g
g
h
h
hc
hr
hs
hw
ho
j
k
k
k
ks
kv
k1
l
l
l
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
11
l
l
l
lo
m
m
m
n
n
n
n
n′
p
pe
pf
qu
r
rT
rTo
ri
rib
rm
rn
rx, ry
rut
rut
ryc
_
ro
rox, roy
s
s
Length of connection in the direction of loading, in.
Length of weld, in.
Characteristic length of weld group (see Tables 8-38 through 8-45), in.
Distance from center of gravity (CG) to instantaneous center of rotation
(IC) of bolt or weld group, in.
Ratio of web to flange yield stress or critical stress in hybrid beams
Coefficient for converting bending to an approximate equivalent axial load
in beam-columns (Part 3)
Cantilever dimension for base plate (see Part 11), in.
Number of shear connectors between point of maximum positive moment
and the point of zero moment to each side
Number of bolts in a vertical row
Number of threads per inch on threaded fasteners
Cantilever dimension for base plate (see Part 11), in.
Number of bolts above the neutral axis (in tension)
Length of supporting flange parallel to stem or leg of hanger tributary to
each bolt in determinimg prying action, in.
Effective span used to compute Meu for extended end-plate connections, in.
Distance from centerline of bolt to nearer surface of tension flange in
extended end-plate connections, in.
Additional tension per bolt resulting from prying action produced by
deformation of the connected parts, kips/bolt
Governing radius of gyration, in.
Radius of gyration of compression flange plus one third of the compression
portion of the web taken about an axis in the plane of the web, in.
Radius of gyration, rT, for the smaller end of a tapered member, in.
Minimum radius of gyration of individual component in a built-up member,
in.
Radius of gyration of individual component relative to centroidal axis
parallel to member axis of buckling, in.
Radius of gyration of steel shape, pipe, or tubing in composite columns.
For steel shapes it may not be less than 0.3 times the overall thickness of
the composite section, in.
Nominal strength per bolt from LRFD Specification
Radius of gyration about x and y axes respectively, in.
Required tensile strength per bolt or per inch of weld (factored force per
bolt or per inch of weld due to a tensile force), kips/bolt
Required shear strength per bolt or per inch of weld (factored force per bolt
or per inch of weld due to a shear force), kips/bolt
Radius of gyration about y axis referred to compression flange, or if reverse
curvature bending, referred to smaller flange, in.
Polar radius of gyration about the shear center, in.
Radius of gyration about x and y axes at the smaller end of a tapered member
respectively, in.
Longitudinal center-to-center spacing (pitch) of any two consecutive holes,
in.
Bolt spacing, in.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
12
GENERAL NOMENCLATURE
t
t
tb
Thickness, in.
Change in temperature, degrees Fahrenheit or Celsius, as indicated
Thickness of beam flange or connection plate delivering concentrated
force, in.
Flange or angle thickness required to develop design tensile strength of
bolts with no prying action, in.
Total required effective thickness of column web with doubler plate, in.
Flange thickness, in.
Flange thickness of channel shear connector, in.
Thickness of base plate, in.
Panel zone thickness including doubler plates, in.
Required doubler plate thickness, in.
Extended end-plate thickness, in.
Web thickness, in.
Web thickness of channel shear connector, in.
Beam web thickness, in.
Column web thickness, in.
Panel zone thickness, in.
Factor for approximate design of beam-columns (Part 3)
Uniformly distributed load per unit of length, kips/in.
Fillet weld size, in.
Plate width; distance between welds, in.
Subscript relating symbol to strong principal axis of angle
Unit weight of concrete, lbs/ft3
Average width of concrete rib or haunch, in.
Panel zone width, in.
Subscript relating symbol to strong axis bending
Horizontal distance, in.
Horizontal distance from the outer edge of a channel web to its centroid,
in.
Connection eccentricity, in.
Horizontal distance from the designated edge of member to its plastic
neutral axis, in.
Horizontal distance, in.
Coordinates of the shear center with respect to the centroid, in.
Moment arm between centroid of tensile forces and compressive forces, in.
Subscript relating symbol to weak axis bending
Vertical distance from the designated edge of member to its plastic neutral
axis, in.
Vertical distance from designated edge of member to center of gravity, in.
Distance from the smaller end of tapered member used in LRFD Specification Equation A-F3-1 for the variation in depth, in.
Subscript relating symbol to weak principal axis of angle
Coefficient for buckling of triangular-shaped bracket plate
Deflection, in.
Live load deflection, in.
tc
te
tf
tf
tp
tp
tp req
ts
tw
tw
twb
twc
tz
u
w
w
w
w
w
wr
wz
x
_x
x
_
x
xp
xo
xo, yo
y
y
yp
y1, y2
z
z
z
∆
∆LL
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
13
∆oh
α
α
α
α
__
α
αm
β
_
β
βw
γ
γ
γi
δ
δ
ε
ζ
η
λ
λc
λe
λeff
λp
λr
µ
ρ
φ
φb
φc
φc
φr
φsf
φt
φv
φw
φFbc
Translation deflection of the story under consideration, in.
Separation ratio for built-up compression members, LRFD Specification
Equation E4
Fraction of member force transferred across a particular net section
Ratio of moment at bolt line to moment at stem line for determining prying
action in hanger connections
Ideal distance from face of column flange or web to centroid of gusset-tobeam connection for bracing connections and uniform force method, in.
Actual distance from face of column flange or web to centroid of gussetto-beam connection for bracing connections and uniform force method, in.
Coefficient for calculating Meu for extended end-plate connections
Ideal distance from face of beam flange to centroid of gusset-to-column
connection for bracing connections and uniform force method, in.
Actual distance from face of beam flange to centroid of gusset-to-column
connection for bracing connections and uniform force method, in.
Special section property for unequal-leg angles (Single Angle Specification)
Depth tapering ratio
Subscript relating symbol to tapered members
Load factor
Deflection, in.
Ratio of net area at bolt line to gross area at face of stem or angle leg used
to determine prying action for hanger connections
Coefficient of linear expansion, with units as indicated
Exponent for alternate beam-column interaction equation
Exponent for alternate beam-column interaction equation
Slenderness parameter
Column slenderness parameter
Equivalent slenderness parameter
Effective slenderness ratio defined by LRFD Specification Equation A-F3-2
Limiting slenderness parameter for compact element
Limiting slenderness parameter for noncompact element
Coefficient of friction; mean slip coefficient for bolts
Ratio of Pu to Vu of a link in an eccentrically braced frame (EBF)
Resistance factor
Resistance factor for flexure
Resistance factor for compression
Resistance factor for axially loaded composite columns
Resistance factor for compression, used in web crippling equations
Resistance factor for shear on the failure path
Resistance factor for tension
Resistance factor for shear
Resistance factor for welds
Design buckling stress for coped beams, ksi
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
14
φRn
φrn
kip
ksi
GENERAL NOMENCLATURE
Design strength from LRFD Specification; must equal or exceed required
strength Ru
Design strength per bolt or per inch of weld from LRFD Specification; must
equal or exceed required strength per bolt or per inch of weld ru
1,000 pounds
Stress, kips/in.2
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
INDEX
AISC
Code of Standard Practice for Steel Buildings and Bridges . . .
Quality Certification Program . . . . . . . . . . . . . . . . . .
ASD (Allowable Stress Design) . . . . . . . . . . . . . . . . . .
ASTM specifications . . . . . . . . . . . . . . . . . . . . . . . .
Allowable stress design . . . . . . . . . . . . . . . . . . . . . . .
Alternative design bolts . . . . . . . . . . . . . . . . . . . . . . .
Anchor rods . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
cast-in-place . . . . . . . . . . . . . . . . . . . . . . . . . . .
drilled-in . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
headed . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
hooked . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
minimum edge distance . . . . . . . . . . . . . . . . . . . . .
minimum embedment length . . . . . . . . . . . . . . . . . . .
welding to . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Angles
dimensions and properties . . . . . . . . . . . . . . . . . . . .
double; see Double angles
geometric properties . . . . . . . . . . . . . . . . . . . . . . .
single; see Single-angle
standard mill tolerances . . . . . . . . . . . . . . . . . . . . .
torsional properties . . . . . . . . . . . . . . . . . . . . . . . .
Architecturally exposed structural steel . . . . . . . . . . . . . .
Arc strikes . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Areas
bars; round and square . . . . . . . . . . . . . . . . . . . . . .
gross, net, and effective net (defined) . . . . . . . . . . . . . .
rectangular sections . . . . . . . . . . . . . . . . . . . . . . .
structural sections; method of increasing, standard mill practice
surface and box, W shapes . . . . . . . . . . . . . . . . . . . .
Availability
shapes, plates, and bars . . . . . . . . . . . . . . . . . . . . . .
steel pipe and structural tubing . . . . . . . . . . . . . . . . . .
Backing bars . . . . . . . . . . . . . . . .
Bars, square and round
weight and area . . . . . . . . . . . . . .
Bars and plates . . . . . . . . . . . . . . .
Base plates; see Columns, base plates for
Beam-columns
interaction equations . . . . . . . . . . .
preliminary design . . . . . . . . . . . .
second order effects . . . . . . . . . . .
Beam formulas . . . . . . . . . . . . . . .
Beams . . . . . . . . . . . . . . . . . . . .
bearing plates for . . . . . . . . . . . . .
bearing strength . . . . . . . . . . . . .
bending coefficient, Cb . . . . . . . . . .
compact . . . . . . . . . . . . . . . . . .
camber . . . . . . . . . . . . . . . . . .
composite design; see Composite design
cross-sectional area
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. . . . . . . . . . . 6-423
. . . . . . . . . . . 6-477
. . . . . . . . . 2-5; 6-25
iv, 1-15, 21, 194; 6-26, 32
. . . . . . . . . 2-5; 6-25
. . . . . . 6-374, 385; 8-7
. . . . . . . . . 6-28; 8-88
. . . . . . . . . . . . 8-88
. . . . . . . . . . . . 8-88
. . . . . . . . . . . . 8-90
. . . . . . . . . . . . 8-89
. . . . . . . . . . . . 8-88
. . . . . . . . . . . . 8-88
. . . . . . . . . . . . 8-89
. . . . . . . . . . . . . . . . . . . . 1-56
. . . . . . . . . . . . . . . . . . . . 7-23
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. . . 1-191
. . . 1-156
. 6-451, 476
. . . 8-114
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. . . . . . . 1-135
2-11; 6-34, 37, 172
. . . . . . . 1-137
. . . . . . . 1-183
. . . . . . . 1-175
. . . . . . . . . . . . . . . . . . . . 1-15
. . . . . . . . . . . . . . . . . . . . 1-21
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-122
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-135
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-133
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. . . . . . . 2-37; 6-60, 127, 201, 250
. . . . . . . . . . . . . . . 2-37; 3-11
. . . . . . . . . . . . 2-14; 6-41, 179
. . . . . . . . . . . . . . . . . 4-187
. 2-27; 4-1; 6-52, 111, 195, 246; 8-225
. . . . . . . . . . . . . . . . . 11-48
. . . . . . . . 4-33; 6-91, 231; 11-48
. . . . . . . . . . 2-30; 4-8; 6-53, 195
. . . . . . . . . . 2-27; 4-6; 6-52, 195
. . . . . 1-179, 185; 4-207; 6-98, 240
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
16
INDEX
gross, net, and effective net . . . . . . . . . . . .
deflections . . . . . . . . . . . . . . . . . . . . . .
design loads; see Uniform loads, factored
diagrams and formulas . . . . . . . . . . . . . . . .
dimensions . . . . . . . . . . . . . . . . . . . . . .
flexural strength . . . . . . . . . . . . . . . . . . .
charts . . . . . . . . . . . . . . . . . . . . . . . .
table . . . . . . . . . . . . . . . . . . . . . . . .
framing off-center on column . . . . . . . . . . . .
to column flange from strong axis . . . . . . . . .
to column flange from weak axis . . . . . . . . .
to column web . . . . . . . . . . . . . . . . . . .
geometric properties . . . . . . . . . . . . . . . . .
lateral-torsional buckling; see Buckling
noncompact . . . . . . . . . . . . . . . . . . . . . .
selection tables
load factor design . . . . . . . . . . . . . . . . .
moment of inertia . . . . . . . . . . . . . . . . .
shear strength . . . . . . . . . . . . . . . . . . . . .
unbraced length greater than Lp . . . . . . . . . . .
uniform loads . . . . . . . . . . . . . . . . . . . . .
vibrations . . . . . . . . . . . . . . . . . . . . . . .
Beam-web penetrations . . . . . . . . . . . . . . . . .
Bearing piles; see HP shapes
Bearing plates; see Beams, bearing plates for
Bearing strength at bolt holes . . . . . . . . . . . . . .
Block shear rupture . . . . . . . . . . . . . . . . . . .
Blocks . . . . . . . . . . . . . . . . . . . . . . . . . .
Bolts . . . . . . . . . . . . . . . . . . . . . . . . . .
alternative design type . . . . . . . . . . . . . . . .
combining with welds in connections . . . . . . . .
design strength . . . . . . . . . . . . . . . . . . . .
bearing strength at bolt holes . . . . . . . . . . .
bolt shear strength . . . . . . . . . . . . . . . . .
bolt tensile strength . . . . . . . . . . . . . . . .
for tension only . . . . . . . . . . . . . . . . .
for combined shear and tension . . . . . . . . .
prying action . . . . . . . . . . . . . . . . . .
in bearing-type connections . . . . . . . . . . . .
in slip-critical connections . . . . . . . . . . . . .
at factored loads . . . . . . . . . . . . . . . . .
at service loads . . . . . . . . . . . . . . . . .
surface classifications . . . . . . . . . . . . . .
high-strength bolts . . . . . . . . . . . . . . . . .
alternative design type . . . . . . . . . . . . .
ASTM A325 . . . . . . . . . . . . . . . . . . .
ASTM A449 . . . . . . . . . . . . . . . . . . .
ASTM A490 . . . . . . . . . . . . . . . . . . .
compatibility of nuts and washers with . . . . .
dimensions of . . . . . . . . . . . . . . . . . .
economical considerations for . . . . . . . . .
entering clearances for . . . . . . . . . . . . .
fully tensioned . . . . . . . . . . . . . . . . . .
galvanizing of . . . . . . . . . . . . . . . . . .
inspection of fully tensioned high-strength bolts
reuse of . . . . . . . . . . . . . . . . . . . . .
snug-tightened . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . 2-12; 6-37
. . . . . . . . . . . . . . . 4-29, 190, 207; 6-98, 240
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. . . . . . . . . . . . . 4-187
. . . . . . . . . . . . . . 1-26
2-27; 4-5; 6-52, 111, 195, 246
. . . . . . . . . . . . . 4-113
. . . . . . . . . . . . . . 4-15
. . . . . . . . . . . . . 9-202
. . . . . . . . . . . . . 9-202
. . . . . . . . . . . . . 9-204
. . . . . . . . . . . . . 9-209
. . . . . . . . . . . . . . 7-23
. . . . . . . . . . . . . . . . . . . . 4-7; 6-111, 246
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. . . . . . . . . . . . 4-15
. . . . . . . . . . . . 4-24
2-33; 4-29; 6-56, 113, 199
. . . . . . . . . . . 4-109
. . . . . . . . . . . . 4-28
. . . . . . . . . . . 4-208
. . . . . 6-57, 200; 12-11
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.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
. . . . . 6-85, 227; 8-23
. . . . 6-87, 228; 8-212
. . . . . . . . . . 8-225
6-79, 130, 223, 371; 8-7
. . . . . 6-374, 385; 8-7
. . . . 6-72, 217; 8-211
. . 6-79, 130, 223; 8-19
. . . . . . . . . . . 8-23
. . . . . . . . . . . 8-22
. . . . . . . . . . . 8-23
. . . . . . . . . . . 8-23
. . . . . . . . 6-83; 8-19
. . . . . . . . 8-19; 11-6
. . . . . . . . . . . 8-12
6-83, 130, 226; 8-12, 25
. . . . . . . . . . . 8-27
. . . . . . . . . . . 8-26
. . . . . . . . . . . 8-26
6-79, 130, 223, 371; 8-7
. . . . . . . . . . . . 8-7
. . . . . . . . . . . . 8-7
. . . . . . . . . . . . 8-7
. . . . . . . . . . . . 8-7
. . . . . . . . . . . . 8-8
. . . . . . . . . . . . 8-9
. . . . . . . . . . . . 8-8
. . . . . . . . . . . 8-12
. . . . . . . . . . . 8-12
. . . . . . . . . . . 8-18
. . . . . . . . . . . 8-15
. . . . . . . . . . . 8-19
. . . . . . . . . . . 8-12
INDEX
17
tension-control/twist-off type; see alternative design type . . . . . . . . . . . . . . . . . . . . . . 8-7
tightening clearances for . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-12
weights of . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .8-9
non-high-strength bolts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-79, 223; 8-19
ASTM A307 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-19
dimensions of . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-19
entering clearances for . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-19
tightening clearances for . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-19
weights of . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-19
Bracing formulas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-14
Bracket plates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12-5
Brittle fracture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1-6
Buckling
beam (lateral-torsional) . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-29; 4-5; 6-52, 111, 195, 246
column (flexural, flexural-torsional) . . . . . . . 1-67, 91; 2-17, 22, 27; 3-5, 53; 6-47, 109, 183, 192, 245
local (flange and web) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-12; 6-36, 52, 111, 174, 246
Building materials, weights . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-7
Built-up members
columns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12-16
crane-runway girders . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12-13
girders; see Plate girders
trusses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12-16
wide-flange sections, dimensions and properties . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-183
C shapes; see Channels
Cb, beam design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-30; 4-8; 6-53, 195
Camber . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-179, 185; 4-207; 6-98, 240
effect on end connections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12-18
Canted connections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9-225
Carbon steel, standard nomenclature for flat-rolled . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-3
Cast-in-place anchor rods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-28; 8-88
Channels
American Standard (C), dimensions and properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-50
flexural-torsional properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-154
miscellaneous (MC), dimensions and properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-52
standard mill practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-183
used as beams, uniform loads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-64, 101
Circles, properties of . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-16
Clamps, crane rail . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-143
Clearances
for bolt entering and tightening . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-12, 19
for welding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-118
Clevises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-92
Code of Standard Practice for Steel Buildings and Bridges . . . . . . . . . . . . . . . . . . . . . . . 6-423
Coefficients of expansion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-12; 7-4
Columns . . . . . . . . . . . . . . . . . . . . . . . 2-22; 3-1; 6-47, 109, 192, 245; 10-35; 11-54, 64; 12-16
alignment of . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11-65
base plates for . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11-54
under axial loads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11-54
concrete compressive strength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11-58
design checks for . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11-58
required thickness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11-59
finishing requirements for . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11-54
holes in for anchor rods and grouting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11-55
leveling methods for . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11-56
heavy base plates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11-57
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
18
INDEX
light base plates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11-56
built-up . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-48, 194; 12-16
combined axial and bending loading (interaction); see Beam-columns
composite design; see Composite design
compressive strength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-22; 3-5; 6-47, 109, 192, 245
tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-16, 6-147
effective length . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-17; 3-5; 6-43, 183
flexural and flexural-torsional buckling; see Buckling
leaning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-18; 3-10; 6-187
lifting devices for . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11-65
load tables, general notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-5
pin-connected . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-51
slender-element . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-105
slenderness ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-13; 3-5; 6-37, 177
splices in . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11-64
butt-plated type . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11-69
column alignment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11-65
directly welded flange type . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11-69
fit-up of . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11-64
flange-plated type . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11-67
force transfer in . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11-66
lifting devices in . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11-65
stability during erection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11-65
web stiffening at moment connections to . . . . . . . . . . . . . . . . . . . . . . 3-14; 6-91, 231; 10-35
Combination sections, properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-105
Combined forces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-34; 6-59, 127, 201, 250
Commentary on the LRFD Specification for Structural Steel Buildings . . . . . . . . . . . . . . . . 6-161
Compact section (definition) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-12; 6-36, 174
Composite beam-columns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-69; 6-66, 213
Composite beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-43, 5-5; 6-64, 205
lower bound elastic moment of inertia tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-50
selection tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-18
shear connectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-43; 5-8; 6-67, 213
steel deck, effect of . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-44; 6-65, 210
shoring . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-43; 5-8; 6-65, 210
Composite columns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-42; 5-67, 6-62, 204
selection tables
W shapes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-74
pipe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-111
tubing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-115
Compression buckling of the web . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-94, 233; 10-39
Compression members; see Columns or Struts
Computer software . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-14; 2-44; 9-10
Concentrated forces . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-14; 4-33; 6-91, 231; 10-35; 11-48
Concentrated load equivalents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-189
Connected elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-212
design strength of . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-87, 228; 8-212
block shear rupture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-212
net area reduction for bolt holes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-213
shear rupture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-212
shear yielding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-212
tension rupture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-225
tension yielding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-225
economical considerations for . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-212
fillers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-237
shims . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-237
with copes, blocks, or cuts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-225
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
INDEX
19
flexural yielding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-225
lateral torsional buckling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-229
local web buckling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-226
Connections
for raised beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9-211
for tubular and pipe members . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9-215
diagonal bracing; see Diagonal bracing connections
FR moment; see Fully restrained (FR) moment connections
PR moment; see Partially restrained (PR) moment connections
simple shear; see Simple shear connections
Construction documents
plans and specifications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-8; 6-33, 429, 460
shop and erection drawings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-431, 461
Construction, types of . . . . . . . . . . . . . . . . . . . . . . . . . . 2-8; 6-25, 162; 9-7, 234; 10-7; 11-17
Continuous beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-200
theorem of three moments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-188
Continuous connections; see Fully restrained (FR) moment connections
Conversion factors, SI (metric) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-8, 12
Copes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-225
reinforcement for; see Reinforcement for coped beams
Corner connections; see Knee connections
Cotter pins . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-93
Crane rails and fastenings
notes, dimensions, and properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-139
Crane-runway girders . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12-13
Cross-sectional areas
gross, net, and effective net (defined) . . . . . . . . . . . . . . . . . . . . . . . . . . 2-11; 6-34, 37, 172
Cross sections
compact, noncompact, and slender-element (defined) . . . . . . . . . . . . . . . . . . . . 2-12; 6-36, 174
Cuts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-225
Decimals of a foot . . . . . . . . . . . . . . .
Decimals of an inch . . . . . . . . . . . . . . .
Definitions; see Glossary
Design documents; see Construction documents
Design loads
weights of building materials . . . . . . . .
Diagonal bracing connections . . . . . . . . .
design checks for . . . . . . . . . . . . . . .
force transfer in . . . . . . . . . . . . . . . .
analysis of existing connections . . . . . .
general uniform force method . . . . . . .
special cases . . . . . . . . . . . . . . . .
members in . . . . . . . . . . . . . . . . .
Diagonal stiffeners . . . . . . . . . . . . . . .
Dimensions; see specific item
Directly welded flange connections . . . . . .
column splices . . . . . . . . . . . . . . . .
FR moment connections . . . . . . . . . . .
moment splices . . . . . . . . . . . . . . . .
Double angles, properties . . . . . . . . . . . .
flexural-torsional properties . . . . . . . . .
used as columns
design strength tables . . . . . . . . . . .
general notes . . . . . . . . . . . . . . . .
Double-angle connections . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-26
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-25
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. . 7-7
11-17
11-27
11-19
11-26
11-20
11-22
11-19
10-54
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10-19, 58; 11-69
. . . . . . 11-69
. . . . . . 10-19
. . . . . . 10-58
. . . . . . . 1-91
. . . . . . 1-172
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-57
. . . . . . . . . . . . . . . . . . . . . . . . . . . 1-91; 3-53
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9-11
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
20
INDEX
all-bolted . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9-13
all-welded . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9-16
bolted/welded . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9-15
design checks for . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9-12
recommended angle length and thickness for . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9-12
shop and field practices for . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9-12
Double concentrated forces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10-35
Double connections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9-196
supported beams of diffrent nominal depths . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9-196
supported beams offset laterally . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9-200
Doubler plate design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9-185; 10-49
at locations of weak-axis connections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10-51
for local web yielding or compression buckling of the web . . . . . . . . . . . . . . . . . . . . . . 10-50
for panel zone web shear . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10-50
for web reinforcement of coped beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9-185
DPT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-109
Drilled-in anchor rods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-88
Dye-penetrant testing weld inspection (DPT) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-109
Eccentric transverse stiffeners . . . . . . . . .
Eccentricity . . . . . . . . . . . . . . . . . . .
for bolt groups . . . . . . . . . . . . . . . .
in plane of faying surface . . . . . . . . .
elastic method . . . . . . . . . . . . . .
instantaneous center of rotation method
normal to plane of faying surface . . . . .
for larger than normal gages . . . . . . . . .
alternative treatment of . . . . . . . . . .
at column-web supports . . . . . . . . . .
at girder-web supports . . . . . . . . . . .
for weld groups . . . . . . . . . . . . . . . .
in plane of faying surface . . . . . . . . .
elastic method . . . . . . . . . . . . . .
instantaneous center of rotation method
normal to plane of faying surface . . . . .
Economical considerations
for bolts . . . . . . . . . . . . . . . . . . . .
for column stiffening at moment connections
for simple shear connections . . . . . . . . .
for weld groups . . . . . . . . . . . . . . . .
for welding . . . . . . . . . . . . . . . . . .
Edge distance
for anchor rods . . . . . . . . . . . . . . . .
for bolts . . . . . . . . . . . . . . . . . . . .
Effective area
of fillet welds . . . . . . . . . . . . . . . . .
of flare welds . . . . . . . . . . . . . . . . .
of partial-joint-penetration groove welds . .
EGW . . . . . . . . . . . . . . . . . . . . . .
Elastic method for eccentric loads . . . . . . .
Electrodes, matching . . . . . . . . . . . . . .
Electrogas welding (EGW) . . . . . . . . . . .
Electroslag welding (ESW) . . . . . . . . . . .
Ellipse, properties of . . . . . . . . . . . . . .
Embedment length for anchor rods . . . . . . .
End returns . . . . . . . . . . . . . . . . . . .
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. . . . . . 10-48
8-28, 154; 9-192
. . . . . . . 8-28
. . . . . . . 8-28
. . . . . . . 8-33
. . . . . . . 8-28
. . . . . . . 8-36
. . . . . . 9-192
. . . . . . 9-195
. . . . . . 9-192
. . . . . . 9-194
. . . . . . 8-154
. . . . . . 8-154
. . . . . . 8-159
. . . . . . 8-154
. . . . . . 8-211
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. .8-8
10-36
. . 9-7
8-111
8-111
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-88
. . . . . . . . . . . . . . . . . . . . . . . . 6-81, 224; 8-23
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AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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. . 8-118
. . 8-128
. . 8-127
. . 8-107
8-33, 159
. . 8-115
. . 8-107
. . 8-107
. . . 7-15
. . . 8-88
. . 8-120
INDEX
21
Engineering conversion factors, SI (metric)
Entering clearances for bolts . . . . . . . .
Equivalents
decimals of a foot . . . . . . . . . . . .
decimals of an inch . . . . . . . . . . . .
Erection . . . . . . . . . . . . . . . . . . .
drawings; see Construction documents
ESW . . . . . . . . . . . . . . . . . . . .
Expansion, coefficients of . . . . . . . . .
Expansion joints . . . . . . . . . . . . . .
Extended end-plate connections . . . . . .
FR moment connections . . . . . . . . .
column stiffening at . . . . . . . . . .
design assumptions for . . . . . . . . .
design checks for . . . . . . . . . . .
eight-bolt stiffened . . . . . . . . . . .
four-bolt unstiffened . . . . . . . . . .
shop and field practices for . . . . . .
moment splices . . . . . . . . . . . . . .
design checks for . . . . . . . . . . .
Extension bars . . . . . . . . . . . . . . .
Fabrication . . . . . . . . . . . .
Factors
load . . . . . . . . . . . . . . .
resistance . . . . . . . . . . . .
SI (metric) conversion . . . . .
Fastenings, crane rails . . . . . .
Fatigue . . . . . . . . . . . . . .
Fatigue cracking in welded joints
FCAW . . . . . . . . . . . . . . .
Feet, decimal equivalents . . . . .
Fillers . . . . . . . . . . . . . . .
Fillet welds . . . . . . . . . . . .
effective area of . . . . . . . .
end returns with . . . . . . . .
in holes or slots . . . . . . . . .
maximum size of . . . . . . . .
minimum effective length of . .
minimum shelf dimensions for .
minimum size of . . . . . . . .
other limitations on . . . . . . .
Fire resistant construction . . . .
Flange-plated connections . . . .
column splices . . . . . . . . .
FR moment connections . . . .
column stiffening at . . . . .
design checks for . . . . . .
shop and field practices for .
moment splices . . . . . . . . .
design checks for . . . . . .
shop and field practices for .
Flange slope, rolled sections . . .
Flare welds . . . . . . . . . . . .
effective area of . . . . . . . .
limitations on . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-8, 12
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-12, 19
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-26
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-25
. . . . . . . . . . . . . . . . . . . . . . . 6-102, 243, 437, 466
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. . 8-107
1-12; 7-4
. . . 1-13
10-21, 59
. . 10-21
. . 10-35
. . 10-22
. . 10-21
. . 10-30
. . 10-24
. . 10-21
. . 10-59
. . 10-56
. . 8-122
. . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-100, 242, 433, 465
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AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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. . . . . 2-6; 6-30, 166
. . . . . 2-7; 6-32, 168
. . . . . . . . . 7-8, 12
. . . . . . . . . 1-141
. . . . .6-97, 135, 254
. . . . . . . . . 8-113
. . . . . . . . . 8-106
. . . . . . . . . . 7-26
. . . . . . . . . 8-237
. . . 6-74, 219; 8-118
. . . . . . . . . 8-118
. . . . . . . . . 8-120
. . . . . . . . . 8-121
. . . . . . . . . 8-119
. . . . . . . . . 8-119
. . . . . . . . . 8-122
. . . . . . . . . 8-119
. . . . . . . . . 8-121
. . . . . . . . . . . 1-8
9-246; 10-9, 56; 11-67
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. . . . . . . . . . 10-9
. . . . . . . . . 10-35
. . . . . . . . . . 10-9
. . . . . . . . . . 10-9
. . . . . . . . . 10-56
. . . . . . . . . 10-56
. . . . . . . . . 10-57
. . . . . . . . . . 1-25
. . . . . . . . . 8-127
. . . . . . . . . 8-128
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22
INDEX
Flexible Wind Connections . . . . . . . . . . .
Flexural members; see Beams or Plate girders
Flexural yielding, of coped beams . . . . . . .
Floor deflections and vibrations . . . . . . . .
Floor plates, weights . . . . . . . . . . . . . .
Flux-cored arc welding (FCAW) . . . . . . . .
Formulas
beam . . . . . . . . . . . . . . . . . . . . .
bracing . . . . . . . . . . . . . . . . . . . .
properties of geometric sections . . . . . . .
trigonometric . . . . . . . . . . . . . . . . .
Frames . . . . . . . . . . . . . . . . . . . . .
braced . . . . . . . . . . . . . . . . . . . .
EBF (eccentrically braced frames) . . . .
unbraced (moment) . . . . . . . . . . . . . .
Fully Restrained (FR) moment connections . .
across girder-web supports . . . . . . . . . .
bottom flange connection . . . . . . . . .
top flange connection . . . . . . . . . . .
web connection . . . . . . . . . . . . . .
directly welded flange connections . . . . .
design checks for . . . . . . . . . . . . .
extended end-plate connections . . . . . . .
design assumptions for . . . . . . . . . . .
design checks for . . . . . . . . . . . . .
eight-bolt stiffened . . . . . . . . . . . . .
four-bolt unstiffened . . . . . . . . . . . .
shop and field practices for . . . . . . . .
flange-plated connections . . . . . . . . . .
design checks for . . . . . . . . . . . . .
shop and field practices for . . . . . . . .
force transfer in . . . . . . . . . . . . . . . .
special considerations for seismic loading of
temporary support during erection . . . . . .
to column-web supports . . . . . . . . . . .
ductility considerations . . . . . . . . . .
recommended details . . . . . . . . . . .
welding considerations for . . . . . . . . . .
Fully tensioned high-strength bolts . . . . . . .
Gages, sheet metal and wire . . . . .
Galvanizing, with high strength bolts
Gas-metal arc welding (GMAW) . . .
Geometric and trigonometric data . .
Girders; see Plate girders or Beams
Girts . . . . . . . . . . . . . . . . . .
connections for . . . . . . . . . . .
Glossary
Code of Standard Practice . . . . .
LRFD Specification . . . . . . . .
Seismic Specification . . . . . . .
GMAW . . . . . . . . . . . . . . . .
Gouging, air-arc . . . . . . . . . . .
Groove welds . . . . . . . . . . . . .
backing bars for . . . . . . . . . .
complete-joint-penetration . . . . .
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. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9-253
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. . . . . . . . . . . 4-187
. . . . . . . . . . . . 7-14
. . . . . . . . . . . . 7-17
. . . . . . . . . . . . 7-24
. . . . . . 2-14; 6-41, 179
. . . . . . . . . 6-42, 319
. . . . . . . . . 6-307, 321
. . . . . . . . . 6-43, 314
. 6-25, 70, 162, 216; 10-7
. . . . . . . . . . . 10-65
. . . . . . . . . . . 10-66
. . . . . . . . . . . 10-66
. . . . . . . . . . . 10-66
. . . . . . . . . . . 10-19
. . . . . . . . . . . 10-19
. . . . . . . . . . . 10-21
. . . . . . . . . . . 10-22
. . . . . . . . . . . 10-21
. . . . . . . . . . . 10-30
. . . . . . . . . . . 10-24
. . . . . . . . . . . 10-21
. . . . . . . . . . . . 10-9
. . . . . . . . . . . . 10-9
. . . . . . . . . . . . 10-9
. . . . . . . . . . . . 10-7
. . . . . . . . . . . . 10-9
. . . . . . . . . . . . 10-7
. . . . . . . . . . . 10-60
. . . . . . . . . . . 10-61
. . . . . . . . . . . 10-60
. . . . . . . . . . . . 10-8
6-79, 223, 371; 8-8, 12, 15
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. . . . . . 8-225
4-207; 6-98, 240
. . . . . . 1-134
. . . . . . 8-106
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. . 7-3
. 8-18
8-106
. 7-14
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12-18
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12-18
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AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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. . . . . . . . . . . 6-425
. . . . . . . . . . . 6-267
. . . . . . . . . . . 6-307
. . . . . . . . . . . 8-106
. . . . . . . . . . . 8-108
6-73, 219; 8-122, 125, 127
. . . . . . . . . . . 8-122
. . . . . . . . . . . 8-122
INDEX
23
extension bars for . . . . . .
ratholes; see weld access holes
runoff bars for . . . . . . . .
spacer bars for . . . . . . . .
weld access holes for . . . . .
Grouting, holes for . . . . . . .
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HP shapes
dimensions and properties . . . . . . . . . . . . . . . . .
used as columns, design strength tables . . . . . . . . . .
Hanger Connections . . . . . . . . . . . . . . . . . . . . .
design checks for . . . . . . . . . . . . . . . . . . . . . .
prying action in . . . . . . . . . . . . . . . . . . . . . . .
Headed anchor rods . . . . . . . . . . . . . . . . . . . . . .
Heat, effect on steel . . . . . . . . . . . . . . . . . . . . . .
Heavy shapes . . . . . . . . . . . . . . . . . . . . . . . . .
High-strength bolts . . . . . . . . . . . . . . . . . . . . . .
alternative design type . . . . . . . . . . . . . . . . . . .
ASTM A325 . . . . . . . . . . . . . . . . . . . . . . . .
ASTM A449 . . . . . . . . . . . . . . . . . . . . . . . .
ASTM A490 . . . . . . . . . . . . . . . . . . . . . . . .
compatibility of nuts and washers with . . . . . . . . . .
dimensions of . . . . . . . . . . . . . . . . . . . . . . . .
economical considerations for . . . . . . . . . . . . . . .
entering clearances for . . . . . . . . . . . . . . . . . . .
fully tensioned installation of . . . . . . . . . . . . . . .
galvanizing . . . . . . . . . . . . . . . . . . . . . . . . .
inspection of (fully tensioned) . . . . . . . . . . . . . . .
reuse of . . . . . . . . . . . . . . . . . . . . . . . . . . .
snug-tightened installation of . . . . . . . . . . . . . . .
tension-control/twist-off type; see alternative design type .
tightening clearances for . . . . . . . . . . . . . . . . . .
weights of . . . . . . . . . . . . . . . . . . . . . . . . .
Holes
for bolts . . . . . . . . . . . . . . . . . . . . . . . . . . .
for anchor rods . . . . . . . . . . . . . . . . . . . . . . .
for grouting . . . . . . . . . . . . . . . . . . . . . . . . .
reduction of area for . . . . . . . . . . . . . . . . . . . .
Hook bolts for crane rails . . . . . . . . . . . . . . . . . . .
Hooked anchor rods . . . . . . . . . . . . . . . . . . . . .
Hybrid girders . . . . . . . . . . . . . . . . . . . . . . . .
design example . . . . . . . . . . . . . . . . . . . . . . .
I shapes; see S shapes
Impact toughness of welded joints . . .
Inches, decimal equivalents . . . . . .
Inspection . . . . . . . . . . . . . . . .
of fully tensioned high-strength bolts
of welded joints . . . . . . . . . . .
dye-penetrant testing (DPT) . . . .
magnetic particle testing (MT) . .
radiographic testing (RT) . . . . .
ultrasonic testing (UT) . . . . . . .
visual testing (VT) . . . . . . . . .
Instantaneous center of rotation method
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. . . . . . . . . . . . . . . . 1-48
. . . . . . . . . . . . . . . . 3-31
. . . . . . . . . . . . . . . . 11-5
. . . . . . . 2-19; 6-44, 191; 11-5
. . . . . . . . . . . . . . . . 11-6
. . . . . . . . . . . . . . . . 8-90
. . . . . . . . . . . . . . . . 1-11
. 1-16; 6-27, 70, 71, 100, 164, 216
. . . . . 6-79, 130, 223, 371; 8-7
. . . . . . . . . . . . . . . . . 8-7
. . . . . . . . . . . . . . . . .8-7
. . . . . . . . . . . . . . . . .8-7
. . . . . . . . . . . . . . . . .8-7
. . . . . . . . . . . . . . . . . 8-8
. . . . . . . . . . . . . . . . .8-9
. . . . . . . . . . . . . . . . . 8-8
. . . . . . . . . . . . . . . . 8-12
. . . . . . . . . . . . . . . . 8-12
. . . . . . . . . . . . . . . . 8-18
. . . . . . . . . . . . . . . . 8-15
. . . . . . . . . . . . . . . . 8-19
. . . . . . . . . . . . . . . . 8-12
. . . . . . . . . . . . . . . . . 8-7
. . . . . . . . . . . . . . . . 8-12
. . . . . . . . . . . . . . . . .8-9
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. . . . . . . . . . . 8-213
. . . . . . . . . . . 11-55
. . . . . . . . . . . 11-55
2-11, 20; 6-34, 172; 8-213
. . . . . . . . . . . 1-141
. . . . . . . . . . . . 8-89
. . . . . . . . . 6-123, 249
. . . . . . . . . . . 4-176
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AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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8-122
8-125
8-122
8-122
8-125
11-55
. . . . . . 8-114
. . . . . . . 7-25
. . . . 8-15, 108
6-387, 421; 8-15
. . . . . . 8-108
. . . . . . 8-109
. . . . . . 8-109
. . . . . . 8-110
. . . . . . 8-110
. . . . . . 8-109
. . . . 8-28, 154
24
INDEX
Intersecting welds (and triaxial stresses) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-116
Jumbo shapes; see Heavy shapes
K factor, column design . .
alignment charts . . . . .
stiffness reduction factors
Knee connections . . . . . .
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L shapes; see Angles
LRFD (Load and Resistance Factor Design)
defined . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
essentials of . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Specification for Structural Steel Buildings (AISC) . . . . . . . . . . . . . . .
Single-Angle Specification (AISC) . . . . . . . . . . . . . . . . . . . . . . .
Specification for Structural Joints Using ASTM A325 or A490 Bolts (RCSC) .
Lamellar tearing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Lateral bracing of structural members . . . . . . . . . . . . . . . . . . . . . . .
Lateral torsional buckling of coped beams . . . . . . . . . . . . . . . . . . . . .
Leaning columns; see Columns, leaning
Leveling methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
heavy base plates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
light base plates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Lifting devices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Load and resistance factor design; see LRFD
Load combinations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Load factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Loads
crane runway horizontal forces . . . . . . . . . . . . . . . . . . . . . . . . .
definition of . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
impact . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
moving, beam diagrams and formulas . . . . . . . . . . . . . . . . . . . . . .
Local flange bending . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Local web buckling of coped beams . . . . . . . . . . . . . . . . . . . . . . . .
Local web yielding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Longitudinal stiffeners . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
M shapes
dimensions and properties . . . . . . . . . .
standard mill practice . . . . . . . . . . . .
MC shapes; see Channels
MT shapes; see Tees
Magnetic particle testing weld inspection (MT)
Matching electrodes . . . . . . . . . . . . . .
Materials
weights and specific gravities . . . . . . . .
Measures and weights . . . . . . . . . . . . .
Metric (SI) units . . . . . . . . . . . . . . . .
conversion factors . . . . . . . . . . . . . .
Mill practice, standard . . . . . . . . . . . . .
Miscellaneous channels; see Channels
Miscellaneous shapes; see M shapes
Modulus of elasticity of steel
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. 2-17; 3-5; 6-43, 183
. . . . . . 3-6; 6-186
. . . . . . 3-7; 6-43
. . . . . . . . 10-67
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. 2-6; 6-31, 162
. . . . . . . 2-1
. . . . . . . 6-3
. . . . . 6-277
. . . . . 6-371
. . . 1-8; 8-113
. . . . . 12-22
. . . . . 8-229
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11-56
11-57
11-56
11-65
. . . . . . . 2-6; 6-30, 166
. . . . . . . 2-6; 6-30, 166
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. . . . . . . 6-31
. . 2-9; 6-30, 166
. . . . . . . 6-30
. . . . . . 4-204
6-91, 231; 10-36
. . . . . . 8-226
6-92, 231; 10-38
. . . . . . 9-185
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-44
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-183
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-109
. . . . . . . . . . . . . . . . . . . . . . . . . . 6-77; 8-115
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AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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. . . 7-5
. . 7-10
. . . 7-8
. 7-8, 12
. 1-183
INDEX
25
effect of temperature on . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Moment connections; see Fully restrained (FR) moment connections or Partially
restrained (PR) moment connections
Moment diagrams, beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Moment of inertia
selection tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
shapes with respect to oblique axes . . . . . . . . . . . . . . . . . . . . . . .
Moment splices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
directly welded flange type . . . . . . . . . . . . . . . . . . . . . . . . . . .
design checks for . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
shop and field practices for . . . . . . . . . . . . . . . . . . . . . . . . . .
extended end-plate type . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
design checks for . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
shop and field practices for . . . . . . . . . . . . . . . . . . . . . . . . . .
flange-plated type . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
design checks for . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
shop and field practices for . . . . . . . . . . . . . . . . . . . . . . . . . .
force transfer in . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
location of . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
MT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . 1-12
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Net area reduction for bolt holes . . . .
Nomenclature
beam diagrams and formulas . . . . .
flat rolled carbon steel . . . . . . . .
general . . . . . . . . . . . . . . . .
LRFD Specification . . . . . . . . .
Seismic Specification . . . . . . . .
Noncompact section (definition) . . . .
Non-high-strength bolts . . . . . . . .
ASTM A307 . . . . . . . . . . . . .
dimensions of . . . . . . . . . . . . .
entering and tightening clearances for
weights of . . . . . . . . . . . . . .
Non-rectangular connections . . . . . .
moment connections . . . . . . . . .
skewed . . . . . . . . . . . . . . .
sloped . . . . . . . . . . . . . . .
simple shear connections . . . . . . .
canted . . . . . . . . . . . . . . .
inclines in two or more directions .
skewed . . . . . . . . . . . . . . .
sloped . . . . . . . . . . . . . . .
Notch development in welded joints . .
Nuts, compatibility with bolts . . . . .
. . . . . . . . . . . 4-190
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. 4-23
. 7-23
10-56
10-58
10-58
10-58
10-59
10-59
10-59
10-56
10-56
10-57
10-56
10-56
8-109
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-213
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P-delta second order effects . . . . . . . . .
Painting welded connections . . . . . . . . .
Panel zone web shear . . . . . . . . . . . . .
Parabola, properties of . . . . . . . . . . . .
Partial-joint-penetration groove welds . . . .
effective area of . . . . . . . . . . . . . .
intermittent . . . . . . . . . . . . . . . . .
Partially restrained (PR) moment connections
Penetrations, in beam webs . . . . . . . . . .
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. 2-14; 6-41, 179
. . . . . . 8-117
6-95, 234; 10-40
. . . . . . . 7-15
6-73, 219; 8-125
. . . . . . 8-127
. . . . . . 8-127
6-25, 162; 9-234
6-57, 200; 12-11
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
. . . . . 4-187
. . . . . . . 7-3
. . . . . . . .1
. . . . . . 6-17
. . . . . 6-305
2-12; 6-36, 174
6-79, 223; 8-19
. . . . . . 8-19
. . . . . . 8-19
. . . . . . 8-19
. . . . . . 8-19
. 9-125; 10-67
. . . . . 10-67
. . . . . 10-68
. . . . . 10-68
. . . . . 9-215
. . . . . 9-225
. . . . . 9-228
. . . . . 9-215
. . . . . 9-224
. . . . . 8-114
. . . . . 8-8, 19
26
INDEX
Piles; see HP shapes
Pipe
availability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
dimensions and properties . . . . . . . . . . . . . . . . . . . . . . . . .
standard mill practice . . . . . . . . . . . . . . . . . . . . . . . . . . .
used as columns, design strength tables . . . . . . . . . . . . . . . . . .
Pipes, connections for . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Plans and specifications; see Construction documents
Plate girders . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
built-up wide-flange sections, dimensions and properties . . . . . . . . .
design examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
flexural strength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
hybrid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
shear strength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
tension field action . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Plates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
areas of rectangular sections . . . . . . . . . . . . . . . . . . . . . . . .
floor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
standard mill practice . . . . . . . . . . . . . . . . . . . . . . . . . . .
weights of rectangular sections . . . . . . . . . . . . . . . . . . . . . .
Plug welds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Ponding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
PR Moment Connections; see Partially restrained (PR) moment connections
Prequalified welded joints . . . . . . . . . . . . . . . . . . . . . . . . . .
complete-joint-penetration groove welds . . . . . . . . . . . . . . . . .
fillet welds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
flare welds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
partial-joint-penetration groove welds . . . . . . . . . . . . . . . . . . .
weld symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Producers of structural shapes, tube, and pipe . . . . . . . . . . . . . . . .
Properties of geometric sections . . . . . . . . . . . . . . . . . . . . . . .
Properties; see specific item
torsion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Prying Action . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Purlins, connections for . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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. 4-167; 6-122, 249
. . . . . . . 4-183
. . . . . . . 4-168
. 4-167; 6-122, 249
. 4-176; 6-123, 249
. 4-167; 6-124, 155
. . . . . 6-124, 157
. . . . . . . 1-133
. . . . . . . 1-137
. . . . . . . 1-134
. . . . . . . 1-196
. . . . . . . 1-138
. . . . 6-76; 8-128
. . . 6-97, 132, 236
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. . . . 1-21
. . . 1-121
. . . 1-194
3-36; 5-111
. . . 9-215
. . . 8-131
. . . 8-137
. . . 8-136
. . . 8-153
. . . 8-148
. 8-134, 135
. . . . 1-17
. . . . 7-17
. . . . . . . . . . . . . . 1-145
. . . . . . . . . . . . . . . 11-6
. . . . . . . . . . . . . . 12-18
Quality Certification Program (AISC) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-477
Quality control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-103, 446, 475
RCSC (Research Council on Structural Connections)
LRFD Specification for Structural Joints Using ASTM A325 or A490 Bolts . . . . . . . . . . . . . 6-371
Radiographic testing weld inspection (RT) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-110
Rails, crane . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-139
Raised beams, connections for . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9-211
Ratholes; see Welding, access holes
Recessed-pin nuts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-93
Rectangular sections, weights and areas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-137
Reinforcement of coped beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9-185
combination longitudinal and transverse stiffening . . . . . . . . . . . . . . . . . . . . . . . . . . 9-185
doubler plates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9-185
longitudinal stiffeners . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9-185
References . . . . . . . . . . 1-199; 2-45; 3-117; 4-213; 5-143; 6-257; 8-238; 9-263; 10-71; 11-108; 12-25
Resistance factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-7; 6-32, 168
Reuse of high strength bolts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-19
Rigid-frame connections; see Fully restrained (FR) moment connections
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
INDEX
27
Rolled structural shapes, general notes
Rolling mill practice . . . . . . . . .
Round bars, weight and area . . . . .
RT . . . . . . . . . . . . . . . . . . .
Runoff bars . . . . . . . . . . . . . .
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S shapes
dimensions and properties . . . . . . . . . . . . . . . . . . . . . . . .
standard mill practice . . . . . . . . . . . . . . . . . . . . . . . . . .
used as beams, uniform loads . . . . . . . . . . . . . . . . . . . . . .
SI (metric) units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
conversion factors . . . . . . . . . . . . . . . . . . . . . . . . . . . .
ST shapes; see Tees
Sag rods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
SAW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Seated connections; see Unstiffened or Stiffened seated connections
Second order effects . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Sections
compact, noncompact, and slender-element (defined) . . . . . . . . . .
Seismic Provisions for Structural Steel Buildings (AISC) . . . . . . . . .
Selection tables, beams
load factor design . . . . . . . . . . . . . . . . . . . . . . . . . . . .
moment of inertia . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Semi-rigid connections; see Partially restrained (PR) moment connections
Serviceability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Shapes
general notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
heavy; see Heavy shapes
Shear diagrams, beams . . . . . . . . . . . . . . . . . . . . . . . . . . .
Sheared plates, standard mill practice . . . . . . . . . . . . . . . . . . .
Shear end-plate connections . . . . . . . . . . . . . . . . . . . . . . . .
bolted/welded . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
design checks for . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
recommended dimensions for . . . . . . . . . . . . . . . . . . . . . .
shop and field practices for . . . . . . . . . . . . . . . . . . . . . . . .
Shear rupture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Shear splices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Shear yielding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Sheet metal gages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Shelf angles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Shelf dimensions for fillet welds . . . . . . . . . . . . . . . . . . . . . .
Shielded metal arc welding (SMAW) . . . . . . . . . . . . . . . . . . .
Shims . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Shop drawings; see Construction documents
Simple shear connections . . . . . . . . . . . . . . . . . . . . . . . . . .
at stiffened column-web locations . . . . . . . . . . . . . . . . . . . .
comparing two-sided, seated, and one-sided connections . . . . . . . .
double angle connections . . . . . . . . . . . . . . . . . . . . . . . .
all-bolted . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
all-welded . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
bolted/welded . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
design checks for . . . . . . . . . . . . . . . . . . . . . . . . . . .
recommended angle length and thickness for . . . . . . . . . . . . .
shop and field practices for . . . . . . . . . . . . . . . . . . . . . .
economical considerations for . . . . . . . . . . . . . . . . . . . . . .
erectability considerations for . . . . . . . . . . . . . . . . . . . . . .
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1-135
8-110
8-122
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. . . 1-46
. . 1-183
. 4-61, 98
. . . .7-8
. . 7-8, 12
. . . . . . . . . . . . . . . 12-21
. . . . . . . . . . . . . . . 8-105
. . . . . . . . . . 2-14, 6-41, 179
. . . . . . . . . . 2-12; 6-36, 174
. . . . . . . . . . . . . . . 6-301
. . . . . . . . . . . . . . . . 4-15
. . . . . . . . . . . . . . . . 4-24
. . . . . . . 2-6; 4-207; 6-98, 239
. . . . . . . . . . . . . . . . 1-25
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. . . . . . 4-190
. . . . . . 1-196
. . . . . . . 9-91
. . . . . . . 9-92
. . . . . . . 9-91
. . . . . . . 9-91
. . . . . . . 9-91
6-87, 228; 8-212
. . . . . . 9-179
. . . . . . 8-212
. . . . . . . .7-3
. . . . . . 12-23
. . . . . . 8-122
. . . . . . 8-102
. . . . . . 8-237
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AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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. . 9-7
9-190
. . 9-8
. 9-11
. 9-13
. 9-16
. 9-15
. 9-12
. 9-12
. 9-12
. . 9-7
. . 9-9
28
INDEX
for large end reactions . . . . . . . . . . . . . . . . . . . . .
shear end-plate connections . . . . . . . . . . . . . . . . . .
bolted/welded . . . . . . . . . . . . . . . . . . . . . . . .
design checks for . . . . . . . . . . . . . . . . . . . . . .
recommended end-plate dimensions for . . . . . . . . . . .
shop and field practices for . . . . . . . . . . . . . . . . .
single-angle connections . . . . . . . . . . . . . . . . . . . .
all-bolted . . . . . . . . . . . . . . . . . . . . . . . . . . .
bolted/welded . . . . . . . . . . . . . . . . . . . . . . . .
design checks for . . . . . . . . . . . . . . . . . . . . . .
recommended angle length and thickness for . . . . . . . .
shop and field practices for . . . . . . . . . . . . . . . . .
single-plate connections . . . . . . . . . . . . . . . . . . . .
bolted/welded . . . . . . . . . . . . . . . . . . . . . . . .
design checks for . . . . . . . . . . . . . . . . . . . . . .
recommended plate length and thickness for . . . . . . . .
shop and field practices for . . . . . . . . . . . . . . . . .
stiffened seated connections . . . . . . . . . . . . . . . . . .
all-bolted . . . . . . . . . . . . . . . . . . . . . . . . . . .
bolted/welded . . . . . . . . . . . . . . . . . . . . . . . .
design checks for . . . . . . . . . . . . . . . . . . . . . .
shop and field practices for . . . . . . . . . . . . . . . . .
tee connections . . . . . . . . . . . . . . . . . . . . . . . . .
bolted/welded . . . . . . . . . . . . . . . . . . . . . . . .
design checks for . . . . . . . . . . . . . . . . . . . . . .
recommended tee length and flange and web thicknesses for
shop and field practices for . . . . . . . . . . . . . . . . .
unstiffened seated connections . . . . . . . . . . . . . . . . .
all bolted . . . . . . . . . . . . . . . . . . . . . . . . . . .
all-welded . . . . . . . . . . . . . . . . . . . . . . . . . .
bolted/welded . . . . . . . . . . . . . . . . . . . . . . . .
design checks for . . . . . . . . . . . . . . . . . . . . . .
shop and field practices for . . . . . . . . . . . . . . . . .
Single-angle connections . . . . . . . . . . . . . . . . . . . . .
all-bolted . . . . . . . . . . . . . . . . . . . . . . . . . . .
bolted/welded . . . . . . . . . . . . . . . . . . . . . . . .
design checks for . . . . . . . . . . . . . . . . . . . . . .
recommended angle length and thickness for . . . . . . . .
shop and field practices for . . . . . . . . . . . . . . . . .
specification (AISC) . . . . . . . . . . . . . . . . . . . . . .
struts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Single-plate connections . . . . . . . . . . . . . . . . . . . . .
bolted/welded . . . . . . . . . . . . . . . . . . . . . . . . .
design checks for . . . . . . . . . . . . . . . . . . . . . . . .
recommended plate length and thickness for . . . . . . . . .
shop and field practices for . . . . . . . . . . . . . . . . . .
Slender-element section (definition) . . . . . . . . . . . . . . .
Skewed connections . . . . . . . . . . . . . . . . . . . . . . .
Sleeve nuts . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Slip-critical connections . . . . . . . . . . . . . . . . . . . . .
designed for factored loads . . . . . . . . . . . . . . . . . . .
designed for service loads . . . . . . . . . . . . . . . . . . .
surface classifications . . . . . . . . . . . . . . . . . . . . .
Sloped connections . . . . . . . . . . . . . . . . . . . . . . . .
Slot welds . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
SMAW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Snug-tight . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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. . . . . . . 9-196
. . . . . . . . 9-91
. . . . . . . . 9-92
. . . . . . . . 9-91
. . . . . . . . 9-91
. . . . . . . . 9-91
. . . . . . . 9-161
. . . . . . . 9-162
. . . . . . . 9-163
. . . . . . . 9-161
. . . . . . . 9-161
. . . . . . . 9-161
. . . . . . . 9-147
. . . . . . . 9-149
. . . . . . . 9-147
. . . . . . . 9-148
. . . . . . . 9-149
. . . . . . . 9-138
. . . . . . . 9-140
. . . . . . . 9-140
. . . . . . . 9-139
. . . . . . . 9-140
. . . . . . . 9-170
. . . . . . . 9-170
. . . . . . . 9-170
. . . . . . . 9-171
. . . . . . . 9-171
. . . . . . . 9-128
. . . . . . . 9-130
. . . . . . . 9-132
. . . . . . . 9-132
. . . . . . . 9-129
. . . . . . . 9-130
. . . . . . . 9-161
. . . . . . . 9-162
. . . . . . . 9-163
. . . . . . . 9-161
. . . . . . . 9-161
. . . . . . . 9-161
. . . . . . . 6-277
. . . . . . . 3-104
. . . . . . . 9-147
. . . . . . . 9-149
. . . . . . . 9-147
. . . . . . . 9-148
. . . . . . . 9-149
. . 2-12; 6-36, 174
. . . 9-215; 10-68
. . . . . . . . 8-93
6-83, 226; 8-12, 25
. . . . 6-130; 8-27
. . . . . 6-83; 8-26
. . . . 6-375; 8-26
. . . 9-224; 10-68
. . . . 6-76; 8-128
. . . . . . . 8-102
. . . . . . . . 8-12
INDEX
29
Snug-tightened bolts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-12
Software . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-14; 2-44; 9-10
Spacer bars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-122
Specific gravities, various substances . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-5
Specification for Structural Joints Using ASTM A325 or A490 Bolts (RCSC), LRFD . . . . . . . . . 6-371
Specification for Structural Steel Buildings (AISC), LRFD . . . . . . . . . . . . . . . . . . . . . . . . . 6-3
Commentary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-161
Specifications; see Construction documents
Splices, crane rail . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-139
Square bars, weight and area . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-135
Stability; see Buckling
frame . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-14; 6-35, 41, 179
Standard mill practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-183
Steel pipes; see Pipe
Stiffened seated connections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9-138
all-bolted . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9-140
bolted/welded . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9-140
design checks for . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9-139
shop and field practices for . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9-140
Stiffeners . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9-185; 10-35
at moment connections; see Column stiffening
diagonal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10-54
for concurrent strong-axis and weak-axis FR connections . . . . . . . . . . . . . . . . . . . . . . 10-49
longitudinal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9-185
transverse . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10-41
concentric . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10-41
eccentric . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10-48
Stiffness reduction factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-7
Structural shapes
availability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-15
general notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-25
geometric properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-23
principal producers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-17
rolling and cutting variations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-183
size groupings, tensile properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-16
Structural steel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-5; 6-25, 427, 460
architecturally exposed; see Architecturally exposed structural steel
Structural tees; see Tees, structural
Structural tubing; see Tubing
Struts, single-angle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-104
Submerged arc welding (SAW) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-105
Surface and box areas of W shapes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-175
Sweep, standard mill practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-187
Symbols; see Nomenclature
Tapered members . . . . . . . . . . . . . . . . . . . . . . . .
Tees, structural
dimensions and properties . . . . . . . . . . . . . . . . . .
flexural-torsional properties . . . . . . . . . . . . . . . . .
standard mill practice . . . . . . . . . . . . . . . . . . . .
used as columns, design strength tables . . . . . . . . . . .
Tee connections . . . . . . . . . . . . . . . . . . . . . . . . .
bolted/welded . . . . . . . . . . . . . . . . . . . . . . . .
design checks for . . . . . . . . . . . . . . . . . . . . . . .
recommended tee length and flange and web thicknesses for
shop and field practices for . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . 6-118
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AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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. 1-68
1-161
1-191
. 3-83
9-170
9-170
9-170
9-171
9-171
30
INDEX
Temperature
coefficients of expansion . . . . . . . . . . . . .
effect on properties of steel . . . . . . . . . . .
Tension members
built-up . . . . . . . . . . . . . . . . . . . . . .
cross-sectional area
gross, net, and effective net . . . . . . . . . .
design strength . . . . . . . . . . . . . . . . . .
pin-connected and eyebar . . . . . . . . . . . .
slenderness ratio . . . . . . . . . . . . . . . . .
Tension rupture . . . . . . . . . . . . . . . . . . .
Tension yielding . . . . . . . . . . . . . . . . . .
Tension-control bolts; see Alternative design bolts
Thermal cutting . . . . . . . . . . . . . . . . . . .
Threaded (anchor) rods . . . . . . . . . . . . . . .
cast-in-place anchor rods . . . . . . . . . . . . .
drilled-in anchor rods . . . . . . . . . . . . . .
headed anchor rods . . . . . . . . . . . . . . . .
hooked anchor rods . . . . . . . . . . . . . . . .
minimum edge distance . . . . . . . . . . . . .
minimum embedment length . . . . . . . . . . .
welding to . . . . . . . . . . . . . . . . . . . .
Tightening clearances for bolts . . . . . . . . . . .
Tolerances
erection . . . . . . . . . . . . . . . . . . . . . .
fabrication . . . . . . . . . . . . . . . . . . . .
Torsion . . . . . . . . . . . . . . . . . . . . . . .
properties . . . . . . . . . . . . . . . . . . . . .
Transverse stiffeners, concentric and eccentric . . .
Triaxial stresses . . . . . . . . . . . . . . . . . . .
Trigonometric formulas . . . . . . . . . . . . . . .
Truss connections . . . . . . . . . . . . . . . . . .
chord splices . . . . . . . . . . . . . . . . . . .
members in . . . . . . . . . . . . . . . . . . . .
panel-point connections . . . . . . . . . . . . .
design checks for . . . . . . . . . . . . . . .
shop and field practices for . . . . . . . . . .
support connections . . . . . . . . . . . . . .
design checks for . . . . . . . . . . . . . . .
shop and field practices for . . . . . . . . . .
Tubing
availability . . . . . . . . . . . . . . . . . . . .
dimensions and properties . . . . . . . . . . . .
connections for . . . . . . . . . . . . . . . . . .
principal producers . . . . . . . . . . . . . . . .
standard mill practice . . . . . . . . . . . . . .
used as columns, design strength tables . . . . .
Turnbuckles . . . . . . . . . . . . . . . . . . . . .
Twist-off bolts; see Alternative design bolts
. . . . . . . . . . . . . . . . . . . . . . . . . 1-12; 7-4
. . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-11
. . . . . . . . . . . . . . . . . . . . . . . . . 6-44, 191
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2-11; 6-34, 172
2-19; 6-44, 191
. . . 6-45, 191
2-13; 6-37, 177
. . 6-87; 8-225
. . . . . 8-225
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. . . . . 6-442, 467
. 1-183; 6-434, 465
. . 2-40; 6-60, 202
. . . . . . . 1-145
. . . . . 10-41, 48
. . . . . . . 8-116
. . . . . . . . 7-24
. . . . . . . 11-92
. . . . . . . 11-107
. . . . . . . 11-92
. . . . . . . 11-94
. . . . . . . 11-94
. . . . . . . 11-94
. . . . . . . 11-98
. . . . . . . 11-98
. . . . . . . 11-100
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. . . . 1-21
. . . 1-122
. . . 9-215
. . . . 1-17
. . . 1-194
3-39; 5-115
. . . . 8-92
Ultimate strength method; see instantaneous center of rotation method
Ultrasonic testing weld inspection (UT) . . . . . . . . . . . . . . . .
Uniform force method . . . . . . . . . . . . . . . . . . . . . . . . .
Uniform loads, factored . . . . . . . . . . . . . . . . . . . . . . . .
general notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Universal mill plates, standard mill practice . . . . . . . . . . . . . .
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AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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. . 8-108
. . . 8-88
. . . 8-88
. . . 8-88
. . . 8-90
. . . 8-89
. . . 8-88
. . . 8-88
. . . 8-89
. 8-12, 19
. . 8-110
11-19, 20
. . . 4-35
. . . 4-28
. . 1-196
INDEX
Unstiffened seated connections
all bolted . . . . . . . . . .
all-welded . . . . . . . . .
bolted/welded . . . . . . .
design checks for . . . . . .
shop and field practices for .
UT . . . . . . . . . . . . . . .
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9-128
9-130
9-132
9-132
9-129
9-130
8-110
Visual testing weld inspection (VT) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-109
VT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-109
W shapes
cambering . . . . . . . . . . . . . . . .
dimensions and properties . . . . . . . .
standard mill practice . . . . . . . . . .
torsion properties . . . . . . . . . . . . .
surface and box areas . . . . . . . . . . .
used as beams
design selection table . . . . . . . . .
uniform loads . . . . . . . . . . . . .
used as columns
design strength tables . . . . . . . . .
WT shapes; see Tees
Wall anchors . . . . . . . . . . . . . . . .
Washers, compatibility with bolts . . . . .
Web crippling . . . . . . . . . . . . . . . .
Web openings . . . . . . . . . . . . . . . .
Web tear-out . . . . . . . . . . . . . . . .
Weights and measures . . . . . . . . . . .
Weights and specific gravities . . . . . . .
Weights
bars, round and square . . . . . . . . . .
building materials . . . . . . . . . . . .
of high-strength bolts . . . . . . . . . . .
of non-high-strength bolts . . . . . . . .
rectangular sections . . . . . . . . . . .
structural shapes, method of increasing .
Welding . . . . . . . . . . . . . . . . . . .
access holes . . . . . . . . . . . . . . .
air-arc gouging . . . . . . . . . . . . . .
clearances for . . . . . . . . . . . . . . .
combined with bolts in connections . . .
complete-joint-penetration groove welds
backing bars . . . . . . . . . . . . . .
extension bars . . . . . . . . . . . . .
ratholes; see weld access holes . . . .
runoff bars . . . . . . . . . . . . . . .
spacer bars . . . . . . . . . . . . . . .
weld access holes . . . . . . . . . . .
design strength of welds . . . . . . . . .
base metal design strength . . . . . . .
weld metal design strength . . . . . .
economical considerations . . . . . . . .
fillet welds . . . . . . . . . . . . . . . .
effective area of . . . . . . . . . . . .
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. 1-179, 185; 4-207; 6-98
. . . . . . . . . . . 1-26
. . . . . . . . . . 1-183
. . . . . . . . . . 1-146
. . . . . . . . . . 1-175
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-15
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-35, 72
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-16
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. . . . . . . . . . . 1-135
. . . . . . . . . . . . . 7-7
. . . . . . . . . . . . . 8-9
. . . . . . . . . . . . 8-19
. . . . . . . . . . . 1-138
. . . . . . . . . . . 1-183
. 6-73, 129, 219, 251; 8-98
. . . . . . . . . . . 8-125
. . . . . . . . . . . 8-108
. . . . . . . . . . . 8-118
. . . . . 6-72, 217; 8-211
. . . . . . . . . . . 8-122
. . . . . . . . . . . 8-122
. . . . . . . . . . . 8-122
. . . . . . . . . . . 8-125
. . . . . . . . . . . 8-122
. . . . . . . . . . . 8-122
. . . . . . . . . . . 8-125
6-73, 129, 219, 251; 8-129
. . . . . . . . . . . 8-129
. . . . . . . . . . . 8-129
. . . . . . . . . . . 8-111
. . . . . . . . . . . 8-118
. . . . . . . . . . . 8-118
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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. . . . . . 12-23
. . . . . . 8-8, 19
6-92, 232; 10-39
6-57, 200; 12-11
6-87, 228; 8-212
. . . . . . . 7-10
. . . . . . . . 7-5
32
INDEX
end returns . . . . . . . . . . . . . . . . . . .
in holes or slots . . . . . . . . . . . . . . . .
maximum size of . . . . . . . . . . . . . . . .
minimum effective length of . . . . . . . . .
minimum shelf dimensions for . . . . . . . .
minimum size of . . . . . . . . . . . . . . . .
other limitations on . . . . . . . . . . . . . .
flare welds . . . . . . . . . . . . . . . . . . . .
effective area of . . . . . . . . . . . . . . . .
limitations on . . . . . . . . . . . . . . . . .
for ASTM A6 groups 4 and 5 shapes . . . . . . .
inspection . . . . . . . . . . . . . . . . . . . . .
dye-penetrant testing weld inspection (DPT) .
magnetic particle testing weld inspection (MT)
radiographic testing weld inspection (RT) . . .
ultrasonic testing weld inspection (UT) . . . .
visual testing weld inspection (VT) . . . . . .
minimizing weld repairs . . . . . . . . . . . . .
arc strikes . . . . . . . . . . . . . . . . . . .
fatigue cracking . . . . . . . . . . . . . . . .
impact toughness . . . . . . . . . . . . . . .
lamellar tearing . . . . . . . . . . . . . . . .
notch development . . . . . . . . . . . . . . .
other considerations . . . . . . . . . . . . . . .
intersecting welds and triaxial stresses . . . .
matching electrodes . . . . . . . . . . . . . .
painting . . . . . . . . . . . . . . . . . . . .
welding shapes from ASTM A6 groups 4 and 5
partial-joint-penetration groove welds . . . . . .
effective area of . . . . . . . . . . . . . . . .
intermittent welds . . . . . . . . . . . . . . .
plug and slot welds . . . . . . . . . . . . . . . .
prequalified welded joints . . . . . . . . . . . .
complete-joint-penetration groove welds . . .
fillet welds . . . . . . . . . . . . . . . . . . .
flare welds . . . . . . . . . . . . . . . . . . .
partial-joint-penetration groove welds . . . . .
weld symbols . . . . . . . . . . . . . . . . .
structural welding materials and processes . . .
air-arc gouging . . . . . . . . . . . . . . . . .
electrogas welding (EGW) . . . . . . . . . .
electroslag welding (ESW) . . . . . . . . . .
flux-cored arc welding (FCAW) . . . . . . . .
gas-metal arc welding (GMAW) . . . . . . .
shielded metal arc welding (SMAW) . . . . .
submerged arc welding (SAW) . . . . . . . .
thermal cutting . . . . . . . . . . . . . . . . .
to anchor rods . . . . . . . . . . . . . . . . . .
weldability of steel . . . . . . . . . . . . . . . .
Wide flange shapes; see W shape
Wire and sheet metal gages . . . . . . . . . . . . .
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. . . 8-120
. . . 8-121
. . . 8-119
. . . 8-119
. . . 8-122
. . . 8-119
. . . 8-121
. . . 8-127
. . . 8-128
. . . 8-128
. . . 8-115
. . . 8-108
. . . 8-109
. . . 8-109
. . . 8-110
. . . 8-110
. . . 8-109
. . . 8-113
. . . 8-114
. . . 8-113
. . . 8-114
. . . 8-113
. . . 8-114
. . . 8-115
. . . 8-116
. . . 8-115
. . . 8-117
. . . 8-115
. . . 8-125
. . . 8-127
. . . 8-127
. . . 8-128
. . . 8-131
. . . 8-137
. . . 8-136
. . . 8-153
. . . 8-148
. 8-134, 135
. . . 8-101
. . . 8-108
. . . 8-107
. . . 8-107
. . . 8-106
. . . 8-106
. . . 8-102
. . . 8-105
. . . 8-108
. . . . 8-89
. . . . 8-98
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-3
AMERICAN INSTITUTE OF STEEL CONSTRUCTION