EN 1993-4-2 (2007) (English): Eurocode 3: Design of steel
structures - Part 4-2: Tanks [Authority: The European Union
Per Regulation 305/2011, Directive 98/34/EC, Directive
2004/18/EC]
EUROPEAN STANDARD
EN 1993-4-2
NORME EUROPEENNE
EUROpAISCHE NORM
February 2007
ICS 23.020.01; 91.010.30; 91.080.10
Supersedes ENV 1993-4-2: 1999
English Version
Eurocode 3 - Design of steel structures - Part 4-2: Tanks
Eurocode3-Calculdesstructuresenacier-Partie4-2:
Re servoirs
Eurocode 3 Bemessung und Konstruktion von
Stahlbauten - Teil 4-2: Silos,Tankbauwerke und
Rohrleitungen - Tankbauwerke
This European Standard was approved by CEN on 12 June 2006.
CEN members are bound to comply with the CEN/CENELEC Internal Regulations which stipulate the conditions for giving this European
Standard the status of a national standard without any alteration. Up-to-date lists and bibliographical references concerning suchnational
standards may be obtained on application to the CEN Management Centre or to any CEN member.
This European Standard exists in three official versions (English, French, German). A version in any other language made by translation
under the responsibility of a CEN member into its own language and notified to the CEN Management Centre has the same status as the
official versions.
CEN members are the national standards bodies of Austria, Belgium, Bulgaria, Cyprus, Czech Republic, Denmark, Estonia, Finland,
France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway. Poland, Portugal,
Romania, Slovakia, Slovenia, Spain, Sweden, Switzerland and United Kingdom.
EUROPEAN COMMITTEE FOR STANDARDIATION
COMITE EUROPEE\I DE NORMALISATION
EUROPAISCI-IES KorvllTEE FOR NORMUNG
Management Centre: rue de Stassart, 36
© 2007 CEN
All rights of exploitation in any form and by any means reserved
worldwide for CEN national Members.
B-1050 Brussels
Ref. No. EN 1993-4-2:2007: E
BS EN 1993-4-2:2007
EN 1993-4-2: 2007 (E)
Contents
Foreword
4
1
8
8
8
General
1.1
Scope
1.2
1.3
1.4
1.5
1.6
1.7
1.8
2
N ormati ve references
Assumptions
Distinction between principles and application rules
Terms and definitions
Syn"lbols used in Part 4.2 of Eurocode 3
Sign conventions
Units
19
2.1
2.2
2.3
2.4
2.5
2.6
2.7
2.8
2.9
19
19
19
19
19
Properties of Jllaterials
3.1
General
3.2 Structural steels
3.3
Steels for pressure purposes
3.4
3.5
4
Stainless steels
Toughness requirements
Basis for structural analysis
4.1
4.2
4.3
4.4
5
13
18
Basis of design
Requirements
Reliability differentiation
Limit states
Actions and environmental effects
Material properties
Geometrical data
Modelling of the tank for determining action effects
Design assisted by testing
Action effects for limit state verifications
2.10 Combinations of actions
2.1 I Durability
3
10
10
10
12
Ultimate limit states
Analysis of the circular shell structure of a tank
Analysis of the box structure of a rectangular tank
Equivalent orthotropic properties of corrugated sheeting
Design of cylindrical walls
5.1
Basis
5.2
Distinction of cylindrical shell forms
5.3
5.4
5.5
Resistance of the tank shell wall
Considerations for supports and openings
Serviceability limit states
20
20
20
20
22
22
23
23
23
23
23
24
25
25
25
27
28
29
29
29
29
30
33
6
Design of conical hoppers
34
7
Design of circular roof structures
7.1
Basis
34
34
34
35
35
7.2
7.3
7.4
2
Distinction of roof structural forms
Resistance of circular roofs
Considerations for individual structural forms
BS EN 1993-4-2:2007
EN 1993-4-2: 2007 (E)
7.5
8
9
Serviceability limit states
36
Design of transition junctions at the bottom of the shell and supporting ring
gkders
36
Design of rectangular and planar-sided tanks
37
9.1
9.2
9.3
9.4
37
37
37
38
Basis
Distinction of structural forms
Resistance of vertical walls
Serviceability limit states
10
Requirements on fabrication, execution and erection with relation to design
38
11
Simplified design
11 . 1 Genera]
39
11.2
11.3
] 1.4
11.5
Fixed roof design
Shell design
Bottom design
Anchorage design
39
40
46
50
51
Annex A [normative]
53
Actions on tanks
53
A.1
A.2
53
53
General
Actions
3
BS EN 1993.. 4·2:2007
EN 1993-4-2: 2007 (E)
Foreword
This European Standard EN 1993-4-2, EUfocode 3: "Design of Steel Structures - Part 4-2: Tanks",
has been prepared by Technical Committee CEN/TC250 «Structural Eurocodes », the Secretariat
of which is held by BSI. CEN/TC2S0 is responsible for all Structural Eurocodes.
This European Standard shall be given the status of a National Standard, either by publication of an
identical text or by endorsement, at the latest by August 2007, and conflicting National Standards shall
be withdrawn at latest by March 2010.
This Eurocode supersedes ENV] 993-4-2: 1999.
According to the CEN-CENELEC Internal Regulations, the National Standard Organizations of the
following countries are bound to implement this European Standard: Austria, Belgium, Bulgaria, Cyprus, Czech
Republic, Denmark, Estonia, Finland,
Germany, Greece, Hungary, Iceland, Ireland, Italy,
Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Romania, Slovakia,
Slovenia, Spain, Sweden, Switzerland and United Kingdom.
Background of the Eurocode progrmnlne
In 1
the Commission of the European Community decided on an action programme in the field of
construction, based on article 95 of the Treaty. The objective of the programme was the elimination of
technical obstacles to trade and the harmonisation of technical specifications.
Within this action programme, the Commission took the initiative to establish a set of harmonised
technical rules for the design of construction works which, in a first
would serve as an
alternative to the national rules in force in the Member States and, ultimately, would replace them.
For fifteen years, the Commission, with the help of a Steering Committee with Representatives of
Member
conducted the development of the Eurocodes programme, which led to the first
generation of European codes in the] 980' s.
]n 1
the Commission and the Member States of the ED and EFTA decided, on the basis of an
agreement l ) between the Commission and CEN, to transfer the preparation and the publication of the
Eurocodes to the CEN through a series of Mandates, in order to provide them with a future status of
European Standard (EN). This links de facto the Eurocodes with the provisions of all the Council's
Directives and/or Commission's Decisions dealing with European standards (e.g. the Council
Directive 89/106/EEC on construction products - CPD - and Council Directives 93/37/EEC,
92/50/EEC and 89/440/EEC on public works and services and equivalent EFTA Directives initiated in
pursuit of
up the internal market).
The Structural Eurocode programme comprises the following standards generally consisting of a
number of Parts:
ENI990
ENJ991
ENJ992
I)
Eurocode 0: Basis of structural design
Eurocode 1: Actions on structures
Eurocode 2: Design of concrete structures
Agreement between the Commission of the European Communities and the European Committee for Standardisation
(CEN) concerning the work on EUROCODES for the
(BCICEN/03/89).
4
of building and civil engineering works
BS EN 1993-4-2:2007
EN 1993-4-2: 2007 (E)
ENl993
ENl994
ENl995
ENl996
ENl997
EN1998
EN1999
Eurocode 3:
Eurocode 4:
Eurocode 5:
Eurocode 6:
Eurocode 7:
Eurocode 8:
Eurocode 9:
Design of steel structures
Design of composite steel and concrete structures
Design of timber structures
Design of masonry structures
Geotechnical design
Design of structures for earthquake resistance
Design of aluminium structures
Eurocode standards recognise the responsibility of regulatory authorities in each Member State and
have safeguarded their right to determine values related to regulatory safety matters at national level
where these continue to vary from State to State.
Status and field of application of Eurocodes
The Member States of the EU and EFTA recognise that EUROCODES serve as reference documents
for the following purposes:
as a means to prove compliance of building and civil engineering works with the essential
requirements of Council Directive 89/ I
particularly Essential Requirement N° 1 Mechanical resistance and stability - and Essential Requirement N°2 Safety in case of fire;
• as a basis for specifying contracts for construction works and related engineering services;
• as a framework for drawing up harmonised technical specifications for construction products
(ENs and
The Eurocodes, as far as they concern the construction works themselves, have a direct relationship
2
with the Interpretative Documents ) referred to in Article 12 of the CPO, although they are of a
3
different nature from harmonised product standards ). Therefore, technical aspects arising from the
Eurocodes work need to be adequately considered by CEN Technical Committees and/or EOT A
Working Groups working on product standards with a view to achieving full compatibility of these
technical specifications with the Eurocodes.
•
The Eurocode standards provide common structural design rules for everyday use for the design of
whole structures and component products of both a traditional and an innovative nature. Unusual
forms of construction or design conditions are not specifical1y covered and additional expert
consideration will be required by the designer in such cases.
National Standards implementing Eurocodes
The National Standards implementing Eurocodes will comprise the full text of the Eurocode
(including any annexes), as published by CEN, which may be preceded by a National title page and
National foreword, and may be followed by a National Annex.
2)
AC(;Orcling to Art. 3.3 of the CPD. the essential .·<,,·.....·"""".•
Hc
(ERs) shall be
concrete form in
documents for the creation of the necessary links between the essential requirements and the mandates for
harmonised ENs and ETAGs/ETAs.
3}
to Art. 12 of the CPO the interpretative documents shall .
a)
concrete form to the essential
by harmonising the
classes or levels for each requirement where necessary:
and the technical bases and indicating
b) indicate methods of correlating these classes or levels of requirement with the technical
calculation and of proof, technical rules for project design. eLC. :
e.g. methods of
c) serve as a reference for the establishment of harmonised standards and guidelines for European technical approvals.
The Eurocodes, de facto, playa similar role in the field of the ER I and a part of ER 2.
5
BS EN 1993-4-2:2007
EN 1993-4-2: 2007 (E)
The National Annex may only contain information on those parameters which are left open in the
Eurocode for national choice, known as Nationally Determined Parameters, to be used for the design
of buildings and civil engineering works to be constructed in the country concerned, i.e. :
• values and/or classes where alternatives are given in the Eurocode,
• values to be used where a symbol only is given in the Eurocode,
• country specific data (geographical, climatic, etc),
snow map,
• the procedure to be Llsed where alternative procedures are given in the Eurocode.
It may also contain:
• decisions on the application of informative annexes,
• references to non-contradictory complementary information to assist the user to apply the
Ellrocode.
Links between Eurocodes and harnlonised technical specifications (ENs and ETAs) for products
There is a need for consistency between the harmonised technical specifications for construction
products and the technical rules for works 4). Furthermore, all the information accompanying the CE
Marking of the construction products which refer to Eurocodes should clearly mention which
Nationally Determined Parameters have been taken into account.
Additional information specific to EN1993·4·2
EN 1993-4-2 gives design guidance for the structural design of tanks.
EN 1993-4-2 gives design rules that supplement the generic rules in the many parts of EN 1993-1.
EN 1993-4-2 is intended for clients, designers, contractors and relevant authorities.
EN 1993-4-2 is intended to be used in conjunction with EN 1990, with EN 1991-4, with the other
Parts of EN 1991, with EN 1993-1-6 and EN 1993-4-1, with the other Parts of EN 1993, with
EN 1992 and with the other Parts of EN 1994 to EN 1999 relevant to the design of tanks. Matters that
are already covered in those documents are not repeated.
Numerical values for partial factors and other reliability parameters are recommended as basic values
that provide an acceptable level of reliability. They have been selected assuming that an appropriate
level of workmanship and quality management applies.
Safety factors for 'product type' tanks (factory production) can be specified by the appropriate
authorities. When applied to 'product type' tanks, the factors in 2.9 are for guidance purposes only.
They are provided to show the likely levels needed to achieve consistent reliability with other designs.
National Annex for EN1993-4-2
This standard gives alternative procedures, values and recommendations for classes with notes
indicating where national choices may have to be made. Therefore the National Standard
implementing EN 1993-4-2 should have a National Annex containing all Nationally Determined
Parameters to be used for the design of buildings and civil engineering works to be constructed in the
relevant country.
National choice is allowed in EN 1993-4-2 through:
2.2 (I)
2.2 (3)
4)
see An.J.3 and Arl.12 of the CPO, as well as clauses 4.2, 4.3. J, 4.3.2 and 5.2 of ID I.
6
BS EN 1993-4-2:2007
EN 1993-4-2: 2007 (E)
2.9.2.) (1)P
2.9.2.1 (2)P
2.9.2.1 (3)P
2.9.2.2 (3) P
2.9.3 (2)
3.3 (3)
4.1.4(3)
4.3.1 (6)
4.3.1 (8)
7
BS EN 1993-4-2:2007
EN 1993-4-2: 2007 (E)
1
General
1.1
Scope
(I)
Part 4.2 of Eurocode 3 provides principles and application rules for the structural
of
vertical cylindrical ~
and rectangular
above ground steel tanks for the storage of liquid
products with the following characteristics
a) characteri stic internal pressures above the liquid level not less than
than 500mbar J) ;
I OOmbar and not more
b) design metal temperature in the range of -50oe to +300oe. For tanks constructed using
austenitic stainless steels, the design metal temperature may be in the range of -165°e to
+300oe. For fatigue loaded tanks, the temperature should be limited to T < 150oe;
c) maximum design liquid level not higher than the top of the
tank @lI.
cylindrical and rectangular
(2)
This Part 4.2 IS concerned only with the requirements for resistance and stability of steel tanks.
Other design requirements are covered by EN 14015 for ambient temperature tanks and by EN 14620
for cryogenic tanks, and by EN 1090 for fabrication and erection considerations. These other
requirements include foundations and settlement, fabrication, erection and
functional
performance, and details like man-holes, flanges, and filling devices.
(3)
Provisions concerning the special requirements of seismic design are provided in EN 1998-4
(Eurocode 8 Part 4 "Design of structures for earthquake resistance: Silos, tanks and pipel1nes"), which
complements the provisions of Eurocode 3 specifically for this purpose.
The design of a supporting structure for a tank is dealt with in EN ] 993-1-1.
(5)
The design of an aluminium roof structure on a steel tank is dealt with in EN 1999-1-5.
(6)
Foundations in reinforced concrete for steel tanks are dealt with in EN 1992 and EN 1997.
(7)
Numerical values of the specific actions on steel tanks to be taken into account in the design are
given in EN 1991-4 "Actions on Silos and Tanks". Additional provisions for tank actions are given in
annex A to this Part 4.2 of Eurocode 3.
(8)
This Part 4.2 does not cover:
floating roofs and floating covers;
resistance to fire (refer to EN 1993-] -2).
The circular planform tanks covered by this standard are restricted to axisymmetric structures,
(9)
though they can be subject to unsymmetrical actions, and can be unsymmetrically supported.
1.2
Normative references
This European Standard incorporates, by dated and undated
provisions from other
standards. These normative references are cited at the appropriate places in the text and the
publications are listed hereafter. For dated references, subsequent amendments to, or revisions of, any
of these publications apply to the European Standard only when incorporated in it by amendment or
revision. For undated references the latest edition of the publication referred to applies.
I)
All pressures are
8
ill
mbar gauge
UIlIe ... "
otherwise specified
BS EN 1993-4-2:2007
EN 1993-4-2: 2007 (E)
EN 1090-2
Execution of steel and alllminium structures
structures
EN 1990
Eurocode: Basis
EN 1991
Eurocode 1: Actiolls
(~f
Technical requiremellts for steel
strllctural design;
011
structures;
Part 1.1: Actions on Structllres Densities, se(f\veight and imposed loadsfor buildings;
Part 1.2: Actiolls on strllctures - Actiow·; 011 structllres expos'ed to fire;
Part 1.3: Actions 011 structures - Snow loads;
Part].4: Actions on strllctllres - Wind loads;
Part 4:
Actions
011
silos and tanks;
EN ] 992
Eurocode 2 : Design of concrete structllres ;
EN 1993
Ellrocode 3: Desigrt
(~fstel
strllctllres;
Part 1.]: General rule.)' and rllles for buildings;
Part 1.3: General rules - Sllpplementary rules for coldformed members and sheeting;
Part 1.4: General rules
Sllpplement([1), rules for stainless steels;
Part 1.6: General rules - Sllpplementary rules for the strength and stability
structures;
(~l
shell
Part 1.7: GeneraL rules - Supplementar.v rilles for pLanar plated structures loaded
transversely;
Part 1.10:
Material toughness and through thickness properties;
Part 4. I: Silos;
EN 1997
Eurocode 7: Geotechnical design;
EN 1998
Eurocode 8: Design
Part 4:
EN 1999
(~fSlrctieso
earthquake resistance;
Silos, tanks and pipelines;
Eurocode 9: Design of aLuminillm strllctures;
Part 1.5: Shell structures;
EN 10025
[gj) Hot rolled prodllcts ql structllral steeLs @11;
EN 10028
Flat products made (if steel for pressure plll]JOSeS;
EN 10088
Stainless steels
EN 10149
Specification for hot-rolled flat products made of high yield strength steel.)' for
coldforming.
Part 1:
General delivery conditions
Part 2:
Delivery conditions for thennomec/wl1ically rolled steeLs
Part 3:
Delivery condilionsfor normaliz.ed or nonnaliz.ed rolled steels
EN 13084
Part 7:
EN 14015
Freestanding industriaL chimneys
Prodllct specificalion (~l cylindrical steeL fabrications for lise in singLe 'vvall
steel chimneys and steel liners
Spec{fication for the de5;ign and I1Wlll{lactllre of site built, vertical, cylindrical,
flat bottomed, above ground, }velded, metallic tanks for the storage (~liqtds
at
ambient temperatures
9
BS EN 1993-4-2:2007
EN 1993-4-2: 2007 (E)
EN 14620
Design and lJw~facture
site bililt, vertical, cylindrical, flat-bottomed steel
tanks for the storage (d' rejh'gerated, liquefied gases with operating
temperatures betlveen -5°C and -165°C;
ISO 1000
Sf Units:
ISO 3898
Basesfor design q/strllctllres - Notation - General symbols:
ISO 8930
General principles on reliability for structures - List (d'equivalent terms.
1.3 Assumptions
(])
In addition to the general assumptions of EN 1990 the following assumption applies:
- fabrication and erection complies with EN 1090, EN 140] 5 and 14620 as appropriate
1.4 Distinction between principles and application rules
(1)
See 1.4 in EN ] 990.
1.5 Terms and definitions
(])
The terms that are defined in ].5 in EN 1990 for common use in the Structural Eurocodes and
the definitions given in ISO 8930 apply to this Part 4.2 of EN 1993, unless otherwise stated, but for
the purposes of this Part 4.2 the fol1owlng supplementary definitions are given:
1.5.1 shell. A structure formed from a curved thin plate. This term also has a special meaning for
tanks: see IR1) 1.5.9
1.5.2 axisYlTIlTIetric shel1. A shell structure whose geometry is defined by rotation of a meridional
line aboLlt a central axis.
1.5.3 box. A structure formed from an assembly of flat plates into a three-dimensional enclosed
form. For the purposes of this standard, the box has dimensions that are generally comparable in all
directions.
1.5.4 meridional direction. The tangent to the tank wall at any point in a plane that passes through
the axis of the tank. It varies according to the structural element being considered.
1.5.5 circumferential direction. The horizontal tangent to the tank wall at any point. It varies
arollnd the tank, lies in the horizontal plane and is tangential to the tank wall inespective of whether
the tank is circular or rectangular in plan.
1.5.6 middle surface. This term is used to refer to both the stress-free middle surface when a shell is
in pure bending and the middle plane of a flat plate that forms part of a box.
1.5.7 separation of stiffeners. The centre to centre distance between the longitudinal axes of two
adjacent parallel stiffeners.
Supplementary to Part 1 of EN 1993 (and Part 4 of EN 1991), for the purposes of this Pml 4.2, the
following terminology applies:
10
BS EN 1993-4-2:2007
EN 1993-4-2: 2007 (E)
1.5.8 tank. A tank is a vessel for storing liquid products. In this standard it is assumed to be
prismatic with a vertical axis (with the exception of the tank bottom and roof parts).
1.5.9 shell. The shell is the cylindrical wall of the tank of circular planform. Although this usage is
slightly confusing when it is compared to the definition given in
1.5.1 @l], it is so widely used
with the two meanings that both have been retained here. Where any confusion can arise, the alternative
term "cylindricaJ wall" is used.
1.5.10 tank wall. The metal plate elements forming the vertical walls, roof or a hopper bottom are
referred to as the tank wall. This term is not restricted to the vertical "valls.
1.5.11 course. The cylindrical wall of the tank is formed making horizontal joints between a series
of short cylindrical section~
each of which is formed by making vertical joints between individual
curved plates. A short cylinder without horizontal joints is termed a course.
1.5.12 hopper. A hopper is a converging section towards the bottom of a tank. It is used to channel
fluids towards a gravity discharge outlet (usually when they contain suspended solids).
1.5.13 junction. A junction is the point at which any two or more shell segments or flat plate
elements meet. It can include a stiffener or not: the point of attachment of a ring stiffener to the shell
or box may be treated as a junction.
1.5.14 transition junction. The transition junction is the junction between the vertical wall and a
hopper. The junction can be at the base of the vertical wall or part way down it.
1.5.15 shell-roof junction. The shell-roof junction is the junction between the vertical wall and the
roof. It is sometimes referred to as the eaves junction, though this usage is more common for solids
storages.
1.5.16 stringer stiffener. A stringer stiffener is a local stiffening member that follows the meridian
of a shell, representing a generator of the shell of revolution. It is provided to increase the stabil ity, or
to assist with the introduction of local loads or to carry axial loads. It is not intended to provide a
primary load carrying capacity for bending due to transverse loads.
1.5.17 rib. A rib is a local member that provides a primary load carrying path for loads causing
bending down the meridian of a shell or flat plate, representing a generator of the shell of revolution
or a vertical stiffener on a box. It is used to distribute transverse loads on the structure by bending
action.
1.5.18 ring stiffener. A ring stiffener is a local stiffening member that passes around the
circumference of the structure at a given point on the meridian. It is assumed to have no stiffness in
the meridional plane of the structure. It is provided to increase the stability or to introduce local
loads, not as a primary load-carrying element. In a shell of revolution it is circular, but in rectangular
structures is takes the rectangular form of the plan section.
1.5.19 base ring. A base ring is a structural member that passes around the circumference of the
structure at the base and is required to ensure that the assumed boundary conditions are achieved in
practice.
1.5.20 ring girder or ring beam. A ring girder or ring beam is a circumferential stiffener which has
bending stiffness and strength both in the plane of the circular section of a shell or the plan section of
a rectangular structure and also normal to that plane. It is a primary load-carrying element, lIsed to
distribute local loads into the she]] or box structure.
11
BS EN 1993-4-2:2007
EN 1993-4-2: 2007 (E)
1.5.21 continuously supported. A continuoLisly Suppol1ed tank is one in which all positions around
the circumference are supported in an identical manner. rv1inor departures from this condition (e.g. a
small opening) need not affect the apphcability of the definition.
~
situation
in which a tank is supported using
a local bracket or column, giving a limited number of narrow supports around the tank circumference.
1.5.22 discrete support. A discrete support is a
1.5.23 catch basin. An external tank structure to contain fluid that may escape by leakage or
accident from the primary tank. This type of structure is used where the primary tank contains toxic
or dangerous tluids.
1.6 Symbols used in Part 4.2 of Eurocode 3
The symbols used are based on ISO 3898: 1987.
1.6.1 Roman upper case letters
A
A I, A2
D
E
H
Ho
I
K
L
M
N
Nr
p
R
T
W
area of cross-section
area of top, bottom flange of roof centre ring
diameter of tank
Young's modulus
height of part of shell wa]] to liquid surface: maximum design liquid height
height of the tank shell
second moment of area of cross-section
coefficient for buckling design
height of shell segment or stiffener shear length
bending moment in structural member
axial force in structural member
minimum nurnber of load cycles relevant for fatigue
vertical load 011 roof rafter
radius of curvature of shell which is not cylindrical
temperature
elastic section modulus; weight
1.6.2 Roman lower case letters
fy
side length of a rectangular opening in the shell
side length of a rectangular opening in the shell; width of a plate element in a cross-section
coefficient for wind pressure loading
diameter of manhole or nozzle
distance of outer fibre of beam to beam axis
design yield strength of steel
fu
ultimate strength of steel
h
rise of roof (height of apex of a dome roof above the plane of its junction to the tank shel1)
height of each course in tank shell
joint efficiency factor; stress concentration factor; count of she]] wall courses
height of shell over which a buckle may form
bending moment per unit width
membrane stress resuHant
number of rafters in circular tank roof
distributed loading (not necessarily normal to wall)
pressure normal to tank wall (outward)
a
b
cp
d
e
j
I
111
11
p
Pn
r
radius of middle surface of cylindrical wall of tank
wall thickness
12
BS EN 1993-4-2:2007
EN 1993-4-2: 2007 (E)
w
x
y
z
minimum width of base ring annular plate
radial coordinate for a tank roof
local vertical coordinate for a tank roof: replacement factor used in design of reinforced
opemngs
global axial coordinate
coordinate along the vertical axis of an axisymmetric tank (shell of revolution)
1.6.3 Greek letters
a
fJ
IF
1M
5
~
v
()
(J'
1:
slope of roof
inclination of tank bottom to vertical; = re/n where n is the number of rafters
partial factor for actions
partial factor for resistance
deflection
change in a variable
Poisson's ratio
circumferential coordinate around shell
direct stress
shear stress
1.6.4 Subscripts
E
F
a
d
f
k
k
m
mIll
n
o
p
r
R
s
s
x
y
o
I
2
e
value of stress or displacement (arising from design actions)
at half span; action
annular
design value
fatigue
inside; inward directed; counting variable
roof centre ring
characteristic value
mean value
minimum allowed value
nominal; normal to the waH
outside; outward directed
pressure
radial; ring
resi stance
at support
shell wall
meridional; radial; axial
circumferential; transverse; yield
reference value
upper
lower
circumferential (shells of revolution)
1.7 Sign conventions
1.7.1 Conventions for global tank structure axis system for circular tanks
(l)
The sign convention given here is for the complete tank structure, and recognises that the tank
is not a structural member. Care with coordinate systems is required to ensure that local coordinates
associated with members attached to the shell wall and loadings given in local coordinate directions
but defined by a global coordinate are not confused.
13
BS EN 1993-4-2:2007
EN 1993-4-2: 2007 (E)
In general, the convention for the global tank structure axis system is in cylindrical coordinates
(see figure J. 1) as follows:
Coordi nate system
Coordinate along the central axis of a shell of revolution
(3)
Radial coordinate
r
Circu mferential coordinate
(}
The convention for positive directions is:
Outward direction positive (internal pressure positive, outward displacements positive)
Tensile stresses positive (except in buckling equations where compression is positive)
(4)
The convention for distributed actions on the tank wall surface is:
Pressure normal to she11 ~
(outward pressure positive) @j]
Pn
z
p
s
c
T
r
p= pole; M= shell meridian; C= Instantaneous
centre of meridional curvature
0= roof; $= shell; B= bottom; T= transition
with global @j]
b) coordinates and loading: vertical
a) 3D sketch ~
axisymmetric shell coordinate system
section
Figure 1.1 : Coordinate systems for a circular tank
1.7.2 Conventions for global tank structure axis system for rectangular tanks
(I)
The sign convention given here is for the complete tank structure, and recognises that the tank
is not a structural member. Care with coordinate systems is required to ensure that local coordinates
associated with members attached to the box wan and loadings given in local coordinate directions
but defined by a global coordinate are not confused.
(2)
In general, the convention for the global tank structure axis system is in Cartesian coordinates
x, )" z, where the vertical direction is taken as z
(3)
figure 1.2).
The convention for positive directions is:
Outward direction positive (internal pressure positive, outward displacements positive)
Tensile stresses positive (except in buckling equations where compression is positive)
Shear stresses: see ~
14
1.7.4 @j]
BS EN 1993-4-2:2007
EN 1993-4-2: 2007 (E)
(4)
The convention for distributed actions on the tank wall surface is:
Pressure normal to box (outward positive)
p
w
.r
B= box meridian
a) 3D sketch IEJ) with global @11
coordinate system
Figure 1.2:
0= roof; W= wall; B= bottom
b) coordinates and loading: vertical
section
Coordinate systems for a rectangular tank
1.7.3 Conventions for structural element axes in both circular and rectangular tanks
(I)
The convention for structural elements attached to the tank wall (see figures 1.3 and 1.4) is
different for meridional and circumferential members.
(2)
The convention for meridional straight structural elements (see figure 1.3a) attached to the tank
wall (for both a shell and a box) is:
Meridional coordinate for cylinder, hopper and roof attachment x
Strong bending axis (parallel to flanges)
y
Weak bending axis (perpendicular to flanges)
15
BS EN 1993-4-2:2007
EN 1993-4-2: 2007 (E)
s
B
1-/=
a) stiffener and axes of bending
I VVI,
v=
;:)11t;;1I, U=UVllVIII
b) local axes in different segments
Figure 1.3: Local coordinate systems for meridional stiffeners on a shell or
box
D
B
0= roof; S= shell; B= bottom
a) stiffener and axes of bending
b) local axes in different segments
Figure 1.4: Local coordinate systems for circumferential stiffeners on a shell
or box
16
85 EN 1993-4-2:2007
EN 1993-4-2: 2007 (E)
(3)
The convention for circumferential curved structural elements (see figure l.4a) attached to a
shell wall is:
Circumferential coordinate axis (curved)
()
Radial axis
r
Vertical axis
(4)
The convention for circumferential straight structural elements attached to a box is:
Circumferential axis
x
Horizontal axis
y
Vertical axis
1.7.4 Conventions for stress resultants for circular tanks and rectangular tanks
(I)
The convention used for subscripts indicating membrane forces is:
"The subscript derives from the direction in which direct stress is induced by the force" for direct
stress resultants. For membrane shears and twisting moments, the SIgn convention is shown in
Figure) .5.
Membrane stress resultants, see figure 1.5:
meridional membrane stress resultant
n8
circumferential membrane stress resultant in shells
ny
circumferential membrane stress resultant in rectangular boxes
l1xy
or
l1x8
membrane shear stress resultant
Membrane stresses:
~nx
meridional membrane stress
~n8
circumferential membrane stress in shells
~1Y
circumferential membrane stress in rectangular boxes
or ~nx8
membrane shear stress
The convention used for subscripts indicating moments is:
"The subscript derives from the direction in which direct stress is induced by the moment".
twisting moments, the sign convention is shown in
1.5.
For
NOTE: This plate and shell convention is at variance with beam and column conventions Llsed in
Eurocode 3: Parts 1.1 and] .3. Care needs to be exercised when using them in conjunction with these
provisions.
Bending stress resultants, see figure 1.5:
meridional bending moment per unit width
circumferential bending moment per unit width in shel1s
circumferential bending moment per unit width in rectangular boxes @J]
In xy
or
771 x8
twisting shear moment per unit width
Bending stresses:
Obx
meridional bending stress
17
BS EN 1993-4-2:2007
EN 1993-4-2: 2007 (E)
OJ)8
circumferential bending stress in shells
(}by
circumferential bending stress in rectangular boxes
Tbxyor
Tbx8
twisting shear stress
Inner and outer surface stresses:
(l,;ix' (}"ox
meridional inner, outer surface stress
(}"i8' (l,;oEl
circumferential inner, outer surface stress in she11s
(}"iy' (l,;oy circumferential inner, outer surface stress in rectangular boxes
T"ixy'
inner, outer surface shear stress in rectangular boxes
11
X
III
a) Membrane stress resultants
b) Bending stress resultants
Figure 1.5: Stress resultants in the tank wall (shells and boxes)
1.8
Units
(l)P S.L units shall be used in accordance with ISO 1000.
(2)
For calculations, the following consistent units are recommended:
m
dimensions
kN/m 3
unit weight
kN
forces and loads
kN/m
line forces and line loads
kPa
pressures and area distributed actions
kg/m3
unit mass
km/s2
acceleration
kN/m
membrane stress resultants
kNm/m
bending stress resultants
kPa
stresses and elastic moduli
18
xy
mm
N/mm 3
N
N/mm
MPa
kg/mm3
m/s 2
N/mm
Nmm/mm
MPa (=N/mm2)
BS EN 1993-4-2: 2007
EN 1993-4-2: 2007 (E)
2
Basis of design
2.1
Requirements
( I)P A tank shall be
constructed and maintained to meet the requirements of section 2 of
EN 1990 as supplemented by the following.
(2)
Special consideration should be given to situations during erection.
2.2
Reliability differentiation
(1)
For re1iability differentiation see EN 1990.
NOTE: The National Annex may define consequence classes for tasks as a function of the location, type
of infill and loading, the structural type, size and type of operation.
(2)
Different levels of
should @j] be used in the
of tanks, depending on the
consequence class chosen, that also includes the structural arrangement and the susceptibility to
different failure modes.
In this Pmt, three consequence classes are used with requirements which produce designs with
(3)
essentially equal risk in the design assessment and considering the expense and procedures necessary
to reduce the risk of failure for different structures: consequence classes 1, 2 and 3.
NOTE: The National Annex may provide information on the consequence classes.
classification is recommended.
The rollowing
Consequence Class 3: Tanks storing Jiquids or liquefied gases with toxic or explosive potential
and large size tanks with flammable or water-polluting liquids in urban areas. Emergency
loadings should be taken into account for these structures where necessary, see annex A.2. J 4.
Consequence Class 2: Medium size tanks with flammable or water-polluting liquids in urban
areas.
Consequence Class 1: Agricultural tanks or tanks containing water
(4)P The choice of the relevant Consequence Class shall be agreed between the designer, the client
and the relevant authority.
2.3
Limit states
(1)
The limit states defined in EN 1993-1-6 should be adopted for this Part.
2.4
Actions and environmental effects
(l)P The general requirements set out in section 4 of EN 1990 shal1 be satisfied.
(2)
Because the information wind loads on liquid induced loads, internal pressure loads, thermally
induced loads, loads resulting from pipes valves and other items connected to the tank , loads
resulting from uneven settlement and emergency loadings set down in EN 1991 is not complete special
information is given in annex A
2.5
Material properties
(1)
The general requirements for material properties given in EN 1993-1 1 should be followed.
19
BS EN 1993-4-2:2007
EN 1993-4-2: 2007 (E)
(2)
The :-;pecific properties of materials for tanks given in section 3 of this Part should be used.
2.6
Geometrical data
(I)
The general information on geometrical data provided in EN 1990 may be used.
(2)
The additional information specific to she]) structures provided in EN 1993-1-6 may be used.
(3)
The plate thicknesses given in 4.1.2 should be used in calculations.
2.7
Modelling of the tank for determining action effects
(I)P The general requirements of EN 1990 shall be followed.
(2)
The specific requirements for structural analysis in relation to serviceability set out in 5.5, 7.5
and 9.4 should be used for the relevant structural segments.
(3)
The specific requirements for structural analysis in relation to ultimate limit states set Ollt in
7.3 and 9.3 (and in more detail in EN 1993-1-6) should be applied.
2.8
Design assisted by testing
(I)
The general requirements set out in Annex 0 of EN 1990 should be followed.
2.9
Action effects for limit state verifications
2.9.1 General
(I)
The general requirements of EN 1990 should be satisfied.
2.9.2 Partial factors for ultimate limit states
2.9.2.1
Partial factors for actions on tanks
(I)P For persistent and transient design situations, the partial factors
NOTE: The National Annex may provide val ues for the ~
the recommended values for
(2)P
Yr' shall
be used.
partial factors @j]
rF Table 2.1
gives
IF.
For accidental design situations, the partial factors
rF
for the variable actions shall be used.
This also applies to the liquid loading of catch basins.
NOTE: The National Annex may provide values for the ~
the rccommended valucs for
partial factors @j]
rF. Table 2.1
gives
IF
(3)P Partial factors for 'product type' tanks (factory production) shall be specified.
NOTE: The National Annex may provide values for the partial factors
recornlllcnded values for
20
IF
IF.
Table 2.1 gives the
BS EN 1993-4-2: 2007
EN 1993-4-2: 2007 (E)
Table 2.1: Recommended values for the partial factors for actions on tanks for
persistent and transient design situations and for accidental design situation
design situation
I iquid type
recommended
recommended
val ues for
X, ill
values for
case of variable
actions from
liquids
I
case of
permanent
actions
I
toxic, explosive or
dangerous liquids
1,40
tlammable liquids
1,30
1,35
other liquids
1,20
1,35
liquid induced loads during test
all liquids
1,00
1,35
accidental actions
all liquids
1,00
liquid induced loads during operation
2.9.2.2
Yr: in
1,35
I
Partial factors for resistances
Where structural properties are determined by testing, the requirements and procedures of
(1)
EN 1990 should be adopted.
(2)
Fatigue verifications should satisfy section 9 of EN 1993-1-6.
(3)P
The partial factors YMi shall be specified according to Table 2.2.
Table 2.2: Partial factors for resistance
Resistance to failure mode
Relevant
y
Resistance of welded or bolted shell wall to plastic limit
state, cross-sectional resistance
Resistance of shell wall to stability
n,11
Resistance of welded or bolted shell wall to rupture
KV12
Resistance of shell wall to cyclic plasticity
~10
YM4
Resistance of welded or bolted connections or joints
XVIS
Resistance of shell wa]] to fatigue
!;'V16
NOTE: Partial factors
n.'li
for tanks may be defined in the National Annex. It''Nalues of n.'1,)' further Information
may be found in EN 1993-1-8. For values of }f,!16, further information may be found in EN 1993-1-9. The
following numerical values are recommended for tanks:
21
BS EN 1993-4-2:2007
EN 1993-4-2: 2007 (E)
2.9.3 Serviceability limit states
(1)
Where simplified compliance rules are given in the relevant provisions dealing with
serviceability limit states, detailed calculations using combinations of actions need not be carried out.
(2)
For all serviceability limit states the values of
/1v1ser
should be specified.
NOTE: The National Annex may provide information on the value for the partial factor for serviceability
]1.,hcl'
nhel
I is recommended.
2.10 Combinations of actions
(l)P The general requirements of EN 1990 shall be followed.
(2)
Tmposed loads and snow loads need not be considered to act simultaneously.
Reduced wind actions, based on a short exposure period, may be used when wind is in
combination with the actions of the hydrostatic test.
(4)
Seismic actions need not be considered to act during test conditions.
(5)
Emergency actions need not be considered to act during test conditions. The combination rules
for accidental actions given in EN 1990 should be applied to emergency situations.
2.11 Durability
(J)
The general requirements set out in EN 1990 should be followed.
22
BS EN 1993-4-2:2007
EN 1993-4-2: 2007 (E)
3
Properties of materials
3.1
General
(])
All steels used for tanks should be suitable for welding to permit later modifications 'vvhen
necessary.
(2)
All steels used for tanks of circular planform should be suitable for cold forming into curved
sheets or curved members.
(3)
The material properties given in this section should be treated as nominal values to be adopted
as characteristic values in design calculations.
Other material properties are given in the relevant Reference Standards defined in EN 1993-]-
(4)
1.
(5)
Where the tank may be filled with hot liquids, the values of the material properties should be
appropriately reduced to values corresponding to the maximum temperatures to be encountered.
The material characteristics at elevated temperature (T > ]oooe for structural steels and T>
(6)
50 0 e for stainless steels) should be obtained from EN ] 3084-7.
3.2
Structural steels
(I)
The methods for design by calculation given in this Part 4.2 of EN 1993 may be
structural steels as defined in EN 1993-1 1, which conform with parts 2 to 6 of EN ] 0025.
methods may also be used for steels included in EN 1993-1-3.
The mechanical properties of structural steels according to EN 10025 or
(2)
should be taken from EN 1993-1 1 or EN 1993-1-3.
3.3
for
The
EN 10]49 @1]
Steels for pressure purposes
(])
The methods for
by calculation given in this Part 4.2 of EN 1993 may be used for steels
for pressure purposes conforming with EN 10028 provided that:
the yield strength is in the range covered by EN 1993-1-1;
-
the ultimate strain is not less than the minimum value for steels according to EN 1993-1-1
which have the same specified yield strength;
-
the ratio
is not less than 1,10.
The mechanical properties of steels for pressure purposes should be taken according to
(2)
EN 10028.
Where the design involves a stability calculation, appropriate reduced properties should be
used, see EN 1993-1-6 section 3.1.
NOTE: Further information may be given in the National Annex.
3.4
Stainless steels
The mechanical properties of stainless steels according to EN 10088 should be obtained from
(1)
EN 1993-1-4.
23
BS EN 1993-4-2:2007
EN 1993-4-2: 2007 (E)
(2)
Guidance for the selection of stainless steels in view of corrosion actions may be obtained from
appropriate sources.
(3)
Where the design involves a buckling calculation, appropriate reduced properties should be
used, see EN 1993-1-6.
3.5
Toughness requirements
3.5.1 General
The toughness requirements should be determined for the minimum design metal temperature
(1)
according to EN 1993-1-10.
(2)
The minimum design metal temperature MDMT should be determined according to 3.S.2.
MDMT may be used in place of Ted' in EN 1993-1-10.
3.5.2 Minimum design metal temperature
(I)
The minimum design metal temperature MDMT should be the lowest of the minimum
temperature of the contents or those classified in table 3.1.
(2)
The lowest one day mean ambient temperature LODMAT should be taken as the lowest
recorded temperature averaged over any 24 hour period. Where insufficiently complete records are
available, this average temperature may be taken as the mean of the maximum and minimum
temperatures or an equivalent value.
.
T a bl e 31 . M"Inlmum
d eSlgn meta temperature MDMTb ase d on LODMAT
.
Lowest one day mean ambient temperature
LODNIAT
lODe s LODMAT
-2soe
s LODMAT s -lo oe
LODMAT
24
s -2soe
Minimum design metal temperature
MDMT
10 years data
30 years data
LODMAT+soe
LODMAT +lo o e
LODMAT
LODMAT+soe
LODMAT-soe
LODMAT
BS EN 1993-4-2:2007
EN 1993-4-2: 2007 (E)
4
Basis for structu ral analysis
4.1
Ultimate limit states
4.1.1 Basis
(I)
Steel structures and components should be so proportioned that the basic design requirements
given in section 2 are satisfied.
4.1.2 Plate thickness to be used in resistance calculations
(I)
In calculations to determine the resistance, the design value of thickness for a plate is the
EN 10149
or EN 10088 reduced
nominal thickness specified in EN 10025, EN 10028
by the maximum value of minus tolerance and a value of corrosion allowance specified in 4.1.3.
4.1.3 Effects of corrosion
(1)
The effects of corrosion sholl Id be taken into account.
(2)
The corrosion depends upon the stored liquid, the type of steel, the heat treatment and the
measures taken to protect the construction against corrosion.
(3)
The value of an allowance should be specified if necessary.
4.1.4 Fatigue
(I)P With frequent load cycles the structure shall be checked against the fatigue limit state.
(2)
The design against low cycle fatigue may be carried out according to EN ] 993-1-6.
(3)
If variable actions will be applied with more than Nt cycles during the design life of the
structure the design should be checked against fatigue (LS4) according to section 9 of EN 1993-1-6.
NOTE: The National Annex may provide the value for the number Nt of cycles. The value N,
recommended.
10000 is
4.1.5 Allowance for temperature effects
The effects of differential temperature between parts of the structure should be included in
(1)
determining the stress distribution depending upon the ultimate limit state considered.
4.2 Analysis of the circular shell structure of a tank
4.2.1 Modelling of the structural shell
(I)
The modelling of the structural shell should follow the requirements of EN 1993-1-6, but these
may be deemed to be satisfied by the following provisions.
(2)
The modelling of the structural shell should include all stiffeners, openings and attachments.
(3)
The design should ensure that the assumed boundary conditions are satisfied.
25
BS EN 1993-4-2:2007
EN 1993-4-2: 2007 (E)
4.2.2 Methods of analysis
General
4.2.2.1
(I)
The analysis of the tank she)] should be carried out according to the requirements of
EN 1993-1-6.
(2)
A higher class of analysis may always be used than that defined for the selected Consequence
Class.
(3)
Irrespective of the Consequence Class chosen, the simplified design described in Section 1 1
may be used if the conditions listed there are met.
4.2.2.2
Consequence Class 1
For tanks in Consequence Class 1, membrane theory may be used to determine the primary
(1)
stresses, with factors and simplified expressions to describe local bending effects and unsymmetrical
actions.
4.2.2.3
Consequence Class 2
(l)
For tanks In Consequence Class 2
alternative analyses should be used:
under axisymmetric actions and support, one of two
a)
Membrane theory may be used to determine the primary stresses, with bending theory
elastic expressions to describe all local effects.
b)
A validated numerical analysis may be used (for instance, finite element shell analysis) as
defined in EN 1993-1-6.
Where the loading condition is not axisymmetric, a validated numerical analysis should be
used, except under the conditions set out in (3) and (4) below.
(3)
Notwithstanding (2), where the loading varies smoothly around the shell causing global
bending only (i.e. in the form of harmonic 1), membrane theory may be used to determine the primary
stresses.
For analyses of actions due to wind loading and/or foundation settlement, semi-membrane
(4)
theory or membrane theory may be used.
NOTE: For information concerning membrane theory, see EN 1993-1-6. The semi-membrane theory
describes the membrane behaviour in interaction with the circumferential bending stiffness.
(5)
Where membrane theory is used to analyse the shell, discrete rings attached to an isotropic
cylindrical tank shell under internal pressure may be deemed to have an effective area which includes
a length of shell above and below the ring of Q,78{H, except where the ring is at a junction.
(6)
Where the shell is discretely stiffened by vertical stiffeners, the stresses in the stiffeners and the
shell wa]] may be ca1cu lated by treating the stiffeners as smeared on the shell wall, provided the
spacing of the stiffeners is no wider than 5{H.
(7)
Where vertical stiffeners are smeared, the stress in the stiffener should be determined making
proper allowance for compatibility between the stiffener and the waH and the wan stress in the
orthogonal direction, according to 4.4.
26
BS EN 1993-4-2:2007
EN 1993-4-2: 2007 (E)
(8)
If a ring girder is used above discrete supports, compatibility of the axial deformation between
the ring and adjacent shell segments should be considered. Where such a ring girder is used, the
eccentricity of the ring girder centroid and shear centre relative to the shell wall and the support
centreline should be included.
(9)
Where a ring girder is treated as a prismatic section (free of distortion), the vertical web
segment should have a plate slenderness not greater than bit = 20.
(10) Where a ring girder is used to redistribute forces into discrete supports and bolts or discrete
connectors are used to join the structural dements, the shear transmission between the ring parts due
to shell and ring girder bending phenomena should be determined.
4.2.2.4
Consequence Class 3
(I)
For tanks in Consequence Class 3, the internal forces and moments should be determined using
a validated analysis (for instance, finite element shell analysis) as defined in EN 1993-1-6. The
plastic I1mit state (LS I) may be assessed using plastic collapse strengths under primary stress states as
defined in EN 1993-1-6.
4.2.3 Geometric imperfections
(I)
Geometric imperfections in the shell should satisfy the limitations defined in EN 1993-1-6.
For tanks in Consequence Classes 2 and 3, the geometric imperfections should be measured
(2)
following construction to ensure that the assumed fabrication tolerance has been achieved.
(3)
Geometric imperfections in the shell need not be explicitly included in determl ni ng the internal
forces and moments, except where a GNIA or GNINIA analysis is used, as defined in EN 1993-1-6.
4.3
Analysis of the box structure of a rectangular tank
4.3.1 Modelling of the structural box
(1)
The modelling of the structural box should follow the requirements of EN 1993-1-7, but they
may be deemed to be satisfied by the following provisions.
(2)
The modelling of the structural box should include all stiffeners, openings and attachments.
(3)
The design should ensure that the assumed boundary conditions are satisfied.
The joints between segments of the box should satisfy the modelling assumptions for strength
(4)
and stiffness.
(5)
Each panel of the box may be treated as an individual plate segment provided that both:
a)
the forces and moments introduced into each panel by its neighbours are included;
b)
the flexural stiffness of adjacent panels is included.
Where the wall panel is discretely stiffened by stiffeners, the stress in the stiffeners and in the
(6)
wall may be calculated by treating the stiffeners as smeared on the box wall, provided that the spacing
of the stiffeners is no wider than 11s t.
NOTE: The National Annex may choose the value of liS' The value
liS
40 is recommended.
27
BS EN 1993-4-2:2007
EN 1993-4-2: 2007 (E)
Where smeared stiffeners are used, the stress in the stiffener should be determined making
(7)
proper allowance for eccentricity of the stiffener from the wall plate, and for the wall stress in the
direction orthogonal to the axis of the stiffener.
The effective width of plate on each side of a stiffener should be taken as not greater than
(8)
where t is the local plate thickness.
NOTE: The National Annex may choose the value of new. The value
new
15£ ~
new
t,
is recommended.
4.3.2 Geometric imperfections
(1)
Geometric imperfections in the box should satisfy the limitations defined in EN 1993-1-7.
(2)
Geometric imperfections in the box need not be explicitly included in determining the internal
forces and moments.
4.3.3 Methods of analysis
(I)
(2)
The internal forces in the plate segments of the box wall may be determined using either:
a)
static equilibrium for membrane forces and beam theory for bending;
b)
an analysis based on linear plate bending and stretching theory;
c)
an analysis based on nonlinear plate bending and stretching theory.
For tanks in Consequence Class 1 method (a) in (1) may be used.
(3)
Where the design loading condition is symmetric relati ve to each plate
in Consequence Class 2, method (a) in (1) may be used.
",,,,,'YrY\,ont
and the tank is
Where the loading condition is not symmetric and the tank is in Consequence Class 2, either
(4)
method (b) or method (c) in (1) should be used.
For tanks in Consequence Class 3, the internal forces and moments should be determined using
(5)
either method (b) or method (c) in (I).
4.4
Equivalent orthotropic properties of corrugated sheeting
Where corrugated sheeting is used as part of the tank structure, the analysis may be carried out
( 1)
treating the sheeting as an equivalent orthotropic wall.
(2)
The orthotropic properties obtained from considering the load displacement behaviour of the
corrugated section in the orthogonal directions may be used in a stress analysis and in a buckling
analysis of the structure. The properties may be determined as described in 4.4 of EN 1993-4-1.
28
BS EN 1993-4-2:2007
EN 1993-4-2: 2007 (E)
5
Design of cylindrical walls
5.1
Basis
5.1.1 General
(1)
Cylindrical shell walls should be so proportioned that the basic design requirements for the
ultimate limit state given in section 2 are satisfied.
(2)
The safety assessment of the cylindrical shell should be carried out using the provisions of
EN ] 993-1-6.
5.1.2 Wall design
The cylindrical she]] wa]] of the tank should be checked for the following phenomena under the
(1)
limit states defined in EN 1993-1-6:
-
Global stability and static equilibrium
-
LS 1: plastic limit
LS2: cyclic plasticity
LS3: buckling
LS4: fatigue
The cylindrical shell wall should satisfy the provisions of EN 1993-1-6, except where this
(2)
standard provides alternatives that are deemed to satisfy the requirements of that standard.
(3)
For tanks in Consequence Class L the cyclic plasticity and fatigue limit states may be ignored.
5.2
Distinction of cylindrical shell forms
(1)
A cylindrical shell wall constructed from flat rolled steel sheet is termed 'isotropic'
of EN 1993-4-]).
5.3.2
(2)
A cylindrical shell wall constructed from corrugated steel sheets where the troughs pass around
the circumference of the tank is termed 'horizontally corrugated' (see 5.3.4 of EN 1993-4-1) .
(3)
A cylindrical shell wall with stiffeners attached to the outside is termed 'externally stiffened'
irrespective of the spacing of the stiffeners (see 5.3.3 of EN 1993-4- I).
5.3
Resistance of the tank shell wall
(1)
The resistance of the cylindrical shell should be evaluated using the provisions of EN ] 993-1-6,
except where the clauses of 5.4 contain provisions that are deemed to satisfy the provisions of that
standard.
The joint efficiency of full penetration butt welds may be taken as unity provided that the
(2)
requirements of EN 140 15 or EN 14620, as appropriate, are met.
(3)
For other types of connection the joint design should be in accordance with EN 1993-1-8.
29
BS EN 1993-4-2:2007
EN 1993-4-2: 2007 (E)
5.4
Considerations for supports and openings
5.4.1 Shell supported by a skirt
(I)
Where the cylindrical shell is supported by a skirt, this should satisfy the provisions of
EN 1993-4-1.
5.4.2
Cylindrical shell with engaged columns
(1)
Where the cylindrical shelJ is supported with engaged columns, this should satisfy the
provisions of EN \993-4-1.
5.4.3 Discretely supported cylindrical shell
(I)
Where the cylindrical shell is discretely supported by columns or other devices, the provisions
of EN ] 993-4-] for this condition should be satisfied.
5.4.4 Discretely supported tank with columns beneath the hopper
(1)
Tanks discretely supported with columns beneath the hopper should satisfy the provisions of
EN 1993-4-1.
5.4.5 Local support details and ribs for load introduction in cylindrical walls
5.4.5.1
(])
Local supports beneath the wall of a cylinder
Local supports beneath the wall of the cylinder shou ld satisfy the provisions of EN 1993-4-1.
5.4.5.2
(1)
4-1.
Local ribs for load introduction into cylindrical walls
Local ribs for load introduction into cylindrical walls should satisfy the provisions of EN 1993-
5.4.6 Openings in tank walls
General
5.4.6.1
(1)
Where an opening in the cylindrical shell wall reduces the load carrying capacity or endangers
the stability of the shell, the opening should be reinforced.
(2)
This reinforcement may be achieved by:
-
increasing the thickness of the shell plate;
-
adding a reinforcing plate;
-
the presence of a nozzle body.
NOTE: The
against the plastic limit state (LS I) generally governs in the region of high pressure
in
loading (l1quid ane! internal) whereas stahility considerations (LS3) arc likely to control the
regions where the plate thickness is small due to low pressures (upper courses).
30
BS EN 1993-4-2:2007
EN 1993-4-2: 2007 (E)
5.4.6.2
(I)
Shell nozzles of small size
Shell nozzles with outside diameter less than 80mm are classed as of small size.
(2)
Reinforcement may be omitted, provided that the thickness of the wall at the nozzle is not less
than that given in table 5.1.
Ta bl e 51 M'Inlmum
.
nozz Ie b odIY t h'Ie kness
Outside diameter d n of
Manhole or nozzle (mm)
dn
:::;;
:::;;
75
75 < d n
:::;;
80
(111111 )
Carbon steel
Austenitic and austenitic-ferritic
stainless steel
5,0
3,5
5,5
5,0
50
50 < d n
5.4.6.3
Minimum nominal thickness t rel . n
6,0
"
Design of shell man holes and shell nozzles of large size for LS1
(I)
Shell man holes and shell nozzles with outside diameter
large size.
than 80mm are classed as of
(2)
The design may be undertaken llsing either the area replacement method according to
paragraphs (3) and (4), or alternatively by the method described in paragraph (5) and (6).
(3)
A reinforcement of cross-sectional area M
the centre of the opening, given by:
0,75 d
should be provided in the vertical plane containing
... (5.1)
trd
where:
d
is the diameter of the hole cut in the shel1 plate~
tref
is the thickness required by the design for LS I for the shell plate without opening.
(4) The reinforcing area M
three methods:
may be provided by anyone or any combination of the following
a)
The provision of a nozzle or a manhole body. The portion of the body which can be
considered as reinforcement is that lying within the shell plate thickness and within a
distance of four times the body thickness from the shell plate surface unless the body
thickness is reduced within this distance, when the limit is the point at which the
reduction begins.
b)
The addition of a thickened shell insert plate or a reinforcing plate, the limit of
reinforcement being such that 1,5d < d n < 2d, where d n is the effective diameter of
reinforcement. A non-circular reinforcing plate may be llsed provided the minimum
requirements are met
c)
The provision of a shell plate thicker than required by the design for LS I for the shell
plate without an opening. The limit of reinforcement is the same as that described in (b).
(5)
As an alternative to the area replacement method specified in (3) and (4) the reinforcement may
be achieved by introducing a nozzle body that protrudes on both sides of the shell plate by an amount
31
BS EN 1993-4-2:2007
EN 1993-4-2: 2007 (E)
This method should not be used unless the nozzle body is more than
not less than 1,17
lOOmm from the base ring plate.
(6)
The thickness of the nozzle body should be chosen such that the stress concentration factor j
does not exceed 2,0. The stress concentration factor j should be obtained from figure 5.1 using the
replacement factor y. The replacement factor y should be evaluated from:
y
=
... (5.2)
+
where:
is the shell plate thickness;
til
is the nozzle body thickness;
rm
IS
r
is the external radius of the nozzle;
rj
IS
the mean radius of the nozzle (nozzle middle surface);
the inside radius of the nozzle .
"""', ~
.
~
2.5
'"
,
'" "'"
"-
I"····
,
2.0
j.
" ' l'... ~
~',
f"t... .'.
.~
..!
..........
.........
,
.........
..........
"
.
, ~
"'
............
............
1.5
,
........
""
....H.. H... ·
""-
1,7 . . . . bsJ.~
,:'1 1_
1
............
!to..
---
~
r........ 1.0- r-....
..__... L ......
...•..........
............ H..H....... ·.
\.
,
0.5
. 0
0.1
..........H.. H... !
!H
. .... ! ...... i.... · · ·
,
r--,
!
r-i
t-..
,
!
OJ
-~
,
......
0.2
...... H..
~i-
--- -~
........... , ............ H.H .... H.
r- roo...........-... r--
- ---........ r---...
.....
0.4
-
- - ........ J
,
,
1.0
t
. . . i, rei ri ,.H.
.....
.....1'--...
r-'
r-14,6
...
.... ........ r--..... 1 - - ...
i""
~ 1,3 " .......
['-.....
~
,
I
~I
...........
0.5
0.6
0.7
0.8
0.9
Y
•
j Stress concentration factor; y = Replacement factor
Figure 5.1: Stress concentration factor for barrel-type nozzle reinforcements
5.4.6.4
Design for LS3 in the presence of shell openings
(1)
The effect of openings on the stability of shells may be neglected provided that the
dimensionless opening size '7 is smal1er than '7max = 0,6, and '7 is given by;
... (5.3)
where:
r
32
IS
the radius of the cylindrical shel1 near the opening;
BS EN 1993-4-2:2007
EN 1993-4-2: 2007 (E)
is the thickness of the unstiffened shel1 wall near the opening;
1'0
(2)
is the radius of the opening.
Where the opening is rectangular, the equivalent opening radius may be taken as:
a+b
1'0= - -
4
... (5.4)
where:
a
is the horizontal side length of the opening;
b
is the vertical height of the opening.
(3)
Where the radius of the opening ro is less than one third of the radius r of the cylindrical
shell, no reduction in the assessed buckling resistance need be made as a result of the opening,
provided that the cross-sectional area taken away by the opening is smaller than the rei nforcement
cross-sectional area M. The reinforcement can be provided according to 5.4.6.3 (4) or by means of
stiffeners in the meridional direction.
(4)
If stiffeners in the meridiona'! direction are used to reinforce the opening, the cross-section of
each stiffener should be reduced towards the ends to prevent the formation of buckles due to stress
concentration in the shell plate near the stiffener ends.
5.4.7 Anchorage of the tank
(1)
The anchorage should be principally attached to the cylindrical shell and not to the base ring
plate alone.
The design should accommodate movements of the tank due to thermal changes and hydrostatic
(2)
pressure to minimise stresses induced in the shell by these effects.
(3)
Where the tank is supported on a rigid anchorage, and is subject to horizontal loads (e.g. wind,
impact) the anchorage forces should be calculated according to shell theory.
NOTE: It should be noted that these forces may be locally much higher than those found using beam
theory. See clause (3) of section 5.4.7 of EN 1993-4-1.
(4)
The design of the cy1indrical shell for local anchorage forces and bending moments resulting
1993-4-1 @iI.
from the anchorage should meet the provisions of ~
5.5 Serviceability limit states
5.5.1 Basis
(1)
The serviceability limit states for cylindrical plated walls should be taken as:
deformations and deflections that adversely affect the effective use of the structure;
deformations, deflections or vibrations that cause damage to non-structural elements.
(2)
Deformations, detlections and vibrations should be limited to meet the above criteria.
(3)
Specific limiting values, appropriate to the intended use, should be agreed between the
designer, the client and the relevant authority, taking account of the intended use and the nature of the
liquids to be stored.
33
BS EN 1993-4-2:2007
EN 1993-4-2: 2007 (E)
6
Design of conical hoppers
(I)
The design of conical hoppers should satisfy the requirements of EN 1993-4-1.
7
Design of circular roof structures
7.1
Basis
7.1.1 General
(1)
Steel tank roofs should be so proportioned that the basic design requirements for the ultimate
Ii mit state given in section 2 are satisfied.
The safety assessment of the spherical or conical shell should be can-ied out using the
provisions of EN 1993-1-6.
(3)
The safety assessment of the roof supporting structure should be carried out using the
provisions of EN 1993-1-1.
7.1.2 Roof design
(])
The roof should be checked for:
resistance to buckling;
resistance of the joints (connections);
-
resistance to rupture under internal pressure.
The roof plating should satisfy the provisions of EN 1993-1-6 except where 7.3 to 7.5 provide
(2)
an alternative approach.
7.2
Distinction of roof structural forms
(1)
The roof may either have a spherical, a conical, a torispherical or a toriconical shape. Where
high internal pressures occur above the liquid surface, the shape should preferably be chosen as
tori spherical or toriconic31.
(2)
A roof structure in one of the shapes described in (I) may either be unsupported or supported
by structural members.
(3)
'rhe roof supporting structure according to (2) may be supported by columns.
(4)
The roof supporting structure may be arranged below the roof plating or above the roof plating.
(5)
The roof plating may be:
(6)
a)
supported by the roof structure without connection;
b)
attached to the roof structure.
Where frangibility of the roof is required, type (a) should be used.
34
BS EN 1993-4-2:2007
EN 1993-4-2: 2007 (E)
(7)
Where the roof supporting structure is external, type (b) should be used.
7.3
Resistance of circular roofs
(1)
The roof plating should satisfy the provisions of EN 1993-1-6 unless special provisions are
given in 7.4.
(2)
The roof supporting structure should satisfy the provisions of EN 1993-1 I.
(3)
Torispherical and toriconical roofs should be designed to prevent buckling of the knuckle
region under internal pressure.
7.4 Considerations for individual structural forms
7.4.1 Unsupported roof structure
(1)
Unsupported roofs should be of butt-welded or double welded lap construction.
(2)
In double welded lap construction, the reduction of resistance against buckling and the plastic
limit state due to the joint eccentricities should be taken into account in the model for the analysis.
7.4.2 Cone or dome roof with supporting structure
7.4.2.1
(1)
Plate deSign
The roof plating may be designed using large deflection theory.
Where roof frangibility is required, roof plates shOll Id not be attached to the internal roof
(2)
supporting structure.
7.4.2.2
(1)
Design of the supporting structure
The roof supporting structure should satisfy the provisions of EN 1993-1 1.
(2)
If the roof plating is attached to the roof supporting structure an effective width of this plating
may be taken as part of the supporting structure. This effective width may be taken as 16t unless a
larger value is confirmed by an analysis.
With column supported roofs, special consideration should be given to the possibility of
(3)
settlement of the foundations.
7.4.3 Roof to shell junction (eaves junction)
(I)
The roof to cylinder junction (eaves junction) should be designed to carry the total downward
vertical load from the roof (dead weight, snow, live load and internal negative pressure).
(2)
The roof to cylinder junction should satisfy the provisions of EN I
] -6. If the conditions set
out in 11.1 (1) are satisfied, the simplified design method given in 1 ] .2.5 may be applied.
(3)
For frangible roof design the compression area A should satisfy the condition:
... (7.1)
35
BS EN 1993-4-2:2007
EN 1993-4-2: 2007 (E)
where:
the total weight of the shell and any framing (but not roof-plates) supported by the
shell and roof;
W
IS
a
is the angle between the roof and a horizontal plane at the roof to cylinder junction.
7.5
Serviceability limit states
(1)
The serviceability limit states for tank roofs should be taken as f01l0ws:
-
deformations and deflections that adversely affect the effective use of the structure;
deformations, deflections or vibrations that cause damage to non-structural elements.
(2)
Deformations, deflections and vibrations should be limited to meet the above criteria.
between the
(3)
Specific limiting values, appropriate to the intended use, should be
designer, the client and the relevant authority, taking account of the intended use and the nature of the
liquids to be stored.
8
Design of transition junctions at the bottom of the shell and
supporting ring girders
(])
The design of transition junctions at the bottom edge and supporting ring girders should satisfy
the requirements of EN 1993-4-1.
36
BS EN 1993·4·2:2007
EN 1993-4-2: 2007 (E)
9
Design of rectangular and planar-sided tanks
9.1
Basis
(l)
A rectangular tank should be designed either as stiffened box in which the structural action is
predominantly bending, or as a thin membrane structure in which the action is predominantly
membrane stresses developing after large deformations.
Where the box is designed for bending action, the joints should be designed to ensure that the
(2)
connectivity assumed in the stress analysis is achieved in the execution.
9.2
Distinction of structural forms
9.2.1 Unstiffened tanks
(1)
A structure that is fabricated from flat steel plates without attached stiffeners should be treated
as an 'unstiffened box'.
(2)
A structure that is stiffened only along joints between plates which are not coplanar should also
be treated as an 'unstiffened box'.
9.2.2 Stiffened tanks
(1)
A structure that is fabricated from flat plates to which stiffeners are attached within the plate
area should be treated as a 'stiffened box'. The stiffeners may be circumferential or vertical or
orthogonal.
9.2.3 Tanks with ties
(I)
Tanks with ties may be square or rectangular.
9.3
Resistance of vertical walls
9.3.1 Design of individual unstiffened plates
(1)
Unstiffened plates should be designed for bending as a two-dimensional plate under the actions
from the stored liquid, the pressure above the liquid, stresses resulting from diaphragm action, and
10cal bending action from attachments or piping.
9.3.2 Design of individual stiffened plates
(l)
Corrugated or trapezoidal sheeting that spans in the horizontal direction should be designed for
global bending under the actions from the stored liquid, the pressure above the liquid, stresses
resulting from diaphragm action, and local bending action from attachments or piping.
(2)
Effective bending properties and bending resistance of stiffened plates should be derived in
accordance with EN ] 993-1-3.
The in-plane shear stiffness and shear resistance may be determined as analogous to that of the
(3)
plane plate if the sheeting is continuously connected along all its boundaries to the adjacent members.
37
BS EN 1993-4-2:2007
EN 1993-4-2: 2007 (E)
NOTE: Ir the conneclion is on only parts of the vertical boundary (e.g. connection only in the troughs of
the corrugalion or trapezoidal sheeting), the stresses can increase dramatically and the stiffness ean
decrease dramatically. It is assumed that such constructions will not be used because of requirements of
lE8) liquid lightness
9.3.3 Global bending from direct action of the stored liquid and the pressure above the liquid
(1)
Horizontal bending resulting from the normal pressure on the wall should be considered. The
loads should be supported by either one-way or two-way bending action.
9.3.4 Membrane stresses from diaphragm action
(I)
The design should take account of membrane tension stresses that develop in the walls as a
result of hydrostatic pressures on opposing walls normal to the wall being considered.
(2)
The design should also take account of membrane compression stresses that can develop as a
result of wind acting on other walls that are orthogonal to the wall being considered.
9.3.5 local bending action from attachments or piping
(I)
Local bending action from attachments or piping should be avoided as far as possible.
However, if this is not possible, a check should be made on the local stresses and deformations near
the attachment.
9.4
Serviceability limit states
(I)
The serviceabi1ity limit states for walls of rectangular steel tanks should be taken as follows:
-
deformations or deflections which adversely affect the effective use of the structure
deformations, deflections and vibrations which cause damage to non-structural elements.
(2)
Deformations, deflections and vibrations should be limited to meet the above criteria.
(3)
Specific limiting values, appropriate to the intended use, should be agreed between the
designer, the client and the relevant authority, taking account of the intended use and the nature of the
liquids to be stored.
10 Requirements on fabrication, execution and erection with
relation to design
(I)
The tank should be fabricated and erected according to EN ] 4015 or EN 14620 and executed
according to EN 1090, as appropriate.
38
BS EN 1993-4-2:2007
EN 1993-4-2: 2007 (E)
Simplified design
11
11.1 General
(1)
The simplified analysis of this section may be applied where al1 the following conditions are
satisfied:
-
the tank structure is of the form shown in figure I 1.1;
-
the only internal actions are liquid pressure and gas pressure above the liquid surface;
-
maximum design liquid level not higher than the top of the cylindrical shell;
-
the following loadings can all be neglected: thermally induced loads, seismic loadings, loads
resulting from uneven settlement or connections and emergency loadings;
-
no course is constructed with a thickness less than that of the course above it, except for the
zone adjacent to the eaves ring;
the design value of the circumferential stress in the tank shell is less than 435 N/mm
2
;
for a spherical roof, the radius of curvature is between 0,8 and 1,5 times the diameter of the
tank;
for a conical roof, the slope of the roof is between 1 in 5 and I in 3 if the roof is only supported
from the she]] (no internal support);
(2)
-
the design gradient of the tank bottom is not greater than I: 100;
-
the bottom is fully supported or supported by closely spaced parallel girders;
-
the characteristic internal pressure is not below -8,5 mbar and not greater than 60 mbaI';
-
the number of load cycles is such that there is no risk of fatigue failure.
The design yie1d stress throughout this chapter should be taken as:
= ~,
~"d
I YMO
(11.1 )
where:
.I;,
YMO
IS
the characteristic yield strength of the steel:
according to section 2.9.2.2
39
BS EN 1993·4·2:2007
EN 1993-4-2: 2007 (E)
~
I
Figure 11.1: Tank structure with catch basin, where simplified tank design is
applicable
11.2 Fixed roof design
11.2.1 Unstiffened roof shell butt welded or with double lap weld
( I)
Provided that the maximum local value of the distributed design load is used in (3) and (5) to
represent the distributed pressure on the roof, possible non-uniformity of the distributed load need not
be considered.
Where a concentrated load is applied, a separate assessment should be made in accordance with
section 7.
(3)
The strength of the roof under the design internal pressure
- for spherical roofs
Po.Ed
should be verified using:
... (11.2)
21
... (l1.3)
for conical roofs
in which:
Re = rlsina
for a conical roof
where:
j
is the joint efficiency factor;
Po.Ed
is the radial outward component of the uniformly distributed design load on the roof (i.e.
the characteristic value multiplied by the partial factor according to section 2.9.2.1);
r
is the radius of the tank cylindrical shell wall;
Re
is the radius of curvature for the conical roof:
Rs
is the radius of curvature of the spherical roof;
a
40
IS
the roof plate thickness;
IS
the slope of the conical roof to the horizonta1.
BS EN 1993-4-2:2007
EN 1993-4-2: 2007 (E)
(4)
The joint efficiency factor should be taken as:
j
=
1,00 for butt welds;
0,50 for lapped joints with fillet welds on both sides.
j
(5)
The stability of a spherical roof under the design external pressure
using:
Pi.Ed
should be verified
... (11.4)
in which:
Ro
= R~
where:
Pi.Ed
is the radial inward component of the uniformly distributed design load on the roof (i.e.
the characteristic value multiplied by the partial factor according to section 2.9.2.1).
(6)
The stability of a conical roof under the design external pressure Pi.Ed should be verified
text deleted @iI.
according to the provisions of section 7.3 of EN I 993-4-1 ~
11.2.2 Self supporting roof with roof structure
(1)
The specified thickness of all roof plating should be not less than 3mm for stainless steels and
not less than 5mm for other steels.
The roof structure should either be braced (see 11.2.4) or structurally connected to the roof
(2)
plating.
(3)
The roof plates may be designed using large deflection theory.
(4)
The design of the roof supporting structure should satisfy the requirements of EN 1993-1-1.
(5)
Provided that the diameter of the tank is less than 60m and the distributed load does not deviate
strongly from symmetry about the tank axis, the procedure described in (6) to (10) may be used for
spherical roofs.
41
BS EN 1993-4-2:2007
EN 1993-4-2: 2007 (E)
h
A'
x
III
= ~r
r
0= roof profile; A= tank axis
Figure 11.2: Tank spherical roof coordinates
For spherical roofs under the action of distributed loads arising from imposed load, snow load,
(6)
wind load, permanent load and pressure, the maximum vertical component should be taken as the
design value Pv,Ed acting either upwards or downwards, with jJv,Ed taken as negative if it acts
upwards. The total design vertical force per rafter should be taken as:
... (11.5)
in which:
j3
= reIn
where:
11
is the number of rafters;
r
1
Pv.Ed
IS
s the radi us of the tank;
the maximum vertical component of the design distributed load (see annex A)
including the dead weight of the supporting structure (downward positive);
is the total design vertical force per rafter.
The normal force NEd and bending moment M Ed in each rafter for design according to EN
(7)
1993-1-1 may be obtained from:
0,375 r P Ed
h
... (11.6)
... (11.7)
provided that the following conditions are met:
p v. Eel
42
]
,2 kK1m
2
... (] 1.8)
BS EN 1993-4-2:2007
EN 1993-4-2: 2007 (E)
... (11.9)
17K 2 2 11K
... (11.10)
Al 2
... (11.11)
2
~
2/3
... (11.12)
in which:
£
... (11.13)
NEd
where:
h
is the rise of the tank roof, see figure 11
x
1S
y
is the vertical height of the roof at coordinate x, see figure 11.2;
17K
1S
hK
is the vertical distance between the flanges of the centre ring, see figure 11.3;
AI
is the area of the top flange of the centre ring, see figure 11.3;
A2
is the area of the bottom flange of the centre ring, see figure 11.3;
Iy
is the second moment of area of the rafter about the horizontal axis.
the radial distance from the centreline of the tank, see figure 11
the flange width of the centre ring, see figure II
(8)
If the second moment of area of the rafter Iy varies along the length of the rafter
due to
the variable effective width of roof plates when they are connected to the rafters) the value of Iy at a
distance 0,5r from the tank axis may be used in (7).
(9)
Provided that the conditions given in (7) are satisfied, the design of the centre ring may be
verified by checking only its lower chord according to (10).
(10) Provided that there are at least J 0 uniformly spaced rafters, the design value of the member
force Nr,Ed and bending moment Mr.Ed for the central ring may be calculated using:
N 2 . Ed
2/3
... (11.14)
... (11.15)
in which:
... (1 1.16)
43
BS EN 1993-4-2:2007
EN 1993-4-2: 2007 (E)
\vhere:
is the design value of the force in the lower chord of the centre ring;
rafte~
NEd
is the design value of the force in the
M Ed
is the design value of the bending moment in the rafter at its inner end;
eo
]s the vertical eccentricity of the rafter neutral axis from the top flange of the centre ring,
see figure 11
rk
is the radius of the neutral axis of the centre ring, see figure 1 1.3.
!
t
i
i
i
i
i
I
I
i
i
i
I
i
/1
)
l
@il
i
i
i
i
i
ii
i
i
;
~J
'r\-~
I
!\
n:~
i
i
f
p= profile section separating flanges; BA= beam axis; A= tank axis; NA= neutral axis of A1 and A2 for
bending in the plane of the plates
Figure 11.3: Roof centre ring
11.2.3 Column supported roof
(J)
The specified thickness of all roof plating shou ld be not less than 3mm for stainless stee1s and
not less than 5mm for other steels.
(2)
The roof plates may be designed using large deflection theory.
(3)
The design of the roof supporting structure should satisfy the requirements of EN 1993-1 1.
11.2.4 Bracing
(1)
If the roof plates are not connected to the rafters, bracing should be used.
(2)
For roofs exceeding 15 m diameter. at least two bays of bracing should be provided (i.e. two
pairs of adjacent rafters connected by truss members). The sets of braced bays should be spaced
evenly around the tank circumference.
44
BS EN 1993-4-2:2007
EN 1993-4-2: 2007 (E)
(3)
For braced roofs with diameter between 15 m and 25 m, an additional circumferential ring
should be provided. For braced roofs with diameter over 25 m, two additional circumferential rings
should be provided.
(4)
The bracing should be designed for a stabilising force equal to 1% of the sum of the normal
forces in the stabilised members.
11.2.5 Edge ring at the shell to roof junction (eaves junction)
(1)
The force in the effective
verified using:
NEd
ring (area where the roof is connected to the shell) should be
$ f~.d
... (11.17)
in which:
p
')
r-
... (11.1
2 tana
where:
is the effective area of the edge ring indicated in figure 1.4~
a
IS
the slope of the roof to the horizontal at the junctio~
pv,Ed
IS
the maximum vertical component of the design distributed load including the dead
weight of the supporting structure (downward positive).
(2)
Where the separation between adjacent rafters at their points of connection to the edge
does not exceed 3,25m, the stability of the edge ring need not be verified.
(3)
Where the design distributed load
may be ignored.
pv,Ed
acts upwards, the bending moments in the
ring
(4)
Where the separation between adjacent rafters at their points of connection to the
ring
does not exceed 3,25m, and the design distributed load pv.Ed acts downwards, the bending moments
in the edge ring may be ignored.
(5)
Where the separation between adjacent rafters at their points of connection to
exceeds 3,25m, the bending moments in the edge ring about its vel1ical axis should
account in addition to the normal force in the ring NEd. The bending moments in the
values inducing tensile stresses on the inside of the ring) should be evaluated using
expressions.
At the connection of the rafter:
the edge
be taken into
ring (positive
the following
... (1 1.19)
At half span between the rafters:
r f3f3
---]
\ sin
'
)
Pv,Ed acts in the upward direction, it is taken as negative, causing a change
the normal forces and bending moments.
NOTE: Where
(1 1.20)
or
in all
45
BS EN 1993-4-2:2007
EN 1993-4-2: 2007 (E)
WI'
=0,6 ~Rltr
W('=
(},6-·Ft
r
r
Figure 11.4: Edge ring at the shell to roof junction
11.3 Shell design
11.3.1 Shell plates
(I)
The circumferential normal stress due to liquid loads and internal pressure should be verified in
each shell course using:
... (11.2])
where the value of H rcd for the Jth course, denoted by Hred .j , is determined according to its
relationship with the value for the course below it, which is the (j-l)th course:
if
if
H rcd .j
in which:
/j,H
= 0,30 metres
where:
P
is the density of the contained liquid;
g
IS
46
the acceleration due to gravity;
Hr"d.j-l
2::
... (11.22)
... (11.23)
BS EN 1993-4-2:2007
EN 1993-4-2: 2007 (E)
Hj
is the vertical distance from the bottom of the jth course to the liquid level,
PEel
is the design value of the pressure above the liquid level (i.e. the characteristic value
).
multiplied by the partial factor according to
2.9.2.1
11.3.2 Stiffening rings
(I)
Fixed roof tanks with roof structures may be considered to be adequately stiffened at the top of
the shell by the roof structure. A primary ring need not be used.
Open top tanks should be provided with a primary ring which is located at or near the top of the
(2)
uppermost course.
If the lower edge of the shell is effectively anchored to resist vertical displacements the primary
(3)
stiffening ring may be designed by satisfying both the strength and the stiffness requirement given in
clauses (12) to (14) of section 5.3.2.5 of EN 1993-4-].
(4) If the lower
of the shell is not effectively anchored to resist vertical displacements the
buckling assessment should be carried out using EN 1993-1-6.
(5) When stiffening rings are located more than 600 mm below the top of the she]], the tank should
be provided with a top curb angle with the following size:
-
60x60x5 where the top shell course has a thickness less than 6 mm;
80x80x6 where the top she]] course has a thickness of 6 mm or more.
section, the horizontal leg should be not further than 25 mm from the top edge of the
For either
shell.
The requirement for a secondary ring to prevent local buckling of the shell should be
(6)
investigated using the following procedure. The height over which buckling of the unstiffened shell
can occur (measured from the top of the shell or the primary wind girder downwards) should be taken
from:
2.5
... (I 1.24)
HE = :Lh
where:
h
is the height of each course in turn below the edge ring or the primary wind girder;
IS
tmin
(7)
the thickness of each course in turn:
is the thickness of the thinnest course.
The height that may be taken to be stable without a secondary ring should be taken from:
25
0,46
rK
... (1 1.25)
in which:
K= 1
if the axial stress
ax.Ed
is tensile
... (11.26)
47
BS EN 1993-4-2:2007
EN 1993-4-2: 2007 (E)
if the axial stress is compressive .. (11.27)
K
where PEu is the maximum design value of the inward component of the pressure on the shell wa]]
(pressure on the outside, negative pressure on the inside) and (rlt) is taken at the same location as the
design value ~x,Ed
of the compressive axial membrane stress.
NOTE: The above formulas can sometimes be very conservative
in the case of very short
The provisions of EN 1993-1-6 may
be used to provide a more economic design.
(8)
The non-uniform distribution of pressure
qw.EcI
resulting from external wind loading on
cylinders (see
11.5) may, for the purpose of tank buckling design, be substituted by an
equivalent uniform external pressure:
... (11.28)
= k\V qw.ll1ax.Ed
where qw.lll:tx.Ed is the maximum wind pressure, and kw should be found as follows:
... (11.29)
with
(9)
ell' according to clause (8) of section 5.3.2.5 of EN
1993-4-1.
The pressure PEd to be introduced into 11.25 follows from:
PEd
=
... (11.30)
where qs.Ed is the internal suction caused by venting, internal partial vacuum or other phenomena.
a) wind pressure
distribution around shell
circumference
b) equivalent
axisymmetric pressure
distribution
Figure 11.5: Transformation of typical wind external pressure load distribution
(10) The procedure set out in (7) should not be used where the axial stress is compressive unless
both of the following conditions are met:
r ~
48
200
... (11.31)
BS EN 1993.. 4..2:2007
EN 1993-4-2: 2007 (E)
-r
.fy
~
1,15£
r
... (11.32)
where:
is the height of the buckle. This is
ring stiffeners whichever is less.
(1 ])
If HE
s
by Hf,,' or the distance between the adjacent
H p , a secondary ring need not be used.
(12) If HE > H p, the height HE should be subdivided by stiffening rings equally spaced at
separations HI' or less to prevent buckling of the shell waH. If more than one stiffening ring is
necessary, the value of K may be calculated separately for each bay between stiffening rings, to give
different distances Hp between stiffening rings according to (7).
(13) If the thickness of the course to which a lower ring is attached is greater than the minimulll
plate thickness tmin, an adjustment should be made as fol1ows. The distance H1ower.adj at which a lower
ring should be placed below the edge ring or primary ring should be evaluated instead as using:
2.5
.,. (11.33)
where:
Hlower
is the distance from the edge ring or the primary
adjusted;
to the secondary ring position to be
H tlnin is the distance from the edge ring or the primary ring to the lower boundary of the shell
courses with thickness tmin'
(14)
Secondary rings should not be located within 150mm of a circumferential tank seam.
(15) Unless a more detailed assessment is carried out using EN 1993-1-6 secondary rings should
satisfy the following stiffness requirement
2
( 11.34)
with
P j.Edr(a j+l +(1 j)
2
( 11
(11.36)
1,79
H
lnB
next smaller integer to mn
IR,j
second moment of area of secondary ring j
max I R .j
maximum value of h.j for all secondary rings
49
BS EN 1993-4-2:2007
EN 1993-4-2: 2007 (E)
H
height of the primary ring or roof to shell junction above the bottom edge
distance from secondary ring} to the next secondary ring below or to the bottom edge
if there is no secondary ring below
o.j
OJ+I
distance from secondary ring} to the next secondary ring above or to the primary ring
or roof to shell junction if there is no secondary ring above
tj
mean value of the shell thickness along the distance OJ
min(aj tj) minimum value of OJ tj along the height H
r
radius of the tank shell
negative design pressure at the secondary ring)
11.3.3 Openings
(l)
Openings and mountings should be designed according to 5.4.6.
11.4 Bottom design
(I)
The design of the bottom plate should take corrosion into account.
(2)
Bottom plates should be lap welded or butt welded.
For welding details see EN 14015 or
EN 14620, as appropriate.
The specified thickness of the bottom plates should not be less than specified in table 11.1
(3)
excluding corrosion al1owance. Larger values should be used if required to resist uplift due to the
internal negative pressure, unless a minimum guaranteed residual liquid level is used to assist in
resisting this uplift.
Ta bl e 111M'
,
I te thOIe kness
. Inlmum
nomina I b 0 tt ompla
Lap welded bottoms
Butt welded bottoms
Carbon steels
6mm
5 mm
Stainless steels
5 mm
3mm
Material
(4)
Bottom plates supported by parallel girders (elevated bottoms) may be designed as continuous
beams according to smal1 deflection theory. If the deformation of the cross section of the supporting
girders due to the lateral load is negligible (e.g. concrete beams, hollow sections, beams with heavy
flanges), the span of the continuous beam representing the plate may be taken as the distance between
adjacent edges of these supporting members, instead of the distance between the centre-lines of the
supporting members.
(5)
Bottoms for tanks greater than 12,5m diameter should have a base ring (in the form of an
annular plate) that satisfies the strength and toughness requirements on the shell course to which they
are attached. This base ring should have a minimum nominal thickness ta excluding corrosion
allowance obtained from:
ta = tJ3 + 3mm
where
t~
50
but not less than 6mm
is the thickness of the attached shell course.
... (11.37)
BS EN 1993-4-2:2007
EN 1993-4-2: 2007 (E)
NOTE 1: This minimum thickness of bottom plate may lead to the formation of a plastic hinge in the
annular plate, avoiding alternating plasticity in the weld detail at the bottom of the shell 'wall. However, it
should be noted that this minimum plale thickness may also lead to uplin of the ouler
or the annular
plate, with consequent potential for corrosion.
NOTE 2: Where axial forces develop in the tank shell, the annular plate must be designed to distribute
these axial forces into the foundation.
(6)
The inner part of the base ring annular plate should not have an exposed width w less than the
limiting value \Va , obtained from:
, ') J
Wa
f yt;; 112
= 1,5 - ' -
H
IS
the maximum design liquid height.
w{/
is the minilllu1l1 exposed width (distance from the inner edge of the annular base plate to
the inner edge of the shell plate).
ta
is the thickness of the annular plate, taking account of the corrosion allowance.
p
IS
g
is the acceleration due to gravity.
[ pgH
(I 1.38)
but not less than 500mm
where:
the density of the contained liquid.
The radial seams connecting annular plates to each other should be full penetration butt welded.
For welding detail s, see EN 14015 or EN 14620, as appropriate.
(7)
(8)
The distance from the outer edge of the shell plate to the outer
ring annular plate should not be less than 50mm.
of the bottom plates or base
(9)
The attachment of the lowest course of the shell plate to the annular plates or bottom sketch
plates should be continuous fillet welds on both sides of the shell plate.
(l0) The throat thickness for each fillet weld should be greater than or equal to the thickness of the
annular plate or of the sketch plate, except that they should not exceed 10111111 and where the shell
plate thickness is
than the sketch plate or annular plate thickness, they should not exceed the
appropriate value given in table 11.2.
Table 11.2: Fillet weld throat thickness if shell plate is thinner than
sketch plate or annu lar plate
Shell plate thickness, t
Fillet weld throat thickness
t< 5 mm
2,0 111m
5 mm
4,5 mm
t> 5 mm
6,0 111m
t
11.5 Anchorage design
(1)
Tank anchorage should be provided for fixed roof tanks. if any of the following conditions can
cause the cylindrical shell wall and the bottom plate close to it to lift off its foundations:
51
as EN 1993-4-2:2007
EN 1993-4-2: 2007 (E)
a)
Uplift of an empty tank due to internal design pressure counteracted by the effective
corroded weight of roof, shell and permanent attachments;
b)
Uplift due to internal design pressure in combination with wind loading counteracted by
the effective corroded weight of roof, shell and permanent attachments plus the effective
weight of the product always present in the tank as agreed between the designer, the
client and the relevant authority.
c)
Uplift of an empty tank due to wind loading counteracted by the effective corroded
weight of roof, shell and permanent attachments;
d)
Uplift of an empty tank due to external liquid caused by flooding. In such cases it is
necessary to consider the effects upon the tank bottom, tank shell etc. as well as the
anchorage design.
For this check, the uplift forces due to the wind load may be calculated using the assumption that the
tank shell has a rigid cross section (beam theory). This assumption implies that local uplift can occur.
In cases where no local uplift can be allowed, a more sophisticated analysis is required.
(2)
Anchorage points should be spaced evenly around the circumference of the tank, insofar as this
is possible.
(3)
The design of the holding down bolts or straps should meet the requirements of EN ] 993-1-1.
If
The minimum cross-sectional area for the holding down bolts or straps should be 0m~.5
corrosion is anticipated, a minimum corrosion allowance of I mm should be added.
(4)
The anchorage should be principally attached to the shell wall. It should not be attached to the
bottom plate alone.
(5)
The design of the anchorage should accommodate movements of the tank due to thermal
changes and hydrostatic pressure and minimise any stresses induced in the shell.
(6)
The design of the shell for local anchorage forces and bending moments resulting from the
anchorage should meet the requirements of 5.4.6 and 5.4.7 of EN 1993-4-].
(7)
No initial tension shOll Id be applied to the holding down bolt or strap, to ensure that it will
become effective only if an uplift force develops in the shell of the tank.
NOTE: If the holding down bolts or straps are not pretensioned, the maximum uplift forces in them under
wind load will be reduced. so that the calculation described in (1) will be applicable. In addition, a
reduction will occur in the stresses induced by restraint of radial movements due to thermal changes and
hydrostatic pressure.
52
BS EN 1993-4-2:2007
EN 1993-4-2: 2007 (E)
Annex A [normative]
Actions on tanks
A.1
General
(1)
The design should take account of the characteristic values of the actions listed in A.2.1 to
A.2.14.
(2) The partial factors on actions according to 2.9.2.1 and the action combination rules according to
2.10 should be applied to these characteristic values.
A.2 Actions
A.2.1 Liquid induced loads
During operation, the load due to the contents should be the weight of the prodllct to be stored
(1)
from maximwn design liquid level to empty.
(2)
During test, the load due to the contents should be the weight of the test 1I1edillmfrol11 maximum
test liquid level to empty.
A.2.2 Internal pressure loads
During operation, the internal pressure load should be the load due to the specified minimum
and maximum values of the internal pressure.
(1)
(2)
During test, the internal pressure load should be the load due to the specified mi nimull1 and
maximum values of the test internal pressure.
A.2.3 Thermally induced loads
(1)
Stresses resulting from restraint of thermal expansion may be ignored if the number of load
cycles due to thermal expansion is such that there is no risk of fatigue failure or cyclic plastic failure.
A.2.4 Dead loads
(1)
The dead loads on the tank should be considered as those resulting from the weight of all
component pat1s of the tank and all components permanently attached to the tank.
(2)
Numerical values should be taken from EN 1991 1-].
A.2.S Insulation loads
(1)
The insulation loads should be those resulting from the weight of the insulation.
Numerical values should be taken from EN 1991-1-].
A.2.6 Distributed live load
(I)
The distributed live load should be taken from EN 1991 I I unless otherwise specified.
53
BS EN 1993-4-2:2007
EN 1993-4-2: 2007 (E)
A.2.7 Concentrated live load
(I)
The concentrated live load should be taken from EN 1991 1 1 unless otherwise specified.
A.2.8 Snow
(l)
The loads should be taken from EN 1991-1-3.
A.2.9 Wind
(I)
The loads should be taken from EN 1991 1-4.
(2)
In addition, the fol1owing pressure coefficients may be used for circular cylindrical tanks, see
figure A.I:
a)
internal pressure of open top tanks and open top catch basin: c p = -0,6.
b)
internal pressure of vented tanks with small openings:
c)
where there is a catch basin, the external pressure on the tank shell may be assumed to
reduce linearly with height.
-0,4.
Due to their temporary character, reduced wind loads may be used for erection situations
(3)
according to EN ] 991-1-4.
A.2.10 Suction due to inadequate venting
(I)
The loads should be taken from EN ] 991-1-4.
A.2.11 Seismic loadings
(I)
The loads should be taken from EN 1998-4, which also sets out the requirements for seismic
design.
A.2.12 Loads resulting from connections
(I)
Loads resulting from pipes, valves and other items connected to the tank and loads resulting
from settlement of independent item supports relative to the tank foundation should be taken into
account. Pipework should be designed to minimise loadings applied to the tank.
A.2.13 Loads resulting from uneven settlement
(1)
Settlement loads should be taken into account where uneven settlement can be expected during
the lifetime of the tank.
A.2.14 Emergency loadings
(])
]'he loads should be specified for the specific situation and can include loadings from events
such as external blast, impact adjacent external fire, explosion, leakage of inner tank, roll over,
overfill of inner tank.
54
BS EN 1993-4-2:2007
EN 1993-4-2: 2007 (E)
Cp
a) Tank with catch basin
Cp
b) Tank without catch basin
Dr= Diameter of tank; Dc= Diameter of catch-basin;
1)
cp = 0,4 applies only for the vented tank; where no numerical values are given with cp @il
they have to be obtained from EN 1991-1-4.
Figure A.1: Pressure coefficients for wind loading on a circular cylindrical tank
55