Trusses

""La tesi si inserisce nell'ambito di ricerca della storia delle tecniche costruttive e analizza l'evoluzione tecnologica e tipologica delle coperture lignee in Italia nel periodo che va dall'inizio del XIX alla metà del XX secolo.
Dopo una parte di inquadramento delle condizioni tecnologiche, del contesto socio-economico e produttivo generale e delle teorie e pratiche costruttive delle coperture lignee italiane della fine del XVIII secolo, la ricerca ne analizza i progressivi mutamenti cercando di individuare alcune "fasi omogenee" e di rintracciare i nessi tra i processi evolutivi del contesto e quelli che interessano le coperture lignee.
Particolare attenzione è attribuita allo sviluppo delle tipologie costruttive delle capriate e alla diffusione di altri tipi di strutture lignee di copertura (cavalletti centinati, archi, portali a due o tre cerniere, ecc.), rapportati ai vari aspetti del contesto tecnico-culturale e produttivo: livello e tipo di formazione culturale e tecnica dell'ingegnere e dell'architetto; sviluppo e diffusione delle teorie della meccanica delle strutture e della resistenza dei materiali; cambiamenti nei modi di produzione e lavorazione dei materiali edilizi; variazione dei prezzi della manodopera e dei materiali; invenzione di nuovi sistemi di connessione dei legnami.""

Il saggio si inserisce nell’ambito di ricerca della storia delle tecniche costruttive e analizza l’evoluzione tecnologica e tipologica delle coperture lignee in Italia nel periodo che va dall’inizio del XIX alla metà del XX secolo. Particolare attenzione è data all’inquadramento delle condizioni tecnologiche, del contesto socio-economico e produttivo generale e delle teorie e pratiche costruttive delle coperture lignee italiane della fine del XVIII secolo, la ricerca ne analizza in seguito i progressivi mutamenti, cercando di individuare alcune “fasi omogenee” e di rintracciare i nessi tra i processi evolutivi del contesto e quelli che interessano le coperture lignee. Lo studio dello sviluppo delle tipologie costruttive delle capriate e la diffusione di altri tipi di strutture lignee di copertura (cavalletti centinati, archi, portali a due o tre cerniere, ecc.) costituisce il nucleo principale del saggio. Questi fenomeni sono rapportati a vari aspetti del contesto tecnico-culturale e produttivo: livello e tipo di formazione culturale e tecnica dell’ingegnere e dell’architetto; sviluppo e diffusione delle teorie della meccanica delle strutture e della resistenza dei materiali; cambiamenti nei modi di produzione e lavorazione dei materiali edilizi; variazione dei prezzi della mano d’opera e dei materiali; invenzione di nuovi sistemi di connessione dei legnami.

In this project there is an example where reaction forces are found using the finite
element method. Firstly, it was solved with manually algebraic solution, then the result was
reached using the ANSYS program and the results of the two solution methods were
compared.
The finite element method, which has a history of 60 years, in recent years the use of
finite element analysis (FEA) as a design tool has grown rapidly. The finite element method is
a numerical procedure that can be used to obtain solutions to a large class of engineering
problems involving stress analysis, heat transfer, electromagnetism, and fluid flow. Easy-touse, comprehensive packages such as ANSYS, a general-purpose finite element computer
program, have become common tools in the hands of design engineers. This project is created
to assist analysis engineers of finite element modeling to gain a clear understanding of the
basic concepts. The example that is solved using ANSYS shows in detail how to use ANSYS
to model and analyses a truss analysis of an engineering problem.
In the first section, fundamentals about the finite element method and simple
definitions of matrix solutions used in analysis solutions are given. In addition to this section,
the use of the MatLab program in the finite element method is explained. In the second
section, the classification and properties of trusses and statically solving methods of truss
problems are given. The formulations and definitions required for the solution of trusses with
the finite element method are included in this section. In the third chapter, the manual solution
of determining the reaction forces of a truss structure under loaded forces using the finite
element method is given. In the fourth section, the example for which reaction forces were
found was modeled on ANSYS and solved by the program. In the final section, the results of
the example for which reaction forces were found by manually and the ANSYS Static
Structural module were compared and the consistency between the results was examined.

The time and the place in which trusses were invented is uncertain; however, it is certain that they were already in use during Roman Empire. The oldest extant material evidences date back to the 6th century AD and witness the simultaneous presence in Italy of two constructive types that coexisted for centuries. The two types of truss are distinguished from each other based on the different relationship between posts and tie-beams: in closed-joint trusses, posts are connected to tie-beams with carpentry joints (e.g. tenon-mortise); in open-joint trusses, the posts are physically detached from the tie-beam but possibly linked to it with a metallic strap.
The paper will outline the idea that, under the effects of vertical static loads, there is no significant difference in structural behaviour between the closed- and the open-joint trusses. Indeed, under ordinary loads, in Italian-style trusses the deflection of the tie-beam is greater than the lowering of the bottom of the post, and carpenters were aware of this since the post/tie-beam joint is always traction resistant; therefore, the tie-beam is usually hanging from the post. Subsequently, the joined analysis of many clues (structural behaviour, evolution of carpentry joints, evolution and spread of iron reinforcements) will be used to support the thesis that the progressive prevalence of the second type over the first (which essentially disappeared since the mid-18th century) is due to the progressive understanding of the behaviour of damaged trusses and to the gradual diffusion of metallic elements for joints reinforcement.
When in a closed joint truss a material decay affects the rafter/tie-beam joint, the tie beam starts to be charged by a concentrated load, which generates a flexional action even though no sensible displacement is visible; decay progression can eventually lead to tie-beam breakage, especially if it is weakened by a mortise.
When the same decay affects an open-joint truss, as soon as the decay starts, if there is no iron reinforcement, the bottom of the post suddenly hits the tie-beam, and there is the risk that it could collapse. On the contrary, if the rafter/tie-beam joint has iron reinforcing elements, it acquires a certain ductility and, in case of decay, the bottom of the rafter slowly and progressively slips, causing a lowering of the post towards the tie-beam, which denounces the beginning of a decay and warns against the risk of collapse.
Hence, progressive affirmation of open-joint trusses can be seen as the achievement of a higher safety in event of material decay of the rafter/tie-beam joint.

Innovative solutions of joints for bamboo trusses are presented. Experimental tests show the performances and the high level of ductility of the proposed technique, joined with simplicity in the concept of the joints, low level of technology and low cost of all used materials. It can permit a proper dissemination and a sustainable maintenance in developing countries.

A Basilica dedicated to Saint Michael was first built in the Longobardic period (6th-8th cen-turies), however the present building dates back to 11th-12th centuries. The church was built in Romanesque style and it is unanimously considered one of the masterpieces of the Lombard architecture of the period. During the subsequent centuries, the building underwent several changes and restoration works. Dealing with the roof of the central nave, the rebuilding of the vaults (1488-91) was the most relevant work. Traces of the pre-existent vaults are still visible in the attic; they were much higher than the present ones and thus they were in-compatible with the structural organisation of the existing timber roof structure. Therefore the conception of this structural system probably dates back to that period. In 1860–75 the building underwent works of stylistic restoration and since the 1930s many preservation in-terventions were done in order to consolidate the decayed sandstone of the façades; however, these interventions did not affect the roof structures. In 1942 two reinforced concrete wall plates were built on the top of the longitudinal walls of the central nave and the timber trusses now lay on them. Since the early 19th century the church has been studied by many art and architecture historians, and many surveys and drawings have been done, both before and af-ter the stylistic restoration works. However the historians’ attention has focused mainly on the formal features of the building and on the construction phases of masonry structure. In many of the drawings the roof structures are not even represented; in the others, they are only sketched out schematically. Therefore, the knowledge of the timber roof structures of the church is still very poor. In this situation, the study of archival documents and the survey and in situ investigation of the timber trusses play a fundamental role in the historical knowledge of this important but neglected timber structural complex. The structural complex is com-posed of a sequence of seven quite different trusses supporting the upper layers of timber elements (i.e. purlins, joists and laths) and the roof tiles. The paper advances a hypothesis about the dating of each of the trusses, based on the matching of the archival data with the critical interpretation of the surveyed signs: structural type of the truss, type of joints, signs of woodworking tools (e.g. axes, saws, hand drills, chisels), assembly marks, signs of reutiliza-tion of timber elements, type of iron reinforcement elements, etc.

Ferrous metals are often seen as antagonists of timber in buildings, since their gradual spread in structural elements has led to the progressive decrease of timber structures diffusion. However metal elements were and still are used in timber structures and have significantly influenced their evolution in time. On the basis of information found in treatises, historical handbooks and – for more recent times –technical journals, of archival sources, of modern historical investigations, and of direct survey, the paper attempts a critical historical reconstruction of the technological evolution of metal elements used in timber trusses between Middle Ages and the mid-20th century, making explicit its influence on the evolution of trusses typology. The paper also deals concisely with the diffusion of metal elements in strengthening works of existing timber structures, especially with reference to the last century of the analyzed period.
In Middle Ages carpentry joints and constructional types of trusses were generally designed so as not to require metal elements because of their high cost. Between 13th and 15th century, the evolution of iron industry allowed a drop in the cost of ferrous metals. In trusses the use of wrought iron in the form of nails and brackets grew, therefore a series of changes took place, including the gradual abandonment of “closed-joint” trusses in favour of “open-joint” ones. In 18th and 19th century, iron and steel industry revolution led to an exceptional production increase: new metal elements spread allowing the creation of the steel-timber trusses and of entirely metal ones. Since the second half of 19th century, the transition from empiricism to structural mechanics and a progressive loss of building traditions led designers to strengthening decayed timber structures using metal ties or rolled beams. In early decades of 20th century, further innovations in the field of hot and cold steel working allowed the invention of new elements and connection systems for timber structures (e.g. bolts, split rings, toothed rings, spiked plates) leading to the creation of new types of timber roof structures (reticular beams and portals).

Abstract: For steel-framed structural systems, strength and deflections have been the two fundamental limit states for the design. However, the use of high-strength steel, lighter sections, and low inherent damping resulted in more lively structures, and floor vibration serviceability has become a governing factor for structural design. While annoying floor vibrations can be significant in open web steel joist-supported
footbridges; a common application in the North American construction industry is the installation of bottom chord extensions in an attempt to strengthen the floor and increase the natural frequency of the floor systems. Even though extending joist bottom chords is very common, there
has not been any publication on the topic studying the dynamic effects of this application. The study presented in this paper aims to fill this gap and identify the effect of bottom chord extensions on the modal parameters of joist-supported structures, by studying two laboratory footbridges. The goal is not to solve a potential vibration problem of a footbridge but to identify the modal parameter variations due to bottom
chord extension installations. Extensive experimental and analytical studies were conducted on single-span and three-span joist-supported laboratory footbridges with different bottom chord extension configurations. Three-dimensional finite-element computer models were created to simulate and compare the results of stiffness and dynamic tests with the philosophy of testing the footbridges and updating the finite element models, thus minimizing the discrepancies between the test results and the finite-element models for better prediction. Results from the static and dynamic tests on the single-span and three-span footbridges indicate that installing the bottom chord extensions to the joists increases the natural frequencies of the flexural stiffness and flexural bending. Considering the low cost, and quick and easy application at the
construction site, extending bottom chords can be considered as an option to reduce the deflections and increase the governing bending mode natural frequencies of footbridges. While bottom chord extensions do not guarantee that the vibration problem (if any) would be solved, with the higher natural frequencies, the footbridges are relatively less  vulnerable to be put in resonance by human induced excitations. As a result, extending bottom chord extensions is an advantage; however, the acceleration response of the footbridges needs to be checked separately, for conformance with the code limits.

The lack of knowledge of the structural behaviour and performances of timber structures often led to their loss and substitution with modern structures, or to invasive strengthening works. Ignorance is a cause of loss of these structures also because if their value isn’t recognized, people will not develop the moral imperative to preserve them. Just because ignorance is one of the main causes of loss of this heritage, knowledge is the first goal to be reached aiming to its preservation. The most important source of knowledge of an existing structure is its direct survey. In situ investigations should aim to collect data about many aspects of the structure: general geometry and details of single members, internal joints, and metal reinforcements; wooden species and defects; evidences of decay; deformations or displacements; but also relation with other structural elements or systems, signs of timber processing, indications of the reuse of materials, etc. All the gathered data should allow an interpretation of the gradual change in time of the structure’s physical reality, of its technological conception and of its structural behaviour since the original design by the carpenter or engineer, through the subsequent works or “natural” evolutions, unto the current state.

AbstractIn this paper, a new design approach for dissipative truss moment frames (DTMFs) able to guarantee, under seismic forces, the development of a yield mechanism of global type is presented and applied. In particular, DTMFs consist of a truss moment frame where the energy dissipation is provided by means of special devices located at the ends of the truss girders at the bottom chord level. The proposed design methodology is based on the kinematic theorem of plastic collapse. The method is based on the assumption that sections of truss elements and the yield threshold of dissipative parts (i.e., special devices) are known, and therefore the column sections are the unknowns of the design problem, which are obtained by imposing that the equilibrium curve corresponding to the global mechanism has to lie below those corresponding to all the possible mechanisms within a displacement range compatible with local ductility supply of dissipative elements. The design methodology has been implemented in a comput...

This paper is a part of a broad research effort aimed at evaluating 82 weathering steel overhead sign structures in Charleston Interstate System in West Virginia. Twenty-six comprehensive inspection forms were developed to objectively evaluate the current condition of 11 general types of sign structures. This paper focuses on analyzing the following two types of sign structures: (1) Type A: Double armed ground mount cantilever; and (2) Type B: Shoulder/median barrier mount two-dimensional truss. A rating methodology was developed to evaluate both the condition of the overall sign structure and its elements. After extensive field inspections of each sign structure, the element condition rating assigned specific rating criteria to sign elements was conducted. The current condition of each sign structure was then evaluated by an overall condition rating, which is estimated by calculating the ratio between the total score of each structure (S) and its maximum possible total score (S sub...

The paper will show how modern structural engineering has been applied to a field of construction before ruled by empiricism and static intuition: timber trusses.
Since the late 18th century, the development of steel industry led to profound changes in the production and processing of building materials. This allowed the use of metallic members in substitution of timber ones and the development of trusses made entirely of steel.
Until mid-19th century timber trusses were designed on empirical basis, with redundant members and with static scheme difficult to be analyzed. In absence of specific building traditions, the spread of metal trusses required the development of appropriate structural analysis methods; the theory of statically-determinate trusses was therefore elaborated. However this theory couldn’t be used with timber trusses because loads weren’t applied in the joints, hypothesis required to ignore the static indeterminacy.
Since the 1860s many engineers expressed the need of structural assessment in traditional structures to optimize the use of materials. Structural analysis method for timber statically–indeterminate trusses were developed, considering rafters as continuous beams on rigid supports. Not considering the deformation of the intermediate supports, such analysis didn’t satisfy constitutive and strain–displacement equations and were gradually excluded from the structural mechanics manuals, but remained common in technical handbooks until 1940s.
In the 1870s, theoretical studies of Castigliano allowed the exact calculation of statically-indeterminate structures, technical papers were then published to apply this theory to various types of wooden trusses. The complexity of the calculations, however, relegated the use of these methods to sporadic examples; in most cases engineers still resorted to empiricism, simplified formulas, tables and nomograms.
In the early 20th century the production of new steel elements for timber connection (screws, bolts, spiked plates) allowed the experimentation of new timber trusses made mainly of boards; these trusses could reproduce the steel truss schemes due to the simplicity of the joints and to the slenderness of members, thus allowing the use of the theory of statically–determinate trusses.

The appraisal of existing riveted metal structures generally involves the understanding of their connection details. Unfortunately, it is tough to decipher how historical riveted connections were designed given the obsolescence of the hot-riveting technique. The design of riveted connections has to be analyzed to support the structural assessment and potential interventions. Practicing engineers, architects and heritage care specialists need to gain insight into the original design philosophy of the connection details to preserve both the service life and heritage value of iron and steel structures. Therefore, we unraveled the design of riveted connections by referring to historical literature and carrying out on-site surveys. This paper reveals the design philosophy of structural riveted connections of the end of the nineteenth century in Belgium. Belgian educator-engineers mainly referred to the findings of French, German and English investigators but two to three decades after th...

Until the mid-19th century timber trusses were empirically designed thanks to centuries-old experience. Since the early 19th century the theory of statically-determinate trusses had been elaborated for the analysis of metal trusses, but this could not be used for timber trusses, because loads were not applied in joints, a hypothesis required to ignore static indeterminacy. In the late 1850s a specific analysis method was developed for timber trusses: it considered rafters as continuous beams on rigid supports, thus it did not satisfy constitutive and strain-displacement equations. However, theoretical developments of the 1870s allowed the exact calculation of statically-indeterminate structures, thus engineers often continued to resort to empiricism, or simplified methods.

The paper addresses the lateral-torsional buckling for a special steel truss structure which is adopted to reinforce a particular class of composite steel-concrete beams. The investigated instability phenomenon deals with a transitory ultimate limit state that may occur when the truss structure is being assembled and is bearing the precast floor system, before the concrete has hardened. During this transitory stage the truss beam works as a steel structure and may exhibit local or global instability phenomena. It provides the reinforcement of the final composite steel-concrete beam once the concrete has hardened. The main result of this paper is an analytical approach for the estimation of the elastic critical moment which is required to calculate the final design lateral-torsional buckling resistance moment in accordance with the technical code in force (the European standard for steel structures is considered in this paper). The simplified analysis this paper presents leads to a closed-form solution for...