Dissertations / Theses on the topic 'Strut and tie model'

The strut-and-tie method (STM) is a simple and conservative method for designing concrete structures, especially deep beams. This method expresses complicated stress patterns as a simple truss or kinematic model made up of compression elements (struts), tension elements (ties), and the joints between elements (nodes). STM is based on lowerbound plasticity theorem, so using it properly will lead to a conservative design. Although the concepts of STM have been around in concrete design since the late 19th century, STM was first introduced in AASHTO LRFD in 1994 and ACI 318-02 in 2002. ACI 318 defines two different types of struts (prismatic and bottle-shaped) based on whether compression stress can spread transversely along the length of the strut. Recent work has brought into question whether these two types of struts do exist and whether current design provisions conservatively estimate failure loads for all members. The performance of struts and nodes were investigated experimentally by testing six fullscale concrete deep beams. The specimens had two different shapes (rectangular and trusslike), two different shear span-to-depth ratio (1 and 1.6), and three different types of development (externally unbonded bars, internally bonded hooked bars, and internally bonded bars with welded external plates). All the specimens were supported vertically and vii tested under a three-point load setup. Based on the results, the truss-like specimen failed at higher loads than rectangular specimens with the same shear span-to-depth ratio. According to these results and recent debate in the literature, bottle-shaped struts are not weaker than prismatic struts because of their shape. They are weaker due to shear failure where struts cross a diagonal tension field. Therefore, the structures should be separately checked for shear strength when they are designed with STM. In this dissertation, the development of the design equation for shear strength of discontinuity regions was introduced, and the procedure is under consideration for adoption in ACI 318-19. This research was expanded numerically by studying the effect of development type and length, strut type, and strut angle on the behavior of concrete deep beams. The crack patterns and load-displacement curves, which were obtained from experimental tests, were used to validate numerical models. The strength of concrete deep beams was assessed by modeling thirty-five specimens in a nonlinear finite element software. According to the results, development length and development types influenced the presence of tensile stress in the support nodes. Additionally, the effect of the tensile stresses from reinforcement development and diagonal tension were not additive in rectangular specimens.

COORDENAÇÃO DE APERFEIÇOAMENTO DO PESSOAL DE ENSINO SUPERIOR
Modelos de bielas e tirantes são, em última análise, representações discretas dos campos de tensão nos elementos estruturais de concreto armado próximos da ruptura e visam possibilitar um projeto consistente de todos os elementos estruturais. Este trabalho tem como objetivo desenvolver um programa de otimização topológica que gere e permita a visualização de um modelo de bielas e tirantes para elementos estruturais de concreto armado. O modelo gerado auxilia o engenheiro de projetos na compreensão dos caminhos de forças. Inicialmente o usuário deve ter como dado de entrada uma malha refinada em elementos finitos. A partir daí o programa calcula as tensões através da análise elástica por elementos finitos. As técnicas de otimização topológica usadas neste trabalho foram a do método da flexibilização súbita ( hard- kill method ) e a do método da remoção. No primeiro processo, os elementos com tensões baixas, que estão sendo usados ineficientemente têm seus módulos de elasticidade bruscamente reduzidos, enquanto que no método da remoção, estes elementos são retirados da malha. Tanto para modificar o módulo de elasticidade do elemento, quanto para retirar o elemento da malha, as tensões principais nos elementos são comparadas com uma tensão de referência definida como uma fração da maior tensão principal na malha. Caso essa tensão principal no elemento seja menor que a referida tensão de referência o elemento tem seu módulo de elasticidade modificado ou é eliminado conforme o método. A distribuição de tensão nos elementos é acompanhada pelo usuário através do módulo de visualização do programa e o processo de otimização topológica é repetido até que o critério de convergência imposto seja alcançado.
Strut and tie models are ultimately discrete representations of the stress fields in the structural elements of reinforced concrete close to failure and they are meant to help the engineer to design a consistent project of all structural elements. This work aims to develop a program of topological optimisation that generates and allows the visualisation of a strut and tie model for structural elements of reinforced concrete. The generated model helps the project engineer to understand the load paths inside the element. Initially the user should have as data a refined finite element mesh. Starting from this point the program calculates the stress fields through a linear elastic finite element analysis. The techniques used for topological optimisation in this work are namely the hard-kill method and the method of removal. In the first process, the elements with low stress levels, that are not being used efficiently, have their elasticity modules abruptly reduced, while in the method of removal, these elements are removed from the mesh. Either to modify the elasticity module of the element or to remove the element from the mesh the principal stresses in each element are compared with a reference stress defined as a fraction of the largest principal stress in the mesh. If the principal stress in the element is smaller than this above mentioned reference stress the element has its elasticity module modified or is removed, depending on the method. The distribution of stresses in the elements can be followed by the user through the module of visualisation of the program and the process of topological optimisation is repeated until the specified convergence criterion is reached.
Modelos de bielas y tirantes son, en último análisis, representaciones discretas de los campos de tensión de los elementos extructurales de concreto armado próximos a la ruptura. Su objetivo principal es ejecutar un proyecto que incluya todos los elementos extructurales. Este trabajo tiene como objetivo desarrollar un programa de optimización topológica que genere y permita la visualización de un modelo de bielas y tirantes para elementos extructurales de concreto armado. El modelo generado auxilia al ingeniero de proyectos en la comprensión de los caminos de fuerzas. Inicialmente el usuario debe tener como dato de entrada una malla refinada de elementos finitos. Así, el programa calcula las tensiones a través del análisis elástica por elementos finitos. Las técnicas de optimización topológica usadas en este trabajo fueron el método de la flexibilización súbita ( hard- kill method ) y el método de la remoción. En el primer proceso, los elementos con tensiones bajas, que están siendo utilizados ineficientemente tienen sus módulos de elasticidad bruscamente reducidos, mientras que en el método de la remoción, estos elementos son retirados de la malla. Tanto para modificar el módulo de elasticidad, cuanto para retirar el elemento de la malla, las tensiones principales en los elementos se comparan con una tensión de referencia definida como una fracción de la mayor tensión principal en la malla. En el caso en que esa tensión principal en el elemento sea menor que la tensión de referencia, el elemento tiene su módulo de elasticidad modificado o es eliminado conforme el método. El usuario acompaña la distribuición de tensión en los elementos a través del módulo de visualización del programa y el proceso de optimización topológica se repite hasta alcanzar el criterio de convergencia impuesto.

COORDENAÇÃO DE APERFEIÇOAMENTO DO PESSOAL DE ENSINO SUPERIOR
O presente trabalho tem por objetivo desenvolver uma formulação e um sistema que seja uma ferramenta auxiliar para o engenheiro de projeto na definição de modelos de bielas e tirantes de estruturas bi-dimensionais. No sistema desenvolvido o usuário pode partir de um modelo complexo, com um número grande de barras nas mais variadas direções. Essa solução inicial pode se basear nos resultados em tensão de uma análise linear elástica por elementos finitos e na experiência do projetista. Todavia, como o usuário terá muitas dúvidas quanto ao melhor modelo as ser usado, ele pode superpor no modelo inicial todas as soluções que achar possíveis. A função do sistema é escolher entre todas as soluções admissíveis (aquelas que respeitam equilíbrio e resistência) a que for mais econômica. Define-se como solução mais econômica aquela que corresponder ao menor consumo de armadura. A formulação do problema conduz a um problema de Programação Linear (PL) e o programa LINDO [2] é utilizado para resolvê-lo. A visualização do modelo é também parte do sistema desenvolvido e é feito a partir dos resultados gerados pelo programa LINDO. O trabalho se divide basicamente em três partes. Na primeira parte é feita uma revisão sobre modelos de bielas e tirantes e sobre fundamentos de programação linear. A segunda parte consta da formulação do problema e por ultimo os resultados do programa são comparados com aqueles fornecidos pela literatura. A ferramenta desenvolvida neste trabalho pode ser de grande utilidade para a definição de modelos de bielas e tirantes mas ela nem de longe tem a pretensão de substituir a experiência, a intuição e o bom senso do engenheiro de projeto que deve sempre prevalecer, inclusive na análise crítica dos resultados do programa.
The present work has the aim of developing a formulation and a computational system, which should be used by the structural engineers an auxiliary tool in the definition of strut and tie models of bidimensional structures. In the developed system the user can define initially a very complex system with a great number of bars and many different directions. This initial solution can be based on both the stress results of a linear elastic finite element analysis and the experience of the engineer. As the user may be in doubt about the best model to be used he may superimpose in the initial model all the allowable solutions he may find. The aim of the system is to choose among all the allowable solution (these ones wich satisfy equilibrium and strenght) the more economical one. As more economical solution is considered the one which correspond to the least consumption of reinforcement. The problem formulation leads to a linear programming problem (LP) and the LINDO program [2] is used for solving it. The visualization of the model and results is also part of the system. It is based on the data generated by the LINDO program. The work is basicaly divided in three parts. In the first one a revision about strut and tie models as well as the basic knowledge in linear programming is presented. In the second part the problem formulation is shown and the last the results of the program are compared with those old the technical literature. The computational tool presented here may be of great utility in the definition of strut and tie models, but it has not by far the intention and the feeling of the engineers which shall ever prevail, inclusive in the critic analysis of the program results.
El presente trabajo tiene como objetivo desarrollar un sistema que sirva como herramienta auxiliar para el ingeniero de proyecto en la definición de modelos de bielas y tirantes de extructuras bidimensionales. En el sistema desarrollado, el usuario puede partir de un modelo complejo, con un número grande de barras en varias direcciones. Esa solución inicial puede basearse en los resultados en tensión de un análisis lineal elástica por elementos finitos y en la experiencia del proyectista. Como el usuario tendrá muchas dudas respecto al mejor modelo as ser usado, él puede superponer en el modelo inicial todas las soluciones que juzgue posibles. La función del sistema es elegir entre todas las soluciones admisibles (aquellas que respetan equilibrio y resistencia) la que sea más económica. Se define como solución más económica aquella que correspdonda al menor consumo de armadura. La formulación del problema conduce a un problema de Programación Lineal (PL) que es resuelto con ayuda del programa LINDO [2]. La visualización del modelo también es parte del sistema desarrollado y parte de los resultados generados por el programa LINDO. El trabajo se divide básicamente en tres partes. En la primeira parte se realiza una revisión de los modelos de bielas y tirantes y de los fundamentos de programación lineal. La segunda parte contiene la formulación del problema y la presentación de los resultados del programa se comparan con los reportados en la literatura. La herramienta desarrollada en este trabajo puede ser de gran utilidad para la definición de modelos de bielas y tirantes pero no tiene la pretensión de substituir la experiencia, la intuición y el buen senso del ingeniero de proyecto que debe siempre prevalecer, incluso en el análisis crítico de los resultados del programa.

Precast/Prestressed concrete girders are commonly used in bridge construction in the United States. The application and diffusion of the prestress force in a pretensioned girder causes a vertical tension force to develop near the end of the beam. Field surveys of the beam ends of pretensioned bridge girders indicate that many of the PCBT beams used in the Commonwealth of Virginia develop cracks within the anchorage zone region. The lengths and widths of these cracks range from acceptable to poor and in need of repair. Field observations also indicate deeper cross sections, very heavily prestressed sections, and girders with lightweight concrete tend to be most susceptible to crack formation. This research examined a new strut-and-tie based design approach to the anchorage zone design of the PCBT bridge girders used in Virginia. Case study girders surveyed during site visits are discussed and used to illustrate the nature of the problem and support the calibration of the strut-and-tie based model. A parametric study was conducted using this proposed design model and the results of this study were consolidated into anchorage zone design tables. The results of the parametric study were compared to the results obtained using existing anchorage zone design models, international bridge codes, and standard anchorage zone details used by other states. A set of new standard details was developed for the PCBT girders which incorporates elements of the new design approach and is compatible with the anchorage zone design aids. A 65 ft PCBT-53 girder was fabricated to verify the new strut-and-tie based design model. This girder contained anchorage zone details designed with the new model. The new anchorage zone details were successful at controlling the development of anchorage zone cracks. The new design approach is recommended for implementation by the Virginia Department of Transportation.
Master of Science

The research conducted was sponsored by JVI of Pittsfield, Massachusetts. JVI has developed a steel embedded connection, referred to as a shooter. The shooter is provided in capacities, a 40 kip capacity shooter and a 50 kip capacity shooter. This steel connection is embedded near the end of a double-tee prestressed girder. Double-tee prestressed girders are a primary component used in the construction of parking garages. Typical double-tee lengths are 60 to 75 feet; however, for this research 20 ft long segments were cast and tested with the shooter installed.

This project had three main goals. The first goal was to develop a preliminary design for the reinforcement around the shooter and test the shootersâ capacity in the laboratory to determine if the stated capacity was correct. Four different designs were created, two designs for the 40 kip capacity shooter and 2 designs for the 50 kip capacity shooter. Each design was placed in one stem of the double-tee and tested at the laboratory. Results from these tests indicate that that each specimen achieved the stated capacity. However, failure was not a connection failure but a shear bond failure.

The second goal was to take the information gathered from testing and develop a design model that could be used for other situations for this type of connection. The design model was created according to the guidelines in the ACI 318-08 code. Two different methods were used, a strut-and-tie model and a modified ACI code approach. From these designs it was determined that the strut-and-tie model should be used for the design of these connections; however, more research needs to be done before using the modified ACI code approach.

The final goal was to determine if finite element analysis could be used to determine if the load at which large cracks that immediately proceed failure occur could be predicted. From this analysis it was determined that a load range could be predicted in which a crack could form as well as a range of what the transfer length of the strands could be.
Master of Science

PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO
CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICO
O projeto de estruturas de concreto armado com a presença de descontinuidades geométricas ou estáticas utilizando o conceito dos modelos de bielas e tirantes tem aumentado muito sua aplicabilidade nos últimos anos. As orientações normativas existentes para esse tipo de projeto parecem, entretanto, ser insuficientes e muitas vezes conservadoras. O presente trabalho tem como objetivo apresentar uma metodologia que englobe os aspectos de geração automática da topologia via otimização topológica e avaliação da segurança via análise de confiabilidade dos modelos de bielas e tirantes aplicados a estruturas planas de concreto armado. O primeiro aspecto visa auxiliar o projetista estrutural na concepção do modelo topológico com a utilização de técnicas de otimização topológica que facilitem a visualização do fluxo de forças no interior da estrutura auxiliando na concepção de uma topologia ótima para o modelo. O segundo aspecto consiste na proposição de um critério de desempenho para modelos com base na avaliação de sua segurança via análise de confiabilidade. Os resultados obtidos e apresentados através dos exemplos desse trabalho permitem concluir que a técnica proposta conduz a uma melhora substancial na concepção e automatização dos modelos topológicos para os modelos de bielas e tirantes, bem como, o critério de avaliação de segurança proposto permite ao projetista estrutural considerar aspectos relacionados à obtenção da probabilidade de falha e mensuração dos modos de falha da estrutura.
The design of reinforced concrete structures with the presence of geometric or statics discontinuities using the concept of strut and tie models has greatly increased its applicability in recent years. The existing Standards and Guidelines for this kind of project seem, however, be insufficient and often conservative. This thesis aims are to present a methodology that includes aspects of automatic generation of topology by topological optimization and assessment of safety by the reliability analysis of the strut and tie models applied to plane reinforced concrete structures. The first aspect is to assist the structural designer in the conception of the structural topological model with the use of topological optimization techniques that facilitate the visualization of the flow forces in the structure, assisting in the design of an optimal topology for the model. The second aspect is the proposal of a performance criterion for models based on the assessment of its security by reliability analysis. The results obtained and submitted through the examples of this work allow to conclude that the proposed technique leads to a substantial improvement in the design and conception and automatic generation of topological models for the strut and tie models, as well as the security evaluation criterion proposed allows the structural designer to consider issues related to obtaining the probability of failure and measurement of failure modes of the structure.

When we speak about “travi reticolari miste“ we refer to a composite steel-concrete beam made up of a steel truss encased in cast in place concrete. The steel structure is typically composed of a plate or straight bars at the bottom, straight bars at the top and diagonal web bars: all these elements are connected with welded joints in a typical pyramidal shape. These beams have a particular feature: they can bear their own weight and the weight of the slabs without any provisional support during the “first phase” and then they can collaborate with the cast in place concrete during the “second phase”. The Italian Code - DM 14.01.2008 and Circolare 02.02.2009 n° 617/C.S.LL.PP – deals with this kind of structures in §4.6 “Other materials costructions” and then in “Linee guida per l’utilizzo di travi tralicciate in acciaio conglobate nel getto di calcestruzzo collaborante e procedure per il rilascio dell’autorizzazione all’impiego” (Sept 2011): composite beams are classified in three groups (A – B – C) depending on their features and for each group suitable norms are prescribed. In particular, for “A” beams we can refer to §4.3 of DM 2008 or to Ec4, for “B” beams we can refer to §4.1 of DM 2008 or to Ec2 while “C” beams require the authorization of Italian Superior Council of Public Works. Welded joints are very important in encased composite steel-concrete structures: the beam behavior depends on forces and stresses that pass through these joints and weldings must have specific geometrical characteristics and dimensions in order to provide an established strength and ductility. However welding process isn’t so easy because of elements geometry: in fact joints connect rounded surfaces, weldings can’t have the exact designed features and this problem represents the weak point of these beams. “TRR Ponte” was studied in order to realize a different type of encased composite beam in wich weldings could be achieved in a more precise way: in TRR Ponte top and web bars are not directly connected but they are jointed through a steel rectangular gusset plate that becomes a plane surface on which welding process is easier and faster. Furthermore bars are welded to the rectangular plates through corner joints that have precise geometrical characteristics and dimensions: in this way weldings can really provide the required strength and ductility. At the same time connection plates reduce the buckling lengths of compressed elements, that are diagonal and top bars: if slenderness is reduced, the design buckling resistance is higher and so the steel beam is more stable during the first phase, when concrete isn’t casted yet. Then there is another very important aspect: in TRR Ponte beams web bars can be put together and welded to the straight bars trough the connection plates working on a plane and then all the beam can be composed. In this way every step of the productive process is more efficient and functional. TRR Ponte is made up of S355 steel type elements, so it can be considered an “A” beam following Italian Code and “Linee Guida”: this means that it should be designed as a steel truss beam to calculate its shear resistance. However, even if during the first phase there are only steel elements, in the second phase a composite beam is made up also of concrete and the struts that develop could influence and improve the shear behavior of the element. At the same time, we can’t use reinforced concrete algorithms because they are based on adherence between concrete and steel elements: in “A” composite beams we don’t use roughened steel bar so the bond stress capacity is very low and we need specific models to correctly evaluate composite beams shear resistance. In this research a new shear design model is developed and it is based on the “Strut-and-Tie method” and on the equilibrium equations applied to composite truss nodes. Experimental tests have shown the development of concrete struts between the rigid joints of the steel truss and so the formation of a composite truss as presumed in the Strut-and-Tie model adopted was confirmed. Also the TRR Ponte failure mechanism was exactly predicted by the design analytical algorithm even if failure beams loads were higher than expected. TRR Ponte shear behavior has been studied also by FEM numerical analysis: the simplified FEM model proposed allow to know the failure mechanism in a fast way and give a collapse load very close to the experimental one. The fatigue behavior of TRR Ponte could be another important aspect to analyze: joint connections and beam fatigue experimental tests could show new possible applications of TRR Ponte, for example integral bridges. In this type of structures, bearings and expansion joints are eliminated so that the sub-structure (piers and abutments) and the super-structure (deck slub) are made monolithic: composite beams could be used to realize the deck slab because during the first phase they could be connected to the abutments and then in the second phase casting concrete would integrate the structure.
Con “travi reticolari miste” si indica una particolare tipologia di travi costituite da una reticolare in acciaio inglobata in un getto di calcestruzzo completato in opera. Il traliccio è costituito da un insieme di elementi saldati in stabilimento tra i quali si può individuare un corrente superiore formato generalmente da barre, un corrente inferiore formato da barre o da un piatto, elementi diagonali in barre disposte in modo da dare alla trave la classica forma piramidale e che possono essere organizzate, ove necessario, in più pareti. Il funzionamento di questo tipo di travi avviene per fasi: Il funzionamento di questo tipo di travi avviene quindi per fasi: durante la prima fase la trave è a tutti gli effetti una reticolare in acciaio che viene posta in opera e sulla quale vengono appoggiati i solai ed è pertanto progettata, oltre che per il peso proprio, per i carichi permanenti strutturali, mentre invece durante la seconda fase avviene il getto integrativo di calcestruzzo che, una volta maturato, permetterà alla trave di portare i carichi permanenti non strutturali e accidentali. Nel DM 14.01.2008 e Circolare 02.02.2009 n° 617/C.S.LL.PP si parla travi tralicciate in acciaio conglobate nel getto di calcestruzzo collaborante al paragrafo §4.6 “Costruzioni di altri materiali” e poi nelle “Linee guida per l’utilizzo di travi tralicciate in acciaio conglobate nel getto di calcestruzzo collaborante e procedure per il rilascio dell’autorizzazione all’impiego” (Settembre 2011): le travi reticolari miste vengono classificate in tre categorie (A – B – C) in base alle loro caratteristiche e si indica di far riferimento al §4.3 del DM 2008 o all’Ec4 (strutture composte) per le travi “A”, al §4.1 del DM 2008 o all’ Ec2 (strutture in calcestruzzo armato) per le travi “B” mentre per le travi “C” è richiesta una specifica autorizzazione da parte del Consiglio Superiore dei Lavori Pubblici. Le connessioni saldate della reticolare in acciaio giocano un ruolo fondamentale per il funzionamento della trave reticolare mista: il trasferimento delle tensioni avviene attraverso i nodi del traliccio e quindi le saldature che li costituiscono devono avere precise caratteristiche in modo da garantire determinate risposte in termini di resistenza e duttilità. Tuttavia nelle travi reticolari miste le saldature vanno a collegare delle superfici curve in quanto i correnti e le anime di parete hanno sezione circolare e pertanto il cordone che si va a realizzare non ha caratteristiche geometriche precise. La “TRR Ponte” nasce proprio dall’idea di realizzare una trave reticolare mista nella quale le saldature possano essere realizzate in modo diverso: in essa infatti gli elementi del traliccio vengono collegati mediante un fazzoletto metallico che diventa una superficie piana sulla quale è possibile eseguire a tutti gli effetti dei cordoni d’angolo con caratteristiche precise e misurabili. Non solo, il processo di saldatura risulta più veloce e agevole per l’operatore e, inoltre, il fazzoletto riduce la lunghezza libera di inflessione degli elementi compressi diagonali e del corrente superiore aumentando il carico critico che porta all’instabilità la trave e quindi ne migliora il comportamento in prima fase. Infine, gli elementi diagonali possono essere posizionati e saldati ai fazzoletti sul piano di lavoro e successivamente, una volta realizzate tutte le pareti, si può procedere con l’assemblaggio dell’intera trave, con una notevole razionalizzazione del processo produttivo. La trave TRR Ponte è realizzata in acciaio da carpenteria e quindi, da normativa, dovrebbe essere dimensionata a taglio come una trave di categoria “A”, ovvero considerando il solo traliccio in acciaio. Tuttavia appare restrittivo trascurare completamente la presenza del getto di seconda fase in quanto la formazione di bielle di calcestruzzo potrebbe influire sul comportamento ultimo della trave e sulle modalità di collasso. Allo stesso tempo però l’applicazione degli algoritmi del cemento armato non sembra essere opportuna in quanto essi si basano sull’aderenza tra calcestruzzo e acciaio quale meccanismo di trasferimento delle tensioni: nelle travi di categoria “A” si utilizza acciaio da carpenteria e comunque si ritiene che il funzionamento generale di una trave reticolare mista si basi soprattutto sulla trasmissione degli sforzi attraverso i nodi saldati del traliccio. Per questi motivi si è proposto un diverso modello analitico per lo studio del comportamento a taglio di queste travi: esso si basa sul metodo “Strut-and Tie”, ovvero sull’ipotesi della formazione all’interno della trave di un traliccio iperstatico composto dalla reticolare in acciaio e dalle bielle compresse in calcestruzzo del getto collaborante, e ad esso sono state applicate le equazioni di equilibrio ai nodi per la valutazione delle azioni interne. I test sperimentali condotti hanno dimostrato la formazione delle bielle di calcestruzzo all’interno della reticolare in acciaio e quindi hanno confermato l’ipotesi di traliccio iperstatico composto formulata con il metodo “Strut-and-Tie”. Inoltre le travi TRR Ponte sono arrivate al rottura secondo le modalità previste in fase di dimensionamento anche se per carichi superiori rispetto a quelli di progetto. Il comportamento a taglio delle travi TRR Ponte è stato studiato anche attraverso analisi numerica: in particolare, si è sviluppato un modello FEM semplificato che, a fronte di un ridotto onere computazionale, si è dimostrato efficace nel descrivere i meccanismi di collasso e stimare dei carichi a rottura prossimi a quelli ottenuti dalle prove sperimentali. Un altro importante aspetto da analizzare potrebbe essere il comportamento a fatica della trave TRR Ponte: test sulle connessioni e sull’intero elemento potrebbero portare a nuovi campi di applicazione della trave TRR Ponte come ad esempio i ponti integrali. In questa tipologia di ponti i dispositivi di appoggio e i giunti di dilatazione vengono eliminati e la sovrastruttura (impalcato) viene resa solidale con la sottostruttura (pile e spalle): dato il loro funzionamento per fasi, le travi reticolari miste potrebbero essere utilizzate per la realizzazione dell’impalcato e dei collegamenti con le altre parti strutturali del ponte.

O modelo de bielas e tirantes apresenta como uma de suas vantagens a generalidade, ou seja, é capaz de representar, de modo aproximado, porém realista e sistemático, grande parte dos elementos de concreto estrutural da atualidade. Além disso, permite ao engenheiro fácil visualização físico-intuitiva do comportamento do concreto estrutural. Por outro lado, o modelo ainda tem um enorme potencial não aproveitado. Ainda não se tem um critério exato para determinação dos nós e das seções transversais das bielas de alguns elementos. Apesar de haver certas incertezas no caso de vigas-parede e principalmente de blocos de fundação, nas vigas esses elementos do modelo podem ser determinados sem grandes dificuldades. Possivelmente, a solução seria variar as dimensões das bielas e as posições dos nós, ambas hipotéticas, a fim de confrontar várias situações com resultados experimentais. Daí a grande importância da difusão do modelo de bielas e tirantes: um maior número de análises de modelagens e de resultados de ensaios levará a um maior domínio sobre o modelo. Este trabalho consiste na análise de vigas de concreto armado utilizando modelos de bielas e tirantes. São apresentados os conceitos que levaram à concepção do modelo, desde a Analogia Clássica da Treliça, chegando aos critérios para verificação dos elementos da treliça e às recomendações atuais de normas e pesquisadores. Com o auxílio do programa computacional CAST (2000), foram modeladas quatro vigas, sendo as três primeiras biapoiadas sem descontinuidades e a quarta com balanço e descontinuidade geométrica (abertura na alma). A primeira viga biapoiada teve algumas de suas características iniciais alteradas a fim de gerar o segundo e o terceiro modelos, procurando-se estabelecer limites de carregamentos e análises comparativas. Os resultados das modelagens permitiram comparações com os resultados das verificações realizadas segundo os critérios da NBR 6118:2003 e do MC CEB-FIP (1990) e, permitiram também, identificar os aspectos de maior dificuldade na concepção de um modelo de bielas e tirantes e os pontos críticos dos mesmos, nos quais há maior possibilidade de falha nas verificações
One of the main advantages presented by the strut-and-tie model is generality. This model is able to approximately represent, in a realistic and systematic way, the majority of today’s reinforced concrete elements. Furthermore, it allows the physics-intuitive visualization of the behavior presented by structural concrete. On the other hand, its potentials are not fully explored yet. Up to date, there is no accurate criterion for the determination of nodes and transverse sections of some strut elements. Despite presenting some uncertainties related to the determination of wall-beams (and mainly of foundation blocks), the model can determine beams without major difficulties. Probably, the key is to vary the dimensions of the struts and the positions of the nodes, both hypothetical, in order to confront various situations with experimental data. Hence, it is very important to diffuse the strut-and-tie model: the bigger the number of modeling analysis and experimental data, the better the comprehension of the model. This work aims to analyze reinforced concrete beams employing the strut-and-tie model. Here are presented the concepts that led to the development of the model, ranging from the Truss Classic Analogy to the criteria employed to verify truss elements and the recommendations from researchers and established standards (rules or norms). Four examples of beams were modeled. Three of them were double-based and the fourth presented balance and no geometric discontinuity (with an opening). Some of the characteristics of the first double-based beam were altered in order to generate the second and the third model, thus establishing loading limits and comparative analysis. The modeling allowed comparisons between the verifications performed in accordance with the NBR 6118:2003 and MC CEB-FIP criteria. It also allowed the identification of major difficulties and critical aspects related to the development of struts and ties, the ones that are most prone to failure in the verification process

The doctoral thesis deals with the analysis of the dapped-end beam detail, in terms of theoretical modelling and practical design using the strut-and-tie method as well as experimental verification of the bearing capacity and the behaviour of the detail under load by means of load tests and subsequent numerical nonlinear analysis. A summary of known structural and static designs explored in the literature has been presented. In addition, the strut-and-tie method has been introduced as an appropriate tool for a consistent design of the detail, element or the whole structure. The theoretical basis for the method has been described, including the general methodology for design and analysis. Practical problems have been discussed, specifically those resulting from the known design of the analysed detail based on the German approach; its modification has been processed theoretically taking into account the practical mode of reinforcement. An experiment has been suggested with a view to verify the presented calculation procedure and the influence of the used ratio of vertical to inclined hanger reinforcement on the bearing capacity and behaviour of the detail under load. The experiment also included accompanying material tests of the concrete which were used along with the inspection certificates issued for the used reinforcement as a basis for the nonlinear finite element analysis. Based on the results, the presented design procedure can be considered safe. These results also imply that the chosen ratio of vertical and inclined hanger reinforcements has no influence on the ultimate bearing capacity within practical reinforcement, as it only influences the formation, development and final width of cracks. With the growing ratio of the inclined hanger reinforcement, the width and density of cracks decreases at all stages of loading. Owing to their limitations, primarily during the service state, it is recommended that the minimal inclined reinforcement should be used.

Abstract : Deep reinforced concrete beams are commonly used as transfer girders or bridge bents, at which its safety is often crucial for the stability of the whole structure. Such elements are exposed to the aggressive environment in northern climates causing steel-corrosion problems due to the excessive use of de-icing salts. Fiber-reinforced polymers (FRP) emerged as non-corroded reinforcing materials to overcome such problems in RC elements. The present study aims to address the applicability of concrete deep beams totally reinforced with FRP bars. Ten full-scale deep beams with dimensions of 1200 × 300 × 5000 mm were constructed and tested to failure under two-point loading. Test variables were shear-span depth ratio (equal to 1.47, 1.13, and 0.83) and different configurations of web reinforcement (including vertical and/or horizontal web reinforcement). Failure of all specimens was preceded by crushing in the concrete diagonal strut, which is the typical failure of deep beams. The test results indicated that, all web reinforcement configurations employed in the tested specimens yielded insignificant effects on the ultimate strength. However, strength of specimens containing horizontal-only web reinforcement were unexpectedly lower than that of specimens without web reinforcement. The web reinforcement’s main contribution was significant crack-width control. The tested specimens exhibited reasonable deflection levels compared to the available steel-reinforced deep beams in the literature. The development of arch action was confirmed through the nearly uniform strain distribution along the length of the longitudinal reinforcement in all specimens. Additionally, the basic assumption of the strut-and-tie model (STM) was adequately used to predict the strain distribution along the longitudinal reinforcement, confirming the applicability of the STM for FRP-reinforced deep beams. Hence, a STM based model was proposed to predict the strength of FRP-reinforced deep beams using the experimental data, in addition to the available experimentally tested FRP-reinforced deep beams in the literature. Assessment of the available STMs in code provisions was conducted identifying the important parameters affecting the strut efficiency factor. The tendency of each parameter (concrete compressive strength, shear span-depth ratio, and strain in longitudinal reinforcement) was individually evaluated against the efficiency factor. Strain energy based calculations were performed to identify the appropriate truss model for detailing FRP-reinforced deep beams, hence, only four specimens with vertical web reinforcement exhibited the formation of two-panel truss model. The proposed model was capable to predict the ultimate capacity of the tested deep beams. The model was also verified against a compilation of a data-base of 172 steel-reinforced deep beams resulting in acceptable level of adequacy. The ultimate capacity and performance of the tested deep beams were also adequately predicted employing a 2D finite element program (VecTor2), which provide a powerful tool to predict the behavior of FRP-reinforced deep beams. The nonlinear finite element analysis was used to confirm some hypotheses associated with the experimental investigations.
Résumé : Les poutres profondes en béton armé (BA) sont couramment utilisées comme poutre de transfert ou coude de pont, comme quoi sa sécurité est souvent cruciale pour la sécurité de l’ensemble de la structure. Ces éléments sont exposés à un environnement agressif dans les climats nordiques causant des problèmes de corrosion de l’acier en raison de l’utilisation excessive de sels de déglaçage. Les polymères renforcés de fibres (PRF) sont apparus comme des matériaux de renforcement non corrodant pour surmonter ces problèmes dans les BA. La présente étude vise à examiner la question de l'applicabilité des poutres profondes en béton complètement renforcées de barres en PRF. Dix poutres profondes à grande échelle avec des dimensions de 1200 × 300 × 5000 mm ont été construites et testées jusqu’à la rupture sous chargement en deux points. Les variables testées comprenaient différents ratios de cisaillement porté/profondeur (égal à 1.47, 1.13 et 0.83) ainsi que différentes configurations d’armature dans l’âme (incluant un renforcement vertical avec ou sans renforcement horizontal). La rupture de tous les spécimens a été précédée par l’écrasement du béton dans le mât diagonal, ce qui est la rupture typique pour les poutres profondes en BA. Les résultats ont révélé que toutes les configurations de renforcement de l’âme employées dans les spécimens d'essais avaient un effet négligeable sur la résistance ultime. Toutefois, la résistance des spécimens contenant uniquement un renforcement horizontal était étonnamment inférieure à celle des spécimens sans renforcement. La contribution principale du renforcement de l’âme était dans le contrôle de la largeur de fissuration. Les spécimens examinés présentaient une déflexion raisonnable par rapport à ce qui est disponible pour les poutres profondes renforcées en acier dans la littérature. Le développement de l'effet d'arche a été confirmé par la distribution quasi uniforme des déformations le long du renforcement longitudinal dans tous les spécimens. En outre, l'hypothèse de base du modèle des bielles et tirants (MBT) a été utilisée adéquatement pour prédire la distribution de déformation le long du renforcement longitudinal, confirmant l'applicabilité du MBT pour les poutres profondes armées de PRF. Par conséquent, un modèle basé sur un MBT a été proposé afin de prédire la résistance des poutres profondes renforcées de PRF en utilisant les données expérimentales en plus de la mise à l'épreuve expérimentalement des poutres profondes renforcées de PRF trouvées dans la littérature. Une évaluation des MTB disponibles dans les dispositions des codes a été menée afin de déterminer les paramètres importants affectant le facteur d'efficacité de la bielle. La tendance de chaque paramètre (la résistance à la compression du béton, le ratio de cisaillement porté/profondeur, et la déformation dans le renforcement longitudinal) a été évaluée individuellement contre le facteur d'efficacité. Des calculs basés sur l’énergie des déformations ont été effectués pour identifier le modèle de treillis approprié afin de détailler les poutres profondes renforcées de PRF. Par conséquent, seulement quatre spécimens avec un renforcement vertical dans l’âme présentaient la formation de modèles avec deux panneaux de treillis. Le modèle proposé a été capable de prédire la capacité ultime des poutres profondes testées. Le modèle a également été vérifié contre une base de données de 172 poutres profondes renforcées en acier aboutissant en un niveau acceptable de pertinence. La capacité ultime et la performance des poutres profondes testées ont été également adéquatement prédites employant un programme d'éléments finis en 2D (VecTor2), ce qui fournira un puissant outil pour prédire le comportement des poutres profondes renforcées de PRF. L'analyse non linéaire par éléments finis a été utilisée afin de confirmer certaines hypothèses associées à l'étude expérimentale.

This work deals with the structural solution of reinforced concrete floor slab, deep beam and its support of multipurpose building. The structure is designed and assessed in according to valid standards. The continuous one-way slab is analyzed by Finite Element Method, deep beam is solved by Strut-and-Tie model.

Este trabalho estuda o comportamento estrutural de blocos sobre estacas em concreto armado situados em divisas de terrenos. Foi feita revisão bibliográfica abordando os assuntos de blocos de coroamento, vigas de equilíbrio, modelo de bielas e tirantes e um breve comentário sobre o programa computacional Diana (2010). O trabalho apresenta um roteiro para análise estrutural e dimensionamento de vigas de equilíbrio sobre estacas com pilar excêntrico ao apoio. É apresentado um exemplo feito por Andrade (1989), comparado com o método proposto por Burke (1979) e com análise numérica. Além deste, foram analisados casos de projetos reais utilizando o método Burke (1979) adaptado neste trabalho. Alguns desses exemplos foram modelados em regime elástico e linear no programa computacional Diana (2010). São apresentadas comparações de resultados obtidos com o método Burke (1979) e análise numérica, comprovando a eficácia desse método. Em todos os exemplos estudados o método proposto por Burke (1979) indicou bons resultados quando comparados com os encontrados em análise computacional. A dissertação apresenta soluções para projetos de bloco sobre estacas, situados em divisas de terrenos e associados a vigas de equilíbrio.
This research investigates the structural behavior of reinforced concrete blocks piles located on the limit of land. Literature review was done about blocks piles, balance beams, strut and tie model and a short comment about the Diana computer program (2010). The dissertation presents a roadmap for structural analysis and sizing of balance beams on stakes with eccentric support pillar. An example, which was studied by Andrade (1989), is compared with the same example done using the method proposed by Burke (1979) and with numerical analysis. In addition to this, are analyzed real cases of projects using the method of Burke (1979). Some of these examples were modeled in linear and elastic characteristics using Diana program computer (2010). Here, it is presented comparisons between the method proposed by Burke (1979) and numerical analysis. It is presented comparisons between the method Burke (1979) and numerical analysis, proving the effectiveness of this method. In all examples studied the method proposed by Burke (1979) provided with good accuracy the results for computer analysis. The conclusion presents suggestions for projects of block piles located in limit of land associated with balance beams.

The present research is conducted to investigate the structural behaviour of continuously supported deep beams made with SCC. A series of tests on eight reinforced two-span continuous deep beams made with SCC was performed. The main parameters investigated were the shear span-to-depth ratio, the amount and configuration of web reinforcement and the main longitudinal reinforcement ratio. All beams failed due to a major diagonal crack formed between the applied mid-span load and the intermediate support separating the beam into two blocks: the first one rotated around the end support leaving the rest of the beam fixed on the other two supports. The amount and configuration of web reinforcement had a major effect in controlling the shear capacity of SCC continuous deep beams. The shear provisions of the ACI 318M-11 reasonably predicted the load capacity of SCC continuous deep beams. The strut-and-tie model recommended by different design codes showed conservative results for all SCC continuous deep beams. The ACI Building Code (ACI 318M-11) predictions were more accurate than those of the EC2 and Canadian Code (CSA23.3-04). The proposed effectiveness factor equations for the strut-and-tie model showed accurate predictions compared to the experimental results. The different equations of the effectiveness factor used in upper-bound analysis can reasonably be applied to the prediction of the load capacity of continuously supported SCC deep beams although they were proposed for normal concrete (NC). The proposed three dimensional FE model accurately predicted the failure modes, the load capacity and the load-deflection response of the beams tested.

Submitted by Cláudia Bueno (claudiamoura18@gmail.com) on 2016-01-29T14:45:57Z No. of bitstreams: 2 Dissertação - Flávio Augusto Xavier Carneiro Pinho - 2015.pdf: 5478560 bytes, checksum: 3507be4593cbd586348d2f5a2bfe2f9f (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5)
Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2016-02-01T11:53:05Z (GMT) No. of bitstreams: 2 Dissertação - Flávio Augusto Xavier Carneiro Pinho - 2015.pdf: 5478560 bytes, checksum: 3507be4593cbd586348d2f5a2bfe2f9f (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5)
Made available in DSpace on 2016-02-01T11:53:05Z (GMT). No. of bitstreams: 2 Dissertação - Flávio Augusto Xavier Carneiro Pinho - 2015.pdf: 5478560 bytes, checksum: 3507be4593cbd586348d2f5a2bfe2f9f (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) Previous issue date: 2015-04-10
Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES
Optimization techniques have been widely used in different engineering applications. In the case of structural conception, these techniques can be applied from the architectural concept, determining, for example, bracing structures to setting the best topology for concrete structures, as those compared to strut and tie models. In this context, this thesis presents techniques applied to topology optimization in subsystems of buildings. It is also presented a new software tool, modelled in object-oriented programming, seeking the solution for topology optimization problems assembling various technical problems unified in a single approach. The software tool was used to determine the best shape to bracing frames on a building submited to different loading combinations as well to compare the strut and tie models to foundation blocks. Results were compared to literature review, validating the unified computational procedure. Strut and tie models found in literature were compared to piled foundation blocks varying the number of piles, and whose geometry for larger number of piles are still not clearly defined.
Técnicas de otimização têm sido especialmente utilizadas em diversos problemas de engenharia. No caso da concepção estrutural de grandes edifícios, essas técnicas podem ser utilizadas desde o partido arquitetônico. Neste caso, podem ser determinadas, por exemplo, estruturas de contraventamento. Outro exemplo é a aplicação da otimização de topologia para determinação do modelo de bielas e tirantes de estruturas de concreto armado. Neste trabalho, são utilizadas técnicas de otimização de topologia aplicadas em subsistemas de edifícios. Apresenta-se um software em linguagem de programação orientada a objeto para a solução de problemas de otimização de topologia em que são reunidas diferentes técnicas características do problema as quais são unificadas em uma única abordagem. Esse software é aplicado para determinar a melhor forma da estrutura de contraventamento de edifícios altos submetidos a diversas combinações de carregamentos e para determinação do modelo de bielas e tirantes de blocos de fundações. Os resultados encontrados validam a utilização da uma abordagem unificada já que são condizentes com a literatura. Os modelos de bielas e tirantes encontrados para os blocos de fundações são iguais aos modelos clássicos encontrados na literatura. Também foram estudados blocos de fundações com uma maior quantidade de estacas cujos modelos ainda não possuem geometria bem definida na literatura.

This work deals with the structural solution of selected parts of load bearing structure of apartment house - floor slabs of 1.PP and 2.NP, deep beam and its supporting column. The analysis is made by Finite Element Method, deep beam is solved by Strut-and-Tie model. The elements are designed and assessed according to valid standards.

O projeto estrutural deve considerar as incertezas provenientes das variáveis envolvidas no dimensionamento dos elementos estruturais, tais como propriedades dos materiais, dimensões dos elementos estruturais e intensidade dos carregamentos atuantes. Existe também a variabilidade inerente aos métodos de análise estrutural, originária de imprecisões na idealização da distribuição das tensões e deformações dos elementos estruturais. Sendo assim, esta dissertação visa analisar a variabilidade dos desvios dos modelos de cálculo propostos por Blevot e Frémy (1967), Fusco (1994) e Santos (2013), todos baseados no método das bielas e tirantes, para blocos sobre duas, três e quatro estacas submetidos a carregamento centrado. Estes elementos estruturais possuem significativa importância, visto que atuam na transmissão dos esforços provenientes dos pilares às fundações profundas. Os modelos de cálculo foram confrontados entre si e com resultados experimentais de Blevot e Frémy (1967), Mautoni (1971), Clarke (1973), Miguel (2000) e Suzuki et al. (1998 / 1999 / 2000 / 2001) para determinação dos parâmetros estatísticos dos desvios desses modelos em relação aos ensaios. Os resultados apontaram desempenho satisfatório para os três modelos de cálculo. Em geral, todos os métodos se mostraram favoráveis à segurança nos casos avaliados para os três tipos de blocos de fundação.
Structural design must consider the uncertainties coming from the variables involved in dimensioning of the structural elements, such as material properties, dimensions of structural elements, and intensity of active loads. There is also inherent variability in structural analysis methods, originated from imprecision in idealization of the distribution of tensions and deformations of structural elements. Thus, this dissertation aims to analyze the variability of calculation models deviations proposed by Blevot and Frémy (1967), Fusco (1994) and Santos (2013), all based on strut and tie method, for two, three and four pile caps submitted to center load. These structural elements are of significant importance, since they act in transmission of loads from columns to deep foundations. Calculation models were compared with each other and with experimental results from Blevot and Frémy (1967), Mautoni (1971), Clarke (1973), Miguel (2000) and Suzuki et al. (1998 / 1999 / 2000 / 2001) to determine the statistical parameters of these model deviations in relation to the tests. Results indicated satisfactory performance for the three calculation models. In general, all methods were favorable to safety in cases evaluated for the three pile caps types.

Esta pesquisa estuda o comportamento de blocos de concreto armado sobre duas estacas com cálice totalmente embutido, utilizado na ligação pilar-fundação de estruturas de concreto pré-moldado. Particularmente, foi avaliado o efeito que a viga de travamento provoca no bloco quando apoiada nas paredes laterais do cálice. Foi desenvolvida análise numérica tridimensional utilizando programa baseado no método dos elementos finitos (MEF), na qual foi considerada a não-linearidade física dos materiais. Para avaliação do programa adotado, realizou-se análise comparativa de resultados experimentais e numéricos obtidos por meio de outro programa. Nos blocos estudados variou-se a espessura e o tipo de conformação das paredes do cálice, o ângulo de inclinação da biela e a intensidade das ações na viga de travamento. Os resultados indicam que a presença da viga de travamento não altera de modo significativo o comportamento do bloco, e que a parede do cálice é capaz de transferir a força proveniente da viga em direção às estacas de modo eficaz. Por meio das tensões nas barras da armadura principal, foi possível obter a força no tirante e o ângulo de inclinação da biela antes da ruína dos modelos. Constatou-se que os ângulos apresentaram maior inclinação do que as utilizadas no dimensionamento, que por sua vez foi feito baseado nos modelos de bielas e tirantes.
The present research studies the behavior of two pile caps reinforced concrete with embedded socked used in connections of pre-cast concrete structures. It was particularly evaluated the effect provoked by the locking beam on the pile-caps when supported by the socket lateral walls. Three-dimensional numerical analyses using software based on finite element method (FEM) were developed considering the nonlinear physical behavior of the material. To evaluate the adopted software, a comparative analysis was made using numerical and experimental results obtained from other software. In the pile caps studied, it was noticed a variation in the wall thickness, socket interface, strut angle inclination and action on beam. The results show that the presence of beam does not change significantly the pile caps behavior and that the socket wall is able to transfer effectively the force from the beam to the pile caps. By the tensions on the bars of longitudinal reinforcement, it was possible to obtain the force on the tie and the strut angle inclination before the collapse of models. It was found that the angles present more inclinations than those used in the design, which was made based on strut and tie model.

Made available in DSpace on 2015-03-26T13:28:03Z (GMT). No. of bitstreams: 1 texto completo.pdf: 2387307 bytes, checksum: f11d179178c73973dbcc9eaba047425e (MD5) Previous issue date: 2011-07-04
Coordenação de Aperfeiçoamento de Pessoal de Nível Superior
This work presents an evaluation of the structural behavior of steel plane frames infilled with structural masonry of blocks of autoclaved aerated concrete, regarding the contribution of the masonry to the structure global stiffening, through the strut-and-tie model. Case studies were evaluated taking into account three steel plane frames and, subsequently, the model was applied to the project of steel buildings with four, six, and eight stories. First and second-order numerical analyses (nonlinear geometrical analysis) were performed to braced steel frames with bracing elements formed for bars of steel and masonry panels. The masonry panels were considered across strut-and-tie model. It is presented comparisons of the lateral displacements and the solicitant forces in the bars of strut-and-tie model to first and second-order analyses. The solicitant forces on the strut and tie were also compared to the structural resistance on these bars aiming to achieve the structural dimension of the masonry panel. Through the results obtained it is concluded that it is possible to substitute the bracing metal bars for the masonry panels until determined numbers of stories. This numbers depends on factors such as the stiffness of the frame and masonry panels, and the intensity applied.
Neste trabalho apresenta-se uma avaliação do comportamento estrutural de pórticos planos de aço preenchidos com alvenaria estrutural de blocos de concreto celular autoclavado, considerando a contribuição da alvenaria na rigidez global da estrutura, por meio de um modelo de bielas e tirantes. Para realização dos estudos de caso, foram avaliados três pórticos planos de aço e, posteriormente, o modelo foi aplicado ao projeto de edifícios de aço com quatro, seis e oito pavimentos. Foram realizadas análises numéricas de primeira e segunda ordem (análise não-linear geométrica) de pórticos de aço contraventados com elementos de contraventamentos formados por barras de aço e por painéis de alvenaria. Os painéis de alvenaria foram considerados por meio do modelo de bielas e tirantes. São apresentadas comparações dos deslocamentos laterais e dos esforços solicitantes nas barras do modelo de bielas e tirantes para as análises de primeira e de segunda ordem. Os esforços solicitantes nas bielas e nos tirantes também foram comparados com os esforços resistentes nessas barras, com vistas a efetuar o dimensionamento estrutural do painel de alvenaria. Os resultados obtidos permitem concluir que é possível substituir as barras de contraventamento metálico por painéis de alvenaria até um determinado número de pavimentos. Este número depende de fatores como a rigidez dos pórticos e dos painéis de alvenaria e a intensidade das ações aplicadas.

Detta examensarbete vid Luleå tekniska universitet har utförts i samarbete med avdelningen för byggkonstruktionvid det nordiska konsultföretaget Norconsult AB. Arbetet bygger på en önskan från Norconsultatt ta fram en beräkningsmodell för höga balkar i överensstämmelse med Eurokod 2 motsvarande densom finns i BBK 04. Eurokod 2 har endast en knapphändig beskrivning av hur höga balkar bör dimensioneras.Detta skapar frustration och osäkerhet hos konstruktörer. Den tidigare svenska betongnormen,BBK 04, innehöll en tydlig och enkel mer empirisk beräkningsmetod för höga balkar, vilket gav en störresäkerhet vid projekteringen. Arbetet begränsas till att studera enkelt upplagda och kontinuerliga balkar i två spann belastade med enpunktlast mitt i vartdera spannet. Geometrin är densamma för samtliga balkar och armeringsmängdenvarieras tillsammans med brottlasten. Initialt utfördes en litteraturstudie för att erhålla en fördjupad kunskap om området samt att bygga uppen förståelse för teorin för höga balkar och den fackverksmodell som används i Eurokod 2. Vidare presenterasen försöksrapport, Rogowsky et al. (1983), som redovisar en experimentell laboratoriestudie därhöga balkar belastas till brott. Resultaten som presenteras är brottlast, töjning i betong och armering,sprickmönster samt nedböjning. Fyra enkelt upplagda och fyra kontinuerliga balkar väljs ut för vidarejämförelse och analys. Härvid används det ickelinjära beräkningsprogrammet ATENA 2D, där studeradebalkar modelleras. Handberäkningar enligt EK2 och BBK 04 utförs för respektive balk och tillhörandearmeringsmängd beräknas. En maximal brottlast itereras fram för respektive balk och beräkningsmetod (EK2 eller BBK 04). Armeringsmängdensom ges av denna beräkning modelleras i ATENA 2D och motsvarande balk analyseras.Resultaten jämförs sedan. Erhållna resultat sammanställs och jämförs med varandra: Rogowsky et al. (1983), ATENA 2D och handberäkningarnaenligt både Eurokod 2 och BBK 04. Jämförelsen visar att det finns få likheter mellan EK2och BKK 04, med avseende på erhållen armeringsmängd. BBK kräver generellt större armeringsmängdän Eurokod 2. Studien visar att beräkningarna med ATENA 2D stämmer väl överens med laboratorieförsöken.Resultaten visar även att antaganden enligt Eurokod 2 stämmer väl överens med hur de studeradebalkarna beter sig i verkligheten. En enkel beräkningsmodell som motsvarar BBKs konservativa modell är inte möjlig att ta fram inom deramar och begränsningar som finns för detta examensarbete. Istället sammanställs en modell i form av enpunktlista som förtydligar, sammanfattar och exemplifierar den mer verklighetstrogna beräkningsgångenför höga balkar enligt Eurokod 2.

A racionalização e a industrialização da construção civil têm promovido o sistema construtivo baseado em elementos de concretos pré-moldados. O comportamento das ligações entre os elementos pré-moldados constitui uma das principais preocupações dos projetistas, sendo as ligações entre a superestrutura e as fundações determinantes na estabilidade e na distribuição de esforços solicitantes da estrutura. O comportamento de blocos sobre estacas com ligações para pilares pré-moldados possui particularidades em razão do diferente mecanismo de transferência de forças do pilar para o bloco mediante a ligação. Neste trabalho é estudado o comportamento de blocos de fundação apoiados sobre quatro estacas com cálice totalmente embutido para ligação com pilar pré-moldado. O estudo baseou-se em análise numérica não-linear de modelos tridimensionais considerando a fissuração do concreto, a presença de armadura e a interface de ligação. O comportamento de blocos com pilares submetidos à força vertical centrada e excêntrica foi descrito em termos de força última, panorama de fissuração, fluxo de tensões principais e tensões nas armaduras do bloco. Os resultados indicam a ocorrência de transferência de esforços do pilar para a fundação a partir das paredes do cálice de interface lisa, entretanto com intensidade insuficiente para a formação de bielas de compressão, e o risco da ocorrência de punção em blocos onde os pilares são ligados por cálices de paredes lisas.
The rationalization and the industrialization of the civil constructions have stimulated the construction process based on precast elements. One of the main designer\'s worries is about the behavior of the joints between precast elements, and the joints between superstructure and the foundations which are determinant in the construction stability and behavior of elements. In reason of the mechanism of transference of the forces from column to pile-cap by socket connections, the behavior of pile-caps with joints for precast columns has some specificity. The behavior of four-pile caps with embedded socket for precast columns joints is studied in this research. The study is based in nonlinear numerical analysis of three dimensional models considering the cracking in concrete, the reinforcement and the joint interface. The behavior of pile caps under centered and eccentric vertical force is described by ultimate force, cracking patterns, principal stresses flow and reinforcements strains. The results suggests that occurs the transfer of forces from column to the pile cap in the socket walls with smooth interface, however the intensity is not enough to form the struts, and the risk of development of punching shear in pile caps which columns are connected by smooth interface socket walls.

Esta pesquisa realiza a análise do comportamento estrutural de blocos rígidos de concreto armado sobre duas estacas submetidos à ação de força vertical centrada, com pilares de seções quadradas e retangulares e diferentes taxas de armaduras de pilares. Nestes elementos utilizam-se o método das Bielas e Tirantes para o projeto estrutural, mas normalmente não se considera a influência da seção geométrica dos pilares e suas taxas de armadura no projeto do bloco. Apresenta-se um estudo experimental de doze modelos de blocos sobre duas estacas, na escala 1:2. Foi desenvolvida uma análise numérica tridimensional e não linear, pelo método dos elementos finitos, com o auxílio de um programa de computador. Com a análise experimental e numérica foi investigada a distribuição do fluxo das tensões principais de compressão e tração nos modelos e constataram-se diferenças na transmissão de forças para os blocos quando se altera a taxa de armadura e a seção transversal dos pilares. Esta constatação modifica o modelo de Biela e Tirante inicialmente adotado. As deformações em armaduras construtivas complementares também foram estudadas possibilitando o entendimento do modelo estrutural. Um modelo de Bielas e Tirantes para blocos sobre estaca com pilares alongados foi proposto.
This research presents an analysis of the rigid two-pile caps structural behavior. The models were subjected to force action centered and supported columns with different rate of armor and square and rectangular cross sections. These elements can be rigid or flexible, rigid pile-caps can be sized using the Method of Strut and Tie. In most cases the Method of Strut and Tie and the influence of column reinforcement are not considered in the pile-cap´s structural projects. This research presents an experimental investigation of two-pile caps with the objective of improve criteria structural projects. Twelve rigid two-pile caps were builded using 1:2 scaled models. Three-dimensional numerical analyses using software based on element finite method (FEM) were developed considering the reinforced concrete nonlinear behavior. Using results of experimental analysis and numerical analysis an investigation of the flow distribution of the principal stresses of compression and tension in the models was performed, differences in the transmission of forces to the pile-caps, when changing the reinforcement ratio and the cross section of the columns, were detected. The initial model of strut and tie may be modified due to results. The understanding of the structural model was also possible by analysis of the stirrups and upper constructive reinforcement stress-strain behavior. A strut and tie model for pile-caps with an elongated rectangular column was proposed.

The topic of the diploma thesis is the design of monolithic concrete structure CERIT in Brno. There are designed three preliminary variants of the concrete structure for the problematic place in the building. Selected variant is developed in detail design (the concrete wall). The solution comprises statical analysis, text section and drawing documentation.

Submitted by Erika Demachki (erikademachki@gmail.com) on 2015-04-23T19:28:37Z No. of bitstreams: 2 Dissertação - Victor Mark Pontes dos Santos - 2014.pdf: 4740430 bytes, checksum: 86ddafe465639f636facb827295fa18a (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5)
Approved for entry into archive by Erika Demachki (erikademachki@gmail.com) on 2015-04-23T19:30:26Z (GMT) No. of bitstreams: 2 Dissertação - Victor Mark Pontes dos Santos - 2014.pdf: 4740430 bytes, checksum: 86ddafe465639f636facb827295fa18a (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5)
Made available in DSpace on 2015-04-23T19:30:26Z (GMT). No. of bitstreams: 2 Dissertação - Victor Mark Pontes dos Santos - 2014.pdf: 4740430 bytes, checksum: 86ddafe465639f636facb827295fa18a (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) Previous issue date: 2013-08-27
Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES
This work explores the use of reliability techniques for selecting strut and tie models and explores the use of topology optimization techniques to generate these models automatically. A literature review is presented exploring probability concepts useful in reliability analysis, concepts about classic approaches to generate strut and topology optimization. The formulation is based on concepts of the limit analysis thus they are the theoretical basis of the strut and tie model. Formulations used in reliability analysis are presented, such as the Monte Carlo simulation and the methods FOSM and FORM. These techniques are applied in nine numerical applications. The first two examples explore alternative techniques on the topology optimization field so as enable appropriate strut and tie results consistent with the project of concrete structures. The following examples are used to validate the tools used in the reliability analysis and in the limit analysis. Finally the four following examples apply reliability analysis with failure function based on limit analysis to compare classic models with those obtained by using topology optimization and analyze the security level of the models with respect to changes in concrete strength, reinforcement provided by the ties and thickness of the struts.
Este trabalho tem o objetivo de utilizar técnicas de confiabilidade para a seleção de modelos de bielas e tirantes e verificar a viabilidade da utilização de técnicas de otimização de topologia para geração automática desses modelos. Apresenta-se uma revisão bibliográfica com conceitos de probabilidade úteis na análise de confiabilidade, conceitos sobre modelos de bielas e tirantes e sobre a otimização de topologia. A metodologia do trabalho emprega formulações utilizadas na análise limite por ser a base teórica do modelo de bielas e tirantes. Apresentam-se também formulações utilizadas na análise de confiabilidade como a simulação de Monte Carlo e os métodos FOSM e FORM. Essas técnicas são utilizadas em nove exemplos de aplicação. As primeiras aplicações exploram variações nas técnicas de otimização de topologia que possibilitam resultados de modelos de bielas e tirantes mais adequados ao projeto de estruturas de concreto armado. As aplicações seguintes validam as ferramentas utilizadas na análise de confiabilidade e na análise limite. Por fim, nas últimas quatro aplicações, aplica-se a análise de confiabilidade com função de falha baseada na análise limite para comparar modelos clássicos e modelos obtidos com otimização de topologia e analisar o nível de segurança dos modelos em relação a algumas variáveis como resistência do concreto, área de aço e espessura de bielas.

Thesis (M.S.)--West Virginia University, 2002.
Title from document title page. Document formatted into pages; contains xi, 122 p. : ill., map. Includes abstract. Includes bibliographical references (p. 114-116).

For architectural reasons, in some structural building systems, the need to change the direction of columns from one floor to another arises. One of the adopted solutions in the transition zone is to use a block of reinforced concrete to assist the transfer of loads between the columns. This solution is proposed by analogy to the blocks used in the transition from the superstructure to the infrastructure of a building, commonly called the pile caps. In this context, this work aims to study a three-dimensional strut-and-tie model applied to the design of reinforced concrete blocks used in the transition between rotated columns, from the results of elastic analysis of stresses and numerically evaluate the failure modes, last resistance and service conditions of the designed block, considering the physical non-linearity of the materials with a model of plasticity. The three-dimensional model was proposed linking plane models defined previously in studies of the author. It was found that the difference of the stresses between the proposed model and the plane model are not significant, confirming thereby the use of the plane model. From the nonlinear analysis, it was found that the load capacity of the investigated element is significantly greater than the applied load, by influence of the tensile strength of the concrete. This means that as the tensile strength of the concrete in the strut and tie model is not considered, is neglected much of the load capacity of the element. Furthermore, it was observed that the configuration of ruin occurred by yielding of steel in the armor called "main". With the results of the study, it was sought to contribute to propose a better solution for the transition region between rotated columns.
Coordenação de Aperfeiçoamento de Pessoal de Nível Superior
Por motivos arquitetônicos, em alguns dos sistemas estruturais de edifícios surge a necessidade de modificar a direção de pilares de um pavimento para o outro. Uma das soluções adotadas na zona de transição de direção é a utilização de um bloco de concreto armado para auxiliar a transferência das cargas entre os pilares. Esta solução é proposta por analogia aos blocos utilizados na transição da superestrutura à infraestrutura de uma edificação, comumente chamado de blocos de fundação. Nesse contexto, o presente trabalho tem como objetivo estudar um modelo de bielas e tirantes tridimensional para o dimensionamento de blocos de concreto armado para transição entre pilares rotacionados, a partir dos resultados de análises elásticas de tensões, e avaliar numericamente os modos de falha, resistências últimas e condições de serviços do bloco dimensionado, considerando a não linearidade física dos materiais com um modelo de plasticidade. O modelo tridimensional proposto interliga modelos planos anteriormente definidos em estudos do autor. Verifica-se que a diferença entre os esforços do modelo proposto e o do modelo plano não são significativas, ratificando, com isso, a utilização do modelo plano. A partir das análises não lineares, verifica-se que a capacidade resistente do elemento estudado é significativamente maior que a solicitação aplicada, por influência da resistência à tração do concreto, ou seja, a não consideração da resistência à tração do concreto no modelo de bielas e tirantes despreza grande parte da capacidade resistente do elemento. Além disso, observa-se que a configuração de ruína ocorre pelo escoamento do aço na armadura chamada de "principal". Com os resultados do trabalho, busca-se contribuir com a proposição de uma solução mais adequada para a região de transição entre pilares rotacionados.

The diploma thesis deals with the strenghtening of the supporting parts of the production hall in Drásov. In the first part the existing load bearing capacity of the structure is solved. The next step is to design of strenghtening variants for nonconforming columns and short corbel. Columns and short corbel are strenghtening with monostrand. At the end of the thesis, verification of the load bearing capacity of the strenghtening structure is performed.

The major part of the work presented in this thesis is an investigation of the strut and tie method for designing 2-D in-plane, reinforced concrete structures. Two important issues relating to this method are addressed. Firstly, the issue of visualising an appropriate strut and tie model is dealt with. In many situations it may be difficult to visualise an appropriate model for a given structural system. Here, a convenient method of visualising strut and tie models is presented. Using elastic finite element analysis, low stressed parts of a structure are removed in a step by step process until the main stress paths, which represent the ties and struts, are defined. The second important issue to be addressed is that of serviceability of the designed structure because the strut and tie model naturally represents a great departure from the elastic stress distribution. Since the strut-tie model is used to design for the ultimate load situation, it is necessary to assess the suitability of the same model in relation to serviceability characteristics of the resulting design. It is important that ductility of the structure should be maintained at ultimate loads while avoiding excessive deflections and cracking at service loads. A wide variety of structures were designed, and to assess the performance of each design, non-linear finite element analysis was used. Verification of some of the numerical results was carried out through physical testing in the laboratory which also allowed the serviceability behaviour of the structures to be assessed. The test program comprised of three corbel joints and two frame corner joints. It was concluded that design from the strut and tie method can produce adequate performance both at service and ultimate loads. In terms of ultimate load prediction, the strut-tie method can produce results of comparable accuracy to non-linear finite element analysis.

Deep beams have traditionally been calculated through experiments and estimations. The purpose of the Strut-and-Tie method is to design a truss with struts, ties and nodes and to calculate these. The method is by Eurocode 2 recommended to use for deep beams and the result will always be on the safer side because the actual capacity will always be equal to or greater than the truss.   The purpose of the study is to create a step by step method description on how to use the method and then apply it in a deep beam for a five-story building.   The study includes an FE-analysis of the sheet and of the truss. After that hand calculations will be made to control the strength and to dimension the reinforcement.  The wall sheet have three supports and the length is 12 m, 3 m high and 0.2 m thick. The result shows that the area reinforcement FS9150 will be needed along with 4 layers of 2Ø16 in the bottom of the deep beam and 5 layers of 2Ø12 in the top of the deep beam. It is also necessary to extend the middle support by 400 mm for the node to have enough capacity.   One difficulty with the method was to develop an optimal truss model. It was difficult to produce models that matched the direction of the forces in the sheet while getting the right angle between the struts and ties. In addition to that, there is also a recommendation to have as few struts and ties as possible. Making a model where all of these are taken into account is a difficult task. It is likely that the method gives a better result, the more experience the structural engineer has with the method.

En stor del av projekteringsskedet är framtagandet av bygghandlingar, främst ritningar i 2D. En modernare metod är istället att samla all information om ett byggnadsprojekt i en samordnad 3D-modell, så kallad BIM-modell. Building Information Modeling (BIM) är en välkänd projekteringsmetod som bygger på att digitala 3D-modeller innehåller tillräcklig information för att beställas och produceras i fysisk form. Modellen består av parametrar som representerar olika egenskaper och när en parameter ändras uppdateras modellen automatiskt. Parametrarna kan nås och modifieras av insticksprogram, så kallade plug-ins som utökar den ursprungliga programvarans funktionalitet med hjälp av programkod. Grafisk programmering är en modern programmeringsmetod med ett visuellt gränssnitt som underlättar för oerfarna användare. Med hjälp av grafisk programmering kan parameterstyrning av 3D-modeller effektiviseras och värdefull tid sparas. Av denna anledning har Dynamo, ett plug-in utvecklat av företaget Autodesk för Revit, studerats för att ta fram ett så kallat skript som automatiserar 3D-modelleringsprocesser i Revit kopplat till placering av armering i pålfundament. Dessutom har möjligheter till standardisering undersökts, samt för- och nackdelar med metoden. I detta examensarbete redogörs för potentialen med Dynamo och de skript som skapats genom en empirisk studie. En enklare fallstudie utfördes för att kunna åskådliggöra graden av tidsbesparing gentemot motsvarande arbete manuellt i Revit. För att komplettera armeringsskripten togs beräkningsmallar fram som, enligt fackverksmetoden och Eurokod 2, försåg skripten med korrekt indata. Resultatet av projektet visar på att Dynamo och grafisk programmering kan effektivisera armeringsplacering i pålfundament. Graden av effektivisering beror på varje enskilt fall, men fallstudien visade på ca 85–90% sparad tid. En generell slutsats pekar mot att ju mer komplicerad utformning av armering desto mer tid finns att spara. Då grafisk programmering bygger på automatisering av arbetsprocesser av upprepande karaktär finns stor potential för att standardisera projektering med hjälp av dynamoskript. Företag kan då skapa rutiner som ökar kontinuitet och kvalitet i sina projekt. Automatiseringen leder även till färre mänskliga fel och utförandet blir effektivare. Uppdragsgivaren uppmanas att vidareutveckla metoden genom att implementera tydliga rutiner vad gäller 3D-modellering med grafisk programmering, samt undersöka möjligheten med automatiserad armering i andra bärande konstruktioner.
Most of the time spent on project planning is dedicated to the development of construction documents, mainly 2D-drawings. A more modern method is to gather all information about a building project in a coordinated 3D-model, so called BIM-model. Building information modelling (BIM) is a well-known design method based on a digital 3D model having enough information to enable procurement work and actual production. The model consists of parameters that represent different properties and when a parameter is changed, the model is updated automatically. These parameters can be accessed and modified through external programs, so called plug-ins that extend the original software’s functionality using program code. Visual programming is a modern programming method which utilizes a visual interface that favours users with little or no experience. Using visual programming, parameter control can be made more efficient and save valuable time. For this reason, Dynamo (a plugin developed by the company Autodesk for Revit), has been studied to create a so-called script that automates 3D modelling processes in Revit linked to placement of reinforcement in pile caps. In addition, possibilities for standardization have been investigated, as well as the advantages and disadvantages of the method. With this project, the potential of Dynamo and the scripts created through an empirical study is described, where a relatively simple case study is carried out in order to illustrate the amount of time saved through visual programming compared to corresponding work manually done in Revit. Furthermore, calculation templates were created, according to the strut and tie model and Eurocode 2, to provide the script in Dynamo with the correct inputs. The result shows that Dynamo and visual programming can make placement of reinforcement in pile caps more efficient. While the degree of efficiency is case dependent, the case study showed an overall 85-90% time saving. A general conclusion suggests that the more complicated rebar designs, the more time there is to be saved. Since visual programming is based on the automation of repetitive processes, there is great potential to standardize structural design with the help of Dynamo scripts. Companies can thus create routines that increase continuity and quality in their projects. The automation also leads to fewer human errors and a more efficient execution. The client is advised to further develop this method by implementing explicit routines regarding 3D modelling with visual programming and investigate the possibilities of automation of reinforcement design in other load-bearing structures.

Made available in DSpace on 2014-07-29T15:18:23Z (GMT). No. of bitstreams: 1 ErikaSakai.pdf: 1917728 bytes, checksum: 5cc92bff51598c6d8147b5abba80383d (MD5) Previous issue date: 2010-12-16
Through studies on the choice of type of foundation to use a certain work, always when the foundation is to pile it is necessary to build another structural element, the block of crowing or also called pile caps. Several studies have been made taking into account the block on stilts without the influence of soil. So this work demonstrates the relationship of methods of calculation of reactions in piles and tensions in chunks of some authors that take into account the influence of soil or not, with the numerical analysis. To analyzethe fundations the program DIANA was used in conjunction with MIDAS / FX +. With these results, ground-structure in the study of these blocks can be concluded on the importance of the interaction, being distinguished that as example, that if the ground are taken in consideration in the analyses of rigid blocks, the biggest reactions if are concentrate near the corners of the block, independent of the type of load application studied and not in the props central offices as some simplified methods consider. This leads to a closer examination of reality and therefore more accurate.
Através de estudos sobre a escolha do tipo de fundação a usar numa determinada obra, sempre quando a fundação for com estaca faz-se necessário a construção de outro elemento estrutural, o bloco de coroamento ou também denominado bloco sobre estacas. Vários estudos foram feitos levando-se em consideração o bloco sobre estacas sem a influência do solo. Portanto este trabalho demonstra a relação de métodos de cálculos de reações nas estacas e tensões nos blocos de estacas envolvidas pelo solo, através de análise numérica baseado no Método dos Elementos finitos, com características tridimensionais e não-lineares. Para a análise foi usado o programa DIANA em conjunto com o MIDAS/FX+. Com os resultados obtidos, pode-se concluir sobre a importância da interação solo estrutura no estudo destes blocos, destacandose que como exemplo, que se o solo é levado em consideração nas análises de blocos rígidos, as maiores reações se concentram nas estacas laterais do bloco, independente do tipo de aplicação de carga estudada e não nas estacas centrais como alguns métodos simplificados propõem. Isto leva a uma análise mais próxima da realidade e, consequentemente, mais preciso.

Anhand von Versuchsergebnissen wird gezeigt, dass Stahlbetonbauteile mit textilbewehrtem Beton verstärkt werden können. Sowohl die Torsionstragfähigkeit als auch die Gebrauchstauglichkeit werden durch die textilbewehrte Verstärkungsschicht deutlich verbessert. Vergleichsrechnungen zeigen, dass die Torsionstragfähigkeit mit bereits bekannten Stabwerksmodellen ermittelt werden kann.

The use of Cross-Laminated Timber products has increased in recent years with a range of structural applications including CLT tall buildings and folded structures. As CLT is used in more innovative structural applications the need for specific methods of design and analysis are apparent. A review of the literature demonstrates that despite the increasing popularity of CLT in construction there are limited methods for the design and analysis of CLT panels and structures that fully utilise its unique properties. Manufacturer data relating to the CLT material properties varies how the cross directional laminas are considered. Finally it was found that there is limited published knowledge regarding CLT material properties for panels loaded non-tangentially to the direction of the timber grain. A method for predicting failure loads and modes has been presented and compared with experimental test data. A Strut and Tie model is proposed for the analysis of CLT panels, a methodology originally developed to design of reinforced concrete deep beams. The Strut and Tie approach considers panel geometry, loads, supports, different properties in tension and compression and was adapted to consider anisotropic behaviour. The procedure, advantages and limitations have been presented and a model developed for an application in CLT. The use of this model is considered for the analysis of simple CLT panel loadings. The behaviour of CLT at different timber grain angles demonstrate a complex composite behaviour influencing the strut and tie capacities. The definition of node sizes was also found to be critical to the definitions of the struts and ties and hence the capacity of the sections. Comparison of experimental tests to the model demonstrates some application to using a Strut and Tie in CLT panels. It identifies where additional investigation is required to improve, develop and validate the model into a method that may be used for full-scale CLT panels and structures in design practice and consider a variety of geometries and loading arrangements.

The finite element method is a powerful analysis tool which has facilitated a better understanding of the behaviour of reinforced concrete structures. Its use in the research field is widespread and complements experimental tests and the development of new analytical models. Its application in practice engineering has permitted to deal with complex elements. However, the general structural engineer is still reluctant to consider finite element modelling for his work as he finds most of these models excessively sophisticated for his needs and knowledge. In particular, complexity of many finite element tools usually derives from the adoption of advanced concrete constitutive models. Implementation of more simple models based on engineering practice could facilitate its use by less experienced finite element users. In structural engineering practice finite element analysis can be of great usefulness to deal with those more problematic elements and/or where the application of traditional analysis methods presents limitations. This includes the so-called D-regions with a 3D behaviour. The strut-and-tie method and the stress field method are consistent and rational tools for the analysis and design of D-regions, but while their application to 2D elements is well covered in literature, its extension to 3D is problematic. This generally explains why excessively conservative assumptions are still common in the design of these elements. Refinement of current analytical and design approaches or the use of finite element analysis could lead to more rational solutions which in turn will reduce material requirements and costs. A 3D nonlinear finite element-based tool was developed in this thesis oriented towards the analysis and design of 3D D-regions by less experienced finite element users. Regarding material modelling, an orthotropic concrete model was adopted to permit the use of uniaxial stress-strain relationships. Only one single parameter, the uniaxial compressive strength of concrete, needs to be defined. Additionally, several aid functions were implemented, among which the following can be highlighted: a comprehensive, embedded reinforcement model to facilitate the introduction of complex rebar geometries; special support and load elements permitting an integrated and simple treatment of the boundary conditions imposed by them; and a simple design algorithm for the automatic determination of the required rebar areas. Three examples of applications to representative 3D D-regions are presented to show the capabilities of the tool. In particular, the analyses of fourteen four-pile caps, three socket base column-to-foundations connections and one anchorage block are described in the third part of the thesis. Results prove that realistic response predictions can be obtained considering relatively simple constitutive models. The capacity of the tool to configure consistent stress field models depending on the reinforcement arrangement is also demonstrated. The generation of rational reinforcement configurations by applying the implemented design algorithm is also shown. A strut-and-tie-based method for the analysis and design of four-pile caps with rectangular geometries is proposed in the fourth part. The method is based on a refined 3D strut-and-tie model and the consideration of three potential modes of failure: exceeding the reinforcement strength, crushing of the diagonal strut at the base of the column with narrowing of the strut and splitting of the diagonal strut due to transverse cracking. The main innovation is that the strut inclination is not fixed as in current strut-and-tie-based design procedures, but determined by maximizing the pile cap strength. The method accounts for strength softening of cracked concrete, compatibility constraints and reinforcement details. Its application to 162 specimens of literature led to very good predictions of the ultimate strength and, to a lesser extent, of the mode of failure.
El método de los elementos finitos es una potente herramienta de análisis que ha facilitado un mejor conocimiento del comportamiento de las estructuras de hormigón armado. Su uso en el ámbito de la investigación está ampliamente extendido. Su aplicación en la práctica ingenieril ha permitido la resolución de elementos complejos. Sin embargo, el ingeniero estructural común todavía es reticente a usar la modelización por elementos finitos ya que considera que la mayoría de estos modelos son excesivamente sofisticados para sus necesidades. La complejidad de muchas herramientas de elementos finitos suele derivarse de la adopción de modelos constitutivos de hormigón avanzados. La implementación de modelos más sencillos podría facilitar su uso por usuarios menos experimentados. En la práctica ingenieril el análisis con elementos finitos puede ser de gran utilidad para tratar aquellos elementos más problemáticos y/o donde la aplicación de los métodos de análisis tradicionales presenta limitaciones. Esto incluye las llamadas regiones D con comportamiento 3D. El método de bielas y tirantes y el método de campos de tensiones son herramientas racionales para el análisis y dimensionamiento de regiones D, pero su extensión a 3D es problemática. Este hecho explica por qué se adoptan todavía hipótesis excesivamente conservadoras en el dimensionamiento de estos elementos. La propuesta de métodos analíticos y de diseño más adecuados o la modelización con elementos finitos podría conducir a soluciones más racionales, lo que a su vez reduciría las necesidades de material y los costes. Como parte de esta tesis se ha desarrollado una herramienta de cálculo no lineal basada en el método de los elementos finitos orientada al análisis y dimensionamiento de regiones D tridimensionales por usuarios con menos experiencia en la modelización con elementos finitos. Se ha adoptado un modelo ortotrópico para el hormigón para permitir el uso de relaciones uniaxiales de tensión-deformación. Sólo es necesario definir un único parámetro, la resistencia a compresión uniaxial del hormigón. Adicionalmente, se han implementado varias funciones de ayuda, entre las que destacan: un modelo de armadura embebida para facilitar la introducción de geometrías de armado complejas; elementos especiales de apoyo y de carga que permiten un tratamiento integral de las condiciones de contorno; y un algoritmo de diseño para la determinación automática del área de armado necesaria. Se presentan tres ejemplos de aplicación a regiones D 3D representativas para mostrar las capacidades de la herramienta. En concreto, en la tercera parte del documento se describen los análisis de catorce encepados, tres cálices de cimentación y un bloque de anclaje. Los resultados muestran que se pueden obtener predicciones bastante realistas considerando modelos constitutivos relativamente sencillos. También se demuestra la capacidad de la herramienta para configurar modelos de campo de tensiones consistentes dependiendo de la configuración de armado. Además se muestra la capacidad del algoritmo de diseño para configurar disposiciones de armado racionales. En la cuarta parte se propone un método para el análisis y dimensionamiento de encepados sobre cuatro pilotes con geometría rectangular. El método se basa en un modelo 3D de bielas y tirantes refinado y la consideración de tres modos de fallo posibles: rotura del acero, aplastamiento de la biela diagonal en la base de la columna con estrechamiento de la misma y splitting de la biela diagonal debido a la fisuración transversal. La principal novedad es que el ángulo de la biela no se fija como en otros modelos, sino que se determina mediante la maximización de la resistencia del encepado. El método considera el debilitamiento de la resistencia del hormigón fisurado, condiciones de compatibilidad de deformaciones y detalles de armado. Su aplicación a 162 especímenes dio luga
El mètode dels elements finits és una potent eina d'anàlisi que ha facilitat un millor coneixement del comportament de les estructures de formigó armat. El seu ús en l'àmbit de la investigació està àmpliament estès. La seua aplicació en la pràctica enginyeril ha permès la resolució d'elements més complexos. No obstant això, l'enginyer estructural comú encara és reticent a fer servir la modelització per elements finits ja que considera que la majoria d'aquests models són excessivament sofisticats per a les seues necessitats i el seu conèixement. En concret, la complexitat de moltes eines d'elements finits sol derivar-se de l'adopció de models constitutius avançats de formigó. La implementació de models més senzills basats en la pràctica enginyeril podria facilitar el seu ús per a usuaris menys experimentats en la modelització amb elements finits. A la pràctica enginyeril l'anàlisi amb elements finits pot ser de gran utilitat per a tractar aquells elements més problemàtics i/o on l'aplicació dels mètodes d'anàlisi tradicionals presenta limitacions. Això inclou les anomenades regions D amb comportament 3D. El mètode de bieles i tirants i el mètode de camps de tensions són eines racionals per a l'anàlisi i dimensionament de regions D, però la seua extensió a 3D és problemàtica. Aquest fet explica per què s'adopten encara hipòtesis excessivament conservadores en el dimensionament d'aquests elements. La proposta de mètodes analítics i de disseny més adequats o la modelització amb elements finits podria conduir a solucions més racionals, amb el que també es reduirien les necessitats de material i els costos. Com a part d'aquesta tesi s'ha desenvolupat una eina de càlcul no lineal basada en el mètode dels elements finits orientada a l'anàlisi i dimensionament de regions D tridimensionals per a usuaris amb menys experiència en la modelització amb elements finits. S'ha adoptat un model ortotròpic per al formigó per permetre l'ús de relacions uniaxials de tensió-deformació. Només cal definir un únic paràmetre, la resistència a compressió uniaxial del formigó. Addicionalment, s'han implementat diverses funcions d'ajuda, entre les quals destaquen: un model d'armadura embeguda per facilitar la introducció de geometries d'armat complexes; elements especials de suport i de càrrega que permeten un tractament integral i senzill de les condicions de contorn; i un algoritme de disseny per a la determinació automàtica de l'àrea d'armat necessari. Es presenten tres exemples d'aplicació a regions D 3D representatives per mostrar les capacitats de l'eina. En particular, en la tercera part del document es descriuen les anàlisis de catorze enceps sobre quatre pilons, 3 calzes de fonamentació i un bloc d'ancoratge. Els resultats mostren que es poden obtenir prediccions prou realistes considerant models constitutius relativament senzills. També es demostra la capacitat de l'eina per configurar models de camp de tensions consistents depenent de la configuració d'armat. A més es mostra la capacitat de l'algoritme de disseny per configurar disposicions d'armat racionals. En la quarta part es proposa un mètode per a l'anàlisi i dimensionament d'enceps sobre quatre pilons amb geometria rectangular. El mètode es basa en un model 3D de bieles i tirants refinat i la consideració de tres modes de fallada possibles: trencament de l'acer, aixafament de la biela diagonal a la base de la columna amb estrenyiment de la mateixa i splitting de la biela diagonal per causa de la fissuració transversal. La principal novetat és que l'angle de la biela no es fixa com en els models actuals de bieles i tirants, sinó que es determina mitjan\c{c}ant la maximització de la resistència de l'encep. El mètode proposat considera el debilitament de la resistència del formigó fissurat, condicions de compatibilitat de deformacions i detalls d'armat. La seua aplicació a 162 espècimens de la liter
Meléndez Gimeno, C. (2017). A finite element-based approach for the analysis and design of 3D reinforced concrete elements and its applications to D-regions [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/86193
TESIS

Construction practices are constantly evolving in order to adapt to physical locations and economic conditions. These adaptations may result in more cost-effective designs, but may also come at a cost of strength. In masonry shear walls, it is becoming more common to reduce the amount of grouting from every cell to only those with reinforcement, a practice known as partial-grouting. Partially-grouted masonry responds differently and in a more complex matter to lateral loads as compared to fully-grouted masonry. The response is made even more complex by wall discontinuities in the form of openings. The main objective of this study is to validate the strut-and-tie procedure for the in-plane lateral strength prediction of partially-grouted, multistory, reinforced concrete masonry walls with openings. The research included testing six three story, half-scale masonry shear walls. Half of the walls had door openings while the other half had window openings. The configurations were selected to represent typical walls in multi-story buildings. The measured lateral strength was compared to estimations from the equations in the US masonry code and to those from an equivalent truss model and a strut-and-tie model. The results show that the U.S. masonry code equations over predicts while the equivalent truss model under predicts the lateral strength of the walls. The results further show that the strut-and-tie model is the most accurate method for lateral strength prediction and is able to account for wall openings and partial-grouting.

The aim of the thesis is the strengthening and resistance of concrete construction. At the beginning is described composite reinforcement and their specific properties. The thesis specifically follows behavior concrete vault and the effects of load. Resistance vault is calculated by S&T model – strut and tie. Finally, the thesis contain strengthening construction by composite reinforcement. Strengthening is considered by two ways - strengthening by cohesive reinforcement and strengthening by incoherent reinforcement (wrapping).

The main topic of this thesis concerns the behavior of concrete pile cap supported by four piles with two varying positions of longitudinal reinforcements. The positions include top of piles and bottom of the pile cap. For this purpose, non-linear finite element models of a pile cap are created using software ATENA 3D. The goal was to observe which position of reinforcement yields the higher bearing capacity and to observe the failure modes in the models. To achieve the above goals, a short review of theoretical background concerning shear phenomena is performed. This, in order to enhance the knowledge regarding shear stresses, shear transfer mechanism, factors affecting shear capacity, modes of shear failure and relate them to the behavior of pile cap. Furthermore, the calculation of shear resistance capacity based on Eurocode 2 using strut and tie method and sectional approach is presented. The numerical analysis started by creating four pile cap models in ATENA 3D. The difference between the models being the position and ratio of longitudinal reinforcement. The purpose behind two reinforcement ratios were to observe the behavior of pile cap model in two cases: a) when failure occurs prior to yielding of reinforcement; b) when failure occurs while reinforcement is yielding. The models are then analyzed using software ATENA Studio. The results revealed that placing the reinforcement on top of piles in case (a) increased the capacity of the model by 23.5 % and in case (b) increased the capacity by 18.5 %. This because the tensile stresses were found to be concentrated on top of piles rather than the bottom of the pile cap. The final failure mode in the model with top reinforcement position was crushing of the inclined compressive strut at the node beneath the column and in the model with bottom reinforcement position, the splitting of the compressive strut due to tensile stresses developed perpendicular to the inclined strut. The potential advantage of placing the reinforcement at the bottom were a better crack control in serviceability limit state and a slightly less fragile failure mode compared to the top position of reinforcement. A parametric study was performed in the model as well to observe the effects of various parameters on the results obtained. It was found that fracture energy had the most significant effect on the results obtained. Finally, a comparison between the results of numerical analysis and analytical design approaches based on strut and tie method and sectional approach was performed. The comparison reveals that the design values obtained based on strut and tie method for the model were very conservative. In particular, the equation for the strength of inclined compressive strut based on Eurocode 2 was very general.
Det huvudsakliga ämnet för den här avhandlingen handlar om beteendet hos pålfundament som stöds av fyra pålar med två olika positioner av längsgående armering. Positionerna inkluderar toppen av pålarna och botten av slagdynan. För detta ändamål skapas icke-linjära finita elementmodeller av en slagdyna med mjukvaran ATENA 3D. Målet var att observera vilket armeringsläge som ger den högre bärkapaciteten och att identifiera brottmekanismen i modellerna. För att uppnå ovanstående mål utförs en kort genomgång av teoretisk bakgrund rörande skjuvningsfenomen. Detta för att förbättra kunskapen om skjuvspänningar, skjuvöverföringsmekanism, faktorer som påverkar skjuvkapacitet, skjuvbrott och relaterar dem till beteendet hos slagdynan. Beräkningen av skjuvmotståndet baserad på Eurocode2 med hjälp av Srut and tie-metod och sektionsmetod. Den numeriska analysen började med att skapa fyra pålfundament i ATENA 3D. Skillnaden mellan modellerna är positionen och förhållandet mellan längsgående armering. Syftet bakom två armeringsförhållanden var att observera beteendet hos slagdynan i två fall: a) när brott inträffar innan armering plasticeras; b) när brott inträffar medan armeringen plasticeras. Modellerna analyseras sedan med hjälp av programvaran ATENA Studio. Resultaten visade att placering av armeringen ovanpå pålarna i fall a) ökade modellens kapacitet med 23,5% och i fall (b) ökade kapaciteten med 18,5%. Detta på grund av att dragspänningarna visade sig vara koncentrerade på toppen av pålarna snarare än på botten av slagdynan. Det slutliga brottet i modellen med topparmeringsposition var krossning av det lutande tryckstaget vid noden under pelaren. I modellen med bottenarmeringsposition delades kompressionsstaget på grund av dragspänningar vinkelrätt mot det lutande staget. The potential advantage of placing the reinforcement at the bottom were a better crack control and slightly less fragile failure mode compared to the top position of reinforcement. En parametrisk studie genomfördes också i modellen för att observera effekterna av olika parametrar på de erhållna resultaten. Det visade sig att brottenergi hade den mest signifikanta effekten på de erhållna resultaten. Slutligen genomfördes en jämförelse mellan resultaten från numerisk analys och analytiska designmetoder baserade på strut and tie-metoden och sektionsmetoden. Jämförelsen avslöjar att de designvärden som erhölls baserat på strut and tie-metoden för modellen var mycket konservativa. I synnerhet var ekvationen för kapaciteten hos det lutande tryckstag baserad på Eurocode 2 mycket generell.

Donat que la nostra societat és cada cop més dependent de la tecnologia, i perquè la tecnologia és vulnerable als processos de l’alta atmosfera que tenen el seu origen en el Sol, la nostra mirada es dirigeix progressivament vers la comprensió dels mecanismes concrets que possibiliten la connexió Sol - Terra, tractant-se avui dia d’una disciplina on la recerca va clarament en augment. L’acoblament de l’alta atmosfera amb la magnetosfera és, doncs, important per tal d’entendre processos que afecten el nostre planeta a escala global. Aquesta darrera baula en la complexa cadena d’esdeveniments que comencen en la nostra estrella té com a principal destinatària la ionosfera d’altes latituds, on es dipositen quantitats considerables d’energia i moment del vent solar. El camp magnètic terrestre juga un paper clau en aquesta interacció, on els corrents elèctrics que circulen al llarg de les línies de camp magnètic, altament conductores, es poden assimilar als cables d’un circuit que es tanca a través de la càrrega elèctrica (en terminologia de circuits) que constitueix la ionosfera d’altes latituds. La missió satel•litària Active Magnetosphere and Planetary Electrodynamics Response Experiment (AMPERE) ha proporcionat, per primera vegada, instantànies dels corrents alineats al camp amb una resolució espaial i temporal sense precedents, oferint així una oportunitat per alimentar un reconegut model físic de l’alta atmosfera de la Terra com el National Center for Atmospheric Research Thermosphere-Ionosphere-Electrodynamics General Circulation Model (NCAR TIE-GCM). En un primer pas, hem utilitzat les dades d’AMPERE en l’equació de continuïtat del corrent entre la magnetosfera i la ionosfera per tal de forçar l’electrodinàmica del TIE-GCM, i hem validat els resultats tot comparant l’output corresponent a les variacions magnètiques en superfície amb dades geomagnètiques d’observatoris a diferents latituds i per a diferents condicions geofísiques. En una segona fase, hem introduït conductivitats ionosfèriques compatibles amb sectors de corrents alineats ascendents elevats, corresponents a electrons que es desplomen com a resultat d’una acceleració descendent deguda a camps elèctrics paral•lels que s’acumulen al llarg de les línies de camp magnètic, tot fent ús de diferents models per a validar les nostres conductàncies de sortida. Els resultats mostren una millora general de la capacitat del model per explicar les variacions magnètiques observades, tot i que amb una major contribució arran de la nostra primera aproximació. Les distribucions de conductància obtingudes, d’altra banda, són prou consistents amb models independents que han intentat quantificar l’efecte ionitzant de partícules que precipiten sobre la ionosfera auroral. En conclusió, hem fet una contribució modesta, però tanmateix constructiva, a la modelització de l’alta atmosfera i la seva connexió amb l’entorn espacial; principalment perquè tenim entre mans un model físic, que en últim terme ha de servir per avaluar el nostre coneixement de la realitat, més que no pas per proveir un resultat purament funcional.
Dado que nuestra sociedad es cada vez más dependiente de la tecnología, y porque la tecnología es vulnerable a los procesos de la alta atmósfera que tienen su origen en el Sol, nuestra mirada se dirige progresivamente hacia la comprensión de los mecanismos precisos que posibilitan la conexión Sol - Tierra, tratándose hoy en día de una disciplina en claro avance en cuanto a investigación. El acoplamiento de la alta atmósfera con la magnetosfera es, pues, importante para la comprensión de procesos que afectan a nuestro planeta a escala global. Este último eslabón en la compleja cadena de sucesos que comienzan en nuestra estrella tiene como principal destinatario la ionosfera de altas latitudes, donde se depositan cantidades considerables de energía y momento del viento solar. El campo magnético terrestre juega un papel clave en esta interacción, donde las corrientes eléctricas que circulan a lo largo de las líneas de campo magnético, altamente conductoras, pueden asimilarse a los cables de un circuito que se cierra a través de la carga eléctrica (en terminología de circuitos) que constituye la ionosfera de altas latitudes. La misión satelital Active Magnetosphere and Planetary Electrodynamics Response Experiment (AMPERE) ha proporcionado, por vez primera, instantáneas de las corrientes alineadas al campo con una resolución espacial y temporal sin precedentes, ofreciendo así una oportunidad para alimentar un reconocido modelo físico de la alta atmósfera de la Tierra como el National Center for Atmospheric Research Thermosphere-Ionosphere-Electrodynamics General Circulation Model (NCAR TIE-GCM). En un primer paso, hemos utilizado los datos de AMPERE en la ecuación de continuidad de corriente entre la magnetosfera y la ionosfera a fin de forzar la electrodinámica del TIE-GCM, validando los resultados a través de la comparación del output correspondiente a las variaciones magnéticas en superficie con datos geomagnéticos de observatorios a distintas latitudes y para diferentes condiciones geofísicas. En una segunda fase, hemos introducido conductividades ionosféricas compatibles con sectores de corrientes alineadas ascendentes elevadas, correspondientes a electrones que se desploman como resultado de una aceleración descendiente debida a campos eléctricos paralelos que se acumulan a lo largo de las líneas de campo magnético, haciendo uso de diferentes modelos para validar nuestras conductancias de salida. Los resultados muestran una mejora general de la capacidad del modelo para explicar las variaciones magnéticas observadas, aunque con una mayor contribución a raíz de nuestra primera aproximación. Las distribuciones de conductancia obtenidas, por otro lado, son razonablemente consistentes con modelos independientes que han intentado cuantificar el efecto ionizante de partículas que precipitan sobre la ionosfera auroral. En conclusión, hemos contribuido modesta, aunque constructivamente, a la modelización de la alta atmósfera y a su conexión con el entorno espacial; principalmente porque estamos tratando con un modelo físico, que en último término debe servir para evaluar nuestro conocimiento de la realidad, antes que proveer un resultado puramente funcional.
Because our society is ever more dependent on technology, and because technology is vulnerable to upper atmospheric processes having their origin in the Sun, our gaze is progressively turning towards the understanding of the exact mechanisms that enable the Sun-Earth connection, being today a matter of increasingly intensive research. Coupling of the upper atmosphere system with the magnetosphere is thus important for understanding processes that affect our planet in a global scale. This last link in the complex chain of events starting in our star has the high-latitude ionosphere as a main target, where considerable amounts of solar wind energy and momentum are deposited. The magnetic field of the Earth plays a key role in this interaction, with electric currents flowing along the highly conducting geomagnetic field lines that can be thought of as the wires in a circuit that is closed by the electrical load of the high-latitude ionosphere. The Active Magnetosphere and Planetary Electrodynamics Response Experiment (AMPERE) satellite mission has offered for the first time snapshots of the geomagnetic field-aligned currents with unprecedented space and time resolution, thus providing an opportunity to feed an acknowledged first-principles model of the Earth’s upper atmosphere such as the National Center for Atmospheric Research Thermosphere-Ionosphere-Electrodynamics General Circulation Model (NCAR TIE-GCM). In a first step, we have made use of AMPERE data in the current continuity equation between the magnetosphere and the ionosphere to drive the TIE-GCM electrodynamics, and we have validated our results by comparing the output ground magnetic variations with geomagnetic observatory data at different latitudes and for different geophysical conditions. In a second stage, we have made ionospheric conductivities consistent with enhanced upward field-aligned current sectors corresponding to electrons plunging as a result of downward acceleration by parallel electric fields built up along the magnetic field lines, whereby we have used different models to validate our output conductances. Results show an overall improvement of the model ability to explain the observed magnetic variations, though with a greater contribution coming from our first approach. Our conductance distribution, on the other hand, is reasonably commensurate with independent models that have tried to quantify the ionizing effect of precipitating particles onto the auroral ionosphere. In conclusion, we have made a modest but constructive contribution to the modeling of the upper atmosphere and its connection with the space environment; especially because we are dealing with a physical model, which is ultimately meant to assess our knowledge of reality, rather than providing a purely functional result.

Dans le domaine des structures en Béton Armé (BA) et plus spécifiquement, lors de la conception d'éléments non-flexibles tels que les corbeaux, les poutres bayonets et les poutres profondes, la Méthode Bielle-Tirant (MBT) présente des avantages par rapport aux algorithmes classiques de calcul de ferraillage basé sur l'analyse FE (par exemple Wood-Armor ou Capra-Maury).La Methode Bielle-Tirant reste une alternative adaptée pour la conception de structures en béton présentant un comportement élastique ou plastique dont le cadre d'application est bien défini dans les codes de conception des structures en béton comme les EuroCodes et les spécifications de conception des ponts AASHTO-LRFD.Néanmoins, cette méthode présente l'inconvénient majeur de nécessiter un investissement important en ressources humaines ou en capacité de calcul pour, respectivement, son application manuelle ou une approche automatique par optimisation de topologie.Le document propose une alternative légère, en termes d'itérations requises, à l'automatisation de la MBT, qui part de l'affirmation que les entretoises résultantes et les attaches d'un modèle ST approprié peuvent être distribuées selon la direction des contraintes principales, $sigma_{III}$ et $sigma_{I}$, obtenus à partir d'un planaire modèle aux EF
Within the field of Reinforced Concrete (RC) structures and more specifically, at the design of non-flexural elements such as corbels, nibs, and deep beams, the rational procedure of conception and justification referred as Strut-and-Tie Method (STM) has shown some advantages over classical algorithms of reinforcement computation based on FE analysis (eg. Wood-Armer or Capra-Maury).The STM remains a suitable alternative for the design of concrete structures presenting either elastic or plastic behaviour whose application framework is well defined in concrete structures’ design codes like the EuroCodes and the AASHTO-LRFD Bridge Design Specifications.Nevertheless, this method has the main inconvenient of requiring a high amount of resources investment in terms of highly experienced personal or in terms of computational capacity for, respectively, its manual application or an automatic approach through topology optimisation.The document proposes a light alternative, in terms of required iterations, to the automation of the STM, which starts from the statement that the resultant struts and ties of a suitable ST model can be distributed according to the direction of the principal stresses, $sigma_{III}$ and $sigma_{I}$ , obtained from a planar or a three-dimensional FE model

Fackverksmodellering (eng. strut-tie modeling) är en accepterad och rationell beräkningsmetod för betongkonstruktioner där vanlig balkteori inte kan appliceras. Det gäller områden för s.k. diskontinuitetsregioner (D-regioner). Den komplexa spännings- och kraftfördelningen som uppstår i D-regioner substitueras till fackverkskomponenter i form av trycksträvor, dragstag och noder. Lastfallen omvandlas, under förenklade villkor, med andra ord till ett lösbart fackverksfall. Metodiken för tillgångasättet har länge ansetts som iterativ och långdragen process, där ett fackverk antas samt optimeras tills ett godtyckligt och rimligt fackverk har uppnåtts. Erfarenhet har betydelse för hur fackverksutformningen kommer att se ut. Oerfarna ingenjörer kan till en början ha svårt att se hur spännings- och kraftfördelningen i en betongkonstruktion sprider ut sig. Med hjälp av FEM kan fackverksmodelleringens process effektiviseras. Spänningsoch kraftfördelningen kan tas fram i belastande betongkonstruktioner i form av finita elementmodeller. Därmed kan konstruktörerna visuellt utforma fackverket efter fördelningen. I studien har ett verkligt fall tillhandahållits från företaget WSP. Konstruktionsdelen som ska dimensioneras är en väggskiva från ett flerbostadshus i Stockholm. Med FEM-design har väggskivan rekonstruerats till en finita elementmodell med en framtagen spännings- och kraftfördelning. Fördelningen har använts som ett underlag för vidare dimensionering för hand efter Svenska Standard, Eurokod 2. Resultaten visar att det är möjligt att utforma ett fackverk med FEM-design som underlag. Även framtagna stångkrafter och upplagskrafter har jämförts mellan handberäkning och FEM, som visar att skillnader mellan beräkningsmetoderna är mellan ungefär 5,1-7,7 %, dock bara för studiens fall. Rapporten visar att en påskyndning i processen kan göras om man använder FEM. Metoden möjliggör en förenkling i processen som kan nyttjas av oerfarna konstruktörer. Detta kan bidra till en bättre slutprodukt och gynna utvecklingen för byggbranschen i slutändan.
Strut-tie modeling is an accepted and rational calculation method for regions in concrete structures where Berouille-theorem can’t be applied. These regions are so called discontinuity regions (D.regions). The stress and force distribution is substituted for strut, ties and nodes much like the members of a truss. Complex load-bearing cases can be transformed, under simplified conditions, to solvable cases. The strut-tie modeling can be seen as an iterative process. At the start of the process the form of the truss is assumed and optimized through trial and error. Experience in the field is therefore of big significance, where unexperienced designers can have a hard time to visualize the stress and force distribution through the concrete structure. The purpose of the study is to use the strut-tie method on a concrete structure. The study will investigate if the strut-tie method can be simplified and if the assumed truss is reasonable. The stress and force distribution is going to be visualized through a finite element model, and hence try to eliminate the iterative modelling phase. In the study, a real load-bearing case will be examined. The concrete structure is a deep beam in an apartment block in Stockholm, Sweden. The designs of the apartment have been provided from the multinational company WSP. The deep beam have been reconstructed to a finite element model through the program FEMdesign 17 3D Structure. The visualized results from the stress and force distribution have been used as a base for further calculations, with the strut-tie method, in accordance to Eurocode 2. The result from the study shows that it’s possible to create a truss from FEM-designs visualized stress- and force distribution. In the study a comparison have also been made between truss member forces calculated by strut-tie and the forces calculated by FEM-design. It shows a difference between 5,1-7,7%. The study shows through the program FEM-design 17 that strut-tie method can be improved, and help unexperienced designers during the truss modeling phase.

Este trabalho estuda o comportamento de blocos rígidos de concreto armado sobre uma, duas, três, quatro e cinco estacas, submetidos à ação de força centrada. Com o objetivo de contribuir para critérios de projeto, utilizaram-se resultados obtidos por meio de modelos analíticos e realizou-se análise numérica utilizando-se programa baseado no método dos elementos finitos. Foi desenvolvida, ainda, uma análise comparativa entre os processos de dimensionamento adotados em projeto, na qual se verificou grande variabilidade dos resultados. Para análise numérica adotou-se comportamento do material como elástico linear e os resultados de interesse foram os fluxos de tensões em suas direções principais. Nos modelos adotados variaram-se os diâmetros de estacas e dimensões de pilar, a fim de se verificar as diferenças na formação dos campos e trajetórias de tensões. Concluiu-se que o modelo de treliça utilizado em projetos é simplificado e foram feitas algumas sugestões para a utilização de um modelo de bielas e tirantes mais refinado. Foi possível a verificação da influência da variação da geometria de estacas e de pilares no projeto de blocos sobre e a revisão dos critérios para os arranjos das armaduras principais. Para os modelos de blocos sobre cinco estacas adotados concluiu-se que o comportamento não é exatamente como considerado na prática
This work describes the behavior of rigid reinforced concrete pile-caps with one, two, three, four and five piles subjected to patches of loading on the center top surfaces of the column. Programs based on finite elements method were used to obtain numerical results and results obtained by means of analytic models were used. A comparative analysis was developed among the processes adopted in design, which large variability of the results was verified. An elastic linear behavior of the material was adopted for numerical analysis and interest results were stress paths along main directions. Piles diameters and column dimensions of the models were been varied, in order to verify the differences in the formation of the regions and trajectories of stress. It is ended that used the truss model is simplified. Some suggestions were made for the use of a more refined strut-and-tie model than the one used in design and it was possible the verification of the variation geometry of piles and columns influence. It was still made a revision of the reinforcement layouts. The conclusion for adopted five-pile-caps was that the behavior is not exactly as considered in the practice

Předložená dizertační práce je součástí většího výzkumného projektu, který si klade za cíl využití mikro prutové konstrukce vyrobené technologií SLM jako absorbér rázové energie s přesně navrženými vlastnostmi. Hlavním cílem práce je vývoj numerického modelu deformačního chování mikro-prutové konstrukce vyrobeného technologií Selective Laser Melting (SLM) z materiálu AlSi10Mg. Aby bylo možné dosáhnout hlavního cíle dizertační práce, bylo nutné analyzovat vliv procesních parametrů technologie SLM na tvorbu vnitřních materiálových vad a drsnost povrchu při výrobě mikro-prutové konstrukce. Tyto imperfekce degradují její mechanické vlastnosti a jejich odstranění zlepší možnosti a přesnost numerické predikce. Výsledky ukazují významný vliv dvou hlavních parametrů – skenovací rychlosti laseru a výkonu laseru. Na základě těchto poznatků byly dále definovány parametry vstupní energie Ein a lineární energie Elin, které zahrnují oba zmíněné parametry a byly definovány jejich limitní hodnoty pro minimalizaci vzniklých imperfekcí. Deformační chování vyrobené mikro-prutové konstrukce bylo analyzováno na navrženém pádové zařízení, které umožňuje testování s dopadovou energií až 120 J. Deformační chování je vyhodnocováno s využitím obrazové analýzy záznamu vysoko rychlostní kamery a silového průběhu z tenzometru. Výsledky analýzy byly využity pro validaci numerického modelu v programu ANSYS Explicit, do kterého byly implementovány poznatky o reálném tvaru vyrobeného mikro-prutového materiálu ve formě eliptického modelu geometrie a informace o reálných mechanických vlastnostech ve formě vyvinutého materiálového modelu. Výsledné porovnání výsledků experimentu s predikcí numerického modelu ukazují dobrou shodu v místě maximálního zatížení Fmax (odchylka 5 %) i průběhu celé deformace vzorku. Tyto poznatky budou v budoucnu využity při návrhu absorbéru energie s definovanými mechanickými vlastnostmi.

Reinforced concrete frames infilled with unreinforced masonry are commonly used in structures worldwide. The interaction between the frame and the infill panel is usually ignored in engineering practice, and the masonry infill is not considered as a structural element. However, observations made after the occurrence of strong earthquakes have shown that the bare frame and infill-frame behave differently when subjected to in-plane lateral loads. Extensive research has been conducted on the behaviour of infill-frames when laterally loaded. This research focuses on the analysis of infill-frames using the equivalent strut modelling method, whereby an infill-frame is simplified, and the infill panel is replaced by one or more compressive strut elements. A large number of strut models have been proposed in the literature, but recent studies have demonstrated that it is not possible to apply one strut model to all infill-frame structures. It has been found that changing the properties of an infill-frame can also change the geometric properties of struts, namely width, location and number of struts in an equivalent strut model. For this reason, recent studies have proposed a case-specific strut modelling approach. In the current study, a macro script available in the literature that can be used to generate a detailed finite element (FE) model has been applied to construct and analyse a number of infill-frames with different material and geometric properties. Sensitivity analyses on some of these infill-frames have also been conducted by varying the material properties of the infill, and the amount and distribution of vertical loads on the frame. The results of detailed FE analyses, more specifically contours of the compressive principal stresses, have been used to define the geometric properties of the struts of case-specific strut models for each of the infill-frames. Equivalent strut models were then analysed and compared. Further, the proposed strut models were applied to other infill-frames selected for this study; two strut models from the literature were also applied to these infill-frames. It was concluded that the geometric properties of, and the vertical load on an infill-frame can be related to the geometric properties of its equivalent strut model. In contrast, a variation of up to 25% in the masonry material properties did not have a significant effect on the strut properties. It was shown that casespecific strut modelling is a versatile and generic technique that can adequately replicate the highly nonlinear behaviour of infill-frames regardless of their geometric or material properties. By expanding the current research, it is hoped that a rigorous classification of infill-frames and their relevant equivalent strut models can be developed to assist structural engineers in their everyday design tasks.

A pesquisa teve como objetivo analisar e discutir o comportamento de blocos de concreto armado sobre duas estacas submetidos à ação de força centrada e excêntrica. Desenvolveu-se uma análise numérica tridimensional não-linear de blocos de concreto armado sobre duas estacas. A análise numérica levou em consideração a fissuração do concreto e a influência das armaduras no comportamento estrutural dos blocos. Por meio da análise numérica, foi possível perceber o comportamento e a forma geométrica das bielas de compressão, com isso, obteve-se melhor entendimento do modelo de bielas (escoras) e tirantes aplicado a blocos de concreto armado sobre duas estacas. A geometria observada nos modelos numéricos analisados preliminarmente difere da usualmente sugerida por vários autores. Realizou-se investigação experimental de blocos, com o fim principal de observar, de modo mais abrangente, a geometria das bielas de compressão. A instrumentação foi posicionada nas faces dos blocos com extensômetros espaçados de modo a ocuparem boa parte da largura e, conseqüentemente, indicarem as suas geometrias. A análise experimental de blocos sobre duas estacas submetidos à ação de força excêntrica permitiu observar o comportamento das bielas e tirantes que diferem dos observados quando a força é centrada. Também foi analisada a eficiência dos ganchos das barras de aço que compõem os tirantes, verificando-se que os ganchos podem ser omitidos sem prejuízo da segurança estrutural dos blocos. Em função dos resultados obtidos por meio das análises experimental e numérica desenvolveram-se modelos de bielas e tirantes aplicados a blocos sobre duas estacas
The research had as objective to analyze and to argue about the behavior of two pile caps submitted to the action of a centered and eccentric load. A nonlinear three-dimensional numerical analysis of two pile caps was developed. The numerical analysis included the cracking and the influence of the reinforcement in the structural behavior of the pile caps. By the numerical analysis, it was possible to perceive the behavior and the geometric form of the strut, with this understand the model strut-and-tie applied to the two pile caps. The geometry observed in the numerical models analyzed at first differs from the usually suggested by some authors. This project realized experimental tests of piles caps to observe the geometry of the struts. The instrumentation was located in the faces of the pile caps with spaced strain-gages in order to occupy good part of the width and, consequently, indicate its geometry. The experimental analysis of two pile caps submitted to the eccentric load allowed the behavior observation of the strut and tie that differ from the one observed when the load was centered. Also the efficiency of the hooks of the reinforced bar was analyzed, therefore, in the experimental analysis of pile caps already developed, it was verified that the hooks can be omitted without damage of the structural security of the pile caps. For treating the procedure defined in the project, and taking advantage of the experimental analysis realized, it was understood that this requirement can be analyzed and that the results will bring benefits to the project. In function of the results obtained through the experimental and numeric analysis strut-and-tie models were developed to be applied in two pile caps

People often make social-related trips to perform activities with their friends. An individual's group of friends can be characterized by his or her social network. While traditional social network data collection is time-consuming and dependent on memory recollection, new online social networking sites may address these shortcomings. This research focuses on the use of tie-strength, the strength of an individual's relationships in his or her social network, to characterize friendships and how this influences an individual's air travel behavior. Four candidate weighting schemes were developed using data collected from a web-based survey which included demographic information, an air travel diary, and friendship information retrieved from Facebook.com. The candidate weight matrices were then tested in a spatial Durbin count model (social model). The results of this study are threefold. First, candidate weighting schemes which consider mutual friendship (i.e. the number of mutual friends two people have in common) exclusively produced higher log-likelihoods than weighting schemes which also consider whether individuals are direct friends (i.e. whether the two individuals are friends themselves). Second, the results of the social model were compared with those of a non-social model. These results suggest that there exist major flaws in using a non-social model to represent variables which may be socially dependent and correlated. Finally, results suggest that individuals tend to have friends who, on average, make more trips than they do. With a growing number of people using online social networks, exploring and understanding friendship influences on travel behavior will help the transportation industry better recognize future travel needs.