As lajes formadas por vigotas pré-moldadas são utilizadas em larga escala no Brasil, em especial as formadas por vigotas treliçadas. As facilidades no manuseio e economia de fôrmas são algumas das vantagens do sistema. Apesar de serem muito utilizadas, ainda existe necessidade de estudo das recomendações no sentido de basear o projeto destas lajes. Os objetivos deste trabalho são: (a) contribuir no projeto de lajes formadas por vigotas com armação treliçadas através de uma análise crítica da bibliografia pesquisada; (b) tratar de temas pouco disseminados no que se refere ao cálculo de lajes pré-moldadas; (c) fornecer recomendações de projeto através de exemplo resolvido que aborda as principais dúvidas de projetistas da área. Neste exemplo avaliam-se as lajes, entre outros aspectos, quanto às flechas iniciais e ao longo do tempo, vibrações e momento negativo nos apoios. Os resultados são analisados e confrontados com as indicações da bibliografia. Comprova-se o fato destas lajes serem mais susceptíveis quanto às vibrações causadas por caminhada e mostra a dificuldade em atender à ABNT NBR 6118:2003. O vão máximo admissível para uma laje do exemplo de aplicação é 28% inferior quando comparado à laje maciça de mesma espessura na análise da vibração excessiva. Enfatiza a importância em prever armadura contra o colapso progressivo e demonstra que o aumento de consumo de aço em 5% é pequeno quando comparado ao total, para uma laje do exemplo de aplicação. / Precast slabs are used in large scale in Brazil, special those formed by lattice reinforcement. Facilities handling and economy mold are some of the advantages of the system. The objectives of this work are: (a) improve study of the design of slabs formed by precast lattice reinforcement through a review of literature; (b) address topics a little spread regards to the calculation of precast slabs; (c) providing design recommendations through examples solved by addressing the main concerns of designers in the area. This example evaluate the slabs to initials and long-term deflections, vibrations and bending moment at the supports. The results are analyzed and compared with indications in the literature. It demonstrates the suscetibility of the slabs for vibrations caused by walking and shows the difficulty in following ABNT NBR 6118:2003. The maximum span for one slab of the aplication example is 28% slower than solid slabs with the same thickness in excessive vibration analysis. This dissertation emphasizes the importance of predicting reinforcement against progressive collapse and shows the increase in steel consumption is small compared to the total, for one slab of the example.

As lajes formadas por vigotas pré-moldadas são utilizadas em larga escala no Brasil, em especial as formadas por vigotas treliçadas. As facilidades no manuseio e economia de fôrmas são algumas das vantagens do sistema. Apesar de serem muito utilizadas, ainda existe necessidade de estudo das recomendações no sentido de basear o projeto destas lajes. Os objetivos deste trabalho são: (a) contribuir no projeto de lajes formadas por vigotas com armação treliçadas através de uma análise crítica da bibliografia pesquisada; (b) tratar de temas pouco disseminados no que se refere ao cálculo de lajes pré-moldadas; (c) fornecer recomendações de projeto através de exemplo resolvido que aborda as principais dúvidas de projetistas da área. Neste exemplo avaliam-se as lajes, entre outros aspectos, quanto às flechas iniciais e ao longo do tempo, vibrações e momento negativo nos apoios. Os resultados são analisados e confrontados com as indicações da bibliografia. Comprova-se o fato destas lajes serem mais susceptíveis quanto às vibrações causadas por caminhada e mostra a dificuldade em atender à ABNT NBR 6118:2003. O vão máximo admissível para uma laje do exemplo de aplicação é 28% inferior quando comparado à laje maciça de mesma espessura na análise da vibração excessiva. Enfatiza a importância em prever armadura contra o colapso progressivo e demonstra que o aumento de consumo de aço em 5% é pequeno quando comparado ao total, para uma laje do exemplo de aplicação. / Precast slabs are used in large scale in Brazil, special those formed by lattice reinforcement. Facilities handling and economy mold are some of the advantages of the system. The objectives of this work are: (a) improve study of the design of slabs formed by precast lattice reinforcement through a review of literature; (b) address topics a little spread regards to the calculation of precast slabs; (c) providing design recommendations through examples solved by addressing the main concerns of designers in the area. This example evaluate the slabs to initials and long-term deflections, vibrations and bending moment at the supports. The results are analyzed and compared with indications in the literature. It demonstrates the suscetibility of the slabs for vibrations caused by walking and shows the difficulty in following ABNT NBR 6118:2003. The maximum span for one slab of the aplication example is 28% slower than solid slabs with the same thickness in excessive vibration analysis. This dissertation emphasizes the importance of predicting reinforcement against progressive collapse and shows the increase in steel consumption is small compared to the total, for one slab of the example.

[Truncated abstract] As a consequence of the increase in terrorist incidents, many comprehensive researches, both experimental and numerical modelling of structure and blast interaction, have been conducted to examine the behaviour of civilian structures under dynamic explosion and its impact. Nevertheless most of the works in literature are limited to response of simple structures such as masonry walls, reinforced concrete beams, columns and slabs. Although these studies can provide researchers and structural engineers a good fundamental knowledge regarding blast load effect, it is more likely for blast load to act upon entire structures in actual explosion events. The interaction between blast load and structures, as well as the interaction among structural members may well affect the structural response and damage. Therefore it is necessary to analyse more realistic reinforced concrete structures in order to gain an extensive knowledge on the possible structural response under blast load effect. Among all the civilian structures, bridges are considered to be the most vulnerable to terrorist threat and hence detailed investigation in the dynamic response of these structures is essential. This thesis focuses on the study of the response of a modern cable-stayed bridge under blast loadings. ... Firstly, analysis is conducted to examine the failure of four main components namely pier, tower, concrete back span and steel composite main span under close proximity dynamic impact of a 1000 kg TNT equivalent blast load. Secondly, based on such results, the remainder of the bridge structure is then tested by utilizing the loading condition specified in the US Department of Defence (DoD) guideline with the aim to investigate the possibility of bridge collapse after the damage of these components. It is found that failure of the vertical load bearing elements (i.e. pier and tower) will lead to catastrophic collapse of the bridge. Assuming that terrorist threat cannot be avoided, hence protective measures must be implemented into the bridge structure to reduce the damage induced by explosive blast impact and to prevent bridge from collapse. As such, a safe standoff distance is determined for both the pier and tower under the blast impact of 10000 kg TNT equivalent. This information would allow the bridge designer to identify the critical location for placing blast barriers for protection purpose. For the case of bridge deck explosion, carbon fibre reinforced polymer (CFRP) is employed to examine in respect of its effectiveness in strengthening the concrete structure against blast load. In this research, appropriate contact is employed for the numerical model to account for the epoxy resin layer between the CFRP and concrete. In addition, to ensure that the CFRP can perform to its full capacity, anchors are also considered in the numerical study to minimize the chance of debonding due to the weakening of the epoxy. The results reveal that although severe damage can still be seen for locations in close proximity to the explosive charge, the use of CFRP did reduce the dynamic response of the bridge deck as compared to the unprotected case scenario. Further investigation is also carried out to examine the change in damaged zone and global response through variation in CFRP thickness.

A structure subjected to extreme load due to explosion or human error may lead to progressive collapse. One of the direct methods specified by design guidelines for assessing progressive collapse is the Alternate Load Path method which involves removal of a structural member and analysing the structure to assess its potential of bridging over the removed member without collapse. The use of this method in assessing progressive collapse therefore requires that the vertical load resistance function of the bridging beam assembly, which for a typical laterally restrained reinforced concrete (RC) beams include flexural, compressive arching action and catenary action, be accurately predicted. In this thesis, a comprehensive study on a reliable prediction of the resistance function for the bridging RC beam assemblies is conducted, with a particular focus on a) the arching effect, and b) the catenary effect considering strength degradations. A critical analysis of the effect of axial restraint, flexural reinforcement ratio and span-depth ratio on compressive arching action are evaluated in quantitative terms. A more detailed theoretical model for the prediction of load-displacement behaviour of RC beam assemblies within the compressive arching response regime is presented. The proposed model takes into account the compounding effect of bending and arching from both the deformation and force points of view. Comparisons with experimental results show good agreement. Following the compressive arching action, catenary action can develop at a much larger displacement regime, and this action could help address collapse. A complete resistance function should adequately account for the catenary action as well as the arching effect. To this end, a generic catenary model which takes into consideration the strength degradation due to local failure events (e.g. rupture of bottom rebar or fracture of a steel weld) and the eventual failure limit is proposed. The application of the model in predicting the resistance function in beam assemblies with strength degradations is discussed. The validity of the proposed model is checked against predictions from finite element model and experimental tests. The result indicate that strength degradation can be accurately captured by the model. Finally, the above developed model framework is employed in investigative studies to demonstrate the application of the resistance functions in a dynamic analysis procedure, as well as the significance of the compressive arching effect and the catenary action in the progressive collapse resistance in different designs. The importance of an accurate prediction of the arching effect and the limiting displacement for the catenary action is highlighted.

Nonlinear explicit finite element (FE) simulations are used to study the axial collapse behavior of multi-corner. single- and multi-cell crush tubes under quasi-static and dynamic loading conditions. It is shown that the higher hardening modulus and yield stress increases the crush force and its resulting energy absorption. Moreover, the multi-cell tubes are found to have complicated collapse modes because of the geometrical complexity of the corner region unlike single-cell tubes. it was also shown that the stress wave propagation has a significant effect on the formation of crush modes in the tubes without imperfections whereas this effect can be ignored in tubes with imperfection or trigger mechanism. An analytical formula for the prediction of mean crush force of multi-corner multi-cell tubes is derived based on the super folding element theory. The analytical predictions for the mean crush force are found to be in good agreement with the FE solutions. Results also show a strong correlation between the cross-sectional geometry and the crash behavior with the method of connecting the inner to the outer walls having large influence on the energy absorption.

This project involves a failure analysis of the internal structural collapse that occurred in World Trade Center 5 (WTC 5) due to fire exposure alone on September 11, 2001. It is hypothesized that the steel column-tree assembly failed during the heating phase of the fire. The results of this research have serious and far-reaching implications, for this method of construction is utilized in approximately 20,000 existing buildings and continues to be very popular. Catastrophic failure during the heating phase of a fire would endanger the lives of firefighters and building occupants undergoing extended egress times (e.g., high-rise buildings), or relying upon defend-in-place strategies (e.g., hospitals). Computer software was used to reconstruct the fire event and predict the structural performance of the assembly when exposed to the fire. Results from a finite element, thermal-stress model confirms this hypothesis, for it is concluded that the catastrophic, progressive structural collapse occurred approximately 2 hours into the fire exposure.

Engineered structures are designed to resist all expected loadings without failure. However, structural failures do occasionally occur due to inadequate design and construction, especially for extreme and abnormal loads. This thesis concerns the progressive collapse of structures due to abnormal loading events, and develops a method of advanced analysis for predicting the progressive collapse behaviour of building structures in the plastic limit state. Combined-stress failure states and stiffness degradation models are proposed to simulate plastic deformation of structural members. Elliptic force-deformation relationships are employed to model the nonlinear material behaviour of members. The stiffness degradation of semirigid connections is modeled by a moment-rotation relationship with four parameters. Having the proposed nonlinear model, a generic member stiffness matrix is derived taking into account elastic-plastic bending, shearing and axial deformations. A computer-based incremental-load nonlinear analysis procedure is developed that progressively updates member stiffness using reduction factors that simulate degraded stiffness behaviour. Three types of localized damage modes are investigated to identify different connection damage scenarios. Account is taken of any debris loading that occurs when disengaged structural components fall onto lower parts of the structure. The associated dynamic effect is taken into account for the quasi-static analysis by utilizing an impact amplification factor. Any progressive collapse occurring thereafter involves a series of failure events associated with topological changes. The progressive-failure analysis procedure is based on the alternate-load-path method suggested in the design and analysis guidelines of the General Services of Administration (GSA, 2003) and the Department of Defense (DoD, 2005). The residual load carrying capacity of the damaged framework is analyzed by incrementally applying prevailing long-term loads and impact debris loads. The deterioration of structural strength is progressively traced to the state at which either global stability is reached or progressive collapse to ground level occurs for part or all of the structure. The analysis procedure is extensively illustrated for several planar steel moment frames, including account for the influence of damaged connections and semi-rigid connection behaviour. The results obtained demonstrate that the proposed method is potentially a powerful tool for the analysis of steel building structures under normal and abnormal loads.

Engineered structures are designed to resist all expected loadings without failure. However, structural failures do occasionally occur due to inadequate design and construction, especially for extreme and abnormal loads. This thesis concerns the progressive collapse of structures due to abnormal loading events, and develops a method of advanced analysis for predicting the progressive collapse behaviour of building structures in the plastic limit state. Combined-stress failure states and stiffness degradation models are proposed to simulate plastic deformation of structural members. Elliptic force-deformation relationships are employed to model the nonlinear material behaviour of members. The stiffness degradation of semirigid connections is modeled by a moment-rotation relationship with four parameters. Having the proposed nonlinear model, a generic member stiffness matrix is derived taking into account elastic-plastic bending, shearing and axial deformations. A computer-based incremental-load nonlinear analysis procedure is developed that progressively updates member stiffness using reduction factors that simulate degraded stiffness behaviour. Three types of localized damage modes are investigated to identify different connection damage scenarios. Account is taken of any debris loading that occurs when disengaged structural components fall onto lower parts of the structure. The associated dynamic effect is taken into account for the quasi-static analysis by utilizing an impact amplification factor. Any progressive collapse occurring thereafter involves a series of failure events associated with topological changes. The progressive-failure analysis procedure is based on the alternate-load-path method suggested in the design and analysis guidelines of the General Services of Administration (GSA, 2003) and the Department of Defense (DoD, 2005). The residual load carrying capacity of the damaged framework is analyzed by incrementally applying prevailing long-term loads and impact debris loads. The deterioration of structural strength is progressively traced to the state at which either global stability is reached or progressive collapse to ground level occurs for part or all of the structure. The analysis procedure is extensively illustrated for several planar steel moment frames, including account for the influence of damaged connections and semi-rigid connection behaviour. The results obtained demonstrate that the proposed method is potentially a powerful tool for the analysis of steel building structures under normal and abnormal loads.

Les notions de robustesse structurale sont intégrées dans les codes de conception européens suite à l'effondrement partiel et progressif de la tour Ronan Point de Canning Town à Londres (Angleterre, 16.05.1968). Le cadre réglementaire des Eurocodes définit la robustesse comme l'aptitude d'une structure à résister à des événements accidentels dits identifiés (incendies, explosions, chocs) ou non identifiés (conséquences d'une erreur humaine, attentats) sans présenter de dégâts disproportionnés par rapport à la cause d'origine. Cette définition incite les ingénieurs à inclure dans les procédures de conception les notions de dommage initial (défaillance locale) et de dommage disproportionné (défaillance globale). L'objectif de ces travaux de thèse est de développer un outil de simulation de la robustesse de structures lorsque des incertitudes de sollicitations (évènement accidentel) et / ou une faute de dimensionnement (conception ou de réalisation) interfèrent avec les dimensionnements réglementaires. La robustesse est évaluée à travers un indice compris entre 0 (structure peu robuste) et 1 (structure très robuste) et calculé à partir des probabilités de défaillance initiale et globale. Cette thèse propose une méthodologie reposant sur la recherche d’arbres complets d'évènements illustrant l'ensemble des cheminements potentiels d'une défaillance initiale localisée jusqu'à la ruine globale. L'approche développée s'applique aux structures hyperstatiques, dans lesquelles la rupture d'un ou plusieurs éléments n'entraine pas systématiquement la ruine de l'ensemble de la structure. En effet, les éléments non endommagés restants peuvent être en mesure de supporter les chargements externes par une redistribution des efforts internes.La procédure est illustrée dans les cas de structures unidimensionnelles hyperstatiques de poutres bi-encastrées et d'un portique référencé dans les normes et classiquement étudié dans la littérature. Le mode local de défaillance de nos simulations est la formation d'une rotule (fragile ou plastique) lorsque le moment sollicitant appliqué atteint la valeur du moment résistant d'une section droite. Deux types de lois probabilistes, Gaussiennes et Log-normales, sont testées par l'approche développée et par des simulations Monte-Carlo. Les variables aléatoires choisies peuvent être indépendantes ou corrélées. Nous présentons les résultats sous forme d’arbres d'évènements comportant l'ensemble des branches exclusives, sans intersection entre branches issues d’un même nœud. Cette spécificité permet de calculer des indices caractérisant la robustesse de la structure selon chaque scénario.L'analyse de l’arbre des évènements et des indices de robustesse permet de mettre en évidence les fragilités potentielles pouvant engendrer une défaillance généralisée d'une structure vis-à-vis d’accidents ou d’actes de malveillance. La méthode développée fournit un outil de simulation et de diagnostic efficace, tant en phase de conception qu'en phase de réhabilitation, permettant d'envisager le renforcement de bâtis existants ou futurs et d'assurer la sécurité des personnes et des ouvrages environnants. / Localized initial failures in constructions can sometimes be followed by disproportionate damage (collapse) spreading to the whole or the major part of a building. Since the partial and progressive collapse of the Ronnan Point tower (London, $1968$) caused by a gas explosion, the concept of robustness has been introduced in standards. Structural robustness is defined as the ability of a structure to withstand unforeseen events causing local damage like fire, explosion or impact, without suffering disproportionate collapse. This definition encourages engineers to include the concepts of initial damage (local failure) and disproportionate damage (global failure) in design procedures. The main objective of this PhD work is to develop a simulation tool in order to highlight the potential weakness in a structure when uncertain sollicitations (accidental events) and/or dimensional fault (design or realization) interfere with the standard predictions. The robustness is evaluated by an index varying from 0 (non-robust structure) to 1 (very robust structure) and is calculated from the initial and global failure probabilities. The proposed methodology is based on an event tree analysis summurizing all the distinct potential scenarios, from the initial damage to the collapse of the structure. The developed approach is applied to statically indeterminate unidimensional structures like beams and frame. The redundancy's consequence is that the break of one or several cross sections will not necessarily lead to the collapse of the whole system: the redistribution of the internal efforts allows the remaining undamaged parts of the structure to support the external (applied) loading. The methodology is illustrated by some examples of clamped-clamped beam and frame, loaded with punctual forces. The cross sections are supposed to have an elastic behaviour until the formation of plastic hinges (local failure). Two types of probabilistic laws, Gaussian and Log-normal, are tested by the developed approach and by Monte-Carlo simulations. The chosen random variables can be either independent or correlated. The resulting complete event tree contains all the exclusive paths from an localised damage to the global failure, without intersection between branches stemming from the same node. This specific property allows to evaluate the robustness indexes of the structure with the ratio between the local and global probabilities, according to each scenario. The analysis of the event tree and of the robustness indexes allows to highlight the potential brittleness which could cause a generalized collapse of the structure with respect to accidents or malicious acts. The developed methodology provides an effective tool of simulation and diagnostic, both in the design phase and in the rehabilitation one, useful to the reinforcement of existing or future buildings and to ensure the safety of people and surrounding structures.

[pt] Edifícios com as mais diversas finalidades estão sujeitos a eventos extremos, tais como impacto de veículos, explosões, e perdas súbitas de membros essenciais para a garantia da sua estabilidade. O colapso progressivo pode ser definido como o processo no qual um dano localizado leva a uma ruína em cadeia, causando a queda de um edifício inteiro ou de parte considerável dele. A perda repentina de determinado membro essencial devido às cargas excepcionais pode desencadear o colapso progressivo de uma estrutura, causando enormes prejuízos humanos e econômicos. O colapso progressivo é fenômeno de natureza dinâmica e não linear, sendo assim, a sua modelagem é complexa. A técnica mais empregada para avaliação do colapso progressivo de estruturas é o método dos caminhos alternativos, que verifica o comportamento da estrutura ante a remoção de um membro essencial de suporte, analisando assim sua capacidade de redistribuição de esforços e resistência ao aumento súbito de carga em uma situação crítica. O trabalho realizou sucessivas análises de modelos da estrutura de um edifício em concreto armado, adotando grau de complexidade progressivo a cada uma delas, utilizando o método dos caminhos alternativos. Analisou-se ao final a efetividade e a importância de cada uma das etapas de análise empregadas no trabalho. A estrutura dimensionada conforme a norma brasileira de concreto armado necessitou de ajustes para atender aos requisitos mínimos de resistência ao colapso progressivo. / [en] Buildings with the most diverse purposes are subject to extreme events, such as vehicle impact, explosions, and sudden loss of members essential to their stability. Progressive collapse can be defined as the process in which a localized damage leads to chain failure, causing the fall of an entire building or a large part of it. The sudden loss of an essential member due to exceptional loads can trigger the progressive collapse of a structure, causing enormous human and economic damage. Progressive collapse is a dynamic nonlinear phenomenon, so its modeling is complex. The most employed technique for evaluation of progressive collapse is the alternative load path method, which verifies the structure behavior after the sudden loss of a load-bearing element, checking its stress redistribution capacity and strength to load increase in critical situations. This work realized successive analysis of structural models of a reinforced concrete building, adopting a progressive complexity to each of them, using the alternative path method. At the end, the effectiveness and importance of each of the analysis steps employed at work were analyzed. The structure designed acoording to the reinforced concrete brazilian standard needed adjustments to meet the minimum resistance requirements of progressive collapse.