Orientador: Mônica Pinto Barbosa / Banca: Tulio Nogueira Bittencourt / Banca: Rogério de Oliveira Rodrigues / Resumo: Apresenta-se como objeto desta pesquisa o estudo numérico não-linear da ductilidade de vigas de concreto armado convencional e de alto desempenho. Toda a análise numérica é efetuada no código de cálculo baseado no método dos elementos finitos CASTEM 2000, que utiliza o modelo reológico elastoplástico perfeito para o aço, o modelo de Drucker-Prager para o concreto e o método de Newton-Raphson para a solução de sistemas não-lineares. O núcleo deste trabalho concentra-se na obtenção de curvas força - deslocamento e momento - curvatura com a finalidade de quantificar respectivamente os índices de ductilidade global e local das vigas analisadas. De início, confrontam-se as respostas numéricas obtidas com resultados experimentais fornecidos pela literatura a fim de garantir confiabilidade à análise numérica realizada. Posteriormente, efetua-se a determinação da capacidade de deformação inelástica do elemento estrutural em questão, variando-se a resistência à compressão do concreto, a taxa geométrica de armadura longitudinal de tração, a tensão de escoamento das armaduras, o espaçamento entre estribos, a base da seção transversal do elemento estrutural e o efeito escala. Estes parâmetros foram avaliados para dois casos de solicitação: flexão simples tipo I e flexão simples tipo II. O primeiro caso caracteriza-se pela ação de forças simétricas aplicadas à 1/3 e 2/3 do vão e a segunda por uma força centrada no meio do vão. A linha de tendência geral observada foi de uma maior ductilização das vigas sujeitas à flexão simples tipo II, em detrimento às solicitadas por flexão simples tipo I. Quanto ao efeito escala observa-se que a ductilização das vigas é inversamente proporcional à esbeltez das mesmas. / Abstract: The objective of this thesis is the study of the ductility of high and conventional strength reinforced concrete beams by non-linear numerical simulations. The numerical analysis is based on the finite element method implemented in CASTEM 2000. This program uses the constitutive elastoplastic perfect model for the steel, the Drucker-Prager model for the concrete and the Newton-Raphson for the solution of non-linear systems. This work concentrates on the determination of force - displacement and moment - curvature curves with the purpose of quantifying the global and local ductility indexes of the beams. First, the numeric responses are confronted with experimental results found in the literature in order to check the reliability of the numerical analyses. Later, a parametric study is carried on. The inelastic deformation capacity of the structural element is investigated by varying the concrete compressive strength, the longitudinal reinforcement ratio, the yield stress of the reinforcement, the spacing between stirrups, the member section dimensions and the element size. These parameters have been analyzed for two cases: simple type I and simple type II bending. The first case is characterized by the action of applied symmetrical forces to the 1/3 and 2/3 of the beam size and second for a force centered in the middle of the beam size. The general tendency observed points to a high ductilization of the beams subjected to simple type II bending in comparison to the ones subjected to simple type I bending. With respect to the element size, it is noticed that the ductility of the beams is inversely proportional to their slendernesses. / Mestre

Muitas edificações têm apresentado degradação ao longo dos anos em todo o mundo, gerando situações de risco e causando acidentes, de modo que se têm estudado alternativas para se recuperar ou reforçar estruturalmente suas vigas, pilares e lajes. Entre as técnicas desenvolvidas para essas finalidades, destacam-se, atualmente, as que utilizam compósitos de polímeros reforçados com fibras (PRF), de modo que, desde as últimas décadas do século passado, desenvolveram-se os sistemas de reforço estrutural por colagem externa de tecidos e laminados de PRF de carbono (PRFC). Isto deve-se a este tipo de fibra apresentar o melhor conjunto de propriedades necessárias para se reforçarem as estruturas de concreto armado, como altas resistência à tração e módulo de elasticidade longitudinal. Na última década, surgiu o sistema de inserção de laminados de PRFC em entalhes executados no concreto de cobrimento de elementos estruturais preenchidos com resina epóxi. Embora haja resultados de outros pesquisadores, há a necessidade de maiores investigações no Brasil sobre o desempenho dessa nova técnica. Assim se propôs o planejamento experimental desta dissertação, cujo objetivo principal foi a análise experimental do desempenho de sistemas de reforço estrutural à flexão com laminados de PRFC aplicados a vigas de concreto armado ensaiadas com carregamento estático. De um total de dez vigas pré-moldadas, quatro foram testemunhos e seis foram reforçadas à flexão com dois laminados de PRFC através de três sistemas: colagem externa, inserção em entalhes longitudinais preenchidos com resina epóxi e com argamassa com sílica ativa. Analisa-se comparativamente o seu desempenho quanto às cargas máximas, aos deslocamentos verticais no centro do vão e às aberturas de fissuras. Constata-se que as reforçadas com laminados de PRFC inseridos em entalhes longitudinais preenchidos com resina epóxi apresentam os maiores valores de carga máxima e de rigidez. Entretanto as preenchidas com argamassa com sílica ativa obtêm desempenho inferior ao das vigas testemunhos por falta de aderência. Também se conclui que as reforçadas com colagem externa de laminados de PRFC têm os menores deslocamentos verticais no centro do vão. / Many buildings have shown deterioration over the years around the world, creating a hazardous situation and causing accidents, so that they have studied alternatives to recover or strengthen their structural beams, columns and slabs. Among the techniques developed for these purposes, stand out, currently, those using fiber reinforced polymer (FRP) composites. Since the last decades of the last century, it has been developed structural reinforcement systems of externally bonded carbon FRP (CFRP) textiles and laminates. This is due to the type of fiber having the best set of properties that are necessary to strengthen reinforced concrete structures, such as high tensile strength and longitudinal elastic modulus. In the last decade, the near-surface mounted CFRP laminates system executed in grooves in the concrete cover of structural elements filled with epoxy resin came up. Although there are results from other researchers, there is a need for further investigation in Brazil on the performance of this new technique. Thus, the experimental program of this thesis has been proposed, which main objective was the experimental analysis of the performance of bending structural reinforcement systems with CFRP laminates applied to reinforced concrete beams tested under static loading. From a total of ten precast beams, four were for control and six were strengthened in bending with two CFRP laminates composites through three systems: externally bonded, near-surface mounted insertion into longitudinal grooves filled with epoxy resin and mortar with silica fume. Their performance is comparatively analyzed for maximum loads, vertical displacements at mid-span and crack openings. It is concluded that those reinforced with near-surface mounted CFRP laminates inserted into longitudinal grooves filled with epoxy resin shows the highest maximum load and stiffness. However those filled with mortar with silica fume obtained lower performance than the control beams for lack of bonding. In addition, it is concluded that the ones strengthened with externally bonded CFRP laminates have the lowest mid-span vertical displacements.

[pt] Este trabalho tem como objetivo o estudo experimental do comportamento de vigas de concreto armado reforçadas a flexão com CFC sujeitas a carga de impacto. As variáveis adotadas foram a taxa de carregamento e a taxa de reforço. Todas as vigas foram dimensionadas para resistirem ao mesmo carregamento, de forma que a ruptura fosse governada pelo escoamento do aço da armadura longitudinal de tração. O programa experimental consistiu no ensaio de dezoito vigas biapoiadas de concreto armado. Todas as vigas foram construídas com a mesma seção transversal, vão e resistência de concreto, diferindo somente na armadura longitudinal de tração. Foram confeccionados três tipos de vigas, sendo que as vigas com maior taxa de aço de armadura longitudinal de tração não receberam reforço, enquanto que as demais foram reforçadas com CFC de forma a suportar a mesma carga última das vigas sem reforço. Foram realizados ensaios estáticos e dinâmicos. Para a aplicação da carga de impacto utilizou-se um martelo, que liberado de diferentes alturas de queda, forneceu diferentes taxa de carregamento e, consequentemente, diferentes taxas de deformação nas vigas ensaiadas. Os resultados mostraram que as vigas com reforço de CFC possuem menor capacidade de desaceleração do movimento de queda do martelo. Verificou-se que quanto maior a altura de queda do martelo maior é a força máxima de reação das vigas, apresentando um crescimento praticamente linear com o aumento da taxa de carregamento. / [en] An experimental study on the behavior of reinforced concrete beams strengthened in flexure with CFC under impact load was carried out in this work. The main objective was to investigate the effects of the loading rate on the strength of the beams. The variables were the loading rate and the ratio of fiber to steel reinforcement cross sections. All beams were design to resist the same load, in a way that the failure should be governed by the yielding of the longitudinal tension steel reinforcement. The experimental program consisted of the test of eighteen simply supported beams. All the beams had the same cross section, span and concrete strength. The only difference was the amount of longitudinal tension steel and fiber reinforcements. Static and dynamic testing had been carried through. A hammer was used for the impact load application, which was released from different heights, giving different loads rates and, consequently, different deformation rates in the tested beams. The results showed that the beams with reinforcement of CFC had less capacity of movement deceleration of hammer fall. It was observed that the higher the height of the hammer the higher was the maximum force of reaction of the beams, showing practically a linear growth with the increase of the loading rate.

Few decades ago, there were no guidelines for torsion design of reinforced concrete (RC) beams. Hence, many existing beams in older buildings have a lack of adequate torsional strength since they were not properly designed for torsion. One way to regain/rehabilitate adequate torsional strength is through application of externally bonded carbon fiber reinforced polymers (CFRP). To date, American Concrete Institute (ACI) code, as well as other building codes, do not have recommendations or provisions for strengthening RC beams for torsion using fiber-reinforced polymer (FRP) composites due to the inexistence of conclusive experimental and analytical data. Of the very limited works on this behavior, the majority of the focus has been devoted to experimental works. Realistic spandrel beams in a building that lack torsional strength were modelled in this research, and strengthened to examine various behaviors such as load capacity, deflection, torque, twist, crack propagation, ductility, and failure modes. For this purpose, six RC beams were tested: four reference beams and two strengthened beams were used to observe additional capacity through the use of carbon fiber-reinforced polymer (CFRP) sheets. To strengthen the beams, one layer of sheets was completely wrapped around them. Results show an additional torsional capacity of 63% and 178% relative to their respective reference beams. Through strengthening, modes of failure of the beams changed from brittle torsion-dominated failure to shear-flexure failure in both beams. The study also included crack pattern and ductility of test beams. Cracks became smaller in width and more evenly distributed across the torsion-loaded area, and torsional ductility was enhanced by 266% and 165% respectively. Flexural ductility was also greatly enhanced by more than five folds. Finally, using ACI 318-14, ACI 440.2R-02, and available formulae in the literature, the beams were analyzed and the respective values were compared.

External prestressed carbon fibre reinforced polymer (CFRP) straps can be used to strengthen shear deficient reinforced concrete (RC) structures. The strengthening system is associated with a number of parameters including the number of straps, strap locations, strap stiffness, and strap prestress. The initial goal of this research was to identify the optimum values for these parameters in order to design an efficient and effective shear retrofitting system. The shear friction theory (SFT) and modified compression field theory (MCFT) were identified as potential predictive theories to model the shear behaviour of RC beams retrofitted with CFRP straps. Possible modifications to the theories to reflect CFRP prestressed straps were investigated. Two popular optimisation algorithms namely the genetic algorithm (GA) and particle swarm optimisation (PSO) were coded and tested with six test functions. These algorithms were used to find the optimum shear retrofitting configurations and also to reduce the computational cost associated with the SFT and MCFT evaluations. An experimental investigation was carried out to validate the SFT and MCFT predictions for various CFRP strap configurations. The investigation consisted of an unstrengthened control beam and five CFRP strengthened beams. The shear behaviour of the beams was significantly influenced by the CFRP strap configurations. A critical load level where the beam stiffness started to deteriorate significantly was identified. It was found that there was a correlation between this load level and the yielding of the internal shear links and a rapid increase in crack openmg. The SFT and MCFT were validated using the experimental results. The peak shear capacities predicted using the SFT were more consistent with the stiffness deteriorating loads identified in the experimental investigation than with the ultimate loads of the beams. The reinforcement forces and crack opening values found from the SFT were consistent with the experimental results. The MCFT predicted the total shear response, ultimate shear capacity, crack opening, and internal and external reinforcement forces in the beams. The accuracy of the MCFT predictions reduced slightly when either the strap configuration was highly nonuniforrn or the initial prestress level in the straps was relatively low. The shear link yielding load levels predicted by the MCFT were found to be similar to the SFT predictions. By using the coded optimisation algorithms in combination with the SFT or MCFT, the optimum CFRP strap configurations were found for a selected case study. Both theories predicted an offset for the optimum strap locations from the locations associated with equal spacings along the shear span. A reasonable agreement between the SFT and MCFT predictions for the optimum shear strengths and strap locations was observed. A parametric study demonstrated that the concrete strength, internal shear link locations, beam depth, and shear span to depth ratio of the beam do not significantly influence the optimum strengthening configurations for the CFRP strap system. External prestressed carbon fibre reinforced polymer (CFRP) straps can be used to strengthen shear deficient reinforced concrete (RC) structures. The strengthening system is associated with a number of parameters including the number of straps, strap locations, strap stiffness, and strap prestress. The initial goal of this research was to identify the optimum values for these parameters in order to design an efficient and effective shear retrofitting system. The shear friction theory (SFT) and modified compression field theory (MCFT) were identified as potential predictive theories to model the shear behaviour ofRC beams retrofitted with CFRP straps. Possible modifications to the theories to reflect CFRP prestressed straps were investigated. Two popular optimisation algorithms namely the genetic algorithm (GA) and particle swarm optimisation (PSO) were coded and tested with six test functions. These algorithms were used to find the optimum shear retrofitting configurations and also to reduce the computational cost associated with the SFT and MCFT evaluations. An experimental investigation was ca1Tied out to validate the SFT and MCFT predictions for various CFRP strap configurations. The investigation consisted of an unstrengthened control beam and five CFRP strengthened beams. The shear behaviour of the beams was significantly influenced by the CFRP strap configurations. A critical load level where the beam stiffness started to deteriorate significantly was identified. It was found that there was a correlation between this load level and the yielding of the internal shear links and a rapid increase in crack opening. The SFT and MCFT were validated using the experimental results. The peak shear capacities predicted using the SFT were more consistent with the stiffness deteriorating loads identified in the experimental investigation than with the ultimate loads of the beams. The reinforcement forces and crack opening values found from the SFT were consistent with the experimental results. The MCFT predicted the total shear response, ultimate shear capacity, crack opening, and internal and external reinforcement forces in the beams. The accuracy of the MCFT predictions reduced slightly when either the strap configuration was highly nonuniform or the initial prestress level in the straps was relatively low. The shear link yielding load levels predicted by the MCFT were found to be similar to the SFT predictions. By using the coded optimisation algorithms in combination with the SFT or MCFT, the optimum CFRP strap configurations were found for a selected case study. Both theories predicted an offset for the optimum strap locations from the locations associated with equal spacings along the shear span. A reasonable agreement between the SFT and MCFT predictions for the optimum shear strengths and strap locations was observed. A parametric study demonstrated that the concrete strength, internal shear link locations, beam depth, and shear span to depth ratio of the beam do not significantly influence the optimum strengthening configurations for the CFRP strap system.

[pt] No Brasil, o dimensionamento de estruturas de concreto armado segue as recomendações da norma brasileira NBR 6118-2003. A norma brasileira, usa a metodologia de dimensionamento semi-probabilístico que não quantifica a probabilidade de falha de um elemento estrutural. A análise de confiabilidade de estruturas é uma ferramenta que possibilita o cálculo da probabilidade de falha associada a um estado limite e também um dimensionamento para uma determinada probabilidade de falha denominada probabilidade de falha alvo. Este trabalho tem como objetivo desenvolver uma metodologia que possibilite o dimensionamento baseado em confiabilidade de seções de vigas de concreto armado sem e com reforço com compósitos de fibras de carbono. Na análise de confiabilidade desenvolvida foram consideradas como variáveis aleatórias o carregamento, as resistências do aço e do concreto, e a resistência à tração dos compósitos de fibras de carbono com propriedades estatísticas determinadas com base nos resultados dos ensaios realizados no laboratório de Estruturas e Materiais do Departamento de Engenharia Civil da PUC-Rio (LEM-DEC). Exemplos de dimensionamento de seções de vigas de concreto armado submetidas à força cortante e à flexão foram realizados inicialmente por métodos semi-probabilísticos e depois utilizando a metodologia proposta baseada em confiabilidade. A análise dos resultados mostra a viabilidade de um projeto baseado em confiabilidade usando um índice de probabilidade de falha determinado para cada tipo de projeto aliando economia e segurança. / [en] In Brazil, the design of reinforced concrete structures follows the recommendations of Brazilian standard NBR 6118-2003. The Brazilian standard uses the methodology of semi-probabilistic design that does not quantify the probability of failure of a structural element. The reliability analysis of structures is a tool that allows the calculation of probability of failure associated with a limit state and also the design for a given probability of failure. This work aims to develop a methodology that enables the Reliability-based-design of concrete beams sections with and without strengthening with carbon fiber composites. In the reliability analysis were considered as random variables the loads, the compression concrete strenght, yield strenght, and tensile strength of carbon fiber composites with certain statistical properties based on the results of tests performed in the Structures and Materials laboratory at PUC-Rio (LEM-DEC). Examples of reinforced concrete beams strengthened with CFC were performed initially by semi-probabilistic methods and then using the proposed methodology based on reliability. The analysis shows the feasibility of a Reliability-baseddesign using a reliability index of failure probability determined for each type of project combining economy and safety.

No description available.

No description available.

Standards and regulations for dimensioning of load-bearing structures are based on the response of load-bearing structures subjected to loads without variation in time. In the event of an accidental load, e.g. a collision or explosion, causes the load to have a rapid variation in the time resulting in a dynamic response. Previous studies have shown that structures that respond in a certain way under static load have shown a completely different behavior under dynamic influence and therefore it is of interest to study the dynamic response of structures.By testing concrete beams with varying amounts of shear reinforcement subjected to impact loading, the purpose of this report is to analyze how the beams responds in terms of crack width and vibrations when they are exposed to a dynamic load. For comparison, reference tests have also been performed on beams subjected to a quasi-static load.The result of the project shows that the shear reinforcement comes into play as the beams with a larger amount of reinforcement have more capacity to hold the flexural shear cracks together. There is also an indication that the dynamic flexural shear capacity could be lower than static shear capacity as the shear cracks had an increased inclination during dynamic loading for some of the beams. This results in a decreased flexural shear capacity as only one stirrup carried the load across the shear crack.Measured signal shows that beams failing respond when impacted by the similar to a plastic collision, while beams responding with a flexure dominated mode without going to failure instead answer similar to an elastic collision. Furthermore, there is indication that the natural frequencies change significantly due to both flexural cracks and flexural shear cracks.

The objective of this research project was to create a Finite Element Routine for the Linear Analysis of Post-Tensioned beams using the program CALFEM® [20] developed at the division of Structural Mechanics in Lund University, Sweden. The program CALFEM and our own made files were written in MATLAB, an easy to learn and user-friendly computer language. The approach used in this thesis for analyzing the composite beam consists in embedding the steel tendons at the exact location where they intersect the concrete parent elements, without moving the concrete parent element nodes. The steel tendons are represented as one dimensional bar elements inserted into the concrete parent elements, which at the same time are represented as 8 node Iso-parametric plane elements. The theory presented in Ref. [4] served as basis for the modeling of the post-tensioned beams; however it only explained the procedure for modeling simple reinforced concrete beams, due to this we needed to make the appropriate adjustments so we could model post-tensioned beams. Assembly of the tendon stiffness into the concrete elements will depend on the bond interface between the steel and concrete, this bonding effect will be modeled using link elements; the stiffness of this link element used in the concrete-tendon interface will be the change in cohesion (between the grout or duct and the steel tendon) at the interface due to the relative slip between the concrete and the steel elements nodes. Loads (Distributed, Concentrated or Post-Tensioning) are applied directly into the concrete parent elements, and then from their resultant displacement the displacements and forces of all the steel tendon elements are obtained, this is done consecutively for all the post-tensioned tendons at every load increment. Four examples from different references and software programs are solved and compared with our results: (1) A simply reinforced cantilever plate. (2) A reinforced concrete beam, under the effect of a vertical concentrated load at mid-span. For this problem the force distribution along the steel reinforcement is obtained for two conditions, perfectly bonded and perfectly un-bonded, our results are compared with the ones obtained with the program SEGNID. (3) Consists of a continuous un-bonded post-tensioned beam with two spans, without stress losses on the tendon. The reactions at the supports and the concrete stress distribution at the location of the mid-support are obtained after the post-tensioning force is applied at both ends. (4) Consist on a un-bonded post-tensioned beam with stress losses on the tendons due to friction, wobbling and anchorage loss, under gradual loading and consecutive post-tensioning of two tendons, the results are compared with the ones reported using the program BEFE [5] developed at the University of Technology Graz, Austria. The results obtained using our program are very similar to the ones obtained with the other programs, including the more powerful curved embedded approach used by BEFE [5].