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Page 190 was not included in the thesis. / <p> A research program is presented for assessing the plastic collapse load and shake-down load of reinforced concrete continuous beams. This investigation attempts to establish a range of validity of simple plastic theory when applied to the under-reinforced concrete beams and to determine the sensitivity of such structures to variable repeated loading. In attempt for more accurate prediction of the behaviour of reinforced concrete beams when subjected to variable repeated loading, the numerical beam analysis was developed.</p> <p> An experimental program was conducted on 10 reinforced concrete continuous beams. Deflections and strains of these specimens of nearly prototype size were measured and compared with predicted values at critical cross-sections. Resulting conclusions and recommendations for further research are made.</p> / Thesis / Master of Engineering (MEngr)

CoordenaÃÃo de AperfeÃoamento de Pessoal de NÃvel Superior / The reinforced concrete structures, when properly designed and performed, have prolonged its life. However, the lack of proper maintenance, acting loads greater than the design ones, pathological manifestations due to aggressive environment and accidents can impair the performance of the structure requiring the need for repair or structural strengthening. The technique of structural strengthening with application of carbon fiber reinforced polymer (CFRP), bonded externally to the reinforced concrete has advantages such as fast execution, which added to the characteristics of the composite as a high modulus of elasticity make wide its use. The aim of this study is to analyze through an experimental program the structural behavior of reinforced concrete beams strengthened in bending with CFRP. The methodology used was the production of three groups of five RC beams each one, with the same dimension of rectangular cross section, for bending test. The first group of beams was called VA. The second and third groups, called VB and VC and had different ratio of reinforcement. In each group of five beams, one beam was not strengthened (reference beam) and the remaining beams were strengthened with two, three, four and five layers of carbon fiber. The experimental results indicate the efficiency of strengthening, noting an increase in stiffness in all strengthened beams. The increase of load capacity was also observed in all groups of beams varying between 9,11% and 16,69%, 55,14% and 86,83%, 89,46% and 126,18%, of the beams of group VA, VB and VC, respectively in relation to the reference beam of each group. Of the carried through study was observed the excellent performance of strengthening in bending with carbon fiber especially in beams with the lowest ratios of reinforcement (group C), besides gathering a lot of information that can be useful for design criteria of the recovered and strengthened structures. / As estruturas de concreto armado, quando convenientemente projetadas e executadas tÃm sua vida Ãtil prolongada, porÃm, a falta de manutenÃÃo adequada, as solicitaÃÃes de cargas superiores Ãs de projeto, as manifestaÃÃes patolÃgicas devido ao meio ambiente agressivo e a ocorrÃncia de acidentes podem comprometer o desempenho da estrutura exigindo a necessidade de uma recuperaÃÃo ou reforÃo estrutural. A tÃcnica de reforÃo estrutural com a aplicaÃÃo de polÃmeros reforÃados com fibra de carbono (PRFC) colados externamente a peÃas de concreto armado apresenta vantagens como a rÃpida execuÃÃo que, somada a caracterÃsticas do compÃsito como alto mÃdulo de elasticidade fazem largo o seu uso. O objetivo desse trabalho à analisar atravÃs de um programa experimental o comportamento estrutural de vigas de concreto armado reforÃadas à flexÃo com PRFC. A metodologia utilizada foi a produÃÃo de trÃs grupos de vigas de concreto armado, com a mesma dimensÃo de seÃÃo transversal retangular para ensaio à flexÃo. O primeiro grupo, denominado grupo VA, foi dimensionado com seÃÃo normalmente armada. O segundo e terceiro grupo de vigas, aqui denominados grupo VB e grupo VC, respectivamente, foram dimensionados com seÃÃo subarmada, com taxas de armaduras distintas. Cada grupo possuÃa cinco vigas, sendo que, uma viga nÃo foi reforÃada (de referÃncia) e as demais vigas foram reforÃadas com duas, trÃs, quatro e cinco camadas de fibra de carbono. Os ensaios experimentais comprovaram a eficiÃncia do reforÃo, constatando-se um aumento de rigidez de todas as vigas reforÃadas. Observou-se tambÃm o aumento da capacidade resistente em todos os grupos de vigas, variando entre 9,11% e 16,69%, 55,14% e 86,83%, 89,46% e 126,18%, das vigas dos grupos VA, VB e VC, respectivamente, em relaÃÃo à viga de referÃncia de cada grupo. O estudo demonstrou o excelente desempenho do reforÃo à flexÃo com fibra de carbono, especialmente nas vigas com menores taxas de armadura (grupo VC), alÃm de reunir uma sÃrie de informaÃÃes que podem ser Ãteis para critÃrios de projeto de estruturas recuperadas e reforÃadas.

The use of fiber reinforced plastics (FRP) in repairing and strengthening bridges has been researched in recent years. In particular, attaching unidirectional FRP to the tension face of reinforced concrete beams has provided an increase in stiffness and load capacity of the structure. However, due to the brittle nature of the unidirectional FRP, the ductility of the beam decreases. One possible solution to this problem is the use of cross-ply or off-axis FRP laminates. This thesis focuses on the investigation of the flexural behavior of reinforced concrete beams strengthened with one of two different FRP orientations (0°/90° and ±45°). More particularly, the change in strength and ductility of the beams as the number of FRP layers are altered is investigated. Seven under-reinforced concrete beams were constructed and tested to failure. With the exception of the control beam, each specimen was applied with two, three, or four layers of either 0°/90° and ±45° FRP orientations. To predict the flexural behavior of the specimens, a theoretical model was derived using basic concepts, past research, and the tested properties of the concrete, steel reinforcement, and FRP. Also, two methods were used to analyze the ductility of the tested beams. Along with the test details of each specimen; the moment, deflection, CFRP strain, crack patterns, and mode of failure are discussed. The results included an increase in load capacity with respect for the number of CFRP layers applied for both orientations. Also, the ductility of the beams were reduced by adding CFRP orientations. / Master of Science

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.

An analytical method for determining the crack spacing and crack width in reinforced concrete beams and one-way slabs is presented in this thesis. The locations and the distribution of cracks developed in a loaded member are predicted using the calculated concrete stress distributions near flexural cracks. To determine the stresses, a concrete block bounded by top and bottom faces and two transverse sections of the beam is isolated and analysed by the finite element method. Two types of blocks are analysed. They are: (i) block adjacent to the first flexural crack, and (ii) block in between successive cracks. The calculated concrete stress distribution adjacent to the first flexural crack is used to predict the locations of primary cracks (cracks formed at sections where the stresses have not been influenced by nearby cracks). The concrete stress distributions in between successive cracks, calculated for various crack spacings and load levels, are used to predict the formation of secondary cracks in between existing cracks. The maximum, minimum and the average crack spacing at a given load level are determined using the particular crack spacing that would produce a concrete tensile stress equal to the flexural strength of concrete. The resulting crack width at reinforcement level is determined as the relative difference in elastic extensions of steel and surrounding concrete. The accuracy of the present method is verified by comparing the predicted spacing and width of cracks with those measured by others. The analytical method presented in this thesis is subsequently used to investigate the effects of various variables on the spacing and width of cracks, and the results are presented. These results are used to select the set of parameters that has the most significant effect. A parametric study is then carried out by re-calculating the spacing and width of cracks for the selected parameters. Based on the results of this parametric study, new formulas are developed for the prediction of spacing and width of cracks. The accuracy of these formulas is ascertained by comparing the predicted values and those measured by other investigators on various types of beams under different load levels. The calculated stress distributions between successive cracks are also used to develop a new method of incorporating the tension stiffening effect in deflection calculation. First, curvature values at sections between adjacent cracks are determined under different load levels, using the concrete and steel stresses. These results are used to develop an empirical formula to determine the curvature at any section between adjacent cracks. To verify the accuracy of the new method, short-term deflections are calculated using the curvature values evaluated by the proposed formula for a number of beams, and the results are compared with those measured by others.

Split Concrete Model (SCM) is a unified approach towards modeling shear behavior in concrete. SCM is essentially a rational model which is evaluated and modified using a large experimental database.The shear strength of the concrete beam is modeled as the sum of the contribution of concrete, transverse reinforcement, longitudinal reinforcement and bond between concrete and longitudinal reinforcement. Concrete does not contribute to the shear strength after the formation of the crack. In SCM, this is shown to be accurately modeled by only considering the second branch of the critical crack while computing the contribution of concrete towards shear strength of the beam. Formation of the second branch of the critical crack and immediate subsequent failure of the beam has been compared to the split-cylinder test, which forms the conceptual basis of SCM.SCM computes the concrete contribution using the split tensile strength and the area under compression of the concrete beam. For cases where a split-cylinder test is not performed, a mathematical model is proposed to compute the split tensile strength using the compressive strength of concrete available from experimental results. This model is proposed using advanced statistical methods, including weighted residuals and Box-Cox transformation and is validated using various statistical procedures. The transverse reinforcement contributes to the shear strength of the concrete beam only after the formation of the crack. In SCM, this is shown to be accurately modeled by only considering the first branch of the critical crack while computing the contribution of the transverse reinforcement towards shear strength of the beam, instead of the conventional approach of considering the entire length of the crack. The contribution of the longitudinal steel and bond between concrete and longitudinal steel and concrete is accurately modeled unlike the conventional approaches which do not consider this contribution.Evaluation using the database shows that SCM can predict accurate results for all ranges of strength, depth, reinforcement ratio, and shear span to depth ratio of the beam. This shows that all the influencing parameters for concrete shear strength have been correctly modeled in SCM. SCM gives more accurate results as compared to current codified approaches as verified with design examples. Finally, specific recommendations have been made indicating how the shear design requirements in the current ACI code can be modified.

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.