When subjected to a combination of moment and shear force, a reinforced concrete (RC) beam with either little or no transverse reinforcement can fail in shear before reaching its full flexural strength. This type of failure is sudden in nature and usually disastrous because it does not give sufficient warning prior to collapse. To prevent this type of shear failure, reinforced concrete beams are traditionally reinforced with stirrups. However, the use of stirrups is not always cost effective since it increases labor costs, and can make casting concrete difficult in situations where closely-spaced stirrups are required. The use of steel fiber reinforced concrete (SFRC) could be considered as a potential alternative to the use of traditional shear reinforcement. Concrete is very weak and brittle in tension, SFRC transforms this behaviour and improves the diagonal tension capacity of concrete and thus can result in significant enhancements in shear capacity. However, one of the drawbacks associated with SFRC is that the addition of fibers to a regular concrete mix can cause problems in workability. The use of self-consolidating concrete (SCC) is an innovative solution to this problem and can result in improved workability when fibers are added to the mix. The thesis presents the experimental results from tests on twelve slender self-consolidating fiber reinforced concrete (SCFRC) beams tested under four-point loading. The results demonstrate the combined use of SCC and steel fibers can improve the shear resistance of reinforced concrete beams, enhance crack control and can promote flexural ductility. Despite extensive research, there is a lack of accurate and reliable design guidelines for the use of SFRC in beams. This study presents a rational model which can accurately predict the shear resistance of steel fiber reinforced concrete beams. The thesis also proposes a safe and reliable equation which can be used for the shear design of SFRC beams.

When subjected to a combination of moment and shear force, a reinforced concrete (RC) beam with either little or no transverse reinforcement can fail in shear before reaching its full flexural strength. This type of failure is sudden in nature and usually disastrous because it does not give sufficient warning prior to collapse. To prevent this type of shear failure, reinforced concrete beams are traditionally reinforced with stirrups. However, the use of stirrups is not always cost effective since it increases labor costs, and can make casting concrete difficult in situations where closely-spaced stirrups are required. The use of steel fiber reinforced concrete (SFRC) could be considered as a potential alternative to the use of traditional shear reinforcement. Concrete is very weak and brittle in tension, SFRC transforms this behaviour and improves the diagonal tension capacity of concrete and thus can result in significant enhancements in shear capacity. However, one of the drawbacks associated with SFRC is that the addition of fibers to a regular concrete mix can cause problems in workability. The use of self-consolidating concrete (SCC) is an innovative solution to this problem and can result in improved workability when fibers are added to the mix. The thesis presents the experimental results from tests on twelve slender self-consolidating fiber reinforced concrete (SCFRC) beams tested under four-point loading. The results demonstrate the combined use of SCC and steel fibers can improve the shear resistance of reinforced concrete beams, enhance crack control and can promote flexural ductility. Despite extensive research, there is a lack of accurate and reliable design guidelines for the use of SFRC in beams. This study presents a rational model which can accurately predict the shear resistance of steel fiber reinforced concrete beams. The thesis also proposes a safe and reliable equation which can be used for the shear design of SFRC beams.

When subjected to a combination of moment and shear force, a reinforced concrete (RC) beam with either little or no transverse reinforcement can fail in shear before reaching its full flexural strength. This type of failure is sudden in nature and usually disastrous because it does not give sufficient warning prior to collapse. To prevent this type of shear failure, reinforced concrete beams are traditionally reinforced with stirrups. However, the use of stirrups is not always cost effective since it increases labor costs, and can make casting concrete difficult in situations where closely-spaced stirrups are required. The use of steel fiber reinforced concrete (SFRC) could be considered as a potential alternative to the use of traditional shear reinforcement. Concrete is very weak and brittle in tension, SFRC transforms this behaviour and improves the diagonal tension capacity of concrete and thus can result in significant enhancements in shear capacity. However, one of the drawbacks associated with SFRC is that the addition of fibers to a regular concrete mix can cause problems in workability. The use of self-consolidating concrete (SCC) is an innovative solution to this problem and can result in improved workability when fibers are added to the mix. The thesis presents the experimental results from tests on twelve slender self-consolidating fiber reinforced concrete (SCFRC) beams tested under four-point loading. The results demonstrate the combined use of SCC and steel fibers can improve the shear resistance of reinforced concrete beams, enhance crack control and can promote flexural ductility. Despite extensive research, there is a lack of accurate and reliable design guidelines for the use of SFRC in beams. This study presents a rational model which can accurately predict the shear resistance of steel fiber reinforced concrete beams. The thesis also proposes a safe and reliable equation which can be used for the shear design of SFRC beams.

A finite element model with discrete and explicit representation of steel fibers is applied for modeling the post-cracking behavior of Steel Fiber Reinforced Concrete (SFRC) in order to contribute on the design of beams with combined reinforcement of steel fibers and rebars (RC-SFRC beams). In this numerical approach, concrete and fibers are initially discretized in finite elements in an independent way, avoiding high computational costs due to conforming meshes. Then, coupling finite elements are introduced to describe the concrete-fiber interaction. The steel fibers are discretized using truss finite elements and their behavior described by an elastoplastic constitutive model. The position of each fiber is defined into the specimen by an uniform isotropic random distribution using as reference the concrete finite element mesh. Concrete and concrete-fiber interface are represented using three and fournoded triangular finite elements, respectively, and their behavior represented by appropriate continuum damage models integrated using an implicit-explicit scheme to enhance the robustness and to reduce the expense of computation. Firstly, the numerical tool is applied in the simulation of three-point bending tests according to EN 14651 to verify its ability to obtain the performance parameters of SFRC and for calibrating the material parameters that describe the concrete-fiber interface. Secondly, both numerical and experimental performance parameters of SFRC are used on the design of RC-SFRC beams according to fib Model Code 2010 to study their influence on the amount of bending and shear reinforcements required. Thirdly, the RC-SFRC beams designed are numerically simulated and the results are compared to the designed ones in terms of crack width, mean crack spacing, deflection and ultimate and service loads. Finally, the numerical results of small scale beams are compared to the experimental and the fib Model Code 2010 predictions to study the capability of the numerical tool to simulate the behavior of structural members. The results demonstrated that computational simulations with an appropriated approach to represent the composite may be an important tool to contribute to better understanding its behavior, extrapolating the conditions considered in laboratory and contributing on the design of SFRC structural members. / Um modelo em elementos finitos com representação discreta e explícita de fibras de aço é utilizado para modelar o comportamento pós-fissuração do Concreto Reforçado com Fibras de Aço (CRFA) com objetivo de contribuir para o dimensionamento de vigas com reforço combinado de fibras e armadura convencional (vigas de CACRFA). Na abordagem numérica utilizada para modelagem de CRFA o concreto e as fibras são inicialmente discretizados em elementos finitos de forma independente, evitando altos custos computacionais devido às malhas conformes. Então, elementos finitos de acoplamento são introduzidos para descrever a interação concreto-fibra. As fibras de aço são discretizadas utilizando elementos finitos de treliça e seu comportamento é descrito por um modelo constitutivo elastoplástico Um algoritmo para distribuição isotrópica randômica é utilizado para gerar e distribuir fibras de aço com base na malha de elementos finitos do concreto. O concreto e a interface concreto-fibra são representados utilizando elementos finitos triangulares de três e quatro nós, respectivamente, e seus comportamentos representados por uma modelos apropriados de dano contínuo integrados utilizando um esquema implícito-explícito com objetivo de aumentar a robustez a reduzir o custo computacional. Primeiramente, a ferramenta numérica é aplicada na simulação de ensaios de flexão de três pontos de acordo com EN 14651 para verificar sua capacidade de obter os parâmetros de desempenho do CRFA e para calibrar os parâmetros do material que descrevem a interface concreto-fibra. Em segundo lugar, os parâmetros de desempenho numéricos e experimentais do CRFA são usados no vigas de CA-CRFA de acordo com o fib Model Code 2010, a fim de estudar sua influência na quantidade de armadura de flexão e cisalhamento necessárias. Em terceiro lugar, as vigas de CA-CRFA são numericamente simuladas e os resultados são comparados com os dimensionados em termos de largura de fissura, espaçamento médio entre fissuras, flecha e cargas últimas e de serviço. Finalmente, os resultados numéricos de vigas de pequena escala são comparados com aqueles obtidos experimentalmente e pelo fib Model Code 2010 para estudar a capacidade da ferramenta numérica em simular o comportamento de elementos estruturais. Os resultados demonstraram que a utilização de simulações computacionais com uma abordagem apropriada para representar o compósito podem ser uma importante ferramenta para contribuir para um melhor entendimento do seu comportamento, extrapolando as condições consideradas em laboratório e contribuindo para o dimensionamento de elementos estruturais de CRFA.

A finite element model with discrete and explicit representation of steel fibers is applied for modeling the post-cracking behavior of Steel Fiber Reinforced Concrete (SFRC) in order to contribute on the design of beams with combined reinforcement of steel fibers and rebars (RC-SFRC beams). In this numerical approach, concrete and fibers are initially discretized in finite elements in an independent way, avoiding high computational costs due to conforming meshes. Then, coupling finite elements are introduced to describe the concrete-fiber interaction. The steel fibers are discretized using truss finite elements and their behavior described by an elastoplastic constitutive model. The position of each fiber is defined into the specimen by an uniform isotropic random distribution using as reference the concrete finite element mesh. Concrete and concrete-fiber interface are represented using three and fournoded triangular finite elements, respectively, and their behavior represented by appropriate continuum damage models integrated using an implicit-explicit scheme to enhance the robustness and to reduce the expense of computation. Firstly, the numerical tool is applied in the simulation of three-point bending tests according to EN 14651 to verify its ability to obtain the performance parameters of SFRC and for calibrating the material parameters that describe the concrete-fiber interface. Secondly, both numerical and experimental performance parameters of SFRC are used on the design of RC-SFRC beams according to fib Model Code 2010 to study their influence on the amount of bending and shear reinforcements required. Thirdly, the RC-SFRC beams designed are numerically simulated and the results are compared to the designed ones in terms of crack width, mean crack spacing, deflection and ultimate and service loads. Finally, the numerical results of small scale beams are compared to the experimental and the fib Model Code 2010 predictions to study the capability of the numerical tool to simulate the behavior of structural members. The results demonstrated that computational simulations with an appropriated approach to represent the composite may be an important tool to contribute to better understanding its behavior, extrapolating the conditions considered in laboratory and contributing on the design of SFRC structural members. / Um modelo em elementos finitos com representação discreta e explícita de fibras de aço é utilizado para modelar o comportamento pós-fissuração do Concreto Reforçado com Fibras de Aço (CRFA) com objetivo de contribuir para o dimensionamento de vigas com reforço combinado de fibras e armadura convencional (vigas de CACRFA). Na abordagem numérica utilizada para modelagem de CRFA o concreto e as fibras são inicialmente discretizados em elementos finitos de forma independente, evitando altos custos computacionais devido às malhas conformes. Então, elementos finitos de acoplamento são introduzidos para descrever a interação concreto-fibra. As fibras de aço são discretizadas utilizando elementos finitos de treliça e seu comportamento é descrito por um modelo constitutivo elastoplástico Um algoritmo para distribuição isotrópica randômica é utilizado para gerar e distribuir fibras de aço com base na malha de elementos finitos do concreto. O concreto e a interface concreto-fibra são representados utilizando elementos finitos triangulares de três e quatro nós, respectivamente, e seus comportamentos representados por uma modelos apropriados de dano contínuo integrados utilizando um esquema implícito-explícito com objetivo de aumentar a robustez a reduzir o custo computacional. Primeiramente, a ferramenta numérica é aplicada na simulação de ensaios de flexão de três pontos de acordo com EN 14651 para verificar sua capacidade de obter os parâmetros de desempenho do CRFA e para calibrar os parâmetros do material que descrevem a interface concreto-fibra. Em segundo lugar, os parâmetros de desempenho numéricos e experimentais do CRFA são usados no vigas de CA-CRFA de acordo com o fib Model Code 2010, a fim de estudar sua influência na quantidade de armadura de flexão e cisalhamento necessárias. Em terceiro lugar, as vigas de CA-CRFA são numericamente simuladas e os resultados são comparados com os dimensionados em termos de largura de fissura, espaçamento médio entre fissuras, flecha e cargas últimas e de serviço. Finalmente, os resultados numéricos de vigas de pequena escala são comparados com aqueles obtidos experimentalmente e pelo fib Model Code 2010 para estudar a capacidade da ferramenta numérica em simular o comportamento de elementos estruturais. Os resultados demonstraram que a utilização de simulações computacionais com uma abordagem apropriada para representar o compósito podem ser uma importante ferramenta para contribuir para um melhor entendimento do seu comportamento, extrapolando as condições consideradas em laboratório e contribuindo para o dimensionamento de elementos estruturais de CRFA.