This paper presents an alternative methodology to represent rebars and their bond-slip behavior against concrete based on coupling finite elements. Among the main features and advantages of the proposed technique are: (i) the coupling between the two independent meshes for concrete and reinforcement does not introduce any additional degree of freedom in the global problem; (ii) both rigid and non-rigid coupling can be used to represent the particular cases of perfect adherence and general bond-slip behavior, respectively; (iii) rebars of arbitrary geometry and orientation can be modeled; (iv) the methodology can be applied to 2D and 3D problems and (v) the formulation can be adapted to other type of finite elements and implemented easily in any existing FEM code. Constitutive models based on continuum damage mechanics are used to represent the concrete behavior and concrete-rebar interaction. A number of numerical analyses are performed and the results obtained show the versatility and accuracy of the proposed methodology.

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Código de Financiamento 001) pelo apoio financeiro, ao Programa de Pós-Graduação em Engenharia Civil da Escola Politécnica da Universidade de São Paulo (USP) pela estrutura, aos funcionários e também aos professores os quais tive o privilégio de ter aulas e adquirir conhecimento. Aos meus colegas do Laboratório de Estruturas e Materiais Estruturais (LEM) André, Marcos, Paulo Vitor, Fernanda, Tarcísio, Felipe e especialmente ao Gusta, pela amizade e a Bel pelo apoio constante, amizade e companheirismo. Finalmente, eu gostaria de dedicar essa dissertação à minha família, aos meus irmãos Carol e Marquinhos e em especial aos meus pais Marcos e Dagmar pelo apoio incondicional e por sempre incentivar e acreditar que a educação é sempre o melhor caminho. A vocês o meu eterno agradecimento.ii Abstract 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 ...