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Deep concrete beams are characterized by small shear-span-to-depth ratios and high shear resistance. Owing to their high strength, they are used as transfer girders in buildings, cap beams in bridges, and pile caps in foundations. It is also characteristic of deep beams that they develop complex deformation patterns and cannot be modeled based on the plane-sections-remain-plane hypothesis. This thesis focuses on modelling the complex shear behavior of fiber-reinforced concrete (FRC) deep beams. While deep beams are typically reinforced only with steel bars in the form of flexural and shear reinforcement, experimental studies have shown that the addition of steel fibers in the concrete can enhance their shear behavior.
The main aim of this thesis is to study a five-spring model for deep beams with conventional reinforcement proposed by Mihaylov et al. (2015), and to extend this model to deep beams with FRC. The five-spring model uses only two kinematic parameters to describe the deformations in deep beams. The extended model captures the complete load-displacement response of FRC beams by accounting for three effects associated with the steel fibers: 1) tension in the fibers crossing the shear cracks; 2) enhanced ductility of the critical compressed zones in deep beams; and 3) tension stiffening effect on the flexural reinforcement. To account for these three local effects, existing models from the literature are studied, compared, and validated. Each of the models is implemented in a Matlab code and is validated with relevant material tests. It is shown that the most suitable models for the modeling of the three effects were proposed by Lee et al. (2013), Ou et al. (2012) and Lee et al. (2013). Once these models were validated, they were implemented in the global framework provided by the five-spring model for deep beams. 
The extended five-spring model is validated against a database of tests of FRC deep beams collected from the literature. It is shown that the predicted shear strengths are in good agreement with the measured values. The validated model is then used to perform a parametric study focused on the effects of the shear-span-to-depth (a/d) ratio, shear and longitudinal reinforcement ratios, as well as fiber volumetric ratio on the shear behavior of deep beams. Increased shear resistance was observed for increasing the shear and longitudinal reinforcements, as well as increasing the fiber volumetric ratio. By increasing a/d ratio, the shear strength decreased. At last, the effectiveness of shear reinforcement was compared with the fiber reinforcement for different a/d ratios. It is concluded that the fiber reinforcement is more effective only for a/d ratios lower than 0.8, while the shear reinforcement is more effective for higher a/d ratios.

Two-parameter kinematic theory --- Five-spring model --- Fiber-reinforced concrete --- Deep beams --- Ingénierie, informatique & technologie > Ingénierie civile