Two-Parameter Kinematic Approach for Shear Strength of Deep Concrete Beams with Internal FRP Reinforcement

Tests of deep concrete beams with internal fiber-reinforced polymer (FRP) reinforcement have shown that such members can exhibit lower shear strength than members with conventional steel reinforcement. To model this effect, the current paper proposes an approach based on a two-parameter kinematic theory (2PKT) for conventional deep beams. The 2PKT is built on a kinematic model with two degrees of freedom that describes the deformation patterns of cracked beams. Using this theory shows that large strains in FRP longitudinal reinforcement result in reduced shear resistance of the critical loading zones (CLZ) of deep beams. The original 2PKT is therefore modified by introducing a reduction factor for the shear carried by the CLZ. The extended 2PKT approach is then applied to a database of 39 tests of FRP-reinforced deep beams from the literature, resulting in an average shear strength experimental-to-predicted ratio of 1.06 and a coefficient of variation of 18.3%. The results show that the 2PKT adequately captures the effects of the stiffness of the reinforcement, section depth, concrete strength, and shear-span-to-depth ratio on the shear strength of FRP-reinforced deep beams.