Post-yielding deflection calculation of flexural hybrid reinforced concrete with a combination of fiber reinforced polymer and steel bars

Flexural hybrid reinforced concrete members with fiber reinforced polymer (FRP) and steel bars (hybrid-RC) exhibit significant post-yielding stiffness due to the contribution of tensile FRP bars. To predict the post-yielding deflection of hybrid-RC members, the Bischoff’s model for effective moment of inertia is extended into the post-yielding stage. Based on this extended model, expressions for equivalent moment of inertia, which consider the variation in stiffness along the member span with and without tension stiffening, are proposed. Obtaining close-formed solutions for the yielding moment of hybrid-RC cross sections, a critical parameter for determining the post-yielding effective moment of inertia, proves challenging due to the unknown state of compressive concrete. Therefore, a simplified equation to determine the yielding moment are proposed by regression of data derived from numerical sectional analyses. An experimental database including 92 hybrid-RC beams collected from published literature is established. The performance of the proposed equation for the yielding moment and expressions for the equivalent moment of inertia are evaluated using the database. The results indicate that the proposed equation can effectively predict the yielding moments of hybrid-RC beams. Furthermore, using a constant effective moment for predicting the post-yielding deflection is effective for the specimens with relatively high reinforcement ratios. The benefit of considering the stiffness variation along the member span is evident when dealing with lightly-reinforced concrete members.