Impact response analysis and prediction of FRP-RC beams with varying flexural stiffness: Numerical simulation and modified two-DOF calculation

The damage behavior and simplified calculation of fiber-reinforced polymer reinforced concrete (FRP-RC) beams subjected to impact loading have attracted substantial attention. In this study, a finite element model incorporating strain rate was employed. Based on the model, the progressive damage behavior and nonlinear impact response of FRP-RC beams with varying stiffness under hammer-to-beam mass ratios were examined. The results indicate that in the investigated conditions, the damage mode of FRP-RC beams does not vary with the changes in the tension reinforcement ratio, but is affected by the hammer-to-beam mass ratio. Due to the absence of a yielding stage for FRP bars, a nonlinear alteration occurred in the rebound of the FRP bars' strain and the beam's displacement with a redistribution of stress. When the reinforcement ratio varies from 0.32% to 3.37%, the peak displacements, reaction and impact forces vary by 25%-49%, 53%-78%, and 0.1%-1% under different mass ratios, respectively. The reinforcement ratio does not change the relationship between the mass ratio and the curve shape of the impact force time history. Additionally, an improved two-degree-of-freedom model considering the FRP's elastic brittleness effect and modified contact stiffness scaling factor was developed, their accuracy was verified. However, there are still many inconveniences to applying the two-DOF model in engineering. Consequently, based on the above two-DOF model, explicit formulas considering contact stiffness, bending stiffness, impactor velocity and mass for displacement and impact force response of impacted FRP reinforcement concrete beams were proposed, which greatly facilitates engineering calculations.