Improved finite difference analysis of dynamic responses of concrete members reinforced with FRP bars under explosion

An improved finite difference (FD) procedure to predict the dynamic response of concrete members reinforced with fiber reinforced polymer (FRP) bars under explosion is proposed. This method no longer needs the empirical formulae of the moment-curvature relationship, which is only suitable for concrete members reinforced with steel bars but inappropriate for those reinforced with FRP bars. The equilibrium of the horizontal force of the structural element, considering the strain rate effects of the concrete and the reinforcing bars, is established to calculate the depth of the neutral axis based on a numerical solution of nonlinear equations. A layered-section-based analysis model is used to calculate the strain rate effect of the compressive concrete. The Euler-Bernoulli's beam theory is solved numerically using an explicit FD scheme. The accuracy of the FD model is validated by the experiments of the concrete members reinforced with steel bars and FRP bars, respectively. The FD results are also compared with those obtained by single-degree-of-freedom (SDOF) analysis and finite element (FE) analysis, respectively. The FD procedure is accurate, applicable and convenient to predict the dynamic responses of the flexural concrete members reinforced with FRP bars, as well as those of the members reinforced with steel bars.