Numerical prediction of dynamic response of RC beams

In this study, an attempt has been made to develop a finite-element numerical procedure for the non-linear transient dynamic analysis of reinforced concrete (RC) beams. New material constitutive relationships have been employed depending on various experimental data. Eight-node serendipity degenerated plate elements have been used to represent the concrete beam elements. A layered approach was adopted to discretise the concrete and steel reinforcement through the thickness of the beam. Strain-hardening plasticity and elastic perfectly plastic models have been used to model the compressive behaviour of the concrete used in this study. Strain rate effect was included by assuming the dynamic yield function to be a function of the current strain rate in addition to being the total plastic strain. Geometrical non-linearity in the layered approach is considered in the mathematical model, which is based on the total Lagrangian approach taking into account Von Karman assumptions. A new model is used to consider the effect of tension stiffening in the cracked concrete. Steel reinforcement is considered as an elastic plastic material with linear strain hardening. Implicit Newmark with a corrector–predictor algorithm is employed for time integration of the equation of the motion. A computer program coded in MATLAB has been developed for the non-linear finite-element dynamic analysis of RC beams subjected to the dynamic loadings. Finally, various numerical examples validating the proposed formulation are given.