Degradation of the first frequency of an RC frame with damage levels

Damage in RC structures causes the degradation of stiffness and frequency parameters. In this study, the relationship between the two coefficients and damage severities is numerically investigated considering a three-dimensional (3D) reinforced concrete (RC) frame in which the concrete damage plasticity model (CDPM) and the elastoplastic model are selected to define concrete and reinforcement materials, respectively. Crack propagation of the frame is obtained utilizing a nonlinear static pushover analysis (NSPA). After the pushing procedure, according to the base shear force versus top displacement curve, the bending stiffness of the RC structure is determined rapidly. Thereafter, the degradation of the first frequency is obtained based directly on the nonlinear curve of stiffness. As a result, it is observed that the degradation of the first frequency of the RC frame is proportional to the severity of damage but not linearly. More significant damage, a more profound decrease in the modal characteristic. Particularly, the fundamental frequency of the RC frame reduces gradually until the base shear force reaches 70% of the ultimate value at which the parameter is about 60% of the counterpart at the intact stage. After that, the reduction gets more significant when the bending capacity approaches the ultimate value.