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

Abstract

Damage in RC structures causes the degradation of stiffness and frequency. In this study, the relationship between the two coefficients and damage severities is numerically investigated considering a three-dimensional (3D) RC frame in which the concrete damage plasticity model (CDPM) and the elastoplastic model are selected for concrete and reinforcements, respectively. Crack propagation is obtained utilizing a nonlinear static pushover analysis (NSPA). After pushing, according to the base shear force versus top displacement curve, the bending stiffness of the structure is determined rapidly based on the first derivative of the relationship. Thereafter, the degradation of the first frequency is obtained based on the derivative of the nonlinear curve of stiffness, the second derivative of the force -displacement curve viz. 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 frequency. Particularly, the frequency of the frame reduces gradually until the base shear force reaches 70% of the ultimate value at which the parameter is 60% of the healthy counterpart. After that, the reduction gets more significant when the bending capacity approaches the ultimate value.