Theoretical models and recorded response in the estimation of cumulative seismic damage on non-linear structures

A damage-function model is proposed for the inelastic response of structures in terms of initial damage and of displacement amplitudes and secant stiffnesses of response cycles. The model is used to obtain an analytical closed-form solution for the probability distribution of cumulative damage after an earthquake ground motion given the distribution prior to such excitation and information on the inelastic structural response. The formulation is applied to a reinforced concrete frame and the results show the capabilities of the method to yield updated distributions of damage.