Estimation of the Park–Ang damage index for planar multi-storey frames using equivalent single-degree systems

A detailed characterization of potential structural damage is essential to performance-based seismic design. The Park–Ang damage index is selected in this work as the seismic damage measure, since it is one of the most realistic measures of structural damage. Response spectra constitute the most common tool used for characterizing the seismic hazard at a site, and these spectra represent the demand on single-degree oscillators. To use these spectra for estimating the Park–Ang damage index demand on an MDOF system, three equivalent single-degree system-based approximate schemes are proposed. These schemes are tested on three moment resisting frames under several ground motion scenarios. The effectiveness of an equivalent system scheme is measured by comparing with the estimates from a nonlinear response-history analysis of the MDOF model. These schemes are tested for both global and storey-level damage indices. Variation of the non-dimensional parameter β is also considered in these case studies. Overall, all the three schemes are found to be effective with varying degrees of accuracy. The proposed methods are recommended for damage-based seismic design and performance evaluation of structures because these schemes can use response spectra for demand estimation and reduce computation cost.