Multidimensional performance limit state for probabilistic seismic demand analysis

Based on a framework of Probabilistic Seismic Demand Analysis, a nonlinear dynamic model of a reinforced concrete (RC) building was established to obtain a demand hazard curve that considers multidimensional performance limit states (MPLSs), including combinations of peak floor acceleration and interstory drift. A definition of the two limit states is expressed using a generalized MPLSs equation. The peak floor acceleration and the interstory drift were considered to be dependent and were assumed to follow a bidimensional lognormal distribution. The maximum interstory drift and the maximum peak floor acceleration were calculated using Increment Dynamic Analysis and nonlinear time history analysis. The numerical formula for a demand hazard curve of the modelled building was then derived by coupling the bidimensional lognormal distribution with the ground motion hazard curve. The uncertainties involved in MPLSs and structural parameters, as well as the different threshold values for peak floor acceleration, were further considered to determine the sensitivity of demand hazard curves. The analysis results showed that the proposed method can be used to describe the damage performance of various building structures, which are sensitive to multiple response parameters including drift and acceleration. Moreover, it was demonstrated in this study that the demand hazard curves were relatively conservative if the coefficient of variation, the peak floor acceleration threshold, the interaction factor N (IDR) and added stiffness, were appropriately selected.