Combination coefficients for modal pushover analysis

Conventional non-linear static analysis estimates the response peak value by evaluating the pushover curve adopting a distribution of invariant forces proportional to the fundamental vibration mode. In order to include the effect of higher modes, multi-modal push-over analysis has been proposed in literature. Nodal response peak values are obtained by combination of “modal” responses usually by the traditional CQC method, requiring cross correlation coefficients defined for linear systems. In this paper, the accuracy of correlation coefficients for linear systems in predicting the statistical correlation of hysteretic oscillator responses is investigated by the Monte Carlo Simulation conducted on non-dimensional non-linear oscillators. Furthermore, new correlation coefficients determined through a pertinent statistical linearization are introduced, and the results provided by the classical and the proposed approach for two illustrative frames are compared with non-linear time history analysis, showing the effectiveness of the new procedure.