Non linear and linearized combination coefficients for modal pushover analysis

Current design practice and seismic codes tend to assess seismic demand of buildings by Non linear Static Analysis (NSA), based on the evaluation of the pushover curve. Earlier non-linear static analysis procedure estimate the response peak value by evaluating the push-over curve adopting a distribution of invariant forces proportional to the fundamental vibration mode. In order to include the effect of higher modes several multimodal push-over analysis procedures were proposed in literature. In In the most famous of these, namely Modal Pushover Analysis (MPA), nodal response peak values are obtained by combination of "modal" responses by the traditional SRSS or CQC methods: the use of the CQC rule is mandatory for irregular plane frames or spatial structures possessing modes with close natural frequencies. In order to take into account the actual characteristics of modal oscillators, the use of pertinent cross correlation coefficients defined for non-linear systems is required. In this paper the accuracy of correlation coefficients for linear systems in predicting the statistical correlation of hysteretic oscillator responses is investigated by a parametric analysis by Monte Carlo simulation. 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 irregular plane and spatial frame are compared with non-linear time history analysis results, showing the effectiveness of the new procedure.