On nonstationarity-related errors in modal combination rules of the response spectrum method

Characterization of seismic hazard via (elastic) design spectra and the estimation of linear peak response of a given structure from this characterization continue to form the basis of earthquake-resistant design philosophy in various codes of practice all over the world. Since the direct use of design spectrum ordinates is a preferred option for the practicing engineers, modal combination rules play central role in the peak response estimation. Most of the available modal combination rules are however based on the assumption that nonstationarity affects the structural response alike at the modal and overall response levels. This study considers those situations where this assumption may cause significant errors in the peak response estimation, and preliminary models are proposed for the estimation of the extents to which nonstationarity affects the modal and total system responses, when the ground acceleration process is assumed to be a stationary process. It is shown through numerical examples in the context of complete-quadratic-combination (CQC) method that the nonstationarity-related errors in the estimation of peak base shear may be significant, when strong-motion duration of the excitation is too small compared to the period of the system and/or the response is distributed comparably in several modes. It is also shown that these errors are reduced marginally with the use of the proposed nonstationarity factor models.