Use of Peak Factors in Response Spectrum–Based Modal Combination Rules for Peak Floor Accelerations

Abstract

Response spectrum–based modal combination rules play an important role in the estimation of linear peak responses of multi-degree-of-freedom (MDOF) systems consistent with the seismic hazard specified through a set of elastic design spectra of different damping ratios. Most modal combination rules have assumed that the nonstationary peak factors relating the root-mean-square responses to the largest response peaks are identical for the modal and overall system responses. However, this assumption may significantly affect the response accuracy. This study considers the use of nonstationary peak factors specifically in a modal combination rule that has been formulated for the peak values of absolute floor acceleration responses in a lumped mass, classically damped, multistoried structure by using the hazard-consistent relative acceleration spectrum ordinates, and employs the hazard-consistent relative velocity spectrum ordinates to account for cross-correlation terms. The proposed formulation consists of the modeling of (1) the nonstationary peak factor for overall floor acceleration response as normalized by the nonstationary peak factor for ground acceleration, (2) the nonstationary peak factor for the relative acceleration response of a base-excited single-degree-of-freedom (SDOF) oscillator as normalized by the nonstationary peak factor for ground acceleration, and (3) the stationary peak factor for the relative displacement response of the SDOF oscillator as normalized by the stationary peak factor for ground acceleration. The proposed modal combination rule is illustrated with the help of five buildings and six earthquake excitations in comparison with the existing modal combination rules for absolute floor acceleration responses.