Response spectrum method for structures subjected to vertical ground motions: Absolute acceleration method

Abstract

Although a wide variety of response spectrum methods have been developed to estimate peak horizontal building responses, much less attention has been devoted to study the applicability of those methods for the vertical direction or to develop new methods to estimate peak vertical building responses. Vertical building responses can be significant for structures located close to the earthquake rupture, and for buildings with fundamental period of vibration within the range of most energy content of the vertical component of the ground motion (typically 0.05 to 0.15 s). The frequency content of the vertical component is significantly different to that in the horizontal components; thus, it is not clear if previous methods are applicable. We present a new alternative response spectrum analysis (RSA) method to estimate absolute accelerations in the vertical direction, which is a modified version of a previously studied modal combination rule developed for the horizontal components of motion. This formulation is derived based on the use of modal absolute accelerations, and we compare it to the traditional complete quadratic combination (CQC). In the proposed method, we develop simplified equations to estimate the necessary correlation coefficients for the vertical direction which are calibrated to fit empirical correlations computed from the vertical response of single degree of freedom systems subjected to a set of 90 vertical components of recorded ground motions. We also compute these correlations by using an improved power spectral density (PSD) function, which is as an enhanced version of the modified Kanai‐Tajimi PSD to represent the frequency content in the vertical direction which differs from that in the horizontal direction. To evaluate the proposed modal combination rule, we compare the RSA results to those obtained using response history analyses (RHA) of peak responses for a simplified model consisting of a prismatic bar fixed only at one end, as well as for 2D frames. We show that the proposed modal combination rule can estimate peak building responses with higher accuracy than the commonly used CQC modal combination rule, for any general building configuration at any structural location.