A Response Spectrum-Based Method for Critical Response of Simple Symmetrical Buildings Under Bidirectional Seismic Excitation With Uncertain Angle of Incidence

Abstract

Spatial combination rules for multi-component seismic excitation have been developed mainly to account for the effects of the uncertainty in the incident angle of excitation on the response amplitudes of asymmetric buildings. These combination rules become redundant for symmetrical buildings, and the unidirectional analysis based on commonly used types of response spectra is unable to predict the maximum response amplitudes under bidirectional excitation. This paper proposes to utilize the concept of the Critical Response Spectrum (CRS) to accurately predict the maximum response of simple symmetric buildings using only one-dimensional response spectrum analysis (RSA) based on the CQC method. As the design spectra are not readily available in terms of CRS, preliminary empirical scaling factors have been developed to obtain a reasonable approximation to CRS from the RotD50 spectrum, in terms of which the NGA-West2 GMPEs are expressed. The validity of both the actual and the approximate CRS has been established by comparing the maximum response quantities of two distinct six-storey symmetrical steel building models with the exact time-history analysis (THA) for a large data set of 56 pairs of horizontal accelerograms of real earthquakes with widely differing characteristics. The mean percentage errors have been found to be much less within about ±10% compared to the unacceptable underestimation of up to about −50% in using the other traditional types of response spectra (viz., geometric mean, envelope, major principal, and RotD50).

Keywords

Bi-directional excitation / critical response spectrum (CRS) / earthquake incident angle / response spectrum analysis (RSA) / simple symmetrical buildings / time history analysis (THA)

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2026 Tianjin University and John Wiley & Sons Australia, Ltd.