Effect of bidirectional ground shaking on structures in the elastic and post-elastic range: Adequacy of design provisions

Abstract

During an earthquake, structures are generally excited to multiple ground motion components: two orthogonal horizontal components and one vertical component. However, the interaction of the deformations along two principal orthogonal directions in the presence of various levels of axial force in columns in post elastic range can be successfully captured if nonlinear dynamic analysis can be carried out using the bidirectional hysteresis model. On the other hand, the seismic codes prescribed simple combination rules to capture this effect in an equivalent sense even without consideration of axial force in columns. Though these rules may be valid in the elastic range, they may not be applicable in the post-elastic range as mentioned in a few seismic codes. Surprisingly, these codes did not specify any user-friendly provision needed by design offices. Hence, the applicability and efficacy of these rules in the post-elastic range is needed to be compared with that obtained from detailed nonlinear tine history analysis under orthogonal pair of bidirectional ground motions obtained from a number of chosen seismic acceleration data for performance-based design. In this study, idealized low-rise buildings with small, medium, and long periods were investigated, considering the presence of axial force in columns. Most of the current design codes and standards suggest that the addition of response of 30% of ground motion in other direction if added to the response of unidirectional ground motion in the considered direction of analysis or the resultant responses obtained by square root of sum of square from the unidirectional analyses carried out separately in both principal directions (referred as SRSS response) may predict the response with reasonable accuracy. The results obtained from the current study makes an attempt to exhibit the trends of post elastic range response for the structures. Further, it shows that seismic codes options significantly underestimate the post-elastic range seismic demand though they are proved to be adequate to predict elastic range response. This paper may prove helpful in improving code provisions.