An alternate perspective on the critical orientation of horizontal pair of seismic excitations: Theory and illustrations

This paper enhances the understanding of critical orientation (that maximizes the response of an EDP over all possible orientations) for horizontal ground motion pairs when applied to the base of a structure. Given that any structural response comprises the contributions from individual modes, even under inelastic excursion, the maximization of modal responses for the first few modes would be sufficient to define the critical orientation for most of the EDPs. In line with this, the theoretical background to establish a concept of modal orientation is presented in this paper. The analysis for the modal response of a building against a pair of orthogonal horizontal excitations is theoretically equivalent to the analysis against the associated single component representation along this orientation. The orientation of the same single-component representation that maximizes the associated oscillator's response is termed as the spectral orientation. The critical orientation is proven to be the difference between the modal and spectral orientations. In line with this, a recommendation is proposed for critical orientation regardless of the EDPs, which is expected to capture most of the EDPs, if not all. Although this development is based on linear analysis, it is demonstrated to be applicable to buildings undergoing inelastic excursion under moderate-to-strong shaking. These recommendations are based on four numerical examples involving symmetric and unsymmetric buildings subjected to individual horizontal pairs of ground motions and also a suite of ground motions. The proposed recommendations on critical orientation should be incorporated into seismic design and performance assessment practices.