Attenuation relations of the pseudo-spectral acceleration (psa) response are used to assess seismic hazard and uniform hazard spectra (uhs). The relations are based on a scalar measure although earthquake excitations are inherently vector quantities. For a single-degree-of-freedom system, this may or may not be important depending on whether the estimated uhs accurately reflect the estimated seismic hazard. For buildings that are sensitive to two orthogonal horizontal components of excitations, a vector or orientation-dependent ground-motion measure could be valuable. These encourage us to assess the orientation effect on the probability of the psa along a random orientation exceeding the geometric mean and quadratic mean and to propose an orientation-dependent ground-motion measure that is based on the maximum resultant psa and a response ratio, defined as the ratio of the psa in an arbitrary orientation to the maximum resultant psa. Numerical results show that the probability that the psa along a random orientation exceeds the geometric mean or the quadratic mean is about 50%. The results also show that the response ratio plotted in the polar coordinate almost always falls among three circles. Attenuation relations are developed based on the developed measure for a set of records selected from the peer Next Generation Attenuation database. Use of the relations for assessing seismic hazard is illustrated. Also, for comparative purposes, attenuation relations based on the geometric and quadratic means are developed and used to assess the seismic hazard.
Online material: Adopted record selection criteria and analysis results of the developed attenuation relations.