Conditional mean spectra given a vector of spectral accelerations at multiple periods

Conditional mean spectra (CMS) are generally defined as expected pseudo-spectral accelerations (PSA) conditioned on uniform hazard spectra (UHS) at a selected period. Many design practices prefer CMS because UHS conservatively envelop the large amplitudes of PSA within a single ground motion. However, in some situations, CMS are preferred given target spectra from UHS at multiple periods (CMSV) for satisfying design requirements. This study presents the mathematical formula of CMSV and describes the methodology to compute CMSV with application examples. The presented method for computing CMSV can provide the transitional design spectra between currently used CMS and UHS depending on the selected conditioning periods.