Weighted Average Conditional Mean Spectrum (WACMS): A bridge between common CMS and Uniform Hazard Spectrum (UHS)

Abstract

In order to accurately predict structural response subject to ground motion excitation in the hazard level of interest, it is necessary to determine appropriate target spectrum. Conditional Mean Spectrum (CMS) conditioned on occurrence of a target spectral acceleration (Sa) at a single period is an alternative of the overly conservative Uniform Hazard Spectrum (UHS). The first-mode period is usually advised as conditioned period to create CMS, but it is not always appropriate. A Weighted Average Conditional Mean Spectrum (WACMS) is newly introduced as a more suitable target spectrum to long-period structures and practical guidelines for use are presented. WACMS is the weighted average of CMS suite conditioned on occurrence of target Sa at first several periods, the sum of whose mass participation factors exceeding 90%. The significant advantage is that it can consider hazard levels at multiple periods and use mass participation factor as the weight. CMS and UHS can be integrated with WACMS. WACMS is equivalent to CMS when one period is considered while almost overlaps UHS when all periods are considered. That is, WACMS bridges the gap between CMS and UHS. In this paper, three different structures designed by Chinese code are utilized as examples to verify this method. Results show that WACMS is more appropriate as a target spectrum to predict mean inter-storey drift ratio (IDR) consistent with Chinese code, compared to CMS conditioned on occurrence of Sa at the first-mode period. Meanwhile, WACMS increases the rate of exceeding IDR limit and IDR dispersion.