Sensitivity of the conditional period selection in the structural response using the CMS as target spectrum

Abstract

A framework is presented for assessing the sensitivity of typical engineering demand parameters (EDP) to the conditional period selection when using conditional mean spectra (CMS) as targets for ground-motion selection in a performance-based seismic evaluation. The framework consists of computing a suite of CMS targets anchored at conditioning periods within a period range of interest to discretize the demand at a given hazard level, as represented by a uniform hazard spectrum (UHS). Ground motions are selected and scaled for the CMS suite and the associated UHS. The envelope of the median responses from the CMS suite is compared with the median response from the UHS. The framework is instrumental in identifying the conditioning period ( T*) range for estimating CMS to capture the maximum median responses at the hazard level of interest. It also helps to characterize the relative difference in responses between using CMS targets and a UHS. The implementation of the methodology is illustrated by evaluating response quantities such as displacement-, acceleration, and force-based EDPs of four reinforced concrete moment frame structures of different heights under three levels of increasing hazard. Results confirm that the conditioning period used for ground-motion selection has a significant impact on the seismic response of displacement-based EDPs, and the sensitivity of the response varies with building height. For other EDPs, like maximum base shear and story acceleration, the results vary. Based on a limited-size ground motion set typically used in practice, the results indicate that UHS-targeted ground motions do not necessarily yield greater demand in comparison with using the CMS for estimating peak story drifts. For maximum floor accelerations, however, the CMS did produce smaller responses.

Comprehensive evaluation of target spectra for selecting bidirectional ground motions in nonlinear response history analysis of frame buildings at far‐field sites

“…Further, Table 2 shows that when estimating MFAs, the median value of $${R_{edp}}$$ for CMS( T 1 ) and CMS($${T_{max}}$$) are 1.25 and 1.39, indicating an average underestimation of about 25% and 39%, respectively; this degree of underestimation is also consistent with past research in which a single CMS with a single $${T^*}$$ might be unconservative for some types of EDP 34 . By contrast, Table 2 shows that the median value of $${R_{edp}}$$ for CMS($${T_{min}}$$) is 1.03 for MFA and 1.69 for MSDR, implying an average underestimation of about 3% for MFA and 69% for MSDR, respectively; these data also confirm findings from prior work that at least two CMSs are required to satisfactorily estimate demands for a variety of EDP types 3,26,31,38,87,89 . The table demonstrates that as the number of CMSs increases, the accuracy improves.…”

“…One way to overcome the challenge of choosing a $${T^{\mathrm{*}}}$$ is to use mCMS, each starting with a different $${T^{\mathrm{*}}}$$ 21,38,39 . In this paper, three pairs of CMSs were selected to cover the response of the structures.…”

“…When no collapses are observed, the central estimate of demand, $$ed{p_{demand}}$$, is defined as the arithmetic mean of the resulting $${N_{gm}}$$ EDPs, but when collapses are observed, the mean is calculated with the remaining records. While the arithmetic mean is commonly used in seismic design guidelines, 2,3,26,35 the median or 50 th percentile is sometimes used to define $$ed{p_{demand}}$$ as well 25,29,38,45 . Further, when collapses are observed, the central estimate could also be redefined as the larger value among the mean of the remaining non‐collapsed cases and 1.2 times the median 23 .…”

“…Further, the CMS results herein support the concept of defining $$ed{p_{demand}}$$ as the maximum among the estimates from mCMS (e.g., Method 2 in refs. 3, 38, 39). Regardless of MSDR or MFA, both the s‐GCMS and Composite Spectrum yield demands that are somewhere between those from a single CMS and those from the UHS.…”

“…One way to overcome such potential underestimation is to use multiple CMSs (mCMS), each with a different $${T^*}$$ (e.g., refs. 26, 30, 38, 39). However, using mCMS increases the number of nonlinear RHAs by a factor equal to the number of CMSs, which can be significant for complex structures where nonlinear RHA is of most interest (e.g., tall buildings, 3D buildings with unsymmetric plan, or other types of structures) 40–42 …”