Evaluation of combination rules for maximum response calculation in multicomponent seismic analysis

Abstract The existing rules for combining peak response to individual components of ground motion are evaluated. The response values r e to two horizontal components of ground motion estimated by four multicomponent combination rules—SRSS‐, 30%‐, 40%‐ and simplified‐SRSS‐rules—are compared with the critical response, r cr , obtained by the CQC3‐rule, which takes into account the direction of the principal ground components with respect to the structural axes and provides the largest response over all possible seismic incident angles. The following results are obtained in the first part of the paper and are valid for any elastic structure and any earthquake design response spectrum: For realistic values of the ratio γ of the design spectra for the two principal components of ground motion the SRSS‐rule estimate lies between 0.79 r cr and 1.00 r cr , the Simplified‐SRSS‐rule estimate lies between 1.00 r cr and 1.26 r cr , the 40%‐rule estimate lies between 0.99 r cr and 1.25 r cr , and the 30%‐rule estimate lies between 0.92 r cr and 1.16 r cr . None of the multicomponent combination rules account for the increase in response of systems if the vibration periods of the two modes that contribute most to the response to the x ‐ and y ‐components of ground motion are close to each other. Evaluated in the second part of the paper is the accuracy of the multicomponent combination rules in estimating the response of a range of one‐storey systems with (a) symmetrical plan and (b) unsymmetrical plan, and of two multistorey buildings. The SRSS‐rule underestimates the response by up to 16% and the other three rules overestimate it by up to 18%. Although these errors appear to be smaller than the many approximations inherent in structural design, they can be eliminated with very little additional computation by using an explicit formula for the critical response based on the CQC3 rule. Copyright © 2001 John Wiley & Sons, Ltd.