Higher modes contribution for estimating the inelastic deformation ratios and seismic demands of structures

Abstract

In order to estimate the seismic demand by using the nonlinear static procedure, different approximate methods have been developed. One of the most useful methods is called displacement coefficient method (DCM), which is based on some modification factors. One of these coefficients denoted C1, concerns the inelastic deformation ratio and usually depends on either the yield-strength reduction factor or the ductility factor. In general the evaluation of the inelastic deformation ratio is based on the response of single degree of freedom (SDOF) systems, where the response of the structure is mainly controlled by the fundamental mode, knowing that the inelastic deformation ratio will not capture the contribution of higher modes in the overall structural response. A developed theoretical approach with the aim of estimating the inelastic deformation ratio for structures, considering contribution of higher modes of vibration, is introduced. In this assessment, the normalized yield strength coefficient (η) and the post-to-preyield stiffness ratio (α) are key factors. The results are compared to the uncoupled modal response history analysis (UMRHA) procedure and some existing formulations for a nine story building subjected to the El Centro 1940 ground motion. It appears that the new theoretical approach leads to enough accurate estimation of the inelastic deformation ratio compared to the UMRHA one.