Optimal seismic analysis of degrading planar frames using a weighted energy method to associate inelastic mode shapes: Part I optimal parameters

The objective of this paper is to compute three optimal parameters that are subsequently used to formulate the pre-yielded and post-yielded portions of an equivalent single degree of freedom system (E-SDOF) that is used to predict the seismic target demands in planar frames. The procedure uses an optimal number of inelastic mode shapes from a structure’s capacity (pushover) curve to account for any significant higher-mode effects (HME) and predict the inelastic demands. Using a variant inertial load pattern, weighted energy gradients under the capacity curve are used to define an optimal ductility parameter, which is in turn used to combine the inelastic (and elastic) mode shapes into a single mode shape. This is used to determine the pre-yielded portion of the E-SDOF system, where the post-yielded portion is determined using an inelastic modes parameter. The procedure also utilizes a reduction factor parameter to adjust the one-second spectral acceleration demand. The three optimal parameters are established using several buildings, whose responses are generally influenced by specific material strain hardening and plastic flow rules, and by the dissipated energy due to the yielding of the individual members. Using this methodology, the predicted target displacement demands are very reasonably predicted when compared to a nonlinear time-history analysis, which enables the parameters to later be used in the formulation of other buildings’ E-SDOF systems.