Feasibility of a nonlinear spectral approach for peak floor acceleration of multi-story bilinear hysteretic buildings

Abstract

To protect the acceleration-sensitive non-structural components in a multistory building, a proper seismic design of them against the peak floor acceleration (PFA) is needed. The PFA, therefore, should be estimated in advance. To efficiently estimate the PFA of multi-story buildings at the inelastic stage, a nonlinear modal combination approach is provided in this study. First, for the single-story building (single-degree-offreedom system), a PFA spectral ratio δ is proposed to measure the nonlinear reductions in PFA. A series of time history analysis (THA) revealed that there is a dependable relationship between the PFA spectral ratio δ, the strength reduction factor R, the postyield stiffness ratio α, and the period T of the structure. The scatter of δ is notably smaller than the ductility demand, showing the good feasibility of a δ-R-T-α relationship for predicting δ. Second, for the multi-story building (multi-degree-of-freedom system), the floor acceleration is decoupled in the modal space, the contribution of each mode to the elastic PFA is multiplied by δ to account for the nonlinear reduction in PFA at the inelastic stage. Here δ can be determined by an appropriate δ-R-T-α relationship, while R and α are determined via a modal pushover analysis. The modified modal contributions are combined via the complete-quadratic combination (CQC) rule, forming the modified CQC (MCQC) approach. The PFAs of some 2-, 5-, and 8-story building structures with different degrees of nonlinearity are computed via the THA and the MCQC approach.The results demonstrate the satisfactory accuracy of the MCQC approach. Notably, the effects of nonlinearities associated with the higher-order modes on the nonlinear PFA are well considered in the MCQC approach, thus the un-acceptable over-estimations of the inelastic PFA, which occurs in conventional methods, are avoided.