A simplified normalized multi-mode nonlinear static procedure (NMP) for seismic performance evaluation of building structures

Abstract

The current work presents a simplified multi-mode nonlinear static procedure based on normalizing the deformation demands (called NMP) for estimating the seismic demands of structures with significant higher mode effects. The proposed procedure is conceptually based on the extended N2 (where N stands for nonlinear analysis and 2 for two mathematical models) method (Kreslin and Fajfar in Earthquake Engineering & Structural Dynamics 40:1571–89, 2011). However, the modal combination procedure used in the proposed method to take the higher mode effects into account is different. The NMP procedure generally encompasses two major steps. First, the structure is pushed using a conventional pushover procedure, namely the basic N2 method, the first-mode pushover analysis, or a pushover analysis with a triangular or a uniform load pattern, which mostly controls the responses at the lower part of the structures. Second, the modal story displacements and drifts computed based on the modal response analysis concept for all the modes of interest are algebraically added. These combined responses are normalized based on the predetermined target displacement. The final responses are the envelope of the results obtained from the two aforementioned steps. The approach used in the second step can preserve the signs of modal responses. Therefore, the effects of sign reversal due to the contribution of higher modes are included in the proposed method. Moreover, the NMP procedure mitigates the computational burden compared to nonlinear response history analysis or adaptive pushover procedures. In order to evaluate the accuracy of the proposed procedure in estimating the seismic demands of structures, it is applied to two sets of steel structures including three special moment frames (SMFs) with 6-, 12-, and 18-story heights, and a 12-story SMF with soft stories as the first set and the 9-, and 20-story SAC steel moment frames as the second set. Comparing the results of the NMP procedure with those obtained by the nonlinear response history analysis (NL-RHA) as the benchmark solution and two other pushover approaches, including a conventional first-mode-based pushover analysis and the extended N2 method, demonstrate the sufficiency of the NMP procedure in accurately estimating the global and local response quantities.