A pushover procedure for seismic assessment of buildings with bi-axial eccentricity under bi-directional seismic excitation Kazem Shakeri n , Samaneh Ghorbani Faculty of Engineering, University of Mohaghegh Ardabili, Ardabil 56199-11367, Iran article info Article history: Received 30 April 2014 Received in revised form 26 September 2014 Accepted 26 October 2014 Keywords: Nonlinear static analysis Bi-axial eccentricity Bi-directional excitation Shear Torque abstract A new modal pushover procedure is proposed for seismic assessment of asymmetric-plan buildings under bi-directional ground motions. Although the proposed procedure is a multi-mode procedure and the effects of the higher and torsional modes are considered, the simplicity of the pushover procedure is kept and the method requires only a single-run pushover analysis for each direction of excitation. The effects of the frequency content of a specific ground motion and the interaction between modes at each direction are all considered in the single-run pushover analysis. For each direction, the load pattern is derived from the combined modal story shear and torque profiles. The pushover analysis is conducted independently for each direction of motion (x and y), and then the responses due to excitation in each direction are combined using SRSS (Square Roots of Sum of Squares) combination rule. Accuracy of the proposed procedure is evaluated through two low- and medium-rise buildings with 10% two-way eccentricity under different pairs of ground motions. The results show promising accuracy for the proposed method in predicting the peak seismic responses of the sample buildings. & 2014 Elsevier Ltd. All rights reserved. 1. Introduction Nowadays, the performance based design (PBD) methodology has been widely accepted by earthquake engineering community as a rigorous approach in design of civil structures. Since struc- tures experience inelastic deformation in low performance lev- els (e.g., Life Safety), PBD methodology requires using nonlinear analysis to quantify the seismic response of structures. Nonlinear static procedures (NSPs) have been widely proposed as a practical tool in seismic evaluation guidelines and design codes [1–4]. Recently, to improve the efficiency of these procedures numerous advanced pushover procedures have been proposed [5–13]. Furthermore, application of the pushover procedures is extended to seismic assessment and design of non-building structures such as bridges [14–16]. However, most of these pushover procedures are originally developed for two dimensional (2D) models of building structures. Although in some procedures the effect of the torsional modes in asymmetric-plan buildings subjected to one-directional ground motion are considered [17–32], it is well recognized in the literature that for a reliable seismic assessment, considering the influence of simultaneous bi-directional ground motions (angle of incidence) on seismic demands of inelastic asymmetric-plan structures is inevitable [33–34]. In this regard, Fajfar et al. have extended the N2 method in order to take into account the bi-directional ground motions effects on asymmetric-plan structures [35]. Recently, Reyes and Chopra have also extended the well-known modal pushover analysis (MPA) to analyze asymmetric-plan buildings subjected to two horizontal components of ground motions [36]. Further- more, the extended versions of the conventional pushover proce- dures are adopted by seismic codes [2–3]. These extended versions of original procedures are developed based on the superposition principle and the original pushover procedure is implemented independently in each horizontal direction and the resulting responses from each direction are combined by SRSS (Square Roots of Sum of Squares) rule. In the extended version of the MPA procedure, the effects of the higher and torsional modes are considered; however, since the original MPA procedure requires running several independent pushover analyses according to the considered modes in each direction, the extended version of the MPA procedure for bi-directional ground motions requires addi- tional analyses. Recently, Manoukas et al. have also developed a multi-mode pushover analysis similar to the extended MPA procedure for asymmetric-plan buildings under bi-directional ground motions, which leads to a significant reduction in computational cost [37]. In this procedure, it is assumed that the two components of the Contents lists available at ScienceDirect journal homepage: www.elsevier.com/locate/soildyn Soil Dynamics and Earthquake Engineering http://dx.doi.org/10.1016/j.soildyn.2014.10.018 0267-7261/& 2014 Elsevier Ltd. All rights reserved. n Corresponding author. Tel.: þ98 914 451 3150; fax: þ98 451 7720202. E-mail addresses: Shakeri@uma.ac.ir, ka.shakeri@gmail.com (K. Shakeri). Soil Dynamics and Earthquake Engineering 69 (2015) 1–15