An alternative modal combination rule for adaptive pushover analysis Alireza Tajik Davoudi 1 * , Reza Abbasnia 1 , Abdolreza Sarvghad-Moghadam 2 , Mohammad-Mahdi Maddah 1 and Ali Khodam 1 1 Department of Civil Engineering, Iran University of Science and Technology, Tehran, Iran 2 International Institute of Earthquake Engineering and Seismology, Tehran, Iran SUMMARY The main purpose of the present study is to develop an alternative modal combination rule for use in the adaptive pushover analysis. Since the quadratic modal combination rules do not take into account the sign reversals of the modal load vectors in the higher modes, the accuracy of the advanced pushover methods are decreased. The proposed modal combination rule is a direct vectorial addition technique in which the relative contribution of each mode and its sign are taken into account. The proposed modal combination rule is employed within the displacement-based adaptive pushover technique, and an alternative pushover procedure is developed. In order to verify the accuracy of the proposed method, two reference buildings are used, and the obtained results from the proposed method and nonlinear time history analysis are compared. It is concluded that the proposed method can estimate the benchmark responses with remarkable accuracy. Copyright © 2016 John Wiley & Sons, Ltd. Received 30 January 2014; Revised 8 July 2015; Accepted 13 September 2015 KEY WORDS: modal combination rule; adaptive pushover; higher modes; sign reversals; moment resisting frame; dynamic response 1. INTRODUCTION The nonlinear static procedure (NSP) is widely used as a robust tool for estimation of the seismic demands of the structure. Conventional pushover method as described in FEMA-356 (2000) and ATC-40 (1996) is restricted to the fundamental mode of the structure and therefore provides good estimation of the seismic demand in the low-rise buildings (Fajfar and GAŠPERŠIČ, 1996; Krawinkler and Seneviratna, 1998; Gupta and Krawinkler, 2000; Mwafy and Elnashai, 2001; FEMA-440, 2005; Poursha et al., 2010; Mortezaei et al., 2011). In order to account for the higher mode contributions in tall buildings, extensive researches have been conducted during recent years. In this regard, two general pushover groups can be identified. In the first group, based on elastic mode shapes of the structure, the modal load vectors are computed and multiple- run pushover analyses are performed. In this group of pushover procedures, the load vectors are invari- ant throughout the analysis (Paret et al., 1996; Sasaki et al., 1998; Chopra and Goel, 2002; Moghadam, 2002; Chopra et al., 2004). A relatively well-known and widely used method of the first group is devel- oped by Chopra and Goel, (2002). In this technique, the modal load patterns proportional to each modes of interest are computed based on the modal shapes, masses and spectral acceleration. Using several pushover analyses, the modal responses are computed. The obtained responses are combined using the square root of the sum of the squares (SRSS) or the complete quadratic combination (CQC) rules. Despite of partial improvement in the estimation of the seismic demands of the structure in comparison *Correspondence to: Alireza Tajik Davoudi, Department of Civil Engineering, Iran University of Science and Technol- ogy, Tehran 1684613114, Iran. E-mail: a_tajik@civileng.iust.ac.ir THE STRUCTURAL DESIGN OF TALL AND SPECIAL BUILDINGS Struct. Design Tall Spec. Build. 2016; 25: 325–339 Published online 25 January 2016 in Wiley Online Library (wileyonlinelibrary.com/journal/tal). DOI: 10.1002/tal.1260 Copyright © 2016 John Wiley & Sons, Ltd.