Vol.:(0123456789) Bulletin of Earthquake Engineering https://doi.org/10.1007/s10518-018-0427-4 1 3 ORIGINAL RESEARCH A new simplifed approach for assessing nonlinear seismic response of plan‑asymmetric structures considering soil‑structure interaction Mohammad S. Birzhandi 1  · Amir M. Halabian 2 Received: 7 September 2017 / Accepted: 21 July 2018 © Springer Nature B.V. 2018 Abstract An innovative approximate method is presented to consider the plan asymmetry, nonlinear structural behaviour and soil-structure interaction (SSI) efects simultaneously. The pro- posed method so-called Flexible base 2DMPA (F2MPA) is an extension of 2 degrees of freedom modal pushover analysis (2DMPA) approach to consider foundation fexibility in seismic response analysis of plan asymmetric structures which itself were developed based on Uncoupled Modal Response History Analysis method for inelastic fxed-base asymmet- ric structures. In F2MPA for each mode shape using 2DMPA procedure, the elastic and inelastic properties of 2DOF modal systems corresponding to the fxed-base structure are initially derived. Then in each time step, displacements and inelastic restoring forces of the superstructure are computed from modal equations of the fexibly-supported structure. In each time step, the nonlinear secant stifness matrix corresponding to the n-th MDOF modal equations of soil-structure system is updated using the corresponding modal 2DOF system of fxed-base structure. To update the transformed modal stifness matrix of the SSI system, this matrix is partitioned and it is assumed that the non-linear variation of the superstructure can be estimated from the variation of modal stifness matrix of the fxed-base structure. Accuracy of the proposed method was verifed on an 8-story asym- metric-plan building under diferent seismic excitations. The results obtained from F2MPA method were compared with those obtained by nonlinear response history analysis of the asymmetric soil-structure system as a reference response. It was shown that the proposed approach could predict the results of the nonlinear time history analysis with a good accu- racy. The main advantage of F2MPA is that this method is much less time-consuming and useful for the practical aims such as massive analysis of a nonlinear structure under difer- ent records with multiple intensity levels. Keywords Modal pushover analysis (MPA) · Soil-structure interaction · 2 Degrees of freedom modal pushover analysis (2DMPA) · Asymmetric structures · UMRHA method Abbreviations SDOF Single degrees of freedom * Mohammad S. Birzhandi s.birzhandi@khuisf.ac.ir Extended author information available on the last page of the article