Seismic demand estimation of isolated buildings with nonlinear bearings subjected to linear response spectra

Abstract

Response spectrum analysis is a commonly used method for the seismic design of linear structures with fixed bases since the seismic input is normally provided in terms of the response spectrum in many codes. This study proposes a more generalized response spectrum method for the seismic design of three-dimensional isolated structures. Firstly, the theory basis of this method is derived in the framework of the random vibration theory. The equivalent parameters of each bearing are expressed in terms of the statistics of the displacement amplitude. Then, the complex mode theory is introduced into this method to consider the effect of the nonclassical damping resulting from the isolation layer. Finally, an iterative analysis procedure is presented, which combines the equivalent linearization with the complex mode theory. Moreover, the convergence and applicability of this method are discussed in detail. The parameter analyses show that the relative error of the base shear of the superstructure estimated by using this method is within 10% compared with that of the nonlinear time history analysis. In addition, a benchmark base-isolated structure is used as a numerical example to examine the effectiveness of the proposed method. The results show that the iteration is convergent and computationally efficient. The results also show that the maximum relative errors of the predicted isolation layer displacement, the inter-story drift of the bottom floor and the absolute acceleration of the top floor are 9.5%, 3.9% and 18.9%, respectively, by comparing them with the nonlinear time history analysis, while these responses are underestimated by 9.8%, 25.9% and 40.2%, respectively, when using the classical complete quadratic combination (CQC) method that neglects the nonclassical damping effect. Although in this study the proposed approach mainly focuses on isolated structures, in essence, this approach can also be applied to inelastic structures or structures with nonlinear dampers.