Seismic response of pile supported frames using the combination of dynamic stiffness approach and Galerkin’s method

Abstract

The aim of this study is to obtain seismic response of pile supported frames using exact mode shapes. The dynamic stiffness method (DSM) is applied to obtain natural frequencies and mode shapes of frame model which has Timoshenko element beams, columns, piles and flexible pile cap. Free vibration analysis is performed for various soil conditions, pile dimensions and column dimensions. The calculated natural frequencies using DSM are tabulated with the natural frequency values obtained from finite element method (FEM). The FEM convergence for the first three natural frequencies are presented. The mode shapes are plotted. The agreement between the mode shapes obtained from the DSM and FEM is observed by means of modal assurance criterion (MAC). Using the Galerkin’s method, the generalized displacement function of the frame model is obtained by a linear combination of mode shapes and generalized coordinates. The generalized mass, stiffness and force for the equivalent model are obtained and earthquake response analysis is performed. At first, the FEM convergence for the roof displacement and base shear is presented. Then, effects of soil conditions, pile diameter and column dimensions on the seismic response of the frame model are revealed using the proposed approach. The time-histories for the roof displacement and base shear are calculated using the Runge-Kutta method. As the accuracy of the seismic response is strictly related to free vibration characteristics of the system, the natural frequencies of a single-storey frame model obtained using the DSM are presented in comparison with the experimental data in literature. Moreover, an additonal validation is presented for the natural frequencies of a beam on elastic foundation using the dynamic stiffness formulation and experimental data for various boundary conditions. The results show that the proposed approach for seismic response analysis of pile supported frames is very effective and straightforward.