Vertical stiffness reduction of rubber bearings under lateral displacement considering different shape factors

Rubber bearings are composite components consisting of rubber layers and steel shims, which have been widely used in seismic isolation structures. The vertical stiffness of rubber bearings reduces significantly under lateral displacement. Previous studies have not clarified the vertical stiffness reduction for bearings with different dimensions. The focus of this study is to comprehensively explore the influence of the first and second shape factors (S₁ and S₂) on the vertical stiffness reduction of bearings with different shapes and to develop a prediction method. On the basis of the two-spring model, an improved theoretical formula for predicting the vertical stiffness of bearings under a lateral displacement was derived considering the influence of the S₁. Subsequently, a series of finite element (FE) models were developed. The parameters of rubber material were calibrated using experimental data. A parametric FE study was conducted to investigate the influence of different S₁ and S₂ on the vertical stiffness reduction of bearings under lateral displacements. The effectiveness of the proposed formula was evaluated by comparing the results with those obtained from the FE analyses. Finally, based on the improved formula, an empirical formula for vertical stiffness reduction that can consider the influence of both S₁ and S₂ was developed. The predicted results of the empirical formula showed good agreement with the experimental and numerical results.