Simple Equations for Predicting Maximum Displacement of Isolation Systems Using Lead Rubber Bearings

Abstract

Predicting maximum displacement is an important task in designing isolation systems. An effective procedure that is widely used for this task is equivalent linear force (ELF) procedure, which is allowed by many contemporary design codes. This procedure uses very basic parameters of the isolation system as well as earthquake condition of the site to analyze for the maximum displacement. However, ELF procedures are time-consuming because they require an iteration process. This study employed an ELF procedure to generate a large database and used it to develop explicit and simple equations that can directly calculate the maximum displacement of isolation systems using lead rubber bearings. The proposed equations can confidently predict the maximum displacement calculated by the ELF procedure. In addition, the investigation showed that the first to post-yield stiffness ratio of an isolation system, which is difficult to accurately determine, has neglected effect on the maximum displacement calculated by the ELF procedure. Based on this observation, a simple equation that uses only three input parameters to predict the maximum displacement was proposed. The input parameters to the simplified equation include normalized characteristic strength and post-yield period of the isolation system, and 1-s spectral acceleration of the site. These parameters are minimum to determine an isolation system and earthquake condition. The comparison between the maximum displacement predicted by the proposed equation and the maximum displacement calculated by the ELF procedure showed that the proposed equation generates slightly conservative results for common designs, therefore is suitable for practical application.