Practical Equations for Predicting Maximum Displacement of Single Friction Pendulum Isolation Systems

Abstract

Predicting maximum displacement is an important task in designing any isolation system, including isolation systems using single friction pendulum (SFP) bearings. Many design codes allow an equivalent linear force (ELF) procedure to be used to predict this engineering demand, providing that the system satisfies some specific conditions. An ELF procedure is much simpler than a dynamic time-history analysis procedure because it does not require time-history inputs. However, this procedure is still time-consuming because it requires an iteration process. This study aimed to develop simple equations to directly calculate the maximum displacement without iterating. The database for developing these equations was obtained by performing the ELF procedure in a current standard on a wide range of isolation systems subjected to a wide range of ground-shaking strengths. As a result, a simple equation that can directly predict the maximum displacement of any isolation system using SFP bearings was proposed. The inputs to the equation include friction coefficient and concave radius of the bearings in the system and the 1-s spectral acceleration of the site. The proposed equation confidently predicts the maximum displacement calculated by the ELF procedure with an average displacement ratio, which is the ratio between the predicted and computed values, of 1.015. The minimum and maximum ratios in the investigated database were 0.975 and 1.092, respectively.