Formulation and Implementation of a Lead-Rubber Bearing Model Including Material and Geometric Nonlinearities Authors: Keri L. Ryan, Utah State University, Logan, UT 84322-4110; kryan@cc.usu.edu James M. Kelly, University of California, Berkeley, CA 94720; jmkelly@peer.berkeley.edu Anil K. Chopra, University of California, Berkeley, CA 94720; chopra@ce.berkeley.edu ABSTRACT Typical models for isolation bearings use elastic-plastic (bilinear) or other empirically derived models for lateral force-deformation behavior. These models do not include the influence of axial loads on the lateral behavior, or more generally the interaction of lateral and vertical response as a result of geometric nonlinearities. Such effects have been shown to be well-represented by a combination of linear shear and rotational springs, i.e., the two-spring model. Here, the two-spring model is extended to consider material nonlin- earity in the shear spring, and an empirical representation of the experimentally observed variation of yield strength is included. The governing equations are reformulated to be compatible with a stiffness-based state determination procedure, in which the bearing forces are found by iterative solution of the nonlinear equilibrium and kinematic equa- tions using Newton’s method, and the instantaneous or tangent bearing stiffness matrix is formed from the differentials of these equations. As an example, this model has been implemented as a material model for use with a zero-length spring element in OpenSees. Comparative response history analyses of slender isolated buildings demonstrate that the geometric nonlinearities have a significant influence on the peak axial forces in the the isolation bearings in strong ground motion. INTRODUCTION Base isolation is a seismic technique that has been traditionally reserved for short or squat structures. However, isolation of taller buildings is becoming more common; for example, the 32-story LA City Hall, the 18-story Oakland City Hall, and numerous projects in Japan. Certainly, overturning in these slender structures will generate large axial forces in the isolation bearings. Designers are concerned about the stability of rubber isolation bearings under large compressive loads and their ability to withstand tensile loads. Thus, mechanical models are needed that can accurately predict the force- deformation behavior of bearings under extreme variations in axial loading, but without being overly expensive (e.g., representing a single bearing as a mesh of 3-dimensional finite elements). This paper presents the formulation and implementation of a new mechanical bearing model that specifically accounts for the nonlinear geometric effects, i.e., the influence of 1 17 ANALYSIS AND COMPUTATION SPECIALTY CONFERENCE th Copyright ASCE 2006 17th Analysis and Computation Specialty Conference Structures Congress 2006 Downloaded from ascelibrary.org by North Carolina State University on 01/11/13. Copyright ASCE. For personal use only; all rights reserved.