Formulation and Implementation of a Lead-Rubber Bearing Model Including Material and Geometric Nonlinearities

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.