Development of design code oriented formulas for elastomeric bearings including bulk compressibility and reinforcement extensibility

The introduction of alternative reinforcement types for elastomeric bearings has rendered it necessary to consider the extensibility of the reinforcement as an additional design parameter. The extensibility of the reinforcement reduces the lateral restraint on the elastomer and, similar to the compressibility of the elastomer, influences important design parameters such as the compression modulus and bending modulus. Neglecting the compressibility of the elastomer or the extensibility of the reinforcement may result in an unconservative overestimation of these design parameters. Existing analytical solutions, which have been developed based on the pressure solution, are usually not suitable for design purposes. In this study, the analytical solutions for infinite strip, circular, square, and annular pad geometries are expanded and simplified to form geometry-specific approximations that account for reinforcement extensibility and bulk compressibility. The derived approximations closely and conservatively follow the analytical solutions over a large range of shape factors and values of the elastomer bulk modulus and reinforcement extensibility. A similar procedure used for the compression modulus and bending modulus is applied to approximate the maximum shear strain due to compression, including bulk compressibility and reinforcement extensibility. Generalized equations are proposed that can be adapted to the elastomeric pad geometries considered