Shear strain demands in elastomeric bearings subjected to rotation

In seismic base isolation applications, fiber reinforcement was initially proposed as a potential cost-saving alternative to conventional steel reinforcement in laminated bearings. Steel reinforcement is often assumed to be rigid, but the extensibility of the reinforcement serves as an additional design parameter that must be considered. Similar to the compressibility of the elastomer, the extensibility of the reinforcement has a pronounced effect on important design parameters such as the compression modulus, bending modulus, and shear strains that develop because of compression or rotation. Analytical solutions for the bending modulus developed based on the pressure solution are available for most common pad geometries and can be used to derive the maximum shear strain due to rotation. These solutions are often complex and unsuitable for design purposes. In this study, the analytical solutions for an infinite strip, circular, square, rectangular, and annular pad geometries are derived and simplified to form geometry-specific approximations for the maximum shear strain due to rotation. The simplified approximations account for the reinforcement extensibility and the compressibility of the elastomer. The derived approximations are evaluated based on the analytical solutions and provide accurate values over a wide range of shape factors and values of bulk compressibility and reinforcement extensibility