Bending of circular-section bonded rubber blocks

Convenient exact closed-form expressions are derived for calculating the bending stiffness of and stresses within loaded cylindrical bonded rubber blocks of circular cross-section. The particular solutions for simple bending, cantilever loading and apparent shear situations are deduced and studied in detail. The shapes of the deformed profiles are discussed and confirmation is provided that the previously adopted assumption of parabolic profiles of the deformed lateral curved surface is only valid for blocks of very small aspect ratio. In simple bending a relationship which is more realistic than those hitherto suggested is derived for the couple required to maintain a specified rotation of the loaded end of the block. In apparent shear an exact expression for the ratio of the true to the apparent shear modulus is derived, and compared with the experimental data. An improved approximate relation is deduced.