Effect of Stress-Free Edges in Plane Shear of a Flat Body

Abstract

Abstract This paper determines the tangential stiffness of a flat rectangular body, or shear pad, with a uniform relative tangential displacement on the upper and lower surfaces. The state of stress differs from pure shear in that the edges are stress-free. The correction to the stiffness in pure shear is obtained as a function of Poisson’s ratio and the length-to-thickness ratio. The paper also illustrates the power of energy methods in furnishing accurate approximations with a small amount of numerical work when only over-all quantities, such as stiffness, are investigated. By manipulating energy relations and using the Prager-Synge approximate method a few hours of slide-rule computation was sufficient to determine both upper and lower bounds for the stiffness.