Displacements in Thick Beams Using Refined Shear Deformation Theory

Abstract

A trigonometric shear deformation theory for displacement of thick beams, by considering the transverse shear deformation effects, is presented. Variables in the present theory are same as that of in the first order shear deformation theory. The sinusoidal function is used in displacement field in terms of thickness coordinate to represent the shear deformation effects. Governing differential equations and various boundary conditions are obtained by using the principle of virtual work. The thick isotropic beams are considered for the numerical studies to demonstrate the efficacy of the theory. It has been shown that the theory is capable of predicting the local effect of stress concentration due to fixity of support. The cantilever and fixed isotropic beams subjected to various loads are examined using the present theory. Results obtained are discussed with those of other theories.

Keywords: Thick beam, trigonometric shear deformation, principle of virtual work, equilibrium equations, displacement, stress