Semi-Elliptical Load Thick Beam Analysis Using 5th Order Shear Deformation Theory

Abstract

A 5th order shear deformation theory considering transverse shear deformation effect is presented for static flexure analysis of isotropic beams with built in ends. The considered displacement field accounts for non-linear variation of in-plane displacements as well as transverse displacement through the thickness of beam. The condition of zero transverse shear stresses on the top and bottom surface of beam is fulfilled. Governing equations and boundary conditions of the theory are obtained using the well known principle of virtual work. Closed form analytical solution for isotropic thick beam subjected to semi-elliptical load is obtained. Numerical results for static bending analysis include the effects of side to thickness ratio and beam aspect ratio for isotropic beams are obtained. The results of present theory are in close accord with those of higher order shear deformation theories.

Keywords: Thick isotropic beam, 5th order shear deformation theory, semi-elliptical load, built-in ends.