Modified hyperbolic shear deformation theory for static flexure analysis of thick isotropic beam

Abstract

A hyperbolic shear deformation theory for thick isotropic beams is developed where the displacements are defined using a meaningful function which is more physical and directly comparable with other higher order theories. Governing variationally consistent equilibrium equations and boundary conditions are derived in terms of the stress resultants and displacements using the principle of virtual work. This theory satisfies shear stress free boundary condition at top and bottom of the beam and doesn’t need shear correction factor. Results obtained for stresses and displacements using the present theory for static flexure of simply supported uniform isotropic beam carrying uniformly distributed load are compared with other beam theories and the exact elasticity solution.