A New Hyperbolic Shear Deformation Theory for Flexure of Thick Simply Supported Beam

Abstract

A new hyperbolic shear deformation theory for flexure of simply supported thick or deep beam, taking into account transverse shear deformation effects, is developed. The number of variables in the present theory is same as that in the hyperbolic shear deformation theory. The governing differential equations and boundary conditions are obtained by using the principle of virtual work. The trigonometric function is used in displacement field in terms of thickness coordinate to represent the shear deformation effects. This theory satisfies the transverse shear stresses on the top and bottom surfaces of the simply supported isotropic beam, which gives excellent results for transverse shear stress by using constitutive relations. Thus, the shear correction factor is omitted. In this paper the simply supported isotropic beam subjected to uniformly varying load is examined using the present theory. The results of the present theory are compared with those of other refined shear deformation theories of beam to verify the accuracy of the theory.

Keywords: Simply-supported, thick beam, varying load, new hyperbolic shear deformation, principle of virtual work, equilibrium equations, dis- placement, stress