A refined shear deformation theory for flexure of thick beams

TLDR: In this paper, a Hyperbolic Shear Deformation Theory (HPSDT) is used for the static flexure analysis of thick isotropic beams, taking into account transverse shear deformation effects.

Abstract: A Hyperbolic Shear Deformation Theory (HPSDT) taking into account transverse shear deformation effects, is used for the static flexure analysis of thick isotropic beams. The displacement field of the theory contains two variables. The hyperbolic sine function is used in the displacement field in terms of thickness coordinate to represent shear deformation. The transverse shear stress can be obtained directly from the use of constitutive relations, satisfying the shear stress-free boundary conditions at top and bottom of the beam. Hence, the theory obviates the need of shear correction factor. Governing differential equations and boundary conditions of the theory are obtained using the principle of virtual work. General solutions of thick isotropic simply supported, cantilever and fixed beams subjected to uniformly distributed and concentrated loads are obtained. Expressions for transverse displacement of beams are obtained and contribution due to shear deformation to the maximum transverse displacement is investigated. 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.