Thermal Response of Thick Beam Subjected to Thermo-mechanical Loads by Using HyperbolicShear Deformation Theory

Abstract

In this paper, a hyperbolic shear deformation theory (HPSDT) taking into account transverse shear deformation effect is presented for thermo-mechanical stress analysis of thick isotropic beam subjected to thermo-mechanical. The displacement field contains two variables. The hyperbolic sine and cosine function is used in the displacement field in terms of thickness Co-ordinate to represent the effect of shear deformation. The most important feature of the theory is that, the transverse shear stresses can be obtained directly from the use of equilibrium equation, satisfying the stress-free boundary conditions at top and bottom surfaces of the beam. The present 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. Navier solution technique is employed for the simply supported beams. The results obtained for bending analysis of isotropic beam subjected to thermo-mechanical load are compared with those obtained by other theories like the elementary theory of beam (ETB), first-order shear deformation theory (FSDT), to validate the accuracy of the presented theory.

Keywords:Hyperbolic shear deformation, isotropic thick beam, principle of virtual work, thermo-mechanical loads