Static Flexure of Thick Fixed Beams Subjected to Cosine Loading using Refined Shear Deformation Theory

Abstract

The theory is developed to analyze the thick fixed beam considering the effect of transverse shear deformation. The important feature of this theory is that the transverse shear stresses can be obtained directly using constitutive relationship. While developing the theory the number of variables is kept same as that of first order shear deformation theory. As the theory satisfies the zero shear stress condition on the top and bottom of beam surface, the present theory does not require any shear correction factor. The governing differential equations and boundary conditions are obtained by using the principle of virtual work. A general solution technique is developed to solve the governing differential equations of the theory. Theory ^is applied to thick fixed beams with cosine loading to obtain the complete flexural response subjected to static bending. The behavior of transverse shear stresses at the fixed ends is studied precisely by using equilibrium equation of theory of elasticity and in accordance with the refined shear deformation theories. The results of displacement and stresses are compared with those of elementary theory of beam bending, first order shear deformation theory, trigonometric shear deformation theory and hyperbolic shear deformation theory.

Keywords: Thick beam, refined shear deformation theory, displacement based theory, equilibrium equations