Flexure of Thick Fixed Beams Subjected to Varying Load using Shear Deformation Theory

Abstract

A refined shear deformation theory for flexural analysis of thick beams, considering transverse shear deformation effects, is developed. The number of variables as in the first order shear deformation theory is kept in present theory. The important feature of present theory is that the transverse shear stresses can directly be obtained using constitutive relations. The theory does not demand shear correction factors. The principle of virtual work is used to obtain the governing differential equations and boundary conditions. To obtain the response of thick fixed beam subjected to varying loading the present theory applied and a general solution technique is developed to solve governing differential equations. 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.