Flexural Analysis of Isotropic Rectangular Beam Subjected to Uniformly Varying Load Using Seventh Order Shear Deformation Theory for Different Boundary Conditions

A refined seventh order shear-deformation theory is outlined in current research paper, to investigate bending behavior of deep beam. The displacement field of theory under consideration relies on two variables, where transverse displacement is segmented in bending along with shear. This theory enables direct computation of transverse shear- stresses effectively using constitutive relations, satisfying no shear-stress state on the beam's upper and lower surfaces. Therefore, the shear correction coefficient is not obligatory according to theory. The virtual-work Principle is applied to get the boundary condition and governing expressions. A rectangular isotropic beam under uniformly varying load is recognized for illustration. The analysis is conducted and performed, and the expressions are retrieved for the transverse displacements, normal displacements, normal bending stresses, and transverse shear stresses for various boundary conditions viz simply supported, fixed and cantilever. Results are numerically assessed for a range of length to thickness ratios of beam. Obtained results are represented in the forms of tables and graphs. These results are validated by results of the elementary theory, Timoshenko theory and other higher-order theories available in the literature to substantiate the theory's effectiveness.