The Unified Solution for a Beam of Rectangular Cross-Section with Different Higher-Order Shear Deformation Models

Abstract

The unified solution is studied for a beam of rectangular cross section. With the rotation defined in the average sense over the cross section, the kinematics with higher-order shear deformation models in axial displacement is first expressed in a unified form by using the fundamental higher-order term with some properties. The shear correction factor is then derived and discussed for the four commonly used higher-order shear deformation models including the third-order model, the sine model, the hyperbolic sine model and the exponential model. The unified solution is finally obtained for a beam subjected to an arbitrarily distributed load. The relation with that from the conventional beam theory is established, and therefore the difference is reasonably explained. A very good agreement with the elasticity theory validates the present solution.

Comparison between Analytical Equation and Numerical Methods for Determining Shear Stress in a Cantilever Beam

“…As basic structural elements, beams have been extensively used in different fields such as architecture, mechanics, chemistry, aerospace and ocean engineering [1]. A beam is a structural element that primarily resists loads applied laterally to its axis.…”