Beam Element Including Shear Deformation

Abstract

The finite element models of the Bernoulli-Euler beam theory and Timoshenko beam theory are now standard. The Timoshenko beam theory allow for the effect of transverse shear deformation which has been neglected in the Bernoulli-Euler beam theory. The first author developed a beam element based on a displacement formulation of Timoshenko beam theory. The objective of this paper is to present a formulation for beam element based on the new beam theory proposed by Endo and Kimura. In this theory, the transverse displacement w is taken as a sum of two partial displacements, one part, wb, due to bending, and the second, ws, due shear displacement. The efficacy of the present beam element is demonstrated through the numerical example of static flexure.