On bending and twisting of beams, part II: Finite element method

Abstract

In the first part of this article [1] a combined stretching, bending and twisting theory for a straight beam under external loading was developed. It was based on a simple displacement assumption using four warping functions. In this second part of this article it is demonstrated, how this theory can be applied to practical problems using finite element methodology. The problem can be divided into following parts: 1) determining the warping functions, 2) determining the cross-sectional quantities, 3) solving the beam problem and 4) determining the stress distribution of the cross-section. Finally, a numerical example is given.