Determination of shear stresses, warping functions and section properties of thin-walled beams using finite elements

Simple, one dimensional finite elements in the plane of the cross section are used to model the axial displacement modes of thin-walled beams. Based on the weak formulation of axial equilibrium of an infinitesimal section cut-out, the axial shear displacement modes, and the torsional and distortional warping functions are determined. The axial displacement functions are then used to determine the shear stress distributions and the section properties. The method makes no distinction between open and closed single or multi celled cross sections. The transverse distortional displacement modes are found by the use of a frame model in the plane of the cross section. The paper also presents a very efficient recursive formulation of super-elements. (C) 1998 Elsevier Science Ltd. All rights reserved.