A new 3D Timoshenko finite beam element including non-uniform torsion of open and closed cross sections

Abstract

In this paper, a new linear-elastic 3D Timoshenko finite beam element, which allows consideration of warping torsion (W-beam), is presented. It is suitable for the analysis of spatial structures consisting of beams with constant open and hollow cross-sections (HCS). The analogy between 2nd-order beam theory (with axial tension) and torsion (including warping) is used for the formulation of equations for non-uniform torsion. The effect of the secondary torsional moment and of the shear forces on the deformations is included in the local finite beam element stiffness matrix. The warping part of the first derivative of the twist angle is considered as an additional degree of freedom at the nodes of the finite elements. This degree of freedom represents the part of the twist angle that is caused by the bimoment. Results of the numerical experiments are discussed, compared, and evaluated. Measurements were performed for confirmation of some of the calculated results. They have shown the importance of the inclusion of warping in stress-deformation analyses of HCS beams.