A shear-flexible element with warping for thin-walled open beams

A new Þnite element for the analysis of thin-walled open beams with an arbitrary cross section is presented. Combining Timoshenko beam theory and Vlasov thin-walled beam theory, the derived element includes both ßexural shear deformations and warping deformations caused by the bimoment. By adopting an orthogonal Cartesian co-ordinate system, one can obviate the ad hoc introduction of St. Venant sti¤ness. The derived block sti¤ness matrix is comparable but more general than the one given by earlier researchers. The versatility and accuracy of the new element are demonstrated by comparing the numerical results with the classical solutions or other numerical results available in the literature