More general expression for the torsional warping of a thin-walled open-section beam. (Q1430842)

Based on a combination of Vlasov's and Kirchhoff's assumptions, the authors deal with the formulation of a torsional warping function for thin-walled open-section beams. Following Goodier and Gjelsvik, they also take into account the thickness warping, not only the contour one. It is shown that the torsional warping function may contain two parts: the contour function and the thickness warping function. Various theories do not lead to significant differences for warping constants, but for some cross-sectional constants the differences may be considerable. It is shown that Goodier's theory is a good approximation for the warping problem. However, it seems that the authors' results give a more general analytical expression for the torsional warping function; the position of the twist centre is considered, too. Numerical results are given for nonsymmetric \(Z\)- and angle-sections, as well as for symmetric and nonsymmetric channel sections.