ONE-DIMENSIONAL FINITE ELEMENT ANALYSIS OF WARPING TORSION FOR THIN-WALLED MEMBERS WITH OPEN-CLOSED CROSS SECTIONS BASED ON COMPATIBLE WARPING FIELD

The warping torsion of thin-walled members with open and closed cross sections was well addressed by the classical theories presented by Timoshenko and Benscoter, respectively. However, the restrained torsional behavior of thin-walled members with open-closed profile cannot be correctly accounted for without considering the distinctive warping properties between open and closed parts of the cross section. The development of warping shear flows within the mid-plane of the cross section needs further elaborations. This work assumes that the torsional warping of open and closed segments correspondingly adheres to the classical assumptions of Vlasov and Umanskii. The warping displacements are required to coincide at the common points of the open and closed segments, leading to a compatible warping field which contains undetermined warping parameter. The warping parameter is explicitly obtained based on the equilibrium requirements. A one-dimensional finite element model is naturally developed for warping torsion analysis of a thin-walled member with open-closed cross section. It is shown by numerical investigations and parametric studies that the type I method based on the Second Umanskii theory can artificially introduce the additional shear flows that reduce the accuracy of shear stresses. As an alternative, the type II method based on the Second Umanskii theory can only obtain the average shear stress of each segment of thin-walled section which fails to provide the correct distribution of shear flows. The Beam-189 element model based on the Vlasov assumption unfortunately neglects the induced warping displacements and shear flows by the constrained effects of the closed contour. Hence, the use of Beam-189 element will reduce the accuracies of both normal and shear stresses. Close agreement can be observed between the Shell-63 element model and the present method for calculating the torsional deformation and stresses, which demonstrates the capability of the one-dimensional finite element model to describe the torsional and warping stiffness of the thin-walled members with open-closed cross section.