Warping Behavior of Open and Closed Thin-Walled Sections with Restrained Torsion

—The behavior of warping torsion of thin-walled members of open and closed cross sections is studied using the classical theories presented by Timoshenko and Benscoter. Based on their studies, the axial shear displacement modes and torsional warping functions are determined. In addition, the warping behavior of thin-walled sections of a bar with a non-uniform warping including the effects of torsion and shear forces using the governing equation for torsion are considered for different section types. Warping is extensively applied to different types of thin-walled steel cross section subjected to concentrated torsional loading, and to the most general torsional boundary conditions, by considering both torsional warping and shear deformation effects (primary shear deformation due to Saint-Venant torsion and secondary shear deformation due to restrained torsion). Warping functions indicate the non-plane warping deformations of thin-walled cross sections and sections with warping functions can warp, and normal stresses and strains from torsion (bi-moment) are proportional to the sectorial coordinate diagrams. Finally, the effects of warping on the open and closed thin-walled beams with restrained torsion are investigated, and it is shown that torsional warping is included as exceptional cases of deformations. © 2022, International Association of Engineers. All rights reserved.