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Torsional buckling is a phenomenon of geometric instability in beams subjected to a bending moment, which occurs when the compressed part or flange of certain open sections buckles laterally, causing the section to translate horizontally and rotate around the shear center, in addition to translating vertically due to the applied loads. Resistance to torsional buckling therefore depends on the lateral bending stiffness E I _z of the beam and the torsional stiffness of the section. Similar to buckling or local buckling, there is a critical moment beyond which the beam will buckle.

In "The Theory of Elastic Stability", S.P. Timoshenko analytically determined the critical torsional buckling moment for a simply supported beam with respect to bending. The main steps are outlined below. The basic assumptions of the model are...