Shear and torsion correction factors of Timoshenko beam model for generic cross sections

A refined Timoshenko beam model which takes into account warping of cross sections is presented. The model extends St. Venant’s theory of uniform torsion to a generic loading of beam. Kinetic and kinematic assumptions, virtual work expression of full elasticity problem, and principle of virtual work are used to bring the presentation to the usual context of engineering models. A new definition of the warping displacement in terms of a variational problem is one of the outcomes. Warping displacements, refined constitutive equations, and correction factors for rectangle, open annular, and angle cross sections of isotropic material are used as application examples. Shear correction factors are found to be purely geometrical quantities depending only on the shape of cross section, which contradicts many findings in literature.