Bending Torsion Theory of a Beam with Shear Deformation

Abstract

One of the problems in beam theory is the incompletion of the theory for shear deformation. The authors previously proposed the method analyzing the problems of coupling shear and torsion in beams having arbitrary cross-sectional forms using St. Venant's theory by the finite element method, and the stiffness matrix for space framework elements, taking shear deformation into account, was determined. However, since the restraint and warping connection at beam ends cannot be taken into account in order to approximate these generalization and extension of the warping rigidity of Wagner's equation, in which the mode of warping is left as it is, and the magnitude is axially changed was attempted.