Torsion of thin-walled beams of open cross-section with influence of shear

An approximate analytical approach to the torsion of thin-walled beams of open cross-section with influence of shear is presented. It is assumed that the normal stresses in the cross-section contour direction are small compared to the normal stresses in the beam longitudinal direction that can be ignored in the stress-strain relations. The stresses and displacements are obtained in the closed analytical form. It is assumed that transverse load can be reduced to moments of torsion only, with respect to the cross-section shear centre. The beam will be subjected to torsion, with respect to the shear centre, i.e. the principal cross-section sectorial coordinate, in the case of cross-sections with two axes of symmetry; to torsion and bending in the case of cross-sections with one axes of symmetry and to torsion, bending and tension in the case of general cross-sections. An illustrative example of beam with one axis of symmetry is given.