Analytic solution for torsion of thin-walled laminated composite beams of symmetrical open cross sections with influence of shear

An approximate analytic solution for torsion of thin-walled laminated composite beams of symmetrical open cross sections with influence of shear is presented. The solution based on the classical Vlasov’s thin-walled beam theory is modified for thin-walled laminated composite beams with orthotropic and symmetrical lay-up. It is shown that the beam subjected to torsion with influence of shear, caused by couples in the cross section planes, is also subjected to bending due to shear in the plane orthogonal to the plane of symmetry. If the cross section has two axes of symmetry, the beam will be subjected only to torsion with influence of shear. The expressions for the displacements and normal stresses are derived in closed analytic form. The material influence on shear is defined by factor that depends on the fibre orientations. Simply supported and clamped beams subjected to distributed couples are considered. Illustrative examples are provided, and the results for the displacements and stresses show very good agreement between analytical ones and numerically obtained results utilizing three-dimensional shell finite elements.