Twisting and Bending of Thin-Walled Prismatic Beams of Open Cross-Sectional Profile

Abstract

Previous studies of the behaviour, in generalized co-ordinates, of thin-walled, prismatic beams of open cross-sectional profile have included, explicitly, only the effects of distributed transverse forces, q x and q y, distributed longitudinal forces, q z, and distributed torsional couples, m z. Using the principle of virtual displacements, the work of previous investigators is extended to include, quite generally, the effects of the hitherto neglected distributed couples, m x and m y. The derivation of the differential equation relating to the twisting of an open-section prismatic beam is presented fully whilst those relating to transverse and axial displacements of cross-sections are merely stated. The kinematic and static boundary conditions for a cantilever are also established from the virtual work equations. These show that the free-end shear boundary condition associated with transverse bending which is usually adopted in engineering calculations is inadequate for such a generalized loading system.