Torsion and Flexure of Curved, Thin-Walled Beams or Tubes

The investigation is concerned with the determination of the stresses and deformation of curved, open and closed cross-sectional, thin-walled beams or tubes taking into account the effects of the warping of the cross section. The solutions for the open and closed cross sections are very similar. The analysis is based solely upon equilibrium, stress-strain, and strain-displacement relations, thus, the concepts of the shear center and the self-equilibrating stress system are not necessary. Also, the slender beam assumption is not made in the analysis. The basic assumption in regard to warping is that the warping be a function of the twist of the beam only, with this function being given by a generalization of the St. Venant theory for uniform torsion. The method is in general intended for solution using a digital computer. The application of the resulting equations is illustrated with example problems.