ABSTRACT
Due to the double symmetry of the box beam, the fields of normal stresses given rise by the axial force or the bending moments are orthogonal with those given rise by the torsion (and distortion). Thus the former can be independently superposed on the latter. Then for the antisymmetric warpings like torsion and distortion the box side mid-axes can be regarded as continuous non-compressible axial supports preventing the axial displacement only. The beam can be cut along these axes into two (or four) guided Vlasov beams with open cross-section, which can be analysed using the formal methods of the theory of guided beams. 2, 3, 4
The idea of the theory of guided beams is the fact that for thin-walled beams, the deformations of which are restricted by external continuous lateral or longitudinal restraints, the mutually independent effective force and displacement quantities (warpings in terms of the generalized bending theory), which can be determined independently by only external loads, are defined in a solving system of axes and special points, which does not coincide with the fundamental system with the origin at the centroid, the pole at the shear centre, and the axes parallel to the (central) principal directions. The choice of the adequate system of axes and special points is analogous to separating correctly a group of mutually dependent differential equations to mutually independent equations.
The main aim of this study is to create an “exact” solution of the problem in terms of the theory of guided Vlasov beams. “Exact” means that no information is lost regards to the premises of the theory.
