Bending and Cramped Torsion of Thin-Walled Rods

Abstract

The derivation of the equilibrium equations of bending and torsion of a thin-walled rod with an arbitrary contour of the cross section is given. The structural elements of the rod, represented by longeron and stringer belts, have tensile–compressive rigidity, and the panels perceive only shear. Panels connect the belts, which ensures joint deformation of all elements of the rod. The movement of the belts is determined by the hypothesis of flat sections. With tight torsion, the movements of the belts depend on the geometric parameters and may not coincide with the plane of the cross section. Only the torque acts on the rod, in this case, the internal forces in the belts satisfy the equations: the sum of the forces and the sum of the bending moments are zero. The rank of the matrix of equations is three, therefore, it is proposed in the work to form groups with a different number of belts, and for each of them to form equilibrium equations for the constrained torsion of a thin-walled rod. This is a peculiar form of belt equilibrium equations. Examples of rod’s torsion are considered.