Elastic biaxial bending and torsion of thin-walled members

This paper presents a detailed treatment of the non-linear elastic biaxial bending and torsion of thin-walled open section members. The treatment is valid for uniform members of linear elastic material, and is limited to small strains and rotations, and moderate deflections. Shear straining of the mid-surface of the member wall is neglected, and it is assumed that the member does not distort or buckle locally. The effects of initial deformations, loads, stresses, and strains are incorporated.

The treatment is based on non-linear strain-displacement relationships, and these are used to derive the non-linear equilibrium and tangent stiffness equations in forms which are suitable for computer solution by the finite element method.

Approximate linear and non-linear differential equilibrium equations are derived, as are the differential equilibrium equations and the energy equation for neutral equilibrium at bifurcation buckling, and these are then related to the classical equations developed by Timoshenko, Vlasov, and others.