Curved thin-walled open-closed cross section beams with finite width

Abstract

In this paper a consistent formulation of the static behaviour of circular beams with thin-walled open-closed cross section is presented. The influence of the different radius of curvature of each element of the cross section is taken into account, assuming the hypothesis of linear elasticity and that the distortion of the cross section is prevented. The warping shape function is derived from a detailed study of properly defined pure torsion case. The topological properties of the multiple-connected cross section are considered within the scope of the Graph Theory, so that a general analysis of the nodal equilibrium requirement and compatability conditions, for both pure and non-uniform torsion, is presented. Some new aspects, relevant to the compatibility of equilibrium equations and the uncoupling conditions between torsion and both normal force and bending, are discussed extensively. Important consequences of this analysis is the coherent definition of the Shear Centre. The equilibrium equations governing non-uniform torsion are derived assuming the warping displacement as the product of an appropriate shape function by a function ψ( s), different from the unitary twist angle. The shear flow in the bending case is determined.