Equivalent beam analysis of thin-walled beam structures

Abstract

In the analysis of thin-walled beam structures it is often necessary to consider the effects of warping restraint in addition to the more usual actions of pure torsion, bending moment and axial force. Out-of-plane warping occurs as a result of twisting about the horizontal axis and, if restrained, may result in the development of large additional stresses. Indeed, for some structural configurations and applications of load, warping restraint may be the predominant action and must be considered fully in the analysis. The equivalent beam method is already widely used for the stress analysis of structures incorporating solid or thick-walled beam elements. Its attraction derives from the ease with which even complex structures may be idealized and rapidly solved by desk-top computers of modest capacity. The method is extended here to the analysis of thin-walled beam structures by the addition of an extra degree of freedom representing the action of warping restraint. The development of two similar beam elements is described, one for straight beams, the other for circularly curved beams. The application of the equivalent beam method is demonstrated in the computer analysis of two very different engineering structures.