Anwendung der Verallgemeinerten Technische Biegetheorie auf kreisförmig gekrümmte Stäbe

Dedicated to Prof. Dr.-Ing. habil. Joachim Lindner on the occasion of his 80th birthday. This paper reports the latest developments concerning the application of Generalised Beam Theory (GBT) to thin-walled members with deformable cross-section and whose undeformed axis is a circular arc, with no pre-twist. Initially, the fundamental equations and relations are presented, leading to the first-order equilibrium equations and associated boundary conditions, which can be written in terms of GBT modal matrices or stress resultants. Then, the procedure to obtain the cross-section deformation modes is explained. Arbitrary (open, closed or ”mixed“) flat-walled cross-sections are covered, even though the kinematic constraints employed to subdivide the modes are much more complex than for prismatic members – in particular, the mode shapes become dependent on the curvature of the beam axis. Using a displacement-based GBT finite element, a set of illustrative examples is presented, involving complex local-distortional-global deformation. These examples show that very accurate results are obtained with the proposed GBT formulation and that the modal solution provides in-depth insight into the structural behaviour of naturally curved members.