Application of Generalised Beam Theory to curved members with circular axis

Abstract

AbstractDedicated to Prof. Dr.‐Ing. habil. Joachim Lindner on the occasion of his 80th birthdayThis 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.