Nonlinear theory of non-uniform torsion of thin-walled open beams |
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| Authors: | Mario M. Attard |
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| Affiliation: | School of Civil Engineering, The New South Wales Institute of Technology, Sydney, Australia;The State Key Laboratory of Mechanical Transmission, Chongqing University, Chongqing 400044, China;School of Civil Engineering, National Technical University, Zografou Campus, GR-157 80 Athens, Greece;Department of Civil Engineering, University of Cape Town, Rondebosch 7701, Cape Town, South Africa;Engineering Systems and Environment Department, School of Engineering & Applied Science, University of Virginia, Charlottesville, VA, USA;Beijing Urban Construction Design & Development Group Co., Limited, Beijing 100037, China;National Engineering Laboratory for Green & Safe Construction Technology in Urban Transit, Beijing 100037, China;Department of Mechanical Engineering, University of Bristol, Bristol, UK |
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| Abstract: | A nonlinear theory of non-uniform torsion based on finite displacements is developed. Expressions for the finite nonlinear strains in Lagrangian coordinates and the Kirchhoff stresses for thin-walled open beams are presented. Using the principle of stationary total potential, the dual forms of the beam equilibrium equations are derived. For conservatively loaded thin-walled open beams a static stability criterion, based on the positive definiteness of the second variation of the total potential, is presented. The criterion developed takes into account the effects of changes in beam geometry such as initial bending curvature, prior to instability. |
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