Generalised Beam Theory (GBT) for Coupled Instability Problems
This paper introduces the basic principles of first- and second-order Generalised Beam Theory (GBT). It demonstrates, among other things, that there is still some life in classical structural mechanics and that this is not just a matter for academics but has practical usefulness. Indeed, ultimately, GBT may offer the most practical way to deal with the difficult problem of the distortional buckling of cold-formed sections.
All of the problems amenable to solution using GBT can also be solved by the finite element and finite strip methods. However, GBT will invariably offer the most elegant solution and, by allowing the separation of fundamental modes, it also offers possibilities that are not present in these alternative methods. In particular, in its second-order form, there are particularly attractive possibilities for dealing with problems involving coupled instabilities.
The paper shows how Generalised Beam Theory (GBT) can be advantageously used to investigate a range of practical problems in the design of cold-formed section columns and beams. Single-mode bifurcation problems, more general bifurcation problems and general buckling problems are among those which are amenable to GBT and practical examples of each are included.
KeywordsDistortional Mode Elastic Foundation Virtual Work Local Buckling Section Property
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