A simple model for the twisting of I beams including web distortion – Application to members supported along a single flange. (February 2022) - Ferreira, Miguel; Providência, Paulo; Andrade, Anísio
Graphical abstract: Highlights: A simple model for the torsional behavior of I-beams with web distortion is derived. It permits a realistic modelling of loading and supports, e.g. at one flange only. The distributions of the distortional moments in the web are a natural output. The finite element implementation is based on the three-field variational principle. Illustrative examples show that it yields accurate results with very coarse meshes. Abstract: In the analysis of thin-walled members, some types of boundary conditions met in practice cannot be correctly represented by conventional line (1D) models. Of course, both shell models or advanced line models (such as generalised beam theory, GBT, among others) can accurately tackle this type of problems – at the cost, however, of the simple interpretation of results provided by conventional line models. This paper investigates the combined bending and twisting of doubly symmetric I beams supported along a single flange. This type of support precludes the application of the conventional Vlasov's theory, because it ignores the distortion of the cross section. A simple line model which accounts for web distortion is developed and a mixed 3-field finite element – which can achieve any required accuracy on very coarse meshes – is derived for its numerical implementation. Illustrative examples are also presented.