Keywords: thin walled beams, one-dimensional beam models, buckling and post-buckling analysis, nonlinear elasticity.

Thin walled beams can be modelled as three-dimensional bodies, shell, folded plates or, as their shape seems to suggest, as one-dimensional continua. In the last case it must be pointed out that, also in the framework of the linear elasticity, the Saint- Venant solutions cannot apply, in most of the cases. This essentially is because, generally speaking, they do not obey the Saint-Venant principle. Starting from the beginning of the twentieth century, many attempts have been made to generate handy and reliable one-dimensional models for thin walled beams in both linear and nonlinear fields. These proposals are examined by considering the cases in which the starting point is a three-dimensional body, a two-dimensional (plate or shell) model, a direct one-dimensional continuum. The most relevant features of the structural behaviour of thin walled beams are discussed and some results obtained by using one-dimensional models in both linear and nonlinear analyses, are reported.

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