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The subject of this paper is the rigorous derivation of lower dimensionalmodels for a nonlinearly elastic thin-walled beam whose cross-section is givenby a thin tubular neighbourhood of a smooth curve. Denoting by h and{\delta}_h, respectively, the diameter and the thickness of the cross-section,we analyse the case where the scaling factor of the elastic energy is of order{\epsilon}_h^2, with {\epsilon}_h/{\delta}_h^2 \rightarrow l \in [0, +\infty).Different linearized models are deduced according to the relative order ofmagnitude of {\delta}_h with respect to h.

Thin-walled beams with a cross-section of arbitrary geometry: derivation of linear theories starting from 3D nonlinear elasticity