  The subject of this paper is the rigorous derivation of lower dimensional
models for a nonlinearly elastic thin-walled beam whose cross-section is given
by 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 of
magnitude of {\delta}_h with respect to h.
