We consider a beam whose cross section is a tubular neighborhood, with thickness
scaling with a parameter δε, of a simple curve γ whose length scales with ε. To model a thin-walled
beam we assume that δε goes to zero faster than ε, and we measure the rate of convergence by a
slenderness parameter s which is the ratio between ε2 and δε. In this Part I of the work we focus
on the case where the curve is open. Under the assumption that the beam has a linearly elastic
behavior, for s ∈ {0, 1} we derive two one-dimensional Γ-limit problems by letting ε go to zero.
The limit models are obtained for a fully anisotropic and inhomogeneous material, thus making the
theory applicable for composite thin-walled beams. The approach recovers in a systematic way, and
gives account of, many features of the beam models in the theory of Vlasov.
