This paper is devoted to the asymptotic analysis of the problem of linear elasticity for an anisotropic and inhomogeneous body occupying, in its reference configuration, a cylindrical domain with a rectangular cross section with sides proportional to $\varepsilon$ and $\varepsilon^2$ and clamped on one of its bases. The sequence of solutions $u^\varepsilon$ of the equilibrium problem is shown to converge in an appropriate topology, as $\varepsilon$ goes to zero, to the solution of a problem for a beam in which the extensional, flexural, and torsional effects are all coupled together.