Summary: We consider the dynamical one-dimensional Mindlin-Timoshenko system for beams. We analyze how its controllability properties depend on the modulus of elasticity in shear \(k\). In particular we prove that the exact boundary controllability property of the Kirchhoff system may be obtained as a singular limit, as \(k\rightarrow\infty,\) of the partial controllability of projections over a sharp subspace of solutions generated by the eigenfunctions that converge, as \(k\rightarrow\infty\), towards the spectrum of the Kirchhoff system.