  Lower bounds for the factors entering the standard notions of shear and
torsion stiffness for a linearly elastic rod are established in a new and
simple way. The proofs are based on the following criterion to identify the
stiffness parameters entering rod theory: the rod's stored-energy density per
unit length expressed in terms of force and moment resultants should equal the
stored-energy density per unit length expressed in terms of stress components
of a Saint-Venant cylinder subject to either flexure or torsion, according to
the case. It is shown that the shear factor is always greater than one,
whatever the cross section, a fact that is customarily stated without proof in
textbooks of structure mechanics; and that the torsion factor is also greater
than one, except when the cross section is a circle or a circular annulus, a
fact that is usually proved making use of Saint-Venant's solution in terms of
displacement components.
