  A theory for the prediction of the size dependence of torsional rigidities of
nanosized structural elements is developed. It is shown that, to a very good
approximation, the torsional rigidity (D) of a nanosized bar differs from the
prediction of standard continuum mechanics $(D_c)$ as $(D-D_c)/D_c = A h_0/a$
where A is a non-dimensional constant, a is the size scale of the cross-section
of the bar and $h_0$ is a material length equal to the ratio of the surface
elastic constant to the bulk elastic constant. The theory developed is compared
with direct atomistic calculations (``numerical experiment'') of the torsional
rigidity bars made of several FCC metals modeled using the embedded atom
method. Very good agreement is obtained between theory and simulation. The
framework presented here can aid the development of design methodologies for
nanoscale structural elements without the need for full scale atomistic
simulations.
