We determine the deformation energetics and energy density of twisted carbon nanotubes and nanotube ropes that effectively constitute a torsional spring. Using ab initio and parametrized density functional calculations, we identify structural changes in these systems and determine their elastic limits. The deformation energy of twisted nanotube ropes contains contributions associated not only with twisting but also with stretching, bending, and compression of individual nanotubes. We quantify these energy contributions and show that their relative role changes with the number of nanotubes in the rope.