The total energy of the system is obtained by adding to it the mechanical energy spent by an extensional load:  and that done by the torque: . Then the total energy is written as:

(24.4)

Minimizing  with respect to  and we can obtain the expressions for and .
For example, the torque is obtained as

(24.5)

And the expression for load experienced by the rod is obtained as

(24.6)

Notice that this load is somewhat larger than that would actually be required to extend the rod to an extension ratio of without application of any twist. Therefore, in a load controlled experiment, the actual extension of the rod in presence of torsion is somewhat larger and is expressed as

(24.7)

In other word, the dead weight required to generate extension ratio  will be

(24.8)