When a circular shaft is subjected to longitudinal thrust, or tension, as well as twisting, the direct stresses due to the longitudinal load must be combined with the shearing stresses due to torsion in order to evaluate the principal stresses in the shaft.
Suppose the shaft is axially loaded in tension so that there is a longitudinal direct stress (T at all points of the shaft.
Figure: Shearing and direct stresses due to combined torsion and tension.
If is the shearing stress at any point, then we are interested in the principal stresses of the system shown in Figure ;
for this system the principal stresses,
and the maximum shearing stress,