Generally two types of stresses are induced in a shaft.
1. Torsional (Shear) stresses due to transmission of torque.
2. Bending stresses due to weight of pulley, gear etc mounted on shaft.
A circular shaft is said to be in a state of pure torsion when it is subjected to torque only, without being acted upon by any bending moment or axial force.
OR; if the shaft is subjected to two opposite turning moment it is said to be in pure torsion. and it will exhibit the tendency of shearing off at every cross-section which is perpendicular to longitudinal axis.