What do you mean by pure Torsion?
In general two types of stresses are induced in shaft.
1. Torsional (Shear) stresses because of transmission of torque.
2. Bending stresses because of weight of pulley, gear etc mounted on shaft.
A circular shaft is said to be in the state of pure torsion when it is subjected to torque, without being acted upon by any bending of the moment or axial force.
OR; if shaft is subjected to the two opposite turning moment it is said to be in pure torsion. And it will exhibit tendency of shearing off at every cross section that is perpendicular to longitudinal axis.