If the upper end of a cylinder is clamped and a torque is applied at the lower end the cylinder gets twisted by angle q. Simultaneously shearing strain  is produced in the cylinder.

(i) The angle of twist q  is directly proportional to the distance from the fixed end of the cylinder.

At fixed end  and at free end q = maximum.

(ii) The value of angle of shear f is directly proportional to the radius of the cylindrical shell.

At the axis of cylinder f = 0 and at the outermost shell f = maximum.

(iii) Relation between angle of twist (q) and angle of shear (f)

AB = rq = fl      

(iv) Twisting couple per unit twist or torsional rigidity or torque required to produce unit twist.

(v) Work done in twisting the cylinder through an angle q  is