Torsion of circular shafts

 Torsion 

Torsion refers to the twisting of a straight bar when it is loaded by moments (or torques) that tend to produce rotation about the longitudinal axis of the bar Similar to turning a screwdriver hand which applies a torque T and twists the shank of the screwdriver. An idealized case of torsional loading is by two pairs of equal and opposite forces. Each pair of forces forms a couple that tends to twist the bar about its longitudinal axis. The torque or twisting moment is the product of one of the forces and the perpendicular distance between the lines of action of the forces.

 The moments are T1 = P 1 d1 and the second is T2 = P2 d2 

The SI unit for moment is the newton meter (Nm). 

Torsional Deformation

Let the left hand end of the bar is fixed in position with the action of the torque T.  

The right-hand end will rotate through a small angle φ known as the angle of  twist (or angle of rotation).

Because of this rotation, a straight longitudinal line pq on the surface of the bar will become a helical curve pq’.

The angle of twist changes along the axis of the bar, and at intermediate cross sections it will have a value φ(x). If every cross section of the bar has the same radius and is subjected to the same torque (pure torsion), the angle φ (x) will vary linearly between the ends.