Torsion

Any moment vector that is collinear with an axis of a mechanical part is called a torque vector, because the moment causes the part to be twisted about that axis. A bar subjected to such a moment is said to be in torsion.

Angle of Twist

The angle of twist, in radians for a solid round bar is:

$$\theta =\frac{Tl}{GJ}\text{(radians)}$$

where:

• $T$ is torque
• $l$ is length
• $G$ is the modulus of rigidity
• $J$ is the polar moment of inertia

Shear Stress

Shear stress develop throughout the cross section. For a round bar in torsion, these stresses are given by

$$\tau =\frac{T\rho }{J}$$

Designating $r$ as the radius of the outer surface, we have

$${\tau }_{\text{max}}=\frac{Tr}{J}$$