# Torsion (Circle Section)

Written by Jerry Ratzlaff on . Posted in Classical Mechanics

Torsion, abbreviated as T, is the stress of twisting of an object due to applied torque.

## Torsion (Circle section) FORMULA

 $$\large{ T = \frac{ J \; \tau }{ \rho } }$$ $$\large{ \tau = \frac{ T \; \rho }{ J } }$$ $$\large{ k = \frac{ G \; J }{ l } }$$ $$\large{ \mu = \frac{ T^2 \; l }{ 2 \; G \; J } }$$ $$\large{ f = \frac{ l }{ G \; J } }$$ $$\large{ \theta = \frac{ T \; l }{ G \; J } }$$

### Where:

$$\large{ T }$$ = applied torque or moment of torsion

$$\large{ \theta }$$  (Greek symbol theta) = angle

$$\large{ \rho }$$  (Greek symbol rho) = distance between the rotational axis and the farthest point in the section

$$\large{ l }$$ = length

$$\large{ \tau }$$ (Greek symbol tau) = maximum shear stress at the outer surface

$$\large{ G }$$ = shear modulus

$$\large{ \mu }$$  (Greek symbol mu) = strain energy

$$\large{ J }$$ = torsion constant (polar momentum of inertia)

$$\large{ f }$$ = torsional flexibility

$$\large{ k }$$ = torsional stiffness