# Torsional Stress Formula

Torsional stress formula of hollow and solid shaft.

 Parameter Symbol Equation Shear stress τ $$\tau =\frac { Tp }{ J }$$ Angle of twist θ $$\theta =\frac { TL }{ GJ }$$ Maximum shear stress τmax $${ \tau }_{ max }=\frac { T{ c }_{ 2 } }{ J }$$ Polar moment of inertia of solid shaft J $$J=\frac { \pi }{ 2 } ({ c }_{ 2 }^{ 4 })$$ Polar moment of inertia of hollow shaft J $$J=\frac { \pi }{ 2 } ({ c }_{ 2 }^{ 4 }-{ c }_{ 1 }^{ 4 })$$ Power P $$P=T\cdot w$$

T: Torque to be transmitted, J: Polar moment of inertia, p: Radial distance to center of shaft, c1: Hollow shaft inner radius, c2: Shaft outer radius, L: Length of the shaft, G: Modulus of rigidity, w: Rotation speed, P: Power