Torsional Stress Formula

Torsional stress formula of hollow and solid shaft.

Torsional stress of solid shaft Torsional stress of hollow 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

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