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Torsion of Shafts

This page provides insight into determining the torsion. It will explore many things relating to torsion, such as:
  1. The torsion capacity of shafts.
  2. Circular shafts, the polar moment of inertia.
  3. The diameter of solid shafts.
  4. The angular deflection of the shaft.
This page will also provide some functions to help you calculate torsion.

Calculation

Inputs



Torsion, T
:30.00nm​



Polar moment of inertia, J
:40m^4​



Distance from centre, r
:20.00m​


Here are the variables for the equation



Output



Shear stress, τ (Max)
:15.00Pa​


τ=T× rJ\tau = \frac{T\times\ r}{J}

Circular Shaft Maximum Torsion Calculation

Inputs



Max shear stress, τ (max)
:50.00Pa​



Radius of the Shaft, R
:25.00m​



Polar Moment of Inertia, J
:40.00m^4​


Here are the variables for the equation

Outputs



Max torsion, T (max)
:80.00nm​


Tmax=τmax× JRT_{max} = \frac{\tau_{max}\times\ J}{R}


Circular Shaft Polar Moment Of Inertia Calculation

Inputs



Shaft Diameter, D
:1.00m​


Here are the variables for the equation

Outputs



Polar Moment Of Inertia, J
:0.10m^4​


J=π×D432J=\frac{\pi\times D^4}{32}

Diameter of a Solid Shaft Calculation

Inputs



Max Torsion, T (max)
:70.00nm​



Max Shear Stress, τ (max)
:40.00Pa​


Here are the variables for the equation

Outputs



Diameter, D
:2.07m​


D=1.72×(Tmaxτmax)13D = 1.72\times(\frac{T_{max}}{\tau_{max}})^\frac{1}{3}

Torsional Deflection of Shaft Calculation

Inputs



Shaft Length, L
:25.00m​



Torsion, T (angular shaft)
:45.00nm​



Modulus of Rigidity, G
:50.00Pa​



Polar Moment of inertia, J
:20.00m^4​


Here are the variables for the equation

Outputs



Shaft Angular Deflection, α
:1.13rad​


α=L⋅TG⋅J\alpha = \frac{L\cdot T}{G\cdot J}

Explanation

Torsion is defined as the twisting of an object due to an applied torque, the shear stress or pressure on an object as a result of an applied twisting moment (torque)
Often used concerning shafts, torsion is also relevant to other areas.
The polar moment of inertia measures a beam's ability to resist torsion. This is necessary to determine the shear stress of a beam under torque.
Calculating the diameter of solid shafts is also possible using the maximum shear stress and maximum twisting moment.
The angular deflection of the shaft is also important to determine the warping of the cross-section of a beam.

Shaft Torsion Calculation

This is the general formula for calculating the shear stress of a shaft using the imposed torsion (T), the distance from the centre of the surface (r) and the moment of inertia (J).

τ=T× rJ\tau = \frac{T\times\ r}{J}
Calculating the shear stress of shafts is important to ensure structural integrity and safety, as it helps design shafts that can withstand the applied forces without failing.

Circular Shaft Maximum Torsion Calculation

This is the formula for calculating the maximum torsion within a circular shaft. The torsion is calculated using the shear stress (τ), the radius (r) and the moment of inertia (J).

Tmax=τmax× JRT_{max} = \frac{\tau_{max}\times\ J}{R}

Circular Shaft Polar Moment of Inertia Calculation

As the polar moment of inertia is needed to determine the torsion of a circular shaft, you may also like to use the formula and function below to calculate it!
The polar moment of inertia can be calculated by just knowing the diameter of the shaft.

J=π×D432J=\frac{\pi\times D^4}{32}

Diameter of a Solid Shaft Calculation

From this, it is also possible to determine the required diameter of a circular shaft if you know the maximum torsion (T) and the maximum shear stress of the shaft (τ). The diameter can be calculated using the formula and function below.

D=1.72×(Tmaxτmax)13D = 1.72\times(\frac{T_{max}}{\tau_{max}})^\frac{1}{3}

Torsional Deflection of Shaft Calculation

Accurately calculating the torsional deflection of a shaft helps ensure the optimal performance and longevity of mechanical systems.
The torsional deflection of a shaft is calculated using the length of the shaft (L), the torsion (T), the rigidity modulus (G) and the moment of inertia (J).

α=L⋅TG⋅J\alpha = \frac{L\cdot T}{G\cdot J}

The Torsion For Other Shapes:

To calculate the torsion for other shaped shafts, check out these calculators:

Solid Cylinder Shaft Torsion

Hollow Cylinder Shaft Torsion

Ellipse Shaft Torsion

Rectangle Shaft Torsion

Square Shaft Torsion

Hexagon Shaft Torsion

C-Channel Section Shaft

I-Section Shaft Torsion

Rectangle Hollow Shaft Torsion

Triangle Shaft Maximum Allowable Torsion

Related Resources

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