Hollow Cylinder Shaft Torsion

This calculator calculates the maximum allowable torsion for a hollow cylinder shaft. This is done using the equation below.
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T=π×τmax((2R)4−(2r)4)16×2R=π×τmax(D4−d4)16×DT = \frac{\pi\times\tau_{max}((2R)^4-(2r)^4)}{16\times 2R}\\ = \frac{\pi\times \tau_{max}(D^4-d^4)}{16\times D}T=16×2Rπ×τmax​((2R)4−(2r)4)​=16×Dπ×τmax​(D4−d4)​
The following are the variables for the equations...
T = the torsion twisting torque or tension. (Nm, lb f ft).
τ (max) = maximum shear stress (Pa).
r = the inner radius of the circle (m).
R = the outer radius of the circle (m).
d = the inner diameter of the circle (m).
D = the outer diameter of the circle (m).
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Figure 1: Diagram of the Circular Hollow Section to Calculate the Torsion
Hollow Cylinder Shaft Torsion CalculatorInputs﻿﻿Inner Diameter, d
:3.00m​
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﻿﻿Max shear stress, τ (max)
:20.00Pa​
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﻿﻿Outer Diameter, D
:5.00m​
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Output﻿﻿Torsion, T
:427.26nm​
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T=π×τmax(D4−d4)16×DT = \frac{\pi\times \tau_{max}(D^4-d^4)}{16\times D}T=16×Dπ×τmax​(D4−d4)​
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