Outer Diameter of Shaft given Torsional Shear Stress Solution

STEP 0: Pre-Calculation Summary
Formula Used
Outer Diameter of Hollow Shaft = (16*Torsional Moment in Hollow Shaft/(pi*Torsional Shear Stress in Hollow Shaft*(1-Ratio of Inner to Outer Diameter of Hollow Shaft^4)))^(1/3)
do = (16*Mthollowshaft/(pi*𝜏h*(1-C^4)))^(1/3)
This formula uses 1 Constants, 4 Variables
Constants Used
pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288
Variables Used
Outer Diameter of Hollow Shaft - (Measured in Meter) - Outer Diameter of Hollow Shaft is defined as the length of the longest chord of the surface of the hollow circular shaft.
Torsional Moment in Hollow Shaft - (Measured in Newton Meter) - Torsional Moment in Hollow Shaft is the reaction induced in a structural shaft hollow element when an external force or moment is applied to the element, causing the element to twist.
Torsional Shear Stress in Hollow Shaft - (Measured in Pascal) - Torsional Shear Stress in Hollow Shaft is the shear stress produced in the hollow shaft due to the twisting.
Ratio of Inner to Outer Diameter of Hollow Shaft - The Ratio of Inner to Outer Diameter of Hollow Shaft is defined as the inner diameter of the shaft divided by the outer diameter.
STEP 1: Convert Input(s) to Base Unit
Torsional Moment in Hollow Shaft: 320000 Newton Millimeter --> 320 Newton Meter (Check conversion ​here)
Torsional Shear Stress in Hollow Shaft: 35.1 Newton per Square Millimeter --> 35100000 Pascal (Check conversion ​here)
Ratio of Inner to Outer Diameter of Hollow Shaft: 0.85 --> No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
do = (16*Mthollowshaft/(pi*𝜏h*(1-C^4)))^(1/3) --> (16*320/(pi*35100000*(1-0.85^4)))^(1/3)
Evaluating ... ...
do = 0.0459688442234587
STEP 3: Convert Result to Output's Unit
0.0459688442234587 Meter -->45.9688442234587 Millimeter (Check conversion ​here)
FINAL ANSWER
45.9688442234587 45.96884 Millimeter <-- Outer Diameter of Hollow Shaft
(Calculation completed in 00.008 seconds)

Credits

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Created by Kethavath Srinath
Osmania University (OU), Hyderabad
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Design of Hollow Shaft Calculators

Tensile Stress in Hollow Shaft when Subjected to Axial Force
​ LaTeX ​ Go Tensile Stress in Hollow Shaft = Axial Force on Hollow Shaft/(pi/4*(Outer Diameter of Hollow Shaft^2-Inner Diameter of Hollow Shaft^2))
Inner Diameter of Hollow Shaft given Ratio of Diameters
​ LaTeX ​ Go Inner Diameter of Hollow Shaft = Ratio of Inner to Outer Diameter of Hollow Shaft*Outer Diameter of Hollow Shaft
Ratio of Inner Diameter to Outer Diameter
​ LaTeX ​ Go Ratio of Inner to Outer Diameter of Hollow Shaft = Inner Diameter of Hollow Shaft/Outer Diameter of Hollow Shaft
Outer Diameter given Ratio of Diameters
​ LaTeX ​ Go Outer Diameter of Hollow Shaft = Inner Diameter of Hollow Shaft/Ratio of Inner to Outer Diameter of Hollow Shaft

Outer Diameter of Shaft given Torsional Shear Stress Formula

​LaTeX ​Go
Outer Diameter of Hollow Shaft = (16*Torsional Moment in Hollow Shaft/(pi*Torsional Shear Stress in Hollow Shaft*(1-Ratio of Inner to Outer Diameter of Hollow Shaft^4)))^(1/3)
do = (16*Mthollowshaft/(pi*𝜏h*(1-C^4)))^(1/3)

Define Shear Stress

Shear stress, force tending to cause deformation of a material by slippage along a plane or planes parallel to the imposed stress. The resultant shear is of great importance in nature, being intimately related to the downslope movement of earth materials and to earthquakes. Shear stress may occur in solids or liquids; in the latter it is related to fluid viscosity.

How to Calculate Outer Diameter of Shaft given Torsional Shear Stress?

Outer Diameter of Shaft given Torsional Shear Stress calculator uses Outer Diameter of Hollow Shaft = (16*Torsional Moment in Hollow Shaft/(pi*Torsional Shear Stress in Hollow Shaft*(1-Ratio of Inner to Outer Diameter of Hollow Shaft^4)))^(1/3) to calculate the Outer Diameter of Hollow Shaft, Outer Diameter of Shaft given Torsional Shear Stress formula is defined as a measure of the outer diameter of a hollow shaft in a mechanical system, considering the torsional shear stress and other design parameters, to ensure the structural integrity and performance of the shaft. Outer Diameter of Hollow Shaft is denoted by do symbol.

How to calculate Outer Diameter of Shaft given Torsional Shear Stress using this online calculator? To use this online calculator for Outer Diameter of Shaft given Torsional Shear Stress, enter Torsional Moment in Hollow Shaft (Mthollowshaft), Torsional Shear Stress in Hollow Shaft (𝜏h) & Ratio of Inner to Outer Diameter of Hollow Shaft (C) and hit the calculate button. Here is how the Outer Diameter of Shaft given Torsional Shear Stress calculation can be explained with given input values -> 45968.84 = (16*320/(pi*35100000*(1-0.85^4)))^(1/3).

FAQ

What is Outer Diameter of Shaft given Torsional Shear Stress?
Outer Diameter of Shaft given Torsional Shear Stress formula is defined as a measure of the outer diameter of a hollow shaft in a mechanical system, considering the torsional shear stress and other design parameters, to ensure the structural integrity and performance of the shaft and is represented as do = (16*Mthollowshaft/(pi*𝜏h*(1-C^4)))^(1/3) or Outer Diameter of Hollow Shaft = (16*Torsional Moment in Hollow Shaft/(pi*Torsional Shear Stress in Hollow Shaft*(1-Ratio of Inner to Outer Diameter of Hollow Shaft^4)))^(1/3). Torsional Moment in Hollow Shaft is the reaction induced in a structural shaft hollow element when an external force or moment is applied to the element, causing the element to twist, Torsional Shear Stress in Hollow Shaft is the shear stress produced in the hollow shaft due to the twisting & The Ratio of Inner to Outer Diameter of Hollow Shaft is defined as the inner diameter of the shaft divided by the outer diameter.
How to calculate Outer Diameter of Shaft given Torsional Shear Stress?
Outer Diameter of Shaft given Torsional Shear Stress formula is defined as a measure of the outer diameter of a hollow shaft in a mechanical system, considering the torsional shear stress and other design parameters, to ensure the structural integrity and performance of the shaft is calculated using Outer Diameter of Hollow Shaft = (16*Torsional Moment in Hollow Shaft/(pi*Torsional Shear Stress in Hollow Shaft*(1-Ratio of Inner to Outer Diameter of Hollow Shaft^4)))^(1/3). To calculate Outer Diameter of Shaft given Torsional Shear Stress, you need Torsional Moment in Hollow Shaft (Mthollowshaft), Torsional Shear Stress in Hollow Shaft (𝜏h) & Ratio of Inner to Outer Diameter of Hollow Shaft (C). With our tool, you need to enter the respective value for Torsional Moment in Hollow Shaft, Torsional Shear Stress in Hollow Shaft & Ratio of Inner to Outer Diameter of Hollow Shaft and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
How many ways are there to calculate Outer Diameter of Hollow Shaft?
In this formula, Outer Diameter of Hollow Shaft uses Torsional Moment in Hollow Shaft, Torsional Shear Stress in Hollow Shaft & Ratio of Inner to Outer Diameter of Hollow Shaft. We can use 3 other way(s) to calculate the same, which is/are as follows -
  • Outer Diameter of Hollow Shaft = Inner Diameter of Hollow Shaft/Ratio of Inner to Outer Diameter of Hollow Shaft
  • Outer Diameter of Hollow Shaft = (32*Bending Moment in Hollow Shaft/(pi*Bending Stress in Hollow Shaft*(1-Ratio of Inner to Outer Diameter of Hollow Shaft^4)))^(1/3)
  • Outer Diameter of Hollow Shaft = (16*(Bending Moment in Hollow Shaft+sqrt(Bending Moment in Hollow Shaft^2+Torsional Moment in Hollow Shaft^2))/(pi*Maximum Principle Stress in Hollow Shaft*(1-Ratio of Inner to Outer Diameter of Hollow Shaft^4)))^(1/3)
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