Outer Diameter of Shaft given Torsional Shear Stress Calculator

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Design of Hollow Shaft

ASME Code for Shaft Desgin

Maximum Shear Stress and Principal Stress Theory

Shaft Design on Strength Basis

Torsional Rigidity

✖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 Moment in Hollow Shaft [Mt_hollowshaft]			+10% -10%
✖Torsional Shear Stress in Hollow Shaft is the shear stress produced in the hollow shaft due to the twisting.ⓘ Torsional Shear Stress in Hollow Shaft [𝜏_h]			+10% -10%
✖The Ratio of Inner to Outer Diameter of Hollow Shaft is defined as the inner diameter of the shaft divided by the outer diameter.ⓘ Ratio of Inner to Outer Diameter of Hollow Shaft [C]			+10% -10%

✖Outer Diameter of Hollow Shaft is defined as the length of the longest chord of the surface of the hollow circular shaft.ⓘ Outer Diameter of Shaft given Torsional Shear Stress [d_o]

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Formula

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Outer Diameter of Shaft given Torsional Shear Stress

Formula

`"d"_{"o"} = (16*"Mt"_{"hollowshaft"}/(pi*"𝜏"_{"h"}*(1-"C"^4)))^(1/3)`

Example

`"45.96884mm"=(16*"3.2E5N*mm"/(pi*"35.1N/mm²"*(1-("0.85")^4)))^(1/3)`

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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)
d_o = (16*Mt_hollowshaft/(pi*𝜏_h*(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

d_o = (16*Mt_hollowshaft/(pi*𝜏_h*(1-C^4)))^(1/3) --> (16*320/(pi*35100000*(1-0.85^4)))^(1/3)

Evaluating ... ...

d_o = 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 00.004 seconds)

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Credits

Created by Kethavath Srinath

Osmania University (OU), Hyderabad

Kethavath Srinath has created this Calculator and 1000+ more calculators!

Verified by Urvi Rathod

Vishwakarma Government Engineering College (VGEC), Ahmedabad

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< 23 Design of Hollow Shaft Calculators

Outer Diameter of Hollow Shaft given Principle Stress

Go 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)

Ratio of Diameters given Principle Stress

Go Ratio of Inner to Outer Diameter of Hollow Shaft = (1-16*(Bending Moment in Hollow Shaft+sqrt(Bending Moment in Hollow Shaft^2+Torsional Moment in Hollow Shaft^2))/(pi*Outer Diameter of Hollow Shaft^3*Maximum Principle Stress in Hollow Shaft))^(1/4)

Principle Stress Maximum Principle Stress Theory

Go Maximum Principle Stress in Hollow Shaft = 16*(Bending Moment in Hollow Shaft+sqrt(Bending Moment in Hollow Shaft^2+Torsional Moment in Hollow Shaft^2))/(pi*Outer Diameter of Hollow Shaft^3*(1-Ratio of Inner to Outer Diameter of Hollow Shaft^4))

Outer Diameter of Hollow Shaft given Angle of Twist Torsional Rigidity

Go Outer Diameter of Hollow Shaft = (584*Torsional Moment in Hollow Shaft*Length of Hollow Shaft/(Modulus of Rigidity of Hollow Shaft*Angle of Twist of Hollow Shaft*(1-Ratio of Inner to Outer Diameter of Hollow Shaft^4)))^(1/4)

Ratio of Diameters given Angle of Twist of Hollow Shaft and Torsional Rigidity

Go Ratio of Inner to Outer Diameter of Hollow Shaft = (1-584*Torsional Moment in Hollow Shaft*Length of Hollow Shaft/(Modulus of Rigidity of Hollow Shaft*Outer Diameter of Hollow Shaft^4*Angle of Twist of Hollow Shaft))^(1/4)

Length of Shaft given Angle of Twist of Hollow Shaft on Basis of Torsional Rigidity

Go Length of Hollow Shaft = Angle of Twist of Hollow Shaft*(Modulus of Rigidity of Hollow Shaft*Outer Diameter of Hollow Shaft^4*(1-Ratio of Inner to Outer Diameter of Hollow Shaft^4))/(584*Torsional Moment in Hollow Shaft)

Torsional Moment given Angle of Twist on Basis of Torsional Rigidity

Go Torsional Moment in Hollow Shaft = Angle of Twist of Hollow Shaft*(Modulus of Rigidity of Hollow Shaft*Outer Diameter of Hollow Shaft^4*(1-Ratio of Inner to Outer Diameter of Hollow Shaft^4))/(584*Length of Hollow Shaft)

Modulus of Rigidity given Angle of Twist of Hollow Shaft on basis of Torsional Rigidity

Go Modulus of Rigidity of Hollow Shaft = 584*Torsional Moment in Hollow Shaft*Length of Hollow Shaft/(Angle of Twist of Hollow Shaft*Outer Diameter of Hollow Shaft^4*(1-Ratio of Inner to Outer Diameter of Hollow Shaft^4))

Angle of Twist of Hollow Shaft on Basis of Torsional Rigidity

Go Angle of Twist of Hollow Shaft = 584*Torsional Moment in Hollow Shaft*Length of Hollow Shaft/(Modulus of Rigidity of Hollow Shaft*Outer Diameter of Hollow Shaft^4*(1-Ratio of Inner to Outer Diameter of Hollow Shaft^4))

Ratio of Diameters given Tensile Stress in Hollow Shaft

Go Ratio of Inner to Outer Diameter of Hollow Shaft = sqrt(1-(Axial Force on Hollow Shaft/(pi/4*Tensile Stress in Hollow Shaft*Outer Diameter of Hollow Shaft^2)))

Outer Diameter of Shaft given Torsional Shear Stress

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)

Ratio of Diameter given Torsional Shear Stress in Hollow Shaft

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

Torsional Shear Stress when Shaft is Subjected to Pure Torsional Moment

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

Torsional Moment given Torsional Shear Stress in Hollow Shaft

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

Outer Diameter of Hollow Shaft given Bending Stress of Hollow Shaft

Go 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)

Ratio of Diameters given Bending Stress of Hollow Shaft

Go Ratio of Inner to Outer Diameter of Hollow Shaft = (1-32*Bending Moment in Hollow Shaft/(pi*Outer Diameter of Hollow Shaft^3*Bending Stress in Hollow Shaft))^(1/4)

Bending Moment given Bending Stress in Hollow Shaft

Go Bending Moment in Hollow Shaft = Bending Stress in Hollow Shaft*(pi*Outer Diameter of Hollow Shaft^3*(1-(Ratio of Inner to Outer Diameter of Hollow Shaft^4)))/32

Bending Stress in Hollow Shaft

Go Bending Stress in Hollow Shaft = 32*Bending Moment in Hollow Shaft/(pi*Outer Diameter of Hollow Shaft^3*(1-Ratio of Inner to Outer Diameter of Hollow Shaft^4))

Tensile Stress in Hollow Shaft when Subjected to Axial Force

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))

Axial Tensile Force given Tensile Stress in Hollow Shaft

Go Axial Force on Hollow Shaft = Tensile Stress in 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

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

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

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

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, The Outer Diameter of Shaft given Torsional Shear Stress formula is defined as the outer diameter of the shaft on which we are applying bending Stress. Outer Diameter of Hollow Shaft is denoted by d_o 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 (Mt_hollowshaft), Torsional Shear Stress in Hollow Shaft (𝜏_h) & 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?

The Outer Diameter of Shaft given Torsional Shear Stress formula is defined as the outer diameter of the shaft on which we are applying bending Stress and is represented as d_o = (16*Mt_hollowshaft/(pi*𝜏_h*(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?

The Outer Diameter of Shaft given Torsional Shear Stress formula is defined as the outer diameter of the shaft on which we are applying bending Stress 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 (Mt_hollowshaft), Torsional Shear Stress in Hollow Shaft (𝜏_h) & 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 4 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)
Outer Diameter of Hollow Shaft = (584*Torsional Moment in Hollow Shaft*Length of Hollow Shaft/(Modulus of Rigidity of Hollow Shaft*Angle of Twist of Hollow Shaft*(1-Ratio of Inner to Outer Diameter of Hollow Shaft^4)))^(1/4)

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