Torsional Moment given Torsional Shear Stress in Hollow Shaft 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 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%
✖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 Hollow Shaft [d_o]			+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%

✖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 given Torsional Shear Stress in Hollow Shaft [Mt_hollowshaft]

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Formula

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Torsional Moment given Torsional Shear Stress in Hollow Shaft

Formula

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

Example

`"320651.1N*mm"="35.1N/mm²"*(pi*("46mm")^3*(1-("0.85")^4))/16`

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Torsional Moment given Torsional Shear Stress in Hollow Shaft Solution

STEP 0: Pre-Calculation Summary

Formula Used

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
Mt_hollowshaft = 𝜏_h*(pi*d_o^3*(1-C^4))/16
This formula uses 1 Constants, 4 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

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.
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.
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 Shear Stress in Hollow Shaft: 35.1 Newton per Square Millimeter --> 35100000 Pascal (Check conversion here)
Outer Diameter of Hollow Shaft: 46 Millimeter --> 0.046 Meter (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

Mt_hollowshaft = 𝜏_h*(pi*d_o^3*(1-C^4))/16 --> 35100000*(pi*0.046^3*(1-0.85^4))/16

Evaluating ... ...

Mt_hollowshaft = 320.651089276111

STEP 3: Convert Result to Output's Unit

320.651089276111 Newton Meter -->320651.089276111 Newton Millimeter (Check conversion here)

FINAL ANSWER

320651.089276111 ≈ 320651.1 Newton Millimeter <-- Torsional Moment in Hollow Shaft

(Calculation completed in 00.004 seconds)

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Created by Kethavath Srinath

Osmania University (OU), Hyderabad

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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

Torsional Moment given Torsional Shear Stress in Hollow Shaft Formula

Define Torsion

In the field of solid mechanics, torsion is the twisting of an object due to an applied torque. Torsion is expressed in either the Pascal (Pa), an SI unit for newtons per square metre, or in pounds per square inch (psi) while torque is expressed in newton metres (N·m) or foot-pound force (ft·lbf). In sections perpendicular to the torque axis, the resultant shear stress in this section is perpendicular to the radius.

How to Calculate Torsional Moment given Torsional Shear Stress in Hollow Shaft?

Torsional Moment given Torsional Shear Stress in Hollow Shaft calculator uses 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 to calculate the Torsional Moment in Hollow Shaft, The Torsional Moment given Torsional Shear Stress in Hollow Shaft formula is defined as the twisting of a beam under the action of torque (twisting moment). It is systematically applied to screws, nuts, axles, drive shafts, etc,. Torsional Moment in Hollow Shaft is denoted by Mt_hollowshaft symbol.

How to calculate Torsional Moment given Torsional Shear Stress in Hollow Shaft using this online calculator? To use this online calculator for Torsional Moment given Torsional Shear Stress in Hollow Shaft, enter Torsional Shear Stress in Hollow Shaft (𝜏_h), Outer Diameter of Hollow Shaft (d_o) & Ratio of Inner to Outer Diameter of Hollow Shaft (C) and hit the calculate button. Here is how the Torsional Moment given Torsional Shear Stress in Hollow Shaft calculation can be explained with given input values -> 3.2E+8 = 35100000*(pi*0.046^3*(1-0.85^4))/16.

FAQ

What is Torsional Moment given Torsional Shear Stress in Hollow Shaft?

The Torsional Moment given Torsional Shear Stress in Hollow Shaft formula is defined as the twisting of a beam under the action of torque (twisting moment). It is systematically applied to screws, nuts, axles, drive shafts, etc, and is represented as Mt_hollowshaft = 𝜏_h*(pi*d_o^3*(1-C^4))/16 or 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. Torsional Shear Stress in Hollow Shaft is the shear stress produced in the hollow shaft due to the twisting, Outer Diameter of Hollow Shaft is defined as the length of the longest chord of the surface of the hollow circular 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.

How to calculate Torsional Moment given Torsional Shear Stress in Hollow Shaft?

The Torsional Moment given Torsional Shear Stress in Hollow Shaft formula is defined as the twisting of a beam under the action of torque (twisting moment). It is systematically applied to screws, nuts, axles, drive shafts, etc, is calculated using 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. To calculate Torsional Moment given Torsional Shear Stress in Hollow Shaft, you need Torsional Shear Stress in Hollow Shaft (𝜏_h), Outer Diameter of Hollow Shaft (d_o) & Ratio of Inner to Outer Diameter of Hollow Shaft (C). With our tool, you need to enter the respective value for Torsional Shear Stress in Hollow Shaft, Outer Diameter of 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 Torsional Moment in Hollow Shaft?

In this formula, Torsional Moment in Hollow Shaft uses Torsional Shear Stress in Hollow Shaft, Outer Diameter of Hollow Shaft & Ratio of Inner to Outer Diameter of Hollow Shaft. We can use 1 other way(s) to calculate the same, which is/are as follows -

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)

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