Torsional Moment given Angle of Twist on Basis of Torsional Rigidity Calculator

✖Angle of Twist of Hollow Shaft is the angle through which the fixed end of a hollow shaft rotates with respect to the free end.ⓘ Angle of Twist of Hollow Shaft [θ_hollow]			+10% -10%
✖Modulus of Rigidity of Hollow Shaft is the elastic coefficient when a shear force is applied resulting in lateral deformation. It gives us a measure of how rigid a body is.ⓘ Modulus of Rigidity of Hollow Shaft [G_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%
✖Length of Hollow Shaft is the distance between two ends of a hollow shaft.ⓘ Length of Hollow Shaft [L_h]			+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 Angle of Twist on Basis of Torsional Rigidity [Mt_hollowshaft]

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Torsional Moment given Angle of Twist on Basis of Torsional Rigidity Solution

STEP 0: Pre-Calculation Summary

Formula Used

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)
Mt_hollowshaft = θ_hollow*(G_h*d_o^4*(1-C^4))/(584*L_h)
This formula uses 6 Variables

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.
Angle of Twist of Hollow Shaft - (Measured in Radian) - Angle of Twist of Hollow Shaft is the angle through which the fixed end of a hollow shaft rotates with respect to the free end.
Modulus of Rigidity of Hollow Shaft - (Measured in Pascal) - Modulus of Rigidity of Hollow Shaft is the elastic coefficient when a shear force is applied resulting in lateral deformation. It gives us a measure of how rigid a body is.
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.
Length of Hollow Shaft - (Measured in Meter) - Length of Hollow Shaft is the distance between two ends of a hollow shaft.

STEP 1: Convert Input(s) to Base Unit

Angle of Twist of Hollow Shaft: 23.58 Degree --> 0.411548637620186 Radian (Check conversion here)
Modulus of Rigidity of Hollow Shaft: 70000 Newton per Square Millimeter --> 70000000000 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
Length of Hollow Shaft: 330 Millimeter --> 0.33 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

Mt_hollowshaft = θ_hollow*(G_h*d_o^4*(1-C^4))/(584*L_h) --> 0.411548637620186*(70000000000*0.046^4*(1-0.85^4))/(584*0.33)

Evaluating ... ...

Mt_hollowshaft = 319.92337016914

STEP 3: Convert Result to Output's Unit

319.92337016914 Newton Meter -->319923.37016914 Newton Millimeter (Check conversion here)

FINAL ANSWER

319923.37016914 ≈ 319923.4 Newton Millimeter <-- Torsional Moment in Hollow Shaft

(Calculation completed in 00.022 seconds)

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Home » Physics » Design of Automobile Elements » Design of Shafts » Mechanical » Design of Hollow Shaft » Torsional Moment given Angle of Twist on Basis of Torsional Rigidity

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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

Torsional Moment given Angle of Twist on Basis of Torsional Rigidity Formula

LaTeX Go

Define Torsional Rigidity

Torsional rigidity is the amount of resistance a cross section has against torsional deformation. The higher the rigidity, the more resistance the cross section has. It is dependent on the shape of the cross section, the shear modulus of the material, the length of the member being subjected to torsion and the support conditions.

How to Calculate Torsional Moment given Angle of Twist on Basis of Torsional Rigidity?

Torsional Moment given Angle of Twist on Basis of Torsional Rigidity calculator uses 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) to calculate the Torsional Moment in Hollow Shaft, Torsional Moment given Angle of Twist on Basis of Torsional Rigidity formula is defined as a measure of the twisting force that causes a hollow shaft to rotate, which is essential in designing hollow shafts to withstand torsional stress and deformation. Torsional Moment in Hollow Shaft is denoted by Mt_hollowshaft symbol.

How to calculate Torsional Moment given Angle of Twist on Basis of Torsional Rigidity using this online calculator? To use this online calculator for Torsional Moment given Angle of Twist on Basis of Torsional Rigidity, enter Angle of Twist of Hollow Shaft (θ_hollow), Modulus of Rigidity of Hollow Shaft (G_h), Outer Diameter of Hollow Shaft (d_o), Ratio of Inner to Outer Diameter of Hollow Shaft (C) & Length of Hollow Shaft (L_h) and hit the calculate button. Here is how the Torsional Moment given Angle of Twist on Basis of Torsional Rigidity calculation can be explained with given input values -> 3.2E+8 = 0.411548637620186*(70000000000*0.046^4*(1-0.85^4))/(584*0.33).

FAQ

What is Torsional Moment given Angle of Twist on Basis of Torsional Rigidity?

Torsional Moment given Angle of Twist on Basis of Torsional Rigidity formula is defined as a measure of the twisting force that causes a hollow shaft to rotate, which is essential in designing hollow shafts to withstand torsional stress and deformation and is represented as Mt_hollowshaft = θ_hollow*(G_h*d_o^4*(1-C^4))/(584*L_h) or 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). Angle of Twist of Hollow Shaft is the angle through which the fixed end of a hollow shaft rotates with respect to the free end, Modulus of Rigidity of Hollow Shaft is the elastic coefficient when a shear force is applied resulting in lateral deformation. It gives us a measure of how rigid a body is, 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 & Length of Hollow Shaft is the distance between two ends of a hollow shaft.

How to calculate Torsional Moment given Angle of Twist on Basis of Torsional Rigidity?

Torsional Moment given Angle of Twist on Basis of Torsional Rigidity formula is defined as a measure of the twisting force that causes a hollow shaft to rotate, which is essential in designing hollow shafts to withstand torsional stress and deformation is calculated using 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). To calculate Torsional Moment given Angle of Twist on Basis of Torsional Rigidity, you need Angle of Twist of Hollow Shaft (θ_hollow), Modulus of Rigidity of Hollow Shaft (G_h), Outer Diameter of Hollow Shaft (d_o), Ratio of Inner to Outer Diameter of Hollow Shaft (C) & Length of Hollow Shaft (L_h). With our tool, you need to enter the respective value for Angle of Twist of Hollow Shaft, Modulus of Rigidity of Hollow Shaft, Outer Diameter of Hollow Shaft, Ratio of Inner to Outer Diameter of Hollow Shaft & Length 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 Angle of Twist of Hollow Shaft, Modulus of Rigidity of Hollow Shaft, Outer Diameter of Hollow Shaft, Ratio of Inner to Outer Diameter of Hollow Shaft & Length of Hollow Shaft. We can use 1 other way(s) to calculate the same, which is/are as follows -

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

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