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

✖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%
✖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%

✖Length of Hollow Shaft is the distance between two ends of a hollow shaft.ⓘ Length of Shaft given Angle of Twist of Hollow Shaft on Basis of Torsional Rigidity [L_h]

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Formula

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

Formula

`"L"_{"h"} = "θ"_{"hollow"}*("G"_{"h"}*"d"_{"o"}^4*(1-"C"^4))/(584*"Mt"_{"hollowshaft"})`

Example

`"329.921mm"="23.58°"*("70000N/mm²"*("46mm")^4*(1-("0.85")^4))/(584*"3.2E5N*mm")`

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

STEP 0: Pre-Calculation Summary

Formula Used

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

Variables Used

Length of Hollow Shaft - (Measured in Meter) - Length of Hollow Shaft is the distance between two ends of a hollow shaft.
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.
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.

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
Torsional Moment in Hollow Shaft: 320000 Newton Millimeter --> 320 Newton Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

L_h = θ_hollow*(G_h*d_o^4*(1-C^4))/(584*Mt_hollowshaft) --> 0.411548637620186*(70000000000*0.046^4*(1-0.85^4))/(584*320)

Evaluating ... ...

L_h = 0.329920975486926

STEP 3: Convert Result to Output's Unit

0.329920975486926 Meter -->329.920975486926 Millimeter (Check conversion here)

FINAL ANSWER

329.920975486926 ≈ 329.921 Millimeter <-- Length of Hollow Shaft

(Calculation completed in 00.020 seconds)

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

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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

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

Define Angle of Twist

For a shaft under torsional loading, the angle through which fixed end of a shaft rotates with respect to the free end is called the angle of twist. As the torque is increased, the outer region of the shaft behaves like a plastic material while the inner core is still linear elastic.

How to Calculate Length of Shaft given Angle of Twist of Hollow Shaft on Basis of Torsional Rigidity?

Length of Shaft given Angle of Twist of Hollow Shaft on Basis of Torsional Rigidity calculator uses 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) to calculate the Length of Hollow Shaft, The Length of Shaft given Angle of Twist of Hollow Shaft on Basis of Torsional Rigidity formula is defined as length of the hollow shaft on which we are applying twisting moment. Length of Hollow Shaft is denoted by L_h symbol.

How to calculate Length of Shaft given Angle of Twist of Hollow Shaft on Basis of Torsional Rigidity using this online calculator? To use this online calculator for Length of Shaft given Angle of Twist of Hollow Shaft 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) & Torsional Moment in Hollow Shaft (Mt_hollowshaft) and hit the calculate button. Here is how the Length of Shaft given Angle of Twist of Hollow Shaft on Basis of Torsional Rigidity calculation can be explained with given input values -> 329921 = 0.411548637620186*(70000000000*0.046^4*(1-0.85^4))/(584*320).

FAQ

What is Length of Shaft given Angle of Twist of Hollow Shaft on Basis of Torsional Rigidity?

The Length of Shaft given Angle of Twist of Hollow Shaft on Basis of Torsional Rigidity formula is defined as length of the hollow shaft on which we are applying twisting moment and is represented as L_h = θ_hollow*(G_h*d_o^4*(1-C^4))/(584*Mt_hollowshaft) or 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). 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 & 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.

How to calculate Length of Shaft given Angle of Twist of Hollow Shaft on Basis of Torsional Rigidity?

The Length of Shaft given Angle of Twist of Hollow Shaft on Basis of Torsional Rigidity formula is defined as length of the hollow shaft on which we are applying twisting moment is calculated using 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). To calculate Length of Shaft given Angle of Twist of Hollow Shaft 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) & Torsional Moment in Hollow Shaft (Mt_hollowshaft). 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 & Torsional Moment in Hollow Shaft and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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