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Angle of Twist of Hollow Shaft on Basis of Torsional Rigidity Calculator

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✖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 [Mthollowshaft]
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✖Length of Hollow Shaft is the distance between two ends of a hollow shaft.ⓘ Length of Hollow Shaft [Lh]
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✖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 [Gh]
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✖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 [do]
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✖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]
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✖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 on Basis of Torsional Rigidity [θhollow]
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Angle of Twist of Hollow Shaft on Basis of Torsional Rigidity

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

Example
`"23.58565°"=584*"3.2E5N*mm"*"330mm"/("70000N/mm²"*("46mm")^4*(1-("0.85")^4))`

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

STEP 0: Pre-Calculation Summary
Formula Used
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))
θhollow = 584*Mthollowshaft*Lh/(Gh*do^4*(1-C^4))
This formula uses 6 Variables
Variables Used
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.
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.
Length of Hollow Shaft - (Measured in Meter) - Length of Hollow Shaft is the distance between two ends of a hollow shaft.
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.
STEP 1: Convert Input(s) to Base Unit
Torsional Moment in Hollow Shaft: 320000 Newton Millimeter --> 320 Newton Meter (Check conversion here)
Length of Hollow Shaft: 330 Millimeter --> 0.33 Meter (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
STEP 2: Evaluate Formula
Substituting Input Values in Formula
θhollow = 584*Mthollowshaft*Lh/(Gh*do^4*(1-C^4)) --> 584*320*0.33/(70000000000*0.046^4*(1-0.85^4))
Evaluating ... ...
θhollow = 0.411647214046393
STEP 3: Convert Result to Output's Unit
0.411647214046393 Radian -->23.5856480131812 Degree (Check conversion here)
FINAL ANSWER
23.5856480131812 ≈ 23.58565 Degree <-- Angle of Twist of Hollow Shaft
(Calculation completed in 00.004 seconds)
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Home » Physics » Design of Automobile Elements » Design of Shafts » Design of Hollow Shaft » Angle of Twist of Hollow Shaft on Basis of Torsional Rigidity

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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

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

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))
θhollow = 584*Mthollowshaft*Lh/(Gh*do^4*(1-C^4))

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 Angle of Twist of Hollow Shaft on Basis of Torsional Rigidity?

Angle of Twist of Hollow Shaft on Basis of Torsional Rigidity calculator uses 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)) to calculate the Angle of Twist of Hollow Shaft, The Angle of Twist of Hollow Shaft on Basis of Torsional Rigidity formula is defined as the angle through which fixed end of a shaft rotates with respect to the free end is called the angle of twist. Angle of Twist of Hollow Shaft is denoted by θhollow symbol.

How to calculate Angle of Twist of Hollow Shaft on Basis of Torsional Rigidity using this online calculator? To use this online calculator for Angle of Twist of Hollow Shaft on Basis of Torsional Rigidity, enter Torsional Moment in Hollow Shaft (Mthollowshaft), Length of Hollow Shaft (Lh), Modulus of Rigidity of Hollow Shaft (Gh), Outer Diameter of Hollow Shaft (do) & Ratio of Inner to Outer Diameter of Hollow Shaft (C) and hit the calculate button. Here is how the Angle of Twist of Hollow Shaft on Basis of Torsional Rigidity calculation can be explained with given input values -> 1351.358 = 584*320*0.33/(70000000000*0.046^4*(1-0.85^4)).

FAQ

What is Angle of Twist of Hollow Shaft on Basis of Torsional Rigidity?
The Angle of Twist of Hollow Shaft on Basis of Torsional Rigidity formula is defined as the angle through which fixed end of a shaft rotates with respect to the free end is called the angle of twist and is represented as θhollow = 584*Mthollowshaft*Lh/(Gh*do^4*(1-C^4)) or 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)). 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, Length of Hollow Shaft is the distance between two ends of a hollow shaft, 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.
How to calculate Angle of Twist of Hollow Shaft on Basis of Torsional Rigidity?
The Angle of Twist of Hollow Shaft on Basis of Torsional Rigidity formula is defined as the angle through which fixed end of a shaft rotates with respect to the free end is called the angle of twist is calculated using 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)). To calculate Angle of Twist of Hollow Shaft on Basis of Torsional Rigidity, you need Torsional Moment in Hollow Shaft (Mthollowshaft), Length of Hollow Shaft (Lh), Modulus of Rigidity of Hollow Shaft (Gh), Outer Diameter of Hollow Shaft (do) & 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, Length of Hollow Shaft, Modulus of Rigidity of 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.
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