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

STEP 0: Pre-Calculation Summary
Formula Used
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))
Gh = 584*Mthollowshaft*Lh/(θhollow*do^4*(1-C^4))
This formula uses 6 Variables
Variables Used
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.
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.
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.
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)
Angle of Twist of Hollow Shaft: 23.58 Degree --> 0.411548637620186 Radian (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
Gh = 584*Mthollowshaft*Lh/(θhollow*do^4*(1-C^4)) --> 584*320*0.33/(0.411548637620186*0.046^4*(1-0.85^4))
Evaluating ... ...
Gh = 70016766790.6141
STEP 3: Convert Result to Output's Unit
70016766790.6141 Pascal -->70016.7667906141 Newton per Square Millimeter (Check conversion here)
FINAL ANSWER
70016.7667906141 70016.77 Newton per Square Millimeter <-- Modulus of Rigidity of 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

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

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

Define Modulus of Rigidity

Shear modulus also known as Modulus of rigidity is the measure of the rigidity of the body, given by the ratio of shear stress to shear strain. Often denoted by G sometimes by S or μ. Shear Modulus of elasticity is one of the measures of mechanical properties of solids. Other elastic moduli are Young’s modulus and bulk modulus. The shear modulus of material gives us the ratio of shear stress to shear strain in a body.

How to Calculate Modulus of Rigidity given Angle of Twist of Hollow Shaft on basis of Torsional Rigidity?

Modulus of Rigidity given Angle of Twist of Hollow Shaft on basis of Torsional Rigidity calculator uses 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)) to calculate the Modulus of Rigidity of Hollow Shaft, The Modulus of Rigidity given Angle of Twist of Hollow Shaft on basis of Torsional Rigidity formula is defined as Shear modulus also known as Modulus of rigidity is the measure of the rigidity of the body, given by the ratio of shear stress to shear strain. Often denoted by G sometimes by S or μ. Modulus of Rigidity of Hollow Shaft is denoted by Gh symbol.

How to calculate Modulus of Rigidity given Angle of Twist of Hollow Shaft on basis of Torsional Rigidity using this online calculator? To use this online calculator for Modulus of Rigidity given Angle of Twist of Hollow Shaft on basis of Torsional Rigidity, enter Torsional Moment in Hollow Shaft (Mthollowshaft), Length of Hollow Shaft (Lh), Angle of Twist of Hollow Shaft hollow), 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 Modulus of Rigidity given Angle of Twist of Hollow Shaft on basis of Torsional Rigidity calculation can be explained with given input values -> 0.070017 = 584*320*0.33/(0.411548637620186*0.046^4*(1-0.85^4)).

FAQ

What is Modulus of Rigidity given Angle of Twist of Hollow Shaft on basis of Torsional Rigidity?
The Modulus of Rigidity given Angle of Twist of Hollow Shaft on basis of Torsional Rigidity formula is defined as Shear modulus also known as Modulus of rigidity is the measure of the rigidity of the body, given by the ratio of shear stress to shear strain. Often denoted by G sometimes by S or μ and is represented as Gh = 584*Mthollowshaft*Lh/(θhollow*do^4*(1-C^4)) or 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)). 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, 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, 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 Modulus of Rigidity given Angle of Twist of Hollow Shaft on basis of Torsional Rigidity?
The Modulus of Rigidity given Angle of Twist of Hollow Shaft on basis of Torsional Rigidity formula is defined as Shear modulus also known as Modulus of rigidity is the measure of the rigidity of the body, given by the ratio of shear stress to shear strain. Often denoted by G sometimes by S or μ is calculated using 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)). To calculate Modulus of Rigidity given Angle of Twist of Hollow Shaft on basis of Torsional Rigidity, you need Torsional Moment in Hollow Shaft (Mthollowshaft), Length of Hollow Shaft (Lh), Angle of Twist of Hollow Shaft hollow), 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, Angle of Twist 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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