Modulus of rigidity of shaft given total strain energy in hollow shaft Calculator

✖Shear stress on surface of shaft is force tending to cause deformation of a material by slippage along a plane or planes parallel to the imposed stress.ⓘ Shear stress on surface of shaft [𝜏]			+10% -10%
✖Outer Diameter of Shaft is defined as the length of the longest chord of the surface of the hollow circular shaft.ⓘ Outer Diameter of Shaft [d_outer]			+10% -10%
✖The Inner Diameter of Shaft is defined as the length of the longest chord inside the hollow shaft.ⓘ Inner Diameter of Shaft [d_inner]			+10% -10%
✖The Volume of Shaft is the volume of cylindical component under torsion.ⓘ Volume of Shaft [V]			+10% -10%
✖Strain Energy in body is defined as the energy stored in a body due to deformation.ⓘ Strain Energy in body [U]			+10% -10%

✖Modulus of rigidity of 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 shaft given total strain energy in hollow shaft [G]

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Formula

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Modulus of rigidity of shaft given total strain energy in hollow shaft

Formula

`"G" = (("𝜏"^2)*(("d"_{"outer"}^2)+("d"_{"inner"}^2))*"V")/(4*"U"*("d"_{"outer"}^2))`

Example

`"1.1E^-8MPa"=((("0.000004MPa")^2)*((("4000mm")^2)+(("1000mm")^2))*"125.6m³")/(4*"50KJ"*(("4000mm")^2))`

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Modulus of rigidity of shaft given total strain energy in hollow shaft Solution

STEP 0: Pre-Calculation Summary

Formula Used

Modulus of rigidity of Shaft = ((Shear stress on surface of shaft^2)*((Outer Diameter of Shaft^2)+(Inner Diameter of Shaft^2))*Volume of Shaft)/(4*Strain Energy in body*(Outer Diameter of Shaft^2))
G = ((𝜏^2)*((d_outer^2)+(d_inner^2))*V)/(4*U*(d_outer^2))
This formula uses 6 Variables

Variables Used

Modulus of rigidity of Shaft - (Measured in Pascal) - Modulus of rigidity of 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.
Shear stress on surface of shaft - (Measured in Pascal) - Shear stress on surface of shaft is force tending to cause deformation of a material by slippage along a plane or planes parallel to the imposed stress.
Outer Diameter of Shaft - (Measured in Meter) - Outer Diameter of Shaft is defined as the length of the longest chord of the surface of the hollow circular shaft.
Inner Diameter of Shaft - (Measured in Meter) - The Inner Diameter of Shaft is defined as the length of the longest chord inside the hollow shaft.
Volume of Shaft - (Measured in Cubic Meter) - The Volume of Shaft is the volume of cylindical component under torsion.
Strain Energy in body - (Measured in Joule) - Strain Energy in body is defined as the energy stored in a body due to deformation.

STEP 1: Convert Input(s) to Base Unit

Shear stress on surface of shaft: 4E-06 Megapascal --> 4 Pascal (Check conversion here)
Outer Diameter of Shaft: 4000 Millimeter --> 4 Meter (Check conversion here)
Inner Diameter of Shaft: 1000 Millimeter --> 1 Meter (Check conversion here)
Volume of Shaft: 125.6 Cubic Meter --> 125.6 Cubic Meter No Conversion Required
Strain Energy in body: 50 Kilojoule --> 50000 Joule (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

G = ((𝜏^2)*((d_outer^2)+(d_inner^2))*V)/(4*U*(d_outer^2)) --> ((4^2)*((4^2)+(1^2))*125.6)/(4*50000*(4^2))

Evaluating ... ...

G = 0.010676

STEP 3: Convert Result to Output's Unit

0.010676 Pascal -->1.0676E-08 Megapascal (Check conversion here)

FINAL ANSWER

1.0676E-08 ≈ 1.1E-8 Megapascal <-- Modulus of rigidity of Shaft

(Calculation completed in 00.004 seconds)

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Home » Physics » Strength of Materials » Torsion of Shafts And Springs » Expression for Strain Energy stored in a Body Due to Torsion » Modulus of rigidity of shaft given total strain energy in hollow shaft

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< 22 Expression for Strain Energy stored in a Body Due to Torsion Calculators

Value of radius 'r' given shear strain energy in ring of radius 'r'

Go Radius 'r' from Center Of Shaft = ((Strain Energy in body*(2*Modulus of rigidity of Shaft*(Radius of Shaft^2)))/(2*pi*(Shear stress on surface of shaft^2)*Length of Shaft*Strain Energy in body*Length of Small Element))^(1/3)

Radius of shaft given shear strain energy in ring of radius r

Go Radius of Shaft = sqrt((2*pi*(Shear stress on surface of shaft^2)*Length of Shaft*(Radius 'r' from Center Of Shaft^3)*Length of Small Element)/(2*Modulus of rigidity of Shaft*(Strain Energy in body)))

Length of shaft given shear strain energy in ring of radius r

Go Length of Shaft = (Strain Energy in body*(2*Modulus of rigidity of Shaft*(Radius of Shaft^2)))/(2*pi*(Shear stress on surface of shaft^2)*(Radius 'r' from Center Of Shaft^3)*Length of Small Element)

Modulus of rigidity of shaft given shear strain energy in ring of radius 'r'

Go Modulus of rigidity of Shaft = (2*pi*(Shear stress on surface of shaft^2)*Length of Shaft*(Radius 'r' from Center Of Shaft^3)*Length of Small Element)/(2*Strain Energy in body*(Radius of Shaft^2))

Shear strain energy in ring of radius 'r'

Go Strain Energy in body = (2*pi*(Shear stress on surface of shaft^2)*Length of Shaft*(Radius 'r' from Center Of Shaft^3)*Length of Small Element)/(2*Modulus of rigidity of Shaft*(Radius of Shaft^2))

Inner diameter of shaft given total strain energy in hollow shaft

Go Inner Diameter of Shaft = (((Strain Energy in body*(4*Modulus of rigidity of Shaft*(Outer Diameter of Shaft^2)))/((Shear stress on surface of shaft^2)*Volume of Shaft))-(Outer Diameter of Shaft^2))^(1/2)

Volume of shaft given total strain energy in hollow shaft

Go Volume of Shaft = (Strain Energy in body*(4*Modulus of rigidity of Shaft*(Outer Diameter of Shaft^2)))/((Shear stress on surface of shaft^2)*((Outer Diameter of Shaft^2)+(Inner Diameter of Shaft^2)))

Modulus of rigidity of shaft given total strain energy in hollow shaft

Go Modulus of rigidity of Shaft = ((Shear stress on surface of shaft^2)*((Outer Diameter of Shaft^2)+(Inner Diameter of Shaft^2))*Volume of Shaft)/(4*Strain Energy in body*(Outer Diameter of Shaft^2))

Total strain energy in hollow shaft due to torsion

Go Strain Energy in body = ((Shear stress on surface of shaft^2)*((Outer Diameter of Shaft^2)+(Inner Diameter of Shaft^2))*Volume of Shaft)/(4*Modulus of rigidity of Shaft*(Outer Diameter of Shaft^2))

Radius of Shaft given Total Strain Energy Stored in Shaft

Go Radius of Shaft = sqrt(((Shear stress on surface of shaft^2)*Length of Shaft*Polar Moment of Inertia of shaft)/(2*Modulus of rigidity of Shaft*(Strain Energy in body)))

Polar Moment of Inertia of Shaft given Total Strain Energy Stored in Shaft

Go Polar Moment of Inertia of shaft = (Strain Energy in body*(2*Modulus of rigidity of Shaft*(Radius of Shaft^2)))/((Shear stress on surface of shaft^2)*Length of Shaft)

Length of shaft given total strain energy stored in shaft

Go Length of Shaft = (Strain Energy in body*(2*Modulus of rigidity of Shaft*(Radius of Shaft^2)))/((Shear stress on surface of shaft^2)*Polar Moment of Inertia of shaft)

Modulus of Rigidity of Shaft given Total Strain Energy Stored in Shaft

Go Modulus of rigidity of Shaft = ((Shear stress on surface of shaft^2)*Length of Shaft*Polar Moment of Inertia of shaft)/(2*Strain Energy in body*(Radius of Shaft^2))

Total Strain Energy Stored in Shaft

Go Strain Energy in body = ((Shear stress on surface of shaft^2)*Length of Shaft*Polar Moment of Inertia of shaft)/(2*Modulus of rigidity of Shaft*(Radius of Shaft^2))

Value of radius 'r' given shear stress at radius 'r' from center

Go Radius 'r' from Center Of Shaft = (Shear stress at radius 'r' from shaft*Radius of Shaft)/Shear stress on surface of shaft

Radius of shaft given shear stress at radius r from center

Go Radius of Shaft = (Radius 'r' from Center Of Shaft/Shear stress at radius 'r' from shaft)*Shear stress on surface of shaft

Modulus of rigidity of shaft given total strain energy in shaft due to torsion

Go Modulus of rigidity of Shaft = ((Shear stress on surface of shaft^2)*Volume of Shaft)/(4*Strain Energy in body)

Volume of Shaft given Total Strain Energy in Shaft due to Torsion

Go Volume of Shaft = (Strain Energy in body*4*Modulus of rigidity of Shaft)/((Shear stress on surface of shaft^2))

Modulus of rigidity given shear strain energy

Go Modulus of rigidity of Shaft = (Shear stress on surface of shaft^2)*(Volume of Shaft)/(2*Strain Energy in body)

Total strain energy in shaft due to torsion

Go Strain Energy in body = ((Shear stress on surface of shaft^2)*Volume of Shaft)/(4*Modulus of rigidity of Shaft)

Shear strain energy

Go Strain Energy in body = (Shear stress on surface of shaft^2)*(Volume of Shaft)/(2*Modulus of rigidity of Shaft)

Volume given shear strain energy

Go Volume of Shaft = (Strain Energy in body*2*Modulus of rigidity of Shaft)/(Shear stress on surface of shaft^2)

Modulus of rigidity of shaft given total strain energy in hollow shaft Formula

What is the difference between strain energy and resilience?

Strain energy is elastic that is, the material tends to recover when the load is removed. Resilience is typically expressed as the modulus of resilience, which is the amount of strain energy the material can store per unit of volume without causing permanent deformation.

How to Calculate Modulus of rigidity of shaft given total strain energy in hollow shaft?

Modulus of rigidity of shaft given total strain energy in hollow shaft calculator uses Modulus of rigidity of Shaft = ((Shear stress on surface of shaft^2)*((Outer Diameter of Shaft^2)+(Inner Diameter of Shaft^2))*Volume of Shaft)/(4*Strain Energy in body*(Outer Diameter of Shaft^2)) to calculate the Modulus of rigidity of Shaft, Modulus of rigidity of shaft given total strain energy in hollow shaft is defined as the measure of the rigidity of the body, given by the ratio of shear stress to shear strain. Modulus of rigidity of Shaft is denoted by G symbol.

How to calculate Modulus of rigidity of shaft given total strain energy in hollow shaft using this online calculator? To use this online calculator for Modulus of rigidity of shaft given total strain energy in hollow shaft, enter Shear stress on surface of shaft (𝜏), Outer Diameter of Shaft (d_outer), Inner Diameter of Shaft (d_inner), Volume of Shaft (V) & Strain Energy in body (U) and hit the calculate button. Here is how the Modulus of rigidity of shaft given total strain energy in hollow shaft calculation can be explained with given input values -> 1.1E-14 = ((4^2)*((4^2)+(1^2))*125.6)/(4*50000*(4^2)).

FAQ

What is Modulus of rigidity of shaft given total strain energy in hollow shaft?

Modulus of rigidity of shaft given total strain energy in hollow shaft is defined as the measure of the rigidity of the body, given by the ratio of shear stress to shear strain and is represented as G = ((𝜏^2)*((d_outer^2)+(d_inner^2))*V)/(4*U*(d_outer^2)) or Modulus of rigidity of Shaft = ((Shear stress on surface of shaft^2)*((Outer Diameter of Shaft^2)+(Inner Diameter of Shaft^2))*Volume of Shaft)/(4*Strain Energy in body*(Outer Diameter of Shaft^2)). Shear stress on surface of shaft is force tending to cause deformation of a material by slippage along a plane or planes parallel to the imposed stress, Outer Diameter of Shaft is defined as the length of the longest chord of the surface of the hollow circular shaft, The Inner Diameter of Shaft is defined as the length of the longest chord inside the hollow shaft, The Volume of Shaft is the volume of cylindical component under torsion & Strain Energy in body is defined as the energy stored in a body due to deformation.

How to calculate Modulus of rigidity of shaft given total strain energy in hollow shaft?

Modulus of rigidity of shaft given total strain energy in hollow shaft is defined as the measure of the rigidity of the body, given by the ratio of shear stress to shear strain is calculated using Modulus of rigidity of Shaft = ((Shear stress on surface of shaft^2)*((Outer Diameter of Shaft^2)+(Inner Diameter of Shaft^2))*Volume of Shaft)/(4*Strain Energy in body*(Outer Diameter of Shaft^2)). To calculate Modulus of rigidity of shaft given total strain energy in hollow shaft, you need Shear stress on surface of shaft (𝜏), Outer Diameter of Shaft (d_outer), Inner Diameter of Shaft (d_inner), Volume of Shaft (V) & Strain Energy in body (U). With our tool, you need to enter the respective value for Shear stress on surface of shaft, Outer Diameter of Shaft, Inner Diameter of Shaft, Volume of Shaft & Strain Energy in body 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 Modulus of rigidity of Shaft?

In this formula, Modulus of rigidity of Shaft uses Shear stress on surface of shaft, Outer Diameter of Shaft, Inner Diameter of Shaft, Volume of Shaft & Strain Energy in body. We can use 4 other way(s) to calculate the same, which is/are as follows -

Modulus of rigidity of Shaft = (Shear stress on surface of shaft^2)*(Volume of Shaft)/(2*Strain Energy in body)
Modulus of rigidity of Shaft = (2*pi*(Shear stress on surface of shaft^2)*Length of Shaft*(Radius 'r' from Center Of Shaft^3)*Length of Small Element)/(2*Strain Energy in body*(Radius of Shaft^2))
Modulus of rigidity of Shaft = ((Shear stress on surface of shaft^2)*Length of Shaft*Polar Moment of Inertia of shaft)/(2*Strain Energy in body*(Radius of Shaft^2))
Modulus of rigidity of Shaft = ((Shear stress on surface of shaft^2)*Volume of Shaft)/(4*Strain Energy in body)

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