Modulus of rigidity given shear strain energy 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%
✖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 given shear strain energy [G]

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Modulus of rigidity given shear strain energy Solution

STEP 0: Pre-Calculation Summary

Formula Used

Modulus of rigidity of Shaft = (Shear stress on surface of shaft^2)*(Volume of Shaft)/(2*Strain Energy in body)
G = (𝜏^2)*(V)/(2*U)
This formula uses 4 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.
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)
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)*(V)/(2*U) --> (4^2)*(125.6)/(2*50000)

Evaluating ... ...

G = 0.020096

STEP 3: Convert Result to Output's Unit

0.020096 Pascal -->2.0096E-08 Megapascal (Check conversion here)

FINAL ANSWER

2.0096E-08 ≈ 2E-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 » Mechanical » Expression for Strain Energy stored in a Body Due to Torsion » Modulus of rigidity given shear strain energy

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

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

LaTeX 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

LaTeX 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 given shear strain energy

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

Shear strain energy

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

Modulus of rigidity given shear strain energy Formula

LaTeX Go

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

Is strain energy a material property?

The strain energy (i.e. the amount of potential energy stored due to the deformation) is equal to the work expended in deforming the material. The total strain energy corresponds to the area under the load-deflection curve and has units of in-lbf in US Customary units and N-m in SI units.

How to Calculate Modulus of rigidity given shear strain energy?

Modulus of rigidity given shear strain energy calculator uses Modulus of rigidity of Shaft = (Shear stress on surface of shaft^2)*(Volume of Shaft)/(2*Strain Energy in body) to calculate the Modulus of rigidity of Shaft, Modulus of rigidity given shear strain energy 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 Shaft is denoted by G symbol.

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

FAQ

What is Modulus of rigidity given shear strain energy?

Modulus of rigidity given shear strain energy 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 G = (𝜏^2)*(V)/(2*U) or Modulus of rigidity of Shaft = (Shear stress on surface of shaft^2)*(Volume of Shaft)/(2*Strain Energy in body). 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, 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 given shear strain energy?

Modulus of rigidity given shear strain energy 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 Shaft = (Shear stress on surface of shaft^2)*(Volume of Shaft)/(2*Strain Energy in body). To calculate Modulus of rigidity given shear strain energy, you need Shear stress on surface of shaft (𝜏), 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, 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, Volume of Shaft & Strain Energy in body. We can use 3 other way(s) to calculate the same, which is/are as follows -

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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