Modulus of Rigidity of Shaft given Total Strain Energy Stored in 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%
✖The Length of Shaft is the distance between two ends of shaft.ⓘ Length of Shaft [L]			+10% -10%
✖Polar Moment of Inertia of shaft is the measure of object resistance to torsion.ⓘ Polar Moment of Inertia of shaft [J_shaft]			+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%
✖The Radius of Shaft is the radius of the shaft subjected under torsion.ⓘ Radius of Shaft [r_shaft]			+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 Stored in Shaft [G]

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

STEP 0: Pre-Calculation Summary

Formula Used

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))
G = ((𝜏^2)*L*J_shaft)/(2*U*(r_shaft^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.
Length of Shaft - (Measured in Meter) - The Length of Shaft is the distance between two ends of shaft.
Polar Moment of Inertia of shaft - (Measured in Meter⁴) - Polar Moment of Inertia of shaft is the measure of object resistance to torsion.
Strain Energy in body - (Measured in Joule) - Strain Energy in body is defined as the energy stored in a body due to deformation.
Radius of Shaft - (Measured in Meter) - The Radius of Shaft is the radius of the shaft subjected under torsion.

STEP 1: Convert Input(s) to Base Unit

Shear stress on surface of shaft: 4E-06 Megapascal --> 4 Pascal (Check conversion here)
Length of Shaft: 7000 Millimeter --> 7 Meter (Check conversion here)
Polar Moment of Inertia of shaft: 10 Meter⁴ --> 10 Meter⁴ No Conversion Required
Strain Energy in body: 50 Kilojoule --> 50000 Joule (Check conversion here)
Radius of Shaft: 2000 Millimeter --> 2 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

G = ((𝜏^2)*L*J_shaft)/(2*U*(r_shaft^2)) --> ((4^2)*7*10)/(2*50000*(2^2))

Evaluating ... ...

G = 0.0028

STEP 3: Convert Result to Output's Unit

0.0028 Pascal -->2.8E-09 Megapascal (Check conversion here)

FINAL ANSWER

2.8E-09 ≈ 2.8E-9 Megapascal <-- Modulus of rigidity of Shaft

(Calculation completed in 00.021 seconds)

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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 of Shaft given Total Strain Energy Stored in Shaft Formula

LaTeX Go

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.

How to Calculate Modulus of Rigidity of Shaft given Total Strain Energy Stored in Shaft?

Modulus of Rigidity of Shaft given Total Strain Energy Stored in Shaft calculator uses 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)) to calculate the Modulus of rigidity of Shaft, The Modulus of Rigidity of Shaft given Total Strain Energy Stored in Shaft formula is defined as 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 of Shaft given Total Strain Energy Stored in Shaft using this online calculator? To use this online calculator for Modulus of Rigidity of Shaft given Total Strain Energy Stored in Shaft, enter Shear stress on surface of shaft (𝜏), Length of Shaft (L), Polar Moment of Inertia of shaft (J_shaft), Strain Energy in body (U) & Radius of Shaft (r_shaft) and hit the calculate button. Here is how the Modulus of Rigidity of Shaft given Total Strain Energy Stored in Shaft calculation can be explained with given input values -> 2.8E-15 = ((4^2)*7*10)/(2*50000*(2^2)).

FAQ

What is Modulus of Rigidity of Shaft given Total Strain Energy Stored in Shaft?

The Modulus of Rigidity of Shaft given Total Strain Energy Stored in Shaft formula is defined as 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)*L*J_shaft)/(2*U*(r_shaft^2)) or 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)). 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 Length of Shaft is the distance between two ends of shaft, Polar Moment of Inertia of shaft is the measure of object resistance to torsion, Strain Energy in body is defined as the energy stored in a body due to deformation & The Radius of Shaft is the radius of the shaft subjected under torsion.

How to calculate Modulus of Rigidity of Shaft given Total Strain Energy Stored in Shaft?

The Modulus of Rigidity of Shaft given Total Strain Energy Stored in Shaft formula is defined as 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)*Length of Shaft*Polar Moment of Inertia of shaft)/(2*Strain Energy in body*(Radius of Shaft^2)). To calculate Modulus of Rigidity of Shaft given Total Strain Energy Stored in Shaft, you need Shear stress on surface of shaft (𝜏), Length of Shaft (L), Polar Moment of Inertia of shaft (J_shaft), Strain Energy in body (U) & Radius of Shaft (r_shaft). With our tool, you need to enter the respective value for Shear stress on surface of shaft, Length of Shaft, Polar Moment of Inertia of shaft, Strain Energy in body & Radius of Shaft 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, Length of Shaft, Polar Moment of Inertia of shaft, Strain Energy in body & Radius of Shaft. We can use 3 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)*Volume of Shaft)/(4*Strain Energy in body)

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