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

✖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 [G]			+10% -10%
✖The Radius of Shaft is the radius of the shaft subjected under torsion.ⓘ Radius of Shaft [r_shaft]			+10% -10%
✖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 given Total Strain Energy Stored in Shaft [J_shaft]

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

STEP 0: Pre-Calculation Summary

Formula Used

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)
J_shaft = (U*(2*G*(r_shaft^2)))/((𝜏^2)*L)
This formula uses 6 Variables

Variables Used

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.
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.
Radius of Shaft - (Measured in Meter) - The Radius of Shaft is the radius of the shaft subjected under torsion.
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.

STEP 1: Convert Input(s) to Base Unit

Strain Energy in body: 50 Kilojoule --> 50000 Joule (Check conversion here)
Modulus of rigidity of Shaft: 4E-05 Megapascal --> 40 Pascal (Check conversion here)
Radius of Shaft: 2000 Millimeter --> 2 Meter (Check conversion here)
Shear stress on surface of shaft: 4E-06 Megapascal --> 4 Pascal (Check conversion here)
Length of Shaft: 7000 Millimeter --> 7 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

J_shaft = (U*(2*G*(r_shaft^2)))/((𝜏^2)*L) --> (50000*(2*40*(2^2)))/((4^2)*7)

Evaluating ... ...

J_shaft = 142857.142857143

STEP 3: Convert Result to Output's Unit

142857.142857143 Meter⁴ --> No Conversion Required

FINAL ANSWER

142857.142857143 ≈ 142857.1 Meter⁴ <-- Polar Moment of Inertia of shaft

(Calculation completed in 00.020 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)

Polar Moment of Inertia 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 and has units of in-lbf in US Customary units and N-m in SI units.

How to Calculate Polar Moment of Inertia of Shaft given Total Strain Energy Stored in Shaft?

Polar Moment of Inertia of Shaft given Total Strain Energy Stored in Shaft calculator uses 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) to calculate the Polar Moment of Inertia of shaft, The Polar Moment of Inertia of Shaft given Total Strain Energy Stored in Shaft formula is defined as a quantity used to describe resistance to torsional deformation (deflection), in cylindrical objects (or segments of the cylindrical object) with an invariant cross-section and no significant warping or out-of-plane deformation. Polar Moment of Inertia of shaft is denoted by J_shaft symbol.

How to calculate Polar Moment of Inertia of Shaft given Total Strain Energy Stored in Shaft using this online calculator? To use this online calculator for Polar Moment of Inertia of Shaft given Total Strain Energy Stored in Shaft, enter Strain Energy in body (U), Modulus of rigidity of Shaft (G), Radius of Shaft (r_shaft), Shear stress on surface of shaft (𝜏) & Length of Shaft (L) and hit the calculate button. Here is how the Polar Moment of Inertia of Shaft given Total Strain Energy Stored in Shaft calculation can be explained with given input values -> 142857.1 = (50000*(2*40*(2^2)))/((4^2)*7).

FAQ

What is Polar Moment of Inertia of Shaft given Total Strain Energy Stored in Shaft?

The Polar Moment of Inertia of Shaft given Total Strain Energy Stored in Shaft formula is defined as a quantity used to describe resistance to torsional deformation (deflection), in cylindrical objects (or segments of the cylindrical object) with an invariant cross-section and no significant warping or out-of-plane deformation and is represented as J_shaft = (U*(2*G*(r_shaft^2)))/((𝜏^2)*L) or 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). Strain Energy in body is defined as the energy stored in a body due to deformation, 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, The Radius of Shaft is the radius of the shaft subjected under torsion, 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.

How to calculate Polar Moment of Inertia of Shaft given Total Strain Energy Stored in Shaft?

The Polar Moment of Inertia of Shaft given Total Strain Energy Stored in Shaft formula is defined as a quantity used to describe resistance to torsional deformation (deflection), in cylindrical objects (or segments of the cylindrical object) with an invariant cross-section and no significant warping or out-of-plane deformation is calculated using 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). To calculate Polar Moment of Inertia of Shaft given Total Strain Energy Stored in Shaft, you need Strain Energy in body (U), Modulus of rigidity of Shaft (G), Radius of Shaft (r_shaft), Shear stress on surface of shaft (𝜏) & Length of Shaft (L). With our tool, you need to enter the respective value for Strain Energy in body, Modulus of rigidity of Shaft, Radius of Shaft, Shear stress on surface of shaft & Length of 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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