Polar Moment of Inertia given Strain Energy in Torsion Calculator

✖Torque SOM is a measure of the force that can cause an object to rotate about an axis.ⓘ Torque SOM [T]			+10% -10%
✖Length of Member is the measurement or extent of member (beam or column) from end to end.ⓘ Length of Member [L]			+10% -10%
✖Strain Energy is the energy adsorption of material due to strain under an applied load. It is also equal to the work done on a specimen by an external force.ⓘ Strain Energy [U]			+10% -10%
✖Modulus of Rigidity is the measure of the rigidity of the body, given by the ratio of shear stress to shear strain. It is often denoted by G.ⓘ Modulus of Rigidity [G_Torsion]			+10% -10%

✖Polar Moment of Inertia is the moment of inertia of a cross-section with respect to its polar axis, which is an axis at right angles to the plane of the cross-section.ⓘ Polar Moment of Inertia given Strain Energy in Torsion [J]

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Formula

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Polar Moment of Inertia given Strain Energy in Torsion

Formula

`"J" = ("T"^2)*"L"/(2*"U"*"G"_{"Torsion"})`

Example

`"0.004095m⁴"=(("121.9kN*m")^2)*"3000mm"/(2*"136.08N*m"*"40GPa")`

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Polar Moment of Inertia given Strain Energy in Torsion Solution

STEP 0: Pre-Calculation Summary

Formula Used

Polar Moment of Inertia = (Torque SOM^2)*Length of Member/(2*Strain Energy*Modulus of Rigidity)
J = (T^2)*L/(2*U*G_Torsion)
This formula uses 5 Variables

Variables Used

Polar Moment of Inertia - (Measured in Meter⁴) - Polar Moment of Inertia is the moment of inertia of a cross-section with respect to its polar axis, which is an axis at right angles to the plane of the cross-section.
Torque SOM - (Measured in Newton Meter) - Torque SOM is a measure of the force that can cause an object to rotate about an axis.
Length of Member - (Measured in Meter) - Length of Member is the measurement or extent of member (beam or column) from end to end.
Strain Energy - (Measured in Joule) - Strain Energy is the energy adsorption of material due to strain under an applied load. It is also equal to the work done on a specimen by an external force.
Modulus of Rigidity - (Measured in Pascal) - Modulus of Rigidity is the measure of the rigidity of the body, given by the ratio of shear stress to shear strain. It is often denoted by G.

STEP 1: Convert Input(s) to Base Unit

Torque SOM: 121.9 Kilonewton Meter --> 121900 Newton Meter (Check conversion here)
Length of Member: 3000 Millimeter --> 3 Meter (Check conversion here)
Strain Energy: 136.08 Newton Meter --> 136.08 Joule (Check conversion here)
Modulus of Rigidity: 40 Gigapascal --> 40000000000 Pascal (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

J = (T^2)*L/(2*U*G_Torsion) --> (121900^2)*3/(2*136.08*40000000000)

Evaluating ... ...

J = 0.00409491016313933

STEP 3: Convert Result to Output's Unit

0.00409491016313933 Meter⁴ --> No Conversion Required

FINAL ANSWER

0.00409491016313933 ≈ 0.004095 Meter⁴ <-- Polar Moment of Inertia

(Calculation completed in 00.004 seconds)

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Home » Engineering » Civil » Strength of Materials » Strain Energy » Strain Energy in Structural Members » Polar Moment of Inertia given Strain Energy in Torsion

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< 19 Strain Energy in Structural Members Calculators

Strain Energy in Torsion given Angle of Twist

Go Strain Energy = (Polar Moment of Inertia*Modulus of Rigidity*(Angle of Twist*(pi/180))^2)/(2*Length of Member)

Strain Energy for Pure Bending when Beam rotates in One End

Go Strain Energy = (Young's Modulus*Area Moment of Inertia*((Angle of Twist*(pi/180))^2)/(2*Length of Member))

Bending Moment using Strain Energy

Go Bending Moment = sqrt(Strain Energy*(2*Young's Modulus*Area Moment of Inertia)/Length of Member)

Torque given Strain Energy in Torsion

Go Torque SOM = sqrt(2*Strain Energy*Polar Moment of Inertia*Modulus of Rigidity/Length of Member)

Shear Force using Strain Energy

Go Shear Force = sqrt(2*Strain Energy*Area of Cross-Section*Modulus of Rigidity/Length of Member)

Strain Energy in Shear given Shear Deformation

Go Strain Energy = (Area of Cross-Section*Modulus of Rigidity*(Shear Deformation^2))/(2*Length of Member)

Length over which Deformation takes place using Strain Energy

Go Length of Member = (Strain Energy*(2*Young's Modulus*Area Moment of Inertia)/(Bending Moment^2))

Modulus of Elasticity with given Strain Energy

Go Young's Modulus = (Length of Member*(Bending Moment^2)/(2*Strain Energy*Area Moment of Inertia))

Moment of Inertia using Strain Energy

Go Area Moment of Inertia = Length of Member*((Bending Moment^2)/(2*Strain Energy*Young's Modulus))

Strain Energy in Bending

Go Strain Energy = ((Bending Moment^2)*Length of Member/(2*Young's Modulus*Area Moment of Inertia))

Strain Energy in Torsion given Polar MI and Shear Modulus of Elasticity

Go Strain Energy = (Torque SOM^2)*Length of Member/(2*Polar Moment of Inertia*Modulus of Rigidity)

Shear Modulus of Elasticity given Strain Energy in Torsion

Go Modulus of Rigidity = (Torque SOM^2)*Length of Member/(2*Polar Moment of Inertia*Strain Energy)

Polar Moment of Inertia given Strain Energy in Torsion

Go Polar Moment of Inertia = (Torque SOM^2)*Length of Member/(2*Strain Energy*Modulus of Rigidity)

Shear Modulus of Elasticity given Strain Energy in Shear

Go Modulus of Rigidity = (Shear Force^2)*Length of Member/(2*Area of Cross-Section*Strain Energy)

Shear Area given Strain Energy in Shear

Go Area of Cross-Section = (Shear Force^2)*Length of Member/(2*Strain Energy*Modulus of Rigidity)

Strain Energy in Shear

Go Strain Energy = (Shear Force^2)*Length of Member/(2*Area of Cross-Section*Modulus of Rigidity)

Length over which Deformation takes place given Strain Energy in Torsion

Go Length of Member = (2*Strain Energy*Polar Moment of Inertia*Modulus of Rigidity)/Torque SOM^2

Length over which Deformation takes place given Strain Energy in Shear

Go Length of Member = 2*Strain Energy*Area of Cross-Section*Modulus of Rigidity/(Shear Force^2)

Stress using Hook's Law

Go Direct Stress = Young's Modulus*Lateral Strain

Polar Moment of Inertia given Strain Energy in Torsion Formula

Polar Moment of Inertia = (Torque SOM^2)*Length of Member/(2*Strain Energy*Modulus of Rigidity)
J = (T^2)*L/(2*U*G_Torsion)

What is meant by Polar Moment of Inertia?

The polar moment of inertia, also known as the second polar moment of area, is a quantity used to describe resistance to torsional deformation (deflection), in cylindrical objects (or segments of cylindrical objects) with an invariant cross-section and no significant warping or out-of-plane deformation.

How to Calculate Polar Moment of Inertia given Strain Energy in Torsion?

Polar Moment of Inertia given Strain Energy in Torsion calculator uses Polar Moment of Inertia = (Torque SOM^2)*Length of Member/(2*Strain Energy*Modulus of Rigidity) to calculate the Polar Moment of Inertia, The Polar Moment of Inertia given Strain Energy in Torsion formula is defined as a shaft or beam's resistance to being distorted by torsion, as a function of its shape. Polar Moment of Inertia is denoted by J symbol.

How to calculate Polar Moment of Inertia given Strain Energy in Torsion using this online calculator? To use this online calculator for Polar Moment of Inertia given Strain Energy in Torsion, enter Torque SOM (T), Length of Member (L), Strain Energy (U) & Modulus of Rigidity (G_Torsion) and hit the calculate button. Here is how the Polar Moment of Inertia given Strain Energy in Torsion calculation can be explained with given input values -> 0.004095 = (121900^2)*3/(2*136.08*40000000000).

FAQ

What is Polar Moment of Inertia given Strain Energy in Torsion?

The Polar Moment of Inertia given Strain Energy in Torsion formula is defined as a shaft or beam's resistance to being distorted by torsion, as a function of its shape and is represented as J = (T^2)*L/(2*U*G_Torsion) or Polar Moment of Inertia = (Torque SOM^2)*Length of Member/(2*Strain Energy*Modulus of Rigidity). Torque SOM is a measure of the force that can cause an object to rotate about an axis, Length of Member is the measurement or extent of member (beam or column) from end to end, Strain Energy is the energy adsorption of material due to strain under an applied load. It is also equal to the work done on a specimen by an external force & Modulus of Rigidity is the measure of the rigidity of the body, given by the ratio of shear stress to shear strain. It is often denoted by G.

How to calculate Polar Moment of Inertia given Strain Energy in Torsion?

The Polar Moment of Inertia given Strain Energy in Torsion formula is defined as a shaft or beam's resistance to being distorted by torsion, as a function of its shape is calculated using Polar Moment of Inertia = (Torque SOM^2)*Length of Member/(2*Strain Energy*Modulus of Rigidity). To calculate Polar Moment of Inertia given Strain Energy in Torsion, you need Torque SOM (T), Length of Member (L), Strain Energy (U) & Modulus of Rigidity (G_Torsion). With our tool, you need to enter the respective value for Torque SOM, Length of Member, Strain Energy & Modulus of Rigidity 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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