Strain Energy in Torsion given Polar MI and Shear Modulus of Elasticity 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%
✖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 [J]			+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%

✖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 in Torsion given Polar MI and Shear Modulus of Elasticity [U]

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

STEP 0: Pre-Calculation Summary

Formula Used

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

Variables Used

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.
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.
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.
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)
Polar Moment of Inertia: 0.0041 Meter⁴ --> 0.0041 Meter⁴ No Conversion Required
Modulus of Rigidity: 40 Gigapascal --> 40000000000 Pascal (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

U = (T^2)*L/(2*J*G_Torsion) --> (121900^2)*3/(2*0.0041*40000000000)

Evaluating ... ...

U = 135.911067073171

STEP 3: Convert Result to Output's Unit

135.911067073171 Joule -->135.911067073171 Newton Meter (Check conversion here)

FINAL ANSWER

135.911067073171 ≈ 135.9111 Newton Meter <-- Strain Energy

(Calculation completed in 00.004 seconds)

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Cummins College of Engineering for Women (CCEW), Pune

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< Strain Energy in Structural Members Calculators

Shear Force using Strain Energy

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

Strain Energy in Shear

LaTeX 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 Shear

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

Stress using Hook's Law

LaTeX Go Direct Stress = Young's Modulus*Lateral Strain

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

LaTeX Go

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

What does Torsion mean?

The twisting or wrenching of a body by the exertion of forces tending to turn one end or part about a longitudinal axis while the other is held fast or turned in the opposite direction also the state of being twisted. The twisting of a bodily organ or part on its own axis.

What is the Strain Energy in Torsion?

The energy stores in the shaft are equal to work done in twisting i.e., Strain energy stored in a body due to torsion. For example, a solid circular shaft.

How to Calculate Strain Energy in Torsion given Polar MI and Shear Modulus of Elasticity?

Strain Energy in Torsion given Polar MI and Shear Modulus of Elasticity calculator uses Strain Energy = (Torque SOM^2)*Length of Member/(2*Polar Moment of Inertia*Modulus of Rigidity) to calculate the Strain Energy, The Strain Energy in Torsion given Polar MI and Shear Modulus of Elasticity formula is defined as energy stored in the body due to deformation. Strain Energy is denoted by U symbol.

How to calculate Strain Energy in Torsion given Polar MI and Shear Modulus of Elasticity using this online calculator? To use this online calculator for Strain Energy in Torsion given Polar MI and Shear Modulus of Elasticity, enter Torque SOM (T), Length of Member (L), Polar Moment of Inertia (J) & Modulus of Rigidity (G_Torsion) and hit the calculate button. Here is how the Strain Energy in Torsion given Polar MI and Shear Modulus of Elasticity calculation can be explained with given input values -> 135.9111 = (121900^2)*3/(2*0.0041*40000000000).

FAQ

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

The Strain Energy in Torsion given Polar MI and Shear Modulus of Elasticity formula is defined as energy stored in the body due to deformation and is represented as U = (T^2)*L/(2*J*G_Torsion) or Strain Energy = (Torque SOM^2)*Length of Member/(2*Polar Moment of Inertia*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, 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 & 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 Strain Energy in Torsion given Polar MI and Shear Modulus of Elasticity?

The Strain Energy in Torsion given Polar MI and Shear Modulus of Elasticity formula is defined as energy stored in the body due to deformation is calculated using Strain Energy = (Torque SOM^2)*Length of Member/(2*Polar Moment of Inertia*Modulus of Rigidity). To calculate Strain Energy in Torsion given Polar MI and Shear Modulus of Elasticity, you need Torque SOM (T), Length of Member (L), Polar Moment of Inertia (J) & Modulus of Rigidity (G_Torsion). With our tool, you need to enter the respective value for Torque SOM, Length of Member, Polar Moment of Inertia & Modulus of Rigidity 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 Strain Energy?

In this formula, Strain Energy uses Torque SOM, Length of Member, Polar Moment of Inertia & Modulus of Rigidity. We can use 3 other way(s) to calculate the same, which is/are as follows -

Strain Energy = (Shear Force^2)*Length of Member/(2*Area of Cross-Section*Modulus of Rigidity)
Strain Energy = (Area of Cross-Section*Modulus of Rigidity*(Shear Deformation^2))/(2*Length of Member)
Strain Energy = (Polar Moment of Inertia*Modulus of Rigidity*(Angle of Twist*(pi/180))^2)/(2*Length of Member)

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