Shear Modulus of Elasticity 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%
✖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%
✖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.ⓘ Shear Modulus of Elasticity given Strain Energy in Torsion [G_Torsion]

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Shear Modulus of Elasticity given Strain Energy in Torsion Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

Variables Used

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.
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.
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.

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
Strain Energy: 136.08 Newton Meter --> 136.08 Joule (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

G_Torsion = (T^2)*L/(2*J*U) --> (121900^2)*3/(2*0.0041*136.08)

Evaluating ... ...

G_Torsion = 39950343055.0178

STEP 3: Convert Result to Output's Unit

39950343055.0178 Pascal -->39.9503430550178 Gigapascal (Check conversion here)

FINAL ANSWER

39.9503430550178 ≈ 39.95034 Gigapascal <-- Modulus of Rigidity

(Calculation completed in 00.020 seconds)

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Home » Engineering » Civil » Strength of Materials » Strain Energy » Strain Energy in Structural Members » Shear Modulus of Elasticity given Strain Energy in Torsion

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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

Shear Modulus of Elasticity given Strain Energy in Torsion Formula

LaTeX Go

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

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 Shear Modulus of Elasticity given Strain Energy in Torsion?

Shear Modulus of Elasticity given Strain Energy in Torsion calculator uses Modulus of Rigidity = (Torque SOM^2)*Length of Member/(2*Polar Moment of Inertia*Strain Energy) to calculate the Modulus of Rigidity, The Shear Modulus of Elasticity given Strain Energy in Torsion formula is defined as the slope of the linear elastic region of the shear stress–strain curve. Modulus of Rigidity is denoted by G_Torsion symbol.

How to calculate Shear Modulus of Elasticity given Strain Energy in Torsion using this online calculator? To use this online calculator for Shear Modulus of Elasticity given Strain Energy in Torsion, enter Torque SOM (T), Length of Member (L), Polar Moment of Inertia (J) & Strain Energy (U) and hit the calculate button. Here is how the Shear Modulus of Elasticity given Strain Energy in Torsion calculation can be explained with given input values -> 4E-8 = (121900^2)*3/(2*0.0041*136.08).

FAQ

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

The Shear Modulus of Elasticity given Strain Energy in Torsion formula is defined as the slope of the linear elastic region of the shear stress–strain curve and is represented as G_Torsion = (T^2)*L/(2*J*U) or Modulus of Rigidity = (Torque SOM^2)*Length of Member/(2*Polar Moment of Inertia*Strain Energy). 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 & 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.

How to calculate Shear Modulus of Elasticity given Strain Energy in Torsion?

The Shear Modulus of Elasticity given Strain Energy in Torsion formula is defined as the slope of the linear elastic region of the shear stress–strain curve is calculated using Modulus of Rigidity = (Torque SOM^2)*Length of Member/(2*Polar Moment of Inertia*Strain Energy). To calculate Shear Modulus of Elasticity given Strain Energy in Torsion, you need Torque SOM (T), Length of Member (L), Polar Moment of Inertia (J) & Strain Energy (U). With our tool, you need to enter the respective value for Torque SOM, Length of Member, Polar Moment of Inertia & Strain Energy 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?

In this formula, Modulus of Rigidity uses Torque SOM, Length of Member, Polar Moment of Inertia & Strain Energy. We can use 1 other way(s) to calculate the same, which is/are as follows -

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

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