Length over which Deformation takes place given Strain Energy in Torsion Calculator

✖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%
✖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%
✖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 over which Deformation takes place given Strain Energy in Torsion [L]

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Formula

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Length over which Deformation takes place given Strain Energy in Torsion

Formula

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

Example

`"3003.729mm"=(2*"136.08N*m"*"4.1e-3m⁴"*"40GPa")/("121.9kN*m")^2`

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Length over which Deformation takes place given Strain Energy in Torsion Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

Variables Used

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.
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.
Torque SOM - (Measured in Newton Meter) - Torque SOM is a measure of the force that can cause an object to rotate about an axis.

STEP 1: Convert Input(s) to Base Unit

Strain Energy: 136.08 Newton Meter --> 136.08 Joule (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)
Torque SOM: 121.9 Kilonewton Meter --> 121900 Newton Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

L = (2*U*J*G_Torsion)/T^2 --> (2*136.08*0.0041*40000000000)/121900^2

Evaluating ... ...

L = 3.00372890001824

STEP 3: Convert Result to Output's Unit

3.00372890001824 Meter -->3003.72890001824 Millimeter (Check conversion here)

FINAL ANSWER

3003.72890001824 ≈ 3003.729 Millimeter <-- Length of Member

(Calculation completed in 00.004 seconds)

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Home » Engineering » Civil » Strength of Materials » Strain Energy » Strain Energy in Structural Members » Length over which Deformation takes place given Strain Energy in Torsion

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Created by Rudrani Tidke

Cummins College of Engineering for Women (CCEW), Pune

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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

Length over which Deformation takes place given Strain Energy in Torsion Formula

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

What is Torque in Human Body?

Torque is the driving force for human movement. Being able to manipulate the target muscle torque will allow for a more specific intervention. Moment Arm of a force system is the perpendicular distance from an axis to the line of action of a force. Torque is the ability of a force to cause rotation on a lever.

How does Shear Deformation take place?

Shearing forces cause shearing deformation. An element subject to shear does not change in length alone but undergoes a change in shape, this is how a shear deformation takes place.

How to Calculate Length over which Deformation takes place given Strain Energy in Torsion?

Length over which Deformation takes place given Strain Energy in Torsion calculator uses Length of Member = (2*Strain Energy*Polar Moment of Inertia*Modulus of Rigidity)/Torque SOM^2 to calculate the Length of Member, The Length over which Deformation takes place given Strain Energy in Torsion formula is defined as the original length of the specimen or structure or body before deformation takes place due to torsional strain energy. Length of Member is denoted by L symbol.

How to calculate Length over which Deformation takes place given Strain Energy in Torsion using this online calculator? To use this online calculator for Length over which Deformation takes place given Strain Energy in Torsion, enter Strain Energy (U), Polar Moment of Inertia (J), Modulus of Rigidity (G_Torsion) & Torque SOM (T) and hit the calculate button. Here is how the Length over which Deformation takes place given Strain Energy in Torsion calculation can be explained with given input values -> 3.003729 = (2*136.08*0.0041*40000000000)/121900^2.

FAQ

What is Length over which Deformation takes place given Strain Energy in Torsion?

The Length over which Deformation takes place given Strain Energy in Torsion formula is defined as the original length of the specimen or structure or body before deformation takes place due to torsional strain energy and is represented as L = (2*U*J*G_Torsion)/T^2 or Length of Member = (2*Strain Energy*Polar Moment of Inertia*Modulus of Rigidity)/Torque SOM^2. 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, 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 & Torque SOM is a measure of the force that can cause an object to rotate about an axis.

How to calculate Length over which Deformation takes place given Strain Energy in Torsion?

The Length over which Deformation takes place given Strain Energy in Torsion formula is defined as the original length of the specimen or structure or body before deformation takes place due to torsional strain energy is calculated using Length of Member = (2*Strain Energy*Polar Moment of Inertia*Modulus of Rigidity)/Torque SOM^2. To calculate Length over which Deformation takes place given Strain Energy in Torsion, you need Strain Energy (U), Polar Moment of Inertia (J), Modulus of Rigidity (G_Torsion) & Torque SOM (T). With our tool, you need to enter the respective value for Strain Energy, Polar Moment of Inertia, Modulus of Rigidity & Torque SOM 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 Length of Member?

In this formula, Length of Member uses Strain Energy, Polar Moment of Inertia, Modulus of Rigidity & Torque SOM. We can use 2 other way(s) to calculate the same, which is/are as follows -

Length of Member = 2*Strain Energy*Area of Cross-Section*Modulus of Rigidity/(Shear Force^2)
Length of Member = (Strain Energy*(2*Young's Modulus*Area Moment of Inertia)/(Bending Moment^2))

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