Length over which Deformation takes place given Strain Energy in Shear 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%
✖Area of Cross-section is a cross-sectional area which we obtain when the same object is cut into two pieces. The area of that particular cross-section is known as the cross-sectional area.ⓘ Area of Cross-Section [A]			+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%
✖Shear Force is the force which causes shear deformation to occur in the shear plane.ⓘ Shear Force [V]			+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 Shear [L]

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Formula

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Length over which Deformation takes place given Strain Energy in Shear

Formula

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

Example

`"2981.263mm"=2*"136.08N*m"*"5600mm²"*"40GPa"/(("143kN")^2)`

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

STEP 0: Pre-Calculation Summary

Formula Used

Length of Member = 2*Strain Energy*Area of Cross-Section*Modulus of Rigidity/(Shear Force^2)
L = 2*U*A*G_Torsion/(V^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.
Area of Cross-Section - (Measured in Square Meter) - Area of Cross-section is a cross-sectional area which we obtain when the same object is cut into two pieces. The area of that particular cross-section is known as the cross-sectional area.
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.
Shear Force - (Measured in Newton) - Shear Force is the force which causes shear deformation to occur in the shear plane.

STEP 1: Convert Input(s) to Base Unit

Strain Energy: 136.08 Newton Meter --> 136.08 Joule (Check conversion here)
Area of Cross-Section: 5600 Square Millimeter --> 0.0056 Square Meter (Check conversion here)
Modulus of Rigidity: 40 Gigapascal --> 40000000000 Pascal (Check conversion here)
Shear Force: 143 Kilonewton --> 143000 Newton (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

L = 2*U*A*G_Torsion/(V^2) --> 2*136.08*0.0056*40000000000/(143000^2)

Evaluating ... ...

L = 2.98126265343049

STEP 3: Convert Result to Output's Unit

2.98126265343049 Meter -->2981.26265343049 Millimeter (Check conversion here)

FINAL ANSWER

2981.26265343049 ≈ 2981.263 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 Shear

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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 Shear Formula

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

What are the four basic forms of deformation of solid bodies?

Four basic forms of deformations or displacements of structures or solid bodies and these are:
TENSION, COMPRESSION, BENDING & TWISTING.

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 Shear?

Length over which Deformation takes place given Strain Energy in Shear calculator uses Length of Member = 2*Strain Energy*Area of Cross-Section*Modulus of Rigidity/(Shear Force^2) to calculate the Length of Member, The Length over which Deformation takes place given Strain Energy in Shear formula is defined as the original length of the specimen, structure or body before the deformation. Length of Member is denoted by L symbol.

How to calculate Length over which Deformation takes place given Strain Energy in Shear using this online calculator? To use this online calculator for Length over which Deformation takes place given Strain Energy in Shear, enter Strain Energy (U), Area of Cross-Section (A), Modulus of Rigidity (G_Torsion) & Shear Force (V) and hit the calculate button. Here is how the Length over which Deformation takes place given Strain Energy in Shear calculation can be explained with given input values -> 3E+6 = 2*136.08*0.0056*40000000000/(143000^2).

FAQ

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

The Length over which Deformation takes place given Strain Energy in Shear formula is defined as the original length of the specimen, structure or body before the deformation and is represented as L = 2*U*A*G_Torsion/(V^2) or Length of Member = 2*Strain Energy*Area of Cross-Section*Modulus of Rigidity/(Shear Force^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, Area of Cross-section is a cross-sectional area which we obtain when the same object is cut into two pieces. The area of that particular cross-section is known as the cross-sectional area, 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 Force is the force which causes shear deformation to occur in the shear plane.

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

The Length over which Deformation takes place given Strain Energy in Shear formula is defined as the original length of the specimen, structure or body before the deformation is calculated using Length of Member = 2*Strain Energy*Area of Cross-Section*Modulus of Rigidity/(Shear Force^2). To calculate Length over which Deformation takes place given Strain Energy in Shear, you need Strain Energy (U), Area of Cross-Section (A), Modulus of Rigidity (G_Torsion) & Shear Force (V). With our tool, you need to enter the respective value for Strain Energy, Area of Cross-Section, Modulus of Rigidity & Shear Force 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, Area of Cross-Section, Modulus of Rigidity & Shear Force. We can use 2 other way(s) to calculate the same, which is/are as follows -

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

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