Strain Energy in Shear Calculator

✖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 of Member [L]			+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%

✖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 Shear [U]

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Formula

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Strain Energy in Shear

Formula

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

Example

`"136.9353N*m"=(("143kN")^2)*"3000mm"/(2*"5600mm²"*"40GPa")`

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Strain Energy in Shear Solution

STEP 0: Pre-Calculation Summary

Formula Used

Strain Energy = (Shear Force^2)*Length of Member/(2*Area of Cross-Section*Modulus of Rigidity)
U = (V^2)*L/(2*A*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.
Shear Force - (Measured in Newton) - Shear Force is the force which causes shear deformation to occur in the shear plane.
Length of Member - (Measured in Meter) - Length of Member is the measurement or extent of member (beam or column) from end to end.
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.

STEP 1: Convert Input(s) to Base Unit

Shear Force: 143 Kilonewton --> 143000 Newton (Check conversion here)
Length of Member: 3000 Millimeter --> 3 Meter (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)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

U = (V^2)*L/(2*A*G_Torsion) --> (143000^2)*3/(2*0.0056*40000000000)

Evaluating ... ...

U = 136.935267857143

STEP 3: Convert Result to Output's Unit

136.935267857143 Joule -->136.935267857143 Newton Meter (Check conversion here)

FINAL ANSWER

136.935267857143 ≈ 136.9353 Newton Meter <-- Strain Energy

(Calculation completed in 00.004 seconds)

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Created by Rudrani Tidke

Cummins College of Engineering for Women (CCEW), Pune

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Don Bosco College of Engineering (DBCE), Goa

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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

Strain Energy in Shear Formula

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

What is Strain Energy?

When a body is subjected to external force it undergoes deformation. The energy stored in the body due to deformation is known as strain energy.

What is the difference between strain energy and resilience?

Strain energy is elastic — that is, the material tends to recover when the load is removed. Where Resilience is typically expressed as the modulus of resilience, which is the amount of strain energy the material can store per unit of volume without causing permanent deformation.

How to Calculate Strain Energy in Shear?

Strain Energy in Shear calculator uses Strain Energy = (Shear Force^2)*Length of Member/(2*Area of Cross-Section*Modulus of Rigidity) to calculate the Strain Energy, The Strain Energy in Shear formula is defined as the energy stored in a body due to deformation. Strain Energy is denoted by U symbol.

How to calculate Strain Energy in Shear using this online calculator? To use this online calculator for Strain Energy in Shear, enter Shear Force (V), Length of Member (L), Area of Cross-Section (A) & Modulus of Rigidity (G_Torsion) and hit the calculate button. Here is how the Strain Energy in Shear calculation can be explained with given input values -> 136.9353 = (143000^2)*3/(2*0.0056*40000000000).

FAQ

What is Strain Energy in Shear?

The Strain Energy in Shear formula is defined as the energy stored in a body due to deformation and is represented as U = (V^2)*L/(2*A*G_Torsion) or Strain Energy = (Shear Force^2)*Length of Member/(2*Area of Cross-Section*Modulus of Rigidity). Shear Force is the force which causes shear deformation to occur in the shear plane, Length of Member is the measurement or extent of member (beam or column) from end to end, 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.

How to calculate Strain Energy in Shear?

The Strain Energy in Shear formula is defined as the energy stored in a body due to deformation is calculated using Strain Energy = (Shear Force^2)*Length of Member/(2*Area of Cross-Section*Modulus of Rigidity). To calculate Strain Energy in Shear, you need Shear Force (V), Length of Member (L), Area of Cross-Section (A) & Modulus of Rigidity (G_Torsion). With our tool, you need to enter the respective value for Shear Force, Length of Member, Area of Cross-Section & 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 Shear Force, Length of Member, Area of Cross-Section & Modulus of Rigidity. We can use 5 other way(s) to calculate the same, which is/are as follows -

Strain Energy = (Area of Cross-Section*Modulus of Rigidity*(Shear Deformation^2))/(2*Length of Member)
Strain Energy = (Torque SOM^2)*Length of Member/(2*Polar Moment of Inertia*Modulus of Rigidity)
Strain Energy = (Polar Moment of Inertia*Modulus of Rigidity*(Angle of Twist*(pi/180))^2)/(2*Length of Member)
Strain Energy = ((Bending Moment^2)*Length of Member/(2*Young's Modulus*Area Moment of Inertia))
Strain Energy = (Young's Modulus*Area Moment of Inertia*((Angle of Twist*(pi/180))^2)/(2*Length of Member))

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