Strain Energy in Shear given Shear Deformation Calculator

✖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 Deformation is deformation of specimen caused by shear force.ⓘ Shear Deformation [Δ]			+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%

✖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 given Shear Deformation [U]

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Strain Energy in Shear given Shear Deformation Solution

STEP 0: Pre-Calculation Summary

Formula Used

Strain Energy = (Area of Cross-Section*Modulus of Rigidity*(Shear Deformation^2))/(2*Length of Member)
U = (A*G_Torsion*(Δ^2))/(2*L)
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.
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 Deformation - Shear Deformation is deformation of specimen caused by shear force.
Length of Member - (Measured in Meter) - Length of Member is the measurement or extent of member (beam or column) from end to end.

STEP 1: Convert Input(s) to Base Unit

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 Deformation: 0.005 --> No Conversion Required
Length of Member: 3000 Millimeter --> 3 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

U = (A*G_Torsion*(Δ^2))/(2*L) --> (0.0056*40000000000*(0.005^2))/(2*3)

Evaluating ... ...

U = 933.333333333333

STEP 3: Convert Result to Output's Unit

933.333333333333 Joule -->933.333333333333 Newton Meter (Check conversion here)

FINAL ANSWER

933.333333333333 ≈ 933.3333 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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< 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 Shear given Shear Deformation Formula

LaTeX Go

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

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 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 Strain Energy in Shear given Shear Deformation?

Strain Energy in Shear given Shear Deformation calculator uses Strain Energy = (Area of Cross-Section*Modulus of Rigidity*(Shear Deformation^2))/(2*Length of Member) to calculate the Strain Energy, The Strain Energy in Shear given Shear Deformation 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 given Shear Deformation using this online calculator? To use this online calculator for Strain Energy in Shear given Shear Deformation, enter Area of Cross-Section (A), Modulus of Rigidity (G_Torsion), Shear Deformation (Δ) & Length of Member (L) and hit the calculate button. Here is how the Strain Energy in Shear given Shear Deformation calculation can be explained with given input values -> 933.3333 = (0.0056*40000000000*(0.005^2))/(2*3).

FAQ

What is Strain Energy in Shear given Shear Deformation?

The Strain Energy in Shear given Shear Deformation formula is defined as the energy stored in a body due to deformation and is represented as U = (A*G_Torsion*(Δ^2))/(2*L) or Strain Energy = (Area of Cross-Section*Modulus of Rigidity*(Shear Deformation^2))/(2*Length of Member). 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 Deformation is deformation of specimen caused by shear force & Length of Member is the measurement or extent of member (beam or column) from end to end.

How to calculate Strain Energy in Shear given Shear Deformation?

The Strain Energy in Shear given Shear Deformation formula is defined as the energy stored in a body due to deformation is calculated using Strain Energy = (Area of Cross-Section*Modulus of Rigidity*(Shear Deformation^2))/(2*Length of Member). To calculate Strain Energy in Shear given Shear Deformation, you need Area of Cross-Section (A), Modulus of Rigidity (G_Torsion), Shear Deformation (Δ) & Length of Member (L). With our tool, you need to enter the respective value for Area of Cross-Section, Modulus of Rigidity, Shear Deformation & Length of Member 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 Area of Cross-Section, Modulus of Rigidity, Shear Deformation & Length of Member. 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 = (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)

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