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Strain Energy in Shear given Shear Deformation Formula

GoStrain Energy in Shear Formula

GoStrain Energy in Torsion given Polar MI and Shear Modulus of Elasticity Formula

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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. Check FAQs

U = \frac{A \cdot G Torsion \cdot (Δ^{2})}{2 \cdot L}

U - Strain Energy?A - Area of Cross-Section?G_Torsion - Modulus of Rigidity?Δ - Shear Deformation?L - Length of Member?

Strain Energy in Shear given Shear Deformation Example

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Here is how the Strain Energy in Shear given Shear Deformation equation looks like with Values.

Here is how the Strain Energy in Shear given Shear Deformation equation looks like with Units.

Here is how the Strain Energy in Shear given Shear Deformation equation looks like.

933.3333 = \frac{5600 \cdot 40 \cdot ({0.005}^{2})}{2 \cdot 3000}

933.3333N*m = \frac{5600mm² \cdot 40GPa \cdot ({0.005}^{2})}{2 \cdot 3000mm}

933.3333 = \frac{5600 \cdot 40 \cdot ({0.005}^{2})}{2 \cdot 3000}

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Strain Energy in Shear given Shear Deformation Solution

Follow our step by step solution on how to calculate Strain Energy in Shear given Shear Deformation?

FIRST Step Consider the formula

U = \frac{A \cdot G Torsion \cdot (Δ^{2})}{2 \cdot L}

Next Step Substitute values of Variables

∴

U = \frac{5600mm² \cdot 40GPa \cdot ({0.005}^{2})}{2 \cdot 3000mm}

Next Step Convert Units

∴

U = \frac{0.0056m² \cdot 4E+10Pa \cdot ({0.005}^{2})}{2 \cdot 3m}

Next Step Prepare to Evaluate

∴

U = \frac{0.0056 \cdot 4E+10 \cdot ({0.005}^{2})}{2 \cdot 3}

Next Step Evaluate

∴

U = 933.333333333333J

Next Step Convert to Output's Unit

∴

U = 933.333333333333N*m

LAST Step Rounding Answer

∴

U = 933.3333N*m

Strain Energy in Shear given Shear Deformation Formula Elements

Variables

Strain Energy

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.

Symbol: U

Measurement: EnergyUnit: N*m

Note: Value can be positive or negative.

Formulas to find Strain Energy

Area of Cross-Section

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.

Symbol: A

Measurement: AreaUnit: mm²

Note: Value should be greater than 0.

Formulas to find Area of Cross-Section

Modulus of Rigidity

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.

Symbol: G_Torsion

Measurement: PressureUnit: GPa

Note: Value should be greater than 0.

Formulas to find Modulus of Rigidity

Shear Deformation

Shear Deformation is deformation of specimen caused by shear force.

Symbol: Δ

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Shear Deformation

Length of Member

Length of Member is the measurement or extent of member (beam or column) from end to end.

Symbol: L

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Length of Member

Other Formulas to find Strain Energy

Go Strain Energy in Shear

U = (V^{2}) \cdot \frac{L}{2 \cdot A \cdot G Torsion}

Go Strain Energy in Torsion given Polar MI and Shear Modulus of Elasticity

U = (T^{2}) \cdot \frac{L}{2 \cdot J \cdot G Torsion}

Go Strain Energy in Torsion given Angle of Twist

U = \frac{J \cdot G Torsion \cdot {(θ \cdot (\frac{π}{180}))}^{2}}{2 \cdot L}

Go Strain Energy in Bending

U = ((M^{2}) \cdot \frac{L}{2 \cdot E \cdot I})

Other formulas in Strain Energy in Structural Members category

Go Stress using Hook's Law

σ = E \cdot ε L

Go Shear Force using Strain Energy

V = \sqrt{2 \cdot U \cdot A \cdot \frac{G Torsion}{L}}

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

L = 2 \cdot U \cdot A \cdot \frac{G Torsion}{V^{2}}

Go Shear Area given Strain Energy in Shear

A = (V^{2}) \cdot \frac{L}{2 \cdot U \cdot G Torsion}

How to Evaluate Strain Energy in Shear given Shear Deformation?

Strain Energy in Shear given Shear Deformation evaluator uses Strain Energy = (Area of Cross-Section*Modulus of Rigidity*(Shear Deformation^2))/(2*Length of Member) to evaluate 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 evaluate Strain Energy in Shear given Shear Deformation using this online evaluator? To use this online evaluator 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.

FAQs on Strain Energy in Shear given Shear Deformation

What is the formula to find Strain Energy in Shear given Shear Deformation?

The formula of Strain Energy in Shear given Shear Deformation is expressed as Strain Energy = (Area of Cross-Section*Modulus of Rigidity*(Shear Deformation^2))/(2*Length of Member). Here is an example- 933.3333 = (0.0056*40000000000*(0.005^2))/(2*3).

How to calculate Strain Energy in Shear given Shear Deformation?

With Area of Cross-Section (A), Modulus of Rigidity (G_Torsion), Shear Deformation (Δ) & Length of Member (L) we can find Strain Energy in Shear given Shear Deformation using the formula - Strain Energy = (Area of Cross-Section*Modulus of Rigidity*(Shear Deformation^2))/(2*Length of Member).

What are the other ways to Calculate Strain Energy?

Here are the different ways to Calculate Strain Energy-

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)

Can the Strain Energy in Shear given Shear Deformation be negative?

Yes, the Strain Energy in Shear given Shear Deformation, measured in Energy can be negative.

Which unit is used to measure Strain Energy in Shear given Shear Deformation?

Strain Energy in Shear given Shear Deformation is usually measured using the Newton Meter[N*m] for Energy. Joule[N*m], Kilojoule[N*m], Gigajoule[N*m] are the few other units in which Strain Energy in Shear given Shear Deformation can be measured.

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Strain Energy in Shear given Shear Deformation Formula

​GoStrain Energy in Shear Formula

​GoStrain Energy in Torsion given Polar MI and Shear Modulus of Elasticity Formula

Strain Energy in Shear given Shear Deformation Example

Strain Energy in Shear given Shear Deformation Solution

Strain Energy in Shear given Shear Deformation Formula Elements

Other Formulas to find Strain Energy

Other formulas in Strain Energy in Structural Members category

How to Evaluate Strain Energy in Shear given Shear Deformation?

FAQs on Strain Energy in Shear given Shear Deformation

Variable Name

GoStrain Energy in Shear Formula

GoStrain Energy in Torsion given Polar MI and Shear Modulus of Elasticity Formula