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Strain Energy in Shear Formula

GoStrain Energy in Shear given Shear Deformation 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 = (V^{2}) \cdot \frac{L}{2 \cdot A \cdot G Torsion}

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

Strain Energy in Shear Example

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

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

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

136.9353 = (143^{2}) \cdot \frac{3000}{2 \cdot 5600 \cdot 40}

136.9353N*m = ({143kN}^{2}) \cdot \frac{3000mm}{2 \cdot 5600mm² \cdot 40GPa}

136.9353 = (143^{2}) \cdot \frac{3000}{2 \cdot 5600 \cdot 40}

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Strain Energy in Shear Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

U = ({143kN}^{2}) \cdot \frac{3000mm}{2 \cdot 5600mm² \cdot 40GPa}

Next Step Convert Units

∴

U = ({143000N}^{2}) \cdot \frac{3m}{2 \cdot 0.0056m² \cdot 4E+10Pa}

Next Step Prepare to Evaluate

∴

U = (143000^{2}) \cdot \frac{3}{2 \cdot 0.0056 \cdot 4E+10}

Next Step Evaluate

∴

U = 136.935267857143J

Next Step Convert to Output's Unit

∴

U = 136.935267857143N*m

LAST Step Rounding Answer

∴

U = 136.9353N*m

Strain Energy in Shear 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

Shear Force

Shear Force is the force which causes shear deformation to occur in the shear plane.

Symbol: V

Measurement: ForceUnit: kN

Note: Value should be greater than 0.

Formulas to find Shear Force

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

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

Other Formulas to find Strain Energy

Go Strain Energy in Shear given Shear Deformation

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

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?

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

FAQs on Strain Energy in Shear

What is the formula to find Strain Energy in Shear?

The formula of Strain Energy in Shear is expressed as Strain Energy = (Shear Force^2)*Length of Member/(2*Area of Cross-Section*Modulus of Rigidity). Here is an example- 136.9353 = (143000^2)*3/(2*0.0056*40000000000).

How to calculate Strain Energy in Shear?

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

What are the other ways to Calculate Strain Energy?

Here are the different ways to Calculate Strain Energy-

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)

Can the Strain Energy in Shear be negative?

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

Which unit is used to measure Strain Energy in Shear?

Strain Energy in Shear 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 can be measured.

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Strain Energy in Shear Formula

​GoStrain Energy in Shear given Shear Deformation Formula

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

Strain Energy in Shear Example

Strain Energy in Shear Solution

Strain Energy in Shear Formula Elements

Other Formulas to find Strain Energy

Other formulas in Strain Energy in Structural Members category

How to Evaluate Strain Energy in Shear?

FAQs on Strain Energy in Shear

Variable Name

GoStrain Energy in Shear given Shear Deformation Formula

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