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Shear strain energy Formula

GoShear strain energy in ring of radius 'r' Formula

GoTotal Strain Energy Stored in Shaft Formula

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Strain Energy in body is defined as the energy stored in a body due to deformation. Check FAQs

U = (𝜏^{2}) \cdot \frac{V}{2 \cdot G}

U - Strain Energy in body?𝜏 - Shear stress on surface of shaft?V - Volume of Shaft?G - Modulus of rigidity of Shaft?

Shear strain energy Example

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Here is how the Shear strain energy equation looks like with Values.

Here is how the Shear strain energy equation looks like with Units.

Here is how the Shear strain energy equation looks like.

0.0251 = ({4E-6}^{2}) \cdot \frac{125.6}{2 \cdot 4E-5}

0.0251KJ = ({4E-6MPa}^{2}) \cdot \frac{125.6m³}{2 \cdot 4E-5MPa}

0.0251 = ({4E-6}^{2}) \cdot \frac{125.6}{2 \cdot 4E-5}

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Shear strain energy Solution

Follow our step by step solution on how to calculate Shear strain energy?

FIRST Step Consider the formula

U = (𝜏^{2}) \cdot \frac{V}{2 \cdot G}

Next Step Substitute values of Variables

∴

U = ({4E-6MPa}^{2}) \cdot \frac{125.6m³}{2 \cdot 4E-5MPa}

Next Step Convert Units

∴

U = ({4Pa}^{2}) \cdot \frac{125.6m³}{2 \cdot 40Pa}

Next Step Prepare to Evaluate

∴

U = (4^{2}) \cdot \frac{125.6}{2 \cdot 40}

Next Step Evaluate

∴

U = 25.12J

Next Step Convert to Output's Unit

∴

U = 0.02512KJ

LAST Step Rounding Answer

∴

U = 0.0251KJ

Shear strain energy Formula Elements

Variables

Strain Energy in body

Strain Energy in body is defined as the energy stored in a body due to deformation.

Symbol: U

Measurement: EnergyUnit: KJ

Note: Value should be greater than 0.

Formulas to find Strain Energy in body

Shear stress on surface of shaft

Shear stress on surface of shaft is force tending to cause deformation of a material by slippage along a plane or planes parallel to the imposed stress.

Symbol: 𝜏

Measurement: PressureUnit: MPa

Note: Value should be greater than 0.

Formulas to find Shear stress on surface of shaft

Volume of Shaft

The Volume of Shaft is the volume of cylindical component under torsion.

Symbol: V

Measurement: VolumeUnit: m³

Note: Value can be positive or negative.

Formulas to find Volume of Shaft

Modulus of rigidity of Shaft

Modulus of rigidity of Shaft is the elastic coefficient when a shear force is applied resulting in lateral deformation. It gives us a measure of how rigid a body is.

Symbol: G

Measurement: PressureUnit: MPa

Note: Value should be greater than 0.

Formulas to find Modulus of rigidity of Shaft

Other Formulas to find Strain Energy in body

Go Shear strain energy in ring of radius 'r'

U = \frac{2 \cdot π \cdot (𝜏^{2}) \cdot L \cdot ({r center}^{3}) \cdot δx}{2 \cdot G \cdot ({r shaft}^{2})}

Go Total Strain Energy Stored in Shaft

U = \frac{(𝜏^{2}) \cdot L \cdot J shaft}{2 \cdot G \cdot ({r shaft}^{2})}

Go Total strain energy in shaft due to torsion

U = \frac{(𝜏^{2}) \cdot V}{4 \cdot G}

Go Total strain energy in hollow shaft due to torsion

U = \frac{(𝜏^{2}) \cdot (({d outer}^{2}) + ({d inner}^{2})) \cdot V}{4 \cdot G \cdot ({d outer}^{2})}

Other formulas in Expression for Strain Energy stored in a Body Due to Torsion category

Go Value of radius 'r' given shear stress at radius 'r' from center

r center = \frac{q \cdot r shaft}{𝜏}

Go Radius of shaft given shear stress at radius r from center

r shaft = (\frac{r center}{q}) \cdot 𝜏

Go Modulus of rigidity given shear strain energy

G = (𝜏^{2}) \cdot \frac{V}{2 \cdot U}

Go Volume given shear strain energy

V = \frac{U \cdot 2 \cdot G}{𝜏^{2}}

How to Evaluate Shear strain energy?

Shear strain energy evaluator uses Strain Energy in body = (Shear stress on surface of shaft^2)*(Volume of Shaft)/(2*Modulus of rigidity of Shaft) to evaluate the Strain Energy in body, The Shear strain energy formula is defined as the energy stored in a body due to deformation. The strain energy (i.e. the amount of potential energy stored due to the deformation) is equal to the work expended in deforming the material. Strain Energy in body is denoted by U symbol.

How to evaluate Shear strain energy using this online evaluator? To use this online evaluator for Shear strain energy, enter Shear stress on surface of shaft (𝜏), Volume of Shaft (V) & Modulus of rigidity of Shaft (G) and hit the calculate button.

FAQs on Shear strain energy

What is the formula to find Shear strain energy?

The formula of Shear strain energy is expressed as Strain Energy in body = (Shear stress on surface of shaft^2)*(Volume of Shaft)/(2*Modulus of rigidity of Shaft). Here is an example- 2.5E-5 = (4^2)*(125.6)/(2*40).

How to calculate Shear strain energy?

With Shear stress on surface of shaft (𝜏), Volume of Shaft (V) & Modulus of rigidity of Shaft (G) we can find Shear strain energy using the formula - Strain Energy in body = (Shear stress on surface of shaft^2)*(Volume of Shaft)/(2*Modulus of rigidity of Shaft).

What are the other ways to Calculate Strain Energy in body?

Here are the different ways to Calculate Strain Energy in body-

Strain Energy in body=(2*pi*(Shear stress on surface of shaft^2)*Length of Shaft*(Radius 'r' from Center Of Shaft^3)*Length of Small Element)/(2*Modulus of rigidity of Shaft*(Radius of Shaft^2))
Strain Energy in body=((Shear stress on surface of shaft^2)*Length of Shaft*Polar Moment of Inertia of shaft)/(2*Modulus of rigidity of Shaft*(Radius of Shaft^2))
Strain Energy in body=((Shear stress on surface of shaft^2)*Volume of Shaft)/(4*Modulus of rigidity of Shaft)

Can the Shear strain energy be negative?

No, the Shear strain energy, measured in Energy cannot be negative.

Which unit is used to measure Shear strain energy?

Shear strain energy is usually measured using the Kilojoule[KJ] for Energy. Joule[KJ], Gigajoule[KJ], Megajoule[KJ] are the few other units in which Shear strain energy can be measured.

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Shear strain energy Formula

​GoShear strain energy in ring of radius 'r' Formula

​GoTotal Strain Energy Stored in Shaft Formula

Shear strain energy Example

Shear strain energy Solution

Shear strain energy Formula Elements

Other Formulas to find Strain Energy in body

Other formulas in Expression for Strain Energy stored in a Body Due to Torsion category

How to Evaluate Shear strain energy?

FAQs on Shear strain energy

Variable Name

GoShear strain energy in ring of radius 'r' Formula

GoTotal Strain Energy Stored in Shaft Formula