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Shear strain energy in ring of radius 'r' Formula

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

U - Strain Energy in body?𝜏 - Shear stress on surface of shaft?L - Length of Shaft?r_center - Radius 'r' from Center Of Shaft?δx - Length of Small Element?G - Modulus of rigidity of Shaft?r_shaft - Radius of Shaft?π - Archimedes' constant?

Shear strain energy in ring of radius 'r' Example

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Here is how the Shear strain energy in ring of radius 'r' equation looks like with Values.

Here is how the Shear strain energy in ring of radius 'r' equation looks like with Units.

Here is how the Shear strain energy in ring of radius 'r' equation looks like.

0.0003 = \frac{2 \cdot 3.1416 \cdot ({4E-6}^{2}) \cdot 7000 \cdot (1500^{3}) \cdot 43.36}{2 \cdot 4E-5 \cdot (2000^{2})}

0.0003KJ = \frac{2 \cdot 3.1416 \cdot ({4E-6MPa}^{2}) \cdot 7000mm \cdot ({1500mm}^{3}) \cdot 43.36mm}{2 \cdot 4E-5MPa \cdot ({2000mm}^{2})}

0.0003 = \frac{2 \cdot 3.1416 \cdot ({4E-6}^{2}) \cdot 7000 \cdot (1500^{3}) \cdot 43.36}{2 \cdot 4E-5 \cdot (2000^{2})}

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Shear strain energy in ring of radius 'r' Solution

Follow our step by step solution on how to calculate Shear strain energy in ring of radius 'r'?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

U = \frac{2 \cdot π \cdot ({4E-6MPa}^{2}) \cdot 7000mm \cdot ({1500mm}^{3}) \cdot 43.36mm}{2 \cdot 4E-5MPa \cdot ({2000mm}^{2})}

Next Step Substitute values of Constants

∴

U = \frac{2 \cdot 3.1416 \cdot ({4E-6MPa}^{2}) \cdot 7000mm \cdot ({1500mm}^{3}) \cdot 43.36mm}{2 \cdot 4E-5MPa \cdot ({2000mm}^{2})}

Next Step Convert Units

∴

U = \frac{2 \cdot 3.1416 \cdot ({4Pa}^{2}) \cdot 7m \cdot ({1.5m}^{3}) \cdot 0.0434m}{2 \cdot 40Pa \cdot ({2m}^{2})}

Next Step Prepare to Evaluate

∴

U = \frac{2 \cdot 3.1416 \cdot (4^{2}) \cdot 7 \cdot ({1.5}^{3}) \cdot 0.0434}{2 \cdot 40 \cdot (2^{2})}

Next Step Evaluate

∴

U = 0.321818468248431J

Next Step Convert to Output's Unit

∴

U = 0.000321818468248431KJ

LAST Step Rounding Answer

∴

U = 0.0003KJ

Shear strain energy in ring of radius 'r' Formula Elements

Variables

Constants

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

Length of Shaft

The Length of Shaft is the distance between two ends of shaft.

Symbol: L

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Length of Shaft

Radius 'r' from Center Of Shaft

Radius 'r' from Center Of Shaft is a radial line from the focus to any point of a curve.

Symbol: r_center

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Radius 'r' from Center Of Shaft

Length of Small Element

Length of Small Element is a measure of distance.

Symbol: δx

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Length of Small Element

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

Radius of Shaft

The Radius of Shaft is the radius of the shaft subjected under torsion.

Symbol: r_shaft

Measurement: LengthUnit: mm

Note: Value can be positive or negative.

Formulas to find Radius of Shaft

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

Other Formulas to find Strain Energy in body

Go Shear strain energy

U = (𝜏^{2}) \cdot \frac{V}{2 \cdot G}

Go Total Strain Energy Stored in Shaft

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

How to Evaluate Shear strain energy in ring of radius 'r'?

Shear strain energy in ring of radius 'r' evaluator uses 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)) to evaluate the Strain Energy in body, The Shear strain energy in ring of radius 'r' formula is defined as the energy stored in a body due to deformation. Strain Energy in body is denoted by U symbol.

How to evaluate Shear strain energy in ring of radius 'r' using this online evaluator? To use this online evaluator for Shear strain energy in ring of radius 'r', enter Shear stress on surface of shaft (𝜏), Length of Shaft (L), Radius 'r' from Center Of Shaft (r_center), Length of Small Element (δx), Modulus of rigidity of Shaft (G) & Radius of Shaft (r_shaft) and hit the calculate button.

FAQs on Shear strain energy in ring of radius 'r'

What is the formula to find Shear strain energy in ring of radius 'r'?

The formula of Shear strain energy in ring of radius 'r' is expressed as 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)). Here is an example- 2E-8 = (2*pi*(4^2)*7*(1.5^3)*0.04336)/(2*40*(2^2)).

How to calculate Shear strain energy in ring of radius 'r'?

With Shear stress on surface of shaft (𝜏), Length of Shaft (L), Radius 'r' from Center Of Shaft (r_center), Length of Small Element (δx), Modulus of rigidity of Shaft (G) & Radius of Shaft (r_shaft) we can find Shear strain energy in ring of radius 'r' using the formula - 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)). This formula also uses Archimedes' constant .

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=(Shear stress on surface of shaft^2)*(Volume of Shaft)/(2*Modulus of rigidity of Shaft)
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 in ring of radius 'r' be negative?

No, the Shear strain energy in ring of radius 'r', measured in Energy cannot be negative.

Which unit is used to measure Shear strain energy in ring of radius 'r'?

Shear strain energy in ring of radius 'r' 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 in ring of radius 'r' can be measured.

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Shear strain energy in ring of radius 'r' Formula

​GoShear strain energy Formula

​GoTotal Strain Energy Stored in Shaft Formula

Shear strain energy in ring of radius 'r' Example

Shear strain energy in ring of radius 'r' Solution

Shear strain energy in ring of radius 'r' 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 in ring of radius 'r'?

FAQs on Shear strain energy in ring of radius 'r'

Variable Name

GoShear strain energy Formula

GoTotal Strain Energy Stored in Shaft Formula