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Total Strain Energy Stored in Shaft Formula

GoShear strain energy Formula

GoShear strain energy in ring of radius 'r' 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{(𝜏^{2}) \cdot L \cdot J shaft}{2 \cdot G \cdot ({r shaft}^{2})}

U - Strain Energy in body?𝜏 - Shear stress on surface of shaft?L - Length of Shaft?J_shaft - Polar Moment of Inertia of shaft?G - Modulus of rigidity of Shaft?r_shaft - Radius of Shaft?

Total Strain Energy Stored in Shaft Example

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Here is how the Total Strain Energy Stored in Shaft equation looks like with Values.

Here is how the Total Strain Energy Stored in Shaft equation looks like with Units.

Here is how the Total Strain Energy Stored in Shaft equation looks like.

0.0035 = \frac{({4E-6}^{2}) \cdot 7000 \cdot 10}{2 \cdot 4E-5 \cdot (2000^{2})}

0.0035KJ = \frac{({4E-6MPa}^{2}) \cdot 7000mm \cdot 10m⁴}{2 \cdot 4E-5MPa \cdot ({2000mm}^{2})}

0.0035 = \frac{({4E-6}^{2}) \cdot 7000 \cdot 10}{2 \cdot 4E-5 \cdot (2000^{2})}

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Total Strain Energy Stored in Shaft Solution

Follow our step by step solution on how to calculate Total Strain Energy Stored in Shaft?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

U = \frac{({4E-6MPa}^{2}) \cdot 7000mm \cdot 10m⁴}{2 \cdot 4E-5MPa \cdot ({2000mm}^{2})}

Next Step Convert Units

∴

U = \frac{({4Pa}^{2}) \cdot 7m \cdot 10m⁴}{2 \cdot 40Pa \cdot ({2m}^{2})}

Next Step Prepare to Evaluate

∴

U = \frac{(4^{2}) \cdot 7 \cdot 10}{2 \cdot 40 \cdot (2^{2})}

Next Step Evaluate

∴

U = 3.5J

LAST Step Convert to Output's Unit

∴

U = 0.0035KJ

Total Strain Energy Stored in Shaft 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

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

Polar Moment of Inertia of shaft

Polar Moment of Inertia of shaft is the measure of object resistance to torsion.

Symbol: J_shaft

Measurement: Second Moment of AreaUnit: m⁴

Note: Value can be positive or negative.

Formulas to find Polar Moment of Inertia 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

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

Other Formulas to find Strain Energy in body

Go Shear strain energy

U = (𝜏^{2}) \cdot \frac{V}{2 \cdot G}

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 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 Total Strain Energy Stored in Shaft?

Total Strain Energy Stored in Shaft evaluator uses 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)) to evaluate the Strain Energy in body, The Total Strain Energy Stored in Shaft 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 Total Strain Energy Stored in Shaft using this online evaluator? To use this online evaluator for Total Strain Energy Stored in Shaft, enter Shear stress on surface of shaft (𝜏), Length of Shaft (L), Polar Moment of Inertia of shaft (J_shaft), Modulus of rigidity of Shaft (G) & Radius of Shaft (r_shaft) and hit the calculate button.

FAQs on Total Strain Energy Stored in Shaft

What is the formula to find Total Strain Energy Stored in Shaft?

The formula of Total Strain Energy Stored in Shaft is expressed as 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)). Here is an example- 3.5E-6 = ((4^2)*7*10)/(2*40*(2^2)).

How to calculate Total Strain Energy Stored in Shaft?

With Shear stress on surface of shaft (𝜏), Length of Shaft (L), Polar Moment of Inertia of shaft (J_shaft), Modulus of rigidity of Shaft (G) & Radius of Shaft (r_shaft) we can find Total Strain Energy Stored in Shaft using the formula - 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)).

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=(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)*Volume of Shaft)/(4*Modulus of rigidity of Shaft)

Can the Total Strain Energy Stored in Shaft be negative?

No, the Total Strain Energy Stored in Shaft, measured in Energy cannot be negative.

Which unit is used to measure Total Strain Energy Stored in Shaft?

Total Strain Energy Stored in Shaft is usually measured using the Kilojoule[KJ] for Energy. Joule[KJ], Gigajoule[KJ], Megajoule[KJ] are the few other units in which Total Strain Energy Stored in Shaft can be measured.

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Total Strain Energy Stored in Shaft Formula

​GoShear strain energy Formula

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

Total Strain Energy Stored in Shaft Example

Total Strain Energy Stored in Shaft Solution

Total Strain Energy Stored in Shaft 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 Total Strain Energy Stored in Shaft?

FAQs on Total Strain Energy Stored in Shaft

Variable Name

GoShear strain energy Formula

GoShear strain energy in ring of radius 'r' Formula