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Strain Energy due to Torsion in Hollow Shaft Formula

GoStrain Energy due to Pure Shear Formula

GoStrain Energy given Applied Tension Load Formula

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

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

U - Strain Energy?𝜏 - Shear Stress?d_outer - Outer Diameter of Shaft?d_inner - Inner Diameter of Shaft?V - Volume of Shaft?G_pa - Shear Modulus?

Strain Energy due to Torsion in Hollow Shaft Example

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Here is how the Strain Energy due to Torsion in Hollow Shaft equation looks like with Values.

Here is how the Strain Energy due to Torsion in Hollow Shaft equation looks like with Units.

Here is how the Strain Energy due to Torsion in Hollow Shaft equation looks like.

3.9031 = 100^{2} \cdot (2004^{2} + 1000^{2}) \cdot \frac{12.5}{4 \cdot 10.0002 \cdot 2004^{2}}

3.9031KJ = {100Pa}^{2} \cdot ({2004mm}^{2} + {1000mm}^{2}) \cdot \frac{12.5m³}{4 \cdot 10.0002Pa \cdot {2004mm}^{2}}

3.9031 = 100^{2} \cdot (2004^{2} + 1000^{2}) \cdot \frac{12.5}{4 \cdot 10.0002 \cdot 2004^{2}}

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Strain Energy due to Torsion in Hollow Shaft Solution

Follow our step by step solution on how to calculate Strain Energy due to Torsion in Hollow Shaft?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

U = {100Pa}^{2} \cdot ({2004mm}^{2} + {1000mm}^{2}) \cdot \frac{12.5m³}{4 \cdot 10.0002Pa \cdot {2004mm}^{2}}

Next Step Convert Units

∴

U = {100Pa}^{2} \cdot ({2.004m}^{2} + {1m}^{2}) \cdot \frac{12.5m³}{4 \cdot 10.0002Pa \cdot {2.004m}^{2}}

Next Step Prepare to Evaluate

∴

U = 100^{2} \cdot ({2.004}^{2} + 1^{2}) \cdot \frac{12.5}{4 \cdot 10.0002 \cdot {2.004}^{2}}

Next Step Evaluate

∴

U = 3903.07580392529J

Next Step Convert to Output's Unit

∴

U = 3.90307580392529KJ

LAST Step Rounding Answer

∴

U = 3.9031KJ

Strain Energy due to Torsion in Hollow Shaft Formula Elements

Variables

Strain Energy

The Strain Energy 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

Shear Stress

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

Symbol: 𝜏

Measurement: StressUnit: Pa

Note: Value should be greater than 0.

Formulas to find Shear Stress

Outer Diameter of Shaft

Outer Diameter of Shaft is defined as the length of the longest chord of the surface of the hollow circular shaft.

Symbol: d_outer

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Outer Diameter of Shaft

Inner Diameter of Shaft

The Inner Diameter of Shaft is defined as the length of the longest chord inside the hollow shaft.

Symbol: d_inner

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Inner Diameter of Shaft

Volume of Shaft

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

Symbol: V

Measurement: VolumeUnit: m³

Note: Value should be greater than 0.

Formulas to find Volume of Shaft

Shear Modulus

Shear Modulus is the slope of the linear elastic region of the shear stress-strain curve.

Symbol: G_pa

Measurement: PressureUnit: Pa

Note: Value should be greater than 0.

Formulas to find Shear Modulus

Other Formulas to find Strain Energy

Go Strain Energy due to Pure Shear

U = 𝜏 \cdot 𝜏 \cdot \frac{V T}{2 \cdot G pa}

Go Strain Energy given Applied Tension Load

U = W^{2} \cdot \frac{L}{2 \cdot A Base \cdot E}

Go Strain Energy given Moment Value

U = \frac{M b \cdot M b \cdot L}{2 \cdot e \cdot I}

Go Strain Energy given Torsion Moment Value

U = \frac{T^{2} \cdot L}{2 \cdot G pa \cdot J}

Other formulas in Strain Energy category

Go Strain Energy Density

S d = 0.5 \cdot σ \cdot ε

How to Evaluate Strain Energy due to Torsion in Hollow Shaft?

Strain Energy due to Torsion in Hollow Shaft evaluator uses Strain Energy = Shear Stress^(2)*(Outer Diameter of Shaft^(2)+Inner Diameter of Shaft^(2))*Volume of Shaft/(4*Shear Modulus*Outer Diameter of Shaft^(2)) to evaluate the Strain Energy, The Strain Energy due to Torsion in Hollow Shaft formula is defined as the energy stored in the hollow shaft when subjected to torsion. Strain Energy is denoted by U symbol.

How to evaluate Strain Energy due to Torsion in Hollow Shaft using this online evaluator? To use this online evaluator for Strain Energy due to Torsion in Hollow Shaft, enter Shear Stress (𝜏), Outer Diameter of Shaft (d_outer), Inner Diameter of Shaft (d_inner), Volume of Shaft (V) & Shear Modulus (G_pa) and hit the calculate button.

FAQs on Strain Energy due to Torsion in Hollow Shaft

What is the formula to find Strain Energy due to Torsion in Hollow Shaft?

The formula of Strain Energy due to Torsion in Hollow Shaft is expressed as Strain Energy = Shear Stress^(2)*(Outer Diameter of Shaft^(2)+Inner Diameter of Shaft^(2))*Volume of Shaft/(4*Shear Modulus*Outer Diameter of Shaft^(2)). Here is an example- 0.00332 = 100^(2)*(2.004^(2)+1^(2))*12.5/(4*10.00015*2.004^(2)).

How to calculate Strain Energy due to Torsion in Hollow Shaft?

With Shear Stress (𝜏), Outer Diameter of Shaft (d_outer), Inner Diameter of Shaft (d_inner), Volume of Shaft (V) & Shear Modulus (G_pa) we can find Strain Energy due to Torsion in Hollow Shaft using the formula - Strain Energy = Shear Stress^(2)*(Outer Diameter of Shaft^(2)+Inner Diameter of Shaft^(2))*Volume of Shaft/(4*Shear Modulus*Outer Diameter of Shaft^(2)).

What are the other ways to Calculate Strain Energy?

Here are the different ways to Calculate Strain Energy-

Strain Energy=Shear Stress*Shear Stress*Volume/(2*Shear Modulus)
Strain Energy=Load^2*Length/(2*Area of Base*Young's Modulus)
Strain Energy=(Bending Moment*Bending Moment*Length)/(2*Elastic Modulus*Moment of Inertia)

Can the Strain Energy due to Torsion in Hollow Shaft be negative?

No, the Strain Energy due to Torsion in Hollow Shaft, measured in Energy cannot be negative.

Which unit is used to measure Strain Energy due to Torsion in Hollow Shaft?

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

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Strain Energy due to Torsion in Hollow Shaft Formula

​GoStrain Energy due to Pure Shear Formula

​GoStrain Energy given Applied Tension Load Formula

Strain Energy due to Torsion in Hollow Shaft Example

Strain Energy due to Torsion in Hollow Shaft Solution

Strain Energy due to Torsion in Hollow Shaft Formula Elements

Other Formulas to find Strain Energy

Other formulas in Strain Energy category

How to Evaluate Strain Energy due to Torsion in Hollow Shaft?

FAQs on Strain Energy due to Torsion in Hollow Shaft

Variable Name

GoStrain Energy due to Pure Shear Formula

GoStrain Energy given Applied Tension Load Formula