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Total strain energy in hollow shaft due to torsion 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 (({d outer}^{2}) + ({d inner}^{2})) \cdot V}{4 \cdot G \cdot ({d outer}^{2})}

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

Total strain energy in hollow shaft due to torsion Example

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Here is how the Total strain energy in hollow shaft due to torsion equation looks like with Values.

Here is how the Total strain energy in hollow shaft due to torsion equation looks like with Units.

Here is how the Total strain energy in hollow shaft due to torsion equation looks like.

0.0133 = \frac{({4E-6}^{2}) \cdot ((4000^{2}) + (1000^{2})) \cdot 125.6}{4 \cdot 4E-5 \cdot (4000^{2})}

0.0133KJ = \frac{({4E-6MPa}^{2}) \cdot (({4000mm}^{2}) + ({1000mm}^{2})) \cdot 125.6m³}{4 \cdot 4E-5MPa \cdot ({4000mm}^{2})}

0.0133 = \frac{({4E-6}^{2}) \cdot ((4000^{2}) + (1000^{2})) \cdot 125.6}{4 \cdot 4E-5 \cdot (4000^{2})}

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Total strain energy in hollow shaft due to torsion Solution

Follow our step by step solution on how to calculate Total strain energy in hollow shaft due to torsion?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

U = \frac{({4E-6MPa}^{2}) \cdot (({4000mm}^{2}) + ({1000mm}^{2})) \cdot 125.6m³}{4 \cdot 4E-5MPa \cdot ({4000mm}^{2})}

Next Step Convert Units

∴

U = \frac{({4Pa}^{2}) \cdot (({4m}^{2}) + ({1m}^{2})) \cdot 125.6m³}{4 \cdot 40Pa \cdot ({4m}^{2})}

Next Step Prepare to Evaluate

∴

U = \frac{(4^{2}) \cdot ((4^{2}) + (1^{2})) \cdot 125.6}{4 \cdot 40 \cdot (4^{2})}

Next Step Evaluate

∴

U = 13.345J

Next Step Convert to Output's Unit

∴

U = 0.013345KJ

LAST Step Rounding Answer

∴

U = 0.0133KJ

Total strain energy in hollow shaft due to torsion 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

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 can be positive or negative.

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 can be positive or negative.

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 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

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 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}

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 in hollow shaft due to torsion?

Total strain energy in hollow shaft due to torsion evaluator uses Strain Energy in body = ((Shear stress on surface of shaft^2)*((Outer Diameter of Shaft^2)+(Inner Diameter of Shaft^2))*Volume of Shaft)/(4*Modulus of rigidity of Shaft*(Outer Diameter of Shaft^2)) to evaluate the Strain Energy in body, Total strain energy in hollow shaft due to torsion formula is defined as the energy stored in a body due to deformation. The strain energy per unit volume is known as strain energy density and the area under the stress-strain curve towards the point of deformation. Strain Energy in body is denoted by U symbol.

How to evaluate Total strain energy in hollow shaft due to torsion using this online evaluator? To use this online evaluator for Total strain energy in hollow shaft due to torsion, enter Shear stress on surface of shaft (𝜏), Outer Diameter of Shaft (d_outer), Inner Diameter of Shaft (d_inner), Volume of Shaft (V) & Modulus of rigidity of Shaft (G) and hit the calculate button.

FAQs on Total strain energy in hollow shaft due to torsion

What is the formula to find Total strain energy in hollow shaft due to torsion?

The formula of Total strain energy in hollow shaft due to torsion is expressed as Strain Energy in body = ((Shear stress on surface of shaft^2)*((Outer Diameter of Shaft^2)+(Inner Diameter of Shaft^2))*Volume of Shaft)/(4*Modulus of rigidity of Shaft*(Outer Diameter of Shaft^2)). Here is an example- 1.3E-5 = ((4^2)*((4^2)+(1^2))*125.6)/(4*40*(4^2)).

How to calculate Total strain energy in hollow shaft due to torsion?

With Shear stress on surface of shaft (𝜏), Outer Diameter of Shaft (d_outer), Inner Diameter of Shaft (d_inner), Volume of Shaft (V) & Modulus of rigidity of Shaft (G) we can find Total strain energy in hollow shaft due to torsion using the formula - Strain Energy in body = ((Shear stress on surface of shaft^2)*((Outer Diameter of Shaft^2)+(Inner Diameter of Shaft^2))*Volume of Shaft)/(4*Modulus of rigidity of Shaft*(Outer Diameter 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)*Length of Shaft*Polar Moment of Inertia of shaft)/(2*Modulus of rigidity of Shaft*(Radius of Shaft^2))

Can the Total strain energy in hollow shaft due to torsion be negative?

No, the Total strain energy in hollow shaft due to torsion, measured in Energy cannot be negative.

Which unit is used to measure Total strain energy in hollow shaft due to torsion?

Total strain energy in hollow shaft due to torsion 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 in hollow shaft due to torsion can be measured.

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Total strain energy in hollow shaft due to torsion Formula

​GoShear strain energy Formula

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

Total strain energy in hollow shaft due to torsion Example

Total strain energy in hollow shaft due to torsion Solution

Total strain energy in hollow shaft due to torsion 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 in hollow shaft due to torsion?

FAQs on Total strain energy in hollow shaft due to torsion

Variable Name

GoShear strain energy Formula

GoShear strain energy in ring of radius 'r' Formula