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Length of shaft given total strain energy stored in shaft Formula

GoLength of shaft given shear strain energy in ring of radius r Formula

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

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

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

Length of shaft given total strain energy stored in shaft Example

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Here is how the Length of shaft given total strain energy stored in shaft equation looks like with Values.

Here is how the Length of shaft given total strain energy stored in shaft equation looks like with Units.

Here is how the Length of shaft given total strain energy stored in shaft equation looks like.

1E+8 = \frac{50 \cdot (2 \cdot 4E-5 \cdot (2000^{2}))}{({4E-6}^{2}) \cdot 10}

1E+8mm = \frac{50KJ \cdot (2 \cdot 4E-5MPa \cdot ({2000mm}^{2}))}{({4E-6MPa}^{2}) \cdot 10m⁴}

1E+8 = \frac{50 \cdot (2 \cdot 4E-5 \cdot (2000^{2}))}{({4E-6}^{2}) \cdot 10}

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Length of shaft given total strain energy stored in shaft Solution

Follow our step by step solution on how to calculate Length of shaft given total strain energy stored in shaft?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

L = \frac{50KJ \cdot (2 \cdot 4E-5MPa \cdot ({2000mm}^{2}))}{({4E-6MPa}^{2}) \cdot 10m⁴}

Next Step Convert Units

∴

L = \frac{50000J \cdot (2 \cdot 40Pa \cdot ({2m}^{2}))}{({4Pa}^{2}) \cdot 10m⁴}

Next Step Prepare to Evaluate

∴

L = \frac{50000 \cdot (2 \cdot 40 \cdot (2^{2}))}{(4^{2}) \cdot 10}

Next Step Evaluate

∴

L = 100000m

Next Step Convert to Output's Unit

∴

L = 100000000mm

LAST Step Rounding Answer

∴

L = 1E+8mm

Length of shaft given total strain energy stored in shaft Formula Elements

Variables

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

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

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

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

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

Other Formulas to find Length of Shaft

Go Length of shaft given shear strain energy in ring of radius r

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

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 Shear strain energy

U = (𝜏^{2}) \cdot \frac{V}{2 \cdot G}

Go Modulus of rigidity given shear strain energy

G = (𝜏^{2}) \cdot \frac{V}{2 \cdot U}

How to Evaluate Length of shaft given total strain energy stored in shaft?

Length of shaft given total strain energy stored in shaft evaluator uses Length of Shaft = (Strain Energy in body*(2*Modulus of rigidity of Shaft*(Radius of Shaft^2)))/((Shear stress on surface of shaft^2)*Polar Moment of Inertia of shaft) to evaluate the Length of Shaft, Length of shaft given total strain energy stored in shaft is defined as the measurement or extent of something from end to end. Length of Shaft is denoted by L symbol.

How to evaluate Length of shaft given total strain energy stored in shaft using this online evaluator? To use this online evaluator for Length of shaft given total strain energy stored in shaft, enter Strain Energy in body (U), Modulus of rigidity of Shaft (G), Radius of Shaft (r_shaft), Shear stress on surface of shaft (𝜏) & Polar Moment of Inertia of shaft (J_shaft) and hit the calculate button.

FAQs on Length of shaft given total strain energy stored in shaft

What is the formula to find Length of shaft given total strain energy stored in shaft?

The formula of Length of shaft given total strain energy stored in shaft is expressed as Length of Shaft = (Strain Energy in body*(2*Modulus of rigidity of Shaft*(Radius of Shaft^2)))/((Shear stress on surface of shaft^2)*Polar Moment of Inertia of shaft). Here is an example- 1E+11 = (50000*(2*40*(2^2)))/((4^2)*10).

How to calculate Length of shaft given total strain energy stored in shaft?

With Strain Energy in body (U), Modulus of rigidity of Shaft (G), Radius of Shaft (r_shaft), Shear stress on surface of shaft (𝜏) & Polar Moment of Inertia of shaft (J_shaft) we can find Length of shaft given total strain energy stored in shaft using the formula - Length of Shaft = (Strain Energy in body*(2*Modulus of rigidity of Shaft*(Radius of Shaft^2)))/((Shear stress on surface of shaft^2)*Polar Moment of Inertia of shaft).

What are the other ways to Calculate Length of Shaft?

Here are the different ways to Calculate Length of Shaft-

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

Can the Length of shaft given total strain energy stored in shaft be negative?

No, the Length of shaft given total strain energy stored in shaft, measured in Length cannot be negative.

Which unit is used to measure Length of shaft given total strain energy stored in shaft?

Length of shaft given total strain energy stored in shaft is usually measured using the Millimeter[mm] for Length. Meter[mm], Kilometer[mm], Decimeter[mm] are the few other units in which Length of shaft given total strain energy stored in shaft can be measured.

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Length of shaft given total strain energy stored in shaft Formula

​GoLength of shaft given shear strain energy in ring of radius r Formula

Length of shaft given total strain energy stored in shaft Example

Length of shaft given total strain energy stored in shaft Solution

Length of shaft given total strain energy stored in shaft Formula Elements

Other Formulas to find Length of Shaft

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

How to Evaluate Length of shaft given total strain energy stored in shaft?

FAQs on Length of shaft given total strain energy stored in shaft

Variable Name

GoLength of shaft given shear strain energy in ring of radius r Formula