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

GoLength of shaft given total strain energy stored in shaft 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}))}{2 \cdot π \cdot (𝜏^{2}) \cdot ({r center}^{3}) \cdot δx}

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?r_center - Radius 'r' from Center Of Shaft?δx - Length of Small Element?π - Archimedes' constant?

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

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Here is how the Length of shaft given shear strain energy in ring of radius r equation looks like with Values.

Here is how the Length of shaft given shear strain energy in ring of radius r equation looks like with Units.

Here is how the Length of shaft given shear strain energy in ring of radius r equation looks like.

1.1E+9 = \frac{50 \cdot (2 \cdot 4E-5 \cdot (2000^{2}))}{2 \cdot 3.1416 \cdot ({4E-6}^{2}) \cdot (1500^{3}) \cdot 43.36}

1.1E+9mm = \frac{50KJ \cdot (2 \cdot 4E-5MPa \cdot ({2000mm}^{2}))}{2 \cdot 3.1416 \cdot ({4E-6MPa}^{2}) \cdot ({1500mm}^{3}) \cdot 43.36mm}

1.1E+9 = \frac{50 \cdot (2 \cdot 4E-5 \cdot (2000^{2}))}{2 \cdot 3.1416 \cdot ({4E-6}^{2}) \cdot (1500^{3}) \cdot 43.36}

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

Follow our step by step solution on how to calculate Length of shaft given shear strain energy in ring of radius r?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

L = \frac{50KJ \cdot (2 \cdot 4E-5MPa \cdot ({2000mm}^{2}))}{2 \cdot π \cdot ({4E-6MPa}^{2}) \cdot ({1500mm}^{3}) \cdot 43.36mm}

Next Step Substitute values of Constants

∴

L = \frac{50KJ \cdot (2 \cdot 4E-5MPa \cdot ({2000mm}^{2}))}{2 \cdot 3.1416 \cdot ({4E-6MPa}^{2}) \cdot ({1500mm}^{3}) \cdot 43.36mm}

Next Step Convert Units

∴

L = \frac{50000J \cdot (2 \cdot 40Pa \cdot ({2m}^{2}))}{2 \cdot 3.1416 \cdot ({4Pa}^{2}) \cdot ({1.5m}^{3}) \cdot 0.0434m}

Next Step Prepare to Evaluate

∴

L = \frac{50000 \cdot (2 \cdot 40 \cdot (2^{2}))}{2 \cdot 3.1416 \cdot (4^{2}) \cdot ({1.5}^{3}) \cdot 0.0434}

Next Step Evaluate

∴

L = 1087569.65349115m

Next Step Convert to Output's Unit

∴

L = 1087569653.49115mm

LAST Step Rounding Answer

∴

L = 1.1E+9mm

Length of shaft given shear strain energy in ring of radius r Formula Elements

Variables

Constants

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

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

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 Length of Shaft

Go Length of shaft given total strain energy stored in shaft

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

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

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

FAQs on Length of shaft given shear strain energy in ring of radius r

What is the formula to find Length of shaft given shear strain energy in ring of radius r?

The formula of Length of shaft given shear strain energy in ring of radius r is expressed as 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). Here is an example- 1.7E+13 = (50000*(2*40*(2^2)))/(2*pi*(4^2)*(1.5^3)*0.04336).

How to calculate Length of shaft given shear strain energy in ring of radius r?

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

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)))/((Shear stress on surface of shaft^2)*Polar Moment of Inertia of shaft)

Can the Length of shaft given shear strain energy in ring of radius r be negative?

No, the Length of shaft given shear strain energy in ring of radius r, measured in Length cannot be negative.

Which unit is used to measure Length of shaft given shear strain energy in ring of radius r?

Length of shaft given shear strain energy in ring of radius r 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 shear strain energy in ring of radius r can be measured.

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

​GoLength of shaft given total strain energy stored in shaft Formula

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

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

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

FAQs on Length of shaft given shear strain energy in ring of radius r

Variable Name

GoLength of shaft given total strain energy stored in shaft Formula