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

GoRadius of shaft given shear stress at radius r from center Formula

GoRadius of Shaft given Total Strain Energy Stored in Shaft Formula

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The Radius of Shaft is the radius of the shaft subjected under torsion. Check FAQs

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

r_shaft - Radius of Shaft?𝜏 - Shear stress on surface of shaft?L - Length of Shaft?r_center - Radius 'r' from Center Of Shaft?δx - Length of Small Element?G - Modulus of rigidity of Shaft?U - Strain Energy in body?π - Archimedes' constant?

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

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

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

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

5.074 = \sqrt{\frac{2 \cdot 3.1416 \cdot ({4E-6}^{2}) \cdot 7000 \cdot (1500^{3}) \cdot 43.36}{2 \cdot 4E-5 \cdot (50)}}

5.074mm = \sqrt{\frac{2 \cdot 3.1416 \cdot ({4E-6MPa}^{2}) \cdot 7000mm \cdot ({1500mm}^{3}) \cdot 43.36mm}{2 \cdot 4E-5MPa \cdot (50KJ)}}

5.074 = \sqrt{\frac{2 \cdot 3.1416 \cdot ({4E-6}^{2}) \cdot 7000 \cdot (1500^{3}) \cdot 43.36}{2 \cdot 4E-5 \cdot (50)}}

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

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

r shaft = \sqrt{\frac{2 \cdot π \cdot ({4E-6MPa}^{2}) \cdot 7000mm \cdot ({1500mm}^{3}) \cdot 43.36mm}{2 \cdot 4E-5MPa \cdot (50KJ)}}

Next Step Substitute values of Constants

∴

r shaft = \sqrt{\frac{2 \cdot 3.1416 \cdot ({4E-6MPa}^{2}) \cdot 7000mm \cdot ({1500mm}^{3}) \cdot 43.36mm}{2 \cdot 4E-5MPa \cdot (50KJ)}}

Next Step Convert Units

∴

r shaft = \sqrt{\frac{2 \cdot 3.1416 \cdot ({4Pa}^{2}) \cdot 7m \cdot ({1.5m}^{3}) \cdot 0.0434m}{2 \cdot 40Pa \cdot (50000J)}}

Next Step Prepare to Evaluate

∴

r shaft = \sqrt{\frac{2 \cdot 3.1416 \cdot (4^{2}) \cdot 7 \cdot ({1.5}^{3}) \cdot 0.0434}{2 \cdot 40 \cdot (50000)}}

Next Step Evaluate

∴

r shaft = 0.00507400014385834m

Next Step Convert to Output's Unit

∴

r shaft = 5.07400014385834mm

LAST Step Rounding Answer

∴

r shaft = 5.074mm

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

Variables

Constants

Functions

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