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Polar Moment of Inertia of Shaft given Total Strain Energy Stored in Shaft Formula

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Polar Moment of Inertia of shaft is the measure of object resistance to torsion. Check FAQs

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

J_shaft - Polar Moment of Inertia 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?L - Length of Shaft?

Polar Moment of Inertia of Shaft given Total Strain Energy Stored in Shaft Example

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Here is how the Polar Moment of Inertia of Shaft given Total Strain Energy Stored in Shaft equation looks like with Values.

Here is how the Polar Moment of Inertia of Shaft given Total Strain Energy Stored in Shaft equation looks like with Units.

Here is how the Polar Moment of Inertia of Shaft given Total Strain Energy Stored in Shaft equation looks like.

142857.1429 = \frac{50 \cdot (2 \cdot 4E-5 \cdot (2000^{2}))}{({4E-6}^{2}) \cdot 7000}

142857.1429m⁴ = \frac{50KJ \cdot (2 \cdot 4E-5MPa \cdot ({2000mm}^{2}))}{({4E-6MPa}^{2}) \cdot 7000mm}

142857.1429 = \frac{50 \cdot (2 \cdot 4E-5 \cdot (2000^{2}))}{({4E-6}^{2}) \cdot 7000}

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Polar Moment of Inertia of Shaft given Total Strain Energy Stored in Shaft Solution

Follow our step by step solution on how to calculate Polar Moment of Inertia of Shaft given Total Strain Energy Stored in Shaft?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

J shaft = \frac{50KJ \cdot (2 \cdot 4E-5MPa \cdot ({2000mm}^{2}))}{({4E-6MPa}^{2}) \cdot 7000mm}

Next Step Convert Units

∴

J shaft = \frac{50000J \cdot (2 \cdot 40Pa \cdot ({2m}^{2}))}{({4Pa}^{2}) \cdot 7m}

Next Step Prepare to Evaluate

∴

J shaft = \frac{50000 \cdot (2 \cdot 40 \cdot (2^{2}))}{(4^{2}) \cdot 7}

Next Step Evaluate

∴

J shaft = 142857.142857143m⁴

LAST Step Rounding Answer

∴

J shaft = 142857.1429m⁴

Polar Moment of Inertia of Shaft given Total Strain Energy Stored in Shaft Formula Elements

Variables

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

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

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

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 Polar Moment of Inertia of Shaft given Total Strain Energy Stored in Shaft?

Polar Moment of Inertia of Shaft given Total Strain Energy Stored in Shaft evaluator uses Polar Moment of Inertia of shaft = (Strain Energy in body*(2*Modulus of rigidity of Shaft*(Radius of Shaft^2)))/((Shear stress on surface of shaft^2)*Length of Shaft) to evaluate the Polar Moment of Inertia of shaft, The Polar Moment of Inertia of Shaft given Total Strain Energy Stored in Shaft formula is defined as a quantity used to describe resistance to torsional deformation (deflection), in cylindrical objects (or segments of the cylindrical object) with an invariant cross-section and no significant warping or out-of-plane deformation. Polar Moment of Inertia of shaft is denoted by J_shaft symbol.

How to evaluate Polar Moment of Inertia of Shaft given Total Strain Energy Stored in Shaft using this online evaluator? To use this online evaluator for Polar Moment of Inertia 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) & Length of Shaft (L) and hit the calculate button.

FAQs on Polar Moment of Inertia of Shaft given Total Strain Energy Stored in Shaft

What is the formula to find Polar Moment of Inertia of Shaft given Total Strain Energy Stored in Shaft?

The formula of Polar Moment of Inertia of Shaft given Total Strain Energy Stored in Shaft is expressed as Polar Moment of Inertia of shaft = (Strain Energy in body*(2*Modulus of rigidity of Shaft*(Radius of Shaft^2)))/((Shear stress on surface of shaft^2)*Length of Shaft). Here is an example- 142857.1 = (50000*(2*40*(2^2)))/((4^2)*7).

How to calculate Polar Moment of Inertia 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) & Length of Shaft (L) we can find Polar Moment of Inertia of Shaft given Total Strain Energy Stored in Shaft using the formula - Polar Moment of Inertia of shaft = (Strain Energy in body*(2*Modulus of rigidity of Shaft*(Radius of Shaft^2)))/((Shear stress on surface of shaft^2)*Length of Shaft).

Can the Polar Moment of Inertia of Shaft given Total Strain Energy Stored in Shaft be negative?

Yes, the Polar Moment of Inertia of Shaft given Total Strain Energy Stored in Shaft, measured in Second Moment of Area can be negative.

Which unit is used to measure Polar Moment of Inertia of Shaft given Total Strain Energy Stored in Shaft?

Polar Moment of Inertia of Shaft given Total Strain Energy Stored in Shaft is usually measured using the Meter⁴[m⁴] for Second Moment of Area. Centimeter⁴[m⁴], Millimeter⁴[m⁴] are the few other units in which Polar Moment of Inertia of Shaft given Total Strain Energy Stored in Shaft can be measured.

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Polar Moment of Inertia of Shaft given Total Strain Energy Stored in Shaft Formula

Polar Moment of Inertia of Shaft given Total Strain Energy Stored in Shaft Example

Polar Moment of Inertia of Shaft given Total Strain Energy Stored in Shaft Solution

Polar Moment of Inertia of Shaft given Total Strain Energy Stored in Shaft Formula Elements

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

How to Evaluate Polar Moment of Inertia of Shaft given Total Strain Energy Stored in Shaft?

FAQs on Polar Moment of Inertia of Shaft given Total Strain Energy Stored in Shaft

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