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Polar Moment of Inertia of Rod given Strain Energy in Rod Formula

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The Polar Moment of Inertia is a measure of an object's resistance to torsional deformation, crucial for analyzing the strength and stability of structural components. Check FAQs

J = τ^{2} \cdot \frac{L}{2 \cdot U \cdot G}

J - Polar Moment of Inertia?τ - Torque?L - Length of Rod or Shaft?U - Strain Energy?G - Modulus of Rigidity?

Polar Moment of Inertia of Rod given Strain Energy in Rod Example

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

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

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

552.5788 = 55005^{2} \cdot \frac{1432.449}{2 \cdot 37.1392 \cdot 105591}

552.5788mm⁴ = {55005N*mm}^{2} \cdot \frac{1432.449mm}{2 \cdot 37.1392J \cdot 105591N/mm²}

552.5788 = 55005^{2} \cdot \frac{1432.449}{2 \cdot 37.1392 \cdot 105591}

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Polar Moment of Inertia of Rod given Strain Energy in Rod Solution

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

FIRST Step Consider the formula

J = τ^{2} \cdot \frac{L}{2 \cdot U \cdot G}

Next Step Substitute values of Variables

∴

J = {55005N*mm}^{2} \cdot \frac{1432.449mm}{2 \cdot 37.1392J \cdot 105591N/mm²}

Next Step Convert Units

∴

J = {55.005N*m}^{2} \cdot \frac{1.4324m}{2 \cdot 37.1392J \cdot 1.1E+11Pa}

Next Step Prepare to Evaluate

∴

J = {55.005}^{2} \cdot \frac{1.4324}{2 \cdot 37.1392 \cdot 1.1E+11}

Next Step Evaluate

∴

J = 5.5257875101012E-10m⁴

Next Step Convert to Output's Unit

∴

J = 552.57875101012mm⁴

LAST Step Rounding Answer

∴

J = 552.5788mm⁴

Polar Moment of Inertia of Rod given Strain Energy in Rod Formula Elements

Variables

Polar Moment of Inertia

The Polar Moment of Inertia is a measure of an object's resistance to torsional deformation, crucial for analyzing the strength and stability of structural components.

Symbol: J

Measurement: Second Moment of AreaUnit: mm⁴

Note: Value should be greater than 0.

Formulas to find Polar Moment of Inertia

Torque

The Torque is a measure of the rotational force applied to an object, influencing its ability to rotate around an axis or pivot point.

Symbol: τ

Measurement: TorqueUnit: N*mm

Note: Value should be greater than 0.

Formulas to find Torque

Length of Rod or Shaft

The Length of Rod or Shaft is the measurement of the distance from one end of the rod or shaft to the other, crucial for structural analysis.

Symbol: L

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Length of Rod or Shaft

Strain Energy

The Strain Energy is the energy stored in a material due to deformation, which can be released when the material returns to its original shape.

Symbol: U

Measurement: EnergyUnit: J

Note: Value should be greater than 0.

Formulas to find Strain Energy

Modulus of Rigidity

The Modulus of Rigidity is a measure of a material's ability to resist deformation under shear stress, indicating its stiffness and structural integrity in mechanical applications.

Symbol: G

Measurement: StressUnit: N/mm²

Note: Value should be greater than 0.

Formulas to find Modulus of Rigidity

Other formulas in Castigliano's Theorem for Deflection in Complex Structures category

Go Strain Energy Stored in Tension Rod

U = \frac{P^{2} \cdot L}{2 \cdot A \cdot E}

Go Force Applied on Rod given Strain Energy Stored in Tension Rod

P = \sqrt{U \cdot 2 \cdot A \cdot \frac{E}{L}}

Go Length of Rod given Strain Energy Stored

L = U \cdot 2 \cdot A \cdot \frac{E}{P^{2}}

Go Modulus of Elasticity of Rod given Strain Energy Stored

E = P^{2} \cdot \frac{L}{2 \cdot A \cdot U}

How to Evaluate Polar Moment of Inertia of Rod given Strain Energy in Rod?

Polar Moment of Inertia of Rod given Strain Energy in Rod evaluator uses Polar Moment of Inertia = Torque^2*Length of Rod or Shaft/(2*Strain Energy*Modulus of Rigidity) to evaluate the Polar Moment of Inertia, Polar Moment of Inertia of Rod given Strain Energy in Rod formula is defined as a measure of a rod's resistance to torsional deformation when subjected to an applied torque. It relates the strain energy stored in the rod to its geometric and material properties. Polar Moment of Inertia is denoted by J symbol.

How to evaluate Polar Moment of Inertia of Rod given Strain Energy in Rod using this online evaluator? To use this online evaluator for Polar Moment of Inertia of Rod given Strain Energy in Rod, enter Torque (τ), Length of Rod or Shaft (L), Strain Energy (U) & Modulus of Rigidity (G) and hit the calculate button.

FAQs on Polar Moment of Inertia of Rod given Strain Energy in Rod

What is the formula to find Polar Moment of Inertia of Rod given Strain Energy in Rod?

The formula of Polar Moment of Inertia of Rod given Strain Energy in Rod is expressed as Polar Moment of Inertia = Torque^2*Length of Rod or Shaft/(2*Strain Energy*Modulus of Rigidity). Here is an example- 5.6E+14 = 55.005^2*1.432449/(2*37.13919*105591000000).

How to calculate Polar Moment of Inertia of Rod given Strain Energy in Rod?

With Torque (τ), Length of Rod or Shaft (L), Strain Energy (U) & Modulus of Rigidity (G) we can find Polar Moment of Inertia of Rod given Strain Energy in Rod using the formula - Polar Moment of Inertia = Torque^2*Length of Rod or Shaft/(2*Strain Energy*Modulus of Rigidity).

Can the Polar Moment of Inertia of Rod given Strain Energy in Rod be negative?

No, the Polar Moment of Inertia of Rod given Strain Energy in Rod, measured in Second Moment of Area cannot be negative.

Which unit is used to measure Polar Moment of Inertia of Rod given Strain Energy in Rod?

Polar Moment of Inertia of Rod given Strain Energy in Rod is usually measured using the Millimeter⁴[mm⁴] for Second Moment of Area. Meter⁴[mm⁴], Centimeter⁴[mm⁴] are the few other units in which Polar Moment of Inertia of Rod given Strain Energy in Rod can be measured.

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Polar Moment of Inertia of Rod given Strain Energy in Rod Formula

Polar Moment of Inertia of Rod given Strain Energy in Rod Example

Polar Moment of Inertia of Rod given Strain Energy in Rod Solution

Polar Moment of Inertia of Rod given Strain Energy in Rod Formula Elements

Other formulas in Castigliano's Theorem for Deflection in Complex Structures category

How to Evaluate Polar Moment of Inertia of Rod given Strain Energy in Rod?

FAQs on Polar Moment of Inertia of Rod given Strain Energy in Rod

Variable Name