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Polar Moment of Inertia given Strain Energy in Torsion Formula

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Polar Moment of Inertia is the moment of inertia of a cross-section with respect to its polar axis, which is an axis at right angles to the plane of the cross-section. Check FAQs

J = (T^{2}) \cdot \frac{L}{2 \cdot U \cdot G Torsion}

J - Polar Moment of Inertia?T - Torque SOM?L - Length of Member?U - Strain Energy?G_Torsion - Modulus of Rigidity?

Polar Moment of Inertia given Strain Energy in Torsion Example

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

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

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

0.0041 = ({121.9}^{2}) \cdot \frac{3000}{2 \cdot 136.08 \cdot 40}

0.0041m⁴ = ({121.9kN*m}^{2}) \cdot \frac{3000mm}{2 \cdot 136.08N*m \cdot 40GPa}

0.0041 = ({121.9}^{2}) \cdot \frac{3000}{2 \cdot 136.08 \cdot 40}

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Polar Moment of Inertia given Strain Energy in Torsion Solution

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

FIRST Step Consider the formula

J = (T^{2}) \cdot \frac{L}{2 \cdot U \cdot G Torsion}

Next Step Substitute values of Variables

∴

J = ({121.9kN*m}^{2}) \cdot \frac{3000mm}{2 \cdot 136.08N*m \cdot 40GPa}

Next Step Convert Units

∴

J = ({121900N*m}^{2}) \cdot \frac{3m}{2 \cdot 136.08J \cdot 4E+10Pa}

Next Step Prepare to Evaluate

∴

J = (121900^{2}) \cdot \frac{3}{2 \cdot 136.08 \cdot 4E+10}

Next Step Evaluate

∴

J = 0.00409491016313933m⁴

LAST Step Rounding Answer

∴

J = 0.0041m⁴

Polar Moment of Inertia given Strain Energy in Torsion Formula Elements

Variables

Polar Moment of Inertia

Polar Moment of Inertia is the moment of inertia of a cross-section with respect to its polar axis, which is an axis at right angles to the plane of the cross-section.

Symbol: J

Measurement: Second Moment of AreaUnit: m⁴

Note: Value should be greater than 0.

Formulas to find Polar Moment of Inertia

Torque SOM

Torque SOM is a measure of the force that can cause an object to rotate about an axis.

Symbol: T

Measurement: TorqueUnit: kN*m

Note: Value can be positive or negative.

Formulas to find Torque SOM

Length of Member

Length of Member is the measurement or extent of member (beam or column) from end to end.

Symbol: L

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Length of Member

Strain Energy

Strain Energy is the energy adsorption of material due to strain under an applied load. It is also equal to the work done on a specimen by an external force.

Symbol: U

Measurement: EnergyUnit: N*m

Note: Value can be positive or negative.

Formulas to find Strain Energy

Modulus of Rigidity

Modulus of Rigidity is the measure of the rigidity of the body, given by the ratio of shear stress to shear strain. It is often denoted by G.

Symbol: G_Torsion

Measurement: PressureUnit: GPa

Note: Value should be greater than 0.

Formulas to find Modulus of Rigidity

Other formulas in Strain Energy in Structural Members category

Go Stress using Hook's Law

σ = E \cdot ε L

Go Shear Force using Strain Energy

V = \sqrt{2 \cdot U \cdot A \cdot \frac{G Torsion}{L}}

Go Strain Energy in Shear

U = (V^{2}) \cdot \frac{L}{2 \cdot A \cdot G Torsion}

Go Length over which Deformation takes place given Strain Energy in Shear

L = 2 \cdot U \cdot A \cdot \frac{G Torsion}{V^{2}}

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

Polar Moment of Inertia given Strain Energy in Torsion evaluator uses Polar Moment of Inertia = (Torque SOM^2)*Length of Member/(2*Strain Energy*Modulus of Rigidity) to evaluate the Polar Moment of Inertia, The Polar Moment of Inertia given Strain Energy in Torsion formula is defined as a shaft or beam's resistance to being distorted by torsion, as a function of its shape. Polar Moment of Inertia is denoted by J symbol.

How to evaluate Polar Moment of Inertia given Strain Energy in Torsion using this online evaluator? To use this online evaluator for Polar Moment of Inertia given Strain Energy in Torsion, enter Torque SOM (T), Length of Member (L), Strain Energy (U) & Modulus of Rigidity (G_Torsion) and hit the calculate button.

FAQs on Polar Moment of Inertia given Strain Energy in Torsion

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

The formula of Polar Moment of Inertia given Strain Energy in Torsion is expressed as Polar Moment of Inertia = (Torque SOM^2)*Length of Member/(2*Strain Energy*Modulus of Rigidity). Here is an example- 0.004095 = (121900^2)*3/(2*136.08*40000000000).

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

With Torque SOM (T), Length of Member (L), Strain Energy (U) & Modulus of Rigidity (G_Torsion) we can find Polar Moment of Inertia given Strain Energy in Torsion using the formula - Polar Moment of Inertia = (Torque SOM^2)*Length of Member/(2*Strain Energy*Modulus of Rigidity).

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

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

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

Polar Moment of Inertia given Strain Energy in Torsion 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 given Strain Energy in Torsion can be measured.

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Polar Moment of Inertia given Strain Energy in Torsion Formula

Polar Moment of Inertia given Strain Energy in Torsion Example

Polar Moment of Inertia given Strain Energy in Torsion Solution

Polar Moment of Inertia given Strain Energy in Torsion Formula Elements

Other formulas in Strain Energy in Structural Members category

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

FAQs on Polar Moment of Inertia given Strain Energy in Torsion

Variable Name