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Moment of Inertia of Shaft when Strain Energy Stored in Shaft Subjected to Bending Moment Formula

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The Area Moment of Inertia is a property that measures an object's resistance to bending and deflection under load, crucial for structural analysis and design. Check FAQs

I = {M b}^{2} \cdot \frac{L}{2 \cdot E \cdot U}

I - Area Moment of Inertia?M_b - Bending Moment?L - Length of Rod or Shaft?E - Modulus of Elasticity?U - Strain Energy?

Moment of Inertia of Shaft when Strain Energy Stored in Shaft Subjected to Bending Moment Example

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Here is how the Moment of Inertia of Shaft when Strain Energy Stored in Shaft Subjected to Bending Moment equation looks like with Values.

Here is how the Moment of Inertia of Shaft when Strain Energy Stored in Shaft Subjected to Bending Moment equation looks like with Units.

Here is how the Moment of Inertia of Shaft when Strain Energy Stored in Shaft Subjected to Bending Moment equation looks like.

552.7188 = 55001^{2} \cdot \frac{1432.449}{2 \cdot 105548.9 \cdot 37.1392}

552.7188mm⁴ = {55001N*mm}^{2} \cdot \frac{1432.449mm}{2 \cdot 105548.9N/mm² \cdot 37.1392J}

552.7188 = 55001^{2} \cdot \frac{1432.449}{2 \cdot 105548.9 \cdot 37.1392}

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Moment of Inertia of Shaft when Strain Energy Stored in Shaft Subjected to Bending Moment Solution

Follow our step by step solution on how to calculate Moment of Inertia of Shaft when Strain Energy Stored in Shaft Subjected to Bending Moment?

FIRST Step Consider the formula

I = {M b}^{2} \cdot \frac{L}{2 \cdot E \cdot U}

Next Step Substitute values of Variables

∴

I = {55001N*mm}^{2} \cdot \frac{1432.449mm}{2 \cdot 105548.9N/mm² \cdot 37.1392J}

Next Step Convert Units

∴

I = {55.001N*m}^{2} \cdot \frac{1.4324m}{2 \cdot 1.1E+11Pa \cdot 37.1392J}

Next Step Prepare to Evaluate

∴

I = {55.001}^{2} \cdot \frac{1.4324}{2 \cdot 1.1E+11 \cdot 37.1392}

Next Step Evaluate

∴

I = 5.5271875966204E-10m⁴

Next Step Convert to Output's Unit

∴

I = 552.71875966204mm⁴

LAST Step Rounding Answer

∴

I = 552.7188mm⁴

Moment of Inertia of Shaft when Strain Energy Stored in Shaft Subjected to Bending Moment Formula Elements

Variables

Area Moment of Inertia

The Area Moment of Inertia is a property that measures an object's resistance to bending and deflection under load, crucial for structural analysis and design.

Symbol: I

Measurement: Second Moment of AreaUnit: mm⁴

Note: Value should be greater than 0.

Formulas to find Area Moment of Inertia

Bending Moment

The Bending Moment is the internal moment that causes a beam to bend, reflecting the distribution of forces along its length in structural engineering.

Symbol: M_b

Measurement: TorqueUnit: N*mm

Note: Value should be greater than 0.

Formulas to find Bending Moment

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

Modulus of Elasticity

The Modulus of Elasticity is a measure of a material's stiffness, indicating how much it deforms under stress in relation to its original dimensions.

Symbol: E

Measurement: StressUnit: N/mm²

Note: Value should be greater than 0.

Formulas to find Modulus of Elasticity

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

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 Moment of Inertia of Shaft when Strain Energy Stored in Shaft Subjected to Bending Moment?

Moment of Inertia of Shaft when Strain Energy Stored in Shaft Subjected to Bending Moment evaluator uses Area Moment of Inertia = Bending Moment^2*Length of Rod or Shaft/(2*Modulus of Elasticity*Strain Energy) to evaluate the Area Moment of Inertia, Moment of Inertia of Shaft when Strain Energy Stored in Shaft Subjected to Bending Moment formula is defined as a measure of an object's resistance to angular acceleration when subjected to bending moments. It reflects how the distribution of mass affects the shaft's ability to store strain energy. Area Moment of Inertia is denoted by I symbol.

How to evaluate Moment of Inertia of Shaft when Strain Energy Stored in Shaft Subjected to Bending Moment using this online evaluator? To use this online evaluator for Moment of Inertia of Shaft when Strain Energy Stored in Shaft Subjected to Bending Moment, enter Bending Moment (M_b), Length of Rod or Shaft (L), Modulus of Elasticity (E) & Strain Energy (U) and hit the calculate button.

FAQs on Moment of Inertia of Shaft when Strain Energy Stored in Shaft Subjected to Bending Moment

What is the formula to find Moment of Inertia of Shaft when Strain Energy Stored in Shaft Subjected to Bending Moment?

The formula of Moment of Inertia of Shaft when Strain Energy Stored in Shaft Subjected to Bending Moment is expressed as Area Moment of Inertia = Bending Moment^2*Length of Rod or Shaft/(2*Modulus of Elasticity*Strain Energy). Here is an example- 5.5E+14 = 55.001^2*1.432449/(2*105548900000*37.13919).

How to calculate Moment of Inertia of Shaft when Strain Energy Stored in Shaft Subjected to Bending Moment?

With Bending Moment (M_b), Length of Rod or Shaft (L), Modulus of Elasticity (E) & Strain Energy (U) we can find Moment of Inertia of Shaft when Strain Energy Stored in Shaft Subjected to Bending Moment using the formula - Area Moment of Inertia = Bending Moment^2*Length of Rod or Shaft/(2*Modulus of Elasticity*Strain Energy).

Can the Moment of Inertia of Shaft when Strain Energy Stored in Shaft Subjected to Bending Moment be negative?

No, the Moment of Inertia of Shaft when Strain Energy Stored in Shaft Subjected to Bending Moment, measured in Second Moment of Area cannot be negative.

Which unit is used to measure Moment of Inertia of Shaft when Strain Energy Stored in Shaft Subjected to Bending Moment?

Moment of Inertia of Shaft when Strain Energy Stored in Shaft Subjected to Bending Moment is usually measured using the Millimeter⁴[mm⁴] for Second Moment of Area. Meter⁴[mm⁴], Centimeter⁴[mm⁴] are the few other units in which Moment of Inertia of Shaft when Strain Energy Stored in Shaft Subjected to Bending Moment can be measured.

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Moment of Inertia of Shaft when Strain Energy Stored in Shaft Subjected to Bending Moment Formula

Moment of Inertia of Shaft when Strain Energy Stored in Shaft Subjected to Bending Moment Example

Moment of Inertia of Shaft when Strain Energy Stored in Shaft Subjected to Bending Moment Solution

Moment of Inertia of Shaft when Strain Energy Stored in Shaft Subjected to Bending Moment Formula Elements

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

How to Evaluate Moment of Inertia of Shaft when Strain Energy Stored in Shaft Subjected to Bending Moment?

FAQs on Moment of Inertia of Shaft when Strain Energy Stored in Shaft Subjected to Bending Moment

Variable Name