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Strain Energy Stored in Rod Subjected to Bending Moment Formula

GoStrain Energy Stored in Tension Rod Formula

GoStrain Energy in Rod when it is Subjected to External Torque Formula

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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. Check FAQs

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

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

Strain Energy Stored in Rod Subjected to Bending Moment Example

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Here is how the Strain Energy Stored in Rod Subjected to Bending Moment equation looks like with Values.

Here is how the Strain Energy Stored in Rod Subjected to Bending Moment equation looks like with Units.

Here is how the Strain Energy Stored in Rod Subjected to Bending Moment equation looks like.

37.1539 = 55001^{2} \cdot \frac{1432.449}{2 \cdot 105548.9 \cdot 552.5}

37.1539J = {55001N*mm}^{2} \cdot \frac{1432.449mm}{2 \cdot 105548.9N/mm² \cdot 552.5mm⁴}

37.1539 = 55001^{2} \cdot \frac{1432.449}{2 \cdot 105548.9 \cdot 552.5}

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Strain Energy Stored in Rod Subjected to Bending Moment Solution

Follow our step by step solution on how to calculate Strain Energy Stored in Rod Subjected to Bending Moment?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

U = {55001N*mm}^{2} \cdot \frac{1432.449mm}{2 \cdot 105548.9N/mm² \cdot 552.5mm⁴}

Next Step Convert Units

∴

U = {55.001N*m}^{2} \cdot \frac{1.4324m}{2 \cdot 1.1E+11Pa \cdot 5.5E-10m⁴}

Next Step Prepare to Evaluate

∴

U = {55.001}^{2} \cdot \frac{1.4324}{2 \cdot 1.1E+11 \cdot 5.5E-10}

Next Step Evaluate

∴

U = 37.1538950799147J

LAST Step Rounding Answer

∴

U = 37.1539J

Strain Energy Stored in Rod Subjected to Bending Moment Formula Elements

Variables

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

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

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

Other Formulas to find Strain Energy

Go Strain Energy Stored in Tension Rod

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

Go Strain Energy in Rod when it is Subjected to External Torque

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

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

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}

Go Torque given Strain Energy in Rod Subjected to External Torque

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

How to Evaluate Strain Energy Stored in Rod Subjected to Bending Moment?

Strain Energy Stored in Rod Subjected to Bending Moment evaluator uses Strain Energy = Bending Moment^2*Length of Rod or Shaft/(2*Modulus of Elasticity*Area Moment of Inertia) to evaluate the Strain Energy, Strain Energy Stored in Rod Subjected to Bending Moment formula is defined as a representation of the energy accumulated in a rod when it experiences bending. This energy is crucial for understanding the material's behavior under stress and for ensuring structural integrity in engineering applications. Strain Energy is denoted by U symbol.

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

FAQs on Strain Energy Stored in Rod Subjected to Bending Moment

What is the formula to find Strain Energy Stored in Rod Subjected to Bending Moment?

The formula of Strain Energy Stored in Rod Subjected to Bending Moment is expressed as Strain Energy = Bending Moment^2*Length of Rod or Shaft/(2*Modulus of Elasticity*Area Moment of Inertia). Here is an example- 0.19889 = 55.001^2*1.432449/(2*105548900000*5.525E-10).

How to calculate Strain Energy Stored in Rod Subjected to Bending Moment?

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

What are the other ways to Calculate Strain Energy?

Here are the different ways to Calculate Strain Energy-

Strain Energy=(Axial Force on Beam^2*Length of Rod or Shaft)/(2*Cross Sectional Area of Rod*Modulus of Elasticity)
Strain Energy=Torque^2*Length of Rod or Shaft/(2*Polar Moment of Inertia*Modulus of Rigidity)

Can the Strain Energy Stored in Rod Subjected to Bending Moment be negative?

No, the Strain Energy Stored in Rod Subjected to Bending Moment, measured in Energy cannot be negative.

Which unit is used to measure Strain Energy Stored in Rod Subjected to Bending Moment?

Strain Energy Stored in Rod Subjected to Bending Moment is usually measured using the Joule[J] for Energy. Kilojoule[J], Gigajoule[J], Megajoule[J] are the few other units in which Strain Energy Stored in Rod Subjected to Bending Moment can be measured.

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Strain Energy Stored in Rod Subjected to Bending Moment Formula

​GoStrain Energy Stored in Tension Rod Formula

​GoStrain Energy in Rod when it is Subjected to External Torque Formula

Strain Energy Stored in Rod Subjected to Bending Moment Example

Strain Energy Stored in Rod Subjected to Bending Moment Solution

Strain Energy Stored in Rod Subjected to Bending Moment Formula Elements

Other Formulas to find Strain Energy

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

How to Evaluate Strain Energy Stored in Rod Subjected to Bending Moment?

FAQs on Strain Energy Stored in Rod Subjected to Bending Moment

Variable Name

GoStrain Energy Stored in Tension Rod Formula

GoStrain Energy in Rod when it is Subjected to External Torque Formula