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Modulus of Elasticity of Rod given Strain Energy Stored Formula

GoModulus of Elasticity given Strain Energy Stored in Shaft Subjected to Bending Moment Formula

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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. Check FAQs

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

E - Modulus of Elasticity?P - Axial Force on Beam?L - Length of Rod or Shaft?A - Cross Sectional Area of Rod?U - Strain Energy?

Modulus of Elasticity of Rod given Strain Energy Stored Example

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Here is how the Modulus of Elasticity of Rod given Strain Energy Stored equation looks like with Values.

Here is how the Modulus of Elasticity of Rod given Strain Energy Stored equation looks like with Units.

Here is how the Modulus of Elasticity of Rod given Strain Energy Stored equation looks like.

105548.8926 = 55000^{2} \cdot \frac{1432.449}{2 \cdot 552.6987 \cdot 37.1392}

105548.8926N/mm² = {55000N}^{2} \cdot \frac{1432.449mm}{2 \cdot 552.6987mm² \cdot 37.1392J}

105548.8926 = 55000^{2} \cdot \frac{1432.449}{2 \cdot 552.6987 \cdot 37.1392}

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Modulus of Elasticity of Rod given Strain Energy Stored Solution

Follow our step by step solution on how to calculate Modulus of Elasticity of Rod given Strain Energy Stored?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

E = {55000N}^{2} \cdot \frac{1432.449mm}{2 \cdot 552.6987mm² \cdot 37.1392J}

Next Step Convert Units

∴

E = {55000N}^{2} \cdot \frac{1.4324m}{2 \cdot 0.0006m² \cdot 37.1392J}

Next Step Prepare to Evaluate

∴

E = 55000^{2} \cdot \frac{1.4324}{2 \cdot 0.0006 \cdot 37.1392}

Next Step Evaluate

∴

E = 105548892618.28Pa

Next Step Convert to Output's Unit

∴

E = 105548.89261828N/mm²

LAST Step Rounding Answer

∴

E = 105548.8926N/mm²

Modulus of Elasticity of Rod given Strain Energy Stored Formula Elements

Variables

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

Axial Force on Beam

The Axial Force on Beam is the internal force acting along the length of a beam, influencing its stability and structural integrity under various loads.

Symbol: P

Measurement: ForceUnit: N

Note: Value can be positive or negative.

Formulas to find Axial Force on Beam

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

Cross Sectional Area of Rod

The Cross Sectional Area of Rod is the area of the cut surface of a rod, which influences its strength and stiffness in structural applications.

Symbol: A

Measurement: AreaUnit: mm²

Note: Value should be greater than 0.

Formulas to find Cross Sectional Area of Rod

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 to find Modulus of Elasticity

Go Modulus of Elasticity given Strain Energy Stored in Shaft Subjected to Bending Moment

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

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 Strain Energy in Rod when it is Subjected to External Torque

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

How to Evaluate Modulus of Elasticity of Rod given Strain Energy Stored?

Modulus of Elasticity of Rod given Strain Energy Stored evaluator uses Modulus of Elasticity = Axial Force on Beam^2*Length of Rod or Shaft/(2*Cross Sectional Area of Rod*Strain Energy) to evaluate the Modulus of Elasticity, Modulus of Elasticity of Rod given Strain Energy Stored formula is defined as a measure of a material's ability to deform elastically when a force is applied. It quantifies the relationship between stress and strain, reflecting the stiffness of the rod under load conditions. Modulus of Elasticity is denoted by E symbol.

How to evaluate Modulus of Elasticity of Rod given Strain Energy Stored using this online evaluator? To use this online evaluator for Modulus of Elasticity of Rod given Strain Energy Stored, enter Axial Force on Beam (P), Length of Rod or Shaft (L), Cross Sectional Area of Rod (A) & Strain Energy (U) and hit the calculate button.

FAQs on Modulus of Elasticity of Rod given Strain Energy Stored

What is the formula to find Modulus of Elasticity of Rod given Strain Energy Stored?

The formula of Modulus of Elasticity of Rod given Strain Energy Stored is expressed as Modulus of Elasticity = Axial Force on Beam^2*Length of Rod or Shaft/(2*Cross Sectional Area of Rod*Strain Energy). Here is an example- 0.122436 = 55000^2*1.432449/(2*0.0005526987*37.13919).

How to calculate Modulus of Elasticity of Rod given Strain Energy Stored?

With Axial Force on Beam (P), Length of Rod or Shaft (L), Cross Sectional Area of Rod (A) & Strain Energy (U) we can find Modulus of Elasticity of Rod given Strain Energy Stored using the formula - Modulus of Elasticity = Axial Force on Beam^2*Length of Rod or Shaft/(2*Cross Sectional Area of Rod*Strain Energy).

What are the other ways to Calculate Modulus of Elasticity?

Here are the different ways to Calculate Modulus of Elasticity-

Modulus of Elasticity=Bending Moment^2*Length of Rod or Shaft/(2*Strain Energy*Area Moment of Inertia)

Can the Modulus of Elasticity of Rod given Strain Energy Stored be negative?

No, the Modulus of Elasticity of Rod given Strain Energy Stored, measured in Stress cannot be negative.

Which unit is used to measure Modulus of Elasticity of Rod given Strain Energy Stored?

Modulus of Elasticity of Rod given Strain Energy Stored is usually measured using the Newton per Square Millimeter[N/mm²] for Stress. Pascal[N/mm²], Newton per Square Meter[N/mm²], Kilonewton per Square Meter[N/mm²] are the few other units in which Modulus of Elasticity of Rod given Strain Energy Stored can be measured.

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Modulus of Elasticity of Rod given Strain Energy Stored Formula

​GoModulus of Elasticity given Strain Energy Stored in Shaft Subjected to Bending Moment Formula

Modulus of Elasticity of Rod given Strain Energy Stored Example

Modulus of Elasticity of Rod given Strain Energy Stored Solution

Modulus of Elasticity of Rod given Strain Energy Stored Formula Elements

Other Formulas to find Modulus of Elasticity

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

How to Evaluate Modulus of Elasticity of Rod given Strain Energy Stored?

FAQs on Modulus of Elasticity of Rod given Strain Energy Stored

Variable Name

GoModulus of Elasticity given Strain Energy Stored in Shaft Subjected to Bending Moment Formula