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

GoModulus of Elasticity of Rod given Strain Energy Stored 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 = {M b}^{2} \cdot \frac{L}{2 \cdot U \cdot I}

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

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

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

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

Here is how the Modulus of Elasticity given Strain Energy Stored in Shaft Subjected to Bending Moment equation looks like.

105590.6916 = 55001^{2} \cdot \frac{1432.449}{2 \cdot 37.1392 \cdot 552.5}

105590.6916N/mm² = {55001N*mm}^{2} \cdot \frac{1432.449mm}{2 \cdot 37.1392J \cdot 552.5mm⁴}

105590.6916 = 55001^{2} \cdot \frac{1432.449}{2 \cdot 37.1392 \cdot 552.5}

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

Follow our step by step solution on how to calculate Modulus of Elasticity given Strain Energy Stored in Shaft Subjected to Bending Moment?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

E = {55001N*mm}^{2} \cdot \frac{1432.449mm}{2 \cdot 37.1392J \cdot 552.5mm⁴}

Next Step Convert Units

∴

E = {55.001N*m}^{2} \cdot \frac{1.4324m}{2 \cdot 37.1392J \cdot 5.5E-10m⁴}

Next Step Prepare to Evaluate

∴

E = {55.001}^{2} \cdot \frac{1.4324}{2 \cdot 37.1392 \cdot 5.5E-10}

Next Step Evaluate

∴

E = 105590691568.675Pa

Next Step Convert to Output's Unit

∴

E = 105590.691568675N/mm²

LAST Step Rounding Answer

∴

E = 105590.6916N/mm²

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

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

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

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 Modulus of Elasticity

Go Modulus of Elasticity of Rod given Strain Energy Stored

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

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 given Strain Energy Stored in Shaft Subjected to Bending Moment?

Modulus of Elasticity given Strain Energy Stored in Shaft Subjected to Bending Moment evaluator uses Modulus of Elasticity = Bending Moment^2*Length of Rod or Shaft/(2*Strain Energy*Area Moment of Inertia) to evaluate the Modulus of Elasticity, Modulus of Elasticity given Strain Energy Stored in Shaft Subjected to Bending Moment formula is defined as a relationship that quantifies the stiffness of a material by relating the strain energy stored in a shaft to the bending moment applied, reflecting its ability to deform elastically under load. Modulus of Elasticity is denoted by E symbol.

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

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

What is the formula to find Modulus of Elasticity given Strain Energy Stored in Shaft Subjected to Bending Moment?

The formula of Modulus of Elasticity given Strain Energy Stored in Shaft Subjected to Bending Moment is expressed as Modulus of Elasticity = Bending Moment^2*Length of Rod or Shaft/(2*Strain Energy*Area Moment of Inertia). Here is an example- 0.000565 = 55.001^2*1.432449/(2*37.13919*5.525E-10).

How to calculate Modulus of Elasticity given Strain Energy Stored in Shaft Subjected to Bending Moment?

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

What are the other ways to Calculate Modulus of Elasticity?

Here are the different ways to Calculate Modulus of Elasticity-

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

Can the Modulus of Elasticity given Strain Energy Stored in Shaft Subjected to Bending Moment be negative?

No, the Modulus of Elasticity given Strain Energy Stored in Shaft Subjected to Bending Moment, measured in Stress cannot be negative.

Which unit is used to measure Modulus of Elasticity given Strain Energy Stored in Shaft Subjected to Bending Moment?

Modulus of Elasticity given Strain Energy Stored in Shaft Subjected to Bending Moment 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 given Strain Energy Stored in Shaft Subjected to Bending Moment can be measured.

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

​GoModulus of Elasticity of Rod given Strain Energy Stored Formula

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

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

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

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

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GoModulus of Elasticity of Rod given Strain Energy Stored Formula