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Length of Rod given Strain Energy Stored Formula

GoLength of Shaft when Strain Energy in Shaft Subjected to External Torque Formula

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

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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. Check FAQs

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

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

Length of Rod given Strain Energy Stored Example

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

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

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

1432.4491 = 37.1392 \cdot 2 \cdot 552.6987 \cdot \frac{105548.9}{55000^{2}}

1432.4491mm = 37.1392J \cdot 2 \cdot 552.6987mm² \cdot \frac{105548.9N/mm²}{{55000N}^{2}}

1432.4491 = 37.1392 \cdot 2 \cdot 552.6987 \cdot \frac{105548.9}{55000^{2}}

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Length of Rod given Strain Energy Stored Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

L = 37.1392J \cdot 2 \cdot 552.6987mm² \cdot \frac{105548.9N/mm²}{{55000N}^{2}}

Next Step Convert Units

∴

L = 37.1392J \cdot 2 \cdot 0.0006m² \cdot \frac{1.1E+11Pa}{{55000N}^{2}}

Next Step Prepare to Evaluate

∴

L = 37.1392 \cdot 2 \cdot 0.0006 \cdot \frac{1.1E+11}{55000^{2}}

Next Step Evaluate

∴

L = 1.43244910018047m

Next Step Convert to Output's Unit

∴

L = 1432.44910018047mm

LAST Step Rounding Answer

∴

L = 1432.4491mm

Length of Rod given Strain Energy Stored Formula Elements

Variables

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

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

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

Other Formulas to find Length of Rod or Shaft

Go Length of Shaft when Strain Energy in Shaft Subjected to External Torque

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

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

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

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 Modulus of Elasticity of Rod given Strain Energy Stored

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

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 Length of Rod given Strain Energy Stored?

Length of Rod given Strain Energy Stored evaluator uses Length of Rod or Shaft = Strain Energy*2*Cross Sectional Area of Rod*Modulus of Elasticity/Axial Force on Beam^2 to evaluate the Length of Rod or Shaft, Length of Rod given Strain Energy Stored formula is defined as a relationship that quantifies the length of a rod based on the strain energy it stores, the cross-sectional area, the modulus of elasticity, and the applied load. This concept is essential in mechanical design and structural analysis. Length of Rod or Shaft is denoted by L symbol.

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

FAQs on Length of Rod given Strain Energy Stored

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

The formula of Length of Rod given Strain Energy Stored is expressed as Length of Rod or Shaft = Strain Energy*2*Cross Sectional Area of Rod*Modulus of Elasticity/Axial Force on Beam^2. Here is an example- 1.2E+6 = 37.13919*2*0.0005526987*105548900000/55000^2.

How to calculate Length of Rod given Strain Energy Stored?

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

What are the other ways to Calculate Length of Rod or Shaft?

Here are the different ways to Calculate Length of Rod or Shaft-

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

Can the Length of Rod given Strain Energy Stored be negative?

No, the Length of Rod given Strain Energy Stored, measured in Length cannot be negative.

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

Length of Rod given Strain Energy Stored is usually measured using the Millimeter[mm] for Length. Meter[mm], Kilometer[mm], Decimeter[mm] are the few other units in which Length of Rod given Strain Energy Stored can be measured.

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Length of Rod given Strain Energy Stored Formula

​GoLength of Shaft when Strain Energy in Shaft Subjected to External Torque Formula

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

Length of Rod given Strain Energy Stored Example

Length of Rod given Strain Energy Stored Solution

Length of Rod given Strain Energy Stored Formula Elements

Other Formulas to find Length of Rod or Shaft

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

How to Evaluate Length of Rod given Strain Energy Stored?

FAQs on Length of Rod given Strain Energy Stored

Variable Name

GoLength of Shaft when Strain Energy in Shaft Subjected to External Torque Formula

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