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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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Length of Rod or Shaft is defined as the total length of the rod or the shaft according to Castiglano's theorom. Check FAQs

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

L - Length of Rod or Shaft?U - Strain Energy in Rod or Shaft?A - Cross Sectional Area of Rod?E - Modulus of elasticity of rod or shaft?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.

1330.4415 = 40 \cdot 2 \cdot 513.34 \cdot \frac{98000}{55000^{2}}

1330.4415mm = 40J \cdot 2 \cdot 513.34mm² \cdot \frac{98000N/mm²}{{55000N}^{2}}

1330.4415 = 40 \cdot 2 \cdot 513.34 \cdot \frac{98000}{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 = 40J \cdot 2 \cdot 513.34mm² \cdot \frac{98000N/mm²}{{55000N}^{2}}

Next Step Convert Units

∴

L = 40J \cdot 2 \cdot 0.0005m² \cdot \frac{9.8E+10Pa}{{55000N}^{2}}

Next Step Prepare to Evaluate

∴

L = 40 \cdot 2 \cdot 0.0005 \cdot \frac{9.8E+10}{55000^{2}}

Next Step Evaluate

∴

L = 1.33044152066116m

Next Step Convert to Output's Unit

∴

L = 1330.44152066116mm

LAST Step Rounding Answer

∴

L = 1330.4415mm

Length of Rod given Strain Energy Stored Formula Elements

Variables

Length of Rod or Shaft

Length of Rod or Shaft is defined as the total length of the rod or the shaft according to Castiglano's theorom.

Symbol: L

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Length of Rod or Shaft

Strain Energy in Rod or Shaft

Strain Energy in Rod or Shaft is defined as the energy stored in a rod or a shaft due to deformation.

Symbol: U

Measurement: EnergyUnit: J

Note: Value should be greater than 0.

Formulas to find Strain Energy in Rod or Shaft

Cross Sectional Area of Rod

Cross Sectional Area of Rod is the area of a two-dimensional shape that is obtained when a three-dimensional rod is sliced perpendicular to some specified axis at a point.

Symbol: A

Measurement: AreaUnit: mm²

Note: Value should be greater than 0.

Formulas to find Cross Sectional Area of Rod

Modulus of elasticity of rod or shaft

Modulus of elasticity of rod or shaft is a quantity that measures an object or substance's resistance to being deformed elastically when stress is applied to it.

Symbol: E

Measurement: StressUnit: N/mm²

Note: Value should be greater than 0.

Formulas to find Modulus of elasticity of rod or shaft

Axial Force on Beam

Axial Force on Beam is defined as the compression or tension force acting on a beam, rod, or shaft.

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 in Rod or Shaft*2*Cross Sectional Area of Rod*Modulus of elasticity of rod or shaft/Axial Force on Beam^2 to evaluate the Length of Rod or Shaft, The Length of Rod given Strain Energy Stored formula is defined as the total length of the rod on which the force is applied and that force applied is converted to strain energy. 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 in Rod or Shaft (U), Cross Sectional Area of Rod (A), Modulus of elasticity of rod or shaft (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 in Rod or Shaft*2*Cross Sectional Area of Rod*Modulus of elasticity of rod or shaft/Axial Force on Beam^2. Here is an example- 1.3E+6 = 40*2*0.00051334*98000000000/55000^2.

How to calculate Length of Rod given Strain Energy Stored?

With Strain Energy in Rod or Shaft (U), Cross Sectional Area of Rod (A), Modulus of elasticity of rod or shaft (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 in Rod or Shaft*2*Cross Sectional Area of Rod*Modulus of elasticity of rod or shaft/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 in Rod or Shaft*Polar Moment of Inertia of rod or shaft*Modulus of rigidity of rod or shaft)/(Torque on Rod or Shaft^2)
Length of Rod or Shaft=2*Strain Energy in Rod or Shaft*Modulus of elasticity of rod or shaft*Area Moment of Inertia of rod or shaft/(Bending Moment in Shaft or Beam^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