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

GoLength of Rod given Strain Energy Stored Formula

GoLength of Shaft when Strain Energy in Shaft Subjected to External Torque 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 = 2 \cdot U \cdot E \cdot \frac{I}{{M b}^{2}}

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

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

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

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

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

1431.8821 = 2 \cdot 37.1392 \cdot 105548.9 \cdot \frac{552.5}{55001^{2}}

1431.8821mm = 2 \cdot 37.1392J \cdot 105548.9N/mm² \cdot \frac{552.5mm⁴}{{55001N*mm}^{2}}

1431.8821 = 2 \cdot 37.1392 \cdot 105548.9 \cdot \frac{552.5}{55001^{2}}

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

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

L = 2 \cdot 37.1392J \cdot 105548.9N/mm² \cdot \frac{552.5mm⁴}{{55001N*mm}^{2}}

Next Step Convert Units

∴

L = 2 \cdot 37.1392J \cdot 1.1E+11Pa \cdot \frac{5.5E-10m⁴}{{55.001N*m}^{2}}

Next Step Prepare to Evaluate

∴

L = 2 \cdot 37.1392 \cdot 1.1E+11 \cdot \frac{5.5E-10}{{55.001}^{2}}

Next Step Evaluate

∴

L = 1.431882053332m

Next Step Convert to Output's Unit

∴

L = 1431.882053332mm

LAST Step Rounding Answer

∴

L = 1431.8821mm

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

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

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

Other Formulas to find Length of Rod or Shaft

Go Length of Rod given Strain Energy Stored

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

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

L = \frac{2 \cdot U \cdot J \cdot G}{τ^{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 Shaft given Strain Energy Stored in Shaft Subjected to Bending Moment?

Length of Shaft given Strain Energy Stored in Shaft Subjected to Bending Moment evaluator uses Length of Rod or Shaft = 2*Strain Energy*Modulus of Elasticity*Area Moment of Inertia/(Bending Moment^2) to evaluate the Length of Rod or Shaft, Length of Shaft given Strain Energy Stored in Shaft Subjected to Bending Moment formula is defined as a method to determine the length of a shaft based on the strain energy it stores when subjected to bending moments, reflecting the relationship between material properties and structural design. Length of Rod or Shaft is denoted by L symbol.

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

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

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

The formula of Length of Shaft given Strain Energy Stored in Shaft Subjected to Bending Moment is expressed as Length of Rod or Shaft = 2*Strain Energy*Modulus of Elasticity*Area Moment of Inertia/(Bending Moment^2). Here is an example- 2.7E+8 = 2*37.13919*105548900000*5.525E-10/(55.001^2).

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

With Strain Energy (U), Modulus of Elasticity (E), Area Moment of Inertia (I) & Bending Moment (M_b) we can find Length of Shaft given Strain Energy Stored in Shaft Subjected to Bending Moment using the formula - Length of Rod or Shaft = 2*Strain Energy*Modulus of Elasticity*Area Moment of Inertia/(Bending Moment^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=Strain Energy*2*Cross Sectional Area of Rod*Modulus of Elasticity/Axial Force on Beam^2
Length of Rod or Shaft=(2*Strain Energy*Polar Moment of Inertia*Modulus of Rigidity)/(Torque^2)

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

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

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

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

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

​GoLength of Rod given Strain Energy Stored Formula

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

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

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

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

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

Variable Name

GoLength of Rod given Strain Energy Stored Formula

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