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

GoLength of Rod given Strain Energy Stored 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 = \frac{2 \cdot U \cdot J \cdot G}{τ^{2}}

L - Length of Rod or Shaft?U - Strain Energy?J - Polar Moment of Inertia?G - Modulus of Rigidity?τ - Torque?

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

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Here is how the Length of Shaft when Strain Energy in Shaft Subjected to External Torque equation looks like with Values.

Here is how the Length of Shaft when Strain Energy in Shaft Subjected to External Torque equation looks like with Units.

Here is how the Length of Shaft when Strain Energy in Shaft Subjected to External Torque equation looks like.

1433.541 = \frac{2 \cdot 37.1392 \cdot 553 \cdot 105591}{55005^{2}}

1433.541mm = \frac{2 \cdot 37.1392J \cdot 553mm⁴ \cdot 105591N/mm²}{{55005N*mm}^{2}}

1433.541 = \frac{2 \cdot 37.1392 \cdot 553 \cdot 105591}{55005^{2}}

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

Follow our step by step solution on how to calculate Length of Shaft when Strain Energy in Shaft Subjected to External Torque?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

L = \frac{2 \cdot 37.1392J \cdot 553mm⁴ \cdot 105591N/mm²}{{55005N*mm}^{2}}

Next Step Convert Units

∴

L = \frac{2 \cdot 37.1392J \cdot 5.5E-10m⁴ \cdot 1.1E+11Pa}{{55.005N*m}^{2}}

Next Step Prepare to Evaluate

∴

L = \frac{2 \cdot 37.1392 \cdot 5.5E-10 \cdot 1.1E+11}{{55.005}^{2}}

Next Step Evaluate

∴

L = 1.43354100307323m

Next Step Convert to Output's Unit

∴

L = 1433.54100307323mm

LAST Step Rounding Answer

∴

L = 1433.541mm

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

Polar Moment of Inertia

The Polar Moment of Inertia is a measure of an object's resistance to torsional deformation, crucial for analyzing the strength and stability of structural components.

Symbol: J

Measurement: Second Moment of AreaUnit: mm⁴

Note: Value should be greater than 0.

Formulas to find Polar Moment of Inertia

Modulus of Rigidity

The Modulus of Rigidity is a measure of a material's ability to resist deformation under shear stress, indicating its stiffness and structural integrity in mechanical applications.

Symbol: G

Measurement: StressUnit: N/mm²

Note: Value should be greater than 0.

Formulas to find Modulus of Rigidity

Torque

The Torque is a measure of the rotational force applied to an object, influencing its ability to rotate around an axis or pivot point.

Symbol: τ

Measurement: TorqueUnit: N*mm

Note: Value should be greater than 0.

Formulas to find Torque

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 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 Shaft when Strain Energy in Shaft Subjected to External Torque?

Length of Shaft when Strain Energy in Shaft Subjected to External Torque evaluator uses Length of Rod or Shaft = (2*Strain Energy*Polar Moment of Inertia*Modulus of Rigidity)/(Torque^2) to evaluate the Length of Rod or Shaft, Length of Shaft when Strain Energy in Shaft Subjected to External Torque formula is defined as a method to evaluate the necessary length of a shaft based on the strain energy it can store when subjected to external torque, ensuring structural integrity and performance in mechanical designs. Length of Rod or Shaft is denoted by L symbol.

How to evaluate Length of Shaft when Strain Energy in Shaft Subjected to External Torque using this online evaluator? To use this online evaluator for Length of Shaft when Strain Energy in Shaft Subjected to External Torque, enter Strain Energy (U), Polar Moment of Inertia (J), Modulus of Rigidity (G) & Torque (τ) and hit the calculate button.

FAQs on Length of Shaft when Strain Energy in Shaft Subjected to External Torque

What is the formula to find Length of Shaft when Strain Energy in Shaft Subjected to External Torque?

The formula of Length of Shaft when Strain Energy in Shaft Subjected to External Torque is expressed as Length of Rod or Shaft = (2*Strain Energy*Polar Moment of Inertia*Modulus of Rigidity)/(Torque^2). Here is an example- 1.4E+6 = (2*37.13919*5.53E-10*105591000000)/(55.005^2).

How to calculate Length of Shaft when Strain Energy in Shaft Subjected to External Torque?

With Strain Energy (U), Polar Moment of Inertia (J), Modulus of Rigidity (G) & Torque (τ) we can find Length of Shaft when Strain Energy in Shaft Subjected to External Torque using the formula - Length of Rod or Shaft = (2*Strain Energy*Polar Moment of Inertia*Modulus of Rigidity)/(Torque^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*Modulus of Elasticity*Area Moment of Inertia/(Bending Moment^2)

Can the Length of Shaft when Strain Energy in Shaft Subjected to External Torque be negative?

No, the Length of Shaft when Strain Energy in Shaft Subjected to External Torque, measured in Length cannot be negative.

Which unit is used to measure Length of Shaft when Strain Energy in Shaft Subjected to External Torque?

Length of Shaft when Strain Energy in Shaft Subjected to External Torque 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 when Strain Energy in Shaft Subjected to External Torque can be measured.

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

​GoLength of Rod given Strain Energy Stored Formula

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

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

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

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

FAQs on Length of Shaft when Strain Energy in Shaft Subjected to External Torque

Variable Name

GoLength of Rod given Strain Energy Stored Formula

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