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Strain Energy in Rod when it is Subjected to External Torque Formula

GoStrain Energy Stored in Tension Rod Formula

GoStrain Energy Stored in Rod Subjected to Bending Moment Formula

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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. Check FAQs

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

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

Strain Energy in Rod when it is Subjected to External Torque Example

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Here is how the Strain Energy in Rod when it is Subjected to External Torque equation looks like with Values.

Here is how the Strain Energy in Rod when it is Subjected to External Torque equation looks like with Units.

Here is how the Strain Energy in Rod when it is Subjected to External Torque equation looks like.

37.1109 = 55005^{2} \cdot \frac{1432.449}{2 \cdot 553 \cdot 105591}

37.1109J = {55005N*mm}^{2} \cdot \frac{1432.449mm}{2 \cdot 553mm⁴ \cdot 105591N/mm²}

37.1109 = 55005^{2} \cdot \frac{1432.449}{2 \cdot 553 \cdot 105591}

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Strain Energy in Rod when it is Subjected to External Torque Solution

Follow our step by step solution on how to calculate Strain Energy in Rod when it is Subjected to External Torque?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

U = {55005N*mm}^{2} \cdot \frac{1432.449mm}{2 \cdot 553mm⁴ \cdot 105591N/mm²}

Next Step Convert Units

∴

U = {55.005N*m}^{2} \cdot \frac{1.4324m}{2 \cdot 5.5E-10m⁴ \cdot 1.1E+11Pa}

Next Step Prepare to Evaluate

∴

U = {55.005}^{2} \cdot \frac{1.4324}{2 \cdot 5.5E-10 \cdot 1.1E+11}

Next Step Evaluate

∴

U = 37.1108991387478J

LAST Step Rounding Answer

∴

U = 37.1109J

Strain Energy in Rod when it is Subjected to External Torque Formula Elements

Variables

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

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

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

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

Other Formulas to find Strain Energy

Go Strain Energy Stored in Tension Rod

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

Go Strain Energy Stored in Rod Subjected to Bending Moment

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

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

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 Modulus of Elasticity of Rod given Strain Energy Stored

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

Go Torque given Strain Energy in Rod Subjected to External Torque

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

How to Evaluate Strain Energy in Rod when it is Subjected to External Torque?

Strain Energy in Rod when it is Subjected to External Torque evaluator uses Strain Energy = Torque^2*Length of Rod or Shaft/(2*Polar Moment of Inertia*Modulus of Rigidity) to evaluate the Strain Energy, Strain Energy in Rod when it is Subjected to External Torque formula is defined as a measure of the energy stored in a rod due to the application of external torque. This energy is crucial for understanding the material's behavior under torsional loads and ensuring structural integrity. Strain Energy is denoted by U symbol.

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

FAQs on Strain Energy in Rod when it is Subjected to External Torque

What is the formula to find Strain Energy in Rod when it is Subjected to External Torque?

The formula of Strain Energy in Rod when it is Subjected to External Torque is expressed as Strain Energy = Torque^2*Length of Rod or Shaft/(2*Polar Moment of Inertia*Modulus of Rigidity). Here is an example- 37.31978 = 55.005^2*1.432449/(2*5.53E-10*105591000000).

How to calculate Strain Energy in Rod when it is Subjected to External Torque?

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

What are the other ways to Calculate Strain Energy?

Here are the different ways to Calculate Strain Energy-

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

Can the Strain Energy in Rod when it is Subjected to External Torque be negative?

No, the Strain Energy in Rod when it is Subjected to External Torque, measured in Energy cannot be negative.

Which unit is used to measure Strain Energy in Rod when it is Subjected to External Torque?

Strain Energy in Rod when it is Subjected to External Torque is usually measured using the Joule[J] for Energy. Kilojoule[J], Gigajoule[J], Megajoule[J] are the few other units in which Strain Energy in Rod when it is Subjected to External Torque can be measured.

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Strain Energy in Rod when it is Subjected to External Torque Formula

​GoStrain Energy Stored in Tension Rod Formula

​GoStrain Energy Stored in Rod Subjected to Bending Moment Formula

Strain Energy in Rod when it is Subjected to External Torque Example

Strain Energy in Rod when it is Subjected to External Torque Solution

Strain Energy in Rod when it is Subjected to External Torque Formula Elements

Other Formulas to find Strain Energy

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

How to Evaluate Strain Energy in Rod when it is Subjected to External Torque?

FAQs on Strain Energy in Rod when it is Subjected to External Torque

Variable Name

GoStrain Energy Stored in Tension Rod Formula

GoStrain Energy Stored in Rod Subjected to Bending Moment Formula