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Torque given Strain Energy in Rod Subjected to External Torque Formula

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

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

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

Torque given Strain Energy in Rod Subjected to External Torque Example

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

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

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

55025.9621 = \sqrt{2 \cdot 37.1392 \cdot 553 \cdot \frac{105591}{1432.449}}

55025.9621N*mm = \sqrt{2 \cdot 37.1392J \cdot 553mm⁴ \cdot \frac{105591N/mm²}{1432.449mm}}

55025.9621 = \sqrt{2 \cdot 37.1392 \cdot 553 \cdot \frac{105591}{1432.449}}

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Torque given Strain Energy in Rod Subjected to External Torque Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

τ = \sqrt{2 \cdot 37.1392J \cdot 553mm⁴ \cdot \frac{105591N/mm²}{1432.449mm}}

Next Step Convert Units

∴

τ = \sqrt{2 \cdot 37.1392J \cdot 5.5E-10m⁴ \cdot \frac{1.1E+11Pa}{1.4324m}}

Next Step Prepare to Evaluate

∴

τ = \sqrt{2 \cdot 37.1392 \cdot 5.5E-10 \cdot \frac{1.1E+11}{1.4324}}

Next Step Evaluate

∴

τ = 55.0259620677254N*m

Next Step Convert to Output's Unit

∴

τ = 55025.9620677254N*mm

LAST Step Rounding Answer

∴

τ = 55025.9621N*mm

Torque given Strain Energy in Rod Subjected to External Torque Formula Elements

Variables

Functions

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

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

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

sqrt

A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number.

Syntax: sqrt(Number)

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 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}

How to Evaluate Torque given Strain Energy in Rod Subjected to External Torque?

Torque given Strain Energy in Rod Subjected to External Torque evaluator uses Torque = sqrt(2*Strain Energy*Polar Moment of Inertia*Modulus of Rigidity/Length of Rod or Shaft) to evaluate the Torque, Torque given Strain Energy in Rod Subjected to External Torque formula is defined as a method to evaluate the torque applied to a rod based on the strain energy stored within it. This concept is crucial in mechanical design for understanding how materials respond to external forces. Torque is denoted by τ symbol.

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

FAQs on Torque given Strain Energy in Rod Subjected to External Torque

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

The formula of Torque given Strain Energy in Rod Subjected to External Torque is expressed as Torque = sqrt(2*Strain Energy*Polar Moment of Inertia*Modulus of Rigidity/Length of Rod or Shaft). Here is an example- 5.5E+7 = sqrt(2*37.13919*5.53E-10*105591000000/1.432449).

How to calculate Torque given Strain Energy in Rod Subjected to External Torque?

With Strain Energy (U), Polar Moment of Inertia (J), Modulus of Rigidity (G) & Length of Rod or Shaft (L) we can find Torque given Strain Energy in Rod Subjected to External Torque using the formula - Torque = sqrt(2*Strain Energy*Polar Moment of Inertia*Modulus of Rigidity/Length of Rod or Shaft). This formula also uses Square Root (sqrt) function(s).

Can the Torque given Strain Energy in Rod Subjected to External Torque be negative?

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

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

Torque given Strain Energy in Rod Subjected to External Torque is usually measured using the Newton Millimeter[N*mm] for Torque. Newton Meter[N*mm], Newton Centimeter[N*mm], Kilonewton Meter[N*mm] are the few other units in which Torque given Strain Energy in Rod Subjected to External Torque can be measured.

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Torque given Strain Energy in Rod Subjected to External Torque Formula

Torque given Strain Energy in Rod Subjected to External Torque Example

Torque given Strain Energy in Rod Subjected to External Torque Solution

Torque given Strain Energy in Rod Subjected to External Torque Formula Elements

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

How to Evaluate Torque given Strain Energy in Rod Subjected to External Torque?

FAQs on Torque given Strain Energy in Rod Subjected to External Torque

Variable Name