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Modulus of Rigidity of Rod given Strain Energy in Rod Formula

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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. Check FAQs

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

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

Modulus of Rigidity of Rod given Strain Energy in Rod Example

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Here is how the Modulus of Rigidity of Rod given Strain Energy in Rod equation looks like with Values.

Here is how the Modulus of Rigidity of Rod given Strain Energy in Rod equation looks like with Units.

Here is how the Modulus of Rigidity of Rod given Strain Energy in Rod equation looks like.

105510.5658 = 55005^{2} \cdot \frac{1432.449}{2 \cdot 553 \cdot 37.1392}

105510.5658N/mm² = {55005N*mm}^{2} \cdot \frac{1432.449mm}{2 \cdot 553mm⁴ \cdot 37.1392J}

105510.5658 = 55005^{2} \cdot \frac{1432.449}{2 \cdot 553 \cdot 37.1392}

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Modulus of Rigidity of Rod given Strain Energy in Rod Solution

Follow our step by step solution on how to calculate Modulus of Rigidity of Rod given Strain Energy in Rod?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

G = {55005N*mm}^{2} \cdot \frac{1432.449mm}{2 \cdot 553mm⁴ \cdot 37.1392J}

Next Step Convert Units

∴

G = {55.005N*m}^{2} \cdot \frac{1.4324m}{2 \cdot 5.5E-10m⁴ \cdot 37.1392J}

Next Step Prepare to Evaluate

∴

G = {55.005}^{2} \cdot \frac{1.4324}{2 \cdot 5.5E-10 \cdot 37.1392}

Next Step Evaluate

∴

G = 105510565819.005Pa

Next Step Convert to Output's Unit

∴

G = 105510.565819005N/mm²

LAST Step Rounding Answer

∴

G = 105510.5658N/mm²

Modulus of Rigidity of Rod given Strain Energy in Rod Formula Elements

Variables

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

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

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

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 Modulus of Rigidity of Rod given Strain Energy in Rod?

Modulus of Rigidity of Rod given Strain Energy in Rod evaluator uses Modulus of Rigidity = Torque^2*Length of Rod or Shaft/(2*Polar Moment of Inertia*Strain Energy) to evaluate the Modulus of Rigidity, Modulus of Rigidity of Rod given Strain Energy in Rod formula is defined as a measure of a material's ability to resist deformation under shear stress. It relates the energy stored in a deformed rod to its geometric and material properties, providing insights into structural performance. Modulus of Rigidity is denoted by G symbol.

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

FAQs on Modulus of Rigidity of Rod given Strain Energy in Rod

What is the formula to find Modulus of Rigidity of Rod given Strain Energy in Rod?

The formula of Modulus of Rigidity of Rod given Strain Energy in Rod is expressed as Modulus of Rigidity = Torque^2*Length of Rod or Shaft/(2*Polar Moment of Inertia*Strain Energy). Here is an example- 0.105511 = 55.005^2*1.432449/(2*5.53E-10*37.13919).

How to calculate Modulus of Rigidity of Rod given Strain Energy in Rod?

With Torque (τ), Length of Rod or Shaft (L), Polar Moment of Inertia (J) & Strain Energy (U) we can find Modulus of Rigidity of Rod given Strain Energy in Rod using the formula - Modulus of Rigidity = Torque^2*Length of Rod or Shaft/(2*Polar Moment of Inertia*Strain Energy).

Can the Modulus of Rigidity of Rod given Strain Energy in Rod be negative?

No, the Modulus of Rigidity of Rod given Strain Energy in Rod, measured in Stress cannot be negative.

Which unit is used to measure Modulus of Rigidity of Rod given Strain Energy in Rod?

Modulus of Rigidity of Rod given Strain Energy in Rod is usually measured using the Newton per Square Millimeter[N/mm²] for Stress. Pascal[N/mm²], Newton per Square Meter[N/mm²], Kilonewton per Square Meter[N/mm²] are the few other units in which Modulus of Rigidity of Rod given Strain Energy in Rod can be measured.

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Modulus of Rigidity of Rod given Strain Energy in Rod Formula

Modulus of Rigidity of Rod given Strain Energy in Rod Example

Modulus of Rigidity of Rod given Strain Energy in Rod Solution

Modulus of Rigidity of Rod given Strain Energy in Rod Formula Elements

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

How to Evaluate Modulus of Rigidity of Rod given Strain Energy in Rod?

FAQs on Modulus of Rigidity of Rod given Strain Energy in Rod

Variable Name