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Modulus of Rigidity given Angle of Twist Formula

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Modulus of Rigidity of Shaft is the elastic coefficient when a shear force is applied resulting in lateral deformation. It gives us a measure of how rigid is s shaft. Check FAQs

G = 584 \cdot M \cdot \frac{L}{θ \cdot d^{4}}

G - Modulus of Rigidity of Shaft?M - Torsional Moment in Shaft?L - Length of Shaft From Torsional Rigidity?θ - Angle of Twist in Shaft?d - Diameter of Shaft From Torsional Rigidity?

Modulus of Rigidity given Angle of Twist Example

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Here is how the Modulus of Rigidity given Angle of Twist equation looks like with Values.

Here is how the Modulus of Rigidity given Angle of Twist equation looks like with Units.

Here is how the Modulus of Rigidity given Angle of Twist equation looks like.

89999.9981 = 584 \cdot 330000 \cdot \frac{450}{15.4192 \cdot {43.5}^{4}}

89999.9981N/mm² = 584 \cdot 330000N*mm \cdot \frac{450mm}{15.4192° \cdot {43.5mm}^{4}}

89999.9981 = 584 \cdot 330000 \cdot \frac{450}{15.4192 \cdot {43.5}^{4}}

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Modulus of Rigidity given Angle of Twist Solution

Follow our step by step solution on how to calculate Modulus of Rigidity given Angle of Twist?

FIRST Step Consider the formula

G = 584 \cdot M \cdot \frac{L}{θ \cdot d^{4}}

Next Step Substitute values of Variables

∴

G = 584 \cdot 330000N*mm \cdot \frac{450mm}{15.4192° \cdot {43.5mm}^{4}}

Next Step Convert Units

∴

G = 584 \cdot 330N*m \cdot \frac{0.45m}{0.2691rad \cdot {0.0435m}^{4}}

Next Step Prepare to Evaluate

∴

G = 584 \cdot 330 \cdot \frac{0.45}{0.2691 \cdot {0.0435}^{4}}

Next Step Evaluate

∴

G = 89999998126.8391Pa

Next Step Convert to Output's Unit

∴

G = 89999.9981268391N/mm²

LAST Step Rounding Answer

∴

G = 89999.9981N/mm²

Modulus of Rigidity given Angle of Twist Formula Elements

Variables

Modulus of Rigidity of Shaft

Modulus of Rigidity of Shaft is the elastic coefficient when a shear force is applied resulting in lateral deformation. It gives us a measure of how rigid is s shaft.

Symbol: G

Measurement: StressUnit: N/mm²

Note: Value should be greater than 0.

Formulas to find Modulus of Rigidity of Shaft

Torsional Moment in Shaft

Torsional Moment in Shaft is the reaction induced in a structural shaft element when an external force or moment is applied to the element, causing the element to twist.

Symbol: M

Measurement: TorqueUnit: N*mm

Note: Value should be greater than 0.

Formulas to find Torsional Moment in Shaft

Length of Shaft From Torsional Rigidity

Length of Shaft From Torsional Rigidity is the length of the shaft calculated on the basis of torsional rigidity.

Symbol: L

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Length of Shaft From Torsional Rigidity

Angle of Twist in Shaft

Angle of Twist in Shaft is the angle through which the fixed end of a shaft rotates with respect to the free end.

Symbol: θ

Measurement: AngleUnit: °

Note: Value should be greater than 0.

Formulas to find Angle of Twist in Shaft

Diameter of Shaft From Torsional Rigidity

Diameter of Shaft From Torsional Rigidity is the diameter of the external surface of a shaft calculated on the basis of torsional rigidity.

Symbol: d

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Diameter of Shaft From Torsional Rigidity

Other formulas in Torsional Rigidity category

Go Angle of Twist of Shaft

θ = 584 \cdot M \cdot \frac{L}{G \cdot d^{4}}

Go Length of Shaft Subjected to Torsional Moment given Angle of Twist

L = θ \cdot \frac{G \cdot d^{4}}{584 \cdot M}

Go Torsional Moment given Angle of Twist in Shaft

M = θ \cdot \frac{G \cdot d^{4}}{L \cdot 584}

Go Shaft Diameter given Angle of Twist in Shaft

d = {(584 \cdot M \cdot \frac{L}{G \cdot θ})}^{\frac{1}{4}}

How to Evaluate Modulus of Rigidity given Angle of Twist?

Modulus of Rigidity given Angle of Twist evaluator uses Modulus of Rigidity of Shaft = 584*Torsional Moment in Shaft*Length of Shaft From Torsional Rigidity/(Angle of Twist in Shaft*Diameter of Shaft From Torsional Rigidity^4) to evaluate the Modulus of Rigidity of Shaft, Modulus of Rigidity given Angle of Twist formula is defined as a measure of the rigidity of a shaft in torsion, which is the torque required to produce a unit angle of twist in a shaft, and is an important parameter in the design of shafts and axles in mechanical systems. Modulus of Rigidity of Shaft is denoted by G symbol.

How to evaluate Modulus of Rigidity given Angle of Twist using this online evaluator? To use this online evaluator for Modulus of Rigidity given Angle of Twist, enter Torsional Moment in Shaft (M), Length of Shaft From Torsional Rigidity (L), Angle of Twist in Shaft (θ) & Diameter of Shaft From Torsional Rigidity (d) and hit the calculate button.

FAQs on Modulus of Rigidity given Angle of Twist

What is the formula to find Modulus of Rigidity given Angle of Twist?

The formula of Modulus of Rigidity given Angle of Twist is expressed as Modulus of Rigidity of Shaft = 584*Torsional Moment in Shaft*Length of Shaft From Torsional Rigidity/(Angle of Twist in Shaft*Diameter of Shaft From Torsional Rigidity^4). Here is an example- 0.09 = 584*330*0.45/(0.269116157089309*0.0435^4).

How to calculate Modulus of Rigidity given Angle of Twist?

With Torsional Moment in Shaft (M), Length of Shaft From Torsional Rigidity (L), Angle of Twist in Shaft (θ) & Diameter of Shaft From Torsional Rigidity (d) we can find Modulus of Rigidity given Angle of Twist using the formula - Modulus of Rigidity of Shaft = 584*Torsional Moment in Shaft*Length of Shaft From Torsional Rigidity/(Angle of Twist in Shaft*Diameter of Shaft From Torsional Rigidity^4).

Can the Modulus of Rigidity given Angle of Twist be negative?

No, the Modulus of Rigidity given Angle of Twist, measured in Stress cannot be negative.

Which unit is used to measure Modulus of Rigidity given Angle of Twist?

Modulus of Rigidity given Angle of Twist 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 given Angle of Twist can be measured.

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Modulus of Rigidity given Angle of Twist Formula

Modulus of Rigidity given Angle of Twist Example

Modulus of Rigidity given Angle of Twist Solution

Modulus of Rigidity given Angle of Twist Formula Elements

Other formulas in Torsional Rigidity category

How to Evaluate Modulus of Rigidity given Angle of Twist?

FAQs on Modulus of Rigidity given Angle of Twist

Variable Name