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Angle of Twist of Shaft Formula

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

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

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

Angle of Twist of Shaft Example

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Here is how the Angle of Twist of Shaft equation looks like with Values.

Here is how the Angle of Twist of Shaft equation looks like with Units.

Here is how the Angle of Twist of Shaft equation looks like.

15.4192 = 584 \cdot 330000 \cdot \frac{450}{90000 \cdot {43.5}^{4}}

15.4192° = 584 \cdot 330000N*mm \cdot \frac{450mm}{90000N/mm² \cdot {43.5mm}^{4}}

15.4192 = 584 \cdot 330000 \cdot \frac{450}{90000 \cdot {43.5}^{4}}

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Angle of Twist of Shaft Solution

Follow our step by step solution on how to calculate Angle of Twist of Shaft?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

θ = 584 \cdot 330000N*mm \cdot \frac{450mm}{90000N/mm² \cdot {43.5mm}^{4}}

Next Step Convert Units

∴

θ = 584 \cdot 330N*m \cdot \frac{0.45m}{9E+10Pa \cdot {0.0435m}^{4}}

Next Step Prepare to Evaluate

∴

θ = 584 \cdot 330 \cdot \frac{0.45}{9E+10 \cdot {0.0435}^{4}}

Next Step Evaluate

∴

θ = 0.269116151488221rad

Next Step Convert to Output's Unit

∴

θ = 15.4192196790813°

LAST Step Rounding Answer

∴

θ = 15.4192°

Angle of Twist of Shaft Formula Elements

Variables

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

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

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

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 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 Modulus of Rigidity given Angle of Twist

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

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 Angle of Twist of Shaft?

Angle of Twist of Shaft evaluator uses Angle of Twist in Shaft = 584*Torsional Moment in Shaft*Length of Shaft From Torsional Rigidity/(Modulus of Rigidity of Shaft*Diameter of Shaft From Torsional Rigidity^4) to evaluate the Angle of Twist in Shaft, Angle of Twist of Shaft formula is defined as a measure of the twisting deformation of a shaft under torque, which is critical in mechanical engineering to ensure the structural integrity of rotating shafts and prevent failure due to torsional stress. Angle of Twist in Shaft is denoted by θ symbol.

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

FAQs on Angle of Twist of Shaft

What is the formula to find Angle of Twist of Shaft?

The formula of Angle of Twist of Shaft is expressed as Angle of Twist in Shaft = 584*Torsional Moment in Shaft*Length of Shaft From Torsional Rigidity/(Modulus of Rigidity of Shaft*Diameter of Shaft From Torsional Rigidity^4). Here is an example- 883.4562 = 584*330*0.45/(90000000000*0.0435^4).

How to calculate Angle of Twist of Shaft?

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

Can the Angle of Twist of Shaft be negative?

No, the Angle of Twist of Shaft, measured in Angle cannot be negative.

Which unit is used to measure Angle of Twist of Shaft?

Angle of Twist of Shaft is usually measured using the Degree[°] for Angle. Radian[°], Minute[°], Second[°] are the few other units in which Angle of Twist of Shaft can be measured.

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Angle of Twist of Shaft Formula

Angle of Twist of Shaft Example

Angle of Twist of Shaft Solution

Angle of Twist of Shaft Formula Elements

Other formulas in Torsional Rigidity category

How to Evaluate Angle of Twist of Shaft?

FAQs on Angle of Twist of Shaft

Variable Name