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

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

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

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

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

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Here is how the Length of Shaft Subjected to Torsional Moment given Angle of Twist equation looks like with Values.

Here is how the Length of Shaft Subjected to Torsional Moment given Angle of Twist equation looks like with Units.

Here is how the Length of Shaft Subjected to Torsional Moment given Angle of Twist equation looks like.

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

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

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

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

Follow our step by step solution on how to calculate Length of Shaft Subjected to Torsional Moment given Angle of Twist?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

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

Next Step Convert Units

∴

L = 0.2691rad \cdot \frac{9E+10Pa \cdot {0.0435m}^{4}}{584 \cdot 330N*m}

Next Step Prepare to Evaluate

∴

L = 0.2691 \cdot \frac{9E+10 \cdot {0.0435}^{4}}{584 \cdot 330}

Next Step Evaluate

∴

L = 0.450000009365805m

Next Step Convert to Output's Unit

∴

L = 450.000009365805mm

LAST Step Rounding Answer

∴

L = 450mm

Length of Shaft Subjected to Torsional Moment given Angle of Twist Formula Elements

Variables

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

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

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

Other formulas in Torsional Rigidity category

Go Angle of Twist of Shaft

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

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

Length of Shaft Subjected to Torsional Moment given Angle of Twist evaluator uses Length of Shaft From Torsional Rigidity = Angle of Twist in Shaft*(Modulus of Rigidity of Shaft*Diameter of Shaft From Torsional Rigidity^4)/(584*Torsional Moment in Shaft) to evaluate the Length of Shaft From Torsional Rigidity, Length of Shaft Subjected to Torsional Moment given Angle of Twist formula is defined as the measure of the length of a shaft that is subjected to torsional moment, which is a crucial parameter in determining the torsional rigidity of a shaft, and is essential in designing and analyzing mechanical systems. Length of Shaft From Torsional Rigidity is denoted by L symbol.

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

FAQs on Length of Shaft Subjected to Torsional Moment given Angle of Twist

What is the formula to find Length of Shaft Subjected to Torsional Moment given Angle of Twist?

The formula of Length of Shaft Subjected to Torsional Moment given Angle of Twist is expressed as Length of Shaft From Torsional Rigidity = Angle of Twist in Shaft*(Modulus of Rigidity of Shaft*Diameter of Shaft From Torsional Rigidity^4)/(584*Torsional Moment in Shaft). Here is an example- 450000 = 0.269116157089309*(90000000000*0.0435^4)/(584*330).

How to calculate Length of Shaft Subjected to Torsional Moment given Angle of Twist?

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

Can the Length of Shaft Subjected to Torsional Moment given Angle of Twist be negative?

No, the Length of Shaft Subjected to Torsional Moment given Angle of Twist, measured in Length cannot be negative.

Which unit is used to measure Length of Shaft Subjected to Torsional Moment given Angle of Twist?

Length of Shaft Subjected to Torsional Moment given Angle of Twist is usually measured using the Millimeter[mm] for Length. Meter[mm], Kilometer[mm], Decimeter[mm] are the few other units in which Length of Shaft Subjected to Torsional Moment given Angle of Twist can be measured.

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

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

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

Length of Shaft Subjected to Torsional Moment given Angle of Twist Formula Elements

Other formulas in Torsional Rigidity category

How to Evaluate Length of Shaft Subjected to Torsional Moment given Angle of Twist?

FAQs on Length of Shaft Subjected to Torsional Moment given Angle of Twist

Variable Name