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Length of Shaft given Total Angle of Twist for Shaft Formula

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The Length of Shaft is the distance between two ends of shaft. Check FAQs

L = \frac{θ \cdot π \cdot G \cdot (D 2 - D 1)}{32 \cdot τ \cdot (\frac{1}{{D 1}^{3}} - \frac{1}{{D 2}^{3}})}

L - Length of Shaft?θ - Angle of twist?G - Modulus of rigidity of Shaft?D₂ - Diameter of shaft at right end?D₁ - Diameter of shaft at left end?τ - Torque Exerted on Wheel?π - Archimedes' constant?

Length of Shaft given Total Angle of Twist for Shaft Example

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Here is how the Length of Shaft given Total Angle of Twist for Shaft equation looks like with Values.

Here is how the Length of Shaft given Total Angle of Twist for Shaft equation looks like with Units.

Here is how the Length of Shaft given Total Angle of Twist for Shaft equation looks like.

162288.9062 = \frac{30 \cdot 3.1416 \cdot 4E-5 \cdot (5000 - 3000)}{32 \cdot 50 \cdot (\frac{1}{3000^{3}} - \frac{1}{5000^{3}})}

162288.9062mm = \frac{30 \cdot 3.1416 \cdot 4E-5MPa \cdot (5000mm - 3000mm)}{32 \cdot 50N*m \cdot (\frac{1}{{3000mm}^{3}} - \frac{1}{{5000mm}^{3}})}

162288.9062 = \frac{30 \cdot 3.1416 \cdot 4E-5 \cdot (5000 - 3000)}{32 \cdot 50 \cdot (\frac{1}{3000^{3}} - \frac{1}{5000^{3}})}

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Length of Shaft given Total Angle of Twist for Shaft Solution

Follow our step by step solution on how to calculate Length of Shaft given Total Angle of Twist for Shaft?

FIRST Step Consider the formula

L = \frac{θ \cdot π \cdot G \cdot (D 2 - D 1)}{32 \cdot τ \cdot (\frac{1}{{D 1}^{3}} - \frac{1}{{D 2}^{3}})}

Next Step Substitute values of Variables

∴

L = \frac{30 \cdot π \cdot 4E-5MPa \cdot (5000mm - 3000mm)}{32 \cdot 50N*m \cdot (\frac{1}{{3000mm}^{3}} - \frac{1}{{5000mm}^{3}})}

Next Step Substitute values of Constants

∴

L = \frac{30 \cdot 3.1416 \cdot 4E-5MPa \cdot (5000mm - 3000mm)}{32 \cdot 50N*m \cdot (\frac{1}{{3000mm}^{3}} - \frac{1}{{5000mm}^{3}})}

Next Step Convert Units

∴

L = \frac{30 \cdot 3.1416 \cdot 40Pa \cdot (5m - 3m)}{32 \cdot 50N*m \cdot (\frac{1}{{3m}^{3}} - \frac{1}{{5m}^{3}})}

Next Step Prepare to Evaluate

∴

L = \frac{30 \cdot 3.1416 \cdot 40 \cdot (5 - 3)}{32 \cdot 50 \cdot (\frac{1}{3^{3}} - \frac{1}{5^{3}})}

Next Step Evaluate

∴

L = 162.288906212228m

Next Step Convert to Output's Unit

∴

L = 162288.906212228mm

LAST Step Rounding Answer

∴

L = 162288.9062mm

Length of Shaft given Total Angle of Twist for Shaft Formula Elements

Variables

Constants

Length of Shaft

The Length of Shaft is the distance between two ends of shaft.

Symbol: L

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Length of Shaft

Angle of twist

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

Symbol: θ

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Angle of twist

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 a body is.

Symbol: G

Measurement: PressureUnit: MPa

Note: Value should be greater than 0.

Formulas to find Modulus of rigidity of Shaft

Diameter of shaft at right end

Diameter of shaft at right end is the longer side diameter of tapering shaft.

Symbol: D₂

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Diameter of shaft at right end

Diameter of shaft at left end

Diameter of shaft at left end is the shorter side diameter of tapering shaft.

Symbol: D₁

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Diameter of shaft at left end

Torque Exerted on Wheel

Torque Exerted on Wheel is described as the turning effect of force on the axis of rotation. In brief, it is a moment of force. It is characterized by τ.

Symbol: τ

Measurement: TorqueUnit: N*m

Note: Value should be greater than 0.

Formulas to find Torque Exerted on Wheel

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

Other formulas in Torsion of Tapering Shafts category

Go Torque on Tapering Shaft

τ = \frac{𝜏 \cdot π \cdot d s}{16}

Go Shear Stress on Left Surface of Shaft

𝜏 = \frac{16 \cdot τ}{π \cdot d s}

Go Diameter of Shaft at Left End

d s = \frac{16 \cdot τ}{𝜏 \cdot π}

Go Total Angle of Twist for Shaft

θ = \frac{32 \cdot τ \cdot L \cdot (\frac{1}{{D 1}^{3}} - \frac{1}{{D 2}^{3}})}{π \cdot G \cdot (D 2 - D 1)}

How to Evaluate Length of Shaft given Total Angle of Twist for Shaft?

Length of Shaft given Total Angle of Twist for Shaft evaluator uses Length of Shaft = (Angle of twist*pi*Modulus of rigidity of Shaft*(Diameter of shaft at right end-Diameter of shaft at left end))/(32*Torque Exerted on Wheel*(1/(Diameter of shaft at left end^3)-1/(Diameter of shaft at right end^3))) to evaluate the Length of Shaft, Length of shaft given total angle of twist for shaft is defined as the measurement or extent of something from end to end. Length of Shaft is denoted by L symbol.

How to evaluate Length of Shaft given Total Angle of Twist for Shaft using this online evaluator? To use this online evaluator for Length of Shaft given Total Angle of Twist for Shaft, enter Angle of twist (θ), Modulus of rigidity of Shaft (G), Diameter of shaft at right end (D₂), Diameter of shaft at left end (D₁) & Torque Exerted on Wheel (τ) and hit the calculate button.

FAQs on Length of Shaft given Total Angle of Twist for Shaft

What is the formula to find Length of Shaft given Total Angle of Twist for Shaft?

The formula of Length of Shaft given Total Angle of Twist for Shaft is expressed as Length of Shaft = (Angle of twist*pi*Modulus of rigidity of Shaft*(Diameter of shaft at right end-Diameter of shaft at left end))/(32*Torque Exerted on Wheel*(1/(Diameter of shaft at left end^3)-1/(Diameter of shaft at right end^3))). Here is an example- 1.6E+8 = (30*pi*40*(5-3))/(32*50*(1/(3^3)-1/(5^3))).

How to calculate Length of Shaft given Total Angle of Twist for Shaft?

With Angle of twist (θ), Modulus of rigidity of Shaft (G), Diameter of shaft at right end (D₂), Diameter of shaft at left end (D₁) & Torque Exerted on Wheel (τ) we can find Length of Shaft given Total Angle of Twist for Shaft using the formula - Length of Shaft = (Angle of twist*pi*Modulus of rigidity of Shaft*(Diameter of shaft at right end-Diameter of shaft at left end))/(32*Torque Exerted on Wheel*(1/(Diameter of shaft at left end^3)-1/(Diameter of shaft at right end^3))). This formula also uses Archimedes' constant .

Can the Length of Shaft given Total Angle of Twist for Shaft be negative?

No, the Length of Shaft given Total Angle of Twist for Shaft, measured in Length cannot be negative.

Which unit is used to measure Length of Shaft given Total Angle of Twist for Shaft?

Length of Shaft given Total Angle of Twist for Shaft 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 given Total Angle of Twist for Shaft can be measured.

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Length of Shaft given Total Angle of Twist for Shaft Formula

Length of Shaft given Total Angle of Twist for Shaft Example

Length of Shaft given Total Angle of Twist for Shaft Solution

Length of Shaft given Total Angle of Twist for Shaft Formula Elements

Other formulas in Torsion of Tapering Shafts category

How to Evaluate Length of Shaft given Total Angle of Twist for Shaft?

FAQs on Length of Shaft given Total Angle of Twist for Shaft

Variable Name