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Length of Shaft given Angle of Twist of Hollow Shaft on Basis of Torsional Rigidity Formula

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Length of Hollow Shaft is the distance between two ends of a hollow shaft. Check FAQs

L h = θ hollow \cdot \frac{G h \cdot {d o}^{4} \cdot (1 - C^{4})}{584 \cdot Mt hollowshaft}

L_h - Length of Hollow Shaft?θ_hollow - Angle of Twist of Hollow Shaft?G_h - Modulus of Rigidity of Hollow Shaft?d_o - Outer Diameter of Hollow Shaft?C - Ratio of Inner to Outer Diameter of Hollow Shaft?Mt_hollowshaft - Torsional Moment in Hollow Shaft?

Length of Shaft given Angle of Twist of Hollow Shaft on Basis of Torsional Rigidity Example

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Here is how the Length of Shaft given Angle of Twist of Hollow Shaft on Basis of Torsional Rigidity equation looks like with Values.

Here is how the Length of Shaft given Angle of Twist of Hollow Shaft on Basis of Torsional Rigidity equation looks like with Units.

Here is how the Length of Shaft given Angle of Twist of Hollow Shaft on Basis of Torsional Rigidity equation looks like.

329.921 = 23.58 \cdot \frac{70000 \cdot 46^{4} \cdot (1 - {0.85}^{4})}{584 \cdot 320000}

329.921mm = 23.58° \cdot \frac{70000N/mm² \cdot {46mm}^{4} \cdot (1 - {0.85}^{4})}{584 \cdot 320000N*mm}

329.921 = 23.58 \cdot \frac{70000 \cdot 46^{4} \cdot (1 - {0.85}^{4})}{584 \cdot 320000}

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Design of Automobile Elements » fx Length of Shaft given Angle of Twist of Hollow Shaft on Basis of Torsional Rigidity

Length of Shaft given Angle of Twist of Hollow Shaft on Basis of Torsional Rigidity Solution

Follow our step by step solution on how to calculate Length of Shaft given Angle of Twist of Hollow Shaft on Basis of Torsional Rigidity?

FIRST Step Consider the formula

L h = θ hollow \cdot \frac{G h \cdot {d o}^{4} \cdot (1 - C^{4})}{584 \cdot Mt hollowshaft}

Next Step Substitute values of Variables

∴

L h = 23.58° \cdot \frac{70000N/mm² \cdot {46mm}^{4} \cdot (1 - {0.85}^{4})}{584 \cdot 320000N*mm}

Next Step Convert Units

∴

L h = 0.4115rad \cdot \frac{7E+10Pa \cdot {0.046m}^{4} \cdot (1 - {0.85}^{4})}{584 \cdot 320N*m}

Next Step Prepare to Evaluate

∴

L h = 0.4115 \cdot \frac{7E+10 \cdot {0.046}^{4} \cdot (1 - {0.85}^{4})}{584 \cdot 320}

Next Step Evaluate

∴

L h = 0.329920975486926m

Next Step Convert to Output's Unit

∴

L h = 329.920975486926mm

LAST Step Rounding Answer

∴

L h = 329.921mm

Length of Shaft given Angle of Twist of Hollow Shaft on Basis of Torsional Rigidity Formula Elements

Variables

Length of Hollow Shaft

Length of Hollow Shaft is the distance between two ends of a hollow shaft.

Symbol: L_h

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Length of Hollow Shaft

Angle of Twist of Hollow Shaft

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

Symbol: θ_hollow

Measurement: AngleUnit: °

Note: Value should be greater than 0.

Formulas to find Angle of Twist of Hollow Shaft

Modulus of Rigidity of Hollow Shaft

Modulus of Rigidity of Hollow 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_h

Measurement: StressUnit: N/mm²

Note: Value should be greater than 0.

Formulas to find Modulus of Rigidity of Hollow Shaft

Outer Diameter of Hollow Shaft

Outer Diameter of Hollow Shaft is defined as the length of the longest chord of the surface of the hollow circular shaft.

Symbol: d_o

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Outer Diameter of Hollow Shaft

Ratio of Inner to Outer Diameter of Hollow Shaft

The Ratio of Inner to Outer Diameter of Hollow Shaft is defined as the inner diameter of the shaft divided by the outer diameter.

Symbol: C

Measurement: NAUnit: Unitless

Note: Value should be less than 1.

Formulas to find Ratio of Inner to Outer Diameter of Hollow Shaft

Torsional Moment in Hollow Shaft

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

Symbol: Mt_hollowshaft

Measurement: TorqueUnit: N*mm

Note: Value should be greater than 0.

Formulas to find Torsional Moment in Hollow Shaft

Other formulas in Design of Hollow Shaft category

Go Ratio of Inner Diameter to Outer Diameter

C = \frac{d i}{d o}

Go Inner Diameter of Hollow Shaft given Ratio of Diameters

d i = C \cdot d o

Go Outer Diameter given Ratio of Diameters

d o = \frac{d i}{C}

Go Tensile Stress in Hollow Shaft when Subjected to Axial Force

σ tp = \frac{P ax hollow}{\frac{π}{4} \cdot ({d o}^{2} - {d i}^{2})}

How to Evaluate Length of Shaft given Angle of Twist of Hollow Shaft on Basis of Torsional Rigidity?

Length of Shaft given Angle of Twist of Hollow Shaft on Basis of Torsional Rigidity evaluator uses Length of Hollow Shaft = Angle of Twist of Hollow Shaft*(Modulus of Rigidity of Hollow Shaft*Outer Diameter of Hollow Shaft^4*(1-Ratio of Inner to Outer Diameter of Hollow Shaft^4))/(584*Torsional Moment in Hollow Shaft) to evaluate the Length of Hollow Shaft, Length of Shaft given Angle of Twist of Hollow Shaft on Basis of Torsional Rigidity formula is defined as the measure of the length of a hollow shaft in a mechanical system, considering the angle of twist and torsional rigidity, which is essential in designing hollow shafts for optimal performance and safety. Length of Hollow Shaft is denoted by L_h symbol.

How to evaluate Length of Shaft given Angle of Twist of Hollow Shaft on Basis of Torsional Rigidity using this online evaluator? To use this online evaluator for Length of Shaft given Angle of Twist of Hollow Shaft on Basis of Torsional Rigidity, enter Angle of Twist of Hollow Shaft (θ_hollow), Modulus of Rigidity of Hollow Shaft (G_h), Outer Diameter of Hollow Shaft (d_o), Ratio of Inner to Outer Diameter of Hollow Shaft (C) & Torsional Moment in Hollow Shaft (Mt_hollowshaft) and hit the calculate button.

FAQs on Length of Shaft given Angle of Twist of Hollow Shaft on Basis of Torsional Rigidity

What is the formula to find Length of Shaft given Angle of Twist of Hollow Shaft on Basis of Torsional Rigidity?

The formula of Length of Shaft given Angle of Twist of Hollow Shaft on Basis of Torsional Rigidity is expressed as Length of Hollow Shaft = Angle of Twist of Hollow Shaft*(Modulus of Rigidity of Hollow Shaft*Outer Diameter of Hollow Shaft^4*(1-Ratio of Inner to Outer Diameter of Hollow Shaft^4))/(584*Torsional Moment in Hollow Shaft). Here is an example- 329921 = 0.411548637620186*(70000000000*0.046^4*(1-0.85^4))/(584*320).

How to calculate Length of Shaft given Angle of Twist of Hollow Shaft on Basis of Torsional Rigidity?

With Angle of Twist of Hollow Shaft (θ_hollow), Modulus of Rigidity of Hollow Shaft (G_h), Outer Diameter of Hollow Shaft (d_o), Ratio of Inner to Outer Diameter of Hollow Shaft (C) & Torsional Moment in Hollow Shaft (Mt_hollowshaft) we can find Length of Shaft given Angle of Twist of Hollow Shaft on Basis of Torsional Rigidity using the formula - Length of Hollow Shaft = Angle of Twist of Hollow Shaft*(Modulus of Rigidity of Hollow Shaft*Outer Diameter of Hollow Shaft^4*(1-Ratio of Inner to Outer Diameter of Hollow Shaft^4))/(584*Torsional Moment in Hollow Shaft).

Can the Length of Shaft given Angle of Twist of Hollow Shaft on Basis of Torsional Rigidity be negative?

No, the Length of Shaft given Angle of Twist of Hollow Shaft on Basis of Torsional Rigidity, measured in Length cannot be negative.

Which unit is used to measure Length of Shaft given Angle of Twist of Hollow Shaft on Basis of Torsional Rigidity?

Length of Shaft given Angle of Twist of Hollow Shaft on Basis of Torsional Rigidity 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 Angle of Twist of Hollow Shaft on Basis of Torsional Rigidity can be measured.

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Length of Shaft given Angle of Twist of Hollow Shaft on Basis of Torsional Rigidity Formula

Length of Shaft given Angle of Twist of Hollow Shaft on Basis of Torsional Rigidity Example

Length of Shaft given Angle of Twist of Hollow Shaft on Basis of Torsional Rigidity Solution

Length of Shaft given Angle of Twist of Hollow Shaft on Basis of Torsional Rigidity Formula Elements

Other formulas in Design of Hollow Shaft category

How to Evaluate Length of Shaft given Angle of Twist of Hollow Shaft on Basis of Torsional Rigidity?

FAQs on Length of Shaft given Angle of Twist of Hollow Shaft on Basis of Torsional Rigidity

Variable Name