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Outer Diameter of Hollow Shaft given Angle of Twist Torsional Rigidity Formula

GoOuter Diameter given Ratio of Diameters Formula

GoOuter Diameter of Hollow Shaft given Bending Stress of Hollow Shaft Formula

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

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

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

Outer Diameter of Hollow Shaft given Angle of Twist Torsional Rigidity Example

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Here is how the Outer Diameter of Hollow Shaft given Angle of Twist Torsional Rigidity equation looks like with Values.

Here is how the Outer Diameter of Hollow Shaft given Angle of Twist Torsional Rigidity equation looks like with Units.

Here is how the Outer Diameter of Hollow Shaft given Angle of Twist Torsional Rigidity equation looks like.

46.0028 = {(584 \cdot 320000 \cdot \frac{330}{70000 \cdot 23.58 \cdot (1 - {0.85}^{4})})}^{\frac{1}{4}}

46.0028mm = {(584 \cdot 320000N*mm \cdot \frac{330mm}{70000N/mm² \cdot 23.58° \cdot (1 - {0.85}^{4})})}^{\frac{1}{4}}

46.0028 = {(584 \cdot 320000 \cdot \frac{330}{70000 \cdot 23.58 \cdot (1 - {0.85}^{4})})}^{\frac{1}{4}}

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Outer Diameter of Hollow Shaft given Angle of Twist Torsional Rigidity Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

d o = {(584 \cdot 320000N*mm \cdot \frac{330mm}{70000N/mm² \cdot 23.58° \cdot (1 - {0.85}^{4})})}^{\frac{1}{4}}

Next Step Convert Units

∴

d o = {(584 \cdot 320N*m \cdot \frac{0.33m}{7E+10Pa \cdot 0.4115rad \cdot (1 - {0.85}^{4})})}^{\frac{1}{4}}

Next Step Prepare to Evaluate

∴

d o = {(584 \cdot 320 \cdot \frac{0.33}{7E+10 \cdot 0.4115 \cdot (1 - {0.85}^{4})})}^{\frac{1}{4}}

Next Step Evaluate

∴

d o = 0.046002754296788m

Next Step Convert to Output's Unit

∴

d o = 46.002754296788mm

LAST Step Rounding Answer

∴

d o = 46.0028mm

Outer Diameter of Hollow Shaft given Angle of Twist Torsional Rigidity Formula Elements

Variables

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

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

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

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

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

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

Other Formulas to find Outer Diameter of Hollow Shaft

Go Outer Diameter given Ratio of Diameters

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

Go Outer Diameter of Hollow Shaft given Bending Stress of Hollow Shaft

d o = {(32 \cdot \frac{M b h}{π \cdot σ b h \cdot (1 - C^{4})})}^{\frac{1}{3}}

Go Outer Diameter of Shaft given Torsional Shear Stress

d o = {(16 \cdot \frac{Mt hollowshaft}{π \cdot 𝜏 h \cdot (1 - C^{4})})}^{\frac{1}{3}}

Go Outer Diameter of Hollow Shaft given Principle Stress

d o = {(16 \cdot \frac{M b h + \sqrt{{M b h}^{2} + {Mt hollowshaft}^{2}}}{π \cdot τ \cdot (1 - C^{4})})}^{\frac{1}{3}}

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 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})}

Go Axial Tensile Force given Tensile Stress in Hollow Shaft

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

How to Evaluate Outer Diameter of Hollow Shaft given Angle of Twist Torsional Rigidity?

Outer Diameter of Hollow Shaft given Angle of Twist Torsional Rigidity evaluator uses Outer Diameter of Hollow Shaft = (584*Torsional Moment in Hollow Shaft*Length of Hollow Shaft/(Modulus of Rigidity of Hollow Shaft*Angle of Twist of Hollow Shaft*(1-Ratio of Inner to Outer Diameter of Hollow Shaft^4)))^(1/4) to evaluate the Outer Diameter of Hollow Shaft, Outer Diameter of Hollow Shaft given Angle of Twist Torsional Rigidity formula is defined as a measure of the outer diameter of a hollow shaft in a mechanical system, which is critical in determining the shaft's strength and stability under torsional loads, and is influenced by factors such as the shaft's material, length, and twist angle. Outer Diameter of Hollow Shaft is denoted by d_o symbol.

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

FAQs on Outer Diameter of Hollow Shaft given Angle of Twist Torsional Rigidity

What is the formula to find Outer Diameter of Hollow Shaft given Angle of Twist Torsional Rigidity?

The formula of Outer Diameter of Hollow Shaft given Angle of Twist Torsional Rigidity is expressed as Outer Diameter of Hollow Shaft = (584*Torsional Moment in Hollow Shaft*Length of Hollow Shaft/(Modulus of Rigidity of Hollow Shaft*Angle of Twist of Hollow Shaft*(1-Ratio of Inner to Outer Diameter of Hollow Shaft^4)))^(1/4). Here is an example- 46002.75 = (584*320*0.33/(70000000000*0.411548637620186*(1-0.85^4)))^(1/4).

How to calculate Outer Diameter of Hollow Shaft given Angle of Twist Torsional Rigidity?

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

What are the other ways to Calculate Outer Diameter of Hollow Shaft?

Here are the different ways to Calculate Outer Diameter of Hollow Shaft-

Outer Diameter of Hollow Shaft=Inner Diameter of Hollow Shaft/Ratio of Inner to Outer Diameter of Hollow Shaft
Outer Diameter of Hollow Shaft=(32*Bending Moment in Hollow Shaft/(pi*Bending Stress in Hollow Shaft*(1-Ratio of Inner to Outer Diameter of Hollow Shaft^4)))^(1/3)
Outer Diameter of Hollow Shaft=(16*Torsional Moment in Hollow Shaft/(pi*Torsional Shear Stress in Hollow Shaft*(1-Ratio of Inner to Outer Diameter of Hollow Shaft^4)))^(1/3)

Can the Outer Diameter of Hollow Shaft given Angle of Twist Torsional Rigidity be negative?

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

Which unit is used to measure Outer Diameter of Hollow Shaft given Angle of Twist Torsional Rigidity?

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

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Outer Diameter of Hollow Shaft given Angle of Twist Torsional Rigidity Formula

​GoOuter Diameter given Ratio of Diameters Formula

​GoOuter Diameter of Hollow Shaft given Bending Stress of Hollow Shaft Formula

Outer Diameter of Hollow Shaft given Angle of Twist Torsional Rigidity Example

Outer Diameter of Hollow Shaft given Angle of Twist Torsional Rigidity Solution

Outer Diameter of Hollow Shaft given Angle of Twist Torsional Rigidity Formula Elements

Other Formulas to find Outer Diameter of Hollow Shaft

Other formulas in Design of Hollow Shaft category

How to Evaluate Outer Diameter of Hollow Shaft given Angle of Twist Torsional Rigidity?

FAQs on Outer Diameter of Hollow Shaft given Angle of Twist Torsional Rigidity

Variable Name

GoOuter Diameter given Ratio of Diameters Formula

GoOuter Diameter of Hollow Shaft given Bending Stress of Hollow Shaft Formula