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Ratio of Diameters given Angle of Twist of Hollow Shaft and Torsional Rigidity Formula

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

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

C - Ratio of Inner to 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?d_o - Outer Diameter of Hollow Shaft?θ_hollow - Angle of Twist of Hollow Shaft?

Ratio of Diameters given Angle of Twist of Hollow Shaft and Torsional Rigidity Example

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Here is how the Ratio of Diameters given Angle of Twist of Hollow Shaft and Torsional Rigidity equation looks like with Values.

Here is how the Ratio of Diameters given Angle of Twist of Hollow Shaft and Torsional Rigidity equation looks like with Units.

Here is how the Ratio of Diameters given Angle of Twist of Hollow Shaft and Torsional Rigidity equation looks like.

0.85 = {(1 - 584 \cdot 320000 \cdot \frac{330}{70000 \cdot 46^{4} \cdot 23.58})}^{\frac{1}{4}}

0.85 = {(1 - 584 \cdot 320000N*mm \cdot \frac{330mm}{70000N/mm² \cdot {46mm}^{4} \cdot 23.58°})}^{\frac{1}{4}}

0.85 = {(1 - 584 \cdot 320000 \cdot \frac{330}{70000 \cdot 46^{4} \cdot 23.58})}^{\frac{1}{4}}

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Ratio of Diameters given Angle of Twist of Hollow Shaft and Torsional Rigidity Solution

Follow our step by step solution on how to calculate Ratio of Diameters given Angle of Twist of Hollow Shaft and Torsional Rigidity?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

C = {(1 - 584 \cdot 320000N*mm \cdot \frac{330mm}{70000N/mm² \cdot {46mm}^{4} \cdot 23.58°})}^{\frac{1}{4}}

Next Step Convert Units

∴

C = {(1 - 584 \cdot 320N*m \cdot \frac{0.33m}{7E+10Pa \cdot {0.046m}^{4} \cdot 0.4115rad})}^{\frac{1}{4}}

Next Step Prepare to Evaluate

∴

C = {(1 - 584 \cdot 320 \cdot \frac{0.33}{7E+10 \cdot {0.046}^{4} \cdot 0.4115})}^{\frac{1}{4}}

Next Step Evaluate

∴

C = 0.849953388500584

LAST Step Rounding Answer

∴

C = 0.85

Ratio of Diameters given Angle of Twist of Hollow Shaft and Torsional Rigidity Formula Elements

Variables

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