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Ratio of Diameters given Tensile Stress in Hollow Shaft Formula

GoRatio of Inner Diameter to Outer Diameter Formula

GoRatio of Diameters given Bending Stress of Hollow Shaft 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 = \sqrt{1 - (\frac{P ax hollow}{\frac{π}{4} \cdot σ tp \cdot {d o}^{2}})}

C - Ratio of Inner to Outer Diameter of Hollow Shaft?P_{ax hollow} - Axial Force on Hollow Shaft?σ_tp - Tensile Stress in Hollow Shaft?d_o - Outer Diameter of Hollow Shaft?π - Archimedes' constant?

Ratio of Diameters given Tensile Stress in Hollow Shaft Example

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Here is how the Ratio of Diameters given Tensile Stress in Hollow Shaft equation looks like with Values.

Here is how the Ratio of Diameters given Tensile Stress in Hollow Shaft equation looks like with Units.

Here is how the Ratio of Diameters given Tensile Stress in Hollow Shaft equation looks like.

0.8478 = \sqrt{1 - (\frac{25980}{\frac{3.1416}{4} \cdot 55.6 \cdot 46^{2}})}

0.8478 = \sqrt{1 - (\frac{25980N}{\frac{3.1416}{4} \cdot 55.6N/mm² \cdot {46mm}^{2}})}

0.8478 = \sqrt{1 - (\frac{25980}{\frac{3.1416}{4} \cdot 55.6 \cdot 46^{2}})}

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Ratio of Diameters given Tensile Stress in Hollow Shaft Solution

Follow our step by step solution on how to calculate Ratio of Diameters given Tensile Stress in Hollow Shaft?

FIRST Step Consider the formula

C = \sqrt{1 - (\frac{P ax hollow}{\frac{π}{4} \cdot σ tp \cdot {d o}^{2}})}

Next Step Substitute values of Variables

∴

C = \sqrt{1 - (\frac{25980N}{\frac{π}{4} \cdot 55.6N/mm² \cdot {46mm}^{2}})}

Next Step Substitute values of Constants

∴

C = \sqrt{1 - (\frac{25980N}{\frac{3.1416}{4} \cdot 55.6N/mm² \cdot {46mm}^{2}})}

Next Step Convert Units

∴

C = \sqrt{1 - (\frac{25980N}{\frac{3.1416}{4} \cdot 5.6E+7Pa \cdot {0.046m}^{2}})}

Next Step Prepare to Evaluate

∴

C = \sqrt{1 - (\frac{25980}{\frac{3.1416}{4} \cdot 5.6E+7 \cdot {0.046}^{2}})}

Next Step Evaluate

∴

C = 0.847842311084974

LAST Step Rounding Answer

∴

C = 0.8478

Ratio of Diameters given Tensile Stress in Hollow Shaft Formula Elements

Variables

Constants

Functions

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

Axial Force on Hollow Shaft

Axial Force on Hollow Shaft is defined as the compression or tension force acting on a hollow shaft.

Symbol: P_{ax hollow}

Measurement: ForceUnit: N

Note: Value should be greater than 0.

Formulas to find Axial Force on Hollow Shaft

Tensile Stress in Hollow Shaft

Tensile Stress in Hollow Shaft is stress that ensures that the stresses developed in a hollow shaft due to service loads do not exceed the elastic limit.

Symbol: σ_tp

Measurement: StressUnit: N/mm²

Note: Value should be greater than 0.

Formulas to find Tensile Stress in 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

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

sqrt

A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number.

Syntax: sqrt(Number)

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

Go Ratio of Inner Diameter to Outer Diameter

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

Go Ratio of Diameters given Bending Stress of Hollow Shaft

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

Go Ratio of Diameter given Torsional Shear Stress in Hollow Shaft

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

Go Ratio of Diameters given Principle Stress

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

Other formulas in Design of Hollow Shaft category

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})}

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 Ratio of Diameters given Tensile Stress in Hollow Shaft?

Ratio of Diameters given Tensile Stress in Hollow Shaft evaluator uses Ratio of Inner to Outer Diameter of Hollow Shaft = sqrt(1-(Axial Force on Hollow Shaft/(pi/4*Tensile Stress in Hollow Shaft*Outer Diameter of Hollow Shaft^2))) to evaluate the Ratio of Inner to Outer Diameter of Hollow Shaft, Ratio of Diameters given Tensile Stress in Hollow Shaft formula is defined as a dimensionless value that represents the ratio of the outer diameter to the inner diameter of a hollow shaft, which is a critical parameter in the design of hollow shafts to withstand tensile stress and ensure structural integrity. Ratio of Inner to Outer Diameter of Hollow Shaft is denoted by C symbol.

How to evaluate Ratio of Diameters given Tensile Stress in Hollow Shaft using this online evaluator? To use this online evaluator for Ratio of Diameters given Tensile Stress in Hollow Shaft, enter Axial Force on Hollow Shaft (P_{ax hollow}), Tensile Stress in Hollow Shaft (σ_tp) & Outer Diameter of Hollow Shaft (d_o) and hit the calculate button.

FAQs on Ratio of Diameters given Tensile Stress in Hollow Shaft

What is the formula to find Ratio of Diameters given Tensile Stress in Hollow Shaft?

The formula of Ratio of Diameters given Tensile Stress in Hollow Shaft is expressed as Ratio of Inner to Outer Diameter of Hollow Shaft = sqrt(1-(Axial Force on Hollow Shaft/(pi/4*Tensile Stress in Hollow Shaft*Outer Diameter of Hollow Shaft^2))). Here is an example- 0.847842 = sqrt(1-(25980/(pi/4*55600000*0.046^2))).

How to calculate Ratio of Diameters given Tensile Stress in Hollow Shaft?

With Axial Force on Hollow Shaft (P_{ax hollow}), Tensile Stress in Hollow Shaft (σ_tp) & Outer Diameter of Hollow Shaft (d_o) we can find Ratio of Diameters given Tensile Stress in Hollow Shaft using the formula - Ratio of Inner to Outer Diameter of Hollow Shaft = sqrt(1-(Axial Force on Hollow Shaft/(pi/4*Tensile Stress in Hollow Shaft*Outer Diameter of Hollow Shaft^2))). This formula also uses Archimedes' constant and Square Root (sqrt) function(s).

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

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

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

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Ratio of Diameters given Tensile Stress in Hollow Shaft Formula

​GoRatio of Inner Diameter to Outer Diameter Formula

​GoRatio of Diameters given Bending Stress of Hollow Shaft Formula

Ratio of Diameters given Tensile Stress in Hollow Shaft Example

Ratio of Diameters given Tensile Stress in Hollow Shaft Solution

Ratio of Diameters given Tensile Stress in Hollow Shaft Formula Elements

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

Other formulas in Design of Hollow Shaft category

How to Evaluate Ratio of Diameters given Tensile Stress in Hollow Shaft?

FAQs on Ratio of Diameters given Tensile Stress in Hollow Shaft

Variable Name

GoRatio of Inner Diameter to Outer Diameter Formula

GoRatio of Diameters given Bending Stress of Hollow Shaft Formula