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Ratio of Diameters given Principle Stress Formula

GoRatio of Inner Diameter to Outer Diameter Formula

GoRatio of Diameters given Tensile Stress in 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 = {(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}}

C - Ratio of Inner to Outer Diameter of Hollow Shaft?M_{b h} - Bending Moment in Hollow Shaft?Mt_hollowshaft - Torsional Moment in Hollow Shaft?d_o - Outer Diameter of Hollow Shaft?τ - Maximum Principle Stress in Hollow Shaft?π - Archimedes' constant?

Ratio of Diameters given Principle Stress Example

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Here is how the Ratio of Diameters given Principle Stress equation looks like with Values.

Here is how the Ratio of Diameters given Principle Stress equation looks like with Units.

Here is how the Ratio of Diameters given Principle Stress equation looks like.

0.8499 = {(1 - 16 \cdot \frac{550000 + \sqrt{550000^{2} + 320000^{2}}}{3.1416 \cdot 46^{3} \cdot 129.8})}^{\frac{1}{4}}

0.8499 = {(1 - 16 \cdot \frac{550000N*mm + \sqrt{{550000N*mm}^{2} + {320000N*mm}^{2}}}{3.1416 \cdot {46mm}^{3} \cdot 129.8N/mm²})}^{\frac{1}{4}}

0.8499 = {(1 - 16 \cdot \frac{550000 + \sqrt{550000^{2} + 320000^{2}}}{3.1416 \cdot 46^{3} \cdot 129.8})}^{\frac{1}{4}}

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Ratio of Diameters given Principle Stress Solution

Follow our step by step solution on how to calculate Ratio of Diameters given Principle Stress?

FIRST Step Consider the formula

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}}

Next Step Substitute values of Variables

∴

C = {(1 - 16 \cdot \frac{550000N*mm + \sqrt{{550000N*mm}^{2} + {320000N*mm}^{2}}}{π \cdot {46mm}^{3} \cdot 129.8N/mm²})}^{\frac{1}{4}}

Next Step Substitute values of Constants

∴

C = {(1 - 16 \cdot \frac{550000N*mm + \sqrt{{550000N*mm}^{2} + {320000N*mm}^{2}}}{3.1416 \cdot {46mm}^{3} \cdot 129.8N/mm²})}^{\frac{1}{4}}

Next Step Convert Units

∴

C = {(1 - 16 \cdot \frac{550N*m + \sqrt{{550N*m}^{2} + {320N*m}^{2}}}{3.1416 \cdot {0.046m}^{3} \cdot 1.3E+8Pa})}^{\frac{1}{4}}

Next Step Prepare to Evaluate

∴

C = {(1 - 16 \cdot \frac{550 + \sqrt{550^{2} + 320^{2}}}{3.1416 \cdot {0.046}^{3} \cdot 1.3E+8})}^{\frac{1}{4}}

Next Step Evaluate

∴

C = 0.849910063643594

LAST Step Rounding Answer

∴

C = 0.8499

Ratio of Diameters given Principle Stress 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

Bending Moment in Hollow Shaft

Bending 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 bend.

Symbol: M_{b h}

Measurement: TorqueUnit: N*mm

Note: Value should be greater than 0.

Formulas to find Bending Moment in 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

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

Maximum Principle Stress in Hollow Shaft

Maximum Principle Stress in Hollow Shaft is defined as the normal stress calculated at an angle when shear stress is considered zero.

Symbol: τ

Measurement: StressUnit: N/mm²

Note: Value should be greater than 0.

Formulas to find Maximum Principle Stress in 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 Tensile Stress in Hollow Shaft

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

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}}

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 Principle Stress?

Ratio of Diameters given Principle Stress evaluator uses Ratio of Inner to Outer Diameter of Hollow Shaft = (1-16*(Bending Moment in Hollow Shaft+sqrt(Bending Moment in Hollow Shaft^2+Torsional Moment in Hollow Shaft^2))/(pi*Outer Diameter of Hollow Shaft^3*Maximum Principle Stress in Hollow Shaft))^(1/4) to evaluate the Ratio of Inner to Outer Diameter of Hollow Shaft, Ratio of Diameters given Principle Stress formula is defined as a dimensionless quantity used in the design of hollow shafts to determine the optimal diameter ratio, considering the principle stresses and material properties, to ensure the structural integrity and performance of the shaft under various loading conditions. Ratio of Inner to Outer Diameter of Hollow Shaft is denoted by C symbol.

How to evaluate Ratio of Diameters given Principle Stress using this online evaluator? To use this online evaluator for Ratio of Diameters given Principle Stress, enter Bending Moment in Hollow Shaft (M_{b h}), Torsional Moment in Hollow Shaft (Mt_hollowshaft), Outer Diameter of Hollow Shaft (d_o) & Maximum Principle Stress in Hollow Shaft (τ) and hit the calculate button.

FAQs on Ratio of Diameters given Principle Stress

What is the formula to find Ratio of Diameters given Principle Stress?

The formula of Ratio of Diameters given Principle Stress is expressed as Ratio of Inner to Outer Diameter of Hollow Shaft = (1-16*(Bending Moment in Hollow Shaft+sqrt(Bending Moment in Hollow Shaft^2+Torsional Moment in Hollow Shaft^2))/(pi*Outer Diameter of Hollow Shaft^3*Maximum Principle Stress in Hollow Shaft))^(1/4). Here is an example- 0.84991 = (1-16*(550+sqrt(550^2+320^2))/(pi*0.046^3*129800000))^(1/4).

How to calculate Ratio of Diameters given Principle Stress?

With Bending Moment in Hollow Shaft (M_{b h}), Torsional Moment in Hollow Shaft (Mt_hollowshaft), Outer Diameter of Hollow Shaft (d_o) & Maximum Principle Stress in Hollow Shaft (τ) we can find Ratio of Diameters given Principle Stress using the formula - Ratio of Inner to Outer Diameter of Hollow Shaft = (1-16*(Bending Moment in Hollow Shaft+sqrt(Bending Moment in Hollow Shaft^2+Torsional Moment in Hollow Shaft^2))/(pi*Outer Diameter of Hollow Shaft^3*Maximum Principle Stress in Hollow Shaft))^(1/4). 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=sqrt(1-(Axial Force on Hollow Shaft/(pi/4*Tensile Stress in Hollow Shaft*Outer Diameter of Hollow Shaft^2)))
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)

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: Unit

Ratio of Diameters given Principle Stress Formula

​GoRatio of Inner Diameter to Outer Diameter Formula

​GoRatio of Diameters given Tensile Stress in Hollow Shaft Formula

Ratio of Diameters given Principle Stress Example

Ratio of Diameters given Principle Stress Solution

Ratio of Diameters given Principle Stress 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 Principle Stress?

FAQs on Ratio of Diameters given Principle Stress

Variable Name

GoRatio of Inner Diameter to Outer Diameter Formula

GoRatio of Diameters given Tensile Stress in Hollow Shaft Formula