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Outer Diameter of Hollow Shaft given Principle Stress 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 = {(16 \cdot \frac{M b h + \sqrt{{M b h}^{2} + {Mt hollowshaft}^{2}}}{π \cdot τ \cdot (1 - C^{4})})}^{\frac{1}{3}}

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

Outer Diameter of Hollow Shaft given Principle Stress Example

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Here is how the Outer Diameter of Hollow Shaft given Principle Stress equation looks like with Values.

Here is how the Outer Diameter of Hollow Shaft given Principle Stress equation looks like with Units.

Here is how the Outer Diameter of Hollow Shaft given Principle Stress equation looks like.

46.0071 = {(16 \cdot \frac{550000 + \sqrt{550000^{2} + 320000^{2}}}{3.1416 \cdot 129.8 \cdot (1 - {0.85}^{4})})}^{\frac{1}{3}}

46.0071mm = {(16 \cdot \frac{550000N*mm + \sqrt{{550000N*mm}^{2} + {320000N*mm}^{2}}}{3.1416 \cdot 129.8N/mm² \cdot (1 - {0.85}^{4})})}^{\frac{1}{3}}

46.0071 = {(16 \cdot \frac{550000 + \sqrt{550000^{2} + 320000^{2}}}{3.1416 \cdot 129.8 \cdot (1 - {0.85}^{4})})}^{\frac{1}{3}}

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Outer Diameter of Hollow Shaft given Principle Stress Solution

Follow our step by step solution on how to calculate Outer Diameter of Hollow Shaft given Principle Stress?

FIRST Step Consider the formula

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}}

Next Step Substitute values of Variables

∴

d o = {(16 \cdot \frac{550000N*mm + \sqrt{{550000N*mm}^{2} + {320000N*mm}^{2}}}{π \cdot 129.8N/mm² \cdot (1 - {0.85}^{4})})}^{\frac{1}{3}}

Next Step Substitute values of Constants

∴

d o = {(16 \cdot \frac{550000N*mm + \sqrt{{550000N*mm}^{2} + {320000N*mm}^{2}}}{3.1416 \cdot 129.8N/mm² \cdot (1 - {0.85}^{4})})}^{\frac{1}{3}}

Next Step Convert Units

∴

d o = {(16 \cdot \frac{550N*m + \sqrt{{550N*m}^{2} + {320N*m}^{2}}}{3.1416 \cdot 1.3E+8Pa \cdot (1 - {0.85}^{4})})}^{\frac{1}{3}}

Next Step Prepare to Evaluate

∴

d o = {(16 \cdot \frac{550 + \sqrt{550^{2} + 320^{2}}}{3.1416 \cdot 1.3E+8 \cdot (1 - {0.85}^{4})})}^{\frac{1}{3}}

Next Step Evaluate

∴

d o = 0.046007084849036m

Next Step Convert to Output's Unit

∴

d o = 46.007084849036mm

LAST Step Rounding Answer

∴

d o = 46.0071mm

Outer Diameter of Hollow Shaft given Principle Stress Formula Elements

Variables

Constants

Functions

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

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

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

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

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 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 Angle of Twist Torsional Rigidity

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

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 Principle Stress?

Outer Diameter of Hollow Shaft given Principle Stress evaluator uses Outer Diameter of Hollow Shaft = (16*(Bending Moment in Hollow Shaft+sqrt(Bending Moment in Hollow Shaft^2+Torsional Moment in Hollow Shaft^2))/(pi*Maximum Principle Stress in Hollow Shaft*(1-Ratio of Inner to Outer Diameter of Hollow Shaft^4)))^(1/3) to evaluate the Outer Diameter of Hollow Shaft, Outer Diameter of Hollow Shaft given Principle Stress formula is defined as a measure of the outer diameter of a hollow shaft, which is a critical parameter in the design of hollow shafts, taking into account the principle stress, bending moment, and torque, to ensure the shaft's structural integrity and performance. Outer Diameter of Hollow Shaft is denoted by d_o symbol.

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

FAQs on Outer Diameter of Hollow Shaft given Principle Stress

What is the formula to find Outer Diameter of Hollow Shaft given Principle Stress?

The formula of Outer Diameter of Hollow Shaft given Principle Stress is expressed as Outer Diameter of Hollow Shaft = (16*(Bending Moment in Hollow Shaft+sqrt(Bending Moment in Hollow Shaft^2+Torsional Moment in Hollow Shaft^2))/(pi*Maximum Principle Stress in Hollow Shaft*(1-Ratio of Inner to Outer Diameter of Hollow Shaft^4)))^(1/3). Here is an example- 46007.08 = (16*(550+sqrt(550^2+320^2))/(pi*129800000*(1-0.85^4)))^(1/3).

How to calculate Outer Diameter of Hollow Shaft given Principle Stress?

With Bending Moment in Hollow Shaft (M_{b h}), Torsional Moment in Hollow Shaft (Mt_hollowshaft), Maximum Principle Stress in Hollow Shaft (τ) & Ratio of Inner to Outer Diameter of Hollow Shaft (C) we can find Outer Diameter of Hollow Shaft given Principle Stress using the formula - Outer Diameter of Hollow Shaft = (16*(Bending Moment in Hollow Shaft+sqrt(Bending Moment in Hollow Shaft^2+Torsional Moment in Hollow Shaft^2))/(pi*Maximum Principle Stress in Hollow Shaft*(1-Ratio of Inner to Outer Diameter of Hollow Shaft^4)))^(1/3). This formula also uses Archimedes' constant and Square Root (sqrt) function(s).

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 Principle Stress be negative?

No, the Outer Diameter of Hollow Shaft given Principle Stress, measured in Length cannot be negative.

Which unit is used to measure Outer Diameter of Hollow Shaft given Principle Stress?

Outer Diameter of Hollow Shaft given Principle Stress 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 Principle Stress can be measured.

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Outer Diameter of Hollow Shaft given Principle Stress 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 Principle Stress Example

Outer Diameter of Hollow Shaft given Principle Stress Solution

Outer Diameter of Hollow Shaft given Principle Stress 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 Principle Stress?

FAQs on Outer Diameter of Hollow Shaft given Principle Stress

Variable Name

GoOuter Diameter given Ratio of Diameters Formula

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