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Outside Diameter of Hollow Shaft based on Equivalent Twisting Moment Formula

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

d o = {((T e) \cdot (\frac{16}{π}) \cdot \frac{1}{(f s) \cdot (1 - k^{4})})}^{\frac{1}{3}}

d_o - Hollow Shaft Outer Diameter?T_e - Equivalent Twisting Moment?f_s - Torsional Shear Stress in Shaft?k - Ratio of Inner to Outer Diameter of Hollow Shaft?π - Archimedes' constant?

Outside Diameter of Hollow Shaft based on Equivalent Twisting Moment Example

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Here is how the Outside Diameter of Hollow Shaft based on Equivalent Twisting Moment equation looks like with Values.

Here is how the Outside Diameter of Hollow Shaft based on Equivalent Twisting Moment equation looks like with Units.

Here is how the Outside Diameter of Hollow Shaft based on Equivalent Twisting Moment equation looks like.

27.5618 = {((900000) \cdot (\frac{16}{3.1416}) \cdot \frac{1}{(458) \cdot (1 - {0.85}^{4})})}^{\frac{1}{3}}

27.5618mm = {((900000N*mm) \cdot (\frac{16}{3.1416}) \cdot \frac{1}{(458N/mm²) \cdot (1 - {0.85}^{4})})}^{\frac{1}{3}}

27.5618 = {((900000) \cdot (\frac{16}{3.1416}) \cdot \frac{1}{(458) \cdot (1 - {0.85}^{4})})}^{\frac{1}{3}}

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Outside Diameter of Hollow Shaft based on Equivalent Twisting Moment Solution

Follow our step by step solution on how to calculate Outside Diameter of Hollow Shaft based on Equivalent Twisting Moment?

FIRST Step Consider the formula

d o = {((T e) \cdot (\frac{16}{π}) \cdot \frac{1}{(f s) \cdot (1 - k^{4})})}^{\frac{1}{3}}

Next Step Substitute values of Variables

∴

d o = {((900000N*mm) \cdot (\frac{16}{π}) \cdot \frac{1}{(458N/mm²) \cdot (1 - {0.85}^{4})})}^{\frac{1}{3}}

Next Step Substitute values of Constants

∴

d o = {((900000N*mm) \cdot (\frac{16}{3.1416}) \cdot \frac{1}{(458N/mm²) \cdot (1 - {0.85}^{4})})}^{\frac{1}{3}}

Next Step Convert Units

∴

d o = {((900N*m) \cdot (\frac{16}{3.1416}) \cdot \frac{1}{(4.6E+8Pa) \cdot (1 - {0.85}^{4})})}^{\frac{1}{3}}

Next Step Prepare to Evaluate

∴

d o = {((900) \cdot (\frac{16}{3.1416}) \cdot \frac{1}{(4.6E+8) \cdot (1 - {0.85}^{4})})}^{\frac{1}{3}}

Next Step Evaluate

∴

d o = 0.0275618463800726m

Next Step Convert to Output's Unit

∴

d o = 27.5618463800726mm

LAST Step Rounding Answer

∴

d o = 27.5618mm

Outside Diameter of Hollow Shaft based on Equivalent Twisting Moment Formula Elements

Variables

Constants

Hollow Shaft Outer Diameter

Hollow Shaft Outer Diameter 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 Hollow Shaft Outer Diameter

Equivalent Twisting Moment

Equivalent Twisting Moment that alone produces maximum shear stress equal to the maximum shear stress produce due to combined bending and torsion.

Symbol: T_e

Measurement: Moment of ForceUnit: N*mm

Note: Value should be greater than 0.

Formulas to find Equivalent Twisting Moment

Torsional Shear Stress in Shaft

Torsional Shear Stress in Shaft is the shear stress produced in the shaft due to the twisting.

Symbol: f_s

Measurement: StressUnit: N/mm²

Note: Value should be greater than 0.

Formulas to find Torsional Shear Stress in 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: k

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

Other formulas in Design of Agitation System Components category

Go Equivalent Twisting Moment for Solid Shaft

Te solidshaft = (\sqrt{({M m}^{2}) + ({T m}^{2})})

Go Equivalent Twisting Moment for Hollow Shaft

Te hollowshaft = (\frac{π}{16}) \cdot (f b) \cdot ({d o}^{3}) \cdot (1 - k^{4})

Go Equivalent Bending Moment for Solid Shaft

Me solidshaft = (\frac{1}{2}) \cdot (M m + \sqrt{{M m}^{2} + {T m}^{2}})

Go Equivalent Bending Moment for Hollow Shaft

Me hollowshaft = (\frac{π}{32}) \cdot (f b) \cdot ({d o}^{3}) \cdot (1 - k^{4})

How to Evaluate Outside Diameter of Hollow Shaft based on Equivalent Twisting Moment?

Outside Diameter of Hollow Shaft based on Equivalent Twisting Moment evaluator uses Hollow Shaft Outer Diameter = ((Equivalent Twisting Moment)*(16/pi)*(1)/((Torsional Shear Stress in Shaft)*(1-Ratio of Inner to Outer Diameter of Hollow Shaft^4)))^(1/3) to evaluate the Hollow Shaft Outer Diameter, The Outside Diameter of Hollow Shaft based on Equivalent Twisting Moment formula is defined as with respect to the twisting moment that alone produce produce maximum shear stress equal to the maximum shear stress produce due to combined bending and torsion. Hollow Shaft Outer Diameter is denoted by d_o symbol.

How to evaluate Outside Diameter of Hollow Shaft based on Equivalent Twisting Moment using this online evaluator? To use this online evaluator for Outside Diameter of Hollow Shaft based on Equivalent Twisting Moment, enter Equivalent Twisting Moment (T_e), Torsional Shear Stress in Shaft (f_s) & Ratio of Inner to Outer Diameter of Hollow Shaft (k) and hit the calculate button.

FAQs on Outside Diameter of Hollow Shaft based on Equivalent Twisting Moment

What is the formula to find Outside Diameter of Hollow Shaft based on Equivalent Twisting Moment?

The formula of Outside Diameter of Hollow Shaft based on Equivalent Twisting Moment is expressed as Hollow Shaft Outer Diameter = ((Equivalent Twisting Moment)*(16/pi)*(1)/((Torsional Shear Stress in Shaft)*(1-Ratio of Inner to Outer Diameter of Hollow Shaft^4)))^(1/3). Here is an example- 27561.85 = ((900)*(16/pi)*(1)/((458000000)*(1-0.85^4)))^(1/3).

How to calculate Outside Diameter of Hollow Shaft based on Equivalent Twisting Moment?

With Equivalent Twisting Moment (T_e), Torsional Shear Stress in Shaft (f_s) & Ratio of Inner to Outer Diameter of Hollow Shaft (k) we can find Outside Diameter of Hollow Shaft based on Equivalent Twisting Moment using the formula - Hollow Shaft Outer Diameter = ((Equivalent Twisting Moment)*(16/pi)*(1)/((Torsional Shear Stress in Shaft)*(1-Ratio of Inner to Outer Diameter of Hollow Shaft^4)))^(1/3). This formula also uses Archimedes' constant .

Can the Outside Diameter of Hollow Shaft based on Equivalent Twisting Moment be negative?

No, the Outside Diameter of Hollow Shaft based on Equivalent Twisting Moment, measured in Length cannot be negative.

Which unit is used to measure Outside Diameter of Hollow Shaft based on Equivalent Twisting Moment?

Outside Diameter of Hollow Shaft based on Equivalent Twisting Moment is usually measured using the Millimeter[mm] for Length. Meter[mm], Kilometer[mm], Decimeter[mm] are the few other units in which Outside Diameter of Hollow Shaft based on Equivalent Twisting Moment can be measured.

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Outside Diameter of Hollow Shaft based on Equivalent Twisting Moment Formula

Outside Diameter of Hollow Shaft based on Equivalent Twisting Moment Example

Outside Diameter of Hollow Shaft based on Equivalent Twisting Moment Solution

Outside Diameter of Hollow Shaft based on Equivalent Twisting Moment Formula Elements

Other formulas in Design of Agitation System Components category

How to Evaluate Outside Diameter of Hollow Shaft based on Equivalent Twisting Moment?

FAQs on Outside Diameter of Hollow Shaft based on Equivalent Twisting Moment

Variable Name