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Diameter of Shaft given Permissible Value of Maximum Principle Stress Formula

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Diameter of Shaft from MPST is the diameter of a shaft calculated based on maximum shear stress theory, considering the principal stress theory's principles. Check FAQs

d MPST = {(\frac{16}{π \cdot σ max} \cdot (M b + \sqrt{{M b}^{2} + {Mt shaft}^{2}}))}^{\frac{1}{3}}

d_MPST - Diameter of Shaft from MPST?σ_max - Maximum Principle Stress in Shaft?M_b - Bending Moment in Shaft?Mt_shaft - Torsional Moment in Shaft?π - Archimedes' constant?

Diameter of Shaft given Permissible Value of Maximum Principle Stress Example

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Here is how the Diameter of Shaft given Permissible Value of Maximum Principle Stress equation looks like with Values.

Here is how the Diameter of Shaft given Permissible Value of Maximum Principle Stress equation looks like with Units.

Here is how the Diameter of Shaft given Permissible Value of Maximum Principle Stress equation looks like.

51.5062 = {(\frac{16}{3.1416 \cdot 135.3} \cdot (1.8E+6 + \sqrt{{1.8E+6}^{2} + 330000^{2}}))}^{\frac{1}{3}}

51.5062mm = {(\frac{16}{3.1416 \cdot 135.3N/mm²} \cdot (1.8E+6N*mm + \sqrt{{1.8E+6N*mm}^{2} + {330000N*mm}^{2}}))}^{\frac{1}{3}}

51.5062 = {(\frac{16}{3.1416 \cdot 135.3} \cdot (1.8E+6 + \sqrt{{1.8E+6}^{2} + 330000^{2}}))}^{\frac{1}{3}}

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Diameter of Shaft given Permissible Value of Maximum Principle Stress Solution

Follow our step by step solution on how to calculate Diameter of Shaft given Permissible Value of Maximum Principle Stress?

FIRST Step Consider the formula

d MPST = {(\frac{16}{π \cdot σ max} \cdot (M b + \sqrt{{M b}^{2} + {Mt shaft}^{2}}))}^{\frac{1}{3}}

Next Step Substitute values of Variables

∴

d MPST = {(\frac{16}{π \cdot 135.3N/mm²} \cdot (1.8E+6N*mm + \sqrt{{1.8E+6N*mm}^{2} + {330000N*mm}^{2}}))}^{\frac{1}{3}}

Next Step Substitute values of Constants

∴

d MPST = {(\frac{16}{3.1416 \cdot 135.3N/mm²} \cdot (1.8E+6N*mm + \sqrt{{1.8E+6N*mm}^{2} + {330000N*mm}^{2}}))}^{\frac{1}{3}}

Next Step Convert Units

∴

d MPST = {(\frac{16}{3.1416 \cdot 1.4E+8Pa} \cdot (1800N*m + \sqrt{{1800N*m}^{2} + {330N*m}^{2}}))}^{\frac{1}{3}}

Next Step Prepare to Evaluate

∴

d MPST = {(\frac{16}{3.1416 \cdot 1.4E+8} \cdot (1800 + \sqrt{1800^{2} + 330^{2}}))}^{\frac{1}{3}}

Next Step Evaluate

∴

d MPST = 0.0515062161581043m

Next Step Convert to Output's Unit

∴

d MPST = 51.5062161581043mm

LAST Step Rounding Answer

∴

d MPST = 51.5062mm

Diameter of Shaft given Permissible Value of Maximum Principle Stress Formula Elements

Variables

Constants

Functions

Diameter of Shaft from MPST

Diameter of Shaft from MPST is the diameter of a shaft calculated based on maximum shear stress theory, considering the principal stress theory's principles.

Symbol: d_MPST

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Diameter of Shaft from MPST

Maximum Principle Stress in Shaft

Maximum Principle Stress in Shaft is the maximum normal stress a shaft can withstand without yielding, calculated based on maximum shear stress theory.

Symbol: σ_max

Measurement: StressUnit: N/mm²

Note: Value should be greater than 0.

Formulas to find Maximum Principle Stress in Shaft

Bending Moment in Shaft

Bending Moment in Shaft is the maximum twisting force that causes shear stress in a shaft, leading to deformation and potential failure.

Symbol: M_b

Measurement: TorqueUnit: N*mm

Note: Value should be greater than 0.

Formulas to find Bending Moment in Shaft

Torsional Moment in Shaft

Torsional Moment in Shaft is the maximum twisting moment that a shaft can withstand without failing, related to maximum shear stress and principal stress theory.

Symbol: Mt_shaft

Measurement: TorqueUnit: N*mm

Note: Value should be greater than 0.

Formulas to find Torsional Moment in 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 in Maximum Shear Stress and Principal Stress Theory category

Go Permissible Value of Maximum Principle Stress

σ max = \frac{16}{π \cdot {d MPST}^{3}} \cdot (M b + \sqrt{{M b}^{2} + {Mt shaft}^{2}})

Go Permissible Value of Maximum Principle Stress using Factor of Safety

σ max = \frac{F ce}{fos shaft}

Go Factor of Safety given Permissible Value of Maximum Principle Stress

fos shaft = \frac{F ce}{σ max}

Go Yield Stress in Shear given Permissible Value of Maximum Principle Stress

F ce = σ max \cdot fos shaft

How to Evaluate Diameter of Shaft given Permissible Value of Maximum Principle Stress?

Diameter of Shaft given Permissible Value of Maximum Principle Stress evaluator uses Diameter of Shaft from MPST = (16/(pi*Maximum Principle Stress in Shaft)*(Bending Moment in Shaft+sqrt(Bending Moment in Shaft^2+Torsional Moment in Shaft^2)))^(1/3) to evaluate the Diameter of Shaft from MPST, Diameter of Shaft given Permissible Value of Maximum Principle Stress formula is defined as a measure of the diameter of a shaft based on the maximum principle stress it can withstand, taking into account the bending moment and torsional moment of the shaft, providing a safe and reliable design for mechanical systems. Diameter of Shaft from MPST is denoted by d_MPST symbol.

How to evaluate Diameter of Shaft given Permissible Value of Maximum Principle Stress using this online evaluator? To use this online evaluator for Diameter of Shaft given Permissible Value of Maximum Principle Stress, enter Maximum Principle Stress in Shaft (σ_max), Bending Moment in Shaft (M_b) & Torsional Moment in Shaft (Mt_shaft) and hit the calculate button.

FAQs on Diameter of Shaft given Permissible Value of Maximum Principle Stress

What is the formula to find Diameter of Shaft given Permissible Value of Maximum Principle Stress?

The formula of Diameter of Shaft given Permissible Value of Maximum Principle Stress is expressed as Diameter of Shaft from MPST = (16/(pi*Maximum Principle Stress in Shaft)*(Bending Moment in Shaft+sqrt(Bending Moment in Shaft^2+Torsional Moment in Shaft^2)))^(1/3). Here is an example- 51506.22 = (16/(pi*135300000)*(1800+sqrt(1800^2+330^2)))^(1/3).

How to calculate Diameter of Shaft given Permissible Value of Maximum Principle Stress?

With Maximum Principle Stress in Shaft (σ_max), Bending Moment in Shaft (M_b) & Torsional Moment in Shaft (Mt_shaft) we can find Diameter of Shaft given Permissible Value of Maximum Principle Stress using the formula - Diameter of Shaft from MPST = (16/(pi*Maximum Principle Stress in Shaft)*(Bending Moment in Shaft+sqrt(Bending Moment in Shaft^2+Torsional Moment in Shaft^2)))^(1/3). This formula also uses Archimedes' constant and Square Root (sqrt) function(s).

Can the Diameter of Shaft given Permissible Value of Maximum Principle Stress be negative?

No, the Diameter of Shaft given Permissible Value of Maximum Principle Stress, measured in Length cannot be negative.

Which unit is used to measure Diameter of Shaft given Permissible Value of Maximum Principle Stress?

Diameter of Shaft given Permissible Value of Maximum Principle Stress is usually measured using the Millimeter[mm] for Length. Meter[mm], Kilometer[mm], Decimeter[mm] are the few other units in which Diameter of Shaft given Permissible Value of Maximum Principle Stress can be measured.

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Diameter of Shaft given Permissible Value of Maximum Principle Stress Formula

Diameter of Shaft given Permissible Value of Maximum Principle Stress Example

Diameter of Shaft given Permissible Value of Maximum Principle Stress Solution

Diameter of Shaft given Permissible Value of Maximum Principle Stress Formula Elements

Other formulas in Maximum Shear Stress and Principal Stress Theory category

How to Evaluate Diameter of Shaft given Permissible Value of Maximum Principle Stress?

FAQs on Diameter of Shaft given Permissible Value of Maximum Principle Stress

Variable Name