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Permissible Value of Maximum Principle Stress Formula

GoPermissible Value of Maximum Principle Stress using Factor of Safety Formula

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

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

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

Permissible Value of Maximum Principle Stress Example

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

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

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

135.349 = \frac{16}{3.1416 \cdot {51.5}^{3}} \cdot (1.8E+6 + \sqrt{{1.8E+6}^{2} + 330000^{2}})

135.349N/mm² = \frac{16}{3.1416 \cdot {51.5mm}^{3}} \cdot (1.8E+6N*mm + \sqrt{{1.8E+6N*mm}^{2} + {330000N*mm}^{2}})

135.349 = \frac{16}{3.1416 \cdot {51.5}^{3}} \cdot (1.8E+6 + \sqrt{{1.8E+6}^{2} + 330000^{2}})

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Permissible Value of Maximum Principle Stress Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

σ max = \frac{16}{π \cdot {51.5mm}^{3}} \cdot (1.8E+6N*mm + \sqrt{{1.8E+6N*mm}^{2} + {330000N*mm}^{2}})

Next Step Substitute values of Constants

∴

σ max = \frac{16}{3.1416 \cdot {51.5mm}^{3}} \cdot (1.8E+6N*mm + \sqrt{{1.8E+6N*mm}^{2} + {330000N*mm}^{2}})

Next Step Convert Units

∴

σ max = \frac{16}{3.1416 \cdot {0.0515m}^{3}} \cdot (1800N*m + \sqrt{{1800N*m}^{2} + {330N*m}^{2}})

Next Step Prepare to Evaluate

∴

σ max = \frac{16}{3.1416 \cdot {0.0515}^{3}} \cdot (1800 + \sqrt{1800^{2} + 330^{2}})

Next Step Evaluate

∴

σ max = 135348998.895824Pa

Next Step Convert to Output's Unit

∴

σ max = 135.348998895824N/mm²

LAST Step Rounding Answer

∴

σ max = 135.349N/mm²

Permissible Value of Maximum Principle Stress Formula Elements

Variables

Constants

Functions

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

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

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 to find Maximum Principle Stress in Shaft

Go Permissible Value of Maximum Principle Stress using Factor of Safety

σ max = \frac{F ce}{fos shaft}

Other formulas in Maximum Shear Stress and Principal Stress Theory category

Go Diameter of Shaft given Permissible Value of Maximum Principle Stress

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

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

Go Maximum Shear Stress in Shafts

𝜏 max MSST = \frac{16}{π \cdot {d MSST}^{3}} \cdot \sqrt{{M b MSST}^{2} + {Mt t}^{2}}

How to Evaluate Permissible Value of Maximum Principle Stress?

Permissible Value of Maximum Principle Stress evaluator uses Maximum Principle Stress in Shaft = 16/(pi*Diameter of Shaft from MPST^3)*(Bending Moment in Shaft+sqrt(Bending Moment in Shaft^2+Torsional Moment in Shaft^2)) to evaluate the Maximum Principle Stress in Shaft, Permissible Value of Maximum Principle Stress formula is defined as a measure of the maximum stress a material can withstand without failing, considering the bending moment and torsional moment of a shaft, providing a critical value to ensure the structural integrity of a mechanical component. Maximum Principle Stress in Shaft is denoted by σ_max symbol.

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

FAQs on Permissible Value of Maximum Principle Stress

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

The formula of Permissible Value of Maximum Principle Stress is expressed as Maximum Principle Stress in Shaft = 16/(pi*Diameter of Shaft from MPST^3)*(Bending Moment in Shaft+sqrt(Bending Moment in Shaft^2+Torsional Moment in Shaft^2)). Here is an example- 0.000135 = 16/(pi*0.0515^3)*(1800+sqrt(1800^2+330^2)).

How to calculate Permissible Value of Maximum Principle Stress?

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

What are the other ways to Calculate Maximum Principle Stress in Shaft?

Here are the different ways to Calculate Maximum Principle Stress in Shaft-

Maximum Principle Stress in Shaft=Yield Strength in Shaft from MPST/Factor of Safety of Shaft

Can the Permissible Value of Maximum Principle Stress be negative?

No, the Permissible Value of Maximum Principle Stress, measured in Stress cannot be negative.

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

Permissible Value of Maximum Principle Stress is usually measured using the Newton per Square Millimeter[N/mm²] for Stress. Pascal[N/mm²], Newton per Square Meter[N/mm²], Kilonewton per Square Meter[N/mm²] are the few other units in which Permissible Value of Maximum Principle Stress can be measured.

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Permissible Value of Maximum Principle Stress Formula

​GoPermissible Value of Maximum Principle Stress using Factor of Safety Formula

Permissible Value of Maximum Principle Stress Example

Permissible Value of Maximum Principle Stress Solution

Permissible Value of Maximum Principle Stress Formula Elements

Other Formulas to find Maximum Principle Stress in Shaft

Other formulas in Maximum Shear Stress and Principal Stress Theory category

How to Evaluate Permissible Value of Maximum Principle Stress?

FAQs on Permissible Value of Maximum Principle Stress

Variable Name

GoPermissible Value of Maximum Principle Stress using Factor of Safety Formula