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Diameter of Shaft given Principle Shear Stress Maximum Shear Stress Theory Formula

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Diameter of Shaft from MSST is the diameter of a shaft calculated based on maximum shear stress theory to determine the shaft's strength and stability. Check FAQs

d MSST = {(\frac{16}{π \cdot 𝜏 max MSST} \cdot \sqrt{{M b MSST}^{2} + {Mt t}^{2}})}^{\frac{1}{3}}

d_MSST - Diameter of Shaft from MSST?𝜏_{max MSST} - Maximum Shear Stress in Shaft from MSST?M_{b MSST} - Bending Moment in Shaft for MSST?Mt_t - Torsional Moment in Shaft for MSST?π - Archimedes' constant?

Diameter of Shaft given Principle Shear Stress Maximum Shear Stress Theory Example

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

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

Here is how the Diameter of Shaft given Principle Shear Stress Maximum Shear Stress Theory equation looks like.

45 = {(\frac{16}{3.1416 \cdot 58.9} \cdot \sqrt{980000^{2} + {387582.1}^{2}})}^{\frac{1}{3}}

45mm = {(\frac{16}{3.1416 \cdot 58.9N/mm²} \cdot \sqrt{{980000N*mm}^{2} + {387582.1N*mm}^{2}})}^{\frac{1}{3}}

45 = {(\frac{16}{3.1416 \cdot 58.9} \cdot \sqrt{980000^{2} + {387582.1}^{2}})}^{\frac{1}{3}}

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Diameter of Shaft given Principle Shear Stress Maximum Shear Stress Theory Solution

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

FIRST Step Consider the formula

d MSST = {(\frac{16}{π \cdot 𝜏 max MSST} \cdot \sqrt{{M b MSST}^{2} + {Mt t}^{2}})}^{\frac{1}{3}}

Next Step Substitute values of Variables

∴

d MSST = {(\frac{16}{π \cdot 58.9N/mm²} \cdot \sqrt{{980000N*mm}^{2} + {387582.1N*mm}^{2}})}^{\frac{1}{3}}

Next Step Substitute values of Constants

∴

d MSST = {(\frac{16}{3.1416 \cdot 58.9N/mm²} \cdot \sqrt{{980000N*mm}^{2} + {387582.1N*mm}^{2}})}^{\frac{1}{3}}

Next Step Convert Units

∴

d MSST = {(\frac{16}{3.1416 \cdot 5.9E+7Pa} \cdot \sqrt{{980N*m}^{2} + {387.5821N*m}^{2}})}^{\frac{1}{3}}

Next Step Prepare to Evaluate

∴

d MSST = {(\frac{16}{3.1416 \cdot 5.9E+7} \cdot \sqrt{980^{2} + {387.5821}^{2}})}^{\frac{1}{3}}

Next Step Evaluate

∴

d MSST = 0.0449999998686723m

Next Step Convert to Output's Unit

∴

d MSST = 44.9999998686723mm

LAST Step Rounding Answer

∴

d MSST = 45mm

Diameter of Shaft given Principle Shear Stress Maximum Shear Stress Theory Formula Elements

Variables

Constants

Functions

Diameter of Shaft from MSST

Diameter of Shaft from MSST is the diameter of a shaft calculated based on maximum shear stress theory to determine the shaft's strength and stability.

Symbol: d_MSST

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Diameter of Shaft from MSST

Maximum Shear Stress in Shaft from MSST

Maximum Shear Stress in Shaft from MSST is the maximum shear stress developed in a shaft due to twisting or torsional loading, affecting its structural integrity.

Symbol: 𝜏_{max MSST}

Measurement: StressUnit: N/mm²

Note: Value should be greater than 0.

Formulas to find Maximum Shear Stress in Shaft from MSST

Bending Moment in Shaft for MSST

Bending Moment in Shaft for MSST is the maximum twisting force that causes shear stress in a shaft, affecting its structural integrity and stability.

Symbol: M_{b MSST}

Measurement: TorqueUnit: N*mm

Note: Value should be greater than 0.

Formulas to find Bending Moment in Shaft for MSST

Torsional Moment in Shaft for MSST

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

Symbol: Mt_t

Measurement: TorqueUnit: N*mm

Note: Value should be greater than 0.

Formulas to find Torsional Moment in Shaft for MSST

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 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 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}

How to Evaluate Diameter of Shaft given Principle Shear Stress Maximum Shear Stress Theory?

Diameter of Shaft given Principle Shear Stress Maximum Shear Stress Theory evaluator uses Diameter of Shaft from MSST = (16/(pi*Maximum Shear Stress in Shaft from MSST)*sqrt(Bending Moment in Shaft for MSST^2+Torsional Moment in Shaft for MSST^2))^(1/3) to evaluate the Diameter of Shaft from MSST, Diameter of Shaft given Principle Shear Stress Maximum Shear Stress Theory formula is defined as a measure of the diameter of a shaft under maximum shear stress, considering the principal stress theory, which is essential in mechanical engineering to design and analyze shafts for various applications. Diameter of Shaft from MSST is denoted by d_MSST symbol.

How to evaluate Diameter of Shaft given Principle Shear Stress Maximum Shear Stress Theory using this online evaluator? To use this online evaluator for Diameter of Shaft given Principle Shear Stress Maximum Shear Stress Theory, enter Maximum Shear Stress in Shaft from MSST (𝜏_{max MSST}), Bending Moment in Shaft for MSST (M_{b MSST}) & Torsional Moment in Shaft for MSST (Mt_t) and hit the calculate button.

FAQs on Diameter of Shaft given Principle Shear Stress Maximum Shear Stress Theory

What is the formula to find Diameter of Shaft given Principle Shear Stress Maximum Shear Stress Theory?

The formula of Diameter of Shaft given Principle Shear Stress Maximum Shear Stress Theory is expressed as Diameter of Shaft from MSST = (16/(pi*Maximum Shear Stress in Shaft from MSST)*sqrt(Bending Moment in Shaft for MSST^2+Torsional Moment in Shaft for MSST^2))^(1/3). Here is an example- 45000 = (16/(pi*58900000)*sqrt(980^2+387.5821^2))^(1/3).

How to calculate Diameter of Shaft given Principle Shear Stress Maximum Shear Stress Theory?

With Maximum Shear Stress in Shaft from MSST (𝜏_{max MSST}), Bending Moment in Shaft for MSST (M_{b MSST}) & Torsional Moment in Shaft for MSST (Mt_t) we can find Diameter of Shaft given Principle Shear Stress Maximum Shear Stress Theory using the formula - Diameter of Shaft from MSST = (16/(pi*Maximum Shear Stress in Shaft from MSST)*sqrt(Bending Moment in Shaft for MSST^2+Torsional Moment in Shaft for MSST^2))^(1/3). This formula also uses Archimedes' constant and Square Root (sqrt) function(s).

Can the Diameter of Shaft given Principle Shear Stress Maximum Shear Stress Theory be negative?

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

Which unit is used to measure Diameter of Shaft given Principle Shear Stress Maximum Shear Stress Theory?

Diameter of Shaft given Principle Shear Stress Maximum Shear Stress Theory 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 Principle Shear Stress Maximum Shear Stress Theory can be measured.

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Diameter of Shaft given Principle Shear Stress Maximum Shear Stress Theory Formula

Diameter of Shaft given Principle Shear Stress Maximum Shear Stress Theory Example

Diameter of Shaft given Principle Shear Stress Maximum Shear Stress Theory Solution

Diameter of Shaft given Principle Shear Stress Maximum Shear Stress Theory Formula Elements

Other formulas in Maximum Shear Stress and Principal Stress Theory category

How to Evaluate Diameter of Shaft given Principle Shear Stress Maximum Shear Stress Theory?

FAQs on Diameter of Shaft given Principle Shear Stress Maximum Shear Stress Theory

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