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Maximum Shear Stress in Shafts Formula

GoPermissible Value of Maximum Shear Stress Formula

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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. Check FAQs

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

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

Maximum Shear Stress in Shafts Example

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Here is how the Maximum Shear Stress in Shafts equation looks like with Values.

Here is how the Maximum Shear Stress in Shafts equation looks like with Units.

Here is how the Maximum Shear Stress in Shafts equation looks like.

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

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

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

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Maximum Shear Stress in Shafts Solution

Follow our step by step solution on how to calculate Maximum Shear Stress in Shafts?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

𝜏 max MSST = \frac{16}{π \cdot {45mm}^{3}} \cdot \sqrt{{980000N*mm}^{2} + {387582.1N*mm}^{2}}

Next Step Substitute values of Constants

∴

𝜏 max MSST = \frac{16}{3.1416 \cdot {45mm}^{3}} \cdot \sqrt{{980000N*mm}^{2} + {387582.1N*mm}^{2}}

Next Step Convert Units

∴

𝜏 max MSST = \frac{16}{3.1416 \cdot {0.045m}^{3}} \cdot \sqrt{{980N*m}^{2} + {387.5821N*m}^{2}}

Next Step Prepare to Evaluate

∴

𝜏 max MSST = \frac{16}{3.1416 \cdot {0.045}^{3}} \cdot \sqrt{980^{2} + {387.5821}^{2}}

Next Step Evaluate

∴

𝜏 max MSST = 58899999.4843198Pa

Next Step Convert to Output's Unit

∴

𝜏 max MSST = 58.8999994843198N/mm²

LAST Step Rounding Answer

∴

𝜏 max MSST = 58.9N/mm²

Maximum Shear Stress in Shafts Formula Elements

Variables

Constants

Functions

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

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

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 to find Maximum Shear Stress in Shaft from MSST

Go Permissible Value of Maximum Shear Stress

𝜏 max MSST = 0.5 \cdot \frac{τ max}{fos shaft}

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 Maximum Shear Stress in Shafts?

Maximum Shear Stress in Shafts evaluator uses Maximum Shear Stress in Shaft from MSST = 16/(pi*Diameter of Shaft from MSST^3)*sqrt(Bending Moment in Shaft for MSST^2+Torsional Moment in Shaft for MSST^2) to evaluate the Maximum Shear Stress in Shaft from MSST, Maximum Shear Stress in Shafts formula is defined as a measure of the maximum shear stress that occurs in a shaft, which is a critical parameter in mechanical engineering to ensure the structural integrity and reliability of rotating machines and mechanisms. Maximum Shear Stress in Shaft from MSST is denoted by 𝜏_{max MSST} symbol.

How to evaluate Maximum Shear Stress in Shafts using this online evaluator? To use this online evaluator for Maximum Shear Stress in Shafts, enter Diameter of Shaft from MSST (d_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 Maximum Shear Stress in Shafts

What is the formula to find Maximum Shear Stress in Shafts?

The formula of Maximum Shear Stress in Shafts is expressed as Maximum Shear Stress in Shaft from MSST = 16/(pi*Diameter of Shaft from MSST^3)*sqrt(Bending Moment in Shaft for MSST^2+Torsional Moment in Shaft for MSST^2). Here is an example- 5.9E-5 = 16/(pi*0.045^3)*sqrt(980^2+387.5821^2).

How to calculate Maximum Shear Stress in Shafts?

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

What are the other ways to Calculate Maximum Shear Stress in Shaft from MSST?

Here are the different ways to Calculate Maximum Shear Stress in Shaft from MSST-

Maximum Shear Stress in Shaft from MSST=0.5*Yield Strength in Shaft from MSST/Factor of Safety of Shaft

Can the Maximum Shear Stress in Shafts be negative?

No, the Maximum Shear Stress in Shafts, measured in Stress cannot be negative.

Which unit is used to measure Maximum Shear Stress in Shafts?

Maximum Shear Stress in Shafts 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 Maximum Shear Stress in Shafts can be measured.

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Maximum Shear Stress in Shafts Formula

​GoPermissible Value of Maximum Shear Stress Formula

Maximum Shear Stress in Shafts Example

Maximum Shear Stress in Shafts Solution

Maximum Shear Stress in Shafts Formula Elements

Other Formulas to find Maximum Shear Stress in Shaft from MSST

Other formulas in Maximum Shear Stress and Principal Stress Theory category

How to Evaluate Maximum Shear Stress in Shafts?

FAQs on Maximum Shear Stress in Shafts

Variable Name

GoPermissible Value of Maximum Shear Stress Formula