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Torsional Moment given Maximum Shear Stress Formula

GoTorsional Moment given Equivalent Bending Moment Formula

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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. Check FAQs

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

Mt_t - Torsional Moment in Shaft for MSST?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?π - Archimedes' constant?

Torsional Moment given Maximum Shear Stress Example

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Here is how the Torsional Moment given Maximum Shear Stress equation looks like with Values.

Here is how the Torsional Moment given Maximum Shear Stress equation looks like with Units.

Here is how the Torsional Moment given Maximum Shear Stress equation looks like.

387582.1251 = \sqrt{{(3.1416 \cdot 45^{3} \cdot \frac{58.9}{16})}^{2} - 980000^{2}}

387582.1251N*mm = \sqrt{{(3.1416 \cdot {45mm}^{3} \cdot \frac{58.9N/mm²}{16})}^{2} - {980000N*mm}^{2}}

387582.1251 = \sqrt{{(3.1416 \cdot 45^{3} \cdot \frac{58.9}{16})}^{2} - 980000^{2}}

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Torsional Moment given Maximum Shear Stress Solution

Follow our step by step solution on how to calculate Torsional Moment given Maximum Shear Stress?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

Mt t = \sqrt{{(π \cdot {45mm}^{3} \cdot \frac{58.9N/mm²}{16})}^{2} - {980000N*mm}^{2}}

Next Step Substitute values of Constants

∴

Mt t = \sqrt{{(3.1416 \cdot {45mm}^{3} \cdot \frac{58.9N/mm²}{16})}^{2} - {980000N*mm}^{2}}

Next Step Convert Units

∴

Mt t = \sqrt{{(3.1416 \cdot {0.045m}^{3} \cdot \frac{5.9E+7Pa}{16})}^{2} - {980N*m}^{2}}

Next Step Prepare to Evaluate

∴

Mt t = \sqrt{{(3.1416 \cdot {0.045}^{3} \cdot \frac{5.9E+7}{16})}^{2} - 980^{2}}

Next Step Evaluate

∴

Mt t = 387.582125088048N*m

Next Step Convert to Output's Unit

∴

Mt t = 387582.125088048N*mm

LAST Step Rounding Answer

∴

Mt t = 387582.1251N*mm

Torsional Moment given Maximum Shear Stress Formula Elements

Variables

Constants

Functions

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

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

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 Torsional Moment in Shaft for MSST

Go Torsional Moment given Equivalent Bending Moment

Mt t = \sqrt{{(Mb eq - M b MSST)}^{2} - {M b MSST}^{2}}

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 Torsional Moment given Maximum Shear Stress?

Torsional Moment given Maximum Shear Stress evaluator uses Torsional Moment in Shaft for MSST = sqrt((pi*Diameter of Shaft from MSST^3*Maximum Shear Stress in Shaft from MSST/16)^2-Bending Moment in Shaft for MSST^2) to evaluate the Torsional Moment in Shaft for MSST, Torsional Moment given Maximum Shear Stress formula is defined as a measure of the twisting force that causes shear stress in a shaft, which is a critical parameter in mechanical engineering to determine the shaft's ability to resist twisting and potential failure. Torsional Moment in Shaft for MSST is denoted by Mt_t symbol.

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

FAQs on Torsional Moment given Maximum Shear Stress

What is the formula to find Torsional Moment given Maximum Shear Stress?

The formula of Torsional Moment given Maximum Shear Stress is expressed as Torsional Moment in Shaft for MSST = sqrt((pi*Diameter of Shaft from MSST^3*Maximum Shear Stress in Shaft from MSST/16)^2-Bending Moment in Shaft for MSST^2). Here is an example- 3.9E+8 = sqrt((pi*0.045^3*58900000/16)^2-980^2).

How to calculate Torsional Moment given Maximum Shear Stress?

With Diameter of Shaft from MSST (d_MSST), Maximum Shear Stress in Shaft from MSST (𝜏_{max MSST}) & Bending Moment in Shaft for MSST (M_{b MSST}) we can find Torsional Moment given Maximum Shear Stress using the formula - Torsional Moment in Shaft for MSST = sqrt((pi*Diameter of Shaft from MSST^3*Maximum Shear Stress in Shaft from MSST/16)^2-Bending 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 Torsional Moment in Shaft for MSST?

Here are the different ways to Calculate Torsional Moment in Shaft for MSST-

Torsional Moment in Shaft for MSST=sqrt((Equivalent Bending Moment from MSST-Bending Moment in Shaft for MSST)^2-Bending Moment in Shaft for MSST^2)

Can the Torsional Moment given Maximum Shear Stress be negative?

No, the Torsional Moment given Maximum Shear Stress, measured in Torque cannot be negative.

Which unit is used to measure Torsional Moment given Maximum Shear Stress?

Torsional Moment given Maximum Shear Stress is usually measured using the Newton Millimeter[N*mm] for Torque. Newton Meter[N*mm], Newton Centimeter[N*mm], Kilonewton Meter[N*mm] are the few other units in which Torsional Moment given Maximum Shear Stress can be measured.

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Torsional Moment given Maximum Shear Stress Formula

​GoTorsional Moment given Equivalent Bending Moment Formula

Torsional Moment given Maximum Shear Stress Example

Torsional Moment given Maximum Shear Stress Solution

Torsional Moment given Maximum Shear Stress Formula Elements

Other Formulas to find Torsional Moment in Shaft for MSST

Other formulas in Maximum Shear Stress and Principal Stress Theory category

How to Evaluate Torsional Moment given Maximum Shear Stress?

FAQs on Torsional Moment given Maximum Shear Stress

Variable Name

GoTorsional Moment given Equivalent Bending Moment Formula