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Bending Moment given Maximum Shear Stress Formula

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

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

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

Bending Moment given Maximum Shear Stress Example

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

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

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

980000.0099 = \sqrt{{(\frac{58.9}{\frac{16}{3.1416 \cdot 45^{3}}})}^{2} - {387582.1}^{2}}

980000.0099N*mm = \sqrt{{(\frac{58.9N/mm²}{\frac{16}{3.1416 \cdot {45mm}^{3}}})}^{2} - {387582.1N*mm}^{2}}

980000.0099 = \sqrt{{(\frac{58.9}{\frac{16}{3.1416 \cdot 45^{3}}})}^{2} - {387582.1}^{2}}

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Bending Moment given Maximum Shear Stress Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

M b MSST = \sqrt{{(\frac{58.9N/mm²}{\frac{16}{π \cdot {45mm}^{3}}})}^{2} - {387582.1N*mm}^{2}}

Next Step Substitute values of Constants

∴

M b MSST = \sqrt{{(\frac{58.9N/mm²}{\frac{16}{3.1416 \cdot {45mm}^{3}}})}^{2} - {387582.1N*mm}^{2}}

Next Step Convert Units

∴

M b MSST = \sqrt{{(\frac{5.9E+7Pa}{\frac{16}{3.1416 \cdot {0.045m}^{3}}})}^{2} - {387.5821N*m}^{2}}

Next Step Prepare to Evaluate

∴

M b MSST = \sqrt{{(\frac{5.9E+7}{\frac{16}{3.1416 \cdot {0.045}^{3}}})}^{2} - {387.5821}^{2}}

Next Step Evaluate

∴

M b MSST = 980.000009922121N*m

Next Step Convert to Output's Unit

∴

M b MSST = 980000.009922121N*mm

LAST Step Rounding Answer

∴

M b MSST = 980000.0099N*mm

Bending Moment given Maximum Shear Stress Formula Elements

Variables

Constants

Functions

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

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

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 Bending Moment given Maximum Shear Stress?

Bending Moment given Maximum Shear Stress evaluator uses Bending Moment in Shaft for MSST = sqrt((Maximum Shear Stress in Shaft from MSST/(16/(pi*Diameter of Shaft from MSST^3)))^2-Torsional Moment in Shaft for MSST^2) to evaluate the Bending Moment in Shaft for MSST, Bending Moment given Maximum Shear Stress formula is defined as a measure of the maximum stress that an object can withstand without deforming plastically, calculated based on the maximum shear stress and principal stress theory, providing a critical value for structural integrity and material failure analysis in mechanical engineering. Bending Moment in Shaft for MSST is denoted by M_{b MSST} symbol.

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

FAQs on Bending Moment given Maximum Shear Stress

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

The formula of Bending Moment given Maximum Shear Stress is expressed as Bending Moment in Shaft for MSST = sqrt((Maximum Shear Stress in Shaft from MSST/(16/(pi*Diameter of Shaft from MSST^3)))^2-Torsional Moment in Shaft for MSST^2). Here is an example- 9.8E+8 = sqrt((58900000/(16/(pi*0.045^3)))^2-387.5821^2).

How to calculate Bending Moment given Maximum Shear Stress?

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

Can the Bending Moment given Maximum Shear Stress be negative?

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

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

Bending 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 Bending Moment given Maximum Shear Stress can be measured.

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Bending Moment given Maximum Shear Stress Formula

Bending Moment given Maximum Shear Stress Example

Bending Moment given Maximum Shear Stress Solution

Bending Moment given Maximum Shear Stress Formula Elements

Other formulas in Maximum Shear Stress and Principal Stress Theory category

How to Evaluate Bending Moment given Maximum Shear Stress?

FAQs on Bending Moment given Maximum Shear Stress

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