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Bending Moment given Bending Stress Pure Bending Formula

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Bending Moment in Shaft is the twisting force that causes the shaft to bend or deform due to external loads in shaft design on strength basis. Check FAQs

M b = \frac{σ b \cdot π \cdot d^{3}}{32}

M_b - Bending Moment in Shaft?σ_b - Bending Stress in Shaft?d - Diameter of Shaft on Strength Basis?π - Archimedes' constant?

Bending Moment given Bending Stress Pure Bending Example

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

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

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

1.8E+6 = \frac{177.8 \cdot 3.1416 \cdot {46.9}^{3}}{32}

1.8E+6N*mm = \frac{177.8N/mm² \cdot 3.1416 \cdot {46.9mm}^{3}}{32}

1.8E+6 = \frac{177.8 \cdot 3.1416 \cdot {46.9}^{3}}{32}

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Bending Moment given Bending Stress Pure Bending Solution

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

FIRST Step Consider the formula

M b = \frac{σ b \cdot π \cdot d^{3}}{32}

Next Step Substitute values of Variables

∴

M b = \frac{177.8N/mm² \cdot π \cdot {46.9mm}^{3}}{32}

Next Step Substitute values of Constants

∴

M b = \frac{177.8N/mm² \cdot 3.1416 \cdot {46.9mm}^{3}}{32}

Next Step Convert Units

∴

M b = \frac{1.8E+8Pa \cdot 3.1416 \cdot {0.0469m}^{3}}{32}

Next Step Prepare to Evaluate

∴

M b = \frac{1.8E+8 \cdot 3.1416 \cdot {0.0469}^{3}}{32}

Next Step Evaluate

∴

M b = 1800.73654796977N*m

Next Step Convert to Output's Unit

∴

M b = 1800736.54796977N*mm

LAST Step Rounding Answer

∴

M b = 1.8E+6N*mm

Bending Moment given Bending Stress Pure Bending Formula Elements

Variables

Constants

Bending Moment in Shaft

Bending Moment in Shaft is the twisting force that causes the shaft to bend or deform due to external loads in shaft design on strength basis.

Symbol: M_b

Measurement: TorqueUnit: N*mm

Note: Value should be greater than 0.

Formulas to find Bending Moment in Shaft

Bending Stress in Shaft

Bending Stress in Shaft is the external force that causes a shaft to deform by bending, typically measured in units of force per unit area.

Symbol: σ_b

Measurement: StressUnit: N/mm²

Note: Value should be greater than 0.

Formulas to find Bending Stress in Shaft

Diameter of Shaft on Strength Basis

Diameter of Shaft on Strength Basis is the diameter of a shaft calculated based on the strength requirements of the shaft design.

Symbol: d

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Diameter of Shaft on Strength Basis

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

Other formulas in Shaft Design on Strength Basis category

Go Tensile Stress in Shaft when it is Subjected to Axial Tensile Force

σ t = 4 \cdot \frac{P ax}{π \cdot d^{2}}

Go Diameter of Shaft given Tensile Stress in Shaft

d = \sqrt{4 \cdot \frac{P ax}{π \cdot σ t}}

Go Axial Force given Tensile Stress in Shaft

P ax = σ t \cdot π \cdot \frac{d^{2}}{4}

Go Bending Stress in Shaft Pure Bending Moment

σ b = \frac{32 \cdot M b}{π \cdot d^{3}}

How to Evaluate Bending Moment given Bending Stress Pure Bending?

Bending Moment given Bending Stress Pure Bending evaluator uses Bending Moment in Shaft = (Bending Stress in Shaft*pi*Diameter of Shaft on Strength Basis^3)/32 to evaluate the Bending Moment in Shaft, Bending Moment given Bending Stress Pure Bending formula is defined as a measure of the turning force that causes deformation in a shaft, typically occurring when a load is applied perpendicularly to the shaft's longitudinal axis and is a critical parameter in shaft design to ensure strength and stability. Bending Moment in Shaft is denoted by M_b symbol.

How to evaluate Bending Moment given Bending Stress Pure Bending using this online evaluator? To use this online evaluator for Bending Moment given Bending Stress Pure Bending, enter Bending Stress in Shaft (σ_b) & Diameter of Shaft on Strength Basis (d) and hit the calculate button.

FAQs on Bending Moment given Bending Stress Pure Bending

What is the formula to find Bending Moment given Bending Stress Pure Bending?

The formula of Bending Moment given Bending Stress Pure Bending is expressed as Bending Moment in Shaft = (Bending Stress in Shaft*pi*Diameter of Shaft on Strength Basis^3)/32. Here is an example- 1.8E+9 = (177800000*pi*0.0469^3)/32.

How to calculate Bending Moment given Bending Stress Pure Bending?

With Bending Stress in Shaft (σ_b) & Diameter of Shaft on Strength Basis (d) we can find Bending Moment given Bending Stress Pure Bending using the formula - Bending Moment in Shaft = (Bending Stress in Shaft*pi*Diameter of Shaft on Strength Basis^3)/32. This formula also uses Archimedes' constant .

Can the Bending Moment given Bending Stress Pure Bending be negative?

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

Which unit is used to measure Bending Moment given Bending Stress Pure Bending?

Bending Moment given Bending Stress Pure Bending 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 Bending Stress Pure Bending can be measured.

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Bending Moment given Bending Stress Pure Bending Formula

Bending Moment given Bending Stress Pure Bending Example

Bending Moment given Bending Stress Pure Bending Solution

Bending Moment given Bending Stress Pure Bending Formula Elements

Other formulas in Shaft Design on Strength Basis category

How to Evaluate Bending Moment given Bending Stress Pure Bending?

FAQs on Bending Moment given Bending Stress Pure Bending

Variable Name