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Diameter of Shaft given Bending Stress Pure Bending Formula

GoDiameter of Shaft given Tensile Stress in Shaft Formula

GoDiameter of Shaft given Torsional Shear Stress in Shaft Pure Torsion Formula

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

d = {(\frac{32 \cdot M b}{π \cdot σ b})}^{\frac{1}{3}}

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

Diameter of Shaft given Bending Stress Pure Bending Example

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Here is how the Diameter of Shaft given Bending Stress Pure Bending equation looks like with Values.

Here is how the Diameter of Shaft given Bending Stress Pure Bending equation looks like with Units.

Here is how the Diameter of Shaft given Bending Stress Pure Bending equation looks like.

46.9 = {(\frac{32 \cdot 1.8E+6}{3.1416 \cdot 177.8})}^{\frac{1}{3}}

46.9mm = {(\frac{32 \cdot 1.8E+6N*mm}{3.1416 \cdot 177.8N/mm²})}^{\frac{1}{3}}

46.9 = {(\frac{32 \cdot 1.8E+6}{3.1416 \cdot 177.8})}^{\frac{1}{3}}

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Diameter of Shaft given Bending Stress Pure Bending Solution

Follow our step by step solution on how to calculate Diameter of Shaft given Bending Stress Pure Bending?

FIRST Step Consider the formula

d = {(\frac{32 \cdot M b}{π \cdot σ b})}^{\frac{1}{3}}

Next Step Substitute values of Variables

∴

d = {(\frac{32 \cdot 1.8E+6N*mm}{π \cdot 177.8N/mm²})}^{\frac{1}{3}}

Next Step Substitute values of Constants

∴

d = {(\frac{32 \cdot 1.8E+6N*mm}{3.1416 \cdot 177.8N/mm²})}^{\frac{1}{3}}

Next Step Convert Units

∴

d = {(\frac{32 \cdot 1800.7365N*m}{3.1416 \cdot 1.8E+8Pa})}^{\frac{1}{3}}

Next Step Prepare to Evaluate

∴

d = {(\frac{32 \cdot 1800.7365}{3.1416 \cdot 1.8E+8})}^{\frac{1}{3}}

Next Step Evaluate

∴

d = 0.0468999999915808m

Next Step Convert to Output's Unit

∴

d = 46.8999999915808mm

LAST Step Rounding Answer

∴

d = 46.9mm

Diameter of Shaft given Bending Stress Pure Bending Formula Elements

Variables

Constants

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

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

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 to find Diameter of Shaft on Strength Basis

Go Diameter of Shaft given Tensile Stress in Shaft

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

Go Diameter of Shaft given Torsional Shear Stress in Shaft Pure Torsion

d = {(16 \cdot \frac{Mt shaft}{π \cdot 𝜏})}^{\frac{1}{3}}

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 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}}

Go Bending Moment given Bending Stress Pure Bending

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

How to Evaluate Diameter of Shaft given Bending Stress Pure Bending?

Diameter of Shaft given Bending Stress Pure Bending evaluator uses Diameter of Shaft on Strength Basis = ((32*Bending Moment in Shaft)/(pi*Bending Stress in Shaft))^(1/3) to evaluate the Diameter of Shaft on Strength Basis, Diameter of Shaft given Bending Stress Pure Bending formula is defined as a measure of the diameter of a shaft under pure bending stress, which is a critical parameter in shaft design to ensure the shaft can withstand the bending stress without failing. Diameter of Shaft on Strength Basis is denoted by d symbol.

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

FAQs on Diameter of Shaft given Bending Stress Pure Bending

What is the formula to find Diameter of Shaft given Bending Stress Pure Bending?

The formula of Diameter of Shaft given Bending Stress Pure Bending is expressed as Diameter of Shaft on Strength Basis = ((32*Bending Moment in Shaft)/(pi*Bending Stress in Shaft))^(1/3). Here is an example- 46893.6 = ((32*1800.736547)/(pi*177800000))^(1/3).

How to calculate Diameter of Shaft given Bending Stress Pure Bending?

With Bending Moment in Shaft (M_b) & Bending Stress in Shaft (σ_b) we can find Diameter of Shaft given Bending Stress Pure Bending using the formula - Diameter of Shaft on Strength Basis = ((32*Bending Moment in Shaft)/(pi*Bending Stress in Shaft))^(1/3). This formula also uses Archimedes' constant .

What are the other ways to Calculate Diameter of Shaft on Strength Basis?

Here are the different ways to Calculate Diameter of Shaft on Strength Basis-

Diameter of Shaft on Strength Basis=sqrt(4*Axial Force on Shaft/(pi*Tensile Stress in Shaft))
Diameter of Shaft on Strength Basis=(16*Torsional Moment in Shaft/(pi*Torsional Shear Stress in Shaft))^(1/3)

Can the Diameter of Shaft given Bending Stress Pure Bending be negative?

No, the Diameter of Shaft given Bending Stress Pure Bending, measured in Length cannot be negative.

Which unit is used to measure Diameter of Shaft given Bending Stress Pure Bending?

Diameter of Shaft given Bending Stress Pure Bending 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 Bending Stress Pure Bending can be measured.

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Diameter of Shaft given Bending Stress Pure Bending Formula

​GoDiameter of Shaft given Tensile Stress in Shaft Formula

​GoDiameter of Shaft given Torsional Shear Stress in Shaft Pure Torsion Formula

Diameter of Shaft given Bending Stress Pure Bending Example

Diameter of Shaft given Bending Stress Pure Bending Solution

Diameter of Shaft given Bending Stress Pure Bending Formula Elements

Other Formulas to find Diameter of Shaft on Strength Basis

Other formulas in Shaft Design on Strength Basis category

How to Evaluate Diameter of Shaft given Bending Stress Pure Bending?

FAQs on Diameter of Shaft given Bending Stress Pure Bending

Variable Name

GoDiameter of Shaft given Tensile Stress in Shaft Formula

GoDiameter of Shaft given Torsional Shear Stress in Shaft Pure Torsion Formula