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Diameter of Hollow Shaft Subjected to Maximum Bending Moment Formula

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Hollow Shaft Outer Diameter is defined as the length of the longest chord of the surface of the hollow circular shaft. Check FAQs

d o = {(\frac{M m}{(\frac{π}{32}) \cdot (f b) \cdot (1 - k^{2})})}^{\frac{1}{3}}

d_o - Hollow Shaft Outer Diameter?M_m - Maximum Bending Moment?f_b - Bending Stress?k - Ratio of Inner to Outer Diameter of Hollow Shaft?π - Archimedes' constant?

Diameter of Hollow Shaft Subjected to Maximum Bending Moment Example

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Here is how the Diameter of Hollow Shaft Subjected to Maximum Bending Moment equation looks like with Values.

Here is how the Diameter of Hollow Shaft Subjected to Maximum Bending Moment equation looks like with Units.

Here is how the Diameter of Hollow Shaft Subjected to Maximum Bending Moment equation looks like.

18.4103 = {(\frac{34000}{(\frac{3.1416}{32}) \cdot (200) \cdot (1 - {0.85}^{2})})}^{\frac{1}{3}}

18.4103mm = {(\frac{34000N*mm}{(\frac{3.1416}{32}) \cdot (200N/mm²) \cdot (1 - {0.85}^{2})})}^{\frac{1}{3}}

18.4103 = {(\frac{34000}{(\frac{3.1416}{32}) \cdot (200) \cdot (1 - {0.85}^{2})})}^{\frac{1}{3}}

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Diameter of Hollow Shaft Subjected to Maximum Bending Moment Solution

Follow our step by step solution on how to calculate Diameter of Hollow Shaft Subjected to Maximum Bending Moment?

FIRST Step Consider the formula

d o = {(\frac{M m}{(\frac{π}{32}) \cdot (f b) \cdot (1 - k^{2})})}^{\frac{1}{3}}

Next Step Substitute values of Variables

∴

d o = {(\frac{34000N*mm}{(\frac{π}{32}) \cdot (200N/mm²) \cdot (1 - {0.85}^{2})})}^{\frac{1}{3}}

Next Step Substitute values of Constants

∴

d o = {(\frac{34000N*mm}{(\frac{3.1416}{32}) \cdot (200N/mm²) \cdot (1 - {0.85}^{2})})}^{\frac{1}{3}}

Next Step Convert Units

∴

d o = {(\frac{34N*m}{(\frac{3.1416}{32}) \cdot (2E+8Pa) \cdot (1 - {0.85}^{2})})}^{\frac{1}{3}}

Next Step Prepare to Evaluate

∴

d o = {(\frac{34}{(\frac{3.1416}{32}) \cdot (2E+8) \cdot (1 - {0.85}^{2})})}^{\frac{1}{3}}

Next Step Evaluate

∴

d o = 0.0184103486522574m

Next Step Convert to Output's Unit

∴

d o = 18.4103486522574mm

LAST Step Rounding Answer

∴

d o = 18.4103mm

Diameter of Hollow Shaft Subjected to Maximum Bending Moment Formula Elements

Variables

Constants

Hollow Shaft Outer Diameter

Hollow Shaft Outer Diameter is defined as the length of the longest chord of the surface of the hollow circular shaft.

Symbol: d_o

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Hollow Shaft Outer Diameter

Maximum Bending Moment

Maximum Bending Moment is the algebraic sum of the moments caused by the internal forces on the shaft and it causes the shaft to rotate.

Symbol: M_m

Measurement: Bending MomentUnit: N*mm

Note: Value should be greater than 0.

Formulas to find Maximum Bending Moment

Bending Stress

Bending stress is the normal stress that an object encounters when it is subjected to a large load at a particular point that causes the object to bend and become fatigued.

Symbol: f_b

Measurement: StressUnit: N/mm²

Note: Value should be greater than 0.

Formulas to find Bending Stress

Ratio of Inner to Outer Diameter of Hollow Shaft

The Ratio of Inner to Outer Diameter of Hollow Shaft is defined as the inner diameter of the shaft divided by the outer diameter.

Symbol: k

Measurement: NAUnit: Unitless

Note: Value should be less than 1.

Formulas to find Ratio of Inner to Outer Diameter of Hollow 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 in Design of Agitation System Components category

Go Force for Design of Shaft Based on Pure Bending

F m = \frac{T m}{0.75 \cdot h m}

Go Maximum Torque of Shaft Subjected to Bending Moment only

T m = F m \cdot (0.75 \cdot R b)

Go Maximum Bending Moment subject to Shaft

M m = l \cdot F m

Go Diameter of Solid Shaft Subjected to Maximum Bending Moment

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

How to Evaluate Diameter of Hollow Shaft Subjected to Maximum Bending Moment?

Diameter of Hollow Shaft Subjected to Maximum Bending Moment evaluator uses Hollow Shaft Outer Diameter = (Maximum Bending Moment/((pi/32)*(Bending Stress)*(1-Ratio of Inner to Outer Diameter of Hollow Shaft^2)))^(1/3) to evaluate the Hollow Shaft Outer Diameter, Diameter of Hollow Shaft Subjected to Maximum Bending Moment refers to the outer diameter of the shaft. In engineering, a shaft is considered hollow when it has a hollow circular cross-section, with a hole or void at its center. Hollow Shaft Outer Diameter is denoted by d_o symbol.

How to evaluate Diameter of Hollow Shaft Subjected to Maximum Bending Moment using this online evaluator? To use this online evaluator for Diameter of Hollow Shaft Subjected to Maximum Bending Moment, enter Maximum Bending Moment (M_m), Bending Stress (f_b) & Ratio of Inner to Outer Diameter of Hollow Shaft (k) and hit the calculate button.

FAQs on Diameter of Hollow Shaft Subjected to Maximum Bending Moment

What is the formula to find Diameter of Hollow Shaft Subjected to Maximum Bending Moment?

The formula of Diameter of Hollow Shaft Subjected to Maximum Bending Moment is expressed as Hollow Shaft Outer Diameter = (Maximum Bending Moment/((pi/32)*(Bending Stress)*(1-Ratio of Inner to Outer Diameter of Hollow Shaft^2)))^(1/3). Here is an example- 18410.35 = (34/((pi/32)*(200000000)*(1-0.85^2)))^(1/3).

How to calculate Diameter of Hollow Shaft Subjected to Maximum Bending Moment?

With Maximum Bending Moment (M_m), Bending Stress (f_b) & Ratio of Inner to Outer Diameter of Hollow Shaft (k) we can find Diameter of Hollow Shaft Subjected to Maximum Bending Moment using the formula - Hollow Shaft Outer Diameter = (Maximum Bending Moment/((pi/32)*(Bending Stress)*(1-Ratio of Inner to Outer Diameter of Hollow Shaft^2)))^(1/3). This formula also uses Archimedes' constant .

Can the Diameter of Hollow Shaft Subjected to Maximum Bending Moment be negative?

No, the Diameter of Hollow Shaft Subjected to Maximum Bending Moment, measured in Length cannot be negative.

Which unit is used to measure Diameter of Hollow Shaft Subjected to Maximum Bending Moment?

Diameter of Hollow Shaft Subjected to Maximum Bending Moment is usually measured using the Millimeter[mm] for Length. Meter[mm], Kilometer[mm], Decimeter[mm] are the few other units in which Diameter of Hollow Shaft Subjected to Maximum Bending Moment can be measured.

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Diameter of Hollow Shaft Subjected to Maximum Bending Moment Formula

Diameter of Hollow Shaft Subjected to Maximum Bending Moment Example

Diameter of Hollow Shaft Subjected to Maximum Bending Moment Solution

Diameter of Hollow Shaft Subjected to Maximum Bending Moment Formula Elements

Other formulas in Design of Agitation System Components category

How to Evaluate Diameter of Hollow Shaft Subjected to Maximum Bending Moment?

FAQs on Diameter of Hollow Shaft Subjected to Maximum Bending Moment

Variable Name