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Equivalent Bending Moment for Hollow Shaft Formula

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Equivalent Bending Moment for Hollow Shaft refers to the bending moment that would produce the same effect on a solid shaft as the combined bending and torsional loads on the hollow shaft. Check FAQs

Me hollowshaft = (\frac{π}{32}) \cdot (f b) \cdot ({d o}^{3}) \cdot (1 - k^{4})

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

Equivalent Bending Moment for Hollow Shaft Example

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Here is how the Equivalent Bending Moment for Hollow Shaft equation looks like with Values.

Here is how the Equivalent Bending Moment for Hollow Shaft equation looks like with Units.

Here is how the Equivalent Bending Moment for Hollow Shaft equation looks like.

75083.0827 = (\frac{3.1416}{32}) \cdot (200) \cdot (20^{3}) \cdot (1 - {0.85}^{4})

75083.0827N*mm = (\frac{3.1416}{32}) \cdot (200N/mm²) \cdot ({20mm}^{3}) \cdot (1 - {0.85}^{4})

75083.0827 = (\frac{3.1416}{32}) \cdot (200) \cdot (20^{3}) \cdot (1 - {0.85}^{4})

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Equivalent Bending Moment for Hollow Shaft Solution

Follow our step by step solution on how to calculate Equivalent Bending Moment for Hollow Shaft?

FIRST Step Consider the formula

Me hollowshaft = (\frac{π}{32}) \cdot (f b) \cdot ({d o}^{3}) \cdot (1 - k^{4})

Next Step Substitute values of Variables

∴

Me hollowshaft = (\frac{π}{32}) \cdot (200N/mm²) \cdot ({20mm}^{3}) \cdot (1 - {0.85}^{4})

Next Step Substitute values of Constants

∴

Me hollowshaft = (\frac{3.1416}{32}) \cdot (200N/mm²) \cdot ({20mm}^{3}) \cdot (1 - {0.85}^{4})

Next Step Convert Units

∴

Me hollowshaft = (\frac{3.1416}{32}) \cdot (2E+8Pa) \cdot ({0.02m}^{3}) \cdot (1 - {0.85}^{4})

Next Step Prepare to Evaluate

∴

Me hollowshaft = (\frac{3.1416}{32}) \cdot (2E+8) \cdot ({0.02}^{3}) \cdot (1 - {0.85}^{4})

Next Step Evaluate

∴

Me hollowshaft = 75.0830826730918N*m

Next Step Convert to Output's Unit

∴

Me hollowshaft = 75083.0826730918N*mm

LAST Step Rounding Answer

∴

Me hollowshaft = 75083.0827N*mm

Equivalent Bending Moment for Hollow Shaft Formula Elements

Variables

Constants

Equivalent Bending Moment for Hollow Shaft

Equivalent Bending Moment for Hollow Shaft refers to the bending moment that would produce the same effect on a solid shaft as the combined bending and torsional loads on the hollow shaft.

Symbol: Me_hollowshaft

Measurement: Bending MomentUnit: N*mm

Note: Value should be greater than 0.

Formulas to find Equivalent Bending Moment for Hollow Shaft

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

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

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 Equivalent Twisting Moment for Solid Shaft

Te solidshaft = (\sqrt{({M m}^{2}) + ({T m}^{2})})

Go Equivalent Twisting Moment for Hollow Shaft

Te hollowshaft = (\frac{π}{16}) \cdot (f b) \cdot ({d o}^{3}) \cdot (1 - k^{4})

Go Equivalent Bending Moment for Solid Shaft

Me solidshaft = (\frac{1}{2}) \cdot (M m + \sqrt{{M m}^{2} + {T m}^{2}})

Go Diameter of Solid Shaft based on Equivalent Twisting Moment

Diameter solidshaft = {(T e \cdot \frac{16}{π} \cdot \frac{1}{f s})}^{\frac{1}{3}}

How to Evaluate Equivalent Bending Moment for Hollow Shaft?

Equivalent Bending Moment for Hollow Shaft evaluator uses Equivalent Bending Moment for Hollow Shaft = (pi/32)*(Bending Stress)*(Hollow Shaft Outer Diameter^3)*(1-Ratio of Inner to Outer Diameter of Hollow Shaft^4) to evaluate the Equivalent Bending Moment for Hollow Shaft, The Equivalent Bending Moment for Hollow Shaft formula is defined as that alone produces maximum normal stress equal to the maximum normal stress produce due to combined bending and torsion. Equivalent Bending Moment for Hollow Shaft is denoted by Me_hollowshaft symbol.

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

FAQs on Equivalent Bending Moment for Hollow Shaft

What is the formula to find Equivalent Bending Moment for Hollow Shaft?

The formula of Equivalent Bending Moment for Hollow Shaft is expressed as Equivalent Bending Moment for Hollow Shaft = (pi/32)*(Bending Stress)*(Hollow Shaft Outer Diameter^3)*(1-Ratio of Inner to Outer Diameter of Hollow Shaft^4). Here is an example- 7.5E+7 = (pi/32)*(200000000)*(0.02^3)*(1-0.85^4).

How to calculate Equivalent Bending Moment for Hollow Shaft?

With Bending Stress (f_b), Hollow Shaft Outer Diameter (d_o) & Ratio of Inner to Outer Diameter of Hollow Shaft (k) we can find Equivalent Bending Moment for Hollow Shaft using the formula - Equivalent Bending Moment for Hollow Shaft = (pi/32)*(Bending Stress)*(Hollow Shaft Outer Diameter^3)*(1-Ratio of Inner to Outer Diameter of Hollow Shaft^4). This formula also uses Archimedes' constant .

Can the Equivalent Bending Moment for Hollow Shaft be negative?

No, the Equivalent Bending Moment for Hollow Shaft, measured in Bending Moment cannot be negative.

Which unit is used to measure Equivalent Bending Moment for Hollow Shaft?

Equivalent Bending Moment for Hollow Shaft is usually measured using the Newton Millimeter[N*mm] for Bending Moment. Newton Meter[N*mm], Newton Centimeter[N*mm], Kilonewton Meter[N*mm] are the few other units in which Equivalent Bending Moment for Hollow Shaft can be measured.

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Equivalent Bending Moment for Hollow Shaft Formula

Equivalent Bending Moment for Hollow Shaft Example

Equivalent Bending Moment for Hollow Shaft Solution

Equivalent Bending Moment for Hollow Shaft Formula Elements

Other formulas in Design of Agitation System Components category

How to Evaluate Equivalent Bending Moment for Hollow Shaft?

FAQs on Equivalent Bending Moment for Hollow Shaft

Variable Name