Equivalent Bending Moment for Hollow Shaft Calculator

✖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.ⓘ Bending Stress [f_b]			+10% -10%
✖Hollow Shaft Outer Diameter is defined as the length of the longest chord of the surface of the hollow circular shaft.ⓘ Hollow Shaft Outer Diameter [d_o]			+10% -10%
✖The Ratio of Inner to Outer Diameter of Hollow Shaft is defined as the inner diameter of the shaft divided by the outer diameter.ⓘ Ratio of Inner to Outer Diameter of Hollow Shaft [k]			+10% -10%

✖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.ⓘ Equivalent Bending Moment for Hollow Shaft [Me_hollowshaft]

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Equivalent Bending Moment for Hollow Shaft Solution

STEP 0: Pre-Calculation Summary

Formula Used

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)
Me_hollowshaft = (pi/32)*(f_b)*(d_o^3)*(1-k^4)
This formula uses 1 Constants, 4 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

Equivalent Bending Moment for Hollow Shaft - (Measured in Newton Meter) - 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.
Bending Stress - (Measured in Pascal) - 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.
Hollow Shaft Outer Diameter - (Measured in Meter) - Hollow Shaft Outer Diameter is defined as the length of the longest chord of the surface of the hollow circular shaft.
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.

STEP 1: Convert Input(s) to Base Unit

Bending Stress: 200 Newton per Square Millimeter --> 200000000 Pascal (Check conversion here)
Hollow Shaft Outer Diameter: 20 Millimeter --> 0.02 Meter (Check conversion here)
Ratio of Inner to Outer Diameter of Hollow Shaft: 0.85 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

Me_hollowshaft = (pi/32)*(f_b)*(d_o^3)*(1-k^4) --> (pi/32)*(200000000)*(0.02^3)*(1-0.85^4)

Evaluating ... ...

Me_hollowshaft = 75.0830826730918

STEP 3: Convert Result to Output's Unit

75.0830826730918 Newton Meter -->75083.0826730918 Newton Millimeter (Check conversion here)

FINAL ANSWER

75083.0826730918 ≈ 75083.08 Newton Millimeter <-- Equivalent Bending Moment for Hollow Shaft

(Calculation completed in 00.020 seconds)

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< Design of Agitation System Components Calculators

Maximum Torque for Hollow Shaft

LaTeX Go Maximum Torque for Hollow Shaft = ((pi/16)*(Hollow Shaft Outer Diameter^3)*(Torsional Shear Stress in Shaft)*(1-Ratio of Inner to Outer Diameter of Hollow Shaft^2))

Maximum Torque for Solid Shaft

LaTeX Go Maximum Torque for Solid Shaft = ((pi/16)*(Diameter of Shaft for Agitator^3)*(Torsional Shear Stress in Shaft))

Rated Motor Torque

LaTeX Go Rated Motor Torque = ((Power*4500)/(2*pi*Speed of Agitator))

Force for Design of Shaft Based on Pure Bending

LaTeX Go Force = Maximum Torque for Agitator/(0.75*Height of Manometer Liquid)

< Shaft Subjected to Combined Twisting Moment and Bending Moment Calculators

Equivalent Twisting Moment for Hollow Shaft

LaTeX Go Equivalent Twisting Moment for Hollow Shaft = (pi/16)*(Bending Stress)*(Hollow Shaft Outer Diameter^3)*(1-Ratio of Inner to Outer Diameter of Hollow Shaft^4)

Equivalent Bending Moment for Hollow Shaft

LaTeX Go 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)

Equivalent Bending Moment for Solid Shaft

LaTeX Go Equivalent Bending Moment for Solid Shaft = (1/2)*(Maximum Bending Moment+sqrt(Maximum Bending Moment^2+Maximum Torque for Agitator^2))

Equivalent Twisting Moment for Solid Shaft

LaTeX Go Equivalent Twisting Moment for Solid Shaft = (sqrt((Maximum Bending Moment^2)+(Maximum Torque for Agitator^2)))

Equivalent Bending Moment for Hollow Shaft Formula

LaTeX Go

What is Maximum Shear Stress Theory for Brittle Materials?

Maximum shear stress theory states that yielding will occur when a particular point undergoes a maximum shear stress that is equal to half of the uniaxial yield strength.

How to Calculate Equivalent Bending Moment for Hollow Shaft?

Equivalent Bending Moment for Hollow Shaft calculator 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 calculate 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 calculate Equivalent Bending Moment for Hollow Shaft using this online calculator? To use this online calculator 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. Here is how the Equivalent Bending Moment for Hollow Shaft calculation can be explained with given input values -> 7.5E+7 = (pi/32)*(200000000)*(0.02^3)*(1-0.85^4).

FAQ

What is 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 and is represented as Me_hollowshaft = (pi/32)*(f_b)*(d_o^3)*(1-k^4) or 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). 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, Hollow Shaft Outer Diameter is defined as the length of the longest chord of the surface of the hollow circular 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.

How to calculate 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 is calculated using 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 calculate Equivalent Bending Moment for Hollow Shaft, you need Bending Stress (f_b), Hollow Shaft Outer Diameter (d_o) & Ratio of Inner to Outer Diameter of Hollow Shaft (k). With our tool, you need to enter the respective value for Bending Stress, Hollow Shaft Outer Diameter & Ratio of Inner to Outer Diameter of Hollow Shaft and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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