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)
Mehollowshaft = (pi/32)*(fb)*(do ^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
Mehollowshaft = (pi/32)*(fb)*(do ^3)*(1-k^4) --> (pi/32)*(200000000)*(0.02 ^3)*(1-0.85^4)
Evaluating ... ...
Mehollowshaft = 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 00.004 seconds)

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18 Design of Agitation System Components Calculators

Outside Diameter of Hollow Shaft based on Equivalent Twisting Moment
Go Hollow Shaft Outer Diameter = ((Equivalent Twisting Moment)*(16/pi)*(1)/((Torsional Shear Stress in Shaft)*(1-Ratio of Inner to Outer Diameter of Hollow Shaft^4)))^(1/3)
Maximum Deflection due to Shaft with Uniform Weight
Go Deflection = (Uniformly Distributed Load per Unit Length*Length^(4))/((8*Modulus of Elasticity)*(pi/64)*Diameter of Shaft for Agitator^(4))
Maximum Torque for Hollow Shaft
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))
Outside Diameter of Hollow Shaft based on Equivalent Bending Moment
Go Diameter of Hollow Shaft for Agitator = ((Equivalent Bending Moment)*(32/pi)*(1)/((Bending Stress)*(1-Ratio of Inner to Outer Diameter of Hollow Shaft^4)))^(1/3)
Maximum Deflection due to Each Load
Go Deflection due to each Load = (Concentrated Load*Length^(3))/((3*Modulus of Elasticity)*(pi/64)*Diameter of Shaft for Agitator^(4))
Equivalent Twisting Moment for Hollow Shaft
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
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)
Diameter of Hollow Shaft Subjected to Maximum Bending Moment
Go Hollow Shaft Outer Diameter = (Maximum Bending Moment/((pi/32)*(Bending Stress)*(1-Ratio of Inner to Outer Diameter of Hollow Shaft^2)))^(1/3)
Equivalent Bending Moment for Solid Shaft
Go Equivalent Bending Moment for Solid Shaft = (1/2)*(Maximum Bending Moment+sqrt(Maximum Bending Moment^2+Maximum Torque for Agitator^2))
Diameter of Solid Shaft Subjected to Maximum Bending Moment
Go Diameter of Solid Shaft for Agitator = ((Maximum Bending Moment for Solid Shaft)/((pi/32)*Bending Stress))^(1/3)
Maximum Torque for Solid Shaft
Go Maximum Torque for Solid Shaft = ((pi/16)*(Diameter of Shaft for Agitator^3)*(Torsional Shear Stress in Shaft))
Equivalent Twisting Moment for Solid Shaft
Go Equivalent Twisting Moment for Solid Shaft = (sqrt((Maximum Bending Moment^2)+(Maximum Torque for Agitator^2)))
Diameter of Solid Shaft based on Equivalent Twisting Moment
Go Diameter of Solid Shaft = (Equivalent Twisting Moment*16/pi*1/Torsional Shear Stress in Shaft)^(1/3)
Diameter of Solid Shaft based on Equivalent Bending Moment
Go Diameter of Solid Shaft for Agitator = (Equivalent Bending Moment*32/pi*1/Bending Stress)^(1/3)
Rated Motor Torque
Go Rated Motor Torque = ((Power*4500)/(2*pi*Speed of Agitator))
Force for Design of Shaft Based on Pure Bending
Go Force = Maximum Torque for Agitator/(0.75*Height of Manometer Liquid)
Maximum Bending Moment subject to Shaft
Go Maximum Bending Moment = Length of Shaft*Force
Critical Speed for Each Deflection
Go Critical Speed = 946/sqrt(Deflection)

8 Shaft Subjected to Combined Twisting Moment and Bending Moment Calculators

Outside Diameter of Hollow Shaft based on Equivalent Twisting Moment
Go Hollow Shaft Outer Diameter = ((Equivalent Twisting Moment)*(16/pi)*(1)/((Torsional Shear Stress in Shaft)*(1-Ratio of Inner to Outer Diameter of Hollow Shaft^4)))^(1/3)
Outside Diameter of Hollow Shaft based on Equivalent Bending Moment
Go Diameter of Hollow Shaft for Agitator = ((Equivalent Bending Moment)*(32/pi)*(1)/((Bending Stress)*(1-Ratio of Inner to Outer Diameter of Hollow Shaft^4)))^(1/3)
Equivalent Twisting Moment for Hollow Shaft
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
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
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
Go Equivalent Twisting Moment for Solid Shaft = (sqrt((Maximum Bending Moment^2)+(Maximum Torque for Agitator^2)))
Diameter of Solid Shaft based on Equivalent Twisting Moment
Go Diameter of Solid Shaft = (Equivalent Twisting Moment*16/pi*1/Torsional Shear Stress in Shaft)^(1/3)
Diameter of Solid Shaft based on Equivalent Bending Moment
Go Diameter of Solid Shaft for Agitator = (Equivalent Bending Moment*32/pi*1/Bending Stress)^(1/3)

Equivalent Bending Moment for Hollow Shaft 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)
Mehollowshaft = (pi/32)*(fb)*(do ^3)*(1-k^4)

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 Mehollowshaft 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 (fb), Hollow Shaft Outer Diameter (do) & 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 Mehollowshaft = (pi/32)*(fb)*(do ^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 (fb), Hollow Shaft Outer Diameter (do) & 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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