Outside Diameter of Hollow Shaft based on Equivalent Bending Moment Calculator

✖The Equivalent Bending Moment is a bending moment which, acting alone, would produce in a shaft a normal stress .ⓘ Equivalent Bending Moment [M_e]			+10% -10%
✖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%
✖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%

✖Diameter of Hollow Shaft for Agitator is defined as the diameter of the hole in the iron laminations that contains the shaft.ⓘ Outside Diameter of Hollow Shaft based on Equivalent Bending Moment [d_hollowshaft]

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Outside Diameter of Hollow Shaft based on Equivalent Bending Moment

Formula

`"d"_{"hollowshaft"} = (("M"_{"e"})*(32/pi)*(1)/(("f"_{"b"})*(1-"k"^4)))^(1/3)`

Example

`"8.10661mm"=(("5000N*mm")*(32/pi)*(1)/(("200N/mm²")*(1-("0.85")^4)))^(1/3)`

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Download Design of Agitation System Components Formulas PDF

Outside Diameter of Hollow Shaft based on Equivalent Bending Moment Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

Diameter of Hollow Shaft for Agitator - (Measured in Meter) - Diameter of Hollow Shaft for Agitator is defined as the diameter of the hole in the iron laminations that contains the shaft.
Equivalent Bending Moment - (Measured in Newton Meter) - The Equivalent Bending Moment is a bending moment which, acting alone, would produce in a shaft a normal stress .
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.
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

Equivalent Bending Moment: 5000 Newton Millimeter --> 5 Newton Meter (Check conversion here)
Bending Stress: 200 Newton per Square Millimeter --> 200000000 Pascal (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

d_hollowshaft = ((M_e)*(32/pi)*(1)/((f_b)*(1-k^4)))^(1/3) --> ((5)*(32/pi)*(1)/((200000000)*(1-0.85^4)))^(1/3)

Evaluating ... ...

d_hollowshaft = 0.00810661034827878

STEP 3: Convert Result to Output's Unit

0.00810661034827878 Meter -->8.10661034827878 Millimeter (Check conversion here)

FINAL ANSWER

8.10661034827878 ≈ 8.10661 Millimeter <-- Diameter of Hollow Shaft for Agitator

(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)

Outside Diameter of Hollow Shaft based on Equivalent Bending Moment Formula

What is Maximum Shear Stress Theory for Ductile 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 Outside Diameter of Hollow Shaft based on Equivalent Bending Moment?

Outside Diameter of Hollow Shaft based on Equivalent Bending Moment calculator uses 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) to calculate the Diameter of Hollow Shaft for Agitator, The Outside Diameter of Hollow Shaft based on Equivalent Bending Moment formula can be calculated with respect to the Bending Moment that alone produce maximum normal stress equal to the maximum normal stress produced due to combined bending and torsion. Diameter of Hollow Shaft for Agitator is denoted by d_hollowshaft symbol.

How to calculate Outside Diameter of Hollow Shaft based on Equivalent Bending Moment using this online calculator? To use this online calculator for Outside Diameter of Hollow Shaft based on Equivalent Bending Moment, enter Equivalent Bending Moment (M_e), Bending Stress (f_b) & Ratio of Inner to Outer Diameter of Hollow Shaft (k) and hit the calculate button. Here is how the Outside Diameter of Hollow Shaft based on Equivalent Bending Moment calculation can be explained with given input values -> 8106.61 = ((5)*(32/pi)*(1)/((200000000)*(1-0.85^4)))^(1/3).

FAQ

What is Outside Diameter of Hollow Shaft based on Equivalent Bending Moment?

The Outside Diameter of Hollow Shaft based on Equivalent Bending Moment formula can be calculated with respect to the Bending Moment that alone produce maximum normal stress equal to the maximum normal stress produced due to combined bending and torsion and is represented as d_hollowshaft = ((M_e)*(32/pi)*(1)/((f_b)*(1-k^4)))^(1/3) or 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). The Equivalent Bending Moment is a bending moment which, acting alone, would produce in a shaft a normal 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 & 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 Outside Diameter of Hollow Shaft based on Equivalent Bending Moment?

The Outside Diameter of Hollow Shaft based on Equivalent Bending Moment formula can be calculated with respect to the Bending Moment that alone produce maximum normal stress equal to the maximum normal stress produced due to combined bending and torsion is calculated using 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). To calculate Outside Diameter of Hollow Shaft based on Equivalent Bending Moment, you need Equivalent Bending Moment (M_e), Bending Stress (f_b) & Ratio of Inner to Outer Diameter of Hollow Shaft (k). With our tool, you need to enter the respective value for Equivalent Bending Moment, Bending Stress & 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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