Diameter of Hollow Shaft Subjected to Maximum Bending Moment Calculator

✖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.ⓘ Maximum Bending Moment [M_m]			+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%

✖Hollow Shaft Outer Diameter is defined as the length of the longest chord of the surface of the hollow circular shaft.ⓘ Diameter of Hollow Shaft Subjected to Maximum Bending Moment [d_o]

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Diameter of Hollow Shaft Subjected to Maximum Bending Moment

Formula

`"d"_{"o"} = ("M"_{"m"}/((pi/32)*("f"_{"b"})*(1-"k"^2)))^(1/3)`

Example

`"18.41035mm"=("34000N*mm"/((pi/32)*("200N/mm²")*(1-("0.85")^2)))^(1/3)`

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Diameter of Hollow Shaft Subjected to Maximum Bending Moment Solution

STEP 0: Pre-Calculation Summary

Formula Used

Hollow Shaft Outer Diameter = (Maximum Bending Moment/((pi/32)*(Bending Stress)*(1-Ratio of Inner to Outer Diameter of Hollow Shaft^2)))^(1/3)
d_o = (M_m/((pi/32)*(f_b)*(1-k^2)))^(1/3)
This formula uses 1 Constants, 4 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

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.
Maximum Bending Moment - (Measured in Newton Meter) - 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.
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

Maximum Bending Moment: 34000 Newton Millimeter --> 34 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_o = (M_m/((pi/32)*(f_b)*(1-k^2)))^(1/3) --> (34/((pi/32)*(200000000)*(1-0.85^2)))^(1/3)

Evaluating ... ...

d_o = 0.0184103486522574

STEP 3: Convert Result to Output's Unit

0.0184103486522574 Meter -->18.4103486522574 Millimeter (Check conversion here)

FINAL ANSWER

18.4103486522574 ≈ 18.41035 Millimeter <-- Hollow Shaft Outer Diameter

(Calculation completed in 00.020 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)

< 7 Shaft Subjected to Bending Moment Only Calculators

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)

Bending Stress for Hollow Shaft

Go Bending Stress = Maximum Bending Moment/((pi/32)*(Hollow Shaft Outer Diameter)^(3)*(1-Ratio of Inner to Outer Diameter of Hollow Shaft^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)

Bending Stress for Solid Shaft

Go Bending Stress = (Maximum Bending Moment for Solid Shaft)/((pi/32)*(Diameter of Solid Shaft for Agitator)^3)

Force for Design of Shaft Based on Pure Bending

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

Maximum Torque of Shaft Subjected to Bending Moment only

Go Maximum Torque for Agitator = Force*(0.75*Radius of Impeller Blade)

Maximum Bending Moment subject to Shaft

Go Maximum Bending Moment = Length of Shaft*Force

Diameter of Hollow Shaft Subjected to Maximum Bending Moment 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)
d_o = (M_m/((pi/32)*(f_b)*(1-k^2)))^(1/3)

What is Bending ?

Bending characterizes the behavior of a slender structural element subjected to an external load applied perpendicularly to a longitudinal axis of the element.

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

Diameter of Hollow Shaft Subjected to Maximum Bending Moment calculator 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 calculate 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 calculate Diameter of Hollow Shaft Subjected to Maximum Bending Moment using this online calculator? To use this online calculator 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. Here is how the Diameter of Hollow Shaft Subjected to Maximum Bending Moment calculation can be explained with given input values -> 18410.35 = (34/((pi/32)*(200000000)*(1-0.85^2)))^(1/3).

FAQ

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

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 and is represented as d_o = (M_m/((pi/32)*(f_b)*(1-k^2)))^(1/3) or Hollow Shaft Outer Diameter = (Maximum Bending Moment/((pi/32)*(Bending Stress)*(1-Ratio of Inner to Outer Diameter of Hollow Shaft^2)))^(1/3). 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, 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 Diameter of Hollow Shaft Subjected to Maximum Bending Moment?

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 is calculated using 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 calculate Diameter of Hollow Shaft Subjected to Maximum Bending Moment, you need Maximum Bending Moment (M_m), 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 Maximum 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.

How many ways are there to calculate Hollow Shaft Outer Diameter?

In this formula, Hollow Shaft Outer Diameter uses Maximum Bending Moment, Bending Stress & Ratio of Inner to Outer Diameter of Hollow Shaft. We can use 1 other way(s) to calculate the same, which is/are as follows -

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)

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