Outside Diameter of Hollow Shaft based on Equivalent Twisting Moment Solution

STEP 0: Pre-Calculation Summary
Formula Used
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)
do = ((Te)*(16/pi)*(1)/((fs)*(1-k^4)))^(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.
Equivalent Twisting Moment - (Measured in Newton Meter) - Equivalent Twisting Moment that alone produces maximum shear stress equal to the maximum shear stress produce due to combined bending and torsion.
Torsional Shear Stress in Shaft - (Measured in Pascal) - Torsional Shear Stress in Shaft is the shear stress produced in the shaft due to the twisting.
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 Twisting Moment: 900000 Newton Millimeter --> 900 Newton Meter (Check conversion here)
Torsional Shear Stress in Shaft: 458 Newton per Square Millimeter --> 458000000 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
do = ((Te)*(16/pi)*(1)/((fs)*(1-k^4)))^(1/3) --> ((900)*(16/pi)*(1)/((458000000)*(1-0.85^4)))^(1/3)
Evaluating ... ...
do = 0.0275618463800726
STEP 3: Convert Result to Output's Unit
0.0275618463800726 Meter -->27.5618463800726 Millimeter (Check conversion here)
FINAL ANSWER
27.5618463800726 27.56185 Millimeter <-- Hollow Shaft Outer Diameter
(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 Twisting Moment Formula

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)
do = ((Te)*(16/pi)*(1)/((fs)*(1-k^4)))^(1/3)

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 Twisting Moment?

Outside Diameter of Hollow Shaft based on Equivalent Twisting Moment calculator uses 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) to calculate the Hollow Shaft Outer Diameter, The Outside Diameter of Hollow Shaft based on Equivalent Twisting Moment formula is defined as with respect to the twisting moment that alone produce produce maximum shear stress equal to the maximum shear stress produce due to combined bending and torsion. Hollow Shaft Outer Diameter is denoted by do symbol.

How to calculate Outside Diameter of Hollow Shaft based on Equivalent Twisting Moment using this online calculator? To use this online calculator for Outside Diameter of Hollow Shaft based on Equivalent Twisting Moment, enter Equivalent Twisting Moment (Te), Torsional Shear Stress in Shaft (fs) & 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 Twisting Moment calculation can be explained with given input values -> 27561.85 = ((900)*(16/pi)*(1)/((458000000)*(1-0.85^4)))^(1/3).

FAQ

What is Outside Diameter of Hollow Shaft based on Equivalent Twisting Moment?
The Outside Diameter of Hollow Shaft based on Equivalent Twisting Moment formula is defined as with respect to the twisting moment that alone produce produce maximum shear stress equal to the maximum shear stress produce due to combined bending and torsion and is represented as do = ((Te)*(16/pi)*(1)/((fs)*(1-k^4)))^(1/3) or 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). Equivalent Twisting Moment that alone produces maximum shear stress equal to the maximum shear stress produce due to combined bending and torsion, Torsional Shear Stress in Shaft is the shear stress produced in the shaft due to the twisting & 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 Twisting Moment?
The Outside Diameter of Hollow Shaft based on Equivalent Twisting Moment formula is defined as with respect to the twisting moment that alone produce produce maximum shear stress equal to the maximum shear stress produce due to combined bending and torsion is calculated using 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). To calculate Outside Diameter of Hollow Shaft based on Equivalent Twisting Moment, you need Equivalent Twisting Moment (Te), Torsional Shear Stress in Shaft (fs) & Ratio of Inner to Outer Diameter of Hollow Shaft (k). With our tool, you need to enter the respective value for Equivalent Twisting Moment, Torsional Shear Stress in Shaft & 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 Equivalent Twisting Moment, Torsional Shear Stress in Shaft & 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 = (Maximum Bending Moment/((pi/32)*(Bending Stress)*(1-Ratio of Inner to Outer Diameter of Hollow Shaft^2)))^(1/3)
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