Diameter of Solid Shaft based on Equivalent Twisting Moment Calculator

✖Equivalent Twisting Moment that alone produces maximum shear stress equal to the maximum shear stress produce due to combined bending and torsion.ⓘ Equivalent Twisting Moment [T_e]			+10% -10%
✖Torsional Shear Stress in Shaft is the shear stress produced in the shaft due to the twisting.ⓘ Torsional Shear Stress in Shaft [f_s]			+10% -10%

✖Diameter of Solid Shaft is defined as the diameter of the hole in the iron laminations that contains the shaft.ⓘ Diameter of Solid Shaft based on Equivalent Twisting Moment [Diameter_solidshaft]

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Diameter of Solid Shaft based on Equivalent Twisting Moment

Formula

`"Diameter"_{"solidshaft"} = ("T"_{"e"}*16/pi*1/"f"_{"s"})^(1/3)`

Example

`"21.55009mm"=("900000N*mm"*16/pi*1/"458N/mm²")^(1/3)`

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Download Design of Agitation System Components Formulas PDF

Diameter of Solid Shaft based on Equivalent Twisting Moment Solution

STEP 0: Pre-Calculation Summary

Formula Used

Diameter of Solid Shaft = (Equivalent Twisting Moment*16/pi*1/Torsional Shear Stress in Shaft)^(1/3)
Diameter_solidshaft = (T_e*16/pi*1/f_s)^(1/3)
This formula uses 1 Constants, 3 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

Diameter of Solid Shaft - (Measured in Meter) - Diameter of Solid Shaft is defined as the diameter of the hole in the iron laminations that contains the 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.

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)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

Diameter_solidshaft = (T_e*16/pi*1/f_s)^(1/3) --> (900*16/pi*1/458000000)^(1/3)

Evaluating ... ...

Diameter_solidshaft = 0.0215500879596176

STEP 3: Convert Result to Output's Unit

0.0215500879596176 Meter -->21.5500879596176 Millimeter (Check conversion here)

FINAL ANSWER

21.5500879596176 ≈ 21.55009 Millimeter <-- Diameter of Solid Shaft

(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)

< 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)

Diameter of Solid Shaft based on Equivalent Twisting Moment Formula

Diameter of Solid Shaft = (Equivalent Twisting Moment*16/pi*1/Torsional Shear Stress in Shaft)^(1/3)
Diameter_solidshaft = (T_e*16/pi*1/f_s)^(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 Diameter of Solid Shaft based on Equivalent Twisting Moment?

Diameter of Solid Shaft based on Equivalent Twisting Moment calculator uses Diameter of Solid Shaft = (Equivalent Twisting Moment*16/pi*1/Torsional Shear Stress in Shaft)^(1/3) to calculate the Diameter of Solid Shaft, The Diameter of Solid Shaft based on Equivalent Twisting Moment formula is defined 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. Diameter of Solid Shaft is denoted by Diameter_solidshaft symbol.

How to calculate Diameter of Solid Shaft based on Equivalent Twisting Moment using this online calculator? To use this online calculator for Diameter of Solid Shaft based on Equivalent Twisting Moment, enter Equivalent Twisting Moment (T_e) & Torsional Shear Stress in Shaft (f_s) and hit the calculate button. Here is how the Diameter of Solid Shaft based on Equivalent Twisting Moment calculation can be explained with given input values -> 21550.09 = (900*16/pi*1/458000000)^(1/3).

FAQ

What is Diameter of Solid Shaft based on Equivalent Twisting Moment?

The Diameter of Solid Shaft based on Equivalent Twisting Moment formula is defined 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 Diameter_solidshaft = (T_e*16/pi*1/f_s)^(1/3) or Diameter of Solid Shaft = (Equivalent Twisting Moment*16/pi*1/Torsional Shear Stress in Shaft)^(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.

How to calculate Diameter of Solid Shaft based on Equivalent Twisting Moment?

The Diameter of Solid Shaft based on Equivalent Twisting Moment formula is defined 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 Diameter of Solid Shaft = (Equivalent Twisting Moment*16/pi*1/Torsional Shear Stress in Shaft)^(1/3). To calculate Diameter of Solid Shaft based on Equivalent Twisting Moment, you need Equivalent Twisting Moment (T_e) & Torsional Shear Stress in Shaft (f_s). With our tool, you need to enter the respective value for Equivalent Twisting Moment & Torsional Shear Stress in 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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