Outside Diameter of Hollow 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%
✖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.ⓘ Outside Diameter of Hollow Shaft based on Equivalent Twisting Moment [d_o]

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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)
d_o = ((T_e)*(16/pi)*(1)/((f_s)*(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

d_o = ((T_e)*(16/pi)*(1)/((f_s)*(1-k^4)))^(1/3) --> ((900)*(16/pi)*(1)/((458000000)*(1-0.85^4)))^(1/3)

Evaluating ... ...

d_o = 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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< Design of Agitation System Components Calculators

Maximum Torque for Hollow Shaft

LaTeX 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))

Maximum Torque for Solid Shaft

LaTeX Go Maximum Torque for Solid Shaft = ((pi/16)*(Diameter of Shaft for Agitator^3)*(Torsional Shear Stress in Shaft))

Rated Motor Torque

LaTeX Go Rated Motor Torque = ((Power*4500)/(2*pi*Speed of Agitator))

Force for Design of Shaft Based on Pure Bending

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

< Shaft Subjected to Combined Twisting Moment and Bending Moment Calculators

Equivalent Twisting Moment for Hollow Shaft

LaTeX 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

LaTeX 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

LaTeX 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

LaTeX Go Equivalent Twisting Moment for Solid Shaft = (sqrt((Maximum Bending Moment^2)+(Maximum Torque for Agitator^2)))

Outside Diameter of Hollow Shaft based on Equivalent Twisting Moment Formula

LaTeX Go

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 d_o 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 (T_e), Torsional Shear Stress in Shaft (f_s) & 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 d_o = ((T_e)*(16/pi)*(1)/((f_s)*(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 (T_e), Torsional Shear Stress in Shaft (f_s) & 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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