Outer Diameter of Hollow Shaft given Principle Stress Solution

STEP 0: Pre-Calculation Summary
Formula Used
Outer Diameter of Hollow Shaft = (16*(Bending Moment in Hollow Shaft+sqrt(Bending Moment in Hollow Shaft^2+Torsional Moment in Hollow Shaft^2))/(pi*Maximum Principle Stress in Hollow Shaft*(1-Ratio of Inner to Outer Diameter of Hollow Shaft^4)))^(1/3)
do = (16*(Mb h+sqrt(Mb h^2+Mthollowshaft^2))/(pi*τ*(1-C^4)))^(1/3)
This formula uses 1 Constants, 1 Functions, 5 Variables
Constants Used
pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288
Functions Used
sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)
Variables Used
Outer Diameter of Hollow Shaft - (Measured in Meter) - Outer Diameter of Hollow Shaft is defined as the length of the longest chord of the surface of the hollow circular shaft.
Bending Moment in Hollow Shaft - (Measured in Newton Meter) - Bending Moment in Hollow Shaft is the reaction induced in a structural shaft hollow element when an external force or moment is applied to the element, causing the element to bend.
Torsional Moment in Hollow Shaft - (Measured in Newton Meter) - Torsional Moment in Hollow Shaft is the reaction induced in a structural shaft hollow element when an external force or moment is applied to the element, causing the element to twist.
Maximum Principle Stress in Hollow Shaft - (Measured in Pascal) - Maximum Principle Stress in Hollow Shaft is defined as the normal stress calculated at an angle when shear stress is considered zero.
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
Bending Moment in Hollow Shaft: 550000 Newton Millimeter --> 550 Newton Meter (Check conversion here)
Torsional Moment in Hollow Shaft: 320000 Newton Millimeter --> 320 Newton Meter (Check conversion here)
Maximum Principle Stress in Hollow Shaft: 129.8 Newton per Square Millimeter --> 129800000 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 = (16*(Mb h+sqrt(Mb h^2+Mthollowshaft^2))/(pi*τ*(1-C^4)))^(1/3) --> (16*(550+sqrt(550^2+320^2))/(pi*129800000*(1-0.85^4)))^(1/3)
Evaluating ... ...
do = 0.046007084849036
STEP 3: Convert Result to Output's Unit
0.046007084849036 Meter -->46.007084849036 Millimeter (Check conversion here)
FINAL ANSWER
46.007084849036 46.00708 Millimeter <-- Outer Diameter of Hollow Shaft
(Calculation completed in 00.004 seconds)

Credits

Created by Kethavath Srinath
Osmania University (OU), Hyderabad
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Vishwakarma Government Engineering College (VGEC), Ahmedabad
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23 Design of Hollow Shaft Calculators

Outer Diameter of Hollow Shaft given Principle Stress
Go Outer Diameter of Hollow Shaft = (16*(Bending Moment in Hollow Shaft+sqrt(Bending Moment in Hollow Shaft^2+Torsional Moment in Hollow Shaft^2))/(pi*Maximum Principle Stress in Hollow Shaft*(1-Ratio of Inner to Outer Diameter of Hollow Shaft^4)))^(1/3)
Ratio of Diameters given Principle Stress
Go Ratio of Inner to Outer Diameter of Hollow Shaft = (1-16*(Bending Moment in Hollow Shaft+sqrt(Bending Moment in Hollow Shaft^2+Torsional Moment in Hollow Shaft^2))/(pi*Outer Diameter of Hollow Shaft^3*Maximum Principle Stress in Hollow Shaft))^(1/4)
Principle Stress Maximum Principle Stress Theory
Go Maximum Principle Stress in Hollow Shaft = 16*(Bending Moment in Hollow Shaft+sqrt(Bending Moment in Hollow Shaft^2+Torsional Moment in Hollow Shaft^2))/(pi*Outer Diameter of Hollow Shaft^3*(1-Ratio of Inner to Outer Diameter of Hollow Shaft^4))
Outer Diameter of Hollow Shaft given Angle of Twist Torsional Rigidity
Go Outer Diameter of Hollow Shaft = (584*Torsional Moment in Hollow Shaft*Length of Hollow Shaft/(Modulus of Rigidity of Hollow Shaft*Angle of Twist of Hollow Shaft*(1-Ratio of Inner to Outer Diameter of Hollow Shaft^4)))^(1/4)
Ratio of Diameters given Angle of Twist of Hollow Shaft and Torsional Rigidity
Go Ratio of Inner to Outer Diameter of Hollow Shaft = (1-584*Torsional Moment in Hollow Shaft*Length of Hollow Shaft/(Modulus of Rigidity of Hollow Shaft*Outer Diameter of Hollow Shaft^4*Angle of Twist of Hollow Shaft))^(1/4)
Length of Shaft given Angle of Twist of Hollow Shaft on Basis of Torsional Rigidity
Go Length of Hollow Shaft = Angle of Twist of Hollow Shaft*(Modulus of Rigidity of Hollow Shaft*Outer Diameter of Hollow Shaft^4*(1-Ratio of Inner to Outer Diameter of Hollow Shaft^4))/(584*Torsional Moment in Hollow Shaft)
Torsional Moment given Angle of Twist on Basis of Torsional Rigidity
Go Torsional Moment in Hollow Shaft = Angle of Twist of Hollow Shaft*(Modulus of Rigidity of Hollow Shaft*Outer Diameter of Hollow Shaft^4*(1-Ratio of Inner to Outer Diameter of Hollow Shaft^4))/(584*Length of Hollow Shaft)
Modulus of Rigidity given Angle of Twist of Hollow Shaft on basis of Torsional Rigidity
Go Modulus of Rigidity of Hollow Shaft = 584*Torsional Moment in Hollow Shaft*Length of Hollow Shaft/(Angle of Twist of Hollow Shaft*Outer Diameter of Hollow Shaft^4*(1-Ratio of Inner to Outer Diameter of Hollow Shaft^4))
Angle of Twist of Hollow Shaft on Basis of Torsional Rigidity
Go Angle of Twist of Hollow Shaft = 584*Torsional Moment in Hollow Shaft*Length of Hollow Shaft/(Modulus of Rigidity of Hollow Shaft*Outer Diameter of Hollow Shaft^4*(1-Ratio of Inner to Outer Diameter of Hollow Shaft^4))
Ratio of Diameters given Tensile Stress in Hollow Shaft
Go Ratio of Inner to Outer Diameter of Hollow Shaft = sqrt(1-(Axial Force on Hollow Shaft/(pi/4*Tensile Stress in Hollow Shaft*Outer Diameter of Hollow Shaft^2)))
Outer Diameter of Shaft given Torsional Shear Stress
Go Outer Diameter of Hollow Shaft = (16*Torsional Moment in Hollow Shaft/(pi*Torsional Shear Stress in Hollow Shaft*(1-Ratio of Inner to Outer Diameter of Hollow Shaft^4)))^(1/3)
Ratio of Diameter given Torsional Shear Stress in Hollow Shaft
Go Ratio of Inner to Outer Diameter of Hollow Shaft = (1-16*Torsional Moment in Hollow Shaft/(pi*Outer Diameter of Hollow Shaft^3*Torsional Shear Stress in Hollow Shaft))^(1/4)
Torsional Shear Stress when Shaft is Subjected to Pure Torsional Moment
Go Torsional Shear Stress in Hollow Shaft = 16*Torsional Moment in Hollow Shaft/(pi*Outer Diameter of Hollow Shaft^3*(1-Ratio of Inner to Outer Diameter of Hollow Shaft^4))
Torsional Moment given Torsional Shear Stress in Hollow Shaft
Go Torsional Moment in Hollow Shaft = Torsional Shear Stress in Hollow Shaft*(pi*Outer Diameter of Hollow Shaft^3*(1-Ratio of Inner to Outer Diameter of Hollow Shaft^4))/16
Outer Diameter of Hollow Shaft given Bending Stress of Hollow Shaft
Go Outer Diameter of Hollow Shaft = (32*Bending Moment in Hollow Shaft/(pi*Bending Stress in Hollow Shaft*(1-Ratio of Inner to Outer Diameter of Hollow Shaft^4)))^(1/3)
Ratio of Diameters given Bending Stress of Hollow Shaft
Go Ratio of Inner to Outer Diameter of Hollow Shaft = (1-32*Bending Moment in Hollow Shaft/(pi*Outer Diameter of Hollow Shaft^3*Bending Stress in Hollow Shaft))^(1/4)
Bending Moment given Bending Stress in Hollow Shaft
Go Bending Moment in Hollow Shaft = Bending Stress in Hollow Shaft*(pi*Outer Diameter of Hollow Shaft^3*(1-(Ratio of Inner to Outer Diameter of Hollow Shaft^4)))/32
Bending Stress in Hollow Shaft
Go Bending Stress in Hollow Shaft = 32*Bending Moment in Hollow Shaft/(pi*Outer Diameter of Hollow Shaft^3*(1-Ratio of Inner to Outer Diameter of Hollow Shaft^4))
Tensile Stress in Hollow Shaft when Subjected to Axial Force
Go Tensile Stress in Hollow Shaft = Axial Force on Hollow Shaft/(pi/4*(Outer Diameter of Hollow Shaft^2-Inner Diameter of Hollow Shaft^2))
Axial Tensile Force given Tensile Stress in Hollow Shaft
Go Axial Force on Hollow Shaft = Tensile Stress in Hollow Shaft*pi/4*(Outer Diameter of Hollow Shaft^2-Inner Diameter of Hollow Shaft^2)
Inner Diameter of Hollow Shaft given Ratio of Diameters
Go Inner Diameter of Hollow Shaft = Ratio of Inner to Outer Diameter of Hollow Shaft*Outer Diameter of Hollow Shaft
Ratio of Inner Diameter to Outer Diameter
Go Ratio of Inner to Outer Diameter of Hollow Shaft = Inner Diameter of Hollow Shaft/Outer Diameter of Hollow Shaft
Outer Diameter given Ratio of Diameters
Go Outer Diameter of Hollow Shaft = Inner Diameter of Hollow Shaft/Ratio of Inner to Outer Diameter of Hollow Shaft

Outer Diameter of Hollow Shaft given Principle Stress Formula

Outer Diameter of Hollow Shaft = (16*(Bending Moment in Hollow Shaft+sqrt(Bending Moment in Hollow Shaft^2+Torsional Moment in Hollow Shaft^2))/(pi*Maximum Principle Stress in Hollow Shaft*(1-Ratio of Inner to Outer Diameter of Hollow Shaft^4)))^(1/3)
do = (16*(Mb h+sqrt(Mb h^2+Mthollowshaft^2))/(pi*τ*(1-C^4)))^(1/3)

Define Principle Stress

It is defined as the normal stress calculated at an angle when shear stress is considered as zero. The normal stress can be obtained for maximum and minimum values.

How to Calculate Outer Diameter of Hollow Shaft given Principle Stress?

Outer Diameter of Hollow Shaft given Principle Stress calculator uses Outer Diameter of Hollow Shaft = (16*(Bending Moment in Hollow Shaft+sqrt(Bending Moment in Hollow Shaft^2+Torsional Moment in Hollow Shaft^2))/(pi*Maximum Principle Stress in Hollow Shaft*(1-Ratio of Inner to Outer Diameter of Hollow Shaft^4)))^(1/3) to calculate the Outer Diameter of Hollow Shaft, The Outer Diameter of Hollow Shaft given Principle Stress formula is defined as the outer diameter of the hollow shaft on which we are applying torsional and bending moments. Outer Diameter of Hollow Shaft is denoted by do symbol.

How to calculate Outer Diameter of Hollow Shaft given Principle Stress using this online calculator? To use this online calculator for Outer Diameter of Hollow Shaft given Principle Stress, enter Bending Moment in Hollow Shaft (Mb h), Torsional Moment in Hollow Shaft (Mthollowshaft), Maximum Principle Stress in Hollow Shaft (τ) & Ratio of Inner to Outer Diameter of Hollow Shaft (C) and hit the calculate button. Here is how the Outer Diameter of Hollow Shaft given Principle Stress calculation can be explained with given input values -> 46007.08 = (16*(550+sqrt(550^2+320^2))/(pi*129800000*(1-0.85^4)))^(1/3).

FAQ

What is Outer Diameter of Hollow Shaft given Principle Stress?
The Outer Diameter of Hollow Shaft given Principle Stress formula is defined as the outer diameter of the hollow shaft on which we are applying torsional and bending moments and is represented as do = (16*(Mb h+sqrt(Mb h^2+Mthollowshaft^2))/(pi*τ*(1-C^4)))^(1/3) or Outer Diameter of Hollow Shaft = (16*(Bending Moment in Hollow Shaft+sqrt(Bending Moment in Hollow Shaft^2+Torsional Moment in Hollow Shaft^2))/(pi*Maximum Principle Stress in Hollow Shaft*(1-Ratio of Inner to Outer Diameter of Hollow Shaft^4)))^(1/3). Bending Moment in Hollow Shaft is the reaction induced in a structural shaft hollow element when an external force or moment is applied to the element, causing the element to bend, Torsional Moment in Hollow Shaft is the reaction induced in a structural shaft hollow element when an external force or moment is applied to the element, causing the element to twist, Maximum Principle Stress in Hollow Shaft is defined as the normal stress calculated at an angle when shear stress is considered zero & 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 Outer Diameter of Hollow Shaft given Principle Stress?
The Outer Diameter of Hollow Shaft given Principle Stress formula is defined as the outer diameter of the hollow shaft on which we are applying torsional and bending moments is calculated using Outer Diameter of Hollow Shaft = (16*(Bending Moment in Hollow Shaft+sqrt(Bending Moment in Hollow Shaft^2+Torsional Moment in Hollow Shaft^2))/(pi*Maximum Principle Stress in Hollow Shaft*(1-Ratio of Inner to Outer Diameter of Hollow Shaft^4)))^(1/3). To calculate Outer Diameter of Hollow Shaft given Principle Stress, you need Bending Moment in Hollow Shaft (Mb h), Torsional Moment in Hollow Shaft (Mthollowshaft), Maximum Principle Stress in Hollow Shaft (τ) & Ratio of Inner to Outer Diameter of Hollow Shaft (C). With our tool, you need to enter the respective value for Bending Moment in Hollow Shaft, Torsional Moment in Hollow Shaft, Maximum Principle Stress in Hollow 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 Outer Diameter of Hollow Shaft?
In this formula, Outer Diameter of Hollow Shaft uses Bending Moment in Hollow Shaft, Torsional Moment in Hollow Shaft, Maximum Principle Stress in Hollow Shaft & Ratio of Inner to Outer Diameter of Hollow Shaft. We can use 4 other way(s) to calculate the same, which is/are as follows -
  • Outer Diameter of Hollow Shaft = Inner Diameter of Hollow Shaft/Ratio of Inner to Outer Diameter of Hollow Shaft
  • Outer Diameter of Hollow Shaft = (32*Bending Moment in Hollow Shaft/(pi*Bending Stress in Hollow Shaft*(1-Ratio of Inner to Outer Diameter of Hollow Shaft^4)))^(1/3)
  • Outer Diameter of Hollow Shaft = (16*Torsional Moment in Hollow Shaft/(pi*Torsional Shear Stress in Hollow Shaft*(1-Ratio of Inner to Outer Diameter of Hollow Shaft^4)))^(1/3)
  • Outer Diameter of Hollow Shaft = (584*Torsional Moment in Hollow Shaft*Length of Hollow Shaft/(Modulus of Rigidity of Hollow Shaft*Angle of Twist of Hollow Shaft*(1-Ratio of Inner to Outer Diameter of Hollow Shaft^4)))^(1/4)
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