Torsional Shear Stress when Shaft is Subjected to Pure Torsional Moment Solution

STEP 0: Pre-Calculation Summary
Formula Used
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))
๐œh = 16*Mthollowshaft/(pi*do^3*(1-C^4))
This formula uses 1 Constants, 4 Variables
Constants Used
pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288
Variables Used
Torsional Shear Stress in Hollow Shaft - (Measured in Pascal) - Torsional Shear Stress in Hollow Shaft is the shear stress produced in the hollow shaft due to the twisting.
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.
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.
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
Torsional Moment in Hollow Shaft: 320000 Newton Millimeter --> 320 Newton Meter (Check conversion here)
Outer Diameter of Hollow Shaft: 46 Millimeter --> 0.046 Meter (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
๐œh = 16*Mthollowshaft/(pi*do^3*(1-C^4)) --> 16*320/(pi*0.046^3*(1-0.85^4))
Evaluating ... ...
๐œh = 35028728.6575477
STEP 3: Convert Result to Output's Unit
35028728.6575477 Pascal -->35.0287286575477 Newton per Square Millimeter (Check conversion here)
FINAL ANSWER
35.0287286575477 โ‰ˆ 35.02873 Newton per Square Millimeter <-- Torsional Shear Stress in Hollow Shaft
(Calculation completed in 00.004 seconds)

Credits

Created by Kethavath Srinath
Osmania University (OU), Hyderabad
Kethavath Srinath has created this Calculator and 1000+ more calculators!
Verified by Anshika Arya
National Institute Of Technology (NIT), Hamirpur
Anshika Arya has verified this Calculator and 2500+ more calculators!

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

Torsional Shear Stress when Shaft is Subjected to Pure Torsional Moment Formula

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))
๐œh = 16*Mthollowshaft/(pi*do^3*(1-C^4))

Define Shear Stress

Shear stress, force tending to cause deformation of a material by slippage along a plane or planes parallel to the imposed stress. The resultant shear is of great importance in nature, being intimately related to the downslope movement of earth materials and to earthquakes. Shear stress may occur in solids or liquids; in the latter it is related to fluid viscosity.

How to Calculate Torsional Shear Stress when Shaft is Subjected to Pure Torsional Moment?

Torsional Shear Stress when Shaft is Subjected to Pure Torsional Moment calculator uses 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)) to calculate the Torsional Shear Stress in Hollow Shaft, The Torsional Shear Stress when Shaft is Subjected to Pure Torsional Moment formula is defined as the shear stress produced in the shaft due to the twisting. This twisting in the shaft is caused by the couple acting on it. Torsional Shear Stress in Hollow Shaft is denoted by ๐œh symbol.

How to calculate Torsional Shear Stress when Shaft is Subjected to Pure Torsional Moment using this online calculator? To use this online calculator for Torsional Shear Stress when Shaft is Subjected to Pure Torsional Moment, enter Torsional Moment in Hollow Shaft (Mthollowshaft), Outer Diameter of Hollow Shaft (do) & Ratio of Inner to Outer Diameter of Hollow Shaft (C) and hit the calculate button. Here is how the Torsional Shear Stress when Shaft is Subjected to Pure Torsional Moment calculation can be explained with given input values -> 3.5E-5 = 16*320/(pi*0.046^3*(1-0.85^4)).

FAQ

What is Torsional Shear Stress when Shaft is Subjected to Pure Torsional Moment?
The Torsional Shear Stress when Shaft is Subjected to Pure Torsional Moment formula is defined as the shear stress produced in the shaft due to the twisting. This twisting in the shaft is caused by the couple acting on it and is represented as ๐œh = 16*Mthollowshaft/(pi*do^3*(1-C^4)) or 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 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, Outer Diameter of Hollow Shaft is defined as the length of the longest chord of the surface of the hollow circular 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.
How to calculate Torsional Shear Stress when Shaft is Subjected to Pure Torsional Moment?
The Torsional Shear Stress when Shaft is Subjected to Pure Torsional Moment formula is defined as the shear stress produced in the shaft due to the twisting. This twisting in the shaft is caused by the couple acting on it is calculated using 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)). To calculate Torsional Shear Stress when Shaft is Subjected to Pure Torsional Moment, you need Torsional Moment in Hollow Shaft (Mthollowshaft), Outer Diameter of Hollow Shaft (do) & Ratio of Inner to Outer Diameter of Hollow Shaft (C). With our tool, you need to enter the respective value for Torsional Moment in Hollow Shaft, Outer Diameter of 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.
Let Others Know
โœ–
Facebook
Twitter
Reddit
LinkedIn
Email
WhatsApp
Copied!