Residual Angle of Twist for Elasto Plastic Case Solution

STEP 0: Pre-Calculation Summary
Formula Used
Residual Angle of Twist = Yield Stress in Shear/(Modulus of Rigidity*Radius of Plastic Front)*(1-((4*Radius of Plastic Front)/(3*Outer Radius of Shaft))*((1-1/4*(Radius of Plastic Front/Outer Radius of Shaft)^3-(3*Inner Radius of Shaft)/(4*Radius of Plastic Front)*(Inner Radius of Shaft/Outer Radius of Shaft)^3)/(1-(Inner Radius of Shaft/Outer Radius of Shaft)^4)))
θres = 𝝉0/(G*ρ)*(1-((4*ρ)/(3*r2))*((1-1/4*(ρ/r2)^3-(3*r1)/(4*ρ)*(r1/r2)^3)/(1-(r1/r2)^4)))
This formula uses 6 Variables
Variables Used
Residual Angle of Twist - (Measured in Radian) - Residual Angle of Twist is the angle of twist due to residual stresses.
Yield Stress in Shear - (Measured in Pascal) - Yield Stress in Shear is the yield stress of the shaft in shear conditions.
Modulus of Rigidity - (Measured in Pascal) - Modulus of Rigidity can be defined as the ratio of shear stress to shear strain.
Radius of Plastic Front - (Measured in Meter) - Radius of Plastic Front is the difference between the outer radius of shaft and depth yields plastically.
Outer Radius of Shaft - (Measured in Meter) - Outer Radius of Shaft is the external radius of shaft.
Inner Radius of Shaft - (Measured in Meter) - Inner Radius of Shaft is the internal radius of shaft.
STEP 1: Convert Input(s) to Base Unit
Yield Stress in Shear: 145 Megapascal --> 145000000 Pascal (Check conversion ​here)
Modulus of Rigidity: 84000 Megapascal --> 84000000000 Pascal (Check conversion ​here)
Radius of Plastic Front: 80 Millimeter --> 0.08 Meter (Check conversion ​here)
Outer Radius of Shaft: 100 Millimeter --> 0.1 Meter (Check conversion ​here)
Inner Radius of Shaft: 40 Millimeter --> 0.04 Meter (Check conversion ​here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
θres = 𝝉0/(G*ρ)*(1-((4*ρ)/(3*r2))*((1-1/4*(ρ/r2)^3-(3*r1)/(4*ρ)*(r1/r2)^3)/(1-(r1/r2)^4))) --> 145000000/(84000000000*0.08)*(1-((4*0.08)/(3*0.1))*((1-1/4*(0.08/0.1)^3-(3*0.04)/(4*0.08)*(0.04/0.1)^3)/(1-(0.04/0.1)^4)))
Evaluating ... ...
θres = 0.00154714663643236
STEP 3: Convert Result to Output's Unit
0.00154714663643236 Radian --> No Conversion Required
FINAL ANSWER
0.00154714663643236 0.001547 Radian <-- Residual Angle of Twist
(Calculation completed in 00.004 seconds)

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Residual Stresses For Idealized Stress Strain Law Calculators

Residual Shear Stress in Shaft when r Lies between r1 and Material Constant
​ LaTeX ​ Go Residual Shear Stress in Elasto Plastic Yielding = (Yield Stress in Shear*Radius Yielded/Radius of Plastic Front-(((4*Yield Stress in Shear*Radius Yielded)/(3*Outer Radius of Shaft*(1-(Inner Radius of Shaft/Outer Radius of Shaft)^4)))*(1-1/4*(Radius of Plastic Front/Outer Radius of Shaft)^3-(3*Inner Radius of Shaft)/(4*Radius of Plastic Front)*(Inner Radius of Shaft/Outer Radius of Shaft)^3)))
Residual Shear Stress in Shaft when r Lies between Material Constant and r2
​ LaTeX ​ Go Residual Shear Stress in Elasto Plastic Yielding = Yield Stress in Shear*(1-(4*Radius Yielded*(1-((1/4)*(Radius of Plastic Front/Outer Radius of Shaft)^3)-(((3*Inner Radius of Shaft)/(4*Radius of Plastic Front))*(Inner Radius of Shaft/Outer Radius of Shaft)^3)))/(3*Outer Radius of Shaft*(1-(Inner Radius of Shaft/Outer Radius of Shaft)^4)))
Recovery Elasto Plastic Torque
​ LaTeX ​ Go Recovery Elasto Plastic Torque = -(pi*Yield Stress in Shear*(Radius of Plastic Front^3/2*(1-(Inner Radius of Shaft/Radius of Plastic Front)^4)+(2/3*Outer Radius of Shaft^3)*(1-(Radius of Plastic Front/Outer Radius of Shaft)^3)))
Residual Shear Stress in Shaft for Fully Plastic Case
​ LaTeX ​ Go Residual Shear Stress in fully Plastic Yielding = Yield Stress in Shear*(1-(4*Radius Yielded*(1-(Inner Radius of Shaft/Outer Radius of Shaft)^3))/(3*Outer Radius of Shaft*(1-(Inner Radius of Shaft/Outer Radius of Shaft)^4)))

Residual Angle of Twist for Elasto Plastic Case Formula

​LaTeX ​Go
Residual Angle of Twist = Yield Stress in Shear/(Modulus of Rigidity*Radius of Plastic Front)*(1-((4*Radius of Plastic Front)/(3*Outer Radius of Shaft))*((1-1/4*(Radius of Plastic Front/Outer Radius of Shaft)^3-(3*Inner Radius of Shaft)/(4*Radius of Plastic Front)*(Inner Radius of Shaft/Outer Radius of Shaft)^3)/(1-(Inner Radius of Shaft/Outer Radius of Shaft)^4)))
θres = 𝝉0/(G*ρ)*(1-((4*ρ)/(3*r2))*((1-1/4*(ρ/r2)^3-(3*r1)/(4*ρ)*(r1/r2)^3)/(1-(r1/r2)^4)))

What is angle of twist in shaft?

The angle of twist for each section is calculated as φ = TL/JG. The total angle of twist from one end of the shaft to the other is found by summing up the twists for the individual sections. Discrete Changes in Internal Torque. and/or Cross-Section.

How to Calculate Residual Angle of Twist for Elasto Plastic Case?

Residual Angle of Twist for Elasto Plastic Case calculator uses Residual Angle of Twist = Yield Stress in Shear/(Modulus of Rigidity*Radius of Plastic Front)*(1-((4*Radius of Plastic Front)/(3*Outer Radius of Shaft))*((1-1/4*(Radius of Plastic Front/Outer Radius of Shaft)^3-(3*Inner Radius of Shaft)/(4*Radius of Plastic Front)*(Inner Radius of Shaft/Outer Radius of Shaft)^3)/(1-(Inner Radius of Shaft/Outer Radius of Shaft)^4))) to calculate the Residual Angle of Twist, Residual Angle of Twist for Elasto Plastic Case formula is defined as a measure of the remaining twist angle in a shaft after it has undergone elastic and plastic deformations, providing insights into the residual stresses and material behavior in mechanical systems. Residual Angle of Twist is denoted by θres symbol.

How to calculate Residual Angle of Twist for Elasto Plastic Case using this online calculator? To use this online calculator for Residual Angle of Twist for Elasto Plastic Case, enter Yield Stress in Shear (𝝉0), Modulus of Rigidity (G), Radius of Plastic Front (ρ), Outer Radius of Shaft (r2) & Inner Radius of Shaft (r1) and hit the calculate button. Here is how the Residual Angle of Twist for Elasto Plastic Case calculation can be explained with given input values -> 0.001547 = 145000000/(84000000000*0.08)*(1-((4*0.08)/(3*0.1))*((1-1/4*(0.08/0.1)^3-(3*0.04)/(4*0.08)*(0.04/0.1)^3)/(1-(0.04/0.1)^4))).

FAQ

What is Residual Angle of Twist for Elasto Plastic Case?
Residual Angle of Twist for Elasto Plastic Case formula is defined as a measure of the remaining twist angle in a shaft after it has undergone elastic and plastic deformations, providing insights into the residual stresses and material behavior in mechanical systems and is represented as θres = 𝝉0/(G*ρ)*(1-((4*ρ)/(3*r2))*((1-1/4*(ρ/r2)^3-(3*r1)/(4*ρ)*(r1/r2)^3)/(1-(r1/r2)^4))) or Residual Angle of Twist = Yield Stress in Shear/(Modulus of Rigidity*Radius of Plastic Front)*(1-((4*Radius of Plastic Front)/(3*Outer Radius of Shaft))*((1-1/4*(Radius of Plastic Front/Outer Radius of Shaft)^3-(3*Inner Radius of Shaft)/(4*Radius of Plastic Front)*(Inner Radius of Shaft/Outer Radius of Shaft)^3)/(1-(Inner Radius of Shaft/Outer Radius of Shaft)^4))). Yield Stress in Shear is the yield stress of the shaft in shear conditions, Modulus of Rigidity can be defined as the ratio of shear stress to shear strain, Radius of Plastic Front is the difference between the outer radius of shaft and depth yields plastically, Outer Radius of Shaft is the external radius of shaft & Inner Radius of Shaft is the internal radius of shaft.
How to calculate Residual Angle of Twist for Elasto Plastic Case?
Residual Angle of Twist for Elasto Plastic Case formula is defined as a measure of the remaining twist angle in a shaft after it has undergone elastic and plastic deformations, providing insights into the residual stresses and material behavior in mechanical systems is calculated using Residual Angle of Twist = Yield Stress in Shear/(Modulus of Rigidity*Radius of Plastic Front)*(1-((4*Radius of Plastic Front)/(3*Outer Radius of Shaft))*((1-1/4*(Radius of Plastic Front/Outer Radius of Shaft)^3-(3*Inner Radius of Shaft)/(4*Radius of Plastic Front)*(Inner Radius of Shaft/Outer Radius of Shaft)^3)/(1-(Inner Radius of Shaft/Outer Radius of Shaft)^4))). To calculate Residual Angle of Twist for Elasto Plastic Case, you need Yield Stress in Shear (𝝉0), Modulus of Rigidity (G), Radius of Plastic Front (ρ), Outer Radius of Shaft (r2) & Inner Radius of Shaft (r1). With our tool, you need to enter the respective value for Yield Stress in Shear, Modulus of Rigidity, Radius of Plastic Front, Outer Radius of Shaft & Inner Radius of 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 Residual Angle of Twist?
In this formula, Residual Angle of Twist uses Yield Stress in Shear, Modulus of Rigidity, Radius of Plastic Front, Outer Radius of Shaft & Inner Radius of Shaft. We can use 1 other way(s) to calculate the same, which is/are as follows -
  • Residual Angle of Twist = Yield Stress in Shear/(Modulus of Rigidity*Inner Radius of Shaft)*(1-(4*Inner Radius of Shaft)/(3*Outer Radius of Shaft)*((1-(Inner Radius of Shaft/Outer Radius of Shaft)^3)/(1-(Inner Radius of Shaft/Outer Radius of Shaft)^4)))
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