Residual Angle of Twist for Elasto Plastic Case Calculator

✖Yield Stress in Shear is the yield stress of the shaft in shear conditions.ⓘ Yield Stress in Shear [𝝉₀]			+10% -10%
✖Modulus of Rigidity is a measure of the stiffness of a solid material, defining the ratio of stress to strain within the proportional limit of elasticity.ⓘ Modulus of Rigidity [G]			+10% -10%
✖Radius of Plastic Front is the distance from the center of the material to the point where plastic deformation occurs due to residual stresses.ⓘ Radius of Plastic Front [ρ]			+10% -10%
✖Outer Radius of Shaft is the distance from the center of the shaft to its outer surface, affecting residual stresses in the material.ⓘ Outer Radius of Shaft [r₂]			+10% -10%
✖Inner Radius of Shaft is the internal radius of a shaft, which is a critical dimension in mechanical engineering, affecting stress concentrations and structural integrity.ⓘ Inner Radius of Shaft [r₁]			+10% -10%

✖Residual Angle of Twist is the angle of twist due to residual stresses.ⓘ Residual Angle of Twist for Elasto Plastic Case [θ_res]

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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)))
θ_res = 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 is a measure of the stiffness of a solid material, defining the ratio of stress to strain within the proportional limit of elasticity.
Radius of Plastic Front - (Measured in Meter) - Radius of Plastic Front is the distance from the center of the material to the point where plastic deformation occurs due to residual stresses.
Outer Radius of Shaft - (Measured in Meter) - Outer Radius of Shaft is the distance from the center of the shaft to its outer surface, affecting residual stresses in the material.
Inner Radius of Shaft - (Measured in Meter) - Inner Radius of Shaft is the internal radius of a shaft, which is a critical dimension in mechanical engineering, affecting stress concentrations and structural integrity.

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

θ_res = 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 ... ...

θ_res = 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 00.020 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 Shaft = (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 Shaft = 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

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 θ_res 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 θ_res = 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 is a measure of the stiffness of a solid material, defining the ratio of stress to strain within the proportional limit of elasticity, Radius of Plastic Front is the distance from the center of the material to the point where plastic deformation occurs due to residual stresses, Outer Radius of Shaft is the distance from the center of the shaft to its outer surface, affecting residual stresses in the material & Inner Radius of Shaft is the internal radius of a shaft, which is a critical dimension in mechanical engineering, affecting stress concentrations and structural integrity.

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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