Recovery Torque in Fully Plastic Case Solution

STEP 0: Pre-Calculation Summary
Formula Used
Fully Plastic Recovery Torque = -(2/3*pi*Outer Radius of Shaft^3*Yield Stress in Shear*(1-(Inner Radius of Shaft/Outer Radius of Shaft)^3))
Tf_rec = -(2/3*pi*r2^3*𝝉0*(1-(r1/r2)^3))
This formula uses 1 Constants, 4 Variables
Constants Used
pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288
Variables Used
Fully Plastic Recovery Torque - (Measured in Newton Meter) - Fully Plastic Recovery Torque is the equal and opposite of fully plastic applied torque.
Outer Radius of Shaft - (Measured in Meter) - Outer Radius of Shaft is the external radius of shaft.
Yield Stress in Shear - (Measured in Pascal) - Yield Stress in Shear is the yield stress of the shaft in shear conditions.
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
Outer Radius of Shaft: 100 Millimeter --> 0.1 Meter (Check conversion here)
Yield Stress in Shear: 145 Megapascal --> 145000000 Pascal (Check conversion here)
Inner Radius of Shaft: 40 Millimeter --> 0.04 Meter (Check conversion here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
Tf_rec = -(2/3*pi*r2^3*𝝉0*(1-(r1/r2)^3)) --> -(2/3*pi*0.1^3*145000000*(1-(0.04/0.1)^3))
Evaluating ... ...
Tf_rec = -284251.303296805
STEP 3: Convert Result to Output's Unit
-284251.303296805 Newton Meter -->-284251303.296805 Newton Millimeter (Check conversion here)
FINAL ANSWER
-284251303.296805 Newton Millimeter <-- Fully Plastic Recovery Torque
(Calculation completed in 00.004 seconds)

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7 Residual Stresses For Idealized Stress Strain Law Calculators

Residual Shear Stress in Shaft when r Lies between r1 and Material Constant
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 Angle of Twist for Elasto Plastic Case
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)))
Residual Shear Stress in Shaft when r Lies between Material Constant and r2
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)))
Residual Angle of Twist in Fully Plastic Case
Go 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)))
Recovery Elasto Plastic Torque
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
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)))
Recovery Torque in Fully Plastic Case
Go Fully Plastic Recovery Torque = -(2/3*pi*Outer Radius of Shaft^3*Yield Stress in Shear*(1-(Inner Radius of Shaft/Outer Radius of Shaft)^3))

Recovery Torque in Fully Plastic Case Formula

Fully Plastic Recovery Torque = -(2/3*pi*Outer Radius of Shaft^3*Yield Stress in Shear*(1-(Inner Radius of Shaft/Outer Radius of Shaft)^3))
Tf_rec = -(2/3*pi*r2^3*𝝉0*(1-(r1/r2)^3))

What is recovery torque?

Recovery torque is equal and opposite to the applied torque. when the load is removed it tries to recovers it's original shape.

How to Calculate Recovery Torque in Fully Plastic Case?

Recovery Torque in Fully Plastic Case calculator uses Fully Plastic Recovery Torque = -(2/3*pi*Outer Radius of Shaft^3*Yield Stress in Shear*(1-(Inner Radius of Shaft/Outer Radius of Shaft)^3)) to calculate the Fully Plastic Recovery Torque, The Recovery Torque in Fully plastic case formula is defined as the equal and opposite of fully plastic applied torque. Fully Plastic Recovery Torque is denoted by Tf_rec symbol.

How to calculate Recovery Torque in Fully Plastic Case using this online calculator? To use this online calculator for Recovery Torque in Fully Plastic Case, enter Outer Radius of Shaft (r2), Yield Stress in Shear (𝝉0) & Inner Radius of Shaft (r1) and hit the calculate button. Here is how the Recovery Torque in Fully Plastic Case calculation can be explained with given input values -> -284251303296.805 = -(2/3*pi*0.1^3*145000000*(1-(0.04/0.1)^3)).

FAQ

What is Recovery Torque in Fully Plastic Case?
The Recovery Torque in Fully plastic case formula is defined as the equal and opposite of fully plastic applied torque and is represented as Tf_rec = -(2/3*pi*r2^3*𝝉0*(1-(r1/r2)^3)) or Fully Plastic Recovery Torque = -(2/3*pi*Outer Radius of Shaft^3*Yield Stress in Shear*(1-(Inner Radius of Shaft/Outer Radius of Shaft)^3)). Outer Radius of Shaft is the external radius of shaft, Yield Stress in Shear is the yield stress of the shaft in shear conditions & Inner Radius of Shaft is the internal radius of shaft.
How to calculate Recovery Torque in Fully Plastic Case?
The Recovery Torque in Fully plastic case formula is defined as the equal and opposite of fully plastic applied torque is calculated using Fully Plastic Recovery Torque = -(2/3*pi*Outer Radius of Shaft^3*Yield Stress in Shear*(1-(Inner Radius of Shaft/Outer Radius of Shaft)^3)). To calculate Recovery Torque in Fully Plastic Case, you need Outer Radius of Shaft (r2), Yield Stress in Shear (𝝉0) & Inner Radius of Shaft (r1). With our tool, you need to enter the respective value for Outer Radius of Shaft, Yield Stress in Shear & 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.
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