Elasto Plastic Yielding Torque in Work Hardening for Hollow Shaft Solution

STEP 0: Pre-Calculation Summary
Formula Used
Elasto Plastic Yielding Torque = (2*pi*Yield Shear Stress(non-linear)*Outer Radius of Shaft^3)/3*((3*Radius of Plastic Front^3)/(Outer Radius of Shaft^3*(Material Constant+3))-(3/(Material Constant+3))*(Inner Radius of Shaft/Radius of Plastic Front)^Material Constant*(Inner Radius of Shaft/Outer Radius of Shaft)^3+1-(Radius of Plastic Front/Outer Radius of Shaft)^3)
Tep = (2*pi*𝞽nonlinear*r2^3)/3*((3*ρ^3)/(r2^3*(n+3))-(3/(n+3))*(r1/ρ)^n*(r1/r2)^3+1-(ρ/r2)^3)
This formula uses 1 Constants, 6 Variables
Constants Used
pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288
Variables Used
Elasto Plastic Yielding Torque - (Measured in Newton Meter) - Elasto Plastic Yielding Torque, in this case, a portion of the shaft from the outer surface would have yielded plastically and rest of the cross section will still be in elastic state.
Yield Shear Stress(non-linear) - (Measured in Pascal) - Yield Shear Stress(non-linear) is the shear stress above the yield point.
Outer Radius of Shaft - (Measured in Meter) - Outer Radius of Shaft is the external radius of shaft.
Radius of Plastic Front - (Measured in Meter) - Radius of Plastic Front is the difference between the outer radius of shaft and depth yields plastically.
Material Constant - Material Constant is the constant used when the beam yielded plastically.
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 Shear Stress(non-linear): 175 Megapascal --> 175000000 Pascal (Check conversion here)
Outer Radius of Shaft: 100 Millimeter --> 0.1 Meter (Check conversion here)
Radius of Plastic Front: 80 Millimeter --> 0.08 Meter (Check conversion here)
Material Constant: 0.25 --> No Conversion Required
Inner Radius of Shaft: 40 Millimeter --> 0.04 Meter (Check conversion here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
Tep = (2*pi*𝞽nonlinear*r2^3)/3*((3*ρ^3)/(r2^3*(n+3))-(3/(n+3))*(r1/ρ)^n*(r1/r2)^3+1-(ρ/r2)^3) --> (2*pi*175000000*0.1^3)/3*((3*0.08^3)/(0.1^3*(0.25+3))-(3/(0.25+3))*(0.04/0.08)^0.25*(0.04/0.1)^3+1-(0.08/0.1)^3)
Evaluating ... ...
Tep = 333876.146024395
STEP 3: Convert Result to Output's Unit
333876.146024395 Newton Meter -->333876146.024395 Newton Millimeter (Check conversion here)
FINAL ANSWER
333876146.024395 3.3E+8 Newton Millimeter <-- Elasto Plastic Yielding Torque
(Calculation completed in 00.004 seconds)

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7 Elastic Work Hardening Material Calculators

Elasto Plastic Yielding Torque in Work Hardening for Hollow Shaft
Go Elasto Plastic Yielding Torque = (2*pi*Yield Shear Stress(non-linear)*Outer Radius of Shaft^3)/3*((3*Radius of Plastic Front^3)/(Outer Radius of Shaft^3*(Material Constant+3))-(3/(Material Constant+3))*(Inner Radius of Shaft/Radius of Plastic Front)^Material Constant*(Inner Radius of Shaft/Outer Radius of Shaft)^3+1-(Radius of Plastic Front/Outer Radius of Shaft)^3)
Elasto Plastic Yielding Torque in Work Hardening for Solid Shaft
Go Elasto Plastic Yielding Torque = (2*pi*Yield Shear Stress(non-linear)*Outer Radius of Shaft^3)/3*(1-(Material Constant/(Material Constant+3))*(Radius of Plastic Front/Outer Radius of Shaft)^3)
Nth Polar Moment of Inertia
Go Nth Polar Moment of Inertia = ((2*pi)/(Material Constant+3))*(Outer Radius of Shaft^(Material Constant+3)-Inner Radius of Shaft^(Material Constant+3))
Full Yielding Torque in Work Hardening for Hollow Shaft
Go Full Yielding Torque = (2*pi*Yield Shear Stress(non-linear)*Outer Radius of Shaft^3)/3*(1-(Inner Radius of Shaft/Outer Radius of Shaft)^3)
Incipient Yielding Torque in Work Hardening for Hollow Shaft
Go Incipient Yielding Torque = (Yield Shear Stress(non-linear)*Nth Polar Moment of Inertia)/Outer Radius of Shaft^Material Constant
Incipient Yielding Torque in Work Hardening Solid Shaft
Go Incipient Yielding Torque = (Yield Shear Stress(non-linear)*Nth Polar Moment of Inertia)/Outer Radius of Shaft^Material Constant
Full Yielding Torque in Work Hardening for Solid Shaft
Go Full Yielding Torque = (2*pi*Yield Shear Stress(non-linear)*Outer Radius of Shaft^3)/3

Elasto Plastic Yielding Torque in Work Hardening for Hollow Shaft Formula

Elasto Plastic Yielding Torque = (2*pi*Yield Shear Stress(non-linear)*Outer Radius of Shaft^3)/3*((3*Radius of Plastic Front^3)/(Outer Radius of Shaft^3*(Material Constant+3))-(3/(Material Constant+3))*(Inner Radius of Shaft/Radius of Plastic Front)^Material Constant*(Inner Radius of Shaft/Outer Radius of Shaft)^3+1-(Radius of Plastic Front/Outer Radius of Shaft)^3)
Tep = (2*pi*𝞽nonlinear*r2^3)/3*((3*ρ^3)/(r2^3*(n+3))-(3/(n+3))*(r1/ρ)^n*(r1/r2)^3+1-(ρ/r2)^3)

How Elasto plastic yielding occurs in shafts?

When the torque is further increased beyond the elastic range, yielding started at outermost fibre of the maximum twisting moment region spreads inward towards the neutral axis. In this case, a portion of the shaft from the outer surface would have yielded plastically and rest of the cross section will still be in elastic state. Hence it is known as elasto-plastic torsion.

How to Calculate Elasto Plastic Yielding Torque in Work Hardening for Hollow Shaft?

Elasto Plastic Yielding Torque in Work Hardening for Hollow Shaft calculator uses Elasto Plastic Yielding Torque = (2*pi*Yield Shear Stress(non-linear)*Outer Radius of Shaft^3)/3*((3*Radius of Plastic Front^3)/(Outer Radius of Shaft^3*(Material Constant+3))-(3/(Material Constant+3))*(Inner Radius of Shaft/Radius of Plastic Front)^Material Constant*(Inner Radius of Shaft/Outer Radius of Shaft)^3+1-(Radius of Plastic Front/Outer Radius of Shaft)^3) to calculate the Elasto Plastic Yielding Torque, Elasto Plastic Yielding Torque in Work Hardening for Hollow Shaft formula is defined as In this case, a portion of the shaft from the outer surface would have yielded plastically and rest of the cross section will still be in elastic state. Elasto Plastic Yielding Torque is denoted by Tep symbol.

How to calculate Elasto Plastic Yielding Torque in Work Hardening for Hollow Shaft using this online calculator? To use this online calculator for Elasto Plastic Yielding Torque in Work Hardening for Hollow Shaft, enter Yield Shear Stress(non-linear) (𝞽nonlinear), Outer Radius of Shaft (r2), Radius of Plastic Front (ρ), Material Constant (n) & Inner Radius of Shaft (r1) and hit the calculate button. Here is how the Elasto Plastic Yielding Torque in Work Hardening for Hollow Shaft calculation can be explained with given input values -> 3.3E+11 = (2*pi*175000000*0.1^3)/3*((3*0.08^3)/(0.1^3*(0.25+3))-(3/(0.25+3))*(0.04/0.08)^0.25*(0.04/0.1)^3+1-(0.08/0.1)^3).

FAQ

What is Elasto Plastic Yielding Torque in Work Hardening for Hollow Shaft?
Elasto Plastic Yielding Torque in Work Hardening for Hollow Shaft formula is defined as In this case, a portion of the shaft from the outer surface would have yielded plastically and rest of the cross section will still be in elastic state and is represented as Tep = (2*pi*𝞽nonlinear*r2^3)/3*((3*ρ^3)/(r2^3*(n+3))-(3/(n+3))*(r1/ρ)^n*(r1/r2)^3+1-(ρ/r2)^3) or Elasto Plastic Yielding Torque = (2*pi*Yield Shear Stress(non-linear)*Outer Radius of Shaft^3)/3*((3*Radius of Plastic Front^3)/(Outer Radius of Shaft^3*(Material Constant+3))-(3/(Material Constant+3))*(Inner Radius of Shaft/Radius of Plastic Front)^Material Constant*(Inner Radius of Shaft/Outer Radius of Shaft)^3+1-(Radius of Plastic Front/Outer Radius of Shaft)^3). Yield Shear Stress(non-linear) is the shear stress above the yield point, Outer Radius of Shaft is the external radius of shaft, Radius of Plastic Front is the difference between the outer radius of shaft and depth yields plastically, Material Constant is the constant used when the beam yielded plastically & Inner Radius of Shaft is the internal radius of shaft.
How to calculate Elasto Plastic Yielding Torque in Work Hardening for Hollow Shaft?
Elasto Plastic Yielding Torque in Work Hardening for Hollow Shaft formula is defined as In this case, a portion of the shaft from the outer surface would have yielded plastically and rest of the cross section will still be in elastic state is calculated using Elasto Plastic Yielding Torque = (2*pi*Yield Shear Stress(non-linear)*Outer Radius of Shaft^3)/3*((3*Radius of Plastic Front^3)/(Outer Radius of Shaft^3*(Material Constant+3))-(3/(Material Constant+3))*(Inner Radius of Shaft/Radius of Plastic Front)^Material Constant*(Inner Radius of Shaft/Outer Radius of Shaft)^3+1-(Radius of Plastic Front/Outer Radius of Shaft)^3). To calculate Elasto Plastic Yielding Torque in Work Hardening for Hollow Shaft, you need Yield Shear Stress(non-linear) (𝞽nonlinear), Outer Radius of Shaft (r2), Radius of Plastic Front (ρ), Material Constant (n) & Inner Radius of Shaft (r1). With our tool, you need to enter the respective value for Yield Shear Stress(non-linear), Outer Radius of Shaft, Radius of Plastic Front, Material Constant & 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 Elasto Plastic Yielding Torque?
In this formula, Elasto Plastic Yielding Torque uses Yield Shear Stress(non-linear), Outer Radius of Shaft, Radius of Plastic Front, Material Constant & Inner Radius of Shaft. We can use 1 other way(s) to calculate the same, which is/are as follows -
  • Elasto Plastic Yielding Torque = (2*pi*Yield Shear Stress(non-linear)*Outer Radius of Shaft^3)/3*(1-(Material Constant/(Material Constant+3))*(Radius of Plastic Front/Outer Radius of Shaft)^3)
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