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Elasto Plastic Yielding Torque in Work Hardening for Hollow Shaft Calculator

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Torsion of Bars Bending of Beams Residual Stresses

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Elastic Work Hardening Material Elastic Perfectly Plastic Materials

✖Yield Shear Stress(non-linear) is the shear stress above the yield point.ⓘ Yield Shear Stress(non-linear) [𝞽_nonlinear]			+10% -10%
✖Outer Radius of Shaft is the external radius of shaft.ⓘ Outer Radius of Shaft [r₂]			+10% -10%
✖Radius of Plastic Front is the difference between the outer radius of shaft and depth yields plastically.ⓘ Radius of Plastic Front [ρ]			+10% -10%
✖Material Constant is the constant used when the beam yielded plastically.ⓘ Material Constant [n]			+10% -10%
✖Inner Radius of Shaft is the internal radius of shaft.ⓘ Inner Radius of Shaft [r₁]			+10% -10%

✖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.ⓘ Elasto Plastic Yielding Torque in Work Hardening for Hollow Shaft [T_ep]

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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)
T_ep = (2*pi*𝞽_nonlinear*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

T_ep = (2*pi*𝞽_nonlinear*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 ... ...

T_ep = 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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< Elastic Work Hardening Material Calculators

Elasto Plastic Yielding Torque in Work Hardening for Solid Shaft

LaTeX 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

LaTeX 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))

Incipient Yielding Torque in Work Hardening for Hollow Shaft

LaTeX 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

LaTeX Go Incipient Yielding Torque = (Yield Shear Stress(non-linear)*Nth Polar Moment of Inertia)/Outer Radius of Shaft^Material Constant

Elasto Plastic Yielding Torque in Work Hardening for Hollow Shaft Formula

LaTeX Go

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 the maximum torque that can be applied to a hollow shaft before it undergoes plastic deformation, taking into account the work hardening effect, and is a critical parameter in the design of shafts subjected to torsional loading. Elasto Plastic Yielding Torque is denoted by T_ep 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) (𝞽_nonlinear), 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 the maximum torque that can be applied to a hollow shaft before it undergoes plastic deformation, taking into account the work hardening effect, and is a critical parameter in the design of shafts subjected to torsional loading and is represented as T_ep = (2*pi*𝞽_nonlinear*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 the maximum torque that can be applied to a hollow shaft before it undergoes plastic deformation, taking into account the work hardening effect, and is a critical parameter in the design of shafts subjected to torsional loading 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) (𝞽_nonlinear), 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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