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Elasto Plastic Yielding Torque for Solid Shaft Calculator

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✖Outer Radius of Shaft is the external radius of shaft.ⓘ Outer Radius of Shaft [r₂]			+10% -10%
✖Yield Stress in Shear is the yield stress of the shaft in shear conditions.ⓘ Yield Stress in Shear [𝝉₀]			+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%

✖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 for Solid Shaft [T_ep]

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Elasto Plastic Yielding Torque for Solid Shaft Solution

STEP 0: Pre-Calculation Summary

Formula Used

Elasto Plastic Yielding Torque = 2/3*pi*Outer Radius of Shaft^3*Yield Stress in Shear*(1-1/4*(Radius of Plastic Front/Outer Radius of Shaft)^3)
T_ep = 2/3*pi*r₂^3*𝝉₀*(1-1/4*(ρ/r₂)^3)
This formula uses 1 Constants, 4 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.
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.
Radius of Plastic Front - (Measured in Meter) - Radius of Plastic Front is the difference between the outer radius of shaft and depth yields plastically.

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)
Radius of Plastic Front: 80 Millimeter --> 0.08 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

T_ep = 2/3*pi*r₂^3*𝝉₀*(1-1/4*(ρ/r₂)^3) --> 2/3*pi*0.1^3*145000000*(1-1/4*(0.08/0.1)^3)

Evaluating ... ...

T_ep = 264815.316746596

STEP 3: Convert Result to Output's Unit

264815.316746596 Newton Meter -->264815316.746596 Newton Millimeter (Check conversion here)

FINAL ANSWER

264815316.746596 ≈ 2.6E+8 Newton Millimeter <-- Elasto Plastic Yielding Torque

(Calculation completed in 00.020 seconds)

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< Elastic Perfectly Plastic Materials Calculators

Elasto Plastic Yielding Torque for Hollow Shaft

LaTeX Go Elasto Plastic Yielding 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))

Incipient Yielding Torque for Hollow Shaft

LaTeX Go Incipient Yielding Torque = pi/2*Outer Radius of Shaft^3*Yield Stress in Shear*(1-(Inner Radius of Shaft/Outer Radius of Shaft)^4)

Full Yielding Torque for Hollow Shaft

LaTeX Go Full Yielding Torque = 2/3*pi*Outer Radius of Shaft^3*Yield Stress in Shear*(1-(Inner Radius of Shaft/Outer Radius of Shaft)^3)

Full Yielding Torque for Solid Shaft

LaTeX Go Full Yielding Torque = 2/3*pi*Yield Stress in Shear*Outer Radius of Shaft^3

Elasto Plastic Yielding Torque for Solid Shaft Formula

LaTeX Go

Elasto Plastic Yielding Torque = 2/3*pi*Outer Radius of Shaft^3*Yield Stress in Shear*(1-1/4*(Radius of Plastic Front/Outer Radius of Shaft)^3)
T_ep = 2/3*pi*r₂^3*𝝉₀*(1-1/4*(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 for Solid Shaft?

Elasto Plastic Yielding Torque for Solid Shaft calculator uses Elasto Plastic Yielding Torque = 2/3*pi*Outer Radius of Shaft^3*Yield Stress in Shear*(1-1/4*(Radius of Plastic Front/Outer Radius of Shaft)^3) to calculate the Elasto Plastic Yielding Torque, Elasto Plastic Yielding Torque for Solid Shaft formula is defined as the maximum torque that can be applied to a solid shaft before it undergoes plastic deformation, which is a critical parameter in the design of shafts and axles in mechanical systems, ensuring their safe and efficient operation under torsional loads. Elasto Plastic Yielding Torque is denoted by T_ep symbol.

How to calculate Elasto Plastic Yielding Torque for Solid Shaft using this online calculator? To use this online calculator for Elasto Plastic Yielding Torque for Solid Shaft, enter Outer Radius of Shaft (r₂), Yield Stress in Shear (𝝉₀) & Radius of Plastic Front (ρ) and hit the calculate button. Here is how the Elasto Plastic Yielding Torque for Solid Shaft calculation can be explained with given input values -> 2.6E+11 = 2/3*pi*0.1^3*145000000*(1-1/4*(0.08/0.1)^3).

FAQ

What is Elasto Plastic Yielding Torque for Solid Shaft?

Elasto Plastic Yielding Torque for Solid Shaft formula is defined as the maximum torque that can be applied to a solid shaft before it undergoes plastic deformation, which is a critical parameter in the design of shafts and axles in mechanical systems, ensuring their safe and efficient operation under torsional loads and is represented as T_ep = 2/3*pi*r₂^3*𝝉₀*(1-1/4*(ρ/r₂)^3) or Elasto Plastic Yielding Torque = 2/3*pi*Outer Radius of Shaft^3*Yield Stress in Shear*(1-1/4*(Radius of Plastic Front/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 & Radius of Plastic Front is the difference between the outer radius of shaft and depth yields plastically.

How to calculate Elasto Plastic Yielding Torque for Solid Shaft?

Elasto Plastic Yielding Torque for Solid Shaft formula is defined as the maximum torque that can be applied to a solid shaft before it undergoes plastic deformation, which is a critical parameter in the design of shafts and axles in mechanical systems, ensuring their safe and efficient operation under torsional loads is calculated using Elasto Plastic Yielding Torque = 2/3*pi*Outer Radius of Shaft^3*Yield Stress in Shear*(1-1/4*(Radius of Plastic Front/Outer Radius of Shaft)^3). To calculate Elasto Plastic Yielding Torque for Solid Shaft, you need Outer Radius of Shaft (r₂), Yield Stress in Shear (𝝉₀) & Radius of Plastic Front (ρ). With our tool, you need to enter the respective value for Outer Radius of Shaft, Yield Stress in Shear & Radius of Plastic Front 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 Outer Radius of Shaft, Yield Stress in Shear & Radius of Plastic Front. We can use 1 other way(s) to calculate the same, which is/are as follows -

Elasto Plastic Yielding 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))

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