Elasto Plastic Yielding Torque for Hollow Shaft Calculator

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Torsion of Bars

Bending of Beams

Residual Stresses

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Elastic Perfectly Plastic Materials

Elastic Work Hardening Material

Residual Stresses for Non-Linear stress strain Law

✖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%
✖Inner Radius of Shaft is the internal radius of shaft.ⓘ Inner Radius of Shaft [r₁]			+10% -10%
✖Outer Radius of Shaft is the external radius of shaft.ⓘ Outer Radius of Shaft [r₂]			+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 Hollow Shaft [T_ep]

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Formula

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Elasto Plastic Yielding Torque for Hollow Shaft

Formula

`"T"_{"ep"} = pi*"𝝉"_{"0"}*("ρ"^3/2*(1-("r"_{"1"}/"ρ")^4)+(2/3*"r"_{"2"}^3)*(1-("ρ"/"r"_{"2"})^3))`

Example

`"2.6E^8N*mm"=pi*"145MPa"*(("80mm")^3/2*(1-("40mm"/"80mm")^4)+(2/3*("100mm")^3)*(1-("80mm"/"100mm")^3))`

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Elasto Plastic Yielding Torque for Hollow Shaft Solution

STEP 0: Pre-Calculation Summary

Formula Used

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))
T_ep = pi*𝝉₀*(ρ^3/2*(1-(r₁/ρ)^4)+(2/3*r₂^3)*(1-(ρ/r₂)^3))
This formula uses 1 Constants, 5 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 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.
Inner Radius of Shaft - (Measured in Meter) - Inner Radius of Shaft is the internal radius of shaft.
Outer Radius of Shaft - (Measured in Meter) - Outer Radius of Shaft is the external radius of shaft.

STEP 1: Convert Input(s) to Base Unit

Yield Stress in Shear: 145 Megapascal --> 145000000 Pascal (Check conversion here)
Radius of Plastic Front: 80 Millimeter --> 0.08 Meter (Check conversion here)
Inner Radius of Shaft: 40 Millimeter --> 0.04 Meter (Check conversion here)
Outer Radius of Shaft: 100 Millimeter --> 0.1 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

T_ep = pi*𝝉₀*(ρ^3/2*(1-(r₁/ρ)^4)+(2/3*r₂^3)*(1-(ρ/r₂)^3)) --> pi*145000000*(0.08^3/2*(1-(0.04/0.08)^4)+(2/3*0.1^3)*(1-(0.08/0.1)^3))

Evaluating ... ...

T_ep = 257526.821790267

STEP 3: Convert Result to Output's Unit

257526.821790267 Newton Meter -->257526821.790267 Newton Millimeter (Check conversion here)

FINAL ANSWER

257526821.790267 ≈ 2.6E+8 Newton Millimeter <-- Elasto Plastic Yielding Torque

(Calculation completed in 00.019 seconds)

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< 6 Elastic Perfectly Plastic Materials Calculators

Elasto Plastic Yielding Torque for Hollow Shaft

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))

Elasto Plastic Yielding Torque for Solid Shaft

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)

Incipient Yielding Torque for Hollow Shaft

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

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)

Incipient Yielding Torque for Solid Shaft

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

Full Yielding Torque for Solid Shaft

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

Elasto Plastic Yielding Torque for Hollow Shaft Formula

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 Hollow Shaft?

Elasto Plastic Yielding Torque for Hollow Shaft calculator uses 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)) to calculate the Elasto Plastic Yielding Torque, The Elasto plastic yielding Torque 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. Hence it is known as elasto-plastic torsion. Elasto Plastic Yielding Torque is denoted by T_ep symbol.

How to calculate Elasto Plastic Yielding Torque for Hollow Shaft using this online calculator? To use this online calculator for Elasto Plastic Yielding Torque for Hollow Shaft, enter Yield Stress in Shear (𝝉₀), Radius of Plastic Front (ρ), Inner Radius of Shaft (r₁) & Outer Radius of Shaft (r₂) and hit the calculate button. Here is how the Elasto Plastic Yielding Torque for Hollow Shaft calculation can be explained with given input values -> 2.6E+11 = pi*145000000*(0.08^3/2*(1-(0.04/0.08)^4)+(2/3*0.1^3)*(1-(0.08/0.1)^3)).

FAQ

What is Elasto Plastic Yielding Torque for Hollow Shaft?

The Elasto plastic yielding Torque 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. Hence it is known as elasto-plastic torsion and is represented as T_ep = pi*𝝉₀*(ρ^3/2*(1-(r₁/ρ)^4)+(2/3*r₂^3)*(1-(ρ/r₂)^3)) or 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)). 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, Inner Radius of Shaft is the internal radius of shaft & Outer Radius of Shaft is the external radius of shaft.

How to calculate Elasto Plastic Yielding Torque for Hollow Shaft?

The Elasto plastic yielding Torque 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. Hence it is known as elasto-plastic torsion is calculated using 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)). To calculate Elasto Plastic Yielding Torque for Hollow Shaft, you need Yield Stress in Shear (𝝉₀), Radius of Plastic Front (ρ), Inner Radius of Shaft (r₁) & Outer Radius of Shaft (r₂). With our tool, you need to enter the respective value for Yield Stress in Shear, Radius of Plastic Front, Inner Radius of Shaft & Outer 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 Stress in Shear, Radius of Plastic Front, Inner Radius of Shaft & Outer Radius of Shaft. We can use 1 other way(s) to calculate the same, which is/are as follows -

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)

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