Full 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

✖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%
✖Inner Radius of Shaft is the internal radius of shaft.ⓘ Inner Radius of Shaft [r₁]			+10% -10%

✖Full Yielding Torque occurs, When the torque is further increased beyond the elasto-plastic range, the shaft will yield to the full depth of the cross section.ⓘ Full Yielding Torque for Hollow Shaft [T_f]

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Formula

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Full Yielding Torque for Hollow Shaft

Formula

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

Example

`"2.8E^8N*mm"=2/3*pi*("100mm")^3*"145MPa"*(1-("40mm"/"100mm")^3)`

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Full Yielding Torque for Hollow Shaft Solution

STEP 0: Pre-Calculation Summary

Formula Used

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)
T_f = 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

Full Yielding Torque - (Measured in Newton Meter) - Full Yielding Torque occurs, When the torque is further increased beyond the elasto-plastic range, the shaft will yield to the full depth of the cross section.
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

T_f = 2/3*pi*r₂^3*𝝉₀*(1-(r₁/r₂)^3) --> 2/3*pi*0.1^3*145000000*(1-(0.04/0.1)^3)

Evaluating ... ...

T_f = 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 ≈ 2.8E+8 Newton Millimeter <-- Full Yielding Torque

(Calculation completed in 00.004 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

Full Yielding Torque for Hollow Shaft Formula

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)
T_f = 2/3*pi*r₂^3*𝝉₀*(1-(r₁/r₂)^3)

What is Full yielding of shaft?

When the torque is further increased beyond the elasto-plastic range,
the shaft will yield to the full depth of the cross section. Therefore such
a torque is called as Fully plastic torque.

How to Calculate Full Yielding Torque for Hollow Shaft?

Full Yielding Torque for Hollow Shaft calculator uses 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) to calculate the Full Yielding Torque, The Full Yielding Torque for hollow shaft formula is defined as When the torque is further increased beyond the elasto-plastic range, the shaft will yield to the full depth of the cross section. Therefore such a torque is called as Fully plastic torque. Full Yielding Torque is denoted by T_f symbol.

How to calculate Full Yielding Torque for Hollow Shaft using this online calculator? To use this online calculator for Full Yielding Torque for Hollow Shaft, 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 Full Yielding Torque for Hollow Shaft calculation can be explained with given input values -> 2.8E+11 = 2/3*pi*0.1^3*145000000*(1-(0.04/0.1)^3).

FAQ

What is Full Yielding Torque for Hollow Shaft?

The Full Yielding Torque for hollow shaft formula is defined as When the torque is further increased beyond the elasto-plastic range, the shaft will yield to the full depth of the cross section. Therefore such a torque is called as Fully plastic torque and is represented as T_f = 2/3*pi*r₂^3*𝝉₀*(1-(r₁/r₂)^3) or 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). 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 Full Yielding Torque for Hollow Shaft?

The Full Yielding Torque for hollow shaft formula is defined as When the torque is further increased beyond the elasto-plastic range, the shaft will yield to the full depth of the cross section. Therefore such a torque is called as Fully plastic torque is calculated using 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). To calculate Full Yielding Torque for Hollow Shaft, 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.

How many ways are there to calculate Full Yielding Torque?

In this formula, Full Yielding Torque uses Outer Radius of Shaft, Yield Stress in Shear & Inner Radius of Shaft. We can use 1 other way(s) to calculate the same, which is/are as follows -

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

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