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Incipient Yielding Torque for Hollow 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%
✖Inner Radius of Shaft is the internal radius of shaft.ⓘ Inner Radius of Shaft [r₁]			+10% -10%

✖Incipient Yielding Torque, In this stage, the shaft regains its original configuration upon the removal of torque. The stresses are assumed to be fully recovered.ⓘ Incipient Yielding Torque for Hollow Shaft [T_i]

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Incipient Yielding Torque for Hollow Shaft Solution

STEP 0: Pre-Calculation Summary

Formula Used

Incipient Yielding Torque = pi/2*Outer Radius of Shaft^3*Yield Stress in Shear*(1-(Inner Radius of Shaft/Outer Radius of Shaft)^4)
T_i = pi/2*r₂^3*𝝉₀*(1-(r₁/r₂)^4)
This formula uses 1 Constants, 4 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

Incipient Yielding Torque - (Measured in Newton Meter) - Incipient Yielding Torque, In this stage, the shaft regains its original configuration upon the removal of torque. The stresses are assumed to be fully recovered.
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_i = pi/2*r₂^3*𝝉₀*(1-(r₁/r₂)^4) --> pi/2*0.1^3*145000000*(1-(0.04/0.1)^4)

Evaluating ... ...

T_i = 221934.671420197

STEP 3: Convert Result to Output's Unit

221934.671420197 Newton Meter -->221934671.420197 Newton Millimeter (Check conversion here)

FINAL ANSWER

221934671.420197 ≈ 2.2E+8 Newton Millimeter <-- Incipient Yielding Torque

(Calculation completed in 00.004 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

Incipient Yielding Torque for Hollow Shaft Formula

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)
T_i = pi/2*r₂^3*𝝉₀*(1-(r₁/r₂)^4)

What is Incipient Yielding in shafts?

.In this stage, the shaft regains its original configuration upon
the removal of torque. The stresses are assumed to be fully
recovered.
Shear stress follows a linear law with zero stress at the neutral
axis, and maximum stress at the outermost fibre.

How to Calculate Incipient Yielding Torque for Hollow Shaft?

Incipient Yielding Torque for Hollow Shaft calculator uses Incipient Yielding Torque = pi/2*Outer Radius of Shaft^3*Yield Stress in Shear*(1-(Inner Radius of Shaft/Outer Radius of Shaft)^4) to calculate the Incipient Yielding Torque, Incipient Yielding Torque for Hollow Shaft formula is defined as the maximum torque that can be applied to a hollow shaft without causing it to yield or deform, taking into account the shaft's dimensions and material properties, and is a critical parameter in the design of shafts for various mechanical systems. Incipient Yielding Torque is denoted by T_i symbol.

How to calculate Incipient Yielding Torque for Hollow Shaft using this online calculator? To use this online calculator for Incipient 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 Incipient Yielding Torque for Hollow Shaft calculation can be explained with given input values -> 2.2E+11 = pi/2*0.1^3*145000000*(1-(0.04/0.1)^4).

FAQ

What is Incipient Yielding Torque for Hollow Shaft?

Incipient Yielding Torque for Hollow Shaft formula is defined as the maximum torque that can be applied to a hollow shaft without causing it to yield or deform, taking into account the shaft's dimensions and material properties, and is a critical parameter in the design of shafts for various mechanical systems and is represented as T_i = pi/2*r₂^3*𝝉₀*(1-(r₁/r₂)^4) or Incipient Yielding Torque = pi/2*Outer Radius of Shaft^3*Yield Stress in Shear*(1-(Inner Radius of Shaft/Outer Radius of Shaft)^4). 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 Incipient Yielding Torque for Hollow Shaft?

Incipient Yielding Torque for Hollow Shaft formula is defined as the maximum torque that can be applied to a hollow shaft without causing it to yield or deform, taking into account the shaft's dimensions and material properties, and is a critical parameter in the design of shafts for various mechanical systems is calculated using Incipient Yielding Torque = pi/2*Outer Radius of Shaft^3*Yield Stress in Shear*(1-(Inner Radius of Shaft/Outer Radius of Shaft)^4). To calculate Incipient 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 Incipient Yielding Torque?

In this formula, Incipient 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 -

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

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