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Incipient Yielding Torque for Hollow Shaft Formula

GoIncipient Yielding Torque for Solid Shaft Formula

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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. Check FAQs

T i = \frac{π}{2} \cdot {r 2}^{3} \cdot 𝝉 0 \cdot (1 - {(\frac{r 1}{r 2})}^{4})

T_i - Incipient Yielding Torque?r₂ - Outer Radius of Shaft?𝝉₀ - Yield Stress in Shear?r₁ - Inner Radius of Shaft?π - Archimedes' constant?

Incipient Yielding Torque for Hollow Shaft Example

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Here is how the Incipient Yielding Torque for Hollow Shaft equation looks like with Values.

Here is how the Incipient Yielding Torque for Hollow Shaft equation looks like with Units.

Here is how the Incipient Yielding Torque for Hollow Shaft equation looks like.

2.2E+8 = \frac{3.1416}{2} \cdot 100^{3} \cdot 145 \cdot (1 - {(\frac{40}{100})}^{4})

2.2E+8N*mm = \frac{3.1416}{2} \cdot {100mm}^{3} \cdot 145MPa \cdot (1 - {(\frac{40mm}{100mm})}^{4})

2.2E+8 = \frac{3.1416}{2} \cdot 100^{3} \cdot 145 \cdot (1 - {(\frac{40}{100})}^{4})

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Incipient Yielding Torque for Hollow Shaft Solution

Follow our step by step solution on how to calculate Incipient Yielding Torque for Hollow Shaft?

FIRST Step Consider the formula

T i = \frac{π}{2} \cdot {r 2}^{3} \cdot 𝝉 0 \cdot (1 - {(\frac{r 1}{r 2})}^{4})

Next Step Substitute values of Variables

∴

T i = \frac{π}{2} \cdot {100mm}^{3} \cdot 145MPa \cdot (1 - {(\frac{40mm}{100mm})}^{4})

Next Step Substitute values of Constants

∴

T i = \frac{3.1416}{2} \cdot {100mm}^{3} \cdot 145MPa \cdot (1 - {(\frac{40mm}{100mm})}^{4})

Next Step Convert Units

∴

T i = \frac{3.1416}{2} \cdot {0.1m}^{3} \cdot 1.5E+8Pa \cdot (1 - {(\frac{0.04m}{0.1m})}^{4})

Next Step Prepare to Evaluate

∴

T i = \frac{3.1416}{2} \cdot {0.1}^{3} \cdot 1.5E+8 \cdot (1 - {(\frac{0.04}{0.1})}^{4})

Next Step Evaluate

∴

T i = 221934.671420197N*m

Next Step Convert to Output's Unit

∴

T i = 221934671.420197N*mm

LAST Step Rounding Answer

∴

T i = 2.2E+8N*mm

Incipient Yielding Torque for Hollow Shaft Formula Elements

Variables

Constants

Incipient Yielding Torque

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.

Symbol: T_i

Measurement: TorqueUnit: N*mm

Note: Value should be greater than 0.

Formulas to find Incipient Yielding Torque

Outer Radius of Shaft

Outer Radius of Shaft is the external radius of shaft.

Symbol: r₂

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Outer Radius of Shaft

Yield Stress in Shear

Yield Stress in Shear is the yield stress of the shaft in shear conditions.

Symbol: 𝝉₀

Measurement: StressUnit: MPa

Note: Value should be greater than 0.

Formulas to find Yield Stress in Shear

Inner Radius of Shaft

Inner Radius of Shaft is the internal radius of shaft.

Symbol: r₁

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Inner Radius of Shaft

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

Other Formulas to find Incipient Yielding Torque

Go Incipient Yielding Torque for Solid Shaft

T i = \frac{π \cdot {r 2}^{3} \cdot 𝝉 0}{2}

Other formulas in Elastic Perfectly Plastic Materials category

Go Elasto Plastic Yielding Torque for Hollow Shaft

T ep = π \cdot 𝝉 0 \cdot (\frac{ρ^{3}}{2} \cdot (1 - {(\frac{r 1}{ρ})}^{4}) + (\frac{2}{3} \cdot {r 2}^{3}) \cdot (1 - {(\frac{ρ}{r 2})}^{3}))

Go Full Yielding Torque for Hollow Shaft

T f = \frac{2}{3} \cdot π \cdot {r 2}^{3} \cdot 𝝉 0 \cdot (1 - {(\frac{r 1}{r 2})}^{3})

Go Full Yielding Torque for Solid Shaft

T f = \frac{2}{3} \cdot π \cdot 𝝉 0 \cdot {r 2}^{3}

Go Elasto Plastic Yielding Torque for Solid Shaft

T ep = \frac{2}{3} \cdot π \cdot {r 2}^{3} \cdot 𝝉 0 \cdot (1 - \frac{1}{4} \cdot {(\frac{ρ}{r 2})}^{3})

How to Evaluate Incipient Yielding Torque for Hollow Shaft?

Incipient Yielding Torque for Hollow Shaft evaluator 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 evaluate 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 evaluate Incipient Yielding Torque for Hollow Shaft using this online evaluator? To use this online evaluator 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.

FAQs on Incipient Yielding Torque for Hollow Shaft

What is the formula to find Incipient Yielding Torque for Hollow Shaft?

The formula of Incipient Yielding Torque for Hollow Shaft is expressed as Incipient Yielding Torque = pi/2*Outer Radius of Shaft^3*Yield Stress in Shear*(1-(Inner Radius of Shaft/Outer Radius of Shaft)^4). Here is an example- 2.2E+11 = pi/2*0.1^3*145000000*(1-(0.04/0.1)^4).

How to calculate Incipient Yielding Torque for Hollow Shaft?

With Outer Radius of Shaft (r₂), Yield Stress in Shear (𝝉₀) & Inner Radius of Shaft (r₁) we can find Incipient Yielding Torque for Hollow Shaft using the formula - Incipient Yielding Torque = pi/2*Outer Radius of Shaft^3*Yield Stress in Shear*(1-(Inner Radius of Shaft/Outer Radius of Shaft)^4). This formula also uses Archimedes' constant .

What are the other ways to Calculate Incipient Yielding Torque?

Here are the different ways to Calculate Incipient Yielding Torque-

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

Can the Incipient Yielding Torque for Hollow Shaft be negative?

No, the Incipient Yielding Torque for Hollow Shaft, measured in Torque cannot be negative.

Which unit is used to measure Incipient Yielding Torque for Hollow Shaft?

Incipient Yielding Torque for Hollow Shaft is usually measured using the Newton Millimeter[N*mm] for Torque. Newton Meter[N*mm], Newton Centimeter[N*mm], Kilonewton Meter[N*mm] are the few other units in which Incipient Yielding Torque for Hollow Shaft can be measured.

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Incipient Yielding Torque for Hollow Shaft Formula

​GoIncipient Yielding Torque for Solid Shaft Formula

Incipient Yielding Torque for Hollow Shaft Example

Incipient Yielding Torque for Hollow Shaft Solution

Incipient Yielding Torque for Hollow Shaft Formula Elements

Other Formulas to find Incipient Yielding Torque

Other formulas in Elastic Perfectly Plastic Materials category

How to Evaluate Incipient Yielding Torque for Hollow Shaft?

FAQs on Incipient Yielding Torque for Hollow Shaft

Variable Name

GoIncipient Yielding Torque for Solid Shaft Formula