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Full Yielding Torque for Hollow Shaft Formula

GoFull Yielding Torque for Solid Shaft Formula

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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. Check FAQs

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

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

Full Yielding Torque for Hollow Shaft Example

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

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

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

2.8E+8 = \frac{2}{3} \cdot 3.1416 \cdot 100^{3} \cdot 145 \cdot (1 - {(\frac{40}{100})}^{3})

2.8E+8N*mm = \frac{2}{3} \cdot 3.1416 \cdot {100mm}^{3} \cdot 145MPa \cdot (1 - {(\frac{40mm}{100mm})}^{3})

2.8E+8 = \frac{2}{3} \cdot 3.1416 \cdot 100^{3} \cdot 145 \cdot (1 - {(\frac{40}{100})}^{3})

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Full Yielding Torque for Hollow Shaft Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

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

Next Step Substitute values of Constants

∴

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

Next Step Convert Units

∴

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

Next Step Prepare to Evaluate

∴

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

Next Step Evaluate

∴

T f = 284251.303296805N*m

Next Step Convert to Output's Unit

∴

T f = 284251303.296805N*mm

LAST Step Rounding Answer

∴

T f = 2.8E+8N*mm

Full Yielding Torque for Hollow Shaft Formula Elements

Variables

Constants

Full Yielding Torque

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.

Symbol: T_f

Measurement: TorqueUnit: N*mm

Note: Value should be greater than 0.

Formulas to find Full 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 Full Yielding Torque

Go Full Yielding Torque for Solid Shaft

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

Other formulas in Elastic Perfectly Plastic Materials category

Go Incipient Yielding Torque for Hollow Shaft

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

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 Incipient Yielding Torque for Solid Shaft

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

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 Full Yielding Torque for Hollow Shaft?

Full Yielding Torque for Hollow Shaft evaluator 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 evaluate the Full Yielding Torque, Full Yielding Torque for Hollow Shaft formula is defined as the maximum twisting torque that a hollow shaft can withstand without undergoing plastic deformation, which is a critical parameter in the design and analysis of shafts subjected to torsional loading. Full Yielding Torque is denoted by T_f symbol.

How to evaluate Full Yielding Torque for Hollow Shaft using this online evaluator? To use this online evaluator 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.

FAQs on Full Yielding Torque for Hollow Shaft

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

The formula of Full Yielding Torque for Hollow Shaft is expressed as 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). Here is an example- 2.8E+11 = 2/3*pi*0.1^3*145000000*(1-(0.04/0.1)^3).

How to calculate Full Yielding Torque for Hollow Shaft?

With Outer Radius of Shaft (r₂), Yield Stress in Shear (𝝉₀) & Inner Radius of Shaft (r₁) we can find Full Yielding Torque for Hollow Shaft using the 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). This formula also uses Archimedes' constant .

What are the other ways to Calculate Full Yielding Torque?

Here are the different ways to Calculate Full Yielding Torque-

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

Can the Full Yielding Torque for Hollow Shaft be negative?

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

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

Full 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 Full Yielding Torque for Hollow Shaft can be measured.

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Full Yielding Torque for Hollow Shaft Formula

​GoFull Yielding Torque for Solid Shaft Formula

Full Yielding Torque for Hollow Shaft Example

Full Yielding Torque for Hollow Shaft Solution

Full Yielding Torque for Hollow Shaft Formula Elements

Other Formulas to find Full Yielding Torque

Other formulas in Elastic Perfectly Plastic Materials category

How to Evaluate Full Yielding Torque for Hollow Shaft?

FAQs on Full Yielding Torque for Hollow Shaft

Variable Name

GoFull Yielding Torque for Solid Shaft Formula