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Elasto Plastic Yielding Torque in Work Hardening for Hollow Shaft Formula

GoElasto Plastic Yielding Torque in Work Hardening for Solid Shaft Formula

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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. Check FAQs

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

T_ep - Elasto Plastic Yielding Torque?𝞽_nonlinear - Yield Shear Stress(non-linear)?r₂ - Outer Radius of Shaft?ρ - Radius of Plastic Front?n - Material Constant?r₁ - Inner Radius of Shaft?π - Archimedes' constant?

Elasto Plastic Yielding Torque in Work Hardening for Hollow Shaft Example

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Here is how the Elasto Plastic Yielding Torque in Work Hardening for Hollow Shaft equation looks like with Values.

Here is how the Elasto Plastic Yielding Torque in Work Hardening for Hollow Shaft equation looks like with Units.

Here is how the Elasto Plastic Yielding Torque in Work Hardening for Hollow Shaft equation looks like.

3.3E+8 = \frac{2 \cdot 3.1416 \cdot 175 \cdot 100^{3}}{3} \cdot (\frac{3 \cdot 80^{3}}{100^{3} \cdot (0.25 + 3)} - (\frac{3}{0.25 + 3}) \cdot {(\frac{40}{80})}^{0.25} \cdot {(\frac{40}{100})}^{3} + 1 - {(\frac{80}{100})}^{3})

3.3E+8N*mm = \frac{2 \cdot 3.1416 \cdot 175MPa \cdot {100mm}^{3}}{3} \cdot (\frac{3 \cdot {80mm}^{3}}{{100mm}^{3} \cdot (0.25 + 3)} - (\frac{3}{0.25 + 3}) \cdot {(\frac{40mm}{80mm})}^{0.25} \cdot {(\frac{40mm}{100mm})}^{3} + 1 - {(\frac{80mm}{100mm})}^{3})

3.3E+8 = \frac{2 \cdot 3.1416 \cdot 175 \cdot 100^{3}}{3} \cdot (\frac{3 \cdot 80^{3}}{100^{3} \cdot (0.25 + 3)} - (\frac{3}{0.25 + 3}) \cdot {(\frac{40}{80})}^{0.25} \cdot {(\frac{40}{100})}^{3} + 1 - {(\frac{80}{100})}^{3})

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Elasto Plastic Yielding Torque in Work Hardening for Hollow Shaft Solution

Follow our step by step solution on how to calculate Elasto Plastic Yielding Torque in Work Hardening for Hollow Shaft?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

T ep = \frac{2 \cdot π \cdot 175MPa \cdot {100mm}^{3}}{3} \cdot (\frac{3 \cdot {80mm}^{3}}{{100mm}^{3} \cdot (0.25 + 3)} - (\frac{3}{0.25 + 3}) \cdot {(\frac{40mm}{80mm})}^{0.25} \cdot {(\frac{40mm}{100mm})}^{3} + 1 - {(\frac{80mm}{100mm})}^{3})

Next Step Substitute values of Constants

∴

T ep = \frac{2 \cdot 3.1416 \cdot 175MPa \cdot {100mm}^{3}}{3} \cdot (\frac{3 \cdot {80mm}^{3}}{{100mm}^{3} \cdot (0.25 + 3)} - (\frac{3}{0.25 + 3}) \cdot {(\frac{40mm}{80mm})}^{0.25} \cdot {(\frac{40mm}{100mm})}^{3} + 1 - {(\frac{80mm}{100mm})}^{3})

Next Step Convert Units

∴

T ep = \frac{2 \cdot 3.1416 \cdot 1.8E+8Pa \cdot {0.1m}^{3}}{3} \cdot (\frac{3 \cdot {0.08m}^{3}}{{0.1m}^{3} \cdot (0.25 + 3)} - (\frac{3}{0.25 + 3}) \cdot {(\frac{0.04m}{0.08m})}^{0.25} \cdot {(\frac{0.04m}{0.1m})}^{3} + 1 - {(\frac{0.08m}{0.1m})}^{3})

Next Step Prepare to Evaluate

∴

T ep = \frac{2 \cdot 3.1416 \cdot 1.8E+8 \cdot {0.1}^{3}}{3} \cdot (\frac{3 \cdot {0.08}^{3}}{{0.1}^{3} \cdot (0.25 + 3)} - (\frac{3}{0.25 + 3}) \cdot {(\frac{0.04}{0.08})}^{0.25} \cdot {(\frac{0.04}{0.1})}^{3} + 1 - {(\frac{0.08}{0.1})}^{3})

Next Step Evaluate

∴

T ep = 333876.146024395N*m

Next Step Convert to Output's Unit

∴

T ep = 333876146.024395N*mm

LAST Step Rounding Answer

∴

T ep = 3.3E+8N*mm

Elasto Plastic Yielding Torque in Work Hardening for Hollow Shaft Formula Elements

Variables

Constants

Elasto Plastic Yielding Torque

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.

Symbol: T_ep

Measurement: TorqueUnit: N*mm

Note: Value should be greater than 0.

Formulas to find Elasto Plastic Yielding Torque

Yield Shear Stress(non-linear)

Yield Shear Stress(non-linear) is the shear stress above the yield point.

Symbol: 𝞽_nonlinear

Measurement: StressUnit: MPa

Note: Value should be greater than 0.

Formulas to find Yield Shear Stress(non-linear)

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

Radius of Plastic Front

Radius of Plastic Front is the difference between the outer radius of shaft and depth yields plastically.

Symbol: ρ

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Radius of Plastic Front

Material Constant

Material Constant is the constant used when the beam yielded plastically.

Symbol: n

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Material Constant

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 Elasto Plastic Yielding Torque

Go Elasto Plastic Yielding Torque in Work Hardening for Solid Shaft

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

Other formulas in Elastic Work Hardening Material category

Go Nth Polar Moment of Inertia

J n = (\frac{2 \cdot π}{n + 3}) \cdot ({r 2}^{n + 3} - {r 1}^{n + 3})

Go Incipient Yielding Torque in Work Hardening for Hollow Shaft

T i = \frac{𝞽 nonlinear \cdot J n}{{r 2}^{n}}

Go Incipient Yielding Torque in Work Hardening Solid Shaft

T i = \frac{𝞽 nonlinear \cdot J n}{{r 2}^{n}}

Go Full Yielding Torque in Work Hardening for Hollow Shaft

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

How to Evaluate Elasto Plastic Yielding Torque in Work Hardening for Hollow Shaft?

Elasto Plastic Yielding Torque in Work Hardening for Hollow Shaft evaluator uses Elasto Plastic Yielding Torque = (2*pi*Yield Shear Stress(non-linear)*Outer Radius of Shaft^3)/3*((3*Radius of Plastic Front^3)/(Outer Radius of Shaft^3*(Material Constant+3))-(3/(Material Constant+3))*(Inner Radius of Shaft/Radius of Plastic Front)^Material Constant*(Inner Radius of Shaft/Outer Radius of Shaft)^3+1-(Radius of Plastic Front/Outer Radius of Shaft)^3) to evaluate the Elasto Plastic Yielding Torque, Elasto Plastic Yielding Torque in Work Hardening for Hollow Shaft formula is defined as the maximum torque that can be applied to a hollow shaft before it undergoes plastic deformation, taking into account the work hardening effect, and is a critical parameter in the design of shafts subjected to torsional loading. Elasto Plastic Yielding Torque is denoted by T_ep symbol.

How to evaluate Elasto Plastic Yielding Torque in Work Hardening for Hollow Shaft using this online evaluator? To use this online evaluator for Elasto Plastic Yielding Torque in Work Hardening for Hollow Shaft, enter Yield Shear Stress(non-linear) (𝞽_nonlinear), Outer Radius of Shaft (r₂), Radius of Plastic Front (ρ), Material Constant (n) & Inner Radius of Shaft (r₁) and hit the calculate button.

FAQs on Elasto Plastic Yielding Torque in Work Hardening for Hollow Shaft

What is the formula to find Elasto Plastic Yielding Torque in Work Hardening for Hollow Shaft?

The formula of Elasto Plastic Yielding Torque in Work Hardening for Hollow Shaft is expressed as Elasto Plastic Yielding Torque = (2*pi*Yield Shear Stress(non-linear)*Outer Radius of Shaft^3)/3*((3*Radius of Plastic Front^3)/(Outer Radius of Shaft^3*(Material Constant+3))-(3/(Material Constant+3))*(Inner Radius of Shaft/Radius of Plastic Front)^Material Constant*(Inner Radius of Shaft/Outer Radius of Shaft)^3+1-(Radius of Plastic Front/Outer Radius of Shaft)^3). Here is an example- 3.3E+11 = (2*pi*175000000*0.1^3)/3*((3*0.08^3)/(0.1^3*(0.25+3))-(3/(0.25+3))*(0.04/0.08)^0.25*(0.04/0.1)^3+1-(0.08/0.1)^3).

How to calculate Elasto Plastic Yielding Torque in Work Hardening for Hollow Shaft?

With Yield Shear Stress(non-linear) (𝞽_nonlinear), Outer Radius of Shaft (r₂), Radius of Plastic Front (ρ), Material Constant (n) & Inner Radius of Shaft (r₁) we can find Elasto Plastic Yielding Torque in Work Hardening for Hollow Shaft using the formula - Elasto Plastic Yielding Torque = (2*pi*Yield Shear Stress(non-linear)*Outer Radius of Shaft^3)/3*((3*Radius of Plastic Front^3)/(Outer Radius of Shaft^3*(Material Constant+3))-(3/(Material Constant+3))*(Inner Radius of Shaft/Radius of Plastic Front)^Material Constant*(Inner Radius of Shaft/Outer Radius of Shaft)^3+1-(Radius of Plastic Front/Outer Radius of Shaft)^3). This formula also uses Archimedes' constant .

What are the other ways to Calculate Elasto Plastic Yielding Torque?

Here are the different ways to Calculate Elasto Plastic Yielding Torque-

Elasto Plastic Yielding Torque=(2*pi*Yield Shear Stress(non-linear)*Outer Radius of Shaft^3)/3*(1-(Material Constant/(Material Constant+3))*(Radius of Plastic Front/Outer Radius of Shaft)^3)

Can the Elasto Plastic Yielding Torque in Work Hardening for Hollow Shaft be negative?

No, the Elasto Plastic Yielding Torque in Work Hardening for Hollow Shaft, measured in Torque cannot be negative.

Which unit is used to measure Elasto Plastic Yielding Torque in Work Hardening for Hollow Shaft?

Elasto Plastic Yielding Torque in Work Hardening 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 Elasto Plastic Yielding Torque in Work Hardening for Hollow Shaft can be measured.

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Elasto Plastic Yielding Torque in Work Hardening for Hollow Shaft Formula

​GoElasto Plastic Yielding Torque in Work Hardening for Solid Shaft Formula

Elasto Plastic Yielding Torque in Work Hardening for Hollow Shaft Example

Elasto Plastic Yielding Torque in Work Hardening for Hollow Shaft Solution

Elasto Plastic Yielding Torque in Work Hardening for Hollow Shaft Formula Elements

Other Formulas to find Elasto Plastic Yielding Torque

Other formulas in Elastic Work Hardening Material category

How to Evaluate Elasto Plastic Yielding Torque in Work Hardening for Hollow Shaft?

FAQs on Elasto Plastic Yielding Torque in Work Hardening for Hollow Shaft

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GoElasto Plastic Yielding Torque in Work Hardening for Solid Shaft Formula