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Incipient Yielding Torque in Work Hardening Solid Shaft Formula

GoIncipient Yielding Torque in Work Hardening for Hollow 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{𝞽 nonlinear \cdot J n}{{r 2}^{n}}

T_i - Incipient Yielding Torque?𝞽_nonlinear - Yield Shear Stress(non-linear)?J_n - Nth Polar Moment of Inertia?r₂ - Outer Radius of Shaft?n - Material Constant?

Incipient Yielding Torque in Work Hardening Solid Shaft Example

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Here is how the Incipient Yielding Torque in Work Hardening Solid Shaft equation looks like with Values.

Here is how the Incipient Yielding Torque in Work Hardening Solid Shaft equation looks like with Units.

Here is how the Incipient Yielding Torque in Work Hardening Solid Shaft equation looks like.

1804.9536 = \frac{175 \cdot 5800}{100^{0.25}}

1804.9536N*mm = \frac{175MPa \cdot 5800mm⁴}{{100mm}^{0.25}}

1804.9536 = \frac{175 \cdot 5800}{100^{0.25}}

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Incipient Yielding Torque in Work Hardening Solid Shaft Solution

Follow our step by step solution on how to calculate Incipient Yielding Torque in Work Hardening Solid Shaft?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

T i = \frac{175MPa \cdot 5800mm⁴}{{100mm}^{0.25}}

Next Step Convert Units

∴

T i = \frac{1.8E+8Pa \cdot 5.8E-9m⁴}{{0.1m}^{0.25}}

Next Step Prepare to Evaluate

∴

T i = \frac{1.8E+8 \cdot 5.8E-9}{{0.1}^{0.25}}

Next Step Evaluate

∴

T i = 1.80495360118951N*m

Next Step Convert to Output's Unit

∴

T i = 1804.95360118951N*mm

LAST Step Rounding Answer

∴

T i = 1804.9536N*mm

Incipient Yielding Torque in Work Hardening Solid Shaft Formula Elements

Variables

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

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)

Nth Polar Moment of Inertia

Nth Polar Moment of Inertia can be defined as Integral arising from nonlinear behaviour of material.

Symbol: J_n

Measurement: Second Moment of AreaUnit: mm⁴

Note: Value should be greater than 0.

Formulas to find Nth Polar Moment of Inertia

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

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

Other Formulas to find Incipient Yielding Torque

Go Incipient Yielding Torque in Work Hardening for Hollow Shaft

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

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 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})

Go Elasto Plastic Yielding Torque in Work Hardening for Hollow Shaft

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})

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 Incipient Yielding Torque in Work Hardening Solid Shaft?

Incipient Yielding Torque in Work Hardening Solid Shaft evaluator uses Incipient Yielding Torque = (Yield Shear Stress(non-linear)*Nth Polar Moment of Inertia)/Outer Radius of Shaft^Material Constant to evaluate the Incipient Yielding Torque, Incipient Yielding Torque in Work Hardening Solid Shaft formula is defined as the measure of the torque required to initiate yielding in a work-hardened solid shaft, which is a critical parameter in the design and analysis of shafts subjected to torsional loading. Incipient Yielding Torque is denoted by T_i symbol.

How to evaluate Incipient Yielding Torque in Work Hardening Solid Shaft using this online evaluator? To use this online evaluator for Incipient Yielding Torque in Work Hardening Solid Shaft, enter Yield Shear Stress(non-linear) (𝞽_nonlinear), Nth Polar Moment of Inertia (J_n), Outer Radius of Shaft (r₂) & Material Constant (n) and hit the calculate button.

FAQs on Incipient Yielding Torque in Work Hardening Solid Shaft

What is the formula to find Incipient Yielding Torque in Work Hardening Solid Shaft?

The formula of Incipient Yielding Torque in Work Hardening Solid Shaft is expressed as Incipient Yielding Torque = (Yield Shear Stress(non-linear)*Nth Polar Moment of Inertia)/Outer Radius of Shaft^Material Constant. Here is an example- 1.8E+6 = (175000000*5.8E-09)/0.1^0.25.

How to calculate Incipient Yielding Torque in Work Hardening Solid Shaft?

With Yield Shear Stress(non-linear) (𝞽_nonlinear), Nth Polar Moment of Inertia (J_n), Outer Radius of Shaft (r₂) & Material Constant (n) we can find Incipient Yielding Torque in Work Hardening Solid Shaft using the formula - Incipient Yielding Torque = (Yield Shear Stress(non-linear)*Nth Polar Moment of Inertia)/Outer Radius of Shaft^Material Constant.

What are the other ways to Calculate Incipient Yielding Torque?

Here are the different ways to Calculate Incipient Yielding Torque-

Incipient Yielding Torque=(Yield Shear Stress(non-linear)*Nth Polar Moment of Inertia)/Outer Radius of Shaft^Material Constant

Can the Incipient Yielding Torque in Work Hardening Solid Shaft be negative?

No, the Incipient Yielding Torque in Work Hardening Solid Shaft, measured in Torque cannot be negative.

Which unit is used to measure Incipient Yielding Torque in Work Hardening Solid Shaft?

Incipient Yielding Torque in Work Hardening Solid 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 in Work Hardening Solid Shaft can be measured.

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Incipient Yielding Torque in Work Hardening Solid Shaft Formula

​GoIncipient Yielding Torque in Work Hardening for Hollow Shaft Formula

Incipient Yielding Torque in Work Hardening Solid Shaft Example

Incipient Yielding Torque in Work Hardening Solid Shaft Solution

Incipient Yielding Torque in Work Hardening Solid Shaft Formula Elements

Other Formulas to find Incipient Yielding Torque

Other formulas in Elastic Work Hardening Material category

How to Evaluate Incipient Yielding Torque in Work Hardening Solid Shaft?

FAQs on Incipient Yielding Torque in Work Hardening Solid Shaft

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GoIncipient Yielding Torque in Work Hardening for Hollow Shaft Formula