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Residual Shear Stress in Shaft for Fully Plastic Case Formula

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Residual Shear Stress in fully Plastic Yielding can be defined as the algebraic sum of applied stress and recovery stress. Check FAQs

ζ f_res = 𝝉 0 \cdot (1 - \frac{4 \cdot r \cdot (1 - {(\frac{r 1}{r 2})}^{3})}{3 \cdot r 2 \cdot (1 - {(\frac{r 1}{r 2})}^{4})})

ζ_{f_res} - Residual Shear Stress in fully Plastic Yielding?𝝉₀ - Yield Stress in Shear?r - Radius Yielded?r₁ - Inner Radius of Shaft?r₂ - Outer Radius of Shaft?

Residual Shear Stress in Shaft for Fully Plastic Case Example

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Here is how the Residual Shear Stress in Shaft for Fully Plastic Case equation looks like with Values.

Here is how the Residual Shear Stress in Shaft for Fully Plastic Case equation looks like with Units.

Here is how the Residual Shear Stress in Shaft for Fully Plastic Case equation looks like.

33.5714 = 145 \cdot (1 - \frac{4 \cdot 60 \cdot (1 - {(\frac{40}{100})}^{3})}{3 \cdot 100 \cdot (1 - {(\frac{40}{100})}^{4})})

33.5714MPa = 145MPa \cdot (1 - \frac{4 \cdot 60mm \cdot (1 - {(\frac{40mm}{100mm})}^{3})}{3 \cdot 100mm \cdot (1 - {(\frac{40mm}{100mm})}^{4})})

33.5714 = 145 \cdot (1 - \frac{4 \cdot 60 \cdot (1 - {(\frac{40}{100})}^{3})}{3 \cdot 100 \cdot (1 - {(\frac{40}{100})}^{4})})

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Residual Shear Stress in Shaft for Fully Plastic Case Solution

Follow our step by step solution on how to calculate Residual Shear Stress in Shaft for Fully Plastic Case?

FIRST Step Consider the formula

ζ f_res = 𝝉 0 \cdot (1 - \frac{4 \cdot r \cdot (1 - {(\frac{r 1}{r 2})}^{3})}{3 \cdot r 2 \cdot (1 - {(\frac{r 1}{r 2})}^{4})})

Next Step Substitute values of Variables

∴

ζ f_res = 145MPa \cdot (1 - \frac{4 \cdot 60mm \cdot (1 - {(\frac{40mm}{100mm})}^{3})}{3 \cdot 100mm \cdot (1 - {(\frac{40mm}{100mm})}^{4})})

Next Step Convert Units

∴

ζ f_res = 1.5E+8Pa \cdot (1 - \frac{4 \cdot 0.06m \cdot (1 - {(\frac{0.04m}{0.1m})}^{3})}{3 \cdot 0.1m \cdot (1 - {(\frac{0.04m}{0.1m})}^{4})})

Next Step Prepare to Evaluate

∴

ζ f_res = 1.5E+8 \cdot (1 - \frac{4 \cdot 0.06 \cdot (1 - {(\frac{0.04}{0.1})}^{3})}{3 \cdot 0.1 \cdot (1 - {(\frac{0.04}{0.1})}^{4})})

Next Step Evaluate

∴

ζ f_res = 33571428.5714286Pa

Next Step Convert to Output's Unit

∴

ζ f_res = 33.5714285714286MPa

LAST Step Rounding Answer

∴

ζ f_res = 33.5714MPa

Residual Shear Stress in Shaft for Fully Plastic Case Formula Elements

Variables

Residual Shear Stress in fully Plastic Yielding

Residual Shear Stress in fully Plastic Yielding can be defined as the algebraic sum of applied stress and recovery stress.

Symbol: ζ_{f_res}

Measurement: StressUnit: MPa

Note: Value can be positive or negative.

Formulas to find Residual Shear Stress in fully Plastic Yielding

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

Radius Yielded

Radius Yielded is the remaining stress in a material after the original cause of the stress has been removed, affecting its structural integrity and durability.

Symbol: r

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Radius Yielded

Inner Radius of Shaft

Inner Radius of Shaft is the internal radius of a shaft, which is a critical dimension in mechanical engineering, affecting stress concentrations and structural integrity.

Symbol: r₁

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Inner Radius of Shaft

Outer Radius of Shaft

Outer Radius of Shaft is the distance from the center of the shaft to its outer surface, affecting residual stresses in the material.

Symbol: r₂

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Outer Radius of Shaft

Other formulas in Residual Stresses For Idealized Stress Strain Law category

Go Recovery Elasto Plastic Torque

T rec = - (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 Residual Shear Stress in Shaft when r Lies between r1 and Material Constant

ζ shaft_res = (𝝉 0 \cdot \frac{r}{ρ} - ((\frac{4 \cdot 𝝉 0 \cdot r}{3 \cdot r 2 \cdot (1 - {(\frac{r 1}{r 2})}^{4})}) \cdot (1 - \frac{1}{4} \cdot {(\frac{ρ}{r 2})}^{3} - \frac{3 \cdot r 1}{4 \cdot ρ} \cdot {(\frac{r 1}{r 2})}^{3})))

Go Residual Shear Stress in Shaft when r Lies between Material Constant and r2

ζ shaft_res = 𝝉 0 \cdot (1 - \frac{4 \cdot r \cdot (1 - ((\frac{1}{4}) \cdot {(\frac{ρ}{r 2})}^{3}) - ((\frac{3 \cdot r 1}{4 \cdot ρ}) \cdot {(\frac{r 1}{r 2})}^{3}))}{3 \cdot r 2 \cdot (1 - {(\frac{r 1}{r 2})}^{4})})

Go Residual Angle of Twist for Elasto Plastic Case

θ res = \frac{𝝉 0}{G \cdot ρ} \cdot (1 - (\frac{4 \cdot ρ}{3 \cdot r 2}) \cdot (\frac{1 - \frac{1}{4} \cdot {(\frac{ρ}{r 2})}^{3} - \frac{3 \cdot r 1}{4 \cdot ρ} \cdot {(\frac{r 1}{r 2})}^{3}}{1 - {(\frac{r 1}{r 2})}^{4}}))

How to Evaluate Residual Shear Stress in Shaft for Fully Plastic Case?

Residual Shear Stress in Shaft for Fully Plastic Case evaluator uses Residual Shear Stress in fully Plastic Yielding = Yield Stress in Shear*(1-(4*Radius Yielded*(1-(Inner Radius of Shaft/Outer Radius of Shaft)^3))/(3*Outer Radius of Shaft*(1-(Inner Radius of Shaft/Outer Radius of Shaft)^4))) to evaluate the Residual Shear Stress in fully Plastic Yielding, Residual Shear Stress in Shaft for Fully Plastic Case formula is defined as a measure of the remaining shear stress in a shaft after it has undergone plastic deformation, providing a critical value for shaft design and material selection in mechanical engineering applications. Residual Shear Stress in fully Plastic Yielding is denoted by ζ_{f_res} symbol.

How to evaluate Residual Shear Stress in Shaft for Fully Plastic Case using this online evaluator? To use this online evaluator for Residual Shear Stress in Shaft for Fully Plastic Case, enter Yield Stress in Shear (𝝉₀), Radius Yielded (r), Inner Radius of Shaft (r₁) & Outer Radius of Shaft (r₂) and hit the calculate button.

FAQs on Residual Shear Stress in Shaft for Fully Plastic Case

What is the formula to find Residual Shear Stress in Shaft for Fully Plastic Case?

The formula of Residual Shear Stress in Shaft for Fully Plastic Case is expressed as Residual Shear Stress in fully Plastic Yielding = Yield Stress in Shear*(1-(4*Radius Yielded*(1-(Inner Radius of Shaft/Outer Radius of Shaft)^3))/(3*Outer Radius of Shaft*(1-(Inner Radius of Shaft/Outer Radius of Shaft)^4))). Here is an example- 3.4E-5 = 145000000*(1-(4*0.06*(1-(0.04/0.1)^3))/(3*0.1*(1-(0.04/0.1)^4))).

How to calculate Residual Shear Stress in Shaft for Fully Plastic Case?

With Yield Stress in Shear (𝝉₀), Radius Yielded (r), Inner Radius of Shaft (r₁) & Outer Radius of Shaft (r₂) we can find Residual Shear Stress in Shaft for Fully Plastic Case using the formula - Residual Shear Stress in fully Plastic Yielding = Yield Stress in Shear*(1-(4*Radius Yielded*(1-(Inner Radius of Shaft/Outer Radius of Shaft)^3))/(3*Outer Radius of Shaft*(1-(Inner Radius of Shaft/Outer Radius of Shaft)^4))).

Can the Residual Shear Stress in Shaft for Fully Plastic Case be negative?

Yes, the Residual Shear Stress in Shaft for Fully Plastic Case, measured in Stress can be negative.

Which unit is used to measure Residual Shear Stress in Shaft for Fully Plastic Case?

Residual Shear Stress in Shaft for Fully Plastic Case is usually measured using the Megapascal[MPa] for Stress. Pascal[MPa], Newton per Square Meter[MPa], Newton per Square Millimeter[MPa] are the few other units in which Residual Shear Stress in Shaft for Fully Plastic Case can be measured.

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Residual Shear Stress in Shaft for Fully Plastic Case Formula

Residual Shear Stress in Shaft for Fully Plastic Case Example

Residual Shear Stress in Shaft for Fully Plastic Case Solution

Residual Shear Stress in Shaft for Fully Plastic Case Formula Elements

Other formulas in Residual Stresses For Idealized Stress Strain Law category

How to Evaluate Residual Shear Stress in Shaft for Fully Plastic Case?

FAQs on Residual Shear Stress in Shaft for Fully Plastic Case

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