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Residual Stress in Elasto Plastic Torsion when r lies between Constant and r2 Formula

GoResidual Stress in Elasto Plastic Torsion when r Lies between r1 and Constant Formula

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

ζ ep_res = 𝞽 nonlinear - \frac{T ep \cdot r}{\frac{π}{2} \cdot ({r 2}^{4} - {r 1}^{4})}

ζ_{ep_res} - Residual Shear Stress in Elasto Plastic Yielding?𝞽_nonlinear - Yield Shear Stress(non-linear)?T_ep - Elasto Plastic Yielding Torque?r - Radius Yielded?r₂ - Outer Radius of Shaft?r₁ - Inner Radius of Shaft?π - Archimedes' constant?

Residual Stress in Elasto Plastic Torsion when r lies between Constant and r2 Example

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Here is how the Residual Stress in Elasto Plastic Torsion when r lies between Constant and r2 equation looks like with Values.

Here is how the Residual Stress in Elasto Plastic Torsion when r lies between Constant and r2 equation looks like with Units.

Here is how the Residual Stress in Elasto Plastic Torsion when r lies between Constant and r2 equation looks like.

74.2541 = 175 - \frac{2.6E+8 \cdot 60}{\frac{3.1416}{2} \cdot (100^{4} - 40^{4})}

74.2541MPa = 175MPa - \frac{2.6E+8N*mm \cdot 60mm}{\frac{3.1416}{2} \cdot ({100mm}^{4} - {40mm}^{4})}

74.2541 = 175 - \frac{2.6E+8 \cdot 60}{\frac{3.1416}{2} \cdot (100^{4} - 40^{4})}

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Residual Stress in Elasto Plastic Torsion when r lies between Constant and r2 Solution

Follow our step by step solution on how to calculate Residual Stress in Elasto Plastic Torsion when r lies between Constant and r2?

FIRST Step Consider the formula

ζ ep_res = 𝞽 nonlinear - \frac{T ep \cdot r}{\frac{π}{2} \cdot ({r 2}^{4} - {r 1}^{4})}

Next Step Substitute values of Variables

∴

ζ ep_res = 175MPa - \frac{2.6E+8N*mm \cdot 60mm}{\frac{π}{2} \cdot ({100mm}^{4} - {40mm}^{4})}

Next Step Substitute values of Constants

∴

ζ ep_res = 175MPa - \frac{2.6E+8N*mm \cdot 60mm}{\frac{3.1416}{2} \cdot ({100mm}^{4} - {40mm}^{4})}

Next Step Convert Units

∴

ζ ep_res = 1.8E+8Pa - \frac{257000N*m \cdot 0.06m}{\frac{3.1416}{2} \cdot ({0.1m}^{4} - {0.04m}^{4})}

Next Step Prepare to Evaluate

∴

ζ ep_res = 1.8E+8 - \frac{257000 \cdot 0.06}{\frac{3.1416}{2} \cdot ({0.1}^{4} - {0.04}^{4})}

Next Step Evaluate

∴

ζ ep_res = 74254137.0083323Pa

Next Step Convert to Output's Unit

∴

ζ ep_res = 74.2541370083323MPa

LAST Step Rounding Answer

∴

ζ ep_res = 74.2541MPa

Residual Stress in Elasto Plastic Torsion when r lies between Constant and r2 Formula Elements

Variables

Constants

Residual Shear Stress in Elasto Plastic Yielding

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

Symbol: ζ_{ep_res}

Measurement: StressUnit: MPa

Note: Value can be positive or negative.

Formulas to find Residual Shear Stress in Elasto Plastic Yielding

Yield Shear Stress(non-linear)

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

Symbol: 𝞽_nonlinear

Measurement: StressUnit: MPa