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A fatigue test was conducted in which the mean stress was 50 MPa (7250 psi) and the stress amplitude was 225 MPa (32,625 psi).
(a) Compute the maximum and minimum stress levels.
(b) Compute the stress ratio.
(c) Compute the magnitude of the stress range.

Respuesta :

boffeemadrid

Answer:

275 MPa, -175 MPa

-0.63636

450 MPa

Explanation:

[tex]\sigma_{max}[/tex] = Maximum stress

[tex]\sigma_{min}[/tex] = Minimum stress

[tex]\sigma_m[/tex] = Mean stress = 50 MPa

[tex]\sigma_a[/tex] = Stress amplitude = 225 MPa

Mean stress is given by

[tex]\sigma_m=\frac{\sigma_{max}+\sigma_{min}}{2}\\\Rightarrow \sigma_{max}+\sigma_{min}=2\sigma_m\\\Rightarrow \sigma_{max}+\sigma_{min}=2\times 50\\\Rightarrow \sigma_{max}+\sigma_{min}=100\ MPa\\\Rightarrow \sigma_{max}=100-\sigma_{min}[/tex]

Stress amplitude is given by

[tex]\sigma_a=\frac{\sigma_{max}-\sigma_{min}}{2}\\\Rightarrow \sigma_{max}-\sigma_{min}=2\sigma_a\\\Rightarrow \sigma_{max}-\sigma_{min}=2\times 225\\\Rightarrow \sigma_{max}-\sigma_{min}=450\ MPa\\\Rightarrow 100-\sigma_{min}-\sigma_{min}=450\\\Rightarrow -2\sigma_{min}=350\\\Rightarrow \sigma_{min}=-175\ MPa[/tex]

[tex]\sigma_{max}=100-\sigma_{min}\\\Rightarrow \sigma_{max}=100-(-175)\\\Rightarrow \sigma_{max}=275\ MPa[/tex]

Maximum stress level is 275 MPa

Minimum stress level is -175 MPa

Stress ratio is given by

[tex]R=\frac{\sigma_{min}}{\sigma_{max}}\\\Rightarrow R=\frac{-175}{275}\\\Rightarrow R=-0.63636[/tex]

The stress ratio is -0.63636

Stress range is given by

[tex]\sigma_{max}-\sigma_{min}=450\ MPa[/tex]

Magnitude of the stress range is 450 MPa

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