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Mechanical Engineering QUESTION #2511
Question 1
According to the Gerber (parabolic) fatigue criterion, the equation relating \(\sigma_a\), \(\sigma_m\), \(S_e\), and \(S_{ut}\) is:
  • \(\frac{\sigma_a}{S_e} + \frac{\sigma_m}{S_{ut}} = 1\)
  • \(\left(\frac{n\sigma_a}{S_e}\right) + \left(\frac{n\sigma_m}{S_{ut}}\right)^2 = 1\)
  • \(\frac{\sigma_a}{S_e} + \left(\frac{\sigma_m}{S_{ut}}\right)^2 = 1\)✔️
  • \(\frac{\sigma_a}{S_e} \cdot \frac{\sigma_m}{S_{ut}} = 1\)
Correct Answer Explanation
The Gerber parabolic criterion: \(\frac{\sigma_a}{S_e}+\left(\frac{\sigma_m}{S_{ut}}\right)^2=1\). Gerber's curve passes through the central region of fatigue failure data.