Topic: Machine Design
A machine member is subjected to fluctuating stress, $sigma = sigma_0 cos(5pi t)$. The endurance limit of the material is 350 MPa and the yield strength is 500 MPa. If the factor of safety used in the design is 3.5, then the maximum allowable stress $sigma_0$ in MPa according to soderberg fatigue criteria is
- A. 10
- B. 200
- C. 100
- D. 50
Answer: C. 100
Explanation: The stress varies sinusoidally from $+sigma_0$ to $-sigma_0$. Therefore, the mean stress $sigma_m = 0$, and the variable (amplitude) stress $sigma_v = sigma_0$. Using the Soderberg criteria: $(sigma_m / S_y) + (sigma_v / S_e) = 1 / FOS$. Since $sigma_m = 0$, the equation becomes $sigma_0 / 350 = 1 / 3.5$. Solving for $sigma_0$ gives 100 MPa.