Discussion
Which one of the following failure theories is the most conservative design approach against fatigue failure?
Answer: A
The most conservative approach is the Soderberg line.
On a plot of alternating stress against mean stress, each criterion draws a boundary from the endurance limit on the alternating-stress axis to a point on the mean-stress axis. The Soderberg line runs to the yield strength, the Modified Goodman line to the ultimate strength, and the Gerber curve is a parabola through the ultimate strength. Since yield strength is lower than ultimate strength, the Soderberg line lies inside the other two and allows the smallest stresses, making it the most conservative.
The Gerber parabola is the least conservative of the three. The yield (Langer) line guards against first-cycle yielding, not against fatigue, so it is not a fatigue failure criterion on its own.
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