The S-N curve from a fatigue test for steel is shown. Which one of the options gives the endurance limit?

The correct option is S₄.

An S-N curve (Stress vs. Number of cycles) plots the cyclic stress amplitude against the number of cycles to failure. In the provided image, the vertical axis represents the fatigue strength, labeled as Fatigue strength, S, and the horizontal axis represents the number of cycles, labeled as Number of cycles, N.

The curve starts at the ultimate tensile strength of the material:
$S_{ut}$
As the number of cycles increases, the stress amplitude required to cause fatigue failure decreases. This is shown by the downward-sloping curve passing through point 1 (at fatigue strength
$S_1$
and cycles
$N_1$), point 2 (at fatigue strength
$S_2$
and cycles
$N_2$), and point 3 (at fatigue strength
$S_3$
and cycles
$N_3$).

For steel and many other ferrous materials, the S-N curve flattens out and becomes a horizontal line at a high number of cycles. This flat region represents the endurance limit (or fatigue limit). Any stress level below this limit will not cause fatigue failure, meaning the material has an infinite life under these loading conditions.

In the given S-N curve, the plateau starts at point 4, which corresponds to the fatigue strength level:
$S_4$
at a cycle count of:
$N_4$
Since the curve is horizontal beyond this point,
$S_4$
is the endurance limit of the steel.