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.

1. Understanding the S-N Curve:
The provided image shows a typical fatigue test result plot, commonly known as the S-N curve. The vertical axis represents the Fatigue strength, S, while the horizontal axis represents the Number of cycles, N. Key reference stress values are marked on the vertical axis as $S_{\mathrm{ut}}$ (ultimate tensile strength), $S_1$, $S_2$, $S_3$, and $S_4$, corresponding to life cycles $N_1$, $N_2$, $N_3$, and $N_4$ respectively at points 1, 2, 3, and 4 along the curve.

2. Defining the Endurance Limit:
For ferrous materials such as steel, the S-N curve exhibits a distinct knee or horizontal asymptote. The stress level below which the material can withstand an infinite number of cycles without experiencing fatigue failure is called the endurance limit (or fatigue limit).

3. Locating the Endurance Limit on the Graph:
Looking closely at the curve in the image, as the number of cycles increases past $N_3$ toward $N_4$ (Point 4), the curve flattens out and becomes parallel to the horizontal axis. Beyond Point 4, the fatigue strength remains constant regardless of how many cycles are applied. The stress level corresponding to this horizontal portion is labeled on the vertical axis as S₄.
Therefore, S₄ represents the endurance limit of the steel.