By definition, objects that are loaded under purely oscillatory loads (smean = 0) fail when their stresses reach the material's fatigue limit sfatigue.
Conversely, objects that are loaded under purely static loads (salt = 0) fail when their stresses reach the material's yield limit syield.
For objects that have a mixture of smean and salt stresses, the Soderberg Criterion provides a way to calculate a failure limit. The Soderberg Diagram plots mean stress on one axis, and alternating stress on the other, and draws a line between the smean = syield and salt = sfatigue points, as shown here,
We then plot the stress state our object of question as a point on the Soderberg Diagram. If the stress state is below the line, then we are OK. If the stress state is above the line, then failure in the part is likely.
If we don't want to plot, we can calculate the point on the Soderberg line that corresponds to our mean stress by the equation,
The part will fail if our alternating stress is larger than the Soderberg stress limit,