The Designer may have more than one thermal expansion or other displacement cycle conditions to consider. Cycles at lower stress ranges are substantially less damaging than cycles at higher stress ranges. ASME B31.3 uses the cycle with the highest stress range (full displacement cycle), SE, to compare to the allowable stress range, SA. However, cycles with lower stress ranges are converted into equivalent numbers of full displacement cycles to determine the /factor. This procedure, described in par. 302.3.5(d), uses the equation
Based on this procedure, the maximum stress range is limited to SA, which satisfies the shakedown limit. Lesser cycles are converted into equivalent, with respect to fatigue damage, numbers of cycles at SE to determine if an/factor less than one is required to protect against fatigue failure. Table 7.1 provides an example of combining several displacement cycle conditions with different stress ranges and numbers of cycles. Note that due to the sensitivity of fatigue damage to stress (the fifth power in the equation), displacement cycles at significantly lower stress ranges than SE produce very little damage or a significantly reduced number of equivalent cycles.