CAESAR II "recommends" the three expansion cases you mention (I will not quibble about that T4, instead I will think of that as the "installed" position - usually something like W+P1) but that may not be all you need to follow the intent of the Code. The Appendix S example on stress reversal shows that additional strain ranges might produce a greater stress range; namely T1-T2, T1-T3, and T2-T3.
But the Code does not state that these stresses sould be formed as "absolute stress summations" (that's a CAESAR II term, not a Code term). They are range calculations like any other.
As Craig points out this has been the Code approach for quite a while now (50 years?) - to evaluate the maximum stress/strain range. Things got more complicated over the last 20 years or so with the inclusion of nonlinear conditions included in the analysis.
And then there is the problem of accummulating damage from the several expansion stress ranges. Your job is not complete in just examining the largest stress range. You must alter your cycle count for this largest range by converting the other, lower, stress ranges into equivalent cycles at the maximum range. See (1d) in B31.3 para. 302.3.5(d).
Do not assume that CAESAR II "recommends" all that is required. It only recommends the most obvious cases to collect expansion stress range(s) and sustained stress(es).
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Dave Diehl