I don't like to use Appendix P simply because I don't believe that there is something known as operating stress. The failure mechanisms are like this:

1) Plastic collapse; due to high bending moment ( plastic hinge at across section)under high load or bursting due to high pressure.

2) Ratchetting: This is a complex phenomenon. This is what is known as cycle dependent creep. From basic theory of fatigue we know the effect of mean stress or mean strain on fatigue. In this phenomenon, due to high level of plasticity, mean strain increases in every cycle ( the opposite effect also sometime hapens when mean stress and not strain reduced in every cycle due to plastic action)and the filure can be due to platic collapse or fatigue.The 2yp range is based on Melan's shakedown theorem and is based on elastic perfectly plastic materials only.

3) Fatigue:

a) stress controlled : this is due to low level of stress ( less than yield point) and high no. of cycles.This is a localized phenomenon.

b) Strain controlled: this is due to high level of strain and lower no. of cycles.Mark's tests were strain controlled.

Fatigue in presence of mean stress is similar but not same as ratchetting.

4) Buckle: Also known as bifurcation buckling where the direction of displacement is orthogonal to applied load, making the effective ( material+geometric ) stiffess=0. This method overpredicts for perfect structure and under predicts the collapse load for imperfect structures.

Based on the above, under which failure category would you place operating stress? It is certainly not plastic collpase ( the code alowable does not indicate that either). Is it then fatigue or ratchetting ( both requires range of loadand cyclicing).The only possibility can be , it is a simplistic representation of checking for fatigue failure using monotonic analysis ( twice yield method of the new 2007 edition of SECTION VIII DIV 2). This is valid for simple cases ( papers by Mroz, Dowling and Kalnins provide the necessary mathematics) but use of cyclic stresss strain curve instead of monotonic is needed. Also the full range of loading is required .Hence in my opinion, this check does not address any proper failure mechanism and hence the expansion stress range check ( this is actually a fatigue check but the code uses one equation to check fatigue and ratchetting to keep this simple)is what should be used.