Stresses in a clamped circular plate
Acroduster1: As you quoted Roark previously, he says that his formulas are for use only when, "... the thickness in not more than than about one quarter of the least transverse dimension...."
Transverse simply means "across," no more and no less (go check the Latin root), and for an annulus, it is certainly reasonable and correct to talk about both the ID and OD as transverse dimensions.
That adjective "least" is in there for a reason, so I think the ID is rather clearly the least transverse dimension of the annulus.
You say that you have used these formulas for all sorts of things, and I have no reason to doubt that statement. I have to ask the question, however: How did you check the results? Just because you got an answer and it seemed to work does not mean that it was accurate.
There is an alternative to using Roark's formulas that might be of interest to the originator of the question. Theory of Plates and Shells by Timoshenko and Krieger gives a more exact formulation of the problem that will perhaps be more useful and less subject to the limitations that have given rise to this discussion. This same derivation is no doubt available elsewhere as well. -- Sam