It is a common problem that the "allowable loads" on a nozzle are to be found. This question is often posed to vessel fabricators by the vessel owner or the contractor, etc, looking for whether the piping loads will create excessive stress in the vessel. It's a simple question.
Unfortunately, there is not a simple answer. And fabricators who have the misfortune to fall into the trap of providing this engineering work for free can find themselves vastly overrunning their engineering time.
The issue is that there isn't a single "allowable load" that may act on a nozzle. There are 3 possible forces acting on the nozzle and shell (2 shears and a radial force) and 3 possible moments (2 bending moments and a torsional moment); call these Fx, Fy, Fz, and Mx, My, and Mz. These will not in general resolve to a single set of forces and moments that are the "maximum".
In fact, there is an infinite number of combinations of these forces and moments that will all act to produce the maximum allowable stress in the shell (this is the true meaning of the "allowable load"...that which stresses the shell to the highest allowable condition).
Since there is an infinite number of load combinations fabricators who are asked to find the "maximum allowable load" can be frustrated when they find one of the sets that produce the maximum load but their customer asks "but what if...?" and they want to change the loads slightly, perhaps then saying that there is no VL or no Mt, etc. Then the fabricator has to perform the exercise all over again. I hope they get paid for each additional cycle.
Anyway, by placing some judgment on this one can come up with a methodology to establish some maximum loads. ie: you might define that the forces and moments will always be in some given proportion to each other or some other relationship, then run your WRC-107 program or spreadsheet based on these rules to find the particular set of maximum loads. Some further refinement can be performed too since some of the loads and moments do not combine directly to produce membrane or through-thickness bending stress.