I was just running a spreadsheet on the different sizes, maybe this will help. Treating repad (and shell) as fixed-fixed flat annular plate, stress of 20,000 PSI, using API-650 round repad sizes, testing for adequacy at 15 PSI:
3/16" shell- good up through 14" nozzle
1/4 shell- good up through 20" nozzle
5/16" shell- good up through 24" nozzle
3/8" shell- good up through 30" nozzle
1/2" shell- good up through 42" nozzle
5/8" shell- good up through 48" nozzle
If the tank diameter is fairly small, this will be overly conservative, but I know of no better analysis. For larger diameters (ie, field erected tanks), these numbers should be reasonable estimates. Normally, you don't have huge nozzles on thin walls, so the most likely problem area is shell manways.