When you are attempting to consider what 'ASME' is requiring it is important not to speak in terms of ASME generically but ASME specifically. In other words, are you asking about pressure piping codes such as the B31 seiries, or boiler and pressure vessel (BPV) codes such as Section I, III, or VIII?
There is a great deal of expertise on all of those codes in here. Specify your code and I'm sure someone will be able to help you out.