About supports, ASME III NF (far more specialized than B31.3 and B31.1 on the supports subject) says in NF-3121.2- "For evaluation purposes, stresses induced in the support by restraint of free end displacement [NF-3111(e)] and anchor motion [NF-3111 (f)] of piping are considered primary stresses.".

NF changed the classification "for evaluation purposes" in 1982.

B31.3 and B31.1 may be silent on classification of stress in supports, but the practice "for evaluation purposes" is the same by the allowable considered.

Which is the connection with your case? You are not talking about stress induced in supports but induced in piping- if I understand well.