In my opinion, B31.1 is a bit light on its application of the rules you show below. I believe it is handled much better in B31.3. B31.3 shows your rules under paragraph 319.5.1 titled "Maximum Reactions for Simple Systems". Here it states: For a two-anchor piping system without intermediate restraints, the maximum instantaneous values of reaction
forces and moments may be estimated from [the equations you list].
Also, the rules you mention are only valid for linear systems or systems that respond in a linear fashion.
In CAESAR II I would simply build the load sets that the system would see and, with the appropriate E, check those reactions.