I AM GOING TO EXPLAIN MY PROBLEM:
CONSIDERING THAT WE HAVE A PIPE CALCULATED AND ERECTED, HAVING READY A FLANGE OR A CONNECTING POINT FOR A NEW PIPE CONNECTION.
WHICH DATA SHOULD BE GIVEN TO THE PERSON WHO IS GOING TO CALCULATE THE NEW PIPE TO ASSURE THAT THE SUPPORTS ALREADY ERECTED IN THE PREVIOUS PIPE ARE NOT CHANGED?
IT ALSO SHOULD BE ASSURED THAT THE LOADS IN THE EQUIPMENT ARE NOT MODIFIED.

I SHOULD UNDERLINE THAT THE CONNECTING POINT IS NOT A FIXED POINT BUT A FREE POINT WITH DESPLACEMENT.

THANK YOU SO MUCH FOR YOUR ANSWERS.

If the new pipe is much smaller than the existing pipe, then a good starting point is to model the existing system, from the connection point, in both directions until you cross at least 3 supports. The assumption here is that the new pipe will not affect the behavior of the existing pipe. I suggest before modeling the new pipe, you apply forces and moments to the existing pipe to achieve the known displacements at the connection point. (You can't apply displacements because this will fix the point.) Then use these same forces and momements in the combined model.

If the new pipe is not small compared to the existing pipe, both systems will interact with each other. You will have to model the existing system, in both directions, until you reach a point of fixity (a nozzle or an anchor).