Regarding your comments:
1) Unless your pipe density is zero, this doesn't make any sense.
2) In a pipe flexibility analysis, pressure has no effect on the system (assuming you don't have expansion joints or Bourdon turned on) displacements and loads. Pressure is only used in the "Code stress" equations as a contribution to the "longitudinal pressure stress".
So if the element forces & moments are zero in case 2, and you said case 1 was the same, then I would again assume the density of the pipe material is zero.
3) The principle of "superpostion" does not necessarily apply to piping systems. See "Formulas for Stress and Strain" by Roark & Young, Section 3.2, paragraph 2. This is especially true if the system you've modeled includes non-linear boundary conditions.
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Regards,
Richard Ay - Consultant