Caesar modifies the SIF's and flexibility due to pressure stiffening. Look at the notes at the end of the B31.3 table to see the equations for pressure stiffening.

Casaer automatically applies pressure stiffening on bends etc using the MAXIMUM pressure load. I think this is not a good way to do it. I think it should apply different pressure stiffening for each pressure load case, corresponding to that load cases pressure.

Are you sure you turned the pressure stiffening off in the correct place on Caesar. You can do it in 2 places. 1- the special execution parameters, or 2 - configure/set-up => computational control.

The one in the special execution parameters is for pressure stiffening of straight pipes, it is not the one you want

The one in the computational control is for bends, tees etc. It will turn the pressure stiffening on SIF's and flexibility off.