I´m analyzing a tank right now with three huge 30" nozzles very close. The Pipe is 36" and the tanks is going to settle 2" during lifetime. I initially ran the analysis with this conditions and specify some spring hangers and a ball joints as client request. My client comments asked me to include the unrestrained nozzle rotation due to thermal expansion and product head. The tank is really big and this angle is 1.5º degrees. The pipe now is having overstresses and deflects almost 4" near the nozzle.

I always include the nozzle stiffnesses Kr, Kl and Kc according to API 650 App. P, the thermal expansion displacements at nozzle-pipe junction and settlement displacements if necessary, but including this angle is giving me hard time to make this pipe pass the analysis.

How real is this angle for my analysis, I mean, 1.5 degres rotation is huge in a 36" pipe. The unrestrained condition on the tank is important here? My nozzle is not unrestrained, the pipe is flanged to it.

The method of analysis for piping connected to API 650 tanks is very correct. It is possible to have a large nozzle roation and it depents on the wall thickness of tank, height of liquid and dia of the tank.

Can u clarify clearly "The unrestrained condition on the tank "
Try providing spring hangers (constant) and make the routing more flexible.

Have you considered a double tied expansion joint ? It would seem to be the ideal solution to absorb tank wall rotation, bulge and setlement.

With unrastrained I mean the Nozzle can move freely wthout any external restriction, thats what the API 650 App P says to estimate this angle, I´m not sure this is the real rotation once I have my pipe connected. My client already built the same type of tanks previously as part of a different project but I have not idea what conditions they used for the analysis. Apparently a more flexible arrangement worked for the other tanks but If I include the nozzle rotation value the same arrangement does not work. I´m not allowed to use expansion joints.

Please check hav u included nozzle stiffness values while modelling the nozzle of tank.

I suggest you to take a look in the Appendix of the original article "Stiffness Coefficients and Allowable Loads for Nozzles in Flat-Bottom Storage tanks", where Mr. Billimoria and Hagstrom made some guidance for the usage of method.
Unfortunately my copy is a low quality one...but I think it's enough to understand what authors intended to say.

In my opinion, you would consider a FEA method for you case.

Just as reference.... API 650, Appendix P Section P.2 (limit loads evaluation) is based on H. D. Billimoria and J. Hagstrom’s article "Stiffness Coefficients and Allowable Loads for Nozzles in Flat Bottom Storage Tanks" and H. D. Billimoria and K. K. Tam’s "Experimental Investigation of Stiffness Coefficients and Allowable Loads for a Nozzle in a Flat Bottom Storage Tank."