I know that Caesar II and Coade Tank can calculate the nozzle allowable loads as per API 650.
By the way I'm trying to investigate to understand the equation that brings to the diagrams P-4A and P-4B.
Does somebody know if I can find the answer in the paper written by Bilimora & Hangstrom in 1997?
Thank you.

This isn't quite true. These COADE programs determine the axis limits for the qualification of the nozzles. Each value reported assumes the others are zero - which isn't true. This is why you need to construct the diagrams shown in API-650 Figures P5-A and P5-B.

Thank you Richard.
I am building a simple excel file that builds automatically the diagrams you mentioned. I did 50% of the job, because my excel file now can generate automatically the Figure P-5A, but the problem is that the user has to insert by hand the values of YL, YF and YC.
My file will check the "working" values of nozzle from the Caeasar Restraint summary, and not only the limit values while the other are set to zero. This will be very time-saving.
After the file will be tested, I will share for free. This could be very good for the "Caesar people"
I would like to know the equations that lead to Figure P-4A and Figure P4-B. I think I should search in the papers I mentioned. Could somebody help me, maybe giving me the equations?

I'm not sure there are equations for Figures P-4A and P-4B. Just "digitize" the data and use a look-up with interpolation.