WRC bulletins 107 and 297 ( by the way the full form of WRC is welding research council) addresses local stresses at vessel -nozzle interesection.WRC 107 is for cylindrical as well as spherical vessels and WRC 297 is only for cylindrical vessels. Both the bulletins discuss how to calculate membrane and bending stress intensities at different locations along the joint.These stress intensities are used as per rules of ASME SEC VIII DIV 2.WRC 297 additionally provides local flexibilities also.

For the formulas: read WRC 107 and 297.

For the basics: Basis method behind Caesar II is finite element analysis using beam elements.Basic method behind WRC 107/297 requires an understanding of shell/plate theory and good command over differential equations.

Based on the type of questions ( most of them)that we get to see in the forum these days and the absolute lack of interest ( this is based on my personal experience of trying to "teach" some young engineers who feels that spending time to brush up the fundamentals or improve knowledge base is a wastage of time)on part of most young engineers, I think my suggestions on "for the basics" will fall to deaf ears.

Regards