Appendix 4 of ASME VIII Div.2 has formulae for the anlysis of spherical shells: you could try to adapt them to your case by using the radius of curvature at the attachment as the spherical radius.
However I don't want to push you in that direction: those formulae are hard to manipulate and unless you write a worksheet for handling them you will have problems especially in guessing the correctness of results.
Another approach could be, if you have already done something of that kind, to solve the differential equation for axisymmetric thin shells by finite differences (again in a worksheet of course): that equation is found in any textbook for plates and shells.


prex
motori@xcalcs.com
http://www.xcalcs.com
Online tools for structural design

Thank you prex, for your answer; maybe, I will just continue to use gussets, to bypass this uncertainty.
The xcalcs.com website looks pretty good, I will check it out in more detail.

See Article D-9 of Section VIII Div 2.  I have used BOSOR5, SHELL01, Monsa, Sabor, and even a 2-D FEM for this class of problem.  All give results that are  approximately the same.  Many of these programs are readily available.  These are far easier to use than some cook book formula.  If you are using ASME BPVC, the stress limits are in concert with their applicable formula  because they separate the effects of discontinuites and bending, whereas a computer solution does not.