Dear Mr. Singh,
It sounds as if you have an interesting design project at hand. Our software does not allow for the design of flanges with stiffener rings. This topic is not covered in the ASME Code. It would appear that this would fall under the category of a special design and you will have to do special calculations to show the adequacy of the design.
Your other question seems to relate to a shallow cone design. If the half apex angle is greater than 60 degrees, the cone should be designed as a flat head.
Hopefully, we had a correct interpretation of your queries.
Best Regards,
Scott Mayeux
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Scott MayeuxCADWorx & Analysis Solutions
Intergraph Process, Power, & Marine