Dear Bhaskar,

Design of stiffening rings can be found in the ASME Code Section VIII Division 1, paragraph UG-29. From the perspective of sizing the ring (meeting the moment of inertia criteria), I do not believe there is any difference between a ring attached to the outer or inner surface of the cylindrical section if the ring is free of gaps, holes, slots etc.

If the ring does have holes or is otherwise non-continuous you will need to review the ASME Code figure UG-29.1 carefully and insure your design meets those requirements. Depending on the layout of the discontinuities, it could get quite complicated.

Please review this Code paragraph carefully. It may clarify some of your concerns.