kandula1, for internal pressure rings (internal or external) will have no effect, this can easily be seen from fact there is no length term in the equations. They may allow a thinner shell for external pressure, as this thickness is a function of length. For a vessel where distortion is a possiblilty independent of pressure retention, they could obviously be useful.
You could use shell bending theory to calculate that some of the load from internal pressure was transferred to the rings, allowing a thinner shell. However, this isn't provided for in the normal code equations. It might help to know more about the application.