There is a new word for you, "to scant." I presume you mean "to determine the scantlings."
Determining the scantlings of a ring frame would be the same as for any other frame, the same engineering principles apply in which the frame is assumed to be a beam carrying a load. The basic strength and stiffness of a frame is determined by its cross section (height and width) and its length. For a laminated frame, it makes no difference if the frame is fitted to the deck and/or keel by a traditional method of bolting and clamping, or by laminating into a ring frame. Assuming both methods have similar and sufficient degrees of rigidity, the scantlings will be the same.
Another factor determining the size of the frame is how many frames there are. The more the frames, the smaller the frame can be because it is taking a smaller share of the overall load--all the other frames are taking their share.
This leads to an interesing observation. In just about any method of construction--metal, wood, or composite--most of the weight of the structure comes from the plating, roughly 2/3rds of the total structural weight. The fewer the number of frames, the heavier the structure because more plate area is unsupported and so must be made thicker, therefore heavier. To reduce the weight of the structure, add more frames. This reduces thickness and structural weight very rapidly.
There are practical limits to this--too many frames and the plating thickness becomes way too thin to work reliably and fairly, and also the cost of making the frames goes way up. Fitting too many frames can also be difficult to physically work around. So there are practical limits. One of the rolls of the designer is to determine what is the best method of framing for the best weight and strength of structure, consistent with the builder's capabilities and the owner's desires for what the boat should look like, how it is to be maintained, and how much it will cost.