The square in a circle is one way to START a circular
platform, but certainly not structurally sufficient as the complete frame. Additional framing will be needed around the
edge. Just how much depends on the type and
thickness of the material used for the lid or walking surface. If you use a single layer of 3/4" plywood as a lid, 1" over hang is the most you can have before deflection is evident as people walk on and off the
edge. 1 1/2" can be acceptable but deflection will be noticeable. There are a number of ways to frame a circular
platform but most involve making a number of small triangles on each side to support the large circular over hangs. One very strong but time consuming method is to make a series of 1" wide rings the same od as the circle and stack them up to the desired height. internal framing can be much like you've pictured with additional framing on 24" centers. The
face of the exposed rings does not make a smooth surface and must be dealt with. For platforms over 6"-8" inches, the 1" thick frame can have legs attached just like other framed platforming. Another circular frame method is to make a ply ring whose od is about 1 1/2" less that the
platform lid, attach it centered to the underside making a 3/4" lip. Now rip 1/4" ply or
luan across the grain, into strips 3/4" less than you want the height of the
platform to be. Attach the first layer to the ring and then full surface glue and
laminate the remaining layers to
build up a 3/": thick facing/framing. This is
practical for circles about 3' diameter or more and up to about 48" high, although an additional ring must be made for the bottom once the height is more than about 8".
The main thing about triangles or circles is that internal framing for a
platform with a single layer of 3/4" ply needs to be on 24" centers across the grain.
Quick answer with out pictures, but I hope it helps a
bit.