An extension to what Ron so "adequately" sketched....in some areas where you have expansive clays, many smaller structures such as residential homes, or small office buildings, are constructed using this kind of system.
Usually, the perimeter beams are supplemented with an interior grid of beams to form what is called a "stiffened slab-on-grade". The beams are spaced between 12 ft. and 16 ft. on center and are usually 12 to 18 inches wide and can get as deep as 36 inches (even in non-frost areas). The concept is to create a rigid mat on which the building rests.
A design methodology has been developed by the Concrete Reinforcing Institute in conjunction with The Wire Reinforcing Institute. It was prepared by Walter L. Snowden, P.E. in Austin, Texas back in the 70's (I think).
I have the document which is titled "Design of Slab-on-Ground Foundations, A Design, Construction, and Inspection Aid for Consulting Engineers", dated August, 1981. I would hope that there are copies available through a search on the internet.