So there are not really any supports which hold the bed together.
The bedsides are attached to the front bed panel and the rear cross sill. Originally the rear cross sills were welded to the bedsides, however, most people do not weld them during reassembly.
The bed wood is supported by cross sills which are bolted to the frame. The bed wood then supports the bedsides. In your case, a fleetside, the wheel wells are bolted to the top of the wood bed.
If you get a LMC catalog(you can download one online from their website) you can see how the bed is put together.
Here is a great thread on the process...
http://67-72chevytrucks.com/vboard/s...d.php?t=663058