Join Date: Apr 2010
Location: Near Boston, Massachusetts
Dados are going to be strongest. If you don't have a router or table saw, I see two fairly simple options, other than building a frame.
1) (The more attractive option) Cut them by hand. I haven't done this with ply, but I don't see why it wouldn't work. Start out by using a circular saw to cut across the board where you want the shelves. Mark where the top and bottom of the dado should be, and make a cut at each line; make sure not to make them too wide, and remember how wide the saw blade is! Once those are cut -- and you should use a straightedge to guide the saw for those two -- make a lot of cuts between them. The idea is to remove a lot of material easily and quickly. Once you've done that, you can clean it out with a chisel -- for cuts for half-inch plywood, I'd use a quarter inch chisel. REMEMBER THAT YOUR PLYWOOD ISN'T ACTUALLY 1/2"!!! (Yeah, I ran into that one myself. Oops.) Once you've cleaned out the cuts, you have a dado!
2) (The sturdier option) Double the plywood. At 29" high I assume you'll have 2 shelves, plus the top and bottom. If you double the wood, you'll need one piece for each side, plus two pieces for each gap. In other words, instead of cutting dados, build up the frame and leave gaps to put the shelves into. Glue and clamp the sides, then glue the shelves and fit them in and clamp everything. I've done something similar, and while it was pretty ugly, it was VERY solid. If you're more careful than I was, you might even manage to make it be... well, less unattractive.
If my explanation in option 1 wasn't good enough, let me know -- I should be able to take some pictures of the process with a piece of scrap to show you how it works.