These sorts of things are usually glued and screwed, but it's actually the glue that holds them together - the screws just hold everything tight while the glue cures. Screwing into hardboard or 1/4" ply is an exercise in futility, so I just used glue, and used my two 4x4's as long clamps. It would have been a bit easier, if I'd done this before I'd rough-cut the 4x4's, but it worked out.
Build this handy stool in one hour and park it in your closet. You can also use it as a step to reach the high shelf. All you need is a 4 x 4-ft. sheet of 3/4-in. plywood, wood glue and a handful of 8d finish nails. Cut the plywood pieces according to the illustration. Spread wood glue on the joints, then nail them together with 8d finish nails. First nail through the sides into the back. Then nail through the top into the sides and back. Finally, mark the location of the two shelves and nail through the sides into the shelves. Don’t have floor space to spare? Build these super simple wall-mounted shoe organizers instead!
A better solution would have been to route a rabbet into the side, so that the added strip always had thickness. The way I did it means that the strip I glued in is very narrow, and hence very weak, at a certain point. In this case, that's not a problem, because it's going to be sitting under the countertop layer. I also noticed that because I had only clamped the strip down, and not into the edge, there was a noticeable glue gap where the strip butted up against the MDF. Again, in this application it isn't visible. But if I was doing something like this on the top of a table, I'd make sure to cut a clean rabbet, and to clamp both down and in.
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The Real Wood Bible I love to pull this book off my shelf from time to time and learn about different characteristics of a certain wood. What’s the wood used for? How easy is it to turn? Toxicity? It’s a very useful book with lots of great photos. Let’s say you have a piece of wood you need to identify. The photos are very crisp and defined so you can match a wood you possess to one found in the book.
Cut 15 top boards 5 ft. long and rip them to 3 in. wide with a table saw so the top will glue up flat without the typical rounded edges of 2x4s. For the leg slot, cut two of the top boards into three pieces: a 39-in. middle piece and two 7-in. end pieces. Glue and screw the top together, one board at a time, with 3-in. deck screws, keeping the ripped edge facing up and level with the adjoining boards. Use a corded drill so there’s plenty of oomph to drive each screw below the surface. Note that the third glue-up from each end is where each leg notch is inserted. You can also create a nifty tool tray in the top by notching the three top pieces with a jigsaw. Clamp every 8 in. or so before driving in the 3-in.deck screws. Predrill the screw holes near the ends to prevent splitting. When you’re screwing on the 7-in. long 2x4s to create the leg slots, use a scrap piece of 2×4 as a spacer.