It was years ago, but I remember I rabbeted the corner joints on 3/4 BBP, then added a triangular corner block on the insides. Not good enough at all. The inner shelves are dadoed in. This photo was taken about a year after the build, when everything was square. The cabinet is so heavy on the wheels I really have to jerk and pull it around to move it, so it’s been heavily abused, pulling at it from the top. The drawer is now showing a decided slant on its rails. I really need to fix this thing, but am too busy, as usual. The fix will mean removing everything, maybe adding metal angle brackets to the outsides of the joints, then long 2×2s to the inside corners for more stability. Bigger wheels would have helped, too. The small plastic ones were listed for the load capacity, but it would roll easier with wheels like you’re designing.
Might As Well Dance : http://barbsid.blogspot.com/