Old Methane Gas Cloud
Join Date: Jun 2009
Location: Huntington Beach, California
Alchymist has an excellent Idea.
If you put about an inch of glue in the center of the dado there shouldn't be a problem. If the plywood going into the dadoes that are PARALLEL to the grain of the sides, glue the whole length of the dado.
In short, as a rule of thumb, when starting with KD wood, you need to figure about 1/8" of wood movement per foot, cross grain. That is from equilibrium of moisture content in your shop to equilibrium in the final usage location. The trick is to put the movement where it can't hurt your work.
From your description, I'm expecting that your 45° miters are on the end grain. That says that the grain is running around the box and not up and down. If I was building the box, the dadoes would be 1/8" wide and about 1/4" up from the bottom of the box. That being said, your wood movement is going to be away from the bottom. The plywood can be glued into the bottom all the way around without any problem at all.
BTW - As end grain to end grain joints are weak, I would add some splines in a contrasting wood every few inches across the corners of the box. Make a jig that will hold the box at a 45° against the fence. (You're trying to cut through the corner equally up each side.) Make your dado cut not quite through the corner. Then rip some contrasting wood to the thickness of the dado cut. Glue the contrasting wood into the dado. The grain should follow the dado cut. Be sure to tighten the locking knob on the table saw blade height control wheel.
Use the right tool for the job.
Rich (Tilting right)
Huntington Beach, California
Remember that when we have the "BIG ONE" everything east of the Rockies falls into the ocean.