Build the Wood Sandwich Core
Place angle brackets on the wall where you want the free-standing shelves to go.
To make the shelf, you take a skin and make the bottom of the shelf, a piece of 5/8" plywood is added, then add a spacer made out of luan that is the same thickness as the angle bracket and a top skin goes on top.
Note: Angle iron brackets are made of steel that is 3/16" thick.
Glue 5/8" plywood to the bottom skin, and then glue the skin trim to the front and sides of the shelf to cover the wood sandwich core. Use pin nails to help hold the trim in place until the glue dries (Image 1).
Use a bead of paneling or construction adhesive glue on top of the plywood and spread it with a trowel (Image 2). This is the base for the next layer, which is the luan.