I'm building a large cabinet now with ply sides and solid wood front and rear fascia (stiles). The fascia has a 3/8" groove where you have your 1/8" groove 7/16" in from the edge. The plywood side has a 3/8" rabbit cut in on the outer edge. This is the joinery for a fastener-less glue joint. The 7/16" dimension leaves the fascia just proud of the ply side after glue up. I then run a flush trim router bit the length of the fascia to clean up the joint.
To strengthen the shelves, I glue a solid wood front and rear trim piece on each shelf. For a 3/4" ply shelf, I would add 1 1/4" wide trim. I rout a rabbit on each to accept the ply shelf and to provide an increased glue surface joint. You can rout a decorative edge on the top and bottom of the front trim piece without sacrificing strength. I have two cabinets made this way that are over twenty years old and no shelf sagging on the 39" long shelves. One is loaded with SWMBO's books and the other has electronic equipment in it. The new cabinet will have 59" long shelves, so I am making the shelf trim 1 1/2" wide for added stiffness.
The spline & groove join will work also. If it were mine, I'd make the grooves sized to accept 1/4" plywood, following the sizing practice for tenons, and so I could use some of the 1/4" ply scrap I have. Also for maximum join strength, the predominate grain of the spline should be 90 degrees to the grain of the fascia.
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"Sawdust is Man Glitter"
Last edited by Jim Frye; 03-11-2017 at 07:45 PM.
Reason: added blather