I used 3/4 inch, 11-ply birch plywood for the wide shelves in our kitchen cabinets. They all got "faced" with 3/4×3/4 maple. That facing was more for looks as I don't have edge banding, but the hard maple will add even more sag resistance. The 3/4 plywood by itself has real good numbers though.
For 3' shelves, 3/4" lumber or plywood will be strong enough, especially a hardwood like oak, maple, ash, etc. If your bookcase is going to have a back, you can cut a dado into the back or put screws through it, into the shelves to give extra support to the shelves,
I've always liked the method of attaching a hardwood band or apron across the front of the bookshelf. This makes it almost impossible for the shelf to sag. Plus, this is just about the only way to add support to an adjustable shelf.
Personally I would put a center support on a 3ft span. Maybe stiffening the back side of the shelf as described will do but why risk it, especially if the shelf will store a bunch of hardback coffee table type books that are really heavy.
You could edge your shelves with 3/4×1 1/2 or 1 1/4 stock, front and back, and they'd be great, but you're adding some look of mass there that would have to blend right with the carcase.
3/4 inch shelf faced with 5/8×1-1/4 walnut. This is for a 33 inch shelf that will hold a microwave on one shelf and cookbooks on the top shelf…
I haven't put a finish on this piece yet. It does add some mass, but this hutch will sit on top of an inch and a quarter walnut counter top so it should look fine.
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