Two methods? :- 1. Drill a series of holes in wall, which are a good fit to some steel rod/studding. Drill corresponding holes in back of wood, slurp some PVA on steel pins, knock into walls, leave to go off. Put PVA on sticking out pins, slide shelf on, wipe of excess PVA, leave to cure before use.
2. Secret brackets, If you trawl the net you can find shelf brackets which are basically, strips of thick steel (about 3mm thick) that are bent up into brackets. If you cut out slots in the plasterboard for the wall fixing area and insert the horizontal part into holes in the back of the shelf, again with you favourite glue. That's it apart from making good the slots in the plaster board (which is actually easier to do before the wood is put on, - better access for you float.
I used method 1 for some floating shelves in my porch. SWMBO Inssted on putting flower pots on the shelves that got covered in earth dead leaves etc. So I made some shelves that were strips of 3/4" high wood X 1/2" thick about 3' long, 8 or so strips were assemble and short strips were then put on the two ends. I used 8mm studding into a brick wall the outside bit was long enough to go through all the strip except the very face of the outside one. Turned out a nice looking job and self cleaning.
I used a similar technique to hold up a plate rack right around a room, 6" X 1" X 4m long planks, for this I use 7" nails with their heads cut off.
I used method 2 to put up a plate rack in our latest house, with the "shelf" made from kitchen unit plinth chipboard so the colour matched.
If your oak is very heavy I would use method 2.
Frank
