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Can I use 2x2 or need to do 2x4? I will anchor the back support to at least three studs; left side support will anchor to stud(s) in left wall and there will be a cheap particle board cabinet on the right side that I can probably screw into for limited support on the right side.

I will use 3/8" ply or 1/2" ply for top, bottom, front pieces. Could this support 200lbs? It will hold things like laundry detergent, cleaning supplies, etc.?

enter image description here

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    Learn to love shelf brackets, non-floating, and putting up shelves to hold heavy things becomes easy.
    – Ecnerwal
    Commented Oct 10, 2023 at 16:50
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    Tight to that cabinet, a support bracket from the hardware store would probably blend in very nicely.
    – popham
    Commented Oct 10, 2023 at 17:01
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    You intend to put 200# on it? Or it's okay if it suddenly collapses if somebody ever were to put 200# on it? Is the 200# evenly distributed? Or a point load positioned at the worst possible location? (A cubic foot of water weighs about 60#. Me hanging on it like an idiot weighs about 200#.)
    – popham
    Commented Oct 10, 2023 at 17:02
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    Yeah, you have a stud in a perfect position to support the right end. A heavy-duty bracket will be almost invisible.
    – isherwood
    Commented Oct 10, 2023 at 20:15
  • What material? Plywood? OSB? Do you plan to stick build it from dimensional lumber?
    – popham
    Commented Oct 10, 2023 at 20:48

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Since you're in a corner, you can definitely pull this off. Structurally it reminds me of a knee wall with a wall at its end like the knee wall from How can I anchor a knee wall to my basement slab?. The corner location makes your design possible. Rather than traditionally oriented framing, though, you would implement a diagonal cantilever. Consider

enter image description here

Basically you have a cantilever. One end is supported at the corner. Then there's a midspan support at the band of wood connecting the two walls (the dashed region from the drawing). After you fill in the load conditions a little better, it would be pretty easy to figure out sizes. The tricky bit would be reinforcing that band of wood connecting the two walls so that it doesn't sag too much under the 400# midspan load.

Glue together a couple pieces of 3/4" plywood to form a composite 1-1/2". That'll be plenty strong and stiff as long as you get your wall anchorages right.

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  • All that math is easy for you to say! Was both hoping I'd find someone who knew the numbers and dreading as I don't understand a bit of it! Anyway, your picture is from above looking down like a floor plan, correct? I don't know if I can add a picture to a comment or reply? If I can figure that out, I will post a drawing showing my interpretation of your drawing.
    – Rallyman99
    Commented Oct 10, 2023 at 21:38
  • @Rallyman99, its the same view as yours. I showed wall framing instead of wall surfaces and ignored the adjacent cabinet.
    – popham
    Commented Oct 10, 2023 at 22:01
  • @Rallyman99, there exist potential wall framing layouts that will make your floating shelf very difficult to execute. If you're fixated on that design instead of brackets, then you should add the locations of your wall studs. Magnets, knocking, a tiny drill bit, etc.
    – popham
    Commented Oct 10, 2023 at 22:12

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