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I have a piece of plywood 2 ft. long and 1ft. wide. I am making a wall rack using brackets. But the problem is I don't know what should be the ratio of the breadth of plywood by the bracket.

Currently, it is 2:1, that is my plywood is 1 ft. and the brackets are 6 inches. Is this safe to use, or there's some ratio for this?

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    What length of bracket to use for a given application depends on the shelf material and the weight it is expected to hold so unfortunately this isn't possible to Answer given the information currently provided in the Question. Also it isn't clear, are you mounting the plywood as a shelf? (That is brackets underneath, screwed to the shelf and then to the wall.)
    – Graphus
    Feb 28 '18 at 14:58
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    Honestly, in this situation I think I would be more worried about the strength of the bracket, not the shelf itself. A bracket without a diagonal support puts a lot of leverage on the corner, which can cause the metal to bend. I would look for something with a diagonal support (images-na.ssl-images-amazon.com/images/I/…) or at least a thicker cross-section (images.homedepot-static.com/productImages/…) Feb 28 '18 at 19:57
  • Thanks @SaSSafraS1232 for comment. I'm not using those brackets which are shown in the image. I was going to buy new (with diagonals) that's why I asked the question what's the minimum size is acceptable for the bracket with respect to plywood. Feb 28 '18 at 20:09
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Assuming that you are acquiring brackets that are strong enough and stiff enough to carry the loads, the question of how long brackets need to be is a good one (though not really a woodworking question).

One consideration is whether you intend to simply place the shelf on the bracket and let gravity keep it in place. If that is the case, your bracket should extend nearly the full depth if the shelf to remove any chance of a heavy load (e.g. you hanging from it by your finger-tips) causing the shelf to tip forward and spilling its contents.

A more practical approach would be to get a bracket having a top arm about 3/4 of the shelf depth, and screw the shelf to the bracket. If the bracket has more than one hole and you want to use fewer than the full complement of screws, it is imperative that you use the hole nearest to the wall just to avoid the calamity of too much load near the front edge.

As far as attaching the bracket to the wall, it is best not to skip any of the holes, but the most important one is the top one, again to withstand excessive moment causing the shelf and bracket to fail.

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The restraints on the bracket are the load rating of the bracket. That rating is assuming that the load is centered over the leg of the bracket. Wider shelves move the load center further out from the wall. The concerns of the amount of the shelf that extends beyond the bracket is a material property of the shelf material. A 1/4" steel shelf could handle a much longer overhang than a 1/4" styrofoam (ridiculous I know) shelf would support.

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