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I have a recessed wall and want to build in some shelves. Went to the lumber yard today and got some 1"-thick hard maple boards and asked them to mill them down to 5/8", which they are going to do tomorrow, and then mentioned it to my dad, who said I should go with at least 3/4", and I can still call and leave them a message and change the order or tell them to hold it. But I would really like them to be thinner.

The shelves are going to be 8" deep and 4' wide, and ideally should be supported only at the ends and not bend visibly under the weight of the books. If anyone can venture an educated guess how much they would bend at 5/8", 11/16" and 3/4", I would appreciate it.

I may have learned this in the strength of materials class, but I barely remember anything from it and it was not my favorite subject. Formally, I think, this would be called maximum deflection of beam with two supports. I can't find the formula online and seem to remember vaguely that the deflection is proportional to the beam thickness to the third power. Does that sound right?

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    Great question, but I doubt that you will get your answer here because, almost, anyone here doesn't want to actually calculate something. Unfortunately I am not structural engineer so I can't help you either, but I can give you a hint: Paper is extremely heavy libraries have extremely heavy duty concrete slabs (I think even more demanding than garages) so I would go from 3/4 or maybe even the whole inch – python starter Jun 3 '15 at 8:21
  • Thanks! Just called them and left a message asking to change to 3/4. Whole inch is not an option, that's the thickness of the rough board before milling. Still curious about the formula, but not enough to try to derive it :) – biggvsdiccvs Jun 3 '15 at 8:55
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It will depend on your book load, and whether your "hard maple" is really sugar maple or not.

There is, of course, an easy way to deal with the calculations these days. Do be sure to read all the "notes" below the calculator. Shelf thickness (or "depth" in beam speak) cubed is indeed the correct factor, and why even small changes in thickness make large differences in stiffness.

http://www.woodbin.com/calcs/sagulator.htm

For lesser woods, 48" is a heck of a long unsupported span for a thin shelf. Actual sugar maple at 8 x 3/4" will do 50 lbs per foot within the "acceptable" range and typical book load is given as 20-40 lbs. Mind, that is based on the strength of "clear, straight grained samples" and "initial sag only." At 35 lbs/ft that shelf reaches the suggested target of 0.02 in/ft to allow for additional sag from sustained loading.

Silver maple is "borderline" at 40 lbs/ft. red, black, and bigleaf are "acceptable" at the same figure. All are somewhat less stiff than sugar maple.

IMPE you should be able to get 13/16" planed from 4/4 rough. If you want the appearance of a thinner shelf you can cut a long taper on the bottom front edge, which will reduce strength somewhat, but not as much as thinning the whole shelf width.

At a higher level of difficulty in the "absurdly thin non-sagging shelf" direction you can mount steel rods, say 16" in from the ends and drill holes in the shelf (the difficulty is in getting the wall-mounted rods and the holes in the shelf to agree) for "invisible supports."

  • I have in front of me shelving with 5/4" depth for about 3' width. I am not 100% sure about the essence, it's not maple but something close - with good surface hardness, anyway. And it's sagging in the middle. Very slightly, but a trained eye can see it. Now, it must be said that it has been installed about 19 years back, and has seen much weight. – ALAN WARD Jun 3 '15 at 16:45
  • Thanks for your reply. A friend who has a lots of tools and is more mechanically inclined offered to help to mount them "invisibly" by making narrow grooves along the sides with a router, which of course will put even more stress on the thinner shelf. At least that's the tentative plan. – biggvsdiccvs Jun 4 '15 at 6:37
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Take a look at this calculator. You are correct in looking for beam deflection but the details matter for accuracy.

http://www.woodbin.com/calcs/sagulator.htm

Using Red Maple as the wood type with your measurements above the calculator estimates a .1" deflection with a 40 pound per foot uniform load.

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