Probably several of your readers use the Sagulator http://www.woodbin.com/calcs/sagulator.htm to determine whether a particular shelf is going to bear its projected load within some desired maximum sag parameter. I lack the math skills to solve the differential equations to determine the amount of sag when the shelf has an edge piece attached.
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For instance, consider a shelf made from ¾-inch plywood with an edge facing of white oak. The oak edge is ¾ (deep) by 1 ½ inches. The plywood portion of the shelf is 36 inches long, 12 inches deep, with a projected load of 90 pounds, evenly distributed.
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The Sagulator tells me that if I used only the plywood, the sag would be about 0.11 inches. It also tells me that if I used only the oak trim for a shelf—that is, the shelf is 36 wide, ¾ deep, and 1 ½ thick, the sag would be about 0.15 inches.
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Well, I can recast to an easier problem that I know how to solve: Plyny can lift 90 pounds and only sags 0.11 inch. Oakey can lift 90 pounds but sags .15 inch. If Plyny and Oakey work together to lift the 90 pounds, how much will they sag together?
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The answer to this problem is 0.063, which seems reasonable, but my question is whether it’s correct. Can we treat the problem as analogous to a work problem (Timmy mows the lawn in an hour, his brother Bill takes 45 minutes …)?
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Replies
I went to college to be a structural engineer so I know there is a technically correct answer to this, but I couldn't begin to figure it out, maybe that's why I never worked as an engineer.
Here's one approach: You know that the plywood and the wood facing are going to have the same sag when they under a load because they are solidly attached to each other. So work the formulas or the calculator backwards, figure out how much of a load it will take to make each element, taken independently, sag the same amount. For instance if the plywood will sag .030" under a load of 50 pounds and the wood facing will need a load of 70 pounds to sag .030" then the two elements combined will support a load of 120 pounds while sagging .030".
John W.
Thank you, John. Using the method you proposed, I determined the weight each element could support to get the predicted outcome by my 'work' method (0.06), and the total weight came up the same (90 pounds in the original example), so I believe that we have an easy way to figure the the predicted sag by combining the individual elements as in a work problem.
On a tangential note, I use your Care and Repair book frequently to help me setup and tune my machines, and I very much appreciate your contributions to this forum.
I'm going to put together a short write-up on the calculations--would that be a Tip submission to FWW, or just a general posting in the newsgroup? I'd appreciate your input.
Again thanks for giving me an idea how to check the calculations, and all the other help you have given me through your writing!
Bob
Thank you for the kind words.
You could try to submit the sag calculations to the Tips column but I suspect that it will be a bit too technical for the column, but you never know.
It certainly is worth describing here on the Knot's site. It will get a lot more exposure if you put it in a new posting on the non-subscription side.
John W.
Hi Bob,Send your write up about sag calculation to us here on the Web, or just post it to this thread. We will gladly consider posting it as a free Web article on FineWoodworking.com.Matt Berger
Fine Woodworking
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