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https://www.popularwoodworking.com/projects/aw-extra-3614-stronger-shelves/
The effect of the other two dimensions, width and length, is straightforward; add 10 percent to the width of a shelf, and it’s 10-percent more rigid; add 10 percent to the length, and it’s 10-percent less rigid.Author: American Woodworker Editors
https://www.hunker.com/13403978/how-to-calculate-angles-for-shelf-supports
Measure the distance down the wall you want the support to go, as well as the distance under the shelf you want the support to extend to. For example, say the wall measurement, side "a" is 12 inches and the shelf measurement side "b" is 8. The angle between the wall and shelf measurement, angle "C," we know will be 90 degrees.
https://www.homedepot.com/b/Storage-Organization-Shelving-Shelving-Brackets-Accessories/Shelf-Pins/N-5yc1vZckssZ1z18dbu
Prime-Line 1/4 in. Clear Self-Locking Shelf Support Peg for 3/4 in. Shelf (4-Pack)
http://www.woodworkingtips.com/etips/etip01.html
Another factor used to determine maximum span is the total expected load -- the longer the shelf, the more books (and weight) it has to hold. A running foot of average sized books weighs about 20 pounds. So a three-foot shelf filled with average sized books would have to support 60 pounds.
https://www.thewoodwhisperer.com/articles/supporting-wide-shelves/
Will that be enough support for a 76″ long shelf?? Will I have problems with sagging??” The wider a shelf is, the more likely it is to sag. This can make an incredibly attractive bookcase look absolutely dreadful. Screwing the shelves into the back is a great start and will provide a significant amount of support along the length of the shelf.
https://design.closetmaid.com/en-us/Documents/Wire%20Shelving%20Specifications%20rev_6_12_English_HQ.pdf
measurements or the desired shelf length. All exposed cut ends are to be capped with #203 or #204 depending on the shelf. SuperSlide Component Installation: Place hang bar supports #925 or #5672 every 24 in. to 36 in. (place support bracket #1164 adjacent to support) use SuperSlide end bracket #979 or #980 at side wall where pole is used.
http://www.woodweb.com/knowledge_base/Free_Span_Limits_of_Cabinet_Shelving.html
The basic formula for the deflection of a shelf is (0.1563) (load per inch of span) (length of the span to the 4th power). (Modulus of elasticity) (width) (thickness to the 3rd power). The load per inch of span is determined by the owner of the shelf; often the shelf is designed to carry a full load of books, which would typically be the heaviest load expected.
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