Also, does anybody know the "typical" Modulus of Elasticity (in N/mm^2 or PSI) and density (in Kg/m^3 or lb/ft^3) for: Baltic Birch plywood (assume 13 ply for 3/4" thickness) Birch plywood with Poplar core (assume 7 ply for 3/4" thickness)
The modulus of elasticity would be about 2,000,000 psi. Sorry to say, my manuals only cover hardwoods such as oak, hickory, and maple; thus I cannot give you a better answer than this.. However, the construction of the plywood has no influence on the modulus of elasticity. But the construction certainly affects the moment of inertia, and therefore, the maximum stress and the maximum deflection. Jim
Interesting article. From a quick scan of the math, it seems like to first approximation in a multiply laminate (e.g., plywood) that the MOE (modulus of elasticity) is only about 50% of the modulus for a similar thickness of pure hardwood of the same species oriented longitudinally. The logic being that the transverse-oriented plys contribute only minimally to stiffness.
While somewhat intuitive, I would have thought with all the glues and resins that you would get some benefit that would make the stiffness more than just 50% of the equivalent pure hardwood.
Interestingly, one of the web deflection calculators gives fir plywood about 2/3 the MOE of equivalent thickness douglas fir. So maybe there is some benefit to the other laminations and resins...
In any case, it still would be good to get some general specs on the typical MOE for Birch plywood.
Based upon looking at some calculators and skimming the analytical paper cited in another response, it seems like Baltic Birch plywood would have an MOE of 1/2 to 2/3 that of the Baltic hardwood number that you quoted.
Also, if I am understanding you correctly, then I think you are incorrect in saying that the construction of the plywood doesn't effect the MOE -- in fact, per the article mentioned in another response, the transvers-oriented plys contribute only minimally to the stiffness. So much so that when there are only a small number of plys there is a significant difference in MOE between plywoods with the face grains oriented parallel vs. orthogonal.
Even if I assume that the plywood has only 50% of the MOE of pure hardwood, then using the equation for deflection of a shelf with uniformly distributed load and supported ends (like adjustable shelving), I get that the shelf could support about 280lbs and still deflect only 1/32 inch per foot which is reportedly the approximate limit for being noticeable to the average human eye. If I assume that the MOE is more like 2/3 of the hardwood equivalent, then I get a maximum support without visible deflection of about 380 lbs.
Given that I need to only generously support 200 lbs (and probably more like 150), I should be OK, even taking the worst case and allowing for additional sagging with age.
Your understanding is faulty. The modulus of elascticity is gives the relationship between stress and strain.
What the article should have said is that the calculations apply to computing the moment of inertia. As the article indicated, cross plies don't contribute to the moment of intertia hence the stresses are higher with plywood that with wood of the same thickness. Jim
Try this for some Baltic birch properties. Be careful to distinguish between the terms 'modulus of elasticity' and 'section modulus'.
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$file/WISAFormbirchEN.pdffrom a Google search on 'plywood birch "modulus of elasticity"'
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glues have low elastic modulus also and, like the cross plies, contribute very little to the overall stiffness, most of which comes from the contribution of the surface plies. For an extreme example of this behavior try a search on "sandwich panel" wherein a relatively thin surface skin is bonded to a foam or honeycomb core, as in hollow core interior doors.
The practical solution to your shelf application is to bond a solid wood strip (wider than the plywood thickness) to the front of your plywood shelf where it will serve the dual purpose of stiffening the shelf and of hiding the cut edge of the plywood. Perhaps add a mid-span support (cleat, clip, pin) under the back of the shelf. Or, use a solid wood shelf. Note that minimal initial deflection, while important, is not the whole story. Highly stressed wood will take a set over time (engineers call this 'creep') which shows up as a sag in the shelf. Either build a shelf stiff enough to resist this or plan to turn the shelf upside-down occasionally. I have to do the latter every few years on a commercial bookcase with 3-foot shelves of teak veneer over particle board -- heavily loaded with my wife's collection of Southern Living annual cookbooks.
I don't have a clue. What I do know is that the design and construction have much more to do with performance than pushing the pencil or slide rule with all the stuff you are asking about. Rather than do all of that math, add stiffness with construction. I couple of simple support under the shelf, or on the front edge will do more than adding thickness of shelving. Just take a look at bridge design.
Don't confuse initial deflection with sag over time.
I have a whole wall of bookcases with 3/4 oak plywood shelves. They didn't deflect much when I first loaded 'em up; barely visible, I would say. Over time they eventually sag about 1/2 inch (they are
30" wide) at which point it bothers me enough to take the books off and flip them over (time to dust them anyway!). It probably takes 6 months or so to sag that far.
The shelves with paperbacks don't sag at all; but the ones with hardbacks all do eventually.
I'd add a stiffener along the edge if I could afford to give up the extra space, but I don't have enough shelf space as it is.
IIRC the OP said that he was using a double thickness of 3/4 ply for the shelves as well as the sides of this bookcase. Even with the 46" shelf span I think it would take some serious weight to noticeably bow these shelves.
I would use the regular birch shelving. Baltic birch is nice stuff to work with and probably stronger, but I think the poplar cored 5 or 7 ply is more than up to the task. And I wouldn't worry much about the shelf pin problem either. Drill the holes for a good, snug fit. If you're like most once the shelf is assembled and loaded with books you probably won't adjust the shelves again. I've come to believe that adjustable shelves are overrated, and the last few bookcases I made (and one of them was 9 ft tall & 4 feet wide) I used fixed shelves.
Please explain. For a shelf, the modulus of elasticity (MOE) determines the relationship between the geometry of the shelf, the weight applied, and the amount of resulting deflection. For plywood, the total effective MOE of the entire sheet is a weighted average of the MOE's of each individual ply (where the moments of inertia of each ply are the weighting factors). To a first approximation, since the moments of intertia of each ply are essentially the same, the effective MOE is equal to the sum of the MOEs of the transverse and longitudinal plies. Since the tranverse plies have a MOE of only 4-6% of the longitudinal plies, it seemed pretty clear from the article that the Modulus of Elasticity is really only driven by the longitudinal plies and hence is about 1/2 as high as pure hardwood. Again, please clarify how I have misread the several formulas in the article.
Well that really gives the same effect. You can look at it this way. The overall moment of inertia of the shelf is independent of the plies and is governed only by the shape and density of the materials. However, the moment of inertia is only effectively resisted by the longitudinal plies. So, the same force is applied to effectively half the bending resistance. So, macroscopically and to a reasonable approximation the plywood shelf is equivalent to a similarly shaped hardwood shelf made of a material with about half the modulus of elasticity. Again, my physics is a bit old and rusty, but I believe I am directionally correct in my understanding and summary. If not, please explain..
In a woodwoorking shop, it would be much easier and just as effective to simply attach a hardwood stiffener to the rear, along with a decorative and functional solid wood front edge.
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