Hope the OP will continue to work on this problem, but since it may drag on for a couple of weeks I'll "spill the beans" on my first order approximation. Composite beams with plywood webs are devilishly tricky, especially in shear... and this one has some problems. The biggest issue is a plywood web's
internal plys... they are oriented the wrong way, just inherent to how plywood is made. The fibers can fail by rolling inside web, and the allowable "rolling shear" stress is lower than the "horizontal shear" stress. That's why manufactured I-joists use OSB for the web instead of plywood.
Here is the "Executive Summary" of my look at this problem:
Bending stress is really low, would likely be acceptable up to the 80+ PSF live load range.
Deflection is low, also. Also good up to 80+ PSF.
Shear is another matter... maybe ok in the 20 to 25 PSF range. This needs to be checked in much more detail than I have done. Even at that loading, the ends of each beam will need additional webs for the point reaction loads at the supports. It is not a big technical issue to add them, but could be an economic consideration.
An example of how elusive solutions to beams with plywood webs are:
I looked in my copy of the standard text on everything wood, Breyer's "Design of Wood Structures" (Third Edition). On the subject of plywood box and I-beams, he "punted". Uses about a page to say "just do what the American Plywood Association (APA) tell you".
2457F - I do encourage you to follow through on your calcs, and I'm sure all of us will be happy to review them. Also, I'll post mine at any time you request. Problems like this, where things don't work out easily, are the absolute best way to get meaningful experience.
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