Without a vertical beam of some sort down the middle of all the shelves, I'd assume nothing is going to keep the shelves from bending.

The analysis the guy did (I believe) is based on a load, and believe he was using 500lbs as a "safe" assumption (not including wood weight).

The analysis is helpful, but I didn't see which rod spacing was ideal. All the analysis showed was deflection at different points for rod distancing.

Without looking, from what I remember, I have approximately 240lbs of books (some are thick text books like physics, calculus, etc... and others are much smaller). The weight of the Poplar wood I haven't done yet, but it will be 1-1/16" thick wood, 48" wide shelves, slightly under 12" spacing between shelves, 11-1/4" depth, six shelves (including the one across the top that will be against the ceiling), and the two sides.

I'm over estimating at the moment, and saying the weight of wood for each shelf is 50lbs (totaling 300lbs), and each side is 100lbs, so wood weight total is 500lbs. Add that to my current books and that's 740lbs.

He did a calculation for me and I think 5/16" stainless steel threaded rod (one on each side) would hold triple that after even after using 50% reliability number from the maximum 70,000psi load that the rod specification has.

My personal preference is to go with 3/8" (or even maybe 7/16") rod, and, from what I can estimate on the load stress analysis, place the rods 12" from the sides for the best deflection reduction. The sides have a dado, so the shelves won't tilt forward to back, and shelf bending is just the nature of anything horizontal.