Managed to lose part of my post when I fixed a typo. Re-summarizing the rest here:

The video clearly shows further rotation of the nut when a washer is in place even if it is maintaining a higher clamp load. Since we do not care about clamp load for this application and do care about the rotation, it would appear to be better to have no washer with regards to reducing the amount of turning done by the nut which would allow the shelf to lower.

Further, the tests are done against metal, with metal nuts, bolts, and washers. Melamine is more textured than metal and should allow for more friction than metal on metal as between nuts and washers. Which should reduce amount of turn for with or without washers.

If a nut/washer combo slipped between them, then the nut lowers and there is nothing stopping the washer from dropping (not attached to the threads) and the shelf following. Single point of failure with no washer and 2 points of failure with equitable chances of failing (nut to washer, washer&nut to shelf) if you assume friction is similar across the two types of materials. (Which I am assuming for discussion purposes since a quick Google search does not give a concrete coefficient of friction for melanine)

That becomes simple probability. If there is 2 places with a 0.1% chance each day of turning a 1/4 turn vs 1 place, then probability states the 2 places will fail twice as much. (This is generalized of course)


TL;DR - my research and education (engineering degree from a top US university with in depth calculus-based physics courses) leads me to the conclusion that there is negligible benefit and an argument may even be made that there is a detriment to including washers in this design when used as described in my prior post.

(Note - since I mention in my guide possibly using a larger drill bit to allow easier shelf assemble, those using that bit may want a washer to ensure the nut has good contact with the shelf. In my case, with the 1/2" bit, I have 0 gap around the rod and no need for washers for that purpose)

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