Is my analysis of a closet system (rails hanging from a top track) correct? (e.g. Elfa, IKEA Algot, or floating shelf on L brackets)

Question

So my contractor didn't use the supplied anchors from the closet company (Elfa), and now I don't know if the random anchors they used will hold up, and wanted to know if I should re-mount the tracks with better anchors.

(This is a representative pic from the site in the watermark--Red circles are where I may support rails from the bottom with a block of wood or something, since they almost touch my square baseboard)

More pictures of the system: https://i.sstatic.net/nqIND.jpg

After a bunch of research, and using these links as resources:

https://physics.stackexchange.com/questions/601974/is-this-the-right-way-to-calculate-the-force-on-a-screw

Physics - Mechanics: Ch 15 Torque (20 of 25) More Examples: 2 F=? of Screw on Bracket - iLecture Online https://youtu.be/kkgj5QBF_Tc

I drew this diagram of forces (free body diagram?):

I simplified the actual closet system to one with just one anchor and one rail (assuming weight will be evenly distributed). Point A, the bottom of the rail is the point of rotation.

(Please tell me if this approach is ok for the purposes of this analysis)

And made this spreadsheet to help calculate things using the torque/moment formula:

T = F * d

And that the sum of T should be 0.

F1 = force on shelf (assume at front edge) F2 = force on anchor

Then, F1 x d1 = F2 x d2

F2 = F1 x (d1/d2)

My results are that with a 50lb rated anchor I should be able to support at least 100lbs safely (dividing the formula result by 2 for safety) on that anchor-- does this seem right?

The rails are very long (80") so I suppose that plays into it, but want to make sure I'm not missing anything.

If this is correct, then basically it means that the closet system should be fine on even average 50lb rated drywall anchors, and if I use heavy duty toggle bolts, there should be no worries under typical closet loads?

EDIT:

It occurred to me after posting this that perhaps what I'm missing is the vertical shear force on the anchor? If I support the rails from the bottom (so the rails are basically sitting on the wood baseboard), that would eliminate that concern, right?

EDIT 2:

After having a chance to get on-site and take a closer look, found a few things:

1. Does not appear that any anchors are in the studs, will go back this weekend to check again with an endoscope, cut open the drywall or use finish nails to double check.

2. It seems the top tracks were glued onto the wall, after removing all screws in the track, I cannot budge it, even prying with a screwdriver. The main reason I would remove it is to remount right-side up, but the only difference would be some cut out slots that let you slide in rails from the top. I was able to get rails in from the bottom, and can leave it upside down as long as there's no concern for bending the small portion of the rail that's next to the slots. (Can see in picture)

3. My new plan is to drill another hole or two through the top track to get into metal studs once I locate them, and secure with snap toggles. And also find something to place on the baseboards to support the rails from the bottom (any ideas? coins? folded paper/cardboard?). Any other issues I'm missing with this plan?

More pictures of the top tracks and my setup: https://i.sstatic.net/4T7N7.jpg

Thanks for everyone's replies!

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Answer 1

Using bottom screws will defeat the purpose of hanging adjustable space rack.

Insert small piece of foam between the rack and wall to prevent scratches.

Starting from the corner of the room, measure 16 inch, and observe if there is a screw in the top rail.

Repeat measurement for next screw and so on.

That would indicate they used studs (and no anchors), which would be the strongest hold.