ETA - Thanks for all the advice! I found some brackets which claim to be rated for 1000lbs per pair and fastened them into the studs with very long cabinet screws. I installed five in total - starting from the center stud and then two studs in each direction. I replaced the very bent rod with a pair of 1.25 poplar dowels which meet at the center bracket. I put everything back and it all seems to be holding really well.

I have a walk-in closet with a 10ft long shelf which, until recently, was held up by two side cleats and three metal shelf brackets screwed into studs (the sort of bracket that has a u-shaped rod holder). The shelf itself seemed sturdy enough, but the brackets holding up the closet rod collapsed under the weight of the clothes.

https://imgur.com/a/NyEclYc

I've never built a closet, but my short assessment is that:

1. The brackets weren't screwed into the shelf, which seems like a potential source of stability for the rod. 2. The shelf wasn't tied into a cleat along the back wall, which seems like a potential source of stability for the shelf. 3. The rod itself is one of those very thin, expandable metal rods, and it seems like almost any other material (thicker metal or wood) would have helped.

My tentative plan is to put in a long back cleat (1x4), put in new brackets and screw them into the shelf, and replace the closet rod with something more rigid (pipe or a dowel). However, I'm not totally convinced that this will be sufficient for supporting the middle of the 10ft span.

It seems like one way to go is to install some kind of post in/near the middle and run the new closet rod through a hole cut in it, and then tie that into the shelf and otherwise let gravity hold it in place.

I've also seen some people tie supports into the cleat sort of in the style of doing a floating shelf, but I'm not clear on how much support that really could add.

Am I missing some better idea here?