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I can't tell if the wheel is seated all the way against the backing plate. If it's not, and the lugnuts are effectively taking all the weight and strain... that would definitely explain it.
Wrong lugs, that wheel is designed for the 1 1/8" nuts.
Is it actually the same lug over and over? I am seeing two nice clean lugs in a row, with that third one broken. If that is the case, then you might have several damaged lugs that are fatiguing and breaking one at a time.
Definitely some funny business going on with the lug nuts there. I agree with Ford Six, I don't think it's the same one shearing off, it looks to me like that is the third different stud to break. The way things are it won't be the last either.
I wouldn't be driving that truck until it had a set of nuts that fit those wheels properly or a set of wheels appropriate for the truck.
I'm still wondering if the center hole is the right size; Chevy and Dodge wheels have the same hole pattern but smaller center holes by just a little.
If it was originally an aftermarket Chevy or Dodge wheel that was designed to be hub-centric(vs lug-centric), which would definitely be the case if you are using flat lugnuts... it might well not be sitting flat on the back.
There's probably a chamfer on the back side of the hub, so it mostly sits in place, but might well not be. And this would be why you are losing studs, due to torque on one side levering against the others. So if one side is tighter, the opposite side might well stretch and break.
But the too-small lugnuts aren't making the studs break. If the threads stripped out of the lugnut, sure, but the lugnut obviously has enough strength to break the stud off.
A bigger lugnut will have more taper for the wheel to rest on... but it doesn't look like that's the issue here....
I would say there is a good possibility that only a few studs are truly taking the load they way things are instead of being evenly distributed. As has already been said, it would be prudent to make sure the wheels are fully seating against the hub and not sitting out the studs due to interference in the centre bore.
Looking at the picture again, it looks like there are marks on the wheel from larger flanged nuts like you would find on hub centric wheel set up? Could also be marks from a socket on an impact? Curious as to what exact truck these wheels came off of.
those are chevy wheels, which are usually lug centric. ford wheels are hub centric. the chevy wheels are depending on the ford lug nuts to stay on the truck. since the ford nuts are too small they are not seating properly letting the wheel wobble a bit and snapping the studs. either get the proper hub centric wheels for the truck, or get the proper lug nuts for the wheels. but even using the larger lug nuts may not solve the problem. .