By "piece that holds them on", I assume you mean the studs. You'll need to replace the wheel with a good used one from a salvage yard. If you don't, the lug nuts will continue to come loose. The shaped friction surfaces have been distorted and ground away. Those are what holds the nuts tight. Replace all of the nuts too for the same reason.
Once the wheel is removed, you'll need to remove the brake caliper and rotor, then you can pound the studs out of the hub. Auto parts stores will have replacements. Don't let the brake caliper hang by the rubber hose. Hang it with a piece of wire or a rubber strap while you do the repairs.
You'll need to temporarily install a stack of large washers over a stud, then use one of the old nuts to pull the studs in. Install that nut backward so the flat side is against the washers. When you install the wheel, use a click-type torque wrench to set the tightness of the nuts. The guys at the auto parts stores may be able to tell you the correct setting, otherwise any tire and alignment shop and any repair shop will have that information. The typical value is around 95 foot-pounds for steel wheel, and less for cast wheels. Failure to use a torque wrench is what caused this failure. The nuts were left too loose last time or they were seriously over-tightened. Any professional who doesn't properly torque wheel nuts stands a real good chance of getting fired. It's that important.
Recheck the tightness after driving the car around the block, then again after a few miles. This is because the studs may not have been fully seated by hand, and the forces on the wheel while driving may pull them in further resulting in loose nuts again. Check the tightness a couple more times about a day or two later.
Thursday, October 24th, 2013 AT 5:23 AM