Join Date: Apr 2009
Location: New Rochelle, NY
Bikes: too many bikes from 1967 10s (5x2)Frejus to a Sumitomo Ti/Chorus aluminum 10s (10x2), plus one non-susp mtn bike I use as my commuter
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Step one, walk away from this for a while. You're not the first person make a bad situation worse by letting your desire to fix something NOW, rather than stepping back and thinking first. There's even a name for the process - tunnel vision.
When you're fresh, (tomorrow) you might try removing the broken off stud with long nose pliers, but don't go crazy trying. In all likelihood the solution is to drill through the bolt straight across to make a hole big enough for a QR unit (with nut). Most use 5mm skewers so there's plenty of material there. Measure the width across the outside of the ears and buy the QR unit first, so you know for sure what size hole you want.
When you start drilling, be sure to keep drill square. To keep the drill from deflecting at the irregular break, you're probably best off drilling from the outside toward the middle. Or you can file the broken bolt flush through the slot, then drilling right to left using the unthreaded ear as a guide. When you're done leave the remainder of the bolt in there, but coat it heavily in grease so it doesn't rust.
BTW- sometimes discretion is the better part of valor, and there'd be no shame in realizing that you're in deeper than you can manage, and letting a decent pro fix this for you.
An ounce of diagnosis is worth a pound of cure.
“Never argue with an idiot. He will only bring you down to his level and beat you with experience.”, George Carlin
“One accurate measurement is worth a thousand expert opinions”
- Adm Grace Murray Hopper - USN
WARNING, I'm from New York. Thin skinned people should maintain safe distance