ACR LGT ACFT RAN OFF END OF RWY INTO OVER-RUN AREA DUE TO LOSS OF ACFT CTL.

Narrative

FLT WAS RELEASED WITH L THRUST REVERSER INOPERATIVE AND WIRED DOWN AS PER THE MEL RESTRICTIONS OF NO LESS THAN 8000 FT RWY IF RWY IS RPTED WET WERE NOTED. NOTE -- WE HAD OPERATED THIS SAME ACFT FOR 2 LEGS PRIOR TO THIS ONE WITHOUT INCIDENT BUT DID NOTE THAT BRAKES 'CHATTERED' AND WERE A LITTLE 'GRABBY'. UPON ARR AT DETROIT IN VFR CONDITIONS WE WERE CLRED FOR A VISUAL APCH TO RWY 21L; FOLLOWING A (WDB ACFT). WE WERE AWARE THAT DUE TO RWY CONSTRUCTION THE LAST 4000 FT OF 21L WAS CLOSED LEAVING 6000 FT AVAILABLE; HOWEVER THE RWY WAS DRY AND WE ANTICIPATED NO PROBLEMS. THE 8000 FT RESTRICTION DID NOT APPLY. WE REMAINED APPROX 1/2 DOT ABOVE GS DUE TO MIN SPACING BEHIND THE TOUCHDOWN WAS ABOUT 1000 FT DOWN THE RWY AT NORMAL SPD. IMMEDIATELY UPON BRAKE APPLICATION THERE WAS A LOUD BANG WHICH WE LATER LEARNED WAS DUE TO A BLOWN L INBOARD TIRE. BECAUSE OF REDUCED BRAKE EFFECTIVENESS AND LIMITED REDUCED THRUST CAPABILITY WE WERE UNABLE TO STOP THE AIRPLANE IN THE REMAINING OPEN PORTION OF THE RWY; COMING TO A STOP ABOUT 1000 FT INTO THE OVERRUN AREA. CONCLUSIONS: IN RETROSPECT WE PROBABLY SHOULD HAVE REQUESTED A LONGER RWY EVEN THOUGH WE WERE PERFECTLY LEGAL FOR 21L. THE COMBINATION OF HAVING TO ACCOUNT FOR FOLLOWING A 'HVY'; LIMITED REVERSE; AND A BLOWN TIRE PROBABLY TOGETHER CAUSED US TO GO INTO THE OVERRUN.