B737-700 FLT CREW WAS NOTIFIED BY ATC THAT TIRE DEBRIS WAS ON RWY AFTER THEIR DEPARTURE. FLT CREW CONTINUED TO DEST AND DECLARED EMER FOR THEIR LNDG. AFTER LNDG; INSPECTION REVEALED THAT TIRE HAD FAILED AND HAD CAUSED SOME ADDITIONAL ACFT DAMAGE DURING THE EVENT.

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I HAVE NO EXPLANATION WHY THE TIRE CAME APART. WE DID NOT HIT ANYTHING ON THE TKOF. THE MECH IN ZZZ1 SAID HE THOUGHT THE TIRE WAS PRETTY NEW. AFTER TKOF ZZZ DEP TOLD US AN ACFT THAT DEPARTED AFTER US RPTED PIECES OF RUBBER ON THE RWY. WE TOLD THEM WE DIDN'T SEE ANYTHING AND DIDN'T NOTICE ANYTHING ABNORMAL ON OUR TKOF. WE ASKED THEM TO CONTACT OUR MAINT DEPT AND SEE IF THEY COULD IDENT THE TIRE REMAINS. WE CALLED DISPATCH AND NOTIFIED THEM OF THE RPT. THEY SAID THEY WOULD CHK WITH MAINT AND GET BACK TO US. ABOUT AN HR LATER WE GOT A CALL; THEY TOLD US MAINT WAS ABOUT 75% SURE THE RUBBER FOUND CAME FROM OUR ACFT AND THEY SUSPECTED IT WAS THE R INBOARD MAIN TIRE. WHILE WE WERE WAITING FOR THEM TO CALL BACK; WE LOOKED THROUGH ALL THE ACFT MANUALS ONBOARD THE PLANE AND COULD NOT FIND ANY INFO ON ADVISED PROCS FOR LNDG WITH A BLOWN TIRE. WE ASKED FOR A RECOMMENDATION AND THE -700 FLEET DIRECTOR TOLD US THE BOEING RECOMMENDED PROC. WHEN WE CHKED IN WITH CTR WE ADVISED THEM THAT WE MIGHT HAVE A BLOWN TIRE AND WE DECLARED AN EMER SO WE COULD HAVE THE EMER EQUIP READY ON THE TXWY. WE FLEW A NORMAL APCH AND LANDED WITHOUT A PROB. WE TAXIED OFF THE RWY AND STOPPED SO THE GND PERSONNEL COULD INSPECT THE AIRPLANE TO SEE IF THEY THOUGHT IT WAS OK TO TAXI. THEY INFORMED US THE R INBOARD MAIN HAD THE ENTIRE OUTER TREADS MISSING; AND IT LOOKED OK TO TAXI TO THE GATE. WE TAXIED TO THE GATE WITH NO PROB. THE GND CREW COULD NOT GET THE JETWAY TO MOVE. AFTER ABOUT 15 MINS THEY FINALLY MANAGED TO GET THE JETWAY HOOKED UP AND WE DEPLANED THE ACFT. I WENT DOWN TO LOOK AT THE TIRE. MAINT ALREADY HAD IT OFF THE AIRPLANE AND IT INDEED HAD ALL THE OUTER TREADS MISSING. A MECH THEN SHOWED ME THERE WAS ALSO DAMAGE TO THE ACFT BY THE LNDG GEAR DOOR AREA AND PIECES OF THE FLAP AFT OF THE GEAR WERE MISSING. AS DESCRIBED; ABOVE; WE FIRST GOT A CALL FROM ATC ADVISING OF A POSSIBLE PROB. THEN GOT MORE INFO FROM OUR MAINT DEPT. LATER IN THE FLT WHEN WE WERE BRIEFING THE CABIN CREW ABOUT WHAT WE PLANNED FOR THE LNDG; A DEADHEADING FLT ATTENDANT SAID SHE HEARD A NOISE DURING TKOF. SHE WAS SITTING ON THE L SIDE IN THE EMER EXIT ROW OVER THE WING. AFTER GETTING ALL THIS INFO WE FELT PRETTY SURE WE HAD A TIRE PROB; BUT HAD NO WAY TO CONFIRM WHICH TIRE IT WAS. TRIED TO FIND A PROC IN THE ACFT MANUALS ONBOARD. THERE WAS NO INFO ABOUT LNDG WITH A BLOWN TIRE. GOT THE RECOMMENDED PROC FROM FLEET DIRECTOR. BRIEFED THE CABIN CREW; MADE A PAX PA BEFORE LNDG; ADVISED ATC AND DECLARED AN EMER; LANDED; HAD THE ACFT INSPECTED ON THE TXWY; THEN TAXIED TO THE GATE. THERE IS NO WAY TO AVOID THIS EVENT. HOWEVER; WE FEEL THERE SHOULD BE INFO ADDED TO THE ACFT MANUALS ON THE BOEING ADVISED PROC FOR LNDG WITH A BLOWN TIRE. SUPPLEMENTAL INFO FROM ACN 740429: ALSO ADVISE CREW MEMBERS THAT ARE TRAVELING IN THE CABIN THAT THEY SHOULD INFORM THE FLT CREW IMMEDIATELY WHEN THEY THINK THERE IS SOMETHING THAT IS ABNORMAL. DON'T ASSUME THE FLT CREW KNOWS.