A B737-300 EXPERIENCED TIRE FAILURE ON TKOF FROM A HIGH ELEVATION FIELD; DAMAGING THE ACFT. ACFT LANDED UNEVENTFULLY AT DEST.

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ENRTE FROM YYY WE WERE INFORMED BY CTR THAT SOME GEAR DOOR PARTS AND POSSIBLE RUBBER (TIRE OR GEAR DOOR) PIECES WERE DISCOVERED ON THE RWY AT YYY. A DETERMINATION FROM YYY ARPT PERSONNEL WAS THAT THEY PROBABLY ORIGINATED FROM OUR ACFT. WE ASKED THEM TO CONFIRM THE DEP RWY AS A WAY TO VERIFY THE RPT. SINCE ANY PROC WOULD NECESSITATE BURNING DOWN ACFT WT; WE CONTINUED. WE CONFIRMED THAT FUEL BAL WAS EQUAL (NO FUEL LEAK) AND HYDS REMAINED CONSTANT (NO HYD LEAK). WE HAD NOT NOTICED ANY UNUSUAL HANDLING CHARACTERISTICS ON TKOF FROM YYY. THE NOSEWHEELS WERE A BIT LOUD AND WOBBLED A BIT ON TKOF; SO WE ASSUMED THAT ANY PROB WAS WITH THEM. STILL; THERE WAS NO UNUSUAL SOUND AS THEY SLOWED DOWN ON THE SNUBBERS; SO WE DID NOT SUSPECT A BLOWN NOSE TIRE. I TURNED ON THE WHEEL WELL LIGHT AND LOOKED THROUGH THE COCKPIT SIGHT WINDOW. EVERYTHING LOOKED NORMAL. I WAS CONFIDENT THAT WE HAD NOT BLOWN A MAIN TIRE BECAUSE OF THE NORMAL TKOF CTL; SO I ELECTED NOT TO GO TO THE CABIN TO VIEW THE MAIN GEAR THROUGH THE PORT. I SENT AN ACARS VOX CONTACT REQUEST AND INFORMED DISPATCH. THEY WERE UNAWARE OF THE ISSUE. SHORTLY THEREAFTER; WE WERE SWITCHED TO ZZZ APCH CTL. THEY ASKED US FUEL AND SOULS ON BOARD. WE CONFIRMED THAT THEY HAD DECLARED AN EMER FOR US. I CALLED THE FLT ATTENDANTS AND BRIEFED THEM. I THEN MADE A PA TO THE PAX. I INFORMED THEM THAT WE HAD BEEN TOLD THAT AN ACFT HAD LOST SOME GEAR DOOR PARTS IN YYY AND THAT WE WERE POSSIBLY THE ACFT THAT LOST THEM. WE DID NOT EXPECT ANY PROBS AT LNDG; BUT THEY WOULD PROBABLY NOTICE FIRE TRUCKS WITH THEIR EMER LIGHTS ON. WE SECURED THE CABIN FOR A NORMAL LNDG. THERE WERE NO ABNORMAL INDICATIONS DURING ACFT CONFIGN. I ELECTED TO CONFIGURE TO FLAPS 30 DEGS DUE TO WINDSHEAR AND XWIND RPTS AT ZZZ. MY LNDG WAS COMPLETELY NORMAL AND UNEVENTFUL. WE PULLED CLR AND AWAITED THE FIRE TRUCKS. I MADE ANOTHER PA TO ALERT THE PAX THAT THE FIRE TRUCKS WERE COMING AND TO NOT BE ALARMED. I BELIEVE THAT 5 FIRE TRUCKS AND SEVERAL OTHER SUPPORT VEHICLES SURROUNDED THE ACFT. THE FIRE CHIEF SAID THAT WE LOOKED NORMAL AND CLRED US TO TAXI BACK ALONE. I INFORMED THE PAX THAT WE WERE APPARENTLY NOT THE ACFT THAT LOST THE PARTS AND THAT WE WERE GOING TO TAXI BACK NORMALLY. WE INFORMED OPS AND THEY ASSIGNED US GATE. UPON OUR ARR AT THE GATE; MAINT INFORMED US THAT WE HAD LOST THE RECAP ON THE #4 TIRE AND THAT SIGNIFICANT DAMAGE HAD OCCURRED. WE MOVED TO ANOTHER ACFT AND CONTINUED. THE FO CONTINUED TO THE NEW ACFT. I SPOKE WITH THE FLT ATTENDANTS AND LEARNED THAT MANY PAX NEAR THE OVERWING ON THE FO'S SIDE RPTED THAT IT WAS REALLY LOUD ON TKOF FROM YYY. THIS WAS THE FIRST TIME I HAD ANY KNOWLEDGE OF THIS. THE FLT ATTENDANTS STATED THAT THEY LEARNED THIS ONLY DURING THE FINAL CABIN CLEANUP AND DID NOT WISH TO FORWARD THE INFO TO US BELOW 10000 FT. IN THIS CASE; I SUPPORT THEIR DECISION. THE PAX RPTS WERE TOO VAGUE TO FULLY SUBSTANTIATE THE EVENT. I WOULD HAVE DONE NOTHING DIFFERENT HAD I KNOWN THE INFO. I SPENT TIME WITH THE FLT ATTENDANTS AND THE FO TO CONFIRM THAT THEY HAD NO RESIDUAL STRESS-RELATED REACTIONS TO THE EVENT. EVERYONE WAS GOOD TO CONTINUE; SO WE DEPARTED. BY THIS POINT; THE THROUGH PAX LEARNED THAT THE FIRST ACFT HAD BEEN DAMAGED. I MADE MYSELF AVAILABLE TO THEM. SEVERAL OF THE THROUGH PAX ASKED ABOUT IT AND I DID MY BEST TO ANSWER THEIR CONCERNS. I DID SHARE THAT WE HAD LOST SOME RUBBER FROM ONE OF THE TIRES; BUT THAT IT DID NOT AFFECT OUR LNDG OR ACFT SYS. OF INTEREST TO THIS EVENT; WE HAD HIGH TKOF SPDS AT XXX THE LEG PRIOR. DUE TO THE HIGH WT; TEMP; AND TAILWIND; WE HAD SPDS OF 160; 163 AND 166 KTS. THE YYY SPDS WERE 134; 136; AND 141 KTS; SO I WAS FAR LESS CONCERNED WITH TIRE ISSUES IN YYY THAN I WAS IN XXX.