B727 LOSES PART OF R MAIN GEAR DOOR INFLT AFTER A TIRE CHANGE IN SLC.

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A FLT FROM SLC-BOI. I DID A NORMAL EXTERIOR PREFLT AND DID NOT OBSERVE ANYTHING UNUSUAL. AFTER PREFLT; MAINT DID A DOUBLE TIRE CHANGE ON THE R MAIN LNDG GEAR. THEY SIGNED THE AIRWORTHINESS RELEASE AND WE DEPARTED FOR BOI. CLBING THROUGH APPROX 16000 FT; THE CREW HEARD A THUMP; WHICH WE ALL ASSOCIATED WITH TURB. AFTER INITIAL DSCNT INTO BOI; THE FLT ATTENDANT RPTED TO THE COCKPIT THAT SHE FELT A STRONGER THAN USUAL VIBRATION IN THE FLOOR APPROX 4 ROWS AFT OF THE AFT OVERWING EXIT. THERE WAS NO HEAT OR SMOKE ASSOCIATED WITH THE VIBRATION AND SHE COULDN'T DETERMINE IF IT WAS ON THE R OR L SIDE OF ACFT. THE LNDG GEAR EXTENDED NORMALLY AND THE LNDG WAS UNEVENTFUL. AS PAX WERE DEPLANING AT THE GATE; A BOISE OPS PERSON ENTERED THE COCKPIT AND RPTED SEEING DAMAGE TO THE UNDERSIDE OF THE R WING NEAR THE LNDG GEAR. ALL 3 PLTS WENT OUTSIDE AND OBSERVED THE R MAIN LNDG GEAR DOOR MISSING WITH ACFT DAMAGE (SCRAPES AND HOLES) IN THE UNDERSIDE OF THE WING/FAIRING/COUPLING AREA. THE RETURN FLT TO SLC WAS CANCELED AND THE APPROPRIATE AGENCIES WERE NOTIFIED. IT WASN'T UNTIL AFTER LNDG AND SEEING THE DAMAGE THAT THE CREW PUT 2+2 TOGETHER AND REALIZED THE THUMP PASSING THROUGH 16000 FT WAS PROBABLY THE DOOR DEPARTING THE AIRPLANE. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: THE DOOR THAT WAS LOST WAS THE FUSELAGE FOLDING SECTION THAT WAS MOST LIKELY OPENED ON THE GND BY MAINT. RPTR INDICATED THAT NO WARNING LIGHTS WERE NOTED IN THE COCKPIT THAT WOULD INDICATE THAT THE GEAR AND DOOR SEQUENCING WERE OTHER THAN NORMAL PRIOR TO THE DOOR SEPARATING.