PLT OF A BEECH BARON; BE58; BLEW A MAIN GEAR TIRE DURING LNDG DUE TO A GUSTY DOWNWIND CONDITION CAUSING THE USE OF HVY BRAKING ACTION. RPTR WAS DIVERTING TO LAND DUE TO UNFORECASTED TSTMS WX IN THE DEST ARPT AREA.

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ON A FLT FROM MEM TO IXD; ATC ADVISED OF A CONVECTIVE SIGMET; AND SPECIFICALLY MENTIONED OUR CALL SIGN. THE WARNING WAS FOR BASEBALL SIZED HAIL AND TORNADOES. WE DECIDED TO DIVERT TO JBR. CTR ADVISED WINDS WERE FAVORING RWY 5 AND PROCEEDED TO CLR US FOR THE VISUAL APCH TO RWY 5. ON DSCNT WE LOST COM WITH CTLR AND CONTINUED IN FOR A LNDG ON RWY 5. WINDS WERE IN FACT BLOWING THE OPPOSITE DIRECTION AT 20-30 KTS. ON LNDG WE APPLIED MAX BRAKING AND DUE TO COMBINED XWIND; PRESSURE FROM BRAKING; AND POOR RWY CONDITION; OUR L MAIN TIRE BLEW OUT. THROUGH THE USE OF DIFFERENTIAL PWR AND MAX BRAKING ON R MAIN WE WERE ABLE TO MAINTAIN THE ACFT UNDER CTL AND COME TO A STOP ON THE RWY. WE PROCEEDED TO CALL JBR FLT SVC OF THE SIT AND REMOVE THE ACFT FROM THE RWY WITHIN 30 MINS. NOTE: PRIOR TO DEP AT MEM I CALLED JACKSON FSS AND WAS ADVISED WX WAS IMPROVING AND WOULD HAVE NO PROB COMPLETING THE FLT. A LINE OF STORMS DEVELOPED WITHIN 45 MINS OF THAT CALL. NOTE: ALTHOUGH THE CTLR ADVISED US TO LAND ON THE WRONG RWY; HIS HELP WAS GREATLY APPRECIATED IN AVOIDING THE DANGEROUS WX.