MD88 OUTER L MAIN TIRE BLEW DURING TKOF AND FLC CONTINUED TO DEST FOR FUEL BURN TO LNDG WT AND A LONGER RWY. UPON LNDG EMER EQUIP RESPONDED AND COMPANY MAINT INSPECTED ACFT FOR DAMAGE. THE GEAR WAS PINNED AND THE ACFT TOWED TO PARKING FOR PAX NORMAL DEPLANING.

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DEPARTED THE GATE AT CVG; BOUND FOR DFW. DEPARTING RWY 18R; V1 WAS COMPUTED AT 137 KIAS. AT APPROX 125 KIAS WE HEARD A MILD BANG. THE SOUND WAS SIMILAR TO THE LNDG GEAR RUNNING OVER A RWY LIGHT COVER OR UNEVEN PAVEMENT. THE CAPT EXPERIENCED NO DIFFICULTY IN CTL AND MADE A NORMAL TKOF. AFTER THE GEAR WAS RETRACTED AND FLAPS/SLATS CLEANED UP; ANOTHER ACFT WAITING FOR TKOF NOTIFIED THE TWR THAT HE SAW ONE OF OUR L MAIN GEAR TIRES SHREDDING ON TKOF. WE WERE NOTIFIED OF THIS AND REQUESTED HOLDING AT A FIX WHILE WE RAN ANY CHKLISTS AND NOTIFIED FLT CTL. BECAUSE WE WERE WELL OVER MAX LNDG WT; THE CAPT AND FLT CTL DECIDED IT WAS PRUDENT TO CONTINUE TO DFW. THIS WOULD BURN OFF A GOOD AMOUNT OF FUEL AND PROVIDE US WITH A LONGER RWY FOR LNDG. THE CAPT BRIEFED THE FLT ATTENDANTS AND MYSELF ON ALL POSSIBLE CONTINGENCIES AND THE APPROPRIATE PA'S MADE TO THE PAX. WE DECLARED AN EMER WITH DFW APCH CTL AND THE CAPT REQUESTED RWY 17R; THE LONGEST RWY AT DFW. A NORMAL LNDG WAS MADE AND WE CLRED THE RWY AND STOPPED ON A TXWY. EMER VEHICLES SURROUNDED THE ACFT AND NOTHING OTHER THAN A SHREDDED TIRE AND HOT RUBBER WAS A CONSIDERATION TO THEM. THE LNDG GEAR WAS PINNED AND WE WERE TOWED TO THE GATE. NO INJURIES RESULTED.