A LNDG A320 SUFFERS ON RWY TXWY EXCURSION WHEN THE R OUTBOARD MAIN WHEEL BRAKE FAILS TO FUNCTION AFTER USING AUTO BRAKING AND MANUAL BRAKING SYS.

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MSP OPERATES ON A TEMPORARILY SHORTENED RWY 30L/12R (6000 FT AVAILABLE) WHILE REPAIRS ON ONE END ARE BEING COMPLETED. OUR FMGC (FLT MGMNT GUIDANCE COMPUTER) CALCULATED MAX ALLOWABLE LNDG WT IS 142200 LBS AND PROJECTED ACFT WT OF 137800 LBS; SO WE WERE LEGAL ON A DRY RWY FOR A VISUAL DAY LIGHT LNDG. THE CAPT SELECTED AUTO BRAKES MEDIUM TO GIVE US A GOOD BRAKING ACTION RIGHT AFTER TOUCHDOWN AT AROUND 138 KTS. AFTER A NORMAL TOUCHDOWN IN THE NORMAL TOUCHDOWN ZONE; AUTO BRAKES STARTED NORMAL DECELERATION. BOTH ENGS REVERSED NORMALLY AND AT 80 KTS THE CAPT STARTED ACTUATION OF THE FOOT PEDAL BRAKES (DISENGAGED AUTO BRAKES AND TOOK ENGS OUT OF REVERSE). BY NOW THE ACFT WAS IN AREA OF RWY WITH A LOT OF REVERTED RUBBER FROM LNDGS ON RWY 30L. FO AND CAPT BOTH NOTED WE WERE GETTING A VERY ROUGH RIDE. AFTER APPLYING THE FOOT BRAKES; I FELT WE WEREN'T SLOWING DOWN ADEQUATELY SO INCREASED PEDAL PRESSURE. AT A SPD LESS THAN 60 KTS; THE ACFT STARTED ANGLING L SO THE CAPT BRAKED HARDER AND TRIED TO CORRECT BACK TO CTRLINE WITH RUDDER. ACFT SLOWED GRADUALLY AND CAME TO A STOP JUST PRIOR TO TXWY A1 AND AFTER TXWY A2. THE L MAIN GEAR CAME TO REST ABOUT 5 FT OFF THE PAVED SURFACE. CAPT INSTRUCTED PAX TO REMAIN SEATED AND CALLED FOR EMER TRUCKS. FIRE FIGHTERS NOTED HOT BRAKES; ESPECIALLY ON THE R SIDE WHERE SMOKE WAS NOTED. THE BRAKE TEMPS WERE: L OUTBOARD 350 DEGS C; L INBOARD 340 DEGS C; R INBOARD 380 DEGS C AND R OUTBOARD 130 DEGS C. THIS INDICATES THAT THE R OUTBOARD BRAKE DID NOT OPERATE TO PROVIDE ANY SIGNIFICANT STOPPING PWR. BOTH R MAIN TIRES HAD SIGNIFICANT FLAT SPOTS ON THEM. OUR ECAM (ELECTRONIC CENTRALIZED ACFT MONITORING) GAVE US NO WARNING INFO; OR STATUS MESSAGES AT ANY TIME DURING THE ENTIRE INCIDENT THAT POINTED OUT ANY PROBS WITH THE BRAKING SYS.