LOW TIME PVT PLT IN PA28-161 ATTEMPTS TURN OFF BEFORE SPD IS DISSIPATED. L BRAKE FAILS TO WORK AT THAT TIME. RUDDER NOT USED EFFECTIVELY. ACFT LEAVES RWY AND CUTS ACROSS GRASS AND TXWY BEFORE STOPPING.

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THIS INCIDENT OCCURRED IN VFR WX. VERY LITTLE WIND ON LNDG (RWY 5R STRAIGHT DOWN THE RWY). IT WAS A SCENIC FLT WITH MY HUSBAND (PLT ALSO) WHO WAS IN THE FRONT R SEAT AND MY MOTHER WHO WAS IN THE BACK R SEAT. NEITHER THE PLANE NOR THE PAX SUSTAINED ANY DAMAGE OR INJURY. IT WAS A PLANNED FLT. WE WERE WELL RESTED. THE FLT ITSELF WAS UNEVENTFUL. THERE HAD BEEN PLANES IN THE PATTERN; BUT NOT AT THE TIME OF LNDG. THERE WAS NO OTHER TFC IN THE AIR OR ON THE GND. APCH TO LNDG A LITTLE HIGH; SLIPPED WITH L AILERON AND R RUDDER. LANDED SMOOTHLY ON RWY 16 FHR. NICE LNDG! PLANNED TO EXIT TO THE R ON THE FIRST TXWY EXIT. APPLIED BRAKES AT WHICH TIME THE PLANE TOOK THE PATH AS DEPICTED (REFER TO DIAGRAM). AT POINT 3X; I THINK I ATTEMPTED TO STAY ON THE RWY (HAPPENED SO QUICKLY) WITH RUDDER CTL; BUT THE SPD HAD NOT DISSIPATED ENOUGH; AND I FELT LIKE IT WOULD GND LOOP; SO I WENT BACK TO THE L BRAKE TO TRY THAT AGAIN TO NO AVAIL; SO I JUST 'WENT WITH' THE PLANE -- BRAKING ON BOTH BRAKES AGAIN AND FINALLY STOPPED ON THE TXWY. THE BRAKES AT THIS TIME WORKED FINE. TESTED REPEATEDLY; THEY DID NOT PULL TO THE R. NOTE BTWN 2X-3X I TRIED L BRAKE TO CORRECT ALIGNMENT TO NO AVAIL. IT WAS THEN; AT 3X I THINK I TRIED RUDDER (TOO MUCH?) AND PLANE SWERVED; SO; FEARING A GND LOOP AT THAT SPD WOULD BE WORSE THAN TRAVERSING THE GRASS AND TXWYS; I OPTED TO DO THAT. NO PLANES WERE ON THE RWY OR TXWYS AT THE TIME; SO THE PATH AHEAD OF PLANE WAS CLR (ASIDE FROM A TXWY LIGHT) OF ANY OBSTRUCTIONS. I NOTED THE STRAIGHT PATH OF THE PLANE -- ONCE IT VEERED TO THAT DIRECTION; IT MAINTAINED THAT TRACK; AND COULD NOT BE CORRECTED WITH L BRAKING ACTION. BRAKES FELT OK; NORMAL; BUT HAD NO EFFECT ON CORRECTING PATH AFTER THE TURN TO THE R. (ONCE I WAS ON THE GRASS; I NO LONGER TRIED L BRAKING; BUT USED BOTH BRAKES.) APPROX 1 - 1 1/2 MONTHS; PRIOR TO THIS INCIDENT ANOTHER PLT (CFII) HAD A SIMILAR INCIDENT IN THIS ACFT; AFTER WHICH NOTHING AMISS WITH THE BRAKING SYS WAS FOUND BY A CERTIFIED MECH. THE SAME MECH EXAMINED THE PLANE AFTER THIS INCIDENT; AND; AGAIN; FOUND NOTHING WRONG WITH THE BRAKE SYS.