MULTIPLE RWY OP INTERSECTING RWYS. SMA RWY INCURSION; ACR Y ISSUED GAR.

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I'M A 180 HR PVT PLT; AND THIS WAS MY FIRST TRIP INTO A CLASS B ARPT (DCA). I WAS VECTORED ONTO DOWNWIND FOR RWY 15 AND THEN CLRED FOR A VISUAL APCH TO RWY 15. APCH CTLR ASKED ME TO KEEP SPD UP AS LONG AS POSSIBLE AND GAVE ME TWR FREQ. CALLED TWR; AND WAS AGAIN ADVISED TO KEEP SPD UP. AS A RESULT OF THAT -- AND MY UNFAMILIARITY WITH THE ARPT AND; I'M SURE; SOME APPREHENSION ABOUT THE CLASS B ARPT -- I CAME IN HIGH AND FAST (10-15 KTS OVER NORMAL FINAL APCH SPD). I MADE THE LNDG FAIRLY SMOOTHLY; BUT WAS ROLLING AT APPROX 80 KTS. I DID NOT APPLY BRAKES FOR 2 REASONS: FIRST; THE CTLR'S EMPHASIS ON KEEPING SPD UP HAD ME THINKING ABOUT LNDG TFC BEHIND ME. SECOND; MY AIRPLANE GETS OCCASIONAL NOSEWHEEL SHIMMY; AND; OF COURSE (MURPHY'S LAW?) I HAD THAT TODAY. I STARTED TO APPLY LIGHT BRAKING AS THE SPD CAME DOWN. TWR THEN CALLED AND ASKED IF I WOULD BE STOPPED BEFORE INTXN OF RWY 18. I SAID 'NOT SURE.' HE THEN SAID 'CONFIRM THAT YOU'LL BE STOPPED BEFORE REACHING RWY 18.' I LOOKED UP AND SAW TXWY FOR 18 APPROX 500 FT AHEAD AND; NOT SURE IF IT WAS TXWY OR RWY ITSELF; I REPLIED ' I THINK I'M GOING TO ROLL ACROSS RWY 18 NOW.' AT THAT POINT; HE CALLED FOR A 737 ON SHORT FINAL FOR RWY 18 TO GAR. AS THAT WAS HAPPENING; I REALIZED THAT IT WAS THE TXWY IN FRONT OF ME; AND I COULD HAVE STOPPED. BEYOND HAVING PREPARED MYSELF BETTER FOR MY PART OF THE APCH AND LNDG; I THINK I MIGHT HAVE RESPONDED BETTER IF TWR HAD SAID SOMETHING LIKE 'I NEED YOU STOPPED BEFORE YOU CROSS RWY 18; CAN YOU DO THAT.' THAT WOULD HAVE CHANGED MY THINKING FROM TFC BEHIND ME TO TFC AHEAD OF ME.