B737 TAXIING FOR DEP AT BWI CROSSED RWY WITHOUT ATC CLRNC.

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THIS WAS OUR 3RD LEG OF DAY 2 OF A 3-DAY AM TRIP. THIS WAS OUR 3RD AIRPLANE IN AS MANY LEGS. WE CAME INTO THE GATE; HAD A PLANE SWAP; AND DEPARTED. DURING THE FLT BRIEFING; I BRIEFED THE FO THAT WE WOULD PROBABLY USE RWY 15R AND WE WOULD TAXI VIA TXWY P. OUR TAXI CLRNC WAS 'COMPANY NUMBER TAXI TO RWY 15R VIA TXWY P.' MY FO READ THE CLRNC BACK TO ATC AND I READ IT TO HIM. I EVEN POINTED TO IT ON MY CHART. APCHING THE INTXN OF TXWYS PA AND R; I SAW THE FLASHING LIGHTS AT RWY 15R AND TXWY R. MY FIRST THOUGHT WAS WHY ARE THESE ON. I THEN SAID TO MY FO; 'WE ARE CLRED TO CROSS RIGHT?' HE SAID; 'HE DIDN'T TELL US TO HOLD SHORT; DO YOU WANT ME TO ASK HIM?' I AGREED HE DID NOT TELL US TO HOLD SHORT; SO WE PROCEEDED TO TAXI ACROSS RWY 15R AT TXWY R. I SHOULD HAVE TURNED R AT TXWY P. WE FOLLOWED OUR NEW PROCS AND CLRED THE RWY BOTH DIRECTIONS AND ILLUMINATED ALL LIGHTS. AT ABOUT ROMEO 1 MY FO SAID; 'WHERE ARE WE GOING?' AND I SAID; 'WE WERE SUPPOSED TO TAXI TO RWY 15R NOT CROSS IT.' ATC CALLED US AT THIS TIME AND WE REPLIED; 'WE JUST REALIZED IT.' ATC GAVE US NEW TAXI INSTRUCTIONS TO TURN R AND HOLD SHORT OF RWY 15R AT TXWY F. WE WERE EVENTUALLY CLRED FOR TKOF AND THE REST OF THE FLT WAS UNEVENTFUL. I CONSIDER MYSELF SOMEONE WHO PAYS ATTN TO DETAILS AND IN 21 YRS; I HAVE NEVER MADE A MISTAKE LIKE THIS. HOW DID THIS HAPPEN? I THINK THESE ARE SOME CONTRIBUTING FACTORS. THIS PARTICULAR INTXN IS A KNOWN HOT SPOT (HS3). THE TXWYS ARE VERY CONFUSING AND SO IS THE SIGNAGE. I AM FAMILIAR WITH BWI AND KNOW THIS. WE CROSSED FLASHING LIGHT AT INTXN R. I WAS ON MY 6TH LEG WITH OUR NEW MANUAL PROCS. THEY REQUIRE BOTH PLTS AGREE THAT THEY ARE CLRED TO CROSS ANY RWY. WHEN I SAID TO MY FO; 'WE ARE CLRED TO CROSS; RIGHT?' I WAS JUST NOT ASKING; I WAS COMPLYING WITH PROCS. MY FO'S RESPONSE I TOOK AS AN AFFIRMATIVE. WE BOTH WERE TRYING VERY HARD TO GET ALL THE NEW PROCS RIGHT. THE PROCS DESIGNED TO PREVENT THIS SIT; MAY HAVE CONTRIBUTED SOMEWHAT. WE WERE MORE CONCERNED WITH THE MECHS OF XING A RWY. SUPPLEMENTAL INFO FROM ACN 614939: A FEW THINGS CONTRIBUTED TO THIS ERROR: 1) TXWY P CURVES AROUND THE WHOLE TERMINAL. 2) PRIOR CONFLICTS BTWN GND CTL IN BWI AND THE ASKING TO CROSS RWY 4/22 TAXIING TO RWY 28. 3) NEW PROCS -- TRYING TO GET EVERYTHING RIGHT; IE; CLRING THE RWY AND TURNING ALL LIGHTS ON. I THINK ANY BRIEFING OF HOT SPOTS AND THE SAYING OF WILL CROSS OR WILL NOT CROSS ANY RWY IN THE TAXI BRIEF WILL CORRECT THIS KIND OF EVENT.