B737-700 CREW HAD DIFFICULTY FINDING RWY TURNOFF BECAUSE MANY OF THE RWY TURNOFFS WERE CLOSED DUE TO ARPT CONSTRUCTION. ALSO; THE END TURNOFF WAS BARRICADED BUT WAS NOT NOTAMED CLOSED.

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ENRTE FROM FLL TO TPA; THE FO COPIED THE ARR ATIS INCLUDING NOTAMS FOR THE FOLLOWING TXWY CLOSURES: W4; W5; S HALF OF W6 AND W FROM W3 TO W6. AT ABOUT THAT TIME; THE 'A' FLT ATTENDANT CAME TO THE COCKPIT TO OFFER US BEVERAGES. THIS PROBABLY BROKE THE FO'S TRAIN OF THOUGHT WHEN HE NORMALLY WOULD HAVE ADVISED ME OF THE TXWY CLOSURES AFFECTING OUR RWY. I BRIEFED A VISUAL APCH TO RWY 36L AND CALLED FOR THE APCH/DSCNT CHKLIST; BUT FAILED TO NOTICE THE TXWY CLOSURES LISTED ON THE ATIS NAPKIN. I HAD NOT FLOWN INTO TPA SINCE THE START OF THE CURRENT CONSTRUCTION PROJECT AND WAS INTENDING TO TURN OFF AT THE MID FIELD EXIT AND TAXI AROUND THE S SIDE OF THE TERMINAL. TPA TWR CLRED US TO LAND ON RWY 36L BUT MADE NO REF TO AVAILABLE OR PREFERRED TURNOFFS; WHICH MANY CTLRS OFTEN DO AS BOTH A COURTESY AND REMINDER TO PLTS DURING ABNORMAL OPS. AS I DECELERATED AND SEARCHED FOR THE FIRST AVAILABLE TURNOFF; I DISCOVERED THE BARRICADES BLOCKING THE ENTRANCES TO W3 AND W4. I MADE A COMMENT TO THE FO TO THE EFFECT OF 'I GUESS WE'LL BE TAXING AROUND THE N SIDE.' I EASED OFF ON THE BRAKES TO EXPEDITE DOWN TO W6; UNAWARE THAT IT WAS PARTIALLY CLOSED. AS WE PASSED W5; I NOTICED THAT IT WAS ALSO BARRICADED. I FELT CONFIDENT THAT W6 WOULD BE WIDE OPEN. BUT AS WE GOT CLOSER IT APPEARED FROM OUR PERSPECTIVE THAT THE BARRICADES PLACED THERE HAD RENDERED IT UNUSABLE AS WELL. I WAS NOW PLANNING TO ROLL TO THE ONLY REMAINING EXIT WHICH WAS SEVERAL THOUSAND FT AWAY AT THE END OF THE 11002 FT RWY. HAVING BEEN ON THE RWY FOR AN EXTENDED PERIOD; I WAS EXPECTING TO HEAR THE TWR TELL US TO EXPEDITE TO THE END OR MAKE A QUICK 180 DEG TURN; BUT THE TWR REMAINED SILENT AS WE ROLLED PAST W6. AS WE DID; I SAW THAT W6 WAS PARTIALLY OPEN; BUT IT WAS TOO LATE TO MAKE THE TURN SAFELY. THE FO ASKED THE TWR WHAT THEY WANTED US TO DO; BUT THERE WAS NO REPLY. AS THE LAST TURNOFF CAME INTO VIEW; MY HEART SANK AT THE SIGHT OF THE BARRICADES WHICH AGAIN APPEARED TO SPAN THE ENTIRE WIDTH OF THE TXWY. THINKING THAT I HAD OVERSHOT THE ONLY AVAILABLE TURNOFF; I SLOWED THE ACFT IN ANTICIPATION OF MAKING A 180 DEG TURN ON THE RWY TO BACK-TAXI TO W6. WE WERE ABOUT 2000 FT FROM THE END OF RWY 36L AS I MANEUVERED TO THE R SIDE OF THE RWY WHILE THE FO AGAIN ASKED THE TWR FOR GUIDANCE. THE TWR TOLD US TO CONTACT GND; SO THE FO DID AS INSTRUCTED. THE FIRST DISTINGUISHABLE WORDS FROM GND CTL WERE 'XYZ;' WHICH HAPPENED TO BE OUR FLT NUMBER. ANXIOUS TO GET THE ACFT OFF THE RWY; I HAD TURNED THE ACFT ABOUT 30 DEGS L OF CTRLINE BEFORE I REALIZED I HAD MISINTERPED OUR ABBREVIATED CALL SIGN AS PART OF THE INSTRUCTIONS ISSUED BY GND. I THEN PROMPTLY CONTINUED TO THE DEP END OF RWY 36L AND EXITED THROUGH THE NOW VISIBLE OPENING BEYOND THE BARRICADE. UNFORTUNATELY; MY MANEUVERING ON THE RWY CAUSED THE TWR TO TAKE PREEMPTIVE MEASURES BY ORDERING THE ACFT BEHIND US TO GO AROUND. I LATER DISCUSSED THE MATTER WITH THE TPA TWR CHIEF WHO CONFIDED THAT THEY HAD EXPERIENCED A SIMILAR SIT EARLIER THAT DAY. HE IMPLIED THAT THEY MAY HAVE BEEN A LITTLE PREMATURE IN SENDING THE OTHER ACFT AROUND; BUT WERE NOW EXERCISING GREATER CAUTION. I APOLOGIZED FOR MY LOITERING AND ADVISED HIM THAT SOME GUIDANCE FROM THE TWR WOULD HAVE BEEN BENEFICIAL IN HASTENING OUR EXIT. AS PIC; I ASSUME FULL RESPONSIBILITY FOR THIS INCIDENT DUE TO THE FACT THAT THE INFO WAS AVAILABLE TO ME AHEAD OF TIME; BUT SOMEHOW OVERLOOKED. HOWEVER; THE CORNERSTONE OF AVIATION SAFETY RESTS UPON THE BUILT IN REDUNDANCY IN PERSONNEL AND EQUIP THAT IS PUT IN PLACE TO GIVE US A SECOND CHANCE WHENEVER THERE IS A BREAKDOWN IN THE PRIMARY SYS. THIS TIME THE PRIMARY SYS (FLC) FAILED TO ASSIMILATE ALL OF THE APPROPRIATE INFO. REALIZING THAT NOT EVERY AIRMAN IN THE COUNTRY IS FAMILIAR WITH THEIR CURRENT CONSTRUCTION SIT; A SIMPLE 'HEADS UP' FROM THE TWR ON FINAL APCH WOULD HAVE PROMPTED ME TO ASK FOR THE AVAILABILITY OF SPECIFIC TXWYS. SUPPLEMENTAL INFO FROM ACN 511743: AS THE PNF; I COPIED ATIS; INCLUDING TXWY CLOSURES. AT THIS TIME; I ASKED 'TWR; WHAT WOULD YOU LIKE US TO DO?' MY RECOLLECTION IS THAT TWR INSTRUCTED US TO CONTINUE TO THE END AND CONTACT GND. AS WE EXITED RWY 36L; GND INSTRUCTED US TO CALL ONCE WE ARRIVED AT OUR GATE; WHICH WE DID. IN HINDSIGHT; I FEEL THIS EVENT WAS VERY AVOIDABLE. FIRST; I SHOULD HAVE VERBALLY COMMUNICATED THE TXWY CLOSURES TO MY CAPT; AS WELL AS DONE A BETTER JOB REVIEWING THE TPA NOTAMS ON THE RELEASE. ADDITIONALLY; I SHOULD HAVE CLARIFIED WITH TWR ANY QUESTIONS I HAD ABOUT A SUITABLE EXIT PRIOR TO LNDG. HAD I DONE THE ABOVE; WE WOULD HAVE BEEN BETTER PREPARED WHEN WE SAW THE S HALF OF W6 AND THE SOUTHERN 255 FT OF THE RWY 18R CONNECTOR BARRICADED WITH SANDBAGS AND OTHER EQUIP. ALSO; I SHOULD HAVE SPOKEN UP EARLIER IN OUR ROLLOUT AND REQUESTED TWR GUIDANCE INSTEAD OF WAITING UNTIL WE WERE NEARLY STOPPED. FROM A HUMAN FACTORS STANDPOINT; REGARDLESS OF WHAT THE ATIS WAS RPTING; BOTH W6 AND THE CONNECTOR APPEARED TO BE BARRICADED FROM MY VANTAGE POINT AS WE APCHED FROM THE S. I FEEL THE TWR COULD HAVE HELPED PRECLUDE THIS EVENT IN 2 WAYS: 1)INCLUDING IN THE ATIS WHICH EXITS ARE SUITABLE FOR ACR ACFT; AND THE WIDTH OF THESE EXITS (EG; 'ACFT LNDG RWY 36L; PLAN TO EXIT N SIDE OF W6; 'X' FT WIDE FOR TAXI...'). MY POINT IS SIMPLY THAT I DIDN'T KNOW HOW WIDE THE EXITS WERE; ONLY HOW MUCH WAS CLOSED. 2) SPEAKING UP SOONER TO US WITH GUIDANCE ONCE WE PASSED W6. WE NEVER HEARD A THING SUCH AS 'EXPEDITE TO THE END; TFC ON FINAL.' AGAIN; I KNOW WE SHOULD NOT HAVE DELAYED ON THE RWY; BUT THE ABOVE MIGHT HAVE HELPED.