B727-200 FLT CREW TAXIED TO WRONG RWY AT CHA.

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I WAS WORKING AS A SO ON ACR X FROM CHA TO ATL. THIS WAS THE SECOND LEG OF A TURN-AROUND TRIP. WE RAN OUR NORMAL PRE-FLT CHKLISTS AND BRIEFED THE FLT BACK TO ATL WHILE PARKED AT THE GATE. WE TALKED ABOUT THE CONVECTIVE ACTIVITY BTWN THE 2 ARPTS. ADDITIONALLY; THE CAPT AND FO STUDIED THEIR TAXI CHARTS FOR CHA AND REMARKED THAT IT WOULD BE A SHORT TAXI TO RWY 20. I ACKNOWLEDGED THIS AND PASSED THE WORD ABOUT OUR VERY SHORT (QUICK) TAXI TO OUR FLT ATTENDANTS. WE STARTED ENGS AND WERE CLRED TO RWY 20 AS PLANNED. I INITIALLY VISUALLY CLRED OUR TAXI RTE THEN BECAME PREOCCUPIED WITH COMPLETING THE TKOF DATA AND READING THE TAXI CHKLIST. THE RWY AND TXWY SIGNS ADJACENT TO THE CHA RAMP AREA WERE CONFUSING AND THE CAPT TAXIED OUR ACFT TOWARD RWY 15 INSTEAD OF RWY 20. OUR PLANE CROSSED RWY 20 (THE ACTIVE) BEFORE WE NOTICED AND COULD STOP HIM. WE IMMEDIATELY CALLED GND CTL AND GOT CLRNC UP TO AND BACK DOWN RWY 15; ACROSS 20; ALONG THE RAMP; TO THE END OF RWY 20. THE CHA GND CTL TOLD US WE WERE THE 12TH ACFT THAT MONTH TO MISREAD THE SIGNS NEXT TO THE RAMP. OUR INCORRECT TAXI RTE DID NOT CAUSE ANY CONFLICTS AS THE RWY; FINAL APCH; AND TXWYS WERE CLR. MAJOR INCIDENT CONTRIBUTOTS -- POOR TXWY AND RWY SIGNS NEXT TO THE CHA RAMP. (MANY ACFT PER MONTH MAKING THE SAME MISTAKE!) MINOR CONTRIBUTORS: LACK OF CREW SITUATIONAL AWARENESS FOR A FEW BRIEF SECONDS. LACK OF CREW VIGILANCE.