EMB140 FLT CREW WITH ZHU AT APPROX FL310 EXPERIENCED TCAS RA DURING VECTORS AROUND WX.

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ENRTE TO DFW FROM LRD AT FL300. ZHU HAD US ON A VECTOR OF HDG 350 DEGS FOR TFC SEPARATION INTO DFW DUE TO TSTMS AND DETERIORATING WX. DUE TO BEING RADAR VECTORED; I CAN BEST ESTIMATE WE WERE ABOUT 20 MI SW OF THE GLOVE INTXN AT THE TIME OF THE INCIDENT. WE WERE SOLID IMC AT THE TIME OF THE INCIDENT AS WELL. THE CAPT AND I WERE EVALUATING OUR NEW POSSIBLE ROUTING AND CHKING OUR FUEL AND ALTERNATES WHEN WE HEARD TCAS ALERT 'TFC; TFC.' WE BOTH LOOKED AT OUR CORRESPONDING MFD'S AND NOTED TFC AT OUR SAME ALT APPROX 1-2 O'CLOCK POS. WITHIN 3-5 SECONDS OF THE INITIAL TA; WE RECEIVED AN RA SAYING 'CLB; CLB.' THE CAPT IMMEDIATELY DISENGAGED THE AUTOPLT; ADDED FULL THRUST AND INITIATED A CLBING L TURN AWAY FROM THE TFC. DURING THIS TIME ZHU WAS STILL BUSY WITH OTHER ACFT CLRNCS AND INSTRUCTIONS. WITHIN SECONDS OF OUR RA RESPONSE; ZHU GAVE US IMMEDIATE TURNING INSTRUCTIONS; THOUGH I CANNOT RECALL WHICH DIRECTION ZHU WANTED US TO TURN. THE TCAS VOICE WAS LOUD ENOUGH TO DISTORT MOST INSTRUCTIONS FROM CTR; HOWEVER; I DO NOT RECALL ZHU TELLING US TO CLB OR DSND. HE ONLY TOLD US TO TURN. TCAS ALTERED 'CLR OF CONFLICT' CLBING THROUGH FL306.7 IN A L TURN PERHAPS 20-30 DEGS L OF OUR 350 DEG ASSIGNED HDG. WHEN THE ZHU FREQ CALMED DOWN ENOUGH; I STATED THAT WE HAD RESPONDED TO AN RA; WAS DSNDING BACK TO FL300 AND REQUESTED FURTHER INSTRUCTIONS. ZHU WAS STILL BUSY WITH OTHER ACFT AND IT TOOK SEVERAL REQUESTS TO GET A RESPONSE. ZHU THEN TOLD US TO HOLD OVER GLOVE INTXN; WHICH AT THAT TIME WE WERE WITHIN 2-5 NM FROM GLOVE HEADING NE. UNABLE TO UNDERSTAND WHAT HE WANTED; WE CONSULTED OUR STAR INTO DALLAS AND ENTERED THE DEPICTED HOLD. AS WE ENTERED THE HOLD; ZHU CLRED US DIRECT BYP AND HANDED US OFF TO ZFW. WE HEARD NO FURTHER INFO FROM ANY OTHER CTLRS AND THEY WERE BUSY REROUTING ACFT DUE TO THE WX IN THE AREA. BOTH THE CAPT AND I FEEL THE ZHU CTLR WAS OVERLOADED WITH TFC AND MERELY DIDN'T REALIZE HE HAD 2 ACFT CONVERGING AT THE SAME ALT. HE WAS TAKING MULTIPLE ACFT OFF COURSE FOR '30 MI SPACING INTO DALLAS PER DALLAS INSTRUCTIONS.' THE FREQ WAS SO CONGESTED IT WAS NEARLY IMPOSSIBLE TO GET ANY WORD IN. AGAIN; WE WERE IMC THE ENTIRE TIME SO I CANNOT ESTIMATE HOW CLOSE WE CAME TO THE OTHER JET. THE ONLY OTHER INFO I HAVE IS THAT EVEN ON THE 6 NM SCALE ON MY TCAS; THE INTRUDING ACFT WAS AT OUR SAME ALT AND WITHIN LESS THAN 1 MI OF US HORIZONTALLY.