DIRECTED BY DFW ATCT LCL CTLR TO GO AROUND ACCOUNT TFC ON THE RWY; FLT CREW OF B737-800 ENCOUNTER SEVERE WINDSHEAR AND TURB. DIVERT TO SHV.

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DURING APCH TO RWY 17L AT DFW; WE WERE STABILIZED ON APCH; ON FINAL; AND IN A SAFE POS TO LAND. WE WERE ON GLIDE PATH; ON COURSE AND ON SPD. THE TWR DIRECTED A GAR AT APPROX 400-500 FT AGL. WE HAD THE RWY ENVIRONMENT IN SIGHT AND WERE IN A POS TO ACCOMPLISH A NORMAL LNDG. OUR RWY WAS RPTING STEADY STATE WINDS DOWN THE RWY AT 24 KTS AS BEST AS WE CAN REMEMBER. WE WERE TOLD THE REASON THE TWR DIRECTED THE GAR WAS BECAUSE OF AN ACFT STILL ON THE RWY. OUR INSTRUCTIONS WERE TO TURN L TO A HDG 150 DEGS AND CLB TO 2000 FT. WE WERE ESTABLISHED ON THE HDG CLBING THROUGH APPROX 1500 FT WHEN WE ENCOUNTERED SEVERE TURB AND THE PREDICTIVE WINDSHEAR WARNING. THE WARNING ALMOST INSTANTLY TURNED INTO AN ACTUAL WINDSHEAR. THE SYS ON THE B737 FUNCTIONED JUST AS IT WAS PUBLISHED AND TAUGHT IN THE SIMULATORS. ALL OF THE WX WAS SHOWING W OF OUR POS WHEN WE WERE ON FINAL APCH. ON THE RADAR ONLY RAIN AND NO CELLS IN OUR MISSED APCH PATH WERE VIEWED. THE LINE OF WX WAS W OF THE FIELD. USING SOP'S FOR WINDSHEAR; WE ANNOUNCED ESCAPE AND THE FO COMPLETED THE PROC FLAWLESSLY. WE WERE UNABLE TO CTL ALT DUE TO THE SEVERE TURB AND FINALLY ESCAPED ABOVE 5000 FT. I DID NOTIFY THE ATC OF OUR SIT; ENCOUNTERING BOTH WINDSHEAR AND SEVERE TURB. CTL OF THE ACFT BECAME OUR PRIMARY FOCUS AT THIS POINT. ONCE STABILIZED IN THE CLB; WE CONTACTED ATC AND DISPATCH. THE SPD VARIATIONS WERE EXTREME. UPON LNDG AT OUR DIVERT; SHV; THE ACFT WAS PLUGGED BY MAINT PERSONNEL AND WE WERE TOLD THAT NO ACFT PARAMETERS WERE SURPASSED. THIS EVENT WAS EQUAL TO OR GREATER IN COMPLEXITY TO ANY EVENT GIVEN ME IN A SIMULATOR. THERE WERE NO INJURIES. ONE LADY WAS CHKED BY PARAMEDICS IN SHV UPON LNDG. SHE HAD PREVIOUS HEART PROBS; AND I HAD HER CHKED AND SHE SIGNED A RELEASE FORM.