FLT CREW OF B757 ENCOUNTER APPARENT WINDSHEAR AT FLARE TO RWY 31C AT MDW. INADVERTENT AND UNCTLED MAIN GEAR TOUCHDOWN RESULTS IN REJECTED LNDG AND GAR INTO WX AND HIGH DENSITY TFC AREA.

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WE WERE ON A STABILIZED ILS APCH TO RWY 31C AT MDW. THERE HAD BEEN A RAIN SHOWER ON FINAL AROUND RUNTS INTXN AND THERE WERE RAIN AND TSTMS IN THE VICINITY. WE WERE VMC AT AROUND RUNTS WITH THE RWY IN SIGHT. THE APCH WAS NORMAL UNTIL 100-200 FT AGL AT WHICH TIME TURB INCREASED SOME AND NORMAL CORRECTIONS WERE APPLIED. NEAR THE FLARE; WIND GUSTS APPEARED TO REQUIRE MORE ROLL CORRECTIONS. THE R WING DROPPED; THE R MAIN WHEELS TOUCHED THE RWY; AND A GAR WAS INITIATED. OUR JUMPSEATER; A B737 CAPT; SAID OUR CORRECTIONS WERE APPROPRIATE FOR THE SIT WITHOUT OVER-CTLING. THE GAR WAS NORMAL; AND WE TURNED TO THE NE FOR WX AND ORD AVOIDANCE AND CLBED TO THE MISSED APCH ALT DURING THE MISSED APCH. COMS TO VERIFY HDG AND ALT CLRNCS WERE BLOCKED. THE PUBLISHED MISSED APCH WAS UNUSABLE DUE TO WX. WE THEN RECEIVED VECTORS AND HELD AT CGT. WE RECEIVED A RPT THAT WE MAY HAVE HAD AFT FUSELAGE CONTACT DURING THE GAR AND RAN THE APPROPRIATE CHKLISTS. DURING THE HOLD TIME A STRONG SHOWER PASSED OVER MDW. AFTER 20-30 MINS; WE FLEW ANOTHER ILS APCH TO A LNDG. THIS WAS NORMAL EXCEPT THE L THRUST REVERSER NEVER FULLY DEPLOYED. POSTFLT EXAMINATION SHOWED NO EVIDENCE OF GND CONTACT WITH ANY PART OF THE ACFT. WITNESSES ON THE GND STATED THEY OBSERVED STRONG GUSTS THAT CAUSED BAGGAGE CARTS TO MOVE DURING OUR GAR. THERE WERE NO WINDSHEAR ADVISORIES OR WARNINGS FROM THE TWR OR ONBOARD WINDSHEAR ADVISORY SYS.