ELEVATOR TRIM TAB BRACKET CAME LOOSE IN FLT REQUIRING AN EMER LNDG.

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AT APPROX XA30 I FELT AND HEARD A LARGE BANG (LIKE SOME TYPE OF IMPACT). IMMEDIATELY AFTER; THE CTL YOKE WAS THRUSTING IN AND OUT VIOLENTLY. I ALSO COULD HEAR THE SOUND OF A LOUD SIREN IN BOTH MY HEADSET AND THE OVERHEAD SPEAKER (WHICH I DETERMINED TO BE MY OWN ELT). I IMMEDIATELY PULLED THE THROTTLE BACK TO IDLE; LOWERED THE LNDG GEAR AND ENGAGED FULL FLAPS. I DID NOT GIVE ANY REGARD TO SPD (I WAS ALREADY BELOW THE SPD FOR GEAR AND 10 DEG FLAPS) FOR FULL FLAPS BECAUSE MY IMMEDIATE CONCERN WAS THAT IF I COULD NOT GET THE TAIL TO STOP SHAKING SO VIOLENTLY THAT IT WOULD PROBABLY COME APART. AS THE AIRPLANE SLOWED BELOW 125 MPH (APPROX) THE SHAKING SUBSIDED AND FINALLY QUIT. I CONTINUED TO REDUCE SPD TO APPROX 80 MPH AND STARTED A DSCNT. I TRIED TO COMMUNICATE WITH APCH BUT BECAUSE OF THE NOISE FROM THE ELT I COULD BARELY MAKE OUT THEIR RESPONSES TO MY XMISSIONS. I DECLARED AN EMER; TOLD THEM I HAD SOME SORT OF STRUCTURAL FAILURE AND THAT I WAS GOING TO FIND A PLACE TO LAND. I CONTINUED MY DSCNT AND SPOTTED A SMALL LNDG STRIP (THAT I WAS AWARE OF PREVIOUSLY AS A GOOD EMER STRIP). DURING MY DSCNT I CHKED TO MAKE SURE THE ENG WAS OK AND LIGHTLY TESTED THE RUDDER; ELEVATOR AND AILERONS FOR PROPER OP. ALL SEEMED OK; BUT I CONTINUED MY NO PWR; 80 MPH DSCNT WITH THE THOUGHT THAT THE TAIL SECTION OF THE PLANE MAY HAVE SUFFERED SERIOUS DAMAGE AND ALSO WITH THE THOUGHT THAT ANY ADDITIONAL STRESS MAY RENDER THE PLANE UNCONTROLLABLE. I LANDED WITHOUT INCIDENT. ONCE ON THE GND I INSPECTED THE TAIL SECTION OF THE AIRPLANE AND DISCOVERED THAT THE METAL BRACKET THAT CONNECTS THE ELEVATOR TRIM TAB TO THE ARM HAD BROKEN AND THE ELEVATOR TRIM TAB WAS FREE TO SWING UP AND DOWN; CONNECTED TO THE PLANE ONLY BY THE HINGE. I FULLY INSPECTED THE TAIL SECTION OF THE AIRPLANE AND FOUND NO CREASES; NO BUCKLING; NO POPPED RIVETS AND NO SIGN OF ANY STRESS WHATSOEVER. UP TO THIS POINT; AFTER REFLECTING ON THIS INCIDENT; I BELIEVE I DID EVERYTHING RIGHT AND TO THE BEST OF MY ABILITY. BASED ON THE CONDITION OF THE PLANE; THE FACT THAT IT DEMONSTRATED NORMAL FLT BELOW 125 MPH; THE REMOTENESS OF THE RWY WE LANDED ON AND THE DISTANCE TO AN ARPT WITH SVCS I DECIDED TO SECURE THE LOOSE TRIM TAB AND FLY ON TO BAKERSFIELD. I DID THIS AND LANDED SAFELY AT MY DEST WITHOUT FURTHER INCIDENT. EVEN THOUGH I ARRIVED SAFELY I DISCOVERED THAT I HAD VIOLATED THE FAR'S FOR TAKING OFF AGAIN WITH A KNOWN DEFECT IN THE PLANE. I AM IN THE PROCESS OF DOING A REVIEW OF THE FAR'S WITH A FLT INSTRUCTOR.