ENTIRE NOSE GEAR AND WHEEL ASSEMBLY FELL OFF THE ACFT UPON LIFTOFF DURING A TRAINING TKOF FLT.

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MY STUDENT AND I WERE DOING TKOFS AND LNDGS ON RWY 17L. 30 MINS INTO THE FLT WE EXPERIENCED A NOSEWHEEL SHIMMY ON TKOF. EVERYTHING WAS NORMAL ON TKOF AND CLBOUT. WE REQUESTED A FULL STOP LNDG ON RWY 17R AT DWH. ON SHORT FINAL AN ACFT LNDG RWY 17L RPTED A TIRE AND NOSE GEAR ON THE RWY. AT THIS TIME WE INITIATED A GAR. WE ASKED ATC ABOUT OUR NOSE GEAR. THEY RPTED TO US THAT IT WAS MISSING. AT THE TIME WE USED ALL APPROPRIATE CHKLISTS FOR THE EMER. THE ACFT WAS LANDED ON RWY 17R DWH. MINOR DAMAGE OCCURRED ON THE ACFT; NO FIRE OCCURRED OR PROP STRIKE; SOME SKIN DAMAGE WAS DONE. FAA WAS NOTIFIED ABOUT THIS INCIDENT. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: RPTR STATED THAT THE ACFT WAS A BEECHCRAFT; B23 SUNDOWNER; AND THAT THE ENTIRE WHEEL ASSEMBLY WITH STRUT HAD FALLEN OFF DURING THE TKOF. LATER EXAMINATION OF THE NOSE GEAR ASSEMBLY DISCLOSED THAT THERE WERE SIGNS OF METAL FATIGUE; PROBABLY CAUSED BY HARD LNDGS. THE RPTR STATED THAT THE TKOF AND LNDG MADE PREVIOUSLY TO THE FINAL ONE WAS COMPLETELY ROUTINE AND NORMAL. HE SUSPECTED THAT THE RPTED GEAR ON THE RWY MAY BE FROM HIS ACFT SINCE HE KNEW THAT HE WAS THE LAST ONE TO USE THE RWY. HE BELIEVED THAT IT COULD BE HIS GEAR ON THE RWY; SINCE NONE WAS OBSERVED DURING HIS TKOF!