PA31 PLT EXECUTES A GEAR UP LNDG.

Narrative

I FLEW FROM NORTH PALM BEACH (F45) TO TREASURE CAY (MYAT). I FAILED TO EXTEND THE LNDG GEAR AND CONTACTED THE RWY WITH THE INBOARD TRAILING EDGE OF THE FLAPS AND THE PROP TIPS. I CAME BACK AROUND AND LANDED NORMALLY. THE FLAPS WERE ABRADED SOMEWHAT BUT WERE FUNCTIONAL. THE Q-TIP PROPS (4 BLADE) WERE CURLED AND SLIGHTLY ABRADED BUT SEEMED STRUCTURALLY SOUND. I DID A FULL PWR RUN-UP; THEN FLEW TO NASSAU WITHOUT INCIDENT; PICKED UP PAX (THE OWNER OF THE ACFT); SAID NOTHING YET OF WHAT HAD HAPPENED; AND FLEW TO PBI TO CLR CUSTOMS. WE THEN RETURNED TO F45 TO OFFLOAD THE PAX AND FROM THERE I RETURNED TO BASE (BCT). THE ACFT PERFORMED NORMALLY IN EVERY WAY. I HAVE SINCE BEEN TOLD THAT I SHOULD NOT HAVE FLOWN THE ACFT (AFTER IT WAS DAMAGED); AND COMMON SENSE WOULD SAY AS MUCH; BUT I WAS IN SOMEWHAT OF A STATE OF SHOCK. THE ISSUE IS MY DECISION TO CONTINUE TO OPERATE THE ACFT IN THIS CONDITION. I AM BETTER INFORMED NOW ABOUT THE CONSEQUENCES OF ANY PROP CONTACT (PROP STRESS AND POSSIBLE ENG DAMAGE) AND WOULD NOT DO THIS AGAIN.