The pilot reported that he began his descent in the airport traffic pattern when another airplane announced its position in the vicinity of the airport. The pilot turned his attention to the traffic and located it visually. The traffic collision avoidance system (TCAS) annunciated in the proximity of the other airplane. The turn to the base leg was made after passing the traffic. During the base and final legs, the gear warning horn annunciated and the pilot stated he had mistaken it for the TCAS. The pilot landed with the gear retracted and the airplane sustained substantial damage to fuselage supporting structure. The pilot reported he was wearing noise cancelling headphones during the flight but did state he was able to hear the gear warning horn annunciate. After the accident, the airplane was placed on jacks and the landing gear was extended using the airplane's own systems and there was no indication of abnormal operation. The pilot reported no preimpact mechanical failures or malfunctions with the airframe or engine that would have precluded normal operation.