On December 11, 2009, about 1600 Pacific standard time, a Cessna 310, N2640C, experienced a landing gear system failure and landed with the landing gear retracted at Tri-Cities Airport, Pasco, Washington. The front seated passenger owned the airplane and was operating it under the provisions of 14 Code of Federal Regulations Part 91. The commercial pilot and three passengers were not injured; the airplane sustained substantial damage. The local personal flight departed from Prosser Airport, Prosser, Washington, about 1350, with a planned destination of Moses Lake, Washington. Visual meteorological conditions prevailed, and a flight plan had not been filed. In a written statement, the pilot reported that after departure he retracted the landing gear and the cabin heater simultaneously failed. He slowed the airplane and extended the landing gear in an effort to see if it would have an effect on the heater. After noting no change, he attempted to retract the landing gear again. There was no movement in the landing gear position and the cockpit light was illuminated green in indication that the landing gear were down. He attempted to troubleshoot the problem to no avail. The pilot further stated that he maneuvered the airplane over the airport, where ground personnel confirmed that the landing gear were extended with the exception of the right main, which was retracted with the gear door extended. During a manual retraction attempt he discovered that the gear handle would not rotate. After numerous failed attempts to force the right main landing gear to extend, he opted to fly to Pasco and land the airplane with all the landing gear in the retracted position. The airplane touched down in a tail-low attitude and settled onto the runway; bulkhead damage was incurred as a result of the landing. Post accident examination revealed that the rod end of the up-lock push-pull tube on the right main landing gear had failed. The part was disposed of prior to the Safety Board having an opportunity to perform an examination. According to a representative from Cessna Aircraft Company, who viewed detailed photographs of the subject push-pull tube, the rod end was broken in tension overload. He further stated that those failures are typically a result of improper rigging, although could be a result of fatigue failure.