On November 11, 1996, about 1230 eastern standard time, a Piper PA-30-160, N7392Y, collided with the ground adjacent to the runway during the takeoff roll at Cartersville, Georgia. The airplane was operated by the pilot under the provisions of Title 14 CFR Part 91, and visual flight rules(VFR). A VFR flight plan was filed for the dual instructional flight. There were no injuries to the commercial instructor, nor to the dual student, and the airplane was substantially damaged. Origination of the flight was Dobbins Air Force Base, Marietta, Georgia, about 1130, on the same day. The flight was being conducted to provide multi-engine training to the single engine rated commercial student. During a takeoff roll on runway 01, at the airport selected for training, the left engine was shut off by the instructor to simulate an engine failure. The pilot under instruction failed to reduced the power on the right engine in a timely manner to prevent the aircraft from yawing to the left. The instructor stated he was unable to recover control of the airplane in time to prevent its veering off of the runway. Examination of the accident site disclosed that the airplane veered off of the left side of the runway at approximately 1500 ft. down the runway. Further examination revealed that the left main gear collapsed and the airplane rested approximately 120 degrees from the original runway heading. The CFI and the student did not report a mechanical problem with the airplane.