On September 30, 2005, approximately 1130 mountain daylight time, a Bellanca 7GCBC, N113AW, piloted by a private pilot, was substantially damaged when it impacted terrain during the landing roll at Vance Brand Airport (2V2), Longmont, Colorado. Visual meteorological conditions prevailed at the time of the accident. The instructional flight was being conducted under the provisions of Title 14 CFR Part 91 without a flight plan. The private pilot and airline transport certificated flight instructor reported no injuries. The local flight departed approximately 1100. According to the Pilot/Operator Aircraft Accident Report Form submitted by the flight instructor, he and his student were performing touch-and-go landings on runway 26. The instructor stated the last landing was planned as a full stop. He stated that the touch down was good and the airplane was aligned with the runway. During the landing roll, the student attempted to correct the airplane from drifting to the right by applying left rudder. The rudder input was unresponsive and the airplane continued to drift to the right and departed the runway. The airplane looped to the right and came to rest on the right side of runway 26. The left main wing spar was broken, the left landing gear strut was bent aft, and the left rudder cable had separated at its midspan. Two pieces of the left rudder cable with the mating sides of the fracture were sent to the NTSB, Office of Research and Engineering, Materials Laboratory Division, for further examination. Detailed optical examination of the fractured individual wire ends and strands adjacent to the fracture revealed significant wear damage. Many of the individual wires were worn to a knife-edge adjacent to the fracture. Wear had penetrated to the center portion of the center strand. Examination of the left side of the fuselage at the cable separation point, conducted by NTSB and FAA, revealed wear marks on the upper, outboard seatback support bar. The seat was removed from the airplane which revealed the seat frame had been repaired on the left side. The weld extended the seatback support bar down and aft, preventing it from lining up with the lower seat support bar. This extension entered the travel path of the left rudder cable. The airplane logbooks contained no entry regarding the maintenance performed on the seat frame. Neither the flight instructor nor airplane mechanic could recall the seat maintenance being performed within the last 2 years. An examination of the remaining airplane systems revealed no anomalies.