On July 9, 2012, about 1700 eastern daylight time, a Cessna 172S, N680MA, was substantially damaged when it veered off the runway during touch-and-go landing at Allentown Queen City Municipal Airport (XLL), Allentown, Pennsylvania. The flight instructor and student pilot were not injured. The airplane sustained substantial damage to the airframe and the horizontal stabilizer. The airplane was operated by Gateway Aviation under the provisions of 14 Code of Federal Regulations Part 91 as a local instructional flight. Visual meteorological conditions prevailed and no flight plan had been filed. According to the pilots, they had been performing touch-and-go practice landing. After landing, around the time of power application, the airplane veered off the left side of the runway. According to a Federal Aviation Administration inspector, the airplane exited the runway into the adjacent grass, crossed a taxiway and intersecting runway, impacted an airport sign, and came to rest near a berm. There were three distinct tire marks noted in the grass from the point where the airplane initially exited the edge of the runway to a point past where the sign had been impacted, up to a hole in the ground similar to a "gopher hole." Initial examination revealed that the left main landing gear axle was impact separated and the associated tire was located about two weeks after the accident, in a ditch, approximately 300 feet from where the airplane had come to rest and was inflated. The 1655 recorded weather observation at XLL included wind from 240 degrees at 4 knots, visibility 10 miles, temperature 29 degrees C, dew point 12 degrees C; barometric altimeter 29.94 inches of mercury. According to maintenance personnel the airplane had been examined several times in the preceding two weeks for an unusual vibration emanating from the left main landing gear. The left main landing gear axle and associated parts, including the left wheel, were examined at the NTSB's Materials Laboratory. The examination revealed that the fractures were consistent with overstress from a single loading event. A detailed examination report, including photographs, is included in the docket that accompanies this accident. The FAA Airplane Flying Handbook, FAA-H-8083-3A, chapter 5, states, in part, the following about takeoffs: "…the throttle should be advanced smoothly and continuously to takeoff power. An abrupt application of power may cause the airplane to yaw sharply to the left because of the torque effects of the engine and propeller…"