On August 20, 2017, about 1120 eastern daylight time, a Piper PA-28R-200, N9431N, was substantially damaged during a forced landing after takeoff from Northeast Florida Regional Airport (SGJ) St Augustine, Florida. The flight instructor and student pilot sustained minor injuries. The airplane was privately owned, and the instructional flight was operated under the provisions of Title 14 Code of Federal Regulations Part 91. Visual meteorological conditions prevailed at the time, and no flight plan was filed for the local flight, which originated from SGJ about 1035.According to the flight instructor, the purpose of the flight was to practice traffic pattern touch-and-go landings. The instructor said that during the run-up he told the student "not to forget to change the fuel tanks every 30 minutes." The flight instructor stated that they were on their fourth takeoff and were climbing through 500 ft when the engine started to "sputter." The flight instructor took control of the airplane, declared an emergency and landed the airplane in a marsh area. According to the student pilot, as they were climbing through 500 ft, she switched the fuel tanks while climbing and the engine "failed." The student pilot did not recall which fuel tank she switchd to prior to the loss of engine power. She passed the controls over to the instructor to perform the emergency landing. Examination of the airplane by a Federal Aviation Administration Inspector revealed the right wing and airframe was buckled. A cursory examination of the engine did not reveal any anomalies that would have precluded normal operation. Due to the airplane resting in the marsh the amount of fuel remaining in the wing tanks could not be determined. Prior to take off the airplane had a total of 25 gallons of fuel on board. According to the Lycoming engine operator's manual, the IO-360C series engine fuel consumption is 12.5 gallons per hour at performance cruise. The airplane was flown for about an hour prior to the loss of engine power.