The flight crew reported that during their initial takeoff the air traffic control tower controller transmitted that he thought he saw smoke originating from the airplane. The flight crew aborted the takeoff as the airplane was accelerating through 80 knots. Upon exiting the runway, the flight crew verified normal operation of both engines. The captain reported that he had no reason to suspect hot brakes due to minimal use and taxied back to the active runway where the flight was subsequently cleared for takeoff. During the second takeoff, which was initiated about 5 minutes and 43 seconds after the initial rejected takeoff, the flight crew heard and felt a loud bang followed by a sudden yaw to the right; the flight crew immediately aborted the takeoff. Shortly after, the flight crew heard a second loud bang, followed by a more severe yaw to the right. The flight crew slowed the airplane and exited onto a taxiway at the end of the runway. Upon exiting the airplane, the captain observed a fire near the left main landing gear and immediately evacuated the airplane. Examination of the airplane by a Federal Aviation Administration inspector revealed that the left main landing gear exhibited fire damage and that the tire was blown. A punctured hole within the right side of the fuselage was observed just aft of the cockpit. The flight crew reported that at the time of the accident the airplane weighed 20,772 pounds. Review of emergency procedures within the aircraft flight manual revealed that a high energy stop inspection of the aircraft was required following the initial rejected takeoff due to the aircraft exceeding the maximum brake energy weight at the time of the initial rejected takeoff. The maximum brake energy weight was calculated to be 20,300 pounds. Probable Cause: The flight crew’s failure to follow the manufacturer?s aircraft flight manual emergency procedures following a rejected takeoff that required a high energy stop inspection. Contributing to the accident was the flight’s exceedence of the aircraft’s maximum brake energy weight.