On November 23, 2016, at 1803 eastern standard time, a Piper PA-28-140, N41565, was substantially damaged during a forced landing after takeoff from Columbus Airport (CSG), Columbus, Georgia. The flight instructor and a private pilot receiving instruction were not injured. The airplane was registered to a corporation and was operated by the flight instructor under the provisions of 14 Code of Federal Regulations Part 91 as an instructional flight. Night, visual meteorological conditions prevailed at the time, and no flight plan was filed. The local flight was originating at the time of the accident.The flight instructor reported that ground operations were normal, and 18 gallons of fuel were observed in each wing tank. The engine started normally, and the magneto checks were within limits. During the initial climb after takeoff, about 1 mile past the departure end of runway 24, the engine vibrated and experienced a total loss of power. The flight instructor assumed the controls and confirmed the fuel selector position, checked the fuel boost pump on, and turned on the carburetor heat. The pilot turned off the carburetor heat after the engine did not respond. The engine did not regain power and the airplane continued straight-ahead until it settled into the trees. The airplane fell for about 4-5 seconds and then came to an abrupt stop. After securing the engine and fuel system, the pilots exited the airplane and were met by first responders. An inspector with the Federal Aviation Administration (FAA) responded to the accident site and examined the wreckage. Structural damage to the wings and fuselage was confirmed. Initial examination of the engine and fuel system did not reveal evidence of a mechanical malfunction. The fuel tanks were breached during the impact sequence and contained no fuel. The fuel strainer was dry and free of contaminants. Follow-up examinations of the engine were performed by the FAA inspector and the NTSB investigator-in-charge. Impact damage to the forward section of the engine prevented rotation of the crankshaft; therefore, internal continuity of the engine was not confirmed. A visual examination of the exterior of the engine revealed no holes in the crankcase or evidence of crankcase rupture. The engine contained oil. The carburetor was removed for examination. The accelerator pump operated normally and squirted fuel. The throttle linkage was intact. The carburetor inlet fuel screen was clean and unobstructed. The carburetor bowl was free of contamination. The top spark plugs were removed for examination. The No. 2 sparkplug exhibited normal wear when compared to a Champion Check-A-Plug chart. The electrode was coated with a thin layer of black soot. The other plugs were normal in wear and color. The ignition leads were undamaged. The magnetos remained securely attached to the engine. Visual examination of the interior of the cylinders showed normal piston deposits and no damage. The recorded weather at CSG, at 1751, included calm wind, temperature 66° F, and dew point 46° F. Review of an FAA Carburetor Icing Chart for the given temperature and dew point revealed that the conditions were conducive to serious icing at glide power.