On June 28, 2017, about 1910 eastern daylight time, a privately owned and operated Beech B23, N4023T, was substantially damaged when it impacted trees and terrain during a forced landing in Ocean Isle Beach, North Carolina. The private pilot received minor injuries, the passenger, who was a student pilot, was seriously injured. The flight departed Odell Williamson Municipal Airport (60J), Ocean Isle Beach, North Carolina about 1908, and was destined for Stag Air Park (7NC1), Burgaw, North Carolina. Visual meteorological conditions prevailed, and no flight plan was filed for the personal flight, which was conducted under the provisions of Title 14 Code of Federal Regulations Part 91.According to the passenger, during the previous flight from 7NC1 to 60J while in cruise flight about 3,000 ft mean sea level (msl), the pilot moved the engine mixture control from a partially leaned setting to full rich, just after the passenger noticed that the exhaust gas temperature gauge was indicating "a little high." As the mixture control was moved, the engine developed a "very noticeable vibration" which then worsened. The pilot increased the throttle setting to the "low to mid 2000" rpm range, after which the engine vibration stopped. The engine operated normally for the remainder of the flight. After landing at 60J, the pilot added about 15 gallons of fuel to the left fuel tank (the tank he had used for the duration of the inbound flight) and about 5 gallons to the right fuel tank. The passenger recalled the pilot commenting about utilizing the right fuel tank for the return flight, but he did not recall whether he moved the fuel selector. The pilot then taxied the airplane to the airport restaurant area where they ate dinner. Before departing the parking area, the pilot removed the engine cowls to examine the engine compartment for any loose wires or other indications of what may have caused the vibration, but found nothing unusual. The pilot then checked the oil quantity and performed a walkaround inspection of the airplane using his checklist, as he had done prior to the previous flight. According to the pilot, the engine started normally and he allowed it to idle for a few minutes to warm up. He performed an engine run-up with no issues noted. The engine performed normally during the takeoff, which the pilot described as a "ground effect takeoff" and during the initial climb. When the airplane reached an altitude of about 500 feet msl, the pilot noticed the airplane was not climbing as expected, and the engine rpm had reduced to less than 2000. As he started a "slow bank" left turn back toward the airport, the airplane would no longer climb. He then checked the carburetor temperature gauge, which read about 58°F and checked the throttle friction which was satisfactory. He considered switching fuel tanks, but chose not to because the engine was developing some power, and he was concerned that switching tanks might cause a total power loss. Once the pilot realized that the airplane would not reach the runway, he prepared for a forced landing into a wooded area. During landing the left wing struck a tree and the airplane rolled inverted. An initial examination of the airplane by a Federal Aviation Administrator (FAA) inspector revealed that fuselage came to rest inverted and the right wing was separated from the fuselage at the root. A section of the left wing was separated about mid span, and the nose section forward of the windscreen was crushed in the aft and upward direction. The empennage was crushed and bent toward the right, aft of the baggage compartment door. The vertical and horizontal stabilizers, rudder and elevators were separated from the empennage. The propeller blades both had minor scratches and nicks but were otherwise undamaged. The engine was rotated by hand at the propeller and produced thumb compression on all four cylinders. The Nos. 3 and 4 sparkplugs were black and sooty. Both magnetos were dislodged. The starter Bendix was in the engaged position. The fuel primer was in the closed position. The throttle control was about 1/4 inch out from the full position, and the mixture control was in the full rich position; however, impact damage was noted to the instrument panel in the area of the controls. The carburetor heat control was in the off position. Both fuel filler caps were found secure with their seals intact. The fuel selector was found halfway between the LEFT and RIGHT tank positions. The wreckage was further examined following its recovery to a storage facility. The cockpit was intact and flight control continuity was confirmed to all flight control surfaces. The fuel selector functioned normally and when air was blown through the fuel lines, no blockages were observed. The fuel strainer and fuel bowl were absent of debris. The carburetor was impact damaged; however, its venturi and floats were intact. The magnetos were impact damaged and could not be tested. The air intake and exhaust were free from obstructions and no anomalies were found with the fuel system. According to the pilot's logbook he had accrued 215 hours of total flight experience; of which, about 40 hours were in the same make and model as the accident airplane. The recorded temperature and dew point about the time of the accident, at an airport located about 15 miles west of the accident site, were 81°F and 59°F, respectively. Review of an FAA carburetor icing chart for the given temperature and dew point revealed serious icing at glide power.