The aircraft was on a regular night cargo flight between Cologne, Germany, and Shannon Airport, Ireland, with an intermediate stop at Dublin Airport. The flight from Cologne to Dublin was uneventful. After unloading and taking on new freight at Dublin the aircraft was cleared by ATC to Flight Level (FL) 120 for a direct track to Shannon. A standard ILS approach was flown to RWY 24 at Shannon. At the point of touchdown, as some of the propeller blades struck the RWY surface, the crew realised that the aircraft undercarriage was not extended so they initiated an immediate go-around. As the aircraft climbed most of No. 3 engine disintegrated and fell from the aircraft to the ground. Debris from this engine damaged No. 4 engine and also perforated the cabin structure, aft of the cockpit jump seats. With only No. 1 engine fully operative and No. 2 engine on reduced power, the crew managed with great difficulty to sufficiently control the aircraft and carry out a successful landing on RWY 24, with the full Shannon Airport Fire Services in attendance. The crew shut down the remaining engines and they and the passengers evacuated the aircraft safely. There was no fire.