@Glennn,
You want me to calculate the energy balance throughout the fall of the towers? That would require a supercomputer or two and a team of dedicated scientists working for a year or two.
I can only guess that the results
may indicate the core's solidity had been weakened. Possibly by the heat of the inferno above. Iron is a good conductor of heat. The steel pillars must have conducted the heat to many floors below, weakening the steel's resistance well below the impact level.