By the time the combined wreackage hit an undamaged floor it was heavy enough to break an unweakened floor, so the collapse continued down the building (You can see windows blowing out sequentially as it happens.)
Now you have the intact building section above the impact zone sitting on top of a hollow tube. Piston. Crush. The central building core guides it down.
The steel did not "melt"
Watch a blacksmith at work, and you will see that steel heated to red heat is so soft that it can be molded like putty by the blacksmith's hammer.
Furthermore, that once-strong steel, when cooled slowly, is so weak it can be bent with your bare hands (that's called "annealing").
Returning the steel to its prior strength and hardness requires re-heating it and "quenching" it by plunging it into water to cool it quickly.
Watch a blacksmith forge a knife. You will never again be amazed that the girders in the WTC -- when exposed to tons of burning jet fuel -- weakened to the point that the buildings collapsed.
“Now you have the intact building section above the impact zone sitting on top of a hollow tube. Piston. Crush. The central building core guides it down.”
Its interesting that you used the term “hollow tube”.
A “rigid hollow tube” is a term the designers used to describe their unique design.
http://www.skyscraper.org/TALLEST_TOWERS/t_wtc.htm