I've been a weldor since the nineteen-sixties, and I can tell you that ( even ignoring the mechanical damage to supports ) ordinary structural steel starts losing its strength as it is heated up. A few hundred degrees will start the changes, to say nothing of a thousand or more degrees of fuel-stoked, wind-driven fires.
The flanges holding one floor failed, and it triphammered the rest down to the ground. That is all it took.
Actually what happened is this.
the initial crash destroyed a small percentage of exterior tube columns. The exterior tubes are for resisting wind loads. The interior core was heavily damaged in both buildings, the South tower losing about 1/4 of its core columns. the impact also destroyed many floor decks that served two important purposes. They held up the floor, but more importantly laterally braced the perimeter tube.
To explain, take two pens or pencils and stand them vertically on top of each other on a desk. with one hand hold the top pencil and the other hold between both pencils. As long as you hold both pencils from moving sideways, you can push down and support a bit of weight. If you remove your fingers, the pencils quickly willpush outwards and collapse.
When the floor trusses/decking was destroyed, the perimeter tubes already overstressed, wre actually pulled inwards by the collapsed floor decks. as fires raged, damaged decking w/ blown off insulation becan to sag further. Eventually the area of the building above the damaged areas began to collapse. Each building collapsed differently.
http://wtc.nist.gov/pubs/NCSTAR1-6ExecutiveSummary.pdf