Let's not forget that a building is not a ladder. If a building could maintain its integrity, except at the location which was cut or otherwise destroyed, it is possible that the intact structure might just be able to absorb the impact but only if it would retain its own structural integrity. Confusing...

hmmm.
Put it this way, the building structure (and I mean only the load-bearing part) is designed to pass the load of the building down to the foundations. Slice out a floor of the building (for instance) and whether the building stands will depend on how well the underlying structure is able to redistribute the loads and stresses without having a critical amount of failures due to exceeding the strength of various structural elements. Each failure causes more redistribution of loads which causes more stress on the remaining structural elements which can lead to more failures, etc., until the remaining structure can't support the loads and gives way (possibly catastrophically).
Taking the WTC towers. The primary support was vested in the core columns and a significant amount in the perimeter columns. The whole point of that design was to allow for the maximum amount of open space per floor (on the order of 40,000 sf). The floor was constructed from light-weight concrete to provide the actual floor and supported by trusses that supported the concrete and also served to provide for load transfer between the core and perimeter columns.
Enter 9/11 and the general structural failure that causes the upper portion of either building to fall onto the lower portion. A major mass falls onto a floor that (likely) was designed for a given dead load (weight of the truss, concrete, and the permanent stuff ) and live load (people and just about everything else). The floor, not designed to support that major mass, gives way and quickly. If the end connectors fail, the floor drops. If the end connectors hold, they pull the perimeter columns in and/or the core columns outward. In either case, there is no opportunity for the load imposed by the descending upper portion to be held and distributed to the true load-bearing structures (the perimeter and core columns). The structure is disrupted and along with that disruption goes the ability of the structure to hold up the building.
Even if the structure of the WTC towers could or should have been strong enough, the fact that there was no place that could take the impact of the falling building and survive long enough to distribute the load to the columns led to the complete collapse.
Thinking about the ladder analogy. Assume the ladder is carrying a load that at least reasonably stresses it. Cut it, then rotate the upper portion 90 degrees or some angle such that the ladder's beams are not aligned and now you depend on the rungs to transfer the load of the upper part to the lower part. If the rung can handle it, the load gets distributed to the beams and continues down to the feet/ground. The ladder, however precariously, stands. If the rung can't, then it breaks allowing the upper portion to fall on the next rung, etc. or some reasonable facsimile. In any case, you have ongoing structural failure, until and unless the rungs, in contact, manages to hold, otherwise the ladder "collapses".
I'll go back to lurking now.
