The Twin Towers mechanism of progressive collapse
First dislodge a single floor from its supports. This floor does not stay perfectly horizontal as it descends. One corner collides with the floor below. However, a corner has density but not mass, and therefore no momentum. The result is that the supports will resist for a while until enough volume of the descending floor has made contact with the floor below to deliver a large enough force to shear the supports at that corner.
By this mechanism, the rest of the descending floor will tend to catch up, and the time delay between the shearing off of supports at the first corner and the shearing at the opposite, last corner, will be less than the time difference between impact of the first corner and the last corner. There is a self-correcting process which results in the two floors which later descend together being more horizontal than the previous floor when it travelled on its own. (The shearing at the last corner actually occurs before the contact has been made at that corner.)
Once two floors descend together, the process of shearing off at the vertical supports becomes easier, but the self-correcting process if the pack of floors deviates from the horizontal still applies, continually restoring the pack of floors to a horizontal position.
Because the vertical supports are effectively brittle, no loss of velocity and so loss of momentum results from the shearing of a floor's supports. As a result, the final impact on the ground is exactly as if all the floors had been held up in the air at a height of fifty stories (half the full height of the building), and let go, to descend together. Air resistance will have a negligible effect, so the calculation of final velocity is easy, K.E. = mgh where h is half the height of the building.
When this pack of floors hits the ground, the ground may shear at the edge of the building, and descend. However, if it does not, then surrounding ground descends immediately(or rises), leaving adjoining buildings up in the air (or crushing the bottom layer of those buildings). They will begin to descend, and meet the ground coming back up. The more rigid the ground under the foundations, the worse the effect.
It is important that vertical shear cuts be made in the ground around the edge of a skyscraper, giving a shear weakness, so as to protect other buildings from the effect of a single skyscraper collapse. This makes it possible for the ground under the failed skyscraper to descend without taking adjacent ground with it, and other skyscrapers with it.
It is important that the floors in a skyscraper be irregular, with one half one foot higher than the other half, so that the full floor does not hit the floor below at the same instant. More specifically, the height between two floors must vary across that pair of floors. Further, sacrificial pillars must be built to take early some of the impact of a floor descending from above.
The first tower was attacked high up, to collect the maximum number of floors together to hit the ground at the same time, to create the maximum earthquake. An attack on the second tower lower down made it more likely that the frame (under greater stress lower down) would be dislodged, admittedly reducing the scale of the second earthquake. However, a second equal earthquake would have caused little more damage than a single earthquake. That is probably why the second tower was attacked lower down. Also, the second tower had already been weakened by the first earthquake. The critical task was to dislodge the first, high up floor in the first tower. Had that failed, then the attack at a lower level on the second tower had a better chance of dislodging the supports at that lower, higher stress, position. What would clearly have been wrong would have been to attack both towers at the same level.
Ivor Catt 17sep01
31 May 2006. The above was written and put onto the www a few days after the disaster. I now clarify it in a slight way. When one corner of a floor collides with the floor below, the impact on the support to that floor is initially minimal because a corner has density but no mass. So the lower corner support does not break. The result is that angular momentum is given to the falling floor, pivoting about the single point of contact with the lower floor. The is the self-correcting mechanism discussed above. I did know this at the time, but could have stated it more clearly. Ivor Catt May 2006