1Estimates for time to collapse of WTC1

1.1Introduction

This is an attempt to estimate what would be expected for the time of collapse of WTC1 based on observation of the videos of the falling building under an assumption that the collapse was due only to gravity and the description of the collapse found in the NIST report along with some other assumptions. The time of collapse was not analyzed by NIST in their report but I will show that a lower bound for the time of collapse may be estimated from the assumptions mentioned above. I will argue that the building fell faster than it should have. Others have argued that the tower should not have fallen at all. See the paper by Ross in [7] for an argument, based on energy, momentum, and the physical properties of the columns, that the total collapse should not have taken place. Jones [8] has given many other arguments of a di®erent sort which also conclude the o±cial explanation is not adequate. I will focus mostly on the °oors in this paper and will not attempt to show the building should not have fallen but that it fell surprisingly fast. These arguments are based on assumptions involving the relative mass of the concrete to the steel in the °oors of the building and the claim that the concrete of the °oors was essentially all crushed to dust.

Here is a section of the NIST report [6] which was shown to me by Nic Dudzik.

\ ...the structure below the level of collapse initiation o®ered minimal resistance to the falling building mass at and above the impact zone. The potential energy released by the downward movement of the large building mass far exceeded the capacity of the intact structure below to absorb that energy through energy of deformation.

Since the stories below the level of collapse initiation provided little resistance to the tremendous energy released by the falling building mass, the building section above came down essentially in free fall, as seen in videos. As the stories below sequentially failed, the falling mass increased, further increasing the demand on the °oors below, which were unable to arrest the moving mass."

The fall of the top of the tower can be seen in the video [14]or [15]. The ¯rst of these shows the top °oors collapsing in a very complicated manner. After a su±cient amount of dust forms, it is di±cult to see what is happening with these upper °oors. Also it is very hard to determine whether the above explanation is correct for the collapse of the bottom °oors based only on the videos.

Here is some information about what was observed based on what I have gotten from the web. If this information is faulty, it will a®ect the validity of the estimates presented in this paper. In [1] it says the steel for the °oors was 44.5 kg/m2. Assuming the °oors were 207 feet by 207 feet, this yields an estimate for the mass of steel per °oor as about 177,146 kg. In [10]it states: \Virtually all the concrete (an estimated 100,000 tons in each tower) on every °oor was pulverized into a very ¯ne dust, a phenomenon that requires enormous energy and could not be caused by gravity alone; workers can't even ¯nd concrete." The NIST report [5] states that on every °oor there were two types of concrete used, normal concrete in the core area and light weight concrete elsewhere. I will assume the °oor slab was composed entirely of light weight concrete for the sake of simplicity. In [17] it gives the ¯gure for density of light weight concrete as 1750 kg=m3. Since the °oor was about 207 feet by 207 feet and the slab of concrete was four inches thick, this works out to 707,786 kg for the mass of the concrete in the °oor. More generally, if the density is Den kg=m3 the mass of the concrete in the °oor is

404:45 £ Den kg:

As to the speed of collapse of WTC1, it looks like it came down in about 15 seconds from the time the antenna started to sink. Smaller ¯gures have been put forth, however. The ¯gure given by NIST [6] for the top panels of the building to hit the ground is 11 seconds. They based this on \precise timing of initiation of collapse from video evidence and also on seismic signals recorded at Palisades N.Y." In addition, it has been shown by Legge [4] that the acceleration of the roof of WTC1, if continued, would give a fall time of 10.5 seconds. One of the longest estimates for the time for WTC1 to collapse is in [19] where it is suggested this time was as long as 16 seconds. I could not ¯nd a time of collapse for WTC1 in the 9/11 commission report but they claim that WTC2 collapsed in 10 seconds [11]p 322. In [6] they say WTC2 collapsed in 9 seconds.

Greening [3] divides the fall of the towers into two stages, a ¯rst stage in which the top °oors act like a single mass, and a second stage in which this stack of top °oors then collapses when it hits the ground. For WTC1 he uses the ¯gure for the ¯rst stage of collapse of this tower as 11.3§1:5 seconds; thus at most 12.8 seconds. Then he argues that it would be about one more second for the top °oors to collapse when they