by Gregory Szuladzin, Anthony Szamboti and Richard Johns
International Journal of Protective Structures Volume 4 · Number 2 · 2013 117
Received on 22 Dec 2012, Accepted on 8 March 2013

ABSTRACT
This article elaborates on variables associated with the collapse of the North Tower of the World Trade Center. The previously published quantifications of inertia, column capacity, and the assumptions related to the beginning of downward motion, are examined and corrected. The reasons for false conclusions reached in several previous analyses are presented.

INTRODUCTION
This presentation is not so much about how the WTC towers failed, but about how they could not fail. The objective is to eliminate erroneous concepts supported by false assumptions and by the use of incorrect values for velocity, mass, and column resistance. The only complete hypothesis of the global collapse mechanism of the Towers is a successive flattening of stories associated with compressive column failure and referred to as a Progressive Column
Failure mode or PCF in brief. (In the past this mode was often referred to as pancaking, but this term is not used here to avoid ambiguities). It is explained here why PCF could not be the mode of the ultimate destruction. The previously published material is quoted and the new points are brought up. Appendix Ccan be of interest to those who want a broader description of facts associated with the collapse. The available information relating to the kinetics of the collapse is summarized first.

THE FIRST PHASE OF DOWNWARD MOTION
A good comparison between various collapse models and reality makes it necessary to have some observations of the towers during collapse. To our knowledge, the most accurate and reliable data available are provided by video footage taken by Etienne Sauret [7], and used in the documentary film WTC: The first 24 hours. This footage clearly shows the top of WTC 1, including the roofline, for about the first 3.2 seconds of the collapse. Each pixel represents 0.27 m of the tower, and the frame rate is 30 per second, allowing for fairly accurate measurements of the motion. It is
unfortunate that the roof line is visible for only 3.2 seconds before disappearing into a dense cloud of debris, but these few seconds are, in fact, quite informative.

Now, let us have a look at the numerical values. The velocity of the falling roof of the North Tower was measured in [7] and the initial phase over the first 1.4 seconds is shown in Figure 1.The averaged acceleration during the early phase of the fall (shown as the slope of the velocity curve in Figure 1) was approximately 5.11 m/s2. The resulting velocity after 1.2 seconds of the fall, which is the approximate time for a fall of one story (3.7 m), is 6.13 m/s (13.71 mi/h).

For comparison, we note that a free drop (acceleration of 9.81 m/s2) of an object from a height of 3.7 m takes 0.869 s and the peak velocity reached then is 8.52 m/s. The total height of the tower was 417 m and the time needed for a free drop from that height was 9.22 s, while the end velocity of the dropping object would reach 90.45 m/s. If the drop is counted to only the top of mezzanine, at 21.33 m above ground (a notional top of the rubble heap), then the time is only 8.98 s.

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