Posted by ngon nguyen on January 04, 2002 at 08:28:08:
On Sept 28, 2001, I posted an article about the WTC progressive collapse. I was able to point out the weak connections between the floor trusses and the columns within the Towers. Even though, Vortex Shedding is an important argument (As Mr. Reiss, a Port Authority official admitted in The New York Times on Dec 13, 2001 about the swaying of the buildings in the wind and the impact that elevator cables have against the beams especially during the months of March and April), it fails to explain two things:
· The collapse started from the very top and worked its way down.
· The floor slabs were pulverized.
There are many theories out there about melting and so on, but they all fail to explain why the top floors failed first even though they were not the hottest floors in the Towers.
As I was doing my Christmas shopping, I came across a toy called a RADIOMETER, which was originally invented by Sir William Crookes in the mid-nineteenth century. This toy demonstrates the ability to convert light energy into mechanical energy, which in turn rotates the vanes in a near vacuum environment (95 % vacuum with very few air molecules). Intrigued by this during my vacation, I went through my daughter's high school Chemistry textbook, keeping in mind that I still had unanswered emails to address concerning the WTC. Here is my new theory:
Recall the Gas Laws:
PV = n RT where
(Pressure) x (Volume) = (number of moles of gases) x (R, a constant) x (Temperature in Kelvins)
Kelvin = Celsius degree + 273.15 degrees Celsius
Standard air pressure @ 0 degrees Celsius and sea level = 1 atm = 14.7 psf
Standard air pressure @ 0 degrees Celsius and @ 1000 ft level = 0.95 atm
Assume that the ambient temperature on September 11th, 2001 was 0 degrees Celsius. If the Towers were heated to 275 degree Celsius by the combustion of the jet fuel while everything else remained constant, we would have a differential pressure (P) between inside and outside of the Towers of about 15 psf. While the Towers were heated, the fires also turned the furniture, appliances, building materials, etc. into many combustion gases. After a while, these gases diffused through the elevator shaft and filled all the top floors. Eventually, the number of moles of gases (n) would increase to, say, 4 times of the original air molecules in these top floors. In this scenario, the differential pressure between the inside and outside of the Towers would be 60 psf (4 x 15 psf).
From observations of the collapse of the Towers, we can assume that the window glass did not fail first (it can withstand a pressure of 60 psf). Therefore, the volume (V) remains constant. The differential pressure between the floors may be considered as very little or negligible. In addition, there is no rotation demand at the truss connection to the column. However, at the top floor, there is uplift to the roof deck and the roof truss of approximately 50 psf. (after subtracting the dead weight of the lightweight insulation concrete and steel deck which is 10 psf) Assume the deck tie down is designed for the uplift but there is problem with the roof truss: at this temperature, the VE dampers (viscoelastic dampers) are disconnected (see previous posting) i.e. the truss bottom chord is not braced. There are two possible failure modes:
1. At the connection of the truss to the column due to rotation demand (see previous posting).
2. The buckling of the bottom chord without horizontal bracing due to compression.
Once the roof is gone, the top floor will now be under the uplift of the differential pressure of 30 psf. (After subtracting the dead weight of structural lightweight concrete on steel deck of the floor of 30 psf. Assume the roof dead weight is ignored.) Because the deck tie down is not designed for this uplift and the structural concrete is not designed for the loading in the upward direction, the concrete will blow up in a sudden failure.
The same will happen to the next floor and so on..
There are lessons to be learned from this incident:
1. Every tall building should have an adequate vent on top of their elevator shafts to be opened at certain temperatures.
2. Do not use rubber derivatives as a primary supporting system in a building because it is impossible to fireproof this material. I am worried about the LA City Hall or similar buildings with base isolation design. On the other hand, it is OK for a bridge to be supported on an Elastomeric Bearing because it is in an open space.
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