Posted by ngon nguyen on September 28, 2001 at 10:37:48:
I posted this article on Sept 25,01, since then I edit it and add some figures which I will post immediately after this, because it is a pdf file which needs Acrobat reader to open it.
Here is my theory about WTC collapse:
WTC has two towers of 1368 & 1362 foot tall with 110 floors each. In plan, each tower has a square shape of 209 foot each side. Its perimeter is a framed tube built from box columns of 18 ¾-inch wide at 3’-3” center-to-center with 48-inch-deep girders at each floor (beam-column frame on the perimeter). Note: The columns are at 3'-3" center-to-center for 4th floor and above. At third floor level, the columns transitioned in an arch-like formation, similar to Jewish candlesticks, to a 10'0" spacing for the lower stories. This is understandable because of the commercial requirements at lower levels. The effect of closely spaced of columns at higher floors make people feel as though there is no windows.
Frame tubes are among the most widely used structural systems for providing lateral stability and lateral loading in tall buildings. This system has been used successfully in many of the world tallest structures. However, the efficiency of the framed tube is limited by two factors:
1. Shear lag in the flanges of the tube reduces the effectiveness of columns away from the corners;
2. The axial stiffness of columns in the webs of the tube, especially the columns well away from the corners, is not used effectively for resisting lateral load.
To overcome this and to increase the stiffness, the viscoelastic damper (figure 1) was conceived and developed as a part of the structural design for the twin towers of WTC. They are an integral and an essential part of the structural system, being designed to assist the tubular steel frame in limiting wind-induced building oscillation ( and reducing vortex shedding) to levels below human perception.
Each of the two towers employs approximately 10,000 viscoelastic dampers ( a product of 3M company). The dampers are distributed evenly throughout the buildings (about 100 on each floor- from the 10th to the 100th floor). They are located between the lower chords of the horizontal trusses and the columns of the outside wall. Upon oscillation of the building there is a relative motion between the lower chord of the truss (point A of figure 2) and a column (point B of figure 2) on the building perimeter. (Note this also means the top chord will rotate relatively to the perimeter column). This motion generates shear deformation in the viscoelastic part of the damper thereby dissipating a part of the energy of oscillation.
For vertical loads, besides the perimeter columns there are rows of columns at the center core (89 foot x 139 foot) surrounding all the elevators. Steel Joists are employed to carry lightweight concrete deck spanning between the perimeter columns and the center core columns. These Steel Joists are trusses made out of angle irons (L-shaped rolled steel). Their top chords are connected or the whole truss is supported by a small shear plate welded to the columns. (The truss has an inverted trapezoidal shape). Theoretically, These plates are to carry shear only however because of the welding, there is some restraint against rotation. As mentioned above the perimeter column rotates relatively with the top chord, thereby inducing bending in the shear plate. The shear plate is under combined shear and bending, is subject to cyclic wind loading all the time.
As the airplane strikes the tower and fire is started. The elevator shafts acted as a flue spreading the fire to all floors and the top floors will eventually become the hottest. The viscoelastic system is destroyed first because they are made out of rubber. Thereby more rotation between the top chords and the perimeter columns combined with heat leading to the shear plate failure. One floor fails leads to another and so on. This is a progressive failure and a DESIGN FLAW!!! Had the designer paid attention to his detail and the possible failure mechanism, progressive collapse could have been avoided. Had in place of the shear plate a true hinge (such as a door hinge where rotation will not severe its shear capacity) been designed the progressive failure would not happen. Another point well worth mentioned is the effect of heat on certain structural components of the tower:
1. Up to a temperature of about 100 degree C, there will be no significant loss of chemically combined water even with a prolonged exposure to this temperature. As the temperature rises above 100 degree C, there is a gradual loss of chemically combined water from the calcium silicate hydrates. There is a drop in the strength of the concrete corresponding to the amount of water lost. Above 400 degree C concrete would become powder. At this temperature, the calcium silicates commence to decompose into quicklime and silica. This process is irreversible and there is a progressive loss of strength with time.
2. Artificial lightweight aggregates, such as expanded clay and shale, sintered pulverized fuel ash, and blast furnace slag, are manufactured at temperatures above 1000 degree C and are very stable at temperature below this level.
3. The effect of temperatures up to about 700 degree C on the strength and ductility of mild steel and hot rolled high yield steel is negligible from practical point of view.
4. Most dampers will not survive at the temperatures above 100 degree C.
About the failure modes I have the following observations:
1. The South Tower was hit by the second plane at its Northeast corner of about the 60th floor. It fell first like a tree combined with the progressive collapse. As noted above the corner is very important in resisting the lateral loads.
2. The North Tower was hit by the first plane at about 90th floor. It fell later vertically, by progressive collapse, rather than falling over.
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