WTC collapse: the mystery beam

[ian neal]

Thanks to Kenyon for sending me this

http://www.gallerize.com/WINDY_TOWERS_OF_9-11_1.htm

[Wokeman]

CTS,
Oh, yes there is this:


Posts: 445
Location: Richmond Surrey
Posted: Sat May 06, 2006 11:35 pm Post subject: WTC collapse: the mystery beam
Thanks to Kenyon for sending me this

http://www.gallerize.com/WINDY_TOWERS_OF_9-11_1.htm

[Poseidon]

The "600,000 lbs" was clearly an error, and possibly a deliberate attempt by the perpetrators to encourage irrational exuberance. Even if the beam were 100 feet long, 6,000 pounds per lineal foot is a cross-section of over 12 square feet, and more massive than the perimeter bifurcation columns ("trees") which ran from floors 4 to 9 on WTC 1 and 2. Some sceptics argue that the WTC collapses must have been controlled demolitions because the buildings virtually fell into their own footprint; others are saying there must have been bombs because some of the debris travelled too far.

According to FEMA 403 chapter 7, "The main WFC 3 building suffered damage from floors 17 through to 26. A three-story section of exterior column trees from WTC 1 hung from the base of the collapsed area at floor 20, as shown in figure 7-2, with approximately 25 feet of the column hanging outside the building". This would not have been the massive bifurcation columns ("trees"), since they would have had to ascend a minimum of 132 feet in addition to horizontal motion of 420 feet. These trees amounted to 3,400 tons per Tower (NIST appendix e Table E-10 or see my steel and concrete inventory here), and with some 20 trees per side over six storeys, 42.5 tons per 72-foot tree is 1180 pounds per lineal foot. Higher up, the most massive core columns were hundreds of pounds per lineal foot.

In order to allow time for lateral motion, the exterior column(s) that hit WFC 3 were most probably from the upper half of WTC 1. A fall from 1,000 feet to 240 feet would take SQR(2*h/g) = around 6.9 seconds where h = 760 feet and g = 32.17 ft/s^2. In the horizontal plane, a uniform acceleration of 20 m/s^2 for the first second followed by negligible deceleration due to drag for the remaining 5.9 seconds would provide 10 + (5.9 * 20) = 128 metres = 420 feet displacement. At 1,000 feet the WTC 1 perimeter columns, per story, were comprised of:

two flanges of 1/2 x 13.5 x 144 inches each, totalling 1,944 ins^3
one outer web of 1/4 x 13 x 144 inches = 468 ins^3
one inner web of 1/4 x 15.75 x 92 inches = 362 ins^3
one spandrel plate of 3/8 x 40 x 52 inches = 780 ins^3

...totalling 3,554 ins^3 per floor or 10,662 ins^3 = 6.17 ft^3 for a three-floor section which at 490 lb/ft^3 is 3,023 lb (84 pounds per lineal foot) or 1,371 kg. (There is some uncertainty as to the flange thickness; it was known to be only 1/4" at the very highest floors.) The force require to produce an acceleration of 20 m/s^2 in an inertia mass of 1,371 kg is 20 * 1371 = 27,420 N = 6,165 lbf.

The cross-section presented to a wind, per floor, would be 40 x 52 = 2,080 ins^2 for the spandrel plate and 15.75 x 92 = 1,449 ins^2 for the inner web, totalling 3,529 ins^2 per floor or 10,587 ins^2 = 6.83 m^2 for a three-story section of exterior column. (So the required pressure is well under 1 psi.) From the drag equation of

d = Cd * A * r * 0.5 * v^2

we obtain

v = SQR(2 * d / (Cd * A * r))

where r = density of air ~ 1.2 kg/m^3 and assuming a relatively high drag coefficient Cd of 4 / pi ~ 1.27 for a flat plate and d = the previously calculated force of 27,420 N and A = 6.83 m^2 as calculated above. This places the required wind at 72.6 m/s = 162 mph for one second duration. Actual windspeed on the day was up to 10 mph on the ground and up to 20 mph at higher altitude.

Suppose we imagine the collapse initiating at 1,200 feet, and proceeding as per the "pancaking" theory to 1,000 feet. After freely falling 200 feet, the terminal velocity would be SQR(2 * 200 * 32.17 ft/s^2) = 113.4 fps = 77.3 mph. In this theory, there is a small delay due to resistance of the intact building below, but the falling upper section smashes its way through each floor in about 0.1 seconds at the 1,000 feet level. The volume of air per floor is approximately 12 * 200 * 200 feet = 480,000 ft^3. Some will go down, but if the total was forced out through a perimeter of 800 feet by an average height of 6 feet which is an exiting area of 4,800 ft^2, it would (continuing outward) extend for some 100 feet at the end of the 0.1 seconds which is a velocity of 1,000 fps or 682 mph.

Let's set the exiting gases velocity at just 700 fps = 213 m/s, in which case the force acting on the exterior column for 0.1 seconds is given by:

d = Cd * A * r * 0.5 * v^2

= 1.27 * 6.83 * 1.2 * 0.5 * 213^2 ~ 236,000 N

to produce an acceleration of F / m = 236,000 N / 1,371 kg = 172 m/s^2. After 0.1 seconds the velocity of the steel is 17.2 m/s = 38.5 mph, and the horizontal displacement is 0.86 metres. Following another 6.8 seconds at 17.2 m/s the total distance travelled horizontally is 0.86 plus 6.8 * 17.2 ~ 118 metres = 387 feet. The columns have to shear off quickly enough, and the pancaking theory has the problem that the gravitational potential appears to be too low for all the energy sinks, but even this scenario does not appear to rule out the idea that debris could end up a few hundred feet away.

Another possibility is that the upper section of the building starts to tilt, gathers some angular momentum, and then debris breaks off with sufficient horizontal velocity to travel hundreds of feet. WTC 2's upper section fell to the south and east, although the lower section fell to the north and west and there could have been sufficient clearance to avoid WTC 1 and hit the corner of WFC 3. FEMA said the column which hit WFC 3 was from WTC 1, so it may have tilted sufficiently to the west.

A better argument for controlled demolition is based on the fact that collapses did occur and were ultimately blamed on "fires". The Monokote fire resistive coating in WTC 7 was all intact since the building was not even hit by a plane. For WTC 1, the vertical approach angle of Flight 11 was about 10 degrees (downwards). The width of the zone where fireproofing on the trusses' bottom chords could have been compromised by impacting debris would have been barely more than 18 feet (from the diameter of the fuselage). The "length" inwards (beyond the zone where a floor was completely collapsed) was determined by:

height of trusses (29 inches) / tan [10 degrees] = 164 inches, say 14 feet. Outside of this 14 x 18 foot strip which is 252 feet^2 or some 0.6% of the total 43,264 ft^2 floor area, most of the fireproofing was protected from impacting debris by four or five inches of solid concrete, and where part of a floor had already collapsed or a member had been taken out, the fire would not have made any difference. Wing debris would not have added significantly to the 0.6% area. A couple of floors might have seen some damage to the Cafco Blaze-shield coating in the immediate impact zone. But in any case, global collapse would have required the total removal of five floors, not two floors.

Hence, WTC 7 could not have collapsed and WTC 1 and 2 would have been exceedingly unlikely to have collapsed unless we propose a novel physics (or metaphysics) where the thermal conductivity of materials undergoes wild fluctuations (possibly under influence of the spirits of dead Muslims), or a new chemistry where the calorific value of fuels changes on a daily basis.