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by Major_Tom » Fri Apr 09, 2010 1:58 pm
by Major_Tom » Fri Apr 09, 2010 1:59 pm
by Major_Tom » Fri Apr 09, 2010 2:00 pm
by Major_Tom » Fri Apr 09, 2010 2:01 pm
by Major_Tom » Fri Apr 09, 2010 2:02 pm
by Major_Tom » Fri Apr 09, 2010 2:03 pm
by Major_Tom » Fri Apr 09, 2010 2:10 pm
by Major_Tom » Fri Apr 09, 2010 2:10 pm
Table 5–1. Summary of main events that led to the collapse of WTC 1.
Event Number........ Event
1 .......................Aircraft impact
2 .......................Unloading of core
3 .......................Sagging of floors and floor/wall disconnections
4........................Bowing of the south wall
5 .......................Buckling of south wall and collapse initiation
Bowing of South Wall
The exterior columns on the south wall bowed inward as they were subjected to high temperatures, pull-in forces from the floors beginning at 80 min, and additional gravity loads redistributed from the core. Figure 5–6 shows the observed and the estimated inward bowing of the south wall at 97 min after impact (10:23 a.m.). Since no bowing was observed on the south wall at 69 min (9:55 a.m.), as shown in Table 5–2, it is estimated that the south wall began to bow inward at around 80 min when the floors on the south side began to substantially sag. The inward bowing of the south wall increased with time due to
continuing floor sagging and increased temperatures on the south wall as shown in Figs. 4–42 and 5–7. At 97 min (10:23 a.m.), the maximum bowing observed was about 55 in. (see Fig. 5–6).
Buckling of South Wall and Collapse Initiation
With continuously increased bowing, as more columns buckled, the entire width of the south wall buckled inward. Instability started at the center of the south wall and rapidly progressed horizontally toward the sides. As a result of the buckling of the south wall, the south wall significantly unloaded (Fig. 5–3),
redistributing its load to the softened core through the hat truss and to the south side of the east and west walls through the spandrels. The onset of this load redistribution can be found in the total column loads in the WTC 1 global model at 100 min in the bottom line of Table 5–3. At 100 min, the north, east, and
west walls at Floor 98 carried about 7 percent, 35 percent, and 30 percent more gravity loads than the state after impact, and the south wall and the core carried about 7 percent and 20 percent less loads, respectively. The section of the building above the impact zone tilted to the south (observed at about 8°,
Table 5–2) as column instability progressed rapidly from the south wall along the adjacent east and west walls (see Fig. 5–8), resulting in increased gravity load on the core columns. The release of potential energy due to downward movement of building mass above the buckled columns exceeded the strain
energy that could be absorbed by the structure. Global collapse ensued.
Tower began to collapse – first exterior sign of collapse was at
Floor 98. Rotation of at least 8 degrees to the south occurred before
the building section began to fall vertically under gravity.
3. Collapse Initiation
• The inward bowing of the south wall induced column instability, which progressed rapidly horizontally across the entire south face.
• The south wall unloaded and tried to redistribute the loads via the hat truss to the thermally weakened core and via the spandrels to the adjacent east and west walls.
• The entire section of the building above the impact zone began tilting as a rigid block (all four faces; not only the bowed and buckled south face) to the south (at least about 8º) as column instability progressed rapidly from the south wall along the adjacent east and west walls.
• The change in potential energy due to downward movement of building mass above the buckled columns exceeded the strain energy that could be absorbed by the structure. Global collapse then ensued.
Buckling of South Wall and Collapse Initiation
The inward bowing of the south wall increased as the post-buckling strength of bowed columns continued to reduce. The bowed columns increased the loads on the unbuckled columns on the south wall by shear transfer through the spandrels. Consequently instability progressed horizontally, and when it engulfed the entire south wall, it progressed along the east and west walls. Moreover, the unloading of the south wall resulted in further redistribution of gravity loads on the south wall to the east and west walls and to the thermally weakened core via the hat truss. At 100 min, the north, the east, and the west walls at Floor 98 carried about 7 percent, 35 percent, and 30 percent more gravity loads than the state after impact, and the south wall and the core carried about 7 percent and 20 percent less loads, respectively. The section of the building above the impact zone began tilting to the south at least about 8° as column instability progressed rapidly from the south wall along the adjacent east and west walls, as shown in Fig. 9–13. The change in potential energy due to downward movement of building mass above the buckled columns exceeded the strain energy that could have been absorbed by the structure. Global collapse ensued.
Finding 26: The WTC 1 building section above the impact and fire area tilted to the south as the structural collapse initiated. The tilt was toward the side of the building that had the long span floors. Video records taken from east and west viewpoints showed that the upper building section tilted to the south. Video records taken from a north viewpoint showed no discernable east or west component in the tilt. A tilt to the south of at least 8 degrees occurred before dust clouds obscured the view and the building section began to fall downwards.
Review of Causes of WTC Collapse
Although the structural damage inflicted by aircraft was severe, it
was only local. Without stripping of a significant portion of the
steel insulation during impact, the subsequent fire would likely
not have led to overall collapse (Bažant and Zhou 2002a; NIST
2005). As generally accepted by the community of specialists in
structural mechanics and structural engineering (though not by a
few outsiders claiming a conspiracy with planted explosives), the
failure scenario was as follows:
1. About 60% of the 60 columns of the impacted face of framed
tube (and about 13% of the total of 287 columns) were severed,
and many more were significantly deflected. This
caused stress redistribution, which significantly increased the
load of some columns, attaining or nearing the load capacity
for some of them.
2. Because a significant amount of steel insulation was stripped,
many structural steel members heated up to 600°C, as confirmed
by annealing studies of steel debris (NIST 2005) (the
structural steel used loses about 20% of its yield strength
already at 300°C, and about 85% at 600°C (NIST 2005);
and exhibits significant viscoplasticity, or creep, above
450°C (e.g., Cottrell 1964, p. 299), especially in the columns
overstressed due to load redistribution; the press reports right
after September 11, 2001 indicating temperature in excess of
800°C, turned out to be groundless, but Bažant and Zhou’s
analysis did not depend on that).
3. Differential thermal expansion, combined with heat-induced
viscoplastic deformation, caused the floor trusses to sag. The
catenary action of the sagging trusses pulled many perimeter
columns inward (by about 1 m, NIST 2005). The bowing of
these columns served as a huge imperfection inducing multistory
out-of-plane buckling of framed tube wall. The lateral
deflections of some columns due to aircraft impact, the differential
thermal expansion, and overstress due to load redistribution
also diminished buckling strength.
4. The combination of seven effects—(1) Overstress of some
columns due to initial load redistribution; (2) overheating
due to loss of steel insulation; (3) drastic lowering of yield
limit and creep threshold by heat; (4) lateral deflections of
many columns due to thermal strains and sagging floor
trusses; (5) weakened lateral support due to reduced in-plane
stiffness of sagging floors; (6) multistory bowing of some
columns (for which the critical load is an order of magnitude
less than it is for one-story buckling); and (7) local plastic
buckling of heated column webs—finally led to buckling of
columns (Fig. 1(b)). As a result, the upper part of the tower
fell, with little resistance, through at least one floor height,
impacting the lower part of the tower.
by Major_Tom » Fri Apr 09, 2010 2:14 pm
by achimspok » Sat Apr 10, 2010 9:34 pm
gif of earliest antenna movement
http://img143.imageshack.us/img143/6538/0500tilt.gif
Angular movement of antenna from NE, measured by tracking 2 points on the antenna.
http://img215.imageshack.us/img215/2258/tiltangle.png
(vertical scale is wrong. Shape of plot is correct. Scale should be stretched 25%)
by David B. Benson » Sat Apr 10, 2010 11:34 pm
by achimspok » Sun Apr 11, 2010 12:30 am
by David B. Benson » Sun Apr 11, 2010 12:55 am
Ok, that'll do. What I would like is an estimate of the number of meters.achimspok wrote:It's partially caused by tilting south and partially by concave roof deformation.
by achimspok » Sun Apr 11, 2010 8:11 am
by Major_Tom » Sun Apr 11, 2010 7:08 pm
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