Quote (ZingerSupreme @ Sep 11 2012 06:53pm)
i understand enough and ill get back on that, cant check it now link blocked at work.
i have a feeling it just says that basically things got hot and the steal lost some strength without actually explaining how the steal could absorb so much heat in the circumstances.
The Question of the Fires
One aspect of the WTC collapse events that we have not, as yet, included in our
calculation is the destructive energy inputs from the explosion and combustion of the fuel
carried by each impacting aircraft. Let us therefore briefly consider jet fuel as an
additional source of energy in the WTC collapse.
We shall assume that each Boeing 767 aircraft was carrying about 30,000 kg of
jet fuel when it crashed. In addition we estimate that for the spectacular fireball that was
seen after each aircraft impact, 75 % occurred outside the struck tower, and 25 %
occurred inside. Now, because the heat of combustion of jet fuel is 42 MJ/kg, we might
conclude that ¼ 30,000 42 10
6
J = 315 Gigajoules of energy was supplied to each
WTC tower by the jet fuel. However, it is likely that inadequate mixing of air and fuel
occurred inside each tower resulting in a fuel-rich vapor cloud at the time of ignition. It
follows that only a small fraction of the available combustion heat was actually dissipated
by the jet fuel explosion. A detailed study of hydrocarbon vapor cloud explosions has
been published by K. Gugan /9/. This author has shown that for the deflagration of large
quantities of flammable liquids, the explosive efficiency or yield is typically only 5 %.
This implies that the fireball caused by each WTC aircraft impact involved a 16
Gigajoule acute release of blast energy inside each tower. The jet fuel that remained
inside each tower after the initial fireballs burned rapidly but started longer lasting fires
and is discussed further below.
K. Gugan’s data (See /9/), scaled to 7,500 kg of exploding jet fuel, indicate a
value of about 2 10
5
Pa for the maximum overpressure at the center of the jet fuel
explosions. This blast overpressure would have caused considerable damage to office
furniture, wallboards, ceiling tiles and windows on the impacted floors; however, 2 10
5
Pa of blast pressure is insufficient to have seriously affected the structural steel support
columns. This conclusion justifies the exclusion of the jet fuel explosions from our
energy transfer calculations.
While on the topic of explosions at the WTC on September 11
th
, 2001, it is worth
considering an observation that some researchers consider to be evidence of the use of
explosives in the collapse of the twin towers. For example, E. Hufschmid in his book
Painful Questions (See Ref/1/) discusses the fact that the collapsing towers spewed out
horizontal jets of dust and asks: “How could (this dust) be ejected with such a high
velocity that the clouds reached 200 to 400 feet?” Hufschmid concludes that “packages
of explosives installed on nearly every floor” must have been used! However, careful
consideration of the WTC collapse mechanism offers an alternative explanation for the
ejected dust that eliminates the need for explosives.
Thus, based on the dimensions of each WTC tower, there were 10,000 m
3
of
“open space” per floor. The collapsing floor acted like a giant piston compressing the air
occupying the open space between floor and ceiling. The pressure build-up would have
shattered windows almost immediately, expelling the enclosed air. However, the process
Why Did the Towers Fall?
We have shown in this report that because of the failure of just one floor, a
sequential collapse of all remaining floors was inevitable. This, of course, brings us to the
$64,000 question:
What caused the initial floor collapse?
Although some researchers apparently find it difficult to accept, I believe the answer to
this question is essentially quite simple:
The initial floor collapse occurred due to the aircraft impact damage
and the resulting eccentric loading of the core columns.
Before elaborating on this statement, let us first deal with another potential factor in
the twin tower’s collapse: the weakening of critical floor supports by heat from the jet
fuel fires. While this may have been a contributing factor, I do not believe that we need to
invoke anything as extreme as the melting of structural steel in the WTC to explain why
the towers collapsed. The smoky appearance of the fires suggests that the flames inside
each tower were fuel-rich and therefore probably below 900 C. In addition, the structural
steel was heated indirectly and entire columns probably never attained temperatures
much above 750 C. Nevertheless, ~ 20 % loss of strength is to be expected for steel
heated to 550 C, a temperature that may have been reached by some WTC core columns.
Returning now to the reasons for the initial floor collapse in the WTC towers we
need to examine the forces required to support a particular floor in order to understand
how it could collapse. For example, consider the support columns at the 80
th
floor of
WTC 2. These columns experienced a downward force equal to M30 g, where M30 is the
mass of thirty floors. Hence the downward force at the 80
th
floor is 30 4.64 10
6
9.81
Newtons = 1366 MN. As noted in Section 4.2, the 236 perimeter and 47 core support
columns have an effective cross-sectional area of (236 0.0184 + 47 0.1236) m
2
=
10.15 m
2
. If we assume that the support columns are fabricated from high strength steel
with an effective compressive yield stress, y, of 400 MN/m
2
we conclude that the
supports at a given floor would fail if the downward compressive load exceeded about 4000 MN. Thus for the above example we see that the 80
th
floor has a collapse safety
factor of about 3 which is well within acceptable limits for modern high-rise buildings.
Now consider the 80
th
floor of WTC 2 after the aircraft impact. About 20 % of the
support columns have been destroyed and another 10 % may have been buckled to some
degree. The safety factor for collapse of the 80
th
floor is now only a little over two, but
apparently still sufficient to sustain the building almost indefinitely. However, the
damage to the twin towers was asymmetric so that the post-impact gravity load above the
impacted floor was no longer uniformly distributed. For WTC 2 the load normally carried
by the first two rows of columns in the southern-most corner of the core would have
shifted to undamaged columns in adjacent rows after the aircraft impact. The upper block
of 30 floors would have leaned (imperceptibly) to the south and would have created a
bending moment along the mid-core rows (comprising about ten columns). Immediately
prior to collapse the effective cross-sectional area supporting the 30 floors above the 80
th
floor would have been only about {(½ 200 0.0184) + 10 0.1236)} m
2
= 3.1 m
2
. We
would therefore expect the floor support to fail because a reaction force of 400 3.1 MN
= 1240 MN is significantly below the 1366 MN required to sustain the structure.
It should be noted that the critical loads estimated above have been treated as
purely compressive loads. However, it is well known from the theory of columns (See,
for example Chapter IX of Ref /10/), that even marginally eccentric loads are capable of
producing very large lateral deflections. If the deflection becomes large, the bending
moment and the stresses are also large and the elastic limit is exceeded resulting in
column failure. It is suggested that in the minutes after the aircraft impacts, localized
stresses were created within the tower’s support structures that gradually established the
conditions for the failure of at least one floor. The development of critical stresses in the
damaged areas of the towers will probably never be known in any great detail. However,
the conservative estimates of the magnitude of asymmetric loadings given above suggest
that aircraft damage alone was sufficient to initiate a total collapse of the buildings.
One final comment with regard to the causes of the WTC collapse is worth
making. It has been stated many times that the WTC towers were designed to withstand
the impact of a commercial aircraft with the weight and speed specifications of a Boeing
707 or 767. Indeed, a few observers find solace in the fact that both towers survived the
impacts for as long as they did. This has led some commentators to assume that simply
because the WTC towers were claimed to be plane crash resistant their collapse must
have been triggered by explosives or some other destructive devise. The logical flaw in
this argument stems from the difference between what one may claim to be true and what
subsequently proves to be true. Evidently the design calculations on which the
crashworthiness of the WTC was based were in error. The infamous Titanic disaster was
also an accident that “could not happen”. However, even though the Titanic failed to live
up to its “unsinkable” billing, no one has seriously proposed that its loss was due to
explosives hidden somewhere on board that ill-fated ship. Unfortunately the twin towers
had an Achilles’ heel that was finally revealed to the world on September 11
th
, 2001.