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This article describes the structure of the World
Trade Center Twin Towers and what happens when the
release of potential energy, due to downward movement of
the mass above one of its supporting columns when buckling,
exceeds the strain energy that can be absorbed by the
same column below. The conclusion is that no global collapse
of the Towers can ensue under the given circumstances. The
web page is intended for children and amateurs of skyscraper
design who want to get a better understanding of the world
around us. The writer is a
structural engineer for Heiwa
Co albeit in the shipbuilding and very big
oil tankers sectors but the principles of structural design
and analysis are the same.
0. The false theory and the misleading
assumptions
An American professor Z P Bazant published soon
after the WTC collapses 911 a theory
that was adopted by the authorities as true. The Bazant
analysis is that if prolonged heating caused the
majority of columns of a single floor to lose their load
carrying capacity, the whole tower is doomed. Bazant
suggests there are five stages until the doom! I quote from
his paper.
Stage 1: The conflagration, caused by the
aircraft fuel spilled into the structure, causes the steel
of the columns to be exposed to sustained temperatures
apparently exceeding
800° C. The heating is probably accelerated
by a loss of the protective thermal insulation of steel
during the initial blast.
Evidently it was not possible that all 47 core and 236
wall columns in the initiation area - one floor 4 000
m² large - sustained temperatures exceeding
800° C! Later examinations show that only a few
parts may have been heated max 500° C temporarily and
locally. So the assumption about apparent temperatures
exceeding 800° C is misleading.
Stage 2: At such temperatures, structural steel
suffers a decrease of yield strength and exhibits
significant viscoplastic deformation i.e., creep - an
increase of deformation under sustained load! This leads to
creep buckling of columns which consequently lose
their load carrying capacity!
It is correct that heat affects steel material properties
as shown in 5. below
but if it contributed to the collapse is not ascertained. No
column from the initiation area that had lost its load
carrying capacity was found in the rubble. The local
temperatures were later established to temporarily and
locally have been max 500° C and the loss of load
carrying capacity is then not critical. So the assumption
about loss of load carrying capacity is also is
misleading.
Stage 3: Once more than half of the columns in
the critical floor that is heated most suffer buckling,
the weight of the upper part of the structure
above this floor can no longer be supported, and
so the upper part starts falling down onto the lower part
below the critical floor, gathering
speed until it impacts the
lower part. At that moment, the upper part has acquired an
enormous kinetic energy and a
significant downward velocity.
As shown in 3.2 below the
static compressive stresses in the supporting structure
below was less than 0.3 x yield. If you remove uniformly
half the supports evidently the supporting structure below
will be stressed to 0.6 yield. So the assumption about the
weight above not being supported by half of the columns is
also misleading. And no buckling of any kind will occur at
0.6 yield stress compression!
Evidently more than half of the columns were never heated
at all to any critical level as seen on videos. The outer
walls were only locally and temporarily affected by fire.
Nevertheless, assuming that more than half of the columns
are simultaneously affected by heat, do these columns
actually bend, twist or crumple up? Why do they not only
compress more, while transferring the load to adjacent
columns that still have ability to carry it? Why would the
part (mass) above the heat affected column actually
gather speed? The column parts are still connected.
Why would the upper part and its mass impact the
lower part?
What is the kinetic energy of the mass above? Why is it
enormous kinetic energy? In 5.3
below it is shown that the energy could not have exceed 340
kWh in WTC1 which corresponds to abt 40 kgs of diesel oil!
It is not an enormous amount of energy. So the assumption
about enormous kinetic energy is also misleading.
And what is the significant downward
velocity? In 5.4 below
it is shown to be about 3 m/s or 10 km/h which is a very low
speed that would not kill anybody in a car collision. So the
assumption about significant downward velocity is also
misleading.
All videos - live forensic evidence - of the collapse
however show that the upper part above the initiation zone
actually disintegrates within 3,5 seconds after the roof
starts to fall, so there is no rigid mass above to act on
the structure below after that. The debris of the upper
part is actually thrown outwards between intact wall
columns at the initiation zone and produces a smoke and dust
screen that hides the destruction of the lower part that
starts after 5 or 6 seconds. The impact is indeed very
strange
Stage 4: The vertical
impact of the mass of the upper
part onto the lower part applies
enormous vertical dynamic load on the
underlying structure, far exceeding its load
capacity, even though it is not heated.
This event is not proven at all. Does really the mass
of the upper part with 200+ deformed columns at its
bottom acting as a damping device vertically impacts on the
lower part? There is no evidence for that as outlined in
5.6 below. What is the
enormous vertical dynamic load of the upper part?
What is the load capacity of the underlying, not
heated part? It will be shown in 7.
below that if the underlying structure is regarded as a
spring, it will only compress max 78 centimeters due to an
instantaneous vertical impact! And then bounce back! This is
logical! The impact speed is low and the kinetic energy
compressing the structure is very low and the structure
below behaves elastically. So the assumptions about
enormous vertical dynamic load and the deficient load
capacity of the underlying structure are also
misleading.
Stage 5: This causes failure of an
underlying multifloor segment of the tower, in
which the failure of the connections of the floor-carrying
trusses to the columns is either accompanied or quickly
followed by buckling of the core columns
and overall buckling of the framed tube
(i.e. the wall columns),
with the buckles probably spanning the height of
many floors, and the upper part possibly getting
wedged inside an emptied lower part of the framed tube! The
buckling is initially plastic but quickly leads to fracture
in the plastic hinges.
It is not clear why the alleged impact - an upper part
with deformed columns below hitting a lower part with intact
floors and columns - would cause the underlying floors to
disconnect from the underlying columns? The floors are
bolted to the columns. How can a column that has deformed
previously above then deform a column below ... over the
height of many floors? Why do not the columns above simply
punch a hole in the floors and get entangled with the
columns below and their spandrels? Stage 5 is very strange
and not recorded on any video. So the assumption about
failure of an underlying multifloor segment is not
obvious.
Stage 6: The part of building lying beneath is
then impacted again by an even
larger mass falling with a
greater velocity and the
series of impacts and failures then
proceeds all the way down.
Are actually any further impacts seen on any videos of
the videos?
It will be shown in this article that most assumptions
and conclusions in stages 1-5 are not correct and that the
Bazant stage 6 is not possible.
1. Introduction - a bird cage
The structural design of the World Trade Center Twin
Towers is very simple as its very lightweight steel
framework is similar to a box shaped bird cage in which
human beings are working. Most skyscrapers or office towers
in the world are built according similar principles. None
has ever globally collapsed in seconds before or after 911
except WTC 1, 2 and 7.
1.1 The bird cage wall bars and their
spandrels
The vertical bars of the cage walls correspond to the
outer wall steel columns of the Towers and are continuous
from bottom to top (albeit 3 wall columns become one at the
bottom of the Towers). The cage wall vertical bars are
horizontally interconnected at regular levels by spandrels
(a word that I cannot find in my Advanced Learner's
Dictionary of Current English but probably has Latin
origin - spandrilla? - used to support the ceiling of, e.g.
the Sistine chapel at the Vatican) that are simple steel
brackets. The spandrels act as belts around the bird cage
that can prevent transverse (outward/inward) deflections of
the wall bars. The spandrels will then be in
tension/compression. On top of the cage is a roof. Inside
the cage are floors fitted bolted to the walls. These floors
also prevent transverse deflections.
1.2 The floors
To better use the volume of the cage 110 off floors were
installed in it at regular intervals. The WTC floors were
also very simple. A floors consists of about 4 inch of
concrete poured on a thin plate of steel supported by
lightweight trusses (beams) bolted to the columns, as you
cannot glue concrete floors to the cage walls and core. Thus
every wall column also carried a portion of the load of the
floors.
The floors can only carry its weight + furniture,
decorations and human beings on the floor. If a floor is
overloaded for any reason, it will sag and the concrete will
fracture in small pieces and the bolted connections to the
columns will shear off. A dislocated column will simply only
punch a hole in a floor.
1.3 The core columns
47 off box or I-shaped columns were installed inside the
cage at its core - core columns to which the floor trusses
were also bolted. The core columns reduce the span of the
floor trusses,
A core column is similar to a wall column with dimensions
tapered from bottom to top like a flag pole. It only carries
its own weight + the load on the floors connected to it. The
core columns are interconnected with spandrel like beams at
regular intervals. Evidently you fit elevator shafts,
vertical cable/pipe/ventilation trunks and stairwells
adjacent to the core columns.
1.5 The cage mass - volume wise most air
It should be clear that 94-96% of the volume of the bird
cage consists of air and that 100% of the cage mass/load is
carried in the vertical columns down to ground.
A column only carries its own weight + the load on the
floors connected to it and the roof. At the bottom or ground
level the columns thus carry the whole load of the column
above and are tapered to smaller dimensions at the top only
to carry the roof.
The compressive stress due to weight (mass) of a column
is therefore uniform from bottom to top and well below any
critical stress (yield or buckling) that is shown below.
1.6 Redundancy
The cage has very large redundancy, i.e. surplus strength
due to the spandrels. You can remove a big number of columns
or floors at any location (e.g. a plane or other object
crashes into the cage or a small bomb goes off and makes a
hole in the cage!) and nothing happens, as the compressive
load in the removed columns is transmitted via the spandrels
to adjacent intact columns and down to the ground.
1.7 Total mass of the Tower
Information about the total mass of the Tower differs
from 250 000 to 500 000 tons but is of little importance.
The Towers were sturdy and had survived many storms, etc.
even if they then were subject to transverse deflections of
several meters at the top. No defects were reported for 30+
years. The Towers also survived the initial impacts of
planes on 911 due to their redundancy. When the Towers
collapsed there were no storm wind forces acting on
them.
1.8 Simplifications
In order to study the collapse of the Tower cage
structure it is easiest and most educational just to look at
one of the wall columns and one of the core columns of the
cage. The compressive load in these columns is the sum of
the load from the bolted floor truss connection at every
floor and the weight of the column itself above.
2. Collapse scenario and cause of collapse - buckled
columns
From NIST report - NISTNCSTAR1-6D chapter 5.2 - we
learn:
"The aircraft impacted the north wall of WTC 1 at 8:46
a.m. … between Floor 93 and Floor 98. … The
subsequent fires weakened structural subsystems, including
the core columns, floors and exterior walls. The core
displaced downward … At 100 min (at 10:28:18), the
north, east, and west walls at Floor 98 carried 7 percent,
35 percent and 30 percent more gravity load loads … and
the south wall and the core carried about 7 percent and 20
percent less loads, respectively., … At 10.28 a.m., 102
min after the aircraft impact, WTC1 began to collapse.
… The release of potential energy due to downward
movement of the building mass above the
buckled columns exceeded the strain
energy that could be absorbed by the structure. Global
collapse ensued."
From chapter 5.3 we learn:
"The aircraft … impacted the south wall of WTC 2
at 9.03 a.m. … between Floor 78 and Floor 84. …
(9:59 am) … The release of potential energy due to
downward movement of the building mass above the
buckled columns exceeded the strain
energy that could be absorbed by the structure. Global
collapse ensued."
Note that the two Towers collapsed for exactly the same
cause: The release of potential
energy due to downward
movement of the building mass
above the buckled columns
exceeded the strain energy that could
be absorbed by the structure.
"Buckled" of steel structure by definition
means bent, twisted or crumpled up and is the key word of
the NIST announced only cause/effect of the global
collapse.
Evidently a bent column does not result in much downward
movement unless it is bent 180° and then removed! A
twisted column does not result in any downward movement at
all. A crumpled up column, i.e. compressed into folds or
creases, produces downward movement but stops when
compression stops.
It is sad that NIST cannot produce any
"buckled" column of the initiation zones, be
it bent 180° or crumpled up, that would have produced
downward motion. We are talking about 566 columns that must
have "buckled" for the effect ... and none is
presented as evidence that potential energy was released for
that cause.
No complete building or steel structure has ever globally
collapsed in millions of pieces before or after 911!
Evidently steel structures may collapse and deform but it is
always locally and stops when the energy is absorbed or
diverted elsewhere. This paper is mainly about WTC1 and it
is necessary to have an idea of the initial damage to its
North wall and its 59 wall columns, allegedly due to an
airplane banking at 20° flying into it, as follows
(from Ms T
Mc Allister, NIST, 15 Sept. 2005):
As can be seen only about 38 of the wall columns were cut
(65%) over 4 or 5 floors and the wall did not buckle or
collapse. The loads in the cut columns were simply
transmitted to intact adjacent wall columns via the
spandrels and then to the East and West walls and the core.
This was not a serious damage. No potential energy was
released at this time. Some people even doubt the hole was
caused by a Boeing 767! It looks too small and the vertical
extent would indicate that the plane was travelling with one
wing much higher than the other, etc. This writer thinks the
hole is too large! The aluminium wing tips would never cut
through the steel wall columns but would be ejected,
bouncing backwards! It is a pity no broken parts of the
North wall were recovered in the rubble. They should have
been on the top of the rubble.
It may be interesting to know how the vertical
subsystems, i.e. the walls and core columns carried the
gravity load in WTC1 before (60/40 walls/core) and after
hole was made in the North wall and after 100 minutes of
fire in below table:
|
Subsystem
|
Original load distribution (%)
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Load distribution after hole made in North
wall (%) (estimated)
|
Load distribution change due to 100 minutes
of fire according NIST
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Load distribution after 100 minutes just
before global collapse (%)
|
|
North wall
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15
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7
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+7%
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7
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|
East wall
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15
|
17
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+35%
|
23
|
|
West wall
|
15
|
17
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+30%
|
22
|
|
South wall
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15
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15
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-7%
|
14
|
|
Core
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40
|
44
|
-20%
|
34
|
|
Total
|
100
|
100
|
0
|
100
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As can be seen from above table, just before global
collapse only the East and West walls carried more gravity
load than original. In 3.2
below it will be shown that this extra load would not
overload the columns in these walls.
2.1 The buckled columns
It is suggested in NIST report - NISTNCSTAR1-6D that all
the wall and core columns buckled simultaneously in the
impact area as they were affected by fire/heat 40-100
minutes later that reduced their strength (yield stress) and
caused subsequent overloading.
Even if this phenomenon is not seen on any video of the
collapse itself - instant forensic analysis - or in
the columns of the rubble afterward - post mortem
forensic analysis -, let's assume that our vertical cage
bars or columns buckled due to heat of the fire.
Buckling of the cage bar or column occurs, when the
compressive stress in the bar exceeds the critical buckling
or collapse stress of the bar. The critical buckling stress
is only a function of the slenderness ratio of the bar, its
cross area and material properties. Only the material
properties are affected by the heat but are virtually
unchanged between 20 and 500° C but let's assume that,
e.g. the yield stress is reduced by 20% (from say 248 to 200
MPa) at 500°C. The wall bar is obviously fitted in the
wall and cooled by external air and can never be heated very
much. That is why the wall perimeter steel columns were not
fire proofed but only fitted with normal heat insulation
against sun and winter weather below an external aluminium
cladding.
When the wall bar buckles, it will deflect sideways which
however is prevented by both the spandrels and the floors,
i.e. it can only buckle between these supports. Both
spandrels and floors keep our wall bar in vertical position
as long as they are intact. If the floor bolted connections
are sheared off and the unsupported length of the bar
between floors increases, the spandrels will still restrain
outward or inward deflection of our bar due to buckling.
Same applies to a core column.
2.2 Release of potential energy due to downward
movement
Downward movement of the mass above, i.e. the columns'
weight and the load of the floors attached to them are only
possible due to transverse deflection of the columns.
If the column does not deflect, there is no downward
movement of the mass above and thus no release of potential
energy.
3. Arrangements at floors 94-98 of WTC 1
Let's look at WTC1 and floors 94-98 - the initiation
zone. Total area of each floor is about 4 000 m².
A wall bar or column there is a box with side 300 mm and
wall thickness, say 12.5 mm. The cross area of the steel is
thus about 150 cm². The bar weighs about 120 kgs/m
incl. spandrels, i.e. is quite light. There are about 236
wall columns. Total cross area of all wall columns is then
3.54 m²
Let's assume that the total mass of the wall steel
columns above floors 94-98 is about 1 500 tons.
The highest loaded core columns are the outer ones, e.g.
number 501. It is an H-beam with two flanges 17x3.5 inch
connected by a 2.2x12.6 inch web. In metric terms the cross
area is about 950 cm², i.e. the bar is very solid. It
weighs 750 kgs/m.
There are 47 core columns most of them with less cross
area than the outer ones. Let's assume that total cross area
of all core columns is only 2.1 m², i.e. 60% of the
wall columns. Then the total mass of the core columns and
spandrels above floors 94-98 is about 900 tons. The core is
thus lighter than the perimeter wall.
A floor including furniture, etc is assumed to weigh
about 1 850 tons. The total mass of floors and the roof
above floors 94-98 is about 26 000 tons. Most of this weight
is in fact concrete poured on a thin corrugated steel plate
supported by trusses that in turn are bolted to the columns.
There are about 700 connecting bolts per floor. Let's
summarize the total mass above as follows:
3.1 Total mass above floors 94-98 - 33 000
tons
|
Steel wall columns
|
1 500 tons
|
|
Steel core columns
|
0 900 tons
|
|
Steel floor trusses
|
3 000 tons
|
|
Concrete floors
|
23 000 tons
|
|
Windows and misc.
|
4 600 tons
|
|
Total
|
33 000 tons
|
Note that less than 10% of the mass is steel in the
supporting columns and that as much as 70% is concrete. If
this mass filled the total volume of the building above the
initiation zone (190 000 m3), the uniform density
would be 0.18 ton/m3 or the density of cotton!
You could say that a big bale of cotton (mass above)
rested on the structure below!
This mass is carried about 60/40 by walls and core.
A floor can only transmit its own weight and load on top
of to the nearest column. A floor cannot transmit any major
load from a core column to a wall column and vice versa -
the bolts will then shear off or the trusses will tear
apart. The concrete just cracks! Wind loads on one wall may
be transferred by the floors to the opposite wall as
horizontal loads.
End of Part 1
Go to Part 2 it is
more interesting than Part 1 with videos that clearly show
what happens before downward motion starts, etc.
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