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2.1 The false Theory and the misleading Assumptions An American professor Z P Bazant published soon after the WTC destructions 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 as illustrated in Fig. 1 below from the Bazant paper:
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 7.1 below but if it contributed to the collapse is not ascertained. No column from the initiation area that had lost its load carrying capacity and exhibited viscoplastic deformation 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 and viscoplastic deformation is also is misleading. Stage 3 (Crush down starts): Once more than half of the columns in the critical floor (floors 94-95 of WTC1) 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 (floor 95 of WTC1), gathering speed until it impacts the lower part (floor 94 of WTC1). At that moment, the upper part has acquired an enormous kinetic energy and a significant downward velocity. Note that upper block is assumed intact and aligned with the structure below. As shown in 7.4 below the static compressive stresses in the supporting structure were less than 0.3 yield stress. If you remove uniformly half the supports evidently the supporting structure below will be stressed to 0.6 yield stress. 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? There is plenty of resistance! The columns are still connected at both ends. Why would the upper part and its mass impact the lower part? What is the kinetic energy of the mass above with a mean density of 0.18 tons/m3? Why is it enormous? In 7.4 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 7.5 below it is assumed 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 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. 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 alleged 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. Note that upper block is still assumed intact and aligned with the structure below at this stage. This event is not proven at all. Does really the mass of the upper part with 280+ deformed columns at its bottom acting as a damping device vertically impacts exactly on the underlying structure? Are the columns of the upper part even aligned with the columns of the lower part so that they can meet in an impact? There is no evidence for that as outlined in 7.7 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 9.1 below that if the underlying structure is regarded as a spring, it will only compress max 78 centimeters due to an instantaneous vertical solid 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 and brakes the load applied and breaks the upper block. So the assumptions about enormous vertical dynamic load and the deficient load capacity of the underlying structure are also misleading.
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 any further impacts seen on of the videos? The upper block must then still be assumed intact and aligned with the structure below all the time. You need kinetic energy, KE, for global collapse and it can only be provided by an intact, rigid, uniform density upper block that remains intact, rigid, with uniform density during the whole destruction of the lower structure. The upper block is the only part that can provide KE during the alleged global collapse. The lower structure does not add any extra KE to the collapse or contribute to the collapse as assumed by Bazant - it is being destroyed (lack of strain energy according NIST). Back to Summary!
3.1 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. 3.2 The Bird Cage Wall Bars and their Spandrels - primary Structure 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. The wall columns are primary structure to carry the load imposed on them down to ground. 3.3 The Floors - secondary Structure 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 bolted connections can only transmit forces to the columns. The floors only carry their weight + furniture, decorations and human beings on the floors. 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. The floors are secondary structure to carry the load imposed on them to the columns. 3.4 The Core Columns - more primary Structure 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 solid beams at regular intervals. Evidently you fit elevator shafts, vertical cable/pipe/ventilation trunks and stairwells adjacent to the core columns. The core columns are also primary structure to carry the load imposed on them down to ground. 3.5 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 primary structure 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. 3.7 Redundancy - difference between primary and secondary Structure The cage has very large redundancy, i.e. surplus strength due to the spandrels. You can remove a big number of primary structure columns or secondary structure 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. It should be noted that primary structure is much stronger than secondary structure as secondary structure only carry it local loads to the primary structure that in turn carries all the loads of the secondary structure. 3.8 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. 3.9 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 primary structure columns is the sum of the load from the bolted floor truss connection at every floor and the weight of the column itself above. Back to Summary!
4.1 Collapse Scenario and Cause of Collapse - buckled Columns - lack of Evidence 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, PE, due to downward movement of the building mass above the buckled columns exceeded the strain energy, SE, that could be absorbed by the structure. Note that NIST does not mention any 'impact'. "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):
4.2 The buckled Columns It is suggested in NIST report - NISTNCSTAR1-6D that all the wall and core primary structure 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 primary structure wall bar in vertical position as long as they are intact. If the secondary structure 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 primary structure core column. 4.3 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 (bending) or vertical crumpling up of the columns. If the column does not deflect or crumple up, there is no downward movement of the mass above and thus no release of potential energy. And definitly not an 'impact'. Back to Summary!
5.1 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: 5.2 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 in table left that less than 8% of the mass
is steel in the supporting primary structure
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 50/50 by walls and core. 5.3 Compressive Stresses in the primary Structure Columns - less than 1/3 of the Yield Stress The mass above the walls at floors 94-98 is thus about 16 500 tons supported by 236 wall columns (total cross area 3.54 m²). Therefore each wall column on average supports 70 tons. The compressive stress in the wall column at floors 94-98 with cross area 150 cm² is thus abt 467 kgs/cm² or 46 MPa or 18.8% of the yield stress (abt 248 MPa) of the steel. NIST suggests that the static loads will be increased 35% in the East wall and 30% in the West wall (all 100% intact) due to load transfers just prior collapse, i.e. the compressive stresses in columns there becomes 62.1 and 59.8 MPa, which is still only 25% and 24% if the yield stress. Actually these are the increased stresses you would expect due to wind under hurricane conditions. The mass above the core is also 16 500 tons supported by the 47 core columns with total area 2.1 m². On average each core column carries abt 351 tons so the average compression is 786 kgs/cm² or 78 MPa or 31.7% of yield. The outer core columns carry more mass and the outer corner core columns the most load, e.g. no. 501 with cross area 950 cm². It may carry as much as 750 tons. The compressive stress in the no. 501 core column at floors 94-98 is thus abt 789 kgs/cm² or 78 MPa or 31.7% of the yield stress of the steel. It is assumed that the compressive stress in the other core columns is abt the same or less. NIST suggests that the load in the core is reduced 20% just prior collapse, i.e. the stresses are reduced. However, some core columns may have been damaged in the initiation zone so in all probability the stresses in the remaining columns may have remained at 30% yield stress. The reason why original the static stresses are higher in the core than in the perimeter walls is that the wall columns are also designed to absorb dynamic wind loads. Back to Summary!
6.1 The Towers were built very strong in the 1960's The above is a clear indication how the Towers were originally built by serious architects and engineers in the 1960's. Compressive static stresses in the primary structure columns were less than 1/3 of the yield stress of the steel before (obviously) ... and after serious damage (not so obvious but shown here)! The buckling stress of the column is virtually the same as the yield stress as the columns were arranged with spandrels. One reason why the static stresses were so low was that the designers had no access to computers to optimize (slender down) the construction. Manual calculations were done and to be on the safe side you added steel and built strong! And steel was quite cheap at that time. And US steel was good quality. The assumed yield stress 248 MPa was probably much higher in reality. NIST never checked the yield stress of the steel from the initiation zone in the rubble! There was therefore plenty redundancy. A plane may crash into the bird cage and nothing happens. A big fire may break out and nothing happens. Why? Because the normal compressive stress in the supporting vertical structure is so low and if any column breaks or buckles, its load is transmitted to adjacent columns via the spandrels and the stress in adjacent columns increase a little. No global collapse is possible under any circumstances. Evidently the columns got stronger (thicker plates, steel with higher yield stress) further down when the 'mass above' increases, but it is certain that the compressive stresses in the Towers never exceed 1/3 of the yield stress. Same applies for the buckling stresses. Back to Summary! 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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