According to http://nymag.com/news/features/16464/index.html, "hydrocarbon-fueled fire maxes out at 1,800 degrees F" (982 degrees C), so even if all the fuel poured down the core and was fully oxygenated, it would not have melted the core steel. In reality, the fire was starved for oxygen (black smoke), so was cooler than the maximum. Most of the fuel burned outside the building, but even if 10,000 gallons burned within the building, the maximum temperature would be 680 degrees F (360 C) and more likely 536 degrees F (280 C) per http://www.arcticbeacon.com/22-Nov-2004.html, which is barely hot enough to cause the steel trusses immediately above the fire to yield at 650 degrees F, even if it were fully unprotected near the center of the truss.
Was the collapse of one truss floor uniform around the perimeter of one floor? Not likely. Could the collapse of a single truss floor onto the floor below cause the floor below to collapse? Given that the load would be evenly distributed, not likely, because the floor supports would be acting in shear as they were designed to act. With a safety factor of 6, one floor should have been able to support 6 floors as dead weight. Could one floor falling 12 feet, or whatever the floor separation was, provide sufficient dynamic load to cause the floor to shear it supports. More calculations like those below area required. If not, could the absence of one floor cause the outer wall to buckle? Not likely given the many-floor lengths of exterior steel wall that remained standing with no support. But why bother arguing the truss floor collapse scenario when you have the core?
http://en.wikipedia.org/wiki/World_Trade_Center: "The core supported the weight of the entire building and the outer shell containing 240 vertical steel columns called Vierendeel trusses around the outside of the building, which were bound to each other using ordinary steel trusses. In addition, 10,000 dampers were included in the structure. With a strong shell and core such as this, the exterior walls could be simply light steel and concrete."
"A 80 cm tall web joist connected the core to the perimeter at each floor" - http://architecture.about.com/library/blworldtrade.htm: 2.63 ft high trusses.
My understanding is that the Twin Towers are the first and last buildings to use the steel truss for floors. The truss steel is much thinner than the conventional heavy duty I-beam box construction, and much less protected than the massive rebar-in-concrete-columns construction of all other skyscrappers. http://letsroll911.org/ipw-web/bulletin/bb/weblog_entry.php?e=174& and others show what happens when buildings of conventional construction burn. The concrete or steel I-beam skeleton remains fairly intact.
Apparently, the central core was not structurally compromised. Flight 175 went through one corner of the building, completely missing the core. With the floors cascading vertically, there were no lateral loads sufficient to make the core lean, much less collapse. It should have remained standing.
F (static load at the floor impacted) * safety factor) > F (impact force)?
Assume each floor was 1,368/110 = 12.38 ft high
Even if the core was compromised, and the upper portion of the building collapsed one floor onto the lower portion of the building, the lower portion should have been able to withstand that shock. It could withstand the static load plus a safety factor of 6,according to http://www.arcticbeacon.com/22-Nov-2004.html, so I find it difficult to believe that the lower core could not withstand the static weight plus its acceleration due to gravity for a distance 12.38 feet. Velocity v = g*t = d/t, so g*t = d/t, and t = (d/g)-2, so t = 0.622 sec, v (avg.) = 19.9 ft/sec., and v (max.) = 39.8 ft/sec., which is the velocity (v1) of the upper floors when they smashed into the lower floors.
This assumes a free fall when in fact there is some structural and air pressure resistance to the fall, lowering the impact velocity. How much the lower core can compress to absorb the impact determines the impact force.
Conservation of Energy (http://hyperphysics.phy-astr.gsu.edu/hbase/flobj.html#c2) implies at impact Kinetic Energy (KE) = mass of upper core (m) times (*) initial velocity (v1) squared (**2).
Assuming the lower core resistance to the impacting upper core is linear, Work (W) = Force (F) *final distance (d2), and W = delta KE = (m*v22)/2 - (m*v12)/2, where v2 = 0, the impact force, F = -(m*v12)/(2*d2) = m*(792 ft2/sec2)/d2.
http://www.infoplease.com/spot/wtc1.html: Each tower was 110 floors and weighed 500,000 tons of which 200,000 tons were steel and 425,000 cubic feet were concrete. (density of concrete is 150 lb./cu. ft.), so concrete was 63,7500,000 lb. or 31,875 tons for a total structural weight of 531,875 tons. The construction was likely nonlinear (heavier at bottom to support top), but to be conservative, assume it was linear at 4,546 tons, or 9,092,000 lb. per floor, so knowing the floor at which each aircraft impacted, you can calculate the mass of the upper core sections.
WTC 1 - Assume that all the structure on one floor disappears and floors 97-110 free fall onto floors 1-96.
m = 23 * 9,092,000 = 209,116,000 lbm (94,853,422 kg)
Dynamic force Fd = 209,116,000*792/d2 = 165,619,872,000 lbm-ft2/sec2/d2
Static force Fs = 209,116,000 lbm*32 ft/sec2 = 6,691,712,000 lbm-ft/sec2
If the design safety factor is 6, then 6Fs = Fd = 165,619,872,000 lbm-ft2/d2 and d2 = 165,619,872,000/6*209,116,000 = 132 ft
If the structure above and below the impact each absorb half of the impact, then each compresses 66 ft or 5.33 floors.
WTC 2 - Assume that all the structure on one floor disappears and floors 81-110 free fall onto floors 0-80.
Calculations remain to be done.
In reality, the entire lower core does not have to compress much, because the concrete shatters and steel buckles at the impact point, performing work that absorbs the kinetic energy of the falling upper core until the upper core comes to rest on the lower core, or more likely topples from it due to asymmetric loading. One photo shows the upper section tilting, and starting to fall to one side, but the the entire building below it disintegrated before it had a chance to completely topple.
Some will contend that the disintegration at the impact point simply continued down the entire lower core. That could only occur if the lower core did not slow the fall of the upper core, or the upper core gained mass during its descent. Given the structure of the core and the fact that concrete shatters at the impact point, and, so does not add mass to the solid falling mass doing the damage, this is impossible.
None of the following properly describe the inner core. The first says no one could get down the stair wells due to collapse, but at least one participant reported that it was the smoke that kept people form descending the stairs. He braved the smoke and escaped, because the stairwell was intact. The others wrongly assumed that the stairwells were on fire, and chose to go to the roof in expectation of helicopter rescue, but the roof access doors were locked and the roof was enshrouded in smoke.
http://skyscrapersafety.org/html/article_20050406_nyt.html
http://www.scienceblog.com/cms/node/7445
http://www.telegraph.co.uk/news/main.jhtml?xml=/news/2001/09/13/wtower13.xml
http://vincentdunn.com/wtc.html
Good references at http://www.serendipity.li/wot/mslp_i.htm
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