ozeco41
Philosopher
Civil - 1965/67 first degree, practiced in most fields but not building structural. However much experience in Engineering management so correcting "narrow minded technical engineers" who get lost in detail and lose the plot.Oz,
Howdy & welcome. Excuse me for missing it, if you mentioned it before, but what is your background. You sound like an engineer to me. I'm mechanical.
Experience includes oversight of emergency response and follow up engineering forensic analyses.
16 years Army reserve engineers - with demolition qualifications.
all read and broad agreement - some details follow...A couple of points, but ones that are significant.
..understood but it is not six stories of fully free fall momentum - doesn't matter anyway IMO the dead load itself was near enough once the impact zone collapsed. The momentum was just the "initial kick" IM(Guess)O...
In your rework of Heiwa's sketches, I believe that it is important to NOT include the damaged 6 floors or so in either section A or C. A & C are basically intact & not weakened by damage, distortion or fire. Those weakened floors (93 - 98 in WTC1) are likely the ones that collapsed first. By the time that any collapse got to an intact section of the towers (A or C), it had already gathered 6 stories worth of momentum.
..See where you are coming from - partly accept - let me think about it BUT I was interested in getting the broad picture on the table -- not the detail....Second in your last sketch, you show the debris collecting predominantly in the part A, the lower section. This is wrong. Think about any floor that is hit by debris and begins to fall. It is starting from a standing start, as a fast descending hammer comes down from above. For the first 2-5 stories (my SWAG), the faster descending upper block is going to sweep the debris into its open structure and pack in there. After a couple of stories, the bottom surface of the upper block C will be so impacted with debris, that it'll approximate a solid surface...
Ditto my previous comment...Thrid point. Think about the effect that the stagger of the peripheral & core columns had on the destruction of any give floor. By the time that the descending upper block arrives at some given floor (say the 80th), fully 2/3rds of the columns supporting the 80th floor have already been destroyed. This is because 1/3 of all those columns reached up to the 82nd floor and another 1/3 reached up to the 81st floor. These have been ripped away BEFORE the descending block even arrives at the 80th floor.
Kerrect -- and one the none engineers miss. The "radial" section modulus of the outer columns was very small compared to the "circumferential" one - along the walls a tremendous mutual interconnecting arrangement.There ain't that much more work to do to snap the 1/3rd connections that are left supporting that floor.
Yes - but so much of the "approach from energy" explanations is wrong because they presume top block and bottom stub act as solid homogeneous entities. You cannot understand the collapse from that perspective. Some of the engineering ones coming from "energy" on the wrong modeling got the right answer but really their answer is a fraud. It just happened that the energies were so massive as to come out on the side of "no demolition" no matter what wrong reasoning was used. (Gawd - there goes my Membership of the Engineers' Club AGAIN! Forget how many times I've been evicted......And I feel strongly that Bazant goes off course in calculating work required to buckle columns. This is an important calculation in the collapse initiation, but not after that point.
AFTER the collapse had initiated, the failure mode was snapped connections, gross breakup of the concrete floors and deformation of the cross trusses. This it the calculation that should have been used in calculating the work of disassembly....
.. a good point but detail below the broad brush explanation I was giving....Your correction to Heiwa's sketch, that the unsupported columns become immediately unstable & snap off, is right on the money. I would tend to think, tho, that the impacting of debris at the bottom of the upper block will give those bottom columns of the upper block some lateral support.
.. or less if that is possibleThe top "stubs" of broken off columns in the lower section have approximately zero ability to resist side loads, however.
... Yes - all subsumed within my explanation of "treat as solid block"...This is one (of many) of Heiwa's fundamental errors. He distributes the strain energy of the of the lower (larger) section uniformly over its entire structure. And he ignores the stress concentrations and side loads that are applied to the non-braced column in the top floor that is being crushed.
Thanks Tom
Eric