Tony,
I finally got a chance to go thru your "Missing Jolt" paper with a little attention.
I'll refrain comment for the moment...
To the heart of the matter. Which I am pretty damn certain that multiple other posters have already pointed out to you.
Your assumptions for the "energy dissipation" (and then, by CoE & CoM, "loss of velocity") due to the impact of the 99th floor onto the 97th in your Appendix D are:
1) Uniform elastic spring action compression in the core and perimeter columns.
2) Compressive plastic yielding of core and perimeter columns in columns of the 97th and
99th stories.
3) Plastic hinging action (buckling) of all columns, in the two stories.
Here is my response:
A. You do realize, of course, that an INVIOLATE REQUIREMENT for 1) & 2) to be true is that the vast majority of the kinetic energy of the 1 story fall has to be transmitted from the upper block's columns to the lower block's columns. If that energy is NOT transmitted into the columns, then they will absorb none of it.
With me so far?
B. Further, you do realize, don't you, that in order for the energy of the fall to be transmitted into those columns, the vast majority of the columns MUST strike each other in such a way that enormous amounts of energy must be transmitted thru the interface between the impacting columns.
Agreed?
___
Now it's time for both of us to put our cards on the table & state CLEARLY our belief in the failure modes that lead to the collapse.
And, most specifically, how the failure mode(s) allows or disallows an interface between the upper columns & lower columns that is capable of transmitting that enormous energy.
Please do not dodge providing your explanation.
Unless you provide a clear, viable mechanism, you have no credibility to produce any analysis of the collapse.
In the interest of fairness, I'll go first.
My definition of "external columns units" or "assemblies" is the 3 story high, 3 column wide plus 3 spandrel welded units in which they were prefabbed.
Observation:
From the videos of the collapse, it is evident that at the instant that the collapse began, the external columns flexed and detached from the side of the building in 1, 2, 3 assembly units (i.e., 3, 6, 9 story high) "sheets". These assemblies had separated from all the trusses to the core and at most joints between the assemblies. They were flung mostly outward, some inward, some downward.
(Aside: It actually looked quite a bit like the start of a "slab avalanche".)
The external columns:
The assemblies flung outward were NOT buckled visibly, but were probably buckled in an engineering sense: to the point that they became unstable & could not carry their load. Therefore, it is evident to me that the failure mode for the external columns was a) buckling columns leading immediately to fractured connectors or b) fractured connectors alone. My money's on b), but the couple millisecond difference is irrelevant.
The core columns:
The core columns had much lower bending loads than the external ones (which were much further from the "neutral axis" of the bend), and had stronger core column-to-core column lateral bracing.
For the collapse initiation, my opinion is that there were 6 story buckles centered on the 98th floor, reaching upwards & downwards about 3 stories. Lateral loads pushed the middle knuckles to one side, and two more knuckles forming at the top & bottom of those columns.
For the collapse progression (not important for this conversation), my bet is that the failure mode was "shearing of the bolts & welds of the cross beams by falling debris, lateral displacement of the tops of the beams by the debris, and then snapping off of the beams at each successive interface again from the levering action of the falling debris acting on the free-standing column.)
My conclusions: It is impossible for any column to column contact at 1 story. I firmly believe that there was never anything other than a glancing contact at any time during the descent. Therefore vast majority (90+%) of the energy of the upper block was NEVER be transmitted to the lower columns.
Therefore there was never be a significant jolt. Just a large number of small ones.
My premise: No interface = no "jolt".
My proximate conclusion: There is no possibility of an interface.
My ultimate conclusion: "No jolt".
That's my judgment. You're welcome to comment on it. But it is not necessary to do so to justify your paper.
___
So, from my perspective, this is exactly what is lacking in your thesis:
Please provide some REASONABLE mechanism for the dynamic loads of the falling upper story to be transmitted from the upper framework into the lower framework thru some as-yet-undefined upper column to lower column interface.
Please describe that interface.
A sketch would be helpful.
Note well, please. I don't particularly care about BZ.
I want to know YOUR proposal for that interface between the upper columns & lower columns that would be capable of transmitting this enormous amount of energy.
Tom
PS. Once you've answered this question, I'll be happy to provide you with my critique of the rest of your paper.
