Sure. Just watch for "chicken and egg" with the load redistribution aspect. (What started it for that part of the structure?) And, no, I haven't a clue where the bits interacted in either time or space. There is a limit to "engineer's gut feelings" esp this time of year despite the alcoholic assistance. (Cabernet/Merlot à la Aussie style "Chateaux Cardboard".) BUT I do know they:
Yes.:
1) Interacted; AND
2) It was complicated to understand.
Vérinage.... Of course it could, in theory also have been huge chains anchored to several core columns and using automated hydraulic machinery, drew the perimeter inward in a deliberate operation thus confounding the efforts of 911 CTs who purport that the towers were taken down by explosives.
Well yea... and do you think if a verinage of the twin towers were to be done they would "pull" the building down by attaching one or two of those trusses to the facade and "pulling".
you don't need a lot of heat to get steel expanding.
This is what a hot spell 30oC plus weather and direct sunlight can do to railway tracks
So I don't find it hard to accept that the wtc fires could cause enough heat expansion to warp the buildings steel structure to cause distortion.
Usmani did the math on a 2D model and found the flimsy joists would push the robust exterior panels out 15 mm. Usmani mentions spandrels and the vertical load distribution they effect once, but I can't assess if and how their action wrt lateral forces is covered by the model.
I don't comprehend the distinction you make between "pull IN" and "an asymmetrical load which influences the bowing to be inward" - the later sounds like a complicated way of saying "pull IN"
Depends on your range of interest. If you are not interested - then you are not interested. Doesn't satisfy J Sander Orling who is interested. (And usually trusts my judgement - we are friends
)
Yeah, except only on one side
I'll take my own gut feeling backed by clear reasoning before either of them.
True enough but its very rough. Szamboti, Newtons Bit, enik and a couple of others have published similar findings. They use FEA - I could do it on my slide rule (my generation of engineering - I don't have access to FEA software.) (And to answer the next question - just and very slowly.
)
Correct. You are guessing, Usmani is doing math.
MY guess is that both push-out and bow-down happen at once: Joist heats -> expands -> goes into compression -> pushes column out -> column pushes back (Newton's 3rd) -> normal (cold, as-is live load) sag of joist increased.
Would seem pretty intuitive. Truss still goes from point A to point B but now takes a longer path in between.
We are missing each others intention. The topic of discussion current in this thread is (should be??) the technical issue of "pre-collapse inwards bowing of wtc2" My response was in that technical context which is still a matter of interest to my friend J S Orling. Hence I interpreted your comment as referring to the immediate discussion. If you are not interested in that aspect of the immediate discussion Jeffrey is. My apology that I took the context for granted - within the OP of this thread.
This is Usmani (his paper with the math, from, I think, 2002):
Correct - bow downwards. And ALSO push outwards. See link above.
Usmani thinks so. At least if you consider 15 mm to be "much". See link above.
Details that I doubt Usmani took into consideration much.
Nobody here is claiming that
The question is whether the joists and their connections are strong enough to push out and pull in the exterior walls at all (they of course are), and by how much (certainly by nowhere near to 55 inches, but also certainly by more than 0). I offer Usmani's work as one serious result that suggests an outward deflection of 15 mm, just to provide us here of an idea what order of magnitude we are talking about.
This is Usmani (his paper with the math, from, I think, 2002):
http://www.era.lib.ed.ac.uk/bitstream/1842/1216/1/WTCpaper.pdf
Usmani thinks so. At least if you consider 15 mm to be "much". See link above.
Now perhaps it "really" isn't 15 mm. Perhaps only 5, perhaps 45. But >0 and <<50'.
Like I said, someone with better qualification and better tools than I have at my disposal ran the math on a 2D-model that is simplified for sure (all models are), but (IMO) in the ballpark.
Details that I doubt Usmani took into consideration much.
Nobody here is claiming that
I am of course with you all that sagging trusses could not have pulled the perimeter in as far as IB went, but are a candidate for starting IB, which was then amplified by vertical loads on off-plumb columns.
You have no resistance to outward bowing on any perimeter column. There needs to be some reason to preferentially bow inwards. IMO that comes from the pull from sagging floor trusses. It need not be much force, just enough to initiate inward bow. Once they begin bowing they aren't going to reverse direction.
Not sure if you are following what I am proposing.
A physical demo of what?
And the point of further relevance here - the inwards force will be a multiple of the applied force. Depending on how close to straight the chain was at the start that multiple can be many times. Pure geometry of the vectors.
The challenge for most models is to get them close enough for the target audience to translate model>>reality. Not easy when the target audience includes people who cannot visualise the situation in the first place.
In the summer of 2011, my girl friend and I bought a couple of hammocks, which we planned to attach to the steel rail around my roof-top terrace. We needed to buy some extra rope for both ends of each hammock, and the flimsy stuff she bought at a home improvement store inspired me to this thread at JREF:
Another great example Oystein. AND you did it without any exploiting of Grandchildren.
yet another example. My usual example is extracting a bogged car - tie a rope tautly from the end of the car to a suitably located tree. Push sideways on rope. Car moves. Re-tighten rope and repeat.
The can demo was for WTC7
