Ok, its a minor point really but I do want to try and understand in layman's language the order of events as Usmani sees it.
How's this?
-Membrane heats and expands
-Thus pushing on the core and perimeter columns
-Columns yeild very little giving rise to compressive force on constrained membrane
-Force increases to the point where compression causes floors to deform
-columns rebound
Yes, so far this is pretty much how I understand this
They are saying that the columns rebound well past their original vertical position and are kept there by the deformed/sagged trusses.
Am I correct now?
The first part yes, that's what they say (although, like you, I don't quite understand why they rebound past the original position; I don't see that the velocities they give in the paper make this an issue of momentum or string-like vibration).
The second part I think no: I don't recall they say that the columns are kept in place at an inwardly bowed position by the pull of sagged trusses.
Why is this considered a more probable scenario than that the floor trusses sagged due to heat as is seen in numerous other office fires? Or is this simply the results shown by the FEA?
The latter.
The NYPD pictures show floors that are a red inferno, certainly temperatures well in excess of 500-600 degrees F and I can get a steel poker glowing red hot in a wood fueled campfire.
It is difficult to gauge actual temperatures within a building from just images of the fire. Usmani et al. ran their simulations for a wide range of (maximum) temperatures and found that the sequence as described above eventuated at lower as well as higher temperatures, so even if the temperature eventually increased enough to make the steel sag due to changed material properties, the inward bowing through geometric effects and buckling came earlier than sagging due to softening.
Is it the concrete that remains much cooler due to it being less of a conductor than the steel, and thus the concrete that keeps the floor intact for a while?
Usmani et al. did include the concrete flooring in their simulations. They considered a simple 1D modelling of heat flow, i.e that the surfaces heated before the inside of the concrete. In contrast, the truss steel, being rather flimsy and out in the open, was assumed to attain rising ambient temperature immediately.
IIRC the top chord of the trusses were embedded in the concrete and only the lower chord was exposed.
No. The concrete was on top of the metal decking, and the metal decking was on top of the top chord, so the top chord was out in the open. Only the "knuckles" (top bends) of the diagonal web bars extended a couple of inches or so into the concrete.
Not sure that its very intuitive that the columns would rebound that far if they only deformed outward by 15 mm. ( though I realize that is calling in personal incredulity
)
I suppose that the floors deforming downwards would have a certain momentum to them that would add to movement back inwards, of the columns and of course the truss span from core to perimeter is now shorter with trusses bent. Why they do not characterise this as a pulling inwards though is puzzling, or is that the tensile force in the membrane that they refer to?.
According to some of the Figures in the paper, the main fire floor pushes outwards in their sims with a force on the order of 50,000 N - that's "5 tons" for laypeople
At the same time, the non-fire floors above and below experience tensile forces - going the other way - of a similar magnitude.
This reverses after the fire floor buckles and the column bows in.
The way I read those graphs, the pulling force eventually exceeds the earlier pushing force.
Truss span (that is the straight line distance between truss ends) gets shorter due to sag/deformation and once this exceeds the extra length of truss due to heat expansion, the columns are being pulled inwards. It seems that switching frames of reference to the floor membrane is much of what they did and refering to the tension in the deformed downwards membrane is pulling on the columns.
Yes, there is a pull on the columns, but, as the earlier push only resulted in a lateral deflection of the column by only 15 mm or so, you wouldn't expect them to bow inwards by more than that from an equal pull - all else being equal.
But all else is not equal: The buckled (failed) floor provides no (or insufficient) lateral bracing for the column in the inward direction (there is still, through tensile strength, bracing wrt outward bowing), and thus the vertical capacity drops sharply. The column is now free to bow inward even further due to its vertical load. To which the sagging truss contributes, but it's not the main factor, and perhaps not even necessary.
Holding a rope between two people and putting a weight in the centre of the rope, the people feel a pulling in, but the rope 'feels' it is being pulled apart(tensile force)
Then again I see that you say that they are simply saying that it was the geometric deformation of the membrane that allowed the columns to rebound and deform inwards and that pull-in was merely a possible contributor to that.
Right.
(Disclaimer: I am certainly as much a layman as you are - just trying to explain things the way I understand them. Don't trust me!)
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