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Old 2nd August 2012, 11:09 AM   #33
tfk
Illuminator
 
Join Date: Oct 2006
Posts: 3,454
Oz, reply to you.

Chris Mohr, you may want to read this. It contains some subtleties that I believe would greatly help one of your explanations. Specifically the canard that "for all the columns to fail simultaneously, they must have been blown." See the last couple of paragraphs.

Originally Posted by ozeco41 View Post
The basic issue to comprehend is that a column is very strong taking loads in axial compression - what it is designed to do. BUT it gets weaker quickly if the load is off centre. And, taking it further, it gets very weak if there is a bit of a bend in the column. So much that a heavily loaded column which gets kinked out of line will self destruct because the axial load which is safe on a straight and centrally loaded column is far more than the column can support once it gets our of line. 'Eccentric loading'.

So all the sagging floor joists had to do was start the bending out of vertical straight line and pretty soon the applied load will take over and complete the destruction without further help from joist sagging.

So that is the two factor basics put as simply as I can:
1) Sagging floor joists starts the inwards bowing which seriously weakens the column; THEN
2) The already applied vertical load finishes the job.
I assume, from the mention of "inward bowing", that you are talking about the towers here, not WTC7.

I know that you're familiar with most of the prose below. I'm including it for both my purposes (to construct the logic completely) & for others who may struggle with a few of the concepts.

In other words, Pardon my Pedantry.

And I agree with every thing that you've said above. I'd add a bit.
__

I would encourage you to include consideration of "time constants" into the causes that you've mentioned. Meaning "the time constants over which the different effects occurred." Specifically, slow gradual change in gross geometry, and then sudden, rapid collapse initiation.

The causes of each must match the time constants seen for the towers: 1 & 2 hours slow geometry change & ~seconds for collapse initiation.

There are only two time constants that seem to me likely to be measured on the order of 20 minutes to 2 hours: a) creep and b) heating (or cooling) of large structural components.

NIST's explanation for final stages of collapse initiation (last ~20 minutes in each tower) included the uneven heating of some core columns, their thermal expansion & taking on a high percent of the load from the outer columns, the core columns' creep (i.e., shortening) at high load & moderate temperature (400 - 800C), their cooling once fires had passed & shedding an excessive amount of load back to the outer columns, and then very sudden buckling of either:

1. perimeter columns due to excess gravitational load, or
2. core columns due to abnormal bending moments.

Note a few other things (pedantry alert..!):

1. the sag of the floors also falls into the category of creep.

2. once the floors have buckled, the floor loads turn from almost pure shear into a lateral, catenary pull. That inward pull must be transferred as bending & inward compressive loads to the composite floors above & below the sagging floor.

___

One other thing regarding time constants...

The time constant for the for collapse of the column in buckling after the critical load has been reached is highly depending on the load condition, which can be lumped into …

a) force driven: the load is increased while the compression and lateral curvature are unconstrained.

Force driven collapse happens very quickly (milliseconds to seconds) once the critical load has been reached.

b) strain driven: the compressive shortening of the column is increased while the lateral curvature & load are unconstrained, as one might get using an Instron tester.

Strain driven collapse occurs at the applied strain rate, whatever that may be.
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For a lattice-work (i.e., 2D array) of columns PRIOR to global collapse, the load condition is essentially "strain driven". This is because, as the strain increases, even if a particular column has buckled and is capable of supporting only tiny load, other nearby columns will pick up the shed load & the column's bolted connections to the structure prevent its further collapse.

The vast majority of columns whose inward bowing was detectable from the ground had almost certainly gone way past critical buckling, were providing only a small fraction (~10%) of their designed support to the structure, but were prevented from collapsing further by their connections to other components.

[Perhaps one of the structures guys could tell us how much vertical compression would bring a 3 story outer columns to its critical buckling point. I'd guess < 2", resulting in minimal inward bowing.]

The strain rate that was applied to the buckled / buckling / about to buckle columns was determined by the slow global shift of the structure in response to the (long time constant) fires, expansion, creep, cooling, etc.

But, once the structure's global safety margin is gone (i.e., one final column buckles & the rest of the columns cannot pick up its shed load), then the load condition on the columns immediately changes from strain driven mode to load driven mode.

And it is precisely this sudden shift in load conditions that produces the "simultaneous failure of all columns" that bother truthers (& Gage) so terribly.

We've expressed this same concept in different terms before, but this is the first time that I've thought about it in terms of time constants & buckling load modes.


Tom


PS. Sorry I remind you of your sister. I hope I didn't twist your words too much, to change your meaning to match what I wanted to discuss...

Last edited by tfk; 2nd August 2012 at 11:14 AM.
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