Open Letter to Dave Thomas

[Horatius]

It's unfortunately not the right track. Most (all?) of the columns did not buckle in that fashion. They buckled elastically, which means no hinges.

Well, there's a limit to what you can show in a comic. It the fundamental description wrong? That is, would the lower structure fail in such a way that the upper structure would be essentially non-supported for some period of time? And would the lower structure also continue to deform and collapse after that point of complete failure?

Also, how would you draw the types of failures you'd expect to see in these columns?




ETA: I guess it would be something like this:

http://www.efunda.com/formulae/solid_mechanics/columns/theory.cfm

That leads me to a modified comic idea that I had. Would you model the columns that collapsed as single 8-story structures, or a series of smaller columns?

 

[Newtons Bit]

Well, there's a limit to what you can show in a comic. It the fundamental description wrong? That is, would the lower structure fail in such a way that the upper structure would be essentially non-supported for some period of time? And would the lower structure also continue to deform and collapse after that point of complete failure?

Also, how would you draw the types of failures you'd expect to see in these columns?




ETA: I guess it would be something like this:

http://www.efunda.com/formulae/solid_mechanics/columns/theory.cfm

That leads me to a modified comic idea that I had. Would you model the columns that collapsed as single 8-story structures, or a series of smaller columns?

What's at efunda is basically correct. You have to be careful with that site, however, the concepts are correct as far as I can tell, yet they can show them in such a non-typical fashion that it can be misleading.

The columns in the building will continue deforming like that until the connections from the beams to the columns become twisted and yanked out, or the rotation at any point exceeds that which the column splices can handle.

 

[Dave Rogers]

The columns in the building will continue deforming like that until the connections from the beams to the columns become twisted and yanked out, or the rotation at any point exceeds that which the column splices can handle.

So is there a more or less continuous curve in the columns, over about eight storeys, followed at some point by an abrupt fracture or series of fractures at weak points? That would, of course, explain the near-total loss of support from the moment of fracture; columns would be releasing elastic energy by straightening, creating lateral forces and movements that would dislocate the column ends significantly. Is that a realistic view?

Dave

 

[Horatius]

So is there a more or less continuous curve in the columns, over about eight storeys, followed at some point by an abrupt fracture or series of fractures at weak points? That would, of course, explain the near-total loss of support from the moment of fracture; columns would be releasing elastic energy by straightening, creating lateral forces and movements that would dislocate the column ends significantly. Is that a realistic view?

Dave

That's sort of what I was thinking about for my updated comic. If the entire 8-story column is deflecting as a unit, largely in one direction, then it seems to me that you'd need at most 3 points of failure to get essentially zero support for the upper section over most of the 8-story drop, and I could make a case that you'd only need two, or maybe even only one such failure.

I decided to take a "Too nice to go to work today" day, so I'll see if I can whip up another comic...

 

[Dave Rogers]

That's sort of what I was thinking about for my updated comic. If the entire 8-story column is deflecting as a unit, largely in one direction, then it seems to me that you'd need at most 3 points of failure to get essentially zero support for the upper section over most of the 8-story drop, and I could make a case that you'd only need two, or maybe even only one such failure.

Alternatively, you could make a case that at least two points of failure are expected from the release of elastic energy.

http://www.lmm.jussieu.fr/spaghetti/

Dave

 

[Horatius]

Okay, so here's the second version. Who knew Cartoon Physics was subject to Peer Review?

And cross-posted peer review at that!

Alternatively, you could make a case that at least two points of failure are expected from the release of elastic energy.

http://www.lmm.jussieu.fr/spaghetti/

Dave

I'll take a look at that, but it seem to me, we could have several different versions of one- and two-point failures, depending on which points actually fail. I only showed one example of each above, as I suspect they're functionally interchangeable.

 

[Stout]

I expect a finder's fee!

You betcha

Hey, I could even temporarily relocate to Vernon, after all the rules don't state how long someone has/had to be a "greater Vernon resident" in order to collect the big money. Heck, I'll even donate it ( less the finders fee of course ) to the JREF as a sort of tuition for all the stuff I've learned here over the past few years.

I'm wondering who the judge is going to be.

It can't be Fullerton, can it...I hope not, all he needs to do is be present in the room with the cash piled neatly on the table.

If Fullerton is wanting to be the judge, I fear that this challenge might be unwinnable. I've been through this violation of the laws of physics with a couple of twoofers last spring and there seems to be a strong "intuitive" component to how materials behave rather than any rational study.

As a for instance, one twoofer seemed to believe that the steel in WTC 1 and 2 somehow *should have* behaved like a collection of bungee cords rather than failing by cracking and there was a focus on the density of the structure of itself , rather than the way the components were put together.

When asked repeatedly just how the collapses of WTC 1 and 2 violated the laws of physics, the twoofers own claim, it was even in the thread title, an answer never materialized.

I expect the same shenanigans with Fullerton.

 

[Newtons Bit]

That's much better Horatius.

 

[Stout]

It's unfortunately not the right track. Most (all?) of the columns did not buckle in that fashion. They buckled elastically, which means no hinges.

OK

I was hoping to be able to use an analogy, like kicking someones legs out from under them, and having their torso fall at freefall speed.

Fullerton seems to be implying that the whole building came down at freefall speed, rather than just the north face. He should ammend the terms of his challenge if he wants to appear more legit.

 

[Horatius]

Alternatively, you could make a case that at least two points of failure are expected from the release of elastic energy.

http://www.lmm.jussieu.fr/spaghetti/

Dave

Interesting.....

Bent dry spaghetti do not break in half but instead in three or more pieces. With the aim to explain this surprising phenomenon, we studied a related problem, namely the dynamics of an elastic rod that is bent quasi-statically and then suddenly set free. Counter-intuitively, we find that the mere release of the rod induces a stress increase. The multiple breaking of bent rods, like dry spaghetti pasta, can then be understood as a cascade of releases (loss of cohesion upon breakings) followed by stress increases leading to new cracks.

So it's entirely possible that the unsupported parts of the fractured column could continue to break, even as they're falling through the air, with no actual load on them at the time.

That video reminds me of this one:


http://en.sevenload.com/videos/wvPvmfg-MythBusters-Cutting-a-Sword-Part-2-2


Watch the high-speed footage at about 5:40, you see one sword snap in two places as it rebounds back well after being hit by the other sword. I suspect we're seeing similar effects here.

 

[Horatius]

That's much better Horatius.

Cool, thanks!

 

[Stout]

Ha! excellent a new cartoon.

Says basically the same thing as the first one,

Horatius, I fear you've one the prize, please think of us here at the JREF while you're lollygagging on your mega yacht.

 

[bill smith]

That's much better Horatius.

I'm just looking dorward to a sketch showing what the 58 columns look like when they all go together. All the widely seperated corner columns and all.

 

[Newtons Bit]

Cool, thanks!

No problem, Mr. Cheese Weasel.

My experience with elastically buckled compression elements is their use in seismic bracing. Which is none, it's explicitly forbidden by code. The research around seismic bracing has found that elastically buckling compression elements absorb far less energy than an inelastic element. In addition, the hysteresis loop of such an element is far more one-sided in the tension zone which can cause problems to connecting elements.

It's generally not something you want, as a designer, in a compression element.

 

[ElMondoHummus]

Dammit, Horatius, why'd you have to go and do that? Now I can no longer use my insult "cartoon physics" to rip on anyone!

 

[Horatius]

Dammit, Horatius, why'd you have to go and do that? Now I can no longer use my insult "cartoon physics" to rip on anyone!

Oh, I'm sure it will still have it's uses.


Oh, look!

I'm just looking dorward to a sketch showing what the 58 columns look like when they all go together. All the widely seperated corner columns and all.

So, no comment at all on the basic physics of a single column collapse? Until you and cmatrix can demonstrate an actual understanding of this simplified case, adding more columns is a waste of time. Show that the effort on my part might have some value, and I'll consider making that effort.

Once again, I won't be holding my breath waiting for that demonstration.

 

[Newtons Bit]

Adding all of the columns would just be a waste of time. There is no connection from column to column once the diaphragms are compromised. The only exception would be at columns where an intact beam is connected with a full moment-connection to another column. This generates a moment frame. However, these beams (with rare exceptions) run from flange to flange of the column which creates a frame from the strong-axis of the columns. They are no stiffer or stronger in the weak-axis. They must rely on a connection to columns in the perpendicular direction to be braced in the weak axis, which again, requires a diaphragm connection.

 

[Horatius]

Adding all of the columns would just be a waste of time. There is no connection from column to column once the diaphragms are compromised. The only exception would be at columns where an intact beam is connected with a full moment-connection to another column. This generates a moment frame. However, these beams (with rare exceptions) run from flange to flange of the column which creates a frame from the strong-axis of the columns. They are no stiffer or stronger in the weak-axis. They must rely on a connection to columns in the perpendicular direction to be braced in the weak axis, which again, requires a diaphragm connection.

I suspect he's trying to ask why all 58 columns would fail at the same instant, rather than being spread out over a measurable period of time.

It seems to me that cmatrix's main objection has two discrete elements that need to be addressed: one is the assertion that all 8 stories of each column must be eliminated in order to allow for a free-fall drop, and the second is that this 8-story elimination must happen simultaneously with all 58 perimeter columns.

Our discussion above shows that the first element is clearly not necessary, we only need 1-3 points of failure in each 8-story column to reduce the support to zero for almost all of the 8-story drop.

Once bs and cmatrix show they can understand this element of the discussion, we can go on to discuss the sequence of how the columns failed, how long it would take that sequence to occur, and what it would look like. I suspect that the time between the complete failure of the first column and that of the last is significantly shorter than either of them realize, but I have no good information on that.

Does anyone know of any good studies/explanations for the rate at which such failures typically occur? Is there a fundamental maximum rate we could define?

 

[Newtons Bit]

I suspect he's trying to ask why all 58 columns would fail at the same instant, rather than being spread out over a measurable period of time.

It seems to me that cmatrix's main objection has two discrete elements that need to be addressed: one is the assertion that all 8 stories of each column must be eliminated in order to allow for a free-fall drop, and the second is that this 8-story elimination must happen simultaneously with all 58 perimeter columns.

Our discussion above shows that the first element is clearly not necessary, we only need 1-3 points of failure in each 8-story column to reduce the support to zero for almost all of the 8-story drop.

Once bs and cmatrix show they can understand this element of the discussion, we can go on to discuss the sequence of how the columns failed, how long it would take that sequence to occur, and what it would look like. I suspect that the time between the complete failure of the first column and that of the last is significantly shorter than either of them realize, but I have no good information on that.

Does anyone know of any good studies/explanations for the rate at which such failures typically occur? Is there a fundamental maximum rate we could define?

I don't know much in the way of studies for rates of failure, however one could calculate what the increase in strain energy would be as the column deflects outwards (and thus shortens vertically as well). I think it is as simple as maintaining P/A (compression) + M/S (elastic bending) = f_c. F_c is the critical buckling stress. Once P/A becomes approximately equal to zero, then the element becomes a pure bending element. The vertical forces above are transmitted through shear and bending rather than axial forces at this point. The "column" will now continue to deflect until M/Z (plastic bending) > F_u, or the rupture yield stress.

You could use that to develop a differential equation that expresses an increase in energy from the potential energy into strain energy of the column which results in a deflection that you can use to compute the change in potential energy. I hate differential equations.

 

[bill smith]

Let's see if this has any effect other than The Usual Suspects making a joke about the title....


[qimg]http://upload.stripgenerator.com/strip/70/63/24/00/00/full.png[/qimg]

Of course if the Strain energy (FS) of a particular column becomes less than the force of gravity acting on it then it will tend to distort. If the strain energy becomes catastrophically low then the lower column will fail altogether.

I have no problem with that. Nobody would have.

But I am happy to watch your attempts tp sketch how all four widely-seperated corners of the building dropped at the same time in addition to all the interior structure barring that which had already fallen in the Penthouse collapse incidents.

By the way how long were the column sections ? From your drawing (8 floors,8 column-sections) it looks like 12 feet or so. Is that correct ?