9-11 Presentation at NMSR, May 19 2010

ergo said:
So anyway. Please explain (or draw, if you prefer) how a gravitational collision will affect the lower body disproportionately to the upper body.
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The main physics principles are that the upper block was able to travel about 1 story before major impacts with structure below. This is of course a simplified explanation.
But in any case the upper block gained kinetic energy, a certain percentage of which was used up in breaking connections, buckling columns etc. According to
Bazant and Zhou's early paper (2001), p 7 'So, even under by far the most optimistic assumptions, the plastic deformation can dissipate only a
small part of the kinetic energy acquired by the upper part of building.
When the next buckle with its group of plastic hinges forms, the upper part has alreadytraveled many floors down and has acquired a much higher kinetic energy;'

Translation: Most of the kinetic energy was preserved and added to every time interval of the collapse - so there was relatively little net force being experienced by the structure of the upper block.

As David Chandler measured, the net acceleration of the upper block was approximately 64% of gravity. Normally that upper block experienced a full 1g of force, so this is actually (and somewhat counter-intuitively) less force than normal!! (remember a body in free fall experiences no forces..in a vacuum)
Add to this the simple fact that the mass of the upper block was being transmitted in a downward vector while the mass of the lower block was also doing the same (due to gravity).
The conceptual error truthers make is that (IMO) the larger lower mass was being transmitted upwards! This is of course physically impossible - what is relevant is the amount of energy required to break connections below the falling mass.

Again keep in mind that the structural integrity of the buildings was necessary to maintain their designed load paths (ie keep them from collapsing). As soon as column-to-floor connections were broken, this integrity was also destroyed - for example it wouldn't matter how strong the core columns were if the connections to them didn't exist anymore.

Bazant/Zhou use this equation to calculate the 'elastically calculated overload ratio due to impact of the upper part 'Pdyn/P0 = 1 +√(1 + (2Ch=mg)) ≈ 31

p 4
 
ergo said:
And you folks don't answer questions.

Please explain how a gravitational collision will affect the lower body disproportionately to the upper body.
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Note: The question is not framed very well either. The collisions are best described by engineers and physicists who can apply precise terms.
 
ergo, note that the force of gravity is always in the same direction, and applies to all mass, upper and lower blocks included.

So in other words gravity is constantly trying to pull everything down - ie to destroy whatever thing you build. Given the chance, that's exactly what it will do - anywhere on the planet, anytime of the day. It's never on holiday like the bomb sniffing dogs ;)
 
Lyrandar said:
Oh no, both floors will likely be reduced to rubble. I don't think Slartibartfast was trying to say anything else. It's just that that rubble will keep moving down.
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ergo said:
It is clear he was saying that only the first lower floor would crush. And rubble will not keep "moving down" if it is being held between the supposed upper block and the larger, intact, lower block. It will be stopped.
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Sorry Ergo, but Lyrander was right and you were wrong - and he (and others) ably addressed most of the other issues that I had with your post and your ignorance of physics. Since it seems pointless to argue about the your misunderstanding of physics generally and it is clear that you are incapable or unwilling to provided references or equations to back up your assertions, I thought that I would instead put together a model of the beginning of the collapse that takes into account conservation of momentum and conservation of energy in order to see if that provides any insight about the Dr. Bazant's assertion that 'crush down' will happen before 'crush up' (besides, making a model is much more fun than answering the vague, unsupported critiques of well-understood physics that you make). I will explain my modeling process (with equations and everything!) so you can offer any specific criticism you care to (and have it answered) along the way and anyone else can chime in with what I'm sure will be more useful criticism... In the end we can compare the model to Dave's model and bring the thread full circle (and back on topic).

The model should be biased in favor of building survival vs. the actual conditions (so my first question to you is why do you think that the model I outline below is less favorable to building survival than what actually happened).

Let's consider the idealized situation where a single floor of supports (say the 94th floor) is instantaneously removed and the upper block falls 3.7m to land on the lower block in an inelastic collision and that all of the columns in the upper block line up perfectly with the columns in the lower block and that all of the columns are able to exert the maximum amount of force possible (the weight of the building above them times the safety factor). We can then set up the equations of motion for each of the floors based on the building specifications and the forces acting on them.

What, in your opinion, is wrong with this methodology?
 
ergo said:
No, why would I? You don't need a diagram to have this discussion. You're just avoiding answering the question.
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Let's just say that answering your questions seems to be less effective than it should be, so I'd like it if you'd try to work through this one on your own. I think drawing a free body diagram is a good way to analyze the forces in question. Why don't you give it a try? Let me know if you get stuck.
 
Hmm, maybe a different approach will help.

Ergo, which of the following statements is/are true?

Assuming the mass is the same:

1) Floor 80 has more potential energy than floor 81.
2) Floors 80 and 81 have the same potential energy.
3) Floor 81 has more potential energy than floor 80.
 
ergo said:
pgimeno said:
Actually, what I understand from his claims is that if one car falls on another, only the falling one will be crushed and the other one will be intact.
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My claims? No. That's the Bazant theory. That a gravitational collision would have only downward impact.
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Your claim is that the top would be crushed and there would be nothing that could crush the bottom. Bazant's theory does not deal with cars, because he considers a layer of rubble in between that is important for how the crushing propagates. You change your version every time.
 
alienentity said:
Again keep in mind that the structural integrity of the buildings was necessary to maintain their designed load paths (ie keep them from collapsing). As soon as column-to-floor connections were broken, this integrity was also destroyed - for example it wouldn't matter how strong the core columns were if the connections to them didn't exist anymore.
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Huh. That's a way of looking at it I hadn't considered before. The lower block must stay intact to resist the upper block, but the upper block need not stay intact to apply force to the lower block.

Not really fair, is it?
 
aggle-rithm said:
Huh. That's a way of looking at it I hadn't considered before. The lower block must stay intact to resist the upper block, but the upper block need not stay intact to apply force to the lower block.

Not really fair, is it?
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It makes a real mess of Ergo's 'rubble is easier to handle' hypothesis, too.
 
ergo said:
So anyway. Please explain (or draw, if you prefer) how a gravitational collision will affect the lower body disproportionately to the upper body.
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I really feel like I already have explained this... Maybe I will try drawing a diagram, but let's see if I can explain this more clearly first.

Before the upper block or any piece of rubble strikes the lower block, the only force acting on it is gravity. The only forces acting on the lower block which it strikes are gravity and the normal force.

At the moment of impact, another force is added. The lower block must exert an upward force on the upper piece to stop it. It must do so over a few thousandths of a second, whereas gravity has had half a second or so to accelerate the upper piece, so this upward force must be several times greater than gravity. I will refer to this upward force as the impact force. At this point, the upper block has two forces acting on it - gravity and the impact force. Since the impact force is stronger, there is a net upward force, but gravity reduces this net force. The lower block now has three forces acting on it - gravity, the normal force, and the impact force (you already know the physical law which dictates that the impact force is present here, and directed downward). Gravity and the normal force were in equilibrium up to this point, so the only contributor to the net downward force is the impact force. This net force is equal to the impact force, unlike the net force on the top piece which is equal to the impact force minus gravity.

What happens after the impact depends on the strength of the materials involved - I regret to say my physics knowledge doesn't extend far enough to discuss this in great detail. The normal force will increase to attempt to resist the downward motion, but it's dependent on the surface and can only increase so far before the surface gives way. (At least, I think that's how it works...)

There you go. It's a hideous oversimplification of a complicated environment, but its point should remain valid even with all the other issues factored in.
 
ergo said:
Since it's going to show me what you can't seem to explain to me using your words, why don't you draw it?
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Because you have been TOLD the answers and SHOWN the answers repeatedly and you refuse to learn from it.

So now you can do the work, then you may understand it.

(kinda like my challenge to you to time the collapses yourself... have you done that yet? did you figure out how to use a stopwatch, or the timer function on youtube?)

Do it yourself and actually LEARN something.
 
Kick for ergo. I'd like to find out if he ever made an attempt to draw a free body diagram, and I see that he's now back to posting on the JREF forums.
 
Ergo's idea of a fbd

freebodydiagram.jpg
 
AZCat said:
Kick for ergo. I'd like to find out if he ever made an attempt to draw a free body diagram, and I see that he's now back to posting on the JREF forums.
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Why would I make a "free body diagram"? Was I claiming to be an expert at technical drawings? If so, please link to the post where I make this claim. Thanks.
 
ergo said:
Why would I make a "free body diagram"? Was I claiming to be an expert at technical drawings? If so, please link to the post where I make this claim. Thanks.
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Your fbd problem, and your posts, exposed your lack of physics.
 
Correct me if I'm wrong but aren't the lower block forces acting on the upper and visa versa the same only when the building is in equilibrium?
 
ergo said:
Why would I make a "free body diagram"? Was I claiming to be an expert at technical drawings? If so, please link to the post where I make this claim. Thanks.
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Why would you? Because it's a great way to understand a problem like this one.
 
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