## Physics of building collapse

I am having trouble understanding a building collapse. According to NIST, on 9/11 WTC7 collapsed after fire weakened its structural steel. They have however admitted that WTC7 fell for 2.25 seconds at free fall. (http://wtc.nist.gov/NCSTAR1/PDF/NCSTAR%201A.pdf) However isn't all the gravitational potential energy of the building used up in attaining free fall? Why did the structure in the way not slow the collapse in any way during this period? Fire can't blow out 8 stories of structure simultaneously and continuously floor by floor. Energy and momentum don't seem to be conserved here which is a violation of the laws of physics. Can anyone explain how I am wrong here?

Mentor
 Quote by cmatrix I am having trouble understanding a building collapse. According to NIST, on 9/11 WTC7 collapsed after fire weakened its structural steel. They have however admitted that WTC7 fell for 2.25 seconds at free fall. (http://wtc.nist.gov/NCSTAR1/PDF/NCSTAR%201A.pdf) However isn't all the gravitational potential energy of the building used up in attaining free fall? Why did the structure in the way not slow the collapse in any way during this period? Fire can't blow out 8 stories of structure simultaneously and continuously floor by floor. Energy and momentum don't seem to be conserved here which is a violation of the laws of physics. Can anyone explain how I am wrong here?
Welcome to the PF. Two things. First, we do not allow discussions of conspiracy theories here on the PF. That's pretty clear in the Rules link at the top of the page.

Second, sure, it's consistent with some failure mechanisms due to melting structural beams. How far does something fall from rest in 2.25 seconds? This is a physics forum, after all. You should be able to answer that question for us. How many stories does that equal?

Mentor
 Quote by cmatrix I am having trouble understanding a building collapse. According to NIST, on 9/11 WTC7 collapsed after fire weakened its structural steel. They have however admitted that WTC7 fell for 2.25 seconds at free fall. (http://wtc.nist.gov/NCSTAR1/PDF/NCSTAR%201A.pdf) However isn't all the gravitational potential energy of the building used up in attaining free fall?
Yes, gravitational potential energy is what causes free-fall.
 Why did the structure in the way not slow the collapse in any way during this period? Fire can't blow out 8 stories of structure simultaneously and continuously floor by floor. Energy and momentum don't seem to be conserved here which is a violation of the laws of physics. Can anyone explain how I am wrong here?
If you don't know how much energy a steel beam can absorb, you can't know that it should have absorbed more. Buildings aren't cars: they don't have "crumple zones" designed to absorb energy. They are designed to withstand a certain static force, but have very little ability to absorb energy. In short, steel beams don't retain much strength as they deform and break.

Try this: Take a soda straw and while stabilizing it with one hand to hold it straight upright, push it against a table with your other hand. You can put quite a bit of force to it without breaking it, can't you? 5-10 pounds maybe? Then let go with your other hand, allowing it to collapse. Once it buckles, it offers only a tiny fraction of the resistance it offered before - an ounce or two of force.

## Physics of building collapse

OK, so what you write is that "free fall" means an "almost free fall" or "for all practical purposes free fall"?

Mentor
 Quote by Borek OK, so what you write is that "free fall" means an "almost free fall" or "for all practical purposes free fall"?
Right - close enough (within a few percent) that you can't tell the difference by freeze-framing/clocking a youtube video.
 Mentor ...and it is actually even a little worse than my straw example: plastic is ductile so the straw doesn't snap it just buckles. When a steel beam fails it only buckes a little before snapping...and the faster the impact the less buckling.....and a snapped beam offers no resistance at all.
 berkeman, I am not presenting a theory merely a question that I am extremely disturbed about. That should have been pretty clear. You have not answered my question but instead ask me an entirely irrelevant and bizarrely basic question. But, 9.8 x 2.25 = 22.05 meters or about 72 feet which is about 8 stories. This is a physics forum, after all. You should been able to answer that question yourself. russ_watters, massive interconnected steel beams, floor pans and reinforced concrete will absorb some energy and momentum, not none at all. With free fall there is no energy and momentum at all being absorbed. The conservation laws seem to be egregiously violated here. Again exactly what am I missing here?
 Recognitions: Gold Member Science Advisor cmatrix You seem, already, to have posted your original question bringing with you answers that satisfy you. Berkeman's comments seem quite reasonable to me. You need a structural engineer to give you accurate calculations so you must either learn the stuff yourself or pay someone to do them for you. If you are "extremely disturbed" then you must have either done some sums of your own or read someone's 'theory'. Perhaps you should get more familiar with the Physics involved before you get too worried. I don't know what you mean when you say that "With free fall there is no energy and momentum at all being absorbed" but, if you drop a brick on your foot, you will be aware of a certain amount of energy being available after a very short distance of "free fall". If you drop the top section of a building through a distance of several metres then there is a a lot of Kinetic Energy available to do damage to the lower bits, when it lands on them. Because of the momentum changes involved, the next section just below the collapsed section gets the majority of the impulse after each increment of the collapse. Most building are never designed to cope with that sort of impact. Once the lower sections have broken and have not absorbed all the energy, they will add to the amount of energy available for damage in subsequent collapses. It all depends upon whether the structure can absorb the energy of collapse of each successive floor or not. If buildings were built with that eventuality in mind then they would have to be so expensive that no one could afford the rent! Only when you have done the actual calculations and proved that mechanism will not work should you go for the conspiracy theory. This Forum doesn't want to get involved with the conspiracy idea and we are all the better for that decision.
 Admin I don't see a conspiracy theory here and I think I understand where cmatrix problem arise. At least my first idea was that some of the energy of the upper part of the building has to be used for smashing lower stories, and that it should slow down the fall - that's exactly the problem s/he addresses. If part of the energy is used to destroy objects that lie below, what we observe is not a free fall - acceleration of the falling object should be lower than g. That's perfectly sound physics, perhaps idealized one. cmatrix: please read what I wrote earlier and what Russ answered. You are right that it is not a free fall, however, once the support beams snapped, whatever was left was too weak to substantially slow down fall of the upper part of the building. For all practical purposes fall can be approximated by free fall.

 Quote by sophiecentaur cmatrix You seem, already, to have posted your original question bringing with you answers that satisfy you. Berkeman's comments seem quite reasonable to me. You need a structural engineer to give you accurate calculations so you must either learn the stuff yourself or pay someone to do them for you. If you are "extremely disturbed" then you must have either done some sums of your own or read someone's 'theory'. Perhaps you should get more familiar with the Physics involved before you get too worried. I don't know what you mean when you say that "With free fall there is no energy and momentum at all being absorbed" but, if you drop a brick on your foot, you will be aware of a certain amount of energy being available after a very short distance of "free fall". If you drop the top section of a building through a distance of several metres then there is a a lot of Kinetic Energy available to do damage to the lower bits, when it lands on them. Because of the momentum changes involved, the next section just below the collapsed section gets the majority of the impulse after each increment of the collapse. Most building are never designed to cope with that sort of impact. Once the lower sections have broken and have not absorbed all the energy, they will add to the amount of energy available for damage in subsequent collapses. It all depends upon whether the structure can absorb the energy of collapse of each successive floor or not. If buildings were built with that eventuality in mind then they would have to be so expensive that no one could afford the rent! Only when you have done the actual calculations and proved that mechanism will not work should you go for the conspiracy theory. This Forum doesn't want to get involved with the conspiracy idea and we are all the better for that decision.
I don't need to do any calculations. I understand how gravity, energy and momentum work in this respect. When the kinetic energy from a falling mass is used to do damage, the mass' rate of decent is slowed. Agree or disagree? If a theory involves no slowing whatsoever you obviously have a violation of the conservation laws. A building free falling for 2.25 secs has no structure whatsoever beneath it because it's rate of decent would slow if any structure was encountered. Consider dropping your brick onto 47 sheets of suspended glass strong enough to support this structure and the brick at the top. Is the brick going to free fall all the way to the bottom?

 Quote by cmatrix [...]will absorb some energy and momentum, not none at all. With free fall there is no energy and momentum at all being absorbed. [...]exactly what am I missing here?
You're missing that nobody really meant "literally, exactly free fall".

The idea is like (as Russ was saying) that you might be able to completely support the weight of a brick with just a straw, but if you lift that brick up just one centimetre higher and then drop it, the straw will likely buckle , letting the brick will fall down almost as fast as if the straw wasn't there at all. Not "exactly" as fast (which as you say would violate conservation laws), but close enough that you probably couldn't easily detect the difference (go take a stopwatch and tell us how much the straw slows the brick compared to when you do it without the straw. Then, if you want to get technical with us about free-fall, go time the brick falling in a complete vacuum).

"Two and a quarter seconds" doesn't mean 2.2500000000000+/-0.0000000000013s. You should be able to calculate an estimate of the uncertainty in how much decelerating force could have been exerted by the lower structure, based on the observations.
 Recognitions: Gold Member Science Advisor The brick and glass model is not the WTC model at all. Each of your sheets of glass would have to be of significant mass and the structure of your model would have to be 'only just' strong enough to support itself. Neither was the whole building nor the top portion of the tower "in free fall". You are not applying conservation laws in a relevant way (you haven't actually said where they 'fail'). Of course you would need to do calculations (in a lot of detail) to analyse the scenario properly. This is my version / explanation of the sort of ting that must have happened (discounting the possibility of a demolition job) The top portion of the tower fell when a mid section became too weak to support it. It fell several metres (a couple of floors), not under free fall but not supported sufficiently and still accelerating ('almost free fall'). It then hit the top floor of what remained of the building below at some significant speed. As I said, momentum considerations meant that the majority of the stress was on the supporting section just below that floor. (Look at pictures of the front coaches of trains in collisions - they are the ones that get concertina'd). That section collapsed, slowing the falling mass a little but not bringing it to a halt. The top - plus this floor - then continued down, accelerating whilst falling the next few metres to the next level and, of course, weighing a bit more. After falling by a further few metres it was, again going fast enough to break the next section supports. Each successive floor collapsed and each time there was more weight on top of it. Although I should imagine that the lower sections were built stronger than the upper sections, they would have been heavier, as a result, so my scenario would also have applied. I would think that, had the planes hit nearer the top, this domino effect might not have occurred. If the floor, immediately below the impact / fire had been able to withstand the initial impact of the higher portion falling on it then the collapse would have stopped there. As it was, there was about a third of the structure above the break - a massive hammer with which to start the collapse. I am sure the terrorists were as surprised as anyone else that the towers went down the way they did.

Mentor
 Quote by cmatrix I don't need to do any calculations. I understand how gravity, energy and momentum work in this respect. When the kinetic energy from a falling mass is used to do damage, the mass' rate of decent is slowed. Agree or disagree?
Disagree -- not necessarily. Remember that there is an accelerating force downward due to gravity, and a retarding force that varies, but can be less than or greater than the gravitational force. The retarding force depends on what bits and pieces and such are being plowed through on the way down. The sum of the forces F = ma, so you can still see a downward acceleration.

Especially for the first 2.25 seconds. You didn't answer my quiz question, and nobody answered it for you, but that's about 1 floor worth of falling. Pretty plausible as one floor's support beams gave way....

Recognitions:
Gold Member
 Quote by berkeman Especially for the first 2.25 seconds. You didn't answer my quiz question, and nobody answered it for you, but that's about 1 floor worth of falling. Pretty plausible as one floor's support beams gave way....
The OP didn't do the calculation right, gravitational freefall for 2.25 seconds is a displacement of 24.8 meters.

 Quote by Borek cmatrix: please read what I wrote earlier and what Russ answered. You are right that it is not a free fall, however, once the support beams snapped, whatever was left was too weak to substantially slow down fall of the upper part of the building. For all practical purposes fall can be approximated by free fall.
I have read what you and Russ have written but it is not helping me in any way. You admit there could be no free fall but the whole problem is that NIST admits there was free fall for 2.25 seconds. I understand your point that what is seen as free fall is not necessarily precisely free fall but that seems immaterial. The problem is your claim that the structure left was too weak to offer any significant resistance. You do not explain then how fire can effectively remove simultaneously and continuously floor by floor 8 stories of structure that held a building up for decades.

Mentor
 Quote by Pengwuino The OP didn't do the calculation right, gravitational freefall for 2.25 seconds is a displacement of 24.8 meters.
Oops, that's my math error, not the OPs. I brain faded to 25 feet, not 25 meters. More like 7 stories then? Thanks Pengwuino.

Recognitions:
Gold Member
 Quote by berkeman Oops, that's my math error, not the OPs. I brain faded to 25 feet, not 25 meters. More like 7 stories then? Thanks Pengwuino.
You both did it wrong, I killed 2 PF members with 1 stone. Or at least corrected them.