"Inside Job": Hidden energy in reports by Prof. Bazant, Dr. Greening and D. Thomas

Originally posted by Akareyon
This is just great, we're coming from two different directions still heading the same way.

Look, it'll take me a few hours, days and weeks to familiarize myself with Ruby, I've just looked at the documentation and not tried one thing yet, you've got a headstart here, but I'm a good runner.

-PLB-'s point about environments like Matlab (or free stuff like Euler/Maxima or Scilab) is worth consideration. Ruby starts to jump out ahead of those if you also plan to do automated feature tracking in videos, generate scripts for serious graphing applications like Asymptote (check that one out, -PLB-, it's pretty sweet) or dumping output straight into PDFs. I cited RMagick (based on ImageMagick) because... it does everything you can think of with images except machine vision (and for that there's Hornet's Eye). If you already know C++ and are comfortable, there's even more to work with.

I've once transcribed the runes on the first page of Tolkien's Lord Of The Rings based on the runes translated from the inscription on Balin's grave before I knew that other editions of the books had a complete description of them in the appendix.

Damn.

My approach was to do the simple math of describing the forces and energies as they were before initiation and comparing them to the values I get once "the stone is sinking". Of course, they were oversimplified and only average values. Now, with PLB's and your patient help, I finally get why we've not been speaking the same language the whole time. Bazant is throwing something through the roof and I'm trying to bring the whole building down, just as I was trying to explain how my "umbrella model" works. I build a core of glass (or pasta), rest a heavy hat truss on the core and let the perimeter hang as a curtain from the edge of the hat truss. Easily could this sort of structure also support a few floor slabs. Now I give the hat truss a knock on the head and, once moving, its weight will crush (or sink) through the brittle glass structure, given the same parameters as in PLB's ice palace example, and exhibit a behaviour quite similar to the one we're discussing. The heavy hat truss is the same as the rigidness of Block C (we can crush that one (up?) later).

One minor adjustment. Bazant gives it a free drop of one story, which is like giving it a push. But the situation is that the capacity of one story diminishes - presumably from fire and impact - until it can no longer support the upper section's mass. For that one story, the peak in Fig 3 reduces to mg, and then a little less, and the upper part starts moving.

More later, but the reason pressure isn't brought up in a 1D model is that there's no such thing as area (or you could think of it as always constant), so pressure is equivalent to force.

Originally posted by IrishWristwatch
More later, but the reason pressure isn't brought up in a 1D model is that there's no such thing as area (or you could think of it as always constant), so pressure is equivalent to force.

Okay, what's the constant?

Welcome to 3D land. Of course we can draw a curve for the volume change onto a 2D grid. That's what we have to do to compute the brittleness (or domino-effect factor) of the construction. We have accounted for potential energy and kinetic energy. Our calculations are somewhat right. The building is down. We have assumed 0.5 GJ "friction" energy for each floor. Where's the rest?

The rest is shearing, buckling, tearing, falling, breaking. How much energy is that? Easy: E=p*V. We know about m*g and F_c, x, y and z, and derive p and V (or the stroke). Remember your tilted cube falling through the stacked columns, pushing them aside? Good example! That's the pressure, or tension, or how wobbly and brittle the whole structure is. One force has to overcome the other now that we have accounted for potential and kinetic energy, and it's in the strain. Where has it gone? It was there the second before! What happen?

Originally posted by IrishWristwatch
The jusification might be a problem, though, since one camp feels it's unnecessary and the other won't believe the results.

Well said, actually...

"One camp" may consider educational benefits of this exercise for students in material sciences and make it a project. I see some value in that. What "the other" believes or not is less important.

Originally posted by buddhasystem

Originally posted by IrishWristwatch
The jusification might be a problem, though, since one camp feels it's unnecessary and the other won't believe the results.

Well said, actually...

"One camp" may consider educational benefits of this exercise for students in material sciences and make it a project. I see some value in that. What "the other" believes or not is less important.

I certainly am on board with that. My interest in this comes from having increased my understanding of a bunch of fields I never had any interest in before. Everything was more interesting than structural engineering, I thought. Boy, was I wrong. No reason to expect everyone to react the same way, but students of the disciplines would have something serious to chew on for a while.

Sorry for the tone earlier. I can never quite keep that under control. I misunderstood the nature of your inquiry, and there's no excuse for it. I tend to assume people understand a subject unless I see otherwise (which, unfortunately, is usually the case) but I've noticed the opposite is true of most people I talk to - they assume I'm utterly clueless even after reams of rigorous posts. After a few years, I've gotten snappy.

Originally posted by Akareyon

Originally posted by IrishWristwatch
More later, but the reason pressure isn't brought up in a 1D model is that there's no such thing as area (or you could think of it as always constant), so pressure is equivalent to force.

Okay, what's the constant?

There are two approaches to answer that question. One, the question is meaningless in the context of 1D, Two, the constant can be anything you want.

1D can mean literally 1D, or it can be in the context of projecting the additional two dimensions onto the one. For a very simplified model, we take the quantities associated with extension into the horizontal dimensions as being uniform at that vertical location. If the entire footprint is involved in the crush front, then it makes sense to talk about the total force. The reason I say force is because we take the footprint area to be constant all the way down, so while the operative quantity really is pressure, it's always multiplied by the same area to get net force.

So the area is not part of it in 1D, but if you want to keep it concrete in your mind, the natural figure to use for area is the footprint area. Practically speaking, that's not too satisfying since most of the footprint area is empty space between the floors and, from the structural perspective, the area which counts (most) is the column cross-sectional area which is NOT constant all the way down, not at all. But, in that regard, the column areas increase as a function of the imposed load so as to maintain a relatively constant demand-to-capacity throughout the height.

Okay, the collapse is not 1D. But, if we're going to go that direction, then we're not talking about Bazant, we're talking about something different.

In any case, it's convenient to pick the units which best fit the problem. Sometimes it's setting g=1 dimensionless and adjusting all other quantities to match. Generalized coordinates for solution need not have direct physical interpretation. After solution, if you want conventional units, convert.

Originally posted by IrishWristwatch
There are two approaches to answer that question. One, the question is meaningless in the context of 1D, Two, the constant can be anything you want.

[...]

Okay, the collapse is not 1D. But, if we're going to go that direction, then we're not talking about Bazant, we're talking about something different.

I promised I'd push, not pull. Let's continue where Bazant has stopped.

Of course the space is mostly empty. But only mostly. Thick steel columns, desks, tables, floor slabs, concrete, lifts and so on occupy a fraction of the space. We don't know each and every force needed to compress it, but we have two values: one for the volume it had before collapse initiation and one after that. We also know the difference between the force that acts upon the structure when it's standing tall and the force that acts when it's falling.

This energy gives us a clue as to what happened energetically inside the structure. If you miss the factor time in the equation for pressure energy, don't panic: energy is time-independent, so let's make Einstein proud and go for space: E=p*V (funny thing: the unit of the second moment of area is length to the fourth power, so it has four dimensions: m^4!)

E we know (2,1*110 = 231 GJ), V we know (1,638,400m³) . It's the average of everything inside the Tower, no matter how solid, fluid, brittle, weak or strong it is. Pressure is force per area. We also know the (average) area, 4095m². So we have pinned down the (average) force that was necessary to overcome F_c:

p=E/V=141,327 N/m².

p=F/A, so

F=p*A=141,327 N/m² * 4095m²=578,733,673 N. Strange, that almost looks like 58,994,258 kg to me, just 100 tonnes more than the mass of Block C... on each meter of height? That's the stress on the structure now that Block C is sinking through it!

Man, I have to admit that every time you plug in (big) numbers, my eyes glaze over. That's not your fault; it's a neurosis on my part. Can we normalize story masses to 1, so that the numbers are at least small when they are plugged in?

Just to be sure if I understand correctly... 500,000 tonnes / 110 floors = 4545454 kg/floor = 1 floor mass?

Second line.

Originally posted by Akareyon
Just to be sure if I understand correctly... 500,000 tonnes / 110 floors = 4545454 kg/floor = 1 floor mass?

Second line.

Yes. Story units.

Gotta run now, see ya later.

reply to post by IrishWristwatch

Okay, I see. Now I also understand why your code puzzled me so I need some sleep, I'll translate my gibberish to unit floors tomorrow and try to resume what we have found out so far (so you can correct me in case I misunderstood) and then explain in more detail what I mean by pressure and tension. I think the katana/hug analogy fits best, since PLBs punching me on the head and our ice palace analogy opened my eyes for a different interpretation of Bazants papers. Now that we know where the equilibrium between acceleration and deceleration needs to be to fit into the given time frame, we know which forces are involved, so we just need to translate them to pressure to make sure we don't just katana-punch a hole through the roof (small volume affected), but squeeze and domino the whole structure to the ground (bigger volume affected) and see what we get.

Okay, let me try.

1 floor mass: 1
1 tower mass: 110
1 floor height: 3.7
gravitation: 9.81
collapse time: 12

Energy in the system for 30 years (m*g*h, h=distance of the centroid to the ground and therefor halved):

m*g*h/2 = (tower mass)*9.81*(110*3.7)/2 = 219596.85

(theoretical live load capacity: 2*tower mass*9.81*(110*3.7)/2= 439193.7)

===Stable system so far! Potential energy safely stored by equilibrium of tension and pressure, deceleration to v=0. Would withstand yet another atlantic cyclone.===

+++layman approach

Energy input by planes and flames (lifts 12 floors 3.7m high): 12 floors*3.7*9.81 = 435.564

Result: total crumblification in 12 seconds

average acceleration downwards: a = 2*h/t² = 2*110*3.7/12² = 5.65
average deceleration (acceleration upwards) = g-a= 4.16

deceleration energy of 98 stories below: (110-12)*4.16*(110-12)*3.7/2 = 73912.384
static energy of 98 stories below before planes crashed: (110-12)*9.81*(110-12)*3.7/2 = 174298.194

Ratio: 0,424 of energy "lost" in lower 98 floors. Where gone?

+++ice palace approach

before plane crash:
Centroid of upper 12 floors: (110-6)*3.7=384.8 metres
potential energy of upper 12 floors above ground: 12*9.81*384.8 = 45298,656
::safely stored

after plane crash:
Centroid of upper 12 floors: (110-5)*3.7=388.5 metres
potential energy of upper 12 floors above ground: 12*9.81*388.5 = 45734,22
::global collapse

Ratio: 1,0096

+++Bazant approach

load capacity 98th floor before crash: 12*2*9.81=235.44
force of block C on 98th floor after crash: 12*2*31*9.81=14597,28
Ratio: 31

"spring compression" under 12 floors before plane crash at 71GN/m: 7,68*10^-4metres (=0,00768 metres=7,68 millimetres)
spring compression under 31*12 floors after plane crash and crush: 98*3.7=362.6 metres
ratio compression: 47213,54
^divided by 31 = ratio spring's stiffness: 1523

time for block c to touch ground: 12s
potential/kinetic energy of block C during crush: 12 floors*(2*388.5/12²)*388.5=25155.375 < brings the whole structure down
again, potential energy of upper 12 floors above ground before crash: 12*9.81*384.8 = 45298,656 < safely stored
Ratio: 0,555
Difference: 20143.281 <= energy needed to crush lower 98 floors
again, static energy of 98 stories below before planes crashed: (110-12)*9.81*(110-12)*3.7/2 = 174298.194
Ratio: 0,11557
Difference=energy "gone": 154155.913 (where be?)

+++ pressure approach (E=p*V)
area (footprint) of tower: 1
average pressure: 55 floors * 9.81 per area = 539.55
Volume: area*110*3.7

Energy in the system before plane crash, safely contained: 219596.85 (compare with above: yep)
Energy input by flames and fire: 435.564 (see above)
check: 12 floors*9.81/area * area*1*3.7 (lifting block c one floor, volume.+= area*1*3.7) = 435.564
Pressure/tension added by flame/plane (lifting block c one floor): +0.702%; new average pressure 577.4166
Energy in the system after crush (rubble pile: 25 metres): 55 floors*9.81/area * area*25=13488.75
Ratio Energy before plane/after crush: 0,0614
Difference Energy before/after: 205672.536 (here maybe?)

+++eof

Bottom line is: so far, we know only how much energy was transformed into deformation energy when the towers came down (0.5GJ*110 floors=55GJ). It was really not much compared to that what held the towers up, so most of the potential energy was transformed into kinetic energy. Where's the rest? TBH, I read your ponderings "is momentum conserved, yes, no, a little, some more, a little less" and they somewhat scared me so I backed up and met PLB. Now I see why we misunderstood. All you have to do to make Newton happy is to account for the strain energy (or tension/pressure) that keeps the building up (as potential energy) and suddenly is gone. In the real world, that can also be the "domino" factor, or how much a huge marble block is already tilted before it tips when you give it a slight punch, or the energy needed to shear a steel bolt, or the brittleness of a pasta column that is already strained to the max and won't take no more. If Bazant is right and each floor resists with only 0.5GJ, they must have been under immense strain before that. Or he's really just throwing something through the roof, mathematically.

With all the graphs I've seen so far that show the decline of potential energy I miss the curve that shows the surplus strain needed to overcome the energy that kept the towers up all the time, because that's where all the potential energy went that has not become kinetic energy, but that wouldn't suffice - otherwise, the towers wouldn't be standing. Where's the rest?

Only then will we have an energy balance and may wonder which caused what: did the towers come down because the strain was too much or was the strain too much because the towers came down?

The average pressure increase that makes the balloon pop is 7%, not 0.7%, sorry, just too late to edit that out.

.

Originally posted by Akareyon
Okay, let me try.

1 floor mass: 1
1 tower mass: 110
1 floor height: 3.7
gravitation: 9.81
collapse time: 12

Personally, I see zero reason to try and match the OBSERVABLE collapse time with the exercise of comparing column to column impacts/buckling/fracture that Bazant's paper assumes, cuz bazant's assumptions definitely are false in his bounding condition that he set up for his paper.

The only thing that you should be exploring is after a single story drop, is there enough kinetic energy to "climb the mountain" in that strain graph. And then again for the next impact, and so on.

There are other interesting things that you can do here too, regarding collapse initiation. Like for example, correct bazant's mass errors using greg urich's study and see what happens. Another would be - IIRC a free fall drop of one story results in an impact speed of 19 mph. So then determine at what speed, and therefore average acceleration value, would enough kinetic energy be imparted onto the l;ower columns for the collapse to continue. Etc...

Then, if you wish to refine it further, you can add in kinetic energy losses due to concrete breakage of the floors, mass loss, etc.

So in the end, if being strict in the science, and doing this says that the fall should of taken 12 seconds, or 18 seconds, or 24 seconds, it is irrelevant to the observable collapse time. Because trying to match an observable collapse time to an impossible collapse situation of direct column to column impacts all the way to the ground, and THEN trying to explain what would have been happening in order to match the times is a fool's errand.

And lastly, If there is interest, it would be MOST interesting to try and do a real study that tries to use factors that are indeed observable. These factors would include:core columns didn't impact directly but instead landed on floors/floor beams, ext columns below the initiation zone didn't offer any resistance nor add to the falling mass since they are clearly seen falling away, most of the resistance would be provided by the truss connections. etc, etc......

Joey, you're absolutely right. Bazant's work isn't worth the bytes it is using up on my hard disk. However, IrishWristwatch, PLB and I have agreed to use it as drunk people use street lamps: for support rather than for illumination, and it did so quite well until we found out what Bazant is doing to make sure that on each impact, the kinetic energy is enough to climb the peak of the buckling force curve.

And lastly, If there is interest, it would be MOST interesting to try and do a real study that tries to use factors that are indeed observable. These factors would include:core columns didn't impact directly but instead landed on floors/floor beams, ext columns below the initiation zone didn't offer any resistance nor add to the falling mass since they are clearly seen falling away, most of the resistance would be provided by the truss connections. etc, etc......

All these variables are now summed up in the part with the pressure/tension energy which noone has been talking about so far. If the area under m*g is constantly greater than the area under the maxwell line, that is: the Energy needed to crush one floor exceeds the energy to decelerate the fall, there are not many alternatives: either the mass of Block C is much greater than 12 floors, or the 12 floors are going through the floor slabs only, or the structure was under great stress before that.

So somehow all the energy that "contained" the potential energy for 30 years must go somewhere before the potential energy becomes kinetic. Bazant is not losing one syllable on the energy needed to bring the whole building down. He assumes 2.1 GJ to trigger almost 1 TJ to be "inevitable" because he assumes almost no energy being in the way of the collapse. We're looking for the rest of the energy, it must have gone somewhere obviously. Some of it went into heat, friction and deformation as it went down, but we're still missing quite a lot, and with E=p*V, we can account for that. We're not so foolish to try and emulate the collapse, we're trying to describe and to analyse it - of course based on the flawed assumptions of Bazant, because it's his name in the NIST report - to show what energy he must hide in his assumptions to bring the towers down in time. It is the pressure, or the tension the structure was under - so it's steel beams missing each other, perimeter walls being ejected to the side, concrete slabs sintered, bolts sheared, domino blocks stacked and so on, even if just an average number.

I understand why Bazant used the value for kinetic energy consumption that he did, but making an estimate of the actual energy consumption seems a bit pointless to me. A more realistic estimate will results in a lower value for kinetic energy consumed, mainly affecting the collapse time.

I think that making an estimation by accounting for all energy sinks is extremely hard, there are many factors that play a role. If you want to make a good estimate, it seems a different approach would make more sense, which is to calculate energy consumption from the known collapse time. After this figure is calculated, it can be compared to what we would expect to see if it is realistic. But that would still required quite some guesswork.

Over all I am not really sure which direction this analysis is going to. What exactly is it that needs to be analyzed and what exactly are the expected results?

reply to post by -PLB-


Okay, let me put it this way.

Block C was sinking through the rest of the structure like a stone in water. Before that, it was resting on it and we know the structure could easily have taken two Block Cs. What happened to the structure? Did it become liquid?

My assumption is that yes, it did, because in a scenario one would expect, Block C would crush a few stories and come to a halt. It did not, it sank to the ground. Why? Bazant says: nothing in the way, maxwell line all the way down. All the tension that kept all the mass up in the air was suddenly gone. Accounting for that very tension (or pressure) would prove that there was more than just the potential/kinetic energy of block C that brought the tower down. After all, what is the difference between a solid and a liquid or a liquid and a gas? The tension between the molecules.

Let me show you something.

E=p*V
p=pressure of block C during collapse on the rest of the structure=force per area=12*(2*388.5/12²)/area
V=area*height=3.7*98*area

E=140870.1

reply to post by Akareyon


Gravity and momentum were pushing it, and it wasn't a big solid block. That's way oversimplifying it. It was a collection of trusses and steel pieces, office stuff, concrete, sheet rock, etc.

The trusses especially had no vertical supports within them. If one falls on another and breaks its connection, then it will simply fall down to the next truss. This was one of the big flaws in the design that had allowed for major retail space. Without any kind of resistance between the floors outside the core, there was nothing stopping the momentum of the collapse.

Originally posted by Akareyon
Sorry to break the news this way. 9/11 was an inside job all the way from top to bottom.

You made it abundantly clear that motivation for the thread was ideological, not scientific or engineering. Why did we bother with all the math...

reply to post by Akareyon


I don't really follow you. One moment you agree that yes, indeed, a gravity driven progressive collapse is possible, and the next you say 911 must be an inside job.

It was the top section that was pulled down by gravity. That is where the energy came from. The mechanism is explained by the ice plate example. I also showed you the energy budget in the Bazant model. It showed that even with a gross overestimated energy consumption in the crushing of floors there is still a lot of excess kinetic energy.

The forces were not constant but large at one moment and small another, as explained in another post. That gives the low average force. Again, you can't just compare an average force over a distance with a force in equilibrium. If the distance between the floors in the WTC was higher, the average force (F_c) would be even lower, but the collapse speed and amount of KE would be higher.

Since I am now only repeating myself I will now retreat from this thread.

reply to post by buddhasystem


I actually typed the exact same thing in my post above but decided to remove it again. But yes, it seems to be very obvious.