The Obligatory 9/11 Thread Part II

[tolman]

Computing the potential energy of some masses at some heights without computing the energy required to destroy the structures below which are supporting that mass is nonsense.

It's certainly not nonsense when it comes to people suggesting demolition as an explanation for the destruction ultimately caused, since it's pretty clear that the damage caused any practical amount of 'chemical persuasion' pales into insignificance compared to the energy stored in the structure.

The distance h must be empty space

Why must any particular space be empty?
That's just an arbitrary condition not based on any obvious understanding of the physics of collapse.

If someone imagined a top section of a building (or a growing debris pile resulting from the collapse of that top section) impinging on a relatively solid structure below, the difference between that falling mass falling entirely free and being supported by some structure clearly flimsy with respect to the falling mass is obviously minimal. Replace empty space with a ring of bamboo and paper screens and minimal change is made to the speed of the falling mass of steel and concrete compared with what would happen if the space were empty.
Gradually increase the energy-absorption capability of the intervening structure and decreasing amounts of potential energy will be converted into kinetic energy, but all that is required for collapse to continue is for the potential energy released by mass falling not to be completely used up in deformation of the structure below (and in deformation of the falling mass itself).

It's simply a bogus argument that a distance fallen must be empty space for collapse to continue.

How are you getting on with my earlier question?
If a given building X was also duplicated exactly as the top half of building Y, with the bottom half of Y being some appropriately strengthened continuation of the upper half, would failures identical in size and distance from the top of both X and Y be expected to progress differently, at least to the point where any collapse zone was starting to be reach the half-way point of Y, even though they'd seem to be happening in identical structures?

If your answer is no, and that any collapse (or failure to collapse) must be effectively the same in both X and the top half of Y, that would suggest that your demands that a falling section should be considered relative to total building size are nonsensical, since with identical collapses in X and the upper half of Y, at all times in Y the falling section is half the relative size, falling half the relative distance, and is less than half the relative mass compared to Y overall than the falling section in X is compared to X overall.

If your answer is yes, you'd have to explain what physical mechanisms allow the process of progressive collapse in Y to 'know' about the existence of the lower half of the building and progress meaningfully differently. I don't see anything like a tiny bit of springiness in the lower half of the building making much difference to what happens higher up.

Maybe it's unfair to give you a choice of two ways to fail, but my question is a fairly obvious logical consequence of your ideas regarding 'relative' sizes of falling sections and 'relative' distances of falling being important.

[psikeyhackr]

Why must any particular space be empty?
That's just an arbitrary condition not based on any obvious understanding of the physics of collapse.

Is the formula for potential energy PE = mgh ?

Is g gravitational acceleration?

How can the mass undergo that acceleration over distance h if it is not empty space?

http://jersey.uoregon.edu/vlab/PotentialEnergy/

A book lying on a table 3 feet above the floor can't fall. If you slide the book over the edge then it will have empty space under it. But what if the desk is on the 10th floor of the building. What is h? Is it 3 feet or 93 feet? Which is the valid answer to the question. What if a building is being constructed next door and they have dug a 20 foot hole for the foundation. Is h 113 ft.

If a 20 ton column section was 500 feet up in the core of the WTC and welded above and below and on all sides with horizontal beams. It is not like a book sitting on a desk that can be slid side ways. What is the MEANING of potential energy in that case? The column section can't move. Energy would have to be expended to force the material beneath out of the way. So computing the so called Potential Energy without computing the energy required to crush the material below makes no sense.

Potential Energy is not energy. It is only the POTENTIAL TO BECOME ENERGY. It can only become kinetic energy by falling through that empty space.

This 9/11 business is a lot of ONE SIDED PHYSICS designed to rationalize what some people prefer to believe. Where is the calculation of the amount of energy required to crush/destroy/obliterate each level so the material above can fall? How can that calculation be done without knowing the AMOUNT OF STEEL on each LEVEL?

So how do people claiming to know physics talk about potential energy without bringing up such OBVIOUS DETAILS?

If the energy required to crush the WTC was greater than the potential energy then what would happen? So where is the calculation of that energy? When does anyone ask for it? The people who have decided to BELIEVE don't need such facts.

psik

[tolman]

Is the formula for potential energy PE = mgh ?

Is g gravitational acceleration?

How can the mass undergo that acceleration over distance h if it is not empty space?

But you seemed to be arguing that the acceleration was only 0.5G.
Wouldn't that require some kind of physical presence to be partly impeding the fall, though not nearly enough to prevent its acceleration?

A book lying on a table 3 feet above the floor can't fall. If you slide the book over the edge then it will have empty space under it.

A sufficient weight impacting the table with sufficient speed may cause the legs to fail and the table top+book+impacting weight to fall to the floor.
If you knew the speed of the weight at impact with the table, and the speed of top+book+weight when they reach the floor, you could calculate how much energy was absorbed by the failure of the table legs (and by damage to the weight, book, etc) up to that point.
Depending on the nature of the legs, it's perfectly possible for the combined kinetic energy of the total hitting the floor to be greater than the kinetic energy of the weight hitting the table, as long as the kinetic energy 'lost' in deforming the legs/table top/book/weight is less than the kinetic energy gained by the lowering of the various components to floor level.

That the legs are 'in the way' merely indicates that the falling will be at some lower acceleration than g, but even were one to imagine a situation where the table top was somehow levitated up to the instant of impact from above and then magically released, one wouldn't get an acceleration of g for the weight anyway - some energy would be absorbed in the collision, and some kinetic energy would need to be transferred to the table top to get it moving along with the falling weight.

But what if the desk is on the 10th floor of the building. What is h? Is it 3 feet or 93 feet? Which is the valid answer to the question. What if a building is being constructed next door and they have dug a 20 foot hole for the foundation. Is h 113 ft.

If you can't work that out, I'd suggest that you probably shouldn't be trying to make any physics-based arguments.

I'd have thought it self-evident that if looking at a progressive collapse modelled as a roughly co-ordinated upper mass falling on and collapsing a structure below, 'h' depends on what part of a collapse one chooses to look at.
If one is looking at what happens when the upper mass moves from point A to point B, then 'h' is the distance between A and B
If one is looking at what happens between times t1 and t2, then h is the distance between where the mass is at t1 and where it is at t2.

If looking at a supposed progressive collapse instant-by-instant, the distance to the ground is irrelevant unless one has some plausible mechanism for that distance to affect what happens in a hypothesised zone of destruction at the top.

It would really help people understand where you're coming from if you'd answer my question regarding the building X and the double-height building Y which has a top half identical to X. Given identical failure events at the same absolute distance from the tops of X and Y which lead to progressive collapse of X, do you actually expect the failures in the two buildings to have different histories before the point where the collapse zone reaches the bottom of X?

If so, in what ways would you expect the histories to be different, and what physical mechanisms would you suggest were behind any differences?

[tolman]

And I'm prepared to keep asking that same question over and over until you answer it, so I can see what you think you mean by making conditions regarding the relative height/mass of a falling section or the relative distance it falls compared to the overall building.

I simply don't understand why you think your conditions are relevant, and I guess I may not be alone in that.

[psikeyhackr]

Is the formula for potential energy PE = mgh ?

Is g gravitational acceleration?

How can the mass undergo that acceleration over distance h if it is not empty space?

But you seemed to be arguing that the acceleration was only 0.5G.

I never said what the acceleration was. I said in order to come down in less than 18 seconds it had to be more than 0.5 G.

Since bending/breaking/dislocating/destroying/crushing the SUPPORTING mass below requires energy and the only source is the mass falling from above then it had to slow down level by level. But since that is not what happened then SOME OTHER FACTOR had to be involved. I am not attempting to explain what that factor was I am simply trying to show that what we see is IMPOSSIBLE on the basis of the KNOWN FACTORS.

But then there are things that we should know but do not. Like the TONS of STEEL and TONS of CONCRETE that were on every level. How can the amount of energy necessary to destroy each level be determined without that information?

psik

[tolman]

Since bending/breaking/dislocating/destroying/crushing the SUPPORTING mass below requires energy and the only source is the mass falling from above then it had to slow down level by level.

I think you may be confusing 'slowing down' (as in 'moving with decreasing velocity') 'with being slowed by X' (in the sense of moving slower than one would have done if X were not there).

The presence of a structure may very easily slow down a falling weight in the second sense while not slowing it down in the first sense.

At the very least, it would be useful if you could make it absolutely clear in which sense you were using the phrase.

It's obvious from an energy perspective terms (that even if the structure being damaged wasn't actually contributing any extra mass to the collapse) that if the energy absorbed in the failure of one level was less than the potential energy lost by the falling mass falling one level, the mass could fall at an ever-increasing rate while causing the structure to progressively fail.

[atrasicarius]

You know what? Fuck this. I'm not going to try and teach high school physics to someone who's going to contradict me every single step of the way. Here's a free online course on classical mechanics: http://ocw.mit.edu/courses/physics/8-01 ... fall-2003/ . Please dont come back until you've gone through and understood the whole thing.
kthxbye

[psikeyhackr]

The fact that your model did not lead to a progressive collapse bellies why it does not actually model anything of value. You can't cause damage to multiple floors most of the way up a steel and concrete structure and expect the collapse to just STOP after a few floors. 15 floors crashing down on one floor is more than enough to knock the whole thing down- as seen in the dozens of videos of the collapse. At no point in the building was a floor able to sustain the weight of 15 floors directly on top of it even as a static load. the event was too dynamic and too large scale to properly have all of the variables accounted for in a few paper loops and washers.

Talking about: 15 floors crashing down on one floor is totally distorted rubbish.

Consider it as 1 level stuck on the bottom of 14 levels crashing down on 1 level stuck on the top of 93 levels.

So those TWO single levels end up crushing each other and then it is 1 level stuck on the bottom of 13 not quite crashing down on 1 level stuck on the top of 92 levels.

Which stack of levels will run out first?

psik

[uke2se]

Talking about: 15 floors crashing down on one floor is totally distorted rubbish.

Consider it as 1 level stuck on the bottom of 14 levels crashing down on 1 level stuck on the top of 93 levels.

So those TWO single levels end up crushing each other and then it is 1 level stuck on the bottom of 13 not quite crashing down on 1 level stuck on the top of 92 levels.

Which stack of levels will run out first?

psik

Physics doesn't work that way, psik.

[byofrcs]

The fact that your model did not lead to a progressive collapse bellies why it does not actually model anything of value. You can't cause damage to multiple floors most of the way up a steel and concrete structure and expect the collapse to just STOP after a few floors. 15 floors crashing down on one floor is more than enough to knock the whole thing down- as seen in the dozens of videos of the collapse. At no point in the building was a floor able to sustain the weight of 15 floors directly on top of it even as a static load. the event was too dynamic and too large scale to properly have all of the variables accounted for in a few paper loops and washers.

Talking about: 15 floors crashing down on one floor is totally distorted rubbish.

Consider it as 1 level stuck on the bottom of 14 levels crashing down on 1 level stuck on the top of 93 levels.

So those TWO single levels end up crushing each other and then it is 1 level stuck on the bottom of 13 not quite crashing down on 1 level stuck on the top of 92 levels.

Which stack of levels will run out first?

psik

Unless the rubble from the crushed levels is ejected completely away (sideways) then you'll eventually end up with the rubble of a number of floors, constrained to stay outside the core and within the outside walls crushing each floor in turn and adding to the rubble.

[Kat Dorman]

Talking about: 15 floors crashing down on one floor is totally distorted rubbish.

Consider it as 1 level stuck on the bottom of 14 levels crashing down on 1 level stuck on the top of 93 levels.

On this I agree. Even Bazant uses the simplification "energy dissipated at the crushing front", but then turns around and simplifies the upper block by making it rigid. Not paradoxical (a rigid upper block doesn't dissipate energy) but not terribly realistic, and not made a whit more so by the treatment in B&L. Reality is, there are initially at least two deformable and frangible bodies. It's only 15 (or 14 or 12) stories against one if the mass of 15 rigidly impacts one.

Fat chance, I say. In the idealized 'upper block' scenario, this might be an example of a more realistic outcome:

http://the911forum.freeforums.org/a-sma ... tml#p10861



Simultaneous crush up/down, even in an imaginary plumb axial strike. I'm not trying to peddle this simulation as accurate for the tower perimeters, rather I think it likely it shares similar characteristics.

So those TWO single levels end up crushing each other and then it is 1 level stuck on the bottom of 13 not quite crashing down on 1 level stuck on the top of 92 levels.

Here I part company with you. Crush UP (versus down) doesn't mean compression of vertical members upward, it means crushing of the members above. All of the crushing is down. IF a story crushes completely, that which is above it has (by definition) moved down by the crush height in the process regardless of whether the story is part of the upper or lower. That's the Δh which plugs into mgΔh. If it's a partial crush, then adjust Δh accordingly. PE is lost according to Δh, not before the change in height occurs.

Which stack of levels will run out first?

This is the wrong question to ask for the towers, a heterogeneous 3D case. The answer to your question does not necessarily influence the outcome (wrt arrest) in the general case - but it can in the 1D case. I can't imagine how it could possibly lead to arrest in the towers, not with that minimally adequate garbage chute called the perimeter. As has been pointed out several times, the failed mass is still there unless it goes over the side. It either stays put or goes down. The latter is a safe bet for the towers because the path is through comparatively flimsy floor diaphragms, but not at all for a 1D slab model...


(camera view axis remains fixed on top slab or 'roofline' so it appears stationary as building crushes 'up', but all motion is actually DOWN)

Crush up then arrest. This is a physics simulation which can, with the same parametric settings and artificial upper block rigidity, reproduce Greening's step-wise algebraic model nearly perfectly (WTC1 in this case):



Thus it is a discretized version of simple BV mechanics with one twist: there's no imaginary constraint against crush up as Bazant imposed unless you decree it so in code. Crush direction otherwise goes however the collision dynamics dictate, given the structure. In a 1D model with constant demand-to-capacity ratio up the entire height (and with the brittle joints I used...), exclusive crush up is favored and this usually leads to arrest. In B&L, Bazant makes the case for insignificant crush up of the overlying story based on realistic but still somewhat arbitrary estimates of the relative residual capacities above and below in a perfect axial strike. So goes the rigid block.

The work I've done to this point strongly indicates the result of exclusive crush down is actually quite a narrow case, and had Bazant gone just a few percent weaker with the overlying story, the cusp into radically different dynamics would be crossed. This, I feel, is one of the failings of the 1D model besides some of the more obvious limitations. With a slight tweak of parameters, the result could easily be exclusive crush up concluding with arrest and no crush down at all! This condition is what I like to call the 'dumpster in the sky'; not at all a realistic physical scenario. Yet, if you're going to claim the validity of the model, you certainly have to stand by it even if doesn't turn out exactly the way you wanted. Especially in the neighboring solution space all around the special solution you highlight in your presentation....

All this to say is 1D models, analytical or physical, have limited applicability to the real tower collapses. There are some gems of knowledge to be extracted, sort of like ideal pendulums as applied to general oscillatory phenomena.

[Weaver]

Thank you, Kat - that was very informative. I can tell you put some significant time and effort into your replies in this thread, and I've learned a lot from them.

[tolman]

(Not claiming to be the relevant kind of engineer here - just thinking out loud. Corrections welcome.)

Thinking of a structure failing and the upper section falling as a structure onto/through the lower section, if energy absorption was in the form of bending columns, etc, my first 'guess' would be to imagine roughly similar kinds of energy absorption from damage to the structure below and the structure above the zone of failure, at least to the point where the structure above has largely degenerated into a heap.
Though even then, if I imagine a 'half-way point' in the destruction of the upper structure, where its lower half has accumulated into a heap of rubble, that heap of rubble is slamming into the building below, accumulating mass all the time.

The remaining structure intact on the top of the pile seems to be having a quite different experience. It looks like it might be feeling less and less effect from the continual impacts of the pile below with the lower building - imagining it as a building remnant sitting on a debris pile, one could argue that if there aren't any huge shocks coming back up through the debris pile from below, then the upper building fragment could be under less duress sitting on a downwards-accelerating pile of rubble than if it was standing on the same pile of rubble on the ground.

Given the buildup of a suitably large debris pile, might the remaining upper section end up being relatively insulated from the damage below, up to the point where the debris starts meeting the ground? The upper section may still be providing force to the top of the debris pile, but if the debris and upper section are accelerating, wouldn't that force be rather less than the weight of the upper section, and hence it may seem to the upper section that it's standing on a debris pile in sub-earth gravity?

That's almost certainly an oversimplification, but it does suggest an asymmetry between the upper and lower 'intact' sections of the building - the zone between then is falling (and quite possibly accelerating) downwards, and the upper section is falling pretty much along with it, not continually impacting into it.
(Maybe the asymmetry is different as the speed of collapse varies?)

It's entirely possible that even apart from inevitable complications when it comes to reality, I'm missing something fundamental in the above.
If so, please would someone point it out.

[atrasicarius]

(Not claiming to be the relevant kind of engineer here - just thinking out loud. Corrections welcome.)

Thinking of a structure failing and the upper section falling as a structure onto/through the lower section, if energy absorption was in the form of bending columns, etc, my first 'guess' would be to imagine roughly similar kinds of energy absorption from damage to the structure below and the structure above the zone of failure, at least to the point where the structure above has largely degenerated into a heap.
Though even then, if I imagine a 'half-way point' in the destruction of the upper structure, where its lower half has accumulated into a heap of rubble, that heap of rubble is slamming into the building below, accumulating mass all the time.

The remaining structure intact on the top of the pile seems to be having a quite different experience. It looks like it might be feeling less and less effect from the continual impacts of the pile below with the lower building - imagining it as a building remnant sitting on a debris pile, one could argue that if there aren't any huge shocks coming back up through the debris pile from below, then the upper building fragment could be under less duress sitting on a downwards-accelerating pile of rubble than if it was standing on the same pile of rubble on the ground.

Given the buildup of a suitably large debris pile, might the remaining upper section end up being relatively insulated from the damage below, up to the point where the debris starts meeting the ground? The upper section may still be providing force to the top of the debris pile, but if the debris and upper section are accelerating, wouldn't that force could be rather less than the weight of the upper section, and hence it may seem to the upper section that it's standing on a debris pile in sub-earth gravity?

That's almost certainly an oversimplification, but it does suggest an asymmetry between the upper and lower 'intact' sections of the building - the zone between then is falling (and quite possibly accelerating) downwards, and the upper section is falling pretty much along with it, not continually impacting into it.
(Maybe the asymmetry is different as the speed of collapse varies?)

It's entirely possible that even apart from inevitable complications when it comes to reality, I'm missing something fundamental in the above.
If so, please would someone point it out.

Seems pretty reasonable to me. Always keep in mind what's the same whether explosives were used or not. Even if the collapse was started with explosives, it would have followed the exact same pattern. Therefore, saying things like "The top block should have come apart if explosives werent used" doesnt work.

[psikeyhackr]

at least to the point where the structure above has largely degenerated into a heap.

How does the structure "degenerate into a heap"?

What is the source of the energy that causes that?

You explain things by dismissing things. It is called BELIEVING. So scientific!

psik

[Weaver]

at least to the point where the structure above has largely degenerated into a heap.

How does the structure "degenerate into a heap"?

As he explained in his post, through multiple collision impacts.

What is the source of the energy that causes that?

Gravity.

You explain things by dismissing things. It is called BELIEVING. So scientific!

psik

Whereas you dismiss things by focusing on irrelevancies and trivial points of weak communication rather than addressing core meanings and the real world. It's called DENIAL - and it's not scientific at all.

[tolman]

It's almost like psikeyhackr doesn't understand that a building could be quite stable in normal conditions, despite containing more than enough stored potential energy to pulverise the material it contains.

[Kat Dorman]

Thank you, Kat - that was very informative. I can tell you put some significant time and effort into your replies in this thread, and I've learned a lot from them.

You're welcome. I was afraid that one was a bit much...

I find the subject of progressive collapse fascinating, to the point of getting a little frothy at the corners of my mouth. If it gets too tedious, just holler.

[Kat Dorman]

It's almost like psikeyhackr doesn't understand that a building could be quite stable in normal conditions, despite containing more than enough stored potential energy to pulverise the material it contains.

I believe you hit the nail on the head, or at least one of them. This seems to be a difficult pill for many to swallow, the notion of a metastable structure. There's an extremely narrow potential barrier between an intact skyscraper and a pile of debris at its natural angle of repose.

psikeyhackr has noted he made his model as weak as possible yet capable of supporting self-weight statically, then asks incredulously if the towers were also made as weak as possible. The answer is YES. To within acceptable engineering practice, most definitely. No doubt 400+m structures could be made with a much higher factor of safety than is estimated for the towers, yet there would be little office space for rent to offset the high costs of doing so. A skyscraper is made with a MINIMUM acceptable margin of safety for sound economical reasons. This acceptable level of integrity only applies when very close to the as-built condition. And, even then, dynamic conditions can locally overcome the strain potential barrier at each level, as in Bazant's limiting case where no capacity degradation is assumed.

[psikeyhackr]

It's almost like psikeyhackr doesn't understand that a building could be quite stable in normal conditions, despite containing more than enough stored potential energy to pulverise the material it contains.

Nobody has accurate data on the building and you CLAIM to understand.

We don't know the distribution of steel in the building therefore you cannot accurately calculate the Potential Energy anyway.

Try finding the total amount of concrete in the towers. Because they were famous buildings with lots of tourists there is data that was handed out decades before 9/11. It says 200,000 tons of steel and 425,000 cubic yards of concrete. But there were two types of concrete used, 110 lb and 150 lb/cu ft. Try finding accurate data on how much of each.

But skyscrapers must withstand the wind and that must put A LOT of torque on the base. So I am sure there was LOTS of 150 lb CONCRETE IN THE SIX BASEMENT LEVELS and I would bet money on plenty in the first five stories above ground level.

But we don't have trustworthy data from any OFFICIAL SOURCE. In fact the only source even vaguely plausible is a programmer in Sweden who say he got data from the SAP2000 database. So why can't the NIST provide that in human readable form? But Gregory Urich admits he did an interpolation for the 236 perimeter columns that went from the 9th floor to the top,

So all you are claiming to do is BELIEVE on the basis of inadequate data. How do you compute the amount of energy necessary to collapse a LEVEL when you don't even know the amount of steel? This is a joke.

Let's see you build a model that can support itself and totally collapse. If it could happen to buildings that were not deliberately designed to collapse why shouldn't it be relatively easy to design a model to deliberately collapse. No live load required, no safety margin required. It should be a piece of cake.

psik