Moderated Steel structures cannot globally collapse due to gravity alone

[Bell]

Still accelerating? It is bouncing in my stuctural analysis calculations. Acceleration comes to a halt! Tell me what is wrong with that!

The fact that the towers are not there anymore.

 

[Dave Rogers]

The basics are quite simple! We can estimate the available energy, PE, at an alleged pure 'impact' of the upper part against the lower structure. Let's say it is 0.61 GNm (because some energy was consumed buckling columns before impact). It is only 170 kWh - that some people use to heat one house during a week.

So, first of all you're double-counting some of the structural resistance by subtracting it from the potential energy. Got that.

And we can likewise estimate how the intact structure below can absorb this energy as elastic deformation, elastic strain energy, ESE, by assuming a spring constant C = 0.5 GN/m (which is very reasonable. Don't believe the Bazant figure of 71 GN/m).

Let's run with your unsourced wild guess at the spring constant, then. Let's also assume that the entire lower structure acts as a single spring, even if in reality it doesn't.

The associated deformation of the total structure below is then 1.56 meter and the maximum force developed is 0.78 GN (spread around in 280+ columns) during this elastic deformation process.

Not quite. You have this odd habit of pretending gravity doesn't exist. While the spring is compressing, the lower block continues to fall, liberating further potential energy. You've assumed that the spring only needs to compress enough to absorb that initial 0.61GNm, but it actually needs to compress to the point where the energy in the spring equals the final, not the initial, potential energy. I don't know your starting numbers for mass and initial drop so I can't estimate how much that is, but I'd guess you need to adjust your compression up by about 50%.

But let's go with your simplifications and calculation errors. You've compressed the bottom block by about 0.36% (1.56m / 433m). Now, I'm a little outside my speciality here, but I suspect this is a little past the yield point of the structure. A36 steel has a Young's modulus of 200GPa, an elastic limit of 250MPa and an ultimate yield point of 400MPa. The Young's modulus therefore corresponds to a compression of 0.125%, after which the columns will be deforming plastically. You're claiming that they're still behaving elastically at 0.36% compression. Do you think, speaking as a professional engineer, that this is a reasonable conclusion?

Dave

 

[Heiwa]

So, first of all you're double-counting some of the structural resistance by subtracting it from the potential energy. Got that.



Let's run with your unsourced wild guess at the spring constant, then. Let's also assume that the entire lower structure acts as a single spring, even if in reality it doesn't.



Not quite. You have this odd habit of pretending gravity doesn't exist. While the spring is compressing, the lower block continues to fall, liberating further potential energy. You've assumed that the spring only needs to compress enough to absorb that initial 0.61GNm, but it actually needs to compress to the point where the energy in the spring equals the final, not the initial, potential energy. I don't know your starting numbers for mass and initial drop so I can't estimate how much that is, but I'd guess you need to adjust your compression up by about 50%.

But let's go with your simplifications and calculation errors. You've compressed the bottom block by about 0.36% (1.56m / 433m). Now, I'm a little outside my speciality here, but I suspect this is a little past the yield point of the structure. A36 steel has a Young's modulus of 200GPa, an elastic limit of 250MPa and an ultimate yield point of 400MPa. The Young's modulus therefore corresponds to a compression of 0.125%, after which the columns will be deforming plastically. You're claiming that they're still behaving elastically at 0.36% compression. Do you think, speaking as a professional engineer, that this is a reasonable conclusion?

Dave

If you check my calculations you will find that the extra 0.514 GJ energy produced by a 1.56 m compression is taken care of (i.e. as elastic compression of the spring). The maximum force produced during compression, uniformly applied on the columns, will not produce stress >yield, so therefore a bounce would result. But evidently the upper part will slide off the columns or the columns will never meet at impact - the columns will punch through the thin floors producing plenty of local failures of the floors that in turn will hinge down, etc. That's why I add that you have to consider that - energy consumed by local failures. It is normal practice in structural damage analysis. NIST has not done it ... yet.

And then you should consider friction between all these partly damaged floors, etc.

Bazant, Greening and Benson assume that all columns contact at impact ... and that the top part of all columns fail ... and that this impact is repeated 92 times, while the upper part remains intact.

Re my spring constant C it is not a wild guess:

Benson has just (today!) told me, very politely, at another forum:

"That result applies, strictly speaking, only to a one-dimensional homogenous crush down. Since the top portion was tilted and the sturcture was not homogeneous, no damage to the top portion is only an approximation to reality. For example, we know that some small part of the core punched through to form the temporary spire at crush-complete; it only lasted a few seconds. Despite this an some other, minor evidence, the best fit to the seismograph record implies that the upper portion remained up on top of the crushed portion most of the way to the bottom."

Not very convincing, to say the least. In the Bazant/Benson paper it is assumed that the whole structure is homogeneous (and rigid) except the one floor that is being crushed. After one floor has been crushed, the next floor becomes non-homogeneous/non-rigid and crushes, etc, etc. It is one reason the Bazant structure is so stiff - 99% is rigid, 1% - a floor being crushed is non-homogeneous. Try to compress something homogeneous. It is not possible in one dimension! That's why Bazant/Benson assumes a spring constant C that is 140 times bigger than the one I calculate.

So I replied:

"Sub-topic is the stiffness of the WTC1 steel structure alleged to have globally collapsed due to gravity force only. Evidently you have to treat the structure/stiffness in 3-D and then it becomes very springy - like a sponge; light structure of elastic material full of holes able to absorb water. It is quite difficult to destroy a sponge dropping another sponge on it. The other sponge bounces.

I am happy to see that you acknowledge that your results only apply to "strictly speaking, only to a one-dimensional homogenous crush down." But what is that???"

No reply, yet.

But I am happy to have found a new Heiwa type experiment that should convince my fellow engineers what happens when you drop a structure on a similar, but bigger piece, of structure. Try to destroy a sponge by dropping another sponge on it. Actually WTC1 upper part has all the charcteristics of a sponge (consisting of strong elastic columns, weak elastic floors and plenty of holes (air)), i.e. not very rigid and definitely not homogeneous.

 

[Bell]

But I am happy to have found a new Heiwa type experiment that should convince my fellow engineers what happens when you drop a structure on a similar, but bigger piece, of structure. Try to destroy a sponge by dropping another sponge on it. Actually WTC1 upper part has all the charcteristics of a sponge (consisting of strong elastic columns, weak elastic floors and plenty of holes (air)), i.e. not very rigid and definitely not homogeneous.

I'm under the impression that Heiwa and Christophera must be related in some way. They atleast share the same last letter in their names.

 

[Dave Rogers]

If you check my calculations you will find that the extra 0.514 GJ energy produced by a 1.56 m compression is taken care of (i.e. as elastic compression of the spring).

Initial PE 0.61GJ, k=0.5GN/m gives 1.56m compression. Your elastic compression energy doesn't include any extra 0.514GJ.

The maximum force produced during compression, uniformly applied on the columns, will not produce stress >yield, so therefore a bounce would result.

Please show your calculations to derive the result that the stress is less than the yield stress. I'm seeing, as I just said, a 0.36% compression of the steel, which is nearly three times the elastic yield point and nearly twice the ultimate yield point of A36 steel. Would you like to try and refute those numbers?

Dave

 

[dtugg]

But I am happy to have found a new Heiwa type experiment that should convince my fellow engineers what happens when you drop a structure on a similar, but bigger piece, of structure. Try to destroy a sponge by dropping another sponge on it. Actually WTC1 upper part has all the charcteristics of a sponge (consisting of strong elastic columns, weak elastic floors and plenty of holes (air)), i.e. not very rigid and definitely not homogeneous.

Are you sure that you are not a comedian by trade, Heiwa?

 

[Gnu World Order]

The fact that the towers are not there anymore.

Well, we now know that the top portions bounced. Up to heaven, apparently.

 

[GStan]

<snip>

No reply, yet.

But I am happy to have found a new Heiwa type experiment that should convince my fellow engineers what happens when you drop a structure on a similar, but bigger piece, of structure. Try to destroy a sponge by dropping another sponge on it. Actually WTC1 upper part has all the charcteristics of a sponge (consisting of strong elastic columns, weak elastic floors and plenty of holes (air)), i.e. not very rigid and definitely not homogeneous.

I want to say that I'm shocked. Perhaps drop a couple of these in the thread:







Or maybe a few of these:







Or even a few of these:







But come on already! Pizza boxes, bathroom scales, car on car porn, feathers.....and now sponges! I hope those of you who have continued to entertain Heiwa over the past several months have at least learned something yourselves in composing your posts. The time you spent writing them is time that you will never get back, and it should have been clear a long time ago that Heiwa has neither the desire nor the ability to learn anything from you.

 

[Dave Rogers]

Now, let's go back to that initial figure of 0.61GJ of potential energy. Heiwa, what's your justification for that figure? According to your paper, you've arbitrarily decided to subtract half the potential energy as being lost to deformation and friction. This is best described as pulling numbers out of thin air, because we have a membership agreement here. We can forget friction; there is no force between vertical surfaces in a vertical fall to cause friction. We can also forget entanglement, as this is just another mechanism for deformation. So we've got a loss of 0.61GJ due to deformation of one damaged storey. Now, you've calculated elsewhere that 0.61GJ represents something like half the maximum possible elastic strain energy of the entire lower structure, which, as you may recall, is the lower 97 storeys. Is this partly damaged, collapsing storey nevertheless about 50 times stronger than any of the undamaged storeys below? I think not. Let's estimate that it can absorb 10 times its share of the maximum elastic strain energy in plastic deformation, a reasonable assumption I think. That gives us an energy loss of 0.07GJ, not 0.61GJ. Therefore, the potential energy that has to be absorbed by the spring is not 0.61GJ but 1.15GJ.

Now, shall we try and get your elastic energy calculation right this time? The actual expression is that, at maximum compression, the spring energy equals the sum of the initial potential energy liberated in the fall and the additional potential energy released during compression. Therefore, U = 1/2.k.x = 1.15x10^6 + 1.65x10^5.x, a simple quadratic equation with roots 2.5m and 1.84m. The larger root corresponds to the lower extreme of motion. So the strain in the structure is 0.67% (again, from the numbers in your paper), greater than the Euler buckling limit you quote even if you assume that the columns are free to rotate at every joint (which, particularly in the core, they weren't).

So what we get, using your own numbers, is that the initial impact contained enough energy to strain the entire lower structure beyond the elastic limit.

Any problems with all that, that don't involve ignoring energy contributions or making wildly inaccurate estimates of inelastic deformation energies?

Dave

 

[ElMondoHummus]

Still accelerating? It is bouncing in my stuctural analysis calculations. Acceleration comes to a halt! Tell me what is wrong with that!

See Dave Rogers' post above. Bottom line: To get a "bounce", you have to both overestimate (to use a kind term) the resistance of the floor immediately below the failure zones and underestimate the energy available in the falling upper segments.

This is where quantitative analysis shows the error of your hypothesis. I'll leave that argument to Dave Rogers and others who are actually qualified to make these arguments. I'm not. I'm merely repeating the experimentally validated and professionally accepted scenario.

And do I leave out energy?

Yes. Again, see Dave Rogers post.

I was just showing that all applied energy was simply transformed into elastic compression = bounce = no global collapse ensues.

And as Dave Rogers pointed out, you severely overestimate several quantities in order to reach that conclusion.

BTW - Frank Greening sent me an e-mail acknowledning there were serious mistakes in his model! One was it didn't allow bouncing.

That shows he's a more honest researcher than you. I don't know the details of his mistakes - and I note here that you're not providing them for anyone else to analyze either - but given that I've yet to see him retract the analysis that there is more than enough energy available in the towers to account for collapse, I'm at a loss as to how this invalidates his conclusions.

And not "allowing" bouncing is common sense. To "bounce", the storey immediately below the failure zone would have to do more than merely slow down the upper segment, it would have to actually provide an upward force greater than the downward one.

All described in my articles. And Bazant paper peer reviewed? I asked ASCE about it. Sorry - no peer review. Paper just published in ASCE publication without peer review.

And yet it was published by Journal of Engineering Mechanics? I'm sorry, but I need someone credible to verify that for me, and you're not it. I understand that not every work published in a journal is refereed, but I need more than your word that this work is one of those. Anyone who claims CD frankly has no such credibility. I'll lay the question out to anyone else here who's a member of ASCE, or who would be able to ask directly if this is the case or not. If it's not, then you have my retraction for that claim.

Regardless, given publication in Journal of Engineering Mechanics, and given your lack of similar publication, I think it's safe to say that there's still an extremely large credibility gap between their work and yours, peer reviewed or not.

Other lurkers, new folks, etc.: Note the lack of acknowledgement on the multiple validations of the NIST collapse model. Some groups differ around the edges, but otherwise accept the ultimate thrust of that collapse scenario. Note, too, the lack of confrontation of Newton's Bit's analysis, and the non-rigorous diminishment of Bazant, Zhou, and Greening. To make his argument, he has to ignore a lot.

I'll bow out here. Dave Rogers is infinitely better educated and more qualified to refute the actual math of the issue than I am. And others, like Architect, are better able to deal with the construction issues Heiwa's butchering in his analysis. Here are the questions that he needs to confront:

But let's go with your simplifications and calculation errors. You've compressed the bottom block by about 0.36% (1.56m / 433m). Now, I'm a little outside my speciality here, but I suspect this is a little past the yield point of the structure. A36 steel has a Young's modulus of 200GPa, an elastic limit of 250MPa and an ultimate yield point of 400MPa. The Young's modulus therefore corresponds to a compression of 0.125%, after which the columns will be deforming plastically. You're claiming that they're still behaving elastically at 0.36% compression. Do you think, speaking as a professional engineer, that this is a reasonable conclusion?

I'm seeing, as I just said, a 0.36% compression of the steel, which is nearly three times the elastic yield point and nearly twice the ultimate yield point of A36 steel. Would you like to try and refute those numbers?

So what we get, using your own numbers, is that the initial impact contained enough energy to strain the entire lower structure beyond the elastic limit.

Any problems with all that, that don't involve ignoring energy contributions or making wildly inaccurate estimates of inelastic deformation energies?

Dave

All yours, folks.

 

[240-185]

But I am happy to have found a new Heiwa type experiment that should convince my fellow engineers what happens when you drop a structure on a similar, but bigger piece, of structure. Try to destroy a sponge by dropping another sponge on it. Actually WTC1 upper part has all the charcteristics of a sponge (consisting of strong elastic columns, weak elastic floors and plenty of holes (air)), i.e. not very rigid and definitely not homogeneous.

You mean this guy could have prepared 9/11?

 

[Heiwa]

Initial PE 0.61GJ, k=0.5GN/m gives 1.56m compression. Your elastic compression energy doesn't include any extra 0.514GJ.

Dave

Hm, The total energy 1.12 GJ (or so - 1.22 GJ ?) is required to compress the spring 1.56 m. 0.61 GJ is applied from outside, 0.51 GJ (or so - 0.61GJ ?) is added during compression as the force applied is moving that distance (actually when the upper part is decelerating). After that any motion of the upper part is zero. Then the bounce starts! Just like children jumping in a bed.

But as already pointed out the upper part will slide off the spring as the columns will never meet at contact/impact and the upper part is not rigid - it compresses also. This is under the assumption that the upper part actually drops almost free fall and remains intact until and after 'impact'. Under this assumption, the upper part misses, I suggest that multiple local failures occur ... and that's it. No global collapse. Just floors getting entangled.

However - no bounce is noticed. The upper part is actuall destroyed prior anything happens to the lower intact structure - big cloud of debris is formed while the lower structure is still intact. This cloud of debris is what remains of the upper part. It is no doubt produced by local CD inside the upper part. Very little debris should have been formed if the upper part really was solid and dropped one floor only due gravity.

The lower structure is then destroyed by something else than gravity. An amateur may believe it is the upper part producing the destruction - the fountain of debris and big pieces of wall sections being thrown sideways - but it does not fool me. They are result of CD. Like WTC7 for that matter

Thanks for considering my WTC1 spring constant C = 0.5 GJ/m reasonable. It is only 140 times smaller than the one that Bazant suggests is required for impact and shock wave in his one-dimensional crush down theory, where no compression can occur but only crush of one floor at a time. Evidently my spring constant is only a unit force applied vertically to an intact structure that then deforms three dimensionally and one unit distance in the vertical direction, etc. Making the unit distance one meter I get the unit force 0.5 GJ applied to every column in proportion to its cross area/total cross area. Just to get a feeling that the lower structure behaves like a sponge, i.e. it deforms in 3-D. Anybody doing structural analysis of WTC1 can verify how flexible WTC1 was.

But my sponge has not uniform properties everywhere. It is evidently less holes in it at the bottom, etc. No way another little sponge dropping from the sky can globally collapse my sponge, though.

 

[Heiwa]

To "bounce", the storey immediately below the failure zone would have to do more than merely slow down the upper segment, it would have to actually provide an upward force greater than the downward one.

All yours, folks.

Or something like it. Read the introduction of my article about dropping anything on anything why anything bounces. Then read the full article

 

[Seymour Butz]

But as already pointed out the upper part will slide off the spring as the columns will never meet at contact/impact and the upper part is not rigid - it compresses also. This is under the assumption that the upper part actually drops almost free fall and remains intact until and after 'impact'. Under this assumption, the upper part misses, I suggest that multiple local failures occur ... and that's it. No global collapse. Just floors getting entangled.

This is actually closer to what would have happened, other than the entanglement statement. So why do you say it would bounce when in fact, as you admit to realizing, that the columns wouldn't "meet"?

1-It's better to realize that as the columns "miss" each other, they will hit the floors below, right?

2- the floors below wouldn't be able to hold the weight of the columns that hold the weight of the now moving upper block, since the individual floors are designed to hold the floors loads only, and NOT the weight of the upper block, cuz that's the job of the columns, right?

3- so then the columns would punch through/destroy the floors they hit, right?

4- in this process, they would also break the floor beams in the core, leaving some of the columns unbraced, making them more susceptible to buckling, right?

5- so the columns buckle, and the collapse continues, right?

 

[Grizzly Bear]

But my sponge has not uniform properties everywhere. It is evidently less holes in it at the bottom, etc. No way another little sponge dropping from the sky can globally collapse my sponge, though.

That's because sponges are not valid comparatives to complex structures. I suggest that you stop playing dumb, and get serious about the arguments you pursue. This is not an insult, only a friendly suggestion.

The same suggestion is extended to:

Then the bounce starts! Just like children jumping in a bed.

You're not being serious -- let alone even trying -- to present an analogy worth considering.

But as already pointed out the upper part will slide off the spring as the columns will never meet at contact/impact and the upper part is not rigid - it compresses also. This is under the assumption that the upper part actually drops almost free fall and remains intact until and after 'impact'. Under this assumption, the upper part misses, I suggest that multiple local failures occur ... and that's it. No global collapse. Just floors getting entangled.

About the only type of structural frame that would even cosmetically resemble your description "entanglement" is the grid skeletal frame used in traditional steel construction. I fail to see any other potential relevance to anything being discussed here -- especially not the world trade centers.

However - no bounce is noticed. The upper part is actuall destroyed prior anything happens to the lower intact structure - big cloud of debris is formed while the lower structure is still intact. This cloud of debris is what remains of the upper part. It is no doubt produced by local CD inside the upper part. Very little debris should have been formed if the upper part really was solid and dropped one floor only due gravity.

The way I see this comment, is that you're treating the upper section as a collective structural system, and the lower section as a monolithic entity. It's a pity that informing you that the lower structure in a system composed of individual parts continues to be ignored even after more than a year of you "blessing" this forum with your appearance. Moreover, it's quite bizarre of you to be selectively treating the two in such a manner.

The lower structure is then destroyed by something else than gravity.

nope, your conclusion is based on an invalid premise

An amateur may believe it is the upper part producing the destruction

Because that's exactly what it is

the fountain of debris and big pieces of wall sections being thrown sideways - but it does not fool me.

It certainly didn't fool me, you on the other hand... well it appears illusions have played the jedi mind tricks on your brain...

They are result of CD. Like WTC7 for that matter

This is called an argument from spurious similarity. You taken an event which has an exceedingly mundane explanation, and have turned it around to claim it as proof of something else based entirely on cosmetics. Competent designers don't stop at such a shallow plateau if they intend to make a serious contention.

And since when did the collapse of the twin towers look anything like WTC 7?

 

[alexi_drago]

The world Heiwa lives in and bases all his physics on:

http://www.youtube.com/watch?v=3lL6hkpJveM

 

[Heiwa]

This is actually closer to what would have happened, other than the entanglement statement. So why do you say it would bounce when in fact, as you admit to realizing, that the columns wouldn't "meet"?

1-It's better to realize that as the columns "miss" each other, they will hit the floors below, right?

2- the floors below wouldn't be able to hold the weight of the columns that hold the weight of the now moving upper block, since the individual floors are designed to hold the floors loads only, and NOT the weight of the upper block, cuz that's the job of the columns, right?

3- so then the columns would punch through/destroy the floors they hit, right?

4- in this process, they would also break the floor beams in the core, leaving some of the columns unbraced, making them more susceptible to buckling, right?

5- so the columns buckle, and the collapse continues, right?

The column/column impact hypothesis is the official theory originating by Bazant & Co, supported by Seffen and adopted by NIST, the latter without calculations. I just show it is not possible using a spring/sponge/pizza boxes/bathroom scales, etc. The upper part will just bounce incl. some local failures at contact points. Very impopular amongst liers.

So I look into the column/floor alternative. It is also arrested, i.e. the upper part stops after multiple local failures as explained in my article.

If floor supports are disconnected from columns, the columns are unloaded and will remain intact. No load/no buckling/no deformation. No global collapse. Right!

 

[Lennart Hyland]

Heiwa: I just wonder what you think about that the lead designer of the WTC, Leslie Robertson, agrees with NIST?

 

[Seymour Butz]

If floor supports are disconnected from columns, the columns are unloaded and will remain intact. No load/no buckling/no deformation. No global collapse. Right!

No.

If the floors disconnect, the upper block continues down. Then it hits another floor, which also disconnects. And another. And another.

After a few disconnects, there will be 30-40' of unsupported column - with little to no bracing. And since the collapses weren't in the purely vertical, but had a tilt, the unsupported columns would bend when it comes into contact with other columns, floor beams, and/or floors falling from above at an angle, and break at the welds.

Then it starts all over again - columns hit floors, floors disconnect. And again, and again.. until it's over.

The key you're missing is that the collapse arrest depended on whether or not the floors were able to stop the drop. Clearly, they aren't.

Which of course brings up the question, as shown by the photos, of:

How can this:

(insert image of floors)

Stop this:

(insert image of the falling upper block)

 

[Heiwa]

That's because sponges are not valid comparatives to complex structures. ...

The way I see this comment, is that you're treating the upper section as a collective structural system, and the lower section as a monolithic entity. It's a pity that informing you that the lower structure in a system composed of individual parts continues to be ignored even after more than a year of you "blessing" this forum with your appearance. Moreover, it's quite bizarre of you to be selectively treating the two in such a manner.

Pls read my article. The upper structural section is treated exactly as the lower structural section of WTC1 in my article. Very sponge like! Or lika pizza boxes. Same thing all three. Light structures of elastic material full of holes. Drop one on another at free fall - no collapse. Easy to understand.

Problem is NIST suggest differently. The upper section of WTC1 is then rigid, which is impossible, so they suggest solid or whatever when challenged - at least homogeneous, while everything else below in WTC1 has no strength at all. You wonder why this upper part didn't drop down before? Or how the builders managed to get the upper part in place for the first time?

I think it is time to stop this thread. Nobody managed to explain that steel structures can globally collapse due to gravity alone. Bye, bye. See you at another thread?