Video Nullfies Pancake/CD Theory

Originally posted by AkareyonWhich jumped out of the way during the collapse to offer as little resistance as possible? Surely, they were not bent, that would have cost too much kinetic energy.

According to Bazant's analysis, it wouldn't have cost too much energy to bend the columns.

Hear, hear. Let's see what Bazant says in conclusion to his "deep examination":

What matters is energy, not the strength, nor stiffness.

That is because force is energy per distance, nothing more. You just shift the perspective.

That is because Bazant was looking at collapse progression, for which energy is important, and you were wondering why the supports would fail in the first place, for which forces are important.

Vérinages show that you have to substract elastic energy from the structure to achieve a collision with the upper half and the lower half of the building so the kinetic energy is not fully dissipated before the collapse arrests.

Huh? How do you subtract energy from a structure? Not sure what you try to say here.

I hoped you would realize yourself how far-fetched Bazants argumentation is when I show you that the removal of the 109th floor and resulting freefall of the 110th floor would crush the 110th and 108th floor at most, while the removal of the 108th floor would result in the 110th and 109th floor crushing all floors between 107th and bath tub.

I am fully aware of it already. You can not make me more aware by making incorrect statements.

It's more the other way round. I'm the one who insists the towers were built for plane crashes, subtropical hurricanes, earth quakes and cold war scenarios and argues against the assertion a plane crash and subsequent fires could do them infinitely more harm than a raging inferno, a bomb in the basement and decades of swaying in the wind. It is you who argues the whole building dissipated only one third of the potential energy gone kinetic by design and that's the way it should be when there is a 0,2% devation from the static scenario.

0.2% deviation? You have a habbit of comparing unrelated values and then come with all kind of strange conclusions. I wonder where you got this figure from.

How about this, I do this and you find another reason why I'm totally wrong? Wait, I already know where this road goes since I built my tower made of vinyl records and paper loops, based on psikeyhackrs model, and was told that paper is just not as brittle as steel.

Why would I need another reason? Not saying that there aren't any.

Originally posted by -PLB-

Originally posted by AkareyonWhich jumped out of the way during the collapse to offer as little resistance as possible? Surely, they were not bent, that would have cost too much kinetic energy.

According to Bazant's analysis, it wouldn't have cost too much energy to bend the columns.

Hear, hear. Let's see what Bazant says in conclusion to his "deep examination":

What matters is energy, not the strength, nor stiffness.

That is because force is energy per distance, nothing more. You just shift the perspective.

That is because Bazant was looking at collapse progression, for which energy is important, and you were wondering why the supports would fail in the first place, for which forces are important.

Vérinages show that you have to substract elastic energy from the structure to achieve a collision with the upper half and the lower half of the building so the kinetic energy is not fully dissipated before the collapse arrests.

Huh? How do you subtract energy from a structure? Not sure what you try to say here.

I hoped you would realize yourself how far-fetched Bazants argumentation is when I show you that the removal of the 109th floor and resulting freefall of the 110th floor would crush the 110th and 108th floor at most, while the removal of the 108th floor would result in the 110th and 109th floor crushing all floors between 107th and bath tub.

I am fully aware of it already. You can not make me more aware by making incorrect statements.

It's more the other way round. I'm the one who insists the towers were built for plane crashes, subtropical hurricanes, earth quakes and cold war scenarios and argues against the assertion a plane crash and subsequent fires could do them infinitely more harm than a raging inferno, a bomb in the basement and decades of swaying in the wind. It is you who argues the whole building dissipated only one third of the potential energy gone kinetic by design and that's the way it should be when there is a 0,2% devation from the static scenario.

0.2% deviation? You have a habbit of comparing unrelated values and then come with all kind of strange conclusions. I wonder where you got this figure from.

How about this, I do this and you find another reason why I'm totally wrong? Wait, I already know where this road goes since I built my tower made of vinyl records and paper loops, based on psikeyhackrs model, and was told that paper is just not as brittle as steel.

Why would I need another reason? Not saying that there aren't any.

edit on 25-5-2013 by -PLB- because: (no reason given)

First plb do you even do math? see akareyon is apply simple algebraic formulas and reason.I know I was following along.

Vérinages should give you a big clue. See people using jouls of energy to remove key physical components of a building so that other joules of energy placed using more joules of energy by people who have been THINKING about how to get all those joules to do exactly what they want (global gravitational symmetrical collapse)

Now if you just told people to remove whatever that wanted and threww a bunch of explosives about the building do you think you would get that collapse?

Then the THINKING was converted to JOULES. It doesn't even matter if you grabbed from the internet or got them directly god, the thinking was still done. (even if you didnt do that thinking and just lifted someone else's)

Are you really not getting akareyons point? Are you really going to try and refute math with "your wrong"?

Are you really saying intelligence, planning, and the like play no part in the energy released?

My god where HAS our quality of thinking gone?

reply to post by Another_Nut


Why don't you go look at a dynamic load created with this event , each normal floor slab was held up with angle cleats fixed to the outer wall and core so if the bolts sheared or the weld or the cleat itself guess what the only way is down, once floors gave way the stability created between the walls and core due to the trusses no longer being there, then the outer walls start to peel away and the core is hit by the falling mass inside the walls.

reply to post by Akareyon


No the problem here is partly due to the design the tube in tube with floors suspended between the outer walls and core the design was the same top to bottom apart from the service floors.

Have you even looked at the possible dynamic loads in this event I know that ANOK doesn't he always ignores it.

Both towers had many floors above the impact point falling NOT 1 or 2 look at the video of the start of the north tower collapse.

Look at the video below collapse starts about 0:31



It takes till about 0:34 before any material appears to fall outside the walls or parts of the walls below impact start to fall away.

The mass of concrete on those 15 floor slabs alone is 9000 tons minimum plus steel decking, trusses, the hat truss plus all the other components heating, ventilation ,lift gear, office furniture etc etc.

Now what is all that mass doing within those walls during that time.

IT drops to the first floor below it which is held up by the angle cleats.



As for people talking about dust and claiming total destruction of everything we know that's BS from pictures after the collapse.

That dust would be sheetrock, the spray on fire protection, concrete dust, paint, dust in areas that could never be cleaned ,glass even smoke particles from the fires.

reply to post by Another_Nut


If you wish to take part of this discussion, you should first grasp what it is about. Akareyon was claiming that the energy that goes into thinking and planning is somehow of relevance. That is why he came with things such as the Landauer's principle.

Of course a good plan is of relevance to the success of a demolition, I never said otherwise. But the amount of energy that goes into that plan is of absolutely no relevance at all. That is just completely silly.

DP

Originally posted by -PLB-

Hear, hear. Let's see what Bazant says in conclusion to his "deep examination":

What matters is energy, not the strength, nor stiffness.

That is because force is energy per distance, nothing more. You just shift the perspective.

That is because Bazant was looking at collapse progression, for which energy is important, and you were wondering why the supports would fail in the first place, for which forces are important.

Force is energy per meter. You can have the force of a million Newtons, if it acts over the distance of a micrometer only it's the same - energetically - as one Newton acting over one meter. And this is where the load-displacement diagram Fig. 3 (B/V'07) comes in, because the columns act differently depending on how far they have been displaced, so 1 MJ isn't 1 MJ anymore. How is that? Because a column that has buckled to a certain degree develops "plastic hinges" so it offers less resistance than an intact column. You know, Euler and Bernouilli beam theory and so on. You can always bend a ruler, and the more you bend it, the more force you need - until it snaps and it offers no resistance at all anymore. So if a huge force momentarily acts over only a few centimeters, nothing serious happens. If a constant force however managed to act far enough, the column would come to the point where it develops "hinges" and becomes so weak that that constant force could push it all the way to its knees.

Now it's time to discern two things. First, there is that huuuge force that acted momentarily because 58000t were free falling from a height of 3.7 meters. And there is the constant force that acted for thirty years because 58000t were being pulled towards the center of the earth. The first one would easily crush the columns of the first floor because the columns were not designed to withstand that force, they would be deplaced. The latter one was accounted for by design. So what a normal, rigid structure would do is decelerate the huge force, dissipating its kinetic energy floor by floor and column by column by converting it into deformation until it reaches the level of the constant force which it can easily stop and keep aloft.

Now what Bazant proves is that the constant force that acted for thirty years because 58000t were pushing towards the ground strained the columns so much that they were on the verge of buckling already (m*g > maxwell line). So when that huuuuuge force acted momentarily, it had only little work to do - pushing the columns those few centimeters that they needed to form their "plastic hinges". Hardly any kinetic energy was dissolved, and even some picked up (from their potential energy) because the columns now were so weak they couldn't even resist the load they were designed for any more.

In the words of Fig. 3, the columns were much closer to u_c than to u_0, to the right of the peak of the F(u) curve.

What a masterpiece those architects achieved, calculating the strength of the columns so precisely that all the weight above each of them was actually way too heavy for them, putting them under huge pressure, yet just weak enough so they did not buckle before there comes along that last little Newtonmeter missing to push it beyond u_c! Balancing ten stories of dishwasher tabs and paper is one thing, but it's a completely different thing doing that math for 110 stories and hundreds of columns so precisely (before there were FEMs) that on the one hand, the building doesn't initiate collapse inadvertedly or prematurely, and on the other hand, when collapse is initiated, hardly any variations in the velocity of the collapse front are noticable, collapse is not arrested by accident and that no matter at what angle the top collides with the base the whole thing comes down symmetrically like a giant 3D domino!

Huh? How do you subtract energy from a structure?

A vérinage removes walls, but you surely knew that since I linked to the EPO.

I am fully aware of it already.

And you find it natural that there are only two extremes - either only 2 floors get smashed (if you drop the 110th story) or all of them (if you drop 11th+109th), nothing in between like maybe 5 floors crushed or 10 or so?

0.2% deviation? [...] I wonder where you got this figure from.

(2,1 GJ / 981 GJ ) * 100 = 0,2. That's where.

Of course a good plan is of relevance to the success of a demolition, I never said otherwise. But the amount of energy that goes into that plan is of absolutely no relevance at all.

Δῶς μοι πᾶ στῶ καὶ τὰν γᾶν κινάσω.

- Ἀρχιμήδης

Originally posted by Akareyon

Originally posted by -PLB-

Hear, hear. Let's see what Bazant says in conclusion to his "deep examination":

What matters is energy, not the strength, nor stiffness.

That is because force is energy per distance, nothing more. You just shift the perspective.

That is because Bazant was looking at collapse progression, for which energy is important, and you were wondering why the supports would fail in the first place, for which forces are important.

Force is energy per meter. You can have the force of a million Newtons, if it acts over the distance of a micrometer only it's the same - energetically - as one Newton acting over one meter. And this is where the load-displacement diagram Fig. 3 (B/V'07) comes in, because the columns act differently depending on how far they have been displaced, so 1 MJ isn't 1 MJ anymore. How is that? Because a column that has buckled to a certain degree develops "plastic hinges" so it offers less resistance than an intact column. You know, Euler and Bernouilli beam theory and so on. You can always bend a ruler, and the more you bend it, the more force you need - until it snaps and it offers no resistance at all anymore. So if a huge force momentarily acts over only a few centimeters, nothing serious happens. If a constant force however managed to act far enough, the column would come to the point where it develops "hinges" and becomes so weak that that constant force could push it all the way to its knees.

Now it's time to discern two things. First, there is that huuuge force that acted momentarily because 58000t were free falling from a height of 3.7 meters. And there is the constant force that acted for thirty years because 58000t were being pulled towards the center of the earth. The first one would easily crush the columns of the first floor because the columns were not designed to withstand that force, they would be deplaced. The latter one was accounted for by design. So what a normal, rigid structure would do is decelerate the huge force, dissipating its kinetic energy floor by floor and column by column by converting it into deformation until it reaches the level of the constant force which it can easily stop and keep aloft.

Now what Bazant proves is that the constant force that acted for thirty years because 58000t were pushing towards the ground strained the columns so much that they were on the verge of buckling already (m*g > maxwell line). So when that huuuuuge force acted momentarily, it had only little work to do - pushing the columns those few centimeters that they needed to form their "plastic hinges". Hardly any kinetic energy was dissolved, and even some picked up (from their potential energy) because the columns now were so weak they couldn't even resist the load they were designed for any more.

In the words of Fig. 3, the columns were much closer to u_c than to u_0, to the right of the peak of the F(u) curve.

What a masterpiece those architects achieved, calculating the strength of the columns so precisely that all the weight above each of them was actually way too heavy for them, putting them under huge pressure, yet just weak enough so they did not buckle before there comes along that last little Newtonmeter missing to push it beyond u_c! Balancing ten stories of dishwasher tabs and paper is one thing, but it's a completely different thing doing that math for 110 stories and hundreds of columns so precisely (before there were FEMs) that on the one hand, the building doesn't initiate collapse inadvertedly or prematurely, and on the other hand, when collapse is initiated, hardly any variations in the velocity of the collapse front are noticable, collapse is not arrested by accident and that no matter at what angle the top collides with the base the whole thing comes down symmetrically like a giant 3D domino!

Huh? How do you subtract energy from a structure?

A vérinage removes walls, but you surely knew that since I linked to the EPO.

I am fully aware of it already.

And you find it natural that there are only two extremes - either only 2 floors get smashed (if you drop the 110th story) or all of them (if you drop 11th+109th), nothing in between like maybe 5 floors crushed or 10 or so?

0.2% deviation? [...] I wonder where you got this figure from.

(2,1 GJ / 981 GJ ) * 100 = 0,2. That's where.

Of course a good plan is of relevance to the success of a demolition, I never said otherwise. But the amount of energy that goes into that plan is of absolutely no relevance at all.

Δῶς μοι πᾶ στῶ καὶ τὰν γᾶν κινάσω.

- Ἀρχιμήδης

edit on 25-5-2013 by Akareyon because: ?SYNTAX ERROR

Brilliant.

And not just you .

But whoever set up the dominos. Or at least saw that there were dominos to play with

Eta... Ya ever get this feeling there has been someone/thing walking around this planet for the last 10-15 thousand years. Changing names. Building teaching changing Guideing humans toward something that only it knows.maybe its not a.i. But it sure seems as if it's there. my ex once told me the moromans believe in a man cursed not to die and roam the planet till the end. noone knows his crimes. O welloff topic I guess.

Originally posted by Akareyon
So what a normal, rigid structure would do is decelerate the huge force, dissipating its kinetic energy floor by floor and column by column by converting it into deformation until it reaches the level of the constant force which it can easily stop and keep aloft.

Its the same argument over and over. And the same counter argument too. With each floor being crushed, you have to add 2.1 GJ of energy that is converter from potential to kinetic. A fact that is ignored over and over.

A vérinage removes walls, but you surely knew that since I linked to the EPO.

So they remove resistance.

And you find it natural that there are only two extremes - either only 2 floors get smashed (if you drop the 110th story) or all of them (if you drop 11th+109th), nothing in between like maybe 5 floors crushed or 10 or so?

I have no opinion on this. I only know of 2 real life situations where this mechanism took place. And in those situations it were 15+ floors. I would have to look at the figures for other buildings in order to form an opinion. I rather not just pull one out of my ss.

(2,1 GJ / 981 GJ ) * 100 = 0,2. That's where.

And as expected, dividing unrelated figures with each other, coming to weird conclusions. Frankly, I am kind of done with this, as I explained it more than 2 times already.

Glad you see the silliness of your argument.

Originally posted by -PLB-
Its the same argument over and over. And the same counter argument too. With each floor being crushed, you have to add 2.1 GJ of energy that is converter from potential to kinetic. A fact that is ignored over and over.

It's not a fact that gets ignored, it's not a fact at all.

You can't just keep adding energy, and not account for energy lost due to deformation, connection failures, heat, sound, resistance etc.

Kinetic energy would be lost, not gained. For each floor impact energy would be lost. The only thing that is adding energy is it's own mass falling from gravity, against a resistance that is stronger than gravity. Resistance would slow the collapse, so kinetic energy could not be gained, only lost.

That is what you keep ignoring. Not too mention that sagging trusses can't put a pulling force on the columns.

Originally posted by ANOK
That is what you keep ignoring. Not too mention that sagging trusses can't put a pulling force on the columns.

Still lying eh ANOK? Nice to see that you've decided that when facts don't support you, you can just lie to try and get people to believe you.

You're being extremely dishonest here and anyone who reads this forum can see you intentionally ignore the facts:

www.abovetopsecret.com...
www.abovetopsecret.com...
www.abovetopsecret.com...

How embarrassing you have to actually lie to try and feel like you're right. I wonder what sort of psychology causes this, were you recently fired or left a relationship? I can't think of any other reason for grasping at straws and destroying your reputation so thoroughly.

Originally posted by Akareyon
Force is energy per meter. You can have the force of a million Newtons, if it acts over the distance of a micrometer only it's the same - energetically - as one Newton acting over one meter.

I've been trying not to butt into this conversation as it's a long discussion between two people but now that you apparently have a cheerleader I have to butt in a little.

How is that? Because a column that has buckled to a certain degree develops "plastic hinges" so it offers less resistance than an intact column. You know, Euler and Bernouilli beam theory and so on. You can always bend a ruler, and the more you bend it, the more force you need - until it snaps and it offers no resistance at all anymore.

This is pretty accurate, and something that many people don't understand about the condition of the towers, but what you go on to say is very confusing to me.

So if a huge force momentarily acts over only a few centimeters, nothing serious happens. If a constant force however managed to act far enough, the column would come to the point where it develops "hinges" and becomes so weak that that constant force could push it all the way to its knees.

This is not accurate. Forces are applied and if a 'constant force' acted 'far enough' then a larger force should result in at least as large work (ie force * distance). Once hinges are developed due to out of plane displacement the resistive capacity goes down, but it had to be there in the first place.

Now it's time to discern two things. First, there is that huuuge force that acted momentarily because 58000t were free falling from a height of 3.7 meters. And there is the constant force that acted for thirty years because 58000t were being pulled towards the center of the earth. The first one would easily crush the columns of the first floor because the columns were not designed to withstand that force, they would be deplaced. The latter one was accounted for by design. So what a normal, rigid structure would do is decelerate the huge force, dissipating its kinetic energy floor by floor and column by column by converting it into deformation until it reaches the level of the constant force which it can easily stop and keep aloft.

And this is complete nonsense. If buildings were as simple as an energy balance they would be a solid concrete pillar to the full height and job done. There's a big difference between a static and a dynamic load. The huuuuge force acting momentarily is a bad way to think about the collapsing top as what it has is momentum. The force applied is the building trying to absorb this momentum. Because it is moving and of significant mass it easily destroys any restraining elements on the floors it impacts and then accelerates that floor over the next floor height.

While it might seem reasonable to think of the upper block as a series of massive overloads being slowly dissipated by the rest of the structure, this just doesn't match the physics. What it is is a huge amount of mass gaining energy by falling inbetween floors.

Now what Bazant proves is that the constant force that acted for thirty years because 58000t were pushing towards the ground strained the columns so much that they were on the verge of buckling already

I don't know why you mention the amount of time here because it has no relevance. Bazant determined that the columns were relatively close to their maximum as they would be in any building. He got the mass slightly wrong as it was an early analysis but still.

So when that huuuuuge force acted momentarily, it had only little work to do - pushing the columns those few centimeters that they needed to form their "plastic hinges". Hardly any kinetic energy was dissolved, and even some picked up (from their potential energy) because the columns now were so weak they couldn't even resist the load they were designed for any more.

In Bazant's paper the overload is around a factor of 8, so it's not 'hardly any kinetic energy' and it's 'dissipated' not 'dissolved'. It's a significant amount of energy they can absorb in deformation, but it's just not enough.

What a masterpiece those architects achieved, calculating the strength of the columns so precisely that all the weight above each of them was actually way too heavy for them, putting them under huge pressure

More nonsense, if the towers were way too heavy then they would have collapsed. The safety margins would never be enough to survive this sort of collapse.

it's a completely different thing doing that math for 110 stories and hundreds of columns so precisely (before there were FEMs) that on the one hand

Bazant does it in his paper, without FEMs. So uh, not sure what you're talking about.

(2,1 GJ / 981 GJ ) * 100 = 0,2. That's where.

I also have no idea what this is.

Originally posted by ANOK
It's not a fact that gets ignored, it's not a fact at all.

You can't just keep adding energy, and not account for energy lost due to deformation, connection failures, heat, sound, resistance etc.

Currect, but the energy lost is already subtracted from the previous2.1 GJ that was available in kinetic energy for destruction. You can't subtract it twice.

Kinetic energy would be lost, not gained. For each floor impact energy would be lost. The only thing that is adding energy is it's own mass falling from gravity, against a resistance that is stronger than gravity. Resistance would slow the collapse, so kinetic energy could not be gained, only lost.

Correct, but the energy lost to crush a single floor is (according to bazant) 0.5GJ. The energy gained when the mass falls a height of 1 floor is 2.1GJ. So after each floor that is crushed there is a net (kinetic) energy leftover of 1.6GJ.

Originally posted by -PLB-
Its the same argument over and over. And the same counter argument too. With each floor being crushed, you have to add 2.1 GJ of energy that is converter from potential to kinetic.

It's still an invalid counter argument. There is only one free fall in this model. After that, each of those 2.1 GJ are diminished by W_c, the energy dissipated by crushing the previous floor.

A vérinage removes walls, but you surely knew that since I linked to the EPO.

So they remove resistance.

= elastic energy.

(2,1 GJ / 981 GJ ) * 100 = 0,2. That's where.

And as expected, dividing unrelated figures with each other, coming to weird conclusions.

:-)

The tower is a closed system with 981 GJ of potential energy. 2.1 GJ of kinetic energy are added to the system by adding one freefall by magically zapping one floor. Thus, a 0,2% deviation from the static scenario results in total collapse.

I agree it's a weird conclusion, but not I have come to it, but the towers.

²exponent: welcome back!

The huuuuge force acting momentarily is a bad way to think about the collapsing top as what it has is momentum.

We're slowly getting to the basics of physics here, it seems. Bazant says it was energy, so I calculate with Joules, -PLB- says it is force, so I say force is energy per distance and use the load-displacement diagram and calculate in Newtons, now you say it's momentum and I say momentum is force multiplied with how long it acts (you know, p=m*v and F=m*a and a=v/t and F=m*v/t and so on). How long it acts depends on...?

The force applied is the building trying to absorb this momentum. Because it is moving and of significant mass it easily destroys any restraining elements on the floors it impacts and then accelerates that floor over the next floor height.

...losing hardly any momentum, that's what's in dispute here.

While it might seem reasonable to think of the upper block as a series of massive overloads being slowly dissipated by the rest of the structure, this just doesn't match the physics.

So my Jenga towers, vinyl record paper loop towers and card houses do not match the physics?

Bazant determined that the columns were relatively close to their maximum as they would be in any building.

...on the verge of developing plastic hinges, just waiting for a nudge?

In Bazant's paper the overload is around a factor of 8, so it's not 'hardly any kinetic energy' and it's 'dissipated' not 'dissolved'.

Sorry again, I'm not a native speaker, I mix things up sometimes. Sometimes I notice in time, sometimes I don't. Thank you for the correction, glad you know what I meant to say: that only a small amount of the kinetic energy was dissipated by the structure underneath.

It's a significant amount of energy they can absorb in deformation, but it's just not enough.

Yep, roughly one third was not enough.

If the towers were way too heavy then they would have collapsed.

Nope. Not as long as there was still a Newton here and there missing and u a few centimeters smaller than u_c. They'd be on the verge of buckling and severely overloaded by their own weight, but would not collapse yet.

The safety margins would never be enough to survive this sort of collapse.

Last time I checked, the towers did not survive this sort of collapse.

Bazant does it in his paper, without FEMs. So uh, not sure what you're talking about.

About the difference between describing the event with a simple mathematical model by assuming and reverse engineering figures and designing a structure with forces so well-balanced and then actually assemble it so the thing really works decades later, but not without surviving bombs in the basement, hurricanes, office fires and plane impacts up to its very last minute ;-)

Originally posted by Akareyon

Originally posted by -PLB-
Its the same argument over and over. And the same counter argument too. With each floor being crushed, you have to add 2.1 GJ of energy that is converter from potential to kinetic.

It's still an invalid counter argument. There is only one free fall in this model. After that, each of those 2.1 GJ are diminished by W_c, the energy dissipated by crushing the previous floor.

No it is not invalid. You have 2.1GJ of kinetic energy after a 3.7m fall, 0.5GJ is consumed by destroying support columns, 1.6GJ is left, and you have another 3.7m fall to the next floor, adding 2.1GJ to the 1.6GJ left over and for the next floor there is 3.7GJ in kinetic energy available for destruction.

Thats the idea of "iteration". It means that all events repeat over and over, including the 3.7m of falling.

Originally posted by Akareyon
²exponent: welcome back!

Merci

We're slowly getting to the basics of physics here, it seems. Bazant says it was energy, so I calculate with Joules, -PLB- says it is force, so I say force is energy per distance and use the load-displacement diagram and calculate in Newtons, now you say it's momentum and I say momentum is force multiplied with how long it acts (you know, p=m*v and F=m*a and a=v/t and F=m*v/t and so on). How long it acts depends on...?

All three are perfectly valid. The upper block has mass, it converts potential energy into kinetic energy while falling and its velocity gives it momentum. My point is that velocity is somewhat neglected in the discussion between you and PLB, and after all this is rather key to understanding the collapse.

...losing hardly any momentum, that's what's in dispute here.

No, momentum is conserved. In fact what is lost in this case is kinetic energy used in deformation and destruction during the impact. This is an Inelastic Collision.

So my Jenga towers, vinyl record paper loop towers and card houses do not match the physics?

I'm afraid not. I was very impressed that your tower survived the impact but vinyl paper does help explain that somewhat. The biggest issue with your model I can see is the load bearing ability of your floors. You could form an extreme curve with several sheets of that paper between two points and have all the load transmitted down through the remaining jenga blocks.

This is what happened in your experiment, the tensile strength of paper is far far too high to reasonably represent a reduced scale concrete floor 4" thick. Assuming your experiment was 200mm square then if your paper was 0.3mm thick or so it would actually be about the right proportions as the tower. Now imagine how brittle concrete is at that scale compared to your paper.

However! All is not lost. The horizontal orientation of your jenga blocks will never do as there's very little room for acceleration between floors, and trapping the paper inbetween the blocks is unrealistic. If you were to fold down each side of the paper and then stick it using a very light adhesive (post-it notes?) to an exterior frame built of vertical jenga blocks, you would be approaching the construction of the WTC. PLB's model works due to the relatively increased height of the storeys and the inability of his paper to support load in tension.

This is making me want to build something but I have work to do I am afraid.

...on the verge of developing plastic hinges, just waiting for a nudge?

Not really 'on the verge'. Just 'not with 4x overload capacity' as some would have you believe.

Sorry again, I'm not a native speaker, I mix things up sometimes. Sometimes I notice in time, sometimes I don't. Thank you for the correction, glad you know what I meant to say

No need to apologise, you've been completely civil and this is quite enjoyable trying to see things from your perspective.

that only a small amount of the kinetic energy was dissipated by the structure underneath.

This is certainly true to some degree. It's true on first view from the rapidity of the collapse. If the floors could absorb significant energy then the collapse would have been much slower or not happened at all.

Yep, roughly one third was not enough.

Right, the resistive force was approximately 1/3rd of the applied force when averaged out so the acceleration of collapse is 0.6g for WTC2 and 0.75g for WTC1 (iirc, might have those backwards)

Nope. Not as long as there was still a Newton here and there missing and u a few centimeters smaller than u_c. They'd be on the verge of buckling and severely overloaded by their own weight, but would not collapse yet.

With respect, that's not 'way too heavy' then, it's just 'no safety margin'. Something which is 'too heavy' for a support breaks that support. Perhaps this is just wording differences.

About the difference between describing the event with a simple mathematical model by assuming and reverse engineering figures and designing a structure with forces so well-balanced and then actually assemble it so the thing really works decades later, but not without surviving bombs in the basement, hurricanes, office fires and plane impacts up to its very last minute ;-)

Well, this is what people have been practising for over 5000 years. Before simulations were common, physical experiments were. The load bearing capacity of the steel used in the WTC was almost certainly proven by experiment and while they broke new ground in design, their techniques are hardly revolutionary. Steel, Bolts, Welds and probably the most advanced element, Trusses.

Originally posted by -PLB-
The energy lost to crush a single floor is (according to bazant) 0.5GJ. The energy gained when the mass falls a height of 1 floor is 2.1GJ. So after each floor that is crushed there is a net (kinetic) energy leftover of 1.6GJ.

Got ya.

You say that the potential difference of 3.7m and weight of 58,000t amounts to a potential energy of 2.1 GJ per floor, and I agree.

You say that the energy lost to crush a single floor is 0.5 GJ, according to Bazant, and I agree - that's what happened.

You say that there is a net energy leftover of 1.6 GJ, and I agree, but exponent disagrees.

Even without adding 2.1 GJ by removing one floor beneath the 58,000t top to get Bazants 4.2 GJ figure, the floor beneath it is already strained with a potential energy surplus of 1.6 GJ - the top is too heavy for the floor beneath it. What kept it aloft then?

You have 2.1GJ of kinetic energy after a 3.7m fall, 0.5GJ is consumed by destroying support columns, 1.6GJ is left, and you have another 3.7m fall to the next floor, adding 2.1GJ to the 1.6GJ left over and for the next floor there is 3.7GJ in kinetic energy available for destruction.

Wait, wait. Step by step now.

Free fall = 2.1 GJ : REM one floor removed, impact on first floor
plus potential to the next floor: + 2.1 GJ = 4.2 GJ (Bazant)
minus energy dissipated: -0.5 GJ = 3.7 GJ : REM first floor crushed, impact on second floor
plus potential to the next floor: +2.1 GJ = 5.8 GJ :
minus energy dissipated: -0.5 GJ = 5.3 GJ : REM second floor crushed, impact on third floor

and so on. So even without free fall

potential to the next floor: 2.1 GJ
minus energy dissipated: -0.5 GJ = 1.6 GJ : REM first floor crushed, impact on second floor
plus potential to the next floor: +2.1 GJ = 3.7 GJ :
minus energy dissipated: -0.5 GJ = 3.2 GJ : REM second floor crushed, impact on third floor

= progressive collapse!

²exponent:

My point is that velocity is somewhat neglected in the discussion between you and PLB, and after all this is rather key to understanding the collapse.

Nah, it's all in there. As I've already shown, you can also go E=m*g*h=1/2 m*v², where v = sqrt(2*g*s) = sqrt(2*9,81m/s² * 3,7m) = 8,5202 m/s and E = 1/2 * m * v² = 1/2* 58.000.000kg * (8,52 m/s)² ≈ 2,1 GJ. It's all the same really, just a change of perspective. I've done this with E=pressure * volume once as well, but people totally flipped out then :-)

I was very impressed that your tower survived the impact but vinyl paper does help explain that somewhat.

I used normal paper for the Jenga experiment. I was also referring to my vinyl record and paper loop experiment based on psikeyhackrs experiment with washers.

the tensile strength of paper is far far too high to reasonably represent a reduced scale concrete floor 4" thick.

Please, let's put aside the square-cube law argument. I know that, we're just building models, not replicas. The friction between the Jenga blocks and the paper is also not comparable to the force of the connections.

If you were to fold down each side of the paper and then stick it using a very light adhesive (post-it notes?) to an exterior frame built of vertical jenga blocks, you would be approaching the construction of the WTC.

...in one aspect: it would topple without the hands of god keeping it upright. As I said before, you can't stack 10 floors with the Jenga blocks oriented vertically. At the sixth floor, there's no way to balance it anymore. Try for yourself, though.

With respect, that's not 'way too heavy' then, it's just 'no safety margin'. Something which is 'too heavy' for a support breaks that support.

That's what it did. It broke all the supports that were in place to keep it up.

The load bearing capacity of the steel used in the WTC was almost certainly proven by experiment and while they broke new ground in design, their techniques are hardly revolutionary.

Some tried to make me believe otherwise :-)

What I was trying to convey however is that it makes a difference whether you engineer the tower so it keeps upright or engineer the tower so it collapses all the way down through itself. One is easy, and if you're bad at it, it topples and bends to the side when under stress. The other one is very, very hard to do, as you can see yourself as soon as you've grabbed a Jenga set at the next garage sale (or a pack of dish washer tablets ;-)

Originally posted by Akareyon
Nah, it's all in there. As I've already shown, you can also go E=m*g*h=1/2 m*v², where v = sqrt(2*g*s) = sqrt(2*9,81m/s² * 3,7m) = 8,5202 m/s and E = 1/2 * m * v² = 1/2* 58.000.000kg * (8,52 m/s)² ≈ 2,1 GJ. It's all the same really, just a change of perspective.

That's perfectly reasonable, but you seem to think I disagree with the concept as you mentioned to PLB. In fact what you illustrated was a simple progressive collapse and I have no complaints.

I used normal paper for the Jenga experiment. I was also referring to my vinyl record and paper loop experiment based on psikeyhackrs experiment with washers.

Aah I see, still you don't seem to argue with my points against your model, so I'm really confused as to what the remaining disagreement with Bazant is. You agree with the energy balance allowing for progressive collapse, you understand the mechanism behind floors not transferring load to columns.

I guess I should ask, why do you think the building collapses were not as they have been reported? What evidence differs in your mind? This is what I'm missing I think!

Please, let's put aside the square-cube law argument. I know that, we're just building models, not replicas. The friction between the Jenga blocks and the paper is also not comparable to the force of the connections.
...
in one aspect: it would topple without the hands of god keeping it upright. As I said before, you can't stack 10 floors with the Jenga blocks oriented vertically. At the sixth floor, there's no way to balance it anymore. Try for yourself, though.

The only jenga blocks I could find were tiny little beer ones, hardly suitable. This collapse you are talking about though is what we expect and what we want. I think we can all agree that there's no way that WTC perimeter columns on their own would survive without the bracing of the floors and the core. If we are to build a model that represents them in any reasonable respect it should embody this behaviour.

The easiest way to do this is to stack the jenga blocks vertically but directly adjacent to each other. Saw a few of them in half so that each adjacent jenga column is offset 1/2 from the previous one. By tying these together with post it notes you can approximate the perimeter spandrels which served as a moment frame.

This is the key structural feature to emulate the WTCs collapse mechanism, the perimeter walls must be braced by the floors and resist forces laterally, not in their normal direction. By this mechanism, once floors begin to be destroyed, as long as there's some resistance, the chaotic debris above will exert outward pressure on the walls, resulting in a progressive collapse with the exterior walls 'pivoted' out to the 4 sides of the tower.

Some tried to make me believe otherwise :-)

What I was trying to convey however is that it makes a difference whether you engineer the tower so it keeps upright or engineer the tower so it collapses all the way down through itself. One is easy, and if you're bad at it, it topples and bends to the side when under stress. The other one is very, very hard to do, as you can see yourself as soon as you've grabbed a Jenga set at the next garage sale (or a pack of dish washer tablets ;-)

Indeed building a structure this large is not exactly easy, but progressive collapse is plausible with even simple construction. Ronan Point is a valuable example. Anyone can model that disaster with relative ease.

Originally posted by exponent
why do you think the building collapses were not as they have been reported? What evidence differs in your mind? This is what I'm missing I think!

My argument is this: if you raise 2.1 GJ of potential energy, you want to make sure that it does not go kinetic. You would want to do that by putting at least 2.1 GJ of elastic energy underneath. Maybe even 4.2, just to be sure.

Bazant, you and -PLB- argue however that 0.5 GJ would suffice. I clearly understand that under these conditions, global collapse is inevitable. My question to you is: how did it remain aloft then in the first place? Collapse wouldn't even have to be initiated by anything, it would have to be hanging by a rope to keep its potential energy.

This collapse you are talking about though is what we expect and what we want.

A collapse by storing the potential energy in a highly unstable equilibrium, like in a bomb?

I think we can all agree that there's no way that WTC perimeter columns on their own would survive without the bracing of the floors and the core. If we are to build a model that represents them in any reasonable respect it should embody this behaviour.

I'm writing this real slowly: if you stack 6 floors of upright Jenga blocks and paper, the whole structure warps around its vertical axis and topples. So even with the "bracing", it's too weak to support itself.

The easiest way to do this is to stack the jenga blocks vertically but directly adjacent to each other. Saw a few of them in half so that each adjacent jenga column is offset 1/2 from the previous one. By tying these together with post it notes you can approximate the perimeter spandrels which served as a moment frame.

I'm trying hard not to look stupid in this discussion, but I really don't see the picture you're painting. Can you do a quick doodle or so? BTW, there's no way I'm sawing my precious Jenga blocks!

Indeed building a structure this large is not exactly easy, but progressive collapse is plausible with even simple construction. Ronan Point is a valuable example.

...not for a symmetrical, global progressive collapse, however.

Originally posted by Akareyon
= progressive collapse!

Right, I agree with your calculations and conclusion.

My argument is this: if you raise 2.1 GJ of potential energy, you want to make sure that it does not go kinetic. You would want to do that by putting at least 2.1 GJ of elastic energy underneath. Maybe even 4.2, just to be sure.

Why stop at 4.2GJ? If the plane crashed into the 31st floor from the roof (similar to the other tower), you end up with a kinetic energy of 4.34GJ at the moment the top impacts of the next floor. And you will have progressive collapse again.

Bazant, you and -PLB- argue however that 0.5 GJ would suffice.

I am not arguing really that it would "suffice". I am not a building safety expert. I am arguing that this was the case with the WTC building (in combination with the unrealistic collapse mode of Bazant). Whether the buildings should have been made stronger is another discussion. But as per scenario I wrote above (31 floors), to me it is not clear at all what figure would suffice, if I was to agree that the actual design was not sufficient.

I clearly understand that under these conditions, global collapse is inevitable. My question to you is: how did it remain aloft then in the first place? Collapse wouldn't even have to be initiated by anything, it would have to be hanging by a rope to keep its potential energy.

This comes down to dynamic load vs static load. For the top to get into motion, it first has to overcome the counter force that the columns are offering. In a static situation, this force is only that of the gravitational pull on the mass above it. So Fs=ma=mg=10m.

For the dynamic situation, the same formula counts. However, "a" is no longer "g'. "a" has now become the deceleration of the mass as result of the impact with the lower floor. Lets for example assume it has 20cm to slow down before the supports fail (displacement of the supports result in failure). We can calculate v at the moment of impact:

v²=2gs=2*10*3.7=74 -> (v=sqrt(74)=8.6m/s

To decelerate something that goes 8.6m/s in a distance of 20cm you get (reverse of above)

a=v²/2s=74/2*0.2=185m/s²

so Fdyn=ma=185m.

Now compare it to the static situation, you get a force that is Fdyn/Fs=185/10=18.5 times larger. Even a FoS of 10 isn't going to help you here. You may have noticed that this value is the same as just dividing floor height (3,7m) by distance you have to decelerate the mass before it fails. (Disclaimer: these calculations are oversimplified in order to accentuate the reason for difference in forces. I also sporadically left out the units)

Hope that answers your question.