The Heiwa Challenge

[Myriad]

OK, so the Funny m Tower SE (or strenght!) is just 1/1000th of what I suggest but it still manages to keep the tower standing. Quite good!

I agree that the model as described would stand, yes.

I hope you agree that you can still load the Funny m Tower , i.e. increase m to 3 m in every assembly n and that the Tower still stands (assuming the ground will resist it)? The foundation/ground is assumed rigid in this little show, so it will resist!

I agree that the model would still stand in that case. However, with no safety margin, the slightest variation in column loads (such as might be caused by light breezes, or elevators moving up and down) would case cumulative plastic deformations of the columns. Eventually it would collapse from metal fatigue.

And I hope you also agree that if you put 6 m up on the top Funny m assembly, it is only the springs below that element that breaks?

The springs below that element break first. Then a top-down progressive collapse would ensue.

And what's the difference of adding potential energy up top or dropping the top part = apply kinetic energy to achieve the same result?

Congratulations. After years of arguing from ignorance about this matter, you've finally hit on the right question. It's a bizarre question for any trained engineer to have to ask, but it's a good question in the sense that if you understand the answer, you'll understand why you've been wrong all this time.

The simple answer is that imparting kinetic energy creates dynamic loads, while adding potential energy (without exceeding the structure's capacity to bear) does not. But you've been told that many times before, and you don't seem to understand, or care about understanding, the difference.

It might help to think of it instead in terms of power. Power by definition is an amount of energy that's being converted (from some form to some other form) per unit time.

If power equals zero, it doesn't matter how much energy you have. You aren't doing anything to anything. Water behind a dam just sits there. A moving mass with nothing in its way just keeps going. To accelerate something, to break something, to heat something, to deform something, you need power. Energy being converted. When gravity can act on the water to get it moving, you have power. When the moving mass collides with something in its way, you have power. Energy being converted.

Adding potential energy to the top of a building that is able to statically handle the load does not generate power. Adding kinetic energy to (that is, accelerating) a significant part of a building does generate power, lots of power, because that kinetic energy is going to have to get converted and transferred rather quickly.

And, finally, I hope you agree that the top part C of the Funny m Tower is not rigid (as assumed by Bazant in his peer reviewed papers) as it contains the weakest springs in the whole Tower?

Failure at 0.5% compression is pretty rigid, which is why progressive collapse happens in your model even though you haven't specified a scale! (In effect, by specifying the ratios of strain to floor height for static conditions and for column failure, you've managed to invent a model that self-compensates for mass and height -- although finding materials with the specified properties for small heights or small masses might be difficult).

I agree that in experiment 1, the top springs might break first, but that would not prevent a complete progressive collapse from occurring since even dropping just one mass alone would be sufficient. In experiment 3, simultaneous crush-up and crush-down might occur at first but crush-down would predominate once a few floors were crushed.

BTW - how are you getting along with your 10 meters tall crush-down model?

Beware that it doesn't collapse on you during construction!

I've invited you to discuss my 10-meter model in the appropriate thread.

Respectfully,
Myriad

 

[Heiwa]

1. I agree that the model as described would stand, yes.

2. I agree that the model would still stand in that case. However, with no safety margin, the slightest variation in column loads (such as might be caused by light breezes, or elevators moving up and down) would case cumulative plastic deformations of the columns. Eventually it would collapse from metal fatigue.

3. The springs below that element break first. Then a top-down progressive collapse would ensue.

4. Congratulations. After years of arguing from ignorance about this matter, you've finally hit on the right question. It's a bizarre question for any trained engineer to have to ask, but it's a good question in the sense that if you understand the answer, you'll understand why you've been wrong all this time.

The simple answer is that imparting kinetic energy creates dynamic loads, while adding potential energy (without exceeding the structure's capacity to bear) does not. But you've been told that many times before, and you don't seem to understand, or care about understanding, the difference.

It might help to think of it instead in terms of power. Power by definition is an amount of energy that's being converted (from some form to some other form) per unit time.

If power equals zero, it doesn't matter how much energy you have. You aren't doing anything to anything. Water behind a dam just sits there. A moving mass with nothing in its way just keeps going. To accelerate something, to break something, to heat something, to deform something, you need power. Energy being converted. When gravity can act on the water to get it moving, you have power. When the moving mass collides with something in its way, you have power. Energy being converted.

Adding potential energy to the top of a building that is able to statically handle the load does not generate power. Adding kinetic energy to (that is, accelerating) a significant part of a building does generate power, lots of power, because that kinetic energy is going to have to get converted and transferred rather quickly.

Failure at 0.5% compression is pretty rigid, which is why progressive collapse happens in your model even though you haven't specified a scale! (In effect, by specifying the ratios of strain to floor height for static conditions and for column failure, you've managed to invent a model that self-compensates for mass and height -- although finding materials with the specified properties for small heights or small masses might be difficult).

5. I agree that in experiment 1, the top springs might break first, but that would not prevent a complete progressive collapse from occurring since even dropping just one mass alone would be sufficient. In experiment 3, simultaneous crush-up and crush-down might occur at first but crush-down would predominate once a few floors were crushed.

I've invited you to discuss my 10-meter model in the appropriate thread.

Respectfully,
Myriad

1. Good!
2. Good!
3. Good! But are you really sure progressive collapse will follow? Why not arrest?
4. Good! So the structure can statically absorb a certain amount of potential energy and still stand -say 1/3 of total - and that means it can also absorb the same amount of kinetic energy and still stand ... or even three times. We are moving ahead. But what happens then? After the weakest spring has broken? Is the energy then released applied on the structure below or applied somewhere else, e.g. the loose part just drops beside the structure, or is the destruction simply arrested? For you to find out!
5. Good!

Good luck with your model! Ensure it doesn't drop on you during assembly.

 

[TheRedWorm]

That doesn't address the issue of scale. Think about it this way: If I throw a bullet at a watermelon, what happens? Now what happens when I fire a bullet at the same melon? Remember, the only difference in my example is scale.

Is scale important in the way physical reality operates, "heiwa," yes or no?

Don't know why you say goodbye, I say hello.

 

[Myriad]

3. Good! But are you really sure progressive collapse will follow? Why not arrest?

Because the bottom 20 floors, despite the springs, cannot decelerate a single floor (let alone two floors) that has fallen a distance h to a stop without undergoing displacement sufficient to break the s20 springs. The remaining 19 floors cannot decelerate two floors falling another distance h, so the s19 springs break. And so forth. Calculations to follow, later today.

4. Good! So the structure can statically absorb a certain amount of potential energy and still stand -say 1/3 of total - and that means it can also absorb the same amount of kinetic energy and still stand ... or even three times.

Nope. It absolutely does not mean that.

The structure does not "absorb" potential energy. Put a weight on the top floor, and the system now has added potential energy. The potential energy doesn't go anywhere. As long as the weight stays there and the structure continues to support it, the potential energy still there.

Thinking that potential energy is "absorbed" -- somehow rendered inert merely because the forces are in static balance -- is basically the same error you made on your web page when you miscalculated the gravitational potential energy in your model by a factor of 1,000. Gravitational potential energy is the summation of mgh over all the structure's mass. Period. It is reduced or "absorbed" only by removing mass or displacing it downwards. (Displacing it downwards turns the potential energy into kinetic energy. Removing it requires power from another source, such as a crane.)

And the structure absorbs all but the smallest amounts of kinetic energy by breaking.

We are moving ahead.

Perhaps. I do think your new "funny springs" model is far superior to all the models and analogies you've offered before. Unlike your vague analogies about colliding ships or stacked fruit, this model is sufficiently well described to be analyzed.

Of course, because it can be analyzed, the analysis will show that progressive collapse occurs in all the experiments you described.

Respectfully,
Myriad

 

[Heiwa]

1. Because the bottom 20 floors, despite the springs, cannot decelerate a single floor (let alone two floors) that has fallen a distance h to a stop without undergoing displacement sufficient to break the s20 springs. The remaining 19 floors cannot decelerate two floors falling another distance h, so the s19 springs break. And so forth. Calculations to follow, later today.




2. Nope. It absolutely does not mean that.

The structure does not "absorb" potential energy. Put a weight on the top floor, and the system now has added potential energy. The potential energy doesn't go anywhere. As long as the weight stays there and the structure continues to support it, the potential energy still there.

Thinking that potential energy is "absorbed" -- somehow rendered inert merely because the forces are in static balance -- is basically the same error you made on your web page when you miscalculated the gravitational potential energy in your model by a factor of 1,000. Gravitational potential energy is the summation of mgh over all the structure's mass. Period. It is reduced or "absorbed" only by removing mass or displacing it downwards. (Displacing it downwards turns the potential energy into kinetic energy. Removing it requires power from another source, such as a crane.)

3. And the structure absorbs all but the smallest amounts of kinetic energy by breaking.




4. Perhaps. I do think your new "funny springs" model is far superior to all the models and analogies you've offered before. Unlike your vague analogies about colliding ships or stacked fruit, this model is sufficiently well described to be analyzed.

5. Of course, because it can be analyzed, the analysis will show that progressive collapse occurs in all the experiments you described.

Respectfully,
Myriad

1. I look forward to your calculations

2. Mass m always, static or moving, applies a force F = mg on the springs s that compress and therefore 'absorbs' it as strain energy. The maximum potential energy that m can apply in a single Funny m element is mgh (by removing all springs) and then the force is applied on the ground.

3. Well, a lot of energy is absorbed as compression! In Experiment 1 there are 84 springs to consider and they will all compress! And then there is more energy required to break a spring. I am glad that you think that the four springs #22 in Part C may break first! Now a surprise. Two of the four #22 springs on one side are a little stronger! What do you think happen then?

4. Glad that you like Funny m element. It is quite similar to a pizza box, though.

5. See 1.

 

[tsig]

1. I look forward to your calculations

2. Mass m always, static or moving, applies a force F = mg on the springs s that compress and therefore 'absorbs' it as strain energy. The maximum potential energy that m can apply in a single Funny m element is mgh (by removing all springs) and then the force is applied on the ground.

3. Well, a lot of energy is absorbed as compression! In Experiment 1 there are 84 springs to consider and they will all compress! And then there is more energy required to break a spring. I am glad that you think that the four springs #22 in Part C may break first! Now a surprise. Two of the four #22 springs on one side are a little stronger! What do you think happen then?

4. Glad that you like Funny m element. It is quite similar to a pizza box, though.

5. See 1.

So you think the top should have bounced off the bottom?

 

[phunk]

2. Mass m always, static or moving, applies a force F = mg on the springs s that compress and therefore 'absorbs' it as strain energy. The maximum potential energy that m can apply in a single Funny m element is mgh (by removing all springs) and then the force is applied on the ground.

If you really believe this, I invite you to place a brick gently on your head, and experience the 'mg' for that brick, then lift it 2 feet above your head and drop it, and see if you feel more than 'mg'.

By the way, if your theory is correct that mass m always applies mg, static or moving, than you've just disproven any possible collapse arrest. Way to go!

 

[Myriad]

Mass m always, static or moving, applies a force F = mg on the springs s that compress and therefore 'absorbs' it as strain energy.

The "it" in that sentence is unclear. The springs absorb what as strain energy? Force? No. Forces are not absorbed as energy, they are balanced by other forces (or else cause accelerations). Mass? No. Mass is not absorbed (at least, not in a case like this; if we were talking about liquids and sponges then maybe). What the springs absorb as strain energy is a small fraction of the gravitational potential energy. How small a fraction? You've specified it in your model: it's m times g times .001 which is the fraction of its height by which each mass is lowered due to the compression of the springs. So the springs absorb a tenth of a percent of the gravitational potential energy.

By the way, the compression energy of the springs is also potential energy! So actually no potential energy has been "absorbed" at all. Instead, a small fraction of it has been converted from gravitational potential energy to elastic strain energy. The total potential energy has not changed.

That, of course, is in the initial static state. When things start moving, all the springs put together can only absorb 2.2 percent of the structure's total potential energy before they break (making very liberal assumptions about how much energy is absorbed in plastic deformation between strains of .003 and .005).

The maximum potential energy that m can apply in a single Funny m element is mgh (by removing all springs) and then the force is applied on the ground.

Your model uses h to mean the height of one floor, but the h in the gravitaitonal potential energy equation mgh refers to the total height off the ground. Be careful not to confuse the two values.

If you remove all the springs then the masses fall, so the force applied on the ground is zero, until the masses hit the ground.

Also, you're mixing up potential energy and force again. Increase the h, and the potential energy increases while the force against the ground does not change. This should make it obvious that there is no consistent proportional relationship between potential energy and the force required to contain it.

3. Well, a lot of energy is absorbed as compression!

Yes. A whole 2.2 percent of it. (Actually only about 1.3 percent is truly absorbed in the springs' plastic deformation, because the portion used to compress the springs elastically is released again when the springs break, and is still available to do work -- although it's such a small fraction that it hardly matters.)

In Experiment 1 there are 84 springs to consider and they will all compress! And then there is more energy required to break a spring.

Yes. It requires 2.2 percent of the structure's total gravitational potential energy to break all those springs.

What do you think the other 97.8% of that potential energy is going to do?

I am glad that you think that the four springs #22 in Part C may break first! Now a surprise. Two of the four #22 springs on one side are a little stronger! What do you think happen then?

They'll break second.

To determine anything beyond that, we need more scale information to determine the angular momentum of a funny mass unit, relative to m and h. Should we use the angular momentum of a 200-foot-square 4" thick steel-trussed concrete slab, a 47" square 5" thick concrete slab inside a wooden tray, a pizza box, or a lemon?

4. Glad that you like Funny m element. It is quite similar to a pizza box, though.

No it's not.

Your funny model has only three assigned parameters, to which you've assigned values of .001, .003, and .005. (Yet, those are enough to determine that it will progressively collapse, even without knowing m or h!) Test the corresponding pizza boxes for the corresponding physical properties and you'll find those values are nowhere close. Test steel columns and trussed concrete floors and they'll be a lot closer. What does that tell you?

Respectfully,
Myriad

 

[Heiwa]

Your funny model has only three assigned parameters, to which you've assigned values of .001, .003, and .005. (Yet, those are enough to determine that it will progressively collapse, even without knowing m or h!) Test the corresponding pizza boxes for the corresponding physical properties and you'll find those values are nowhere close. Test steel columns and trussed concrete floors and they'll be a lot closer. What does that tell you?

Respectfully,
Myriad

And just to cheer you up I have changed those parameters to make the Funny m assembly a little softer! So it will break up! But a one-way crush down by little C of big part A is not possible in Experiment 1. Big strong part A destroys little weak part C. And what happens then?

If you use LS DYNA, you can probably find out. Always good to do computer simulations before building a 10 meters tall model.

But let's face it. Funny m is just an example to get feel for the real problem. In reality the springs s will punch holes in element m and that's another problem ... to be solved.

Maybe I should make another Funny m assembly where m is split up into smaller elements?

 

[Heiwa]

If you really believe this, I invite you to place a brick gently on your head, and experience the 'mg' for that brick, then lift it 2 feet above your head and drop it, and see if you feel more than 'mg'.

By the way, if your theory is correct that mass m always applies mg, static or moving, than you've just disproven any possible collapse arrest. Way to go!

Thanks for your contribution. The gravity force F on a mass m is always mg. If this mass collides with anything, e.g. you, and energy is transmitted then other forces of short duration develops. If you are strong, then m will bounce away from you thanks to these forces. You arrested m! Thanks for proving my point.

 

[Heiwa]

So you think the top should have bounced off the bottom?

It is likely. Every time I try with various structures it happens. The Heiwa Challenge is to produce a structure, where it doesn't happen. See post #1.

 

[FineWine]

Thanks for your contribution. The gravity force F on a mass m is always mg. If this mass collides with anything, e.g. you, and energy is transmitted then other forces of short duration develops. If you are strong, then m will bounce away from you thanks to these forces. You arrested m! Thanks for proving my point.

He didn't prove your point.

 

[Heiwa]

He didn't prove your point.

What do you expect from a religious fundamentalist? Lobster and champagne?

 

[Myriad]

And just to cheer you up I have changed those parameters to make the Funny m assembly a little softer! So it will break up! But a one-way crush down by little C of big part A is not possible in Experiment 1. Big strong part A destroys little weak part C. And what happens then?

Ah, interesting changes. From the web site:

Due to mass m the springs s compress elastically d = 0.03h.

The structural Funny m assembly is really funny or at least the spring elements. They can compress 0.09h elastically and 0.1h plastically before they break (in this example). It means you must put on 3 m for the springs to start deforming plastically!

That is pretty funny. I see you've realized your previous model would progressively collapse in all three experiments, so you've fixed the design by making the columns 30 times more elastic! They now compress 30 times more under the static load than before, and it would take about 15% of the buildings total gpe to break them all.

That makes your funny model units a lot more like pizza boxes... and a lot less like the floors of a WTC tower. If their columns were that elastic, the towers would have been about 40 feet shorter -- more than three stories -- due to elastic compression of the columns! Each ceiling more than four inches lower! And I'd hate to think of what would have happened in a high wind, or try to figure out how to keep the window glass intact as the walls flex. Heck, the whole building would have bounced every time a cargo elevator stopped. And if a tenant wanted to put something heavy (like a UPS room or a paper file archive) on one side, they'd have to put something equally heavy on the opposite side, or else all the floors above them would lean. (Just a little, but I bet the tenants upstairs would notice!)

But rubber buildings do have one advantage, they are much less likely to progressively collapse! With the new values, progressive collapse can be arrested in your model under certain conditions. (Make the columns even more flexible, and maybe the planes could bounce off too!)

That extra durability might explain why so many new cruise liners are being built out of rubber!

Respectfully,
Myriad

 

[FineWine]

What do you expect from a religious fundamentalist? Lobster and champagne?

That makes as much sense as everything else you post, so I guess I'm not disappointed.

 

[phunk]

Thanks for your contribution. The gravity force F on a mass m is always mg. If this mass collides with anything, e.g. you, and energy is transmitted then other forces of short duration develops. If you are strong, then m will bounce away from you thanks to these forces. You arrested m! Thanks for proving my point.

Yes we all know that the force of gravity is mg, but that's not what you said in what I quoted. You said the force that the mass exerts on the springs is always mg, whether it's static or moving. This is very clearly wrong.

 

[phunk]

Wait, who's the religious fundamentalist?

 

[Heiwa]

Ah, interesting changes. From the web site:




That is pretty funny. I see you've realized your previous model would progressively collapse in all three experiments, so you've fixed the design by making the columns 30 times more elastic! They now compress 30 times more under the static load than before, and it would take about 15% of the buildings total gpe to break them all.

That makes your funny model units a lot more like pizza boxes... and a lot less like the floors of a WTC tower. If their columns were that elastic, the towers would have been about 40 feet shorter -- more than three stories -- due to elastic compression of the columns! Each ceiling more than four inches lower! And I'd hate to think of what would have happened in a high wind, or try to figure out how to keep the window glass intact as the walls flex. Heck, the whole building would have bounced every time a cargo elevator stopped. And if a tenant wanted to put something heavy (like a UPS room or a paper file archive) on one side, they'd have to put something equally heavy on the opposite side, or else all the floors above them would lean. (Just a little, but I bet the tenants upstairs would notice!)

But rubber buildings do have one advantage, they are much less likely to progressively collapse! With the new values, progressive collapse can be arrested in your model under certain conditions. (Make the columns even more flexible, and maybe the planes could bounce off too!)



Respectfully,
Myriad

The purpose of the article is only to establish what spring breaks first in this 3-D structure of Funny m assemblies assuming, unrealistically, that part C actually free fall drops on part A! What happens afterwards is another story.
And it seems it is always a spring in part C that breaks first regardless of how flexible or stiff the structure is. So you have evidently learnt something.

Evidently a floor cannot be represented by one m element in the Funny m assembly. It was only there to provide mass to compress the springs. And assuming that the springs just compress and break somewhere ... and do not slip off or damage their connections - are simplifications.

So far the only other models I am aware of are by Bazant and Seffen, which are just in 1-D! Lines C and A with some funny density/mass per meter where only line A is getting shorter - no springs/floors, etc. Imagine a line with no cross area colliding with another line with no cross area! How do they meet?

Hopefully Bazant and Seffen will no try to improve. It is line C that is getting shorter - if the lines fuse!

 

[bill smith]

Heiwa....any word back from the ASCE on the publication of your paper ?

 

[FineWine]

Heiwa....any word back from the ASCE on the publication of your paper ?

Can we assume that when his paper is rejected it will prove that ASCE is part of the conspiracy?