Building Collapses in Rio

With that in mind, you'll note that I introduce the additional forces later. I say:

The reason the horse can pull the cart is the same reason that the guy can turn the crank. The force between animal and object is not the only force on the animal. The other one is the ground. The horse's legs push against the ground and the ground pushes back. This satisifes the third law but leaves forces unbalanced on the horse and subsequently the cart, so the cart moves. So it is with the crank.

If one draws a free body diagram (correctly, that is), one must include ALL forces acting on the body. This puts the net force acting on a body in terms of the vector sum of all forces acting on that body. For the man standing on the ground turning a stiff crank, there are two forces acting on the man:

1) the force of the ground pushing against his foot
2) the force of the crank pushing against his hand

Both of these forces are each one-half of two action-reaction pairs. SnowCrash, your author claimed we can dispense with all the canceling action reaction pairs. That means your author has no forces in his free body diagram and the man remains stationary. Well, on the whole, over time and the total mass of his body, he IS stationary - he doesn't fly off in some direction.

But your author fails to capture the two real forces acting to hold the main in place (relative to the massve earth). In so doing, having no forces at all in the freebody diagram for the man, your author correctly accounts for overall net motion, but fails to account for the real forces in action. Ask the man turning the crank if he's applying force to both turn the crank AND remain standing in one place,

Originally posted by -PLB-
reply to post by IrishWristwatch

 

I don't have such a deep understanding of Bazants model as you have, so I can well be wrong here. But doesn't what you say here means that his model does not account for static loads?

He accounts for both force due to momentum change and static load. If I gave a contrary impression, the error is mine.

A debris layer laying on an intact floor increases the load of that floor.

Yes.

In fact, even without a debris layer, the load on the lower floor is greater by the weight of 2 floors during an impact.

This is a VERY interesting thing you bring up. I believe you're referring to the concept of sudden loading, an engineering term describing the effect of impulse due to a load being brought into contact with a support and then released. NIST makes mention of this in their FAQ and, it turns out, this was one of the things which lowered the prior esteem I had for them (I've made extensive use of their free online engineering resources, which are great, and they've typically maintained a stellar reputation throughout their existence first as NBS and then NIST).

Please allow me another subsequent long post to explain the issue of sudden loading as it applies to this subject...

reply to post by IrishWristwatch


Yeah, I was just drawing that diagram myself to understand it better (force acting from foot on floor (A), floor on foot (B), man on machine (C), machine on man (D), machine on floor (E), and floor on machine(F))

Thinking out loud (again, correct me if I'm wrong)

The frictional resistance of the rotating parts in the lever will account for the force transmitted through the machine on the floor, and the floor will have an equal and opposite reaction force that cancels out the force acting through rotation friction on the machine, otherwise the machine would move away from the man.

(And of course, gravity and reaction force from earth's core, and the (vertical) force from the machine on the floor and the reaction force: the normal force)

The rest accounts for the rotation.

So sure, we have (B) canceling (D) and (F) canceling the part of (C) that doesn't go into rotation, otherwise machine and/or man would start moving.

However, as for the respective action-reaction force pairs, A doesn't cancel B, and vice versa, C doesn't cancel D and vice versa, and E doesn't cancel F and vice versa.

Right?

(The reason B can cancel D is the same reason why F can cancel C, B and D act on the same object and F and C act on the same object)

Obviously in the above I must simplify, otherwise I'd get lost in the details, such changing force vector components in different directions/angles on the lever and therefore the machine during lever rotation, etc. etc.

Let's take e.g. a very common action-reaction pair in isolation: gravity and the reaction force from earth's center of mass. If these two were to cancel each other out F(g) + F'(g) = 0 ... (F' being negative), we would all be weightless. Rather, gravity makes the WTC come down while earth simultaneously moves up an infinitesimal amount towards the WTC, because both forces act on different objects: F acts on the WTC and F' acts on earth as a whole.

Because earth is such a massive object, it is accelerated by such a small amount compared to the WTC that earth's simultaneous movement is unnoticeable to the casual human observer.

If one stands on the ground, what prevents one from moving downward further is not the reaction force from earth's center of mass, but the normal force that is the reaction force of the action force exerted on the ground through your shoes.

Originally posted by ANOK
then why did the weak joints not fail when the trusses supposedly pulled in columns much more massive than themselves?

That is a contradiction you need to address.

I don't subscribe to the 'newton's third and then compare masses' school of physics. The contradiction is in your mind only, thus far. If you want to do a serious analysis of the forces on the trusses' connections in the two situations, I think that would be appreciated by all.

Thanks.

Sudden Loading. In engineering, this refers to the application of a given load suddenly, as the term implies, such that the member bearing the load goes from unloaded to fully loaded in a very short period of time (effectively instantaneously).

This specifically excludes the effects of impulsive contribution due to collision. In the context of a column supporting a load, sudden loading refers to bringing the load into contact with the column, which is initially unloaded, then releasing the load suddenly as opposed to gradually applying the load in a quasi-static fashion.

Being an engineering term alien to physics, I didn't know this until Tony Szamboti explained it to me - the missing link being the fact that the load is first brought into contact. It made no sense that dynamic loading ALWAYS produced twice the peak of the same load statically when impact is involved. Clearly, intuition indicates that, the greater the impact velocity, the greater the impulse delivered, all other things equal.

In NIST's FAQs, they describe a situation in which floors (or stories of an upper block? There's a difference, and it's never made clear...) from above drop onto a floor below, and say the dynamic load amplification factor is two. This is false, and for more than simply the reason that there is a non-zero impact velocity, though this is obviously also true. A dynamic amplification factor of 2 relies on contact and release only and excludes impact, but it also very subtly involves a usually unspoken assumption of linear response in the support.

First, the non-impulsive nature of sudden loading.

From The practical design of plate girder bridges, where the context is a train rolling onto a bridge:

Also it should be noticed that the load comes on the structuree suddenly, and if the span is only a short one, the full live load effect is induced in a fraction of a second.
...
Then, as regards sudden loading, it can be shown theoretically that if a load is suddenly applied to a piece of material, the strain produced will be just twice that produced by the same load gradually applied, and, therefore, the equivalent stress will be twice that produced by the same load gradually applied, as calculated in the usual way.

"In the usual way." This phraseology belies its origins in everyday engineering statics. Bridge builders when designing cannot exclusively do calculations the 'usual way' for engineering, which is primarily static analysis. There are dynamic considerations when a train rolls onto the bridge - it is suddenly loaded - where a moment ago it was fully unloaded with respect to live load.

The support gives in response to the applied load; that is, it deforms. In so doing, the load is allowed to drop ever so slightly beyond the equilibrium (unloaded) position, thus losing potential energy. Where does this energy go? Until the support displaces far enough to counter the static load, it will not even resist the downward acceleration of the load. That occurs when the displacement is equal to the loaded static equilibrium displacement. So the lost potential energy goes into kinetic, and the load accelerates downward.

Until that displacement of static equilibrium is achieved. At that point, the force is equal and further deformation increases the resistive force. Then the load will decelerate. Assuming the support doesn't fail, there will come a point where the downward momentum of the load is reduced to zero and the object is momentarily at rest. For materials with linear response, this happens to be twice the deflection of the static equilibrium position and twice the associated strain.

Of course, the restoring force at maximum deflection is also twice the static load, so the load now begins to accelerate upwards as the support rebounds. The force will reduce as the load moves up, being equal to the static load at the midpoint of travel and zero at the top. At the top, the original position is restored, velocity is zero, and all the kinetic energy has gone back into potential. The dynamics of simple harmonic oscillator with a mass at one end under the external force of gravity.

In the real world, response is (usually highly) damped, and the oscillation rapidly reduces in magnitude to zero. But, in the real world, response is not usually linear, and is never linear over a sufficiently large deflection.

Bridge builders, while having to account for dynamic sudden loading, do not have to account for trains dropping onto bridges. Likewise, structural engineers do not generally need to consider non-linear response, because they stay within elastic range by design.

Continued...

The engineer of STATIC structures stays well within the elastic range of materials, by design, simply because the plastic region means trouble. Failure. Moreover, the materials used tend to fairly well exhibit elastic response because that is desired. Steel, in particular, is effectively elastic under small deformations; that is, the deformation is reversible, even if damped and lossy. Concete does not have a plastic phase but it too is relatively elastic until failure.

The problem with the notion of dynamic amplification factor always being two relies on elastic response. It is the linear relation expressed in Hooke's law, F = -kx, which dictates the 'magic' number of two. Any non-linear response will change the result, as it is dependent on the integral of force over distance; the mechanical work done to arrest a load, therefore maximum deflection and strain, is given by that integral, and it would only be coincidence if an arbitrary curve integrated to the same value as a straight line between endpoints.

Floor collapse, that is floor-on-floor, involves a highly non-linear process of deformation, fracture, ductile elongation, and so on between a variety of members and materials. Not only do they impact with velocity providing impulse above sudden loading, the process is not in any way likely to involve a magic number of two even in the case of true sudden loading. Well-distributed force applied to a floor assembly near the center of the span might result in a linear deflection response over a few centimeters but, in a messy collapse, who knows?

It is for this reason that I found NIST's comment to be woefully in error, greatly overestimating the dynamic load to induce failure on an impacted floor.

Now, to catch up to the other posts.

Originally posted by snowcrash911
reply to post by IrishWristwatch

 

Yeah, I was just drawing that diagram myself to understand it better (force acting from foot on floor (A), floor on foot (B), man on machine (C), machine on man (D), machine on floor (E), and floor on machine(F))

Thinking out loud (again, correct me if I'm wrong)

I believe you're getting it.

I'm a little shocked at the online reference. It is true that the canceling forces are easily ignored when known, and physicists will immediately cut to the chase and analyze the unbalanced forces, if any. But it is not true that the forces can be ignored as if they don't exist, because they do exist.

Net force is not the same as all the forces acting on a body, it is the same as the vector sum of their contributions. Quite different.

Originally posted by snowcrash911
Because earth is such a massive object, it is accelerated by such a small amount compared to the WTC that earth's simultaneous movement is unnoticeable to the casual human observer.

Correct.

If one stands on the ground, what prevents one from moving downward further is not the reaction force from earth's center of mass, but the normal force that is the reaction force of the action force exerted on the ground through your shoes.

Correct. Your intrinsic 'static capacity' keeps you upright. The force your legs exert, when stationary, exactly cancels the force applied to your body from gravity. If you relax, and allow your legs lose capacity, you collapse.

If someone smacks a leg brutally with a metal pipe, that leg will lose capacity due to external influence. If the other leg is not able to absorb the load previously borne by the damaged leg, you'll tip or fall in some way. Usually people can stand on one leg, but inanimate structures can't move to redistribute load. If you were a static structure (arthritis), you'd fall over even if one leg could support all your weight.

Suppose you can easily support one person on your shoulders, but not two. Suppose further that the response of your legs to load were linear up to the point of your knees buckling. Then, if another person were brought into contact with your shoulders and released, that alone would be enough to take you down.

People talk about an FOS of 2 like it means something. It means something only in the context of a structure which is essentially static. Once some major portion is in motion, an FOS of 2 is butter. Even if only bringing upper section into contact with lower and releasing it, there is ZERO margin of safety. The lower is taken to full elastic deflection, no drop distance required.

Originally posted by IrishWristwatch
Correct.

Cool.

Originally posted by -PLB-
reply to post by snowcrash911

 

Then I do not understand how the model can ever predict arrest without initial debris layer. Even if the collapse starts with crush up, as debris piles up, crush down will happen as result of static load.

edit on 5-2-2012 by -PLB- because: (no reason given)

No, in this case the intertial 'shield' of the debris layer protects the bottom, not the top. The intact lower portion is capable of supporting the static load. The only way the capacity is exceeded is if the momentum change from impacts above provides an excessive peak impulse to the intact colums below the debris layer. In order to deflect those columns further than their static load deflection, the impacts above must literally move the ever growing debris layer, which has significant inertia, above and beyond its gravity-driven descent. Thus, the upper block splats itself on the debris layer like a classic exclusive crush up coupled to ground.

Like I say, I was taking a guess, but this is based on physics simulations which easily quantify the effect for various material configurations. Depending on the parameters, there can be mixed crush or exclusive crush up, but rarely exclusive crush down WITHOUT the initial debris layer. In those cases of crush-up only, the best (theoretical) chance for crush down to emerge is in the earliest impact. If it didn't happen on first impact, what would make it more likely to fail on the second? Not the static load, it can be supported by definition; only the acquired momentum of the (now smaller!) upper block can cause the forming debris layer to transfer SOME of that momentum through the debris layer to the lower section.

Simulation bears this out every time, and allows recording of all dynamic data so that the entire process can be followed in intimate detail to not only verify no violation of conservatiion laws occurs, but to also see how the situation unfolds and why it is so.

Obviously, all of this 1D stuff (Bazant and sims) is very much divorced from reality, but that is the current subject of discussion. Within that context, Bazant's treatment came within a gnat's ass of crushing up, as I would expect from simulation. Had it crossed that threshold - even in event of concurrent failure below - crush up would ensue and two things have fallen out of my experimentation in regards to this family of models:

1) When crush up starts, it is unlikely to end until full consumption of the upper portion
2) Crush down dynamics are not affected greatly by the concurrent crush up of a small upper section

With this, I conclude it's likely that bidirectional crush would occur in Bazant's treatment with a small and reasonable adjustment to his assumed parametric input. With a little further tweaking, exclusive crush and therefore eventual arrest could be the result.

It means very, very little to the real collapses. It really speaks to the shortcomings of the model. I do believe it would have been much better if Bazant had covered this, because the type and magnitude of tweaks I mention to show arrest are not unreasonable, not at all. It's almost as if he was reluctant to show the entire neighboring solution space because that would start a whole new round of pseudoscientific accusations leveled at him.

"Bazant says it could arrest, blah, blah, blah, but deliberately chooses conditions which lead to collapse."

Overlooking the fact that the analysis is already highly optimistic for survival!

I have, based on this, suggested in the past that this sort of wording would've been the high road in B&L:

The actual collapse mechanisms bear virtually no resemblance to that detailed in earlier papers. These were simplified formulations to determine gross energetic thresholds for continuation and a first order approximation to the dynamics. In all likelihood, and as appears from direct observation, the collapses consisted of bidirectional crush of varying proportion. In this reply, an ideal case leading to exclusive crushdown is examined to illustrate the validity of the earlier papers, but also a more general framework of bidirectional crushing is developed and it is seen that a number of realistic solutions depict total collapse as well. Ultimately, the analysis will be taken to the limit of applicability, where exclusive crush up and arrest result, and the reasons why the model is inapplicable in these regimes, versus being applicable in previous articles, will be thoroughly explained.

But it's a minor nitpick.

In addition to the above, it's important to note the lower section partially unloads when crushdown is in progress, whether or not crush up occurs. The impacts transiently overload the columns locally, but the lower section is experiencing LESS than static load on average, so long as the debris is accelerating downwards. In these models, there is no terminal velocity so dynamic equilibrium is never achieved. If it were, the crush would proceed with the lower section experiencing an average loading equal to static. Only sustained slowing of the upper block from previously higher velocity results in an average load higher than static.

With regards to an exclusive crush up, that means the lower section IS experiencing a greater average force than static load, since the upper section will eventually come to rest at the conclusion of crush up. However, with a modest FOS, this additional loading is easily borne, and collapse arrests.

This is a huge reason to leave 1D models behind when it comes to collapse mechanism. That's obvious to some people, but look how much chatter there is over these purely instructive but not descriptive models.

I don't believe for a moment that exclusive crush up terminating in arrest could happen in the towers, not by a long shot. It's what I like to call the dumpster-in-the-sky fallacy, that the floor assemblies could bear even the static load of the rubble likely to have accumulated. (That's my belief, Darkwing, not a claim of fact, and I'm entitled to my opinion). But I absolutely do believe Bazant's model could predict arrest, a result 180 degrees opposite from that reported, by virtue of only minor and fully defensible adjustment of assumed and estimated parameters.

Pretty ironic, all in all.

The visual evidence points towards a significant amount of crush-up occurring early in the collapse at minimum.




Unedited showing NE corner used to plot the theoretical approximate position of a top section not having undergone crush-up.

One correction to the crap on sudden loading:

Not ALL the lost gravitational potential energy during sudden loading goes into kinetic energy. This is obviously false. At maximum deflection, all the gravitational PE has been converted into strain potential energy, and the KE of the load is zero.

What I meant to convey was that, UNTIL the strain potential energy equals the loss in gravitational potential, some portion will be in kinetic. As stated, though, it is simply in error.

Originally posted by DrinkYourDrug
The visual evidence points towards a significant amount of crush-up occurring early in the collapse at minimum.

Absolutely.

The term 'crush' strictly means compaction within the models, but I take it to be effectively synonymous with loss of integrity and breakup in the context of the real collapses in the way you use it here. I say this because people have taken me to task for using the term to mean something other than purely pulverization and compaction. In this thread, I don't think there's much concern over whether or not destruction occurred as full compaction so much as which direction, if any, destruction of all kinds could propagate.

Likewise, the north tower's upper section seems to break up on the way down, readily and easily. Skewered? Splayed? Not sure of the best way to put it.

This alone makes the Bazant analysis inapplicable as a narrative of mechanism. It still serves as bounding case, technically, though just not as broadly applicable as he might like. Simply moving the problem to two degrees of freedom takes the result perilously close to crush up. Instead of abandoning this direction, I feel he should have pushed it. I believe a wide range of solutions for bidirectional crush would show collapse to completion.

reply to post by IrishWristwatch

Open systems are studied all the time. I get the impression you think systems must somehow be made closed before a model is acceptable.

Again.

I will caps this because I am doubting your eyesight.

THERE ARE TWO THINGS NOT ONE.

ON THE ONE HAND YOU HAVE THE MODEL.

ON THE OTHER YOU HAVE THE THING MODELED.

THE PROBLEM IS NOT WITH MODELLING OPEN SYSTEMS.

THE PROBLEM IS WITH USING AN OPEN MODEL TO MODEL THE OPEN SYSTEM.

No, Irish. The system is not closed, there is no such thing in reality. But you cannot do science by invoking god when your equations run into trouble. If, and please read this carefully

YOUR MODEL

not

THE THING YOU ARE MODELING

is open in the sense of some action or activity being unaccounted for then you have not explained anything, because ther could be literally ANYTHING in that gap, it could be god, it could be a black hole, it could be Richard Dawkins cocking a snook from on high. The fact that there is A HUGE ENORMOUS GAPING HOLE IN YOUR EXPLANATION MEANS ANYTHING CAN GO THERE.

More specifically: It means that you can put an explosive device there or some natural phenomenon.

That is fine when you have EMPIRICAL DATA, which is why the scientific method relies on EMPIRICAL DATA to bridge the gap.

But we don't HAVE NEW EMPIRICAL DATA.

We are trying to find what is in THE GAP of HISTORICAL (i.e. non-controlled) data.

There is a way to deal with the exact issue that has been developed and honed over millenia, it is called the scientific method.

reply to post by Darkwing01


THAT, my dear Irish, is why the law is

F= ma -> Closed model

and not

F= ma (by the grace of god) -> Open model

I will also back off of the criticism of SnowCrash's physics source. Going back and reading the whole thing, it's much better when taken in context. It IS like one person paying the other's tab, in terms of accounting. What difference does it make in the end? This is true. But, ultimately, me paying your tab and you paying mine is not the same as each paying our own. Where this difference matters, as I point out above, is that the forces are really felt by the interacting objects, and a free body diagram of one of the isolated bodies in the examples above includes the forces to show equilbrium of a stationary body, since they are part of different action-reaction pairs which happen to cancel, but are not required to per the 3rd law.

Resorting to big fonts now instead of making an argument, Darkwing? Not sure I'm going to read that. You're bad enough when you're not frothing...