Merged Applicability of Bazant's model to the real world

[Myriad]

So what is R? How do you calculate it's magnitude? If a 10kg block falls under gravity and hits the floor, what will R be?

Interesting question. It's a little trickier to calculate than you might think.

A few things we can point out right away:

1. R is zero until the block actually touches the floor.

2. After the event is over (or to put it another way, reaches a new static equilibrium with the block resting on the floor), R is equal and opposite to the weight of the block.

3. We know that when the block hits the floor, its velocity must go from v (the velocity it was traveling just before it hit the floor) to zero over a period of time. That time might be very short but it cannot be instantaneous (zero duration). An instantaneous change in velocity from v to 0 would require infinite force. Instead there is some finite amount of time, that we can call delta t, between reaching the floor and coming to rest.

4. We also know that because of 3, the block must continue to move downward after the initial moment it touches the floor, even if it lands perfectly flat, because it doesn't come to a stop until the additional time delta t has elapsed. That means that even though the block and the floor are both solid rigid objects in our everyday understanding, the laws of physics say one or both must deform during the collision, at least a little.

That gives us some basic boundary conditions. We know that we can make a graph of the block's position, velocity, and acceleration for the time interval delta t. The block's velocity will decrease from v to 0 on some curve. The position of the block's center of gravity will be moving downward at the start of the time interval, and will be at rest at the end. The force the floor exerts on the block (R) will be 0 in the instant before contact with the floor, the weight of the block at the end of delta t, and the difference (force R minus the weight of the block) will be proportional to the slope of the velocity graph at all points along the way (which, since the slope of the velocity curve is the block's acceleration, is just restating Newton's third law as pertains to the block).

Beyond that, things start depending on the exact qualities of the block and the floor, and other factors. The force between the floor and the block in any given moment is a function of the current amount of elastic and inelastic deformation of the materials, which depends on the position the block has reached, which depends on its movement and acceleration, which are affected by the force. And the force versus deformation curve is not linear, in the real world. A physicist or engineer who needs a definite answer would lay out the differential equations involved and execute a numerical solution, or would do tests with the actual materials, or some combination.

One thing we can do, short of that, is to look at an ideal solution that answers the question, "For a block of mass m, dropped from height h, what is the least possible maximum force the floor could exert on it, and still bring it to a stop within a given distance of floor deflection (assuming the floor yields and the block is perfectly rigid)?" That best case occurs if the floor exerts a constant force from the moment the block contacts it to the moment the block comes to rest. (For this to happen, the block must not bounce, so the floor must be deforming inelastically; that's unrealistic for e.g. a wooden floor but roughly fits how a floor with a few inches of wet sand on it might behave.)

The velocity v of the block on reaching the floor is sqrt(2gh).

By our ideal assumptions, the block decelerates at a constant rate a from velocity v to velocity 0 through a total distance of s. Similarly to the initial fall, v = sqrt(2as), so a = v^2 / (2s).

Substituting sqrt(2gh) for v, and solving for a, that works out to a = g * h/s. In other words, the acceleration of the block when it hits the floor, expressed in g's, is the ratio of the height from which it was dropped, to the total distance it deflects the floor before it stops. If you drop the block from a meter, and it hits something resisting and stops after another meter (a pit full of shaving cream perhaps?), it decelerates at 1g. If you drop the block from a meter, and it hits the floor and stops after deflecting the floor a centimeter, it decelerates at 100g.

The actual force the floor exerts on the block will be the mass times the acceleration, plus the mass times the static force of gravity, so 2mg (twice the weight of the block) for the shaving cream pit that deflects a meter, and 101mg (101 times the weight of the block) for the sand floor that deflects a centimeter.

For a real wooden block landing on a real wooden floor, flat on, the peak forces will be higher. That's because (even though in the real world the block and the floor will both deform) a centimeter of additional movement before the floor stops the block after a 1 meter fall is unrealistically large (for a small building block size block at least). Also, the force is not constant for the entire delta t as in the ideal case, but increases roughly in proportion to the current amount of deformation. The result is a higher peak force applied for a shorter time. The real block will also likely bounce; that is to say, some or all of the deformation will be elastic.

The key understanding here is that to bring the block to rest, the floor must do work on it. The force alone doesn't determine what happens; the distance through which the force is applied matters just as much. (Hence, a smaller force of 2x the weight of the block will bring it to a stop, but only after a much greater distance of additional fall.)

If we're talking about work, force applied over distance, then we're talking about energy. This is important because other things that can happen when the block meets the floor, such as the block breaking or the floor breaking, become very difficult to analyze in terms of the forces over time and distance, especially if they're all happening during the same time interval. These can be much easier to characterize in terms of energy. That's why many solutions to collision problems involve using energy rather than explicit forces. For instance: the falling block develops x amount of kinetic energy, y amount of energy is converted by fracturing the block, leaving z amount of energy to be absorbed by deformation of the floor, which deforms s amount to do so. The underlying physics principles are the same and the results will be the same, but it's often easier to get raw data on e.g. how much total energy it takes to break something, than for a full equation or complete data relating resisting force to velocity and displacement for something in the process of breaking.

Respectfully,
Myriad

 

[ozeco41]

Interesting question. It's a little trickier to calculate than you might think....

A good explanation of the basics there Myriad.

And that is for a single homogeneous block and various landing surfaces.

It gets orders of magnitude more complicated when dealing with the real WTC "top block" falling on lower tower because of the hundreds of different element on element contacts each one has different elasticity factors, weights, velocities......

 

[Dave Rogers]

Myriad still has not shown how the net force of block C exceeds the resistive force of Block A--without referring to Bazant.

This is a bit of a loaded question, given that it's Bazant's notation that describes the falling block as block C and the lower block as block A; therefore, even describing them as blocks A and C is an implicit reference to Bazant.

However, the clue is in the notation. Block C is the falling block, and A is the lower block still standing; what, then, is B reserved for? The answer is that B is the layer of rubble created from the top of block A and the bottom of layer B by their collisions. Bazant's analysis shows that, as the collapse progresses, layer B grows in weight - obviously - by accumulation of debris, and is exerting a force on block A. Block C, meanwhile, is exerting a force on block B. There is no direct force between A and C, because layer B is between them.

From there, it's relatively simple to understand why a difference between the force acting on A and the force acting on C doesn't violate Newton's Third Law; the reaction forces, in both cases, are acting on B, and are different forces. The difference between them shows as a net force on layer B.

Finally, Bazant's analysis shows that the force between B and C decreases as the collapse progresses. This is why crush-down precedes crush-up; in effect, the upper block C rides down on a cushion of rubble, which is the mass that crushes the lower block A. And this is why understanding, and taking into account, the behaviour of the falling debris is crucial to an understanding of the collapses.

Dave

 

[GlennB]

Yes, cheers Myriad.

And a superficial interpretation of Newton's 3rd law can lead to some comical results (Old Heiwa came up with a few ) ...

Consider a beer can tied to the back of your car with length of fishing line. You try to pull away :

By Newtons 3rd, f₁= f₂(action = reaction)

But f=ma, so :

m₁a₁= m₂a₂

But a₁= a₂, therefore m₁= m₂

Therefore the car weighs the same as the beer can. Q.E.D.

(for the purposes of illustration. There should be some - signs in there)

 

[Newtons Bit]

A good explanation of the basics there Myriad. [qimg]http://conleys.com.au/smilies/thumbup.gif[/qimg]

And that is for a single homogeneous block and various landing surfaces.

It gets orders of magnitude more complicated when dealing with the real WTC "top block" falling on lower tower because of the hundreds of different element on element contacts each one has different elasticity factors, weights, velocities......[qimg]http://conleys.com.au/smilies/scratch.gif[/qimg]

I've run the numbers on a rigid upper block impacting an elastic spring bottom block.

 

[pgimeno]

It seems I have made a fundamental error and admitted it. Why would you put someone on ignore because they dont understand collision problems and newtons laws as well as you do?

The corollary here is, don't buy ergo's physics misunderstandings.

The most common outcome of this kind of interchange is just "na na na, I can't hear you" on every explanation attempt. You can't blame someone who is tired of seeing that again and again, and figures that your case will be the same. Fortunately Myriad has been patient with you until you understood the issue. ergo is one of those who won't listen to any explanations, and gets pages and pages of pointless discussion filled with his flawed physics without getting anywhere.

 

[cooperman]

The corollary here is, don't buy ergo's physics misunderstandings.

The most common outcome of this kind of interchange is just "na na na, I can't hear you" on every explanation attempt. You can't blame someone who is tired of seeing that again and again, and figures that your case will be the same. Fortunately Myriad has been patient with you until you understood the issue. ergo is one of those who won't listen to any explanations, and gets pages and pages of pointless discussion filled with his flawed physics without getting anywhere.

Thsi has nothing to do with ergo. It wa my mistake and he didn't share it.

Erho's main question is "how can you prove that the resistive force R was not greater than the weight of the upper block without referring to Bazant?"

His question is a valid one and I too would like to see an answer.

 

[Dave Rogers]

Erho's main question is "how can you prove that the resistive force R was not greater than the weight of the upper block without referring to Bazant?"

His question is a valid one and I too would like to see an answer.

I would argue that it's an utterly invalid one. It's equivalent to saying, "If you're not allowed to answer correctly, how can you answer this question correctly?" It's an absurd and dishonest question, and doesn't merit a response unless he can come up with some reason why Bazant's analysis is irrelevant.

Dave

 

[Myriad]

Ergo has not yet directly stated (though he seems to have now implied it, in some of his responses to cooperman) that he accepts that whether or not the upper block decelerates depends on whether or not the resistive force R was greater than the weight of the upper block. Specifically, that when R is less than the weight of the upper block, no deceleration will occur. His most recent coherent claim on this was that any amount of resistive force whatsoever acting on a falling object means that deceleration must occur, and the fact that the rest of us disagree means we are disregarding basic laws of physics.

Without resolution on that, there is no point in proceeding beyond it.

As I've said before, I'll answer the question regarding the resistive force but ergo has to first show that the question is relevant, for him, to the issue originally under discussion, which is whether deceleration of the falling mass should be expected. As long as he insists that any amount of resistive force whatsoever must result in a deceleration, there is no reason for him to care about whether or not that resistive force exceeds the weight of the upper block, so there's no need to waste time addressing the issue.

Respectfully,
Myriad

 

[cooperman]

Ergo has not yet directly stated (though he seems to have now implied it, in some of his responses to cooperman) that he accepts that whether or not the upper block decelerates depends on whether or not the resistive force R was greater than the weight of the upper block. Specifically, that when R is less than the weight of the upper block, no deceleration will occur. His most recent coherent claim on this was that any amount of resistive force whatsoever acting on a falling object means that deceleration must occur, and the fact that the rest of us disagree means we are disregarding basic laws of physics.

Without resolution on that, there is no point in proceeding beyond it.

As I've said before, I'll answer the question regarding the resistive force but ergo has to first show that the question is relevant, for him, to the issue originally under discussion, which is whether deceleration of the falling mass should be expected. As long as he insists that any amount of resistive force whatsoever must result in a deceleration, there is no reason for him to care about whether or not that resistive force exceeds the weight of the upper block, so there's no need to waste time addressing the issue.

Respectfully,
Myriad

I don't think ergo is claiming that. We know that if R exceeds F then there will be deceleration. Ergo accepts this.

 

[femr2]

Remember to distinguish between decrease in rate of acceleration, and deceleration.

 

[GlennB]

Remember to distinguish between decrease in rate of acceleration, and deceleration.

I'm looking forward to the day when Szamboti remembers this. Every time he posts I have no clue which version of 'deceleration' he's thinks he's using.

I think he scrambled my brain the day he claimed that the static undamaged building was undergoing a constant 1g acceleration.

 

[excaza]

Well, I suppose if you cut the FBD in half, it would always be at a 1g acceleration.

But he can't draw a FBD, so I dunno.

 

[Myriad]

I don't think ergo is claiming that. We know that if R exceeds F then there will be deceleration. Ergo accepts this.

I'd rather hear it from him. Post 722:

Do you now admit that that causing a deceleration depends on which force is greater -- that is, in this case, that the force acting on Block C in the downward direction must be less than the resistive force of Block A, for Block C to decelerate? And do you now recognize that if the downward force on Block C is greater, it will not decelerate?

No, I don't. As I've already stated.

In what subsequent post did he change his claim? Post 756 a few posts later directly contradicts the above, with no explanation or indication of a change in understanding. Insisting he's correct about two different contradictory claims rules out further rational discourse until it's resolved.

Respectfully,
Myriad

 

[leftysergeant]

However, the clue is in the notation. Block C is the falling block, and A is the lower block still standing; what, then, is B reserved for? The answer is that B is the layer of rubble created from the top of block A and the bottom of layer B by their collisions. Bazant's analysis shows that, as the collapse progresses, layer B grows in weight - obviously - by accumulation of debris, and is exerting a force on block A. Block C, meanwhile, is exerting a force on block B. There is no direct force between A and C, because layer B is between them.

From there, it's relatively simple to understand why a difference between the force acting on A and the force acting on C doesn't violate Newton's Third Law; the reaction forces, in both cases, are acting on B, and are different forces. The difference between them shows as a net force on layer B.

And this is where whackadoodles like box boy Gage and Judy Wood and Jim Hoffman wander off into la-la lands.

Gage just does not get that the forces involved are tearing apart the innards of the structure, and envisons it as mostly involving the perimeter columns. Examination of any of the video shows that the destruction of the perimeter columns involves strictly lateral forces. See the bent connector bolts or torn out bolt holes in the bottoms of the perimeter columns for proof of that.

Wood and Hoffman seem to think that massive amounts of rubble are lost in the dust plume.

Their eyeballs aint calibrated to measure that. They may know how to crunch a few numbers but their powers of observation suck.

 

[leftysergeant]

I think he scrambled my brain the day he claimed that the static undamaged building was undergoing a constant 1g acceleration.

Okay, even I got that he was thinking of the foundation exerting a 1g decelleration. He fails, however, to grasp that, when they started moving, the upper columns of all three structures deflected the decellerating structures so that they no longer had any significant effect other than to limit the rate of acceleration to somewhat less than 1g.

 

[ozeco41]

Myriad still has not shown how the net force of block C exceeds the resistive force of Block A--without referring to Bazant.

This is a bit of a loaded question, given that it's Bazant's notation that describes the falling block as block C and the lower block as block A; therefore, even describing them as blocks A and C is an implicit reference to Bazant.

I would argue that it's an utterly invalid one. It's equivalent to saying, "If you're not allowed to answer correctly, how can you answer this question correctly?" It's an absurd and dishonest question, and doesn't merit a response unless he can come up with some reason why Bazant's analysis is irrelevant.

Dave

I beg to differ Dave. This thread has shown why Bazant and Zhou is not valid for the global collapse stage of the Twin Towers. The status of the other Bazant et al papers need not concern us at this point. I remain unconvinced of "crush up crush down" but that is a side issue at this point.

The first (implicit) question is a challenge "Myriad still has not shown how the net force of block C exceeds the resistive force of Block A--without referring to Bazant". Setting aside the technical point that the "A" and "C" are Bazant language the challenge is to answer without reference to Bazant.

Given that Bazant and Zhou is not valid for the "global collapse" of the twin towers (ie the OP discussion of this thread) why not answer the challenge without reference to Bazant?

The reason that the resistive force was not sufficient to slow or stop the top block in the global collapse was that there was not sufficient (if any) axial loaded columns to offer the resistance. That situation was outlined in qualitative terms in my earlier post. The key point being that Bazant and Zhou's assumption of axial column loading, a conservative and valid assumption for their purposes, was not valid for WTC Twin Towers during the "global collapse".

 

[ergo]

Do you now admit that that causing a deceleration depends on which force is greater -- that is, in this case, that the force acting on Block C in the downward direction must be less than the resistive force of Block A, for Block C to decelerate? And do you now recognize that if the downward force on Block C is greater, it will not decelerate?

No, I don't. As I've already stated.

In what subsequent post did he change his claim? Post 756 a few posts later directly contradicts the above, with no explanation or indication of a change in understanding. Insisting he's correct about two different contradictory claims rules out further rational discourse until it's resolved.

Perhaps because what you wrote is unintelligible. Eg: "...the downward force on Block C..." implies something pressing down from above. Block C is the upper block.

What is obvious to eight-year-olds and other people who understand everyday physics is that a small something cannot descend through a larger something of the same material composition via gravity alone. So the answer to whatever you may be asking above is: the lower intact building A is naturally going to impede the descent of upper portion C, no matter what possible height C could be "dropped" from "naturally", i.e., from some hypothetical damage zone of many more floors (especially if that damage zone begins to be larger than C itself, in which case we would more likely see a toppling).

This would be true whether there is a rubble layer or not, and probably more so if there was, as any further force from gravity or impact would be mitigated and deflected through the rubble. When you're crushing peppercorns, you don't do it through a layer of already crushed pepper. Why? Well, let's let our bee dunkers answer that question.

 

[Newtons Bit]

Perhaps because what you wrote is unintelligible. Eg: "...the downward force on Block C..." implies something pressing down from above. Block C is the upper block.

What is obvious to eight-year-olds and other people who understand everyday physics is that a small something cannot descend through a larger something of the same material composition via gravity alone. So the answer to whatever you may be asking above is: the lower intact building A is naturally going to impede the descent of upper portion C, no matter what possible height C could be "dropped" from "naturally", i.e., from some hypothetical damage zone of many more floors (especially if that damage zone begins to be larger than C itself, in which case we would more likely see a toppling).

This would be true whether there is a rubble layer or not, and probably more so if there was, as any further force from gravity or impact would be mitigated and deflected through the rubble. When you're crushing peppercorns, you don't do it through a layer of already crushed pepper. Why? Well, let's let our bee dunkers answer that question.

1) It's not a tree-trunk.
2) The level of forces involved are about 1000 times more than what you see in everyday physics. That's why you have to be licensed to do engineering.

 

[leftysergeant]

Perhaps because what you wrote is unintelligible. Eg: "...the downward force on Block C..." implies something pressing down from above. Block C is the upper block.

What is obvious to eight-year-olds and other people who understand everyday physics is that a small something cannot descend through a larger something of the same material composition via gravity alone.

Well DUH! A larger top block fell onto one floor. That broke, so even more of the top block plus the failed floor fell onto the next floor. The first collapse took apart the rest of the building the way you eat an elephant - one bite at a time.

This would be true whether there is a rubble layer or not, and probably more so if there was, as any further force from gravity or impact would be mitigated and deflected through the rubble. When you're crushing peppercorns, you don't do it through a layer of already crushed pepper. Why? Well, let's let our bee dunkers answer that question.

It's mopre like stomping grapes. The deeper they are piled, the less you have to stomp. Just the weight of the grapes on top pressing downward will crush the grapes at the bottom. (Try bringing home a five-gallon bucket of really ripe blackberries and see what happens at the bottom of your bucket.)The accumulating rubble just provided more PE which, when exceded the carrying capacity of the next floor, became KE.