Moderated Continuation - Why a one-way Crush down is not possible
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aggle-rithm
Ardent Formulist
You're the one who thinks it's not possible, despite clear evidence to the contrary. YOU are the one who needs to figure it out. Especially since you claim to be an engineer who is working tirelessly for the cause of building safety.
bill smith
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Now that's a good question.
Dave Rogers
Bandaged ice that stampedes inexpensively through
It's defined in the quote you included. It means that Bazant is assuming that the energy absorbed by deformation of the structure anywhere other than at the crushing front is small enough that it won't make a significant difference to the results if it's assumed to be zero. This is equivalent to assuming that the structure doesn't actually deform significantly. It's not the same as assuming that it doesn't deform at all, just that any deformation doesn't affect the final outcome, so it doesn't need to be calculated.
Dave
Sure,
First, take a look at this stress - strain curve:
http://en.wikipedia.org/wiki/Stress%E2%80%93strain_curve
The second figure, marked "Fig 1" (for structural steel")
The elastic part of the curve is the straight line segment between origin (0 stress, 0 strain) up to point 2 the yield strength.
The plastic part of the curve is everything to the right of that point (i.e., higher strains).
The energy absorbed is the area under the curve.
You can see that the area under the elastic portion of the curve is much, much smaller than the area under the plastic part of the curve. This means that a piece of steel will absorb only a small (negligible) percent of energy in the elastic region, and LOTS more (perhaps 30x more) while undergoing plastic deformation.
Second effect: It is only plastic deformation that is "energy dispersive". When a material is undergoing eleastic deformation, it is acting like a spring. It'll absorb the energy in compression, and then turn around & give it right back to you by bouncing back. In plastic deformation, it absorbs the energy (as heat) and takes a permanent "set".
Now comes the second piece. Elastic waves get sent from a collision thru the metal. They will get transmitted all the way from the crush zone, down thru the columns to the ground. (They'll actually reflect from every interface, including the ground & bounce back upwards. But they are dissipating a bit at each interface, and as they travel. Exactly like sound. Because the are sound wavess.) So, non-energy dispersive elastic waves get sent throughout the towers. The whole thing would be ringing like a giant bell.
But here's the kickers: Plastic waves do NOT transmit thru the metal.
This is why, when your car get hit from the front, you'll crumple the front end of the car, but the damage will stop & not crumple the whole body.
So the plastic waves (the type of deformation that is responsible for absorbing the vast majority of the energy) does NOT transmit thru the entire structure. So the rest of the structure (away from the crush zone) is NOT dissipating any significant amount of energy.
This is just one of the reasons why Heiwa's "this part is bigger than that part, so it will absorb more energy & survive" is nonsense.
For all intents, the area of the crush is absorbing all the energy, and away from the crush zone, none.
Clear?
Tom
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You have to read a little more and get the context, e.g. some extracts from the BLGB paper:
Merely to get convinced of the inevitability of gravity driven progressive collapse, further analysis is, for a structural engineer, superfluous. Further analysis is nevertheless needed to dispel false myths, and also to acquire full understanding that would allow assessing the danger of progressive collapse in other situations.
The gravity-driven progressive collapse of a tower consists of two phases—the crush-down, followed by crush-up (Fig. 2 bottom), each of which is governed by a different differential equation (Bazant and Verdure 2007, pp. 312-313). During the crush-down, the falling upper part of tower (C in Fig. 2 bottom), having a compacted layer of debris at its bottom (zone B), is crushing the lower part (zone A) with negligible damage to itself. During the crush-up, the moving upper part C of tower is being crushed at bottom by the compacted debris B resting on the ground.
…
It is found that, immediately after the first critical story collapses, crush fronts will propagate both downwards and upwards. However, the crush-up front will advance into the overlying story only by about 1% of its original height h and then stop. Consequently, the effect of the initial two-way crush is imperceptible and the hypothesis that the crush-down and crush-up cannot occur simultaneously is almost exact.
---
Fig 2 is below:
So you see, gravity driven progressive collapse, where upper part C first one-way crushes down lower part A into rubble part B, and then gets crushed up by the rubble part B is a normal phenomenon and further analysis is really superfluous for structural engineers according expert Bazant & Co. Idiots, like you and me, are not supposed to ask any questions or do our own analysis.
That nobody has ever seen a real gravity driven progressive collapse, where upper part C of a structure first one-way crushes down lower part A of same structure into rubble part B, and then gets crushed up by the rubble part B is of little interest.
Anyway, Bazant describes what it is as outlined above.
Re 'crush fronts' there are two sorts according Bazant. One crush-up front stops after progressing 1% into part C! The other, the crush-down front progresses 100% through part A.
Reason, if any, seems to be that part C is rigid ... and stops the crush-up front or turns it into a crush-down front. Nobody knows! Anyway, when the crush-down front has finished off part A, it seems it turns and becomes a crush-up front and destroys rigid part C.
Anyway, further explanations are superfluous according Bazant. The only person to dispel false myhs is Bazant so there you are.
bill smith
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Bazant therefore reckons that any eventual deformation of part C away from the crush front will be so insignificant that it can be valued at zero. Therefore any eventual change to it's rigid status can be set at zero. Is it not so that Bazant is saying that Part C is ' rigid minus zero ' or to all intents and purposes 'Rigid' ?
Dave Rogers
Bandaged ice that stampedes inexpensively through
No. Since the crushing front is able to move through the building, the word "eventual" is completely unwarranted. Bazant is simply saying that the amount of energy absorbed anywhere other than the crushing front is not large enough to matter.
Dave
bill smith
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So he is not indicating that part C is to all intents and purposes 'rigid' ?
Gamolon
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Wait a minute. I thought you've been saying that a gravity driven collapse was NOT possible.
Are you saying that a gravity driven collapse may have been possible with the towers, just not the way Bazant describes it in his paper?
If I blew out all 47 core columns, all 240 perimeter columns between floors 93 through 98 and then let the upper section drop, How could floor 92 stop or arrest the fall of that upper part? You said yourself that there were local failures. That doesn't make sense. The supports for floor 92 are there to support floor 92 only, not the rest of the upper part of the building. At the moment of impact floor 92 ceases to be floor 92, but becomes floor 92 + 99 + 100 + 101 + 102 + 103 + 104 + 105 + 106 + 107 + 108 + 109 + 110 + antenna + elevator motors + control panels + furniture + roof structure + anything else I didn't mention. It is THAT mass that puts a strain onto the floor supports of floor 92.
How do you expect the 120 floor truss to hold that up? That upper mass would shear/bend and the floor truss supports AND decimate the concrete floor into pieces.
So when floor 92 is destroyed/unsupported, there is now nothing holding the perimeter columns to the core columns. Floor 92 then becomes part of the falling mass onto floor 91. So instead of the 12 floors + everything else, the upper mass becomes 13 floors plus everything else that fell on floor 92, we now have 13 floors + everything else falling on floor 91. You don't lose the mass as everything falls. The upper mass is still the same weight no matter if it was constructed in a way to be 95% air, 60% air, or 5% air.
I don't see how your explanation holds up Heiwa.
You have yet to explain to me how floor 92 and it's supports are supposed to arrest 99 + 100 + 101 + 102 + 103 + 104 + 105 + 106 + 107 + 108 + 109 + 110 + antenna + elevator motors + control panels + furniture + roof structure + anything else I didn't mention.
Gamolon
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This is immaterial to bill & Heiwa, to whom we have explained this about 200x. Another 200x won't matter.
But for anyone else who might be wondering...
Wrong. Away from the crush zone, Part A and Part C are both considered to be "rigid bodies".
"Rigid body" does NOT mean "indestructible".
Rigid body means that the component is considered by the analysis to move (or stand still) as a single unit. It means that the analysis does not worry about how one part of the "rigid part" flexes or deforms with respect to another part of the same rigid body.
But once the stresses on A PORTION of the rigid body exceed ultimate strength levels, or the energy imparted on A PORTION of the rigid body exceed the strain energy absorbing capacity of THAT PORTION of the rigid body, then THAT PORTION of the rigid body will fail. And the part that fails will no longer be part if its parent rigid body.
It is an approximation. It is a very good approximation that greatly simplifies the math, while having very, very little impact on the answer. It is not "a mistake" that invalidates the analysis.
It is exactly like the "perfect gas law" (PV=nRT). This "law" is an approximation that applies for a limited band of pressures, volumes & temperatures. It is fundamentally wrong. But it is a very, very good approximation that gives you very, very good answers for those who understand the limits of its applicability.
Heiwa's continuing harping that this assumption is a mistake that makes Bazant's analysis "wrong" is a joke.
Tom
But for anyone else who might be wondering...
Wrong. Away from the crush zone, Part A and Part C are both considered to be "rigid bodies".
"Rigid body" does NOT mean "indestructible".
Rigid body means that the component is considered by the analysis to move (or stand still) as a single unit. It means that the analysis does not worry about how one part of the "rigid part" flexes or deforms with respect to another part of the same rigid body.
But once the stresses on A PORTION of the rigid body exceed ultimate strength levels, or the energy imparted on A PORTION of the rigid body exceed the strain energy absorbing capacity of THAT PORTION of the rigid body, then THAT PORTION of the rigid body will fail. And the part that fails will no longer be part if its parent rigid body.
It is an approximation. It is a very good approximation that greatly simplifies the math, while having very, very little impact on the answer. It is not "a mistake" that invalidates the analysis.
It is exactly like the "perfect gas law" (PV=nRT). This "law" is an approximation that applies for a limited band of pressures, volumes & temperatures. It is fundamentally wrong. But it is a very, very good approximation that gives you very, very good answers for those who understand the limits of its applicability.
Heiwa's continuing harping that this assumption is a mistake that makes Bazant's analysis "wrong" is a joke.
Tom
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bill smith
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bill smith
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T.....you said this:-
''Rigid body means that the component is considered by the analysis to move (or stand still) as a single unit. It means that the analysis does not worry about how one part of the "rigid part" flexes or deforms with respect to another part of the same rigid body.''
Which of these dictionary definitions is the more applicable in this case ?
Rigid,adj.....def...[Incapable of or resistant to bending]
Complete,adj....def...[Having every necessary or normal part or component]
PS. the difference here might be seen as the difference between a box of nails and a bag of nails.
''Rigid body means that the component is considered by the analysis to move (or stand still) as a single unit. It means that the analysis does not worry about how one part of the "rigid part" flexes or deforms with respect to another part of the same rigid body.''
Which of these dictionary definitions is the more applicable in this case ?
Rigid,adj.....def...[Incapable of or resistant to bending]
Complete,adj....def...[Having every necessary or normal part or component]
PS. the difference here might be seen as the difference between a box of nails and a bag of nails.
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Please take some engineering courses or get some help from some professionals; reading your posts is painful due to your lack of knowledge in the subject area. This is not a personal attack; Please study the subject area and get help before making more moronic posts about modeling.
.
If you were not such a inveterate, shameless wanker, I might tell you that the definition of the word "rigid" is irrelevant. And that the definition of the word "body" is irrelevant.
If you weren't such a wanker, I might tell you that the term "rigid body" is an engineering & physics phrase. With its own specific definition that is unrelated to the English definitions of either word.
If you weren't such a wanker, I'd suggest that you look it up, and pay particular attention to the "kinematic" and / or "engineering dynamics" definition.
Unfortunately, you ARE such a wanker, so...
tk
You are right. Bazant suggests the opposite and that it is superfluous to argue against that. So I argue against that. Please, wrap a wet towel around your head, cool down, and start to ... think.
bill smith
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