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Why are you unable to quote your own paper correctly?
Your "WTC1 - the Case for Collapse/Crush down Arrest" says:
"It is suggested that the first crush down can be initiated by a 0.5 m drop of part C, thus the initial potential energy, PE
0, applied is 0.5 x 54.06x106 x 9.82 = 265.44x106 J." (PE = h m g)
This is, of course, some of your typical sloppiness.
The Kinetic Energy that the upper block gained in its fall is NOT determined by "what energy would crush an object below". Difficult to believe that you could write and then publish something this ill-considered.
As you know, the KE that it has gained is equal to the PE lost, which is determined by its mass & the height that it HAS fallen. Which in this case is about 3.6 meters. So the right answer (using your mass number) is PE is 3.6 m x 54x106 Kg x 9.81 m/sec2 = 1.9 GJ.
And yet you produce 1 GJ here. Sloppy.
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Bad assumption. But it is a starting point.
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Wrong. There are about 100 columns that can punch holes. 50 up & 50 down. If you'd paid attention in class, instead of daydreaming of your impending glory, you would have gotten this right.
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Baseless assertion. "Fail"
Tell me your assumptions. Which parts are undergoing deformation, what are their loads & deflections.
Show that you haven't blown some trivial number that would not make your elastic absorption be 0.001 GJ.
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Baseless assertion. "Fail"
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I would like to point out that your analysis makes zero sense.
IF, as you say, "the columns punch holes in the concrete floors" (as is certainly true), well then the concrete floors did NOT arrest the fall. Unless you contend that the 50,000 Metric ton upper block can stand on air.
If it did punch holes, then you must consider the NEXT group of parts that comes into contact. If that one is shown to fail, then you must consider the NEXT one after that. And so on.
And you must continue this process UNTIL you come to some parts that do NOT fail. Then, AND ONLY THEN, can you say that the collapse will be arrested.
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Thus far, your high-falutin' Structural Damage Assessment rates an "F".
I've been trying to help you raise your grade. You don't seem to want to do the work necessary.
But this is the part that really matters.
You must CORRECTLY calculate how much kinetic energy the upper block has acquired at each collision.
You must identify the parts that fracture, and calculate how much energy that they can absorb.
... [Big hint here: Do not consider the columns to be 1 story high. This will give you wrong answers.]
You must identify the parts that ultimately do NOT fracture. And show that their total energy absorption capacity is greater than the remaining kinetic energy in the upper block.
Then, and only then, can you say that the block will stop.
I am running out of patience with you, young man. Your constant antics in class are holding everyone back.
Tom
Thanks for reading my papers. Yes, if the free fall drop is 3.6 m and the associated mass is 54 000 000 kgs then the free energy is 1.9 GJ. I just use better figures. But there is no evidence that any mass free fell any distance!
You see, if a structure consists of two parts C and A and C and A are connected by 280+ element, upper part C can never free fall on lower part A.
Or, can you provide evidence to the contrary?
Anyway, if C impacts A, both parts C and A first deform elastically, while part C is decelerated (the jolt!). You agree?
This deformation, compression, transforms the energy into heat! Both parts C and A warm up a little. And that energy is then 'lost' and cannot produce any further damage.
If local elements in parts C and/or A fail, more energy is transformed into heat and is then 'lost'. Of course, local failures may cause parts to displace, so that more potential energy is released, but what happens then?
Yes, at new contacts the structure deforms again elastically, the moving element is decelerated and more energy is lost as heat.
And that's
Why a one-way Crush down is not possible! When any structural element fails and produces a displacement/new contact there is elastic compression, and this goes on and on and on and on ... and the destruction is very soon arrested.
Bazant completely ignores the multiple elastic compressions that are associated with a one-way crush down/multiple contacts and that always arrest the local destruction.
Do this test! Jump in your bed and measure the temperature of the springs in the mattress. The temperature will slowly increase! Every time you contact the mattress, potential energy is transformed into heat that warms up the mattress. It is quite fun to jump on a mattress. It started off my career to debunk the OCT of 911.