About 5 pages ago I posted two fundamental problems concerning BV. Hate to repeat but it seems to me nobody addressed them.
DBB claims to so I'll repost my complaints followed by what seems to be his replies.
Formal complaint #1:
It is impossible to describe motion of both upper block and lower block using only one generalized coordinate.
The illustration below shows how BV attempts to explain the system motion using only one generalized coordinate.
How do they describe a system with 2 inherent degrees of freedom with only one coordinate?
They fix the distance Zo and do not allow it to vary during what they call "crush down phase".
The authors do this by claiming that crush-up of upper block C begins to occur only after the lower block A is completely crushed.
This claim is provably invalid for the following reasons:
a) WTC1 upper block was toast early on
b) The outside walls of the upper block actually fell out and over the lower walls on the E, N and W sides (probably on the S side too, but that is top secret). This means the upper block was milktoast (there was very little structure left early on).
c) Demos we have observed that use an upper and lower block see both their upper and lower blocks consumed in the collapse.
These observations invalidate the claim and means eq 12 in the paper cannot be used to describe crush-down.
There is in fact no single differential equation which can describe crush-down.
Even using only 1 physical dimension there must be at least 2 differential equations used with 2 variables to describe crush-up, crush-down motion.
Note: If I were to give this problem of crush-up crush-down to an undergraduate class of pretty advanced mechanics students and even give them the form that building resistance F(z) takes, very few of them would try to solve it using only one generalized coordinate (and the ones that do would be wrong). If I gave this problem for homework to a decent graduate class of physics students, I'd bet that nobody in the class would even attempt to solve it using only one degree of freedom.
To which DDB seemed to answer:
First of all, this crush-down equation is simply the continuous analogue of Frank Greening's floor-by-floor model; simply continue to refine that into millifloors, microfloors and so to the continuos limit. As a matter of practice, using Runge-Kutta to solve the ODE means passing back into the discrete domain once again.
B&V make four simplifying assumptions:
(1) one dimensional;
(2) energy dissipated only at the crushing front;
(3) known resisting force;
Major_Tom objects to (2), implying, I think, two crushing fronts. Obviously Frank Greening does not think so and indeed Bazant & Le thoroughly remove that possiblity in the idealized, analytic case being considered just now.
OneWhiteEye --- I've been thorugh all this before. Homogenization is fine when the tilt is taken into account; crushing proceeded on 3+ floors simultaneaously which is surely better represented by homogenization that by stepwise floor-by-floor model. However, both give essentially ythe same results; shagster actually went to the effort of running his own version of Greening's ideas using minifloors to demonstrate this; although, after some study, this is analytically obvious.
The issue of early crush-up never seems to die, does it? The problem is that it would have to proceed against the force of gravity, not with it. Instead what you seem to have noticed in frame 1007 is a lack of one dimensionality, with zone C west perimeter wall going outside the lower portion, yes? That actually does not trouble me, yet.
Major_Tom --- Kieth Seffen also uses one coordinate; his paper is also in ASCE J. Engg. Mechanics. I opine you need to rethink your position. The question is simply the extent to which the four simplifying assumptions are adequate to describe the evolution of position of the uppermost parts. Works d**n well for WTC 1 all the way to the bottom; not so for WTC 2 where it seems zone C fell off.
Assuming homogeneity, Bazaant & Le show thaqt zone C is almost industrucible. That's mechincs for you. The sturcture obviiously was not homogeneous and you have, in other threads, shown some distruction along the west and north walls. In of itself that mass loss is not important, but it does mean the floor trusses in those areas have been weakened. So an average of about 4--6 stories above floor 98 do not come close to satisfying the homogeneity condition. Fine. consider then that zone C is from floor, say, 102 up. To keep the equation simple, assume crush-down begins from there. As I mentiioned in this thread yesterday, this works well enough to match the additional observations by OneWhiteEye.
That is his answer. Sorry for posting it in a scattered way, but that is just how he presented it to us over the last few pages.
Dearest impartial reader, did DBB actually answer the complaint or did he avoid doing so? Does his answer satisfy you? Please remember:
DBB believes in the indestructible upper block based on a theory even though demolition planners have been smashing upper blocks against lower blocks for a few years now and even have a special name for this style of demolition.
We can see the upper block take quite a beating in every one of these cases http://www.youtube.com/watch?v=NwFHEoiUZ7o&NR=1
and crush itself with the lower block in what appears to be a 1:1 ratio. Every case.
Reader, you can see that upper blocks are far from indestructible yet DBB cannot because he "doesn't watch videos".
So do you think he refuted this first complaint?
(I think he just bullsh*tted past answering it). Watch carefully to see how artistically he avoids addressing the issue again....