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OOS Collapse Propagation Model

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rwguinn said:
What the hells?

That makes even less sense to me the more I read it.
Manager-speak?

If you can't describe a mechanism mathematically, then it is not engineering-or science.
Click to expand...

The "ROOSD" folks have trouble using the correct terms for the things they're trying to describe...
 
Newtons Bit said:
The "ROOSD" folks have trouble using the correct terms for the things they're trying to describe...
Click to expand...

RE: doing the math for a progression (implying a temporal sequence) of collapse due to a vertical, assymettric, avalanche of open office space debris destroying subsequent core to perimeter, and inter-core column, horizontal bracing and connections in a 3 dimensional structure is even possible?

I'm not an engineer so I really don't know if it is or if it is, how long a modern supercomputer would take to ca-chunk through the numbers for 100 stories.

However, the described mechanism makes sense to me. All that need be shown is that not enough mass was expelled between initail failure and peak acelleration of internal collapse front (implied by watching the level at which expulsions are beginning), to reduce the dynamic forces to the point that they will not fail a floor pan.

Bazant right or wrong put the initial max impulse on the first impacted floor at 30+ times greater than it could withstand.

Starting point then would be to put a finer edge on that number.

Like I said though, I'm not an engineer, so I have to leave it to you guys.
 
JSanderO said:
Have you seen the math for an avalanche or a rock slide? Link please.
Click to expand...
I have, you will not like it. You might call me a math-bot, a physics-bot, ... worse an engineering-bot. For now, I am a copy-old-slides-with-DSLR-bot right now, or a yelling-grandsons-baby-sitter-bot.
Yes, I have seen the math, why can't you find it? Don't join the avalanche truth, or rock slide truth movement yet, do some study first.
 
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JSanderO said:
Have you seen the math for an avalanche or a rock slide? Link please.
Click to expand...
You and MT are going to go model crazy on this one, and wait, there are differential equations. Math, I wonder if MT will say in Indian Jones style, "math... I hate math". Who loves math, engineering models.
http://angel.elte.hu/~tegzes/www/tp_phd.pdf not sure what the math is here, did not have time to go though all the equations, but here is your... link please - you should have read all the papers on 911 before joining Gage.

...

ROFL - where's the math
 
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Major_Tom said:
Step 4: EXAMINE A VARIETY OF PHYSICS-BASED MATHEMATICAL APPROACHES TO THE COLLAPSE OF STACKED SYSTEMS



Here are a few different ways to set up the basic physics to the collapse propagation of a stacked system of masses in 1 dimension:

Study of a Simple 1 Dimensional Stacked System

Models of Inelastic Accretion


WTC Asynchronous Impact Crush-Down Model




It is also important to be aware of and review the approaches taken to collapse progression in the following papers in light of the new information gathered in steps 1 - 3 and compare them to the models linked above:

All 4 Bazant papers BZ, BV, BL and BLGB, linked and reviewed here
Frank Greening, Energy Transfer in the WTC Collapse, linked and reviewed here
Keith Seffen, Progressive Collapse of the World Trade Centre: a Simple Analysis, linked and reviewed here
Gordon Ross: Momentum Transfer Analysis of the Collapse of the Upper Storeys of WTC 1 linked here
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I haven't noticed anyone form a fatherly relationship toward Seffen, so maybe some of you will be able to spot the mistakes in the Seffen paper.

Let's check.


Progressive collapse of the World Trade Centre: a Simple Analysis

K. A. Seffen

Abstract:

The collapse behavior of the World Trade Centre (WTC) towers is considered formally as a propagating instability phenomenon. The application of associated concepts enables the residual capacities of both towers after collapse to be formally estimated. This information is combined into a simplified variable-mass collapse model of the overall dynamic behavior. The resulting, non-linear governing equation of motion can be solved in closed form, to yield compact information about the overall collapse conditions.
Click to expand...




Page 1 to 15

Key derivations within the paper:


equation 12 - Equation of motion for the collapse front

equation 16 - speed of the crush front

equation 17 - collapse time





Page 16 to 19: Dynamical predictions


Key dynamical predictions made by Seffen:



A steady state acceleration of g/2.

This is true of the WTC 1 and 2 buildings according to Seffen, but it is also true of many other systems. According to Seffen (p 17-18),

This particular steady value of g/2 is a consistent property of any variable-mass system where the mass, initially at rest, is entrained by a non-impulsive action.
Click to expand...


>>>>>>>>>>>>>>>>>>>>>>>


Some advice on how to read a technical paper like this. First, locate what the author is doing in the paper and locate the key equations in the paper. I have already quoted Seffen in the abstract concerning what he is trying to do in the paper, and I have already located the key equations for you.




Can anyone tell me what Seffen is doing in the paper? Can anyone spot the mistakes he made?
 
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MileHighMadness said:
So...M_T, now that your Book is done...what are you going to do with it?
Click to expand...

Test some of the ideas, in this thread, for example.

.............................
.............................






Some advice on how to read a technical paper like this. First, locate what the author is doing in the paper and locate the key equations in the paper.




Can anyone tell me what Seffen is doing in the paper?

Abstract:

The collapse behavior of the World Trade Centre (WTC) towers is considered formally as a propagating instability phenomenon. The application of associated concepts enables the residual capacities of both towers after collapse to be formally estimated. This information is combined into a simplified variable-mass collapse model of the overall dynamic behavior. The resulting, non-linear governing equation of motion can be solved in closed form, to yield compact information about the overall collapse conditions.
Click to expand...

He is deriving equations of motion of the crush front of the WTC towers.


What is the key equation in the paper?

Equation 12, which is the equation of motion of the crush front.



How did he model the WTC collapse in order to derive equation 12?

He modelled the WTC collapse as "a variable-mass system where the mass, initially at rest, is entrained by a non-impulsive action." He models it as a specific class of problems, all of which have steady-state accelerations that converge on g/2.




What does his equation of motion predict about the acceleration of the crush front?

A steady state acceleration of g/2.




Can that prediction be tested?

Yes. Follow the 5 steps:

Major_Tom said:
Mathematical approach to the study of ROOSD propagation:


Step 1: GAIN AN OVERALL CONCEPTUAL AND VISUAL UNDERSTANDING OF WHAT ONE IS LOOKING AT

Step 2: RESEARCH AVAILABLE LITERATURE ON THE SUBJECT OF FLOORS IMPACTING FLOORS

Step 3: MEASURE THE COLLAPSE PROPAGATION RATE AS ACCURATELY AND COMPLETELY AS POSSIBLE

Step 4: EXAMINE A VARIETY OF PHYSICS-BASED MATHEMATICAL APPROACHES TO THE COLLAPSE OF STACKED SYSTEMS

Step 5: COMPARE MODELS IN STEP 4 TO INFORMATION IN STEPS 1 - 3 to see which models could match propagation behavior or teach something about it.
Click to expand...


The actual collapse front propagation rate is measured in step 3. Simply compare it to the Seffen prediction.



Why didn't Seffen compare his prediction to actual measurements of the collapse front speed?

Because this information was not available when he wrote the paper. Researchers at that time including Bazant only had access to the first few seconds of WTC1 roofline or antenna drop measurement and the seismic records. Bazant states this clearly in BV.
 
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Can anyone spot the mistakes Seffen made?


1) He modelled the WTC collapses as a particular class of physics problems, as "a variable-mass system where the mass, initially at rest, is entrained by a non-impulsive action."

It appears that "entrained by impulsive action" would have been a better class of problems to work within. This becomes more clear when his model is compared to the BV model, the Greening model, and the stacked system mechanics of OneWhiteEye linked earlier.

2) He claimed a steady-state acceleration of the crush front of g/2.




Does anyone disagree with these comments on the Seffen paper?
 
In 1910, Albert Einstein published three ground breaking papers on physics. Those three papers were so far advanced, at that time; nobody else could truly understand them. It would take over a decade before the rest of the scientific world caught up with Einstein, and he would be recognized for the genius he was.

Major_Tom, if you are expecting that to happen with you and your Book…it is not going to happen. A hundred years from now, no one will even know you or your Book ever existed. Unfortunately, you and your massive ego will never allow you to fully understand that.

I’m not trying to be cruel, but just stating the cold hard truth.
 
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The Seffen paper is very useful to study in parallel with BV (2007) both the stated purpose and the key equations are strikingly similar. Remember, first locate the stated purpose of the paper and the key equations derived.


Mechanics of Progressive Collapse: Learning from World Trade Center and Building Demolitions
Zdenek P. Bažant, F.ASCE
1
; and Mathieu Verdure
2



Abstract:
Progressive collapse is a failure mode of great concern for tall buildings, and is also typical of building demolitions. The most
infamous paradigm is the collapse of the World Trade Center towers. After reviewing the mechanics of their collapse, the motion during
the crushing of one floor or group of floors and its energetics are analyzed, and a dynamic one-dimensional continuum model of
progressive collapse is developed. Rather than using classical homogenization, it is found more effective to characterize the continuum by
an energetically equivalent snap-through. The collapse, in which two phases—crush-down followed by crush-up—must be distinguished,
is described in each phase by a nonlinear second-order differential equation for the propagation of the crushing front of a compacted block
of accreting mass. Expressions for consistent energy potentials are formulated and an exact analytical solution of a special case is given.
It is shown that progressive collapse will be triggered if the total internal energy loss during the crushing of one story
equal to the energy dissipated by the complete crushing and compaction of one story, minus the loss of gravity potential during the crushing of that
story exceeds the kinetic energy impacted to that story. Regardless of the load capacity of the columns, there is no way to deny the
inevitability of progressive collapse driven by gravity alone if this criterion is satisfied for the World Trade Center it is satisfied with an
order-of-magnitude margin. The parameters are the compaction ratio of a crushed story, the fracture of mass ejected outside the tower
perimeter, and the energy dissipation per unit height. The last is the most important, yet the hardest to predict theoretically. It is argued
that, using inverse analysis, one could identify these parameters from a precise record of the motion of floors of a collapsing building. Due
to a shroud of dust and smoke, the videos of the World Trade Center are only of limited use. It is proposed to obtain such records by
monitoring with millisecond accuracy the precise time history of displacements in different modes of building demolitions. The
monitoring could be accomplished by real-time telemetry from sacrificial accelerometers, or by high-speed optical camera. The resulting
information on energy absorption capability would be valuable for the rating of various structural systems and for inferring their collapse
mode under extreme fire, internal explosion, external blast, impact or other kinds of terrorist attack, as well as earthquake and foundation
movements.
Click to expand...


Just like Seffen, Bazant is deriving a one-dimensional continuum model for crushing front propagation.



Key equations:

Equation 12, Equation 17, which are his differential equations of progressive collapse or demolition


Equivalent versions of equations 12 and 17 are equations 20 and 21



His implications and conclusions for these equations are clearly listed on page 318:

Implications and Conclusions

1. If the total internal energy loss during the crushing of one
story representing the energy dissipated by the complete
crushing and compaction of one story, minus the loss of
gravity potential during the crushing of that story
exceeds the kinetic energy impacted to that story, collapse will con-
tinue to the next story. This is the criterion of progressive
collapse trigger Eq. 5. If it is satisfied, there is no way to
deny the inevitability of progressive collapse driven by gravity
alone regardless of by how much the combined strength
of columns of one floor may exceed the weight of the part of
the tower above that floor . What matters is energy, not the
strength, nor stiffness.

2. One-dimensional continuum idealization of progressive col-
lapse is amenable to a simple analytical solution which
brings to light the salient properties of the collapse process.
The key idea is not to use classical homogenization, leading
to a softening stress-strain relation necessitating nonlocal fi-
nite element analysis, but to formulate a continuum energeti-
cally equivalent to the snapthrough of columns.

3. Distinction must be made between crush-down and crush-up
phases, for which the crushing front of a moving block with
accreting mass propagates into the stationary stories below,
or into the moving stories above, respectively. This leads to a
second-order nonlinear differential equation for propagation
of the crushing front, which is different for the crush-down
phase and the subsequent crush-up phase.

4. The mode and duration of collapse of WTC towers are con-
sistent with the present model, but not much could be learned
because, after the first few seconds, the motion became ob-
structed from view by a shroud of dust and smoke.

5. The present idealized model allows simple inverse analysis
which can yield the crushing energy per story and other
properties of the structure from a precisely recorded history
of motion during collapse. From the crushing energy, one can
infer the collapse mode, e.g., single-story or multistory buck
ling of columns.

6. It is proposed to monitor the precise time history of displace-
ments in building demolitions—for example, by radio telem-
etry from sacrificial accelerometers, or high-speed optical
camera—and to engineer different modes of collapse to be
monitored. This should provide invaluable information on
the energy absorption capability of various structural sys-
tems, needed for assessing the effects of explosions, impacts,
earthquake, and terrorist acts.
Click to expand...











The BV paper is re-examined in discussions by Gourley and Szuladzinski and a closure by Bazant and Le, which is clearly an intended point-by-point rebuttal of the Gourley and Szuladzinski discussions.






DISCUSSIONS AND CLOSURES

Discussion of “Mechanics of Progressive
Collapse: Learning from World Trade
Center and Building Demolitions” by
Zdenĕk P. Bažant and Mathieu Verdure
March 2007, Vol. 133, No. 3, pp. 308–319.
DOI: 10.1061/
ASCE
0733-9399
2007
133:3
308

Gregory Szuladzinski

Analytical Service Pty Ltd., Killara/Sydney, Australia 2071. E-mail:
ggg@bigpond.net.au

Szuladzinski's opening comments on BV:

The paper presents a very interesting concept of an accidental
demolition, whereby heavy damage sustained by an intermediate
story of a building leads to the upper part of the structure crushing
the lower one in a sequence of story collapse steps. The focus of
the paper is on the treatment of equations of motion and very few
numbers are quoted; that is, numbers that relate to the physical
properties of the structure discussed, namely the World Trade
Center (WTC) towers. The following comments are intended to
fill that gap as well as to ascertain the likelihood of the applica-
bility of this concept.
Click to expand...




Gregory is clearly referring to application of BV equations 12 and 17 to the specific case of the WTC towers. There can be no mistake that he is discussing the specific cases of WTC1 and 2 throughout the discussion.








Discussion of “Mechanics of Progressive
Collapse: Learning from World Trade
Center and Building Demolitions” by
Zdene
̆k P. Bažant and Mathieu Verdure
March 2007, Vol. 133, No. 3, pp. 308–319.
DOI: 10.1061/
ASCE
0733-9399
2007
133:3
308
James R. Gourley
1
1
B.S. Chemical Engineering; Attorney, Carstens & Cahoon, LLP, Dallas,
TX 75240. E-mail: jrpatent@gmail.com

Gourley's opening comments on BV:

This discussion describes flaws in the modeling and analysis of
the World Trade Center collapses by Bažant and Verdure in their
paper entitled “Mechanics of Progressive Collapse: Learning
from World Trade Center and Building Demolitions.” First, the
paper’s two-phased approach to the collapse analysis will be con-
sidered. The writers will demonstrate that a two-phase collapse
analysis is not representative of reality, because it disregards well-
accepted laws of physics and therefore is not instructive. Second,
the original paper’s summary of the findings of the NIST report
will be analyzed.
Click to expand...



James is also clearly addressing the application of equations 12 and 17 in BV to the specific cases of WTC1 and 2. He explicitly identifies BV as a modelling and analysis of the World Trade Center collapses when he states:

This discussion describes flaws in the modeling and analysis of
the World Trade Center collapses by Bažant and Verdure in their
paper entitled “Mechanics of Progressive Collapse: Learning
from World Trade Center and Building Demolitions.”
Click to expand...









Bazant replies to these discussions in his closure on BV:

Closure to “Mechanics of Progressive Collapse: Learning from World Trade Center and Building Demolitions”
by Zdenĕk P. Bažant and Mathieu Verdure
March 2007, Vol. 133, No. 3, pp. 308–319.
DOI: 10.1061/
ASCE
0733-9399
2007
133:3
308
Zdeněk P. Bažant and Jia-Liang Le
1
McCormick Institute Professor and W. P. Murphy Professor of Civil
Engineering and Materials Science, Northwestern Univ., CEE,
2145 Sheridan Rd., Evanston, IL 60208. E-mail: z-bazant@
northwestern.edu
2
Graduate Research Assistant, Northwestern Univ.

Bazant begins with:

Discussion by James R. Gourley

The interdisciplinary interests of Gourley, a chemical engineer
with a doctorate in jurisprudence, are appreciated. Although none
of the discusser’s criticisms is scientifically correct, his discussion
provides a welcome opportunity to dispel doubts recently voiced
by some in the community outside structural mechanics and en-
gineering. It also provides an opportunity to rebut a previous
similar discussion widely circulated on the Internet, co-authored
by S. E. Jones, Associate Professor of Physics at Brigham Young
University and a cold fusion specialist. For the sake of clarity, this
closure is organized into the points listed subsequently and rebut-
ted one by one.
Click to expand...

He then argues the 8 points in order, each point being clearly labelled.


1. Newton’s Third Law

2. Are the Internal Forces in Upper and Lower Parts of
Tower Equal?

3. Localization of Energy Dissipation into Crushing Front

4. Can Crush-Up Proceed Simultaneously with Crush Down?

5. Why Can Crush-Up Not Begin Later?

6. Variation or Mass and Column Size along Tower Height

7. Were the Columns in the Stories above Aircraft Impact
Hot Enough to Fail?

8. Steel Temperature and NIST Report






Likewise he opens his replies to the G. Szuladzinski discussion:


Discussion by G. Szuladzinski

The interest of Szuladzinski, a specialist in homeland security, is
appreciated. After close scrutiny, however, his calculations are
found to be incorrect, for reasons explained in the following.
Click to expand...


and clearly lists each reply in order:



1. Load-Displacement Curve of Columns and Energy Ab-
sorption Capacity

2. Does Excess of over Gravity Load Imply Arrest of
Collapse?

3. Is the Equation of Motion for Calculating the Duration of
Fall Correct?

4. Could Stress Waves Ahead of Crushing Front Destroy
the Tower?




Each discussion by Gourley and Szuladzinski, and each rebuttal by Bazant, can be easily reviewed simply by going to clearly marked section. Each of the 12 clearly marked objections and rebuttals make specific reference to the case of the WTC towers.
 
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Can any regular JREF poster besides Ozeco see the direct parallel between the Seffen equation of motion of the collapse front and the BV equations of motion of the crush front.

How does the BV method differ from the Seffen method?
 
Major_Tom said:
Can any regular JREF poster besides Ozeco see the direct parallel between the Seffen equation of motion of the collapse front and the BV equations of motion of the crush front.

How does the BV method differ from the Seffen method?
Click to expand...

I think most of the class took the day off.


Is the quiz multiple choice?


Well, sorry, gotta go. I gotta go change my registration before they close. See ya around.
 
Major_Tom said:
Can any regular JREF poster besides Ozeco see the direct parallel between the Seffen equation of motion of the collapse front and the BV equations of motion of the crush front.

How does the BV method differ from the Seffen method?
Click to expand...

Look, I was told there would be no math on the test.
 
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