OOS Collapse Propagation Model

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So what, in your own words, are the assumptions made about the time behavior of mass in the crush-up direction, vs. mass in the crush-down direction?


The time behavior of what Bazant calls zone A and C depend upon the connection strength between individual floors. He states his own assumption of the forces between individual floors in his third assumption listed in the very first paragraph of the BV section reproduced in my last post.




I wrote that I strongly recommend approaching analysis of the BV, BL, and BLGB papers through the following 7 perspectives:



1) Direct comparision between Bazant and Seffen methods and their key equations of motion (Seffen eq 12 compared to Bazant eqs 12 and 17).

2)) A basic study of 1-dimensional stacked system collision interactions with a variety of parameters altered linked here. This gives one a simple, practical sense of 1-dimensional multiple body interactions, like the type described in BV eqs 12 and 17, and the possible varieties of mechanical movements that can result from them.

3) Direct comparison of claims within BV to the actual collapse propagation rates which were recorded after the 2007-2008 Bazant papers were written.

4) Quotes by David Benson demonstrating how he understood the relationship between BV eqs 12, 17 and the actual collapses of WTC1, 2 linked here

5) Statements by Bazant in BL (the closure to BV) and BLGB demonstrating how he understood the relationship between BV eqs 12, 17 and the actual collapses of WTC1, 2.

6) Comparison of statements about WTC1 and 2 made within BV, BL, and BLGB directly with the visual record of events through the lens of the most accurate mappings of the WTC1, 2 collapse behavior (available in parts 2.1, 2.2, 2.3, and 2.4 of my book).

7) Practical comparison of BV eqs 12 and 17 and Seffen eq 12 to video records of Verinage demolitions.


My own suggested approach to the study of crush up, crush down mechanics of stacked systems of masses in 1 dimension is given in the second perspective offered above.




Coversely, what are the assumptions about mass in ROOSD, in both directions?



The mathematical approach to the study of ROOSD propagation is given below as 5 clearly marked steps to be taken in order:


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.


Step 1 is incredibly important. I approach step 1 by using a descriptive model which some of us have called ROOSD or 'OOS propagation model.'

The OOS model is based on 6 observable physical features of the WTC1, 2 collapses:


1) Observed Behavior of WTC1 Core

2) Observed Motion of WTC1, 2 Perimeter Walls

3) Observed Behavior of the Crush Fronts

4) Observation of core and perimeter columns within the rubble

5) Pieces of flooring remain intact and people survive at the base of WTC 1

6) Appearance at the base of each tower after collapse






Note that in following the simple 5 step process, mappings of the most global features of the collapses are created in step 1. These mappings involve no assumptions of any kind.




Your question: Coversely, what are the assumptions about mass in ROOSD, in both directions?

Unlike both Bazant and Seffen, I do not speculate about collapse front behavior either upward or downward at all. I map it instead.
 
The first of 7 perspectives to help understand BV more clearly:

1) Direct comparision between Bazant and Seffen methods and their key equations of motion (Seffen eq 12 compared to Bazant eqs 12 and 17).

.



From the information given so far in this thread it is possible to directly compare BV and the Seffen paper in a variety of ways:

  • Purpose of paper
  • Name of model
  • Key equations, choice of variable and parameters
  • Representation of key equations
  • Derivation of key equations
  • Application of key equations to predict collapse features



It is also possible to spot and compare the limitations each author was working within:


  • Inability to verify predictions
  • Limited understanding of WTC collapse features
  • Inability to identify a specific WTC collapse mode
  • Misrepresentation of the actual crushing process along the collapse front contact interface


These point by point items allow for a very broad and comprehensive comparison between Seffen's and Bazant's 1 dimension propagation equations of motion and their understanding of the actual WTC1 and 2 collapse progression crush fronts at the time they published their papers.
 
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From the information given so far in this thread it is possible to directly compare BV and the Seffen paper in a variety of ways:

  • Purpose of paper
  • Name of model
  • Key equations, choice of variable and parameters
  • Representation of key equations
  • Derivation of key equations
  • Application of key equations to predict collapse features

Wow, Major_Tom. You're so gifted. If it wasn't for your information in this thread, I'd never have been able to figure out the "purpose of paper" or "name of model" in the B&V or Seffen paper. :rolleyes:
 
Your question: Coversely, what are the assumptions about mass in ROOSD, in both directions?

Unlike both Bazant and Seffen, I do not speculate about collapse front behavior either upward or downward at all. I map it instead.

The crush-up and crush-down equations are working on a simplified set of assumptions with regards to mass distriubtion. Your model is not working from any assumptions, you say. What is your resulting mathematical model of the forces, then?
 
The crush-up and crush-down equations are working on a simplified set of assumptions with regards to mass distriubtion. Your model is not working from any assumptions, you say. What is your resulting mathematical model of the forces, then?
There. Can. Be. No. Mathematics.
Without assumptions, there is no model.
Just hand-waving.
(Hint, for the non technically inclined--The Mathematics IS the Model. Of any sort.)
 
(Hint, for the non technically inclined--The Mathematics IS the Model. Of any sort.)

His "model" is observations (and opinions based on such). Not useless but, without a direction it's only observational data. Could be useful for someone looking to construct a model. Maybe he's just mad Bazant and Co didn't consult him first. :D
 
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I am still stuck at the part where structural steel got red hot and too soft to hold up the building. With all the load paths gone I do not wonder why the collapse continued to the ground.

The details are academical, as in of great concern to people revising building codes.
The kind of people who are familiar with the relevant math.
 
1) Direct comparison between Bazant and Seffen methods and their key equations of motion (Seffen eq 12 compared to Bazant eqs 12 and 17).

2) A basic study of 1-dimensional stacked system collision interactions with a variety of parameters altered linked here. This gives one a simple, practical sense of 1-dimensional multiple body interactions, like the type described in BV eqs 12 and 17, and the possible varieties of mechanical movements that can result from them.

...



Please consider the second viewpoint through which one can examine BV clearer and in more detail. The linked study explores the variety of interactions possible behind the type of 1 dimensional mechanics used by Bazant in BV by running simulations of this type of interaction using a slab and spring model in a physics game engine.




It studies the effects of varying mass along the 1-dimensional structure. or varying connection strength between adjacent masses up the structure, varying stretch, or varying cap mass.

The study also examines the ability or inability to measure along the roofline and the concept of terminal or steady state acceleration.

Simulations involving high velocity initial impact of the 1-dimensional structure are also studied.




The simulations were found to produce a range of results, including:

  • mixed crush up and down
  • mostly crush down
  • exclusive crush down using only topmost floors
  • delayed crush down





Among the conclusions drawn from the results are:

- A discrete model, even highly idealized, is a dynamic problem with more than one degree of freedom if upper is not rigid.
- The simplest representation, which conforms to typical discrete inelastic models, has TWO aggregate, generalized coordinates
- A 1D solid slab and spring model with many members, and which fails, has a propensity for crush-up whether or not crush down occurs.

Even in the highly idealized 1 dimensional mass interactions behind the derivation of BV eqs 12 and 17, a variety of solutions for crush front motion other than 'crush down, then crush up' are possible.
 
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Please consider the second viewpoint through which one can examine BV clearer and in more detail. The linked study explores the variety of interactions possible behind the type of 1 dimensional mechanics used by Bazant in BV by running simulations of this type of interaction using a slab and spring model in a physics game engine.




It studies the effects of varying mass along the 1-dimensional structure. or varying connection strength between adjacent masses up the structure, varying stretch, or varying cap mass.

The study also examines the ability or inability to measure along the roofline and the concept of terminal or steady state acceleration.

Simulations involving high velocity initial impact of the 1-dimensional structure are also studied.




The simulations were found to produce a range of results, including:

  • mixed crush up and down
  • mostly crush down
  • exclusive crush down using only topmost floors
  • delayed crush down





Among the conclusions drawn from the results are:

- A discrete model, even highly idealized, is a dynamic problem with more than one degree of freedom if upper is not rigid.
- The simplest representation, which conforms to typical discrete inelastic models, has TWO aggregate, generalized coordinates
- A 1D solid slab and spring model with many members, and which fails, has a propensity for crush-up whether or not crush down occurs.

Even in the highly idealized 1 dimensional mass interactions behind the derivation of BV eqs 12 and 17, a variety of solutions for crush front motion other than 'crush down, then crush up' are possible.
Equations, please. Show your model in equations. I see a lot of words, and I find it hard to compare models, if it is not written in the right language of the models (math).

If you are using a specific coordinate frame also, you need to define that, and define your terms in relation to it. You also need to show your assumptions for how unobservable portions of the building are accommodated within the mathematical language of the engineering models. Otherwise, how can they be compared?
 
Equations, please. Show your model in equations. I see a lot of words, and I find it hard to compare models, if it is not written in the right language of the models (math).


You are suggesting the author of the study should convert the simulation results of 110 interacting masses into a series of equations. You suggest this because a series of equations are the 'right' way to describe the impulse reactions between 110 interacting masses, an inherently unsmooth process. Simulation results aren't the 'right' language.


Would these equations require more than 1 generalized coordinate to represent the interactions, or would you stick to one generalized coordinate like Bazant does in BV eq 12?

The study clearly points out the need for at least 2 generalized coordinates to represent the type of 1-d physical system Bazant represents in BV eq 12. Bazant uses only 1.
 
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I am by no means a mathematician, physicist nor structural engineer... just a dumb architect. However, when one sees the process which destroyed the 400,000 ton structure consisting of hundreds of thousands of discreet elements which were part of the complex organized stable system and became chaotic in a period of less than 20 seconds of hundreds of thousands if not millions of physical interactions and seeks a series of equations to *model* or describe the destruction... they are chasing an unattainable goal with the data and technology to model we have today.

We know that industry uses finite element analysis to simplify complex systems going from stable to unstable. And these models are useful to understand how nodes perform. But it is a fool's errand to attempt an FEA type model for a WTC (or any building for that matter of similar size) collapse.

The basic materials science is there to know how the mechanics and the chemistry of the elements / nodes. It's settled knowledge what sort of impact would destroy a slab or sever a column. But we don't have the inputs for all the interactions. The magnitude is beyond the reach of our model *systems*.

What we can see is macro processes in play such as the facade peel or the movement of a mass downward destroyed everything in its path or the toppling of the unbraced columns. The ROOSD model is more than accurate enough as a depiction as to what was happening. Math and formulas add nothing to understand this.

And there is no point to it either. Are there lessons to be learned from ROOSD? Is any tall building subject to a ROOSD? If not which ones aren't and why aren't they? THAT is the interesting discussion. That is... was there something about the design of the twin towers that made them a good candidate for a ROOSD. Sure they stood for decades... what's up?

Enough with the demand for a series of equations....
 
Is any tall building subject to a ROOSD? If not which ones aren't and why aren't they? THAT is the interesting discussion.


If you know of a way to address such questions and yield reliable answers without mathematical models and equations, please enlighten the world. Interpretive dance, maybe?
 
I am by no means a mathematician, physicist nor structural engineer... just a dumb architect. However, when one sees the process which destroyed the 400,000 ton structure consisting of hundreds of thousands of discreet elements which were part of the complex organized stable system and became chaotic in a period of less than 20 seconds of hundreds of thousands if not millions of physical interactions and seeks a series of equations to *model* or describe the destruction... they are chasing an unattainable goal with the data and technology to model we have today.

We know that industry uses finite element analysis to simplify complex systems going from stable to unstable. And these models are useful to understand how nodes perform. But it is a fool's errand to attempt an FEA type model for a WTC (or any building for that matter of similar size) collapse.

The basic materials science is there to know how the mechanics and the chemistry of the elements / nodes. It's settled knowledge what sort of impact would destroy a slab or sever a column. But we don't have the inputs for all the interactions. The magnitude is beyond the reach of our model *systems*.

What we can see is macro processes in play such as the facade peel or the movement of a mass downward destroyed everything in its path or the toppling of the unbraced columns. The ROOSD model is more than accurate enough as a depiction as to what was happening. Math and formulas add nothing to understand this.

And there is no point to it either. Are there lessons to be learned from ROOSD? Is any tall building subject to a ROOSD? If not which ones aren't and why aren't they? THAT is the interesting discussion. That is... was there something about the design of the twin towers that made them a good candidate for a ROOSD. Sure they stood for decades... what's up?

Enough with the demand for a series of equations....
JSO, he's using the wrong language to compare his theory to the models, so they cannot be directly compared. You should be asking him to put the Bazant et al. equations into English if you want the layman's view.
 
If you know of a way to address such questions and yield reliable answers without mathematical models and equations, please enlighten the world. Interpretive dance, maybe?

Your sarcasm aside... it is my hunch that ROOSD vulnerable designs share a number of structural design features/attributes. Among them are:

1. Hull and core designs which means open long span floor systems
2. wind shear designs which do not include some manner of multi floor bracing which extends from the exterior to and into the core.
3. designs which use the floor plates to transmit wind shear loads to the core
4. cores which are not diagonally braced
5. very light weight floor systems

etc. etc. and so forth
 
Your sarcasm aside... it is my hunch that ROOSD vulnerable designs share a number of structural design features/attributes. Among them are:

1. Hull and core designs which means open long span floor systems
2. wind shear designs which do not include some manner of multi floor bracing which extends from the exterior to and into the core.
3. designs which use the floor plates to transmit wind shear loads to the core
4. cores which are not diagonally braced
5. very light weight floor systems

etc. etc. and so forth


Okay. And how should one go about determining whether or not your hunch with regard to each point is correct, not just in specific examples (as one might confirm by full-scale testing, at great cost) but systematically?

Lots of people had hunches that the Brooklyn Bridge would quickly collapse -- or that the Tacoma Narrows Bridge wouldn't. Whose hunches should we legislate into the building codes?
 
Your sarcasm aside... it is my hunch that ROOSD vulnerable designs share a number of structural design features/attributes. Among them are:

I can't wait to see what genius ideas you've come up.

1. Hull and core designs which means open long span floor systems

Please provide evidence that shorter span trusses would have more collapse resistance.

2. wind shear designs which do not include some manner of multi floor bracing which extends from the exterior to and into the core.

What? I don't even know what this means. Are you asking for outrigger trusses?

3. designs which use the floor plates to transmit wind shear loads to the core

The core was part of the lateral system at the roof, where the hat truss transferred vertical overturning forces into it. These forces were transferred by structural members.

At typical floors below the hat truss, the core lacks lateral stiffness, which means that the wind shear forces weren't transmitted to the core.

4. cores which are not diagonally braced

Why would placing a lateral system in the core help prevent progressive collapse due to a complete vertical element failure?

5. very light weight floor systems

Why would light weight concrete systems be more susceptible than normal weight concrete with the same compressive strength?
 
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