The 9/11 Forum

femr2 · by **femr2** on Tue Jun 23, 2009 12:29 am

As the inclusion of asynchronous and partially elastic collisions are beyond the scope of a spreadsheet contained model, I thought I'd start up a new thread to contain progress of this offshoot of the model.

I've had to go 'code' on it of course, but I'm planning on using the spreadsheet model as the basis for all source data, which I'm hoping will much reduce data skepticism, and allow fairly rapid progression of it's features.

Initial visualisation is in simple 'smearogram' form, but once I have fairly useful mechanisms in place, I'll bolt it into the existing 3D rendering process that I use for the spreadsheet model (And in the process add smearogram output to the latter also)

It's very early days (couple of hours coding), but just 'playing' with partially inelastic collisions has already highlighted quite an interesting factor I'd already considered/assumed, but 'seeing' it is always insightful...

This first image is for fully inelastic collisions, conservation of momentum only, no structural supports. Floors 93 upwards allowed to free-fall. Constant floor thickness, storey height and mass:

http://femr2.ucoz.com/photo/1-0-82

Bolting in partially inelastic collisions, accurate floor heights, per-floor masses and some very beta (read dodgy) energy expenditure mechanics results in this 'thing' :

http://femr2.ucoz.com/photo/1-0-84

Now, whilst the mechanics used are definitely a bit dodgy at the moment, the first point of note is the effect that asynchronous impacts and partially elastic collisions has upon the amount of mass and associated KE involved in impacts at the 'crushing front'.

The amount of mass which could actually be considered part of the 'pile driving mass' is significantly less than that involved in any synchronous impact model.

I need to improve the mechanisms, but I think the effect on 'collapse time' should be considered to be 'profound'.

Suggestions for improvement, motion behaviours, factors and comments very welcome...

Heiwa · by **Heiwa** on Tue Jun 23, 2009 8:13 pm

Good! I assume that an asynchronous impact is the first contact of two assemblies C and A of material elements - an upper part C contacting a lower part A; C being dropped on A by gravity - where only one element of each part participate, i.e. very limited masses. The forces developing at this elastic contact are then transmitted to every element in parts C and A.

So TWO "crush fronts" develop in the parts! One going up into C and one going down in A. The result should be that both C and A deform, etc, etc.

Now, A is fixed on ground and it is reasonable to assume that the first A crush front will bounce there. C on the other hand is only in contact with A and the crush front in C will behave differently.

When more elements in A and C come in contact more crush fronts ... and forces ... develop. And these forces may damage A or C ... and the structure is modified. Suggest you try to identify where the first structural failure develops. In C or A?

femr2 · by **femr2** on Thu Jun 25, 2009 3:09 pm

Heiwa wrote:Good! I assume that an asynchronous impact is the first contact of two assemblies C and A of material elements - an upper part C contacting a lower part A; C being dropped on A by gravity - where only one element of each part participate, i.e. very limited masses.

Yep, though I'm currently using whole floor masses, rather than sub-element mass. When I have reasonable mechanics, I'll start breaking down the masses into sub-elements.

The forces developing at this elastic contact are then transmitted to every element in parts C and A.

Some assistance in what kind of equations to use to model this would be handy. Specifically the transmission of energy from one mass through another into a third. Time-interval based equations would be very handy

So TWO "crush fronts" develop in the parts! One going up into C and one going down in A. The result should be that both C and A deform, etc, etc.

Yep. Again, very early days, and suggestion of mechanisms would be very handy. Specifically how to treat energy 'expenditure' either as part of, or post collision. The first runs use a simple elastic/inelastic equation with a coefficient of restitution variable. Thoughts on what kind of value to use for CR welcome, or indeed what mechanism to use to vary it.

Now, A is fixed on ground and it is reasonable to assume that the first A crush front will bounce there. C on the other hand is only in contact with A and the crush front in C will behave differently.

As it's still 1D, the 'bounce' can result in some quite chaotic behaviour, so I'm trying to employ mechanisms to 'transfer' mass from one body to another when they are travelling in parallel, to propagate mass downwards towards the 'crush zone'.

Sample output looks like this at the mo. (Colour indicates velocity and mass)

Heiwa · by **Heiwa** on Fri Jun 26, 2009 7:17 am

femr2 wrote:
The forces developing at this elastic contact are then transmitted to every element in parts C and A.

Some assistance in what kind of equations to use to model this would be handy. Specifically the transmission of energy from one mass through another into a third. Time-interval based equations would be very handy

It is quite easy! Each element is linked to adjacent elements by a potential (e.g. a spring) and thus constitutes an assembly of elements = a structure. Apply energy to the structure or an equivalent force and the springs deform, i.e. absorb energy. Thus, just add up all the deformations using a suitable 3-D FEM or beam analysis software and you'll find out what spring or element that fails first.

Then adjust model - include the broken element - and redo the analysis (10 000 times!).

femr2 · by **femr2** on Fri Jun 26, 2009 12:37 pm

Heiwa wrote:It is quite easy!

Cool. Could you post some quick pseudo code here then please ?

femr2 · by **femr2** on Fri Jul 03, 2009 8:48 pm

Heiwa wrote:
femr2 wrote:... in a 1D sense, that floor masses are modelled independently of each other, with the potential for one floor to be traveling at a different velocity from others, incurring inter-floor impacts as-and-when, rather than a single rigid cap mass impacting and coalescing with the floor below and only incurring an exact number of sequential impacts. For a >1D model, much more complex, but I assume you mean within 1D. I'll be increasing the D as soon as I get the 1D model sorted.

Suggest you simplify your 1-D model as follows to get a feel for it:

Upper part (C) consists of only two (n=2) material points each with mass m connected by one potential (spring).

Lower part (A) consist of twenty (n=20) material points each with mass m interconnected by 19 potentials; the lowest material point in A is connected to ground (assumed rigid! Ground will not move) by a twentieth potential.

There is also a 22nd potential connecting C and A that will be removed.

The 22 potentials differ (as we are in a gravity field). Each potential can carry the material points above it utilising 30% (or any figure) of available 'strength' prior 'breakage'. Thus the single C potential carries only 1 m, the bottom A potential connected to ground carries 22 m, i.e. it is 22 times "stronger' than the C potential. The top potential in A is 3 times 'stronger' than the single C potential.

Prior impact C/A part C is free and its single potential is 'unloaded'. Part A potentials are also unloaded - each potential carries 2 m less.

Now, do your pressure (force)/time calculations of the 21 potentials as before, when SIMPLIFIED C (2 m - one potential) impacts SIMPLIFIED A (20 m - 20 potentials), i.e. bottom C m contacts top A m (as the 22nd potential between C/A is removed).

The pressure developing at impact (time t = 0) will thus affect 20 m/20 potentials in A and 2 m/1 potential in C.

It would appear that the upper part C single potential will be subject to several pressure waves/fluctuations before even the bottom A/ground potential is affected.

femr2 · by **femr2** on Fri Jul 03, 2009 8:49 pm

femr2 wrote:
Heiwa wrote:Suggest you simplify your 1-D model as follows to get a feel for it...

Happy to include something similar to the spring suggested, though of course I'll be looking at it more as a deforming column, but as it'll be my poor ol' PC crunching the numbers I see no point reducing the number of 'masses'. 110 (116) + roof, antenna and distributed aircraft is very little extra leg-work, and I already have fairly useful mass data.
Would like the ground to be able to absorb some energy, and maybe even 'vibrate' somewhat.
I'll have to be careful with linear ramping of the 'strength' increase suggested, to conform to the actual events a little closer (and appease those on the other side of the coin to myself). Floor connection strength did not increase, although I'm fully aware of the necessity to ramp column strength. So I imagine the per-floor 'spring' 'strengths' will be set rather less than suggested.
For initiation, I'd like to include a time based gradual reduction in initiation zone 'spring' strength, to try and model the point at which it 'lets go'.

Now, do your pressure (force)/time calculations of the 21 potentials

I'll struggle a little with the actual coded implementation of the energy transmission, but I'm sure you guys will lend a hand when I get 'stuck' (Just the word potential helps my mindset here)

The pressure developing at impact (time t = 0) will thus affect 20 m/20 potentials in A and 2 m/1 potential in C.

I see what you're saying, but I'll definitely be defining t=0 to be the point at which the initiation zone 'strength' reduction begins to result in vertical displacement, and letting the simulation run until full completion (whatever that is), rather than focus t=0 to be an implied point of arrest.

It would appear that the upper part C single potential will be subject to several pressure waves/fluctuations before even the bottom A/ground potential is affected.

Aiii. The timer interval is going to have to be very small to capture this rapid transmission behaviour. My poor ol' PC has big fans tho, so I'll cope

I'm going to spend a little more time clarifying in my own mind how to go about capturing the difference in behaviour between floor connection breakage and actual column failure within a model which includes a 'spring'.

Thanks. It all helps me to clarify what I'm actually trying to do, and what it will involve me getting my hands dirty with.

femr2 · by **femr2** on Fri Jul 03, 2009 8:50 pm

Heiwa wrote:
femr2 wrote:
Aiii. The timer interval is going to have to be very small to capture this rapid transmission behaviour. My poor ol' PC has big fans tho, so I'll cope

I'm going to spend a little more time clarifying in my own mind how to go about capturing the difference in behaviour between floor connection breakage and actual column failure within a model which includes a 'spring'.

Thanks. It all helps me to clarify what I'm actually trying to do, and what it will involve me getting my hands dirty with.

An idea is that the pressure waves in parts C and A move at the speed of sound in steel and that they bounce when they reach the top of C (the roof) and ground (rigid).

If the pressure (force) wave in part A takes time t to travel down/up, it takes only time t/10 for the same event up/down in part C. When the pressure waves return to interface C/A they send new pressure waves into parts C and A. At the same time C and A deform (material points displace and move) but the movements are being damped! Pressure will build up simultaneously everywhere in C and A but at different rates (rapidly at the impact point, slowly at the extremities).

It would appear that upper part C will really be shaken by plenty of interfering pressure waves and, I assume, that it is this effect that will produce a first failure somewhere in the simple structures C and A, e.g. the only potential in C? It is always the weakest element in the structures in collision that fails first in any collision according my experience and it seems to be the only C potential in this simple model.

Major_Tom · by **Major_Tom** on Sat Jul 04, 2009 7:05 pm

I'm going to spend a little more time clarifying in my own mind how to go about capturing the difference in behaviour between floor connection breakage and actual column failure within a model which includes a 'spring'.

That is a very good idea because this difference is merged together far too often in this type of analysis.

Let's review:

We have, in general, 3 independent types of structures,

2 vertical: Core columns and perimeter column sheets (core columns act as "matchsticks" of 36 foot length connected and to end whereas perimeter columns act as 2-D "sheets")

1 horizontal: Flooring slabs.

In the large majority of this type of analysis these three independent elements are thrown together and considered in the most bizarre, impractical way and if the energy imbalance favors continued, increasing destruction, the author concludes that since this model is the "most favorable for survival", total destruction is assured in all cases.

This is what I will call the "chicken soup" or "Hungarian goulash" method of reasoning (you just mix all the elements together and hope the final product "tastes good").

This leads people to talk about "perimeter column buckling" (which hardly existed) or floor-by floor core columns "buckling" (which didn't exist) and a number of other factors which don't exist.

This is the basic Bazant approach which has resulted in such absurdities as years of debate over an indestructable upper block.

Very few people had the creativity to view the problem outside of the Bazantian mental box.

When OWE played with a toy physics tool he found that if slab connections are treated as breakable elements in both the upper and lower blocks, there are many possible outcomes depending on input parameters (as one could have anticipated years ago).

Anyway, in the first upper-lower block "impact" for WTC1,......

Let's honestly ask: What is colliding with what?

Let's not ask about the "best case scenario" but in reality.

What is colliding with what?

Perimeter column sheets: Is the upper block perimeter smashing into the lower perimeter sheet?

No, most probably not.

Core columns: Are the core columns buckling in such a way that the intact upper column falls and smashes into an intact lower column with no horizontal displacement, sending shock waves up and down through the columns?

No, most probably not.

(If so, how can such waves be analyzed without considering discontinuities (column welds and connections) in the steel medium which naturally partially reflects and artially transmits such waves?)

Floor slabs: Can we anticipate a collision between floor slabs?

Most certainly. How can one be avoided?

Major_Tom · by **Major_Tom** on Sat Jul 04, 2009 7:27 pm

Consider the way in which just core columns are treated:

Even though we know from the WTC rubble that the relative percentage of core columns exhibiting buckling is very, very small and the relative number of core columns that were seen straight and cleanly broken at the welds is very, very large (+95% easily, probably higher), this info seems to disappear into oblivion when we begin to talk of energy equations.

After a core column breaks at 2 locations maximum, doesn't any talk of the next "collision" become meaningless?

And what about the perimeter column sheets? Once top and bottom sheets are displaced, does talking about the "next collision" have any meaning?

Femr2 wrote:

I've been looking at the implications of adding asynchronous impacts and partially elastic collisions to the simple 1D crush models recently, and the most significant result so far is the huge difference in mass acting at the 'crush front'.

Exactly, it is the ability of the mass to act at the crushing front that is a huge difference between "Hungarian goulash" indestructable upper block methods and anything real.

All upper block mass is concentrated as an indestructable point mass acting together on the poor building below. This grossly overestimates the destructive abilities of an "upper block" on the floor below, and so on, and so on....

Let's consider the first impact as being flooring vs flooring. At collision, both floors are held onto their respective structures via connections and each contains inertia.

Dr G wrote:

An energy analysis is far more useful. You need to look at the work expended in collapsing one floor compared to the accompanying changes in kinetic and potential energy. This can be done using column crushing/buckling theory, for example.

What was the estimate for the amount of energy needed to sever the floor connections for one slab? Based on what reasoning? If this energy cannot be guessed reasonably, how can one proceed with energy analysis?

femr2 · by **femr2** on Wed Jul 08, 2009 9:08 am

Major_Tom wrote:What was the estimate for the amount of energy needed to sever the floor connections for one slab? Based on what reasoning? If this energy cannot be guessed reasonably, how can one proceed with energy analysis?

Though by no means definitive, some discussion of floor slab connectivity breakage was discussed recently here WTCCS Spreadsheet Crush-Down Model

DBB's last estimate was in the 60MJ range. I've been doing the sums recently and will post per-floor estimates when I've had time to do the leg-work.

Although we've been discussing the ejection of perimeter sections with flooring still attached, I think it's still more valid, in modeling terms, to look at floor connection breakages rather than the less 'real' column buckling.

Another factor for the 'improved' model I'm considering is how to look at the considerable lateral forces evident within video footage. Thoughts welcome...

femr2 · by **femr2** on Sat Jul 25, 2009 5:23 pm

http://www.youtube.com/watch?v=H2WjwV5ml5I

Traces for a range of CR values. (The last boxed value on the right).

I'll add observations once I've gone slightly blind watching it on repeat...but feel free to jump in

David B. Benson · by **David B. Benson** on Sat Jul 25, 2009 11:49 pm

Major_Tom wrote:And what about the perimeter column sheets? Once top and bottom sheets are displaced, does talking about the "next collision" have any meaning?

No. Such just become ejected mass.

This grossly overestimates the destructive abilities of an "upper block" on the floor below, and so on, and so on....

Nope. The first few destroyed floors become a zone of crushed materials, zone B in BLGB, which groes by accretion at the bottom at the expense of zone A. The upper zone C sorta rides down on top.

What was the estimate for the amount of energy needed to sever the floor connections for one slab?

There is enough information in the NIST reoprt to obtain good estimates; between 33 and 60 MJ assuming vertical distruction of truss seats (in agreement with visual evidence of the modes of failure along the south wall).

femr2 · by **femr2** on Sun Jul 26, 2009 8:52 am

David B. Benson wrote:
Major_Tom wrote:And what about the perimeter column sheets? Once top and bottom sheets are displaced, does talking about the "next collision" have any meaning?
No. Such just become ejected mass.

In order for intact sections of perimeter to become separated from the tower there will of course have to be collisions. They won't be 'end-on' or involve the outdated 'buckling' mechanisms discussed ad-finitum, but there must be collisions, or they would stay put. The energy sink required to do so must also be included within any model, including lateral impulses.

This grossly overestimates the destructive abilities of an "upper block" on the floor below, and so on, and so on....
Nope. The first few destroyed floors become a zone of crushed materials, zone B in BLGB, which grows by accretion at the bottom at the expense of zone A. The upper zone C sorta rides down on top.

It's very clear that the majority of each cap mass become separated from the system fairly early in each descent. I think it's about time to take out the majority of the cap mass once-and-for-all in any modeling, after the first few seconds.

What was the estimate for the amount of energy needed to sever the floor connections for one slab?
There is enough information in the NIST report to obtain good estimates; between 33 and 60 MJ assuming vertical destruction of truss seats (in agreement with visual evidence of the modes of failure along the south wall).

I'm still compiling data on the connection breakage sinks, but it's clear that it's above 60. In discussion in another thread you have already indicated values upwards of 70 if I recall. In addition, many other sinks also need to be included, such as the perimeter requirements mentioned above.

Heiwa · by **Heiwa** on Sun Jul 26, 2009 7:36 pm

David B. Benson wrote: The upper zone C sorta rides down on top.

Quite difficult to model! Any ideas how?

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