I have explained that the key to understanding of cascade failures at WTC is to recognise that it is a sequence of individual column failures. Somewhat akin to toppling a row of dominoes. Once the first domino topples the impetus to the next comes from the limited stability of that second domino PLUS the impact of being struck by the first. And so on down the line.
We easily see the "row of dominoes" as a sequence of individual topples. We need to take the same focus in our understanding of WTC cascade failures. See it as a sequence. Maybe several concurrent sequences - those big domino toppling demonstrations usually have multiple branches. The principles remain the same.
So for the next column in sequence to fail in axial overload requires that the load applied be more than the strength of the column can support. In the WTC situation that involved a varying mix of two factors:
(a) Increase the load; AND
(b) Weaken the column (Not by CD cutting - those ones - if any - are not failures in axial overload)
And in these next three stages I want to explain:
Stage 3 - how loads redistribute following a failure of a column and increasing the load on remaining columns. And specifically why the added load is ALWAYS more than most persons would expect.
So this one mostly about "(a) Increase the load";
Stage 4 - Why columns fail - a specifically how (i) increasing unbraced length; (ii) heat (temperature actually); and (iii) creep weaken a column.
So this one mostly about "(b) Weaken the column"; AND
Stage 5 - Perimeter Inward Bowing" - one of several examples of multi-factor physics which both "sides" have misunderstood.
Stage 3 - Load Redistribution - Why it is not "proportional" and (almost) Always Worse.
The history of WTC 9/11 collapses is littered by presumptions that removal of half the columns would double the load on those remaining. Removal of 25% would add 33.3% extra load uniformly to the remaining columns.
That is not so. The redistribution of loads depends on the original layout of the columns and the locations of those removed and those remaining. I want to avoid the full engineering explanation but can provide it if needed.
So I will use two simplified examples/thought exercises to illustrate.
(I've already posted them in the Peanut Gallery - but now I give the answers)
Example/Exercise #1
This is a simplified WTC Tower - simplified to three rows of columns. Left Centre and Right.
BEFORE the column was cut the total load in each of row L and Row R is 100 whilst Row C has 200.
Now some nefarious b..... cuts Row R.
Obviously the load in "R" drops to zero.
Not so obvious maybe?? The load in "L" also drops to zero - leaving "C" carrying the unaltered total load of 400. Nothing proportional about that - cutting 33.3% of columns leaving 66.7% intact and the load on one column DOUBLES.
Now understanding that is second nature to engineers like me but it may be new to you Jango. Do you see why it is so or do you need further explanation? <<Point for Agreement or further explanation
Example/Exercise #2
Seven rows of columns A>> G Equally spaced (no snide comments about my graphic skills - I'm not C7 using MSPaint.) All same load - make it 100 if you must have a number.
That same nefarious b..... Cuts Row "D"
Assume that the "Top Block" is a steel frame with the limited elastic flexibility that such a frame would have.
What happens to load in rows B, C, E and F?
This is what happens:
(Excuse the simplified graphics.)
The dropping at "D" causes the upper structure to "hog" over C and E AND it tries to lift over B and F.
I cannot say "how much" without doing the full specification of the structures and an FEA analysis. We don't need that detail here - just the principles it reveals.
But sufficient for us to show that the loads on B and F REDUCE and the loads on C and E increase by half of D PLUS the amount of the reductions on B and F. So the two columns adjacent to the one which was cut received additional load which is MORE than was carried by the cut columns.
And that is as complicated as we need to think about.
BOTTOM LINES for this Stage 3 of explanation are:
A) Failure of any column will cause the load it was carrying to be redistributed to other columns:
(i) It will add load to some, add less load to others and may actually REDUCE load on some;
(ii) The redistribution will not be proportional to number of columns failed; AND
(iii) Will cause a disproportionate increase in load for some columns somewhere in the layout - not necessarily the adjacent columns.
B) The disproportionate transfer will drive some of the remaining columns closer to failure than others. And it will almost certainly be worse than would occur with proportional reallocations.
Jango are you comfortable with understanding those "bottom lines" A)(i), (ii), (ii) and B)? <<Points for Agreement or further explanation
So far we have agreed a scenario and I have made two key points which are:
A) The cascading failures need to be understood as a sequence or sequences of single column failures - fast sequences without doubt but still sequences - not one big homogeneous single event; AND
B) The load redistribution which follows each column failure step is not proportional to the number of columns "lost" and it will always be worse than proportional. (It CANNOT be better for the next column to fail and the only remote possibility - not of practical concern - is that it COULD be proportional.)
In this stage I want to identify the main factors causing column failure. Our scenario has two causes of failure - cutting of columns which requires no further explanation - by definition a cut column is failed. So we need to now focus on columns failing in axial overload.
I have already foreshadowed that failure occurs when the applied load is greater than the strength of the column. That can and in the WTC scenario will include a balance or race between increasing loads and reducing column strength.
I explained the main mechanism for increasing loads in the previous Stage 3.
Objective for this stage:
In this stage I want to identify four main factors which reduce strength and round up this stage by introducing two factors which complicate the simple "single column" focus. Life wasn't meant to be easy.
Weakening Factor #1 - Effects of non-Axial or eccentric loading.
A column can take very high loads if the load is centrally (axially) applied at the end. That is almost always what the design calls for. It is the most economic usage of steel.
But strength falls away rapidly as the load goes off-centre - either by shifting the application point OR by taking the column out of alignment. Compare these four situations:
A is the designed ideal - centrally axially loaded;
B is offset or eccentric loaded;
C externalised eccentricity which directly introduces bending; AND
D one example of column taken out of line.
Now I am aware that you Jango would prefer the numbers - I'm going to take a hairy-arsed engineer's guess:
Whatever load A can take - B will only take half; C reduces to 1/4th and D 1/10th or less. Are there any engineers reading who care to check "B" for me? I'm too focussed on doing the explaining to oil up the rusty brain to do the calcs. C and D are too vague for the numbers to mean much I simply want Jango to appreciate that the fall off under eccentric loading or column displacement is dramatic.
So - eccentric or out of line loading weakens columns.
Weakening Factor #2 - Changing Effective Length
Most people will probably have good gut feel for this one - a long thin rod, pole or bar will bend more easily than a short stocky one:
The issue for WTC collapses is that some columns - e.g. the "inward bowing perimeters - had their effective length increased by failure/removal of bracing:
The effective length "as designed" is on the length. And the "effective length" of the column is 1 - each storey. Cut out the bracing as shown on the right and the effective length becomes 3.
And the strength of the column is inversely proportional to the square of the EL. So increasing length by 2 reduces strength to 1/4 and increasing by 3 reduces strength to 1/9th.
Weakening Factor #3 - Increasing Temperature
The strength of structural steel falls off rapidly as temperature rises. This is typical - the shape of the curve will vary somewhat with the steel grade or alloy but the rapid falloff characteristic is common.
And a reminder at this point of our cascading sequence of one at a time failures. The only column which needs its length increased or its temperature elevated is the next one in line to fail. (I'll get to two of the obvious "yes buts" at the end of this post. )(Edit - nailed one of them - the other ones can wait. )
Weakening Factor #4 - Contribution of "Creep" to column failure
"Creep" is (usually) a slow "flowing" deformation of material - including structural steel - when subjected to prolonged loading. The relevant issue for WTC failures is that creep increases as loads increase AND as temperature rises. Bottom line is that when structural steel reaches temperatures above the designed for range creep can occur. The creep causes flow of the stressed material in the direction of stress - the loaded column gets shorter. And getting shorter is very close to the same thing as failing. Columns fail in axial overload by getting shorter - provided the applied load can follow the shortening column it will continue to shorten AND bend or buckle out of alignment. So creep adds another weakening process.
Let's Complicate it a Bit
I said earlier that I would introduce '...two factors which complicate the simple "single column" focus'. Here's one example that illustrates both of those complicating factors - a real column which failed with heat as the main factor:
__________
(That is NOT a WTC example - it is chosen to illustrate some principles)
I'm using this to show two things:
1) A heat driven failure results in column folding and the space the column occupies getting smaller. The floor above has driven the top of the column downwards and the heat affected middle bit of column has wrapped around. The yellow arrows show the "knees" of the top and bottom parts and that the top part is already lower than the bottom part. Also there is no gap - then ends already passing. Note those points for the next stages of this explanation when I start to address the "Fundamental Issues that Both Sides Got Wrong"
2) The folding halted and it wasn't because the steel suddenly cooled and regained strength. What has happened is that the floor above has sagged as much as the adjacent columns would allow. So it has squashed the column down by that amount THEN could go no further. The adjacent less heat affected columns have held up the floor above from sagging any more. It couldn't "chase" the column down. So it couldn’t cause complete breakage. However the red arrows show how - if the crushing had continued - the top and bottom parts of the column would have bypassed each other. That is another key point to note for application in the next stage or two where I deal with "both sides got it wrong" examples.
And both of those show the next level of complexity we need to address - even when we take our column by column focus the actual columns are not standing in isolation. They will interact with those near them. In loading and in heating. Whatever raised temperatures any one column experiences are likely to be similar for the nearby columns even though different to those on the other side of the building.
And explaining that full range of those interactions gets several orders more complicated.
I don’t think we need to go there - I would rather look at some of the points of 9/11 WTC discussion where both sides have got the basics wrong. Those will allow us to explore specific issues which should be clearer than attempting generic explanations.
And "Perimeter Inward Bowing" is one relatively easy example so I will deal with that one in "Stage 5"
My objective for this stage was "Identify four main factors which reduce strength and round up this stage by introducing two factors which complicate the simple "single column" focus". <<Have I achieved that or are there any points where you want further explanation?
Will do. A confession - I've post edited a couple of details near the end of my last post. Merely to clarify what are those "two complicating factors".
Tried to colour code the changes but missed the edit window by a minute.
These are the changes:
Here's one example that illustrates both of those complicating factors - a real column which failed with heat as the main factor:
And both of those show the next level of complexity we need to address - even when we take our column by column focus the actual columns are not standing in isolation.
2) The folding halted and it wasn't because the steel suddenly cooled and regained strength. What has happened is that the floor above has sagged as much as the adjacent columns would allow. So it has squashed the column down by that amount THEN could go no further. The adjacent less heat affected columns have held up the floor above from sagging any more. It couldn't "chase" the column down. So it couldn’t cause complete breakage. However the red arrows show how - if the crushing had continued - the top and bottom parts of the column would have bypassed each other. That is another key point to note for application in the next stage or two where I deal with "both sides got it wrong" examples.
Pardon the step in - Minor suggested addition:
The column stopped squashing once the load on it became lower than would be required to keep deforming steel at that temperature. The load lessened because in the design of this structure, the adjacent columns were close enough to relatively quickly have load redistributed to them.
Will do. A confession - I've post edited a couple of details near the end of my last post. Merely to clarify what are those "two complicating factors".
Tried to colour code the changes but missed the edit window by a minute.
De-facto foster grandfather to about 120-140 kids 5 days per week - driving school buses as a retirement hobby job. Plus I train prospective bus drivers for their "authority" - allows them to carry fare paying passengers.
I enjoy Jeff Dunham's work. (all characters esp Accchhhmed)
BTW - prognosis for relative difficulty of the task before us:
Stage 2 - relatively easy stuff - I hope
AM to school and PM to home. With some getting off before others get on - about 9 Schools in the "mix". So probably no more than 50-60 at one time.
I've been busy in RL for most of past week - not able to concentrate on next "chapter". Should be able to get back to it tomorrow. ooops. Later today - it is nearly 1 AM here as I type. 00:54 Kilo
Stage 5 Ozeco's Explanation of Twin Towers Initiation - Adding Up The Bits.
Where we are at - Where to go with this stage.
I've put forward sufficient "building blocks" for my goal of explaining the Cascade Failure mechanism. In this stage I want to outline were those bits fit together as a coherent whole.
I had intended to give some detailed explanations of points that historically both "sides" have got wrong. I still need to identify those points but going to detailed argument at this stage will not help my current objective of explaining the cascade mechanism. We can explore in more detail later if we need to. But be warned I'm about to question several aspects of the "accepted wisdom". To be diplomatic I will flag them as POSC ["Point(s) Of Some Confusion"]
...E) Top Block descending bodily marks the end of our interest for this topic. (I will take it to the point where "ROOSD" driven progression is under way.)...
Recall we are distinguishing an "initiation stage" which ends once the "Top Block" is "dropping bodily" and a "progression stage" which follows. And we will need to be clear as to the difference because that is one often repeated source of confusion. POSC
Progression Stage Is Outside The Scope of This Explanation.
So let's be clear what I am not explaining.
I describe the "progression stage" mechanism as "Three Mechanisms" Major_Tom and his colleague femr2 coined the acronym "ROOSD" ["Runaway Open Office Space Destruction"]. Whatever terminology you prefer the key features of that progression stage mechanism were:
A) Material fell down the OOS ["Open Office Space"]1 shearing off the floors allowing the Perimeter to peel off and fall away2 and material falling in the core area sheared off the horizontal beams3 allowing the core columns to also fall over; AND
B) The columns which are the main vertical load support parts of the structure were effectively bypassed. Did not provide much resistance to the progression. Were not involved in buckling failure other than some minor exceptions. POSC
C) Hence my description of "Three Mechanisms" based on 1 2 and 3
Let's Define Our End Point - "How ROOSD Started"
the topic has not been discussed much AFAIK but one common explanation presumes that somehow separating floor mass accumulated in sufficient quantities to shear off the floors below. There is an elephant in that room which seems to go unnoticed. Let's see why - watch this clip to refresh what bit of collapse we are discussing. It is WTC2 but the WTC1 mechanism involved the same factors- different balance but same factors:
what do we see? Step P - At 1 second -Settling - early motion - mostly vertical as columns failing in some sort of sequence; Step Q - By 4 seconds - significant tilt of the Top Block - Base of Top Block moves horizontally to the right - ensures column ends are out of line; Step R - At ~5 seconds rapid downwards dropping with no obvious extra tilt; Step S - At 6 seconds - disappears into dust.
Notice that the visible perimeter of the left side is dropping well inside the perimeter of the lower tower. That is one of four sides and it is my "elephant in the room".
Here is why (Graphic borrowed from one of Achimspok's animations - my addition of the arrows etc):
At this stage the Top Block is still very much an integral structure complete with its external perimeter columns. Ditto the lower Tower and its Perimeter.
What hits what?
The left side arrow shows how the descending Top Block perimeter impacts the lower tower floors at the bits marked in blue - and without doubt that concentrated load from several stories of structure shears off those floors. ROOSD is already under way on that side of the building.
Conversely the right side arrow rising up into the Top Block (relatively speaking) impacts the Top Block OOS floors at the blue marked lines. And Shears them off. ROOSD is already under way on that side of the building.
And both those actions plus the equivalents on the other sides start the break up of both the "Top Block": and the "Lower Tower".
So that is the main process starting ROOSD. It is both the end point marker for my explanation and a logically defined known point for the following stage of explanation. (And - for those in the Peanut Gallery who are thinking ahead - it starts to demolish "crush down - crush up" in the WTC Twins 9/11 scenario...)
Bridging the Gaps in "THE EXPLANATION"
Stages 1-2-3-4 of these posts described the building blocks of the cascade failure mechanism - with a focus on the critical vertical vector of load carrying failure. We now have the "end point" of ROOSD Starting. And we have refreshed memory with four stages of the macro level motion.
Our "building blocks with focus on column failure in the vertical mode" is what caused macro "Step P - At 1 second -Settling - early motion - mostly vertical"
And by that Step P - that point in the process - all the critical failing has occurred. Ongoing collapse is inevitable. We do not need to explain Steps Q R S to "prove" the cascade mechanism. BUT we use them for explanation of some of the common POSC.
Errors and Misapplications of Bazant's "Limit Case"
Prof. Z Bazant won the academic race to be first to publish an explanation of WTC collapses. Made it 9/13 - second day after the event. It was correct in principle, probably wrong in a couple of details and has been the cause of a lot of confusion. Here's why POSC AND IMNSHO
It is an explanation of the "progression" or "ROOSD" or "Three Mechanisms" stage. He simplifies the progression stage with the assumption that all the columns were crushed. That is worse case for collapse and best case for survival. It was and is a valid "limit case" concept which was his intention. He found that there was more than sufficient energy available to crush all the columns into buckling failure. So far so good...BUT
To get it started he simplified the "initiation stage" to an assumption that the Top Block dropped onto the lower towers and landed column on column. Without getting pedantic at this stage that was a valid assumption to set the starting point for his explanation of progression stage as a limit case.
It never was a realistic explanation of the actual "initiation stage" which went along the lines I have explained in these posts.
That simplification was still no problem until people started to adopt that "dropping into impact" assumption as what really happened. It didn’t.
And the "crushing of columns" didn't happen either - a related error which Bazant made in papers which followed B&Z 2002 and lots of confusion happened in many forums of debate.
Let's briefly look at the sources of confusion - there are three which are significant:
1) It assumes some entity "dropped" through a gap creating what would essentially be one big object hitting another big object more or less as single entities. Reality was a "member on member sequence of impacts" - hence my focus on column by column through this series of posts;
2) It presumes a "gap" to drop through... which means that the columns had failed and were no longer in the picture. That cannot be a valid explanation for the real cascade failure. It is circular arse about chasing its own tail. "the column is already failed allowing the drop which fails the column" - so an error of sequencing (If you want a search term - I haven’t tried it but I've referred to the error as "anachronistic" in posts over the last four or five years.)
3) It assumes columns in line being crushed. They weren't in line or crushed. See "ROOSD" or my "Three Mechanisms".
And some of the common confusions which resulted POSC
1) Any claim discussion or explanation which literally applied the B&Z assumption of "dropping to impact" to the real event. POSC
2) A paper co-authored by T Szamboti (The Missing Jolt: A Simple Refutation of the NIST-Bazant Collapse Hypothesis. G MacQueen & T Szamboti 2009) It accepts that there was a drop which should produce a macro scale impact - "The Missing Jolt". Both premises wrong. POSC
3) Arguments about whether or not "Tilting" of the top blck would prevent or allow axial impact of the dropping column ends. (It is actualy the super set of which "Missing Jolt" is one example.) Makes the same two errors - Tilt was caused by column failure allowing one side of the Top Block to be lower. So the space occupied by the column is already shorter. The column cannot being that space unfailing. (Expect some "yes buts" on that assertion ) Plus the "anachronism" issue that failure of the column caused the drop which caused the tilt. POSC
4) Confusion between the "macro jolt" of "Missing Jolt" and "micro jolts" which would occur in abundance as the level of individual members of the structure. There was no "macro jolt" because the scenario for one never exists. There wer lots of micro jolts" BUT "micro jolts" are not the jolts envisaged by "Missing Jolt". POSC
Each of those is a merely outlined for purposes of this expantory series. They each warrant seperate discussion. There has been a lot of it in other threads.
Let's Round Up the Explanation to Date.
Recall that my objective was to explain the mechanism with CD still in the mix to avoid confusion.
My position on CD for the Twins is:
A) For the "progression" stage I can satisfy to my own standards by engineering reasoning that CD was not needed. In the scientific method we do not "prove negatives" so I do not claim proof of "No CD". BUT any clever terrorist or MIHOPer who did the brilliant undetected job of CD assisting the progression stage wasted his time. It wasn't needed.
B) For the "initiation" stage I CANNOT satisfy to my own standards by engineering reasoning that CD was not needed. It needs quantification and balancing/weighting of all the building block mechanisms. I doubt that such proof is possible. POSC (Disagreement rather than Confusion I suspect - the FEA fans likely to disagree. Let's see. Therefore I rely on improbability of CD in the logistic and security arena.
Over To You Jango
Jango are there any aspects where you would want further explanation - of the mechanism? I may now be able to respond to some of those POSC - I am aware of some already posted in the Peanut Gallery thread.
Thank you for the opportunity to write this up - I've wanted to do it for some years and never made the opportunity.
There will probably be a few proofing mistakes but the content should be good enough for purpose.
I'm along for the ride so far, however, the ending is where I'll add a comment.
Logistics and security are gray areas dependent on other human gray areas. There are some interesting pre-9/11 events at the World Trade Center that have not been fully fleshed out even though they give off an odor at first smell.
I'm along for the ride so far, however, the ending is where I'll add a comment.
Logistics and security are gray areas dependent on other human gray areas. There are some interesting pre-9/11 events at the World Trade Center that have not been fully fleshed out even though they give off an odor at first smell.
I'm along for the ride so far, however, the ending is where I'll add a comment.
Logistics and security are gray areas dependent on other human gray areas. There are some interesting pre-9/11 events at the World Trade Center that have not been fully fleshed out even though they give off an odor at first smell.
My Objective - to explain the cascade failure process of WTC1 and WTC2 "initiation stage" up to the point where the Top Block was falling AND ROOSD/Three Mechanisms progression was under way.
I will not be addressing CD claims which means that I must allow for CD options in the mix of contributors to collapse. The understanding of cascade failure is not affected whether or not there was CD. (Think about that before (any of) you ask )
I don't recall a "cascade failure initiation event" at either of those locations Noah.
And I'm not an "odour engineer" - other than odours from sewage treatment plants. They smell like ripening faeces - my preferred word not allowed by this US style forum which spells it ****.
There are some interesting pre-9/11 events at the World Trade Center that have not been fully fleshed out even though they give off an odor at first smell.
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)(Edit - nailed one of them - the other ones can wait. 
)
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