How Buckling Led to "Free Fall" acceleration for part of WTC7's Collapse.

We're missing the point. The point was the loss of north-south restraint.

If the only damage on the tower was a complete removal of the wind girders of the east or west walls, the building would still have been destroyed. Because of wall crippling.
Yes in either instance the building would probably be vulnerable to collapse because the buckling of the lower portion of columns in WTC 7 would result in the lower mass of WTC 7 not being able to support the upper mass of WTC 7 (as I think @Mick West explained in the first post in this thread).

However, as was discussed a few pages back in this thread, regarding the amount of crumpling of the exterior curtain wall as it fell, I would think that for a collapse where the core failed independent of floor failures, the collapse might be more likely to be visually characterized by global failure of the outer perimeter shell falling down without significant crumpling (e.g. like in the BBC and CNN footage). Whereas in your example of partial removal of the wind girders of the east or west walls, I would think that the building collapse might be more characterized by inwards crumpling of the outer perimeter shell as it collapses (similar to what was seen in the NIST simulations, even though the NIST simulations aren't meant to be an accurate geometric representation of the collapse given the predicted pattern of structural failure that did take place).


However, the Q&A section on the NIST website regarding WTC 7 https://www.nist.gov/pao/questions-and-answers-about-nist-wtc-7-investigation
says this (italics emphasis mine)


Some people have said that a failure at one column should not have produced a symmetrical fall like this one. What's your answer to those assertions?​


WTC 7's collapse, viewed from the exterior (most videos were taken from the north), did appear to fall almost uniformly as a single unit. This occurred because the interior failures that took place did not cause the exterior framing to fail until the final stages of the building collapse. The interior floor framing and columns collapsed downward and pulled away from the exterior frame. There were clues that internal damage was taking place, prior to the downward movement of the exterior frame, such as when the east penthouse fell downward into the building and windows broke out on the north face at the ends of the building core. The symmetric appearance of the downward fall of the WTC 7 was primarily due to the greater stiffness and strength of its exterior frame relative to the interior framing.

So possibly in any structural failure situation leading to collapse where the interior failures occurred before the exterior failures, the exterior frame of WTC 7 would appear to fall as one unit.

In fact, a partial removal would have been fine. For Euler buckling of the affected columns

Length² × strain = π² × gyradius.

At a rather low stress of 50MPa and with a gyradius of 7 inches or less consistent with the W14 section columns, the critical length would be 35m, or 10 storeys. This is for a fixed-guided boundary condition, which is applicable here as the the undamaged top block of the tower slides in the danaged section without rotating.
Yes, from your calculations it doesn't seem like it would have taken much stress nor required failure of a significant portion of columns in the building for the building to completely collapse. It seems that might be because of how the truss and column system was configured in the building design, which did not lend itself well to resisting collapse once failure of structural members had initiated, similar to how such a structure designed like WTC 7 was also more vulnerable to fire than conventional structures (which I think the NIST Q&A on WTC 7 had also mentioned):



Why did WTC 7 collapse, while no other known building in history has collapsed due to fires alone?​


Factors contributing to WTC 7's collapse included: the thermal expansion of building elements such as floor beams and girders, which occurred at temperatures hundreds of degrees below those typically considered in current practice for fire-resistance ratings; significant magnification of thermal expansion effects due to the long-span floors in the building; connections between structural elements that were designed to resist the vertical forces of gravity, not the thermally induced horizontal or lateral loads; and an overall structural system not designed to prevent fire-induced progressive collapse.

Does this mean there are hundreds or thousands of unsafe tall buildings with long span supports that must be retrofitted in some way? How would you retrofit a building to prevent this problem?​

Of particular concern are the effects of thermal expansion in buildings with one or more of the following characteristics: long-span floor systems, connections that cannot accommodate thermal effects, floor framing that induces asymmetric forces on girders, and composite floor systems, whose shear studs could fail due to differential thermal expansion (i.e., heat-induced expansion of material at different rates). Engineers should be able to design cost-effective fixes to address any areas of concern identified by such evaluations.
 
We're missing the point.
Yes. The topic is:
"How Buckling Led to "Free Fall" acceleration for part of WTC7's Collapse."

and you are digging into details without showing their relevance to the OP topic
The point was the loss of north-south restraint.

If the only damage on the tower was a complete removal of the wind girders of the east or west walls, the building would still have been destroyed. Because of wall crippling.
You have lost the context. The perimeter shell fell - still as an integral whole - after the core had collpses internally. The cause of the bit of freefall in that stage of collapse was removal of supporting columns by some as yet jnot agreed mechnaism.
In fact, a partial removal would have been fine. For Euler buckling of the affected columns

Length² × strain = π² × gyradius.

At a rather low stress of 50MPa and with a gyradius of 7 inches or less consistent with the W14 section columns, the critical length would be 35m, or 10 storeys. This is for a fixed-guided boundary condition, which is applicable here as the the undamaged top block of the tower slides in the danaged section without rotating.
So the three options on the table are:
1) Direct failure of columns << The option you are focussing on with Euler type buckling probably the main factor;
2) Failure of the cantilever of the bridging trusses (and possible interactions with other parts of the transfer structure) << currently being ignored;
OR
3) Recent speculations about "impacts from falling floor slabs" << which are actually sub aspects of either 1 or 2.
 
So possibly in any structural failure situation leading to collapse where the interior failures occurred before the exterior failures, the exterior frame of WTC 7 would appear to fall as one unit.
THAT is where the debate STARTED. It is the starting scenario
 
The cause of the bit of freefall in that stage of collapse was removal of supporting columns by some as yet jnot agreed mechnaism.
A recent paper on this topic "The Collapse of World Trade Center 7: revisited" published earlier this year also says there doesn't appear to be an agreed upon mechanism that has been clearly identified for where exactly the failure of supporting columns initiated that started the collapse
https://www.researchgate.net/publication/347108749_The_collapse_of_World_Trade_Center_7_revisited5, Published November 2020


CONCLUSIONS​

The collapse of WTC 7 remains to this day a unique event in the history of structural fire engineering.
Despite occurring nearly twenty years ago, there is no real way to know what exactly caused its failure.

Multiple expert teams had investigated the disaster and tried to recreate the various events that led to the progressive failure of the structure. With most debris gone, the expert teams had to rely on photos, videos, and numerical modelling to piece together their different hypotheses. Fire Dynamics Simulator (FDS) and explicit FEM played a crucial role in each of the investigative teams’ approaches, which shows a trend towards more computationally intensive methods for forensic analysis of fire-attacked structures. By reviewing the various modelling approaches and hypotheses of the investigators some important insights about the case can be gained:
1. There is consensus amongst the investigators regarding two main aspects of the collapse of WTC7:
fire was the primary cause of the failure, and the failure initiated in the east side of the building somewhere in the lower 14 floors.

2. FDS simulations of affected floors 7-9 and 11-13 calibrated against videos produce comparable
temperatures in the structural components. Even the small variations in temperature, however, may result in different outcomes depending on the nature of the structural model.
3. Despite the tremendous efforts of the various investigative teams, there is no consensus regarding the exact initiating mechanism. Arup & Guy Nordenson and Associates (Arup) analysis showed that girder 44-79 would be pulled off of its seat, opposite to the prediction by NIST which show the girders pushed off of their seats. Weidlinger & Associates and Hughes Associates (WAI’s) analysis points towards a floor beam connection failing followed by entire floor collapsing. Finally, the University of Edinburgh (UoE) mechanical room fire scenario predicts that the failure may have occurred due to a completely different fire caused by a breach of the emergency power system.
4. Numerical models are only idealisations of real events, and thus by nature they would be dependent on the decisions made by the analyst. There are many discrepancies between the different numerical models and outcomes for WTC 7, and each may be sensitive to different factors. There still remains a gap in the knowledge on the most suitable approach to modelling large structural systems in fire, and what is the right level of abstraction to capture the most important aspects of the behaviour without complicating the models beyond reasonable computational cost and pushing it outside its predictive capacity.

https://link.springer.com/article/10.1007/s10694-022-01225-2, Published March 15, 2022

ABSTRACT​

The catastrophic events of September 11, 2001, stand out as a major motivation for research on improving the understanding of structural behaviour in fire. These events included the first complete collapse of a tall steel framed structure solely due to fire. World Trade Center 7 (WTC7) was a 47-storey office building within the WTC complex that collapsed due to a fire initiated by debris from the collapse of WTC1. In the following years, detailed investigations were carried out by expert teams to pinpoint the cause of the progressive failure of WTC7. Each of the expert teams analysed the fire and structure and made varying conclusions with regards to the mechanisms responsible for initiating and propagating the collapse of the building. This paper revisits the collapse of WTC7 and its investigation, and then explores the hypothesis that a potential hydrocarbon fire may have compromised the large transfer structure within the mechanical space of the building. This is done via two OpenSees finite element models. The first model explores the thermomechanical response of the mechanical floors to a potential diesel fire, and the second investigates the response of the structure to a failure caused by that fire. The outcome of the analyses shows that it is feasible that a mechanical room fire could lead to a failure in the transfer structure, which would then result in the loss of support to at least two columns within the building core. The failure of these columns may unbrace the eastern-most core columns and precipitate in the failure of the structure as observed on 9/11.
 
Indeed. And I'd like to see the above chart that supposedly shows over-g but with some error bars on it. The line that spends more time beyond g in particular seems to have a surprising level of precision - how do they justify that?
It's best interpreted in the context of the original discussions @FatPhil. "over-G" was only one factor and of secondary importance.

The discussion was on another forum where two serious researchers who were perceived as "truthers" were concernedly proposing technical explanations which were affronts to the entrenched and wrong opinions of debunker "prevailing wisdom". The broader context for "over-G" aspects of WTC7 collapse was methods of precise measurement including "sub-pixel" techniques - yet another contentious issue. But the topic under discussion was the NIST <> Chandler manufactured (by Chandler) controversy over NIST "admitting" free fall.

Both NIST and Chandler used similar crude measurement techniques. The advocate for precision measurement identified about a dozen shortcomings with those techniques. "sub-pixel" measurement only one feature of assessment. "over-G" only one possible outcome. And there were several other errors of more macro importance e.g. Numerous possible errors of geometry resulting from angles of view plus NIST and or Chandler when measuring motion used a "zone" - not a specific point - as reference for "start of motion" and "end of measurement"

So forgive the lengthy explanation BUT

The issue of "error bands" was raised many times but never resolved EITHER by defining what those bands were OR for what aspect of the discussion they applied to. And my own opinion at the time was that nothing depended on "over-G" so it wasn't worth the distraction or effort to resolve it. In the setting of the original discussion and the dramatis personae involved. I can link you to the material if you need it BUT it is typically scattered over several lengthy threads. IMO it is not worthy of importing here to comply with Metabunk protocols.

In fact the more interesting discussion arose from the number of persons who either claimed "over-G" was not possible OR demonstrated their own limited comprehension of the topic.

Arising from the more generic issues of "Free Body Physics" involved I initiated discussions on several forums including this "challenge" thread here on Metabunk.
The Challenge post https://www.metabunk.org/threads/acceleration-greater-than-g.5635/#post-143011

EDIT >> PS. I've re-read through that linked thread @FatPhil. I'd forgotten that I had covered a lot of the issues I've mentioned in this post. You may find the thread interesting. I'll live with what I said 7 years back - haven't changed my understanding much.
 
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You have lost the context. The perimeter shell fell - still as an integral whole - after the core had collpses internally.
Not very much "after". Just a few fractions of seconds. Which is the problem.
main-qimg-c27b84b6c77ac7694b858400aaea78cd.gif

The cause of the bit of freefall in that stage of collapse was removal of supporting columns by some as yet jnot agreed mechnaism.
That mechanism was synchronised multistorey 3-hinge buckling of all columns as a direct result of 1-hinge buckling caused by the crippling I mentioned. (Entire floors were launched sideways to make this possible. It would have been quite a sight)

The cause of all this was the failure of the framed tube to do its job of stabilizing both itself and the core.

However, the Q&A section on the NIST website regarding WTC 7 https://www.nist.gov/pao/questions-and-answers-about-nist-wtc-7-investigation
says this (italics emphasis mine)

Their statement is partly wrong.

The core fell first, because it has a lower safety factor, and the splices were not designed to resist bending

But it neither disconnected from the exterior, nor was the primary cause of the exterior failure.
Screenshot_2022-06-05-18-09-46-604_com.microsoft.office.word-01.jpeg

That's how crippling fits into the context.
 
A recent paper on this topic "The Collapse of World Trade Center 7: revisited" published earlier this year also says there doesn't appear to be an agreed upon mechanism that has been clearly identified for where exactly the failure of supporting columns initiated that started the collapse
https://www.researchgate.net/publication/347108749_The_collapse_of_World_Trade_Center_7_revisited5, Published November 2020
That disagreement seems mostly irrelevant for this discussion? as all four structural analyses can be summarized as "heat caused various things to go wrong, then column 79 failed, then progressively the core collapsed, and then the exterior". Our discussion here seems to be concerned with what happened after column 79 failed, but the disagreement is about before.

From the paper:

NIST:
External Quote:
The severe heating and restrained expansion of the floor slab caused what remained of the floor to lose its stiffness by concrete crushing, and severely weakened the fire floors causing partial collapse which could not be impeded and resulted in cascading floor failure that left column 79 unsupported over 9 floors causing its buckling failure which caused the kink observed in the collapse video. The buckling of column 79 was followed by similar failures of columns 80 and 81, and then the progressive collapse of the adjacent column lines.
Arup & Guy Nordenson and Associates:
External Quote:
Just after the failure of girder 44-79, the north eastern floor slab would collapse over multiple floors causing column 79 to also lose its west-facing connection and thus buckling. The failure of column 79 and its supported floor area leaves column 80 unbraced and its buckling then causes the kink observed in the penthouse as seen in the collapse videos. The falling debris then damages the transfer trusses and results in the failure of the next column line followed by pulling of the remaining core and causing the failure of interior of the building.
Weidlinger & Associates and Hughes Associates:
External Quote:
With this, the eastern portion of the floor would collapse impacting a similarly weakened floor resulting in progressive failure of the east section of the interior floor of WTC 7. Columns 79, 80, and 81 then unsupported over multiple floors would buckle and cause the kink in the penthouse. The collapsing debris severely damaged the transfer structure on the fifth and sixth floors, and also resulted in westwards internal collapse propagation.
University of Edinburgh (UoE):
External Quote:
Likewise, the exposed and partially heated truss 1 is also losing capacity due to heating thus transferring its own capacity to the core and to column 79. Given that column 79 is likely to have been heated due to a diesel fire in its location, and that it also is the most heavily loaded column, it is likely that it would have failed. From this, it was clear that failure of any one of truss 1, truss 2, or column 79 would overload the other two and lead to their failure. It was, therefore, that combined heating of truss 1 and truss 2, and potential heating of column 79 was the primary factor for global collapse of WTC 7.
 
That disagreement seems mostly irrelevant for this discussion? as all four structural analyses can be summarized as "heat caused various things to go wrong, then column 79 failed, then progressively the core collapsed, and then the exterior". Our discussion here seems to be concerned with what happened after column 79 failed, but the disagreement is about before.
EXACTLY. This thread is about what failed the columns of the perimeter AFTER the core had already collapsed.

A recent paper on this topic "The Collapse of World Trade Center 7: revisited" published earlier this year also says there doesn't appear to be an agreed upon mechanism that has been clearly identified for where exactly the failure of supporting columns initiated that started the collapse
In fact, it confirms the status of the debate identified earlier by @Jeffrey Orling and me - maybe some others.
External Quote:
The outcome of the analyses shows that it is feasible that a mechanical room fire could lead to a failure in the transfer structure, which would then result in the loss of support to at least two columns within the building core. The failure of these columns may unbrace the eastern-most core columns and precipitate in the failure of the structure as observed on 9/11.
.. and we have already identified two options - possibly three depending on if and how we tie in the impacts of falling floors.

The debate has drifted off focus and lost track of progress made earlier.
 
That disagreement seems mostly irrelevant for this discussion? as all four structural analyses can be summarized as "heat caused various things to go wrong, then column 79 failed, then progressively the core collapsed, and then the exterior". Our discussion here seems to be concerned with what happened after column 79 failed, but the disagreement is about before.
I thought it was relevant because none of the analyses seem to be certain whether it was just column 79 that failed or whether there was the failure of other columns other than column 79 that also initiated the collapse. This ties into the disagreement about what happened before column 79 failed. All the analyses can generally agree that the heat from the fire caused things to go wrong, but they can't exactly agree on the specifics of what was the exact process involved.
In fact, it confirms the status of the debate identified earlier by @Jeffrey Orling and me - maybe some others.

.. and we have already identified two options - possibly three depending on if and how we tie in the impacts of falling floors.

The debate has drifted off focus and lost track of progress made earlier.
I'm sorry for going off topic, I was just trying to understand earlier things said in this thread about free fall acceleration and why there was lack of crumpling of the outer perimeter shell during collapse, but what was the original debate? Was it debating whether truss failure was the primary method of failure for column 79 that lead to the sequence of events resulting in WTC 7 coming down at free fall acceleration?

Edit:
EXACTLY. This thread is about what failed the columns of the perimeter AFTER the core had already collapsed.

Okay, from what I understand from what @Jeffrey Orling said, one possible cause was that with core collapse, the failure of the perimeter columns was because they were knocked out on all sides of the base of WTC 7 when the pile of debris from the collapsed core spread outwards in all directions. Another possible cause that seems to be proposed instead is outer perimeter wall crippling, specifically in the north-south direction.
 
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I thought it was relevant because none of the analyses seem to be certain whether it was just column 79 that failed or whether there was the failure of other columns other than column 79 that also initiated the collapse.
It is a matter of how you define "initiate". I somewhat disagree with NIST choosing Col 79. Reality is that something triggered Coll 79 - it didn't fail of its own "volition". Plus the other columns near 79 and associated other elements also failed - the whole cluster was the first stage of failure of the core of WTC7. I agree with NIST that referring to Col 79 is a useful descriptor.
This ties into the disagreement about what happened before column 79 failed. All the analyses can generally agree that the heat from the fire caused things to go wrong, but they can't exactly agree on the specifics of what was the exact process involved.
We will never be certain. And it has no consequence on either of the two issues viz proving there was no CD or explaining the collapse
I'm sorry for going off topic, I was just trying to understand earlier things said in this thread about free fall acceleration and why there was lack of crumpling of the outer perimeter shell during collapse, but what was the original debate? Was it debating whether truss failure was the primary method of failure for column 79 that lead to the sequence of events resulting in WTC 7 coming down at free fall acceleration?
No problem - just be clear as to what issues are being discussed and their relationship.
Okay, from what I understand from what @Jeffrey Orling said, one possible cause was that with core collapse, the failure of the perimeter columns was because they were knocked out on all sides of the base of WTC 7 when the pile of debris from the collapsed core spread outwards in all directions. Another possible cause that seems to be proposed instead is outer perimeter wall crippling, specifically in the north-south direction.
Jeffrey was speculating about one of the issues. I was describing the relevant set.
 
because none of the analyses seem to be certain whether it was just column 79 that failed or whether there was the failure of other columns other than column 79 that also initiated the collapse
oh, they're all sure that once column 79 went, the others did, too
Weidlinger doesn't commit to whether 79 failed first out of 79, 80, 81, but they're all in agreement that this is when the collapse really started to get going.
 
Have we agreed on what was the sequence of events pre collapse?
Fires burned in the NE side of the building on floor below 14 all day (sprinklers had failed)
beams and girders expanded when over heated and critical girders were pushed off seats on columns 79 (probably 80 and 81)
local floor collapses ensued around these columns leaving them unbraced
unbraced columns are weaker and subject to buckling...
columns below the EPH apparently buckled because it dropped down through the building.
floor areas supported by those beams which had been pushed off their seats collapsed over multiple floors.
collapse of multiple floors down onto the structures on floors 5-7 (load transfer region) initiated further collapses of lateral steel which spread westward through the structure leading to extensive floor collapses throughout the interior
the massive debris from the collapse of the floors aggregated inside the base of the "cage" of the tower
Debris undermined the perimeter "cage" structure at its base. It collapsed as a unit unconnected to the foundations.
 
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