Merged Applicability of Bazant's model to the real world

[Dave Rogers]

Another engineer and I did the calculations for a main double truss at high temperatures with a standard floor load and found that even at 700 degrees C the deflection is only about 2 inches.

How do you reconcile that with the actual deflections measured by NIST on sample floor assemblies?

"The test was stopped at 116 min when, after another sudden drop, the center span deflection reached about 15in."

NCSTAR1.6, page 44, describing tests on a 35 foot restrained span with 3/4" SFRM. Given that the actual floor trusses were longer than this, and may have had damage to the SFRM, a deflection of 40" under normal loading doesn't seem inconsistent with this result.

It would be helpful if you could describe the basis of your calculations.

Dave

 

[Dave Rogers]

I do get sensitive to comments such as "the basic finding, which is the broader conclusion of Bazant's model, is still valid." which may indicate that defence of Bazant is given higher priority than determining what happened with the WTC collapse. That may not be your intention but I tend to read carefully when similar statements are made.

I think Bazant's later statements appear over-dogmatic in claiming that his model is a complete analysis of the collapses; it's clearly far too idealised to give any significant understanding of the detailed processes. It's useful, though, as a limiting case - as has been repeated ad nauseam to truthers on this forum - to refute the uninformed opinion that global collapse was in any way unexpected or implausible. In the context of the subject matter of the forum, that's sometimes a higher priority than determining the fine detail of the collapse dynamics. On an engineering discussion board, though, I would agree with you unreservedly.

Dave

 

[leftysergeant]

Bazant's model of crush-up may still be valid here, too, at least as I am begining to grasp it. I get the sense that he is saying that crush-up occurs when the resistance offered by black A can no longer be displaced by block C. and that the resistance of block A will beging to crush block C.

But bear in mind that the towers were unique and far less rigid than the typical building. The load-bearing capacity was dependent on very few members for the size of the whole structure. We may even need to discuss it as two distinct structures for the purpose at hand, specificly, as the core and the office floors.

To further complicate things, it may even be that the vertical jolt is missing because the initiating event did not involve a vertical movement at all, but a slight horizontal movement.

In a sense, the towers were topped with a very heavy steel umbrella in the form of the "hat trusses." The weight of these trusses was born by both the core and the perimeter columns. When the perimeter columns lost their ability to support the hat trusses on at least two sides, the trusses leaned into that area, subjecting the core columns to a shearing force that they could no longer resist. What followed would closely resemble a tree being cut down incorrectly. The still-viable perimeter columns would be resisting the toppling of the hat trusses, so that the stresses they placed on the core would, at the point of failure, be directed toward those viable columns. Thus, the bottoms of the core columns in block C would slide off of the tops of the columns in block A.

But the columns in block C are now being stressed in a direction from which they were never intended to be stressed, as a result of which, they become disconnected from each other very easily. Thus, crush-up begins almost immediately, because the block C columns cannot exert any appreciably force on those of block A, but block A can dislocate the core of block C.

The only deceleration that occurs is when the perimeter columns that had not failed arrest the horizontal movement of the bottom of block C.

So, the jolt is there. We have just been looking for changes in movement on the wrong axis.

It also occurred to me while I was writing this that there may have been a problem in the way that NIST determined how much the floor trusses would sag. I have read the report on line, but not printed it out, so help me if I overlooked or forgot an important point.

The failure of the test pieces to sag in the NIST tests may have been because they did not properly arrange the weights on top of the trusses.

We are not talking about a bare floor when we talk about the failures of the floors. There was a wide assortment of office furnishings all over the place on the effected floors. I don't know whether any of you have ever had to move one, but just the average office copying machine is one bloody heavy object. But it is light in comparison to a kamikaze airliner at full speed. At leasst a few of them wound up where they were not supposed to be, along with all manner of other furnishings and bodies and potted plants and what have you. A few of the floor slabs fell immediately on impact and were resting on floors that ultimately failed. A few panels of perimeter columns also wound up inside on the floors. (They're a bit heavy, you know.)

There were also several tons of extraneous aluminum scrap and at least one honking great engine adding to the burden.

Very little of the office contents left the area through the down-range holes. About all we see exiting in any of the videos is an engine and maybe landing gear parts. As best I can figure, the most noticeable bowing of the perimeter columns appears to be down-range of the impact points, and I must conclude, based on the way such things would typically unfold, that a lot of the office contents had also been shoved abruptly into those same areas. I hope that helps make a little more sense of this.

 

[ozeco41]

I think Bazant's later statements appear over-dogmatic in claiming that his model is a complete analysis of the collapses; it's clearly far too idealised to give any significant understanding of the detailed processes. It's useful, though, as a limiting case - as has been repeated ad nauseam to truthers on this forum - to refute the uninformed opinion that global collapse was in any way unexpected or implausible...

All agreed.

... In the context of the subject matter of the forum, that's sometimes a higher priority than determining the fine detail of the collapse dynamics. On an engineering discussion board, though, I would agree with you unreservedly.

Dave

I think the distinction you draw finesses the pragmatic balance quite well. This is not primarily a forum for engineering discussion. And the established "climate" does not serve well as a background for complex rational analyses.

However engineering realities should not be sacrificed to serve the implicit goal of converting the heathen or at least holding the line against heresy and apostasy.

Eric C

 

[leftysergeant]

However engineering realities should not be sacrificed to serve the implicit goal of converting the heathen or at least holding the line against heresy and apostasy.

The best that we can hope for, I think, is that we shall disabuse them of a few superstitions.

 

[ozeco41]

Bazant's model of crush-up may still be valid here, too, at least as I am begining to grasp it. I get the sense that he is saying that crush-up occurs when the resistance offered by black A can no longer be displaced by block C. and that the resistance of block A will beging to crush block C.

But bear in mind that the towers were unique and far less rigid than the typical building. The load-bearing capacity was dependent on very few members for the size of the whole structure. We may even need to discuss it as two distinct structures for the purpose at hand, specificly, as the core and the office floors.

To further complicate things, it may even be that the vertical jolt is missing because the initiating event did not involve a vertical movement at all, but a slight horizontal movement.

In a sense, the towers were topped with a very heavy steel umbrella in the form of the "hat trusses." The weight of these trusses was born by both the core and the perimeter columns. When the perimeter columns lost their ability to support the hat trusses on at least two sides, the trusses leaned into that area, subjecting the core columns to a shearing force that they could no longer resist. What followed would closely resemble a tree being cut down incorrectly. The still-viable perimeter columns would be resisting the toppling of the hat trusses, so that the stresses they placed on the core would, at the point of failure, be directed toward those viable columns. Thus, the bottoms of the core columns in block C would slide off of the tops of the columns in block A.

But the columns in block C are now being stressed in a direction from which they were never intended to be stressed, as a result of which, they become disconnected from each other very easily. Thus, crush-up begins almost immediately, because the block C columns cannot exert any appreciably force on those of block A, but block A can dislocate the core of block C.

The only deceleration that occurs is when the perimeter columns that had not failed arrest the horizontal movement of the bottom of block C.

So, the jolt is there. We have just been looking for changes in movement on the wrong axis.

It also occurred to me while I was writing this that there may have been a problem in the way that NIST determined how much the floor trusses would sag. I have read the report on line, but not printed it out, so help me if I overlooked or forgot an important point.

The failure of the test pieces to sag in the NIST tests may have been because they did not properly arrange the weights on top of the trusses.

We are not talking about a bare floor when we talk about the failures of the floors. There was a wide assortment of office furnishings all over the place on the effected floors. I don't know whether any of you have ever had to move one, but just the average office copying machine is one bloody heavy object. But it is light in comparison to a kamikaze airliner at full speed. At leasst a few of them wound up where they were not supposed to be, along with all manner of other furnishings and bodies and potted plants and what have you. A few of the floor slabs fell immediately on impact and were resting on floors that ultimately failed. A few panels of perimeter columns also wound up inside on the floors. (They're a bit heavy, you know.)

There were also several tons of extraneous aluminum scrap and at least one honking great engine adding to the burden.

Very little of the office contents left the area through the down-range holes. About all we see exiting in any of the videos is an engine and maybe landing gear parts. As best I can figure, the most noticeable bowing of the perimeter columns appears to be down-range of the impact points, and I must conclude, based on the way such things would typically unfold, that a lot of the office contents had also been shoved abruptly into those same areas. I hope that helps make a little more sense of this.

Our posts crossed in the posting.

Some interesting points there leftysergeant - your usual practical approach showing through.

No detailed comments at this stage. However the point you make about the office content and fitout partitions being "bulldozed" ("airplanedozed") into one end of the building bears careful consideration.

 

[ozeco41]

The best that we can hope for, I think, is that we shall disabuse them of a few superstitions.

..but never losing sight of the old adage "There's none so blind as them that won't see" - usually spoken in a north of England accent given my origins.

 

[Tony Szamboti]

How do you reconcile that with the actual deflections measured by NIST on sample floor assemblies?

"The test was stopped at 116 min when, after another sudden drop, the center span deflection reached about 15in."

NCSTAR1.6, page 44, describing tests on a 35 foot restrained span with 3/4" SFRM. Given that the actual floor trusses were longer than this, and may have had damage to the SFRM, a deflection of 40" under normal loading doesn't seem inconsistent with this result.

It would be helpful if you could describe the basis of your calculations.

Dave

The results for a 700 degree C temperature and 88 lbs./sq. ft. floor loading are below.

Temperature (degrees C) = 700
Span (ft.) = 60
Floor load (lbs./sq. ft.) = 88
% of room temp MOE for concrete at temperature = 43
% of room temp MOE for steel at temperature = 64
Concrete MOE (psi) = 1.81E+06
Steel MOE (psi) = 3.00E+07
Concrete MOE at temp (psi) = 7.78E+05
Steel MOE at temp (psi) = 1.92E+07
Concrete slab thickness (in.) = 4
Slab centroid to top chord (in.) = 2.414
Top chord to bottom chord (in.) = 28.05
MOE ratio of steel to concrete = 2.47E+01
Effective slab width (in.) = 74.18
Transformed slab section area (in^2) = 1.20E+01
Top Chord area (in^2) = 3.25
Bottom Chord area (in^2) = 6.94E+00
Composite centroid distance from bottom (in.) = 2.1078E+01
Moment of Inertia double truss (in^4) = 4.30E+03
Deflection of main trusses (in.) = 2.08E+00



I can send you the spreadsheet if you like.

The calculations take into consideration the effect of temperature on the modulus of elasticity of both the concrete and steel in the composite beams.

I believe there is even something in the NIST report about a 2 inch deflection at 700 degrees and then later there is a lot of mumbo jumbo and viola we get 25 inches which is then expanded to 40+ inches by creep. The only way to do this is to apply additional loading and the only way that could have happened is for the load from disconnected trusses to be applied to a remaining connected truss.

As for the floor assembly testing you don't say what the concrete and steel temperatures and floor loading were. You need to do that.

 

[femr2]

The load-bearing capacity was dependent on very few members for the size of the whole structure.

Don't forget the coupl-o hundred perimeter columns.

We may even need to discuss it as two distinct structures for the purpose at hand, specificly, as the core and the office floors.

Four. Core columns. Core floor assembly. OOS Floor assembly. Perimeter columns.

To further complicate things, it may even be that the vertical jolt is missing because the initiating event did not involve a vertical movement at all, but a slight horizontal movement.

Initial movement has been looked at in detail. Suggest looking at WTC 1 early motion trace data presented by MT in the OOS thread.

In a sense, the towers were topped with a very heavy steel umbrella in the form of the "hat trusses."

Not really. The additional mass of the hat truss was not particularly significant. Less so than the increased rigidity, until perimeter was stripped, imo.

Mass distribution...

What followed would closely resemble a tree being cut down incorrectly.

Unwise allegory.

So, the jolt is there. We have just been looking for changes in movement on the wrong axis.

No. Mini-*jolts* are there, and expected. Massive ones that Tony is looking for are not, and not expected imo.

It also occurred to me while I was writing this that there may have been a problem in the way that NIST determined how much the floor trusses would sag.

You're not kidding...

I hope that helps make a little more sense of this.

Sorry, but it seems more like you are just beginning to relax a little in less exciting *truther bashing* dialogue to speak your mind and think through some implications. Nothing wrong with that of course, but kind of telling about how much prior thought has been applied.

 

[femr2]

The NIST report claims a large number of the trusses disconnected, but not all.

Where is that in the report ? I just had a scan, and the opposite stands out...

 

[Dave Rogers]

I believe there is even something in the NIST report about a 2 inch deflection at 700 degrees and then later there is a lot of mumbo jumbo and viola we get 25 inches which is then expanded to 40+ inches by creep.

Rather than paraphrasing, perhaps you could quote specific references by page number. You're adding rather a lot of commentary here.

The only way to do this is to apply additional loading and the only way that could have happened is for the load from disconnected trusses to be applied to a remaining connected truss.

That's your opinion, rather than NIST's hypothesis, so it's rather dishonest to say that the NIST report claims that a large number of trusses were disconnected.

As for the floor assembly testing you don't say what the concrete and steel temperatures and floor loading were. You need to do that.

ASTM E119, as specified in NCSTAR1.6B, page 5. I presume that the estimate of 700ºC as the maximum temperature attained by the floor trusses is also your opinion, rather than a claim specifically made by NIST; if not, please provide a citation.

Dave

 

[BasqueArch]

The results for a 700 degree C temperature and 88 lbs./sq. ft. floor loading are below.

Temperature (degrees C) = 700
Span (ft.) = 60
Floor load (lbs./sq. ft.) = 88
% of room temp MOE for concrete at temperature = 43
% of room temp MOE for steel at temperature = 64
Concrete MOE (psi) = 1.81E+06
Steel MOE (psi) = 3.00E+07
Concrete MOE at temp (psi) = 7.78E+05
Steel MOE at temp (psi) = 1.92E+07Concrete slab thickness (in.) = 4
Slab centroid to top chord (in.) = 2.414
Top chord to bottom chord (in.) = 28.05
MOE ratio of steel to concrete = 2.47E+01
Effective slab width (in.) = 74.18
Transformed slab section area (in^2) = 1.20E+01
Top Chord area (in^2) = 3.25
Bottom Chord area (in^2) = 6.94E+00
Composite centroid distance from bottom (in.) = 2.1078E+01
Moment of Inertia double truss (in^4) = 4.30E+03
Deflection of main trusses (in.) = 2.08E+00



I can send you the spreadsheet if you like.

The calculations take into consideration the effect of temperature on the modulus of elasticity of both the concrete and steel in the composite beams.

I believe there is even something in the NIST report about a 2 inch deflection at 700 degrees and then later there is a lot of mumbo jumbo and viola we get 25 inches which is then expanded to 40+ inches by creep. The only way to do this is to apply additional loading and the only way that could have happened is for the load from disconnected trusses to be applied to a remaining connected truss.

As for the floor assembly testing you don't say what the concrete and steel temperatures and floor loading were. You need to do that.

What you don't calculate is the thermal expansion of the thin trusses at 700C. As they expand they buckle out of plane, largely losing their geometry and both their load carrying capacity and the horizontal bracing they previously provided to the exterior columns.

The trusses sagged more than 2" at 700C.

 

[Newtons Bit]

What you don't calculate is the thermal expansion of the thin trusses at 700C. As they expand they buckle out of plane, largely losing their geometry and both their load carrying capacity and the horizontal bracing they previously provided to the exterior columns.

The trusses sagged more than 2" at 700C.

That's pretty good for a layperson!

The top chord will have a problem with expansion inducing additional compression in the element. Under the parameters given, it will expand about 5.8" (sorry I work in US customary). Restraint on an end will pretty much be fatal. An element that is restrained from expansion on both ends will have an induced stress of 235ksi. It will buckle long, long before then.

The web members will also expand outwards. A differential expansion of web members will cause the bottom chord to develop kinks. This will also be fatal for the truss.

 

[Dave Rogers]

I could make some satirical comment about thermal expansion of steel being unknown before NIST's WTC7 report, but it would be like shooting fish in a barrel.

Dave

 

[ergo]

Where is that in the report ? I just had a scan, and the opposite stands out...

It is alluded to in the FAQ ( Dec '07 supplement) here:

Analyses of the composite floor system under fire exposures determined from fire dynamics simulations and thermal analyses, predicted sagging subsequent to truss web diagonal buckling and failure of some seated connections (see NIST NCSTAR 1-6C). However, the vast majority of the connections remained intact. Further, the shear studs that attached the floor slab to the spandrel, and the diagonal steel struts that connected the truss top chord to the intermediate columns were also capable of transferring inward pull forces. Thus, the sagging floors were capable of exerting an inward pull on the exterior columns and spandrel beams.

http://wtc.nist.gov/pubs/factsheets/faqs_12_2007.htm

referencing http://wtc.nist.gov/pubs/NISTNCSTAR1-6CDraft.pdf

But I can see why the video (which appears to have been televised) wouldn't want to get into those specifics since that would cause viewers to ask the same questions that Tony points out.

 

[ergo]

You're not kidding...

This one particularly is helpful. Thanks. It suggests the more probable cause of that inward sagging: the sinking of the core first.

 

[Dave Rogers]

It is alluded to in the FAQ ( Dec '07 supplement) here:



http://wtc.nist.gov/pubs/factsheets/faqs_12_2007.htm

referencing http://wtc.nist.gov/pubs/NISTNCSTAR1-6CDraft.pdf

But I can see why the video (which appears to have been televised) wouldn't want to get into those specifics since that would cause viewers to ask the same questions that Tony points out.

And I'm sure nobody would want to ask Tony how, in his view, "However, the vast majority of the connections remained intact" can be translated to "a large number of the trusses disconnected, but not all". After all, there's not much difference between those statements, is there?

Dave

 

[Newtons Bit]

It is alluded to in the FAQ ( Dec '07 supplement) here:



http://wtc.nist.gov/pubs/factsheets/faqs_12_2007.htm

referencing http://wtc.nist.gov/pubs/NISTNCSTAR1-6CDraft.pdf

But I can see why the video (which appears to have been televised) wouldn't want to get into those specifics since that would cause viewers to ask the same questions that Tony points out.

You mean the same questions that have already been sufficiently answered in this thread?

 

[ergo]

And I'm sure nobody would want to ask Tony how, in his view, "However, the vast majority of the connections remained intact" can be translated to "a large number of the trusses disconnected, but not all". After all, there's not much difference between those statements, is there?

Tony's model provides the explanation for how the floors could have sagged the way they did if the NIST truss sagging model is even partly to be believed. The video femr2 posted confirms this, as far as modelling the effects of heat. If you have a better scenario for how the floors could have sagged to that degree, why don't you share it?

 

[Dave Rogers]

Tony's model provides the explanation for how the floors could have sagged the way they did if the NIST truss sagging model is even partly to be believed. The video femr2 posted confirms this, as far as modelling the effects of heat. If you have a better scenario for how the floors could have sagged to that degree, why don't you share it?

Post #913 suggests a few pertinent points, I see. The point is that Tony pretended that NIST claimed things that he was the one actually claiming, when NIST claimed the opposite. It doesn't look good.

Dave