Analysis of Bazant & Zhou (2002)

Point 1 This paper was "rapid communication". It actually appears to have been only written in less that two days, published on 9/13/01: http://web.archive.org/web/20011031095744/http://www.tam.uiuc.edu/news/200109wtc/

So,

Point 1.1 Bazant & Zhou (2002) was not carefully crafted and well thought out, but something hastily thrown together in a matter of hours.

Point 1.2 Bazant & Zhou (2002) was not subject to a normal peer review process and probably received no peer review at all.


Points 1.1 and 1.2 do not follow from point 1 and cannot be considered more than idle speculation unless supported by evidence.

Point 2 Bazant and Zhou were forced to include an "Addendum" (pages 6-7) which answers six questions about the paper from skeptics in the structural engineering community. This appears to be the only "peer review" the paper received.

From points 1 & 2, we can conclude that this paper should not be described as being "peer reviewed" as the evidence indicates that it was not. This is obviously a low quality paper on its face.


The claim of the absence of peer review is unsupported, and appears to be contradicted by the publication of the paper and its addenda in a peer-reviewed journal. The quality of a paper is usually assessed based on number of cites (reflecting, generally, the importance of the paper) and on whether (and under what circumstances) its major findings are overturned (reflecting the correctness of the paper). Conclusions about the quality of a paper based on concerns other than its importance and correctness, such as the amount of time the authors spent writing it or the amount of dialog it generates in response, are unjustified. One might as well judge a paper by what typeface it's printed in.

Abstract: This paper presents a simplified approximate analysis of the overall collapse of the towers of World Trade Center in New York
on September 11, 2001. The analysis shows that if prolonged heating caused the majority of columns of a single floor to lose their load
carrying capacity
, the whole tower was doomed.


Point 3 In their abstract, Bazant & Zhou claim they only provide a "simplified approximate" analysis here, so in no way does this paper represent anything approaching precise and thorough explanation for the "collapse" of the WTC buildings. NIST deliberately committed a grave error by simply defering the very serious question of "gobal collapse" mechanism to this paper.


Analysis using simplifications and approximations of the system being analyzed are not at all unusual in science. The implicit claim is that the simplifcations and approximations do not substantially affect the conclusions. The way to challenge this claim is to make a case that the simplifications and approximations do in fact invalidate the authors' conclusions. Simply pointing out that the analysis is simplified and approximate, which is clearly acknowledged by the authors and understood by the editor, peer reviewers, and every reasonable reader, is not a worthwhile point of critique. The engineering community has had, and continues to have, ample time and opportunity to publish peer-reviewed papers challenging Bazant and Zhou's assumptions, approximations, and conclusions.

The last sentence, even if it were true, is a criticism of NIST, not of Bazant and Zhou.

Point 4 Bazant & Zhou assume "prolonged heating" initiated the "collapse" of the twin towers, but despite providing five multi-part figures they show no Time-Temperate Curves as neccessary to understand the behavior of steel in fires: http://en.wikipedia.org/wiki/Fire-resistance_rating Furthermore, Bazant & Zhou fail to mention any Time-Temperate Curve data in paper what-so-ever. From the lack of Time-Temperate Curves or data it is hard to understand how Bazant & Zhou could have provided any model for "collapse" stemming from "prolonged heating".


It is fairly well established that fires significantly increase the temperature of their surroundings. Do you demand a time vs. luminance curve when the weatherman says "it's sunny outside?" If you wish to challenge the claim that heating would occur as a result of large building fires, then provide a rationale for such a claim (as in, "this fire was different from all other fires because...[fill in the blank]").

Point 5 Bazant & Zhou claim that a "majority" of columns need to "lose their load carrying capacity" on a single floor to ensure "total collapse", however the authors fail to provide any equation to support this assertation. In fact, of the eight equations explicitly listed, none even use the number of columns (failed or otherwise) as a variable. Furthermore, no where in the paper do Bazant & Zhou even attempt to explain why a simple "majority" of columns are needed to fail in order for "global collapse" to ensue.


Your assemblage of quoted phrases misstates the paper's claim. The actual claim is that "Once more than about a half of the columns in the critical floor that is heated most suffer buckling (stage 3), the weight of the upper part of the structure above this floor can no longer be supported." Most of the body of the paper shows, step by step, why global collapse must ensue from this.

It is true that they do not explain why the weight of the upper part of the structure cannot be supported by less than about half the columns. This is a technical paper in a technical journal. You should not expect it to explain or cite information that is common knowledge among its intended readership.

Have you asked any engineers about this point? Are you making the contrary claim that half the columns on a floor should be able to support the load of buildings in general, or of the WTC towers in particular?

Point 6 Bazant & Zhou claim that columns "lose their load carrying capacity", but no where in the paper do the authors even attempt to show which columns are supposed to have done so. Moreover, since Bazant & Zhou explictly ignore the possibility of column facture, all columns should obviously retain some "load carrying capacity".


Buckled columns retain an insignificant fraction of their load carrying capacity. Again, this is a technical paper in a technical journal. It is not necessary or expected that it will repeat basic facts that are already common knowledge among its intended readership.

Not specifying which columns buckled is among the "simplifications and assumptions" that the paper acknoweldges. To challenge this, show how which specific columns buckled would make a difference in the paper's conclusions.

Point 7 Bazant & Zhou claim that heating lowered the yield strength of the column materials, but no where do they provide any numerical estimates of any yield strength.


Curves of temperature of steel versus strength are commonly available throughout the literature. Are you making a contrary claim that heating does not lower the yield strength, or are you just faulting them for not including more Engineering 101 information in the paper for your convenience?

If you think this point invalidates their conclusions, then provide your own numerical estimates of the columns' yield strength, and show that they falsify Bazant and Zhou's scenario.

Point 8 Bazant & Zhou claim viscoelastic creep lead to buckling, however they provide no equations for creep, nor do they discuss creep further in the paper. Moreover, the authors fail to explain the relationship between creep and yield strength.


There's that "fail to explain" basic facts again. Gee, you'd think they were writing a technical paper in a technical journal for a technical audience, rather than an introductory textbook. Oh, wait...

Point 9 Bazant & Zhou claim a "likely scenario of failure" but provide absolutely no estimates of probability for any failure scenarios, nor do they even bother to consider other possible failure scenarios.


If they'd claimed to show an exact probability of their scenario, or to have determined the only possible failure scenario, or even to have determined the most likely possible failure scenario, then you'd have a point here. As it is, you've just pointed out that the claim they did make is completely consistent with the content of the paper.


Point 10 Bazant & Zhou claim their model is for "sustained temperatures apparently exceeding 800°C", however, actual tests of uninsulated steel show temperatures never exceed 360°C. Furthermore, NIST's report indicates by paint analysis that only three out of sixteen perimeter columns examined reached temperatures above 250°C and neither two core columns examined reached temperatures above 250°C. Moreover, NIST metallography showed no evidence of temperature higher than 600°C.
http://911research.wtc7.net/essays/nist/index.html#exaggeration
Ref. NIST Report, pages 90/140.


I just heated a piece of uninsulated steel over my gas stove for a few minutes, and it became orange-hot, which shows that it reached a temperature well over 360° C. Therefore your claim that "actual tests of uninsulated steel show temperatures never exceed 360°C" is falsified.

None of the other NIST findings that you report are evidence that steel in the critical floor did not reach 800°C. Only that some of the columns they tested did not, and that the tests available to them were unable, by the nature of the test, to distinguish temperatures above 600°C.

Point 11 Without providing any quantitative basis, model or even an estimate, Bazant & Zhou claim a significant portion of steel-insulation was dislocated.


The actual statement in the paper is this: "The heating is probably accelerated by a loss of the protective thermal insulation of steel during the initial blast." Note "probably," and that no mention is made of what portion.

Nonetheless this is indeed a point of contention. Some engineers believe that dislocation of insulation was not a significant factor, because the steel would have heated to failure anyhow, and/or because the insulation was already damaged or inadequate before the impact.

Or are you making a contrary claim that dislocation of insulation would not have occurred? If so, what protected the insulation from dislocation?

Point 12 Bazant & Zhou fail to provide any consideration of the amount of air flow that would have been required for any fire to reach 800°C in 56 minutes.
http://www.opednews.com/articles/opedne_joseph_s_070522_oh_yeah_2c_here_s_anot.htm


Perhaps because the temperature reached by a fire is not particularly sensitive to the amount of air flow. Even a fire in a sealed room, zero air flow, can reach 800°C. But the exhausting of smoke shows that the air flow in the WTC tower fires was greater than zero.

Page 1, Paragraph 2:

The vertical impact of the mass of the upper part onto the lower part (stage 4) applies enormous vertical dynamic load on the underlying structure, far exceeding its load capacity, even though it is not heated. This causes failure of an underlying multifloor segment of the tower (stage 4), in which the failure of the connections of the floor-carrying trusses to the columns is either accompanied or quickly followed by buckling of the core columns and overall buckling of the framed tube, with the buckles probably spanning the height of many floors (stage 5), at right, and the upper part possibly getting wedged inside an emptied lower part of the framed tube (stage 5), at left. The buckling is initially plastic but quickly leads to fracture in the plastic hinges.


Point 13 Bazant & Zhou claim failure proceeds by many floors at time, however, the demolition waves clearly visible in the "collapse" video indicates some other process is under way.


There's no contradiction with the observed behavior, if the fractures occurred primarily near the top floors of the "many floors" whose columns were buckling at any given time. There is no claim that the fractures themselves would occur many floors at a time.

Point 14 Bazant & Zhou claim the failure mechanism is characterized by buckling that "probably span[] the height of many floors", yet no such multi-story buckles were found in the debris. Moreover, the debris columns are largely buckle-free.


Most of the column failures were at the welds/connections. Bazant and Zhou may not have been aware of this detail at the time, but it doesn't affect their conclusions. The plastic deformations they hypothesize would have absorbed more energy than elastic deformation followed by weld failure, so their assumption is conservative against progressive collapse.

Point 15 Despite stating that buckling quickly leads to fracture, the authors fails consider any role that fracture might play in the "collapse" mechanism such as leading to the building-top tipping over.


Perhaps they felt that the causal connection between the columns fracturing and the loads supported by those columns falling down did not need to be explained to an educated audience.

Tipping is addressed in appendix II.


Point 16 Bazant & Zhou fail to even consider why multi-column perimeter sections can be seen peeling off the sides of tower during "collapse".


Actually they do consider one likely mechanism for this:

"...and the upper part possibly getting wedged inside an emptied lower part of the framed tube..."

Point 17 Bazant & Zhou fail to even consider how steel sections of up to 10 tons are ejected during the "collapse" and lodged in adjacent buildings.


Actually they do. "Buckling" of a column implies lateral displacement of a portion of the column. The load on a buckled column would likely result in lateral movement. Though they don't explain it explicitly, "ejected" debris is an obvious expected consequence of their scenario.

Point 18 Bazant & Zhou fail to even consider how all of the concrete is pulverized in dust, nor the energy required to do so.
http://911research.wtc7.net/papers/dustvolume/index.html


So, then, that would be one of the "simplifications" they openly acknowledge exist in their scenario. They state that "errors by a factor of two would not be surprising" but would not affect their conclusions." Can you show that inclusion of concrete pulverization in their scenario would affect their calculations by more than a factor of 2?

Point 19 Bazant & Zhou fail any details of the mechanism of the clearly systematic floor by floor failure in terms of perimeter columns, core columns and trusses. Exactly how these parts interact with each other is left unconsidered.


Not within the scope of this paper, though they do describe the general characteristics of such interactions:

"For example, the upper part of one tower is tilting as it begins to fall (see Appendix II); the distribution of impact forces among the underlying columns of the framed tube and the core, and between the columns and the floor-supporting trusses, is highly nonuniform..."

"For our purpose, we may assume that all the impact forces go into the columns and are distributed among them equally. Unlikely though such a distribution may be, it is nevertheless the most optimistic hypothesis to make because the resistance of the building to the impact is, for such a distribution, the highest. If the building is found to fail under a uniform distribution of the impact forces, it would fail under any other distribution."

If you would like to perform an analysis or simulation of exactly how all the parts of the collapsing structure would interact with each other, floor by floor, for the entire collapse, I'd be eager to see the results.

Respectfully,
Myriad
 
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Would it not been simpler to - lessay - create an OP with ALL of the points of critique?
 
707, low fuel, low speed, lost in the fog - 187 pounds of TNT energy at impact (not many people in the world understand this; ask the chief engineer of the WTC about this design)

Wrong again, your bunk is junk.
707 DC 8, 600 m.p.h. High speed and the motivation (lost in fog as opposed to deliberatively flown into in junk as well.)

See this NIST NCSTAR 1-2 WTC Investigation report...
 

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Wrong again, your bunk is junk.
707 DC 8, 600 m.p.h. High speed and the motivation (lost in fog as opposed to deliberatively flown into in junk as well.)

See this NIST NCSTAR 1-2 WTC Investigation report...

Wrong again, your bunk is junk.

NIST FAQ said:
As stated in Section 5.3.2 of NIST NCSTAR 1, a document from the Port Authority of New York and New Jersey (PANYNJ) indicated that the impact of a [single, not multiple] Boeing 707 aircraft was analyzed during the design stage of the WTC towers. However, NIST investigators were unable to locate any documentation of the criteria and method used in the impact analysis and, therefore, were unable to verify the assertion that “… such collision would result in only local damage which could not cause collapse or substantial damage to the building.…”

http://wtc.nist.gov/pubs/factsheets/faqs_8_2006.htm
 
You do understand the insulation on the core was wall board, and under the floors was spray on, very fragile.
Think the fire proofing was disloged.
[qimg]http://www.internationalskeptics.com/forums/imagehosting/879046a66b7c96bf7.jpg[/qimg]
Oops, look like you made an error. It looks like the impact dislodged tons of insulation and columns too. A reminder, the fire insulation is wall board. Yes the stuff my roommate in college punch holes though with his fist. Bet you forgot to see what the insulation was made of.

Visually debunked! See?

Great fire. Just how much fuel does a plane have to carry in order to achieve this.
 
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If Mr. anderson can't do it in his own words, then he is just spamming someone else's work, and that is just simply plagiarizing.

He could have simply set up his own free website to post his thoughts and come back when he was ready to discuss. No, he simply is not seriuos about this involvement or seeking the "truth".

Ignore this thread.
 
This isn't an analysis. It's maybe notes one could use to make an analysis (even though most of the "points" are pretty stupid). I spend over 10 hours on this and still need to put a little bit more time into editing. Bofors work is what, 10 minutes?
 
This isn't an analysis. It's maybe notes one could use to make an analysis (even though most of the "points" are pretty stupid). I spend over 10 hours on this and still need to put a little bit more time into editing. Bofors work is what, 10 minutes?


Fifty-one posts to address recycled nonsense cribbed from Jim Hoffman, who refuses to defend his work in any venue.
 
The Bazant report is what got NIST in trouble. They adopted his thrown together quickly theory and ran with it. Unfortunately as they did their physical fire testing to work backwards to support this theory they couldn't reach the results to support it. That's why for one thing they blame building content fire more then jet fuel. They then went to the computer and had to keep tweaking the numbers so they stopped at initiation and bailed out.

Ummm...wrong. Where is your proof that NIST kept "tweaking the numbers"?
 
Point 13 Bazant & Zhou claim failure proceeds by many floors at time, however, the demolition waves clearly visible in the "collapse" video indicates some other process is under way.

I'd love to see where you are going with that.

Point 14 Bazant & Zhou claim the failure mechanism is characterized by buckling that "probably span[] the height of many floors", yet no such multi-story buckles were found in the debris. Moreover, the debris columns are largely buckle-free.

Bazant calculated a buckling mechanism, as well as making several other assumptions in the paper to justify that the calculation was wholly in favor of building survival. It is quite obvious that the column splices in the core or the bolt group in the perimeter would be likely to fail first, however his Wg/Wp ratio was meant to be a lower bound, and if he calculated for fracture it would not be so.

Point 15 Despite stating that buckling quickly leads to fracture, the authors fails consider any role that fracture might play in the "collapse" mechanism such as leading to the building-top tipping over.

erm, taking fracture into account would actually show that the building would be less likely to tip, read appendix 2

Point 16 Bazant & Zhou fail to even consider why multi-column perimeter sections can be seen peeling off the sides of tower during "collapse".

see above, and read again why he wrote the paper:

Bazant and Zhou said:
Since we are not attempting to model the details
of the real failure mechanism but seek only to prove that the
towers must have collapsed and do so in the way seen ~‘‘Massive’’
2001; American 2001!, we will here neglect fracture, even
though the development of fractures, especially in column connections,
is clearly discerned in the photographs of the collapse.

Point 17 Bazant & Zhou fail to even consider how steel sections of up to 10 tons are ejected during the "collapse" and lodged in adjacent buildings.

clearly that is beyond the scope of their paper, however, using their model, it is treated in a paper here on page 101

Point 18 Bazant & Zhou fail to even consider how all of the concrete is pulverized in dust, nor the energy required to do so.
http://911research.wtc7.net/papers/dustvolume/index.html

also beyond the scope of the paper, the WTC concrete is treated in Bazant's latest paper, co authored by a poster called Apollo, who has written other papers on the WTC concrete.

Point 19 Bazant & Zhou fail any details of the mechanism of the clearly systematic floor by floor failure in terms of perimeter columns, core columns and trusses. Exactly how these parts interact with each other is left unconsidered.

again, see why he wrote the paper in the first place. He took a scenario that he admits does not match photo evidence in order to justify a model in favor of building survival.
 
Wrong again, your bunk is junk.
707 DC 8, 600 m.p.h.
Now you just need to explain why someone in the 1960s would think a 707 flying at 600 miles per hour at an altitude of 1,000 feet is a realistic scenario that needed to be accounted for.

Great fire. Just how much fuel does a plane have to carry in order to achieve this.
Considering that most structures human being live and work in are filled with combustible materials, I'd venture that all you really need is enough fuel to ignite a fire which sets all that combustible material on fire.

Heck, even aircraft cabins are filled with combustible materials which burn quite well. That's the reason for the requirement that an aircraft be capable of getting all its passengers out in 90 seconds. Because anything longer than that and it's too late.
 
Page 1, Paragraph 3:


Elastic Dynamic Analysis
The details of the failure process after the decisive initial trigger
that sets the upper part in motion are of course very complicated
and their clarification would require large computer simulations
.
For example, the upper part of one tower is tilting as it begins to
fall (Appendix II); the distribution of impact forces among the
underlying columns of the framed tube and the core, and between
the columns and the floor-supporting trusses, is highly nonuni-
form
; etc. However, a computer is not necessary to conclude that
the collapse of the majority of columns of one floor must have
caused the whole tower to collapse
. This may be demonstrated by
the following elementary calculations, in which simplifying as-
sumptions most optimistic
in regard to survival are made.


Point 20 Bazant & Zhou fail to elucidate or even propose what the "decisive initial trigger" was for either of the twin towers.

Point 21 Bazant & Zhou claim the "collapse" mechanism is "very complicated" yet they proceed with "elementary calculations".

Point 22 Bazant & Zhou claim that "clarification [of the post-initialization failure process] would require large computer simulations" but do none (and neither does NIST).

Point 23 Bazant & Zhou claim "the distribution of impact forces... is highly nonuniform" yet explicitly assume perfect uniformity in their failure model.

Point 24 Bazant & Zhou claim the individual "collapse" of columns must have caused the entire towers to failure, but ductile steel columns simply do not "collapse" per se, no they buckle, bend and break instead.

Point 25 If a simple "majority of columns of one floor" have collapsed, the tower must be tilting. Repetition of this process means that the tilt angle would increase floor-by-floor. The angular momentum of this tilting would accelerate the tilting speed and the building-top would evenetually fall off.

Point 26 Bazant & Zhou claim to have used "most optimistic" assumptions, yet proceed to develop a model derived from the pessimistic assumptions of sustained 800oC temperatures and significant loss of fireproofing material.
 
And that my friends, is a prime example of what the A/E For 9/11 truth has to offer. Just like Gage himself, the members create nothing new. They simply regurgitate others work. If they were general academics, I could almost excuse it, but these are people who are SUPPOSE to have expertise in the field of interest, yet not an original analysis among them.

And they wonder why we give them little credibility.

TAM:)
 
And that my friends, is a prime example of what the A/E For 9/11 truth has to offer. Just like Gage himself, the members create nothing new. They simply regurgitate others work. If they were general academics, I could almost excuse it, but these are people who are SUPPOSE to have expertise in the field of interest, yet not an original analysis among them.

And they wonder why we give them little credibility.

TAM:)

No kidding. My brain hurts from all of this.
 
Point 24 Bazant & Zhou claim the individual "collapse" of columns must have caused the entire towers to failure, but ductile steel columns simply do not "collapse" per se, no they buckle, bend and break instead.
I'm not familiar with the terms "buckle failure" "bend failure" and "break failure" anymore than I am with "collapse failure". Wouldn't one more correctly use compression, tension, torsion, or shear?
 
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Point 1.1 Bazant & Zhou (2002) was not carefully crafted and well thought out, but something hastily thrown together in a matter of hours.

Point 1.2 Bazant & Zhou (2002) was not subject to a normal peer review process and probably received no peer review at all.

Point 1) Bazant is an extremely competant civil engineer and one of the foremost experts in his field.


Point 2) The buildings were steel, structural damage was known to have occurred, fires were known to have been extensive, steel begins losing tensile strength at just 300 degrees C has lost half its strength at 600 degrees C, and has roughly 10% of its tensile strength by 1000 degrees C, and at those temperatures it has not yet come close to melting.

Point 3) Every civil engineer has to gain an understanding of hookes law, and of clockwise bending moments. As can be seen from photographs of the collapse, the collapse initiated with a bending moment, and having read his paper, and being an engineer myself, I cannot fault the reasoning in the paper.

Point 4) Bazant & Zhou's paper was peer reviewed by the Journal of Engineering Mechanics who supported the conclusions of the paper.

Point 5) NO ALTERNATIVE HYPOTHESIS HAS EVER BEEN SUBMITTED FOR PEER REVIEW IN A RECOGNISED JOURNAL OF ENGINEERING SCIENCE.

Here's some relavent journals that the so called experts of the 'truth' movement could submit their work to:

http://www.pubs.asce.org/journals/

http://www.aisc.org/

Bazant appears to have submitted 251 academic papers for peer review, on the topic of structural engineering.

How many papers has (for example) Stephen Jones Phd (nuclear physics) submitted on that same topic ? Answer: 0
...................................................................

Work submitted by Zdenek Bazant between 2007, and 1997:


2007 Asymptotic Prediction of Energetic-Statistical Size Effect from Deterministic Finite-Element Solutions

2007 Microplane Model M5f for Multiaxial Behavior and Fracture of Fiber-Reinforced Concrete

2006 Reliability, Brittleness, Covert Understrength Factors, and Fringe Formulas in Concrete Design Codes

2006 Size Effect on Strength of Quasi -- Brittle Structures with Reentrant Corners Symmetrically Loaded in Tension

2005 Designing Against Size Effect on Shear Strength of Reinforced Concrete Beams without Stirrups: I. Formulation

2005 Designing Against Size Effect on Shear Strength of Reinforced Concrete Beams without Stirrups: II. Verification and Calibration

2005 Microplane Model M5 with Kinematic and Static Constraints for Concrete Fracture and Anelasticity. I: Theory

2005 Microplane Model M5 with Kinematic and Static Constraints for Concrete Fracture and Anelasticity. II: Computation

2005 Model-Based Simulation of Durability of Materials and Structures

2004 Temperature Effect on Concrete Creep Modeled by Microprestress-Solidification Theory

2003 Asymptotic Matching Analysis of Scaling of Structural Failure Due to Softening Hinges. I: Theory

2003 Asymptotic Matching Analysis of Scaling of Structural Failure Due to Softening Hinges. II: Implications

2003 Cohesive Fracturing and Stresses Caused by Hydration Heat in Massive Concrete Wall

2003 Confinement-Shear Lattice Model for Concrete Damage in Tension and Compression: I. Theory

2003 Confinement-Shear Lattice Model for Concrete Damage in Tension and Compression: II: Computation and Validation

2003 Decontamination of Radionuclides from Concrete by Microwave Heating. I: Theory

2003 Decontamination of Radionuclides from Concrete by Microwave Heating. II: Computations

2003 Nonlocal Integral Formulations of Plasticity and Damage: Survey of Progress

2002 Addendum to "Why Did the World Trade Center Collapse?--Simple Analysis"¹

2002 Continuous Relaxation Spectrum for Concrete Creep and its Incorporation into Microplane Model M4

2002 Discussion of "Fracture Analysis of High Strength Concrete Members"

2002 Lateral Confinement Needed to Suppress Softening of Concrete in Compression

2002 Nonlocal Integral Formulations of Plasticity and Damage: Survey of Progress

2002 Size Effect Hidden in Excessive Dead Load Factor

2002 Size Effect on Strength of Floating Sea Ice under Vertical Line Load

2002 Vertex Effect in Strain-Softening Concrete at Rotating Principal Axes

2002 Why Did the World Trade Center Collapse?--Simple Analysis

2001 Fracture Analysis of High Strength Concrete Members

2001 Size Effect in Concrete Columns: Finite-Element Analysis with Microplane Model

2000 Fracture Mechanics of ASR in Concretes with Waste Glass Particles of Different Sizes

2000 Fracturing Rate Effect and Creep in Microplane Model for Dynamics

2000 Large-Strain Generalization of Microplane Model for Concrete and Application

2000 Microplane Model M4 for Concrete. I: Formulation with Work-Conjugate Deviatoric Stress

2000 Microplane Model M4 for Concrete. II: Algorithm and Calibration

2000 Probabilistic Nonlocal Theory for Quasibrittle Fracture Initiation and Size Effect. I: Theory

2000 Probabilistic Nonlocal Theory for Quasibrittle Fracture Initiation and Size Effect. II: Application

1999 The "Chunnel" Fire. I: Chemoplastic Softening in Rapidly Heated Concrete

1999 Compound Size Effect in Composite Beams with Softening Connectors. I: Energy Approach

1999 Compound Size Effect in Composite Beams with Softening Connectors. II: Differential Equations and Behavior

1999 Effects of Size and Slenderness on Ductility of Fracturing Structures

1999 Modeling Chloride Penetration in Saturated Concrete

1999 Size Effect on Failure of Bond Splices of Steel Bars in Concrete Beams

1998 Acoustic Emissions in Fracturing Sea Ice Plate Simulated by Particle System

1998 Size Effect in Penetration of Sea Ice Plate with Part-Through Cracks. I: Theory

1998 Size Effect in Penetration of Sea Ice Plate with Part-Through Cracks. II: Results

1998 Triaxial Composite Model for Basic Creep of Concrete

1997 Crack Growth and Lifetime of Concrete under Long Time Loading

1997 Discussion of "Algebraic Methods For Creep Analysis of Continuous Composite Beams"

1997 Fracturing Truss Model: Size Effect in Shear Failure of Reinforced Concrete

1997 Inelastic Buckling of Concrete Column in Braced Frame

1997 Microprestress-Solidification Theory for Concrete Creep I: Aging and Drying Effects

1997 Microprestress-Solidification Theory for Concrete Creep. II: Algorithm and Verification

1997 Postcritical Imperfection-Sensitive Buckling and Optimal Bracing of Large Regular Frames

1997 Size Effect in Compression Fracture: Splitting Crack Band Propagation

1997 Theory of Crack Spacing in Concrete Pavements

.......................................................

Bazant & Zhou, with no access to actual samples from the WTC's gave a very very accurate description of what actually occurred. The only mistake in his paper, was the temperatures he predicted, which were in fact lower than he had thought. But having said that, steel would have still lost significant tensile strength from the fires and this was enough to affect the structure, and it caused creep failiure resulting in a bending moment.
 

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