Journal of 9/11 Studies Letters, September, 2014 ASCE Journals refuse to correct fraudulent paper they published on WTC collapses By Tony Szamboti and Richard Johns September 3, 2014 In January 2011 one of the ASCE Journals (the Journal of Engineering Mechanics) published a paper by Jia-Liang Le and Zdenek Bazant entitled “Why the Observed Motion History of the World Trade Center Towers is Smooth”. This paper attempted to calculate the velocity loss of the falling upper section of WTC 1, when it landed on the first intact story, and claimed that this ‘jolt’ (loss of velocity) would be too small to observe. This conclusion is unsound, as it is based on assumptions about the tower that conflict with information provided in the NIST reports on 9/11 and contains internal contradictions and inconsistencies. A Discussion paper pointing out these problems was submitted to the same journal in May 2011, but after keeping the paper in review for 27 months the journal’s editors finally declined it in August 2013 on the grounds that it is “out of scope” for the journal. The following is a summary of the events surrounding these papers. The Le and Bazant paper was apparently written in response to a paper by Graeme MacQueen and Tony Szamboti (“The Missing Jolt: A Simple Refutation of the NIST-Bazant Collapse Hypothesis”, Journal of 9/11 Studies, 2009), although the authors simply referred to MacQueen and Szamboti’s work as “… a new objection, pertaining to the smoothness of the observed motion history of the tower top, … raised and disseminated on the Internet”. Prior to Le and Bazant’s paper being published in 2011, Szamboti, a mechanical engineer working in Philadelphia, had been discussing this issue of the smooth downward motion of WTC 1, or “missing jolt”, with Richard Johns, a Canadian philosopher of science. Johns, whose first degree is in engineering mathematics, was puzzled as to why the intact steel columns below the fire zone had offered so little resistance to the falling mass and sought expert advice. Szamboti was able to confirm Johns’ suspicion of inconsistencies (concerning the resistance of a buckling column) in an earlier 2001 JEM published paper by Bazant. Not surprisingly, when Le and Bazant’s new paper on the “missing jolt” problem was published, Szamboti and Johns read it carefully. They were astonished to find errors of a very clear and unambiguous kind, apparently stemming from the use of input values that differed from those provided by the NIST in their WTC report. For example, in calculating the resistance of a column as it buckles, using Bazant’s “3 hinge” buckling model, the key value is the column’s plastic moment Mp. Le and Bazant simply state this to be 0.32 MNm, for an average column on the first impacted floor. They do not derive it, as one would expect, from more fundamental data, such as the average column’s physical dimensions and the type of steel used. Moreover, when Szamboti and Johns calculated the Mp themselves, from the data provided by NIST, they obtained the value of 0.64 MNm, which gives the columns double the resistance assumed by the Le and Bazant paper. After finding this, and other significant errors which drastically affected the conclusion of the Le and Bazant paper, Szamboti and Johns wrote a Discussion paper correcting the Le and Bazant inaccuracies and submitted it to the Journal of Engineering Mechanics in May 2011, within their five-month window for discussion of a paper from the time it was published. They then waited for a full year, until May 2012, to hear results of a peer review. At that time they were told their paper was rejected by just one reviewer, as a second reviewer did not respond. However, when they read the review they were surprised at its lack of justification for rejecting their paper and responded with a rebuttal, showing it to be incorrect on almost every point. The rebuttal forced the Journal of Engineering Mechanics to reconsider the Szamboti and Johns Discussion paper, informing the authors that it would only require an editorial review and would not have to go back through a peer review process. 1

Journal of 9/11 Studies Letters, September, 2014 Another full year passed with no action by the Journal of Engineering Mechanics editors. Frustrated by this further delay, in May 2013 Szamboti and Johns sent a letter asking about their Discussion paper’s status directly to the chief editors, Kaspar Willam and Roberto Ballarini. After three additional months passed, in August 2013 Willam and Ballarini informed Szamboti and Johns that their Discussion paper was “out of scope” for the Journal of Engineering Mechanics. It is not possible for a Discussion paper, one that simply corrects errors in a paper that is already published, to be out of scope for a journal. Therefore Szamboti and Johns viewed this verdict as clear proof that the editors were unwilling to allow Le and Bazant’s paper to be corrected. When asked directly whether he would be publishing at least an errata for the Le and Bazant paper, Ballarini replied that he would not, since (in his words) “I am not an expert in forensics, and therefore do not plan to perform an analysis of the WTC collapse myself.” Of course a civil engineer of Prof. Ballarini’s ability and experience would at least be able to repeat the simple calculations involved, using the public NIST data that Szamboti and Johns referenced, to see if he got the same answers. An appeal explaining the issue was sent to the Director of ASCE Journals, Angela Cochran, asking her to intercede. She quickly remanded the matter to the Engineering Mechanics Institute Board of Governors, which is the ASCE committee that has oversight over the Journal of Engineering Mechanics. Incredibly, the President of the Board of Governors, Roger Ghanem, stated in a letter to Szamboti and Johns that, while he was apologetic for the delay in processing their paper, he felt they were treated fairly and stood by the original review and rejection. This was all done without finding any error in Szamboti and Johns’ work, or explaining how a Discussion paper could be out of the journal’s scope. In further email discussion, Prof. Ghanem cagily stated, “While your paper may very well be within the scope of the Journal, the Board's review of your case was concerned with whether or not the submission was treated fairly and in a manner that is consistent with the policies of the Journal of Engineering Mechanics.” The Szamboti and Johns paper showed the Journal of Engineering Mechanics editors, in a definitive way, that the Le and Bazant paper was grossly incorrect and that correction of their inputs gave results which were in complete opposition to their claims. Amazingly, the Le and Bazant paper still sits on the Journal of Engineering Mechanics uncorrected. Since nothing was done by them to correct it, after their being alerted to the inaccuracies, the ASCE editors and their Board of Governors are now in violation of their own ethics and complicit in what can only be considered a deliberate misleading of the engineering profession and the public in general regarding the WTC collapses. The Le and Bazant January 2011 JEM paper can be found on the Internet at the link below http://www.civil.northwestern.edu/people/bazant/PDFs/Papers/499.pdf The Szamboti and Johns Discussion paper critiquing it, the JEM review comments and their rebuttal to it, and the resubmitted Discussion paper are included below on pages 3 through 17 for the reader to see just what the issues are for themselves. 2

Journal of 9/11 Studies Letters, September, 2014 Original submission of Discussion of the paper Why the Observed Motion History of World trade Center Towers is Smooth By Ja-Liang Le and Zdenek Bazant DOI: 10.1061/_ASCE_EM.1943-7889.0000198 Journal of Engineering Mechanics, Vol. 137, No. 1, January 1, 2011, pg. 82-84 Tony Szamboti Richard Johns 1. Introduction In their paper, Le and Bazant respond to the claim that the motion of the roofline of the World Trade Center North Tower (WTC 1), as captured in video footage, is inconsistent with the hypothesis of gravity- driven progressive collapse. Unfortunately they do not give any sources for this claim, but it is likely that they are responding to the work of Chandler (2010) and MacQueen and Szamboti (2009). It is agreed on all sides that the collapse of WTC 1 initiated at the 98th floor leaving a 12-story upper part to fall onto a stationary 97-story lower part, as stated by NIST NCSAR 1-6, p. 156. Le and Bazant calculate the size of the velocity reduction (during impact between the falling upper part of the tower and the stationary lower part) to be about 3%. They also find that, after impact, the upper part continues to accelerate downwards at 6.2 m/s2. These calculations are unfortunately based on assumptions about WTC 1, especially regarding the steel columns on story 97, which are without justification, and which are contradicted by NIST. 2. Inertia Resistance Le and Bazant first calculate the slowing of the upper portion of the building due to the inertia of the first story impacted. For reasons that unfortunately are not specified, the authors consider only the mass of the concrete floor slab to be involved in this exchange of momentum. Hence they calculate the effect of a descending mass of 54.18 Mkg striking a stationary mass of 0.627 Mkg. However, the concrete floor slab is only a small part of the floor, which includes rebar, steel decking, truss work, and of course the live load. According to Bazant and Le (2008), from which Le and Bazant obtain the data used in their paper, m2 = the mass of a single story is 3.87 Mkg for WTC 1. Using this value, rather than the mass of the concrete slab alone, we get a velocity ratio of 54.18/(54.18 + 3.87) = 0.93. The velocity lost is therefore about 7% of the original, rather than the 1.1% claimed. (Note that this is already more than the 3% total loss calculated by Le and Bazant.) 3

Journal of 9/11 Studies Letters, September, 2014 3. Column resistance The 287 columns on the 97th story are treated by Le and Bazant as identical, even though the 47 core columns were on average much stockier than the 240 perimeter columns. The data used for a single column seem to be describing a perimeter column (stated in NIST NCSTAR 1-3D, p. 4 to be 14” square box columns) since the value Mp = 0.32 MNm may be obtained for a 14” square box column with wall thickness 6.75mm, or 0.27”, according to the usual formula: (b is the breadth of each flange, t is the flange thickness, and Fy is the yield stress, assumed by Le and Bazant to be 0.248 GN/m2.) This flange thickness 0.27” is roughly consistent with the NIST NCSTAR 1-3D report, which states that “As the elevation in the building increased, the thickness of the plates in the columns decreased, but the plates were always at least 0.25 thick”. (p. 5) The first error is then revealed when we apply this column specification, implicitly used by Le and Bazant, to calculate the total cross-sectional area of the columns. We then obtain a total area A = 2.75m2, for the 287 columns, which is much less than the authors’ own value of 6.05m2. One is bound to wonder how this value of 6.05m2 was obtained, since no reference or calculation is given for it. We shall show below that the correct value is roughly A = 2.3 (perimeter) + 1.7 (core) = 4m2. The authors’ second error is to use a value of Fy = 0.248 GN/m2 (36 ksi) for the yield stress of the columns on the 97th story. This is incorrect, as thin-walled perimeter columns on the upper stories are reported by NIST to be 55ksi – 100ksi (NCSTAR 1-6, p. 61, and NCSTAR 1-3B, Table 4-2, p. 52). We will conservatively estimate the average yield stress to be 65ksi, i.e. 0.45 GN/m2. Since the formula for Mp is linear with the yield stress Fy, correction of this error increases the value of Mp for the perimeter columns to 0.58 MNm. This is a very conservative estimate, since NIST reports the actual yield stresses to be above the nominal ones. (NCSTAR 1-6, p. 61) We see that the authors’ estimate of 0.32 MNm is hardly an upper bound. The calculation of Mp for the core columns is laborious, since the columns are a variety of sizes and steel types. They are wide-flange columns, with flange dimensions ranging from 16.695” x 3.033” down to 8” x 0.528”, and either 36, 42, 45, or 50 ksi. (See the publicly available NIST SAP2000 model data, reproduced by MacQueen and Szamboti (2009), pp. 22-3.) The Mp values range from 2.01 MNm down to 0.09 MNm, with the average being 0.75 MNm. Again, this is far above the authors’ estimate of 0.32 MNm. With these corrections in place, let us calculate the total yield load for all the columns. First the 240 perimeter columns: P = 240 x 0.00675 x 4 x 0.3556 x 0.45 x 109 = 1.04 GN. The calculation for the core is more laborious, due to the variation in column dimensions and yield stress. But using the same columns data, the total cross-sectional area of the core columns is found to be 1.69 m2, and the maximum load is 0.46 GN. 4

Journal of 9/11 Studies Letters, September, 2014 Using these corrected values, we can calculate the load-displacement curve. For this we also need the column length, L, which is 3.7m in the case of the core columns, and 2.3m for the perimeter columns, due to the 1.4 m deep spandrel plates. The resistive force Fb is given by the formula below, where the number of columns is n, and u the reduction in column length. Adding the two resistive forces, due to the perimeter and core columns, we get the graph shown in Fig. 1. Ueq (54 Mkg upper part mass) Ueq ( 33 Mkg upper part mass) Fig. 1. Diagram of load vs. displacement during axial deformation and buckling By inspecting this graph we see that ueq, the displacement at which the column resistance equals the 0.53 GN weight of the upper part (i.e. the 54 Mkg mass used by Le and Bazant) is roughly 0.38m, rather than the 0.065m claimed. Up to this point we have used Le and Bazant’s mass value of 54 Mkg for the upper part of the tower, but this is probably an overestimate since it conflicts with the data provided in the NIST WTC report concerning their description of the floor structures, total steel weight found in contracts, and live and superimposed dead loads. A more reasonable estimate, based on these data, is 33 Mkg for the 12-story upper part, i.e. 2.75 Mkg per story. This lower estimate is also much closer to typical mass per square meter values for other buildings sharing this type of construction, such as the Sears Tower and John Hancock building. For a detailed treatment of these arguments, see Urich (2007). From here on, therefore, we shall calculate using the 33 Mkg value as well as Le and Bazant’s 54 Mkg. For example, using the lower mass value, ueq occurs at roughly 1.12m as shown in Fig. 1. 5

Journal of 9/11 Studies Letters, September, 2014 4. Calculating the Velocity Curve In order to verify the accuracy of the gravity-driven model, we shall calculate the velocity curve for the roof line, and compare it with the behavior of WTC 1 itself. Fortunately there is high-resolution footage of the collapse of WTC 1 shot by professional filmmaker Etienne Sauret, and used for the documentary film WTC - The First 24 Hours (2002). Each pixel of this footage represents 0.27m of the tower, and the frame rate is 30 per second, allowing for very accurate measurements of the motion. David Chandler, one of the “internet” sources that Le and Bazant presumably refer to, has analyzed this motion using Tracker, an open source video analysis tool. His graph is shown below, together with two velocity plots for a gravity-driven collapse. The calculated velocity of the roofline was obtained numerically using the load-displacement curve shown above. We also assumed Le and Bazant’s freefall acceleration during the collapse of the first story, and the two possible mass values, as mentioned above. The floors are treated as rigid and incompressible, so that no energy is lost deforming them, even though in reality this would be a significant energy drain. The upper part of the building is also modeled as a rigid block, which Le and Bazant regard as a reasonable approximation. Velocity vs. Time for Roofline of WTC 1 0 -5 Calculated (33 Mkg mass) (m/s) -10 Calculated (54 Mkg mass) Velocity -15 Chandler measured data -20 w/error bars -25 0 1 2 3 4 5 Seconds Fig. 2. Measured and calculated velocity curves It is questionable whether the velocity fluctuations seen on the graph in Fig. 2 (using the 54 Mkg mass value claimed by Le and Bazant) would be visible on the video, since the measurement error is +0.675 m/s. But it is clear that the calculated average downward acceleration is much less than the observed value. With the 33 Mkg mass the calculated velocity decrease is roughly 2 m/s, and should be visible in a velocity plot obtained from the Sauret video footage. Also, the average acceleration after impact is negative (i.e. upward), which would be easy to observe. 6

Journal of 9/11 Studies Letters, September, 2014 5. Conclusion The analysis of Le and Bazant, while sound theoretically, uses incorrect input values. These errors each have the effect of reducing the resistance of the lower part of the building. As a result, their calculated velocity drop on impact is too low, and the calculated acceleration following that drop is too high. References Chandler, D. (2010). “Destruction of the World Trade Center North Tower and Fundamental Physics”, Journal of 9/11 Studies, available at http://www.journalof911studies.com. MacQueen, G., and Szamboti, T. (2009). “The Missing Jolt: A Simple Refutation of the NIST-Bazant Collapse Hypothesis”, Journal of 9/11 Studies, available at http://www.journalof911studies.com. National Institute of Standards and Technology (NIST). (2005). Final report on the Collapse of World Trade Center Towers NIST-NCSTAR 1, NIST, Gaithersburg, Md. Urich, G. (2007). “Analysis of the Mass and Potential Energy of World Trade Center Tower 1”, Journal of 9/11 Studies, available at http://www.journalof911studies.com. Rebuttal to Criticisms of Reviewer #2 Richard Johns Anthony Szamboti June 7, 2012 The full text of the reviewer’s comments, as provided to us over email, including quotations from our discussion, are shown below in 10-point Arial font, indented. Our responses are in Times font. Reviewers' comments: AE: On the basis of the enclosed review, the paper is declined for the lack of substantive arguments in terms the underpinning (e.g. tower velocity) calculations. Reviewer #2: The Jan 2011 technical note (TN) by Le and Bazant discussed how the upper portion of the WTC towers fell and impacted the remaining building section below, with a focus on the mechanics used to determine the velocity of the upper portion as it impacted the section below and the effect of degradation on the velocity. The change in velocity at impact was shown to be too small to detect on available videos. This paper builds on a series of papers in the Journal of Engineering Mechanics, and the entire sequence of papers needs to be considered by the discussion authors. The discussion paper by Szambati and Johns asserts that the input values used for the calculations of velocity were incorrect. Therefore, the levels of computed deceleration at impact and acceleration following impact are thought to be incorrect. However, as noted below, the authors have not successfully demonstrated their concerns because they have not accurately represented the work by Le and Bazant or presented the basis for the input 7

Journal of 9/11 Studies Letters, September, 2014 values they feel are correct. The reviewer has the following comments about the discussion paper: 2. Inertia Resistance The authors stated that the reasons for only using the concrete mass are not stated. However, Le and Bazant reference their 2008 paper for the source of values used, and the authors go on to use values from that paper. Le and Bazant (2008) define mc as the "mass of one floor slab". A floor slab is terminology often used to refer to the constructed floor, not just the concrete. Response: No doubt the term ‘floor slab’ is sometimes used this way, but not in this case. The mass used by Le and Bazant, 0.627 Mkg, cannot be the mass of the entire constructed floor, since the latter (including the live load) is at least 2 Mkg. A very rough calculation of the mass of a lightweight concrete slab, 11cm thick, and roughly 60 by 60 metres, density 1750 kg/m3, is about 0.7 Mkg. Of course there was no floor in much of the building core, which no doubt accounts for the small difference between this value and Le and Bazant’s. The authors use the m2 value defined by Le and Bazant as "mass of a single story", which includes the steel columns and floor slab, in a mass ratio of the upper section mass (M) to (M+m2). M/(M+m2) cannot be equated to the velocity reduction in equation 2 in the TN. The authors statement below is incorrect: "The velocity lost is therefore about 7% of the original, rather than the 1.1% claimed. (Note that this is already more than the 3% total loss calculated by Le and Bazant.)" The 1.1% velocity reduction by Le and Bazant was based on rigid mass interactions in equation 2, and the 3% velocity reduction was based on deformation and interaction of both masses in equation 11. This criticism is baffling to us. Our velocity reduction calculation, based on the inertia of floor 97, does not depend on the floor being rigid. It is simple Newtonian physics. When a body of mass 14m strikes a stationary one of mass m, and they stick together, the resulting body has mass 15m and has 14/15 = 0.93 of the original velocity. This follows from the conservation of linear momentum, which applies to all collisions, regardless of the rigidity of the bodies involved. If the bodies are compressible, then the velocity reduction is spread over a longer time interval, but the size of the reduction is unaffected. We can see no reason at all to suppose that only the concrete slab would be accelerated by the impact, rather than the whole floor assembly. Neither Le and Bazant nor Referee #2 has supplied such a reason. 3. Column Resistance The authors state: "The 287 columns on the 97th story are treated by Le and Bazant as identical, even though the 47 core columns were on average much stockier than the 240 perimeter columns. The data used for a single column seem to be describing a perimeter column (stated in NIST NCSTAR 1-3D, p. 4 to be 14" square box columns) since the value Mp = 0.32 MNm may be obtained for a 14" square box column with wall thickness 6.75mm, or 0.27", according to the usual formula: Mp = 1.5 x b2t x Fy (b is the breadth of each flange, t is the flange thickness, and Fy is the yield stress, assumed by Le and Bazant to be 0.248 GN/m2)." 8

Journal of 9/11 Studies Letters, September, 2014 The column data used by Le and Bazant was representative section for all of the core and perimeter columns, as described in Le and Bazant (2008) under Variation of Mass and Buckling Resistance Along Height section. The section referred to does contain some information about the columns, but it does not describe any single column spec that is representative for the columns between floors 97 and 98. Interestingly, it does give 10mm as the web thickness for the perimeter columns on the aircraft impact level. Using 10mm with the other parameters (breadth 0.3556m and yield stress 250 MPa) gives Mp = 0.448 MNm rather than 0.32 MNm, so it could not have been used in Le and Bazant (2011). In our opinion, Le and Bazant’s TN should have stated clearly, in the paper itself, their assumed specs for the columns on story 97. As it is, we are forced to guess these specs, based on the few numbers they do supply, such as the plastic moment. The plastic moment, Mp=0.32 MNm is the "average yield bending moment of one column" for "n=287 columns (approximately considered as identical)". Identical does not imply that they are all perimeter box columns. Further, it is not clear what 1.5 x b2t x Fy represents in the Mp equation, as it is not an expression for the plastic modulus of either a hollow box section or a wide-flange section about the plastic neutral axis. The authors need to give a source for the equation. Our equation for Mp is a simplified version of the one given in: Gaylord E. H. and Gaylord C. N. (1979) Structural Engineering Handbook, McGraw-Hill. On page 7-3 the plastic section modulus is given for a hollow rectangular section with external dimensions b x d, and flange/web thicknesses t and w as: For a hollow square section, with equal flange and web thicknesses, we put d = b and w = t to get: We then derived a simplified formula for thin-walled sections where t << b. Multiplying out the brackets and dropping terms containing t2 and higher orders, one obtains: When this is multiplied by Fy it gives the formula for Mp stated in our discussion. No doubt the use of the simplified formula was a stumbling block to the reviewer, and it also gives slightly different Mp values from the exact one. We would be happy to use the exact formula instead. Given the comments above, the 'first error' cited by the authors as an incorrect total cross-sectional column area for a floor is not persuasive. Le and Bazant used a representative section (noted above) and there is no basis for the author's assertion that A= 4 m2. 9

Journal of 9/11 Studies Letters, September, 2014 The value A = 4m2 is obtained by adding 2.3m2 (perimeter) to 1.7m2 for the core. The total cross sectional area for the (roughly square) perimeter columns was calculated as 240 (columns) x 4 x 0.3556m (breadth) x 0.00675m (thickness). The total cross sectional area for the core columns was obtained by adding the cross sectional area for each core column, as given in the NIST SAP2000 model data. The noted 'second error' of the Fy value could not be verified. "The authors' second error is to use a value of Fy = 0.248 GN/m2 (36 ksi) for the yield stress of the columns". I did not find it in the 2011 technical note, or in the other papers by Le and Bazant. Le and Bazant did account for varying Fy of the columns in their representative section. Le and Bazant did indeed use Fy = 250 MPa, i.e. 0.25 GN/m2. While it is not explicitly stated in their 2011 paper, it can be calculated from their Equation (3). They call it 0, and it equals (1.513 x 109)/6.05 = 0.25 x 109. Bazant and Le also give this value explicitly in their 2008 closure to G. Szuladzinski’s discussion (JEM 2008, p. 921). For the calculation of Mp, I looked at the referenced MacQueen and Szamboti (2009), which listed column Fy and dimensions for core columns, but did not list any plastic moment values. Given the Mp equation above, the values listed for are suspect. It is disappointing that the reviewer finds our Mp values to be “suspect” without actually checking any of them. All the necessary data to do so are provided in the supplied MacQueen and Szamboti reference. Each flange has plastic section modulus t.b2/4, so the total is t.b2/2 for the two flanges. (Here we neglected the small contribution from the web, i.e. ¼(d – 2t)w2, where d – 2t is the web length and w the thickness. The full formula is given in Gaylord and Gaylord text referenced above, p. 7-3.) In our discussion we stated the Mp values calculated using this formula for the largest and smallest core columns. For example, the largest type of core column on this story has b = 16.695” = 0.424m, and t = 3.033” = 0.077m, and has a 42 ksi (290 MPa) yield stress. We then have Mp = (0.077 x 0.4242 x 290 x 106)/2 = 2.01 MNm, exactly as stated in our discussion. We calculated the Mp values in the same way for all of the 47 core columns using a spreadsheet, and found the average to be 0.75 MNm. If anyone doubts this figure they are welcome to calculate it for themselves. We can also provide our Excel file, upon request. The authors computed a total yield load for "First the 240 perimeter columns: P = 240 x 0.00675 x 4 x 0.3556 x 0.45 x 10^9 = 1.04 GN." Equations need to be presented with defined variables, and then followed by values is desired. It is not clear what 0.3556 represents, and the area of the perimeter columns included flange sections that extended beyond the 'box' section, which is not discussed or included in the calculations. Based on these points, the values listed for the core columns are also suspect, as insufficient basis for the values presented are provided. 10

Journal of 9/11 Studies Letters, September, 2014 We think this calculation is clear enough, but it would be easy to add the explanation that 0.3556m is the breadth of a perimeter column, and 0.00675m the flange thickness, so that 0.00675 x 4 x 0.3556 is the cross-sectional area of one column. Multiplying by the yield stress 0.45 x 109 N and the number of perimeter columns (240) gives the total yield load for the perimeter columns on the 97th story. The appeal to extended flange sections, to account for Le and Bazant’s very high area value, is grasping at straws. The figure below is part of Fig. 2-3 on p. 7 of NIST NCSTAR 1-3A, and shows that the total XS length of the flanges and webs is 13.5” x 2 + 14” + 15.75” = 56.75”. Hence our value of 14 x 4 = 56” is admittedly too low, but only by about 1.3%, which is not significant. The authors use the unsubstantiated values from above in an equation from Le and Bazant (2002) that computes plastic axial load Fb or a given axial shortening u. The input values for the equation include a core column length of 3.7 m and a perimeter column length of 2.3 m. Clearly, column lengths must all be the same on a given story - the spandrel plates were attached to the columns but did not act as columns. Thus, Figure 1 is incorrect. The length of concern is the unsupported column length and it is different between the columns in the core and those on the perimeter due to the depth of the beams involved. In taking 2.3m as the unsupported length of a perimeter column we are following Bazant and Zhou (2002), p. 5, except that we measured the spandrel height to be 1.4m rather than 1.2m. This can be changed without drastically affecting the results. The authors go on to estimate their own value of the mass of the upper descending portion of the tower, simply based on floor densities from other high-rise buildings. While that information is interesting, it is not sufficient to claim that the correct value is 2.75 Mkg per story. In our discussion paper we actually refer to a detailed analysis by G. Urich, which is based on the NIST reports’ description of the floor structures, total steel weight found in contracts, and live and superimposed dead loads. We do not argue solely by comparison with the Sears Tower and John Hancock building, although that provides additional evidence. Moreover, we recently found that NIST NCSTAR 1-6D, p. 176, Table 4-7, directly states the actual total load on the columns between floors 98 and 99 to be 73,143 kips, i.e. roughly 33 Mkg. With the collapse initiating on the 98th floor, as referenced in NIST NCSTAR 1-6, p. 156, the falling upper section mass would be roughly 33 Mkg, as stated in our discussion. There are many separate lines of evidence leading to mass estimates in this range, while Le and Bazant provide no justification at all for their much-higher estimate. Hence our criticism is well supported and very reasonable. 11

Journal of 9/11 Studies Letters, September, 2014 4.Calculating the velocity curve. Given the concerns about the values for mass and column properties, the velocity computations in this section are suspect. The basis of the computed velocity curves for the 33 and 54 Mkg masses are not described. Note that in Figure 2 that the 33 Mkg mass has a zero velocity at approx. 3.2 s, well before the collapse is completed. All the necessary input values are given, so that anyone can calculate their own curves to verify ours. We would be happy to provide hand calculations that give approximately the same results as the curves shown, which were produced numerically. We were not able to include such calculations in the original discussion, since we had reached the upper word limit. In summary, Reviewer #2 has not found any error at all in our criticisms of Le and Bazant’s TN. We have correctly cited the TN itself, as well as Bazant’s earlier papers on the subject, and the NIST reports. Our criticisms, summarized below, are therefore still valid. 1.Le and Bazant do not adequately state their assumed specifications for the columns on story 97. 2.The values they do state, i.e. average Mp = 0.32 MNm and total XS area 6.05 m2, are unsupported by any references or calculations, and not even consistent with one another, given the known number and external dimensions of the columns, their own value for the yield stress, and the standard textbook formula for Mp. 3.In calculating the momentum exchange between the falling upper block and the first stationary floor, Le and Bazant have incorrectly used the mass of the concrete slab only, rather than the full floor assembly. 4.Le and Bazant’s mass value of 54.18 Mkg for floors 99-110 (plus the roof) is unsupported by any evidence, and is much greater than the 33 Mkg value given by NIST. 5.Le and Bazant’s average value for the yield stress of the columns on story 97 contradicts the yield stresses provided by NIST. 6.With all these corrected data the value of ueq, i.e. the downward displacement at which the resistive and gravitational forces balance, is roughly 1.12m, not the 0.065m they claim. 7.Using the corrected data, Le and Bazant’s own methods predict a velocity reduction that would be visible in a velocity plot derived from Etienne Sauret’s high-definition video footage of WTC 1. (Our discussion paper, unlike the TN, includes this necessary empirical data, and no such reduction is visible.) The conclusion of Le and Bazant’s TN is not supported by the available evidence. 12

Journal of 9/11 Studies Letters, September, 2014 Resubmitted Discussion of the paper Why the Observed Motion History of World trade Center Towers is Smooth By Ja-Liang Le and Zdeněk Bažant DOI: 10.1061/_ASCE_EM.1943-7889.0000198 Journal of Engineering Mechanics, Vol. 137, No. 1, January 1, 2011, pg. 82-84 Tony Szamboti Richard Johns 1. Introduction In their paper, Le and Bažant respond to the claim that the motion of the roofline of WTC 1, as captured in video footage, is inconsistent with the hypothesis of gravity-driven progressive collapse. Unfortunately they do not give any sources for this claim, but it is likely that they are responding to the work of Chandler (2010) and MacQueen and Szamboti (2009). It is agreed on all sides that the collapse of WTC 1 initiated at the 98th floor leaving a 12-story upper part to fall onto a stationary 97-story lower part, as stated by NIST NCSAR 1-6, p. 156. Le and Bažant calculate the total velocity reduction after impact to be about 3%. They also find that, after impact, the upper part continues to accelerate downwards at 6.2 m/s2. It seems these calculations are based on assumptions, especially regarding the steel columns on story 97, which are without justification and contradicted by NIST. 2. Inertia Resistance Le and Bažant first calculate the slowing of the upper portion due to the inertia of the first story impacted. For reasons that are not specified, they consider only the mass of the concrete floor slab to be involved in this exchange of momentum. They calculate the effect of a descending mass of 54.18 Mkg striking a stationary mass of 0.627 Mkg. However, the concrete floor slab is only part of the overall floor mass, which also includes rebar, steel decking, truss work, and the live load. According to Bažant and Le (2008, p. 905), from which Le and Bažant obtain the data used, m2 = the mass of a single story is 3.87 Mkg for WTC 1. Using this value, we get a velocity ratio of 54.18/(54.18 + 3.87) = 0.93. The velocity lost is therefore about 7% of the original, rather than the 1.1% claimed. (Note that this is already more than the 3% total loss, calculated by Le and Bažant.) 3. Column resistance For simplicity, Le and Bažant’s calculations assume that the 287 columns on the 97th story are identical. Unfortunately the full specifications of this representative column are not stated. We are told that the plastic moment Mp for this column is 0.32 MNm, and from Equation (3) we can infer that the yield stress σ0 = 250 MPa. The total cross-sectional area of the 287 columns is stated to be 6.05 m2. The shape of the column, its overall dimensions, and flange and web thicknesses are not given. We can find no specification consistent with this data. 13

Journal of 9/11 Studies Letters, September, 2014 Most of the columns (240 of the 287) were perimeter columns, the overall dimensions and shape of which are stated by NIST (NCSTAR 1-3D, p. 4) to be approximately 14” square box columns, i.e. having width and breadth equal to 0.3556 m. To calculate Mp we used a standard formula for the plastic section modulus of a hollow rectangular section (see Gaylord et al, 1979, 7-3), putting width equal to breadth b, web thickness equal to flange thickness t, and multiplying by the yield stress, gives: . (1) Calculating backwards (from Mp=0.32 MNm) gives t = 7.02 mm. This is much less than the 10 mm thickness given in Bažant and Le (2008, p. 896) for the aircraft impact level, and even a little less than the 7.5 mm they state for the top story. It also entails a total cross-sectional area of 287 x 4 x 0.3556 x 0.00702 = 2.87 m2, which is less than half of the 6.05 m2 stated. The authors need to explain how their Mp value was obtained. Our estimate of the average plastic moment of the columns on story 97 is 0.64 MNm, obtained as follows. For the perimeter columns, we conservatively assume web and flange thicknesses t = 7.5 mm. The yield stress of the perimeter columns at story 97 is reported by NIST to be 55ksi – 100ksi (NCSTAR 1-6, p. 61, and NCSTAR 1-3B, Table 4-2, p. 52). We estimate the average yield stress to be 65ksi, i.e. 450 MPa, which is also conservative, since NIST reports the measured yield stresses to be above nominal. (NCSTAR 1-6, p. 61). This gives Mp = 0.61 MNm for the perimeter columns. The core columns vary in size and steel types. They are wide-flange columns, with flanges ranging from 16.695” x 3.033” down to 8” x 0.528”, and either 36, 42, 45, or 50 ksi yield strength. (See the available NIST SAP2000 model data, reproduced by MacQueen and Szamboti (2009), pp. 22-3.) To calculate Mp for the weak axis the plastic section modulus Zp = ½ t.b2, also obtained from Gaylord et al (1972, 7-3), was used, omitting the small contribution from the web. The Mp values for core columns were found to range from 2.01 MNm to 0.09 MNm, the average being 0.75 MNm. The weighted average, for core and perimeter columns, is then 0.64 MNm. We conclude that 0.32 MNm is much too low. Using this corrected Mp value, together with the other column data stated above, we can repeat Le and Bažant’s calculations for the velocity reduction of the upper part of WTC 1. First we calculate the total yield load for all columns. For the 240 perimeter columns: P = 240 x 4btσ0 = 1150 MN. For the core, using the NIST data, the total cross-sectional area of the core columns is found to be 1.69 m2, and maximum load is 460 MN. In total, we have P = 1,610 MN. For calculating the load-displacement curve we also need the column length L, given by Le and Bažant as 3.7 m for all the columns. Bažant and Zhou (2002, p. 5) state the effective height of the perimeter columns to be 2.5 m, the distance between the 1.32 m deep spandrel plates, that were heavier gauge than the adjacent column webs. (See NIST NCSTAR 1-3A, pp. 7-9.) Since our aim is to calculate a conservative estimate of the velocity drop, however, we will ignore the spandrel plates and use L = 3.7 m – which makes the perimeter columns more slender, substantially reducing their resistance during buckling. The resistive force Fb is then given by the formula below (see Bažant and Zhou 2002, p. 6) where number of columns is n, and u the reduction in column length. 14

Journal of 9/11 Studies Letters, September, 2014 Using Mp = 0.64 MNm we get the graph shown in Fig. 1. ueq with 54.18 Mkg mass ueq with 33.18 Mkg mass Fig. 1. Diagram of load vs. displacement during axial deformation and buckling The average resistance of the columns is 310 MN, using numerical integration. The displacement ueq, at which column resistance equals the 530 MN weight of the upper part (i.e. the 54.18 Mkg mass used by Le and Bažant) is 0.27 m, rather than the 0.065 m claimed. Up to this point we have used Le and Bažant’s mass value of 54.18 Mkg for the upper part of the tower, but this conflicts with the NIST report (NCSTAR 1-6D, p. 176, Table 4-7), which states the actual total load on the columns between floors 98 and 99 to be 73,143 kips, i.e. 325.4 MN or 33.18 Mkg. NIST’s estimate is also much closer to typical mass per square meter values for other buildings sharing this type of construction, such as the Sears (now Willis) Tower and John Hancock building. For a detailed examination of the masses of WTC 1 and 2 see Urich (2007). From here on, we will use NIST’s 33 Mkg figure in our calculations. For example, ueq then occurs at roughly 0.76 m, as shown in Fig. 1. 4. Calculating the Velocity Curve To verify the accuracy of the gravity-driven model, we can calculate the velocity curve for the roof line, and compare it with the behavior of WTC 1 itself. Fortunately, there is high-resolution footage of the collapse of WTC 1 shot by professional filmmaker Etienne Sauret, and used for the documentary film WTC - The First 24 Hours (2002). Each pixel of this footage represents 0.27 m of the tower, and frame rate is 30 per second, allowing for accurate measurements of the motion. David Chandler has analyzed this motion using Tracker, an open source video analysis tool. His graph is shown below, together with a calculated velocity plot for a gravity-driven collapse. The calculated velocity of the roofline was obtained numerically using the load-displacement curve shown above, and scaling up linearly for lower stories, according to the increasing design load. We also assumed Le and Bažant’s freefall acceleration during the collapse of the first story. Floors are treated as rigid and incompressible, and assumed to stick together upon impact. The upper part of the building is modeled as a rigid block, which Le and Bažant regard as a reasonable approximation. It is easy to derive an approximation of this curve, using hand calculations, given the average 97th story column resistance of 310 MN, which is approximately NIST’s (325.4 MN) weight for the upper part of the 15

Journal of 9/11 Studies Letters, September, 2014 building. Hence the average velocity is approximately constant after the first impact – decreasing slightly due to the inertia of the impacted stationary floors. Velocity (m/s) 0 -2 -4 Calculated -6 -8 -10 -12 -14 Measured -16 -18 -20 0 1 2 3 4 Seconds Fig. 2. Measured and calculated velocity curves The calculated first velocity decrease is 1.65 m/s (approximately 20%), and would be visible (if it existed) in a velocity plot obtained from the Sauret video footage. Also, the predicted average acceleration after impact (roughly zero) is significantly different from what was observed. 5. Conclusion The analysis of Le and Bažant uses incorrect input values. These errors each have the effect of reducing the resistance of the lower part of the building. As a result, their calculated velocity drop on impact is too low, and their calculated acceleration following that drop is too high. References Bažant and Zhou (2002) “Why Did the World Trade Center Collapse?—Simple Analysis”, J. Eng. Mech., Vol. 128, No. 1, 2-6. Bažant and Le (2008) “What Did and Did Not Cause Collapse of World Trade Center Twin Towers in New York?”, J. Eng. Mech., Vol. 134, No. 10, 892-906 Chandler, D. (2010). “Destruction of the World Trade Center North Tower and Fundamental Physics”, Journal of 9/11 Studies, available at http://www.journalof911studies.com. Gaylord E. H. and Gaylord C. N. (1979) Structural Engineering Handbook, McGraw-Hill. MacQueen, G., and Szamboti, T. (2009). “The Missing Jolt: A Simple Refutation of the NIST-Bazant Collapse Hypothesis”, Journal of 9/11 Studies, available at http://www.journalof911studies.com. National Institute of Standards and Technology (NIST). (2005). Final report on the Collapse of World Trade Center Towers NIST-NCSTAR 1, NIST, Gaithersburg, Md. 16