Contents › tt_assets › pdf › WTC_LevyAbboud... · 2018-04-19 · Contents 1 INTRODUCTION ... 10 4.1 MEETING THE NYC BUILDING CODE REQUIREMENTS..... 10 4.2 ADOPTING THE ASCE7-98

World Trade Center Structural Engineering Investigation — Supplemental Report

Contents

1 INTRODUCTION................................................................................................................. 1

2 PEER REVIEW OF THE RWDI AND CPP WIND TUNNEL STUDIES AND SUBSTANTIATION OF THE RWDI WIND LOADS ............................................................. 2

2.1 PEER REVIEW OBJECTIVES............................................................................................... 2 2.2 COMPARISON OF BASIC WIND TUNNEL DATA ................................................................. 3 2.3 PREDICTION OF DESIGN LOADS AND COMPARISON WITH RWDI AND CPP RESULTS....... 4 2.4 EXPLANATION OF DIFFERENCES IN RWDI AND CPP DATA ............................................. 7 2.5 BLWTL PEER REVIEW CONCLUSIONS............................................................................. 7

3 SUMMARY OF PRIOR WIND LOADING ANALYSES................................................ 8

4 RETROFIT OPTIONS....................................................................................................... 10 4.1 MEETING THE NYC BUILDING CODE REQUIREMENTS................................................... 10 4.2 ADOPTING THE ASCE7-98 STANDARD PROVISIONS ...................................................... 10

5 REFERENCES.................................................................................................................... 15

6 MATERIALS CONSIDERED........................................................................................... 16

Appendices

A. BLWTL Peer Review Report: “Report Regarding the Review of the World Trade Center Twin towers (NY) Wind Studies Carried Out by RWDI and CPP”.

B. RWDI Wind Loads and Load Combinations for a TMD-enhanced 5% Structural Damping Level.

C. CVs D. Figures.

HART-WEIDLINGER i


1 Introduction

This report supplements our rebuttal report dated August 4, 2002 [Levy and Abboud, 2002b]. Based on a detailed review of the supporting documentation and calculations to Dr. Osteraas’s report [Osteraas, 2002] concerning the structural adequacy of a hypothetical single remaining WTC-2 tower in response to wind loading, we have undertaken additional work and analysis to explain the differences in results between the CPP and RWDI wind tunnel tests, commissioned by Exponent and Weidlinger Associates Inc., respectively. These differences in wind load predictions lead to different assessments, by Exponent and Weidlinger Associates Inc., concerning the structural adequacy of a hypothetical single remaining tower and the effect of wind shielding. Accordingly, we commissioned the Alan G. Davenport Wind Engineering Group and the Boundary Layer Wind Tunnel Laboratory at The University of Western Ontario to conduct an independent peer review of the wind tunnel testing reports prepared by RWDI and CPP and explain the difference in the results from these tests. The results of this peer review are reported in [BLWTL, 2003], and analyzed in this report.

We also supplement our analysis on the feasibility and simplicity of some retrofit options afforded to us in the hypothetical single-tower scenario should the Port Authority of New York and New Jersey opt to upgrade such a tower to exceed the requirements of the governing New York City Building Code by adopting the wind loading provisions of the state-of-the-art ASCE7-98 Standard (or the current ASCE 7-02 Standard*).

* The wind loading provisions in ASCE 7-02 for tall and dynamically sensitive buildings such as the twin towers of the World Trade Center have not changed from those in ASCE 7-98 primarily due to the need to use wind tunnel testing and to the fact that design wind speed for the New York City vicinity have not changed.

HART-WEIDLINGER Page 1


2 Peer Review of the RWDI and CPP Wind Tunnel Studies and Substantiation of the RWDI Wind Loads

Dr. Osteraas has opined in his September 2002 report [Osteraas, 2002] that WTC 2 is structurally inadequate in a hypothetical single-tower configuration and would require retrofit of all 8 corner columns over the entire height of the Tower. Dr. Osteraas based his opinion on an Exponent-commissioned wind tunnel study performed by Cermak, Peterka and Peterson (CPP) in Fort Collins, Colorado [CPP, 2002]. In our rebuttal report of October 2002 [Levy and Abboud, 2002b], we established that only 12 floor-high columns, out of more than 30,000 columns, would need to be reviewed for potential retrofit in the hypothetical scenario where WTC 2 stands alone. We also thus concluded that the effects of shielding of one tower by the other from wind loads have virtually no effect on the structural performance of a single hypothetical remaining tower. We based our wind analysis on a wind tunnel study performed by Rowan, Williams, Davies and Irwin, Inc. (RWDI) in Guelph, Ontario, Canada [RWDI, 2002 a&b].

These two independent sets of wind tunnel tests investigated similar configurations of the World Trade twin towers and their surroundings. However, they came up with significantly different predictions of design wind loads on the structures. Further evaluation of the test results revealed that the primary reason for the differences in the design loads predicted by the two laboratories stemmed not from the physical testing of the models but from the process of combining the test data with wind climate statistics. In order to obtain an independent third-party opinion on the results obtained by RWDI and CPP, a reputed wind tunnel laboratory was retained to undertake an independent review of the available data and prepare a report of their findings.

The Alan G. Davenport Wind Engineering Group and the Boundary Layer Wind Tunnel Laboratory (BLWTL) at The University of Western Ontario (UWO), London, Ontario, Canada were retained by Weidlinger Associates, Inc. to conduct an independent peer review of the wind tunnel testing reports prepared by RWDI and CPP and explain the difference in the results from these tests [BLWTL, 2003]. A synopsis of the BLWTL findings follows in the remainder of Section 2.

2.1 Peer Review Objectives The following reports and available affiliated material were reviewed by BLWTL:

[1] Cermak, Peterka, Petersen Inc Data Report, Wind-Tunnel Tests – World Trade Center, New York, NY, CPP Project 02-2420, Aug 2002 [CPP, 2002].

[2] Rowan Williams Davies & Irwin Inc, Final report, Wind-Induced Structural Responses, World Trade Center – Tower 1, New York, NY, Project No. 02-1310A, Oct 4., 2002 [RWDI, 2002a].

[3] Rowan Williams Davies & Irwin Inc, Final report, Wind-Induced Structural Responses, World Trade Center – Tower 2, New York, NY, Project No. 02-1310B, Oct 4., 2002 [RWDI, 2002b].



[4] A letter from Dr. Peter Irwin to Mr. Levy, dated Oct. 2, 2002 Re: Peer Review of Wind Tunnel Tests, World Trade Center. RWDI Reference #02-1310 [Irwin, 2002].

Briefly, the primary objectives of the BLWTL peer review were to:

1) To compare the basic wind tunnel data from the two studies.

2) Use the RWDI wind tunnel data to make predictions of design base loads and compare with those of both RWDI and CPP.

3) To provide an explanation of why RWDI’s and CPP’s predictions of design base loads differ substantially.

2.2 Comparison of Basic Wind Tunnel Data Wind tunnel experiments performed by both RWDI and CPP consisted of testing scale models of the WTC towers for a set of wind speeds from all compass directions. Base moments and forces were measured from these tests for 36 different equi-spaced compass directions. This base moment and force data is referred to as “azimuthal” data and does not include the probability of strong winds occurring from a certain direction. The azimuthal base forces are then statistically combined with the climatic data for New York City (i.e. data concerning the probability of winds of a given speed occurring from a given direction) to predict the wind induced response of a building.

From wind tunnel testing, RWDI collected force balance data measured at the concourse level (reported at the foundation level) referenced to a mean wind speed at a height of 600 m. CPP measured the same data at concourse level but referenced to a height of 1000 ft (305 m). To compare the RWDI and CPP azimuthal data, RWDI’s base moment data was scaled to a 1000 ft reference height by BLWTL using conversion factors provided by RWDI and verified by BLWTL. The variation of CPP’s base moments with reference wind speed for the available compass directions (presented on Pages 31 – 48 of CPP’s report) was overlayed and plotted with RWDI’s data. From this comparison, BLWTL concluded that the data measured in both wind tunnels were “remarkably similar” to each other despite some basic differences such as the extent of the proximity models (4000 ft radius for RWDI versus 2400 ft for CPP), different dynamic properties for the evaluation of resonant response, etc. Moreover, BLWTL determined that in general, whenever differences existed between the two sets of results, the RWDI numbers exceeded the CPP results.

The BLWTL study noted that modeling of structural response in the wind tunnel is a well established science and standards, such as the “ASCE Manual of Practice No. 67: Wind Tunnel Studies of Buildings and Structures” exist to impart uniformity to the process of such measurements at different laboratories.



2.3 Prediction of Design Loads and Comparison with RWDI and CPP Results

BLWTL noted that the mathematical techniques used in the combination of wind tunnel and climatic data involve complex statistical techniques that are still evolving. These mathematical techniques essentially translate the building model data measured in the wind tunnel to the wind-induced response of the prototype by considering the full-scale characteristics of wind speed and direction at the building site.

Since the basic wind tunnel data (azimuthal data) measured at both RWDI and CPP compare well with each other, the difference in approach for the statistical combination of the wind tunnel measurements with climatic data is the primary source of the major differences between the predicted design loads by both wind tunnels. CPP appears to have adopted a simplified statistical combination approach in which CPP combines the directionally modified design wind speed (to account for the varying probabilities of occurrence from different directions) with the wind tunnel data measured for that direction. As BLWTL comments in its report, this simplified approach inherently overestimates the predicted design wind loads. RWDI on the other hand used the “upcrossing method” which incorporates contributions of winds from all directions to the probability of obtaining the design response and therefore the design wind load. The upcrossing method “allows the directionality of the wind to be taken into account in a rational manner” according to the BLWTL report.

Statistics for non-hurricane wind events are based on historical records from adjoining meteorological stations. To account for the influence of hurricanes on the wind climate in New York City, Monte Carlo simulations of hurricane events have to be performed to develop the wind speed statistics. RWDI, CPP and BLWTL utilized a hurricane model for New York City developed by ARA-Intrarisk [see Levy and Abboud, 2002b]. Whereas CPP used a simplistic directional factor approach to combine the wind tunnel measurements with the climatic data statistics, and RWDI used the more rational and advanced “upcrossing method”, BLWTL also utilized a rational and advanced “storm passage technique” in which the Monte Carlo simulations of hurricane events are directly combined with the wind tunnel data, thus avoiding a number of statistical assumptions required by the older methods.

The results of the BLWTL “storm passage” analysis for the ASCE 7-98 design wind speed case [ASCE, 1998] and comparisons with the RWDI and CPP results are presented in Table 2.1 below for reference. Table 2.1 indicates that the BLWTL results match well with the RWDI results. The BLWTL predictions are 2% to 22% less than RWDI’s for WTC-1 and 8% to 18% less for WTC-2. The differences arise due to the use of different approaches in defining the design wind speed. RWDI has matched their design wind speed to the ASCE 7-98 prescribed value of 104 mph for New York City, whereas, BLWTL predicted 500-year return period loads and divided them by a load factor of 1.5 to predict the base moments (equivalent to a wind speed value of 102 mph). In comparison, the CPP results significantly overestimate the design moments, predicting values that are 40% to 71% larger than BLWTL.



Table 2.1 - Peak Design Overturning Moments at Foundation Level 1 (Based on Force Balance Model Data for a Structural Damping of 2.5%)

ASCE 7-98 Design Speed

BLWTL2 (storm passages)

RWDI3 (upcrossings)

% Diff. RWDI

vs. BLWTL

CPP4 % Diff. CPP

vs. BLWTL

WTC-2 With WTC-1 Mx (lb-ft) 9.66E+09 11.1E+09 14.9% 13.9E+09 43.9% My (lb-ft) 9.03E+09 10.1E+09 11.8% 15.5E+09 71.6% Base Torque (lb-ft) 1.94E+08 2.11E+08 8.9% WTC-2 Alone Mx (lb-ft) 10.7E+09 12.7E+09 18.7% 15.0E+09 40.2% My (lb-ft) 14.0E+09 16.6E+09 18.6% 23.0E+09 64.3% Base Torque (lb-ft) 2.08E+08 2.26E+08 8.7% WTC-1 With WTC-2 Mx (lb-ft) 8.73E+09 10.7E+09 22.6% My (lb-ft) 11.2E+09 11.4E+09 1.8% Base Torque (lb-ft) 2.07E+08 2.11E+08 1.9% WTC-1 Alone Mx (lb-ft) 11.7E+09 12.6E+09 7.9% My (lb-ft) 11.0E+09 11.3E+09 2.7% Base Torque (lb-ft) 1.99E+08 2.11E+08 6.0%

1 In all cases the foundation moments are assumed to be 7% greater than the concourse level moments 2 500-year response predicted using an updated version of the hurricane model used to develop the ASCE-7 design wind speeds divided by 1.5 3 Design wind speed matches ASCE 7-98; for detailed source information, see Attachment C to BLWTL’s report 4 Design Wind Speed Matches ASCE 7-98; for detailed source information, see Attachment C to BLWTL’s report

A comparison of RWDI and BLWTL results for the New York City Building Code (NYCBC) required design 50-year return period, fastest mile wind speed of 80 mph is shown in Table 2.2. This comparison reveals that the difference between the RWDI “upcrossing” and the BLWTL “storm passages” results is small, 1% – 14% for WTC-2 and 1% – 10% for WTC-1. Furthermore, BLWTL’s predictions based on its own implementation of the “upcrossing method” yield base moments that are smaller than both RWDI’s “upcrossing” predictions and BLWTL’s “storm passage” predictions.

No comparison with CPP results could be made for the NYCBC case since CPP did not develop that governing case. It should be noted that the case termed “50-year nominal” in [CPP, 2002]



does not correspond to the NYCBC requirements (see p. 8 of [CPP, 2002] for a partial explanation)†, even though it seems to have been misconstrued by Exponent in its report to represent an analysis corresponding to NYCBC wind loads [Osteraas, 2002, footnotes of page 18 and footnote 7 of page F-4].

In summary, the BLWTL results clearly substantiate the RWDI results for both the NYC Building Code requirements and the ASCE 7-98 standard.

Table 2.2 - Peak Design Overturning Moments at Foundation Level (Based on Force Balance Model Data for a Structural Damping of 2.5%)

NYCBC Wind Speed

BLWTL (Upcrossings)

BLWTL (Storm

Passages)

RWDI1 (Upcrossings)

% Diff. RWDI vs. BLWTL

(Storm Passages)

WTC-2 With WTC-1 Mx (lb-ft) 9.28+09 10.2E+09 10.1E+09 -1.0% My (lb-ft) 8.35E+09 9.01E+09 9.24E+09 2.5% Base Torque (lb-ft) 2.04E+08 1.94E+08 -5.1% WTC-2 Alone Mx (lb-ft) 9.58E+09 10.2E+09 11.2E+09 8.9% My (lb-ft) 10.8E+09 12.8E+09 14.9E+09 14.1% Base Torque 2.29E+08 2.08E+08 -10.1% WTC-1 With WTC-2 Mx (lb-ft) 9.05E+09 9.49E+09 9.96E+09 4.7% My (lb-ft) 10.8E+09 11.2E+09 10.6E+09 -5.7% Base Torque 2.11E+08 1.91E+08 -10.5% WTC-1 Alone Mx (lb-ft) 9.89E+09 11.3E+09 11.6E+09 2.6% My (lb-ft) 9.75E+09 10.3E+09 10.4E+09 1.0% Base Torque 2.04E+08 1.94E+08 -5.1%

1 For detailed source information, see Attachment C to BLWTL’s report

† The footnote of Table C6-3 of ASCE 7-98 states “For the MRI=50 [Mean Recurrence Interval] as shown, the actual return period, as represented by the design wind speed map in Figure 6-1, varies from 50 to approximately 90 years.”



2.4 Explanation of Differences in RWDI and CPP Data The BLWTL “storm passage technique” leads to predicted base moments that are in general agreement with the RWDI “upcrossing” predictions. On the other hand, CPP’s predictions based on its simplified methods lead to a substantial overestimation of the base moments when compared to either RWDI or BLWTL predictions, despite the fact that CPP’s wind tunnel measurements appear to be generally smaller for the directions available for comparison.

To further assure itself that CPP’s approach is being interpreted correctly, BLWTL applied the CPP approach to the RWDI raw wind tunnel measurements in two different ways, and replicated CPP’s estimates with a mean difference of 6%; details of this analysis can be found in [BLWTL, 2003]. This reinforced BLWTL’s conclusion that the primary difference between the design loads predicted by RWDI and CPP is the simplified method by which CPP combined the wind tunnel and climatic data, and not the wind tunnel data itself.

2.5 BLWTL Peer Review Conclusions BLWTL reached the following conclusions in its report [BLWTL, 2003]:

1) BLWTL’s predicted base moments are comparable to the RWDI predictions.

2) CPP’s predictions considerably overestimate the wind loads required by either the NYCBC or the ASCE 7-98 Standard.

3) The primary reason behind CPP’s overestimation of the wind loads is its simplified approach to integrating wind tunnel measurements with climatic data or statistics.

4) The BLWTL results presented in Tables 2.1 and 2.2 above should be used for design, reduced by 5% for aeroelastic effects.

Given the above, and given that our prior analyses were based on the RWDI results which are conservative compared to the BLWTL predictions and are based on the rational, well-established and exercised “upcrossing” method, we confirm with an extremely high degree of scientific certainty our prior findings and opinions related to the structural adequacy of a hypothetical single-tower configuration and to the assessment that the structural performance of such a lone standing tower is virtually unaffected by the wind shielding effect (or lack thereof) [Levy and Abboud, 2002b]. Although we believe wind loading effects are irrelevant to the issue of structural dependence of the WTC towers, as we have previously stated, the fact that the performance of a hypothetical single-tower is virtually unaffected by the shielding effect renders this argument mute in our opinion.



3 Summary of Prior Wind Loading Analyses

A detailed evaluation of the structural performance of the Twin Towers, in twin-tower and single-tower configurations, under the design wind loads developed by RWDI was developed in [Levy and Abboud, 2002b]. A brief summary of these results in given in Tables 3.1 and 3.2 below:

Table 3.1 Number of Unique Exterior Wall Panel Columns Out of Over 30,000 Columns With DC Ratio > 1.33

WTC-1 WTC-2 Configuration (and Structural Damping) NYCBC ASCE 7-98 NYCBC ASCE 7-98

Configuration 1 Twin-Tower

(2.5% Damping)

7 36 5 37

Configuration 2 Single-Tower

(2.5% Damping)

8 79 12 400

Table 3.2 Number of Unique Exterior Wall Panel Spandrels Out of About 25,000 Spandrels

With DC Ratio > 1.33

WTC-1 WTC-2 Configuration (and Structural Damping) NYCBC ASCE 7-98 NYCBC ASCE 7-98

Configuration 1 Twin-Tower

(2.5% Damping)

0 126 0 255

Configuration 2 Single-Tower

(2.5% Damping)

1 176 40 958

Evaluation of each of the World Trade Center towers for the effects of wind loading (obtained from the RWDI wind tunnel tests) under the governing NYCBC provisions, in the twin and single tower configuration, leads us to the conclusion that there is a negligible increase in the number of exterior wall panel column and spandrel elements that have a demand-capacity ratio in excess of the acceptable value of 1.33. Other than some of the corner columns and the exterior wall columns at the intersection with the roof truss, the overwhelming majority of the columns in the tower remain well below a demand-capacity ratio of 1.0. The average demand capacity ratios in the columns of towers WTC-1 and WTC-2 under ultimate wind loading conditions are much below a demand-to-capacity ratio of 1.0. This is especially meaningful given the extraordinary ability of the exterior wall structure to redistribute load. The increase in the maximum values of



demand-capacity ratios between the single tower and twin tower configurations is also minimal. The effects of shielding of one tower by the other from wind loads have thus virtually no impact on the structural performance of a remaining tower under the hypothetical scenarios considered by insurers’ engineering experts.

As shown in Tables 3.1 and 3.2, it is noticeable that the overall assessment of the structural performance of the WTC towers under the NYCBC wind loads is largely unaffected by the issue of shielding. Even under the stringent recommendations of the state-of-the-art ASCE 7-98 Standard which goes beyond the NYCBC requirements, 79 columns in WTC-1 and 400 columns in WTC-2 out of more than 30,000 columns in each tower would be reviewed during a retrofit analysis for a single-tower configuration, instead of the 36 columns in WTC-1 and 37 columns in WTC-2 that would be reviewed for a two-tower configuration.



4 Retrofit Options

4.1 Meeting the NYC Building Code Requirements Under the governing NYCBC, there is a negligible change in the wind load resistance capability of WTC-1 for a change from a twin-tower to single-tower configuration, as indicated by the number of affected column and spandrel elements in Tables 3.1 and 3.2. Although the few elements in question would be reviewed in detail, a retrofit is unlikely to be required given the extraordinary load redistribution capabilities of the perimeter wall.

Similarly, for WTC-2, the change is marginal and at best would require review of about 40 spandrels located at the 84th floor on the North and South facades, out of about 25,000 spandrels in the entire WTC-2 tower. These spandrels exceed the DC ratio of 1.33 by up to 10% as shown in Figures D.1 and D.2.

Exponent has not evaluated the wind loading performance of the WTC towers for the governing NYCBC based on wind tunnel testing, despite stating that “current structural engineering practice requires wind tunnel studies for significant structures” [Osteraas, 2002, page F-3]. In fact, Exponent could not perform such an evaluation since the CPP study [CPP, 2002] did not investigate wind loads corresponding to a true 50-year wind speed, as required by the NYCBC. CPP’s report presents design wind loads for this “nominal” 50-year return period (not the true 50-year return period) and these have been misconstrued by Exponent as the true 50-year return period loads for comparison with NYCBC prescriptive design wind loads [Osteraas, 2002, 2nd bullet and footnote 7 of page F-4]. The ASCE 7-98 Standard makes clear the distinction between true and nominal return periods. The design wind speeds indicated in Figure 6.1 of ASCE 7-98 are nominal 50-year return period values. A review of the commentary to ASCE 7-98 , in particular, the footnote of Table C6-3 of ASCE 7-98 clearly states that “For the MRI=50 [Mean Recurrence Interval] as shown, the actual return period, as represented by the design wind speed map in Figure 6-1, varies from 50 to approximately 90 years.” As such, Exponent conclusions concerning retrofit requirements based on wind tunnel testing must be understood to mean “under ASCE 7-98 wind tunnel testing provisions” and not “under NYCBC wind tunnel testing requirements”. This important distinction is missing from the Exponent report [Osteraas, 2002, top bullet of page F-17].

4.2 Adopting the ASCE7-98 Standard Provisions If the PANYNJ were to opt for an evaluation of a hypothetical single remaining WTC-2 tower for wind loads beyond the governing NYCBC requirements, such as those specified in the state-of-the-art ASCE 7-98 (or ASCE 7-02) Standard, then the excess stress beyond the acceptable value of 1.33 in the column and spandrel elements can be mitigated by the retrofit options discussed in this section. The conclusions arrived at by Exponent [Osteraas, 2002] for their evaluation of ASCE 7-98 based wind loads results in a recommendation to strengthen the eight corner columns over the entire height of WTC-2. Our study [Levy and Abboud, 2002b] also concluded that for the ASCE 7-98 levels of loading, some of the corner columns of WTC-2 will have demand-capacity ratios in excess of the acceptable value of 1.33. However, the extent of the



retrofit will be smaller than what is proposed by Exponent. Exponent’s assessment is based on CPP’s wind tunnel loads that are substantially higher than those arrived at by the wind tunnel testing performed by RWDI and BLWTL. The likely reasons for this overestimation by CPP have already been discussed above.

As previously discussed, a viable retrofit option is the addition of steel cover plates to members deemed in need of increased capacity. We agree that such an option, among others, would be considered if retrofit was desired to meet ASCE 7-98 criteria. Another viable and potentially less intrusive option to reduce the level of stresses in the single tower configuration for either WTC-1 or WTC-2 is the installation of a passive damping system such as a Tuned Mass Damper (TMD). The use of TMD’s can conservatively enhance the expected damping in the sway directions in either of the WTC towers in the single tower configuration to 5% from the pre-retrofit level of 2.5%. At this stage it is envisioned that a 1200 ton TMD occupying a space of approximately 58 ft x 58 ft x 35 ft in a single mass pendulum configuration would be appropriate to achieve the 5% damping level. The TMD would probably be a mixture of a pendulum and an inverted pendulum to obtain the long periods needed without an excessive height requirement. It could also be split into multiple smaller dampers if a single space is not available. Other shapes such as a mass damping steel ring or a mass damping block over the building core could also be used to configure the mass to best fit available space. Current TMD devices have achieved a great degree of reliability that they are routinely resorted to in the seismic rehabilitation practice around the world.

The recommended wind loads and load combinations for 5% structural damping, corresponding to the installation of a TMD device, were derived from the RWDI wind tunnel measurements of the High Frequency Force Balance (HFFB) model since they can be readily determined without the need for additional wind tunnel testing, as would be required in the instance of the aeroelastic model.

A comparison of the reduction in base shears and moments achieved by the increase in structural damping anticipated by the installation of a TMD is shown in Table 4.1. These results indicate that base shears are reduced by 17% to 25% when a WTC tower in single-tower configuration is retrofitted with a TMD which can easily increase the damping level to 5%. This reduction in base shears directly reduces the demand capacity ratios of the exterior wall columns and spandrels. The bi-direction reduction in base shears will especially improve the performance of the corner columns that get overstressed due to bi-axial bending.



Table 4.1 Comparison of HFFB Base Loads for Different Levels of Structural Damping.

Hypothetical Single-Tower Configuration for WTC 1 and WTC 2

Base Moments at Foundation Level

Base Shears and Torsion Tower and Structural

Damping My (lb ft) Mx (lb ft) Fx (lb) Fy (lb) Mz (lb ft) WTC-1

2.5% Damping 1.15e+10 1.28e+10 1.19e+07 1.26e+07 1.94e+08

WTC-1

5% Damping 8.78e+09 9.37e+09 9.58e+06 9.74e+06 1.67e+08

Ratio 76% 74% 81% 77% 86%

WTC-2

2.5% Damping 1.49e+10 1.12e+10 1.52e+07 1.17e+07 2.08e+08

WTC-2

5% Damping 1.11e+10 8.75e+09 1.14e+07 9.70e+06 1.82e+08

Ratio 74% 78% 75% 83% 88%

The ASCE 7-98 loads and load combinations provided by RWDI for 5%-damping TMD-case along with the weight of the TMD were applied to the SAP2000 models of WTC-1 and WTC-2. As indicated in Table 4.2, the number of unique exterior wall columns in all possible load combinations of Configuration 2 (single tower) in which the demand-capacity ratio exceeds the acceptable value of 1.33 reduces dramatically with an increase in structural damping to 5%. For a hypothetical lone WTC-1, the TMD reduces the number of columns exceeding a DC ratio of 1.33 from 79 down to 10, and out of these, seven columns are located at the 107th floor where the outrigger trusses frame into the perimeter wall, and the remaining three are corner columns – two at the B1 level and one at the 9th floor level; the corresponding pre-retrofit column DC ratios are shown in Figures D.3-D6 and the post-retrofit ones are shown in Figures D.7-D.10. For a lone WTC-2, the TMD reduces the 400 perimeter wall columns exceeding a DC ratio of 1.33 down to 26; the corresponding pre-retrofit column DC ratios are shown in Figures D.11-D14 and the post-retrofit ones are shown in Figures D.15-D.18.



Table 4.2 Number of Unique Exterior Wall Columns With DC Ratio > 1.33 Effect of TMD on Single-Tower Configuration – ASCE7-98 Standard

Configuration and Structural Damping WTC 1 WTC 2

No Retrofit (2.5% Damping) 79 400

TMD Retrofit (5% Damping) 10 26

Table 4.3 Number of Unique Exterior Wall Spandrels With DC Ratio> 1.33 Effect of TMD on Single-Tower Configuration – ASCE7-98 Standard

Test Configuration and Structural Damping WTC 1 WTC 2

No Retrofit (2.5% Damping) 176 953

TMD Retrofit (5% Damping) 65 165

Similarly, Table 4.3 illustrates the extraordinary reduction in the number of spandrel elements that have a DC ratio in excess of the acceptable value of 1.33 that can be achieved by the installation of a tuned mass damper. For WTC-1, the number of overstressed spandrels is reduced from 176 down to 65, and the maximum DC ratio is reduced from a high of 1.85 down to a high of 1.57; the corresponding pre-retrofit spandrel DC ratios are shown in Figures D.19-D22 and the post-retrofit ones are shown in Figures D.23-D.26. For WTC-2, the number of overstressed spandrels is reduced from 953 down to 165, and the maximum DC ratio is reduced from a high of 1.70 down to a high of 1.55; the corresponding pre-retrofit spandrel DC ratios are shown in Figures D.27-D30 and the post-retrofit ones are shown in Figures D.31-D.34.

Further, since the aeroelastic model results from both RWDI and CPP produce a wind response smaller than what is predicted by the HFFB model and used in the evaluation presented herein, the evaluation of the stress state in the exterior wall columns and spandrels provides an upper bound estimate of the number of columns potentially requiring retrofit measures. As recommended in the independent BLWTL peer review by UWO, the HFFB results can be conservatively reduced by 5% for design applications to account for mitigating aeroelastic effects. This would further reduce the number of column or spandrel elements that would require consideration for retrofit and lower the demand capacity ratio in those that do. The exterior wall panel column and spandrel elements that have a demand-capacity ratio in excess of the acceptable value of 1.33 for the tuned mass damper case can be locally retrofitted by the addition of cover plates, if necessary, while keeping in mind the extraordinary ability of the exterior wall to redistribute loads efficiently.



In the hypothetical scenario of one surviving tower, the DC ratios in the core columns were also evaluated to investigate their ability to carry the additional gravity load imposed by the installation of a Tuned Mass Damper. Since the optimal placement of a passive TMD device is as close to the top of the towers as possible, its dead load was assumed to be uniformly distributed to the core columns at the 110th level. Consequently, in some core columns at the very top of the towers, there is a localized increase in the DC ratios due to the addition of the TMD dead load, but the addition of the TMD dead load alone does not cause any core columns to experience a significant increase in their DC ratios. In no case do the DC ratios of the core columns for the gravity loads only case exceed unity, whether the TMD device is installed or not.

Again, in the hypothetical scenario of one surviving tower, the DC ratios of all core columns for all applicable LRFD load combinations are less than the acceptable value of 1.33. In fact, only a handful of interior core columns ever exceed a DC ratio of 1.0 (but still remain under 1.33), whether the TMD is installed or not. These occur at the sky lobby floors 40, 43, 74, 76 and 77 and at floors 104 and 105, primarily in the 500 and 600 series of core columns. The addition of a TMD only reduces the maximum DC ratio in core columns, down to a maximum of 1.04 for WTC-1 and 1.15 for WTC-2. The average value of the DC ratios of all core columns remains virtually unchanged with the addition of the TMD dead loads and accompanying reduction in wind loading.

The final choice of a specific retrofit option would be based on trade-offs of cost, practicality and the degree of repair intrusiveness. However, the degree and extent of retrofits discussed here under the stringent standards of ASCE 7-98 that exceed the requirements of the NYCBC remain small compared to the scale and value of each of the WTC towers.



5 References

[ASCE, 1998] Minimum Design Loads for Buildings and Other Structures, ASCE 7-98, American Society of Civil Engineers, Washington, DC.

[BLWTL, 2003] Vickery, Surry and Isyumov, “Report Regarding the Review of the World Trade Center Twin towers (NY) Wind Studies Carried Out by RWDI and CPP”, The Alan G. Davenport Wind Engineering Group and the Boundary Layer Wind Tunnel Laboratory at The University of Western Ontario, London, Ontario, Canada, Nov. 2003.

[CPP, 2002] Cermak, Peterka, Petersen Inc Data Report, Wind-Tunnel Tests – World Trade Center, New York, NY, CPP Project 02-2420, Aug 2002.

[FEMA, 2000] Prestandard and Commentary for the Seismic Rehabilitation of Buildings, FEMA 356, Prepared by the American Society of Civil Engineers for the Federal Emergency Management Agency, Washington, DC.

[Irwin, 2002] A letter from Dr. Peter Irwin to Mr. Levy, dated Oct. 2, 2002 Re: Peer Review of Wind Tunnel Tests, World Trade Center. RWDI Reference #02-1310.

[Levy and Abboud, 2002a] Levy, M. and Abboud, N., Aug. 1, 2002, Structural Engineering Investigation of the World Trade Center, expert report, Hart-Weidlinger, Weidlinger Associates, Inc., August 1, 2002.

[Levy and Abboud, 2002b] Levy, M. and Abboud, N., Oct. 4, 2002, Structural Engineering Investigation of the World Trade Center, expert report, Hart-Weidlinger, Weidlinger Associates, Inc., August 1, 2002.

[Osteraas, 2002] Exponent Failure Analysis, “World Trade Center: Assessment of Structural and Architectural Damage,” dated September 2002.

[RWDI, 2002a] Wind Induced Structural Responses, World Trade Center – Tower 1, New York, New York. Prepared for Hart-Weidlinger Division of Weidlinger Associates, Inc. Rowan Williams Davies & Irwin, Inc., Guelph, Ontario, Canada. Oct. 4, 2002.

[RWDI, 2002b] Wind Induced Structural Responses, World Trade Center – Tower 2, New York, New York. Prepared for Hart-Weidlinger Division of Weidlinger Associates, Inc. Rowan Williams Davies & Irwin, Inc., Guelph, Ontario, Canada. Oct. 4, 2002.



6 Materials Considered Materials Referenced See list in body of report. Materials Reviewed In addition to the Materials and References listed in our prior reports, “World Trade Center – Structural Engineering Investigation, M. Levy and N. Abboud, Aug. 1st, 2002” and “World Trade Center – Structural Engineering Investigation – Rebuttal Report, M. Levy and N. Abboud, Oct. 4, 2002”, and the References listed in the body and appendices of this report, the following materials have been reviewed:

1. WTC buildings construction photos.

2. WTC towers original wind tunnel testing photos.

3. NYPD photos.



Appendix A

BLWTL Peer Review Report

HART-WEIDLINGER A-1


Appendix B

RWDI Wind Loads and Load Combinations for a TMD-enhanced 5% Structural Damping Level

HART-WEIDLINGER B-1


Table B.1 50 Year Return Period Effective Floor-by-Floor Wind Loads Acting on WTC 1, Configuration 2, Structural Properties without P-δ Effects,

5% Structural Damping

Floor Level

Fx (lb)

Fy (lb)

Mz (lb-ft)

1 27800 12200 504500 2 55200 25200 1014000

3 35700 16500 637900

4 19500 9200 345700

5 19600 9400 347300

6 29800 14300 530200

7 46500 26100 904100

8 32200 15800 581400

9 40700 24600 805400

10 40400 23600 783100

11 39800 23900 773400

12 40500 24900 789200

13 41300 25900 804800

14 42000 27000 820400

15 42800 28000 835800

16 43500 29000 851000

17 44200 30000 866400

18 44900 31000 881500

19 45600 32000 896500

20 46400 33000 911600

21 47200 34200 927800

22 48100 35400 944000

23 49000 36700 960200

24 49900 37900 976100

25 50800 39100 991700

26 51700 40300 1008000

27 52500 41500 1023000

28 53300 42600 1038000

29 54200 43800 1054000

30 55000 45000 1069000

31 55900 46200 1084000

HART-WEIDLINGER B-2


Floor Level

Fx (lb)

Fy (lb)

Mz (lb-ft)

32 56700 47400 1100000 33 57600 48500 1115000

34 58400 49600 1130000

35 59200 50800 1146000

36 60000 52000 1161000

37 60800 53100 1175000

38 61700 54300 1190000

39 62600 55500 1207000

40 67400 59800 1306000

41 84500 78200 1621000

42 42700 33200 725700

43 92400 87900 1747000

44 77700 70800 1470000

45 74000 68600 1391000

46 71600 67200 1340000

47 71800 68000 1339000

48 72800 69300 1356000

49 73800 70700 1372000

50 74800 72100 1388000

51 75800 73400 1404000

52 76800 74800 1421000

53 77900 76200 1438000

54 78800 77500 1454000

55 79800 78800 1469000

56 80800 80200 1485000

57 81800 81500 1501000

58 82700 82800 1517000

59 83700 84200 1533000

60 84600 85500 1548000

61 85700 87000 1564000

62 86900 88500 1581000

63 88000 90000 1597000

64 89000 91400 1613000

65 90200 93000 1630000

HART-WEIDLINGER B-3


Floor Level

Fx (lb)

Fy (lb)

Mz (lb-ft)

66 91400 94500 1646000 67 98200 101100 1781000

68 100700 104100 1823000

69 96000 100400 1721000

70 96000 100800 1716000

71 97200 102300 1732000

72 98200 103700 1747000

73 99200 105200 1764000

74 105100 111200 1883000

75 137700 148700 2407000

76 54600 54100 835900

77 152800 166800 2627000

78 112600 120400 1973000

79 110600 119000 1922000

80 109100 118000 1881000

81 109300 118500 1874000

82 110400 120100 1888000

83 111400 121400 1900000

84 112300 122700 1911000

85 113400 124100 1923000

86 114300 125400 1935000

87 115300 126700 1947000

88 116400 128200 1960000

89 117300 129400 1972000

90 118100 130600 1983000

91 119200 132100 1996000

92 120100 133300 2008000

93 121000 134500 2020000

94 122100 136000 2033000

95 123000 137200 2045000

96 123800 138500 2057000

97 124900 139900 2070000

98 125800 141100 2082000

99 126700 142300 2094000

HART-WEIDLINGER B-4


Floor Level

Fx (lb)

Fy (lb)

Mz (lb-ft)

100 127700 143800 2107000 101 127900 144600 2113000

102 128100 145400 2121000

103 128700 146600 2131000

104 129100 147600 2142000

105 129500 148700 2152000

106 132700 152700 2220000

107 208900 242900 3313000

108 194000 226200 3132000

109 58200 65800 910200

110 286600 337700 4891000

Sums 9.32E+06 9.34E+06 1.65E+08

Factors to Convert Above Load Vectors to

ASCE 7-98 1.11 1.13 1.09

HART-WEIDLINGER B-5


Table B.2 50 Year Return Period Effective Floor-by-Floor Wind Loads Acting on WTC 1, Configuration 2, Structural Properties with P-δ Effects,


Floor Level

Fx (lb)

Fy (lb)

Mz (lb-ft)

1 24300 11800 508400 2 48600 24700 1022000

3 31400 16100 642700

4 17200 9000 348200

5 17400 9200 349800

6 26300 14000 534000

7 42900 26300 913200

8 28400 15300 585200

9 38300 25100 814200

10 37400 23700 790600

11 37000 24100 780900

12 37900 25200 796900

13 38700 26200 812700

14 39500 27300 828400

15 40400 28400 844000

16 41200 29400 859400

17 42000 30500 874900

18 42800 31500 890200

19 43600 32500 905300

20 44400 33600 920600

21 45400 34900 937000

22 46400 36200 953300

23 47400 37500 969700

24 48400 38800 985800

25 49300 40000 1002000

26 50300 41300 1018000

27 51300 42600 1033000

28 52200 43800 1049000

29 53200 45100 1065000

30 54100 46300 1080000

31 55000 47500 1095000

HART-WEIDLINGER B-6


Floor Level

Fx (lb)

Fy (lb)

Mz (lb-ft)

32 56000 48800 1111000 33 56900 50000 1126000

34 57800 51200 1142000

35 58800 52400 1157000

36 59700 53600 1172000

37 60600 54800 1187000

38 61500 56000 1202000

39 62500 57300 1219000

40 67200 61600 1319000

41 85800 81500 1639000

42 39700 32400 726300

43 94800 92200 1768000

44 77800 73000 1484000

45 74500 70900 1405000

46 72400 69700 1354000

47 72800 70600 1353000

48 73900 72000 1369000

49 75000 73400 1386000

50 76200 74900 1402000

51 77300 76400 1419000

52 78400 77800 1435000

53 79600 79300 1453000

54 80700 80700 1469000

55 81800 82100 1484000

56 82900 83600 1501000

57 84000 85000 1516000

58 85000 86300 1532000

59 86200 87800 1548000

60 87200 89200 1564000

61 88400 90700 1580000

62 89700 92400 1597000

63 90900 93900 1613000

64 92100 95400 1629000

65 93400 97100 1646000

HART-WEIDLINGER B-7


Floor Level

Fx (lb)

Fy (lb)

Mz (lb-ft)

66 94700 98800 1663000 67 101300 105200 1798000

68 103900 108300 1840000

69 99800 104900 1738000

70 100000 105500 1733000

71 101200 107100 1749000

72 102300 108500 1765000

73 103500 110000 1782000

74 109400 116200 1902000

75 145600 157000 2436000

76 53200 53600 833300

77 162600 176800 2660000

78 117200 125500 1991000

79 115600 124400 1941000

80 114400 123600 1900000

81 114800 124300 1894000

82 116000 125900 1907000

83 117100 127300 1919000

84 118200 128700 1931000

85 119400 130200 1943000

86 120400 131600 1955000

87 121500 133000 1967000

88 122700 134500 1980000

89 123700 135800 1992000

90 124700 137100 2003000

91 125900 138700 2016000

92 126900 140000 2028000

93 127900 141200 2040000

94 129100 142800 2054000

95 130100 144100 2066000

96 131100 145400 2078000

97 132300 146900 2091000

98 133300 148200 2103000

99 134200 149500 2115000

HART-WEIDLINGER B-8


Floor Level

Fx (lb)

Fy (lb)

Mz (lb-ft)

100 135400 151000 2128000 101 135600 151800 2134000

102 135900 152700 2142000

103 136500 153900 2152000

104 137000 155100 2163000

105 137400 156200 2173000

106 140400 160100 2241000

107 224000 257200 3351000

108 206900 238500 3165000

109 57000 64400 902900

110 307800 358100 4951000

Sums 9.58E+06 9.74E+06 1.67E+08

Factors to Convert Above Load Vectors to

ASCE 7-98 1.11 1.13 1.09

HART-WEIDLINGER B-9


Table B.3 Load Combinations for Simultaneous Application of Effective Static Floor-by-Floor Loads in Configuration 2 from Tables B.1 and B.2

Recommended Load Combination Factors of 50-Year Return Period Wind Loads Load

Combination Fx Forces Fy Forces Mz Moment

1 100% 40% 40%

2 100% 40% -55%

3 100% -45% 40%

4 100% -45% -55%

5 -100% 40% 55%

6 -100% 40% -55%

7 -100% -45% 50%

8 -100% -45% -55%

9 40% 100% 40%

10 40% 100% -55%

11 40% -100% 40%

12 40% -100% -55%

13 -50% 100% 40%

14 -50% 100% -55%

15 -50% -100% 40%

16 -50% -100% -55%

17 40% 45% 100%

18 40% 50% -100%

19 40% -40% 100%

20 50% -45% -100%

21 -50% 45% 100%

22 -50% 50% -100%

23 -50% -40% 100%

24 -50% -50% -100%

HART-WEIDLINGER B-10


Table B.4 50 Year Return Period Effective Floor-by-Floor Wind Loads Acting on WTC 2, Configuration 2, Structural Properties without P-δ Effects,


Floor Level

Fx (lb)

Fy (lb)

Mz (lb-ft)

1 22400 31400 600700 2 35300 51100 999300 3 24700 35200 668700 4 23400 33600 637100 5 23400 33800 639900 6 21800 31700 598700 7 24200 40900 876300 8 24900 35900 684000 9 24000 42000 908700 10 25400 42300 886200 11 24400 41500 872400 12 24400 42200 888200 13 24400 42900 903800 14 25600 43600 919400 15 26900 44300 934700 16 28100 44900 949800 17 29500 45600 965200 18 30700 46300 980300 19 32000 47000 995300 20 33300 47600 1010000 21 34800 48500 1027000 22 36400 49400 1043000 23 38000 50300 1059000 24 39500 51100 1075000 25 41000 52000 1091000 26 42600 52800 1107000 27 44100 53700 1123000

28 45500 54500 1138000 29 47100 55400 1154000 30 48500 56200 1169000 31

50000 57000 1184000



Floor Level

Fx (lb)

Fy (lb)

Mz (lb-ft)

32 51500 57800 1200000 33 53000 58600 1215000 34 54400 59400 1230000 35 55900 60300 1246000 36 57400 61100 1261000 37 58700 61800 1275000 38 60300 62700 1291000 39 61800 63500 1308000 40 66100 68600 1414000 41 89900 84500 1736000

42 28800 46100 809700 43 102600 89700 1831000 44 76400 75900 1526000 45 76600 74300 1492000 46 76500 72600 1454000 47 77800 72800 1454000 48 79600 73800 1472000 49 81300 74800 1491000 50 83200 75900 1509000 51 84900 76900 1527000 52 86700 77900 1546000 53 88600 79000 1565000 54 90300 80000 1583000 55 92000 81000 1600000 56 93900 82000 1619000 57 95600 83000 1637000 58 97300 84000 1654000 59 99100 85000 1672000 60 100700 86000 1689000 61 102600 87000 1708000 62 104700 88200 1726000 63 106600 89300 1743000 64 108600 90400 1761000 65

110700 91600 1780000 HART-WEIDLINGER B-12


Floor Level

Fx (lb)

Fy (lb)

Mz (lb-ft)

66 112600 92700 1798000 67 114600 93800 1817000 68 116600 95000 1835000 69 118500 96000 1852000 70 120400 97100 1869000 71 122400 98200 1886000 72 124200 99200 1903000 73 126100 100300 1922000 74 132400 106100 2045000 75 183000 137700 2618000

76 55100 59100 921800 77 208300 152600 2863000 78 142900 113400 2134000 79 143100 112000 2095000 80 142800 110300 2051000 81 143800 110400 2043000 82 145800 111500 2056000 83 147400 112400 2068000 84 149000 113300 2079000 85 150900 114400 2091000 86 152600 115300 2103000 87 154200 116300 2115000 88 156100 117300 2127000 89 157600 118200 2139000 90 159200 119000 2150000 91 161000 120100 2163000 92 162600 121000 2175000 93 164100 121800 2186000 94 166000 122900 2200000 95 167500 123700 2212000 96 169000 124600 2224000 97 170900 125700 2237000 98 172400 126500 2248000 99



Floor Level

Fx (lb)

Fy (lb)

Mz (lb-ft)

100 175900 128400 2273000 101 176300 128900 2279000 102 176700 129400 2285000 103 177900 130400 2299000 104 179000 131300 2312000 105 179800 132000 2322000 106 182900 135600 2389000 107 298000 212200 3572000 108 273300 198500 3371000 109 64600 62400 946100

110 411700 293600 5271000

Sums 1.10E+07 9.47E+06 1.80E+08 Factors to Convert Above Load Vectors to

ASCE 7-98

1.12 1.11 1.08



Table B.5 50 Year Return Period Effective Floor-by-Floor Wind Loads Acting on WTC 2, Configuration 2, Structural Properties with P-δ Effects,


Floor Level

Fx (lb)

Fy (lb)

Mz (lb-ft)

1 22400 30400 627600 2 35300 49500 1042000 3 24700 34100 698000 4 23400 32600 664600 5 23400 32800 667100 6 21800 30800 623800 7 24200 40300 906500 8 24900 34800 712100 9 25700 41500 938400 10 25400 41500 916400 11 24400 40800 901300 12 24700 41600 917000 13 26000 42300 932400 14 27400 43000 947900 15 28700 43800 963100 16 30000 44500 978100 17 31400 45200 993300 18 32700 45900 1008000 19 34000 46600 1023000 20 35300 47400 1038000 21 36900 48300 1054000 22 38500 49200 1070000 23 40100 50200 1087000 24 41700 51100 1103000 25 43300 52000 1118000 26 44900 52900 1134000 27 46400 53800 1149000

28 48000 54700 1165000 29 49600 55600 1181000 30 51100 56400 1196000 31

52600 57300 1211000



Floor Level

Fx (lb)

Fy (lb)

Mz (lb-ft)

32 54100 58200 1226000 33 55600 59100 1241000 34 57100 59900 1256000 35 58700 60800 1271000 36 60200 61700 1286000 37 61600 62500 1301000 38 63200 63400 1316000 39 64800 64300 1333000 40 69200 69300 1441000 41 94400 86000 1766000

42 29200 45500 828300 43 108000 91900 1862000 44 79800 76900 1553000 45 80000 75500 1518000 46 80000 73900 1478000 47 81400 74100 1477000 48 83200 75200 1496000 49 85000 76300 1514000 50 87000 77500 1533000 51 88800 78500 1551000 52 90600 79600 1569000 53 92600 80800 1588000 54 94400 81800 1606000 55 96200 82900 1624000 56 98100 84000 1642000 57 99800 85100 1659000 58 101600 86100 1677000 59 103500 87200 1695000 60 105100 88200 1712000 61 107100 89300 1730000 62 109300 90600 1748000 63 111300 91800 1766000 64 113400 93000 1783000 65



Floor Level

Fx (lb)

Fy (lb)

Mz (lb-ft)

66 117600 95400 1820000 67 119600 96600 1838000 68 121700 97800 1856000 69 123700 98900 1873000 70 125600 100000 1890000 71 127700 101300 1907000 72 129600 102300 1924000 73 131600 103500 1943000 74 138000 109300 2067000 75 191800 142900 2646000

76 55300 59300 929500 77 218800 158700 2894000 78 148700 117000 2155000 79 149000 115700 2115000 80 148900 114100 2071000 81 150100 114200 2062000 82 152100 115400 2076000 83 153800 116400 2087000 84 155500 117300 2098000 85 157400 118500 2110000 86 159100 119500 2122000 87 160800 120500 2133000 88 162800 121600 2146000 89 164400 122500 2157000 90 165900 123400 2168000 91 167900 124600 2181000 92 169500 125500 2192000 93 171000 126400 2204000 94 173000 127500 2217000 95 174600 128400 2229000 96 176200 129400 2240000 97 178100 130500 2253000 98 179700 131400 2265000 99



Floor Level

Fx (lb)

Fy (lb)

Mz (lb-ft)

100 183200 133400 2289000 101 183600 134000 2295000 102 184100 134500 2301000 103 185300 135500 2314000 104 186400 136500 2328000 105 187200 137200 2337000 106 190200 140800 2403000 107 311800 221700 3597000 108 285100 206800 3392000 109 63500 62800 942200

110 430900 307000 5309000

Sums 1.15E+07 9.70E+06 1.82E+08 Factors to Convert Above Load Vectors to

ASCE 7-98

1.11 1.12 1.08



Table B.6 Load Combinations for Simultaneous Application of Effective Static Floor-by-Floor Loads in Configuration 2 from Tables B.4 and B.5

Recommended Load Combination Factors of 50-Year Return Period Wind Loads Load

Combination Fx Forces Fy Forces Mz Moment

1 100% 55% 40%

2 100% 55% -55%

3 100% -40% 40%

4 100% -40% -55%

5 -100% 55% 45%

6 -100% 55% -55%

7 -100% -40% 45%

8 -100% -40% -55%

9 40% 100% 55%

10 45% 100% -50%

11 40% -95% 55%

12 40% -95% -40%

13 -40% 100% 55%

14 -40% 100% -40%

15 -40% -95% 55%

16 -40% -95% -40%

17 40% 50% 95%

18 50% 55% -100%

19 40% -45% 95%

20 50% -40% -100%

21 -40% 50% 95%

22 -45% 55% -100%

23 -40% -45% 95%

24 -45% -40% -100%



Appendix C

CV, Rate Schedule & Materials Considered

1. Matthys Levy CV

2. Najib Abboud CV

HART-WEIDLINGER C-1


Matthys Levy, P.E.

Circum Vitae

Birthplace Basle, Switzerland

Education CE, Columbia University, New York, NY, 1962, Applied Mechanics MSCE, Columbia University, New York, NY, 1956 BSCE, City College of New York, NY, 1951

Registration: Professional Engineer NY 1956; CA (CE) 1974; NCEES 1962; MA 1964; VT 1999; NJ 2004; MN 1995 Chartered Engineer, United Kingdom; European Engineer (EUR ING)

Brief Professional History Chairman (2002), Principal (1964), Weidlinger Associates, Consulting Engineers (1956- ) Asst. Operations Officer, 453rd Eng. Construction Battalion, US Army, Korea (1952-54) Structural Consultant, New York, NY and Chicago, IL (1951-55)

Teaching/Lecturing Experience Adjunct Professor, School of Architecture, Columbia University, New York, NY (1962-80) Visiting Critic in Architecture, Yale University, New Haven, CT (1960-65) Distinguished Professor, Pratt Institute, Brooklyn, NY (1980-81) Lecturer, University of Idaho, Rutgers University, Princeton University, Harvard University,

Catholic University, University of Florida, University of Minnesota, University of Rochester

Affiliations National Academy of Engineering American Society of Civil Engineers (Fellow) Institution of Civil Engineers (Fellow) American Institute of Architects (Honorary Member) American Concrete Institute International Association for Shell and Spatial Structures (Executive Council) International Association of Bridge and Structural Engineering

Awards IASS Tsuboi Award for paper, “The Innovation of Lightness”, 1995 ASCE, Innovation in Civil Engineering Award, 1994 Medal of Excellence, Engineering News Record, 1992, 2000 Lincoln Arc Welding Award, 1961, 1981, 1991 Prestressed Concrete Institute Award, 1963, 1971, 1992 AIA Institute Honor Award, 1985; New York Chapter, AIA Award of Merit, 1976 Founder’s Award, Salvadori Center, 2003

HART-WEIDLINGER C-2


Named as “Structural Engineering Legend in Design,” Structural Engineering Magazine, 2003 Grand Conceptor Award, ACEC, 2004

Publications - Books Contributor of more than fifty technical papers and articles in the fields of structures, computer analysis, and building

design (see separate sheet for full listing). Engineering the City: The Story of Infrastructure, with Richard Panchyk, Chicago Review Press,

2000. Translated into Japanese (2001). Earthquake Games, with Mario Salvadori, Margaret K. McElderry Books, Simon and Schuster, 1997

Translated into Japanese (1998), Scholastic Paperback, 2000. Beyond the Cube, J. Francois Gabriel, ed., chapter: Tetrahedral Purity: The Javits Center. John Wiley

and Sons, Inc., 1997. Why the Earth Quakes: The Story of Earthquakes and Volcanoes, with Mario Salvadori, WW

Norton, 1995. Paperback edition, 1997. Translated into Japanese (1996), Italian (1998), Turkish (2000), Chinese (2000).

Why Buildings Fall Down, with Mario G. Salvadori, WW Norton, 1992. Paperback edition, 1994. Translated into Japanese (1993), Korean (1993), Italian (1997), Rumanian (1998), Second Edition, 2002.

Engineering and Humanities, J. H. Schaub and S. K. Dickson, ed., chapter: Structure and Sculpture, John Wiley and Sons, Inc. 1982.

Structural Design in Architecture, with Mario G. Salvadori, Prentice Hall, 1967: Translated into Spanish (1970), Japanese (1969) and Korean (1975). Second Edition, 1980.

Patents Triangulated Roof Structure, 1993; Triangulated Cable Dome with Retractable Roof, 1994 Triangulated Roof Structure, 1995

Representative Project Experience Milestone Projects Rose Center for Earth and Space, American Museum of Natural History, New York, NY NY Hall of Science Interactive Exhibit Playground, Queens, NY Baruch College Academic Complex, New York, NY Bank of China HQ Building, Beijing, China CIBA-GEIGY Life Science Building, Summit, NJ Rockefeller University’s Campus Community Bridge, New York, NY World Bank HQ Complex Addition, Washington, DC Georgia Dome Stadium, Atlanta, GA La Plata Stadium, La Plata, Argentina Jacob K. Javits Convention Center, New York, NY Marriott Marquis Hotel and Theater, New York, NY Expert Testimony and Forensic Investigation World Trade Center collapses Superdome, Sydney, Australia

HART-WEIDLINGER C-3


Montreal Stadium, roof failure Atlanta Arena, collapse of stands Two Times Square, collapse of scaffolding, Pool, failure of waterproofing High rise building, structural condition after fire RCA Dome, roof control system Marriott Marquis Hotel, structural bracing for crane UNI Dome, condition after storm caused deflation Javits Center, delay due to cast node defects Office Building Projects Canary Wharf, FC4 and FC6, London, England Banque Lambert, Bruxelles, Belgium EPA Research and Administrative Facility, Research Triangle Park, NC SUNY/Buffalo Natural Sciences and Math Complex, Amherst, NY Rockefeller Laboratory, Memorial Sloan Kettering Cancer Research Center, New York, NY Merck, Sharp and Dohme Headquarters, Valley Forge, PA Cali International Financial Center, Jersey City, NJ Southern Bell Headquarters Building, Atlanta, GA Leighton House Residence Tower, New York, NY 85 Broad Street Tower, New York, NY One Financial Center, Boston, MA DHUD HQ Building, Washington, DC US Embassy Complexes:

Nicosia, Cyprus; Damascus, Syria; Montevideo, Uruguay; Athens, Greece Baghdad, Iraq; Tokyo, Japan

Institutional Projects Children’s Museum, New York, NY Asia Society Headquarters, New York, NY Polytechnic University - Dibner Library, Brooklyn, NY Prototype Design for 6 Elementary Schools, Bronx and Brooklyn, NY Cooper Union Residence Hall, New York, NY Hostos College Allied Health Complex, New York, NY NYU Dormitory Towers, New York, NY Long Span and Transportation Projects Shanghai Stadium Roof, Shanghai, China Schalke Stadium Retractable Dome, Gelsenkirchen, Germany Carrier Dome Fabric Roof Upgrade, Syracuse, NY Flatbush Avenue and Utica Avenue Station Rehabilitations, Brooklyn, NY Motorgate Parking Structure, Roosevelt Island, NY White Plains Transportation Center Rehabilitation, White Plains, NY Roosevelt Avenue and 74th St. Intermodal Station Expansion, Queens, NY

HART-WEIDLINGER C-4


Section of WMATA Metro, Washington, DC NAFEC Hangar #1 Restoration, Lakehurst, NJ LIST OF PUBLICATIONS Books Co-author of Structural Design in Architecture, Why Buildings Fall Down, Why the Earth Quakes, Earthquake Games and Engineering the City (see above for full list).

Illustrations Architecture and Engineering: An Illustrated Teacher’s Manual on Why Buildings Stand Up by

Mario Salvadori and Michael Tempel, The New York Academy of Sciences, 1983. Your Child’s Sensory World by Lise Liepmann, The Dial Press: 1973.

Exhibitions and Television Appearances Domes, Building Big Series, PBS, 2000; Why the Towers Fell, NOVA, 2002; Engineering Disasters, Modern Marvels, 2002; Why Buildings Collapse, ABC News, 2002; The Leaning Tower of Pisa, History Channel, 2002; Inviting Disaster: Structures That Fall, History Channel, 2003. “The Engineer’s Art,” Centre George Pompidou, Paris, 1997

Papers and Articles “Anatomy of the World Trade Center Collapses: A Structural Engineering Investigation,” with N.N. Abboud, M. Levy, D. Tenant, J. Mould, H. Levine, S. King, C. Ekwueme, A. Jain and G. Hart, Proc. of the Third Forensic Engineering Congress, ASCE, Oct. 19-21, 2003, San Diego, CA.. “Anatomy of a Disaster: A Structural Investigation of the World Trade Center Collapses,” with N.N. Abboud, M. Levy, D. Tenant, J. Mould, H. Levine, S. King, C. Ekwueme, A. Jain and G. Hart, SFPE/SEI Proc., Conference on Designing Structures for Fire, Sept.30- Oct. 1, 2003, Baltimore, MD. “Simplified and Advanced Methodology for Determining the Response of Buildings to Aircraft Impact,” with Levine, H., Tennant, D. Lawver, D., Levy, M. and Abboud, N., ASCE 2003 Structures Congress, Designing and Protecting Structures from Terrorist Attacks, May 29-June 1, 2003, Seattle, WA. “Great Structural Engineering Firms,” The Structural Design of Tall and Special Buildings, Wiley, 2003 “The Pusan Dome, Structural Design of Retractable Roof Structure,” Kazuo Ishii, ed., WIT Press,

Southampton, October 2000. “Staggered Truss System Earns an A+ ,” Modern Steel Construction, November 2000. “Tenstar Canopy, A New Form of Roof,” IASS Symposium, Madrid, Spain, September 1999. “Twinstar Dome for La Plata,” IASS Symposium, Sydney, Australia, October 1998. “Innovation of Structural Form,” IASS Symposium, Sydney, Australia, October 1998. “High Translucency Structural Fabric,” Structural Engineers World Congress, San Francisco, July 1998. “The La Plata Tenstar Dome,” Structural Engineers World Congress, San Francisco, July 1998. “The Pusan Dome and Retractable Structure,” Structural Engineers World Congress, San Francisco,

July 1998. “A Museum for the Heavens,” Civil Engineering, May 1998. “Shanghai Stadium, China’s First Fabric Roof, IASS Symposium, Singapore, November 1997. “Engineering of Architecture,” Panstadia International, London, April 1997. “Interstitial Structure for the Ciba-Geigy Laboratory,” IASS Symposium, Stuttgart, Germany, 1996.

HART-WEIDLINGER C-5


“Computers and the Conceptual Design of Structures,” IASS Symposium, Stuttgart, Germany, October 1996.

“The Limit of Spatial Structures” IASS Symposium, Beijing, China, May 1996. “Retractable Lightweight Structures,” IASS Symposium, Milano, Italy, June 1995. “Wind Load Design of the Georgia Dome,” with Tian-Fang Jing, ASCE Convention, Atlanta, GA,

October 1994. “The Lightest Retractable Roof,” IABSE Symposium, Birmingham, UK, September 1994. “Floating Saddle Connections for the Georgia Dome,” with Tian-Fang Jing, Structural Engineering

International, Journal of IABSE, August 1994. “The Innovation of Lightness,” IASS Bulletin, 1994. “Protecting Buildings Against Terrorism,” with Eve Hinman, Fire Engineering, December 1993. “Interstitial Precast Prestressed Concrete Trusses for Ciba-Geigy Life Science Building,” with Tony

Yoshizawa, PCI Journal, November/December 1992. “Hypar-Tensegrity Dome, Construction Methodology,” IASS Symposium, Toronto, Canada, July

1992. “Analysis of the Georgia Dome Cable Roof,” AEC Conference on Computing, Dallas, Texas, June 1992. “Non-linear Analysis of Cable Dome,” proceedings, ASCE Structures Congress, San Antonio, Texas,

April 1992. “The Proportional Eye,” proceedings, ASCE Structures Congress, San Antonio, April 1992. “A Case of the Shakes,” Civil Engineering, February 1992. “Floating Fabric Over Georgia Dome,” Civil Engineering, November 1991. “The Hypar-Tensegrity Dome, A Nonlinear View,” proceedings, Second Civil Engineering Automation

Conference, ASCE, New York, November 1991. “Hypar-Tensegrity Dome, Optimal Configurations,” IASS Symposium: Spatial Structures at the Turn of

the Millennium, Copenhagen, September 1991. “Cable Dome Weldments,” James F. Lincoln Arc Welding Awards Program, August 1991. “Aesthetics and Structural Form,” University of Idaho lecture, April 1991. “Hypar-Tensegrity Dome,” proceedings, International Symposium on Sports Architecture, Beijing, China,

November 1990. “Precast Facade Panels - Past and Current Examples,” proceedings, Architectural Precast Concrete

Cladding - Its Contribution to Lateral Resistance of Buildings, PCI, Chicago, Illinois, November 1989. “Hybrid Structures,” Architecture, June 1989. “The Optimum Skyscraper,” proceedings, ENSIDESA Seminar, Alicante, Spain, April 1989. “Exploring Composite Structures,” Architecture, March 1988. “Load Test Verification of Space Frame Roof Design,” Space Structures, Spring 1988. “Space Frame Reserve Capacity,” proceedings, International Colloquium on Space Structures, Beijing,

China, October 1987. “New Approaches to Long Span Structures,” Architecture, March 1987. “The Problem with Public Projects”, Civil Engineering, March 1987. “Solving the Tough Problems in Designing the Javits Center,” proceedings, National Design

Engineering Conference, September 1986. “New York Convention Center Space Frame,” IASS Symposium on Spacial Roof Structures, Dortmund,

1984.

HART-WEIDLINGER C-6


“Space Frame Columns,” James F. Lincoln Arc Welding Awards Program, August 1981. “Building the Empire City,” The Sciences, December, 1980. “A Sense of Structure and Sculpture,” Crom Lectures on Civil Engineering Design, 1980 “A Sense of Structure,” ASCE Convention and Exposition, October 1979. “Bobcat Bridge,” AE Concepts in Wood Design, April-May 1978. “High-Rise Panel Structures,” Journal of the Structural Division, ASCE, with Istvan S. Varga, May 1972. “Optimum Floor Depth,” Architectural and Engineering News, November 1968. “Some Structural Implications of Exposed Concrete,” Journal of the American Concrete Institute,

July 1968. “Building,” The Encyclopedia Americana, 1968. “Architectural Education, A Look Back and a Look Forward,” Architectural and Engineering News,

June 1965. “The Role of the Computer in Engineering Practice,” Architectural Record, with Charles P. Lecht,

August 1963. “All Welded Grid Trusses,” James F. Lincoln Arc Welding Foundation Awards Program 1961,

Digest in Progressive Architecture, December 1961. “Precast Grid Wall for Banque Lambert,” Journal of the American Concrete Institute, February 1961. “La Concha Shell,” Informes de la Construccion, with Raymond Parnes, January 1961. “Thin Shells,” Architectural Record, June 1959. “Air-Supported Nylon Membranes Roof Theater,” Engineering News Record, August 20, 1959. “Conoid with Corrugations Makes an Unusual Roof,” Engineering News Record, December 5, 1957. Legal Cases (1999-Present) 1. 2004 Beacon/Barton Mallow v. HOK et al Resolutions, Inc., Mediator, Boston Adequacy of the design of the Patriots Stadium Attended Mediation; pending outcome 2. 2004 Maryland Stadium Authority, et al v. Ellerbe Becket Circuit Court for Baltimore City, Design adequacy of raker beams for the Comcast Center Preparing report. 3. 2003 US Fidelity & Guaranty Co. v. Dick Corp/Barton Mallow Co. et al US District Court, Western Pennsylvania, Adequacy of documents for detailing and construction of steel connections Prepared report; was deposed; pending 4. 2003 Hexaport v. Shelley engineering US District Court, New Hampshire, C-02-476-JD Design defects discovered during construction Prepared report; Pending trial

HART-WEIDLINGER C-7


5. 2003 Lakes of the Meadow, et al v. Arvida/Walt Disney World Circuit Court, Miami-Dade County, 95-23003-CA-08 Construction did not conform to design drawings Prepared report and was deposed; Outcome pending 6. 2003 Lake Superior Center Authority v. Hammel Green & Abrahamson, Inc & Rutherford &

Chekene District Court, County of St. Louis: C2-02-602206 Claimed design deficiency Prepared Report and Affidavit; pending trial 7. 2002-Present World Trade Center Properties LLC, et al v. Travelers Indemnity Co. et al US District Court, Southern District of New York, No. 01CV12738 (JSM) Structural Investigation of the Collapses of the WTC Twin Towers. Prepared reports, prepared affidavit and was deposed 2002, 2003; pending trial 8. 2001-2002 Metreon, Inc v. Bovis Construction Corporation et al Trial Court of the State of California No. 305856 Failure to meet design requirements and delay claim Prepared statement and testified at arbitration; award in favor of plaintiff 9. 2000-2001 World Lavon McCord et al and Rebecca Caraway et al v. The LZA Group et al Fulton County, GA 99-vs-157365 and 99-vs-157903A Failure of precast concrete stands at the Atlanta Arena Prepared report and was deposed; Settled before trial 10. 1998-1999 University of Northern Iowa v. Commerce & Industry Insurance Co. Iowa District Court for Black Hawk County, LACV 084595 Failure of the Fabric roof of the UNI Dome Prepared report, was deposed and testified at trial; award in favor of plaintiff

HART-WEIDLINGER C-8


Najib Abboud

Circum Vitae Education PhD, Stanford University, Stanford, CA, 1990, Civil Engineering (Structural Mechanics) and

Mechanical Engineering MSSE, Stanford University, Stanford, CA, 1986 BSCE, American University, Beirut, Lebanon, 1985

Professional Experience Associate Principal and Chief Technology Officer, Weidlinger Associates Inc., New York, NY,

(2003-); Senior Associate (1996-2003); Associate (1993-96); Research Engineer (1990-93).

Responsible for research and development in the area of computational methods for transient and harmonic multi-media interaction problems in general, and structural acoustics, ultrasonics and transduction in particular. Led or contributed to several software development projects, mainly in computer-aided modeling for various engineering and imaging applications, in areas of shock and nonlinear fluid/structure analysis, soil/structure interaction, structural damping, structural acoustics and ultrasonics; work conducted under the sponsorship of private industry such as AT&T Bell Laboratories and government agencies such as the Office of Naval Research, the Defense Nuclear Agency, the National Science Foundation and the National Institutes of Health. Conducted extensive work in mixed and hybrid finite element methods, boundary element methods, radiation boundary conditions and numerical dispersion analysis. Responsible for all major computer technology initiatives in the firm.

Responsible for the forensic engineering practice (East). Leads and/or coordinates all major forensic engineering projects for the firm (Eastern Sector).

Teaching/Lecturing Experience Adjunct Associate Professor, The City College of the City University of New York, Dept. of

Civil Engineering (1998- 2000).

Taught graduate courses in Finite Element Methods – Statics and Advanced Finite Element Methods – Dynamics.

Teaching Assistant, Stanford University, Dept. of Civil Engineering (1987).

Taught graduate courses in Finite Element Methods – Statics and Advanced Finite Element Methods – Dynamics.

HART-WEIDLINGER C-9


Recent Publications N.N. Abboud, M. Levy, D. Tenant, J. Mould, H. Levine, S. King, C. Ekwueme, A. Jain and G.

Hart, “Anatomy of the World Trade Center Collapses: A Structural Engineering Investigation,” Proc. of the Third Forensic Engineering Congress, ASCE, Oct. 19-21, 2003, San Diego, CA.

N.N. Abboud, M. Levy, D. tenant, J. Mould, H. Levine, S. King, C. Ekwueme, A. Jain and G. Hart, “Anatomy of a Disaster: A Structural Investigation of the World Trade Center Collapses,” SFPE/SEI Proc., Conference on Designing Structures for Fire, Sept.30- Oct. 1, 2003, Baltimore, MD.

Levine, H., Tennant, D. Lawver, D., Levy, M. and Abboud, N. (2003), “Simplified and Advanced Methodology for Determining the Response of Buildings to Aircraft Impact,” ASCE 2003 Structures Congress, Designing and Protecting Structures from Terrorist Attacks, May 29-June 1, 2003, Seattle, WA.

N.N. Abboud, G.L. Wojcik, D.K. Vaughan, J. Mould, D. Powell, and L. Nikodym, "Finite Element Modeling for Ultrasonic Transducers” Keynote Address, Proc. SPIE International Symp. on Medical Imaging 1998, Ultrasonic Transducer Engineering Conference, K. Shung (ed), San Diego, Feb 21-27, 1998.

N.N. Abboud, J. Mould, G.L. Wojcik, D.K. Vaughan, D. Powell, V. Murray and C. MacLean, "Thermal Generation, Diffusion and Dissipation in 1-3 Piezocomposite Sonar Transducers: Finite Element Analysis and Experimental Measurements” Proc. IEEE International Ultrason. Symp., 1997.

G.L. Wojcik, J. Mould, D. Tennant, R. Richards, H. Song, D.K. Vaughan, N.N. Abboud and D. Powell, “Studies of Broadband PMN Transducers Based on Nonlinear Models” Proc. IEEE International Ultrason. Symp., 1997.

G.L. Wojcik, C. DeSilets, L. Nikodym, D.K. Vaughan, N.N. Abboud and J. Mould, “Computer Modeling of Diced Matching Layers” Proc. IEEE International Ultrason. Symp., 1996.

G.L. Wojcik, J. Mould, F. Lizzy, N.N. Abboud, M. Ostromogilsky and D.K. Vaughan, “Nonlinear Modeling of Therapeutic Ultrasound,” Proc. IEEE Ultrason. Symp., 1617-1622, 1995.

M. Ettouney, R. Daddazio and N.N. Abboud, “Practical Applications of Scale Independent Elements,” Proc. 1995 Design Engineering Technical Conferences, 3(B), pp. 177-183, DE-Vol. 84-2, ASME 1995.

M. Ettouney, R. Daddazio and N.N. Abboud, “Scale Independent Elements for Dynamic Analysis of Vibrating Systems,” Proc. Third Int. Conf. on Mathematical and Numerical Aspects of Wave propagation Phenomena, Mandelieu - La Napoule (France), April 1995.

M. Ettouney, R. Daddazio and N.N. Abboud, “Behavior of Submerged Shell-Structure Systems,” ASME J. of Vibration and Acoustics, 1993.

G.L. Wojcik, D.K. Vaughan, N.N. Abboud and J. Mould, “Electromechanical Modeling Using Explicit- Time-domain Finite Elements,” Proc. IEEE Ultrason. Symp., 2, 1107-1112, 1993.

M. Ettouney, R. Daddazio and N.N. Abboud, “Probabilistic Boundary Element Method in Soil Dynamics,” in A.H-D. Cheng and C.Y. Yang (ed.), Computational Stochastic Mechanics, Computational Mechanics Publications and Elsevier Applied Science, Chapter 27, 1993.

HART-WEIDLINGER C-10


R. Daddazio, M. Ettouney and N.N. Abboud, “Submerged Shell-Structure Interaction,” Computational Methods for Fluid/Structure Interaction, AMD-Vol 178, pp. 1-6, ASME, 1993.

M. Ettouney, R. Daddazio and N.N. Abboud, “Behavior of Submerged Shell-Structure Systems,” ASME 93-WA/NCA-21, 1993.

R. Daddazio, M. Ettouney and N.N. Abboud, “Wet Modes of Submerged Structures, Part 2: Applications,” ASME J. of Vibration and Acoustics, 114, 440-448, 1992.

P.M. Pinsky, L.L. Thompson and N.N. Abboud, “Local Higher-Order Radiation Boundary Condition for the Two-Dimensional Time-Dependent Structural Acoustics Problem,” J. Acoust. Soc. Am., 91(3), 1320-1335, 1992.

N.N. Abboud and P.M. Pinsky, “Finite Element Dispersion Analysis for the Three-Dimensional Second-Order Scalar Wave Equation,” International Journal for Numerical Methods in Engineering, 35(6), 1183-1218, 1992.

N.N. Abboud, R.P. Daddazio, M.M. Ettouney, D. Ranlet, and R. Smilowitz, "Acoustic Radiation/Scattering Response of a Linearly Elastic Shell of Revolution Containing Internal Structure -- User's Manual for the WASCAT Code --", WA Technical Report, WA 9202, Weidlinger Associates, New York, New York, 1992.

Legal Cases (1999-present) 2003 US Fidelity & Guaranty Co. v. Dick Corp/Barton Mallow Co. et al US District Court, Western Pennsylvania, Adequacy of documents for detailing and construction of steel connections Expert consultant and reports co-author; pending.

2002 Silverstein properties Inc vs. Travelers Insurance Co.

Structural investigation into the causes of the collapses of the WTC Twin Towers as a result of the Sept 11 attacks. Expert consultant and reports co-author; pending.

HART-WEIDLINGER C-11


Appendix D

Figures

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110 0.0 0.0 0.1 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.1 0.1 0.2 0.1 0.1 0.1 0.0 0.0 0.0 0.0 0.0 0.0 0.1 0.0 0.1 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.1 0.0 0.1 0.2 0.1 0.1 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

109 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

108 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.1 0.0 0.1 0.3 0.6 0.3 0.1 0.2 0.0 0.0 0.0 0.0 0.1 0.1 0.2 0.4 0.1 0.1 0.4 0.2 0.1 0.0 0.0 0.1 0.0 0.0 0.1 0.1 0.3 0.6 0.3 0.1 0.1 0.1 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

107 0.1 0.4 0.3 0.2 0.2 0.1 0.0 0.0 0.0 0.1 0.1 0.1 0.1 0.2 0.7 0.8 1.1 0.5 0.5 0.8 0.5 0.5 0.3 0.1 0.1 0.1 0.5 0.5 0.4 0.3 0.3 0.4 0.4 0.5 0.3 0.1 0.1 0.1 0.4 0.4 0.7 0.7 0.5 1.0 0.9 0.7 0.6 0.2 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.3 0.3 0.5 0.1

106 0.3 0.4 0.4 0.3 0.3 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.3 0.3 0.6 0.6 0.5 0.6 0.4 0.6 0.2 0.2 0.2 0.2 0.2 0.2 0.4 0.3 0.3 0.5 0.6 0.8 0.2 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.8 0.5 0.9 0.9 0.9 0.8 0.4 0.4 0.4 0.3 0.3 0.3 0.3 0.2 0.2 0.4 0.4 0.5 0.3

105 0.3 0.4 0.4 0.4 0.3 0.2 0.2 0.2 0.3 0.3 0.3 0.3 0.3 0.3 0.7 0.7 0.7 0.6 0.5 0.4 0.2 0.2 0.2 0.2 0.3 0.3 0.4 0.3 0.3 0.2 0.3 0.4 0.3 0.4 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.6 0.6 0.8 0.9 0.9 0.8 0.4 0.4 0.4 0.4 0.4 0.3 0.3 0.3 0.3 0.2 0.3 0.3 0.4

104 0.4 0.4 0.4 0.4 0.3 0.2 0.2 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.4 0.4 0.5 0.5 0.4 0.2 0.2 0.2 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.4 0.4 0.3 0.3 0.3 0.3 0.3 0.3 0.4 0.8 0.7 0.8 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.4

103 0.4 0.5 0.5 0.4 0.4 0.2 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.4 0.5 0.3 0.3 0.3 0.2 0.2 0.3 0.3 0.3 0.4 0.3 0.3 0.3 0.3 0.3 0.4 0.5 0.4 0.3 0.3 0.3 0.3 0.3 0.3 0.5 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.3 0.3 0.3 0.3 0.3 0.3 0.5

102 0.5 0.5 0.5 0.5 0.5 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.4 0.4 0.4 0.3 0.2 0.2 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.4 0.4 0.4 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.4 0.4 0.4 0.4 0.4 0.4 0.3 0.4 0.4 0.4 0.4 0.3 0.3 0.6 0.6 0.6 0.5

101 0.4 0.5 0.5 0.5 0.5 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.4 0.4 0.4 0.4 0.4 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.4 0.4 0.4 0.4 0.4 0.3 0.3 0.3 0.3 0.3 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.6 0.7 0.7 0.6

100 0.5 0.6 0.5 0.5 0.5 0.3 0.3 0.3 0.3 0.3 0.3 0.4 0.4 0.4 0.4 0.4 0.4 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.5 0.5 0.5 0.5 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.7 0.7 0.7 0.5

99 0.4 0.5 0.6 0.6 0.5 0.3 0.3 0.3 0.3 0.3 0.3 0.4 0.4 0.4 0.4 0.4 0.4 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.4 0.3 0.4 0.3 0.4 0.3 0.3 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.5 0.5 0.5 0.5 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.7 0.7 0.7 0.6

98 0.5 0.5 0.6 0.5 0.5 0.6 0.6 0.6 0.3 0.3 0.4 0.4 0.4 0.4 0.7 0.7 0.7 0.6 0.6 0.6 0.3 0.3 0.3 0.3 0.3 0.3 0.4 0.3 0.4 0.3 0.3 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.7 0.7 0.9 0.9 0.9 0.9 0.9 0.9 0.8 0.8 0.8 0.8 0.8 0.8 0.7 0.7 0.7 0.7 0.5

97 0.4 0.5 0.5 0.5 0.5 0.6 0.6 0.6 0.6 0.7 0.7 0.7 0.7 0.7 0.7 0.7 0.7 0.6 0.6 0.6 0.6 0.6 0.7 0.3 0.4 0.3 0.4 0.3 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.7 0.7 0.7 0.7 0.7 0.9 0.9 0.9 0.9 0.9 0.9 0.8 0.8 0.8 0.8 0.8 0.8 0.7 0.7 0.7 0.7 0.6

96 0.5 0.5 0.5 0.5 0.5 0.6 0.6 0.7 0.7 0.7 0.7 0.7 0.7 0.7 0.7 0.7 0.8 0.6 0.6 0.6 0.7 0.6 0.7 0.7 0.7 0.7 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.8 0.8 0.8 0.8 0.8 0.7 0.8 0.8 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.8 0.8 0.8 0.8 0.8 0.7 0.7 0.7 0.6

95 0.5 0.5 0.6 0.5 0.5 0.6 0.7 0.7 0.7 0.7 0.7 0.7 0.8 0.8 0.8 0.8 0.8 0.6 0.7 0.7 0.7 0.7 0.7 0.7 0.7 0.7 0.7 0.7 0.7 0.4 0.4 0.4 0.4 0.4 0.4 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 1.0 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.8 0.8 0.7 0.7 0.7 0.7

94 0.6 0.6 0.6 0.6 0.6 0.7 0.7 0.7 0.7 0.7 0.7 0.8 0.8 0.8 0.8 0.8 0.8 0.7 0.7 0.7 0.7 0.7 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.9 0.8 0.9 0.8 0.8 0.8 0.8 0.8 1.0 0.9 0.9 0.9 1.0 1.0 1.0 0.9 0.9 0.9 0.9 0.9 0.8 0.7 0.7 0.7 0.6

93 0.5 0.2 0.6 0.6 0.6 0.7 0.7 0.7 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.7 0.7 0.7 0.7 0.7 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.8 0.9 0.8 0.8 0.8 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 0.9 0.9 0.9 0.9 0.9 0.7 0.7 0.7 0.7

92 0.6 0.3 0.6 0.6 0.6 0.7 0.7 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.7 0.7 0.7 0.8 0.8 0.8 0.8 0.8 0.8 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 0.9 0.9 0.8 0.8 0.8 0.7

91 0.6 0.3 0.6 0.6 0.6 0.7 0.7 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.9 0.9 0.7 0.8 0.8 0.8 0.8 0.8 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 1.0 1.0 1.0 1.0 1.0 0.9 0.9 0.9 0.9 0.9 1.0 1.0 1.0 1.0 1.1 1.1 1.0 1.0 1.0 1.0 0.9 0.9 0.9 0.4 0.3 0.3 0.7

90 0.6 0.3 0.3 0.3 0.3 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.8 0.9 0.9 0.9 0.9 0.9 0.9 0.9 1.0 0.9 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.1 1.0 1.2 1.1 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 0.9 0.4 0.4 0.3 0.8

89 0.6 0.3 0.3 0.3 0.3 0.7 0.8 0.8 0.8 0.8 0.8 0.9 0.9 0.9 0.8 0.9 0.9 0.9 0.9 0.9 1.0 1.0 1.0 0.9 0.9 0.9 0.9 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.1 1.1 1.1 1.1 1.1 1.0 1.2 1.1 1.1 1.1 1.1 1.1 1.1 1.0 1.0 1.0 1.0 0.9 0.9 0.4 0.4 0.4 0.8

88 0.7 0.3 0.3 0

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Contents › tt_assets › pdf › WTC_LevyAbboud... · 2018-04-19 · Contents 1 INTRODUCTION ... 10 4.1 MEETING THE NYC BUILDING CODE REQUIREMENTS..... 10 4.2 ADOPTING THE ASCE7-98