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    Ambient Vibration Testing and Model Updating of a 44-StoreyBuilding in Vancouver, Canada

    Martin Turek1, Carlos E. Ventura2 and Sebastin Guerrero3(1) Graduate Student

    (2) Professor

    Room 2010, Department of Civil Engineering, University of British Columbia6250 Applied Science Lane, Vancouver, BC, Canada V6T [email protected]; [email protected]

    (3) EngineerGlotman Simpson

    Vancouver, BC, Canada

    The Melville is a 44-Storey reinforced concrete building located in downtown Vancouver, Canada.An ambient vibration test was performed on the building in its final stages of construction. In atypical setup, three measurements were taken on every second floor. The analysis using thefrequency-domain decomposition and stochastic subspace identification techniques obtained thefirst 10 modes of vibration and damping estimates. These results were then used to update a FEmodel of the structure, to be used for seismic analysis studies. The results discussed in this

    paper are also used as a case study for the development of a design methodology for SHMsystems.

    INTRODUCTION

    This paper presents the results of an ambient vibration test performed on a 44-storey concretebuilding. The Melville is located in downtown Vancouver, Canada, which is a region of highseismic risk. At the time of testing the building was under construction, with all of the concrete inplace up to the 44

    thfloor and cladding up to the 35th floor. The tests provided information on the

    dynamic characteristics of the building (natural frequencies, mode shapes and damping) andinformation about the actual vibrations (amplitudes and noise levels, etc.).

    The test was performed for two reasons: to update an ETABS model used for seismic studies,

    and also as a case study for the development of a design methodology for ambient vibrationbased structural health monitoring systems. A description of the design methodology is presentedin the next section. This paper will present a description of the building, the ambient vibration test,the results, the initial development of the full FEM and the updating of an equivalent FEM.

    DEVELOPMENT OF A DESIGN METHODOLOGY FOR SHM SYSTEMS

    Currently there exist many concepts for various types of SHM systems for civil engineeringstructures [1,2,3], but few of them are actually in operation. Part of the reason for this is a lack ofknowledge of the performance of the damage detection techniques in a real scenario. This leadsto a desire to develop a design methodology for SHM systems that will provide the level ofconfidence needed. The proposed design methodology described here attempts to evaluatethese techniques under almost real conditions for a given structure. There are two ways to

    evaluate a damage detection technique: by a physical test of by a simulation. Physical tests [4,5]tend to be expensive, but can provide valuable insight into the real performance of thetechniques. Simulations are easier to implement and are more flexible but tend to be lessrealistic. The development of any damage detection technique found in the literature is based onsome sort of simulation. An example is from a benchmark simulation on the IASC/ASCE steelframe [6]. This design methodology looks at creating a calibrated vibration simulation using theresults of an ambient vibration test.

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    The methodology can be split into two main components: the design of simulations to be used forthe evaluation of the system, and the design of the damage detection methodology to beimplemented. The process can be described as in Figure 1.

    Figure 1: Proposed Design Methodology for SHM Systems

    The six main steps of the methodology are as follows:

    i) Perform an ambient vibration test on the structure of interestii) Design and update a FEM of the structureiii) Simulate the ambient level vibrations using the FEMiv) Add noise to the simulated signalsv) Select the damage detection method(s) appropriate to the application

    vi) Choose sensor layout

    The results of the ambient vibration test are of critical importance to the entire process. Thedynamic characteristics are used in the updating of the model (Step ii). The ground levelvibrations measured can be used as input to the FEM for the simulation, and the dampingestimates obtained are also used in the simulation (Step ii). The noise levels are calibrated fromthe recorded signals (Step iv). Once the damage detection methodology has been determined,and the simulations created, the design process for the system can begin. The main aspect of thedesign is the layout of the sensors. The location and number must be chosen. This can be donein an iterative process that includes modifications to the damage detection methodology, and tothe simulation, particularly the damage cases used. These iterations are necessary if certaindamage cases cannot be identified. The final result of the process is to find the optimal sensor setwith the minimum number.

    This design methodology does not focus on details such as instrumentation and electronics.Items such as choice of instrumentation, connections and computing systems are considered tobe outside of this methodology. It is assumed that the technology available is now, or will be,sufficient to successfully implement the designed system.

    This paper focuses on the first two steps of the design methodology.

    AV Test

    FEM-up

    Simulation

    Add Noise

    Design ofDD

    Methodology

    Design

    Iterations

    Choose Sensor

    Locations

    Choose

    Damage

    Cases

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    Figure 2: Photo of the Melville Building

    MELVILLE BUILDING

    The Melville is a mixed development in downtown Vancouver, composed of a high rise 46-storeyresidential tower at the west end of the development and a 10-storey hotel at the east end. Bothshare a common podium structure which includes three levels above ground and 5 undergroundparking levels. The total height of the residential tower is 146 mfrom the slab on grade at parkinglevel 5 to the roof of the tower. The total height underground is 15 m. The podium structureheight is 21m. A photo of the tower at the time of testing is shown in Figure 2. The typical tower

    floor plan and sensor layout is shown in Figure 3.

    The gravity system only carries vertical loads due to self-weight and occupancy, consisting of flat concrete slabsat the tower levels. The ground floor is a transfer slab,and in this case a slab/slab-band system was used. Allthe slabs are simply supported by columns distributedalong the surface of the building. The foundations for thecolumns are simple spread footings.

    Along the perimeter of the building at the undergroundparking levels, continuous basement walls have thedouble function of carrying vertical loads as well as

    working as retaining walls for the soil surrounding theconstruction. A central core placed approximately at thecentre of the tower defines the lateral system. The corefoundation is a massive raft footing bearing directly onthe natural soil. In addition a slab on grade was pouredat the lower parking level directly bearing on the existingsoil.

    AMBIENT VIBRATION TEST

    The AVT was performed in June of 2006, by a team of 7people. For the test, the reference sensors were placedwith the data acquisition system on the 39

    thfloor. Three

    teams of 2 were deployed to move the roving sensorsfrom the top of the building down, and from the bottom ofthe parking garage up. Typically every second or thirdfloor was measured. For each floor, a sensor layout asshown in Figure 3 was applied. This is a typical layout

    for a building that allows the translation in both directions and the torsional movements to bemeasured. The only measurement that varied from Figure 3 was for level P5, where only a singlepoint was measured in both horizontal directions.

    For each setup 30 minutes of data was recorded at 500 samples per second. The long length ofthe tests was required due to the low frequencies of the building. A high sampling rate waschosen for two reasons. First, it has been found that in building tests previously [7] that moresamples can provide a better definition of the mode shapes. Also, that for a difficult building totest such as this one, it is better to acquire more data than possibly necessary and decimate at a

    later time.

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    AMBIENT VIBRATION TEST RESULTS

    The data analysis was performed using theARTeMIS Extractor software [8] using thefive methods available. Those methods arethe Frequency Domain Decomposition(FDD) Method, Enhanced FDD (EFDD), andthree variations of the Stochastic Subspace

    Identification (SSI) method. The FDDmethods are frequency domain methodswhich are based on taking a singular valuedecomposition of the cross-spectral densitymatrices of the signal set. The mode shapesare the singular vectors associated with thesingular values, which essentially providethe amplitudes at a given frequency. Thesingular values at all frequencies are plotted,and these are analogous to the spectraldensity plots. The advantage of the SVDplots are that the effect of the noise in thesignal is reduced, and closely spaced

    modes are easily identified. Figure 4 showsthe plot of the singular value lines from theFDD analysis on the Melville data. The

    Figure 3: Typical Sensor Layout modes are numbered on the plot.

    The SSI method is a time-domain method which essentially computes the cross-correlations ofthe signal set, to obtain the matrices of a state-space formulation of the system. Those matricesare then decomposed into the modes and frequencies. Descriptions of the FDD and SSI can befound in [9] and [10] respectively. Damping is estimated from the EFDD and SSI methods in twodifferent ways. In the EFDD, the spectral bell for a given mode is isolated and transformed to thefrequency domain to identify its single-degree-of-freedom correlation function. The decay of thisfunction defines the damping estimate. In the SSI technique, damping is estimated from thecomplex frequency.

    Figure 4: SVD Plot of Complete Building Test (With Mode Numbers)

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    From the results of the analysis, 10 modes were identified under 5 Hz. Before the analysis, thedata was decimated in MATLAB to 100 sps for better management of the data. Then during theactual analysis, it was decimated down to 10 sps, which allows for better results using the SSItechnique. A total of 512 frequency lines were used. Tables 1 - 4 present the natural frequency,standard deviation of frequency, damping estimate and standard deviation of damping. For theFDD technique there is no information on the last three quantities so they are not presented. Acomplete set of modes shapes is presented in the Appendix, Figures A1-A10.

    Table 1: Melville Building Natural Frequencies

    Method FDD EFDD SSI-UPC SSI-PC SSI-CVAMode Descrip. Frequency [Hz]

    1 1 E/W 0.313 0.309 0.303 0.303 0.3032 1 N/S 0.342 0.346 0.330 0.330 0.3293 1 Tor 0.645 0.648 0.644 0.648 0.649

    4 2 E/W 1.230 1.228 1.228 1.227 1.2265 2 N/S 1.406 1.413 1.416 1.416 1.417

    6 2 Tor 2.021 2.022 2.024 2.024 2.0237 2 E/W 2.803 2.801 2.813 2.823 2.810

    8 2 N/S 3.311 3.320 3.315 3.317 3.3189 3 Tor 3.516 3.518 3.509 3.507 3.510

    10 4 Tor 4.805 4.773 N/A N/A N/AE/W East/West; N/S North/South; Tor Torsion; N/A Not Applicable

    Table 2: Melville Building Standard Deviation of Natural FrequenciesMethod FDD EFDD SSI-UPC SSI-PC SSI-CVAMode Std. Dev. of Frequency [10

    -2Hz]

    1 N/A 0.546 0.590 0.563 0. 7552 N/A 0.345 0.595 0.596 0. 545

    3 N/A 0.333 0.381 0.885 1.1744 N/A 0.309 0.387 0.442 0.708

    5 N/A 0.462 0.287 0.170 0.3516 N/A 0.386 0.300 0.258 0.295

    7 N/A 0.852 1.148 3.084 0.8978 N/A 1.750 1.399 1.270 1.3579 N/A 1.121 0. 432 0. 695 0. 725

    10 N/A 3.243 N/A N/A N/A

    Table 3: Melville Building Damping Estimates

    Method FDD EFDD SSI-UPC SSI-PC SSI-CVAMode Damping Ratio [%]1 N/A 3.861 1.156 1.038 1.441

    2 N/A 2.361 2.099 2.034 2.1483 N/A 1.665 1.873 1.828 2.076

    4 N/A 1.003 1.164 1.239 1.3265 N/A 1.038 0.518 0.668 0.614

    6 N/A 0.950 1.006 1.096 1.0947 N/A 0.515 0.957 1.137 1.4958 N/A 1.167 1.423 1.391 1.320

    9 N/A 0.815 1.124 1.059 1.12710 N/A 0.340 N/A N/A N/A

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    Table 4: Melville Building Standard Deviation of Damping EstimatesMethod FDD EFDD SSI-UPC SSI-PC SSI-CVA

    Mode Std. Dev. of Damping Ratio [%]1 N/A 1.948 0.459 0.544 0.909

    2 N/A 0.368 0.395 0.441 0.4983 N/A 0.561 1.360 1.279 1.531

    4 N/A 0.157 0.509 0.463 0.6585 N/A 0.091 0.147 0.344 0.225

    6 N/A 0.207 0.139 0.150 0.1437 N/A 0.313 0.234 0.682 1.4138 N/A 0.361 0.252 0.332 0.201

    9 N/A 0.131 0.205 0.196 0.15110 N/A 0.388 N/A N/A N/A

    FINITE ELEMENT MODEL AND UPDATING

    One of the objectives of this study was to generate several computer models of the building andperform a sensitivity analysis until the natural frequencies and modes shapes were close to theones obtained from the ambient vibration test. Four different models were developed using twodifferent commercial software systems widely known in structural engineering, ETABS version 8.0

    [11] for 3D analysis and SAP version 9.0 [12] for 2D. The first two were 2D models, and only thecore in each direction (E/W and N/S) was modeled for the tower levels, and the core walls plusthe basement walls for the basement levels. The first 3D model contained all of the structuralelements present in the building including gravity system, columns, walls and the LateralResisting System (LRS) elements.

    A second 3D model was generated (Figure 5), including theexterior cladding and the partition walls, up to level 35 sincethis was the state of the construction at the time of testing. Theresults obtained with the 2D models were very similar to theones obtained with the 3D model containing only the structuralelements. This comparison was used as a verification of the3D model before going to the more complex full 3D model, and

    also confirming that it is a valid assumption to just model theLRS elements since the gravity elements in this type ofbuilding do not have a large influence on the dynamicresponse of the building. The results obtained with thecomplete 3D model including the non-structural elementsconfirmed their influence at least in the initial response of thebuilding; however, when the building is excited by majorshaking such as by an earthquake it is expected that the non-structural components will not have any significant influence inthe response of the building. Table 5 presents a comparisonbetween the frequencies of the various models. Table 6 givesthe initial design comparison for the full 3D model. Test modesshown are from EFDD. Examples of the modes obtained with

    the 3D model are shown in the Appendix, Figure A11.Figure 5: ETABS Full 3D Model

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    Table 5: Comparison of All Models

    E/W[Hz]

    N/S[Hz]

    Torsion[Hz]

    ETABS no cladding 0.175 0.186 0.667

    SAP 2D no columns 0.162 0.170 N/A

    Test 0.312 0.342 0.659

    ETABS cladding +

    drywall

    0.270 0.301 0.763

    Table 6 Initial FEM Design CorrelationsMode ETABS Test direction

    1 0.270 0.309 1 E/W

    2 0.301 0.346 1 N/S

    3 0.763 0.648 1 Tor

    4 1.316 1.228 2 E/W

    5 1.471 1.413 2 N/S

    6 2.381 2.022 2 Tor

    7 3.030 2.801 2 E/W

    8 3.571 3.320 2 N/S9 4.000 3.518 3 Tor

    10 5.000 4.773 4 Tor

    UPDATING OF AN EQUIVALENT MODEL

    An equivalent model (Figure 6) to the one in ETABS was createdfor the purpose of updating the material parameters, while havinga direct correlation to the test results. The equivalent model andupdating was performed in FEMTools [13]. The equivalent modelfocused on the tower only, taking care to correctly model the core,while simplifying the floor layout. Each floor was taken to be asquare, with total area equal to the floor area of the ETABS model,

    and with identical thickness. Similarly, the cladding was modeledwith the identical thickness and properties, although the totalsurface area varied, since it was applied to the perimeter of eachfloor. To model the effect of the tower built on the parking garage,its base boundary conditions were converted to springs and thespring stiffness adjusted to match the translational modes. Onlythe first three modes were used for the updating. Table 7 showsthe correlation between the equivalent model and the test databefore updating for five modes.

    Note: In Figure 6, the equivalent model is shown with themeasured test points (red dots). Those points lie outside of thegeometry of the equivalent model; this is due to the fact that the

    real geometry is highly irregular, and the equivalent model,although having equal floor areas, is slightly smaller in theNorth/South direction. The points seen below the model are thosemeasured in the parking garage.

    Figure 6: Equivalent Model

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    Table 7 Equivalent Model Correlations Before UpdatingMode FEM [Hz] EMA [Hz] Diff. [%] MAC [%]

    1 0.26 0.31 -15.76 97.12 0.31 0.34 -9.38 96.1

    3 0.74 0.64 15.05 88.64 1.16 1.22 -5.20 90.6

    5 1.70 1.41 21.04 82.9

    The intention of the model was to examine the properties of the cladding and of the core forupdating. In particular, it was of interest to find how each component and each property affectsthe ratio between the translational modes and the torsional mode. It is seen in Table 8 that forboth of the translational modes in the model the frequencies are lower than the test; while for thetorsional mode the frequency is higher. It was found when initially constructing the equivalentmodel that the translational modes between it and the ETABS model were matching, but thetorsional mode of the equivalent model was too high (1Hz instead of 0.74 Hz). The ratio wascorrected by removing some of the cladding, because the cladding had a more significant effecton the torsional modes than on the translational modes. Therefore it is believed that a similareffect is being observed between the frequencies of the ETABS model and those of the test.

    First a sensitivity analysis was performed examining the thickness and modulus of elasticity forthe core and cladding elements. The sensitivity plot is shown in Figure 7. In the figure,

    Parameters 1 to 4 represent the modulus of the core and cladding elements, and parameters 5 to8 represent the thickness of the three core elements and the cladding. All of these are globalparameters, meaning a change is applied equally to all elements. Responses 1 to 3 are thenatural frequencies of the first 3 modes. It was found that the MAC values were not very sensitiveto changes in the parameters, so they were excluded from the analysis.

    Since the ratio between torisional andtranslational frequencies is not correct,the model must be updated in such away that these modes will change atdifferent rates. This is difficult, sincemost parameters will change both ofthem (ie either increase or decrease) in

    a similar way. Therefore, it is useful toexamine the sensitivity matrix to find anyparameters which affect either thetranslational or torsional modes only. Itis seen that parameter 7, which is a coreelement thickness, is mostly sensitive tothe two translational modes (shown inblue). The ideal process would then beto first update the entire model to matchthe torsional mode using the cladding(see Table 9) and then update thespecific core element set that willchange only the translational mode. Thisis deceptive however, since when the

    Figure 7: Equivalent Model Sensitivity Diagram thickness of a core element is changedboth the stiffness and mass will change;

    meaning that depending on the location of the element the model frequencies may not changewhen the parameter is changed. Since the core element is an essential part of the structure, thatis the case observed here. So instead, the model was updated in two ways to examine the results(both by adjusting the cladding modulus only): first to match the translational modes, then tomatch the torsional mode. The results are shown in Tables 8 and 9.

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    Table 8: Updating Results: Matching Translational ModesMode FEM [Hz] EMA [Hz] Diff. [%] MAC [%]

    1 0.30 0.31 -3.60 97.12 0.35 0.34 3.78 96.2

    3 0.85 0.64 32.38 88.24 1.32 1.22 8.10 90.2

    5 1.86 1.41 31.96 83.6

    Table 9: Updating Results: Matching Torsional ModeMode FEM [Hz] EMA [Hz] Diff. [%] MAC [%]

    1 0.23 0.31 -25.98 97.12 0.27 0.34 -19.88 96.0

    3 0.64 0.64 -0.72 88.84 1.05 1.22 -14.26 90.6

    5 1.59 1.41 13.33 80.6

    In both cases, the mode shape correlation (MAC) did not change significantly. These tables showthe expected results: when the translational modes are matched, the torsional frequencyincreases, with an increase in error of 17%. When the torsional mode is matched, thetranslational frequencies decrease, with an increase in error of 10% in each. In terms of actualproperty changes, the modulus increased by 100% for the translational matching, and decreased

    by 50% for the torsional matching. So it is seen that the torsional matching is slightly moreefficient, creating less error and requiring less of a parameter change. A third method was alsoexplored, in which all of the cladding elements were treated individually. Therefore the modulus ofelasticity was updated locally for each cladding element. The results are shown in Table 10.

    Table 10: Local Updating Results: Cladding Modulus of ElasticityMode FEM [Hz] EMA [Hz] Diff. [%] MAC [%]

    1 0.29 0.31 -7.65 97.32 0.33 0.34 -3.74 96.1

    3 0.74 0.64 14.53 92.94 1.16 1.22 -5.38 89.4

    It is seen from the results in Table 10 that the error is more evenly distributed, while neither

    translational nor torsional modes are matching exactly. Also it is noted that while the translationalmodes have been better matched, the torsional mode did not change (see Table 7). This isdifferent than from Table 8, where the translational modes matched while creating an increasedtorsional mode. The local updating then gives generally better results, however the parameterchanges were seen to be concentrated near the base of the model.

    From the above results, it is likely that the best matching would come from a change in thearrangement of the cladding. Instead of having a global change in cladding properties for theETABS model, a variation of properties across each floor will be necessary.

    SUMMARY

    This paper presented the results of an ambient vibration test on a 44-story reinforced concretebuilding in Vancouver, Canada. The tests were successful at identifying 10 modes of the structurebelow 5 Hz. The results obtained using the five methods available with the ARTeMIS Extractorsoftware were very consistent, identifying fundamental frequencies in the building of 0.312 and0.342 Hz in the two translational directions. The damping values were typically between 1 and 2%from the SSI method. The FDD estimates were slightly higher, buy the SSI estimates tend to bemore accurate.

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    The results were first used to validate several models used in a seismic response study. Theresults confirmed the overall behaviour of the structure, and allowed for a modification of theparameters to get a better match of the frequencies. The initial design of the model showed arelatively good match of the modes.

    The results of the updating study on the equivalent finite element model suggested that thedistribution of the cladding will have the most effect on correctly matching the first three modes.The ETABS model described in this paper will be updated in more detail, and then used for

    simulations in a design of a SHM system for the real structure.

    ACKNOWLEDGEMENTS

    The authors wish to thank Juan Carlos Carvajal, Jose Centeno, Jorge Holmann, Kate Thibert andShabnam Hoesseni, graduate students from the University of British Columbia for their hard workduring the tests.

    The assistance and permission to access to the building of Keith Mackie of Amacon Constructionis greatly appreciated.

    Micheal OKeefe, P.Eng from Glotman Simpson Consulting Engineers, Vancouver, B.C. for hissupport and provide of structural and architectural drawings.

    Celso Mendoza, P.Eng from Glotman Simpson Consulting engineers, Vancouver, B.C. for histime and counseling during the ETABS modeling.

    REFERENCES

    [1] Naeim, F., Hagie, S., Alimoradi, A., Automated Post-Earthquake Damage Assessment andSafety Evaluation of Instrumented Buildings, SMIP-05 Seminar on Utilization of Strong-MotionData, Los Angeles, CA, May 2005

    [2] Straser, E., Sohn, H., Kiremidjian, A., Law, K.H., A Framework for Health Monitoring ofStructures, Proc. of ASCE Structures Congress, 2000

    [3] Celebi, M., Sanli, A., Sinclair, M., Gallant, S., Radulescu, D., Real-Time Seismic MonitoringNeeds of a Building Owner and the Solution, Earthquake Spectra, Vol. 20, Issue 2, pp333-346,May 2004

    [4] Maeck, J., De Roeck, G., (2003) Description of Z24 Benchmark, Mechanical Systems andSignal Processing, Vol. 17, No. 1, pp. 127-131

    [5] Farrar, C.R., Dynamic Characterization and Damage Detection in the I-40 Bridge over the RioGrande, Los Alamos National Laboratory Report, LA-12767-MS, 1994

    [6] Johnson, E.A., Lam, H.F., Katafygiotis, L.S., Beck, J.L., (2004) Phase I IASC-ASCEStructural Health Monitoring Benchmark Problem Using Simulated Data, ASCE Journal ofEngineering Mechanics, Vol. 130, No. 1, pp. 3-15

    [7] Turek, M., Thibert, K., Ventura, C., Kuan, S., Ambient Vibration Testing of Unreinforced BrickMasonry Buildings in Vancouver, Canada, Proceedings of IMAC XXIV, St. Louis, Mo., 2005,paper 77

    [8] ARTeMIS Extractor Software Version 3.5, Structural Vibration Solutions, Inc., (Copyright 1999-2006) Structural Vibration Solutions, Inc.

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    [9] Brincker, R., Zhang, L., Andersen, P., Modal Identification from Ambient Responses usingFrequency Domain Decomposition, 18

    thInternational Modal Analysis Conference, San Antonio,

    Texas, pp 625-630, 2000

    [10] Pridham, B.A., Wilson, J.C., (2004) Identification of Base Excited Structures Using Output-Only Parameter Estimation, Earthquake Engineering and Structural Dynamics, Vol. 33, No. 1,pp133-155

    [11] ETABS Version 9.09, (Copyright 1984-2006), Computers and Structures Inc.

    [12] SAP2000 Advanced Version 10.0.9 (Copyright 1976-2006) Computers and Structures Inc.

    [13] FEMTools Version 3.1.2, (Copyright 1994-2006), Dynamic Design Solutions N.V.

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    APPENDIX MODE SHAPES

    Figure A1: Mode 1 1st

    E/W (0.312 Hz)

    Figure A2: Mode 2 1st

    N/S (0.342 Hz)

    Figure A3: Mode 3 1st

    Torsion (0.645 Hz)

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    Figure A4: Mode 4 2

    ndE/W (1.221 Hz)

    Figure A5: Mode 5 2nd

    N/S (1.406 Hz)

    Figure A6: Mode 6 2nd

    Torsion (2.031 Hz)

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    Figure A7: Mode 7 3

    rdE/W (2.803 Hz)

    Figure A8: Mode 8 3rd

    N/S (3rd

    Torsion) (3.311 Hz)

    Figure A9: Mode 9 3rd

    Torsion (3rd

    N/S) (3.525 Hz)

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    Figure A10: Mode 10 4

    thTorsion (4.814 Hz)

    FigureA10: Mode 1 - 1stE/W; Mode 3 1st Torsion; Mode 5 2ndN/S; Mode 7 3rd E/W