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DECK-INDUCED STAY CABLE VIBRATIONS: FIELD ... Cable Stay Bridge Workshop, St. Louis, MO, April 25-27, 2006 DECK-INDUCED STAY CABLE VIBRATIONS: FIELD OBSERVATIONS AND ANALYTICAL MODEL

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  • FHWA Cable Stay Bridge Workshop, St. Louis, MO, April 25-27, 2006

    DECK-INDUCED STAY CABLE VIBRATIONS: FIELD OBSERVATIONS AND ANALYTICAL MODEL

    MingMing--Yi LiuYi LiuSinotech Engineering Consultants, Inc., Taipei, Taiwan

    Delong ZuoJohns Hopkins University, Baltimore, MD, USA

    Nicholas P. JonesJohns Hopkins University, Baltimore, MD, USA

  • FHWA Cable Stay Bridge Workshop, St. Louis, MO, April 25-27, 2006

    Finite element modelingFinite element modeling

    Field observationsField observations

    Analytical modelingAnalytical modeling

    ScopeScope

  • FHWA Cable Stay Bridge Workshop, St. Louis, MO, April 25-27, 2006

    The Fred Hartman BridgeThe Fred Hartman BridgeOver the Houston ship channel in Houston, Texas, USAOver the Houston ship channel in Houston, Texas, USA384 m main span, 54 m clearance384 m main span, 54 m clearanceTwinTwin--deck, each 24 m wide and 2.87 m highdeck, each 24 m wide and 2.87 m highDoubleDouble--diamond shaped towers diamond shaped towers 192 cables (59 m to 198 m long) in four inclined planes192 cables (59 m to 198 m long) in four inclined planes

  • FHWA Cable Stay Bridge Workshop, St. Louis, MO, April 25-27, 2006

    FullFull--Scale Measurement SystemScale Measurement System

    South Tower North Tower

    AS13-AS24 AS1-AS12 AN24-AN13 AN12-AN1

    Major measurementMajor measurementStaysStays

    AccelerationAccelerationDisplacementDisplacementDamper forceDamper force

    Sampling rate = 40 HzSampling rate = 40 HzLowLow--pass filtered at 10 Hzpass filtered at 10 HzFiveFive--minute recordsminute records

    DeckDeck

    AccelerationAcceleration

    MeteorologicalMeteorologicalWindWindRainfallRainfall

    AnemometerBi-axial accelerometerUni-axial accelerometer

  • FHWA Cable Stay Bridge Workshop, St. Louis, MO, April 25-27, 2006

    Observed Types of VibrationObserved Types of Vibration

    ((KKrmrmnn--) ) VortexVortex--induced vibration (VIV)induced vibration (VIV)RainRain--wind induced vibration (RWIV)wind induced vibration (RWIV)LargeLarge--amplitude dry cable vibrationamplitude dry cable vibrationVibration induced by deck oscillationVibration induced by deck oscillationVibrations not categorizedVibrations not categorized

  • FHWA Cable Stay Bridge Workshop, St. Louis, MO, April 25-27, 2006

    Mode ShapesMode Shapes

    Coupled motionCoupled motion

    Deck / Tower vibrationDeck / Tower vibration++

    Cable vibrationCable vibration

    Cable vibrationCable vibrationDeck / Tower vibrationDeck / Tower vibration

    Local motionLocal motionGlobal motionGlobal motion

  • FHWA Cable Stay Bridge Workshop, St. Louis, MO, April 25-27, 2006

    Natural FrequenciesNatural Frequencies

    6th VerticalO0.790166th VerticalI0.786155th VerticalO0.720145th VerticalI0.715134th VerticalO0.668124th VerticalI0.66511

    1st TorsionalO0.688101st TorsionalI0.68693rd VerticalO0.58883rd VerticalI0.57071st LateralO0.43261st LateralI0.4135

    2nd VerticalO0.38542nd VerticalI0.37231st VerticalO0.30121st VerticalI0.2871

    Description of ModePhasingFrequency (Hz)Mode

    1.2480.570FrequencyAS16AS24Stay

    Deck Modes (Ozkan 2003)

    Fundamental Stay Mode

  • FHWA Cable Stay Bridge Workshop, St. Louis, MO, April 25-27, 2006

    Response of Bridge DeckResponse of Bridge Deck

    -15

    -10

    -5

    0

    5

    10

    15

    0 5 10 15 20 25 30Time (min)

    Verti

    cal D

    isp.

    (cm

    )

    -15

    -10

    -5

    0

    5

    10

    15

    0 5 10 15 20 25 30Time (min)

    Verti

    cal D

    isp.

    (cm

    )

    0 5 10 15 20 25 300

    5

    10

    15

    20

    V-A

    S18

    (m/s

    )

    Time (min.)

    0

    0.261

    0.523

    0.784

    1.045

    f s (H

    z)

    : Wind speed perpendicular to deck axis0.15 :Strouhal number according to wind tunnel tests

    (Mehedy Mashnad): Height of bridge deck

    sVSD

    VS

    D

    f

    =

    =

    0 510 15

    20 2530

    00.5

    11.5

    20

    1000

    2000Deck at MidA

    Time (min.)

    Frequency (Hz)

    PSD

    of D

    isp

    (cm

    2 /H

    z)

    0.566 Hz 0.586 Hz

    0.293 Hz

    0 510 15

    20 2530

    00.5

    11.5

    20

    200

    400Deck at AS19

    Time (min.)

    Frequency (Hz)

    PSD

    of D

    isp

    (cm

    2 /H

    z)

    0.566 Hz 0.761 Hz0.293 Hz

  • FHWA Cable Stay Bridge Workshop, St. Louis, MO, April 25-27, 2006

    Response of Bridge DeckResponse of Bridge Deck

    0 5 10 15 20 25 30-30

    -20

    -10

    0

    10

    20

    30

    Dis

    p-X

    (cm

    )

    Time (min.)

    0 5 10 15 20 25 30-30

    -20

    -10

    0

    10

    20

    30

    Dis

    p-X

    (cm

    )

    Time (min.)

    0 5 10 15 20 25 30-30

    -20

    -10

    0

    10

    20

    30

    Dis

    p-X

    (cm

    )

    Time (min.) 05 10

    15 2025 30

    00.5

    11.5

    20

    20

    40AS16

    Time (min.)

    Frequency (Hz)

    PSD

    of D

    isp-

    X (c

    m2 /

    Hz)

    0.566 Hz 0.761 Hz 0.293 Hz

    0 510 15

    20 2530

    00.5

    11.5

    20

    3000

    6000AS24

    Time (min.)

    Frequency (Hz)

    PSD

    of D

    isp-

    X (c

    m2 /

    Hz)

    0.566 Hz0.293 Hz

    0 510 15

    20 2530

    00.5

    11.5

    20

    1000

    2000Deck at MidA

    Time (min.)

    Frequency (Hz)

    PSD

    of D

    isp

    (cm

    2 /H

    z)

    0.566 Hz 0.586 Hz

    0.293 Hz

  • FHWA Cable Stay Bridge Workshop, St. Louis, MO, April 25-27, 2006

    Analytical ModelingAnalytical Modeling

    L

    x HH

    k

    y(x,t)

    m

    qp

    Wave equationWave equation

    Boundary conditionsBoundary conditions

    Natural frequencyNatural frequency

    Mode shapeMode shape

    ( ) ( )

    ( ) ( ) ( ) ( )

    ( )

    ( )

    =

    =

    +

    =

    =

    cfxAxY

    cfL

    Hkmfcf

    tLkyt

    tLymx

    tLyHty

    ttxy

    xtxyc

    2sin

    2tan2

    4

    ,,,;,0

    ,,

    22

    2

    2

    2

    2

    2

    22

    CableCable

    DeckDeck

  • FHWA Cable Stay Bridge Workshop, St. Louis, MO, April 25-27, 2006

    Natural Frequency Loci of SystemNatural Frequency Loci of System

    ffrr = (= (ffdd -- ffcc) / ) / ffcc

    Relative frequencyRelative frequency

    ffdd = 0.293 = 0.293 0.878 Hz0.878 Hzmm = 7.59 x = 7.59 x 10105 5 kgkg; ; kk = = 2564 2564 23072 kN/m23072 kN/mDeckDeck

    ffcc = 0.585 Hz= 0.585 HzLL = = 199.8; 199.8; = 76.0 kg/m; = 76.0 kg/m; HH = 4150 kN= 4150 kNCableCable

    Natural frequencyNatural frequencyParametersParameters

    (Hz)

    Asymptote

    ( )1585.0 += rd ff

    585.0=cf

    rf

    f 585.0== dc ff

    -0.5 -0.4 -0.3 -0.2 -0.1 0.0 0.1 0.2 0.3 0.4 0.50.0

    0.1

    0.2

    0.3

    0.4

    0.5

    0.6

    0.7

    0.8

    0.9

    1.0

    The First Mode

    The Second Mode

    0.24-0.24

    Asymptote

    Veering of naturalVeering of naturalfrequency locifrequency loci

    Pure cable frequencyPure cable frequency

    Pure deck frequencyPure deck frequency

  • FHWA Cable Stay Bridge Workshop, St. Louis, MO, April 25-27, 2006

    Finite Element ModelingFinite Element ModelingMECSMECS

    (multi(multi--element cable system)element cable system)

    Deck / Tower (beam elements)Deck / Tower (beam elements)Cable (truss elements)Cable (truss elements)

    OECSOECS(one(one--element cable system)element cable system)

  • FHWA Cable Stay Bridge Workshop, St. Louis, MO, April 25-27, 2006

    Fred Hartman BridgeFred Hartman Bridge

    152 m

    49 m

    381 m

    78 m

    24 m

    152 m

    24 m

    X

    Z

    X

    Y

    Y

    Z

    Cable 1

    Symmetry

    Symmetry

    Symmetry

    Symmetry

    Cable 2 Cable 3 Cable 22 Cable 23 Cable 24

    Finite element modelingFinite element modelingPrototypePrototype

  • FHWA Cable Stay Bridge Workshop, St. Louis, MO, April 25-27, 2006

    Natural Frequency Loci of BridgeNatural Frequency Loci of Bridge

    Global Coupled Local Coupled

    n0 5 10 15 20 25 30

    0.0

    0.1

    0.2

    0.3

    0.4

    0.5

    0.6

    0.7

    OECS

    MECS

    nf(Hz)

    1st Dz

    2nd Dz

    3rd Dz + 1st C24

    1st Dy + 1st C24

    IO

    I

    I

    I

    O

    O

    O

    I O

    I O 4th Dz + 1st C3, C23

    1st Dy + 1st C24 3rd Dz + 1st C24

    I O

    1st C24

    0.5850Irvine (1981)

    Dy: Lateral deck motionDz: Vertical deck motionI: In-phase motion

    O: Out-of-phase motion

    Veering of naturalVeering of naturalfrequency locifrequency loci

    CoupledCoupled

    GlobalGlobal

    LocalLocal

    Pure cable frequencyPure cable frequency

  • FHWA Cable Stay Bridge Workshop, St. Louis, MO, April 25-27, 2006

    Global MotionsGlobal MotionsOECSf1 = 0.2902 Hz

    xz

    yMode 1

    MECS

    xz

    y

    f1 = 0.2919 Hz

    Mode 1

    OECS

    xz

    y

    f2 = 0.3004 Hz

    Mode 2

    MECS

    xz

    y

    f2 = 0.3021 Hz

    Mode 2

  • FHWA Cable Stay Bridge Workshop, St. Louis, MO, April 25-27, 2006

    Local MotionsLocal Motions

    xz

    y

    f15 = 0.5825 Hz

    Mode 15

    MECS

    xz

    y

    f16 = 0.5825 Hz

    Mode 16

    MECS

    xz

    y

    f19 = 0.5825 Hz

    Mode 19

    MECS

    xz

    y

    f20 = 0.5825 Hz

    Mode 20

    MECS

  • FHWA Cable Stay Bridge Workshop, St. Louis, MO, April 25-27, 2006

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