19
FHWA Cable Stay Bridge Workshop, St. Louis, MO, April 25-27, 2006 DECK-INDUCED STAY CABLE VIBRATIONS: FIELD OBSERVATIONS AND ANALYTICAL MODEL Ming Ming - - Yi Liu Yi Liu Sinotech Engineering Consultants, Inc., Taipei, Taiwan Delong Zuo Johns Hopkins University, Baltimore, MD, USA Nicholas P. Jones Johns Hopkins University, Baltimore, MD, USA

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

  • Upload
    lyque

  • View
    228

  • Download
    2

Embed Size (px)

Citation preview

Page 1: 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

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

Page 2: 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

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

Finite element modelingFinite element modeling

Field observationsField observations

Analytical modelingAnalytical modeling

ScopeScope

Page 3: 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

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

Page 4: 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

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

Page 5: 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

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

Observed Types of VibrationObserved Types of Vibration

((KKáármrmáánn--) ) 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

Page 6: 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

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

Page 7: 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

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

Page 8: 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

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 (Hz)

: 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 5 10 15 20 25 30

00.5

11.5

20

1000

2000Deck at MidA

Time (min.)

Frequency (Hz)

PSD

of D

isp

(cm

2 /Hz)

0.566 Hz 0.586 Hz

0.293 Hz

0 5 10 15 20 25 30

00.5

11.5

20

200

400Deck at AS19

Time (min.)

Frequency (Hz)

PSD

of D

isp

(cm

2 /Hz)

0.566 Hz 0.761 Hz0.293 Hz

Page 9: 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

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.) 0 5 10 15 20 25 30

00.5

11.5

20

20

40AS16

Time (min.)

Frequency (Hz)

PSD

of D

isp-

X (c

m2 /H

z)

0.566 Hz 0.761 Hz 0.293 Hz

0 5 10 15 20 25 30

00.5

11.5

20

3000

6000AS24

Time (min.)

Frequency (Hz)

PSD

of D

isp-

X (c

m2 /H

z)

0.566 Hz0.293 Hz

0 5 10 15 20 25 30

00.5

11.5

20

1000

2000Deck at MidA

Time (min.)

Frequency (Hz)

PSD

of D

isp

(cm

2 /Hz)

0.566 Hz 0.586 Hz

0.293 Hz

Page 10: 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

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

Analytical ModelingAnalytical Modeling

L

x HH

k

y(x,t)

μm

qp

Wave equationWave equation

Boundary conditionsBoundary conditions

Natural frequencyNatural frequency

Mode shapeMode shape

( ) ( )

( ) ( ) ( ) ( )

( )

( ) ⎟⎠⎞

⎜⎝⎛=

⎟⎠⎞

⎜⎝⎛−

=

+∂

∂=

∂∂

∂∂

=∂

cfxAxY

cfL

Hkmfcf

tLkyt

tLymx

tLyHty

ttxy

xtxyc

π

ππ

π

2sin

2tan2

4

,,,;,0

,,

22

2

2

2

2

2

22

CableCable

DeckDeck

Page 11: 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

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; μμ = 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

Page 12: 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

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)

Page 13: 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

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

Page 14: 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

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 O4th 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

Page 15: 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

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

Page 16: 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

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

Page 17: 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

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

Coupled MotionsCoupled Motions

xz

y

f7 = 0.5468 Hz

Mode 7

MECS

xz

y

f23 = 0.5911 Hz

Mode 23

MECS

xz

y

f8 = 0.5599 Hz

Mode 8

MECS

xz

y

f24 = 0.5954 Hz

Mode 24

MECS

Page 18: 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

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

SummarySummary

L

x HH

k

y(x,t)

μm

qp++

?

OECS OECS ++ CableCable--deck system deck system MECSMECS?

Page 19: 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

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

LargeLarge--amplitude stay cable vibration induced by deck oscillation have amplitude stay cable vibration induced by deck oscillation have been been observed in the fieldobserved in the field

Analytical modeling revealed that coupled motions of deck and stAnalytical modeling revealed that coupled motions of deck and stay cables are ay cables are associated with the veering associated with the veering of of natural frequency locinatural frequency loci

ThreeThree--dimensional finite element models verified that coupled motion adimensional finite element models verified that coupled motion and nd natural frequency curve veering are exhibited in real structuresnatural frequency curve veering are exhibited in real structures

AAn OECS model with linear vibration theorn OECS model with linear vibration theoryy forfor a cable based on the presented a cable based on the presented model would reasonably evaluate coupled motions model would reasonably evaluate coupled motions forfor engineering applicationsengineering applications, , offering a more efficient approach than a MECS modeloffering a more efficient approach than a MECS model

ConclusionsConclusions