deck-induced stay cable vibrations: field ... cable stay bridge workshop, st. louis, mo, april...
TRANSCRIPT
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
((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
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 (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
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
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
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
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 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
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
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
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?
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