View
73
Download
3
Category
Preview:
DESCRIPTION
cable stayed bridge under wind load ppt
Citation preview
WIND-INDUCED VIBRATION AND CONTROL OF CABLE-STAYED BRIDGES
KAMAL KRISHNA BERA
Under the guidance of
Prof. Naresh K. Chandiramani
DEPARTMENT OF CIVIL ENGINEERINGINDIAN INSTITUTE OF TECHNOLOGY BOMBAY
Main Components:
Bridge Deck
Stay cables
Towers or pylons
CABLE-STAYED BRIDGE
Advantages: stiffness > suspension bridge cables temporary and permanent supports to bridge deck symmetrical bridge large ground anchorages not required.
MODELLING
Deck
•Spine (Central) Beam Model
• Multi-scale modeling components of interest: shell elements or solid elements
other components: line elements
Cable•Truss Element
][][][ get KKK
000000
000000
001001
000000
000000
001001
][c
eqe L
AEK
3
2
12
)(1
T
AEwL
EEeq
Equivalent Modulus of Elasticity
Elastic linear stiffness matrix Geometric stiffness matrix
100100
010010
000000
100100
010010
000000
][c
g L
TK
AEROSTATIC INSTABILITY
• Wind speed components
),,,()( tzyxuzU
),,,( tzyxv
),,,( tzyxw
Longitudinal direction:
Lateral direction:
Vertical direction:
• Mean wind load
)(2
1)( 2 DD BCUF
)(2
1)( 2 LL BCUF
)(2
1)( 2 MBCUM
• Torsional Divergence
)(2
1 22 MCBUK
)0()0()( MMM CCC
)0(2
1)0(
2
1 2222MM CBUCBUK
)0(
22
Mcr CB
KU
AERODYNAMIC INSTABILITY
I. Vortex Induced Vibration
Lock in Phenomenon
)2sin(2
1 2 tfDCU sL D
USf tst
Vortex shedding frequency
tS Strouhal number
)sin(2
1)2( 22 tDCUyyym sLnn
222
2
max 164 tc
L
n
L
SS
DC
m
UDCy
2D
mSc
Scruton number
U
II. Galloping Instability
Instability by Negative Aerodynamic Damping in cross wind direction
At very low reduced frequency
o across-wind oscillation of structure
o modifies effective angle of attack
o change in aerodynamic forces
U
yC
d
dCBUF D
L
excitedselfy
0
2
2
1)(
U
yC
d
dCBUkyycym D
L
0
2
2
1
02
1
0
kyyCd
dCUBcym D
L
UB
cC
d
dCD
L
2
0
Instability Criterion
III. FLUTTER
Coupled Vertical and Torsional vibration
Both under Laminar and Turbulent Wind flow
o Wind-structure interaction
o Self-excited Aerodynamic Forces
o Instability at Critical Wind Speed
Failure of Original Tacoma Narrows Bridge (1940)
B
hHKHK
U
BKH
U
hKHBULse 4
23
221
2
2
1
B
hAKAK
U
BKA
U
hKABUM se 4
23
221
22
2
1
Scanlan and Tomko (1971)
)(2)](1[)(2 2 kCUUbkChkUChbbLse
)()](2
1[
8)( 2
22 kCUUbkC
bhkUCbM se
Theodorsen (1934)
FrequencyReduced2 U
BkK
)()()( kiGkFkC
2-D Flutter Analysis
Eigen value of matrix A 21 iiiii j ,hi
0iCritical State Corresponding wind speed
Flutter Speed
IV. BUFFETING
Vertical, Lateral and Torsional motion
under wide ranges of wind speed
increases monotonically with increasing wind speed
Mean Wind Speed Fluctuating Wind Speed (turbulence)
Static Wind Force Dynamic Wind Force
Random Vibration of bridge
Buffeting Forces
BCtUtL L )()(2
1)( 0
2
U
tuUtwtuUtU
)(21)()()( 2222
U
tw
U
tu
U
tw
tuU
tw )()(1
)(
)(
)(1
Lift force in transient wind axis
)sin()()cos()()( tDtLtL
)()(
)(2
1)()()(
)(2)(
2
1)(
0
02
0002
staticb
LDLL
LtL
BCUU
twCC
U
tuCBUtL
Lift force in mean wind axis
)()()( 000 DDD CCC
WIND INDUCED VIBRATION CONTROL
I. Modification of structural parameters
mass, damping and stiffness
II. Aerodynamic measures
Wedge-shaped fairings , Actively controlled surfaces , “deck-flap”
system
III. Mechanical measures
Passive, Active, Semi-active and Hybrid Control systems
Active Control System
Korlin and Starossek (2004)
o Rotational Mass Damper (RMD)
o Movable Eccentric Mass Damper (MEMD)
Effectively Control Flutter
• Requires High Energy Input • lower energy consumption,• movement cause undesirable
horizontal movement of bridge
Semi-active Control System
Pourzeynali and Datta (2005)
o Semi-active Tuned Mass Damper (STMD)
CaseWind Speed
(m/s)Max. Torsional
amp. (rad.)
Uncontrolled 55.52 (flutter, sustained
oscillation)0.02
Controlled with tuned mass damper (20% damping) 98 (flutter, sustained oscillation) 0.02
Controlled with semi-active tuned mass damper (max. damping 21.6%)
110 (decaying oscillation) 0.0063
More Literature Study
Finite Element Modelling
Flutter Analysis
……………………. …………………………..
Cable-bridge deck vibration interaction
Control with Active Tuned Mass Damper (ATMD), Active
Tendon Systems
Non-linear Flutter / Buffeting
FUTURE WORKS
THANK YOU
Vortex-Induced Vibration Galloping Instability Flutter Buffeting
Occurs at low wind speed and low turbulence condition.
Occur at much lower frequency than vortex shedding.
Usually occur at very high wind speed.
Occur over a wide range of wind speed.
Due to Lock-in, vortex shedding frequency natural frequency of bridge components.
Motion of structure in vertical direction causes change in angle of attack of original flow velocity.
Due to self-excited aerodynamic forces resulting from wind –structure interaction.
Due to velocity fluctuation in the incoming flow i.e. turbulence.
Resulting motion normal to flow, for bridge deck it is in the vertical direction.
Large amplitude vibration in normal to mean wind direction.
Flutter can be 1D (vertical or torsional), 2D (coupled vertical and torsional motion) or 3D (coupled vertical, torsional and lateral motion).
Random vibration.Motion can be any combination of lateral, torsional and vertical.
Simple harmonic force due to alternate vortex shedding as well as motion induced force.
Self-excited forces. Self-excited forces. Not self-excited.
Increase in damping reduces instability.
Increase in damping reduces instability.
Effect of increase in damping is very low.
Increase in damping reduces response.
KAMAL KRISHNA BERA
Under the guidance of
Prof. Naresh K. Chandiramani
DEPARTMENT OF CIVIL ENGINEERINGINDIAN INSTITUTE OF TECHNOLOGY BOMBAY
WIND-INDUCED VIBRATION AND CONTROL OF CABLE-STAYED BRIDGES
Recommended