SEISMIC RESPONSE OF A REINFORCED

1
SEISMIC RESPONSE OF A REINFORCED CONCRETE ARCH
BRIDGE
Kawashima, K. and Mizoguchi, A.
Tokyo Institute of Technology
12WCEE, Auckland, New Zealand
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(No Transcript)
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Arch Bridge analyzed
2 lanes
9.5 m wide
192m
27m
Movable
Movable
150m
4
Arch Bridge Analyzed
Designed in accordance with the 1980 Design

Specifications of Highway Bridges, JRA
Allowable stress design approach
Seismic coefficient 0.18
5
Ground Condition Ground Motion
Uniform Excitation
GM 2

Multiple Excitation
GM 2
GM 1
3
?19MN/m
V 1000m/s
S
GM 1
GM 2
3
3
?19MN/m
?19MN/m
3
?20MN/m
V 300m/s
V 700m/s
S
S
V 1400m/s
S
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Analytical Model
Axial

Axial Force due

Moment
Force
to Dead Load
Yield

M
y
Moment
Curvature
Moment
Takeda-model
M
y
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Type I and Type II Ground Motions
Type I
2
Stiff
Moderate
1.8
Soft
1.6
1.4
Lateral

Force

1.2
Coefficients
1.0
Type II
0.8
0.6
0.4
0.2
0
0
1
2
3
4
5
Natural Period, s
8
Section of
Arch Rib at Springing
9
2
0
0
700
5
0
0
5
0
0
5
0
0
3
8
5
0
3
8
5
0
150
3450
D22
21_at_150
2050
150
6
0
1
5
0
_at_
1
0
0
D22
1
0
0
700
1.0
?
l
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Evaluation of Moment-Curvature Relation
Stress
Reinforcements
Strain
Type I GM
Stress
Type II GM
s
cc
s
0.8x
cc
Strain
Concrete
e
e
cc
cu
10
Dependence of Ultimate Displacement on

Confinement and Type of Ground Motion
Lateral Force vs. Lateral

Stress-Strain of Concrete
Displacement of a Pier
Ultimate Displacement
Lateral

Concrete

Type-I
Type-II
Ultimate Strain
Force
Stress
Type-I
Type-II
s
cc
0.8s
cc
e
e
Lateral Disp.
cu
cc
Yield Disp.
First Yield Disp.
Concrete Strain
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Shear Strain Dependence of Shear Modulus and

Damping Ratio of Soils in Equivalent Linear
Analysis
1
G/G
Dilluvium
0.8
0.6
Weathered

0.4
Granite
0.2
0
Damping Ratio
0.25
0.2
0.15
0.1
0.05
0
-4
-6
-2
-3
-5
10
10
10
10
10
Shear Strain
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Peak Acceleration in Surrounding Ground
Horizontal
Springing
gt1.1g
1-1.1g
0.9-1g
0.8-0.9g
-0.8g
Vertical
Springing
gt0.7g
0.6-0.7g
0.5-0.6g
0.4-0.5g
0.3-0.4g
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Natural Mode Shapes
1st
T 2 s
1
T 1.07 s
2nd
2
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Section Forces due to Static Loads
Design Force
Dead Load
Dead LoadActive Load
Dead LoadActive LoadThermal Effect
Axial Force
Moment

MN
MNm
60
40
0
40
20
-100
0
0
150
50
100
150
50
0
100
Distance, m
Distance, m
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Larger Response in Vertical Direction than in

Horizontal Direction under the Lateral Excitation
Horizontal
Vertical
Displacement, m
Acceleration, g
0.6
3
0.4
2
0.2
1
0
0
-0.2
-1
-2
-0.4
-3
-0.6
0
150
50
100
150
50
100
0
Distance, m
Distance, m
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Uniform Horizontal Vertical Excitations
Design Force
Yield Moment
Computed
Moment, MNm
Axial Force, MN
150
100
100
80
50
60
0
40
-50
20
-100
0
-150
-20
150
0
50
100
0
150
50
100
Distance, m
Distance, m
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Multiple Excitation, Horizontal Vertical
Horizontal
Vertical
Absolute

Displacement, m
Acceleration, g
3
0.6
2
0.4
1
0.2
0
0
-1
-0.2
-0.4
-2
-0.6
-3
0
150
0
50
100
50
150
100
Distance, m
Distance, m
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Multiple Excitation, Horizontal Vertical
Design Force
Yield Moment
Computed
Moment, MNm
Axial Force, MN
150
100
100
80
50
60
0
40
-50
20
-100
0
-150
-20
0
50
100
0
50
100
150
150
Distance, m
Distance, m
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Yielding of Arch Rib
Moment, MNm
80
40
µ
1.1
f
0
-40
-80
-0.002
0.002
0
Curvature, 1/m
Yielding of Arch Rib
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Conclusions
Large vertical responses are induced by lateral
excitation due

to significant mode coupling. Hence, vertical
excitation is

important in seismic design of an arch bridge
Some tension force as well as large compression
force that is

about double the design axial force is induced
in the arch rib.
Slight yielding occurs in the arch rib
More precise analysis is required considering the
interaction

between axial force and moment