th
The 14 World Conference on Earthquake Engineering
October 12-17, 2008, Beijing, China
Seismic performance of skew bridge with friction type rubber bearings
K.Y. Liu1, K.C. Chang2, C.H. Lu3 and W.C. Cheng4
1
Associate Research Fellow, Center for Research on Earthquake Engineering(NCREE)/Taipei, Chinese Taiwan
2
Professor, Dept. of Civil Engineering, Taiwan University/Taipei, Chinese Taiwan
3
Ph.D Student, Dept. of Civil Engineering, Taiwan University/Taipei, Chinese Taiwan
4
Master, Dept. of Civil Engineering, Taiwan University/Taipei, Chinese Taiwan
Email: [email protected]
ABSTRACT:
The seismic response of the skew bridges with rubber bearing is studied. In Taiwan, simply-supported PCI
bridges are widely used with rubber bearing pads as a supporting system. It is common seen that, during the
construction practice, the rubber bearing pads have been laid on the cement mortar-made bearing pads without
any details of bolting design. This kind of arrangement potentially allows rubber bearing to slide, so as the
superstructure when the earthquake occurs. In addition, bridges are usually being skewed to provide
transportation service, requiring a further investigation of seat width to avoid falling of the superstructure. In
this study, firstly, a series of friction coefficient was conducted. Furthermore, a scale-down skew bridge model
has been constructed to perform the shaking table test. According to the experimental results, the inertial forces
from superstructure can be reduced because of the sliding-induced isolation effect. The analytical program,
SAP2000N was used to simulate the experimental results, and it has been shown the numerical model can well
predict the displacement demand. Based on the parametric study, finally, the study will discuss the bridge
behaviors with different skew angles.
KEYWORDS:
skew bridge, rubber bearing, friction coefficient, shaking table test
1. INTRODUCTION
A devastating earthquake with a magnitude of 7.6 struck the central region of Taiwan in the early morning of
September 21, 1999. It was known as the 921 or Chi-chi earthquake (NCREE 1999). There are approximately
1,100 highway bridges spread on the provincial and county routes in the region. Major catastrophe occurred
especially in Taichung and Nantou counties. About 90 percent of the bridges escaped from serious damage. The
extents of bridge damages are relatively minor when compared to those observed in the 1994 Northridge
earthquake and 1995 Kobe earthquake. It was observed that the friction-sliding mechanism of rubber bearings
played a critical role to limit the seismic load transfer to the bridges’ columns. Most of the bridge damages
appeared to be caused by the movement of superstructure and separation of thermal expansion joints due to
sliding or failure of the bearings, with the exception of seven bridges collapsed due to large fault displacements
which crossed indirectly to the bridges. It was also observed that the number of bridge column damage was
surprisingly small. Chang et al. (Chang et. al 2004) developed a bridge model to simulate slide-friction of
rubber bearings, impact effect between shear key and girder, and plastic hinge at the end of the columns,
providing well simulation on a bridge that was damaged in the Chi-Chi Earthquake. Since most of the bridges in
the damaged area caused by Chi-Chi earthquake were designed without ductile detailing, it may be in contrast to
the current seismic design concept emphasizing the design of plastic hinges. Besides, damages of skew bridges
were also found in the Loma Prieta earthquake (M7.0) in 1989, Northridge earthquake (M6.7) in 1994, Kobe
earthquake (M7.2) in 1995. However, studies of skew bridge with rubber bearing are seldom discussed. Besides,
considering the route selection, engineers may face to design a skew bridge rather than a regular or straight
bridge in some occasions. For example, the bridge which is across the river often has no choice but to make a
column bent inclined to the axis of the superstructure. Therefore, this paper presents the experimental study
(Cheng 2008) on seismic performance of skew bridge with friction/sliding RB bearing (steel-reinforced
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The 14 World Conference on Earthquake Engineering
October 12-17, 2008, Beijing, China
elastomeric bearing) and PTFE-RB bearing (steel-reinforced elastomeric bearing coated on a thin PTFE
material). The friction coefficient test was carried out first to get friction coefficient of RB bearings and
PTFE-RB bearings on the surface of cement mortar, concrete, and steel plates. Two scaled bridge model was
utilized in the shaking table test to understand the influence of sliding behavior of bearings on a straight and
skew bridge, respectively. The force equilibrium relationship between inertial force and base shear was verified
from the test results, helping to build up reasonable analytical models to perform the parametric study. The
analytical program, SAP2000N, have been used to simulate the experimental results and demonstrated good
accuracy in predicting the displacement demand of the skew bridge. Based on the parametric study, finally, the
study will discuss the bridge behaviors with different skew angles and input directions of time histories.
2. FRICTION COEFFICIENT TEST
2.1. Test specimen and setup
Figure 1 shows the test setup of the friction coefficient test. The size of bearing specimens are determined due to
(1) minimal height of 15mm can only be provided by the manufactory and (2) consistent width of 150mm for
same specimens to be used in the shaking table test. So, the size of the bearing specimen is
150mm¯150mm¯15mm. The Hardness IRHD material and shape factor of the rubber is 60 and 3.75,
respectively. One SS400 shim plate is placed inside of the bearing. Based on the test requirements for rubber
bearings in Chapter 18, AASHTO (AASHTO, 2002), a total of 12 cases shown in Table 1 was performed to get
friction coefficient of two types of bearing (RB and PTFE-RB in Figure 2-3) on two different surfaces (material:
cement mortar, steel in Figure 4-5) with four sliding velocities (1.06, 50, 150 and 300 mm/sec). In each test, the
bearing clamped by the restrain plates on the top beam, shown in Figure 6, was forced to slide on the prefixed
blocks, either made by cement mortar or steel, within 14 cycles. The target displacement for horizontal actuator
is 60 mm in both positive and negative direction, providing a sufficient friction length to develop sliding
mechanism. The constant normal force around 4MPa for each bearing was applied by two vertical hydraulic
actuators, while shear and friction force were measured through two load cells under a loading beam. The
relative displacement was recorded by a temposonic sensor to compare to the data from horizontal actuator.
Figure 1 Test setup of the friction coefficient test
Figure 4 Cement mortar block
Figure 2 RB bearing
Figure 5 Concrete block with steel plate
Figure 3 PTFE-RB bearing
Figure 6 Installation of bearing
2.2. Test results and Discussions
Force and displacement curves for all cases are shown in Figure 7. During the test, it has been found that the
friction force rapidly decreases after first cycle and is getting smaller and smaller as increasing the number of
cycles. There is no doubt that long accumulated sliding distance will wear bearing surface and smoothen the
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The 14 World Conference on Earthquake Engineering
October 12-17, 2008, Beijing, China
surface of cement mortar or steel with some residue rubber attached. The friction coefficient was determined
according to ISO 15113 (ISO 2005). Since friction force is unstable in the first three cycles and affected in the
last three cycles by the horizontal actuator before stopping the test, it is suggested to neglect those six cycles to
obtain the coefficient with respect to cycles. Therefore, the maximum, minimum, and average friction
coefficients for each case are listed in Table 1.
Table 1 Summary of the friction coefficient test results
Group
Friction surface
cement mortar
RB
steel plate
PTFE-RB
steel plate
Case
Velocity (mm/sec)
1
2
3
4
5
6
7
8
9
10
11
12
1.06
50
150
300
1.06
50
150
300
1.06
50
150
300
Friction coefficient
Maximum Minimum Average
0.378
0.346
0.358
0.299
0.248
0.267
0.229
0.169
0.192
0.231
0.168
0.193
0.417
0.371
0.388
0.536
0.422
0.467
0.477
0.359
0.409
0.498
0.386
0.434
0.130
0.101
0.112
0.175
0.138
0.152
0.193
0.158
0.171
0.213
0.172
0.188
120
80
80
80
80
40
0
-40
-80
-120
40
0
-40
-80
-120
-80 -60 -40 -20 0 20 40 60 80
Horizontal Displacement (mm)
-40
-80
-120
40
0
-40
-80
-120
-80 -60 -40 -20 0 20 40 60 80
Horizontal Displacement (mm)
(b) case2
-80 -60 -40 -20 0 20 40 60 80
Horizontal Displacement (mm)
(c) case3
(d) case4
150
100
100
100
100
0
-50
-100
50
0
-50
-100
-150
-80 -60 -40 -20 0 20 40 60 80
Horizontal Displacement (mm)
(e) case5
-80
-40
-80
-80 -60 -40 -20 0 20 40 60 80
Horizontal Displacement (mm)
(i) case9
-80 -60 -40 -20 0 20 40 60 80
Horizontal Displacement (mm)
(h) case8
80
40
0
-40
-80
-80 -60 -40 -20 0 20 40 60 80
Horizontal Displacement (mm)
-50
-100
(g) case7
Horizontal Force (kN)
0
0
-150
80
40
50
-80 -60 -40 -20 0 20 40 60 80
Horizontal Displacement (mm)
(f) case6
Horizontal Force (kN)
-40
-50
-100
-150
80
0
0
-80 -60 -40 -20 0 20 40 60 80
Horizontal Displacement (mm)
80
40
50
Horizontal Force (kN)
50
Horizontal Force (kN)
150
Horizontal Force (kN)
150
Horizontal Force (kN)
Horizontal Force (kN)
0
150
-150
Horizontal Force (kN)
40
-80 -60 -40 -20 0 20 40 60 80
Horizontal Displacement (mm)
(a) case1
Horizontal Force (kN)
120
Horizontal Force (kN)
120
Horizontal Force (kN)
Horizontal Force (kN)
y
120
40
0
-40
-80
-80 -60 -40 -20 0 20 40 60 80
Horizontal Displacement (mm)
(j) case10
(k) case11
Figure 7 Hysterresis curve of the friction coefficient test
-80 -60 -40 -20 0 20 40 60 80
Horizontal Displacement (mm)
(l) case12
From Figure 5, the initial stiffness represents the elastic shear stiffness of the bearing and the unloading stiffness
is as same as the initial one. Consequently, owing to the contribution of the rubber in the elastic range, the
hysteresis loop for both RB and PTFE-RB bearing are a parallelogram shape rather than a pure rectangular loop.
th
The 14 World Conference on Earthquake Engineering
October 12-17, 2008, Beijing, China
Moreover, in comparison of reaction coefficient on different surfaces, this value on the cement mortar is smaller
than the one on the steel plate. To reflect the construction practice of unbolted bearings, a range from 0.2 to 0.4
for the friction coefficient is more realistic than using a single value. As for the PTFE-RB, the friction
coefficient from 0.1 to 0.2 can be obtained based on the test results.
3. SHAKLING TABLE TEST
3.1. Test specimen and setup
Shaking table tests were conducted to get realistic dynamic performance from two 1/7.5 scale-down
simply-supported bridge models with rubber bearings, shown in Figure 8 and 9, a straight and a skew bridge
model, respectively. Based on the definition of a complex bridge, which should be examined through dynamic
analysis method (MOTC 2000), the skew angle is 20 degree. The superstructure is 10.67 tons and consists of
concrete slabs, two girders and four diaphragms, supported by two rectangular hollow-section steel bents. The
column bents were designed to remain elastic. Figure 10 shows the design drawings of the bridge. The bearings
used in this test are as same as in the friction coefficient test, including RB and PTFE-RB bearings. Besides, in
order to compare the sliding behaviors between two different boundary conditions (B.C), as shown in Figure 11,
both RB-RB cases which represent a semi-fixed B.C, and PTFE-RB cases which are like a roller-hinge B.C,
were performed with peak ground acceleration (PGA) levels from 0.1g to 0.7g. The south bent may use RB or
PTFE-RB bearing, depending upon the cases; while the north bent was equipped with RB bearing only. The
input ground motion along the longitudinal direction of the bridge model is record in east-west direction of 1941
El Centro earthquake. Both time-history and response spectrum normalized to 1.0g are given in Figure 12.
Regarding to the instrumentation plan, acceleration on the superstructure, relative displacement of the bearing,
and surface strains at the end of the columns were measured.
Bridge model
Skew
Straight
Figure 8 regular bridge model
Test schedule for the shaking table test
Bearing arrangement
Peak input ground acceleration of El
(South end - North end)
Centro earthquake (g)
RB - RB
0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7
PTFE - RB
PTFE - RB
Figure 9 skew bridge model
Figure 10 design drawings
(a) RB-RB case
(b) PTFE-RB case
Figure 11 Arrangement of bearings
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The 14 World Conference on Earthquake Engineering
October 12-17, 2008, Beijing, China
_
p
p
p g
4
1.5
3
PSa (g)
A c c e le r a t i o n ( g )
1
0.5
0
-0.5
2
1
-1
-1.5
0
2.5
5
7.5
10
Time (sec)
12.5
15
17.5
0
20
0
0.5
1
1.5
Period (sec)
2
2.5
3
(a) Time history
(b) Response spectrum
Figure 12 Input ground motion of EL-Centro earthquake (PGA normalized to 1.0g)
3.2. Test result
Figure 13 illustrates the test results of peak acceleration on the superstructure with respect to PGAs. The obtained
acceleration is not proportional to the PGA, not only in RB-RB case or PTFE-RB case, representing the
influence of sliding effect on the global performance. Especially, the trend of the line in Figure 13(b) is getting
flat with a turning point around 0.2~0.3g. Although received same input ground motions, the accelerations in
PTFE-RB case are smaller than in RB-RB case, indicating that an isolation effect is apparent when utilizing a
bearing with small friction coefficient. The global structure response, particularly the force demand of the
column, can re reduced due to a sliding mechanism. However, the relative displacement between superstructure
and substructure is increasing. In Figure 14 (b), the obtained displacement showed no difference between two
locations before PGA of 0.2g, but after that, the displacement at south bent with PTFE-RB is increasing and the
displacement ratio between south and north bent is greater than 1.5. In contrast, the displacement demands at
both bents in Figure 14 (a) are similar due to using same type of RB bearing to require a semi-fixed boundary
condition. So, the structure performance was significantly affected by the bearing system, corresponding to a
low or high friction coefficient, and the arrangement of bearings to make a specified constrain on the boundary.
So far, friction coefficient of rubber bearing was often determined through static tests under very slow velocity.
However, for bridge subjected to the earthquake excitation, the coefficient from a dynamic test, such as a shaking
table test, is more realistic to describe the sliding phenomena. As shown in Figure 15, the base shear forces, which are
sum of two column forces at either north or south side bent, were divided by the weight of the superstructure to
determine the friction. The PGA in Figure 15 is 0.7g, and the bridge was moved according to the recorded videos.
Clearly, it is due to the sliding effect that an upper and lower bound of shear forces can be identified. The friction
coefficient for RB bearing and PTFE-RB bearing is around 0.4 and 0.2, respectively, close to the test results obtained
in the friction coefficient test with the speed at 300mm/sec.
Skew Bridge(RB-RB) EL Centro_X Direction - Relation Between Max. Deck Acceleration and PGA
Skew Bridge(PTFE-RB) EL Centro_X Direction - Relation Between Max. Deck Acceleration and PGA
0.8
0.5
0.66
0.7
0.69
0.4
0.6
0.53
0.5
Acceleration (g)
Acceleration (g)
0.70
0.42
0.4
0.30
0.3
0.2
0.14
0.29
0.3
0.36
0.37
0.5
0.6
0.39
0.33
0.24
0.2
0.12
0.1
0.1
0
0
0
0.1
0.2
0.3
0.4
PGA (g)
0.5
0.6
0.7
0.8
0
0.1
0.2
0.3
0.4
PGA (g)
0.7
0.8
(a) RB-RB case
(b) PTFE-RB case
Figure 13 Peak acceleration on the superstructure
Skew Bridge(RB-RB) EL Centro_X Direction - Relation Displacement Between Superstructure and Substructure
2
1.45
0.66
0.5
0.38
0
0
0.1
0.87
0.56
south side
north side
0.38
0.13
0.17
1.50
1.24
0.98
1
1.63
1.59
Displacement (cm)
Displacement (cm)
1.59
1.41
1.5
Skew Bridge(PTFE-RB) EL Centro_X Direction - Relation Displacement Between Superstructure and Substructure
2
1.5
1.39
1.20
1
0.90
0.70
0.44
0.5
0.3
0.4
PGA (g)
0.5
0.6
0.7
0.8
0
0.1
0.69
0.2
0.3
1.16
south side
north side
0.41
0.14
0.18
0
0.2
0.56
1.06
0.89
0.4
PGA (g)
0.5
0.6
(a) RB-RB case
(b) PTFE-RB case
Figure 14 Maximum relative displacement between superstructure and column bent
0.7
0.8
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The 14 World Conference on Earthquake Engineering
October 12-17, 2008, Beijing, China
Skew Bridge(RB-RB) EL Centro 700gal X Direction - South Bearing Horizontal Force
Skew Bridge(PTFE-RB) EL Centro 700gal X Direction - South Bearing Horizontal Force
30
40
Normal Force = 52.8kN
Normal Force = 52.8kN
15
Force (kN)
Force (kN)
20
0
0
-15
-20
-30
-40
5
7
9
11
13
Time (sec)
15
17
19
5
21
7
(a) RB-RB case (south side)
9
11
13
Time (sec)
15
Skew Bridge(RB-RB) EL Centro 700gal X Direction - North Bearing Horizontal Force
19
21
Skew Bridge(PTFE-RB) EL Centro 700gal X Direction - North Bearing Horizontal Force
40
40
Normal Force = 52.8kN
Normal Force = 52.8kN
20
Force (kN)
20
Force (kN)
17
(c) PTFE-RB case (south side)
0
-20
0
-20
-40
-40
5
7
9
11
13
Time (sec)
15
17
19
21
5
7
9
11
13
Time (sec)
15
17
19
21
(b) RB-RB case (north side)
(d) PTFE-RB case (north side)
Figure 15 Column shear forces with PGA of 0.7g
3.3. Analytical simulation
Based on the structure information, both skew and straight models shown in Figure 16 and 17 were established
in SAP200N (CSI 2002) to compare the structure performance with experimental results. In order to simulate
the sliding behavior of the rubber bearing, the friction-pendulum element (Wen 1976) was utilized with proper
friction coefficient given from either friction coefficient test or shaking table test. Only the bearing is considered
a nonlinear element with elastic shear stiffness determined by the shear modulus, area and height of the rubber,
and a constant friction coefficient of 0.4 for RB bearing, as well as 0.2 for PTFE-RB bearing. In Figure 19, the
analytical models can well predict the time history of the acceleration in the cases of 0.1g, 0.4g and 0.7g,
respectively. Not only the results from straight bridge model but the skew bridge models show good accuracy.
Figure 16 Skew bridge model
Figure 17 Straight bridge model
Straight Bridge(PTFE-RB) EL Centro 100gal X Direction - Acceleration Simulation(m=0.2&0.4)
Skew Bridge(RB-RB) EL Centro 100gal X Direction - Acceleration Simulation(m=0.4)
0.2
experimental result
analytical result
0.1
Acceleration (g)
Acceleration (g)
0.2
0
-0.1
experimental result
analytical result
0.1
0
-0.1
-0.2
-0.2
5
7
9
11
13
Time (sec)
15
17
19
5
21
(a) RB-RB case (Skew bridge, 0.1g)
0.3
9
11
13
Time (sec)
15
17
19
21
Straight Bridge(PTFE-RB) EL Centro 400gal X Direction - Acceleration Simulation(m=0.2&0.4)
0.4
experimental result
analytical result
Acceleration (g)
Acceleration (g)
0.6
7
(d) PTFE-RB case (Straight bridge, 0.1g)
Skew Bridge(RB-RB) EL Centro 400gal X Direction - Acceleration Simulation(m=0.4)
0
-0.3
experimental result
analytical result
0.2
0
-0.2
-0.4
-0.6
5
7
9
11
13
Time (sec)
15
17
19
5
21
(b) RB-RB case (Skew bridge, 0.4g)
9
11
13
Time (sec)
15
17
19
21
Straight Bridge(PTFE-RB) EL Centro 700gal X Direction - Acceleration Simulation(m=0.2&0.4)
0.4
Acceleration (g)
experimental result
analytical result
0.4
7
(e) PTFE-RB case (Straight bridge, 0.4g)
Skew Bridge(RB-RB) EL Centro 700gal X Direction - Acceleration Simulation(m=0.4)
0.8
Acceleration (g)
Figure 18 Friction-Pendulum element
0
-0.4
experimental result
analytical result
0.2
0
-0.2
-0.4
-0.8
5
7
9
11
13
Time (sec)
15
17
19
21
5
7
9
11
13
Time (sec)
15
17
19
(c) RB-RB case (Skew bridge, 0.7g)
(f) PTFE-RB case (Straight bridge, 0.7g)
Figure 19 Comparison of deck acceleration between analytical and experimental results
21
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The 14 World Conference on Earthquake Engineering
October 12-17, 2008, Beijing, China
Like results in Figure 19, the comparisons regarding to displacement in skew and straight model with three PGA
levels are also shown in Figure 20. Though the time history results of displacement are not so as good as
acceleration, ie., in Figure 20 (f) the analytical residual displacement is larger than the test data; however, the
peak response was capable of predicting the maximal response, helping engineers to confirm the safety of
unseating length based on the design code.
Skew Bridge(RB-RB) EL Centro 100gal X Direction - Displacement Simulation(m=0.4)
Straight Bridge(PTFE-RB) EL Centro 100gal X Direction - Displacement Simulation(m=0.2&0.4)
0.2
experimental result
analytical result
0.2
Displacement (cm)
Displacement (cm)
0.4
0
-0.2
-0.4
experimental result
analytical result
0.1
0
-0.1
-0.2
5
7
9
11
13
Time (sec)
15
17
19
21
5
7
(a) RB-RB case (Skew bridge, 0.1g)
Displacement (cm)
Displacement (cm)
15
17
19
21
Straight Bridge(PTFE-RB) EL Centro 400gal X Direction - Displacement Simulation(m=0.2&0.4)
0
-0.7
experimental result
analytical result
0.5
0
-0.5
-1.4
-1
5
7
9
11
13
Time (sec)
15
17
19
21
5
7
(b) RB-RB case (Skew bridge, 0.4g)
11
13
Time (sec)
15
17
19
21
Straight Bridge(PTFE-RB) EL Centro 700gal X Direction - Displacement Simulation(m=0.2&0.4)
2
Displacement (cm)
experimental result
analytical result
1
9
(e) PTFE-RB case (Straight bridge, 0.4g)
Skew Bridge(RB-RB) EL Centro 700gal X Direction - Displacement Simulation(m=0.4)
2
Displacement (cm)
13
Time (sec)
1
experimental result
analytical result
0.7
11
(d) PTFE-RB case (Straight bridge, 0.1g)
Skew Bridge(RB-RB) EL Centro 400gal X Direction - Displacement Simulation(m=0.4)
1.4
9
0
-1
-2
experimental result
analytical result
1
0
-1
-2
5
7
9
11
13
Time (sec)
15
17
19
21
5
7
9
11
13
Time (sec)
15
17
19
21
(c) RB-RB case (Skew bridge, 0.7g)
(f) PTFE-RB case (Straight bridge, 0.7g)
Figure 20 Comparison of deck displacement between analytical and experimental results
3.4. Comparison and Discussion
The shear force of the substructure is resulted from the inertial force of the superstructure, cap-beam and column
bents, assumed the damping force is neglectable; hence, these two loads should be identical to each other to make the
loading path clearly identified through the bearing system in between. In this study, the contribution of inertial force
from cap-beam and column themselves are too small to neglect because of relative small weight compared to the
girder. Figure 21 represents the comparison between inertial force of the superstructure and the base shear of the
substructure. The inertial force is the product of deck mass and deck acceleration at the time point corresponding to
maximal acceleration of the deck; meanwhile, the base shear at the same time point was also calculated. It was found
that no matter the superstructure was sliding or not, the force equilibrium relationship is satisfied in both RB-RB case
and PTFE-RB case. Therefore, by taking advantage of the accuracy of the analytical model, the force demand of
sliding rubber bearing and columns at different PGA levels can be quickly and precisely judged. Besides, the
maximal base shear force between skew and straight bridge model are also compared. As shown in Figure 22, though
the force of south bent in skew bridge is slightly smaller than the force obtained from straight bridge model (Figure
22 (a)), the trend of two lines almost same. However, if the skew angle is larger than 20 degree, the parametric
study results in Figure 23 reveal that the structure behavior is not proportional to the skew angle. Consequently,
it is suggested to use suitable bearing elements in the bridge model to get maximal response of a skew bridge.
Skew Bridge(RB-RB) EL Centro_X Direction - Comparison with Inertial Force and Column Shear Force
Skew Bridge(PTFE-RB) EL Centro_X Direction - Comparison with Inertial Force and Column Shear Force
100
60
90
50
80
40
60
Force (kN)
Force (kN)
70
50
40
30
20
30
inertial force
column shear force
20
10
inertial force
column shear force
10
0
0
0
0.1
0.2
0.3
0.4
PGA (g)
0.5
0.6
0.7
0.8
0
0.1
0.2
0.3
0.4
PGA (g)
0.5
0.6
(a) RB-RB case
(b) PTFE-RB case
Figure 21 Comparison of inertial force and base shear force in skew bridge model
0.7
0.8
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The 14 World Conference on Earthquake Engineering
October 12-17, 2008, Beijing, China
EL Centro_X Direction - Comparison with Straight and Skew Bridge for North Pier Max. Horizontal Force
EL Centro_X Direction - Comparison with Straight and Skew Bridge for South Pier Max. Horizontal Force
40
15
30
Force (kN)
Force (kN)
10
20
5
straight bridge
skew bridge
straight bridge
skew bridge
10
0
0
0
0.1
0.2
0.3
0.4
PGA (g)
0.5
0.6
0.7
0.8
0
0.1
0.2
0.3
0.4
PGA (g)
0.5
0.6
0.7
0.8
(a) South bent
(b) North bent
Figure 22 Comparison of maximal base shear force in the longitudinal direction (PTFE-RB case)
EL Centro_EW 1000gal Column Shear Force Response (South Column V2)
EL Centro_EW 1000gal Deck Displacement Response (Longitudinal Direction)
8
7
70
60
5
4
3
60
0o
10o
20o
30o
40o
50o
50
40
30
40
30
20
20
1
10
10
0
0
2
-10
0
10
20
30
Skew Angle (degree)
40
50
60
0o
10o
20o
30o
40o
50o
50
Shear Force (kN)
0o
10o
20o
30o
40o
50o
Shear Force (kN)
6
Displacement (cm)
EL Centro_EW 1000gal Column Shear Force Response (North Column V2)
70
0
-10
0
10
20
30
Skew Angle (degree)
40
50
60
-10
0
10
20
30
Skew Angle (degree)
40
50
60
(a) girder displacement
(b) south bent base shear force
(c) north bent base shear force
Figure 23 Prediction of maximal response for RB-RB case under different skew angles (PGA = 1.0g)
CONCULSIONS
This paper aims at discussing the seismic response of the skew bridges with sliding rubber bearings. The
construction practices of rubber bearing without any anchor bolts provide a fuse-like mechanism for rubber
bearing to slide on the bearing pad and thereafter to reduce the force demand of the column and enlarge the
displacement requirement of seat width. Therefore, a series of friction coefficient was conducted first and
followed by shaking table tests on two scale-down skew bridge models. According to the experimental results,
the friction coefficient for RB and PTFE-RB bearing is 0.4 and 0.2, respectively, considering the influence of
high speed may be required in a real seismic event. Beside, the force equilibrium relationship between inertial
force and base shear was confirmed experimentally. The analytical models can well predict the structure
performance in comparison with the test results, helping to set seat width for the skew bridge. Based on the
parametric study, finally, it is suggested to use suitable bearing elements in the bridge model to get maximal
response of a skew bridge under seismic excitations.
REFERENCES
AASHTO. (2002), “Standard Specifications for Highway Bridges, 17th Ed”, American Association of State
Highway and Transportation Officials, Washington, DC.
Cheng Wei-Jin. (2008). “Shaking Table Test for Scale Down Skew Bridge Models with Rubber Bearings.”
Master thesis, Department of Civil Engineering, Taiwan University, Chinese Taiwan.
Computers and Structures, Inc., (2002). “SAP2000, Integrated Finite Element Analysis and Design of Structures,
Analysis Reference Manual,” University of California at Berkeley, California, USA.
ISO. (2005). “Rubber–Determination of Frictional Properties”, ISO 15113 INTERNATIONAL STANDARD.
K.C Chang, K.Y Kuo, K.Y Liu, and C.H Lu. (2004). “On Seismic Retrofit Strategies of Highway Bridges Experiences Learned from Chi-Chi Earthquake”, 13th World Conference on Earthquake Engineering,
Vancouver, B.C., Canada, Paper No. 639, 2004
Center for Research on Earthquake Engineering(NCREE). (1999). “Reconnaissance report of the 921 Chi-Chi
Earthquake for bridges and transportation facilities,” Report No. NCREE -99-055, Taipei, Chinese Taiwan.
Wen Y.K. 1976. Method for Random Vibration of Hysteretic Systems. Journal of the Engineering Mechanics Division,
ASCE, 102(EM2).