Proceedings of the 9th International Conference on Structural Dynamics, EURODYN 2014
Porto, Portugal, 30 June - 2 July 2014
A. Cunha, E. Caetano, P. Ribeiro, G. Müller (eds.)
ISSN: 2311-9020; ISBN: 978-972-752-165-4
Seismic performance of straddle-type monorail pre-stressed concrete bridges
considering interaction with train under moderate earthquakes
Chul-Woo Kim 1, Kazuyuki Ono 2, Mitsuo Kawatani 3, and Takuya Enmei 3
Dept. of Civil and Earth Resources Engineering, Kyoto University, Kyoto 615-8540, Japan
2
Road & Transport Dept., Eight-Japan Engineering Consultants Inc., Osaka 532-0034, Japan
3
Dept. of Civil Engineering, Kobe University, Kobe 657-8501, Japan
email: [email protected], [email protected], [email protected], [email protected]
1
ABSTRACT: This study aims to investigate seismic responses and performance of straddle-type pre-stressed concrete (PC)
bridges considering train load under moderate earthquakes. The study also examines how elastomeric bearings work for
improving seismic performance of the bridge. All investigations were based on a three-dimensional dynamic response analysis
of train-bridge interaction system under earthquakes. Observations demonstrated that considering train as dynamic system led to
decrease of seismic responses in comparison with those responses considering train as additional mass to the bridge. Elastomeric
bearings also improved seismic performance of the bridge. However greater train accelerations were observed at the train on the
bridge with elastomeric bearings than the bridge with steel bearings, which would make passengers feel excessive vibrations.
KEY WORDS: Monorail; Seismic performance; Train-bridge interaction; elastomeric bearing.
1
INTRODUCTION
Monorail system has been successfully adopted as a new
transport system in major cities of Japan as it takes short
period and low cost in construction compared to the subway
system. Improving efficiency and labor saving while satisfies
seismic performance is a challenge even in structural design
of monorail system. A new type of a steel-concrete composite
monorail bridge with a simplified lateral bracing system thus
has been proposed in Japan [1]. As for pre-stressed concrete
(PC) monorail bridges, adopting longer span (hereafter,
advanced bridge) than conventional bridges and elastomeric
bearings is proposed to improve efficiency and seismic
performance. However, there is concern about large
deformations of PC girders caused by longer span and change
in vibration characteristics caused by elastomeric bearings.
In seismic design of monorail bridges, the effect of the train
load is considered as additional mass. However, it is improper
to treat train on the monorail bridge just as additional mass in
seismic design, since train on monorail bridges is a
complicated dynamic system with steering and stabilizing
wheels that firmly grasp the track girder of monorail bridges.
In addition, differently from railways, the passengers in
monorail train might have difficulty in evacuating during
earthquakes because of the structural characteristic of the
monorail system. Therefore, studies on seismic performance
of the monorail bridge and vibration serviceability of
monorail train are important technical issues.
Bridges in Japan should satisfy level-1 seismic performance
under moderate earthquakes, so called level-1 ground motions,
and level-2 seismic performance under extreme earthquakes,
so called level-2 ground motions [2]. Level-1 seismic
performance is defined as the state in an elastic manner
without severe damage under moderate earthquakes.
Additionally the bridge bearings are kept intact under the
level-1 earthquake. A remaining problem to be answered is
whether seismic responses of the bridge designed under the
level-1 earthquakes stay within elastic range as expected or
not, since some measured moderate earthquakes have
dominant frequency range which is similar with bridge
structures. In other words, even though amplification of a
moderate earthquake can be categorized as level-1 ground
motion, it could have resonant frequency with bridges and
result in a plastic behavior.
This study investigates seismic performance of PC
monorail bridges with elastomeric bearings as well as
adopting longer span than that of conventional bridges. The
effect of train load on the seismic performance of the bridge
under moderate ground motions is also examined by means of
a three-dimensional dynamic response analysis. The validity
of the analytical method of train-bridge interaction has been
verified by comparing with experiment results on steel
monorail bridges [1], [3]. Moreover, the analytical method has
been updated to consider seismic behaviors of the steel
monorail bridges under moving train [4], [5].
2
TRAIN-BRIDGE INTERACTION WITH GROUND
MOTION
Bridges are considered as an assemblage of beam elements
with six degrees of freedom (DOFs) at each node [3-5]. A car
of monorail train has two bogies with pneumatic tires for
running, steering and stabilizing wheels. The car’s dynamic
behavior is assumed to be sufficiently represented by a
discrete rigid multi-body system with 15 DOFs.
The combination of the interaction force and wheel load at
a contact point of the bridge suggests the equation of forced
vibration for monorail train-bridge interaction system. If the
interaction system is subjected to ground motion then the
problem is solvable by considering an additional inertia force
input from acceleration of mass as shown in Equation (1).
(1)
1161
850
1500
1500
Proceedings of the 9th International Conference on Structural Dynamics, EURODYN 2014
385
5300
5300
5300
5300
385
21200
850
850
1500
1500
(a) Conventional bridge with span length of 21.2m
485
8100
5400
5400
8100
485
850
27000
(b) Advanced bridge with span length of 27m
Figure 1. PC girders of the monorail bridge.
Front view
Side view
22000
5600
950
3700
Side view
Front view
22000
950
950
485 30485
5600
3700
28000
28000
950
48530485
750 1000750
100
100
1500
65. 431
2000
1500
2300
71. 920
71. 420
100
1800
100
2500
1350
65. 431
2300
1350
1500
65. 431
100
3000
5000
Φ1000
L =8.0m, n=4
200 100
1900
200 100
1900
1000
2000
100
1800
2000
1500
62. 420
1000
1000
100
100
3000
5000
1000
100
100
L=8.0m, n=4
71. 920
71. 420
2300
2500
100
2350
65. 431
2300
2350
64. 320
62. 420
1000
Φ1000
72. 920
100
64. 320
64. 320
62. 420
500 1000
72. 920
10500
7100
1800
10500
7100
2000
10500
7100
1800
64. 320
200 100
1900
71. 920
71. 420
10500
7100
100
72. 920
200 100
1900
71. 920
71. 420
500 1000
72. 920
500 1000
500 1000
7501000750
3000
5000
62. 420
1000
1000
100
2@2500=5000
100
7000
1000
100
Φ1000
Φ1000
L=6.5m, n=6
L=6.5m, n=6
(a) Conventional bridge
(b) Advanced bridge
Figure 2. Substructure of monorail bridges.
where M, C and K indicate the mass, damping, and stiffness
matrices of the bridge, respectively. The force vector is f.
Subscripts B, T and BT denote the bridge, train, and bridgetrain interaction, respectively. q and wdenote generalized
coordinate vector of the bridge and displacement of train,
respectively. äg is the ground acceleration.
In this study, the modal analysis is employed assuming that
bridge structures deform within elastic range under level-1
ground motions. Details of Equation (1) can be found in
references [4], [5]. The differential equations of train-bridge
interaction under the ground motion are solved by Newmark’s
β method. β of 0.25 was used to obtain stable and accurate
solutions. Solutions were obtained with a relative margin of
error of less than 0.001.
3
3.1
ANALYTICAL MODEL
Bridges
This study considered two bridge models: conventional bridge
and advanced bridge. Bridge length of the conventional bridge
is 22m (span length is 21.2m), while the advanced bridge
adopts bridge length of 28m (span length is 27.0m). The
general layout and geometry of two bridges are shown in
Figure 1, whereas Figure 2 shows those of substructures. The
monorail structure has two tram girders and the distance
between those tram girders is 3.7m. Reinforced concrete (RC)
piers with height of 10.6m were considered in the study.
1162
Figure 3 shows the finite element (FE) model of the
monorail bridges. Surface roughness of tram girders and gaps
between girders were considered in the dynamic response
analysis under moving train and subjected to earthquakes.
Half of the total mass of neighboring span (Ld in Figure 3)
was also considered: 254.31kN for the conventional bridge
and 345.55kN for the advanced bridge. Table 1 shows crosssectional properties and mass per unit length of PC girders.
Elastic properties of concrete and elastomeric bearings are
summarized in Table 2. It is noteworthy that the elastomeric
bearing is proposed for the advanced bridge. The bridge
footings of the models were idealized as springs of which
properties are shown in Table 3.
Figure 4 shows first five natural modes of the conventional
and advanced bridges with steel bearings taken from the
eigenvalue analysis. The frequencies in parentheses are the
results from the FE model considering parked train on the
bridge as additional mass. Only horizontal bending modes
of tram girders and piers were observed in the first five natural
modes.
3.2
Monorail train
Figure 5 shows the three-dimensional car model with 15 DOF
that is used in this study. The monorail train was assumed to
have weight of 338kN/car including passengers. Natural
frequencies for bounce and sway motions were 1.207 Hz and
0.912 Hz, respectively. Details of physical properties of train
are summarized in reference [4].
Proceedings of the 9th International Conference on Structural Dynamics, EURODYN 2014
Moving Train
End of
girder
G1 girder
Ld
Ld
Center of
girder
End of
girder
Ld
Ld
G2 girder
y z
x
Observation point
Ground motion
P1
P2
P3
P4
Figure 3. FE model of monorail bridge.
1st mode:
3.099Hz(2.471Hz)
Horizontal bending
(C/W Pier bending)
2nd mode:
3.370Hz(2.665Hz)
Pier bending
(C/W Horizontal bending)
3rd mode:
3.833Hz(2.903Hz)
Horizontal bending
(C/W Pier bending)
4th mode:
4.297Hz(3.819Hz)
Horizontal bending
5th mode:
4.299Hz(3.867Hz)
Horizontal bending
(C/W: Coupled with)
(a) Conventional bridge with steel bearings
1st mode:
2.394Hz(1.860Hz)
Horizontal bending
(C/W Pier bending)
2nd mode:
2.563Hz(1.949Hz)
Pier bending
(C/W Horizontal bending)
3rd mode:
2.798Hz(2.040Hz)
Horizontal bending
(C/W Pier bending)
4th mode:
2.934Hz(2.693Hz)
Horizontal bending
5th mode:
2.935Hz(2.751Hz)
Horizontal bending
(C/W: Coupled with)
(b) Advanced bridge with steel bearings
Figure 4. First five natural modes and frequencies.
Table 1. Cross-sectional properties of PC girders.
PC girder
Conventional
Advanced
Cross-sectional area
(m2)
End
Center
1.075
0.884
1.075
0.927
Moment of inertia of area (m4)
End (Iz)
0.073
0.073
Center (Iz)
0.064
0.071
End (Iy)
0.220
0.220
Center (Iy)
0.206
0.209
End (Ix)
0.307
0.307
Center (Ix)
0.307
0.307
Mass per unit
length (t/m)
End
Center
2.687
2.211
2.864
2.233
Table 2. Elastic properties of concrete and elastomeric bearing.
Concrete (N/mm2)
Spring constant of elastomeric bearing
fck
E
G
kx
ky
kz
kx
ky
Conventional
50
3.3e104
1.43e104
208
663
162415
342726
3464
Advanced
80
3.8e104
1.65e104
(kN/m) (kN/m)
(kN/m)
(kN.m/rad) (kN.m/rad)
4
4
Pier
27
2.65e10
1.15e10
fckCompressive stress, E: Young’s modulus, G: Shear modulus
Table 3. Spring constant of foundation.
Vertical
Horizontal
Rotational
3.3
3581400 (kN/m)
28275000 (kN/m)
1003300 (kN.m/rad)
Ground motions
Two moderate design ground motions specified in JRA (Japan
Road Association) code [2] and a measured moderate ground
motion were considered in the analysis.
Figure 6(a) shows Group-1 of Level-1 (hereafter, G1LV1
ground motion) which is the moderate earthquake at a stiff
soil site. Figure 6(b) shows Group-2 of Level-1 (hereafter,
G2LV1 ground motion) which is the moderate earthquake at a
moderate soil site. The moderate ground motion measured in
Hobetsu, Yuuhutsu, Hokkaido, Japan, on 26 September 2003
(hereafter HB ground motion, see Figure 6(c)) was also
adopted in the seismic response analysis of monorail bridges.
In the JRA code, vertical components of the ground
motions are not specified, and half scale of the transverse
ground motions was adopted in the analysis. For the measured
HB ground motion, measured vertical ground motion was
considered in the analysis.
Figure 6 shows accelerograms and response spectra of the
three ground motions. Figure 6(c) shows the natural periods
corresponding to the first horizontal (0.323s, 3.099Hz) and
advanced bridge with steel bearings (0.418s, 2.394Hz)
without considering train. Existence of the natural periods on
the dominant range of the response spectrum discloses
potential of strong seismic responses.
3.4
Track surface roughness
Track surface roughness measured at the conventional bridge
is considered in the analysis. Laser displacement sensors were
installed to the experimental car to measure surface roughness
of tram wheel path, steering wheel path and stabilizing wheel
path. The speed of experimental car was 1km/h and sampling
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Proceedings of the 9th International Conference on Structural Dynamics, EURODYN 2014
frequency was 200 Hz. Furthermore, surface roughness of
joints between girders were also measured by caliper and
depth gauge. For the advanced bridge which has longer span
than the conventional bridge, the data length of surface
roughness is expanded by adding roughness data.
Analysis conditions
Rayleigh damping was adopted in the analysis, in which the
damping constant of the monorail bridge during an earthquake
was assumed to be 5%. Dynamic responses of each bridge
were obtained by mode-superposition up to the mode related
to the frequency near 20Hz: for the conventional bridge with
steel bearing, up to the 38th (19.77Hz) mode; up to the 42th
(19.86Hz) and 56th (19.64Hz) modes were considered for the
advanced bridge with steel and elastomeric bearings in respect.
The time interval with Newmark’s β method is 0.005.
In investigating the dynamic effect of monorail train on
seismic responses of monorail bridges, four scenarios were
considered in the analysis: SCN-1 which disregards train’s
mass; SCN-2 which considers train as an additional mass on
the bridge model; SCN-3 which considers interaction between
parked train and the bridge; and SCN-4 which considers
interaction between moving train and the bridge. In SCN-2
and SCN-3, train was aligned in such way that the reaction
force of P2 pier is the most critical.
PEAK = 102 Gal R.M.S = 25.4 Gal
Seismic responses
In this section, two design ground motions G1LV1 and
G2LV1 in JRA code (Figure 6 (a), (b)) were utilized to
investigate how adopting longer span and elastomeric
bearings result in seismic responses.
100
50
0
-50
-100
-150
200
h=5%
100
0
0
5
10
15
Time (s)
20
25
0.1
1
10
Period(s)
(a) Design ground motion on stiff soil site: G1LV1
Responses at pier top and span center
150
Acceleration(Gal)
4.2.1
300
150
Acceleration (Gal)
4.2
Figure 5. Monorail train model with 15DOF.
Acceleration (Gal)
4.1
SESMIC RESPONSE ANALYSIS OF TRAIN-BRIDGE
INTERACTIVE
PEAK = 118 Gal R.M.S = 32.9 Gal
300
Acceleration (Gal)
4
system of train might act as a damper under earthquakes. The
result corresponds to the conclusion in the previous study on
steel girder bridges [4]. It is noteworthy, however, that
responses of the advanced bridge with elastomeric bearings
showed different tendency: considering the interaction
between the advanced bridge with elastomeric bearings and
moving train (SCN-4) was greater than the other scenarios as
shown in Figure 10.
1164
Response acc. (Gal)
Acc. (Gal)
Acc. (Gal)
Acceleration (Gal)
Response acc. (Gal)
Response acc. (Gal)
Response acc. (Gal)
Response
acc.
(Gal)
Acceleration
(Gal)
Acc. (Gal)
Acceleration
(Gal)
Acc. (Gal)
Response acc. (Gal)
Response acc. (Gal)
Acc. (Gal)
Acc. (Gal)
Acc. (Gal)
Acc. (Gal)
Acceleration
(Gal)
Accelerations at the span center and top of P2 pier in the
200
50
transverse direction were examined. Those accelerations of
h=5%
0
100
the conventional bridge under the G1LV1 ground motion are
-50
-100
shown in Figure 7, and those under the G2LV1 ground motion
0
-150
0.1
1
10
0
5
10
15
20
25
30
are shown in Figure 8. Figure 7 and Figure 8 show that RMS
time(s)
Period(s)
values under the G2LV1 ground motion were greater than
(b) Design ground motion on moderate soil site: G2LV1
those values under the G1LV1 ground motion in all scenarios.
Thus for the advanced bridge the responses under the G2LV1 Peak= 140 Gal
PEAK
= RMS=
140
R.M.S
= 42.4
Gal
1000
Peak=
140Gal
Gal 42.4
RMS= 42.4
GalGal 1000
Peak= -53.3 Gal 200
RMS= 15.7Peak=
Gal
200
200
1000
0.323s 0.418s 200
ground motion which led to critical result are discussed200
in
0.323s 0.418s
800
800
800
100
100
100
100
100
order to save space. The responses of the advanced bridge
600
600
600
0
0
0
with steel bearings under the G2LV1 ground motion are
00
400
400
400
-100
shown in Figure 9, and those of the advanced bridge -100
with
-100
-100
-100
200
200
200
elastomeric bearings are shown in Figure 10.
-200
-200
-200
-200
0 00
-200
0
5
10
15
20
25
30
0.1 0.1
1
10 10 15 20 025 305
0.1
30
1
101
15 25
20 25 30
0 510
0.10.1
In focusing on the response at the span center, responses of0 5 10 0 155 1020
Period (s)
Time (s)
Natural Natural
period (s) period (s) Time (s)
Time (s) Time (s)
EW direction
natural period
(s) period (s)
natural
the conventional bridge of SCN-2 under the G1LV1 ground
PEAK
=-53.3
53.3
GalRMS=
R.M.S
15.7
Gal
Peak=
Gal RMS= 42.4 Gal
Peak=
Gal
RMS=
15.7= Gal
1000
Peak= 140 Gal RMS=
42.4140
Gal
Peak=
-53.3
Gal
15.7
Gal
1000
1000
200
motion were greater
than
those
responses
of
SCN-1.
However,
200
200
200
1000
200
1000
0.323s 0.418s 0.323s 0.418s
800
800800
800
the responses100at the span center
of the 800
conventional
and
100
100
100 100
600
600
600
600motion600
advanced bridges
under the G2LV1
ground
showed
0
0 00
0
400400
400
400
400
opposite tendency with those responses under the G1LV1
-100
-100 -100
-100
200200
-100
200
200
200
ground motion: i.e. those responses of SCN-1 were greater
0 00
-200 -200
-200
0
-200
-200 0
0
5
10
15
20
25
30
than those of SCN-2.
0.1
1
11
30
110
10 0
15 20 0.1
25 0.1
05 510 10 15
15 (s)
20 25
10.10.1
0 5 10 15 020 5 2510 30
20
25 3030 0.1 0.1
Time
Period (s)
Natural
Natural period
(s)period (s)
In considering interactionTime
between
train
with
Natural
period (s)
Natural
period (s)
Time and
(s) the bridge
Time
(s)
UD
direction
(s)
Time
(s)
natural(s)period (s)
naturalnatural
period (s)period (s)
natural period
steel bearings (SCN-3 and SCN-4), the responses were
(c) Measured ground motion: HB
smaller than those not considering the interaction (SCN-1,
Figure 6. Accelerograms and response spectra of moderate
SCN-2) (see Figures 7, 8 and 9). It shows that the dynamic
ground motions.
100
0
-200
-400
-400
0
5
10
15
20
200
0
-200
-400
0
25
time(s)
5
10
15
20
25
time(s)
0
10
200
0
-200
400
200
0
-200
0
5
10
15
20
0
25
time(s)
PEAK = 227.4 Gal
R.M.S = 52.76 Gal
400
200
0
-200
5
10
15
20
0
25
time(s)
10
0
-200
-400
Acceleration(Gal)
Acceleration(Gal)
Acceleration(Gal)
200
PEAK = 175.7 Gal
R.M.S = 46.79 Gal
400
200
0
-200
-400
0
5
10
15
20
5
10
15
20
200
0
-200
25
time(s)
0
0
-200
-400
PEAK = 221.6 Gal
R.M.S = 48.32 Gal
400
200
0
-200
-400
0
5
10
15
20
25
time(s)
10
5
10
15
20
Responses of monorail train
Responses of monorail train during earthquakes are also
examined to provide information on vibratory sensation of
passengers during earthquakes. Accelerations of the third car
of monorail train on the conventional bridge are shown in
Figure 11, and those on the advanced bridge are shown in
Figure 12. For the response of train on the conventional bridge,
responses under the G2LV1 ground motion were greater than
those under the G1LV1 ground motion as shown in Figure 11.
Observations also demonstrated that the response of
moving train (SCN-4) was greater than of the response of
parked train (SCN-3). For the response of train on the
advanced bridge with steel bearings (see Figure 12 (a)), peak
responses of moving train on the advanced bridge with steel
bearings under the G2LV1 ground motion were greater than
those of parked train even though the RMS value of SCN-4
was similar with SCN-3. However adopting elastomeric
bearings led to relatively large accelerations on moving train
as shown in Figure 12 (b).
It could be concluded that responses of both moving and
parked trains should be considered to investigate vibratory
sensation of passengers during earthquakes. Moreover
adopting elastomeric bearings to reduce seismic responses of
bridges could increase acceleration responses of train under
earthquakes.
5
30
time(s)
PEAK = 191.7 Gal
R.M.S = 48.65 Gal
400
200
0
-200
0
25
time(s)
(4) Case-4: Train moving
(a) Pier top
(b) Span center
Figure 7 Acceleration responses of the conventional bridge
with steel bearings under G1LV1 ground motion.
4.2.2
20
-400
0
0
10
20
30
time(s)
600
400
200
0
-200
-400
-600
PEAK = 421.1 Gal
R.M.S = 147.3 Gal
0
10
20
30
time(s)
600
400
200
0
-200
-400
-600
PEAK = 260.5 Gal
R.M.S = 66.31 Gal
0
10
20
30
time(s)
(3) Case-3: Train stop
Acceleration(Gal)
Acceleration(Gal)
Acceleration(Gal)
PEAK = 189.7 Gal
R.M.S = 36.55 Gal
200
30
time(s)
PEAK = 184.3 Gal
R.M.S = 47.93 Gal
400
(3) Case-3: Train stop
400
20
-400
0
25
time(s)
PEAK = 613.3 Gal
R.M.S = 150.7 Gal
(2) Case-2: Train as mass
(2) Case-2: Train as mass
PEAK = 182.6 Gal
R.M.S = 36.16 Gal
400
30
time(s)
-400
-400
-400
20
600
400
200
0
-200
-400
-600
(1) Case-1: No train
R.M.S = 141.9 Gal
Acceleration(Gal)
400
Acceleration(Gal)
Acceleration(Gal)
(1) Case-1: No trainPEAK = 423.9 Gal
PEAK = 164.8 Gal
R.M.S = 46.79 Gal
Acceleration(Gal)
-200
200
Acceleration(Gal)
0
PEAK = 230.7 Gal
R.M.S = 69.68 Gal
400
Acceleration(Gal)
200
PEAK = 388.6 Gal
R.M.S = 73.70 Gal
400
Acceleration(Gal)
PEAK = 228.5 Gal
R.M.S = 41.83 Gal
400
Acceleration(Gal)
Acceleration(Gal)
Acceleration(Gal)
Proceedings of the 9th International Conference on Structural Dynamics, EURODYN 2014
SEISMIC PERFORMANCE OF MONORAIL BRIDGE
Shearing forces of bearings and piers, and bending moments
of piers are examined to discuss seismic performance of
10
20
30
time(s)
600
400
200
0
-200
-400
-600
PEAK = 272.7 Gal
R.M.S = 70.86 Gal
0
10
20
30
time(s)
(4) Case-4: Train moving
(a) Pier top
(b) Span center
Figure 8 Acceleration responses of the conventional bridge
with steel bearings under G2LV1 ground motion.
monorail bridges under moderate ground motions.
5.1
Seismic performance of bearings
The observation point was the bearing on the P3 pier as the
shearing force on the P3 pier was greater than that of other
piers from a preliminary investigation. Analytical shearing
forces of steel bearings on the conventional bridge under
G2LV1 and HB ground motions are shown in Figure 13. It
shows that responses under the HB ground motion were larger
than those under the G2LV1 design ground motion.
Responses under the HB ground motion which led to
critical results were discussed for the advanced bridge, and
those shearing forces of steel and elastomeric bearings are
shown in Figure 14. The horizontal lines in Figures 13 and 14
indicate shear capacities of bearings of the bridges: 165.4kN
for the conventional bridge; and 221.9kN for the advance
bridge.
As shown in Figure 13(a), shearing forces of the
conventional bridge under the G2LV1 ground motion were
smaller than the shear capacity except SCN-2. For shearing
forces of SCN-1 (disregarding train) and SCN-2 (considering
train as additional mass) scenarios, those shearing forces of
steel bearings on both conventional and advanced bridges
under the HB ground motion were greater than the respective
shear capacities. On the other hands, the scenarios considering
train dynamics (SCN-3 and SCN-4) led to remarkably smaller
shearing forces than those of SCN-1 and SCN-2. One reason
for the result could be train’s dynamic system which acts as
damper during earthquakes.
1165
0
-200
-400
-400
0
10
20
0
30
time(s)
10
20
400
PEAK = 154.3 Gal
R.M.S = 43.01 Gal
200
0
-200
-400
30
time(s)
0
10
200
0
-200
PEAK = 393.0 Gal
R.M.S = 112.6 Gal
400
400
Acceleration(Gal)
Acceleration(Gal)
200
0
-200
PEAK = 142.1 Gal
R.M.S = 40.05 Gal
200
0
-200
0
30
time(s)
10
20
-400
30
time(s)
0
10
200
0
-200
200
0
-200
-400
-400
0
10
20
0
30
time(s)
10
20
400
200
0
-200
-400
30
time(s)
30
time(s)
0
-200
200
0
-200
-400
0
10
20
400
200
0
-200
0
10
0
10
20
0
-200
0
5
10
15
20
25
time(s)
PEAK = 264.3 Gal
R.M.S = 77.35 Gal
400
200
0
-200
-400
10
PEAK = 156.2 Gal
R.M.S = 43.28 Gal
0
-200
20
0
30
time(s)
-200
-400
0
5
10
15
20
25
time(s)
PEAK = 245.3 Gal
R.M.S = 62.51 Gal
400
200
0
-200
-400
0
10
20
30
time(s)
PEAK = 176.4 Gal
R.M.S = 62.5 Gal
200
0
-200
0
5
10
15
20
25 30
Time (s)
20
30
time(s)
SCN-4: Moving train (Rear axle)
(a) G1LV1 ground motion (b) G2LV1 ground motion
Figure 11. Acceleration responses of train on the
conventional bridge with steel bearings.
Under the HB ground motion, maximum shearing forces at
the steel bearing on the conventional bridge were 187.1kN for
the SCN-1 scenario and 446.8kN for the SCN-2 scenario,
whereas those maximum shearing forces crossed the shear
capacity of 165.4kN. Moreover, those maximum shearing
forces of the steel bearing on the advanced bridge were
242.9kN in SCN-1 and 321.9kN in SCN-2, which also crossed
the shearing capacity of 221.9kN.
20
30
time(s)
800
600
400
200
0
-200
-400
-600
-800
PEAK = 733.9 Gal
R.M.S = 106.7 Gal
0
10
20
30
time(s)
200
0
-200
0
10
20
30
time(s)
PEAK = 266.2 Gal
R.M.S = 91.81 Gal
400
200
0
-200
-400
0
10
20
30
time(s)
SCN-3: Parked train (3rd car, front axle)
Acceleration(Gal)
0
Acceleration(Gal)
PEAK = 163.7 Gal
R.M.S = 43.86 Gal
200
10
PEAK = 284.7 Gal
R.M.S = 83.44 Gal
400
SCN-3: Parked train (3rd car, front axle)
400
400
-400
30
time(s)
200
-400
0
10
(4) SCN-4: Train moving
(b) Span center
(a) Pier top
Figure 10. Acceleration responses of the advanced bridge
with elastomeric bearings under G2LV1 ground motion.
Acceleration(Gal)
200
Acceleration(Gal)
PEAK = 249.6 Gal
R.M.S = 51.52 Gal
400
-400
30
time(s)
(4) SCN-4: Train moving
(b) Span center
(a) Pier top
Figure 9. Acceleration responses of the advanced bridge
with steel bearings under G2LV1 ground motion.
400
20
-400
30
time(s)
0
(3) SCN-3: Train stop
PEAK = 267.7 Gal
R.M.S = 65.87 Gal
Acceleration(Gal)
PEAK = 187.1 Gal
R.M.S = 47.93 Gal
400
Acceleration(Gal)
Acceleration(Gal)
20
PEAK = 169.7 Gal
R.M.S = 58.57 Gal
200
-400
30
time(s)
PEAK = 153.4 Gal
R.M.S = 43.13 Gal
(3) SCN-3: Train stop
Acceleration(Gal)
10
(2) SCN-2: Train as mass
PEAK = 242.0 Gal
R.M.S = 66.01 Gal
400
Acceleration(Gal)
Acceleration(Gal)
Acceleration(Gal)
PEAK = 176.0 Gal
R.M.S = 46.98 Gal
400
20
Acceleration (Gal)
20
(2) SCN-2: Train as mass
Acceleration(Gal)
0
400
Acceleration(Gal)
10
Acceleration(Gal)
0
1166
0
-200
-400
-400
-400
200
-400
30
time(s)
PEAK = 341.0 Gal
R.M.S = 84.32 Gal
400
200
0
-200
-400
0
10
20
Acceleration(Gal)
Acceleration(Gal)
400
20
PEAK = 223.1 Gal
R.M.S = 65.95 Gal
400
(1) SCN-1: No train
(1) SCN-1: No train
PEAK = 202.7 Gal
R.M.S = 48.39 Gal
Acceleration(Gal)
0
-200
200
Acceleration(Gal)
200
PEAK = 430.3 Gal
R.M.S = 117.6 Gal
400
Acceleration(Gal)
PEAK = 242.8 Gal
R.M.S = 53.98 Gal
400
Acceleration(Gal)
Acceleration(Gal)
Proceedings of the 9th International Conference on Structural Dynamics, EURODYN 2014
30
time(s)
600
400
200
0
-200
-400
-600
PEAK = 373.7 Gal
R.M.S = 98.74 Gal
0
10
20
30
time(s)
SCN-4: Moving train (Rear axle)
(b) Elastomeric bearings
(a)Steel bearings
Figure 12. Acceleration responses of train on the
advanced bridge under G2LV1 ground motion.
The scenario SCN-2 that considers train as mass and is
adopted in the bridge design code resulted in safest design
even though the scenario is too idealized. The scenario SCN-1
of disregarding train, which occurs in actual situation,
provided greater seismic responses than those scenarios
considering train dynamics.
It is noteworthy that the shearing forces of elastomeric
bearings were clearly smaller than the shear capacities in all
scenarios. Seismic performance of elastomeric bearings is
sufficient under moderate ground motions.
20
30
time(s)
10
20
30
time(s)
PEAK = 242.9 kN, R.M.S = 58.52 kN
V
Vlim
0
10
PEAK = 180.0 kN, R.M.S = 57.16 kN
V
Vlim
0
10
20
30
time(s)
400
300
200
100
0
-100
-200
-300
-400
PEAK = 446.8 kN, R.M.S = 102.7 kN
V
Vlim
0
10
20
30
time(s)
400
300
200
100
0
-100
-200
-300
-400
PEAK = 321.9 kN, R.M.S = 118.4 kN
V
Vlim
0
10
V
Vlim
0
10
20
30
time(s)
400
300
200
100
0
-100
-200
-300
-400
PEAK = 93.50 kN, R.M.S = 22.27 kN
V
Vlim
0
10
20
30
time(s)
400
300
200
100
0
-100
-200
-300
-400
0
10
20
30
time(s)
400
300
200
100
0
-100
-200
-300
-400
V
Vlim
0
10
20
30
time(s)
(4) SCN-4: Train moving
(a) G2LV1 ground motion
(b) HB ground motion
Figure 13. Shear forces at steel bearings of the
conventional bridge.
5.2
Seismic performance of piers
A brief procedure to assess seismic performance of RC pier is
as [2], 1) to decide failure mode utilizing the ratio of shear
capacity times pier height to the capacity of bending moment;
2) to compare the analytical cross-sectional shearing force
with the limit state if failure mode is shearing failure, or to
compare the analytical cross-sectional bending moment with
the limit state if failure mode is flexural failure mode.
Preliminary investigations showed that failure modes of all
models were the flexural mode. To examine the seismic
performance at the pier base, the bending moment estimated
from the seismic response analysis was compared to the
flexural capacity for cracking of concrete Mc and the flexural
capacity for failure of RC piers Mu.
The maximum capacities for cracking of concrete, yielding of
reinforcing bars and failure of the pier are calculated. To
examine the flexural capacity, it is necessary to consider all
axial reinforcements of the cross-section. The flexural
capacity for cracking of concrete Mc is defined as the bending
moment when the stress at the edge in the cross-section of the
pier reaches the flexural strength of concrete, which can be
calculated as Equation (2).
M c  Wi ( f bd  N i / Ai )
V
Vlim
0
10
20
30
time(s)
30
time(s)
400
300
200
100
0
-100
-200
-300
-400
0
PEAK = 55.16 kN, R.M.S = 23.08 kN
V
Vlim
10
20
30
time(s)
V
Vlim
0
10
20
30
time(s)
400
300
200
100
0
-100
-200
-300
-400
PEAK = 82.15 kN, R.M.S =36.35 kN
V
Vlim
0
10
20
30
time(s)
(3) SCN-3: Train stop
PEAK = 108.4 kN, R.M.S = 26.44 kN
(2)
where, Wi, fbd, Ni and Ai are the section modulus considering
reinforcing bars, the flexural strength of concrete,
compressive axial force at the cross-section and the sectional
area considering of reinforcing bars, respectively.
Shear force (kN)
V
Vlim
Shear force (kN)
Shear force (kN)
PEAK = 86.49 kN, R.M.S = 19.47 kN
20
PEAK = 96.55 kN, R.M.S = 28.73 kN
(3) SCN-3: Train stop
400
300
200
100
0
-100
-200
-300
-400
PEAK = 51.93 kN, R.M.S = 19.02 kN
(2) SCN-2: Train as mass
Shear force (kN)
PEAK = 78.05 kN, R.M.S = 19.83 kN
Shear force (kN)
Shear force (kN)
(2) SCN-2: Train as mass
400
300
200
100
0
-100
-200
-300
-400
30
time(s)
400
300
200
100
0
-100
-200
-300
-400
(1) SCN-1: No train
Shear force (kN)
400
300
200
100
0
-100
-200
-300
-400
Shear force (kN)
Shear force (kN)
(1) SCN-1: No train
20
Shear force (kN)
V
Vlim
0
400
300
200
100
0
-100
-200
-300
-400
Shear force (kN)
10
PEAK = 187.1 kN, R.M.S = 56.97 kN
Shear force (kN)
V
Vlim
0
400
300
200
100
0
-100
-200
-300
-400
400
300
200
100
0
-100
-200
-300
-400
PEAK = 109.4 kN, R.M.S = 30.80 kN
V
Vlim
0
10
20
Shear force (kN)
PEAK = 101.6 kN, R.M.S = 30.07 kN
Shear force (kN)
400
300
200
100
0
-100
-200
-300
-400
Shear force (kN)
Shear force (kN)
Proceedings of the 9th International Conference on Structural Dynamics, EURODYN 2014
30
time(s)
400
300
200
100
0
-100
-200
-300
-400
PEAK = 48.98 kN, R.M.S = 19.43 kN
V
Vlim
0
10
20
30
time(s)
(4) SCN-4: Train moving
(b) Elastomeric bearing
(a) Steel bearing
Figure 14. Shear forces at bearings of the advanced
bridge under HB ground motion.
The flexural capacity for failure of the pier Mu is defined as
the bending moment for failure of the pier. The bending
moment is calculated according to Equation (3).
M u  C  (d  e    x)  Tsc  (d  e  dc )  Tst  e
(3)
where, C’, T’sc and Tst are the axial compressive force of
concrete, the axial compressive force of reinforcing bars, and
the axial tensile force of reinforcing bars, respectively.
For the conventional bridge with steel bearings under the
G2LV1 and HB ground motions, the analytical bending
moment with flexural capacities of the P2 pier are shown in
Figure 15. The bending moment and flexural capacities for the
advanced bridge under the HB ground motion are shown in
Figure 16. Therein Mc was 20180kN.m and Mu was 3370
kN.m.
Observations demonstrated that the monorail bridges satisfy
Level-1 seismic performance as expected since in all
scenarios the bending moment was smaller than the limit
states of flexural failure but greater than the flexural capacities
for clacking. Considering train dynamics in the seismic
response analysis reduced the bending moments at the RC
piers drastically comparing the scenario of considering train
as additional which is the conventional approach. For the
bridge with elastomeric bearings, bending moments were
remarkably smaller than the limit state of flexural failure and
were not cracked. It demonstrates that the elastomeric
bearings were a good option to improve seismic performance
of the bridge.
1167
M
Mc
Mu
-20000
0
10
20
0
-10000
M
Mc
Mu
-20000
0
30
time(s)
10
20
10000
0
-10000
M
Mc
Mu
-20000
0
30
time(s)
10
10000
0
-10000
M
Mc
Mu
-20000
0
10
20
PEAK = 10930 kN･m, R.M.S = 2550 kN･m
20000
10000
0
-10000
M
Mc
Mu
-20000
30
time(s)
0
10
20
PEAK = 8549 kN･m, R.M.S = 2861 kN･m
10000
0
-10000
M
Mc
Mu
-20000
30
time(s)
0
0
-10000
M
Mc
Mu
-20000
0
10
20
20000
10000
0
-10000
M
Mc
Mu
-20000
30
time(s)
0
10
10
20
0
-10000
M
Mc
Mu
-20000
0
10
20
30
time(s)
10000
0
-10000
M
Mc
Mu
-20000
0
10
10000
0
-10000
M
Mc
Mu
-20000
10
20
10
20
30
time(s)
PEAK = 2156 kN･m, R.M.S = 629.5 kN･m
20000
10000
0
-10000
M
Mc
Mu
-20000
0
10
20
30
time(s)
PEAK = 2422 kN･m, R.M.S = 706.1 kN･m
20000
10000
0
-10000
M
Mc
Mu
-20000
0
30
time(s)
20000
10000
0
-10000
CONCLUSION
M
Mc
Mu
-20000
30
time(s)
This study investigates how train on monorail bridges acts on
seismic responses of monorail bridges. The study also
examined the seismic performance of the conventional type
monorail bridge with steel bearings and the advanced type
monorail bridge which adopts longer span than that of the
conventional bridge under moderate ground motions. Efficacy
of the elastomeric bearing is also examined. Summarized
results are as follows.
(1) The failure mode was flexural failure, and monorail
bridge design satisfies Level-1 seismic performance since
in all scenarios the bending moment was smaller than the
limit states.
(2) Dynamic system of train could act as a damper during
earthquakes.
(3) Elastomeric bearings were a good option to improve
seismic performance of the bridge. However, adopting
elastomeric bearings to reduce seismic responses of
bridges could increase acceleration responses of train
under earthquakes.
(4) Seismic responses of both moving and parked trains
should be considered to investigate vibratory sensation of
passengers during earthquakes.
1168
20
PEAK = 6059 kN･m, R.M.S = 1795 kN･m
0
(4) SCN-4: Train moving
(a) G2LV1 ground motion
(b) HB ground motion
Figure 15. Bending moment at the pier base of the
conventional bridge with steel bearings.
6
0
10
20
30
time(s)
(3) SCN-3: Train stop
PEAK = 6260 kN･m, R.M.S = 1669 kN･m
20000
0
30
time(s)
20000
30
time(s)
Bending Moment (kN・m)
10000
Bending Moment (kN・m)
Bending Moment (kN・m)
20000
20
PEAK = 6655 kN･m, R.M.S = 1355 kN･m
(3) SCN-3: Train stop
PEAK = 4174 kN･m, R.M.S = 1253 kN･m
M
Mc
Mu
-20000
(2) SCN-2: Train as mass
PEAK = 5279 kN･m, R.M.S = 1368 kN･m
Bending Moment (kN・m)
10000
Bending Moment (kN・m)
Bending Moment (kN・m)
20000
0
-10000
30
time(s)
20000
(2) SCN-2: Train as mass
PEAK = 3221 kN･m, R.M.S = 847.9 kN･m
20
10000
(1) SCN-1: No train
Bending Moment (kN・m)
PEAK = 5149 kN･m, R.M.S = 1424 kN･m
20000
Bending Moment (kN・m)
Bending Moment (kN・m)
(1) SCN-1: No train
Bending Moment (kN・m)
-10000
10000
PEAK = 2553 kN･m, R.M.S = 785.1 kN･m
20000
Bending Moment (kN・m)
0
PEAK = 10920 kN･m, R.M.S = 2442 kN･m
20000
Bending Moment (kN・m)
10000
PEAK = 8657 kN･m, R.M.S = 2542 kN･m
20000
10
20
30
time(s)
Bending Moment (kN・m)
PEAK = 4149 kN･m, R.M.S = 1404 kN･m
20000
Bending Moment (kN・m)
Bending Moment (kN・m)
Bending Moment (kN・m)
Proceedings of the 9th International Conference on Structural Dynamics, EURODYN 2014
PEAK = 2931 kN･m, R.M.S = 1368 kN･m
20000
10000
0
-10000
M
Mc
Mu
-20000
0
10
20
30
time(s)
(4) SCN-4: Train moving
(a) Steel bearings
(b) Elastomeric bearings
Figure 16. Bending moment at the pier base of the
advanced bridge under HB ground motion.
REFERANCES
[1]
[2]
[3]
[4]
[5]
[6]
C.H. Lee, C.W. Kim, M. Kawatani, N. Nishimura, T. Kamizono,
Dynamic response analysis of monorail bridges under moving trains
and riding comfort of trains, Engineering Structures 27 , 1999-2013,
2005.
Japan Road Association (JRA), Specifications for Highway Bridges,
Part V: Seismic Design, Maruzen, Tokyo, Japan, 2013.
C.H. Lee, M. Kawatani, C.W. Kim, N. Nishimura, Y. Kobayashi,
Dynamic response of a monorail steel bridge under a moving train,
Journal of Sound and Vibration 294, 562-579, 2006.
C.W. Kim, M. Kawatani, Effect of train dynamics on seismic response
of steel monorail bridges under moderate ground motion, Earthquake
Engineering & Structural Dynamics 35, 1225–1245, 2006.
C.W. Kim, M. Kawatani, T, Kanbara, N. Nishimura, Seismic behavior
of steel monorail bridges under train load during strong earthquakes,
Journal of Earthquake and Tsunami 7, No.2,1350006 1-17, 2013.
C.W. Kim, M. Kawatani, K.B. Kim, Three-dimensional dynamic
analysis for bridge–vehicle interaction with roadway roughness,
Computers & Structures 83, 1627–1645, 2005.