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International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print), ISSN
INTERNATIONAL JOURNAL OF CIVIL ENGINEERING AND
0976 – 6316(Online) Volume 5, Issue 1, January (2014), © IAEME

TECHNOLOGY (IJCIET)

ISSN 0976 – 6308 (Print)
ISSN 0976 – 6316(Online)
Volume 5, Issue 1, January (2014), pp. 73-88
© IAEME: www.iaeme.com/ijciet.asp
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IJCIET
©IAEME

SEISMIC RESPONSE BEHAVIOR USING STATIC PUSHOVER ANALYSIS
AND DYNAMIC ANALYSIS OF HALF-THROUGH STEEL ARCH BRIDGE
UNDER STRONG EARTHQUAKES
EviNur Cahya1,
1, 2, 3

Toshitaka Yamao2,

Akira Kasai3

(Graduate School of Science and Technology, Kumamoto University, 2-39-1 Kurokami,
Kumamoto, 860-8555, Japan)

ABSTRACT
This paper presents the seismic response behavior of the static pushover and dynamic
response analyses of a half-through steel arch bridge subjected to earthquake waves. The static
pushover analysis were carried out using three loading cases which are considering the dead load,
live load, impact load and earthquake load, according to Japan Specifications for Highway Bridges
(JSHB) loading condition. These results were being compared with the results from dynamic
analysis. The dynamic response analyses were carried out using earthquake waves in transverse and
longitudinal directions in order to investigate the seismic behavior of the arch bridge model. The
seismic waves according to the JSHB seismic waves were applied and the response behavior was
investigated from two different earthquake records. The finite element software of ABAQUS was
used in the dynamic analysis, using both modal dynamic and direct integration analysis. The first
yielded members under longitudinal and lateral loading were found, as well as the spreading of the
plastic zones. According to the analytical results from static and dynamic analysis as well, it was
found that the plastic members were clustered near the intersections of arch ribs and stiffened girders
and the diagonal brace that connected two arch ribs. The behavior under static analysis showed large
value of the strain in the members both in the arch ribs and the stiffened girders which composed of
stiffened box-section than the result of dynamic analysis from both earthquake wave records.
Keywords: Dynamic analysis, half-through type arch bridge, static pushover, seismic behavior,
ultimate strength.

73


I. INTRODUCTION
Seismic design for steel bridges in Japan has been improved based on the lesson learned from
serious damages in various past earthquakes. It has been widely realized that changes are needed in
the existing seismic design methodology implemented in codes. [1-3]. Since before HyogokenNanbu earthquake, conventional bridges designed based on the traditional static design approach
required that the structural components should only behave in an elastic manner. After the severe
damages, the revised Japanese specification recommended that the structures exhibiting complicated
seismic behaviors such as the arch bridges should be designed based on the result of the dynamic
analysis for the purpose of the earthquake resistance design methodology [4]. Thus, the seismic
response behavior under the simulated major earthquake is necessary for the future design.
Bridges play very important roles of evacuation routes and emergency routes for rescue, first
aid, medical services, firefighting, and transporting urgent goods to refugees. For these purposes, it is
essential to ensure seismic safety of a bridge in the seismic design. Therefore, in the seismic design
of a bridge, seismic performance required depending on levels of design earthquake ground motions
and importance of the bridge, shall be ensured [4].
The attention of researchers has been attracted in two directions. One is to apply the nonlinear time-history analysis into design use. Although this method is a more powerful procedure for
demand predictions, it is time-consuming and this hampers its wide application to everyday design
use, although rapid improvement of the computation speed in recent years is increasingly lessening
this problem. The other option is to improve the reliability of the simple static design method and a
static pushover analysis is expected as one of the most promising tools. But there is an inherent
assumption of pushover analysis, that the structure should be controlled by the fundamental mode,
and this limits its application to complex structures due to the higher mode effects [3].
Thus, it is realized to be more rational to adopt both the pushover analysis and the time
history analysis, where the former is used for simple or regular structures and the latter is used for
complex structures [5,6]. To implement such a dual-level design conception to practical
specifications, however, the applicable range of pushover analysis should be first clarified by
extensive investigations [3].
The static nonlinear pushover analysis may provide much of the needed information. In the
pushover analysis, the structure is loaded with a predetermined or adaptive lateral load pattern and is
pushed statically to target displacement at which performance of the structure is evaluated [7]. The
target displacements are estimates of global displacement expected due to the design earthquake
corresponding to the selected performance level. Recent studies addressed limitations of the
procedure and the selection of lateral load distribution including adaptive techniques to account for
the contribution of higher modes in long period structures [8].
The revised specifications based on the performance-based design code concept indicate that
the structures exhibiting complicated seismic behavior such as the arch bridges should be designed
based on the result of the dynamic analysis and seismic behavior of steel arch bridges need to be
focused on the advanced analysis predicting the time-history responses [9]. The three-dimensional
(3-D) nonlinear seismic response analysis of half-through type arch bridges was presented recently
and has been justified the need to perform in order to get more accurate results due to the effects of
either geometric or material nonlinearity taken into account [2]. After the structural system has been
created from the mathematical and physical models, seismic performance evaluation of an existing
system is needed to modify component behavior characteristics such as strength, stiffness,
deformation capacity, etc. in order to better suit the specified performance criteria. The dynamic
verification method for bridges has been introduced and the seismic performance levels were
established according to the viewpoints of safety, function-ability and repair ability during and after
74


any earthquakes. The basic concept of the dynamic verification methods for seismic performance is
that the response of the bridge structures against the designed earthquake ground motions based on
dynamic analysis must not exceed the determined limit states [4].
The study is focused at the determination of seismic behaviors and performance evaluation of
the half-through type steel arch bridges under the simulated ground motions specified by the Japan
Specifications for Highway Bridges (JSHB) [10]. The seismic response of the half-through type steel
arch bridge composed of twin stiffened box-section ribs with transverse and diagonal bracings was
observed in three dimensional models by static pushover analysis and nonlinear dynamic response
analysis. In static pushover analysis, the loading conditions were adjusted by using load controlled
method, which are considering the dead load, live load, impact load and earthquake load, according
to JSHB loading condition. The seismic behavior of the arch bridge model subjected to Level II
ground motion [4] was investigated in the dynamic response analyses. Time-history responses and
their maximum values of the axial force, displacement and bending moment along the arch length
were studied under the longitudinal and transverse ground motions input from two different
earthquake records. The distributions of yielded elements were also investigated.
II. SEISMIC PERFORMANCE LEVEL OF THE BRIDGES
The Japanese design specifications for highway bridges (JSHB) consider two levels of
earthquake ground motion (Level 1 and Level 2) and two types in Level 2 earthquake motion (Type I
and Type II). Level 1 earthquake motion represents ground motion highly probable to occur during
service period of bridges and its target seismic performance is set to have no structural damage.
Level 2 earthquake motion is defined as ground motion with high intensity with less probability to
occur during the service period of bridges. The target seismic performances against Level 2
earthquake motion is set to limited damage for function recovery in short period for high importance
bridges and to prevent fatal damage for bridges such as unseating of a superstructure or collapse of a
bridge column for standard importance bridges. Type I of Level 2 earthquake motion represents
ground motion from large scale subduction-type earthquakes, while Type II from near-field shallow
earthquakes that directly strike the bridges [12].
Table 1 summarizes items of seismic performances 1 to 3 in view of safety, serviceability and
reparability for seismic design. The relation of the depending on the level of design earthquake
ground motions and the two categories on bridge importance are shown in Table 2 for seismic
performances damaged for bridges.
III. PARAMETRIC AND CASE STUDIES
1.1

Structural system and modeling
The theoretical arch model studied herein is representative for actual half-through type arch
bridges as shown in Fig. 1, in which 11 vertical columns are hinged to arch ribs at both ends. The
arch has a span length (l) of 106 m and the arch rise (f) is 22 m, giving a rise-span ratio 0.21. The
global axes of the arch ribs are also shown in Fig.1, where b and L represents the width of a stiffened
girder and the deck span, respectively. Arch ribs of the bridge consist of steel box-section members,
connected by lateral bracing and diagonals. Between the two longitudinal stiffened girders across the
arch ribs, lateral girders and diagonals are also provided. The longitudinal girders and arch ribs are
connected with vertical column. The cross sectional profiles of arch ribs, stiffened box-section,
vertical members and lateral members are rectangular and I-sections as shown in Fig. 2.

75


Table 1. Seismic performance of bridges
Seismic performance

Seismic
safety design

Seismic performance
Level 1 :
Keeping the sound
functions of bridges

To ensure the
safety against
girder
unseating

Seismic performance Same as
Level 2 :
above
Limited damages and
recovery

Seismic performance
Level I :
No critical damages

Seismic
serviceability
design
To ensure the
normal
functions of
bridges
Capable of
recovering
functions
within a short
period after the
event

Same as
above

-

Seismic serviceability design
Emergency
reparability
No repair work
is needed to
recover the
functions

Permanent
reparability
Only easy
repair works
are needed

Capable of
recovering
functions by
emergency
repair works

Capable of
easily
undertaking
permanent
repair works

-

-

Table 2. Design earthquake ground motions and seismic performance of bridges
Earthquake ground motions
Class A bridges
Class B bridges
Level 1 earthquake ground motion (highly Keeping sound functions of bridges
probable during the bridge service life)
(Seismic performance level 1)
Level 2 earthquake Type I earthquake ground
ground motion
motion (a plate boundary
type earthquake with a
large magnitude)

Type II earthquake
ground motion (an inland
direct strike type
earthquake like Hyogoken nambu earthquake)

No critical
damages (Seismic
performance level
3)

Limited seismic
damages and
capable of
recovering bridge
functions within a
short period
(Seismic
performance level
2)

Boundary conditions of the stiffened girders and the springing arch ribs are shown in Table 1.
Two types of steels, SM490Y (yield stress, σy=355 MPa, Young’s modulus, E = 206 GPa and
Poisson’s ratio, ν= 0.3) and SS400 (yield stress, σy=245 MPa, Young’s modulus, E = 206 GPa and
Poisson’s ratio, ν= 0.3) are adopted. The first type of steel, SM490Y is used for the main members of
the bridge, while SS400 is used for diagonal brace member which connected two stiffened girder and
diagonal brace member between two arch ribs. A multi-linear stress-strain relation is assumed and
shown in Fig. 3.
76


a) Arch rib

Figure 1. Theoretical arch model

b) Vertical
column

c) Lateral
member

Figure 2. Cross sectional profiles of
members

Table 3. Boundary condition at the springing arch rib and at the end of the stiffened grider
Boundary condition
Arch rib
Stiffened girder
Dx

Fixed

Free

Dy

Fixed

Fixed

Dz

Fixed

Fixed

θx

Free

Free

θy

Free

Free

θz

Free

Free

Stress - σ (N/mm²)

600
525
500
400
355
300
200
100
0
0.0018 0.012
0

0.05

0.1
Strain - ε

0.15

0.18 0.2

Figure 3. Stress-strain relationship of SM490Y steel
77


1.2 Loading condition
In static pushover analysis, the loading conditions were adjusted by using load controlled
methods with three loading cases. In parametric analysis, impact loads (I), and earthquake effects
(EQ) specified in JSHBwere defined by using dead load (DL) and live load (LL) as follows;

I = i ⋅ LL

(1)

20
50 + l

(2)

(1) Impact loads (I) :
i=
Where: LL: Live loads,
l: Span length,
i: Impact coefficient
(2) Earthquake effect (EQ) :
EQ = k h ⋅ DL
kh = C z ⋅ kh0

(3)
(4)

Where: kh: Design horizontal seismic coefficient, kh = 0.25 (Class II)
kh0: Standard value of design horizontal seismic coefficient,
Cz: Modified factor for zone, Cz = 0.85
The design load (inertial force) EQ given by equation (3) is replaced by equivalent
nodal forces and applied to in-plane and out-of-plane directions. The uniform load distributed along
cross section and the full bridge length of the arch, q (q1,q2) is assumed to be dead and live load
conditions as shown in Fig. 3 and Fig. 4. It is converted to 56 equivalent concentrated loads for each
arch rib and applied to nodal points of the arch bridge model.

Figure 4. Live load (LL) according to JSHB

78


(a)

Cross section of deck plate

(b)
Load on the bridge length
Figure5. Uniform load conditions on the cross section of the deck plate and on the bridge length
m
Loading conditions in this analysis were used load combinations in designaccording to
JSHB as shown in Table 4. In loading case I, live and impact loads are applied in
.
in-plane direction
under the constant load. In Table 4, a coefficient α is the load factor and the maximum load factor αu
,
at the failure of the bridge was obtained. In loading case II and III, inertial force (EQ in increased in
(EQ)
longitudinal and transverse direction until the maximum load capacity as determined by lateral
tion
instability after the dead and live load are applied in both directions.
Table 4. Combination of loads
Loading case

Loading conditions

I
II
III

1.7 D + α ( L + I )
1.13 ( D + L ) + αEQlong
1.13 ( D + L ) + αEQtransv

Input direction
In-plane
Longitudinal
Transverse

In order to examine the validity and problems of the allowable stress design method, elasto
elastoplastic and large spatial displacement analysis were carried out for the arch bridge model.
bridge
1.2

Input seismic waves
The seismic ground motions were recorded from the Hyogo-Ken Nambu earthquake, JMA in
Hyogo
mbu
EW and NS direction. These two seismic waves, Type II-I-1 and Type II-I-2 waves provided by the
S
II
2
JSHB data were input in the dynamic response analysis. The input JSHB seismic waves are
illustrated in Fig. 6. The waves have applied in longitudinal direction and transverse directions of the
arch bridge model, for Type II-I-2 and Type II
II-I-1 waves, respectively.

a) Type II-I-1 wave
1
b) Type II-I-2 wave
Fig. 6 Input JSHB seismic wavesLevel II earthquake ground motion (Type II) recorded from Hyogo
otion
HyogoKen Nambu earthquake
79


In order to compare the seismic responses of the arch bridge model, other seismic waves with
much longer period were also used. The two seismic waves recorded from the Northeastern Pacific
Ocean off the coast earthquake FY2011, in EW and NS direction, which are Type I- and Type I-II-I-2
3 waves were input in the dynamic response analysis in longitudinal and transverse directions
respectively, and shown in Fig. 7.
1.3

Damping matrix and numerical analysis
umerical
The behavior of steel arch bridges under seismic loads is quite different from that of
suspension and cable-stayed bridges since the large axial compression due to the effect of its dead
stayed
load reduces the stiffness of arch. According to the effect of seismic loads, the stiffness variation
d
becomes more complicated because the arch bridge can also develop oscillatory forces between
tension and compression. In the linear behaviors, the properties of the deterministic system of
seismic response do not change during the seismic loads. This criterion clearly demands nonlinear
seismic response because the structural stiffness must undergo changes as the result of significant
damage. Therefore the seismic behavior of steel arch bridges needs to be focused on the precise
mic
analysis predicting the time history responses. For the complicated seismic excitation, 2-D analysis
2
was found not to be adequate to obtain accurate results according to the strong coupl
coupling between the
in-plane and out-of-plane motions of the arch ribs and the deck. The 3-D nonlinear seismic analysis
plane
3D
of steel arch bridges has been presented recently. It was justified the need to perform due to the
effects of either geometric or material n
nonlinearity taken into account.

a) Type I-I-2 wave
b) Type I-I-3 wave
Figure7. Input JSHB seismic wavesLevel II earthquake ground motion (Type I) recorded from
otion
Northeastern Pacific Ocean off the coast earthquake
In the numerical analyses, the Newmark-β method was used for solving the differential
Newmark
ethod
equations in finite element analysis, where the second order equations of motions were integrated
with respect to time taking into account material and geometrical non-linearity. The value β = 0.25
non linearity.
was selected to keep the constant average acceleration. A constant time step of 0.01 sec has set. And
o
a damping model (Rayleigh type) calibrated to the initial stiffness and mass has used as shown in
Fig. 8. The damping matrix equation is determined by an expression below.
.
bel
(5)
In which:
C = Damping matrix
α = Coefficient for mass matrix
M = Mass matrix
β = Coefficient for stiffness matrix
K = Stiffness matrix
80


The arbitrary proportional factors α and β are determined by following equations.

ߙൌ

ସగ·௙భ ·௙మ ሺ௙భ ௛మ ି௙మ ௛భ ሻ
൫௙భ మ ି௙మ మ ൯

௙ ௛ ି௙ ௛

భ
మ
ߚ ൌ గ൫௙భమ ି௙ మమ൯
భ

(6)
(7)

మ

The seismic response analysis with ground acceleration input and a constant dead load were
performed using the nonlinear FEM program ABAQUS. The two seismic waves were input in
longitudinal (X-axis) direction and transverse (Z-axis) direction, respectively.

Figure 8. Rayleigh damping model
1.4

Eigenvalue analysis
The eigenvalue analysis was carried out to investigate the effect of arch ribs and stiffened
girders on the natural periods of the arch bridge model. In order to understand the fundamental
dynamic characteristics, Table 5 presents the natural periods and the effective mass ratios of each
predominant mode, from ABAQUS Analysis. The maximum effective mass ratios obtained in X, Y
and Z directions imply the order of the dominant natural period. It can be seen from Table 3 that the
arch bridge model is possible to vibrate sympathetically at the 1stmode in longitudinal direction (Xaxis), 2ndmode in transverse direction (Z-axis) and 8thmode in-plane direction (Y-axis), respectively.

Order of
period
1
2
3
4
5
6
7
8
9
10

Table 5. Results of eigenvalue analysis
Effective mass ratio (%)
Natural
Natural periods
frequency (Hz)
(sec)
X
Y
Z
1.0341
0.9670
74
0
0
1.9767
0.5059
0
0
75
2.6452
0.3780
0
0
0
2.6452
0.3780
0
0
0
3.3823
0.2957
0
0
0
3.7199
0.2688
26
0
0
4.1054
0.2436
0
0
25
4.1988
0.2382
0
100
0
5.0428
0.1983
0
0
0
5.2847
0.1892
0
0
0
81


Two values of resonant frequencies that earned from eigenvalue were selected from two
that
dominant vibration modes. Substitution of dominant resonant frequencies f1, f2 and the damping ratio
h1, h2 were set to be 0.03 (3 %). When the coefficient value (α) for mass matrix and the coefficient
( )
value for mass matrix (β) were obtained, the damping matrix C should be eventually calculated by
)
using equation(5). Three predominant Eigen modes deflecting in the longitudinal direction and one
.
in the transverse direction of the two bridges are shown in Fig. 9.

a) 1st mode
b) 2nd mode
c) 8th mode
(longitudinal direction)
(out-of plane direction)
(in-plane direction)
plane
Figure 9. Vibration shapes to predominant modes
IV. RESULTS AND DISCUSSIONS
1.5

Static pushover analysis
The ultimate behavior and the development of plastic zone on the cross section of the arch
bridge model were carried out using ABAQUS program. The analytical result of the three loading
cases I, II and III were discussed.
(a) Loading case I
Fig. 10 shows the nodal points of the monitorial displacement in each loading case. In
displacement
loading case I, Fig. 11a) shows the load factor (α) versus in-plane displacement (v) at the arch crown
(
)
and the center of the stiffened girder. The segment of the member element was yielded first at the
load factor α = 3.95, and this model attained the ultimate state at the load factor αu = 5.27. The first
his
yielded members of the arch bridge model are shown in Fig. 11b). Fig. 11c) shows that the column
of the arch rib yields in the first place, and then followed by the arch rib and the stiffened girder as
shown in Fig 11d).

Figure10. The nodal points of the monitorial displacement in each loading case
(b) Loading case II
In loading case II, Fig. 12 a) shows the load factor (α) versus longitudinal displacement ( at
( )
(u)
the arch crown and the center of the stiffened girder. The segment of the member element was
d
yielded first at the load factor α = 8.38. The first yield members of the model are shown in Fig. 12b).
Fig. 12c) shows that the main arch rib yields in the first place, and then followed by the other
c)
followed
members of the arch bridge model as seen as Fig. 12d).
12d)
82


Y (v)

Z (w)

a) Load factor vs. in-plane displacement curve
plane

X (u)

b) First yielded members

c) Load factor vs. axial strain curves
d) Spreading of plastic members
Figure 11. Results of loading case I

X (u)

a) Load factor vs.longitudinal displacement
curve


c) Load factor vs. axial strain curves
Figure 12. Results of loading case II
83


(c) Loading case III
In loading case III, Fig. 13a) shows the load factor (α) versus transverse displacement ( at
(
(w)
the arch crown and the center of the stiffened girder. The segment of the member element was
yielded first at the load factor α = 8.702. The first yield members of the model are shown in Fig.
members
13b). Fig. 13c) shows that the brace which connected the two main arch ribs yields in the first place,
and then followed by the lateral beam, deck brace and arch rib in the arch bridge model as shown in
Fig. 13d).

Z (w)

a) Load factor vs.out of plane displacement curve

c)


Load factor vs. axial strain curves
Figure 1 Results of loading case III
13.

From these three cases, it is found that each loading will lead lo different responses
loading
considering the spreading of the yield members and it is able to show the critical members by each
direction of static pushover loading From the results, stiffened girder members, arch rib members
loading.
and diagonal brace members that connected the two arch ribs under the deck plate seem to be the
most critical members in all the loading cases. These members should be considered more in the
design and in the dynamic analysis.
1.6

Dynamic responseanalysis
The dynamic analysis of the arch bridge model is conducted in two type of analytical
methods, those are modal dynamic analysis and direct integration analysis. In both analyses, the
seismic waves were input in longitudinal and transverse directions, by ABAQUS program. By using
the acceleration data obtained from the JSHB, Type II-I-2 wave for longitudinal directionand Type
II
II-I-1wave for transverse direction,with the damping ratio (h) = 0.03, the longitudinal and
1wave
direction,
)
transversedisplacement has been checked at the arch crown, and the internal force from the first
displacement
the
yielded member has been analyzed. Fig. 14 shows the displacement response obtained from the
1
modal dynamic analysis of ABAQUS.
84


In the same way, the modal dynamic analysis was carried out also for data Type I-I-2 wave
he
for longitudinal directionand Type I-I-3wave for transverse direction, with the time periods 240
itudinal
I
seconds. The results are shown in Fig. 15.
1

a) Type II-I-2 wave (longitudinal direction)

b) Type II-I-1 wave (transverse direction)

Figure 14. The displacement time history at the arch crown for seismic waves in longitudinal and
history
transverse direction in dynamic analysis
analysis(from Level II earthquake ground motion Type II Hyogootion
II,
Ken Nambu earthquake)

a) Type I-I-2 wave (longitudinal direction)

b) Type I-I-3 wave (transverse di
direction)

Figure 15. The displacement time history at the arch crown for seismic waves in longitudinal and
transverse direction in dynamic analysis (from Level II Earthquake Ground Motion Type I,
Northeastern Pacific Ocean off the coast earthquake)
earthquake

Maximum and minimum plastic ratios ε/εy of strain responses were also observed to
m
investigate the strain distribution along the arch rib and stiffened girder.The strain records are
The
obtained from the maximum and minimum strain value at each point in the cross section of each
sec
member. The element numbering of arch rib and the stiffener girder can be seen in Fig 16 to explain
clearly the strain behavior of each element in the arch rib and stiffened girder. From the strain
girder.
distributions in the arch rib under static push over loading and seismic waves in longitudinal
sh
direction, it was found that some element in the arch rib near intersections between arch rib and the
stiffened girder are yield through static analysis, as shown in Fig 17a). In the other hands, all the
analysis
.
members in the arch rib does not reach yield under dynamic analysis using two waves record from
two strong earthquakes. The same phenomenon also occurs in the stiffened girder elements. The
stiffened girder elements near the intersection reach more than twice of the strain yield limit. While
twice
the arch rib elements and the stiffened girder elements in the center of the bridge have the lowest
value of strain distribution.
85


a) Arch rib elements

b) Stiffened girder elements
Figure 16. Element numberi for arch rib and stiffener girder
numbering

a) Longitudinal direction

b) Transverse direction
Figure 17. Maximum and minimum strain ratios ε/εy of strain responses
along the arch rib and stiffener girder

86


These behavior acts differently in the case of static loading and seismic waves from
transverse direction. In both arch rib and stiffened girder, there is no element reach yield neither
strain obtained from static or dynamic in transverse direction. Based on the result of static pushover
analysis, the yield members were clustered at the braces that connected the two arch ribs, as the most
critical member under loading in transverse direction.It also shown that the elements near the
springing arch rib reach the highest strain value under static pushover analysis.
Comparing these results with the results obtained from static pushover analysis, it can be seen
that the maximum displacement from dynamic analysis reaches much lower value than from static
analysis. The reason for this is because none of the element member reaches yield by dynamic
analysis using two big earthquake waves, while the static pushover analysis was run until it reached
its ultimate strength. The same phenomenon seem to be occur in the dynamic analysis compared to
static analysis in the case of the critical members that shown from the figures.
V. CONCLUSION
The seismic behavior of a half-through steel arch bridge subjected to ground motions in
longitudinal and transverse directions were investigated by static pushover and dynamic response
analysis. The static pushover analysis by load controlled method was carried out and compared. In
dynamic analysis, the two seismic waves according to JSHB seismic waves were simulated and
discussed. The main conclusions of this study are summarized as the following.
1) From the static analysis in in-plane direction loading, it was found that arch ribs and vertical
columns are the first yield member and become the most critical members, then lead to the
yielding of the stiffened girder and lateral bracing beam which connect two arch ribs. This first
yield occurs when the load reach 3.95 times of the design load from the provisions.
2) In static pushover analysis under loading in longitudinal direction, the first yield occurs in the
vertical columns which connect arch rib and stiffened girder and the stiffened girders near the
intersection points when applied load reach 8.38 times of the design load and the displacement at
the arch crown was around 0.13 m. Compare to the result from dynamic analysis under two
strong earthquake in longitudinal direction, the maximum displacement obtained around 0.13 m
also. But none of the main members, arch rib or stiffened girder reaches yield.
3) In static pushover analysis under loading in transverse direction, the first yield occurs in the
diagonal brace members which connect two arch ribs under deck plate when applied load reach
8.7 times of the design load and the displacement at the arch crown was around 0.2 m. Compare
to the result from dynamic analysis under two strong earthquake in longitudinal direction, the
maximum displacement obtained around 0.27 m and none of the main members, arch rib or
stiffened girder reaches yield.
4) The results obtained from both static and dynamic analysis for longitudinal directions indicate
that the plastic members are clustered near the joints of the arch ribs and the stiffened girders, as
the most critical point in the half through arch bridge structures which is caused by the large
deformation at this intersection zones.
5) From the result from static analysis for transverse direction, it was shown the critical members
were at the diagonal brace members which connected the two arch ribs. The behaviors of these
members under dynamic analysis were not discussed further in this study.Under the dynamic
analysis, there is no member yield in the arch rib and stiffened girder as the main structure in the
half-through type arch bridge model.
6) The arch bridge is not judged to damage under both strong earthquake waves from JSHB data
record because the maximum strains in members do not reach the yield strain.
87


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