International Journal of Civil Engineering and Technology (IJCIET), …iaeme.com/MasterAdmin/UploadFolder/20320140501008-2/... · 2014-03-05 · International Journal of Civil Engineering

International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print), ISSN

0976 – 6316(Online) Volume 5, Issue 1, January (2014), © IAEME

73

SEISMIC RESPONSE BEHAVIOR USING STATIC PUSHOVER ANALYSIS

AND DYNAMIC ANALYSIS OF HALF-THROUGH STEEL ARCH BRIDGE

UNDER STRONG EARTHQUAKES

EviNur Cahya1, Toshitaka Yamao

2, Akira Kasai

3

1, 2, 3

(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.

INTERNATIONAL JOURNAL OF CIVIL ENGINEERING AND

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

Journal Impact Factor (2013): 5.3277 (Calculated by GISI)

www.jifactor.com

IJCIET

©IAEME



74

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 Hyogoken-

Nanbu 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 non-

linear 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



75

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.



76

Table 1. Seismic performance of bridges

Seismic performance Seismic

safety design

Seismic

serviceability

design

Seismic serviceability design

Emergency

reparability

Permanent

reparability

Seismic performance

Level 1 :

Keeping the sound

functions of bridges

To ensure the

safety against

girder

unseating

To ensure the

normal

functions of

bridges

No repair work

is needed to

recover the

functions

Only easy

repair works

are needed

Seismic performance

Level 2 :

Limited damages and

recovery

Same as

above

Capable of

recovering

functions

within a short

period after the

event

Capable of

recovering

functions by

emergency

repair works

Capable of

easily

undertaking

permanent

repair works

Seismic performance

Level I :

No critical damages

Same as

above - - -

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

probable during the bridge service life)

Keeping sound functions of bridges

(Seismic performance level 1)

Level 2 earthquake

ground motion

Type I earthquake ground

motion (a plate boundary

type earthquake with a

large magnitude)

No critical

damages (Seismic

performance level

3)

Limited seismic

damages and

capable of

recovering bridge

functions within a

short period

(Seismic

performance level

2)

Type II earthquake

ground motion (an inland

direct strike type

earthquake like Hyogo-

ken nambu earthquake)

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.



77

a) Arch rib b) Vertical

column

c) Lateral

member

Figure 1. Theoretical arch model 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

Figure 3. Stress-strain relationship of SM490Y steel

0

100

200

300

400

500

600

0 0.05 0.1 0.15 0.2

Stre

ss -

σ(N

/m

m²)

Strain - ε

355

525

0.180.0120.0018



78

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;

LLiI ⋅= (1)

(1) Impact loads (I) :

l

i+

=50

20 (2)

Where: LL: Live loads,

l: Span length,

i: Impact coefficient

(2) Earthquake effect (EQ) :

DLkEQ h ⋅= (3)

0hzh kCk ⋅= (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

International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976


(a)

(b)

Figure5. Uniform load conditions on the cross section of the deck plate and on the bridge length

Loading conditions in this analysis were used load combinations in

JSHB as shown in Table 4. In loading case I, live and impact loads are applied in

under the constant load. In Table 4, a coefficient

at the failure of the bridge was obtained. In loading case II and III, inertial force (

longitudinal and transverse direction until the maximum load capacity as determined by lateral

instability after the dead and live load are applied in both directions.

Table

Loading case

I

II

III

In order to examine the validity and problems of the allowable stress design method, elasto

plastic and large spatial displacement analysis were carried out for the arch bridg

1.2 Input seismic waves

The seismic ground motions were recorded from the Hyogo

EW and NS direction. These two seismic waves, Type II

JSHB data were input in the dynamic response

illustrated in Fig. 6. The waves have applied in

arch bridge model, for Type II-I-2 and Type II

a) Type II-I-1 wave

Fig. 6 Input JSHB seismic wavesLevel II

of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print), ISSN

6316(Online) Volume 5, Issue 1, January (2014), © IAEME

79

Cross section of deck plate

(b) Load on the bridge length

m load conditions on the cross section of the deck plate and on the bridge length

Loading conditions in this analysis were used load combinations in designaccording

. In loading case I, live and impact loads are applied in

, a coefficient α is the load factor and the maximum load factor

at the failure of the bridge was obtained. In loading case II and III, inertial force (EQ

tion until the maximum load capacity as determined by lateral

instability after the dead and live load are applied in both directions.

Table 4. Combination of loads

Loading conditions Input direction

1.7 D + α ( L + I ) In-

1.13 ( D + L ) + αEQlong Longitudinal

1.13 ( D + L ) + αEQtransv Transverse

In order to examine the validity and problems of the allowable stress design method, elasto

plastic and large spatial displacement analysis were carried out for the arch bridge model.

The seismic ground motions were recorded from the Hyogo-Ken Nambu earthquake, JMA in

S direction. These two seismic waves, Type II-I-1 and Type II-I-2 waves provided by the

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

and Type II-I-1 waves, respectively.

1 wave b) Type II-I-2 wave

Input JSHB seismic wavesLevel II earthquake ground motion (Type II) recorded from Hyogo

Ken Nambu earthquake

6308 (Print), ISSN

m load conditions on the cross section of the deck plate and on the bridge length

designaccording to

. In loading case I, live and impact loads are applied in-plane direction

is the load factor and the maximum load factor αu

EQ) in increased in

tion until the maximum load capacity as determined by lateral

Input direction

-plane

Longitudinal

Transverse

In order to examine the validity and problems of the allowable stress design method, elasto-

e model.

mbu earthquake, JMA in

2 waves provided by the

analysis. The input JSHB seismic waves are

transverse directions of the

wave

otion (Type II) recorded from Hyogo-



In order to compare the seismic responses of the arch bridge model, other seismic waves with

much longer period were also used. The

Ocean off the coast earthquake FY2011, in EW and NS direction, which are Type I

3 waves were input in the dynamic response analysis

respectively, and shown in Fig. 7.

1.3 Damping matrix and numerical

The behavior of steel arch bridges under seismic loads

suspension and cable-stayed bridges since the large axial compression due to the effect of its dead

load reduces the stiffness of arch. According to the effect of seismic loads, the stiffness variation

becomes more complicated because the arch bridge can also develop oscillatory forces between

tension and compression. In the linear behaviors, the properties

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

analysis predicting the time history responses. For the complicated seismic excitation, 2

was found not to be adequate to obtain accurate results according to the strong coupl

in-plane and out-of-plane motions of the arch ribs and the deck. The 3

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

a) Type I-I-2 wave

Figure7. Input JSHB seismic wavesLevel II

Northeastern Pacific Ocean off the coast earthquake

In the numerical analyses, the Newmark

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

was selected to keep the constant average acceleration. A constant time step of 0.01 sec has set. And

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 bel

In which:

C = Damping matrix

α = Coefficient for mass matrix

M = Mass matrix

β = Coefficient for stiffness matrix

K = Stiffness matrix



80


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-

3 waves were input in the dynamic response analysis in longitudinal and transverse directions

umerical analysis

of steel arch bridges under seismic loads is quite different from that of

stayed bridges since the large axial compression due to the effect of its dead

d reduces the stiffness of arch. According to the effect of seismic loads, the stiffness variation


tension and compression. In the linear behaviors, the properties of the deterministic system of



mic behavior of steel arch bridges needs to be focused on the precise

analysis predicting the time history responses. For the complicated seismic excitation, 2

was found not to be adequate to obtain accurate results according to the strong coupl

plane motions of the arch ribs and the deck. The 3-D nonlinear seismic analysis


effects of either geometric or material nonlinearity taken into account.

wave b) Type I-I-3

Input JSHB seismic wavesLevel II earthquake ground motion (Type I) recorded from


In the numerical analyses, the Newmark-β method was used for solving the differential


with respect to time taking into account material and geometrical non-linearity. The value

o keep the constant average acceleration. A constant time step of 0.01 sec has set. And


. The damping matrix equation is determined by an expression below.

= Coefficient for mass matrix

= Coefficient for stiffness matrix

6308 (Print), ISSN


two seismic waves recorded from the Northeastern Pacific

-I-2 and Type I-I-

in longitudinal and transverse directions

quite different from that of

stayed bridges since the large axial compression due to the effect of its dead

d reduces the stiffness of arch. According to the effect of seismic loads, the stiffness variation


of the deterministic system of



mic behavior of steel arch bridges needs to be focused on the precise

analysis predicting the time history responses. For the complicated seismic excitation, 2-D analysis

was found not to be adequate to obtain accurate results according to the strong coupling between the

D nonlinear seismic analysis


wave

otion (Type I) recorded from

ethod was used for solving the differential


linearity. The value β = 0.25

o keep the constant average acceleration. A constant time step of 0.01 sec has set. And


(5)



81

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

� � ��·��·��

��

�� (6)

� � ��

��

(7)

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 (X-

axis), 2nd

mode in transverse direction (Z-axis) and 8th

mode in-plane direction (Y-axis), respectively.

Table 5. Results of eigenvalue analysis

Order of

period

Natural

frequency (Hz)

Natural periods

(sec)

Effective mass ratio (%)

X Y Z

1 1.0341 0.9670 74 0 0

2 1.9767 0.5059 0 0 75

3 2.6452 0.3780 0 0 0

4 2.6452 0.3780 0 0 0

5 3.3823 0.2957 0 0 0

6 3.7199 0.2688 26 0 0

7 4.1054 0.2436 0 0 25

8 4.1988 0.2382 0 100 0

9 5.0428 0.1983 0 0 0

10 5.2847 0.1892 0 0 0



Two values of resonant frequencies t

dominant vibration modes. Substitution of dominant resonant frequencies f

h1, h2 were set to be 0.03 (3 %). When the coefficient value (

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.

a) 1st mode

(longitudinal direction)

Figure 9. Vibration shapes to predominant modes

IV. RESULTS AND DISCUSSIONS

1.5 Static pushover analysis The ultimate behavior and the development

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 displacemen

loading case I, Fig. 11a) shows the load factor (

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

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

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 (

the arch crown and the center of the stiffened girder. The segment of the member element was

yielded first at the load factor α = 8.38. The first yield members of the model are shown in Fig.

Fig. 12c) shows that the main arch rib yields in the first place, and then f

members of the arch bridge model as seen as Fig. 12d)



82

Two values of resonant frequencies that earned from eigenvalue were selected from two

dominant vibration modes. Substitution of dominant resonant frequencies f1, f2 and the damping ratio

were set to be 0.03 (3 %). When the coefficient value (α) for mass matrix and the coefficient

) were obtained, the damping matrix C should be eventually calculated by

. Three predominant Eigen modes deflecting in the longitudinal direction and one

in the transverse direction of the two bridges are shown in Fig. 9.

b) 2

nd mode

(out-of plane direction)

c) 8th

(in-plane direction)

Vibration shapes to predominant modes

DISCUSSIONS

The ultimate behavior and the development of plastic zone on the cross section of the arch


Fig. 10 shows the nodal points of the monitorial displacement in each loading case. In

loading case I, Fig. 11a) shows the load factor (α) versus in-plane displacement (v) at the arch crown


his model attained the ultimate state at the load factor αu


of the arch rib yields in the first place, and then followed by the arch rib and the stiffened girder

The nodal points of the monitorial displacement in each loading case

a) shows the load factor (α) versus longitudinal displacement (

d the center of the stiffened girder. The segment of the member element was

= 8.38. The first yield members of the model are shown in Fig.

c) shows that the main arch rib yields in the first place, and then followed by the other

as seen as Fig. 12d).

6308 (Print), ISSN

hat earned from eigenvalue were selected from two

and the damping ratio

) for mass matrix and the coefficient

) were obtained, the damping matrix C should be eventually calculated by

. Three predominant Eigen modes deflecting in the longitudinal direction and one

th

mode

plane direction)

of plastic zone on the cross section of the arch


t in each loading case. In

) at the arch crown


u = 5.27. The first


the stiffened girder as

The nodal points of the monitorial displacement in each loading case

) versus longitudinal displacement (u) at

d the center of the stiffened girder. The segment of the member element was

= 8.38. The first yield members of the model are shown in Fig. 12b).

ollowed by the other



a) Load factor vs. in-plane displacement curve

c) Load factor vs. axial strain curves

Figure 11.

a) Load factor vs.longitudinal displacement

curve


Figure 12.



83

plane displacement curve b) First yielded members

Load factor vs. axial strain curves d) Spreading of plastic members

Figure 11. Results of loading case I

Load factor vs.longitudinal displacement b) First yielded members


Figure 12. Results of loading case II

X (u)

Y (v)

Z (w)

X (u)

6308 (Print), ISSN

b) First yielded members

d) Spreading of plastic members





(c) Loading case III

In loading case III, Fig. 13a) shows the load factor (


yielded first at the load factor α = 8.702. The first yield mem

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).

a) Load factor vs.out of plane displacement curve


Figure 1

From these three cases, it is found that each l

considering the spreading of the yield members

direction of static pushover loading

and diagonal brace members that connected the two arch ribs

most critical members in all the loading cases.

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.

the acceleration data obtained from the JSHB, Type II

II-I-1wave for transverse direction,

transversedisplacement has been checked at the arch crown, and th

yielded member has been analyzed. Fig. 1

modal dynamic analysis of ABAQUS.



84

In loading case III, Fig. 13a) shows the load factor (α) versus transverse displacement (


= 8.702. The first yield members of the model are shown in Fig.



displacement curve b) First yielded members


Figure 13. Results of loading case III

From these three cases, it is found that each loading will lead lo different responses

considering the spreading of the yield members and it is able to show the critical members by each

static pushover loading. From the results, stiffened girder members, arch rib members

members that connected the two arch ribs under the deck plate

most critical members in all the loading cases. These members should be considered more in the

of the arch bridge model is conducted in two type of analytical


seismic waves were input in longitudinal and transverse directions, by ABAQUS program.

the acceleration data obtained from the JSHB, Type II-I-2 wave for longitudinal directionand Type

1wave for transverse direction,with the damping ratio (h) = 0.03, the longitudinal

displacement has been checked at the arch crown, and the internal force from the first

yielded member has been analyzed. Fig. 14 shows the displacement response obtained from the

modal dynamic analysis of ABAQUS.

Z (w)

6308 (Print), ISSN

displacement (w) at


bers of the model are shown in Fig.





oading will lead lo different responses

and it is able to show the critical members by each

From the results, stiffened girder members, arch rib members

under the deck plate seem to be the

These members should be considered more in the

of the arch bridge model is conducted in two type of analytical


seismic waves were input in longitudinal and transverse directions, by ABAQUS program. By using

wave for longitudinal directionand Type

) = 0.03, the longitudinal and

e internal force from the first

shows the displacement response obtained from the



In the same way, the modal dynamic analysis was carried out

for longitudinal directionand Type I

seconds. The results are shown in Fig. 1

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

Figure 14. The displacement time hi

transverse direction in dynamic analysis

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

Figure 15. The displacement time history at the arch crown for seismic waves in longitudinal and

transverse direction in dynamic analysis


Maximum and minimum plastic ratios

investigate the strain distribution along

obtained from the maximum and minimum strain value at each point in the cross sec

member. The element numbering of arch rib and the stiffener girder can be seen in Fig 16

clearly the strain behavior of each element in the arch rib and stiffened girder

distributions in the arch rib under

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

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 twic

the arch rib elements and the stiffened girder elements in the center of the bridge have the lowest

value of strain distribution.



85

he modal dynamic analysis was carried out also for data

itudinal directionand Type I-I-3wave for transverse direction, with the time periods 240

Fig. 15.

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

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 II

Ken Nambu earthquake)

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


dynamic analysis (from Level II Earthquake Ground Motion Type I,

Northeastern Pacific Ocean off the coast earthquake)

m and minimum plastic ratios ε/εy of strain responses were also observed to

along the arch rib and stiffened girder.The strain records are

obtained from the maximum and minimum strain value at each point in the cross sec

numbering of arch rib and the stiffener girder can be seen in Fig 16

clearly the strain behavior of each element in the arch rib and stiffened girder.

under static push over loading and seismic waves in longitudinal

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

in the arch rib does not reach yield under dynamic analysis using two waves record from

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

elements and the stiffened girder elements in the center of the bridge have the lowest

6308 (Print), ISSN

data Type I-I-2 wave

time periods 240

(transverse direction)

story at the arch crown for seismic waves in longitudinal and

otion Type II, Hyogo-

wave (transverse direction)


(from Level II Earthquake Ground Motion Type I,

of strain responses were also observed to

The strain records are

obtained from the maximum and minimum strain value at each point in the cross section of each

numbering of arch rib and the stiffener girder can be seen in Fig 16 to explain

. From the strain

sh over loading and seismic waves in longitudinal

some element in the arch rib near intersections between arch rib and the

. In the other hands, all the

in the arch rib does not reach yield under dynamic analysis using two waves record from

The same phenomenon also occurs in the stiffened girder elements. The

e of the strain yield limit. While

elements and the stiffened girder elements in the center of the bridge have the lowest



Figure 16. Element numberi

Figure 17. Maximum and minimum strain ratios

along the arch rib and stiffener girder



86

a) Arch rib elements

b) Stiffened girder elements

Element numbering for arch rib and stiffener girder

a) Longitudinal direction

b) Transverse direction

Maximum and minimum strain ratios ε/εy of strain responses

along the arch rib and stiffener girder

6308 (Print), ISSN

of strain responses



87

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.



88

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