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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 Journal Impact Factor (2013): 5.3277 (Calculated by GISI) www.jifactor.com 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
    • International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print), ISSN 0976 – 6316(Online) Volume 5, Issue 1, January (2014), © IAEME 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
    • International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print), ISSN 0976 – 6316(Online) Volume 5, Issue 1, January (2014), © IAEME 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
    • International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print), ISSN 0976 – 6316(Online) Volume 5, Issue 1, January (2014), © IAEME 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
    • International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print), ISSN 0976 – 6316(Online) Volume 5, Issue 1, January (2014), © IAEME 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
    • International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print), ISSN 0976 – 6316(Online) Volume 5, Issue 1, January (2014), © IAEME 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
    • International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print), ISSN 0976 – 6316(Online) Volume 5, Issue 1, January (2014), © IAEME (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
    • International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print), ISSN 0976 – 6316(Online) Volume 5, Issue 1, January (2014), © IAEME 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
    • International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print), ISSN 0976 – 6316(Online) Volume 5, Issue 1, January (2014), © IAEME 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
    • International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print), ISSN 0976 – 6316(Online) Volume 5, Issue 1, January (2014), © IAEME 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
    • International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print), ISSN 0976 – 6316(Online) Volume 5, Issue 1, January (2014), © IAEME 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 b) First yielded members c) Load factor vs. axial strain curves d) Spreading of plastic members Figure 12. Results of loading case II 83
    • International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print), ISSN 0976 – 6316(Online) Volume 5, Issue 1, January (2014), © IAEME (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) b) First yielded members Load factor vs. axial strain curves d) Spreading of plastic members 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
    • International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print), ISSN 0976 – 6316(Online) Volume 5, Issue 1, January (2014), © IAEME 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
    • International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print), ISSN 0976 – 6316(Online) Volume 5, Issue 1, January (2014), © IAEME 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
    • International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print), ISSN 0976 – 6316(Online) Volume 5, Issue 1, January (2014), © IAEME 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
    • International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print), ISSN 0976 – 6316(Online) Volume 5, Issue 1, January (2014), © IAEME REFERENCES [1] T. Yamao, T. Sho, S. Murakami and T. Mazda, Seismic behavior and evaluation of seismic performance of half through steel arch bridges subjected to fault displacement, Journal of Seismic Engineering, 2007, 317-324 [2] F. Chandra, S. Atavit and T. Yamao, Seismic behavior and a performance evaluation of decktype steel arch bridges under the strong earthquakes, The 5th International Symposium on Steel Structures, Seoul, Korea, 2009, 388-395. [3] Y. Zheng, T. Usami and H. Ge, Seismic response predictions of multi-span steel bridges through pushover analysis, Earthquake Engineering and Structural Dynamics, 32, 2003, 1259–1274 [4] Japan Road Association, Specifications for Highway Bridges,Part V-Seismic Design, Japan, 2002. [5] T. Usami, H. Oda, Numerical analysis and verification methods for seismic design of steel structures. Journal ofStructural Mechanics and Earthquake Engineering (JSCE), 668(I-54), 2001, 1–16. [6] Z. Lu, H. Ge and T. Usami, Applicability of pushover analysis-based seismic performance evaluation procedure for steel arch bridges,Engineering Structures, 26, 2004, 1957-1977. [7] A. Ghobarah, Performance-based design in earthquake engineering: State of development,Engineering Structures, 23, 2001, 878-884. [8] A. M. Mwafi, A. S. Elnashai, Static pushover versus dynamic collapseanalysis of RC buildings, Engineering Structures, 23 (5) ,407–24. [9] S. Atavit, Seismic Behaviors and a Performance Evaluation Method of a Deck-Type Steel Arch Bridge, doctoral diss., Kumamoto University, Kumamoto, Japan, 2007. [10] Japan Road Association, Specifications for Highway Bridges,Part I - Steel Bridge, Japan, 2002 (In Japanese). [11] Abaqus 6.11, Abaqus/CAE User’s Manual,DassaultSystèmesSimulia Corp., Providence, RI, USA, 2011. [12] T. Kuwabara, T. Tamakoshi, J. Murakoshi, Y. Kimura, T. Nanazawa and J. Hoshikuma, Outline of Japanese Design Specifications for Highway Bridges in 2012, The 44thMeeting, Joint Panel on Wind and Seismic Effects (UJNR), UJNR Gaithersburg, 2013. 88