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 First International Conference for PhD students in Civil Engineeri ng CE-PhD 2012, 4-7 November 2012,Cluj-Napoca, Romania www.sens-group.ro/ce2012 Seismic assessment of Hungarian highway bridges – A case study József Simon *1 , László Gergely Vigh 2 1,2  Budapest University of Tech nology and Economics, D epartment of Structural Engineer ing  H-1521 Budapest, M ű egyetem rkp. 3., Hungary Abstract This paper deals with the case study of a typical Hungarian highway bridge, illustrating the  seismic performance and damage evaluation method. T he investigated large-span bridge consists of continuous steel box-section superstructure supported by reinforced concrete piers. For the analysis, simplified beam-element numerical model is developed. Linear spectral response analysis as well as non-linear static and cyclic analyses are invoked for the evaluation and then their results are compared. The model incorporates non-linear characteristics of the critical details, such as  pier, pier-to-superstructure joints, etc. Pushover and incremental dynamic analysis using several earthquake records is applied to determine the fragility curves reflecting the probability of various damage occurrence. The analyses indicate that the most vulnerable component is the fixed bearing, the collapse of the whole structure is caused by the local failure of the restrained pier, and the  structure provide relatively large extra resist ance against seismic loads.  Keywords: Eurocode 8 analysis methods, time-history analysis, non-linear analysis, pushover analysis, seismic assessment of continuous girder bridge, incremental dynamic analysis, fragility curve 1. Introduction In low or moderate seismicity regions, such as Hungary, there is no tradition of seismic design. We do not have much knowledge of the seismic behaviour of our bridges, however it is likely that significant damage may be caused by an earthquake. Besides, in 2006 a new seismic hazard map was released with an increased seismic proneness, classifying Hungary as moderate seismic zone. Experiences on newly erected structures in the last decade [1, 2] and parametric study on typical continuous girder bridges of Hungary [3] show that seismic load may cause failure of some specific elements, such as foundations, piers, bearings, joints, etc. In order to achieve sufficient seismic  performance, t hese details may have to be reinforced even though they would be safe in ultimate limit state. The global scope of our research is to evaluate the seismic performance and the expected damage during the lifetime of existing Hungarian bridges on the basis of performance based design methodology [4]. Based on the r esults, possible retrofit methods may be proposed. In this paper a typical continuous girder bridge, the M0 Háros highway bridge, Hungary is examined. A three dimensional numerical model which incorporates non-linear characteristics of the critical details is developed in Open System for Earthquake Engineering Simulation FEM software (OpenSEES) [5]. According to EC 8-2 [6] conventional linear spectral response analysis is *  Corresponding author. Tel./ Fax.: +36 70 945 69 51 E-mail address: [email protected] ail.com

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  • 7/23/2019 Sj Vlg Ce-phd2012 Final

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    First International Conference for PhD students in Civil Engineering

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    Seismic assessment of Hungarian highway bridges A case study

    Jzsef Simon*1, Lszl Gergely Vigh2

    1,2Budapest University of Technology and Economics, Department of Structural EngineeringH-1521 Budapest, Megyetem rkp. 3., Hungary

    Abstract

    This paper deals with the case study of a typical Hungarian highway bridge, illustrating theseismic performance and damage evaluation method. The investigated large-span bridge consists of

    continuous steel box-section superstructure supported by reinforced concrete piers. For theanalysis, simplified beam-element numerical model is developed. Linear spectral response analysisas well as non-linear static and cyclic analyses are invoked for the evaluation and then their resultsare compared. The model incorporates non-linear characteristics of the critical details, such as

    pier, pier-to-superstructure joints, etc. Pushover and incremental dynamic analysis using severalearthquake records is applied to determine the fragility curves reflecting the probability of variousdamage occurrence. The analyses indicate that the most vulnerable component is the fixed bearing,the collapse of the whole structure is caused by the local failure of the restrained pier, and the

    structure provide relatively large extra resistance against seismic loads.

    Keywords: Eurocode 8 analysis methods, time-history analysis, non-linear analysis, pushover

    analysis, seismic assessment of continuous girder bridge, incremental dynamic analysis, fragilitycurve

    1. Introduction

    In low or moderate seismicity regions, such as Hungary, there is no tradition of seismic design.We do not have much knowledge of the seismic behaviour of our bridges, however it is likely thatsignificant damage may be caused by an earthquake. Besides, in 2006 a new seismic hazard mapwas released with an increased seismic proneness, classifying Hungary as moderate seismic zone.

    Experiences on newly erected structures in the last decade [1, 2] and parametric study on typicalcontinuous girder bridges of Hungary [3] show that seismic load may cause failure of some specificelements, such as foundations, piers, bearings, joints, etc. In order to achieve sufficient seismic

    performance, these details may have to be reinforced even though they would be safe in ultimatelimit state.

    The global scope of our research is to evaluate the seismic performance and the expecteddamage during the lifetime of existing Hungarian bridges on the basis of performance based designmethodology [4]. Based on the results, possible retrofit methods may be proposed.

    In this paper a typical continuous girder bridge, the M0 Hros highway bridge, Hungary isexamined. A three dimensional numerical model which incorporates non-linear characteristics ofthe critical details is developed in Open System for Earthquake Engineering Simulation FEM

    software (OpenSEES) [5]. According to EC 8-2 [6] conventional linear spectral response analysis is*Corresponding author. Tel./ Fax.: +36 70 945 69 51E-mail address: [email protected]

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    carried out to compute probable reaction forces and displacements, non-linear, static pushoveranalysis is applied to determine the collapse mechanisms and non-linear time-history analyses aredone to capture the seismic behaviour of the bridge more precisely. Based on the results, the criticalstructural components influencing the overall seismic performance are determined. To evaluate thefeasibility of the different analysis methods, results are compared to each other on the level ofinternal forces in the critical elements. Finally, incremental dynamic analysis based stochasticassessment is used to create fragility curves of the critical components and to more preciselyevaluate the actual seismic performance of the bridge.

    2. Bridge description

    The case study bridge is a newly erected highway bridge over the Danube River for the M0Motorway at Hros. The structure was designed by Unitef, Inc., Ch, Inc. and Pon-Terv, Inc,

    Hungary. The total length of the bridge is 770.42 m (3x73,5 m flood, 3x108,5 m river and 3x73,5 mflood bridges) and the total width of the deck is 21.80 m (1.9 m sidewalk + 18.0m carriageway +1.9 m sidewalk). The river bridge is a continuous three span girder with a one-cell box cross-sectionwith inclined webs and an orthotropic deck. The flood bridges are three span continuous composite

    bridges. The steel box is identical to that of the river bridge, but the deck is a R.C. slab. The bridgeis straight in plan. In this study only the river bridge is analyzed. The river bridge shares twocommon piers with the flood bridges (pier 4 and pier 7) and is separated from the flood bridges by a+-70 mm (pier 4) and a +-160 mm (pier 7) expansion joint. The longitudinal view of the bridge can

    be seen in Figure 1.

    Figure 1. Longitudinal section of the river bridge.

    Figure 2. Side-views of pier 5. Table 1. Cross-sectional data.

    The steel grade of the box girder is S355, the piers are C35/45 concrete and the reinforcing steelis grade S500B. The variable cross-section parameters of the box girder and the piers are listed inTable 1. The two side-views of pier 5 are shown in Figure 2. The cross-sections are nearly the same

    Girder S1 S2 S3 S4

    A[m2] 0.82 0.91 1.11 1.15

    Iy[m4] 3.20 4.08 5.75 5.84

    Iz[m4] 2 3. 50 2 4. 50 2 5. 80 2 6. 90

    It[m4] 4.83 5.77 6.52 7.05

    P4 S1 S2 S3 S4

    A[m2] 23 .7 27 .4 36 .4 1 08 .0

    Iy[m4] 14 .1 11 .9 23 .4 3 93 .0

    Iz[m4] 4 8 6. 0 4 32 .0 5 18 .0 2 43 0. 0

    It

    [m

    4

    ] 34 .4 3 5. 3 8 1. 1 1 17 0. 0

    P5 S1 S2 S3 S4

    A[m2] 24 .2 28 .5 39 .9 1 58 .0

    Iy[m4] 14 .4 12 .7 29 .4 8 12 .0

    Iz[m4] 4 8 9. 0 4 35 .0 5 98 .0 5 35 0. 0

    It[m4] 3 5 .7 3 9. 4 1 01 .0 2 45 0. 0

    P6 S1 S2 S3 S4

    A[m2] 24 .2 28 .5 39 .9 1 58 .0

    Iy[m4] 14 .4 12 .7 29 .4 8 12 .0

    Iz[m4] 4 8 9. 0 4 35 .0 5 98 .0 5 35 0. 0

    It[m4] 3 5 .7 3 9. 4 1 01 .0 2 45 0. 0

    P7 S1 S2 S3 S4

    A[m2] 24 .2 27 .6 39 .9 1 72 .0

    Iy[m4] 14 .4 12 .1 29 .4 9 76 .0

    Iz[m4] 4 8 9. 0 4 33 .0 5 98 .0 6 23 0. 0

    It[m4] 3 5 .7 3 6. 1 1 01 .0 2 93 0. 0

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    at each pier, only the pier height varies. The superstructure is fixed in the longitudinal direction atpier 5, whereas one of the two bearings provides lateral restraint at each pier.

    Seismic design of the structure was completed in accordance with Eurocode 8 Pt. 2, using modalspectrum analysis. The applied seismic parameters are: ground acceleration of 0.1 g, soil type C,importance class II, Type 1 spectrum. The applied mass is calculated from the dead loads and 1kN/m2 live load distributed on the carriageway. This leads to an equivalent 146 kN/m line loadalong the length of the girder. Quasi-elastic behaviour is considered with a behaviour factor q = 1.5.

    3. Numerical model

    According to the comprehensive literature overview of [7] on seismic numerical modeling ofgirder bridges, a three dimensional numerical model is developed in OpenSees [5]. A schematic

    picture of the numerical model can be seen in Figure 3. The main structure is modeled by beam

    elements. Elastic beam element is used for the girder and displacement based fiber section elementfor the piers because of the expected plastic deformations. The fibers have their own uniaxialstressstrain relationship. This way the cross-section is discretely modeled, confined andunconfined concrete regions and the longitudinal steel reinforcement can be taken into account. Forthe behaviour of steel the Giuffr-Menegotto-Pinto model, and for the behaviour of concrete lineartension softening concrete material model is adopted. The beam elements are placed in the center ofgravity, the elements of the girder and the piers are joined with rigid elements. These rigid elementsare created to model the top of the pier and the rigid box section and are led to the edges of the topof the pier where the bearings are placed. The bearings on the piers and the abutments are modeled

    by zero-length elements with non-linear spring characteristics assigned to three degrees of freedom(ux, uy, uz), but rotations are free to develop. For the elastomeric bearings bilinear hysteretic

    material model is used (Figure 11). This behaviour can be described by the initial stiffness (K0), thepost-yield and initial stiffness ratio () and the yielding strength (Fy). Table 2 shows the propertiesof the fixed and expansion bearings. The soil-structure interaction at the foundations of the piers istaken into account with integrate linear springs, adjusted with stiffness values (Table 3) calculatedfrom foundation analysis.

    The developed model is applied for the non-linear analysis of the bridge. In the following, thedifferent seismic analysis methods available in EC8-2 are compared to each other. Whencompleting linear analysis (modal spectrum analysis and linear time-history analysis), material non-linearity is not incorporated, and elements are assigned with their initial stiffness values.

    Table 2. Bearing properties.

    Figure 3. Numerical model of the bridge. Table 3. Foundation stiffnesses.

    PierNo. 4 5 6 7

    Kx[MN/m] 4760 3850 3850 3070

    Ky[MN/m] 5130 4550 4550 3220

    Kx[MNm/rad] 350000 500000 500000 350000

    Kx[MNm/rad] 111000 125000 125000 111000

    K0[kN/mm]

    Fy[kN]

    []

    70

    960

    0.170

    14

    5

    0.018

    Fi xe d Expansi onType

    Bearingcharacteristics

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    4. Comparison of analysis methods

    4.1. Linear response spectrum analysis (LRSA)

    Linear response spectrum analysis is the most commonly used earthquake analysis methodamong designers due to its relative simplicity and effectiveness. Original seismic design of theinvestigated structure was also made by LRSA. In linear analysis, geometric and material non-linearity is ignored. Accordingly, fixed bearings are assumed fully rigid, while expansion bearings

    provide no restraint in the model. The linear dynamic analysis is carried out according to EC8-2 [6].The behaviour factor (q) is 1.5 for the continuous girders (superstructure) as well as for the pierwalls, and q = 1.0 should be used for the analysis and design of the bearings, abutments andfoundations. The parameters of the standard acceleration response spectrum curve are : ag= 1.0m/s2, soil type C, M > 5.5, = 0.05. The applied spectrums can be seen in Figure 4. Typical modalshapes and frequencies, obtained from the modal analysis, are illustrated in Figure 5. The reaction

    forces of the bearings and the piers are summarized in Table 4. The critical components are thelongitudinally restrained pier 5 and the fixed bearings at the same place. The results are inaccordance with [3].

    Figure 4. Applied standard response spectra. Figure 5. Typical modal shapes.

    Table 4. Pier and bearing reaction forces from LRSA, LTHA and NLTHA.

    Assuming q = 1.0, the maximal displacements are 27 mm and 36 mm in the transversal andlongitudinal direction respectively, and the maximal deflection (mostly from the dead loads) is 247mm.

    Fx Fy Fz Mx My Mz

    4 2558.5 4210.6 32266.3 56144.6 20787.6 1003.8

    5 13414.2 18429.9 89420.5 275367.4 229907.1 13838.0

    6 11631.3 17174.8 89337.8 251826.4 88429.0 10.7

    7 12599.3 16290.0 87876.1 175951.2 101845.2 5152.2

    Fx Fy Fz Mx My Mz

    4 2362.9 4027.2 31833.4 47126.0 17728.6 876.4

    5 12188.4 11864.7 84308.9 190599.2 217217.8 11393.5

    6 11402.6 11632.0 84137.7 174807.9 80323.0 8.5

    7 11406.4 14846.3 82225.8 141236.6 98054.1 4218.0

    Fx Fy Fz Mx My Mz

    4 2344.5 5636.8 31871.4 63457.8 17146.3 1261.6

    5 11743.7 10142.4 84419.2 159012.1 117740.9 12587.2

    6 11219.0 11065.4 84360.3 160511.9 95641.4 101.2

    7 10378.4 14045.8 82327.5 149178.0 113279.7 2460.7

    kNm

    Linearresponsespectrumanalysisresults

    kN

    Pier

    Pier

    Pier

    kN kNm

    Nonlineartimehistoryanalysis results

    Lineartimehistoryanalysisresults

    kN kNm

    Fx Fy Fz Fx Fy Fz

    4 0.0 1664.0 4422.1 0.0 0.0 4410.8

    5 5045. 2 7809. 3 1 3197. 5 5075. 1 0. 0 13186. 4

    6 0.0 7206.5 13037.4 0.0 0.0 13028.2

    7 0.0 2002.6 4513.6 0.0 0.0 4507.7

    Fx Fy Fz Fx Fy Fz

    4 0.0 1240.8 3795.8 0.0 0.0 3897.7

    5 4910. 9 5201. 7 1 2136. 1 4916. 6 0. 0 12221. 0

    6 0.0 4701.9 11873.7 0.0 0.0 11956.1

    7 0.0 1656.4 4056.7 0.0 0.0 4025.1

    Fx Fy Fz Fx Fy Fz

    4 32.7 1026.7 3644.5 32.7 11.0 3588.8

    5 1 599. 8 1329 .5 1 0396 .5 1 599. 8 18. 1 104 90. 8

    6 27. 6 1371. 4 10373. 9 27. 6 18. 8 10455. 4

    7 25.5 1025.8 3691.1 25.5 11.3 3709.1

    Pier

    Linearresponsespectrumanalysisresults

    Rightbearing Leftbearing

    kN kN

    Rightbearing LeftbearingPier

    Lineartimehistoryanalysisresults

    kN kN

    Pier

    Nonlineartimehistoryanalysisresults

    Rightbearing Leftbearing

    kN kN

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    4.2.Linear time-history analysis (LTHA)

    With time-history analysis the seismic behaviour can be revealed more precisely since thestructure is analyzed in the time domain in contrast to LRSA which generally overestimates thereaction forces in a conservative manner.

    A new algorithm is developed which creates synthetic acceleration records for time-historyanalysis. The records are determined to match the given acceleration spectrum curve (see Section4.1. and Figure 6.). According to EC 8, at least 3 such records should be used. The maximum valuesof the results from the three LTHAs can be seen in Table 4. The maximum displacements are 33.9mm, 10.3 mm and 220.6 mm in the longitudinal, transversal and vertical directions.

    Figure 6. The fitted three synthetic acceleration records.

    4.3.Pushover analysis

    As per EC8-2, pushover analysis (static non-linear analysis) can be applied for design check asalternative method to LSRA, or for characterizing the failure mechanisms. The load pattern appliedin pushover analysis is basically determined by the most dominant mode shape, therefore if more

    modes are relevant (e.g. in the lateral direction) the method can be used only with limitations.Generally in case of continuous girders with not too high (less than 30 m) piers one modecharacterizes the seismic behaviour in the longitudinal direction [3], so pushover analysis could be auseful tool for capacity design, and to determine the collapse mechanism. In this paper pushoveranalysis is carried out only in this direction.

    Figure 7. Capacity curves for the whole structure, pier 5 and the fixed bearing.

    Capacity curves (base shear force vs. top displacement) of the whole structure, the longitudinallyrestrained pier (no. 5) and the fixed bearing are shown in Figure 7. The analysis indicates that theultimate collapse of the whole structure is caused by the local failure of the longitudinally restrained

    pier. However, failure/fracture of any components are not taken into consideration in thesimulation. Considering 50 mm, 100 mm and 250 mm deformations as slight, moderate and fulldamage states for the bearing, it can be realized that the fixed bearing suffers large deformations

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    and bearing failure anticipates pier failure (corresponding pier curvatures are still in the linearregion). Accordingly, the most vulnerable component is the fixed bearing. This indicates that the

    piers are robust, stiff, and provide relatively large extra resistance against seismic loads.

    4.4.

    Non-linear time history analysis (NLTHA)

    Non-linear dynamic analysis is the most rigorous analysis type. Note that springs representingthe bearings make the structure less stiff, the dominant natural period in the longitudinal directionchanges from 0.725 s to 1.44 s. This causes a drastic response decrease according to the responsespectrum curve (Figure 4, 6.). Figure 8. shows how the natural period changes, the moments in pier5 are decreased, while displacements in the longitudinal direction increase.

    The non-linear behaviour of the fixed and expansion bearings and of the pier can be seen inFigure 9. The pier remains elastic to the applied three synthetic acceleration records (Figure 6.) Themaximum deformations of the bearings are 42 mm and 67 mm in case of the fixed and expansion

    bearings respectively. These deformations are under the assumed slight damage level. Themaximum displacements of the structure are 56 mm, 49.6 mm and 212.4 mm in the longitudinal,lateral and vertical directions. Table 4 also summarizes the bearing reaction forces and pier internalforces. The calculated response can be very sensitive to the characteristics of the individual groundmotion used as seismic input, therefore a set of records should be used for higher reliability.

    Figure 8. Longitudinal moment of pier 5 and longitudinal displacement of the structure with orwithout bearing elements.

    Figure 9. Non-linear behaviour of the fixed and expansion bearings and the pier.

    4.5.Comparison of the results

    Reaction forces from LRSA, LTHA and NLTHA are compared in Table 4. It is found that LRSAis conservative in comparison to LTHA as the latter gives lower response values especially in thelateral direction. Since in the longitudinal direction one mode characterizes the seismic behaviour,the two analyses leads to nearly the same results. In both methods, piers and fixed bearings arefound as critical elements. Non-linear analysis methods also confirm that the most vulnerablecomponent is the fixed bearing, whereas the piers are robust and stiff. The failure of the bearinganticipates the failure of the restrained pier. The pier remains elastic at the level of bearing failure.

    For the given intensity level which is determined by the standard acceleration spectrum thedisplacements are so low in the longitudinal direction that not even slight damage of the bearingsand hereby of the piers are likely to occur. The spring elements applied for the non-linear analysis

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    decrease the stiffness of the structure and thus increase the fundamental period. Thus, seismicresponses are decreased, with increasing deformation demands. The responses obtained from

    NLTHA thus fundamentally differ from those of the linear analyses, they are compared in Table 4.Drastic change of the moments of the piers can be observed, the moments are lower at therestrained (pier 5) and higher at the non-restrained (pier 4, 6, 7) piers. The horizontal forcetransmission capability of the expansion bearings results more favorable reaction force distribution.

    5. Incremental dynamic analysis (IDA)

    In Section 4. only deterministic analyses which are most commonly used in Europe arepresented. These analyses can highlight the most vulnerable components and details of the structureand they provide results for a given intensity level, but do not characterize the probability of failureof the structure. This probability can be expressed by creating the fragility curves of different

    components or the whole structure. In this case stochastic methods are needed. The seismicperformance can be very sensitive to the characteristics of the individual acceleration record.During incremental dynamic analysis, the structure is subjected to 44 different ground motionsfollowing the instructions of FEMA P695 [8] document. The earthquake records are sampled to

    provide a very diverse accelerogram set. Firstly, this set is normalized by the peak ground velocitiesso that the variance of each record is reduced to an acceptable level. The normalized set then isscaled the way that the median acceleration response spectrum of the set equals the responsespectrum used for the design at the fundamental period of the structure. This can be seen in Figure10, here the scaling is done at natural period of 1.44 s which corresponds to the dominant natural

    period of the non-linear model in the longitudinal direction. The analysis is carried out only in thelongitudinal direction.

    Figure 10. Set of ground motion records scaled to a pre-defined spectral acceleration level atT=1.44 s.

    At each scaling level the maximum longitudinal displacement of the girder is registered for eachground motion. The displacement vs. spectral intensity - defined here by the spectral acceleration -relation for each record is shown in Figure 11. Plateau of the curve of a seismic record (meaningrapidly increased deformations) indicates the structural collapse for the given record. Three damagelevels (slight, moderate and full) are determined for each component. The damage is measured indeformation and in curvature ductility (=u/ y) in case of the fixed bearing and the piers,respectively. The corresponding values are 50 mm, 100 mm, 250 mm of deformation and = 1, 4and 7 curvature ductilities for slight, moderate and full damages. According to this, fragility curvesare created and shown in Figure 12. The curves confirm again that the most vulnerable componentin collapse prevention performance objective is the fixed bearing: the failure of the whole structure

    is determined by the full damage of the bearing (Figure 12. thick, solid line). Piers are so robust thatthey do not even suffer slight damage when the bearing is failed.

    The standard spectral acceleration at the fundamental period (1.44 s) is 1.175 m/s2. The curves

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    indicate that the actual seismic performance of the structure is sufficient: relatively large extraresistance against seismic loads is provided by the preserve material and cross-section capacities,even though the structure was not designed to ductile behaviour.

    Figure 11. Max. longitudinal displacementvalues from each ground motion record at

    different spectral acceleration levels.

    Figure 12. Fragility curves for the fixedbearing and the pier.

    6. Conclusions

    In this paper the M0 Hros highway bridge, Hungary is investigated. Linear and non-linearanalyses are carried out and compared to each other. The results confirm that the most vulnerablecomponent is the fixed bearing, anticipating the failure of the restrained pier. Comparison of theanalysis results shows that the LRSA overestimates the reaction forces and displacements comparedto the LTHA, NLTHA methods. Using more sophisticated model incorporating non-linear elements

    results in more flexible structure, with decreased reaction forces and increased deformations.In addition, incremental dynamic analysis based seismic performance assessment is completed in

    accordance to FEMA P695. The fragility curves created by incremental dynamic analysis indicatethat the structure provide relatively large extra resistance against seismic loads due to the increasedflexibility, and to the material and cross-section preserve capacity, even though the structure wasnot designed to ductile behaviour.

    7. References

    [1]

    Jo A, Vigh L, Kollr L. Experiences on seismic design of structures in Hungary. MAGSZACLSZERKEZETEK, Vol. 6:(1), pp. 72-81, 2009 (in Hungarian)

    [2]

    Vigh LG, Dunai L, Kollr L. Numerical and design considerations of earthquake resistant design of twoDanube bridges.Proc. ECEES 2006. Geneva, p. 10. Paper 1420, 2006

    [3] Zsarnczay . Seismic performance analysis of common bridge types in Hungary(inHungarian). MasterThesis at Budapest University of Technology and Economics, 2010

    [4]

    Deierlein GG. Overview of a Comprehensive Framework for Earthquake Performance Assessment.Performance-Based Seismic Design Concepts and Implementation. Proc. of Intl Workshop, PEERReport 2004/05, UC Berkeley, p. 15-26, 2004

    [5]

    McKenna F, Feneves GL. Open system for earthquake engineering simulation. Pacific earthquakeengineering research center, version 2.3.2., 2012

    [6] CEN: EN 1998-1:2008 Eurocode 8. Design of structures for earthquake resistance - Part 2: Bridges,2008

    [7]

    Simon J. Numerical model development for seismic assessment of continuous girder bridges.Proceedings of the Conference of Junior Researchers in Civil Engineering, pp. 216-224. Budapest,Hungary, 2012

    [8]

    ATC: FEMA P695. Quantification of Building Seismic Performance Factors, 2009