Earth seismology and earthquake engineering

MSc Dissertation September 1999 Engineering Seismology and Earthquake Engineering Cable-Stayed Bridges Earthquake Response and Passive Control Guido Morgenthal Imperial College of Science, Technology and Medicine Civil Engineering Department London SW7 2BU Cable-Stayed Bridges Earthquake Response and Passive Control Dissertation submitted by Guido Morgenthal in partial fulfilment of the requirements of the Degree of Master of Science and the Diploma of Imperial College in Earthquake Engineering and Structural Dynamics September 1999 Supervisors: Professor A S Elnashai, Professor G M Calvi Engineering Seismology and Earthquake Engineering Section Department of Civil Engineering Imperial College of Science, Technology and Medicine London SW7 2BU ACKNOWLEDGEMENTS I would like to express my deep gratitude to my two supervisors for this dissertation Firstly my thanks must go to Professor A S Elnashai for his help and guidance throughout the year His lectures have laid a sound foundation for the work on this project and his constant support even during my stay in Italy is greatly appreciated Equally important, I would like to thank Professor G M Calvi from the Structural Mechanics Section of Università di Pavia Through him I had the opportunity to work on a fascinating project and to experience a beautiful country and a lovely town at the same time His generosity in taking time to discuss the progress of my work and his support in organising my stay were essential for my completing the work in time The comments of Professor N Priestley and the help of the other people at San Diego are also gratefully acknowledged Finally and most importantly, I would like to thank my parents who are always there for me I am grateful for their encouragement and unending support Introduction Page TABLE OF CONTENTS Acknowledgements Table of contents INTRODUCTION 1.1 Preamble 1.2 Significance of long-span bridges 1.2.1 Impact of bridges on economy 1.2.2 The trans-European transport network 1.3 Recent cable-stayed bridge projects 1.3.1 Öresund Bridge, Sweden 1.3.2 Tatara Bridge, Japan 1.3.3 The Higashi-Kobe Bridge, Japan STATE OF RESEARCH ON CABLE-STAYED BRIDGES 2.1 Configuration of Cable-Stayed Bridges 2.1.1 General remarks 2.1.2 Cable System 2.1.3 Stiffening Girder 2.1.4 Towers 2.1.5 Foundations 2.2 Nonlinearities in Cable-Stayed Bridges 2.3 Dynamic behaviour and earthquake response 2.3.1 General dynamic characteristics 2.3.2 Damping characteristics 2.3.3 Influence of soil conditions and soil-structure interaction effects 2.3.4 Structural control THE RION ANTIRION BRIDGE 3.1 Introduction to structure and site 3.2 Description of the structure 3.2.1 The deck 3.2.2 The pylons and piers 3.2.3 The transition piers 3.2.4 The stay cables 3.2.5 The foundation FINITE ELEMENT MODEL OF THE BRIDGE 4.1 Introduction 4.2 Description of the finite element model 4.2.1 The deck 4.2.2 The cables 4.2.3 The pylons and piers 4.2.4 The foundations and abutments 4.3 Accelerograms 4.3.1 Structural damping 4.4 Calibration investigations on the piers 7 8 10 11 11 11 12 14 16 17 17 19 19 22 24 27 29 29 29 30 31 32 32 33 34 34 34 34 36 36 37 39 42 42 Introduction CHARACTERISTICS OF THE RION-ANTIRION BRIDGE 5.1 Static characteristics - special considerations 5.1.1 Relative displacements 5.1.2 Static push-over analyses on the pier/pylon system 5.2 Dynamic characteristics - modal analyses EARTHQUAKE RESPONSE AND ITS CONTROL 6.1 Introduction 6.2 Investigations on basic systems 6.2.1 Introduction 6.2.2 Modelling assumptions 6.2.3 Results 6.3 Design considerations and performance criteria 6.3.1 Introduction 6.3.2 Serviceability conditions 6.3.3 Slow tectonic movements 6.3.4 Earthquake conditions 6.4 Devices for deck connection 6.4.1 Fuse device 6.4.2 Shock transmitter 6.4.3 Hydraulic dampers 6.4.4 Elasto-plastic isolators 6.5 Parametric studies on different deck isolation devices 6.5.1 Introduction 6.5.2 Analysis assumptions 6.5.3 Results 6.6 Conclusions Page 44 44 44 45 47 51 51 51 51 51 52 55 55 55 55 56 60 60 60 60 61 62 62 62 63 73 SUMMARY 76 REFERENCES 78 APPENDIX Introduction Page INTRODUCTION 1.1 Preamble Man's achievements in Structural Engineering are most evident in the world's largest bridge spans Today the suspension bridge reaches a free span of almost 2000m (Akashi-Kaikyo Bridge, Japan) while its cable-stayed counterpart can cross almost 1000m (Tatara Bridge, Japan, Normandie Bridge, France, Figure 1) Cable-supported bridges therefore play an important role in the overcoming of barriers that had split people, nations and even continents before Figure 1: Normandie Bridge, France It is evident that they are an important economical factor as well By cheapening the supply of goods they contribute significantly to economical prosperity Cable-stayed bridges, in particular, have become increasingly popular in the past decade in the United States, Japan and Europe as well as in third-world countries This can be attributed to several advantages over suspension bridges, predominantly being associated with the relaxed foundation requirements This leads to economical benefits which can favour cable-stayed bridges in free spans of up to 1000m Many of the big cable-stayed bridge projects have been executed in a seismically active environment like Japan or California However, very few of them have so far experienced a strong earthquake shaking and measurements of seismic response are scarce This enforces the need for accurate modelling techniques Three methods are available to the engineer to study the dynamic behaviour: forced vibration tests of real bridges, model testing and computer analysis The latter approach is becoming increasingly important since it offers the widest range of possible parametric studies However, testing methods are still indispensable for calibration purposes Herein the seismic behaviour of the Rion-Antirion cable-stayed Bridge, Greece, is studied by means of computer analyses employing the finite element method A framework of performance criteria is set up and within this different possible structural configurations are investigated Conclusions are drawn regarding the effectiveness of deck isolation devices Introduction Page 1.2 Significance of long-span bridges 1.2.1 Impact of bridges on economy Roads and railways are the most important means of transport in all countries of the world They act as lifelines on which many economic components depend Naturally rivers, canals, valleys and seas constitute boundaries for these networks and therefore considerably confine the unopposed supply of goods They cause significant extra costs because goods have to be diverted or even shipped or flown These extra costs can exclude economies from foreign markets It is evident that in this situation bridging the gap is worth considering Cable-supported bridges offer the possibility to cross even very large distances without intermediate supports Hence, it is only since their development, that people can consider crossings like the Bosporus (Istanbul Anatolia, completed 1973 and 1988), Öresund (Denmark - Sweden, to be completed 2000), the Strait of Messina (mainland Italy - Sicily, design stage finished), the Strait of Gibraltar (Spain Morocco) or the Bering Strait (Alaska - Russia) Of course infrastructure projects like these are costly Countries take up high loans to afford these road links Cost-benefit analyses are inevitable as proof for banks However, the number of already executed major projects emphasises that even the exorbitant costs can be worthwhile The bridges become an important factor for the whole region and can significantly boost the industry on both sides of the new link Furthermore and equally importantly, those bridge projects can become a substantial factor in the cultural exchange among people 1.2.2 The trans-European transport network The European Parliament has on the 23 July 1996 introduced plans for the development of a "trans-European transport network" ([29]) This project comprises infrastructures (roads, railways, waterways, ports, airports, navigation aids, intermodal freight terminals and product pipelines) together with the services necessary for the operation of these infrastructures Investments of about 15 billion Euro per year in rail and road systems alone underline the remarks made in the previous section regarding the importance of transport networks and the links within them The objectives of the network were defined by the European Parliament as follows: - ensure mobility of persons and goods; offer users high-quality infrastructures; combine all modes of transport; allow the optimal use of existing capacities; be interoperable in all its components; cover the whole territory of the Community; allow for its extension to the EFTA Member States, countries of Central and Eastern Europe and the Mediterranean countries Introduction Page Some of the broad lines of Community action concern: - the development of network structure plans; the identification of projects of common interest; the promotion of network interoperability; research and deve lopment, with priority measures defined as follows: - completion of the connections needed to facilitate transport; optimization of the efficiency of existing infrastructure; achievement of interoperability of network components; integration of the environmental dimension in the network It is apparent that the connections as means of interoperation between sub-networks are one of the most important components within the network Many of the currently planned major bridges in Europe are therefore part of the network and supported by the EU Among them are the Öresund and Rion-Antirion Bridges which are discussed subsequently 1.3 Recent cable-stayed bridge projects 1.3.1 Öresund Bridge, Sweden The £1.3 billion Öresund crossing will link Denmark and Sweden from the year 2000 on It comprises an immersed tunnel, an artificial island and a bridge part of which is a cable-stayed bridge (Figure 2) Figure 2: Öresund Bridge, Sweden For a combined road and railway cable-stayed bridge the center span of 490m (8th largest cablestayed bridge in the world) is remarkable A steel truss girder of dimensions 13.5x10.5m was Introduction Page employed to accommodate road and railway traffic on two levels The concrete slab is 23.5m wide and provides space for a lane motorway The structurally more difficult harp pattern (see section 2.1.2.1) was chosen for aesthetic reasons It should be mentioned that the struts of the girder were inclined according to the angle of the cables which is favourable from the structural as well as pleasing from the aesthetic point of view The money for the project was borrowed on the international market and jointly guaranteed by the governments of Denmark and Sweden It will be paid back from the toll fees introduced Being part of the trans-European transport network the link will be one of the most important European Structures carrying railway and at least 11,000 vehicles per day More information on the Öresund project can be found in [91] 1.3.2 Tatara Bridge, Japan Upon completion in 1999 the Tatara Bridge will be the cable-stayed bridge with the longest free span in the world It is shown in Figure 3, an elevation is given in section 2.1, Figure The center span is 890m, supported by a semi-fan type cable system Compared with this the side spans with 270 and 320m are extremely short and asymmetric so that intermediate piers and counterweights needed to be applied there Figure 3: Tatara Bridge, Japan The girder is a steel box section with a streamlined shape to decrease wind forces It is 31m wide and only 2.70m deep To act as counterweight the deck in parts of the sidespans is made of concrete At the towers the girder is kept free because of high temperature induced forces in the case of a fixing In model tests it was found to be necessary to install additional damping devices for the cables Particularly the upper ones (the longest one having a length of over 460 m - the longest stay cable ever) were found to be prone to wind and rain induced vibration Additional ropes Introduction Page 10 perpendicular to the stay cables were installed and connected to damping devices at the deck This yielded cable damping ratios of over 2% of critical The Tatara Bridge is being constructed in an area of high seismicity It was designed for an earthquake event of magnitude 8.5 at a distance of 200km The fundamental period of the bridge is 7.2s being associated with a longitudinal sway mode All information about the Tatara Bridge were taken from [33] 1.3.3 The Higashi-Kobe Bridge, Japan The Higashi-Kobe Bridge in Kobe City, Japan, is one of the busiest bridges in the world As part of the Osaka Bay Route it spans the Higashi-Kobe Channel connecting two reclaimed land areas (Figure 4) Figure 4: Higashi-Kobe Bridge, Japan The bridge's main span is 485m with the side span being 200m each The main girder is a Warren truss with height a of 9m It accommodates roads at the top and bottom of the truss respectively Both of these have three lanes, the width of the truss being 16m For the cable system the harp pattern was chosen The steel towers are of the H-shape and have a height of 146.5m These are placed on piers which are founded on caissons of size 35 (W) x 32 (L) x 26.5 (H) m An important feature of the bridge is that the main girder can move longitudinally on all its supports This results in a very long fundamental period which was found to be favourable for the seismic behaviour On 17 January 1995 Kobe was struck by an earthquake of magnitude 7.2 Although the HigashiKobe Bridge performed well in this earthquake, certain damage did occur which was reported in [44] Important information about the soil behaviour could be obtained from this event because the bridge was instrumented These will be further discussed in section 2.3.3 Earthquake Response and its Control Page 73 6.6 Conclusions The earthquake behaviour of the Rion-Antirion Bridge has been studied for various configurations The cases of a transversely free and a restrained deck have been considered as well as possible isolation devices In the light of the set of performance criteria described in 6.3 the following can be concluded from the results obtained for earthquake conditions A configuration with a free deck is unfavourable because - relative displacements between deck and pier are too large, particularly if transverse tectonic movements precede; - deformations in the soil are very large; - the deformation demand on the pylon is very large; hinging occurs The case of a fixed deck (shear key) is unfavourable because - high forces are applied from the deck on the pier; - accelerations of the deck are such that sliding of cars can occur Damping devices can be favourable because - relative transverse displacements of the deck can be reduced; however, the efficiency of the devices varies - the deformation demand on the pylon is considerably reduced by any device studied - deformations in the soil are reduced with respect to a free deck configuration; hydraulic devices are more efficient - forces on the pier are reduced with respect to a fixed connection and can be adjusted by choosing the appropriate device - accelerations of the deck can be reduced with some dampers; the likelihood of cars sliding on the deck can thus be reduced Table 20 shows a comparison of possible solutions for the deck connection It is apparent that damping devices provide a good solution with results lying either between a free and a fixed deck or even being more favourable than both as for the deformation demand on the pylon Earthquake Response and its Control Page 74 Free deck Max transverse dspl deck-pier [m] Max transv dspl d5 in the pylon (excl rot.) [m] Max transverse dspl in the soil spring [m] Force applied on the pier by the deck [MN] Safety against sliding [-] Hydraulic dampers, Elasto-plastic isolators, Fixed deck C=12MN, α=0.2 Fy=20MN, Eel=52500N/mm2 , Epl =0.05Eel 0.95 0.60 0.60 0.00 0.44 0.31 0.31 0.33 0.50 0.40 0.45 0.30 0.0 13.1 25.3 63.7 0.95 0.58 0.74 0.21 Table 20: Comparison of possible deck configurations If an optimal solution in terms of deck displacements and pier forces is sought, Figure 72 gives an interesting relationship The devices studied seem to lie close to the straight line between the results for a free and a restrained deck This means that the damping device can to a certain extent be adjusted to the response that is required If lower deck displacements are sought higher forces on the pier need to be accommodated and vice versa However, there are more and less effective solutions as has already been pointed out in section 6.5 While displacement reduction seems to depend on the energy dissipation capacity of the isolator the maximum force is correlated to the strength of the device Max rel displ deck-pier [m] Comparison, all cases 1.00 0.90 free deck 0.80 fixed deck 0.70 hydraulic dampers 0.60 elasto-plastic isolators 0.50 0.40 0.30 0.20 0.10 0.00 10 20 30 40 50 Max force deck-pier [MN] 60 70 Figure 72: Comparison of all considered deck configurations As was explained earlier, for the design of the deck configuration serviceability conditions also need to be considered If wind induced deck movements shall be avoided, a fuse device can be employed as explained in 6.4.1 Also, the impact of slow tectonic movements needs to be taken into account In the case of the Rion-Antirion Bridge these are required so as not to cause Earthquake Response and its Control Page 75 additional forces in the structure Therefore, a so called shock transmitting device as described in section 6.4.2 needs to be employed If all the above mentioned requirements are taken into account, a possible deck configuration featuring a fuse, a shock transmitter and isolation devices could look as shown in Figure 73 and Figure 74 Figure 73: Possible deck isolation system in plan Figure 74: Possible deck isolation system in elevation Summary Page 76 SUMMARY The main objective of this dissertation was to study the seismic behaviour and performance of cable-stayed bridges To this end, investigations on the Rion-Antirion Bridge structure were conducted employing the finite element method With the three-dimensional model and the analysis code used it was possible to take into account all major member characteristics and boundary conditions as well as geometric nonlinearities As a first step static analyses were conducted on the bridge subjected to relative displacements between the piers to study the impact of tectonic movements on the structure It was found that the flexibility of the bridge which is provided by a freely movable deck acts favourably in terms of induced forces The bridge deck responds by considerable relative displacements with respect to the pylons which can, however, be disadvantageous if deck displacements need to be limited Displacements of preceded tectonic movements add to the dynamic displacements during an earthquake and can thus increase the danger for pounding of the deck against the pylon legs Modal analyses were performed to investigate the basic dynamic characteristics of the bridge Four different cases in terms of deck connectivity were considered and the following conclusions can be drawn: - The fundamental mode has a very long period It is either a transverse (18.6s) or a vertical deck (7.5s) mode depending on whether the deck is free in the transverse direction or not Several well spaced long period modes follow succeeded by many closely spaced modes below 3s - Tower modes have a high mass participation These are beyond mode no 100 which points out the importance of higher mode contribution - For the shape and the natural frequency of the long period modes the boundary conditions of the deck are most influential To study the seismic behaviour of the bridge a framework of performance criteria was set up considering the following parameters: - displacements: relative deck displacements, soil deformations; - forces: forces in the pylon (results of static push-over analyses were utilised), forces on the piers from the deck connection system; - accelerations of the deck: sliding of cars on the road surface was considered Dynamic time-history analyses were performed to study the bridge response to a design earthquake A set of significant response parameters was monitored and commented on Firstly, the basic structural configurations with a free and a fully restrained deck were investigated Summary Page 77 Then it was analysed whether the seismic performance can be improved by employing isolation devices between the deck and the pylon base To this end, parametric studies with 13 hydraulic dampers and elasto-plastic devices were conducted The following was found: - Relative displacements of a free deck are very large These can be limited by using isolation devices However, this gives rise to additional forces applied on the piers A straightforward relationship was found between these forces and the maximum displacements By choosing the appropriate isolation device it is thus possible to adjust the bridge response as desired It was, however, also found that, depending on the energy dissipation capacity with respect to the maximum force, the effectiveness of the devices varies - The deformation demand on the pylon was found to be considerably reduced by any of the damping devices Only slight cracking on the legs needs to be expected in that case - Soil deformations are largest for the system with a free deck and smallest for a restrained deck Isolation devices provide an intermediate solution - Generally, a free deck is favourable in terms of deck accelerations A restrained deck experiences very high accelerations and sliding of cars can occur Damping devices can prove to be favourable It was found, however, that sliding of cars does only occur momentarily and further investigations are needed as to what possible consequences are In the light of the framework of performance criteria it can be concluded that by applying deck isolation devices the earthquake behaviour of cable-stayed bridges can be significantly improved An optimum performance with these passive devices can be obtained by balancing the reduction in forces along the bridge against tolerable displacements It was also shown which device properties provide the most efficient solutions Further investigations are necessary to substantiate the results obtained Parametric studies on the soil properties and the input motion were beyond the scope of this work Also, modelling approaches for the foundation and the cables could be improved by enhanced soil-structure interaction modelling and nonlinear cable models respectively Most importantly, it should be noted, that only one particular structure has been studied Since every cable-stayed bridge is an individual structure with respect to all its characteristics, also the effect of changes in geometry should be looked into Not only have these an influence on the basic dynamic properties but also the effectiveness of isolation devices as proven herein could be altered References Page 78 REFERENCES [1] Abdel-Ghaffar, A.M., "Cable-stayed bridges under seismic action", Cable-Stayed Bridges - Recent Developments and Their Future, Ito, M (ed.), Elsevier Science Publishers, 1991, pp 171-192 [2] Abdel-Ghaffar, A.M., M Khalifa, "Importance of Cable Vibration in Dynamics of Cable-Stayed Bridges", Journal of Engineering Mechanics, Vol 117, pp 2571-2589 [3] Abdel-Ghaffar, A.M., S.F Masri, A.-S.M Niazy, "Seismic performance evaluation of suspension bridges", Proceedings of the 10th World Conference on Earthquake Engineering, Madrid, 1992, pp 4845-4850 [4] Abdel-Ghaffar, A.M., A.S Nazmy, "3-D Nonlinear Seismic Behaviour of Cable-Stayed Bridges", Journal of Structural Engineering, Vol 117, pp 3456-3476, 11/1991 [5] Abdel-Ghaffar, A.M., A.S Nazmy, "Nonlinear seismic response of cable-stayed bridges subjected to nonsynchronous support motions", Proceedings of 9th World Conference on Earthquake Engineering, Tokyo-Kyoto, 1988, Vol 6, pp 483-488 [6] Achkire, Y., A Preumont, "Active tendon control of cable-stayed bridges", Earthquake Engineering and Structural Dynamics, Vol 25, pp 585-597, 1996 [7] ADINA System 7.2, 1998, ADINA R&D, Inc., 71 Elton Avenue, Watertown, MA 02472, USA [8] Ali, H.M., A.M Abdel-Ghaffar, "Modelling of Rubber and Lead Passive-Control Bearings for Seismic Analysis", Journal of Structural Engineering, Vol 121, pp 1134-1144, 1995 [9] Ali, H.M., A.M Abdel-Ghaffar, "Modelling the nonlinear seismic behaviour of cable-stayed bridges with passive control bearings", Computers & Structures, Vol 54, No 3, pp 461-492, 1995 [10] Ali, H.M., A.M Abdel-Ghaffar, "Seismic energy dissipation for cable-stayed bridges using passive devices", Earthquake Engineering and Structural Dynamics, Vol 23, pp 877-893, 1994 References Page 79 [11] Alireza, R., G Amin, "An investigation into the effect of earthquake on bridges", Proceedings of the 10th World Conference on Earthquake Engineering, Madrid, 1992, pp 4763-4766 [12] Ambraseys, N.N., J.J Bommer, "Attenuation relations for use in Europe: An overview", "Fifth SECED Conference - European Seismic Design Practice", Elnashai (ed.), Balkema, 1995, pp 67-74 [13] Ambraseys, N.N., J.A Jackson, "Seismicity and strain in the gulf of Corinth (Greece) since 1694, Journal of Earthquake Engineering, Vol 1, No 3, 1997, pp 433-474 [14] Anderson, E., S.A Mahin, "A displacement-based design approach for seismically isolated bridges", Seismic Design Methodologies for the Next Generation of Codes, Fajfar, P., H Krawinkler (eds.), Balkema, 1997, pp 383-394 [15] Aschrafi, M., "Comparative Investigations of Suspension Bridges and Cable-Stayed Bridges for Spans Exceeding 1000m", Long-Span and High-Rise Structures, IABSE Symposium, Kobe, 1998, pp 447452 [16] Betti, R., A.M Abdel-Ghaffar, A.S Niazy, "Kinematic soil-structure interaction for long-span cable-supported bridges", Earthquake Engineering and Structural Dynamics, Vol 22, pp 415-430, 1993 [17] Broderick, B.M., A.S Elnashai, B.A Izzuddin, "Observations on the effect of numerical dissipation on the nonlinear dynamic response of structural systems", Engineering Structures, Vol 16, 1994, pp 51-62 [18] Bruno, D., V Colotti, "Vibration Analysis of Cable-Stayed Bridges", Structural Engineering International, pp 23-28, 1/94 [19] Bruno, D., A Leonardi, "Natural Periods of Long-Span CableStayed Bridges", Journal of Bridge Engineering, Vol 2, 1997, pp 105-115 [20] Caetano, E., Alvaro Cunha, C.A Taylor, "Dynamic analysis of a cable-stayed bridge: Correlation with experimental results on the physical model and on the prototype", Seismic Design Practice into the Next Century, Booth (ed.), Balkema, 1998, pp 363-370 [21] Caetano, E., A Cunha, "Experimental analysis of coupled cabledeck motions in cable-stayed bridges", Proceedings of the 11th world conference on Earthquake Engineering, 1996, Paper No 913 References Page 80 [22] Caetano, E., A Cunha, J Macdonald, C Taylor, "Experimental analysis of the effect of cable vibrations on the dynamic behaviour of two cable-stayed bridges", Proceedings of the 11th European conference on Earthquake Engineering, 1998 [23] "Calibration Seismic Analysis of the Rion-Antirion Bridge", SEQAD Consulting Engineers, San Diego, 1999 [24] Calvi, G.M., "Seismic design of bridges in Europe", Fifth SECED Conference - European Seismic Design Practice, Elnashai (ed.), Balkema, 1995, pp 35-42 [25] Calvi, G.M., A Pavese, "Conceptual design of isolation systems for bridge structures", Journal of Earthquake Engineering, Vol 1, No (1997), pp 193-218 [26] Calvi, G.M., A Pavese, "Displacement based design of building structures", Fifth SECED Conference - European Seismic Design Practice, Elnashai (ed.), Balkema, 1995, pp 127-132 [27] Clough, R.W., J Penzien, "Dynamics of Structures", 2nd edition, McGraw-Hill, 1993 [28] Combault, J., P Morand, "The Exceptional Structure of the Rion Bridge in Greece", Long-Span and High-Rise Structures, IABSE Symposium, Kobe, 1998, pp 495-499 [29] "Community guidelines for the development of the trans-European transport network", Decision No 16, 92/96/EC, European Parliament and the Council, 23 July 1996 [30] Dumanoglu, A.A., J.M.W Brownjohn, R.T Severn, "Seismic analysis of the Fatan Sultan Mehmet (Second Bosporus) suspension bridge, Earthquake Engineering and Structural Dynamics, Vol 21, pp 881-906, 1992 [31] Elassaly M., A Ghali, M.M Elbadry, "Influence of soil conditions on the seismic behabiour of two cable-stayed bridges", Canadian Journal of Civil Enginering, Vol 22, pp 1021-1040, 1995 [32] Elnashai, A.S., "Advanced Finite Element Analysis", Lecture Notes, Imperial College London, 1998 [33] Endo, T., T Iijima, A Okukawa, M Ito, "The technical challenge of a long cable-stayed bridge - Tatara Bridge", Cable-Stayed Bridges Recent Developments and Their Future, Ito, M (ed.), Elsevier Science Publishers, 1991, pp 417-436 References Page 81 [34] Ernst, H.J., "Der E-Modul von Seilen unter Berücksichtigung des Durchhängens", Bauingenieur, Vol 40, 1965, pp 52-55 [35] Fajfar, P., H Krawinkler, "Seismic design methodologies for the next generation of codes", Seismic Design Practice into the Next Century, Booth (ed.), Balkema, 1998, pp 459-466 [36] Fan, L., S Hu, W Yuan, "Nonlinear seismic response analysis of long-span cable-stayed bridge", Proceedings of the 10th World Conference on Earthquake Engineering, Madrid, 1992, pp 48154820 [37] Filiatrault, A., R Tinawi, B Massicotte, "Damage to Cable-Stayed Bridge during 1988 Saguenay Earthquake I: Pseudostatic Analysis", Journal of Structural Engineering, Vol 119, pp 1432-1449, 5/1993 [38] Filiatrault, A., R Tinawi, B Massicotte, "Damage to Cable-Stayed Bridge during 1988 Saguenay Earthquake", Journal of Structural Engineering, Vol 119, pp 1450-1463, 5/1993 [39] Fleming, J.F., E.A.Egeseli, "Dynamic behaviour of a cable-stayed bridge", Earthquake Engineering and Structural Dynamics, Vol 8, pp 1-16, 1980 [40] Fleming, J.F., J.D Zenk, B Wethyavivorn, "Seismic analysis of cable-stayed bridges", Proceedings of the 8th World Conference on Earthquake Engineering, San Francisco, 1984, Vol 5, pp 207-214 [41] Frandsen, J., A McRobie, "Comparison of Numerical and Physical Models for Bridge Deck Aeroelasticity", IABSE Symposium Kobe 1998 [42] Friedland, I.M., M.C Constantinou (ed.), Proceedings of the U.S.Italy Workshop on Seismic Protective Systems for Bridges [43] Fouad, N A.: "Rechnerische Simulation der klimatisch bedingten Temperaturbeanspruchungen von Bauwerken - Anwendung auf Beton-Kastenträgerbrücken und -Sandwichwände", Fraunhofer IRB Verlag, 1998 [44] Ganev, T., F Yamazaki, H Ishizaki, M Kitazawa, "Response analysis of the Higashi-Kobe Bridge and surrounding soil in the 1995 Hyogoken-Nanbu Earthquake", Earthquake Engineering and Structural Dynamics, Vol 27, 1998, pp 557-576 References Page 82 [45] Garevski, M., V Mitrovski, "Dynamic behaviour of cable-stayed bridges", Proceedings of the 8th World Conference on Earthquake Engineering, San Francisco, 1984, Vol 5, pp 199-205 [46] Garevski, M., T Paskalov, "Application of FEM in modelling of cable-stayed bridges", Proceedings of the 8th European Conference on Earthquake Engineering, Lisbon, 1986, Vol 3, pp 6.9/9-6.9/13 [47] Garevski, M.A., R.T Severn, "Damping and response measurement on a small-scale model of a cable-stayed bridge", Earthquake Engineering and Structural Dynamics, Vol 22, pp 13-29, 1993 [48] Garevski, M.A., R.T Severn, "Dynamic analysis of cable stayed bridges by means of 3D analytical and physical modelling", Proceedings of the 10th World Conference on Earthquake Engineering, Madrid, 1992, pp 4809-4814 [49] Gentile, C., F Martinez Y Cabrera, "Dynamic investigation of a repaired cable-stayed bridge", Earthquake Engineering and Structural Dynamics, Vol 26, 1997, pp 41-59 [50] Gimsing, N.J., "Cable supported bridges - concept & design", John Wiley, 2nd edition, 1998 [51] Gregory, I.H., A.H Muhr, "Design of elastic anti-seismic bearings", Fifth SECED Conference - European Seismic Design Practice, Elnashai (ed.), Balkema, 1995, pp 479-486 [52] Gupta, S.P., Kumar, A., "A study on dynamics of cable stayed bridge including foundation interaction", Proceedings of the 8th European Conference on Earthquake Engineering, Lisbon, 1986, Vol 5, pp 8.3/9-8.3/16 [53] Gupta, S., A Kumar, "Dynamic response of cable stayed bridge including foundation interaction effect", Proceedings of 9th World Conference on Earthquake Engineering, Tokyo-Kyoto, 1988, Vol 6, pp 501-506 [54] Hodhod, O., J.C Wilson, "Characteristics of the seismic response of a cable-stayed bridge tower", Proceedings of the 10th European Conference on Earthquake Engineering, Vienna, 1994, Vol 3, pp 2069-2074 [55] Hu, S., W Yuan, L Fan, "Non-linear seismic response analysis of long-span suspension bridge", Proceedings of the 10th European Conference on Earthquake Engineering, Vienna, 1994, pp 20572074 References Page 83 [56] Ito, M., "Design practices of Japanese steel cable-stayed bridges against wind and earthquake effects", Proceedings of the International Conference on Cable-Stayed Bridges, Bangkok, 1987, Vol 1, pp 15-22 [57] Izzuddin, B.A., "Nonlinearities in plain frames", Lecture Notes, Imperial College London, 1998 [58] Karoumi, R., "Response of Cable-Stayed and Suspension Bridges to Moving Vehicles – Analysis methods and practical modeling techniques", Doctoral Thesis, TRITA-BKN Bulletin 44, Department of Structural Engineering, Royal Institute of Technology, Stockholm, 1998 [59] Kawano, K., K Furukawa, "Random seismic response analysis of soil cable-stayed bridge interaction", Proceedings of 9th World Conference on Earthquake Engineering, Tokyo-Kyoto, 1988, Vol 6, pp 495-500 [60] Kawashima, K., S Unjoh, "Damping characteristics of cable stayed bridges", Proceedings of the 10th World Conference on Earthquake Engineering, Madrid, 1992, pp 4803-4808 [61] Kawashima, K., S Unjoh, "Seismic behaviour of cable-stayed bridges", Cable-Stayed Bridges - Recent Developments and Their Future, Ito, M (ed.), Elsevier Science Publishers, 1991, pp 193-212 [62] Kawashima, K., S Unjoh, Y Azuta, "Analysis of Damping Characteristics of a Cable Stayed Bridge Based on Strong Motion Records", Structural Engineering/ Earthquake Engineering (Japan Society of Civil Engineers), Vol 7, No 1, 4/1990, pp 169-178 [63] Kawashima, K., S Unjoh, Y.-I Azuta, "Damping characteristics of cable-stayed bridges", Proceedings of 9th World Conference on Earthquake Engineering, Tokyo-Kyoto, 1988, Vol 6, pp 471-476 [64] Kawashima, K., S Unjoh, M Tunomoto, "Estimation of Damping Ratio of Cable-Stayed Bridges for Seismic Design", Journal of Structural Engineering, Vol 119, pp 1015-1031, 4/1993 [65] Khalil, M.S., "Seismic analysis and design of the skytrain cablestayed bridge", Canadian Journal of Civil Enginering, Vol 23, pp 1241-1248, 1995 References Page 84 [66] Kitazawa, M., K Nishimori, J Noguchi, I Shimoda, "Earthquake resistant design of a long-period cable-stayed bridge", Proceedings of the 10th World Conference on Earthquake Engineering, Madrid, 1992, pp 4797-4802 [67] Konok-Nukulchai, W., P.K.A Yiu, D.M Brotton, "Mathematical Modelling of Cable-Stayed Bridges", Structural Engineering International, Vol 2, 1992, pp 108-113 [68] Loo, Y.-C., G Iseppi, "Nonlinear effects of cable sag - a case study", Proceedings of the International Conference on Cable-Stayed Bridges, Bangkok, 1987, Vol 1, pp 289-303 [69] Lubkowski, Z.A., J.M Tandy, T.F Piepenbrock, M.R Willford, "Non-linear dynamic soil-structure interaction analysis of a deep basement embedded in soft soil", Seismic Design Practice into the Next Century, Booth (ed.), Balkema, 1998, pp 167-174 [70] Makropoulos, K.C., D Diagourtas, "The Corinthian Gulf (Greece) strong-motion databank", Fifth SECED Conference - European Seismic Design Practice, Elnashai (ed.), Balkema, 1995, pp 317-322 [71] Mylonakis, G., A Nikolaou, "Soil-pile-bridge interaction: kinematic and inertial effects Part I: soft soil", Earthquake Engineering and Structural Dynamics, Vol 26, 1997, pp 337-359 [72] Naeim, F., J.M Kelly, "Design of Seismic isolated structures: from theory to practice", John Wiley, 1999 [73] Nazmy, A.S., A.M Abdel-Ghaffar, "Effects of ground motion spatial variability on the response of cable-stayed bridges", Earthquake Engineering and Structural Dynamics, Vol 21, pp 1-20, 1992 [74] Nazmy, A.S., A.M Abdel-Ghaffar, "Non-linear earthquake-response analysis of long-span cable-stayed bridges: theory", Earthquake Engineering and Structural Dynamics, Vol 19, pp 45-62, 1990 [75] Nazmy, A.S., A.M Abdel-Ghaffar, "Non-linear earthquake-response analysis of long-span cable-stayed bridges: applications", Earthquake Engineering and Structural Dynamics, Vol 19, pp 6376, 1990 [76] Nuti, C., "Seismic analysis of isolated bridges", Proceedings of the 10th World Conference on Earthquake Engineering, Madrid, 1992, pp 4893-4896 References Page 85 [77] Officer, P., "Response of Long-Span Cable-Supported Bridges to Seismic Excitation", MSc Thesis, Imperial College, 1998 [78] Pacheco, B.M., Y Fujino, A Sulekh, "Estimation Curve for Modal Damping in Stay Cables with Viscous Damper", Journal of Structural Engineering, Vol 119, pp 1961-1979, 6/1993 [79] Parvez, S.M., M Wieland, "Earthquake behaviour of continous multi-span cable-stayed bridge", Proceedings of 9th World Conference on Earthquake Engineering, Tokyo-Kyoto, 1988, Vol 6, pp 477-482 [80] Priestley, M.J.N., G.M Calvi, "Concepts and procedures for direct displacement-based design", Seismic Design Methodologies for the Next Generation of Codes, Fajfar, P., H Krawinkler (eds.), Balkema, 1997, pp 171-181 [81] Rion-Antirion Bridge, Design drawings and technical documentation [82] Saafan, S.A., "Nonlinear Behaviour of Structural Plane Frames", Proceedings American Society of Civil Engineers, Vol 89, 1963, pp 557-579 [83] Saiidi, M.S., E.M Maragakis, T Isakovic, M Randall, "Performance-based design of seismic restrainers for simplysupported bridges", Seismic Design Methodologies for the Next Generation of Codes, Fajfar, P., H Krawinkler (eds.), Balkema, 1997, pp 395-406 [84] Schemmann, A.G., H.A Smith, "Vibration control of cable-stayed bridges", parts and 2, Earthquake Engineering and Structural Dynamics, Vol 27, 1998, pp 811-824, pp 825-843 [85] Sethia, M.R., P Krishna, A.S Arya, "Model tests of a cable-stayed bridge", Proceedings of the International Conference on CableStayed Bridges, Bangkok, 1987, Vol 2, pp 927-938 [86] Simoes, L.M.C., J.H.I.O Negrao, "Comparison between modal and step-by-step approaches in the optimization of cable-stayed bridges subjected to seismic loads", Proceedings of the 11th world conference on Earthquake Engineering, 1996, Paper No 1881 [87] Troitsky, M.S., "Cable-stayed bridges: theory and design", 2nd edition, 1988 References Page 86 [88] Tuladhar, R., D.M Brotton, "A computer program for non-linear dynamic analysis of cable-stayed bridges under seismic loading", Proceedings of the International Conference on Cable-Stayed Bridges, Bangkok, 1987, Vol 1, pp 315-326 [89] Vaz, C.T., A Rito, R.T Duarte, "Seismic studies of the Arade river cable-stayed bridge", Proceedings of 9th World Conference on Earthquake Engineering, Tokyo-Kyoto, 1988, Vol 6, pp 507-512 [90] Warnitchai, P., Y Jujino, B.M Pacheco, R Agret, "An experimental study on active tendon control of cable-stayed bridges", Earthquake Engineering and Structural Dynamics, Vol 22, pp 93-111, 1993 [91] Webpage of "Öresundkonsortiet", the contractor Öresundproject: www.oeresundkonsortiet.com [92] Wethyavivorn, B., J.F Fleming, "Three dimensional seismic response of a cable-stayed bridge", Proceedings of the International Conference on Cable-Stayed Bridges, Bangkok, 1987, Vol 1, pp 387-398 [93] Wilson, J.C., W Gravelle, "Modelling of a cable-stayed bridge for dynamic analysis", Earthquake Engineering and Structural Dynamics, Vol 20, pp 707-721, 1991 [94] Wilson, J.C., T Liu, W Gravelle, "Ambient vibration and seismic response of a cable-stayed bridge", European Earthquake Engineering, Vol 5, 1991, pp 9-15 [95] Wolf, J.P., "Dynamic Soil-Structure Interaction", 1985, PrenticeHall Publishers [96] Wolf, J.P., "Soil-Structure Interaction Analysis in the Time Domain", 1988, Prentice-Hall Publishers [97] Woo, G., "Long period earthquake risk in Europe", Fifth SECED Conference - European Seismic Design Practice, Elnashai (ed.), Balkema, 1995, pp 59-65 [98] Wyatt, T.A., "The dynamic behaviour of cable-stayed bridges: fundamentals and parametric studies", Cable-Stayed Bridges Recent Developments and Their Future, Ito, M (ed.), Elsevier Science Publishers, 1991, pp 151-170 for the References Page 87 [99] Wyllie, L.A., "Seismic design in California with the new millennium", Seismic Design Practice into the Next Century, Booth (ed.), Balkema, 1998, pp 59-62 [100] Yamanobe, S., T Takeda, T Ichinomiya, A.S Cakmak, "Seismic safety of prestressed concrete cable-stayed bridges", Proceedings of the 10th World Conference on Earthquake Engineering, Madrid, 1992, pp 4821-4826 [101] Yamasaki, Y., T Ikeda, "Cable Supported Bridge under Movement of Foundation due to Earthquake", Long-Span and High-Rise Structures, IABSE Symposium, Kobe, 1998, pp 403-408 [102] Yiu, P.K.A., D.M Brotton, "Mathematical modelling of cable-stayed bridges for computer analysis", Proceedings of the International Conference on Cable-Stayed Bridges, Bangkok, 1987, Vol 1, pp 249-260 [103] Yokoyama M., S Tanaka, M Iwano, "Analytical study on seismic behaviour of cable-stayed concrete bridge", Proceedings of 9th World Conference on Earthquake Engineering, Tokyo-Kyoto, 1988, Vol 6, pp 489-494 [104] Yokoyama, K., S Unjoh, K Tamura, T Moritani, "Earthquake Protective Design for Super-Long-Span Bridges", Long-Span and High-Rise Structures, IABSE Symposium, Kobe, 1998, pp 173-178 [105] Zhang, X.-L., X.-Y Yan, "A method for evaluating earthquake resistant behaviour of bridge", Proceedings of the 10th World Conference on Earthquake Engineering, Madrid, 1992, pp 48274831 [106] Zheng, J., T Takeda, "Effects of soil-structure interaction on seismic response of PC cable-stayed bridge", Soil Dynamics and Earthquake Engineering, Vol 14, pp 427-437, 1995 [107] Zienkiewicz, O.C., R.L Taylor, "The Finite Element Method", 4th edition, Vol 1,2, 1991, Mc Graw Hill