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Opsahl Steigen,Ragnhild.Pdf University of Stavanger Faculty of Science and Technology MASTER'S THESIS Study program/ Specialization: Spring semester, 2011 Master's Degree Program in Mechanical and Structural Engineering - Civil Engineering Open Writer: Ragnhild Opsahl Steigen ~.tJ.hiM..O.f.&J!J~-~-- ... (Y{riter's signature) F acuity supervisor: Jasna Bogunovic Jakobsen External supervisor: Roger Guldvik Ebeltoft Title of thesis: Modeling and analyzing a suspension bridge in light of deterioration of the main cable wires Credits (ECTS): 30 Keywords: Pages: ..... 9.9 ......... Suspension bridge Steel bridge + enclosure: ..1.0 1.. Eigen value analysis Structural engineering Stavanger, JJ(h.~~.(f. ... Date/year Modeling and analyzing a suspension bridge in light of deterioration of the main cable wires Ragnhild Opsahl Steigen Master thesis in structural and material engineering University of Stavanger, spring 2011 Preface The master thesis is the final part of my Master degree in structural and material science at the University of Stavanger. The thesis consists of collecting and studying data for Lysefjord Bridge in light of the deterioration of the main cables, and to carry out some analysis for the bridge. Data is given from The Norwegian Public Roads Administration (Statens Vegvesen). The data is used to make a finite element model (FEM) of the bridge in ABAQUS. The model is analyzed with emphasis on eigen frequencies and mode shapes. A brief analysis of the bridge behavior during wind loading is also carried out. The wire fractures observed in the main cables are summarized and analyzed with respect to the weather conditions in the area in a period with many wire fractures. Data on the weather in the area is given from Lysefjord Weather Station, that was contacted during the work with this thesis. The thesis consists of; • a presentation of the static and dynamic characteristics of a suspension bridge • a summary of the wire fractures in the main cables on Lysefjord Bridge • a weather analysis for periods with many wire fractures • the modeling of a finite element model in ABAQUS • an eigen value analysis and a brief wind analysis of the finite element model in ABAQUS • a verification of the finite element model in ABAQUS by theoretical calculations Thanks to the thesis supervisor at University of Stavanger, Jasna Bogunovic Jakobsen, and to Ove Mikkelsen for help with building the finite element model in ABAQUS. I also want to thank Roger Guldvik Ebeltoft in The Norwegian Public Roads Administration for information around the problem, and Per Slyngstad, also in The Norwegian Public Roads Administration, for results of the bridge model and analysis in Alvsat, and for the information used to build the model of the bridge in ABAQUS. Thanks also to Ole Tom Guse in Lysefjord Weather station for data on the weather near Lysefjord Bridge. ii Contents 1 Introduction 2 2 Suspension bridges 4 2.1 Stiffening girder . 5 2.2 Main cables . 6 2.3 Hanger cables . 7 2.4 Towers . 7 2.5 Anchor piers . 7 3 Fracture of wires in the main cables 9 3.1 The main cables . 9 3.2 Possible reasons for wire fractures . 10 3.3 SoundPrint® acoustic monitoring . 12 3.4 Wire fractures detected visually . 13 3.5 Monitored wire fractures . 15 3.6 Weather around Lysefjord Bridge . 16 3.7 Maintenance and replacement of cables . 18 3.8 Wire fractures in similar bridges . 19 4 Finite element model of Lysefjord Bridge 22 4.1 ABAQUS software . 22 4.2 ABAQUS model . 23 4.2.1 Definition of directions . 23 4.2.2 Elements . 23 4.2.3 Geometry . 29 4.2.4 Conditions . 30 4.2.5 Stiffness properties . 31 4.2.6 Other parameters . 31 5 Applying load in the finite element model 32 5.1 Mass . 32 5.2 Modeling of mass . 33 5.3 Analysis of characteristic dead load . 35 5.4 Wind . 36 5.4.1 Static wind loading . 36 5.4.2 Mean wind speed . 38 5.4.3 Simulated wind load in ABAQUS . 39 5.4.4 Dynamic wind loading . 40 5.4.5 Non-linear geometric effects . 42 iii 5.5 Other loads . 42 5.5.1 Earthquake . 42 5.5.2 Traffic . 43 6 Results from the analysis in ABAQUS 44 6.1 General . 44 6.2 Eigenfrequencies and eigenmodes . 45 6.2.1 Eigenfrequencies . 45 6.2.2 Comparison of the eigenfrequencies in Alvsat and ABAQUS . 46 6.2.3 Comparison of the eigenmodes in Alvsat and ABAQUS . 47 6.2.4 Horizontal displacement of the cables . 55 6.2.5 Coupling of the directions . 57 6.3 Displacement due to dead load . 64 6.4 Displacement due to wind load . 64 6.5 Stress due to dead load and wind load . 66 7 Validation of eigenfrequencies and vibration modes 68 7.1 Vertical eigenfrequencies and modes . 68 7.1.1 Vertical asymmetric modes . 69 7.1.2 Vertical symmetric modes . 71 7.2 Torsion eigenfrequencies and modes . 73 7.2.1 Torsion symmetric modes . 73 7.2.2 Torsion asymmetric modes . 75 7.3 Eigenfrequencies from calculations . 76 8 Conclusion 78 9 Further recommendations 80 Appendices A Figures B Calculations C ABAQUS List of Figures 2.1 The main components of a suspension bridge shown on Lysefjord Bridge [7] 4 2.2 Akashi Kaikyo Bridge is the world’s longest suspension bridge [6] . 5 2.3 The cross section of the bridge girder in Lysefjord Bridge [7] . 6 3.1 The cross section of the main cable in Lysefjord Bridge [7] . 9 3.2 The surface defects detected on one examined Z-wire from Lysefjord Bridge [28] . 11 3.3 The fracture surface of one examined Z-wire from Lysefjord Bridge [28] . 12 3.4 Amount of fractures in each of the twelve cables from the opening of the bridge Dec. 1997 to Oct. 2010 . 14 3.5 Cable arrangement in Lysefjord Bridge . 14 3.6 Accumulated wire fractures from the opening of the bridge Dec. 1997 to Oct. 2010 . 15 3.7 Amount of wire fractures recorded by Advitam Oct. 09 to Mar. 11 [2] . 16 3.8 Daily fractures during the period from Oct. to Jan. 2009 and 2010 [2] . 17 3.9 Lysefjord weather station is stationed in Forsand [11] . 18 3.10 Amount of wire fractures, average temperature and maximum mean wind speed recorded Dec. 2009 . 20 3.11 Amount of wire fractures, average temperature and maximum mean wind speed recorded Dec. 2010 . 21 4.1 Real and fictive directions of the bridge [7] . 23 4.2 System of coordinates in ABAQUS . 24 4.3 General ABAQUS model of the bridge girder . 24 4.4 Bridge girder with dimensions . 25 4.5 Directions in the model, seen from south . 25 4.6 Dummy nodes to link the hangers to the bridge girder in ABAQUS . 26 4.7 The shape of the bridge girder when dead load is applied . 26 4.8 The shape of the main cables when the dead load is applied . 27 4.9 The hangers in the ABAQUS model . 28 5.1 Modeling of mass of bridge girder in ABAQUS . 33 5.2 Fictive points to attach m1 = 1454 kg/m under NA in ABAQUS . 34 5.3 The model of the bridge with dead load applied . 35 5.4 Positive directions for the forces, and the orientation of the wind. 37 5.5 Dummy elements to simulate wind on the bridge girder in ABAQUS . 40 5.6 Vortex shedding around the bridge girder [16] . 41 6.1 Horizontal symmetric modes . 49 6.2 Horizontal asymmetric modes . 50 v 6.3 Vertical symmetric modes . 51 6.4 Vertical asymmetric modes . 52 6.5 Torsional symmetric modes . 53 6.6 Torsional asymmetric modes . 54 6.7 Horizontal symmetric modes, displacement in girder and cables . 55 6.8 Horizontal asymmetric modes, displacement in girder and cables . 56 6.9 Horizontal symmetric mode, coupled . 58 6.10 Horizontal asymmetric mode, coupled . 59 6.11 Vertical symmetric mode, coupled . 60 6.12 Vertical asymmetric mode, coupled . 61 6.13 Torsional symmetric mode, coupled . 62 6.14 Torsional asymmetric mode, coupled . 63 6.15 The directions of the wind loading on the bridge girder . 64 6.16 Displacement of the bridge girder when the loading from a mean wind speed of 38 m/s is applied, where H, V and T is horizontal, vertical and torsion respectively . 65 6.17 The displacement of the bridge girder due to a mean wind in the cen- ter(node 19 at L/2) . 67 6.18 Stress in the cables near the towers when dead load and wind load is applied 67 7.1 First and second vertical asymmetric modes from the analytical calculations 70 7.2 First and second vertical asymmetric modes from ABAQUS and Alvsat . 71 7.3 First and second vertical symmetric modes from the analytical calculations 72 7.4 First and second vertical symmetric modes from ABAQUS and Alvsat . 73 7.5 First and second torsion symmetric modes from the analytical calculations 75 7.6 First and second torsion symmetric modes from ABAQUS and Alvsat . 75 7.7 First and second torsion asymmetric modes from the analytical calculations 76 7.8 First and second torsion asymmetric modes from ABAQUS and Alvsat . 76 List of Tables 4.1 Stiffness properties for Lysefjord Bridge . 31 5.1 Mass of Lysefjord Bridge . ..
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