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(a) Isotropic view(b) Plan view4.4.3. CablesFigure 4.2Modeling of girdersThe vibration of cables plays an important role in the overall response of cable-stayedbridges (Abdel-Ghaffar and Khalifa, 1991; Ali and Abdel-Ghaffer 1995; and Ito, 1987).Therefore, appropriate modeling of cables is quite necessary. Ali and Abdel-Ghaffer(1995) also found that the natural frequencies of cables strongly depend on the sag of thecables. Cables are constructed of strands that are made of high strength steel wires. Threetypes of strand configurations are commercially available. They are: (a) helically-woundstrand, (b) parallel wire strand, and (c) locked coil strand.In the Bill Emerson Memorial Cable-stayed Bridge, each cable consists of 19~54 strands,each 15.7 mm in diameter. Parallel to each other, these strands are placed inside apolyethylene pipe, grouted and then sealed to form a single cable. In this bridge, there are atotal of 128 cables in the main span. In the FE model, these cables were simulated byFrame/Cable element, assuming the contribution of every internal wire inside the cable.The modeling of cables is a difficult task because nonlinearities arise from the sagging ofcables. The stiffness, therefore, changes with the applied load. Each cable element wasrestrained in compression to prevent any compression deformation and to simulate itspractical condition on the actual bridge. Since each cable is attached at one end to the topflange of one composite steel girder and at the other end to the work point of the tower,both attachment points are away from the neutral axes of their respective supportingstructural elements (deck and tower). Therefore, two rigid links were introduced to connectthe cable to the neutral axis of the deck and the tower, respectively. The use of rigid linksensures that the theoretical lengths, horizontal angles, and the maximum sag of the cablesare exactly the same as designed. The dimensions and section properties of all cables aregiven in Table 4.3. The cable number can be seen in Figure 4.4.44
Table 4.3Initial property of cablesCableNo.Diameter(m)Area (m 2 )Tension I(KN)Tension J(KN)Max Sag(m)Length (m)1 0.1014 0.00808 7837.90 7983.60 0.778 158.862 0.1014 0.00808 8233.26 8375.67 0.703 154.843 0.0976 0.00749 7742.66 7876.65 0.683 150.844 0.0926 0.00674 5514.69 5614.38 0.692 147.025 0.0905 0.00644 5409.74 5504.57 0.651 143.026 0.0884 0.00614 4920.66 5009.63 0.595 132.867 0.0840 0.00554 5337.23 5418.88 0.443 122.688 0.0840 0.00554 5058.98 5137.07 0.389 112.779 0.0817 0.00524 3649.84 3710.51 0.360 103.1110 0.0769 0.00464 3851.38 3904.72 0.255 93.4911 0.0769 0.00464 3672.04 3722.04 0.210 84.2512 0.0756 0.00449 3118.39 3163.43 0.185 75.4513 0.0717 0.00404 2459.85 2495.78 0.153 66.9514 0.0662 0.00345 1829.71 1858.27 0.133 58.9615 0.0632 0.00314 1189.74 1211.57 0.127 51.7716 0.0602 0.00285 1209.04 1223.27 0.066 44.2517 0.0602 0.00285 1110.97 1125.04 0.070 43.5718 0.0632 0.00314 1361.75 1383.21 0.107 50.4719 0.0662 0.00345 1783.06 1810.92 0.130 57.2120 0.0676 0.00359 1965.90 1998.42 0.171 64.8521 0.0744 0.00434 2927.96 2970.52 0.185 73.0622 0.0756 0.00449 3395.19 3441.46 0.212 81.6623 0.0769 0.00464 3935.02 3985.24 0.240 90.7124 0.0805 0.00509 3973.45 4028.74 0.311 100.1725 0.0840 0.00554 5252.55 5324.99 0.361 109.7426 0.0840 0.00554 5228.18 5303.43 0.437 119.6027 0.0894 0.00628 5094.98 5177.92 0.567 129.6828 0.0916 0.00659 5121.93 5209.80 0.678 139.8229 0.0926 0.00674 5543.83 5635.09 0.732 150.0030 0.0966 0.00734 7709.35 7832.12 0.791 160.1031 0.1015 0.00808 8558.47 8690.27 0.848 170.4332 0.1015 0.00808 7482.38 7617.77 1.095 180.9445
Page 1 and 2:
Organizational Results Research Rep
Page 3 and 4:
TECHNICAL REPORT DOCUMENTATION PAGE
Page 5 and 6:
Executive SummaryOpen to traffic on
Page 7 and 8: 8. All cables behave elastically un
Page 9 and 10: Table of ContentsExecutive summary.
Page 11 and 12: List of Figure CaptionsFigure 1.1 A
Page 13 and 14: Figure 5.30 29 th mode shape (1.032
Page 15 and 16: 1. Introduction1.1. GeneralCable-st
Page 17 and 18: Figure 1.1Artist rendering of the B
Page 19 and 20: Expansionand lateralearthquakerestr
Page 21 and 22: 3. Evaluate the model by conducting
Page 23 and 24: 2. Automatic Retrieval of Peak Acce
Page 25 and 26: 2.2.3. Map/Find stationsClicking th
Page 27 and 28: 2.2.5. Displaying seismogramsTo dis
Page 29 and 30: Figure 2.8Directory chooser2.2.6. S
Page 31 and 32: 3.2. Seismic instrumentation networ
Page 33 and 34: The main bridge from Bent 1 to Pier
Page 35 and 36: (a) South side of deck at support o
Page 37 and 38: (a) North side of deck at middle of
Page 39 and 40: The seismic responses at the top (T
Page 41 and 42: Polyreference Complex Exponential (
Page 43 and 44: are evaluated and presented in Figu
Page 45 and 46: 0.353.50.330.252.5Amplitude0.20.15A
Page 47 and 48: 1 x 10-4 Frequency(Hz)Amplitude0.90
Page 49 and 50: Amplitude0.20.180.160.140.120.10.08
Page 51 and 52: Amplitude0.20.180.160.140.120.10.08
Page 53 and 54: 1.20.80.400 100 200 300 400 500 600
Page 55 and 56: 4. Finite Element Modeling of Bill
Page 57: Since the cable stays are connected
Page 61 and 62: Table 4.4Spring and damping coeffic
Page 63 and 64: (a) View of the entire bridge(b) Vi
Page 65 and 66: 4.6. RemarksA detailed 3-D FE model
Page 67 and 68: knω = (5.4)nm nSimilarly, when dam
Page 69 and 70: mainly corresponds to the vertical
Page 71 and 72: thFigure 5.10 9 mode shape (0.740Hz
Page 73 and 74: thFigure 5.19 18 mode shape (0.947H
Page 75 and 76: Figure 5.27 26 th mode shape (0.977
Page 77 and 78: When the bridge deck moves up and d
Page 79 and 80: 1.1Frequency (Hz)0.90.70.5BC Case 1
Page 81 and 82: 1.1Frequency(Hz)0.90.70.5Plus 0Plus
Page 83 and 84: no difference among the three cases
Page 85 and 86: The FE model of the bridge was vali
Page 87 and 88: 10.6TestFE model0.2-0.20 100 200 30
Page 89 and 90: 1.20.80.40-0.4TestFE model0 100 200
Page 91 and 92: differences is that the exact locat
Page 93 and 94: (a) Vertical acceleration time hist
Page 95 and 96: The FE model of the cable-stayed br
Page 97 and 98: Displacement (m)0.30.20.10-0.1-0.2X
Page 99 and 100: Station D1 (before amplification) a
Page 101 and 102: ending of the tower as shown in Fig
Page 103 and 104: symmetric about the centerline of t
Page 105 and 106: Tensile stress (MPa)800750700650600
Page 107 and 108: 7. Conclusions and RecommendationsB
Page 109 and 110:
The vast arrays of acceleration dat
Page 111 and 112:
14. Cunha A, Caetano and Delgado T.
Page 113 and 114:
42. Song, W., Giraldo, D.F., Clayto
Page 115 and 116:
Figure A.2 Vertical stiffness and d
Page 117 and 118:
A.2 Group Interaction FactorThe cro
Page 119 and 120:
For a group of piles with identical
Page 121:
Missouri Department of Transportati
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