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Table 5.5Natural frequencies for various degrees of approachinvolvementModeNo.withapproachk=0(kN/m)84×10(kN/m)72×10(kN/m)62×10(kN/m)52×10(kN/m)42×10(kN/m)1 0.339 0.339 0.340 0.340 0.339 0.339 0.3392 0.400 0.398 0.402 0.401 0.401 0.401 0.3993 0.484 0.484 0.485 0.485 0.484 0.484 0.4844 0.573 0.573 0.573 0.573 0.573 0.573 0.5735 0.602 0.602 0.602 0.602 0.602 0.602 0.6026 0.625 0.610 0.615 0.614 0.612 0.610 0.6107 0.658 0.657 0.658 0.658 0.658 0.658 0.6578 0.689 0.688 0.690 0.690 0.690 0.690 0.6899 0.740 0.739 0.740 0.740 0.740 0.740 0.73910 0.828 0.826 0.827 0.827 0.827 0.826 0.82611 0.842 0.827 0.829 0.829 0.829 0.829 0.82812 0.853 0.842 0.842 0.842 0.842 0.842 0.84213 0.878 0.878 0.878 0.878 0.878 0.878 0.87814 0.915 0.908 0.917 0.917 0.917 0.917 0.91215 0.931 0.931 0.931 0.931 0.931 0.931 0.93116 0.935 0.935 0.935 0.935 0.935 0.935 0.93517 0.935 0.935 0.935 0.935 0.935 0.935 0.93518 0.948 0.945 0.947 0.947 0.947 0.947 0.94619 0.954 0.952 0.953 0.953 0.953 0.953 0.95320 0.957 0.954 0.954 0.954 0.954 0.954 0.95421 0.962 0.962 0.962 0.962 0.962 0.962 0.96222 0.964 0.964 0.964 0.964 0.964 0.964 0.96423 0.965 0.965 0.965 0.965 0.965 0.965 0.96524 0.965 0.965 0.965 0.965 0.965 0.965 0.96525 0.965 0.965 0.966 0.966 0.966 0.966 0.96526 0.977 0.977 0.977 0.977 0.977 0.977 0.97727 1.018 1.018 1.018 1.018 1.018 1.018 1.01828 1.018 1.018 1.018 1.018 1.018 1.018 1.01829 1.031 1.031 1.031 1.031 1.031 1.031 1.03130 1.040 1.039 1.040 1.040 1.040 1.040 1.0395.3.4. Influence of pile foundationThree cases are considered to investigate the effect of pile foundations in the approachspans. The first case is to model the support of the piers in the approach spans as springsand dashpots in vertical, longitudinal, and traffic directions. This case is supposed tosimulate the effect of group pile foundations. The second case is to fix the bases of allpiers to restrain motions in all degrees of freedom. The third case is to model the bases ofpiers as hinges. The frequencies obtained for the three cases are listed in Table 5.6. Theyare also compared in Figure 5.38. It is clearly seen from Figure 5.38 that there is basically68
no difference among the three cases as far as the first 30 natural frequencies areconcerned. As explained before, this result is because the first 30 modes mainly involvethe vibration of the main bridge or the cable-stayed span. Therefore, the accuracy offoundation modeling in the approach span is insignificant for the analysis of the cablestayedspan.Table 5.6Natural frequencies for various pile foundation conditions (Hz)Mode No.Springs anddashpotsFixed Hinge1 0.339 0.339 0.3392 0.400 0.400 0.4003 0.484 0.485 0.4854 0.573 0.573 0.5735 0.602 0.602 0.6026 0.625 0.629 0.6267 0.658 0.658 0.6588 0.689 0.690 0.6909 0.740 0.740 0.74010 0.828 0.829 0.82811 0.842 0.842 0.84212 0.853 0.864 0.85513 0.878 0.878 0.87814 0.915 0.916 0.91415 0.931 0.931 0.93216 0.935 0.935 0.93517 0.935 0.935 0.93518 0.948 0.949 0.94819 0.954 0.955 0.95520 0.957 0.959 0.95721 0.962 0.962 0.96222 0.964 0.964 0.96423 0.965 0.965 0.96524 0.965 0.965 0.96525 0.965 0.966 0.96626 0.977 0.978 0.97827 1.018 1.018 1.01828 1.018 1.018 1.01829 1.031 1.032 1.03230 1.040 1.040 1.04069
Page 1 and 2:
Organizational Results Research Rep
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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 and 58: Since the cable stays are connected
Page 59 and 60: Table 4.3Initial property of cables
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: 1.1Frequency(Hz)0.90.70.5Plus 0Plus
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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