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Table 5.4ModeNo.Natural frequencies for different additional mass density (Hz)Change of relative mass density in bridge deck0 +5.0% +6.7% +10.0%1 0.348 0.341 0.339 0.3252 0.411 0.403 0.400 0.3903 0.497 0.488 0.484 0.4754 0.588 0.577 0.573 0.5575 0.619 0.606 0.602 0.5826 0.642 0.629 0.625 0.5847 0.676 0.662 0.658 0.6338 0.709 0.694 0.689 0.6669 0.761 0.745 0.740 0.72310 0.852 0.834 0.828 0.80611 0.864 0.847 0.842 0.82312 0.873 0.858 0.853 0.82713 0.894 0.882 0.878 0.84314 0.937 0.921 0.915 0.86915 0.937 0.936 0.931 0.90716 0.940 0.936 0.935 0.91517 0.955 0.937 0.935 0.93418 0.959 0.955 0.948 0.93419 0.965 0.957 0.954 0.93720 0.965 0.961 0.957 0.95321 0.965 0.963 0.962 0.95722 0.965 0.964 0.964 0.96023 0.967 0.965 0.965 0.96424 0.975 0.965 0.965 0.96525 0.982 0.966 0.965 0.96526 1.002 0.983 0.977 0.96727 1.025 1.020 1.018 0.98828 1.025 1.020 1.018 1.01429 1.057 1.038 1.031 1.01430 1.068 1.047 1.040 1.01566
1.1Frequency(Hz)0.90.70.5Plus 0Plus 5%Plus 6.7%Plus 10%0.30 5 10 15 20 25 30ModeFigure 5.37 Frequency variation with different mass densities5.3.3. Presence of the approach span of the bridgeIn the FE modeling of the cable stayed bridge, the presence of the approach span caninfluence the dynamic properties of the cable-stayed main span. Since all piers in theapproach span are shorter, the approach structure has higher stiffness and thus is moredifficult to be excited under dynamic loadings. In this section, seven cases are studied. InCase 1, the approach spans are included in the cable-stayed span model. In Case 2, theapproach spans are neglected completely or k=0 in Table 5.5. The remaining cases alsoneglect the approach spans. However, the effect of the approach spans is approximatedby eight linear springs at the end of the Illinois side span. The coefficient of the springs(k) varies from 2×10 4 kN/m (1.372×10 3 kip/ft) to 4×10 8 kN/m (2.744×10 7 kip/ft). Thefirst 30 frequencies obtained from the FE model are listed in Table 5.5. It can be foundthat there is only a slight variation among various cases, indicating that the main bridgealmost vibrates independently of the approach spans. This is because the first 30 modesare closely related to the motion of the main bridge. The approach spans are seldominvolved in the motion of the bridge system within this frequency range.67
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Organizational Results Research Rep
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TECHNICAL REPORT DOCUMENTATION PAGE
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Executive SummaryOpen to traffic on
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8. All cables behave elastically un
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Table of ContentsExecutive summary.
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List of Figure CaptionsFigure 1.1 A
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Figure 5.30 29 th mode shape (1.032
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1. Introduction1.1. GeneralCable-st
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Figure 1.1Artist rendering of the B
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Expansionand lateralearthquakerestr
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3. Evaluate the model by conducting
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2. Automatic Retrieval of Peak Acce
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2.2.3. Map/Find stationsClicking th
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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: 1.1Frequency (Hz)0.90.70.5BC Case 1
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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