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6. Time History Analysis and Structural Assessmentof the Cable-stayed Bridge6.1 GeneralIn this section, the validated FE model of the cable-stayed bridge is analyzed tounderstand the seismic behavior under various excitations, and to assess the structuralconditions of the main components of the bridge. Both ground motions from elsewhereand rock motions at the bridge site will be used as inputs for time history analysis. Thestructural assessment will be focused on towers and cables.6.2 Time history analysisThe New Madrid Seismic Zone (NMSZ) is the location of three over 8.0M earthquakesthat took place in 1811–1812. Since then, minor and moderate earthquakes continue tooccur. Even in the past two years, a few earthquakes had amplitudes higher than 4.0. At12:37:32 (UTC) on Sunday, May 1, 2005, an earthquake of magnitude 4.1 on the Richterscale occurred in Manila, Arkansas. The rock motions recorded at the base of bridgetowers are valuable and represent the regional geologic and seismic conditions.To evaluate the effect of ground motions on the seismic behavior of the cable-stayedbride, three typical earthquake waves such as EI Centro (1940), Pacoima (1971), andMexico (1985) were considered in the following analysis in addition to the D1 records atthe bridge site. As shown in Table 6.1, the three events cover weak, moderate, and strongearthquakes with their vertical peak ground acceleration (PGA) ranging from 0.171 to1.170g. The dominant frequency, f g , and the frequency bandwidth, represented byξ g(Wang and Chen, 2007), of the ground motions are also in wide ranges. The timehistory of the three earthquake records in the vertical direction along with their Fouriertransform spectra are depicted in Figures 6.1 to 6.3. The three component rockaccelerations recorded at Station D1 during the May 1, 2005, earthquake are shown inFigures 6.4 to 6.6 along vertical, transverse and longitudinal directions, respectively.Table 6.1Earthquake records (vertical component shown)Case Earthquake Year PGA(g) f (Hz)g1 Mexico City (MC) 1985 0.171 0.49 0.102 El Centro (EC) 1940 0.348 1.75 0.163 Pacoima (PA) 1971 1.170 2.49 0.42ξg78
(a) Vertical acceleration time history(b) FFTFigure 6.1 Mexico City Earthquake ground motion(a) Vertical acceleration time history(b) FFTFigure 6.2 El Centro Earthquake ground motion(a) Vertical acceleration time history(b) FFTFigure 6.3 Pacoima Earthquake ground motion79
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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
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Figure 2.8Directory chooser2.2.6. S
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3.2. Seismic instrumentation networ
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The main bridge from Bent 1 to Pier
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(a) South side of deck at support o
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(a) North side of deck at middle of
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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 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: differences is that the exact locat
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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