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Figure 5.31 30 th mode shape (1.040 Hz)thFigure 5.32 115 mode shape (1.237 Hz)thFigure 5.33 568 mode shape (3.187 Hz)thFigure 5.34 759 mode shape (3.862 Hz)thFigure 5.35 1969 mode shape (8.853 Hz)62
When the bridge deck moves up and down, the towers are being slightly bent in thelongitudinal direction. This result explains the RY value of 0.5% in the first mode.Indeed, the first mode represents the coupled vibration between UZ and UX. While nomovement occurs in the transverse direction, Figure 5.3 shows the second mode ofvibration in longitudinal and vertical directions at a frequency of 0.400 Hz. The shapes ofthe 3 rd and 4 th modes are shown in Figure 5.4 and Figure 5.5 and mainly correspond totorsional motion. The shapes of 5 th mode and 7 th to 10 th modes primarily correspond tovertical motion while Mode 6 mainly corresponds to longitudinal motion. These modesare mainly related to the motion of the main span. After the 11 th mode, more and morecables begin to participate in the motion. The 115 th or higher modes of vibration involvethe mass of the approach spans of the bridge, which can be clearly seen in Figures 5.32 -5.34. This is because the elements in the approach part of the bridge are stiffer and moredifficult to be triggered. At even higher frequencies (e.g. 8.853 Hz), two towers begin toexperience significant motion.5.3. Parametric studyDifferent choices of structural and material properties may significantly affect thebehaviors of the FE bridge model. To ensure the FE model of the cable-stayed bridge isrobust and reliable, various parameters are perturbed to understand the sensitivity of themodel. These parameters include the presence of the approach spans, the soil propertiesaround pile foundation, the boundary condition, and the mass density of concrete. Aspointed out in Section 5.2.2, the cable-stayed main span of the bridge is much moreflexible than the Illinois approach spans. Therefore, only the first 30 modes of vibrationare considered in this section to expedite the analysis process.5.3.1. Boundary conditionThe boundary conditions (BC) of an actual bridge are often complicated. Usually theyare idealized as fixed, hinged or roller supports in the analysis models (Hu et al., 2006).For external or end bearings, various simplifications have been made in the past. Forexample, Ren et al. (2005) used fixed bearings in one pier and expansion bearings in theremaining ones. Hu et al. (2006) treated bridge towers as being fixed at their base in alldegrees of freedom. In the present study, four combinations of four boundary conditionsare considered for four piers of the main span, as described in Table 5.2.Table 5.2Boundary conditions for the FE analysis modelBC Case Pier1 Pier2 Pier3 Pier41 Fixed Fixed Fixed Fixed2 Hinge Fixed Hinge Hinge3 Expansion Fixed Expansion Expansion4 Hinge Hinge Hinge HingeIn order to make the FE model more manageable, in Case 2 and 4, the rotation motionaround the traffic direction is also restrained. For the different cases, the calculatedfrequencies are listed in Table 5.3. It can be seen that boundary conditions do have63
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
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8. All cables behave elastically un
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Table of ContentsExecutive summary.
Page 11 and 12:
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
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: Figure 5.27 26 th mode shape (0.977
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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