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0.60.40.20-0.20 100 200 300 400 500 600 700-0.4-0.6-0.8-1-1.2Location along the bridge(m)rdFigure 3.37 3 measured mode shape of the Bill Emerson Memorial Bridge3.7. RemarksThe following remarks can be made from the analysis of the ground motions andstructural responses at the Bill Emerson Memorial Cable-stayed Bridges:1. The real-time seismic monitoring system provides engineering data that can beeffectively used toward understanding of the dynamic behavior of the cable-stayedbridge.2. The peak-picking method in frequency domain can be conveniently applied toanalyze a huge set of field measured data.3. The modal parameters such as natural frequencies and mode shapes can beeffectively extracted from the field measured data of the bridge based on the peakpickingmethod.40
4. Finite Element Modeling of Bill Emerson MemorialCable-stayed Bridge4.1. GeneralDue to rapid developments in computational mechanics, FE modeling has become one ofthe most powerful tools used in the analysis and design of large-scale bridges. A FE modelcan be the convenient and accurate idealization of a complicated structure in civilengineering. In order to successfully establish a bridge FE model, assumptions must bemade to simplify the process of modeling. Additionally, due to structures’ complexity,uncertainty may exist in material and geometric properties. Therefore, the calculatedresults from a FE model must be properly verified by various means, particularly with fieldmeasurements.In cable-stayed bridges, there exist two types of nonlinearity: geometrical and material.Geometrical nonlinearity is an important feature under operational loads (Guido, 1999; Huet al., 2006). Depending on design specifications and construction process, a cable-stayedbridge model may have to be analyzed to determine its deflected position under dead loads.Geometrical nonlinearity is associated with:♦ The sagging effect of inclined stay cables which governs the axial elongation;♦ The effect of relatively large deflections of the whole structure due to itsflexibility;♦ The action of compressive loads in the slab and in the towers.On the other hand, Ren and Makoto (1999) studied the elastic-plastic seismic behavior oflong span cable-stayed steel bridges and concluded that geometric nonlinearity had littleinfluences on the seismic response behavior of the example bridge. Nevertheless, thesagging effect of stay cables is herein taken into account in the FE model of the BillEmerson Memorial Cable-stayed Bridge.As one of the most powerful engineering design and analysis software, SAP2000 is chosento model and analyze the Bill Emerson Memorial Cable-stayed Bridge. This software hascapability of modeling pre-stressed cables for their sagging effect and of simulating pilefoundations. In this report, a 3-D numerical model of the Bill Emerson Memorial CablestayedBridge is established using the SAP2000 version 10 software.4.2. Bridge geometryThe geometry of the cable-stayed bridge was modeled according to the as-built drawings:Steel Cable-Stayed Main Span Unit (SCMS) or Approach Spans (AS) Cape GirardeauCounty, Missouri to Alexander County, Illinois, with necessary updated modifications inconsultation with the Missouri Department of Transportation. The key dimensions andgeometry of bridge members were extracted from the plans as detailed in Table 4.1.41
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: 1.20.80.400 100 200 300 400 500 600
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 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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