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4.4.4. Connection bearings between towers and decksThe connection of the deck to the towers presents a special challenge to the developmentof the FE model. Generally, two approaches exist to model bridge bearings as discussed inSAP2000 Manual. One approach is to attach elements to separate joints at the samelocation and constrain their degrees of freedom using an “Equal” or “Local Constraint.”The other approach is to attach several elements to a common joint and use frame elementend releases to free the unconnected degrees of freedom. The first approach was adopted inthis study. The pot bearings used between steel girders and pier cap beams at Piers 2 and 3were modeled to allow for the longitudinal translation and free rotation about any axis. Theearthquake lateral restrainers at the center of the floor beam at Piers 1 to 4 were modeled toprovide lateral restraints between the floor beam and the cap beam. Two earthquake shocktransmission devices were installed next to each pot bearing, which will limit thelongitudinal movement in the event of a strong earthquake but leave it nearly free to moveunder slowly varying conditions such as thermal effects. As such, the devices weremodeled in this study as a hinge in the longitudinal direction for seismic analysis. Effectivemodeling of support conditions at bearings and expansion joints requires carefulconsiderations on the continuity of displacement components in horizontal, longitudinal,and vertical directions.4.4.5. Foundations in main and approach spansIn the Bill Emerson Memorial Cable-stayed Bridge, Pier 2 is based on rock. Piers 3 and 4are supported on caissons, which is sufficiently rigid to be modeled as a fixed support.Soil-pile interaction effects can be neglected in the cable-stay span. On the other hand,Piers from 5 to 14 in the Illinois approach are supported on pedestal pile-groupfoundations. Each pier has two columns and each column is supported by 5 round piles of1.83 m (6 ft) in diameter. The length of piles varies from 24.1 m to 30.5 m (79 ft to 100 ft).In the FE model, the soil-pile interaction was simulated by linear dampers and springs invertical, longitudinal, and traffic directions, respectively, as illustrated in Figure 4.3 forsprings. The linear dampers, not shown in the figure, were modeled similarly withLink/Damper elements. The spring and damping coefficients of soils were listed in Table4.4. Their calculations are detailed in Appendix A.TrafficLongitudinalVerticalFigure 4.3Modeling of pile-group foundation for the base of the piers46
Table 4.4Spring and damping coefficient (c in kN.sec/m and k in kN/m) of pile foundationsVertical direction Traffic direction Longitudinal directionNo. k z =(×10 6 )c z =(×10 3 )gk z =(×10 6 )gc z =(×10 7 )k x =(×10 10 )c x =(×10 7 )gk x =(×10 10 )gc x =(×10 8 )k y =(×10 10 )c y =(×10 7 )gk y =(×10 10 )gc y =(×10 8 )Pier 5 1.85 5.20 4.44 1.24 1.84 8.04 3.24 1.42 1.839 8.041 3.648 1.605Pier 6 1.85 5.20 4.44 1.24 1.75 7.72 3.11 1.36 1.751 7.720 3.503 1.532Pier 7 1.85 5.20 4.44 1.24 2.79 12.24 4.92 2.16 2.787 12.244 5.560 2.437Pier 8 1.85 5.20 4.44 1.24 2.99 13.13 5.28 2.32 2.992 13.135 5.954 2.612Pier 9 1.85 5.20 4.44 1.24 2.32 10.19 4.10 1.80 2.320 10.187 4.626 2.029Pier 10 1.85 5.20 4.44 1.24 2.32 10.19 4.10 1.80 2.320 10.187 4.626 2.029Pier 11 1.85 5.20 4.44 1.24 2.50 10.97 4.42 1.94 2.496 10.975 4.977 2.189Pier 12 1.85 5.20 4.44 1.24 2.32 10.19 4.10 1.80 2.320 10.187 4.626 2.029Pier 13 1.85 5.20 4.44 1.24 1.84 8.04 3.24 2.16 2.787 12.244 5.560 2.43747
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 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: Table 4.3Initial property of cables
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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