Assessment of the Bill Emerson Memorial Bridge - FTP Directory ...

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Figure A.5 α A as a function of pile length and spacing (Poulos, 1968)Figure A.6 Graphical solution of α L for horizontal vibration (Poulus, 1972)104
For a group of piles with identical geometry, the group interaction factor isa summation of those factors from individual piles. Note that the group interactionfactor in horizontal x-direction and y-direction may be different, depending on thenumber and the spacing of piles in each direction.A.3 Group stiffness and damping factorsFigure A.4 shows schematically the plan and cross sections of an arbitrarypile group foundation. This figure will be used to explain and obtain the stiffnessand damping factors of a group of piles in all directions. For vertical vibration, thegroup stiffness (k g ) and damping factors (c g ) can be expressed intozz∑ k ∑ cc gzk gzz = ,z = (α A∑∑α AFor torsional vibration, the group stiffness (k gψ ) and damping factors (c gψ )can be evaluated by= [ k + k ( )]1k g 2 2ψ ψ xx r+ yr∑αA2, c ψ= [cψ+ c x( x r+ y 2∑α Ag 1r)]A.6)(A.7)For translational modes, the group stiffness and damping coefficientsalong x axis (kx g, cx g ) and along y axis (ky g, cy g ) can be determined by∑ k ∑ c ∑ c gxk ∑x = k g yck gxy = c g yx = , , ,y = (A.8)∑α Lx ∑α Lx ∑α LA ∑α LyFor rocking vibration about y axis and about x axis, the stiffness anddamping coefficients (kφ g, cφ g ) and (kθ g, cθ g ) can be respectively evaluated byk k 2 2g zxrk xz c2z ckk = + + − φ x φc c x 2 2g φ z rc xz c2z cc xφ, c+ + −∑α = φ(A.9)φLx∑α Lx2 2k kg θ zyrk yz c2z ckk+ + − 2 2=yθc + c +g θ zyrc xz c−2z ccθ, c∑α = yθ(A.10)θLy∑α LyFor the coupled vibration between translational mode along x axis androtational mode about y axis, the group stiffness and damping coefficients (kxφ g,cxφ g ) can be evaluated by1k g = 1xφ ∑ ( k xφ− k xzc), c gαLxxφ = ∑ ( )α Lxc xφ− c xz c(A.11)Similarly, the group stiffness and damping coefficients for the coupled vibrationbetween translational mode along y axis and rotation al mode about x axis, (kyθ g,cyθ g ), can be expressed into11k g yθ= ∑ ( k yθ− k yzc), c g yθ= ∑ (c yθ− c yzααLyLyc)(A.12)105
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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
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Polyreference Complex Exponential (
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are evaluated and presented in Figu
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0.353.50.330.252.5Amplitude0.20.15A
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1 x 10-4 Frequency(Hz)Amplitude0.90
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Amplitude0.20.180.160.140.120.10.08
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Amplitude0.20.180.160.140.120.10.08
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1.20.80.400 100 200 300 400 500 600
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4. Finite Element Modeling of Bill
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Since the cable stays are connected
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Table 4.3Initial property of cables
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Table 4.4Spring and damping coeffic
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(a) View of the entire bridge(b) Vi
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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
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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: A.2 Group Interaction FactorThe cro
Page 121: Missouri Department of Transportati
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