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

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For a round pile, the translational parameters along x and y axis areidentical. In the case of a sliding mode along x direction, the stiffness anddamping coefficients (k x , c x ) can be evaluated by⎡E pIp ⎤kx= ⎢ ⎥fr ,3 x 1⎣ o ⎦⎡E pI p ⎤c x= ⎢ fr 2 ⎥⎣ oVs ⎦x 2(A.3)Similarly, the formulations for both rocking modes about φ and θ areidentical. In the case of a rocking mode about φ, the coefficients (k φ , c φ ) can bedetermined by⎡EI⎤k = p pφ ⎢ ⎥ fr ,⎣2 ⎦φ1 o⎡ EIpc =p⎤φ ⎢ rV2 ⎥ f (A.4)φ 2The translational motion along x (or y) axis and the rocking motion about y(or x) is inherently coupled in one plane as shown in Figure A.1. These couplingsare denoted as xφ (or yθ). In the case of coupling mode between translation xand rotation φ, the stiffness and damping of (k xφ , c xφ ) can be evaluated by⎡EIpk = xφ ⎢⎣ r 2op⎤⎥ f⎦xθ1⎣ os ⎦⎡EI⎤, c = p pxφ ⎢ ⎥ f⎣ rVo s ⎦xφ 2(A.5)In Eqs. (A.3 - A.5), I p is the moment of inertia of a pile about x axis, r o is the pileradius, and f x1, f x2, f φ1, f φ2, f xφ1, and f xφ2 , are the Novak’s parameters determinedfrom Table A.1 for ν = 0.25 and parabolic soil profile for the bridge site.Table A.1 Stiffness and damping parameters of a pile: l/r o >25 forhomogeneous soil profile and l/r o >30 for parabolic soil profile102
A.2 Group Interaction FactorThe cross section of all piles used for the Bill Emerson Memorial CablestayedBridge is round. Therefore the stiffness and damping coefficients of anyindividual pile are the same in any horizontal direction. In a pile group, however,the number of piles in x and y directions may be different. As a result, thestiffness and damping coefficients of a pile group depend up on the number ofpiles and their spacing in each direction.To study the group effect, Paulos (1968) considered one pile in the groupas a reference. For example, in Figure A.4, No. 1 is assumed as a reference pileand distance ‘S’ is measured from the center of any other pile to center of thereference pile. If the effect of the reference pile is considered as 100%, that ofany other pile is reduced by an interaction factor α A for vertical vibration and αLfor horizontal vibration. The interaction factor α A can be determined from FigureA.5 based on the length of pile (l) and the radius of pile section (r o). The factor αLcan be obtained from Figure A.6 for each pile, taking into account the departureangle β in degree (Paulos, 1972). The factor α L is a function of l, rK R as defined in Figure A.6.o, and flexibilityFigure A.4 Plan and cross section of pile group103
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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
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: Figure A.2 Vertical stiffness and d
Page 119 and 120: For a group of piles with identical
Page 121: Missouri Department of Transportati
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