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5.E+054.E+054.E+05Moment (kN-m)3.E+053.E+052.E+052.E+051.E+05M =3×10 5 kN-mxM xy = 250000 kN-mΦ xy = 0.04×10 -2 rad/mM xu = 414000 kN-mΦ xu = 0.48×10 -2 rad/m5.E+040.E+000.0 0.5 1.0 1.5 2.0 2.5 3.0Curvature (10 -2 rad/m)Figure 6.15 Hollow section capacity about strong axis bending3.E+053.E+05Moment (kN-m)2.E+052.E+051.E+05M yy = 159000 kN-mΦ yy = 0.08×10 -2 rad/mM yu = 243000 kN-mΦ yu = 1.12×10 -2 rad/m5.E+040.E+000.0 1.0 2.0 3.0 4.0 5.0 6.0Curvature (10 -2 rad/m)Figure 6.16 Hollow section capacity about weak axis bendingAfter the bending moment demands have been determined from the FE model of thebridge, the capacity over demand ratio of each column can be evaluated. The ratios of thebending capacity to the maximum moment are listed in Table 6.4, in which M x and M yare the bending moments about x and y axis, respectively, under the design earthquake,and M xu and M yu are their corresponding capacities. Since the entire structure is88
symmetric about the centerline of the bridge, moments at joints 374 and 417, 370 and421, 432 and 475, and 428 and 479 are relatively close. Their averaged values are listedin Table 6.4 as A, B, C, and D, respectively. For both top (A and C) and bottom (B andD) of the two towers, the capacity over demand ratios corresponding to the momentsabout the y-axis (in-plane moment) are all above 2.4. In fact, all the in-plane seismicmoments are significantly less than their yield moments of corresponding sections,indicating an elastic behavior of the bridge or a conservative design for earthquake loads.The out-of-plane bending behavior is different. The hollow sections appear to yieldslightly as indicated in Figure 6.15. The bottom solid sections likely experience moderateyielding. As illustrated in Figure 6.13, the curvature ductility could be as high as 10,corresponding to a seismic moment 483,058 kN-m (356,450 kip-ft). Even so, the ratios ofseismic moment and ultimate moment are above 1.0. These results indicate that columnswill likely yield to a moderate degree but they are not susceptible to collapsing under thedesign loads. Immediately after a design earthquake, however, the bottom section (out ofplane bending) must be inspected and perhaps repaired.Table 6.4Moment capacity over demand ratioM x(kN-m)M xy(kN-m)M xu(kN-m)M xuM xM y(kN-m)M yy(kN-m)M yu(kN-m)M yuM yA 277384 250000 414000 1.49 100668 159000 243000 2.41B 483058 301000 487000 1.01 116308 192000 289000 2.48C 300243 250000 414000 1.38 89996 159000 243000 2.70D 391285 301000 487000 1.24 84997 192000 289000 3.40The maximum force and stress of all stay cables induced by dead load plus earthquakeloads are listed in Table 6.5, together with their corresponding design values. It is seenthat most design stresses are close to the maximum tensile stresses during a designearthquake. According to bridge drawings, the cables are made of ASTM A416, Grade270, weldless, low-relaxation strands. This material has strength of σ y =1860 MPa (270ksi). The strength over stress ratio for each cable is also listed in Table 6.5. As one cansee, all stay cables are in elastic range under the dead plus earthquake loads. The factor ofsafety is over 2.35, which ensures the safety of the bridge during a design earthquake.The assignment of cable number can be found in Figure 4.4.It can be seen from Table 6.5 that Cable 14 experienced the largest stress during theearthquake. The stress time history in this cable is depicted in Figure 6.17. The initialstress at the beginning of the earthquake represents the dead load effect. It isapproximately 605 MPa (87.7 ksi). This means that the earthquake effect isapproximately 792-605=187 MPa (27.1 ksi), which is 31% of the dead load stress.To ensure no slack in all cables, the stress time history of the cable with the smalleststress, No.17, is presented in Figure 6.18. It is clearly shown that the minimum stressduring the earthquake is approximately 10.5MPa, indicating that the cable is in tension.This analysis ensures that no cable is subjected to compression during the earthquake and89
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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
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 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: ending of the tower as shown in Fig
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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