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

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