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

Figure 5.30 29 th mode shape (1.032 Hz) ................................................................................. 61Figure 5.31 30 th mode shape (1.040 Hz) ................................................................................. 62Figure 5.32 115 th mode shape (1.237 Hz) ................................................................................ 62Figure 5.33 568 th mode shape (3.187 Hz) ................................................................................ 62Figure 5.34 759 th mode shape (3.862 Hz) ................................................................................ 62Figure 5.35 1969 th mode shape (8.853 Hz) .............................................................................. 62Figure 5.36 Frequency comparison with different boundary conditions ................................. 65Figure 5.37 Frequency variation with different mass densities.................. .............................. 67Figure 5.38 Natural frequencies with various pile foundation conditions ............................... 70Figure 5.39 Comparison of calculated and measured frequencies............. .............................. 72Figure 5.40 Calculated versus measured 1 st mode shape ......................................................... 73Figure 5.41 Calculated versus measured 2 nd mode shape ........................................................ 73Figure 5.42 Calculated versus measured 3 rd mode shape........................... .............................. 74Figure 5.43 Calculated versus measured 5 th mode shape........................... .............................. 74Figure 5.44 Calculated versus measured 6 th mode shape ........................................................ 75Figure 5.45 Calculated versus measured 8 th mode shape ........................................................ 75Figure 5.46 Mode assurance criterion (MAC) values .............................................................. 76Figure 6.1 Mexico City Earthquake ground motion................................. .............................. 79Figure 6.2 El Centro Earthquake ground motion ................................................................... 79Figure 6.3 Pacoima Earthquake ground motion....................................... .............................. 79Figure 6.4 Vertical rock motion at Station D1 ....................................................................... 80Figure 6.5 Transverse rock motion at Station D1 .................................................................. 80Figure 6.6 Longitudinal rock motion at Station D1 ............................................................... 80Figure 6.7 Midspan displacements under Mexico City earthquake ....................................... 82Figure 6.8 Midspan displacements under El Centro earthquake.............. .............................. 82Figure 6.9 Midspan displacements under Pacoima earthquake ............................................. 83Figure 6.10 Midspan displacements under Arkansas earthquake ............................................ 83Figure 6.11 FE model of two towers.......................................................... .............................. 86Figure 6.12 Cross sections of columns in towers....................................... .............................. 86Figure 6.13 Solid section capacity about strong axis bending ................................................. 87Figure 6.14 Solid section capacity about weak axis bending..................... .............................. 87Figure 6.15 Hollow section capacity about strong axis bending................ .............................. 88Figure 6.16 Hollow section capacity about weak axis bending ............................................... 88Figure 6.17 Time history of tensile stress in Cable 14............................... .............................. 91Figure 6.18 Time history of tensile stress in Cable 17............................... .............................. 91xii