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

Table 5.5Natural frequencies for various degrees of approachinvolvementModeNo.withapproachk=0(kN/m)84×10(kN/m)72×10(kN/m)62×10(kN/m)52×10(kN/m)42×10(kN/m)1 0.339 0.339 0.340 0.340 0.339 0.339 0.3392 0.400 0.398 0.402 0.401 0.401 0.401 0.3993 0.484 0.484 0.485 0.485 0.484 0.484 0.4844 0.573 0.573 0.573 0.573 0.573 0.573 0.5735 0.602 0.602 0.602 0.602 0.602 0.602 0.6026 0.625 0.610 0.615 0.614 0.612 0.610 0.6107 0.658 0.657 0.658 0.658 0.658 0.658 0.6578 0.689 0.688 0.690 0.690 0.690 0.690 0.6899 0.740 0.739 0.740 0.740 0.740 0.740 0.73910 0.828 0.826 0.827 0.827 0.827 0.826 0.82611 0.842 0.827 0.829 0.829 0.829 0.829 0.82812 0.853 0.842 0.842 0.842 0.842 0.842 0.84213 0.878 0.878 0.878 0.878 0.878 0.878 0.87814 0.915 0.908 0.917 0.917 0.917 0.917 0.91215 0.931 0.931 0.931 0.931 0.931 0.931 0.93116 0.935 0.935 0.935 0.935 0.935 0.935 0.93517 0.935 0.935 0.935 0.935 0.935 0.935 0.93518 0.948 0.945 0.947 0.947 0.947 0.947 0.94619 0.954 0.952 0.953 0.953 0.953 0.953 0.95320 0.957 0.954 0.954 0.954 0.954 0.954 0.95421 0.962 0.962 0.962 0.962 0.962 0.962 0.96222 0.964 0.964 0.964 0.964 0.964 0.964 0.96423 0.965 0.965 0.965 0.965 0.965 0.965 0.96524 0.965 0.965 0.965 0.965 0.965 0.965 0.96525 0.965 0.965 0.966 0.966 0.966 0.966 0.96526 0.977 0.977 0.977 0.977 0.977 0.977 0.97727 1.018 1.018 1.018 1.018 1.018 1.018 1.01828 1.018 1.018 1.018 1.018 1.018 1.018 1.01829 1.031 1.031 1.031 1.031 1.031 1.031 1.03130 1.040 1.039 1.040 1.040 1.040 1.040 1.0395.3.4. Influence of pile foundationThree cases are considered to investigate the effect of pile foundations in the approachspans. The first case is to model the support of the piers in the approach spans as springsand dashpots in vertical, longitudinal, and traffic directions. This case is supposed tosimulate the effect of group pile foundations. The second case is to fix the bases of allpiers to restrain motions in all degrees of freedom. The third case is to model the bases ofpiers as hinges. The frequencies obtained for the three cases are listed in Table 5.6. Theyare also compared in Figure 5.38. It is clearly seen from Figure 5.38 that there is basically68