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

1.1Frequency(Hz)0.90.70.5Plus 0Plus 5%Plus 6.7%Plus 10%0.30 5 10 15 20 25 30ModeFigure 5.37 Frequency variation with different mass densities5.3.3. Presence of the approach span of the bridgeIn the FE modeling of the cable stayed bridge, the presence of the approach span caninfluence the dynamic properties of the cable-stayed main span. Since all piers in theapproach span are shorter, the approach structure has higher stiffness and thus is moredifficult to be excited under dynamic loadings. In this section, seven cases are studied. InCase 1, the approach spans are included in the cable-stayed span model. In Case 2, theapproach spans are neglected completely or k=0 in Table 5.5. The remaining cases alsoneglect the approach spans. However, the effect of the approach spans is approximatedby eight linear springs at the end of the Illinois side span. The coefficient of the springs(k) varies from 2×10 4 kN/m (1.372×10 3 kip/ft) to 4×10 8 kN/m (2.744×10 7 kip/ft). Thefirst 30 frequencies obtained from the FE model are listed in Table 5.5. It can be foundthat there is only a slight variation among various cases, indicating that the main bridgealmost vibrates independently of the approach spans. This is because the first 30 modesare closely related to the motion of the main bridge. The approach spans are seldominvolved in the motion of the bridge system within this frequency range.67