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

1.1Frequency (Hz)0.90.70.5BC Case 1BC Case 2BC Case 3BC Case 40.30 5 10 15 20 25 30ModeFigure 5.36 Frequency comparison with different boundary conditions5.3.2. Mass density of concreteThe mass density of material plays an important role in the dynamic characteristics of thecable-stayed bridge. According to ASTM standards, the unit weight of concrete is givenas 2.36×10 4 N/m 3 (150 lb/ft 3 ). As a matter of fact, this value does not include the weightof rebar in reinforced concrete. For reinforced concrete (RC) slabs, the weight of rebarcan be significant. For example, Deck Panel A09 has a total rebar weight of up to 1696kg. These bars are embedded into a concrete deck of 0.2794m (11 in) thick and an area of67.6m 2 (727.3 ft 2 ). The additional average unit weight reaches 611N/m 3 (3.90 lb/ft 3 ),which is 2.6% of the 2.36×10 4 N/m 3 (150 lb/ft 3 ). If high strength steel bars for ducts andbarriers are considered, more additional weight should be added into the original values.In this section, three additional mass densities are considered: 5%, 6.7%, and 10% aslisted in Table 5.4 on top of the normal mass density or unit weight given by ASTMstandards.The calculated frequencies for different additional mass densities of concrete aresummarized in Table 5.4. It can be seen that any increase in mass density results in adecrease of the natural frequencies of the bridge structure. The comparison of frequencychanges is also made in Figure 5.37. Clearly, a decreasing trend of natural frequency withincreasing mass density can be observed. It can also be seen from Figure 5.37 that thechange in natural frequencies of the first five modes is substantially smaller than thefollowing ten modes of vibration. This result is likely due to the fact that the mass changein bridge deck affects more significantly the natural frequencies in transverse vibration.The first five modes primarily correspond to the vertical motion that is less sensitive tothe mass change in bridge deck due to vertical supports at ends and towers of the mainspans.65