Multi-mode responses of suspended-span bridges to turbulent wind excitation have been estimated in the past by considering the response of each mode and then taking the root-sum-square for the total response. Other procedures, mainly in the time domain, also exist but they have certain simplifying assumptions that limit the complete analysis of the system as well as the estimation of certain important criteria, e.g., flutter speed. A more comprehensive procedure, in the frequency domain, has been developed to capture the full bridge aerodynamics by considering simultaneously the effect of more than one mode. Frequency-domain functions (flutter derivatives) are preferred by most bridge dynamists because they are easier to obtain experimentally. The determination of multi-mode response is especially important for longer-span bridges since their increased flexibility is more likely to elicit a coupled response. In this paper, the fundamental single-mode frequency-domain formulation is extended into the multi-modal domain and a detailed example is presented to highlight the importance of using a coupled analysis procedure for suspended bridges with longer spans.
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