Abstract Summary
The task group "IABSE TG 3.1 - Super-long span bridge aerodynamics" gathers about twenty engineers specialized in wind engineering. It is equally composed of university researchers, wind tunnel engineers and engineers from design offices. The aim is to compare the results obtained by the different teams in the field of wind-loaded structures by considering their aeroelastic behaviour on examples of increasing complexity. The parameters were the number of degrees of freedom, the type of flutter derivatives (analytical expressions of Theodorsen, measurements on wind tunnel models), the analyzed structure (sectional model, numerical model of an existing bridge). The results to be provided were the flutter wind speed and/or the displacements value for different wind speeds. The main results have been presented in Ghent [1]. In partnership with T-Ingénieirie and Michel Virlogeux, the Greisch office carried out the execution studies of the Third Bosporus Bridge in Istanbul. The CSTB and Polimi were in charge, respectively, of the wind tunnel tests with sectional and aeroelastic models. One of the important conclusions was the value of the instability velocity evaluated at 92.5 m/sec, a velocity clearly higher than the design speed. The aeroelastic behavior of the structure was neglected for the design because of the difference between the wind speed adopted for the design, 46.79 m/sec vs the estimated flutter wind speed. Having developed a numerical tool to evaluate the flutter speed of a large span structure, a calculation was undertaken with the flutter derivatives measured by the CSTB. With these data, the numerical value obtained for the critical speed is 100.5 m/sec. The same calculation with the derivatives of Theodorsen gives an almost identical result, 103.3 m/sec. We consider that the two results are equivalent and show that the bridge deck is well profiled. However, a detailed examination of the Theodorsen derivatives and those measured by the CSTB shows different signs for 4 out of 8 flutter derivatives. The orientation of the axes is not the origin of this discrepancy. These 4 derivatives are the A1, A4, H2, and H3, i.e. the off-diagonal terms of the damping and stiffness aeroelastic matrices. This paper develops an analytical approach to the calculation of the critical velocity and of the power spectral density (PSD) of the displacements as a function of the 8 principal derivatives, A1 to A4, H1 to H4. The final expression allows to show that the simultaneous change of the signs of of these 4 derivatives, and only them, • the result is identical : o on the flutter speed o on the displacements, IF the PSD matrix of the wind forces is diagonal (PSD-F) • the result is different on displacements, IF PSD-F matrix is complete. Today, we have not found any reference highlighting this type of result. Reference - [1] Diana G. and all, Super-long span bridge aerodynamics benchmark: additional results for TG3.1 Step 1.2, Proceedings of IABSE Congress Ghent 2021
