Aerodynamic admittance of streamlined bridge decks

In this paper, the generalized one-wavenumber aerodynamic admittance (3D one-wavenumber AAF), two-wavenumber aerodynamic admittance (3D two-wavenumber AAF) and two-dimensional aerodynamic admittance with the second (spanwise) wavenumber k2=0 (2D AAF) of streamlined bridge decks in free stream turbulence are investigated based on Ribner's three-dimensional aerodynamic theory. The misunderstandings of and internal relationship between the three kinds of admittances are clarified theoretically. Using wind tunnel tests in large-scale spire-generated turbulence, generalized coherence models of buffeting forces are proposed by the introduction of the reduced separation to take into account the three-dimensional effects of turbulent flow. Then, the closed-form expressions of admittances of the gust-loading on streamlined bridge deck are derived provided that the floating parameters in generalized coherence models are determined experimentally. Compared with previous numerical solution, the proposed closed-form models can explicitly divide the 3D one- and two-wavenumber AAFs into two parts, the gust-independent 2D AAF and the gust-related correction factors, providing us a new insight into both the effects of turbulence and cross geometry of the streamlined bridge decks. Experimental results confirm that the 2D AAF depends only on the cross-section geometry and the streamwise wavenumber k1. In contrast, the spanwise correction factors of 3D AAF are mainly determined by the dimension of the girder and the statistical characteristics of the gusts, including the decay parameter and integral length scales. This approach proposed in this paper can be extended to line-like structures with complicated cross-section shapes, such as twin-box girder.