Aerostatic torsional divergence of suspension bridges via a fully nonlinear continuum formulation

A fully nonlinear three-dimensional dynamic model of a suspension bridge under fairly general loading conditions is proposed. The nonlinear balance equations are obtained via a direct total Lagrangian formulation and the kinematics, for the deck and the two cables, include the finite displacements of the centroidal lines and the flexural and torsional finite rotations of the deck cross-sections (otherwise rigid in their own planes). The deformation parameters, namely, the elongations in the cables, the deck elongation and the three curvatures, are nonlinear functions of the displacement gradients. The proposed model takes into account the fully nonlinear extensional-flexural-torsional coupling and examines both torsional divergence and lateral buckling phenomena induced by static wind actions. An application of the three-dimensional nonlinear model, for the study of aeroelastic stability, is illustrated considering the Hu Men Suspension Bridge on the Zhu Jiang river in China. For this structure, the calculated critical wind velocities are compared with the results obtained via a linear analysis. Moreover, the proposed nonlinear model allowed to carry out effective parametric studies so as to assess the influence, on the critical wind velocity, of the global parameters governing the structural bridge response.