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This paper presents a spatial catenary cable element for the nonlinear analysis of cablesupported structures. An incremental-iterative solution based on the Newton-Raphson method is adopted for solving the equilibrium equation. As a result, the element stiffness matrix and nodal forces are determined, wherein the effect of self-weight and pretension are taken into account. In the case of the initial cable tension is given, an algorithm for form-finding of cable-supported structures is proposed to determine precisely the unstressed length of the cables. Several classical numerical examples are solved and compared with the other available numerical methods or experiment tests showing the accuracy and efficiency of the present elements.

A convenient and effective finite element-based method for coupled flutter analysis of long-span bridges is presented. The exact formulation of the aerodynamic self-excited forces with eighteen flutter derivatives utilized by complex notation is proposed. The predictions of the flutter wind speed and the critical frequency are compared with those either given by existing methods or the wind tunnel test showing the effectiveness and accuracy of the present approach. Numerical flutter analysis for an asymmetric bridge is the application for engineering practice, and its obtained results highlight the important role of the first lateral bending and torsional mode in generating the coupled flutter. Multi-mode analyses that are based on only the symmetrical modes can predict accurately the bridge flutter onset. The consistent self-excited aerodynamic force formulations produce the flutter velocity that is closer to the experimental one of full-bridge model in the wind tunnel.

This paper presents a number of approximated analytical formulations for the flutter analysis of long-span bridges using the so-called uncoupled flutter derivatives. The formulae have been developed from the simplified framework of a bimodal coupled flutter problem. As a result, the proposed method represents an extension of Selberg's empirical formula to generic bridge sections, which may be prone to one of the aeroelastic instability such as coupled-mode or single-mode (either dominated by torsion or heaving mode) flutter. Two approximated expressions for the flutter derivatives are required so that only the experimental flutter derivatives of (* 2 * 1 , A H) are measured to calculate the onset flutter. Based on asymptotic expansions of the flutter derivatives, a further simplified formula was derived to predict the critical wind speed of the cross section, which is prone to the coupled-mode flutter at large reduced wind speeds. The numerical results produced by the proposed formulas have been compared with results obtained by complex eigenvalue analysis and available approximated methods show that they seem to give satisfactory results for a wide range of study cases. Thus, these formulas can be used in the assessment of bridge flutter performance at the preliminary design stage.