A closed-form refined model of the cables' nonlinear response in cable-stayed structures

In this paper a refined second-order model for the analysis of the elastic response of cables in cable-stayed structures is proposed. Starting from the exact catenary theory, the Dischinger-Ernst formulation is rationally deduced and, performing a second order approximation both with respect to the stress variation and the apparent chord-strain one, a refined explicit equivalent constitutive relationship for elastic stays is obtained. Moreover, the geometrical non-linearities induced on the cable by the deformation of the stay-supported structure are taken into account through a second order displacement approach. Accordingly, a closed-form formulation describing nonlinear cable-structure interaction effects is obtained which, unlike the classical secant model, does not need iterative procedures, opening the possibility to develop refined analytical solutions for cable structures. Several numerical examples and benchmarks on different stay configurations are presented, showing the effectiveness and the accuracy of the proposed model.