Un accurato modello analitico per la statica dei ponti strallati di grande luce

The conflicting demands connected from a side to the crossing of span always longer and from the other to the containment of the environmental impact of the structures set the necessity to critically re-examine the designing aspects that has brought to define the actual standards for the realization of long span cable bridges. In the case of fan-shaped scheme with "H" towers, the analysis of the statical behaviour of such structures through analytical approaches in closed form is currently founded on continuous models where the interaction between the girder and the cables is modeled through the Dischinger's tangent theory, that is through a first order approach in the displacements. In the case of non too long span, such approach allows to model in a satisfactory way the intrinsic non linear behaviour of such structures, connected to the presence of complexes structural elements as cables. On the other hand, when the spans become meaningful, the effects of interaction cable-girder can strongly be influenced by the high geometric non linearity in the behaviour of the cables "almost perpendicular" with respect to the weight force's direction, that is with respect to the forces's direction which act on the deck and therefore on the cables themselves. In this case, the sag effect with respect to the configuration of cable's chord is strong and, also holding valid the hypothesis of small displacements for the girder, the correct modeling of the behaviour of the whole structure has to bring in account the strong non linearity of the mechanical response of such structural elements. Starting from a "quasi-secant" model to describe the behaviour of the single cable, giving a second order approximation both with respect to the stress variation and to the apparent chord-strain one, the cable-girder interaction is modeled through a second order displacement approach able to take into account the finite variation of the cable's chord direction induced by the deformation of the stay-supported deck. In this way a closed-form formulation is obtained which, unlike classical secant model, does not need iterative procedures. Considering then a Eulero-Bernoulli model to describe the bending behaviour of the girder and a De Saint Venant model to decribe the torsional one, a refined continous model of the whole structure able to describe its statical behaviour has been developed. Moreover closed form solutions of the model, developed according to perturbative tecnique and valid under generic load acting on the bridge's deck, are proposed. The proposed results obtained from the present model and the comparisons effected confirm the best correspondence of the proposed approach in relationship to the behaviour attended of the structure, putting in evidence a prevailing truss behaviour of the bridge and the coupled nature of the bending and torsion of the girder, induced by the strong non linearity of the actions of cable-girder interaction.