On the dynamic response of suspended footbridges

Several Authors have underlined the possible activation of large amplitude oscillations of suspended footbridges due to the nonlinear behavior of the hangers, which act as linear elastic springs in tension and do not react in compression. In fact, in particular conditions the pedestrian- induced loads and/or the wind actions may cause oscillations that, in some parts of the footbridge span, achieve amplitude higher than the initial deformation of the hangers due to dead loads; in these cases such hangers slack and, consequently, the stiffness of the footbridge decreases. Thus the footbridge may undergo to unexpected large amplitude oscillations that the usually utilized models cannot predict, as they assume a bilateral behavior for the suspended system. Here, the response of suspended footbridges is evaluated introducing a continuous model that is obtained adopting the nonlinear equivalent regularization technique proposed for suspended bridges. The solution of the aforementioned continuous model is evaluated in closed form by means of perturbation methods. The dynamic analysis shows the possibility of the coexistence of multiple solutions, some of which are characterized by high amplitude. In order to identify the conditions for the activation of such phenomena, the evaluated responses are plotted for different values of the mechanical parameters of the examined structure and of the considered actions.