Prediction of resonantly forced vibrations for suspended footbridges

The aim of the present paper is to investigate the performance of suspended footbridges under pedestrian loads. Indeed, several Authors have underlined the possible activation of large amplitude oscillations into suspended footbridges due to the nonlinear behavior of the hangers. In fact, the last ones act as linear elastic springs in tension and do not react in compression. Consequently, if the whole suspended footbridge or parts of it undergo large amplitude oscillations, the initial hangers’ pretension stress may become zero and the slackening may start. In these cases, the stiffness of the footbridge deck decreases drastically, and a complex dynamic response may occur. Hence, the footbridge may show unexpected vertical and torsional oscillations that the “classical” models cannot predict; these models, in fact, assume a bilateral behavior for the suspended system and, consequently, no variations of the global stiffness during the motion. Here, the response of suspended footbridges is evaluated by using a continuous model obtained by adopting the nonlinear equivalent regularization technique proposed for long span suspended bridges. The dynamic analysis, performed by means of a perturbation method, shows the possibility of the coexistence of multiple solutions, some of which are characterized by high amplitudes and by the activation of the afore-described slackening phenomenon. The response is evaluated for several values of loading, mechanical and geometrical parameters, with the main aim of highlighting the characteristics and the stability of the investigated oscillations and obtaining information and/or design indications to prevent such phenomena.