Limit of hanger linearity in suspension footbridge dynamics: A new section model

The mechanical behaviour of suspension bridges is characterised by nonlinearities due to the main cables geometric effects and to the inability of the hangers to sustain compressive loads. The nonlinear effects due to hanger slackening are expected to increase in suspension footbridges due to lightweight decks, that is, low dead to live load ratio, and to shallow plate-girder decks with very low flexural and torsional stiffness. In this paper a new section model is proposed to study the limit of hanger linearity in lightweight suspension footbridges. The model is inspired to a four degrees-of-freedom model already proposed in the literature, but is expressed with a new formalism that allows some interesting properties to be outlined. Specifically, the expression of a particular frequency, herein called relative antiresonance frequency, as a function of the model generalised properties is derived: if the system is loaded with a harmonic force having that frequency, the linear behaviour of the hangers is assured for every value of the force amplitude. The proposed section model is applied to a footbridge benchmark subject to the pedestrian harmonic load and results are compared with those obtained through a nonlinear dynamic analysis on a 3D Finite Element model of the bridge.