This paper proposes a generalized equivalent spectral model of pedestrian-induced forces on footbridges that can be applied in serviceability analysis, from unrestricted traffic to crowded conditions. The model is based on experimental relationships among pedestrian density, step velocity, and step frequency taken from the literature. A suitable physically based expression for the coherence function is introduced that is dependent on pedestrian density and distance among pedestrians; it reduces to perfect uncorrelation for spatially unrestricted traffic and to perfect correlation for crowded conditions. Furthermore, the harmonic content of pedestrian-induced forces is defined as a function of the pedestrian density. Based on the proposed spectral model of the loading, the classic methods of linear random dynamics can be adopted for vibration serviceability analysis of footbridges. Similar to in the wind engineering field, simple closed-form expressions are provided for the evaluation of the maximum dynamic response

In the framework of the Generalized Beam Theory (GBT) a new cross-section analysis is proposed, specifically suited for nonlinear elastic thin-walled beams (TWB). The approach is developed according to the nonlinear Galerkin method (NGM), which calls for the evaluation of nonlinear (passive) trial functions, to be used in conjunction with linear (active) trial functions, in describing the displacement field. The set of (quadratic) trial functions is determined here by requiring that the classic Vlasov's kinematic hypotheses of the linear theory (i.e. (a) transverse inextensibility and (b) unshearability) are satisfied also in the nonlinear sense. The linear field is described by the so-called conventional displacements, by neglecting non-conventional displacements, which violate Vlasov's hypotheses. The nonlinear trial functions thus generated are innovative deformation fields, which describe extensional and shear displacements in a different way from that of the non-conventional fields of the linear theory. In particular, they consist of non-constant tangential and out-of-plane displacements of the cross-section profile, able to ensure inextensibility and unshearability of all the plate elements, by balancing the second-order strains induced by the conventional displacements. Since nonlinear trial functions do not increase the number of the unknowns, the GBT spirit, as a reduction method, is preserved. A very promising example is discussed, which shows that equilibrium paths can be determined by using few linear trial functions in conjunction with the corresponding nonlinear trial functions, supplying good results when compared with burdensome finite-element solutions

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