Keywords: vibration, footbridges, footbridge structural dynamics, composite structures, serviceability, pedestrian walking, dynamic loading factor, dynamic structural design.

Pedestrian footbridges have been constructed with increasingly daring structures that encompass the experience and knowledge of structural designers to the use of newly developed materials and technologies, also boosted by the ever-growing investigations on this field. As the structural designer main objective is related to produce increasingly lighter structures its conception requires a substantial amount of theoretical knowledge associated to structural design and construction processes. This fact have generated very slender structural footbridges and consequently changed the serviceability and ultimate limit states associated to their design.

A direct consequence of this design trend is a considerable increase of structural vibration associated problems. In the particular case of pedestrian footbridges this phenomenon precisely occurs when the structural fundamental frequency is equal or near the load exiting frequencies, or even equal to some of its multiples. Another important aspect that still deserves further investigation is related to the harmonic dynamical modelling of load induced by pedestrians on the footbridges [1,2,3,4].

Although the design criteria for evaluation of the vibration levels induced by human rhythmic activities have been known for many years, it has only recently possible to apply such criteria to the design of floor structures. The reason for this is that the complexity associated with the problem is considerable. The loading is extremely complex and the structural system dynamic response, in a general way, involves a high number of vibration modes. Along the years, a lot of studies have been showing that the problem can be simplified in way to supply problem approaches that can be properly applied to the design practice [1,2,3,4,5,6].

On the other hand, a pure statically based design of these structures can lead in some cases of excessive vibrations or even of user discomfort. This was the main motivation for the development of a design methodology based on the structural system dynamical response. Initially, the model natural frequencies are compared to the load frequencies induced by the constant movement of pedestrians over the footbridges. This comparison is performed to avoid, in principle, the resonance physical phenomenon that could lead to unacceptable footbridge vibration levels.

In sequence, the model dynamical response also contemplates a critical analysis of the maximum values of acceleration, velocities and displacements. Linear elastic finite element analysis results were compared to the results from several investigators and design standards recommendations [1,2,3,4,5,6].

The investigated structural model was based on an existing outdoor footbridge at the city of Rio de Janeiro, Brazil. The structure dimensions are 22.5m x 2.30m. The structural system, used for pedestrian crossing, is composed of a composite (steel/concrete) solution made of a "T" steel beam section and a reinforced concrete deck. The main span is 22.5m length simply supported by columns at its extremities.

The structural system dynamic response in terms of peak accelerations was obtained and compared to the limiting values proposed by several authors and design standards. The maximum values found for footbridge accelerations were 385%g, at resonance, while the maximum accepted values for the acceleration were 5%g according to the adopted design criteria and specific design standards [1,2,3,4,5,6]. The results obtained throughout the investigation indicated that the footbridge analysed in this work violates the human comfort criteria when a frequency band ranging from 3.0Hz to 5.5Hz for the forcing frequencies induced by people walking was considered. Hence it was detected that this type of structure can, without any doubt, reach high vibration levels, compromising the footbridge user's comfort and especially its safety.

1

Pimentel, R.L.; Pavic, A.; Waldron, P., "Evaluation of design requirements for footbridges excited by vertical forces from walking", Canadian Journal of Civil Engineering, Vol. 28(5), 769-776, 2001. doi:10.1139/cjce-28-5-769

2

Ellis, B.R., "On the response of long-span floors to walking loads generated by individuals and crowds", The Structural Engineer, Vol. 78, 17-25, 2000.

3

Ellis, B.R. and Ji, T., "Floor vibration induced by dance-type loads: theory and verification", The Structural Engineer, Vol. 72 (3), pp 36-50, 1994.

4

Bachmann, H. and Ammann, W.; "Vibrations in structures induced by man and machines", Structural Engineering Document 3e, International Association for Bridges and Structural Engineering, 1987.

5

CEB/Bulletin D'Information N0 209; "Vibration problems in structures. Practical guidelines", 1991.

6

Supplement to the National Building Code of Canada, Commentary on Serviceability Criteria for Deflections and Vibrations, National Research Council of Canada, Ottawa, 1995.

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