Keywords: vibration, dynamical analysis, footbridges, composite structures, parametric study, serviceability, pedestrian walking and dynamic structural design.

Pedestrian footbridges have been constructed with increasingly daring structures that encompass the experience and knowledge of structural designers by using newly developed materials and technologies 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 existing loading frequencies, or even equal to some of its multiples. Another important aspect that still deserves further investigation is related to the modelling of the harmonic dynamical loads induced by pedestrians on the footbridges [1,2,3,4].

It must be emphasized that the geometry of the human body walking is an organized movement of legs that causes an ascent and descent of the effective mass of the body in each passing. The accelerations of the human body mass are associated with floor reactions, and it is approximately periodic in the frequency of the step. The two feet produce this type of loading, as a function of the static parcel associated with the weight of the individual and three or four harmonic components of the loading. These harmonic ones appear due to an interaction between the increasing load represented by a foot and the simultaneous unloading of the other foot.

The present investigation is carried out based on a more realistic loading model developed in order to incorporate the dynamical effects induced by people walking when the dynamical response of pedestrian footbridges is investigated. In this particular loading model the movement of legs that causes an ascent and descent of the effective mass of the human body in each passing was considered and the position of the dynamical loading is changed according with the individual position and the generated time function, corresponding to the excitation induced by people walking, has a space and time description.

The investigated structural model was based on several footbridges, with main spans varying from 10m to 40m. The structural system, used for pedestrian crossing, is composed of a composite (steel/concrete) solution made of an "I" steel beam section and a reinforced concrete deck. The proposed computational model, developed for the composite slab dynamic analysis, adopted the usual mesh refinement techniques present in finite element method simulations [5].

The developed analysis methodology is described and discussed in details. Based on an extensive parametric study the footbridges dynamic response in terms of peak accelerations was obtained and compared to the limiting values proposed by several authors and design standards [6,7] in order to provide a more realistic evaluation for vibration due to walking in this type of structure.

The results obtained throughout the present investigation indicated that in specific cases the design standards did provide results of sufficient safety, based on the adoption of loading models that are excessively simplified [6,7]. 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., 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., Ammann, W., "Vibrations in structures induced by man and machines", Structural Engineering Document 3e, International Association for Bridges and Structural Engineering, 1987.

5

ANSYS, "Swanson analysis systems", Inc., P.O. Box 65, Johnson Road, Houston, PA, 15342-0065, Version 8.0, Basic analysis procedures

6

Murray, T.M., Allen, D.E., Ungar, E.E., "Floor Vibrations Due to Human Activity", Steel Design Guide Series, American Institute of Steel Construction, AISC, 1997.

7

International Standard Organization, "Evaluation of Human Exposure to Whole-Body Vibration, Part 2: Human Exposure to Continuous and Shock-Induced Vibrations in Buildings (1 to 80Hz)", International Standard, ISO 2631-2, 1989.

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