198 L. Pedersen and C. Frier to the action of a pedestrian is a random variable. This means that the bridge response to the action of a pedestrian is best described by a probability distribution function describing the stochastic nature of bridge response. When evaluating the vibration serviceability-limit-state of a footbridge, it would often be bridge acceleration levels that would be of concern, and for this paper focus is on the peak midspan acceleration levels of the footbridge generated by single-person pedestrian traffic. Even when having decided that the footbridge response is to be handled as a random variable, there are decisions to be made related to which walking load model to employ. This is so because not only a single load model is available in literature. There are simple load models that can be used but there are also more advanced load models that can be employed. The difference between the simple and advanced models relates to their way and level of detail in describing the locomotion of a walking person and the load hereby directed to the footbridge. Differences between the models are described in the paper. The paper examines how different choices made related to modelling the action of a pedestrian will influence predictions of footbridge response. The choices will involve deciding on a load model but there are also decisions to be made in terms of how to model the parameters of the load model. The paper addresses both issues. Two different bridges are assumed for the study in order to widen the basis for a discussion of results. The load models assumed are described in Sect. 24.2. Section 24.3 defines the footbridges and Sect. 24.4 presents and discusses results of findings. 24.2 The Load Models Considered for the Study Sections 24.2.1 and 24.2.2 presents the two load models considered for the studies of this paper. Section 24.2.3 presents the assumptions made in terms of input parameters for the models. 24.2.1 Load Model I This load model, Eq. (24.1), is the one that has been employed for many years for modelling vertical action of a pedestrian and it is for instance suggested in [8–10]. F.t/ DW n XiD1 ˛i cos.2 ifst C i/ (24.1) Wis the weight of the pedestrian, ˛i is the dynamic load factor for load harmonic no i, and fs is the step frequency of the pedestrian. The value n defines the number of load harmonics assumed for the calculations. For the present studies only the first load harmonic will be considered for this load model as the bridges investigated are such that the load harmonics with values of i above 1 hardly would be able to cause dynamic response of the bridges. This means that it is not necessary to model phase information between load harmonics; information contained in the parameters i. Even though the model is often employed as a deterministic load model, entering model parameters as random variables makes it useful as a stochastic load model. The model is not as advanced as load model II described in the next section. 24.2.2 Load Model II This load model accounts for the inability of a pedestrian to repeat the same force in each step and that the force generated by a pedestrian is not fully periodic. The load model is introduced in [11] and is seen in Eq. (24.2). F.t/ D 5 XiD1 Fi.t/ C 5 XiD1 FS i .t/; (24.2)
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