PSI - Issue 78

Anna Brunetti et al. / Procedia Structural Integrity 78 (2026) 1729–1736

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range, vibrations induced by the crowd are unlikely to trigger resonance phenomena and therefore do not affect the user comfort. However, if one or more resonant frequencies of the footbridge lie within the critical range, it becomes necessary to quantify the disturbance caused by pedestrian traffic in terms of perceived acceleration on the deck. The maximum acceptable acceleration depends on the desired level of user comfort. The intensity of the pedestrian load used to simulate the dynamic excitation of the footbridge depends on the expected (or observed) level of crowding. To this end, the document introduces Bridge Classes, numbered from I to IV, with each class corresponding to a different level of pedestrian traffic, from highest to lowest. 3.2. Numerical simulation and assessment of footbridge serviceability A steady-state analysis was adopted to evaluate the maximum acceleration induced by a moving pedestrian load at a given frequency. For 10 natural frequencies within the range of interest, steady-state analyses were performed by applying a dynamic load at the frequency of the i -th natural frequency of the structure to simulate resonance conditions. Each analysed frequency corresponds to a specific loading case, which is defined based on the bridge class and the associated resonance risk. The loading cases defined by the Sétra guidelines mainly differ in terms of intensity of the applied load. However, the application method remains consistent: the load is distributed across the entire pedestrian surface, aligned with the direction of the considered mode shape, and oriented in line with its modal deformation (Fig. 4).

Fig. 4.Example of load distribution scheme for the i-th frequency.

The mass of the crowd, which slightly modifies the natural frequencies presented above, is included in the analysis. In addition, a conservative value of 0.4% was adopted for the structural damping, as suggested by the document provided by Sétra. Due to the complexity and number of modes to be considered, the analyses were automated using a MATLAB routine. The results, obtained under the assumption of a Bridge Class II (urban footbridge connecting densely populated areas) are presented in Table 2. The reported values represent the maximum accelerations recorded on the footbridge for each analysis.

Table 2. Results Steady-State analysis. Mode Type of mode

Frequency (Hz) Vert. Acc. (m/s 2 ) Long. Acc. (m/s 2 ) Transv. Acc. (m/s 2 )

1 2 3 4 5 6 7 8 9

1 st Flexural 1 st Torsional 2 nd Flexural 3 rd Flexural

1.17 1.37 1.52 1.82 2.82 2.88 3.77 4.10 4.66

0.37 0.19 1.51 1.97 1.78 0.09 0.01 0.55 0.48 0.25

1.33E-04 1.51E-04 3.22E-04 6.81E-04 2.61E-03 5.49E-04 9.01E-05 9.59E-04 9.30E-04 3.01E-04

5.10E-04 1.32E-04 5.73E-04 1.41E-04 8.86E-03

Transverse-torsional 2.22

4 th Flexural 2 nd Torsional

- - - - -

Transverse-flexural

5 th Flexural 6 th Flexural

10

Results are also represented graphically in Fig. 5, in order to compare the obtained accelerations with the comfort limits suggested by Sétra. It can be noted that, if excited into resonance by pedestrian loading, frequencies corresponding to the third, fourth, fifth, and eighth modes can generate vertical accelerations of approximately 1.5