Abstract Summary
The evolution of pedestrian bridge design is tending towards increasingly slender and flexible structures. As a result, these footbridges are more sensitive to vibrations caused by pedestrians. When designing them, it is needed to check their vibratory behaviour. For the comfort of pedestrians, measures must be taken to limit these vibrations. To adapt the design is often not possible or sufficient. The most common solution is to use Tuned Mass Dampers (TMD). In order to verify the vibration behaviour, several guides have been produced in recent years. They propose dynamic loading to be used for the design. The goal is to check that the accelerations obtained with the dynamic response are below certain comfort criteria. The loads proposed in the guides are sinusoidal and harmonic. The interest is not the transient response but only on the established vibrations. We therefore propose to solve the system in the frequency domain to obtain the maximum response of the established regime and not the full response over time. The proposal is to calculate frequencies and modes of the structure and to use it to find the phase and the frequency of the sinusoidal load for each mode along the footbridge that maximise the response of the structure. The phasing is associated with each mode. To work in the modal domain reduces the calculation time. Classically, the engineers are calculating static displacements under unit loading whose orientation depend of the modal response of each mode. They then multiply the displacements by the pedestrian surface load and dynamic coefficient to obtain the maximum dynamic response. However, there is a different load case for each mode and a different post-treatment to obtain the maximal accelerations. Hence, these steps are time-consuming for complex models. Furthermore, this methodology doesn’t consider the cross correlation between the modes. In comparison, we have implemented in our own-software FinelG, an automatic load procedure which adapts the phasing and surface of pedestrian loads to obtain the critical load cases that maximise each modal loading. With the transfer matrix, the dynamic response of the structure for a range of pedestrian walking frequency corresponding to each eigenmode is solved. We keep the maximum response and thus we obtain the dynamic response curve of the structure (displacements or accelerations) at various points of the structure versus the pedestrian frequency and thus verify its comfort. It reduces the time-cost of these verifications for complex structures. In addition, with manual calculations, the modes are usually assumed to be uncoupled. This is usually the case for undamped structures. When dampers are added, this is no longer the case, dampers are generally effective for several modes and couple them. This statement has been verified on structures designed by Greisch office. By considering the correlation between the modes, as in the new implementation, it would be possible to reduce the number of dampers on some structures. Finally, the paper gives some actual designed footbridges.
