# Experimental and Numerical Study on Dynamics of Two Footbridges with Different Shapes of Girders
## 4 Conclusions  
The experimental and numerical results of the dynamic system identification and verification of the behavior of two footbridges in Poland have been presented in this paper. The study has concerned the footbridge above the S8 expressway, and the structure above the University Route in Bydgoszcz. The vibration testing altogether with the system identification and correlation techniques have been applied in the study.  
Firstly, experimental tests under different scenarios of human-induced load, impulse load, and excitations induced by vibration exciter, have been conducted. The results obtained show that it is possible to detect all four bending mode shapes, and the corresponding natural frequencies, of the deck for the footbridge above S8 expressway in the case of impulse excitation. Moreover, the study proves that for a footbridge above the University Route in Bydgoszcz, only the test with the use of impulse excitation allows the identification of five frequencies that have not been triggered by any other excitation (human-induced load or using a vibration exciter). The results of the tests indicate that both structures under investigation have the first bending frequency of the deck in the range of human-induced excitation. Therefore, there is a risk of excessive structural vibrations during exploitation.  
In the second stage of the study, numerical analyses have been carried out. The detailed FEM models, based on technical drawings, have successfully matched the experimentally identified modal parameters of the footbridges. The comparison between experimental and numerical results show a good agreement, both in the case of frequencies and mode shapes, with the MAC value close to one.  
Finally, the vibration serviceability of footbridges has been assessed according to the current codes of practice. The footbridge over the S8 expressway, regardless of the scenario of human-induced loading (even with excitations that can be considered as vandalistic), provides a maximum level of comfort to its users. Different situation concerns the footbridge above the University Route in Bydgoszcz. This time, the accelerations measured under synchronized walking, running, and jumping scenarios have exceeded comfort level, even for a small group of pedestrians. The results of the study show that this structure meets the assumptions of the guidelines for vibration severability in normal use; nevertheless, it is susceptible to excitations induced by synchronized users, even in the case of a small group of pedestrians.  
It should be added that, once the footbridge has been constructed, it is recommended to conduct dynamic field tests, especially if the frequencies determined from the numerical model at the design stage are similar to the human-induced loading. The identified dynamic parameters can be further used to update the numerical model. Then, the updated numerical model can be employed to carry out the extensive numerical analyses focused on the response of structures under different dynamic loads, including wind and earthquakes.  
Conceptualization, A.B. and R.J.; Methodology, A.B; Formal analysis, A.B.; Validation, A.B. and R.J.; Resources, A.B.; Writing--original draft preparation, A.B.; Writing--review and editing, R.J.; Supervision, R.J. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
The authors would like to thank the staff of Field Research Laboratory for help in conducting the experimental tests.  
The authors declare no conflict of interest.