# Experimental and Numerical Study on Dynamics of Two Footbridges with Different Shapes of Girders
## 2 Materials and Methods
### Vibration Testing  
Both of the analyzed footbridges underwent static and dynamic field tests. During the static tests, displacements of the deck, settlements of the supports and forces in hangers were measured. The dynamic tests included measurements of the vertical displacements of the deck, an increase of strains in the hangers and accelerations of the platform and the arch or steel girder. Figure 4: General structural arrangement and typical cross-section of the footbridge above the University Route in Bydgoszcz (dimensions in mm). Figure 3: Side and front view of the footbridge above the University Route in Bydgoszcz. Three-axial, micro-electro-mechanical capacitive accelerometers (MEMS) of the LIS344 ALH type manufactured by STMicroelectronics (Figure 5a) were used to measure the structure vibration response [74; 75]. They consist of a seismic mass suspended on a spring, for which length depends on the level of acceleration (see also [76]). A change in the length of the spring causes a change in the capacitance of the capacitor connected. In consequence, the electronic system contained in the accelerometer generates a voltage proportional to the capacitor's capacity. The LIS344 ALH has a full-scale of \(\pm\)2 g/\(\pm\)6 g, and the device is capable of measuring accelerations over a maximum bandwidth of 1.8 kHz for all axes. The sensor has small dimensions of \(4\times 4\times 1.5\) mm and a weight of 0.040 g. The operating temperature is between \(-\)40\(\sim\)85 \({}^{\circ}\)C. The measurement data were recorded using the QUANTUM HBM 840a 8-channel measurement amplifier (Figure 5d). A standard laptop was connected to the measuring station and it was used for the data processing, visualization, and storage of the measurement results. During the tests, accelerometers were placed in such a way that one axis was perpendicular to the axis of the deck, the second axis was vertical, and the third one was longitudinal. In each case, the accelerometers were rigidly connected to the platform of structure, either with concrete screws (Figure 5b) or with strong neodymium magnets and additionally compressed with the clamp elements of the hangers anchor (Figure 5c). The sampling rate was set to 600 Hz. As the main excitation of the footbridges is related to the movement of pedestrians, dynamic measurements were taken during the following tests: free and synchronized march, free and synchronized run and jumping (Figure 6). Depending on the test, 6, 9, and 12 pedestrian groups were used as a dynamic load. This allowed studying the influence of the increasing number of pedestrians on the values of received accelerations. In all tests related to walking or free running, each pedestrian was moving at their own pace. However, the synchronous excitations were harmonized using a metronome. In the case of walking and jumping, the frequency of human-induced load was consistent with the first bending frequency of the deck. Whereas the running tests were performed with pedestrian crossing at a pace rate close to 3 Hz. The measurements of accelerations were also taken for a dynamic impact test and using a light vibration exciter. During the impulse tests, a container filled with water with dimensions of \(1\times 1\times 1\) m was dropped from the height of ca. 6 cm on the footbridges deck. Also, the light vibration exciter was used, which generated a sweep signal with variable frequency in the range of 0-10 Hz. Both tests were repeated in the axis of each danger in a central axis of a platform. In each test, the measurement time was set in such a way that the suppression of free vibrations of the structure was allowed. In total, 37 dynamic tests were carried out for the footbridge over the S8 road and 38 for the footbridge above the University Route in Bydgoszcz.