In this paper, the seismic assessments of two footbridges, i.e., a single-span steel frame footbridge and a three-span cable-stayed structure, to the spatial variation of earthquake ground motion (SVEGM) are presented. A model of nonuniform kinematic excitation was used for the dynamic analyses of the footbridges. The influence of SVEGM on the dynamic performance of structures was assessed on both experimental and numerical ways. The comprehensive tests were planned and carried out on both structures. The investigation was divided into two parts: in situ experiment and numerical analyses. The first experimental part served for the validation of both the finite element (FE) modal models of structures and the theoretical model of nonuniform excitation as well as the appropriateness of the FE procedures used for dynamic analyses. First, the modal properties were validated. The differences between the numerical and the experimental natural frequencies, obtained using the operational modal analysis, were less than 10%. The comparison of the experimental and numerical mode shapes also proved a good agreement since the modal assurance criterion values were satisfactory for both structures. Secondly, nonuniform kinematic excitation was experimentally imposed using vibroseis tests. The apparent wave velocities, evaluated from the cross-correlation functions of the acceleration-time histories registered at two consecutive structures supports, equaled 203 and 214 m/s for both structures, respectively. Also, the coherence functions proved the similarity of the signals, especially for the frequency range 5 to 15 Hz. Then, artificial kinematic excitation was generated on the basis of the adopted model of nonuniform excitation. The obtained power spectral density functions of acceleration-time histories registered at all supports as well as the cross-spectral density functions between registered and artificial acceleration-time histories confirmed the strong similarity of the measured and artificial signals. Finally, the experimental and numerical assessments of the footbridges performance under the known dynamic excitation generated by the vibroseis were carried out. The FE models and procedures were positively validated by linking full-scale tests and numerical calculations. In the numerical part of the research, seismic analyses of the footbridges were conducted. The dynamic responses of structures to a representative seismic shock were calculated. Both the uniform and nonuniform models of excitation were applied to demonstrate and quantify the influence of SVEGM on the seismic assessment of footbridges. It occurred that SVEGM may generate non-conservative results in comparison with classic uniform seismic excitation. For the stiff steel frame footbridge the maximum dynamic response was obtained for the model of nonuniform excitation with the lowest wave velocity. Especially zones located closely to stiff frame nodes were significantly more disturbed. For the flexible cable-stayed footbridge, in case of nonuniform excitation, the dynamic response was enhanced only at the points located in the extreme spans and in the midspan closely to the pillars.

In this work, an examination on the modal properties of a single-span steel-frame footbridge is presented. The footbridge is situated in Jawornik (Lesser Poland). The footbridge is symmetrical since its main structure consists of two steel frames of the same shape. The boundary conditions for both frames are the same as well. The study was completed on the basis of numerical as well as experimental investigations. For finite element (FE) analysis, a 3-D model of the single-span steel-frame footbridge was created. For the experimental study, a research scheme for in situ tests was developed. Three kinds of excitation techniques were used during the in situ tests: shock excitation, operational vibration, and slow sine sweep testing. Different functions that estimate natural frequencies, i.e., the power spectral density function (PSD) and the frequency response function (FRF), were applied. The modal assurance criterion (MAC) was used as a mathematical tool for the verification of the mode shapes of natural vibrations obtained in experimental and numerical ways. Good compatibility was recognized between the results obtained for experimental and numerical procedures in terms of both the natural frequency and the mode of vibration. The identified and verified values of the five consecutive natural frequencies of the footbridge were smaller than 5 Hz, but they were recognized as being located outside the frequency range defined as having “maximum risk of resonance”. The numerical and experimental modal analysis revealed that all modes corresponding to the natural frequencies from the 0–5 Hz range have both a symmetrical and an anti-symmetrical nature. In particular, the first vertical mode, which can play a central role from the serviceability of the footbridge point of view has a symmetrical shape. The results of the research might be applicable to the dynamic study of the structure type considered in the analysis, i.e., for the dynamic assessment of a single-span steel-frame footbridge with a relatively large mass as well as stiffness. The investigation proved that ambient vibration modal experiments are enough for the experimental investigation of the modal properties of the structure.

In this study, the human-induced dynamic performance of modern footbridges equipped with either classical reinforced concrete (RC) or innovative glass fiber-reinforced polymer (GFRP) composite deck slabs were investigated and compared. The numerical studies were carried out for two bridges: a three-span cable-stayed footbridge and a three-span continuous beam structure. Two variants of both bridges were taken into consideration: the footbridges equipped with traditional RC slabs and the structures benefitted with GFRP slabs. The risk of resonance as well as the vibration serviceability and the comfort criteria assessment of the footbridges with different slab materials were assessed. The investigation revealed that the footbridges, both cable-stayed and beam, benefitted with the GFRP slabs had higher fundamental frequency than those with the traditional RC slabs. The footbridges with the GFRP slabs were less exposed to the resonance risk, having fundamental frequencies above the limit of the high risk of resonance. The effect of shifting up the natural frequencies by introducing GFRP slabs was more remarkable for the lightweight beam structure than for the cable-stayed footbridge and resulted in a more significant reduction of the resonance risk. The calculated maximum human-induced accelerations of the footbridges benefitted with the GFRP slabs were meaningfully higher than those obtained for the footbridges with the RC slabs. The study proved that, with the same GFRP slab, meeting vibration serviceability and comfort criteria limits in the case of very lightweight beam structures may be more problematic than for cable-stayed footbridges with more massive structural systems. In the research, particular attention was paid to examining the impact of higher harmonics of the moving pedestrian force on the structures benefitted with the GFRP composite slabs. It occurred that in the case of footbridges, both cable-stayed and beam, equipped with the RC slabs higher harmonics of human force did not play any role in the dynamic performance of structures. However, in the case of the footbridges benefitted with the GFRP slabs, the impact of higher harmonics of the pedestrian force on the dynamic behavior of structures was clearly visible. Higher harmonics excited accelerations comparable to those executed by the first harmonic component. This conclusion is of great importance for footbridges equipped with GFRP slabs. The fundamental frequency may place a footbridge in the low or even negligible risk resonance range and the higher frequencies corresponding to vertical modes may be located above the limit of 5 Hz that ensures avoiding resonance. Nevertheless, the fact that fundamental modes are so responsive to higher harmonics significantly increases the risk of resonance. The amplification of the dynamic response may occur due to frequencies related to second or third harmonics (i.e., being half or a third of the natural frequencies). In such cases, full dynamic analysis of a footbridge at the design stage seems to be of crucial importance.