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 paper, the dynamic responses of a large-scale multiple-support road viaduct to mining-induced seismic events registered in two regions of mining activity were compared. The regions differ in geological structure, which results in discrepancies in the dominant frequency content. Spatial variation of ground motion causing the kinematic excitation non-uniformity was accounted for in the dynamic analyses of this large-scale structure. Non-uniform mining-induced kinematic excitation models were proposed, with respect to the specificity of mining origin quakes. The dynamic performance of the viaduct was determined using three different methods of calculation: the time history analysis, the response spectrum analysis, and the multiple support response spectrum analysis. Both the uniform and non-uniform kinematic excitation models were adopted for the dynamic performance assessment. The research revealed that the dynamic response of some members of the structure, determined using the non-uniform excitation model, was significantly greater than that obtained for the uniform one. Hence, in the dynamic analysis of multiple-support structures under mining-induced events, the effect of spatial variation of ground motion should be considered. The study pointed out that the commonly used response spectrum analysis may lead to the underestimation of the dynamic response of large-scale multiple-support structures. Instead, the multiple support response spectrum method, which takes into account the non-uniformity of ground motion, is recommended as a conservative approximation. This method provides a safe upper estimation of the full-dynamic analysis results of large-scale structures under mining-induced tremors. Finally, the research indicated that the dynamic performance of a structure strongly depends on the frequency range attributed to a specific mining region. The dynamic performance of identical engineering structures under tremors of similar maximal amplitudes may differ significantly due to discrepancies in frequency contents of shocks occurring in various mining regions.
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