# Experimental and Numerical Study on Dynamics of Two Footbridges with Different Shapes of Girders
## 1 Introduction
The modal parameters obtained from experimental tests could also be used further in updating [50; 51; 52; 53; 54; 55; 56; 57; 58], structural health monitoring (SHM) [59; 60; 61; 62], non-destructive diagnostics [63; 64; 65], and others. The second approach intended to estimate the dynamic properties of structures is to conduct numerical analysis. The use of the numerical models of real structures to perform modal analysis had many advantages. It allowed us to predict (i.e., at the design stage) the expected levels of acceleration caused by the human-induced load. Thus, if the comfort level was exceeded, the modification of the structure was possible. However, there is one disadvantage. The creation of a numerical model that sufficiently reliably describes the dynamic properties of a real structure is a very complex issue [50]. It is due to a large number of unknowns at this stage, including estimation of the damping ratio, appropriate boundary conditions, modeling of joints, material properties, and the influence of non-structural elements on dynamic parameters of the structure [66]. Therefore, the best practice is the development of the numerical model, followed by dynamic field tests to confirm the assumptions. Another important issue is how to model the human-induced load. There are many models which can be used, but it should be remembered that walking behavior is an individual feature. It also depends mainly on synchronization with the structure and with other pedestrians. The human-structure interaction (HSI) phenomena were widely investigated in the literature [67; 68; 69; 70; 71; 72]. Therefore, it is not easy to develop one universal model describing human-induced load [73]. The paper presents an experimental and numerical investigation focused on two examples of footbridges in Poland. Both footbridges had reinforced concrete decks and steel girders. One of the structures was an example of a typical arch bridge, while the second was characterized by the unusual shape of the steel girder. It was decided to compare both structures and examine the influence of the unusual shape of the girder on the dynamic parameters. For both structures, the detailed experimental tests and numerical analyses were conducted. The field tests were carried out under different sets of pedestrian crowd loads. Various human-induced load scenarios allowed us to draw conclusions about the risk of excessive vibrations during exploitation. Hence, based on the obtained acceleration time histories, it was possible to assess the level of comfort. The footbridges were also tested under an impulse load and excitations induced by a light vibration exciter, so as to identify dynamic parameters, such as natural frequencies, mode shapes, and damping ratios. The dynamic parameters of both footbridges considered in numerical analyses were verified by comparing them with the results from the field tests. The article is arranged as follows. In Section 2, the footbridges and created numerical FEM models are described. The theoretical basics of the dynamic and modal analysis are presented altogether with data processing and mode shapes and frequencies validation criteria. A field test conducted on the designed footbridges, consisting of acceleration measurements, is also described in this section. Subsequently, the results from the numerical analysis and the field test are compared and discussed in Section 3. In this section, the comfort criteria for both footbridges based on the accelerations obtained in field tests were also assessed. Finally, conclusions were presented in Section 4.