# Effect of Vinyl Flooring on the Modal Properties of a Steel Footbridge
## 4 Assessment of the Dynamic Behavior of a Laboratory Footbridge without and with the Vinyl Flooring
### Description of the Structure, Numerical FE Model and Numerical Modal Analysis  
The laboratory footbridge is a frame steel structure (Figure 4). The structure has only one span of about 4 m of length. The deck is composed by two longitudinal lateral beams and five transverse beams. The cross-section of the longitudinal beams is a European profile UPN 50 \(\times\) 25 \(\times\) 5 mm. The transverse beams are configured by two different profiles: (i) for the transverse beams at the supports, a single L 50 \(\times\) 5 mm profile is considered and (ii) for the remaining transverse beams, a double L 50 \(\times\) 5 mm profile is chosen. Four columns, UPN 50 \(\times\) 25 \(\times\) 5 mm, link the deck of the structure to the foundation. Additionally, a tramex panel (30 \(\times\) 3 mm) is included between each two transversal beams. The columns are clamped to the foundation slab and simply pinned to the deck. The vinyl flooring was installed on the footbridge mimicking the same connection conditions of the Jorge Manrique footbridge. The vinyl flooring was connected to the laboratory footbridge via several steel clamps. The clamps were separated longitudinally around 0.5 m and transversally around 0.8 m.  
A FE model of the structure was built (Figure 4) with the FE package Midas [21]. A numerical model with 133 nodes and 156 elements was developed in order to both assist in the design of the subsequent AVT test and check the experimental modal parameters. Two types of elements were used to build this numerical model: (i) 3D beam elements and (ii) 3D shell elements. In this manner, the behavior of all the beams and columns of the structure were simulated by the 3D beam elements. Meanwhile, the 3D shell elements were considered in order to simulate numerically the behavior of the tramex panels. A linear isotropic constitutive law was considered for 3D beam elements while a linear orthotropic constitutive law was taken into account for the 3D shell elements. As material properties for the steel, the values recommended by European standards were again chosen [22]. As an assumption, the effect of the vinyl flooring was simulated again via the modification of the mass matrix of the structure by an equivalent distributed mass of 8.2 kg/m\({}^{2}\)[19].  
Subsequently, the numerical natural frequencies of the laboratory footbridge for the two different scenarios were obtained through two different numerical modal analyses [23]. Thus, the first five numerical vibration modes of the footbridge without, \(f_{num,j}^{wo\_2,pf}\), and with, \(f_{num,i}^{w\_2,pf}\), the vinyl flooring (being \(j\) the number of the considered vibration mode) are shown in Table 3. Additionally, Figures 5 and 6 illustrate the first five numerical vibration modes of the laboratory footbridge without, \(\phi_{num,j}^{wo\_pf}\), and with, \(\phi_{num,j}^{w\_2,pf}\), the vinyl flooring respectively.  
Figure 4: Description, FE model and AVT of the laboratory footbridge.  
Figure 5: First five numerical, \(\phi^{wo,pf}_{num,j}\), and experimental, \(\phi^{wo,pf}_{exp,j}\), vibration modes of the laboratory footbridge without the vinyl flooring (being \(j\) the number of the considered vibration mode).  
Figure 6: First five numerical, \(\dot{\psi}_{num,j}^{w,pf}\), and experimental, \(\dot{\phi}_{exp,j}^{w,pf}\), vibration modes of the laboratory footbridge with the vinyl flooring (being \(j\) the number of the considered vibration mode).