# Effect of Vinyl Flooring on the Modal Properties of a Steel Footbridge
## 2 Unexpected High Experimental Damping Ratios of the Jorge Manrique Footbridge
### Description of the Structure, Numerical Finite Element (FE) Model and Numerical Modal Analysis  
The Jorge Manrique footbridge is located at Murcia (Spain). It was designed and built to connect the two banks of the Segura River which crosses the urban center of this town. The footbridge is one of the most innovative bowstring arch footbridges built in Spain at the end of the last century (Figure 1a). Its structural system consists of two main tied-arches linked to a steel spatial truss deck by two groups of 48 inclined hangers with a diameter of 24 mm. The deck is isostatically supported on rolled and pinned bearings. The span of the footbridge is around 54 m. The deck has a variable width, from 12.9 m at the abutments to 6.4 m at mid-span. The depth of the deck is equally variable, evolving from 0.6 m at the abutments to 1.2 m at the mid-span. The cross-section of the upper arch is a steel tubular profile with a diameter of 350 mm and 40 mm of thickness. Finally, the steel truss deck is configured spatially by an upper grating composed by \(\frac{1}{2}\) IPE-100 and HEA-100 European profiles and a spatial mesh of structural elements composed by tubular profiles whose diameter varies from 89 to 140 mm. The deck floor is composed of two layers: (i) a top vinyl non-woven flooring (Figure 1b) with 18 mm of thickness and a weight of 8.2 kg/m\({}^{2}\)[19] and (ii) a lower tempered glass layer with 30 mm of thickness. As mentioned previously, this upper layer was installed several years after the opening of the footbridge in order to avoid falls among pedestrians caused by its original sliding surface. During several years after its opening, local newspapers had published news about the complaints of the users due to both the falls and the high vibration level experienced when they crossed the footbridge [11; 12]. Surprisingly the placement of the vinyl flooring not only improved the adherence of the floor but also the comfort level of the structure. Thus, a study was performed to analyze the effect of this non-structural element on the modal parameters of the footbridge. The modal parameters of the structure were identified experimentally via signal processing, using an operational modal analysis (OMA) algorithm, of the measurements recorded during an ambient vibration test (AVT) [20]. In order to both establish the main parameters of this experimental test and check the experimental results, a finite element (FE) model of the footbridge was performed. The commercial FE analysis package Midas [21] was used for this purpose. The FE model was composed by 44,710 nodes and 58,192 elements. Two types of elements were considered: (i) 3D beam elements to model the arches and the deck and (ii) 3D cable elements to simulate the behavior of the hangers (Figure 2). For the FE model, it was assumed that the non-structural floor,  
Figure 1: Jorge Manrique footbridge. (**a**) Longitudinal view of the structure and (**b**) view of the vinyl flooring installed on the footbridge. both the glass layer and the vinyl layer, does not modify the stiffness of the structure and only affects the mass. As mechanical properties of the steel, the values proposed by the European standards were adopted [22]: (i) density, \(\rho_{s}=7850\) kg/m\({}^{3}\), (ii) [PERSON]'s modulus, \(E_{s}=210000\) MPa, and (iii) [PERSON]'s ratio, \(\
u_{s}=0.3\). Finally, the footbridge is simply supported on four bearings. Each bearing is located at both sides of each arch. Two numerical FE modal analyses [23] were performed: (i) footbridge without the vinyl flooring and (ii) footbridge with the vinyl flooring. As results of these analyses the first three numerical vibration modes and associated numerical natural frequencies were obtained. Table 1 shows both the first three numerical natural frequencies without the vinyl flooring, \(f_{num\_wo,j}\), and with the vinyl flooring, \(f_{num\_j}\) (being \(j\) the number of the considered vibration mode).