# Finite Element Models of a Benchmark Footbridge
## 2 Description of the Benchmark Footbridge
### Field Tests  
Field tests were performed to study the footbridge performances under both static and dynamic loads.  
Static tests were performed in March 2011 by using four golf carts of 4.5 kN each as a moving static load [31]. Two carts were positioned side by side across the bridge width at 13 different locations along the instrumented length of the footbridge. Moment influence lines were obtained by calculating the curvature at each sensor location and by multiplying it by the flexural stiffness \(EI\) of the cross-section. Another static test was performed in April 2014 by positioning an approximately four-metric-ton truck (about 46.7 kN) in the middle of the longest span of the bridge, i.e., between P10 and P11 on the south-east leg [33]. The rear axle, which introduced the greatest portion of the load (42 kN), was placed directly above the sensors in the middle of the longest span. Displacements  
\begin{table}
\begin{tabular}{l c} \hline \hline Reinforced concrete [kN/m\({}^{3}\)] & 23.56 \\ Post-tensioned concrete [kN/m\({}^{3}\)] & 24.35 \\ Structural steel [kN/m\({}^{3}\)] & 76.97 \\ Bridge railings [kN/m] & 0.730 \\ Utilities [kN/m] & 0.219 \\ Future wearing surface [kN/m\({}^{2}\)] & 0.718 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Design dead loads.  
Figure 4: Position of parallel sensors [14].  
were obtained by double integration of the curvature, measured by sensors. Moreover, an independent displacement measurement using a laser was performed by a research group from Columbia University.  
The footbridge natural frequencies were obtained through different dynamic tests (Table 2). The ones described in [31] were performed in 2010 and refer to synchronized people running at 3 Hz, 4 Hz and at random frequencies for 30 s. Natural frequencies were extracted from Fast Fourier Transform (FFT) of the strain sensor measurements at the midspan between peers P10 and P11. From the tests with excitations of 3 and 4 Hz, two frequencies were identified, at 3.11 and 3.72 Hz, respectively. These values were confirmed by the test with random excitation (3.17 and 3.72 Hz). A subsequent measurement campaign was performed in 2014 with similar tests. Data were analyzed in [22], identifying the first two natural frequencies at around 3 and 3.6 Hz. Moreover, natural frequencies of higher modes (from third to sixth) were also identified. [PERSON] [20] performed quasi-static and dynamic tests by installing a newly designed wireless system (Acceleration Evaluator, ALE), which embeds an MEMS-based accelerometer. The ALE transmitter was installed at one-quarter of the south-east leg length, starting from the connection with the main span. Dynamic tests were performed with eight people jumping for 30 s at 3 Hz at the transmitter location and eight people running at random frequencies for 2 min between the main span-leg connection point and half of the leg total length. Identified frequencies were 3.08 and 3.75 Hz. Finally, [PERSON] et al. [34] tested an alternative methodology to measure dynamic displacements based on digital videos. The bridge deck was excited by people jumping on the south-east leg. Postprocessing of recorded videos allowed us to extract the vertical displacement response and to identify two peaks at 3 and 6.3 Hz, respectively.  
The small magnitude load induced by people during the above tests produced small strain amplitudes that could be used to identify natural frequencies, but not to accurately find deformed and mode shapes. Nevertheless, it is worth recalling that, due to the parallel sensors position, only vertical flexural modes of the south-east leg can be detected.