# Finite Element Models of a Benchmark Footbridge
## 4 Validation of FE Models
### Static Analysis  
The two static on-site tests (moving golf carts and static trucks) described in Section 2.5 are numerically simulated through the two FE models. In order to obtain moment influence lines to be compared with those experimentally measured, a resultant load of 18 kN, representing the total weight of four golf carts, was applied at different positions along the footbridge length. The load was differently distributed depending on the type of FE model. In the B model, the moving static load is applied as a single force of 18 kN concentrated on a deck node. In the S model, two different load distributions were tested (Figure 7):  
1. the total load has been applied as three forces of 6 kN each on three nodes of the generic cross section, in order to reproduce the equivalent load condition as in the B model;
2. the total load has been spread over a larger portion of the deck and applied as nine concentrated loads corresponding to the axes of the four golf carts. Figures 8-10 plot the obtained bending moment influence lines at three pier locations: P8, P10 and P11h12 (at half the span between P11 and P12), respectively. Numerical influence lines are compared with those obtained from sensor measurements [12], which are reported in red solid lines together with measurement errors in red dashed lines. Figure 6: S model. Figure 8: Bending moment influence line at P8. Figure 7: Scheme of load conditions L1 and L2 on S model. Figure 9: Bending moment influence line at P10. In detail, the B model and S model with L1 provide almost the same results for the influence lines as in P8 and P11h12 (Figures 8 and 10) because of the equivalent way in which the applied load is modeled. The rough representation of the loading conditions in these cases causes a discrepancy of about 50% between numerical and experimental outcomes at the peak bending moment in P8. On the contrary, considering the P10 location (Figure 9), the results highlight a higher variability between the B model numerical outcomes and the S ones, even when the load is applied in the same way. This is mainly due to the description of the connection between the main span of the bridge deck and the east legs (Figure 1), which is more accurately reproduced by the introduction of the shell elements for main girder modelling. Indeed, the S model influence lines at P10 are closer to the experimental ones. The S model with L2, with a more realistic description of the applied load, gives the best fit to the experimental results, with numerical influence lines generally falling inside the error limits of experimental measurements. Focusing on the influence lines at P10 (Figure 9), the experimental influence line is best approximated by the S-L2 model (relative error at the peak moment of about 26% with S-L2 against 110% with the B model). In this case, the more realistic description both of the deck geometry at the connection between the south-east leg and main span and of the transit loading conditions allows for the solving of the large discrepancy between experimental and B-bending moments when the load is applied between P10 and P11. The large discrepancy that still remains when the load is applied in P10 is expected, because at this location there is the connection between two structures (main span and leg) built at different times, so its physical continuity is not guaranteed. The second static test consists of the application of a concentrated load of 42.7 kN at a half span between P10 and P11 on the south-east leg. The load is applied as a single concentrated nodal force in the B model and divided into two concentrated nodal loads in the S model along the same cross-section. The displacements obtained along the south-east leg are compared with those estimated in [33], through double integration of the curvature according to both rectangular and trapezoidal rules, and with that measured by a laser.