## 4 Application to a Stock of Bridges with Current Verification Loads
The lowest value of \(\alpha_{cr,k}\) for each load position was taken as the \(\alpha_{cr}\) for the specific \(s\)-\(H_{MAX,d}\) configuration. The lowest among the load multipliers \(\alpha_{cr}\) of each of the \(s\)-\(H_{MAX,d}\) couples identified the reserve capacity that could be guaranteed for the investigated arch. The results of the analyses for each of the \(f/L\) ratios and \(L=5\) m are shown in Table 1.  
The analyses were performed for different spans, and the outcomes are summarized in Table 2 and Figure 9.  
Being that the minimum load multiplier precisely describes the Load Rating Factor \(V\), the following factors (Table 2) can be obtained for the 1945A design code with respect to the B2 line load. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & & \multicolumn{4}{c}{**L = 5 m**} \\ \hline \hline
**f/L** & **Load** & \(s_{min}\) **(m)** & \(H_{MAX,d}\) **(kN)** & \(s(\alpha_{cr,B2})\) **(m)** & \(\alpha_{cr,B2}\) \\ \hline
1/2 & 1945A-single-axis wagon & 0.59 & 235.99 & & \\
1/2 & 1945A-locomotive & 0.54 & 307.34 & 0.67 & 1.17 \\
1/2 & 1945A-multiple wagons & 0.55 & 232.79 & & \\
1/3 & 1945A-single-axis wagon & 0.42 & 272.43 & & \\
1/3 & 1945A-locomotive & 0.36 & 366.96 & 0.54 & 1.21 \\
1/3 & 1945A-multiple wagons & 0.38 & 269.62 & & \\
1/4 & 1945A-single-axis wagon & 0.37 & 313.23 & & \\
1/4 & 1945A-locomotive & 0.31 & 443.75 & 0.53 & 1.12 \\
1/4 & 1945A-multiple wagons & 0.33 & 315.96 & & \\
1/5 & 1945A-single-axis wagon & 0.35 & 352.07 & & \\
1/5 & 1945A-locomotive & 0.29 & 526.24 & 0.5 & 1.08 \\
1/5 & 1945A-multiple wagons & 0.31 & 362.91 & & \\
1/6 & 1945A-single-axis wagon & 0.33 & 394.37 & & \\
1/6 & 1945A-locomotive & 0.27 & 613.37 & 0.45 & 1.05 \\
1/6 & 1945A-multiple wagons & 0.29 & 413.19 & & \\
1/8 & 1945A-single-axis wagon & 0.29 & 479.67 & & \\
1/8 & 1945A-locomotive & 0.24 & 780.97 & 0.39 & 1.02 \\
1/8 & 1945A-multiple wagons & 0.25 & 514.88 & & \\
1/10 & 1945A-single-axis wagon & 0.26 & 564.18 & & \\
1/10 & 1945A-locomotive & 0.21 & 943.41 & 0.42 & 0.97 \\
1/10 & 1945A-multiple wagons & 0.22 & 612.97 & & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Minimum load multipliers for arches designed according to the 1945A code and verified with the B2 load. Similarly, this approach was adopted for the 1925, 1926, and 1945A and 1945B design codes, as well as for the B2, C3, and D4 load lines. The minimum reserve capacity for each combination of design and verification loads are reported in Table 3.  
It appears evident that, for arches designed according to the 1926 code, no capacity reserves could be found, since \(\alpha_{cr}\) is always less than 1. This result is due to the fact that the 1926 code prescribes the use of distributed loads, which are less critical because they induce a shape of the bending moment that follows the shape of the arch fairly well, and in principle allows for the design of arches with a very small depth. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & \multicolumn{8}{c}{**Codes: 1945A vs. B2**} \\ \hline \multirow{2}{*}{**f/L**} & \multicolumn{8}{c}{**Arch Bridge Length L (m)**} \\ \cline{2-9}  & **5** & **10** & **15** & **20** & **25** & **30** & **40** & **50** \\ \hline
1/2 & 1.17 & 1.83 & 2.38 & 2.22 & 2.55 & 2.20 & 2.37 & 2.09 \\
1/3 & 1.21 & 1.64 & 1.75 & 2.04 & 2.46 & 2.27 & 2.38 & 2.36 \\
1/4 & 1.12 & 1.50 & 1.82 & 2.12 & 2.41 & 2.27 & 2.31 & 2.21 \\
1/5 & 1.08 & 1.51 & 1.74 & 2.08 & 2.41 & 2.23 & 2.38 & 2.22 \\
1/6 & 1.05 & 1.47 & 1.67 & 1.98 & 2.41 & 2.23 & 2.31 & 2.22 \\
1/8 & 1.02 & 1.41 & 1.66 & 1.94 & 2.39 & 2.23 & 2.36 & 2.21 \\
1/10 & 0.97 & 1.42 & 2.05 & 2.01 & 2.39 & 2.23 & 2.28 & 2.24 \\ Minimum & 0.97 & 1.41 & 1.66 & 1.94 & 2.39 & 2.20 & 2.28 & 2.09 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Load Rating Factors \(V\) for arches designed according to the 1945A code and verified with the B2 load. Figure 9: Reserve capacity of arches designed according to the 1945A code and verified with the B2 load.