## 6 Conclusions  
Many bridge operators are currently upgrading their procedures for inspection, maintenance, and monitoring of existing structures towards multilevel approaches. The logic is to start verifying the bridges with simple conservative methods, and then proceed with  
Figure 19: Load Rating Factor of arches designed according to the 1945 codes and verified with D4 loads, both with and without dynamic amplification comparison. Figure 18: Load Rating Factor of arches designed according to the 1945 code and verified with C3 loads, both with and without dynamic amplification comparison. more refined and expensive procedures, only if the minimal load carrying capacity is not assessed. In this paper, an easy-to-use method for first-level expeditious assessments of masonry arch railway bridges is proposed. This method provides conservative evaluation of the reserve capacity of existing arches, with respect to the current design load, given only its span, the rise-to-span ratio, and the original design code. The procedure perfectly responds to the need for a straightforward way of assessing the reserve capacity of existing bridges without the need for comprehensive knowledge of the structural properties. For specific masonry arches designed in compliance with the railway bridges codes in references [60; 61; 62], the following conclusions can be drawn:  
* Arches designed according to the 1926 code are not automatically verified for any of the current European line loads;
* If we neglect dynamic amplification, arches designed according to the 1925 code are verified for any of the current European line loads for spans \(L\geq 10\) m;
* If we consider dynamic amplification, arches designed according to the 1925 code are never automatically verified for line loads C3 and D4, while they are verified for B2 line loads, though only for spans \(L\geq 25\) m;
* If we neglect dynamic amplification, arches designed according to the 1945 code are verified for any line loads for spans \(L\geq 10\) m;
* If we consider dynamic amplification, arches designed according to the 1945 code with load type 1945A, are verified for any line loads for spans \(L\geq 15\) m;
* If we consider dynamic amplification, arches designed according to 1945 code with load type 1945B, are verified for line loads C3 and D4, spans \(L\geq 20\) m, and line load B2 for spans \(L\geq 15\) m.  
The method presented can be extended to any pair of transit load and design code. It therefore provides a simple and immediate estimate of the nominal reserve capacity for any masonry arch bridge, and allows a priori knowledge of whether in-depth analysis might be worthwhile, thus enabling operators to single out those structures requiring immediate interventions or thorough verifications. For agencies managing a large stock of bridges, this conservative evaluation of the Load Rating Factor is a useful tool for classifying bridges based on their capacity deficit. This method provides a priority ranking for tests, inspections, and formal assessment, as well as for programming maintenance, repair, and reconstruction works. Conceptualization, D.Z., F.B. and L.P.; methodology, F.B., D.Z. and L.P.; software, L.P. and F.B. ; validation, F.B., L.P. and D.Z. ; formal analysis, L.P. and F.B. ; investigation, F.B. and L.P.; resources, F.B. and L.P.; data curation, L.P. and F.B. ; writing--original draft preparation, F.B. and L.P.; writing--review and editing, F.B., L.P. and D.Z. ; visualization, L.P. and F.B. ; supervision, L.P. and D.Z. ; project administration, D.Z. ; funding acquisition, D.Z. All authors have read and agreed to the published version of the manuscript. This research was funded by RFI--Rete Ferroviaria Italiana, in the frame of the research agreement \"Estensione del sistema DOMUS per la Gesitone dei Ponti Ferroviari\". Not applicable. The data that support the findings of this study are available on request from the corresponding author (L.P). Restrictions apply to the availability of these data, which were used under license for this study.