## 1 Introduction  
Recent bridge failures all over the world [1, 2, 3], including the collapse of the Morandi bridge in Italy, which caused 43 deaths in 2018 [4], turned the spotlight on the state of the existing bridge asset worldwide [5]. In the wake of such accidents, verifying whether heritage structures have enough load-carrying capacity to comply with current codes has become an urgent need [6, 7, 8, 9]. For those structures constructed prior to the most recent codes, which represent the majority of the railway infrastructures in many countries [10, 11, 12], the old age of the bridges and consequential lack of documentation makes it particularly complicated to acquire information from the infrastructure operators [9, 13, 14]. In principle, in order to properly understand the state of deterioration and residual capacity of an existing bridge [14, 15, 16, 17], an extensive campaign of tests, monitoring, and assessment needs to be conducted [12, 14, 18, 19, 20]. However, the large number of structures typically managed by each operator makes it unfeasible to conduct, in the short term, an in-depth evaluation of every bridge [8, 21, 22]. Consequently, several national authorities have developed assessment procedures involving multiple levels of complexity: the logic is to assess all bridges with a first-level conservative procedure [23, 24, 25], which requires minimal knowledge of the structural extent, and then proceed with more refined assessment methods [26; 27] only if a critical situation [28] or insufficient load-carrying capacity [29; 30; 31] is highlighted. Understanding what the original code design demand was, and comparing it with the current code design demand, is therefore a key step in carrying out the first level of verification [12; 32; 33], particularly for masonry arch railway bridges [11; 34], most of which were designed according to pre-WW2 codes [8; 21; 35]. As for first level verifications, operators could perform extensive numerical simulations on their stock of bridges to evaluate their load-carrying capacity, as performed in [36] for a single masonry arch bridge. Nevertheless, recent developments in numerical simulation, applied to civil engineering, mainly focus on accurately studying complex structural behaviors and actions [8; 9; 37; 38; 39; 40], rather than on providing expeditious methods of working with limited input data. In the literature, different theories about the safety of masonry arches can be found [41], among which are the Mery Method [42], the first rational approach to arches [43], and Heyman's Safe Theorem [44; 45]. Yet even the most recent methods for evaluating the capacity of masonry arch bridges [32; 46], including those based on limit analysis [47; 48] and probabilistic approaches [32], involve a thorough and comprehensive knowledge of the structural geometry and properties. In particular, all geometric [47] and material data [32] are required, in most procedures, in order to evaluate the arch capacity, with special consideration of the arch depth and fill properties [49]. It is, however, difficult to obtain such information without performing expensive inspections and samplings [11; 50]. In addition, despite existing exhaustive numerical studies on the behavior of masonry arch bridges [8; 36], the technical literature does not currently report any 'fast and frugal' methods for assessing the reserve capacity of a masonry arch. In this article, we propose an expeditious procedure to conservatively assess the reserve capacity of masonry arch railway bridges with a minimal set of information, namely the span, rise-to-span ratio and design code, employable within a framework of risk assessment and prioritization of interventions.