# Seismic Assessment of Historical Masonry Buildings at Different Scale Levels: A Review
## 2 Large-Scale Approaches
### Mechanical Methods
#### 2.2.1 Simplified Mechanical Methods  
Simplified numerical methods are used to analyse a rather relevant number of buildings based on a few mechanical and geometrical input parameters, leading to a reliable qualitative evaluation in a relatively short time. Even if more time demanding than empirical methods, they provide higher result accuracy since they are based on data with direct physical meaning. Among them, methods referring to the evaluation of a single resistance factor related to the likely predominant collapse mechanisms (e.g., in-plane shear failure) and therefore depending on the building typology characteristics, can be found. The result is approximated since the collapse mode is a priori defined but has the advantage of requiring a quite limited number of geometrical and material features, then being relatively fast. After the Umbria-Marche earthquake (1997), [PERSON] and [PERSON] (1997) elaborated one of the first procedures--later implemented by other contributors such as [PERSON], [PERSON] (1997)--related to a predominant collapse mechanism. The procedure is based mostly on geometrical data, allowing the calculation of three indexes (i.e., in-plan area ratio, area-to-weight ratio and base shear ratio) that, compared to reference values, allowed \begin{table}
\begin{tabular}{c c} \hline \hline \multicolumn{2}{c}{**Mechanical Methods**} \\ \hline
**Simplified Mechanical Methods** & **Detailed Mechanical Methods** \\ \hline [PERSON] [77] & [PERSON], [PERSON] [78] \\ [PERSON] and [PERSON] [79] & [PERSON], [PERSON] [80] \\ [PERSON], [PERSON] [68] & [PERSON], [PERSON] [81] \\ [PERSON] [69] & [PERSON] and [PERSON] [66] \\ [PERSON]\({}^{\prime}\)[PERSON] and [PERSON] [70] & [PERSON], [PERSON] [82] \\ [PERSON] and [PERSON] [71] & [PERSON], [PERSON] [83] \\ [PERSON] and [PERSON]\({}^{\prime}\)[PERSON] [72] & [PERSON], [PERSON] [84] \\ [PERSON] and [PERSON] [73] & [PERSON], [PERSON] [85] \\ [PERSON] and [PERSON]\({}^{\prime}\)[PERSON] [74] & [PERSON], [PERSON] [86] \\ [PERSON], [PERSON] [75] & [PERSON], [PERSON] [87] \\ [PERSON], [PERSON] [76] & [PERSON], [PERSON] [88] \\ [PERSON] [89] & [PERSON] and [PERSON] [90] \\ [PERSON], [PERSON] [91] \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Summary of different proposals for the mechanical analysis of masonry structures. for identifying the most vulnerable buildings within the same seismicity zone. Again, the SAVE procedure, determining the collapse peak ground acceleration (PGA) in each direction starting from the building's shear resistance evaluated through geometrical data was proposed by [PERSON] and [PERSON] [71]. [PERSON], [PERSON] [76] implemented the SAVE approach elaborating the RE.SIS.TO method and accounting for the possible structural criticisms highlighted during the in situ surveys by means of reductive coefficients. Besides the above-presented approaches, another category of simplified mechanical methods is based on kinematic models applied to the structures subdivided into macro-elements. Such methods aim to verify the activation of failure modes involving one or more structure portions. The demand is defined through parameters such as drift, displacement or PGA, associated with an output in terms of collapse-load multipliers representing a vulnerability index to be correlated with damage thresholds. The subdivision into macro-elements, necessary for the method application, fits the results of the knowledge investigations (e.g., structural system, connections between perpendicular walls, structural discontinuities, historical evolution, surveyed crack pattern, etc.). As stressed by [PERSON], [PERSON] [92] and [PERSON], [PERSON] [2], the kinematic analysis presents some shortcomings, therefore needing careful handling of the results.