# Seismic Assessment of Historical Masonry Buildings at Different Scale Levels: A Review
## 2 Large-Scale Approaches
### Mechanical Methods
#### 2.2.2 Detailed Mechanical Methods  
The detailed mechanical methods are based on the capacity spectrum methods (CSM) [77; 102; 103], assessing the expected building performance through the spectral coordinates' comparison. A graphical representation of the global capacity--in terms of force-displacement relationship--is provided to be compared with the response spectrum representation of the earthquake demand. In particular, the capacity curve is determined by applying an incremental static load to the structure and recording the base shear and the displacement of a reference point on the top step by step. Detailed mechanical methods developed for existing buildings usually require the buildings' classification--depending on typology and seismic design--and the definition of the damage states. Then, a capacity curve is associated with the building class to correlate with a spectral demand curve described by acceleration-displacement response spectra opportunely reduced to account for the inelastic behaviour. Finally, the evaluation of the seismic response is performed in terms of performance points [60]. The approach was first proposed by HAZUS [77], introducing 33 classes based on the functional destinations and 36 model buildings referring to the material and the structural system. Four damage levels for structural and non-structural elements and the relative fragility curves characterised each building class; pushover curves and capacity curves were also defined, accounting for the indications outlined by ATC-40 [104] and FEMA356 [105]. One of the main advantages of these methods is that they do not require detailed information on all the analysed buildings. Once defined the capacity curves for each typology, only the damage thresholds and the number of buildings for each typology are needed. The assessment of the structural behaviour of a given building within the range defined by its reference fragility curve is allowed through a parametric analysis [60]. The method's strength is, at the same time, its weakness since it provides a reliable result if the area being analysed is characterised by the homogeneity of the building typology and by a consolidated seismic design code [58]. Such shortcoming makes the method suitable for the American scenario rather than for the European ones; despite that, a few attempts to use the HAZUS approach in the European framework can be found in the scientific literature [78; 79; 82]. A mechanics-based approach similar to that proposed in HAZUS [77] was developed within the framework of the RISK-UE project [80]. [PERSON] and [PERSON] [66] proposed a double-level approach, later detailed within the hybrid methods, including a mechanical model applicable when PGA and spectral values are provided to describe the hazard. A simplified version of the CSM was introduced to evaluate the building's seismic performance in terms of damage limit states. More recently, [PERSON], [PERSON] [83] proposed a mechanical method for the large-scale assessment of RC buildings--later extended to masonry ones [84]. It proposed to identify the capacity limit on the capacity curve to be compared with the demand deduced from a response spectrum for each building in the random population, finally resulting in vulnerability curves. Particularly important for cultural heritage assets was the modified CSM proposed within the framework of the PERPETUATE project [87]. It introduced corrective factors for the building's irregularities and proposed new limit states, specifically calibrated for cultural heritage buildings, accounting for human life safety and specific conservation requirements. Each limit state was correlated to damage measures for single structural elements and the entire building. As for the other CSM methods, the approach was calibrated, assuming perfect connections between perpendicular walls. Implementing the CSM proposed within the PERPETUATE project was the investigation concerning the rocking of masonry structures performed in Lagomarsino [89].