# Seismic Assessment of Historical Masonry Buildings at Different Scale Levels: A Review
## 3 Small-Scale Approaches
### Rigid Plane Approaches  
The rigid plane approaches, also known as shear-connection methods, assume the masonry structural system as a combination of two perpendicular sets representing vertical planes (i.e., the facades and the inner walls) and an additional one simulating the horizontal planes (i.e., floor slabs). The approximation of infinitely rigid horizontal planes and the assumption of a full connection between floors and walls are the hypotheses at the base of the method, making it less accurate when dealing with historical structures provided by irregular wall openings, deformable slabs and poor connections. In Italy, rigid-plane approaches began to spread after the Friuli earthquake of 1976 to estimate the seismic building capacity on a large scale. In the Regional Law of Friuli-Venezia Giulia made in 1977 (L.R. 20.06.1977) the VeT and the POR [223] methods were introduced, to be later included in Circolar n\({}^{\circ}\) 21,745 of 30.07.1981 [224]. Even though their application may suggest a large-scale approach, the above-cited methods can be reliably applied to a relatively reduced group of buildings. They both assumed a regular distribution of piers at each level, and the stiffness of the wall as the sum of the shear stiffnesses of in-series piers and the diagonal shear strength as unique parameters accounted for the elastic-perfectly plastic constitutive law. For representing walls with openings, the POR method used an assemblage of strips that were infinitely stiff and resistant; pier elements were represented as idealised one-dimensional elements. A limited plastic deformation, where the plastic branch's length was determined depending on the masonry category (e.g., untreated stone, new brick masonry, existing brick masonry), is assumed differently from VeT. One of the main limitations of the POR method concerns the collapse mechanism, being shear failure the only considered, neglecting otherwise flexural phenomena. In general, the method highlighted good reliability when applied to two-floor structures, leading--in other cases--to an overestimation of the stiffness. From 1985 to 1995, several contributions were published aiming at a more accurate representation of the masonry walls' behaviour, overcoming the POR limits. The PORFLEX presented by [PERSON], [PERSON] [12] proposed an elastic-brittle constitutive law, strips infinitely stiff but not infinitely resistant and walls with variable stiffness to account for damage evolution. The axial force increment due to the horizontal load was even included in the model, as were tension and compression failures. [PERSON] [225] proposed the POR90 method by introducing a new methodology for the piers' stiffness evaluation, helpful in the case of irregular walls, based on a definition of equivalent height dependent on the spandrels' dimensions and position. Diagonal shear or axial compression and bending failure of piers were considered within the method. Similar to the POR, the VEM method [226] proposed a floor-by-floor analysis by neglecting the increment of the axial forces on the piers due to the horizontal loads. The aim was to identify the load collapse multiplier needed for determining the maximum resistant horizontal force of each level. Spandrels were assumed to be rigid elements, and the piers were analysed in terms of diagonal and sliding shear and compressive-bending actions. The main features of the POR-related methods are summarised in Table 5 by developing the analysis of [PERSON] [259]. The RAN method devised by [PERSON] [227] inspired by POR, allowed a global analysis of the building performance through the assumption of a cumulative response of storeys and walls. An elastic-perfectly plastic constitutive law was used for both shear and compressive-bending collapse criteria. The piers were modelled through one-dimensional