# Seismic Assessment of Historical Masonry Buildings at Different Scale Levels: A Review
## 3 Small-Scale Approaches
### Rigid Plane Approaches
#### 3.3.2 Bidimensional (Macroelement) Models  
Another widely explored category of macroelement-related models adopts bidimensional elements to simulate the masonry components. One of the first proposed bidimensional models was the SISV (Setto Inclinato a Sezione Variabile) developed by [PERSON] and [PERSON] [246]. Piers, spandrels and joints were simulated through triangular finite elements by excluding the in-tension parts and simulating those in compression through a beam with a variable section and axis linking the midpoints of the reactive outer sections. The panels had an adaptive geometry, changing during the analysis due to the increase in horizontal loads. The problem was nonlinear, and the hypothesis of stiff spandrels was adopted to analyse each level according to its local reference system. The method was slightly updated a few years later [266], changing its name to PEFV (Parete a Elementi Finiti a Geometria Variabile). Studies performed by [PERSON], [PERSON] [253] and [PERSON] [255] evidenced that the use of beam-type macro-elements implied an inaccurate simulation of the interaction between macro-elements and weak modelling of the panels' cracked condition [256]. These authors respectively proposed a two-dimensional macro-element model based on using a set of non-linear springs--also adopted by the computer code 3 DMacro [267]--and a strut and tie model. In the former proposal, two diagonal springs connected the opposite element corners, simulating shear behaviour, while a discrete distribution of springs along the element's sides simulated its interaction with the adjacent macro-elements ([PERSON] and [PERSON], 2011). Springs were also used for the rigid body spring model (RBSM) of [PERSON] and [PERSON] [254] and [PERSON] [268], where plane quadrilateral rigid elements were reciprocally connected through two normal springs and one shear spring at each side. Separate hysteretic laws were assigned to the axial and shear deformation between elements, and a Coulomb-like law was used to combine the strength of the shear springs with the vertical axial loading [3]. The Mas3D model was proposed by [PERSON], [PERSON] [251], using the macro-element model with 'no-tension' proposed by [PERSON] and [PERSON] [269]. It adopted a'multi-fan panel' as an element with no tensile strength and linear compressive behaviour. Stiff endfaces characterised multiple compressed fans in each panel, without interaction among the fans' sides. Each fan's radial tension defines the tensional state since there were no tangential tensions, and the stiffness matrix can be directly evaluated with a reduced computational effort. A model which has found wide use in the last two decades is the one proposed and implemented in the 3 Muri(r) software [67], based on the macroelement approach proposed by [PERSON] and [PERSON] [247] and later developed in several contributions [248; 249; 250; 252; 257]. This programme accounted for the compression-bending failure and the shear failure only. In the former case, the effective redistribution of the compression due to the section reduction was accounted for when the maximum strength was reached, determining the ultimate displacement according to the maximum drift value expected for the mechanism (0.6%). In the case of shear failure, a Mohr-Coulomb criterion was assumed so that the model followed the progressive decrease of element strength and stiffness through hysteretic structural behaviour. The ultimate shear deformation was associated with a 0.4% drift [270]. The pier damage modelling approach introduced by FEMA356 [105] and later updated [205; 258] can also be mentioned. According to it, each wall was modelled through a nonlinear translational spring with force-deformation characteristics determined by the critical failure mode identified as the smallest shear capacity between rocking failure, sliding failure and diagonal tension failure.