# Seismic Assessment of Historical Masonry Buildings at Different Scale Levels: A Review
## 3 Small-Scale Approaches
### Rigid Plane Approaches
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & **VET** & **POR** & **PORFLEX** & **POR90** & **VEM** \\ \hline Analysis & Floor by floor & Floor by floor & Floor by floor & Floor by floor & Floor by floor \\ \hline Constraints & Constant & Constant & Variable & Constant & Constant \\ \hline \multirow{2}{*}{Sections} & Not- & Not- & \multirow{2}{*}{Partialized} & Not- & Not- \\  & partialized & & & & partialized & partialized \\ \hline \multirow{2}{*}{Constitutive law} & Elastic & Elastic & & Elastic & \\  & perfectly & perfectly & & perfectly & \\  & plastic & plastic & & plastic & \\ \hline Axial load in & \multirow{2}{*}{Constant} & Constant & Constant & Variable & Constant & Constant \\  & & & & & \\ \hline \multirow{4}{*}{Piers failure phenomena} & Diagonal & Diagonal & Diagonal & Diagonal & Shear & Diagonal \\  & shear & shear & shear & shear \\ \cline{2-6}  & - & - & - & & \\ \cline{2-6}  & - & - & - & & \\ \cline{2-6}  & - & - & \multirow{2}{*}{Compressive- } & Compressive- & Compressive- \\  & & & & bending & bending & bending \\ \hline \multirow{3}{*}{Spandrels failure phenomena} & - & - & Diagonal & - & Diagonal \\  & - & - & shear & - & shear \\ \cline{1-1} \cline{2-6}  & - & - & - & - & - \\ \cline{1-1} \cline{2-6}  & - & - & - & - & - \\ \cline{1-1} \cline{2-6}  & - & - & - & - & - \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Comparison of the main typologies of rigid plan approaches. application of the frame discretisation. The employability and critical issues related to the EFM procedure have been investigated, for instance, by [220; 261]. Between the 60s and the 90s, several EFM were proposed [232; 233; 234; 235; 236]. [PERSON] [236] was among the first to study the walls' shear deformation problem, accounting for it through the transfer in the rigid arms instead of in the column element modelling the walls. The models showed a good level of accuracy both for solid or hollow walls and facades. Relevant at the Italian and international level was the SAM (Simplified Analysis of Masonry Buildings) method [237; 238; 240], proposing a schematisation of the 'wall with openings' through an equivalent frame idealisation in which the in-plane response of walls governed the resisting mechanisms. The method was first developed for plane structures [238] and later extended to three-dimensional ones [239]. Both piers and spandrels were modelled as beam-column elements, accounting for the equivalent height proposed by [PERSON] [225], characterised by shear deformation, and connected through joint elements that were infinitely resistant and stiff. Joint elements were modelled through rigid offsets at the ends of the pier and spandrel elements; an elastic-plastic behaviour with limited deformations was associated with the piers, approximating the experimental resistance under cyclic load. No axial tension was allowed, while the expression of the strength criterion was detailed in [PERSON] [262] and [PERSON] [238]. The method aimed to analyse the whole wall by assigning an incremental horizontal load up to the wall failure and analysing the global equilibrium. The diagonal shear, the shear sliding and the flexural or rocking failure were accounted for by the piers; only the diagonal shear and flexural failure criteria were otherwise considered for the spandrels. The method was further developed through SAM II, a user-friendly computer code [244] where reinforced masonry or concrete elements with nonlinear behaviour can be modelled. In this way, the method offered the possibility of analysing reinforced masonry and mixed structures besides the unreinforced masonry ones. Both an infinitely rigid diaphragm and deformable floors can be modelled, the latter is generally more suitable for existing structures. A method accounting for an equivalent frame system made of nonlinear elements was proposed by [PERSON] and [PERSON] [263], with reference to spatial structures composed of curved, three-dimensional members with variable cross-sections.