# Seismic Assessment of Historical Masonry Buildings at Different Scale Levels: A Review
## 3 Small-Scale Approaches
### Finite Element Methods
#### 3.2.2 FE Modelling and Analysis: Strategies Applied to Cultural Heritage  
The first attempts at structural evaluation using FEM models have been performed through linear elastic analyses thanks to their relatively reduced numerical effort, partially controlling the analysis's intrinsic limits through large expertise [197, 198, 199]. With the overwhelming improvement of the computing and software tools, the use of linear analysis has been often limited to a preliminary and relatively fast assessment of the model reliability and definition (e.g., check on the mesh definition, load definition and distribution, reliability of reactions and deformations), since it generally lacks accuracy for the structural assessment of masonry structures. Besides the complex nonlinear behaviour usually shown by masonry structures, even at low-stress levels, linear analyses cannot account for key aspects of the masonry behaviour, such as the non-tension response. A nonlinear approach appears necessary to properly catch the collapse behaviour, possibly associated with large displacements and not the negligible role of geometrical nonlinearity. This approach is thus nowadays the most common to define in detail the structural capacity, even if examples of linear approaches may still be found, such as in [PERSON], [PERSON] (2001), where the consistent knowledge of the analysed building allowed performing limit state and local mechanism analysis in addition to a linear dynamic analysis assuming a reduced masonry stiffness to account for the damage condition. Nonlinear static pushover (PO) analysis is often the method adopted to analyse existing masonry structures according to what is suggested by current codes (to cite a few, (104; 201; 202; 203; 204; 205); PO accounts for possible geometric and material nonlinearities, is relatively easy to execute, and has a reduced computational burden. Many examples of PO applications can be found in the literature from the last two decades (2; 138; 171; 172; 174; 175; 184; 206; 207; 208; 209; 210; 211; 2012)). On the other hand, several weaknesses can be highlighted concerning the adopted load patterns, which usually do not account for degradation except in the case of adaptive pushover analysis, where the progressive changes in the modal frequencies due to crushing and cracking phenomena are introduced ([PERSON] and [PERSON] (213); [PERSON], [PERSON] (214)). Nonlinear time-history (dynamic) analyses--or nonlinear response-history analyses--can be carried out for masonry structures, providing a more detailed assessment of the structural response to strong seismic impulses but requiring, meanwhile, higher accuracy in modelling materials due to the need to include cyclic performance and corresponding strength and stiffness degradation. They currently represent the most accurate available method for the structural evaluation of masonry buildings, but, although several contributions may be found (173; 178; 187; 188; 190), they are still rarely used in engineering practice. The limited use is the consequence of operational issues such as the complexity of the time-integration algorithm, the difficulties in damping representation and identification of the suitable static and dynamic parameters, and the nature of the earthquake records, which exhibit different peculiarities entailing a complex transposition in the numerical analysis (215). Since incorporating inelastic members' behaviour under cyclic earthquake ground motions, the time-history analysis allows the explicit simulation of hysteretic energy dissipation in the nonlinear range. The analysis provides the dynamic response for the input ground motion, determining the response history data on the relevant demand parameters. The analysis shall be repeated for several ground motions due to the variability in earthquake ground motion (215). It is a matter of fact that the reliability of the analysis results cannot be easily proved when dealing with complex constructions such as historical buildings.