## Nomenclature  
List of abbreviations  
2D & Two-dimensional  
3D & Three-dimensional  
DFM & Deformable frame model  
DIC & Digital image correlation  
DOF & Degrees of freedom  
EFM & Equivalent frame model  
FE & Finite element  
FEMA & Federal emergency management agency  
GI & GAlvanized iron  
IP & In-plane  
OOP & Out-of-plane  
RBSM & Rigid body spring model  
REM & Rigid element model  
RMEM & Rigid macro-element model  
SAM & Simplified analysis of masonry  
URM & Unreinforced masonry  
List of symbols  
A\({}_{n}\) & Area of influence at node n  
b & Parameter accounting for the element slenderness  
c & Masonry cohesion (as proposed by [PERSON] and [PERSON])  
d\({}_{max}\) & Maximum displacement reached in the opposite direction by the DFM  
d\({}_{u}\) & Displacement at the ultimate strength of the DFM diagonal strut  
E\({}_{l}\) & Lintel Young modulus  
E\({}_{m}\) & Masonry Young modulus  
E\({}_{x,y,h}\) & Axial stiffness of the DFM horizontal beams  
E\({}_{x,\varnothing}\) & Axial stiffness of the DFM vertical beams  
f\({}_{t}\) & Masonry tensile strength  
F\({}_{\sigma}\) & Force at crack initiation of the DFM diagonal strut  
F\({}_{u}\) & Ultimate strength of the DFM diagonal strut  
f\({}_{v,1}\) & Masonry shear strength for the diagonal cracking failure  
f\({}_{v,2}\) & Masonry shear strength for shear-sliding failure  
G\({}_{m}\) & Masonry shear modulus  
H\({}_{b}\) & Brick height  
h\({}_{inf}\) & Height of the area of influence of a horizontal strut  
h\({}_{m}\) & Macro-element height  
K\({}_{d}\) & DFM diagonal strut initial stiffness  
K\({}_{d,j}\) & Initial stiffness of the diagonal strut \(i\)  
K\({}_{h}\) & DFM horizontal strut in-plane stiffness  
K\({}_{v}\) & DFM vertical strut in-plane stiffness  
L\({}_{b}\) & Brick length  
l\({}_{inf}\) & Width of the area of influence of a vertical strut  
l\({}_{m}\) & Macro-element width  
M\({}_{n}\) & Nodal mass at node n  
t\({}_{m}\) & Macro-element thickness  
\(\alpha\) & Parameter accounting for the cyclic damage in the masonry  
\(\beta\) & Parameter accounting for the cyclic shear behavior of masonry  
\(\gamma\) & Parameter accounting for plasticity in the hysteretic behavior  
\(\mu\) & Masonry friction coefficient  
\(\overline{\mu}\) & Masonry friction coefficient as proposed by [PERSON] and [PERSON]  
\(v_{l}\) & [PERSON] Poisson's ratio  
\(\rho_{m}\) & Masonry density  
\(\rho_{l}\) & Lintel density  
* [PERSON] and [PERSON] (1970) [PERSON]; [PERSON] Some experimental results on the strength of brick masonry walls. In Proceedings of the 2 nd International Brick Masonry Conference, Stoke-on-Trent, UK, 12-15 April 1970; pp. 149-156. * [PERSON] and [PERSON] (1982) [PERSON]; [PERSON] Failure of shear-stressed masonry: An enlarged theory, tests and application to shear walls. _Proc. Br. Cernm. Soc._**1982**, _30_, 223-235. * [PERSON] and [PERSON] (1996) [PERSON]; [PERSON] [PERSON] Seismic response of infilled RC frames structures. In Proceedings of the 11 th world conference on earthquake engineering, Acapulco, Mexico, 23-28 June 1996; Volume 23, p. 28. * Mathworks (2022) Mathworks. _Matlab Version: 9.4 (R2022b)_; The MathWorks Inc.: Natick, MA, USA, 2022. * [PERSON] (2016) [PERSON] _ATLAS, a Tool and Language for Simplified Structural Solution Strategy_, Technical report; GEOMAS Insa-Lyon: Lyon, France 2016. * [PERSON] et al. (2023) [PERSON]; [PERSON] [PERSON]; [PERSON]; [PERSON] [PERSON]; [PERSON] [PERSON]; [PERSON] [PERSON]; [PERSON] [PERSON]; [PERSON] Shake table tests on 1:2 reduced scale masonry house with the application of horizontal seismic bands. _Eng. Struct._**2023**, _283_, 115897. [CrossRef]
* Cast3M version 24.1. Finite Element Tool Box for Structural and Fluid Mechanics. Available online: [[https://www-cast3m.cea.fr](https://www-cast3m.cea.fr)]([https://www-cast3m.cea.fr](https://www-cast3m.cea.fr)) (accessed on 24 October 2024). * [PERSON] (2021) [PERSON] Numerical Model for the Assessment of the Seismic Vulnerability of Traditional Masonry Structures with Seismic Bands.