## 3 Case Study  
### Description of the Building Structure  
To assess the effect of the infill panels, considering the presence of openings and the change in the distribution of masonry walls on the vulnerability of RC buildings, a residential building was selected as a representative case study. The building has the plan dimensions of 17.4 m \(\times\) 13.1 m, which consists of 4.3 \(\times\) 4.3 m modules (longitudinal and transverse direction, respectively), with a story height equal to 3 m. The building was designed according to the Algerian code (RPA2003) [1].  
Twenty-four 2D models were generated in the software OpenSees ([PERSON], [PERSON], et al., 2000) [27], one without infill walls herein designated Bare Frame (BF) model and another one with infill panels distributed along the building's facades (Full Frame (FF)) model. Also, eight different models with different opening ratios (the reduction factor is from 10% to 90%) were generated, and thirteen models differ in the distribution of the infill walls. The masonry unit selected for the infill panels is hollow clay horizontal bricks 15 cm thick, representing Algeria's most common masonry units. Once the main objective of the study was established as the assessment of the in-plane influence of the infill masonry walls in the seismic response of RC frames, only a 2D frame was considered. Nevertheless,  
Figure 1: Macro Models for masonry infill walls: (**a**) single strut model, (**b**) Three Diagonal model (based on [31]) (**c**) Proposed multi-strut model [32], (**d**) Macro-model proposed by [PERSON] et al., 2010) [33].  
to input or postprocess data is prominent. As such, the numerical models were generated using OpenSees software. Figure 3 shows an overall description of the adopted modelling strategy for the RC elements. As can be seen, a beam with hinges element from OpenSees element library was used to model the RC elements. This element has the capability to specify plastic hinge lengths at the element ends. By using Modified Radau Hinge Integration method [36; 37], two-point Gauss integration is used on the element interior, while two-point Gauss-Radau integration is applied over lengths of two hinges. In order to accommodate any extended plasticity beyond the hinge zones, fiber sections were also considered in the central part of the element. The length of hinges at the end of each element has been quantified using the following proposal [38]:  
\[lp=0.08l_{e}+0.022d_{b}\,f_{y} \tag{4}\]  
where \(l_{e}\) is the length of the element, \(d_{b}\) is the diameter of the longitudinal steel rebar and \(f_{y}\) is the yield strength of the used steel in MPa.  
Figure 3: Adopted strategy for modelling RC elements. (**a**) Beam with hinge element general description. (**b**) Fiber section discretization. i. unconfined concrete (Concrete01) ii. confined concrete (concrete02) iii. Steel material (steel02).  
As can be seen in Figure 3b the RC section was discretized in three different materials to accommodate the expected behavior of each ingredient of the RC. For the cover, where the concrete has no confinement, a zero tensile concrete model known as Concrete01 has been used. On other hand, to account for the effect of steel stirrups, the confined ratio has been considered for the middle region. The modified concrete strength has been used to define the concrete parts confined by stirrups. Concrete02 model in OpenSees was used to model the confined concrete with a tensile strength of 10% of the compressive strength of the concrete. Longitudinal rebars were modelled using the uniaxial Giuffre-Menegotto-Pinto model [39] with isotropic hardening, known as Steel02 in OpenSees. Eventually, in order to account for beam-column connection, a rigid end-offset joint model was applied for the beam-column joints [40]. The lengths of the rigid parts were considered to be half of the depth of the perpendicular element.