# A Parametric Computational Study of RC Building Structures under Corner-Column Removal Situations
## 2 Description of the Study
### FE Model  
A Finite Element (FE) model was developed with the dimensions of the real building on ABAQUS/Explicit software [41]. Columns were modelled as beam elements (element B31 [41]) and slabs as area elements with hourglass control (element S4R [41]). The FE model considered non-linear slab concrete and steel reinforcement behaviour. For the sake of simplicity, the columns were modelled using a linear-elastic behaviour with an elastic modulus (see Table 1) and a Poisson ratio of 0.2. It should be noted at this point that the columns' linear-elastic behaviour was supported by the lack of damage to these elements during the test. The ABAQUS concrete damage plasticity model [41; 42; 43; 12; 44; 45] was used for the concrete in the slabs, including concrete cracking and crushing for tensile and compressive behaviour, respectively. Compression was defined from Eurocode 2 [40] considering the mechanical parameters given in Table 1. Concrete tension behaviour was defined by a bilinear softening stress-strain response after reaching its maximum tensile strength, \(\mathrm{f_{ct}}\) (Table 1). This bilinear response was defined by an intermediate point with a strain of \(5.5\times 10^{-4}\), stress equal to 0.33 \(\mathrm{f_{ct}}\) and a final point with a strain of \(25\times 10^{-4}\) and a stress equal to \(\mathrm{f_{ct}}\)/100 [46]. Damage was also introduced in the model in terms of tension and compression damage [41] by defining two independent parameters, named dt and dc, respectively. Both parameters are used to identify the inelastic behaviour of concrete when subjected to tensile and compressive stresses in the presence of tensile cracking and compressive crushing, respectively. In both cases, multilinear relationships are assumed as it is considered in ABAQUS by default [41]. The rest of the parameters of the damage plasticity model, such as the dilatation angle, eccentricity, fb0/fc0 and K, were considered by default [41]. The steel reinforcement bars (yield stress of 500 MPa, Young modulus of 200,000 MPa and Poisson ratio of 0.3) were introduced in the slabs using perfect bond smeared layers [28]. The measured strain rate in the tests were lower than 1/s, as discussed in [13]. Strain rate values registered during the test with Digital Image Correlation (DIC) showed a peak strain rate value of 0.32/s, which in concrete structures is normally representative of small dynamic events such as earthquakes or heavy traffic. [PERSON] et al. [47] showed that, for values less than 10/s, this effect can be ignored as it was adopted in the FE analysis. Figure 2 shows the FE model that was developed. The self-weight of the structure was automatically considered by the FE model based on the density of the materials (25 kN/m\({}^{3}\) and 78.5 kN/m\({}^{3}\) for concrete and steel, respectively). The superimposed experimental load was also modelled as uniform and line loads in the FE model. Fully-fixed boundary conditions were adopted for the bottom nodes of the ground columns, while nodes in the slab belonging to the intersections with the columns were coupled as plate constraints to ensure that all the nodes in these regions had rigid body displacements. Dynamic non-linear mechanical and geometrical analyses (DNLA) using explicit calculations were performed for both FE validation and the subsequent parametric study. Rayleigh damping [41] was considered according to the values obtained experimentally, neglecting stiffness proportional damping and considering mass proportional damping [48], which is directly proportional to the damping  
Figure 1: Sketch and photograph of the building prepared for the sudden corner-column removal. coefficient (\(\zeta\) = 7.3%; based on the test results [28]) and the fundamental period of the structure after column removal (T\({}_{1}\) = 0.2785 s; based on the test results [28]). A preliminary step with static-linear analysis (SLA) was carried out to obtain the load of column P3 before its sudden removal. This force (F3) was then applied to the model prepared for the DNLA.