# On the Modeling and Analysis of Brittle Failure in Existing R/C Structures Due to Seismic Loads
## 3 Example Application of the Proposed Numerical Simulation Procedures
### Geometric and Loading Characteristics of the SPEAR Building  
The SPEAR building was a full-scale, three-story, 2 \(\times\) 2 bay, torsionally sensitive R/C building which is considered representative of the structures that were designed and constructed throughout southern Europe from the 1950s until the mid-1980s (Figure 6). The building was designed for gravity loads alone, in addition to the self-weight of the R/C structural elements, as well as for 0.5 kN/m\({}^{2}\) and 2.0 kN/m\({}^{2}\) gravity loads on slabs accounting for finishing and live loads, respectively. All stories had an identical plan  
Figure 5: Moment–Rotation (\(M\)–\(\theta\)) relationship representing the shear response of R/C beam-column joints in an intermediate floor of a building (the 0.5 factor for the moment is replaced by 1.0 for a roof joint in the building).  
configuration with external dimensions of 12.825 m \(\times\) 10.75 m, comprising eight columns of a 250 mm rectangular cross-section and one strong column of 250 mm \(\times\) 750 mm cross-section. The columns were connected to beams having 250 mm \(\times\) 500 mm web cross-sectional dimensions. Slab thickness was 150 mm, while story height in all cases was 3.00 m o.c. The columns had longitudinal reinforcement \(\mathcal{O}\)12 mm smooth bars (see Figure 2), which were lap-spliced over 400 mm at the base for all three levels with a hook formation at the end of the bars. All columns had \(\mathcal{O}\)8 mm perimeter stirrups, spaced at 250 mm o.c. which did not continue in the beam-column joints. Longitudinal reinforcement at both ends of all beams was 4 \(\mathcal{O}\)12 mm bars at the top and 2 \(\mathcal{O}\)12 mm bars at the bottom. Exceptions were: (i) beam B4 with 4 \(\mathcal{O}\)200 mm plus 2 \(\mathcal{O}\)12 mm bars at the top and 3 \(\mathcal{O}\)20 mm bars at the bottom of both ends; (ii) beam B8 that was reinforced with 2 \(\mathcal{O}\)20 mm top bars plus 4 \(\mathcal{O}\)12 mm top bars at the connection with column C4, 4 \(\mathcal{O}\)12 mm bars at the connection with column C7 and 2 \(\mathcal{O}\)12 mm bars at both ends; (iii) beam B10 at the top had 4 \(\mathcal{O}\)20 mm plus 2 \(\mathcal{O}\)12 mm bars at the connection with column C5, 2 \(\mathcal{O}\)20 mm plus 2 \(\mathcal{O}\)12 mm bars at the connection with column C8 and 2 \(\mathcal{O}\)20 mm bars at both ends; and (iv) beam B12 had 3 \(\mathcal{O}\)20 mm plus 2 \(\mathcal{O}\)12 mm bars at the top and 2 \(\mathcal{O}\)20 mm bars at the bottom of both ends. The mean concrete compressive strengths \(f_{cm}\) obtained from tests on cylindrical core specimen taken from the building after completion of the experiment was found equal to 24.73 MPa, 26.70 MPa, and 25.32 MPa for the first, second, and third story columns, respectively. Finally, uniaxial tensile tests on steel bar coupons yielded stress of reinforcement \(f_{y}\) that was equal to 479.45 MPa, 474.11 MPa, and 396.87 MPa in the cases of the \(\mathcal{O}\)8 mm, the \(\mathcal{O}\)12 mm and the \(\mathcal{O}\)20 mm bars, respectively.  
Figure 6: Typical story plan of the SPEAR test building at ELSA-JRC, Ispra, Italy (units in m).  
The testing protocol at JRC consisted of a series of simulated ground motions of increasing intensity which were applied to the R/C structure through a pseudo-dynamic procedure. The basic accelerograms used were the two components of the Montenegro 1979 (Hercge Novi) ground motion, sequentially scaled upwards to 0.02 g, 0.15 g, and 0.20 g, labeled as the s10, s11, and s12 pseudo-dynamic tests. These accelerograms were applied in both the \(X\) and \(Y\) plan directions and were normalized with respect to the peak ground acceleration (\(PGA\)), as shown in Figure 7.