# Seismic Upgrade of an Existing Reinforced Concrete Building Using Steel Plate Shear Walls (SPSW)
## 3 Seismic Analysis of the r/c Building  
On the basis of the data presented in the previous section, a numerical model of the r/c building was created in SAP 2000 [29], and it is shown in Figure 5. In this model, frame elements are used for beams and columns and shell elements for the floor slabs. Concrete cracking is conservatively taken into account by considering for all members an effective stiffness equal to 50% of the gross stiffness. The position of the staircase is found not to be critical for the seismic response of the r/c building, and, thus, it is not included in the numerical model. Infills are included in the model, but only as loads to the beams. The r/c building is assumed to be fixed-base (base fixity is denoted with green symbols in the figures that follow), and, hence, soil-structure-interaction effects are absent. It is then assumed that the r/c building must resist the seismic load defined by the design spectrum of EC8 [30] for a peak ground acceleration (PGA) equal to 0.24 g (representative of the broader area [31] where the r/c building under study lies), soil class B, importance factor \(\gamma\) = 1.0, and behavior factor q = 1.5. Modal response spectrum analysis of the fixed-base r/c building is performed using the 100-30% spectral combination rule, and the storey shears in both horizontal directions of the building are computed. These storey shears are used for the design of the SPSW in the following and read: 988.113 kN and 926.853 kN for the first storey in the x and y directions, respectively; 729.937 kN and 685.458 kN for the second storey in the x and y directions, respectively; and 292.945 kN and 279.892 kN for the third storey in the x and y directions, respectively. The fundamental period of the r/c building is T\({}_{1}\) = 0.837 s.  
Next, to identify the potential seismic damage in the critical regions of the beams and columns of the r/c building, NLTH analyses are conducted using three seismic motions for  
Figure 5: Model of the r/c building. which their response spectrum is compatible with the aforementioned design spectrum. The two horizontal components of these seismic motions are used interchangeably with respect to the two horizontal axes of the r/c building. Thus, in total, six NLTH analyses are executed assuming: (i) both material and geometrical nonlinearities; (ii) the innate viscous damping of the r/c building to be 3% and the (Rayleigh) damping matrix to be defined using the well-known mass and stiffness proportionality factors; (iii) point plastic hinges at the ends of beams and columns in order to take into account their inelastic behavior. These plastic hinges to beams are formed by bending moments, whereas those to columns are formed by the combination of axial force and bending moments [29; 32]. A flexure-shear failure condition is also considered for columns [29; 32]. The NLTH analyses revealed almost similar patterns regarding the number of plastic hinge formations on the beams and columns of the r/c building. Figure 6 displays these plastic hinges for the case of the first seismic motion, where one can notice unwanted plastic hinges not only at the top end of the columns of the first storey but also at both ends of the columns of the second storey. Besides the excessive plastic hinge rotation at the bottom end of one column of the first storey, the plastic hinges to the columns of the first two storeys are classified in the IO (Immediate Occupancy)-LS (Life Safety) performance level range according to the acceptance criteria of [32]. In the figures that follow, the legends B, IO, LS, CP, C, etc. are in accordance with the normalized force versus deformation curve of [32]. The maximum values for transient interstorey drift ratios (IDRs), residual interstorey drift ratios (RIDR), and base shear are listed in Table 3. The definition and calculation of IDR, RIDR, and base shear in the context of time-domain seismic analysis are described in [33].