# Seismic Upgrade of an Existing Reinforced Concrete Building Using Steel Plate Shear Walls (SPSW)
## 5 Seismic Response Results of the Retrofitted r/c Building
### Finite Element Model (FEM)  
The results of the retrofitted building shown in Figure 8 are described first. The maximum values for IDRs, RIDR, and base shear are listed in Table 5, and in comparison to the results presented in Section 3 (for the non-retrofitted building) and Section 5.1 (for the retrofitted building-EBM case), the maximum RIDR and base shear are increased to 1.71% > 0.50% and 2680 kN (i.e., by 38.6%), respectively. Figure 11 displays the worst plastic hinge excursions (coming from the seismic motion \"1b\"). According to the acceptance criteria of [29], plastic hinges to columns for five NLTH analyses performed remain in the range defined by the IO-LS performance levels, and in one NLTH analysis, they surpass the LS performance level. In general, contrary to the EBM case described in the previous section, modeling of the SPSWs with FEMs (Figure 8) indicates ductile behavior of the building and reveals no or small damage to several beams and columns in almost all NLTH analyses performed. Table 6 presents the Von Mises stresses and the maximum shear stresses of the SPSWs, demonstrating that the SPSWs have not been fully utilized, as none of the plates yielded. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \
\begin{tabular}{c} **Horzontal Direction of** \\ **the Building** \\ \end{tabular} &
\begin{tabular}{c} **Seismic** \\ **Motion** \\ \end{tabular} & \multicolumn{3}{c}{**Maximum HDR (\%)**} & \multicolumn{1}{c}{**Base Shear (kN)**} & \multicolumn{1}{c}{**Maximum RIDR (\%)**} \\ \hline \multirow{8}{*}{X} & 1a & 0.66 & 0.64 & 0.40 & 647.8 & 0.10 \\  & 1b & 1.63 & 1.28 & 0.28 & 726.8 & 0.34 \\  & 2a & 1.19 & 0.63 & 0.27 & 688.1 & 0.12 \\  & 2b & 0.79 & 0.52 & 0.32 & 602.1 & 0.11 \\  & 3a & 0.86 & 0.70 & 0.39 & 723.4 & 0.22 \\  & 3b & 1.03 & 0.78 & 0.35 & 670.8 & 0.18 \\ \hline \multirow{8}{*}{\(\Upsilon\)} & 1a & 0.15 & 0.15 & 0.75 & 1934 & 0.41 \\  & 1b & 0.24 & 0.19 & 0.38 & 1012 & 0.11 \\ \cline{1-1}  & 2a & 0.16 & 0.15 & 0.40 & 1318 & 0.12 \\ \cline{1-1}  & 2b & 0.14 & 0.15 & 0.51 & 1165 & 0.24 \\ \cline{1-1}  & 3a & 0.16 & 0.17 & 0.55 & 1380 & 0.17 \\ \cline{1-1}  & 3b & 0.16 & 0.12 & 0.45 & 1147 & 0.21 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Maximum values for IDR, RIDR, and base shear. Figure 10: Plastic hinge formations—Equivalent Brace Model (EBM). The results of the retrofitted building shown in Figure 9 are described next. The maximum values for IDRs, RIDR, and base shear are listed in Table 7, and in comparison to the results presented in Section 3 (for the non-retrofitted building) and the previous model (Figure 8), the maximum RIDR is drastically decreased to 0.036% < 0.5% and the maximum base shear reduces to 2066 kN (i.e., by 23%). The inelastic behavior of the building is improved, and as revealed by the plastic hinge excursions shown in Figure 12 (worst case), plastic hinges to columns for all six NLTH analyses performed remain below the range defined by the LS. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Seismic Motion**} & **Von Mises Stress** & \(\leq\)**235 MPa** & **Maximum Shear** & \multirow{2}{*}{\(\leq\)**235\(\sqrt{3}\) MPa**} \\  & **(MPa)** & & & **Stress \(\tau_{\text{max}}\) (MPa)** & \\ \hline
1a & 44.27 & ✔ & 27.58 & ✔ \\
1b & 52.15 & ✔ & 21.41 & ✔ \\
2a & 45.92 & ✔ & 19.81 & ✔ \\
2b & 42.28 & ✔ & 23.54 & ✔ \\
3a & 65.12 & ✔ & 24.18 & ✔ \\
3b & 42.63 & ✔ & 23.28 & ✔ \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Maximum Von [PERSON] and shear stress to SPSWs. Figure 11: Plastic hinge formations—Finite Element Model (FEM).