# Seismic Upgrade of an Existing Reinforced Concrete Building Using Steel Plate Shear Walls (SPSW)
## 5 Seismic Response Results of the Retrofitted r/c Building
### Orthotropic Membrane Model (OMM)
To ensure that the ultimate strength of the web-plates of the SPSW is not exceeded, the NLTH analyses are repeated, assuming the thickness t of the web-plate for all SPSWs to be 9.0 mm. Modal analysis is performed, and the fundamental period of the building is now T\({}_{1}\) = 0.406 s. The maximum values from NLTH analyses for IDRs, RIDR and base shear are presented in Table 14 and are compared with those of Table 12. One easily notices that the maximum RIDR increases to 0.093% \(<\) 0.5%, and the maximum base shear also increases to 2202 kN (i.e., by 9.5%). \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Beismic Motion** & **Von Mises Stress** & **Status** & **S11 (MPa)** & **S22 (MPa)** \\ \hline
1a & 155.0 & Yield & 263.9 & 5.8 \\
1b & 436.2 & Yield/Fail & 355.9 & 8.9 \\
2a & 157.7 & Yield & 249.2 & 5.8 \\
2b & 132.0 & Yield & 247.2 & 6.1 \\
3a & 208.1 & Not yield & 206.5 & 5.6 \\
3b & 299.1 & Yield & 297.6 & 7.7 \\ \hline \hline \end{tabular}
\end{table} 
Table 13: Maximum Von Mises and principal stress to SPSWs, status of the SPSW. Figure 16: Principal tensile stresses S11 (in MPa)—Orthotropic Membrane Model (OMM). \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Horizontal Direction of** & **Seismic** & \multicolumn{4}{c}{**Maximum IDR (\%)**} & \multirow{2}{*}{**Base Shear (kN)**} & \multirow{2}{*}{**Maximum RIDR (\%)**} \\ \cline{3-3}
**the Building** & **Motion** & & **1 st Storey** & **2 nd Storey** & **3 rd Storey** & \\ \hline  & 1a & 0.27 & 0.39 & 0.31 & 1318 & 0.018 \\  & 1b & 0.40 & 0.61 & 0.49 & 1813 & 0.020 \\  & 2a & 0.28 & 0.39 & 0.27 & 1461 & 0.016 \\ X & 2b & 0.25 & 0.38 & 0.31 & 1172 & 0.093 \\  & 3a & 0.29 & 0.44 & 0.36 & 1426 & 0.025 \\  & 3b & 0.32 & 0.49 & 0.39 & 1505 & 0.027 \\ \hline  & 1a & 0.17 & 0.24 & 0.19 & 2101 & 0.021 \\  & 1b & 0.13 & 0.19 & 0.14 & 1596 & 0.010 \\  & 2a & 0.13 & 0.18 & 0.12 & 1596 & 0.010 \\ \(\Upsilon\) & 2b & 0.16 & 0.25 & 0.20 & 1646 & 0.015 \\  & 3a & 0.18 & 0.25 & 0.18 & 2202 & 0.010 \\  & 3b & 0.17 & 0.25 & 0.19 & 1733 & 0.021 \\ \hline \hline \end{tabular}
\end{table} 
Table 14: Interstorey drift ratios and base shear forces. Figure 17 displays the worst plastic hinge distribution obtained from the NLTH analyses (seismic motion \"1b\"). A comparison of the number of plastic hinge excursions in Figures 14 and 17 reveals that the increase in thickness from 5.0 to 9.0 mm leads to slightly better behavior. If plastic hinge excursions for the rest of seismic motions are compared (the corresponding figures are not shown herein for space reasons), one concludes that this increase in thickness certainly improves the behavior of the building and, in all likelihood, the exhibition of a soft-storey mechanism is avoided. The maximum Von Mises and normal (tensile and compressive) stresses are listed in Table 15, whereas Figures 18 and 19 display the Von Mises stresses and principal tensile stresses, respectively, for the worst seismic motion \"1b\". From the results of Table 15 and in conjunction with Figures 18 and 19, yielding of the web-plate of the SPSW is now achieved for three seismic motions, but the ultimate strength of 360 MPa is not exceeded. Therefore, the desired behavior of the retrofitted SPSWs r/c building is obtained for all seismic motions considered. Taking into account that for the seismic retrofit of existing r/c buildings in seismic regions, energy dissipation is sought [2; 3], the SPSW should be designed to yield but not fail. On the other hand, if only added stiffness and/or strength are required for seismic retrofit purposes, then yielding of the SPSW is not allowed, keeping in mind that the thickness of the SPSW depends on the geometric properties of the VBEs and HBEs [13; 14; 17].