# 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)  
This model is considered the most accurate one regarding the representation of the actual behavior of the SPSW [17]. In particular, membrane elements in conjunction with an orthotropic steel material (herein S235 is assumed) are utilized to model the SPSW. An OMM depends on the inclination angle \(\alpha\), leading, thus, to a reorientation of the local axes of the area elements. Therefore, the local axes of the membrane elements are rotated by 45\({}^{\circ}\). Following [17], the stiffness value along the axis that corresponds to the compression diagonal is degraded to 2%, whereas the Poisson ratio and the shear modulus are set to zero. In this way, the tension-field action of the web-plate of the SPSW is accurately represented. The OMM is employed for the building in which small SPSWs are configured (Figure 9). Modal analysis is performed, and the fundamental period of the building is T\({}_{1}\) = 0.428 s. The maximum values from NLTH analyses for IDRs, RIDR and base shear are listed in Table 12. In comparison to the results presented for the FEM ii model in Section 5.2, the maximum RIDR increases to 0.077% < 0.5% and the maximum base shear reduces to 2011 kN (i.e., by 2.7%). The worst plastic hinge distribution obtained from the NLTH analyses (seismic motion \"1b\") is shown in Figure 14. A comparison of the number of plastic hinge excursions for the FEM model in Figure 9 and the OMM model in Figure 14 reveals slightly better behavior in favor of the FEM model. In order to evaluate the tension-field action in the OMM, the maximum Von Mises and normal stresses are listed in Table 13, where S11 and S12 correspond to tensile and compressive stresses, respectively. Figures 15 and 16 display the Von Mises stresses and principal tensile stresses, respectively, for the worst seismic motion \"1b\". From the results of Table 13 and in conjunction with Figures 15 and 16, yielding of the web-plate of the SPSW is achieved, confirming the ductile behavior sought; nevertheless, the ultimate strength of 360 MPa (steel material S235) is considerably exceeded for seismic motion \"1b\". \begin{table}
\begin{tabular}{c c c c c c} \hline  & & \multicolumn{4}{c}{**3 rd Storey**} \\ \hline
**Column** & **Position** & **Reference Model** & **EBM** & **FEM i** & **FEM ii** \\ \hline C5 & Base & B & B & B & B \\ Top & B & IO & B & B \\ \hline C6 & Base & - & B & - & B \\ Top & - & IO & - & B \\ \hline C7 & Base & B & B & B & B \\ Top & B & C & B & B \\ \hline C8 & Base & - & B & - & - \\ Top & - & IO & - & - \\ \hline C9 & Base & B & B & B & B \\ Top & B & IO & B & B \\ \hline C10 & Base & B & B & B & B \\ Top & B & IO & B & B \\ \hline C11 & Base & B & B & B & B \\ Top & B & IO & B & B \\ \hline C12 & Base & B & B & B & B \\ Top & B & IO & B & B \\ \hline \end{tabular}
\end{table} 
Table 11: _Cont._Figure 14: Plastic hinge formations—Orthotropic Membrane Model (OMM). Figure 15: [PERSON] stresses (in MPa) to the SPSWs—Orthotropic Membrane Model (OMM). \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Horizontal Direction**} & \multirow{2}{*}{**Seismic**} & \multicolumn{4}{c}{**Maximum IDR (\%)**} & \multirow{2}{*}{**Base Shear (kN)**} & \multirow{2}{*}{**Maximum RIDR (\%)**} \\ \cline{3-3} \cline{5-7}  & & & **1 st Storey** & & **2 nd Storey** & **3 rd Storey** \\ \hline \multirow{4}{*}{X} & 1a & 0.31 & 0.39 & 0.31 & 1252 & 0.009 \\  & 1b & 0.48 & 0.64 & 0.46 & 1901 & 0.006 \\  & 2a & 0.30 & 0.37 & 0.26 & 1391 & 0.013 \\  & 2b & 0.28 & 0.37 & 0.28 & 1083 & 0.077 \\  & 3a & 0.30 & 0.42 & 0.32 & 1275 & 0.012 \\  & 3b & 0.34 & 0.46 & 0.35 & 1483 & 0.039 \\ \hline \multirow{4}{*}{\(\Upsilon\)} & 1a & 0.19 & 0.25 & 0.18 & 1977 & 0.023 \\  & 1b & 0.16 & 0.21 & 0.15 & 1754 & 0.007 \\  & 2a & 0.15 & 0.19 & 0.15 & 1582 & 0.007 \\  & 2b & 0.18 & 0.24 & 0.17 & 1615 & 0.014 \\  & 3a & 0.21 & 0.25 & 0.16 & 2011 & 0.005 \\  & 3b & 0.19 & 0.24 & 0.17 & 1601 & 0.011 \\ \hline \hline \end{tabular}
\end{table} 
Table 12: Maximum values for IDR, RIDR, and base shear.