# Optimization of Slotted Steel Plate Shear Walls Based on Adaptive Genetic Algorithm
## 3 Optimization Analysis of SSPSWs
### Optimization Results
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Frame Configuration**} & \multirow{2}{*}{**No.**} & **Variable** & **Slot** & **Inter-Slot** & **Inter-Slot** & **Slot Width,** & **Plate** & **Plate** & **Plate** \\  & & **Parameters** & **Quantity, n** & **Column** & **Column** & **d** & **Thickness, t** & **Width, B** & **I/b** & **b/t** \\ \hline \multirow{8}{*}{B-J} & SPSW-TB12 & & 5 & 1416.84 & 119.23 & 15.91 & 12 & 794.93 & 11.88 & 9.94 \\  & SPSW-TF & aspect ratio & 18 & 1527.07 & 81.41 & 27.79 & 12 & 2047.01 & 18.77 & 6.79 \\  & SPSW-TB36 & of frame & 28 & 1434.35 & 62.99 & 9.31 & 12 & 2087.39 & 22.77 & 5.25 \\  & SPSW-TB48 & & 24 & 1319.31 & 59.90 & 5.29 & 12 & 1624.46 & 22.03 & 4.99 \\ \cline{2-10}  & SPSW-TT8 & & 15 & 1394.35 & 91.94 & 18.65 & 8 & 1750.79 & 15.17 & 11.49 \\  & SPSW-TT10 & plate & 18 & 1383.32 & 79.25 & 22.29 & 10 & 1096.97 & 17.46 & 7.93 \\  & SPSW-TF & thickness & 18 & 1527.70 & 81.41 & 27.79 & 12 & 2047.01 & 18.77 & 6.79 \\  & SPSW-TT14 & & 21 & 1595.71 & 77.77 & 5.07 & 14 & 1817.41 & 20.52 & 5.56 \\ \hline \multirow{8}{*}{Q-J} & SPSW-FB12 & & 12 & 1337.54 & 41.97 & 54.53 & 12 & 1200 & 31.87 & 3.50 \\  & SPSW-FF & aspect ratio & 22 & 1468.48 & 41.05 & 66.18 & 12 & 2400 & 35.77 & 3.42 \\ \cline{1-1}  & SPSW-FB36 & of frame & 43 & 1477.43 & 22.60 & 60.59 & 12 & 3600 & 65.37 & 1.88 \\ \cline{1-1}  & SPSW-FB48 & & 25 & 1502.02 & 21.47 & 169.67 & 12 & 4800 & 69.96 & 1.79 \\ \cline{1-1} \cline{2-10}  & SPSW-FT8 & & 21 & 1598.45 & 43.25 & 68.98 & 8 & 2400 & 36.96 & 5.41 \\ \cline{1-1}  & SPSW-FF10 & plate & 20 & 1545.95 & 43.13 & 74.71 & 10 & 2400 & 35.84 & 4.31 \\ \cline{1-1}  & SPSW-FF14 & thickness & 22 & 1468.48 & 41.05 & 66.18 & 12 & 2400 & 35.77 & 3.42 \\ \cline{1-1} \cline{2-10}  & SPSW-FT14 & & 16 & 1339.97 & 37.65 & 109.99 & 14 & 2400 & 35.99 & 2.69 \\ \hline \hline \end{tabular}  
* For SSPSW models with varying plate thicknesses (SPSW-TT8, SPSWTT10, SPSW-TF, and SPSW-TT14), optimization yields target displacements of 9.02 mm, 8.99 mm, 9.12 mm, and 8.97 mm, respectively. Table 2 summarizes optimized parameters, revealing a decreasing trend in inter-slot column width (b) with increasing plate thickness (t). Analysis demonstrates that thicker plates satisfy stiffness constraints more readily under equivalent requirements, inherently reducing slit configuration stiffness. Enhanced ductility correlates with higher inter-slot column aspect ratios (l/b) and lower width-to-thickness ratios (b/t), as evidenced by parametric optimization results. This inverse relationship between plate thickness and ductility underscores a critical design trade-off: while thicker plates improve stiffness by 12-15%, they reduce ductility capacity by 18-22%. Consequently, SSPSW design prioritizes thinner steel plates (t \(\leq\) 12 mm) to balance stiffness demands with ductility performance requirements.  
\end{table} 
Table 2: Design parameters: two- vs. four-side connections in slotted shear walls. For quadrilateral-joined SSPSW configurations (SPSW-FB12, SPSW-FF, SPSW-FB36, and SPSW-FB48) with varying frame aspect ratios, optimization yields target displacements of 4.26 mm, 4.38 mm, 4.74 mm, and 5.28 mm, respectively. Optimized parameters in Table 2 demonstrate that lower-aspect-ratio frames with quadrilateral connections achieve 23-35% higher global stiffness compared to bilateral configurations, accompanied by increased slot widths. This enhanced stiffness performance necessitates proportionally higher stiffness contributions (18-22%) from slotted steel plates in quadrilateral-joined systems. In contrast to bilateral-joined configurations, quadrilateral implementations require prioritized optimization of slotted plate stiffness contributions to compensate for frame flexibility, particularly in high-aspect-ratio scenarios. For quadrilateral-joined SSPSWs with varying plate thicknesses (SPSW-FT8, SPSW-FT10, SPSW-FF, and SPSW-FT14), optimization yields target displacements of 4.02 mm, 4.44 mm, 4.38 mm, and 4.20 mm, respectively.