## 3 Low-Reversed Cyclic Loading Test on FSMRL Wall Structure
### Stiffness Calculation for the FSMRL Wall Structure  
(1) For MRL walls, the elastic stiffness in the lateral force resistance (or \(K\)) can be calculated using Equations (2)-(5) (shown in section 6) [27]  
Based on previous wall-related experiments, the equations incorporate bending deformation and structural destruction and take into account the influence of concerned variables, such as the axial compressive ratio, minor cracks, and the construction procedure. \[K_{1}=\frac{0.3\eta_{\text{c}}(2\mu_{\text{N}}+0.4)}{\frac{H^{3}}{12E_{\text{ c}}I_{\text{eq}}}+\frac{\mu H}{G_{\text{c}}A_{\text{eq}}}} \tag{2}\]  
\[A_{\text{eq}}=A_{\text{c}}+\frac{E_{\text{q}}}{E_{\text{c}}}A_{\text{q}} \tag{3}\]  
\[b_{\text{eq}}=A_{\text{eq}}/h \tag{4}\]  
\[I_{\text{eq}}=\frac{1}{12}b_{\text{eq}}h^{3} \tag{5}\]  
For MRL walls with holes, the calculation of the elastic stiffness in the lateral force resistance can be conducted using Equation (6) (see Figure 9). \[K_{1}=\frac{1}{\frac{1}{K_{\text{III}}}+\frac{1}{K_{\text{I}}+K_{\text{II}}}} \tag{6}\]  
Figure 9: Sketch of the stiffness calculation for MRL walls with holes. Note: \(K_{I}\), \(K_{II}\) and \(K_{III}\) stand for the piece-by-piece calculation results of the specimen stiffness in lateral force resistance, whereas the layer height H represents the height of the embrasure or windowsill. 1. Stiffness calculation for reinforced concrete frame and seismic wall The authors introduced the D-value method which can be expressed by Equation (7). \[K_{2}=\alpha_{c}\frac{12i_{c}}{h^{2}}\] (7)
2. Calculation of layer stiffness The calculated value for the layer stiffness is derived from the linear superposition of the frame stiffness and the MRL wall stiffness (see Equation (8)). \[K=\sum K_{1}+\sum K_{2}\] (8)  
Engineering practice normally reserves a large space in the lower layer of the FSMRL wall structure. However, to avoid the early occurrence of FS column failure, this paper shortens the columns and introduces reinforcement measures. The height cut is conducted proportionally; the layer height--which is 2.6 m in practice--is 1.3 m in this paper. The paper makes use of the finite-element software OpenSees ([16]) to simulate the influence of height changes in the FS layer on the load-bearing performance of the overall structure. The height of the FS layer is set at 1.3 m, 1.4 m, 1.5 m, 1.6 m, or 1.7 m to simulate an actual structure with a layer height of 2.6 m, 2.8 m, 3.0 m, 3.2 m, or 3.4 m respectively. The model provides a comparative diagram for skeleton curves, which are displayed as follows (see Figure 10). Using Equation (2) to Equation (8), the stiffness ratio (at the interim layer) can be determined for specimens with different frame heights. Table 4 shows the relation between the stiffness ratio and the structure's crack, yield, and peak loading (see Figure 11). \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Height of FS Layer (mm)** & **1300** & **1400** & **1500** & **1600** & **1700** \\ \hline Stiffness ratio at the interim layer & 1.66 & 2.02 & 2.42 & 2.88 & 3.39 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Stiffness ratio at the interim layer with different frame supported (FS) layer heights. Figure 10: Comparative diagram for the skeleton curves of the models. Figure 11 shows that the overall curves for the crack, yield, and peak loading decrease with increasing stiffness ratio. A closer look shows that, comparatively, the crack-loading curve follows a more steady variation pattern, whereas the decrease of the other two variables is steeper, which indicates that the stiffness ratio has a stronger influence on the structural strength at the yielding stage and under peak loading. Stiffness adjustment of the FS layer and hole opening of the MRL wall are performed in an effort to obtain different stiffness ratios, either greater than or smaller than 1. The authors again use OpenSees to simulate the load bearing process to identify the preferable stiffness ratio for the interim layer of the FSMRL wall structure [16; 28].