# Influence of Multiple Openings on Reinforced Concrete Outrigger Walls in a Tall Building
## 3 Evaluation of the Influence of Multiple Openings
### Influence on Lateral Stiffness of Tall Buildings  
The influence of openings on the stiffness and strength of reinforced concrete outrigger walls was investigated in the previous sections. In this section, the influence of openings on the lateral stiffness of the whole structure was investigated by applying the degraded stiffness of outrigger walls due to  
Figure 15: The strut-and-tie model for the outrigger wall with multiple openings.  
openings given in Table 3 to the proposed, analytical Equations (6) and (7). The equivalent bending stiffness of the outrigger wall without openings given in Equation (1) can be easily converted to the equivalent bending stiffness of the outrigger wall with openings, as shown by the following equation.  
\[\left(EI\right)_{oi}=\beta_{K}\left(EI\right)_{o} \tag{13}\]  
where \(\left(EI\right)_{oi}\) is the equivalent bending stiffness of the \(i\)-th analysis models.  
The lateral displacement at the top of the building and shear forces developed in each outrigger are summarized in Table 5. The lateral displacement and shear forces were almost the same, even though the minimum value of \(\beta_{K}=0.58\) (M11) was applied. According to a study by [PERSON] [31], the relation between the lateral displacement at the top and stiffness of the outrigger is nonlinear. Moreover, the lateral displacement is not sensitive to the stiffness of the outrigger when the outrigger has sufficiently high stiffness, such as the outrigger walls in this study. Even though the internal shear force developed in each outrigger remained almost the same as seen in Table 5, the strength of the outrigger wall with openings was reduced significantly, as seen in Table 4, since the size of the openings increased. Therefore, the structural safety in terms of strength should be carefully checked when designing the reinforced concrete outrigger walls.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Model**} & \multirow{2}{*}{**Outrigger**} & \multicolumn{2}{c}{\(\Delta_{top}\) **(m)**} & \multirow{2}{*}{**Diff. (\%)**} & \multicolumn{2}{c}{\(V\) **(kN)**} & \multirow{2}{*}{**Diff. (\%)**} \\ \cline{3-3} \cline{5-8}  & & \(M0\) & & & & **M0** & & **M11** \\ \hline A1 & O11 & 0.4964 & 0.5050 & 1.73 & 6790 & 6732 & 0.85 \\ A2 & O21 & 0.4715 & 0.4833 & 2.50 & 8267 & 8173 & 1.14 \\ A3 & O31 & 0.5782 & 0.5935 & 2.65 & 9842 & 9679 & 1.66 \\ \hline A4 & \begin{tabular}{c} O41 \\ O42 \\ \end{tabular} & 0.3701 & 0.3777 & 2.01 & 3669 & 3707 & 1.04 \\ \hline A5 & \begin{tabular}{c} O51 \\ O52 \\ \end{tabular} & 0.3831 & 0.3918 & 2.22 & 3908 & 3938 & 0.77 \\ \hline A6 & \begin{tabular}{c} O61 \\ O62 \\ \end{tabular} & 0.3412 & 0.3470 & 1.70 & 2111 & 2144 & 1.56 \\ \hline \multirow{2}{*}{A7} & \
\begin{tabular}{c} O61 \\ O63 \\ \end{tabular} & 0.3412 & 0.3470 & 1.70 & 3597 & 3594 & 0.08 \\ \cline{2-6}  &
\begin{tabular}{c} O63 \\ \end{tabular} & & & & 5232 & 5089 & 2.73 \\ \hline \hline \end{tabular}
\end{table}
Table 5: The lateral displacement at the top of the building and shear forces developed in the outrigger walls predicted by Equations (6) and (7).  
Figure 16: Strength of outrigger walls predicted by the strut-and-tie model.