# Influence of Multiple Openings on Reinforced Concrete Outrigger Walls in a Tall Building
## 2 Design of Reinforced Concrete Outrigger Wall with Multiple Openings
### Arrangement of Multiple Openings  
Outrigger walls behave as cantilever deep beams, which have nonlinear distribution of stresses. It is not easy to analyze and design outrigger walls through design methods and formulas developed for slender beams. In this study, the strut-and-tie model was used to perform a preliminary design of the reinforced concrete outrigger walls. The strut-and-tie model was proven to be a desirable approach for designing reinforced concrete members with discontinuous regions (D-regions). The method is based on a truss analogy, which was first presented to explain the contribution of transverse reinforcement to the shear strength of a beam by [PERSON] in 1899. Following this, [PERSON] et al. [18] developed a strut-and-tie model as a design method for the D-region, and later discussed some designing details [19]. Furthermore, the strut-and-tie model method has been adopted by some design provisions, such as American Concrete Institute (ACI) 318-14 [16] as a design method for structures with D-regions. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Model**} & \multirow{2}{*}{**Outrigger**} & \multirow{2}{*}{**X (m)**} & \multicolumn{2}{c}{**\(\boldsymbol{\Lambda_{top}\) (m)**}} & \multirow{2}{*}{**Diff. (\%)**} & \multicolumn{2}{c}{**\(\boldsymbol{V\) (kN)**}} & \multirow{2}{*}{**Diff. (\%)**} \\ \cline{3-3} \cline{5-10}  & & & **Equation (6)** & & & **FEA** & & **Equation (7)** & **FEA** \\ \hline A1 & O11 & 89.25 & 0.4964 & 0.5134 & 3.30 & 6790 & 6876 & 1.25 \\ A2 & O21 & 138.25 & 0.4715 & 0.4905 & 3.87 & 8267 & 8331 & 0.77 \\ A3 & O31 & 183.75 & 0.5782 & 0.5985 & 3.39 & 9842 & 9840 & 0.02 \\ \hline A4 & O41 & 89.25 & & & & & & \\ O42 & 183.75 & 0.3701 & 0.3789 & 2.34 & 3669 & 3808 & 3.65 \\  & O52 & 208.25 & & & & & 6273 & 6225 & 0.77 \\ \hline A5 & O51 & 68.25 & & & & & & 3908 & 4028 & 2.97 \\  & O52 & 208.25 & & & & & 6967 & 6890 & 1.11 \\ \hline A6 & O61 & 68.25 & & & & & & 2111 & 2220 & 4.92 \\  & O62 & 138.25 & 0.3412 & 0.3429 & 0.42 & 3597 & 3528 & 1.95 \\  & O63 & 208.25 & & & & & 5232 & 5155 & 1.51 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Results from Equations (6) and (7) and finite element analysis (FEA). Figure 4: Dimensions of the analysis model to verify the proposed analytical equations. By using the strut-and-tie model, which assumes that all the stresses are condensed in struts and ties, horizontal and diagonal reinforcements were placed in the region with high tensile stresses. Meanwhile, in a practical situation, lateral loads coming from different directions lead to the fact that every half-side outrigger should be able to support upward and downward forces. This means that the tension zones could likely become compressive zones in an outrigger wall, and compressive zones should also be able to resist tension forces. Thus, every half-side of an outrigger wall with four reinforcements can be obtained by a symmetric superposition of the side supported upward forces and side supported downward forces, as shown in Figure 5 in which the blue lines represent steel reinforcements. According to American Concrete Institute (ACI) 318-14, the distributed transverse reinforcement should be positioned for compressive strength of concrete \(f_{c}^{\prime}\) not exceeding 42 MPa (6000 psi). However, there is some difficulty in the placement of the distributed transverse reinforcement in an outrigger wall with multiple openings, which is shown in Figure 5. In this study, the compressive strength of concrete that was used in the outrigger walls was greater than 42 MPa in order to evade the requirement for web reinforcement. Therefore, the outrigger wall was reinforced with four main reinforcements along the tension zone. The sectional area of each reinforcement was given by \(A_{s1}\), \(A_{s2}\), \(A_{s3}\), and \(A_{s4}\). These reinforcements divide the outrigger wall into four parts, as shown in Figure 6, in which the yellow colored regions were subjected to low stresses.