# Design Proposal for Masonry Infill Walls Subject to Seismic Actions
## 2 Out-of-Plane Behaviour of Masonry Infill Walls
### Code Proposals  
In North America, [PERSON] of M.S.J.C. [20] determines that for the out-of-plane design of participating infill walls, the use of connectors spaced at a maximum of 1.22 m along the supported perimeter of the infill is mandatory, and the out-of-plane capacity of the walls have to be computed using Equation (1) [7]. FEMA 273 [21] defines the maximum slenderness values in Table 1, while the capacity should be computed using Equation (15), if the arch effect can be taken into account, otherwise the out-of-plane capacity is assumed as the maximum flexural capacity of the wall. \begin{table}
\begin{tabular}{c c} \hline \hline
**Slederness** & \(\lambda_{2}\) \\ \hline
5 & 0.129 \\
10 & 0.030 \\
15 & 0.034 \\
35 & 0.013 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: \(\lambda_{2}\) values for the computation of the out-of-plane capacity of infill walls (FEMA 273 [21]). Figure 6: Test setup for the in-plane and out-of-plane tests carried out by [PERSON] et al. [16]. \[q=\frac{0.7f^{\prime}_{m}\lambda_{2}}{\left(\frac{h}{t}\right)}\times 144 \tag{15}\]  
FEMA 306 [22] does not impose a limit drift. Nonetheless, it mentions that the limit is about 1.5% for clay brick masonry, and assumes the analytical proposal of [10; 23], see Equation (4), for the out-of-plane capacity of the infills. Regarding the seismic loads to be used in the out-of-plane design, which cannot be higher than the capacity computed using the methods mentioned, FEMA 302 [24] prescribes Equation (16) in the case of new buildings with rigid diaphragms, within the limits obtained by Equations (17) and (18):  
\[F_{p}=\frac{0.4a_{p}S_{DS}W_{p}}{\frac{R_{p}}{I_{p}}}\left(1+2\frac{z}{h}\right) \tag{16}\]  
\[F_{p}<1.6S_{DS}I_{p}W_{p} \tag{17}\]  
\[F_{p}>0.3S_{DS}I_{p}W_{p} \tag{18}\]  
Here, \(a_{p}\) is the amplification factor, \(S_{DS}\) is the spectral acceleration, \(W_{p}\) is the weight of the wall, \(z\) is the height of the highest point of the infill wall, \(h\) is the height of the building, \(R_{p}\) is the response modification factor and \(I_{p}\) is the importance factor. Another proposal is made by FEMA 356 [25], see Equation (19), in which the performance level is taken into consideration through a specific parameter that varies according to the desired performance level (Table 2). Here, \(S_{XS}\) is the spectral acceleration and \(W\) is the weight of the wall. \[F_{p}=\chi S_{XS}W \tag{19}\]  
The NZS 1170.5 [26] standard provides a design methodology for infill masonry walls identical to the North American code. Infill walls have a considerable contribution to the lateral load resistant structure, except in situations when the infill wall is separated from the frame, the infill wall is constructed with a flexible and light material, or it has a fragile behaviour such that it will collapse in the event of a very low seismic action. The out-of-plane capacity follows FEMA 306 [22]. The seismic force to be used in the seismic design of infill walls should be computed using Equation (20), which includes the influence of the vertical position of the element in the structure as well as an amplification of the acceleration, when compared to the maximum acceleration at the floor height:  
\[F_{ph}=C_{p}\big{(}T_{p}\big{)}C_{ph}R_{p}W_{p}<3.6W_{p} \tag{20}\]  
\[C_{p}\big{(}T_{p}\big{)}=C(0)C_{Hi}C_{i}\big{(}T_{p}\big{)} \tag{21}\]  
\[C_{Hi}=\left\{ \begin{array}{ll}\left(1+\frac{h_{i}}{6}\right),&h_{i}\leq 1 2m\\ \left(1+10\frac{h_{i}}{h_{n}}\right),&h_{i}<0.5h_{n}\\ 3.0,&h_{i}\geq 0.2h_{n}\end{array} \right. \tag{22}\] \begin{table}
\begin{tabular}{c c c} \hline \hline
**Structural Performance Level** & **Flexible Diaphragms** & **Other Diaphragms** \\ \hline Collapse prevention & 0.9 & 0.3 \\ Life safety & 1.2 & 0.4 \\ Immediate occupancy & 1.8 & 0.6 \\ \hline \hline \end{tabular} \({}^{\dagger}\) Values of \(\chi\) for flexible diaphragms need not be applied to out-of-plane strength of walls in Sections 2.6.7.2 of the FEMA 356 [25].  
\end{table}