# Design Proposal for Masonry Infill Walls Subject to Seismic Actions
## 5 Design Proposal
### Out-of-Plane Capacity Reduction  
In models 2 and 3, openings of the infills in a transversal direction had a higher influence than openings in a longitudinal direction, even though the percentage of the opening was similar (27% and 30% for longitudinal and transversal ones, respectively). This was associated with the arrangements of the openings, which for infills in a transversal direction did not allow an arching mechanism over the height of the wall. Given that height is usually smaller than length, the vertical arching mechanism has a higher contribution to the out-of-plane capacity of the wall, if the wall is connected to the four sides. This can be confirmed by the analytical solution of EC6 [28], which takes the arching mechanism into consideration in only one direction. Here, the vertical direction is considered, as it provides a better correlation with the experimental results, and it is the shortest span. If the central part of the infill wall is not altered by openings, enabling a vertical arch effect during out-of-plane loading, the out-of-plane capacity of the wall does not seem to be affected and the analytical solutions available in the standards have a similar reliability \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & & & & & **New Proposal** \\ \hline \multirow{6}{*}{**Normal**} & \multirow{2}{*}{**Wall**} & \multirow{2}{*}{**Type**} & \multicolumn{2}{c}{**Experimental**} & \multirow{2}{*}{**Constrained on**} & \multirow{2}{*}{**Error (\%)**} \\  & & & **Frequency** & & **4 Sides (Hz)** & \\ \cline{1-1}  & & P1 exterior leaf & With openings & 60.5 & 48.4 & \(-20.1\) \\  & & P1 interior leaf & With openings & 57.5 & 37.6 & \(-36.4\) \\  & & P2 exterior leaf & With openings & 66.7 & 48.4 & \(-27.5\) \\  & & P2 interior leaf & With openings & 59.5 & 37.6 & \(-36.8\) \\  & & P1 exterior leaf & Solid & 69.4 & 48.4 & \(-30.3\) \\  & & P1 interior leaf & Solid & 62.8 & 37.6 & \(-40.1\) \\  & & P2 exterior leaf & Solid & 70.7 & 48.4 & \(-31.6\) \\  & & P2 interior leaf & Solid & 67.1 & 37.6 & \(-43.9\) \\ \hline \multirow{6}{*}{**Normal**} & \multirow{2}{*}{P1 North} & \multirow{2}{*}{With openings} & \multirow{2}{*}{56.9} & \multirow{2}{*}{80.6} & 41.7 \\  & & P1 South & Solid & 67.0 & 80.6 & 20.3 \\ \cline{1-1}  & & P2 South & Solid & 65.0 & & 24.0 \\ \hline \multirow{6}{*}{**Normal**} & \multirow{2}{*}{P1 North} & \multirow{2}{*}{With openings} & \multirow{2}{*}{56.3} & \multirow{2}{*}{80.6} & 43.2 \\  & & P1 South & Solid & 64.1 & 80.6 & 25.8 \\ \cline{1-1}  & & P2 South & Solid & 66.7 & & 20.9 \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Comparison between experimental frequencies and the analytical proposal from Equation (31). to the computation of solid infill walls. If the vertical arch effect is not enabled, the out-of-plane capacity of the infill wall has to be reduced. The reduction of the in-plane capacity of masonry infill walls can be factored by reducing the capacity of the solid wall using a reduction factor. When following the prescriptions of NZS 1170.5 [26], the reduction is achieved using a parameter proposed by [7]. In a similar procedure, a reduction factor is proposed for the out-of-plane capacity of masonry infill walls with openings, see Equation (35), when the distribution of the openings does not enable a vertical arch effect mechanism, see Figure 15.  
\[\lambda_{out-of-plane}=1-Area\ opening\ (\%) \tag{35}\]  
For the infill wall with the transversal direction of models 2 and 3, the reduction factor would be equal to 0.3, meaning the capacity was reduced by 70%, and the results of the reduction of the out-of-plane capacity computed using the analytical solutions can be found in Table 11 and Figure 16. [PERSON] [15], FEMA 306 [22] and EC6  
It should be noted that the reduced out-of-plane capacity obtained was dependent on the value for the reference solid wall, hence if the initial estimation was already excessively high or low, the estimation of the out-of-plane capacity of the wall with openings will be excessively high or low, respectively.