# Design Proposal for Masonry Infill Walls Subject to Seismic Actions
## 2 Out-of-Plane Behaviour of Masonry Infill Walls
### Experimental Research Studies
The value of \(R_{2}\) is related to the stiffness \(El\) of the most flexible frame element, see Equation (5), and \(\lambda\) depends on the height \(h\) to thickness \(t\) ratio of the infill wall, see Equation (6). \[q=\frac{2f_{m}^{\prime}}{\left(\frac{h}{t}\right)}R_{1}R_{2}\lambda \tag{4}\]  
Figure 3: Testing setup [10]: (**a**) in-plane test; (**b**) out-of-plane test. Figure 2: Experimental design [7]: (**a**) geometry of tested frames; (**b**) test setup. \[R_{2}=0.357+2.49\times 10^{-14}EI\leq 1.0 \tag{5}\]  
\[\lambda=0.154e^{-0.0985}\} \tag{6}\]  
Another analytical solution, based on the bi-directional arch effect allowed by the surrounding frame, was proposed by [PERSON] et al. [11]. This is in fact an extension of the analytical solution by [PERSON] and [PERSON] [12], which considered only the arch effect in one of the main directions of the frame as:  
\[\propto=\frac{1}{h}\left(EI_{b}h^{2}+G_{s}J_{c}h\right)^{0.25}<50\]0  
\[\propto=\frac{1}{h}\left(EI_{b}h^{2}+G_{s}J_{c}h\right)^{0.25}<50\]1  
\[\propto=\frac{1}{h}\left(EI_{b}h^{2}+G_{s}J_{c}h\right)^{0.25}<50\]2  
Here, \(x_{yv}\) is the maximum displacement of the infill wall in the vertical direction and \(M_{yh}\) is obtained by replacing \(x_{yv}\) by \(x_{yh}\) in Equation (8) and \(l\) by \(h\) in Equation (9). With the objective of comparing the influence of reinforcement in the in-plane damage of masonry infill walls and their out-of-plane-capacity, after initial in-plane damage, [PERSON] et al. [13] and [PERSON] et al. [14] tested three full-scale RC frames with different infills, see \[\propto=\frac{1}{h}\left(EI_{b}h^{2}+G_{s}J_{c}h\right)^{0.25}<50\]3 (i) unreinforced; (ii) with bed joint reinforcement; (iii) with reinforced plaster. The frames were subjected to an in-plane cyclic load with a constant vertical load, and then subjected to out-of-plane loads applied on four points of the infill wall. The conclusions were that: (i) the presence of reinforcement lowers the damage in the infill wall but only the reinforced plaster infill increases the in-plane stiffness, energy dissipation capacity and maximum load; (ii) the in-plane damage drastically reduces the acceleration needed for the out-of-plane collapse; (iii) both reinforced solutions improve the out-of-plane behaviour of the infill walls, to the greatest extent in the reinforced plaster one. The authors also proposed analytical solutions to calculate the out-of-plane fundamental vibration period of the infill wall, see Equation (10), and the in-plane capacity of infill masonry walls reinforced with bed joint reinforcement, see Equation (11). \[\propto=\frac{1}{h}\left(EI_{b}h^{2}+G_{s}J_{c}h\right)^{0.25}<50\]4  
\[\propto=\frac{1}{h}\left(EI_{b}h^{2}+G_{s}J_{c}h\right)^{0.25}<50\]5  
\[\propto=\frac{1}{h}\left(EI_{b}h^{2}+G_{s}J_{c}h\right)^{0.25}<50\]6 Models [13,14]: (a) infill walls; (b) detail of the reinforcement at the infills. Here, \(m\) and \(f_{v}\) are the specific mass and shear resistance of masonry, respectively, \(l^{\prime}\) is the length of the compressed zone of the wall, \(f_{y}\) is the yield strength of steel, \(A_{sh}\) is the area of reinforcement applied in the bed joint, \(s\) is the horizontal spacing of the reinforcement and \(d^{\prime}\) is the lowest between \(l^{\prime}\) and \(h\). An extensive study on the out-of-plane behaviour of reinforced and unreinforced infill walls, with previous in-plane damage, see Figure 5, was also performed by [PERSON] [15]. He compared experimental results with available analytical solutions and codes, and concluded that the analytical proposal for the out-of-plane capacity of [PERSON] [10] was the most adequate, if modified as shown in Equation (12). \[\propto=\frac{1}{h}\left(EI_{b}h^{2}+G_{s}J_{c}h\right)^{0.25}<50\]7  
\[\propto=\frac{1}{h}\left(EI_{b}h^{2}+G_{s}J_{c}h\right)^{0.25}<50\]8  
Here, \(f^{i}_{x1}\) is the flexural strength in the direction parallel to the bed joints and \(f_{x1}\) is the flexural strength in the direction parallel to the bed joints for the unreinforced solution. [PERSON] et al.