# Design Proposal for Masonry Infill Walls Subject to Seismic Actions
## 2 Out-of-Plane Behaviour of Masonry Infill Walls  
### Experimental Research Studies  
The out-of-plane behaviour of an infill wall is highly dependent on the arching effect [4; 5; 6], due to the confinement provided by the frame. Hence, the out-of-plane capacity is greatly affected by the compressive strength of masonry and the stiffness of the RC elements. The first analytical models calculated the out-of-plane capacity of infill walls [5; 6] and only considered this effect in one of the main directions. This might not be realistic as infill walls can be connected to the frame on all four sides and, in this case, the arch effect can develop in two directions. Given this, [PERSON] and [PERSON] [7] proposed an analytical solution to compute the out-of-plane capacity of infill walls that assumed a bi-directional arch effect. Their tests included nine frames with concrete blocks, subjected to a uniform load on the surface of the infills using airbags, see Figure 2, with the objective of understanding the out-of-plane behaviour and the maximum load capacity of the infill walls. The authors concluded that the out-of-plane behaviour could be divided into four stages: (i) linear elastic until the first crack; (ii) propagation of cracks and definition of a failure line; (iii) increment in the load capacity due to the arch effect; (iv) crushing of masonry, due to compression and collapse. The authors proposed that the out-of-plane capacity that the panel can withstand, in the case of a panel supported on four sides, is given by \(q\) (in kN/m\({}^{2}\)) as:  
\[q=4.50f_{m}^{\prime\ 0.75}t^{2}\bigg{(}\frac{\alpha}{l^{2.5}}+\frac{ \beta}{h^{2.5}}\bigg{)} \tag{1}\] \[\propto=\frac{1}{h}\left(EI_{b}h^{2}+G_{s}J_{c}h\right)^{0.25}<50\] (2) \[\beta=\frac{1}{l}\left(EI_{b}l^{2}+G_{s}J_{b}l\right)^{0.25}<50 \tag{3}\]  
where, \(f_{m}^{\prime}\) is the compressive strength of masonry (in kN/m\({}^{2}\)), \(t\), \(h\) and \(l\) are the thickness, height and length of the infill wall, respectively (all in mm), \(E\) is the elasticity modulus of concrete (N/mm\({}^{2}\)), \(I_{c}\) and \(I_{b}\) are the inertia moments of the column and beam sections (mm\({}^{4}\)), respectively, and \(J_{c}\) and \(J_{b}\) are the torsion constants of the columns and beams (mm\({}^{4}\)), respectively. Figure 1: Partial and complete out-of-plane collapses of infilled walls during the L’Aquila earthquake (2009), Italy. In a later study, [PERSON] and [PERSON] [8; 9] proposed changing the value 4.50 in Equation (1) to 4.10, and eliminating the term related to torsion in Equations (2) and (3), due to its low influence and unnecessary complexity. The in-plane damage has a considerable influence on the out-of-plane resistance of an infill wall, as shown by [PERSON] [10], who tested eight full scale, one storey, one bay, RC frames, with brick and concrete masonry, first in-plane and then out-of-plane, see Figure 3. The in-plane test consisted of the application of load, monotonically, until a displacement value, equal to twice the value needed for the first crack to appear, was achieved. Then, the walls were loaded out-of-plane using airbags until the collapse of the specimen. The conclusions were: (i) the out-of-plane capacity depends on the slenderness and compressive strength of masonry; (ii) the in-plane damage does not affect the out-of-plane cracking pattern; (iii) for high slenderness infills, in-plane cracks lower the maximum out-of-plane capacity; (iv) vertical loading increases the stiffness but does not affect the out-of-plane capacity. [PERSON] [10] also proposed an analytical solution for the out-of-plane capacity of infills \(q\), see Equation (4), with or without in-plane damage. The reduction of the out-of-plane capacity is made using a parameter, \(R_{1}\), which can be obtained by, see [10]: (i) estimating the in-plane displacement due to cracking, using the uncracked stiffness of the system; (ii) visual inspection and classification of the damage in the infill. If the infill wall is undamaged, \(R_{1}\) assumes a unitary value.