# Effect of Thin Cement-Based Renders on the Structural Response of Masonry Wall Panels
## 5 Design  
Test results have demonstrated that the shear strength can be affected by the cement-based render. A simplified approach to the problem can be made by considering the contribution of the cement-based render as a separate wall panel, and by calculating the lateral capacity of a rendered wall panel as the addition of the capacities of the URM wall and the render:  
\[P_{\rm max}=(P_{wall}+P_{render}), \tag{14}\]  
where \(P_{wall}\) is the lateral load-capacity of the URM wall panel and \(P_{render}\) is the lateral load capacity of the render. This design philosophy is based on limit-state design principles. By re-arranging Equations (2) and (3), it is possible to calculate the portion of diagonal load absorbed by the mortar:  
\[P_{render}=3\times n\times A_{render}\times\tau_{render}, \tag{15}\]  
where  
\[\tau_{render}=1.5\times f_{t,render}, \tag{16}\]  
and where \(A_{render}\) is the area of the of the horizontal cross section of the render (=1200 mm \(\times\) the thickness of the render), and \(n\) is the number of sides were the render has been applied (1 or 2). By doing this, it is possible to develop an analytical formulation for the prediction of the lateral capacity of a wall, using the data obtained from the mechanical characterization of the render. In Table 5, experimental results in terms of lateral load capacity are compared with theoretical ones, calculated from the tensile strength of the render (Equation (1)). It can be noted that the analytical formulation is able to capture the lateral capacity of a rendered wall with an acceptable error. It can be also noted that the analytical values of the lateral load capacity, using Equation (2), provide an overestimation of the load-capacity of the stone-panel. This can be explained by considering the assumptions of the limit-state analysis (perfect plastic material behavior). Figure 10: Shear tests (rendered wall panels): (**a**) L-07-S; (**b**) L-08-B. By contrast, the theoretical value underestimates the lateral load capacity of the rendered brickwork wall. However, it should be pointed out that the theoretical wall capacity (\(P_{wall}\)) was calculated in Equation (15) using the shear strength \(\tau_{0}\) of the corresponding non-rendered wall (test No. L-04-B). For this test the bonding pattern was \"Header bond\", while for the rendered wall this was \"Flemish bond\". Given the particular arrangement of the bricks, this system of header bonding is much weaker than Flemish again lateral in-plane loads [21; 22]. A similar method was recently used by [PERSON] and [PERSON] [16]. By using a large amount of experimental results from laboratory tests, these researchers concluded that the theoretical formulation also overestimates the lateral capacity of a wall panel, when high-strength renders are used and underestimates it when low-strength renders are employed. In order to overcome these problems, the authors proposed to apply a modification factor defined as the ratio between the experimental lateral capacity and the value of the analytical prediction, using Equations (15) and (16):  
\[\beta\ =\frac{P_{R\max}}{\big{(}P_{wall}+P_{coating}\big{)}}, \tag{17}\]  
where \(P_{R\max}\) is the experimental value of the load lateral capacity of the rendered wall. The main limitation of the method used by [PERSON] and [PERSON] to calibrate the modification factor is that this has been done by only using laboratory tests and a limited number of mortar types. In detail, the shear strength of the URM wall panels is dramatically larger compared to the shear strength of stone masonry wall panels tested on-site. The Italian Building Code [37] provides a table for the shear strength of URM masonry with values ranging from 0.020 and 0.074 MPa, for rubble, irregular, peddle and barely cut stone masonry, while the shear strength of the URM stone masonry used by the authors ranged from 0.076 and 0.175 MPa. However it must be concluded that this method seems to be the most appropriate for design purposes.