# Tensile Capacity of Adhesive Anchors in Damaged Masonry
## 4 Discussion
### Effect of the Crack Width  
On the basis of the previous analysis, it seems that apart from the position, the crack width affects the results. Figure 10 shows the maximum load vs. the crack width. The load decreases exponentially with the increasing of the crack width with an excellent correlation (R\({}^{2}\) = 0.94). It seems that up to the crack width of about 0.7 mm the decrease follows either an exponential (R\({}^{2}\) = 0.94) or a linear trend (R\({}^{2}\) = 0.92) (Figure 10 right), while beyond that limit the load reduction is less pronounced and only an exponential function can fit the experimental results (Figure 10 left). Unfortunately, there are no results in the crack width range 0.7-1.3 mm, while it would be interesting to observe whether there is a steep change in gradient (at a given crack width) or a soft decrease until reaching an asymptotic value. To investigate this topic a specific additional experimental campaign is needed. On the basis of these results, it seems that the crack opening is the governing parameter that affects the results. Nevertheless, although the correlation between load and crack width is excellent, there is no correlation between displacement and crack width. Indeed, the coefficients of variation of the displacements evaluated at different load levels (Peak load, 50% of the peak load and at 5 kN- Table 3 and Figure 11) are very high. It has to be noted that the displacements at the peak load and at 50% of the peak load were associated to the different loads of each test. Nevertheless, even when evaluated at the same (rather low) load level (5 kN), the coefficients of variation remained very high. The coefficient of variation of the load associated to different crack width (Table 3) is very low up to crack width equal to 0.4 mm. Figure 10: Load vs. crack width (all results and up to 0.7 mm). By comparing the load displacement curves associated at a given crack width (Figure 11) it seems that the displacement is only partially affected by the crack width. Indeed, Figure 12 shows that, also for small crack width (0.1 mm and 0.2 mm), there are some curves that differ (independent from the type of failure) and thus the coefficient of variation of the displacements at given loads are very high. This behavior seems more pronounced with increasing crack width, nevertheless no clear trend can be found and there is also no correlation with the failure mode. In addition, it is evident that in some cases a non-linear branch at the beginning of the test was observed (i.e., test W1-A7, W1-A4), followed by a linear part. For this reason, the stiffness of the load-displacement curves was evaluated considering the tangent of the linear part. Figure 13 shows this stiffness vs. the crack width. It seems that the correlation of the two variables is rather limited, even if a trend is identifiable. Likely, the level of pre-damage from the load cycle affects the results, and the crack opening measured on the surface does not consider the possible damage (along the hole) within the masonry, which could affect the load-displacement behavior as well. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Crack Width** & \multicolumn{2}{c}{**Max Load**} & \multicolumn{2}{c}{**Mean Displacement (mm)**} & \multicolumn{2}{c}{**Cov Displacement (\%)**} \\ \hline
**(mm)** & \begin{tabular}{c} **Mean** \\ **(kN)** \\ \end{tabular} & \
\begin{tabular}{c} **Cov** \\ **(\%)** \\ \end{tabular} & **Peak** &
\begin{tabular}{c} **0.5** \\ **Peak** \\ \end{tabular} & **5 kN** & **Peak** & **0.5 Peak** & **5 kN** \\ \hline
0.1 & 27.23 & 3.3 & 4.09 & 1.26 & 0.60 & 65 & 71 & 72 \\
0.2 & 23.93 & 2.7 & 5.54 & 2.44 & 1.41 & 40 & 46 & 47 \\
0.25–0.28 & 22.69 & 1.9 & 5.21 & 2.47 & 1.71 & 47 & 79 & 83 \\
0.30–0.38 & 20.09 & 4.5 & 2.98 & 1.00 & 0.70 & 65 & 35 & 30 \\
0.4–0.7 & 16.59 & 19.7 & 4.85 & 2.44 & 1.95 & 33 & 57 & 61 \\
1.3–1.8 & 10.62 & 31.4 & 7.53 & 3.07 & 1.81 & 100 & 104 & 58 \\
2.0–2.5 & 4.78 & 43.0 & 10.37 & 4.30 & 0.34 & 140 & 155 & - \\ \hline \hline \end{tabular}
\end{table}