# Out-of-Plane Experimental Study of Strengthening Slender Non-Structural Masonry Walls
## 3 Experimental Results Analysis with Discussion
### Stiffness Degradation  
With each new cycle and increased applied mid-height displacement amplitude, the damage of the specimen accumulates. Consequently, the stiffness degradation of the tested specimen is inevitable and is one of the main parameters in the characterization of the specimen's hysteretic response. The displacement amplitudes \(u_{i}\) at the mid-height of the specimen and the corresponding horizontal force \(F_{i}\) define the secant stiffness values of each hysteresis response loop \(K_{i}\), as given by Equation (1). From the experimentally obtained discrete values of stiffness and displacements of all cycles for an individual specimen, it is evident that the decrement of stiffness can be approximated by a hyperbolic curve using the least squares method. Based on the hysteresis response, the characteristic stiffness degradation parameters (_C_ and _n_) were determined for each specimen. The parameters define the interpolation hyperbolic function with Equation (2) to obtain the best fit to the experimentally obtained stiffness degradation values for each loading direction.  
\[K_{i}=\frac{F_{i}}{u_{i}} \tag{1}\]  
\[y(x)=\frac{C}{x^{n}}\quad y(x)=K_{i}\ \,\ \ x=u_{i} \tag{2}\]  
The coefficient \(C\) defines the overall vertical position of the curve, which indicates the global stiffness degradation, while the coefficient \(n\) dictates the shape of the curve and indicates the initial stiffness degradation slope. The higher the value of the coefficient \(n\), the steeper the initial stiffness degradation. Increasing of the coefficient \(C\) results in a higher remaining stiffness over the entire testing out-of-plane displacement amplitude range.  
In order to compare the strengthening systems' efficiencies according to stiffness degradation, the average factors of the interpolation functions \(n\) and \(C\) were determined from the positive and negative loading direction for each group of tested specimens, depending on their type and strengthening system. The average stiffness degradation interpolation functions of all groups of specimens are presented in Figure 12. The NF-poor curve has a lower position in comparison to the NF-good curve, as a consequence of the incompletely filled bed joint in the bottom location of the plastic hinge formation. From the average stiffness degradation curves' progress, it can be observed that all strengthening systems reduce the stiffness degradation rate. Expectedly, the application of strengthening systems A displays the greatest behavior improvement, which is followed by the application of the strengthening systems B, C, and D. The curves of NF-B and NF-D specimens have similar progress until reaching the 15 mm of mid-height displacement amplitude. After exceeding it, the NF-D curve gets closer to the NF-C curve. The progress of both becomes practically equal above the mid-height displacement amplitude of 45 mm.  
of workmanship, it is difficult to draw any conclusion. The coefficient \(C\) governs the global secant stiffness degradation over the entire range of applied displacement amplitudes, after the plastic hinges development. In order to compare strengthening systems' efficiencies according to global stiffness degradation, the values of the average coefficients \(C\) were normalized with the average value of non-strengthened (NF-good) specimens. A comparison of the normalized coefficients \(C_{norm}\) is shown in Figure 13. The improvement is the most significant when applying strengthening system A, which increases the coefficient by 171%. It is followed by system D with an increase of 168%. Systems B and C increase the coefficient by 103% and 117%, respectively.