# Out-of-Plane Experimental Study of Strengthening Slender Non-Structural Masonry Walls
## 3 Experimental Results Analysis with Discussion
### Eigenfrequencies and Damping  
The dynamic response of non-strengthened and strengthened specimens was assessed with the forced vibration method using attached accelerometers ACC1, ACC2, and ACC3 (see Figure 3) on the specimen before and after the quasi-static cyclic testing. Thus, the first natural frequency \(f\) and damping ratio \(\xi\) were evaluated on the intact state of an individual specimen and again after test termination, when the specimen was returned back to its neutral position. With fast Fourier transformation, the time response spectrum was converted to the amplitude response spectrum in the frequency domain, where amplitude peaks represent the natural oscillating frequencies. The natural frequency of the first mode shape was determined by comparing the amplitude peaks of the spectra for three accelerometers placed at 1/4 (ACC1), 1/2 (ACC2), and 3/4 (ACC3) of the wall specimen height. At first mode shape, the amplitude peaks of the accelerometers ACC1 and ACC3 exhibit a similar value which is, at the same time, significantly smaller compared to the value of accelerometer ACC2 at mid-height. From the amplitude spectrum using the half-power bandwidth method [70], the proportion of the critical damping ratio for the first oscillating shape was determined. The results of the dynamic properties of all tested non-structural walls specimens are summarized in Table 4.  
By applying strengthening systems, the natural time period \(T\) is reduced by 7% to 12% compared to the non-strengthened NF specimens in the undamaged state prior to testing. The critical damping ratio of strengthened specimens is also, to some degree, lower, except in the case of the strengthening system D. The results of non-strengthened specimens show that the natural time period \(T\) of undamaged slender non-structural walls built of regular solid bricks nears 0.07 s and can increase up to 0.2 s (at the least) by damage caused during an earthquake. The critical damping ratio of undamaged non-strengthened specimens is about 2.9% and can increase up to 7.3% in the case of damaged specimens. The comparison of strengthened systems after the tests is not applicable, since the failures were not the \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{3}{c}{**Before Testing**} & \multicolumn{3}{c}{**After Testing**} \\ \hline
**Specimen** & \(f\) [Hz] & \(T\) [s] & \(\xi\) [\%] & \(f\) [Hz] & \(T\) [s] & \(\xi\) [\%] \\ \hline NF-1 & 13.61 & 0.073 & 2.81 & 4.64 & 0.22 & 6.74 \\ NF-2 & 14.20 & 0.070 & 3.21 & 4.60 & 0.22 & 8.16 \\ NF-3 & 13.80 & 0.072 & 2.60 & 4.41 & 0.23 & 6.97 \\
**Average** & **13.87** & **0.072** & **2.87** & **4.55** & **0.22** & **7.29** \\
**COV** & **2.2\%** & **2.2\%** & **10.9\%** & **2.7\%** & **2.7\%** & **10.4\%** \\ \hline NF-1A & 14.94 & 0.067 & 2.57 & 4.83 & 0.21 & 6.16 \\ NF-2A & 15.30 & 0.065 & 2.89 & 4.92 & 0.20 & 6.51 \\ NF-3A & 15.83 & 0.063 & 2.66 & 4.23 & 0.24 & 6.52 \\
**Average** & **15.36** & **0.065** & **2.71** & **4.66** & **0.22** & **6.40** \\
**COV** & **2.9\%** & **2.9\%** & **6.1\%** & **8.0\%** & **8.4\%** & **3.2\%** \\ \hline NF-1B & 14.34 & 0.070 & 2.58 & 3.61 & 0.28 & 8.74 \\ NF-2B & 15.08 & 0.066 & 2.60 & 4.83 & 0.21 & 8.00 \\ NF-3B & 15.39 & 0.065 & 2.75 & 4.60 & 0.22 & 6.54 \\
**Average** & **14.94** & **0.067** & **2.64** & **4.35** & **0.23** & **7.76** \\
**COV** & **3.6\%** & **3.7\%** & **3.5\%** & **14.9\%** & **16.2\%** & **14.4\%** \\ \hline NF-1C & 16.37 & 0.061 & 2.80 & 3.85 & 0.26 & 8.93 \\ \hline NF-1D & 16.09 & 0.062 & 3.12 & 4.23 & 0.24 & 8.76 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Natural frequencies \(f\), corresponding time period \(T\), and damping ratios \(\xi\) of tested non-structural walls in the out-of-plane direction obtained with the forced vibration method. same for all specimens. These parameters are important in the process of out-of-plane design load definition when performing the structural analysis of a building.