# Out-of-Plane Experimental Study of Strengthening Slender Non-Structural Masonry Walls
## 3 Experimental Results Analysis with Discussion
### Response Envelope Curves and Limit States  
The limit states are determined based on the force-displacement response hysteresis envelopes for the positive and negative loading direction. The following limit states (LS) were determined. * First crack initiation LS: Reduction in stiffness is observed and a mechanism of plastic hinges in upper, mid-height, and bottom bed joint is formed. * Maximum resistance LS: The specimen achieves the maximum out-of-plane resistance force \(F_{max}\) at the corresponding mid-height out-of-plane displacement. * Near collapse LS: The test specimen is severely damaged or in the next amplitude cycle; a collapse is likely to occur. To analyze the effectiveness of different strengthening systems, a comparison of the average second-cycle hysteresis envelopes in the positive and negative loading direction was performed for individual sets of test specimens. A comparison of the specimens' average envelope curves (averaged all positive and negative envelopes) is shown in Figure 9. For each LS, the average values of out-of-plane force resistance and the corresponding average displacements are presented in Table 2 for all specimens' groups. In the case of the strengthening system A, the maximum resistance LS and the near collapse LS are remarkably close, both in terms of the limit displacements value and the out-of-plane resistance. This is not the case with other NF specimens, where the curve slightly decreases to the near collapse LS after reaching the maximum out-of-plane capacity. A comparison of the average envelopes shows that the strengthening system A has the greatest impact on the maximum out-of-plane resistance. The ratios between displacements at near collapse LS and maximum resistance LS are 1.53, 1.03, 1.63, 4.37, and 2.52 for specimens' groups NF-good, NF-A, NF-B, NF-C, and NF-D, respectively. The comparison of these ratios correlates to the damage capacity after the maximum resistance LS is reached, where NF-A and NF-B exhibit limited damage capacity before total failure of strengthening systems. On the other hand, the NF-C and NF-D systems have a higher damage capacity after exceeding the maximum resistance LS, which can be explained by observing the diagonal strengthening strips' orientation, where different tensile stress distribution occurs. For a more detailed comparison, the average load capacities and limit displacements of individual test specimens' groups for each of the limit states were normalized in respect to average values of as-built (NF-good) specimens. A relative comparison of different strengthening systems' efficiency at all three limit states for out-of-plane force resistance is shown in Figure 10.  
When comparing the out-of-plane force resistance of strengthened and non-strengthened (NF-good) specimens, it can be seen that by applying the strengthening system A, the resistance at first crack initiation LS is increased by 60%, the maximum resistance LS is increased by 221%, and the near collapse LS is increased by 315%. For system B, the out-of-plane resistance improvement was approximately halved namely, 51%, 98%, and 116% for each of the limit states, respectively. The first crack initiation LS resistance increased by 61% and by 56% for the C and D systems, respectively. Systems C (by 65%) and D (by 61%) have a similar effect on increasing the capacity of maximum resistance LS and have a negligible effect on the out-of-plane force resistance at near collapse LS. However, the out-of-plane force resistance value at near collapse LS is similar to the as-built (NF-good) specimens, the corresponding displacements are much higher than the displacements of the as-built specimens at near collapse LS. At maximum resistance LS, the corresponding limit mid-height displacements for specimens with strengthening system A and system B increase by 200% and 84%, respectively. The remaining systems exhibit a negative effect.