## 6 Conclusions  
In this study, a suitable damage index is determined. Masonry wall buildings reinforced with x-bracing concrete frames are assessed by analysing various models to study the damage behaviours under monotonic loading and cyclic loading conditions. Results, the case study demonstrates that the masonry wall building, reinforced with x-bracing concrete frames, exhibits enhanced seismic resistance, reduced potential for severe damage, and improved overall structural performance compared to the original structure. The detailed analysis and calculations support the effectiveness of x-bracing in mitigating the impact of seismic forces will affect to building collapse. The study results are summarized in the following main points:  
1. The monotonic loading and cyclic loading conditions are analysed at the maximum lateral force. The analysis reveals that the results are consistent in the same direction and with the model structure analysis results.
2. The correlation coefficient between the damage level and accumulated energy (\(\beta\)) is appropriate for use in the calculation of the damage index using the Park-Ang equation. The Park-Ang equation for a masonry wall building (\(\beta\)) is equal to 0.10-0.35.
3. The criteria for the consideration of the damage level are defined as follows: when the damage index is between 0.25 and 0.50, the specimen has a minor damage level; when the damage index is between 0.50 and 0.80, the specimen has a moderate damage level; when the damage index is between 0.80 and 1.00, the specimen has a severe damage level; and when the damage index is more than 1.00, the specimen has a collapse damage level, resulting in the structure of the building experiencing a disaster.
4. The damage index for assessing the seismic-resistant design of masonry wall buildings reinforced with x-bracing concrete frames shows that they resist higher lateral force base shear values before lateral displacement than the original walls without x-bracing concrete frame structures, with values of 478.78 kN and at 67.16 kN, respectively, demonstrating an approximately 7.13 times difference in lateral forces. The masonry wall buildings reinforced with x-bracing concrete frames show extensive large cracks, and the damage index criterion (DI) is equal to 0.8 in the maximum lateral force base shear design.  
Therefore, the use of reinforced x-bracing concrete frames in masonry wall buildings offers a holistic approach to seismic resistance. This strategy addresses the vulnerabilities of traditional masonry structures, providing improved stability, increased shear strength, controlled de-formation, and enhanced energy dissipation. The adaptability of x-bracing systems makes them valuable not only in new construction but also in retrofitting existing buildings for better seismic performance.  
Figure 8: Comparison between masonry wall building with x-bracing and original wall building without x-bracing concrete frame.  
**Author Contributions:** Conceptualization, Y.C. and V.C.; methodology, Y.C. and V.C.; software, Y.C. and V.C.; validation, Y.C. and V.C.; formal analysis, Y.C. and V.C.; investigation, Y.C. and V.C.; resources, Y.C. and V.C.; data curation, Y.C. and V.C.; writing--original draft preparation, Y.C. and V.C.; writing--review and editing, Y.C. and V.C.; visualization, Y.C. and V.C.; supervision, Y.C. and V.C.; project administration, Y.C. and V.C. All authors have read and agreed to the published version of the manuscript.  
**Funding:** This research received no external funding for the cost of publication.  
**Institutional Review Board Statement:** Not applicable.  
**Informed Consent Statement:** Not applicable.  
**Data Availability Statement:** Data is contained within the article.  
**Conflicts of Interest:** The authors declare no conflict of interest.