## 1 Introduction  
With the worldwide occurrence of earthquakes, the seismic strengthening of buildings plays an important role in earthquake risk reduction. Many buildings that are designed in accordance with the early codes lack detail in terms of ductility. Therefore, these structures exhibit low-ductility performance and tend to damage or even collapse when subjected to a severe earthquake. However, these types of structures remain valuable after maintenance. Mitigating earthquake loss by strengthening buildings to reduce seismic risk is an economic strategy. The first important step in strengthening structures is to define the extent to which structural performance must be improved. Structures are expected not only to ensure collapse prevention when subjected to a maximum considered earthquake (MCE) but also to possess a certain collapse safety margin after strengthening. The direct quantification of the safety levels of structures has become increasingly important in recent years, especially after the development of performance-based earthquake engineering. A global structural performance index is desired to measure the acceptable collapse safety margin and facilitate an assessment of collapse resistance capacity in future seismic research. Many seismic strengthening methods have been used to improve the seismic performance of structures. The use of dissipative braces seems promising because such braces provide a supplemental path for earthquake-induced horizontal actions; thus, they enhance the seismic behavior of the frame by adding energy dissipation capacity and stiffness [1; 2; 3]. Fiber-reinforced polymers are widely used to retrofit existing reinforced concrete (RC) structures. It can improve the global seismic performance of structures by increasing the ductility of the columns and preventing brittle failure mode [4]. [PERSON] et al. [5] used a high-performance, fiber-reinforced concrete jacket to retrofit the RC corner beam-column joint of an existing structure with structural deficiencies. This technique was effective for increasing the shear strength of the joint by approximately 40%. An integrated approach was also proposed to ensure sustainability, safety, and resilience for the renovation of existing RC building stocks; the approach targets energy efficiency and architectural restyling by complementing the building with a technological double skin that supports itself on an independent exoskeleton [6; 7]. Many other retrofitting methods, such as adding concrete shear walls, enlarging the column section, reinforcing the column with carbon fiber, and installing an energy dissipation damper, have been used [8]. These strategies mostly characterize the collapse resistance capacity of structures through the bearing capacity of the beam/column components or ductility factor(s). However, these indexes are simple, partial, and unable to express the global collapse performance of structures exactly and directly. The collapse safety margin evaluation approach based on incremental dynamic analysis (IDA) and vulnerability analysis can be considered a comprehensive tool to reflect the complete seismic performance of structures experiencing minor to severe damage or even collapse. The collapse margin ratio (CMR) was introduced into the FEMA P695 report [9] and defined as the ratio of the median spectral intensity \(IM_{50\%}\) (such as spectral acceleration, as suggested in the report) of the collapse-level ground motions to the spectral acceleration with the MCE level \(IM_{MCE}\) at the fundamental period of structures. CMR is used to quantify the margin between MCE- and collapse-level earthquakes. It is a case-specific factor that reflects all structural design information and varies from one case to another. CMR is not only a technical term; it can be understood and accepted by risk decision-makers or house owners because they can easily, rapidly, and approximately assess the total seismic performance of their buildings in future earthquakes and whether the damage-induced economic loss can be tolerable.