Analysis of Flexural Load‐Bearing Capacity and Reliability of Damaged Concrete Beams Reinforced With Carbon Fiber Fabric

The reliability analysis of damaged reinforced concrete beams strengthened with carbon fiber reinforced polymer (CFRP) is addressed by categorizing the damage levels into three stages: before cracking load M i < M k , from cracking load to yield load M k ≤ M i < M y , and from yield load to ultimate load M y ≤ M i < M u . The flexural capacity and reliability of CFRP‐strengthened damaged reinforced concrete beams are analyzed accordingly. Based on the three types of CFRP‐reinforced damaged reinforced concrete beams, specific calculation formulas for the flexural capacity are proposed under various failure modes, including CFEP rupture, crushing of the compressed concrete zone, and cases where the height of the compressed concrete zone is less than 2 a ′ . These formulas have been validated against experimental data, showing a good correlation between experimental values and calculated results with high accuracy. Building upon these proposed calculation formulas for different damage levels in CFRP‐strengthened reinforced concrete beams, statistical parameters for mechanical properties relevant to structural reinforcement using carbon fiber fabric have been obtained through extensive testing based on existing research findings. Utilizing structural reliability theory methods, a systematic approach for conducting reliability analysis on CFRP‐strengthened damaged reinforced concrete beams has been established. By comparing and analyzing reliable indicators derived from this study, insights into the reliability level of CFRP‐strengthened damaged reinforced concrete beams are provided. The study simultaneously explores how the mean values and coefficients of variation of various random variables influence the reliability indicators. Factors, such as the reinforcement ratio of reinforced concrete beams, the amount of carbon fiber cloth used for strengthening, the strength utilization coefficient of carbon fiber cloth, performance index values related to the guaranteed strength standard value of carbon fiber cloth, and the enhancement factor after steel yield all affect the reliability indicators for strengthened damaged reinforced concrete beams. The results indicate that when initial load M k ≤ M i < M y is applied without unloading on a damaged beam, an increase in initial load M i leads to a decrease in reliability indicators for carbon fiber‐reinforced damaged reinforced concrete beams. Furthermore, these reliability indicators increase with an increasing damage reduction coefficient. Under constant conditions regarding other factors, as the strength utilization coefficient of carbon fiber sheets increases, so does the reliability indicator for strengthened reinforced concrete beams. When unloading occurs under conditions where M k ≤ M i < M y , and other factors remain unchanged, it is observed that as reinforcement ratio ρ increases, so do the reliability indicators for CFRP‐strengthened damaged reinforced concrete beams. Conversely, when loading exceeds yield stress M k > M y during unloading, while keeping other factors constant, an increase in enhancement factor postyield results in a gradual decline in reliability indicators for strengthened reinforced concrete beams. Additionally, under consistent conditions concerning postyield enhancement factors at similar levels; increasing layers of reinforcement also contributes positively to enhancing reliability indicators following strengthening measures on reinforced concrete beams. This research provides valuable insights into conducting a reliable analysis on carbon fiber‐reinforced damaged reinforced concrete beams.