This paper investigated the working behavior characteristics of six reinforcement concrete (RC) beams subjected to bending based on the numerical shape function (NSF) method and structural stressing state theory. Firstly, the structural stressing state mode is expressed based on the generalized strain energy density (GSED) derived from the measured strain data. Then, one of the Carbon Fiber Reinforced Plastic (CFRP)-strengthened RC beams is taken as an example and the leap characteristics of RC beam’s stressing state are detected by applying the Mann–Kendall (M–K) criterion, updating the existing definition of the structural failure load. Accordingly, the stressing state modes and strain fields of the CFRP-strengthened RC beam are proposed to reveal their leap characteristics. Furthermore, through comparing the working performance of six RC beams, the effects of different strengths and different reinforcement ratios on CFRP strengthening performance are investigated. Finally, the NSF method is applied to reasonably interpolate the limited strain data for further revealing the stressing state characteristics of the RC beams. The research results explore a new analysis method to conduct an accurate estimation of the structural failure load and provide a reference for the future design of CFRP-strengthened RC beams.

中文翻译：

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碳纤维增强塑料加固钢筋混凝土梁受力状态分析

【摘要】：基于数值形函数(NSF)方法和结构受力状态理论,研究了六根钢筋混凝土(RC)梁在受弯作用下的工作行为特性。首先，基于从测量应变数据导出的广义应变能密度（GSED）来表示结构应力状态模式。然后，以其中一根碳纤维增强塑料 (CFRP) 强化 RC 梁为例，应用 Mann-Kendall (M-K) 准则检测 RC 梁受力状态的跳跃特性，更新了现有的定义结构破坏荷载。因此，提出了CFRP加强RC梁的应力状态模式和应变场，以揭示其跳跃特性。此外，通过比较六根钢筋混凝土梁的工作性能，研究了不同强度和不同配筋率对CFRP增强性能的影响。最后，应用NSF方法对有限应变数据进行合理插值，进一步揭示RC梁的受力状态特征。研究结果探索了一种新的分析方法，可以对结构破坏荷载进行准确估算，为今后CFRP加固RC梁的设计提供参考。