基于相平面法的 RC 结构抗连续倒塌动力敏感危险域分析

摘要：相较于直接非线性动力分析法，非线性静力下推法因其简便也被广泛应用于钢筋混凝土 (RC) 结构的 抗连续倒塌性能分析，并可采用动力放大系数或能量法近似预测最大动力响应。RC 结构在拆除柱子后，随着 变形的增加，在抗连续倒塌承载机制由压拱机制转换到悬索机制的过程中，可能存在按静力分析安全而按动力 分析不安全的动力敏感危险域，导致结构发生达不到预期变形能力的脆性破坏模式。这一问题尚未得到足够的 重视。该研究以结构稳定理论为基础，采用相平面法研究了 RC 结构抗连续倒塌承载机制转换过程中可能存在 的动力敏感危险域。以两杆模型、RC 梁柱子结构和 RC 框架结构为例，基于相平面法揭示了动力响应中的短暂 跳跃失稳现象，阐明了静、动力失稳和动力敏感危险域之间的关系，通过控制变量法分析了静、动力失稳现象 及动力敏感危险域与重要结构参数之间的关系，提出了动力失稳及动力敏感危险域的实用近似判定方法。研究 结果表明：结构抗连续倒塌由压拱机制转换到悬索机制的过程中，除可能存在静力极值点失稳外，还可能存在 动力跳跃失稳，且静、动力失稳因加载方式与失效准则不同而并非总是同时出现。动力跳跃失稳可采用相平面 法精准地识别，若相轨迹的性状稳定并收敛于中心或稳定焦点，则动力稳定；否则，发生动力失稳，且伴随出 现鞍点。若静力极值点失稳恢复而动力失稳仍存在，则为动力敏感危险域，即动力敏感危险域为失稳域的子 集，且不包含在静力极值点失稳域中。 

关键词：连续倒塌；动力效应；结构稳定性；相平面法；钢筋混凝土结构；拆除构件法 

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INVESTIGATION OF DYNAMIC SENSITIVE DANGER ZONE FOR RC STRUCTURES AGAINST PROGRESSIVE COLLAPSE BY THE PHASE PLANE METHOD

Abstract:   Apart from the nonlinear dynamic analysis, the nonlinear static analysis is also widely adopted to perform the progressive collapse analysis of reinforced concrete (RC) structures, in which a dynamic increase factor or the energy balance approach can be considered to involve the influence of dynamic effects. However, it is possible that a structure is evaluated to be safe in a static procedure but unsafe in a dynamic procedure when the progressive collapse mechanism switches from the compressive arch action to the tensile catenary action due to the removal of a column. In this case, a brittle failure mode may occur as the deformation capacity is much lower in the dynamic procedure. Thus, the dynamic sensitive danger zone (DSDZ) during the transformation process of the progressive collapse mechanism is investigated on the basis of structural stability theory. A two-bar truss system, an RC beam-column substructure, and an RC frame are adopted as numerical examples. The phase plane method is employed to identify the dynamic instability phenomenon in dynamic responses. The relationship between the DSDZ and static and dynamic instabilities are interpreted, as well as the influence of important structural parameters on them. Moreover, the practical approaches or criteria for identifying the dynamic instability and the DSDZ are proposed. According to the results, not only the static instability but also the dynamic instability may occur during the transformation process of the progressive collapse mechanism. Furthermore, the static and the dynamic instabilities are independent. The dynamic instability can be identified by the phase plane method, in which the structure is stable if the phase trajectory converges to the stable focus. Otherwise, the dynamic instability will occur. When only the dynamic instability exists, it is the case of the DSDZ, which is the subregion of the instable zone.

Keywords:  progressive collapse  /  dynamic effects  /  structural stability  /  phase plane method  /  reinforced concrete structures  /  alternate load path method

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官网链接：https://engineeringmechanics.cn/cn/article/doi/10.6052/j.issn.1000-4750.2023.08.0607

丁陆川, 陈建兵. 基于相平面法的RC结构抗连续倒塌动力敏感危险域分析[J]. 工程力学. DOI: 10.6052/j.issn.1000-4750.2023.08.0607DING Lu-chuan, CHEN Jian-bing. INVESTIGATION OF DYNAMIC SENSITIVE DANGER ZONE FOR RC STRUCTURES AGAINST PROGRESSIVE COLLAPSE BY THE PHASE PLANE METHOD[J]. Engineering Mechanics.