Abstract The development of collapse fragility curves is an essential requirement for the assessment of the collapse risk of structures. These fragility curves depend on the structural collapse capacity that is evaluated in terms of either the intensity measure (IM) or the damage measure (DM); such as the engineering demand parameter (EDP). In turn, collapse capacity estimates are sensitive to the method employed for their assessment. Conventionally, the IM and DM rules are employed in conjunction with incremental dynamic analyses (IDA) to quantify the collapse capacity of a structure. However, this approach has been criticised for being subjective in nature, since it depends on the structural response approaching predetermined threshold values. Therefore, it does not relate to the actual dynamic instability. Although the selection of these thresholds stems from the results of experimental investigations and equivalent numerical models and serve as an indirect check for dynamic instability, the present study seeks to provide a mathematical basis for defining collapse criteria. A dynamical system approach is used to formulate a mathematical criterion for defining P-Delta instability induced seismic collapse in single-degree-of-freedom (SDOF) structures. The non-linear SDOF structure is considered as a non-autonomous, non-smooth system, and is studied as an ensemble of different sub-systems. Collapse is defined as the point when the dominant system eigenmode of the structure changes from stable to unstable, and remains unstable as the structure collapses. This approach can be applied to first mode governed multi-degree-of-freedom (MDOF) structures when studied as an equivalent SDOF structure. It is found that the dynamical systems approach results in higher deformations at collapse when compared to the conventional IM/DM rule based approach, suggesting the conservatism involved in the latter. However, it results in lower deformations at collapse when compared to the energy criterion, which relies on the occurrence of large deformations to predict collapse. Furthermore, the derived fragility curves show that the proposed approach yields lower probabilities of collapse when compared to the conventional method. Therefore, the proposed method can be used an alternative method for the performance design of structures.

中文翻译：

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用于评估地震结构倒塌的动力系统方法及其与 PBEE 框架的集成

摘要 倒塌脆性曲线的建立是结构倒塌风险评估的必要条件。这些脆性曲线取决于根据强度度量 (IM) 或损坏度量 (DM) 评估的结构倒塌能力；例如工程需求参数（EDP）。反过来，倒塌能力估计对其评估所采用的方法很敏感。通常，IM 和 DM 规则与增量动态分析 (IDA) 结合使用来量化结构的倒塌能力。然而，这种方法因本质上的主观性而受到批评，因为它依赖于接近预定阈值的结构响应。因此，它与实际的动态不稳定性无关。虽然这些阈值的选择源于实验研究和等效数值模型的结果，并作为动态不稳定性的间接检查，但本研究旨在为定义倒塌标准提供数学基础。动力学系统方法用于制定数学准则，用于定义单自由度 (SDOF) 结构中 P-Delta 不稳定性引起的地震倒塌。非线性单自由度结构被认为是一个非自治的、非光滑的系统，并作为不同子系统的集合进行研究。坍塌定义为结构的主导系统本征模从稳定变为不稳定，并在结构坍塌时保持不稳定的点。当作为等效的单自由度结构进行研究时，这种方法可以应用于第一模态控制的多自由度 (MDOF) 结构。结果表明，与传统的基于 IM/DM 规则的方法相比，动态系统方法在坍塌时会导致更高的变形，表明后者具有保守性。然而，与能量准则相比，它导致倒塌时的变形较低，能量准则依赖于大变形的发生来预测倒塌。此外，导出的脆性曲线表明，与传统方法相比，所提出的方法产生的倒塌概率较低。因此，所提出的方法可以用作结构性能设计的替代方法。结果表明，与传统的基于 IM/DM 规则的方法相比，动态系统方法在坍塌时会导致更高的变形，表明后者具有保守性。然而，与能量准则相比，它导致倒塌时的变形较低，能量准则依赖于大变形的发生来预测倒塌。此外，导出的脆性曲线表明，与传统方法相比，所提出的方法产生的倒塌概率较低。因此，所提出的方法可以用作结构性能设计的替代方法。结果表明，与传统的基于 IM/DM 规则的方法相比，动态系统方法在坍塌时会导致更高的变形，表明后者具有保守性。然而，与能量准则相比，它导致倒塌时的变形较低，能量准则依赖于大变形的发生来预测倒塌。此外，导出的脆性曲线表明，与传统方法相比，所提出的方法产生的倒塌概率较低。因此，所提出的方法可以用作结构性能设计的替代方法。与能量准则相比，它导致倒塌时的变形较低，能量准则依赖于大变形的发生来预测倒塌。此外，导出的脆性曲线表明，与传统方法相比，所提出的方法产生的倒塌概率较低。因此，所提出的方法可以用作结构性能设计的替代方法。与能量准则相比，它导致倒塌时的变形较低，能量准则依赖于大变形的发生来预测倒塌。此外，导出的脆性曲线表明，与传统方法相比，所提出的方法产生的倒塌概率较低。因此，所提出的方法可以用作结构性能设计的替代方法。