This paper presents a detailed investigation into the seismic response of non-deteriorating and deteriorating single degree-of-freedom systems controlled by \(P -\Delta\) effects, with due account for the influence of earthquake duration. In order to isolate the effect of duration from other ground motion characteristics, 77 pairs of records with equivalent spectral shapes are considered in the study. The structural characteristics examined include the structural period, applied gravity loading, post-yield stiffness, viscous damping, material hysteretic behaviour, as well as the level of cyclic deterioration within the pinching systems. Detailed incremental dynamic analyses are carried out, considering an intensity measure corresponding to the spectral acceleration at the structural period of vibration of the system. Based on the incremental dynamic analysis results, predictive relationships are proposed for determining the structural collapse capacity, accounting for the influence of key parameters including instability and duration effects. The median and dispersion of the collapse capacity distribution embedded in the predictive models are also presented. The effect of duration is shown to increase with longer structural periods and to decrease with higher \(P -\Delta\) levels. The more rapid instigation of dynamic instability in relatively stiff systems is also shown to reduce their comparative sensitivity to variations in ground motion characteristics. Overall, it is indicated that disregarding the influence of duration could lead to over-estimations of up to 50% in the collapse capacity. The paper concludes with a discussion of other sources of structural damage that instigate collapse when using records with equivalent spectral shape but without especial consideration for duration effects.

中文翻译：

---

考虑了持续时间和不稳定影响的SDOF系统的地震倒塌能力评估

本文对由\（P-\ Delta \）控制的非恶化和恶化的单自由度系统的地震响应进行了详细的研究。影响，并适当考虑地震持续时间的影响。为了将持续时间的影响与其他地面运动特征隔离开来，研究中考虑了77对具有等效频谱形状的记录。检查的结构特征包括结构周期，施加的重力载荷，屈服后刚度，粘性阻尼，材料滞后性能以及收缩系统内的循环劣化程度。考虑到与系统振动的结构周期中的频谱加速度相对应的强度度量，进行了详细的增量动态分析。基于增量动力分析结果，提出了确定结构倒塌能力的预测关系，考虑关键参数的影响，包括不稳定和持续时间影响。还介绍了嵌入预测模型中的崩溃能力分布的中位数和离散度。研究表明，持续时间的影响随着结构周期的延长而增加，而随着结构周期的增加而减小\（P-\ Delta \）级别。还显示了在相对较硬的系统中更快速地激发动态不稳定性，从而降低了它们对地震动特征变化的比较敏感性。总的来说，表明忽略持续时间的影响可能导致倒塌能力的高估高达50％。本文最后讨论了其他结构破坏源，当使用具有相同光谱形状但未特别考虑持续时间影响的记录时，这些破坏会导致坍塌。