Quantitative and parametric investigations of the flexural robustness of seismically designed reinforced concrete (RC) building frames under column loss were conducted in this study. A robustness index expressed as the product of the seismic coefficient and the resistance ratio was proposed for the evaluation. Under column-loss conditions, the building frame may not sustain the effective seismic weight using the flexural mechanism as the robustness index is smaller than one. Analytical formulae of the robustness index for the three-dimensional frame model were derived using the energy method and plastic analysis technique. Seven moment-resisting RC building frames with different structural parameters were designed. Nonlinear static analyses were performed to investigate the effects of the span length, number of stories, and seismic coefficient on the robustness index. The results indicated that among these parameters, the span length was the most critical factor. The robustness index decreased with an increase in the span length. For the five-story building frames, it decreased to smaller than 1.0 when the span length increased from 4 to 6 m or larger. Nevertheless, the robustness index was approximately directly proportional to the seismic coefficient and number of stories. It was doubled as the seismic coefficient or number of stories increased from 0.1 to 0.2 or five to ten, respectively. Numerical verification confirmed that the proposed analytical formulae can provide conservative robustness evaluation for seismically designed RC building frames.

中文翻译：

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抗震设计的 RC 建筑框架抗连续倒塌的抗弯强度分析方法

本研究对抗震设计的钢筋混凝土 (RC) 建筑框架在柱损失情况下的抗弯强度进行了定量和参数化研究。提出了以地震系数和抗力比的乘积表示的稳健性指标用于评估。在失柱条件下，由于稳健性指标小于 1，建筑框架可能无法使用弯曲机制承受有效地震权重。利用能量法和塑性分析技术推导出三维框架模型稳健性指标的解析公式。设计了七个不同结构参数的抗弯钢筋混凝土建筑框架。进行非线性静态分析以研究跨度长度、楼层数、和抗震系数对稳健性指标的影响。结果表明，在这些参数中，跨度是最关键的因素。鲁棒性指数随着跨度的增加而下降。对于五层建筑框架，当跨度长度从 4 增加到 6 m 或更大时，它减小到小于 1.0。然而，稳健性指数与地震系数和层数大致成正比。随着地震系数或楼层数分别从 0.1 增加到 0.2 或从 5 增加到 10，它增加了一倍。数值验证证实，所提出的分析公式可以为抗震设计的 RC 建筑框架提供保守的稳健性评估。跨度是最关键的因素。鲁棒性指数随着跨度的增加而下降。对于五层建筑框架，当跨度长度从 4 增加到 6 m 或更大时，它减小到小于 1.0。然而，稳健性指数与地震系数和层数大致成正比。随着地震系数或楼层数分别从 0.1 增加到 0.2 或从 5 增加到 10，它增加了一倍。数值验证证实，所提出的分析公式可以为抗震设计的 RC 建筑框架提供保守的稳健性评估。跨度是最关键的因素。鲁棒性指数随着跨度的增加而下降。对于五层建筑框架，当跨度长度从 4 增加到 6 m 或更大时，它减小到小于 1.0。然而，稳健性指数与地震系数和层数大致成正比。随着地震系数或楼层数分别从 0.1 增加到 0.2 或从 5 增加到 10，它增加了一倍。数值验证证实，所提出的分析公式可以为抗震设计的 RC 建筑框架提供保守的稳健性评估。稳健性指数与地震系数和楼层数大致成正比。随着地震系数或楼层数分别从 0.1 增加到 0.2 或从 5 增加到 10，它增加了一倍。数值验证证实，所提出的分析公式可以为抗震设计的 RC 建筑框架提供保守的稳健性评估。稳健性指数与地震系数和楼层数大致成正比。随着地震系数或楼层数分别从 0.1 增加到 0.2 或从 5 增加到 10，它增加了一倍。数值验证证实，所提出的分析公式可以为抗震设计的 RC 建筑框架提供保守的稳健性评估。