An Analytical Approach for the Flexural Robustness of Seismically Designed RC Building Frames Against Progressive Collapse

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.