## 5 Summary and Conclusions  
This paper presents two retrofitting strategies against progressive collapse of existing steel gravity frames, in which beams and columns are connected by simple connections. Retrofitting scheme 1 incorporates the addition of seat angles which are bolted to beam and column flanges, whereas retrofitting scheme 2 strengthens the connections by using steel plates with long-slotted holes which are welded to the column flanges and bolted to the beam flanges. The effectiveness of the proposed retrofit strategies in improving the robustness of structural systems is evaluated using detailed finite element models for a planar composite frame with simple beam-to-column connections and a 3-D micro-based model representing a 10-story seismically designed steel-framed structure, which is composed of moment frames and gravity frames. All numerical models have been shown to be able to capture progressive collapse behaviors of structures reasonably well after carefully calibrated against disparate experimental data and more refined numerical models.  
A key conclusion that can be drawn from this study is that the proposed retrofit strategies can improve the robustness of steel gravity frames significantly. The results of static and dynamic push-down analysis carried out using detailed finite element models reveal that the static and dynamic ultimate collapse resistance of the planar composite frames with enhanced connections elevate by as  
Figure 31: Responses of model M1-RS1 and M1-RS2 subjected to truck impact of column D5.  
Figure 30: Response of model M1 subjected to truck impact of column D5.  
much as 47.6% and 55.7%, respectively, compared with those of the composite frame with conventional connections when retrofit strategy 1 is employed. The numbers become 37.5% and 45.8% if the connections are enhanced using retrofit strategy 2. The adoption of these two retrofitting strategies also results in better ductility of planar composite frames under column loss scenarios. On the basis of the quantifications of collapse resistance mechanisms, the source of additional resistance that contributes to improved structural robustness due to both retrofit strategies is the increase in the amount of catenary action. Since evident increase in the flexural stiffness of the connections is not observed, both strategies have limited impact on the seismic behavior of the entire structural system. The comparisons between the responses of a multistory seismically designed steel frame structure, whose columns and beams in the gravity system are connected by enhanced simple connections and conventional simple connections, subjected to instantaneous removal of an interior gravity column and impact of a heavy vehicle with high speed on the same column, demonstrate that the proposed retrofit strategies are able to effectively protect the structure under both column loss scenarios and extreme loading conditions because progressive collapse occurs to the structure with unenhanced gravity system whereas collapse is arrested in structures with enhanced gravity systems.  
Furthermore, both schemes are economical, easy-to-implement, and non-destructive. Therefore, the proposed strategies are practical enough to be applied to retrofit existing steel gravity frames against progressive collapse.  
Original draft preparation: L.Z.; supervision, methodology, retrofit strategies, numerical models and validation: H.L.; review and editing: W.W. All authors have read and agreed to the published version of the manuscript.  
The presented work was supported by grants from the National Natural Science Foundation of China under Grant No. 51408152, China Postdoctoral Science Foundation through grant 2014M550194, China Postdoctoral Science Foundation through grant 2015T80353, and Natural Science Foundation of Heilongjiang Province, China under Grant No. LC2016021.  
The authors declare no conflict of interest.