# Nonlinear Dynamic Response of a Precast Concrete Building to Sudden Column Removal
## 4 Results and Discussion
### Edge Column Removal Scenario
#### 4.1.2 Precast Frame System (PCF_E)  
The precast frame system subject to edge column removal scenario is investigated herein. Figure 7 shows the structural response results in terms of vertical displacement recorded at the location of the removed column and main failure events occurring at the 1 st ground level during progressive collapse phenomenon. As mentioned before, in addition to springs to simulate connection behavior, the PC1 model considers the presence of a tying system consisting of two 28-mm diameter rebars (indicated with red lines in the schematic view shown in Figure 7). This assumption meets the fib Bulletin 63 requirements [34]. Conversely, the PC2 model considers only springs to simulate connection behavior with no tying system. It is noted that, in Figure 7, the link and tie locations are identified with label L.  
Figure 6: Results for MRF_E: (**a**) Vertical displacement; (**b**) Steel stress strain relation; (**c**) Concrete core compressive stress-strain relation; (**d**) Axial load of RC beams across removed column. Figure 7: Displacement response and main events detected for PC1 and PC2 frame systems subject to edge column loss scenario. It is evident from Figure 7 that the PC1 system was not able to sustain the load magnitude corresponding to accidental combination (100%-Q\({}_{b,e}\) in Table 1). This is attributed to support losses which are experienced by precast beams at this load level. For this reason, it is interesting to find the threshold load level at which column loss does not occur. Under a load magnitude equal to 80% of the design accidental load \(Q_{b,e}\) the PC1 frame system did not show any support loss (i.e., PLS4 was not reached). Conversely, when the load magnitude was increased to 90% of \(Q_{b,e}\), the loss of column support occurred at the first floor level. In addition to PC1 model, the PC2 model was investigated. In this case, the tying system was not included, so the frame resistance relied only on connection strength. It can be observed how such system was not able to sustain even the self-weight (reported with the label SW in Figure 7) of structural members and hollow-core slab. All supports were lost and the structure was unable to redistribute the applied loads. The analysis of this system is considered of a great importance, since it highlights the need to improve the structural robustness by adding tying systems. In detail, the following main failure events corresponding to Figure 7 were detected based on the link (or ties) positions for PC1 model with support loss detection:  
1. PLS1 was reached because of the yielding of all ties and all negative moment spring at each floor level;
2. PLS2 was reached because of fracture of all dowels at each floor level. This indicates that the structural response relies on the flexural contributions of rotational springs and tying reinforcements;
3. PLS3 was reached because of some tie fractures at the second floor level in correspondence of removed column (T2-2 and T2-3 locations) immediately followed by an additional tie fracture at the first floor level (T1-2 location);
4. Due to the above-mentioned tie fractures, the structure lost the support at the first and second floor levels (T1-2, T2-2 and T2-3 locations), indicating that a progressive collapse was occurring. PLS4 was thus reached. To summarize the above-mentioned failure events, maximum support lateral displacements for different link locations and floor levels are reported in Figure 8. After the dowels' fractures at 4.6 mm, the precast beams began to slide over the supporting column until the tie reached the fracture elongation at locations 2-2 and 2-3 (equal to 90 mm, calculated by multiplying the fracture strain \(\varepsilon_{su}\) equal to 20% and the node-to-node distance of 450 mm). A further tie fracture was detected at the first floor level (1-2 location). The consequent support loss at the first and second floor levels led to the progressive collapse of the structure. Figure 9 shows the stress-strain diagrams of ties at the locations of fracture.