# Performance-Based Analysis of Single-Layer Cylindrical Steel Reticulated Shells in Fire
## 5 Structural Response Analysis in Different Fire Scenarios
### Displacement Analysis of the Cylindrical Latticed Shell  
Figures 17-19 show a displacement cloud diagram of a structure during a fire, with different fire source locations. When the maximum fire source power is 20 MW, the structure has different failure modes and fire durations depending on the location of the fire source. The maximum displacement point of the reticulated shell under a normal temperature load is located at the highest midpoint of the roof. The equivalent displacement is 0.09 m. The structure remains in an overall stable state. When the fire source is in the center at the ground level, as shown in Figure 17, the structure remains basically stable during the first 1860 s of the fire. At 1863 s, the components on the left side yield first, and then the upper reticulated structure begins to collapse from the middle. After a few seconds, the cylindrical  
Figure 16: Stress-strain relationship model of steel at high temperatures prescribed in EC3. reticulated shell collapses completely at 1866 s, while the maximum displacement of the node in the middle of the roof is up to 11.63 m. The structure reaches its bearing capacity limit at 1863 s, and the structure is completely destroyed. The fire resistance limit of the structure in these fire conditions is thus 1863 s. When the fire source is set at the midpoint of the longitudinal side, as shown in Figure 18, the structure remains stable during the first 580 s. The steel pipes on the side near the fire source yield first, at 583 s. As the temperature continues to rise, the steel pipes on the right side of the reticulated shell (above the fire source) collapse entirely. At 586 s, they basically completely collapsed. At this point, the maximum displacement of the top node of the reticulated shell is 11.82 m. The structure loses its bearing capacity at a fire duration of 583 s. When the fire source is in the corner, as shown in Figure 19, the steel pipes on the right side of the roof begin to become destabilized at 569 s. At 570 s, the steel pipes on the right side of the roof start to extensively collapse. The reticulated shell completely collapses at 572 s. At this point, the structure is completely destroyed, with the maximum displacement of the middle roof node at 11.59 m. The fire resistance of the reticulated shell is thus 569 s. Comparing the three fire scenarios above, it was found that the maximum nodal displacement of the reticulated shell was basically the same with the different fire scenarios. The fire resistance limit of the reticulated shell was the largest at 1863 s, when the fire source was at the center at ground level. When the fire source was at the midpoint or in the corner of the longitudinal side, the reticulated shell was destroyed at the beginning of the fire. The fire resistance limit of the reticulated shell reduced by 70%. In the actual design, attention should be paid to the placement of combustibles to avoid fires starting from the close areas of the two fire scenarios. Figure 17: Structural deformation under fire location I.  
Figure 18: Structural deformation under fire location II. Figure 20 shows the displacement of selected key nodes in different fire source conditions. It can be seen that with self-weight, the midspan nodes N40 and N29 produce an initial downward displacement of 0.1 m. The nodes N23 and N25, near the longitudinal side, have an initial upward displacement of 0.032 m. The midspan nodes produce an initial downward displacement. The nodes close to the longitudinal side have an initial upward displacement. In the meantime, the structure presents a different displacement response with a different fire source power, which is caused by the rapid decrease in the elastic modulus of the steel at temperatures above 400 \({}^{\circ}\)C. During a fire in a cylindrical reticulated shell, when the maximum fire source power is 20 MW and there are different fire source positions, the limits of the bearing capacity are reached in the stationary phase or during the rising phase of the fire.