# Application of Sensitivity Analysis to Progressive Collapse Resistance of Planar Truss Structures
## 4 Selection of Statistical Objects Based on Anti-Progressive Collapse Mechanism  
The anti-progressive collapse mechanism is the internal mechanism of the structure to regain stability and equilibrium after encountering local damage, which is also the redistribution of the structural internal force. Meanwhile, [PERSON] indicated [18] that  
Figure 10: Importance coefficient: (**a**) Test truss, (**b**) steel roof truss.  
the progressive collapse was related to the structural system, and different structural systems exhibited different anti-progressive collapse mechanisms. [PERSON] [19] has given three local redistribution mechanisms of internal force for truss structures. On this basis, [PERSON] [20] combined the experimental and numerical simulation results to identify the global redistribution mode of internal force of planar truss structures, i.e., the two main anti-progressive collapse mechanisms of the arch effect and catenary action.  
The substructures on both sides of the local damage are converged at the lower chord joint right below the damaged element after the initial failure of the upper chord. However, the rotational stiffness of this joint is significantly weakened compared to the complete structure, causing the original truss with continuous bending performance to form a \"hinge\" at this joint. At this time, the remaining structure is hinged at this joint and relies on the catenary action developed along the lower chords to provide load-bearing (Figure 11).  
The failure of the lower chord is similar to that of the upper chord. A hinge is developed directly above the damaged element. At this time, the remaining structure relies on the arch effect developed in the upper chords to provide a vertical bearing (Figure 12).  
After the initial failure of the web member, the substructures will be joined by two connections, the upper chord above the damaged element and the lower chord below the damaged element, respectively. Both the arch effect developed in the upper chords and the catenary action in the lower chords exist in the structure (Figure 13).  
However, according to previous experiments, numerical simulations, or theoretical studies [21; 22], when the arch mechanism works, the load transferred to the support makes the elements near the support buckle due to a large compressive force, resulting in the interruption of the arch mechanism. An accident investigation related to such structures also found [23] that, due to the lack of sufficient support, out-of-plane constraints, and the large slenderness ratio of rods, the bearing capacity in the upper chords can be very  
Figure 11: Catenary mechanism after the failure of the upper chord.  
Figure 12: Arch mechanism after the failure of the lower chord.  
Figure 13: Two mechanisms after the failure of the web member.  
limited, which will fail the arch mechanism. In Section 5.2, the progressive collapse analysis of the test truss after the web member W5 failed also found that the upper chord UC2, which develops the arch effect under compression, buckled and caused the arch mechanism to be interrupted. Meanwhile, the tension in LC3 increases exponentially. It is further confirmed that of the two mechanisms, the arch mechanism is prone to failure. The catenary mechanism developed in the lower chords plays a key role in the global redistribution of the remaining structural internal force. Therefore, combined with the above analysis, the planar truss structure should select the lower chords as the statistical objects for sensitivity analysis.