# Application of Sensitivity Analysis to Progressive Collapse Resistance of Planar Truss Structures
## 6 Conclusions  
This paper performed a finite-element Alternate Path analysis on two typical types of planar truss structures and demonstrated the differences in sensitivity analysis results under different statistical objects. The selection of statistical objects for the sensitivity analysis of planar truss structures was investigated. The significance of the sensitivity analysis was clarified by the progressive collapse analysis of critical elements. Based on the analysis and comparative verification of examples, the following conclusions are drawn:  
1. In the same structure, the results of traditional sensitivity analysis are different under various statistical objects. There are significant discrepancies in the distribution of important elements, as well as the magnitude and the variation trend of element importance coefficients. When the statistical objects are the lower chords or all elements, the most important element in the test truss is the upper chord UC2. Still, when the statistical objects are the upper chords, the most important element is web member W5. Similarly, when the statistical objects of the steel roof truss are individually the lower and upper chords, the element with the largest importance coefficient is upper chord TC4 and web member WM2, respectively.
2. The catenary mechanism in the lower chords is critical to the progressive collapse resistance of planar truss structures. Accordingly, the lower chords should be selected as the statistical objects of sensitivity analysis for planar truss structures. The introduction of the anti-progressive collapse mechanism into the sensitivity analysis achieved good research results. The sensitivity analysis of the lower chords as the  
Figure 19: Structural deformation diagram under two working conditions: (**a**) TC4 failure condition, (**b**) WM2 failure condition.  
Figure 20: Sensitive indices after TC4 failure.  
statistical objects is essentially consistent with the element importance evaluated by the energy-based judgment method. The Pearson correlation coefficient and the corresponding scatter diagram of the two methods show a significant positive correlation. The progressive collapse analysis of important elements also fully illustrates the rationality of the sensitivity analysis of planar truss structures with the lower chords as the statistical objects. Meanwhile, it is more efficient to calculate only the stress change of the lower chords than the traditional sensitivity analysis that counts all the remaining elements.
* The sensitivity analysis results of the two types of trusses with the lower chords as the statistical objects show that the upper chord in the midspan is the critical element of the structure. The sensitivity analysis can identify the redistribution paths of the remaining structural internal force after the initial failure of the critical element. Moreover, the unbalanced load at the local failure will gradually dissipate along the redistribution paths. Therefore, the structural progressive collapse resistance performance can be improved by strengthening the weak links in the redistribution paths.  
Conceptualization, methodology, and review, C.K.; numerical models, validation, and original draft preparation, Q.L. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding, and the source of APC is self-raised.  
Not applicable.  
All the analysis data in this paper are from numerical simulation, and I guarantee the authenticity and validity of the data.  
The authors declare no conflict of interest.