# Stressing State Analysis of CFST Arch Supports in Deep Roadway Based on NSF Method
## 5 Stressing State Analysis of the CFST Arch Support-A
### Change Characteristics Reflected by Strain and Stress Fields  
Certainly, the analysis based on the measured strain data could really embody the performance features of support-A around the characteristic loads to some extent. However, these limited data could only reflect the distribution and the development of strains at each measured points, that is, the local structural working features. Hence, the NSF method is applied to the mid-span section of support-A, so as to acquire the strains and stress data at unmeasured points on the steel tube and core concrete. Through constructing the strain and stress fields of the cross section, the change characteristics of structural stressing state for the support could be described more intuitively, so that more detailed performance and mechanism could be researched. According to the Figures 6 and 7 above, four stressing state stages of the supports are divided by the three characteristic loads, respectively, the elastic, elastic-plastic, plastic and failure one, hence the strain or stress fields of steel tube and core concrete around the characteristic loads are plotted to investigate the changing characteristics of the cross section. As illustrated in Figure 8a, the strains of the whole cross section of steel tube are compressive, indicating that under the given load case the mid-span section is subjected to compression all the time. At 400 kN (load \(L\)), the whole cross section is unyielded, hence support-A is really in elastic  
Figure 7: The changing characteristics of strain-based stressing state modes: (**a**) The trend changing characteristics of strain-based stressing state modes during the whole loading process; (**b**) the trend changing characteristics of strain-based stressing state modes between 0 kN and 800 kN; (**c**) the distribution pattern changing characteristics of strain-based stressing state modes; (**d**) the increment changing characteristics of point 4 at level of 100 kN; (**e**) the increment changing characteristics of point 4 at level of 20 kN. stage. While thereafter the part of the cross section exceeds yield strain at once, and the top is still in unyielded condition until load \(Q\). Besides, from 400 kN to 600 kN, the middle and bottom of steel tube increase one or two color gradations, then more than three color gradations at load \(Q\). At the moment, the total cross section reaches yield, indicating that the stressing state of the steel tube really mutates to plastic stage completely. Similarly, the mutation characteristics of the core concrete could also be observed in increments of color gradations shown in Figure 8b,c. Besides, in the elastic, elastic- plastic and plastic stressing state stages, the stains or stress on the center and top of the core concrete always keep smaller than the edge of middle and lower parts, which could be implied that the development of strains and stress for the support both present the trend from the areas around points 4 and 7 to the center, then to the top and bottom. In order to observe the changing characteristics around the characteristic load \(R\), the strain and stress fields at 780 kN, 800 kN (characteristic load \(R\)), 820 kN and 840 kN are plotted in Figure 9. It could be seen from Figure 9a,b that before load \(R\), the strains of steel tube and core concrete only consist three color gradations, and with the growth of load, the strain fields display the enlargement of soft orange gradation (\(-5.4\)--\(7.1\)) the and the reduction of red one (\(-2.0\)-\(3.7\)), indicating that the sectional plastic development maintain relative stable. Therefore, the changing characteristics of strain fields at this stage obviously reflects the accumulation of quantity instead of qualitative mutations. Once it surpasses load \(R\), the strains of the whole cross section occurred different degrees of growth and the number of sectional color gradations increases to eight, in particular for the outstanding increase of sectional middle and lower part.