## 5 Stressing State Analysis of CFST Arch Models
### Change Characteristics Reflected by Strain/Stress Fields of Arch Models  
In the light of experimental strain data, performance features of two arch models around the updated failure loads and their respective working behavior characteristics under loading can be embodied in some extent. Unfortunately, these limited data could only reflect the distribution and the development of strains of each measured point. The NSF method was applied for the strains at unmeasured points on the surface or the inside of cross-sections. Constructing strain/stress fields of cross-sections can provide an intuitive description of the structural stressing state during the loading process, as well as a clear observation of change characteristics of arch models around the failure loads. It can be seen from Figure 8 that some cross-sections of arch models had small strain values throughout the loaded process, while some others had large variation ranges and had a well-controlled effect on the arch models. Thus, the change characteristics of these key sections were the focus of attention, namely sections 7, 9-11 of arch-A, and sections 2, 7, 10, 12, and 13 of arch-B. To observe the changes around characteristic load \(P\), section 11 of arch-A was taken as an example. As shown in Figure 9, the strain fields were basically symmetrically distributed along the vertical. Only the densities and values of isopleth curves had slight changes before and after characteristic load \(P\) (140 kN). The strains of the whole cross-section were almost compressive, indicating that the section was mainly subjected to compression. Similar features were observed on other sections of arch-A and arch-B, and quantitative changes existed instead of qualitative changes on the shapes of isopleth and the magnitude of strain values around loads \(P\). Figure 8: The distribution curves of experimental strains: (**a**) \(|\varepsilon_{i}\)/\(\varepsilon_{y}\)-\(F_{j}\) curve of two arch models; (**b**) the distribution mode curve of \(|\varepsilon_{i}|_{\text{max}}\). (Note: \(m\)-\(i\) denotes \(\varepsilon_{i}\) of \(m\)-th cross-section, \(i=1,2,3,4\)). To delineate the variations around characteristic point \(Q\), section 11 of arch-A was selected. As depicted in Figure 10a, from 170 kN to 180 kN, the whole cross-section was fundamentally in the compressive state with very little tensile strains. Neither the shapes nor the values of isopleth curves had a notable distinction. From 180 kN to 190 kN, the strains of the section were still mainly compressive, even though tensile strains had obvious increments and occupied more area of the section. Especially, the compressive strain values had a dramatic growth, with a range changing from \(-\)2930-0 \(\mu\)\(\epsilon\) at 180 kN to \(-\)12,200-0 \(\mu\)\(\epsilon\) at 190 kN. During this stage, the oversized strain values around the lower part of the section demonstrated that the section/structure underwent an unstable stressing state with potential risk after 180 kN. Therefore, the failure load 180 kN was a watershed for the arch, implying that the arch model was considered unsuitable for resisting load from then on. Differing from arch-A, the strain values of section 13 of arch-B had a relatively small developing range due to the effect of great horizontal displacements, as shown in Figure 10b. It is seen that the area of compressive region occupied almost the whole section. With the action of spatial loads, the distribution shape of isopleth curves was asymmetric. From 80 kN to 85 kN, strains at the lower-left corner of the section had visible changes in values. When the load reached 90 kN, the changes of strains were more obvious in values and isopleth curve shapes. Potential mechanical instability caused by outer displacements limited the development of strains. Hence, the maximum compressive strain was \(-\)2570 \(\mu\)\(\epsilon\) at 90 kN, remaining subsequent bearing capacity if the development of outer displacements can be restricted.