## 5 Stressing State Analysis of CFST Arch Models
### Investigation into Measured Strains of Two Arch Models  
Based on the NSF method, the hidden value of structural response can be exploited by SEDs, and deep mining and analysis can be made on structural stressing state modes. However, for arches under different loading conditions, their working behaviors will have distinct performance features around the failure load (characteristic load \(Q\)). Since the measured strains of arches are the most direct reflection of their mechanical behaviors, these strains were initially selected to concretely observe their different features.  
As shown in Figure 8a, the measured strain's absolute value (\(|\varepsilon_{i}|\)), which reached the yield point (\(\varepsilon_{y}\)), was chosen. The ratio of the strain to the yield strain (\(|\varepsilon_{i}|/\varepsilon_{y}\)) was taken as a parameter to reflect the development/magnitude level of strains. The yield strains of arch-A (\(\varepsilon_{yA}\)) and arch-B (\(\varepsilon_{yB}\)) were \(1844\mu\varepsilon\) and \(1563\mu\varepsilon\), respectively. It should be noted that the load \(F_{j}\) for arch-B here represented vertical load values, and the horizontal load was 10% of corresponding vertical loads. As seen in the figure, no yield deformations appeared before load \(P\), and relatively small yield deformations appeared from loads \(P\) to \(Q\). Compared with small ratios of \(|\varepsilon_{i}|/\varepsilon_{y}\) for arch-B, the strains of arch-A developed with much greater extent, especially after the failure load. Obviously, materials of arch-A were utilized to a higher degree. This is because that materials of arch-B, the failure of arch model was mainly controlled by great horizontal displacements with the action of out-plane loads, rather than material damage. To observe the distribution of strains on each cross-section, the distribution mode of the sectional maximum strain (\(|\varepsilon_{i}|_{\text{max}}\), \(i\) = 1, 2, 3, 4) was plotted. As shown in Figure 8b, the \(|\varepsilon_{i}|_{\text{max}}\) of arch-A or arch-B maintained a slight and stable increase before the failure loads. From then on, strains of some sections showed great mutation/increment. Although the arches were loaded symmetrically, the distribution modes of \(|\varepsilon_{i}|_{\text{max}}\) were asymmetric, especially under high-level loading. The primary cause of this phenomenon was the initial geometrical imperfections of arch models.  
Generally, from the perspective of experimental strain data, the arch will have a higher supporting capacity under in-plane loads than that under spatial loads and strains will have more obvious mutation characteristics around the failure load. Since the out-plane stiffness of the arch is smaller than the in-plane one, the arch model will have larger displacement under small horizontal loads, even if the materials still have subsequent bearing capacity. So, it is important to strengthen the out-plane stiffness of arch bridges, for example, by adding enough transverse supporting in practical engineering. Because the area around the arch feet is vulnerable to damage due to the impact of initial imperfection, it also should be given attention during structural design.