## 5 Stressing State Analysis of CFST Arch Models  
### Investigation into Parameter SED for Modeling Structural Stressing State  
Pursuant to the method of modeling the structural stressing state, the stressing state modes of experimental arch models were expressed by the normalized SED values to characterize their working behavior. Based on the strain/stress data interpolated by NSF method, SED values of arch-A or arch-B were calculated by Equations (3) and (4) for the expression of stressing state mode. The corresponding characteristic parameter \(E_{j,\mathrm{norm}}\) under load \(F_{j}\) was used to plot the _E-F_ curve in order to investigate the developing tendency and sensitivity of the arch's stressing state mode. Using the M-K criterion, characteristic loads in the curves were detected, namely \(P_{\mathrm{A}}\) (140 kN), \(Q_{\mathrm{A}}\) (180 kN) for arch-A and loads \(P_{\mathrm{B}}\) (66 kN), \(Q_{\mathrm{B}}\) (85 kN) for arch-B, successively. As depicted in Figure 7, the _E-F_ curve of arch-A is plotted for example. It is shown that the curve grew rather slowly as long as the acting load remained below 140 kN (\(P_{\mathrm{A}}\)), indicating that the arch model was basically in the linear-elastic working state. From 140 kN to 180 kN (loads \(P_{\mathrm{A}}\) to \(Q_{\mathrm{A}}\)), there was a slight growth trend of the curve, implying that the CFST arch was in the elastic-plastic working state and local plastic development existed. As the load exceeded 180 kN (\(Q_{\mathrm{A}}\)), the curve thoroughly deviated from this loading path and began to undergo a fast development with rapid growth/mutation. At this stage, the arch model entered the unstable stressing state until the ultimate load (206 kN). The _E-F_ curve of arch-B had similar developing features, so it was not discussed here. Figure 6: The stress-strain curve of steel. Figure 7: The _E-F_ curve of arch-A and characteristic loads distinguished by Mann-Kendall (M-K) criterion. Two common stressing state characteristics could be summarized from the above: (1) Characteristic load \(P\) is the load where the arch's stressing state transitioned from elasticity to elastoplasticity. Although some parts in the arch model may have interred plastic states during the stages, the whole arch structure maintained a stable stressing state until characteristic load \(Q\). In other words, the arch's stressing state maintained quantitative change instead of qualitative change during the stages. (2) Characteristic load \(Q\) is the load where the arch's stressing state qualitatively changed/leapt to the other state, which was different from the previous state. The arch model maintained the stable stressing state modes before load \(Q\) and then entered the gradually developing failure states until the ultimate load. It is an essential and general working behavior feature, which structures certainly present during their loading process. Hence, the load corresponding to characteristic load \(Q\) can be defined as the failure load of the structure. The present failure at the ultimate load is a state in which structures have already been destroyed and have lost stability. To ensure sufficient safety and the normal applicability of structures, safety factors were used to multiply the ultimate load so as to be the design value for structural design. This traditional uncertain value is commonly conservative, and material is often wasted. Meanwhile, the updated failure load was revealed by the inherent mutation of the structural stressing state characteristics instead of any assumption and was in accordance with the natural law regarding the quantitative change to qualitative change of a system. That is to say, the load to structural stressing state mutation is determinate while the structural ultimate load is indeterminate. After the ultimate load was reached, the structure created a great potential safety hazard and was unsuitable for load bearing. A relatively rational safety reserve existed from the failure load to the ultimate load.