# Stressing State Analysis of SRC Column with Modeling Test and Finite Element Model Data
## 5 Mutation Stressing State Characteristic Pair
### Partial Stressing State Analysis of the Finite Element Model  
The selection of the elements used for stressing state modeling analysis for each part of the SRC column has been highlighted in Figure 2. Taking SRC_1_100 as an example, based on the element strain energy (\(ESE\)) data of the concrete part of the SRC column, three stressing state sub-modes with characteristic parameters have been established, as shown in Figure 7. The sub-modes of concrete stressing states are established in Figure 7a-c and are based on the concrete elemental strain energy \(ESE\), the first-order elemental strain energy \(\Delta ESE\), and the second-order elemental strain energy \(\Delta^{2}ESE\), respectively. Equations (16) and (17) shows the first- and second-order elemental strain energy expressions:  
\[\Delta ESE_{j}=ESE_{j}-ESE_{j-1} \tag{16}\]  
\[\Delta^{2}ESE_{j}=ESE_{j}-2 ESE_{j-1}+ESE_{j-2} \tag{17}\]  
Figure 6: \(IE_{\text{norm}}\)-displacement figure and axial force-Displacement figure: **(a)**\(IE_{\text{norm}}\)-Displacement of SRC_1_100; **(b)** Axial force-Displacement SRC_1_100. The expressions of the numerical modes established based on \(ESE\), \(DESE\), \(D2 ESE\) are shown in Equations (18)-(20), and the stressing state sub-mode of vertical reinforcement and spiral reinforcement is similar to them:  
\[\textbf{E}_{j}^{\text{C0}}=\left[ESE_{1}\dots ESE_{10}\right]_{j} \tag{18}\]  
\[\textbf{E}_{j}^{\text{C1}}=\left[\Delta ESE_{1}\dots\Delta ESE_{10}\right]_{j} \tag{19}\]  
\[\textbf{E}_{j}^{\text{C2}}=\left[\Delta^{2}ESE_{1}\dots\Delta^{2}ESE_{10} \right]_{j} \tag{20}\]  
The evolution of the concrete stressing state sub-modes is shown in Figure 7a-c. From the figure, it can be seen that all three concrete stressing state sub-modes show the same mutation near the characteristic point P.  
The stressing state sub-mode obtained based on \(ESE\), \(\Delta ESE\) and \(\Delta^{2}ESE\) has very obvious mutation near the characteristic point P. Establishing the characteristic parameters corresponding to the stressing state sub-mode can also characterize the evolution of the stressing state of the SRC column. Based on the \(ESE\), \(\Delta ESE\), and \(\Delta^{2}ESE\), the characteristic parameters \(CP0\), \(CP1\), and \(CP2\) corresponding to the stressing state sub-modes can be constructed, and their expressions are shown in Equation (21):  
\[CP0_{j}=\left|\frac{1}{n}\sum_{k=1}^{n}ESE_{j,k}\right|\text{, }CP1_{j}= \left|\frac{1}{n}\sum_{k=1}^{n}\Delta ESE_{j,k}\right|\text{, }CP2_{j}= \left|\frac{1}{n}\sum_{k=1}^{n}\Delta^{2}ESE_{j,k}\right| \tag{21}\]  
Figure 7d-f shows the evolution law of the three characteristic parameters. The positions of the characteristic point P and the characteristic point Q have been marked in the figure. Among them, the change in the characteristic parameter \(CP0\) is relatively soft. The  
Figure 7: Concrete stressing state sub-mode revealed by \(ESE\), \(\Delta ESE\) and \(\Delta^{2}ESE\): (**a**) Model of concrete; (**b**) Mode 1 of concrete; (**c**) Mode 2 of concrete; (**d**) \(CP0\) of concrete; (**e**) \(CP1\) of concrete; (**f**) \(CP2\) of concrete. characteristic parameter _CP1_ begins to show a linear change with the loading of the displacement load before the characteristic point P. After the characteristic point P, because the stressing state of the concrete begins to enter an unstable state, the characteristic parameter _CP1_ begins to show a kind of unstable wave change. This feature is more apparent through the characteristic parameter _CP2_ than _CP1_. The evolution of the characteristic parameter _CP2_ is almost a horizontal straight line at the beginning, and after entering the characteristic point P it becomes a sharply fluctuating zigzag-shaped broken line. It can be seen that for the concrete of SRC_1_100, the three characteristic parameters and the three stressing state sub-modes can well characterize the evolution law of the concrete stressing state.