# Stressing State Analysis of SRC Column with Modeling Test and Finite Element Model Data
## 2 Modeling Test/Simulation Data
### Correlation Modeling Method  
The correlation modeling method proposed in this paper for the stressing state analysis of SRC columns treats the studied structure or member as a whole and characterizes the evolution of the stressing state of the structure or member through the interaction between the modeled elements. The characteristic pairs established based on the correlation method are called correlation characteristic pairs. The correlation modeling analysis method is introduced below as an example of modeling SRC column test data.  
Step 1: Select 4 measurement points on the surface of concrete or spiral reinforcement to output the strain data of the whole process of loading, integrate it against the load and take the absolute value. The matrix shown as Equation (8) is obtained:  
\[\mathbf{S}_{j}^{\text{Step1}}=\left[\left|\int_{0}^{F}\varepsilon_{1}\text{d }F\right|\cdots\left|\int_{0}^{F}\varepsilon_{4}\text{d}F\right|\right]_{j}^{4} \tag{8}\]  
where \(\varepsilon\) denotes the strain in concrete or spiral reinforcement, the subscript \(j\) denotes the ordinal number of load steps, \(F\) denotes the load step in the loading process, and the number 4 in the superscript denotes the number of elements in the vector. The symbols in the following formula have the same meaning. Then the elements in the Equation (8) vector are taken two by two to obtain the vector shown in Equation (9):  
\[\mathbf{S}_{j}^{\text{Difference1}}=\left[\left|\int_{0}^{F}\varepsilon_{1} \text{d}F\right|-\left|\int_{0}^{F}\varepsilon_{2}\text{d}F\right|\cdots\left| \int_{0}^{F}\varepsilon_{3}\text{d}F\right|-\left|\int_{0}^{F}\varepsilon_{4} \text{d}F\right|\right]_{j}^{6} \tag{9}\]  
\[\mathbf{S}_{j}^{\text{Difference1}}=\left[D_{1-2}\ldots D_{3-4}\right]_{j}^{ 6}=\left[D_{a}\ldots D_{f}\right]_{j}^{6} \tag{10}\]  
The vector Equation (9) is simplified to obtain the vector shown in Equation (10), and the superscript 6 indicates the number of elements in the vector.  
Step 2: Integrate the elements in the vector Equation (10), take the absolute value and then normalize to get the vector shown in Equation (11):  
\[\mathbf{R}_{j,\text{norm}}^{\text{Step2}}=\left[\left|\int_{0}^{F}D_{a}\text{ d}F\right|\ldots\left|\int_{0}^{F}D_{f}\text{d}F\right|\right]_{j,\text{norm}}^{6} \tag{11}\]  
\[\mathbf{R}_{j}^{\text{sub}}=\left[\left(\left|\int_{0}^{F}D_{a}\text{d}F \right|_{\text{norm}}-\left|\int_{0}^{F}D_{b}\text{d}F\right|_{\text{norm}} \right)\ldots\left(\left|\int_{0}^{F}D_{a}\text{d}F\right|_{\text{norm}}- \left|\int_{0}^{F}D_{b}\text{d}F\right|_{\text{norm}}\right)\right]_{j}^{15} \tag{12}\]  
\[\mathbf{R}_{j}^{\text{sub}}=\left[E_{ab}\ldots E_{ef}\right]_{j}^{15} \tag{13}\]  
The vector shown in Equation (12) is obtained by taking the difference in the elements in the vector of Equation (11) two by two. Superscript 15 indicates the number of elements in the vector. The expression of Equation (12) is simplified as shown in Equation (13). Integrate the elements in Equation (13), take the absolute values, and then sum up and normalize to obtain the correlation characteristic parameter shown in Equation (14):  
\[R_{j,\text{norm}}^{\text{sub}}=\left(\sum_{N=1}^{15}\left|\int_{0}^{F}E_{ab} \text{d}F\right|\right)_{j,\text{norm}} \tag{14}\]  
The correlation modeling method for the output data of the SRC column finite element model is similar to the above steps and will not be repeated here.