# Use of the Gene-Expression Programming Equation and FEM for the High-Strength CFST Columns
## 2 A Brief Background of Gene Expression Programming (GEP) and Finite Element Analysis (FEA)
### Brief Introduction  
The accuracy of prediction from FEA is significantly impacted by input parameters, specifically selection of appropriate concrete model [4]. Moreover, there could be slip between two connected materials with different properties although a fully shear connection has to be assumed and simulated. In order to demonstrate the superior accuracy of predictions based on the GEP equation (Equation (1)) [10], 32 CFST columns were collected from recent literature and numerically modelled using FEA. Figure 1 shows a summary of the process of this modelling. As is evident, first of all, the data were collected for modelling and then, in order to achieve trustworthy results, convergence and mesh studies were performed for each column separately and after that the models were analyzed using ABAQUS [48].  
\[\mathrm{P_{exp}}=(\mathrm{\surd}_{0}\times(2\times\mathrm{d}_{1})+(\mathrm{d} _{4}\times(\mathrm{\surd}_{1}-(6.219-\mathrm{d}_{3})))+[(8.078\times\mathrm{d}_ {4})+(0.626\times\mathrm{d}_{2})]/\mathrm{tanh}(-2.831) \tag{1}\]  
where: \(\mathrm{d}(0)=\mathrm{f_{C}(MPa)}\), \(\mathrm{d}(1)=\mathrm{D}\) (mm), \(\mathrm{d}(2)=\mathrm{L}\) (mm), \(\mathrm{d}(3)=\mathrm{t}\) (mm),\(\mathrm{d}(4)=\mathrm{f_{y}}\) (MPa).  
Even though tremendous effort was previously made to model concrete-filled steel tubular column using FEA, this methodology may not be helpful in specific cases, particularly while assuming quick development and usage of thin-walled steel tube or the high-strength concrete [4; 49; 50]. FEA is performed according to the circular CFST (CCFST) specimens from the numbers of studies [51; 52; 53; 54; 55; 56] which carry different geometries, material properties, boundary and support conditions, and loading functions. However, for the AI investigation, all of them were considered to be in the range of selected parameters. For the ultimate strength of the CFST columns, 1242.2 kN to 9187 kN was considered and, 36.2 MPa  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Technique** & **Input** & **Output** & **Description** & **Reference** \\ \hline GEP & D, t, f\({}_{y}\), f\({}_{c}\), L, t\({}_{x}\)f\({}_{y}\), E\({}_{t}\) & P & 92 FRP-CFST columns & [39] \\ ANN & D, t, f\({}_{y}\), f\({}_{c}\), L & P & 633 CCFST columns & [40] \\ GEP & D, t, f\({}_{y}\), f\({}_{c}\), L & P & 314 CCFST columns & [21] \\ ANN & D, t, f\({}_{y}\), f\({}_{c}\), L & P & 272 CCFST columns & [33] \\ ANN & D, t, f\({}_{y}\), f\({}_{c}\), L & P & 205 CFST columns & [42] \\ SVM & B, t, f\({}_{y}\), f\({}_{c}\), L, E\({}_{c}\), E\({}_{s}\) & P & 180 SCFST columns & [34] \\ ANFIS-GA; ANFIS-PSO & D, t, t\({}_{p}\), f\({}_{y}\), f\({}_{c}\), L & P & 57 steel Y-section columns & [35] \\ ANN & f\({}_{c}\), L, D, t\({}_{p}\), E\({}_{t}\), E\({}_{t}\) & c\({}_{cc}\) & P & 465 FRP-CCFST columns & [36] \\ GP & f\({}_{c}\), L, D, t\({}_{p}\), E\({}_{t}\) & P & 832 FRP-CCFST columns & [37] \\ \hline \hline \end{tabular}  
* D:diameter; t thickness; f\({}_{y}\): yield stress of steel tube; f\({}_{c}\): concrete compressive strength; L: length; t\({}_{t}\): thickness of ply multiplied by FRP layers; f\({}_{t}\): tensile strength of FRP; E\({}_{c}\): modulus of elasticity for FRP; B: width; E\({}_{c}\): concrete modulus of elasticity; E\({}_{s}\): steel modulus of elasticity; f\({}_{p}\): thickness of the plate f\({}_{t\mathrm{t}_{t}}\): ultimate strain of FRP sheet; \({}_{cc}\): strain of confined column; GEP: gene expression programming; ANN: artificial neural network; SVM: support vector machine; ANFIS: adaptive neuro-fuzzy inference system; GA: genetic algorithm; PSO: particle swarm optimization.  
\end{table}
Table 1: Review studies for application of artificial intelligence (AI) for the composite columns.  
to 193.3 MPa was chosen for the concrete compressive strength. For the columns' length and diameter, 200 mm to 756 mm and 114.3 mm to 219.1 mm were considered respectively. In addition, the range of 2.5 mm to 10 mm was selected for the thickness, and the yield stress of steel tube is considered as 227 MPa to 428 MPa.