# 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)
### The Results of FE Simulation  
Some of the CFST samples which were modelled by the finite element method (FEM) are indicated in Figure 2a,b. In all of the cases, the column was subjected to axial loading in the center of the column along the \(Y\) axis. In this study, different columns with various L/D and D/t were modelled and their ultimate bearing capacity was obtained accordingly. The results were compared to the corresponding experimental results and the outcome is summarized in Table 2. The P\({}_{\text{exp}}\) shows the experimental load-bearing capacity of the circular CFST columns while the P\({}_{\text{FE}}\) indicates the result of the FE analysis for the ultimate bearing capacity of the column. The last column of Table 2 is a comparison between the experimental results and the finite element results which is reported as an error in percentage. In some cases, such as model Nos. 4, 5, 10-12, 14-18, 20-24, and 32, the bearing capacity predicted by FE was less than the measured experimental value of the bearing capacity. As is evident from Table 2, the ultimate bearing  
Figure 2: **(a)** FE modelling of Model No. 1 with PFE 3171 kN; Model No. 2 with PFE 2640 kN; **(b)** FE modelling of Model No. 3 with PFE 7919 kN; Model No. 4 with PFE 7928 kN. Figure 4: Axial strength versus time for model numbers 10–12 and 14. Figure 5: Axial strength versus time for model numbers 15–20. Figure 6: Axial strength versus time for model numbers 21–25. Figure 7: Axial strength versus time for model numbers 26–28. **4. Results, Comparison, and Discussion of the GEP Equation Outcomes with the FEA Results**  
In this section, the data of those 32 samples were input into Equation (1) and the results were compared with those obtained from the FEA and the outcome summarized in Table 3. The last two columns in Table 3 present the error between the bearing capacity obtained from the FEA and the GEP equation with the experimental results. As is evident, in most of the cases, the ultimate bearing capacity achieved from the GEP equation is closer to the real data obtained from the experimental test. In five samples (3, 9, 23, 27, 30), FE results were manifest a better prediction of the maximum bearing capacity which could be due to specific conditions of the composite columns such as lower L/D ratio, slenderness rate, and the strength of the materials. Therefore, in these special cases, the prediction from the GEP equation may not be good enough due to wide ranges of input datasets. Nevertheless, more than 85% of the predictions by Equation (1) showed very good agreement with the experimental results. This proves the feasibility of this equation and the GEP approach for estimation of the maximum bearing capacity of such composite columns. If the maximum and minimum strength of the CFST columns resulting from the experimental work and their corresponding values from FEA and GEP are taken into consideration, it can be seen that the column sample No. 5 with the maximum experimental bearing capacity of 9187 kN has the closest predicted value of 8929.05 kN from the GEP equation. On the other hand, the column No. 21 with the minimum experimental bearing capacity of 1242.2 kN also has the most accurate value of 1242.0 kN from its corresponding GEP equation result. Therefore, the GEP-based equation yields very good results compared to those from the FEA. Furthermore, according to the Table 3, model numbers 3, 9, 23, 27, and 30 presented a closer value of ultimate bearing capacity to the corresponding experimental outcome in the FEA instead of AI analysis using the GEP equation. In fact, this is because these models are short columns, stub columns, or composite column with a low or a very high strength materials, or they are the columns subjected to a kind of impact loading; Therefore, the prediction by the GEP equation led to less accuracy compared to the FEA. Nevertheless, as can be clearly inferred, the GEP equation results for 27 models out of 32 models indicated  
Figure 8: Axial strength versus time for model numbers 13, 29–32.