## 2 Finite Element (FE) Modelling
### Result and Discussion of the FE Analysis  
The numerical model was successfully able to simulate the actual conditions with minimum error. Hence, in this section, the verified FE method is utilised for a parametric study to investigate various uprights with different heights and thicknesses as well as various reinforcement spacings under axial loading. In general, eight reinforcement spacings including no-reinforcement, 50 mm, 100 mm, 150 mm, 200 mm, 250 mm, 300 mm, 350 mm and 400 mm were considered for the parametric study. The numerical evaluation was conducted on four various thicknesses of 1.6 mm, 2.0 mm, 2.5 mm and 3.0 mm of profiles as well as four different upright lengths, including 1800 mm, 2400 mm, 3000 mm and 3600 mm. All of the results were obtained from the FE analysis. Generally, four lengths (1800 mm, 2400 mm, 3000 mm and 3600 mm) with different reinforcement spacings (50 mm, 100 mm, 150 mm, 200 mm, 250 mm, 300 mm, 350 mm and 400 mm) and web thicknesses (1.6 mm, 2.0 mm, 2.5 mm and 3.0 mm) were considered for modelling of the upright frames. Figure 12a-d illustrate the axial behaviour of 3600 mm length upright frames with 1.6 mm, 2.0 mm, 2.5 mm and 3.0 mm thickness, respectively. According to this figure, using shorter reinforcement spacing increased the ultimate load capacity among all of the models, especially in the model with 1.6 mm thickness. It can be also concluded that increasing thickness could control the mode of distortional buckling. Figure 13a-d depict the FE results of the 3000 mm models based on the normalised load-displacement diagram. In these models, upright frames are more strengthened as the reinforcement spacing decreases. The models with 1.6 mm thickness represented the best behaviour. The models with 50 mm reinforcement spacing achieved the maximum ultimate capacity in all cross-section thicknesses. Figure 14a-d represent the simulation diagrams of models with 2400 mm length. It is obvious that using 50 mm spacing for reinforcement is the optimum choice to improve the compressive capacity for 2400 mm uprights. By comparing the thicknesses, the models with 2.5 mm thickness  
In general, in all four lengths, 50 mm spacing showed the highest increment in terms of ultimate load capacity compared to other spacing values. Figure 16a-d consist of models categorised according to 50 mm reinforcement spacing. According to this figure, models with 1800 mm length and 50 mm spacing indicate the highest capacity among other models. According to the FE results, uprights followed almost the same trend of increasing the ultimate load capacities with reinforcement spacing. However, the results did not indicate the same pattern for different thicknesses and lengths. Figures 17 and 18 represent the normalised ultimate load capacities of each model based on the length and thickness. Further, 2.5 mm thickness is the optimum value for uprights with 1800 mm and 2400 mm lengths. However, 3000 mm and 3600 mm models revealed a different pattern, where models with 1.6 mm thickness showed the highest normalised ultimate capacities in comparison with other models and thicknesses, as indicated in Figure 15.  
Figure 12: Normalised load-displacement diagrams of the FE results for: (a) 3600L-1.6T, (b) 3600L-2.0T, (c) 3600L-2.5T, and (d) 3600L-3.0T models. Ultimate normalised values are given in Tables 1-4 where each table reveals the ultimate values in order of thickness and reinforcement spacing. Table 1 shows the FE results of the models with 3600 mm length, in which 50 mm spacing is the optimum value for reinforcing pitch along the upright length. According to this table, 50 mm spacing increased the ultimate compressive capacity by 9.1%, 9.55%, 19.2% and 25.94% for 1.6 mm, 2.0 mm, 2.5 mm and 3.0 mm thicknesses, respectively. Table 2 demonstrates the ultimate normalised compressive capacities for 3000 mm models, which increased by 11.24%, 12.21%, 19.8%,and 27.64% for 1.6 mm, 2.0 mm, 2.5 mm and 3.0 mm thicknesses, respectively.