## 3 Results  
The candidate solutions that delivered the optimum cross-sectional dimensions resulting in a minimum area obtained with the harmony search algorithm converged. In the first attempt to optimise the cross-sectional dimensions, the web was constrained to be slender, and the flange was constrained to be noncompact in order to replicate the conditions of the experimental study [PERSON] et al. (2014). In this case, approximately 500 iterations were sufficient to reach convergence to an optimum solution with a minimum area of the cross-section. Figure 5 shows the convergence of the minimum area among the population of candidate solutions in the first 800 harmony search iterations. As can be seen from the figure, the solution stabilises at a cross-sectional area of 5741 mm\({}^{2}\) and stays at that level for the remaining iterations. Although this optimised value of the cross-sectional area with a slender web is approximately 63% of the area of the girder beam tested by [PERSON] et al. (2014), it yields a slightly greater bending moment capacity and an ultimate shear stress 11% greater than the experimental specimen. A comparison of the experimental dimensions of the cross-section with the optimised dimensions can be found in Table 3. An observation of the values listed in Table 3 shows that the unbraced span length stayed unchanged after the optimisation, which was expected, owing to the adverse effect of increasing this quantity on the lateral-torsional buckling capacity of the girder beam. Furthermore, the optimised cross-section has greater web slenderness (\(D/t_{w}\)) and flange slenderness (\(b_{f}/2t_{f}\)) values. From this observation, it can be inferred that the increased slenderness of the web plate and the flanges can contribute to a more economical dimensioning of the cross-section under some circumstances. The optimised cross section is also analyzed using the software package CUFSM (Constrained and Unconstrained Finite Strip Method). The first buckling mode of the optimised cross section together with the normal stress distribution can be seen in Figure 6. \begin{table}
\begin{tabular}{c c c c} \hline \hline \(t_{f}\)[mm] & \(b_{f}\)[mm] & \(t_{w}\)[mm] & \(D\)[mm] \\ \hline
5 & 100 & 1 & 200 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Lower bounds for the flange and web dimensions in the harmony search optimisation. Figure 5: Variation in the minimum cross-sectional area of the slender web in the first 800 harmony search iterations. Although the optimised cross-section with a slender web delivers good results from an economical point of view, the 1-mm-thick web of this optimal configuration is not practical. To obtain a better solution, a second attempt at optimising the cross-sectional dimensions was made by confining the slenderness value of both the web plate and the flange within the noncompact range. The harmony search process for this second case can be seen in Figure 7. The outcome of this second attempt was satisfactory. The optimised cross-sectional area was approximately 84% of that of the original configuration with the same load-carrying capacity. Table 4 lists all the cross-sectional dimensions of the original optimised specimens. It can be observed that the flange slenderness of the optimised cross-section is approximately 2.5 times that of the original specimen. Nevertheless, this flange slenderness remains in the noncompact range according to Equation (7). On the other hand, the web slenderness of the optimised cross-section is 43% of that of the original specimen. This web slenderness is also in the noncompact range according to Equation (8). The first buckling mode of the optimised cross section with noncompact web together with the normal stress distribution can be seen in Figure 8.  
Figure 6: Results of the analysis with finite strip method using the software package CUFSM for the slender web.