## 3 Results
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & \(b_{f}\)[mm] & \(t_{f}\)[mm] & \(D\)[mm] & \(t_{w}\)[mm] & \(a\)[mm] & \(M_{cr}\)[Nmm] & \(\tau_{u}\)[MPa] & \(A\)[mm\({}^{2}\)] \\ \hline Experimental value & 250 & 15 & 800 & 2 & 750 & \(1.1834\cdot 10^{11}\) & 64.017 & 9100 \\ Optimised value & 265.4 & 8.59 & 1182 & 1 & 750 & \(1.1835\cdot 10^{11}\) & 70.98 & 5741 \\ Difference [\%] & 6.16 & \(-\)43 & 48 & \(-\)50 & 0 & 0.008 & 11 & \(-\)37 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Geometric and mechanical properties of the optimised cross-section with slender web. Figure 7: Variation in the minimum cross-sectional area with noncompact web in the first 2000 harmony search iterations. Figure 9 shows a finite element model with the Huber-von Mises-Hencky stress distribution of the optimised girder with the noncompact web. It can be observed that, under the concentrated load at the mid-span, the local buckling of the web plate occurs near the top flange. It has been recommended that plate girders should be designed with a span-to-depth ratio in the range of 10-12 [26]. This range for the a/D ratio corresponds to a recommended range for the angle of the panel diagonal (\(\theta_{d}\)) between 4.76\({}^{\circ}\) and 5.71\({}^{\circ}\). Considering this requirement, the optimised plate girder is suitable for span lengths of up to 4.7 m.  
In order to extend the analysis to more cases, and to better understand the effect of moment distribution on the structural performance, the harmony search process is repeated under the assumption of constant distributed loading for a cross-section with a slender web and noncompact flange. The moment gradient factor \(C_{b}\) is adjusted according to the new load case using Equation (4). In order to incorporate the change in the value of \(C_{b}\), the minimum bending moment capacity constraint was also lowered accordingly. The outcome of the harmony search optimisation can be seen in Figure 10. A minimum cross-sectional area of 7250 mm\({}^{2}\) could be reached after 347 harmony search iterations. The geometric properties of the optimised cross-section are listed in Table 5. It can be observed that the optimised web plate has a decrease in depth, an increase in thickness and is less slender than the original geometry, which is contrary to what was observed in the load case with concentrated load. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & \(b_{f}\)[mm] & \(t_{f}\)[mm] & \(D\)[mm] & \(t_{w}\)[mm] & \(a\)[mm] & \(M_{\sigma}\)[\(Nmm\)] & \(\tau_{w}\)[\(MPa\)] & \(A\)[mm\({}^{2}\)] \\ \hline Experimental value & 250 & 15 & 800 & 2 & 750 & \(1.1834\times 10^{11}\) & 64.017 & 9100 \\ Optimised value & 374 & 8.97 & 399 & 2.31 & 750 & \(1.1857\times 10^{11}\) & 64.029 & 7629 \\ Difference [\%] & 66 & \(-\)54 & \(-\)52 & 14 & 0 & 0.19 & 0.02 & \(-\)16 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Geometric and mechanical properties of the optimised cross-section with noncompact web. Figure 8: Results of the analysis with finite strip method using the software package CUFSM for the noncompact web. Figure 9: Finite element model of the optimised plate girder with noncompact web. As can be seen from the presented results, the effect of slenderness on the structural performance is not clearly discernable. Figure 11 shows the results of a parametric study that was carried out in order to visualise the effect of changing the web plate slenderness on the structural behaviour. Using the equations in Section 1.1, the ultimate shear stress \(\tau_{u}\) was calculated for different values of web plate slenderness \(\lambda_{w}\). Each curve in Figure 11 represents a different web plate thickness, while the flange slenderness and flange thicknesses are kept constant. It can be observed that, at small web thicknesses, increasing the web slenderness has a favourable effect on the ultimate shear stress, whereas, at higher web thickness values, slenderness has the opposite effect.