# Heuristic Techniques for the Design of Steel-Concrete Composite Pedestrian Bridges
## 4 Discussion
### Parametric Study  
A parametric study for varying span lengths is presented with the GSO and DLS combination optimization model. Five span lengths were considered: 28, 32, 38, 42 and 48 m. The characteristics that were studied are the economy, the geometry, and the amount of materials. Tables 7 and 8 compile the values of the features of the optimization solutions: Table 7 gives the main values of the geometry of the structure, and Table 8 gives the values of the measurements of the amount of materials of the structure. The results of the parametric study led to practical rules for the preliminary design of cost-optimized steel-concrete composite pedestrian bridges with box-girder cross sections isostatic spans. The discussion of the results was carried out together, with a regression analysis. The functions obtained were valid approximations within the range of the studied parameters. The extrapolation of these results to other span lengths should be carried out carefully. Figure 8 shows the average results of the cost of the structure per square meter of the steel-concrete composite pedestrian bridge for distinct span lengths. The cost evolution as a function of the horizontal span leads to a very good quadratic correlation. The average footbridge cost adjusted to \(C=0.1954\)L\({}^{2}\)\(-8.0873\)L + 325.96 with a regression coefficient of R\({}^{2}\) = 0.9994. The cost rising is produced by the need \begin{table}
\begin{tabular}{c c c c c c c} \hline  & & **Reference** & **DLS** & **SA** & **GSO** & **GSO and DLS** \\ \hline
**Cost** & \(\upmu\)/m\({}^{2}\) & 399.10 & 304.82 & 299.77 & 313.18 & 297.76 \\
**\% Cost/reference** & \% & - & \(-23.62\)\% & \(-24.89\)\% & \(-21.53\)\% & \(-25.39\)\% \\
**CO\({}_{2}\) emissions** & kg CO\({}_{2}\)/m\({}^{2}\) & 700.22 & 536.39 & 527.70 & 552.54 & 523.68 \\
**\% Emissions/reference** & \% & - & \(-23.40\)\% & \(-24.64\)\% & \(-21.09\)\% & \(-25.21\)\% \\ \hline \end{tabular}
\end{table} 
Table 6: CO\({}_{2}\) emissions and cost data comparison from the reference solution and the heuristics. \begin{table}
\begin{tabular}{c c c c c c c c} \hline
**Span** & **CL** & **CA** & **CT** & **EAS** & **EAL** & **EAI** & **FCK** & **Total** \\
**(m)** & **(m)** & **(m)** & **(m)** & **(mm)** & **(mm)** & **(mm)** & **(MPa)** & **Depth/L** \\ \hline
28 & 0.17 & 1.53 & 1.70 & 18 & 8 & 12 & 35 & 0.035 \\
32 & 0.16 & 1.37 & 1.53 & 18 & 8 & 10 & 30 & 0.036 \\
38 & 0.15 & 1.21 & 1.36 & 18 & 8 & 10 & 30 & 0.036 \\
42 & 0.15 & 0.96 & 1.11 & 18 & 8 & 10 & 25 & 0.035 \\
48 & 0.15 & 0.80 & 0.95 & 18 & 8 & 10 & 25 & 0.034 \\ \hline \end{tabular}
\end{table} 
Table 7: GSO with DLS combination for 28, 32, 38, 42, and 48 m spans. \begin{table}
\begin{tabular}{c c c c c} \hline
**Span (m)** & **Beam Rolled Steel (kg/m\({}^{2}\))** & **Slab Concrete (m\({}^{3}\)/m\({}^{2}\))** & **Slab Reinforcement (kg/m\({}^{2}\))** \\ \hline
28 & 194.10 & 0.17 & 30.87 \\
32 & 165.64 & 0.15 & 24.63 \\
38 & 150.66 & 0.14 & 22.23 \\
42 & 135.37 & 0.14 & 19.80 \\
48 & 126.56 & 0.14 & 17.84 \\ \hline \end{tabular}
\end{table} 
Table 8: GSO with DLS combination measurements of the materials for 28, 32, 38, 42, and 48 m spans. for larger amounts of materials to satisfy the deflection requirements. Note that the R\({}^{2}\) regression coefficient in Figure 8 is almost 1, this indicates a very good correlation. The variations between the minimum and the mean cost of the pedestrian bridge produced by the GSO and DLS combination are 0.42%. Figure 9 shows the mean values of the depth of the steel beam (\(CA\)) for different span lengths. The depth of the beam has a good linear variation, according to the span length of the bridge. The average depth of the beam adjusts to \(CA=0.0369\)L \(-\) 0.2179 with R\({}^{2}\) = 0.9927. Again, the good correlation factor represents a functional relationship. As shown in Figure 10, a function was found relating the thickness of the slab with different span lengths.