# Heuristic Techniques for the Design of Steel-Concrete Composite Pedestrian Bridges
## 2 Optimization Problem Definition
### Structural Analysis and Constraints  
The structure was analyzed like a linear element. The model of the structure considered the shear deformation and the effective flange width [6]. To obtain the stresses of the structure to check regulations and recommendations constraints, a Fortran language program was implemented. This program calculated the stresses in two sections: mid span and supports. In this structure, the highest stresses occurred in these areas. Prior to the verifying limit states, the program needed to calculate stress envelopes due to the loads. This program evaluated the stress envelopes due to a uniform load of 5 kN/m\({}^{2}\) and the deck self-weight, including the bridge railing and asphalt (see Table 2). Note that the thermal gradient [5] and the differential settling in each support were also taken into account. The model implemented obtained the beam stresses and the transversal section tensions to assess the structural design validity. Once the stresses were obtained, a structural integrity analysis was performed. The ultimate limit states (ULS) assessed the capacity of the structure against the flexure, shear, torsion, and the combination of the stresses. It further considered the minimum reinforcements to resist the stresses and the examination of the geometrical conditions. To evaluate the structural capacity, the regulations employed to obtain the equations that allow the verification of the pedestrian bridge have been the Spanish code on structural concrete [4], the Spanish recommendations for composite road bridge project [6], and the code on the actions for the design of road bridges [3]. The serviceability limit states (SLS) assessed the capacity of the structure to continue its service. The ULS considered in this study were: bending, shear, torsion, shear-torsion interaction, and the stiffeners verification. It must be taken into account that once the variables that define a frame solution have been chosen, then geometry, the materials, and the passive reinforcement are defined. It should be noted that no attempt has been made to calculate the reinforcement in such a way as to comply with common design rules. Such common design procedures follow a conventional order for obtaining reinforcement bars from flexural ULS, and then checking the SLS and redefining if required. While this order is effective, it ignores other possibilities that heuristic search algorithms do not oversee. The seismic verifications are not necessary due to the small value of the calculus acceleration for the location of the constructions. On the other side, the SLS assessed were: deflections, vibrations, cracking, and web deformation. The vibration limit state was verified in accordance with the restrictions for footbridges [4]. The SLS of cracking included compliance with limitations of the crack width for existing durability conditions. With respect to deflection, the instantaneous and time-dependent deflection was limited to 1/500 th of the main span length for the characteristic combination [4], and the frequent value for the live loads was limited to 1/1200 th of the main span length [5]. Concrete and steel fatigue were not considered, as this ultimate limit state is rarely checked in pedestrian bridges. In addition, the recommendations indicated in the specialized bibliography [43; 44; 45] were considered. The modulus implemented compared the structure model values with the values obtained from the regulations equations. This modulus verified the demands of the safety, as well as those relating to the aptitude for service requirement. Therefore, the limit states and the geometrical and constructability