Threshold accepting optimization of road vaults and rectangular hollow bridge piers

This paper deals with the economic optimization of reinforced concrete road vaults and with the optimization of rectangular hollow section bridge piers typically used in road construction. It shows the efficiency of a heuristic optimization by the threshold accepting algorithm. The evaluation of solutions follows the Spanish Code for structural concrete. Design loads are in accordance to the national IAP Code for road bridges. The algorithm is firstly applied to a RC hydraulic vault of 4.00 m of horizontal span and 800 m of length. This example has 23 discrete design variables, 3 geometrical, 3 of materials and 17 of reinforcement. Stress resultants and envelopes of vault structures are computed by an internal matrix method program. Best results amount to 958 euros/m and they indicate savings of about 8% with respect to the prior real design office calculations. The second structure analysed is a 24 m RC vertical height bridge pier of hollow rectangular cross-section, which supports the main span of a prestressed concrete road bridge of 60-90-60 meters of longitudinal spans. This example has 95 discrete variables, 15 geometrical, 7 types of concrete and 73 types of reinforcement bars of fixed length. The evaluation module includes the limit states that are commonly checked in design: flexure, shear, deflections, buckling, etc. Results indicate savings of about 30% with respect to the design based on the experience of the bridge designers. Finally, results indicate that heuristic optimization is a forthcoming option for improving the design costs of real RC structures.