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This paper deals with the economic optimization of reinforced concrete short corbels typically used in construction. The study shows the efficiency of heuristic optimization by the random search, the descent local search and the Simulated Annealing (SA) algorithms. The evaluation of solutions follows a nonlinear finite element analysis with smeared cracking up to failure. Designs are considered feasible when they withstand a prescribed reference load. The algorithms are applied to a typical short corbel of 0.350m of total depth for which there is available data about the mode of failure and ultimate loads. The distance of the applied load to the built-in section is 0.150m. This example has seven discrete design variables for the geometry of the corbel, material and passive reinforcement. The application of the SA algorithm requires the calibration of the initial temperature and threshold, the number of variables modified in each iteration, the length of the Markov chains and the reducing coefficient. Each heuristic is run nine times so as to obtain statistical information about the minimum, average and deviation of the results. The best result has a cost of 10.4770€ for the SA algorithm. Finally, solutions and run times indicate that heuristic optimization is a forthcoming option for the design of real nonlinear finite element analysed structures.

Heuristic optimization of short corbels by smeared cracking finite element analysis