Keywords: cost optimization, non-linear programming, reinforced concrete, rectangular cross-section beam.

In the traditional design of reinforced concrete (RC) members, a trial and error process is usually applied. An assumed cross-section is checked for strength, serviceability and other requirements of the design code. If the requirements are not satisfied a new cross-section is adopted and repeatedly checked. This design process does not take into account the cost of the structural element and thus usually leads to unnecessary over dimensioning. However, to be competitive on the mark it is inevitable to take into account the cost of the structure. Structural optimisation is an effective technique that yields economical and rational design and leads to effective cost reductions

The paper presents the cost optimization design of simply supported reinforced concrete beams of rectangular cross-section reinforced with tension and compression reinforcement. The goal of the optimization was to find the optimal dimensions of the cross-section as well as the optimal amount of reinforcement for a given span and imposed load, by minimizing the self-manufacturing cost of the beam subjected to the structural analysis constraints based on Eurocode provisions for the conditions of both the ultimate and the serviceability limit states.

A detailed objective function of the beam's self-manufacturing costs was given including the material and labour cost items. The self-manufacturing costs include the material costs of the concrete, reinforcement and formwork panels. The labour costs were added together from the costs of the cutting, placing and connecting of the reinforcement as well as from the labour costs for concreting of the beam, consolidating and curing of the concrete. The maintenance, amortisation, transportation, erection costs, etc. are not considered in this paper. The cost objective function is defined in an open manner and thus could be modified to take into account different economical conditions. The structural optimization was performed using the nonlinear programming approach, NLP.

To demonstrate the applicability of the proposed approach the cost-optimization of a simply supported RC beam of different spans (2-12m), distances between the individual beams (4-8m) and variable uniformly distributed imposed load (2 and 5 kN/m²) was performed. For each combination of the parameters, the particular NLP optimization was performed and the optimal results obtained were compared. The goal of the research was to define the spans and loads, at which the RC beams would demonstrate the advantage of the approach.

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