Minimum cost design of reinforced concrete T-beams at ultimate loads using Eurocode2

The present paper outlines a general procedure for obtaining on the basis of direct minimization optimal cost designs of reinforced concrete T-beams at ultimate design loads. The objective function to be minimized is divided into costs of concrete, steel and formwork. The set of constraints consists in design constraints defined in accordance with Eurocode2 including the nonlinear ultimate behaviors of concrete and reinforcing steel as well as current practices rules. However, the proposed formulation can easily cater for other design codes without major alterations. Self weight of T-beam which may contribute substantially to the ultimate bending moment capacity for long spans is considered variable both in the objective and the constraints functions. The cost optimization process is developed by the use of the Generalized Reduced Gradient technique in the space of only a reduced number of design variables. Typical design examples are presented to illustrate the step by step optimal design procedure and to provide applications that can be used in future investigations. Comparisons with standard design office methods are performed and the results reported showing that the proposed method can be successfully applied to the optimal design of reinforced concrete T-beams. The proposed methodology is economically effective compared to conventional office design methods and can be easily extended to other sections commonly used in structural design. It is also practically simple and more comprehensive than other optimization methods available in the literature which do not account for all the design variables considered in this work.