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Technical codes for buildings deal with cracked reinforced concrete structures assuming concrete as a compression–only material, whereas rebar provides the structural component with the required tensile strength [1]. Numerical methods can handle reinforced concrete structures calling for demanding non–linear analysis. Indeed, well–known convergence issues arise when copying with concrete as a compression–only material. Recently, an alternative energy–based approach has been proposed to solve the equilibrium of a linear elastic no– tension medium exploiting its hyper–elasticity [2]. A topology optimization problem distributes an equivalent orthotropic material to minimize the strain energy of the no-tension body, thus avoiding more demanding non–linear analysis. This contribution provides an extension to the analysis and optimal design of reinforced concrete structures. Following [3], truss members are modeled within a two–dimensional no–tension continuum in order to model structural elements made of reinforced concrete. The solution of the equilibrium is straightforward within the approach proposed in [2], thus allowing performing analysis at the serviceability limit state with cracked sections. Also, introducing the areas of the reinforcement bars as an additional set of unknowns, a problem of size optimization is outlined to cope with the optimal rebar of r.c. structures. Preliminary numerical simulations are shown to assess the proposed procedure.

ANALYSIS AND DESIGN OF REINFORCED CONCRETE STRUCTURES AS A TOPOLOGY OPTIMIZATION PROBLEM