Yield design based numerical analysis of three-dimensional reinforced concrete structures

The purpose of this contribution is to present some new recent developments regarding the evaluation of the ultimate bearing capacity of massive reinforced concrete structures which cannot be modelled as ID (beams) or 2D (plates) structural members. The approach is based on the implementation of the lower bound static approach of yield design through a discretization of the three-dimensional structure into tetrahedral finite elements, on the one hand, the formulation of the corresponding optimization problem in the context of Semidefinite Programming (SDP) techniques, on the other hand. Another key feature of the method lies in the treatment of the concrete embedded reinforcing bars not as individual elements, but by resorting to an extension of the homogenization approach. The whole procedure is first validated on a rather simple illustrative problem, then applied to the design of a bridge pier cap taken as an example of more complex and realistic structure.