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

Hugues Vincent (1) , Mathieu Arquier (1) , Jeremy Bleyer (2) , Patrick de Buhan (3)

1 Strains
2 navier umr 8205 - Laboratoire Navier
3 multi-échelle - Modélisation et expérimentation multi-échelle pour les solides hétérogènes

The objective of this contribution is to present some new recent developments regarding the evaluation of the ultimate bearing capacity of massive three‐dimensional reinforced concrete structures which cannot be modeled as 1D (beams) or 2D (plates) structural members. The approach is based upon 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 semi‐definite programming 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 yield design homogenization approach. The whole procedure is first validated on the rather simple illustrative problem of a uniformly loaded simply supported beam, then applied to the design of a bridge pier cap taken as an example of more complex and realistic structure.

Mots clés: Finite element method; Homogenization; Reinforced concrete structures; Semi-definite programming; Yield design

Domaines: Physique [physics]; Mécanique [physics]; Matériaux et structures en mécanique [physics.class-ph]

Hugues Vincent, Mathieu Arquier, Jeremy Bleyer, Patrick de Buhan. Yield design-based numerical analysis of three-dimensional reinforced concrete structures. International Journal for Numerical and Analytical Methods in Geomechanics, 2018, 42 (18), pp.2177-2192. ⟨10.1002/nag.2850⟩. ⟨hal-01855342⟩