Résumé La prise en compte dans les calculs du caractère endommageable du béton doit permettre de prévoir les conditions de ruine des structures en béton armé ou précontraint. Nous présentons ici la simulation numérique du comportement jusqu’à rupture (courbes effort-flèche et zones endommagées) d’une poutre en béton armé. Le calcul a été mené sans connaître les résultats expérimentaux de l’essai correspondant. Il a été procédé à une simulation classique par éléments finis ainsi qu’à une approche utilisant le principe des ‘macros-éléments’. L’incertitude sur les lois de comportement du matériau a été évaluée et prise en compte et ses conséquences estimées. Les comparaisons entre résultats numériquest et expérimentaux montrent que les approches développées constituent un outil prévisionnel satisfaisant.

Summary The finite-element method provides a good prediction of the response of concrete reinforced structures (load-displacement) and also much information on the local aspects (stresses, strains, critical zones). Progressive damage such as initiation and growth of microcracks produces in concrete members a decrease of stiffness. These macroscopic and microscopic aspects of damage can be easily modelled by continuous damage model theory. Two kinds of problem are, however, generally encountered when dealing with this type of constitutive laws: (i) It is not very easy to identify the evolution of the damage parameters and the constitutive laws fitting to experimental results. (ii) The implementation of strain-softening constitutive laws in classical finite-element analysis cannot be madeex abrupto. It is today very well established that strain localization, which is favoured by strain-softening, introduces an inobjectivity of the finite-element calculations, that is a loss of uniqueness of the solution, mesh dependency, and finally an unrealistic solution in which failure of a structure occurs without energy dissipation. Furthermore, it is necessary to adopt a correct model for the behaviour of the steel-concrete bond when dealing with reinforced concrete structures. It is only when solutions have been developed to these problems that the prediction of the response of real-size structures can be carried out. Then the comparison between experimental data and numerical results is important and establishes the performance of the theory developed. The work presented in this paper originated from a challenge from the well-known Bouygues company. They designed and tested reinforced concrete beams disregarding the usual building code requirements. For example, these beams when subjected to bending do not have any stirrups. The engineers at Bouyques performed the tests, measured the load displacement response of the beam and determined the characteristic properties of its constituents (i.e. Young’s modulus of concrete, strength of concrete and uniaxial stress-strain curve of reinforcements). They provided us with the characteristic properties of the concrete and steel, and numerical predictions were carried out at the Laboratoire de Mécanique et de Technologie in Cachan. In these numerical calculations, two models were implemented. The first one is a classical finite-element approach using an isotropic damage (scalar) law for concrete and elastic response of the steel reinforcement. In the second approach, macro-elements, whose behaviour is described in term of global variables (bending moment, axial force, rotation of the cross-section etc.) were implemented. It is shown in the paper that the results from those two approaches fit very well the experimental response obtained. Furthermore, the finite-element approach provides interesting information about the development of local damage and its evolution inside the beam. Finally it is pointed out that the macro-element calculations reduce drastically the computation time, making it more interesting for industrial purposes.