Towards a uniform and optimal approach for safe NLFEA of reinforced concrete beams

Abstract

Application of Nonlinear Finite Element Analysis (NLFEA) is lagging behind the many digital advances in the structural engineering practice. This is due to the need for codes and standards. To help development of these codes and standards, 119 solution strategies were developed with different assumptions and choices for the concrete constitutive model, the finite element discretization, the way of modelling the reinforcement and the incremental-iterative procedures. The constants aspects of the constitutive model, like confinement and the reduction compressive strength due to lateral cracking, are based on the RTD1016 Dutch Guideline. All models are two-dimensional with a plane stress assumption and in all cases the analysis is force controlled with the application of an arclength method. This is done to increase the value of results for application in practice, as generally displacement loading is hard to apply in a real-life structure. The strategies were benchmarked with 101 experiments on reinforced concrete beams selected from literature. Those beams cover a broad range of design aspects, failing both in shear and bending, reinforcement configurations with- and without shear reinforcement, both prestressed and conventional reinforcement and heights ranging from 90 to 1200 mm. This resulted in 1919 NLFEAs which were performed with an automated approach in the DIANA multi-purpose finite element software package. It was concluded that the failure load and failure mode of the experiments can be approximated with a mean uncertainty of 1.05 with a coefficient of variation around 10 percent, provided that an appropriate solution strategy is applied. It is possible to assign an appropriate solution strategy when the structural design is known, where the main influence is the presence of shear reinforcement. Beams with stirrups are robustly modelled by a rotating crack model, while beams without stirrups were found to be better approximated by a fixed crack approach with specific choices regarding reinforcement modelling and equilibrium. To have a more objective way of judging the ductility of a failure, a measure of the dissipated energy in the reinforcement was implemented in the DIANA code. It was found that the mean model uncertainty of a ductile failure can be as low as 1.045, with a coefficient of variation around 10 percent. Brittle failures showed a mean uncertainty of 1.131, with a coefficient of variation just below 16 percent. Therefore the ductility index was found to be a valid way to judge the reliability of an NLFEA result. This study has demonstrated the applicability of force controlled NLFEA for reinforced concrete beams. The derived properties of the model uncertainties are a crucial input for safety formats.