Steffen Mohr, Jesús M. Bairán, Antonio R. Marí
A frame element model for the analysis of reinforced concrete structures under shear and bending,
Engineering Structures,
Volume 32, Issue 12, December 2010, Pages 3936-3954


Modeling the response of reinforced concrete structures under combined shear and normal forces involves handling the anisotropic behavior that takes place in the post-cracked and ultimate ranges. Current 2D (plane-stress and plane-strain) and 3D (solid) non-linear finite element formulations capable of modeling such response are too costly and not suitable for daily engineering practice. In this paper a new developed frame element model which combines an efficient fully coupled in-plane shear's normal sectional model with a beam's column element, suitable for structural analysis applications is described and verified with tests results. Both normal and shear stresses and strains are involved in the sectional equilibrium and compatibility equations, respectively. The shear and vertical strain distributions are assumed to be composed by a series of polynomial shape functions; each one is affected by a constant whose value is internally calculated according to the materials state. The non-linear analysis of the frame structure is carried out using the Generalized Matrix Formulation, which is a force-based approach with exact interpolation of forces along the element and implicitly accounts for the shear deformation of the element. The model has been verified using the results of selected well documented tests, in which the influence of the level of shear stresses on the structure response is experimentally evidenced. Good agreement has been obtained between the experimental and the theoretical results provided by the model, showing its capability to reproduce displacements, stresses and strains in the concrete and in the reinforcements, and different types of failure, with more accuracy than previous models.