Representation of bond in finite element analyses of reinforced concrete structures
A non-linear finite element model has been developed to analyse reinforced concrete structures taking into account : (1) non-linear concrete behaviour under biaxial stress, (2) progressive cracking of the concrete, and (3) interaction between the reinforcement and the concrete matrix commonly known as bond. Three dimensional reinforced concrete components are analysed by an approximate two dimensional plane stress model. Bond is considered to be a concentric layer surrounding the reinforcement modelled by a 6 noded rectangular 'shearing' element. The concrete is represented by 8 noded isoparametric membrane elements and the reinforcement by 3 noded isoparametric bar elements. The finite element model uses, an incremental iterative solution technique known as the 'Initial stress method' and a special solution technique to allow for cracking of the concrete. stiffnesses within elements are evaluated by numerical integration using Gaussian Quadrature, with elastic moduli stored at the sampling positions. The bond model is based upon an assumed non-linear relationship between bond stress and slip in which the localised ultimate bond stress' is a function of both the lateral pressures exerted by the concrete on the reinforcement and the radial contraction of the bar' due to Poisson's effect. Allowance is also made for the deterioration of bond when the slip exceeds a tolerance value. The concrete model is a non-linear elastic fracture model based upon the 'Equivalent uniaxial strain approach' as developed by Darwin and Pecknold (1974). Cracking of the concrete is assumed to be 'smeared' within the concrete element. Reinforced concrete components which have been analysed include; the ordinary pullout test, double ended pull out test, a transfer test, and a beam-column intersection. A small experimental programme was conducted to obtain reliable data as to the nature of the bond stress and reinforcement strain distributions in the double-ended pullout test, the transfer test and the beam-column intersection. To determine the reinforcement strain distributions, plain round bars or ribbed reinforcement bars in the case of the beam-column, were embedded in the concrete specimens with electrical strain gauges attached . The author's computer programs are explained and listed in the appendices.