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
A Doctoral Thesis. Submitted in partial fulfilment of the requirements for the award of Doctor of Philosophy of Loughborough University.