Behaviour and strength of reinforced concrete continuous
The present research is concerned with the development of models for shear
in reinforced concrete continuous beams. A series of tests on reinforced
concrete continuous deep beams was performed to aid in the development of
such models. The main parameters studied were the shear span to depth ratio
and web reinforcement. The vertical web reinforcement had more influence
on the load capacity of the tested beams than the horizontal web reinforcement.
Present codes of practice (ACI 318-89 and CIRIA Guide 2) for continuous deep
beams showed little agreement when compared to test results. A three dimensional
non-linear finite element model of reinforced concrete deep beams was developed.
The multi-axial isotropic behaviour of concrete before cracking or crushing,
and the failure surface, are based on experimental data. The softening behaviour
of concrete in both cracking and crushing is implemented by decomposition
of the total strain increment into a crack or crush strain increment and a
strain increment in the intact concrete. Fracture energy is considered in
modelling the behaviour of the stress across the crack. Shear stress transfer
across the crack is variable and represented by empirical equations from experiments.
The interaction between concrete and steel is modelled using a new linkage
element. The model needs only two parameters to define the whole behaviour;
the cylinder strength and fracture energy. The model is implemented in ABAQUS
4.9, a widely available finite element program and the behaviour of the experimental
continuous deep beams is reasonably predicted.
A more practical and simpler approach based on the theory of plasticity
was developed to predict an upper bound on the collapse load of reinforced
concrete panels loaded in plane. The materials are assumed rigid-perfectly
plastic. Modified Coulomb failure criteria with tension cut-off are adopted
to predict yielding of concrete. A collapse mode is assumed, with rigid
moving blocks separated by narrow zones of displacement discontinuity. The
shape of 'yield lines' and displacements of concrete rigid blocks are the
variables involved in the energy equation. Minimisation of the predicted
collapse load produces the optimum shape of the yield lines. Examples of
comparison with other upper bound analysis and with experiments are given
to show the applicability of this numerical technique to a wide range of
problems. Practical formulae based on upper bound analysis to predict the
capacity of reinforced concrete continuous deep beams were derived. The strength
prediction from those formulae depends on the effectiveness factor. Calibration
of the theoretical predictions against the available experimental results
produced the optimum value of the effectiveness factor in terms of the concrete
strength and the reinforcement.
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(last update 10 November 2003)