[Univ of Cambridge] [Dept of Engineering]

Behaviour and strength of reinforced concrete continuous deep beams

A.F. Ashour


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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