Plastic behaviour of deformable reinforced concrete box sections under eccentric load

Abstract

This thesis deals with the plastic behaviour of deformable reinforced concrete box sections under eccentric load. Analytical, numerical and experimental studies of this topic has been carried out.An elasto-plastic finite element model for reinforced concrete plates/panels and shells has been developed. The model is based on yield functions derived from the rigid-plastic yield line theory. A stress resultant finite element model of reinforced concrete shells has not previously been reported in the literature.The developed finite element model has been used to evaluate the plastic behaviour of deformable box sections under eccentric load. This investigation has shown that when a box section is exposed to eccentric load, plasticity will spread along the box, and that the spread of plasticity is primarily associated with the development of plastic comer hinges. Based on a comprehensive parametric investigation, which involved variation in geometry and material strength of a box section, it was found that the magnitude of spread of plasticity was mainly influenced by the ratio of bending to in-plane capacity of the walls in the box section, as well as the level of anti-symmetrical loading.Based on the observed failure mechanism predicted by the finite element simulations, a new analytical plastic solution technique has been developed to determine the collapse load of a deformable box section under eccentric load. As the magnitude of spread of plasticity varies, the governing parameter in the solution is the length over which the plasticity has spread at failure, i.e. the effective plastic length. The solution has shown to predict the same collapse loads as the finite element model.A large-scale experimental test series consisting of 17 beams has been carried out to provide experimental evidence for the ultimate load carrying capacity and failure mechanisms in deformable thin-walled reinforced concrete box sections under eccentric load. The main parameters investigated in this program were the reinforcement layout, the ratio of bending to inplane capacity of the wall in the box section, and the degree of load eccentricity. Two different transverse reinforcement layouts were investigated experimentally. Beams with one layer of stirrup reinforcement were compared to beams with two layers of stirrup reinforcement in the wall of the box section, and hence the increased transverse stiffness of the flanges and webs and increased corner stiffness was assessed.This investigation showed that using double layered stirrup reinforcement in the flanges and webs, compared to a single stirrup, increases the distortional stiffness of the cross section significantly. Thus, as the magnitude of eccentric load increases, i.e. increase in distortion, the distortional cracking load increases relatively for the beams with two layers of stirrup reinforcement. The comparison has also shown that the increased distortional stiffness has an impact on the ultimate load. The beams with double layered stirrup reinforcement will give higher ultimate collapse loads compared to the corresponding one stirrup reinforcement as the anti-symmetrical load component increases.To verify the new analytical solution and the finite element model, experiments with three different ratios of bending to inplane capacities were tested under different levels of anti-symmetrical loads. The experiments have verified the formation of plastic comer hinges, and that the length over which these have extended at failure will vary with the ratio of bending to inplane capacities, and the degree of eccentricity. It was found experimentally that the spread of plasticity in a deformable box section increases logarithmically as the ratio of bending to inplane capacity decreases. Using these plastic lengths in conjunction with the developed plastic solution for single-cell box sections, excellent agreement with the experimental collapse loads is achieved. Also the developed finite element model was shown to be a powerful tool enabling the description of the plastic behaviour of reinforced concrete shells and folded plate structures. Compared to the experiments, the finite element model is able to predict the correct collapse load and stress state, as well as being able to capture the kinematics of a deformable reinforced concrete box section.