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    Lateral confinement needed to suppress softening of concrete in compression
    (Asce-Amer Soc Civil Engineers, 2002) Caner, FC; Bazant, ZP
    Suppression of softening in the load-deflection diagram of concrete-filled tubular columns and spiral columns is proposed to serve as a design criterion helping to avoid the size effect and explosive brittle character of collapse. To this end, the recently developed tube-squash tests, in which a short concrete-filled steel tube is squashed to about a half of its original length and allowed to bulge, are conducted with tubes of different wall thicknesses. A finite-strain finite element computer code with a microplane constitutive model is used to simulate the tests. After its verification and calibration by tests, the code is used to analyze nonbuckling concrete-filled tubular columns and spirally reinforced columns. It is found that softening in the load-deflection diagram can be fully suppressed only if the reinforcement ratio (ratio of the tube volume or spiral volume to the total volume of column) exceeds about 14%. If mild softening is allowed, the reinforcement ratio must still exceed about 8%. These ratios are surprisingly high. If they are not used in design, one needs to pay attention to the localization of softening damage, accept the (deterministic) size effect engendered by it, and ensure safety margins appropriate for protecting against sudden explosive brittle collapse. This is of particular concern for the design of very large columns.
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    Vertex effect in strain-softening concrete at rotating principal axes
    (Asce-Amer Soc Civil Engineers, 2002) Caner, FC; Bazant, ZP; Cervenka, J
    The inelastic behavior of concrete for highly nonproportional loading paths with rotating principal stress axes is studied. Test cylinders are first loaded in compression under uniaxial stress and then torsion is applied at constant axial displacement. Proportional compressive-torsional loading tests are also carried out for comparison. The tests demonstrate that the response of concrete for load increments parallel in the stress space to the current yield surface is highly inelastic (i.e., much softer than elastic) in the peak load range and especially in the postpeak range. The classical tensorial models of plasticity type incorrectly predict for such load increments the elastic stiffness. The experiments are simulated by three-dimensional finite element analysis using the microplane model M4, in which the stress-strain relations are characterized not by tensors but by vectors of stress and strain on planes of various orientations in the material. It is shown that the observed vertex effect is correctly predicted by this model, with no adjustment of its material parameters previously calibrated by other test results. The experiments are also simulated by a state-of-the-art fracture-plastic model of tensorial type and it is found that the vertex effect cannot be reproduced at all, although an adjustment of one material parameter suffices to obtain a realistic postpeak slope and achieve a realistic overall response. What makes the microplane model capable of capturing the vertex effect is the existence of more than 60 simultaneous yield surfaces. Capturing the vertex effect is important for highly nonproportional. loading with rotating principal stress axes, which is typical of impact and penetration of missiles, shock, blasts, and earthquake.