Journal Article10.1061/JMCEA3.0002347
Closure to “Instability, Ductility, and Size Effect in Strain-Softening Concrete”
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TL;DR: In this article, structural instability due to strain-softening (i.e., declining branch of the stress-strain diagram) is presented, and the existence of a lower limit on the size of this region permits ductility, along with its dependence on the structure size and stored energy, to be predicted by a stability analysis.
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Abstract: Analysis of structural instability due to strain-softening (i.e., declining branch of the stress-strain diagram) is presented. In a continuum, strain-softening is impossible; it can exist only in a heterogeneous material. Failure occurs by unstable localization of strain or beam curvature, in which the stored strain energy of the structure is transferred into a small strain-softening region whose size is several times the aggregate size, or the spacing of reinforcement, or the depth of the beam. The existence of a lower limit on the size of this region permits ductility, along with its dependence on the size and stored energy, to be predicted by a stability analysis. Calculations of limit loads and moment redistributions in strain-softening beams and frames must include instability checks of possible curvature localization. The same applies to finite element analyses of reinforced concrete structures with account of tensile cracking, and predictions of limit loads of these structures which are questionable because they depend on the size of the finite elements.
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Citations
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References
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Equilibrium Branching Due to Flexural Softening
TL;DR: In this article, the importance of softening local behavior (decreasing bending moment for increasing flexural deformation) in the inelastic analysis of reinforced concrete beams and frames has been presented.
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Probabilistic modeling of concrete structures
Abstract: The model is compatible with the finite element analysis and therefore useful in parametric studies involving pertinent strength variables and in analysis and design of concrete structural systems. Specifically, a probabilistic model of spatial variation of concrete strength is considered and the corresponding statistical size effect is analyzed. The same model of concrete strength is also used in a failure analysis: (1) to illustrate the fact that the locations of crack initiation and the minimum load associated with it are statistically different from specimen to specimen; and (2) to reproduce, with the aid of the digital simulation technique, these locations and minimum loads. Finally, a method of digital simulation of multivariate-multidimensional random functions is described, demonstrating its usefulness in a structural concrete problem with the aid of numerical examples.
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