Showing papers by "Université Paris-Saclay published in 1987"
TL;DR: In this paper, the softening postpeak load-deflection relation for cracking reinforced concrete beams and frames is analyzed by layered finite elements, where the bending theory assumptions are used and bond slip of reinforcement is neglected.
Abstract: The softening postpeak load-deflection relation for cracking reinforced concrete beams and frames is analyzed by layered finite elements. Concrete is assumed to exhibit strain softening in both tension and compression, and the steel reinforcement is elastic-plastic. The bending theory assumptions are used and bond slip of reinforcement is neglected. It is shown that the model can satisfactorily approximate the existing test results for softening beams and frames. At the same time, the constitutive laws with strain softening, including those of continuum damage mechanics, are shown to lead to spurious sensitivity of results to the chosen finite element size, similar to that documented before for other strain-softening problems. In analogy to the finite element crack-band model, this problem can be overcome if the minimum admissible element size is specified as a cross friction property; its suitable value appears to be equal to the beam depth.
85 citations
TL;DR: In this article, a layered finite element model with strain-softening material properties, whose applicability to reinforced concrete was corroborated by comparisons with experimental data in the preceding paper, is used in a parametric study aimed at the effect of several factors: structure size, finite element size, downward slope of strain•softening stress-strain relation, length of the plastic yield plateau before the onset of strain softening (if any), and end-restraint stiffness.
Abstract: A layered finite element model with strain‐softening material properties, whose applicability to reinforced concrete was corroborated by comparisons with experimental data in the preceding paper, is used in a parametric study aimed at the effect of several factors: structure size, finite element size, downward slope of strain‐softening stress‐strain relation, length of the plastic yield plateau before the onset of strain softening (if any), and end‐restraint stiffness. To quantify the response, several new response characteristics are introduced: the ductile strengthening factor, characterizing how strain softening reduces the maximum load compared to the plastic limit load; the redistribution ratio, characterizing the degree of bending moment redistribution in comparison to that in plastic limit analysis; the energy safety factor, describing the energy to deform the structure to the peak load; and the ductility factor, characterizing the deflection increase at maximum load relative to the deflection from...
41 citations
TL;DR: In this paper, an extensive characterization procedure was developed to study multilayers for extended ultraviolet (XUV, 1 A≲λ≲1000 A) optics, and results of this procedure applied to sputtered Si/W multi-layer designed as normal-incidence XUV reflectors for ∼200 A.
Abstract: We describe an extensive characterization procedure developed to study multilayers for extended ultraviolet (XUV, 1 A≲λ≲1000 A) optics. We present results of this procedure applied to sputtered Si/W multilayers designed as normal‐incidence XUV reflectors for ∼200 A. Techniques used were low‐angle x‐ray diffraction, Bragg–Brentano and Seemann–Bohlin diffraction, wide‐film Debye–Scherrer (Read) camera, Rutherford backscattering spectroscopy, and transmission electron microscopy. Reflectances at several incidence angles were measured with synchrotron radiation and found to agree very well with reflectance curves calculated without adjustable parameters. The information obtained from the different techniques forms a coherent picture of the structure of these materials.
11 citations