Limit State Evaluation of Steel-Reinforced Concrete Elements by Von Mises and Menétrey–willam-Type Yield Criteria

Abstract

An advanced version of a recently developed numerical limit analysis procedure for the prediction of peak loads and failure modes of steel-reinforced concrete elements is proposed. The modified procedure allows to take into account possible yielding of reinforcement thus capturing the actual behavior at the collapse of both steel and concrete. This implies a finite element (FE) modeling of the reinforced concrete (RC) elements in which concrete is governed by a Menétrey-Willam-type yield criterion, with cap in compression, while steel bars are governed by a von Mises yield criterion. The peak load of a wide range of RC structures whose behavior at ultimate state is dominated either by the concrete crushing or by the steel bars yielding is then predicted with a very good accuracy.to such approaches embracing limit analysis, see e.g. Spiliopoulos and Weichert [2013], or shakedown analysis, also endowed with apposite constitutive assumptions [Fuschi, 1999]. Several contributions concern direct methods based on finite elements method (FEM) in conjunction with optimization algorithms such as linear [Sloan, 1988] and nonlinear programming [Le et al., 2010], [Garcea and Leonetti, 2011]. These approaches indeed do not allow the treatment of post elastic phenomena that may arise in concrete structures, such as localization, fracture, damage, creep, etc. and that can be faced by coupling plasticity with fracture or damage mechanical theories within step-by-step analyses (see e.g., Lubliner et al. [1989], Lee and Fenves [1998] and Zhang et al. [2010]); however, they can give information on the behavior at limit (collapse) states of structures, which are very useful for design purposes. In this context, with an approach not based on an optimization algorithm but grounding on sequences of FE elastic analyses, it has to be inserted to the present study.The promoted approach belongs to a wider research program started by the authors in the context of laminates of fibres reinforced polymers [Pisano and Fuschi, 2007;Pisano et al., 2012Pisano et al., , 2013bDe Domenico et al., 2014] and then extended in the context of RC structures with reference to a Menétrey-Willam (M-W)-type yield criterion with cap in compression [Pisano et al., 2013a[Pisano et al., , 2013cDe Domenico et al., 2014]. In both the latter quoted studies, two limit analysis methods, namely the linear matching method (LMM), and the elastic compensation method (ECM), have been applied under the simplified hypothesis where reinforcements behave as indefinitely elastic. This hypothesis implies, as explicitly declared, the limitation of applicability to those structures whose behavior, at incipient collapse, is dominated by crushing of concrete, being the steel bars far from yielding which is the case of the so-called over-reinforced structures. To overcome this limitation and to improve the overall modeling of the RC structural elements at collapse, the present study proposes an advanced version of the above numerical limit analysis procedure for dealing with possible ...

Gradient elasticity and dispersive wave propagation: Model motivation and length scale identification procedures in concrete and composite laminates

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Limit analysis on FRP-strengthened RC members

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Single Spring Joint Element Based on the Mixed Coordinate System

“…Finite element method (FEM) has become the most commonly adopted method to predict the strength and the deformation of composites, namely, concrete and reinforcing bar. Typically, based on the methods used, nonlinear FEM of RC can be divided into three categories: discrete model, embedded model, and smeared model [3][4][5][6][7][8]. In the discrete model (Figure 1(a)), a joint element is inserted to simulate the bond-slip performance of the concrete and the reinforcing bar.…”