Enrico Spacone

FIBRE BEAM–COLUMN MODEL FOR NON-LINEAR ANALYSIS OF R/C FRAMES: PART I. FORMULATION

A companion paper presents the formulation of a fibre beam-column element for the non-linear static and dynamic analysis of R/C frames. This paper illustrates the application of the proposed element in the simulation of the hysteretic behaviour of several R/C beam and column specimens. The specimens are subjected to uniaxial and biaxial loading histories with varying axial load. The proposed element shows computationally stable and robust numerical behaviour, while being able to describe very well the hysteretic behaviour of the reinforced concrete members under the imposed complex loading histories.

Analysis of Reinforced Concrete Elements Including Shear Effects

The response of reinforced concrete (RC) structures is often governed by shear failure. This article reports on a study of RC plane frames under monotonic and cyclic loading, including axial, bending, and shear effects. The authors introduce a force-based two-dimensional (2D) element based on the Timoshenko beam theory. The element formulation is general and yields the exact solution within the Timoshenko beam theory. The authors use a simple, nonlinear, shear force-shear deformation law at the section level, together with a classical fiber section for the axial and bending effects. The authors validate their hypotheses through comparisons with experimental data on the shear performance of bridge columns. A case example using a viaduct that collapsed during the 1995 Kobe earthquake is presented. The results highlight the importance of accounting for the limited shear capacity of the piers in predicting the failure mechanism of the structure.

Finite element formulations of one-dimensional elements with bond-slip

Abstract This paper presents two general formulations of one-dimensional structural members with deformable interfaces. The interface accounts for the bond-slip between the element components. The first formulation is the classical displacement-based formulation; the second one is a novel force-based approach. The two formulations are derived from the equilibrium and compatibility differential equations of the problem. A special force recovery procedure, based on residual deformations, is presented for the force-based formulation. Two applications are used to illustrate the two formulations: the first is a reinforcing bar with bond slip, the second is a steel–concrete composite beam with partial interaction between the steel beam and the concrete slab. Examples of a bar with bond failure and of a composite beam with weak connection show the precision of the force-based element and its capability to trace the complex response of softening members with a limited number of elements.

A 3D hypoplastic model for cyclic analysis of concrete structures

Abstract This paper presents a hypoplastic model for three-dimensional analysis of concrete structures under monotonic, cyclic, proportional and non-proportional loading. The constitutive model is based on the concept of equivalent uniaxial strains that allow the assumed orthotropic model to be described via three equivalent uniaxial stress–strain curves. The characteristics of these curves are obtained from the ultimate strength surface in the principal stress space based on the Willam–Warnke curve. A cap model is added to consider loading along or near the hydrostatic axis. The equivalent uniaxial curve is based on the Popovics and Saenz models. The post-peak behavior is adjusted to account for the effects of confinement and to describe the change in response from brittle to ductile as the lateral confinement increases. Correlation studies with available experimental tests are presented to demonstrate the model performance. Tests with monotonic loading on specimens under constant lateral confinement are considered first, followed by biaxial and triaxial tests with cyclic loads. The triaxial test example considers non-proportional loading.

A new look at reliability of reinforced concrete columns

This paper presents an investigation on reliability of reinforced concrete columns. For short columns, the fiber model is used for generating failure surfaces and strain and stress histories of both steel and concrete fibers under proportional and sequential loads. Two failure criteria, one based on the collection of peak-load points, the other based on prescribed maximum concrete strains are presented. For slender columns, failure surfaces are generated using a method proposed in 1991 by Bažant et al. (ACI Structural Journal, 1991, 88, 391–401). The reliability estimation of short and slender columns under random loads is formulated by Monte Carlo simulation in the load space. In this space, isoreliability contours for both deterministic and nondeterministic columns under different load paths and load correlations are plotted. It is demonstrated that these factors may have substantial effects on the reliability of reinforced concrete columns. Therefore, the results of this study can be used to support the consideration of load path and load correlation in the development of improved evaluation and design specifications for reinforced concrete columns.

Responses of Reinforced Concrete Members Including Bond-Slip Effects

This paper discusses the importance of modeling bond-slip in the response of reinforced concrete (RC) members. A displacement-based, RC beam fiber model with bond-slip is presented. The formulation is general and applies to both monotonic and cyclic loads. It also extends to shallow beams strengthened in flexure by externally bonded thin plates. Two main applications are presented to illustrate the model characteristics and to show the importance of including bond-slip in modeling RC members. The first application considers a RC column experimentally tested under cyclic loads and previously modeled with a fiber element without bond-slip. The second application considers a shallow beam strengthened with a fiber reinforced plastic plate. In both cases, the model realistically predicts not only the strength of the members, but also their stiffness and, in the case of the column, the hysteretic energy dissipated during the loading cycles.

Analysis of Hysteretic Behavior of Anchored Reinforcing Bars

This paper presents the analysis of the hysteretic behavior of anchored reinforcing bars with a new finite element model. The finite element is based on the interpretation of the steel stress distribution and, thus, is flexibility-based. It is characterized by robust and stable numerical behavior even in the presence of significant strength loss and softening as might be the case with reinforcing bars of insufficient anchorage length. After a brief description of the salient features of the model, the paper establishes the validity of the model by correlation of analytical with experimental results on anchored reinforcing bars under severe load reversals. Several parametric studies are presented in order to study analytical features of the model, such as sensitivity to mesh reinforcement and number of integration points. A second objective of the parametric studies is to investigate the effect of key material on the hysteretic behavior of anchored reinforcing bars.

Failure analysis of R/C columns using a triaxial concrete model

Abstract Inelastic failure analysis of concrete structures has been one of the central issues in concrete mechanics. Especially, the effect of confinement has been of great importance to capture the transition from brittle to ductile fracture of concrete under triaxial loading scenarios. Moreover, it has been a challenge to implement numerically material descriptions, which are susceptible to loss of stability and localization. In this article, a novel triaxial concrete model is presented, which captures the full spectrum of triaxial stress and strain histories in reinforced concrete structures. Thereby, inelastic dilatation is controlled by a non-associated flow rule to attain realistic predictions of inelastic volume change at various confinement levels. Different features of distributed and localized failure of the concrete model are examined under confined compression, uniaxial tension, pure shear, and simple shear. The performance at the structural level is illustrated with the example of a reinforced concrete column subjected to combined axial and transverse loading.

New light on performance of short and slender reinforced concrete columns under random loads

Reinforced concrete (RC) columns are often designed and assessed under the assumption that axial loads and bending moments are applied simultaneously and are perfectly correlated. Cases, however, may exist where loads are applied sequentially with varying degrees of correlation between them. This study lays the groundwork for the development of performance-based methods of assessment and design of RC columns under random loads. The effects of load path and load correlation are both taken into account. Section interaction diagrams are used as limit states to derive iso-reliability contours for RC columns under different load histories and correlations. Multiple column limit states are considered, including section-based and fiber-based limit states.

Nonlinear Dynamic Analysis of a Full-Scale Unreinforced Adobe Model

This paper describes the results of a numerical study of a full-scale adobe building model tested on a shaking table. Material properties of adobe masonry were calibrated to represent the wall in-plane seismic behavior, based on a prior numerical analysis of an adobe wall carried out by the authors. The inelastic part of the constitutive model was represented by a softening curve in tension and by a hardening/softening behavior in compression; thus, the fracture energy is a key issue in the modeling process. A finite element model that relies on a homogenous continuum approach was developed in Abaqus/Explicit software. The damage evolution in the numerical simulation represented fairly well the experimental crack pattern, for in-plane and out-of-plane seismic effects. Overall, the calibrated material properties and the explicit solution scheme proved to be appropriate for simulating the seismic behavior and predicting capacity of unreinforced adobe structures subjected to seismic loading.