Keywords: reinforced concrete, non-linear finite element analysis, buckling, plastic hinges.

This paper presents a numerical study of slender reinforced concrete columns using nonlinear finite element analysis. The issue of the research is focussed on the rotational capacity of the discontinuity regions (D-regions). Such regions are close to the beam-column connections and are produced due to a sharp variation of the geometry, so that the general bending theory is not valid. The model is compared with experimental tests performed by the same authors. The influence on this parameter with respect to the axial load level, slenderness, and the amount of reinforcement is studied.

The authors have performed two projects in parallel (one experimental and one numerical) to characterize the plastic hinge behaviour of HSC columns. In this paper a numerical model is adjusted using the results from limited experimental tests. By using the adjusted numerical model it will be possible to perform a greater number of numerical experiments in order to develop simplified models of analysis and design of such columns.

Much work has been is developed in this field, but most of them mix the rotational capacity of the plastic hinge and the second order effects. This paper presents the initial results of the study of the plastic rotation capacity of the discontinuity regions in order to create a numerical model which may accurately recreate this behaviour. In order to do that, a plastic trend parameter (PTP) to quantify the plastic rotation will be used.

One of the objectives of the research project was to obtain the best numerical model which represents the same behaviour of the experiments with the lower computational cost. Thereby, two models were studied and compared: a nonlinear 1D finite element without distributing the plastic behaviour along the element; and a 2D finite element model with distributed cracking and a fixed crack model. A parameter to quantify easily the plastic rotation capacity was performed. It is based on a parameter introduced by Lopes and Bernardo [1], but including the axial load and the second order effects.

It was observed that the plastic rotation capacity depends sensibly both of geometric slenderness and axial load level. It defines the importance of the P- effect in the deformability of the supports. Also, it is shown that the plastic rotation capacity depends appreciably of the geometric slenderness. It defines the importance of the P- effect in the deformability of the supports. It is presented a decreasing tendency of the plastic rotation capacity with respect to the geometric slenderness. For the numerical model the same tendency is observed although with lower values.

The effect of the longitudinal reinforced ratio is not very important for this specimen, since this parameter was compared for high axial load levels. It is necessary to perform more experiments to check the effects of the longitudinal reinforcement on the capacity of plastic rotation for low axial load levels.

The numerical characterization of the plastic hinge is mesh-dependent, both for one-dimensional and for bi-dimensional models. The 1D model better characterizes the global behaviour but it does not represents correctly the plastic hinge region. Therefore, the plastic trend parameter (PTP) is not valid for the one-dimensional formulation. The 2D model characterizes properly the D-region although it needs higher computational cost, and cannot be used as a global model for the entire structure.

The influence of the parameters was verified: axial load level, geometric slenderness and longitudinal reinforcement ratio on the capacity of plastic rotation, noticing a great influence in the P- effects and the capacity of rotation in the plastic hinge over the deformability of normal strength columns. The parameter developed to analyze the behaviour in the plastic phase (PTP) seems to characterize their plastic rotation capacity. The study carried out using this parameter generally confirmed the most important tendencies observed for the behaviour by previous analyses (which used ductility indexes).

The range of the studied variables has to be defined to adjust their importance for the appearance of the plastic hinge. In this study was demonstrated that for some values of slenderness and axial loads, the columns failed due to instability without appearing the plastic hinge.

1

Lopes S.M.R. and Bernardo L.F.A. "Plastic rotation capacity of high-strength concrete beams", Materials and structures , vol 36, January-February 2003, 22-31. doi:10.1007/BF02481567

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