Strength and ductility of RC jacketed columns: A simplified analytical method
Introduction
Jacketing of reinforced concrete (RC) columns is a technique widely adopted in current engineering practice to retrofit existing weak members and increase their strength and ductility. The method consists in casting a RC layer (jacket) around the column, in order to increase the confinement effect on the member and/or enlarge the cross section. The effect provided by the jacket depends on whether or not it is directly loaded (i.e. when the jacket is continuous and well connected in correspondence of the slabs) or indirectly loaded (i.e. when a gap exists between the jacket and the slabs). In the first case, a core–jacket composite action as well as the confinement effect due to external stirrups, which enhance the axial capacity [1], [2], [3], [4], takes place. Conversely, if the jacket is indirectly loaded the main effect of the technique is the confinement pressure induced by the external layer on the inner column core. In both cases, the amount of transverse and longitudinal steel is crucial for the overall efficacy of the technique, as well as the thickness of the jacket.
To evaluate the strength and deformation capacities of a jacketed element Eurocode 8 [5] allows to make three simplifying assumptions: (i) absence of slippage between old and new concrete; (ii) application of concrete properties over the full section of the element; (iii) neglecting of the confinement effects and buckling of longitudinal bars. Moreover EC8 assumes the full axial load acting on the jacketed element (core–jacket composite action). The strength and ductility capacity of the jacketed member obtained under these assumption (monolithic member) is then calibrated by applying suitable multipliers or monolithic factors , commonly derived from empirical analysis [6], [7], [8]. While the Eurocode approach has the advantage of being quite expeditive for the engineering practice experimental studies have shown that monolithic factors values show a large dispersion as they are sensitive to the applied axial load, percentage of longitudinal reinforcement and relative strength of the core and jacket concrete [8], [9].
A different approach can be found in the literature where a number of experimental [2], [3], [4] and theoretical [10], [11], [12] researches have tried to evaluate the influence of different aspects such as preload, core–jacket interface treatment and rebar slippage in column-footing joint on the capacity of the RC jacketed member.
An iterative algorithm for calculating the lateral response curve of RC jacketed members, including the relative slip at interface between old and new concrete, was proposed in [10]. The authors proposed a model based on the estimation of crack spacing, taking into account the possible presence of dowels and the concrete frictional resistance at interface.
The case of jacketed columns subjected to axial load and bending moment is studied in [11] by means of non-linear finite element analyses validated through a set of experimental tests. The authors found that the influence of the old-new concrete interface cannot be neglected and that strength degradation at the interface can be modelled by reducing the coefficients of friction and adhesion. Other studies, however, showed that the interface influence is significantly reduced by roughing the existing column surface, or by using bonding agents or steel connectors before the jacket is applied [13], [14].
More recently a theoretical model to calculate proper constitutive laws for old and new concrete and steel was proposed and validated with experimental data available in the literature [12]. The analyses included confinement effect and buckling of longitudinal bars. The case of eccentrically loaded columns was studied through a numerical approach based on the discretization of the section by means of the fibre model.
Finally in [15] the author has proposed a stress block approach to model the different mechanical properties of concrete in the core and in the jacket which also takes into account the effect of confinement and buckling of bars.
This paper extends the approach presented in [15] and provides a simplified estimation of strength and ductility of RC jacketed columns subjected to axial load and uniaxial bending moment, under the assumption of absence of slippage at core–jacket interface.
Stress block coefficients are evaluated for different values of pitch of stirrups and axial strain. Moment–curvature curves are derived with few points and ductility analysis is carried out for both directly loaded jackets. Results obtained are compared with numerical analyses performed with OpenSees [16]. In this case, sections are modelled with a square fibre discretization and the constitutive law of confined concrete available in the OpenSees library has been adopted.
The proposed method considers the effect of the different concrete properties between core and jacket and includes confinement effects and buckling of longitudinal bars. Consequently, it removes the previously mentioned hypotheses (ii) and (iii) of EC8 approach. The proposed methodology can be reliably used under the assumption of negligible interface bond degradation. However, it should be also noted that even if slippage is not considered, the use of new monolithic factors especially devoted to address its effect would be a possible solution for including slippage in the calculation.
Section snippets
Constitutive law of materials
The concrete constitutive law adopted in this study takes into account the effect of confinement. In particular Mander et al. model [17] was adopted as it was shown in [12] to be suitable for both the compressive behaviour of jacket and core.withwhere in MPa and .
As it is well-known, the peak stress and the peak strain of confined concrete have to be calculated on the basis of the effective confinement pressure .
This can be simply
Comparisons with numerical analyses and experimental data
The proposed model is validated with experimental data available in the literature [2] and with numerical analyses carried out with OpenSees [16]. OpenSees was chosen for the wide library of constitutive models that allows for a complete modelling of the case study, including confined and unconfined concrete.
In particular, a ZeroLengthSection element is created between two nodes (see Fig. 8). Node 1 is fixed while loads are applied at node 2. The analysed section is subdivided with the classic
Ductility calculation
One of the main advantages in adopting an easy hand-computing procedure is the evaluation of important design parameters.
In fact, if the top concrete compressive strain is set equal to the ultimate value the procedure described in Section 2 is able to provide the ultimate moment and curvature of the section.
The computation of curvature corresponding to the yielding of the jacket steel is more difficult to be performed, since the concrete strain at the top of the
Design considerations and limits of applicability
The proposed approach allows for easy design calculation of the flexural behaviour of RC jacketed sections.
When adopting the model, it should be noted that the following assumptions are made: – absence of slippage between old and new concrete; – application of full axial load over the jacketed member; – perfect bond between concrete and steel bars.
However, since cracks open in the outer shell and slippage may occur between the inside core and the outside jacket if the two surfaces are not
Conclusions
In this paper, a simplified analytical method is presented to calculate the moment–curvature curve for RC jacketed columns. The model is based on a step-by-step procedure, based on the stress-block approach. From a comparison with numerical analyses carried-out with OpenSees and experimental published data the following conclusions can be drawn:
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The stress-block approach is suitable to be applied to RC jacketed sections if the parameters are well-calibrated.
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Results derived with the proposed
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