It is expected that during strong earthquakes, longitudinal reinforcing steel in reinforced concrete structural elements may undergo large tension and compression strain reversals. Because of insufficient tie spacing, this repeated loading into the inelastic range may lead to buckling of steel reinforcing bars. Even though this problem has been studied by several researchers, most of these studies have been based on monotonic behavior. In this research, steel coupons were machined from steel reinforcing bars conforming to most of the ASTM A 706 specifications. These specimens were tested under axial-strain-controlled monotonic and reversed cyclic axial loading. The tests were performed until the specimens failed, in all cases under compressive loading. To study the effects of the ratio of spacing of lateral supports (Sh) to bar diameter (D) on reinforcement stability, tests were performed for Sh /D ratios of 2.5, 4, 6, and 8. Based on observed buckling behavior in reinforcing bars under cyclic (reversed) loading, a procedure is proposed for predicting onset of buckling. The use of this procedure, along with an analytical model proposed in the literature for the cyclic behavior of reinforcing steel, gave results that were in good agreement with experimental results obtained in this study.
Results from moment-curvature analysis are important for evaluating the seismic performance of reinforced concrete (RC) elements. In this type of analysis, it is necessary to know the stress-strain behavior of reinforcing steel that includes the effect of buckling.
Even though the problem of reinforcement stability has been studied by several researchers, most of these studies have been based on a monotonic behavior, and limited research has been conducted considering the cyclic behavior of reinforcing bars including buckling (Monti and Nuti 1992; Mander et al. 1994; mention that in most studies of reinforcement stability, a con-Suda et al. 1996; Pantazopoulou 1998). It is also worthy of siderable scatter on the experimental load associated with buckling of reinforcing steel is expected for two reasons: (1) the variability of defining the buckling load based only on observation and (2) the difficulty in measuring strains in reinforcing bars in a concrete member after yielding. These factors have to be considered when evaluating existing data related to reinforcement stability or when conducting new research on the subject.
Several factors affect the onset of buckling of reinforcing bars in RC elements, such as the hoop influence on restraining a longitudinal bar, the splitting strength of cover concrete, or the lateral expansion of the concrete core at large compressive strains. The evaluation of the influence of these factors and their relationships is outside the scope of this investigation. This paper is aimed at studying the problem of reinforcement stability considering only the cyclic (reversed) behavior of re- inforcing steel and the unsupported length of reinforcement. Results of an analytical and experimental investigation on re- inforcement stability conducted at the National University of Mexico are described here. Based on these results, a procedure is proposed for evaluating the cyclic (reversed) stress-strain behavior of reinforcing steel including the effect of buckling.
Compression Monotonic Curve
Testing of reinforcing steel under compression has been less frequent than testing under tension. This is because of the ad- ditional difficulties in performing compression tests, mainly caused by potential buckling problems, inherent in this type of test. The lack of sufficient information on compressive test- ing of short reinforcing bars might explain why most studies on the seismic response of RC structures have been performed based on the assumption that a monotonic stress-strain curve of a short reinforcing bar in compression is equal and opposite to the corresponding curve in tension. However, experimental results have shown that when using the common definition of stress (which uses the initial cross-sectional area of the element), these curves are different (Mander et al. 1984; Dodd and Restrepo 1995). Dodd and Restrepo (1995) have found that in the natural coordinate system, which takes into account the instantaneous cross-sectional area of the element, the compression and tension curves are equal and opposite. Based on this finding, they defined the compressive stress, fcs, and compressive strain, cs, as follows.
CYCLIC BEHAVIOR OF SHORT REINFORCING BARS
Several authors have proposed analytical models for estimating the cyclic stress-strain behavior of reinforcing bars in the absence of buckling (Mander et al. 1984; Dodd and Restrepo 1995). The model proposed by Dodd and Restrepo (1995) describes the Bauschinger effect by means of a softened curve and is based on data collected from reinforcing steel manufactured in New Zealand. This model uses the instantaneous geometry of the reinforcing bars. The model proposed by Mander et al. (1984) considers the Bauschinger effect and defines the cyclic stress-strain behavior using several rules for reversal from skeleton curves associated to the tension and compression cases. Fig. 3 shows results using this model and results of cyclic tests on Mexico manufactured reinforcing bars in the absence of buckling. A comparison of these curves shows a good agreement between the analytical and experimental results.
BUCKLING OF REINFORCING BARS
Several experimental and analytical investigations have been conducted in the past on buckling in reinforcing bars. However, most of these investigations have been performed considering monotonic loading and either the reduced or tangent modulus theory (Bresler and Gilbert 1961; Mander et al. 1984; Scribner 1986; Papia et al. 1988; Mau 1990; Watson et al. 1994). Limited research has been done on the stability of reinforcing bars under cyclic (reversed) loading. Monti and Nuti (1992) have proposed an analytical model for predicting the cyclic behavior of reinforcing bars including buckling. This model is based on results of a series of monotonic and cyclic tests on steel rebars and requires the calibration of several parameters using data from cyclic tests on reinforcing bars. Pantazopoulou (1998) has studied the mechanics of longitudinal bar buckling in RC elements and has shown the need to consider the interaction between tie effectiveness, tie spacing, core deformation capacity, and bar diameter. From an analysis of experimental evidence, this author has proposed design empirical rules for the tie spacing required to prevent buckling of longitudinal reinforcement. However, since the observed buckling strain was reported in only a few of the reviewed studies, the end of the member’s usefulness was obtained from global response observations. That is, buckling strain was not considered directly.
Suda et al. (1996) have performed the only analytical and experimental study known of by the writers regarding the instability of reinforcing bars in RC elements under cyclic loading. They performed cyclic (reversed) loading tests on RC columns in which the reinforcing bars had a new instrumentation system for measuring strains beyond the yielding stage. Results of this research indicate that longitudinal bar buckling in RC elements subjected to cyclic (reversed) loading might occur when the bars are under a compressive stress in a tensile strain range. Based on their findings, Suda et al. (1996) have proposed a model for representing the cyclic behavior of steel reinforcing bars in RC elements.