Uniaxial Bond Stress- Slip Relationship of Reinforcing Bars in Concrete. Department of Civil and Environmental Engineering, Sungkyunkwan University, Suwon 4. Republic of Korea.
Copyright . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. This paper documents a study carried out on the estimation of the bond stress- slip relationship for reinforced concrete members under axial tension loading. An analytical model is proposed that utilizes the conventional bond stress- slip theories as well as the characteristics of deformed bar and concrete cross- sectional area. 4 The Indian Concrete Journal * 2005! Utilization of Nonlinear Finite Elements for the Design and Assessment of Large Concrete Structures. I: Calibration and Validation. An equation for the estimation of the bond stress is formulated as the function of nondimensional factors (e. The validity, accuracy, and efficiency of the proposed model are established by comparing the analytical results with the experimental data and the JSCE design codes, as well as the analytical models given by Ikki et al. The analytical results presented in this paper indicate that the proposed model can effectively estimate the bond stress- slip relationship of reinforced concrete members under axial tension loading. Introduction. Bond of reinforcing bars to the surrounding concrete influences the behavior of reinforced concrete structures in many ways . It can be a key element for the ultimate load- carrying capacity of reinforced concrete structures since it affects the anchorage of bars and the strength of lap slices. Moreover, the deformation capacity of the members, and hence the redistribution capacity in statically indeterminate structures, is directly influenced by the bond. For these reasons, it can be said that a fundamental issue for reinforced concrete structures is the bond between the reinforcing bars and the concrete . This leads comparisons between various researches and test results on bond difficult. Most investigators have used pull- out tests that are commonly adopted in reinforced concrete bond studies . In most research, not a great deal of attention has been focused on the embedment length and the stress state in the concrete. The embedment lengths and the stress states have, therefore, not coincided with those in real reinforced concrete members. Because this has not been recognized by many researchers, results often show a significant difference to real behavior. In general, bond action in reinforced concrete members is represented by the bond stress- slip relationship. Many bond stress- slip relationships have been proposed and some of these have been formulated. These relationships have been used in the finite- element method (FEM) . However, most of the proposed relationships were derived from pull- out tests and differ from each other. The main limitation of the pull- out test is that it does not simulate the actual conditions in a reinforced concrete flexural member. Therefore, utilizing relationships derived from the pull- out test might be considered to contain inevitable problems. Consequently, it is necessary to establish a realistic bond stress- slip relationship that takes into account the actual conditions in a reinforced concrete flexural member, which is usually long embedment length and axial tension force at the cracking section. This article presents an analytical model to estimate the bond stress- slip behavior of reinforced concrete members based on the axial tension test. The models suggested for the estimation of the bond stress- slip relationship in the JSCE code . An analytical equation is formulated as an exponential function of the relative rib area and the nondimensional slip. The validity, accuracy, and efficiency of the proposed model are established by comparing the results of the present study with the results obtained from the analytical and experimental studies. In addition, a parametric study was performed to evaluate the effects of the bond factors. The results of analysis presented in this paper indicate that the proposed model can be used effectively to estimate the bond stress- slip relationship. Interaction between Reinforcing Bar and Concrete. With the growth of bond researches, a reinforced concrete structure was known as a composite structure . To put it concretely, when the external force is progressively applied to a reinforced concrete member, interfacial stresses between the reinforcing bar and the concrete are created and the capacity of the interface to transmit stresses begins to weaken at certain load levels. These irreparable damages spread to the surrounding concrete. As a result of this process, the capacity of the interface to transmit stresses gradually deteriorates and a slip of both materials inevitably occurs. As shown in Figure 1, the stress transfer mechanisms, which refer to the bond action, are usually expressed by the bond stress- slip relationship obtained from pull- out tests. The bond actions are comprised of an adhesive bond, a frictional bond, and a shear bond. In the case of deformed bars, the bond resistance capacity is mainly governed by the mechanical interlocking action. Figure 1: Bond stress- slip relationship. Relative Rib Area. In fact, the bar geometry, and more specially the rib geometry, governs to a high degree the general bond behavior and determines the bond resistance . In particular, as shown in Figure 2, the bar diameter , the rib height , and the rib spacing are found to be the most important parameters . In addition, deformed bars are currently mainly used for reinforcement in reinforced concrete structures. The best bond actions can be obtained by means of an appropriate combination of the 3 above mentioned parameters. Figure 2: Details of deformed bar. Rehm . The experimental evidence also proves that bond actions are relatively the same, provided that the relative rib areas are the same, and the rib face angle is greater than 3. The generally accepted values ranging between 0. In addition, the maximum bond stress obtained from specimens with short embedment show a steady increase that coincides with the increase of the relative rib area. Figure 3: Bond stress- slip relationships of short embedment and long embedment. Also, when the relative rib area increases, the maximum bond stress obtained from specimens with long embedment will have smaller values than that obtained from specimens with short embedment. However, even in cases where the embedment length is sufficient, an increase is shown in proportion to the relative rib area, even though the maximum bond stress is smaller than that of cases where the embedment length is short. Hence, the effect of the relative rib area on the bond action in the case of long embedment length needs also be considered. Stress State by Boundary Conditions. Generally, test methods used to measure bond stress and slip can be categorized into two methods, namely, pull- out tests and axial tension tests. The formulation of the bond- slip relationship has been developed for the following typical bond problems, as shown in Figure 4: (a) one side pull- out; (b) both sides pull- out. In these tests, the main limitation is that they do not simulate the actual conditions in a structural member. Due to the effect of the compressive force , concrete is in compression and the reinforcing bar is in tension. In reality, in the tensile zone of a reinforced concrete member, the concrete and reinforcing bar are both in tension. The presence of a lateral stress modifies the stress distribution shown in Figures 4(a) and 4(b) to a considerable degree. Figure 4: Typical stress distributions for (a) one side pull- out, (b) both sides pull- out, and (c) axial tension. In the axial tension tests shown in Figure 4(c), a monotonically increasing tensile force is applied to the two protruding ends of the reinforcing bar embedded in the concrete prism. The distribution of tensile stresses induced in the reinforcing bar and concrete will be varied as shown in Figure 4(c). This distribution is very similar to that of the tension face of a reinforced concrete flexural member. It can, therefore, be considered that utilizing the bond- slip relationships obtained from the axial tension tests in the analysis is more realistic than utilizing those obtained from the pull- out tests. Existing Models. The bond behaviors of reinforced concrete members have been studied extensively in the last century. A number of bond stress- slip relationships and corresponding bond models have been proposed in the last three decades. A number of popular bond models are introduced in the following paragraphs. In 1. 95. 7, Rehm . He also proposed the following bond model, which is a function of slip, and comparatively analyzed the bond stress distribution with the proposed model as. In 1. 96. 7, based on the pull- out tests and axial tension tests, Mugurama and Morita . Results from the above analysis concurred with the experimental results. However, in this model, it needs to be assumed that the slip corresponding to the maximum bond stress and the maximum bond stress obtained from the long specimens under axial tension is significantly smaller than that of the short pull- out specimens. In 1. 98. 7, Shima . Equation (4) were proposed for the bar with a long embedment and for the bar with a short embedment, respectively, while considering the strain effect in accordance with the boundary conditions. This model is beneficial when the concrete is under the compressive stress condition at the reinforcing bar level and can be applied to the analysis of the behavior of a reinforced concrete member without any experiment in order to determine experimental factors. For this reason, this model is the representative bond model that is currently being used in the analysis and design of reinforced concrete members as. However, (4) was obtained from the experimental results of a pull- out test for an anchored bar embedded in the footing of a reinforced concrete pier or column.
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