Experiment investigation of the influence of reinforcing bar buckling on seismic behavior of RC columns
Introduction
Laboratory evidences and earthquake damage observations indicate that the buckling of longitudinal steel bar is an important damage state of reinforced concrete (RC) columns when subjected to an ever-increasing side sway inelastic deformations [1], [2], [3], [4], [5], [6]. It is well known that bending moment combined with axial compression force will induce large strain on the edge of a section, and large tensile strains followed by high compression will bring the reinforcing bars to buckle and the concrete to crush or spall. Insufficient closely spaced transverse reinforcement will aggravate the inelastic buckling of longitudinal bars due to inadequate confinement when the cover concrete spalls. The full deformation history which associated with the amount of post-yield tension strain directly affects the buckling phenomena of reinforcing bars within RC column [7].
Experimental researches [8], [9], [10], [11], [12], [13], [14] and finite element analysis [15], [16], [17], [18], [19], [20], [21], [22], [23] of individual bars under monotonic and/or cyclic loads indicate that buckling behavior of steel bars obviously vary from the stress–strain curves of non-buckled ones, post-buckling behavior mainly depends on the slenderness ratio (), yield strength () and the initial eccentricity (). Dhakal and Maekawa [17] suggested that buckling behavior of steel bar depends greatly on the slenderness ratio and the square root of yield strength. Previous researchers studied the inelastic buckling of individual bars commonly based on average stress-strain relationships. The average stress is defined as the ratio of axial force to the cross sectional area (), the average strain is expressed as the ratio of total axial deformation to the buckling length of bar (). Since axial force () and total axial deformation () are easy to measure in the test of individual bars, it is convenient to investigate the buckling behavior of single steel bar on the basis of measured curves. Experimental and finite element results indicate that the compressive average stress is less than that of the bar without buckling by different levels depend on the degree of inelastic buckling, buckling after tensile yielding will cause average compressive stress to decrease continuously.
All aforementioned researches focused on the buckling of individual bars, however, buckled reinforcing steel bars behave differently in RC columns. The confinement of stirrups, the lateral dilation of core concrete at large compressive strains and the transverse constraint effect of cover concrete will change the buckling behaviors of longitudinal bars in RC section. Experimental and analytical researches on RC columns [1], [2], [3], [6], [7], [24], [25], [4], [26], [27], [28], [29], [30], [31], [32] reveal that main bars tend to buckle under large reversed cyclic deformations. Apart from the effects of core concrete and cover concrete, the post-buckling behavior of longitudinal bar mainly depends on the diameter, spacing and layout of transverse reinforcement, the diameter and yield strength of main bar. Among all the factors, the design and detailing of transverse reinforcement play a pivotal role in controlling the inelastic buckling of longitudinal bars. In addition to providing shear capacity [33], [34], [35] and confining the core concrete [36], [37], [38], transverse reinforcement also restrain the buckling tendency of main bars and do not allow the main bars to deform laterally at the tie locations [25], [4], [26], [30], the stability of main bar is a function of the effectiveness of tie arrangement. It is generally considered that the buckling length of longitudinal bar is equal to the distance between two consecutive stirrups, which is described as local buckling of reinforcing bars [8], [10], [20]. The situation that the buckling length varies from two to several tie spacing refers to global buckling of bars [2], [22], [39]. Therefore, insufficient amount of transverse reinforcement or yield of stirrup will lead to the increase of buckling length, and bigger inelastic lateral buckling displacement of longitudinal bar.
Since only a few experimental research have measured the buckling displacements of longitudinal bars in RC columns [3], it is remain unclear what are the differences between the buckling behavior of individual steel bar and that of longitudinal bar in RC column. Based on the theoretical synthesis reasoning of RC section, it was supposed that strength loss of the average compressive stress of buckled main bar will result in a reduction of moment capacity of RC section, thereby adversely affecting the section and member ductility [40], some studies even argued that the buckling of main bar usually causes a sudden loss of the load-carrying capacity and the ultimate displacement of RC columns [41]. Nevertheless, the theoretical reasoning has not been directly confirmed by the aforementioned experimental results of RC columns.
In this paper, a new method was adopted in an effort to measure the lateral buckling displacements of reinforcing bars within RC columns or individual steel bars more accurately, which is able to deal with the randomness of the buckling direction of corner bar in rectangular RC section reliably. Based on the proposed buckling displacement measuring method, seven nearly full-scale RC columns and a series of corresponding individual bars were tested under reversed cyclic loading, lateral buckling displacements were record to explore the buckling behaviors of reinforcing bars, the buckling displacements of individual bars were compared with the corresponding experimental results of longitudinal bar in RC sections, and the effects of longitudinal bar buckling on the bearing capacity and ductility of RC columns were investigated.
Section snippets
State-of-the-art
For a cyclic laterally loaded RC column, confined core concrete will crack and crush gradually. Even though transverse reinforcement confine the core concrete and prevent any further deterioration effectively at the stirrup locations, core concrete will transversely expand simultaneously on the compression side of RC section between two consecutive stirrups after cracks completely closed and large compressive strain prompted. In such cases, the transverse expansion of core concrete will result in
Experiment program
Previous researches prove that the slenderness ratio and yield strength of bars are two significant parameters of bar buckling [15], [16], [17], [18], [19], [20], [21], [22], [23]. Four column experimental tests by Moyer and Kowalsky [7] indicate that the amount of post-yield tension strain directly affects the buckling phenomena of reinforcing bars in RC columns, and the tension strain of bars directly related to the axial compression ratio of columns. Research results by Esmaeily and Xiao [48]
Hysteric curves
Fig. 5 shows the lateral force ()–top displacement () hysteresis loops of the tested columns, the cyclic responses of all tested units are ductile and show a stable hysteretic response. One of the major damage phenomena is the inelastic buckling of longitudinal bars, the onset of bar buckling generally occurred during the loading cycle of 3 ~ 5, which are marked in Fig. 5. Because the steel bar was hidden from view due to the cover concrete, it was difficult to directly observe the
Behavior of stirrup after bar buckling
The peak strain of stirrup “GB” in each loading cycle and the final shape of the stirrup and longitudinal bar in specimen C-2 are shown in Fig. 13. Test results indicate that stirrups in the tested specimen have not yielded during the loading even though the column was cyclic loaded to inelastic range with severe damage. Experimental observations also prove that longitudinal bars buckled between two adjacent stirrups due to adequate transverse reinforcement. Hence, the buckling length of single
Summary and conclusions
Seven large-scale cantilever square RC columns and corresponding individual steel bars were tested under cyclic loads, longitudinal bars all buckled between two adjacent stirrups due to adequately reinforced transverse reinforcement. Based on the measured lateral buckling displacements of bars, the inelastic buckling behaviors of longitudinal bars and the effects of bar buckling on the bearing capacity and ductility of RC columns were investigated.
The main outcomes of this study can be
CRediT authorship contribution statement
Hong Yang: Conceptualization, Methodology, Writing - original draft, Writing - review & editing, Supervision, Funding acquisition. Panxu Sun: Formal analysis, Investigation, Data curation. Yunjun Deng: Software, Validation, Visualization.
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgments
The authors would like to express their appreciation for the financial support provided by the National Natural Science Foundation of China (No. 51878100) and the Graduate Research and Innovation Foundation of Chongqing, China (Grant No. CYB18036). Any opinions expressed in this paper are those of the authors and do not reflect the views of the sponsoring agencies.
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