Debonded reinforcing bars are shown to enhance development of catenary action in beams
Recent tests of planar subassemblies of a 10-story reinforced concrete (RC) frame structure, comprising two beams and three columns, have shown that the development of catenary action under a central column loss scenario is limited by fracture of the bottom flexural reinforcement in the beams.1 Similar behavior has been observed in other tests of RC frames or assemblies under column removal scenarios.2-4 Most of the tested specimens failed in a similar manner: tensile fracture of the reinforcing bars at the beam ends. Figure 1 shows one of the fractured bottom bars at a wide flexural crack that developed at the beam-central column interface during a subframe assembly test. Strain localization occurred in the exposed bar segment at the crack due to the greater axial constraint provided by concrete bonded to the embedded bar segments on each side of the crack.
Validated, detailed finite element (FE) models of an intermediate moment frame (IMF) assembly (complying with Section 21.12 of ACI 318-025) have confirmed the existence of this strain localization.6 As shown in Fig. 2, the FE models verify that a bonded bottom reinforcing bar exhibits a sharp increase in strain near an unsupported central column, while a bottom bar with a debonded length of one beam depth exhibits minimal strain localization. This indicates that debonding the bottom reinforcing bars at the beam ends will delay fracture, enabling a beam to sustain larger rotations, increased catenary forces, and increased vertical load-carrying capacity under a column removal scenario.
Figure 3 schematically illustrates the concept of using a debonding technique to avoid strain localization at dominant crack openings. Based on this concept, a simple approach for debonding bars is proposed herein, and this approach is validated through an experimental study. Furthermore, its effectiveness in resisting disproportionate collapse (commonly known as progressive collapse) is verified by computational analysis. The optimum debonded length and the behavior under seismic loading conditions are also evaluated numerically.
In general, the negative bending moment capacity of beam end sections is larger than the positive bending moment capacity. Under a column loss scenario, the bottom reinforcing bars are thus likely to fracture before the top reinforcing bars. On that basis, as well as the fact that debonding of the top bars could have undesirable effects on the connection stiffness, only bottom bar debonding was considered in this study.
Three specimens were investigated under uniaxial tensile load to demonstrate the effectiveness of a technique for debonding reinforcing bars from the surrounding concrete. The efficacy of debonding reinforcing bars at a cracked zone was also evaluated numerically to determine its effectiveness in delaying the fracture of bars and providing enhanced ductile behavior.
Each specimen consisted of two 10 x 48 in. (25.4 x 1219 mm) concrete cylinders connected by one No. 8 (No. 25) reinforcing bar (Fig. 4). A 1/4 in. (6.4 mm) gap between the two cylinders was designed to represent a crack opening. The specimens were pulled in the longitudinal direction until the reinforcing bar fractured. The force was applied through a T-shaped steel loading fixture at each end of a specimen. The force was transmitted from the fixture to the concrete by means of four high-strength 7/8 in. (22.2 mm) diameter threaded bars which were connected to a 2 in. (51 mm) thick circular steel disk that served as the flange of the T-section of the loading fixture. The concrete formwork comprised round paperboard tubes.
The reinforcing bars were debonded using polyolefin heat-shrink tubing (when heated, the tubing shrinks in the radial direction to fit tightly over the bar [Fig. 5]). Specimens A, B, and C were fabricated with 0, 2, and 8 in. (0, 51, and 203 mm) debonded lengths on each side of the gap between the concrete cylinders, respectively.
The specimens were fabricated with self-consolidating concrete having a nominal compressive strength of 6000 psi (41.4 MPa). At the time of testing, the compressive strength of the concrete was 12,000 psi (93 MPa) based on the average of three 6 x 12 in. (152 x 305 mm) cylinder breaks. The No. 8 (No. 25) reinforcing bars met ASTM A706 GR 60 requirements, with measured yield and ultimate strengths of 70,000 psi (483 MPa) and 103,000 psi (710 MPa), respectively. The yield strain was 0.265% and the fracture strain was 16% with a gauge length of 8 in. (203 mm).
Instrumentation and test setup
Strain in the reinforcing bar was measured using strain gauges bonded to the bar surface. Gauges were applied to the bar over an 8 in. (203 mm) length on each side of the gap. The relative movement between two cross sections located at 3 in. (76 mm) from the gap was measured by displacement transducers (Fig. 4). Tensile loading was applied under displacement control at a rate of 0.15 in./ minute (3.8 mm/minute).
The specimens were loaded continuously until failure occurred. For all three specimens, failure was characterized by fracture of the reinforcing bar within the 1/4 in. (6.4 mm) gap. As shown in Fig. 6, the specimen with no debonding (Specimen A) developed a cone-shaped concrete spall at the free surface of the crack opening. In contrast, the free surface of the crack opening exhibited no significant concrete damage in specimens with debonding (Specimen B and C). Figure 7 shows the applied load as a function of relative displacement over a 6.25 in. (159 mm) gauge length for the three specimens. While the peak load is almost identical for the three specimens, significant differences are observed among the peak displacements of the three specimens prior to failure. The specimen without debonding (Specimen A) failed at a displacement of about 1.45 in. (37 mm). Specimen B, with a debonded length of 2 in. (51 mm), failed at a smaller displacement of approximately 0.9 in. (23 mm), while Specimen C, with a debonded length of 8 in. (203 mm), failed at a larger displacement of approximately 2 in. (51 mm).
These results show that debonding over a very short length can actually result in earlier fracture than having no debonding. This can be explained by the de facto debonding (loss of bond) that occurred within the cone-shaped spall of Specimen A. It is apparent that if the debonded length is less than the depth of this damage zone in the concrete, then strains in the reinforcing bar will be localized within the shorter length of the debonded zone, resulting in earlier fracture. Specimen A, which had no debonding but did have a deep spall, therefore shows more ductile behavior than Specimen B, which had a short debonded length of only 2 in. (51 mm). However, Specimen C, which had a debonded length of 8 in. (203 mm), exhibited a 38% greater peak displacement than Specimen A. This clearly indicates that the debonding method, when applied over a sufficient length, can effectively delay the fracture of the reinforcing bar.
Analysis of axially loaded cylindrical prism test
For this study, detailed FE models of the three test specimens were developed using the LS-DYNA7 general-purpose software package. Concrete was modeled using eight-node solid elements with mesh size of about 1 in. (25 mm), while reinforcing bars were represented by two-node beam elements (Fig. 8) with mesh size of 2 in. (51 mm). A mesh sensitivity study showed that a further refinement of mesh size was not needed. A continuous surface cap model was used as the material model for concrete. The main features of the model include: isotropic constitutive equations, a yield surface formulated in terms of a three stress-invariant shear surface with translation for pre-peak hardening, a hardening cap that expands and contracts, damage-based softening with erosion and modulus reduction, and rate effects for high strain rate applications. Bond behavior between concrete elements and reinforcing bars was simulated by adding one-dimensional contact, allowing movement only along the longitudinal direction based on a predefined bond-slip relationship, and preventing penetration normal to the bar axis.6
Debonding between reinforcing bars and surrounding concrete was achieved by setting a very small value of the bond modulus (ratio of bond stress to slip). Further modeling details can be found in Reference 6. Figure 7 shows plots of the applied load versus displacement for the three modeled specimens along with the plots of the previously described experimental results. Good agreement between computational and experimental results validates the computational method used in this study. Relative to the fully bonded specimen, an unbonded length of 2 in. (51 mm) has a lower deformation capacity and an unbonded length of 8 in. (203 mm) has a higher deformation capacity.
Selected results from the analysis of a specimen with an 8 in. (203 mm) debonded length (Specimen C) are presented in Fig. 8. The damage index contours indicate some level of concrete damage starting at about 8 in. (203 mm) from the gap, corresponding to the location where the concrete was fully bonded to the central reinforcing bar. Also, the axial force in the reinforcing bar can be seen to be relatively constant within the debonded zone and to gradually decrease with distance away from the debonded zone.
For this study, FE models of an IMF assembly under a central column loss scenario were evaluated. The design of the modeled specimens was in accordance with ACI 318-02.5 Detailed information on the analyses is presented in Reference 6. IMF assemblies with debonded lengths of 0 (no debonding), 1D, 2D, and 3D were modeled, where D was the depth of the beam. The models were used to find the optimum debonded length, resulting in the largest displacement and peak load prior to bar fracture and beam failure without adversely affecting the stiffness of the beam. The computational model was validated with the experimental data for the case of no debonding.6 Figure 9 depicts the applied vertical load versus the vertical displacement of the central column, based on analyses with different debonded lengths. The figure shows that the debonded length of 3D provided the best performance (largest vertical load and displacement prior to failure). Because the differences in peak loads prior to failure were not significant between the cases with unbonded lengths of 2D and 3D, it's prudent to use 2D as the optimum length of debonding to avoid adversely impacting the stiffness of the connection. The results show improvements of more than 30% in the peak load with a debonded length of 2D for the IMF beam-column assembly analyzed herein.
Both the experimental and computational investigations showed that the proposed debonding method can effectively eliminate strain localization of reinforcing bars at wide cracks. Computational models showed that debonding of reinforcing bars at the beam ends in a beam-column assembly significantly increases the catenary resistance under a column loss scenario. However, it's also important to verify that the application of the proposed debonding method will not result in degraded performance under seismic loading.
To examine the effect of debonding the bottom reinforcement next to the column face under seismic loading conditions, a finite element model of a cruciform beamcolumn assembly was developed and subjected to lateral loading at the top of the cruciform. The cross-sectional dimensions and reinforcement details of the cruciform were the same as those used in the modeled IMF assembly.1 The lengths of the upper and lower columns were both 72 in. (1829 mm), and the lengths of the beams were both 120 in. (3048 mm). The same modeling technique that was used for the IMF assembly was employed for this model. Two loading conditions were considered as shown in Fig. 10: a) a monotonic, pushover displacement; and b) cyclic loading. For each loading case, analyses were conducted without debonding and with a debonded length of 2D on each side of the central column. The applied load versus the lateral displacement responses at the top of the column, for the monotonic and cyclic load cases, are shown in Fig. 10(a) and (b), respectively. In both loading cases, a small degradation in stiffness was seen in the responses from the cruciform with a debonded length of 2D. However, the overall response indicates that debonding the bottom reinforcing bars in the vicinity of the beam-column interface would have only a minor effect on the seismic resistance of the structure.
It should be pointed out that bar buckling was not included in the current model. Additional study is required to investigate whether the proposed debonding technique may affect the buckling behavior. It also must be noted that the debonding method presented herein was applied to a continuous reinforcing bar. When a reinforcing bar that is to be debonded will also have a lap splice or bar cutoff, adequate anchorage must be assured to develop the tensile strength of the bar.
Recent experimental results for reinforced concrete beam-column assemblies under a column removal scenario indicate that prior to failure of the assembly, tensile catenary forces develop in the beam as the beam-column joint deflection exceeds the beam depth, supplying additional gravity load-carrying capacity. However, this load-resisting mechanism is limited by the rotational capacity at the beam ends. Experimental observations indicate that the failure of the assembly is characterized by fracture of the bottom reinforcing bars at a major crack opening near the beam-column interface. Results of detailed finite element models of the beam-column assembly indicate that strain localization within the crack opening causes an early fracture of reinforcement, which limits the beam-end rotational capacity. The method proposed herein is based on the idea that such strain localization can be mitigated or eliminated if the reinforcing bar is debonded from the surrounding concrete in zones where major cracks are expected. Tensile tests of a No. 8 (No. 25) reinforcing bar embedded in concrete with a simulated crack opening were conducted with and without debonding in the region of the simulated crack opening. Debonding was achieved by decoupling the reinforcing bar from the concrete using polyolefin heat-shrink tubing. Experimental results showed that debonding of 8 in. (203 mm) on each side of the simulated crack increased the peak displacement by about 38%, compared to the case without debonding.
Computational analyses were conducted using a detailed finite element model validated against experimental results. The model showed that debonding of the bottom beam bars for a length of two beam depths on each side of a central column resulted in an improvement of more than 30% in the peak vertical load-carrying capacity under a column removal scenario. Modeling also showed that the debonding did not cause a significant degradation in the seismic resistance of the beam-column assembly.
The proposed approach thus enhances the resistance of RC frames to disproportionate collapse. Additional work is required to evaluate the efficiency of this debonding technique in more complex loading conditions and other configurations and detailing.
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Una forma sencilla para reducir el riesgo de derrumbe progresivo
Bao, Yihai; Lew, H.S.; Sadek, Fahim; y Main, Joseph;
En general, la capacidad del momento de flexiÓn negativa de las secciones de los extremos de las vigas es mayor que la capacidad del momento de flexiÓn positiva. Por ese motivo, en caso de pÉrdida de una columna, las barras de refuerzo de la parte inferior son propensas a fracturarse antes que las barras de refuerzo de la parte superior. Los estudios presentados en este artÍculo investigan la eficacia de una tÉcnica para mejorar la ductilidad en las secciones de los extremos de las vigas. El estudio muestra que el despegue de las barras de refuerzo del hormigÓn armado circundante retrasa la fractura de dichas barras y mejora el comportamiento dÚctil. Por lo tanto, el enfoque propuesto se muestra prometedor como mÉtodo para mejorar la resistencia de los marcos de hormigÓn armado a un derrumbe desproporcionado.
1. Lew, H.S.; Bao, Y.; Pujol, S.; and Sozen, M.A., "Experimental Study of RC Assemblies under a Column Removal Scenario,"
2. Yi, W.; He, Q.; Xiao, Y.; and Kunnath, S.K., "Experimental Study on Progressive Collapse-Resistant Behavior of Reinforced Concrete Frame Structures,"
3. Su, Y.; Tian, Y.; and Song, X., "Progressive Collapse Resistance of Axially Restrained Frame Beams,"
4. Yu, J., and Tan, K.H., "Experimental and Numerical Investigation on Progressive Collapse Resistance of Reinforced Concrete Beam Column Sub-assemblages," Engineering Structures, in press. (DOI:10.1016/j.engstruct.2011.08.040)
5. ACI Committee 318, "Building Code Requirements for Structural Concrete (ACI 318-02) and Commentary,"
6. Bao, Y.; Lew, H.S.; and Kunnath, S., "Modeling of Reinforced Concrete Assemblies under a Column Removal Scenario,"
7. Hallquist, J., LS-DYNA Keyword User's Manual,
Received and reviewed under Institute publication policies.
ACI Honorary Member H.S. Lew is a Senior Research Engineer in the
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