Effect of eccentricity in reinforced concrete beam-column-slab connection under cyclic loading

Abstract

Beam–column connections are one of the most critical elements of reinforced concrete structures, especially in seismically active regions, and have been extensively evaluated experimentally and numerically. However, very limited experimental studies about eccentric reinforced concrete connections including the effect of connected slabs are available. This study presents the experimental results of two half-scale eccentric beam-column-slab connections subjected to quasi-static cyclic loading. The horizontal eccentricity (e_h) is maintained at 12.5% and 25% of column width (b_c) for specimens 1 and 2, respectively. The damage pattern, performance levels, displacement ductility (μ_D), energy dissipation, and connection strength and stiffness are compared for both specimens, and the effect of eccentricity is evaluated. It is concluded that the eccentricity has no significant effect on the lateral load carrying capacity; however, the overall strength degradation increases with the increase in eccentricity. Similarly, the elastic stiffness of specimen 2 decreased by 14% as the eccentricity increased from 12.5% to 25%; however, the eccentricity had no significant effect on the overall stiffness degradation. μ_D decreased by 43%, and the energy dissipation capacity decreased by 40% in specimen 2 with higher eccentricity. The story drifts corresponding to the performance levels of the life safety (LS) and collapse prevention (CP) were found to be 28% lesser in specimen 2 than in specimen 1.

Graphical abstract

Keywords

corner connection / eccentricity / strength degradation / stiffness degradation / energy dissipation / performance levels

Introduction

Beam–column connections are a critical element in reinforced concrete (RC) structures, especially for earthquake loading. Beam hinging is the most desirable mode of failure, whereas column hinging and joint shear failure should be avoided as per the capacity design philosophy of connections [1]. Beam-column connections in RC structures have been an active area of experimental research since the 1960s [1]. Many of these studies have led to the development of ACI 352R-02 [2] guidelines for connection design. Edge beams are sometimes constructed flush with the exterior columns, resulting in eccentricity, as shown in Fig. 1. Torsional forces develop in the connection owing to this eccentricity, resulting in additional shear demand. ACI 352R-02 [2] indirectly considers the effect of this eccentricity by reducing the effective width of a connection for calculating the shear strength.

Many researchers have attempted to quantify the effect of eccentricity on the strength and behavior of RC beam–column connections. The eccentricity affects the ultimate strength of the connection, and the flexure mode of failure changes to the shear failure mode accompanied by a torsional effect. Similarly, the vertical eccentricity (connection with different beam depths) also affects the joint shear strength and overall performance of the connections [3]. In eccentric connections, the joint shear deformation is approximately four to five times on the joint face near the beam/flush side compared to the far side/offset side of the joint [4]. The displacement ductility (μ_D) factor for connections with no horizontal eccentricity (e_h) ranges from 4 to 8, compared to 2.5 to 5 for eccentric specimens [4]. The confinement of the concentric connection was excellent compared to the eccentric connection; even at 4% drift, the concentric connection showed negligible diagonal compressive strain compared to the eccentric one [5]. Additionally, many other researchers have discussed the negative effect of eccentricity in reinforced concrete connections [6–21].

It is believed that the slab may reduce the eccentricity effect by shifting the resultant force of the beam and slab longitudinal bars toward the column centerline. Shin and LaFave [1] and Canbolat and Wight [6] tested exterior beam-column-slab subassemblies to evaluate the effect of the slab on eccentric connections. They concluded that the slab reduces the negative effect of eccentricity. This study focuses on eccentric corner beam-column-slab subassemblies. Eccentric beam–column corner connections with a slab portion of a width equal to the effective width (b_e) as defined in section 8.4.1.8 of ACI 318-14 were evaluated to study the eccentricity effect [22]. Very few experimental studies have been conducted on eccentric corner beam-column-slab connections. Consequently, the recommendations of ACI 352R-02 regarding eccentric connections are based on very limited experimental work. Therefore, an experimental study was conducted to study the effect of the slab on the inelastic behavior of eccentric corner beam–column connections by evaluating the damage pattern, μ_D, elastic stiffness, overall stiffness, strength degradation, performance levels, and energy dissipation. The outcomes of the current study will facilitate a better understanding of the behavior of beam-column-slab connections.

Methodology

A half-scaled model was selected, and the specimens were scaled down using dimensional analysis and the Buckingham Pi Theorem. The stress, strain, and Poisson’s ratio of the materials used in the specimens were kept identical to those of the prototype materials. The eccentricity introduced was e_h = b_c/8 (b_c is the column width, ACI 352R-02 limit for concentric connections) in specimen 1, and e_h = b_c/4 in specimen 2. Both specimens were extracted from the corner of an RC frame with a slab width equal to the effective width “b_e” as defined in section 8.4.1.8 of ACI 318-14. It was assumed that the point of contra-flexure occurs at the mid-span of the spandrel beam and mid-height of the columns. The reinforcement details are shown in Fig. 2. Reinforcement bars were provided with standard seismic hooks. A one inch (25.4 mm) clear cover was provided in all the members. The average cylinder compressive strength of concrete was found to be 4300 psi (29 MPa) on the specimen testing date. Similarly, the average yield and ultimate strengths of the reinforcement bars were found to be 63000 psi (434 MPa) and 107000 psi (738 MPa), respectively.

The specimens were subjected to quasi-static cyclic loading applied at the beam end, as shown in Fig. 3. The end constraints were selected to achieve realistic boundary conditions of a two-dimensional frame. A pin connection was provided at the bottom of the column, whereas a roller support was used for the top end of the column to achieve unrestrained motion in both the upward and downward directions. Similarly, a constant axial load of 32 tons resulting in 500 psi stress was maintained over the column during the application of the cyclic loading on the beam. The story drift was calculated using Eq. (1) and applied in sequence, as depicted in Fig. 4. Each drift cycle was repeated three times to study the strength degradation and energy dissipation for each cycle.

(1)Drift=\left(\frac{\mathrm{\Delta }}{L_{\mathrm{b}}+0.5h_{\mathrm{c}}}\right)\times 100,

where Δ is the beam tip displacement, L_b is the length of the beam, and h_c is the depth of the column parallel to the beam axis.

All the specimens were instrumented with linear variable displacement transducers (LVDTs), potentiometers, and strain gauges at critical locations, as shown in Fig. 5. Two LVDTs (3 and 4) were installed diagonally at the exterior face of the joint, whereas four (5, 6, 7, and 8) of them were installed on the beam near the beam–column interface to capture the joint deformation and beam rotation at different story drifts, respectively. Similarly, two displacement transducers (1 and 2) were installed at the beam tip to record the displacements. Further, two LVDTs (10 and 11) were used to capture the out-of-plane displacements of the specimen and one for the column base displacement. Strain gauges (5 and 10 mm) were installed at critical locations in each specimen. At the longitudinal bars of the beam and slab, the strain gauges were installed within 1/2 effective beam depth (d) from the beam–column interface, where based on previous studies, the plastic hinge was expected to develop [1,6]. Similarly, strain gauges on the column bars were installed just below the beam longitudinal bars. Additional strain gauges were also installed at the middle joint hoops on both the exterior and interior sides.

Results and discussion

Cracking pattern

The final crack patterns are shown in Figs. 6 and 7. The inception of the first hairline cracks at the beam–column interface in specimens 1 and 2 was observed at 0.5% and 0.7% story drift, respectively. The distribution of cracks in both specimens was similar in the initial stages. It was observed that the cracks on the interior and exterior faces of both specimens extended gradually toward the beam tip from the beam–column interface, exhibiting excellent energy dissipation. The widening of the cracks started at 1.5% story drift in both specimens with relatively negligible further extension. Diagonal cracks were not observed in either specimen. However, the pulling out of the beam longitudinal bars was observed after 1.5% drift in both specimens and continued until the end of the test. At the end, no significant difference in damage patterns was observed for either specimen. This is primarily because of the slab, which reduces the eccentricity effect. Similar results were observed by Shin and LaFave [1] and Canbolat and Wight [6]. An interesting future study may involve comparing the experimentally observed crack patterns with the fracture patterns of the phase field model (PFM) [23–30].

Force-deformation behavior

Figure 8 shows the lateral load vs. displacement (hysteresis curves) of the two specimens. It was observed that the hysteresis curves exhibit a pinching effect in the middle. The pinching was greater in specimen 2 owing to the high eccentricity as compared to Specimen 1. A similar behavior was observed by Shin and LaFave [1] and Canbolat and Wight [6]. The pinching is mainly because of the bond slip, reinforcement yielding, and concrete cracking. Specimen 1 exhibited linear behavior until a drift of approximately 0.5%, whereas specimen 2 demonstrated linear behavior until a story drift of approximately 1% in both the negative and positive loading directions. Both specimens reached their maximum lateral strength at 1.5% drift.

The maximum lateral strength capacity of specimen 1 at 1.5% drift was recorded as 31.56 kN and that of specimen 2 was 34.28 kN. Similarly, envelope curves for both specimens were plotted by noting the maximum lateral load capacity and the corresponding displacement at each displacement cycle in both the negative and positive directions of loading. Finally, the average envelop curves were obtained by averaging both the negative and positive envelope curves for both specimens, as shown in Fig. 9. It can be observed from Fig. 9 that the strength degradation at 1.5% drift in specimen 2 was rapid compared to specimen 1 owing to high eccentricity.

Bilinear idealization

The bilinear idealization, i.e., elasto-plastic curves were developed from average backbone curves, using the equal energy principle, i.e., by equalizing the elastic and total energies under the experimental and idealized curves. Figure 10 shows the experimental and idealized curves for both specimens.

The displacement ductility (μ_D) was calculated for both specimens using Eq. (2):

(2){\mu }_{\mathrm{D}}=\frac{{\mathrm{\Delta }}_{\mathrm{u}}}{{\mathrm{\Delta }}_{\mathrm{y}}},

where “Δ_u” is the ultimate displacement and “Δ_y” is the yield displacement. The ultimate displacement “Δ_u” in specimens 1 and 2 occurred at 3.5% and 2.52% drift levels, respectively. Specimen 2 reached the ultimate state earlier owing to the high rate of strength degradation. Similarly, the yield displacement “Δ_y” in specimens 1 and 2 occurred at 0.5% and 0.63% drift levels, respectively. These drift levels correspond to the initiation of cracking in both specimens. Using Eq. (2), the displacement ductility (μ_D) of specimens 1 and 2 were found to be 7 and 4, respectively. Joh et al. [4] obtained displacement ductility in the range of 2.5 to 5 for eccentric connections and 4 to 8 for concentric connections.

The elastic stiffness was determined from the idealized elasto-plastic curve and was found to be 3.9 kN/mm for specimen 1 and 3.35 kN/mm for specimen 2, indicating a decrease in the elastic stiffness with the increase in eccentricity. However, eccentricity has no significant effect on the overall stiffness degradation, as shown in Fig. 11.

Performance levels

Three performance levels, as described in the American Society of Civil Engineers standard (ASCE/SEI 41–06), were determined for both specimens: immediate occupancy (IO), life safety (LS), and collapse prevention (CP). The IO level is taken as the story drift corresponding to yield displacement “Δ_y”, whereas the CP level is considered as the story drift corresponding to a lateral strength equal to 80% of the peak strength (20% strength degradation). Similarly, the LS level is considered as 75% of the CP level.

The performance levels of both specimens are shown in Fig. 12, and the corresponding values of the story drifts are listed in Table 1. It can be observed from Table 1 that the drifts at the LS and CP levels of specimen 2 decreased by 28% compared to specimen 1. This is primarily because of the rapid strength degradation in specimen 2. However, the IO level was almost similar in both cases because the performance of both specimens was similar in the initial stages of loading.

Energy dissipation

Equivalent viscous damping was calculated for both specimens using Eq. (3) [31].

(3){\mathit{\xi }}_{\mathrm{d}}=\frac{E_{\mathrm{d}}}{2\mathrm{\pi }{E}_{\mathrm{inp}}} ,

where E_d is the energy dissipation per cycle, and E_inp is the input energy. Because three cycles were used for every drift, the energy dissipation E_d was calculated as the average area of the three cycles for every drift. The input energy E_inp was calculated using Eq. (4) [31].

(4)E_{\mathrm{inp}}\left(\mathrm{Input\; energy}\right)={\displaystyle \frac{\mathrm{1}}{\mathrm{2}}}\{{\left(L{\mathrm{\Delta }}^{\prime }\right)}_{+\mathrm{i}\mathrm{v}\mathrm{e}}+{\left(L{\mathrm{\Delta }}^{\prime }\right)}_{-\mathrm{i}\mathrm{v}\mathrm{e}}\},

where L and {\mathrm{\Delta }}^{\prime } are the maximum load and corresponding displacement, respectively, in both the positive and negative loading directions.

It can be observed from Fig. 13 that the percent damping in specimen 1 increased gradually from 0.3% to 1% story drift owing to the hairline cracks. A relatively rapid increase in percent damping was observed from 1% to 2% drift because of the extensions and widening of cracks. Beyond 2% drift, the percent damping remained practically constant with a slight decrease at the end because no significant cracks were produced beyond this point, and the energy was dissipated primarily because of the opening and closing of existing cracks. Similarly, it was observed for specimen 2 that the percent damping increased rapidly from 1% to 2% story drift owing to the formation of major cracks in this drift range, followed by no change from 2% to 3%, and a slight increase from 3% to 3.5% story drift. The overall performance of specimen 1 was excellent compared to that of specimen 2, as shown in Fig. 13.

The accumulative dissipated energy was calculated by numerical integration of the dissipated energy for the three cycles corresponding to each drift level. The accumulative dissipated energy at 3.5% drift in specimen 1 was 1.68 times that of specimen 2, as shown in Fig. 14.

Conclusions

The following conclusions were drawn from the results obtained in this study.

1) The eccentricity has no significant effect on the lateral load carrying capacity; however, the overall strength degradation increases with the increase in eccentricity. Similarly, the eccentricity has no significant effect on the damage mechanism. This may be because of the slab portion as well as the pulling-out of the longitudinal bars. The pulling-out may have occurred because of the construction joint provided at both the bottom and top of the columns, as per section 3.2.2.2 of ACI 224.3R-95 [32].

2) The elastic stiffness of the specimen decreased by 14% as the eccentricity increased from 12.5% to 25% of the column width. However, the eccentricity has no significant effect on the overall stiffness degradation. The displacement ductility decreased by 43% as the eccentricity increased from 12.5% to 25% of column width.

3) The energy dissipation capacity decreased by 40% as the eccentricity increased from 12.5% to 25% of column width. The story drifts corresponding to the performance levels of the life safety and collapse prevention were found to be 28% lesser in specimen 2 than in specimen 1.

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