Seismic Performance of Reinforced Concrete Eccentric Beam-Column Connections with Floor Slabs

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1 ACI STRUCTURAL JOURNAL Title no. 101-S41 TECHNICAL PAPER Seismic Performance of Reinforced Concrete Eccentric Beam-Column Connections with Floor Slabs by Myoungsu Shin and James M. LaFave Two 2/3-scale reinforced concrete eccentric beam-column-slab subassemblies (edge connections with flush exterior edge-beam and column faces) were tested under large lateral displacement reversals. The main objective of the study was to investigate the effect of floor slabs on the seismic performance of eccentric beamcolumn connections. The specimens (with different eccentricities and edge-beam widths) exhibited similar behavior before they started to break down, and they also reached similar joint shear strengths. Based on these results, it was concluded that the floor slabs diminished differences between seismic performance of the specimens and increased joint shear strengths of the specimens when compared with other eccentric connections without floor slabs. Finally, ACI code design procedures for estimating nominal joint shear strength were quite conservative for the case of eccentric beam-column connections with floor slabs. Keywords: joint; reinforced concrete; slab. INTRODUCTION Beam-column connections are critical regions in reinforced concrete (RC) moment resisting frames designed to endure severe earthquakes. According to the capacity design philosophy, beam hinging (while avoiding column hinging and joint shear failure) is the most desirable failure mode to guarantee high energy dissipation during earthquakes, through large ductile inelastic deformations without overall strength degradation. 1 Since the mid-1960s, numerous experimental studies have been conducted to investigate the behavior of RC beam-column connections subjected to seismic loading and to establish adequate design methods. As a result, several key parameters governing the behavior of connections have been identified, and the effects of varying these parameters have been evaluated. The key parameters include relative column versus beam flexural strength, confinement of the joint core, joint shear stress, and anchorage of reinforcement in the joint region. Recently, Joint ACI-ASCE Committee 352 integrated results from many of these studies into a state-of-theart report entitled Recommendations for Design of Beam-Column Connections in Monolithic Reinforced Concrete Structures. 2 Most studies of RC beam-column connections have focused on concentric connections; few RC eccentric beam-column connection tests have been reported in the literature to date. 3-7 When a beam-column connection is subjected to seismic loading, the beam top and bottom forces from bending are transmitted to the column at the beam-column interfaces, producing relatively large joint shear forces. In an eccentric connection, the column centerline is offset from the beam centerline. Due to this eccentricity between beam and column centerlines, the transmitted forces may also induce torsion in the joint region, which produces additional joint shear stresses. To help better address this in design, Joint ACI-ASCE Committee 352 has called for additional research to clarify to what extent the presence of torsion and the increase in associated stresses will affect the capacity of this type of joint. 2 Joh, Goto, and Shibata 3 tested five cruciform beam-column connections, including two eccentric connections. The displacement ductility of specimens with eccentricity was only between 2.5 and 5, while specimens without eccentricity had displacement ductility ranging from 4 to 8. In their specimen with a flush face of the column and eccentric beams, the flush side of the joint had four to five times larger joint shear deformations than the offset side of the joint. Lawrance, Beattie, and Jacks 4 tested one cruciform eccentric beam-column connection. Eccentricity between beam and column centerlines did not affect the global strength of the specimen, but strength degradation occurred at lower displacement ductility than in companion concentric specimens. Although the column-to-beam moment strength ratio was high (roughly two), column longitudinal bars at the flush side experienced local yielding, partially resulting from torsion due to the eccentricity. Raffaelle and Wight 5 tested four cruciform eccentric beam-column connections. Inclined (torsional) cracks were observed on the joint faces adjoining the beams. Strains in joint hoop reinforcement on the flush side were larger than those on the offset side, which was attributed to additional shear stress from torsion. The researchers suggested that joint shear strengths of eccentric beam-column connections were overestimated with the then current Joint ACI-ASCE Committee 352 design recommendations 8 and that this could be rectified by using a proposed equation for reduced effective joint width. Chen and Chen 6 tested six corner beam-column connections, including one concentric connection, one conventional eccentric connection, and four eccentric connections with spread-ended (tapered width) beams to cover the entire column width at the beam-column interface. The researchers concluded that eccentric corner connections with spread-ended beams showed superior seismic performance to conventional eccentric corner connections. Finally, Vollum and Newman 7 tested 10 corner beamcolumn connections; each consisted of a column and two perpendicular (one concentric and one eccentric) beams. Various load paths were tested to investigate connection behavior, and performance improved significantly (in ACI Structural Journal, V. 101, No. 3, May-June MS No received March 3, 2003, and reviewed under Institute publication policies. Copyright 2004, American Concrete Institute. All rights reserved, including the making of copies unless permission is obtained from the copyright proprietors. Pertinent discussion including author s closure, if any, will be published in the March- April 2005 ACI Structural Journal if the discussion is received by November 1, ACI Structural Journal/May-June

2 ACI member Myoungsu Shin is a PhD candidate in civil engineering at the University of Illinois at Urbana-Champaign, Ill. He received his BS and MS from Seoul National University, Seoul, Korea. His research interests include earthquake-resistant design of reinforced concrete structures. ACI member James M. LaFave is an assistant professor of civil engineering at the University of Illinois at Urbana-Champaign. He is Chair of Joint ACI-ASCE Committee 352, Joints and Connections in Monolithic Concrete Structures, and is a member of ACI Committees 374, Performance-Based Seismic Design of Concrete Buildings; 439, Steel Reinforcement; and E 802, Teaching Methods and Educational Materials. His research interests include earthquake-resistant design of reinforced concrete structures and durability of structural concrete. Fig. 1 Eccentric beam-column connections in exterior frame. Fig. 2 Three-dimensional view of specimens (units: inches, 1 in. = 25.4 mm). terms of both strength and crack control) with reduction in connection eccentricity. Floor slabs were typically not included in previous eccentric connection tests. A floor slab may reduce the torsional demand induced by eccentricity in the joint region, not only by shifting the acting line of the resultant force of beam top and slab reinforcement, but also by providing some confinement to the joint. It may also increase joint shear capacity by expanding the effective joint width. On the other hand, a floor slab is expected to impose additional shear demand on the joint and to reduce the column-to-beam moment strength ratio. RESEARCH SIGNIFICANCE Few RC eccentric beam-column connection tests have been reported in the literature to date, and floor slabs were typically not included in the previous tests. Current ACI design provisions for estimating the joint shear strength of eccentric 404 beam-column connections have been empirically established based on these limited experimental results. 2,9 Therefore, these ACI provisions should be reconfirmed for the case of eccentric beam-column connections with floor slabs. This paper presents test results on the performance of eccentric beam-column-slab connections subjected to lateral earthquake loading. EXPERIMENTAL PROGRAM Two RC eccentric beam-column-slab subassemblies were designed, constructed, and tested in the University of Illinois Newmark Structural Engineering Laboratory. Each subassembly represents a model of an edge connection in an exterior moment resisting frame. In many edge connections, the exterior faces of columns are flush with the exterior faces of edgebeams, while the columns are often wider than the edgebeams (Fig. 1). This study primarily focuses on that type of edge connection. The test subassemblies were isolated at inflection points between floors and between column lines. It was assumed that inflection points in a moment resisting frame subjected to seismic loading exist at approximately the midheights of columns and the midspans of edge-beams because moments due to significant seismic loading are typically much larger than moments due to gravity loading. Each subassembly included a floor slab and a transverse beam on one side only, as in an edge connection of a typical two-way slab system. The transverse beam could contribute to joint shear capacity by providing some confinement to the interior side of the joint, while its torsional capacity may affect the slab contribution to flexural capacity of the edge-beams. Design of test specimens The specimens were designed and detailed in conformance with ACI and ACI 352R-02 recommendations, 2 except for a few design parameters that were specifically investigated in this study. Figure 2 shows a three-dimensional view of the specimens. Considering a prototype structure with a story height of 15 ft (4.6 m) and a span length of 25 ft (7.6 m), the specimens represent approximately 2/3-scale models with a story height of 118 in. (3.0 m) and a span length of 196 in. (5.0 m). Each specimen consisted of a column, two edge-beams framing into the column on opposite sides, a transverse beam, and a floor slab. The main design parameters varied in the specimens were the eccentricity between beam and column centerlines, and the edge-beam width; the member dimensions were selected to maximize effects of these parameters. Variation in eccentricity was expected to affect torsional demand in the joint region, and variation in edge-beam width was expected to affect joint shear strength. Because each specimen had a flush exterior face of the column and the edge-beams, the specimen with a larger eccentricity (Specimen 2) necessarily had a narrower edge-beam width. Figure 3 illustrates reinforcing details in the specimens. All details were identical except for the edge-beams. The columns were 18 in. wide x 13 in. deep (457 x 330 mm) an aspect ratio of 0.72 and were reinforced with eight No. 6 reinforcing bars (ρ = 1.5%). The floor slabs were 48 in. (1219 mm) wide (including the edge-beam width) and 4 in. (102 mm) thick, reinforced with a single layer of No. 3 reinforcing bars in each direction. The four slab longitudinal bars were spaced every 10 in. (254 mm), and the 14 slab transverse bars were spaced every 12 in. (305 mm). The transverse beams were 13 in. wide x 16 in. deep (330 x 406 mm), reinforced with two No. 6 bars at the top and two No. 5 bars at the bottom. The edge-beams were 16 in. (406 mm) deep ACI Structural Journal/May-June 2004

3 Table 1 Connection design parameters Specimen 1 2 Eccentricity e, in. (mm) 3.5 (89) 5.5 (140) Edge-beam size, in. x in. (mm x mm) 11 x 16 (279 x 406) 7 x 16 (178 x 406) Moment strength ratio * M r Joint shear stress level γ Joint reinforcement A sh, in. 2 (mm 2 ) Member depth to bar diameter ratio 13.7 /13.0 (1.14 /1.08 ) 0.33 at 3.25 in. (213 at 83 mm) 21.7 /19.0 (1.80 /1.58 ) 0.33 at 3.25 in. (213 at 83 mm) h b /d b(col) h c /d b(bm) * M r = ΣM n (columns)/σm n (beams). In ACI , b j = b b + 2x, x = smaller distance between beam and column edges. In ACI 352R-02, b j = b b + Σmh c /2, m = 0.3 when e > b c /8, otherwise m = 0.5. A sh = total area of horizontal joint reinforcement within layer in longitudinal direction. d b(col) and d b(bm) = maximum diameter of longitudinal bars used in column and edge-beam. Notes: γ and M r values are computed with f c = 4000 psi (27.6 MPa) and f y = 60 ksi (414 MPa); γ values were computed using lb-in. units (N-mm units in parentheses). in both specimens; they were 11 in. (279 mm) wide in Specimen 1, and 7 in. (178 mm) wide in Specimen 2. The edge-beams were each reinforced with four No. 5 bars at the top (ρ S1 = 0.79%, ρ S2 = 1.31%) and two No. 5 bars at the bottom (ρ S1 = 0.39%, ρ S2 = 0.62%) to achieve similar moment strengths in both specimens. Top reinforcing bars in Specimen 2 were arranged in two layers to provide a clear spacing greater than a minimum of 1 in. (25 mm). All longitudinal beam, column, and slab reinforcement was continuous through the connection, except for transverse beam and slab bars that were terminated with standard hooks within the column and edge-beams, respectively. A minimum concrete clear cover of 1 in. (25 mm) was provided in all members. Connection design parameters Table 1 summarizes the main design parameters and other important values that are considered to govern the behavior of beam-column connections. The specimens satisfied the ACI seismic design requirements applying to special moment frame members, except for the design joint shear stress level (γ). The M r and γ values reported in the table were computed using design material properties. When calculating the column-to-beam moment strength ratios M r, beam moment strengths were computed considering a slab contribution within the effective slab width defined in ACI , for both slab in tension and in compression. The first and second tabulated design joint shear stress levels γ with superscripts 2 and 3 were computed following ACI and ACI 352R-02, respectively, using the following equation γ = V uj, f c b j h c Here, V u,j is the ultimate joint shear force for design (lb or N); f c is the concrete compressive strength (psi or MPa); b j is the effective joint width (in. or mm); and h c is the column depth (in. or mm). When computing the V u,j values, longitudinal slab bars within the ACI effective slab width (two No. 3 bars for both specimens) were included, as well as all top and bottom beam bars, when following ACI 352R-02; however, the slab bars were not included in this calculation per ACI The γ values would be limited to 12.0 for lb-in. units (1.00 for N-mm units) in these connections by both ACI and ACI (1) Fig. 3 Reinforcing details (units: inches, 1 in. = 25.4 mm). 352R-02 because only the transverse beam covered at least 3/4 of its corresponding column face. Therefore, the γ values exceeded the ACI limiting value, especially in Specimen 2. The specimens were reinforced with three layers of horizontal joint reinforcement. Each layer consisted of a No. 3 hoop and two No. 3 crossties, which is approximately the minimum amount of joint reinforcement prescribed by ACI and ACI 352R-02. The amount of joint reinforcement (size and spacing) was kept the same in the two specimens to help clearly identify the effects of other (varied) design parameters on joint shear behavior. Values of the key design parameters in other eccentric connection tests found in the literature 3-6 are briefly summarized herein for comparison purposes. The eccentricity normalized by the column width varied from 0.14 to 0.25 (versus 0.19 in Specimen 1 and 0.31 in Specimen 2). The joint reinforcement ratio, computed as the total area of joint reinforcement in a layer divided by the product of reinforcement spacing and column width, ranged from 0.22 to 0.77% (versus 0.56% in both Specimens 1 and 2). Finally, the joint shear stress level varied from approximately 13 to 18 in lb-in. units (about 1.1 to 1.6 in N-mm units) per ACI , while the ratio of column depth to beam bar diameter ranged from 18.7 to 25.0, in the other eccentric connection tests. Construction and material properties Wooden formwork was used to cast the subassemblies. Electrical resistance strain gages were installed at key positions on reinforcing bars before the bars were assembled into steel ACI Structural Journal/May-June

4 Table 2 Concrete compressive strength f c on day of subassembly test Specimen 1 2 Except upper column, psi (MPa) 4340 (29.9) 5240 (36.2) Upper column, psi (MPa) 5200 (35.8) 5910 (40.7) Table 3 Properties of reinforcing bars Bar size No. 3 No. 5 No. 6 Column hoop f y, ksi (MPa) 65 (450) 73 (500) 78 (540) 68 (466) ε y * ε sh NA f u, ksi (MPa) 102 (700) 96 (660) 100 (690) 104 (715) * Strain at beginning of strain hardening. Ultimate (maximum) strength. Note: NA = not applicable. cages. At the bottom of the lower column form, four highstrength steel anchor bolts were mounted to permit connection of the concrete column to the testing fixture. At the ends of the edge-beams, longitudinal beam bars were welded to embedded steel fixtures that permitted later bolting to the test setup. Concrete was placed in the upright position of the form, as in field construction. Concrete with a maximum aggregate size of 3/8 in. (10 mm) and a slump of 5 in. (125 mm) was used to accommodate any steel congestion in the joint region and the small minimum clear cover of 1 in. (25 mm). For each subassembly, all members except the upper column were cast at one time, and the upper column was then cast one week later. For curing, the fresh concrete was covered with wet fabric and plastic sheets for one week. The design compressive strength of concrete was 4000 psi (27.6 MPa) and Grade 60 deformed reinforcing bars were specified. Table 2 summarizes the actual compressive strength of concrete on the day of the subassembly test. At least six concrete cylinders were cast for each placement of concrete; they were covered and cured in the same way as the subassemblies. Three of the cylinders were tested at 28 days, and the others were tested on the day of the subassembly test. Table 3 lists the actual yield strength f y, yield strain ε y, ultimate strength f u, and strain at the onset of strain hardening ε sh for flexural reinforcing bars and column hoops. Three reinforcing steel coupons were tested for each bar size to get the average properties listed in the table. The stress-strain relationship of column hoops did not have a well-defined yield plateau but, rather, exhibited gradually decreasing stiffness, so their yield properties were determined using the 0.2%-offset method. Test setup and loading sequence Figure 4 shows a picture of the test setup. The specimens were tested in their upright position. The column was linked to a universal hinge connector at the bottom (by anchor bolts cast inside the lower column) and to a hydraulic actuator at the top. The end of each edge-beam was linked to the strong floor by a pinned-end axial support. Thus, the two ends of the beams and the top and bottom of the column were all pinconnected in the loading plane to simulate inflection points of a frame structure subjected to uniaxial lateral earthquake loading. Column pins were along the column centerline and edge-beam pins were along the edge-beam centerline. Story shear was statically applied by displacing the top of the column (parallel to the longitudinal direction of the edgebeams) using a hydraulic actuator with a 100 kip (445 kn) Fig. 4 Test setup (Specimen 1 in testing rig). loading capacity and a ±10 in. (±508 mm) linear range. (Positive and negative loading directions are indicated on the figure.) No external column axial load was applied, conservatively in accordance with results of previous studies that found the presence of column compression could slightly improve joint shear strength by confining the joint core 2 or could have no apparent influence on joint shear strength. 10,11 The transverse beam and the floor slab were not directly loaded. Because the specimen was not symmetric about the loading direction, a slotted steel bracket was installed near the top of the column to guide specimen displacements along the longitudinal direction only. A twist of the column about its longitudinal axis was not restrained by any of the external column supports (the actuator, the slotted steel bracket, or the universal hinge connector). Any unbalanced torsional moments in the specimens were resisted by combinations of horizontal forces in the transverse direction at the beam-end supports and at the ends of the column. In RC building frame columns above and below eccentric connections subjected to lateral earthquake loading, there could be a contra-twist point at roughly midheight, producing torsional moments in the columns. Column damage was not a topic investigated in this study, however, and it should not considerably affect joint behavior. Furthermore, severe column damage from torsion has not been reported even for eccentric connection tests where column twist was restrained. 3 During testing, two reference column displacements were measured at the level of the actuator with respect to the exterior and interior faces of the upper column and the average of the two displacements was defined as the story displacement. The two displacements were slightly different because the specimen twisted a small amount due to torsion in the joint region caused by eccentricity. Instrumentation used in each specimen was as follows. A total of 64 electrical resistance strain gages were mounted on reinforcing bars at key locations in and around the connection. Eight cable-extension gages were installed on the top and bottom of edge-beams to estimate beam rotations in the vicinity of beam-column interfaces. Five linear variable differential transformers (LVDTs) were used on the flush face of the joint to determine overall joint shear deformations. Finally, each beam-end support had a load cell to monitor the reaction forces generated in the support. Figure 5 shows the pattern of cyclic lateral displacements applied by the actuator during each test. A total of 22 displacement cycles were statically applied up to 6% story drift. (The maximum drift of Specimen 1 was limited to approximately 406 ACI Structural Journal/May-June 2004

5 Fig. 5 Pattern of cyclic lateral displacements. 5.5% in the positive direction due to misalignment.) Two consecutive same-drift cycles were typically applied to examine strength degradation, and 1% drift cycles were inserted between other cycles to investigate stiffness degradation. DISCUSSION OF TEST RESULTS Overall connection behavior Figure 6 shows the story shear versus story drift (load versus displacement) hysteretic curves for the two specimens. The curves exhibited considerable pinching (the middle part of each hysteretic loop was relatively narrow), as well as some stiffness and strength degradation during same-drift repeat cycles. This behavior is characteristic of most RC frame connections and is typically attributed to reinforcement bond slip through the joint region, concrete cracking, and/or reinforcement yielding. The predicted strengths of each specimen indicated on the figure were computed using actual material properties, assuming: a) the edge-beams would reach their nominal moment strengths at the beam-column interfaces (beam hinging); and b) joint shear failure would occur. For beam hinging, the nominal beam moment strengths were computed using the equivalent rectangular stress block concept, considering slab contribution within the effective slab width defined in ACI For joint shear failure, the nominal joint shear strength was computed following ACI procedures. According to the predicted strengths, both specimens would be expected to have joint shear failure before longitudinal beam bars yielded. However, each specimen exhibited significantly higher strength than the predicted one computed assuming joint shear failure. Yield points of the specimens are not easily determined from the load versus displacement curves because the reinforcement layout of the edge-beam and slab was not symmetric about the centerline of the beam and because of a shear lag effect in slab reinforcement. Therefore, it was examined when each longitudinal beam and slab bar yielded, based on reinforcing steel strain gage data measured in the beam-slab sections at the beam-column interfaces and at half an effectivebeam-depth away from the interfaces. Bottom beam bars typically underwent faster increases in strain (and consequently yielded earlier) than top beam bars. First beam bar yielding occurred during the 1.5 and 2% drift cycles in Specimens 1 and 2, respectively. In each specimen, all longitudinal beam and slab bars yielded at the beam-column interfaces, and yielding of the beam bars spread to half an effective-beam-depth away from the interfaces, by the 3% drift cycle, meaning that beam hinging eventually developed adjacent to the beam-column interfaces. Fig. 6 Load-versus-displacement hysteretic curves (1 kip = 4.45 kn). Fig. 7 Eight cable-extension gages and five LVDTs (1 in. = 25.4 mm). The rotational behavior of edge-beams near the beamcolumn interfaces was investigated to further examine the development of beam hinging. In each specimen, eight cable extension gages were installed on top and bottom of the edge-beams (two gages at each location), approximately one effective beam depth (14 in. [356 mm]) away from the interfaces, to where a plastic hinge region may have extended (refer to Fig. 7). Data from these gages was used to estimate edgebeam rotations adjacent to the column, comprising both plastic hinge rotation (from yielding of longitudinal beam bars) and rigid beam-end rotation (from opening of large flexural cracks and some beam bar slippage). Figure 8 illustrates the envelope curves of story shear versus beam rotation in the specimens, from connecting the peak story drift point of each cycle. The rate of increase in beam rotation (with respect to story drift) got higher during the 2.5 and 3% drift cycles. ACI Structural Journal/May-June

6 Fig. 8 Envelope curves of story shear versus beam rotation (1 kip = 4.45 kn, S1 = Specimen 1, S2 = Specimen 2). Fig. 9 Typical joint concrete cracking pattern (taken after testing Specimen 1). This was because all longitudinal beam and slab bars yielded by that cycle. Also, beam rotation increased while story shear did not increase (or even decreased) during higher drift cycles (in other words, while beam moments at the beamcolumn interfaces did not increase). These observations imply that beam hinging developed in both specimens. Specimen 1 reached its maximum story shear force during the 3% drift cycle, while Specimen 2 did so during the 4% drift cycle. Both specimens exhibited successive strength drops after the peak force drift cycles, up to approximately 15% (an average for both directions) by the 6% drift cycle. Considering that large strength drops typically do not accompany beam hinging, some other failure mechanism likely developed leading to the breakdown of the specimens. Neither column hinging nor severe anchorage failure was observed throughout the tests, however. (With a column depth-to-beam bar diameter ratio of approximately 20, the specimens did exhibit some beam bar slippage through the joint, as has also been reported for other similar connections. 2 ) Therefore, it was concluded that the specimens ultimately failed by joint shear (similar to in previous studies, 10,12 where it was also observed that beam-column connections can fail due to joint shear although they undergo some beam hinging); this conclusion will be strengthened later by examining joint cracking damage, joint shear deformations, joint hoop strains, and joint contributions to overall story displacement. Strength degradation of the specimens was further examined by comparing story shear forces of consecutive same-drift Fig. 10 Envelope curves of story shear versus joint shear deformation (1 kip = 4.45 kn). cycles. The reduction in story shear force during a second (repeat) cycle was compared to the first cycle story shear, as a percentage. Strength degradation remained low (approximately 5%) until the 2 or 3% drift cycles, but it increased up to 13 and 19% in Specimens 1 and 2, respectively, during the 5% drift cycle. Overall stiffness of a specimen for a particular loading cycle was defined as an average of the story shear divided by the story displacement at the positive and negative peak drifts of the cycle. Stiffness degradation continuously increased throughout the tests and exceeded 80% of the first-cycle stiffness by the end of each test. Stiffness degradation was faster before the 1% drift cycles because most concrete cracking and bond slip initiation occurred in the early stages of the tests. The amount of energy dissipated during a particular loading cycle was calculated as the area enclosed by the corresponding load versus displacement hysteretic loop. The specimens exhibited similar patterns of energy dissipation, with the rate of increase in energy dissipated per cycle increasing with respect to story drift until the 4% drift cycle. For example, the energy dissipated during the 4% drift cycle was roughly twice that during the 3% drift cycle, although story shear did not increase much between 3 and 4% story drift. The rate of increase in energy dissipated per cycle (with respect to story drift) quickly reduced during the 5% drift cycle. Joint shear deformation Figure 9 shows a typical joint cracking pattern, observed after testing Specimen 1. Initial joint shear cracks were observed during the 0.75% drift cycle in both specimens. The cracks were diagonally inclined and intersected one another due to the reversed loading. Some joint concrete spalled off from the exterior joint face after extensive cracking at higher story drifts. Specimen 2 underwent more joint concrete cracking and spalling than Specimen 1. To monitor overall joint shear deformation in an average sense, five LVDTs were installed into the flush face of the joint in each specimen (refer to Fig. 7). Considering the two triangles (having a common side) formed by the LVDTs, angular changes in the 90-degree angles were computed at each loading step. Then the average of the two angular changes was defined as the joint shear deformation γ d on the flush face of the joint, as explained in Fig. 7. Figure 10 shows the envelope curves of story shear versus joint shear deformation in the specimens, from connecting the peak drift point of each cycle. The specimens exhibited 408 ACI Structural Journal/May-June 2004

7 Fig. 11 Envelope curves of joint hoop strain versus story drift (Int. = interior, Ext. = exterior, S1 = Specimen 1, and S2 = Specimen 2). similar joint shear deformation at a relatively slow rate of increase during early stages of the tests. The rate of increase in joint shear deformation (with respect to story drift) became higher, however, during the 2.5 and 3% drift cycles. The rapid increase in joint shear deformation occurred without considerable rises (or even with drops) of story shear in both specimens. This resulted from some crushing and spalling of joint concrete due to joint shear. The marked increase in joint shear deformation occurred after exceeding approximately 0.01 radians. (For these specimens, 0.01 radians of joint shear deformation produces roughly 0.8% story drift, as will be described later in more detail.) Specimen 2 underwent larger joint shear deformations than Specimen 1 during the 5 and 6% drift cycles, reaching radians in the last negative cycle. This largest value is roughly four times larger than the maximum value up through the 2.5% drift cycle. The joint shear deformations exhibited by these specimens were similar to or larger than those in other eccentric connections found in the literature that failed by joint shear. 3,5,6 These observations support the conclusion that both specimens had joint shear failures. Joint hoop strain Three layers of horizontal joint reinforcement were equally spaced at 3.25 in. (83 mm) between the top and bottom longitudinal beam bars in each specimen; a layer consisted of a hoop and two crossties. Each joint hoop was instrumented with two strain gages, one on each leg parallel to the loading direction, to monitor strain at the exterior (flush) and interior (offset) sides of the joint. Figure 11 shows the envelope curves of joint hoop strain versus story drift in the specimens, from connecting the peak drift point of each cycle. In the figure, the three joint hoops are referred to as bottom, middle, and top according to vertical position, and an arrow indicates that a strain gage was broken after the corresponding cycle. In each specimen, joint hoop strains at the flush side of the joint were generally larger than those at the offset side of the joint, which can be explained as follows. First, the joint shear resistance mechanism excluded some part of the offset side; in other words, the offset side was less effective than the flush side in resisting joint shear forces. Second, the eccentricity between beam and column centerlines induced torsion into the joint region, resulting in an increase of net shear stress near the flush side. Finally, the transverse beam and floor slab provided some confinement to the offset side. The specimens, however, showed more uniform strain distributions in the joint than did other eccentric connections (without slabs and transverse beams) reported in the literature, 3,5,6 where joint hoop strains at the flush side were much larger (two or three times) than those at the offset side. This can be explained as follows. In each specimen, the location of the tension-ontop resultant force transmitted to the joint from the beam and slab reinforcement was closer to the column centerline than it would have been in the case without slabs, where the resultant force would be located along the beam centerline (eccentric to the column centerline). (Similar behavior occurred on the compression-on-top side of the joint, where the top compression force was closer to the column centerline than it would have been without the presence of a floor slab.) This implies that ACI Structural Journal/May-June

8 Fig. 12 Calculation of story displacement due only to joint shear deformation. Joint contribution to story displacement One of the goals of the strong column-weak beam design philosophy is to ensure that most of the inelastic deformation of a moment resisting frame is concentrated in beam plastic hinges during earthquakes, while avoiding overall collapse of the frame due to column or joint damage. To further evaluate the behavior of the specimens, contributions of various deformation sources to the story displacement were evaluated separately. In a well-detailed beam-column connection, most of the story displacement will result from beam inelastic deformations. In this study, the considered sources of overall specimen displacement are beam elastic and inelastic deformations, column elastic deformation, and joint shear deformation. Each of the elastic deformations includes both flexural and shear deformations. The beam inelastic deformation encompasses both plastic hinge rotation and rigid beam-end rotation near the beam-column interfaces. Assuming the column and the edge-beams remain rigid, as shown in Fig. 12, the story displacement due only to joint shear deformation ( c,j ) was calculated using the following equation l c c, j = l b --- γ d ( l b h c ) γ d h b (2) Fig. 13 Various sources of story displacement in Specimen 2 (1 in. = 25.4 mm). joint torsional demand was less than in the case without slabs, resulting in more uniform strain distribution in the joint. In both specimens, joint hoop strains started to rise after several small drift cycles, and they typically increased even while story shear decreased during the 5 and 6% drift cycles, although the rate of increase with respect to story drift got lower at high story drifts. The specimens generally underwent similar joint hoop strains at early stages of the tests, but Specimen 2 exhibited larger increments in joint hoop strain than Specimen 1 at high story drifts. This agreed with the fact that Specimen 2 underwent larger joint shear deformations than Specimen 1 as the specimens started to break down due to joint shear. According to the design philosophy of ACI , the function of joint reinforcement is to provide confinement of the joint core, so the joint can fully develop the concrete strut mechanism. Yielding of joint reinforcement was investigated based on the yield strain of joint hoops determined by the 0.2%- offset method; the yield strain was In Specimen 2, the middle joint hoop yielded during the 4% drift cycle, and strain in the bottom joint hoop approached (at which point the joint hoop steel reached its proportional limit and started to lose stiffness in the stress-strain curve) during the 3% drift cycle. Therefore, the joint hoops in Specimen 2 almost reached the limit of their useful function per the ACI design philosophy. In Specimen 1, it was not clear to distinguish whether the hoops yielded or not because two strain gages broke at the exterior side of the joint during testing. Here, γ d is the joint shear deformation near the flush face of the joint. Figure 13 illustrates the contribution of the various sources to the positive story displacement in Specimen 2, as an example. Most of the story displacement resulted from beam inelastic deformation and joint shear deformation throughout the test. The table within the figure lists the percent contribution of joint shear deformation to the applied story displacement in both specimens; each value is an average for both loading directions at the indicated story drift. In Specimen 2, for instance, joint shear deformation produced 24% of the applied story displacement at 1% drift and 53% at 6% drift. This indicates that the contribution of joint shear deformation was significant within the cracked elastic range of behavior and even more so over the inelastic range. (The large contribution of joint shear deformation in the inelastic range was because the specimen failed due to joint shear.) The calculated story displacements were smaller than the actual applied story displacements up until approximately 4% drift. This disparity was likely due to small displacements occurring at the specimen external support locations (elastic elongation of anchors and/or interface shear slip). In contrast, the calculated story displacements were larger than the actual applied story displacements at high story drifts, in part because the joint shear deformation contribution was computed using values measured at the flush face of the joint (without a transverse beam and floor slab), which may overestimate the average joint shear deformations across the column width. (Before the onset of joint shear failure, joint cracking was not severe even at the flush side of the joint, so the difference between joint shear deformations at the flush side and at the offset side was relatively small at low story drifts.) Estimation of joint shear strength The horizontal joint shear force V j at midheight of the joint during a test can be computed considering horizontal force equilibrium of the joint region and moment equilibrium of each edge-beam, as described in Fig. 14. Here, V 1 and V 2 are the measured vertical forces in the east and west beam-end 410 ACI Structural Journal/May-June 2004

9 supports, respectively, and V c is the applied story shear force. Also, jd 1 and jd 2 are the moment arms at east and west beam-column interfaces, respectively, which were taken as 14 in. (356 mm) for sagging moments and 12 in. (305 mm) for hogging moments in Specimen 2. The maximum joint shear force computed in this way is 142 kips (632 kn) in Specimen 2. This procedure could not be used to compute horizontal joint shear forces in Specimen 1 because the load cells in the beam-end supports did not operate. The maximum joint shear force can also be estimated using an alternative method as follows. In each specimen, all longitudinal beam and slab bars yielded at beam-column interfaces before the specimen reached its peak story shear force. No longitudinal beam and slab bars underwent strain hardening during the tests, however. Based on these observations, the maximum joint shear force V j,max can be estimated at the story drift when each specimen reached its maximum story shear force, using the following equation, = A s f y V c, max V jmax Here, A s and f y are the area and the actual yield strength of each reinforcing bar, and V c,max is the maximum story shear force applied. The summation term encompasses all longitudinal slab bars as well as all (top and bottom) beam bars. Thus, the maximum joint shear force V j,max is estimated to be 145 kips (647 kn) in Specimen 1 and 146 kips (651 kn) in Specimen 2. The estimated value for Specimen 2 is very close to the maximum joint shear force computed previously using the method described in Fig. 14. The latter method using Eq. (3) was assumed to give a better estimate of maximum joint shear force because the former method was based on assumed beam moment arms. The maximum joint shear forces V j,max imposed during the tests can be considered as reasonable conservative estimates of the joint shear strengths of these connections because the specimens eventually failed due to joint shear. Unexpectedly, both specimens achieved similar joint shear strengths, even though one of them had a larger eccentricity and a narrower edge-beam. Table 4 compares the maximum joint shear force V j,max with the nominal joint shear strengths V n,j computed following ACI and ACI 352R-02. The maximum joint shear force of each specimen exceeded the values computed following each of the ACI procedures, especially so in Specimen 2. Current ACI procedures for estimating nominal joint shear strength were conservative for the case of the eccentric beam-column connections tested with floor slabs. ACI design procedures applying to eccentric connections were established in part based on eccentric connection tests conducted without floor slabs and/or with other conservative assumptions. Therefore, it appears that the floor slabs increased joint shear strengths of the specimens and diminished differences in joint shear strength between the specimens. This was partially because joint shear forces at the top of the joint were distributed across the entire column width by means of the floor slabs (as explained previously in the section on joint hoop strain), so the effective joint width was enlarged when compared with the case without slabs. In fact, the joint shear strength of the specimens was well estimated using the effective joint width b j currently defined for concentric connections in ACI 352R-02 (3) Fig. 14 Edge-beam and joint forces. Table 4 Comparison of actual and nominal joint shear strengths Specimen V j,max, kips (kn) ACI ACI 352R-02 b j = (b b + b c )/ (645) 113 (503) 133 (592) 149 (663) (650) 79 (352) 101 (449) 141 (628) b b b + b c j = V n,j, kips (kn) * * V n,j = γ f c b j h c ; f c = actual concrete compressive strength; and γ = 12 for lb-in. units (γ = 1.0 for N-mm units). Note: The two ACI procedures provided different dimensions of b j (refer to Table 1). as listed in Table 4. (This approach could be somewhat unconservative for edge connections where the interior faces of columns are flush with the interior faces of edge-beams; this type of edge connection could have more severe joint torsional demand.) SUMMARY AND CONCLUSIONS The seismic performance of eccentric beam-column connections with floor slabs (edge connections with flush exterior beam and column faces) was experimentally investigated for two subassemblies under simulated lateral earthquake loading. The main design variables in the specimens were the eccentricity between beam and column centerlines, and the edge-beam width. Results and conclusions can be summarized as follows. The conclusions are applicable for connections similar to those tested; more research may be required before the conclusions can be extrapolated to other cases. 1. The specimens developed beam hinging near beamcolumn interfaces before they reached their maximum story shear forces, and they eventually failed due to joint shear, exhibiting successive strength drops. This conclusion was drawn from the following: a) all longitudinal beam and slab bars yielded by 3% drift, and the rate of increase in beam rotation got much higher at 2.5 and 3% drifts near beam-column interfaces; b) joint shear deformation rapidly increased starting from 2.5 to 3% drift; and c) neither column hinging nor severe anchorage failure was observed throughout the tests; 2. The specimens exhibited similar joint shear deformations at a relatively slow rate of increase before they started to break down. Joint shear deformation, however, rapidly increased from 2.5 to 3% drift onward without considerable rises (or even with drops) of story shear in both specimens. The marked increase in joint shear deformation occurred after exceeding approximately 0.01 radians. The specimen with the larger eccentricity underwent larger joint shear deformations than the other specimen during 5 and 6% drift cycles; (4) ACI Structural Journal/May-June

10 3. The specimens showed more uniform joint hoop strain distribution across the joint than did other eccentric connections (without slabs and transverse beams) reported in the literature. The specimens underwent similar joint hoop strains at early stages of the tests, but the specimen with the larger eccentricity exhibited larger increments in joint hoop strain than the other specimen at high drifts; 4. The specimens reached similar joint shear strengths, even though one of them had a larger eccentricity and a narrower beam. From this conclusion (along with Conclusions 2 and 3), the specimens exhibited very similar behavior before they started to break down. It was concluded then that floor slabs diminished differences between seismic performance of these eccentric connections; 5. Current ACI building code procedures for estimating nominal joint shear strength were quite conservative for the case of the tested eccentric beam-column connections with floor slabs. The ACI design procedures applying to eccentric connections were established in part based on eccentric connection tests conducted without floor slabs and/or with other conservative assumptions. Therefore, it was concluded that floor slabs increased joint shear strengths of the specimens. The beneficial effects of floor slabs (reducing torsional demand on the joint and increasing joint shear capacity) appear to outweigh the detrimental effects of the slabs (imposing additional shear demand on the joint); and 6. The contribution of joint shear deformation to story displacement was significant both within the elastic range and over the inelastic range of behavior in the specimens. It is, therefore, recommended that joint shear deformation should be considered in the analysis of RC moment resisting frames, especially those with eccentric connections. ACKNOWLEDGMENTS The authors would like to acknowledge research support from the University of Illinois and from the Chester P. Siess Civil Engineering Graduate Student Award. NOTATION b b = beam width b c = column width b j = effective joint width e = eccentricity between beam and column centerlines f c = concrete compressive strength f y = yield strength of reinforcing bar h b = beam depth h c = column depth jd 1, jd 2 = assumed moment arms at east and west beam-column interfaces, respectively l b = beam pin-to-pin length l c = column pin-to-pin height M r = column-to-beam moment strength ratio V c,max = maximum story shear force V j,max = maximum joint shear force V n,j = nominal joint shear strength V u,j = ultimate joint shear force for design V 1, V 2 = measured reaction forces in east and west beam-end supports, respectively γ = design joint shear stress level γ d = joint shear deformation c,j = story displacement due only to joint shear deformation ρ S1 = reinforcement ratio in Specimen 1 ρ S2 = reinforcement ratio in Specimen 2 REFERENCES 1. Paulay, T., and Priestley, M. J. N., Seismic Design of Reinforced Concrete and Masonry Buildings, John Wiley & Sons, Inc., New York, 1992, 744 pp. 2. Joint ACI-ASCE Committee 352, Recommendations for Design of Beam-Column Connections in Monolithic Reinforced Concrete Structures (ACI 352R-02), American Concrete Institute, Farmington Hills, Mich., 2002, 40 pp. 3. Joh, O.; Goto, Y.; and Shibata, T., Behavior of Reinforced Concrete Beam-Column Joints with Eccentricity, Design of Beam-Column Joints for Seismic Resistance, SP-123, J. O. Jirsa, ed., American Concrete Institute, Farmington Hills, Mich., 1991, pp Lawrance, G. M.; Beattie, G. J.; and Jacks, D. H., The Cyclic Load Performance of an Eccentric Beam-Column Joint, Central Laboratories Report , Central Laboratories, Lower Hutt, New Zealand, Aug. 1991, 81 pp. 5. Raffaelle, G. S., and Wight, J. K., Reinforced Concrete Eccentric Beam-Column Connections Subjected to Earthquake-Type Loading, ACI Structural Journal, V. 92, No. 1, Jan.-Feb. 1995, pp Chen, C. C., and Chen, G. K., Cyclic Behavior of Reinforced Concrete Eccentric Beam-Column Corner Joints Connecting Spread- Ended Beams, ACI Structural Journal, V. 96, No. 3, May-June 1999, pp Vollum, R. L., and Newman, J. B., Towards the Design of Reinforced Concrete Eccentric Beam-Column Joints, Magazine of Concrete Research, V. 51, No. 6, 1999, pp Joint ACI-ASCE Committee 352, Recommendations for Design of Beam-Column Joints in Monolithic Reinforced Concrete Structures (ACI 352R-85), American Concrete Institute, Farmington Hills, Mich., 1985, 21 pp. 9. ACI Committee 318, Building Code Requirements for Structural Concrete (ACI ) and Commentary (318R-02), American Concrete Institute, Farmington Hills, Mich., 2002, 443 pp. 10. Bonacci, J., and Pantazopoulou, S., Parametric Investigation of Joint Mechanics, ACI Structural Journal, V. 90, No. 1, Jan.-Feb. 1993, pp Meinheit, D. F., and Jirsa, J. O., Shear Strength of R/C Beam-Column Connections, Journal of the Structural Division, ASCE, V. 107, No. ST11, 1981, pp Hwang, S. J., and Lee, H. J., Analytical Model for Predicting Shear Strengths of Interior Reinforced Concrete Beam-Column Joints for Seismic Resistance, ACI Structural Journal, V. 97, No. 1, Jan.-Feb. 2000, pp ACI Structural Journal/May-June 2004