Reinforced concrete edge beam column slab connections subjected to earthquake loading

Transcription

1 Magazine of Concrete Research, 24, 55, No. 6, June, Reinforced concrete edge beam column slab connections subjected to earthquake loading M. Shin* and J. M. LaFave* University of Illinois at Urbana-Champaign Four two-thirds-scale reinforced concrete edge beam column slab subassemblies (two concentric and two eccentric connections) were tested under quasi-static cyclic lateral loading. Each subassembly represented a cruciform connection in an exterior moment-resisting frame with a monolithic floor slab on one side only, loaded in the longitudinal direction of the edge-beams. The tests explored the effect of eccentricity between beam and column centrelines, and the effect of floor slabs, on the structural performance of edge beam column slab connections subjected to earthquake loading. Performance of the specimens was evaluated in terms of overall strength and stiffness, energy dissipation, beam plastic hinge development, joint shear deformation, and joint shear strength. All specimens underwent some beam hinging at the beam/column interfaces. However, both eccentric specimens, and one concentric specimen with a heavily reinforced floor slab, eventually failed as a result of joint shear, whereas the other concentric specimen exhibited more ductile load displacement response. The eccentric specimens (with different eccentricities and edge-beam widths) underwent similar behaviour before they started to break down, and they also reached similar joint shear strengths. Slab participation was evaluated using slab bar strain gauge data with respect to storey drift. Actual effective slab widths were much larger than the ones typically used in design, especially for the specimens with a column wider than the edge-beams. Finally, floor slabs imposed significant joint shear demand, but they also increased joint shear capacity by expanding effective joint width. Notation b b b c b j,318, b j,352 b j,exp and b9 j,exp b j,rw d t beam width column width effective joint width computed per ACI and ACI 352R-2 effective joint width estimated using experimental maximum joint shear force effective joint width computed per an equation suggested by Raffaelle and Wight vertical distance between longitudinal slab bars and centroid of a transverse beam * University of Illinois at Urbana-Champaign, Department of Civil and Environmental Engineering, 318 Newmark Civil Engineering Laboratory, MC-25, 25 North Mathews Avenue, Urbana, IL 6181, USA. (MCR 1135) Paper received 29 April 23; last revised 14 October 23; accepted 13 November 23 e f 9 c f y h b h c h ph jd 1, jd 2 l b l c M n þ, M n M r V 1, V 2 V c V c,m(cal) V c,m(exp) V j eccentricity between edge-beam and column centrelines concrete compressive strength steel yield strength beam depth column depth vertical distance between gauges on top and bottom of an edge-beam assumed moment arms at east and west beam/column interfaces beam pin-to-pin span length column pin-to-pin storey height beam positive and negative nominal moment strengths column-to-beam moment strength ratio measured reaction forces in east and west beam-end supports storey (column) shear force predicted storey strength measured storey strength (maximum storey shear force) horizontal joint shear force # 24 Thomas Telford Ltd

2 Shin and LaFave V j,m V j,u bot top experimental maximum joint shear force design ultimate joint shear force average of relative displacements measured by two gauges on bottom of an edge-beam average of relative displacements measured by two gauges on top of an edge-beam ª joint shear deformation (at exterior face of joint) ª d design joint shear stress level ª m maximum joint shear stress level ª n nominal joint shear stress level Ł ph î eq beam rotation near beam/column interface equivalent viscous damping Introduction and background The vulnerability of reinforced concrete (RC) beam column connections in moment-resisting frames has been identified from structural damage investigations after many past earthquakes. 1,2 Since the mid-196s, numerous experimental studies have been conducted to investigate the behaviour of RC beam column connections subjected to earthquake loading. However, few tests on edge beam column slab connections (cruciform connections in exterior frames with floor slabs on one side only) have been reported in the literature to date. This paper presents experimental and analytical results for RC edge beam column slab connections loaded in the longitudinal direction of the edge-beams. The research specifically explored the effect of eccentricity between beam and column centrelines, as well as the effect of floor slabs, on the structural performance of edge connections subjected to earthquake loading. Key previous research on these two subjects is briefly summarised below. When a beam column connection is subjected to lateral loading, the beam top and bottom forces from bending are transmitted to the column at the beam/ column interfaces, producing large joint shear forces. In many edge connections the exterior faces of the columns are flush with the exterior faces of the edgebeams (Fig. 1). The columns are often wider than the edge-beams, resulting in an offset between the beam and column centrelines. This kind of connection is classified as an eccentric connection. Owing to the eccentricity between beam and column centrelines, the transmitted beam forces may also induce torsion in the joint region, which will produce additional joint shear stresses. A few RC eccentric beam column connections have been tested without floor slabs, 3 8 but more research is needed to clarify the extent to which the presence of eccentricity between beam and column centrelines affects the behaviour of eccentric connections, particularly when floor slabs are present. In this study, two eccentric edge connections were tested, as well as two concentric edge connections, all with floor slabs. Lawrance et al. 3 tested one cruciform eccentric beam column connection. Eccentricity between beam and column centrelines 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- Centroidal axis of column Assumed contra-flexure positions Direction of motion Torsional effect T C C T T Forces transferred from edge-beams C C T Fig. 1. Eccentric beam column connections in an exterior frame 274 Magazine of Concrete Research, 24, 55, No. 6

3 to-beam moment strength ratio was high (roughly 2), some column longitudinal bars at the flush side experienced local yielding, due possibly to torsion from the eccentricity. Joh et al. 4 tested six cruciform beam column connections, including two eccentric connections. The displacement ductility of specimens with eccentricity was only from 2. 5 to 5, whereas specimens without eccentricity had displacement ductility ranging from 4 to 8. In their specimen with a flush face of the column and eccentric beams, joint shear deformations on the flush side of the joint were four to five times larger than those on the offset side of the joint. 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 by American Concrete Institute (ACI) design recommendations in existence at the time, 9 but that this could be rectified by using a proposed equation for reduced effective joint width. Teng and Zhou 6 tested six cruciform beam column connections, including two concentric, two medium eccentric, and two one-sided eccentric connections. The researchers formulated joint shear strength recommendations for eccentric connections by limiting the allowable shear deformation in an eccentric joint to the magnitude of shear deformation in a companion concentric joint at 2% storey drift. Chen and Chen 7 tested six corner beam column connections, including one concentric connection, one conventional eccentric connection, and four eccentric connections with spread-ended (tapered width) beams covering 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, in terms of displacement ductility, energy-dissipating capacity, and joint shear deformation. Finally, Vollum and Newman 8 tested 1 corner beam column connections; each consisted of a column and two perpendicular (one concentric and one eccentric) beams. Various load paths were tested to investigate the behaviour of the connections. Performance improved significantly (in terms of both strength and crack control) with reduction in connection eccentricity. For approximately the past 15 years, various investigators have evaluated the effect of floor slabs on the seismic response of RC moment frames. According to Pantazopoulou and French, 1 who discussed results of the previous studies and consequent code amendments, most of the research focused on investigating how much a floor slab contributed to beam flexural strength (reducing the column-to-beam moment strength ratio) when the slab was in the tension zone of the beam RC edge beam column slab connections subjected to earthquake loading section. However, limited research was concerned with the effect of floor slabs on joint shear behaviour, although some researchers did indicate that floor slabs could impose additional shear demands on joints. Floor slabs may increase joint shear capacity by expanding effective joint width and/or by providing some confinement to joints (along with transverse beams). For eccentric connections, floor slabs may also reduce joint torsional demand by shifting the acting line of the resultant force of the beam top and slab reinforcement. In this paper, the slab effect on joint shear demand is evaluated by inspecting slab strain gauge data at various storey drifts to compute joint shear forces. Then the slab effect on joint shear capacity is also evaluated, by estimating the effective joint widths of the test specimens and comparing them with other specimens without floor slabs reported in the literature. Experimental programme This study investigated the effect of eccentricity between beam and column centrelines, as well as the effect of floor slabs, on the seismic performance of RC edge beam column slab connections. Four beam column slab subassemblies (two concentric and two eccentric connections) were tested. Each subassembly represented an edge connection subjected to lateral earthquake loading, isolated at inflection points between floors and between column lines. Considering a prototype structure with a storey height of 4. 5 m and a span length of 7. 5 m, the specimens represent approximately two-thirds-scale models; the scale factor is large enough to simulate the behaviour of the prototype RC structure. 11 Design of test specimens The specimens were designed and detailed in conformance with ACI requirements and recommendations for RC structures in high seismic zones. In particular, ACI (Building Code Requirements for Structural Concrete) 12 and ACI 352R-2 (Recommendations for Design of Beam Column Connections in Monolithic Reinforced Concrete Structures) 13 were strictly adhered to, except for a few design parameters that were specifically the subject of this investigation. Each specimen consisted of a column, two edgebeams framing into the column on opposite sides, and a transverse beam and floor slab on one side only. Fig. 2 shows plan views around the joints (floor slabs are not shown for clarity), and Fig. 3 illustrates reinforcing details in the specimens. In specimens 1, 2 and 3 all design details were identical except for the edge-beams, so the parameters varied in the first three specimens were the eccentricity (e) between the edge-beam and column centrelines, and the edge-beam width. (In particular, the connection geometry of specimen 1 was quite similar to that found in a nine-storey building that Magazine of Concrete Research, 24, 55, No

4 Shin and LaFave Transverse beam Column centroid 457 West Edge beam East (a) (b) (c) (d) Fig. 2. Plan views around joints (units: mm): (a) specimen 1 (e ¼ 89 mm); (b) specimen 2 (e ¼ 14 mm); (c) specimen 3 (e ¼ mm); (d) specimen 4 (e ¼ mm) (S4: #4@127) 8-# #3@83 4-#5 2-#5 #3@ #3@35 #3@83 2-#6 2-#5 #3@35 46 #3@ (a) (b) (c) 4-#7 at cor. 4-#6 at mid. 4-#5 #3@254 #3@35 2-#6 #3@35 #3@ #3@83 2-#5 46 #3@83 2-# (d) (e) (f) Fig. 3. Reinforcing details (units: mm): (a) column (specimens 1, 2 and 3); (b) edge-beam (specimens 1, 3 and 4); (c) transverse beam (specimens 1, 2 and 3); (d) column (specimen 4); (e) edge-beam (specimen 2); (f) transverse beam (specimen 4). See Table 3 for bar size designations 276 Magazine of Concrete Research, 24, 55, No. 6

5 RC edge beam column slab connections subjected to earthquake loading exhibited noticeable joint damage associated with a recent strong earthquake. 2 ) Specimen 2 had the largest eccentricity and the narrowest edge-beam width. In specimen 4 there were many different design details in comparison with the other specimens. The most important difference between the first three specimens and specimen 4 was the reinforcement ratio of longitudinal slab bars. In addition, each of the three beams framing into the column in specimen 4 covered more than three-quarters of the corresponding column face, whereas only the transverse beam did so in the first three specimens, with possible confinement implications. The edge-beams of all specimens were reinforced with the same number and size of reinforcing bars, to achieve similar beam moment strengths. All floor slabs were 122 mm wide (including the edge-beam width) and 12 mm thick, reinforced with a single layer of reinforcing bars in each direction. All longitudinal beam, column and slab reinforcement was continuous through the connection, except for transverse beam and slab bars, which were terminated with standard hooks within the column and edge-beams respectively. A minimum concrete clear cover of 25 mm was provided in all members. Table 1 summarises the main design parameters and other important values that are generally considered to govern the behaviour of RC beam column connections. When calculating the design 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 318-2, for both slab in compression and slab in tension. (The effective overhanging slab width for beams with a slab on one side only is taken as the smallest of one-twelfth the span length of the beam, six times the slab thickness, or one-half the clear distance to the next beam.) The total ACI effective slab width (including edge-beam width) was then 69 cm in specimens 1, 3 and 4, and 59 cm in specimen 2. The normalised design joint shear stress levels (ª d ) listed first and second were computed following ACI and ACI 352R-2 respectively. When computing the ª d values, longitudinal slab bars within the effective slab width (two bars for specimens 1, 2 and 3, and three bars for specimen 4) were included, as well as all top and bottom beam bars, per ACI 352R-2, but not per ACI The ª d values would be limited to 1. in the first three specimens and to in specimen 4 by both ACI and ACI 352R-2, based on the joint confinement level from adjoining members. The M r and ª d values were computed using design material properties. All specimens were reinforced with three layers of horizontal joint reinforcement; each layer consisted of a No. 3 hoop and two No. 3 cross-ties (nominal diameters of all bars used are provided in Table 3). This is approximately the minimum amount of joint reinforcement prescribed by ACI and ACI 352R-2 for the first three specimens, and about 1.5 times the minimum amount for specimen 4. Construction of test specimens For each subassembly, all members except the upper column were cast at one time; the upper column was typically cast one week later. Concrete with a maximum aggregate size of 1 mm and a slump of 125 mm was used to accommodate any steel congestion in the joint region and the small minimum clear cover of 25 mm. The design compressive strength of concrete was 28 MPa, and the design yield strength of reinforcing steel (ASTM standard reinforcing bars 12 ) was 42 MPa. Table 2 summarises the actual compressive strength of concrete on the day of subassembly testing. At least six concrete cylinders were cast for each placement of concrete, with three of them tested at 28 days for reference and the others tested on the day of the subassembly test. Table 3 lists the actual yield strength Table 1. Main design parameters and important values Specimen Eccentricity, e (mm) Edge-beam width, b b (mm) Longitudinal slab steel ratio (%) Moment strength ratio, M r * Joint shear stress level, ª d / / / /1.34 Joint reinforcement, A sh (mm 2 ) 213@83 mm 213@83 mm 213@83 mm 213@83 mm Member depth to bar h b /d b(col) diameter h c /d b(bm) * M r ¼ ÓM n (columns)/óm pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi n (beams)., ª d ¼ V j,u (N)= f c 9(MPa) b j (mm) h c (mm), V j,u ¼ design ultimate joint shear force. In ACI 318-2, b j ¼ b b +2x, x ¼ smaller distance between beam and column edges. In ACI 352R-2, b j ¼ b b + Ómh c /2, m ¼. 3 when e. b c /8, otherwise m ¼. 5. A sh ¼ total area of horizontal joint reinforcement within a layer (in the longitudinal direction.) d b(col) and d b(bm) ¼ maximum diameter of longitudinal bars used in column and edge-beam. Magazine of Concrete Research, 24, 55, No

6 Shin and LaFave Table 2. Compressive strength of concrete on the day of the subassembly test (MPa) Specimen Except upper column Upper column 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. 2% offset method. Table 3. Properties of reinforcing bars Specimens 1 and 2 Bar size No. 3 No. 5 No. 6 Column hoop f y (MPa) å y å sh n.a f u (MPa) Specimens 3 and 4 Bar size No. 3 No. 4 No. 5 No. 6 No. 7 Col. hoop, S3/S4 f y (MPa) /58 å y /.44 å sh n.a./n.a. f u (MPa) /731 Diameter (mm) of bars: No , No , No , No , No ( f y ), yield strain (å y ), ultimate strength ( f u ), and strain at the onset of strain-hardening (å sh ) for flexural reinforcing bars and column hoops. Three reinforcing steel Test set-up and loading sequence Figure 4 shows a picture of the test set-up with the specimen supports and other key components labelled. Reaction frame Actuator ( ) ( ) Out-of-plane translation constraint Drift reference frame Pin Pin Pin Beam-end support with load cell (typ.) Hinge Pin Fig. 4. Test set-up (specimen 4 in testing rig, looking south) 278 Magazine of Concrete Research, 24, 55, No. 6

7 The specimens were tested in their upright position. The column was linked to a universal hinge connector at the bottom and to a hydraulic actuator (with a swivel connector) 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 edge-beams and the top and bottom of the column were all pin-connected in the loading plane, to simulate inflection points of a frame structure subjected to lateral earthquake loading. The column pin-to-pin storey height (l c ) was 3. m, and the beam pin-to-pin span length (l b ) was 5. m. The interior edge of the floor slab was left free (unsupported), which neglected any possible effect of slab membrane action that might have provided additional confinement to the joint region. (Such compressive membrane forces were observed and credited for some strength enhancement in slab column connection tests where the slabs extended to the centrelines between columns in the transverse direction and rotation of the slab edges was restrained. 14 ) Uniaxial storey shear was statically applied at the top of the column (parallel to the longitudinal direction of the edge-beams) by a hydraulic actuator with a 45 kn loading capacity and a 25 mm linear range. (Positive (eastward) and negative (westward) loading directions are indicated in Fig. 4.) No external column axial load was applied, conservatively in accordance with results of previous studies that found the presence of column compression could either slightly improve joint shear strength 13 or have no apparent influence on joint shear strength. 15,16 The transverse beam and floor slab were not directly loaded. Because the specimens were not symmetric about the loading direction, a slotted steel bracket was installed near the top of the column in order to guide specimen displacements along the longitudinal direction only. 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). Column torsion was not a topic investigated in this study, and it should not considerably affect joint behaviour. (Furthermore, severe column damage from torsion has not been reported even for eccentric connection tests where column twist was restrained. 4 ) 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. Instrumentation used in each specimen was as follows. Roughly 6 electrical resistance strain gauges were mounted on reinforcing bars at key locations in and around the connection. Eight cable-extension gauges were installed on the top and bottom of the edge-beams to estimate beam rotations in the vicinity of the beam/column interfaces. Five linear variable differential transformers (LVDTs) were used on the exterior face of the joint to examine overall joint shear deformations. Finally, each beam-end support was RC edge beam column slab connections subjected to earthquake loading equipped with 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% storey drift. (The maximum drift of specimen 1 was limited to about 5. 5% owing to misalignment of the specimen.) Consecutive same-drift cycles were tested to examine strength degradation, and 1% drift cycles were inserted between other cycles to investigate stiffness degradation. Experimental results Load displacement response Figures 6(a) and 6(b) show the hysteretic loops of storey shear against storey drift (load against displacement) for specimens 2 and 3 respectively. They were typical in that they exhibited pinching (the middle part of each hysteretic loop was relatively narrow), as well as stiffness and strength degradation during repeat same-drift cycles. These were attributed to reinforcement bond slip through the joint region, concrete cracking, and/or reinforcement yielding. Fig. 6(c) compares the envelope curves of load against displacement for all four specimens, from connecting the peak drift point of each cycle. (Maximum loads for the specimens are summarised later in Table 6.) Among the first three specimens (with the same slab reinforcement), specimen 3 reached slightly larger maximum loads in both loading directions; this was attributed primarily to a difference in concrete compressive strength. Specimen 3 also exhibited higher stiffness than specimens 1 and 2 at the beginning of the test owing to high concrete strength. Consequently, the load displacement response of specimen 3 got flat slightly earlier (between 2% and 2. 5% drift cycles) than the others (between 2. 5% and 3% drift cycles). Specimen 4 reached the largest maximum load (2 3% higher than the other specimens), primarily because its floor slab was much more heavily reinforced. Yield points of the specimens are not easily deter Cycle number Fig. 5. Pattern of cyclic lateral displacements Magazine of Concrete Research, 24, 55, No

8 Shin and LaFave Storey shear: kn Ext. edge Int. edge Ext. edge 2 5 Int. edge (a) (a) (b) Storey shear: kn Ext. edge Int. edge Ext. edge Int. edge Storey shear: kn (b) S1 S2 S3 S4 (c) Fig. 6. Load against displacement response: (a) specimen 2; (b) specimen 3; (c) envelope curves (S1 ¼ specimen 1) mined from the load displacement curves because the reinforcement layout of the edge-beam and slab was not symmetric about the centreline of the beam, and because of slab reinforcement shear lag effects. Therefore yielding of individual bars in each edgebeam and slab was examined. Bottom beam bars typically underwent faster strain increases and consequently yielded earlier than top beam bars. Fig. 7 summarises the subassembly storey drift applied when each longitudinal beam bar yielded at beam/column interfaces; strain gauge data were compared with yield strains of the reinforcing bars. (Yielding of slab bars will be discussed in detail later.) First yielding of bottom beam (c) Fig. 7. Storey drift (%) at onset of beam bar yielding at beam/column interfaces: (a) specimen 1; (b) specimen 2; (c) specimen 3; (d) specimen 4 bars occurred during 1. 5% or 2% drift cycles in all specimens. (Therefore all specimens were eventually tested to a displacement ductility of almost 4.) In the first three specimens all beam and slab bars yielded by 3% drift cycles, whereas some slab bars in Specimen 4 did not yield by the end of the test. In all specimens beam bar yielding spread to half an effective beam depth away from the interfaces by 3% drift cycles, meaning that beam hinging developed adjacent to beam/column interfaces. Table 4 summarises storey shear forces at various drifts as a percentage of the maximum storey shear force reached in each specimen. (The table also indicates (by 1 ) that the specimens reached their maximum storey shear forces during 3% or 4% drift cycles.) Specimens 1, 2 and 4 underwent larger strength drops Table 4. Storey shear forces divided by maximum story shear forces (%) Storey drift (%) S1 S2 S3 S4 +3/ 3 1/1 99/99 99/1 96/97 +4/ 4 1/1 1/1 1/99 1/1 +5/ 5 96/95 92/95 97/95 94/96 +6/ 6 85/85 83/88 94/9 83/86 (d) 28 Magazine of Concrete Research, 24, 55, No. 6

9 than specimen 3, approximately 15% (an average for both directions) by the 6% drift cycle, whereas specimen 3 exhibited the most ductile load displacement behaviour. Considering that beam hinging typically does not cause large strength drops, some other failure mechanism probably developed, leading to the breakdown of specimens 1, 2 and 4. However, neither column hinging nor severe anchorage failure was observed throughout the tests. (With the ratio of column depth to beam bar diameter slighty greater than 2, the specimens did exhibit some beam bar slippage through the joint, as has been reported previously for other similar connections. 13 ) Therefore it was concluded that specimens 1, 2 and 4 failed as a result of joint shear (similar to previous studies, where it was also observed that beam column connections can fail from joint shear, although they undergo some beam hinging 16,17 ); this conclusion is strengthened in later sections. Strength degradation of the specimens was further examined by comparing storey shear forces of consecutive same-drift cycles (reduction in storey shear force during the second (repeat) cycle with respect to the first cycle). In all specimens strength degradation remained low (roughly 5%) until the 2% or 3% drift cycles, but it increased up to 13%, 19%, 12% and 18% in specimens 1 4 respectively, during the 5% drift cycle. Specimen 3 generally showed the smallest strength degradation throughout. Overall stiffness of a specimen for a particular loading cycle was defined as an average of the storey shear divided by the storey displacement at the positive and negative peak drifts of the cycle. In each specimen stiffness degradation continued throughout the test, and exceeded 8% of the first-cycle stiffness by the end of the test (the first-cycle stiffness was 25. kn/cm, 27.3 kn/cm, 39.3 kn/cm and 29.6 kn/cm in specimens 1 4 respectively). Stiffness degradation was faster before about 1% drift in all specimens, possibly because most of the concrete cracking and bond slip initiation occurred during the early stages of the tests. Energy dissipation The amount of energy dissipated during a loading cycle was calculated as the area enclosed by the corresponding load displacement hysteretic loop, presented in Fig. 8. In each specimen the energy dissipated during the 4% drift cycle was roughly twice that during the 3% drift cycle, even though storey shear barely increased between 3% and 4% drift. However, the rate of increase in energy dissipated per cycle (with respect to storey drift) quickly reduced during the 5% drift cycle, although strengths of the specimens did not drop by much. The table within Fig. 8 contains equivalent viscous damping (î eq ) values for various drift cycles of each specimen, computed following standard procedures described elsewhere. 18 (For comparison, î eq values for an elastic-perfectly plastic system with no pinching would RC edge beam column slab connections subjected to earthquake loading be %, 21% and 25% at displacement ductilities of 1, 2 and 3 respectively.) The specimens exhibited similar patterns of equivalent viscous damping throughout the tests. In particular, î eq values decreased after the 4% drift cycle in the first three specimens. Although specimen 4 showed a slightly different pattern, the variation between î eq values of all specimens for each cycle was negligible. Thus it may be concluded that the energydissipating capacity of these edge connections was very similar, whether they were eccentric or concentric, and regardless of their failure modes (even though specimens 1, 2 and 4 had some joint shear breakdown, their energy dissipation performance was similar to that of specimen 3). Plastic hinge development The rotational behaviour of the edge-beams near beam/column interfaces was investigated to examine the development of beam plastic hinges. In each specimen, eight cable-extension gauges were used to estimate beam rotations in the vicinity of the beam/column interfaces. The gauges were installed on top and bottom of the edge-beams (two gauges at each location), approximately one effective beam depth (355 mm) away from the column faces, to where a plastic hinge region might extend (see Fig. 11). Each gauge monitored the relative displacement between the column face and the section where the gauge was mounted; the values measured by the two gauges at a location were averaged. Beam rotations in the plastic hinge regions (Ł ph ) were computed by: Ł ph ¼ bot top h ph or top bot h ph (1) Here h ph is the vertical distance between gauges on the top and bottom of the edge-beam, bot is an average of the relative displacements measured by the two gauges on the bottom of the edge-beam, and top is an average of the relative displacements measured by the two gauges on the top of the edge-beam. Beam rotations were considered positive when the specimen was loaded in the positive direction. The estimated beam Energy dissipated per cycle: kn m Drift (%) Equiv. viscous damping (%) S1 S2 S3 S S1 S2 S3 S4 Fig. 8. Energy dissipated per cycle Magazine of Concrete Research, 24, 55, No

10 Shin and LaFave rotation comprised both plastic hinge rotation and rigid beam-end rotation. Plastic hinge rotation was due to yielding of longitudinal beam bars near the interfaces after concrete cracking. Rigid beam-end rotation was attributed to bond slip of reinforcing bars and opening of large flexural cracks at the interfaces. Figure 9(a) compares the envelope curves of storey shear against beam rotation in the two eccentric specimens, from connecting the peak drift point of each cycle. In the figure, E and W stand for the east and west beams respectively. In general, all edge-beams in both specimens showed similar beam rotations throughout testing (up to rotational ductility of about 8). The rate of increase in beam rotation (with respect to storey drift) got higher during the 2. 5% and 3% drift cycles, because all longitudinal beam and slab bars yielded by that cycle. Also, beam rotation increased whereas storey shear did not increase (or even decreased) during higher drift cycles (in other words, beam moments at the beam/column interfaces did not increase). These observations imply that beam hinging had developed in the plastic hinge regions. Figure 9(b) compares the envelope curves of storey shear against beam rotation in the two concentric specimens. Specimen 3 underwent beam hinging in the plastic hinge regions and generally had larger beam rotations (up to a rotational ductility of about 1) than the eccentric specimens and specimen 4. In specimen 3 Storey shear: kn Storey shear: kn Beam rotation: rad S1-W S1-E S2-W S2-E (a) S1 S S4 S Beam rotation: rad S3-W S3-E S4-W S4-E (b) Fig. 9. Envelope curves of storey shear against beam rotation: (a) specimens 1 and 2; (b) specimens 3 and 4 S3 S4 S2 S1 the increment in beam rotation from 2% to 3% drift was roughly twice that from 1% to 2% drift. Also, beam rotation increased whereas storey shear barely increased from the 2.5% drift cycle onward. Specimen 4 generally exhibited the smallest beam rotations out of all four specimens (up to a rotational ductility of about 6). In specimen 4 the rate of increase in beam rotation (with respect to storey drift) rose somewhat during the 3% drift cycle; however, it dropped after the 4% drift cycle as the specimen started to break down because of joint shear. Slab bar strains The first three specimens had four longitudinal slab bars (at the same floor slab locations), whereas specimen 4 was reinforced with seven longitudinal slab bars. Each longitudinal slab bar was instrumented with a strain gauge located crossing the west beam/column interface. Fig. 1 illustrates the strain profiles of longitudinal slab bars in a section crossing the west beam/ column interface at peak drift points of various cycles. (The top of the west beam/column interface was in tension when the specimen was loaded in the positive direction.) All longitudinal slab bars experienced continuous strain increases before yielding, as storey drift got larger. Therefore it was clear that slab participation (to beam moment strengths and joint shear demands) got larger as each specimen was subjected to larger storey drifts. The slab bar nearest to the edge-beams generally underwent the fastest strain increase, except in specimen 2. Onset of slab bar yielding occurred during the 1. 5%, 1% and 2% drift cycles in specimens 1, 2 and 3 respectively, and all longitudinal slab bars yielded by 3% drift in the first three specimens. Specimens 1 and 2 showed larger slab bar strains than specimen 3, possibly because the longitudinal slab bars were located closer to the column in the first two specimens. However, in specimen 4 only the two slab bars nearest the edge-beam underwent yielding by the end of the test. (The slab bar nearest the edge-beam underwent yielding during the positive 4% drift cycle, and then the strain quickly dropped, possibly as a result of partial de-bonding of the strain gauge.) Lower slab bar strains in specimen 4 were partly attributed to its column and transverse beam, which were narrower than in the other specimens, and also to torsional distress in the transverse beam at the column face. These issues will be explored further in later sections. Joint shear deformation Initial joint shear cracks were observed during the. 75% drift cycle in all four specimens. The cracks were diagonally inclined and intersected one another, owing to the reversed loading. Some joint concrete spalled off from the exterior joint face after extensive cracking at higher storey drifts. Specimens 3 and 4 underwent the least and the most joint concrete crack- 282 Magazine of Concrete Research, 24, 55, No. 6

11 RC edge beam column slab connections subjected to earthquake loading Microstrain (S1) Yield Microstrain (S2) Yield Column width Beam width Distance from exterior face of slab: cm (a) Column width Beam width Distance from exterior face of slab: cm (b) Microstrain (S3) Yield Microstrain (S4) Yield Column width Beam width Distance from exterior face of slab: cm (c) Column width Beam width Distance from exterior face of slab: cm (d) Fig. 1. Slab bar strain profiles across west beam/column interface (storey drift (%) in legend): (a) specimen 1; (b) specimen 2; (c) specimen 3; (d) specimen 4 ing and spalling respectively. To monitor overall joint shear deformation in an average sense, five LVDTs were installed at the exterior face of the joint in each specimen (see Fig. 11). Considering the two triangles formed by the LVDTs, angular changes at the 98 angles were computed for each measuring step. Then the average of the two angular changes was defined as the joint shear deformation (ª) at the exterior face of the joint, as explained in Fig. 11. Figure 12 shows the envelope curves of storey shear against joint shear deformation, from connecting the peak drift point of each cycle. The eccentric connections (specimens 1 and 2) exhibited similar joint shear deformations at a relatively slow rate of increase during Joint γ 2 36 cm γ 1 28 cm LVDTs γ (γ 1 γ 2 )/2 2 Cable extension gauges at a location Undeformed LVDTs Deformed LVDTs Fig. 11. Eight cable-extension gauges and five LVDTs Magazine of Concrete Research, 24, 55, No

12 Shin and LaFave Storey shear: kn 12 Joint contribution to storey displ. (%) Drift (%) 9 S1 S2 S3 S Joint shear deformation: rad S1 S2 S3 S4 Fig. 12. Envelope curves of storey shear against joint shear deformation the early stages of the tests. However, the rate of increase in joint shear deformation (with respect to storey drift) became higher during the 2. 5% and 3% drift cycles. This fast increase occurred without considerable rises (or even with drops) of storey shear in these specimens. This resulted from cracking, crushing and/or spalling of some joint concrete because of joint shear. Specimen 2 eventually underwent larger joint shear deformations than specimen 1, during the negative 5% and 6% drift cycles. The joint shear deformations exhibited by these two specimens (roughly radians maximum) were similar to or larger than those in other eccentric connections found in the literature that failed by joint shear. 3,5,6 Specimen 3 exhibited very small joint shear deformations (less than. 7 radians maximum). This may be partly because the joint shear deformations were measured at the exterior face of the joint (over 85 mm away from the exterior face of the edge-beams), so they did not necessarily represent joint shear deformations in the joint core. However, it was unlikely that specimen 3 underwent joint shear deformations as large as the other specimens anyway because it exhibited relatively moderate joint cracking damage and showed the most ductile overall load displacement behaviour. (For comparison, all eight cruciform concentric connections tested by Joh et al. 19 underwent beam hinging without joint shear failure, and they exhibited joint shear deformations of less than. 4 radians by 5% drift.) Specimen 4 had the largest joint shear deformations among all four specimens (especially in the positive direction), and the rate of increase got higher from the 2. 5% drift cycle, without considerable rises (or even with drops) in storey shear. The rapid increases in joint shear deformation occurred after exceeding approximately.1 radians in specimens 1, 2 and 4. (For these specimens, a joint shear deformation of. 1 radians by itself produces roughly. 8% drift, as will be described below in more detail.) The above observations support the conclusion that specimens 1, 2 and 4 started to break down as a result of joint shear during the tests. The portion of storey displacement due to joint shear deformation was computed using the joint shear deformations measured at the exterior face of the joint, assuming the column and the edge-beams remained rigid (and assuming the measured joint shear deformations were representative of the values through the joint). The table within Fig. 12 presents the percentage contribution of joint shear deformation to the applied storey displacement (at the top of the column); each number is an average for both loading directions at the indicated storey drift. By the end of the tests, the joint shear deformation contribution to overall drift was 42%, 53% and 58% in specimens 1, 2 and 4 respectively. The joint shear deformation contribution was also significant (greater than 25%) within the cracked elastic range of behaviour (for instance, even at 1% drift). Specimen 3 showed smaller joint shear deformation contributions to drift than the other specimens, which agrees with the observation that it experienced larger beam rotations than the other specimens. Joint hoop strains In each specimen, three layers of horizontal joint reinforcement (each consisting of a hoop and two cross-ties) were equally spaced at 83 mm between the top and bottom longitudinal beam bars. Each joint hoop was instrumented with two strain gauges, one near the centre along each of the legs parallel to the loading direction, to monitor strain at the exterior and interior sides of the joint. Fig. 13 shows the envelope curves of joint hoop strain against storey drift in all 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 gauge was broken after the specified cycle. In general, joint hoop strains at the exterior side of the joint were larger than those at the interior side for both eccentric and concentric specimens, in part because the transverse beam and floor slab provided some confinement to the interior side of the joint. There are additional possible reasons for this phenomenon in the eccentric specimens. From the standpoint of eccentric joint capacity, the interior (offset) side could be less effective than the exterior (flush) side in resisting joint shear forces. From the standpoint of eccentric joint demand, eccentricity between the beam and column centrelines could induce torsion in the joint region, resulting in an increase in net shear stress near the flush side. However, a big difference was not found between the joint hoop strains of specimens 1 and 3 (eccentric and concentric specimens with identical edge-beam width), suggesting that these latter two effects were not very significant, probably because the floor slabs expanded effective joint width and reduced joint torsional demand by shifting the acting line of the resultant force from top beam and slab reinforcement. The eccentric connections with floor slabs and transverse beams in 284 Magazine of Concrete Research, 24, 55, No. 6

13 RC edge beam column slab connections subjected to earthquake loading Microstrain at int. side (S1) Microstrain at int. side (S2) Microstrain at int. side (S3) Microstrain at int. side (S4) Bottom Middle Top Bottom Middle Top Bottom Middle Top Bottom Middle Top Microstrain at ext. side (S1) Microstrain at ext. side (S2) Microstrain at ext. side (S3) Microstrain at ext. side (S4) Bottom Middle Top Bottom Middle Top Bottom Middle Top Bottom Middle Top Fig. 13. Envelope curves of joint hoop strain against storey drift (int. ¼ interior, ext. ¼ exterior) (S1 = specimen 1) this study showed more uniform strain distributions across 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. In all specimens, joint hoop strains started to rise after several small drift cycles, and they increased even Magazine of Concrete Research, 24, 55, No

14 Shin and LaFave while storey shear decreased during 5% and 6% drift cycles, although the rate of increase in strain got lower at high storey drifts. Specimens 2 and 4 generally exhibited larger joint hoop strains than specimens 1 and 3, which was consistent with the observation that specimens 2 and 4 underwent larger joint shear deformations. Comparing the two eccentric specimens, specimen 2 exhibited larger increments in joint hoop strain than specimen 1 at high storey drifts, which agreed with the fact that specimen 2 underwent larger joint shear deformations after starting to break down. Comparing specimens with the same edge-beam width, specimen 4 underwent larger joint hoop strains than specimens 1 and 3, because specimen 4 had the smallest effective joint area and was subjected to the largest joint shear force due to the heavily reinforced slab. Yielding of joint reinforcement was investigated based on the yield strain of the joint hoops determined by the. 2% offset method. (The yield strain was about.45 in all tests, with the stress strain proportional limit occurring at a strain of approximately. 3.) Only the middle joint hoop of specimen 4 yielded (during the negative 5% drift cycle) at the interior side of the joint; however, many joint hoops yielded or approached yielding during 4% or 5% drift cycles at the exterior sides of the joints. (For some joint hoops, it was not possible to distinguish whether they yielded or not, because their strain gauges broke during the tests.) In particular, the middle joint hoops of specimens 2 and 4 saw very large strains of nearly. 7. Analysis of test results Effective slab width contribution (to beam flexural strength and joint shear) The concept of an effective slab width is generally used to incorporate floor slab contributions (to beam moment strength and joint shear demand) in RC design. It is well known that the slab contribution depends strongly on imposed lateral drift level. In this study the number of effective slab bars at a particular storey drift was defined, considering slab in tension, as the sum of forces in all longitudinal slab bars (at the storey drift) divided by the product of actual yield strength and area of the bars. To compute this, first the strain in each longitudinal slab bar (plotted in Fig. 1) was divided by the yield strain of the bar; one (1.) was assigned if this strain ratio was larger than unity. Then the number of effective slab bars was computed by adding the strain ratios of all longitudinal slab bars, and the corresponding effective slab width was estimated considering the locations of the slab bars. Table 5 lists the number of effective slab bars and the effective slab width at various storey drifts. When each specimen reached its maximum storey shear force, the number of effective slab bars (and corresponding effective slab width) computed in this way was 4. (122 cm), 4. (122 cm), 3. 9 (119 cm) and 4. (77 cm) in specimens 1 4 respectively. These numbers of effective slab bars will be used to estimate maximum joint shear demands of the specimens in a later section. (The maximum effective slab width of specimen 3 could have been larger if a wider slab had been tested, as all longitudinal slab bars yielded and the specimen did not experience joint shear failure.) The maximum effective slab width that can potentially contribute to beam flexural capacity may not be fully activated when a connection fails in part due to other modes before complete beam hinging; this may have occurred in specimens 1, 2 and 4. The maximum effective slab width in specimen 4 seems to have also been limited by the torsional strength of the transverse beam, which was subjected to large torsional moments near the column face, where concrete cracking and spalling damage occurred as shown in Fig. 15. The torsional moments were generated as a result of the vertical distance (d t ) between longitudinal slab bars and the centroid of the transverse beam. At positive 4% drift, for instance, tensile forces in all longitudinal slab bars at the west beam/column interface can be computed using strain gauge data from Fig. 1. Considering only the tensile slab bar forces, without taking into account any concrete or slab bar forces at the east beam/column interface, the possible torsional moment applied at the column face adjacent to the transverse beam in specimen 4 is equal to the sum of the slab bar forces times d t, or 46.8 kn m. (Some portion of the slab bar forces may Table 5. Number of effective slab bars and corresponding effective slab width Drift (%) Number of effective slab bars Effective slab width (cm) S1 S2 S3 S4 S1 S2 S3 S n.a n.a Magazine of Concrete Research, 24, 55, No. 6

15 RC edge beam column slab connections subjected to earthquake loading enter into the joint by means of diagonal compression in the slab panel and/or weak axis bending of the transverse beam, as well as torsion of the transverse beam. 1 ) This torsional moment is equal to 8% of the torsional strength of the transverse beam, computed based on the thin-walled tube (space truss) analogy per ACI The transverse beam in specimen 4 was also under considerable horizontal shear from the four slab bars, 286 kn, which is 8% of the shear strength of the transverse beam, also computed per ACI Therefore it was judged that the transverse beam in specimen 4 suffered distress due to a combination of torsion and shear, thereby limiting the amount of slab participation. On the other hand, the transverse beams in the first three specimens did not experience much distress; they only reached less than 35% of their torsional strengths and 35% of their shear strengths. The ACI effective slab width for design would be 69 cm for specimens 1, 3 and 4, and 59 cm for specimen 2, which encompasses two, two, two and three longitudinal slab bars in specimens 1 4 respectively. (According to ACI 318-2, a single effective slab width for design is used regardless of positive or negative bending, or of the magnitude of imposed lateral drift.) The number of effective slab bars determined above (when each specimen reached its maximum storey shear force) was more than the number of slab bars included within the ACI effective slab width, particularly in specimens 1 3. In other words, the effective slab width estimated based on slab bar strains was times larger than the ACI effective slab width in the first three specimens, but similar to the ACI value in specimen 4 (with a narrower column and a transverse beam that suffered some deterioration). The actual effective slab width when each specimen reached its maximum storey shear force was roughly equal to the column width plus two times the transverse beam width for these test specimens. Chapter 21 of ACI comments that the ACI effective slab width is reasonable for estimating beam negative moment strengths of interior connections at roughly 2% drift. In this study the effective slab width estimated at 2% drift was 19 cm, 17 cm, 89 cm and 52 cm in specimens 1 4 respectively; these values are also substantially larger than the ACI effective slab widths in the first three specimens, and somewhat smaller in specimen 4. (In fact, laboratory experiments on edge connections with floor slabs on one side only, loaded in the longitudinal direction of the edge-beams, have not previously been reported in the literature and would therefore not be the basis for current ACI procedures to estimate effective slab width.) This is of particular importance because a smaller effective slab width is not conservative for estimating joint shear demand or column-to-beam moment strength ratio. Because all specimens underwent beam hinging near beam/column interfaces, the predicted storey strength (V c,m(cal) ) of each specimen may be computed assuming the edge-beams reached their nominal moment strengths at the beam/column interfaces: V c,m(cal) ¼ (M þ n þ M n ) l b (2) l c (l b h c ) Here M þ n and M n are beam positive and negative nominal moment strengths, computed using the ACI nominal moment strength calculation method (equivalent rectangular stress block concept) with actual material properties. These beam nominal moment strengths depend on the amount of slab participation. Table 6 compares the predicted storey strength (V c,m(cal) ), computed using the number of effective slab bars (about four in each specimen) and corresponding effective slab width when each specimen reached its maximum storey shear force, with the measured storey strength (V c,m(exp) ), which is the maximum storey shear force. The V c,m(cal) values are 6%, 11%, 4% and 1% higher than the V c,m(exp) values in specimens 1 4 respectively. (V c,m(exp) values for positive loading were used for this comparison because the specimens underwent some damage after being loaded first in the positive direction.) In other words, the beam slab moment strengths in specimens 1 3 are slightly overestimated considering the effective slab bars computed based on slab bar strains. This is because some concrete at the bottom of these edge-beams near beam/column interfaces started to spall off at about 2. 5% drift, which reduced beam sectional moment arms, leading to smaller actual storey strengths than the computed values (in specimen 4, concrete spalling did not occur at the bottom of the edge-beams). Slab effect on joint shear demand Considering horizontal force equilibrium of an RC joint free body diagram, and moment equilibrium of Table 6. Measured and predicted storey strengths Specimen V c,m(exp) (kn) (+) loading ( ) loading V c,m(cal) (kn) No. of included slab bars Magazine of Concrete Research, 24, 55, No

16 Shin and LaFave the edge-beams, the horizontal joint shear force (V j )at mid-height of the joint during a test can be computed as explained in Fig. 14. Here V 1 and V 2 are the edgebeam end shears, which are simply the axial forces measured in the east and west beam-end supports respectively, and V c is the applied storey shear force. Also, jd 1 and jd 2 are the beam moment arms at the east and west beam/column interfaces, which were assumed to be 355 mm for sagging (positive) moments, and 33 mm (35 mm in specimen 2) for hogging (negative) moments. (These assumed moment arms were the ones determined above when calculating the nominal moment strengths of the edge-beams.) Using this method, the maximum joint shear force was computed to be 631 kn, 67 kn and 793 kn in specimens 2, 3 and 4 respectively. (This method could not be used in specimen 1 because the load cells in the beam-end supports did not operate.) V 1 (l b h c )/2 East edge-beam V j C b1 T b2 V c C b1 V 1 (l b h c )/2jd 1 T b2 V 2 (l b h c )/2jd 2 C b1 C jd b1 Joint 1 T b1 jd 1 V j Vj The maximum joint shear force can also be determined using an alternative method. All beam longitudinal bars yielded at beam/column interfaces before each specimen reached its maximum storey shear force, but no longitudinal beam or slab bars underwent strainhardening during testing. Therefore the maximum joint shear force (V j,m ) can be estimated at the storey drift when each specimen reached its maximum storey shear force as: T b1 Fig. 14. Edge-beam and joint free body diagrams V j,m ¼ X A s f y V c,m(exp) (3) V c V c jd 2 T b2 C b2 Here A s is the area of each reinforcing bar, f y is the actual yield strength of each reinforcing bar, and V c,m(exp) is the maximum storey shear force measured at the column top. The summation term includes all (top and bottom) longitudinal beam bars, as well as the four effective slab bars for each specimen (as determined above). Using this equation, the V j,m value was 647 kn, 651 kn, 643 kn and 792 kn in specimens 1 4 respectively. Maximum joint shear forces estimated with the two methods are in good agreement, with a discrepancy of less than 5%. However, the latter method was considered to estimate maximum joint shear forces better, because the former method was based on assumed beam moment arms. As mentioned earlier, ACI does not consider slab participation in joint shear demand design calculations, whereas ACI 352R-2 recommends including slab reinforcement within the ACI effective slab width. The experimental maximum joint shear forces (V j,m ) exceeded the values computed per ACI by roughly 25% in the first three specimens and 55% in specimen 4, and they also exceeded the values computed per ACI 352R-2 by roughly 1% in all four specimens. Specimen 4 probably would not have undergone joint shear failure if it had been reinforced with a lower slab steel ratio similar to that of the other specimens. Slab effect on joint shear capacity The effect of floor slabs (and transverse beams) on RC joint shear capacity was evaluated by estimating effective joint widths of the eccentric specimens in this study and comparing them with other eccentric specimens without slabs found in the literature. For a specimen that failed due to joint shear, its joint shear strength can be considered equal to the maximum joint shear force (V j,m ) applied during the test, and thus an effective joint width (b j,exp ) for the specimen may be estimated by: V j,m (N) b j,exp (mm) ¼ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi (4) ª n f c 9(MPa) h c (mm) Here ª n is the nominal joint shear stress level specified by ACI and ACI 352R-2, to place eccentric connections on an equal basis for comparison with similar concentric connections. Table 7 summarises the maximum joint shear forces (V j,m ) and the estimated effective joint widths (b j,exp ) of eccentric specimens (from this testing programme and from the literature) that were judged to fail because of joint shear (ª n is 1. for all specimens in the table). To appreciate the effect of the floor slabs, the b j,exp values were normalised using an equation suggested by Raffaelle and Wight: 5 Fig. 15. Torsional damage of transverse beam in specimen 4 b c b j,rw ¼ (5) 1 þ 3e=x c Here e is the eccentricity between beam and column 288 Magazine of Concrete Research, 24, 55, No. 6