RESPONSE OF RC FRAME UNDER LATERAL

RESPONSE OF R C

F R A M E UNDER LATERAL L O A D S

By X. Qi1 and S. J. Pantazopoulou,2 Member, ASCE ABSTRACT: The experimental response of a single-story, indeterminate reinforced concrete (RC) frame with floor slabs is investigated in this paper. The frame was quarter-scale and tested under static lateral-load reversals simulating earthquake load. The internal force redistribution occurring within the inelastic range of response and the beam flexural overstrength resulting from slab contribution are evaluated. It is shown that the pattern of lateral-load distribution in indeterminate structures is severely affected by the partial restraint that continuity imposes on the inelastic member expansion, particularly at large levels of lateral displacement. Specimen behavior is characterized in terms of strength, stiffness, lateral drift ratio, and plastic hinge-formation. The mechanism by which shear is introduced to beamcolumn joints of connections with floor slabs is examined. The performance of the current code recommendations for design of beam-column joints is investigated in view of the combined effects of continuity and contribution of floor-slabs to the flexural resistance of the beams. INTRODUCTION

Current requirements for joint design of reinforced concrete (RC) structures ("Recommendations" 1985) have been based on extensive experimental studies of the inelastic behavior of individual RC frame connections (Hanson et al. 1967; Meinheit et al. 1981; Paulay et al. 1978; Uzumeri et al. 1974). A large number of the specimens tested have been statically determinate (SD) subassemblies, modeling interior or exterior connections of frame structures. However, more recently, a limited number of tests have been carried out on statically indeterminate (SI) specimens of various configurations and degrees of static redundancy ("Interim" 1984; Shahrooz and Moehle 1987; Zerbe and Durrani 1988). These tests have revealed important differences between the behavior of SD and SI types of specimens, particularly in the observed strengths and failure mechanisms. Typically, failure of statically determinate structures is initiated by the formation of the first plastic hinge in any member. In contrast, formation of the first plastic hinge in a statically indeterminate structure merely triggers redistribution of internal forces throughout the members of the structure; this results in local stress relief of the plastic-hinge regions and relocation of forces to less damaged members. Redistribution of forces may occur as long as the structure is statically redundant. The magnitude of the resulting internal actions depends on the intensity of deformation and the relative stiffnesses of the members. However, experiments conducted on indeterminate test structures indicate that in statically redundant specimens, internal actions are also affected by the relative stiffness of the testing equipment, the loading history, the experimental setup, and the method of application of loads. For this reason, a quantitative assessment of the effects of indeterminacy on 'Struct. Engr., Skidmore, Owings & Merrill, 333 Bush St., San Francisco, CA 94104-2894. 2 Asst. Prof., Dept. of Civ. Engrg., Univ. of Toronto, Toronto, Ontario, M5S1A4, Canada. Note. Discussion open until September 1, 1991. To extend the closing date one month, a written request must be filed with the ASCE Manager of Journals. The manuscript for this paper was submitted for review and possible publication on March 5, 1990. This paper is part of the Journal of Structural Engineering, Vol. 117, No. 4, April, 1991. ©ASCE, ISSN 0733-9445/91/0004-1167/$1.00 + $.15 per page. Paper No. 25713. 1167

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the behavior of RC structures may require a large number and variety of tests. This paper investigates the internal force redistribution and the effects of continuity on the behavior of an indeterminate RC frame structure that was tested at the University of California, Berkeley (Qi 1986). The frame was a single story, two-bay subassemblage of a quarter-scale, multistory reinforced concrete structure that had been tested on a shake table (Shahrooz and Moehle 1987). The specimen had a floor slab cast monolithically with the beams and was tested under static lateral-load reversals simulating earthquake load. The subassemblage test was carried out with the following objectives: (1) To study the behavior of reinforced concrete ductile momentresistant frames when subjected to earthquake-type lateral-load reversals; (2) to determine the influence of slabs on the performance of the supporting beams; and (3) to study the internal force redistribution occurring within the inelastic range of response. DESCRIPTION OF EXPERIMENTAL PROGRAM

Model Description A general view of the specimen is shown in Fig. 1(a). The specimen represented the lower interior frame of the model structure shown in Fig. 1(b). The columns of the specimen [Fig. 1(a)] were extended one-half story height above the slab (to the approximate location of the inflection points in the second-story columns of the model structure). During the experiment, vertical and lateral loads were applied at the top of the columns. Using this loading setup, the stress conditions induced in the beam-column joints of the specimen were comparable to those of the first-story joints of the structure shown in Fig. 1(b). The model structure [Fig. 1(b)] was designed according to the American Concrete Institute's ACI 318-83 Building Code ("Building Code" 1983) and satisfied the ACI-ASCE Committee 352 recommendations for joint dimensions and confinement ("Recommendations" 1985). Member dimensions and reinforcing details of the specimen discussed here were identical to those of the model structure. The story height of the subassemblage was 915 mm (36 in.) (Fig. 2). The center-to-center beam span was 1,900 mm (75 in.), and the total width of the slab was 1,145 mm (45 in.). The longitudinal beam-web cross section

"LP-

^ &

^

&

(a)

^

(b)

FIG. 1. Specimen Tested: (a) General View of Specimen; and (b) Six-Story Prototype Model

1168

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line of action of servo-controlled /-actuators (to avoid unrealistic restraint)

w 5"— (typical)

T

^m — 5"

ra

75"

(a)

FIG. 2. Quarter-Scale Frame Structure: (a) Elevation in Longitudinal Direction; and (b) Elevation in Transverse Direction

was 180 mm by 130 mm (7 in. by 5 in.); the spandrel beam-web cross section was 190 mm by 100 mm (7.5 in. by 4 in.). The slab was 45 mm (1.75 in.) thick. Column dimensions were 130 mm (5 in.) in the direction of the loading and 165 mm (6.5 in.) in the transverse direction. A 400-mm(16-in.-) square, 300-mm- (12-in.-) high footing block was attached at the base of each column. Longitudinal beam reinforcement consisted of two no. 2 and one no. 1 grade 60 deformed bars placed at the bottom of the cross section along the entire length of the member (bottom reinforcement ratio of 0.39%). Three no. 2 bars and two no. 1 bars were used as top reinforcement at the interior and exterior supports (0.64% top reinforcement ratio). The no. 2 bars were continuous over the entire length of the beam and hooked at the exterior joints (0.48% top reinforcement ratio at midspan). Stirrups were devised of no. 11 gauge plain wire and were spaced at 38 mm (1.5 in.) on centers (o.c.) near the joints and at 50 mm (2 in.) o.c. along the remaining length of the beam. Transverse beams contained eight no. 2 bars placed symmetrically at the top and bottom of the cross section (corresponding steel ratio of 1.3%). Stirrups were spaced uniformly at 38 mm (1.5 in.) o.c. Slab reinforcement consisted of two layers (top and bottom, longitudinal and transverse) of no. 9 steel wire with knurled deformations. The top layer of longitudinal slab bars was extended up to a distance of 700 mm (27.5 in.), measured from the column faces. The main reinforcement of the columns was comprised of four no. 3 and six no. 2 grade 60 deformed bars. The longitudinal steel ratio (over the gross area of the column cross section) was 2.26%. The rebars were anchored into the footing block with standard 90° hooks at the bottom, and were welded to steel plates at the top of the columns. No. 9 gauge plain wire was used as transverse reinforcing steel. Stirrups were spaced at 25 mm (1 in.) o.c. near the column ends and at 38 mm (1.5 in.) o.c. along the remaining length of the column. Material Properties Due to the small scale of the specimen (one-quarter scale), some reinforcing bars were not within the diameter range typically used in construction. Nominal areas (in square millimeters) of the nos. 3,2, and 1 and slab reinforcing bars were 70, 30, 16, and 11, respectively. Yield stresses, mea1169 Downloaded 22 Feb 2010 to 83.212.134.238. Redistribution subject to ASCE license or copyright; see http://pubs.asce.org/copyright

SO-kip Jack "" kip Load Cell kip Load Cell " kip Actuator

Cross-Section A-A aluminum plates plan

^ * -

A|_

JA

(b)

(a)

FIG. 3. Loading Setup: (a) Loading Frame and Test Setup; and (b) Load Transducers Used at Base of Columns

sured by coupon tests, were in the range of 445 MPa, except for the slab bars, which yielded at 415 MPa. All bars had a distinct yield plateau region, but after strain-hardening they reached maximum stresses of 660, 590, 670, and 590 MPa, respectively, at an approximate strain level of 0.1. The concrete mix was designed to have a 28-day compressive strength of 27 MPa (4,000 psi). The maximum aggregate size was limited to 10 mm (3/8 in.). The average measured compressive strength at the day of the test was 35 MPa (5,100 psi), at a strain of 0.0025. Load Setup The overall view of the test setup is shown in Fig. 3. The test was initiated by placing lead weights [120 lb/sq ft (5.75 kN/m2)] on the floor slab to simulate the self-weight of the prototype full-scale structure. Then, the interior and exterior columns were axially compressed by an average stress of 0.09/c and 0.045/^ respectively. The magnitudes of the applied axial loads were equivalent to 30% of Pbc,i for the interior column and 15% of Pbal for the exterior columns; the loads were kept constant throughout the test and were intended to simulate the weight of the assumed superstructure and provide a stiffening effect to the columns. Static lateral loads with a cyclic history were then applied at the upper ends of the columns above the slab. The total load was applied to the north column using displacement control and was distributed to the three columns by two dynamic actuators from MTS, which were positioned horizontally at the top of the specimen between the columns (Fig. 3). Linear voltage, differential transformers (LVDTs) mounted on the top surface of the main beam between the column centerlines measured the growth of the beam occurring within the two spans at each load increment. The MTS actuators were operated under displacement control; the relative displacement of the ends of each actuator was set equal to the measured beam growth within the respective span. This loading arrangement was used to avoid introducing unrealistic restraint to the horizontal elements of the specimen, which would tend to affect the stiffness of the structure and the distribution of lateral forces to the columns. Fig. 4(a) shows the displacement histories of the three columns at the top of the specimen; the solid line represents the imposed displacement history 1170


(c) 20.0

5

-4.0 20.0 0.0

£.

0.0

-20.0 -10.0

Tfrrnn HTp"H"H"H'l | i M i i 11 i i | 0.0 10.0 Displacement (Inches)

FIG. 4. Measured Response: (a) Displacement Histories at Top of Columns; (b) History of Lateral Load Applied on North Column; and (c) Load-Displacement Diagram

of the north column, which was controlled during the test. The imposed displacement corresponded to interstory drift values (ratio of relative lateral story deflection to story height) ranging between 0.25% and 8.6%. Average lateral drift ratios (total lateral displacement of the top of the specimen to total height) were approximately the same as the interstory drift ratios, except for the last few cycles of the test, where localization of damage in the plastic hinge regions of the specimen caused some discrepancies between average lateral and interstory drift ratios. In the following, both the interstory and the average lateral drift ratios will be used to characterize the behavior of the specimen at various stages of the test. Drift levels exceeding the range of 1.5%—2% are not likely to be reached by actual structures. However, data obtained at larger levels of lateral drift will be included in the discussion because they provide some insight regarding the mechanisms of load transfer and redistribution occurring in frame structures. Variation of the total lateral load applied at the north side of the structure is also plotted in Fig. 4(b). The diagram has been corrected for the P-A effects of the column axial loads. Instrumentation Load cells mounted in the hydraulic actuators were used to measure the lateral and vertical loads applied to the columns. Distribution of the loads within the specimen was established using multifunctional transducers, which were located under each column footing block. The transducers were made of aluminum; the cross section is shown in Fig. 3. The arrangement of the aluminum plates was intended to practically separate the shear-stress components (mainly carried by the plates parallel to the load) from axial and flexural stresses. The transducers were instrumented and calibrated to read axial load, shear force, and bending moment. Displacement transducers (LVDTs) were used to measure lateral displacements at several locations in the structure, rotation of the longitudinal beams 1171 Downloaded 22 Feb 2010 to 83.212.134.238. Redistribution subject to ASCE license or copyright; see http://pubs.asce.org/copyright

relative to the column face, pull-out of the main beam reinforcement from the beam-column joints, and twist of the southern exterior transverse beam relative to the south column. Strain gauges were placed on the top and bottom slab bars, on the longitudinal reinforcement of the main beam and columns, and on stirrups at the supports of the transverse beams. OBSERVED RESPONSE

Overall, the specimen exhibited a stable, ductile, hysteretic behavior, even under exceedingly large levels of lateral drift. The measured lateral-loaddisplacement diagram is shown in Fig. 4(c). The lateral load reached its maximum value at 3.8% interstory drift (3.6% average lateral drift ratio^ This maximum corresponded to an average base-shear stress of 0.21 \fc MPa (2.6 \ffc psi). At 2% interstory drift ratio, which is often considered a design limit, lateral force did not exceed 85% of the strength. During the first cycle at 5.8% interstory drift ratio, the bottom beam bars buckled near the south exterior joint. Upon reversing the load, those bars fractured [point FR in Fig. 4(c)]. Despite the fracture, the load-carrying capacity of the specimen was maintained without sharp reduction up to 7.2% interstory drift (7% average lateral drift), indicating a successful internal force redistribution within the structure. During the last cycle of the test, the specimen sustained 11.96% average lateral drift; at this stage, the lateral strength of the specimen was reduced by 27%. Plastic-hinge formation could be deduced from the observed cracking patterns and from reinforcement strain readings. Under lateral loads, cracks were initiated at the bottom of the longitudinal beam near the column faces. During load reversals, flexural cracks opened over the entire beam depth near the exterior supports indicating significant yielding of the reinforcement and plastic-hinge formation at these locations. Cracks in the beam near the interior joint were narrow and did not penetrate through the depth, suggesting that the slab reinforcement and top beam bars did not undergo significant inelastic deformations. In contrast, extensive cracking was observed on the interior column over a distance of 2.54. fr°m t n e supports, where dc is the effective depth of the column cross-section. Although the design column-to-beam flexural strength ratio was approximately 2 at the interior joint, observed crack widths indicated plastic hinge formation at the base of the interior column and above and below the interior joint. This observation is also supported by strains in the column longitudinal reinforcement obtained at the end cross sections. Plastic hinges formed at the base of the exterior columns as well. Beyond 3.5% interstory drift, cracks were uniformly distributed on the outer faces of the exterior columns suggesting inflection point movement along the column height with increasing intensity of lateral displacement. Formation of plastic hinges in the interior column above and below the joint is attributed to the increased beam strength resulting from slab participation not accounted for in the design. Participation of the slab to beam flexure was evident from extensive cracking that was observed on the slab around the interior and exterior joints. Slab cracks were a continuation of beam flexural cracks. Once they entered the slab, cracks propagated in directions perpendicular to the longitudinal beam and were evenly spaced at distances approximately twice the slab thickness. As induced lateral dis1172

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placement increased, cracks spread over the entire width of the slab. The cracked region extended over a third of the span from each column face. Some inclined cracks were visible on the bottom of the slab around the interior column. These cracks emanated from the corners of the interior joint and suggest that diagonal compression struts may have developed at the bottom of the slab under negative flexure (hogging moment). Cracking patterns on the slab surface are different from those observed on statically determinate beam-column subassemblies with floor slabs [Kurose et al. (1989)]. (It is possible that some characteristics of the crack patterns reported in tests of SD subassemblies may be related to concentrated load effects caused by the load actuators [Kurose et al. (1989)]. The slab participated in the flexural response of the main beam by developing in-plane forces (Pantazopoulou and Moehle 1987; Pantazopoulou et al. 1988); these forces induced shear, weak-axis bending and torsion in the transverse beams. Under the action of the slab forces, the exterior beams developed extensive cracking. Inclined cracks were first observed at 0.45% interstory drift on the outside faces of the beams. Vertical cracks opened on the inside faces at 1.0% interstory drift. At increased levels of lateral displacement, cracks extended over more than half the total length of the transverse beams, measured from the column face. Diagonal cracks were also observed on the north and south faces of the interior transverse beams; however, these cracks were concentrated within a short distance (approximately equal to one beam depth) from the face of the column. A drastic reduction in stiffness and energy dissipation capacity of the specimen with progressing load sequence was evident from the shape of the hysteresis loops [Fig. 4(c)]. Because of pinching, the reloading stiffness of the specimen dropped rapidly past the 1.8% interstory drift level. Sources of pinching and loss of energy dissipation capacity included slip of the main beam reinforcement and shear deformation occurring in the beams and joints. Measurements of pull-out and push-in of the beam reinforcement obtained at the interior and exterior supports are plotted in Fig. 5(a). The plot indicates a considerable loss of bond in the joint region, particularly for the bottom reinforcement at the interior joint and for top and bottom reinforcement at the exterior supports. Fig. 5(b) shows the contribution of slippage to the total end rotation of the beams at the interior and exterior joints; the total represents the rotation measured over a 150-mm (6-in.) distance from the respective face of the column, and it includes rotation due to reinforcement slip, flexural, and shear deformations. The experimental results indicate that beyond the 2% average lateral drift level, over 50% of the beam end rotation resulted from reinforcement pull-out. The loss of energy dissipation capacity and the marked absence of a welldefined yield point in either loading direction are characteristic of the behavior of several specimens with floor slabs (Kurose et al. 1989; French and Boroojerdi 1989; Zerbe and Durrani 1985). Previous studies have shown that lack of a distinct yield point on the load-deformation envelope of specimens with floor slabs is a result of the continuous increase of slab participation to the longitudinal beam flexure with increasing deformation level (Pantazopoulou and Moehle 1988). Furthermore, because the width of participating slab is variable, unusually large movements of the neutral axis (NA) occur over the cross-section height; these movements of the NA tend to emphasize pinching of the load displacement envelopes (Kurose et al. 1989). 1173 Downloaded 22 Feb 2010 to 83.212.134.238. Redistribution subject to ASCE license or copyright; see http://pubs.asce.org/copyright

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0.0

200

400

1 7 Load Point #

M

FIG. 5. Recorded Slip of Beam Reinforcement: (a) Slip of Reinforcement at South Exterior Support and at North Face of Interior Support; and (b) Total Rotation and Rotation due to Slip at South Exterior and at North Face of Interior Support

400

I'T^f T~l I I I I f'TT

interior • North Face

-0.020.0

Load Point #

o i. rr

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South Exterior

-w-^vvMyl JUA-

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c

0.02-, -

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1 total rotation rotation due to slip

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I j I I I I

002

(b)

o = 0.0

®

0.10 n

0) South Exterior -0.10 I I I ! I I I I I I I I I I I I

c

0.10 n top reinforcement — bottom reinforcement

(a)

Strain Histories of Main Beam Reinforcement and History of Beam Expansion 10.0 r

"b

FIG. 6. Strain Histories of Main Beam Reinforcement and History of Beam Expansion: (a) Strains in Top Beam Reinforcement at Interior Support; (b) Strains in Bottom Beam Reinforcement at Interior Support; (c) Beam Strains at South Exterior Support; and (d) Beam Expansion

Strains in Main Beam Strain histories of the main beam reinforcement were measured at the interior and exterior column faces and at 150 mm (6 in.) and 300 mm (12 in.) away from the south face of the interior joint. Fig. 6(a) shows strain histories recorded at the two faces of the interior support. The solid lines correspond to top and bottom steel strains measured at the north span, which is adjacent to the externally loaded column. Dotted lines represent strains in the south span. Although the two spans were symmetrically reinforced and the induced displacement levels in the two loading directions were similar, beam strain histories measured at the two sides of the interior support displayed some differences in waveform and intensity [Fig. 6(a)]. It is believed that the asymmetric layout of the loading setup was the probable cause of these differences (Fig. 3). Yielding of the top beam reinforcement occurred on the south and north faces of the interior support at 1.8% interstory drift toward the north and at 2.2% interstory drift toward the south, respectively [Fig. 6(a)]. Bottom beam reinforcement yielded on the north and south faces of the interior connection at 2.6% and 1.5% interstory drift ratios, respectively. Strains in the top beam reinforcement over the interior support remained tensile beyond 0.45% interstory drift but did not exceed yielding levels notably until after 5% interstory drift. It is likely that the residual tensile strains resulted from the unequal amounts of reinforcement at the top and bottom of the cross section and were accentuated by the gravity loads placed on the slab. On the north face of the interior support, bottom reinforcement strains also remained tensile after cracking of the concrete. In contrast, strains measured in the bottom reinforcement on the south face fluctuated between tension and compression and reached twice the intensity of the respective values measured on the north face. The magnitudes of beam reinforcement strains recorded at the interior support suggest that the slab contributed toward re1175 Downloaded 22 Feb 2010 to 83.212.134.238. Redistribution subject to ASCE license or copyright; see http://pubs.asce.org/copyright

ducing the levels of beam curvature ductility demand in negative bending (slab-in-tension case). Beam strains recorded at 150 mm and 300 mm away from the south face of the interior support were examined to establish the distance from the critical section over which inelastic deformations were distributed. For negative bending (slab-in-tension case), strains in the main beam reinforcement at a distance 150 mm away from the column face were not less than 80% of those measured at the face of the column. For positive bending (slab-incompression case), strains were reduced by 50% at a distance 150 mm away from the face of the support but remained approximately constant thereafter up to a distance of 300 mm. These patterns suggest that when in tension, the slab promoted spreading of deformations over a broad distance from the critical locations. Beam strains measured at the exterior support were one order of magnitude larger than the respective values measured at the interior connection [Fig. 6(a)]. At the south exterior support, yielding of the top beam reinforcement occurred at 1.3% interstory drift to the south, while yielding of the bottom reinforcement occurred at 1.0% interstory drift to the north. At 5.8% interstory drift, the bottom bars fractured after they had previously buckled. Strain histories of beam reinforcement obtained at the south exterior support are plotted in Fig. 6(c). In the plot, it is evident that both top and bottom reinforcement strains remained tensile beyond lateral displacement levels corresponding to 0.45% interstory drift. As previously mentioned, the same observation was made for the top beam reinforcement at the interior joint. The residual tensile strains recorded at both ends of the span, when considered in combination with the pull-out and push-in measurements obtained for the top beam reinforcement at critical locations [Fig. 5(a)], suggest significant beam growth at the slab level regardless of the loading direction. The total elongation of the upper surface of the beam within each span, which was measured independently in order to control the MTS actuators, is in agreement with this observation. Fig. 6(d) illustrates the history of total beam elongation for each span as a function of the load point number. Curvature ductility demands at the exterior connections were exceedingly large. (Yield-curvature used in ductility calculations corresponded to yielding of the main beam reinforcement at the cross section examined for each loading direction.) During the last cycles of the test, curvature ductility exceeded 6 under negative bending, while at the interior connection, ductilities were still below 2. At 2% interstory drift, beam curvature ductilities were in the range of 1 at the interior and 2 at the exterior supports (for negative bending). Distribution of Strains in Longitudinal Slab Reinforcement Longitudinal slab reinforcement strains measured across the width of slab at critical locations and for different levels of interstory drift are plotted in Figs. l(a-c). Figs. 7(a) and 7(b) illustrate slab strains measured at the north and south faces of the interior support respectively; strains measured at the southern exterior support are shown in Fig. 7(c). Recorded strain patterns differ depending on the direction of load (positive or negative bending) and the location considered (exterior or interior support). Under negative bending, strains in the longitudinal slab reinforcement attenuated with transverse distance from the column face. During the early stages of the test, strains were a maximum in the main beam reinforcement 1176


(a)

Column face

(b)

(c)

Column face

Column face

FIG. 7. Distributions of Slab Strains and Slab Curvatures: (a) North Face of Interior Support; (to) South Face of Interior Supporrt; and (c) South Exterior Support

and the adjacent top slab bars at both interior and exterior supports. However, as the induced lateral drift was increased, tensile strains in the top layer of slab reinforcement exceeded the strain of the beam reinforcement at both faces of the interior support. The difference was partly a result of the larger lever arm of the upper slab bars as compared with that of the beam bars, and partly because of slippage of the main reinforcement through the joint. However, it may have been aggravated by the gravity loads of the slab. After yielding of the main reinforcement, significant redistribution of strains occurred in the transverse direction, which became more evident as the amount of lateral drift increased. Slab strain profiles at both faces of the interior support indicated a slow rate of decay with increasing transverse distance from the main beam [Figs. 7(a) and 7(b)]. At average lateral drifts exceeding 0.45%, the longitudinal slab reinforcement at the faces of the interior support remained in tension regardless of the direction of the load. This loading stage also corresponds to the initiation of residual tensile strains in the top beam reinforcement [Figs. 6(a-d). Slab bars adjacent to the main beam yielded at approximately the same level of lateral drift as the main beam reinforcement. Beyond 5% average lateral drift, the entire upper layer and two-thirds of the lower layer of slab bars reached or exceeded yield. Measurements obtained at the south exterior support indicated a fast rate of decay of slab strains with increasing transverse distance from the main beam [Fig. 7(c)]; strain profiles became steeper as the magnitude of lateral drift was increased. At approximately 2% interstory drift toward the south, slab strains were reduced by 60% at a distance db away from the main beam, where db is the effective beam depth; at the edge of the slab (3.5*4 away from the main beam), reinforcement strains were only 10% of the respective values measured in the main beam reinforcement. Under positive bending, the number of slab bars registering compressive 1177

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Twist of South Exterior Transversa Beam 0.00

5.8% drift

i 0.01

Stirrup Strain Histories In Transverse Beams .(c) Exterior Transverse Beam (Average)

(a)

z

Interior Transverse Beam side A side B

P=

(b) f 3.6%

•b 0.0

'.

-2%

liHiiUl'-------^~\' 5.8% drift

Load Point Number

-0.01-

200

5.0 10.0 Distance From Face of Support (Inches)

i'do"

FIG. 8. Behavior of Transverse Beams: (a) Twist of Exterior Transverse Beam for Slab-in-Tension Case; (b) Twist of Exterior Transverse Beam for Slab-inCompression Case; and (c) Stirrup Strain Histories in Transverse Beams

strains was limited and was reduced with increasing magnitude of lateral drift. At the interior connection, only the top slab bars adjacent to the main beam recorded compressive strains during the first few cycles. At the south exterior connection, all the top slab bars recorded compressive strains up to 2% average lateral drift but remained tensile all the way across for higher drift levels, because of severe inelastic excursions of the main beam reinforcement during these cycles. Curvature distribution over the cross section was evaluated from strains measured in the top and bottom layers of longitudinal reinforcement across the width of beam and slab. The estimated curvatures indicated a highly irregular profile of cross-section deformation [Fig. 7(a-c]. Curvatures decreased with transverse distance from the beam web under negative bending, but there was a marked increase toward the tip of the transverse beam under positive bending. From this result, it is evident that although the concept of plane sections remaining plane is a powerful design tool, it is not in agreement with the experimental behavior of RC Tbeam sections. Torsion of Transverse Beams Under the action of the in-plane slab forces, transverse beams twisted about their longitudinal axis and deflected in the plane of the slab. Variations of twist drift levels along the south (exterior) transverse beam are plotted in Fig. 8(a) for specimen displacement toward the south (slab-in-tension at the south exterior support) and in Fig. 8(b) for specimen displacement toward the north (slab-in-compression at the south exterior support). Overall, the magnitude and distribution of twist of the exterior transverse beams was influenced by the direction of bending of the adjacent main beam (positive or negative bending). For the slab-in-tension case, the magnitude of twist increased toward the tip of the transverse beam and reached 0.016 radians at 5.8% interstory drift [Fig. 8(a)]. In contrast, for the slab-in-compression case, the largest amount of twist occurred within the first half of the trans1178


verse beam length measured from the face of the column; the maximum twist recorded was 0.01 radians at the midspan and 0.002 radians at the tip of the beam [Fig. 8(b)]. From this result, it is evident that the pattern and magnitude of the slab forces acting on the exterior transverse beams in the two load cases were significantly different; this observation is in agreement with the slab strain distributions of Figs. 7(a-c). Deflections of the transverse beams in the plane of the slab displayed similar distributions as the twist. Under negative bending, the maximum deflection at the tip of the south exterior beam reached approximately 1.0% of the overhanging length. Cracking patterns observed on the interior transverse beams suggested a lower intensity of stresses than those experienced by the exterior beams although the extent of slab participation was much more substantial at the interior support. These differences may suggest that reduced intensity loads were transferred to the interior transverse beams; furthermore, the increased stiffness of these beams relative to their exterior counterparts may have contributed in minimizing the extent of cracking. (At the interior support, stiffness of the transverse beams was enhanced by the slab, which was continuous over the support and confined the interior transverse beams on both sides.) Weak-axis shear acting at the support of any transverse beam was estimated as the sum of forces transferred to the beam from the slab; these forces resulted partly from normal compressive stresses developing in the slab concrete and partly from stresses in the longitudinal slab reinforcement. Because longitudinal slab bars registered tensile strains on both sides of the interior transverse beam at postcracking drift levels, some contributions of slab reinforcement stresses to the shear of the interior transverse beams may have been partly cancelled, thus reducing the magnitude of loads transferred to that beam (Ammerman and French 1989). The magnitude of horizontal shear acting on the transverse beams may be gauged indirectly from stirrup strains recorded at the supports of these beams; average stirrup strains reached the values of 0.0023 and 0.0027 for the interior and exterior beams, respectively. Histories of stirrup strains are plotted for both beams in Fig. 8(c) as a function of the load-point number. Stirrup strains remained tensile beyond drift levels that corresponded to cracking of the beams and exceeded yielding at the exterior and interior supports at 3.6% and 5.8% interstory drift, respectively. Internal Redistribution Although the average base-shear stress did not exceed 0.21 \ffc MPa (2.5 \ffc psi), measured forces in the three transducers under the column footings indicated that base shear was unevenly distributed to the three columns, with the maximum shear stress exceeding 0.3 Vjl MPa at some locations. Figs. 9(a) and 9(b) illustrate the distribution of lateral load (including F-A contributions of the column axial loads) to the three columns as a function of the load point number. The fraction of total load transferred to each column at the top of the structure is shown in Fig. 9(a); Fig. 9(b) plots the fraction of total load undertaken by each individual column as base shear. From Fig. 9(a), it is evident that the distribution of the lateral load to the columns at the top of the structure was relatively insensitive to the loading direction, with 50% of the total load being transferred to the middle column and approximately 25% to each of the two exterior columns. A slight increase of the relative amount of load taken by the exterior columns was observed with increasing lateral drift ratio. However, a sharp change in the lateral-load 1179


Lateral Load Distribution to Columns of Specimen

1.0 North Column

0.5

Central Column

South Column Load Point #

0.0 200

400

(b)

FIG. 9. Lateral Load Distribution to Columns of Specimen: (a) At Top of Specimen; and (o) At the Base of Specimen

distribution occurred during the last two cycles at 5.8% interstory drift towards the north. At that loading stage, it was estimated that 45% of the total lateral load was carried by the north column, while 38% and 17% of the total load was transferred to the center and south columns, respectively. This pattern was a result of internal redistribution of forces throughout the structure following the rupture of the bottom beam reinforcement at the south exterior support. The change in distribution of base shear was observed only on displacement to the north because in this loading direction the magnitude of positive moment that could be maintained at the south exterior support after fracture of the bottom reinforcement was reduced significantly. At the base of the structure, distribution of base shear was severely affected by the direction of the load throughout the test. Redistribution of loads occurred primarily between the two exterior columns, which carried approximately 60% of the total base shear, while the remaining 40% was constantly carried by the middle column. Fig. 9(b) shows that the south and north exterior columns carried 40% and 20% of the total base shear when the structure was displaced towards the south and 20% and 40%, respectively, when the structure was displaced towards the north. It is believed that the alternating pattern of base shear distribution was the combined result of: (1) The overturning moment created by the lateral loads; and (2) the inelastic expansion of the beams that accumulated at large levels of lateral drift. Overturning moments were resisted in the structure by tensile and compressive axial loads, which developed mainly in the exterior columns. These axial loads formed a couple opposing the overturn. Therefore, the total column axial load was increased or reduced depending on the location of the column and the direction of the load. In the specimen, the column subjected to the lowest net compressive force was the one carrying the least amount of base shear because of reduced stiffness and shear resistance [Fig. 10(a)]. Residual beam deformations resulting from inelastic strains in the reinforcement, cracking of the concrete, and bond deterioration all accumulated with increasing magnitude of lateral drift, thus producing an overall expansion of the beams of the specimen [Fig. 10(b)]. A history of the beam expansion occurring within each span was plotted in Fig. 6(d) for both spans. The columns of the structure reacted to the lateral movement necessary to 1180


Mechanisms Affecting the Base Shear Distribution

V- TA 1

K; (a)

'i!

•

^

(b)

FIG. 10. Mechanisms Affecting Base Shear Distribution: (a) Overturning Effect of Lateral Load; and (b) Effect of Inelastic Expansion of Beam

accommodate the increasing beam elongation by developing internal shear and flexural moments. The additional column shear associated with beam expansion was introduced to the beams as an internal axial compression that increased in magnitude with progressing load sequence and amount of lateral drift. The magnitude of the resulting beam axial force was evaluated for each span by establishing equilibrium on the free body diagrams of the two exterior connections when these are considered isolated from the remaining structure. An envelope of the estimated force acting in the beams is pldtted in Fig. 11(a) as a function of the lateral drift. The base-shear distribution that actually occurred during the test is likely to be a combination of the patterns shown in Figs. 10(a) and 10(b). Because both patterns were affected by the direction of the load and the amount of lateral drift, base shear in the more lightly loaded column continued decreasing with progressing load cycle number, and eventually reached 10% of the total lateral load during the last cycle of the test. The envelopes of base shear carried by each column are plotted as a function of lateral drift in Figs. 11(b) and 11(c). The portion of column shear related to beam expansion for the exterior columns is approximated by the axial load of the adjacent beam [Fig. 11(a)]. Comparisons between these diagrams suggest that beam expansion significantly influenced the distribution of base shears. This result is further supported by the observation that the changes in the axial loads of the exterior columns that

(b)

/

10.0-. / /f

If

o.o

0.0

(c) .

TotaU>^

Total

,-North " / Central^ / 6?

South^ 10.0

'/• 0.0

South Central North 10.0 Drift %

Drift %

FIG. 11. Internal Member Forces: (a) Beam Axial Load as Function of Lateral Drift; (b) Base Shear Envelopes upon Displacement to North; and (c) Base Shear Envelopes upon Displacement to South

1181


resulted from the overturning effects did not exceed 15% of Pbal. For the columns of the specimen, axial load variations of this magnitude were not sufficient to cause the discrepancies in stiffness that would be necessary in order to produce the uneven base shear distributions shown in Figs. ll(a— c). Evaluation of Experimental Setup Test data obtained at symmetric locations in the structure indicated that member actions were significantly affected by the loading direction. The most dramatic differences were observed in the magnitudes of flexural moments developing in the main beam at the north and south faces of the interior support, for similar drift levels in the two loading directions. This nonsymmetric behavior that was further manifested by asymmetric strain patterns recorded in the beam reinforcement at the two faces of the interior beam-column joints is believed to be related to the loading setup. During the test, the compression and tension sides of the columns above the slab changed length due to lateral deflection; this resulted in disalignment and relative movement of the attachment points of the horizontal actuators. Because of the relative movement of the attachment points, the lateral forces applied to the columns through the horizontal actuators changed orientation with increasing magnitude of lateral drift. At the top of the middle and north columns (where actuators were acting on both sides of the columns), the lateral forces created a couple; the lever arm of the couple was equal to the relative movement of the attachment points. It was estimated that the resulting moment was approximately 15% of the total moment developed at the base of the columns above the slab, and was additive on displacement to the south and subtractive on displacement to the north. Thus, at a given level of lateral drift, the moments introduced in the middle and north beamcolumn joints upon displacement to the north could differ from the respective moments occurring on displacement to the south by 30%. ANALYTICAL RESULTS

Effective Slab Contribution To quantify the contribution of slab to the beam flexural strength from measured results, properties of the main beam were computed analytically assuming several possibilities for the participation of the slab. In the analysis, the slab was assumed to act as a flange to the beam. In this study, the width of the flange considered effective on each side of the beam web is expressed as a multiple of the beam depth db through a multiplication factor K. The analysis was carried out assuming that plane sections remain plane during bending. Measured material properties were used in the computations. The modified Park and Kent model (Park and Paulay 1975) represented the stress-strain envelope of concrete. Monotonic stress-strain relations of reinforcing steel were modeled using a simple trilinear curve (linear-elastic, plastic, strain-hardening). The hysteretic behavior of the reinforcement was modeled using the nonlinear equations introduced by Menegotto and Pinto (1977). Results computed for various levels of curvature ductility are presented in Tables 1 and 2. Lower bounds of beam strength were estimated for both positive and negative bending by ignoring the participation of the slab (K = 0 in Tables 1 and 2). The value K = 3 in Tables 1 and 2 corresponds to participation of the entire available slab width. Experimental beam moments 1182

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TABLE 1. Computed Beam Moments (Moment Unit = kN-m x 103) NEGATIVE

POSITIVE

Effective Width Expressed by Multiplier K ductility

(1) 1 2 3 4

0 (2)

1 (3)

2 (4)

3 (5)

0 (6)

(7)

2 (8)

(9)

4.8 5.4 5.66

5.72 6.30 7.08 7.66

6.24 7.19 8.23 8.95

6.88 8.11 9.05 9.78

7.91 8.17 8.36 9.01

12.87 13.58 14.75 15.45

17.38 19.31 21.04 21.5

21.24 25.4 26.1 26.4

L^d

1

3

that developed at the south exterior and at the interior connections of the specimen at 2% and 5.8% interstory drift are included in the table for comparison. The 2% interstory drift level is an approximation of the maximum lateral displacement likely to be attained by actual structures and falls within the range of lateral-load levels addressed by the ACI-ASCE Committee 352 recommendations for design of frame connections ("Recommendations" 1985). Beam moments occurring at the exterior supports were evaluated using column shears and moments that were measured by the load transducers located below the foundation and above the slab (Fig. 3). Beam moments occurring at the interior support were evaluated using as additional information the beam shears, which were equal to the change in column axial load occurring in the beam-column joints. Curvature ductilities associated with the measured flexural moments are also included in the tables to provide a common ground for comparison between experimental and analytical results. At the south exterior support, the flexural strengths estimated from experimental data for positive and negative bending were 7.25 kN-m (65 kipin.) and 16.75 kN-m (150 kip-in.), respectively. These values compare well with computed strengths obtained using K = 1 (one beam depth of effective flange width on each side of the beam web). An upper bound for the flexural resistance of the main beam can be obtained by considering the effective slab width required to cause torsional failure of the transverse beams at the exterior supports. Thus the amount of shear required to develop the torsional resistance of the transverse beams provides an indirect measure of the maximum possible slab contribution to the main beam flexural strength at the exterior connections. Using the space-truss model (Park and Paulay 1975) it was estimated that the torsional resistance of the typical exterior transverse beam of the specimen was 4.06 kN-m (36 kip-in.). From Tables 1 and 2, it is evident that the maximum moment resisted by slab and beam at the exterior support was limited by the sum of the flexural strength of the main TABLE 2.

Experimentally Measured Beam Moments (Moment Unit = kN-m x 103) INTERIOR SUPPORT

SOUTH EXTERIOR SUPPORT Positive Drift