Cyclic behaviour of interior post-tensioned flat plate

(PT) flat plate slab systems are very efficient, since the PT flat plate slab systems provide improved crack and deflection control, and allow relativ...

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Magazine of Concrete Research, 2006, 58, No. 10, December, 699–711

Cyclic behaviour of interior post-tensioned flat plate connections S. W. Han*, S.-H. Kee*, T. H.-K. Kang†, S.-S. Ha*, J. W. Wallace† and L-H. Lee* Hanyang University; University of California

In high seismic regions, post-tensioned (PT) slab–column frames are commonly used to support gravity loads in conjunction with a lateral-force resisting system (LFRS) such as a core wall. The LFRS is designed to resist 100% of the design lateral forces as well as to limit lateral displacements to an acceptable level, whereas the slab– column frame must sustain the gravity loads under the expected (design) displacements. Given the relatively sparse data on the seismic performance of PT flat plate slab–column frames, cyclic tests of four interior PT slab–column connections were conducted. Primary test variables were the level of gravity shear at the slab–column connection and the slab tendon arrangement. Test results indicate that both the test variables strongly influence the cyclic behaviour of the PT connections, and that the use of slab bottom reinforcement at the slab–column connection was effective in resisting positive moment developed under lateral loading as well as improving the hysteretic energy dissipation capacity.

Notation Aps Asm b0 b1 b2 c c2 d db dp f c9 fpc fps

area of tendons area of continuous bottom bonded reinforcement perimeter of critical section width of critical section parallel to loading direction width of critical section perpendicular to b1 distance from the centroid of critical section to the perimeter of critical section column dimension perpendicular to the loading direction effective slab depth bar diameter effective slab depth of tendons peak concrete compressive stress average compressive stress in concrete owing to effective post-tensioning force only nominal stress in an unbonded tendon (limited to lesser of fpy and fse + 210)

* Division of Architectural Engineering, Hanyang University, Seoul 133–791, Korea. † Department of Civil and Environmental Engineering, University of California, Los Angeles (UCLA), California 90095, USA. (MCR 51489) Paper received 29 November 2005; accepted 7 August 2006

fpy fse fy h Jc l1 l2 Mn, c þ 3 h Mn,fs Mu,ub Vc Vg Vp Vu c ªf ªv c u Łu Ły

tendon yield stress effective tendon stress yield stress of slab bottom reinforcement slab thickness polar moment of inertia of critical section centre-to-centre spans parallel to the loading direction centre-to-centre spans perpendicular to the loading direction nominal moment for a slab width of c2 + 3h nominal moment for a full slab width peak unbalanced moment nominal concrete shear strength gravity force to be transferred from a slab to a column vertical component of effective posttensioning force at section factored shear force to be transferred from a slab to a column ratio of long side to short side of a column factor used to determine the unbalanced moment transferred by flexure at slab– column connections fraction of unbalanced moment transferred by eccentric shear nominal shear strength provided by concrete maximum shear stress drift ratio at punching drift ratio at yielding 699

www.concrete-research.com 1751-763X (Online) 0024-9831 (Print) # 2006 Thomas Telford Ltd

S. W. Han et al. rp  øu

reinforcement ratio associated with tendons (¼ Aps /l2 dp ) strength reduction factor uniformly distributed design load

Introduction Slab–column framing is popular because it offers distinct advantages such as low cost owing to ease of construction (e.g. slip forms), low floor-to-floor height and flexible use of space. In particular, post-tensioned (PT) flat plate slab systems are very efficient, since the PT flat plate slab systems provide improved crack and deflection control, and allow relatively large slab spanto-thickness ratios, in the order of 35 to 45. Slab– column frames are commonly used to resist gravity loads in high seismic regions (SDC-D or -E, IBC-031 ), where SDC indicates seismic design category; however, they may be utilised as intermediate moment frames (ACI 318–052 section 21.12.6) in areas with moderate seismic demands (SDC-A, -B and -C). Given the broad potential applications, a detailed understanding of slab–column frame behaviour subjected to lateral forces and/or displacements is important. According to the seismic provisions in ACI 318–05,2 structural systems are either designated to resist earthquake forces [i.e. be part of the lateral-force resisting system (LFRS)] or they are referred to as ‘non-participating’ systems or ‘gravity’-force resisting systems (GFRS). In high seismic regions, post-tensioned slab– column frames are commonly used for GFRS, particularly for residential and office buildings where the LFRS consists of shear walls or moment-resisting frames at the building perimeter. When subjected to earthquake ground motions, the LFRS undergoes lateral deformations, which are imposed on the GFRS through the floor diaphragms. The lateral displacements imposed on the slab–column frame are likely to introduce significant unbalanced moments on the slab–column connections, increasing the potential for punching failures. Before the introduction of ACI 318–05,2 no specific requirements existed to avoid punching failures at slab–column connections in GFRS owing to the lateral displacement of the LFRS. However, the ability to maintain gravity loads after punching failure (i.e. post-punching resistance) could be justified owing to the ACI 3182 chapter 7 requirement for integrity reinforcement (continuous bottom reinforcement through the column cage). According to the eccentric shear stress model in ACI 318–05,2 punching failures at slab–column connections subjected to shear (Vu ) and unbalanced moment (Mub ) occur where the shear stress owing to direct shear and eccentric shear exceeds the nominal shear stress on the slab critical section. The eccentric shear stress is a result of moment ªv Mub . The remaining portion of Mub equal to ªf Mub is assumed to be resisted by flexure by providing slab reinforcement over a slab flexural trans700

fer width of c2 + 3h. Prior studies3–5 indicate that the eccentric shear stress model gives conservative results for the punching shear capacity of the post-tensioned interior slab–column connections. Available seismic provisions for the flat plate slab systems (e.g. ACI 318–052 section 21.11) focus on conventional non-prestressed slab–column connections: similar provisions for prestressed post-tensioned slab– column connections do not exist. In particular, very limited testing has been conducted on the PT interior connections subjected to reversed cyclic loads (Qaisrani,5 Pimanmas et al.6 ). For PT flat plate slab systems with shear reinforcement, existing data are limited to the shake table tests of an approximately one-third scale, two-storey, post-tensioned flat plate frame (Kang and Wallace7 ). Therefore, seismic performance of the PT connections, which tend to have relatively high gravity shear ratios owing to the substantial spans, have not been adequately studied. Furthermore, the impact of the tendon arrangement, which typically involves the use of banded tendons in one direction and distributed tendons in the other direction (ACI 423.3R-968 ), has not been systematically assessed, and the influence of bonded bottom reinforcement on the behaviour of PT flat plate systems subjected to moment reversal has not been addressed.

Test programme Prototype and specimen design Figure 1 depicts the prototype building selected to assist in the determination of specimen proportions and details. The prototype building is a ten-storey, posttensioned flat plate slab system with 3.5 m storey heights with special reinforced concrete (RC) shear walls (R ¼ 6) designed according to IBC-031 and ACI 318–052 requirements for SDC-E (high seismic risk). A slab thickness of 200 mm and a span length of 8 m were selected for the prototype building, resulting in a span-to-depth ratio of 40, which is within the range of 35 to 45 typically used for PT flat plate construction. The shear walls were designed to resist the lateral earthquake forces, whereas the PT flat plate slab systems were proportioned to support gravity forces. Given that the prototype building is used for typical residential/office construction, the unit weight of the building is estimated as 23.5 kN/m3 . Additional dead loads (e.g. partition walls) of 0.5 kPa and live loads of 2 kPa were chosen based on recommendations in IBC03.1 Slab moments and shear forces owing to factored gravity loads were determined based on the results of an elastic analysis using MIDAS/Gen (MIDAS IT,9 Version 6.3.2). The specimens were approximately two-thirds scale representations of a typical interior slab–column connection within the prototype building (Fig. 1). Inflection points were assumed to occur at or near slab mid-span, Magazine of Concrete Research, 2006, 58, No. 10

Cyclic behaviour of interior post-tensioned flat plate connections 8·0 8·0

8·0

8·0

8·0

8·0

8·0

8·0

8·0

8·0

8·0

8·0

8·0

3·5

10 @ 3·5m

8·0 8·0

8·0

8·0

(b) Plan

(a) Elevation

Unit: m

Fig. 1. Prototype building

resulting in a span length of 4.6 m for the loading direction. A slightly shorter span length of 3.6 m was used in the transverse direction. A 300 3 300 mm column cross-section and a 130 mm slab thickness were selected based on the two-thirds scale factor. Slabs were post-tensioned with 12.7 mm diameter, seven-wire strands with design yield stress of 1861 MPa. The arrangement of slab reinforcement is provided in Fig. 2. Minimum concrete clear cover was 12 mm for both top and bottom slab reinforcement. The post-tensioning strands were greased and placed in polyethylene tubes with a diameter of 16 mm; therefore, the tendons were ‘unbonded’. The number of post-tensioning tendons and the post-tensioning force per tendon were selected such that approximately 100% of slab dead weight was balanced (Table 1). The resulting average compressive stress ( fpc ) of 1.21 MPa is within the allowable range of 0.88 MPa and 3.44 MPa as specified by ACI 318–05.2 According to section 18.9 of ACI 318–05,2 minimum bonded top reinforcement ( fy ¼ 352 MPa) was placed within an effective transfer width of c2 þ 3h at the connection region. Although the slab–column frame is designed for gravity loads, it is subjected to the lateral deformations imposed on it by the lateral system (shear walls). To investigate the influence of the lateral deformations of the LFRS on the slab moment distribution, threedimensional elastic analyses of combined PT flat plate frame and shear wall system were conducted for various levels of seismic demand. Resulting slab moments are depicted in Fig. 3. The slab moment diagrams indicate that the positive slab moment eventually develops on one side of the slab–column connection as the seismic demand is increased; therefore, sufficient bottom reinforcement should be provided to avoid the Magazine of Concrete Research, 2006, 58, No. 10

formation of large cracks. Requirements for minimum bonded bottom reinforcement for the post-tensioned connections do not exist; therefore, it is common to provide structural integrity reinforcement per ACI 318–052 section 7.13.2.5. This provision was developed primarily based on common practice for RC slab–column frames, which typically have slab span-tothickness ratios closer to 20. Owing to the larger spans of typical of PT construction, bottom reinforcement satisfying ACI 3182 (section 7.13.2.5) and ACI-ASCE 35210 requirements [equation (1)] was provided 0:5øu l1 l2 Asm ¼ (1)  fy where  ¼ 0.9. Accordingly, five D10 (db ¼ 10 mm) bottom bars were placed within a column width of c2 for both directions, whereas no bottom reinforcement was provided outside of c2 . Material properties Normal Portland cement concrete with a design concrete strength of 29.8 MPa and a maximum aggregate size of 19 mm were used. The measured slump of the concrete ranged from 100 to 125 mm. As indicated in Table 2, mean compressive test-day strength of the concrete was 32.3 MPa based on compressive test results of five, 100 3 200 mm concrete cylinders in accordance with KS F 2404 (KS-0211 ). Seven-wire strands [steel wire for prestressed concrete (SWPC) 7B11 , db ¼ 12.7 mm] and D10 mild reinforcement were used for slab reinforcement, whereas D25 reinforcement (db ¼ 25 mm) was used for column longitudinal reinforcement. The SWPC 7B strands ( fy ¼ 1555 MPa) and reinforcement ( fy ¼ 466 MPa) were fabricated in accordance with KS D 7002 and KS B 0802, respec701

S. W. Han et al. 600

4600 TC 5

Moment: kN m

820 1800

c214h

c213h

0

0

2

(a)

900

4

6

2200

C1

8

A1

B1 C1

14

16

1·0D10·25L1E (SDC-B) 1·0D10·25L1E (SDC-C) 1·0D10·25L1E (SDC-D) 1·0D10·25L1E (SDC-E)

2400

40 1390

[email protected] 100

Unit: mm

B1

200

2600 Top rebars

150

A1

400 900

TC 6

[email protected]

TC 7

TC 3 TC 2 TC 1

[email protected] 100 1390 TC 4

TC 8

Distance from A1: m

Fig. 3. Slab moment distribution for both gravity and lateral loads

[email protected] 150 E W Loading direction

Testing and instrumentation TC 6 TC 5 4600

40 150

Unit: mm

350 100 350 [email protected] [email protected]

c2 1 3h

[email protected]

TC 2

900 TC 3 1800 TC 1 900

Top rebars

c2 1 8h

TC 4

TC 7

150 100 [email protected] E W Loading direction (b)

Fig. 2. Details of unbonded tendons and bonded top bars of specimens: (a) PI-B50 and PI-B30; (b) PI-D50 and PI-D30

tively (KS-0211 ). Properties determined from the material test programme are summarised in Table 2, whereas the stress–strain relations obtained from representative samples are shown in Fig. 4.

The four interior post-tensioned slab–column connections were subjected to uni-directional, reversed cyclic loading using the test set-up illustrated in Fig. 5. The primary variables of the test programme were the level of gravity shear, which could be varied using the hydraulic jack at the base of the column, and the arrangement of slab tendons (Table 1). For two of the specimens (PI-B50 and PI-B30), tendons were banded in the loading direction (E–W) and approximately uniformly distributed in the transverse direction (N–S), whereas for the other two specimens (PI-D50 and PID30), the tendons were uniformly distributed in the loading direction (E–W) and banded in the transverse direction (N–S), as shown in Fig. 2. The name PI-B50 refers to the following variables: Post-tensioned, Interior, Banded, with 50% gravity shear ratio. The gravity shear ratio is calculated as Vg /Vc , where Vg is the factored gravity shear determined from analysis, Vc is calculated according to ACI 318–052 (equation (11– 36)), which includes the impact of the prestress, and  ¼ 0.75. The base of the column was pinned, and the slab edges were pin-supported at the four corner points by struts (steel bars) with a diameter of 10 cm (Fig. 5). To evaluate the appropriateness of the boundary condi-

Table 1. Properties of specimens Mark PI-B50 PI-B30 PI-D50 PI-D30

c2 : mm

d†: mm

rp : %

f c9 : MPa

fpc : MPa

Vc: kN

Vg: kN

300 300 300 300

104 104 104 104

0.21 0.21 0.16 0.16

32.3 32.3 32.3 32.3

1.21 1.21 1.21 1.21

343 343 343 343

132 82 132 82

c2 : column dimension in the direction perpendicular to loading d†: effective depth based on average of d ps in two directions rp : ratio of post-tensioning tendons f c9 : mean compressive concrete strength at the time of testing fpc : average compressive stress in concrete owing to effective post-tensioning Vc: nominal shear strength Vg: gravity force to be transferred from slab to column e.g. PI-B50, (P): PT, (I): interior, (B): banded, (50): Vg /Vc  0.50 ( ¼ 0.75)

702

Magazine of Concrete Research, 2006, 58, No. 10

Cyclic behaviour of interior post-tensioned flat plate connections Table 2. Properties of materials Concrete f c9 : MPa 32.3

o

Es : MPa

0.00185

29 600

f y : MPa

y

Es : MPa

f u : MPa

u

466 465

0.0024 0.0027

193 166 172 222

698 584

0.1245 0.0819

f y : MPa

y

Es : MPa

f u : MPa

u

1555

0.0098

182 223

1751

0.049

Steel rebar d b : mm 10 25 SWPC 7B strand d ps : mm 16

f c9 : mean compressive concrete strength at the time of testing f y : yield stress, f u : ultimate stress o : mean strain at peak concrete strength, y : yield strain, u : ultimate strain d b or d ps : rebar or strand diameter Es : steel modulus of elasticity

1800 1600

SWPC7B(12·7 mm) 7-wire strand

Tensile stress: MPa

1400 1200 1000 800

D10 Rebar

600 D25 Rebar

400 200 0

0

0·02

0·04

0·06 0·08 Tensile strains

0·1

0·12

0·14

40 f ¢c 5 33·57 (MPa)

35

Concrete stress: MPa

Es 5 28·183 (MPa) 30 25 20 15

0·45f ¢c 5 15·10 (MPa)

10 5 0 0·0000 0·0004 0·0008 0·0012 0·0016 0·0020 0·0024 0·0028 0·0032 Concrete strains

Fig. 4. Stress–strain relations of representative materials Magazine of Concrete Research, 2006, 58, No. 10

tions, an elastic finite element analysis was conducted using MIDAS/Gen.9 This analysis showed that, for a given drift ratio, the difference in the unbalanced moments between the test condition (pinned at four corners) and the complete building system was less than 3%. Gravity loads were simulated by applying an axial load at the base of the column using a 5000 kN hydraulic jack, as well as by placing loading blocks on the slab. Given that the ratio of shear force and moment at the critical section of the slab–column connection significantly influences the behaviour of the connections,12,13 the location of the loading blocks was determined based on an finite element analysis to match the ratio of shear force and moment for the specimens and the prototype building. As shown in Fig. 5, load cells were mounted on the hydraulic jack at the base of the column and on each of the four struts at the slab corners to monitor the applied loads. The 250 kN capacity horizontal actuator was used to displace the top of the column (Fig. 5). A typical lateral displacement history consisting of three cycles at monotonically increasing drift levels between 0.2% and 6%, as shown in Fig. 6, was used for the tests. The applied lateral load and displacements were monitored using a load cell and linear variable differential transducers (LVDTs), respectively, and additional LVDTs were used to monitor (and avoid) slab twisting. Strain gauges were attached on selected bonded slab bars, and eight load cells were installed on tendons to measure the tendon forces during post-tensioning as well as changes in tendon forces during testing. 703

S. W. Han et al. 4800

Load cell

250 kN actuator

Pin

Pin

300

Loading blocks

E

645

985

340

Rigid blocks

Loading blocks

130

2100

W

Strong concrete reaction wall

3350

Transducer strut (ö10 cm rigid steel bar) 

Pin 5000 kN Hydraulic jack

Load cell

ö15 cm steel bolt

Strong concrete floor

Unit: mm

6·0%

Lateral drift ratio: %

6 4·5%

4 2 0

0·5% 0·75% 0·2% 0·25%0·35%

1·0%

1·4%

1·75%

2·2%

2·75%

3·5%

90 60 30 0 230

22

260

24 26

120

290 0

5

10

15

20

25 30 Cycles

35

40

45

Lateral displacement: mm

Fig. 5. Test set-up

2120 50

Fig. 6. Loading histories

Test results Crack patterns and observed damage Crack patterns at the completion of testing are shown in Fig. 7. In general, for drifts less than 1%, slab flexural cracks formed adjacent to the column and subsequently extended across the entire slab width. For drift ratios greater than 3%, significant cracks were observed to extend approximately 300 mm (ffi 2.5d) away from the column face (Fig. 7). Based on observations, as well as the test data presented in the following subsections, it is concluded that punching failures occurred for all test specimens after flexural yielding of slab bonded reinforcement. Lateral load versus lateral drift Values of unbalanced moments obtained from two different approaches are plotted in Fig. 8. The first 704

estimate of the unbalanced moment was obtained as the lateral load multiplied by a column height of 2.1 m, whereas the second estimate was derived from the difference of vertical reactions measured in the struts at the slab corners times the distance between the struts (4.8 m). A comparison of the results obtained using the two approaches is provided in Fig. 8 and indicates that consistent results were obtained. Envelopes to the load–displacement relations as well as an idealised bi-linear relationship4,14,15 fitting to the envelope relations also are depicted in Fig. 9. The bilinear relations are used to determine drift angles associated with yielding (Ły ) and punching (Łu ) as noted in Table 3. As depicted in Fig. 9, Łu is defined as the drift ratio at punching (Łu,1 ) for specimens that experienced sudden punching failures (PI-B50, PI-B30 and PI-D50), or the drift angle at which the lateral load experiences a 20% drop from the peak lateral load (Łu,2 ) for the specimen PI-D30, which did not experience a sudden punching failure. As noted for reinforced concrete connections,4,14–17 the limited data available have shown that lateral drift capacity at punching for post-tensioned slab–column connections is also strongly influenced by the magnitude of direct gravity shear stress applied on the critical section.4,5 A detailed review of the existing database for the PT connections4 indicates that higher drift ratios at punching were obtained for the PT connections, inpart owing to the larger span-to-thickness ratios (40 to 45) compared with the RC connections ( 25), and that lower drift values were observed for the PT connections Magazine of Concrete Research, 2006, 58, No. 10

Cyclic behaviour of interior post-tensioned flat plate connections PI-B50

PI-B30 20 cm 20 cm

30 cm 20 cm

20 cm 20 cm 20 cm 30 cm

PI-D50

PI-D30

20 cm 20 cm 20 cm 20 cm

Unbalanced moment: kN m Unbalanced moment: kN/m

Fig. 7. Observed damage 150 100

PI-B50

50 0 250 from horizontal actuator load cells from vertical transducer strut load cells

2100 150 100

PI-D50

50 0 250

2100 2150

from horizontal actuator load cells from vertical transducer strut load cells Testing sequence

Fig. 8. Comparisons of unbalanced moments

subjected to reversed cyclic loading relative to the PT connections subjected to monotonic or repeated lateral loading (Fig. 10). Since the database for PT interior connections subjected to reversed cyclic loading is limMagazine of Concrete Research, 2006, 58, No. 10

ited to the four, isolated specimens with relatively high gravity shear ratios (Vg /Vc ¼ 0.46 to 0.72) tested by Qaisrani5 and Pimanmas et al.6 , the test results presented for this study provide valuable information to assess trends for gravity shear ratios Vg /Vc between approximately 0.25 and 0.40 (actual values for the connections based on actual material properties, versus the design values of 0.30 and 0.50, respectively). Figure 10 presents data (Vg /Vc; Łu ) for the four specimens tested (Table 3), along with the existing test data of post-tensioned slab–column connections without shear reinforcement. Based on the results presented in Fig. 10, a fairly consistent trend of decreasing drift ratio at punching (Łu ) for increasing gravity shear ratio (Vg /Vc ) is observed. The four test specimens from this study achieved substantially higher lateral drifts (3.2% to 5.9%) compared with earlier test results (1.8 to 2.3%) for interior connections subjected to cyclic loading with higher gravity shear ratios.5,6 ). Furthermore, specimens with lower gravity shear ratios (PI-B30 and PI-D30) achieved 180 and 135% of the lateral drift ratios of the companion 705

S. W. Han et al. 26

24

22

Drift ratio: % 0 2

4

6

26

24

22

Drift ratio: % 0 2

4

6 60

60 èu

Ppeak 5 47·8 kN

40

Pn 5 Mn,ub /(h1 5 2·1 m) 2/3(Ppeak) 5 31·9 kN

2/3(Ppeak) 5 29·1 kN

20

Lateral load: kN

20

0

2·0%

2·1% 3·3%

5·9%

220

220 Pn 5 Mn,ub /(h1 5 2·1 m)

240

260

Pn 5 Mn,ub /(h1 5 2·1 m)

(a) PI-B50

240

(b) PI-B30

60

Ppeak 5 52·2 kN 40

Pn 5 Mn,ub /(h1 5 2·1 m)

èy

260

60

èu

40

Pn 5 Mn,ub /(h1 5 2·1 m) 2/3(Ppeak) 5 34·8 kN

20

20

Lateral load: kN

0

24·0%

0

21·4% 5·4%

1·5%

0

220

220

2/3(Ppeak) 5 231·5 kN Pn 5 Mn,ub /(h1 5 2·1 m)

240

èy

èu

Pn 5 Mn,ub /(h1 5 2·1 m)

(c) PI-D50 24

22

240

Ppeak 5 247·3 kN

260

26

Lateral load: kN

èy

Lateral load: kN

Ppeak 5 43·6 kN Pn 5 Mn,ub /(h1 5 2·1 m)

40

èu

èy

0 2 Drift ratio: %

4

6

(d) PI-D30 26

24

22

0 2 Drift ratio: %

4

260

6

Fig. 9. Lateral load plotted against lateral drift ratio

specimens with higher gravity shear ratios (PI-B50 and PI-D50), respectively, before punching failures (Fig. 10). For PI-B30 and PI-D30, relatively large lateral drift ratios were achieved for both specimens, 5.6 to 5.9%, respectively, indicating that the tendon arrangement did not impact the drift at punching failure significantly for the moderate gravity shear ratio. However, for the higher gravity shear ratio, based on the load–displacement relations (Fig. 9), higher drift capacity (120%) and improved ductility (190%) were observed for PI-D50 compared with PI-B50. The lower drift capacity and ductility for PI-B50 compared with PI-D50 is likely owing to larger precompression within the connection region. In both cases of gravity shear ratios, larger drift ratio at punching failure was achieved for the case with distributed tendons. Current practice, which typically bands tendons in one direction, may result in connec706

tions that have less drift capacity for loads parallel to the banded direction. Dissipated energy The dissipated energy per cycle, which is used to assess the hysteretic damping characteristics of the system, was calculated based on the area of a load– displacement relation for that cycle (Fig. 9). Based on evaluation of these data, it is concluded that a gravity shear ratio (Vg /Vc ) has a modest impact of the accumulated dissipated energy for specimens with the same tendon distribution (for a given cycle). However, as shown in Fig. 11, the values of the accumulated dissipated energy at failure differ substantially, as specimens PI-B30 and PI-D30 have values that are approximately 150% and 40% higher than those for PI-B50 and PID50, respectively. The PT connections with higher gravity shear (PI-B50 and PI-D50) tend to fail at a Magazine of Concrete Research, 2006, 58, No. 10

1.14 1.03 1.24 1.13 0.70 0.76 1.00 1.10 105.7 106.5 104.1 104.8

Bonded slab reinforcement

78.7 79.0 59.4 59.6

10

80.2 98.4 80.2 98.4

13 12 ¼ 9 / 10 11

14 ¼ 4 / 13

Mn,ub : kN/m ªM / P f u,ub M n,cþ3 h M n,cþ3 h : kN/m

P

M n, fs : kN/m

Mu,ub /Mn,ub

F+P F+P F+P F+P

lower drift ratio, and thus achieve less ductility. In particular, yielding of the slab reinforcement of PI-B50 was limited prior to punching failure. These results indicate that the hysteretic energy dissipation capacity is dependent upon the gravity shear ratio. Test data indicate that the hysteretic energy dissipation capacity also is sensitive to the tendon distribution pattern. Based on the relations plotted in Figs 9(a) and (b), specimens PI-B50 and PI-B30 exhibited fairly linear behaviour up to 2% drift with limited yielding of both top and bottom slab bonded reinforcement, probably as a result of high local precompression provided by the banded post-tensioning within the connection region. On the other hand, for specimens PI-D50 and PI-D30, a significant drop in lateral stiffness was observed at 1% drift (Figs 9(c) and (d)). As a result, the values of accumulated dissipated energy for PI-B50 and PI-B30 are approximately 90% and 40% of those for PI-D50 and PI-D30, respectively (Fig. 11).

55.0 60.2 59.6 65.8 1.18 1.11 1.25 1.18 GSR: gravity shear ratio ª f ¼ 0.6 (according to ACI 318–05) Mu,ub ¼ (Ppeak )(h1 ), where h1 ¼ 2.1 m Mn,cþ3h : flexural moment capacity of slabs over the width of c2 + 3h ÓMn,fs : flexural moment capacity of slabs over entire slab width F + P: flexural yielding, followed by punching failure

2.01 2.01 2.01 2.01 0.39 0.24 0.39 0.24 2.38 2.22 2.51 2.38 91.6 100.4 99.3 109.6 2.1 2.0 1.4 1.5 PI-B50 PI-B30 PI-D50 PI-D30

43.6 47.8 49.1 52.2

3.3 5.9 4.0 5.4

9 8 ¼ 5 / 7 2 1

3

4

5

6

7

ª f Mu,ub : kN/m u /c u : MPa Vg /Vc Mu,ub : kN/m Łu : % Ły : % Ppeak : kN

Test results Mark

Table 3. Test and analytical results

u : MPa

GSR

Shear strength

P

Flexural strength

Moment

Failure mode

Cyclic behaviour of interior post-tensioned flat plate connections

Magazine of Concrete Research, 2006, 58, No. 10

As mentioned earlier, the test specimens included minimum bonded top reinforcement (eight D10 bars) in accordance with ACI 318–052 and bonded bottom reinforcement (five D10 bars) as required for structural integrity reinforcement based on ACI 352.1R-89.10 During the cyclic tests, both top and bottom bonded reinforcing bars reached the yield strain of approximately 0.002 (Fig. 12). Yield of top reinforcement initiated at drift ratios of 1.1, 1.7, 0.6 and 1.7% for PI-B50, PI-B30, PI-D50 and PI-D30, respectively, whereas yield of bottom reinforcement occurred between drift ratios of 2.2% and 3.5% for all specimens. Figures 12(a) and (b) show that, before punching, the degree of yielding of top reinforcement was more extensive than that of bottom reinforcement. Bottom reinforcement strains are plotted against the measured drift ratios in Fig. 13 for the bars located at the column centreline. Owing to gravity loading, bottom reinforcement was in compression before the application of lateral loading. The strains in bottom reinforcement began to vary from negative to positive values (i.e. moment reversal) at drift ratios of 0.8% and 0.5% for PI-B50 and PI-D50, respectively. This result is consistent with the observation that larger pre-compression within the connection region may have existed where banded tendons were parallel to the loading direction. For PI-B30 and PI-D30, with relatively low gravity shear stresses, moment reversal was observed at relatively low drift ratio of 0.5%. In high seismic regions, the lateral (roof) drift demand on the structure is typically limited to 2% for life safety considerations,18 and some storey drift ratios typically exceed the roof drift ratio. Bonded bottom steel with the amount of Asm (equation (1)) is not anticipated to yield for drifts less than approximately 1.5%;14 however, moment reversal is likely to occur (Fig. 3). Therefore, bonded bottom reinforcement should be provided for PT flat plate systems designed 707

S. W. Han et al. 0·09

20 Trongtham · and Hawkins - Int. Qaisrani·5 - Int. 6 Pimanmas · et al. - Int.

0·08

23 · Martinez-Cruzado - Ext. 24 Han et al. ·- Ext. 23 - Corner Martinez-Cruzado · 21 · Shatila - Ext. (with shear reinf.) Ritchie and ·Ghali25 - Ext. (w/ shear reinf.) 4 Kang and Wallace - PT frame · (w/ shear reinforcement)

Han et al. · (Present) - Int.

Trongtham · and Hawkins20 - Ext. Shatila21· - Ext. Foutch et · al.22 - Ext.

0·07

Best-fit line for PT connections without shear reinforcement subjected to reversed cyclic lateral loading

Drift ratio at punching

0·06

0·05

0·04

Database is referenced in Kang and Wallace4 and Kang et al.19 Best-fit line for all PT connections without shear reinforcement

0·03

0·02

0·01

0

ACI 318-05 drift limit for a given V  u /öVc (ö 5 0·75) 0

0·1

0·2

0·3

0·4 0·5 0·6 Gravity shear ratio: Vg /Vc

0·7

0·8

0·9

1

1·5%

30

PI-B50 PI-B30 PI-D50 PI-D30

25 20

E W Loading direction

15 10

4000

3·0% PI-B50 PI-B30 PI-D50 PI-D30

3000

Strains 3 106

Accumulated dissipated energy: kN/m

Fig. 10. Gravity shear ratio plotted against drift ratio at punching (PT slab–column connections)

åy

2000 1000

5 0

0

5

10

15

20

25 30 Cycles

35

40

45

50

0 200 400 600 21000 2800 2600 2400 2200 0 Distance from column centre: mm Unbonded tendons

Bonded top reinforcement

800 1000

Strain gauges

Fig. 11. Accumulated dissipated energy (a)

1·5% E W Loading direction

3·0% 2500

1000

For each specimen, average tendon stresses were monitored using seven or eight load cells mounted at 708

PI-B50 PI-B30 PI-D50 PI-D30

0 0 500 1000 1500 22000 21500 21000 2500 Distance from column centre: mm Unbonded tendons

Stresses in unbonded tendons

åy

2000

Strains 3 106

to resist gravity loads since tensile strains in the bottom slab reinforcement was observed before reaching a lateral drift ratio of 1.5% (Fig. 12(b)). The quantity of bottom reinforcement provided in the specimens was in compliance with equation (1) and was sufficient to resist positive moment developed up to lateral drifts of approximately 1.5% to 2.0% before reaching the yield strain (Fig. 12(b)), as well as to prevent progressive collapse. Accordingly, bottom reinforcement required by equation (1) is sufficient to limit extensive yielding; therefore, there does not appear to be a need to provide larger quantities of bottom reinforcement.

2000

Strain gauges Bonded bottom reinforcement (b)

Fig. 12. Strain distribution in (a) top and (b) bottom reinforcement passing through the column cage Magazine of Concrete Research, 2006, 58, No. 10

Cyclic behaviour of interior post-tensioned flat plate connections 3000

Shear strength of post-tensioned slab–column connections (ACI 318–05) The shear strength of the specimens was evaluated using the eccentric shear stress model of ACI 318–052 chapter 11

Strains 3 1026

2500 åy

2000 1500 1000 500

PI-B50 PI-B30 PI-D50 PI-D30

0 2500

21000

0

0·5

1

1·5 2 Drift ratio: %

2·5

3

Vu ªv M u,ub c  < c Jc b0 d 1 pffiffiffiffiffiffiffiffiffiffiffiffi ªf ¼ 1 þ ð2=3Þ b1 =b2

u ¼ 3·5

tendon ends (TC, see Fig. 2). Figure 14 reveals that the stress in the unbonded tendons increased as a lateral drift ratio increased and that the tendon distribution influenced the change in the tendon stress in the loading direction. For the PI-B specimens, tendon stresses in the loading direction (TC 1, 2 and 3) tended to increase fairly uniformly irrespective of tendon location. However, for the PI-D specimens, only the stresses in tendons placed close to the column (TC 1 or 2) increased significantly (Fig. 14). The peak values of the increase in the tendon stresses are in the range of 4.7 to 6.4% of the effective tendon stress ( fse ). These values are substantially smaller than those ( 15%) predicted by using equation (2) (ACI 318–052 equation 18–5)

f c9 MPa 300rp

Stress increments in unbonded tendons: MPa

(5) (6)

where vc is the nominal shear stress capacity of the post-tensioned connection without shear reinforcement reduced by the capacity reduction factor in units of MPa, p is the smaller of 0.29 or (Æs d/b0 + 1.5)/12 and Æ s is 40 for interior columns. In Table 3 column 10, the nominal moment for a  slab width of c2 + 3h (Mþ n,cþ3 h + Mn,cþ3 h ) is calculated for the specimens using the actual concrete strength ( f c9 ), the actual yield stress of bonded bars ( fy ), and the measured stress in unbonded tendons at failure ( fps ), given that all the slab bonded reinforcement yielded at the time of the failure. It is noted that the moment transferred by flexure (ªf Mu,ub ffi 0.6Mu,ub ) and the  flexural transfer capacity (Mþ n,cþ3 h + Mn,cþ3 h ) are almost identical (Table 3, column 12), suggesting that the assumed fraction of unbalanced moment transferred by flexure (ªf ¼ 0.6) according to ACI 318–052 is reasonable for the PI-D specimens. For the PI-B specimens, most of post-tensioning tendons and all the bonded reinforcement were placed within c2 + 3h (Fig. 2). Thus, information provided in column 12 in Table 3 is not sufficient to assess the fraction of unbalanced moment transferred by flexure. The peak values of the applied unbalanced moment (Mu,ub ) monitored from a load cell attached to the horizontal actuator and the values of the total flexural  moment capacity (Mþ n,fs + Mn,fs ) computed using measured material properties for the specimens are indicated

(2)

The smaller increases may be partly attributed to the smaller total elongation of the tendon obtained for the interior connection under both gravity and lateral loads (plotted against the interior connection under gravity loads only, where the tendon in always in the tension zone). The lower stresses in the unbonded tendons under lateral loads result in reduced moment capacities under combined gravity and lateral load, relative to the nominal moment capacities computed for gravity load alone.

LC 1

80 LC 1

60

LC 3 LC 2 LC 4 LC 1

LC 3 LC 2 LC 7 LC 1 LC 6 LC 4

40 20

(a) PI-B50

0

1

2 3 4 Drift ratio: %

5

LC LC LC LC LC

LC 6 LC 7 LC 8 LC 5

LC 5

0

220

(4)

ªv ¼ 1  ªf   pffiffiffiffiffiffi Vp c ¼  p f c9 þ 0:3 f pc þ b0 d

Fig. 13. Strains in bonded bottom reinforcement versus drift ratio

f ps ¼ f se þ 70 þ

(3)

0

2 3 4 Drift ratio: %

5

LC 3

7 3 2 5 6

LC 5 LC 6 LC 7

(c) PI-D50

(b) PI-B30

1

LC 2

0

1

2 3 4 Drift ratio: %

5

0

(d) PI-D30

1

2 3 4 Drift ratio: %

5

Fig. 14. Stress increments in unbonded tendons versus lateral drifts Magazine of Concrete Research, 2006, 58, No. 10

709

S. W. Han et al. in columns 4 and 11 in Table 3, respectively. Note that Mn,f s denotes the moment capacity considering full slab width, not c2 + 3h. As might be expected, the values obtained using the two different approaches are quite close (ratios ¼ 0.87 to 1.05), and also consistent with other independently obtained measurements (load cells installed at the base of slab end points) (see Fig. 9). These results support that the shear stress capacities (vc ) of the specimens were greater than the peak shear stresses (vu ) such that the full flexural moment capacities were reached prior to punching failures that eventually occurred at relatively large drifts (3.2 to 5.9%). The peak shear stress (vu ) owing to direct shear and eccentric shear obtained using equations (3) to (6) with peak unbalanced moment (Mu,ub ) was compared with pffiffiffiffiffiffi the nominal shear strength (c ¼ 0.29 f c9 + 0.3fpc + Vp /b0 d, where Vp is negligible) for the specimens in column 8 in Table 3. Based on the results, the eccentric shear stress model gives conservative results for the nominal shear strength for the PT specimens, as well as for the post-tensioned interior slab–column specimens tested earlier (Fig. 15). Results for this test programme are consistent with results for earlier test programmes for gravity loads, although the ratios tend to be a bit lower, possibly owing to the modest increase in tendon stress under lateral loads noted earlier.

(b)

(c)

Conclusions Experimental studies of four isolated, post-tensioned interior slab–column connections subjected to both gravity and cyclic lateral loading were conducted. Based on the test results, the following conclusions are reached. (a) Consistent with observations for reinforced concrete slab–column connections, the level of gravity shear on the slab critical section significantly influences the cyclic behaviour of the post-tensioned slab–column connections. As the gravity shear ratio increased, a drift ratio at punching and the

(d )

(e)

hysteretic energy dissipation capacity for the posttensioned connections decreased. The improved hysteretic energy dissipation for the connections with lower gravity shear (PI-B30 and PI-D30) was owing to more extensive yielding of bonded reinforcement prior to punching failure. Results indicate that seismic performance of the post-tensioned flat plate slab systems is impacted by the tendon distribution. For the higher gravity shear ratio (40%), higher drift capacity and improved ductility were observed for PI-D50 compared with PI-B50. For these cases, limited yielding of both top and bottom slab reinforcement was noted and the use of banded tendons appears to create larger precompression within the connection region. Moment reversal (change from negative slab moment due to gravity load to positive slab moment under lateral load on one side of a connection) occurred between lateral drifts of 0.5 to 0.8%. In turn, bonded bottom reinforcement, which was placed according to ACI 318–052 and ACI 352.1R-89,10 reached yield at lateral drifts between 2.2% to 3.5%. Based on these results, it is concluded that bonded bottom reinforcement should be provided for the post-tensioned flat plate slab systems; however, integrity reinforcement required by chapter 7 of ACI 318–05 appears sufficient to limit rebar yielding. In addition, the bottom reinforcement improves the hysteretic energy dissipation capacity of the PT interior connections. Test results indicate that tendon stresses for combined gravity and lateral loading were approximately 35 to 60% of the values predicted by ACI 318–052 provisions. The reduced tendon stress should be considered for flexural design of the post-tensioned flat plate slab systems in high seismic regions, as moment reversal is anticipated. The validity of the eccentric shear stress model defined in ACI 318–052 was assessed. The test results indicate that the eccentric shear stress model gives reasonable predictions for the nominal shear strength (vc ) and the flexural transfer capacity.

0·8 0·7

vc /(f c¢ )1/2: MPa1/2

Acknowledgements

0·6 0·5 Gravity· loading tests3 · lateral loading tests5 Repeated Reversed · cyclic loading tests5 Present· test programme

0·4 0·3 0·2

0

0·1

0·2

0·3

0·4 0·5 0·6 0·7 fpc /(f c¢ )1/2: MPa1/2

0·8

0·9

Fig. 15. Shear strength of post-tensioned interior slab– column connections

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The work presented in this paper was sponsored by Hanyang University, MOST R01–2006–000–10722–0 and SRC/ERC R11–2005–056–04002–0. The views expressed are those of authors and do not necessarily represent those of the sponsor.

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References 1. International Code Council. International Building Code (IBC-03). Whittier, California, 2003.

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Cyclic behaviour of interior post-tensioned flat plate connections 2. American Concrete Institute. Building Code Requirements for Structural Concrete and Commentary (ACI 318-05). ACI, Farmington Hills, Michigan, 2005. 3. Burns N. H. and Hemakom R. Test of post-tensioned flat plate with banded tendons. Journal of Structual Engineering, ASCE, 1985, 111, No. 9, 1899–1915. 4. Kang T. H.-K. and Wallace J. W. Punching of reinforced and post-tensioned concrete slab–column connections. ACI Structural Journal, 2006, 103, No. 4, 531–540. 5. Qaisrani A. N. Interior Post-Tensioned Flat-Plate Connections Subjected to Vertical and Biaxial Lateral Loading. PhD thesis, University of California, Berkeley, 1993. 6. Pimanmas A., Warnitchai P. and Pongpornsup S. Seismic performance of 3/5 scaled post-tensioned interior flat slab– column connections. Asia Conference on Earthquake Engineering (ACEE 2004), Manila 2004 (CD-ROM). 7. Kang T. H.-K. and Wallace J. W. Dynamic responses of flat plate systems with shear reinforcement. ACI Structural Journal 2005, 102, No. 5, 763–773. 8. Joint American Concrete Institute–American Society of Civil Engineers Committee 423. Recommendations for Concrete Members Prestressed with Unbonded Tendons (ACI 423.3R-96). ACI, Farmington Hills, Michigan, 1996. 9. Midas It. MIDAS/GENw User’s Manual. Version 6.3.2, Seoul, Korea, 2004. 10. Joint American Concrete Institute–American Society of Civil Engineers Committee 352. Recommendation for Design of Slab–Column Connections in Monolithic Reinforced Concrete Structures (ACI 352.1R-89). ACI, Farmington Hills, Michigan, 1989. 11. Korean Standard Association. Standard Specification (KS02). KSA, Seoul, Korea, 2002. 12. Akiyama H. and Hawkins N. M. Response of Flat Plate Connection Structures to Seismic and Wind Forces. University of Washington, Seattle, 1984. Structures and Mechanics Report SM 84–1, 1–267. 13. Pan A. D. and Moehle J. P. An experimental study of slab– column connections. ACI Structural Journal, 1992, 89, No. 6, 626–638. 14. Pan A. D. and Moehle J. P. Lateral displacement ductility of reinforced concrete flat plates. ACI Structural Journal, 1989, 86, No. 3, 250–258.

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15. Megally S. and Ghali A. Design considerations for slab– column connections in seismic zones. ACI Structural Journal, 1994, 91, No. 30, 303–314. 16. Hueste M. B. D. and Wight J. K. Nonlinear punching shear failure model for interior slab–column connections. Journal of Structural Engineering ASCE, 1999, 125, No. 9, 997–1008. 17. Moehle J. P. Seismic design considerations for flat-plate construction. Mete A. Sozen Symposium, Tarpon Spring, Florida (J. K. Wight and M. E. Kreger (eds)). American Concrete Institute, Farmington Hills, MI, 1996, ACI SP-162, pp. 1–34. 18. Federal Emergency Management Agency. Pre-Standard and Commentary for the Seismic Rehabilitation of Buildings (FEMA-356). FEMA, Washington DC, 2000. 19. Kang T. H.-K., Lafave J. M., Robertson I. N. and Hawkins N. M. Post-tensioned slab–column connections: Drift capacity at punching of connections subjected to lateral loading. ACI Concrete International, to be published in 2007. 20. Trongtham N. and Hawkins N. M. Moment Transfer to Columns in Unbonded Post-tensioned Prestressed Concrete Slabs. University of Washington, Seattle, 186 pp., 1977, Report SM77-3. 21. Shatila M. Prestressed Concrete Slab-edge Column Connection. MSc thesis, University of Calgary, 1987. 22. Foutch D. A., Gamble W. L. and Sunidja H. Tests of posttensioned concrete slab-edge column connections. ACI Structural Journal, 1990, 87, No. 18, 167–179. 23. Matinez-Cruzado J. A. Experimental Study of Post-tensioned Flat Plate Exterior Slab–Column Connections Subjected to Gravity and Biaxial Loading. PhD thesis, University of California, Berkeley, 1993. 24. Han S. W., Kee S.-H., Park Y.-M., Lee L.-H. and Kang T. H.-K. Hysteretic behavior of exterior post-tensioned flat plate connections. Engineering Structures, in press, doi: 10.1016/j. engstruct.2006.03.029. 25. Ritchie M. and Ghali A. Seismic-resistant connections of edge columns with prestressed slabs. ACI Structural Journal, 2005, 102, No. 2, 314–323.

Discussion contributions on this paper should reach the editor by 1 June 2007

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