Design for Punching Shear at Interior Columns in Prestressed Concrete Slabs: Resistance to Earthquakes
by
Ramez Botros Gayed
A DISSERTATION
SUBMITTED TO THE FACULTY OF GRADUATE STUDIES IN PARTIAL FULFILMENT OF THE REQUIREMENT FOR THE
DEGREE OF DOCTOR OF PHILOSOPHY
DEPARTMENT OF CIVIL ENGINEERING
CALGARY, ALBERTA SEPTEMBER, 2005
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Trang 3The undersigned certify that they have read, and recommend to the Faculty of Graduate Studies for acceptance, a dissertation entitled “Design for Punching Shear at Interior Columns in Prestressed Concrete Slabs: Resistance to Earthquakes” submitted by Ramez Botros Gayed in partial fulfillment of the requirements for the degree of Doctor of Philosophy
Trang 4
Experimental and numerical studies were carried out to investigate the punching shear strength of post-tensioned concrete flat slab-interior column connections under the effects of gravity loads and lateral displacements induced by earthquakes Seven full-size post- tensioned slab-interior column connections were tested under gravity loads combined with cyclic displacement reversals of increasing amplitude up to failure The ratio of prestressed to non-prestressed reinforcement was varied, while the flexural strength was constant The slabs were reinforced with headed studs, a type of shear reinforcement that had been developed at the University of Calgary The objective of this experimental program was to verify the applicability of the seismic provisions of the North American codes as well as other seismic design procedures, proposed earlier, when used for prestressed slabs
The tested connections showed that varying the prestressing compressive stress, foc, from 0.4 to 1.1 MPa (60 to 150 psi) has no significant effect on the unbalanced moment strength or the ductility; finite-element analyses permitted the extension of the range of Joc to 1.4 MPa (200 psi) Effectiveness of stud shear reinforcement, when used in
prestressed flat slab structures, was confirmed Furthermore, it was shown that
prestressing mitigates degradation of the connection’s stiffness; however, energy dissipation is better in non-prestressed connections
A commercial non-linear finite-element analysis software was used to investigate the punching strength of prestressed slab-interior column connections, subjected to simulated earthquake loading The analyses served to study the effect of varying design parameters that could not be covered in the physical experiments The finite-element model was described and verified using the results of the experimental program conducted in this research Analysis results, combined with the test results, showed that existing seismic design procedure, for non-prestressed slabs, is also applicable for prestressed slabs having foc = 0.4 to 1.4 MPa (60 to 200 psi)
Trang 5I would like to express my honest gratitude to my supervisor Dr Amin Ghali I am very grateful for his caring guidance, constructive criticism, encouragement and generous support at all stages of this research I would like also to thank him and his wife for their generosity and concern about myself during my stay in Calgary
My appreciation is also extended to the members of my supervisory committee, Dr W Dilger and Dr M El-Badry, for their constructive comments and helpful encouragement
The financial support from the National Science and Engineering Research Council of Canada and the Department of Civil Engineering at the University of Calgary is thankfully acknowledged
I would like to express my gratitude to Decon Canada for providing the headed shear studs used in my experimental work The donation of the prestressing tendons from DSI as well as the valuable information provided by Don Singer are specially appreciated
I am also grateful to all the technical staff of the Department of Civil Engineering at the University of Calgary for their valuable help and support in the experimental work of my program My special thanks to Terry Quinn, Don Anson, Dan Tilleman, Harry Pollard and Don McCullough for the joyful work environment they have created
Finally, my words stand helpless and cannot express my deep appreciation to my beloved family: my father and mother for their endless love and support during my life and my brother for his guidance through my life
Trang 7APPROVAL, PAGE S11 12121111 1011211111111 1010111111 HH0 Ha il ABSTRACT) woccccccccccscscsesesesscscscscsesesesevacsesesssesevevscsssesesesevevsssesesesesevssssseseeevssesseseseees iii ACKNOWLEDGEMENTS ou ccccccccccccsesscssseseseseseececseseseseseecsesesesesasevacseseseeseseas iv
DEDICA TIƠN c2 20111111 eu V
TABLE OF CONTENTS c2 2H21 111 go vi IBBSMNS9)U) 05 XI LIST OF FIGUREES S1 2 121212111 121212111 101012111 g1 roi XI
LIST OF 32.i.9 5.5 -::1liI XX
CHAPTER I1: INTRODUCTTION 2S: 12k 2212021221211 ey 1
1.1 6705212255 Ị
12 NON-PRESTRESSED REINFORCEMENT cà cccsecerees 2 13 TENDONSLAYOUT Q LSnLS HS 1n Hy HH HH HH Hy 2 1.4 — TENDON PROFILES S2 vn k SH ng HH HH ghe, 5 1.5 PUNCHING SHEAR CONSIDERATION Ă se eeerrree 7 1.6 SHEAR REINFORCEMENÏT SG c1 S SH nu 9 17 SHEAR STRESSES DUE TO WIND AND EARTHQUAKES 12 1.8 — OBJECTTIVES AND SCOPPE Q LH vn Hy HH hệt 13 19 LAYOUT OF DISSERTATION cuc Star erey 14 CHAPTER 2: PUNCHING SHEAR IN FLAT PLATES -. -: 15
2.1 0N;49)8)0/98195)Ẽ25255% aaaJÀAăăăốố 15
2.2 ANALYTICAL MODELS - cà St SH ve erret 16 2.2.1 Linear variation of shear stress (eccentric shear) model 17 2.2.2 Beam analogy mođeÌ ác 1c v2 1S vn vn 11x ve 19 2.2.3 Models based on elastie plate theOrY SĂc se, 25 2.2.4 Yield line modelÌL - c1 v11 12 1121 18 111111111 81 11x xe 25 2.2.5 Strut-and-tie modeÌ - 1k1 1S HS HH HH, 29 2.2.6 Plastic model v1 1S S11 11 11H 11 11 1 kg grvkt 31 2.2.7 Shear strength degradation modelÌ - - sex ssskkxsevesesre 33 23 CODE PROVISIONS FOR PRESTRESSED SLAB-COLUMN
CONNECTIONS HH HH HH HH HH Hà Hà HH rệt 34
PIN NT 906i n9 34
2.3.2 Joinnt ACT-ASCE Committee 421 (ACT 421.1R-99) 38
Trang 8“1N Gan ae 46 2.4.2 Prestressing eÍÍeCfS LH TH HH TH HH Hà key 47 2.4.3 Lateral displaceImnerifS - uc n1 vn SH nh ve, 48 2.5 FACTORS AFFECTING PUNCHING SHEAR STRENGTH OF
SLAB-COLUMN CONNECTIONS share 49 2.5.1 Driff-shear ratiO In†€TaCfIOT Ăn nàng He, 50 2.5.2 Concentration of flexural reinforcement in the column vicinity .51 2.5.3 Monotonic versus cyelie reversed moment application 52 2.5.4 Uniaxial versus biaxial moment application -.‹‹‹s-++: 53 2.5.5 Slab SIZ€ ©ÍT€CT HH HH TH TT HH ng ng tàu 53 2.5.6 Provision of shear reinforcement in the column vicinity 55 2.6 RESEARCH ON PRESTRESSED FLAT SLAB-COLUMN
0 9))0)5958i90)1 1115 57 2.6.1 Scordelis, Pister and Lin (1956) - che 57 2.6.2 Gerber and Burns (7Ï) .c c1 112 11111311111 81551 1x, 57 2.6.3 Smith and Burns (1974) - -.c v1 3S nh Hệ 58 2.6.4 Burns and Hemakom (1977) .cccccccssccesscessccsseeessceseeesseeeseseneseneee 59 2.6.5 Hawkins (1977, I9 ]) sáng ng Hà HH 59 2.6.6 Franklin and Long (1982) uc n1 vn 11 11181111 1 xe, 61 2.6.7 Dilger and Shatila (1989) cu v1 vn 1111 111 8111111 11x, 62 2.6.8 Foutch et al (1990) cv x n1 SH TT TH TH TH TH vệ 63 2.6.9 Martinez-Cruzado et al (19944) ác cnv v11 1 1x ve, 65 2.6.10 Hassanzadeh and Sundquist (2000) 2c Sex, 65 2.6.11 Kang and Wallace (2004) c cc 1 n1 vn 11x gvec 66 2.6.12 Ritchie and Ghali (20ÕŠ) Án kg HH HH He 66 ` G7
CHAPTER 3: EARTHQUAKE-RESISTANT FLAT PLATE
S;TRUCTURES - : : v St t212121212121212 01 1H HH1 121111111111111111 111tr 69 3.1 INTRODUCTION 0 cccccccccsessesecseeeecnseeesescesesesesesseeseesesseesesseenessesaeeneenees 69 3.2 DESIGN CODES' SEISMIC ACTIONS che 70 3.2.1 International Building Code 2003 (TBC-03) c +: 70
3.2.1.1 — Analytical procedures for determination of seismic 12127801: S800n0n0n8Ắ « ố.ố 71 3.2.1.2 Eundamendl periOdi ĂĂ Si Seiteikei 76 3.2.1.3 Application of seismie laterdl ƒOFC€S 78 3.2.1.4 Drƒi calculaHion and lHHÌIAHOHS ccS« 79 3.2.1.5 Seismie design load combiHđfiOHS 81 3.2.2 National Building Code of Canada 2005 (NBCC-05) 82
Trang 93.2.2.3 Application of seismic lateral fOrceS cisco 3.2.2.4 Fundamental period occccccccccccccccccscscsectseeseseeseessseeeeesaee 3.2.2.5 Drift LiMILATIONS iececcccccccscecessescseetseesesesssesseessseeseseaes 3.2.2.6 Seismic load conmiDÌnQfÏOHS c ve cecsekskiea 3.2.3 Comparison between the IBC-03 and NBCC-05 codes 3.3 SHEAR WALLS AS PRIMARY LFRS sĂ So sssksieeirskes 3.3.1 Shear walÏ CTOSS S€CfÏOTS LH HH HH re 3.3.1.1 Rectangular shedr' WAdllS cv, 3.3.1.2 — Hlanged shedr VUQÌÏÏS cà vkisssrieserve 3.3.1.3 Coupled shear Wdlϧ cà kSekiseee 3.3.2 Plan arrangements of shear walls and torsional oscillation 3.4 ANALYTICAL MODELTNG FOR SEISMIC DESIGN
3.4.1 Two-dimensional analysis for symmetrical multi-storey
DUI GIN GS cece ceseceneceseeeteeeeeeeeeeeeeeeseeeeeeeaeenseceeeeeaeesteseneeeeaee 3.4.2 Three-dimensional analysis for unsymmetrical multi-storey
l0 T.TECƯHHt)aaaaiaẳaầẳả4 i 3.4.3 Effective slab width for lateral force analyS1S - ‹ + 3.5 CODE PROVISIONS FOR EARTHQUAKE-RESISTANT SLAB-
COLUMN CONNECTIONS ác LH HH nh HH re 3.5.1 ACI 318-05 COde LH ng TH HH ng cay 3.5.2 Joint ACI-ASCE Committee 421 (ACT 421.1R-99) 3.5.3 Joint ACI-ASCE Committee 423 (ACI 423.3R-96) 3.5.4 Canadian Standard 2004 (CSA A23.3-04) cccceesekee 3.5.5 Megally and Ghali (2000Ư) - c1 2 112 1111 xreeree
3.5.6 Brown (2003) cung HH TH HH HH
Trang 104.3.1 Casting of test SPeCIMeNS ceceeseesseeeteeetseeseeesteestseceseeeseessaees 152 4.3.1.1 — FOFHHWOFĂ Ă Ăn Hệ, 152 4.3.1.2 Placement OƒT€ÌHƒOFCGIHGHI i cv 152 hN ˆ), , 1 v dtđi.- 154 4.3.1.4 COHCF€IC CHIỈHE vă ch rhện 154 “` Š-:-utiaiadadđaiiiiiaiaiaiáảŸ34 155 “6 62402 155 4.5 — TNSTRUMENTATION SH HH HH HH hu 157 4.6 TESTPROCEDURE SG n2 9n HT TH ng ngư 159 4.7 — SƯUMMARY Ăn HH TH TT ng TH HH nu 161 CHAPTER 5: EXPERIMENTAL RESULTS oo ccccesecetetereeeeeneeenes 163 5.1 INTRODUCTION uc ccceccceceseesecesecseesecneesseeseeeeceaeeseceseseresaeeeresaeeeees 163 5.2 LOADS AND MODES OF FAILURE eccccceeeteeeeeseteeeeetseeeeeaeeaees 163 5.3 CRACK PATTERNS ou cecceceesessseeteeeseeseeeeeenecesecresseceesaeeeseeneseeeeseeeaes 164 5.4 SLAB AND COLUMN DEFORMATIONS, STEEL STRAINS AND
PRESTRESS FORCES LG HH ng ng TH Hà ng Hy 170 5.4.1 Axial displacement of €Olumm -.cccsc xxx 171
5.4.2 Drift ratio, DR vccccccccccsccscscccsesesssssssccssesessssessecesesernsvesseessesenns 175
5.4.3 Slab deflections ốc 180 5.4.4 Strains in slab top flexural reinforcement cc eeeeeeeteeneeeees 189 5.4.5 Strains in slab bottom flexural reinforcemeri - - 194 5.4.6 Strains in stud shear reinforcement ce eesceeseeeeeeeteeeteeeeeeees 198 5.4.7 Prestressing tendO'S” ÍOFC€S c1 vn S vn ky 198 ¬ `: 9809 213 CHAPTER 6: ANALYSIS OF EXPERIMENTAL RESULTS 214 6.1 1N ;49)9)0/9819)Ẽ55555 214 6.2 — DRIFTCAPACTY SH HH TH HH Tnhh Hhu 214 6.3 DUCTILITY Ă 2S HS HS HH TH HT HH HH nhiệt 215 6.3.1 HySfer€SIS ÌOOPS LH HH HT TH TH KH Hhệp 215 6.3.2 Axial displacement of coÏumn sec vevssevsesrresverks 216 6.3.3 Displacement đuctIÏItY .- cà HS n ng HH Hệ 216 2e 218 6.5 MAXIMUMITNPUT ENERGY Su SH HH iu 220 Ơ=?\ (C00) 27.0009)0 0 221 6.7 — DAMPING COEFFICIENT Ăn HH HH 222 6.8 PUNCHING SHEAR STRENGTH - cS cSSsssieererske 222 6.8.1 Unbalanced moments causing shear failure .‹++ «+ 222
Trang 113819) 227 6.8.4 Punching shear stress outside the shear-reinforced zone 232 6.9 RESIDUAL SHEAR STRENGTHH 2c nen 232 6.10 EFFECTOF PRESTRESSING ON STRENGTH c~e 234
6.11 CONCLUSIONS .L 234
CHAPTER 7: FINITE-ELEMENT ANALYSES Ă.c.eiie 236 7.1 INTRODUCTIƠN uc HH HH HH Tnhh nh nhu 236 7.22 DESCRIPTION OE THE FINITE-ELEMENT MODEL 237 7.2.1 Finife €Ïl€Im€TẨS - TH nh TH HH nghiệt 237 7.2.2 Constitutive concrete model assumptIOnS -.‹ +25 x+++ 52 238 7.2.2.1 Behayvior under comessiVe siress sÍqf€S 239 2.2.2.2 — CrdckiHg CFỈ€FÍOH ii HH nh nhện 243 2.2.3 Shear releHfiOH HlOđÏ ĂĂSS sinh, 246 7.2.3 Materlal PTODeTLI€S cv nSnH ng nh ng yeu 247 22.3 COHCFÍƠ Ă HT HH HH kh 247
KP PIN 10/2,/20/ na 248
7.2.4 Non-Ìinear IteraftIVe pfOC€dUTe - cớ, 249 7.3 VERIFICATION OF THE FINITE-ELEMENT MODEL 251 7.3.1 Three-dimenslonal models of post-tensioned slabs 251 7.3.2 Failure mode and hysteretic behaVIOT cssc cà ssseve+ 254 7.3.3 Sensitivity of the finite-element results to support condition 262 7.4 PARAMETRIC STUDY OF PRESTRESSED SLAB-INTERIOR
COLUMN CONNECTIONS SUBJECTED TO EARTHQUAKE-
SIMULATED DISPLACEMENTS Sáng e, 264 7.4.1 AnalysIs varlableS - c cv vn 1n Hy yeu 264 7.4.2 AVeragø€ COIPT€SSIV€ SfT€SS 1 CONCT€f€, ƒ›„¿ c.c2Ă +, 266 7.4.3 Finite-element modl c St nnHnHn H n grưy 267 7.4.4 Finite-element r€SỤ(S Q SĂ 1k1 SH HH HH, 268 7.4.4.1 Ef£ctLofthe ratio Ứ„ Í(@,} 272 N2 6, aa e 276
“nh? , rGn 2n ẶÁa ỎƠơOạO 276
7.5 — SUMMARY AND CONCLUSIONS cu ehehereee 277
CHAPTER 8: SUMMARY, CONCLUSIONS AND
RECOMMENDATIONS 1111111111 rrrrrreg 279
8.1 l8 /0/710 0 279
Trang 12APPENDIX A: DESIGN OF PROTOTYPE FLOOR AND TEST
`7 00750511777 292 A.I — GENERAL SH HH HH HH TK TH KH kh Hhu 292 A.2 — PROTOTYPE FLAT PLATE FLOOR 2 c2 seieieeirey 292 A.2.] @OITTV LH TH TH TH HH nhà 292 ˆ W2 nh 294 A.2.3 LOAđS HH TH HH ng TH HH HH Tinh HH 294 A.2.4 Tendon prOllile c1 n1 11 119 1101111118111 0111111 1111 ghe 295 A.2.5 Load balanc1ng cv kg HH kh iu 295
ˆW Nhà h5 296
A.2.7 Non-prestressed reInÍOrCeT€I( cv nh key 305 A.2.8 Factored flexural r€SISfATC€ - án LH re 306 A.2.9 Shear deSIEn LH TT TH KH HH iu 307 A.2.10 Design of headed shear reinforceimenI ‹-scscscsxccsses 311 A.2.11 Structural IntegrIfy reinfOrCeIm€ï - uc Ăn se 313 A.3 — POST-TENSIONED SLAB-INTERIOR COLUMN SPECIMENS 313 A.3.1 Prestressed tendOnS ung ng ngư 313 A.3.2_ Non-prestressed reInfOrC€T€T ĩc 12112 vs vrsevres 315 A.3.3 Flexural resistances Of SpeClimens co vn nhe 316 A.3.4 Predicted failure ÏOaS - ĩc k2 ng HH ng re 316 A.3.5 Column stub đeSIgn ch HH Hàu 318
Trang 133.1 3.2 4.1 4.2 4.3 4.4 5.1 5.2 5.3 6.1 6.2 6.3 6.4 6.5 6.6 6.7 7.1 7.2 7.3 7.4 Al A.2
Comparison between force modification factors of IBC-03 and NBCC-05
S€ISITIC CO€S TH TH nh TH TH Thu TH HT Ti HH nh tệp 9] Effective slab widths for equivalent frame models of flat plate buildings 106-108 Reinforcementts OŸ †€Sf SD€CIT€NS (2c 12 1 11 1191 1181111111111 8111111 111 xe, 127 Design of concrete mix used for casting SDe€CIIn€đS ác, 128 Concrete strength and mix ftype 0Ÿ †€sf Sp€CI€NS 2c c vs seresves 128 Properties of reinforcement used 1n †esf SD€C1nens ác svseves 149 Loads and modes of failure of slab-interior column connections subjected to shear and reversed cyclic moment transfer .ccccceececsseeesscessessseeesseeseeesseseseeens 164 Column displacemenrts at different loading stages of †esfing cà 171 Drift ratio at yield and at failure of slab-interior column connections 175 Displacement ductility factor oŸ tesf SD€CIT€RS c2 13 vssssevrsesres 217 Stiffness and energy characferISftIcs Of tesf SD€CIT€nS .- - cv 220 Ultimate unbalanced moment in tests compared with values permitted by ACI 318-05, CSA A23.3-04 and Megally and Ghali (2000B) c c2 225 Punching shear stresses and strengths according to experimental results and ACI Si vo 227 Punching shear strength of test specimens, at d/2 from the column periphery, according to ACI 318-05, CSA A23.3-04 and Megally and Ghali (2000b) 231
Punching shear stresses of test specimens, outside the shear-reinforced zone,
according to experimental data and codeS” DTOVISIOTS coi 232 Experimental results of the post-punching stage (Stage IÏÏ) - cc << 233 Test and non-linear FE results of prestressed slab-interior column connections subjected to shear and cyclic reversed displacemeniS cc c2 262 Details of analyzed prestressed slab-interior column connecftIons 265 Finite-element results of the slab-column connections listed in Table 7.2 270
Concrete shear contribution, vs, OŸ prestressed connecfIOnS - cc <<: 272
Prestress forces of the banded and distributed tendons In test specImens 315
Moment resistance, Ä⁄„ for the †eSf SD€CII€RS 2c v12 1321 xsevrsesree 317
Trang 141.4 1.5 1.6 1.7 1.8 1.9 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 2.10 2.11 2.12 2.13 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9
Plan view ofa prestressed flat plate Í[OOT c1 v12 11 1 111111111111 8 xe 3 Tendon schemes In prestressed two-way fÏaf pÏaf©S càng nh Hye, 5 Slab bending moments for a two-dimensional frame modeling of prestressed
flat plate o2 7
Slab flexural and shear cracks in the column vicinity of a slab-interior column COTTI€CfIOTN s2 11T nh TH nhu nh TH ghi TH nh TH Thi Thi HH 8 Effectiveness of shear reinforcement in flat slab ÍÏoOTsS + + s+xcsesss 9 Deficieney of stirrup shear reinforcement ¡n flat slab floor systems 10 SSR used as shear reinforcement in slab-column connecftIOnS - ‹- 11 Comparison between shear reinforeements In flat plate floOTS - - I1 Stud shear reinforcement at an Interior column in a prestressed slab 12 Eccentrie shear model at a slab-interior column connecfIon -.‹ ‹« «- 19 Internal forces at an interior critical section, according to beam analogy
model (Park and Islam, 19776) .c 112111 11311113111 81111111111 0111111 111 1H tràn 20 Yield line pattern of slab-interior square column connections (Gesund and
GO]i, uiddỒỀ 27 Yield line patterns of fracture mechanisms, proposed by: (a) Dilger and Cao (1994), and (b) Brown (2003) ccecsccssceetsesssecsseesteesssecsseceeessaectseeeesessestseseneeenes 28 Truss model developed by Alexander and Simmonds (1987) -.‹‹ ++: 30 Assembly of load-resisting struts for shear and moment transfer (Alexander and Simmonds, 1987) .cccccccccccsscccssscccssseeessecesseesesseeeesseeesssesesseeeessesesssesessesensaeees 31 Plastic model of Alexander (19944) c1 SH HS n1 SH TH TH TH TH ket 32 Shear strength degradation model (Moehle, 1996 and Kang 2004) 34 Modeling of equivalent frames In flat plate struCfUT€S - c2 44 Plane frame idealization of slab-column connecfIONIS .- «s 5+2 45 Equivalent frame for analysis of lateral displacemen ccs+ccsscxs<«2 49 Size effect law (Bazant and Cao, 1 98§7) co cv v11 1111 1181111111111 811 11 xe 54 Types of tendon schemes tested by Hassanzadeh and Sundquist (2000) 66
Distribution exponert, &, versus the fundamental period, 7]ì ‹ .‹«<«+ 73
General procedure response spectrum (IBC-03) 2c cv stress 75 Lateral force distribution for determination of 7; using Rayleigh procedure 77 Inelastic force-deformation respONse CUTV© 1 12112 11 1111111111111 ke 82 Definition of parameters required to determine the torsional parameter, B, of
5Ev0iiuš>ï01i2 727 84
UHS graphs for three cities in Canada (Vancouver, Montreal and Calgary) 86 Reinforcement layout of a rectangular shear Wall .cccccecseetsestseceseeeteesteeeeneees 93 Sections of flanged shear walls in multI-storey buildings - ‹+scc+<<+2 94 Coupled shear walls and their mathematical model (Park and Paulay, 1975) 95
Trang 153.12 3.13 3.14 3.15 3.16 3.17 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 4.10 4.11 4.12 4.13 4.14 4.15 4.16
four cases discussed in SectIOII 3.4 LH n ng ng HH nh nhiệt 100 Coordinates for 3-D analysis of a multi-storey shear wall structure (Ghali et
I0 “ 104
Requirement criteria of punching shear reinforcement according to ACI
318-05 and Megally and Ghali (2000Đ) 2c 112 v11 111 111111118121 tr rey 109 Requirement criteria of punching shear reinforcement according to CSA
A23.3-04 and Megally and Ghali (2000Đ) - c2 2211211311311 xxee 112 Conditions where Eq 3.61a governs the amount of shear reinforcement, v, .113 Definttion of displacement ductiÏIty t€TTS cv + sevssevressxes 119 Defintion of stiffness, energy and damping paraimef€rS ‹+cscxcs<<s¿ 120 Layout of prestressed protofype concrefe †ÏOOT- -.ccccc ki, 124 Dimenslons Of f†eSf SD€CIIITS 0 1201121111111 111 1110 111011 811g ky xe 125 (a) Cross section along banded tendons of specimen IPS-9 or [PS-9R 129 (b) Cross section along distributed tendons of specimen IPS-9 or IPS-9R 130 Flexural reinforcement layout of specimen IPS-9: (a) Prestressed tendons
and top non-prestressed reinforcement; (b) Studs and bottom non-
presfressecÌ reInÍOTC€TN€TIT - 2 113191 1S S1 TT HH ky 131,132 Flexural reinforcement layout of specimen IPS-9R: (a) Prestressed tendons
and top non-prestressed reinforcement; (b) Studs and bottom non-
presfressecÌ reInÍOTC€TN€TIT (2 113191 SE ST ng HH ky 133,134 Flexural reinforcement layout of specimen IPS-7: (a) Prestressed tendons
and top non-prestressed reinforcement; (b) Studs and bottom non-
prestressed r€IRÍOTC€IT€TIT 2 1121211111 11 1115111111 8111111 11111 rry 135,136 Flexural reinforcement layout of specimen IPS-5: (a) Prestressed tendons
and top non-prestressed reinforcement; (b) Studs and bottom non-
presfressecÌ reInÍOTC€TN€TIT - 2 113191 1S S1 TT HH ky 137,138 Flexural reinforcement layout of specimen IPS-5R: (a) Prestressed tendons
and top non-prestressed reinforcement; (b) Studs and bottom non-
prestressed r€IRÍOTC€IT€TIT 2 1121211111 11 1115111111 8111111 11111 rry 139,140 Flexural reinforcement layout of specimen IPS-3: (a) Prestressed tendons
and top non-prestressed reinforcement; (b) Studs and bottom non-
presfressecÌ reInÍOTC€TN€TIT 2c 11v SE ST Hey 141,142 Flexural reinforcement layout of specimen IPS-0: (a) Top non-prestressed
reinforcement; (b) Studs and bottom non-prestressed reinforcement 143,144 Details of stud shear reinforcement in test SpeCI€NS - 2c ++sxcsx+s 145 Typical stress-strain curve for 9.5 mm (% in.) stud shear reinforcement 146 Average stress-strain curve for 8 mm deformed bars .cccceeceesseesseeeseeeteeesees 146 Typical stress-strain curve for 1OM deformed bars 5c se 147 Typical stress-strain curve for 15M deformed bats .ccccccecseesestseceseeeseeeeeees 147 Typical stress-strain curve for 25M deformed bars ca 148
Trang 164.19 4.20 4.21 4.22 4.23 4.24 4.25 4.26 4.27 5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8 5.9 5.10 5.11 5.12 5.13 5.14 5.15 5.16 5.17 5.18 5.19 5.20 5.21 5.22 5.23 5.24 5.25 5.26
Details of dead and live ends of prestressed tendons - c2 cscscxcsxss 151 Details of tendons' load monitoring and anchorage at their live ends 152 C0 iiisi080)140y TT 4 153 Reinforcement of specimen [PS-9R before concrete caSfIng ‹- 154
Testing frame oo .A 157
Pictorial view of the festing Írame - ĩc nàng ng ng HH kết 158 Instrumentation to measure slab and column stub deformations - 159 Loading history of test specimens during loading stage Lo eee eeceeteeteeeeeee 160 Column ends’ displacement history during loading stage II and positive sign COTV€TTIOT ÍOT Ổ TH TT TH Thu TH TH TH HT Thi HT nh ng 161 Crack patterns for specimen IPS-0 during load stage Loo ee eeseesseeeseeeteeeteees 165 Crack patterns for specimen IPS-5 during load stage To eceeeseeeteeeteeeteees 166 Crack patterns for specimen IPS-9R during load stage Ï - ‹+ s5 +2: 167 Crack patterns for specimen IPS-0 at the end of stage ÏÏ - c + <c+sx+: 168 Crack patterns for specimen IPS-Š at the end of stage ÏÌ -s-c+++<x++: 168 Crack patterns for specimen IPS-9R at the end of stage ÏÏ <c+<<+2 169 Crack patterns for specimen [PS-0 at the end of stage lIÏ ‹++ ++5: 169 Crack patterns for specimen [PS-Š at the end of stage ÏÏT -.«<+<<<+: 170 Crack patterns for specimen IPS-9R at the end of stage lÏI ‹:s-5 +5: 170
Column displacement versus shearing force, Ƒ for I[PS-0 .ccs<<+: 172
Column displacement versus shearing force, Ƒ, for IPS-3 ‹cs-s+©: 172
Column displacement versus shearing force, Ƒ, for IPS-5 and IPS-5R 173
Column displacement versus shearing force, , for IPS-7 ôcs<+â: 173
Column displacement versus shearing force, V, for [PS-9 and IPS-9R 174 Amplitudes of displacement D minus Dytage 1, versus drift ratio, DR during
testing Stage TD ccc ceescssccsscesssessscesscesseesssecssesessessaecsseseseestaecssesesesersesesesetesenaes 174 Hysteresis loops of drift ratio versus unbalaneed moment of [PS-0 176 Hysteresis loops of drift ratio versus unbalanced moment of [PS-3 177 Hysteresis loops of drift ratio versus unbalanced moment of IPS-5 0 177 Hysteresis loops of drift ratio versus unbalanced moment of [PS-SR 178 Hysteresis loops of drift ratio versus unbalaneced moment of [PS-7 178 Hysteresis loops of drift ratio versus unbalanced moment of [PS-9 179 Hysteresis loops of drift ratio versus unbalanced moment of IPS-9R 179 Envelopes of drIft ratio-unbalanced moment hysteresis loops 180 Profiles of slab deflection along centerline (x-axis) at peak positive drift
ratios — specimen IPS-Ơ ác v1 11 112 1111110111011 0111 11 01 HE HH kh 181 Profiles of slab deflection along centerline (x-axis) at peak negative drift
ratios — specimen IPS-0 vo ỒƯ.Ư 181 Profiles of slab deflection along centerline (x-axis) at peak positive drift
\:100)-0039200i1i01nn si 182
Trang 175.29 5.30 5.31 5.32 5.33 5.34 5.35 5.36 5.37 5.38 5.39 5.40 5.41 5.42 5.43 5.44 5.45 5.46 5.47 5.48
\:100)-003900in1i0in in a Profiles of slab deflection along centerline (x-axis) at peak negative drift ratios — specimen IPS-5 voice ố Profiles of slab deflection along centerline (x-axis) at peak positive drift raflos — specimen IPS-SR ác c1 v11 112 1201111111011 0111011 101 1n kg HH kh Profiles of slab deflection along centerline (x-axis) at peak negative drift
\:100)-039s00i1-i01nn 11
Profiles of slab deflection along centerline (x-axis) at peak positive drift ratios — specimen IPS-7 oo eeccccscesssestscenseeseeesteessseeseseeseessaecsseesseestaeseseseeessaees Profiles of slab deflection along centerline (x-axis) at peak negative drift ratios — specimen IPS-7 oo cccccseestsestscesscesecesteessseesesesseessaeceseesseestaeeeseseeessaees Profiles of slab deflection along centerline (x-axis) at peak positive drift
ratios — specimen IPS-9 TT e ẢẢ
Profiles of slab deflection along centerline (x-axis) at peak negative drift ratios — specimen IPS-9 oo e Profiles of slab deflection along centerline (x-axis) at peak positive drift
ratios — specimen IPS-9R 0 17 -
Profiles of slab deflection along centerline (x-axis) at peak negative drift
\:1010-0030siin1-a01mns T1
Typical profiles of slab deflection along the moment axis (y-axis) at peak drift ratios — specimen IPS-( - ác k2 v11 1S 11 SH TH kg TH Hiệp Profiles of slab deflection along centerline (x-axis) at peak positive moment
TrAMSLEL ae eốố.‹‹áăăăăăă
Profiles of slab deflection along centerline (x-axis) at peak negative moment
TrAMSLEL 43ä5ãạ án
Strains of top flexural reinforcement running in x-direction, perpendicular to moment ax1s, specimen TPS-( - cá 1192111111 1119111101 8 11 9 1E HH Strains of top flexural reinforcement running in x-direction, perpendicular to Moment axis, specimen PS -3 ¿Ác 13111111 1119111 01 1 11 g1 kg nh kh Strains of top flexural reinforcement running in x-direction, perpendicular to moment ax1s, specimen TP S-5 - - c c 1E 11111 1119111 11 1 118g kg HH Strains of top flexural reinforcement running in x-direction, perpendicular to moment axis, specimen [PS-SR -c c1 1111 119 111 1 011 91kg HH Strains of top flexural reinforcement running in x-direction, perpendicular to Moment axis, specimen PS -7 - - ¿+ ác 1+ 1921111111 1119111101 E11 HH HH Strains of top flexural reinforcement running in x-direction, perpendicular to moment ax1s, specimen TPS-Ĩ cá t1 k9 1111111 11 111 1101 1kg nh Strains of top flexural reinforcement running in x-direction, perpendicular to moment axis, specimen [PS-9Ï Ác 111191 1191110111 111g 1E HH kh Strains of bottom flexural reinforcement running in x-direction,
perpendicular to moment axis, specimen [PS-Ơ -.c c Le,
Trang 185.51 5.52 5.53 5.54 5.55 5.56 5.57 5.58 5.59 5.60 5.61 5.62 5.63 5.64 5.65 5.66 5.67 6.1 6.2 6.3 6.4 6.5 6.6 6.7 6.8 6.9 6.10 6.11
perpendicular to moment axis, specimen IPS-5 cece .- cv v2 ssrersrsesxee 195 Strains of bottom flexural reinforcement running in x-direction,
perpendicular to moment axis, specimen IPS-5R uo ec eeceesseesseeeteeetseetseeeseeeees 196 Strains of bottom flexural reinforcement running in x-direction,
perpendicular to moment axIs, specimen [PS-7 - c cc v2 sserersrsesxee 196 Strains of bottom flexural reinforcement running in x-direction,
perpendicular to moment axIs, specimen [PS-9 - cv v 1v rrsesxee 197 Strains of bottom flexural reinforcement running in x-direction,
perpendicular to moment axIs, specimen [PS-9R co cv series 197
Strains in studrails of specimen IPS-0 at different drIft ratiOS -.«- 199
Strains in studrails of specimen IPS-3 at different drift ratios -.‹ -+ 200
Strains in studrails of specimen IPS-Š at different drIft ratiOS -.«- 201
Strains In studrails of specimen IPS-SR at different drIft ratioS -.- 202
Strains in studrails of specimen IPS-7 at different drIft ratiOS -.«- 203
Strains in studrails of specimen IPS-9 at different drift ratIos - ‹ +: 204
Strains in studrails of specimen IPS-9R at different drIft ratiOS - 205
Tendon forces for specImen [PS-3 112011 1111 1111111111011 111111 kg 207 Tendon forces for specimen [PS-Š S11 S ng HH HH key 208 Tendon forces for specImen [PS-SÏ - c1 211 11 1111111111111 11 nh 209 Tendon forces for specImen [PS-7 - cv 1111 11111 1111111111011 111 101 key 210 Tendon forces for specimen [PS-9 c1 TH HH HH key 211 Tendon forces for speciImen [PS-9Ï c1 20112111 1111111111111 1 111 nh 212 Elastic and ductile responses of a single-degree of freedom structure 218
Variation of stiffness parameter, K, with drift ratio, DR occ eecetsceeteeeeetees 219 Effect of direction of displacement reversals on maximum input energy 221 Cut at a plane perpendicular to moment axis in specimen IPS-0 Dark colour is result of wetting the concrete during CUItING c ec eecessseceseeeseestseetseeeteeeseees 225 Critical section at d/2 from the column periphery 0.0 cece eeceeceeeeeteeeteeeteeesees 226 Shear stresses at the critical section, d/2 from column periphery, versus drift ratio during testing stage IT — specimen IPS-0 0 ceceeeetteceteeeeteeetseeteeenaee 228 Shear stresses at the critical section, d/2 from column periphery, versus drift ratio during testing stage IT — specimen IPS-3 -cc c ke, 228 Shear stresses at the critical section, d/2 from column periphery, versus drift ratio during testing stage IT — specImen IPS-5, - cv He, 229 Shear stresses at the critical section, d/2 from column periphery, versus drift ratio during testing stage II — specimen IPS-SR - c se, 229 Shear stresses at the critical section, d/2 from column periphery, versus drift ratio during testing stage IT — specImen IPS-7, - cv ke, 230 Shear stresses at the critical section, d/2 from column periphery, versus drift ratio during testing stage IT — specimen IPS-9 ooo ccceeeetseeeteeeeteestsenteeeaee 230
Trang 197.1 7.2 7.3 7.4 7.5 7.6 7.7 7.8 7.9 7.10 7.11 7.12 7.13 7.14 7.15 7.16 7.17 7.18 7.19 7.20 7.21 7.22 7.23 7.24 7.25 7.26 7.27 7.28 7.29 7.30 7.31
Concrete finite-element used in three-dimensional analysSIS - 238 Yield or failure surface Of COICT€f€ LH TH HT ng nhàng tiệt 240 Schematic representation of different hardening rules - 55+ ++s+2 243 00095: 580v19 si 58uiiiy10 0n .-a 244 Stress-strain curve Of COn€F€f€ 171 †€TISIOTI - ung HH ni, 245 Shear retention model used in ANACAP cung HH hệt 247 Typical concrete uniaxial compressive StreSs-Strain CUTV - sex 248 Typical reinforcing steel sfF€SS-SfA1TI CUTV L1 vn vn vn ve 249 Schematic representation of the non-linear iterative procedure 250 Analyzed model of slab-interior column connections subjected to shearing
force and cyelic reversed đispÏaCeI€TIfS - ác 12L ng ky 252 Finite-element mesh used in the analyses of slab-interior column
CONNECTIONS oo ‹a ố 253
Column ends’ displacement history used in the FE analyses - - 254 Crack pattern of specimen IPS-3 at the plane of symmetry at maximum
unbalanced MOMEN aaadddiẳŸÝẢ 255 Deformed shape at symmetry plane of specimen IPS-3 just before failure 256 Profile of vertical deflection at different loading stages of IPS-3 at d/2 from IISIv904ii8i122 0 256 Vertical deflection of IPS-3 at symmetry plane ]Just before failure 257 Distribution of maximum principal strain, ¢;, on compressive surface of
j6: 80u 2i0i-iï1 0 e 258 Envelopes of moment-drift ratio hysteresis loops of IPS-0 cccsx+: 258 Envelopes of moment-drift ratio hysteresis loops of IPS-3 - cccccẰ 259 Envelopes of moment-drift ratio hysteresis loops Of IPS-5 oo ec eeeeseeeeeetees 259 Envelopes of moment-drift ratio hysteresis loops ofIPS-SR .‹- 260 Envelopes of moment-drift ratio hysteresis loops of [PS-7 se: 260 Envelopes of moment-drift ratio hysteresis loops of IPS-9 c.cccssx°¿ 261 Envelopes of moment-drift ratio hysteresis loops of IPS-9R .‹ 261 Envelope of Ä⁄-DR loops o£IPS-Š5, analyzed assuming either rigid or spring support conditions along EFGH (Fig 7.]Ú) .ẶSĂ s HS HH HH He, 263 Tendon profile in a typical interior span of a prestressed flat plate structure 266 Variation of compressIve stress, /„, with the span length, ƒ -‹ 267 Model of slab-interior column connections used in the parametric study 268
Finite-element mesh for slab-interior column connections, used in the
PATAMETLIC STUY ce ceccccscccscsssccsecesscesseesseceecesseesseseecesseesteesesenseessaeseseseseessaes 269 Effect of varying V, /(V,) on the concrete shear contribution - 271 Influence of varying V, /(oV,) on the hysteretic behavior and moment
strength of prestressed slab-interior eolumn connectiO'S -.‹‹- 273,274
Trang 20Al A.2 A.3 A.4 A.5 A.6 A.7 A,8 A,9 A.10 A.ll A.12
prestressed slab-interior column conreCfiOTNS - c vs se, 277 Plan of flat plate ÍÏOOT dc Ăn ST TH KH HH HH kh 293 Banded tendon profile in the prototype ÍÏOOT c2 1v vvvvsesrresvee 297 Equivalent frames used in calculating internal actions for prototype floor 299 Shearing force and bending moment diagrams for the self-weight loading
Cổ HH HH HT Họ TH TT ng 301
Shearing force and bending moment diagrams for the live and super-
Imposed dead load €aS€S - LH HT HH HH HH Hiệu 301 Shearing force and bending moment diagrams for the prestress secondary
iu “<1 303
Shearing force and bending moment diagrams for the drift loading case 304 Factored shearing force and bending moment distributions for the prototype
S085 0117 304
Moments due to specified gravity loads and prestresSing - -.‹‹s-‹++: 305 Dimensions of shear critical sections and arrangement of headed
reinforcement at a typIcal interior column ofthe prototype floor 309 Arrangement of stud shear reinforcement, at an interior column of the
prototype floor, satisfying Clause 21.12.3 ofCSA A23.3-04 c c 312 Column dimensions and reinforcement details ceceeceeseeseeseceteeteeeeeeteesaeens 318
Trang 21All symbols are defined where they first appear The following list contains the most frequently used symbols: Ap 1D) (Di); DR DR,, DR, DR, s0 2 tạ Ep Es
cross-sectional area of prestressed reinforcement cross-sectional area of non-prestressed reinforcing bars
cross-sectional area of vertical legs of shear reinforcement on one peripheral line, parallel to the column periphery
perimeter of shear critical section
square column dimension; or depth of neutral axis measured from extreme compression fiber
column dimensions in the x- and y-direction, respectively
average of distances from extreme compression fiber to the centroids of the tension reinforcements running in two orthogonal directions
maximum aggregate size
nominal diameter of a reinforcing bar
distance from extreme compression fiber to the centroid of prestressing tendons at their intersection with the shear critical section at d/2 from the column face axial displacement of column displacement vector ultimate deflection recorded at center of slabs at end of loading Stage III drift ratio inter-storey drift ratio at peak moment and at yield of a slab-column connection, respectively
drift ratio when the moment drops to 80 percent of the peak value eccentricity of a prestressing tendon, measured from the centroid of the concrete section
Young’s modulus of elasticity of concrete dissipated energy in a hysteretic cycle modulus of elasticity of reinforcement
Trang 22Ine Tor OF fs Jou Jm forces effective stress in a prestressed tendon after accounting for all prestress losses
stress in prestressed reinforcement at nominal flexural strength, according to CSA A23.3 or ACI 318, respectively
specified ultimate strength of prestressed reinforcement specified yield strength of prestressed reinforcement direct tensile strength of concrete
ultimate tensile stress of non-prestressed flexural reinforcement specified yield strength of non-prestressed flexural reinforcement specified yield strength of shear reinforcement force vector lateral static force at the 7” floor level of a building gravitational constant shear modulus of elasticity thickness of slab
first stress invariant
gross moment of inertia of a column
equivalent moment of inertia of a column, considering attached torsional elements
importance factor, according to IBC-03 or NBCC-05 gross moment of inertia of a slab strip of width /,
d multiplied by the second moment of the perimeter of the shear critical section about the x- or y-axis
second deviatoric stress invariant
property of the shear critical section analogous to polar moment of inertia, according to ACI 318 code
stiffness parameter, representing the unbalanced moment producing unit drift ratio
end-rotational stiffness of a column
Trang 23hạ Ỉ sh-zone ly l, LC LFRS LSC distance between the column points where lateral displacements are introduced center-to-center span between columns in two orthogonal directions height of storey
length of prestressed tendon between anchors, divided by the number of plastic hinges required to develop a failure mechanism
length of clear span between columns
distance from column face to outermost peripheral line of shear reinforcement
projections of shear critical section on the centroidal principal x- and y- axis
load cell that is attached to an actuator ram to measure induced load
values during the test
lateral force resisting system
linear strain converter that is used to measure displacements during the test
flexural strength per unit width of slab for top or bottom reinforcement bending moment
moment due to prestressing induced forces primary prestressing moment
secondary (hyper-static) prestressing moment probable unbalanced moment strength
factored unbalanced moment resistance, according to CSA A23.3 Standard
maximum unbalanced moment transferred between slab and column, calculated at centroid of the shear critical section
unbalanced moment at failure as predicted by the finite-element analysis unbalanced moment that produces a yield line pattern
effective prestressing force
response modification factor, in accordance with IBC-03 or NBCC-05
Trang 24IS] Tì Ve Ves „ F, Cu): WwW; W XV, Z OD, Ar, Ap Ostrut Os, Bo, Bp stiffness matrix torsional moment
fundamental period of a structure, in seconds
nominal shear strength (in stress units) provided by concrete in absence of shear reinforcement or unbalanced moment
nominal shear strength (in stress units) provided by concrete in presence of shear reinforcement
maximum factored shear stress, according to CSA A23.3 Standard nominal shear strength (in stress units), according to ACI 318 code factored shear stress resistance, according to CSA A23.3 Standard nominal shear strength (in stress units) provided by shear reinforcement maximum torsional shear stress
maximum factored shear stress
vertical shearing force transferred between slab and column design base shear force
nominal shear strength provided by concrete
vertical component of effective prestressing force crossing the shear critical section at d/2 from column face
shearing force due to secondary prestressing effects
factored shear force in design; in tests, V,, is shear force at failure
shear force producing secondary failure, in absence of unbalanced moment
portion of total gravity load assigned to the i” floor level of a building total gravity load of the structure
centroidal principal axes
load factors of dead, live and prestressing load effects
Inclination angle of a shear strut to the slab’s horizontal plane empirical coefficients given by ACI 318-05 (Sections 11.12.2.1 and
11.12.2.2)
Trang 25Vf Des Oss Op P,P Pp HA Nn @D < À GI, Ø2, 03
fraction of unbalanced moment transferred by flexure
fraction of unbalanced moment transferred by shear eccentricity lateral cyclic displacement reversals, introduced near the column ends design inter-storey drift, including inelastic deformations
maximum elastic inter-storey drift uniaxial fracture strain
yield strain
strength reduction factor of concrete, non-prestressed reinforcement and prestressed reinforcement, respectively, according to CSA A23.3
Standard
top or bottom flexural reinforcement ratio prestressed reinforcement ratio
displacement ductility factor rotational ductility factor
angle of rotation between column and plane of slab damping ratio
Poisson’s ratio
strength reduction factor, according to ACI 318 code concrete density factor, according to CSA A23.3 Standard = principal stresses
Trang 261.1 GENERAL
A flat plate is a slab supported directly on columns, without column capitals or drop panels Post-tensioned flat plates have been introduced for the first time in the US during the mid fifties Since then, it has become a widely adopted structural system in various applications such as parking structures, apartment and industrial buildings of medium height This is because of its general economy and ability to satisfy architectural requirements Furthermore, post-tensioned concrete flat plates have the advantages of longer spans and control of both deflection and cracking The most common method of construction used is the cast-in-place slabs with the slab monolithically cast with the columns The main reinforcement for such structural system consists of draped tendons placed in both directions of the slab (see Fig 1.1) Prestressing tendons can be bonded or unbonded; however, it was shown that better economy is achieved by using the unbonded tendons (Burns and Hemakom, 1985 and Hawkins, 1977) Single unbonded strands in plastic ducts of relatively small diameter are more suitable in thin slabs Bonded tendons require ducts of relatively large diameter that fit only in thick slabs Corrosion of unbonded tendons can be a problem that must be avoided by effective secure means This dissertation is concerned only with flat plates prestressed with unbonded steel tendons Most prestressed slabs in buildings are of this type
Trang 27tendons in prestressed floor structures for one or more of the following reasons: ]- To supplement prestressing tendons to meet the required strength capacity
2- To control cracking in regions of peak bending moments and in the vicinity of columns Cracking may also take place at the anchorages due to splitting effects of prestressing tendons Headed studs are used to control horizontal splitting cracks Furthermore, the Joint ACI-ASCE Committee 423 (ACI 423.3R-96) report on “Recommendations for Concrete Members Prestressed with Unbonded Tendons” developed regulations for placement of horizontal reinforcing bars, used to control vertical splitting cracks
3- To avoid progressive collapse Typically, well-anchored bottom-reinforcing bars passing through column cages are provided in both slab directions
4- To control cracking due to temperature and shrinkage effects
It is believed that non-prestressed reinforcement passing through critical sections (e.g in the column vicinity) provides the ductile-type of behaviour that is required for energy dissipation during an earthquake
13 TENDONS LAYOUT
Trang 29prestressing reinforcement combined with that of the non-prestressed reinforcement rather than by tendon distribution This is attributed to the notion that the pre- compression (i.e in-plane confinement) produced by the tendons disperses rapidly within the slab from their points of application, regardless of the distribution of the tendons in the slab This is particularly true for interior parts of the slab (away from the anchorage); however, edge portions of the slab should be treated as non-prestressed slabs, for which reinforcing bars must be placed across the anticipated crack path Therefore, a number of schemes exist, in literature, for placing the prestressing tendons in two-way flat plates as shown in Fig 1.2 In all of the shown schemes, parallel tendons are assumed to have the same profile However, ACI 423.3R-96 has recommended the banded-distributed scheme (Figs 1.1 and 1.2a) as a predominant practical method for placing tendons In this scheme, tendons are closely spaced in narrow bands (typically, up to 1.20 m wide) over support lines in one direction — commonly chosen with the longer spans — and placed with uniform spacing in the perpendicular direction In addition to the constructability advantage of this scheme, from a design standpoint, both directions can be designed with the maximum permissible tendon drape Banded and distributed tendons generally do not cross at their high or low points, except over the supports
The distribution shown in Fig 1.2b has, in one direction, 65 to 75% of the tendons
banded over the column lines, while the rest of tendons are placed within the middle strip; in the other slab direction, the tendons are uniformly distributed Scheme (c) of Fig
1.2 has only banded tendons over the columns in both directions, and therefore, requires
additional non-prestressed reinforcement between the tendon bands Figure 1.2d shows a good distribution of tendons from a conceptual point of view; however, it is impractical, as it requires weaving of the tendons The ACI Building Code (ACI 318-05, Section 18.12.4) requires that at least two tendons should pass through the design shear critical
Trang 3065 to 75% , 25 to 35% _, 65 to 75% | Col strip [Middle strip! Col strip (b) Mixed-distributed 65 to 75% —==———t+>~~| Col strip Middle strip Col strip 25 to 35% 65 to 75% 65 to 75% | 25 to 35% | 65 to 75% | Col strip Middle strip Col strip (c) Banded-banded (d) Mixed-mixed Figure 1.2 — Tendon schemes in prestressed two-way flat plates 14 TENDON PROFILES
Trang 31tendon segments as well as constant compressive force and concentrated moments at the tendons’ ends The upward force of tendons in a concrete slab is designed to balance a portion of the gravity load; commonly, for two-way flat plate structures, 75 to 85% of the dead load is balanced by the effective prestressing forces, P Moments produced by the balancing load when applied on a released statically determinate structure is called ‘primary moments’ and they are designated as A; alternatively, they may be calculated simply as the product of the effective prestressing force, P., times the eccentricity, e,
from the member’s neutral axis: i.e !' =Pe p e
In statically indeterminate structures, post-tensioning produces reactions at the supports due to their restraining effects to the free deformations of the prestressed structure These reactions, called ‘secondary actions’, form a self-equilibrating system Rationally, these secondary actions are characteristics of indeterminate structures; i.e in statically determinate structures they are null
Secondary bending moments, 1/7’ can be accounted for directly or indirectly In the direct method, the balanced loading is applied to the frame, shown in Fig 1.3 Analysis of such frame gives the bending moment, M/,, which is the sum of the primary and the secondary moments The moment diagram of the support reactions, with no other loads on the frame, gives the hyperstatic moment, MM” Therefore, the diagram of M7? is composed of linear segments, as shown for the slab only in Fig 1.3b Alternatively, the balanced moment ©, (resulting from the above frame analysis) minus the product of (P e) would give M” ; this method has been referred to as the indirect method
Trang 32A B C D E (a) Slab bending moment diagram under gravity loads A B C D E (b) Slab secondary prestressing moment Unbalanced _‡ moment A B C D E
(c) Slab bending moment diagram under combined gravity loads and lateral forces Figure 1.3 — Slab bending moments for a two-dimensional
frame modeling of prestressed flat plate floor
15 PUNCHING SHEAR CONSIDERATION
Trang 33Figure 1.4 shows an elevation and an isometric view of a slab-interior column connection transferring a shearing force, V, caused by gravity loads between a slab and its supporting column Flexural cracks appear on the slab top surface as shown Figure 1.4 also shows the diagonal shear cracks developed within the slab thickness Therefore, up to or close to failure, the diagonal shear cracks are not visible on the slab surface Once the shear strength of the connection is reached, the diagonal shear cracks cross the full thickness of the slab, forming a truncated pyramid that with the supporting column punches through the slab This punching failure occurs suddenly without much warning
Diagonal Flexural crack Slab top Column
shear crack surface \ ten N Punching Column —> Slab shear surface 1 Shearing Shearing T force, V force, V
Figure 1.4 — Slab flexural and shear cracks in the column vicinity
of a slab-interior column connection
Unbalanced moments, transferred between the slab and columns, produce shear
Trang 34Too short to be effective Effective shear reinforcement Punching cracks Figure 1.5 — Effectiveness of shear reinforcement in flat slab floors 16 SHEAR REINFORCEMENT
Trang 35Stirrup hook Concrete spalling Clear 1 cover Stirrup shear reinforcement _4, = area of stirrup leg \ | N + Top } Flexural reinforcement —> Bottom | ÀN Slab Figure 1.6 — Deficiency of stirrup shear reinforcement in flat slab floor systems
Trang 36Base rail ae t,=d/2 YN —\ Py ’ S| Cover~ 4 => b=2.5d,
Figure 1.8 - Comparison between shear reinforcements in flat plate floors
Trang 37Figure 1.9 — Stud shear reinforcement at an interior column in a prestressed slab
1.7 SHEAR STRESSES DUE TO WIND AND EARTHQUAKES
Trang 38punching strength to support gravity loads after a severe seismic event
Extensive tests on reinforced non-prestressed slab-interior column connections, subjected to either gravity loads or a combination of shearing force and reversed cyclic
unbalanced moment, have been reported in the literature However, little research has
been done on the punching shear resistance of prestressed slabs subjected to earthquake- simulated forces The question of the behaviour of prestressed concrete flat plates in earthquake-prone regions has become one of prime importance and hence the need for
further research
18 OBJECTIVES AND SCOPE
The major objective of the research project presented in this dissertation is to study the performance of post-tensioned slab-interior column connections transferring shearing force combined with cyclic reversed unbalanced moment The research project consists of experimental and numerical components The findings of the research will develop design recommendations for post-tensioned flat plates in seismic zones The research
items, presented in this dissertation, can be summarized as follows:
1 Literature review of the analytical research related to punching of slab-column connections transferring shearing forces with unbalanced moments
2 Literature review of the major experimental research conclusions related to shear combined with cyclic reversed unbalanced moment transfer between slabs and columns
3 Evaluation of the existing ACI 318-05 (ACI Committee 318, 2005), and CSA A23.3- 04 (CSA, 2004) building codes’ provisions, as well as the provisions of the Joint
ACI-ASCE Committees 421 on “Shear Reinforcement for Slabs”, and 423 on
“Recommendations for Concrete Members Prestressed with Unbonded Tendons” 4 Development of an experimental program on post-tensioned slab-interior column
Trang 39both the banded and distributed directions of the slab will be addressed Seismic behaviour of the tested specimens is to be studied with special attention given to seismic design considerations such as punching shear strength during and after earthquake occurrence, ductility, inter-storey drift capacity, and stiffness
5 Assessment of the procedure developed by Megally and Ghali (2000b), and adopted by ACI 421, for non-prestressed reinforced concrete slabs to reach a design procedure that applies to post-tensioned slabs
19 LAYOUT OF DISSERTATION
Trang 40CHAPTER 2
PUNCHING SHEAR IN FLAT PLATES
2.1 INTRODUCTION
A major concern with flat plate structural system is its susceptibility to punching, a local failure that occurs at the slab-column connection This brittle type of failure has been the subject of much of the past research, in which efforts have been spent to develop analytical models capable of predicting the strength of slab-column connections transferring shearing forces combined with unbalanced moments Research has resulted in a number of models, which are reviewed in Section 2.2
The provisions of the North American design codes (ACI 318 and CSA A23.3) as well as ACI committee reports, related to shear strength of prestressed flat plates, are reviewed in Section 2.3 A common design tool that satisfies equilibrium and geometric compatibility of two-way slab structures is the equivalent frame method In this method, the slab internal forces are determined by idealizing the slab-column assemblies as a series of elastic two-dimensional frames Effect of cracking on internal force distribution is accounted for by reducing the flexural stiffness of the slab strip, bounded by centrelines of adjacent panels Megally and Ghali (2000b) have proposed a simplified elastic frame analysis to calculate the unbalanced moments due to earthquake lateral displacements; the elastic frame analyses are discussed in Section 2.4 Past research on non-prestressed concrete slab-column connections, subjected to earthquake-simulated loading conditions, have addressed a number of key factors affecting the strength and ductility of the connections These factors are believed to affect the performance of the connections between prestressed slabs and columns; they are addressed in Section 2.5