Punching Shear Retrofit Method Using Shear Bolts for Reinforced Concrete Slabs under Seismic Loading

Transcription

1 Punhing Shear Retroit Method Using Shear Bolts or Reinored Conrete Slabs under Seismi Loading by Wensheng Bu A thesis presented to the University o Waterloo in ulillment o the thesis requirement or the degree o Dotor o Philosophy in Civil Engineering Waterloo, Ontario, Canada, 8 Wensheng Bu 8

2 AUTHOR'S DECLARATION I hereby delare that I am the sole author o this thesis. This is a true opy o the thesis, inluding any required inal revisions, as aepted by my examiners. I understand that my thesis may be made eletronially available to the publi. ii

3 Abstrat Reinored onrete slab-olumn strutures are widely used beause o their pratiality. However, this type o strutures an be subjet to punhing-shear ailure in the slab-olumn onnetions. Without shear reinorement, the slab-olumn onnetion an undergo brittle punhing ailure, espeially when the struture is subjet to lateral loading in seismi zones. The shear bolts are a new type o transverse reinorement developed or retroit o existing strutures against punhing. This researh ouses on how the shear bolts an improve the punhing-shear apaity and dutility o the existing slab-olumn onnetions under vertial servie and lateral seismi loads. A set o nine ull-sale reinored onrete slab-olumn onnetion speimens were tested under vertial servie and yli loads. The vertial (gravity) load or eah speimen was kept at a onstant value throughout the testing. The yli lateral drit with inreasing intensity was applied to the olumns. The speimens were dierent in number o bolts, onrete strength, number o openings, and level o gravity punhing load. Strains in lexural rebars in the slabs, rak widths, lateral loads, and displaements were obtained. The peak lateral load (moment) and its orresponding drit ratio, onnetion stiness, rak width, and dutility were ompared among dierent speimens. The testing results show that shear bolts an inrease lateral peak load resisting apaity, lateral drit apaity at peak load, and dutility o the slab-olumn onnetions. Shear bolts also hange the ailure mode o the slab-olumn onnetions and inrease the energy dissipation apaity. The thesis inludes also researh on the development o guidelines or shear bolt design or onrete slab retroitting, inluding the punhing shear design method o onrete slab (with shear bolts), dimensions o bolts, spaing, and inluene o bolt layout patterns. Suggestions are given or onstrution o retroitting method using shear bolts. Reommendations are also presented or uture researh. iii

4 Aknowledgements This researh was undertaken under the supervision o Proessor Maria Anna Polak. Without Proessor Polak s diretion, help, and enouragement, this thesis ould hardly be aomplished so well as presented. Thus, I would like to express my greatest gratitude to her. The presented researh was unded by a grant rom the Natural Sienes and Engineering Counil (NSERC) o Canada. The shear bolts were manuatured and donated by Deon In. The ready mixed onrete was donated by Hogg Fuel and Supply Ltd. in Kithener, Ontario. Ri Sherping and Sika Canada graiously donated Sikadur 3 or repairing drilling holes on onrete slabs. This researh involved experimental work in the Strutural Laboratory o Civil and Environmental Engineering, University o Waterloo. I would like to thank Proessor Timothy H. Topper or his help and instrutions. I also appreiate the great help rom Rihard Morrison, Doug Hirst, Ken Bowman, Dik Powers, Terry Ridgway, Mark Sobon, Brue Stikney, and the sta in the Mahine Shop; without their help, my experiments ould not be done. For helping me in the laboratory, I need to thank Nik Lawler, José Andrés Alvarado, Mike Kuebler, Je West, Hongtao Liu, Yanjun Yang, Xianxun Yuan, Qinghua Huang, Jinyu Zhu, Hongli Huang, Xiaohong Huang, Xiaoguang Chen, Yuxin Liu, Ying An, Dan Mao and Tianjin Chen. Proessor Mahesh Pandey and Proessor Wei-Chau Xie oered me help during my researh and study; I also beneited rom the disussion and teahing o Proessor Donald E. Grierson and Gregory Glinka. Finally, I would like to express speial thanks to my wie and daughter. I appreiate their understanding, support and patiene. iv

5 To My Parents v

6 Table o Contents Author s Delaration... ii Abstrat... iii Aknowledgements...iv Dediation...v Table o Contents...vi List o Figures...ix List o Tables...xv Chapter 1 Introdution Reinored Conrete Flat Slab Column Strutures and Punhing Shear Failure Reinored Conrete Flat Slab Column Strutures under Earthquakes Objetive o This Researh Contribution o This Researh Organization o the Thesis...9 Chapter Literature Review Introdution...1. Punhing Shear Behaviour in Reinored Conrete Slabs under Vertial Load or Vertial Load Combined with Stati Moments Parameters Inluening Punhing Shear Strength o Slab-Column Connetions Previous Researh on Seismi Behaviour o Reinored Conrete Slabs Flat Slab Column Strutures in Seismi Zones Behaviour o Slab-Column Connetions under Cyli Loading Analytial Models or Punhing Shear Punhing Shear Design Punhing Shear Design Requirements in CSA A Punhing Shear Design Requirements in ACI (in SI units) Euroode (4) Seismi Requirements or Design o Flat Slab-Column Strutures National Building Code o Canada (NBCC 5) Seismi Requirements o CSA ACI Seismi Requirements or Slab-olumn Strutures FEMA 356 Requirements...47 vi

7 .7 Previous Researh Work on Punhing Shear at Waterloo Chapter 3 Experiment Program Speimens Design Flexural Reinorement Estimation o the Capaities o the Speimens beore Testing Properties o Materials used or Speimens Conrete Compression and Tension Strength Properties o Steel Reinoring Bars Properties o Steel Shear Bolts Fabriation o the Reinored Conrete Speimens Shear Reinorement Installation o Shear Bolts Experimental Setup Components o the Experiment Setup Steel Liting Frame or Installation o Conrete Slab-Column Speimens Member Strength and Stiness o the Steel Experimental Setup Instrumentation Displaements Crak width Strains Load ontrol Testing Proedure Chapter 4 Experimental Results and Disussion Introdution Results o Series I Lateral Load versus Drit Ratio Moment versus Lateral Drit Ratio Connetion Stiness Drit Dutility Strains in Shear Bolts Flexural Reinorement Strains Vertial Crak Width... 1 vii

8 4..8 Craking and Failure Modes o the Speimens Results o Series II Connetion Moment versus Lateral Drit Ratio Drit Dutility Eet o Openings on Connetion Moment Capaity and Dutility Eet o Shear Bolt layout Pattern on Connetion Moment Capaity and Dutility Connetion Stiness Strains in Shear Bolts Strains in Flexural Reinorements Estimation o Vertial Crak Width Craking and Failure Mode o the Speimens Comparison o Testing Results with the Building Codes o ACI318-5, CSA A3.3-4 and Euroode (4) Chapter 5 Design o Steel Shear Bolts and Conrete Slab with Shear Bolts Design o Steel Shear Bolts Thikness o the Bolt Head Determination o Bolt Head Thikness using Elasti Thin Plate Theory Determination o Bolt Head Thikness using Finite Element Method Determination o Bolt Head Area Stresses in a Conrete Slab Caused by a Shear Bolt Design o Steel Shear Bolts or Conrete Flat Slab Strengthening Strength o the Retroitted Slab Shear Bolt Layout in the Flat Conrete Slab Constrution Requirements Chapter 6 Conlusions and Reommendations Experimental Series I Experimental Series II Shear Bolt Design and Analysis Reommendations or Future Researh...5 Appendix A Abbreviations and Notations Reerenes..11 viii

9 List o Figures Figure 1.1 Flat slab (plate) loor and beam-slab loor (adapted rom MaGregor and Bartlett, )...1 Figure 1. Reinored onrete lat slab building (Cope and Clark, 1984, ourtesy o British Lit Slab Ltd.)... Figure 1.3 Failure surae o punhing shear (adapted rom MaGregor, )... Figure 1.4 Collapse o Skyline Plaza (adapted rom Building Siene Series 179, 3, by Building and Fire Researh Laboratory o the National Institute o Standards and Tehnology, USA)...3 Figure 1.5 Damage o the slab due to punhing shear (Sabol, 1994)...4 Figure 1.6 Piture o shear bolt...5 Figure 1.7 Dimensions o boll, washer and nut...6 Figure 1.8 Shear bolts installation in the onrete lat slab...6 Figure 1.9 Layout pattern o shear bolts in the onrete slab...6 Figure 1.1 Top view o the slab with steel shear bolts...7 Figure 1.11 bottom view o the slab with shear bolts...7 Figure.1 Interation between Shearing and Flexural Strength (Moe, 1961) Figure. I-shape shear reinorement (Hawkins and Coley, 1974) Figure.3 Headed shear studs welded to a bottom steel plate Figure.4 Load-deletion urves o slabs with dierent punhing strengthening methods (adapted rom Magally and Ghali, ) Figure.5 Prestressed shear bolts or slab under vertial load (Ghali et al. 1974) Figure.6 Speimens inluding exterior and interior slab olumn onnetion Figure.7 Test set up o biaxial loading... Figure.8 Experimental envelopes... Figure.9 Slab strengthened by steel bolts and plates (Ebead and Marzouk, )... 3 Figure.1 Slab strengthened by CFRP stirrups (Stark et al., 5)... 3 Figure.11 Assumption o onial shell and rigid setors by Kinnunen and Nylander model.. 4 Figure.1 Punhing shear model o Kinnunen, Figure.13 Truss model o slab punhing shear (Alexander and Simmonds, 1987)... 7 Figure.14 Curved ompression strut (adapted rom Alexander et al., 199)... 8 Figure.15 Layout o radial strip (adapted rom Alexander et al., 199)... 9 ix

10 Figure.16 Equilibrium o Radial Strip (adapted rom Alexander et al., 199)...9 Figure.17 Axisymmetri punhing (Braestrup et al., 1976)...31 Figure.18 Predited ailure surae (Braestrup et al., 1976)...3 Figure.19 Free body diagram o slab-olumn onnetion or shear rition model (Dilger,, and Dehka, 1)...35 Figure. Yield line pattern in the slab (Rankin and Long, 1987)...36 Figure.1 Yield line pattern o interior slab-olumn onnetion subjeted to shear and unbalaned moment (Cao, 1993)...37 Figure. Critial setions deined in Canadian ode CSA A3.3-4 (Cement Assoiation o Canada, 6)...41 Figure.3 Basi ontrol setions deined in Euroode (4)...44 Figure.4 Load versus enter deletion measured by internal LVDT o the testing rame. (Adetia and Polak, 5)...49 Figure 3.1 Plan view o the prototype struture...53 Figure 3. Elevation view o the prototype struture...54 Figure 3.3 The ive speimens (SW1~SW5) o Series I and shear bolt layout...55 Figure 3.4 The our speimens (SW6~SW9) o Series II and shear bolt layout Figure 3.5 Dimensions o the speimens SW1~SW9 (all dimensions in mm )...56 Figure 3.6 Reinorement detail and strain gauges in speimen SW1~SW5 and SW Figure 3.7 Reinorement detail and strain gages in Speimen SW6, SW7 and SW Figure 3.8 Reinorement detail o olumn and lateral load diretions...58 Figure 3.9 Compression test o the onrete ylinder (4 x8 )...64 Figure 3.1 Conrete ylinder tension test...65 Figure 3.11 Conrete ylinder (6 x1 ) ompression test...66 Figure 3.1 Crushing o the onrete ylinder #6 (6 x1 ) o the irst bath onrete...67 Figure 3.13 Compression strength versus strain o ylinders o the onrete...68 Figure 3.14 Standard oupon mahined rom M #1 rebar (a) Dimensions, (b) Piture...7 Figure 3.15 Testing o rebar oupon...71 Figure 3.16 Testing o original rebar...71 Figure 3.17 Tension stress versus strain in Rebar- (irst bath rebar)...73 Figure 3.18 Tension stress versus strain in Coupon-1 (irst bath rebar)...74 Figure 3.19 Standard oupon mahined rom 3/8 steel shear bolt (a) Dimensions, (b) Piture.74 x

11 Figure 3. Testing o the original bolt Figure 3.1 Tension stress versus strain o original shear bolts (bolt-org-) Figure 3. Tension stress versus strain o oupon (oupon-bolt-1) shear bolts Figure 3.3 Rebar ages Figure 3.4 Strain gauges attahed on rebars Figure 3.5 Rebar ages and ormworks beore asting o the speimens Figure 3.6 Speimens just ater asting Figure 3.7 Speimens stored in the laboratory... 8 Figure 3.8 Shear bolt spaing in speimen SW, SW3, SW4 and numbering o strain gauges on bolts Figure 3.9 Shear bolt spaing in speimen SW7, SW8, SW9 and numbering o strain gauges on bolts Figure 3.3 Shear bolts with strain gauges... 8 Figure 3.31 Drilling holes in the slab Figure 3.3 Piture o experimental setup Figure 3.33 Elevation A o the testing setup Figure 3.34 Elevation B o the testing setup Figure 3.35 Plan view o the main rame near ground level, ground anhor bolts, base panel, and the base reation beams Figure 3.36 Plan view o the main rame at the rosshead level Figure 3.37 Plan view o the square ring beam, braing beams, and adjustable stoppers Figure 3.38 Neoprene pads between the onrete slab and the square ring beam or the top reation beam (L is the support length: L=155 mm on eah side) Figure 3.39 Adjustable stopper Figure 3.4 Roller on top o the upper onrete olumn... 9 Figure 3.41 Steel ollar system onneted to horizontal hydrauli atuators... 9 Figure 3.4 Steel rame or speimens liting and installation Figure 3.43 Liting o the onrete speimen Figure 3.44 Estimated maximum load on the speimen in testing Figure 3.45 Displaement transduers on slab and string pots onneted to the speimen Figure 3.46 Plan view o the independent rak or transduers Figure 3.47 Displaement transduers layout on slab xi

12 Figure 3.48 Loading path...1 Figure 4.1 Horizontal load versus horizontal drit ratio at top olumn end...14 Figure 4. Horizontal load versus horizontal drit ratio at top olumn end...15 Figure 4.3 Bakbone urves o horizontal load versus horizontal drit ratio at top olumn end Figure 4.4 Moment versus lateral drit ratio at top olumn end...17 Figure 4.5 Moment versus horizontal drit ratio at top olumn end...18 Figure 4.6 Bakbone urves o moment versus lateral drit ratio at top olumn end...18 Figure 4.7 Peak-to-peak moment stiness vs. drit ratio o SW1, SW and SW3 (Group I)...19 Figure 4.8 Peak-to-peak moment stiness vs. drit ratio o SW4 and SW5 (Group II)...11 Figure 4.9 Stiness degradation at small yles o the ive speimens SW1~SW Figure 4.1 Deinition o dutility...11 Figure 4.11 Lateral drit ratio versus strain in bolt #1 or speimen SW Figure 4.1 Lateral drit ratio versus strain in eah bolt o the three speimens SW, SW3, and SW Figure 4.13 Stain gauge positions on the reinorement o speimens SW1 ~ SW5 and SW Figure 4.14 Lateral drit ratio versus strain at loation d o Rebar #1 in speimen SW Figure 4.15 Lateral drit ratio versus strain at loation d o Rebar #1 in speimen SW Figure 4.16 Lateral drit ratio versus strain at loation d o Rebar #1 in speimen SW Figure 4.17 Lateral drit ratio versus strain at loation d o Rebar #1 in speimen SW Figure 4.18 Lateral drit ratio versus steel strain at loation d o Rebar #1 in eah speimen o SW Figure 4.19 Bakbone urves o lateral drit ratio versus steel strain at loation d o Rebar # Figure 4. Strains in dierent loations o eah numbered rebar in speimen SW1~SW5 at - 1.% lateral drit ratio...11 Figure 4.1 Crak width at loations L1, L, L3, and L4 in the slab o SW Figure 4. Crak width at loations L1, L, L3, and L4 in the slab o SW...14 Figure 4.3 Crak width at loations L1, L, L3, and L4 in the slab o SW Figure 4.4 Crak width at loations L1, L, L3, and L4 in the slab o SW Figure 4.5 Crak width at loations L1, L, L3, and L4 in the slab o SW Figure 4.6 Final rak pattern on top and bottom surae o eah speimen...18 xii

13 Figure 4.7 Moment versus lateral drit ratio o speimen SW6~SW Figure 4.8 Bakbone urves o moment versus lateral drit ratio or SW6~SW Figure 4.9 Bakbone urves o moment versus lateral drit ratio between speimen SW5 and SW Figure 4.3 Bakbone urves o moment versus lateral drit ratio between speimen SW4 and SW Figure 4.31 Comparison o bakbone urves o moment versus lateral drit ratio between speimen Figure 4.3 Bakbone urves o moment versus lateral drit ratio or SW4 and SW Figure 4.33 Moment peak-to-peak stiness versus drit ratio o speimen SW6, SW7, SW Figure 4.34 Moment peak-to-peak stiness versus drit ratio o speimen SW5 and SW Figure 4.35 Peak-to-peak stiness o small drit yles o SW5 ~ SW Figure 4.36 Figure 15 Horizontal load versus strain in bolt #1a o SW Figure 4.37 Bakbone urves o lateral drit ratio versus strain in eah bolt o speimens SW Figure 4.38 Bakbone urves o lateral drit ratio versus strain in eah bolt o speimens SW Figure 4.39 Bakbone urves o lateral drit ratio versus strain in eah bolt o speimens SW Figure 4.4 Strain gauges layout in speimens SW6, SW7, and SW Figure 4.41 Lateral drit ratio versus strain at loation d o Rebar #1 in speimen SW Figure 4.4 Lateral drit ratio versus strain at loation o Rebar #1 in speimen SW Figure 4.43 Lateral drit ratio versus strain at loation o Rebar #1 in speimen SW Figure 4.44 Lateral drit ratio versus strain at loation o Rebar #1 in speimen SW Figure 4.45 Strains in dierent loations o eah numbered rebar in speimen SW5~SW9 at % lateral drit ratio Figure 4.46 Crak width at loations L1, L, L3, and L4 in the slab o SW Figure 4.47 Crak width at loations L1, L, L3, and L4 in the slab o SW Figure 4.48 Crak width at loations L1, L, L3, and L4 in the slab o SW Figure 4.49 Crak width at loations L1, L, L3, and L4 in the slab o SW Figure 4.5 Crak pattern (inal) o top and bottom suraes o speimen SW6~SW Figure 5.1 Shear bolt and bolt head xiii

14 Figure 5. Axisymmetri element and its internal ores Figure 5.3 Bolt head thikness versus net hole learane and ratio r / R or 3/8 diameter bolts Figure 5.4 Bolt head thikness versus net hole learane and ratio r / R or 1/ diameter bolts Figure 5.5 Head thikness at the bolt stem edge versus hole radius Figure 5.6 Normalized bolt head thikness versus normalized distane rom bolt stem (or all stem diameters)...17 Figure 5.7 Mid-thik plate setion deormation Figure 5.8 Eight-node isoparametri plate element...17 Figure 5.9 Finite element mesh or a quadrant Figure 5.1 Gauss point numbering o element and Figure 5.11 Ratio o bolt head area over bolt stem setion area versus onrete ompressive strength Figure 5.1 Pressure on onrete slab suraes by bolts head and washer Figure 5.13 Axisymmetri analysis o the onrete slab around the bolts hole Figure 5.14 Stress distribution along the top line BC...18 Figure 5.15 Stress distribution along the top line AD...18 Figure 5.16 Spaing S, S 1 and S o shear bolts Figure 5.17 Punhing shear raks in the onrete slab without shear reinorement Figure 5.18 Shear rak angles in slab zones with or without shear studs Figure 5.19 Distane o punhing shear rak tail to the olumn enter Figure 5. Shear raks in the opening edges o the slab (SW6) without shear bolts Figure 5.1 Shear raks in the opening edges o the slab (SW8) with shear bolts o radial layout...19 Figure 5. Shear raks in the opening edges o the slab (SW7) with shear bolts o orthogonal layout...19 Figure 5.3 Crak angle θ 1 in the slab strengthened with shear bolts Figure 5.4 Assumed pressure in the slab onrete by the shear bolt heads Figure 5.5 Spaing S 1=.75d (or.5d) or Headed shear studs by CSA A Figure 5.6 Symmetri layout o shear bolts xiv

15 List o Tables Table.1 Vertial load inluene on peak load and drit (rom Robertson and Durrani, 199).. 19 Table. Limit on plasti rotation angles or slab-olumn onnetion by perormane level Table.3 Edge slab-olumn onnetions with or without shear studs (El-Salakaway and Polak et al, 1998, 1999,, 3)... 5 Table.4 Four edge slab-olumn speimens strengthened with shear bolts (El-Salakaway and Polak et al., 3) Table.5 Six interior slab-olumn speimens strengthened with/without shear bolts (adapted rom Adetia and Polak, 5)... 5 Table 3.1 Initial design o moment apaity o the nine slab-olumn onnetions beore testing... 6 Table 3. Details o Speimens o Series I Table 3.3 Details o Speimens o Series II Table 3.4 Conrete strength o eah speimen (4 x8 ylinders) Table 3.5 Compression strength o onrete ylinders (6 x1 ) or the three bathes Table 3.6 Testing results o the steel shear bolts and the two bathes steel rebar... 7 Table 3.7 Properties o steel reinoring bars Table 3.8 Testing data o original shear bolts and oupons Table 3.9 Properties o steel shear bolts Table 4.1 Peak load and drit dutility (deined by Pan and Moehle, 1989) o speimen SW1~SW Table 4. Drit dutility (using tested irst yield drit ratio) o speimen SW1~SW Table 4.3 Drit ratios at irst yielding o reinoring bars in the ive speimens SW1~SW Table 4.4 Crak width at 1.5%,.% and 3.% drit ratio or speimen SW1~SW Table 4.5 Peak moment and drit dutility (deined by Pan and Moehle, 1989) o speimen SW6~SW Table 4.6 Drit dutility (using tested irst yield rebar strain) o speimen SW6~SW Table 4.7 Comparison o peak moment and drit dutility between SW5 and SW Table 4.8 Comparison o drit dutility (using tested irst yield drit ratio) between SW5 and SW Table 4.9 Comparison o peak moment and drit dutility between SW7 and SW8 (eet o openings and shear bolts layout patterns) xv

16 Table 4.1 Comparison o drit dutility (using tested drit ratio) between SW8 and SW Table 4.11 Comparison o peak moment and drit dutility between SW4 and SW7, SW4 and SW9 (eet o openings and shear bolts layout patterns) Table 4.1 Comparison o drit dutility (using tested irst yield drit ratio) in SW4, SW7, and SW Table 4.13 Comparison o peak moment and drit dutility between SW7 and SW8 (eet o openings and shear bolts layout patterns) Table 4.14 Comparison o drit dutility (using tested drit ratio) in SW7 and SW Table 4.15 Crak width at 1.5%,.% and 3.% drit ratio or speimen SW6~SW Table 4.16 Measured peak moments and the predited nominal moments using odes o ACI318-5, Euroode (4) and CSA A Table 5.1 Spaing s 1 when θ 1 = 4 o using rak angle method...19 Table 5. Spaing s 1 when θ 1 = 5 o using rak angle method...19 S 1 Table 5.3 Coeiients ψ = or various slab (interior weather) thikness, ' v.56λφ d S 1 Table 5.4 Coeiients ψ = or various slab (exterior weather) thikness, ' v.56λφ d S 1 Table 5.5 Coeiients ψ = or various slab (interior weather) thikness, ' v >.56λφ d S 1 Table 5.6 Coeiients ψ = or various slab (exterior weather) thikness, ' v >.56λφ d xvi

17 Chapter 1 Introdution 1.1 Reinored Conrete Flat Slab Column Strutures and Punhing Shear Failure Among many types o reinored onrete buildings, reinored onrete lat slab struture is very popular. It onsists o lat plate and olumns, with no beams between the olumns to support the slab. Figure 1.1 (a) shows a lat plate loor, and Figure 1.1 (b) shows a lat slab with drop panels and olumn apitals. Figure 1.1 () shows a beam slab loor. In this thesis, the lat slab olumn strutures are suh as represented in Figure 1.1 (a). Figure 1. shows an example o a system that onsists o lat plates supported on olumns. The researh addresses the behaviour, design, and retroit o this type o strutures. Emphasis is on the punhing shear retroit o slab-olumn onnetions in seismi zones. (a) Flat plate (slab) loor (b) Flat slab loor () Beam-slab loor Figure 1.1 Flat slab (plate) loor and beam-slab loor (adapted rom MaGregor and Bartlett, ) Flat slab-olumn strutural systems are popular due to redution o building storey height, easy setting up o ormwork, onveniene or HVAC utilities layout, and good slab s appearane. However, this type o struture an easily be subjet to brittle punhing shear ailure. When the latslab-olumn onnetions are subjeted to heavy vertial loading, raks will our inside the slab in the viinity o the olumn. These raks then propagate through the slab thikness at an angle o to 45 degree to the bottom o the slab. This an lead to punhing shear ailure o the slab along the raks (Fig.1.3). When subjeted to seismi lateral load, shear stresses in the slab inrease due to an 1

18 unbalaned moment (rom horizontal loading), and the slab-olumn onnetion is more likely to ail by punhing shear. Figure 1. Reinored onrete lat slab building (Cope and Clark, 1984, ourtesy o British Lit Slab Ltd.) Figure 1.3 Failure surae o punhing shear (adapted rom MaGregor, ) There have been several ases o punhing shear ailure in the last ew deades. Punhing shear ailure an happen during the utilization o buildings. For example, in 196, in New York City, a three year old onrete dek o a plaza, whih was part o a roo o a ar garage, ollapsed suddenly (Feld and Carper, 1997). The roo was supporting 1. m deep earth over with vegetation on it. It was ound that the slab punhed through a olumn and there was little damage in other plaes o the slab.

19 The reason was that the earth on the slab top was saturated and rozen, whih inreased the load. Moreover, the slab was onstruted with insuiient punhing shear apaity. Figure 1.4 Collapse o Skyline Plaza (adapted rom Building Siene Series 179, 3, by Building and Fire Researh Laboratory o the National Institute o Standards and Tehnology, USA) Punhing shear ailure an also our during onstrution, when the weight o the resh onrete and shoring are transerred to the adjaent lower stories. These onstrution loads are sometimes larger than the designed live loads. I the shoring is removed too early, the onrete strength o the lower story may not be suiient, resulting in lower punhing shear apaity. In 1973, the Skyline Plaza (high-rise apartment building in onstrution) suered a progressive ollapse rom the 3 rd loor to the basement whih aused ourteen workers death (Fig. 1.4). The investigation revealed that the ailure started rom 3 rd loor by ailure o the slab near one or more olumns due to premature removal o shoring and the low punhing shear strength o onrete (Carino, et al., 1983). Openings in slabs are oten neessary and are oten loated near olumns. This makes the slab olumn onnetions weaker in punhing shear. Feld and Carper (1997) reported punhing shear ailures o onrete slabs due to onstrution o openings beside olumns (Feld and Carper, 1997). 3

20 1. Reinored Conrete Flat Slab Column Strutures under Earthquakes There are more than 1, earthquakes reorded eah year and approximately 6 o them are signiiant and potentially destrutive (Bertero, 1994). Earthquakes our in Canada mainly in the east and west oast areas and in the Arti. During an earthquake, the horizontal movement o the ground indues large horizontal inertia ores and lateral drits in the buildings. The inter-story drit makes the lat slab-olumn onnetion rotate and produe moments in the onnetion. The moments inrease punhing shear stress in a onrete slab around the olumn area. Thereore, the lat slab strutures are easy to be damaged in earthquakes. In 1985 Mexio City earthquake, 91 wale slab strutures ollapsed and 44 were severely damaged (Rosenblueth et al., 1986). This type o struture was the most vulnerable to ollapse in that earthquake. Wale slabs have solid slabs at the olumn onnetions, thus they have similar behaviour to lat slab strutures. Some o them were damaged by punhing shear ailure o the slabs. Others were damaged by olumn ailures. In the 1994 Northridge earthquake, a our-story reinored onrete slab-olumn building was severely damaged. Its typial plan view is shown in Figure1.5. The outside perimeter onsisted o dutile moment rames. Slabs (with drop panels) were post tensioned. Eah o the irst loor and the seond loor was damaged in six slab-olumn onnetions (Figure 1.5). Also, there was raking and spalling o onrete on the perimeter rame (Sabol 1994, Wallae et al., ) Figure 1.5 Damage o the slab due to punhing shear (Sabol, 1994) 4

21 1.3 Objetive o This Researh Strength and dutility are both important or strutures designed or seismi zones. It would not eonomial to make all buildings to deorm elastially under earthquakes. Most strutural members are allowed to have plasti hinges and deorm plastially. An important philosophy is that these members must be able to sustain load under large deormations to let people be evauated during an earthquake. Thus, these strutures must possess dutility. A general deinition o dutility an be stated as: the dutility is the ratio o the ultimate displaement (drit, or rotation) over displaement (drit or rotation) at the onset o yielding. It was not until in 1976 that the United Building Code speiied dutility requirements or strutures. A large number o buildings, inluding lat slab olumn strutures, onstruted beore that are thereore laking dutility. Reent earthquakes show that buildings designed using newer strutural odes behave muh better than the older ones. Thereore, it is desirable to ind eetive method to strengthen the existing reinored onrete lat slab olumn strutures. It is important to inrease the punhing shear apaity, dutility, and lateral drit apaity o the slab olumn onnetions. Adding shear reinorement is one way to meet these requirements. Among many kinds o shear reinorements, steel shear bolt, was developed or existing onrete slabs. Figure 1.6 shows one shear bolt and its washer and nut. This type o shear bolt set was used in this researh. The bolt stems were o 3/8 (9.5mm) diameter. Figure 1.7 gives the dimensions o the bolt. The washer at the threaded end was mahined to be 9mm thik and 44mm diameter with 14mm diameter holes entered. The washer at the other end was o 44mm diameter, thikness 3mm and a hole o diameter 18mm. This washer was provided to inrease the bearing area under the head whih had a diameter 3mm (typial or shear studs). Figure 1.6 Piture o shear bolt 5

22 (Unit: mm) Figure 1.7 Dimensions o boll, washer and nut The shear bolts were installed vertially through the holes drilled in the onrete slabs around the olumns. Figure 1.8 shows the shear bolts installed in a slab. The bolts interseted with the potential punhing shear rak, holding the outer part o onrete slab rom punhing. Figure 1.9 shows the possible pattern: orthogonal and radial layout o bolts in the onrete slab. Figure 1.1 and Figure 1.11 show the top and bottom view o the onrete slab with shear bolts, respetively. Figure 1.8 Shear bolts installation in the onrete lat slab Orthogonal layout Radial layout Figure 1.9 Layout pattern o shear bolts in the onrete slab 6

23 Figure 1.1 Top view o the slab with steel shear bolts Figure 1.11 bottom view o the slab with shear bolts Sine 1996, researh has been arried out on lat slab olumn strutures strengthened by shear bolts. First, El-Salakawy et al. (3) published test results on edge slab olumn onnetions strengthened with shear bolts subjeted to a onstant ratio o gravity load and lateral loads. Then, Adetia and Polak (5) tested six interior lat slab olumn onnetions. Those experiments showed that under 7

24 stati loads shear bolts an improve the punhing shear apaity and dutility o the slab olumn onnetions. Sine punhing shear strength and dutility o lat slab-olumn onnetions is espeially important in seismi zones, the behaviour o slabs strengthened with shear bolts beame the primary objetive o this researh. This behaviour was investigated in the experimental program designed to study the load-displaement responses. Nine ull sale speimens were tested. Comparisons were done with slabs without shear reinorements. In addition, the eet o openings in slabs, intensity o gravity loads and bolts patterns in the slabs were varied in the tests. The thesis is onluded by a detailed investigation o the design reommendations regarding shear bolt size, anhorage head size and spaing o bolts in slabs. 1.4 Contribution o This Researh This researh involved experimental investigation on the behaviour o interior slab olumn onnetions with shear bolts subjeted to gravity load and pseudo seismi loading. Nine slab olumn speimens, in two series, were ast. Three o them were designed with 15x15mm openings next to olumn aes. Three o the speimens had applied onstant vertial load o 11kN and the others were subjeted to 16kN. This researh is the irst to present test results o slab olumn speimens strengthen with shear bolts under pseudo seismi loading. It involved design and testing o nine speimens (six o them with shear bolts) under gravity load and yli lateral displaement loading. The obtained results were analyzed regarding lateral load apaity, lateral drit ratios, raking, strains, deletions, and dutilities o the speimens. Series I, whih was an initial test series, was designed to study the eet o shear bolts in slabs, number o shear bolt rows, and gravity load intensity under yli displaements. Series II was designed to study eet o openings and bolt pattern on the overall behaviour o onnetions. In order to ondut this researh, a detailed testing setup was deined. An existing steel test rame in the laboratory was irst modiied and an additional steel supporting rame was designed and onstruted. An independent steel rak was designed and installed or displaement transduers to reord the speimen deormation. In addition to testing, a theoretial investigation was ompleted on the design aspets o shear bolts and slabs reinored with shear bolts. To provide a design and onstrution guide or strengthening o 8

25 lat slab olumn strutures, bolt heads were analyzed using elasti thin plate theory and inite element analysis. Equation or head area was derived based on onrete bearing strength. Relation among head thikness, bolt diameter and diameter o holes was provided. Bolt spaing in slabs was analyzed and appropriate design proedures were provided. These inluded strength requirements or onrete slabs retroitted with shear bolts and requirements related to inlined rak propagation. Seismi design requirements regarding to slabs with shear bolts were given. Finally, some suggestions were provided or the retroitting onstrution, ire and orrosion protetion o steel shear bolts, and maintenane. 1.5 Organization o the Thesis Chapter 1 o this thesis introdues the bakground, explains the objetive o the researh, and presents the ontributions. Chapter desribes a literature review on: 1) punhing shear researh; ) seismi behaviour and researh on lat slab olumn strutures; 3) previous researh work arried out at the University o Waterloo. In Chapter 3, the experimental setup is introdued, inluding the design and setting up o steel test rame, steel supporting rame, instrumentation, and design and abriation o the onrete lat slab olumn onnetions. Chapter 4 presents the experimental results. Comparisons are made whih show the advantages o the steel shear bolts. Analysis o the results is done whih shows the perormane o slabs with shear bolts. Loads, drit ratios, strains, and raks are presented. In Chapter 5, the design o steel shear bolt is introdued. Also the design o the existing onrete slabs strengthened with shear bolts is explained in terms o number o bolts, the spaing and layout o the bolts in the slab. Some suggestions are also given on the operation o retroitting, protetion and maintenane o the shear bolts. Chapter 6 presents the onlusions and provides suggestions or uture researh. 9

26 Chapter Literature Review.1 Introdution This hapter desribes literature on punhing shear researh work that has been done by previous researhers. First, in setion., it introdues the researh ompleted on reinored onrete lat slab olumn onnetions under vertial (gravity) load or a ombination o vertial load and stati moments only. Seond, in setion.3, it addresses previous researh on punhing shear behaviour o lat slabolumn strutures subjeted to seismi loads and gravity load. Then in setion.4, some typial mehanis models or punhing shear o slab-olumn onnetions are reviewed. In setion.5, the ode design methods or punhing shear o lat slab olumn strutures are introdued. Finally, setion.6 presents researh on shear bolt strengthening method that has been done at the University o Waterloo, whih inludes work on edge slab-olumn onnetions under gravity loads and stati moments, and behavior o interior lat slab-olumn onnetions subjeted to monotonially inreasing gravity loading.. Punhing Shear Behaviour in Reinored Conrete Slabs under Vertial Load or Vertial Load Combined with Stati Moments When a reinored onrete lat slab olumn struture is subjeted to heavy gravity (vertial) load, punhing shear raks our inside the slab at the olumn viinity. They propagate at ~ 5 degree angles through the slab thikness. A trunated onial or pyramid ailure surae around the olumn orms. In addition to vertial loads, the slab-olumn onnetions may be subjeted to unbalaned moments, whih are aused by unequal spans on both sides o the olumn or by lateral loading suh as wind or earthquakes. The unbalaned moment is resisted by a ombination o stresses in slab lexural reinorements, shear strength o onrete, and shear reinorement in the viinity o olumn. Eet o unbalaned moments rom earthquakes (reversed yli loading) will be disussed in Setion.3. Punhing shear transer mehanisms (internal ores equilibrating punhing ore) inlude: aggregate interlok at the rak, ompression and tension in onrete, dowel ore rom lexural steel, and tension in transverse reinorements i present. 1

27 ..1 Parameters Inluening Punhing Shear Strength o Slab-Column Connetions Many ators aet the punhing shear apaity o lat slab-olumn onnetions under stati loads. Slab thikness, olumn dimensions, onrete strength, lexural reinoring ratio and pattern, and shear reinorement are all the parameters inluening punhing shear apaity. In experiments, the testing methods and onditions, suh as the loading rate and sale o speimens, also inluene the results, and supporting onditions. The disussion below is based on some seleted reerenes related to the above ators Conrete Strength Researh has been done to ind the relation between the onrete ompressive strength, ' and the shear strength. Moe (1961) was the irst to onlude that the shear strength relates not to ' but to '. Based on the testing results, he obtained the ollowing equation or ultimate nominal punhing shear apaity V n : V n ' = [ 15(1.75 ) 5.5φ ] (.1) d Vn where is the olumn dimension, d is the eetive slab depth, φ =, V lex is the vertial V punhing shear ore at the alulated ultimate lexural apaity o the slab. Moe explained that shear strength is primarily aeted by onrete tensile splitting strength whih is oten assumed lex proportional to '. Current researh also suggests that high strength onrete an inrease % o the shear strength o the slab-olumn onnetion (Emam, Marzouk, and Hilal, 1997)...1. Column Size and Slab Thikness As shown in equation (.1), Moe (1961) proposed that shear strength depends on the ratio o onentri load area (olumn) dimension to slab eetive thikness d. In equation (.1), i let φ = 1, the value o Vn ' would be in linear relation with d. This means when dimensions o 11

28 onentrated load area inrease, or when the slab eetive thikness derease, well. V n ' dereases as..1.3 Flexural Reinorement The strength o lexural reinorement, reinorement pattern and layout, and the amount o ompression reinorements have eets on punhing shear apaity. These are explained as ollows. (1) Strength and Ratio o Flexural Reinorement Researh indiates that shear strength an be related to lexural eets. Yitzhaki (1966) tested 14 slab-olumn speimens and proposed that the shear strength depends proportionally on the lexural reinorement strength and the olumn size. Dowel ores develop in the lexural reinorements when they ut aross the inlined shear rak. Vertial ores also develop due to the membrane eet in the lexural reinorement mat when the rigid parts o a slab (outside o shear raks) rotate around the olumn. Kinnunen (1963) onluded that dowel ores and vertial ores rom membrane eet aount or 35 perent o the punhing shear apaity. Thereore, aording to Kinnenun s onlusion, slab punhing shear apaity inreases i the ratio and strength o lexural reinorements inreases. V Moe (1961) proposed the relation between n V and n, as in equation -, V lex ' V V V n ' ' V + C V n lex = 1. (-) where Vnis the nominal punhing shear strength (vertial punhing shear ore o the olumn), is the vertial punhing shear ore at the alulated ultimate lexural apaity o the slab, onstant between and 1, and ' V is a ititious reerene value o shear, 1 V = A bd, ' ' ' V lex ' C is a ' A is a onstant, b is the perimeter length o the ritial setion, d is the eetive thikness o a slab. From Vn V Figure.1, it is ound that i = 1, n ' V lex V approahes a onstant. This means i we design a slab

29 governed by lexural ailure ( V n = V lex, whih is a preerred mode o ailure), V n an be alulated ' ' using V = A bd ', whih is independent o the lexural reinoring ratio. Figure.1 Interation between Shearing and Flexural Strength (Moe, 1961) () Pattern o Flexural Reinorement Tests by Kinnunen and Nylander (196) showed that the ailure loads an be about %-5% higher in irular slabs reinored with two-way bars than that in slabs with ring reinorements. (3) Conentration o Tensile Reinorement Hawkins et al. (1974) summarized that onentration o tensile reinorement over a olumn is preerable beause it inreases slab stiness, delay the irst yielding o tension reinorement, and derease the rak width under the same loading ondition. (4) Compression Reinorements 13

30 Vn Elstner and Hognestad (1956) reported that, or φ = < 1, there is little eet on shear strength V with the variation o the ompression reinorement, where V, are deined as in equation (-1). lex V n lex However, when φ 1, the shear strength inreases i the ratio o the ompression reinorement inreases. Compression reinorements also inrease the dowel ore ater punhing ailure, whih an prevent progressive ollapse o a struture Shear Reinorements Conial punhing shear raks orm i the slab is subjeted to a vertial load or a vertial load with an unbalaned moment. To prevent punhing shear rak rom propagating, shear reinorements an be used. Shear reinorement is, in general, a bar (or other shape) rossing the inlined raks to prevent punhing shear ailure. The bar should have adequate tension strength, dutility and good anhorage to develop its strength i punhing shear ours. There are many types o shear reinorements or new or existing reinored onrete slabs. (1) Shear Reinorements or New Constrution For new onstrution, shear reinorements are embedded with the lexural reinorements beore the onrete is ast. They an be divided into three groups: 1) Strutural steel setions suh as I shape steel, or hannels; ) Bent bars and stirrups; 3) Headed reinorements inluding shear studs and headed bars Hawkins and Coley (1974) investigated the eet o I-shape steel in edge slab-olumn onnetions (Figure.). They ound that I-shape steel inrease shear apaity and rotation apaity o the slabolumn onnetions. However, I-shape steel setions need to pass through the slab-olumn onnetion, and thereore setions in one diretion need to be welded or bolted onto the I-steel setions in the other diretion. This ongests the slab olumn onnetions. In addition, the I-shapes an only be embedded between the top and bottom rebar mats, otherwise holes have to be drilled to let the rebars go through. Thus this kind o punhing shear reinorement is not a avorable one in onstrution, with the exeption o thik slabs and large olumns where they may work. 14

31 Figure. I-shape shear reinorement (Hawkins and Coley, 1974) Headed shear studs welded to a bottom steel strip were irst tested at the University o Calgary by Dilger and Ghali (1981) (Figure.3). The area o a head on the top o the bar is usually at least ten times o the bar setional area. Tests using this shear reinorement show that the shear apaity and dutility are inreased. Figure.3 Headed shear studs welded to a bottom steel plate Megally and Ghali () ompare ive 15mm thik interior slab-olumn onnetions under vertial loading. Four o them were strengthened by shear apital, drop panel, stirrups, and shear studs, respetively. It is shown that the shear apital and drop panel inrease punhing shear apaity, but the strengthened slabs show no better dutility than non-strengthened slab (Figure.4). Stirrups 15

32 inrease strength, but not dutility or 15mm thik slab (due to poor anhorage). Shear studs substantially inrease strength and dutility o the onnetions. Figure.4 Load-deletion urves o slabs with dierent punhing strengthening methods (adapted rom Magally and Ghali, ) () Shear Reinorement or Retroit o Existing Reinored Conrete Slab-Column Strutures Existing onrete slabs may need to be strengthened due to insuiient punhing shear apaity. This may be aused by hange o the building use, new openings in a slab, design and onstrutions errors. There have been several methods proposed or punhing shear retroit o existing slab olumn onnetions. A steel support an be installed around the olumn on the bottom o the slab. Also reinored onrete apital or a drop panel an be added to the bottom o a slab. Ghali et al. (1974) tested 1 speimens with prestressed shear bolts in three groups (Figure.5). The twelve bolts or eah speimen were 3/4 inh diameter high tensile strength steel bolts with a 4x4x3/4 inh steel plate at eah end. The unbonded bolts were tensioned to 75.3kN beore testing. One group o speimens (Group B) were subjeted to monotonially inreased moments, and another group (Group C) were subjeted to monotonially inreasing vertial load. The results showed that the prestressed slab had muh higher deletion apaity and ailure load than unreinored slabs. In Group C, speimen # 1 ( no bolts) obtained an ultimate load o 413 kn, but speimen #9 (prestressed bolts) obtained 69 kn ultimate vertial load, an inrease o 67% ompared with speimens #1. In 16

33 group C, speimens #5 (without bolts) reahed 196 knm ultimate moment, and speimen #4 (with prestressed bolts) reahed 41 knm moment, a 3% inrease. Figure.5 Prestressed shear bolts or slab under vertial load (Ghali et al. 1974) A new shear strengthening tehnique using steel shear bolts or existing slab was proposed by El- Salakaway et al. (3), and Adetia and Polak (5). Results o the tests show that the maximum deletions measured at ultimate loads are between 54-16% larger or slabs with shear bolts than those o non-shear-reinored slabs. The ultimate punhing shear apaity an also be inreased by using shear bolts. These will be introdued in Setion.6..3 Previous Researh on Seismi Behaviour o Reinored Conrete Slabs.3.1 Flat Slab Column Strutures in Seismi Zones In seismi zones, lat slab olumn strutures must deorm without damage together with the primary lateral load resisting system suh as shear walls or braed moment rames. I the slabs do not have adequate dutility and strength, punhing shear ailure o slab-olumn onnetion an our. When the onrete slab olumn strutures experiene yli loading during an earthquake, the behaviour o the struture is dierent rom those in non seismi zones. The punhing shear strength and stiness o onrete derease under yli load, hene the slab-olumn onnetions need to possess ertain strength and dutility to undergo inelasti deormations. Lateral deorming apability and dutility are two main neessary properties o slab-olumn struture in seismi zones. Furthermore, this type o strutures needs to have post-ailure resistane ater an earthquake to support servie loads. 17

34 Substantial researh work has been done on punhing shear behaviour o slab-olumn strutures in seismi zones. Most o the previous experiments were done using interior or edge onnetion subassemblies isolated rom prototype strutures onsisting o a slab with olumns extending rom the top and bottom o the slab. These subassemblies are subjeted to vertial loading rom either the top o olumns or slab surae, and yli loading on the olumn ends or slab edges. This method is easy to arry out and the test results have been utilized in design odes. There is also some researh was done using ontinuous slab olumn speimens. Other experimental methods inlude testing model strutures on shaking tables. Many ators inluene seismi punhing shear apaity and dutility o slab-olumn onnetion in seismi zones. In addition to the ones desribed in setion., the ollowing are also important in seismi zones: biaxial loading or uniaxial loading and the magnitude o the gravity load shear..3. Behaviour o Slab-Column Connetions under Cyli Loading.3..1 Eet o Gravity Load Robertson and Durrani (199) tested three speimens eah with two exterior and one interior slabolumn onnetions as shown in Figure.6. The three speimens were subjeted to dierent vertial and lateral yli loadings. The speimen A, B and C were subjeted to vertial load o 14, 85, 4 lb / t (6.7kPa, 13.6kPa,.1kPa) respetively. Speimen A reahed a peak lateral load o 19.8 kips (88. kn) at 3.5% drit, while peak load on speimens B and C were 13.1 kip (58.3kN) and 9.6 kip(4.7kn) respetively (Table.1). Speimen A reahed maximum drit o 5% at ailure, while speimen B and C reahed 1.5% and 1%, respetively. This work demonstrates that when the gravity load level (gravity shear level) inreases, the apaity or moment transer and dutility o the onnetion derease. The hysteresis urves o unbalaned moment versus drit or three speimens A, B and C (with inreasing gravity loading) show that the apaity o lateral drit, stiness, and energy dissipation derease as the gravity loading inrease. Robertson and Durrani (199) suggested a design limit,. 35, where V u is the diret shear ore V at peak lateral load, and V is the nominal shear apaity o slab in the absene o moment transer. V u 18

35 Figure.6 Speimens inluding exterior and interior slab olumn onnetion Table.1 Vertial load inluene on peak load and drit (rom Robertson and Durrani, 199) Speimen Superimpose Peak load and Drit o irst ailure slab load (lb/t ) orresponding drit A kip at 3.5% drit 5% at one exterior onnetion B kip at 1.5% 1.5 % at interior onnetion C kip at 1% 1% at interior onnetion 1kip=4.448kN, lb/t =47.88Pa.3.. Eet o Biaxial Lateral Cyli Loading Pan and Moehle (199) investigated the eet o biaxial lateral loading and gravity loading on the behaviour o slab-olumn onnetions. Their test set-up is shematially showed in Figure.7. Some o the speimens were subjeted to uniaxial yli drit, while the others were subjeted to biaxial loading. It was ound that lateral yli loading redues the lateral stiness, strength, and drit apaity o the slab-olumn onnetions. Figure.8 shows the lateral ore versus drit envelopes or Speimens 1 to 4. Speimen 1 and speimen have the same average gravity nominal shear stress on the ritial setion, ' 1.4 psi (.1 ' MPa), speimen 3 and 4 are with the same gravity shear stress o '.88 psi ( '.7 MPa). Speimens and 4 were subjeted to biaxial loading. It is onluded that the biaxial yli loading results in derease in stiness, strength, and available drit 19

36 apaity as ompared to uniaxial yli loading situation. Figure.8 also demonstrates that higher gravity level loads lead to derease in stiness, strength, and available drit apaity. Figure.7 Test set up o biaxial loading Figure.8 Experimental envelopes.3..3 Shear Capitals and Drop Panels Sine shear apitals inrease the thikness o a slab near the olumn, they are helpul or inreasing punhing shear apaity. This was onirmed by Wey and Durrani s tests (199). They tested three

37 speimens with shear apitals under vertial load and yli moment. It was onluded that when the shear apital is too small, and the onnetion is under high moment reversals, the net positive moment at the onnetion may result in an inverted punhing ailure and the thikness o the shear apital is not eetive in inreasing the shear apaity. As mentioned in setion..1, Megally and Ghali () onluded that shear apitals an only inrease shear apaity, but not enhane dutility o the slab-olumn onnetions Eet o Conrete Strength on Seismi Punhing Shear Emam, Marzouk and Hilal (1997) researhed seismi harateristis o slab-olumn strutures onstruted with high-strength onrete. Aording to their tests on our interior slab-olumn onnetions: two with high-strength onrete olumn and slab: H.H.H.C..5(1) and H.H.H.C.1.(), two with high-strength olumn and normal strength slab: N.H.H.C..5(3) and N.H.H.C.1.(4). By using high strength onrete, the dutility o displaement and rotation inreased by 1 and 15 perent, respetively, as the onrete strength inreased rom 35 to 75 MPa. Shear strength, moment apaity, drit perent, and rotation apaity inreased by, 31, 37 and 5 perent, respetively. However, Megally and Ghali () onluded that although high strength onrete inrease punhing strength, the ultimate drit ratio and displaement dutility ator, it an hardly prevent brittle ailure in severe earthquakes Shear Reinorement or New Slabs Several tests on slab-olumn strutures under yli loading were onduted using stirrups, shear studs, bent-bars, or shearhead reinorements. The summary o the indings is presented below. (1) Stirrups, bent bars, and steel shearheads Four slab-olumn onnetions (three with vertial losed stirrups and one without shear reinorement) were tested under yli loading by Islam and Park (1976). Meanwhile they also tested other two speimens under monotoni lateral loading, one with bent-bars, the other with shearhead reinorement (hannel setions). The experimental results led to the onlusion that the losed stirrups inrease the shear strength and signiiantly inrease dutility o the onnetion under 1

38 yli unbalaned moment. The losed stirrups result in more dutile behaviour at large deletions than a strutural steel shearheads. Bent bars and hannel setions also inrease shear strength, however, bent bars do not inrease dutility and only resist punhing shear in one diretion; and hannels only slightly inrease dutility. Hawkins et al. (1975) investigated the eetiveness o integral beam type stirrup reinorement in slabs under yli loading. They onluded that the losed stirrups an inrease the shear strength, dutility and hange the hystereti behaviour o the onnetions with low reinorement ratios rom a shear to a moment type o energy dissipation mehanism. In order to make stirrups work eiiently, they should be losed and with 135 degree hooks, well anhored and extend ar enough rom the olumn. () Shear studs Shear studs were developed at the University o Calgary as mentioned in setion.. Cao and Dilger (1993) tested our speimens with shear studs. They ound that the shear studs improve signiiantly the onnetion dutility and shear strength. Sine shear studs are easy to install and do not interere with lexural steel bars and with onrete asting, this type o reinorement is preerred in onstrution. One other onlusion rom Cao and Dilger (1993) is that under yli loading the onrete nominal shear strength o the onnetion is redued. This should be inluded in punhing shear design ormulas or slabs in seismi zones. Megally and Ghali () published their test results o eight single edge slab-olumn onnetions with and without shear studs under yli loading. The onlusion was that shear studs inrease the punhing shear resistane and prevent brittle ailure even in a severe earthquake. The onnetions an undergo dutile deormations up to 5% inter-storey drit ratio without punhing shear ailure Seismi Retroit o Reinored Conrete Slab Column Connetions Ebead and Marzouk () tested two slabs, 19x19x15mm slab with 4x4 olumns, whih were strengthened by eight ASTM A35 bolts (19mm diameter) and 6 mm thik steel plates on top and bottom slab surae around the olumn. (Figure.9). The bolts were bonded with onrete using epoxy. The speimens were subjeted to onstant vertial load and yli lateral load. They ound that

39 the moment apaity inreased about 15% and the strengthened onnetion ould undergo 75% more lateral drit than those without bolts and steel plates. The strengthened onnetion ould reah 8% drit beore ailure, whereas the non-strengthened slab ould only reah about 4-5%. 19mm Dia. Bolts Steel Plate t=6mm Figure.9 Slab strengthened by steel bolts and plates (Ebead and Marzouk, ) Carbon ibre-reinored polymer (CFRP) were also used to strengthen the existing onrete slabs. Stark et al. (5) tested two slab speimens strengthened with CFRP. As shown in Figure.1, CFRP straps were wrapped with epoxy through the holes in the slabs. These CFRPs ated as stirrups. The slabs were detailed aording to the old version o ACI The olumns were made rom steel and were attahed to the slab using steel bolts. A vertial onstant load and reversed yli lateral load were applied to the speimens. Punhing shear ailure was ound at about % or the nonstrengthened speimen, while the strengthened speimens ould undergo about 8% drit without signiiant strength losses. The moment apaity also inreased. The retroitted onnetions had two times displaement dutility and 3.5 times joint rotation dutility as ompared to the non-strengthened ones. Figure.1 Slab strengthened by CFRP stirrups (Stark et al., 5) 3

40 .4 Analytial Models or Punhing Shear In the last ew deades, intensive researh work was done related to punhing shear. Based on the experiments and analysis o the slab behaviour, several analytial models have been proposed. Some o them ormed the basis o the design ormulae employed in various strutural odes and speiiations. This setion examines the bakground o the important models or punhing shear. (1) Punhing Shear Model by Kinnunen and Nylander Kinnunen and Nylander (196) proposed a punhing shear model based on stati gravity-type test results o irular slab-olumn onnetions, with irular olumn and irular and radial reinorements. Kinnunen (1963) developed the model suitable or irular slabs with two way orthogonal reinorement mats on the tension side and onsidered dowel ores o the reinorement. As shown in Figure.11, the part outside the inlined rak is divided into setors bounded by the inlined rak, radial raks and the perimeter o the slab speimen. The setors as shown in Figure.1b, whih are assumed to be rigid and supported by the imaginary onial onrete shell, rotate around the root o the inlined raks. The onial shell, whih supports all the setors, is shown in Figure.1 and the shaded area in Figure.1. Figure.11 Assumption o onial shell and rigid setors by Kinnunen and Nylander model 4

41 Figure.1 Punhing shear model o Kinnunen, 1963 Through the equilibrium o the setors, Kinnunen derived three equations as ollows: equation (-) was set up by satisying moment equilibrium; equation (-3) and (-4) were set up to satisy ore equilibrium in radial and vertial diretions, respetively. B γ P ( 1 ) + T sin α ( ) T os α ( h z) π R4 ( h λ y) = (-) 1 T osα + π R4 π κ R1 π R = (-3) ϕ P (1 γ ) = T sinα (-4) 5

42 where P is the punhing shear load on the onnetion (the applied load at the slab periphery or at the olumn), T is the inlined ompression ore in the onial shell, κ R1 is the ore omponent in the tangential diretion o reinorement utting aross the shear rak, R is the ore in radial diretion o the reinorement utting aross the shear rak, R 3 is the ore o shear reinorement (not inluded in this model), R 4 is the tangential resultant o onrete ompression stress at the bottom o the setion, M is the vertial omponent o membrane ore in reinorement mat aused by the rotation o the setion, D is the dowel ore in the reinorement interseting with the onial shear rak, V = M + D = γ P, γ is the ratio o V over P, ϕ is the slie angle o the rigid setion, α is the inline angle o the imaginary ompression onrete onial shell, y is the vertial height o the onial shell rom the slab bottom surae, the slab bottom, B is olumn diameter, z 1 and z see Figure.1. λ y is the vertial height o the resultant ore R4 rom Kinunnen also assumed that the ailure riterion is: The tangential ompressive onrete strain on the bottom surae o the slab under the root o the shear rak reahes a harateristi value at whih avorable embedment o the onial shell is impaired. Using the ompression stress in the slab bottom onrete, we obtain punhing load P 1. Then using the ores in the reinorements, a punhing load P an be alulated. The ultimate punhing load P is obtained by an iterative proess: assume an initial value o y h to alulate α, alulate P 1, and P ; i P 1 is not lose to P, assume another y h, and repeat till P1 = P, whih is then equal to the ultimate punhing load P. () Truss Model by Alexander and Simmonds Alexander and Simmonds (1987) proposed a truss model to simulate the punhing shear mehanism o slab-olumn onnetions. The model assumes the top steel bars as horizontal hords and the onrete rom the bottom o slab to the top reinorement as inlined struts (gravity struts). As shown in Figure.13, the gravity onrete struts resist the downward movement, while the uplit struts resist upward movement. (Uplit struts onsist o bottom rebar and onrete rom top slab to bottom rebar.) When the punhing load or the moment is large, the 6

43 stress in the struts would be large enough to push the reinorement mat apart rom the onrete. To determine the inlination angle α o the struts, Alexander et al. (1987) gave the ollowing equation based on experimental results: Figure.13 Truss model o slab punhing shear (Alexander and Simmonds, 1987) tanα 1..35K = e (-5) s d ' K = A d ' e.5 bar y ( / s ) where se is the eetive tributary width o reinoring bar, d ' is the over o reinoring mat measuring rom enter o the mat to the near slab surae, is the dimension o olumn ae perpendiular to the bar being onsidered, A bar is the area o a single reinoring bar, ds is the eetive depth o the slab, y is the yield strength o the reinorement, and ' is the onrete ompression strength. For interior slab-olumn onnetions under vertial load only, one the strut angle α is determined, the ultimate punhing shear load P an be alulated using the ollowing equation: T P = A tanα (-6) st y 7

44 where T Ast is the setion area o lexural reinorements that are lose enough to the olumn to partiipate as a shear strut. (3) Bond model by Alexander and Simmonds On the basis o their truss model, Alexander and Simmonds (199) proposed a bond model or onentri punhing shear. In the truss model, the shear is resisted by vertial omponent o the ore o the straight-line ompression struts. However, tests show that a urved arh is more onsistent with strain measurements than the straight-line strut (Figure.14). The shear is transerred to the olumn by the urved, radial ompression arh. Let T be the tension ore in the reinoring bar as shown in Figure.14. The shear ore V an be expressed as d( T jd) d( T ) d( jd) V = = jd + T dx dx dx where jd is the moment arm, d( T ) dx varies with loation x (stress gradient in the rebar), whereas whih the arm jd hanges with x. jd is the beam ation part in whih tension ore in the rebar d( jd) T dx is the arhing ation part in Figure.14 Curved ompression strut (adapted rom Alexander et al., 199) 8

45 Figure.15 Layout o radial strip (adapted rom Alexander et al., 199) Figure.16 Equilibrium o Radial Strip (adapted rom Alexander et al., 199) It is assumed the loads on the slab are transerred to our radial strips interseting with the olumn (Figure.15). Eah radial strip an be assumed to be a antilever beam (Figure.16) when the ar end is ree o moment, as in many punhing shear tests or slab-olumn onnetions, ie M pos = in Figure.16. w is the maximum shear load that may be delivered to one side o a radial strip by the adjaent quadrant o the two-way slab. Alternatively, w is alulated rom the maximum ore 9

46 gradient in the reinorement perpendiular to the radial strip. The punhing apaity o the slabolumn onnetion P is P = 8 w* l = 8 M w (-7) neg where M neg = wl M neg is the lexural apaity o the strip, whih an be alulated by the ollowing equation: M ρ jd neg = y (-8) where ρ is the eetive reinoring ratio (tension reinorement on the slab top) within the radial strip, is the width o the strip, moment arm within the slab. y is the yield stress o the reinorement, jd is the internal In order to alulate the ultimate punhing shear load P as in equation (-7), the distributed load w is estimated using either the maximum stress gradient in the rebar perpendiular to the strip or the nominal maximum one-way shear stress v whih is speiied by the ACI ode 318. Alexander and Simmonds applied bond stress to alulate stress gradient in the reinorements, whih is then used to alulate w : π db w = jd ( τ o ) (-9) s τ = (.9614b ) (-1) ' o i s bsi = 1 d b bi = min d ' bvi = 3 d b where s is the spaing o rebar perpendiular to the strip, db is the diameter o the rebar, onrete over thikness (rom rebar enter to top slab surae). (-11) d ' is the The seond alternative to estimate the distributed load w is using the nominal maximum onrete shear stress v or a beam subjeted to shear and lexure only, whih is speiied in ACI lause as: 3

47 v = psi = MPa (-1) ' ' ( ).166 ( ) It is assumed that the maximum shear stress o the strip (beam) setion is transerred to the strip. Thereore, the value o w is: w = d = (MPa) (-13) ' * v d(.166) where d is the eetive thikness o the slab. (4) Plastiity Model o Braestrup (1976) Braestrup et al. (1976) proposed an upper bound plastiity punhing model or axisymmetri slabs Figure.17 shows the setion o an axisymmetri slab, whih is simply supported by a irle ring with diameter D on the bottom. As shown in Figure.18, a vertial load P is applied on the top enter area with diameter d ; the diameter o the punhed opening on the bottom surae is d 1 ; urve A-B-E is the inlined punhing shear rak. It is assumed that the generatrix o the ailure surae is r = r( x) and the displaement vetor is at an angle α = α(x) to the ailure surae. The energy ( W I ) dissipated at the ailure surae should be equal to the work ( W ) done by the punhing load P. P Figure.17 Axisymmetri punhing (Braestrup et al., 1976) h 1 dx WI = δ ( λ µ sin α) π r (-14) osα WP = P δ (-15) 31

48 where δ is the relative veloity (displaement), is the uniaxial onrete strength, t is the tensile strength o onrete, angle o onrete. t ρ =, λ 1 ρ( k 1) =, µ = 1 ρ( k + 1), 1+ sinϕ k =, ϕ is the rition 1 sinϕ Figure.18 Predited ailure surae (Braestrup et al., 1976) By equating (-14) and (-15), the upper bound ultimate punhing load P an be obtained. Braestrup et al. (1976) optimized the ailure surae and they ound that it inludes a onial part and a atenary part. In the ailure surae A-B-E in Figure.18, AE is an inlined straight line; BE is a atenary urve. Thus the ultimate punhing load P inludes two parts: P 1 rom the upper one and P rom the lower atenary part. P = P1 + P (-16) h ( d osϕ + h sin ϕ)(1 sin ϕ) P1 = π (-17) os ϕ 1 d d 1 1 d 1 P = π [ λ( h h ) + λ ( ( ) ab) µ (( ) a )] (-18) 3

49 where h is the slab depth and h is the height o the top one part o the ailure rak, d a = + h tan ϕ, b = tanϕ, = a b. This model assumes the onrete as a peretly plasti material. It gives good qualitative explanation to punhing shear ailure. The variation o the alulated ultimate punhing loads was about 16% as mentioned in their onlusion. (5) Shear Frition Model by Dilger () and Dehka (1) Based on the shear-rition riterion (Loov, 1978) or beam shear, Dilger () and Dehka (1) developed the shear-rition model or punhing shear o reinored onrete slabs with or without shear reinorements, under onentri load. Aording to shear-rition riterion, the shear stress v on a onrete ailure surae is related to the normal stress σ on that surae and the ompressive strength ', whih an be expressed as equation (-19): v k ' = σ (-19) where v is the average shear stress on the shear ailure plane, σ is the normal stress on that plane, ' is the 8-day ompressive ylinder strength, k is the orrelation oeiient determined rom experiment data. In order to obtain reasonable results, they modiied equation (-19) by adding the onrete tension strength t to σ : v = k ( σ + ) (-) t ' Two orms o the shear-rition model were developed: general model and the simpliied model. The general model is suitable or omputer programming while the simpliied model an be used or hand alulation. Figure.19 shows the ree body diagram o the slab-olumn onnetion or general model. The ailure surae inludes eight aets. The ultimate punhing shear apaity V s, gen, as in equation (-1), is the summation o the shear apaity o eah aet whih is obtained by inorporating equilibrium equations o the aet into equation (-). K T rt Vs, gen 1 ot 4 ot ot T ot T v θ K k θ θ θ = (-1) 33

50 '.5 ( bot top ) K = k b + b h r = t 1 ' T = tension ore in the lexural reinorements T v =tension ore in eah shear stud θ = angle o the ailure aet h = slab thikness b bot = bottom edge length o the aet b top = top edge length o the aet x bot =the distane between olumn ae and the bottom o the ailure aet By assuming a suitable range o x bot and angle θ, a series o V, s gen an be obtained using omputer program. The minimum V s, gen and its orresponding θ are the ultimate punhing shear apaity. The simple orm o shear-rition model, as in equation (-), was derived rom the general model: 4 x h V l x A 4 x k s h k h h rt s, e s, simple = + ( o + π ) + vs yv (-) l = ( + ) + 4 ( s + ( n 1) s), x y k x = hlo A π r + t h vs yv s, e h s where V s,simple is the nominal shear ore resisted by the onnetion as given by shear rition, h = average eetive length o the stud,, are olumn dimensions, s, s are spaing o bolts, s, e n is the number o shear studs, the shear studs. x y A vs is the setion area o the stud stem, yv is the yield strength o 34

51 Shear Studs Failure Surae T S R T Slab Shear Studs v LC Symm. x z x V s x bot top Column θ h/sinθ y Failure Surae h top,x b bot.,x b x A x A xy b b bot.,xy A y Slab Column top,xy b bot.,y b top,y Figure.19 Free body diagram o slab-olumn onnetion or shear rition model (Dilger,, and Dehka, 1) (6) Yield Line Model (Ranking and Long, 1987) When a reinored onrete slab is subjeted to a heavy vertial load, the lexural reinorement in the slab may yield at the maximum moment loations and onrete would rak there. Finally, some rak patterns, i.e. yield line patterns, would our in the slab, whih divide the slab into several elasti plates onneted by plasti hinges. The ultimate load that the slab an sustain is alulated by onsidering the equilibrium o all these divided plates or by equating the external work o the slab loads and the internal work o the divided plates. 35

52 Rankin and Long (1987) developed the ollowing equation (-3) to alulate the ultimate vertial load P lex when the lexural steel bars in the onrete slab yield, by assuming the yield line pattern as shown in Figure.. Figure. Yield line pattern in the slab (Rankin and Long, 1987) P lex = s 8(.17) M a b (-3) where s is the square slab edge length, a is the support length on our sides, is the dimension o the square olumn setion, M b is nominal apaity o the slab setion using tension reinorements. Ranking and Long also proposed an empirial ormula to alulate the shear punhing strength P vs o the slab when the onrete subjeted to punhing shear ailure. P = 1.66 ( + d) d(1 ρ) (-4) vs '.5 where d is the eetive slab thikness, ρ is the lexural reinorement ratio. For the slab-olumn onnetions subjeted to gravity load and moment, Cao (1993) proposed equation (-5) to estimated the unbalaned moment apaity M assuming the yield line rak 36

53 pattern in Figure.1 (ring raks belong to ompression surae; other raks are on the negative surae). M = (1 + π )(1 + k) m.5v (-5) where k is the ratio o positive to negative moment apaity per unit length, m is the negative moment per unit length whih is equal in the two orthogonal diretions x and y, is the olumn dimension, V is the shear ore applied on the slab-olumn onnetion. Figure.1 Yield line pattern o interior slab-olumn onnetion subjeted to shear and unbalaned moment (Cao, 1993) (7) Critial Setion Models Talbot (1913) irst proposed the shearing stress ormula (Moe reerred to it in his report, 1957) or reinored onrete ooting slabs based on the assumption that the ailure ours on a so alled ritial setion: V ν = (-6) 4 ( r + d) jd where r is the side length o the loaded area, d is the eetive depth o the slab, jd is the distane between tension and ompression resultants (.9d), and V is the shear ore. The ritial setion in this ase is at olumn aes and it is is a hypothetial ailure plane, perpendiular to the surae o the slab. 37

54 Forsell and Holmberg assumed (1946) that the shearing stresses are parabolially distributed aross the depth o slab. They proposed the shear stress ormula: 1.5V ν = (-7) bh where b is the perimeter length o the ritial setion whih is at h / rom the olumn aes, h is the slab thikness. Moe (1961) suggested that the ritial setion should be at a olumn ae. Based on his testing results o 4 slab-olumn speimens and others testing results, Moe proposed the ultimate shear strength v u (psi) as v 15(1.75 r d ) ' V u u = = bd ' bd / V lex (-8) where Vuis ultimate shear ore (lb), V lex is a shear ore at ultimate lexural (yield line) apaity o the slab (lb), r is the olumn size (in.), b is the olumn perimeter length (in.), and d is the eetive slab thikness (in.). Based mainly on Moe s work, the ACI-ASCE Committee 36 (196) speiied the ritial setion at d / rom the olumn ae to simpliy the equation (-8). They proposed the ollowing equation to alulate the ultimate punhing shear strength o the onrete slab, whih orms the basis o the urrent ACI ode provision on punhing shear design: V u v u = = bd ' 4. where bis perimeter length o the ritial setion at d / rom the olumn ae, other variables are same as those in equation (-). 38

55 .5 Punhing Shear Design This setion examines the punhing shear design proedures o some important strutural odes o pratie. All odes adopt an approah involving a ritial setion, whih is at a ertain distane rom the olumn perimeter. The basi rule is that the atored shear stress on the ritial setion should be less than the nominal shear apaity. Canadian ode CSA A3.3-4 and the Amerian Code (ACI 318-5) have similar provisions or punhing shear. In both odes, the ritial setion is.5d rom the olumn aes. In other odes suh as Euroode (4) and CEB-FIB Model Code 9, the positions o the ritial setion are dierent. In all odes, shear apaity has ontributions rom onrete and the shear reinorement. Both ACI318-5 and CSA A3.3-4 do not aount or the eet o lexural reinorement in alulation o the shear resistane, while the European odes onsider the eet..5.1 Punhing Shear Design Requirements in CSA A3.3-4 Aording to the CSA A3.3-4 ode, or two way slab-olumn onnetions, the atored shear stress d v on the ritial setion (the perimeter at a distane rom olumn aes, Figure.) should be no more than the atored shear resistane v r. v v = v + v (-9) r s where v is the atored shear resistane rom onrete, vs is the atored shear resistane orm shear reinorements. Fatored shear resistane o the ritial setion without shear reinorement is: v '.38λφ =.47 ' = min.19λφ (1 + ) =.14 β ' α sd φ λ (.19 + ) =.65 b ' ' ' (1 + ) β α sd (.19 + ) b (MPa) (-3) Where λ = 1or regular onrete, φ =.65 is the redution ator or onrete strength, β is the ratio o the long side over short side o the olumn, b o is the perimeter length o the ritial setion. α s =4, 3, or interior, edge, and orner olumn, respetively. Equations in (-3) are equivalent to those in ACI

56 I v rom equations in (-3) is less than v, shear reinorements are required. For slabs with shear reinorements, the shear resistane is also as v r = v + vs, but v is alulated as in equation (-3). For slabs with shear reinorement, atored shear resistane rom shear reinorement is : v s φs Avs yv = (-31) b s where φ s =. 85 is redution ator o steel bar. A vs is the setion area o the shear reinorement, yv is the strength o the shear reinorement, s is the radial spaing o the shear reinorement. For onrete with headed shear reinorement (shear studs), shear resistane rom onrete in the shear reinored zone is v = λφ (-3a) '.8 Maximum shear resistane o setion with headed shear reinorement should satisy the ollowing equation: v λφ (-33a) ' r max. 75 For onrete with stirrup shear reinorement, shear resistane rom onrete in the shear reinored zone is v = λφ (-3b) '.19 Maximum shear resistane o setion with stirrup shear reinorement should satisy the ollowing equation: v ' r max. 55λφ (-33b) To alulate the atored shear stress v by gravity load and unbalaned moment in the perimeter o the ritial setion, the ollowing equation is applied: v V = b d γ vm + J e x γ vm + J e y (-34) where V is the vertial shear ore. M is the unbalaned moment in x, y diretion, whih is transerred by slab shear and lexural stresses. γ v is the ration o the moment transerred by shear, 4

57 1 γ v = 1, b 1 is the width o the ritial setion side perpendiular to the moment vetor, b b b is the other side length. e is the distane rom the entroid o the ritial setion to the point where shear stress is alulated. J is analogous to polar moment o inertia o the shear ritial setion around the x, y entrioda1 axes, respetively. In alulations o V and loads and live loads are 1.5 and 1.5 or most load ombinations. M, the ators or dead Figure. Critial setions deined in Canadian ode CSA A3.3-4 (Cement Assoiation o Canada, 6).5. Punhing Shear Design Requirements in ACI (in SI units) Similar to CSA A3.3-4, ACI requires the atored shear stress v at the ritial setion (the perimeter at a distane d rom olumn aes) should be no more than the produt o nominal shear strength v n times a shear strength redution ator φ =.75 : 41

58 v φ (-35) v n where v + n = v vs, v is the shear resistane rom onrete, vs is the shear resistane rom shear reinorements. To ompare with CSA A3.3-94, the strength redution ator φ an be assigned to v and v r, and equation (-35) an be written as: ' v v r (-36) where v ' r ' ' = φ v + φv = v +. s v s The atored shear resistane o the ritial setion without shear reinorement is v ' ' '.33φ =.48 ' ' = min.17φ (1 + ) =.18φ (1 + ) β β ' α sd ' α sd.83φ (. + ) =.63 (. + ) b b (MPa) (-37) Where β is the ratio o the long side over short side o the olumn, b o is the perimeter length o the ritial setion. α s =4, 3, or interior, edge, and orner olumn, respetively. For slabs with shear reinorement, shear resistane rom shear reinorement is: v where ' s φ Avs yv = (-38) b s A vs is the setion area o the shear reinorement, yv is the strength o the shear reinorement, s is the spaing o the shear reinorement. Shear resistane v ' = φ or '.17 onrete with stirrups. Maximum shear resistane o a setion with stirrup shear reinorement shall satisy the ollowing equation v φ (-39) ' ' r max. 5 When alulating the atored shear stress v, the ollowing equation is applied: 4

59 v V = b d γ vm + J e x γ vm + J e y (-4) where V is the vertial shear ore, ration o the moment M transerred by shear, M is the unbalaned moment in x, y diretion. γ v is the 1 γ v = 1, b 1 is the width o the ritial b b setion side perpendiular to the moment vetor, b is the other side length. e is the distane rom the entroid o the ritial setion to the point where shear stress is alulated. J is the analogous polar moment o inertia o the shear ritial setion around the alulations o ombinations. V and M x, y entriodal axes, respetively. In, the ators or dead loads and live loads are 1. and 1.6 or most load.5.3 Euroode (4) The Euroode (4) employs a basi ontrol setion at a distane d rom the aes o the olumn or the loaded area. Similarly, the shear stress v on the ontrol setion should be no more than the shear resistane ( v r ). v v r As shown in Figure.3, or retangular olumns, the basi ontrol setion inludes round orners (ACI and CSA ode permit right angle orners). The ode also requires heks on the olumn ae and on the ontrol setion outside the shear reinorement area. For interior slab-olumn onnetions without shear reinorements, the shear resistane v r or the basi ontrol setion is alulated as 43

60 Figure.3 Basi ontrol setions deined in Euroode (4).18 = = (1 ρ ) (-41) 1/3 vr v k k vmin γ.5 k = 1 + ( ) <., d in mm d k = the harateristi onrete strength, MPa ρ = lexural reinorement ratio, 1/ ( ρzρ y ). ρ = ρ, ρ are reinoring ratios in z, y diretions or a slab width equal to olumn width plus 3d z y eah side. γ = 1.5, partial ator or persistent and transient onrete. v = k 3/ 1/ min.35 k The shear stress unbalaned moment v u1d β v at the basi ontrol setion due to atored external onentri load V and M is = V (-4) γ M u1 β = (1 + ) or one diretion moment, or V W 1 e e ( ) ( ) b b β = + y + z or two diretion moments z y 44

61 W 1 = u1 edl where u1 is the length o the basi ontrol setion length, γ is the ration ator o M, ( γ =.6 or retangular olumn), b, b are the dimensions o the basi ontrol perimeter (Figure.3), e, e y z y z are the eentriities M V along y and z axes respetively, ( e y results rom a moment rom z axis). e is the distane o dl rom the moment axis. v I ollowing: > v, shear reinorement is required. The shear resistane strength v r an be alulated as d 1 v =.75v + 1.5( ) A ( )sinα (-43) u d r sw ywd, e sr 1 where v is alulated as in equation (-41), s r is the radial spaing o shear reinorement, d is the eetive depth o the slab, A sw is the setion area o all shear reinorements in one perimeter, ywd, e = 5 +.5d ywd, ywd is the design yield strength o the shear reinorements, u1 is the length o the basi ontrol setion length, α is the angle between the shear reinorement and the slab plane. At the olumn ae, the shear stress punhing shear resistane v r max.5 d v due to v r max as ollowing. V and 45 M shall be no more than the maximum = ν (-44) k ν =.6(1 ) (-45) 5 = / γ d k where k is the harateristi ompressive ylinder strength o onrete at 8 days, γ = 1.5. For interior olumns, the shear stress v at the olumn ae is V v = (-46) ud β

62 where uis the length o olumn periphery (or interior olumn), β is alulated as in equation (- 4)..6 Seismi Requirements or Design o Flat Slab-Column Strutures In addition to the punhing shear provisions desribed in the above Setion.5, some odes provide speial provisions or seismi punhing shear requirements..6.1 National Building Code o Canada (NBCC 5) NBCC 5 requires that the primary lateral load resistant system should not be a lat slab-olumn struture when the building is more than three stories. NBCC (5) also requires that lateral interstorey drit ratio should not exeed 1.% or post-disaster strutures,.% or high importane buildings, and.5% or other buildings..6. Seismi Requirements o CSA Clause in the Canadian strutural ode CSA requires: or slab olumn onnetions subjeted to seismi loading, i the shear stress produed by gravity load only is greater than REv, shear reinorement should be provided. vis the shear resistane rom onrete (Eq. -3) and alulated using the ollowing ormula: R.5 46 R E is.85 E = ( ) 1. (-47) δi where δ i is the inter-story drit ratio, δi.5. When shear reinorements are required, it is required that the ollowing relation should be satisied. V R E V (-48) r where V is the onentri external shear ore, V r is the atored shear ore resistane. V r inludes onrete resistane V alulated using.5 v and the shear resistane by shear reinorements. The ode also states that the shear reinorements shall extend a minimum o 4d beyond the ae o the olumn.

63 .6.3 ACI Seismi Requirements or Slab-olumn Strutures The Amerian Conrete Institute Code, ACI uses the gravity shear ratio VR in Clause where Vu VR = (-51) φv b d n v n is the nominal shear strength provided by the onrete (stress unit) V the atored shear ore due to gravity loading ( U = 1.D + 1.L +.S) u The maximum story drit ratio, DR, when there is no shear reinorement, is DR =.35.5*VR ( VR <.6) DR =.5 ( VR.6) I DR an not be satisied, the slab needs shear reinorement or larger thikness. Minimum shear reinorement should be v s Av yv 3.5 ' = (MPa) (-53) bs FEMA 356 Requirements FEMA 356 Prestandard and Commentary or the Seismi Rehabilitation o Buildings () requires that the struture shall satisy both global level and member level riteria aording to the perormane level o the struture. There are three strutural perormane levels: Immediate Oupany (IO), Lie Saety (LS), and Collapse Prevention (CP). Global level riteria or RC rames are: IO: allows 1% maximum interstory drit LS: allows % maximum interstory drit CP: allows 4% maximum interstory drit Member level riteria are based on plasti rotations or eah member. For slab-olumn onnetion, limits on plasti rotation angles (radian) by perormane level are shown in Table. 47

64 Table. Limit on plasti rotation angles or slab-olumn onnetion by perormane level V g / V o (Gravity shear ratio) Continuity Rebar Plasti Angle Rotation Limit (radian) or Immediate Oupany (IO) Component (member) Type and Plasti Angle Lie Saety (LS) Primary Rotation Limit (radian) Collapse Prevention (CP) Lie Saety (LS) Seondary Collapse Prevention (CP). YES YES NO NO Previous Researh Work on Punhing Shear at Waterloo The presented urrent researh is a ontinuation o the work done at the University o Waterloo sine Thereore the review o this work is provided here. Sine 1997, several tests have been done related to punhing shear o reinored onrete slab-olumn onnetions. These involved edge and interior slab olumn onnetions, with or without openings near olumns, with or without shear reinorements suh as shear studs or shear bolts. The previously tested speimens were subjeted to vertial and lateral stati loads. El-Salakawy, Polak, and Soliman (1998) tested slab-olumn onnetions subjeted to high moments. It was ound that the shear stress around the olumn inreased due to higher moment-to-shear ratio (Table.3). In 1999, El-Salakawy, Polak and Soliman published the test results on reinored onrete slab-olumn edge onnetions with openings (Table.3). Researh was also arried out on the eet o shear studs on the reinored onrete slab-olumn edge onnetions. El-Salakawy, Polak, and Soliman () ound that shear studs an inrease stiness o slab-olumn edge onnetions with an opening and also inrease the shear strength and dutility o the speimens. One the opening in the slab is as big as the olumn dimension, the inluene o shear studs was very small. Shear studs are the type o reinorement that is embedded into the reinored onrete speimens beore asting. Alternatively, shear bolts an be installed ater drilling holes on existing previously 48

65 built slab-olumn onnetions. In 3, El-Salakaway et al. published the results o tests on our edge slab-olumn speimens strengthened by shear bolts. (Table.4) The onlusion was that shear bolts, as a new type o retroitting method, an inrease the apaity and dutility o slab-olumn edge onnetions, and an hange the ailure mode rom punhing shear mode to a avourable lexural mode. Adetia and Polak (5) tested six interior slab olumn onnetions strengthened by shear bolts subjeted to vertial loading only. (Table.5) These speimens were all 18x18x1mm reinored onrete slabs with short olumn stubs. All the slabs were simply supported on our sides (15x15mm) on the bottom. In their test results, ompared with the ontrol speimen without shear bolts, the slab-olumn onnetion strengthened with our rows o shear bolts had inreased ultimate punhing shear load by 4.3% and displaement dutility by 9%. They observed that the shear bolts an prevent propagation o shear rak in strengthened slabs and improve the perormane o the slabs with openings (Figure.4 and Table.5). Figure.4 Load versus enter deletion measured by internal LVDT o the testing rame. (Adetia and Polak, 5) 49

66 Speimen Table.3 Edge slab-olumn onnetions with or without shear studs (El-Salakaway and Polak et al, 1998, 1999,, 3) Slab size(mm) (1 thikness) Shear Bolts/ Shear Studs Flexural Capaity (Yield Line) V lex (kn) M lex kn*m 5 Failure Load (kn) Failure Moment M u *m) (kn Opening Size (mm) Failure Mehanis m Column dimension/ Position XXX 1x154 N/A N/A Punhing 5x5 Edge SF 1x154 N/A x15 Punhing 5x5 Edge SE 1x154 N/A x15 Punhing 5x5 Edge SF1 1x154 N/A x15 Punhing 5x5 Edge SF 1x154 N/A x15 Punhing 5x5 Edge CF 1x154 N/A x5 Punhing 5x5 Edge XXX-R 1x154 6 row studs N/A Flexural 5x5 Edge SF-R 1x154 6 row studs x15 Flexural 5x5 Edge SE-R 1x154 6 row studs x15 Flexural 5x5 Edge CF-R 1x154 6 row studs x5 Punhing 5x5 Edge HXXXR 1x154 6 row studs N/A Punhing- Flexural HSF 1x154 6 row studs x15 Punhing- Flexural (mm) 5x5 Edge 5x5 Edge HSE 1x154 N/A N/A Punhing 5x5 Edge HXXX 1x154 N/A N/A Punhing 5x5 Edge

67 Speimen Table.4 Four edge slab-olumn speimens strengthened with shear bolts (El-Salakaway and Polak et al., 3) Slab size(mm) (1 thikness) Shear Bolts/ Shear Studs Flexural Capaity (Yield Line) V lex (kn) M lex kn*m Failure Load (kn) Failure Moment M u (kn*m) Opening Size (mm) Failure Mehanism SX-1SR 1x154 1 row bolts N/A Punhing lexural Column dimension/ Position (mm) 5x5 Edge SX-SR 1x154 3 row bolts N/A Flexural 5x5 Edge SX-SB 1x154 3 row bolts N/A Flexural 5x5 Edge SH-SR 1x154 3 row bolts x15 Flexural 5x5 Edge 51

68 Speimen Size (mm) Shear Bolts/ Studs Flexural Capaity (Yield Line) V lex (kn) M lex (kn*m) Applied Failure Load (kn) Dutility mm/mm Opening Size (mm) Failure Mehanism Column Size And Position SB1 18x18 N/A 358 N/A N/A Punhing 15x15 entered (mm) SB 18x18 row bolts 358 N/A N/A Punhing/ 15x15 entered Flexure SB3 18x18 3 row bolts 358 N/A N/A Flexure 15x15 entered SB4 18x18 4 row bolts 358 N/A N/A Flexure 15x15 entered SB5 18x18 4 row bolts 358 N/A x15 opening 4 SB6 18x18 4 row bolts 358 N/A x15 opening Flexure Flexure 15x15 entered 15x15 entered Table.5 Six interior slab-olumn speimens strengthened with/without shear bolts (adapted rom Adetia and Polak, 5) 5

69 Chapter 3 Experiment Program 3.1 Speimens Design A total o nine ull sale speimens were tested. These speimens an be regarded as part o a prototype struture o whih the lat onrete slab spans 3.75m between olumns. The slab thikness is 1 mm. Figure 3.1 and Figure 3. show the plan view and elevation view o one prototype struture, whih is a three-storey lat slab olumn building. The speimens represent interior slabolumn onnetions whih are isolated speimens with dimensions orresponding to the lines o ontralexure under gravity loads. D 375 C (15).4L Support line o isolated speimens 375 B 375 mm A mm Figure 3.1 Plan view o the prototype struture 53

70 Column Flat Slab Isolated Speimen mm Figure 3. Elevation view o the prototype struture The nine speimens, SW1~SW9, were subjeted to a vertial onstant load and yli reversal lateral displaements. The speimens are divided into two series: Series I (SW1~SW5) and Series II (SW6~SW9). Series I onsists o two groups: Group 1 (SW1, SW, and SW3) and Group (SW4 and SW5). Figure 3.3 shows the ive speimens o Series I; Figure 3.4 shows the our speimens in Series II, inluding the slab names, vertial loads on olumns, and the layouts o shear bolts. SW1 V=11kN SW V=11kN SW3 V=11kN (a) 54

71 SW4 V=16kN SW5 V=16kN (b) Figure 3.3 The ive speimens (SW1~SW5) o Series I and shear bolt layout (a) Group 1 (SW1, SW, SW3); (b) Group (SW4, SW5) SW6 V=16kN SW7 V=16kN SW8 V=16kN SW9 V=16kN Figure 3.4 The our speimens (SW6~SW9) o Series II and shear bolt layout. The speimens SW1~SW9 have slab dimensions o 18mm by 18mm with top and bottom olumn stubs (xmm) extending out 7mm rom the enter o the slab (Figure 3.5). In onstrution pratie, the slabs sometimes may require openings near olumns. To investigate the seismi behaviour o this type o slab-olumn onnetions, three speimens (SW6, SW7, and SW8) are designed to have two 15x15mm openings near the olumn in the lateral load diretion (Figure 3.4 and Figure 3.5). All the speimens are supported on the 15x15mm perimeter on the bottom o the slab, with two sides also supported rom the top to resist yli moments. The top o the slab in this projet is the slab ompression surae under vertial load (Figure 3.5). This is opposite to the situation in a real slab-olumn system where ompression is on the bottom. 55

72 The dimensions o the slabs were hosen to represent the loations o ontralexure lines or the ase o gravity loads. In ase o gravity plus horizontal yling loads (as in the ase o the presented tests), the loations o ontralexure lines normal to horizontal loading diretion hange depending on the diretion o the horizontal loading. Thereore, sine in the setup the loation o supports remain the same (in-between the atual loations o the lines o ontralexure), thik neoprene pads were provided on top and bottom o the slab to allow rotations. The neoprene pads were about 5mm thik and 5mm wide installed along the supporting lines as shown in Figure 3.5() and Figure D Center line o simple supports on bottom surae (supports on top surae see (b) A Column B Center line o simple supports on top surae (supports on bottom surae see (a) A Openings 15 Neoprene supports C D 15 C (All dimensions in 'mm') (a) (b) () 15 B AD F P Column F Slab BC Figure 3.5 Dimensions o the speimens SW1~SW9 (all dimensions in mm ) (a) Plan view o SW1~SW5 and SW9; (b) Plan view o SW6, SW7 and SW8; () Elevation view Flexural Reinorement In the tension surae o the onrete slab, the lexural reinorement ratio o is 1.3% in the diretion o lower bars and 1.1% in the diretion o upper bars. The reinoring ratio on the ompression surae o the slab is hal o the tension reinorement. The reinorement is designed ollowing the results o alulation o Adetia (3) assuming a atored vertial distributed load o 18.5kPa to the prototype strutures. The speimens lexural reinorement was idential to previous tests in order to allow diret omparisons o results. 56

73 The bottom and the top reinorements are two-way mats. The reinorement was designed to have the same moment apaities in the two orthogonal diretions. The reinoring ratio o the olumns is high and losed ties are used in order to make the olumn strong enough to transer shear ore and yli moments to the slab. Figure 3.6 and Figure 3.7 show the reinorement o the speimens without or with openings, respetively. The bottom mat, tension surae under vertial load, onsists o #1 in one diretion at lower position and #1M@9 in the transverse diretion at upper position. Due to this layout, the moment apaities in the two diretions are the same. The top mat onsists o #1M@ in two diretions. For speimens with openings, the reinorement in diretion 1 (along the lateral ore appliation) is interrupted by the opening. There was no spae in the slab to plae additional bars along the sides o the opening. However, or diretion (normal to lateral loads) the same number o rebars that were ut by the openings are plaed beside the opening edges (Fig. 3.7). Figure 3.8 (a) shows the olumn rebar details. Figure 3.8 (b) shows the positive lateral drits applied on the top and bottom olumns o the speimens. AD and BC sides o the slab in Figure 3.8(b) an be ound in Figure 3.6 and Figure 3.7. These aids in inding the position o the speimens and the loading diretion in the testing rame as shown in Figure Rebar #5 Loation "d" Strain Gauge 18mm 1mm (lower) A D B Lateral drit diretion C #1 # 18mm mm A D a b a b d #3 B C 9mm (upper) 18mm (onrete over o slab: mm) (a) Rebar #4 mm 18mm (b) Figure 3.6 Reinorement detail and strain gauges in speimen SW1~SW5 and SW9 Bottom reinorement mat; (b) Top reinorement mat 57

74 A Rebar #5 B A #4 Strain Gauge B 18mm 1mm (lower bars) D 9mm (upper bars) 18mm (a) Lateral Load Rebar #1 C 18mm mm D a b b d mm 18mm (Conrete over o slab: mm) Rebar #3 C (b) Figure 3.7 Reinorement detail and strain gages in Speimen SW6, SW7 and SW8 (a) Bottom reinorement mat; (b) Top reinorement mat mm #1@1mm 15mm #5 M AD Side Positive lateral drit (+) BC Side mm (+) (a) (b) Figure 3.8 Reinorement detail o olumn and lateral load diretions (a) Column setion; (b) Positive lateral drit diretion 3.1. Estimation o the Capaities o the Speimens beore Testing The speimens design was arried out based on assumed material parameters values. This was done beore testing in order to deide on the ultimate punhing loads and ultimate slab-olumn onnetion moment apaity or eah speimen. These estimated loads and moments were used to selet the 58

75 apaity o the load ells and atuators, to design the experimental setup, and to determine test proedures suh as loading rate, onstant vertial load, et. The testing proedures are presented in Setion Ultimate Punhing Loads in Flexural Failure and in Punhing Shear Failure The design o the speimens was done based on the Canadian onrete ode CSA A To ensure suessul testing, the speimens were designed to ail in punhing shear i no moment and no shear reinorement were present. Flexural apaity o the speimen had to be larger than punhing apaity to ensure suh a ailure. The equation (3-1) (Chapter ) o ull yielding at lexural ailure (Rankin and Long, 1987) was used to alulate the ultimate lexural punhing load apaity (upper bound) o the slab-olumn speimen without shear reinorement and unbalaned moment, = M (3-1) Plex k y1 b s where k y 1 = 8(.17) = 9. 7, s = 18 mm (slab dimension), = mm (olumn a dimension), a = 15 mm (support distane), and M b = 39kNm, M b moment apaity alulated by CSA A (tension reinorement only). Thereore kn. The ultimate punhing shear apaity was alulated using Rankin and Long s equation(1987): is the nominal lexural P lex = P vs or speimens without shear reinorement and moment P = 1.66 ( + d) d(1 ρ) (3-) vs '.5 where ' is the onrete ompressive strength, is the length o the olumn side, d is the eetive slab thikness. ρ is the reinorement ratio. For speimens without openings and shear reinorement, = mm, d = 9 mm, assuming = 4MPa, then P = 9.6 kn. ' vs Using CSA A3.4-94, (the speimens were designed beore CSA A3.4-4 is enored), the estimated nominal punhing shear apaity is 59 ' P vs = 6kN (or = 4 MPa). Speimens SW1~SW3 were tested under the vertial load o 11kN. Speimens SW4 ~ SW9 had a vertial load o 16 kn.

76 3.1.. Ultimate Moment Capaities o the Speimens During testing, lateral displaements were applied to the olumn stubs. The value o the applied moment dependeds on the displaement and the stiness o the slab-olumn onnetions. The displaements inrease the raking, whih results in the derease o the stiness o the onnetion. At the same time the punhing shear apaity also derease due to extensive raking. In order to estimate the behaviour o the slabs, moment apaities o the onnetions were alulated using yield line analysis and CSA A Provisions. 1) CSA A Provisions The punhing shear ormulas o CSA A (without material redution ators and using unatored loads) are as ollows: v Vn = b * d v γ vm ne + J x (3-3) v r nastud y ' ' = vs + v = (3-4) s * b vr v (3-5) where Vn is the given vertial load, the perimeter length o the ritial setion, M n is the unbalaned moment apaity o the onnetion. b is dv is the eetive thikness o the slab, s is the bolt spaing in radial diretion, n is the number o bolts in eah periphery row, eah bolt. Solving equations (3-1, 3-, 3-3) results in the value o moment apaity A stud is the setion area o M n. M n J nastud x = γ ve s( + d y v ) + v Vn b d v (3-6) or M n J x = v γ ve max Vn b d v (3-7) where v =, or slabs with shear reinorement, ' max. 8 v =.3. ' 6

77 ) Yield Line Theory to Estimate the Moment Capaity o the Speimens Using yield line theory, Cao (1993) obtained the ormula (3-8) o unbalaned moment apaity o the slab-olumn onnetion under vertial load and unbalaned moment. M = (1 + π )(1 + k) m. 5V (3-8) where k is the ratio o positive to negative moment lexural apaity per unit width, m is the negative moment per unit width (assuming m x = m y ). is the olumn dimension, V is the shear ore applied to the slab-olumn onnetion. The results o the alulations or the unbalaned moment apaities are listed in Table 3.1. The shear bolt spaing was assumed to be 7mm and the irst row o bolts was 5mm ar away rom the olumn aes. The maximum alulated moment was 1 knm whih orresponds to lateral loads o 8 kn applied to the speimens. This is less than the apaity o available lateral atuators. Thereore it was deided to used two 5 kip (kn) load ells or the two horizontal lateral atuators, and 15 kip (667kN) load ell or the vertial atuators Capaity o Conrete Column The apaity o the olumn was examined using the o-relation ormula o axial load and moment ating on the olumn and the material strengths o the olumn. Top olumn was subjet to both axial ompression and moment. Bottom olumn was subjet to moment only. The theoretial maximum apaity point o the olumn is ( P, M r r ) = (497.6 kn, 93.4 knm). At the applied axial ompression o 11 kn the moment apaity is 81 knm, and at the applied axial ompression o 16 kn the moment apaity is 85 knm. On the bottom olumn, sine there is no axial load, the moment apaity is about M = 75 knm. These moment apaities were adequate or the testing. The olumns were r designed using 1M diameter stirrups at spaing o 1 mm to ensure adequate shear apaity. 3. Properties o Materials used or Speimens The ollowing subsetions address their tested strength. In addition, the strength and elongation o steel shear bolts are also shown. Table 3. and Table 3.3 display detailed inormation o speimens in Series I and Series II, inluding slab designations, their group number, onrete and rebar bath numbering, bolt rows, dimensions, and vertial load. 61

78 Table 3.1 Initial design o moment apaity o the nine slab-olumn onnetions beore testing Name o speimen Assumed material strength Conrete ompr. ' (MPa) Shear bolt yield ' yv (MPa) Rebar yield y (MPa) External vertial load (kn) Row o shear bolts Moment apaity at ritial setion d/ (CSA ode) rom the olumn: M n (kn*m) No No With bolts, bolts, bolts, With ν r = ν = ν r = ν = bolts, ν + ν s, min( ν 1, max( ν 1, ν r = ν = ' ν, ν 3) ν, ν 3).8 '.3 Moment apaity at d/ out o shear bolt M n (kn*m) Moment apaity based on Cao s yield line equation M n (kn*m) Column size (mm) Opening size (mm) SW N/A N/A 86.5 x - SW x - SW x - SW x - SW N/A N/A 81.5 x - SW N/A N/A N/A x SW N/A x SW N/A x SW x 15x15 openings 15x15 openings 15x15 openings 6

79 Table 3. Details o Speimens o Series I Series # Group # Slab name Slab dimension (mm) Column size (mm) Bolt rows Vertial onstant load (kn) Conrete bath number Rebar bath number SW1 18x18x1 xx7 11 Series I Group 1 SW 18x18x1 xx SW3 18x18x1 xx Group SW4 18x18x1 xx SW5 18x18x1 xx7 16 Table 3.3 Details o Speimens o Series II Series # Slab name Slab dimension (mm) Column size (mm) Number o opening Size o opening Bolt rows Vertial onstant load (kn) Conrete bath number Rebar bath number SW7 18x18 x1 x x7 15x15 6 (orth.) 16 1 Series SW6 18x18 x1 x x7 15x15 16 II SW8 18x18 x1 x x7 15x15 6 (rad.) 16 3 SW9 18x18 x1 x x7 N/A 6 (rad.) Conrete Compression and Tension Strength The nine reinored onrete speimens were ast using ready mixed onrete in three bathes. Conrete was provided by Hogg Fuel and Supply Ltd., Ontario. The irst bath o onrete was or 63

80 speimens SW1, SW and SW3; the seond bath o onrete went or SW4, SW5, and SW7; SW6, SW8 and SW9 were ast using the third bath o onrete. All the speimens were ured in normal interior temperature (about C ). Conrete ylinders (4 diameter x 8 length and 6 diameter x 1 length ) were prepared with eah asting bath. Some o the 4 diameter x 8 length ylinders were plaed in the standard humid room and were tested on the 8 th day or ompression strength; the others were plaed with the slab-olumn onnetions in normal interior temperature, and were tested or ompression and tension strength at the same time o the slab-olumn onnetions testing. Figure 3.9 Compression test o the onrete ylinder (4 x8 ) Table 3.4 shows the average ompression strength and average tension strength o eah slab-olumn onnetion speimen at the testing time; it also shows the 8-day ompression strength (ured in humid room) o the ylinders or eah bath o onrete. Speimen SW1, SW, and SW3, ast rom the irst bath o onrete, had the average standard 8-day ompression strength 34.5 MPa and average ompression strength rom 33.7 to 37. MPa at the time o slab testing. In the seond ast bath, speimens SW4, SW5, and SW7 had standard 8-day strength o 37MPa and 45. to 46.5 MPa ompression strength at slab testing. The third ast bath o speimens SW6, SW8, and SW9 reahed 5MPa in 8-day standard strength and 51.9 MPa in ompression strength at slab testing. Figure 3.9 shows the rushing o a ylinder (4 x8 ) whih was ured in a standard humid room or 8 days. Figure 3.1 shows the splitting (tension) test o 4 x8 onrete ylinders ured in the normal room environment. It an be seen that the olor in the raked surae is lighter than the olour o the third 64

81 bath onrete. This may be beause the third bath onrete ylinders were tested at a younger age and more plastisizer was added to the onrete to inrease the onrete slump. Table 3.4 Conrete strength o eah speimen (4 x8 ylinders) Test series # Series I Series II Slab name Age o slab (rom asting to testing, days) Average ompressive strength at slab testing (MPa) ' (MPa) (used in alulations) Average tensile strength at slab testing (MPa) SW SW SW SW SW SW SW SW SW Average standard Conrete (8-day ) bath ompression number strength (MPa) Figure 3.1 Conrete ylinder tension test 65

82 To obtain the ompression stress versus strain urves o eah bath o onrete, ylinders (6 x1 ) were tested in the MTS rame (Figure 3.11). The end suraes o all ylinders were ground to smooth; diameter and length o eah ylinder were measured three times in dierent loations. The load, and external and internal LVDT displaements were reorded throughout the whole testing proess. The tests were done by strain ontrol. Table 3.5 shows the ompression strength and strain at peak points o eah urve. Figure 3.1 shows rushing pattern o the onrete ylinder #6 (6 x1 ) o the irst bath o onrete. Also, Figure 3.13(a), (b) and () show three ompression stress versus strain urves or the three bathes o onrete, respetively. Figure 3.11 Conrete ylinder (6 x1 ) ompression test 66

83 Figure 3.1 Crushing o the onrete ylinder #6 (6 x1 ) o the irst bath onrete (a) 67

84 (b) () Figure 3.13 Compression strength versus strain o ylinders o the onrete (a) ylinder #6 o the 1 st bath, (b) ylinder #4 o the nd bath, () ylinder # o the 3rd bath 68

85 Table 3.5 Compression strength o onrete ylinders (6 x1 ) or the three bathes First bath o onrete or Seond bath o onrete or Third bath o onrete or Cylinder # slabs SW1, SW, and SW3 Strain at peak ompression stress Peak ompression strength (MPa) slabs SW4, SW5, and SW7 Strain at peak Peak ompression ompression stress strength (MPa) slabs SW6, SW8, and SW9 Strain at peak ompression stress Peak ompression strength (MPa) Average Properties o Steel Reinoring Bars The reinoring bars (M #1 rebar, nominal diameter 11.3mm) o the slabs ame rom two bathes. The irst bath o steel rebars was used in speimen SW1, SW, SW3, SW4, SW5 and SW7. The seond bath was used in speimens SW6, SW8, and SW9. For eah bath o steel bars, two types o steel speimens were used to test their strength. One type was the standard round oupons mahined rom M #1 rebars. The oupons were 1/4 in the enter segment and 3/8 at the two anhor ends. A lip strain gauge was used to measure the strain. Figure 3.14 shows the dimensions and piture o the oupons. Figure 3.15 shows the testing o a rebar oupon. The seond type o steel speimen was original rebar as rolled. The total length o eah 69

86 original rebar speimen was 14 long, inluding 8 gauge length entered and two inhes anhor length at eah end. Figure 3.16 shows the original rebar testing and the broken position. It is ound that in the original rebar (as rolled) test, the broken loations were all along the roots o ribs o the rebar. Thus the minimum diameters o the rebar were measured or atual tension strength alulation or the rebar. In addition, aording to ASTM and CSA ode, the rebar strengths were also alulated using nominal setion area (1 mm ). " -1/4" " 3/8" 1/4" R=3/16" Gage length=" (a) (b) Figure 3.14 Standard oupon mahined rom M #1 rebar (a) Dimensions, (b) Piture 7

87 Figure 3.15 Testing o rebar oupon Figure 3.16 Testing o original rebar Table 3.6 gives all the original testing data o the rebars. Table 3.7 shows the average values alulated rom Table 3.6. Figure 3.17 shows the tension stress versus strain in the original rebar 71

88 (rebar-) o the 1 st bath steel. Figure 3.18 shows the tension stress versus strain in the oupon (Coupon-1) o the 1 st bath steel. It was deided that, or uture alulations and omparisons with ode ormulas, the yield strength o rebar should be taken as 47 MPa, ultimate strength 65 MPa at % elongation. Table 3.6 Testing results o the steel shear bolts and the two bathes steel rebar Rebar bath number Original rebar or rebar oupon Nominal yield strength (MPa) F y Nominal tensile strength (MPa) F u Elong -ation o 8" length (oupon: o ") " Strain Gauge and the broken position Rebar % Broken outside " Rebar % Inside " Rebar % Inside " 1 Coupon % Inside " Coupon % Inside " Coupon % Inside " Coupon % Inside " Rebar % Broken outside " Rebar % Outside " Rebar % Outside " Rebar % Inside " Rebar % Inside " Coupon % Inside " Coupon % Inside " Coupon % Inside " Coupon % Inside " 7

89 Table 3.7 Properties o steel reinoring bars Rebar oupon Original rebar Rebar bath number Average yield strength (MPa) Average tensile strength (MPa) Average elongation (%) Average nominal yield strength (MPa) Average nominal tensile strength (MPa) Average nominal yield strength used in alulation (MPa) (56) 67 (87) (555) 596 (695) 47 Note: Nominal strengths were alulated using nominal rebar setion area ( 1mm ); numbers in parenthesis are the strength alulated using average net broken area o rebar setion ( 83mm ) negleting the ribs. 7. Tension stress (MPa) Strain (measure in " gauge length) Figure 3.17 Tension stress versus strain in Rebar- (irst bath rebar) 73

90 Tension strain (Mpa) y = 433x R = Strain in " gauge length Figure 3.18 Tension stress versus strain in Coupon-1 (irst bath rebar) 3..3 Properties o Steel Shear Bolts The shear bolts were also tested using two types o speimens. One type was the standard round oupon mahined rom shear bolts, shown in Figure The seond type onsisted o the original shear bolts stems. 3/4" -1/4" 3/4" 3/8" 1/4" R=3/16" Gage length=" (a) (b) Figure 3.19 Standard oupon mahined rom 3/8 steel shear bolt (a) Dimensions, (b) Piture 74

91 Figure 3. Testing o the original bolt Figure 3. shows one original shear bolt stem with broken setion in the hydrauli grip system. The testing data o original shear bolts and oupons are shown in Table 3.8. The average yield strength, tensile strength, and elongation are in Table 3.9. Again, the nominal strengths rom original bolts are smaller than those o oupons. The average nominal yield strength rom original bolts was 369 MPa; nominal tensile strength was 494 MPa. From the oupon tests, the average yield strength was 378MPa; tensile strength was 51MPa, and elongation was 11.5%. Figure 3.1 and Figure 3. show the tension stress versus strain urves o original shear bolt and oupon. For alulations, the yield strength will be taken as 37 MPa, ultimate tensile strength 5 MPa at 11% elongation. 75

92 Table 3.8 Testing data o original shear bolts and oupons original rebar or Nominal Nominal Elongation " Strain Gauge Yield strain rebar oupon yield tensile o " and broken position strength strength length F y (MPa) F u (MPa) oupon-bolt % Broken inside ". oupon-bolt % Broken inside ".5 oupon-bolt % Broken inside ".7 bolt-org % Broken inside ".8 bolt-org % Broken inside ".16 bolt-org Broken inside " Table 3.9 Properties o steel shear bolts Original shear bolt Shear bolt oupon Average Average Average Average Average yield tensile yield tensile elong- strength strength strength strength ation (MPa) (MPa) (MPa) (MPa) (%)

93 T e n s i o n s t r e s s ( M P a ) Strain in " gauge Length Figure 3.1 Tension stress versus strain o original shear bolts (bolt-org-) 6 Tension stress (MPa) Strain Figure 3. Tension stress versus strain o oupon (oupon-bolt-1) shear bolts 77

94 3..4 Fabriation o the Reinored Conrete Speimens The reinorement ages o eah speimen inlude top mat, bottom mat, and olumn rebar ages. All the #1M rebars or the slabs had hooks designed at the rebar ends. Figure 3.3 shows the top and bottom rebar mats. Figure 3.4 shows the strain gauges attahed onto the rebars. Cages and ormwork beore asting are show in Figure 3.5 Figure 3.6 shows three speimens just ater asting. A piture o speimens stored in the laboratory is shown in Figure 3.7. Figure 3.3 Rebar ages Figure 3.4 Strain gauges attahed on rebars 78

95 Figure 3.5 Rebar ages and ormworks beore asting o the speimens Figure 3.6 Speimens just ater asting 79

96 Figure 3.7 Speimens stored in the laboratory 3..5 Shear Reinorement Steel shear bolts are installed ater drilling holes in the onrete slab o the speimens. The bolts are tightened against the slab by a standard wrenh to a torque whih auses about 1~15% o yield strain o the bolts. In series I, our peripheral rows o shear bolts were installed in speimen SW; six rows o bolts in speimens SW3, SW4. There were no bolts installed in speimens SW1, SW5. Eah peripheral row o bolts around the olumn inludes eight bolts (Figure 3.8). Bolt spaing and numbering o bolts with strain gauges in speimen SW, SW3 and SW4 are shown in Figure 3.8. In Series II, six peripheral rows o shear bolts were installed in speimen SW7, SW8 and SW9. The shear bolt layout was orthogonal in SW7 and radial in SW8 and SW9 (Figure 3.9). Eah peripheral row o bolts around the olumn inludes eight bolts. Speimen SW6 had no bolts. In Figure 3.8 and Figure 3.9, the numbered shear bolts had strain gauges attahed to the enter o the bolt stem, along the stem axis. The leads (eletriity wires) were onneted to the strain gauges and were sent through a small holes drilled in the bolts ap as shown in Figure 3.3. Isolating resin was applied to the strain gauges and the surrounding area on the bolts stem, and blak eletriity isolating tape was used to wrap the strain gauges. (Figure 3.3) 8

97 The spaing between the peripheral rows o shear bolts was not onstant, due to intererene rom lexural bars (Figure 3.8 and 3.9). Radial patterns o shear bolt layout were initially planned or speimen SW8 and SW9. Ater drilling, the bolt patterns were not peretly radial. This was also due to the intererene o the lexural reinoring bars. The drilling or shear bolts requires that no lexural bars are ut Bolts with strain gages 14 1a 4a 3a a Lateral drit Bolts with strain gages 14 1a a 3a 4a 5a 6a (a) (b) Figure 3.8 Shear bolt spaing in speimen SW, SW3, SW4 and numbering o strain gauges on bolts (a) Speimen SW (4-row bolts); (b) Speimen SW3, SW4 (6-row bolts) a a 4a 3a 5a 6a Numbering o bolts with strain gauges Lateral Load a 3a 1a 4a 5a 1b 6a 4b b 6b 5b 3b Numbering o bolts with strain gauges Lateral Load b b 3b 5b 6b a 1a 3a 4a 5a 6a 4b Numbering o bolts with strain gauges (a) (b) () Figure 3.9 Shear bolt spaing in speimen SW7, SW8, SW9 and numbering o strain gauges on bolts (a) Speimen SW7( 6-row bolts); (b) Speimen SW8(6-row bolts); () Speimen SW9(6-row bolts) 81

98 Figure 3.3 Shear bolts with strain gauges 3..6 Installation o Shear Bolts A total o 3 holes o 1/ diameter were drilled through the onrete slabs using Target drilling mahine and ore drill bits with diamond tips. There was a water hose onneted to the ore bit to supply water while drilling. During the drilling proess, i it was ound that the drill bit hit a lexural reinoring bar in the slab, the drill mahine was moved to a dierent position. The non-suessul holes were pathed using Sikadur 3 plus pool sand (1:1). Figure 3.31 shows the operation o the drilling mahine, whih was held tight to the onrete slab using a steel angle attahed to the mahine bottom. 8

99 Figure 3.31 Drilling holes in the slab 3.3 Experimental Setup This setion inludes three subsetions. First, in setion 3.3.1, the main omponents (elements) o the setup are introdued. Seond, setion 3.3. introdues a speial steel rame designed and used or liting and installation o the onrete slab-olumn speimens. Third, in setion 3.3.3, the strength and stiness o all the members are disussed Components o the Experiment Setup A piture o the experimental setup is shown in Figure 3.3. The names and the numbering o all members o the setup are shown in Figure 3.33 (Elevation A) and Figure 3.34 (Elevation B). The steel setup or the testing inludes two main parts: the main rame and the supporting rame. 83

100 The main rame onsists o our vertial steel olumns ( 1 : W31x86), the rosshead (two deep hannels, 19, MC46x86), and stieners or the rosshead. Three hydrauli atuators are installed on the main rame to apply load to the onrete slab-olumn speimen: two o them are horizontal to apply yli lateral drits ( 4 : 5 kips); the third is a vertial atuator ( 6 : 15 kips) to apply the vertial onstant load to the olumn o the speimen. The ground anhor bolt pattern in the laboratory is shown in Figure A short beam ( 1 : W31x17, with end plates) onneted the two olumns ( 1 ) at the bottom with our ground anhor bolts holding it in positions. Figure 3.36 shows the top plan view o the rosshead o the main rame. The 15-kip vertial atuator ( 6 ) was installed in the middle o the rosshead through a steel plate attahed to the bottom o the two deep hannels. In order to install the horizontal atuators on eah side o the rame, (Figure 3.33), a short beam ( 18 : W5x73) with end plates was inserted and bolted between the two olumns at the level o the atuator. The height dierene between the two horizontal hydrauli atuators was 15 mm. The seond part o the experimental setup, the speimen supporting rame, is shown in Figure 3.34 and 3.35, and inludes a square ring beam ( 14 ), our supporting olumns ( 1 ), two bottom reation beams ( 15 ), two top reation beams ( ), eight vertial reation rods ( 13 ), and a base steel panel ( 16 ) stiened by paralleled hannels ( 17 ) underneath. This rame was designed to support a onrete slabolumn speimen. The onrete slab was supported on its bottom rom our sides by the square ring beam. The plane view o the square ring beam is shown in Figure To restrain overturning o the speimen due to yli lateral loading, two top reation beams ( ) were installed in the diretion parallel to Y1 and Y axes. On eah end o this beam, two vertial steel rods ( 13 ), attahed to the bottom beam 15, were used to hold the top reation beam (), as shown in Figure 3.3, Figure 3.34, and Figure

101 Figure 3.3 Piture o experimental setup 85

102 mm BC side 1 9 AD side mm mm 734mm Y1 Y 1 Column o steel rame (W31x86) Top reation beam (W5x89) 3 5 1"x1" Neoprene pads Horizontal load ell (5 kip) 4 6 Horizontal atuator Vertial atuator 7 9 Vertial load ell (15 kip) Conrete slab-olumn speimen 8 1 Steel pan and rollers Supporting olumn (W5x89) 11 Braing beam (W15x) 1 Adjustable stopper (W15x) 13 Reation steel rods ( mm) Base reation beam (W31x73) Steel hannels (C15x1) Channels o rosshead (MC46x86) Support square ring beam (W5x89) 1" thik steel base panel Short beam or atuators (W5x73) Collar system 1 Beam (W31x17, with end plates) onneting the two rame olumns at the bottom, ahored to the ground by our long bolts Figure 3.33 Elevation A o the testing setup 86

103 mm X1 15mm mm X 1 3 Column o steel rame (W31x86) 1"x1" Neoprene pads 6 Top reation beam (W5x89) Vertial atuator 7 Vertial load ell (15 kip) 8 Steel pan and rollers 9 13 Conrete slab-olumn speimen Reation steel rods ( mm) 1 14 Supporting olumn (W5x89) Support square ring beam (W5x89) 15 Base reation beam (W31x73) 16 1" thik steel base panel 17 Steel hannels (C15x1) 19 Channels o rosshead (MC46x86) Figure 3.34 Elevation B o the testing setup 87

104 1x35 = 366 mm mm 35x9 = 745 mm mm X X1 1 Holes or vertial rods 193 mm 734 mm Y1 Y 1 Column o steel rame (W31x86) 1 Supporting olumn (W5x89) 15 Base reation beam (W31x73) 16 1" thik steel base panel 1 Beam onneting the two rame olumns at the bottom, ahored to the ground by our long bolts 1" ground anhor bolts (ixed layout already) Figure 3.35 Plan view o the main rame near ground level, ground anhor bolts, base panel, and the base reation beams 1 Stieners Stieners 19 X 916 mm 734 mm 6 X1 Y1 Y 1 Column o steel rame 19 Channel o rosshead 6 Vertial atuator Figure 3.36 Plan view o the main rame at the rosshead level 88

105 X X Y1 1 Column o steel rame (W31x86) 11 Brae beam (W15x, underneath) 18 Short beam or horizontal atuators Y 1 Supporting olumn (W5x89) 1 Adjustable stopper (W15x) 14 Square ring beam (W5x89) Figure 3.37 Plan view o the square ring beam, braing beams, and adjustable stoppers Top reation beam (W5x89) 5mm 5 3 5mm Steel lat bar 5x5xL Conrete slab 5mm 5 Steel lat bar 5x5xL Neoprene (5x5xL) 3 Square ring support beam Column Figure 3.38 Neoprene pads between the onrete slab and the square ring beam or the top reation beam (L is the support length: L=155 mm on eah side) 89

106 Neoprene pads o 5mm thikness were inserted between the onrete slab and the support beams and also between the slab and the top restrain beam along the support lines. Figure 3.38 shows the detail. The reason or using neoprene pads: is to simulate the slab rotation at the ontralexure line o the ontinuous prototype building due to yli moment transer. The 5 mm thik neoprene lat bars was glued to 5mm thik steel lat bars o the same dimensions with the neoprene. This provided suiient spae or rotation between the onrete slab and the support ring beam or the top reation beam. As shown in Figure 3.35, there were no ground anhor bolts diretly underneath the eight vertial reation rods ( 13 ). Thereore, two base reation beams ( 15 ) were designed parallel to Y1 axis (in Figure 3.34 and 3.35). In the middle o eah base beam, our ground anhor bolts held the stiened bottom lange o the beam. All the ground anhor bolts were o 1 diameter and Grade 8. At eah end o the base beam, two vertial reation rods were astened as shown in Figure Thereore, the base reation beam ated as a beam antilevered at its two ends. The our support olumns ( 1 in Figure 3.34 and 3.35) were installed on top o the two base reation beams ( 15 ). These olumns transerred ompression load to the base beams. Although the strength and the stiness o the two base beams were designed high enough to sustain the loading during in the experiments, a steel panel ( 16, 734x745x5mm) stiened by steel hannels was also provided underneath. This stiened panel was astened by all ground anhor bolts that it overed as shown in Figure The two base reation beams were installed on top o the base panel. There were two purposes o using the base panel. First, the bottom lange o eah base reation beam was astened to the base panel by twelve additional bolts; this made the base beam at together with the base panel to transer load to more ground anhor bolts. Also, the steel panel provided a base to attah instruments. Some string pots were attahed to the steel panel by magnet piees. The steel raks or displaement transduers or slab bottom surae were also installed on the panel by magnets. To restrain the lateral sway o the supporting rame, our horizontal braing beams ( 11 : W15x) installed between the square ring beam and the our olumns o the main rame. Figure 3.37 gives the plane view o braing beam layout and Figure 3.33 provides the elevation view. 9

107 In order to restrain any possible exessive horizontal movement o the onrete slab due to horizontal lateral ore dierene, our adjustable stoppers were installed horizontally on the our main rame olumns, at the onrete slab level. Figure 3.33 and Figure 3.37 show the elevation and plan view o these stoppers in the experiment setup. One inh thik neoprene pads were glued to the stoppers to ae the onrete slab edges. Figure 3.39 gives the details o a stopper. W15x 1" bolt PL 1x1x x1x5 Neoprene Figure 3.39 Adjustable stopper The vertial load was irst applied by the vertial hydrauli atuator ( 6 ) whih would keep the onstant load on top o the upper onrete olumn. As shown in Figure 3.33 and Figure 3.34, the ylinder ( 6 ) o the vertial atuator was onneted a 15 kip load ell ( 7 ) and a threaded stud with a pin hole. Through a round steel pin (diameter 49mm), a lat square steel plate was onneted to the atuator. The upper and lower onrete olumns were also onneted to horizontal atuators through steel ollars ( in Figure 3.33, detailed in Figure 3.41) to apply horizontal yli loading. In order to redue the rition between the top onrete olumn and the steel plate, steel rollers were used. A steel pan ( 8 ) with ive steel rollers, shown in Figure 3.4 was inserted between the plate and top surae o the onrete olumn. The ollar system as shown in Figure 3.41 was a modiiation rom a previous ollar system (El- Salakawy, 1998). The previous one was used to apply monotoni horizontal load (the loading was in one diretion only). The modiied ollar system would apply reversed loading. Four threaded rods (3/4 diameter) and ive thik steel plates were added to lamp the onrete olumn. 91

108 1 r=5mm r Steel rollers Elevation 31 Plan view o roller pan Figure 3.4 Roller on top o the upper onrete olumn A Pin Conrete olumn Loading diretion, atuators onneted Plan View A A-A Elevation (units: mm) Figure 3.41 Steel ollar system onneted to horizontal hydrauli atuators 3.3. Steel Liting Frame or Installation o Conrete Slab-Column Speimens The weight o eah reinored onrete slab-olumn was about 1 kg. Four steel oupling nuts were embedded in the our orners o eah slab. These were used or our eye bolts or liting the slab. Due to limitations or spae in height and horizontal diretion, a speial steel liting rame was abriated using large steel angles and W-shapes. The drawings o the liting rame are shown in Figure

109 B x B4 ( W15x ) End Plates: 15x15x5mm C1 5 B4 76 Stiener PL-1 eah side holes 76x76mm / B3 (angle L15x15x13) B B B Liting Frame Elevation View 4 holes 76x76mm / 15 Stiener PL-1 136x7x C1 ( W15x ) End Plates: 15x15x5mm B4 B B Holes on Top Flange B1 78 C Bottom Flange Holes to Math Holes on B, B Liting Frame Plan View B1 (W5x73) B (angle L15x15x13) Figure 3.4 Steel rame or speimens liting and installation 93

110 Figure 3.43 Liting o the onrete speimen Member Strength and Stiness o the Steel Experimental Setup The experimental setup must have enough strength and stiness to sustain the experimental loading. The main rame was an existing rame used by previous researhers (El-Salakawy,1998 and Adetia, 5). Thus the strength and stiness o the main rame were assumed suiient. Similarly, the stiened base panel was also used by Adetia (5). The work on the main rame was to adjust the height o the rosshead and to drill holes in olumns to bolt the new braing beams and the stoppers. 94

111 The support rame was a new design, whih inluded the square ring beam, our support olumns, two base reation beams and two top reation beams, eight vertial reation rods, our braing beams, and our stoppers. Beore design o all these members, the maximum loads were estimated based on the alulation in setion 3.1. and Table 3.1 and the previous tests results. The vertial load was kept onstant ( V = 16kN ); the maximum horizontal load F on top and bottom olumn were assumed to be 15kN. Figure 3.44 shows the loads on the onrete slab-olumn speimen. Ln = 1.5m. The height H between the horizontal atuators was assumed 1.47m beore design (during installation, H was adjusted to 1.5m). It was assumed that the onrete slab would tilt up on three edges on the bottom surae; only one onrete slab edge (on the right hand side in Figure 3.44) transerred the ompression load to the side o the square ring beam. Thus the reation ore R is equal to ( V + F * H / L + G), where G is the sel weight o the onrete speimen and the steel reation n beams on the slab; the reation ore R 1 is equal to ( F * H / L n). Fore R was applied on one side o the square ring beam. R was transerred to the support olumns. R 1 was used or design o the vertial rods strength and design all the reation beams. The braing beams and the stoppers were designed by assuming lateral load F=15kN was applied when one horizontal atuator might aidentally stop working. R1 F V H F R Ln V=16kN F=15kN Figure 3.44 Estimated maximum load on the speimen in testing In addition, eah o the three hydrauli atuators was onneted to a load ell, onnetors, a ollar system through threaded studs. These studs, were heked or their tension and ompression strength. For the modiied ollar system, the tension ore o the threaded rods and the shear ore o the lamping plates were heked. 95

112 3.4 Instrumentation The data aquisition system inludes the ollowing: a) three load ells onneted to the vertial and the two horizontal hydrauli atuators; b) displaement transduers; ) strain gauges in shear bolts and lexural reinorements in the onrete slab. The data aquisition system inluded two data aquisition modules or all the strains, displaements and load ells Displaements The three atuators have their own internal LVDTs to reord the ylinder displaements. In addition, external displaement transduers were used. To eliminate the deormation eet o the testing rame, all external displaement transduers were astened onto a rigid steel rak that was installed independently on the ground. Figure 3.45 shows the elevation inluding the transduer rak. Figure 3.46 gives the plan view. On the top and the bottom onrete olumn ends, string pots (S1 and S in Figure 3.45) were attahed horizontally to measure the olumn lateral drits. On the bottom olumn ends o the speimen, a string pot (S5) was installed in vertial diretion to reord the displaement, whih is the resultant o vertial and horizontal displaements o that olumn end. On eah side o the onrete slab, perpendiular to the loading diretion, a horizontal string pot (S3 or S4) was attahed to the enter o the slab edge to test the slab movement in the horizontal loading diretion Crak width Displaement transduers inluding LVDTS and DCDTs were installed on both top and bottom slab suraes in aligned vertial pairs (Figure 3.47). The displaement dierene between these pairs gives an estimation o the rak vertial widths inside the slab Strains Strain gauges (5mm-length) were attahed at loations a, b,, and d o rebar #1 ~ Rebar #5 in two diretions as shown in Figure 3.6 and Figure 3.7. Shear bolts, at typial loations, had also attahed strain gauges in the middle o their bolt stems in longitudinal diretion. In speimen SW7, strain gauges were plaed on shear bolts in orthogonal lines; in speimens SW8 and SW9, shear bolts in both orthogonal diagonal diretions had attahed strain 96

113 gauges. Layouts and numbering o shear bolts with strain gauges in SW7, SW8 and SW9 are shown in Figure 3.8 and Figure Load Control The ontrollers or the vertial 15 kip (667. kn) atuator were MTS 44; two 5 kip (.4 kn) horizontal atuators were ontrolled by two MTS 46 ontrollers. The two MTS 46 ontrollers or the horizontal atuators were onneted to a voltage ramp, whih ould generate voltages orresponding to the designed load path (lateral drit). The two horizontal atuators were ontrolled by swithing the ramp manually. String Pot S1 S3 T S4 T S S5 S1-S5: String pots to test displaement T: Displaement transduers on top and bottom slab surae Figure 3.45 Displaement transduers on slab and string pots onneted to the speimen 97

114 Round Bar "B" 16mm Conrete slab Column o steel rame Independent steel olumn 35 Conrete olumn 916 X L76x76x X1 11 Round Bar "A" 388mm 734 mm Y1 Y Figure 3.46 Plan view o the independent rak or transduers Lateral Load L1 L L3 L Horizontal Lateral Load L1 L L3 L Units: mm Transduers on Top surae Transduers on Top and Bottom Units: mm Transduers on Top surae Transduers on Top and Bottom Figure 3.47 Displaement transduers layout on slab 98

115 3.5 Testing Proedure Eah speimen was subjeted to gravity load rom the top vertial atuator, using load ontrol mode, at a loading rate o about kn / minute until the desired load level was attained. The vertial load was then kept onstant throughout the test. Speimen SW1, SW, and SW3 were subjeted to 11kN vertial load while SW4~SW9 to 16 kn. Ater appliation o the vertial load, the two horizontal atuators were ativated to apply horizontal loading. During this proess, the two atuators were ontrolled in displaement mode. They pushed and pulled the speimen olumns simultaneously at the same rate aording to a pre-planned yli loading path as shown in Figure The horizontal loading rate was about.6 volt / minute (4.6 mm / minute) beore 3% drit ratio and 1.45 volt / minute (11.1 mm / minute) or larger drits. The lateral loading yles were applied rom lower to higher drit levels by ontrolling the horizontal atuators displaement. At eah level, the same drit yle was repeated three times. Ater.75% drit level, one.5% drit yle was inserted between three-repeated-yle groups. This small yle o lower drit is used to evaluate the onnetion behaviour ater larger seismi loading. The reason or applying three repetitions o eah yle was to show the onnetion stiness degradation at eah drit level. Ater 3.% lateral drit, long and deep raks ormed in the onrete slabs and the intermediate.5% drit yles showed no muh hange in the behaviour as ompared to previous small yles; thereore the small yles were stopped ater 3.% drit. The inreasing lateral drit yles were then applied without repetitions to redue testing time. The intermediate small drit yles (.5%) were applied to show the deormation behaviour, stiness, and strength o the speimen ater higher lateral drits. It also provides inormation or possible repair o the struture ater large lateral drits. Due to unexpeted slab movements, and small deormation o the rame during testing, the drits reorded by external string pots were slightly dierent rom the drits reorded by internal LVDTs o the atuators. The displaements and drits reported in this thesis are based on the readings rom the external string pots whih reorded real displaement o the speimen. The design o the horizontal loading path ollowed the main idea o the ACI publiation: Aeptane Criteria or Moment Frames Based on Strutural Testing (ACI T1.1-1) and Commentary (T1.1 R- 1). (1) Although slow, pseudo-dynami yli loading is not ully equivalent to dynami loading and the loading path annot represent earthquake loading ompletely, the result are 99

116 representative or the behaviour o slabs in seismi zones. Many similar yli testing proedures have been widely used by other researhers and their testing results have been inorporated into strutural odes. Figure 3.48 Loading path 1

117 Chapter 4 Experimental Results and Disussion 4.1 Introdution This hapter gives the experimental results or Series I and Series II tests. For eah series, lateral load versus drit ratio, moment versus lateral drit ratio, bakbone urves o horizontal load versus horizontal drit ratio at top olumn end, peak-to-peak stiness versus drit ratio, stiness o small yles, strains in reinorements, and rak width are presented. 4. Results o Series I This setion introdues the test results o Series I whih inludes speimens SW1 ~ SW5. Among them, speimens SW1, SW, and SW3 orm Group I; the speimens SW4 and SW5 orm Group II Lateral Load versus Drit Ratio For larity o explanations, it is neessary to speiy the positive and negative ore diretions o the two horizontal hydrauli atuators. It is assumed that when atuators in Figure 3.33 push the onrete olumn o the speimen the ores are negative; otherwise, the ores are positive. The two horizontal atuators were installed in the experiment setup as shown in Figure In the test, side BC was on side o Y1 axis, and side AD was on side o Y axis. The horizontal load diretion is perpendiular to sides BC and AD. When the top horizontal atuator pushes the top onrete olumn end rom BC side to the AD side, the horizontal load and the drit on the top onrete olumn are negative. At the same time, or the bottom onrete olumn, bottom horizontal atuator pushes the bottom onrete olumn rom side AD to the side BC, the horizontal load and the drit on the bottom onrete olumn are also negative. The sides o AD and BC o the onrete slab olumn onnetions are also speiied in Figure 3.6 ~ Figure 3.8, Figure 4.13, and Figure 4.4. Horizontal lateral load on top olumn end versus its horizontal lateral drit ratio or speimens SW1, SW and SW3 (Group 1) are shown in Figure 4.1, and or SW4, SW5 (Group ) in Figure 4.. Speimens SW1, SW and SW3 (onrete strength: 35MPa) were subjeted to vertial load o 11kN on the top olumn end; SW4 and SW5 (onrete strength: 46MPa) to vertial load o 16kN. As 11

118 shown in Table 4.1, it is observed that in Group 1, the peak lateral negative load or SW1 (without shear bolts) was 51.8kN at.6% drit ratio, while SW (with 4-row bolts) reahed 6.4kN at 5.7% drit and SW3 (6-row bolts) reahed 61.57kN at 4.3% drit ratio. Comparing with SW1, peak load o speimen SW inreased 17%, and orresponding drit ratio inreased 117%; SW3 showed an inrease o 19% in peak load and 61% inrease in orresponding drit. For positive peak load, SW and SW3 showed 7% and 3% inrease, respetively. Also, drit ratio o SW and SW3 orresponding to positive peak load inreased 19% and 66%, respetively In Group, speimen SW5 (without bolts) had its peak negative lateral load o 5.kN at.7% drit ratio, while SW4 (6-row bolts) reahed negative lateral peak load o 74.9kN at 4.5% drit ratio. Speimen SW4 showed 43.9% inrease in lateral peak load apaity and 64.% inrease in orresponding lateral drit ompared to speimen SW5. Figure 4.3 shows the ive bakbone urves o hysteresis urves o lateral load versus lateral drit. These bakbone urves were ormed by onneting peak points at the irst yle o eah same-drityles group. These urves learly show initiation o punhing load ailure or SW1 and SW5 (no bolts), the post peak dutility o speimens SW, SW3 and SW4 (with bolts), and the inrease o peak load apaity and the maximum drit ratio o the speimens strengthened with shear bolts. Speimens SW1 and SW5 without bolts ailed abruptly ater attaining the peak loads. There was a sudden peripheral rak ormed in SW1 and SW5 respetively. Conversely, speimens with bolts (SM, SM3, and SM4) ontinued to deorm at almost onstant lateral load. No sudden peripheral raks ormed and all the raks were in radial diretion. The maximum lateral drit attained by these speimens was 8%. Further testing had to be terminated beause the top rollers ould not aommodate it. 1

119 Table 4.1 Peak load and drit dutility (deined by Pan and Moehle, 1989) o speimen SW1~SW5 Drit Slab name V V Peak lateral load (kn) Horizontal drit ratio at peak lateral load (%) Yield drit ratio (%) Drit dutility at peak lateral load µ peak Drit dutility at 95% post peak lateral load µ. 95 dutility at 8% post lateral load µ Group 1 SW SW SW Group SW SW Note: Nominal punhing shear apaity o onrete V ' =. 33 b d (ACI 318-5, in metri units) Table 4. Drit dutility (using tested irst yield drit ratio) o speimen SW1~SW5 Slab name Tested irst yield drit ratio (%) Drit dutility at peak lateral load µ peak Drit dutility at 95% post peak lateral load µ. 95 Drit dutility at 8% post peak lateral load µ SW Group 1 SW SW Group SW SW

120 8 Lateral load (kn) SW1: No bolts V=11kN Lateral drit ratio (%) (a) 8 Lateral load (kn) SW: 4-row bolts V=11kN Lateral drit ratio (%) (b) 8 Lateral load (kn) SW3: 6 row bolts V=11kN Lateral drit ratio (%) () Figure 4.1 Horizontal load versus horizontal drit ratio at top olumn end (a) Speimen SW1, (b) Speimen SW, () Speimen SW3 14

121 8 Lateral load (kn) SW4: 6-row bolts V=16kN Lateral drit ratio (%) (a) 8 Lateral load (kn) SW5: No bolts V=16kN Lateral drit ratio (%) (b) Figure 4. Horizontal load versus horizontal drit ratio at top olumn end (a) Speimen SW4, (b) Speimen SW5 15

122 Lateral load (kn) SW1 SW SW3 SW4 SW Lateral drit ratio (%) Figure 4.3 Bakbone urves o horizontal load versus horizontal drit ratio at top olumn end. 4.. Moment versus Lateral Drit Ratio Moment versus drit ratio urves are equivalent to Figures The lever arm or the lateral ores was 1.5m. For ompleteness, they are presented here. Moment versus lateral drit ratio o speimen SW1-SW3 are shown in Figure 4.4, and or speimens SW4 and SW5 are shown in Figure 4.5. Bakbone urves o moment versus lateral drit ratio are shown in Figure 4.6. All observations regarding the behaviour are equivalent to omments rom setion Moment (kn*m) SW1: No bolts No openings V=11kN Lateral drit ratio (%) (a) 16

123 Moment (kn*m) Moment (kn*m) SW: 4-row bolts No openings V=11kN Lateral drit ratio (%) SW3: 6 row bolts No openings V=11kN Lateral drit ratio (%) (b) () Figure 4.4 Moment versus lateral drit ratio at top olumn end (a) Speimen SW1, (b) Speimen SW, () Speimen SW3 Moment (kn*m) SW4: 6-row bolts No openings V=16kN Lateral drit ratio (%) (a) 17

124 Moment (kn*m) SW5: No bolts No openings V=16kN Lateral drit ratio (%) (b) Figure 4.5 Moment versus horizontal drit ratio at top olumn end (a) Speimen SW4, (b) Speimen SW5 Moment (kn*m/drit) SW1 SW SW3 SW4 SW Lateral drit ratio (%) Figure 4.6 Bakbone urves o moment versus lateral drit ratio at top olumn end 18

125 4..3 Connetion Stiness Based on the urves o unbalaned moment versus drit ratio, peak-to-peak stiness o eah yle is alulated (Figure 4.7 and Figure 4.8). Stiness at the small drit yles (in between larger drits) are showed in Figure 4.9. The onnetion stiness dereased rapidly (to 4-5% original stiness) during the repeated yles up to.75% drit ratio. It should also be noted that the stiness dereased ater eah repeated yle, in every three suessive same drit yles. The stiness dereased more in the seond yle than it did in the third one. Among eah group o three same yles, the stiness derease between the irst and seond yles was more than twie the derease between the seond and third yles. Low drit yles also showed stiness degradation. 14 Peak-to-Peak moment stiness (kn*m/drit ratio) SW1:V=11kN,no bolts SW:V=11kN,4-row bolts SW3:V=11kN, 6-row bolts Lateral drit ratio (%) Figure 4.7 Peak-to-peak moment stiness vs. drit ratio o SW1, SW and SW3 (Group I) Shear bolts had some eet in inreasing the onnetion stiness, but this eet was not signiiant, as shown in Figure 4.7 and Figure 4.8. Shear bolts had an eet on the speimen s stiness at large lateral deormations. Speimen SW1 and SW5, without shear bolts, both showed rapid stiness derease at the drit ratio o about 3.%. At this drit ratio, the speimens ailed by punhing. However, speimens SW, SW3, SW4, strengthened with shear bolts, ould undergo ar more 19

126 deormation without abruptly losing stiness. Shear bolts had little or no eet on stiness o the deteriorated onnetions at small deormations (Figure 4.9) Peak-to-Peak moment stiness (kn*m/drit ratio) SW4:V=16kN,6-row bolts SW5:V=16kN,no bolts Lateral drit ratio (%) Figure 4.8 Peak-to-peak moment stiness vs. drit ratio o SW4 and SW5 (Group II) 11 1 Peak-to-peak moment stiness o small yles (kn*m/drit ratio) SW1:V=11kN,no bolts SW:V=11kN,4-row bolts SW3:V=11kN,6-row bolts SW4:V=16kN,6-row bolts SW5:V=16kN,no bolts Lateral drit ratio beore small yles (%) Figure 4.9 Stiness degradation at small yles o the ive speimens SW1~SW5 11

127 4..4 Drit Dutility Dutility is deined by a ratio o δ % = whereδ y is the displaement orresponding to lexural % µ δ Y yielding o the slab and δ % is the displaement orresponding to a ertain load (% o the maximum load in the post-peak region). Two methods are used in this thesis to alulate drit dutility o the reinored onrete slab-olumn speimens. The dierene between the two methods is in the deinition o the yield drit ratio. (1) Method I (Pan and Moehle, 1989) The method proposed by Pan and Moehle (1989) was adopted to deine the drit dutility. It deines points orresponding to max 3 P and max between the origin, the point o P in the bakbone urve as shown in Figure 4.1. A line max 3 P, and rossing the horizontal line orresponding to max deines the assumed yield drit ratio δ y (or yield displaement). Then dutility at point o peak load P and point orresponding to 8% o peak load at dereasing side are alulated as µ peak δ = δ peak yield and µ δ.8.8 =. Similarly, dutility at point orresponding to 95% o peak load at dereasing side is δ yield also alulated as δ =.. 95 µ.95 δ yield In Series I o this test program, due to maximum displaement o the roller system, only SW1 and SW5 reahedδ.8. The peak lateral load and dutility at peak load on positive and negative sides o loading yles were alulated and are shown in Table 4.1. The slabs strengthened with shear bolts reahed higher dutility at peak loads. For speimen in Group 1, the dutility at positive peak load o speimen SW1 (without shear bolts) is δ + peak = 1.78, while SW (4-row bolts) reahed its δ + peak o.36 (inrease o 33%), and SW3 (6-row bolts) reahed its δ + peak o.5 (inrease o 6%). Similarly, or speimens in Group, the dutility at positive peak load o speimen SW5 (without shear bolts) is 111

128 δ + peak = 1.81, while SW4 (6-row bolts) reahed its δ + peak peak negative load also showed similar results. o.31 (inreased 7.6%). Drit dutility at For post peak load dutility µ. 95, omparing to speimen SW1, speimen SW and SW3 obtained inrease o 36.% and 84.4% respetively in negative drit diretion. In Group II, speimen SW4 obtained 3% inrease ompared with speimen SW5. () Method II In this method, the yield drit ratio δ yield is taken rom experimental observations as the drit ratio when the lexural rebar irst reah yielding. Table 4. gives the tested irst yield drit ratios o speimens SW1~SW5 and the dutilities deined by Method II. It is ound that onrete slabs strengthened with shear bolts attained irst lexural rebar yielding earlier than those without shear bolts. The drit dutilities o the speimens with bolts are muh larger than those o speimens without bolts. In Group I, speimen SW and SW3 ahieved 17% and 15% inrease in µ peak respetively omparing with SW1; in Group II, speimen SW4 obtained 78% inrease in µ peak and + 141% inrease in µ peak omparing with SW5. As or inrease in post peak drit dutility, speimen SW and SW3 ahieved 188% and 58% inrease in µ.95, respetively omparing with SW1; speimen SW4 obtained 19% inrease in µ.95 omparing with SW5. From the trend o bakbone urves in Figure 4.3, it an be inerred that inrease in µ. 8 would be even larger i it ould be reahed in the tests. Figure 4.1 Deinition o dutility 11

129 4..5 Strains in Shear Bolts Strain data were measured or shear bolts, in both lateral loading diretion (diretion 1) and in transverse diretion (diretion ). Shear bolts with strain gauges were numbered as shown in Figure 3.8. An example o the lateral drit ratio versus strain in Bolt #1 o SW is shown in Figure The bakbone (envelope) urves o lateral drit ratio versus bolt strains are shown in Figure 4.1. Generally, in diretion 1, the irst two bolts (bolt #1 and bolt #) lose to the olumn experiened signiiant strains. The third one (bolt #3) had small strain and the ourth bolt (bolts #4) remained non-ative throughout the whole loading history. Bolt #1 and Bolt # were ativated apparently only ater the drit reahed at least 1%. This drit orresponds to lateral load o 35~4 kn, whih is 5~55% o the maximum lateral load attained by the speimen. In diretion 1, only bolt #1 in SW3 yielded. Bolts in diretion experiened larger strains, at the same drit ratios, than their ounterparts in diretion 1. Strains in bolt # 1a o SW3 and SW4 reahed exeeding bolt yield strain ( lose to yield strain ε y = ). Strain in bolt # 1a o SW reahed and respetively, whih is Lateral drit ratio (%) SW 4 row bolts V=11kN Strain in bolt #1 x 1-3 Figure 4.11 Lateral drit ratio versus strain in bolt #1 or speimen SW 113

130 Lateral drit ratio (%) SW: 4 row bolts V=11kN -4 Bolt1 Bolt -6 Bolt3 Bolt Strain in bolts.5 3 x 1-3 Lateral drit ratio (%) SW: 4 row bolts V=11kN -4 Bolt1a Bolta -6 Bolt3a Bolt4a Strain in bolts.5 3 x 1-3 (a) Lateral drit ratio (%) SW3: 6 row bolts V=11kN Bolt1 Bolt Bolt3 Bolt4 Bolt5 Bolt6 Lateral drit ratio (%) SW3: 6 row bolts V=11kN Bolt1a Bolta Bolt3a Bolt4a Bolt5a Bolt6a Strain in bolts.5 3 x Strain in bolts.5 3 x 1-3 Lateral drit ratio (%) SW4: 6-row bolts V=16kN Bolt1 - Bolt -4 Bolt3 Bolt4-6 Bolt5 Bolt Strain in bolts.5 3 x 1-3 (b) Lateral drit ratio (%) SW4: 6-row bolts V=16kN Bolt1a - Bolta -4 Bolt3a Bolt4a -6 Bolt5a Bolt6a Strain in bolts.5 3 x 1-3 () Figure 4.1 Lateral drit ratio versus strain in eah bolt o the three speimens SW, SW3, and SW4 (a) Speimen SW; (b) Speimen SW3; () Speimen SW4 114

131 4..6 Flexural Reinorement Strains A total o 16 strain gages were attahed to reinoring bars and embedded in the onrete slab. The layout o strain gauges in the reinorements is shown in Figure Figure 4.14 ~ Figure 4.18 shows lateral drit ratio versus strains at loation d in rebar #1 in speimen SW1 to SW5, respetively. Rebar #1 passed through the olumn in speimens SW1 to SW3. Loation d was 1 mm away rom the olumn edge. In Figure 4.14 to Figure 4.18, the urves on the let side are the lateral drit ratio versus strain throughout the wholes testing proess. The graphs on the right side provide extrated response beore irst rebar yielding. The yield strains were determined using the yield strength o the rebar and the elasti modulus o steel bar ( E = GPa ). The yield s strain o the irst bath o rebars (in SW1-SW5, and SW7) was ; the yield strain o the seond bath o rebar (in SW6, SW8, and SW9) was bakbones urves together or the ive speimens SW1~SW5 (Series I) Figure 4.19(a), (b) show the Rebar #5 A B a 5b C L a b Rebar #5 a b d C L Rebar #1 Rebar # LC a b d D C L C Rebar #1 435 Rebar # (a) 115

132 Rebar #4 A B a a b a b b d C L Rebar #3 13 Rebar #4 C L a C L b d D - C L + (Lateral drit diretion o top olumn) C Rebar #3 (b) Figure 4.13 Stain gauge positions on the reinorement o speimens SW1 ~ SW5 and SW9 (a) Strain gauge loations on bottom reinorement mat (in test); (b) Strain gauge loations on bottom reinorement mat (in test) Lateral drit ratio (%) SW1: No bolts V=11kN Lateral drit ratio (%) SW1: No bolts V=11kN Strain in loation "d" o Rebar #1 (x1-3 ) (a) Strain in loation "d" o Rebar #1 (x1-3 ) (b) Figure 4.14 Lateral drit ratio versus strain at loation d o Rebar #1 in speimen SW1 (a) Response during ull testing sequene; (b) Response until irst yielding 116

133 Lateral drit ratio (%) SW: 4-row bolts V=11kN Strain in loation "d" o Rebar #1 (x1-3 ) Lateral drit ratio (%) SW: 4-row bolts V=11kN Strain in loation "d" o Rebar #1 (x1-3 ) (a) (b) Figure 4.15 Lateral drit ratio versus strain at loation d o Rebar #1 in speimen SW (a) Response during ull testing sequene; (b) Response until irst yielding Lateral drit ratio (%) SW3: 6 row bolts V=11kN Lateral drit ratio (%) SW3: 6 row bolts V=11kN Strain in loation "d" o Rebar #1 (x1-3 ) (a) Strain in loation "d" o Rebar #1 (x1-3 ) (b) Figure 4.16 Lateral drit ratio versus strain at loation d o Rebar #1 in speimen SW3 (a) Response during ull testing sequene; (b) Response until irst yielding 117

134 Lateral drit ratio (%) SW4: 6-row bolts V=16kN Lateral drit ratio (%) SW4: 6-row bolts V=16kN Strain in loation "d" o Rebar #1 (x1-3 ) (a) Strain in loation "d" o Rebar #1 (x1-3 ) (b) Figure 4.17 Lateral drit ratio versus strain at loation d o Rebar #1 in speimen SW4 (a) Response during ull testing sequene; (b) Response until irst yielding Lateral drit ratio (%) SW5 No bolts V=16kN Lateral drit ratio (%) SW5 No bolts V=16kN Strain in loation "d" o Rebar #1 (x1-3 ) (a) Strain in loation "d" o Rebar #1 (x1-3 ) (b) Figure 4.18 Lateral drit ratio versus steel strain at loation d o Rebar #1 in eah speimen o SW5 (a) Response during ull testing sequene; (b) Response until irst yielding 118

135 Lateral drit ratio (%) SW1 SW SW Strain in rebar #1 at "d" Position ( 1-3 ) 8 6 (a) Lateral drit ratio (%) SW4 SW Strain in rebar #1 at "d" Position ( 1-3 ) (b) Figure 4.19 Bakbone urves o lateral drit ratio versus steel strain at loation d o Rebar #1 (a) Group 1: SW1, SW, and SW3; (b) Group : SW4 and SW5 119

136 An example o strain variations along the lexural steel bars is shown in Figure 4., whih shows strains at dierent loations o dierent bars at drit ratio -1.% or all ive speimens. The bar numbers are shown in Figure The drit ratios and loations at irst yielding in the numbered steel bars, or all ive speimens, are summarized in Table 4.3 (the positive and negative sign reer to the diretion o loading). In the ive speimens SW1~SW5, the bottom bar (#1) and the top bar (#3) going through the olumn in diretion 1, yielded irst. In speimen SW1 (without bolts), bar #1 yielded at approximately drit ratio +1.33%, and bar #3 yielded at approximately drit ratio -1.54%. However, bar #3 in speimen SW (with 4-row bolts) reahed irst yielding at -.97% drit ratio; bar #1 in SW3 (with 6-row bolts) reahed irst yield at -.7% drit ratio. This suggests that the lexural rebar in onrete slabs with bolts will sustain more loads and deorm more than those in slabs without bolts. Strain in reinorement ( 1-6 ) Strain in reinorement ( 1-6 ) SW1 SW SW3 SW4 SW5 a Loation b - Column ae Distane o strain gauges(a,b,,d) on Rebar #1 rom olumn enter (m) a Loation SW1 SW SW3 SW4 SW5 b (a) - Column ae Distane o strain gauges(a,b,,d) on Rebar # rom olumn enter (m) (b) d d 1

137 Strain in reinorement ( 1-6 ) a Loation SW1 SW SW3 SW4 SW5 b - Column ae Distane o strain gauges(a,b,,d) on Rebar #3 rom olumn enter (m) Strain on reinorement ( 1-6 ) Strain on reinorement ( 1-6 ) SW1 SW SW3 SW4 SW5 Loation a () - Column ae Distane o strain gauges(a,b) on Rebar #4 rom olumn enter (m) Loation a SW1 SW SW3 SW4 SW5 Loation b (d) Loation b - Column ae Distane o strain gauges(a,b) on Rebar #5 rom olumn enter (m) (e) Figure 4. Strains in dierent loations o eah numbered rebar in speimen SW1~SW5 at -1.% lateral drit ratio (a) Loation a, b, and d o rebar #1; (b) Loation a, b, and d o rebar #; () Loation a, b, and d o rebar #3; (d) Loation a and b o rebar #4; (e) Loation a and b o rebar #5 11 d

138 Table 4.3 Drit ratios at irst yielding o reinoring bars in the ive speimens SW1~SW5 Slab Name Drit ratio at irst yielding Bar #1 Bar # Bar #3 Bar #4 Bar #5 SW % at d +1.84% at d -1.54% at d (No yielding) -3.6% at b SW -1.11% at +1.59% at d -.91% at d +4.56% at a (No yielding) SW3 -.68% at -1.4% at +1.73% at b +3.77% at b +4.47% at a SW % at d +1.5% at d -.96% at d +5.5% at b -6.6% at b SW % at d +1.46% at d +1.4% at (No yielding) +3.7% at b Notes: Positive and negative signs orrespond to loading diretions Loations o strain gauges are shown in Figure 4.13 Based on the presented results, it is visible that beore punhing ailure o slabs without bolts, shear bolts do not inluene the strains in lexural reinorements. This is onsistent with the results related to onnetion stiness, whih also did not depend on the presene o shear reinoring elements Vertial Crak Width As shown in Figure 3.47, in loations L1, L, L3, and L4, the displaement transduers (LVDTs) were set on both top and bottom suraes. The displaement dierene was used as an estimation o opening width (vertial) o inlined rak through slab thikness. Figures 4.1 through Figure 4.5 show all the rak widths in position L1, L, L3, L4 o eah slab under yli horizontal loading. It an be observed that or speimen SW1 and SW5 (no bolts), there was an abrupt rak width inrease at lateral drit +3.%. The two speimens had reahed their peak load just beore. The speimens SW, SW3 and SW4, strengthened with shear bolts, lasted many more yles without sudden rak expansion. The rak width in loation L1 at 1.5%,.%, and 3.% drits are summarized in Table

139 Table 4.4 Crak width at 1.5%,.% and 3.% drit ratio or speimen SW1~SW5 Slab name Crak width (mm) at +1.5% drit ratio at +.% drit ratio at +3.% drit ratio SW1.18 (at -1.5% drit ratio).3 (at -.% drit ratio).7 (at -3.% drit ratio) SW SW SW SW Lateral drit ratio (%) SW Slab rak width at loation "L1" (mm) Lateral drit ratio (%) SW Slab rak width at loation "L3" (mm) Lateral drit ratio (%) SW Slab rak width at loation "L4" (mm) Lateral drit ratio (%) SW Slab rak width at loation "L" (mm) Figure 4.1 Crak width at loations L1, L, L3, and L4 in the slab o SW1 13

140 Lateral drit ratio (%) SW Slab rak width at loation "L1" (mm) Lateral drit ratio (%) SW Slab rak width at loation "L3" (mm) Lateral drit ratio (%) SW Slab rak width at loation "L4" (mm) Lateral drit ratio (%) SW Slab rak width at loation "L" (mm) Figure 4. Crak width at loations L1, L, L3, and L4 in the slab o SW Lateral drit ratio (%) SW Slab rak width at loation "L1" (mm) Lateral drit ratio (%) SW Slab rak width at loation "L3" (mm) Lateral drit ratio (%) SW Slab rak width at loation "L4" (mm) Lateral drit ratio (%) SW Slab rak width at loation "L" (mm) Figure 4.3 Crak width at loations L1, L, L3, and L4 in the slab o SW3 14

141 Lateral drit ratio (%) SW Slab rak width at loation "L1" (mm) Lateral drit ratio (%) SW Slab rak width at loation "L3" (mm) Lateral drit ratio (%) SW Slab rak width at loation "L4" (mm) Lateral drit ratio (%) SW Slab rak width at loation "L" (mm) Figure 4.4 Crak width at loations L1, L, L3, and L4 in the slab o SW4 Lateral drit ratio (%) SW Slab rak width at loation "L1" (mm) Lateral drit ratio (%) SW Slab rak width at loation "L3" (mm) Lateral drit ratio (%) SW Slab rak width at loation "L4" (mm) Lateral drit ratio (%) SW Slab rak width at loation "L" (mm) Figure 4.5 Crak width at loations L1, L, L3, and L4 in the slab o SW5 15

142 Crak measurements show that, beore punhing, all slabs experiened similar initial raks (Table 4.4). The raks inreased rapidly ater punhing o the speimens without bolts. The largest raks were experiened at loation L Craking and Failure Modes o the Speimens Craks on slab suraes started rom orners o the olumn on the tension side, irst on the bottom slab surae (whih was subjeted to tension rom gravity load) and then on top surae. First rak on top o the slab was usually observed at about.6~.75% drit ratio. On bottom suraes, raks irst propagated toward the our slab edges and orners, while on slab top surae, initial raks developed rom olumn orner to the diretion perpendiular to the lateral loading diretion. The inal rak patterns o top and bottom slab suraes or all ive speimens are shown in Figure 4.6. Column inlined rak were irst observed at about 4.~4.5% drit ratios or slabs with shear bolts. For the speimens SW1 and SW5 (without bolts), there were no inlined rak observed in olumn (the slabs ailed at small drits). From the rak pattern and the hysteresis urves, it an be ound that SW1 and SW5 ailed by punhing shear mode; the other three slabs (SW, SW3 and SW4) were subjeted to lexural ailure mode. The three slabs attained the peak lateral load during testing, whih dereased only slightly (by 1%) in the post peak behaviour. SW1 top surae SW1 bottom surae (a) 16

143 SW top surae SW bottom surae (b) SW3 top surae SW3 bottom surae () 17

144 SW4 top surae SW4 bottom surae (d) SW5 top surae SW5 bottom surae (e) Figure 4.6 Final rak pattern on top and bottom surae o eah speimen (a) SW1, (b) SW, () SW3, (d) SW4, and (e) SW5 4.3 Results o Series II This setion introdues the test results o Series II whih inludes speimens SW6 ~ SW9. Speimens SW6, SW7, and SW8 had openings next to the olumn. Speimen SW6 had no shear reinorements. 18

145 Speimen SW7 had an orthogonal pattern o six peripheral rows o bolts. Speimens SW8 and SW9 had a radial layout o steel shear bolts (6-row). Whenever appropriate, omparisons are made with speimens rom Series I. In Series I, three speimens had orthogonal pattern o shear bolts: speimen SW had 4-row shear bolts; speimen SW3 and SW4 had 6-row shear bolts Connetion Moment versus Lateral Drit Ratio Connetion moment is alulated rom the moments o the top and bottom lateral ores multiplied by the distane between them. The distane between the two horizontal hydrauli atuators was 1.5m. The lateral drit ratio was alulated rom the lateral displaement measured by the external string pot divided by the distane between slab-olumn enter and the string pot. Sine top and bottom lateral drit ratios are slightly dierent, the average drit ratio is used herein. Figures 4.7 (a) to (d) show the urves o moment versus lateral drit ratio or speimen SW6 to SW9 respetively. In eah urve, the peak points were marked and linked by a dashed line (bakbone urve). The our bakbone urves are plotted together in Figure 4.8, rom whih it is observed that, among the three speimens with the same openings, SW6 (no bolts) had the minimum moment apaity, 5.8 knm, at negative peak point, while SW7 (orthogonal bolt pattern) reahed knm (8.% inrease) and SW8 (radial bolt pattern) reahed knm (1.6% inrease). Corresponding drits at the negative peak points are: -1.31% (SW6), -.88% (SW7, 1% inrease) and -.77% (SW8, 111.5% inrease) Table 4.5 shows the moments at negative and positive peak points, the yield drit ratio, and drit dutility at peak points and 8% o peak moment in post peak region. As expeted, the speimen SW9, without openings but strengthened with radial pattern o shear bolts, showed highest moment apaity and dutility. Compared with speimen SW8 (with two openings and also strengthened with radial pattern o shear bolts), SW9 s moment apaity was 76-8% larger; its lateral drit ratio at peak moment was % larger; drit dutility at 8% peak load (post peak) inreased by 44-55%. 19

146 Table 4.5 Peak moment and drit dutility (deined by Pan and Moehle, 1989) o speimen SW6~SW9 V Slab name V Peak moment (kn*m) Peak lateral drit ratio at peak moment (%) Yield drit ratio (%) Drit dutility at peak moment µ peak Drit dutility at 95% post peak moment µ.95 Drit dutility at 8% post peak moment µ SW SW SW SW Note: Nominal punhing shear apaity o onrete V ' =. 33 b d (ACI 318-5, in metri units); the perimeter length b o ritial setion o eah speimen (SW6, SW7, and SW8) with openings exluded the opening eeted length Table 4.6 Drit dutility (using tested irst yield rebar strain) o speimen SW6~SW9 Slab name Tested irst yield drit ratio (%) Drit dutility at peak moment µ peak Drit dutility at 95% post peak moment µ. 95 Drit dutility at 8% post peak moment µ SW SW SW SW

147 Moment (kn*m) SW6: No bolts openings V=16kN Lateral drit ratio (%) (a) Moment (kn*m) SW7: 6-row bolts openings V=16kN Lateral drit ratio (%) (b) 131

148 Moment (kn*m) SW8: 6-row bolts (radial) openings V=16kN Lateral drit ratio (%) Moment (kn*m) () SW9: 6-row bolts (radial) No openings V=16kN Lateral drit ratio (%) (d) Figure 4.7 Moment versus lateral drit ratio o speimen SW6~SW9. (a) Speimen SW6; (b) Speimen SW7; () Speimen SW8; (d) Speimen SW9 13

149 Moment (kn*m/drit) SW6 SW7 SW8 SW Lateral drit ratio (%) Figure 4.8 Bakbone urves o moment versus lateral drit ratio or SW6~SW Drit Dutility Drit dutility is deined in setion 4..4, by Method I (Pan and Moehle, 1989) and Method II (using tested irst yield rebar strain). For Series II, the peak lateral moment and dutility (Method I) at peak points on positive and negative sides o loading yles are alulated and shown in Tables 4.5. Dutilities deined by Method II are shown in Table 4.6. For the three slabs with openings, SW6, SW7, and SW8 in Table 4.5, it is observed that the slabs strengthened with steel bolts (SW7 and SW8) show higher dutility deined by Method I than speimen SW6 (no bolts). However, i the dutility is deined by Method II, given in Table 4.6, the strengthened slabs (SW7 and SW8) show even lower dutility than SW6; this is beause the rebar strain reorded or SW6 is not very reasonable as shown in Figure From Figure 4.8, it an be easily determined that speimens SW7 and SW8 obtained apparent higher drit dutilities than speimens SW6. In the ollowing setions, dutilities are also ompared between slabs with and without opening, with or without bolts, and with orthogonal bolt 133

150 layout or radial bolt layout. Generally, slab strengthened with shear bolts had higher dutility at peak loads and at ailure Eet o Openings on Connetion Moment Capaity and Dutility To ind the eet o openings on onnetion moment apaity and dutility, several omparisons are made as presented in this setion. It should be noted that or speimens with openings, the reinorement in diretion 1 (along the lateral ore appliation) was interrupted by the opening. There was no spae in the slab to plae additional bars along the sides o the opening. However, or diretion (normal to lateral loads) the same number o rebars that were ut by the openings weree plaed beside the opening edges (Fig. 3.7): (1) Speimen SW5 (no bolts, no openings) and SW6 (no bolts, two openings) Their moment and drits are shown in Figure 4.9 and Table 4.7. It is ound that the two openings in SW6 result in peak moment derease o 8% (-) or 3% (+) and lateral drit ratio at peak point derease o 5% (-) or 37% (+). From Table 4.7, the dutility o SW5 and SW6, deined by method I (Pan and Moehle, 1989), showed no muh dierene. However, the dutility o speimen SW5 deined using tested irst yield strain in rebar, is muh larger than dutility o SW6 (Table 4.8). For + example, µ.8 is 3.48 or SW5 (no opening), and.4 or SW6 (with two openings). () Speimen SW4 (6-row orthogonal bolts, no openings) and SW7 (6-row orthogonal bolts, two openings) As shown in Figure 4.3 and Table 4.11, similar to ase (1), the two openings lead to a derease o 4% (-) or 37% (+) in peak moment, a derease o 36% (-) or 49% (+) in lateral drit at peak. The drit dutility o SW4 and SW7 is lose i they are deined by Method I (Pan and Moehle, 1989). However, in Table 4.1, their dutilities (deined using tested irst yield drit ratio) are dierent. + Speimen SW4 (no opening, 6-row orthogonal bolts) obtained µ.95 =7.14, and SW7 (two openings, + orthogonal bolts) obtained µ.95 =1.61 only. (3) Speimen SW8 (6-row radial bolts, two openings) and SW9 (6-row radial bolts, no openings) As shown in Figure 4.31 and Table 4.9, ompared with SW9, the peak moment o SW8 dereased 31% and 34%; lateral drit ratio at peak moment dereased 3% and 35%; drit ratio at yield 134

151 dereased 3% and 33%. Dutility (deined by method I) at.8 Peak load dereased 1% and 6%, + but rom Table 4.1, the dutility (method II) o SW9 reahed 7.17 at µ.8, while SW8 only reahed at µ.8. Table 4.7 Comparison o peak moment and drit dutility between SW5 and SW6 Slab name V V Peak moment (kn*m) Peak lateral drit ratio at peak moment (%) Yield drit ratio (%) Drit dutility at peak moment µ peak Drit dutility at 95% peak moment µ.95 Drit dutility at 8% peak moment µ SW SW Table 4.8 Comparison o drit dutility (using tested irst yield drit ratio) between SW5 and SW6 Slab name Tested irst yield drit ratio (%) Drit dutility at peak moment µ peak Drit dutility at 95% post peak moment µ. 95 Drit dutility at 8% post peak moment µ SW SW

152 Table 4.9 Comparison o peak moment and drit dutility between SW7 and SW8 (eet o openings and shear bolts layout patterns) Drit Slab name V V Peak moment (kn*m) Peak lateral drit ratio at peak moment (%) Yield drit ratio (%) Drit dutility at peak moment µ peak Drit dutility at 95% post peak moment µ.95 dutility at 8% post peak moment µ SW SW Table 4.1 Comparison o drit dutility (using tested drit ratio) between SW8 and SW9 Slab name Tested irst yield drit ratio (%) Drit dutility at peak moment µ peak Drit dutility at 95% post peak moment µ. 95 Drit dutility at 8% post peak moment µ SW SW

153 Moment (kn*m/drit) SW5 SW Lateral drit ratio (%) Figure 4.9 Bakbone urves o moment versus lateral drit ratio between speimen SW5 and SW6 Moment (kn*m/drit) SW4 SW Lateral drit ratio (%) Figure 4.3 Bakbone urves o moment versus lateral drit ratio between speimen SW4 and SW7 137

154 Moment (kn*m/drit) SW8 SW Lateral drit ratio (%) () Figure 4.31 Comparison o bakbone urves o moment versus lateral drit ratio between speimen SW8 and SW9 Moment (kn*m/drit) SW4 SW Lateral drit ratio (%) Figure 4.3 Bakbone urves o moment versus lateral drit ratio or SW4 and SW9 138

155 Table 4.11 Comparison o peak moment and drit dutility between SW4 and SW7, SW4 and SW9 (eet o openings and shear bolts layout patterns) Slab name V V Peak moment (kn*m) Peak lateral drit ratio at peak moment (%) Yield drit ratio (%) Drit dutility at peak moment µ peak Drit dutility at 95% peak moment µ.95 Drit dutility at 8% peak moment µ SW SW SW Table 4.1 Comparison o drit dutility (using tested irst yield drit ratio) in SW4, SW7, and SW9 Slab name Tested irst yield drit ratio (%) Drit dutility at peak moment µ peak Drit dutility at 95% post peak moment µ. 95 Drit dutility at 8% post peak moment µ SW SW SW

156 4.3.4 Eet o Shear Bolt layout Pattern on Connetion Moment Capaity and Dutility Shear bolts were installed orthogonally in SW7 and SW4 and in radial pattern in SW8 and SW9. They are ompared as ollows: (1) Speimen SW4 (6-row orthogonal bolts, no openings) and SW9 (6-row radial bolts, no openings) From Figure 4.3 and Table 4.11, it is ound that, ompared with SW4, speimen SW9 had a % derease in negative peak moment and 5% inrease in positive peak point, a derease o 1% and 7% in lateral drits at peak points, a 3% inrease in dutility (Pan and Moehle, 1989) at negative peak moment and a 6.7% dutility (method I) derease at positive peak points. The overall behaviour o both speimens was almost idential. However, omparing dutilities deined by method II (using tested irst yield rebar strain), speimen SW4 (orthogonal bolt pattern) has better dutile behaviour + than speimen SW9 (radial bolt pattern). For example, rom Table 4.1, µ.95 is 7.14 or SW4 and 5.49 or SW9. () Speimen SW7 (6-row orthogonal bolts, two openings) and SW8 (6-row radial bolts, two openings). From Figure 4.8 and Table 4.13, it is observed that SW8 had an inrease o 1% and 1% in peak moments but 4% and 6% derease in lateral drits at peak points, 8% and 13% dutility (Method I, Pan and Moehle, 1989) derease at peak points and % and 1% dutility (Method I) derease at.8 peak load (post peak). Comparison o dutilities deined using Method II shows also + speimen SW7 has better dutile behaviour. For example, in Table 4.14, µ.8 is.5 or SW7 but only 1.3 or SW8 (36% less) Connetion Stiness Based on urves o moment versus drit ratio, peak-to-peak stiness o eah yle was alulated or every speimen. Figure 4.33 shows the peak-peak stiness versus lateral drit ratio o SW6, SW7 and SW8. Figure 4.34 shows the peak-peak stiness o speimen SW5 and SW9. Stiness at small drit yles (.5% drit) are displayed in Figure In general, the onnetion stiness dereased quikly during the repeated yles until.75% drit ratio. The stiness dereased ater eah repeated moment yle; in every three suessive same drit yles, the stiness dropped about 1.5 times more in the seond yle than it did in the third one. Small yles also showed a dereasing trend in stiness. 14

157 Table 4.13 Comparison o peak moment and drit dutility between SW7 and SW8 (eet o openings and shear bolts layout patterns) Slab name V V Peak moment (kn*m) Peak lateral drit ratio at peak moment (%) Yield drit ratio (%) Drit dutility at peak moment µ peak Drit dutility at 95% post peak moment µ.95 Drit dutility at 8% post peak moment µ SW SW Table 4.14 Comparison o drit dutility (using tested drit ratio) in SW7 and SW8 Slab name Tested irst yield drit ratio (%) Drit dutility at peak moment µ peak Drit dutility at 95% post peak moment µ. 95 Drit dutility at 8% post peak moment µ SW SW Comparing stiness o the three speimens with openings, SW6, SW7 and SW8, we an ind that speimen SW6 (without shear bolts) had stiness very similar to SW7 and SW8 but showed more rapid stiness derease ater 1.% drit ratio. By omparison between SW5 and SW9, it is ound the stiness o SW5 (without shear bolts) derease quikly ater drit ratio.5% when it ailed in punhing. Generally, shear bolts had little inluene on the stiness o the onnetions beore punhing ailures ourred in speimens without shear bolts. 141

158 Peak-to-peak Stiness (kn*m) /drit ratio) SW6 SW7 SW Lateral drit ratio (%) Figure 4.33 Moment peak-to-peak stiness versus drit ratio o speimen SW6, SW7, SW8 Peak-to-peak stiness (kn*m) /drit ratio) SW5 SW Lateral drit ratio (%) Figure 4.34 Moment peak-to-peak stiness versus drit ratio o speimen SW5 and SW9 14

159 Peak-to-peak stiness o small yles (kn*m/drit ratio) SW5 SW6 SW7 SW8 SW9 V=16kN, no bolts V=16kN, no bolts, two openings V=16kN, 6-row bolts(orth.), two openings V=16kN, 6-row bolts(radiate), two openings V=16kN, 6-row bolts(radiate), no openings Lateral drit ratio beore small yles (%) Figure 4.35 Peak-to-peak stiness o small drit yles o SW5 ~ SW Strains in Shear Bolts For slab SW7, a total o twelve strain data were measured on six bolts along and transverse to the loading diretion. For slab SW8 strengthened with 6-row radial bolts, strains were measured on bolts: six in lateral loading diretion, six in diretion perpendiular to lateral load, and six in diagonal diretion. Bolts with strains gages are numbered as in Figure 3.9. Strains in Bolts #1a o slab SW7 versus lateral drit diretion are shown in Figure Figure 4.37 to Figure 4.39 show the bakbone urves o lateral drit ratio versus strain on bolts or speimen SW7, SW8, and SW9. These igures demonstrate that shear bolts in the transverse diretion show higher tension strains than those in the lateral loading diretion. In the lateral loading diretion, the 4 th and 5 th row shear bolts, ar rom the olumn ae, had very small tension strains. Only the 1 st row shear bolts in the diretion transverse to the lateral loading diretion yielded at very large drit ratios. 143

160 6 Horizontal drit ratio (%) SW7: 6-row bolts openings V=16kN Strain in Bolt #1a x 1-3 Figure 4.36 Figure 15 Horizontal load versus strain in bolt #1a o SW7. Lateral drit ratio (%) SW7: 6-row bolts openings V=16kN Bolt1 Bolt Bolt3 Bolt4 Bolt5 Bolt Strain in bolts x 1-3 Lateral drit ratio (%) SW7: 6-row bolts openings V=16kN Bolt1a Bolta Bolt3a Bolt4a Bolt5a Bolt6a Strain in bolts x 1-3 Figure 4.37 Bakbone urves o lateral drit ratio versus strain in eah bolt o speimens SW7 144

161 Lateral drit ratio (%) Bolt1 Bolt Bolt3 Bolt4 Bolt5 Bolt6 - SW8:radiate -4 6-row bolts -6 openings V=16kN Strain in bolts x 1-3 Lateral drit ratio (%) Bolt1a Bolta Bolt3a Bolt4a Bolt5a Bolt6a SW Strain in bolts x 1-3 Lateral drit ratio (%) Bolt1b Boltb Bolt3b Bolt4b Bolt5b Bolt6b SW Strain in bolts x 1-3 Figure 4.38 Bakbone urves o lateral drit ratio versus strain in eah bolt o speimens SW8 145

162 Lateral drit ratio (%) SW9: radiate 6-row bolts No openings V=16kN Bolt1 Bolt Bolt3 Bolt4 Bolt5 Bolt Strain in bolts x 1-3 Lateral drit ratio (%) Bolt1a Bolta Bolt3a -.5 Bolt4a -5 Bolt5a Bolt6a -7.5 SW Strain in bolts x 1-3 Lateral drit ratio (%) Bolt1b Boltb Bolt3b Bolt4b Bolt5b Bolt6b SW Strain in bolts x 1-3 Figure 4.39 Bakbone urves o lateral drit ratio versus strain in eah bolt o speimens SW Strains in Flexural Reinorements A number o strain gages were attahed to lexural rebar and embedded in onrete in eah slab. The numbering and loations o them are shown in Figure 4.4. For eah speimen, strains are shown in Figure 4.41 to Figure 4.44 or speiied loations on rebars lose to the olumn. Strain gauge readings at dierent loations in eah rebar are drawn in Figure 4.45 or drit ratio o 1.15%. It an be seen that only rebar in SW5, going through the olumn in the diretion o lateral loading, has yielded at drit ratio o -1.15%. 146

163 Rebar #5 A B a b Rebar #5 C L b a C L b d Rebar #1 LC b d Rebar # D C L C Rebar #4 A B C L b a a b Rebar #4 b d LC Rebar #3 C L b d Rebar #3 D C 357 LC - + (Lateral drit diretion o top olumn) Figure 4.4 Strain gauges layout in speimens SW6, SW7, and SW8 (a) Strain gauge loations on bottom reinorement mat; (b) Strain gauge loations on top reinorement mat 147

164 Lateral drit ratio (%) SW6: No bolts openings V=16kN Strain in loation "d" o Rebar #1 (x1-3 ) (a) Lateral drit ratio (%) SW6: No bolts openings V=16kN Strain in loation "d" o Rebar #1 (x1-3 ) (b) Figure 4.41 Lateral drit ratio versus strain at loation d o Rebar #1 in speimen SW6 (a) Response during the ull testing sequene, (b) Response until yielding 8 4 Lateral drit ratio (%) SW7: 6-row bolts openings V=16kN Strain in loation "" o Rebar #1 (x1-3 ) Lateral drit ratio (%) SW7: 6-row bolts openings V=16kN Strain in loation "" o Rebar #1 (x1-3 ) (a) (b) Figure 4.4 Lateral drit ratio versus strain at loation o Rebar #1 in speimen SW7 (a) Response during the ull testing sequene, (b) Response until yielding 148

165 8 4 Lateral drit ratio (%) SW8: 6-row bolts (radial) openings V=16kN Lateral drit ratio (%) SW8: 6-row bolts (radial) openings V=16kN Strain in loation "" o Rebar #1 (x1-3 ) (a) Strain in loation "" o Rebar #1 (x1-3 ) (b) Figure 4.43 Lateral drit ratio versus strain at loation o Rebar #1 in speimen SW8 (a) Response during the ull testing sequene, (b) Response until yielding Lateral drit ratio (%) SW9: 6-row bolts (radial) No openings V=16kN Strain in loation "" o Rebar #1 (x1-3 ) Lateral drit ratio (%) SW9: 6-row bolts (radial) No openings V=16kN Strain in loation "" o Rebar #1 (x1-3 ) (a) (b) Figure 4.44 Lateral drit ratio versus strain at loation o Rebar #1 in speimen SW9 (a) Response during the ull testing sequene, (b) Response until yielding 149

166 Strain in reinorement (miro strain) Strain in reinorement (miro strain) Strain in reinorement (miro strain) Loation b SW5-1 SW6 SW7 - SW8 Column SW9 ae Distane o strain gauges (b,,d) on rebar #1 rom olumn enter(m) Loation a SW5 SW6 SW7 SW8 SW9 (a) Loation b - Column ae Distane o strain gauges (b,,d) on rebar #5 rom olumn enter(m) SW5 SW6 SW7 SW8 SW9 b Loation (b) - Column ae Distane o strain gauges (b,,d) on rebar #3 rom olumn enter(m) () d d 15

167 Strain in reinorement (miro strain) Loation a SW5 SW6 SW7 SW8 SW9 Loation b - Column ae Distane o strain gauges (a, b) on rebar #4 rom olumn enter(m) (d) Figure 4.45 Strains in dierent loations o eah numbered rebar in speimen SW5~SW9 at -1.15% lateral drit ratio (a) Strain in loation b, and d o rebar #1; (b) Strain in loation a, b on rebar #5; () Strain in loation b,, and d on rebar #3; (d) Strain in loation a and b on rebar # Estimation o Vertial Crak Width As shown in Figure 3.47, in loation L1, L, L3, and L4, displaement transduers were plaed on both top and bottom suraes o the slabs. The displaement dierenes are used as estimates o slab opening width through slab thikness. Figure 4.46 Figure 4.49 show all the rak widths in position L1, L, L3, and L4 o eah slab under yli horizontal loading. I the rak width is negative in the igures, it is either due to errors in testing or rupture o onrete slab underneath the transduers. Table 4.15 shows rak width o speimen SW6, SW7, SW8, and SW9 at lateral drit o 1.5%,.%, and 3.%. From the rak igures, it an be ound that rak width in the slab is wider in L1 (lose to olumn side) and L3 (lose to the olumn orners) than those in L and L4. For slabs with openings, the rak widths at 3% drit are large beause they all reahed peak load beore 3% drit ratio. The speimens without bolts (SW6) had wider rak width than those strengthened with shear bolts (SW7, SW8) ater % drit. Speimen SW9 (without openings) had smaller rak width at 3% drit than SW6~SW8 beause it had not reahed its peak load yet. 151

168 Table 4.15 Crak width at 1.5%,.% and 3.% drit ratio or speimen SW6~SW9 Slab name Crak width (mm) at +1.5% drit ratio at +.% drit ratio at +3.% drit ratio SW SW SW SW Lateral drit ratio (%) SW Slab rak width at loation "L1" (mm) Lateral drit ratio (%) SW Slab rak width at loation "L3" (mm) Lateral drit ratio (%) SW Slab rak width at loation "L4" (mm) Lateral drit ratio (%) SW Slab rak width at loation "L" (mm) Figure 4.46 Crak width at loations L1, L, L3, and L4 in the slab o SW6 15

169 Lateral drit ratio (%) SW Slab rak width at loation "L1" (mm) Lateral drit ratio (%) SW Slab rak width at loation "L3" (mm) Lateral drit ratio (%) SW Slab rak width at loation "L4" (mm) Lateral drit ratio (%) SW Slab rak width at loation "L" (mm) Figure 4.47 Crak width at loations L1, L, L3, and L4 in the slab o SW7 Lateral drit ratio (%) SW Slab rak width at loation "L1" (mm) Lateral drit ratio (%) SW Slab rak width at loation "L3" (mm) Lateral drit ratio (%) SW Slab rak width at loation "L4" (mm) Lateral drit ratio (%) SW Slab rak width at loation "L" (mm) Figure 4.48 Crak width at loations L1, L, L3, and L4 in the slab o SW8 153

170 Lateral drit ratio (%) SW Slab rak width at loation "L1" (mm) Lateral drit ratio (%) SW Slab rak width at loation "L3" (mm) Lateral drit ratio (%) SW Slab rak width at loation "L4" (mm) Lateral drit ratio (%) SW Slab rak width at loation "L" (mm) Figure 4.49 Crak width at loations L1, L, L3, and L4 in the slab o SW Craking and Failure Mode o the Speimens Craks on slabs started rom the orners o olumns on the tension side, irst at the bottom slab surae and then on top surae. First rak usually was observed at about.6~.75% drit ratio. On bottom surae, raks irst propagated toward the slab edge and orners, while on slab top surae, initial raks developed rom olumn orner to the diretion perpendiular to the lateral loading diretion. The inal rak patterns o top and bottom slab suraes or all speimens are shown in Figure 4.5. From the rak pattern and the hysterosis urves, it an be ound that SW5 and SW6 ailed by punhing shear mode; the other two, SW7 and SW8 were subjeted to lexural ailure mode. 154

171 SW 6 top view SW 6 bottom view SW7 top view SW7 bottom view 155

172 SW8 top view SW8 bottom view SW9 top view SW9 bottom view Figure 4.5 Crak pattern (inal) o top and bottom suraes o speimen SW6~SW9 4.4 Comparison o Testing Results with the Building Codes o ACI318-5, CSA A3.3-4 and Euroode (4) The nominal moment apaity or eah speimen was alulated using the applied gravity load and the material strengths. The design ormulae o building odes, ACI318-5, CSA A3.3-4, and Euroode (4) were used. The alulated nominal moment and the peak moment measured in the test or eah speimen are ompared in Table

173 As introdued in Setion.5, the Amerian ode ACI318-5 provides ormulae or punhing shear design o two-way slab under gravity load and unbalaned onnetion moment. The shear stress on the ritial setion due to external moment and vertial load an be alulated by equation (-34). In this researh, the moment was applied in one diretion (along x diretion) only, thus equation (-34) an be written into ollowing equation (4-1). The design shear strength v r is alulated by equation (4-). where v V γ M e v = + (4-1) bd J x φ v = ( V + V ) (4-) r s bd vr v V is the atored vertial load, V, reinorement respetively, (4-3) V s are nominal resistane ores rom onrete and shear M is the atored unbalaned moment o the onnetion, b is the perimeter length o the ritial setion, d is the eetive thikness o the slab, γ v =.4, J x is the analogy o polar moment o inertia about the moment axis. φ is the strength redution ator ( φ =.75 or shear). Solving equations (4-1), (4-), (4-3) results in the value o a atored moment M : J x φ V M = ( Vs + V ) γ ve bd bd (4-4) For omparison with the test, resistane atorφ, is taken as unity, and V is replaed by the vertial onstant load V in the experiments ( V = 11 kn, or16 kn ), then the nominal unbalaned moment M an be omputed as in equation (4-5), whih an be ompared with the experimental results. J x 1 V M = ( Vs + V ) γ ve bd bd ACI318-5 has no speial provisions or headed shear studs or shear bolts. It provides provisions or shear reinorements o in the orm o stirrups (wires and bars) and shear head (steel shapes). For a (4-5) 157

174 slab with stirrups (wires and bars), the nominal shear resistane ore V.17b d ' = (metri), and shear resistane s where V rom the shear reinorements is V V rom onrete is Avs is the setion area o all shear reinorements around one peripherial setion, A d vs yv s =, s yv is the yield strength o the shear reinorement (taken as MPa), s is the radial spaing o shear reinorements. The sum o shear ore rom both onrete and shear reinorements ( V + V ) must s be no more than '.5b d. Sine there are openings in SW6, SW7 and SW8, the setional area o ritial setion is redued due to the openings. Canadian ode CSA A3.3-4 adopts similar equations to those o ACI318-5 or punhing shear design. It has equivalent provisions or slabs with stirrups: nominal shear ore V rom onrete is V.19b d ' = and nominal shear resistane s V rom the stirrups is V s A d vs yv = ; the total o s these two nominal ores must be no more than '.55b d. The dierene in the ators in ACI and CSA odes omes rom the dierene in the saety ators in the two odes. CSA A3.3-4 provides partiular lauses or design o headed shear studs, in whih the nominal shear ore V rom onrete is V =.8b d, and the sum o the nominal shear ores rom ' onrete and shear reinorements shall be no more than '.75b d. These values are larger than those or stirrups. Moreover, aording to Clause in CSA A3.3-4, or slabs with headed shear reinorements under seismi loading, the atored gravity shear stress v g shall satisy the ollowing ormula (4-6). v V R λφ φ A ' s vs yv g = E.5(.8 ) + bd bs (4-6) For this researh, A vs b s yv is given or eah speimen. Setting the material reduing ators φ, φ to s unity, the nominal allowed maximum gravity load Va 1 an be alulated as 158

175 A ' vs yv Va 1 RE.5(.8 ) + bd b s (4-7) where R E is deined in equation (-47), Avs is the area o shear reinorements, yv is the yield strength o the shear reinorement, s is the radial spaing, b is the ritial setion length, d is the eetive slab thikness. Clause o CSA A3.3-4 also speiies the allowable maximum gravity load or seismi slabs without shear reinorements. v V = R v (4-8) g E bd where v is deined in equations in (-3). From equation (4-8), the allowable maximum gravity load or a seismi slab without shear reinorement is V = b d R (4-9) ' a ( ) E (.38 ) Aording to Euroode (4), Clause (3) and (1), design moment M an be alulated by equating the shear resistane v r o equation (-43) and the shear stress v in equation (-4) due to external load V and unbalaned moment M. d 1 V W1d M =.75v + 1.5( ) Asw ywde ( )sinα sr u1d u1d γ (4-1) v.18 (1 )(1 ρ ρ ) 1/3 = + k x y (4-11) γ d = 5 +.5d (4-1) ywde ywd where d is the eetive depth o slab, s r is the radial spaing o shear reinorements, A sw is the ross setion area o shear reinorements o eah periphery row, u 1 is the length o the basi ontrol 159

176 setion, γ =.6 or square olumn, W u1 1 = edl, e is the distane o dl to the moment axis, α is the angle between the reinorement and the slab plane, γ = 1.5 or persistent onrete, k is the harateristi ylinder ompressive strength (8-day), ρ, ρ are the lexural reinoring ratios o the x y slab in two orthogonal diretions, ywd is the design yield strength o the shear reinorement. To obtain the nominal moment M rom equation (4-1) ~ (4-1), let the partial ator or onrete be γ = 1. ; use the ollowing relation between ' and k proposed by Reinek (1999) (Gardner, 5); and replae V by vertial onstant load V applied in the tests. k = 1.6 (MPa) (4-13) ' Thus, there is ollowing equation (4-14) or the nominal moment, in whih all parameters are speiied as or equation (4-1). d 1 V W1d M =.75v + 1.5( ) Asw ywde ( )sinα sr u1d u1d γ (4-14) v.18 1 d ' = (1 + ) 1( 1.6) x y ρ ρ 1/3 (4-15) All the alulated and measured moments or the speimens were shown in Table 4.9. The maximum allowable gravity loads are also presented or seismi slabs with or without shear reinorements. For slabs strengthened with shear bolts, ACI318-5 provisions give smaller nominal values than the CSA A3.3-4, sine ACI318-5 provisions used above were mainly or stirrups and wires. The Euroode (4) gives too large nominal results, even larger than the measured peak moments, whih is not reasonable. CSA A3.3-4 is the best to predit the nominal moment apaity, but or slabs with openings or with shear reinorements, the predited values are smaller than the tested peak moments. 16

177 Table 4.16 Measured peak moments and the predited nominal moments using odes o ACI318-5, Speimen name Measured peak moment (kn*m) Nominal moment predited by ACI318-5 (kn*m) Euroode (4) and CSA A3.3-4 Nominal moment predited by Euroode (4) (kn*m) Nominal moment predited by CSA A3.3-4 (kn*m) Gravity load V applied in the tests (kn) Gravity load ratio V V Nominal Max. allowed gravity load V by CSA a1 or seismi slabs with shear bolts (kn) Nominal Max. allowed gravity load V by CSA a or seismi slabs without shear bolts (kn) SW N/A 7.9 SW SW SW SW N/A 8.4 SW N/A 76.4 SW SW SW V Note: 1. Gravity load ratios V were alulated using ' V =.33b d (ACI 318-5, in Metri units).. Nominal Maximum allowed gravity load V a1 and V a were alulated assuming allowed lateral drit ratio δ i = % in CSA A3.3-4 Clause This variation among dierent odes in alulation o nominal moment is mainly aused by the ollowing reasons: (1) The material strength redution ators in dierent odes are dierent; in eah ode, these ators are alibrated with their orresponding load ators and load ombination ators. In Table 4.16, the nominal moment apaities are alulated negleting the material and strength redution ators only. () The ode preditions, or slabs without shear bolts, over a wide range o slab thiknesses. However, test results vary with speimen thikness. Aording to Bazant and Cao (1987) and Choi et al. (7), punhing shear strength dereases as slab thiknesses inrease. Thereore, the predited 161

178 nominal moments using odes, or the speimens SW1, SW5, and SW6 (without shear bolts), are muh lower than maximum moments measured. 16

179 Chapter 5 Design o Steel Shear Bolts and Conrete Slab with Shear Bolts This hapter onsists o three parts. First, in Setion 5.1, the design o steel shear bolts is introdued, whih inludes the determination o bolt head thikness, head area and bolt stem diameter. Seond, setion 5. gives suggestions on how to design retroit o lat onrete slabs using shear bolts. This setion analyzes slab shear resistane and provides guidane regarding the layout o the shear bolts. Third, suggestions are given or onstrution methods during retroit using shear bolts. 5.1 Design o Steel Shear Bolts A steel shear bolt onsists o a bolt stem, a head at one end, and a washer and nut at the other end. The washer and the head must be designed or adequate thikness and area. The work involves design o the head thikness, the head area, and their relation to the bolt stem strength. The size o the stem is determined based on slab strength onsiderations. The general proedure to determine the shear bolts or onrete retroitting is: (1) to determine the shear bolts layout and bolt head area aording to the slab thikness, onrete strength, and steel strength o the bolts; () to determine bolt stem diameter and heat thikness Thikness o the Bolt Head The bolt head thikness was analyzed using the elasti thin plate theory and the inite element method. It an be determined using bolt stem diameter and the hole diameter. These are explained in two ollowing subsetions Determination o Bolt Head Thikness using Elasti Thin Plate Theory The bolt head and the bolt stem an be onsidered as an axisymmetri elasti body. The bolt head is assumed to be a irular thin plate. The round stem applies an evenly distributed irular load at the enter o the head. The head diameter is R. The diameter o the bolt stem is r, and the drilled hole in the onrete slab or the bolts has a diameter o R. The load rom the bolts stem is q whih is equal to the yield stress. The head is assumed to be simply supported on the onrete slab surae. 163

180 The bolt and bolt head are shown in Figure 5.1. The internal ore onventions or an axisymmetri slie element are shown in Figure 5.. Figure 5.1 Shear bolt and bolt head M θr M r M θ M rθ Figure 5. Axisymmetri element and its internal ores 164

181 Using elasti thin plate theory, one an obtain the internal ore equations as ollowing. M r = ( M ) x θ = w w = D( + µ ) x y θ = w 1 w 1 w = D[ + µ ( + )] r r r r θ (5-1) w w M = ( M ) = D( + µ ) y x θ y θ = θ = 1 1 ( w w D ) w = + + µ r r r x θ (5-) w M rθ = Mθr = ( M xy ) θ = = D(1 µ )( ) θ = x y (5-3) 1 w 1 w = D(1 µ )( ) r r θ r θ Sine q is symmetri around z axis, deormation plane o the irular plate is also symmetri about z axis, w is only the untion o r, not θ, thereore M = M = ( M ) = (5-4) rθ θr xy θ = Qr = ( Qx ) θ = = D( w) θ = = D w x r 1 Qθ = ( Qy ) θ = = D( w) θ = = D w y r θ (5-5) (5-6) w 1 w 1 w r r r r θ w = + + The stresses in the plate are 1M σ r r = 3 z (5-7) t 165

182 1Mθ σ θ = 3 z t (5-8) 1M rθ τ rθ = τθ r = 3 z = t (5-9) 6Qr t τ rz = ( z ) 3 t 4 (5-1) 6Qθ t τ θ z = ( z ) 3 t 4 (5-11) σ = 1 z z z q( ) (1 ) t t (5-1) The maximum stresses are M r ( σ r ) t = ( σ r ) t = 6 z= z= t (5-13) Mθ ( σθ ) t = ( σ ) t 6 z θ = = z= t (5-14) τ rθ = τ = (5-15) θ r 3Qr ( τ rz ) z= = t (5-16) 3Qθ ( τ θ z ) z= = t (5-17) ( σ ) = t = (5-18) z q z At the bottom point o the plate, sine τ rz =, τθ z =, σ z =, σ r and σ θ beome the prinipal stresses. Aording to Von Mises Criterion, we have σ = σ + σ σ σ = ys 1 1 σ + σ σ σ (5-19) r θ where σ ys is the yield stress o the steel. Substituting equation 5-19, we get 36M r 36Mθ 36M rmθ σ ys r θ ( σ ),( σ θ ) r z= t z= t (Equation 5-13, 5-14) into the + = (5-) t t t By rearranging this equation, we obtain: 166

183 36 4 ( r θ r θ ) σ ys t = M + M M M (5-1) The bolt head is onneted to the bolt stem. Thereore only stresses in the plate around the stem are o interest. Based on the equations rom W.D. Pilkey s Handbook (Page 11), equations o the internal ores o the irular plate under entered irular distributed load q are: ν 4 M r = qr (3 + ν )(1 α ) qr (3 ν β )(1 α ) 4(1 ν ) β lnα α (5-) 1 ν 4 1 (1 3 )(1 ) 4(1 ) ln 1 + ν + β α + + ν β α Mθ = qr 3 ν (1 3 ν ) α qr α (5-3) 16 + (1 ν )(1 β ) 1 β 1 Qr = qr ( α ) qrα (5-4) α where R is the radius o the irular head plate (radius o the hole drilled in the onrete slab sine the head is assumed to be simply supported at the edge), r is the radius o the loading area on the head (irular bolt stem area attahed to the head), r α =, R r β =. R Figure 5.3 shows bolt head thikness versus net hole learane and ratio r / R or 3/8 (9.5mm) diameter bolts whih were used in this program. Figure 5.4 shows bolt head thikness versus net hole learane and ratio r / R or 1/ (1.7mm) diameter bolts whih were used previously or edge onnetion. Figure 5.5 gives the head thikness at the bolt stem edge versus hole radius or three type o bolts: diameter 4.76mm, 6.35mm, 7.94mm bolts. Figure 5.6 shows the ombined graph o normalized oordinates. The x axis is the normalized by the distane rom the bolt edge to the hole edge: x, and y axis is the ratio o head thikness over the bolt stem diameter: R(1 β ) t r. The relation urves are drawn or dierent β values. Figure 5.6 an be used or steel shear bolt design. The maximum thikness at the stem, or x = should be.9 to 1.r or typial drilled holes. The thikness an be redued with the distane rom the stem. 167

184 Figure 5.3 Bolt head thikness versus net hole learane and ratio r / R or 3/8 diameter bolts 168

185 Figure 5.4 Bolt head thikness versus net hole learane and ratio r / R or 1/ diameter bolts Figure 5.5 Head thikness at the bolt stem edge versus hole radius 169

186 Figure 5.6 Normalized bolt head thikness versus normalized distane rom bolt stem (or all stem diameters) Determination o Bolt Head Thikness using Finite Element Method In order to hek the results aording to thik plate theory, eight-node isoparametri inite element (Figure.5.7) was used to analyze the bolt head or the bolt o 3/8 diameter (R=9.5mm). The hole r diameter ( r ) is 6.75mm and β = =. 67. This element is based on the Mindlin thik plate R assumptions: 1) The plate deletion is small; ) The line perpendiular to the mid plane beore deormation remains straight but not neessary normal to the mid plane ater deormation; 3) The stress perpendiular to the mid plane an be negleted (Figure.5.7). The displaements w, θ, θ are expressed as x y 17

187 171 x x y y w w w x w y θ φ θ φ = + + (5-5) where, x y φ φ denote the average shear deormation. Figure 5.7 Mid-thik plate setion deormation The shape untions o this type element are ) )(1 (1 1 ), ( ) )(1 )(1 (1 4 1 ), ( 1 η ξ η ξ η ξ η ξ η ξ = + + = N N (5-6) ) )(1 (1 1 ), ( ) 1 )( )(1 (1 4 1 ), ( 4 3 ξ η η ξ η ξ η ξ η ξ + = + + = N N

188 17 ) )(1 (1 1 ), ( ) 1 )( )(1 (1 4 1 ), ( 6 5 η ξ η ξ η ξ η ξ η ξ + = = N N ) )(1 (1 1 ), ( ) 1 )( )(1 (1 4 1 ), ( 8 7 η ξ η ξ η ξ η ξ η ξ = + + = N N To analyze one quarter o the steel bolt head (evenly distributed thikness), eight-node isoparametri plate element (Figure 5.8) is used. Figure 5.8 Eight-node isoparametri plate element The geometri oordinates are expressed as: = = i i i i y x N y x 8 1 (5-7) The quadrant is disretized into eleven elements as shown in Figure 5.9. ABE area represents a quadrant o the bolt stem; BE is the edge o the bolt, and CF is orresponding to the edge o the drilled hole in the onrete slab. CDGF area is supported by the onrete slab surae. In the FE model, the vertial displaement on the hole edge CF are restrained. The alulated our Gauss point internal ores o element and 4 are as ollows.

189 Figure 5.9 Finite element mesh or a quadrant Figure 5.1 Gauss point numbering o element and 4 G.P. X-COORD. Y-COORD. X-MOMENT Y-MOMENT XY-MOMENT XZ-S.FORCE YZ-S.FORCE ELEMENT NO.= E+4.991E E E E E E E E E E E E E E E+4.371E E E E+3 173

190 ELEMENT NO.= E+4.588E E E E E+3.745E E E E E E E E E E+3.49E E E E+3 The moments at stem edge BE are alulated assuming that the average o the two adjaent elements represent the atual moments: M = ( ) / = N * mm r M = ( ) / = θ N * mm Using Von Mises Criterion (Equation 5.19) and Equation 5-1, the required thikness is t = 5.3 mm. This thikness orresponds well with the thikness alulated using thin plate theory whih is in this ase equal to 5.mm (Figure 5.3) Determination o Bolt Head Area The CSA A3.3-4 requires that the head area o the headed shear stud shall be at least ten times the stud stem area. This is not suitable or the shear bolts. Sine the headed studs are embedded in the onrete slab, part o the ore in the stud stem may ome rom bond between the stem and the onrete. Also, there is no spae (hole) between onrete and the stem. The main onsideration or the bolt head area is to hek the bearing resistane o the onrete under the bolt head. In the Canadian strutural ode CSA A3.3-4, Clause speiies that the atored ' bearing resistane o the onrete an be taken as.85φ A1, and when the supporting surae is wider than the loaded area, the resistane an be multiplied by a magniying ator o up to, where φ is the material strength reduing ator or onrete, A 1 is the loaded area. Thus, maximum nominal onrete resistane o ' is the onrete ompressive strength, and 1.7 alulation. Assuming the bolt stem yields at ailure and equating the yield load resistane F n, the ollowing equation an be obtained. ' A 1 was used in this F bolt and the bearing F bolt = F (5-8) n F = π r (5-9) bolt yv 174

191 F n ' ' r = 1.7φ π ( R R ) = 1.7φ π ( R ) (5-3) β The bolt head area A is π R and the stem setion area A b is π r. R and r are the radii o the head and bolt stem setion respetively. R is the hole diameter. yv is the yield strength o the bolts. r β = A. From equations (5-8) ~ (5-3), the ratio o R A ( R = ) was derived. r b A A b = 1 yv + ' 1.7φ β (5-31) (a) 175

192 Ratio o bolt head area over bolt stem setion area Conrete ompressive strength '(MPa) (bolt diameter = 3/8") (b) Figure 5.11 Ratio o bolt head area over bolt stem setion area versus onrete ompressive strength (a) A versus ' ( yv varies, β =. 75 ); (b) A b A versus ' ( β varies, A b yv = 37MPa ) In Equation 5-31, the ratio o the bolt head area over the bolt stem area is related to three parameters: the ratio ( β ) o bolt stem radius r over the radius o the hole, the yield strength o the bolts yv, and the onrete strength '. Figure 5.11a gives the ratio o bolt head area over bolt stem setion area or a 3/8 (9.5mm) diameter bolt. The ratio varies with the onrete strength and the steel bolt yield strength. For low strength onrete, the ratio is higher. Steel bolts with higher yield strength need bigger head areas. The eet o bolt diameter is very small. For onservative design, the bolt head area should be 16 times the bolt stem setion area or bolts o maximum 5 MPa yield strength. Figure 5.11b shows the ratio o bolt head area over bolt stem setion area or a 3/8 diameter bolt 176

193 with dierent ratio o β. For the same shear bolt stem and onrete strength, when β inrease, the bolt head area will derease Stresses in a Conrete Slab Caused by a Shear Bolt Linear inite element analysis was arried out or alulation o the onrete stress distribution under the shear bolts. It was done to determine the inluene o the onining stress rom the head on onrete underneath the head. Assume the head and the washer o eah shear bolt are applying uniorm pressure on top and bottom suraes o the onrete slab (Figure 5.1 a). The resultant o the pressure on onrete is assumed to be equal to the yield ore in the bolt stem. Pressure q = MPa produed by yield ore was used herein (Figure 5.1 b). Sine the bolt heads are small ompared with the slab area, the stresses aused by bolt heads were only aeting a small viinity zone. The stresses in the slab rom the eet o bolts are also symmetri about the slab mid-surae. Thereore, the stresses aused by eah bolt in the onrete slab an be alulated using axisymmetri analysis. Let the longitudinal axis o the bolt stem be the axis o symmetry, and a vertial slab setion ABCD is isolated as show in Figure Sine the slab is symmetri in geometry and loading about the slab mid plane, the length o ABCD is 4mm (whih is twie the slab thikness) and its height is 6 mm. The bottom side AD is restrained in y diretion only. (The displaement o the mid plane o the onrete slab remains zero under equal pressure rom bottom and top surae). The other boundaries are ree. (a) Bolt and slab 177

194 (b) Pressure on the slab by bolt head Figure 5.1 Pressure on onrete slab suraes by bolts head and washer Figure 5.13 Axisymmetri analysis o the onrete slab around the bolts hole From the results, it is ound that the loations beyond r = 15 mm rom the bolt hole enter are aeted by very small stresses (lose to zero). Thereore it is assumed that the aeted distane is 15mm (1.5h). Figure 5.14 shows stress σ x, σ y, σ z, τ xy distribution along top line BC o the setion. Figure 5.15 shows stress σ x, σ y, σ z, τ xy distribution along bottom line AD o the setion. 178

195 (a) Stress σ x, ( Sx ) distribution along top line BC (b) Stress σ y, (Sy) distribution along top line BC 179

196 () Stress σ z, (Sz) distribution along top line BC (d) Stress τ xy distribution along top line BC Figure 5.14 Stress distribution along the top line BC 18

197 (a) Stress σ x, ( Sx ) distribution along bottom line AD (b) Stress σ y, (Sy) distribution along bottom line AD 181

198 Sy(Mpa) x () Stress σ z, (Sz) distribution along bottom line AD (d) Stress τ xy, (Sxy) distribution along bottom line AD Figure 5.15 Stress distribution along the top line AD 18

199 5. Design o Steel Shear Bolts or Conrete Flat Slab Strengthening This setion desribes the design o the lat onrete slab strengthened with steel shear bolts, inluding the strength o the onrete slab and layout o the shear bolts in the slab Strength o the Retroitted Slab The punhing shear strength o the slab strengthened with shear bolts an be alulated using similar equations and provisions o CSA A3.3-4 or headed shear studs. However, the ritial setion area is redued due to drilled holes along the perimeter o the ritial setion. Thus the eetive ritial ' setion perimeter length b is equal to ( b n * d ), where b is the ritial setion ( d / rom olumn perimeter) length. n is the number o holes drilled along ritial setion perimeter. d is the diameter o the drilled holes. In design, the shear bolt tension apaity (along bolt stem) an be taken as the smaller o the ollowing three ases: (1) The yielding ore ( F t ) o the bolt stem at the root o thread grooves, F = * A (5-3) t yv n where yv is the yield (tension) strength o the shear bolts, A n is the setion area o the bolt stem exluding threads. () The yield shear ore ( F s1 ) by threads on the bolt stem. (3) The yield shear ore ( F s ) by threads on the nut. Case () and ase (3) an be onsidered together. Aording to Barrett s Fastener Design Manual (199), the pullout load P o the bolt against the nut an be alulated using the ollowing equation: where P πd L m v = (5-33) 3 d m is the pith diameter o the threads, L is the length o thread engagement, shear strength (stress) o the two materials o the bolt and nut. Consequently, the punhing shear strength v r (stress) o the retroitted slab is 183 v is the smaller

200 vr = v + vs (5-34) where v is the atored shear resistane rom onrete, vs is the atored shear resistane rom shear reinorements. v s φsnfb = (5-35) ' b s where φ =. 85 is redution ator o steel strength. n is the number o shear bolts in a periphery s row parallel to olumn perimeter. radial spaing o the shear reinorement. resistane rom onrete in the shear reinored zone is: F b is the smaller result o equation (5-3) and (5-33). s is the ' b is the eetive ritial setion perimeter length. Shear v = '.8λφ Maximum shear resistane o setion with shear reinorement should satisy the ollowing equation: v ' r max. 75λφ Seismi requirements o the onrete slabs strengthened with shear bolts an ollow CSA (Clause 1.1.3), i.e. equation (-47) and (-51) in Chapter, but eetive ritial setion and shear strength o bolt threads are neessary to be used. 5.. Shear Bolt Layout in the Flat Conrete Slab Shear bolts layout requires determination o a radial pattern or an orthogonal pattern in the onrete slab. This setion ompares the two patterns and disusses the number o bolt rows and spaing between the bolts in radial and tangential diretion. Radial diretion is deined as away rom the olumn ( S, S 1 in Figure 5.16). Tangential diretion is along the perimeters o shear bolts and parallel to the olumn sides ( S in Figure 5.16) Comparison o Radial and Orthogonal Layout Patterns o Shear Bolts As desribed in setion 4.3., or slab without openings, the slab (SW9) strengthened with radial bolts layout pattern showed lose apaity and dutility to that o the slab (SW4) with orthogonal bolt pattern. For slab with openings, the slab (SW8) with radial bolts showed some moment apaity 184

201 inrease, however, SW8 had higher onrete strength (5MPa) than SW7 (4MPa). Moreover, SW8 showed some derease in dutility. Thereore, or the lat slab olumn struture, i the lateral loading diretion is parallel to the two main orthogonal diretions, just as the ase in the experiments, the orthogonal bolt layout would be preerable. However, in real situations lateral load omes rom an arbitrary diretion and possibly a more uniorm bolt distribution around the olumn might be preerable. For strengthening method, it is reommended here to ombine the two patterns, i.e. the orthogonal pattern plus an extra line o bolts in radial diretion in eah quadrant. Due to intererene rom the lexural reinorement in the onrete slab, the radial bolts may not orm a straight line. A simple rule an be ollowed that the shear bolts pattern should be symmetri about the two main axes o the olumn Bolt Spaing in Radial Diretion Let s assume the shear bolts are orthogonally installed as shown in Figure To deide the bolts spaing S and S 1, the ator onsidered here is the punhing shear rak inside the slab. Aording to the observations, the angles o punhing shear raks in the slab without shear reinorements range rom 5~35 degree. Also, Regan (1974) pointed out that the ritial shear raks, at a onnetion without shear reinorement, extend rom heads at about d/4 to d/ rom the olumn aes, to tails situated where the raks interset the main tensile steel at distanes o d or more rom the olumn (Figure 5.17) The shear reinorement should be plaed aross the rak in the middle o the slab. For speimens strengthened with shear bolts, the spaing S 1 need speial onsiderations, whih are explained later in this setion. S S1 S Figure 5.16 Spaing S, S 1 and S o shear bolts ( S, S 1 - radial diretion spaing; S - tangential diretion spaing ) 185

202 Figure 5.17 Punhing shear raks in the onrete slab without shear reinorement For slabs with shear reinorements, the shear raks in the zone with shear reinorement have steeper inlined angle ( θ 1 ) than that o raks in the non-shear reinored zones ( θ ). Dilger and Ghali (198) ound that in the onrete slab with headed shear studs, angle θ 1 an be about 4 5 degree, while angle θ is usually around 3 degrees (Figure 5.18). Figure 5.18 Shear rak angles in slab zones with or without shear studs The tests done in this researh showed similar rak angles to those mentioned above. The three speimens without shear bolts, SW1, SW5, and SW6, were subjeted to sudden punhing shear 186

203 ailure. The distanes between the olumn enter and the rak tails were measured, whih are shown in Figure 5.19(a), (b) and (). The heads o all shear raks were assumed at the olumn aes. Thereore, the rak angles an be estimated using the slab thikness and the distanes o the rak tails to the olumn aes. For example, or SW1 (Figure 5.19(a)), the tail distanes to olumn aes are 313mm, 31mm, 35mm, and 47mm. The slab thikness is 1mm. Thus the orresponding angles are 1 o, 1.1 o, 18.9 o, and 14.3 o. The largest angle or SW5 (Figure 5.19(b)) is 5 o ; the largest angle or SW6 is 33. o. SW6 is the speimen with openings as shown in Figure 5.19(). In reality, these angles are likely to be slightly larger than the above alulations suggest due to spalling o the onrete over whih likely made the presented length measurements larger. (a) SW1 187

204 (b) SW5 () SW6 Figure 5.19 Distane o punhing shear rak tail to the olumn enter 188

205 The slabs with openings provide an opportunity to observe the rak angles on the opening edges. The three slabs with openings were SW6 (without shear bolts), SW7 and SW8 (with shear bolts). Figure 5. shows the raks o SW6 at the opening ae parallel to the lateral load diretion. It is ound the main raks are at angles o about 31 degree, whih orresponds well with the angle estimated rom surae measurements. In Figure 5.1, the slab (SW8) was strengthened with shear bolts around the openings and in the radial layout. The angles o the main inlined raks are about 45 5 degree. In Figure 5., the slab (SW7), strengthened by shear bolts but in orthogonal pattern, has rak angles smaller than 45. The reason an be the at that the shear bolts were not as lose to the openings as in SW8. It also shows that the rak angle in shear reinored slabs varies rom o 5, depending on the loation o the bolts. All these main shear raks started rom the olumn aes. Thereore, the distane between the irst shear bolts and the olumn ae, S, should ross the inlined rak. Thereore, assuming bolts ross the rak in the middle: For θ 1 = 4 o, S =.5*d/(tan For θ 1 = 5 o, S =.5*d/(tan o 4 ) =.59 d. o 5 ) =.4d. Considering the beneiial eet (oninement) o the bolt head it an be reommended that S =.45d ~. 55d rom the olumn ae. This also overs the at that the drilling o the holes requires ertain distane rom the olumn whih is at least 45mm. (a) (b) Figure 5. Shear raks in the opening edges o the slab (SW6) without shear bolts 189

206 (a) (b) Figure 5.1 Shear raks in the opening edges o the slab (SW8) with shear bolts o radial layout (a) (b) Figure 5. Shear raks in the opening edges o the slab (SW7) with shear bolts o orthogonal layout Two approahes were used to theoretially determine the spaing S1 between shear bolt rows. (1) Crak Angle Approah 19