DOCTORAL THESIS

END ANCHORAGE AT SIMPLE SUPPORTSIN

REINFORCED CONCRETE

Rizgar Salih Amin (BSc. MSc.)

A thesis submitted in partial fulfillment of therequirements of London South Bank University

for the degree of Doctor of Philosophy

November 2009

i

CONTENTS

Acknowledgement…………………………………………………….. vNotation………………………………………………………………. vi

List of Tables………………………………………………………... x

List of Figures……………………………………………………….. xiii

List of Appendixes xx

Abstract……………………………………………………………… xix

Chapter One Introduction…………………………………… 1

Chapter Two Literature Review ……………………………. 6

2.1 Introduction …………………………………………………... 6 2.2 Code of practice recommendations …………………………….. 9

2.2.1 BS 8110 : 2005………………………………………….. 9 2.2.2 EC2 : 2004………………………………………….. 11

2.2.3 ACI 318 : 2005………………………………………….. 15

2.2.4 Commentary……………………………………………... 19

2.3 Straight Anchorages without Transverse Pressure……………… 40 2.3.1 Tepfers (1973) …………………………………………… 40 2.3.2 Orangun et al. (1977) …………………………..………… 42 2.3.3 Cairns/Cairns and Jones (1973) ……………………..…… 43 2.3.4 Morita and Fujii (1982) …………………………………. 49 2.3.5 Darwin et al. (1992)……………………………………… 50 2.3.6 Nielsen (1999)……………………………………………. 52

2.4 Straight Anchorages with Transverse Pressure…………………. 60 2.4.1 Untrauer and Henry (1965)……………………………... 60 2.4.2 Robins and Standish (1982, 1984) ……………………... 61 2.4.3 Navaratnarajah and Speare (1986 , 1987)………………. 63 2.4.4 Nagatomo and Kaku (1992) ……………………………. 64 2.4.5 Batayneh (1993) ………………………………………... 66 2.4.6 Cairns and Jones (1995) ………………………………... 69 2.4.7 Rathkjen (1972) ………………………………………... 70 2.4.8 Jensen (1982) ………………………………………….. 72 2.4.9 Ghaghei (1990) ………………………………………… 75 2.4.10 Regan (1997) …………………………………………… 77 2.4.11 Nielsen (1999)…………………………………………... 81 2.4.12 Magnusson (2001) ……………………………………... 86 2.4.13 Cleland et al. (2001) …………………………………… 100

2.5 Commentary and Conclusions on Straight Anchrages 104

ii

2.6 Anchorages with End Hooks and Bends………………………... 120 2.6.1 Mylrea (1928)…………………………………………...... 120 2.6.2 Muller (1968)………………………………....................... 122 2.6.3 Hribar and Vasko (1969)……………………………......... 125 2.6.4 Minor and Jirsa (1975)……………………………............. 131 2.6.5 Marques and Jirsa ( 1975)………………………………… 135 2.6.6 Schiessl (1982)……………………………………………. 140 2.6.7 Soroushian et al. (1988)………………………………....... 143 2.6.8 Gulparvar (1997)……………………………………........ 146 2.6.9 Summary and Conclusions……………………………….. 149

Chapter Three : Comparisons between Experimental

and Calculated Bond Strengths………

152

3.1 Introduction……………………………………………………… 152 3.2 Anchorages without transverse pressure ……………………….. 152 3.3 Anchorages with transverse pressure …………………………… 165

Chapter Four : Tests of End Anchorages at Simple

Supports …………………………………

174

4.1 Test programme……………………………………………….. 174 4.2 Test specimens………………………………………………... 176 4.3 Materials and Fabrication…………………………………….. 183 4.3.1 Concrete ……………………………………………….. 183 4.3.2 Reinforcement…………………………………………. 183 4.3.3 Bar deformations………………………………………. 184 4.3.4 Fabrication……………………………………………... 184 4.4 Instrumentation and testing……………………………………. 184 4.5 Test results…………………………………………………….. 187 4.5.1 Ultimate loads…………………………………………... 187 4.6Cracking and modes of failure………………………………….. 197 4.6.1 Beams with straight bars………………………………... 197 4.6.2 Beams with bent and hooked bars……………………… 201 4.7 Overview of test results for anchorage strength……………… 203 4.7.1 straight bars…………………………………………….. 203 4.7.2 and Bent bars………………………………... 207 4.8 Strain measurements……………………………………………. 210 4.8.1 Strains at straight ends…………………………………. 210 4.8.2 Strains in and Bends……………………........ 211 4.9 Slip……………………………………………………………… 219 4.9.1 Straight bar specimens …………………………………. 219

iii

4.9.2 and bent bar specimens………………………... 223 Chapter Five : Development of Expressions for Anchorage

Strengths

228

5.1 Straight anchorages without transverse pressure or transverse reinforcement …………………………………………………

228

5.1.1 Introduction……………………………………….. 228 5.1.2 Treatment of anchorage length……………………... 229 5.1.3 Treatment of cover and bar spacing …………….…. 234 5.1.4 Effects of relative rib areas and bar sizes………….. 244 5.2 Straight Anchorages with Transverse Pressure ………………… 257 5.2.1 Introduction…………………………………………… 257 5.2.2 Influence of transverse pressure………………………. 258 5.2.3 Treatments of cases of medium to high transverse pressure……………………………………

261

5.2.4 Treatment of cases with low transverse pressure …… 268

5.2.5 Overall comparison of experimental and calculated

bond strengths for anchorages without transverse

reinforcement ………………………………………..

269

5.3 End anchorages with transverse reinforcement ……………….. 278 5.4 Applications of the proposed equations to other tests………... 287 5.4.1 Beam tests by Magnusson …………………………. 287 5.4.2 Pull-out tests by Untrauer and Henry ………………. 293 5.4.3 Pull-out tests by Batayneh………………................... 295 5.5 Specimens with 900 and 1800 bends at simple supports………... 399 5.5.1 Available test data………………..…………………. 399 5.5.2 Evaluation of design recommendations…………….. 301 5.5.3 A new approach to evaluate capacities of end

anchorages by bends at simple supports ……………...

311

5.5.4 Treatment of bent anchorages if is unknown…… 317

5.5.5 Conclusion ………………………………………….. 319

Chapter Six : Conclusions and Recommendations .………... 320 6.1 Conclusion……………………………………………………. 320 6.2 Proposals for future research ………………………………… 324 6.2.1 Straight anchorages…………………………………... 324 6.2.2 Bent bars……………………………………………… 329

References…………………………………………………………… 333

Appendixes………………………………………………………….. 340

iv

ACKNOWLEDGEMENTS

I would like to express my deepest gratitude to Professor Paul Regan my PhD supervisor and mentor. Thank you for giving me the opportunity to develop my research under your direction and for your wholehearted support, guidance, friendship , patience and attention as the writing of this thesis progressed . Thank you for understanding.

I also wish to acknowledge and thank my director of research Dr. Ivana Kraincanic , Prof. M.Nazha ( Head of Engineering Systems Department) and the previous directors Dr. M.Datoo , Prof.M.Gunn and Prof. A. Parsa for their assistance during this research.

I am most grateful to Prof. A.Parsa (my previous director) and Prof. N.Alford (ex.Pro.Dean) for their insistence and seriousness towards my research and my second phase of the experimental works would not have been possible without their support

I would particularly like to acknowledge the following staff, Chung Lam (Research Degrees Administrator),Daren James(Course Director of Built Environment Extended Degree),Concrete laboratory technicians, all FSBE’s IT technicians and Perry library staff.

My sincere gratitude to my students Fatlum Azemi (undergraduate ) and Vassili kaffas (postgraduate) for their help and assistance volunteered by them during the experimental works in laboratory and special gratitude to my best friends Khalat Hussain and Naser Buzhalla for their supports during this research.

I would like to extend my sincere thanks to my directors at work during this research all of S.Lane, J.Lane and other directors in TWS, P.Cowton and other staff in MacBains Cooper and to P.Hudgson , C.Mate, M.Regan and other staff in Trigram Partnership for enabling me to work flexibility to support my research. Their assistances and positive encouragements have undoubtedly contributed to this work.

I am indebted to my brothers: Kak Muhemmed (Head of my family) for your consistency and wisdom, Homer who supported me find the mental strength to focus on completing this research,

A big Thank you goes out to my sisters and brothers : Paneer, Fittum and Dr.Taha and their partners Payman Muhammed and Dr.Taha Hamakhan for their encouragements and for giving me confidence throughout this research.

I dedicate this work to my darlings my nephews and nieces: Kany, Yadgar, Ahmad, Rast, Rand, Aya and Awan

v

Notation

1. S.I. Units have been used

-Force-Stress-Length ,slip and Deflection -Area

Latin lower case symbols

Dimension perpendicular to the plane of a bend , in BS8110.

or and in EC2 or

effa effective shear span from the centre of the load going to a support to the centre of the support

clear spacing of ribs measured parallel to the bar axis

clear shear span between a concentrated load and a support

width of section or width of tension zoneconcrete cover to reiforcement

clear cover from a main bar to the tension face of a member ( bottom

cover)

design cover= least of , and

next least of , and

end cover to a bend or hook.

lesser and greater of and

clear cover from a main bar to the side face of a member

lesser of and

effective depth of a section

bond stress

bond stress at which a splitting crack reaches a concrete surface

design ultimate bond strength

basic design ultimate bond strength to EC2

characteristic bond strength

ultimate bond stress

calculated bond stress =

vi

(for limits see text)

cylinder crushing strength of concrete (150x300 cylinders) –

for and in

conversions .

design cylinder strength of concrete

characteristic cylinder strength of concrete

tensile strength of concrete

design tensile strength of concrete

cube crushing strength of concrete ( cubes)- in conversions =

cube strength of and cubes

stress in reinforcement

bar stress at the loaded end of an anchorage

yield strength of reinforcement

yield strength of transverse reinforcement in anchorage length

yield strength of shear reinforcement

f calculated bond stress = (for limits

see text)

Overall depth of section

rib height

span

straight bonded lead length of a bent bar over a support

length of curve and tail of a bent bar

effective value of (BS8110)

anchorage length ( bond length)

design anchorage length

effective anchorage length

basic anchorage length (EC2)

inside length of curve in a bent bar

straight length of anchorage subject to transverse pressure

length of tail following a bend

number of anchored main bars

transverse pressure on an anchorage

vii

ultimate value of

internal radius of a bend

clear spacing of anchored main bars

centre to centre spacing of ribs

centre to centre spacing of transverse reinforcement in an anchorage

length

neutral axis depth

horizontal cover measured to the centre of a bar

vertical cover measured to the centre of a bar

z internal lever arm

Latin upper case symbols

area of one main bar

area of one transverse bar in an anchorage length, e.g. one leg of

a stirrup

total area of shear reinforcement in a shear span

Elastic modulus of reinforcement

design ( applied) tensile force in a bar at the start of a bend

bar force developed in the lead length over a support, before a bend

bar force developed in the curve and tail of a bend

value of defined by bond

value of defined by bearing

force in a main bar

design force in main bar, that can be developed by an anchorage

ultimate force in a main bar at the loaded end of an anchorage

total force in shear reinforcement in a shear span

total tensile force in main reinforcement

bending moment

reaction

total tensile force in main reinforcement

shear force

ultimate shear force

viii

Greek symbols

angle between outer face of wedge and axis of bar

EC2 coefficient for the form of the bar

EC2 coefficient for cover

EC2 coefficient for transverse reinforcement

EC2 coefficient for transverse pressure

coefficient for bar size

partial safety factor for materials (concrete)

EC2 coefficient for position/orientation of bar during casting

EC2 coefficient for bar size

internal angle of friction

effectiveness factor for concrete in compression

effectiveness factor for concrete in tension

bearing stress in a bend

design (resistance) value of

characteristic value of

bar diameter (main bar)

List of Tables

Chapter Two

Table 2.1 Parameters included in bond strength design by BS8110 , ACI-318 and EC2……………………………………………………………..

20

Table 2.2 Ratios of from to from ………………………….. 21Table 2.3 Results of comparisons by Darwin et al.…………………………… 51Table 2.4 Summary of actual and predicted bond strengths(Nielsen)………….. 58Table 2.5 Results of beam tests by Batayneh…………………………………. 68

ix

Table 2.6 Data for Rathkjen’s beams without transverse reinforcement…….. 70Table 2.7 Results of eqn.(2.48) for Jensen’s tests…………………………….. 73Table 2.8 Data and results for tests by Ghaghei………………………………. 76Table 2.9 Details and results of tests by Regan……………………………….. 78Table 2.10 Geometry and detailing of the support and shear span( Mgnusson) 88Table 2.11 Results of tests with direct and indirect supports ( Mgnusson) 90Table 2.12 Data from beams with different lengths of support plates

( Mgnusson)…………………………………………………………90

Table 2.13 Ratios of for middle and corner bars………………………............. 91Table 2.14 Results for beams with bars in one layer and two layers………….. 93Table 2.15 Beam-end tests by Magnusson……………………………………... 99Table 2.16 Data for test results plotted in Fig.2.51……………………………. 115Table 2.17 Effect of tail length on bar stresses at slip of ( Hribar and

Vasko)………………………………………………………………

130

Table 2.18 Effect of radius bar of bend on bar stressesat slip of for bars with ( Hribar and Vasko)……………………………….

131

Table 2.19 Summary of data for tests by Marques and Jirsa…………………... 137Table 2.20 Summary of results of tests by Soroushian et al…………………... 144Table 2.21 Ultimate bond stresses at anchorages ( )for Gulparvar's

beams 4 and 6………………………………….................................147

Table 2.22 Results of tests by Gulparvar………………………………............. 148

Chapter ThreeTable 3.1 The effect of the shift rule on for Ferguson and

Thompson tests…………………………………………………….

161

Table 3.2 Summary of statistical analyses of For BS8110,EC2,Darwin et al and Morita and Fujii………………

163

Table 3.3 Data of specimens without transverse reinforcement from literature…………………………………………………………….

165

Table 3.4 Summary of statistical analyses of / for BS8110, EC2, Batayneh and Nielsen

……………………………………………..

173

Chapter FourTable 4.1 Beams Bs details……………………………………........................ 180Table 4.2 Beams Bb details…………………………………………………… 181Table 4.3 Beams Bh details………………………………………………….... 182Table 4.4 Tensile strengths of reinforcement…………………………………. 184Table 4.5 Comparisons of lever arms…………………………………………. 189Table 4.6 Test results, Beams Bs……………………………………………... 191-

192Table 4.7 Test results ,Beams Bb……………………………………………... 193Table 4.8 Test results , Beams Bh…………………………………….............. 194

x

Table 4.9 Summary of test details and results, Beams Bs…………………… 195Table 4.10 Summary of test details and results, Beams Bb…………………… 196

Table 4.11 Summary of test details and results, Beams Bh…………………… 196

Table 4.12 Effect of anchorage length on bond strengths for beams with bonded bars ………………………………………………..…….....

204

Table 4.13 Effect of transverse pressure on bond strengths for beams with bonded bars…………………………………………………………

205

Table 4.14 Data and results for directly comparable beams with and without stirrups………………………………………………………………

206

Table 4.15 Data and results for directly comparable beams with different materials…………………………………………………………….

206

Table 4.16 Summary of results from strain gauges on 900 and 1800 bends……. 217Table 4.17 Data for beams in a 200mm width ………………………………… 221Table 4.18 Data for beams with single bar in a 150mm width

and …………………………………....222

Table 4.19 Beams with two bars in a 125mm width…………………………… 223Table 4.20 Slips at for beams with and bends……………….. 224

Chapter FiveTable 5.1 Results of tests by Yerlici and Ozturan ……………………………. 232Table 5.2 Results of tests by W.S.Atkins ……................................................. 240Table 5.3 Cover parameters at minimum calculated bond strengths ………… 243Table 5.4 Results of tests by Ahlborg and Den Hartigh ……………………… 247Table 5.5 Results of tests by Cairns and Jones of splices of bars…….. 248Table 5.6 Comparisons of experimental and calculated scale effects………… 249Table 5.7 Experimental evidence on limits for ………………… 251

Table 5.8 Summary of statistical analyses of / for cases A,B and C………………………………………………………………………………….

255

Table 5.9 Properties of specimens in Figs 5.21 and 5.22……………………. 257Table 5.10 Summary of data for test groups ………………………………….. 269

Table 5.11Summary of analyses by the proposed equations and existing equations EC2B and Andreasen…………………………………….

276

Table 5.12 Detail of the stirrup system ……………………………………….. 279

Table 5.13 Analysis of specimens with transverse reinforcement……………. 284-285

Table 5.14 Summary of statistical for specimens with two bars each in the bend of a stirrup………………………………………..

286

Table 5.15Results of analysis for anchored bars in end region in NSC and HSC beams by Magnusson…………………………………………

290-291

Table 5.16Summary of ratio for beams by Magnusson

…………292

Table 5.17 Summary of test/calculated ratios for tests by Untrauer and Henry 294Table 5.18 Results of analysis for specimens by Untrauer and Henry

and the proposed method…………………………………………...294

Table 5.19 Summary of and fro specimens with by Batayneh………………………………………………….

294

Table 5.20 Results of analysis for for tests with by 296-

xi

Batayneh……………………………………………………………. 298Table 5.21 Summary of results for for tests with by

Batayneh……………………………………………………………298

Table 5.22 Comparison of test results to prediction by BS8110 ………………. 304Table 5.23 Comparison of test results to prediction by BD 44/95……………... 306Table 5.24 Comparison of test results to prediction by EC2…………………... 308Table 5.25 Summary of mean values for A and B ………………… 309

Table 5.26 Summary of for beams with bonded and unbonded

leads ………………………………………………………………..

310

Table 5.27 Comparison of test to bond resistance calculated by proposals 1,2 and 3 for beams with and bends ………………………….

313

Table 5.28 Summary of mean values for for the proposed methods 314Table 5.29 Bar forces developed in anchorages-comparison between

calculated resistances and forces determined from measured strains 316

Table 5.30 Summary of comparisons of calculated and experimental strengths

of bent anchorages with bonded lengths……………………………

319

Chapter Six

Table 6.1 Results of comparisons in terms of …………………. 321

List of Figures

Chapter Two

Figure 2.1 : Equivalent anchorage length for standard bends and hooks to EC2 ………………………………………………………...

14

Figure 2.2 : Standard (minimum) hooks and bends to ACI-318 …………..

17

Figure 2.3 : Transverse reinforcement details in hooks and bends to ACI-318……………………………………………………………….

18

xii

Figure 2.4 : Design ultimate bond stresses for bars with negligible transverse reinforcement, comparisons of BS810,EC2 and ACI-318………………………………………………………………

24

Figure 2.5 : Effect of stirrups on bar stresses developed by various bond lengths…………………………………………………………...

27

Figure 2.6 : Comparisons of bearing stress limits in BS8110 and

EC2……...

31

Figure 2.7 : Comparisons of from BS8110 and BD 44/95……..……….

32

Figure 2.8 : Design bar stresses calculated by BS8110……………...

……….

35

Figure 2.9 : Comparisons between EC2 and BS8110 for anchorages with

and bends ………………………………………...

39

Figure 2.10 : Splitting pattern types by

Tepfers……………………………….

41

Figure 2.11 : Test arrangement and failure mode for specimen with

by Baldwin and Clark

………………………………

43

Figure 2.12 Forces and stresses in the failure model by

Cairns……………..

44

Figure 2.13 : Polygon of forces on a wedge ……………….…………………

44

Figure 2.14 : Terminology for crescent shaped ribs…………………………..

45

Figure 2.15 : Cairns and Jones - test specimens………………………………

46

Figure 2.16 : Cairns and Jones – influence of relative rib area on bond strength………………………………………………………….

47

Figure 2.17 : Failure patterns of anchored bars(Morita and Fujii)……………

49

Figure 2.18 : Yield Locus, Displacement Directions and Internal Work……..

53

Figure 2.19 : Geometry of a deformed bar……………………………………

53

Figure 2.20: Displacement at failure and internal work in local mechanics …

55

Figure 2.21: Relationships between and by Nielsen………………………. 56Figure 2.22: Failure Mechanisms in

surrounds………………………………57

Figure 2.23: Final results for different failure 58

xiii

mechanism……………………Figure 2.24: Truss model for yielding

stirrups………………………………..59

Figure 2.25 : Untrauer and Henry’s test arrangements………………………...

60

Figure 2.26 : Relationship between the and by Untrauer and Henry……………………………………………………………

61

Figure 2.27 : Robins and Standish’s test arrangements ……………………….

62

Figure 2.28: Navaratnarajah and Speare’s test arrangements…………………

63

Figure 2.29: Nagatomo and Kakus’ test arrangements……………………….

64

Figure 2.30: Typical details of test specimen by Batayneh..............................

66

Figure 2.31: Typical beam test arrangements by Batayneh …………………..

68

Figure 2.32: Rathkjen’s test arrangements……………………………………

70

Figure 2.33 : Relationships between and for Rathkjen’s tests .............................................................................................

71

Figure 2.34: Jensen’s test arrangements……………………………………...

72

Figure 2.35 : Relationships between and for Jensen’s tests 74

Figure 2.36 : Ghaghei’s typical test arrangements……………………………

75

Figure 2.37 : Relationship between the and for Ghaghei’s tests …………………………………………………

76

Figure 2.38 : Test arrangements for Regan’s slabs……………………………

77

Figure 2.39 : Relationship between the and for /bl =7.5 in tests by Regan…………………………………

80

Figure 2.40 : Corner mechanisms with centres of rotation on the side face of beam for Nielsen and Andreasen………………………………

81

Figure 2.41 : The limitation of support pressure by concrete web compression

84

Figure 2.42 : Beam specimens and typical cross section by Magnusson ……

89

Figure 2.43 : Effect of variations of transverse reinforcement and bearing materials(Magnuson)………………………………………………

92

Figure 2.44 : Magnusson’s strut-and-tie model……………………………….

95

Figure 2.45 : Relationship between and (Magnusson)………..

96

Figure 2.46 : Details of beam-end specimens by Magnusson………………...

98

xiv

Figure 2.47 : Local movements at failure……………………………………..

104

Figure 2.48 : Cases of non-polar symmetric restraints………………………...

106

Figure 2.49 : Movements in surrounds at failure according to Nielsen……….

108

Figure 2.50 : Distributions of reactions across widths of supports……………

109

Figure 2.51 : Splitting pattern types by Tepfers……………………………….

110

Figure 2.52 : Comparison of different treatments of the relationship between bond strength and concrete cylinder strength…………………...

114

Figure 2.53 : Comparisons of test results with various formulations for maximum bond strength…………………………………………

116

Figure 2.54 : Mylrea’s test arrangements .

……………………………………

120

Figure 2.55 : Muller’s test arrangements………………………………………

122

Figure 2.56 : Average bond stresses at 0.25mm loaded-end slip tests for series 1,2 and 3 by Hribar and Vasko…………………………...

128

Figure 2.57 : Ultimate bond stresses- tests by Hribar and Vasko……………..

129

Figure 2.58 : Minor and Jirsa’s test arrangements…………………………….

132

Figure 2.59 : Loaded end slips at - tests by Minor and Jirsa 134

Figure 2.60 : Influence of bond length on bond strength in tests by Minor and Jirsa……………………………………………………………..

135

Figure 2.61 : Marques and Jirsa’s test arrangements…………………………

136

Figure 2.62 : Bond length for both bent and straight bar in Schiessl’s approach…………………………………………………………

141

Figure 2.63 : Results of all calculations for ribbed bars in upper and lower position from Schiessl……..

142

Figure 2.64 : Soroushian et al’s test arrangements…………………………….

143

Figure 2.65 : Influence of transverse reinforcement on ultimate strength- testsby Soroushian et al………………………………………………

145

Figure 2.66 : Detailing of beams by Gulparvar ……………………………….

146

xv

Chapter ThreeFigure 3.1 : Specimens and test arrangements

………………………………154-157

Figure 3.2 : Histogram of number of results and some of main variables 158

Figure 3.3 : Relationship between and for predictions by BS8110,EC2,Darwin et al and Morita and Fujii……………

159

Figure 3.4 : Relationship between and for predictions by BS8110,EC2,Darwin et al and Morita and Fujii……………

160

Figure 3.5 : Relationship between and for predictions byBS8110,EC2,Darwin et al and Morita and Fujii………………..

162

Figure 3.6 : Relationships between and …………….

163

Figure 3.7 : Histogram of number of results and some of main variables

for specimens without transverse reinforcement……………….

166

Figure 3.8 : Relationship between and ………… 169

Figure 3.9 : Relationships between and ………… 170

Figure 3.10 : against after relaxation of a limit of……………………………………………………

170

Figure 3.11 : against for Batayneh's eq.3.6…………

171

Figure 3.12 : against for Batayneh's eq.3.7………..

171

Figure 3.13 : Relationships between and ……………. 172

Chapter FourFigure 4.1 : End of the typical

beam…………………………………………175

Figure 4.2 : Series Bs details…………………………………………………

177

Figure 4.3 : Series Bb details…………………………………………………

178

Figure 4.4 : Series Bh details…………………………………………………

179

Figure 4.5 : Slip measurement instrumentation for specimens with straight bars ……………………………………………………………..

185

Figure 4.6 : Slip measurement instrumentation for specimens with 900 and 1800 bends………………………………………………………

185

xvi

Figure 4.7 : Model showing calculation parameters…………………………

187

Figure 4.8 : Crack patterns for beams with straight anchorage…………….

197

Figure 4.9 : Fig(4.9)Effect of transverse pressure on failure cracks.(Beams Bs9 and Bs10)…………….…………………………………

197

Figure 4.10 : Cracking at failure, Beams Bs6, Bs7 and Bs8 without transverse pressure …………………………………………………..

198

Figure 4.11 : Cracking at failure, Bs14 with transverse pressure …………

198

Figure 4.12 : Cracking at failure, Beams Bs31, Bs32, Bs33and Bs34 with closely spaced bars…………………………………………….

199

Figure 4.13 : Cracking at failure, Beams Bs27, Bs28 and Bs29 with

transverse pressure

……………………………………………..

200

Figure 4.14 : Cracking at failure in Beams Bs23 and Bs26 with and without fibre board pads………………….………………………………

200

Figure 4.15 : Cracking at failure, Beams Bb3, Bb10 and Bb15…………...…..

201

Figure 4.16 : Cracking at failure, Beams Bh8 with transverse pressure………

202

Figure 4.17 : Cracking at failure top and side, Beam Bb12 and Bh11………...

202

Figure 4.18 : Relation between and when …………… 203

Figure 4.19 : Relation between and when ………….

203

Figure 4.20 : Influence of radius of bend on the bar stresses developed by and bent anchorages…………..

208

Figure 4.21 : Influence of side cover on the bar stressesdeveloped by and bent anchorages with =2.5….

208

Figure 4.22 : Ratios of strengths of partly debonded anchorages and anchorages fully bonded over supports as functions of the corresponding ratios of bond lengths …………………………

209

Figure 4.23 : Strain gauges on Bs5…………………………………………. 210Figure 4.24 : Load-strain relationships for

Bs5……………………………….210

Figure 4.25 : Strain gauges on 900 and 1800 bends.……………………… 211Figure 4.26 : Force-strain relationships for specimens with 900 bent

bars……212

Figure 4.27 : Force-strain relationships for specimens with 1800 bent bars …

213

Figure 4.28 : Relationships between bond stresses and Load for Bh10-Bh12...

215

xvii

Figure 4.29 : Relationships between bond stresses and Load for Bb12- Bb15……………………………………………………………

216

Figure 4.30 : Relationships between relative bond stress and slipfor beams with , and ……

219

Figure 4.31 : Relationships between relative bond stress and slipfor beams with , and

220

Figure 4.32 : Relationships between relative bond stress and slip for beams with ……………….……………….......

221

Figure 4.33 : Relationships between relative bond stress and slip for beams with ……………………………………..

222

Figure 4.34 : Relationships between relative bond stress and slip for beams with ………………………………….….

223

Figure 4.35 : and slip relationship for bent bars end with and bends………………………………………………

225

Figure 4.36 : Loads at which slips reached ……………………………

226

Chapter Five

Figure 5.1 :/

5.0

mc

against ……230

Figure 5.2 :/ against …..

230

Figure 5.3 : Yerlici and Ozturan’s test arrangements………………………..

232

Figure 5.4 : Relationships between/ and

for Yerlici and Ozturan’s data…………………………………...

233

Figure 5.5 : Relationship between and ( ) for Chamberlin’s tests………………………………………………

235

Figure 5.6 : Relationship between and ( ) for Ferguson and Thompson’s tests…………………………………………..

235

Figure 5.7 : Relation between and ( ) for Batayneh’s tests..............................................................................................

236

xviii

Figure 5.8 : Relation between and ( ) for Kemp and Wilhelm’s tests………………………………………………….

236

Figure 5.9 : Influence of cover on bond strength in tests (for types S and P ) by Batayneh…………………………………………………….

237

Figure 5.10 : Relationship between and 238

Figure 5.11 : Influence of on bond strengths in tests by Ferguson and Thompson and W.S.Atkins……………………………………

239

Figure 5.12 : Influence of on bond strengths in tests by Ferguson and Thompson and W.S.Atkins……………………………………..

239

Figure 5.13 : Arrangement of testing by W.S.Atkins …………………………

240

Figure 5.14 : Results of Chamberlin’s tests plotted against …………. 242Figure 5.15 : Results of tests by Chapman and Shah

…………………………243

Figure 5.16 : Influence of relative rib areas on bond strengths in tests by Darwin and Graham …………………………………………….

245

Figure 5.17 : Results of tests by Ahlborn and Den Hartigh …………………..

246

Figure 5.18 : Influence of bar size on ………………………….

254

Figure 5.19 : Influence of bar size on

………………………….

255

Figure 5.20 : Influence of bar size on …………………………...

255

Figure 5.21 : Conditions at a support producing transverse pressure …............

257

Figure 5.22 : Relationships between and for tests byBatayneh and Ghaghei…………………………………………..

259

Figure 5.23 : Relationships between and for tests byJensen and Rathkjen……………………………………………

260

Figure 5.24 : Test results from Jensen plotted to show values of …………

261

Figure 5.25 : Relationship between and sectional parameters

with …………………………………………………….

263

xix

Figure 5.26 : Relationship between and sectional parameters

with ……………………………………………..

264

Figure 5.27 : Relationship between and sectional parameters

with …………………………………….

265

Figure 5.28 : Relationship between and for Jensen Specimens………………………………………………………

271

Figure 5.29 : Relationship between and for Rathkjen specimens……………………………………………………….

272

Figure 5.30 : Relationship between and for specimens by Ghaghei, Regan and Batayneh………………………………

273

Figure 5.31 : Relationship between and for specimens by Amin ………………………………………………………..

274-275

Figure 5.32 : Typical specimens with transverse reinforcement for series considered……………………………………………………….

280

Figure 5.33 : Relationship between and for Jensen specimens with and without transverse reinforcement…………………………..

281

Figure 5.34 : Relationships between and for specimens with andwithout transverse reinforcement ……………………...………..

282

Figure 5.35 : Beams and typical sections by Magnusson……………………..

287

Figure 5.36 : Elevation and anchorage details for Bb and Bh beams………….

300

Figure 5.37 : Dimensions of bars with ( bends) ends…………...........

302

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List of Appendices

Appendix 1 Results of tests by Shin and Choi used in Fig.2.56……………. 341

Appendix 2

Table A1 Specimens without transverse pressure or transverse reinforcement- summary of data and comparisons with existing expressions for bond strengths ………………………

342

Table A2 Specimens with transverse pressure but without transverse reinforcement- summary of data and comparisons with existing expressions for bond strengths ………………………

348

Appendix 3

Table A3 Bar strains ……………………………………………………. 357Table A4 Load-slip measurements …………………….......................... 359Table A5 Bar forces and bond stresses from strains measured on bent

and hookedbars………………………………………………… 366

Appendix 4Table A6 Specimens without transverse pressure or transverse

reinforcement using proposed equations of ( 5.1 to 5.3)……….370

Table A7 Data for beam-end specimens without transverse reinforcement …………………………………………………

377

Table A8 Comparisons between experimental bond strengths and strengths calculated from equations 5.8 to 5.22 …………….

384

Table A9 Comparison of experimental strengths and strengths calculated (5.24) for beam-end specimens without transverse reinforcement………………………….……………………..

388

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Abstract

This thesis reports research on end anchorage at simple supports of reinforced

concrete members and treats both straight bars and bars with 900 and 1800 bends.

The most significant characteristics of straight anchorages at simple supports are their

generally short lengths and the presence of transverse pressure from the support

reactions. Published work in this area is rather limited. The only major research is that

by Danish authors, working in the field of plasticity, and the only code of practice

recommendations are those of Eurocode 2, which take account of the transverse

pressure but do not consider the effects of the short lengths involved.

Bends and hooks are widely treated in design codes, but their rules appear very

arbitrary and seem to lack published substantiation.

The approach adopted here is essentially empirical.

A data base of results from tests of anchorages without transverse pressure is

assembled and used to evaluate existing expressions for bond strength. An equation

by Darwin, MaCabe , Idun and Schoenekase is found to be the most reliable of those

considered and is modified in the light of the comparison. The most significant

change is that the influence of the ratio of the anchorage length to the bar size is

treated by a multiplying factor , instead of being treated as an additional

resistance independent of concrete strength , cover etc.

In overall terms the modified equation produces a modest improvement in the

correlation between calculated and actual strengths, but the above change and an

alteration to the way in which covers and spacings are treated do improve reliability in

areas which are important for end anchorages.

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Sixty five tests were made on end anchorages in simply supported beams. The bars

had straight anchorages in thirty seven of the tests, 900 bends in thirteen and 1800

hooks in eleven. The main variables were concrete cover, anchorage length,

transverse pressure and internal diameters of bends. The results of these tests, together

with others from the literature are used to develop expressions for anchorage

capacities.

For straight ends the result is a bi-linear relationship between the ultimate bond stress

and the transverse pressure ( ) . For the bond resistance is that of the equation

above and the gradient is 2.0. For higher pressure is 0.4. The correlation

with the 186 test results is with the ratios between experimental and calculated

strengths having a mean of 1.02 and a coefficient of variation of 14.7%. These figures

compare favourably with the 1.94 and 20% for EC2.

For anchorages with terminal bends and hooks , the bar force developed bonded lead

lengths over supports is calculated as for a straight bar with transverse pressure , and

the bond strength in the bend+tail is that for a straight bar without transverse pressure.

The bearing capacity of the lead is calculated as in BD44/95, which takes account of

spread of stress away from the inside of the bend being three-rather than two-

dimensional . The total capacity of an anchorage is the sum of the forces developed by

the lead length and the bend+tail , with the latter taken as the lesser of the values

determined by bearing and bond. All lengths used in the calculations are the real

dimensions and not effective lengths as used in some cases in BS8110 and bearing

stresses are checked in all cases.

For the anchorage failures of bent and hooked bars, all but five of which are from the

present tests the ratios of experimental to calculated strengths have a mean of 1.10

and a coefficient of variation of 15 % which compare with values of 1.60 and 17 %

for BS8110, 1.40 and 18 % for EC2. and 1.59 and 17% for BD44/95 The number

and range of the test results is too limited to properly confirm the reliability of the

present approach , but it does appear to the considerably more reliable than current

xxiii

design methods and avoids the use of fictitious lengths and arbitrary omissions of

checks on bearing stresses .

xxiv