Doctoral Thesis 2009

DOCTORAL THESIS

END ANCHORAGE AT SIMPLE SUPPORTS IN REINFORCED CONCRETE

Rizgar Salih Amin (BSc. MSc.)

A thesis submitted in partial fulfillment of the requirements of London South Bank University for the degree of Doctor of Philosophy

November 2009

i

CONTENTS Acknowledgement…………………………………………………….. Notation………………………………………………………………. List of Tables………………………………………………………... List of Figures……………………………………………………….. List of Appendixes Abstract………………………………………………………………

v vi x xiii xx xix

Chapter One Introduction…………………………………… Chapter Two Literature Review ……………………………. 2.1 Introduction …………………………………………………... 2.2 Code of practice recommendations …………………………….. 2.2.1 BS 8110 : 2005………………………………………….. 2.2.2 EC2 : 2004………………………………………….. 2.2.3 ACI 318 : 2005………………………………………….. 2.2.4 Commentary……………………………………………...

1 6 6 9 9 11 15 19

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

40 40 42 43 49 50 52

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

60 60 61 63 64 66 69 70 72 75 77 81 86 100

2.5 Commentary and Conclusions on Straight Anchrages

104

2.6 Anchorages with End Hooks and Bends………………………... 2.6.1 Mylrea (1928)…………………………………………...... 2.6.2 Muller (1968)……………………………….......................

120 120 122

ii

2.6.3 2.6.4 2.6.5 2.6.6 2.6.7 2.6.8 2.6.9

Hribar and Vasko (1969)……………………………......... Minor and Jirsa (1975)……………………………............. Marques and Jirsa ( 1975)………………………………… Schiessl (1982)……………………………………………. Soroushian et al. (1988)………………………………....... Gulparvar (1997)……………………………………........ Summary and Conclusions………………………………..

Chapter Three : Comparisons between Experimental

125 131 135 140 143 146 149

152

and Calculated Bond Strengths……… 3.1 Introduction……………………………………………………… 3.2 Anchorages without transverse pressure ……………………….. 3.3 Anchorages with transverse pressure ……………………………

Chapter Four : Tests of End Anchorages at Simple

152 152 165 174

Supports ………………………………… 4.1 Test programme……………………………………………….. 4.2 Test specimens………………………………………………... 4.3 Materials and Fabrication…………………………………….. 4.3.1 Concrete ……………………………………………….. 4.3.2 Reinforcement…………………………………………. 4.3.3 Bar deformations………………………………………. 4.3.4 Fabrication……………………………………………... 4.4 Instrumentation and testing……………………………………. 4.5 Test results…………………………………………………….. 4.5.1 Ultimate loads…………………………………………... 4.6Cracking and modes of failure………………………………….. 4.6.1 Beams with straight bars………………………………... 4.6.2 Beams with bent and hooked bars……………………… 4.7 Overview of test results for anchorage strength……………… 4.7.1 straight bars…………………………………………….. 4.7.2 Bent 90  and 180  bars………………………………... 4.8 Strain measurements……………………………………………. 4.8.1 Strains at straight ends…………………………………. 4.8.2 Strains in 90  and 180  Bends……………………........ 4.9 Slip……………………………………………………………… 4.9.1 Straight bar specimens …………………………………. 4.9.2 90  and 180  bent bar specimens………………………...

174 176 183 183 183 184 184 184 187 187 197 197 201 203 203 207

Chapter Five : Development of Expressions for Anchorage

228

210 210 211 219 219 223

iii

Strengths 5.1 Straight anchorages without transverse pressure or transverse reinforcement ………………………………………………… 5.1.1 Introduction……………………………………….. 5.1.2 Treatment of anchorage length……………………... 5.1.3 Treatment of cover and bar spacing …………….…. 5.1.4 Effects of relative rib areas and bar sizes………….. 5.2 Straight Anchorages with Transverse Pressure ………………… 5.2.1 Introduction…………………………………………… 5.2.2 Influence of transverse pressure………………………. 5.2.3 Treatments of cases of medium to high transverse pressure…………………………………… 5.2.4 Treatment of cases with low transverse pressure …… 5.2.5 Overall comparison of experimental and calculated

228 228 229 234 244 257 257 258 261 268 269

bond strengths for anchorages without transverse reinforcement ……………………………………….. 5.3 End anchorages with transverse reinforcement ……………….. 5.4 Applications of the proposed equations to other tests………... 5.4.1 Beam tests by Magnusson …………………………. 5.4.2 Pull-out tests by Untrauer and Henry ………………. 5.4.3 Pull-out tests by Batayneh………………................... 5.5 Specimens with 900 and 1800 bends at simple supports………... 5.5.1 Available test data………………..…………………. 5.5.2 Evaluation of design recommendations…………….. 5.5.3 A new approach to evaluate capacities of end

278 287 287 293 295 399 399 301 311

anchorages by bends at simple supports ……………... 5.5.4 Treatment of bent anchorages if pu is

317

unknown…… 5.5.5 Conclusion …………………………………………..

319

6.1 Conclusion……………………………………………………. 6.2 Proposals for future research ………………………………… 6.2.1 Straight anchorages…………………………………... 6.2.2 Bent bars………………………………………………

320 320 324 324 329

References…………………………………………………………… Appendixes…………………………………………………………..

333 340

Chapter Six : Conclusions and Recommendations .………...

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 iv

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

Notation 1. S.I. Units have been used -Force

kN

v

-Stress -Length ,slip and Deflection -Area

N / mm 2

mm

mm 2

Latin lower case symbols Dimension perpendicular to the plane of a bend , in BS8110. ab = ( c s + ϕ ) or ( s +ϕ) and in EC2 ab = ( c s + ϕ / 2 ) or ( s +ϕ) / 2 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 zone concrete cover to reiforcement clear cover from a main bar to the tension face of a member ( bottom

ab

aeff ar av

b

c

cb cd

cD ce cm , cM cs

cover) design cover= least of cb , c s and s / 2 next least of cb , c s and s / 2 end cover to a bend or hook. lesser and greater of cb and c ′s

f bk f bu

clear cover from a main bar to the side face of a member lesser of c s and s / 2 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

f buo

calculated bond stress =

c ′s d fb f bc f bd f bd

,0

[1 + cd / ϕ ][ 0.37 + 0.025c D / cd ] [10 / ( lb / ϕ ) ] 0.4

fc

f c (for limits see text) cylinder crushing strength of concrete (150x300 mm cylinders) – f c = 0.8 f cu for f cu ≤ 75 N / mm 2 and f c = f cu − 15 N / mm 2 in

f cd f ck f ct

f ctd f cu

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 ( 150 mm cubes)- in conversions f cu = cube strength of 100 mm and 200 mm cubes

fs

stress in reinforcement

vi

f sd fy f yt f yw

f∗ h hr l l1 l2 l 2 ,eff

lb lbd l b ,eff l b , rqd

lc lp

lt

n

p

pu

r

s

sr st

x X y z

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 0 .4 f c (for calculated bond stress = [1.13 + 0.08b / nϕ ] [10 / ( l b / ϕ ) ] 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 l2 (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 ultimate value of p 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 internal lever arm

Latin upper case symbols As Ast Asv Es Fbt

FR1 FR 2 FR 2 b FR 2σ

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 FR 2 defined by bond value of FR 2 defined by bearing

vii

Fs Fsd Fsu Fsv

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

Ft M

R T V Vu

Greek symbols

α

angle between outer face of wedge and axis of bar (1 + cd / ϕ )( 0.932 + 0.0632 c D / cd )

αc

α1 α2

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 =1.8 / f c effectiveness factor for concrete in tension = 0.6 ϕ / lb / f c bearing stress in a bend design (resistance) value of σb characteristic value of σb bar diameter (main bar)

α3 α5 αϕ γ mc

η1 η2 θ

υ

ρ

σb σbd σbk

ϕ

List of Tables Chapter Two Table 2.1 Table 2.2

Parameters included in bond strength design by BS8110 , ACI-318 and EC2…………………………………………………………….. Ratios of f bd from f c to f bd from f ctd

20 21

viii

Table 2.3 Table 2.4 Table 2.5 Table 2.6 Table 2.7 Table 2.8 Table 2.9 Table 2.10 Table 2.11 Table 2.12 Table 2.13 Table 2.14 Table 2.15 Table 2.16 Table 2.17

………………………….. Results of comparisons by Darwin et al.…………………………… Summary of actual and predicted bond strengths(Nielsen)………….. Results of beam tests by Batayneh…………………………………. Data for Rathkjen’s beams without transverse reinforcement…….. Results of eqn.(2.48) for Jensen’s tests…………………………….. Data and results for tests by Ghaghei………………………………. Details and results of tests by Regan……………………………….. Geometry and detailing of the support and shear span( Mgnusson) Results of tests with direct and indirect supports ( Mgnusson) Data from beams with different lengths of support plates ( Mgnusson)………………………………………………………… Ratios of for middle and corner bars………………………............. Results for beams with bars in one layer and two layers………….. Beam-end tests by Magnusson……………………………………... Data for test results plotted in Fig.2.51……………………………. Effect of tail length on bar stresses at slip of 0.2mm ( Hribar and

Vasko)……………………………………………………………… Table 2.18 Effect of radius bar of bend on bar stressesat slip of 0.2mm for bars with lt = 0 ( Hribar and Vasko)………………………………. Table 2.19 Summary of data for tests by Marques and Jirsa…………………... Table 2.20 Summary of results of tests by Soroushian et al…………………... Table 2.21 Ultimate bond stresses at anchorages ( N / mm 2 )for Gulparvar's beams 4 and 6…………………………………................................. Table 2.22 Results of tests by Gulparvar………………………………............. Chapter Three Table 3.1 The effect of the shift rule on ( f bu ,test / f bu , EC 2 ) for Ferguson and Thompson tests……………………………………………………. Table 3.2 Summary of statistical analyses of f bu ,test / f bu ,calc For BS8110,EC2,Darwin et al and Morita and Fujii……………… Table 3.3 Data of specimens without transverse reinforcement from literature……………………………………………………………. Table 3.4

Summary of statistical analyses of f bu ,test / f bu ,calc for BS8110, EC2, Batayneh and Nielsen ……………………………………………..

51 58 68 70 73 76 78 88 90 90 91 93 99 115 130 131 137 144 147 148

161 163 165 173

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

ix

Table 4.7 Table 4.8 Table 4.9 Table 4.10 Table 4.11 Table 4.12 Table 4.13 Table 4.14 Table 4.15 Table 4.16 Table 4.17 Table 4.18 Table 4.19 Table 4.20

Test results ,Beams Bb……………………………………………... Test results , Beams Bh…………………………………….............. Summary of test details and results, Beams Bs…………………… Summary of test details and results, Beams Bb…………………… Summary of test details and results, Beams Bh…………………… Effect of anchorage length on bond strengths for beams with bonded bars ………………………………………………..……..... Effect of transverse pressure on bond strengths for beams with bonded bars………………………………………………………… Data and results for directly comparable beams with and without stirrups……………………………………………………………… Data and results for directly comparable beams with different materials……………………………………………………………. Summary of results from strain gauges on 900 and 1800 bends……. Data for beams in a 200mm width ………………………………… Data for beams with single bar in a 150mm width and cb = 16 mm and c s = 67 mm ………………………………….... Beams with two bars in a 125mm width…………………………… Slips at 0.67 p u for beams with 90  and 180  bends………………..

Chapter Five Table 5.1 Results of tests by Yerlici and Ozturan ……………………………. Table 5.2 Results of tests by W.S.Atkins ……................................................. Table 5.3 Cover parameters at minimum calculated bond strengths ………… Table 5.4 Results of tests by Ahlborg and Den Hartigh ……………………… Results of tests by Cairns and Jones of splices of 20 mm Table 5.5 bars…….. Table 5.6 Comparisons of experimental and calculated scale effects………… Table 5.7 Experimental evidence on limits for f butest / f bucalc ………………… Table 5.8 Summary of statistical analyses of f bu ,test / f bu ,calc for cases A,B and C…………………………………………………………………………………. Table 5.9 Properties of specimens in Figs 5.21 and 5.22……………………. Table 5.10 Summary of data for test groups ………………………………….. Summary of analyses by the proposed equations and existing Table 5.11 equations EC2B and Andreasen……………………………………. Table 5.12 Detail of the stirrup system ……………………………………….. Table 5.13 Analysis of specimens with transverse reinforcement……………. Table 5.14 Summary of statistical f bu ,test / f bu ,calc for specimens with two bars each in the bend of a stirrup……………………………………….. Results of analysis for anchored bars in end region in NSC and Table 5.15 HSC beams by Magnusson………………………………………… Table 5.16 Summary of Ft ,test / Ft ,calc ratio for beams by Magnusson

192 193 194 195 196 196 204 205 206 206 217 221 222 223 224

232 240 243 247 248 249 251 255

257 269 276 279 284285 286

290291 292

x

Table 5.17 Table 5.18 Table 5.19

Table 5.20 Table 5.21 Table 5.22 Table 5.23 Table 5.24 Table 5.25 Table 5.26 Table 5.27 Table 5.28 Table 5.29 Table 5.30

………… Summary of test/calculated ratios for tests by Untrauer and Henry 294 Results of analysis for specimens by Untrauer and Henry 294 and the proposed method…………………………………………... * Summary of f bu ,test / f bu and f bu ,test / f bu , 0 fro specimens with 294 p = 0 by Batayneh…………………………………………………. 296Results of analysis for f bu ,test / f bu ,calc for tests with p  0 by Batayneh……………………………………………………………. 298 298 Summary of results for f bu ,test / f bu ,calc for tests with p  0 by Batayneh…………………………………………………………… Comparison of test results to prediction by BS8110 ………………. 304 Comparison of test results to prediction by BD 44/95……………... 306 Comparison of test results to prediction by EC2…………………... 308 309 Summary of mean values for Ftest / FR calc A and B ………………… 310 Summary of Ftest / FR calc for beams with bonded and unbonded leads ……………………………………………………………….. Comparison of test to bond resistance calculated by proposals 1,2 313 and 3 for beams with 90  and 180  bends …………………………. 314 Summary of mean values for Ftest / FRcalc for the proposed methods Bar forces developed in anchorages-comparison between 316 calculated resistances and forces determined from measured strains Summary of comparisons of calculated and experimental strengths 319 of bent anchorages with bonded lengths……………………………

Chapter Six Table 6.1

Results of comparisons in terms of f bu ,test / f bu ,calc

321

………………….

xi

List of Figures Chapter Two Figure 2.1 : Figure 2.2 : Figure 2.3 : Figure 2.4 : Figure 2.5 : Figure 2.6 : Figure 2.7 : Figure 2.8 : Figure 2.9 :

Equivalent anchorage length for standard bends and hooks to EC2 ………………………………………………………... Standard (minimum) hooks and bends to ACI-318 ………….. Transverse reinforcement details in hooks and bends to ACI318………………………………………………………………. Design ultimate bond stresses for bars with negligible transverse reinforcement, comparisons of BS810,EC2 and ACI318……………………………………………………………… Effect of stirrups on bar stresses developed by various bond lengths…………………………………………………………... Comparisons of bearing stress limits in BS8110 and EC2……... Comparisons of f btd from BS8110 and BD 44/95…….. ………. Design bar stresses calculated by BS8110……………...………. Comparisons between EC2 and BS8110 for anchorages with 90  and 180

Figure 2.10 : Figure 2.11 :

14 17 18 24 27 31 32 35 39

bends ………………………………………... Splitting pattern types by Tepfers………………………………. Test arrangement and failure mode for specimen with 

41 43

l b / ϕ = 2.5 by Baldwin and Clark

Figure 2.12 Figure 2.13 : Figure 2.14 : Figure 2.15 : Figure 2.16 : Figure 2.17 : Figure 2.18 : Figure 2.19 : Figure 2.20: Figure 2.21: Figure 2.22: Figure 2.23: Figure 2.24: Figure 2.25 : Figure 2.26 : Figure 2.27 : Figure 2.28: Figure 2.29: Figure 2.30: Figure 2.31:

……………………………… Forces and stresses in the failure model by Cairns…………….. Polygon of forces on a wedge ……………….………………… Terminology for crescent shaped ribs………………………….. Cairns and Jones - test specimens……………………………… Cairns and Jones – influence of relative rib area on bond strength…………………………………………………………. Failure patterns of anchored bars(Morita and Fujii)…………… Yield Locus, Displacement Directions and Internal Work…….. Geometry of a deformed bar…………………………………… Displacement at failure and internal work in local mechanics …

44 44 45 46 47 49 53 53 55 56

Relationships between f bu / f c and c / ϕ by Nielsen……………………….

Failure Mechanisms in surrounds……………………………… Final results for different failure mechanism…………………… Truss model for yielding stirrups……………………………….. Untrauer and Henry’s test arrangements………………………... Relationship between the f bu / f c and p by Untrauer and Henry…………………………………………………………… Robins and Standish’s test arrangements ………………………. Navaratnarajah and Speare’s test arrangements………………… Nagatomo and Kakus’ test arrangements………………………. Typical details of test specimen by Batayneh.............................. Typical beam test arrangements by Batayneh …………………..

57 58 59 60 61 62 63 64 66 68

xii

Figure 2.32: Figure 2.33 : Figure 2.34: Figure 2.35 : Figure 2.36 : Figure 2.37 : Figure 2.38 : Figure 2.39 : Figure 2.40 : Figure 2.41 : Figure 2.42 : Figure 2.43 : Figure 2.44 : Figure 2.45 : Figure 2.46 : Figure 2.47 : Figure 2.48 : Figure 2.49 : Figure 2.50 : Figure 2.51 : Figure 2.52 : Figure 2.53 : Figure 2.54 : Figure 2.55 : Figure 2.56 : Figure 2.57 : Figure 2.58 : Figure 2.59 : Figure 2.60 : Figure 2.61 : Figure 2.62 : Figure 2.63 : Figure 2.64 : Figure 2.65 : Figure 2.66 :

Rathkjen’s test arrangements…………………………………… Relationships between f bu / f c and p u / f c for Rathkjen’s tests ............................................................................................. Jensen’s test arrangements……………………………………... Relationships between f bu / f c and pu / f c for Jensen’s tests Ghaghei’s typical test arrangements…………………………… Relationship between the f bu / f cu and pu / f cu for Ghaghei’s tests ………………………………………………… Test arrangements for Regan’s slabs…………………………… Relationship between the f bu / f cu and pu / f cu for l b / ϕ =7.5 in tests by Regan………………………………… Corner mechanisms with centres of rotation on the side face of beam for Nielsen and Andreasen……………………………… The limitation of support pressure by concrete web compression Beam specimens and typical cross section by Magnusson …… Effect of variations of transverse reinforcement and bearing materials(Magnuson)……………………………………………… Magnusson’s strut-and-tie model………………………………. Relationship between Ftest / FMC 90 and f c (Magnusson) ……….. Details of beam-end specimens by Magnusson………………... Local movements at failure…………………………………….. Cases of non-polar symmetric restraints………………………... Movements in surrounds at failure according to Nielsen………. Distributions of reactions across widths of supports…………… Splitting pattern types by Tepfers………………………………. Comparison of different treatments of the relationship between bond strength and concrete cylinder strength…………………... Comparisons of test results with various formulations for maximum bond strength………………………………………… Mylrea’s test arrangements .…………………………………… Muller’s test arrangements……………………………………… Average bond stresses at 0.25mm loaded-end slip tests for series 1,2 and 3 by Hribar and Vasko…………………………... Ultimate bond stresses- tests by Hribar and Vasko…………….. Minor and Jirsa’s test arrangements……………………………. Loaded end slips at f s = 414 N / mm 2 - tests by Minor and Jirsa Influence of bond length on bond strength in tests by Minor and Jirsa…………………………………………………………….. Marques and Jirsa’s test arrangements………………………… Bond length for both bent and straight bar in Schiessl’s approach………………………………………………………… Results of all calculations ϕ = 8 − 28 mm , f cu = 25 − 55 N / mm 2 for ribbed bars in upper and lower position from Schiessl…….. Soroushian et al’s test arrangements……………………………. Influence of transverse reinforcement on ultimate strength- tests by Soroushian et al……………………………………………… Detailing of beams by Gulparvar ……………………………….

70 71 72 74 75 76 77 80 81 84 89 92 95 96 98 104 106 108 109 110 114 116 120 122 128 129 132 134 135 136 141 142 143 145 146

xiii

Chapter Three Figure 3.1 :

Specimens and test arrangements ………………………………

Figure 3.2 :

Histogram of number of results and some of main variables

Figure 3.3 :

Relationship between f bu ,test / f bu ,calc and c m / ϕ for predictions by BS8110,EC2,Darwin et al and Morita and Fujii…………… Relationship between f bu ,test / f bu ,calc and l b / ϕ for predictions by BS8110,EC2,Darwin et al and Morita and Fujii…………… Relationship between f bu and ϕ ( mm ) for predictions by BS8110,EC2,Darwin et al and Morita and Fujii……………….. Relationships between log ( f bu ,test / A) and log ( f c ) ……………. Histogram of number of results and some of main variables

Figure 3.4 :

Figure 3.5 : Figure 3.6 : Figure 3.7 :

154157 158 159

160

162 163 166

for specimens without transverse reinforcement………………. Figure 3.8 :

Relationship between f bu ,test / f bk , BS 8110 and p u / …………

fc

169

Figure 3.9 :

Relationships between f bu ,test / f bk , EC 2 and pu / …………

fc

170

Figure 3.10 : Figure 3.11 : Figure 3.12 : Figure 3.13 :

Chapter Four Figure 4.1 : Figure 4.2 : Figure 4.3 : Figure 4.4 : Figure 4.5 : Figure 4.6 : Figure 4.7 : Figure 4.8 : Figure 4.9 :

against p u / f c after relaxation of a limit of α2α5 ≥ 0.7 …………………………………………………… f bu ,test / f bu , Bat 3.6 against p u / f c for Batayneh's eq.3.6………… f bu ., est / f bu , Bat 3.7 against p u / f c for Batayneh's eq.3.7……….. Relationships between f bu ., test / f bu , N and pu / f c …………….

170

End of the typical beam………………………………………… Series Bs details………………………………………………… Series Bb details………………………………………………… Series Bh details………………………………………………… Slip measurement instrumentation for specimens with straight bars …………………………………………………………….. Slip measurement instrumentation for specimens with 900 and 1800 bends……………………………………………………… Model showing calculation parameters………………………… Crack patterns for beams with straight anchorage…………….

175 177 178 179 185

f bu ,test / f bk , EC 2

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

171 171 172

185 187 197 197

xiv

Figure 4.10 : Figure 4.11 : Figure 4.12 : Figure 4.13 : Figure 4.14 : Figure 4.15 : Figure 4.16 : Figure 4.17 : Figure 4.18 : Figure 4.19 : Figure 4.20 : Figure 4.21 : Figure 4.22 : Figure 4.23 : Figure 4.24 : Figure 4.25 : Figure 4.26 : Figure 4.27 : Figure 4.28 : Figure 4.29 : Figure 4.30 : Figure 4.31 :

Cracking at failure, Beams Bs6, Bs7 and Bs8 without transverse pressure ………………………………………………….. Cracking at failure, Bs14 with transverse pressure …………

198

Cracking at failure, Beams Bs31, Bs32, Bs33and Bs34 with closely spaced bars……………………………………………. Cracking at failure, Beams Bs27, Bs28 and Bs29 with

199

transverse pressure …………………………………………….. Cracking at failure in Beams Bs23 and Bs26 with and without fibre board pads………………….……………………………… Cracking at failure, Beams Bb3, Bb10 and Bb15…………...….. Cracking at failure, Beams Bh8 with transverse pressure……… Cracking at failure top and side, Beam Bb12 and Bh11………... Relation between f bu / f cu and c s / ϕ when p = 0 …………… Relation between f bu / f cu and l b / ϕ when p = 0 …………. Influence of radius of bend on the bar stresses developed by 90  and 180  bent anchorages………….. Influence of side cover on the bar stresses developed by 90  and 180  bent anchorages with r / ϕ =2.5…. Ratios of strengths of partly debonded anchorages and anchorages fully bonded over supports as functions of the corresponding ratios of bond lengths ………………………… Strain gauges on Bs5…………………………………………. Load-strain relationships for Bs5………………………………. Strain gauges on 900 and 1800 bends.……………………… Force-strain relationships for specimens with 900 bent bars…… Force-strain relationships for specimens with 1800 bent bars … Relationships between bond stresses and Load for Bh10-Bh12... Relationships between bond stresses and Load for Bb12Bb15…………………………………………………………… Relationships between relative bond stress f b / f cu and slip for beams with b = 250 mm , cb = c s = 25 mm and p  0 …… Relationships between relative bond stress f b / f cu and slip for beams with b = 250 mm , cb = 25 mm , c s = 55 mm and

198

200 200 201 202 202 203 203 208 208 209 210 210 211 212 213 215 216 219 220

p 0

Figure 4.32 : Figure 4.33 :

Relationships between relative bond stress f b / f cu and slip for beams with b = 200 mm ……………….………………....... Relationships between relative bond stress f b / f cu and slip for beams with b = 150 mm

221 222

xv

Figure 4.34 :

Figure 4.35 : Figure 4.36 :

…………………………………….. Relationships between relative bond stress f b / f cu and slip for beams with b = 125 mm …………………………………. …. P.( 30 / f cu ) and slip relationship for bent bars end with 90  and 180  bends……………………………………………… Loads at which slips reached 0.1mm ……………………………

223

225 226

Chapter Five Figure 5.1 :

f bu ,test

/

fc

…… Figure 5.2 :

Figure 5.3 : Figure 5.4 :

Figure 5.5 : Figure 5.6 :

Figure 5.7 :

Figure 5.8 : Figure 5.9 : Figure 5.10 :

f bu ,test

Figure 5.12 : Figure 5.13 :

 c  0.92 + 0.08 M cm 

   against

 cm

 c  0.92 + 0.08 M cm 

   against

 + 0.5  ϕ 

 fc 

(ϕ / l b )

Yerlici and Ozturan’s test arrangements……………………….. Relationships between f bu ,test / f c (1.0 +c m / ϕ)( 0.932 +0.0632 c M / c m ) and ( lb / ϕ ) for Yerlici and Ozturan’s data…………………………………... Relationship between f bu ,test f bu ,calc 2 and ( c m / ϕ ) for Chamberlin’s tests……………………………………………… Relationship between f bu ,test f bu ,calc 2 and ( c m / ϕ ) for Ferguson and Thompson’s tests………………………………………….. Relation between f bu ,test f bu ,calc 2 and ( c m / ϕ ) for Batayneh’s tests.............................................................................................. Relation between f bu ,test f bu ,calc 2 and ( c m / ϕ ) for Kemp and Wilhelm’s tests…………………………………………………. Influence of cover on bond strength in tests (for types S and P ) by Batayneh……………………………………………………. Relationship between f bu ,test /

cd  fc  1.0 + ϕ 

  lb        ϕ 

230

230

(ϕ / lb ) 0.4 …..

( c D / cd ) Figure 5.11 :

/

 cm   + 0.5  ϕ 

232 233

235 235

236

236 237

0.4

and

Influence of c d / ϕ on bond strengths in tests by Ferguson and Thompson and W.S.Atkins…………………………………… Influence of c D / c d on bond strengths in tests by Ferguson and Thompson and W.S.Atkins…………………………………….. Arrangement of testing by W.S.Atkins …………………………

238 239 239 240 xvi

Figure 5.14 : Figure 5.15 : Figure 5.16 : Figure 5.17 : Figure 5.18 : Figure 5.19 : Figure 5.20 : Figure 5.21 : Figure 5.22 : Figure 5.23 : Figure 5.24 :

Figure 5.25 :

Figure 5.26 : Figure 5.27 : Figure 5.28 : Figure 5.29 :

Figure 5.30 :

Figure 5.31 :

Figure 5.32 : Figure 5.33 : Figure 5.34 : Figure 5.35 :

Results of Chamberlin’s tests plotted against c s / ϕ …………. Results of tests by Chapman and Shah ………………………… Influence of relative rib areas on bond strengths in tests by Darwin and Graham ……………………………………………. Results of tests by Ahlborn and Den Hartigh ………………….. Influence of bar size on f butest / f bucalcA …………………………. Influence of bar size on f butest / f bucalcB …………………………. Influence of bar size on f butest / f bucalC …………………………... Conditions at a support producing transverse pressure …............ f c and p u / f c for tests by Relationships between f bu Batayneh and Ghaghei………………………………………….. f c and p u / f c for tests by Relationships between f bu Jensen and Rathkjen…………………………………………… Test results from Jensen plotted to show values of f c ………… Relationship between (λ f ∗ / with λ = [ ( l / ϕ ) / 10 ] 0.4

f c ) and sectional parameters

……………………………………………………. Relationship between (λ f ∗ / f c ) and sectional

parameters

with λ = [ ( l / ϕ ) / 8] 0.4 ≥ 1.0 …………………………………………….. Relationship between (λ f ∗ / f c ) and sectional parameters with λ = [ ( l / ϕ ) / 10] 0.4 ≥ 1.0 ……………………………………. Relationship between ( f bu / f c ) and ( p u / f c ) for Jensen Specimens……………………………………………………… Relationship between ( f bu / f c ) and ( p u / f c ) for Rathkjen specimens………………………………………………………. Relationship between ( f bu / f c ) and ( p u / f c ) for specimens by Ghaghei, Regan and Batayneh……………………………… Relationship between ( f bu / f c ) and ( p u / f c ) for specimens by Amin ……………………………………………………….. Typical specimens with transverse reinforcement for series considered………………………………………………………. Relationship between f bu and f c for Jensen specimens with and without transverse reinforcement………………………….. Relationships between f b and p for specimens with and without transverse reinforcement ……………………...……….. Beams and typical sections by Magnusson……………………..

242 243 245 246 254 255 255 257 259 260 261

263

264 265 271 272

273

274275 280 281 282 287

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Figure 5.36 : Figure 5.37 :

Elevation and anchorage details for Bb and Bh beams…………. Dimensions of bars with 90  ( 180  bends) ends…………...........

300 302

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

341

Appendix 2 Table A1 Table A2

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

342

Bar strains ……………………………………………………. Load-slip measurements …………………….......................... Bar forces and bond stresses from strains measured on bent and hookedbars…………………………………………………

357 359

Specimens

370

348

Appendix 3 Table A3 Table A4 Table A5

366

Appendix 4 Table A6

without

transverse

pressure

or

transverse

xviii

reinforcement using proposed equations of ( 5.1 to 5.3)………. Table A7 Table A8 Table A9

Data for beam-end specimens without transverse reinforcement ………………………………………………… Comparisons between experimental bond strengths and strengths calculated from equations 5.8 to 5.22 ……………. Comparison of experimental strengths and strengths calculated (5.24) for beam-end specimens without transverse reinforcement………………………….……………………..

377 384 388

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.

xix

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 ( l b / ϕ )

0.4

, 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. 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 ( p ) . For p = 0 the bond resistance is that of the equation above and the gradient f bu / p is 2.0. For higher pressure f bu / p 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 twodimensional . The total capacity of an anchorage is the sum of the forces developed by

xx

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 design methods and avoids the use of fictitious lengths and arbitrary omissions of checks on bearing stresses .

xxi