Download - Doctoral Thesis 2009
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
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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