S HE A ti OF REINFORCED CONCRETE BEAMS by ALEXANDRE PLACAS BASc., Civil Engr ...

586 Pages·2014·8.93 MB·English

S HE A ti
OF REINFORCED CONCRETE BEAMS
by
ALEXANDRE PLACAS B.A.Sc., Civil Engr., M.A.Sc.
A thesis submitted for the Diploma of membership
of Imperial College.
Imperial College of Science
and Technology, London November 1969
1
ABSTRACT
The invesigation reported in this thesis is concerned with
the general subject of the shear resistance of reinforced
concrete beams and the findings are applicable to rectangular,
T- and I-sections.
To assist the theoretical analysis, tests of 75 normal sized
beams, in which the parameters affecting shear varied system-
atically, were carried out. Concentrating on the types of
members where lack of sufficient experimental data existed, all
but 10 of the beams contained shear reinforcement and 45 had
compression flanges.
Virtually all the beams, having high strength longitudinal
reinforcement with good bond quality, failed in shear in one
of the following modes
1)D iagonal Tension
2)S hearing (Shearing of concrete above a shear crack)
3)S hear Compression
4)W eb Crushing
The theoretical analysis is to a large extent based on
observations of the behaviour of these beams during the tests
and at failure. As a result equations are presented representing
each mode of failure. If the strengths corresponding to modes
2, 3, and 4 are greater than the diagonal tension load, the
final solution is given by the mode of failure equation pre-
dicting the least strength; in other cases failure is by dia-
gonal tension. In this manner not only is an adequate numerical
prediction of the failure load obtained, but a comparison of
2
the results pertaining to the various modes provides a good
indication of the actual type of failure that is likely to
take place.
Intrinsic to this approach is a rational solution of the
problem of compression reinforcement and its influence or lack
of influence on the ultimate shear strength of rectangular
beams. The increased strength of T-beams over that of rectangles
composed of their webs is also adequately reflected in the
proposed theory.
To establish the equation for the shearing mode of failure
a new adoption of a Coulomb type "plastic shoar" failure cri-
terion for concrete is presented.
Since collapse loads are not the only design criteria, in
addition to the equations for the four modes of failure mentioned,
formulae ore also developed, substantiated by test results,
to cover two other possible criteria
1)S hearing off of flanges in T-beams
2)S hear crack widths
The various equations put forward in this thesis show
adequate correlation with test results, giving on average a
10% safety margin at a coefficient of variation of less than
0.10.
3
ACKNOWLEDGEMENTS
The author is grateful to Professor A.L.L. Baker, D.Sc.,
F.I.C.E., F.I. Struct. E., under whose supervision the in-
vestigation reported herein was conducted.
My sincere thanks are due to Dr. P.E. Regan, Ph.D.,
D.I.C., SVR, for his advice and guidance throughout the
duration of the investigation.
lily thanks are also due to the laboratory staff, in parti-
cular Messrs J. Turner and F. Turner, for their assistance
in the preparation of the test beams.
The author is indebted to the following organizations,
without whose cooperation the research reported in this
thesis would not have been possible: The Construction Industry
Research and Information Association (C.I.R.I.A.) under whose
sponsorship the research was carried out; the National
Research Council of Canada for the award of a grant that made
the author's stay in England possible; The Ecole Polytechnique
of the University of Montreal for the granting of the necessary
leave of absence.
4
CONTENTS
PAGE
ABSTRACT 2
ACKNOWLEDGEMENTS 4
CONTENTS 5
NOMENCLATURE 11
CHAPTER 1 INTRODUCTION 15
CHAPTER 2 CRITICAL REVIEW OF EXISTING SHEAR THEORIES 25
2.1 Introduction and general comments 25
2.2 The Morsch theories 30
Laupals theory and other semi-empirical shear cam- 33
pression theories - Zwayer, Moody
244 Walther's theory and other theoretical shear cam- 41
pression theories - Ohja, Bjuggren
2;5 Plane of minimum strength methods - Borishanski 50
Hillerborg

2.6 Regan's theory 57

2.7 Other shear theories - Taylor, Petersson, Jones, Kani 64

4.8 Review of some research an T-beams 69

2.9 Dowel and aggreagte interlock actions 72

2.9.1 Dowel action in reinforced concrete beams 73
Beams without shear reinforcement
Beams with shear reinforcement

82
2.9.2 Aggregate interlock action in reinforced concrete
beams

CHAPTER 3 DETAILS OF THE EXPERIMENTAL INVESTIGATION 88

3.1 Concrete 89

98
3.2 Reinforcement
5
3.3 Geometry of beams and arrangement of reinforcement 108
3.4 Casting and curing 115
3.5 Test procedure 117
3.6 Parameters investigated 122
CHAPTER 4 INVESTIGATION OF SHEAR FAILURE IN 125
RECTANGULAR BEAMS
4.1 Behaviour of rectangular beams failing in shear 125
4.2 Rectangular beams without shear reinforcement 131
4.2.1 Strain measurements on concrete and reinforcement 137
4.3 Influence of the degree of shear reinforcement 145
4.4 Influence of the ratio of main reinforcement 156
4.5 Influence of the shear span to effective depth ratio 164
466 Influence of the concrete strength 167
4.7 Influence of the compression reinforcement 173
4.8 Influence of the inclination of shear reinforcement 185
4.9 Strain measurements 189
4.9.1 on the shear reinforcement 189
4.9.2 on the main reinforcement 192
4.9.3 on the concrete 194
CHAPTER 5 INVESTIGATION OF SHEAR FAILURE IN T-BEAMS 207
5.1 Behaviour of T.-beams failing in shear 207
5.2 Influence of the degree of shear reinforcement 216
5.3 Influence of the ratio of main reinforcement 223
5.4 Influence of the shear span to effective depth ratio 229
5.5 Influence of concrete strength 235
5.6 Influence of the inclination of shear reinforcement 240
5.7 Influence of transverse flange reinforcement 246
5.8 Influence of flange breadth 255
6
5.9 Influence of flange depth 259

5.10 Strain measurements 263

5.10.1 on the shear reinforcement 263

5.10.2 on the main reinforcement 266

5.10.3 on the concrete 269
a)t op surface
b)s ides
CHAPTER 6 INVESTIGATION OF WEB CRUSHING FAILURES 298
6.1 Behaviour of the thin-webbed I-beams 300
6.2 Influence of concrete strength 307
6.3 Influence of shear reinforcement 309
6.4 Influence of spacing of shear reinforcement 311
6.5 Influence of inclination of shear reinforcement 331
6.6 Strain measurements 313
6.6.1 on the shear reinforcement 3:-
6.6.2 on the main reinforcement 3-7
6.6.3 on the concrete 321
CHAPTER 7 SHEAR STRENGTH OF REINFORCED CONCRETE BEAMS 331
7.1 Behaviour of beams failing in shear 332
7.1.1 Shear cracking 373
7.1.2 Shear failure 339
7.2 Equilibrium conditions at an inclined plane 340
7.2.1 Behaviour of beams following shear cracking 340
7.2.2 Equilibrium conditions at an inclined plane 314
7.3 Shearing mode of failure 347
7.3.1 Singly reinforced rectangular beams
7.3.2 T-beams 77,4
7.3.3 Beams with compression reinforcement :-1
7
7.4 Shear compression mode of failure 358
7.4.1 Singly reinforced rectangular beams 358
a)C losely spaced vertical stirrups 362
b)C losely spaced inclined stirrups 363
c)B ent-up bars 364
d) Widely spaced shear reinforcement 365
7.4.2 Beams with compression reinforcement 365
7.4.3 T-beams 367
7.5 Web crushing 368
7.5.1 Equilibrium conditions 370
7.5.2 Considerations on the stress-strain relationship 372
in the web
7.5.3 Formulation of equations for the web crushing 376
strength of reinforced concrete beams
7.5.4 Validity of web crushing equation 382
7.6 Horizontal shear and transverse flange reinforcement 385
in T-beams
7.6.1 Beams without transverse flange reinforcement 385
7.6.2 Transverse reinforcement in flanges 390
7.7 Detailing requirements 395
7.7.1 Effect of shear on forces in main reinforcement 395
a)B eams without shear reinforcement
b) Beams with shear reinforcement
7.7.2 minimum requirements for shear reinforcement 402
7.8 Short and deep beams; ;doment-shear interaction 405
7.8.1 Beams without shear reinforcement 406
7.8.2 Beams with shear reinforcement 419
7.9 Physical interpretation of shearing equation 425
8
7.9.1 Failure criterion for concrete 425
7.9.2 Rectangular beams 428
7.9.3 T-beams 433
7.10 Discussion 437
CHAPTER 8 COMPARISON OF TEST RESULTS WITH THEORIES 441
8.1 Comparisons with the proposed theory 443
8.2 Comparisons with Codes of Practice 449
8.3 Comparisons with other shear theories 458
8.4 Discussion of the comparisons presented in 8.1 to 8.3 462
8.5 Influence of compression flanges - comparison of 471
rectangular and T-section
8.6 Application of the proposed theory to T-beams tested 474
by other investigators
8.7 Comparison of the proposed web crushing equation with 477
the provisions of the Draft Unified Code of Practice
for Structural Concrete
CHAPTER 9 SERVICEABILITY CRITERIA 480
9.1 Shear crack widths 480
9.2 Deflection of beams failing in shear. 494
End rotations
CHAPTER 10 CONCLUSIONS AND SUGGESTIONS FOR 510
FURTHER RESEARCH
10.1 Conclusions 510
10.2 Suggestions for further research 513
10.2.1 Aggregate interlock 513
10.2.2 Effect of axial loading on shear strength 515
10.2.3 Effect of manner of load cpr'ication 518
10.2.4 Prestressed concrete beams 520
9
10.2.5 Continuous beams and influence of shear on moment521
- rotation characteristics
REFERENCES 526

APPENDIX A MODIFICATIONS TO EXISTING SHEAR COMPRESSION 540
THEORY
A.1 Failure criterion 541
A.2 Influence of stirrups on the compatibility conditions 549

A.2.1 Comparison of top fibre strains 550
A.2.2 Investigation of the effect of taking account of 561
the stirrups in the compatibility conditions as
expressed by equation (A.2.2)
A.3 Influence on the ultimate load of the inclination 559
of stirrups
A.3.1 Ultimate load for stirrups inclined at 450 571
A.3.2 Development of an approximate equation 573

APPENDIX B TABLE OF STRAIN MEASUREMENTS ON BEM D-2 580
10