report no. ucbj eerc-83j 23 earthquake engineering

REPORT NO.

UCBj EERC-83j 23

OCTOBER 1983

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EARTHQUAKE ENGINEERING RESEARCH CENTER

LOCAL BOND STRESS-SLIP RELATIONSHIPS OF DEFORMED BARS UNDER GENERALIZED EXCITATIONS

by

ROLF ELiGEHAUSEN

EGOR P. POPOV

VITELMO V. BERTERO

Report to the National Science Foundation

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COLLEGE OF ENGINEERING

UNIVERSITY OF CALIFORNIA . Berkeley, California

For sale by the National Technical I nformation Service, U.S. Department of Commerce, Springfield, Virginia 22161.

See back of report for up to date listing of EERC reports.

DISCLAIMER Any opinions, findings, and conclusions or recommendations expressed in this publication are those of the authors and do not necessarily reflect the views of the National Science Foundation or the Earthquake Engineering Research Center, University of California, Berkeley

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I---R_EPO __ R_T_~_A_G_~_M_E_N_T_A_T_IO_N_LII_. _R_EPO_NRT_S_FN'---7_c_E_E_-_8_3_0_3_6 _____ ---lI_2. ______ --!~3.-R-ec_ipl_':..:..nr:'d:.!.:~s..:..;..3'cce.:...", _s~~:on;;, f~ 4. Title and Subtitle

Local Bond Stress-Slip Relationships of Deformed Bars under 5. Report Date

October 1983 Generalized Excitations 6-

~COI>s.CO __ -; 7. Author(s) 8. Performine ,. I>s. ... \ ~ "'apt. No.

r-__ R_._E_l_i_g_e_h_a_u_s_e_n_,_E_. __ P_. __ P_o_p_o_v_,_a_n_d __ V_. ___ V_. __ Be __ rt_e_r_o ________________ ~-U-CB-I __ E'1))CO __ ---J __________ 4

9. Performing Organization Name and Address 10. Projec. .• ask/Work Unit No. Earthquake Engineering Research center University of California 1301 South 46th Street Richmond, Calif. 94804

11. Contntct(C) or Gntnt(G) No. (C)

(G) PFR79-08984 ~~~-~~~-~-~-~~---------------------~----------.------4

12. Sponsoring Organization Name and Address 13. Type of Report & Period Covered National Science Foundation 1800 "G" Street, NW Washington, D.C. 20550

15. Supplementary Notes

16. Abstract (limit: 200 words)

14.

This report covers integrated experimental and analytical investigations that permit predicting analytically the local bond stress-slip relationship of deformed reinforcing bars subjected to generalized excitations, such as may occur during the response of reinforced concrete (RIC) structures to severe earthquake ground motions.

Some 125 pull-out specimens were tested. Each one of these specimens simulated the confined region of a beam-column joint. Only a short length (five times the bar diameter) of a Grade 60 deformed reinforcing bar was embedded in confined concrete. The tests were run under displacement control by subjecting one bar end to the required force needed to induce the desired slip which was measured at the unloaded bar end. The influence of (1) loading history, (2) confining reinforcement, (3) bar diameter and deformation pattern, (4) concrete compressive strength, (5) clear bar spacing, (6) transverse pressure, and (7) loading rate on the bond stress-slip relationship was studied.

Based on the experimental results, a relatively simple analytical model for the local bond stress-slip relationship of deformed bars embedded in confined concrete is developed. The main assumption is that bond deterioration during generalized excitations depends on the damage experienced by the concrete, which, in turn, is a function of the total dissipated energy.

17. Document Analysis a. Descriptors

b. Identifiers/Open·Ended Terms

c. COSATI Field/Group 18. Availability Stateme":

Release Unlimited

(See ANSI-Z39.18)

, I

19. Security Class (ThIs Report) 21. No. of Pages 1·

~------------~----------22. Price 2G. Security Class (ThIs Page)

See Instructions on Reverse OPTIONAL FORM 272 (4-77) (Formerly NTIS-35) Department of Commerce

LOCAL BOND STRESS-SLIP RELATIONSHIPS OF DEFORMED BARS UNDER GENERALIZED EXCITATIONS

Experimental Results and Analytical Model

by

Rolf Eligehausen

Visiting Scholar from the University of Stuttgart, Federal Republic of Germany

Egor P. Popov

Professor of Civil Engineering University of California, Berkeley

Vilelrno V. Bertero

Professor of Civil Engineering University of California, Berkeley

A report on research sponsored by the National Science Foundation.

Report No. UCB/EERC-83/23 Earthquake Engineering Research Center

College of Engineering University of California

Berkeley, California

October 1983

ABSTRACT

This report covers integrated experimental and analytical investigations that permit

predicting analytically the local bond stress-slip relationship of deformed reinforcing bars sub

jected to generalized excitations, such as may occur during the response of reinforced concrete

(RIC) structures to severe earthquake ground motions.

Some 125 pUll-out specimens were tested. Each one of these specimens simulated the

confined region of a beam-column joint. Only a short length (five times the bar diameter) of a

Grade 60 deformed reinforcing bar was embedded in confined concrete .. The tests were run

under displacement control by subjecting one bar end to the required force needed to induce

the desired slip which was measured at the unloaded bar end. The influence of the following

parameters on the bond stress-slip relationship was studied: (I) loading history, cn confining

reinforcement, (3) bar diameter and deformation pattern, (4) concrete compressive strength,

(5) clear bar spacing, (6) transverse pressure, and (7) loading rate.

The detailed experimental results are presented and compared with results given in the

literature. Based on the experimental results obtained,a relatively simple analytical model for

the local bond stress-slip relat~onship of deformed bars embedded in confined concrete is

developed. The model takes into account the significant parameters that appear to control the

behavior observed in tth~ experiments. The main assumption is that bond deterioration during

generalized excitations depends on the damage experienced by the concrete which, in turn, is a

function of the total dissipated energy. This assumption appears to apply only in the range of

low cycle fatigue; that is, when a small number of cycles at relatively large slip values is applied.

The proposed analytical model for the local bond stress-slip relationship exhibits satisfac

tory agreement with experimental results under various slip histories and for various bond con

ditions.

The concrete in RIC joints of ductile moment resisting frames outside of stirrup-ties is

unconfined. Therefore, based on the evaluation of test data given in literature, the analtyical

model is modified to include such regions. Furthermore, rules are formulated to extend the

validity of the model to conditions different from those present in the tests.

The results of the investigation reported herein are used to offer some conclusions regard

ing the behavior of bond of deformed bars under monotonic and cyclic loading, and recommen

dations for further work are indicated.

ii

ACKNOWLEDGEMlliNTS

The authors are grateful for the financial support provided for this investigation by the

National Science Foundation under Grant PFR 79-08984 to the University of California, Berke

ley. The support of Dr. R. Eligehausen by the Deutsche Forschungs-gemeinschaft are grate

fully acknowledged. The project was under general supervision of Professors E. P. Popov and

V. V. Bertero.

F. C. Filippou assisted with the preparation of the report for publication. Gail Feazell

made the drawings and prepared them for publication, and Linda Calvin did the typing of the

final manuscript. The authors would like to thank them for their help.

iii

ABSTRACT . • . •

ACKNOWLEDGEMENTS

TABLE OF CONTENTS

TABLE OF CONVERSION FACTORS

LIST OF TABLES

LIST OF FIGURES

1. INTRODUCTION

1.1 General

TABLE OF CONTENTS

i

iii

iv

vii

viii

ix

1

1

1. 2 Objectives and Scope • 2

II. LITERATURE REVIEW. 4

2.1 Experimental Studies on Local Bond Stress-Slip Relationship 4

2.1.1 General Description. 4

2.1.2

2.1. 3

Monotonic Loading

Cyclic Loading

2.2 Analytical Models for Cyclic Loading •

2.3 Summary of Chapter II

III. EXPERIMENTAL PROGRAM

3.1 Test Specimen

3.2 Test Program

3.3 Material Properties

3.3.1 Concrete

3.3.2 Reinforcing Steel

3.4 Manufacture and Curing of Test Specimens

3.5 Experimental Setup and Testing Procedure.

iv

'.

5

9

10

13

15

15

18

21

21

22

22

23

Table of Contents (cont'd)

IV. EXPERIMENTAL RESULTS · 26

4.1 General . . . . · 26

4.2 Visual Observations and Failure Mode 26

4.3 Honotonic Loading · 27

4.3.1 General Behavior 27

4.3.2 Influencing Parameters 28

4.3.2.1 Tension or Compression Loading · 28

4.3.2.2 Confining Reinforcement 29

4.3.2.3 Bar Diameter · · · 32

4.3.2.4 Concrete Strength · · · · · 33

4.3.2.5 Bar Spacing · · · · · · 33

4.3.2.6 Transverse Pressure · · · · · · 34

4.3.2.7 Rate of Pullout 34

4.3.3 Comparison with Other Results · · · · 34

4.3.3.1 General Behavior · · · · · · 34

4.3.3.2 Influence of Investigated Parameters · 35

4.4 Cyclic Loading · · . . · · · · 38

4.4.1 General Behavior · 39

4.4.2 Unloading Branch · · · · 41

4.4.3 Frictional Branch · · · · 42

4.4.4 Reloading Branch · · · · · · · · 43

4.4.5 Reduced Envelope · · · · 44

4.4.6 Influencing Parameters 45

4.5 Required Restraining Reinforcement · · · · · · · · · 48

V. ANALYTICAL MODEL OF LOCAL BOND STRESS-SLIP RELATIONSHIP 51

5.1 General . . . · · . . · · · · · · · · · · · · · · 51

v

Table of Contents (cont'd)

5.2 Theory of Bond Resistance Mechanism. 51

5.2.1 Monotonic Loading 52

5.2.2 Cyclic Loading 54

5.3 Analytical Model for Confined Concrete 56

5.3.1 Monotonic Envelope. 57

5.3.2 Reduced Envelope .•.. 58

5.3.3 Frictional Resistance 60

5.3.4 Unloading and Reloading Branch • 62

5.3.5 Effects of Variation of Different Parameters on Analytical Model . • . • . • . • . 62

5.3.5.1 Effects on Monotonic Envelope 63

5.3.5.2 Effects on Cyclic Parameters .• 65

5.3.6 Comparison of Analytical Predictions of Local Bond Stress-Slip Relationships with Experimental Results 65

5.4 Analytical Model for Unconfined Concrete in Tension and Comp~ession ••••••••••••••••••••. 66

5.4.1 Monotonic Envelope 66

5.4.2 Cyclic Parameters 68

VI. CONCLUSIONS AND RECOMMENDATIONS FOR FUTURE WORK 70

6.1 Summary and Conclusions 70

6.1.1 Monotonic Loading 70

6.1.2 Cyclic Loading • . 71

6.1.3 Analytical Bond Model 72

6.2 Recommendations for Future Research • 72

REFERENCES 74

TABLES 78

FIGURES • 85

vi

TABLE OF CONVERSION FACTORS

To convert To

inches (in.) millimeters (mm)

feet (ft) meters (m)

yards (yd) meters (m)

square inches (sq in.) square millimeters

cubic inches (cu in.) cubic millimeters

cubic feet (cu ft) cubic meters (m 3 )

pounds mass (Ibm) kilograms (kg)

tons (ton) mass kilograms (kg)

pound force (lbf) newtons (N)

kilograms force (kgf) newtons (N)

pounds force per square inch (psi) kilopascals (kPa)

vii

(mm2)

(mm 3)

Hultiply by

25.4

0.305

0.914

645

16.4X 10 3

0.028

0.453

907

4.45

9.81

6.89

LIST OF TABLES

TABLE 3.1 TEST PROGRAM •..

TABLE 3.2 MIX OF CONCRETE

TABLE 3.3 CONCRETE COMPRESSIVE AND TENSILE STRENGTHS

TABLE 3.4 GEOMETRY OF BAR DEFORMATIONS • .

TABLE 4.1 STANDARD DEVIATION OF BOND RESISTANCE AT GIVEN SLIP VALUES FOR ALL TESTS MONOTONICALLY LOADED (SERIES

78

80

81

82

1-7. n = 21 ROWS) •.••..••••.•..•.•• 83

TABLE 4.2 COEFFICIENT OF VARIATION OF BOND RESISTANCE FOR CYCLIC LOADING TESTS (SERIES 2.3 TO 2.15) • • . . . . . • . . 84

viii

FIG. 2.1

FIG. 2.2

FIG. 2.3

FIG. 2.4

FIG. 2.5

FIG. 2.6

FIG. 2.7

FIG. 2.8

FIG. 2.9

FIG. 2.10

FIG. 2.11

FIG. 2.12

FIG. 3.1

FIG. 3.2

FIG. 3.3

FIG. 3.4

LIST OF FIGURES

TYPICAL RELATIONSHIP BETWEEN BOND STRESS L AND SLIP s FOR MONOTONIC AND CYCLIC LOADING • . . . •

INTERNAL BOND CRACKS AND FORCES ACTING ON CONCRETE (AFTER [14]) . . .• . ......... .

SHEAR CRACKS IN THE CONCRETE KEYS BETWEEN LUGS (AFTER [10]) . . . . . • . . . . . • . . . . .

INFLUENCE OF THE RELATED RIB AREA aSR AND DIRECTION OF CASTING ON BOND STRESS-SLIP RELATIONSHIP FOR MONOTONIC LOADING (AFTER [13]) ....•...

LOCAL BOND STRESS-SLIP RELATIONSHIPS FOR SMALL SLIP VALUES AFTER DIFFERENT RESEARCHERS .

BOND STRESS-SLIP RELATIONSHIP FOR MONOTONIC LOADING FOR DIFFERENT REGIONS IN A JOINT (AFTER [8]) •.....

INFLUENCE OF THE RATIO BOND STRESS UNDER UPPER LOAD, MAX L, TO STATIC BOND STRENGTH, LMAX' ON THE Nill1BER OF CYCLES UNTIL BOND FAILURE (AFTER [31]) •.•..

INCREASE OF SLIP AT THE UNLOADED BAR END UNDER PEAK LOAD DURING CYCLIC LOADING AS A FUNCTION OF THE NUMBER OF LOAD REPETITIONS (AFTER [31]) • • . • • . . • • . . .

LOCAL BOND STRESS-SLIP RELATIONSHIP FOR CONFINED CONCRETE UNDER CYCLIC LOADING (AFTER [8])

ANALYTICAL MODEL FOR LOCAL BOND STRESS-SLIP RELATIONSHIP PROPOSED BY MORITA/KAKU [12]

ANALYTICAL MODEL FOR LOCAL BOND STRESS-SLIP RELATIONSHIP PROPOSED BY TASSIOS [9] • • • •

ANALYTICAL MODEL FOR LOCAL BOND STRESS-SLIP RELATIONSHIP PROPOSED BY VIWATHANATEPA/POPOV/BERTERO [8]

MECHANISM OF DEGRADATION OF STIFFNESS AND STRENGTH OF AN INTERIOR JOINT (AFTER [36]) . . . . . . . . . . . . .

MAJOR CRACKS IN SUBASSEMBLAGE BCU NEAR FAILURE (TAKEN FROM [37]) ••••.•••.••••.

AN INTERIOR BEAM-COLUMN JOINT AFTER SEVERAL INCREASING CYCLES OF REVERSED LOADING (Courtesy of Professor T. Paulay) . . . . . . . . . . . . . . . . . . . . . . FORMATION OF CONCRETE CONE IN PULLOUT SPECIMEN (TAKEN FROH [8]) . . . • • . . . • . . . . . .

ix

85

85

86

86

87

88

89

89

90

90

91

91

92

93

93

94

List of Figures (cont'd)

FIG. 3.5

FIG. 3.6

FIG. 3.7

FIG. 3.8

FIG. 3.9

FIG. 3.10

FIG. 3.11

FIG. 3.12

FIG. 3.13

FIG. 3.14

FIG. 4.1

FIG. 4.2

FIG. 4.3

FIG. 4.4

FIG. 4.5

FIG. 4.6

FIG. 4.7

FIG. 4.8

FIG. 4.9

FIG. 4.10

FIG. 4.11

FIG. 4.12

TEST SPECIMEN • 95

TEST SETUP 95

HISTORIES OF SLIP FOR CYCLIC TESTS (SERIES 2) 96

AGGREGATE GRADING . . 96

PHOTO OF TEST BARS 97

PHOTO OF SPECIMENS PRIOR TO CASTING (FRONT AND BACK SIDES OF FORMS NOT IN PLACE) • . . • . . . . . 97

PHOTO OF TEST SPECIMEN PREPARED FOR A TENSION TEST 98

DEVICE FOR APPLYING TRANSVERSE PRESSURE . . . • . 98

PHOTO OF TEST SPECIMEN IN MACHINE WITH TRANSVERSE PRESSURE APPLIED • . . . • . . . . •• •••. 99

PHOTO OF CONSOLE AND RECORDING DEVICES 99

PHOTO OF SAWN SPECIMEN AFTER TESTING. FAILURE BY PULLOUT 100

PHOTO OF A SPECIMEN FROM SERIES 1.4. FAILURE BY SPLITTING . • • • • 100

BOND STRESS-SLIP RELATIONSHIP FOR TEST SERIES 1.1 • 101

BOND STRESS-SLIP RELATIONSHIP FOR TEST SERIES 1.2 • . 101

BOND STRESS-SLIP RELATIONSHIP FOR TEST SERIES 1.3 • . 102

BOND STRESS-SLIP RELATIONSHIP FOR TEST SERIES 1.4 102

BOND STRESS-SLIP RELATIONSHIP FOR TEST SERIES 1.5 . 103

BOND STRESS-SLIP RELATIONSHIP FOR ALL MONOTONIC TESTS OF SERIES 2 : • . • • • . . • . . . . . • . . . 103

SCATTER OF MEASURED BOND STRESS-SLIP RELATIONSHIP OF TEST SERIES 2 ••• ". • • • • • . • . • • . . 104

INFLUENCE OF DIRECTION OF LOADING (TENSION OR COMPRESSION) ON BOND STRESS-SLIP RELATIONSHIP

INFLUENCE OF TRANSVERSE REINFORCEMENT ON BOND STRESS-

105

SLIP RELATIONSHIP • • . • • • . . • . . . • . • . . • 106

INFLUENCE OF BAR DIAMETER AND DEFORMATION PATTERN ON BOND STRESS-SLIP RELATIONSHIP . . . . . . . • • . . . 107

x


FIG. 4.13 INFLUENCE OF CONCRETE STRENGTH ON BOND STRESS-SLIP RELATIONSHIP . . . . . . . . . . . .. .... 108

FIG. 4.14 INFLUENCE OF CLEAR DISTANCE BETWEEN BARS ON BOND STRESS-SLIP RELATIONSHIP . . . . . . . . . . . . 109

FIG. 4.15 INFLUENCE OF CLEAR BAR SPACING S/db

ON BOND RESISTANCE 110

FIG. 4.16 INFLUENCE OF TRANSVERSE PRESSURE P ON BOND STRESS-SLIP RELATIONSHIP 111

FIG. 4.17 INFLUENCE OF TRANSVERSE PRESSURE P ON BOND RESISTANCE 112

FIG. 4.18 INFLUENCE OF TRANSVERSE PRESSURE P ON COEFFICIENT ~T/p. 112

FIG. 4.19 INFLUENCE OF RATE OF PULLOUT ON BOND STRESS-SLIP RELATIONSHIP 113

FIG. 4.20 INFLUENCE OF RELATIVE RATE, T, OF SLIP INCREASE ON BOND RESISTANCE . . . . . . . . . . . . . . . . . 113

FIG. 4.21 COMPARISON OF BOND STRESS-SLIP RELATIONSHIP MEASURED IN PRESENT TESTS WITH DATA GIVEN IN LITERATURE . . . • 114

FIG. 4.22 INCREASE OF BOND RESISTANCE AS A FUNCTION OF TRANSVERSE PRESSURE P - COMPARISON BETWEEN RESULTS OF PRESENT TESTS M~D THOSE GIVEN IN LITERATURE . . . . . . • . •. 115

FIG. 4.23 INFLUENCE OF RATE OF PULLOUT ON BOND RESISTANCE. COMPARISON OF RESULTS OF PRESENT TESTS WITH THOSE GIVEN IN LITERATURE . • • • . . . . . . . . . . . 116

FIG. 4.24 BOND STRESS-SLIP RELATIONSHIP FOR CYCLIC LOADING, SERIES 2.3 . . . . . . . . . . . . . . . . . . . . 116



FIG. 4.27a BOND STRESS-SLIP RELATIONSHIP FOR CYCLIC LOADING, SERIES 2.6 . . . . . . . . . . . . . . . . . . . . 118

FIG. 4.27b BOND STRESS-SLIP RELATIONSHIP FOR CYCLIC LOADING, SERIES 2.6* . . . . . . . . . . • . . . . . . 119


FIG. 4.29 BOND STRESS-SLIP RELATIONSHIP FOR CYCLIC LOADING, SERIES 2.8 . . • . . . . . • . . . . . . . . 120

xi


FIG. 4.30 BOND STRESS-SLIP RELATIONSHIP FOR CYCLIC LOADING, SERIES 2.9 . . · · · · · · · · · · · · · · · · · · 120

FIG. 4.31 BOND STRESS-SLIP RELATIONSHIP FOR CYCLIC LOADING, SERIES 2.10 · · · · · · · · · · · · · · · · 121

FIG. 4.32 BOND STRESS-SLIP RELATIONSHIP FOR CYCLIC LOADING, SERIES 2.11 · · · · · · · · · · · · · · · · · 121





FIG. 4.37 BOND STRESS-SLIP RELATIONSHIP FOR CYCLIC LOADING, SERIES 2.17 · · 0 · · · · · · · · · · · · · · 124

FIG. 4.38 BOND STRESS-SLIP RELATIONSHIP FOR CYCLIC LOADING, SERIES 2.18 · · · · · · · 0 · · · · · · · · · 124

FIG. 4.39a BOND STRESS-SLIP RELATIONSHIP FOR CYCLIC LOADING, SERIES 2.19-1 · · · 0 · · · · · · · · · · 0 · · · 125

FIG. 4039b BOND STRESS-SLIP RELATIONSHIP FOR CYCLIC LOADING, SERIES 2.19-2 · · · · · · · · · · · · 0 · · · · 125

FIG. 4.39c BOND STRESS-SLIP RELATIONSHIP FOR CYCLIC LOADING, SERIES 2.19-3 · · · · 0 · · · · 0 · · · · · · · · 126

FIG. 4.39d BOND STRESS-SLIP RELATIONSHIP FOR CYCLIC LOADING, SERIES 2.19-4 · · · · · · · · · · · · · · · · · · 126

FIG. 4.40a BOND STRESS-SLIP RELATIONSHIP FOR CYCLIC LOADING, SERIES 2.20 · · · · · · · · · · · · · · · · · 127

FIG. 4.40b BOND STRESS-SLIP RELATIONSHIP FOR CYCLIC LOADING, SERIES 2.20 · · · · · · · · · · · · · 0 0 · · 127

FIG. 4.40c BOND STRESS-SLIP RELATIONSHIP FOR CYCLIC LOADING, SERIES 2.20 · · 0 · · · · · · · · 0 · · · · · 128

FIG. 4.40d BOND STRESS-SLIP RELATIONSHIP FOR CYCLIC LOADING, SERIES 2.20 · · · · · · · · · · · · · · · · · 128

FIG. 4.40e BOND STRESS-SLIP RELATIONSHIP FOR CYCLIC LOADING, SERIES 2.20 · 0 · · · 0 · 0 · · · 129

xii

List of Figures (cont'd) Page

FIG. 4.41a

FIG. 4.41b

FIG. 4.41c

FIG. 4.41d

FIG. 4.41e

FIG. 4.41£

FIG. 4.41g

FIG. 4.42a

FIG. 4.42b

FIG. 4.42c

FIG. 4.42d

FIG. 4.43

FIG. 4.44

FIG. 4.45

FIG. 4.46

FIG. 4.47

FIG. 4.48

BOND STRESS-SLIP RELATIONSHIP FOR CYCLIC LOADING, SERIES 2.21-1 · · · · · · · · · · · · · · · · · · · 129


BOND STRESS-SLIP RELATIONSHIP FOR CYCLIC LOADING, SERIES 2.21-3 · · · · · · · · · · · · · · · · · · · · 130








BOND STRESS-SLIP RELATIONSHIP FOR CYCLIC LOADING, SERIES 2.22-4 · · · · · · · · · · · · · · · 134

STIFFNESS OF UNLOADING BRANCH AS A FUNCTION OF NUMBER OF UNLOADINGS · · · · · · · · . . · · · · · · · · · · · 135

FRICTIONAL BOND RESISTANCE DURING CYCLIC LOADING AS A FUNCTION OF PEAK SLIP s · · · · · · · · 135 max

RATIO BETWEEN FRICTIONAL BOND RESISTANCE DURING CYCLIC LOADING, Tf, AND BOND RESISTANCE, TunI' FROM WHICH UNLOADING STARTS AS A FUNCTION OF PEAK SLIP s

max

DETERIORATION OF BOND RESISTANCE AT PEAK SLIP AS A FUNCTION OF NUMBER OF CYCLES

DETERIORATION OF BOND RESISTANCE AT PEAK SLIP AS A FUNCTION OF NUMBER OF CYCLES, PLOTTED IN DOUBLE LOGARITHMIC SCALE . .

DETERIORATION OF BOND RESISTANCE AT PEAK SLIP AS A

· 136

· .. 137

· . . 138

FUNCTION OF THE PEAK VALUES OF SLIP s ...•..•. 138 max

xiii


FIG. 4.49

FIG. 4.50

EFFECTS OF NUMBER OF CYCLES AND OF THE PEAK VALUES OF SLIP smax ON THE ENSUING BOND STRESS-SLIP RELATIONSHIP FOR s > s ............. 0 0 • • • • max

IDEALIZATION OF BOND STRESS-SLIP RELATIONSHIP FOR CALCULATING THE CHARACTERISTIC VALUES OF THE REDUCED ENVELOPE . . . . • . . . . . . . . . . . . • . . . .

FIG. 4.51a REDUCTION OF MAXIMUM BOND RESISTANCE OF THE REDUCED ENVELOPE AS A FUNCTION OF THE PEAK VALUES OF SLIP AT WHICH CYCLING IS PERFORMED. TESTS WITH FULL REVERSALS OF SLIP

FIG. 4.51b REDUCTION OF ULTIMATE FRICTIONAL BOND RESISTANCE OF THE REDUCED ENVELOPE AS A FUNCTION OF THE PEAK VALUES OF SLIP AT WHICH CYCLING IS PERFORMED. TESTS WITH FULL

FIG. 4.52

REVERSALS OF SLIP

REDUCTION OF BOND RESISTANCE OF THE REDUCED ENVELOPE AS A FUNCTION OF THE PEAK VALUES OF SLIP AT WHICH CYCLING IS PERFORMED. COMPARISON OF RESULTS OF TESTS WITH FULL

l39

139

140

140

AND HALF CYCLES . . . • . • . • • . . • . . • . . 141

FIG. 4.53 BOND STRESS-SLIP RELATIONSHIP FOR CYCLIC LOADING, SERIES 1.6 . . . . . • • • • . . . • . . . . . • • 141

FIG. 4.54 BOND STRESS-SLIP RELATIONSHIP FOR CYCLIC LOADING, SERIES 1. 7 • . . . . • • . . • . . . . • . . . . . 142

FIG. 4.55 BOND STRESS-SLIP RELATIONSHIP FOR CYCLIC LOADING, SERIES 3.4 . . . . • . . . . • . . . • . . . . • . 142

FIG. 4.56 BOND STRESS-SLIP RELATIONSHIP FOR CYCLIC LOADING, SERIES 3.5 •..•••.•.••.•....••. 143

FIG. 4.57 BOND STRESS-SLIP RELATIONSHIP FOR CYCLIC LOADING, SERIES 3.6 . . . . . . . . . • . . . . . . . • . . 143

FIG. 4.58 BOND STRESS-SLIP RELATIONSHIP FOR CYCLIC LOADING, SERIES 4.2 • . . . . . • . • . . . . . • . • • . • 144

FIG. 4.59 BOND STRESS-SLIP RELATIONSHIP FOR CYCLIC LOADING, SERIES 4.3 . . . . . . . . . . . . • . . • . • . . 144

FIG. 4.60 BOND STRESS-SLIP RELATIONSHIP FOR CYCLIC LOADING, SERIES 5.4 ...•.•..•..•.••.•... 145

FIG. 4.61 BOND STRESS-SLIP RELATIONSHIP FOR CYCLIC LOADING, SERIES 5.5 . . . . . . . . . . . . • . . . . . • . 145

FIG. 4.62 BOND STRESS-SLIP RELATIONSHIP FOR CYCLIC LOADING, SERIES 5.6 . • . . . . • . • • . . . . • . . . . . 146

xiv


FIG. 4.63

FIG. 4.64

FIG. 4.65

FIG. 4.66

FIG. 4.67

FIG. 5.1

FIG. 5.2

FIG. 5.3

FIG. 5.LI

FIG. 5.5

FIG. 5.6

FIG. 5.7

FIG. 5.8

FIG. 5.9

FIG. 5.10

FIG. 5.11

BOND STRESS-SLIP RELATIONSHIP FOR CYCLIC LOADING, SERIES 6.5 . . . . . . . . . . . . . . . . . . . . BOND STRESS-SLIP RELATIONSHIP FOR CYCLIC LOADING, SERIES 6.6 . . . . . . . . . . . . . . . . . . . .

BOND STRESS-SLIP RELATIONSHIP FOR CYCLIC LOADING, SERIES 7.3 . .......... .... .

INFLUENCE OF INVESTIGATED PARAMETERS (DIRECTION OF LOADING, CONCRETE STRENGTH, BAR SPACING, TRANSVERSE PRESSURE, RATE OF PULLOUT) ON BOND BEHAVIOR DURING CYCLIC LOADING . . . . . . . . . . . . . . • . . . .

INFLUENCE OF BAR DIAMETER AND DEFORMATION PATTERN ON BOND BEHAVIOR DURING CYCLIC LOADING . . . . . .

MECHANISM OF BOND RESISTANCE, MONOTONIC LOADING

MECHANISM OF BOND RESISTANCE, CYCLIC LOADING . .

PROPOSED ANALYTICAL MODEL FOR LOCAL BOND STRESS-SLIP RELATIONSHIP FOR CONFINED CONCRETE . . . . . . . . .

COMPARISON OF EXPERU1ENTAL AND ANALYTICAL RESULTS OF BOND STRESS-SLIP RELATIONSHIP UNDER MONOTONIC LOADING

RATIO BETWEEN ULTIMATE FRICTIONAL BOND RESISTANCE OF REDUCED ENVELOPE AND OF MONOTONIC ENVELOPE AS A

146

147

147

148

148

149

150

151

152

FUNCTION OF THE DAMAGE FACTOR, d . . . . • . . . . • 153

DAMAGE FACTOR, d, FOR REDUCED ENVELOPE AS A FUNCTION OF THE DIMENSIONLESS ENERGY DISSIPATION E/E ..... 153

o

RELATIONSHIP BETWEEN FRICTIONAL BOND RESISTANCE DURING CYCLING, '[feN), AND THE CORRESPONDING ULTI¥ATE FRICTIONAL BOND RESISTANCE l3 (N) ................. 154

DAMAGE FACTOR, df' FOR FRICTIONAL BOND RESISTANCE DURING CYCLING AS A FUNCTION OF THE DIMENSIONLESS ENERGY DISSI-PATION Ef/Eof .. . . . . . . . . . . . . . . . . .. 154

CALCULATION OF ZERO INITIAL FRICTIONAL BOND RESISTANCE FOR UNLOADING FROM LARGER VALUE OF PEAK SLIP s THAN DURING PREVIOUS CYCLES ............ rn~x. • •• 155

COMPARISON OF EXPERIMENTAL AND ANALYTICAL RESULTS FOR BOND STRESS-SLIP RELATIONSHIPS FOR TEST SERIES 2.4 . .. 155

COMPARISON OF EXPERIMENTAL AND ANALYTICAL RESULTS FOR BOND STRESS-SLIP RELATIONSHIPS FOR TEST SERIES 2.6

xv

156


FIG. 5.12

FIG. 5.13

FIG. 5.14

FIG. 5.15

FIG. 5.16

FIG. 5.17

FIG. 5.18

FIG. 5.19

FIG. 5.20

FIG. 5.21

FIG. 5.22

FIG. 5.23

FIG. 5.24

COMPARISON OF EXPERIMENTAL AND ANALYTICAL RESULTS FOR BOND STRESS-SLIP RELATIONSHIPS FOR TEST SERIES 2.8 .. 156

COMPARISON OF EXPERIMENTAL AND ANALYTICAL RESULTS FOR BOND STRESS-SLIP RELATIONSHIPS FOR TEST SERIES 2.19 157

COMPARISON OF EXPERIMENTAL AND ANALYTICAL RESULTS FOR BOND STRESS-SLIP RELATIONSHIPS FOR TEST SERIES 2.13 157

COMPARISON OF EXPERIMENTAL AND ANALYTICAL RESULTS FOR BOND STRESS-SLIP RELATIONSHIPS FOR TEST SERIES 1.6 (112 VERTICAL BARS) . . . . . . . . . . . . . . . . . .. 158

COMPARISON OF EXPERIMENTAL AND ANALYTICAL RESULTS FOR BOND STRESS-SLIP RELATIONSHIPS FOR TEST SERIES 3.4 (#6 (19 mm) BAR) ....... 0 • • • • • • • • • • •• 158

COMPARISON OF EXPERU1ENTAL AND ANALYTICAL RESULTS FOR BOND STRESS-SLIP RELATIONSHIPS FOR TEST SERIES 3.5 (f18 (25 mm) BAR) . 0 • • • • • • • • • • • • • • • • •• 159

COMPARISON OF EXPERIMENTAL AND ANALYTICAL RESULTS FOR BOND STRESS-SLIP RELATIONSHIPS FOR TEST SERIES 3.6 (f/10 (32 mm) BAR) .•..••.•....•..... 159

COMPARISON OF EXPERIMENTAL AND ANALYTICAL RESULTS FOR BOND STRESS-SLIP RELATIONSHIPS FOR TEST SERIES 4.2 (f' == 54.6 N/mm 2

) •• o. • • • • • • • • • • •• 160 c

COMPARISON OF EXPERIMENTAL AND ANALYTICAL RESULTS FOR BOND STRESS-SLIP RELATIONSHIPS FOR TEST SERIES 5.4 (CLEAR SPACING = 1 db) . . . . . . . . . . . . . . . o. 160

COMPARISON OF EXPERIMENTAL AND ANALYTICAL RESULTS FOR BOND STRESS-SLIP RELATIONSHIPS FOR TEST SERIES 6.6 (p = 10 N/mm2

) • • • • • • • • • • • • • • • • • • • •• 161

COMPARISON OF EXPERIMENTAL AND ANALYTICAL RESULTS FOR BOND STRESS-SLIP RELATIONSHIPS FOR TEST SERIES 7.3 (8 = 170 mm/min) . . . . . . . . • . . . 0 • • • • • •• 161

BOND STRESS-SLIP RELATIONSHIPS UNDER MONOTONIC LOADING FOR DIFFERENT REGIONS IN A JOINT . . . 0 • • • • • • •• 162

PROPOSED DISTRIBUTION OF CHARACTERISTIC VALUES OF BOND RESISTANCE AND SLIP ALONG THE ANCHORAGE LENGTH • • . . 0 162

xvi

LOCAL BOND STRESS-SLIP RELATIONSHIPS OF DEFORMED

BARS UNDER GENERALIZED EXCITATIONS

Experimental Results and Analytical Model

I. INTRODUCTION

1.1 General

In earthquake resistant design of structures, economical requirements usually lead to the

need for large seismic energy input absorption and dissipation through large but controllable

inelastic deformations of the structure. The need for controlling the inelastic deformations fol

lows from the recommendations of the Structural Engineer's Association of California [1] that

buildings be designed to resist major earthquakes such that structural and nonstructural dam

ages incurred from an earthquake do not lead to collapse of the structure or to the endanger

ment of human life. Therefore, to meet the above requirements, the sources of potential struc

tural brittle failure must be eliminated and degradation of stiffness and strength under repeated

loadings must be minimized or delayed long enough to allow sufficient energy to dissipate

through stable hysteretic behavior.

In reinforced concrete (RIC), one of the sources of brittle failure is the sudden loss of

bond between reinforcing bars and concrete in anchorage zones, which has been the cause of

severe local damage to, and even collapse of, many structures during recent strong earthquakes.

Present bond seismic code provisions [2] appear to be inadequate. These provisions are based

on results obtained under monotonic loading, which are inadequate for gauging the actual struc

tural behavior during severe seismic shaking [3].

Even if no anchorage failures occur, the hysteretic behavior of reinforced concrete struc

tures, subjected to severe seismic excitations, is highly dependent on the interaction between

steel and concrete (bond stress-slip relationship) [4]. Tests show that developing displacement

ductility ratios of four or more, fixed end rotations caused by slip of the main steel bars along

their embedment length in beam-column joints, may contribute up to 50 percent of the total

- 2 -

beam deflections [5-71. These effects must be included in the analyses. However, this is not

possible at present because, in spite of recent integrated experimental and analytical studies [8]

devoted to finding such a relationship, no simple reliable bond stress-slip laws for generalized

excitations are available [9].

1.2 Objectives and Scope

The ultimate objectives of the work reported herein were to conduct all the necessary

integrated experimental and analytical investigations that will permit to predict analytically the

local bond stress-slip relationship of deformed reinforcing bars subjected to generalized excita

tions; for instance, as expected during the response of RIC structures to severe earthquake

ground motions.

To achieve these objectives, some 125 pull-out specimens were tested. Each one of the

specimens tested represented the confined region of a beam-column joint. Only a short length

(5 times the bar diameter db) of a Grade 60 deformed reinforcing bar was embedded in

confined concrete. Each specimen was installed in a specially designed testing frame and was

loaded by a hydraulic servo-controlled universal testing machine. The tests were run under dis

placement control by subjecting one bar end to the required force needed to induce the desired

slip, which was measured at the unloaded bar end.

The influence of the following parameters on the bond stress-slip relationship was studied.

(1) Loading history. The main parameters were: the peak value of slip (0.1 mm ~ s ~ 15

mm), the difference a s between the peak values of slip between which the specimen was

cyclically loaded (As = 0.05 mm, 1 Smax, and 2 smax), and the number of cycles (l to 30).

(2) Confining Reinforcement (none to 3% of concrete volume).

(3) Bar Diameter (#6, #8 and #10 bars (db:::::: 19, 25, 32 mm».

(4) Concrete Compressive Strength U: = 30 N/mm2 (4350 psi) and f: = 55 N/mm2 (8000

psi) .

- 3 -

(5) Clear Bar Spacing (s = 1 db to 6 db)'

(6) Transverse Pressure (p = 0 to 13.5 N/mm2 (1960 psi)).

(7) Loading Rate (increase of slip 170 mm/min., 1.7 mm/min., and 0.034 mm/min. (6.7

in/min., 0.067 in/min., and 0.0013 in/min.».

Based on the results obtained, an analytical model for the local bond stress-slip relation

ship was developed. It takes into account the significant parameters that control the behavior

observed in the experiments. By evaluating test data given in literature, rules were formulated

to extend the validity of the model to conditions different from those present in the tests.

- 4 -

II. LITERATURE REVIEW

2.1 Experimental Studies on Local Bond Stress-Slip Relationship

2.1.1 General Description

The interaction of deformed bars with concrete depends mainly on the mechanical inter

locking between lugs and concrete; adhesion and friction between the rough bar surface and

concrete adds only a little to the bond resistance [10, Ill. The bond characteristic of bars can

best be described by a relationship between local bond stress, T, and pertinent local slip, s, of

the bar [10]. In this report slip is defined as the relative displacement of the bar with respect to

concrete. This relationship is also needed for analytical models for predicting the behavior of

anchored bars. Therefore, the influence of the different parameters on the local bond stress

slip relationship will be described in the following.

Fig. 2.1 shows a bond stress-slip relationship (valid for a slip controlled test) for mono

tonic and cyclic loading. The graph is based on the results given in [8,9,10,121, with some

modifications based on the test results reported herein. The curves are simplified to better dis

tinguish the different regions.

When loading a specimen the first time, a bond stress-slip relationship is followed which is

called herein "monotonic envelope" (paths OABCDEF or OAjBjCjDjEjFj). Imposing a slip

reversal at point G, a stiff "unloading branch" is followed up to the point where the frictional

bond resistance (Tj) is reached (path GHI). Further slippage in the negative direction takes

place along the "friction branch" without significant increase in T (path IJ). When the bar is

almost back in the position before loading (s ::::: 0), it picks up load again, but the values of T

might be reduced compared to the values corresponding to the monotonic envelope, as illus

trated by path JB']C'jK. The curve OA']B']C'jD'IE']F'] is called herein ojreduced envelope".

When reversing the slip again at K, first the stiff unloading branch and then the friction branch

with T = T] are followed (path KLM). Well before reaching Smax (from which unloading

started), the bond stresses increase again ("reloading branch", path MG'). For:!l = Smax. the

- 5 -

corresponding T is much lower than at first loading. Increasing the slip further, a curve similar

to the monotonic curve is followed, but with T values that might be reduced (path G'D'E'F').

This curve is also called herein "reduced envelope". In the following, the different branches of

the local bond stress-slip relationship and the main parameters influencing them will be dis

cussed in more detail.

2.1.2 Monotonic Loading

The monotonic envelope can be described by the characteristic points OABCDEF.

When loading an anchored bar, relative movements between steel and concrete (slip) will

occur. The slip is caused mainly by crushing of the concrete in front of the lugs. At first, the

bond resistance is made up by adhesion up to point A. Further loading will mobilize the

mechanical interlocking of cement paste on the microscopic irregularities of the bar surface as

well as the mechanical interlocking between the lugs and concrete. The high pressure on the

concrete in front of the lugs causes tensile stresses in the concrete around the bar, which, in

turn, create internal inclined cracks, called herein "bond" cracks, say at point B. These bond

cracks were shown by Goto [14] experimentally (Fig. 2.2) and by several researchers

[7,8,11,13,15] analytically, using the method of finite elements.

The bond cracks modify the response of concrete to loading. Its stiffness will be dimin

ished and, therefore, larger slip increments will be needed for further T-increments than before

cracking. After the occurrence of bond cracks, the stress transfer from steel to the surrounding

concrete is achieved by inclined compressive forces spreading from the lugs into concrete at an

angle a (Fig. 2.2c). The components of these forces parallel to the bar axis are proportional to

the bond stress T. The radial component, with respect to the bar axis, loads the concrete like

an internal pressure and induces tensile hoop stresses which cause splitting cracks. When these

cracks reach the concrete surface, say at a T illustrated by point C in Fig. 2.1, and none or only

a small amount of confining reinforcement is provided, the bond resistance will drop to zero

(path CP).

- 6 -

However, if the concrete is well confined, the load can be increased further. When

approaching the maximum bond resistance (point D), shear cracks in a part of the concrete

keys between ribs are initiated [10,16] (Fig. 2.3). With increasing slip with respect to 57 ,an max

increasing area of concrete between lugs is affected by this shear failure and, consequently, the

bond resistance is reduced. At point E, the concrete between lugs is completely sheared off,

and the only mechanism left is frictional resistance between rough concrete at the cylindrical

surface where shear failure occurred. On the contrary to [10,16], Tassios [9] assumes that the

maximum bond resistance is controlled by a compression failure of the compression struts

spreading out from the lugs into the concrete.

The ascending branch of the bond stress-slip curve (path OABCD in Fig. 2.1) has been

studied extensively. However, not much is known about the descending branch (path DEF),

which can only be measured in a deformation controlled test.

The bond resistance offered by adhesion is rather small (7 A = 0.5 to 1.0 N/mm2 (- 72 to

145 psi) [9]). The bond stress at occurrence of internal bond cracks can be roughly estimated

to 7 B = 2 to 3 N/mm2 (290 to 435 psi) for a concrete with /; = 30 N/mm2 (4350 psi) [7,9].

Analysis of these values reveals that under service load adhesion is overcome and internal bond

cracks will occur.

Splitting of concrete due to bond has been thoroughly studied in [17-19]. According to

this work, the splitting resistance depends mainly on the concrete tensile strength, concrete

cover, bar spacing, amount of transverse reinforcement and transverse pressure. The bond

stress 7 c at splitting may be as low as 2 N/mm2 (290 psi) or as high as 7 N/mm2 (1015 psi) for

a concrete having a f; = 30 N/mm2 (4350 psi) and with no transverse pressure applied,

depending on the actual values for concrete cover, bar spacing, and confining reinforcement.

The maximum bond resistance 7 max is mainly influenced by the concrete strength, bar

deformations, and the position of the bar during casting. The influence of the bar diameter is

relatively small if all dimensions (height and distance of bar lugs and concrete dimensions) are

kept constant as multiples of the bar diameter [13]. The bond strength might also be

- 7 -

influenced by confining reinforcement and transverse pressure, but their influence is not

sufficiently studied yet.

The Tmax increases with increasing concrete strength. It amounts to 'Tmax::::: 10 to 15

N/mm 2 (1450 to 2175 psi) for l = 30 N/mm 2 (4350 psi) and bars with normal deformation

patterns cast horizontally. The given values are average 'Tmax over a certain bond length (usu-

ally 3 db to 5 db)' Locally 'T max might be larger. Rehm [10] and Martin [13] assume that 'T max

is proportional to l, but other authors [20,21] normalize the results for different concrete

strengths with fl. The influence of the deformation pattern can best be described by the so-

called "related rib area", asR [10] (Eqn. 2.0; that is, the relation between bearing area (area of

the lugs perpendicular to the bar axis) to the shearing area (perimeter times lug spacing).

where

asR k· FR 'sinj3

'IT' db . C

k number of transverse lugs around perimeter;

FR area of one transverse lug;

sinj3 angle between lug and longitudinal axis of bar;

C = center to center distance between transverse lugs.

(2.1)

For bars cold worked by twisting, a second term is added [10] which is not given here. Figure

2.4 shows the influence of the related rib area and of the position of the bar during casting on

the local bond stress-slip relationship. It can be seen that bond strength and bond stiffness

increase with increasing values asR' Reinforcing bars commonly used in the U.S. have values

asR between approximately 0.05 and 0.08.

The frictional bond resistance T E has been barely investigated yet. For a concrete with f;

= 30 N/mm2 (4350 psi), values for T D of about 0.4 N/mm2 (58 psi) to 10 N/mm2 (1450) are

given [8,9,221.

The bond resistance at given slip values scatters considerably. Extensive studies [23]

show that the average standard deviation for the bond resistance in the slip range s = 0.01 mm

(0.0004 in.) to ST is about 1.3 N/mm2 (189 psi) for ideal test conditions (e.g., pull-out tests max

- 8 -

of identical bars with short embedment length and specimens cast from the same concrete

batch). A much higher scatter is to be expected for less ideal conditions. This partially

explains the scatter of the data given in the literature for characteristic T-values (e.g., T max).

The bond stiffness given in the literature scatter even more. This is demonstrated by Fig.

2.5, which shows local bond stress-slip relationships for small slip values after different authors.

The local bond stress-slip relationships were derived from the results of tests with different test

specimens. They are valid for bond regions well away from a concrete face. According to [24],

the large scatter of available data is mainly due to difficulties in measuring slip between steel

and concrete correctly and to the use of different test specimens with different stress conditions

in the concrete surrounding the bar. Furthermore, the scatter may have been caused by the

use of bars with different diameter and different deformation pattern. According to [10], the

bond stiffness decreases for constant bar diameter with increasing relation between lug distance

c and lug height a and for constant values cia with increasing bar diameter. Also, the number

of tests was not always sufficient to produce reliable local bond laws.

The shape of the local bond law is significantly influenced by the position of the bar dur

ing casting (Fig. 2.4). The largest bond stiffness is reached for bars cast vertically and loaded

against the setting direction of fresh concrete. Bars cast horizontally show a much smaller

stiffness and a lower bond strength. Bars cast in the vertical position but loaded in the setting

direction of the concrete may perform even poorer than bars cast horizontally [10]. The same

is true for bars cast in a horizontal position when the depth of concrete beneath the bar is

increased [20].

The local bond law for loading in tension or compression is almost identical [10].

Observed differences in tests (e.g. in [12]) can mainly be attributed to loading the bar in

different directions with respect to the setting direction of the fresh concrete.

The local bond stress-slip relationship may vary along the embedment length. According

to [25-28]' bond stiffness and bond strength are 2-3 times larger in the interior of a specimen

with tension forces acting on both ends of the embedded bar than towards the ends. However,

- 9 -

no significant influence of the location on the local bond law was observed in the comparable

tests [29]. In [8] three different regions with very different bond stress-slip behaviors were

identified in a beam-column joint: unconfined concrete in tension, confined concrete and

unconfined concrete in compression (Fig. 2.6). A similar influence of the location on the local

bond law was found in [22].

2.1.3 Cyclic Loading

The influence of repeated (not reversed) loading with constant peak loads has been stu

died in [30-32]. According to [31], repeated load has a similar influence on the slip and the

bond strength of deformed bars as on the deformation and failure behavior of unreinforced

concrete loaded in compression. The bond strength decreases with increasing number of cycles

between constant bond stresses (fatigue strength of bond, Fig. 2.7). The slip under peak load

and the residual slip increase considerably as the number of cycles increases (Fig. 2.8) If no

fatigue failure of bond occurs during cycling and the load is increased afterwards, the mono

tonic envelope is reached again and followed thereafter. That means, provided the peak load is

smaller than the load corresponding to the fatigue strength of bond, a preapplied repeated load

influences the behavior of bond under service load but does not adversely affect the bond

behavior near failure compared to a monotonic loading.

Although many factors related to early concrete damage (microcracking and microcrushing

due to high local stresses at the lugs) may be involved in this bond behavior during repeated

loads, the main cause of the slip increase under constant peak bond stresses is creep of concrete

between lugs [31].

The influence of reversed loading on the local bond stress-slip relationship has not been

studied extensively. In [I2] the following characteristic behavior was found:

(a) After loading in one direction, the bond stress-slip relationship for loading in the reversed

direction is almost identical with the monotonic envelope in that direction.

(b) Once a peak slip value is reached, a considerable reduction in bond resistance is produced

at lower slip values in the subsequent load history.

- 10 -

(c) The peak bond stress under cycli.c loading between constant slip values deteriorates

moderately and is not significantly influenced by the loading history.

(d) A small number of cycles between limited slip values do not give a significant effect on

the bond stress-slip behavior for slip values larger than the peak slip in the previous

cycles.

This behavior was also found in the earlier studies [33,34]. However, it must be remem-

bered that in all these tests cycling was performed between rather small slip values with

corresponding bond stresses well below the monotonic T max or the fatigue strength of bond

(compare Fig. 2.7).

In [8] specimens representing a beam-column interior joint were cycled between different

increasing Smax' Figure 2.9 shows a typical local bond stress-slip relationship, which was

deduced from the measured steel strains along the anchorage length and the measured slip at

the bar ends. These results indicate that cycles between constant slip values equal to or larger

than the slip ST (ST = slip value corresponding to the monotonic T max) do produce a pro-max max

nounced deterioration of the bond resistance at peak slip and may have a significant effect on

the bond stress-slip behavior at slip values larger than the peak slip in the previous cycles. The

deterioration of bond strength and bond stiffness is much more pronounced for full reversed

cycles (Ismin I = I smaxD than for half cycles (Smin = 0) [3,6].

According to [9,12] the frictional bond stress T f after first unloading from a bond stress

T < Tmax seems to be a constant multiple of T (r f = a 'T, with a ::::::: 0.18-0.25). On the con-

trary, in [8] it is assumed that T f is independent of the bond stress from which the unloading is

started, and the given value (T f::::::: 0.4 N/mm2 (60 psi)) is rather low. The frictional bond

resistance deteriorates during subsequent cycles between fixed slip values. A rough estimate of

the deterioration rate is given in [9].

2.2 Analytical Models for Cyclic Loading

The first analytical model of the local bond stress-slip relationship for cyclic loading was

- 11 -

proposed by Morita/Kaku [121. It is shown in Fig. 2.10.

The monotonic envelopes, which are different for loading in tension or compression and

for confined or unconfined concrete, are given by two successive straight lines which follow

closely the experimentally measured curve. The assumed bond stress-slip relationship for the

first cycle coincides relatively well with the behavior observed in experiments. However, the

observed deterioration of the bond resistance at peak slip and of the frictional bond resistance

with increasing number of cycles is not taken into account. After cycling between arbitrary slip

values, it is assumed that the monotonic envelope is reached again at slip values larger than the

peak value in the previous cycle and followed thereafter.

The model is sufficiently accurate for a small number of cycles between relatively small

slip values with corresponding bond stresses smaller than about 80 percent of the monotonic

T max' However, it is inaccurate for several load cycles, and it is not valid for slip values larger

than the one corresponding to 0.8 T max' In [35] a simplified version of this model was used for

the analytical investigation of a concrete panel under load cycles with some success.

Figure 2.11 shows the bond model proposed by Tassios [91. The monotonic envelope

consists of six successive straight lines. The coordinates of the controlling points A to E, which

have the same physical meaning as described in Section 2.1.2, are theoretically evaluated and

given as a function of the relevant influencing parameters. The same bond stress-slip relation

ship is assumed regardless of whether the bar is pulled or pushed. After loading to a slip value

S > SB, the values of T of the bond stress-slip relationship for loading in the reversed direction

are reduced by 113 compared to the monotonic envelope. The bond stress-slip relationship for

reloading and for subsequent cycles between fixed slip values is somewhat simplified compared

to the real behavior. However, the deterioration of the bond resistance at peak slip and of the

frictional bond resistance is taken into account. When increasing the slip beyond the cyclic

peak value (s > Sc in Fig. 2.10, it is assumed that the monotonic envelope is reached again

and, therefore, no deterioration of the monotonic envelope is taken into account.

Tassios' model is an improvement compared to the older one of Morita/Kaku insofar as

- 12 -

the descending branch of the local bond stress-slip relationship is given and the influence of

load cycles on bond deterioration for slip values smaller than or equal to the peak slip value in

the previous cycle is taken into account. However, the assumption that for slip values larger

than the peak value in the previous cycle the monotonic envelope is reached again and followed

thereafter, while the bond stresses in the reversed direction are reduced by 1/3 compared to the

monotonic envelope, is not sufficiently accurate. For monotonic loading, the model is useful

for the total slip range. However, for cyclic loading it is valid for slip values S «ST only. max

Recently, another proposal for a local bond stress-slip law was published in [8] (Fig. 2.12).

The model's main characteristics are as follows:

(a) A four stage piecewise linear approximation is used as monotonic envelope. The physical

meaning of the controlling points are the same as described in Section 2.1.2. However,

points Band C (occurrence of internal bond cracks and splitting cracks) are omitted.

Different monotonic envelopes are assumed for unconfined concrete in tension, confined

concrete and unconfined concrete in compression, which simulate the behavior observed

in the experiments (compare Fig. 2.6).

(b) Cycling between points A and Aj or unloading and reloading only (paths GIG or KLK)

do not deteriorate the envelope.

(c) Unloading from a point beyond A or Aj and following the friction path for an arbitrary

small slip value produces reduced envelopes (OAD'E'F' and OAjD'jE'jF'j) by reducing

the characteristic bond stresses TD,TDl,TE,TEj and the slip values SE,SEl by a reduction

factor. The latter depends on the cumulative slip having magnitudes larger than those of

the previous cycle. Therefore, no further reduction of the envelope is assumed for subse-

quent cycles between slip values smaller than or equal to the previous peak slips.

As an example, Eqn. 2.2 gives the reduction of T D. Similar equations exist for the reduc-

tion of the other characteristic values which describe the model.

[ L sJ SD L Sill SD I

T ~ = aD' T D = 1 - aT D • , - f3 . , T D T D PD TD TD PD

(2.2)

- 13 -

where

l:>;,LSil: sum of the peak slip values having a magnitude larger than in the previ

ous cycles for loading in tension or compression, respectively;

SD: slip at point D;

aT D,{3T D,g T D,PD: constants, evaluated from test results.

(d) The frictional bond resistance is assumed to be equal to T E of the monotonic envelope

and independent of the number of cycles.

(e) The bond stress-slip relationships for the reloading branch (path MRN) and for additional

cycles between fixed slip limits are very similar to those proposed in [12].

The above model is a major improvement, because it takes several features observed in

experiments into account and it is approximately valid for cycling between arbitrary slip values.

However, in spite of being rather complicated, it is not general. Some 20 parameters are

needed to describe the bond stress-slip relationship for cyclic loading, which have no clear phy

sical meaning and must be evaluated from test results. Furthermore, the assumptions on which

the calculation of the reduced envelope is based need improvement. For example, an arbitrary

number of cycles (~1) in well-confined concrete between Smax = 2sD and Smin = -2sD reduces

T D independent of the number of cycles by 13 percent. On the contrary to that T D is reduced

to zero after eight cycles between almost the same peak slip values if only the value of Smax is

increased arbitrarily small in each cycle.

2.3 Summary of Chapter 2

To date several thousand experiments have been carried out to study the ascending

branch of the local bond stress-slip relationship for monotonic loading. By contrast, its des

cending branch, which can only be measured in a deformation controlled test, has hardly been

investigated. While the bond behavior for repeated (not reversed) loadings with peak bond

stresses well below the monotonic bond strength under monotonic loading is fairly well known,

the knowledge about this behavior for reversed loadings between relatively large peak slip

- 14 -

values is rather limited.

Bond between reinforcing bars and concrete does scatter significantly, even under nearly

ideal laboratory conditions. This has to be taken into account when evaluating results from

bond tests, planning new test series, or estimating the influence of bond on the overall behavior

of reinforced concrete elements or structures.

While the characteristic bond resistances of the ascending branch of the monotonic

envelope can be fairly well estimated, the prediction of the corresponding slip values is very

difficult and a large scatter must be expected. The shape of its descending branch and the ulti-

mate frictional bond resistance are h~rdly known yet.

The bond behavior for reversed loadings between rather small slip values (s «S7 ) max

can be predicted with sufficient accuracy. However, the knowledge about the influence of

cycles between larger slip values (s ~ S7 ) on the local bond stress-slip relationship is still in max

its infancy.

The analytical models for a local bond stress-slip relationship for cyclic loadings proposed

so far reflect this inadequate knowledge and cannot be accepted for general excitations. There-

fore, the present study concentrates on the local bond law for relatively large slip values for

monotonic and cyclic loadings. The results of an extensive experimental investigation and an

analytical model for prediction of such laws is presented herein.

- 15 -

III. EXPERIMENTAL PROGRAM

3.1 Test Specimen

The test specimens should represent as closely as possible the conditions found in a

beam-column joint. Therefore, these conditions and the considerations to model them

appropriately in a test specimen are described in the following.

Figure 3.1 (after [36]) shows the hysteretic behavior of an interior joint when loaded by a

lateral force H, which simulates the effect of an earthquake loading. First, as H increases from

o to B, cracks develop on both sides of the column, Fig. 3.1 (b). After unloading and applying

H in the opposite direction (path BCD), diametrically opposed cracks develop on either side of

the column, Fig. 3. ICc) . If the load reversals applied in both directions are sufficiently severe

to cause permanent strain in beam bars, cracks through the entire beam cross section are

formed, as shown in Fig. 3.1 (d). The bars that run through the column are simultaneously

pulled and pushed from opposite sides under cyclic loading. The critical condition develops

when a bar is subjected to full reversals of tensile and compressive forces developing high bond

stresses along the bar embedment length within the column. This may lead to a severe

stiffness degradation of the joint caused by bond failure of the beam bars within the column.

In Fig. 3.2 (taken from [37]), an interior joint after testing is shown. If the column is less

strong than in this experiment, bending and shear cracks will develop in the column as well

(Fig. 3.3, taken from [38]), which can change the bond stress-slip relationship. Even if no

bending and shear cracks occur in the joint, the bond conditions vary along the embedment

length (Fig. 2.6), depending on the state of stress and strain in the concrete around the bar.

The unconfined concrete at the tensioned bar end offers the least bond resistance because

of the early formation of radial splitting cracks caused by high tensile hoop stresses. Bond

failure is caused by the separation of a concrete cone (Fig. 3.4) from the concrete block due to

bond forces acting on the concrete in front of the lugs. Much better bond conditions are found

in the concrete core between confining reinforcement. Splitting cracks in the plane between

- 16 -

bars may develop, but their growth will be controlled by the confining reinforcement, and bond

failure is probably due to a shear failure in the concrete between lugs. The best bond is offered

by the unconfined concrete at the compressed bar end, because at this end the concrete lateral

to the bar is under high compressive stresses caused by the column normal force and the

moment acting on the joint and caused by the expansion of the bar due to the Poisson effect.

The bond is not only influenced by the above mentioned parameters, but it might also be

different for top and bottom bars (top bar effect), edge and interior bars (different

confinement) and may vary with such parameters as bar diameter, concrete strength, bar dis

tance, degree of confinement, etc.

To simulate the simultaneous push-pUll condition of a beam bar in an interior joint, a

simplified model was used in [8,221. Single bars were cast in well-confined concrete blocks,

their width being up to 25 times the bar diameter, and subjected to monotonic or cyclic loadings

(see Fig. 2.6). Extensive data (applied forces, steel strains along embedment length, displace

ments of bar ends relative to the middle of the concrete block and cracks) were taken during

the tests. The results gave a very good insight in the overall behavior of an anchored bar.

Some local bond stress-slip relationships were deduced from the data. However, the evaluation

of such relationships was complex, and their accuracy is somewhat questionable. Local bond

stresses and local slip were calculated from the difference of the measured steel strains at adja

cent points along a bar and converting them into local slip and steel stresses. Since the strain

measurements have considerable scatter, particularly so for cyclic loading after a bar yields, the

calculated results tend to be inaccurate. Furthermore, these tests are expensive and time con

suming, which prohibits a thorough study of relevant parameters. Therefore, a different

approach was used in this study.

The specimen (Fig. 3.5) should represent the confined region of a beam-column joint.

Therefore, the concrete was confined by secondary reinforcement representing the column rein

forcement. To ensure a good anchorage of the vertical bars, they were rigidly connected with

the top and bottom stirrups by arc welding.

- 17 -

Only a short length of a Grade 60 deformed bar was embedded in concrete. During the

test, the force acting on the loaded bar end and the slip, measured at the unloaded bar end,

were recorded. Assuming that the bond stresses are evenly distributed along the bonded length, they

can easily be calculated from the measured forces. Furthermore, because the steel behaves

elastically and the embedment length is short, the slip values at the unloaded and loaded bar

ends do not differ significantly from each other. Therefore, the measured slip represents the

local slip in the middle of the embedment length with sufficient accuracy. Note that strictly

speaking the so obtained relationship is not a local bond stress-slip relationship but an average one.

However, the embedment length was chosen to,5 db' This embedment length is short enough

so that the basic assumptions (see above) are still valid with sU.fficient accuracy but long enough

to reduce the scatter of test results usually observed in tests with a very short bonded length.

The bonded length was positioned in the middle of the specimen, and a bond free length

of 5 db at either side was employed. By this arrangement and by placing teflon between the

specimen and the bearing plates (see Fig. 3.6 and Section 3.5), the influence of a possible res

traint of concrete lateral strains by friction at the bearing plates was reduced as much as possi

ble.

The bond free length was obtained by placing a thin metal tube concentrically around the

bar and sealing the ends with mastic to prevent concrete from flowing in. The inner diameter

of the tubes was about 4 mm (0.16 in.) larger than the outer diameter of the bars, including

lugs. The tubes neither restrained the slip of the bar nor significantly affected the transfer of

bar forces to the concrete. Some preliminary tests showed that the bond stress-slip relationship

was not influenced by tubes with slightly different inner diameters or wall thicknesses.

Because splitting cracks might influence the bond stress-slip behavior, the resistance

against splitting was simulated as closely as possible to that which might exist in a real struc

ture. For this purpose, thin plastic sheets were placed in the plane of the longitudinal axis of

the bar (Fig. 3.5), which limited the concrete splitting area to the desired value. The length of

the splitting area was 1.5 db larger than the bond length because of the higher relation between

- 18 -

splitting and bond forces in tests with short embedment length compared to the middle of a

long anchorage [19,391. The width of the splitting area was equal to the assumed clear bar dis

tance, which was varied between 1 db and 6 db. This method of simulating various bar dis

tances was chosen because the outer dimensions of the specimen and the confining reinforce

ment could be kept constant, which simplified the production of the specimens.

The bars were placed in the middle of the specimens (height 12 inches:::::: 300 mm) and

cast in a horizontal position. Therefore, the bond could be expected to be somewhat superior

or inferior to top or bottom bars, respectively.

3.2 Test Program

A summary of the test program is given in Table 3.1. The tests are subdivided into 7

series, depending on the parameter studied. Only one parameter was varied in a test series,

while all other parameters were kept constant. The "normal" or standard set of parameters was:

Tested Bar:

Confining Reinforcement:

Concrete Strength:

Transverse Pressure:

Loading Rate:

#8 (db = 25.4 mm)

made out of #4 bars (db = 12.7 mm)

f; = 30 N/mm2 (:::::: 4350 psi)

None

1.7 mm (0.067 in.) slip/minute

Main Test Series 2 (Table 3.1a) was used to investigate the influence of various slip his-

tories on the local bond stress-slip relationship. The main parameters were:

Monotonic loading in tension and compression (Series 2.1, 2.2, and 2.16).

Cyclic loading between full reversals of slip (full cycles) at different peak slip values cov

ering the whole range of the bond stress-slip law (Series 2.3 to 2.11 - Fig. 3.7).

Cyclic loading between slip s=O and a selected peak slip value (half cycles) (Series 2.12 to

2.15).

- 19 -

Cyclic loadings with a difference in slip .1s = 0.05 mm at selected peak slip values (Series

2.17 and 2.18). In these tests the load dropped from the peak value to almost zero.

Cyclic loading under different increasing Smax (Series 2.19 to 2.22).

In the Test Series 2.3 to 2.18, after the specimens were subjected to either lor, alterna

tively, to 10 cycles up to the selected peak values of slip, the slip was increased monotonically

to failure. On the contrary, the bars of Test Series 2.19 to 2.22 were subjected to a series of

cycles at different values of slip with 5 cycles at each step.

In the cyclic test, usually the first and final loadings after completing the cycles were done

in tension. Only in Test Series 2.6* was the loading started and completed in compression.

In the other six test series (Table 3.1b), the influence of various other parameters on the

basic bond behavior under monotonic and cyclic loadings were studied:

Series 1:

Series 3:

Series 4:

Series 5:

Series 6:

Confining reinforcement: The diameter of the vertical bars were varied

from #8 (db:::::: 25 mm) to #2 (db:::::: 6.4 mm) (Series 1.1 to 1.3). In addi

tion, specimens without confining reinforcement were tested (Series 1.4).

In Series 1.5, the influence of the stirrups was studied.

Bar diameter: The bar diameter was varied from #6 (db:::::: 19 mm) to #10

(db:::::: 32 mm), thus covering the range normally used in buildings designed

to resist severe earthquakes.

Concrete strength: While usually the concrete strength was f;:::::: 30

N/mm2 (:::::: 4350 psi), it was increased to f;:::::: 55 N/mm2 (:::::: 7975 psi) in

Test Series 4.

Bar spacing: The clear distance between bars was varied between c = 1 db

(minimum value allowed in the code) to c = 6 db'

Transverse pressure: Pressure ranging from 5 N/mm2 (725 psi) to 13.2

N/mm2 (1914 psi) was applied in the direction of the column reinforcement

to simulate the influence of column compression forces on bond behavior.

Series 7:

- 20 -

The applied maximum pressure was equal to about 45 percent of the con

crete compressive strength. For comparison, tests with no transverse pres

sure were carried out as well.

Loading rate: The adopted standard rate of pull-out 0.7 mm (0.067 in.) slip

per minute) was mainly chosen for practical reasons to terminate a test in a

reasonable time. It was about 10 times faster than the loading rate recom

mended for standardized load-controlled pUll-out tests [40). The chosen slip

increase of 1.7 mm (0.067 in.) per minute gave an average increase in steel

strain up to the peak load of about 1.5 mm/m per minute. During an earth

quake, larger strain rates are reached. Therefore, the rate of pUll-out was

increased to 170 mm (6.69 in.) slip/min. (100 times faster than the standard

value) in Test Series 7.1 and 7.3. In addition, the influence of a 50 times

slower rate of pull-out (0.034 mm (0.0013 in.) slip/min.) was studied in

Test Series 7.2.

The influence of the above mentioned parameters was studied for monotonically increas

ing slip and for cyclic loading at a peak slip value Smax = 1.65 mm (0.065 in.). In the cyclic

tests, after performing 10 cycles between fixed slip values, the slip was increased monotonically

to failure.

Usually two or three identical tests were carried out to reduce the effect of inevitable

scatter of results. Note that the average values calculated from two or three tests represent no

statistically reliable mean value. To determine such a value, more repetitive tests are necessary.

However, the objective of this study was not to achieve statistically reliable bond stress-slip

relationships for a small number of variables but to investigate the influence of several parame

ters on the bond behavior, especially under cyclic loading. Altogether 125 specimens were

tested; from that 47 specimens were loaded monotonically and 78 specimens loaded cyclically.

3.3 Material Properties

3.3.1 Concrete

- 21 -

The concrete was made from normal weight aggregate. The mixes used are given in

Table 3.2. For the medium strength concrete U; = 30 N/mm2 = 4350 psi), the amount of

cement was 356 kg/m3 (596 Ib/cu. yd.), the water-cement ratio was 0.57 and the maximum

aggregate size was 9.5 mm (3/8 in.). For the high strength concrete U; = 55 N/mm2 = 7975

psi), the values were: amount of cement = 505 kgl m3 (845 Ib/cu. ydJ, water-cement ratio =

0.38, and maximum aggregate size = 9.5 mm (3/8 inJ. The aggregate grading is shown in Fig.

3.8.

The average slump was 4.75 inches (120.7 mm), with minimum and maximum values of

3.25 and 6.0 inches (82.6 and 157.4 mm), respectively. The concrete was relatively easy to cast

and compact, with no apparent segregation of its components.

The measured concrete strengths are summarized in Table 3.3. Twelve standard cylinders

were cast from each concrete batch. Nine cylinders were used to measure the concrete

compressive strength and three cylinders to test the splitting tensile strength. The compression

tests were done usually at the beginning, in the middle, and at the end of the time needed to

test all specimens cast from one batch~ This time was 3 to 5 days. The splitting tensile

strength tests were performed in the middle of that time. The tests started about four weeks

after casting. No significant increase in strength was noticed during the time of testing. There

fore, only the average strengths of all tested cylinders are given in Table 3.3.

The average concrete strengths agreed very well with the values aimed at. Note that the

small coefficients of variation for the 30 N/mm2 concrete (3.3 percent for f; and 6.9 percent

for ft, respectively) indicate that a very good uniformity of concrete properties was achieved

throughout the tests. This was due to the fact that the amount of material needed for all tests

was stored at the beginning. In the last column of Table 3.3, the relation between ft and f?!3

is given. The average relationship agrees well with the value given in [41].

- 26 -

IV. EXPERIMENTAL RESULTS

4.1 General

In this chapter the experimental results will be presented and the influence of the

different parameters investigated will be discussed in detail. Bond stress-slip diagrams were

deduced by taking applied forces at given slip values from the records monitored by the XY

recorder and converting them into bond stresses using Eqn. 4.1:

where

F T =

F force [N];

db actual bar diameter [mm] (see Table 3.4);

Ie embedment length;

3.75 inches (95.3 mm) for #6 bars;

5.0 inches (127.0 mm) for #8 bars;

6.25 inches 058.8 mm) for #10 bars.

(4.1)

The concrete strength differed somewhat from the desired value f; = 30 N/mm2• There-

fore, the bond stresses plotted were converted to the latter value by Eqn. 4.2:

TU;=30N/mm2) = T(Eqn.4.1l ·-J30/f;

where l is the actual concrete compressive strength in N/mm2.

For plotting bond stress-slip diagrams, the following convention was used:

positive or negative bond stress - bar in tension or compression, respectively

positive or negative slip values - bar pulled out or pushed in, respectively.

4.2 Visual Observations and Failure Mode

(4.2)

In all tests, except those with an applied transverse pressure, a splitting crack developed

prior to failure in the plane of the longitudinal axis of the bar. Its development could often be

noted from a low bang or could sometimes be detected from the monitored load-slip relation-

ship. The bond stress at splitting was about 4 to 9 N/mm2 (580 to 1305 psi) for concrete with

- 27 -

f; = 30 N/mm2 (4350 psi). After developing this crack, the load dropped rapidly if the con

crete was not confined by reinforcement (Series 1.4). However, in the case of confined con

crete, the load could be increased further with a gradually decreasing bond stiffness. This can

be explained by the fact that the growth of cracks was controlled by the vertical bars crossing

the crack plane. The width of these cracks could not be measured exactly because of the plastic

sheets used to limit the concrete splitting area (Fig. 3.5), but it is believed that they did not

exceed about 0.05 mm (0.002 in.), in general, or 0.1 mm (0.004) (vertical bars #2), respec

tively.

In all tests conducted on specimens with confined concrete, the failure was caused by pul

ling out of the bars at steel stresses well below yield strength (max. lIs:::::: 0.4 to 0.8 f y ). The

concrete between lugs was completely sheared off and almost pulverized (Fig. 4.1). By sawing

the concrete and the vertical reinforcement of some specimens, it was possible to take the

specimen apart and to inspect the surface of the concrete that was in contact with the bar. No

signs of failure of the concrete in compression in the direction of inclined bond forces (as

assumed by Tassios [9]) could be detected.

The specimens of Series 1.4 (no confining reinforcement) failed by splitting of the con

crete in the plane of the longitudinal axis of the bar at about 45 percent of the pull-out load of

comparable specimens with confined concrete. The concrete between lugs was intact and no

severe damage (shear cracks or crushing) could be detected (Fig. 4.2).

4.3 Monotonic Loading

The test results for monotonic loading are plotted in Figs. 4.3 to 4.20.

4.3.1 General Behavior

Figures 4.3 to 4.9 show the results of all monotonic loading tests of Series 1 and Series 2.

For tests with confined concrete, the typical behavior was as follows.

The stiffness of the ascending branch of the bond stress-slip curve decreased gradually

from its initial large value to zero when approaching the maximum bond resistance at a slip

- 28 -

value of approximately 1.5 mm (0.06 in,) (Fig. 4.8). After passing T max, the bond resistance

decreased slowly and almost linearly until it leveled off at a slip of s = 11 to 12 mm (0.43 to

0.4 7 in.). This value is almost identical to the clear distance between lugs. For larger slip

values, the bond resistance was usually almost constant (Fig. 4.7) or decreased slightly in some

cases (Figs. 4.3 to 4.5). Therefore, the bond stress-slip curves of all other tests were drawn

only up to 12 mm (0.47 in,) slip.

The scatter of the bond stress-slip curves of specimens cast from the same batch and

tested identically was significantly smaller than what could be expected according to [23]. The

scatter in Test Series 1.3 and 1.5 corresponded approximately to the lower and upper bounds of

the values experienced in all tests. On an average, the standard deviation of the bond resis

tances for given slip values for all monotonically loaded tests was about 0.65 N/mm2 (94 psi),

with only a small influence of the extent of slip (Table 4.1). Because of the relatively small

scatter, normally only two identical tests were carried out in Series 2 to 7. The number of

repetitive tests was increased to three when the difference between the first two test results was

relatively large.

Figure 4.8 shows the average results of those test series that were monotonically loaded

almost up to the frictional resistance. The specimens of the different test series were cast from

different concrete batches. In Fig. 4.9 the average bond stress-slip relationship of Test Series 2

as well as the lowest and highest single result are plotted. By comparing Figs. 4.8 and 4.9 with

Figs. 4.5 and 4.7, it can be seen that the scatter is much larger when the specimens are cast

from different concrete batches.

4.3.2 Influencing Parameters

4.3.2.1 Tension or Compression Loading. Figure 4.10 shows the bond stress-slip rela

tionships for Series 2.1 (tension loading) and Series 2.2 (compression loading), which were cast

from the same batch. Bond stresses and slip values for compression loading were multiplied by

-1 to facilitate the comparison. In addition, the average curve of Series 2 is plotted.

- 29 -

The bond stress-slip relationship of Series 2.2 (bars pushed) is almost identical to that of

Series 2.1 (bars pulled) for slip values ~0.1 mm (0.004 in.) and slightly lower for larger slip

values. The results of both test series do not differ much from the average curve of Series 2.

If inevitable scatter is taken into account, it is reasonable to assume that the basic bond law for

tension and compression loading is almost identical. ~l js result could be expected [10] because

the bars were cast in a horizontal position.

Equal bond stress-slip relationships for bars in tension and compression remain valid only

for steel stresses below yield, as was the case in the reported tests. After yielding, the diameter

of a bar in tension is significantly reduced due to the Poisson effect, which may reduce the

bond resistance. The opposite is true for a bar yielding in compression. The influence of the

Poisson eH:ect on the bond was not studied in these experiments. Evaluation of results given in

[8,22] indicates that the Poisson effect will not change the bond resistance more than about 20

to 30 percent even for steel strains as high as 40 mm/m.

4.3.2.2 Confining Reinforcement. In Fig. 4.11 the average bond stress-slip relationships

for Series 1.1 to 1.5 are plotted. Figure 4.11a shows the whole slip range, while in Fig. 4.11 b

only the ascending branches of the bond stress-slip relationships are drawn.

There is a distinctively different behavior for tests with or without confining reinforce

ment. Specimens having no confining reinforcement failed by splitting of the concrete at a

rather small bond stress T ~ 6.0 N/mm2 (870 psi). This value compares favorably with the

theoretical one calculated according to Eqn. 4.3 proposed in [191.

T crack = 1.5 . Ict • .J c/ db (4.3)

where

T crack bond stress at occurrence of splitting cracks;

c = minimum concrete cover;

let axial tensile strength of concrete.

db = diameter of bar.

According to [41] let can be taken to about 90% of the splitting tensile strength It. With

values applicable for the present tests {Jet = 2.8 N/mm2 (406 psi) (see Table 3.3),

- 30 -

c/ db 2.0), one gets T crack = 5.9 N/mm2 (855 psi).

After splitting, the bond resistance dropped rapidly and reached T = 1 N/mm2 (145 psi)

at s = 4 mm (0.16 inJ. Without any friction at the bearing plates, the specimens would have

fallen apart completely with a consequent dropping of the bond resistance to zero.

Specimens with confined concrete failed by the bars pulling out. Because the splitting

crack developed in the plane of the longitudinal axis of the bars, only vertical bars crossing this

plane were effective in restraining the concrete, while the influence of stirrups was negligible.

This can be seen by comparing results of Series 1.2 with those of Series 1.5.

The influence of the area of vertical bars, L Asv, was rather small in the varied range of

L Asv- While the initial stiffness of the bond stress-slip curve was almost identical for all test

series (Fig. 4.11b), specimens with vertical #2 bars (db = 6.35 mm) (Series 1.3) had about 10

to 15 percent less bond strength after development of the splitting crack than specimens with

#4 (db = 12.7 mm) (Series 1.2) and #8 (db = 25.4 mm) (Series 1.1) vertical bars. The bond

stress-slip relationships for specimens with #4 (db = 12.7 mm) and #8 (db = 25.4 mm) verti

cal bars were practically identical. This shows that an upper limit for an effective restraining

reinforcement exists beyond which the bond behavior cannot be improved further, because the

main role of this reinforcement is to prevent opening of splitting cracks. For this reason, all

the tests in Series 2 to 7 were carried out with vertical #4 (db = 12.7 mm) bars.

The bond behavior of specimens with less confining reinforcement than tested will be

between those for Series 1.3 arid 1.4. This vast region was not explored further, because it was

felt that it is not of great practical importance in earthquake resistant design, where large res

training forces could be developed because of the very stringent requirements regarding

confinement of concrete. Furthermore, the confinement offered might depend on the location

of the vertical bars with respect to the test bar. The influence of this parameter was not stu

died.

The stress, (J'm in the vertical reinforcement can be estimated as follows (compare Fig.

2.2):

- 31 -

Splitting force, s', per unit length:

s' (4.4)

where

tga = tangent of the angle under which the bond forces spread into the concrete.

For a constant bond stress (as in the present tests), the total splitting force, S, is:

S = T • tga . db . Ie (4.5)

Introducing:

S L Asv . (T sv (4.6)

and

T = (4.7) .

into Eqn. 4.5, and solving for (T sv results in:

(T sv tga -_. (T

1T' s (4.8)

where

(T sv = stress in the vertical reinforcement;

(T s stress in the tested bar;

As area of tested bar.

The value of tga is not yet known exactly. According to [19,421, it depends mainly on the slip,

s, with respect to ST • When reaching ST ,tga will be in the order of 1.0 [I 7,19]. If the max max

latter value is adopted, one gets:

As (T sv ::::; 0.3 . ~ A . (T s

L. sv

(4.9)

In the tests of Series 1, the test bars were stressed up to (T s::::; 300 N/mm2 (43500 psi)

(Series 1.1 and 1.2) and (Ts::::; 250 NI mm2 (36250 psi) (Series 1.3), respectively, resulting in

a stress in the vertical bars of (T sv::::; 90 N/mm2 (13050 psi) (Series 1.2, #4 bars) and (T sv ::::;

300 N/mm2 (43500 psi) (Series 1.3, #2 bars). These stresses being lower than the yield

strength of the vertical reinforcement in combination with the good anchorage of these bars

- 32 -

explain the small widths of splitting cracks observed.

Equation 4.9 can also be used to estimate the area of reinforcement required for an

effective confinement. This question is discussed in Section 4.5.

4.3.2.3 Bar Diameter. In Fig. 4.12 the results of tests with bars of different diameters

are plotted. For comparison the average bond stress-slip curve for all monotonic tests of Series

2 is plotted as well.

The related rib area of the bars used in Series 3 was much larger than those of the bars

employed in the other tests (CXSR ::::: 0.12 compared to CXSR ::::: 0.066, see Table 3.4). This

resulted in a much stiffer ascending branch of the bond stress-slip relationship because of the

larger lug bearing area (reduced pressure) and an increase of bond strength of about 10 percent

for #8 (db = 25.4 mm) bars. While the peak bond resistance was reached in the tests of Series

3 at a slip of about 0.7 to 0.9 mm (0.028 to 0.035 in.), ST was about 1.5 mm (0.059 in.) in max

the other tests (Fig. 4.12b). The observed influence of the related rib area on the ascending

branch of the local bond law compares favorably with earlier findings [13] (compare Fig. 2.4).

The maximum bond resistance decreased slightly with increasing bar diameter. The rela-

tion was 1:0.94:0.85 for #6, #8, and #10 bars (db::::: 19, 25, and 32 mm), respectively. If the

difference in the values of CXsR is taken into account (see Table 3.4), it appears from this lim-

ited investigation that 'Tmax decreases by about 5 to 10 percent when using #8 (db = 25.4 mm)

bars instead of #6 (db = 19.0 mm) bars or #10 (db = 31.7 mm) bars instead of #8 (db =

25.4 mm) bars.

The descending branch of the local bond law leveled off to the frictional resistance at a

slip of s ::::: 9 to 10 mm (0.35 to 0.39 in.) for #6 (db = 19.0 mm) and #10 (db = 31.7 mm)

bars and a slip s ::::: 12 mm (0.47 in.) for #8 (db = 25.4 mm) bars. These slip values are again

almost identical with the clear distance between lugs.

The frictional bond resistance was not influenced much by the different bar diameter, lug spac-

ings, or values for the related rib area.

- 33 -

4.3.2.4 Concrete Strength. In Fig. 4.13 the results of tests with normal strength U; =

30 N/mm2 (4350 psi)) and high strength U; = 54.6 NI mm2 (7917 psi)) concrete are com-

. pared with each other. As can be seen, stiffness of the ascending branch and bond resistance

for equal slip values increase with increasing concrete strength. Furthermore, maximum bond

resistance is reached at smaller slip values (at approximately 1 mm (0.039 in.) compared to 1.5

mm for normal strength concrete). The latter result agrees with earlier findings [13].

The increase in bond resistance is about 35 percent, which is almost equal to the increase

in tensile strength of the high strength concrete compared to the normal strength concrete (see

Table 3.3). The measured tensile strengths of these concretes are approximately proportional

to E. Therefore, the results of tests with high strength concrete were converted to J; = 30

N/mm2 (4350 psi) by multiplying the bond stresses with the factor .J30/ J;. As can be seen,

the resultant bond stress-slip curve agrees reasonably well with those of Series 2, with the

exception of the initial part of the ascending branch.

4.3.2.5 Bar Spacing. In Fig. 4.14 bond stress-slip relationships for specimens simulating

different bar spacings are plotted. The bond behavior improved with increasing bar spacing;

however, the influence was relatively small. When increasing the clear bar spacing from the

minimum allowable value s = 1 db to S = 4 db, bond resistance increased by about 20 percent

(Fig. 4.15). Further increase of the bar spacing did not effect the bond behavior.

This result can be explained by the fact that in spite of different loads at splitting (com

pare Eqn. 4.3) the ultimate failure was caused by pulling out, because the growth of splitting

cracks was controlled by restraining reinforcement. If less restraining reinforcement is provided

so that the ultimate failure will be due to splitting, a more significant influence of bar spacings

must be expected.

From the results plotted in Fig. 4.15, it becomes clear that the increase in bar spacing had

more influence on the bond resistance of the initial part of the bond stress-slip relationship

(T cs = O.lmm) than on the maximum bond resistance T max'

- 34 -

4.3.2.6 Transverse Pressure. Figure 4.16 shows the results of Test Series 6. The speci-

mens were compressed perpendicular to the potential plane of splitting; the pressure applied

ranged from p = 0 N/mm2 (comparison tests) to p = 13.2 N/mm2 (1914 psi).

As expected, the results of Test Series 6.1 (no transverse pressure) agree well with those

of Series 2, within the normal range of scatter. The maximum bond resistance and the ultimate

frictional resistance were increased by transverse pressure. The increase amounted to about 25

percent for the maximum pressure applied (Fig. 4.17). The slip at maximum bond resistance

shifted to slightly larger values with increasing transverse· pressure. The ratio between the

added bond resistance and applied pressure decreased significantly with increasing pressure (Fig.

4.18).

4.3.2.7 Rate of Pull-out. The influence of rate of pull-out (or rate of slip) on the local

bond law can be seen from Fig. 4.19. While the overall shape of the bond stress-slip relation-,

ship was not changed much, bond resistance increased with increasing rate of pUll-out. A

change of rate of pull-out by a factor of 100 resulted in a change of maximum bond resistance

and ultimate frictional bond resistance of about 15 percent (Fig. 4.20). In a semi-logarithmic

scale, the test results can be represented by a straight line.

4.3.3 Comparison With Other Results

4.3.3.1 General Behavior. In Fig. 4.21 the results of the present tests with #8 (db =

25.4 mm) bars are compared with results given in literature for bars cast in a horizontal posi-

tion. Figure 4.21a is valid for the initial part of the bond stress-slip relationship. The shaded

area represents the range of the bond stress-slip relationship as found by other researchers

(compare Fig. 2.5). The results of Test Series 2 (54 tests with #8 (db = 25.4 mm) bars) fall

into the lower part of that area. The scatter of the measured bond stress-slip curves is consid-

erable. The results of Test Series 3 (4 tests with #8 (db = 25.4 mm) bars) fall in the upper

part of the shaded area. The bars used in Test Series 3 had higher lugs and a lug bearing area

that was about 65% larger than those of the bars employed in Series 2 (see Table 3.4). All

other parameters were kept constant. From these data it can be concluded that the large scatter

- 35 -

of the initial bond stiffness found in literature is mainly caused by the inevitable scatter and the

use of bars with different rib patterns and/or different bar diameters. Other reasons are the use

of different test specimens, difficulties in measuring the slip between steel and concrete when

using more sophisticated techniques (measurement of steel and concrete strains) and

differences in applied loading and/or slip rates.

Very large displacements may be induced during severe earthquakes. Therefore, bond

stress-slip relationships covering the complete range of slip are compared in Fig, 4.21 b. Unfor

tunately, very limited data are available in literature for this range. The curves 1 and 3 were

each deduced from strains along the bar and displacements of the bar ends measured in a single

pull-out test with an embedment length of 25 db [8,22]. In spite of almost identical test condi

tions and material properties, the deduced local bond laws are rather different. This can partiy

be attributed to the inevitable scatter of bond tests. However, the main reason can be attri

buted to the inaccuracies related to deducing the results by this technique. Note that the

overall behavior agrees reasonably well with the results reported herein Wne 2).

The local bond stress-slip relationship proposed by Martin [13] Oine 4) is based on a

large number of pUll-out tests under load control. The bond law is lower than the one found in

the present tests but falls in the observed range of results.

4.3.3.2 Influence of Investigated Parameters.

Restraining Reinforcement: To date the influence of this parameter on the bond

behavior was mainly studied in relation to a splitting failure. It was found by previous investi

gators and substantiated by the present study that a splitting failure can be delayed or avoided

altogether by restraining reinforcement. However, no quantitative comparison with the present

results is possible because of different test conditions. In previous tests, usually the anchorage

lengths of tested bars were large (> 12 to 15 db)' and concrete cover (bottom and side) was

small, resulting in a different type of failure and a much less effective restraining reinforcement

than in the experiments reported herein.

- 36 -

The influence of transverse reinforcement on bond strength for a pull-out type of failure

has been investigated very little. Usually, it is assumed that once a pull-out failure is reached,

either by providing a large concrete area or a sufficiently strong restraining (confining) rein

forcement, T max cannot be increased much further by additional transverse reinforcement. On

the contrary, Tassios' proposal [9] results in an increase of Tmax of about 5 N/mm2 (725 psi) or

24 N/mm2 (3480 psi), respectively, when changing the diameter of the vertical bars in the tests

from db = 6.35 mm (#2 bars) to db = 12.7 mm (#4 bars) or db = 25.4 mm (#8 bars),

respectively. The present experimental results do not support Tassios' proposal because the

bond behavior of specimens with #4 (db = 12.7 mm) and #8 (db = 25.4mm) vertical bars as

restraining reinforcement was identical and differed only slightly from that of specimens with

#2 (db = 6.35 mm) bars.

According to ACI 318-77 [43], the basic development length may be reduced by 25% if

the anchored bars are enclosed by a spiral reinforcement. This means that 33% higher bond

stresses are allowed for bars that are effectively confined by reinforcement compared to bars

anchored in unconfined concrete. This increase in bond strength is justified in the case of a

splitting failure which will occur when the minimum values for concrete cover and bar spacing

allowing by the code are applied.

Bar Diameter: A slight influence of the bar diameter, which was varied between 19 and

32 mm, on the maximum bond resistance was found in the present limited investigation.

According to [44], the influence of bar diameter is insignificant in the range db = 8 to 32 mm.

The latter result is based on an evaluation of the results of a large number of pull-out tests and

may be more reliable. According to ACI 318-77 [43], the allowable bond stress varies with

1/ db' When the concrete dimensions are assumed as a constant multiple of the bar diameter,

this provision is neither supported by the present test results nor by earlier tests [17-19] with

bond failures caused by splitting.

Concrete Compressive Strength: While Rehm [10] and Martin [13,44] assume a linear

relationship between bond resistance and concrete compressive strength, f:, other researchers

- 37 -

propose a proportionality between bond resistance and.Jh. The present results confirm the

latter assumption. In addition, one has to take into account that ST decreases with increasing max

concrete strength. ACI 318-77 [43] also assumes T to vary with E.

Bar Spacing: To date the influence of this parameter on bond behavior has only been stu-

died in connection with splitting failures, where it is of decisive importance. In this respect it is

correctly taken into account in ACI 318 [43], On the contrary, in the present study, bar spacing

was of little influence because the growth of splitting cracks was controlled by a very effective

restraining reinforcement and bars were pulled out.

Transverse Pressure: In Fig. 4.22 the increase of bond resistance as a function of the

transverse pressure used in the tests reported herein is compared with the results of other

investigations. The reported increase in bond strength (Fig. 4.22a) for a transverse pressure of

10 N/mm2 (1450 psi) varies between about 2.5 N/mm2 and 8.5 N/mm2 (362 and 1232 psi,

respectively). However, when the different test conditions are considered, the differences are

reduced.

In the tests of Untrauer/Henry [45] (!jne 4 in Fig. 4.22a), failure of comparison speci-

mens without normal pressure was caused by splitting of the concrete, and the concrete

between lugs was fully intact. On the contrary, specimens compressed by a sufficiently high

normal pressure failed by pulling out of the bars, and the concrete between lugs was sheared

off. If failure had been caused in all tests by pull-out, the influence of transverse pressure on

T max would have been much smaller than shown in Fig. 4.22a.

In the tests of Viwathanatepe et al [8] and Cowell [221, a transverse pressure of about 10

N/mm2 (1450 psi) was induced by a bending moment, and the bar was also yielding in

compression. Therefore, the observed increase in maximum bond resistance reflects the

influence of external pressure and of internal pressure due to expansion of the bar (Poisson's

effect). If one estimates that about half of the total increase of T max was caused by the latter

effect, the increase caused by transverse pressure alone compares fairly well with the value

measured in the present tests. The increase of T max observed by Doerr [28] for a pressure of

- 38 -

15 N/mm2 (2175 psi) seems unrealistically high in comparison to the values measured for a

pressure of 5 N/mm2 and 10 N/mm2 (125 psi and 1450 psi) and is in contradiction to the gen

eral trend found in the other investigations.

The increase of frictional bond resistance caused by transverse pressure found in different

experimental investigations scatters considerably (Fig. 4.22b) even if all special circumstances

are properly taken into account. The proposal of Tassios [9] is based on theoretical considera

tions. According to the available experimental results, this proposal significantly overestimates

the influence of transverse pressure. on the ultimate frictional bond resistance.

Additional tests are necessary in which the influence of external pressure and internal

pressure due to Poisson's effect should be investigated separately.

The influence of transverse pressure on the bond behavior is not taken into account in

ACI 318-77 [43].

Rate of Slip Increase: Figure 4.23 shows the influence of rate of slip increase on bond

resistance. While the present tests were run under deformation (slip) control, the comparable

investigations were run under load control. Therefore, an average loading rate for a slip of 0.5

mm (0.02 in.) was taken as relative value. Considering the different test procedures, the

results of all investigations agree fairly well. A change of the rate of pull-out by a factor of 100

results in a change of the bond strength of about 15% to 20%.

The influence of the loading rate on the bond behavior is neglected in present codes (e.g.

[43]).

4.4 Cyclic Loading

The results of the cyclic loading tests are plotted in Figs. 4.24 to 4.42. In the bond

stress-slip diagrams, only a limited number of cycles are drawn for reasons of clarity. In all

diagrams, the corresponding bond stress-slip relationship for monotonic loadings are shown,

which were obtained from specimens made from the same concrete batch.

While most of the specimens were cycled one or ten times, respectively, at fixed values of

- 39 -

peak slip Smax and Smin, the specimens of Series 2.19 to 2.22 were first subjected to five cycles at

certain values of peak slip (smaxJ, Sminl), then the Smax was changed and the specimens were

again cycled at (Smax2, Smin2) and so on. The results of the latter tests are plotted in Fig. 4.39a

to Fig. 4.42a for cycles at (smaxJ, Sminl), in Fig. 4.39b to Fig. 4.42b for cycles at (Smax2, Smin2)

and so on.

4.4.1 General Behavior

In general, the behavior during cyclic loading agreed fairly well with the description given

in Section 2.1.1. The coefficients of variation for bond resistance during cyclic loading calcu

lated from the results of 2 to 3 repetitive tests are summarized in Table 4.2. These coefficients

were calculated for characteristic values of the bond resistance during cyclic loading (7 unl =

bond resistance at peak slip Sma x and 7 f = frictional bond resistance) and of the reduced

envelope after cycling (7max = maximum bond resistance and 73 = ultimate frictional bond

resistance). They were almost independent of the value Smax at which the specimens were

cycled and remained practically constant as the number of cycles increased. On the average,

they amounted to about 6% for T unl and to about 10% for 7 f, 7 max, and 73. A somewhat larger

scatter has to be expected if specimens for repetitive tests are cast from different concrete

batches.

A comparison of results of Test Series 2 (Figs. 4.24-4.42) leads to the following general

observations.

(a) If the peak bond stress during cycling did not exceed 70-80% of the monotonic bond

strength 7 max, the ensuing bond stress-slip relationship at first loading in the reverse direc

tion and at slip values larger than the one at which the specimen was cycled was not

significantly affected by up to 10 repeated cycles (see Figs. 4.24, 4.25, 4.33, 4.39a, and

4.42a). The bond resistance at peak slip deteriorated moderately with increasing number

of cycles. These results agree well with earlier findings [12,31,33,341. An explanation for

this behavior is given in Section 2.1.3.

- 40 -

(b) When the bar was loaded monotonically to an arbitrary slip value and then cycled up to 10

times between this slip value and a slip value corresponding to a load equal to approxi

mately zero, the monotonic envelope was, for all practical purposes, reached again (Figs.

4.37 and 4.38). From then on the behavior was the same as that obtained in a monotonic

test. This agrees well with earlier results [10,12,31]' The reasons for this behavior are

that during unloading the small fraction of the total slip that is caused by elastic deforma

tion of the concrete is recovered and the concrete is not much more damaged by a limited

number of reloadings.

(c) Loading to slip values inducing a T larger than 80% of the monotonically obtained T max in

either direction led to a degradation in the bond stress-slip behavior in the reverse direc

tion (Figs. 4.26-4.32). The bond stress-slip relationship at slip values larger than the peak

value during previous cycles was significantly different from the virgin monotonic

envelope. There always was a significant deterioration or the bond resistance which

increased with increasing peak slip smax (Figs. 4.26-4.32), increasing numbers of cycles

(Figs. 4.26-4.30), and was larger for full reversals of slip than for half cycles (compare

Figs. 4.27a with Fig. 4.34, Fig. 4.29 with Fig. 4.35, and Fig. 4.37 with Fig. 4.36).

Furthermore, the cycles produced a pronounced deterioration of the bond stiffness and

bond resistance at slip values smaller than or equal to the peak slip value. These results

agree qualitatively with those reported in [8,22]. However, a quantitative comparison is

not possible because of different test conditions.

The observed behavior can be explained by assuming that in a well-confined concrete the

maximum bond resistance is controlled by local crushing and the initiation of a shear

failure in a part of the concrete between the lugs of the bar. The larger the value of slip

with respect to Srmax (i.e. slip at T rna), the larger is the area of concrete between the lugs

affected by the crushing and shear failure and the smaller is the bond resistance. If the

bar is cycled between constant peak values of Smax and Smin, the main damage is done in

the first cycle. During successive cycles, the concrete at the cylindrical surface, where

- 41 -

failure occurred, is mainly ground off, decreasing its interlocking and frictional resistance.

A more detailed explanation will be given in Section 5.2.2.

(d) The frictional bond resistance, 'T f' during cycling was dependent upon the value of the

peak slip Smax and the number of cycles (see Figs. 4.24-4.32). With repeated cycles, T f

deteriorated rapidly.

(e) Cycling a specimen at different increasing slip values had a cumulative effect on the

deterioration of bond stiffness and bond resistance (compare Figs. 4.39c, 4.40d, and 4.41e

with Fig. 4.29). On the other hand, some additional cycles between smaller slip values

than the peak value in the previous cycle did not much influence the bond behavior at the

larger peak value (compare Fig. 4.41 b with Fig. 4.41 c).

In the following, the influence of cyclic loading on the different branches of the bond

stress-slip relationship as defined in Section 2.1.1 will be discussed in detail.

4.4.2 Unloading Branch

The bond stress-slip relationship for unloading is slightly nonlinear with the flattest slope

near zero load (see Fig. 4.24). However, it seems reasonable to linearize the actual behavior.

The average slope between the point from which unloading started and the point with zero

bond stress is plotted in Fig. 4.43 as a function of the number of unloadings. The slope at first

unloading was practically independent of the peak slip value Smax and, on the average,

amounted to about 200 N/mm3 (737 kipslin3) for a concrete with f; = 30 N/mm2 (4350 psi).

It was approximately equal to the average slope of the monotonic envelope for very small slip

values (~ 0.01 mm (0.0004 in.». During 20 consecutive unloadings, the slope decreased by

about 30%. The scatter of the test results was considerable.

For comparison, the average slope of the unloading branch for the tests with high strength

concrete U; = 55 N/mm2 (7975 psi» is plotted as well. On the average, the slope was about

50% larger than that for a medium strength concrete U; = 30 N/mm2 (4350 psi)).

The average slopes of the unloading branch measured in the present tests compare favor-

- 42 -

ably with the values given in [9]. According to [12], the unloading branch is stiffer than found

here, which can be explained by the fact that in [12] the bar was pulled out against the setting

direction of the concrete.

4.4.3 Frictional Branch

In Fig. 4.44 the frictional bond resistance, T I' is plotted as a function of the peak slip

value, Smax, at which the specimens were cycled. The number of cycles is chosen as a parame

ter. In the first cycle, T I was strongly dependent upon Smax and reached its peak value of about

2.9 N/mm2 (420 psi) at Smax ~ 4 to 10 mm (0.16 to 0.4 in.). T f was reduced to about 0.2

N/mm2 to 0.5 N/mm2 (29 psi to 72.5 psi) by 10 load cycles, the largest deterioration occurring

in the first cycle. The rate of decrease of T f was larger for larger values of Smax' Therefore,

after 10 cycles the influence of Smax on T I was rather small. No clear influence of .the slip

difference As = Smax - Smin (A S = Smax for half cycles and As = 2 Smax for full cycles) on the

deterioration of the frictional bond resistance could be detected. '

Figure 4.45 shows the relation between the frictional bond resistance during cycling, T I'

and the bond stress T un! at peak slip Smax from which unloading started. While this relation was

clearly dependent on the peak slip value, Smax, it was almost independent of the number of

cycles. This observation means that T I deteriorated almost at the same rate as the bond resis

tance at peak slip, Tun!'

According to [9] and [12], the frictional bond resistance amounts to 0.25 or 0.18 times the

bond resistance at peak slip, T un!, respectively. As can be seen from Fig. 4.45, these assump

tions are very crude approximations because the relation Til 'T un! varies approximately from 0.05

for smax ~ 0 mm to 0.4 for Smax ~ 9 mm (0.35 in.). In [8] a constant value T I ~ 0.4 N/mm2

(58 psi) is assumed, which is rather small and only valid after several load cycles (see Fig.

4.44). In [22] a frictional bond resistance T I ~ 1 N/mm2 to 3.5 NI mm2 (145 psi to 507 psi)

was found, which compares favorably with the present tests.

- 43 -

4.4.4 Reloading Branch

When reloading the specimen after a cycle between slip values Smax and Smin with

I Smin I = Smax for full cycles and Smin = 0 for half cycles, the bond resistance increased well

before reaching Smax (Figs. 4.24-4.36). On the average, T started to increase significantly at a

slip value equal to about 45% of Smax' While the value was not much influenced by any of the

investigated parameters, its scatter was rather large.

On reloading, the bond resistance at peak slip, T un!, never reached its initial value at first

loading (N = 1). This can be seen from Fig. 4.46, which shows the bond ratio Tun! (N) IT un!

(N = 1) as a function of the number of cycles, N, for different values of the peak slip, Smax, at

which the specimen was cycled. In Fig. 4.46a the results of tests with full reversals of slip and

in Fig. 4.46b the corresponding results for tests with half cycles are plotted. After one cycle,

the bond resistance at peak slip, T un!, was reduced to about 25% to 85% of its original value,

depending on the specific conditions. After 10 cycles, these values were down to 7% and 60%.

The major part of the total deterioration observed after 10 cycles was produced in the first

cycle. Under comparable conditions (smax = const. N = const.) , T un! was significantly more

deteriorated for cycles between full reversals of slip than for half cycles (compare Fig. 4.46a

with Fig. 4.46b).

The bond deterioration ratios shown in Fig. 4.46a are plotted in Fig. 4.47 in a double loga

rithmic scale. As can be seen, only the results for cycles between rather small slip values can

be approximated by a straight line. On the other hand, the ratios for cycles with Smax near or

beyond STmax (slip value at the monotonic T max) can only be approximated by two straight lines

with a breaking point at about cycle 2. It is well known that the results of creep tests on con

crete under cyclic compression, plotted in a double logarithmic scale, can be approximated by a

straight line [47]. The same is true for relaxation tests on concrete under cyclic compression.

Therefore, if the bond resistance deterioration would only be caused by a process similar to

relaxation of concrete, the test results would follow a straight line when plotted in a double log

arithmic scale. Following this argument, it can be concluded that the deterioration of bond

- 44 -

resistance was caused by a process similar to relaxation when the specimens were cycled

between small peak slip values «= 0.4 mm (0.016 in.)). On the other hand, the bond resis

tance deterioration during the first cycle between larger peak slip values was caused by damag

ing the concrete between lugs (local crushing and initiation of shear cracks), while in subse

quent cycles it was caused by gradual grinding off of the concrete at the cylindrical surface

where shear failure and local crushing occurred.

Figure 4.48 shows the bond deterioration ratio at peak slip Smax for tests with full reversal

of slip (full cycles) and for half cycles (Smin = 0) as a function of Smax. The influence of Smax

on the bond deterioration ratio is pronounced. While for small values of Sma x half and full

cycles reduced the bond resistance at peak slip almost by the same amount, the bond resistance

was significantly more deteriorated by full cycles than by half cycles when the peak slip values

increased. The differences become much smaller if the test results for half cycles are plotted at

smaxl2. That means that cycles between S = ± smax/2 caused as much damage in the bond resis

tance at peak slip as an equal number of cycles between S = 0 and S = Smax, provided Smax was

larger than about 0.4 mm.

The bond deterioration ratios found for cycles between small peak values of slip (~ 0.5

mm) agree fairly well with those reported in [121. A comparison for larger slip values is not

possible because of lack of comparable results in literature.

4.4.5 Reduced Envelope

In Fig. 4.49, reloading curves for similar specimens subjected to different loading histories

are plotted. The lines denoted by "a" represent the behavior of specimens cycled once or ten

times, respectively, between the peak slip values corresponding to point "a". It can be seen by

comparing the lines denoted by the letters "a" to "e" with the monotonic loading curve that

cycling between sufficiently large slip values reduced the maximum bond resistance T max as well

as the frictional bond resistance T3. In order to get a proper estimate of the bond deterioration

rate, the test results were idealized as shown in Fig. 4.50 and then the reductions of T1 (approx

imately equal to bond strength T max) and T3 (frictional bond resistance) were calculated. The

- 45 -

results are plotted in Figs. 4.51 and 4.52 as a function of the peak slip value Smax during cycling.

According to these graphs, the monotonic envelope was reached again after up to 10

cycles between rather small slip values in the order of Smax < 0.4 mm (0.016 inJ. With

increasing values of Smax and increasing numbers of cycles, the envelope was increasingly

deteriorated. The main reduction was caused by the first cycle. Frictional bond resistance

deteriorated less than bond strength.

Figure 4.52 shows that one-sided cycles with Smax ~ 0.5 mm (0.02 in.) generally pro

duced less deterioration of the envelope than an equal number of cycles with full reversals of

slip. The test results of these cycles fit fairly well the lines valid for full cycles if they were

plotted at smax/2. This means that cycles between s=O and s= Smax produced about the same

deterioration of the monotonic envelope than an equal number of cycles between S = ± smax/2,

provided Smax was larger than about 0.4 mm (0.016 in.).

The present test results agree qualitatively with those published in [8,22]. However, a

quantitative comparison is not possible because of completely different test conditions.

Roughly speaking, the deterioration of the envelope found in [8] and [22] seems to be smaller

or larger, respectively, than observed in the present investigation.

4.4.6 Influencing Parameters

While in Sections 4.4.1 to 4.4.5 the results of cyclic tests of Series 2 were discussed, in

this section the results of the cyclic tests done in Series 1 and Series 3 to 7 will be discussed.

In these tests the specimens were cycled at a peak slip value smax = 1.65 mm (0.065 in.),

which almost coincided with the value of slip at the maximum bond resistance under mono

tonic loading. The influence of the following parameters on the bond behavior under cyclic

loading was studied.

Diameter of vertical bars of transverse reinforcement (db = 6.4 mm (#2 bar)), Series 1.6

and 1.7.

Direction of loading. First loading in compression (Series 2.6*) as compared to loading in

- 46 -

tension (Series 2.6).

Diameter of test bar (db = 19 mm to 32 mm (#6 bars to #10 bars», Series 3.4 to 3.6.

Concrete strength U; = 54.6 N/mm2 (7917 psi)), Series 4.2 and 4.3.

Clear spacing of bars (1 db to 6 db), Series 5.4 to 5.6.

Transverse pressure p (5 N/mm2 (725 psi) and 10 N/mm2 (1450 psi)), Series 6.5 and 6.6.

Rate of slip increase (S = 170 mm/sec. (6.7 in.!sec.), Series 7.3.

The results of these tests are plotted in Figs. 4.27b and 4.53 to 4.65. The results of the

comparable "standard" tests (Series 2.6 (full cycles) and Series 2.13 (one-sided cycles» are

shown in Figs. 4.27a and 4.34, respectively. The influence of a certain investigated parameter

on the cyclic bond behavior can be studied by comparing Figs. 4.54 and 4.59 with Fig. 4.34 and

Figs. 4.53, 4.55 to 4.58 and 4.60 to 4.65 with Fig. 4.27a. It can be seen that the overall cyclic

bond behavior was not much influenced by the above mentioned i\lvestigated parameters.

A more detailed elaboration is given by Figs. 4.66 and 4.67. In Fig. 4.66 the deterioration

of the bond resistance measured in Test Series 2.6 (Standard Test) is compared vlith those

observed in Series 1.6, 2.6*, 4.2, 5.4 to 5.6, 6.5, 6.6 and 7.3 (Specific Test). A comparison of

the deterioration behavior of Test Series 2.13 with those of Test Series 1.7 and 4.3 is also

included in the figure. In Fig. 4.67 a similar comparison is done for Series 3.4 to 3.6 (influence

of bar diameter). The following values were chosen to characterize the deterioration of the

bond resistance during cyclic loading.

(a) Relation of bond resistance at peak slip, 7 un/, after cycling to the corresponding bond

resistance for monotonic loading.

(b) Relation between frictional bond resistance, 7 f, during cycling and the bond resistance at

peak slip, 7 un/'

(c) Relation between 71 (approximately equal to maximum bond resistance) and 73 (ultimate

frictional bond resistance) of the reduced envelope to the corresponding values of the

monotonic envelope.

- 47 -

In (a) and (b) above the defined relationships were calculated for Cycles 1 to 10 and then aver

aged. The relationship (c) was evaluated as average value for the first slip reversal at 7] (for

cycles between s = ± 1.65 mm (0.065 in.)) and after 10 cycles at 7] and 73.

In Figs. 4.66 and 4.67 values greater than unity for the ratio bond deterioration standard

test (Series 2.6 or 2.13, respectively) to bond deterioration specific test (e.g. Series 1.6) means

that in the standard test 7 unl as well as 7] and 73 of the envelope 'were reduced less by the load

cycles and the relation TIl T unl was lower than in the specific test. The dashed lines represent

the acceptable scatter that can be expected for identical test specimens but made from different

concrete batches. The investigated parameters significantly influence the cyclic bond behavior

only if the calculated ratios fall outside the range given by the dashed lines.

According to Fig. 4.66, the cyclic bond behavior was approximately the same when the

test bars were first loaded in tension (Series 2.6) or compression (Series 2.6*). This behavior

was expected because of the similarity of the monotonic envelopes. Substituting #2 bars (db =

6.35 mm) (Series 1.6 and 1.7) for #4 bars (db = 12.7 mm) as transverse (restraining) rein

forcement had no significant effect on the cyclic bond behavior. This is also true for specimens

made out of high strength concrete (Series 4.2 and 4.3) instead of medium strength concrete.

While the cyclic bond behavior of specimens simulating a clear bar spacing of 1 db and 6 db

(Series 5.4 and 5.6) was not much different from those of the specimen with a clear spacing of

4 db (Series 2.6), the specimens with a clear spacing of 2 db (Series 5.5) experienced more

bond deterioration than the specimens of Series 2.6. This result can be attributed to excessive

scatter because it does not fit in the general trend and cannot be rationalized. Transverse pres

sure in the investigated range (5 N/mm2 and 10 N/mm2 (725 psi and 1450 psi)) (Series 6.5 and

6.6) and a 100 times faster loading rate (Series 7.3) did not change the cyclic bond behavior

very much.

On the contrary, the specimens of Series 3 experienced significantly more bond deteriora

tion than the specimens of Series 2.6 (left part of Fig. 4.67). The specimens of Series 3 and of

Series 2.6 were cycled at the same peak slip value Smax = 1.65 mm (0.065 in.). The bars used

- 48 -

in Series 3 had a much larger related rib area than the standard bars used in Series 2.6 (see

Table 3.4). This resulted in a steeper ascending branch of the bond stress-slip relationship.

The maximum bond resistance was reached at a slip value of Sr of about 0.7 mm to 0.9 mm max

(0.028 in. to 0.035 inJ (Fig. 4.12) compared to about 1.6 mm (0.062 in.) in Series 2.6 (Fig.

4.27a). Therefore, the specimens of Series 3 were cycled at about 2 times the slip value Sr , max

while the specimens of Series 2.6 were cycled approximately at Sr . If the results of Series 3 max

are compared with those of the test specimens of Series 2.7 which were cycled at Smax - 1.6

Sr ,the influence of the bar diameter and the deformation pattern on the cyclic bond behavior max

is not significant (see right part of Fig. 4.67).

Note that specimens with the small bar (#6, db = 19 mm) developed a somewhat larger

maximum bond resistance than those with larger bars during monotonic loading (Fig. 4.12) but

experienced more bond deterioration during cyclic loading (Fig. 4.67). Therefore, the bond

resistance was almost independent of the bar size after some load cycles (see Figs. 4.55-4.57).

The results of Test Series 3 indicate that the bond deterioration during cycling does not

only depend on the absolute value of the peak slip, as shown in Figs. 4.48 and 4.52, but on its

relation to characteristic slip values (sr or S3) of the monotonic envelope. However, more max

tests with bars of different diameters and deformation patterns are needed to deduce more

clearly bond deterioration as a function of either the ratio smaxl Sr or smaxl S3. max

Summarizing, it can be stated that the behavior of bond during cyclic loading is not

significantly affected by the various parameters investigated if the deterioration of bond resis-

tance is related to the pertinent monotonic envelope. However, the influence of bar diameter

and deformation pattern on the cyclic bond behavior should be studied more thoroughly in the

future.

4.5 Required Restraining Reinforcement

Equation 4.9 can be used to estimate the required area of reinforcement to effectively res-

train concrete in the joint so that a pull-out failure and not a splitting bond failure will occur.

- 49 -

Let us first consider an interior joint with one beam passing through it. In the extreme case,

approximately equal forces of same sense are acting on each side of the anchored beam bars.

The worst bond conditions are found at the tension side of the beam bars because the vertical

column bars there are also in tension. At the compressed bar end, sufficient confinement is

provided by compressed column bars and by compression column forces acting on the joint.

Therefore, the required area of restraining reinforcement needs to be calculated for one side of

the beam only, but this reinforcement must be provided at both sides of the joint because the

external excitation might change the direction of loading. Furthermore, in each layer several

beam bars are passing through the joint, in which case the splitting forces of all bars in one

layer must be added. Solving Eqn. 4.9 for LAsv one obtains:

u"s 0.3 . n' As-

U" sv (4.10)

where

LAsv = required area of reinforcement for restraining the concrete at one column side;

n = number of beam bars in one layer passing through the joint;

As = area of one beam bar in a layer, for bars with different bar diameters the average

area may be taken;

U" s = stress in beam bar at the column face;

U" sv = allowable stress in the vertical column reinforcement.

The allowable stress U" sv is not well known yet. In tests with sufficient restraining reinforce-

ment, it ;-eached about 300 N/mm2 (43.5 ksj). However, it should be noted that restraining

vertical bars were well anchored and were placed close to the test bar. Bars less well anchored,

or in a larger distance from the origin of splitting forces, will offer less restraint at equal steel

stresses. Therefore, it is proposed that U" sv should neither exceed the yield stress nor a value of

300 N/mm2 (43.5 ksj).

Often at interior joints, beams from four directions are joining together. In this case, the

restraining reinforcement according to Eqn. 4.10 must be provided in the joint at each side of

- 50 -

the column. Eqn. 4.10 is also valid for external joints, where it gives the area of the restraining

reinforcement at that side of the column that faces the beam. Preferably, stirrups enclosing the

top and bottom layers of beam bars should be used as restraining reinforcement. The column

reinforcement can also be used as restraining reinforcement if it can take up the additional

splitting forces without exceeding the yield stress. However, in the latter case, one should use

a larger number of small diameter column bars instead of a small number of large diameter bars

to ensure a good anchorage of the bars.

It should be noted that the above proposal for the area of restraining reinforcement in the

joint (Eqn. 4.10) is based on the following assumptions:

-Ratio between bond forces and splitting forces, as explained in Section 4.3.2.2, has been

set equal to unity.

-Allowable steel stress for restraining reinforcement (0" sv ~ 300 N/mm2 (43.5 ksi) and

~ fy has been proposed).

-Superposition of splitting forces and forces caused by external excitations (under the

combined actions, 0" sv may not exceed fy).

The validity of the above assumptions should be checked by additional experimental and

theoretical studies.

- 51 -

V. ANALYTICAL MODEL OF LOCAL BOND STRESS-SLIP RELATIONSHIP

5.1 General

The fixed end rotation of an interior or exterior joint can be an important source of

stiffness degradation in the lateral load-deformation relationship of moment-resisting frames.

This fixed-end rotation must either be minimized by a sufficient anchorage of the beam bar or

its effect must be considered in the design and, therefore, it should be included in the analysis

of building response to obtain realistic behavior of a frame under severe cyclic loadings.

The fixed-end rotations of beams can be calculated when the the slip of the beam top and

bottom bars with respect to the column faces are known. This slip can analytically be predicted

if the following items are available:

(a) Analytical procedure to solve the differential equation of bond.

(b) Analytical model for local bond stress-slip relationship.

(c) Analytical model for the stress-strain relationship of bars.

In this report, only point (b) will be described. Points (a) and (c) will be described in detail in

a companion report [49].

5.2 Theory of Bond Resistance Mechanism

A theory of bond resistance mechanism for monotonic and cyclic loading will be

presented because it can form a rational basis for developing hysteretic rules for bond behavior

under generalized loading. Furthermore, it helps to understand the results of the present tests

(Chapter 4) more clearly. The theory is valid for well-confined concrete, where the propagation

and particularly the width of possible splitting cracks are kept small so that the ultimate failure

is caused by bar pull-out. A theory of bond resistance mechanism for unconfined concrete near

the bar end loaded in tension, where failure is caused by breakout of a concrete cone, has been

presented in [8].

- 52 -


Inclined cracks initiate at relatively low bond stresses at the point of contact between steel

and concrete [14] as shown in Fig. 2.2 and Fig. 5.1a. The length and width of these cracks are

arrested by the restraint offered by secondary reinforcement (indicated in Fig. 5.1 by normal

stresses at the top of the element). With increasing induced slip, the concrete in front of the

lugs will be crushed. The bond forces which transfer the steel force into the concrete are

inclined with respect to the longitudinal bar axis; at this relatively low loading stage the angle is

relatively small (= 30 degrees [13,19,39]). Under otherwise constant conditions, the slope of

the initial part of the bond stress-slip curve depends on the lug bearing area ex sR (Eqn. 2.1).

Increasing the stress in the bar further more slip occurs because more local crushing takes

place and later shear cracks (see Fig. 2.3) in the concrete keys between lugs are initiated.

According to Rehm [10], this happens when the slope of the bond stress-slip curve decreases ,

rapidly (approximately at Point B in the diagram of Fig. 5.1b). At maximum bond resistance

(Point C), a part of, or the total, concrete key between the lugs has been sheared off, depend-

ing on the ratio of clear lug distance, Cj, to average lug height, a. For no. mal ratios

(cd a > 6), only a part of the key will be sheared off (see Fig. 2.3). The length of the shear

crack is given by Rehm [10] as 6 times the lug height and by Lutz/Gergely [17] as 2 to 3 times

the lug height. Therefore, an average value of approximately 4 times the lug height is assumed

as shear crack length. At this loading stage, the bond forces will spread into the concrete under

an increased angle of about 45 degrees, because of the wedging action of sheared off concrete.

The bars used in the main tests had a ratio clear lug spacing to lug height of about 9 and

the maximum bond resistance was reached at a slip Sr equal to about 1.2 times the lug max

height. Therefore, it is estimated that about 50% of the key's length was sheared off when the

maximum resistance was reached (Fig. 5.1b).

When more slip is induced, an increasingly larger part of the concrete is sheared off

without much drop in bond resistance. In the reported tests, the resistance at a slip equal to

approximately 3 times the value Sr was about 85% of the maximum bond resistance. The max

- 53 -

shear cracks might have reached the base of the concrete key at the adjacent lug at a slip of

about 0.5 times the clear lug distance (Point D in the diagram of Fig. 5.1e). Increasingly less

force is needed to shear off the remaining bits of the concrete keys and to smooth out the sur-

face of the shear crack. When the slip is equal to the clear lug distance, that means the lugs

have traveled into the position of the neighboring rib before loading (Point E) only frictional

resistance is left, which will be practically independent of the deformation pattern or the related

rib area. Because of the shear cracks, it is likely that inclined bond cracks will not grow much

wider than those that developed at Point C and that new inclined cracks might develop (shown

by dashed lines in Fig. 5.le) due to the still high compression forces on the concrete in front of

the lugs.

It should be noted that the gradual shearing off of the concrete keys is only possible in

well restrained (confined) concrete. If the confinement offered by transverse reinforcement

cannot prevent the excessive growth of eventually developing splitting cracks, the bars will be

pulled-out before the concrete keys will be totally or partially sheared off.

With the exception of Series 3, all reported experiments were carried out with bars with

an almost identical rib pattern. The frictional bond resistance was always reached at a slip value

of about 11 mm to 12 mm (0.43 in. to 0.47 in.), which is a little more than the clear distance

between lugs measured at their midheight of approximately 10.5 mm (0.41 in.). This supports

the proposed theory. The bars used in Series 3 had a much larger related rib area (bearing

area), which explains the steeper ascending branch and the smaller value of the slip at max-

imum bond resistance, S7 , compared to the tests of Series 2. In spite of that, in the tests of max

Series 3.2 with #8 bars (db = 25 mm), which had almost the same clear lug distance than the

#8 bars used in the tests of Series 2, the frictional bond resistance was also reached at a slip

value of approximately 12 mm (0.47 in.) (Fig. 4.12a). On the contrary, the clear lug distance

of the #6 bars (db = 19 mm) and #10 bars (db = 31.7 mm) used in Test Series 3.1 and 3.3

was only about 7 and 8.5 mm, respectively. In these tests the descending branch of the bond

stress-slip curve leveled off at a slip of about 8 to 9 mm (Fig. 4.12a). The ultimate frictional

- 54 -

bond resistance in the tests of Series 2 and 3 was almost the same, which shows that it was not

influenced much by different values of the related rib area. These observations are in accor-·

dance with the proposed theory.


In Fig. S.2a it is assumed that the slip is reversed before shear cracks develop in the con

crete keys. For the loading cycle OA, the response is exactly the same as described in Section

5.2.1. After unloading (path AF), a gap remains open with a width equal to the slip at point F

between the left side of the lug and the surrounding concrete (compare Fig. S.la), because only

the small fraction of slip that is caused by elastic concrete deformations is recovered during

unloading.

As soon as additional slip in the reverse direction is imposed, some frictional resistance is

built up. This resistance is rather small because the surface of the concrete surrounding the bar

is relatively smooth. At H the lug is again in contact with the concrete, but a gap has opened at

the lug's right side. Due to the concrete blocking any further movement of the bar lug, a sharp

rise in stiffness of the hysteretic curve (path HI) occurs. The increase in resistanCe might as

well start a little before H due to the load transfer by some pieces of broken concrete that

might have been produced during loading from 0 to A. With increasing load, the old cracks

close, allowing the transfer of compressive stresses across the crack with no noticeable reduc

tion in stiffness. Inclined cracks perpendicular to the old cracks will open if the negative bond

stress continues to rise and the old and new cracks may even join. However, since the concrete

is well confined, the broken pieces of concrete cannot move. Therefore, the bond stress-slip

relationship for loading in the opposite direction follows very closely the monotonic envelope.

At I a gap with a width equal to SF/, that is the difference between slip of points F and I has

opened (Fig. S.2a). When again reversing the slip at I, the bond mechanism for the loading

path IKL is similar to that of path AFH described earlier. However, the bond resistance starts

only to increase again at L, when the lug starts to press broken pieces of concrete against the

previous bearing face. With further movement, stresses are built up to close the crack previ-

- 55 -

ously opened and open those previously closed. At M lug and concrete are fully in contact

again. If more slip in the same direction is imposed, the monotonic envelope is reached again

and followed thereafter for the same reasons as given for path HI.

A different behavior is followed if the slip is reversed after the initiation of shear cracks in

the concrete keys (path OABC in diagram of Fig. 5.2b). Therefore, the bond resistance is

reduced compared to the monotonic envelope. When loading in the reverse direction (path

CFGHI), the lug presses against a key whose resistance is lowered by shear cracks over a part

of its length induced by the first half cycle. Furthermore, the old relatively wide inclined cracks

will probably close at higher loads than in the cycle considered in Fig. 5.2a, thus complicating

the transfer of inclined bond forces into the surrounding concrete. Therefore, shear cracks in

the hitherto undamaged side of the concrete key might be initiated at lower loads and might

join the old shear cracks (Fig. 5.2b). Therefore, the bond resistance is reduced compared to

the monotonic envelope. When reversing the slip again (path IKLMN), only the remaining

intact parts of the concrete between lugs must be sheared off, resulting in an even lower max

imum resistance than at point I.

In the next example it is assumed that a large slip is imposed during the first half cycle

(path OABCD in diagram of Fig. 5 .2c), resulting in the shearing off of almost the total concrete

key (compare Fig. 5.1c). When moving the bar back, a higher frictional resistance must be

overcome than in the cases described previously because the concrete surface is rough along the

entire width of the lugs. At H the lugs are again in contact with the remaining "intact" part of

the keys (Fig. 5.2c) which do not offer much resistance. Therefore, the maximum resistance

during the second half cycle is almost the same as the ultimate frictional resistance during

monotonic loading. During reloading (path JKLMNO), an even lower resistance is offered

because the concrete at the cylindrical surface where shear failure occurred has been smoothed

already during the first cycle.

From the above considerations it follows that if the bar is cycled between constant peak

values of Smax and Smin' the main damage is done during the first cycle. During successive

- 56 -

cycles, the concrete at the cylindrical surface were shear failure occurred is mainly ground off,

decreasing its interlocking and frictional resistance. This explains the observed decrease in

maximum resistance during reloading (path LMN in Figs. 5.2b and 5.2c) with increasing

number of cycles (see Figs. 4.46 to 4.48 and Fig. 4.51).

According to the above theory, under otherwise constant conditions, bars with smaller

ratios clear lug spacing, Cj, to lug height, a, will produce more bond deterioration than bars

with larger ratios cJi a when cycled between the same values of peak slip, Smax and Smin' This is

shown by the results of Series 3 in comparison to those of Series 2 (see Fig. 4.67). However,

additional tests are needed for further proof and quantification of the influence of deformation

pattern on cyclic behavior of bond.

5.3 Analytical Model for Confined Concrete

The assumed bond model which was first presented in [48] is illustrated in Fig. 5.3. ,

Although it simplifies the real behavior, it takes into account the significant parameters that

appear to control the behavior observed in the experiments. This model, in spite of being

simpler than the ones proposed hitherto (see Section 2.2), is believed to be more general

because it can be easily applied to any bond condition. The model's main characteristics, illus-

trated by following a typical cycle (Fig. 5.3b), are described below.

When loading the first time, the assumed bond stress-slip relationship follows a curve

valid for monotonically increasing slip, which is called herein "monotonic envelope" (paths

OABCD or OAIBI CIDI). Imposing a slip reversal at an arbitrary slip value, a stiff "unloading

branch" is followed up to the point where the frictional bond resistance T f if reached (path

EFG). Further slippage in the negative direction takes place without an increase in T up to the

intersection of the "friction branch" with the curve OA'I (path GHI). If more slip in the nega-

tive direction is imposed, a bond stress-slip relationship similar to the virgin monotonic curve is

followed, but with values of T reduced as illustrated by paths fA' I J. This curve

(0 A'I B'I C'I D'I) is called the "reduced envelope". When reversing the slip again at J, first

the unloading branch and then the frictional branch with T = rJ are followed up to point N,

- 57 -

which lies on the unloading branch EFG (path JLN). At N the "reloading branch" (same

stiffness as the unloading branch) is followed up to the intersection with the reduced envelope

o A' B' C'D' (path NE'), which is followed thereafter (path E' B' S). If instead of increasing the

slip beyond point N, more cycles between the slip values corresponding to points Nand K are

imposed, the bond stress-slip relationship is like that of a rigid plastic model, the only

difference being that frictional bond resistance decreases with increasing number of cycles. A

similar behavior as described is followed if the slip is reversed again at point S (path STU) or

negative slip values are imposed first. To complete the illustration of the model, details for the

different branches referred to in the above overall description

(illustrated in Fig. 5.3a) are given in the following section. The given numerical values for the

different parameters are deduced from the results of Test Series 2. The influence of bond con

ditions different from those in Test Series 2 on these parameters will be discussed in Section

5.3.5.

5.3.1 Monotonic Envelope

The simplified monotonic envelope simulates the experimentally obtained curve under

monotonically increasing slip. It consists of an initial nonlinear relationship 7 = 7, (sf s,)a valid

for s:::;; s" followed by a plateau 7 = 7, for s,:::;; s:::;; S2 (Fig. 5.3b). For s ~ S2, 7 decreases

linearly to the value of the ultimate frictional bond resistance 73 at a slip value of S3. This

value S3 is assumed to be equal to the clear distance between the lugs of the deformed bars.

The reason for this assumption is given in Section S.2. The same bond stress-slip relationship

is assumed regardless of whether the bar is pulled or pushed.

With the values:

s, 1.0 mm

S2 3.Omm

S3 10.5 mm

7, 13.5 N/mm2

73 5.0 N/mm2

a 0.40

- 58 -

the analytically obtained bond stress-slip relationship agrees well with the average curve

obtained in Test Series 2 (Fig. 5.4). However, it must be observed that bond between

deformed bars and concrete inevitably scatters (see Fig. 4.9). Therefore, the values for 7j, 73,

and a may vary between 7]:::::: 15.5 N/mm2, 73:::::: 6 N/mm2, a :::::: 0.33, and 7]:::::: 11.5

N/mm2, 73:::::: 4.2 ~ N/mm2, a :::::: 0.45. Furthermore, the values of s] and S2 might scatter as

well.

5.3.2 Reduced Envelopes

Reduced envelopes are obtained from the monotonic envelopes by reducing the charac-

teristic bond stresses 7] and 73 through reduction factors, which are formulated as a function of

one parameter, called the "damage factor", d. For no damage, d=O, the reloading branch

reaches the monotonic envelope. For full damage, d = 1, bond is completely destroyed (7 =0).

The rationale for this assumption is given by Fig. 4.49, which shows that reloading curves ,

for similar specimens subjected to different loading histories appear to form a parametric family

of curves and that almost the same reduced envelope is followed after a small number of cycles

between large peak slip values or after a larger number of cycles between smaller peak values of

slip. Furthermore, it can be seen that the maximum bond resistance, 7], deteriorates faster

than the ultimate frictional resistance, 73. However, there is a strong correlation between the

deterioration rate of the maximum and frictional bond resistance. This can be seen from Fig.

5.5, which illustrates the reduction of 73 as a function of the damage parameter d, deduced

from the reduction of 7]. Considering the inevitable scatter, the simple analytical function

shown in Fig. 5.5 seems to be adequate.

The deterioration of the monotonic envelope seems to depend on the damage experienced

by the concrete, particularly the length of the concrete keys between the lugs of the bar that

has been sheared off. This, in turn, is a function of the magnitude of the slip induced in the

bar in both directions; the larger the Smax and the difference between peak slip values, the

larger the damage. Another influencing factor is the number of cycles. These parameters can

be related to the energy dissipated during the loading and unloading processes. Therefore, it

- 59 -

was assumed that the damage parameter d is a function of the total dissipated energy only.

However, it has also been assumed that only a fraction of the energy dissipated during repeated

cycles between fixed peak slip values appears to cause damage, while the other part appears to

be used to overcome the frictional resistance and is transformed into heat.

Figure 5.6 illustrates the correlation between the measured damage factor, d, as a function

of the computed dimensionless dissipated energy factor, E/ Eo. The proposed function for d is

shown in the figure. Because of the reason given above, in the computation of E, only 50% of

. the energy dissipated by friction is taken into account. The normalizing energy, Eo,

corresponds to the absorbed energy under monotonically increasing slip up to the value S3.

Although there is some scatter, the agreement between the analytical and experimental results

seems acceptable.

While two results for specimens, which were subjected to one-sided cycles between s=O

and S=Smax, fit the proposed analytical function nicely; two others, however, indicate much less

damage than predicted. This discrepancy cannot be explained in a fully satisfactory manner. It

could be excessive scatter or it could suggest that the influence of the difference between the

peak values of slip (smax - Smin) is not accurately taken into account by the proposed approach.

Therefore, another assumption for d, expressed as:

(5.1)

where

c] ~ 1.0 is a function of (smax - Smin)/ S3 and takes the influence of the maximum excursion

in both directions into account, and

C2 ~ 1.0 is a function of (E/ Eo) and represents the influence of the number of cycles only

was tried. However, the scatter was much the same; therefore, the above described simple

assumption was adopted.

No reduction of the current envelope (monotonic or reduced) is assumed for unloading or

reloading only (e.g. path EFE, Fig. 5.3b). In the tests, cycles were always carried out between

- 60 -

fixed peak values of slip. However, during generalized excitations, it may happen that a cycle is

not completed to the current values of Smax or Smin (e.g. path GHM in Fig. 5.3b). In this case,

the damage parameter is interpolated between the values valid for the last slip reversal and for

the completed cycle (point E and point P in this example) using Eqn. 5.2:

d (5.2)

where

d damage factor of current inversion point(point H in example)

dL damage factor of last inversion point (point E in example)

de damage factor for the completed cycle (point P in example)

SL slip value of last inversion point (slip of point E in example)

Se slip value of completed cycle (slip of point P in example)

S = slip value of current inversion point (slip of point H in example)

Because of the absence of any test results concerning this problem, the assumed linear relation

would seem to be appropriate.

If unloading is done from a larger slip value than the peak slip in the previous cycle (e.g.

path STU in Fig. 5.3b), the new reduced envelope is calculated as a function of the total dissi

pated energy using the analytical expression shown in Fig. 5.6.

It should be observed that the proposal for calculating the damage parameter as a function

of the total dissipated energy is theoretically correct only in the range of the low cycle fatigue.

That is, when a small number of cycles at relatively large slip values is carried out. In fact, if a

high number of cycles at small slip values is performed, the energy dissipated can be relatively

large, but no significant damage is produced and the reloading branch reaches the monotonic

envelope again [12,31]. On the other hand, when limiting our attention to a small number of

cycles « 30), as in the present study, the energy dissipated for cycles between small slip values

is rather small and the calculated damage, as a consequence, is insignificant.

5.3.3 Frictional Resistance

The frictional bond resistance, T f' depends upon the peak value of sliP? Smax, reached in

- 61 -

either direction, and is related to the bond stress, from which unloading started (Fig. 4.45).

However, the reduction of bond resistance at peak slip is only very roughly taken into account

in the proposed model insofar as the bond resistance at peak slip is limited by the reduced

envelope (see Fig. 5.3b). Therefore, the frictional bond resistance (7 f in Fig. S.3b) was related

to the value of the ultimate frictional bond resistance of the corresponding reduced envelope

(73 in Fig. 5.3b), because this value is calculated in the current model (see Section 5.3.2). The

relationship between 7 f and 73 as a function of the ratio smaxl S3 deduced from the tests is

shown in Fig. 5.7. For the first slip reversal, the ratio 7 f/73 depends significantly on the value

smaxl S3 (line a, b,c in Fig. 5.7). However, when cycling between fixed values of slip (e.g.

between Smax and Smin in Fig. 5.3b), 7f is reduced more rapidly than the ultimate 73 of the

corresponding reduced envelope. After 10 cycles, the ratio 7 fl73 is almost independent of

Smaxis3 (see Fig. 5.7). Therefore, the analytical function abc in Fig. 5.7 is used only for the cal

culation of the frictional resistance for the first slip reversal (7 f in Fig. S.3b). For subsequent

cycles, 7 f (e.g., 7} in Fig. 5.3b) is deduced from this initial value by multiplying it with an

additional reduction factor df . It seemed reasonable to assume that the latter depends on the

energy dissipated by friction alone.

Figure 5.8 illustrates the correlation between the measured reduction factor df as a func

tion of the computed dimensionless dissipated energy factor Efl Eof , as well as the proposed

function for df . Ef is the energy dissipated by friction alone and the normalizing energy Eof is

equal to the product 73 . S3 and is, therefore, related to the monotonic envelope. A relatively

large scatter for the damage factor df can be expected because of the large scatter of 7 f (see

Table 4.2). If one neglects tests which had small values of Smax, all results cluster around the

proposed analytical function with no apparent influence of the varied parameters. Although

only a small amount of frictional energy was dissipated during cycles between small values of

peak slip, the deterioration of the frictional bond resistance was rather large. However, it

should be remembered that the absolute value of 7 f is very small in this case (see Fig. 4.44).

If unloading is done from a larger slip value than the peak slip in the previous cycle (e.g.

- 62 -

path STU in Fig. 5.3b), the new frictional bond resistance, l' fU, is interpolated between two

values (Fig. 5.9): the first value is related to 1'3 of the corresponding new reduced envelope

using the analytical function given in Fig. 5.7 and the second value is the l' f reached in the last

cycle (1' f(1) in Fig. 5.9). This interpolation is done in order to have a smooth transition in the

values of l' f' In subsequent cycles between newly established peak slip values, the calculated

new initial value (1' fa (2) in Fig. 5.9) is deteriorated again as a function of the energy Ef dissi

pated by friction alone using the analytical relationship given in Fig. 5.8. In the calculation of

Ef , the friction energy dissipated in the previous cycles is neglected because it is taken into

account in the calculation of l' fa (2).

5.3.4 Unloading and Reloading Branch

The slope of any unloading branch (paths EFG or JKL in Fig. 5.3b) is taken as K = 180

N/mm3. The relatively small influence of the number of cycles on the stiffness of the unload

ing branch is neglected. The same slope is assumed for any reloading branch (e.g. path NE' in

Fig. 5.3b).

5.3.5 Effects of Variation of Different Parameters on the Analytical Model

The analytical model described above and illustrated in Fig. 5.3 has been deduced from

standard tests conducted on standard specimens which had the following main characteristics:

bar diameter: db = 25 mm (#8 bars)

deformation pattern: see Table 3.4, CisR = 0.065

concrete strength: f;:::::: 30 N/mm2 (4350 psi)

clear spacing between bars: 4 db

restraining reinforcement: about 4 times the minimum value given in Section 4.5

external pressure: none

increase of slip: 1.7 mm/min.

Position of bars during casting: The bars were cast horizontally with a depth of concrete

of:::::: 150 mm (:::::: 6 in.) below the bar.

- 63 -

In what follows, the effects of variations of these main parameters on the analytical model are

discussed.

5.3.5.1 Effects on Monotonic Envelope. If no specific test results are available which

provide accurate data on the bond stress-slip relationship in a specific case, the following pro

cedure may be used to modify the monotonic envelope defined in Section 5.3.1.

(a) Bar Diameter

In the present tests a slight decrease of maximum bond resistance was observed with

increasing bar diameter for equal values of the related rib area, although in the more extensive

investigations, no influence of db was found [44]. Based on the present work, it is proposed to

increase 7] by up to 10% if #6 bars (db = 19 mm) are used instead of #8 bars (db = 25 mm)

and to decrease 7] by 10% if #10 bars (db = 32 mm) are used.

(b) Deformation Pattern

The related rib area, aSR, affects mainly the ascending branch of the bond law. If the

actual value of aSR differs much from the value aSR = 0.065, its influence should be taken

into account by modifying s], 7], and a using the data given in Fig. 2.4. For aSR :::::: 0.11, 7]

should be increased by about 10% whereas s] and a should be decreased by about 0.7 mm and

0.33 mm, respectively.

The clear spacing, c], between lugs has a significant effect on the local bond stress-slip

relationship since, with increasing values of c], the values of slip at maximum bond resistance

and at leveling off to the frictional bond resistance increase. The bond deterioration during

cyclic loading decreases with increasing clear lug spacing c]. However, more tests are needed to

quantify the influence of the bar deformation pattern on slip more accurately. In the reported

tests, the clear distance between lugs of the standard bars was 10.5 mm and the corresponding

one for #6 bars was about 7 mm. It is proposed to modify the values for s], S2, and S3 given in

Section 5.3.1 with the factor c]1l0.5 (c] in mm), but because of lack of data the modification

should not exceed ±30%.

- 64 -

(c) Concrete Strength

The influence of this parameter can easily be taken into account by multiplying 'T) and 'T}

with the factor U;/30)f3, where f3 = 1/2 to 2/3 and f; is the concrete compressive strength in

N/mm2. Furthermore, the value of s) should be changed approximately in proportion to .JJ: to take into account the variation of ST with concrete strength.

max

(d) Clear Spacing

If the clear spacing between bars is smaller than 4 db, 'T) and 'T} should be reduced using

the information given in Fig. 4.15.

(e) Restraining Reinforcement

If the minimum restraining reinforcement as given in Section 4.5 is provided, a pull-out

type of failure can be expected. The maximum and frictional bond resistances will not be much

lower « 15%) than the cited values, which are applicable for cases having a 4 times heavier , transverse reinforcement than required in Section 4.5. However, if less restrainment

(confinement) than required in Section 4.5 is provided, a splitting type of failure may occur. In

this case, the bond stress-slip relationship may differ much from that for a well-confined con-

crete (see Fig. 4.11). However, not enough data are available to reliably cover this case.

(f) External Pressure

The influence of external transverse pressure p (for example, by column compressive

forces) can be taken into account by increasing 'T) and 'T3 according to Fig. 4.17.

(g) Loading Rate

If the loading rate differs significantly from that used for testing standard specimens 0.7

mm slip per minute), the values of 'TJ and 'T3 should be modified according to Fig. 4.20.

(h) Position of Bars During Casting

The proposed bond law is valid for bars positioned horizontally in mid-height of a 300

mm 02 in.) high specimen and surrounded by well compacted concrete. The bond stress-slip

relationship may be significantly different for different bond conditions, e.g. more or less fresh

- 65 -

concrete beneath the bars or concrete less well compacted. However, no quantification of these

influence factors is given because of lack of data. For possible modification of the monotonic

envelope, see Section 2.1.1.

5.3.5.2 Effects on Cyclic Parameters. According to Section 4.4.6, several parameters

investigated do not influence significantly the cyclic bond behavior if the deterioration of bond

resistance is related to the pertinent monotonic envelope and calculated for equal ratios of

smax/ S3· In the proposed model, bond resistance during cyclic loading is related to the mono

tonic envelope, and the influence of S3 is taken into account by calculating the reduced

envelope and the frictional resistance during cycling through the normalizing energy Eo and

Eo/, respectively. Therefore, it is assumed that the cyclic parameters given in Sections 5.3.2

and 5.3.3 are also valid for different test conditions than those on which they have been deter

mined (see above). The influence of the different parameters on the stiffness of the unloading

and reloading branch can be taken into account by modifying its slope (K = 180 N/ mm3, Sec

tion 5.3.4) in the same way as the values 7\ (see Section 5.3.5.0. It is believed that this

approximation is sufficiently accurate for practical purposes because the slope of the unloading

branch only slightly influences the overall behavior of a long anchorage [49].

5.3.6 Comparison of Analytical Predictions of Local Bond Stress-Slip Relationships

with Experimental Results

The local bond stress-slip relationships predicted using the model described above are

compared in Figs. 5.10 to 5.22 with the results obtained in some of the present tests. For mak

ing the calculations, a computer program was written which is described in a companion report

[49]. To take the inevitable scatter into account, the parameters which describe the monotonic

envelope were varied in the given range (Section 5.3.5.0 to match the experimental results.

As can be seen, except for the reloading curves starting from s = 0 and reaching the values of

the peak slip between which the specimen was cycled, the agreement is quite good. This is also

true for the results of Test Series 1 and 3 to 7, in which the influence of several parameters on

the bond behavior was studied. In general, the model was successful in reproducing the experi-

- 66 -

mental results with sufficient accuracy.

5.4 Analytical Model for Unconfined Concrete in Tension and Compression

The bond conditions in a joint vary along the embedment length as described in Sections

2.1.2 and 3.1 (see also Fig. 2.6). In the following, the implications on the bond stress-slip rela

tionship during monotonic and cyclic loading are discussed.

5.4.1 Monotonic Envelope

Figure 5.23 shows the different regions in an interior joint as identified in [8] and typical

bond stress-slip relationships for monotonic loading in both directions. Loading 1 (tension

force applied at the left bar end, compression force at the right bar end) results in a rather infe

rior bond behavior at the left unconfined end of the concrete block compared to the middle

confined region due to the early formation of a concrete cone which separates from the main

concrete block (Fig. 3.4). The opposite is true for the right unconfined end of the block

because of the column compressive force transverse compressive stresses are acting on the bar.

For a monotonic loading in the opposite direction (loading 2), the bond behavior of the two

end regions reverses. The length of the end regions with different bond behavior and the per

tinent bond laws are not well known yet.

According to [8] the length of the concrete cone that eventually breaks out is influenced

by the thickness of the (unconfined) cover, the amount and particular arrangement (spacing) of

the stirrups and the arrangement of the longitudinal bars (see Fig. 3.4). In the experiments

performed in [8] this length amounted to about 3-4 db' From the results given in [221, this

length can be estimated to about 5 db' The bond strength in this zone will not be uniform, but

will vary from a relatively low value at the· column face to almost the value applicable for

confined concrete at the tip of the cone because some concrete at the column face will break

out first. Approximately the same length as given above is assumed for the zone with very

good bond at the other end of the block.

The bond strength of the unconfined tensioned region close to the column face may drop

- 67 -

down as low as about 5 N/mm2 (725 psi) for a concrete strength 1'(' = 30 N/mm2 (4350 psi)

[8,221. After the formation of a cone, the bond resistance will decrease rapidly to about zero.

The maximum bond resistance in the compressed region near the column face depends on

the transverse pressure which acts on the bar. A pressure of 10 N/mm2 (1450 psi), which was

approximately present in the tests [8,22] at maximum load, will increase 7 max by about 20%.

Furthermore, compression stresses due to the Poisson effect (bar yielding in compression) are

acting on the bar, which might increase 7 max by an additional 20%. The same percentage

increase can be expected for the ultimate frictional bond resistance. The characteristic slip

values are not likely to change much.

With due consideration of the above mentioned data, the following monotonic envelopes

are suggested as being valid for a concrete strength f; = 30 N/mm2 (4350 psi).

Tension Side:

7] = 5 N/mm2 (725 psi)

73 = 0

S] = S2 = 0.3 mm (0.012 in.)

S3 = 1 mm (0.04 in.)

IX = 0.4

Unconfined region at column face:

Compression Side:

7] = 20 N/mm2 (1900 psi)

73 = 7.5 N/mm2 (1087 psi)

S] = 1 mm (0.04 in.), S2 = 3 mm (0.12 in.)

S3 = 10.5 mm (0.41 in.)

IX = 0.4

The influence of a different concrete strength can be taken into account as proposed in Section

5.3.5.1. If the maximum transverse pressure is less than 10 N/mm2 (1450 psi) or the bar does

not yield in compression, the values for the maximum and frictional bond resistance of the

unconfined region in compression should be modified accordingly.

For conditions as present in the tests [8,221, the following distribution of the characteris-

tic bond stresses and slip values is proposed (Fig. 5.24):

(a) x=O to x=2 dh and x = Ie to x = Ie - 2 db

(b) x =0.25 Ie ~ 5 d" to

x=0.75 /" ~ 1,,-5 d"

Characteristic bond stresses and slip values of the unconfined concrete in tension and compression, as given above.

Characteristic bond stresses and slip values of the confined region, see Section 5.3.

Cc) Embedment length between regions (a) and (b).

- 68 -

Linear interpolation of the characteristic bond stresses and slip values between regions (a) and (b).

It should be noted that the above proposals are highly speculative, which has to be taken

into account when using them. Additional tests are needed to reliably quantify the bond in the

various zones along a bar.

5.4.2 Cyclic Parameters

Figure 5.23a (bottom left) shows typical monotonic bond laws for the left unconfined

region 1. If first a slip in the negative direction is imposed (bar is pushed in), relatively good

bond is developed and "normal" damage in the concrete surrounding the bar is induced. On the

contrary, if one imposes first slip in the positive direction (bar is pulled oud, the concrete is

prone to early cone formation. Therefore, much more damage than "normal" is produced when , loaded to equal slip values. It is reasonable to assume that not much bond resistance is left

after the formation of a cone. Therefore, the following modifications to the analytical bond

model for cyclic loading are proposed.

The normalizing cyclic parameters (Eo, Eo!, and S3) are related to the monotonic

envelope for push-in loading (inducing slip in the negative direction for region 1 or in the posi-

tive direction for region 2 in Fig. 5.23). To take the more severe damage into account which is

caused by bar pull-out (inducing slip in the opposite direction than described above), the per-

tinent total dissipated energy, E, and energy dissipated by friction alone, E!, are multiplied by

an amplification factor 8. It is proposed to take this amplification factor as twice the ratio

between the value Eo for push-in loading and the value Eo for pull-out loading. This definition

of the amplification factor results in a reduced envelope for push-in loading with characteristic

bond str~sses of about 10% of the values of the monotonic envelope, when the bar is first

pulled out up to a slip value s = S3 and then the direction of loading is reversed. ,

Note that the above proposal is rather crude because the deterioration of bond caused by

pull-out to very small slip values « Sj) is probably overestimated. However, a more

- 69 -

sophisticated approach seems not to be justified in the light of the current limited knowledge.

The validity of the above described assumptions was shown in a companion report [49] by a

good agreement between predicted and measured behavior of deformed bars with an anchorage

length of 25 db'

- 70 -

VI. CONCLUSIONS AND RECOMMENDATIONS FOR FUTURE RESEARCH

6.1 Summary and Conclusions

From the results obtained in this study, the following main observations can be made for

the local bond behavior under monotonic and cyclic loading.


(1) The local bond stress-slip relationship of bars embedded in well-confined concrete and

failing by pUll-out has a characteristic shape. The stiffness of the ascending branch

decreases gradually from its initial large value to zero when approaching the maximum

bond resistance, 7 max. After passing 7 max, the bond resistance decreases almost linearly to

the ultimate frictional bond resistance, 73 at a slip, S3, which is approximately equal to the

clear distance between lugs, and remains almost constant thereafter.

(2) If the bond failure is caused by splitting, the bond resistance drops rapidly to zero after

the occurrence of splitting cracks.

(3) The scatter of the bond resistance at constant slip values is almost independent of the

value of the slip. The standard deviation amounts to about 1 to 1.3 N/mm2 (145 to 190

psi) for specimens tested under identical conditions but cast from different concrete

batches.

(4) To ensure that the bond failure is caused by pull-out, normally a restraining reinforce

ment must be provided. The minimum area for this reinforcement is given in Section

4.5. Providing a restraining reinforcement with an area larger than the minimum value

does not result in a significant improvement of the bond behavior.

(5) The following statements are valid for a pull-out failure.

(a) The influence of the bar diameter on the local bond stress-slip relationship was

rather small in the tested range (db = 19 mm to 32 mm) (#6 to #10 bars).

(b) The bond resistance increased approximately proportional to.JJ:. However, the

slip value corresponding to the maximum bond resistance decreased almost

- 71 -

proportional to 1/.J7:.

(c) Increasing the clear bar spacing from the minimum value s

resulted in an increase of the bond resistance by about 20%.

(d) The bond behavior was improved by applying transverse pressure to the test speci-

mens. The maximum bond resistance was increased by about 25% for a pressure of

13.5 N/mm2 (1914 psi). The concrete compressive strength was l = 30 N/mm2

(4350 psi).

(e) The bond resistance was increased (decreased) by an increase (decrease) of the load

ing rate. A change of the rate of pull-out by a factor of 100 resulted in a change of

the bond resistance by about 15%.


(1) During cyclic loading the degradation of bond strength and bond stiffness depends pri

marily on the maximum value of peak slip in both directions reached previously. Other

significant parameters are the number of cycles and the difference between the peak

values of slip between which the bar is cyclically loaded, i.e. as = Smax - Smin- The bond

deterioration is larger for full reversals of slip than for half cycles.

(2) Cycling up to 10 times between slip values corresponding to bond stresses smaller than

about 80 percent of the maximum bond resistance, T max> attained under monotonically

increasing slip reduces moderately the bond resistance at the peak slip values as the

number of cycles increase but does not significantly affect the bond stress-slip behavior at

larger slip values.

(3) Cycling between slip limits larger than the values corresponding to a bond stress of 80

percent of T max produces a pronounced deterioration of bond strength and bond stiffness

at slip values smaller than the peak slip value and has a distinct effect on the bond stress

slip behavior at larger slip values.

- 72 -

(4) The various parameters investigated do not influence significantly the cyclic bond behavior

if the deterioration of bond resistance is related to the pertinent monotonic envelope and

is calculated for equal ratios of peak slip Smax to slip S3, where S3 is the slip value of the

monotonic envelope at which the descending branch levels off to the frictional resistance.

6.1.3 Analytical Bond Model

(1) The proposed analytical model for the local bond stress-slip relationship of deformed bars

embedded in well-confined concrete for generalized excitations is very simple compared

with the real behavior but provides a satisfactory agreement with experimental results

under various slip histories and for various bond conditions.

6.2 Recommendations for Future Research

While the studies reported herein have clarified some aspects of the bond between

deformed bars and well confined concrete under monotonic and cyclic loadings, some areas

should be the subject of future research:

(1) More experiments are needed to study the influence of deformation patterns, especially

the distance between and height of lugs on the bond behavior under monotonic and cyclic

loading. The results of these tests can be used to reconsider and eventually modify the

proposed theory for the mechanism of bond resistance.

(2) The effect of the strain of the bar, especially beyond yield strain, on the local bond

stress-slip relationship should be investigated.

(3) The relation between bond forces and splitting forces is not well known yet and should be

studied in appropriate tests. The results are useful to reliably estimate the necessary

amount of restraining reinforcement to ensure a pUll-out type of failure. If these restrain

ing bars are resisting any other actions, this simultaneous effect should be studied.

(4) The bond behavior in the unconfined end regions of beam-column joints is rarely known

yet and should be studied in appropriate tests.

- 73 -

(5) If the concrete is not well confined, the bond failure may be caused by splitting. The per

tinent bond behavior under monotonic and cyclic loading is very little known yet.

- 74 -

REFERENCES

1. Seismology Committee, "Recommended Lateral Force Requirements and Commentary," Structural Engineers Association of California, 1969.

2. International Conference of Building Officials, Uniform Building Code, 1970 Edition, Vol. 1, Pasadena, California.

3. Bertero, V. V., "Seismic Behavior of Structural Concrete Linear Elements (Beams, Columns) and Their Connections," Comite Euro-International due Beton, Bulletin D'Information No. 131, Paris, April 1979.

4. Popov, E. P., "Mechanical Characteristics and Bond of Reinforcing Steel Under Seismic Loading," Workshop on Earthquake Resistant Reinforced Concrete Building Construction, University of California, Berkeley, 1977.

5. Takeda, T., Sozen, M. A., and Nielsen, N. N., "Reinforced Concrete Response to Simulated Earthquakes," Journal of the Structural Division, ASCE, Vol. 96, No. ST-12, December 1970.

6. Ismail, M. and Jirsa, J., "Behavior of Anchored Bars Under Low Cycle Overloads Producing Inelastic Strains," ACI Journal, July 1972.

7. Ma, S. M., Bertero, V. V. and Popov. E. P., "Experimental and Analytical Studies on the Hysteretic Behavior of Reinforced Concrete Rectangular and T-Beams," Earthquake Engineering Research Center, Report No. EERC 76-2, University of California, Berkeley, May 1976.

8. Viwathanatepa, S., Popov, E. P., and Bertero, V. V., "Effects of Generalized Loadings on Bond of Reinforcing Bars Embedded in Confined Concrete Blocks," Earthquake Engineering Research Center, Report No. UCBIEERC-79/22, University of California, Berkeley, August 1979.

9. Tassios, T. P., "Properties of Bond Between Concrete and Steel Under Load Cycles Idealizing Seismic Actions," Comite Euro-International Du Beton, Bulletin No. 131, Paris, April 1979.

10. Rehm, G., "Ueber die Grundlagen des Verbundes zwischen Stahl und Beton (On the Basic Laws of Bond Between Steel and Concrete)," Schriftenreihe des Deutschen Ausschusses fuer Stahlbeton, Heft 138, Berlin, 1961 (in German).

11. Lutz, L. A., "Analysis of Stresses in Concrete near a Reinforcing Bar Due to Bond and Transverse Cracking," ACI Journal, Vol. 67, No. 10, p. 778, October 1970.

12. Morita, S. and Kaku, T., "Local Bond Stress-Slip Relationship and Repeated Loading," Proceedings, IABSE Symposium on "Resistance and Ultimate Deformability of Structures Acted on by Well Defined Repeated Loads," Lisboa, 1973.

- 75 -

13. Martin, H., "Zusammenhang zwischen Oberflaechen-Beschaffenheit, Verbund und Sprengwirkung von Bewehrungsstaehlen unter Kurzzeitbelastung (Relationship Between Deformation Pattern, Bond and Splitting of Reinforcing Bars Under Short Time Loading)," Schriftenreihe des Deutschen Ausschusses fuer Stahlbeton, Heft 228, Berlin, 1973 (in German).

14. Goto, Y., "Cracks Formed in Concrete Around Tension Bars," ACI Journal, Proceedings, Vol. 68, No.4, April 1971.

15. Yannopoulos, P., "Fatigue, Bond and Cracking Characteristics of Reinforced Concrete Tension Members," Ph.D. Thesis, Imperial College, London, January 1976.

16. Lutz, L. A. and Gergely, P., "Mechanics of Bond and Slip of Deformed Bars in Concrete," ACI Journal, Vol. 64, No. 11, pp. 711-721, November 1967.

17. Tepfers, R., "A Theory of Bond Applied to Overlapped Tensile Reinforcement Splices for Deformed Bars," University of Technology, Division of Concrete Structures, Goteborg, Publication 73.2, 1973.

18. Orangun, C. 0., Jirsa, J. O. and Breen, J. E., "A Re-Evaluation of Test Data on Development Length and Splices," ACI Journal, March 1977.

19. Eligehausen, R., "Ubergreifungsstoesse zugbeanspruchter Rippenstaebe mit geraden Stabenden, (Lapped Splices of Tensioned Deformed Bars With Straight Ends)," Schriftenreihe des Deutschen Ausschusses fur Stahlbeton, Berlin, 1979 (in German).

20. Menzel, G. A., "A Proposed Standard Deformed Bar for Reinforced Concrete," presented at the 17th Semi-Annual Meeting, Concrete Reinforcing Steel Institute, Colorado Springs, Colorado, September 1941.

21. ACI Committee 408, "Bond Stress - The State-of-the-Art," ACI Journal, Vol. 63, No. 11, pp. 1161-1188, November 1966.

22. Cowell, A. D., Bertero, V. V., and Popov, E. P., "An Investigation of Local Bond Slip Under Variation of Specimen Parameters," Earthquake Engineering Research Center, Report No. UCB/EERC 82/23, University of California, Berkeley, 1982.

23. Sortz, S., "Verbund zwischen Stahleinlagen und Beton als Pruef-und Verwendungs eigenschaft (Bond Between Steel and Concrete as Test and User Property)," Zement und Beton, Heft 75, June/july 1974 Gn German).

24. Eibl, J. and Ivanyi, G., "Studie zum Trag-und Verformungsverhalten von Stahlbeton (Study on the Bearing and Deformation Behavior of Reinforced Concrete)," Schriftenreihe des Deutschen Ausschusses fuer Stahlbeton, Heft 260, Berlin, 1976 Gn German).

25. Nilson, A. H., "Internal Measurement of Bond Slip," ACI Journal, Vol. 63, No.7, July 1972.

26. Tanner, G. H., "An Experimental Investigation of Bond Slip in Reinforced Concrete," M.S. Thesis, Cornell University, November 1971.

- 76 -

27. Wahla, M. I., "Direct Measurement of Bond Slip in Reinforced Concrete," Ph.D. Thesis, Cornell University, January 1970.

28. Dorr, K., "Bond Behavior of Ribbed Reinforcement Under Transverse Pressure," lASS Symposium on Nonlinear Behavior of Reinforced Concrete Spatial Structures, Volume 1, Preliminary Report, Werner Verlag, Dusseldorf, 1978.

29. Mirza, S. M. and Houde, G., "Study of Bond Stress-Slip Relationships in Reinforced Concrete," ACI Journal, January 1979.

30. Perry, E. S. and Jundi, N., "Pullout Bond Stress Distribution Under Static and Dynamic Repeated Loadings," ACI Journal, Proceedings, Vol. 66, No.5, May 1969.

31. Rehm, G. and Eligehausen, R., "Einfluss einer nicht ruhenden Belastung auf das Verbundverhalten von Rippenstaeben (Influence of Repeated Loads on the Bond Behavior of Deformed Bars)," Betonwerk-Fertigteil-Technik, Heft 6, 1977 (in German).

32. Edwards, A. D. and Yannopoulos, P. J., "Local Bond-Stress-Slip Relationship Under Repeated Loading," Magazine of Concrete Research, Vol. 30, No. 103, June 1978.

33. Bertero, V. V. and Bresler, B., "Behavior of Reinforced Concrete Under Repeated Loads," Journal of the Structural Division, ASCE, June 1968.

34. Ismail, M. and Jirsa, J., "Bond Deterioration in Reinforced Concrete Subjected to Low Cycle Loads," ACI Journal, Proceedings, Vol. 69, No.6, June 1972.

35. Shipman, G. M. and Gerstle, K. H., "Bond Deterioration in Concrete Panels Under Load Cycles," ACI Journal, Vol. 76, No.2, February 1979.

36. Bertero, V. V. and Popov, E. P., "Seismic Behavior of Ductile Moment-Resisting Reinforced Concrete Frames," ACI Special Publication SP-53, pp. 247-292, Detroit, 1977.

37. Viwathanatepa, S., Popov, E. P., and Bertero, V. V., "Seismic Behavior of Reinforced Concrete Interior Beam-Column Joints," Earthquake Engineering Research Center, Report No. UCB/EERC 79/14, University of California, Berkeley, 1979.

38. Pauley, T., Park, R., and Priestley, MJ.N., "Reinforced Concrete Beam-Column Joints Under Seismic Actions," ACI Journal, Proceedings, November 1978.

39. Rehm, G., Eligehausen, R., and Schelling, G., "Hoehe und Verteilung der Querzugspannungen im Bereich von Stabverankerungen in Beton (Distribution of Tensile Hook Stresses in Concrete in the Region of Anchorages of Ribbed Bars)," Report of the Lehrstuhl fuer Werkstoffe im Bauwesen, Universitaet Stuttgart, 1978 (in German).

40. RILEM Document RC6, "Bond Test Reinforcing Steel, 2. Pull-Out Test," RILEM Bulletin, Paris, 1976.

41. Heilmann, H. G., "Beziehungen zwischen Zug und Druckfestigkeit des Betons (Relationships Between Tensile and Compressive Strength of Concrete)," Beton, Heft 2, 1969 (in German).

-77-

42. Losberg, A. and Olsson, P. A., "Bond Failure of Deformed Reinforcing Bars Based on the Longitudinal Splitting Effect of the Bars," ACI Journal, January 1979.

43. ACI 318-77, "Building Code Requirements for Reinforced Concrete," American Concrete Institute, Detroit, 1977.

44. Martin, H. and Noakowski, P., "Verbundverhalten von Rippenstaeben, Auswertung von Ausziehversuchen (Bond Behavior of Ribbed Bars, Evaluation of Pull-out Tests)," Schriftenreihe des Deutschen Ausschusses fuer Stahlbeton, Heft 319, Berlin, 1981 (in German).

45. Untrauer, R. E. and Henry, R. L., "Influence of Normal Pressure on Bond Strength," ACI Journal, Proceedings, Vol. 62, No.5, May 1965.

46. Hjorth, 0., "Ein Beitrag zur Frage der Festigkeit und des Verbundverhaltens von Stahl und Beton bei hohen Beanspruchungsgeschwindigkeiten," Schriftenreihe of the Institut fuer Baustoftkunde und Stahlbetonbau der Technischen Universitaet Braunschweig, Heft 32, Mai 1976 (in German).

47. Whaley, C. P. and Neville, A. M., "Non-elastic Deformation of Concrete Under Cyclic Compression," Magazine of Concrete Research, V. 25, No. 84, Sept. 1973.

48. Ciampi, V., Eligehausen, R., Bertero, V. V. and Popov, E. P., "Analytical Model for Deformed Bar Bond Under Generalized Excitations," Proceedings, IABSE Collogium on "Advanced Mechanics in Reinforced Concrete," Delft, 1981.

49. Ciampi, V., Eligehausen, R., Bertero, V. V., and Popov, E. P., "Analytical Model for Deformed Bar Bond Under Generalized Excitations," Earthquake Engineering Research Center, Report No. UCB/EERC-82123, University of California, Berkeley, 1982.

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, 5

. 21

.Q

V

±4.

6,±

1.65

,±9.

2 ea

ch

----.~

~

v 0-

0.44

, 0-

1.65

, 5

22

>,

u 0-

4.57

, 1-

9.2

each

#4:

db

= 1

2.7

nllI;

#8

; db

=

25.4

1111

1

TABL

E 3.

1a

TEST

PRO

GRAM

Cle

ar

Tra

nsve

rse

Sli

p N

umbe

r B

ar

Pre

ssur

e R

ate

of

Dis

tanc

e N/

1TIII2

Sp

ecim

ens

mm

/min

s/

db

2 3 3 3 2 2 2 2 2 2 2 2 2 2 2 1 2 2 2 4

0 1.

7 2 3 2 2 2 2

I---

2 2 2

Act

ual

Con

cret

e S

tren

gth,

f~

N/1T

III2

29.6

29

.6

29.7

29

.6

30.7

29.7

30.7

30.7

30.7

29.6

30.7

29.6

30

.7

30.7

30.7

30.7

28.5

28.5

28.5

30.7

30.7

29.7

29.7

--.J

0

0

Ser

ies

Row

Inve

stig

ated

C

onfi

ning

)

Num

ber

Bar

C

oncr

ete

Para

met

er

Rei

nfor

cem

ent

of

Dia

met

er)

Str

engt

h L

oadi

ng H

isto

ry

Cyc

les

f'

Ver

tica

l S

tirr

up

N/~2

1 #S

#4

2

#4

#4

3 C

onfi

ning

#2

#2

M

onot

onic

in

Ten

sion

0

#S

30

1 4

Rei

nfor

cem

ent

----

5 #4

#2

f--

6 #2

#4

C

ycli

c s

= ±

1.65

iTIl

I 10

7

#2

#4

Cyc

lic

s =

0 to

1.6

5 iTI

lI

1 #6

2

Mon

oton

ic

in T

ensi

on

0 #S

3

#10

3 B

ar D

iam

eter

#4

#4

30

4

#6

5 C

ycli

c be

twee

n s

= i

1.65

iTIl

I 10

#S

6

#10

1 C

oncr

ete

Mon

oton

ic

in t

ensi

on

0 4

2 #4

#4

C

ycli

c, s

= ±

1.65

iTIl

I 10

IS

55

3

Str

engt

h C

ycli

c, s

= 0

and

s

= 1

.65

iTIlI

10

1 2 M

onot

onic

in

Ten

sion

0

3 5

Bar

Dis

tanc

e #4

#4

#S

30

4 5

Cyc

lic

betw

een

s =

±1.

65 i

TIlI

10

6 1 2 M

onot

onic

in

Ten

sion

0

3 T

rans

vers

e #4

#4

I/S

30

6

4 P

ress

ure

5 C

ycli

c be

twee

n s

= ±

1.65

iTIl

I 10

6 1

Mon

oton

ic

in T

ensi

on

0 7

2 R

ate

of

#4

#4

#S

30

3 P

ull-

out

Cyc

lic,

s =

±1.

65 i

TIlI

10

#2:

db

= 6

.35

iTIlI;

#4:

db =

12.

7 iTI

lI; #6

: db

= 1

3.0

iTIlI,

#S:

db

= 2

5.4

iTIlI;

#11)

: db

=3

1.Si

TIlI

TABL

E 3.

1b

TEST

PRO

GRAM

Cle

ar

Tra

nsve

rse

Bar

P

ress

ure

Dis

tanc

e s

/db

N/iT

IlI2

4 0

4 0

4 0

1 2 6 0

1 2 6

0 5 10

4 13

.2

5.0

10.0

4 0

Num

ber

Sli

p R

ate

of

ITilI

/min

Sp

ecim

ens

3 3 1.

7 3 2 3 2 2 2 2 2

1.7

2 2 2 2 1.

7 2 2 2 2 2

1.7

2 2 2 2 2 2 2 1.

7 2 2

170.

2

0.03

4 2

170.

2

-

Act

ual

Con

cret

e S

tren

gth,

fc

N/iT

IlI2

29.4

30

.5

30.5

30

.7

30.5

30.7

30

.7

31.6

54.6

2S.2

31.0

29.7

I

'-l

-0

- 80 -

f' = 30 N/mm2 f' = 55 N/mm2 c c Material

Parts by Weight* Parts by Weight* Weight kg/m 3 Weight kg/m 3

Cement, Type I-II, 1.00 356 1.00 505 Lone Star Brand

Water 0.57 203 0.38 191

Fine Sand 0.43 152 0.36 181

Coarse Sand 2.43 864 1.43 725

Fine Gravel 2.10 746 1.50 760

TOTAL 6.53 2321 4.67 2362

* 1 kg/m 3 = 1.67 lbs/cubic yard

TABLE 3.2 MIX OF CONCRETE

- 81 -

1 1

NUMBER OF f' f t ft BATCH SPECH1ENS SERIES c

N/mm2 N/mm2 --CAST rfTT

c

1 3 1 29.4 3.04 0.319

2 9 1 30.5 2.98 0.305

3 6 1 30.7 3.24 0.330

4 11 2 29.6 3.16 0.330

5 11 2 29.7 2.68 0.279

6 11 2 30.7 2.83 0.288

7 9 2 30.7 2.89 0.294

8 11 2 29.7 3.18 0.324

9 11 2 & 7 28.2 3.33 0.345

10 12 5 31.0 3.04 0.328

11 12 6 31.0 3.14 0.318

12 12 3 31.6 2.90 0.290

13 6 2 28.5 2.66 0.284

2 -

124 x 30.1 3.11 0.310 v% 3.3 6.9 6.9

14 6 4 54.6 4.03 0.280

1 IN/mm2 = 145 psi

2 Five specimens did not yield reliable results because of mal programming or malfunctioning of testing machine.

TABLE 3.3 CONCRETE COMPRESSIVE AND TENSILE STRENGTHS

Dia

met

er

Tra

nsve

rsal

Lu

gs

Ser

ies

Bar

No

mi n

a 1

Act

ual1

Hei

ght

(n

vn)

Wid

th

Dis

tanc

e A

ngle

(n

vn)"

{mm

) (m

m)

c S

a 1 a 2

a 3 a 4

a 5 a 6

a 7 b H

b F

(nvn

) (0

)

2

#6

19.0

5 18

.78

1.16

1.

22

1.44

1.

07

1.22

0.

86

0.69

2.

2 3.

8 9.

7 74

2

3 #8

25

.4

25.1

1 1.

75

1.90

1.

70

1.52

1.

85

1.73

1.

57

2.5

4.2

13.4

75

2

#10

31. 7

5 31

.82

2.54

2.

82

2.86

2.

06

2.41

2.

13

2.18

3.

0 7.

0 13

.5

72

3 O

ther

#8

25

.4

24.7

0 0.

34

0.88

1.

10

1.23

1.

26

1.26

0.

57

2.4

4.4

14.0

71

1 db

=

1.2

74 \I

G7l

; G

= w

eigh

t in

gra

ms,

1

= le

ngth

in

nvn.

2 V

alue

s gi

ven

for

geom

etry

of

lugs

are

ave

rage

d fr

om 1

0 m

easu

rem

ents

ta

ken

at 1

sam

ple.

3

Val

ues

give

n fo

r ge

omet

ry o

f lu

gs a

re a

vera

ged

from

30

mea

sure

men

ts

take

n at

3 sa

mpl

es

from

3

dif

fere

nt

rods

.

04

0,1

1--

---

.... 1.

I°7I

bL

I---

c --

I--

c --

.I

TABL

E 3

.4

GEOt~ETRY

OF

BAR

DEF

OR

MAT

ION

S

Lon

gitu

dina

l Lu

gs

a L

b L

(nvn

) {m

m}

1.2

3.5

2.0

4.0

3.2

3.8

0.7

3.9

Rel

ated

R

ib A

rea

Ci. SR

0.10

0.11

0.16

0.06

6

I

00

N

- 83 -

Standard Deviation S1 i p (mm)

of Bond Resistance (N/mm2 ) 0.1 1.0 J..5 5.0 11.5

Average 0.73 0.70 0.65 0.61 0.50

Minimum 0.10 0.07 0.10 0.06 0.06

Maximum 1.50 1. 73 1.77 1.55 1.27

TABLE 4.1 STANDARD DEVIATION OF BOND RESISTANCE AT GIVEN SLIP VALUES FOR ALL TESTS MONOTONICALLY LOADED (SERIES 1-7, n = 21 ROWS)

- 84 -

L at s Lf during cycling Reduced Envelope Coefficient unl max After 10 Cycles of Variation

% N=1 N-2 N=10 N=1 N=2 N=10 Lmax L3

Average 5 4 7 17 21 21 10 11

Minimum 2 2 2 11 5 11 2 2

Maximum 8 8 12 24 36 42 18 20

Lunl = Bond resistance

Lf = Frictional bond resistance during cyclic loading.

Lmax = Maximum bond resistance.

L3 = Ultimate frictional bond resistance.

N = Number of cycles.

TABLE 4.2 COEFFICIENT OF VARIATION OF BOND RESISTANCE FOR CYCLIC LOADING TESTS (SERIES 2.3-2.15)

- 85 -

T

FIG. 2.1 - TYPICAL RELATIONSHIP BETWEEN BOND STRESS T AND SLIP s FOR MONOTONIC AND CYCLIC LOADING

LONGITUDINAL SECTION

PRIMARY~

CRACK

(0)

BOND-' CRACK

CONCRETE

'--FORCE ON \ CONCRETE

FORCE COMPONENTS ON BAR

CROSS SECTION

UNCRACKED ZONE

INTERNALLY) CRACKED ZONE

( b)

FORCES ACTING ON CONCRETE

,---------, 100 "0 I

~I 0° 00.6 Sl 100 I 0 0'

Cl:::Jr. tgCl

_~r ~ TANGENTIAL RADIAL OOMPONENT COMPONENT

(c)

FIG. 2.2 - INTERNAL BOND CRACKS AND FORCES ACTING ON CONCRETE (AFTER [14J)

- 86 -

C -- TENSION TRAJECTORIES

--- COMPRESSION TRAJECTORIES

LUG

a..!

FIG. 2.3 SHEAR CRACKS IN THE CONCRETE KEYS BETWEEN LUGS (AFTER [10J).

T [N/mm2 ]

20.------r-----,------,------,------,-----~

__ -0.10

10

--- s£. DIRECTION OF CASTING

o ~--~----~----~----~I----~--~ 0.2 0.4 0.6 0.8 1.0 1.2

5 [mm]

FIG. 2.4 INFLUENCE OF THE RELATED RIB AREA aSR AND DIRECTION OF CASTING ON BOND STRESS-SLIP RELATIONSHIP FOR MONOTONIC LOADING (AFTER [13J).

T[N

/mm

2]

8.

i

NU

MB

ER

R

EF

T

YP

E O

F S

PE

CIM

EN

6 I

~ •

0)

[25 ]

INT

ER

IOR

R

EG

ION

®

[ 29]

--1'

1-

I I

......

-.

6)

[ 27]

4 I

,.

I /

,-J---=

-""---,

. r,

....

-- -- --0

[28 ]

0 [26

] B

EA

M

®

[13

] P

UL

L-O

UT

(

1 )

I I

2 I

I! J

1 J;1"'f~_ 3

0 N

/mm

2

CD

[ 8 ]

SP

EC

IME

N

(2)

-'----

(I)

.P e=

5d

b

0.0

2

0.0

4

0.0

6

0.0

8

0.1

(2)

.Pe =

25d

b, C

ON

FIN

ED

RE

GIO

N

s [m

m]

FIG

. 2.

5 LO

CAL

BOND

STR

ESS-

SLIP

REL

ATIO

NSHI

PS

FOR

SMAL

L SL

IP V

ALUE

S AF

TER

DIFF

EREN

T RE

SEAR

CHER

S.

(Xl

-....J

- 88 -

HEAVILY REINFORCED CONCRETE BLOCK REPRESENTING JOINT

STEEL STRAPS RIGIDLY CONNECTED

I------___+_'~ WITH BLOCK --. I-------f----l

® ¢~~- - - - - - - - - .:f~t::::::J

TESTED BAR I-------+-....J ~ REACTION FORCE

f--- 25 db----j

CD UNCONFINED CONCRETE IN TENSION

® CONFINED CONCRETE

@ UNCONFINED CONCRETE IN COMPRESSION

a} SPECIMEN AND TEST SET-UP (SCHEMATIC)

10hH~------~~------~--------+--------~

o ____ ~ ____ ~ __ ~ ____ ~ __ ~ ____ ~ __ ~ __ ~ 2.5 5.0 7.5

b) LOCAL BOND STRESS-SLIP RELATIONSHIP

10.0 s[mm]

FIG. 2.6 BOND STRESS-SLIP RELATIONSHIP FOR MONOTONIC LOADING FOR DIFFERENT REGIONS IN A JOINT (AFTER [8J)

- 89 -

max, / 'max 1.0

. / 1-min, 'max- 0.10

~ -6~ • ft::,e 6 0

r--.. • --.... ~ -DO

~ 0 <b

0 ........

0.9

0.8

0.7 .. C u-o c u f I

.3 ~ ~: 6

4 3 3

db 0 6 &3~ ~: c 0 SYMBOL [N/mm2] [mm]

0 8 -+

0 23.5 14 0.6 4

6 28

• 48.0 14

10 1 10 3 104 10 5 106

NUMBER OF LOAD CYCLES, N

FIG. 2.7 INFLUENCE OF THE RATIO BOND STRESS UNDER UPPER LOAD, MAX T, TO STATIC BOND STRENGTH, TMAX, ON THE NUMBER OF CYCLES UNTIL BOND FAILURE (AFTER [31J).

1.0 r--------1:~---..,-----...__---,_---_,___--___,

E 0.5 1--~'----t__-="'---+--____:7'-=--+_---_j_---_+_--_______l E ~

o z w a:: ~ CD

~ 0.1 (')..-"""""''----j------I-----rI<-----=_'"'''''''-+-----+------I

o

i O'05t==:t~=~t~:::.:f:::=-t~=--::I::::=1 ~ f~ = 23.5 N Imm2 CL :::i db=14mm

en min, = 0.1 'max

0.01~---~---~---~---~---~---~ 100 10 1 104 105 106

NUMBER OF LOAD CYCLES, N

FIG. 2.8 INCREASE OF SLIP AT THE UNLOADED BAR END UNDER PEAK LOAD DURING CYCLIC LOADING AS A FUNCTION OF THE NUMBER OF LOAD REPETITIONS (AFTER [31J).

T

[N/m

m2

] 15t

I

•

'CO

NFI

NED

I ~/---

---L

I

10 f-

: .

REG

ION

/"

""

+-+

.---.~-

-+-+

5'-

'

o I

/ I

I I 7~

I I

I I

r r

I I

7 7

r (7

-5

-10

-- ---

----

----

---

MO

NO

TON

IC

LOA

DIN

G

,..1

I I 2

-15

' 0

5 [m

ml

-2

-I

FIG

. 2.

9 LO

CAL

BOND

STR

ESS-

SLIP

REL

ATIO

NSHI

P FO

R CO

NFIN

ED C

ONCR

ETE

UNDE

R CY

CLIC

LO

ADIN

G (A

FTER

[8

J).

T

I M

ON

OTO

NIC

EN

VE

LOP

E

~---

I I.

4f·

"p=

=jf

( I

-\

~

( II~ ~

J IS

<:':1

rA

---/w

J

MO

NO

TON

IC E

NV

ELO

PE

TD

= f

3'T

s

Tv

=f3

'TJ

TK

= a

t· T

J

TN

= e

x· T

H

TE

O

t'T

s TO

at'

Tp

K3

40

0 N

/mm

3

at

0.1

8

f3 0

.9

f3 0

.9 -

0.4

4 (

5-0

.05

)

5L =

(5S

+ 5

Jl/

2

5U =

(5

J +

5p

l/2

5 G =

5s/

2

ssO

.05

mm

0.0

5 s

s S

0.5

mm

FIG

. 2.

10

ANAL

YTIC

AL M

ODEL

FO

R LO

CAL

BOND

STR

ESS

SLIP

REL

ATIO

NSHI

P PR

OPOS

ED B

Y M

ORIT

AjKA

KU

[12J

1..0

o

T t

0 T

mo

x TC~

C /

E

F

r- TE

I

5,& 5

8 5 C

--

L-l

s Sr

mox

5E

oj

MO

NO

TO

NIC

E

NV

EL

OP

E

T

PI.

P;I

-Jn

78

t M

ON

OTO

NIC

/)

; 7

+ 7

0

LOA

DIN

G

I ,'U

'~

o r

rd

1" I

~Is

-Tf~

//~ I

/'

J

K~ //

!

--~~l/<~~NOTONIC

//

LOA

DIN

G

2 1K

= 3

' TK

e

TfO

= 0

.25

TK

Tfn

=P

·Tt o

-Tt o

=0.2

51(,

-7: f

= p

. T-

n G

FIG

. 2.

11

ANAL

YTIC

AL M

ODEL

FO

R LO

CAL

BOND

ST

RESS

-SLI

P RE

LATI

ONSH

IP

PROP

OSED

BY

TAS

SIOS

[9

J

F' I

E' I

T

L

, M

ON

OTO

N

0' f

:-

" /L

OA

DIN

G

IC

(",N

/

iP~

" i

R

" , ,

, , , ,

, , , ,

_TE~

Fj=E

~·~,

. t

E'

r,ls

, '.

". , '. , '

. ,'. ,'. , '. ,'. , '.

, '. , '. " ",

--"

,'

"

/'

',".

MO

NO

TO

NIC

/ ,

'"

f'

0'

LOA

DIN

G

',,'J

{-.

I

Tr

= T

El

TL

= T

E

1R =

0.9

Tp

sM -

;:0

.4 s

G

'-1 0

1 TO

' = O

to 'T

o

TE'=

OtE

' TE

s E'

= /3

E .

5 E

To

' =

010'

To

I I

TE

; =

olE

. T

El

SE~

= /3

'E

. S

EI

ex,

ex',

/3,

/3'

: F

UN

CT

ION

O

F

LOA

DIN

G

HIS

TO

RY

FIG

. 2.

12

ANAL

YTIC

AL M

ODEL

FO

R LO

CAL

BOND

STR

ESS-

SLIP

REL

ATIO

NSHI

P PR

OPOS

ED

BY V

IWAT

HANA

TEPA

/ PO

POV/

BERT

ERO

[8J

'!)

I-'

L

o

H

8 (IN)

( a ) LATERAL LOAD DEFORMATION DIAGRAM .

H

(d) 8~D8 H I I

0' TLD 1\ CRID -e . ......,., ~-:/t--~----, -El

CLIO

( C)

- 92 -

Cel)

MECHANISM OF STIFFNESS DEGRADATION

(d)

FIG. 3.1 MECHANISM OF DEGRADATION OF STIFFNESS AND STRENGTH OF AN INTERIOR JOINT (AFTER [36J)

Co

SPALLING COVER

- 93 -

c:::I ~"'[email protected]'l:21'1 BULGING OF

COLUMN COVER " t

JO,j'lT OR

CONNECTION )"

4" BULGING OF COLUMN COVER

COLUMN

LEGEND:

NEW CRACKS---OLD "

FIG. 3.2 MAJOR CRACKS IN SUBASSEMBLAGE BCU NEAR FAILURE (TAKEN FROM [37J).

FIG. 3.3 AN INTERIOR BEAM-COLUMN JOINT AFTER SEVERAL INCREASING CYCLES OF REVERSED LOADING (Courtesy of Professor To Paulay)

- 94 -

(a) PHOTO OF SPECIMEN AFTER BREAK OUT OF CONCRETE CONE.

,",

--,.:::">

,.'{/,:~;:- -- -------- ---......... _- ..:-- - -------- - -----

(0) SIDE VIEW (b) SECTION.

(b) GEOMETRY OF CONCRETE CONE

FIG. 3.4 FORMATION OF CONCRETE CONE IN PULLOUT SPECIMEN (TAKEN FROM [8J).

#8

SE

RIE

S 1

,2

4T

07

#6

#

8

#/0

SE

RIE

S 8

,3

FIG

. 3.

9 PH

OTO

OF T

EST

BARS

. FI

G.

3.10

PH

OTO

OF S

PECI

MEN

S PR

IOR

TO C

ASTI

NG

(FRO

NT A

ND B

ACK

SID

ES O

F FO

RMS

NOT

IN

PLA

CE).

\.0

--

.J

FIG

. 3.

11

PHOT

O OF

TES

T SP

ECIM

EN

PREP

ARED

FOR

A

TEN

SION

TES

T.

Fl'r 5-~-;~~-(5r

= ~: -~ ·I

'~I-='

~5---t

--5i---

~· 1

_ --

--.1

~ !

n ' i

. I

r Ir-----

riff--r---

l-x

-l ~

I ! in

!!

1 I

' Ii

II 1\

II \-

, ,

, 13

@

:

L-®

, , Ll 11 II

3:

II II

I .1

qg

---i

-: ::

:::

;'

1 r t

IU

I '

~ -~

I I

:' :'1

"----' 1-

----

-'----

L--

(c:.!

,I

, u 0)

S

IDE

V

IEW

r 11.5~11

®

~

® ~

L I Y

:i,,1

J

H::t

-.J

I

CD O

UT

ER

H

EA

D

® H

YD

RA

ULI

C

JAC

K

@

DIS

TR

IBU

TIO

N

HE

AD

b)

PLA

N

VIE

W

® T

ES

T

SP

EC

IME

N

@

TE

ST

B

AR

®

TH

RE

AD

ED

R

OD

FIG

. 3.

12

DEVI

CE

FOR

APPL

YING

TRA

NSVE

RSE

PRES

SURE

1.0

00

~ j

j D

IRE

CT

ION

O

F

CA

ST

ING

TU

BE

152

BA

R

+ .. ~ r-lf--~j

15

2

""

,;

PL

AS

TIC

S

HE

ET

l ~ ~

_V

ER

TIC

AL

B

AR

S

~_~--L_~~===ii':2::=::::

J~ ST

IRR

U P

S

L95-t

5d bJ-5

d bl5

dbf65

J 15

db

SH

EE

T

BO

ND

ED

LE

NG

TH

FIG

, 3

.5

TEST

SPE

CIM

EN

-, 1

I L

I l

I 1

I i

, 8

37

.0-4

4.5

l ['

;;

1~- I

11.5

-19.

0

,

-1--J

1,--r:--

--UP

PE

R H

EA

D O

F M

TS

--2

.25

.-

13

.5

. ...

---1

Iii I

I \

I I

II

J

/ ::

1

I 'I

r

~~-UPPER H

EA

D

2 L

VD

T's

-T

EF

LON

I ..

I

1 I T

ES

T

SP

EC

IME

N

-~-t--

TfS

T'1

AR

~~THREADED

RO

DS

I l/ t

----TE

FLO

N

L~=

.,~LOWER H

EA

D

I -r--

11t::

J1

II

!llllr

21

ITl-

-SL

IT

3.5

i-

I ,-

-CO

NN

EC

TIN

G D

EV

ICE

3

'I 1

<--

--I,

I ,.

--1

7--_

I

ME

AS

UR

EM

EN

TS

IN

IN

CH

ES

FIG

. 3.

6

=t--

LO

WE

R H

EA

D O

F M

TS

(M

OV

ING

) --

-

TEST

SET

UP

~

VI

- 96 -

• FULL CYCLES (smin'smax)

• HALF CYCLES (Smin~ 0)

" CYCLES WITH D.s ~O.05mm

2.3 2.11

-10 -5 5 10

S [mm] 2.11 2.3

FIG. 3.7 HISTORIES OF SLIP FOR CYCLIC TESTS (SERIES 2)

O'l I'<.0 o o 0

OPENING SIZE [in.] N rt') I'- <;t I'-N <;t O'l (X) 0 0 0 o 0 0 0 0 0 0000 <:i

~~-.--,-,--,--.-~r-,--T~~O o 0

a 80r--r~~+--r~---------------~20 w - FINE + COARSE SAND z ---TOTAL AGGREGATE ~ ~

~ 60 I---+-+\-w--~+-"o:--, +--+--+-+---+-+--+-140 ~ ~ , ~

~ , ~ z z w 40 60 w u u ~ ~ w w ~ ~

CD CONCRETE WITH f~ ~ 30 N/mm2

® CONCRETE WITH f~ = 55 N Imm 2

FIG. 3.8 AGGREGATE GRADING

- 99 -

FIG. 3.13 PHOTO OF TEST SPECIMEN IN MACHINE WITH TRANSVERSE PRESSURE APPLIED.

FIG. 3.14 PHOTO OF CONSOLE AND RECORDING DEVICES.

FIG

. 4.

1 PH

OTO

OF S

AWN

SPEC

IMEN

AFT

ER

TEST

ING.

FA

ILUR

E BY

PUL

LOUT

. FI

G.

4.2

PHOT

O OF

A SP

ECIM

EN

FROM

SER

IES

1.4.

FA

ILUR

E BY

SPL

ITTI

NG

.

>-'

o o

- 101 -

+-----~~_\~- SERIES: 1.1 ____ _ -VERTICAL BARS: db = 25.4mm

I STIRRUPS: db= 12.7mm

::f---:~-L-__ -:~C--_~-~ ___ ~---J-~-- ! -_-"_~ __ J"- _ -- ----t---i

__ -+-__ ,-"",,--+i ___ j---J----r-I. -"---+--1

14f---+~~-\

8

I 6~~~~1--~

4 ---i---i----=i""=7=======-t--- - +-----r-<c-=--I-==I

2f-----~---""-------t_---_t__ ~--+---------

4 8 12 16 20 24

s ImmJ

FIG. 4.3 BOND STRESS-SLIP RELATIONSHIP FOR TEST SERIES 1.1

-I-"--i----- , SERIES: 1.2

2 I VERTICAL BARS: db = 12.7mm

I STIRRUPS:db=12.7mm-

K) Ht---'v-..-~rr-- -r--------t----- --~--- -1------4----1 I I I I

I . I ~----------+-~-+----. '2 I

14

12

8m--~

6 ------+--- -- --- -----""-"----'-~ I

4

,

2 L

4 8 12 14 20 24

s [mm[


- 102 -

T [N/mm 2[

16r-----~~------~------~------~------~------_r~

14 ! -------+--~-- SERIES 1.3 ---+-------1-----1 I VERTICAL: db=6.4mm

12 f---T'-"~-- I --- i ---I STIRRUPS: db = 12.7mm

! ! I I --+-

10 f--f---- ~ .. _____ ~, ______ ~ ________ ~-- ~ _ _____+--- -----L

6f1----

4

i I

-f !

i ' -- -- -- ~- -------+- ~-~-____+___t 2 I

2 --- ________ c ____________ - ---.- --- ---

4 8 12 16 20 24

slmmi


16 T [N/mm2]

14 SERIES 1.4 NO CONFINING

12 REINFORCEMENT -

10 ----r-

8 r---~--r-------f---

r&s ----- t----------

I UJ\ "\

~ ~ ~"

6

4

2

2 4 6 8 10 12 s[mm]


- 103 -

8

'~ .-

~ ~ "-~~ ~" ~ ~ t--

14

12

10

6

4

2

4 8 12 16

SERIES: 1.5

VERTICAL: db = 12.7mm STIRRUPS: db = 6.4 mm -

--=

20

-cD-

~

24

s [mm]

,


14 SYMBOLS SERIES -+----+- - I -- 2.16

--@-- 2.15 -.. -@--- 2.10

---@---- 2.1 10 _.-\ID-.- 2.11

AVERAGE

I

3 4 5 6 7 8 9 10 II 12

s Imml

FIG. 4.8 BOND STRESS-SLIP RELATIONSHIP FOR ALL MONOTONIC TESTS OF SERIES 2

- 104 -

161--------;j~-+""""",---+--

14 ~-I----t _--,..-..

10 H-+-!----r

6

LOWEST SINGLE-1 RESULT I

. j ·-·l I ,

···_-·t ... _--

2 --- ... _+--+-2 3 4 5 6 7 8 9

l·-I

--.!.---

·ir--· s [mmt

I

10 II 12

FIG. 4.9 SCATTER OF MEASURED BOND STRESS-SLIP RELATIONSHIPS OF TEST SERIES 2

- 105 -

T [N/mm2]

16r---~--~---r--~~~==~========~

12

8

4

2 4 a)

6 8

Se ries 2.1 2.2 2

10

(a) FULL RANGE OF SLIP

Loading Tension,

Compression

12

Tension

-------

14 16 s[mm]

T[N/mm2] 16~--------~--~----~----~--~----~--~

8

b) 0.2 0.4 0.6 0.8

Series Loading

2.1 Tension

2.2 Compression

1.0

2 Tension

1.2 1.4 1.6 s[mm]

(b) ASCENDING BRANCH OF BOND STRESS-SLIP RELATIONSHIP

FIG. 4.10 INFLUENCE OF DIRECTION OF LOADING (TENSION OR COMPRESSION) ON BOND STRESS-SLIP RELATIONSHIP

T [N/mm2 J 16

14

10

4

2

2

101-

81--

2

If I!J

- 106 -

Series Vertical bars

db[mm1 Stirrups db [mm1 LAsv/As

1.1 25.4 12.7 4.0 1.2 12.7 12.7 1.0 1.3 6.35 12.7 0.25 1.4 0.0 1.5 12.7 635 1.0

L~==~::=t=-Vertical bars

I

6 8


! I i

Asv/Ab

4.0 1.0

0.25 0.0

------ @ -----------

I

I J I

10

0.2 04 0.6 0.8 1.0 1.2 1.4 1.6 s [mm]

12 s [mmJ


FIG. 4.11 INFLUENCE OF TRANSVERSE REINFORCEMENT ON BOND STRESS-SLIP RELATIONSHIP

- 107 -

symbol i series db [mm[ ~------~~---~~~----+-- -----I

3.1 19

25 25 32

6

4

ftl-f------+I--~ -- - '<~, :::--... -- I

_-+1 _ ~'......... "_~_1 ___ _ I -------~. ~ __ .. i

---L-~- - '~:-J'~2~-::::-4~~~-~. I ~---

------- .-' ---- ----------------1

I 2~------~------+-------+-------~-------+

OL-------L---____ ~ ______ ~ ______ ~ ______ ~ ____ ~ o 2 4 6 8 10


16 r-------.-------,_----~,_------_,--~ ...... - .. ----- -------<D--J--------__ I-

14

12

10

/" - -------~-----,,I" .,..-'--- ....@ ---

f v' _----~ --~--/;:/v-- ....-- -. -I /1 I 'I ,,, '1 1/1/

i.l1 8 rffir-~--+------r±===T===~~~~~--1 ill symbol db [mm] AVERAGE OF

6 1,1 SERIES

II r··-<D-··- 19 3.1 3.4 , , 4 ,

2

3.2 3.5

---~------I~~ 25 ~~-+--~------~ I--@}-- 32

2

3.3 3.6

l I I I i

0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8

s[mm]

12

s[mm]


FIG. 4.12 INFLUENCE OF BAR DIAMETER AND DEFORMATION PATTERN ON BOND STRESS-SLIP RELATIONSHIP

- 108 -

20r-------r---~==~==~====~==~

16

12

4

16

12

8

4

o

2 4 6 8 10


II' .....

12

remark

14 16 s [mm]

~ ~

/ @ ._ -----------1----------;11 ...... t- -----------. ."". . ."". .. ---_ .. --- --~ .. ~ .. ----, ...... ! ./ ............ ®

.-'" ,#fI' ."

......... I / , ...

symbol series ([N/mm2] remark ' " / " £1 " L(j)- 4.1-4.3 54.6 -, , I,'

~-®-- 4.1-4.3 54.6 r:1(j). , ,

1/ v'30/54.6

~' ""[email protected] 2 30.0 -

I I I I I I I

0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6

s[mm]


FIG. 4.13 INFLUENCE OF CONCRETE STRENGTH ON BOND STRESS-SLIP RELATIONSHIP

- 109 -

16 T[ N/mm]

8

l I symbol series clear spacing

.. --@ .• -([)- 5.1 Id b I' ....... r. -- -4 "" .-(g)-. 5.2 2d b ~#.". ....... " 6/ -0, -", .:-@-.. 2 4d b '/ -- -... .., ,." -...... .. 7 /1' ..... ~ ~ f---®-- 5.3 6d b , ''1 ..... " 11/ 1'-..... ". "~ ii' ... .. .

.................. "" ... ~ ~; .... 1'-<> ...... ',--= ........ ~ ............. ~ .......

.... :.'~~ ', ...... ~::... ~

14

12

10

6

'-.. '--. ....... ...:::.-.. -4

2

i i o 2 4 6 8 10

s [mm]


16 T[N/mm2]

8

.. --- ----@----...... ~ ........ .... --- ._._.::<62,-

~ 1--.-.- ,-

",," ...... --- f---<D---,,:' ...... .- --"", ....

#; ",. ", 1-:., ..... /

,-/ .'1/ symbol series clear spacing I

I ~-([)- 5.1 +5.4 Id b I l .-(g)-. 5.2+5.5 2d b

--@- 2 I-

f 4db

~ 5.3+5.6 6db

14

12

10

6

4

2

0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6

s[mm]


FIG. 4.14 INFLUENCE OF CLEAR DISTANCE BETWEEN BARS ON BOND STRESS-SLIP RELATIONSHIP

12

- 110 -

T(S)/T(S=ldb

) I. 3 ,..------,-----.-------.-----------,

1.2 r---t------±------:::::;;;; ..... -----;

1.1 1-----+--1--+---- _ Tes =0.1 mm----l

III Tmax

II. Lfriction 1.0 1----..... ----+------+-------1

o 1.0 2.0 4.0 6.0

FIG. 4.15 INFLUENCE OF CLEAR BAR SPACING S/db ON BOND RESISTANCE

- 111 -

T[N/mm2] 18 I

,@."..=@f:::::' •• , / ~.'. I' # .- - .. 3 .. , ........ , -------- __ . __ . ________ l. ____ . ____ ._._~_ -+--~

.' ........ '-~ ! 16

, " -- I I

14 :{f/'-- ~~--I'::~:~- --i-------+--~--+-----',I I "i ',.:,~~ , I I

121---,H-----+--~n--~ " ,,~.~~:~~:~~~----+-~--~--+-----~ , , ! '>~.-_ I I i ',I ""~.:.. i I

I 0 ~-4I'------+---------_t---~ <,~'~~:k~~-------l-

'- "-"" I TRANSVERSE 2 -- "'-- --, -..+--------1 symbol series PRESSURE P [N/mm ] , ..................... ...:~~~_

' ....... ........ , .. ~ 8

2 o ' ........ '"':"-- ...... ...:." ............... 6 ~-t-~--r-:-:--t---__=_---I~---_+__- --~~.:. .. ~::;7 ~ 6.1 0 - __

-@-- 6.2 5.0 I,

4 - --®-. 6.3 10.0 ----~----r- -------t--------~ .12\ ,I ----&-- 6.4 13.2 I

2 --""-=-=~-==--='--~--=--=--. ..,...--=====:'....---~-----.. ---+_---------------l-~ ----I

OL-_____ ~ ____ ~ ______ L_ ____ _L ______ ~ ______ ~

2 4 6 8 10 12

S [mm]


8

.--®-i:--------_._ ... .. , .. - .................... _. 4 .. -.--_.-".,..,.- _.-' .• - ••• - --:@ .. --.-::-.=

",,,,.,. ,..;;~ r- .

. " ~ .. ::,..-" -~---.' ~;:::;..- --- -------,

"" .. ~:~ r::--- "'(J)--", ~~""~ , {?-...

/~., ./

~ ;l ~// .·z

./. /' // l' I'P TRANSVERSE I'il symbol series P [N/mm2] I ' • PRESSURE , .

<1 f-<D- 2 0

// - -®- 6.1 0

!/ .. -@- .. 6.2 5.0 II Ii I---®-- 6.3 10.0 ,

r ---$-- 6.4 13_2

16

14

12

10

6

4

2

0.4 0.8 1.2 1.6 2.0

S [mm]


FIG. 4.16 INFLUENCE OF TRANSVERSE PRESSURE P ON BOND STRESS-SLIP RELATIONSHIP

- 112 -

T( p)/T(p =0) 1.3 r---------r-------,--------,

•

1.2

1.1 r---~--__+-------I-----_____l

• Tmax

• T friction I.0a_-----I-------__+-------i

o 5 10 15

TRANSVERSE PRESSURE, P [N/mm2]

FIG. 4.17 INFLUENCE OF TRANSVERSE PRESSURE P ON BOND RESISTANCE

fj, TIp 0.50 ...---------,--------r---------,

• Tmax

.. T friction

0.25

/).T = T(p) - T(p=O)

o 5 10 15

TRANSVERSE PRESSURE, P [N/mm2]

FIG. 4.18 INFLUENCE OF TRANSVERSE PRESSURE P ON COEFFICIENT ~T/p

- 113 -

,,- -'CD " ............ symbol series s[mm/min) s/~ /~~ "'I', -(D-- 7.1 170 100

14

/I/·---·- .... , ...... ~ "" ---<G>-:- 2 1.7 I

12/"" .@ ~' [email protected] P ' ... 1· ...... • ..... ' ", .... , I I 10 ...... I',

"""''''''' '"..... II

6

4

2

1 o 2 4

r',~ ..... ........ -+~----i

'<:::::~'''''''''''''''''''L

i 6

s[mm)

"', I ...........

I

... , I ..............

.. ,.,...... I ..... _-.... ........--- ...... --.. -

! 8 10 12

FIG. 4.19 INFLUENCE OF RATE OF PULL-OUT ON BOND STRESS-SLIP RELATIONSHIP

T(r)IT(r=l) 1.2 r---,-----------r------------,

• Tmax

1.1 • Lfriction

1.Qt----+----------__ ------------'-l

0.9

0.8

• r = 5/50

50= 1.7 mm/min

• 0.01 0.1 10

RELATIVE RATE. r. OF SLIP INCREASE

FIG. 4.20 INFLUENCE OF RELATIVE RATE, T, OF SLIP INCREASE ON BOND RESISTANCE

100

5

o

- 114 -

T[N/mm2)

8.---~----~~~~~~~~ ANGE OF RESU L TS FROM LITERATURE

6

4

SERIES 3 (4 tests)1

o 0.02 0.04

AVERAGE RESULT OF SERIES 2 (54 tests)

SCATTER OF RESULTS . ..... OF SERIES 2 (single tests)

(a) FOR SMALL SLIP VALUES

I ' --------+-------t--

'/2 fe = 30 N mm

db- 25mm

CD Viwathanatepa et. 01

® Present test, Series 2 @ Cowell

@ Martin

I i SCATTER OF OWN R ESUL TS

I

2 4 6 8

(b) FOR FULL RANGE OF SLIP

10 12 s [mml

FIG. 4.21 COMPARISON OF BOND STRESS-SLIP RELATIONSHIP MEASURED IN PRESENT TESTS WITH DATA GIVEN IN LITERATURE

- 119 -

16

/- .................. MONO~ONIC I / ,

'7 ~NGI·-I j---- IX ......

/ ......

-_. ,

Vcy ,

'-.. --- ----- ----~

~ ~ f=@-

I

I r---

12

8

4

o

1-----.1

AFTER 10 CvdLES ~ ~B1. s[mmJ

1---- ~ -- -------- f------ -- - _ ... ~--.-. --~

;---- t---- ./ -,_ I ~'r2J'~ , - ----- ------ --l--

MOt-mONIC/" ' ...... - --; @ SERIES 2.6

CYCLING BETWEEN I--LOADING _I--- ' p'Tmm

I "-- _/-kD t I

-4

-8

-12

-16 -10 -8 -6 -4 -2 o 2 4 6 8 10 12

(b)

FIG. 4.27b BOND STRESS-SLIP RELATIONSHIP FOR CYCLIC LOADING, SERIES 2.6*

-l-I·-- .-----+--1 ,

----+----I

-10 -8 -6 -4 I

---

,JAFTER! 10 CYCLES I

4 6 8 10 12

/ :: . 'I' ··t-J~~~:~G1: ~):'-'h-----I----------I----j -12 I -T S =±2.54mm

MONOlONIC LOADING/

L--_.l...-_.L.-_..L-_-'--_-'--_---L -16--1._-----1_--1_--1_--1._--1---1

FIG. 4.28 BOND STRESS-SLIP RELATIONSHIP FOR CYCLIC LOADING, SERIES 2.7

- 120 -

~-+---l----f.i\-+--(I)l-{jQ)-l---- 8 II~~ f '1'-..-..-.._ I

~ ~ ~ ~ IIEXTRAPOLATED 1---+--~-.J.-..--+---~---',+----+---+--4 ::r--t-

~ \ \ ---?-----~~.:i=:::=::~QITOfg)j-.." _ 1\ I


I 1 16 rh /..,.b"."llDAD-+I~G_-+---I ~--+---+-.- J---+---l---Y ~,_c["t--h tl----+--"

i I~· I ...... -.._.

(2) I L(i) (2) 1---- --~-+I _-+_1' ir 4@/AFTERlcycT--i--

I ~ AFTER 10 C~CLES j~


,......., N

E E

.......

- us -

10~------~------~------~

f' -30 N/mm2 c ~T =T(p)-T(p=O) max

z 5 I-------F-+-----+--~\ )(

o E

\--> <J

00 5 10 15 TRANSVERSE PRESSURE. P [N/mm2

]

CD PRESENT TEST

® TASSIOS [9]

@ DORR [28]

® UNTRAUER IHENRY [45]

@ VIWATHANATEPA ET AL. [8]

® COWELL [22]

(a) MAXIMUM BOND RESISTANCE

7.5 r---------r---------,---------,

,......., N

E 5.0 E

....... z

~ ~ 251----1----+------+--------1 <J .

5 10 15 TRANSVERSE PRESSURE. P [N/mm2

]

CD PRESENT TEST

® TASSIOS [9]

@ VIWATHANATEPA ET.AL. [8]

® COWELL [22]

(b) ULTIMATE FRICTIONAL BOND RESISTANCE

FIG. 4.22 INCREASE OF BOND RESISTANCE AS A FUNCTION OF TRANSVERSE PRESSURE P - COMPARISON BETWEEN RESULTS OF PRESENT TESTS AND THOSE GIVEN IN LITERATURE.

T max (r) /Tmax(r=l)

CD Present test ® Tassias [9]

1.2 @ Hjorth [46]

- 116 -

1.01--------.;;;..............I'r:;..",=----------------1

r = 5/50

50 = 1.7 mm/min.

O.s

0.01 0.1 10 100 1000

RELATIVE RATE, r, OF SLIP INCREASE

FIG. 4.23 INFLUENCE OF RATE OF PULLOUT ON BOND RESISTANCE. COMPARISON OF RESULTS OF PRESENT TESTS WITH THOSE GIVEN IN LITERATURE.

.---Sl---+---~---- ------ -------'+'---------- --~r_=_--

MONOTONIC LOADING /'// -------- ./ /'/

61---~-+---------- ----------- ---------------- -------~-+-

I AFTER 10 CYCLES

41---+-------+-----+

21---1----------

- 21-----+----------------

-4t---+-------I/+-~-,E--_+_----_+_------+_--_l SERIES 2.3 CYCLING BETWEEN

-6t---+-----~ ------+------- =± 0.107mm --1-----1 ;,

/' ........

-S ........ ~MONOTONIC

.- LOADING ----+----- ----~+'__-___l

-0.2 -01 0.1 02 s/mm/


12

8

4

0.

-4

-8

-12

-16

- 117 -

~CTONIJ -- -- -LOtIOING -------- --

I , ~ /' ~K.FTER 10. CYCLES

=t~ I V ~ --l ;, /

-2---rw- W~~ ~., ! :

.!

I _~~:-- f v

I~~@-+ ,

I ! ~/ I I i 'CD / / -~+- -t---- i----+--- t---- .

p'NCTONIC ~/ SERIES 2.4 OAOING 1--/ CYCLING BETWEEN --- s =±C.44mm

~L __ ---- t----- I

I I I -1.0. -0.8 -0.6 -0..4 -0.2 0. 0.2 C~ 0.6 0..8 1.0. l2

s Imm\

(a)

16

I'-~ /MbNCTO~IC L010ING /--

~ 12 If

~ '/ => , f--- AFTER 10 "-J--------- 8

~ CYCLES --~ 1= 4

TO>

-10. -8 -6 -4 -2 ~ 4 6 8 10. 12

-4- 10. s[mm]

1----- I " I _1_ SERES 2A -,

" , W! -8 --t- CYCLING BETWEEN , s = ± C.44mm , , I

MCNCTONIC LCAOING/ ",,-. / 12

I I I " _/ -16

(b)


- 1 I I

-10 -8 -6 -4 -2

---1-- ---1-- ~--- -----l- I I

I -... I 1--------;-- ',;:-t- --- ----- --...

I ,t" , MONOfONIC LOADING~.... I

I ........... -,,/

- l18 -

L--_'--_'--_'--_'--_'-----I. -16-'---'----'----'---'---'----'


-10 -8 -6 -4 -7'-1; :r 2 4 6 8 10 12

~:<I- : / 4· ........l--i-' ,[mm]

~-- - . I ·8- - f-SERIES 2.6--1-~----+---I V"~' i /1 CYCLING BETWEEN

1--- MONOTONIC"I--. .', i/J s = ± 1.65mm I -LOImIING -- - - -"-', ':-~II / / -12

I '- i-/ L--_i---'--i-_l-_'--_'-----..J -16-'--'--'---~'--'----'---'

(a)

FIG. 4.27a BOND STRESS-SLIP RELATIONSHIP FOR CYCLIC LOADING, SERIES 2.6

- 121 -

12

8

I ~ l~ I ~NOTONIC LOADING

'~- ---- --4 Iq)~ ~-I~

~ 1/ o

-4

-8

'---- ® -cb ---- CD ,

.... - 1 "I'

, , -, , 1 SERIES 2.10 , ,

-12

, , , CYCLING BETWEEN ' .... I s = ±9.2 mm

MONOTONIC LOADING/ , I

I I ' ........ /

I I I -"

-16 -12 -10 -8 -6 -4 o 2 4 6 8 10 12

s[mm]


FIG. 4.32

T [N/rnm2 ]

16r--r--'--,---,--,--,--,---.-~--,--,--,---,--,--,--,

12 --f--J __ 1 __ 1-

--1---1 I !

8

4

-4 - ~--- -;-- - 1 2 10 --+---+---f----t----'[-- , L ' -8 I : t->-r'-~ 'k - - j---}

MONOTONIC LOADING I '" :! -12 -r-r----, -- --1 ~,1_=J-

-16 '::------l-:---'-:----1:------"---L----L----L-__ L-----L __ -L----.L __ --1-__ L----.L __ -L----l -16 -14 -12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12 14 16

s[mm]

BOND STRESS-SLIP RELATIONSHIP FOR CYCLIC LOADING, SERIES 2.11

- 122 -

8

4

-4

-8

-12 '---_'--_-'--_-'--_..L-_..L-_...L-..J

0.2 04 0.6 0.8 1.0 1.2

slmml

FIG. 4.33 BOND STRESS-SLIP RELATIONSHIP FOR CYCLIC LOADING~ SERIES 2.12

I

12 f---II~f------"1,,"~=,-MON

1

OTONIC LOADI,NG-~

'-, "-

W--,------l---J~- - -'::-~-I - __

AFTER 10 CYCLES -.-. ---l-t+--f---+---- ---,

I SERIES 2.13mm I

-8~~---+~C~~LINGBETWEEN·~-4~ s = 0 and s = 1.65mm

-12 L.-.._'--_-'--_..L-_...l.--_---"--_-L--J

o 2 4 6 8 10 12

slmml


- 123 -

12

--- -~-+---j

--

-8

-120~-2-:---4-':---'-6----'-8---!10----'1-2 -'

slmml


16

4 ----AFTER

10 CYCLES

O~~~=*~~t=~

'SE"'ES 2.15 +-+----1 CYCLING BETWEEN

- 8 ~-+-----+--s = 0 and 5 = 9.2mm

I -12 L--_"--_-'---_-':-_-'--_-L-_-'--..... o 2 4 6 8 10 12

slmml


- 124 -

16 ,..:T __ I~N~/m~m~2~1'-______ -r ______ -' ______ -' ________ '-____ --.

AT s = 1.65mm

14~----~+-------~--~~--+-----------r---------

AFTER ADDITIONAL 12 ~.~----~~~:l:=;¢::=::"':2)---=---..J------~-- 10 C'r'CLES AT s = 2.54mm

---~ 1

..... - ---. . -- ---------t--- ----~fi -~-.::~--~~NOTONII LOADIf'JGL+_ ---

I I I II ~--------r------- 1--- ---- -

---11-- - ___ SERIES 2.17 +CYCLING WITH I !:!"s = 0.05m1

.---- .--.----- - 1---

10 I----~-_#_~f__

8~-H----+-----~~

2

2 3 4 5 6 slmml


SERIES 2.18

14 ~-----+------- I ~:C~I~~5~: t AFTER 10 CYCLES MONOTONIC LOADING - . .

12 A~ s = 1.0mm -_\ ---- ---~t-----+------------j --_ 1 --.---4 I

1-""-"'- I 10 ~~-I'.L....---J,t-~;'"=' ----- - .. _------_ ... __ . _.-._-- ---+----~.::..:::::----~-- - -

I AFTER ADDITIONAL I / 10 CYCLES AT s= l.65mm

8~//" t---·------r---- 21

1--

6 f--+-/ f------tt--~-+_ ------- -+-- - -- -t-I .! I

-H-----'C/-+l-----I -f--4

I 31

-~.~

1

2 3 4

----. ~""'--I -_

131 --_. --I-_~"--=-

I TER

ADDITIONAL ---10CYCLES AT s = 4.6mm

---------1-------

5 6

slmml


- 125 -

MONOTONIC LOADli __ - ____ _

~~---+--- .. -. -~ -- ----------

- 8t----t---

-12t-----+---

-1.0 -0.8 -0.6 -04 -02 0 02 04 0.6 0.8 1.0 1.2

(0) s Imml

FIG. 4.39a BOND STRESS-SLIP RELATIONSHIP FOR CYCLIC LOADING, SERIES 2.19-1

--:

-10 -8 -6 -4 -2 o 2 4 6 (b)

FIG. 4.39b BOND STRESS-SLIP RELATIONSHIP FOR CYCLIC LOADING, SERIES 2.19-2

12

8

4

o

-4

-8

-12

-16

(C)

- 126 -

I ,,- , I ~ ',-",

I

I I up II

(

~ ® 1(12) ~ I I I

-- ~- 1---.

j 1 I L r:; "/

~t:==- j--- v-~~ /' -- --~~-- --~ .. -... _. ------- v r----t_ '- - --- I [" ,

r--'-- " -------- f

I "'~. J I

" I J

i-iIL~ ~~ I

,- I , _/

-10 -8 -6 -4 -2 o 2

j I I

:~~+J:~= j@ ~. :------

16 --+----------t__ ~ ,

~ I

f®- I

'~ SERIES 2.19

CYCLING BETWEEN

r=±4'r 4 6 8 10 12

s[mm]

FIG. 4.39c BOND STRESS-SLIP RELATIONSHIP FOR CYCLIC LOADING, SERIES 2.19-3

I I LOADING--

-10 -8 -6 -4 -2 o 2 4 6 8 10 12

{d} s [mmj

FIG. 4.39d BOND STRESS-SLIP RELATIONSHIP FOR CYCLIC LOADING, SERIES 2.19-4

- 127 -

I ~~/- -", 1 MbNOTO~IC LOJDING I I

I I

6 ttJ~~~[~~~ I

--t 1 L i

i I~ iff II i h 51--,-r-f-~ I

I

~ ~ ~v 1 i 1

I, II 1/ /~ I I ~ 71 I

-- ._--

~ +--r -------,----- -- ~ ,ELs i.20-1 L---.., 1', J 1--- -

MONOTONIC/' ' ...................... fl !CD CYCLING BElWEEN

LOADING I 5 = ±1.02 mm

12

8

4

o

-4

-8

~- ----_ .. , --f- e----- ------ f----

'" /

-_/

-12

I -16

(0) -10 -8 -6 -4 -2 o 2 4 6 8


12

,..- " I I ,.................: MONOTONIC LOADING

1 '-l'~Jl 1 I - ---- : - 1 ...... ,,;..[ j - -

I i"--L_ II ___ ~ _ l---

I I I I

8

O~--~--~--~--r---~--+-~+---~--+---~--~--~~

-4 --- -...... , -8

-12 MONOTONIC -LOADING

-[ . ,

! I 1 ! i I 1-+ -- -+---j-~-l----

I SERIES 2.20- 2 CYCLING BETWEEN ----r--S II± 1.~5mm i·-+---t-I

1 ~ 1

I -16 L---L----L----.l..---4.l---..L---~O-----I..2-----I..4------:-6----J.8----J.IO=----:'12:--'

-10 -8 -6 - -2

(b) slmmJ

FIG. 4.40b BOND STRESS-SLIP RELATIONSHIP FOR CYCLIC LOADING, SERIES 2.20

FIG.

- 128 -

12 -----

8 -----+--

I 4

0

-4 --- ~ : I I I

-8

· -t _.--=-+15_+-J,L-+-_1- -.--1---,- -j--~ -- -

--{ =~, --- I I, ~~~5~~- ~l~~f~-;;-rl MONOlONIC ", LOADING __ t- " ''., / 1----1---- s:±2.54m!'-f_-+_-l----.j

_/ I i

-12

-16 -10 -8 -6 -4 -2 o 2

( C) 4 6 8 10

s /mm l

12

4.40c BOND STRESS-SLIP RELATIONSHIP FOR CYCLIC LOADING, SERIES 2.20

T /N/mml]

16

12

8

4

o

t +1 I . __ .-.. - .. - ---- ------ ---- --1----t-----~ .. _. __ ._- -----(r'~<7~~~C1·DIt<Cl~

I I I 16 " 1---r---.-.--- ------ ._---- ----~.--.- -_. f-~\ ",_ I r-

I @I 0 ® -_I f------ f----- ~.-

-_ .. __ ._- ----- f. ... 29 \ f-- 21 l---T=-/~J..- t i

I ~j..-I---j---.&. I i i '

@V~~~ i ,

l-I

i i

1-----1----- :1 ~~ I -- , ___ i71 _CiGl I 1 ~ERIES 220-4

.... , 1----

" I ·--CYCLING BETWEEN .... I s =±4.57mm

l MONOlONIC LOADING>, ! ,

..... / 1---· I ..... -" i I

-4

-8

-12

-16 -10 -8 -6 -4 -2 o 10 12 2 4 6 8

(d) s Imml

FIG. 4.40d BOND STRESS-SLIP RELATIONSHIP FOR CYCLIC LOADING, SERIES 2.20

- 129 -

12 f---------!----t--

8

4

4 ---t: 5 21- --J

r

- -- -- ~-+I-- -2 I ' .... I I . -.; I 1 I.

8 --- -+ j',,<t---- ----J---------' ---1----I 'I h, i I - I ' I /

12 MONOTONIC LOADING~'}' - - - -----r-- ----1------I I ',- .// . i I I

16~~--~--~--~---L--~--~--~--~--~-~~~_J

10 8 6 4 2 o 2 4

(e) 6 8 10 12

s [mml

FIG. 4.40e BOND STRESS-SLIP RELATIONSHIP FOR CYCLIC LOADING, SERIES 2.20

FIG.

12

8

4

0

-4

-8

-12

-16

(0)

1-----+-----+---- - ~t~~ r---l --------...... l/'/ h "''''~ i. I, f-------+---t-=""'-~-+---I® I -\1) I~c---

I ' , 1/1 SERIES 2.21-1 MONOTONIc! .... " lit-L{j} CYCLING BETWEEN

~ING -c -- '-,- ~/ ' • ± l.orm f------+-1-l

-10 -8 -6 -4 -2 o 2 4 6 8 10 12

s[mm[

4.41a BOND STRESS-SLIP RELATIONSHIP FOR CYCLIC LOADING, SERIES 2.21-1

- 130 -

12 f-------- -----

-10 -8 -6 -4 -2 2 4 6 8 10 12

s [mml (b)

o

FIG. 4.41b BOND STRESS-SLIP RELATIONSHIP FOR CYCLIC LOADING, SERIES 2.21-2

T IN/mrTfl 2r-~--+---------,---------.---------,---------,---~

O~----+---~----+---------+---------+------r--~~

-I f-----+----+-----7'~=----- -+------~----~--~ SERIES 2.21- 3 I CYCLING BETWEEN s = ± 1.65mm

-2~----~--------~--------~--------~--------~--~ -2 -I 0 2

(C) slmml

FIG. 4.41c BOND STRESS-SLIP RELATIONSHIP FOR CYCLIC LOADING, SERIES 2.21-3

- 131 -

-:r----t------l---+-----+--@--:0161----i.~ r:v::;.-""-- --t--1-i-l! ..1

-- - --- ---,I i I I i __ _

-8

/ I I SERIES 2.21 - 4 j

I '" ....... I CYCLING BETWEEN

-12C~TNIc/. "'",/1 I f2f'" I I -16 L------l'------l_---'-_---'-_---'-_---L_--'-_--'-_----'-_----'--_----'---_-'---'

-10 -8 -6 -4 - 2 0 2 4 6 8 10 12

(d) s /mml

FIG. 4.41d BOND STRESS-SLIP RELATIONSHIP FOR CYCLIC LOADING, SERIES 2.21-4

12

8

4

o

-4

-8

-12

-16

(e)

I I I /~ -..... MONOTONIC LOADING

" / ---/

.......... /, I I @ I ,

@l f ~\ .....

~~ .......... -

165\ ----- -

~ ~\ I '-A

~ ~ ~ ~ ~

r--- __ @ .......... 21l ..... , I ....

~MOOO1UNIV' I

SERIES 2.21-'5 CYCLING BETWEEN ' ..... I s =± 4.6mm ............... I

I

LilNG ' ..... / .......... r-""/

-10 -8 -6 - 4 - 2 o 2 4 6 8" 10 12

s /mml

FIG. 4.41e BOND STRESS-SLIP RELATIONSHIP FOR CYCLIC LOADING, SERIES 2.21-5

- 132 -

T /N/mm 2/

0.8 r-'--r--'-----.------..------..,-------,----~

O.5t-------+-·------t-------+-----

Or--r-~---r_----+------+----+-~---~

I

I SERIES 2.21-6 -----j-CYCLING BETWEEN--

i S :±1.65mm I

I

(~.)1-----:2:-------..L1 -----l0------L-----.J2L--.-J

s /mml

FIG. 4.41f BOND STRESS-SLIP RELATIONSHIP FOR CYCLIC LOADING, SERIES 2.21-6

16 T N/mm2 I I I

;' -I- -.. /.MONOTONIC LOADING /.......... I I

" I +----__ ! 1', i

8t------f----f---T---+---+-

4 1-----+----+--+----1-----1-

/ ....... , i

/ , i 1

I " 1=1-I r§I) -...-.. ...... , ~~ -----(P\=~~==l ~

® , t----+---t---=>-~+----+----I----.-if---__+_- ~~IES 2.21-7 _-,---- I_

I CYcLING BETWEEN --,----'',r-, / s =± 9.2mm

~:: lie ILOAD'r ',,-j -10 -8 -6 -4 -2 o 2 4 6 8 10 12

(g)

FIG. 4.419 BOND STRESS-SLIP RELATIONSHIP FOR CYCLIC LOADING, SERIES 2.21-7

- 133 -

16 T IN/mm2

1

8

SERIES 2.22 - I CYCLING BETWEEN

- 8 t----~t-~t-~ s = 0 and s = 044mm

-12 '-_.l....-_.l.....-_-"--_..I....-_..I....-_..J.---J

02 04 06 08 1.0 1.2

(0) s Imml


.......... ..... - ---

4H-~+--~t-~t-~+-~+-~~

SERIES 2.22 - 2 C)cLlNG BETWEEN

- 8 ~~+--T )-+-~- S = 0 and s = 1.65mm

-12 ~_.L----'----L-_--L-_..L-_..L-_...L.....J 2 4 6 8 10 12

slmml

FIG. 4.42b BOND STRESS-SLIP RELATIONSHIP FOR CYCLIC LOADING, SERIES 2.22

- 134 -

12 SERIES 2.22-3

-8 II CYCLING BETWEEN I -5 =0 and 5=4.57mm

-12 '--_.1.-....._.L..-_-'----_-'--_-'--_~ 2 4 6 8 10 12

51mml

FIG. 4.42c BOND STRESS-SLIP RELATIONSHIP FOR CYCLIC LOADING, SERIES 2.22

T IN/mm21

16

12 ~-MONOTONIC LOADING

I 8

4

0

-4 SERIES 2.22 - 4 CYCLING BETWEEN

-8 5 = 0 and 5 = 9.2mm-

-12 2 4 6 8 10 12

51mml

FIG. 4.42d BOND STRESS-SLIP RELATIONSHIP FOR CYCLIC LOADING, SERIES 2.22

K [m

m2~ m

m]

. I

300----~---

------~--.-t_------I

I I

f~

= 5

5 N

/mm

2

i SC

AT

TE

R O

F R

ES

ULT

S

o '.

' 5

10

15

20

N

UM

BE

R

OF

UN

LOA

DIN

GS

FIG

. 4.

43

STIF

FNES

S OF

UNL

OADI

NG B

RANC

H AS

A F

UNCT

ION

OF N

UMBE

R OF

UNL

OADI

NGS

"If [N

/mm

2]

4 t I

'I c

~~~Esl

[~c~~s

l I I

N

I 2 3

• .. • o 6 o

..Q

31

1

' • 0

21

I ..

.. "6

---_

6

• ""'-

... ,1

N

=2

Ii

--" ....

........

.. -6

, I

-0--

--0--

~ I

N =

10

'I

----

----

----

----

o o

4 8

12

16

smax

[m

m]

FIG

. 4.

44

FRIC

TION

AL B

OND

RESI

STAN

CE D

URIN

G CY

CLIC

LOA

DING

AS

A F

UNCT

ION

OF

PEAK

SL

I P s

max

>-'

W

\..

Jl

- 136 -

Tf/Tunl 0.6r--------,--------~--------~--------~--------~

I-"A ....... SC-E-N-D-IN-G..t-+--------+- DESCENDING BRANCH--+---.=---.II BRANCH OF LOCAL BOND LAW

T N=I 8 o ...... Tunl( I)

0.4 - N=IO_ ....-Tunl(lO) ~-----l--- .----+ ). -- ~_---t-:t -p-=-:.=.--=:-=-l"':=-_-_-__ -+-~- S

5 I,(Tf(IO) max --, T

f (I) •

o 2 4

FIG. 4.45 RATIO BETWEEN FRICTIONAL BOND RESISTANCE DURING CYCLIC LOADING, Tf, AND BOND RESISTANCE, Tunl' FROM WHICH UNLOADING STARTS AS A FUNCTION OF PEAK SLIP Smax

BO

ND

D

ETE

RIO

RA

TIO

N

RA

TIO

, T

un

l (N

) I

Tunl

(N

=I)

1.0

• .-----,-

-----,-

---,-

-,-

-,-

-,-

-,.

.-----,-

---,

O. 8

H4--\-+~

0.6

1'\

\1\

1 ~'"

1 sm

ax[m

m] ~

0.4

4

0.41

'\

'\ I

"-

J: r-

-*:

I =y

=-~

1.65

0.21

1

"-,

I "-

A ~

4.5

7

~6.85

2 3

4 5

6 7

8 9

10

NU

MB

ER

O

F C

YC

LES

, N

(a)

CYCL

ES W

ITH

FULL

REV

ERSA

LS O

F SL

IP

(b)

OO

ND

DET

ERIO

RAT

ION

R

ATIO

T

un

l (N

) I

Tun

l (N

=I)

1.0

• ..------;---,.-,---,---r--,---,---,---,

----

t---

1 0

---0

I C

YC

LIN

G W

ITH

~s=0.05mm

Q--

-O

0.8

1\\ ""

0---

<>

\

.. '"

It--II

---..

.

0.61

\

\1

04

"-

CY

CLI

NG

B

ET

WE

EN

o an

d sm

ax

I ---t

Sm

ax[m

m]

.~ARBITRARY

04

4

I . -

-i

1.65

~4.57

9.2

01

..

I

2 3

4 5

6 7

8 9

10

NU

MBE

R O

F LO

AD C

YC

LES

N

CYCL

ES W

ITH

fj s

= 0.

05 m

m AN

D fj

s =

s

(HAL

F CY

CLES

) m

ax

FIG

. 4.

46

DETE

RIOR

ATIO

N OF

BON

D RE

SIST

ANCE

AT

PEAK

SLI

P AS

A F

UNCT

ION

OF N

UMBE

R OF

CYC

LES

>-'

W

-..

.J

1.0

O.B

0.6

0

0.4 ~

0.2

O. I

0.0

5 B

ON

D

DE

TE

RIO

RA

TIO

N

RA

TIO

, T

unl

(N)

/ Tu

nl (

N =

I )

--~"

""""

,,-~

--;J--

:'J-

--

~"'"

~ ~

r---.....

r-

---i

]...

"\."\.

"'" r'-

--:-

--'

'"\. "" -

------

"" ~ l-

t

~ ~

I--,

~

~

"" '~ ~ '"

ls T

m

in

Sm

a.

>---

, r--< I

--.

~ N

r'

--l

~ i'

-t.

>--...

.., r--

. N

i-, r---

.. r---...

~ ~ ~

~

N

-r--r--.

.. :>-

Sm

ax

[mm

]

0.11

?I II 0

.44

.02

.65

;:;:;~

"" ~; 2

.54

4.5

7

hr'

~6.85

BO

ND

D

ET

ER

IOR

AT

ION

R

AT

IO,

Tun

l (N

) /

Tunl

(N

= I )

1.0

Sym

bol

N

Cyc

ling

betw

een

0--

-0

2 0

and

smax

0.

8 ~

----

+ 0

---0

10

,

..-.

2 ~

! _

__

_

10

±

sm

ax

~,.I

--+-

-.

r'--'i

~-O

I ~l

....

I~N

'21---

-----l

:--

7 I

•

0.6

04

0.2

I

'-Ir

:-L

• ....

......

Tun

l (N

)Tu

nl(

N=

I)

N=IO

0

.02

0.01

I

FIG

. 4.

47

U--i

S£

I

I O

. .'

2 3

4 5

6 7

8 9

10

NU

MB

ER

O

F C

YC

LES

, N

DETE

RIOR

ATIO

N OF

BON

D PE

SIST

ANCF

AT

PE~K

FIG

. 4.

48

SLIP

AS

A F

UNCT

ION

OF N

UMBE

R OF

CYC

LES,

PL

OTTE

D IN

DO

UBLE

LO

GARI

THM

IC S

CALE

4 8

12

16

smax

lmm

\

DETE

RIOR

ATIO

N OF

BON

D RE

SIST

ANCE

AT

PEAK

SL

IP A

S A

FUN

CTIO

N OF

THE

PE

AK V

ALUE

S OF

SL

IP

s max

......

W

00

- 139 -

T (N/mm2)

16r-------r-------~------~------~------~----__,

12

4

o 2 4

LOADING

CYCLE

6 S ( mm)

CYCLING BETWEEN

± smax

S ~s max - s>smax

8 10 12

FIG. 4.49 EFFECTS OF NUMBER OF CYCLES AND OF fHt PEAK VALUES OF SLIP smax ON THE ENSUING BOND STRESS-SLIP RELATIONSHIP FOR S > smax

MONOTONIC v-

LOADING

-10.5

FIRST SLIP REVERSAL

T

Tj(M)

r:~-r-

-Tj (N)

-Tj (M)

-3.0 -1.0 0 1.0 3.0

s[mm]

- EXPERIMENTAL

----- ANALYTICAL

10.5

FIG. 4.50 IDEALIZATION OF BOND STRESS-SLIP RELATIONSHIP FOR CALCULATING THE CHARACTERISTIC VALUES OF THE REDUCED ENVELOPE.

Tj (

N)/

T,

(MO

NO

TO

NIC

) i

i

1.0

. --

-l

0.8

,-

0.6

'-

0.4

0.2

--

o (0)

\' \

--~--I A

FT

ER

I

CY

CLE

_

. a-'

AF

TE

R

10 C

YC

LES

. \

\ \

. \

-)

I \

\ .

h . \ . \

\ \

\ \:

\-

~, a

Ir,

\ "

.-i----------

!

, \

... ,

I=--

---=

=

\ .

....'6

.. L.

•

I '1

-,,~

\.

I "--

--f.--

-----0

6

:..

I _.

_ ....

. I

"""·-

·-I!-'

r.-It.

_._.

._

. 4

8 12

16

Smax

[m

ml

FIG

. 4.

51a

REDU

CTIO

N OF

MAX

IMUM

BON

D RE

SIST

ANCE

OF

THE

RED

UCED

EN

VELO

PE A

S A

FUN

CTIO

N OF

THE

PE

AK V

ALUE

S OF

SLI

P AT

WHI

CH

CYCL

ING

IS

PERF

ORM

ED.

TEST

S W

ITH

FULL

RE

VERS

ALS

OF S

LIP.

73 (N

)/7

3 (M

ON

OTO

NIC

)

1.0

. \

~ \

.

\

\ \

081

~\

. \

\ .

\ ~ \

~ . \ \ \

. '.

0.6

f-"

--+

-FI

RS

T S

LIP

RE

VE

RS

AL

--~--

AF

TE

R

I C

YC

LE

_ ..

... -

AF

TE

R 1

0 C

YC

LES

1----

-r--

" ~

. ....

........

.. ,

0.4

,

, _

_ ,

III

__

""'"

"6

".

-

I 0

.2

o 4

(b)

~'.

--

.......

·_a

, I

._

._

.-._

._

._

._

.... ,

8 12

16

smax

[m

m]

FIG

. 4.

51b

REDU

CTIO

N OF

ULT

IMAT

E FR

ICTI

ONAL

BON

D RE

SIST

ANCE

OF

THE

REDU

CED

ENVE

LOPE

AS

A F

UNCT

ION

OF T

HE

PEAK

VAL

UES

OF S

LIP

AT W

HICH

CYC

LING

IS

PE

RFOR

MED

. TE

STS

WIT

H FU

LL

REVE

RSAL

S OF

SLI

P.

f-'

,/::

o

- 141 -

T(Nl/T (MONOTONIC)

1.0 .- --+-~ Ii T3 CYCLING BETWEEN

\ \ \

\

I I + . . --

\(0) : 0 0.6--- \. - --L--

\ I \ I

e)\ ! e

\ ! \J--\

0.4--

1(0)" I ' "-

0.2

o 4

- --- ± smax

• 0 5 = 0 AND s=smax

(e) (0) PLOTTED AT smax/2 -

o

"-- ...... ~--- -------------- ---+ ........... .----8

I

-r-------12 16

smax [mmJ

FIG. 4.52 REDUCTION OF BOND RESISTANCE OF THE REDUCED ENVELOPE AS A FUNCTION OF THE PEAK VALUES OF SLIP AT WHICH CYCLING IS PERFORMED. COMPARISON OF RESULTS OF TESTS WITH FULL AND HALF CYCLES.

~ I I I I f/ -- tONOTONIC (SERIES 1.3)

-', "

.................

ICfJ ..............

'"

-~ V(Ii) --~ -- ... _---- --

~ J~ -

II

@ 7; -P"""

F s[mm]

16

12

8

4

o

-----!®) ---.......

.... ......... "

" , -8 ............. ,

I- MONOTONIC (SERIES 1.3~"'-I ,I SERIES 1.6

I VERTICAL: db = 6.4 mm _ ---' f---

I I I I rIRRrS: d

bl = 12.7im

-12

-10 -8 -6 -4 -2 o 2 4 6 8 10 12


- 142 -

T [N/mm2] 16~--~--~--~--~----~--~~

12 r-~:+'-'-,fMONOTONIC (SERIES 1.3)

OF-~~--~---+--~----r---~~ s[mm]

-8~--+---~---+------'----r---~~ SERIES: 1.7 VERTICAL: db = 6.4 mm

-12 r----j----_+_ STIRRUPS: 9b = 12.7 mm

-16 L-__ ...L-__ -L-__ ---'-__ ____' ____ -'---__ --'----'

2 4 6 8 10 12


16

(0' " ",r1NoTLc (.lRIEJ.I)

, "

" 12

, , 8

,

p " .... _--I lcAFTER 10 CYCLES--------

-~ ~ V r---

@) 'i -~ s [mm]

4

o

1----- --- .... II fJJ

.... , "

, , vi SERIES 3.4 , , , I , I db = 19mm

MONOTONIC (SERIES 3.1)1J'", I , I I I I I I ' ,

I , I I ,

-8

-12

-16 -10 -8 -6 -4 -2 o 2 4 6 8 10 12


- 143 -

16

12

",

rMOJOTONll (SER\ES 3. )

I '

1m ............... "

if ............... ,

'-'-'-

.~ CAFTER 10 CYCL'ES'" ------"-

I~ / r-- ;-

~ ~

f--s [mm] v-

.@ ~

v® Vw --, , ................ '/

"-, L/ SERIES 3.5 --

8

4

o

-8

- I , '- I d'T5

mm

i (SERIES 3.2»)'-, I

MONOTONIC I ,

I I I I - I , __ I

-12

-16 8 10 12 2 4 6 -10 -8 -6 -4 -2 o


IS

12 ~A rMoLTO.1 (SElES 31,------

..................

~ -..........

r--- -----,-- -----/ ---

.~ j L-AFTER 10 ~CLES --

10 ~ ~

V/ ~ ~ s[mm]

8

4

o

-----'" ~ '" -, -

'- !...-/I SERIES 3.S -, -, I

MONOTONIC (SERIES 3.3)-~ __ I ,

db =32mm I

.... __ ... ,

I I

-8

-12

-16 -10 -8 -S -4 -2 o 2 4 6 8 10 12


- 144 -

/'-. k:D I (/- I I I I

I - --",iMONOTONIC (SERIES 4.1) I

I "

20

16 I , I , I , I

, , I , / , 12 I

, I

, "

f~/ , ,

, , ,

~/) V L ~"

CD AFTER 10 CY~ ;.::.:--- ---

~ -~ ~ -I

~ 7 ~ f@ I s[mm]

Qg) ~ f(2)

8

4

o

I

J r; II 1}) --- I - , I , , I , ,

II ) , , I SERIES 4.2 , , I f~ = 54.6 N/mm2 , ,

1(6 ! , , , " ,

" MONO,TONIC (SERIES 4.1) ~""" , /

-8

-12

-16

-10 -8 -6 -4 -2 o 2 4 6 8 10 12


T [N/mm2] 20~~=---~--~--~--~--~--~--'

161--h'----+-1--~-------+-~--~- SERIES = 4.3 f~ = 54.6 N/mm2

4 ~-H-Ir.

I I AFTER 10 CYCLES

1'----- ------ ------MONOTONIC (SERIES 4.1)

I s[mm]

Or--rr---~--~--~--+---+---+-~

4 6 8 10 12 14 16


- 145 -

121---+---+-

------~ ---- -+----I I I I I I

--!~+---+

81---+----+

41----+

I I

0~-~-+_-+--4_-~~~-++-~-~--~-~-~

-12

. ···~+_I'[mml~ 1-- t--- +----:-

Series 5.4 I

--+-- clear spacing: I db-----+

-4 ---t-..... ---I ..........

-8 I---oM~Od.N=OTO N I C

I -16 '---_..L.-_...L-_-'--_.....L..._-'-_---'--_--L_-----"-__ L-_L-_-L-_..L-.J

-10 -8 -6 -4 -2 0 2 8 10 12 4 6

FIG. 4.60 BOND STRESS-SUP RELATIONSHIP FOR CYCLIC LOADING, SERIES 5.4

T [N/mm2]

16.--r--~-~-~-~-~~~~~-~--~-~-~

fP- - I I I I 12 ~-~-+_-+_-4_--+--_+I--,/*' ...-;,-t-~-"'_o_ __ +',(:~~,OTONIC (SERIES 5.21

8r--r--+--+--4---+--~~4+-_+-~~~~-+_-~

4 ~-t-----1t-----1----+--@-+2 ~~vV A AFTER~~;~~ 0r-~--_T--_r--~-c.~~~=H--_+--_r---r--+---~

@)-~---4 I----+---+------+---l---® 71r-

----- V0CR)' ------ I ! ---8~-~-+_-~-~-~--~~~-+_-+--4---+--_+-_+~

- ----___;' SERIES 5.5

--~. / CLEAR

1

SPACI1NG: 2d

1b

. _ -12 MONOTONIC {SERIES 5.2)...J· -- --

-16 L--,--...l-I ----L1_-L--1---L1_L--,----L--L-.---L-----L_L----L-----L......J

-10 -8 -6 -4 -2 o 2 8

s[mm]

10 12 4 6


- 146 -

16

8

I~- ----- -_.rMoloTOl (slES Ll fr "

" ..............

y

1/1 --r---:"" '---'- --~

'~

~ j@ LAFTER 10 CYCLES t--t-~

12

4

C!W ry l::- s[mm] (2 v=

o

---- II ); ---, , , , ,

~j ,

................ SERIES 5.6 .....

I CLEAR SPACING 6db_

MONiTONIC (SERIES 5.3;J----_ ... '

I I I

-8

-12

-16 -10 -8 -6 -4 -2 o 2 4 6 8 10 12


T [N/mm2]

8

(I) I I I I

! .............. JMONOTONIC (SERIES 6.2)

" , , ,

~ """"

V1AFTER~~ ...... _-- ---

~ t--

=

I~

®t rz; k s[mm]

®- -r

16

12

4

o

'-

V -- .... -....

" , "

ICP) SERIES 6.5 , , , '" TRANSVERSE PRESSURE:5N/mrl , , , I

-8

-12 , , ,

" I I

MONOTONIC (SERIES 6.2)...J'", I /

I I I I '" -"' -16

-10 -8 -6 -4 -2 o 2 4 6 8 10 12


16 t----+----~t__-

I 12

_ J _

I

8 --~--, I

I i , 4

- 147 -

I

{----'>.-------f>L-----.f--i--\AFTER 10 CYCLES-

I I I

°r---r--'r-~--~--~+--+--44---+--~---+--~---+~

-4

I I~ -8 ----f

l

"'--,~ -~ -- ~: - I ~ 1 I SERIES 6.6 -~ !--12 __ - _''-,- _ __ _ _ I I __ ~ _~~ i""'NjERSE PRESSURE I

, I I ION/mm2 T--- -f--MONOTONIC LOADING~, i I / I, i I I ,

-16 (SERIES 6.3) - - -- j- --l"-'"--,~-~--/ - -----L-- -f------+-- j t--

----~-+

-6 -4 -2 0 6 8 10 12 s[mm]


12-----

8 I--------t I-I-j , I

4 t---+-----t----t---+--I

0~--+1--_+1--_+---+--_+4#~--44--~--~----~--~--~ -4

-8

-l--~-- J

-':L-J,i -12 MONOTONIC t "

LOADING ( SERIES 7.()

--I---~---SERIES 7.3 -I; · l70mm/j ~.

-I -1-- i--j _161--__ .l.--__ .l.--__ ..L-__ ..L-__ ..:r::.:... __ -L-__ ---L-__ ---L-__ -li __ ---..J'--__ '--__ L' ---..J

-10 -8 -6 -4 -2 o 2 4 6 8 10 12

s [mml

FIG. 4.65 BOND STRESS-SLIP RELATIONSHIP FOR CYCLIC LOADING, SERIES 7-3

- 148 -

RATIO 1.4

BOND DETERIORATION BOND DETERIORATION

STANDARD TEST SPECIFIC TEST

1.3

1.2 I

• I

r-- - - -- - r-- - t--- 1--- 1'--1--~--- -- - t--~

1.1 ~.

4~

4~ 4J 1.0

u ~

> ~ HALF I FULL CYCLES

'-0.9

-- - r-- - t-- - -- --- REDUCTION OF Tunl 0 I • -RELATION Tunl ITt <> I • 0.8 REDUCT. OF ENVELOPE " I • -

AVERAGE • 0.7 I I I

INVESTIGATED COMPRES. TRANSV. CONCRETE CLEAR BAR SPACING TRANSV. PRESSURE LOADING PARAMETER LOADING REINFORC. STRENGTH Idb 2db 6db 5 N/mm2 10 N/mm2 RATE

SERIES 2.6* 1.6+1.7 4.2 + 4.3 5.4 5.5 5.6 6.5 6.6 7.3

FIG. 4.66 INFLUENCE OF INVESTIGATED PARAMETERS (DIRECTION OF LOADING, CONCRETE STRENGTH, BAR SPACING, TRANSVERSE PRESSURE, RATE OF PULLOUT) ON BOND BEHAVIOR DURING CYCLIC LOADING.

FIG. 4.67

1.4

1.2

1.0

0.8

INVESTIGATED

PARAMETER

SERIES

RATIO BOND DETERIORATION STANDARD TEST BOND DETERIORATION SPECIFIC TEST

SYMBOLS:

SEE FIG. 4.66

0 .~ -- - ---.I ---, -- - --- -----

~.

U

--t----- t-- - f--- ---, -

- COMPARISON WITH SERIES 2.~ COMPARISON WITH SERIES 2.7 j 1 I I I I

BAR DIAMETER

#6 #8 #10 **6 #8 #10

3.4 3.5 3.6 3.4 3.5 3.6

INFLUENCE OF BAR DIAMETER AND DEFORMATION PATTERN ON BOND BEHAVIOR DURING CYCLIC LOADING

- 149 -

....................................................... ··············\··········.···.· ...... ·.·.~A~· .. ·.· .. ··· ·:·:·::~:2il:2:2:L:2::2:22::s;,::2ii2:2::::: ~

(0 ) o s

t t

(b) s

, '...... E ----

(c) s

FIG. 5.1 MECHANISM OF BOND RESISTANCE, MONOTONIC LOADING

- 150 -

T C

K s

••••••••••.•..••••••.•.•••••••.•.••••••.••••••.•.•••• (.~u~.·.c~~tt. ~_I~IiiIB~~llr /1

MONOTONIC LOADING

(0 )

T MONOTONIC LOADING

' ....... ..t. N ..... 0

C

'-... E M - __ K._~

•• , ;;\'E.';; I ...... :~:.~.~.:~.:~.:~.:~.:.~~ .......... .

(b)

' ....... L M ........ _--

F N 0

.&.-__ -411 G s

--- " MONOTONIC ' ..... _/ LOADING

(c)

FIG. 5.2 MECHANISM OF BOND RESISTANCE, CYCLIC LOADING

- 157 -

T(N/mm 2 )

16~--r---~--~--~--~--~--~--~--~---.---r---.-.

8

-8

(0) AFTER 5 CYCLES (b) AFTER 10 CYCLES (c) AFTER 15 CYCLES (d) AFTER 20 CYCLES

-l·-· ........ ·~MONOTONIC LOADING o .,

....... ....... ".

'. T " 0 •

MONOTONIC ~......... / LOADING~ '-

-8 -4 o s (mm)

". '. ........ .......... -. °---. __

0

-- CYCLIC TEST _.- MONOTONIC LOADING -- ANALYTICAL MODEL

4 8 12

FIG. 5.13 COMPARISON OF EXPERIMENTAL AND ANALYTICAL RESULTS FOR BOND STRESS-SLIP RELATIONSHIPS FOR TEST SERIES 2.19

12

8

4

o

-4 CYCLE CD

o 2 4 6

_._.- MONOTONIC LOADING -- CYCLIC TEST ----- ANALYTICAL MODEL

SERIES 2.13 CYCLING BETWEEN 5 =0 AND 5=1.65 mm

8 10 12 14 s [mm]


16 1: [ N/mm2]

12 -.-.- MONOTONIC LOADING -- CYCLIC TEST ----- ANALYTICAL MODEL

8

4

0

-4 -- . ....... , '-. ,

-8 "-'-.

"-"-

-12 I I

-12 -10 - 8 -6 -4

- 158 -

"- .--2 0 2 4

SERIES 1.6 VERTI CAL: db = 6,4 mm STIRRUPS: db =12,7mm

6 8 10 12 s [mm]

FIG. 5.15 COMPARISON OF EXPERIMENTAL AND ANALYTICAL RESULTS FOR BOND STRESS-SLIP RELATIONSHIPS FOR TEST SERIES 1.6 (#2 VERTICAL BARS)

16 1: [N/mm2] "-

"-"-

12 -.-.- MONOTONIC LOADING I "--- CYCLIC TEST I

'" I yMONOTONIC LOADING --- -- ANALYTICAL MODEL I

I 8 "-

.......... -.-- -'-'-' 4 --

'""""-AFTER 10 CYCLES

0

-4 '-'- -- --. "-

-6 "-'" "-

"-

1 -12 "- SERIES "- 3.4

"- db = 19mm

-16 " I I I

-12 -10 -6 -6 -4 -2 0 2 4 6 8 10 12 s [mm]

FIG. 5.16 COMPARISON OF EXPERIMENTAL AND ANALYTICAL RESULTS FOR BOND STRESS-SLIP RELATIONSHIPS FOR TEST SERIES 3.4 (#6 (19 mm) BAR)

CD Monotonic Envelope

@ Unloading Branch

@ Friction Branch @ Reloading Branch

@ Reduced Envelope

(a)

- 151 -

T

EXPERIMENTAL ANALYICAL

MONOTONIC LOADING

s

D D'

-------+-rl--+--=+-++-.'.:+-+-..L! ----__ I--r-~~ S T

-.;;:

...... """',,'-' MONOTONIC~~~ LOADING

(b)

I T fU l----L-L

U

-- EXPERIMENTAL ---- ANALYTICAL

FIG. 5.3 PROPOSED ANALYTICAL MODEL FOR LOCAL BOND STRESSSLIP RELATIONSHIP FOR CONFINED CONCRETE

- 152 -

T [N/mm 2 ] 16~--~----~--~----~--~----~--~--~

--- ANALYTICAL

8~---r----+----+--~~---+----~--~--~

4~---r----+----+----+----+----~--~--~

4 8


....." ~ ~ -:::::-'

/ ~.,.,.~ ;..

12

12 16 s [mm]

.' ----

/~ EXPERIMENTAL

--- ANALYTICAL

8

4

1/ o o 0.4 0.8 1.2

-1.6

s [mm]


FIG. 5.4 COMPARISON OF EXPERIMENTAL AND ANALYTICAL RESULTS OF BOND STRESS-SLIP RELATIONSHIP UNDER MONOTONIC LOADING

- 153 -

)" = T3 (N)/T3 (N=I) 1.0 ..-----,----~--_r_--~--___.

0.8

• d ),,=1--

2-d

0.6 ~---+-.--_+_~------"'!'Irl_--___+--______j

0.4 I-----+-----I-----+------'....-.+ ____ -----l T

0.2

o L-__ ~ __ ~ __ -L __ ~ __ ~

o 0.2 0.4 0.6 0.8 1.0

d = I-Tj(N)/T1(N=I)

FIG. 5.5 RATIO BETWEEN ULTIMATE FRICTIONAL BOND RESISTANCE OF REDUCED ENVELOPE AND OF MONOTONIC ENVELOPE AS A FUNCTION OF THE DAMAGE FACTOR, d

FIG. 5.6 DAMAGE FACTOR, d, FOR REDUCED ENVELOPE AS A FUNCTION OF THE DIMENSIONLESS ENERGY DISSIPATION E/Eo

- 154 -

r feN) / r 3 (N) 1.25 r-o=-----=----...---------....-----------,

o o FIRST SLIP REVERSAL • AFTER N = /0 CYCLES 0

1.0~--~--------~b~--------__ ----~------__ -----o~C

0.5~-----+--------+-----------.---+-------------~

• • • • • • • a • •

0 0.5 1.0 1.5 S max / S 3

FIG. 5.7 RELATIONSHIP BETWEEN FRICTIONAL BOND RESISTANCE DURING CYCLING, Tf(N), AND THE CORRESPONDING ULTIMATE FRICTIONAL BOND RESISTANCE T3(N)

d- ~ f- I- Lfo

1.0

...

08

os r-------..,c---f------------I--------- 1'" Smox _____ --I

•

04 .0 N =1 .0 N=2 ... .0. N=IO 00.0. Smax~ mm ..... Smax > I.Omm

00

-0/ ~--------~----------~ ________ ~ ________ __J

o

FIG. 5.8

LO 2.0 3.0

DAMAGE FACTOR, df' FOR FRICTIONAL BOND RESISTANCE DURING CYCLING AS A FUNCTION OF THE DIMENSIONLESS ENERGY DISSIPATION Ef/Eof

- 155 -

Lto ( I ) = Tf FOR FIRST SLIP REVERSAL

T f ( I ) = Tfo ( I ) • ( 1- d f )

Lto (2) = Tf ( I ) + K, (smax( 2) - smax( I ) /S3

T fo ( N ) / T3 ( N ) 1.0 ~--~---r-------r------'

0.5~--~L+--~+-~--------~----------~

I I I

Smax (2)

S3 I o L-____ -L ____ ~~I ________ -L __________ ~

o 0.5 1.0 1.5

FIG. 5.9 CALCULATION OF ZERO INITIAL FRICTIONAL BOND RESISTANCE FOR UNLOADING FROM LARGER VALUE OF PEAK SLIP smax THAN DURING PREVIOUS CYCLES

T (N/mm2) 16.---~---.----,----.---,~---.----,----,---,---~

8

-8

10 CYCLES

CYCLIC TEST (s ::0.44 mm) ANALYTICAL MODEL

-16 L-__ -L __ ---L ____ ....L-__ --1-____ L.....-_.....I.-__ ---l.. ____ .l..-__ -.J-__ ~

-1.0 -0.5 0 0.5 1.0 1.5 s (m m )


- 156 -

T (N/mm2) �6r-------r---~--._--._--~--,_--~--~--~--~--~~

~--MONOTONIC LOADING

AFTER I CYCLE

8

CD - CYCLIC TEST (5 = ± 1.65 mm)

-8 _.- MONOTONIC LOADING

MONOTONIC LOADING

-- ANALYTICAL MODEL

-16~--~--~--~--~--~--~--~--~--~--~--~--~~

-2 o 2 4 5 (mm)

6 8 10


T (N/mm2) 16~--~--~--~--~--~--~--~--~--~--~--~--~

8

~MONOTONIC LOADING "

" . ........ ""------.

------- ..... -.r::::.::::.rt---------J} T 3 (N)

0~----_4~~~~~~~~~~~~~~ AFTER I CYCLE

....... -8

....... .......

CYCLE

........ I ....... .

" I " .

'-'./

AFTER 10 CYCLES

5 max

- CYCLIC TEST (5 =:1:4.6 mm) _.- MONOTONIC LOADING -- ANALYTICAL MODEL

-16~--~--L---L---~--~--~--~--~--~--~--~--~~ -8 - 4 0 4 8 12

5 (mm)


- 159 -

16 1: [N/mm2]

12 -.-.- MONOTONIC LOADING -- cyeuc TEST ----- ANALYTICAL MODEL

8

---4i

AFTER 10 CYCLES

O~------------------~~~--r-------------------~

-4

--.. --. -8 --. --. '-.. .......

....... -12 .......

.......

-16 -12 -10 -8 -6 -4

I L __ ' i

j .......

I ....... ........ ./

-2 0 2 4

S ER I ES 3.5 db=25mm

6 8 10 12 s[mm]


~.~[N~/~m~m_2]~~ __ ,-__ '-__ '-__ .-__ ,, __ -r __ -' __ -. __ -' __ -' 16 r-

_. _. - MONOTONIC LOADING 12 -- CYCLIC TEST

----- ANALYTICAL MODEL

8

4

......... ................... ...;MONOTONIC LOADING

.........

O~---------t=~==~----------~

-4

-8

-12 SERIES 3.6 db =32mm

-16L-__ L-__ ~ __ ~ __ ~ __ ~ __ ~ __ ~ __ -L __ -L __ ~ __ ~ __ ~

-12 -10 - 8 -6 - 4 - 2 0 2 4 6 8 10 12 s [mm]


20 1: [N/mm2]

16 _0_.- MONOTONIC LOADING -- (YCLIC TEST ------ ANALYTICAL MODEL

12

8

4

0

-4 .......

-8 "- . ~MONOTO NI C LOADING

" "'-..

-12 " "-"-

" ...... -16 " -12 -10 -8 -6 -4

- 160 -

'-. '-

-2 o 2

......... VMONOTONIC LOADING

'" '" .......... " . ........

'-. .... "-. ............................... .......

AFTER 10 CYCLES ......

4 6

......... _---

SERIES 4.2 fe' = 54,6 Nlmm2

8 10 12 • s[mm]

FIG. 5.19 COMPARISON OF EXPERIMENTAL AND ANALYTICAL RESULTS FOR BOND STRESS-SLIP RELATIONSHIPS FOR TEST SERIES 4.2 (f~ = 54.6 N/mm2)

............... MONOTONIC LOADING .y .........

---AFTER 10 CYCLES

SERIES 5.4 CLEAR SPACING, 1 db

2 4 6 8 10 12 s [mm]

FIG. 5.20 COMPARISON OF EXPERIMENTAL AND ANALYTICAL RESULTS FOR BOND STRESS-SLIP RELATIONSHIPS FOR TEST SERIES 5.4 (CLEAR SPACING = 1 db)

20 1: [N/mm2]

16 _._. - MONOTONIC LOADING CYCLIC TEST

--- - -- ANALYTICAL MODEL

12

8

4 ~ 0

-4

....... '. -8 '- ........ "-

....... , -12 ,

"-"- ,

-16 ,

-12 -10 -8 -6 -4

- 161 -

-2 0 2

....... .'. "" MONOTONIC LOADING .-.<

.,." . .......

SERIES 6.6

'-. '-.

'-..

TRANSVERSE PRESSURE: 10N/mm 2

4 6 8 10 12 5 [mm]

FIG. 5.21 COMPARISON OF EXPERIMENTAL AND ANALYTICAL RESULTS FOR BOND STRESS-SLIP RELATIONSHIPS FOR TEST SERIES 6.6 (p = 10 N/mm2)

161: [N/mm 2]

12 -.-.- MONOTONIC LOADING --CYCLIC TEST ------ ANALYTICAL MODEL

8 ----

4 AFTER 10 CYCLES

0

-4

--- . ........ -8 '- ,

"-.......

-12 "-"- SERIES 7.3

"- / S = 170 mm Imin ........ / -16 ........

-12 -10 ··8 -6 -4 -2 0 2 4 6 8 10 12 5 [mm]

FIG. 5.22 COMPARISON OF EXPERIMENTAL AND ANALYTICAL RESULTS FOR BOND STRESS-SLIP RELATIONSHIPS FOR TEST SERIES 7.3 (5 = 170 mm/min)

T

- 162 -

REGION 1 _____ REGION 2

~~==~::J - LOADING I

r-,_ J / ........... I LOADING 2 '-'

T

(b)

--- - LOADING 2

(c )

FIG. 5.23 BOND STRESS-SLIP RELATIONSHIPS UNDER MONOTONIC LOADING FOR DIFFERENT REGIONS IN A JOINT

T

---, \

\ \

\ \

\ \ ,

\ \ ........,~~=-=--=-=--=-=-=--=(

\ \ \ , , , ,

\

- LOADING I 1 SEE FIG. 5.23 \ --- LOADING 2 \ ,

'---

0 .te 1+2db>-l f4-2d b+l

I+--5 db ------->1 I+-- 5 d b-----l

REGION 1 (Compare Fig.

CONFINED CONCRETE (Compare Fig.

REGION 2 (Compare Fig.

TRANSIENT REGION

5.23 a)

5.23 b)

5.23 c)

FIG. 5.24 PROPOSED DISTRIBUTION JF CHARACTERISTIC VALUES OF BOND RESISTANCE AND SLIP ALONG THE ANCHORAGE LENGTH

- 163 -

EARTHQUAKE ENGINEERING RESEARCH CENTER REPORTS

NOTE: Numbers in parentheses are Accession Numbers assigned by the National Technical Information Service; these are followed by a price code. Copies of the reports may be ordered from the National Technical Information Service, 5285 Port Royal Road, Springfield, Virginia, 22161. Accession ~umbers should be quoted on orders for reports (PB --- ---) and remittance must accompany each order. Reports without this information were not available at time of printing. The complete list of EERC reports (from EERC 67-1) is available upon request from the Earthquake Engineering Research Center, University of California, Berkeley, 47th Street and Hoffwan Boulevard, Richmond, California 94804.

UCB/EERC-77/0l "PLUSH - A Computer Program for Probabilistic Finite Element Analysis of Seismic Soil-Structure Interaction," by M.P. Ramo Organista, J. Lysmer and H.B. Seed - 1977 (PB81 177 651)A05

UCB/EERC-77/02 "Soil-Structure Interaction Effects at the Humbo1.dt Bay Power Plant in the Ferndale Earthquake of June 7, 1975," by J.E. Valera, H.B. Seed, C.F. Tsal and J. Lysmer - 1977 (PB 265 795)A04

UCB/EERC-77/03 "Influence of Sample Disturbance on Sand Response to Cyclic Loading," by K. Mori, H.E. Seed and C.K. Chan - 1977 (PB 267 352)A04

UCB/EERC-77/04 "Seismological Studies of Strong Motion Records," by J. Shoja-Taheri - 1977 (PB 269 655)AIO

UCB/EERC-77/05 Unassigned

UCB/EERC-77/06 "Developing Methodologies for Evaluating the Earthquake Safety of Existing Buildings," by No.1 -B. Bresler; No.2 - B. Bresler, T. Okada and D. Zisling; No. 3 - T. Okada and B. Bresler; No.4 - V.V. Bertero and B. Bresler - 1977 (PB 267 354)A08

UCB/EERC-77/07 "A Literature Survey - Transverse Strength of Masonry Nalls," by Y. Ornote, R.L. Mayes, S.W. Chen and R.N. Clough - 1977 (PB 277 933)A07

UCE/EERC-77/08 "DRAIN-TABS: A Computer Program for Inelastic Earthquake Response of Three Dimensional Buildings," by R. Guendelman-Israel and G.H. Powell - 1977 (PB 270 693)A07

UCB/EERC-77/09 "SUBWALL: A Special Purpose Finite Element Computer Program for Practical Elastic Analysis and Design of Structural ,Ialls with Substructure Option," by D. Q. Le, H. Peterson and E. P. Popov - 1977 (PB 270 567)A05

UCB/EERC-77/10 "Experimental Evaluation of Seismic Design Hethods for Broad Cylindrical Tanks," by D.P. Clough (PB 272 280)A13

UCB/EERC-77/ll "Earthquake Engineering Research at Berkeley - 1976," - 1977 (PB 273 507)A09

UCB/EERC-77/12 "Automated Design of Earthquake Resistant Hultistory Steel Building Frames," by N.D. Walker, Jr. - 1977 (PB 276 526)A09

UCB/EERC-77/13 "Concrete Confined by Rectangular Hoops Subjected to Axial Loads," by J. Vallenas, V.V. Bertero and E.P. Popov - 1977 (PB 275 165)A06

UCB/EERC-77/14 "Seismic Strain Induced in the Ground During Earthquakes," by Y. Sugimura - 1977 (PB 284 201)A04

UCB/EERC-77/15 Unassigned

UCB/EERC-77/16 "Computer Aided Optimum Design of Ductile Reinforced Concrete Moment Resi3ting Frames," by S.W. Zagajeski and V.V. Bertero - 1977 (PB 280 137)A07

UCB/EERC-77/17 "Earthquake Simulation Testing of a Stepping Frame with Energy-Absorbing Devices," by J.M. Kelly and D.F. Tsztoo - 1977 (PB 273 506)A04

UCB/EERC-77/l8 "Inelastic Behavior of Eccentrically Braced Steel Frames under Cyclic Loadings," by C.W. Roeder and E.P. Popov - 1977 (PB 275 526)A15

UCB/EERC-77/l9 "A Simplified Procedure for Estimating Earthquake- Induced Deformations in Dams and Embankments," by F. r. Makdisi and H.B. Seed - 1977 (PB 276 820)A04

UCB/EERC-77/20 "The Performance of Earth Dams during Earthquakes," by H.B. Seed, F.r. Makdisi and P. de Alba - 1977 (PB 276 821)A04

UCB/EERC-77/21 "Dynamic Plastic Analysis Using Stress Resultant Finite Element.Formulation," by P. Lukkunapvasit and J.M. Kelly - 1977 (PB 275 453)A04 .

UCB/EERC-77/22 "Preliminary Experimental Study of Seismic Uplift of a Steel Frame," by R.W. Clough and A.A. Huckelbridge 1977 (PB 278 769)A08

UCB/EERC-77/23 "Earthquake Simulator Tests of a Nine-Story Steel F,ame with Columns Allowed to Uplift," by A.A. Huckelbridge - 1977 (PB 277 944)A09

UCB/EERC-77/24 "Nonlinear Soil-Structure Interaction of Skew Highway Bridges," by M.-C. Chen and J. Penzien - 1977 (PB 276 l76)A07

UCB/EERC-77/25 "Seismic Analysis of an Offshore Structure Supported on Pile Foundations," by D.D.-N. Liou and J. Penzien 1977 (PB 283 l80)A06

UCB/EERC-77/26 "Dynamic Stiffness Matrices for Homogeneous Viscoelastic Half-Planes," by G. Dasgupta and A.K. Chopra -1977 (PB 279 654)A06

- 164 -

UCB/EERC-77/27 "A Practical Soft Story Earthquake Isolation System," by J .M. Kelly, J .~l. Eidinger and C. J. Derham _ 1977 (PB 276 8l4)A07

UCB/EERC-77/28 "Seismic Safety of Existing Buildings and Incentives for Hazard Mitigation in San Francisco: An Exploratory Study," by A.J. Meltsner - 1977 (PB 281 970)AOS

UCB/EERC-77/29 "Dynamic Analysis of Electrohydraulic Shaking Tables," by D. Rea, S. Abedi-Hayati and Y. Takahashi 1977 (PB 282 569)A04

UCB/EERC-77/30 "An Approach for Improving Seismic - Resistant Behavior of Reinforced Concrete Interior Joints," by B. Galunic, V.V. Bertero and E.P. Popov - 1977 (PB 290 870)A06

UCB/EERC-78/01 "The Development of Energy-Absorbing Devices for Aseismic Base Isolation Systems," by J.1-1. Kelly and D.F. Tsztoo - 1978 (PB 284 978)A04

UCB/EERC-78/02 "Effect of Tensile Prestrain on the Cyclic Response of Structural Steel Connections, by J.G. Bouwkamp and A. Mukhopadhyay - 1978

UCB/EERC-78/03 "Experimental Results of an Earthquake Isolation System using Natural Rubber Bearings," by J.1-1. Eidinger and J.M. Kelly - 1978 (PB 281 686)A04

UCB/EERC-78/04 "Seismic Behavior of Tall Liquid Storage Tanks," by A. Niwa - 1978 (PB 284 017) A14

UCB/EERC-78/0S "Hysteretic Behavior of Reinforced Concrete Columns Subjected to High Axial and ·Cyclic Shear Forces," by S.W. Zagajeski, V.V. Bertero and J.G. Bouwkamp - 1978 (PB 283 858)A13

UCB/EERC-78/06

UCB/EERC-78/07

UCB/EERC-78/08

UCB/EERC-78/09

UCB/EERC-78/10

UCB/EERC-78/1l

UCB/EERC-78/12

UCB/EERC-78/13

UCB/EERC-78/14

UCB/EERC-78/15

UCB/EERC-78/16

UCB/EERC-78/17

UCB/EERC-78/18

UCB/EERC-78/19

UCB/EERC-78/20

UCB/EERC-78/21

UCB/EERC-78/22

UCB/EERC-78/23

UCB/EERC-78/24

UCB/EERC-78/25

!!Three Dimensional Inelastic Frame Elements for the ANSR-I P:::"ogram,11 by A. S.iahi rD. G. Rowand G.H. Powell - 1978 (PB 295 755)A04

"Studies of Structural Response to Earthquake Ground ~1otion," by O.A. Lopez and A.K. Chopra - 1978 (PB 282 790)A05

"A Laboratory Study of the Fluid-Structure Interaction of Submerged Tanks and Caissons in Earthquakes," by R.C. Byrd - 1978 (PB 284 957)A08

Unassigned

"Seismic Performance of Nonstructural and Secondary Structural Elements," by I. Sakamoto - 1978 (PB81 154 593)A05

"Mathematical t10delling of Hysteresis Loops for Reinforced Concrete Columns," by S. Nakata, ,. Sproul and ,T. Penzien - 1978 (PB 298 274) A05

"Damageability in Existing Buildings," by T. Blejwas and B. Bresler - 1978 (PB 80 166 978)AOS

"Dynamic Behavior of a Pedestal Base Multistory Building," by R.M. Stephen, E.L. \-lilson, J.G. Bouwkamp and M. Button - 1978 (PB 286 650)A08

"Seismic Response of Bridges - Case Studies," by R.A. Imbsen, V. Nutt and J. Penzien - 1978 (PB 286 503)AIO

"A Substructure Technique for Nonlinear Static and Dynamic Analysis," by D.G. Rowand G.H. powell -1978 (PB 288 077)A10

"Seismic Risk Studies for San Francisco and for the Greater San Francisco Bay Area," by C.S. Oliveira -1978 (PB 81 120 11S)A07

"Strength of Timber Roof Connections Subjected to Cyclic Loads," by P. Gulkan, R.L. Mayes and R.W. Clough - 1978 (HUD-OOO l491)A07

"Response of K-Braced Steel Frame Models to Lateral Loads," by J.G. Bouwkamp, R.M. Stephen and E.P. Popov - 1978

.. Rational Design Methods for Light Equipment in Structures Subj ected to Ground ~1otion, II by J.L. Sackman and J.M. Kelly - 1978 (PB 292 357)A04

"Testing of a Wind Restraint for Aseismic Base Isolation," by J.M. Kelly and D.E. Chitty - 1978 (PB 292 833)A03

"APOLLO - A Computer Program for the Analysis of Pore Pressure Generation and Dissipation in Horizontal Sand Layers During Cyclic or Earthquake Loading," by P.P. Martin and H.B. Seed - 1978 (PB 292 83S)A04

"Optimal Design of an Earthquake Isolation System," by M.A. Bhatti, K.S. Pister and E. Polak - 1978 (PB 294 735)A06

"MASH - A Computer Program for the Non-Linear Analysis of Vertically Propagating Shear Waves in Horizontally Layered Deposits," by P.P. Martin and H.B. Seed - 1978 (PB 293 101)A05

"Investigation of the Elastic Characteristics of a Three Story Steel Frame Using System Identification," by I. Kaya and H.D. McNiven - 1978 (PB 296 225)A06

"Investigation of the Nonlinear Characteristics of a Three-Storv Steel Frame Using System Identification," by I. Kaya and H. D. McNiven - 1978 (PB 301 363) A05

- 165 -

UCB/EERC-78/26 "Studies of Strong Ground ~lotion in Taiwan," by Y.M. Hsiung, B.A. Bolt and J. Penzien - 1978 (PB 298 436)A06

UCB!EERC-78!27 "Cyclic Loading Tests of l1asonry Single Piers: Volume 1 - Height to 'tlidth Ratio of 2," by P.A. Hidalgo, R.L. ~ayes, H.D. McNiven and R.W. Clough - 1978 (PB 296 2111A07

UC8!EE?C-78/28 "Cyclic Loading Tests of Masonry Single Piers: Volume 2 - Height to Width Ratio of P.A. Hidalgo, R.L. :.1ayes, R.W. Clough and H.D. McNiven - 1978 (PB 296 2l2)A09

UCB/EERC-78!29 ".1>,nalytical Procedures in Soil Dynamics," by J. Lysmer - 1978 (PB 298 445)!,06

, " ., by S.-W.J. Chen,

UCB/EERC-79/01 "Hysteret~c Behavior of Lightweight Reinforced COncrete Beam-Col umn Subassernblages, " by B. Forzani, E.P. Popov and V.V. Bertero - ApL"il 1979(PB 29B 2671A06

UCB/EERC-79/02 "The Development of a Mathematical Model to Predict the Flexural Response of Reinforced Concrete Beams to Cyclic Loads, Using System Identification," by J. Stanton & H. McNiven - Jan. 1979(PB 295 8751AIO

UCB/EERC-79/03 "Linear and Nonlinear Earthquake Response of Simple Torsionally Coupled Systems," by C. L. Kan and A.K. Chopra - Feb. 1979(PB 298 262)A06

UCB/EERC-79/04 "A Mathematical t-bdel of Masonry for Predicting its Linear Seismic Response Characteristics," by Y. Mengi and H.D. McNiven - Feb. 1979(PB 298 266)A06

UCB/EERC-79/05 "Mechanical Behavior of Lightweight Concrete Confined by Different Types of Lateral Reinforcement," by M.A. Manrique, V.V. Bertero and E.P. Popov - May 1979(PB 301 114)A06

UCB/EERC-79/06 "Static Tilt Tests of a Tall Cylindrical Liquid Storage Tank," by R.W. Clough and A. Niwa - F·eb. 1979 (PB 301 167)A06

UCB/EERC-79/07 "The Design of Steel Energy Absorbing Restrainers and Their Incorporation into Nuclear Power plants for Enhanced Safety: Volume 1 - Summary Report," by P.N. Spencer, V.F. Zackay, and E.R. Parker -Feb. 1979(UCB/EERC-79/07)A09 •

UCB!EERC-79/08 "The Design of Steel Energy Absorbing Restrainers and Their Incorporation into Nuclear Power plants for Enhanced Safety: Volume 2 - The Development of Analyses for Reactor System Piping, ""Simple Systems" by M.C. Lee, J. Penzien, A.K. Chopra and K, Suzuki "COmplex Systems" by G.H. Powell, E.L. Wilson, R.W. Clough and D.G. Row - Feb. 1979(UCB/EERC-79/08)AIO

UCB/EERC-79/09 "The Design of Steel Energy Absorbing Restrainers and Their Incorporation into Nuclear Power plants for Enhanced Safety: Volume 3 - Evaluation of Corn.'1lercial Steels," by W.S. OWen, R. M.N. Pelloux, R.O. Ritchie, M. Faral, T. Ohhashi, J. Toplosky, S.J. Hartman, V.F. zackay and E.R. Parker -Feb. 1979(UCB/EERC-79/09)A04

UCBiEERC-79/10 "The Design of Steel Energy Absorbing Restrainers and Their Incorporation into Nuclear Power plants for En.'lanced Safety: Volume 4 - A Review of Energy-Absorbing Devices," by J. M. Kelly and M.S. Skinner - Feb. 1979(UCB/EERC-79/10)A04

UCB/EERC-79/1l "Conservatism In Summation Rules for Closely Spaced Modes," by J .M. Kelly and J .L. Sackman - May 1979(PB 301 328)A03

UCB/EERC-79/12 "Cyclic Loading Tests of Masonry Single Piers; Volume 3 - Height to Width Ratio of 0.5," by P.A. Hidalgo, R.L. Mayes, H.D. McNiven and R.W. Clough - May 1979(PB 301 321)A08

UCB/EERC- 79/13 "Cyclic Behavior 0 f Dense Course-Grained Materials in Relation to the Seismic Stability of Dams," by N.G. Banerjee, H.B. Seed and C.K. Chan - June 1979(PB 301 373)A13

UCB/EERC-79/14 "seismic Behavior of Reinforced Concrete Interior Beam-Column Subassernblages," by S. Viwathanatepa, E.P. Popov and V.V. Bertero - June 1979(PB 301 326)AIO

UCB/EERC-79/15 "Optimal Design of Localized Nonlinear Systems with Dual Performance Criteria Under Earthquake Excitations," by M.A. Bhatti - July 1979(PB 80 167 l09)A06

UCB/EERC-79/16 "OPTDYN - A General Purpose Optimization Program Eor Problems wi th or 'Ni thout Dynamic Constraints," by M.A. Bhatti, E. polak and K.S. Pister - July 1979(PB 80 167 091)A05

UCB/EERC-79/17 "ANSR-II, Analysis of Nonlinear Structural Response, Users Manual," by D.P. Mondkar and G.H. Powell July 1979 (PB 80 113 301) A05

UCB/EERC-79/18 "Soil Structure Interaction in Different Seismic Environments," A. Gomez-Masso, J. Lysmer, J .-C. Chen and H.B. Seed - August 1979(PB 80 101 520)A04

UCB/EERC-79/19 "AR'1A t-bdels for Earthquake Ground Motions," by M. K. Chang, J. W. Kwiatkowski, R. F. Nau, R. M. Oliver and K.S. Pister - July 1979(PB 301 166)A05

UCB/EERC-79/20 "Hysteretic Behavior of Reinforced Concrete Structural Walls," by J. ~I. Vallenas, V. V. Bertero and E.P. Popov - August 1979(PB 80 165 905)Al2

UCB/EERC-79/21 "Studies on High-Frequency Vibrations of Buildings - 1: The COlumn Effect," by J. Lubliner - Augustl979 (PB 80 158 553)A03

UCB/EERC-79/22 "Effects of Generalized Loadings on Bond Reinforcing Bars Embedded in COnfined COncrete Blocks," by S. Viwathanatepa, E.P. Popov and V.V. Bertero - August 1979(PB 81 l24 018)A14

UCB/EERC-79/23 "Shaking Table Study of Single-Story Masonry Houses, Volume 1: Test Structures 1 and 2," by P. Gulkan, R.L. Mayes and R.W. Clough - Sep~. 1979 (HUD-OOO 1763)A12

UCB/EERC-79/24 "Shaking Table Study of Single-Story Masonry Houses, Volume 2: Test Structtires 3 and 4," by P. Gulkan, R.L. Mayes and R.W. Clough - Sept. 1979 (HUD-OOO 1836)A12

UCB/EERC-79/25 "Shaking Table Study of Single-Story Masonry Houses, Volume 3: Summary, COnclusions and Recommendations," by R.W. Clough, R.L. Mayes and P. Gulkan - Sept. 1979 (HUD-OOO 1837)A06

- 166 -

UCB/EERC-79/26 "Recommendations tor a U.S.-Japan Cooperative Research Program Utilizing Large-Scale Testing Facilities ," by U.S.-Japan Planning Group - Sept. 1979(PB 301 407)A06

UCB/EERC-79/27 "Earthquake-Induced Liquefaction Near Lake Arnatitlan, Guatemala," by H.B. Seed, I. Arango, C.K. Chan, A. C~mez-Masso and R. Grant de Ascoli - Sept. 1979(NUREG-CRl34l)A03

GCa/EE"C- 79 /2 8 "Infill Panels: Their Influence on Seismic Response of Buildings," by J. 'tI. Axley and V. V. Bertero Sept. 1979(PB 80 163 37l)AlO

UCB/EERC-79/29 "3D Truss Bar Element (Type 1) for the ANSR-II Program," by D.P. Mondkar and G.H. Powell - Nov. 1979 (PB 80 169 709) A02

UCB/EERC-79/30 "20 Beam-Column Element (Type 5 - Parallel Element Theory) for the ANSR-II Program, " by D.G. Row, G.H. Powell and D.P. Mondkar - Dec. 1979(PB 80 167 224) AO 3

UCB/EERC-79/31 "3D Beam-Column Element (Type 2 - Parallel Element Theory) for the ANSR-II Program, " by A. Riahi, G.H. ?owell and D.P. Mondkar - Dec. 1979 (PB 80 167 216)A03

UCB/EERC-i9/32 "On Response of Structures to Stationary Excitation," by A. Der Kiureghian - Dec. 1979(PB 80166 929)A03

UCB/EERC-79/33 "Undisturbed Sampling and Cyclic Load Testing of Sands," by S. Singh, :J.B. Seed and C.K. Chan Dec. 1979(ADA 087 298)A07

UCB/EERC-79/34 "Interaction Sffects of Simultaneous Torsional and CompreSSional Cyclic Loading 'Of Sand," by P.~'1. Griffin and Iv.N. !-louston - Sec. 1979(;"DA :::92 352)A15

:JCB/EERC-80/Gl "Earthquake Response of Concrete ::;ravity Ja. ... ns Including Hydrodynamic and Foundation Interac'Cion Effects," by A.K. Chopra, P. Chakrabartl and S. Gupta - Jan. 1980(AD-A087297)A10

UCB/EERC-80/02 "Rocking Response of Rigid Blocks to Earthauakes," bv C.S. Yim, A.K. ChoDra and J. Penzien - Jan. 1980 (PB80 166 002) A04 .. .

CCB/EERC-80/03 "Optimum Inelastic Jesign 0 f Seismic-Resistant Reinforced Concrete Frame Str:.J.ctures," by s. ':N. Zagaj eskl. and 'I.V. Bertero - .Jan. 1980(PB80 164 635)A06

UC3/EERC-30/04 "Ef:ects of ,;mount and A.rrangement of f,-Jall-Panel Reinforcement on Hysteretic 5ehavior of Reinforced Concrete ',oJalls," by R. Iliya and V.V. Berter" - Feb. 1980(PB81 122 525)A09

UCB/EERC-80/05 "Shaking Table Research on Concrete Darn :1odels," by A. Niwa and R. w. Clough - Sept. 1980 (P381 122 368) P.06

~]CB/EERC-80/06 "The Design of Steel Energy-Absorbi:1g Restrdl.nerS and +:heir Incorporacion into ~uclear ?ower ?lants for Enhanced Safety (Vol lA): Piping '<'Iith En-ergy . .;bscrbing Eestrainers; ?arame:ter Study on Small Systems, >.

by G.H. Powell, C. Oughourlian and J. Simons - June 1980

UCB/EEP..C-80/07 '1 Inelastic Torsional Response 'of Structures Subj ected to Earthquake Gro1..lnd i1otions I II by Y. Yamazaki April 1980(PB81 122 327)A08

UCB/EERC-80/08 "Study of X-Braced Steel Frame Structures Under Earthquake Simulation," by Y. Ghanaat - April 1980 (PB8l 122 335)A11

UCB/EERC-80/09 "Hybrid :4odelling of Soil-Structure Interaction," by S. Gupta, T.II. Lin, J. Penzien and C.S. Yeh :4ay 1980(PB8l 122 3l9)A07

UC3/EERC-80/10 "General Applicability of a :<onlinear ~odel of a One Story Steel ?"ame," by S.L Sveinsson and H.D. McNiven - :'lay 1980(PB8l 124 877)A06

UCB/EERC-80/11 "A Green-Function Method for l'lave Interaction with a Submerged Body," by 'N. Kioka - April 1980 (PB81 122 269)A07

UCB/EERC-80/12 "Hydrodynamic Pressure and Added 'lass for .'.xisyrnroetric 30dies," by F. 01ilrat - ~ay 1980 (PB81 122 343) A08

UCB/EE"C-80/13 "Treatment of Non-Linear Drag Forces Acting on Offshore Platforms," by B.V. Dao and J. Penzien May 1980(PS81 153 ~13)A07

UC3/EERC-80/14 "20 Plane/Axisywmetric Solid Element (Type 3 - Elastic or Elastlc-Perfectly Plastic) for the ANSR-II Program," by D. P. Mondkar and G. H. Powell - July 1980 (PB81 122 350);1.03

GCB/EERC-80/15 "A Response Spectrum :4ethod for Random Vibrations," by A. Der Kiureghian - June 1980 (PB81122 301) .".03

UCB/EERC-80/16 "Cyclic Inelastic Buckling of Tubular Steel Braces," by 'l.A. Zayas, E.P. Popov and S.A. !1ahin June 1980(PB81 124 885)A10

CCS/EERC-80/17 "Dynamic Response of Simple Arch Dams Including Hydrodynamic Interaction," by C.S. Porter and A.K. Chopra - July 1980(PB8l 124 000)A13

UCB/EERC-SO/18 "Experimental Testing of a Friction Damped Aseismic Base Isolation System with Fail-Safe Characteristics," by J.M. Kelly, K.E. Beucke and M.S. Skinner - July 1980(PB8l 148 595)A04

UCB/EERC-80/19 "The Design of Steel Energy-Absorbing Restrainers and their Incorporation into Nuclear Power Plants for Enhanced Safety (Vol lB): Stochastic Seismic Analyses of Nuclear Power Plant Structures and Piping Systems Subjected to Multiple SUDDort Excitations," by M.e, Lee and J. Penzien - Jlli~e 1980

UCB!EERC-BO/20 "The Design of Steel Energy-.;bsorbing Restrainers and their Incorporation into Nuclear Power Plants for Enhanced Safety (Vol lC): Numerical ~1ethod for Dynamic Substr'.1cture Analysis," by J .M. Dickens and E.L. Wilson - June 1980

UCB/EERC-80/21 "The Design of Steel Energy-Absorbing Restrainers and their Incorporation into Nuclear Power Plants for Enhanced Safety (Vol 2): Develo~ment and Testing of Restraints for Nuclear Piping Systems," by J.M. Kelly and M.S. Skinner - June 1980

GCB/EERC-BO/22 "3D Solid Element (Type 4-Elastic or Elastic-Perfectly-Plastic) for t"e ANSR-II Program," by ~.P. Mondkar and G.H. Powell - July 1980(PB81 123 242)A03

UCB/EERC-80/23 "Gap-Friction Element (Type 5) for the ANSR-II Program," by D.P. Mondkar and G.H. Powell - July 1980 (PB8l 122 285)A03

- 167 -

UCB/EERC-80/24 "U-Bar Restraint Element (Type 11) for the ANSR-II Program," by C. Oughourlian and G.H. Powell July 19BO(PB81 122 293)A03

UCB/EERC-80/25 "Testing of a Natural Rubber Base Isolation System by an Explosively Simulated Earthquake," by J.M. Kelly - August 1980(PB81 201 360)A04

UCB/EERC-30/26 "Input Identification from Structural Vibrational. Response," by Y. Hu - August 19BO (PB81 152 308) AOS

UCB/EERC-BO/27 "Cyclic Inelastic Behavior of Steel Offshore Structures," by V.A. Zayas, S.A. Mahin and E.P. Popov August 19BO(PBBl 196 180)A1S

UCS/EERC-80/28 "Shaking Table Testing of a Reinforced Concrete Frame with Biaxial Response," by M.G. Oliva October 1980(PB81 154 304)AIO

UCB/EERC-80/29 "Dynamic Properties of a Twelve-Story Prefabricated Panel Building," by J .G. Bouwkamp, J.? Kollegger and R.M. Stephen - October 1980(PB82 117 128)A06

UCS/EERC-80/30 "Dynamic Properties of an Eight-Story Prefabricated Panel Building," by J.G. Bouwkamp, J.P. Kollegger and R.M. Stephen - October 1980(PB81 200 313)A05

UCB/EERC-30/31 "Predictive Dynamic Response of Panel Type Structures Under Earthquakes," by J.P. Kollegger and J.G. Bouwkamp - October 1980(PBBl 152 316)A04

UCB/EERC-80/32 "The Design of Steel Energy-Absorbing Restrainers and their Incorporation into Nuclear Power Plants for Snhanced Safety (Vol 3): Testing of~ommercial Steels in Low-Cycle Torsional Fatigue," by P. c~~~~~r, E.R. Parker, E. Jongewaard and M. Drory

Uc.:S/EERC-80/33 "The Clesign of Steel Energy-Absorbing Restrainers and their Incorporation into Nuclear POwer Plants for Enhanced Safety (Vol 4): Shaking Table Tests of Piping Systems ·,.,i th Energy-.".bsorbing Restrainers," by S.F. Stiemer and W.G. Godden - Sept. 19BO

UCB/EERC-80/34 "The Design of Steel Energy-Absorbing Restrainers and their Incorporation into Nuclear Power Plants for Enhar.ced Safety (Vol 5): Summary Report," by P. Spencer

UC3/EERC-80/35 "Experimental Testing of an Energy-Absorbing Base Isolation System," by J. :.1. Kelly, 11. S. Skinner and K.E. Beucke - October 1980(PB81 154 072)A04

UCB/EERC-80/36 "Simulating and Analyzing Artificial Non-Stationary Earthquake Ground Notions," by R. F. Nau, R.~1. Oliver and K.S. Pister - October 1980(PB81 153 397)A04

UCB/EERC-SO/37 "Earthquake Engineering at Berkeley - 1980," - Sept. 1980(PB81 205 3~4)A09

UCB/SERC-80/38 "Inelastic Seismic Analysis of Large Panel Buildings," by V. Schricker and G.H. Po'.ell - Sept. 1980 (PBBI 154 338)A13

UCB/EERC-80/39 "Dynamic Response of Embankment, Concrete-Gravity and Arch Dams Including Hydrodynamic Interaction," by J.F. Hall and A.K. Chopra - October 1980(PB81 152 324)All

UCB/EERC-80/40 "Inelastic Buckling of Steel Struts Under Cyclic Load Reversal," by R.G. Black, W.A. Wenger and E.P. Popov - October 1980(PB81 154 312)A08

UCB/EERC-80/41 "Influence of Site Characteristics on Building Damage During the October 3, 1974 Lima Earthquake," by P. Repetto, I. Arango and H.B. Seed - Sept. 1980(PB81 161 739)AOS

UCB/EERC-BO/42 "Evaluation of a Shaking Table Test Program on Response Behavior of a Two Story Reinforced Ccncrete Frame," by J.N. Blondet, R.W. Clough and S.A. Mahin

UCB/E,ERC-80/43 "~~odelling of Soil-Structure Interaction by Finite and Infinite Elements," by F. Medina -December 1980(PBBl 229 270)A04

[JCB/EERC-81/01 "Control of Seismic Response of Piping Systems and Other Structures by Sase Isolation," edited by J.M. Kelly - January 1981 (PB81 200 73S)AOS

UCB/EERC-Bl/02 "OPTNSR - An Interactive Software System for Optimal Design of Statically and Dynamically Loaded Structures with Nonlinear Response," by M.A. Bhatti, V. Ciampi and K.S. Pister - January 1981 (PB81 218 851)A09

UCB/EERC-81/03 "Analysis of Local Variations in Free Field Seismic Ground Motions," by J.-C. Chen, J. Lysmer and H.B. Seed - January 1981 (AD-A099S08)A13

UCB/EERC-31/04 "Inelastic Structural Modeling of Braced Offshore Platforms for Seismic Loading," by V.A. Zayas, P.-S.B. Shing, S.A. Mahin and E.P. Popov - January 1981(PB82 138 777)A07

UCB/EERC-81/0S "Dynamic Response of Light Equipment in Structures," by A. Der Kiureghian, J.L. Sackman and B. NourOmid - April 1981 (PB8l 218 497)A04

UCB/EERC-81/06 "Preliminary Experimental Investigation of a Broad Base Liquid Storage Tank," by J.G. Bouwkamp, J.P. Kollegger and R.M. Stephen - May 19B1(PB82 140 3B5)A03

UCB/EERC-81/07 "The Seismic Resistant Design of Reinforced Concrete Coupled Structural Walls," by A.E. Aktan and V.V. Bertero - June 1981(PB82 113 358)All

UCB/EERC-Bl/08 "The Undrained Shearing Resistance of Cohesive Soils at Large Deformations," by M.R. Pyles and !LB. Seed - August 19B1

UCB/EERC-81/09 "Experimental Behavior of a Spatial Piping System with Steel Energy Absorbers Subjected to a Simulated Differential Seismic Input," by S.F. Stiemer, W.G. Godden and J.M. Kelly - July 19B1

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UCB/EERC-B2/17 "Effects of Concrete Types and Loading Conditions on Local Bond-Slip Relationships," by A. D. Cowell, E. P. Popov and V." V. Bertero - September 1982 (PBB3 153 577)A04

UCB/EERC-82/l8 "Mechanical Behavior of Shear Wall Vertical boundary Members: An Experimental Investigation," by M. T. Wagner and V. V. Bertero - October 19B2 (PBB3 159 764)A05

UCB/EERC-B2/19 "Experimental Studies of Multi-support Seismic Loading on Piping Systems," by J. M. Kelly and A. D. Cowell - November 1982

UCB/EERC-B2/20 "Generalized Plastic Hinge Concepts for 3D Beam-Col\lIllIl Elements," by P. F.-S. Chen and G. H. Powell -November 19B2

UCB/EERC-B2/2l "ANSR-III: General Purpose Computer Program for Nonlinear Structural Analysis," by C. V. Oughourlian and G. H. Powell - November 19B2

UCB/EERC-B2/22 "Solution Strategies for Statically Loaded Nonlinear Structures," by 'J. W. Simons and G. H. Powell -November 19B2

UCB/EERC-B2/23 "Analytical Model of Deformed Bar Anchorages under Generalized Excitations," by V. Ciampi, R. Eligehausen, V. V. Bertero and E. P. Popov - November 19B2 (PBB3 169 532)A06

UCB/EERC-82/24 "A Mathematical Model for the Response of Masonry walls to DYnamic Excitations," by H. Sucuoglu, Y. Mengi and H. D. McNiven - November 19B2 (PBB3 169 Oll)A07

UCB/EERC-82/25 "Earthquake Response Considerations of Broad Liquid Storage Tanks," by F. J. Cambra - November 1982

UCB/EERC-82/26 "Computational Models for Cyclic Plasticity. Rate Dependence and Creep," by B. Mosaddad and G. H. Powell - November 1982

UCB/EERC-82/27 "Inelastic Analysis of Piping and Tubular Structures," by M. Mahasuverachai and G. H. Powell - November 1982

UCB/EERC-83/01 "The Economic Feasibility of Seismic Rehabilitation of Buildings by Base Isolation," by J. M. Kelly -January 1983

UCB/EERC-83/02 "Seismic Moment Connections for Moment-Resisting Steel Frames," by E. P. Popov - January 1983

UCB/EERC-83/03 "Design of Links and Beam-to-Colurnn Connections for Eccentrically Braced Steel Frames," by E. P. Popov and J. O. Malley - January 1983

UCB/EERC-83/04 "Numerical Techniques for the Evaluation of Soil-structure Interaction Effects in the Time Domain," by E. Bayo and E. L. Wilson - February 1983

UCB/EERC-83/05 "A Transducer for Measuring the Internal Forces in the COlumns of a Frame-Wall Reinforced COncrete Structure," by R. Sause and V. V. Bertero - May 1983

UCB/EERC-83/06 "Dynamic Interactions between Floating Ice and Offshore structures," by P. Croteau - May 1983

UCB/EERC-83/07 "Dynamic Analysis of Multiply Tuned and Arbitrarily Supported Secondary Systems," by T. 19usa and A. Der Kiureghian - June 1983

UCB/EERC-83/0B "A Laboratory study of Submerged Multi-body Systems in Earthquakes," by G. R. Ansari. - June 1983

UCB/EERC-83/09 "Effects of Transient Foundation Uplift on Earthquake Response of Structures," by C.-S. Yim and A. K. Chopra - June 1983

UCBjEERC-83/l0 "Optimal Design of Friction-Braced Frames under Seismic Loading," by M. A. Austin and K, S, Pister -June 1983

UCB/EERC-B3/11 "Shaking Table Study of Single-Story Masonry Houses: DYnamic Performance under Three Component Seismic Input and Recommendations," by G. C. Manos, R. W. Clough and R. L. Mayes - June 1983

UCB/EERC-83/12 "Experimental E=or Propagation in" pseudodynamic Testing," by P. B. Shing and S. A. Mahin - June 1983

UCB/EERC-83/13 "Experimental and Analytical Predictions of the Mechanical Characteristics of a l/5'"scale Model of a 7-story RiC Frame-Wall Building Structure," by A. E. Aktan, V. V. Bertero, A. A. Chowdhury and T. Nagashima - August 1983

UCB/EERC-83/14 "Shaking Table Tests of Large-Panel Precast Concrete Building System Assemblages," by M. G. Oliva and R. W. Clough - August 1983

UCB/EERC-B3/l5 "Sei!l11Uc Behavior of Active Beam Links in Eccentrically Braced Frames," by K. D. Hjelmstad and E. P. Popov - July 1983

UCB/EERC-83/l6 "System Identification of Structures with Joint Rotation," by J. S. Dimsdale and H. D. McNiven _ July 1983

UCB/EERC-83/17 "Construction of Inelastic Response Spectra for Single-Degree-of-Freedom Systems," by S. Mahin and ~. Lin - July 1983

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UCB/EERC-83/l8 "Interactive Computer Analysis Methods for Predicting the Inelastic Cyclic Behavior of Sections," by S. Kaba and S. Mahin - July 1983

UCB/EERC-83/l9" "Effects of Bond Deterioration on Hysteretic Behavior of Reinforced Concrete Joints," by F. c. Filippou, E." P. Popov ann V. V. Bertero - August 1983

UCB/EERC-83/20 "Analytical and Experimental Correlation of Large-Panel Precast Building System Performance," by H. G. Oliva, R. W. Clough, M. Velkov, P. Gavrilovic and J. Petrovski - November 1983

UCB/EERC-83/2l "Mechanical Characteristics of the Materials Used in the 1/5 Scale and Full Scale Models of the 7-Story Reinforced Concrete Test Structure," by V. V. Bertero, A. E. Aktan and A. A. Chowdhury - september 1983

UCB/EERC-83/22 "Hybrid Modelling of Soil-Structure Interaction in Layered Media," by T.-J. Tzong and J. Penzien October 1983

UCB/EERC-83/23 "Local Bond Stress-Slip Relationships of Deformed Bars under Generalized Excitations", by R, Eligehausen, E. P. Popov and V. V. Bertero -October 1983

report no. ucbj eerc-83j 23 earthquake engineering

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