Open Collections

UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

Bond of deformed bars in steel fiber-reinforced concrete under cyclic loading Panda, Amulya Kumar 1984

Your browser doesn't seem to have a PDF viewer, please download the PDF to view this item.

Item Metadata

Download

Media
831-UBC_1984_A1 P35.pdf [ 16.05MB ]
Metadata
JSON: 831-1.0062944.json
JSON-LD: 831-1.0062944-ld.json
RDF/XML (Pretty): 831-1.0062944-rdf.xml
RDF/JSON: 831-1.0062944-rdf.json
Turtle: 831-1.0062944-turtle.txt
N-Triples: 831-1.0062944-rdf-ntriples.txt
Original Record: 831-1.0062944-source.json
Full Text
831-1.0062944-fulltext.txt
Citation
831-1.0062944.ris

Full Text

BOND OF DEFORMED BARS IN STEEL EIBER-;;'TR,EINFORCED CONCRETE UNDER CYCLIC LOADING by AMULYA KUMAR PANDA B.Tech(Hons), IIT Kharagpur, Ind i a , 1966 M.Sc(Engg.), Sambalpur U n i v e r s i t y , I n d i a , 1975 M.A.Sc. U n i v e r s i t y Of B r i t i s h Columbia, Canada, 1980 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in THE FACULTY OF GRADUATE STUDIES Department Of C i v i l E n g i n e e r i n g We accept t h i s t h e s i s as conforming to the r e q u i r e d standard THE UNIVERSITY OF BRITISH COLUMBIA A p r i l 1984 © Amulya Kumar Panda, 1984 In p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l m e n t of the requirements f o r an advanced degree a t the U n i v e r s i t y o f B r i t i s h Columbia, I agree t h a t the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e and study. I f u r t h e r agree t h a t p e r m i s s i o n f o r e x t e n s i v e copying of t h i s t h e s i s f o r s c h o l a r l y purposes may be granted by the head o f my department or by h i s or her r e p r e s e n t a t i v e s . I t i s understood t h a t copying or p u b l i c a t i o n of t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l not be allowed without my w r i t t e n p e r m i s s i o n . Department o f The U n i v e r s i t y of B r i t i s h Columbia 1956 Main Mall Vancouver, Canada V6T 1Y3 Date Xl<k<?ti i i A b s t r a c t The i n f l u e n c e of reversed c y c l i c l o a d i n g on the anchorage bond behaviour of deformed bars i n p l a i n and s t e e l f i b e r r e i n f o r c e d c o n c r e t e was s t u d i e d . The i n t e n t was to examine the f e a s i b i l i t y of using s t e e l f i b r o u s concrete to improve anchorage bond performance i n beam-column j o i n t s i n moment r e s i s t i n g frame s t r u c t u r e s f o r seismic r e s i s t a n c e . Twenty-four specimens were t e s t e d , i n which a s i n g l e bar was sim u l t a n e o u s l y p u l l e d at one end and pushed i n at the other; the l o a d was reversed c y c l i c a l l y to simulate the l o a d i n g of a bar p a s s i n g through an i n t e r i o r beam-column j o i n t under seismic l o a d i n g . The important v a r i a b l e s were the s i z e of s t e e l f i b e r s and the p a t t e r n of l o a d i n g . The r e s u l t s i n d i c a t e that the l o a d i n g h i s t o r y has a s i g n i f i c a n t i n f l u e n c e on the bond d e t e r i o r a t i o n . A s i g n i f i c a n t r e d u c t i o n in s t i f f n e s s and r e s i s t a n c e c a p a c i t y i s observed f o r specimens under reversed c y c l i c l o a d i n g as compared to those under monotonic l o a d i n g , and t h i s was p r i m a r i l y due to a d e t e r i o r a t i o n i n the s t r e s s t r a n s f e r mechanism. The a d d i t i o n of s t e e l f i b e r s improved the anchorage bond c a p a c i t y by 20 to 26 percent and re t a r d e d the rate of bond d e t e r i o r a t i o n under reversed c y c l i c l o a d i n g . The s t e e l f i b e r s were a l s o found to make a d e f i n i t e c o n t r i b u t i o n to crack c o n t r o l and thus b e t t e r s e r v i c e a b i l i t y . From a study of the geometric c h a r a c t e r i s t i c s of the a p p l i e d s t r e s s displacement curves, a t r i l i n e a r model was proposed to p r e d i c t the response of a specimen under reversed c y c l i c l o a d i n g of i n c r e m e n t a l l y i n c r e a s i n g nature. F i n a l l y , an e l a s t i c axisymmetric f i n i t e element a n a l y s i s was c a r r i e d out as a supplement to the i n f o r m a t i o n obtained from the experimental study. I t was found u s e f u l i n f o r m u l a t i n g a theory on the bond d e t e r i o r a t i o n mechanism.. i v Table of Contents A b s t r a c t i i L i s t of Tables ix L i s t of F i g u r e s x L i s t of Notations x i v Acknowledgement x v i i i Chapter I INTRODUCTION 1 1 . 1 GENERAL 1 1.2 OBJECTIVE AND SCOPE 5 1.3 ORGANIZATION OF THE PRESENTATION: 7 1.4 REVIEW OF PAST STUDIES: 8 1.4.1 F l e x u r a l Bond S t r e s s : 9 1.4.2 Anchorage Bond 21 a. S t a t i c P u l l - o u t Test 21 b. Repeated/Cyclic Bond Behaviour: 23 Chapter II TEST PROGRAM 41 2 . 1 GENERAL 41 2.2 OBJECTIVE OF THE TEST PROGRAM 44 2.3 CONCRETE MODEL REPRESENTING AN INTERIOR BEAM-COLUMN JOINT 48 2.4 PRELIMINARY INVESTIGATIONS 50 2.5 PARAMETERS IN STUDY 51 2.6 SPECIMENS UNDER TEST 5 2 2.7 SPECIMEN IDENTIFICATION 5 2 2.8 MATERIAL PROPERTIES 57 2.8.1 Concrete 57 2.8.2 S t e e l f o r Main Reinforcement 63 2.8.3 S t e e l F i b e r s 64 2.9 INSTRUMENTATION 6 5 2.9.1 Test Bar Instrumentation ....67 2.9.2 Mounting of S t r a i n Gauges 68 2.10 FABRICATION OF TEST SPECIMENS 70 2.11 TESTING SET UP AND TESTING SYSTEM 72 2.11.1 Loading System 72 2.11.2 Data A c q u i s i t i o n and Data P r o c e s s i n g 74'-2.12 LOAD HISTORY 7 5, 2.13 TEST PROCEDURE 75 Chapter III EXPERIMENTAL RESULTS: 81 3.1 INTRODUCTION 81 3.1.1 A p p l i e d Stress-Displacement R e l a t i o n s h i p 81 3.1.2 S t r a i n D i s t r i b u t i o n Diagrams 83 3.1.3 Bond S t r e s s D i s t r i b u t i o n 83 3.1.4 Surface Cracking 86 3.1.5 I n t e r n a l C r a c k i n g 86 3.2 EXPLORATORY SPECIMENS 8 7. 3.2.1 Specimen E-2-RV/1 87 V 3.2.2 Specimen F2-MO/2 & F2-MO/3 8? 3.2.3 Specimen P-RV/4 88 3.2.4 Summary 8 9 3.3 TEST SERIES SPECIMENS 9 0 3.3.1 Monotonic Loading (MO) 9 0 a. A p p l i e d Stress-Displacement R e l a t i o n s h i p § 0 b. S t r a i n D i s t r i b u t i o n 9 3 c. Bond S t r e s s D i s t r i b u t i o n 96 d. Crac k i n g 9& 3.3.2 Repeated Loading (RP) 1 0 2 a. A p p l i e d S t r e s s Displacement R e l a t i o n s h i p ]Q2 b. C r a c k i n g ; 0 4 3.3.3 Reversed C y c l i c Loading (RV) IQ5/ a. A p p l i e d S t e e l Displacement R e l a t i o n s h i p 106 b. S t r a i n D i s t r i b u t i o n 1 0 9 c. Bond S t r e s s D i s t r i b u t i o n 111 d. Crac k i n g 113 3.3.4 Reversed C y c l i c Loading with M u l t i p l e C y c l e s (RVM) 116 a. A p p l i e d S t r e s s Displacement R e l a t i o n s h i p 117 b. C r a c k i n g 119 c. S t r a i n D i s t r i b u t i o n 119 3.4 SUMMARY OF TEST RESULTS 12A 3.4 .1 A p p l i e d S t r e s s - d i s p l a c e m e n t R e l a t i o n s h i p s 124 3.4.2 S t r a i n D i s t r i b u t i o n Diagrams 1 31 3.4.3 Cr a c k i n g and F a i l u r e Mode 1 32 Chapter IV EVALUATION AND INTERPRETATION OF TEST RESULTS ....135 4 . 1 GENERAL 135 4.2 MECHANICS OF BOND 136 4.3 EFFECT OF VARIOUS PARAMETERS ON BOND BEHAVIOUR ...138 4.3 .1 Loading Type 139 A. MONOTONIC LOADING 139 B. REPEATED LOADING 140 C. REVERSED CYCLIC LOADING 142 4.3.2 Load Amplitude 145 4.3.3 Number of C y c l e s 147 4.3.4 S t e e l F i b e r s 1 5A' a. Specimens: P-500/25/RVM/20 & F1-500/25/RVM/21 . . 1 5 4 b. Specimens: P-500/25/RV/5 & F2-500/25/RV/17 1 5 6 4.3 . 5 E f f e c t of S t e e l F i b e r S i z e (Length) 161 a. Specimens: F2-500/25/RVM/1 9 & F1 -500/2 5/.RVM/2 1 .161 b. Specimens: F2-500/25/RV/8 & F1-500/25/RV/16 151 4.3.6 E f f e c t of the Groove in the Bar 164 a. Specimens: P-500/25/RV/5 (Grooved) & P-500/25/RV/6 164 4.3.7 E f f e c t of Diameter of Bar & Embedment Length ...166 a. Specimens: F1-500/30/RVM/25 & F1-500/25/RVM/21 .166 b. Specimens: P-500/25/RVM/20 & P-375/20/RVM/23 ...166 4.3.8 E f f e c t of Bar Surface C o n d i t i o n s 169 a. Specimens: P-375/20/RVM/23 & P-375/20/RVM/24 (Greased) 169 4.3.9 E f f e c t of H e l i x around Bar 17-2 Specimens: F2-500/25/RVM/19 & F2-500/25/RVM/22 (H e l i x Provided) 172 4.4 ENERGY ABSORPTION & DISSIPATION CAPACITY 172 4.5 ENVELOPE OF MAXIMUM STRESS VERSUS DISPLACEMENT CURVES 1 7 9 4.6 YIELD PENETRATION ALONG BAR 182 4 . 7 BOND DEGRADATION RATIO: 184 4.8 CIRCUMFERENTIAL CRACK FORMATION 190. Chapter V AXIAL STIFFNESS DEGRADATION PHENOMENON: 194 5.1 INTRODUCTION ...194 5.2 OBJECTIVE OF THE MODEL 198 5.3 GEOMETRIC CHARACTERISTICS OF HYSTERESIS LOOPS 198 5.4 STIFFNESS DEGRADATION 201 5.4.1 E f f e c t of Number of C y c l e s on S t i f f n e s s Degradation: 201 5.4.2 S t i f f n e s s KCI vs Displacement at Beginning of Compression C y c l e : 204 5.4.3 Change i n S t i f f n e s s (Stage II) with Increase i n Peak S t r e s s L e v e l : 208 a. KTII versus A p p l i e d S t r e s s 208 b. KCII versus A p p l i e d S t r e s s 210 5.5 FORMULATION OF AN APPLIED STRESS DISPLACEMENT MODEL; 215 5.6 CONSTRUCTION OF THE MODEL 217 5.7 COMPARISON OF THE MODEL WITH THE EXPERIMENTAL CURVE 2 20 5.8 LIMITATIONS OF THE MODEL 2 23 5.9 STIFFNESS PRIOR TO LOSS OF STRENGTH, KTCR (STAGE II) 223 Chapter VI THEORY OF BOND DETERIORATION AND CRACKING: ....227 6.1 GENERAL 227 6.2 BOND DETERIORATION MECHANISM UNDER MONOTONIC PUSH-IN PULL-OUT LOADING: 228 6.2.1 P e r f e c t Bond 228 6.2.2 E l a s t i c Bond Behaviour (No Cracking) 228 6.2.3 Cracking i n Concrete ( A p p l i e d S t r e s s < Y i e l d S t r e s s ) 229 a. P u l l Out End 229 b. Push In End 232 6.2.4 Bond Behaviour a f t e r Y i e l d i n g of Bar 235 a. P u l l Out End 235 b. Push In End 236 6.3 BOND DETERIORATION AND CRACKING MECHANISM UNDER REVERSED CYLIC LOADING 237 6.4 ROLE OF STEEL FIBERS ON BOND DETERIORATION AND CRACKING 240 6.5 PREDICTION OF SPLITTING CRACKING 24 2 Chapter VII ANALYTICAL STUDY OF BOND BEHAVIOUR 248 7.1 INTRODUCTION 248 7.2 OBJECTIVE OF ANALYTICAL STUDY 251 7.3 FINITE ELEMENT MODEL 251 7.4 FINITE ELEMENT MESHES AND MATHEMATICAL FORMULATION 256 7.4.1 Displacement Funtion 256 7.4.2 S t r a i n 259 7.4.3 E l a s t i c i t y M a trix and S t r e s s e s 260. '7.4.4 S t i f f n e s s Matrix 261 7.4.5 Equation f o r the System 262 7.4.6 S o l u t i o n of E q u i l i b r i u m Equations 263 7.4.7 M o d i f i c a t i o n of E q u i l i b r i u m Equations at Surface of D i s c o n t i n u i t y 26A 7.4.8 S l i p Due to Separ a t i o n 265 7.4.9 Element Nodal Point S t r e s s e s 266 7.5 ANALYSIS SCHEME 267 7.6 SELECTION OF BOND STRESS-SLIP RELATIONSHIP: 268 7.7 ANALYTICAL RESULTS 271 7.7.1 Case I: No S l i p , P e r f e c t Bond 271-7.7.2 Case I I : S l i p and Separ a t i o n 273 Chapter VIII SUMMARY, CONCLUSIONS AND RECOMMENDATIONS 278 8.1 SUMMARY 278 8.2 CONCLUSIONS 280 8.3 RECOMMENDATIONS FOR FURTHER STUDY 284 BIBLIOGRAPHY 28 7 APPENDIX A - DESIGN OF TEST SPECIMENS: 296 APPENDIX B - MATHEMATICAL MODEL OF STRESS-STRAIN RELATIONSHIP OF DEFORMED BARS 303 B.1 GENERAL BEHAVIOUR OF THE STRESS-STRAIN RELATIONSHIP 303 B.1.1 MATHEMATICAL MODEL OF THE STRESS-STRAIN RELATIONSHIP: 304 B.1.2 SIMPLIFIED ANALYTICAL MODEL FOR REVERSED CYCLIC LOADING: 306 B.I.3 ANALYTICAL MODEL OF STRESS-STRAIN RELATIONSHIP OF REINFORCING BAR FOR MONOTONIC LOADING 307 B. I.4 CONCLUSIONS: 308 APPENDIX C - EXPERIMENTAL RESULTS 309 C. 1 MONOTONIC LOADING 309 C.1.1 SPECIMEN - F2-500/25/MO/10 309 C.I. 2 SPECIMEN - F1-500/25/MO/12 310 C.2 SPECIMENS SUBJECTED TO REPEATED LOADING (RP) 311 C.2.1 SPECIMEN - F2-500/25/RP/9 311 C.3 SPECIMENS SUBJECTED TO REVERSED CYCLIC LOADING (RV) 312 C.3.1 SPECIMEN - F2-500/25/RV/5 312 C.3.2 SPECIMEN P-500/25/RV/6 316 C.3.3 SPECIMEN P-500/25/RV/8 317 C.3.4 SPECIMEN - F1-500/25/RV/l6 318 C.4 SPECIMENS SUBJECTED TO REVERSED MULTIPLE CYCLIC LOADING (RVM) 320 C.4.1 SPECIMEN - F1-500/25/RVM/13 320 C.4.2 SPECIMEN - F2-500/25/RVM/14 321 C.4.3 SPECIMEN - F1-500/25/RVM/15 323 C.4.4 SPECIMEN - F1-500/25/RVM/19 324 C.4.5 SPECIMEN - F1-500/25/RVM/21 326 C.4.6 SPECIMEN - F1-500/2 5/RVM/22 327 C.4.7 SPECIMEN - F1-500/25/RVM/23 328 C.4. 8 SPECIMEN - F1-500/25/RVM/24 330 C.4.9 SPECIMEN - F1-500/25/RVM/25 331 APPENDIX D - TYPICAL CALCULATION FOR REDUCTION IN DIAMETER & BEARING 333 ix L i s t of Tables Table 2.1 Mix P r o p o r t i o n s 42 Table 2.2 Specimen P a r t i c u l a r s and Loading H i s t o r y 43 Table 2.3 Mechanical P r o p e r t i e s of R e i n f o r c i n g S t e e l 55 Table 2.4 Test Bar P a r t i c u l a r s .'. . 56 Table 2.5 Mechanical P r o p o r t i o n s of Concrete 60 Table 2.6 Types of Loading H i s t o r y 76 Table 3.1 Summary of Test R e s u l t s 125 Table 4.1 Energy Absorption C a p a c i t y 176 Table 4.2(a) Y i e l d P e n e t r a t i o n along R e i n f o r c i n g Bar 183 Table 4.2(b) Y i e l d P e n e t r a t i o n along R e i n f o r c i n g Bar 183 Table 4.3(a) Bond Degradation R a t i o 185 Table 4.3(b) Bond Degradation R a t i o 185 Table 4.4 C i r c u m f e r e n t i a l Cracking Load f o r V a r i o u s Specimens 193 Table 5.1 S t i f f n e s s P r i o r to Loss of Strength 226 Table 6.1 Load Sharing b^y Ribs of R e i n f o r c i n g Bar 233 Table B.1 R e s u l t s of Regression A n a l y s i s for 20mm Diameter Test Bar 334 Table B.2 R e s u l t s of Regression A n a l y s i s for 25mm Diameter Test Bar : 336 Table B.3 R e s u l t s of Regression A n a l y s i s f o r 30mm Diameter Test Bar 337 Table B.4 S t r a i n Hardening Modulus 338 X L i s t of F i g u r e s Chapter I 1.1(a) Goto's Instrumentation to Detect L o c a t i o n and Extent of I n t e r n a l Cracks 15 1.1(b) Deformation of Concrete around R e i n f o r c i n g . Bars 15 1.2 N i l s o n ' s Experimental Bond S t r e s s - S l i p Curves (Tanner's Tests) 19 1.3 Bond S t r e s s - S l i p Curve ( A f t e r Mirza and Houde) 19 1.4(a) Test Specimen ( A f t e r M o r i t a and Kaku) 25 1.4(b) Two T y p i c a l Test R e s u l t s 25 1 .4(c) • Bond S l i p Law 25 1.5 C y c l i c Model I d e a l i z a t i o n ( A f t e r Hassan and Hawkins) 28 1.6 I d e a l i z e d Bond S l i p Curve f o r S t e e l Bar Under G e n e r a l i z e d Loading ( A f t e r Hungspreug) 32 1.7 L o c a l Bond-Slip Law by T a s s i o s 39 1.8(a) Test Specimen 39 1.8(b) A n a l y t i c a l Model f o r L o c a l Bond S t r e s s - S l i p R e l a t i o n s h i p ( A f t e r E ligehausen et a l . ) 39 Chapter II 2.1(a) Test Frame Set Up 45 2.1(b) Test Frame Set Up 45 2.1(c) T y p i c a l Tested Specimen 46 2.1(d) Loading Arrangement (Close Up) 46 2.2 C y c l i c Bond Test Equipement 47 2.3 Beam-Column J o i n t f o r c e s and the Model 49 2.4(a) Mounting Of S t r a i n G a u g e s ( S p l i t Bar) 50 2.4(b) Mounting Of S t r a i n Gauges (Test S e r i e s ) 50 2.5 Reinforcement D e t a i l s 53 2.6(a) S t e e l F i b e r P a r t i c u l a r s 59 2.6(b) S t e e l F i b e r s 59 2.7 S t r e s s - S t r a i n R e l a t i o n s h i p of P l a i n and F i b e r R e i n f o r c e d Concrete 61 2.8 L o a d - D e f l e c t i o n R e l a t i o n s h i p of P l a i n and F i b e r R e i n f o r c e d Concrete 62 2.9 Deformation P a t t e r n f o r Rebar 63 2.10 Instrumentation f o r Measurement Of Displacement .. 66 2.11 Load C e l l Connection to Rebar 67 2.12 S t r a i n Gauge L o c a t i o n f o r V a r i o u s Specimens 69 2.13 Form Work 71 2.14 Test System 73 2.15 Loading H i s t o r y 77 x i Chapter III 3.1 T r i l i n e a r Model Repres e n t a t i o n of A p p l i e d S t r e s s Displacement Diagrams 84 3.2 H y s t e r e s i s Loop f o r F2-MO/18 .. 91 .3.3 A p p l i e d S t r e s s Displacement Diagram f o r F1-M0/12 .. 94 3.4 S t r a i n D i s t r i b u t i o n Curve f o r F2-MO/18 95 3.5 Bond S t r e s s D i s t r i b u t i o n Diagram for F2-MO/18 97 3.6 Cracking P a t t e r n of a T y p i c a l Specimen 99 3.7 Cracki n g P a t t e r n f o r F2-MO/18 101 3.8 A p p l i e d S t r e s s Displacement Curve f o r F1-RP/11 ....103 3.9 Cracking P a t t e r n f o r F1-RP/11 105 3.10 A p p l i e d S t r e s s Displacement Curve f o r F2-RV/17 ...107 3.11 S t r a i n D i s t r i b u t i o n Diagram f o r F2-RV/17 110 3.12 Bond S t r e s s D i s t r i b u t i o n Diagram f o r F2-RV/17 ....112 3.13 Cracking P a t t e r n f o r F2-RV/17 114 3.14 A p p l i e d S t r e s s Displacement Curve f o r P-RVM/20 ...118 3.15 Cracking P a t t e r n f o r P-RVM/20 120 3.16 S t r a i n D i s t r i b u t i o n Curve f o r P-RVM/20 121 3.17 Bond S t r e s s D i s t r i b u t i o n Diagram f o r P-RVM/20 ....123 Chapter IV 4.1 Deformation of Concrete and Cracking i n Concrete around Rebar 137 4.2 S t r e s s - S t r a i n R e l a t i o n s h i p of S t e e l Under C y l i c Loading 144 4.3 A p p l i e d S t r e s s Displacement Diagram f o r F1-RP/11 & F1/RV/16 146 4.4 No. of Cy c l e s vs Displacement R e l a t i o n s h i p 148 4.5 No. of C y c l e s vs Displacement to F a i l u r e 152 4.6 No. of C y c l e s vs Log (Displacement ) 153 4.7 Comparative H y s t e r e t i c Behaviour of P-RVM/20 & F1-RVM/21 155 4.8 Comparative H y s t e r e t i c Behaviour of P-RV/5 & F2-RV/17 157 4.9 S t r e s s - S t r a i n R e l a t i o n s h i p Of Concrete Confined by Transverse Reinforcement 159 4.10 Comparative H y s t e r e t i c Behaviour of F2-RVM/19 & F1-RVM/21 162 4.11 Comparative H y s t e r e t i c Behaviour of F2-RV/8 & F1-RV/16 163 4.12 Comparative H y s t e r e t i c Behaviour of P-RV/5 & P-RV/6 165 4.13 Comparative H y s t e r e t i c Behaviour of F1-RVM/21 & F1-RVM/25 167 4.14 Comparative H y s t e r e t i c Behaviour of P-RVM/20 & P-RVM/23 168 4.15 Comparative H y s t e r e t i c Behaviour of P-RVM/23 & P-RVM/24 170 4.16 Comparative H y s t e r e t i c Behaviour of F2-RVM/19 & F2-RVM/22 173 4.17 Energy Absorption C a p a c i t y Computation 175 x i i 4.18 A p p l i e d S t r e s s vs l og (Cumulat ive Energy Absorbed) Diagram 178 4.19 Envelope Of Peak S t r e s s - Di sp lacement Curves . . . . 1 8 0 4 .20(a) Bond Degrada t ion R a t i o vs No. of C y c l e s 188 4 .20(b) Bond Degrada t ion R a t i o vs No. of C y c l e s 189 4.21 S t r a i n - D i s t r i b u t i o n Diagram for P-RV/5 & F2-RV/17 191 Chapter V 5.1 Comparison of K V a l u e s for F2-RVM/19 196 5.2 Comparison of KCI & KTI Va lue s for a l l Specimens . .200 5.3 KTII vs No. of C y c l e s 202 5.4 KCII vs No. of C y c l e s 203 5 .5(a ) KCI vs Di sp lacement at B e g i n n i n g of Compress ion C y c l e 205 5 .5(b) KCI vs Di sp lacement at B e g i n n i n g of Compress ion C y c l e . . . 2 0 6 5.6 Log (KCI) vs Di sp lacement R e l a t i o n s h i p 207 5.7 A p p l i e d S t r e s s vs KTII 209 5.8 A p p l i e d S t r e s s - Di sp lacement Curve for F2-RVM/19 .211 5 .9 A p p l i e d S t r e s s vs KCII 212 5.10 C o r r e l a t i o n of E x p e r i m e n t a l Data wi th KCII ( P r e d i c t e d ) 214 5.11 C o n s t r u c t i o n of A p p l i e d S t r e s s - D i s p l a c e m e n t Model 218 5.12 C o n s t r u c t i o n of Model vs E x p e r i m e n t a l Curve 221 5.13 Comparison of Model vs E x p e r i m e n t a l Curve 222 5.14 S t i f f n e s s P r i o r to Loss of S t r e n g t h (KTCR) 224 Chapter VI 6.1 Mechanism of Bond R e s i s t a n c e 231 6.2 Diagram Showing Load Shar ing by R ibs of Rebar 234 6.3 f o r c e s Caus ing S p l i t t i n g C r a c k i n g 244 Chapter VII 7.1 I d e a l i z a t i o n of the Problem 253 7.2 F i n i t e Element Mesh 254 7.3 T y i c a l F i n i t e Element 256 7.4 R e p r e s e n t a t i o n of Nodal f o r c e s 262 7.5 V a r i o u s S t r e s s e s at I n t e r f a c e 272 7.6 S t r e s s D i s t r i b u t i o n Along R e i n f o r c i n g Bar 275 7.7 Bond S t r e s s D i s t r i b u t i o n at S t e e l Concre te I n t e r f a c e 276 APPENDIX A - 298 A.1 F o r c e s A c t i n g on the Specimen 298 A . 2 S t r e s s - S t r a i n D i s t r i b u t i o n A c r o s s Specimen 299 APPENDIX B - 339 B. 1 S t r e s s S t r a i n Behaviour of S t e e l Under Monotonic and C y c l i c Load ing 339 x i i i APPENDIX C - 340 C.1(a) A p p l i e d S t r e s s Displacement Diagram f o r P-RV/5 .340 C.1(b) A p p l i e d S t r e s s Displacement Diagram f o r P-RV/6 .340 C.2(a) I n t e r n a l Crack formation In Specimen P-RV/5 ....341 C.2(a) I n t e r n a l Crack formation In Specimen F2-RVM/14 .341 C.3 S t r a i n D i s t r i b u t i o n Diagram f o r P-RV/5 342 C.4 Bond S t r e s s D i s t r i b u t i o n Diagram f o r P-RV/5 343 C.5(a) A p p l i e d Stress-Displacement Diagram f o r F1-RV/16 344 .C.5(b) A p p l i e d Stress-Displacement Diagram f o r F1-RVM/25 344 C.6(a) A p p l i e d Stress-Displacement Diagram f o r F1-RVM/13 345 C.6(b) A p p l i e d Stress-Displacement Diagram f o r F1-RVM/15 345 C.7 S t r a i n D i s t r i b u t i o n Diagram f o r F2-RVM/19 346 C.8(a) A p p l i e d Stress-Displacement Diagram f o r F1-RVM/21 347 C.8(b) A p p l i e d Stress-Displacement Diagram f o r P-RVM/23 347 C.9 S t r a i n D i s t r i b u t i o n Diagram f o r P-RVM/23 348 C.10 S t r a i n D i s t r i b u t i o n Diagram f o r F1-RVM/25 349 Xlv -LIST OF NOTATIONS g l o b a l displacement width of beam area of r e i n f o r c i n g bar area of core of column s e c t i o n measured to the o u t s i d e of the c l o s e d hoop reinforcement gross c r o s s s e c t i o n a l area of column area of reinforcememt area of t r a n s v e r s e reinforcment s t r a i n shape f u n c t i o n e l a s t i c i t y matrix diameter of bar f o r anchorage o v e r a l l depth of beam e f f e c t i v e depth of beam nodal displacement modulus of e l a s t i c i t y of concrete modulus of e l a s t i c i t y of r e i n f o r c i n g s t e e l t a n g e n t i a l s t i f f n e s s of s t r e s s - s t r a i n diagram of s t e e l at onset of s t r a i n hardening nodal element f o r c e v e c t o r compressive s t r e s s i n concrete u l t i m a t e compressive s t r e n g t h in co n c r e t e ( c y l i n d e r ) modulus of rupture of concre t e s t r e s s i n the s t e e l y i e l d s t r e n g t h of reinforcement height of r i b of r e i n f o r c i n g bar KTI,KCI - The slope of the l i n e j o i n i n g the a p p l i e d s t r e s s -displacement curve at zero load and the maximum peak s t r e s s ( i f the a p p l i e d s t r e s s i s l e s s than the y i e l d s t r e s s ) or 414 MPa ( i f the a p p l i e d s t r e s s exceeds the y i e l d s t r e s s ) KTII,KCII - The slope of the l i n e j o i n i n g the a p p l i e d s t r e s s -displacement curve at 414 MPa and the maximum peak s t r e s s l e v e l (exceeding y i e l d ) KTL,KCL - The slope of the l i n e j o i n i n g the unloading p o r t i o n of the a p p l i e d s t r e s s - d i s p l a c e m e n t curve at maximum peak and zero load KCII(n) - a x i a l s t i f f n e s s to be computed at any c y c l e 'n' a f t e r y i e l d KCI(1) - KCI f o r 1st l o a d i n g i n compression ( a f t e r y i e l d ) KCI(n) - KCI i n the nth c y c l e e [ K]fK] - s t i f f n e s s matrix (element/global) l g - e f f e c t i v e span of beam - development le n g t h - unsupported l e n g t h of t r a n s v e r s e s t e e l N - shape f u n c t i o n 10 - perimeter of r e i n f o r c i n g bar p - p i t c h of r i b s of r e i n f o r c i n g bar P - a p p l i e d load on beam (modulus of rupture t e s t ) e c - s t r a i n i n the concrete e x - s t r a i n at any p o i n t i n the r e i n f o r c i n g bar e e £ - s t r a i n i n the r e i n f o r c i n g s t e e l e ^ - s t r a i n i n the r e i n f o r c i n g s t e e l at the onset of x v i s t r a i n hardening t?y - s t r a i n i n the r e i n f o r c i n g s t e e l at y i e l d s - l o c a l s l i p betwen r e i n f o r c i n g bar and concrete s^ - hoop spacing u - bond s t r e s s A - 1/2 the area of the t r i a n g u l a r f i n i t e element u - cumulative engery absorbed o- - s t e e l s t r e s s at i t h l o c a t i o n i o s - s t e e l s t r e s s at any p o i n t a - a p p l i e d s t r e s s a(n) - a p p l i e d s t r e s s l e v e l at which s t i f f n e s s to be computed ( i n the nth c y c l e ) o ( l ) - peak s t r e s s l e v e l i n the 1st c y c l e ( a f t e r y i e l d ) v - poisson's r a t i o P s - v o l u m e t r i c r a t i o of t r a n s v e r s e c i r c u m f e r e n t i a l v c - shear c a p a c i t y of concrete V - design shear f o r c e x v i i DEDICATED TO MY PARENTS AND TO MY WIFE, RAMA IN ACKNOWLEDGEMENT OF THEIR MANY SACRIFICES ON MY BEHALF x v i i i Acknowledgement The author expresses h i s indebtedness to P r o f e s s o r s S. Mindess and R.A. Spencer for t h e i r v a l u a b l e guidance in planning and c a r r r y i n g out the i n v e s t i g a t i o n reported i n t h i s t h e s i s . The author i s proud to have been a s s o c i a t e d with Dr, Mindess in t h i s work. A p p r e c i a t i o n i s extended to P r o f e s s o r s N.D. Nathan, R . J . Gray, L . J . Gibson fo r t h e i r advice and encouragement during p r e p a r a t i o n of the t h e s i s . Thanks are extended to the t e c h n i c a l a s s i s t a n t s of the L a b o r a t o r y ; e s p e c i a l l y , Messrs. B. M e r k l i e , D. Postgate, G. K i r s c h and W.Schmit f o r t h e i r a s s i t a n c e i n making the t e s t equipment,specimens and c a r r y i n g out the t e s t s . The author g r a t e f u l l y acknowledges the h e l p rendered by Mr. V. Subramony, Managing D i r e c t o r ; Mr. P.K. Hota, I.A.S., DGM; Mr. S. Pandey, GM (P & A); Mr. A.N. Sood, GM ( P r o j e c t s ) of Rourkela S t e e l P l a n t , SAIL (INDIA) in g r a n t i n g leave to the author to complete t h i s work. The encouragement and a s s i s t a n c e of f r i e n d s such as Mr. A. Behera, I.A.S, ADM, Rourkela, Dr. K.S. Naik and many ot h e r s are duly acknowledged. L a s t l y , thanks are due to Miss Helen Ray for t y p i n g the t h e s i s . The i n v e s t i g a t i o n r e p o r t e d in t h i s t h e s i s was sponsored by the N a t i o n a l Sciences and E n g i n e e r i n g Research C o u n c i l of Canada. 1 I. INTRODUCTION 1.1 GENERAL The bond between r e i n f o r c i n g bars and concrete has been a subj e c t of resea r c h f o r n e a r l y a century. With the advent of high s t r e n g t h deformed bars and l a r g e diameter bars, higher concrete s t r e n g t h s , and u l t i m a t e s t r e n g t h design procedures, the c u r r e n t knowledge about the nature of bond, s p l i t t i n g , and bond f a i l u r e , seems to be inadequate. Apparently, there i s no general concensus as to the r e l a t i v e magnitude of the i n f l u e n c e of v a r i a b l e s such as concrete s t r e n g t h , cover, bar s i z e anchorage l e n g t h , and so on, on the bond s t r e n g t h (85). While the i n f o r m a t i o n a v a i l a b l e on the i n d i v i d u a l behaviour of r e i n f o r c i n g s t e e l and the conc r e t e , subjected to monotonic or c y c l i c l o a d i n g , i s q u i t e advanced, t h e i r composite behaviour, or the i n t e r a c t i o n between the two m a t e r i a l s , s t i l l remains u n c l e a r . The p r e c i s e p r e d i c t i o n of the n o n l i n e a r response of r e i n f o r c e d c o n c r e t e s t r u c t u r e s subjected to s t a t i c , dynamic or c y c l i c l o a d s , using methods such as f i n i t e element a n a l y s i s , i s handicapped by a lack of knowledge about the l o c a l bond s t r e s s -s l i p r e l a t i o n s h i p governing the behaviour at the s t e e l - c o n c r e t e i n t e r f a c e . I t i s w e l l known that the beam-column j o i n t of a high r i s e r e i n f o r c e d c o n c r e t e frame s t r u c t u r e can become ' c r i t i c a l ' due to o v e r s t r e s s i n g i n that region when the s t r u c t u r e i s sub j e c t e d to severe earthquake l o a d i n g . I t i s a l s o expected that p l a s t i c hinges may form in the beams a d j o i n i n g the column faces, r e s u l t i n g i n a l t e r n a t e y i e l d i n g of the r e i n f o r c i n g s t e e l i n 2 t e n s i o n and compression i n o p p o s i t e faces of the column. Due to repeated l o a d i n g , there may be a gradual l o s s of bond, which can r e s u l t i n p e n e t r a t i o n of y i e l d i n g i n t o the anchorage zone, thus reducing the e f f e c t i v e l e n g t h a v a i l a b l e to develop the y i e l d s t r e n g t h of the r e i n f o r c i n g bars. Anchorage bond f a i l u r e i n the beam-column j o i n t s has been the cause of severe l o c a l damage and even c o l l a p s e of some s t r u c t u r e s during recent earthquakes(11). The S t r u c t u r a l Engineers A s s o c i a t i o n of C a l i f o r n i a (SEAOC) (88) recommends that s t r u c t u r e s designed f o r earthquake f o r c e s should be a b l e t o : 1. R e s i s t minor earthquakes without damage. 2. R e s i s t moderate earthquakes without s t r u c t u r a l damage, but with some n o n - s t r u c t u r a l damage. 3. R e s i s t major earthquakes without c o l l a p s e , but with some s t r u c t u r a l and n o n - s t r u c t u r a l damage. These c r i t e r i a r e q u i r e that the b u i l d i n g components be d e t a i l e d so that they have s u f f i c i e n t d u c t i l i t y under reversed c y c l i c l o a d i n g to provide the r e q u i r e d energy d i s s i p a t i o n c a p a c i t y . F u r t h e r , the degradation of s t i f f n e s s and s t r e n g t h are to be minimized or delayed to permit the s u r v i v a l of the s t r u c t u r e . Experimental i n v e s t i g a t i o n s of beam-column j o i n t s subjected to repeated, reversed c y c l i c l o a d i n g , c a r r i e d out by v a r i o u s i n v e s t i g a t o r s (15,35,36,75,97,100) i n d i c a t e s i g n i f i c a n t d e gradation i n s t r e n g t h and s t i f f n e s s . One of the dominant f a c t o r s r e s p o n s i b l e f o r t h i s degradation i s the e x c e s s i v e s l i p of the beam f l e x u r a l r e i n f o r c i n g s t e e l through the j o i n t , caused p r i m a r i l y by p r o g r e s s i v e bond d e t e r i o r a t i o n . Such s l i p may 3 cause e x c e s s i v e d e f l e c t i o n and even endanger the s t a b i l i t y of the whole frame. In order to ensure j o i n t i n t e g r i t y through s e v e r a l c y c l e s of r e v e r s e d f l e x u r e , the present American Concrete I n s t i t u t e (ACI) Code (3) and Uniform B u i l d i n g Code (96) recommend the p r o v i s i o n of s p e c i a l t r a n s v e r s e reinforcement or hoops in the j o i n t f o r confinement. The c o n g e s t i o n produced as a r e s u l t of the amount of reinforcement poses a problem i n concrete placement and a l s o i n c r e a s e s the c o s t . The e f f e c t of severe repeated, reversed c y c l i c l o a d i n g on bond and c r a c k i n g has not yet been thoroughly i n v e s t i g a t e d , though c o n s i d e r a b l e work has been done under s t a t i c l o a d i n g c o n d i t i o n s . At present, the seismic code p r o v i s i o n s on bond appear to be inadequate (11). Some of the p r o v i s i o n s are based on the r e s u l t s obtained under monotonic l o a d i n g t e s t s , which do not p r o p e r l y assess the a c t u a l behaviour during extreme earthquake l o a d i n g . The bond behaviour of r e i n f o r c e d concrete under m o n o t o n i c a l l y i n c r e a s i n g l o a d i s a l t o g e t h e r d i f f e r e n t from that observed under repeated reversed a c t i o n . ACI-ASCE 1 Committee 352 (10) has p o i n t e d out c l e a r l y the need for r e s e a r c h i n making recommendations f o r anchorage of continuous beam bars p a s s i n g through j o i n t s of d u c t i l e moment r e s i s t i n g r e i n f o r c e d c o n c r e t e frames, subjected to r e v e r s a l s in the i n e l a s t i c range o c c u r r i n g d u r i n g earthquakes. F u r t h e r , the present ACI Code (3) has no p r o v i s i o n f o r computing the development l e n g t h of the 1 American S o c i e t y of C i v i l Engineers 4 r e i n f o r c i n g s t e e l i n the i n t e r i o r beam-column j o i n t s , where seismic a c t i o n can produce t e n s i o n i n the bar on one s i d e of the column and compression on the other s i d e . I t i s s t i l l d i f f i c u l t to set f o r t h general r u l e s f o r the development lengths needed under c y c l i c l o a d i n g : i . e . , the s p e c i f i c g e o m e t r i c a l , d e t a i l i n g and l o a d i n g c o n d i t i o n s which need to be con s i d e r e d f o r t h i s purpose. In a d d i t i o n , the performance e x p e c t a t i o n s should be more e x p l i c i t l y d e f i n e d f o r each case of l o a d i n g . The experimental work on c y c l i c bond behaviour a p p a r e n t l y began around 1970 but many areas s t i l l remain unexplored. According to Popov (80), "There are e x t r a o r d i n a r i l y many unresolved problems i n the general area of bond and s l i p of r e i n f o r c i n g s t e e l under c y c l i c l o a d i n g . General r u l e s s t i l l await t h e i r development." Recently, i n a 'State of the Art Report on F i b e r R e i n f o r c e d Concrete' ACI Committee 544 (9) has suggested the need for a d d i t i o n a l r e s e a r c h on f i b e r r e i n f o r c e d concrete f o r seismic r e s i s t a n t uses to allow development of design procedures for s t r u c t u r a l elements such as d u c t i l e j o i n t s . I t appears that h a r d l y any work has been done to study the behaviour of the bond of r e i n f o r c i n g bar in s t e e l f i b r o u s concrete under c o n d i t i o n s of l o a d i n g s i m u l a t i n g seismic motions. 5 1.2 OBJECTIVE AND SCOPE Because of the many u n c e r t a i n t i e s regarding the b o n d - s l i p r e l a t i o n s h i p s mentioned above, a r e s e a r c h program was i n i t i a t e d with the f o l l o w i n g o b j e c t i v e s : 1. To study the bond behaviour of r e i n f o r c i n g bars in concrete under c y c l i c l o a d i n g , i n specimens r e p r e s e n t i n g beam-column j o i n t s . In p a r t i c u l a r , the f e a s i b i l i t y of using s t e e l f i b r o u s concrete i n beam-column j o i n t s f o r b e t t e r anchorage bond performance than that of p l a i n concrete was examined. The f o l l o w i n g major v a r i a b l e s were c o n s i d e r e d i n the study: a. Loading Type, amplitude of l o a d i n g and the number of l o a d i n g c y c l e s . b. S t e e l f i b r e s i z e ( l e n g t h ) . c. Bar diameter and embedment l e n g t h . d. bar s u r f a c e c o n d i t i o n . e. E f f e c t of s p i r a l reinforcement around the t e s t bar. 2. To study the e f f e c t of bond d e t e r i o r a t i o n on the s t i f f n e s s degradat i o n . 3. To formulate an a p p l i e d s t r e s s - d i s p l a c e m e n t model f o r reversed c y c l i c l o a d i n g . The study c a r r i e d out i n t h i s i n v e s t i g a t i o n forms an extension of the work done f o r the M.A.Sc. d i s s e r t a t i o n (74) of the author. A b r i e f summary of t h i s work w i l l be given in S e c t i o n 1.4. The experimental phase of t h i s i n v e s t i g a t i o n c o n s i s t e d of t e s t i n g c o n c r e t e ^specimens with a c e n t r a l l y p l a c e d s i n g l e 6 r e i n f o r c i n g bar (bond t e s t bar) sub j e c t e d to simultaneous push-in and p u l l - o u t l o a d i n g a p p l i e d at the p r o t r u d i n g ends, s i m u l a t i n g s e i s m i c l o a d i n g c o n d i t i o n s . The model s e l e c t e d f o r the t e s t may be con s i d e r e d as a very s i m p l i f i e d r e p r e s e n t a t i o n of a beam-column j o i n t . I t should be noted that such e f f e c t s as dowel a c t i o n (which i s g e n e r a l l y expected i n p r a c t i c e due to the presence of beam shear at the face of the column), i n t e r a c t i o n between c l o s e l y spaced bars, and c r a c k i n g of concre t e i n the j o i n t r e g ion due to the f l e x u r a l and shear s t r e s s e s , have not been modelled. In the a n a l y t i c a l p a r t of t h i s study, an e l a s t i c axisymmetric f i n i t e element a n a l y s i s has been c a r r i e d out to p r e d i c t s t r e s s e s and deformations at and around a r e i n f o r c i n g bar embedded i n a concrete c y l i n d e r subjected to push-in and p u l l - o u t l o a d i n g . F i n a l l y , a comparison has been made between the experimental r e s u l t s and those obtained from a n a l y t i c a l s t u d i e s . I t should be noted t h a t , i n view of the l a r g e number of v a r i a b l e s c o n s i d e r e d i n t h i s i n v e s t i g a t i o n , using only a small number of t e s t specimens, s t a t i s t i c a l i n f o r m a t i o n r e g a r d i n g the r e p r o d u c i b i l i t y of the r e s u l t s c o u l d not be obtained. Rather, the r e s u l t s of t h i s study are u s e f u l p r i m a r i l y f o r comparing the trends due to the d i f f e r e n t v a r i a b l e s . 7 1.3 ORGANIZATION OF THE PRESENTATION Chapter 2 d e s c r i b e s i n d e t a i l the t e s t program. I t i n c l u d e s the parameters examined i n t h i s study; the design of the t e s t specimens; the m a t e r i a l p r o p e r t i e s of the con c r e t e , the r e i n f o r c i n g bars and the s t e e l f i b e r s ; i n s t r u m e n t a t i o n ; t e s t set-up; and the t e s t procedure. Chapter 3 presents the r e s u l t s of these t e s t s under v a r i o u s c a t e g o r i e s of load h i s t o r i e s . Chapter 4 c o n t a i n s a d e t a i l e d e v a l u a t i o n and i n t e r p r e t a t i o n of the t e s t r e s u l t s d e s c r i b e d i n Chapter 3. In t h i s Chapter, the e f f e c t s of v a r i o u s parameters such as l o a d i n g type, load amplitude, number of c y c l e s , presence of s t e e l f i b e r s , bar diameters, bar s u r f a c e c o n d i t i o n , and so on, on the bond behaviour are c r i t i c a l l y examined, with s p e c i f i c r e f e r e n c e to the b e n e f i t s due to the i n c l u s i o n of s t e e l f i b e r s in c o n c r e t e . Other c h a r a c t e r i s t i c s i n c l u d i n g the envelope of a p p l i e d s t r e s s versus displacement curves, y i e l d p e n e t r a t i o n along the bar, energy a b s o r p t i o n c a p a c i t y , and bond degradation r a t i o , are examined to make a comparative a n a l y s i s between s t e e l f i b e r r e i n f o r c e d concrete and p l a i n concrete specimens, under i d e n t i c a l c o n d i t i o n s of l o a d i n g . Chapter 5 i n c l u d e s the d e s c r i p t i o n of a x i a l s t i f f n e s s d egradation phenomena and the f o r m u l a t i o n of an a p p l i e d s t r e s s versus displacement model. F i n a l l y , a comparison i s made between the r e s u l t s obtained from the experimental study and those from the model. In chapter 6, hypothesis f o r a s t r e s s t r a n s f e r mechanism 8 and a c r a c k i n g mechanism are presented. Chapter 7 i s devoted to an a n a l y t i c a l study of the bond problem, using the f i n i t e element method. F i n a l l y , a summary of t h i s i n v e s t i g a t i o n and suggestions f o r f u t u r e research are d e s c r i b e d i n Chapter 8. 1•4 REVIEW OF PAST STUDIES: B a s i c a l l y , there are two types of i n t e r a c t i o n s between the r e i n f o r c i n g bar and concrete i n v o l v i n g s l i p : (1) F l e x u r a l bond s t r e s s e s , which e x i s t on the su r f a c e of the r e i n f o r c i n g bar in a f l e x u r a l member such as a beam or a s l a b , due to the v a r i a t i o n i n bending moment. The change i n bending moment between two s e c t i o n s i n a beam of l e n g t h dx, produces a change i n bar fo r c e dT. Since the bar must be in e q u i l i b r i u m , t h i s change i n bar forc e w i l l be r e s i s t e d by an equal and opp o s i t e fo r c e produced by the bond at the contact s u r f a c e between s t e e l and con c r e t e . T h i s bond s t r e s s due to a change i n bending moment i s c a l l e d the f l e x u r a l bond s t r e s s . u.Zo dx = dT = dM z or u dM V 1 .1 z•dx > Lo Zo • z where u f l e x u r a l bond s t r e s s V shear f o r c e 10 t o t a l perimeter of the bar at the s e c t i o n z arm of the i n t e r n a l r e s i s t i n g couple 9 (2) Anchorage bond s t r e s s e s , which develop i n an anchorage zone at the ends of bars which extend i n t o a support, or at the ends of bars c u t o f f w i t h i n a span. If a bar i s r e q u i r e d to develop a given f o r c e T at some po i n t and has an anchorage l e n g t h Id beyond that point and u, the average bond s t r e s s assumed to be uniformly d i s t r i b u t e d over t h i s l e n g t h , then from e q u i l i b r i u m c o n s i d e r a t i o n s , u T 1 .2 LO l d where / u = anchorage bond s t r e s s T = a p p l i e d f o r c e 1^ = anchorage le n g t h 1.4.1 F l e x u r a l Bond S t r e s s Many types of bond t e s t s have been used by v a r i o u s r e s e a r c h e r s to study the t r a n s f e r of f o r c e s from s t e e l to co n c r e t e , and v i c e v e r s a , around a r e i n f o r c i n g bar s t r e s s e d i n te n s i o n such as o c c u r r i n g i n f l e x u r e . The two major types of f l e x u r a l bond t e s t s are t e n s i o n t e s t and beam t e s t . In the former case, a bar i s encased i n a c y l i n d e r or a prism, and i s subj e c t e d to t e n s i o n at the p r o t r u d i n g ends. Thus, the c o n d i t i o n s are s i m i l a r to the t e n s i o n zone of a beam. Under beam t e s t s , v a r i o u s types such as o r d i n a r y r e c t a n g u l a r beams subjected to four p o i n t l o a d i n g , hammer-head beams, c a n t i l e v e r beams, stub c a n t i l e v e r beams, are t e s t e d to study the f l e x u r a l bond. In a l l of these t e s t s , the concrete 10 surrounding the bar remains in t e n s i o n and re p r e s e n t s the a c t u a l c o n d i t i o n s e x i s t i n g i n a beam. In 1948, Mylrea (67) was the f i r s t to p o i n t out that the we l l known f l e x u r a l bond formula v u= (i 3 ) lo • z where terms have have a l r e a d y been d e f i n e d i n Eq.1.1 The above equation y i e l d s true v a l u e s of bond s t r e s s only when the bar i s s t r a i g h t and extends over the f u l l l e n g t h of the member, and the t e n s i l e f o r c e i n the bar v a r i e s d i r e c t l y with the o r d i n a t e of the moment curve and no cra c k s are formed. He emphasized the concept of a minimum development le n g t h rather than a u n i t bond s t r e s s . He was of the o p i n i o n that the bond c o n d i t i o n s of a bar r i b were d i f f e r e n t from those between the r i b s and, t h e r e f o r e , i t was not p o s s i b l e that a bond s l i p curve at a p a r t i c u l a r p o i n t i n the bar represented the behaviour at other p o i n t s along the embedment l e n g t h . Main (60) dev i s e d a new technique of in s t r u m e n t a t i o n f o r measurement of t e n s i l e s t r e s s e s and bond s t r e s s e s i n the r e i n f o r c i n g bar without d i s t u r b i n g the bond s t r e s s e s . His method i n v o l v e d s l i c i n g the r e i n f o r c i n g bar l o n g i t u d i n a l l y and m i l l i n g a groove in one of the halves f o r f i x i n g of s t r a i n gauges, and then tackwelding both i n t o a s i n g l e bar. He re p o r t e d marked d i f f e r e n c e s between the s t r e s s e s at cracked and uncracked s e c t i o n s of beams. L o c a l peaks i n the s t e e l s t r e s s e s were observed at cra c k s with high l o c a l bond s t r e s s e s adjacent to the crack l o c a t i o n s . He a l s o i n d i c a t e d a r e l a t i v e l y higher bond s t r e n g t h f o r deformed bars than f o r p l a i n bars. 11 Ferguson, Turpin and Thompson (29) i n v e s t i g a t e d the i n f l u e n c e of bar spacing, s t i r r u p s , and the depth of concrete cover on the bond s t r e n g t h . They conducted e c c e n t r i c p u l l - o u t t e s t s , s i m u l a t i n g the worst beam c o n d i t i o n s . S p l i t t i n g was observed to be an important f a c t o r i n bond s t r e n g t h . They concluded that the minimum bar spacing should be based on the aggregate s i z e . By i n c r e a s i n g the bar spacing, a s i g n i f i c a n t improvement i n the u l t i m a t e bond s t r e s s c o u l d be ob t a i n e d . Ferguson and Thompson (27,28) p u b l i s h e d a two p a r t paper on the development length of high s t r e n g t h r e i n f o r c i n g bars. The t e s t specimens c o n s i s t e d of simply supported beams with overhangs. The bond f a i l u r e was caused by s p l i t t i n g but d i a g o n a l t e n s i o n was o f t e n a c o m p l i c a t i n g f a c t o r . They found that bond s t r e n g t h was a f u n c t i o n of cover over the bars, an e x t r a inch of cover i n c r e a s i n g the bond r e s i s t a n c e from 0.41 to 0.69 MPa. S t i r r u p s were found to r e s i s t bond s p l i t t i n g and help in p r e v e n t i n g sudden f a i l u r e . The bond s t r e n g t h was observed to vary with the square root of the concre t e compressive s t r e n g t h ( f c ' ) r a t h e r than d i r e c t l y with f c . In a review paper, Ferguson (30) d i s c u s s e d the bond s t r e s s and the nature of bond f a i l u r e . For deformed bars, the bearing of the r i b s a g a i n s t the concrete and the shear s t r e n g t h of the co n c r e t e between the r i b s were repo r t e d to be mainly r e s p o n s i b l e f o r the bond s t r e n g t h . E s p e c i a l l y f o r a cracked beam, the l o c a l bond s t r e s s was so v a r i a b l e that the average bond s t r e s s computation over an embedment length was f e l t to be a d v i s a b l e . The bond capacity, of compression bars was found to be greater 12 than that f o r t e n s i o n bars because compression bars do not c r o s s open c r a c k s . B r e s l e r and Bertero (12,14) c a r r i e d out t e s t s on instrumented a x i a l l y r e i n f o r c e d t e n s i o n specimens i n which the r e i n f o r c i n g bars were subjected to repeated t e n s i l e loading(one d i r e c t i o n only) at both ends (maximum s t e e l s t r e s s 276-345 MPa) to study the mechanism of bond d e t e r i o r a t i o n . They were the f i r s t to re p o r t r e s u l t s on bond s t r e s s d i s t r i b u t i o n s and measurements of end s l i p . Many v a l u a b l e c o n c l u s i o n s can be drawn from t h e i r s t u d i e s . The most noted one i s the h i s t o r y -dependence of the bond d e t e r i o r a t i o n . A given maximum peak s t r e s s l e v e l i n the s t e e l reinforcement reduces the s t r e s s t r a n s f e r e f f e c t i v e n e s s at lower s t r e s s e s i n subsequent c y c l e s . The f o l l o w i n g b a s i c mechanism of bond d e t e r i o r a t i o n under repeated l o a d was proposed: The bond d e t e r i o r a t i o n i s due to f a i l u r e i n a r e l a t i v e l y t h i n l a y e r of concrete (designated the 'boundary l a y e r ' ) adjacent t o the s t e e l - c o n c r e t e i n t e r f a c e . The f a i l u r e i s due to c r a c k i n g and/or i n e l a s t i c deformation and c r u s h i n g of the concret e i n the 'boundary l a y e r ' . The s t r e s s t r a n s f e r occurs b a s i c a l l y by f r i c t i o n and wedging a c t i o n . Some s l i p a l s o takes p l a c e i n the process. Upon unloading, the re v e r s e motion i s r e s i s t e d by f r i c t i o n and a l s o by wedging a c t i o n of the r i b s . The recovery of the s t e e l e l o n g a t i o n i s prevented by the shear r e s i s t a n c e at the s t e e l - c o n c r e t e i n t e r f a c e . F u r t h e r , c r a c k s a l r e a d y formed do not c l o s e up completely on complete r e l e a s e of a p p l i e d l o a d . There remains some r e s i d u a l s l i p due to 13 i r r e c o v e r a b l e deformation and that i s r e s p o n s i b l e f o r the h y s t e r e s i s e f f e c t of the a p p l i e d l o a d - s l i p curve. With repeated c y c l e s the boundary l a y e r i s s u b j e c t e d to d i s r u p t i o n . The amount of d i s r u p t i o n i s dependent on the magnitude of the a p p l i e d t e n s i l e l o a d i n the p r e v i o u s c y c l e . The g r e a t e r the d i s r u p t i o n , the l e s s e r w i l l be the bond e f f e c t i v e n e s s at lower a p p l i e d s t r e s s l e v e l s i n the subsequent c y c l e . Lutz and Gergely (56,58) s t u d i e d the mechanics of the s l i p of deformed bars i n c o n c r e t e both e x p e r i m e n t a l l y and a n a l y t i c a l l y . They used the f i n i t e element method to analyze the s t r e s s e s and deformations i n a c o n c r e t e c y l i n d e r with a c e n t r a l l y - p l a c e d bar subjected to t e n s i o n . T h i s model represented two s i t u a t i o n s in a r e i n f o r c e d c o n c r e t e member. F i r s t , the bar, when p u l l e d from both s i d e s , represented the c o n d i t i o n s between f l e x u r a l c r a c k s . When p u l l e d from only one s i d e , i t represented the anchorage zone problem. Transverse c r a c k i n g i n c o n c r e t e , s l i p , and s e p a r a t i o n between the r e i n f o r c i n g bar and the concrete were c o n s i d e r e d . R a d i a l s e p a r a t i o n was found •'to occur i n the v i c i n i t y of a t r a n s v e r s e crack due to high r a d i a l s t r e s s e s . They r e p o r t e d that the bond of deformed bars was mainly due to bearing of the r i b s a g a i n s t the c o n c r e t e . S l i p of deformed bars c o u l d occur i n two ways: (1) the r i b s c o u l d push the concrete away from the bar or (2) the r i b s c o u l d crush the c o n c r e t e . From the t e s t of Rehm (83) and t h e i r t e s t s with a s i n g l e r i b , they concluded that f o r bars having a r i b face angle of more than about 40 degrees with the bar a x i s , the s l i p was mainly due 1 4 to c r u s h i n g of the mortar i n f r o n t of the r i b s . For r i b s having face angle l e s s than 40 degrees, s l i p was mainly due to the r e l a t i v e movement between the concre t e and the s t e e l along the face of the r i b and due to some c r u s h i n g of the mortar. A s i g n i f i c a n t study which served as a c a t a l y s t in e s t a b l i s h i n g the c u r r e n t ideas on bond f a i l u r e was due to Goto (33). By i n j e c t i n g ink i n t o the concrete specimens d u r i n g t e s t s and then c u t t i n g l o n g i t u d i n a l l y , he co u l d e s t a b l i s h the p a t t e r n of i n t e r n a l c r a c k s from which he proposed the mechanism of the i n t e r a c t i o n between the concrete and s t e e l as demonstrated in F i g s . l . 1 ( a ) & ( b ) . The formation of i n t e r n a l c r a c k s i n the concrete around the bar g i v e s the appearance of comblike c o n c r e t e , the t e e t h of which are deformed in the d i r e c t i o n of the primary crack ( F i g . 1.1(b)) by compressive f o r c e s t r a n s m i t t e d from the r i b s . The i n c l i n a t i o n of the cra c k s being about 60 degrees to the bar a x i s , the deformation of the t e e t h serves to t i g h t e n the concre t e around the r e i n f o r c i n g bar and in c r e a s e s the f r i c t i o n a l r e s i s t a n c e . The r e a c t i o n of the t i g h t e n i n g f o r c e causes c i r c u m f e r e n t i a l t e n s i o n and i s r e s p o n s i b l e f o r l o n g i t u d i n a l s p l i t t i n g in the c o n c r e t e . It i s b e l i e v e d that once the s p l i t t i n g cracks develop, i t i s an i n d i c a t i o n of the onset of bond f a i l u r e . N i l s o n (69,71) a r r i v e d at a bond s t r e s s - s l i p r e l a t i o n s h i p based p a r t l y on an hypothesis and p a r t l y on experimental data r e p o r t e d by B r e s l e r and Ber t e r o (12,14). The s t e e l displacement was c a l c u l a t e d by i n t e g r a t i n g the s t r a i n values of the s t e e l and the concrete displacements were estimated on the b a s i s of 15 . red ink brotf pip* Vinyl pip* ' — - locution of notch F I G . 1.1(a) GOTO'S INSTRUMENTATION TO DETECT INTERNAL CRACKS. F I G . 1.1(b) GOTO yS IDEALISATION OF INTERACTION BETWEEN BAR & CONCRETE( Ref. 33 ) 16 measured s l i p at the faces of the t e s t specimens. A t h i r d degree polynomial was obtained by f i t t i n g the data. The r e l a t i o n s h i p i s given by u = 3.606xl0 6s - 5.356x10 s s 2 + 1.986 x 1 0 1 2 s 3 ~ 1.4 where u = l o c a l bond s t r e s s in p s i s = l o c a l bond s l i p in inches D i f f e r e n t i a t i o n of the above equation y i e l d s du = 3.606xl0 6 - 10.712x10 s s + 5.958 x 1 0 1 2 s 2 ~ 1.5 ds which r e p r e s e n t s the s t i f f n e s s of the concrete l a y e r s t r a n s f e r r i n g the f o r c e s to the s t e e l bar. N i l s o n (68,70) subsequently a l s o d e v i s e d a method to determine the bond s t r e s s - s l i p r e l a t i o n s h i p at any p o i n t along the embedment le n g t h , based on t e s t s of 150x150x450mm prisms, each r e i n f o r c e d c e n t r a l l y by a 25mm diameter bar i n which i n t e r n a l embedded gauges were mounted to measure concrete s t r a i n s at the i n t e r f a c e of the s t e e l and the c o n c r e t e . By i n t e g r a t i n g s t r a i n s of the s t e e l and the c o n c r e t e , s l i p c o u l d be computed. A s e r i e s of bond s t r e s s - s l i p curves was obtained at 50,75,100 and 150 mm from the loaded ends as shown i n F i g . 1.2. The proposed b o n d - s l i p equation i s u = 3100(1 .43c+1 .5) x s T f c ' -- 1.6 and the maximum l i m i t i n g value of bond s t r e s s i s u < (1 .43C+1 . 5 ) / f c ' where u = l o c a l bond s t r e s s in p s i -- 1.7 c = d i s t a n c e from the loaded end in inches s = s l i p in inches f c ' = concrete s t r e n g t h i n p s i . 17 N i l s o n ' s work d e f i n i t e l y confirms the o r i g i n a l thought of Mylrea (67) that bond s t r e s s at any p o i n t i s a f u n c t i o n of s l i p at that p o i n t and the bond s l i p curve at any p a r t i c u l a r p o i n t on the bar cannot be used to represent the bond s l i p behaviour at any other p o i n t on the embedment l e n g t h . However, N i l s o n ' s equation does not co n s i d e r other important v a r i a b l e s such as, the bar diameter, c o n f i n i n g pressure and so on. F u r t h e r , the computation of s l i p was based on concrete deformation by i n t e r n a l embedded gauges. Due to p o s s i b i l i t i e s of i n t e r n a l c r a c k i n g i n the concrete surrounding the bar over the gauge l e n g t h , the r e s u l t s obtained might be d o u b t f u l . Mirza and Houde (42) c a r r i e d out t e s t s on 62 t e n s i o n specimens, each r e i n f o r c e d a x i a l l y with only one c e n t r a l bar (38 r e i n f o r c e d with 25mm d i a . bars, 12 with 20mm d i a . bars and 12 with 12mm d i a . b a r s ) . The end s l i p , e l o n g a t i o n of the embedded bars, and crack formations were recorded and analyzed. They repor t e d that the s l i p was due to gradual d e t e r i o r a t i o n of the concrete i n f r o n t of the r i b s of the r e i n f o r c i n g bar as a r e s u l t of high bearing and shearing s t r e s s e s . Since no evidence of cr u s h i n g of the concret e near the r i b s was observed in the s l i c e d specimens, they concluded that the s l i p at the i n t e r f a c e c o u l d be ex p l a i n e d e n t i r e l y by the bending of the comb-like s t r u c t u r e of the concrete surrounding the r e i n f o r c i n g bar. However, they suggested that more b a s i c r e s e a r c h was r e q u i r e d i n that area. Based on t h e i r experimental r e s u l t s , they reported that the maximum value of bond s t r e s s at the s t e e l - c o n c r e t e i n t e r f a c e occurred at a s l i p of 0.03mm. Up to the peak bond 18 value , the f o l l o w i n g l o c a l bond s t r e s s - s l i p r e l a t i o n s h i p was proposed i n the form of a p o l y n o m i a l : u = 1.95X10 6S - 2.35X10 9S 2 + 1.39X10 1 2S 3 - 0.33X10 1 5S" ~ 1.8 The bond s t r e s s - s l i p curve i s shown in F i g . 1.3. The bond s t r e s s - s l i p behaviour beyond the peak value was found to be dependent on the d i s t a n c e from the end f a c e . However, no r e l a t i o n s h i p of the bond s t r e s s - s l i p behaviour beyond the peak value was r e p o r t e d by them. The above equation a l s o does not c o n s i d e r other important v a r i a b l e s such as bar diameter, c o n f i n i n g p r e s s u r e , and so on, on the bond s t r e s s - s l i p r e l a t i o n s h i p . The experimental study c a r r i e d out by Zagajeski (105) based on the t e s t r e s u l t s of 3.6 meter simple span beams loaded with r e v e r s i n g t h i r d p o i n t loads, r e s u l t e d in some s i g n i f i c a n t c o n c l u s i o n s . His f i n d i n g s c o r r o b o r a t e d the e a r l i e r f i n d i n g s of B r e s l e r and B e r t e r o (12,14) that the bond e f f e c t i v e n e s s was s e n s i t i v e to previous l o a d h i s t o r y . He r e p o r t e d t h a t , due to c y c l i n g , the concrete boundary l a y e r surrounding the bar experienced s o f t e n i n g r e s u l t i n g i n d e t e r i o r a t i o n of bond e f f e c t i v e n e s s and degradation i n the s t i f f n e s s . The s t i f f n e s s was measured by l o a d - d e f l e c t i o n or moment-curvature r e l a t i o n s h i p s . Bauschinger e f f e c t i n the r e i n f o r c i n g s t e e l and c r a c k i n g i n the concrete were found l a r g e l y r e s p o n s i b l e f o r the s t i f f n e s s d e g r a d a t i o n . 19 0 0 0 0 1.0 2.0 WW ( 0.001 in) F1fl.%2-*'l*on'« experimental bond stress-slip curves (Tanner's tests) (Ref. 70 ) 0.8 -0 2 4 6 8 10 12 14 16 18 Slip i iff 4 (in ) F1g.1j3 -Unit bond stress versus unit slip (After Mirza I Ho jde,Ref.63 ) 20 Summary A b r i e f summary of notable f i n d i n g s i n c l u d i n g some comments i s d e s c r i b e d as f o l l o w s : 1. In the c l a s s i c a l beam theory i t was assumed that the bond s t r e s s was a f u n c t i o n of s hearing f o r c e a l o n e . T h i s was i n c o n t r a d i c t i o n to the experimental evidence. 2. The bond s t r e s s - s l i p r e l a t i o n s h i p s p u t f o r t h by many i n v e s t i g a t o r s r e l a t e average bond s t r e s s e s and s l i p at the end of t e s t specimens. Some i n d i r e c t methods were adopted to e s t a b l i s h a r e l a t i o n s h i p that c o u l d be a p p l i e d to l o c a l c o n d i t i o n s but t h e i r accuracy i s q u e s t i o n a b l e . 3. The mechanism of bond d e t e r i o r a t i o n was p r i m a r i l y due to c r a c k i n g , i n e l a s t i c deformation and f a i l u r e i n a r e l a t i v e l y t h i n l a y e r of concrete adjacent to the s t e e l concrete i n t e r f a c e . The amount of bond d e t e r i o r a t i o n was i n f l u e n c e d by the l o a d h i s t o r y . 4. For deformed bars, s p l i t t i n g c r a c k i n g was an i n d i c a t i o n of the onset of bond f a i l u r e . 5. The bond e f f e c t i v e n e s s was found to be s e n s i t i v e to previous l o a d h i s t o r y . The magnitude and sense of the p r evious s t r e s s l e v e l were found to be very important. 6. I r r e s p e c t i v e of q u e s t i o n a b l e methods adopted to e s t a b l i s h b o n d - s l i p r e l a t i o n s h i p , i t was c o n v i n c i n g l y shown that the b o n d - s l i p r e l a t i o n s h i p was n o n l i n e a r . 21 1.4.2 Anchorage Bond a. S t a t i c P u l l - o u t Test The anchorage of r e i n f o r c i n g s t e e l i n concrete i s fundamental to the whole idea of r e i n f o r c e d c o n c r e t e . That i s why a vast l i t e r a t u r e on anchorage bond can be found d e a l i n g with p u l l - o u t t e s t s of r e i n f o r c i n g bars embedded in c o n c r e t e . O r i g i n a l l y , the purpose was to determine the r e q u i r e d l e n g t h of embedment necessary f o r f u l l development of the c a p a c i t y of the r e i n f o r c i n g bar. Important c o n t r i b u t i o n s based on p u l l - o u t t e s t s are due to Abrams (4), R i c h a r t and Jensen (86), Menzel (62), G i l k e y , Chamberlin and Beal (31), Watstein and Seese (103), C l a r k (20), Muhlenbruch (66), Mylrea (67), Main (60), Konyi (51), Mathey and Watstein (61), Ferguson and Thompson (27,28), Lutz and Gergely (56), N i l s o n (69,70,71), and many ot h e r s . A b r i e f summary of the r e s u l t s of these p u l l - o u t t e s t s i n c l u d i n g some comments on the t e s t method i s presented here: 1. A reasonable measure of the anchorage length of a bar embedded in concrete can be obtained from the p u l l - o u t t e s t . 2. The p u l l - o u t t e s t emphasizes the need f o r a p a r t i c u l a r l e n g t h of bar (anchorage length) from the p o i n t of maximum t e n s i l e s t r e s s to a v o i d p u l l - o u t . 3. The t e s t p r o v i d e s an approximate i n d i c a t i o n of what happens adjacent to any crack i n the concrete, where a bar always c a r r i e s more t e n s i o n than e x i s t s in nearby s e c t i o n s . 4. The s l i p of the loaded end i s o f t e n c o n s i d e r e d to be h a l f 22 the crack width which would r e s u l t by p u l l i n g the r e i n f o r c i n g bar at both ends. 5. The drawback of the p u l l - o u t t e s t as a standard t e s t i s that the compressive s t r e s s i n the concrete complicates the s t r e s s c o n d i t i o n s and i n h i b i t s t e n s i o n c r a c k i n g i n the co n c r e t e . Swamy and Al - N o o r i (94) were the f i r s t to report improved performance i n anchorage bond of deformed bars embedded i n s t e e l f i b e r r e i n f o r c e d c o n c r e t e . T h e i r experimental work c o n s i s t e d of p u l l out t e s t s on specimens with a bar embedded e i t h e r v e r t i c a l l y or h o r i z o n t a l l y . The v e r t i c a l l y c a s t specimens were 150mm i n diameter, while the h o r i z o n t a l l y c a s t specimens were 150mm x 150mm i n c r o s s s e c t i o n . The embedment lengths of specimens were 100mm for 10mm and 12mm diameter bars, and 150mm for 16mm, 20mm and 25mm diameter bars. Round s t r a i g h t s t e e l f i b e r s of 0.40x25mm & 0.5mmx50mm and volume c o n c e n t r a t i o n of 7 percent and 3.5 percent, r e s p e c t i v e l y , were used. Based on the bond s t r e s s - s l i p r e l a t i o n s h i p s , they r e p o r t e d that the anchorage bond s t r e n g t h of f i b e r r e i n f o r c e d c o n c r e t e was 40 percent higher than that f o r p l a i n c o n c r e t e . F u r t h e r , the mode of f a i l u r e was found to be d i f f e r e n t in the two cases. The p l a i n concrete specimens showed gre a t e r c r a c k i n g and wider cracks than the f i b e r r e i n f o r c e d concrete ones. The f a i l u r e i n the l a t t e r case was observed to be more g r a d u a l . 23 b. Repeated/Cyclic Bond Behaviour The s t u d i e s of repeated or c y c l i c bond t e s t s are r e l a t i v e l y more recent ( a f t e r 1970). Takeda, Sozen and N i l s o n (82) are amongst the f i r s t to i n v e s t i g a t e the response of r e i n f o r c e d c oncrete to simulated earthquakes. They observed that the s t i f f n e s s and the energy absorbing c a p a c i t y of the r e i n f o r c e d c o n c r e t e t e s t specimens changed c o n s i d e r a b l y throughout the d u r a t i o n of the simulated earthquakes. In a s e r i e s of papers by Brown and J i r s a (17), I s m a i l and J i r s a (45,46), and Gosain and J i r s a (32), the r e s u l t s of a s e r i e s of r e i n f o r c e d c o n c r e t e c a n t i l e v e r beams su b j e c t e d to r e v e r s a l s of ov e r l o a d to determine the e f f e c t of load h i s t o r y on the s t r e n g t h , d u c t i l i t y , and mode of f a i l u r e of the beams, were presented. The specimens. represented the c o n d i t i o n s t y p i c a l of an e x t e r i o r j o i n t . The f i r s t paper (17) r e p o r t s that the deformation of s t e e l i n the anchorage zone c o n t r i b u t e d s i g n i f i c a n t l y to the t o t a l deformation and the energy a b s o r p t i o n c a p a c i t y of the specimens. The response of the t e s t specimens under l o a d r e v e r s a l was found to be n o n - l i n e a r due to the Bauschinger e f f e c t i n the s t e e l , shear deformations, c l o s u r e of the r e s i d u a l crack opening and the n o n - l i n e a r l o a d - s l i p behaviour of the anchored l o n g i t u d i n a l r einforcement. The second paper (45) repor t e d that 30 to 45 percent of the t o t a l end d e f l e c t i o n of the beam was due to the e l o n g a t i o n of the bars in the anchorage zone. They(45) recommended f u r t h e r r e s e a r c h on the e f f e c t of load h i s t o r y and beam geometry on the response of anchored bars to e y r i e s of l a r g e o v e r l o a d s . Some of t h e i r 24 a d d i t i o n a l f i n d i n g s were: 1. For l o a d - c o n t r o l l e d l o a d i n g below the l e v e l which produces s t e e l y i e l d , an i n c r e a s e i n the peak a p p l i e d load causes an in c r e a s e i n end s l i p at a lower lo a d l e v e l in the subsequent c y c l e . 2. For d e f l e c t i o n c o n t r o l l e d l o a d i n g with l a r g e amplitude and fo r f u l l y reversed c y c l e s , y i e l d p e n e t r a t i o n along the main r e i n f o r c i n g bar i n t o the anchorage zone i n c r e a s e s r a p i d l y with the number of c y c l e s , the bar diameter and the amplitude of imposed d e f l e c t i o n s a f t e r y i e l d i n g . 3. With l a r g e bars, severe c y c l i c l o a d i n g may produce a b r i t t l e j o i n t f a i l u r e i n r e l a t i v e l y few c y c l e s of l o a d i n g . 4. S l i p of anchored bars has a s i g n i f i c a n t i n f l u e n c e on the response of the member and cannot be ignored i n determining the s t i f f n e s s and energy absorbing c a p a c i t y of the member. In 1973, M o r i t a and Kaku (64) r e p o r t e d on the e f f e c t of the load h i s t o r y on the l o c a l bond s t r e s s - s l i p r e l a t i o n s h i p from push - i n • p u l l - o u t t e s t s of specimens having r e i n f o r c i n g s t e e l ( t e s t bar) bonded to concret e over a short l e n g t h . The specimens c o n s i s t e d of f i v e r e i n f o r c i n g bars embedded i n a short r e i n f o r c e d concrete beam at r i g h t angles to i t s a x i s as shown i n F i g . 1.4(a). The bond zone was l o c a t e d at mid height of the beam to a v o i d the i n f l u e n c e of the f l e x u r a l s t r e s s i n the beam. Deformed bars of 19 and 25mm diameter were used i n the t e s t s and bond le n g t h s of 48mm f o r the 19mm diameter bars, and of 66mm for the 25mm diameter bars were pr o v i d e d . They concluded that the d e t e r i o r a t i o n of 'l o c a l bond depends on the magnitude of the T 25 -1045 -Cover-Reinf. Bar(19mm dia.) Plan View Stirrup (6 mm dia) S i d ( ? v j p w Cross Section Bond Length slit ^»-Side View N.B All Dimensions In mm Fig.1.4(a)TEST SPECIMEN F i g . U ( b ) bond s t r e s s (kg/cm*) • « u M Bond 1 * 1 / S ' / / / j / / 9 / / * / / r ~ I r i / / / / »lip F i g . 14(c) B a s i c b o n d - s l i p l a v by M o r i t a and Kaku(R ef. 64 ) 26 p r e v i o u s maximum l o c a l s l i p ; the l a r g e r the p r e v i o u s s l i p the g r e a t e r the r e d u c t i o n i n bond s t r e s s at lower s t r e s s l e v e l s . T y p i c a l t e s t r e s u l t s are shown in F i g . 1.4(b). They a l s o proposed a model f o r a l o c a l bond s t r e s s - s l i p law, based on which the a p p l i e d load versus deformation c h a r a c t e r i s t i c s of r e i n f o r c e d concrete members can be p r e d i c t e d . Two t y p i c a l t e s t r e s u l t s and the b a s i c b o n d - s l i p law f o r reversed c y c l i c l o a d i n g i s s c h e m a t i c a l l y shown in F i g . 1.4(b) & ( c ) . T h e i r work i s a good beginning for a r a t i o n a l e v a l u a t i o n of bond behaviour under c y c l i c l o a d i n g . However, the a p p l i c a t i o n of a s i n g l e b o n d - s l i p law f o r every poin t along an anchorage le n g t h seems to be a handicap to the model. The work of Hassan and Hawkins (40) on c y c l i c p u l l - o u t t e s t s i s q u i t e important. They re p o r t e d r e s u l t s of t e s t s on 13 specimens, s i m u l a t i n g the c o n d i t i o n s e x i s t i n g i n an e x t e r i o r beam-column j o i n t of a r e i n f o r c e d concrete s t r u c t u r e . A l l specimens were 150x450x600mm, with #10 Grade 40 bars. The t e s t r e s u l t s i n d i c a t e that high i n t e n s i t y reversed c y c l i c load produces p r o g r e s s i v e bond d e t e r i o r a t i o n , which in turn causes s i g n i f i c a n t degradation i n s t i f f n e s s and load c a r r y i n g c a p a c i t y of the beam-column j o i n t s . The s u r f a c e geometry of the r e i n f o r c i n g bar i s found to play a s i g n i f i c a n t r o l e i n the r a t e of bond d e t e r i o r a t i o n on c y c l i n g . The r a t e of d e t e r i o r a t i o n i n c r e a s e s markedly with i n c r e a s i n g r a t i o of lug spacing to nominal diameter for the bar. A mathematical model i s developed based on the t e s t data, fo r p r e d i c t i n g the a p p l i e d f o r c e versus displacement r e l a t i o n s h i p . The model for reversed c y c l i c 27 l o a d i n g i s b r i e f l y d e s c r i b e d below: For a bar subjected t o high i n t e n s i t y r e versed c y c l i c l o a d i n g , the bond s t r e s s d i s t r i b u t i o n at the i n t e r f a c e and the c o n s t i t u t i v e r e l a t i o n s h i p of the r e i n f o r c i n g s t e e l assumed for the model are shown i n F i g . 1.5. The t o t a l depth of the specimens was d i v i d e d i n t o three r e g i o n s : 1. E l a s t i c Region I -In t h i s region no c r a c k i n g in the concrete around the bar i s assumed. S t r e s s - s t r a i n behaviour of the r e i n f o r c i n g bar i s assumed to be l i n e a r e l a s t i c . 2. Region II -I n t e r n a l cracks are assumed to have developed. Bond s t r e s s has a constant value of Umax ( i . e . maximum bond s t r e s s ) ; s t e e l s t r e s s corresponds to i t s s t r e s s - s t r a i n r e l a t i o n s h i p f o r v i r g i n l o a d i n g . 3. Region III -Crackin g in both d i r e c t i o n s i s assumed. The s t e e l s t r e s s corresponds to the s t r e s s - s t r a i n r e l a t i o n s h i p under reversed c y c l i c l o a d i n g . The bond degeneration i s assumed to vary a c c o r d i n g to a power law from the value of Umax at the j u n c t i o n with region II to zero at the loaded end of the bar. A summary of the main p o i n t s of the model i s shown in F i g . 1.5. Despite the p h y s i c a l inadequacies of the model (such as the e m p i r i c a l e x p r e s s i o n f o r f u l l y cracked l e n g t h , or the equilibrium-dependent Umax value r a t h e r than a slip-dependent v a l u e , and using j u s t one b o n d - s l i p law f o r every p o i n t along 28 i i crk 'cr(k-l) crk (a) SPECIMEN REGION in IV (b) THE MODEL crk 'cr(k-l)-lcrk / REGION I / REGION II 1 I J REGION III & IV (c) CONSTITUTIVE RELATIONS FIG. 1.5 CYCLIC MODEL IDEALIZATION, 29 the bar, which i s a b a s i c handicap, l i m i t i n g the v e r s a t i l i t y of the t e c h n i q u e ) , i t has s e v e r a l p r a c t i c a l p o s s i b i l i t i e s for computational p r e d i c t i o n s of h i g h l y complicated c y c l i c l o a d i n g , for which simple models are not a v a i l a b l e . Work s i m i l a r to that of Hassan and Hawkin (40) was c a r r i e d out by Viwathanatepa, Popov and Bertero (100) on c y c l i c bond behaviour. The work was an outgrowth of the o b s e r v a t i o n of s e r i o u s bond degradation at the i n t e r i o r beam-column j o i n t s d u r i n g the c y c l i c l o a d i n g of beam-column subassemblages. The experimental set up was designed to simulate the c o n d i t i o n s of an i n t e r i o r beam-column j o i n t with a s i n g l e bar sub j e c t e d to simultaneous push-in p u l l - o u t l o a d i n g , s i m u l a t i n g seismic motions. Some of the f i n d i n g s of t h e i r work a r e : 1. Before reaching y i e l d of the s t e e l , a cone of unconfined c o n c r e t e p u l l s away from the c o n f i n e d core at the p u l l - o u t end; the corresponding l e n g t h i s no longer a v a i l a b l e for t r a n s m i t t i n g the bond s t r e s s . 2. For push-in p u l l - o u t l o a d i n g , almost symmetric or antisymmetric p a t t e r n s of s t r e s s e s (bond) and displacements are generated. 3. When the a p p l i e d displacements exceed those producing y i e l d of the s t e e l , s i g n i f i c a n t bond degradation i s observed to occur. F u r t h e r , an a n a l y t i c a l model was a l s o proposed which o f f e r e d f u r t h e r i n s i g h t i n t o the bond mechanism under c y c l i c l o a d i n g . Pauley, Park^ and P r i e s t l e y (78) examined i n d e t a i l the 30 behaviour of i n t e r i o r beam-column j o i n t s under s e i s m i c a c t i o n , based on t e s t s c a r r i e d out on beam-column subassemblages. They emphasized that the recommendations of ACI-ASCE 352 (10) appeared to be inadequate and unsafe. They p o s t u l a t e d the e x i s t e n c e of two shear r e s i s t i n g mechanisms, one i n v o l v i n g j o i n t shear reinforcement and the other a l i n e a r concrete s t r u t . The e f f e c t s of reversed c y c l i c l o a d i n g i n these mechanisms on both the e l a s t i c and i n e l a s t i c range of response are d i s c u s s e d . They repor t e d that a f t e r s e v e r a l c y c l e s of i n e l a s t i c r e v ersed load, y i e l d p e n e t r a t i o n i n e v i t a b l y occurs along the beam bars i n t o the j o i n t c o re. Some bond t r a n s f e r i s destroyed and the e f f e c t i v e anchorage l e n g t h of the beam bars i s d r a s t i c a l l y reduced, thus i n c r e a s i n g the bond s t r e s s i n the c e n t r a l p o r t i o n of the j o i n t to a very high order. Consequently, the concrete s t r u t c o n t r i b u t i o n i s reduced f u r t h e r and a major part of the h o r i z o n t a l j o i n t shear i s to be r e s i s t e d by a t r u s s mechanism n e c e s s i t a t i n g more h o r i z o n t a l shear reinforcement. They concluded that the diameter of beam bars p a s s i n g through the j o i n t c ores should not be e x c e s s i v e i f s l i p of bars through the j o i n t core due to bond f a i l u r e i s to be avoided. The s l i p can be avoided by l i m i t i n g the beam bar diameter to a c e r t a i n p r o p o r t i o n of the column depth or l i m i t i n g the average bond s t r e s s on the beam bars. Hungspreug (44) c a r r i e d out i n v e s t i g a t i o n s of the l o c a l bond s t r e s s between the r e i n f o r c i n g bar and the c o n c r e t e under v a r i o u s l o a d i n g h i s t o r i e s , i n c l u d i n g c y c l i c l o a d i n g , and under v a r i o u s degrees of c o n f i n i n g p r e s s u r e s , with the goal of 31 o b t a i n i n g q u a n t i t a t i v e l y u s e f u l r e s u l t s as data input for numerical s t u d i e s . The t e s t specimens c o n s i s t e d of 300mm long, 150mm diameter c y l i n d e r s with a c e n t r a l l y p l a c e d p o l i s h e d bar of 24mm diameter, each bar c o n t a i n i n g one, two or three machined r i b s i n the c e n t r a l p o r t i o n . A p r e s s u r i z e d f i r e hose wrapped around the concrete specimen and encased w i t h i n a s t e e l j a c k e t made i t p o s s i b l e to study the e f f e c t of r a d i a l c o n f i n i n g pressure on the bond behaviour. Based on the t e s t r e s u l t s , an i d e a l i z e d l o a d - s l i p curve f o r a s i n g l e r i b b e d bar, under v a r i o u s l o a d i n g h i s t o r i e s and d i f f e r e n t degrees of c o n f i n i n g p r e s s u r e , was proposed, as shown i n F i g . 1.6. T h i s , however, i s a p p l i c a b l e only to the s i z e of bar, the concrete cover, the r i b geometry and the range of concrete s t r e n g t h used. The l o a d - s l i p curve c o u l d a l s o be a p p l i e d to the bar with double or t r i p l e r i b s . The l o a d - s l i p curve c o n s i s t e d of a set of s t r a i g h t l i n e s j o i n i n g three stages of l o a d i n g , i . e . an i n i t i a l stage with s t i f f n e s s K1, a c r a c k i n g stage with l e s s s t i f f n e s s K2, and an un l o a d i n g - r e l o a d i n g stage with a s t i f f n e s s K3. With bars having m u l t i p l e r i b s , though the i n i t i a l s t i f f n e s s remained the same, the upper l i m i t f o r the i n i t i a l stage was hi g h e r . The c r a c k i n g s t i f f n e s s was found to be higher than f o r a s i n g l e - r i b b e d bar, ob v i o u s l y because l e s s damage was caused by c r a c k i n g . The s l i p at f a i l u r e was a l s o observed to be q u i t e small as compared to a s i n g l e - r i b b e d bar because of sh a r i n g of the lo a d by the m u l t i p l e r i b s . I t was thought that as the r i b s of the m u l t i p l e - r i b b e d bar began to l o s e t h e i r bonding e f f i c i e n c y , the bar would behave something l i k e a s i n g l e - r i b b e d bar but with a load even higher 32 kj_ - 3200 ± 800 k i p / i n . (simple method) k 2 - 120 ± 20 k i p / i n . k 3 - 4500 ± 730 k i p / i n . k A - 770 ± 190 k i p / i n . k 5 - 67 ± 12 k i p / i n . Note 1 kip = 0.304 k s i f o r 1 r i b = 0.202 k s i f o r 2 r i b s = 0.152 k s i f o r 3 r i b s F i g . 1.6 I d e a l i z e d bond-slip curve f o r a s t e e l bar (1,2, and 3 r i b ) under a generalized loading (monotonic, repeated, and reversed c y c l i c ) and with or without c o n f i n i n g pressure (Ref. 44 ) 33 than the u l t i m a t e load that c o u l d be s u s t a i n e d by a s i n g l e -r i b b e d bar. It was a l s o reported (44) that the l o a d - s l i p / b o n d s t r e s s -s l i p r e l a t i o n s h i p f o r a l l specimens, i r r e s p e c t i v e of the number of r i b s , f o r a p p l i e d loads below 27.6 MPa, c o u l d be expressed as: ( i ) a polynomial given by P = 5805 s - 4.2x10 s s 2 + 1.478x10 s s 3 ~ 1.9 ' where P = a p p l i e d load i n k i p s , s= s l i p i n inches or, ( i i ) i n the form of bond s t r e s s - s l i p r e l a t i o n s h i p u = 1.77X10 6 s - 1.28X10 6 s 2 + 0.45x10 s s 3 -- 1.10 where u = bond s t r e s s i n p s i There were many l i m i t a t i o n s to the use of the proposed bond s t r e s s - s l i p behaviour by Hungspreug (44), because the t e s t s were c o n f i n e d to only one bar s i z e , one type of r i b geometry, one s i z e of concre t e cover, and a f i x e d embedment l e n g t h , and the range of concre t e s t r e n g t h used i n the t e s t s . S l i c i n g the specimens r e v e a l e d that s p l i t t i n g c r a c k s were more e x t e n s i v e than the t r a n s v e r s e c r a c k s , although the t r a n s v e r s e c r a c k s were the f i r s t to i n i t i a t e . However, the t r a n s v e r s e c r a c k s were observed to s t a b i l i z e at about 12mm from the s u r f a c e of the r e i n f o r c i n g bar. The c o n f i n i n g pressure was re p o r t e d to have the e f f e c t of reducing the l o n g i t u d i n a l c r a c k i n g by producing compressive t a n g e n t i a l s t r e s s e s . Repeated l o a d i n g at i n c r e a s i n g l o a d amplitude was observed to have an adverse e f f e c t on the s t i f f n e s s and the u l t i m a t e bond s t r e n g t h . 3 4 Edwards' and Yannopoulos (22) c a r r i e d out p u l l - o u t t e s t s of specimens with short embedment lengths to determine the l o c a l bond s t r e s s - s l i p r e l a t i o n s h i p under repeated l o a d i n g . Deformed bars of 16mm diameter and concrete embedment l e n g t h of 38mm (or four times the deformed bar lug spacing) were used. Specimens were t e s t e d under nine load c y c l e s of constant amplitude; a l l of the specimens f a i l e d due to s p l i t t i n g . They repo r t e d c o n s i d e r a b l e s c a t t e r i n the bond s t r e s s - s l i p r e l a t i o n s h i p and suggested the n e c e s s i t y of a s u f f i c i e n t number of t e s t r e p l i c a t i o n s to o b t a i n r e l i a b l e estimates of the curves. They a l s o observed that the bond between s t e e l and concrete at any s t r e s s l e v e l was i n f l u e n c e d by the prev i o u s l o a d i n g h i s t o r y . The e f f e c t i v e n e s s of bond depended mainly upon the given s t r e s s l e v e l and the magnitude of the pr e v i o u s peak s t r e s s , and to a l e s s e r extent upon the number of c y c l e s . The amount of bond d e s t r u c t i o n i n the f i r s t c y c l e was found to be l a r g e r than that in succeeding c y c l e s . I t in c r e a s e d with i n c r e a s i n g load amplitude both i n the f i r s t c y c l e and i n the succeeding c y c l e s . Henager (41) c a r r i e d out t e s t s on specimens r e p r e s e n t i n g beam-column j o i n t s of a d u c t i l e moment r e s i s t i n g frame s t r u c t u r e , using c o n v e n t i o n a l hoops i n one case and s t e e l f i b e r s in l i e u of hoops i n the other. S t e e l f i b e r s were b r a s s - p l a t e d 0.51mm diameter by 38mm long. The specimens were su b j e c t e d to lo a d i n g r e p r e s e n t i n g the e f f e c t of two major earthquakes. The j o i n t s u sing s t e e l f i b e r s were found to have improved d u c t i l i t y and s t r e n g t h , and were somewhat s t i f f e r and more damage t o l e r a n t than the j o i n t s * using c o n v e n t i o n a l hoops. The in c r e a s e d 3 5 s t i f f n e s s f o r the s t e e l f i b e r specimen was accounted f o r by a l i k e l y r e d u c t i o n i n bond s l i p of the r e i n f o r c i n g bar. Henager's study, however, d i d not inc l u d e i n p a r t i c u l a r the bond behaviour or bond d e t e r i o r a t i o n between the r e i n f o r c i n g bar and the concrete under v a r i o u s c o n d i t i o n s of l o a d i n g s i m u l a t i n g seismic motion. None the l e s s , the e f f e c t of bond might have been r e f l e c t e d i n h i s study of the moment-rotation c h a r a c t e r i s t i c s of the beam-column j o i n t s . Panda (74,93) s t u d i e d the e f f e c t of reversed c y c l i c load on the bond of deformed bars i n p l a i n and s t e e l f i b e r r e i n f o r c e d c o n c r e t e , and a l s o c r a c k i n g i n concrete surrounding the r e i n f o r c i n g bar. Specimens made with f i b e r r e i n f o r c e d concrete were t e s t e d to explore the f e a s i b i l i t y of using SFRC ( S t e e l F i b e r R e i n f o r c e d Concrete) i n moment r e s i s t i n g d u c t i l e frames i n seismic areas. Ten specimens, two of p l a i n concrete and ei g h t of s t e e l f i b e r r e i n f o r c e d concrete were t e s t e d under repeated/reversed c y c l i c l o a d i n g . The experimental set up was designed so that a s i n g l e bar cou l d be simultaneously p u l l e d at one end and pushed at the other, and t h i s l o a d i n g c o u l d be reversed c y c l i c a l l y to simulate the loa d i n g of a bar passing through an i n t e r i o r beam-column j o i n t under se i s m i c l o a d i n g . The t e s t specimens were 250x500x900mm with a 25mm diameter r e i n f o r c i n g bar c e n t r a l l y l o c a t e d i n the specimens, with an embedment l e n g t h of 500mm. Two types of s t e e l f i b e r s were used: 0.25x0.5x12.5mm and 0.25x0.5x25mm. F i b e r c o n c e n t r a t i o n s of 100 and 200 l b / c u yd (59.3 and 1 1 8 . 6 kg/cu m ) were used i n the t e s t specimens. A b r i e f summary of some of the main p o i n t s a r e : 36 1. The mode of f a i l u r e and the behaviour under t e s t f o r p l a i n and SFRC specimens appeared to be d i f f e r e n t . SFRC specimens e x h i b i t e d g r e a t e r r e s i s t a n c e to crack formation and propagation than the p l a i n concrete ones. 2. No s i g n i f i c a n t decrease i n bond s t r e s s was observed with a small i n c r e a s e i n the number of c y c l e s under a constant s t r e s s l e v e l . However, an i n c r e a s e i n peak s t r e s s l e v e l produced a s i g n i f i c a n t r e d u c t i o n in bond s t r e s s i n subsequent c y c l e s . 3. With i n c r e a s e i n peak load or load r e p e t i t i o n s under constant l o a d , both p l a i n as w e l l as SFRC specimens s u f f e r e d a l o s s i n the r e l a t i v e c o n t r i b u t i o n of the concrete to the apparent s t i f f n e s s of the bar and the surrounding c o n c r e t e . The l o s s of s t i f f n e s s was found to be greater f o r p l a i n concrete specimens. The s t i f f n e s s c o n t r i b u t i o n was d e f i n e d as: X = L / e dx ' s 1 f /E s s _J x 1 0 0 - - 1.11 where X = percent of s t i f f n e s s c o n t r i b u t i o n e g = measured t e n s i l e s t r a i n long reinforcement f s = maximum t e n s i l e s t r e s s a p p l i e d to s t e e l E s = Young's modulus of s t e e l L = anchorage l e n g t h ( t e n s i o n zone considered) 4. Under re v e r s e d c y c l i c l o a d i n g with few c y c l e s , the anchorage bond s t r e n g t h of deformed bars was found to be 37 about 20 to 30 percent higher i n s t e e l f i b e r r e i n f o r c e d concrete than i n p l a i n c o n c r e t e . However, f u r t h e r work in the area was suggested as only a few t e s t s were c a r r i e d out with a l i m i t e d number of v a r i a b l e s in the i n v e s t i g a t i o n . T a s s i o s (97) c a r r i e d out a review of the ideas on bond between r e i n f o r c i n g bars and concrete f o r a p o s s i b l e r a t i o n a l approach to the mechanics governing bond, mainly under c y c l i c l o a d i n g . Though p r e c i s e q u a n t i f i c a t i o n of v a r i o u s f a c t o r s i n f l u e n c i n g the c r i t i c a l l o c a l bond s t r e s s TA (which l e d to the f i r s t l o c a l c r a c k i n g ) was d i f f i c u l t , some elementary q u a n t i f i c a t i o n s with c o r r e c t i o n f a c t o r s were r e p o r t e d . A conceptual model based on which mechanisms of c r a c k i n g and bond f a i l u r e c o u l d be p r e d i c t e d , was a l s o proposed. He formulated e m p i r i c a l equations f o r the p r e d i c t i o n of the u l t i m a t e bond s t r e s s at f a i l u r e , and that at f i r s t c r a c k i n g . Based on the conceptual model, a s i m p l i f i e d c y c l i c bond s t r e s s s l i p r e l a t i o n s h i p was developed, which i s s c h e m a t i c a l l y shown in F i g . 1.7 . Recently, some i n t e r e s t i n g and very important work on the behaviour of deformed bars anchored at i n t e r i o r j o i n t s under seismic e x c i t a t i o n s has been completed by E l i g e h a u s e n , Popov and B e r t e r o (24). From t e s t s of some 125 specimens ( F i g . 1.8(a)) a mathematical model of a deformed bar anchored at the i n t e r i o r j o i n t s of d u c t i l e moment r e s i s t i n g r e i n f o r c e d c o n c r e t e frames s u b j e c t e d to severe earthquakes has been presented. The t e s t specimens c o n t a i n e d Grade 60 deformed bars, with the bond length 38 l i m i t e d to f i v e times the diameter of the bar. The e f f e c t s of v a r i a b l e s such as monotonic versus c y c l i c l o a d i n g with v a r y i n g s l i p h i s t o r i e s , t e n s i l e versus compressive l o a d i n g , the amount of confinement reinforcement, bar diameter, concr e t e s t r e n g t h , bar spacing, t r a n s v e r s e pressure and r a t e of p u l l - o u t , were co n s i d e r e d in the f o r m u l a t i o n of the model. They a l s o formulated a model for the l o c a l bond-stress s l i p r e l a t i o n s h i p , which i s d e s c r i b e d s c h e m a t i c a l l y in F i g . 1.8(b). They repo r t e d that the monotonic bond s t r e s s - s l i p r e l a t i o n s h i p f o r l o a d i n g i n t e n s i o n was almost i d e n t i c a l to that f o r l o a d i n g i n compression. The d e t e r i o r a t i o n of bond duri n g c y c l i c l o a d i n g was observed to i n c r e a s e with an i n c r e a s e in the h y s t e r e t i c requirements ( i n t e n s i t y of s t r a i n and number of c y c l e s ) , i n c r e a s i n g y i e l d s t r e n g t h and d e c r e a s i n g anchorage l e n g t h . Summary From the above d i s c u s s i o n s of the c u r r e n t s t a t e of knowledge i t i s c l e a r that e x t e n s i v e study has been done on the bond behaviour of deformed bars in concrete under monotonic p u l l - o u t l o a d i n g c o n d i t i o n s . However, the amount of research devoted to the e f f e c t of reversed c y c l i c l o a d i n g on the anchorage bond e s p e c i a l l y in a beam-column j o i n t , i s remarkably s m a l l . L i t t l e work on the behaviour of bond in s t e e l f i b e r r e i n f o r c e d concrete under reversed c y c l i c l o a d i n g has been c a r r i e d out so f a r . From the study of v a r i o u s l o c a l bond s t r e s s - s l i p r e l a t i o n s h i p s f o r monotonic as w e l l as c y c l i c l o a d i n g , put f o r t h 39 F I G . 1 .7 C Y C L I C B O N D - S L I P R E L A T I O N S H I P ( C O N C E P T U A L MODEL) (Ref. 97) | t | MCCTIM Of USTIW -lift E3 I •#L*STIC tMCCT -•4 l i t T M l •Aft 1 t i * [ TTTiv-4 a 5 s L H T K tMCCT •MONOTONIC LOADING MONOTONIC" LOADING EXPOtMEMTAl — — ANALYTICAL F I G . 1 . 8 ( b ) PROPOSED A N A L Y T I C A L MODEL FOR L O C A L BOND-S T R E S S - S L I P R E L A T I O N S H I P ( R e f . 1 9 ) 40 by v a r i o u s r e s e a r c h e r s , i t i s c l e a r that there e x i s t s a wide v a r i a t i o n i n the computed valu e s of s l i p with respect to any p a r t i c u l a r bond s t r e s s . Most of the bond s t r e s s - s l i p models do not c o n s i d e r many important v a r i a b l e s that a f f e c t the bond s t r e s s - s l i p r e l a t i o n s h i p , such as concrete s t r e n g t h , bar diameter, stopdeformation p a t t e r n of bar, bar spacing, amount of c o n f i n i n g reinforcement, t r a n s v e r s e p r e s s u r e , r a t e of bar p u l l -out and so on. Much more r e s e a r c h i s needed i n t h i s area, p a r t i c u l a r l y on load h i s t o r y and the e f f e c t of confinement on bond. A d e t a i l e d d i s c u s s i o n on the l o c a l b o n d - s l i p model w i l l however be made in Chapter 7 i n the context of the a n a l y t i c a l study of bond. 41 11 . TEST PROGRAM 2.1 GENERAL A t o t a l of twenty four specimens, i n c l u d i n g four e x p l o r a t o r y ones, were t e s t e d i n the S t r u c t u r a l E n g i n e e r i n g Laboratory of the C i v i l E n g i n e e r i n g Department, U n i v e r s i t y of B r i t i s h Columbia. A l l of the specimens contained a c e n t r a l l y p l a c e d r e i n f o r c i n g bar ( t e s t bar) of one of three nominal diameters: 20mm, 25mm or 30mm, (See Table 2.4 f o r dimensions). Six of the specimens were of p l a i n c o n c r e t e ; the remainder were a l l s t e e l f i b e r r e i n f o r c e d c o n c r e t e . The v a r i a b l e s examined were mix p r o p o r t i o n s , s i z e of s t e e l f i b e r s ( l e n g t h ) , l o a d i n g h i s t o r y , diameter of the t e s t bar, embedment l e n g t h of the t e s t bar and the su r f a c e c o n d i t i o n of the bar. The mix- p r o p o r t i o n s and other p a r t i c u l a r s of the specimens are t a b u l a t e d in Tables 2.1 and 2.2. In order to study a l a r g e number of v a r i a b l e s with a minimum number of t e s t specimens, a l l the t e s t specimens were d i f f e r e n t from one another, and no r e p l i c a t i o n s of the t e s t s were c a r r i e d out. T h i s s i t u a t i o n , t h e r e f o r e does not allow the s t a t i s t i c a l s i g n i f i c a n c e of the v a r i o u s comparisons to be c a l c u l a t e d . The a p p l i c a t i o n of l o a d i n g was by means of two jacks mounted on a t e s t frame. The loa d set up was such that a compression (or tension) f o r c e c o u l d be a p p l i e d at one end of the t e s t bar while a t e n s i o n (or compression) f o r c e was a p p l i e d to the other end. An MTS servos-controlled load system was used to apply the TABLE 2.1  MIX PROPORTIONS Specimen No. S t e e l F i ber '(kg/m') Cement (kg/rn 1 ) Sand (kg/m') Pea G r a v e l 10mm (kg/m 1) Water (kg/m') Water Reducer 1 (ml/m 1) A i r Entralnment 2 (ml/m') P-500/25/RV/5 P-500/25/RV/6 P-500/25/RVM/20 P-375/20/RVM/23 P-375/20/RVM/24 NIL 417.0 878 .0 878 .0 192 .2 774 258 F1-500/25/RP/11 F1-500/25/MO/12 F1-500/25/RVM/13 F1-500/25/RV/16 F1-500/25/RVM/21 F1-500/30/RVM/25 62 .3 (0.79%) 443 . 7 840.6 840. 6 205.8 774 310 F2-500/25/RV/8 F2-500/25/RP/9 F2-500/25/MO/10 F2-500/25/RVM/14 F2-500/25/RVM/15 F2-500/25/RV/17 F2-500/25/M0/18 F2-500/25/RVM/19 F2-500/25/RVM/22 62.3 (0. 79%) 443 . 7 840.6 840. G 205.8 774 310 1 P o z z o l 1 t h 300N 2 MB-VR NOTE: S t e e l F i b e r , % by Volume. SPECIMEN TABLE 2.2 c  PARTICULARS AND LOADING HISTORY Specimen No. S i z e C o n c r e t e SG* OR Load 1ng Remarks (mmxmmxmm) St r e n g t h NSG* H i s t o r y fc'(MPa) P-500/25/RV/5 50. 26 SG P-500/25/RV/6 51 .44 NSG F2-500/25/RV/8 250x500x900 46.61 NSG RV F1t500/25/R V/16 63 .64 NSG F2-500/25/RV/17 55.57 SG F2-5OO/25/M0/1O 46.89 NSG F1-5OO/25/M0/12 250x500x900 47 .16 NSG " MO F2-500/25/MO/18 55.57 SG F1-500/25/RVM/13 46 . 33 NSG F2-500/25/RVM/14 49.09 NSG F2-500/25/RVM/15 49.09 NSG F2-500/25/RVM/19 250x500x900 55 . 57 SG RVM P-500/25/RVM/20 50.06 SG F1-500/25/RVM/21, 51 .09 SG F2-500/25/RVM/22 52 . 13 SG { s p i r a l p r o v i d e d around t e s t bar P-375/20/RVM/23 250x375x900 49.92 SG P-375/20/RVM/24 52 .06 SG rebar g r e a s e d F1-500/30/RVM/25 250x500x900 54 . 26 SG F2-500/25/RP/9 250x500x900 47 . 16 NSG RP F1-500/25/RP/11 53.99 NSG SG* - S t r a i n gage pre s e n t NSG* - No s t r a i n gage pre s e n t l o a d s . Loads, displacements and s t r a i n s were recorded using a V i d a r 5403 D-Das Data A c q u i s i t i o n System and PDP 11/10 mini computer. The l o a d i n g arrangements and t e s t set up are shown i n F i g s . 2.1,2.2. 2.2 OBJECTIVE OF THE TEST PROGRAM The major o b j e c t i v e s of the t e s t program were: 1. To study the e f f e c t of randomly d i s p e r s e d s t e e l f i b e r s i n the c o n c r e t e matrix on the anchorage bond as compared to p l a i n c o n c r e t e specimens, with v a r i o u s load h i s t o r i e s . 2. To study the general behaviour of specimens with d i f f e r e n t l o a d i n g h i s t o r i e s , with s p e c i f i c r e f e r e n c e to bond d e t e r i o r a t i o n , and to o b t a i n the a p p l i e d s t r e s s -displacement r e l a t i o n s h i p s . 3. To study the l o c a l bond s t r e s s d i s t r i b u t i o n along the r e i n f o r c i n g bar at v a r i o u s l o c a t i o n s f o r d i f f e r e n t specimens. 4 To study the a x i a l s t i f f n e s s degradation with v a r i o u s load h i s t o r i e s f o r d i f f e r e n t specimens. 5. To compute and compare the t o t a l energy a b s o r b i n g c a p a c i t y of v a r i o u s specimens up to the p o i n t of bond f a i l u r e . 6. To study the c r a c k i n g p a t t e r n at v a r i o u s a p p l i e d s t r e s s l e v e l s and the modes of f a i l u r e . 7. To b e t t e r understand the bond behaviour between the r e i n f o r c i n g bar and the c o n c r e t e under d i f f e r e n t l o a d i n g c o n d i t i o n s , e s p e c i a l l y under r e v e r s e d c y c l i c l o a d i n g , using the above mentioned data. A f i n i t e element procedure was used f o r the p r e d i c t i o n of l o c a l s t r e s s e s and deformations 45 FIG.2-1(Q)TEST FRAME SETUP FIG.2.Kb)TEST FRAME SETUP 46 FIG.2-KC)TYPICAL TEST SPECIMEN FIG .2.1(d)LOADING ARRANGEMENT (CLOSE-ELEVAT ION SIDE VIEW FIG2-2 CYCLIC BOND TEST EQUIPMENT. 48 in c o n c r e t e at and around the r e i n f o r c i n g bar. 2.3 CONCRETE MODEL REPRESENTING AN INTERIOR BEAM-COLUMN JOINT During a severe o v e r l o a d due to high l a t e r a l f o r c e s , a crack i s l i k e l y to form through the beam at the column face ( r i g h t next to the column) of a high r i s e frame s t r u c t u r e as shown in F i g . 2.3. On r e v e r s a l of the load, another crack forms through the adjacent beam on the opposite side of the column. If the a p p l i e d l a t e r a l f o r c e s are s u f f i c i e n t l y i n t e n s e , cracks can develop through the e n t i r e depth of the beams. Due to i n e l a s t i c deformation, the cr a c k s may not c l o s e up completely. T h e r e f o r e , the continuous beam r e i n f o r c i n g bars p a s s i n g through the j o i n t would be subjected to simultaneous p u l l from one side and push from the other s i d e . The experimental setup in t h i s i n v e s t i g a t i o n was designed to simulate t h i s c o n d i t i o n f o r a s i n g l e bar, c e n t r a l l y l o c a t e d i n a block of concrete r e p r e s e n t i n g the j o i n t . F i g s . 2.3(b)&(c) shows the f o r c e s a c t i n g on a t y p i c a l i n t e r i o r beam-column j o i n t . T h i s i n d i c a t e s that the t e s t specimen r e p r e s e n t s an extremely s i m p l i f i e d model ( F i g . 2.3(d)), as i t does not i n v o l v e a l l of the s t r e s s s t a t e s that e x i s t d u r i n g an a c t u a l seismic motion i n an i n t e r i o r beam-column j o i n t . In the block of concret e model, the m u l t i p l i c i t y of the other f a c t o r s , such as the e f f e c t s of dowel a c t i o n ( t r a n s v e r s e f o r c e due to shear on beam b a r ) , m u l t i p l e r e i n f o r c i n g bars, e c c e n t r i c placement of the r e i n f o r c i n g bars, and the a c t u a l s t r e s s c o n d i t i o n s that e x i s t along the embedment le n g t h of the r e i n f o r c i n g bar are a l s o not c o n s i d e r e d . The present specimen -geometry was chosen i n an attempt to separate 49 ///// BEAM-COLUMN JOINT c 1 ~ \( ' 1 T v ' 7 7 7 ^ (b)FORCES ACTING ON INTERNAL JOINT (a ) TYPICAL HIGH RISE FRAME y C r j — / , "\t — i 1 -— 1 "f 1 * \ t- 1 I) ( d ) BLOCK OF CONCRETE MODEL (C) FORCES ACTING ON INTERNAL JOINT (LOAD REVERSED) FIG.2*3 - BEAM COLUMN JOINT FORCES & THE MODEL 50 out these f a c t o r s . Only the e f f e c t of anchorage c o n d i t i o n s on the d e t e r i o r a t i o n of bond was c o n s i d e r e d as the e f f e c t of other v a r i a b l e s renders the bond problem a h i g h l y complex one. The s i m p l i f i e d model d e s c r i b e d above, was used by the author f o r h i s M.A.Sc. d i s s e r t a t i o n (74)-. C o i n c i d e n t a l l y , a s i m i l a r model was adopted by Viwathanatepa (99) f o r h i s bond study. 2.4 PRELIMINARY INVESTIGATIONS Before making plans f o r more ex t e n s i v e t e s t i n g , i t was decided to t e s t four e x p l o r a t o r y specimens to study t h e i r performance and s u i t a b i l i t y f o r the bond t e s t , as w e l l as to e v a l u a t e the performance of the t e s t i n g system. Each of the four specimens contained a c e n t r a l l y p l a c e d t e s t bar made of s p l i t bars, glued together, having a c e n t r a l groove for mounting the s t r a i n gauges as shown i n F i g . 2.4. roove For Strain Gauge ^ - t t H O O V E FOfl STRAIN GAUGE -FIXING FIG.2-A(aCOUNTING OF STRAIN GAUGES FIG.2.4(b)MOUNTING OF STRAIN GAUGES (SPLIT BAR) ™ ™ % (TEST SERIES) One of the four specimens was of p l a i n c o n c r e t e , while the remainder were of f i b e r r e i n f o r c e d c o n c r e t e . A b r i e f d i s c u s s i o n of the performance of these specimens, and reasons f o r some of the m o d i f i c a t i o n s , ' w i l l be given i n Chapter 3. •51 5 PARAMETERS IN STUDY The main v a r i a b l e parameters i n t h i s i n v e s t i g a t i o n were: Loading H i s t o r y Four d i f f e r e n t load h i s t o r i e s , with equal magnitudes of push-in and p u l l - o u t loads were used: i ) Monotonic (MO) i i ) Reversed C y c l i c , with only one c y c l e f o r each i n c r e m e n t a l l y i n c r e a s e d peak amplitude of l o a d i n g , except f o r the l a s t c y c l e t i l l f a i l u r e (RV). i i i ) Reversed C y c l i c , ' with m u l t i p l e c y c l e s f o r each i n c r e m e n t a l l y i n c r e a s e d peak amplitude of lo a d i n g (RVM). iv ) Repeated Loading ( e i t h e r t e n s i o n or compression) with only one c y c l e f o r each i n c r e m e n t a l l y i n c r e a s e d peak amplitude of l o a d i n g (RP) Types of Concrete i ) P l a i n Concrete i i ) S t e e l F i b e r R e i n f o r c e d Concrete a) with 30mm long s t e e l f i b e r s b) with 50mm long s t e e l f i b e r s Embedment Length and Diameter of the Test bar i ) 25mm diameter t e s t bar with 500mm embedment length i i ) 20mm diameter t e s t bar with 375mm embedment len g t h i i i ) 30mm diameter t e s t bar with 500mm embedment l e n g t h 52 2.6 SPECIMENS UNDER TEST A l l but two of the specimens under t e s t had the dimensions 250x500x900mm; the other two specimens were 250x375x900mm. The lo a d i n g was a p p l i e d to the ends of the Grade 60 deformed t e s t b a r s . In one of the specimens, a 200mm outer diameter s p i r a l made of 10mm diameter bar, was pl a c e d around the t e s t bar to provide confinement. For the remaining cases, c o n v e n t i o n a l t r a n s v e r s e reinforcement was used. The d e t a i l s of the design of specimens are i n c l u d e d in Appendix A. The d i s p o s i t i o n of the r e i n f o r c i n g bars i n the specimens i s shown i n F i g . 2.5. The y i e l d s t r e n g t h s at 0.2 percent o f f s e t and other p r o p e r t i e s of v a r i o u s diameters of r e i n f o r c i n g bars are t a b u l a t e d i n Tables 2.3 & 2.4. In eleven of the specimens, the t e s t bars were l o n g i t u d i n a l l y machined for f i x i n g of the s t r a i n gauges. The remaining specimens had ungrooved bars. T e s t s of specimens with ungrooved bars were necessary to ob t a i n i n f o r m a t i o n r e g a r d i n g the e f f e c t of grooves. The d e t a i l s of the grooves are shown i n F i g . 2.4(b) 2.7 SPECIMEN IDENTIFICATION For s i m p l i c i t y , the specimens were given numbers to i n d i c a t e p l a i n or s t e e l f i b e r r e i n f o r c e d c o n c r e t e , embedment leng t h of t e s t bar, bar s i z e , s t e e l f i b e r s i z e ( i f p r e s e n t ) , l o a d h i s t o r y and the s p e c i f i c number assigned to the specimen. A b r i e f d e s c r i p t i o n i s given below: -104 Lalaral T ' t t i .. n . n r •1 1 i b rr-t I to ELEVATIONS 10$ L o l t r e l T i l l NOTE: ALL DIMENSIONS ARE IN MM SECTIONAL PLAN FIG. 2.5(a) Reinforcement In Specimens ( S p i r a l Provided) Embedment = 500mm I I T 2 8 I 7 I T o o 1 7 ELEVATIONS SECTIONAL PLAN -290-FIG. 2.5(b) Reinforcement In Specimens With Embedment = 375mm 54 f 1 l O c ^ L o t e r o l T i e s E L E V A T I O N S V K7\ — A A — 30 NOTE: ALL DIMENSIONS ARE IN MM 500 SECTIONAL PLAN F I G . 2*5(c) R e i n f o r c e m e n t I n S p e c i m e n s W i t h Embedment = 500mm T A B L E 2 . 3 MECHAN ICAL P R O P E R T I E S OF R E I N F O R C I N G BARS ( R e s u l t s o f T e n s i o n T e s t ) Nom i na1 B a r d i a (mm) T y p e C . S. A r e a (mm' ) Y i e l d S t r e n g t h (MPa ) U I t i m a t e T e n s i 1 e S t r e n g t h (MPa ) % E 1 o n g a t i o n t y (mm/mm) ( Sh (mm/mm) E s ( M P a ) 2 0 D e f o r m e d 2 9 0 . 0 424 .6 7 7 9 . 2 2 2 . 5 0 . 0 0 2 0 2 0 . 0 1 1 2 1 0 . 3 6 6 25 - d o - 4 8 6 . 7 422 .9 7 9 9 . 8 26 .0 0 . 0 0 2 0 5 0 . 0 0 8 3 2 0 6 , 5 0 5 30 - d o - 6 7 2 . 3 4 2 0 . 6 7 6 3 . 9 23 .0 0 . 0 0 2 0 O 0 . 0 0 5 3 2 0 6 . 5 0 5 N o t e : t y -t s h -E s -S t r a i n a t y i e l d S t r a i n a t b e g i n n i n g o f s t r a i n h a r d e n i n g Y o u n g ' s M o d u l u s o f s t e e l T A B L E 2 . 4  T E S T BAR P A R T I C U L A R S NOMINAL D I A M E T E R (mm) S O L I D BAR GROOVED B IR M e a s u r e d A r e a ( 1 ) (mm' ) M e a s u r e d A r e a ( 2 ) (mm' ) Nom1na1 A r e a ( 3 ) (mm' ) E q u 1 v a 1 e n t O i a . a s p e r ( 1 ) ( m m ) M e a s u r e d A r e a f 1 ) (mm' ) M e a s u r e d A r e a ( 2 ) (mm' ) Nom1na1 A r e a ( 3 ) (mm' ) E q u 1 v a ) e n t D i a . a s p e r ( 1 ) (mm) 10 6 5 . 0 6 5 . 8 7 8 . 5 9 . 10 - - - -2 0 2 9 0 . 0 2 9 3 . 4 3 1 4 . 1 19. 22 24 1 .62 2 4 5 . 0 2 5 7 . 7 1 5 . 5 25 4 8 6 . 7 4 8 5 . 5 5 0 6 . 6 24 . 8 9 4 3 0 . 5 4 2 9 . 4 4 5 0 . 3 23 . 4 3 0 6 7 2 . 3 6 6 9 . 6 7 0 6 . 9 2 9 . 2 6 6 1 6 . 2 6 1 3 . 5 6 5 0 . 4 28 . 0 N o t e : M e a s u r e d A r e a ( 1 ) - C r o s s s e c t i o n a l a v e r a g e o f 3 s e c t i o n s m e a s u r e d b y P l a n i m e t e r M e a s u r e d A r e a ( 2 ) - B a s e d o n w e i g h t c a l c u l a t i o n s N o m i n a l A r e a O ) - B a s e d o n n o m i n a l d i a m e t e r s 57 (a) P l a i n Concrete Specimens: P - 500 / 25 / RV / 5 s p e c i f i c No. f o r specimen Loading H i s t o r y Diameter of Test Bar i n mm. Embedment Length i n mm. P l a i n Concrete (No f i b e r s but c o n t a i n c o n v e n t i o n a l reinforcement) (b) S t e e l F i b e r R e i n f o r c e d Concrete Specimens: F2 - 500 / 25 / RVM / 19 I s p e c i f i c No. f o r specimen Loading H i s t o r y Diameter of Test Bar i n mm. Embedment Length i n mm. I S i z e of S t e e l F i b e r - 2 f o r 50mm. long 1 f o r 30mm. long S t e e l F i b e r R e i n f o r c e d Concrete 2.8 MATERIAL PROPERTIES 2.8.1 Concrete The cement used i n the con c r e t e was CSA Type 30 high e a r l y s t r e n g t h p o r t l a n d cement (corresponding to ASTM Type I I I ) . The f i n e aggregate was c l e a n sand from the Fr a s e r River V a l l e y which was f r e e from harmful impurities.. The coarse aggregate used was 10mm pea g r a v e l . The design compressive s t r e n g t h of the 5 8 c o n c r e t e was 45 MPa at 28 days . The d e t a i l s of the c o n c r e t e mix p r o p o r t i o n s are shown i n Tab le 2 . 1 . In the case of the f i b e r r e i n f o r c e d c o n c r e t e specimens , c o l l a t e d , water s o l u b l e cr imped Baekart s t e e l f i b e r s were used , w i t h the d imens ions shown i n F i g . 2 . 6 . T e s t s were c a r r i e d out on r e p r e s e n t a t i v e samples of the specimens i n the form of c y l i n d e r s (100mm d i a x200mm) and pr i sms (100x100x350mm) to measure compres s ive s t r e n g t h s and f l e x u r a l s t r e n g t h s of the specimens . I t may be mentioned here that so f a r , s t andard methods are not a v a i l a b l e to determine the p r o p e r t i e s of SFRC (9) , a l t h o u g h many t e s t s have been proposed . However, many of the t e s t s for p l a i n c o n c r e t e are be ing a p p l i e d to SFRC. Another aspect of the problem i s tha t the computat ion of some p r o p e r t i e s , such as t e n s i l e s t r e n g t h of SFRC from f l e x u r a l t e s t s u s i n g the formula fr= Bl ( n o t a t i o n s d e s c r i b e d i n b d 2 page x i v - x v i ) i s c o r r e c t , as l ong as the m a t e r i a l i s e l a s t i c . However, the t e s t r e s u l t s are r e p o r t e d i n T a b l e 2 . 5 . The s t r e s s - s t r a i n r e l a t i o n s h i p s of p l a i n as w e l l as f i b e r - r e i n f o r c e d c o n c r e t e under u n i a x i a l compress ion are shown i n F i g . 2 . 7 . The t e s t r e s u l t s i n d i c a t e d a r ea sonab le u n i f o r m i t y in c o n c r e t e p r o p e r t i e s of v a r i o u s specimens of both types of c o n c r e t e . A s i g n i f i c a n t d i f f e r e n c e i n the performance of the f i b e r r e i n f o r c e d c o n c r e t e and p l a i n c o n c r e t e i n s t a t i c f l e x u r a l t e s t s of 100x100x350mm beams may be obse rved , as shown i n F i g . 2 . 8 . The s t e e l f i b e r s appear to c o n t r i b u t e s i g n i f i c a n t l y to the g r e a t e r u l t i m a t e f l e x u r a l s t r e n g t h and h igher toughness , as c a l c u l a t e d by the area under the l o a d - d e f l e c t i o n c u r v e s . The 59 A Diameter - 0.5mm spect Ratio«60 ~ 1mm —<3.S 1— 30mm ^ Diameter • 0.5mm Aspect Ratio«l00 • —Hi r™ 50"im — 3 COLLATED CRIMPED STEEL FIBERS FIG.2.6(a) STEEL FIBER PARTICULARS FIG.2.6(b) STEEL FIBERS T A B L E 2 . 5 MECHAN ICAL P R O P E R T I E S OF CONCRETE S P E C I M E N S f c ' AVERAGE t c AVERAGE F c A V E R A G E f r AVERAGE ( M P a ) f c ' (mm/mm) €C ( M P a ) E c ( M P a ) ( M P a ) f r ( M P a ) ( M P a ) (mm/mm) P - 5 0 0 / 2 5 / R V / 5 5 0 26 50.-75 0 0 0 2 2 0 0 0 0 2 2 6 3 1 . 2 0 7 3 1 . 9 0 4 5 4 0 5 46 P - 5 0 0 / 2 5 / R V / 6 51 44 0 0 0 2 3 5 3 0 , 8 7 6 5 23 P - 5 0 0 / 2 5 / R V M / 2 0 5 0 0 6 0 0 0 2 2 7 31 , 8 2 0 5 43 P - 3 7 5 / 2 0 / R V M / 2 3 4 9 92 0 0 0 2 1 0 3 2 , 4 8 9 5 G9 P - 3 7 5 / 2 0 / R V M - 2 4 52 0 6 0 0 0 2 3 6 3 3 . 130 5 57 F 2 - 5 0 0 / 2 5 / R V / 8 46 61 5 1 . 6 1 0 0 0 3 15 0 0 0 3 1 4 31 , 1 10 3 1 . 5 7 9 7 88 8 77 F 2 - 5 0 0 / 2 5 / R P / 9 47 16 0 0 0 3 2 4 31 ,751 8 14 F 2 - 5 0 O / 2 5 / M 0 / 1 O 46 8 9 0 0 0 3 2 7 31 . 1 10 10 46 F 1 - 5 0 0 / 2 5 / R P / 1 1 53 9 9 0 0 0 2 9 3 3 3 , 6 8 9 6 13 F 1 - 5 0 0 / 2 5 / M O / 1 2 47 16 0 0 0 2 8 5 31 ,751 8 14 F 1 - 5 0 0 / 2 5 / R V M / 1 3 4 6 33 0 0 0 3 2 0 31 , 1 10 10 0 8 F 2 - 5 0 0 / 2 5 / R V M / 1 4 4 9 0 9 0 0 0 3 1 4 31 , 4 2 7 7 4 9 F 2 - 5 0 0 / 2 5 / R V M / 1 5 4 9 0 9 0 0 0 3 1 4 31 , 4 2 7 7 4 9 F 1 - 5 0 0 / 2 5 / R V / 1 6 6 3 64 0 0 0 3 2 9 3 3 . 4 5 4 1 1 32 F 2 - 5 0 0 / 2 5 / R V / 1 7 55 57 0 0 0 3 3 3 3 0 , 6 4 1 9 82 F 2 - 5 O O / 2 5 / M 0 / 1 8 55 5 7 0 0 0 3 3 3 3 0 , 6 4 1 9 82 F 2 - 5 0 0 / 2 5 / R V M / 1 9 55 57 0 0 0 3 3 3 3 0 , 6 4 1 9 82 F 1 - 5 0 0 / 2 5 / R V M / 2 1 51 0 9 0 0 0 3 10 3 1 , 6 0 7 7 G3 F 2 - 5 0 0 / 2 5 / R V M / 2 2 52 13 0 0 0 2 5 3 3 1 , 6 6 2 8 53 F 1 - 5 0 0 / 3 0 / R V M / 2 5 54 26 0 0 0 3 2 6 31 , 6 6 2 8 7 9 cr. o ( C - s t r a i n i n c o n c r e t e a t p e a k l o a d ( f c ' ) E c - m o d u l u s o f e l a s t i c i t y o f c o n c r e t e f c ' - c o n c r e t e c o m p r e s s i v e s t r e n g t h f r - m o d u l u s o f r u p t u r e o f c o n c r e t e (Mpa) 10 1(68-95) S T R A I N F I G . 2-7 S T R E S S - S T R A I N R E L A T I O N S H I P O F P L A I N & F I B E R - R E I N F O R C E D C O N C R E T E (KN) 0 0 5 00 0-15 DISPLACEMENT(IN) FIG.2-8 LOAD-DEFLECTION RELATIONSHIP OF PLAIN & FIBER-REINFORCED CONCRETE 63 c u r v e s a l s o i n d i c a t e an a p p a r e n t l y d u c t i l e ' b e h a v i o u r , a n d a l a r g e r e n e r g y a b s o r p t i o n c a p a c i t y f o r f i b e r r e i n f o r c e d c o n c r e t e c o m p a r e d t o p l a i n c o n c r e t e . T h e t o u g h n e s s i n d e x ( 8 1 ) c a l c u l a t e d a s t h e a r e a u n d e r t h e l o a d d e f l e c t i o n c u r v e u p t o 0 . 0 7 5 i n . (1 .9mm) d i v i d e d by t h e a r e a u n d e r t h e l o a d d e f l e c t i o n c u r v e up t o t h e f i r s t c r a c k d e v e l o p m e n t r a n g e s f r o m 8 . 5 t o 1 2 . 8 ; w h e r e a s f o r p l a i n c o n c r e t e s p e c i m e n s , i t was o n e , a s t h o s e f a i l e d i m m e d i a t e l y a f t e r d e v e l o p m e n t o f t h e f i r s t c r a c k . 2 . 8 . 2 S t e e l f o r M a i n R e i n f o r c e m e n t D e f o r m e d r e i n f o r c i n g b a r s o f G r a d e 6 0 w e r e u s e d a s t h e m a i n r e i n f o r c e m e n t ( t e s t b a r ) a s w e l l a s f o r o t h e r r e i n f o r c e m e n t s , i n c l u d i n g t h e t r a n s v e r s e r e i n f o r c e m e n t ( h o o p s ) . The d e f o r m a t i o n p a t t e r n a n d g e o m e t r y , s u c h a s r i b h e i g h t , s p a c i n g , a n d so o n , o f t h e t e s t b a r a r e i n d i c a t e d i n F i g . 2 . 9 ; F I G . , 2.9 DEFORMATION PATTERN FOR REBAR T e s t s w e r e c a r r i e d o u t t o a s c e r t a i n t h e m e c h a n i c a l p r o p e r t i e s o f t h e r e i n f o r c i n g b a r u n d e r u n i a x i a l t e n s i l e l o a d a n d t h e s e a r e t a b u l a t e d i n T a b l e 2 . 3 . C o m p r e s s i o n t e s t s on b a r s a m p l e s r e v e a l e d p r a c t i c a l l y t h e same b e h a v i o u r a s t e n s i l e l o a d i n g a n d 64 hence, the r e s u l t s have not been reproduced. The s t r e s s - s t r a i n behaviour of the r e i n f o r c i n g s t e e l under monotonic as we l l as under r e v e r s e d c y c l i c l o a d i n g i s shown i n F i g . B.1 (Appendix B). The h y s t e r e t i c curves of the r e i n f o r c i n g s t e e l were p l o t t e d based on readings of the s t r a i n gauges l o c a t e d on the r e i n f o r c i n g bar j u s t o u t s i d e the co n c r e t e . The h y s t e r e t i c behaviour of the r e i n f o r c i n g s t e e l i n d i c a t e s pronounced s t i f f n e s s d e g r a d a t i o n , due to Bauschinger e f f e c t f o r reversed c y c l i c l o a d i n g . A m a t e r i a l model f o r the r e i n f o r c i n g s t e e l bar i s d e s c r i b e d i n d e t a i l i n Appendix B. 2.8.3 S t e e l F i b e r s I t was p o s t u l a t e d that s t e e l f i b e r s added to the concrete matrix would improve the anchorage bond c a p a c i t y . T h i s i s e s p e c i a l l y important i n a beam-column j o i n t , where severe overloads due to seismic f o r c e s may cause d r a s t i c r e d u c t i o n s in st r e n g t h and s t i f f n e s s , p r i m a r i l y due to severe bond deg r a d a t i o n , which c o u l d l e a d to exce s s i v e f i x e d end r o t a t i o n , f a i l u r e of the j o i n t , and e v e n t u a l l y the c o l l a p s e of the s t r u c t u r e . The c u r r e n t design p r a c t i c e s and code recommend the p r o v i s i o n of o r t h o g o n a l l y p l a c e d reinforcement i n the beam-column j o i n t . Sometimes, the severe congestion of reinforcement in the beam-column j o i n t poses problems i n placement and v i b r a t i o n of concre t e i n the j o i n t . With the use of s t e e l f i b e r s , i t was hoped that t h i s p r a c t i c a l problem c o u l d be overcome while s t i l l p r o v i d i n g a j o i n t that would be e f f i c i e n t and economical. However, there are a few l i m i t a t i o n s , such as the maximum volume 'concentration of f i b e r s and the maximum s i z e 65 of aggregate, as these a f f e c t the w o r k a b i l i t y of concrete to a great e x t e n t . In the present research, two types of s t e e l f i b e r s were used. These were Bekaert s t e e l f i b e r s with crimped ends, 50mm and 30mm long, having the trade names Wirand and Dramix, r e s p e c t i v e l y . They were provided c o l l a t e d with a water s o l u b l e s i z i n g , so that they would be both easy to handle, and would d i s p e r s e adequately when mixed with the c o n c r e t e . The d e t a i l s of these s t e e l f i b e r s are i n d i c a t e d i n F i g s . 2.6. The aspect r a t i o s f o r the 50mm and 30mm long f i b e r s were 100 and 60 r e s p e c t i v e l y . The aspect r a t i o i s d e f i n e d as the r a t i o of leng t h to diameter of the s t e e l f i b e r s . The s t e e l f i b e r s were made of s t r a i n hardened m i l d s t e e l wires having u l t i m a t e s t r e n g t h s ranging from 1180-1380 MPa (as per the in f o r m a t i o n f u r n i s h e d by the s u p p l i e r s ) . However, the f i b e r s t r e n g t h s were not v e r i f i e d . 2.9 INSTRUMENTATION The experimental measurement of f o r c e s , displacements and s t r a i n s at v a r i o u s p o i n t s along the r e i n f o r c i n g bar was necessary. The s t r a i n r e c o r d i n g s were made p o s s i b l e using e l e c t r i c r e s i s t a n c e s t r a i n gauges. Displacements were measured r e l a t i v e to the c e n t e r - l i n e of the specimen, using l i n e a r v a r i a b l e d i f f e r e n t i a l t ransformers (LVDT) (see F i g . 2.10) with a maximum t r a v e l d i s t a n c e of 12mm. Using a data a c q u i s i t i o n system, i t was p o s s i b l e to rec o r d displacements with reasonable accuracy. The measurements were made to the nearest 0.0001 inches (0.0025mm). The loa d measurement was done by using 66 Concrete Glue Specimen E E o o cn •5P0mm — r PLAN Magnetic Clomp LVOT .-MS Flat tightly / fixed to Load Cell •Load Cell ® LVOT Concrete Specimen MS Flat glued to Specimen Mognetic Clamp .JH 'Load Cell ELEVA'T ION Note: S i m i l a r Arrangement on S. S i d e . FIG. 2-10 INSTRUMENTATION FOR MEASUREMENT OF DISPLACEMENT 67 c a r e f u l l y c a l i b r a t e d load c e l l s i n c o r p o r a t e d ' i n t o the h y d r a u l i c rams. 2.9.1 Test Bar Instrumentation From the experience of t e s t i n g the e x p l o r a t o r y specimens, i t was concluded that probably the best l o c a t i o n of the s t r a i n gauges would be on the pe r i p h e r y of the t e s t bar. Th e r e f o r e , the r e i n f o r c i n g bars f o r the bond t e s t s were machined on d i a m e t r i c a l l y opposite s i d e s along t h e i r l e n g t h , and grooves of 2.5x6.Omm f o r the 25mm and 30mm diameter t e s t bars, and 2.0x6.0mm f o r the 20mm diameter t e s t bars, were made. The p r o v i s i o n was a l s o made f o r placement of a t h i n m e t a l l i c s t r i p as a cover f o r the groove, by some s l i g h t a d d i t i o n a l machining on both s i d e s of the groove. A threaded connector was welded to each end of the r e i n f o r c i n g bar as shown i n F i g . 2.11. LOAD C E L L CONNECTION REBAR CONNECTION FIG. 2.11 L O A D C E L L CONNECTION TO REBAR Due care was a l s o taken to ensure that the l o n g i t u d i n a l a x i s of the threaded connectors, a t both ends, c o i n c i d e d with that of the r e i n f o r c i n g bar. 6 8 2.9.2 Mounting of S t r a i n Gauges The s t r a i n gauges used i n the t e s t specimens were high e l o n g a t i o n e l e c t r i c r e s i s t a n c e gauges of the type EP-08-250 BG120. 2 The performance of t h i s type of gauge was found to be s u p e r i o r compared to the type CEA-06-062-UW-120 which was used i n the e x p l o r a t o r y t e s t specimens. The l a t t e r type was found u n s a t i s f a c t o r y f o r post y i e l d s t r a i n measurements of the r e i n f o r c i n g bar and hence c a l l e d f o r a change in the s e l e c t i o n of s t r a i n gauges. The s t r a i n gauges were mounted on d i a m e t r i c a l l y opposite s i d e s of the t e s t bar at a spacing of 37.5mm as may be seen i n F i g . 2.12. T h i s was intended to take care of the bending e f f e c t , i f any, i n the r e i n f o r c i n g bar. One set of s t r a i n gauges was a l s o f i x e d on e i t h e r end of the r e i n f o r c i n g bar, j u s t o u t s i d e the co n c r e t e , to r e c o r d the a p p l i e d push-in or p u l l - o u t f o r c e s on the r e i n f o r c i n g bar. The f i x i n g of the s t r a i n gauges to the r e i n f o r c i n g bar was done with utmost care and as per the i n s t r u c t i o n s provided by the s u p p l i e r s . F i r s t of a l l , the r e i n f o r c i n g bar was sand-b l a s t e d , and then a i r - b l a s t e d to remove any d i r t or grease. Chlorothene NU was a p p l i e d i n the groove to c h e m i c a l l y remove the grease, f o l l o w e d by C o n d i t i o n e r - A and N e u t r a l i z e r - 5 . A f t e r the s u r f a c e was made dry, the t e n t a t i v e p o s i t i o n of the s t r a i n -gauges was marked in the groove and the cementing m a t e r i a l , M-Bond type AE-15 Adhesive, was a p p l i e d i n the a p p r o p r i a t e p l a c e s . 2 S t r a i n Gauges and other a c c e s o r i e s s u p p l i e d by Micro-Measurement D i v i s i o n , Measurement Group, North C a r o l i n a . 69 12 5 -A Inv.^r": ^ i '2 3 4 5 6 7 8 9 10 M 13 14 15 16 17 18 192021 y v V, A L » . . 500 J 22 1 SPECIMEN P-RV/4 1 ' 2 3 4 5 3 6 7 8 9 10 II 12 13 14/ 15 - i 12.5 > f t t T 20/37.5 37.5 SPECIMENS / - I P-RV/5, P-RV/6, F2-RV/8, F2-RV/9, F2-MO/10, FI-RP/II.FI- M0/I2,FI-RVM/I3,F2-RVM/I4,F2-RVM/I5, FI-RV/I6, F2 - RV/17, F 2 - M0/I8, F2 - RVM/19, FI-RVM/25 / 2 3 4 5 6 7 8 9 I 0 I I 3 12 13 14/ 1 5 ^8 37.5 37.5 37.5 SPECIMENS 1 P-RVM/20, Fl - RVM/21, F2-RVM/22 f - < 18.75 Jziiihi 37.5 4 I Note: A l l dimensions i n mm. SPECIMENS P-RVM/23,P-RVM/24 FIG. 2-12 STRAIN GAUGE LOCATION FOR VARIOUS SPECIMENS 70 With the h e l p of mylar tape, the s t r a i n gauges were a f f i x e d in the groove. Pressure was a p p l i e d by means of s p r i n g clamps and c u r i n g was done in an e l e c t r i c oven at 200°F f o r about 30 minutes. The s o l d e r t i p s were att a c h e d to the gauges and a f t e r c l e a n i n g with Rosin s o l v e n t and a i r - b l a s t i n g , l e a d wires were connected by s o l d e r i n g to the s t r a i n gauge t i p s . For each specimen, the l e a d wires connecting h a l f the s t r a i n gauges were taken out at each end of the bar through the grooves. Then a p r o t e c t i v e c o a t i n g of type M-Coat G was a p p l i e d on the s u r f a c e to p r o t e c t a g a i n s t weathering. F i n a l l y , the grooves were covered with a s t r i p of g a l v a n i z e d i r o n sheet to which l u b r i c a t i n g m a t e r i a l was a p p l i e d on the underside of the s t r i p to a v o i d p u l l i n g out of the lead wires due to f r i c t i o n . Both of the s t r i p s were h e l d t i g h t l y by means of wires at i n t e r v a l s along the r e i n f o r c i n g bar. Each l e a d wire was numbered to i d e n t i f y the s t r a i n gauge and i t s l o c a t i o n along the l e n g t h of the bar. 2.10 FABRICATION OF TEST SPECIMENS The formwork for the c o n c r e t e specimens c o n s i s t e d of plywood and 50x100mm (nominal) lumber b o l t e d together f o r easy and e f f i c i e n t s t r i p p i n g . Care was taken to prevent any leakage through the j o i n t s and to keep the forms square and t r u e . The forms were o i l e d , and the r e i n f o r c i n g cage along with the s p i r a l reinforcement t i e d to i t was p r o p e r l y l o c a t e d . The t e s t bar with the s t r a i n gauges f i x e d to i t was supported i n the formwork through h o l e s p r o v i d e d f o r that purpose. The d e t a i l s of the reinforcement cage -and the forms are shown i n F i g . 2.13. 72 The cement, aggregate, and s t e e l f i b e r s were weighed and s t o r e d s e p a r a t e l y in c o n t a i n e r s . A pan-type mixer was used and a l l c o n c r e t e i n g r e d i e n t s were added i n the order, cement, coarse aggregate, sand, and water followed by two admixtures: a water reducer, P o z z o l i t h 300N and an a i r - e n t r a i n i n g agent (MB-VR). In the case of the f i b e r r e i n f o r c e d concrete specimens, s t e e l f i b e r s were added by shaking them through a s i e v e , and the concrete was mixed for about 2 to 3 minutes. The concrete was then p l a c e d i n t o the formwork and compacted by means of an immersion v i b r a t o r . Care was taken not to d i s t u r b the reinforcement cage d u r i n g placement and v i b r a t i o n of the c o n c r e t e . F i n a l l y , the specimens were f i n i s h e d with a t r o w e l . Test c y l i n d e r s (100x200mm) and prisms (100x100x350mm) were a l s o c a s t from each mix. The forms were removed two days a f t e r c a s t i n g and the specimens were covered with wet b u r l a p and cured f o r a p e r i o d of two weeks. They were then s t o r e d in a i r t i l l t e s t i n g . 2.11 TESTING SET UP AND TESTING SYSTEM 2.11.1 Loading System An MTS s e r v o - c o n t r o l l e d l o a d i n g system was used f o r the c y c l i c bond t e s t s . Readings from a l l the s t r a i n gauges and LVDTs c o u l d be recorded using a Vidar Data A c q u i s i t i o n system and a PDP-11 Mini Computer. The t e s t system i s shown s c h e m a t i c a l l y i n F i g . 2.14. The MTS system i s a c l o s e d - l o o p servo c o n t r o l l e d two channel system u t i l i z i n g a h y d r a u l i c power supply. The Br idge Completion C i r c u i t s & STRAIN GAUGES 5 STRAIN GAUGES 5 STRAIN GAUGES 5 STRAIN GAUGES 5 STRAIN GAUGES 10 STRAIN GAUGES 10 STRAIN GAUGES BRIDGE BOXES POWER SUPPLY EX - VOLTS 0 0 0 OU I I II • O i l I 0 0 k 0 D 0 UI • • • • VIDAR (Data Acquisition) 40 STRAIN GAUGES + 4 LVOTS CONCRETE SPECIMEN JACK # l POP II I COMPUTEHI a n fir3 a a a a MTS CONTROL ( L o a d i n g ) (Oala Analysis and Processing FI6.2.14TEST SYSTEM Ik h y d r a u l i c a c t u a t o r which serves as a f o r c e g e n e r a t i n g and/or p o s i t i o n i n g device i s c o n t r o l l e d by the servo v a l v e i n response to a c o n t r o l s i g n a l . The loa d or displacement a p p l i e d by a h y d r a u l i c a c t u a t o r i s sensed by tra n s d u c e r s , which provide s i g n a l s to transducer c o n d i t i o n e r s which supply e x c i t a t i o n v o l t a g e s and c o n d i t i o n the transducer output v o l t a g e to D.C. l e v e l s . The output of a p a r t i c u l a r transducer c o n d i t i o n e r i s s e l e c t e d by a feed back s e l e c t o r and s u p p l i e d to a Command Input Module which attenuates the s e l e c t e d feed back s i g n a l and compares i t to a program command s i g n a l . As the program command and feed back s i g n a l s become equal, the c o n t r o l s i g n a l a p p l i e d to the servo valve decreases to zero and the loop becomes balanced. 2.11.2 Data A c q u i s i t i o n and Data P r o c e s s i n g Computer programs were w r i t t e n f o r data a c q u i s i t i o n and for p r o c e s s i n g t e s t data sent from the V i d a r to the PDP-11 Computer. Data f o r each specimen was s t o r e d i n separate f i l e s on the PDP-11 d i s c . Before each t e s t , c a l i b r a t i o n data from LVDTs and Load C e l l s , and gauge f a c t o r s f o r s t r a i n gauges, were entered i n t o the computer program. The v o l t a g e s measured by the V i d a r were then d i r e c t l y converted i n t o the d e s i r e d u n i t s , and s e l e c t e d values were p r i n t e d by the computer duri n g the t e s t . Data p r o c e s s i n g was completed a f t e r the t e s t was f i n i s h e d . 75 2.12 LOAD HISTORY There were four b a s i c types of l o a d i n g h i s t o r i e s a p p l i e d to the t e s t specimens. E x c l u d i n g the four e x p l o r a t o r y specimens, f i v e specimens were t e s t e d i n reversed c y c l i c l o a d i n g (RV), in which f o r each incremental i n c r e a s e i n the peak l o a d i n g , only one c y c l e was a p p l i e d ; three specimens were t e s t e d in monotonic l o a d i n g (MO), two specimens were t e s t e d i n repeated l o a d i n g (RP), and the remaining ten specimens were t e s t e d i n reversed c y c l i c (RVM) l o a d i n g i n which m u l t i p l e c y c l e s were a p p l i e d f o r each incremental i n c r e a s e i n the peak l o a d i n g . In a l l cases, the amplitudes of l o a d i n g on the push-in s i d e and the p u l l - o u t s i d e were maintained e q u a l . The d e t a i l s of the l o a d i n g h i s t o r y f o r each specimen are d e s c r i b e d on Table 2.6 and F i g . 2.15. The s i n u s o i d a l l o a d i n g , used i n the t e s t s , has been shown as s t r a i g h t l i n e s between the peak values f o r ease of p r e s e n t a t i o n in Table 2.6 and F i g . 2.15. A constant r a t e of l o a d i n g (1.1kN/sec) was used f o r a l l the specimens. The l o a d i n g f o r each specimen was continued t i l l complete f a i l u r e i n anchorage of the r e i n f o r c i n g bar took p l a c e , or the bar f a i l e d i n t e n s i o n . 2.13 TEST PROCEDURE The t e s t frame shown i n d e t a i l i n F i g . 2.2, was designed f o r a maximum load c a p a c i t y of ±100 kips(±445 kN). The specimens were mounted i n the frame with the r e i n f o r c i n g bar h o r i z o n t a l . The bar was loaded through the threaded connectors welded to the bar, which were b o l t e d to the load c e l l s of the j a c k s . The arrangement was such that an equal push-in load at one end of the bar .and p u l l - o u t l o a d at the other end c o u l d be TABLE 2.6 TYPES OF LOADING HISTORY Specimen No. Loading Type Load vs. Cycles (Typ ica l ) P-500/25/RV/5 % A A A P-5O0/25/RV/6 t/l A A A A A l\ l\ l\ F2-50O/25/RV/8 RV W tr 1JAAMA/\/\ L\ / I /1 /1 F1-500/25/RV/16 4/1 F2-50O/25/RV/17 ' V V F2-500/25/MO/10 A F1-50O/25/M0/12 MO «A F2-500/25/MO/18 *rt UJ or / \ F2-500/25/RP/9 RP . A A A A F1-500/25/RP/11 'STRESS. F1-5O0/25/RVM/13 F2-500/25/RVM/14 F2-500/25/RV/15 F2-5UO/25/RVM/19 i P-50O/25/RVM/2O RVM F1-50O/25/RVM/21 Itl a F2-50O/25/RVM/22 i -tn »i KwiAlnl /• 1 / T 1 / • 1 /t \ ho \ /II \ / « \ /1» C Y C L E S - * P-375/20/RVM/23 P-375/20/RVM/24 F1-500/30/RVM/25 LL 79 a p p l i e d s i m u l t a n e o u s l y , as shown s c h e m a t i c a l l y i n F i g . 2.3(d), and r e v e r s e d s i m u l t a n e o u s l y . For any specimen, the f i r s t l oad c y c l e was ±1Okips(±44.5kN). For specimens with ungrooved bars the peak l o a d i n g s were then i n c r e a s e d to ±20kips(±89kN),±30kips(±135kN),±40kips(±178kN),±4 5kips(±200kN), ±4 9kips(±207.9kN),±51kips(±2 26.8kN),±53kips(±2 35.9kN), ±55kips(±244.6kN),±57kips(±2 53.5kN),±59kips(±2 62kN), ±60kips(±266.9kN),±62kips(±275.8kN),±64kips(±284.7kN), or u n t i l f a i l u r e o c c u r r e d . For specimens with grooved bars, the peak l o a d i n g s were s u i t a b l y reduced to match up with the corresponding a p p l i e d s t r e s s l e v e l s f o r specimens with ungrooved bars. A l l specimens except those s u b j e c t e d to monotonic l o a d i n g s were t e s t e d under lo a d c o n t r o l u n t i l about the y i e l d s t r e s s i n s t e e l and then switched over to displacement c o n t r o l . Because i t i s not p o s s i b l e to study the f a l l i n g branch of an a p p p l i e d s t r e s s - d i s p l a c e m e n t curve under load c o n t r o l , specimens sub j e c t e d to monotonic l o a d i n g were t e s t e d under displacement c o n t r o l r i g h t from the beginning. For each peak load l e v e l , anywhere from one to ten c y c l e s were run before the load was i n c r e a s e d to the next peak. With regard to the r a t e of l o a d i n g , the l o a d c o n t r o l l e d as w e l l as the displacement c o n t r o l l e d l o a d i n g system pr o v i d e d a q u a s i - s t a t i c l o a d i n g arrangement. T h i s was necessary to f a c i l i t a t e r e c o r d i n g the s t r a i n s and load/displacement values at any i n s t a n t , by w i t h h o l d i n g the load/displacement momentarily. For s t e e l , i n c r e a s e d speed does not appear to have so much e f f e c t upon the u l t i m a t e s t r e n g t h as 80 upon the y i e l d s t r e n g t h . The concrete undergoes an i n c r e a s e in s t r e n g t h and modulus of e l a s t i c i t y with higher s t r a i n r a t e s . These aspects however may be c o n s i d e r e d as secondary e f f e c t s . As the l o a d i n g on the specimen progressed, a c a r e f u l watch was maintained to note the appearance of cracks on the s u r f a c e of the specimen. The l o a d i n g was continued t i l l f a i l u r e of the specimen took p l a c e . A f t e r each t e s t , the general behaviour of the specimen under t e s t was noted. 81 I I I . EXPERIMENTAL RESULTS: 3.1 INTRODUCTION T h i s chapter d e s c r i b e s i n d e t a i l the t e s t r e s u l t s obtained i n t h i s study. The data w i l l be grouped as f o l l o w s : 1. E x p l o r a t o r y Test R e s u l t s 2. Specimens Under Monotonic Loading (MO) 3. Specimens Under Repeated Loading (RP) 4. Specimens Under Reversed C y c l i c Loading (RV) 5. Specimens Under Reversed M u l t i p l e C y c l i c Loading (RVM) Out of a t o t a l of twenty-four specimens t e s t e d , four were e x p l o r a t o r y ones; two were t e s t e d under repeated l o a d i n g , three under monotonic l o a d i n g , f i v e under reversed c y c l i c l o a d i n g and ten under re v e r s e d m u l t i p l e c y c l i c l o a d i n g . The r e s u l t s w i l l i n c l u d e the f o l l o w i n g c h a r a c t e r i s t i c s of the specimens, which are d e s c r i b e d b r i e f l y f o r convenience. 3.1.1 A p p l i e d Stress-Displacement R e l a t i o n s h i p In a l l of the t e s t s , the specimens were sub j e c t e d to equal magnitudes of push-in and p u l l - o u t loads a p p l i e d to the two p r o t r u d i n g ends of the t e s t bar. A x i a l displacements of the t e s t bar at both ends with r e s p e c t to the c e n t r e l i n e of the specimens were recorded as the average readings of two LVDTs on each of the North and South faces of the specimens ( F i g . 2.10). Thus, two s e t s of a p p l i e d s t r e s s - d i s p l a c e m e n t curves were obtained f o r each specimen t e s t e d . I t may be mentioned here that s i n c e LVDTs were l o c a t e d at a d i s t a n c e of 60mm from the o u t s i d e end of a specimen, the displacements measured i n c l u d e d 82 the a x i a l deformations of the 60mm l e n g t h of the bar. However, no c o r r e c t i o n f o r t h i s a d d i t i o n a l deformation was necessary when a comparative study of the behaviour of the specimens was done. For each specimen, the a p p l i e d s t r e s s - d i s p l a c e m e n t curves were p l o t t e d by Calcom p l o t t e r from the data s t o r e d i n the d i s c during t e s t i n g and some by manual p l o t t i n g . The a p p l i e d s t r e s s - d i s p l a c e m e n t r e l a t i o n s h i p d e s c r i b e s the o v e r a l l performance of a specimen. F u r t h e r , the energy d i s s i p a t e d by an anchored bar embedded i n concrete can be evalu a t e d from the area under the h y s t e r e s i s loops. For convenience, the a p p l i e d s t r e s s - d i s p l a c e m e n t curves f o r each h a l f c y c l e have been d i v i d e d i n t o three stages ( F i g s . 3. 1(a) & ( c ) ) : Stage I - Loading from zero to 60 k s i (414 MPa) which represents the nominal y i e l d s t r e s s l e v e l f o r the r e i n f o r c i n g bar. Stage II - Loading from 60 k s i (414 MPa) to the peak s t r e s s l e v e l . Stage I I I - Unloading from the maximum peak s t r e s s l e v e l to zero l o a d . The d e f i n i t i o n s of the terms used are given below: Loading S t i f f n e s s : The tangent to the a p p l i e d s t r e s s -displacement curve at zero load f o r any c y c l e whether i n t e n s i o n or i n compression ( F i g . 3.1(b)). S t i f f n e s s (KTI,KCI): The slope of the l i n e j o i n i n g the a p p l i e d s t r e s s - d i s p l a c e m e n t curve at zero l o a d and the maximum peak s t r e s s ( i f the a p p l i e d s t r e s s i s l e s s than the y i e l d s t r e s s ) or 83 60 k s i (414 MPa) ( i f the a p p l i e d s t r e s s exceeds the y i e l d s t r e s s ) ( F i g s . 3 . l ( a ) f c ( b ) ) . S t i f f n e s s (KTII,KCII): The slope of the l i n e j o i n i n g the a p p l i e d s t r e s s - d i s p l a c e m e n t curve at 60 k s i (414 MPa) and the maximum peak s t r e s s l e v e l (exceeding y i e l d ) ( F i g . 3.1(a) ). Unloading S t i f f n e s s (KTL,KCL): The slope of the l i n e j o i n i n g the unloading p o r t i o n of the a p p l i e d s t r e s s - d i s p l a c e m e n t curve at maximum peak and zero l o a d ( F i g . 3.1(a) & ( b ) ) . 3.1.2 S t r a i n D i s t r i b u t i o n Diagrams These diagrams were obtained by p l o t t i n g the s t r a i n values recorded by the s t r a i n gauge along the t e s t bar as d e s c r i b e d in Chapter 2. The s t r a i n value f o r each l o c a t i o n was computed by averaging the readings of the two d i a m e t r i c a l l y opposite s t r a i n gauges. The s t r a i n d i s t r i b u t i o n diagrams w i l l be used to e x p l a i n the s t r e s s t r a n s f e r mechanism from the r e i n f o r c i n g s t e e l to the co n c r e t e . 3.1.3 Bond S t r e s s D i s t r i b u t i o n The l o c a l bond s t r e s s values along the r e i n f o r c i n g bar were, computed from the s t r a i n values recorded by the s t r a i n gauges as f o l l o w s : (o - 0 ) u i j • 4 A x " ~ ° C 3 ' 1 ) where u.(. = average bond s t r e s s between i and j l o c a t i o n s at the s t e e l - c o n c r e t e i n t e r f a c e . a, = s t e e l s t r e s s at i th l o c a t i o n . i * (a) T y p i c a l A p p l i e d S t r e s s Displacement Curve (0A > 60KSI (414Mpa) (b) T y p i c a l Applied Stress -Displacement Curve «TA <60KSI ) FIG. 3.1 TRI LI NEAR MODEL OF APPLIED STRESS Dl SPLACEMENT-CURVE 85 o. = s t e e l s t r e s s at j t h l o c a t i o n . J D = diameter of bar (measured). Ax = l e n g t h of bar between i and j p o i n t . The computation of o from s t r a i n values recorded by s t r a i n gauges mounted on the r e i n f o r c i n g bar, e s p e c i a l l y f o r specimens under reversed c y c l i c l o a d i n g , i s not easy, as the s t r e s s i s h i s t o r y dependent. T h e r e f o r e , a n a l y t i c a l models for the s t r e s s -s t r a i n r e l a t i o n s h i p s f o r the r e i n f o r c i n g s t e e l subjected to c y c l i c l o a d i n g as well as monotonic l o a d i n g were developed, (see Appendix-B) based on the experimental r e s u l t s . A small computer program was w r i t t e n to compute the average bond s t r e s s c orresponding to the s t r a i n v a l u e s . I t should be mentioned here, that the accuracy of p r e d i c t i o n of the l o c a l bond s t r e s s i s dependent on the accuracy of the f o l l o w i n g : ( i ) S t r a i n values recorded by the s t r a i n gauges. ( i i ) Model for the s t r e s s - s t r a i n r e l a t i o n s h i p of r e i n f o r c i n g s t e e l . ( i i i ) C r o s s - s e c t i o n a l area of the r e i n f o r c i n g bar. ( i v ) Spacing of s t r a i n gauges. F u r t h e r , the bond s t r e s s computed from Equation 3.1 i s a l o c a l average value between two c o n s e c u t i v e s t r a i n gauges. However, in r e a l i t y , there may be a high c o n c e n t r a t i o n of bond f o r c e at the i n t e r f a c e i n the c o n c r e t e immediately ahead of the r i b s , because of the wedging a c t i o n between the r i b s of the r e i n f o r c i n g bar and the c o n c r e t e . F u r t h e r , any c r a c k i n g at the i n t e r f a c e may i n c r e a s e the s t r e s s l e v e l i n the bar l o c a l l y to a great e x t e n t . However, in order to o b v i a t e the d i s c r e p a n c i e s as 86 mentioned above, the f o l l o w i n g measures were taken: 1. A f a i r l y a ccurate s t r e s s - s t r a i n model f o r the r e i n f o r c i n g bar was developed to compute s t r e s s e s at any l o c a t i o n along the r e i n f o r c i n g bar. 2. The spacing of s t r a i n gauges was made as c l o s e as p r a c t i c a b l e . 3. The c r o s s - s e c t i o n a l area of the r e i n f o r c i n g bar was a c c u r a t e l y measured to the extent p o s s i b l e . 3.1.4 Surface C r a c k i n g During t e s t i n g , crack formation and propagation were c a r e f u l l y observed and marked on the specimen s u r f a c e s , along with the corresponding a p p l i e d s t r e s s l e v e l s . The emphasis has been p l a c e d on d e s c r i b i n g the crack formation and propagation f o r only one s i d e of the specimen (south side) as the behaviour on the other s i d e was always very s i m i l a r f o r reversed c y c l i c l o a d i n g . 3.1.5 I n t e r n a l Cracking Two of the specimens P-RV/5 and F2-RVM/14 were cut (by means of a diamond saw) l o n g i t u d i n a l l y i n a h o r i z o n t a l plane about 5mm c l e a r of the r e i n f o r c i n g bar, to r e v e a l the i n t e r n a l crack development w i t h i n the specimen, e s p e c i a l l y near the bar-concrete i n t e r f a c e . These w i l l be d e s c r i b e d i n d e t a i l f o r the r e l e v a n t specimens. 87 3.2 EXPLORATORY SPECIMENS A b r i e f summary of the performance of the specimens and the t e s t i n g system, and the reasons which n e c e s s i t e d some changes and m o d i f i c a t i o n s i n the design of the specimens and the t e s t arrangement are d e s c r i b e d below: 3.2.1 Specimen F2-RV/1 O r i g i n a l l y , i t was intended to subject the specimens to equal amounts of push-in and p u l l - o u t loads under displacement c o n t r o l throughout the t e s t . T h e r e f o r e , l o a d i n g under displacement c o n t r o l was t r i e d on t h i s specimen. A f t e r many t r i a l runs, i t was found that automatic equal amounts of l o a d i n g by means of s u i t a b l e displacement feed back c o n t r o l was not p o s s i b l e with the system and f a c i l i t i e s a v a i l a b l e . From the t e s t i n g of the above specimen, i t was concluded that only by means of a manual c o n t r o l , and with the help of an x-y c h a r t r e c o r d e r , c o u l d equal amounts of push-in and p u l l - o u t l o a d be a p p l i e d to the specimen under displacement feed back c o n t r o l . 3.2.2 Specimen F2-MO/2 & F2-MO/3 Both of the specimens were subjected to monotonic p u l l - o u t l o a d i n g from one end only (under l o a d c o n t r o l ) to observe the performance of the system and the behavior of the specimens. In g e n e r a l , the specimens behaved i n a s a t i s f a c t o r y manner. The s t r a i n gauge r e c o r d i n g s were found to be c o n s i s t e n t with the a p p l i e d s t r e s s l e v e l s . However, most of the s t r a i n gauges went out of order beyond about 65 k s i (448 MPa) of a p p l i e d s t r e s s . The specimens developed the f i r s t r a d i a l s p l i t t i n g c r a c k s at 40 to 45 k s i (276 to 310 MPa) and profuse c r a c k i n g on the p u l l - o u t 88 end at about 100 k s i (690 MPa). The bar f o r specimen F2-MO/3 f i n a l l y f a i l e d due to t e n s i l e f a i l u r e at 116 k s i (800 MPa). In view of the f a c t that most of the s t r a i n gauges went out of order at about 65 k s i (448 MPa) and si n c e i t was intended to study the behavior of bond at very high s t r e s s l e v e l , i t was decided to use a high e l o n g a t i o n type s t r a i n gauge (to be d e s c r i b e d l a t e r ) f o r t e s t specimens. 3.2.3 Specimen P-RV/4 Th i s specimen was s u b j e c t e d to reversed c y c l i c l o a d i n g . One c y c l e each was a p p l i e d at peak s t r e s s l e v e l s of 15, 30, 45, 60 k s i (103, 207, 310, 414 MPa) and four c y c l e s were a p p l i e d at 67 k s i (462 MPa). In the 4th c y c l e , the bar at the push-in end f a i l e d suddenly due to premature b u c k l i n g , and the t e s t was stopped. The b u c k l i n g of the bar was due to a r e d u c t i o n i n the a x i a l s t i f f n e s s when the two s p l i t bars s t a r t e d s e p a r a t i n g from each other under r e v e r s a l of l o a d i n g . In g e n e r a l , the behaviour of the specimen under re v e r s e d c y c l i c l o a d i n g was q u i t e good. The f i r s t r a d i a l s p l i t t i n g crack developed on the south face of the specimen at the 42 k s i (290' MPa) s t r e s s l e v e l . Since the bar buckled at about 67 k s i (462 MPa), the s t r a i n values were a v a i l a b l e only up to t h i s s t r e s s l e v e l . On the b a s i s of the t e s t of t h i s specimen, i t was decided to use a s o l i d bar rather than a s p l i t bar because of i t s observed poor performance. 89 3.2.4 Summary Based on the experiences and ob s e r v a t i o n s made during t e s t i n g of the e x p l o r a t o r y specimens, the f o l l o w i n g c o r r e c t i v e measures were made f o r r e s t of the t e s t program: 1. The specimens were redesigned f o r a s o l i d t e s t bar with l o n g i t u d i n a l grooves machined on d i a m e t r i c a l l y opposite faces f o r mounting of s t r a i n gauges. T h i s was done to obv i a t e any b u c k l i n g of the t e s t bar (as experienced f o r specimen P-RV/4). 2. A new type of s t r a i n gauge (EP-08-250 BG 120) was used, which c o u l d r e c o r d the high s t r a i n values that were expected i n the t e s t s . T h i s was done i n c o n s u l t a t i o n with the s u p p l i e r s . 3. The importance of p r e c i s e alignment of the jacks with respect to the c e n t r e l i n e of the t e s t bar was r e a l i z e d . In order to achieve t h i s , some m o d i f i c a t i o n s i n the p o s i t i o n i n g of the specimens were c a r r i e d out so that i t c o u l d not t w i s t or change i t s o r i e n t a t i o n d u r i n g t e s t i n g . 4. The method of t e s t i n g was l i m i t e d to load c o n t r o l before y i e l d i n g in the s t e e l , and then switched over to displacement feed back c o n t r o l t i l l f a i l u r e of the spec imens. 9 0 3.3 TEST SERIES SPECIMENS Since many specimens were t e s t e d under v a r i o u s c a t e g o r i e s of l o a d i n g h i s t o r i e s , i t i s a p p r o p r i a t e to d e s c r i b e i n d e t a i l only one specimen as r e p r e s e n t a t i v e of each category of lo a d i n g - Monotonic (MO), Repeated (RP), Reversed C y c l i c (RV), Reversed M u l t i p l e - C y c l i c (RVM). The p r e s e n t a t i o n of r e s u l t s w i l l i n c l u d e c h a r a c t e r i s t i c s of the r e p r e s e n t a t i v e specimens such as the a p p l i e d s t r e s s - d i s p l a c e m e n t r e l a t i o n s h i p , ' s t r a i n d i s t r i b u t i o n , bond s t r e s s d i s t r i b u t i o n , c r a c k i n g , and so on. The r e s u l t s of a l l other specimens w i l l be presented i n a separate appendix (Appendix-C). However, an attempt w i l l be made to i n t e r p r e t b r i e f l y the r e s u l t s of the r e p r e s e n t a t i v e specimens with r e f e r e n c e to the other specimens under each category. The d e t a i l e d e v a l u a t i o n and i n t e r p r e t a t i o n of the r e s u l t s w i l l , however, be c a r r i e d out i n Chapter 4. 3.3.1 Monotonic Loading (MO) Three specimens (F2-MO/10,F1-MO/1 2,F2-M0/18) Were t e s t e d under monotonic l o a d i n g . Two of the specimens (F2-MO/10,F2-MO/18) con t a i n e d 50mm long s t e e l f i b e r s ; the remaining one (F1-MO/12) con t a i n e d 30mm long s t e e l f i b e r s . The r e s u l t s of specimen F2-MO/18 are d e s c r i b e d below as r e p r e s e n t a t i v e of these three specimens. a. A p p l i e d Stress-Displacement R e l a t i o n s h i p The specimen was subj e c t e d to mono t o n i c a l l y i n c r e a s i n g push-in p u l l - o u t l o a d i n g under displacement feedback c o n t r o l . The a p p l i e d s t r e s s displacement curve f o r both the south and north f a c e s of the specimens are shown i n Fig.3.2. From t h i s 91 FIG. 3.2 APPLIED STRESS DISPLACEMENT RELATIONSHIP FOR F2-MO/18 92 F i g u r e , i t may be seen that up to the y i e l d s t r e s s l e v e l ( i n the r e i n f o r c i n g s t e e l ) , the slopes of the s t r e s s - d i s p l a c e m e n t curves in both cases are q u i t e steep. The slope of the curve on the push- in s i d e i s steeper than that on the p u l l - o u t s i d e . T h i s i s because improved bond c o n d i t i o n s e x i s t on the push i n s i d e . However, beyond about 60 k s i (414 MPa), a sharp r e d u c t i o n i n the slope s of the curves takes p l a c e , followed by a gradual r e d u c t i o n i n the slope, f o r both cases. T h i s i n d i c a t e s a sharp r e d u c t i o n i n a x i a l s t i f f n e s s a f t e r y i e l d i n g of the bar. The displacement on the push-in si d e at a p a r t i c u l a r s t r e s s l e v e l i s observed to be much smaller than that on the p u l l - o u t s i d e . The specimen e x h i b i t e d very good load r e s i s t i n g c a p a c i t y and c o u l d s u s t a i n l o a d even up to ±102 k s i (703 MPa) without p u l l - o u t f a i l u r e . However, at t h i s stage, the specimen was unloaded to avo i d bar f a i l u r e , and was reloaded i n the reverse d i r e c t i o n . It i s i n t e r e s t i n g to note that as the load was reversed, the y i e l d s t r e s s i n compression ( i n s t e e l ) probably was s e v e r e l y reduced due to the Bauschinger e f f e c t . That i s why the a p p l i e d s t r e s s i n compression c o u l d not be in c r e a s e d beyond 79 k s i (545 MPa) and the bar buckled. A comparison of the responses of the other specimens i n t h i s category i n d i c a t e some d i f f e r e n c e s . Up to about 60 k s i (414 MPa), the l o a d i n g s t i f f n e s s f o r F2-MO/18 i s s l i g h t l y higher than F2-MO/10 and F1-MO/12. However, the slope of the displacement curve beyond 60 k s i (414 MPa) remains p r a c t i c a l l y the same f o r a l l the specimens. The reason f o r the higher i n i t i a l s t i f f n e s s f o r F2-MO/18 may be due to i t s higher concrete 93 s t r e n g t h (55.6 MPa) as compared to F2-MO/10 and F1-M0/12 (46.8 MPa) The specimen F1-M0/12 ( c o n t a i n i n g the 30mm f i b e r s ) , even a f t e r unloading at i t s maximum peak a p p l i e d s t r e s s l e v e l of 90 k s i (620 MPa)(Fig.3.3), c o u l d be c y c l e d four times at an amplitude of 78 k s i (538 MPa) and s t i l l r e t a i n the c a p a c i t y to s u s t a i n more c y c l e s . However, i t was unloaded and preserved f o r the i n t e r n a l crack study. Specimen F2-MO/10, on unloading at i t s maximum peak s t r e s s l e v e l of 91 k s i (627 MPa), was loaded i n the reversed d i r e c t i o n up to 81 k s i (558 MPa) and then c y c l e d . However, i n the second c y c l e , i t f a i l e d at 78 k s i (538 MPa) due to p u l l - o u t of the bar. T h e r e f o r e i t appeared that the specimen F1-MO/12, c o n t a i n i n g 30mm s t e e l f i b e r s , had somewhat b e t t e r performance than the other specimens c o n t a i n i n g the 50mm f i b e r s . T h i s was due to u n s a t i s f a c t o r y w o r k a b i l i t y of the concrete mix c o n t a i n i n g 50mm long f i b e r s . b. S t r a i n D i s t r i b u t i o n The s t r a i n d i s t r i b u t i o n curves fo r specimen F2-MO/18 are presented i n F i g . 3.4. The slope of the s t r a i n d i s t r i b u t i o n curve fo r a p a r t i c u l a r s t r e s s l e v e l on the push-in side of the specimen seem to be d i f f e r e n t than that on the p u l l - o u t s i d e . The slope of the s t r a i n d i s t r i b u t i o n curve on the push-in si d e appears to be steeper than that on the p u l l - out s i d e , i n d i c a t i n g g r e a t e r bond r e s i s t a n c e on the push-in s i d e . F u r t h e r , the t e n s i l e s t r a i n zone i s observed to be about 10 to 25 percent l a r g e r ( s t r e s s range 276-524 MPa) than that of the compression zone. T h i s i n d i c a t e s that the push-in f o r c e can be 94 8-o CD . LO O = -1 CO d rw CO CO UJ CC I— o CO o Q LU I—I o _ J d - SPEClrtEN F1-H0/12(S) SPECIIIEN F1-M0/12(N) PULL OUT END PUSH IN END 1 .02 2.03'. 3.05 5.08mm — i 1 r D.08 -0.04 T O.Q I 1 1 0.04 0.08 0.12 DISPLfiCEMENT(IN) 0.16 0.2 F I G . 3.3 APPLIED STRESS-DISPLACEMENT DIAGRAM (M0NT0T0NIC LOADING) <X5 tn 1 5 i FIG. 3-4 STRAIN DISTRIBUTION DIAGRAM FOR F2-MO/18 (MONTOTONIC LOADING) 96 t r a n s m i t t e d w i t h i n a much smal l e r l e n g t h than that r e q u i r e d on the p u l l - o u t end. T h i s i s because the concrete on the p u l l - o u t s i d e i s s u b j e c t e d to c r a c k i n g ; the outward deformation of the c o n c r e t e and a r e d u c t i o n i n the diameter of the r e i n f o r c i n g bar caused s e p a r a t i o n and s l i p between the r e i n f o r c i n g bar and the c o n c r e t e . A l l of these f a c t o r s cause greater bond d e t e r i o r a t i o n on the p u l l - o u t end. With a p r o g r e s s i v e i n c r e a s e i n the a p p l i e d s t r e s s l e v e l , a p r o g r e s s i v e i n c r e a s e in the s t r a i n values i s apparent. Beyond the y i e l d s t r e s s l e v e l i n s t e e l , a sharp i n c r e a s e i n the s t r a i n values i s observed f o r the f i r s t few gauges from the p u l l - o u t end, u n l i k e the push-in end. T h i s i s probably due to g r e a t e r d e t e r i o r a t i o n in bond on the p u l l - o u t end than on the push-in end. As the a p p l i e d s t r e s s i s f u r t h e r i n c r e a s e d , gradual p e n e t r a t i o n of y i e l d i n g i s observed from both ends towards the c e n t r e of the specimen. The l e n g t h of y i e l d p e n e t r a t i o n i s observed to be l a r g e r on the p u l l - o u t end, s i n c e severe bond degradation takes p l a c e on the p u l l - o u t end. No comparison was p o s s i b l e with the other two specimens as they d i d not c o n t a i n s t r a i n gauges mounted on the r e i n f o r c i n g bar. c. Bond S t r e s s D i s t r i b u t i o n The bond s t r e s s d i s t r i b u t i o n curves f o r specimen F2-MO/18 at v a r i o u s s t r e s s l e v e l s are shown in Fig.3.5. They show that the peak bond s t r e s s e x i s t s on both ends of the specimen at low a p p l i e d s t r e s s l e v e l s . However, on i n c r e a s i n g the a p p l i e d s t r e s s l e v e l , the peak bond s t r e s s s h i f t s towards the c e n t r e of the specimen. C o n s i d e r i n g the bond s t r e s s Curve 1 (±29.97 k s i F I G . 3-5 BOND STRESS DISTRIBUTION DIAGRAM FOR F2-MO/18 98 [207 MPa] s t r e s s l e v e l ) , the absolute maximum bond s t r e s s of 1.5 k s i (10.3 MPa) e x i s t s at the push-in end, another peak bond s t r e s s of 1.2 k s i (8.3 MPa) occurs at 50mm from the p u l l - o u t end; the bond s t r e s s at the centre i s almost n e g l i g i b l e . On an in c r e a s e i n l o a d i n g to say ±60 k s i (414 MPa) (Curve 3), the bond s t r e s s e s on both ends as w e l l as i n the c e n t r a l region i n c r e a s e c o n s i d e r a b l y . The peak bond s t r e s s at the p u l l - o u t end i n c r e a s e s to about 1.9 k s i (13 .1 MPa) at 110mm from the p u l l - o u t end, whereas at the centre i t i n c r e a s e s to 1.0 k s i (6.9 MPa) and at the push-in end to 2.7 k s i (18.6 MPa) at only 12mm from the push-in end. T h i s i n d i c a t e s that g r e a t e r bond r e s i s t a n c e s t i l l e x i s t s on the push-in end, while severe bond degradation has taken p l a c e on the p u l l out end. F u r t h e r , a r e d i s t r i b u t i o n in the bond s t r e s s curve may a l s o be n o t i c e d . T h i s i s due to a severe r e d u c t i o n in bond r e s i s t a n c e , e s p e c i a l l y at the p u l l - o u t end. T h i s i s expected, because with an i n c r e a s e i n peak l o a d i n g , i n t e r n a l c r a c k i n g ( d i a g o n a l and r a d i a l s p l i t t i n g c r a c k s ) and s l i p between the r e i n f o r c i n g bar and concrete occur which r e s u l t s i n bond de g r a d a t i o n , d. C r a c k i n g The terms used to d e s c r i b e the c r a c k i n g p a t t e r n s f o r a t y p i c a l specimen are shown i n F i g . 3.6. The c r a c k i n g p a t t e r n s f o r specimen F2-MO/18 are shown in F i g . 3.7. As the specimen was subjected to p r o g r e s s i v e l y i n c r e a s i n g l o a d , the f i r s t h a i r l i n e r a d i a l s p l i t t i n g crack o c c u r r e d at the p u l l - o u t end (S. face) of the specimen at the 45 k s i (310 MPa) a p p l i e d s t r e s s l e v e l . With a f u r t h e r i n c r e a s e 99 FIG.3.6 CRACKING PATTERN OF A TYPICAL SPECIMEN 100 in the a p p l i e d load, more r a d i a l c r a c k s occurred, . while l o n g i t u d i n a l c r a c k s formed and extended on the east and west faces of the specimen. At about the 74 k s i (510 MPa) s t r e s s l e v e l , c r a c k s developed around the bar, i n d i c a t i n g wide s e p a r a t i o n between the r e i n f o r c i n g bar and the concrete at the p u l l out end. At 88 k s i (607 MPa) the c i r c u m f e r e n t i a l c r a c k s tended to form at a r a d i u s of about 75 to 90mm from the bar. At t h i s s t r e s s l e v e l , the l o n g i t u d i n a l s p l i t t i n g c r a c k s had extended l i t t l e more than halfway in the East and West faces of the specimen from the p u l l - o u t end. At 97 k s i (669 MPa), the c i r c u m f e r e n t i a l cracks extended and widened a p p r e c i a b l y , but no new r a d i a l s p l i t t i n g c r a c k s formed or extended on the S. face ( p u l l - o u t end). The l o a d i n g was i n c r e a s e d to 102 k s i (703 MPa) and even at t h i s stage, there was no change i n the c r a c k i n g p a t t e r n , except that c r a c k s around the bar and the c i r c u m f e r e n t i a l cracks widened to a great e x t e n t . At t h i s l o a d , no v i s i b l e c r a c k s c o u l d be observed on the N. face (push-in end). Only when the l o a d i n g was reversed and the p u l l - out lo a d on the N. face was i n c r e a s e d d i d the r a d i a l and l o n g i t u d i n a l c r a c k s emerge on the North and E & W faces r e s p e c t i v e l y . These are shown i n F i g . 3.7. At 79 k s i (545 MPa) l o n g i t u d i n a l c r a c k s on the E. and W. faces had extended up to about midway of the specimen. At t h i s l o a d , the r e s i s t a n c e c a p a c i t y of the specimen dropped and the specimen f a i l e d due to p u l l - o u t of the bar. A r e l a t i v e comparison of the v i s u a l c r a c k i n g p a t t e r n s of specimens F2-MO/10, F1-MO/12, F2-Mo/l8 shows that a l l the specimens had e s s e n t i a l l y the same c h a r a c t e r i s t i c s . However, FIG.3.7 CRACKING PATTERN OF SPECIMEN F2-M0/18 102 the c i r c u m f e r e n t i a l c r a c k s were prominently developed f o r specimens F2-MO/10 and F2-MO/18 whereas for specimen F1-MO/12 ( c o n t a i n i n g 30mm f i b e r s ) , the c i r c u m f e r e n t i a l crack was j u s t tending to form. 3.3.2 Repeated Loading (RP) Under t h i s category of l o a d i n g , only two specimens, F2-RP/9 and F1-RP/11 were t e s t e d . These specimens were su b j e c t e d to i n c r e m e n t a l l y i n c r e a s e d repeated l o a d i n g with only one c y c l e f o r each peak amplitude. The r e s u l t s for specimen F-RP/11 are d e s c r i b e d below as r e p r e s e n t a t i v e of the two specimens. These specimens d i d not c o n t a i n s t r a i n gauges and hence the s t r a i n d i s t r i b u t i o n behaviour c o u l d not be s t u d i e d . a. A p p l i e d S t r e s s Displacement R e l a t i o n s h i p The a x i a l a p p l i e d s t r e s s versus displacement at both the push-in and p u l l - o u t ends i s shown in F i g s . 3.8(a)&(b). It can be seen that the responses of these specimens are q u i t e d i f f e r e n t compared to those s u b j e c t e d to monotonic as w e l l as reversed c y c l i c - l o a d i n g (to be d i s c u s s e d l a t e r ) . The slopes of the unloading curves appear to be the same as those of the r e l o a d i n g c u r v e s . A comparison of responses of t h i s specimen with those f o r a specimen subjected to monotonic l o a d i n g (e.g. F1-MO/12) show e s s e n t i a l l y s i m i l a r behaviour. T h i s i n d i c a t e s that the c y c l i n g i n t e n s i o n has no major i n f l u e n c e on the l o a d i n g s t i f f n e s s of the specimen. However, the c y c l i n g caused an i n c r e a s e i n displacements due to the accumulation of damages. The p a t t e r n s of the a p p l i e d s t r e s s displacement curves i n compression seem to be s i m i l a r to those i n t e n s i o n , but with 10A much smal l e r displacements under i d e n t i c a l l o a d i n g . The above two specimens, even a f t e r c y c l i n g up to 81 k s i (558 MPa) ( f o r F1-RP/11) and 91 k s i (627 MPa) ( f o r F2 - R P/9), showed no sign of f a i l u r e . Then, they were unloaded and kept f o r i n t e r n a l crack i n v e s t i g a t i o n s . A comparison with the a p p l i e d s t r e s s displacement r e l a t i o n s h i p of specimen F2-RP/9 shows e s s e n t i a l l y s i m i l a r behaviour up to 68 k s i (469 MPa). However, beyond t h i s s t r e s s l e v e l , i n c r e a s e d displacements were observed f o r specimen F2-RP/9 as compared to those f o r specimen F1-RP/11. b. C r a c k i n g The d e t a i l e d crack p a t t e r n and crack propagation f o r specimen F1-RP/11 with an i n c r e a s e i n a p p l i e d s t r e s s l e v e l i s shown i n F i g . 3.9. For t h i s specimen, the f i r s t r a d i a l s p l i t t i n g crack occurred at an a p p l i e d s t r e s s l e v e l of 40 k s i (276 MPa) on the p u l l - o u t end (S. face) of the specimen. At 53 k s i (365 MPa) a h o r i z o n t a l l o n g i t u d i n a l s p l i t t i n g crack developed on the E. face as an ext e n s i o n of the r a d i a l c r a c k . At 65 k s i (448 MPa), another crack formed around the bar, causing s e p a r a t i o n , i n a d d i t i o n to an a d d i t i o n a l r a d i a l s p l i t t i n g crack and the l o n g i t u d i n a l crack e x t e n s i o n . At 70 k s i (483 MPa) a few more c r a c k s o c c u r r e d . At 81 k s i (558 MPa), a small c i r c u m f e r e n t i a l crack tended to form. In g e n e r a l , even up to 81 k s i (558 MPa) a l l the c r a c k s were h a i r l i n e , except the crack around the bar. At the push- i n end (N. f a c e ) , no v i s i b l e c r a c k s were observed. On the E. and W. faces of the specimen, the l o n g i t u d i n a l c r a c k s had extended more than halfway a c r o s s the specimen, towards the N. f a c e . FIG.3.9 CRACKING PATTERN OF SPECIMEN F 1-RP / 1 1 106 A comparison of the crack p a t t e r n f o r specimens F2-RP/9 and F1-RP/11 r e v e a l s the same crack p a t t e r n s f o r both specimens. There was a s l i g h t d i f f e r e n c e i n the crack p a t t e r n s f o r specimens s u b j e c t e d to monotonic and repeated l o a d i n g . The specimens subjected to repeated l o a d i n g developed e s s e n t i a l l y s i m i l a r c r a c k s at a l e s s e r a p p l i e d load than those under monotonic l o a d i n g . 3.3.3 Reversed C y c l i c Loading (RV) Under t h i s category of l o a d i n g , f i v e specimens were t e s t e d : two with p l a i n concrete (P-RV/5, P-RV/6), two with f i b e r r e i n f o r c e d c o n c r e t e , c o n t a i n i n g 50mm long f i b e r s (F2-RV/8, F2-RV/17) and one with FRC c o n t a i n i n g 30mm long s t e e l f i b e r s ( F l -RV/16). A l l of these specimens were subjected to i n c r e m e n t a l l y i n c r e a s e d c y c l i c l o a d i n g with one c y c l e at each peak amplitude of l o a d i n g . The r e s u l t s of specimen F2-RV/17 are d e s c r i b e d below as t y p i c a l of the specimens t e s t e d under t h i s category of l o a d i n g . However, an attempt w i l l be made to make a b r i e f comparative study of the c h a r a c t e r i s t i c s of the other specimens t e s t e d i n t h i s category. a. A p p l i e d S t e e l Displacement R e l a t i o n s h i p The response of t h i s specimen under f u l l y r e v ersed c y c l i c push-in p u l l - o u t l o a d i n g was found to be e s s e n t i a l l y the same at both ends (S. and N. Faces) and so only one end (N. Face) i s shown i n F i g . 3.10. A f t e r a few e l a s t i c c y c l e s , the specimen was loaded beyond the y i e l d s t r e s s of the bar. The specimen was loaded under l o a d c o n t r o l t i l l i t reached the y i e l d s t r e s s l e v e l 107 -7.11mm-533 -3.56 FIG. 3-10 HYSTERESIS LOOP FOR SPECIMEN F2-RV/17 108 i n the s t e e l , and then was switched over to the displacement feedback c o n t r o l . During the t e s t i n g of the specimen, the response under reversed c y c l i c l o a d i n g was observed to be a l t o g e t h e r d i f f e r e n t from that under monotonic and repeated l o a d i n g . With the r e v e r s a l s of l o a d i n g at a p p l i e d s t r e s s l e v e l s as low as 43 k s i (296 MPa), a s l i g h t p i n c h i n g of the h y s t e r e t i c curves was observed. The l o a d i n g s t i f f n e s s decreased n o t i c e a b l y in the s u c c e s s i v e l o a d i n g c y c l e s , ( r e l e v a n t terms f o r s t i f f n e s s have a l r e a d y been d e f i n e d p r e v i o u s l y i n t h i s C h a p t e r ) . T h i s i n d i c a t e d the onset of bond d e t e r i o r a t i o n even at t h i s s t r e s s l e v e l . However, durin g l o a d i n g below the y i e l d s t r e s s l e v e l , the s t i f f n e s s (KTI or KCI as d e f i n e d i n Sec. 3.1.1) remained e s s e n t i a l l y the same f o r the same peak s t r e s s l e v e l . Loading beyond y i e l d produced a marked r e d u c t i o n in the s t i f f n e s s (KTI or KCI). With an i n c r e a s e i n the number of c y c l e s and peak amplitude of l o a d i n g beyond y i e l d s t r e s s l e v e l , an i n c r e a s e in displacement was observed. The l o a d was g r a d u a l l y i n c r e a s e d to 78 k s i (538 MPa) and a few c y c l e s were run at t h i s s t r e s s l e v e l . I t i s i n t e r e s t i n g to mention here that the p i n c h i n g of the h y s t e r e t i c curve became i n c r e a s i n g l y severe when the load was c y c l e d , though the i n i t i a l 3-4 c y c l e s produced p r a c t i c a l l y no e f f e c t . However, the displacements went on i n c r e a s i n g during those c y c l e s . By the 16th c y c l e , the p i n c h i n g of the h y s t e r e t i c curve was most severe, probably due to the d r a s t i c bond degr a d a t i o n ; t h i s was f o l l o w e d by a drop i n load r e s i s t a n c e c a p a c i t y of the specimen. F i n a l l y , the specimen f a i l e d due to bar p u l l - o u t . T h e r e f o r e , a s i g n i f i c a n t d i f f e r e n c e i n the 109 u l t i m a t e f a i l u r e p u l l - o u t load as compared t o that under monotonic l o a d i n g was observed. The main reason f o r t h i s i s that many reversed c y c l e s at r e l a t i v e l y h i g h amplitudes of l o a d i n g (at l e a s t beyond y i e l d ) caused severe bond degradation at both ends of the specimen. The y i e l d had pen e t r a t e d i n t o the core of the specimen from both ends. Due to a severe i n c o m p a t i b i l i t y of deformations i n the s t e e l and concrete, probably one of the di a g o n a l c r a c k s transformed i n t o a wide c o n i c a l crack which was manifested as a c i r c u m f e r e n t i a l crack on the p u l l - o u t end of the specimen, thus s e v e r e l y reducing the e f f e c t i v e anchorage l e n g t h . T h i s anchorage l e n g t h r e d u c t i o n was v u l n e r a b l e to f u r t h e r bond degradation and caused p u l l - o u t f a i l u r e . b. S t r a i n D i s t r i b u t i o n The s t r a i n d i s t r i b u t i o n curves for specimen F2-RV/17 at v a r i o u s s t r e s s l e v e l s and c y c l e s of l o a d i n g are shown i n F i g . 3.11. I t may be seen that even at a s t r e s s of ±30 k s i (207 MPa), bond d e t e r i o r a t i o n had taken p l a c e at the p u l l - o u t end, i n d i c a t e d by the h o r i z o n t a l p o r t i o n of the s t r a i n curve, whereas at the push-in end the s t r a i n curve has a steep slope, i n d i c a t i n g g r e a t e r bond r e s i s t a n c e . At ±43.5 k s i (300 MPa), r a d i a l s p l i t t i n g c r a c k s developed which would have f u r t h e r aggravated the bond d e t e r i o r a t i o n . An i n c r e a s e i n the peak amplitude of l o a d i n g caused a g r e a t e r slope i n the s t r a i n curve, i n d i c a t i n g p r o g r e s s i v e s t r e s s t r a n s f e r from the r e i n f o r c i n g bar to the c o n c r e t e . One important c h a r a c t e r i s t i c observed i s that an i n c r e a s e i n the peak amplitude of l o a d i n g caused bond S T R A I N ( M I C R O S T R A I N S ) O i l 111 d e t e r i o r a t i o n at a lower s t r e s s l e v e l i n the subsequent c y c l e s . For example, the bond d e t e r i o r a t i o n can be observed from an in c r e a s e in the s t r a i n v a l u e s at ±43.5 k s i (300 MPa), when the peak s t r e s s i n the pre v i o u s c y c l e was i n c r e a s e d t o ±66 k s i (455 MPa). T h i s can be seen from curves 3 and 10 of F i g . 3.11. The number of c y c l e s of l o a d i n g at peak amplitude, e s p e c i a l l y beyond the y i e l d s t r e s s l e v e l , caused bond d e t e r i o r a t i o n which may be observed from the in c r e a s e i n s t r a i n v a l u e s . However t h i s c o u l d not be s t u d i e d f o r t h i s specimen at 79.0 k s i (545 MPa), as most of the s t r a i n gauges went out of order at t h i s s t r e s s l e v e l . From the general trend of the s t r a i n d i s t r i b u t i o n curves, i t seemed that the bond s t r e s s developed on the compression si d e was g r e a t e r than that on the t e n s i o n s i d e at a s i m i l a r s t r e s s l e v e l . F u r t h e r , with an i n c r e a s e i n the peak amplitude of l o a d i n g , the length of the t e n s i l e s t r a i n zone i n c r e a s e d and i n general was about 10 to 20 percent g r e a t e r than that of the compression zone. The maximum y i e l d p e n e t r a t i o n along the r e i n f o r c i n g bar was observed to be about 100mm from the end of the specimens at a maximum s t r e s s l e v e l of ±77 k s i (531 MPa). c . Bond S t r e s s D i s t r i b u t i o n The bond s t r e s s d i s t r i b u t i o n curves f o r specimen F2-RV/17 are shown i n F i g . 3.12 at v a r i o u s peak s t r e s s l e v e l s . As the c a l c u l a t i o n of the bond s t r e s s e s i s based on the s t r a i n v a l u e s , the bond s t r e s s behaviour can be p r e d i c t e d from the s t r a i n diagrams. In f a c t , most of the bond c h a r a c t e r i s t i c s and bond d e t e r i o r a t i o n behaviour have a l r e a d y been e x p l a i n e d in the l i g h t of the s t r a i n diagrams i n the pr e v i o u s pages. 311 113 I t may be seen from F i g . 3.12 that at a p a r t i c u l a r a p p l i e d s t r e s s l e v e l , peak bond s t r e s s e s e x i s t at both ends of the specimens and the absolute maximum always e x i s t s at the push-in end. However, with an in c r e a s e i n a p p l i e d s t r e s s l e v e l , the peak bond s t r e s s e s at both ends as w e l l as at the centre of the specimen i n c r e a s e . F u r t h e r , a r e d i s t r i b u t i o n i n the bond s t r e s s curve may be observed, i . e . the peak bond s t r e s s e s s h i f t inwards owing to bond degradation, e s p e c i a l l y at the p u l l - o u t end. For example, at the ±23 k s i (158 MPa) s t r e s s l e v e l , the absolute maximum bond s t r e s s of 1.3 k s i (9 MPa) e x i s t s at 40mm from the push-in end, another peak bond s t r e s s s of 1.0 k s i (6.9 MPa) e x i s t s 40mm from the p u l l - o u t end, and n e g l i g i b l e bond s t r e s s e s e x i s t at the centre of the specimen. With an inc r e a s e in s t r e s s l e v e l to 66 k s i (455 MPa),the peak bond s t r e s s i n c r e a s e s to 2.3 k s i (16 MPa) at the c e n t r e . T h i s shows that g r e a t e r bond r e s i s t a n c e s t i l l e x i s t e d at the push-in end and grea t e r bond degradation took p l a c e at the p u l l - o u t end. d. C r a c k i n g The d e t a i l s of the crack p a t t e r n f o r specimen F2-RV/17 are shown i n F i g . 3.13. For t h i s specimen, su b j e c t e d to reversed c y c l i c l o a d i n g , two h a i r l i n e r a d i a l s p l i t t i n g c racks f i r s t emerged at the ±43 k s i (296 MPa) s t r e s s l e v e l on the S. Face of the specimen. Up to about 48 k s i (331 MPa) the r a d i a l and l o n g i t u d i n a l s p l i t t i n g c r a c k s developed only were h a i r l i n e c r a c k s . Beyond t h i s , a d d i t i o n a l r a d i a l and l o n g i t u d i n a l s p l i t t i n g c r a c k s developed and e x i s t i n g c r a c k s widened and FIG.3.13 CRACKING PATTERN FOR SPECIMEN F2-RV/17 115 extended. The l o n g i t u d i n a l c r a c k s extended from both ends towards the c e n t r e . At 77 k s i (531 MPa) c i r c u m f e r e n t i a l c r a c k s developed, which widened and extended on the subsequent l o a d i n g to 79 k s i (545 MPa). The i n i t i a l 3-4 c y c l e s at a peak l o a d i n g of 79 k s i (545 MPa) d i d not produce s i g n i f i c a n t crack formation and propagation. However, repeated c y c l i n g at t h i s amplitude of l o a d i n g caused p r o g r e s s i v e widening of the c i r c u m f e r e n t i a l c r a c k s and f i n a l l y the specimen f a i l e d due to bar p u l l - o u t i n the 16th c y c l e . The crack p a t t e r n s on the S. and N. Faces as w e l l as on the E. and W. Faces can be seen to be s i m i l a r . A b r i e f comparison of the c h a r a c t e r i s t i c s of specimen F2-RV/17 with those f o r other specimens (P-RV/5,P-RV/6, F2-RV/8, F1-RV/16) t e s t e d under t h i s category of RV l o a d i n g are summarized below: 1. The a p p l i e d s t r e s s - d i s p l a c e m e n t c h a r a c t e r i s t i c s f o r specimens P-RV/5 (with a grooved bar) and P-RV/6 (with an ungrooved bar) are p r a c t i c a l l y the same. Both the specimens f a i l e d a f t e r reaching 10 and 12 c y c l e s ( t o t a l ) of l o a d i n g , r e s p e c t i v e l y , and a peak load of about 80 k s i (552 MPa). The h y s t e r e t i c responses of F2-RV/8 and F1-RV/16 are a l s o e s s e n t i a l l y the same, and both the specimens f a i l e d a f t e r an equal numbec of c y c l e s ( t o t a l 15 c y c l e s ) , having been subjected to i d e n t i c a l l o a d i n g c o n d i t i o n s . However, specimen F2-RV/17 showed the best performance as i t s u s t a i n e d 16 c y c l e s at the 80 k s i (552 MPa) peak s t r e s s l e v e l . In g e n e r a l , i t may be s a i d that the performance of the SFRC specimens were found to be s u p e r i o r to those of the p l a i n c o n c r e t e ones, as f a r as 116 anchorage bond i s concerned. 2. An examination of the crack p a t t e r n s f o r specimens P-RV/5, P-RV/6, F2-RV/8, F1-RV/16, F2-RV/17 r e v e a l s the f o l l o w i n g : The crack p a t t e r n s f o r P-RV/5 and P-RV/6 are s i m i l a r . The formation of wide c i r c u m f e r e n t i a l c r a c k s with a r a d i u s of about 100mm may be observed f o r both specimens. However, only p a r t i a l c i r c u m f e r e n t i a l cracks formed f o r F2-RV/8, F1-RV/6, F2-RV/17 with smaller r a d i i than those of P-RV/5, P-RV/6, i n d i c a t i n g smaller cone formations. 3.3.4 Reversed C y c l i c Loading with M u l t i p l e C y c l e s (RVM) Under t h i s category of l o a d i n g , ten specimens were t e s t e d : three with p l a i n concrete (P-RVM/20, P-RVM/23, P-RVM/24), four c o n t a i n i n g 50mm long s t e e l f i b e r s (F2-RVM/14, F2-RVM/15, F2-RVM/19, F2-RVM/22) and three with 30mm long s t e e l f i b e r s (F1-RVM/13, F1-RVM/21, F1-RVM/25). Specimens P-RVM/23, P-RVM/24 conta i n e d 20mm diameter t e s t bars with a 375mm embedment leng t h , specimen F1-RVM/25 c o n t a i n e d a 30mm diameter t e s t bar(500mm embedment l e n g t h ) , and the remaining specimens a l l contained a 25mm t e s t bar with a 500mm embedment l e n g t h . The i n t e n t of the study under t h i s category of l o a d i n g was to i n v e s t i g a t e the e f f e c t of the number of reversed c y c l e s . o f l o a d i n g at v a r i o u s peak amplitudes of l o a d i n g , the e f f e c t of diameter and embedment le n g t h of the r e i n f o r c i n g bar, the e f f e c t of a s p i r a l around the the t e s t bar (F2-RVM/22), and f i n a l l y the e f f e c t of s t e e l f i b e r s i n the con c r e t e on bond behaviour. As a r e p r e s e n t a t i v e of the specimens t e s t e d under t h i s category, the observed c h a r a c t e r i s t i c s f o r specimen P-RVM/20 are d e s c r i b e d i n d e t a i l . 117 However, a b r i e f comparative study with the c h a r a c t e r i s t i c s of other specimens t e s t e d i n t h i s category w i l l be made. A d e t a i l e d e v a l u a t i o n and i n t e r p r e t a t i o n of the r e s u l t s w i l l be presented i n Chapter 4. a. A p p l i e d S t r e s s Displacement R e l a t i o n s h i p The a p p l i e d s t r e s s displacement r e l a t i o n s h i p s f o r t h i s specimen on both faces (N. & S. faces) were found to be s i m i l a r ; the r e l a t i o n s h i p on the S. face i s shown i n F i g . 3.14. The a p p l i e d s t r e s s displacement c h a r a c t e r i s t i c s are e s s e n t i a l l y the same as those f o r specimens t e s t e d i n RV lo a d i n g up to about 72 k s i (496 MPa). With r e v e r s a l s of l o a d i n g at a p p l i e d s t r e s s l e v e l s as low as 48 k s i (331 MPa), a s l i g h t p i n c h i n g of the h y s t e r e t i c curves was observed. With two load r e v e r s a l s even at t h i s s t r e s s l e v e l , the l o a d i n g s t i f f n e s s decreased s i g n i f i c a n t l y . T h i s means that the energy absorbing c a p a c i t y of the specimen was being g r a d u a l l y reduced with an i n c r e a s e i n the number of c y c l e s . However, the displacements at the peak loads and the s t i f f n e s s e s (KTI & KCI as d e f i n e d in Sec.3.1.1) d i d not change s i g n i f i c a n t l y at t h i s s t r e s s l e v e l . Loading beyond 60 ks i (414 MPa) produced a d r a s t i c change in s t i f f n e s s and i n d i c a t i o n s of s i g n i f i c a n t displacements. However, 2 c y c l e s of l o a d i n g even at 72 k s i (496 MPa) produced no f u r t h e r n o t i c e a b l e i n c r e a s e i n displacement. On i n c r e a s i n g the peak lo a d to 78 k s i (538 MPa), the displacement caused was again s i g n i f i c a n t . When unloading and r e l o a d i n g i n compression i n the 1st c y c l e (538 MPa), severe p i n c h i n g of the h y s t e r e t i c curve c o u l d be observed. T h i s i n d i c a t e d severe d e t e r i o r a t i o n i n bond. In the second 118 FIG .3-U APPLIED STRESS -DISPLACEMENT DIAGRAM FOR SPECIMEN P-RVM/20 119 c y c l e of running (same amplitude) the l o a d c a r r y i n g c a p a c i t y of the specimen dropped suddenly i n compression and the specimen f a i l e d due to bar p u l l - o u t . b. C r a c k i n g The c r a c k i n g p a t t e r n s on a l l s i d e s of t h i s specimen are d e s c r i b e d i n F i g . 3.15. In g e n e r a l , the c r a c k i n g phenomena observed f o r t h i s specimen were somewhat d i f f e r e n t from those of the specimens c o n t a i n i n g s t e e l f i b e r s . For t h i s specimen, the f i r s t r a d i a l s p l i t t i n g crack was observed at the 48 k s i (331 MPa) peak s t r e s s l e v e l , f o l l o wed by another one i n the 2nd c y c l e . At 60 k s i (414 MPa) one more r a d i a l crack developed and the l o n g i t u d i n a l crack extended to the E. & W. f a c e s . At 72 k s i (496 MPa) a c i r c u m f e r e n t i a l crack formed and the r a d i a l cracks widened. In the 2nd c y c l e , another r a d i a l crack emerged. At 78 k s i (538 MPa) the c i r c u m f e r e n t i a l crack and the r a d i a l c r a c k s , e s p e c i a l l y w i t h i n a r a d i u s of 75mm, widened c o n s i d e r a b l y . In the 2nd c y c l e of the peak amplitude, the load c a r r y i n g c a p a c i t y dropped and the specimen f a i l e d due to bar p u l l - o u t . c. S t r a i n D i s t r i b u t i o n The s t r a i n d i s t r i b u t i o n curves f o r t h i s specimen at v a r i o u s a p p l i e d l e v e l s are presented in F i g . 3.16. The p a t t e r n of the s t r a i n d i s t r i b u t i o n curves i s e s s e n t i a l l y s i m i l a r to that d e s c r i b e d f o r specimens su b j e c t e d to load h i s t o r y RV. Severe bond d e t e r i o r a t i o n c o u l d be observed at the ±60 k s i (414 MPa) s t r e s s l e v e l when the peak load i n the p r e v i o u s c y c l e was i n c r e a s e d to ±72 k s i (496 MPa), (curves 4 & 8) i n d i c a t i n g that FIG.3-15 CRACKING PATTERN FOR SPECIMEN P-RVM/20 ill 122 the l o a d h i s t o r y has a d e f i n i t e e f f e c t on the bond d e t e r i o r a t i o n . Even i n the second c y c l e with a peak a p p l i e d s t r e s s l e v e l of ±48 k s i (331 MPa), there i s some bond d e t e r i o r a t i o n as can be seen from the i n c r e a s e i n the s t r a i n v a l u e s (curves 1 & 3). In the f i r s t c y c l e at the ±72 k s i (496 MPa) s t r e s s l e v e l , the maximum y i e l d p e n e t r a t i o n was about 100mm from the end of the specimen. In g e n e r a l , the bond s t r e s s at the push-in end was found to be higher than that at the p u l l - o u t end f o r a p a r t i c u l a r a p p l i e d s t r e s s l e v e l , as i s evident from the higher s l o p e s of the s t r a i n curves. T h i s may a l s o be seen in F i g . 3.17. A b r i e f comparison of the observed c h a r a c t e r i s t i c s of specimen P-RVM/20 with other specimens t e s t e d under the same load h i s t o r y (RVM) i s summarized below: 1. The a p p l i e d s t r e s s displacement r e l a t i o n s h i p f o r P-RVM/20 as compared to that f o r specimens F2-RVM/19, F1-RVM/21, F2-RVM/22 and F1-RVM/25 (subje c t e d to i d e n t i c a l load c o n d i t i o n s ) i n d i c a t e e s s e n t i a l l y the same displacement up to about 60 k s i (414 MPa). Beyond t h i s s t r e s s l e v e l , the displacement for P-RVM/20 in c r e a s e d s i g n i f i c a n t l y compared to those of the other specimens. T h i s i s due mainly to severe bond d e t e r i o r a t i o n and c r a c k i n g of specimen P-RVM/20. Fu r t h e r , specimen P-RVM/20 f a i l e d i n the 2nd c y c l e and specimen F1-RVM/25 i n the 1st c y c l e at 78 k s i (538 MPa), whereas specimens F2-RVM/19, F1-RVM/21, F2-RVM/22 su s t a i n e d 8, 11 and 8 c y c l e s r e s p e c t i v e l y at the same peak s t r e s s l e v e l . T h i s shows that the specimens with s t e e l 124 f i b e r s have improved bond performance compared to p l a i n c o n c r e t e specimens. The presence of a l a r g e r diameter bar (30mm d i a . ) i s r e s p o n s i b l e f o r the grea t e r bond d e t e r i o r a t i o n and poor performance of specimen F1-RVM/25. 2. A few c y c l e s of l o a d i n g were found to cause bond d e t e r i o r a t i o n even at an a p p l i e d s t r e s s l e v e l of 48 k s i (331 MPa). The e f f e c t of c y c l i n g was a l s o found to inc r e a s e s i g n i f i c a n t l y with an in c r e a s e i n the magnitude of the peak a p p l i e d l o a d . 3.4 SUMMARY OF TEST RESULTS It i s worthwhile at t h i s stage, f o r convenience, to summarize the r e s u l t s obtained form the experimental program. T h i s summary w i l l emphasize the f o l l o w i n g a s p e c t s : 1. A p p l i e d s t r e s s - d i s p l a c e m e n t r e l a t i o n s h i p s 2. S t r a i n - d i s t r i b u t i o n along the r e i n f o r c i n g bar 3. Cracki n g 4. F a i l u r e mode A b r i e f summary of the r e s u l t s of the bond t e s t s i s a l s o t a b u l a t e d i n Table 3.1. 3.4.1 A p p l i e d S t r e s s - d i s p l a c e m e n t R e l a t i o n s h i p s The h y s t e r e t i c behaviour of the specimens i s v i t a l i n e x p l a i n i n g the o v e r a l l response. The experimental r e s u l t s c l e a r l y i n d i c a t e a severe r e d u c t i o n i n s t i f f n e s s and r e s i s t a n c e c a p a c i t y of the specimens under reversed c y c l i c l o a d i n g . A specimen s u b j e c t e d to monotonic l o a d i n g c o u l d s u s t a i n a push-in p u l l - o u t l o a d as high as the 102 k s i (703 MPa) s t r e s s l e v e l (which c o u l d have been in c r e a s e d f u r t h e r ) , whereas an i d e n t i c a l TABLE -3-1  SUMMARY OF RESULTS FOR BOND TEST Spec imen No. f c' (MPa) Loadlng Hi s t o r y A p p l i e d S t r e s s (MPa) C y c l e s ( T o t a l ) Max i mum D1 s p l a c e -men t (mm) A p p l i e d S t e s s at 1st Crack (MPa ) Mode of Fa 11ure Remarks P-500/25/RV/5 50. 26 RV 101 . 3 1 361 . 3 Execes i ve The specimen 20G .6 1 ( R a d i a l s p l 111 ing was cut long-299 .6 1 2.46 s p l i t t i n g & Rebar i t u d i na11y 402 . 7 1 Crack ) pul1 out f o r i n t e r n a l 454 .6 1 ( 10) crac k study 490.8 1 511.5 1 532 .2 1 552 .8 1 542.4 1 P-500/25/RV/6 51 .44 RV 91.0 182 . 7 274 .4 365.4 411.6 448 . 2 466 . 1 484 . 7 502 .6 52 1 . 3 548.2 585 .0 1 (12) 1 .93 320. 3 ( R a d i a l Crack) Execes1ve s p l i t t ing S Rebar pul1 out TABLE - 3.1 CONT'D  SUMMARY OF RESULTS FOR BOND TEST Spec 1 men No. f c ' (MPa) Loading HI s t o r y A p p l l e d S t r e s s Leve 1 (MPa) Cyc1es ( T o t a l ) Max 1 mum D1splace-ment (mm) A p p l i e d S t r e s s at 1st Crack (MPa) Mode of Fa 11ure Remarks F2-500/25/RV/8 46 .61 RV 91.4 ! 274 .4 Execes i ve 182 . 7 1 ( R a d i a l s p l i 11 ing 274 . 4 1 3 . 2 spl i 111ng & Rebar 365.4 1 Crack) pu11 out 4 11.3 1 (15) 448 . 2 1 466 . 1 1 484 .0 1 502.6 1 521 . 3 1 539 . 2 1 548.2 1 566.8 1 584.7 1 F2-500/25/RP/9 47. 16 RP 91.0 182 .7 274 . 4 365.4 411.6 448.2 466 . 1 484 . 7 499.2 539.2 557 .6 585 .0 630.9 1 (18) 3 . 1 274 4 ( R a d i a l s p l 1 t t i ng Crack ) S t i l l c an be c y c l e d (kept f o r c r a c k s t u d y ) TABLE - 3«V CONT'D SUMMARY OF RESULTS FOR BONO TEST Spec imen No. f c ' (MPa) Loading H i s t o r y Peak A p p l i e d S t r e s s Leve 1 (MPa ) C y c l e s ( T o t a l ) Max imura D i s p l a c e -ment (mm) S t r e s s at 1st Crack (MPa) Mode of F a i l u r e Remarks F1-5OO/25/M0/10 46.89 MO 630. 9 1 319.9 ( R a d i a l Spl i t C r a c k s ) Rebar Pul1-out One LVOT was d e t a t c h e d d u r i n g t e s t F1-500/25/RP/11 53.99 RP 91.0 182 . 7 274 . 4 365.4 4 11.6 448 . 2 466 . 1 484 . 7 502 .6 521 .3 539.2 557.6 1 (12) 3.65 275.8 ( R a d i a l sp 1 i 111ng Crack ) S t i l l c o u l d be c y c l e d (kept f o r cr a c k s t u d y ) F1-50O/25/M0/12 47 . 16 MO 621 .6 539 . 2 1 4 (5) 3.28 275.8 ( R a d i a l s p l 1 t t i n g Crack ) Rebar Pul1 out af t e r e x c e s s 1ve s p l 1 t t i n g F1-500/25/RVM/13 46.33 RVM 91.0 210.3 377 . 9 415.8 497 . 8 466. 1 1 1 2 ( 1 5 ) 2 8 1 2.82 289.6 ( R a d i a l s p l 1 t t I n g Crack ) Rebar Pul1 out af t e r e x c e s s i v e s p l i 11 ing F2-500/25/RVM/14 49.09 RVM 91.0 210.3 377.9 415.8 497 . 8 537 .8 1 2 4 (20) 5 4 4 2.3 275 .8 ( R a d i a l sp11111ng Crack ) S t i l l c o u l d be c y c l e d The specimen c u t f o r i nterna1 c r a c k study F2-500/25/RVM/15 49.09 RVM 91.0 210. 3 377 . 9 415.8 497 . 8 537.8 1 1 2 (13) 2 2 5 2.4 337 .9 ( R a d i a l s p 1 i 11 i ng Crack ) Rebar Pul1 out a f t e r exces i ve s p l 1 t t I n g TABLE - 34 CONT'D SUMMARY OF RESULTS FOR BOND TEST Spec 1 men No F1-500/25/RV/16 F2-500/25/RV/17 F2-500/25/MO/18 F2-500/25/RVM/19 P-500/25/RVM/20 f c ' (MPa) 63 .64 55.57 55.57 55.57 50.06 Load i ng HI s t o r y RV RV MO RVM RVM Peak App1i ed S t r e s s Leve 1 (MPa ) 91 182 274 365 4 1 1 448 466 484 502 521 539 557 575 584 103.3 206.6 299.6 402 . 7 454 .6 490. 8 511.5 532 . 2 547 . 5 707 . 4 102 . 206. 330. 413. 495 . 537 . 102 . 206. 330. 4 13. 495 . 537 . Cyc1es ( T o t a l ) ( 15) (24) 1 1 2 2 2 10 ( 18) ( 10) Max i mum D i sp1 ace-men t (mm) 3.39 3.5 2.78 3.63 3 . 76 S t r e s s at 1st Crack (MPa) 275.8 ( R a d i a l s p l i 111ng Crack ) 299 . 2 ( R a d i a l sp 1 i 111ng Crack ) 310.3 ( R a d i a l s p l 1 t t i n g Crack) 289.6 ( R a d i a l sp1111 i ng Crack ) 279 ( R a d i a l sp1i 11 i ng Crack) Mode of Fa i 1 u r e Rebar Pul1 out a f t e r e x c e s s i ve sp 1 i 111 ng Rebar P u l l out a f t e r e x c e s s 1ve s p l i 111ng Rebar Pul1 out a f t e r e x c e s s i ve s p l 1 t t i n g Rebar Pul1 out af t e r e x c e s s 1ve s p l 1 t t ing Rebar Pul1 out af t e r e x c e s s i ve s p l i t t ing Remarks CD The t e s t bar b u c k l e d a f t e r u n l o a d i n g and l o a d i n g at +547.6 MPa TABLE - 3 A CONT'D  SUMMARY OF RESULTS FOR BOND TEST Spec linen No. f c ' L o ading H i s t o r y Peak A p p l l e d S t r e s s Cyc1es ( T o t a l ) Max(mum Oi s p l a c e -ment S t r e s s at 1st Crack Mode of Fa 1 l u r e Remarks F1-500/25/RV/21 51 .09 RVM 102.9 206.6 330.6 413.3 495.9 537 . 2 1 1 2 ( 18) 2 2 10 3.76 310. 3 ( R a d i a l s p l i t t ing Crack) Rebar Pul1 out a f t e r e x c e s s 1ve s p l i 11 i ng F2-500/25/RVM/22 52. 13 RVM 102.9 20G.6 330.6 4 13.3 495.9 537 . 2 1 1 2 (16) 2 2 8 2.95 310. 3 ( R a d i a l s p l 1 t t i n g Crack ) Rebar Pul1 out a f t e r e x c e s s i ve s p l 1 t t 1 n g H e l i x Prov tded around r e b a r P-375/20/RVM/23 49 .92 RVM 99.3 198 .6 320. 3 399. 9 480.6 519.9 1 1 2 (9) 2 2 1 2 .03 320.6 ( R a d i a l s p l 1 t t ing Crack 1 Rebar Pul1 out a f t e r e x c e s s i ve s p l 1 1 1 i n g P-375/20/RVM/24 52.06 RVM 99.3 198 .6 320.3 399 . 9 368.2 1 1 2 (71 2 1 1 . 32 320.6 ( R a d i a l spl1111ng Crack) Rebar Pu11 out a f t e r e x c e s s 1ve s p l i t t ing g r e a s e a p p l i e d on the rebar F1-500/30/RVM/25 54 . 26 RVM 108 . 2 206.5 328 . 5 4 15.1 495 . 3 534 .3 1 1 2 (7) 2 2 1 2 .95 206 . 9 ( R a d i a l s p l 1 t t i ng Crack ) Rebar Pul1 out a f t e r e x c e s s i ve s p l i t t i n g 130 specimen su b j e c t e d to i n c r e m e n t a l l y i n c r e a s e d l o a d i n g with a few c y c l e s of reversed l o a d i n g may f a i l at as low a s t r e s s l e v e l as 78 k s i (538 MPa), i n d i c a t i n g a decrease in l o a d r e s i s t i n g c a p a c i t y of more than 24 percent. T h i s decrease in r e s i s t a n c e c a p a c i t y g e n e r a l l y occurs when the specimen i s loaded to a s u f f i c i e n t l y high s t r e s s l e v e l , (at l e a s t beyond y i e l d ) and a few load r e v e r s a l s are imposed at t h i s s t r e s s l e v e l . The l o s s in r e s i s t a n c e c a p a c i t y i s due to a d e t e r i o r a t i o n i n the s t r e s s t r a n s f e r mechanism, caused by i n e l a s t i c deformation, c r a c k i n g i n the c o n c r e t e , and the Bauschinger e f f e c t i n the r e i n f o r c i n g s t e e l . The r e d u c t i o n i n s t i f f n e s s and the bond d e t e r i o r a t i o n are evident from the severe p i n c h i n g of the h y s t e r e t i c c u r v e s . A few c y c l e s of reversed l o a d i n g even at a s t r e s s l e v e l of 30 to 40 k s i (207 to 276 MPa) causes a n o t i c e a b l e r e d u c t i o n in the l o a d i n g s t i f f n e s s e s , though no s i g n i f i c a n t changes in s t i f f n e s s (KTI, KCI as d e f i n e d i n Sec.3.1.1) are observed. However, an increase i n the load beyond the y i e l d s t r e s s l e v e l c o u l d cause a severe r e d u c t i o n i n the s t i f f n e s s and an i n c r e a s e in the displacement. For specimens s u b j e c t e d to repeated l o a d i n g ( w i t h o u t r e v e r s a l ) , i t appears that the l o a d c y c l i n g probably has no i n f l u e n c e on the l o a d i n g s t i f f n e s s . The slopes of the unloading curves (KTL, KCL) seem to be the same as those of the r e l o a d i n g c u r v e s . The response of a m o n o t o n i c a l l y loaded specimen compared with the envelope curve of a specimen s u b j e c t e d to repeated l o a d i n g i n d i c a t e s s i m i l a r c h a r a c t e r i s t i c s . C lose examination of the h y s t e r e t i c curves of v a r i o u s 131 specimens su b j e c t e d to c y c l i c l o a d i n g r e v e a l s some important c h a r a c t e r i s t i c s which w i l l be d e s c r i b e d i n d e t a i l i n Chapter 5. These i n c l u d e the o b s e r v a t i o n s that the slopes of the unloading curves (KTL or KCL) are e s s e n t i a l l y the same. The bond behaviour or the bond d e t e r i o r a t i o n of specimens s u b j e c t e d to reversed c y c l i c l o a d i n g and repeated l o a d i n g ( w i t h o u t r e v e r s a l ) may be con s i d e r e d analogous to the e f f e c t of a double a c t i n g and a s i n g l e a c t i n g hack-saw, r e s p e c t i v e l y . J ust l i k e the former i s more e f f e c t i v e i n c u t t i n g than the l a t t e r , reversed c y c l i c l o a d i n g causes greater d e t e r i o r a t i o n i n bond than repeated l o a d i n g . 3.4.2 S t r a i n D i s t r i b u t i o n Diagrams The s t r a i n values recorded by the s t r a i n gauges f i x e d to the r e i n f o r c i n g bar are measured d i r e c t l y , and hence are more r e l i a b l e than any p r e d i c t e d r e s u l t s . The s t r a i n d i s t r i b u t i o n diagrams are necessary in e x p l a i n i n g the phenomena of bond d e t e r i o r a t i o n , c r a c k i n g , and s e p a r a t i o n between the r e i n f o r c i n g bar and the c o n c r e t e . Increase i n e i t h e r s t r a i n values (with r e s p e c t to the value at same lo a d i n the pre v i o u s c y c l e ) or the slope of the s t r a i n curve at a p a r t i c u l a r l o c a t i o n along the r e i n f o r c i n g bar i n d i c a t e a r e d u c t i o n in bond s t r e s s . The gene r a l trend of the s t r a i n d i s t r i b u t i o n diagrams f o r the push-in p u l l - o u t type of l o a d i n g i n d i c a t e s g r e a t e r bond r e s i s t a n c e on the push i n end than on the p u l l - o u t end. T h i s i s p r i m a r i l y due to c r a c k i n g and s e p a r a t i o n of the concrete around the bar at the p u l l - o u t end. A few c y c l e s at a r e l a t i v e l y high amplitude of load may cause an i n c r e a s e i n s t r a i n values at a p a r t i c u l a r 132 l o c a t i o n i n the r e i n f o r c i n g bar, i n d i c a t i n g d e t e r i o r a t i o n i n the s t r e s s t r a n s f e r c a p a c i t y ( i . e . the bond). An i n c r e a s e i n the peak amplitude of l o a d i n g caused bond d e t e r i o r a t i o n at a lower s t r e s s l e v e l i n the subsequent c y c l e (e.g. curves 3 & 10 of F i g . 3.11). An i n c r e a s e i n the peak amplitude of l o a d i n g i n c r e a s e s the le n g t h of the t e n s i l e s t r a i n zone as compared to that of the compression zone, the inc r e a s e being about 10 to 35 percent ( a p p l i e d s t r e s s range of 200-500 MPa). T h i s i m p l i e s that the push-in f o r c e can be t r a n s m i t t e d w i t h i n a much smal l e r l e n g t h than that r e q u i r e d f o r p u l l - o u t f o r c e . The presence of r e s i d u a l s t r e s s of s i g n i f i c a n t magnitude, e s p e c i a l l y f o r l o a d i n g beyond the y i e l d s t r e s s l e v e l , i n d i c a t e s l o c a l i z e d d e s t r u c t i o n of the concrete surrounding the bar. 3.4.3 Cr a c k i n g and F a i l u r e Mode The f i r s t c r a c k i n g load ( r a d i a l s p l i t t i n g c r a c k s ) f o r a l l specimens except F1-RVM/25 occurred more or l e s s at the same a p p l i e d s t r e s s l e v e l (40 to 55 k s i ) (276 to 379 MPa). Specimen F1-RVM/25, c o n t a i n i n g a 30mm diameter t e s t bar, developed f i r s t c r a c k i n g at 30 k s i (207 MPa) a p p l i e d s t r e s s l e v e l . With an i n c r e a s e i n the peak load, more r a d i a l s p l i t t i n g c r a c k s emerged and some of the r a d i a l cracks propagated to the E. and W. faces of the specimen as l o n g i t u d i n a l c r a c k s g r a d u a l l y extended towards the push-in s i d e . The emergence of a c i r c u m f e r e n t i a l crack on the S. or N. faces of a specimen i s i n d i c a t i v e of the onset of a p u l l - o u t bond f a i l u r e . I t i s probable that the formation of a c o n i c a l 133 crack i s i n f l u e n c e d by the extent of s e p a r a t i o n between the r e i n f o r c i n g bar and the concrete and the y i e l d p e n e t r a t i o n along the r e i n f o r c i n g bar. F i n a l l y , a f t e r the formation of a c o n i c a l c rack, the anchorage c a p a c i t y of the specimen depends on the remaining l e n g t h of embedment, c o r r e c t e d f o r any c r a c k i n g ( c o n i c a l ) that may have occ u r r e d at the other end. Therefore, the e f f e c t i v e anchorage l e n g t h of the r e i n f o r c i n g bar i s d r a s t i c a l l y reduced. Thus, at t h i s stage, the specimen may s u f f e r a d r a s t i c r e d u c t i o n i n s t r e n g t h and s t i f f n e s s and f a i l due to bar p u l l - o u t . The s i z e of cone, i . e . i t s diameter and depth, appears to be s m a l l e r f o r specimens with s t e e l f i b e r s than f o r those of p l a i n c o n c r e t e . For p l a i n concrete specimens, only a few wide, r a d i a l , l o n g i t u d i n a l c r a c k s occurred, whereas for f i b e r r e i n f o r c e d c o n c r e t e many narrow, r a d i a l and l o n g i t u d i n a l c r a c k s developed under i d e n t i c a l l o a d i n g c o n d i t i o n s . F u r t h e r , the f i b e r r e i n f o r c e d c o n c r e t e specimens were more r e s i s t a n t than p l a i n c o n c r e t e ones. The FRC specimens were found to have enough c a p a c i t y to s u s t a i n many more c y c l e s of r e v e r s e d l o a d i n g than p l a i n c o n c r e t e specimens. For example, under i d e n t i c a l c o n d i t i o n s of l o a d i n g , specimen F2-RV/17 s u s t a i n e d 16 c y c l e s at 79 k s i (545 MPa) before f a i l u r e , whereas p l a i n c o n c r e t e specimen P-RVM/20 f a i l e d a f t e r undergoing only two c y c l e s at t h i s s t r e s s l e v e l . Thus, s t e e l f i b e r s appear to have d e f i n i t e advantages f o r use i n s i t u a t i o n s where r e v e r s a l s of r e l a t i v e l y high amplitudes of l o a d i n g (at l e a s t beyond y i e l d ) are expected, e s p e c i a l l y i n the beam-column j o i n t s of moment r e s i s t i n g d u c t i l e 134 frame s t r u c t u r e s . The f a i l u r e mode f o r a l l specimens was due to p u l l - o u t of the r e i n f o r c i n g bar from the concrete block, i . e . bond f a i l u r e . A complete a n a l y s i s and i n t e r p r e t a t i o n of the r e s u l t s i s presented in Chapter 4. 135 IV. EVALUATION AND INTERPRETATION OF TEST RESULTS 4.1 GENERAL The bond between r e i n f o r c i n g bars and c o n c r e t e i s a fundamental aspect of r e i n f o r c e d c o n c r e t e . Despite the a v a i l a b i l i t y of a vast amount of l i t e r a t u r e and t e s t data, the p r e c i s e i n f l u e n c e s of the c o n t r o l l i n g parameters remain u n c l e a r . T h e r e f o r e , i n t h i s work, an attempt has been made to evaluate the s t r e s s t r a n s f e r mechanism between r e i n f o r c i n g s t e e l and concrete under the i n f l u e n c e of parameters such as load h i s t o r y , load amplitude, number of c y c l e s , presence of s t e e l f i b e r s i n c o n c r e t e , and so on. In Chapter 3, the d e t a i l s of the t e s t r e s u l t s were presented. However, no attempt was made to analyze and i n t e r p r e t these r e s u l t s i n terms of the s t r e s s t r a n s f e r mechanism or the bond behaviour, e s p e c i a l l y under reversed c y c l i c l o a d i n g . In t h i s Chapter, the important parameters mentioned above w i l l be c r i t i c a l l y examined and d i s c u s s e d with r e f e r e n c e to the bond behaviour and bond d e g r a d a t i o n . T h i s may augment the c u r r e n t understanding about the nature of bond and the bond d e t e r i o r a t i o n mechanism. F i n a l l y , u t i l i z i n g the i n f o r m a t i o n obtained from the a n a l y t i c a l study, a theory of the bond d e t e r i o r a t i o n mechanism w i l l be presented. At the present time, research i n d i c a t e s that the concept of s l i p g e n e r a l l y a p p l i e d to p l a i n bars i s r e a l l y meaningless when modern deformed bars are c o n s i d e r e d . In t h i s i n v e s t i g a t i o n , emphasis i s p l a c e d on the displacement measured at the loaded ends with respect to the c e n t r e of the specimen. The displacement and the s t r a i n measurements along the r e i n f o r c i n g 1 36 bar ( t e s t bar) are c o n s i d e r e d to be the two most important measurable parameters with which to e x p l a i n the s t r e s s t r a n s f e r mechanism and the bond d e t e r i o r a t i o n . 4.2 MECHANICS OF BOND The bond s t r e n g t h developed between two c o n s e c u t i v e r i b s of a deformed bar i s d e r i v e d from the c o n t r i b u t i o n s of the f o l l o w i n g : ( i ) Shearing r e s i s t a n c e developed through chemical adhesion on the s u r f a c e of the r e i n f o r c i n g bar. ( i i ) F r i c t i o n a l r e s i s t a n c e to s l i d i n g . ( i i i ) Bearing a g a i n s t the face of the r i b s . For a deformed bar, the prime mechanism for the development of bond s t r e n g t h i s the bearing of the concrete a g a i n s t the r i b s and the s t r e n g t h of concrete between the r i b s ( 2 9 ) . The c o n t r i b u t i o n s of the two other f a c t o r s have been found to be n e g l i g i b l e . U n l i k e the behaviour with a p l a i n bar, i t i s u s u a l l y the v i s u a l appearance of s p l i t t i n g of the concrete near the p u l l - o u t end that i s i n d i c a t i v e of f a i l u r e in bond of deformed bars. In order to e x p l a i n the bond d e t e r i o r a t i o n mechanism and bond f a i l u r e , the work of Goto (33) should be mentioned. His i d e a l i z a t i o n of the i n t e r a c t i o n between the bar and the concrete i s e x p l a i n e d i n F i g . 1.1 which he e s t a b l i s h e d a f t e r observing the i n t e r n a l c r a c k i n g p a t t e r n s of specimens t e s t e d under p u l l -out l o a d i n g . "The p u l l i n g out of the r e i n f o r c i n g bar i s s u b j e c t to r e s t r a i n t by the compressive ' s t r u t s ' in the concrete as shown i n F i g . 1.1,. T h i s t i g h t e n i n g f o r c e on the bar i s due to 137 the wedging a c t i o n and deformation of the t e e t h of the comb-like c o n c r e t e . The r a d i a l component of t h i s f o r c e may cause c i r c u m f e r e n t i a l t e n s i o n and s p l i t t i n g i n the con c r e t e . The mechanism can be seen i n F i g . 1 .1 . To gain f u r t h e r i n s i g h t i n t o the bond d e t e r i o r a t i o n mechanism, i t i s worthwhile to r e c o l l e c t the information r e g a r d i n g s t r a i n d i s t r i b u t i o n along the r e i n f o r c i n g bar under v a r i o u s l o a d h i s t o r i e s presented i n Chapter 3. For example, under monotonic l o a d i n g , i t was observed that the push-in f o r c e c o u l d be t r a n s m i t t e d over a much sh o r t e r l e n g t h than c o u l d the p u l l - o u t f o r c e . T h i s i n d i c a t e s that bond r e s i s t a n c e on the compression end i s much higher than that on the t e n s i o n end. T h i s can be e x p l a i n e d through F i g . 4 . 1 . I t can be seen from F i g . 4.1 that with a gradual i n c r e a s e i n the push-in p u l l - o u t load, the p r o g r e s s i v e s t r e s s t r a n s f e r from s t e e l to concrete w i l l take p l a c e mainly through the contact p o i n t s ( i . e . r i b s ) of the bar. The concrete w i l l deform i n the manner shown in F i g . 4 . 1 . At the t e n s i l e end, the s e p a r a t i o n between bar and SEPARATION AROUND REBAR INTERNAL DIAGONAL CRACKS NOTE: ENLARGED VIEW OF DEFORMATION SHOWN FOR CLARITY. FIG.4.1 DEFORMATION OF CONCRETE fc CRACKING AROUND REBAR 138 c o n c r e t e , caused by s l i p and the Poisson's e f f e c t i n the bar, w i l l be aggravated due to the outward deformation of the concrete and the i n t e r n a l d i a g o n a l cracks emanating from the r i b s . A t y p i c a l c a l c u l a t i o n f o r the extent of the r e d u c t i o n in diameter and the bearing area due to Poisson's e f f e c t i s given i n Appendix 'D'. With an i n c r e a s e i n the load amplitude, the zone of s e p a r a t i o n w i l l propagate inwards. Thus, the bond r e s i s t a n c e c a p a c i t y w i l l decrease g r a d u a l l y from the t e n s i o n end, and the peak bond s t r e s s ( t e n s i o n s i d e) w i l l s h i f t inwards as shown in a t y p i c a l bond s t r e s s d i s t r i b u t i o n curve, such as F i g . 3.5. However, on the compression end, the inward deformation of the concrete w i l l impose an a d d i t i o n a l g r i p on the r e i n f o r c i n g bar, i n a d d i t i o n to that e x e r t e d by the compression ' s t r u t ' , mentioned e a r l i e r . Moreover, an i n c r e a s e in c r o s s s e c t i o n a l area of the bar due to Poisson's e f f e c t may f u r t h e r improve the bond between the r e i n f o r c i n g bar and the c o n c r e t e . Thus the bond r e s i s t a n c e on the compression end i s much higher than that on the t e n s i o n end. A comprehensive d i s c u s s i o n of bond d e t e r i o r a t i o n and i t s mechanism w i l l be presented i n Chapter 6. 4.3 EFFECT OF VARIOUS PARAMETERS ON BOND BEHAVIOUR In order to i d e n t i f y the major i n f l u e n c e s of some of the v a r i a b l e s mentioned e a r l i e r on the bond behaviour, and t h e i r r e l a t i v e c o n t r i b u t i o n s to the s t r e s s - t r a n s f e r mechanism, i t i s worthwhile making a r e l a t i v e comparison of the h y s t e r e t i c behaviour of the specimens i n v o l v i n g one or more of the 1 39 v a r i a b l e s . I t should again be emphasized that the a p p l i e d s t r e s s - d i s p l a c e m e n t r e l a t i o n s h i p i s a powerful t o o l with which to e x p l a i n the behaviour of specimens su b j e c t e d to d i f f e r e n t l o a d i n g h i s t o r i e s . 4.3.1 Loading Type A. MONOTONIC LOADING (Specimens: F2-500/25/MO/10, F1-500/25/MO/12  F2-500/25/MO/18) In g e n e r a l , i t i s observed that up to the y i e l d s t r e s s l e v e l there i s p r a c t i c a l l y no change i n the a x i a l s t i f f n e s s , and the a p p l i e d s t r e s s - d i s p l a c e m e n t r e l a t i o n s h i p i s p r a c t i c a l l y l i n e a r , but the s t i f f n e s s in t e n s i o n i s l e s s than that i n compression. The s t i f f n e s s here i s d e f i n e d as the slope of the a p p l i e d s t r e s s - d i s p l a c e m e n t curve. However, i t should be noted that even i n the working load range, the s t r e s s t r a n s f e r process from the s t e e l to the concrete i s w e l l d i s t r i b u t e d along the bar, c a u s i n g i n t e r n a l crack formation emanating from the bar r i b s . The s l i p and s e p a r a t i o n propagate inwards from the p u l l -out end of the specimen. In the s t r e s s range of 40 to 50 k s i (276 to 345 MPa), the c i r c u m f e r e n t i a l t e n s i o n in the concrete, due to the wedging a c t i o n a g a i n s t the bar r i b s , a l s o causes s p l i t t i n g c r a c k s which are manifested as r a d i a l cracks on the p u l l out face of the specimen. These f a c t o r s cause a d e t e r i o r a t i o n i n bond, e s p e c i a l l y at the p u l l - o u t end. T h i s may be seen from the Bond S t r e s s Diagram ( F i g . 3.5) and the h o r i z o n t a l p o r t i o n of the S t r a i n Diagram (Fig.3.4) f o r a t y p i c a l 140 specimen (F2-MO/18). However, i t may be seen that at the push-in end, improved bond r e s i s t a n c e p e r s i s t e d . J u s t beyond the y i e l d l e v e l (=414 MPa), there was an abrupt r e d u c t i o n i n s t i f f n e s s due to y i e l d i n g i n the r e i n f o r c i n g s t e e l . With a f u r t h e r i n c r e a s e i n s t r e s s l e v e l , a p r o g r e s s i v e degradation i n the s t i f f n e s s and an i n c r e a s e i n deformation was observed, i n d i c a t i n g a p r o g r e s s i v e i n c r e a s e in i n t e r n a l c r a c k i n g , i n e l a s t i c deformation in the s t e e l , and propagation of s l i p and s e p a r a t i o n towards the core of the specimen. The bond s t r e s s d i s t r i b u t i o n diagram and the s t r a i n diagrams c o n f i r m the gradual d e t e r i o r a t i o n of bond in the p u l l - o u t end, f o l l o w e d by the s h i f t i n g of the peak bond s t r e s s towards the core of the specimen, thus modifying the bond s t r e s s d i s t r i b u t i o n p a t t e r n . However, on the push- in end, p r a c t i c a l l y no such bond degradation was observed, and the bond r e s i s t a n c e remained very h i g h , though the bond s t r e s s d i s t r i b u t i o n p a t t e r n changed with an i n c r e a s e i n a p p l i e d s t r e s s l e v e l . B. REPEATED LOADING (Specimens: F2-500/25/RP/9, F1-500/25/RP/11) These specimens were subjected to an i n c r e m e n t a l l y i n c r e a s e d l o a d i n g with one c y c l e f o r each peak amplitude of l o a d i n g . The response curves fo r these specimens i n d i c a t e completely d i f f e r e n t behaviour as compared to those specimens su b j e c t e d to reversed c y c l i c l o a d i n g . A comparison of the a p p l i e d s t r e s s versus displacement curve under monotonic and repeated l o a d i n g ( F i g . 3.8) r e v e a l s that the envelope of the curves at v a r i o u s c y c l e s i n the repeated l o a d i n g i s s i m i l a r to 141 that of the monotonic curve. A continuous change i n the slope of the a p p l i e d s t r e s s - d i s p l a c e m e n t curve (beyond y i e l d ) may a l s o be observed. S t r a i g h t l i n e s can be j o i n e d from zero load to the i n t e r s e c t i o n p o i n t s of the unloading and r e l o a d i n g curves. The s l o p e s of these may be t r e a t e d as the s t i f f n e s s of the unloading and r e l o a d i n g curves(see F i g . 3.8(a)). I t was i n t e r e s t i n g to f i n d that the s t i f f n e s s obtained as above remained the same, i r r e s p e c t i v e of the magnitude of the a p p l i e d s t r e s s l e v e l . Under t e n s i o n , even at low a p p l i e d s t r e s s l e v e l s , the l a y e r of concrete surrounding the r e i n f o r c i n g bar ( t e s t bar) undergoes c r a c k i n g and a r e d u c t i o n in i t s modulus of e l a s t i c i t y ; however, there i s s t i l l s u f f i c i e n t bond r e s i s t a n c e f o r the t r a n s f e r of s t r e s s from the r e i n f o r c i n g bar to the c o n c r e t e . I t i s probably the bearing of the r i b s a g a i n s t the concrete that i s p r i m a r i l y r e s p o n s i b l e f o r l o a d t r a n s f e r or bond between the r e i n f o r c i n g bar and the concrete (29). There appears to be some resemblance in the p a t t e r n of the slopes of the unloading and r e l o a d i n g curves (as shown in F i g . 3.8) to those f o r r e i n f o r c i n g s t e e l under repeated l o a d i n g . T h i s suggests that the mechanical p r o p e r t i e s of the r e i n f o r c i n g s t e e l probably dominate the a p p l i e d s t r e s s - d i s p l a c e m e n t behaviour of specimens s u b j e c t e d to repeated l o a d i n g . However, the residua-1 displacements (at zero load) i n c r e a s e due to the accumulation of incremental deformations with c y c l i n g . The deformations may be p a r t l y due to the r e l e a s e of the i n i t i a l s t r e s s e s induced by shrinkage and thermal e f f e c t s , and p a r t l y due to the i n e l a s t i c nature of the s l i p between the r e i n f o r c i n g bar and the c o n c r e t e . 142 The a p p l i e d s t r e s s - d i s p l a c e m e n t r e l a t i o n s h i p s of the specimens (F2-RP/9 & F1-RP/11) subjected to repeated l o a d i n g i n compression have s i m i l a r c h a r a c t e r i s t i c s to those i n t e n s i o n , except that the displacements are much smal l e r as compared to those i n t e n s i o n under s i m i l a r a p p l i e d s t r e s s l e v e l s . F u r t h e r , the s t i f f n e s s (as d e f i n e d above) i n compression appears to be higher than that in t e n s i o n . T h i s i s because duri n g l o a d i n g in t e n s i o n , the concrete i s subjected to c r a c k i n g and s i g n i f i c a n t bond degradation takes p l a c e , whereas f o r l o a d i n g in compression, l e s s damage occurs, and consequently a higher bond s t r e n g t h i s achieved. C. REVERSED CYCLIC LOADING Under t h i s type of l o a d i n g , the specimens were subjected to reversed c y c l i c l o a d i n g with i n c r e m e n t a l l y i n c r e a s e d magnitudes. E s s e n t i a l l y s i m i l a r a p p l i e d - s t r e s s displacement r e l a t i o n s h i p s were observed at e i t h e r end of each specimen. However, the h y s t e r e t i c responses of these specimens were observed to be q u i t e d i f f e r e n t from those of specimens under monotonic or repeated l o a d i n g . The a p p l i e d s t r e s s displacement curves f o r a t y p i c a l specimen F2-500/25/RVM/14 r e v e a l s that even at s t r e s s l e v e l s below the y i e l d s t r e s s i n s t e e l , a marked r e d u c t i o n in the l o a d i n g s t i f f n e s s ( d e f i n e d i n Chapter 3) took place under c y c l i c l o a d i n g . T h i s s i g n i f i e s that the bond degradation and s l i p o c c u r r e d because some damage i n the concrete 'boundary l a y e r ' surrounding the r e i n f o r c i n g bar probably took p l a c e in the form of c r a c k i n g or i n e l a s t i c deformation i n the concrete due to c y c l i n g . 143 On i n c r e a s i n g the peak amplitude of l o a d i n g beyond the y i e l d s t r e s s i n s t e e l , a s i g n i f i c a n t r e d u c t i o n i n the s t i f f n e s s was observed. T h i s was probably due to an abrupt i n c r e a s e i n deformations i n the r e i n f o r c i n g s t e e l and c r a c k i n g i n the c o n c r e t e . On r e v e r s a l of the l o a d i n the other d i r e c t i o n ( i . e . compression), fo r most of the specimens a p i n c h i n g in the h y s t e r e t i c curve was observed due to e x c e s s i v e s l i p . T h i s was due to the bond degradation which would have taken plac e i n the p r e v i o u s c y c l e s . However, there was some bond r e s i s t a n c e , due to the f r i c t i o n a l e f f e c t s and c l o s i n g - u p of the p r e v i o u s l y formed c r a c k s . As soon as the concrete made co n t a c t with the r i b s of the r e i n f o r c i n g bar, again the response curve became s t i f f e r . On unloading and r e l o a d i n g i n t e n s i o n , s i g n i f i c a n t r e d u c t i o n i n the s t i f f n e s s c o u l d be observed. The reason f o r t h i s i s that the r e i n f o r c i n g s t e e l underwent s o f t e n i n g due to post y i e l d s t r e s s r e v e r s a l . The phenomenon i s known as Bauschinger e f f e c t ( F i g . 4.2). Consequently, the deformation i n the s t e e l i n c r e a s e d , which in t u r n , caused g r e a t e r deformation in the c o n c r e t e , c r a c k i n g ( d i a g o n a l as w e l l as s p l i t t i n g ) , and degradation i n s t i f f n e s s and bond. As the l o a d d i r e c t i o n was reversed a few times and the l o a d taken up to a r e l a t i v e l y high amplitude (beyond the y i e l d s t r e s s in s t e e l ) each time, a t h i n l a y e r of concrete surrounding the r e i n f o r c i n g bar was subjected to severe l o c a l c r a c k i n g and d i s i n t e g r a t i o n , e s p e c i a l l y at the p u l l - o u t end. The cracks a l r e a d y formed under-went widening and e x t e n s i o n . The accumulated damage continued to i n c r e a s e and was found to c o n s i d e r a b l y exceed that i n the p r e - y i e l d stage. T h i s U5 r e s u l t e d i n severe degradation i n the composite a c t i o n between the r e i n f o r c i n g bar and the c o n c r e t e and hence a r e d u c t i o n in s t r e n g t h and s t i f f n e s s of the specimens. A hypothesis f o r the mechanism of bond d e t e r i o r a t i o n under reversed c y c l i c l o a d i n g w i l l be presented i n Chapter 6. 4.3.2 Load Amplitude For specimens su b j e c t e d to repeated l o a d i n g , the peak s t r e s s l e v e l i n the previous c y c l e s seem to have no major i n f l u e n c e on the l o a d i n g s t i f f n e s s (at zero l o a d ) . In c o n t r a s t , under reversed c y c l i c l o a d i n g , the peak s t r e s s l e v e l has a s i g n i f i c a n t i n f l u e n c e on the r e d u c t i o n i n l o a d i n g s t i f f n e s s , e s p e c i a l l y when the p r e v i o u s l o a d i n g has been beyond the post y i e l d l e v e l . However, there appears to be not much d i f f e r e n c e in the accumulated displacements of the specimens ( e s p e c i a l l y beyond y i e l d ) under these two type of l o a d i n g s on the t e n s i o n s i d e , as may be seen i n F i g . 4.3 f o r specimens F1-RP/11 and F1-RV/16 f o r c o r r e s p o n d i n g number of c y c l e s . T h i s probably i n d i c a t e s that s i g n i f i c a n t damage i s caused dur i n g l o a d i n g i n the t e n s i o n c y c l i n g and l e s s damage i s caused dur i n g l o a d i n g i n the compression c y c l e . However, a s i g n i f i c a n t degradation i n the s t i f f n e s s can be observed f o r specimen F1-RV/16. Nonetheless, a specimen s u b j e c t e d to repeated l o a d i n g (RP) has more r e s i s t a n c e to p u l l - o u t f a i l u r e than a specimen s u b j e c t e d to reversed l o a d i n g (RV or RVM), s i n c e about h a l f of the former specimen has not been su b j e c t e d to t e n s i o n . Hence, i t has not undergone much damage or bond de g r a d a t i o n . In f a c t specimen F1-RP/11 s t i l l had the c a p a c i t y to s u s t a i n a l a r g e r number of H 7 c y c l e s compared to specimen F1-RV/16. For specimens s u b j e c t e d to reversed c y c l i c l o a d i n g , once the s t r e s s l e v e l i s i n c r e a s e d to a r e l a t i v e l y high l e v e l , (beyond y i e l d ) i t caused s i g n i f i c a n t bond d e t e r i o r a t i o n at a lower s t r e s s l e v e l i n subsequent c y c l e s . T h i s aspect may be examined from the s t r a i n d i s t r i b u t i o n diagram f o r specimens F2-RV/17, F i g . 3.11 (curves 3 and 10 at ±43.5 k s i (300 MPa)). Even at t h i s s t r e s s l e v e l , there appears to be c o n s i d e r a b l e bond d e t e r i o r a t i o n , as i s apparent from the r e l a t i v e l y high s t r a i n v alues when the peak s t r e s s l e v e l was i n c r e a s e d to ±66 k s i (455 MPa). T h e r e f o r e , the amplitude of l o a d i n g seems to have a s i g n i f i c a n t i n f l u e n c e on the bond behaviour and bond d e t e r i o r a t i o n . 4.3.3 Number of C y c l e s In order to a s c e r t a i n the e f f e c t of the number of l o a d i n g c y c l e s on the bond d e t e r i o r a t i o n , a comparative study was made on the response of specimens having i d e n t i c a l load h i s t o r i e s and c o n d i t i o n s of l o a d i n g . Since the r e l a t i v e displacement of the r e i n f o r c i n g bar with r e s p e c t to the concrete i s mainly due to bond d e t e r i o r a t i o n (64), the displacement has been c o n s i d e r e d as the measurable parameter f o r comparison. The displacement versus number of c y c l e s i s shown i n F i g . 4.4 and may be d e s c r i b e d b r i e f l y as f o l l o w s : 1. (a) A comparison of the responses of specimens F2-RVM/19, P-RVM/20, F1-RVM/21 and F2-RVM/22 at the 78 k s i (538 MPa) peak s t r e s s l e v e l r e v e a l s that the r a t e of displacement per c y c l e i n the p l a i n c o n c r e t e specimen 148 (78.0 KSI COKP.) ( 538MPa ) FIG.4.-4 NO. OF CYCLES VS. DISPLACEMENT 149 l i 78.0 KSI (TENSION) F2-RVM/14 • UJ o < _) 0. in 4 6 NO. OF CYCLES (e ) (78.0 KSI COMP.) 10 • / » . F2-RVM/15 F2-RV /I 7 • F2-RVM/14 4 6 8 NO. OF CYCLES 10 (f ) 72.0 KSI (TENSION) P-RVM/20 RVM/15 F1-RVM/13 F2-RVM/U 2 4 6 NO. OF CYCLES (g) (72.0 KSI COMP.) F1-RVM/13 F2-RVM/14 4 6 8 NO. OF CYCLES (h) NOTE:EACH CURVE AVERAGED FOR N & S.SIDE OF SPECIMENS 10 10 FIG. 4.4 NO. OF CYCLES VS. DISPLACEMENT 150 i s very high as compared to SFRC specimens ( F i g . 4.4(a)). (b) Up to about 4 c y c l e s at the 78 k s i (538 MPa) peak s t r e s s l e v e l , the responses of specimens F2-RVM/19, F2-RVM/21, and F2-RVM/22 are the same and are l i n e a r . Beyond four c y c l e s , the behaviour becomes non l i n e a r . Specimen F1-RVM/21 appears to have the best performance ( F i g s . 4 . 4 ( a ) U b ) ) . 2. With an inc r e a s e i n peak l o a d i n g , e s p e c i a l l y beyond the y i e l d s t r e s s l e v e l , the e f f e c t of c y c l i c l o a d i n g had an i n c r e a s i n g e f f e c t on displacement and bond d e t e r i o r a t i o n ( F i g s . 4.4(c)&(d)). 3. A comparison of the responses of specimens F2-RVM/14, F2-RVM/15, and F2-RV/17 ( F i g . 4.4(e)) r e v e a l s that the p r i o r type of l o a d i n g or the load h i s t o r y had an important e f f e c t on the ra t e of displacement per c y c l e . A specimen loaded under RVM had ap p a r e n t l y s u f f e r e d more damage than the specimens loaded under RV p r i o r to the 78 k s i (538 MPa) peak s t r e s s l e v e l at which the e f f e c t of c y c l i n g was s t u d i e d . T h i s i s evident from the response of F2-RVM/14 & F2-RVM/15 and F2-RV/17 ( F i g . 4.4(e)). The f i g u r e s a l s o i n d i c a t e an improved response f o r F1-RVM/13 c o n t a i n i n g 30mm long s t e e l f i b e r s , compared to the 50mm long f i b e r s i n the other specimens ( F i g s . 4.4(g)t(h) ). The e x p l a n a t i o n f o r the in c r e a s e i n displacement with an in c r e a s e i n the ^number of c y c l e s , e s p e c i a l l y when the peak 151 l o a d i n g amplitude i s above the y i e l d s t r e s s l e v e l , can be given by an o b s e r v a t i o n of the s t r a i n d i s t r i b u t i o n diagrams of the specimens. I t was shown i n Chapter 3 that c y c l i n g has a damaging e f f e c t on the c o n c r e t e 'boundary l a y e r ' surrounding the r e i n f o r c i n g bar as i n d i c a t e d by the i n c r e a s e i n s t r a i n values corresponding to a p a r t i c u l a r l o c a t i o n on the bar. T h i s shows that bond degradation takes p l a c e , and i t i s p r i m a r i l y the bond degradation which causes a r e d u c t i o n i n s t i f f n e s s and an i n c r e a s e i n displacement. 'For specimens F2-RVM/19,P-RVM/20,F1-RVM/21 and F2-RVM/22, subj e c t e d to reversed c y c l i c l o a d i n g and i d e n t i c a l l o a d i n g c o n d i t i o n s , the i n f l u e n c e of the number of c y c l e s on the displacement at the 78 k s i (538 MPa) peak s t r e s s l e v e l i s shown in F i g . 4.5(Enlarged view). The r e s u l t s , when p l o t t e d on a l o g a r i t h m i c s c a l e y i e l d a l i n e a r r e l a t i o n s h i p as shown in F i g . 4.6. From the above r e l a t i o n s h i p , the f o l l o w i n g formula can be obtained by f i t t i n g a s t r a i g h t l i n e to the data. N 6 = ( 1 . 053) /I 1.65 f o r specimens F2-RVM/19,F1-RVM/21, and F2-RVM/22, and a l s o a p p l i c a b l e to specimen F2-RV/17 N and 6 = (1.247) / l 0.52 f o r specimen P-RVM/20 where 5 = displacement of the r e i n f o r c i n g bar at p u l l - o u t end i n inches when the a p p l i e d s t r e s s = 78 k s i (538 MPa) N = number of c y c l e s A hypothesis of the mechanism of bond d e t e r i o r a t i o n and the i n c r e a s e i n displacjement with an i n c r e a s e in the number of 152 T(FAILED) 78.0 KSI STRESS LEVEL 2 4 6 8 10 12 K NO. OF CYCLES FIG.4.5 NO. OF CYCLES VS. DISPLACEMENT TO FAILURE AT 78KSK 538 MPA) APPLIED STRESS LEVEL T FT" CL) as U U < a, co i—i n r N b =(1.247J/10.52 FOR P-RVM/20 8 = (1 .0529)N/1 1 .649 FOR F2-RVM/19 F1-RVM/21 • F2-RVM/22 en o L 4 5 6 NO. OF CYCLES 10 FIG.4.6 NO. OF CYCLES VS. LOG (DISPLACEMENT) AT 78KSI ( 538 MPA) 154 c y c l e s w i l l be presented i n Chapter 6. I t should be noted that each of the curves shown in F i g . 4.4 has has been drawn as the mean of the two s e t s of data p o i n t s obtained from each end of the t e s t specimen. In ge n e r a l , these two set s of p o i n t s seem to be q u i t e c l o s e together, i n d i c a t i n g r e l a t i v e l y small v a r i a b i l i t y i n each specimen. 4.3.4 S t e e l F i b e r s a. Specimens: P-500/2 5/RVM/20 & F1 -500/25/RVM/21 The purpose of t h i s s e c t i o n i s to compare the behaviour of the f i b e r r e i n f o r c e d concrete specimens with that of the p l a i n c o n c r e t e specimens. The comparison w i l l be made between specimens subjected to i d e n t i c a l l o a d i n g c o n d i t i o n s . The comparative h y s t e r e t i c behaviour of specimens P-RVM/20 and F1-RVM/21 i s shown in F i g . 4.7. These specimens have a s i m i l a r a p p l i e d s t r e s s - d i s p l a c e m e n t behaviour up to the y i e l d s t r e s s l e v e l . Beyond the y i e l d s t r e s s l e v e l , the displacements on the p u l l - o u t end are n o t i c e a b l y higher f o r P-RVM/20 than f o r F1-RVM/21 at the same s t r e s s l e v e l s f o r a given number of c y c l e s . F u r t h e r , the s t i f f n e s s degradation observed i n specimen P-RVM/20 was markedly higher than that f o r specimen F1-RVM/21 f o r a given number of c y c l e s . The h y s t e r e t i c curve f o r P-RVM/20 i n d i c a t e s p i n c h i n g i n the 1st c y c l e at the 78 k s i (538 MPa) peak s t r e s s l e v e l , and the specimen f a i l e d due to p u l l - o u t of the r e i n f o r c i n g bar i n the 2nd c y c l e . On the other hand, specimen F1-RVM/21 s u s t a i n e d s i x c y c l e s of l o a d i n g at the same peak s t r e s s l e v e l (538 MPa) before developing a pinched h y s t e r e s i s 155 016 2.032 3.048 4.064 mm - 552 - 4 1 4 690 MPa — P-RVM /20 FI-RVM/2I SPECIMEN'*! -HVM/2I FIG.4.7 APPLIED STRESS-DISPLACEMENT DIAGRAM 156 loop and f a i l i n g due to bar p u l l - o u t . T h i s i n d i c a t e s a much gr e a t e r energy absorbing c a p a c i t y f o r specimen F1-RVM/21 than f o r P-RVM/20. The p r e c i s e reasons f o r these d i f f e r e n c e s are not c l e a r l y understood. However, they may be due to the improved post c r a c k i n g p s e u d o - d u c t i l i t y , higher u l t i m a t e s t r a i n c a p a c i t y and improved crack c o n t r o l (49) of f i b e r r e i n f o r c e d c o n c r e t e . b. Specimens; P-500/25/RV/5 & F2-500/25/RV/17 These specimens were subjected to i n c r e m e n t a l l y i n c r e a s e d reversed c y c l i c l o a d i n g under i d e n t i c a l c o n d i t i o n s . The h y s t e r e t i c response curves f o r these specimens are shown in F i g . 4.8. F i g u r e 4.8 r e v e a l s that the a p p l i e d s t r e s s -displacement behaviour remained e s s e n t i a l l y the same for both of the specimens up to the peak s t r e s s l e v e l of about 77 k s i (531 MPa). A f t e r only 3 c y c l e s at t h i s s t r e s s l e v e l , specimen P-RV/5 e x h i b i t e d severe p i n c h i n g of the h y s t e r e t i c curve and a degradation i n a x i a l s t i f f n e s s , i n d i c a t i n g s i g n i f i c a n t bond d e t e r i o r a t i o n . In the subsequent c y c l e s , t h i s specimen under-went g r e a t e r and g r e a t e r bond degradation and u l t i m a t e l y f a i l e d at about the 52 k s i (358 MPa) s t r e s s l e v e l due to p u l l out of the r e i n f o r c i n g bar. However, specimen F2-RV/.17 su s t a i n e d 15 c y c l e s at the peak s t r e s s l e v e l of 531 MPa which i n d i c a t e s much l e s s bond d e g r a d a t i o n . Presumably, the b e t t e r bond behaviour of specimen F2-RV/17 i s due to the presence of s t e e l f i b e r s i n the c o n c r e t e . The f a c t that both the specimens behaved in the same way up to 77 k s i (531 MPa), but very d i f f e r e n t l y beyond t h i s s t r e s s l e v e l , suggests that the s t e e l f i b e r s became e f f e c t i v e 158 only a f t e r some c r a c k i n g i n the specimen had taken p l a c e . Summary: It was observed that the specimens with s t e e l f i b e r s e x h i b i t e d much b e t t e r anchorage bond c h a r a c t e r i s t i c s than specimens with no f i b e r s , e s p e c i a l l y under reversed c y c l i c l o a d i n g . The probable reasons f o r t h i s are d i s c u s s e d below: With deformed bars, l o n g i t u d i n a l s p l i t t i n g in the concrete due to c i r c u m f e r e n t i a l t e n s i o n i s q u i t e common and t h i s was observed d u r i n g the t e s t s . The development of such s p l i t t i n g c r a c k s r e l e a s e s the g r i p of the r e i n f o r c i n g bar and hence causes bond deg r a d a t i o n . I t i s thought that the presence of f i b e r s makes crack propagation slower and i n h i b i t s crack opening. The f i b e r s enable s t r e s s to be t r a n s f e r r e d a c r o s s cracked s e c t i o n s , a l l o w i n g the a f f e c t e d p a r t s of the composite to r e t a i n some p o s t - c r a c k i n g s t r e n g t h and to withstand g r e a t e r deformation (49). T h i s property i s known as the toughness or energy absorbing c a p a c i t y of c o n c r e t e . I t i s computed as the area under' the lo a d versus d e f l e c t i o n curve. The improved toughness or energy absorbing c a p a c i t y of s t e e l f i b e r r e i n f o r c e d concrete p r i s m a t i c beams subjected to four p o i n t l o a d i n g can be seen from F i g . 2.8. A comparison of the observed s t r e s s - s t r a i n curves f o r the s t e e l f i b e r s r e i n f o r c e d concrete c y l i n d e r s s u bjected to u n i a x i a l compression ( F i g . 2.7) and f o r p l a i n c o n c r e t e c o n f i n e d by s p i r a l s or t r a n s v e r s e s t e e l ( F i g s . 4.9(a)&(b)) i n d i c a t e a strong s i m i l a r i t y i n the p a t t e r n s of the cu r v e s . Though the mechanisms i n v o l v e d i n these two cases are q u i t e d i f f e r e n t and as such, can 159 200 _ 150 z 100 50 1 1 1 Specimens without | longitudinal reinforcement 1 1 ! — - fc^ r\ \ / \ * 1 \ \ N n (4.76 mm (ties at 1-j / in (38.1 mr n) centi'rs-. \ Plain ) (4.76 mm 1 lies at 2j n (63 5 mi ll renters (8001 (600) (400) (200) 0.0O5 0.01 0.015 0.02 0 025 Average strain over a 6 in (152 mm) qauge length 003 Fig. £,9(tibial loud-strain curves for 4j in (108 mm) square concrete prisms with various contents ol'square tics. (Ref 75) 160 not be s t r i c t l y compared, the behaviour i n d i c a t e s improved d e f o r m a t i o n a l c h a r a c t e r i s t i c s and s t r e n g t h f o r f i b e r r e i n f o r c e d c o n c r e t e compared to p l a i n c o n c r e t e . It i s w e l l known t h a t , f o r deformed bars, the p r i n c i p a l mechanism of s t r e s s t r a n s f e r from s t e e l to concrete i s by the b ea ring on the r i b s of the r e i n f o r c i n g bar. I t has been re p o r t e d by Rehm (83) that very high p r e s s u r e s , up to 12 to 16 times the cube s t r e n g t h , may occur under the r i b s . T h e r e f o r e , i t i s l i k e l y that at f a i r l y high a p p l i e d s t r e s s l e v e l s , the c o n c r e t e may get crushed, causing s l i p and bond d e g r a d a t i o n . However, Chen et a l . (18) have repo r t e d a s i g n i f i c a n t improvement in the bearing c a p a c i t y of s t e e l f i b e r r e i n f o r c e d c o n c r e t e . T h e r e f o r e , i t i s l i k e l y that SFRC specimens w i l l have improved bond performance compared to the p l a i n c o n c r e t e ones. It may be mentioned here that the SFRC specimens t e s t e d contained l o n g i t u d i n a l reinforcement ( F i g . 2.5) of about 2.5 percent of the c r o s s s e c t i o n a l area, and l a t e r a l s c l o s e l y spaced at 87mm c e n t e r s , making the t o t a l v o l u m e t r i c content of s t e e l about 3.7 percent ( e x c l u d i n g f i b e r s ) . With t h i s much r e i n f o r c i n g s t e e l , i t may be that the s t e e l f i b e r s act l e s s e f f i c i e n t l y than they would i f there had been l e s s r e i n f o r c i n g s t e e l . T h i s may be due to the masking e f f e c t of the r e i n f o r c i n g s t e e l . Kormeling (52) a l s o observed that the b e n e f i c i a l i n f l u e n c e s of f i b e r a d d i t i o n s decrease with i n c r e a s i n g volumes of c o n v e n t i o n a l reinforcement. T h e r e f o r e , f u r t h e r research would be necessary to a s c e r t a i n p r e c i s e l y the combination of s t e e l f i b e r s and r e i n f o r c i n g bars to produce optimum anchorage 161 bond c o n d i t i o n s . T h i s w i l l be h i g h - l i g h t e d i n Chapter 8, under suggestions f o r f u r t h e r r e s e a r c h . 4.3.5 E f f e c t of S t e e l F i b e r S i z e (Length) a. Specimens: F2-500/25/RVM/19 & F1-500/25/RVM/21 The h y s t e r e t i c curves f o r specimens F2-RVM/19 and F1-RVM/21 are shown i n F i g . 4.10. These specimens were sub j e c t e d to in c r e m e n t a l l y i n c r e a s e d reversed c y c l i c l o a d i n g under i d e n t i c a l l o a d i n g c o n d i t i o n s . The h y s t e r e t i c curves f o r both specimens have s i m i l a r a p p l i e d s t r e s s - d i s p l a c e m e n t c h a r a c t e r i s t i c s r i g h t up to f a i l u r e . T h i s probably i n d i c a t e s that the 30mm and 50mm long s t e e l f i b e r s have s i m i l a r e f f e c t s on anchorage bond behaviour. b. Specimens: F2-500/25/RV/8 & F1-500/25/RV/16 The a p p l i e d s t r e s s - d i s p l a c e m e n t r e l a t i o n s h i p s f o r these specimens are shown i n F i g . 4.11. These specimens were subj e c t e d to i n c r e m e n t a l l y i n c r e a s e d reversed c y c l i c l o a d i n g under i d e n t i c a l c o n d i t i o n s . F i g . 4.11 i n d i c a t e s e s s e n t i a l l y no d i f f e r e n c e i n response even up to about the 80 k s i (552 MPa) s t r e s s l e v e l f o r both the specimens. T h e r e a f t e r , severe p i n c h i n g of the h y s t e r e t i c curve i s observed f o r both the specimens. The displacements f o r F2-RV/8 are r e l a t i v e l y l a r g e r than those of F1-RV/16 with an i n c r e a s e i n the number of c y c l e s . However, both specimens f a i l e d a f t e r the same number ( f i f t e e n ) of c y c l e s . From the above o b s e r v a t i o n s , i t may be concluded that both the 30mm long and 50mm long s t e e l f i b e r s of the type used, have p r a c t i c a l l y the same e f f e c t • on anchorage bond performance. 162. 4.10 APPLIED STRESS-DISPLACEMENT DIAGRAM 163 FIG. 4.11 APPLIED STRESS-DISPLACEMENT DIAGRAM 164 However, i t should be mentioned here that the concrete c o n t a i n i n g the 50mm long f i b e r s was found to be l e s s workable than that with 30mm long f i b e r s , as observed dur i n g c a s t i n g of the specimens. Therefore, the performance of the specimens c o n t a i n i n g 50mm long f i b e r s may have been dependent upon the w o r k a b i l i t y of the concrete and the degree of compaction. 4.3.6 E f f e c t of the Groove in the Bar a. Specimens: P-500/25/RV/5 (Grooved) & P-500/25/RV/6 These specimens were su b j e c t e d to i n c r e m e n t a l l y increased r e v e r s e d c y c l i c l o a d i n g (RV). The a p p l i e d s t r e s s - d i s p l a c e m e n t r e l a t i o n s h i p s f o r the specimens are shown in F i g . 4.12, which i n d i c a t e s p r a c t i c a l l y no d i f f e r e n c e i n the response of the specimens even up to the 76 k s i (524 MPa) s t r e s s l e v e l . Specimen P-RV/6, however, s u s t a i n e d two more c y c l e s at about 78/80 k s i (538/552 MPa) than d i d P-RV/5, before f a i l u r e by p u l l i n g out of the bar. I t may a l s o be noted that there was a s l i g h t d i f f e r e n c e i n the peak amplitude of l o a d i n g and that specimen P-RV/5 was subj e c t e d to s l i g h t higher l o a d i n g in every c y c l e as compared to specimen P-RV/6. Nonetheless, i t would appear that the presence of a groove i n the r e i n f o r c i n g bar ( f o r f i x i n g of the s t r a i n gauges) does not make a s i g n i f i c a n t d i f f e r e n c e i n the st r e s s - d i s p l a c e m e n t r e l a t i o n s h i p as compared to that f o r a s o l i d bar. S P E C I M E N ' P - R V / 6 FIG. 4-12 APPLIED STRESS-DISPLACEMENT DIAGRAM 166 4.3.7 E f f e c t of Diameter of Bar & Embedment Length a. Specimens: F1-500/30/RVM/25 & F1-500/25/RVM/21 The h y s t e r e t i c responses of these specimens are compared in F i g . 4.13. Specimens F1-RVM/25 and F1-RVM/21 were su b j e c t e d to s i m i l a r l o a d i n g h i s t o r i e s . F i g . 4.13 shows that the lo a d -deformation r e l a t i o n s h i p s remain e s s e n t i a l l y the same f o r both specimens up to about the 60 k s i (415 MPa) s t r e s s l e v e l . At the 72 k s i (496 MPa) s t r e s s l e v e l , i n the f i r s t c y c l e , the h y s t e r e t i c curve f o r specimen F1-RVM/25 shows p i n c h i n g , i n d i c a t i n g severe bond d e t e r i o r a t i o n . At 78 k s i (538 MPa) in the f i r s t c y c l e , t h i s specimen f a i l e d due to e x c e s s i v e s l i p . On the other hand, specimen F1-RVM/21 c o u l d withstand ten c y c l e s at the 78 k s i (538 Map) peak s t r e s s l e v e l before f i n a l l y f a i l i n g due to ex c e s s i v e s l i p caused by severe bond degrad a t i o n , as i n d i c a t e d by severe p i n c h i n g of the h y s t e r e t i c curves. A comparison of the h y s t e r e t i c curves i n d i c a t e s reduced bond e f f e c t i v e n e s s f o r the 30mm diameter r e i n f o r c i n g bar as compared to the 25mm diameter bar with the same embedment le n g t h of 500mm. T h i s i s expected as the r a t i o of the perimeter to c r o s s s e c t i o n a l area i n c r e a s e s f o r s m a l l e r bars. b. Specimens: P-500/25/RVM/20 & P-3 75/20/RVM/2 3 The h y s t e r e t i c responses of these specimens are compared i n F i g . 4.14. Specimens P-RVM/20 and P-RVM/23 were s u b j e c t e d to s i m i l a r l o a d h i s t o r y ; they d i f f e r e d only i n the embedment l e n g t h and the diameter of the t e s t bar. The h y s t e r e t i c curves i n d i c a t e more s t i f f n e s s degradation f o r P-RVM/20 beyond the y i e l d s t r e s s l e v e l 168 F I G . A . H APPL IED STRESS-D ISPLACEMENT DIAGRAM 169 and g r e a t e r displacement on the p u l l - o u t end f o r the same s t r e s s l e v e l . However, the h y s t e r e t i c curve f o r P-RVM/23 shows a s l i g h t p i n c h i n g at 70 k s i (482 MPa), seemingly due to a reduced embedment l e n g t h . F i n a l l y , f a i l u r e took p l a c e by p u l l - o u t of the bar, along with a cone of concrete when i t was c y c l e d at a peak amplitude of 75.4 k s i (520 MPa). On the other hand, specimen P-RVM/20 was loaded up to the 78 k s i (538 MPa) s t r e s s l e v e l , and s u s t a i n e d two c y c l e s at t h i s s t r e s s l e v e l . The comparatively g r e a t e r deformations of specimen P-RVM/20 than P-RVM/23 under s i m i l a r peak s t r e s s l e v e l s i n d i c a t e a b e t t e r bond e f f e c t i v e n e s s of the l a t t e r specimen, e s p e c i a l l y c o n s i d e r i n g that i t had a reduced embedment len g t h (375mm) as compared to that of specimen P-RVM/20, with an embedment of 500mm. 4.3.8 E f f e c t of Bar Surface C o n d i t i o n s a. Specimens: P-375/20/RVM/2 3 & P-37 5/2 0/RVM/2 4 (Greased) The h y s t e r e t i c responses of these specimens are compared i n F i g . 4.15. They were sub j e c t e d to s i m i l a r l o a d i n g h i s t o r i e s . However, the h y s t e r e t i c curves i n d i c a t e a remarkable d i f f e r e n c e in t h e i r responses. The h y s t e r e t i c curves f o r P-RVM/24 (which was greased) i n d i c a t e more s t i f f n e s s degradation even at the 46 k s i (317 MPa) s t r e s s l e v e l as compared to P-RVM/23. Severe p i n c h i n g e x i s t s i n the h y s t e r e t i c curve f o r specimen P-RVM/24 beyond t h i s s t r e s s l e v e l , i n d i c a t i n g a r e d u c t i o n i n the energy absorbing c a p a c i t y . The load c a r r y i n g c a p a c i t y was a l s o reduced, and u l t i m a t e l y the specimen f a i l e d due to e x c e s s i v e p u l l out of the r e i n f o r c i n g bar from the co n c r e t e , at a peak 170 I 016 2.032 3.048 4.064mm i 1 r H 690MP0 -A 552 H 414 276 -A 138 C Y C L E S -SPECIMCN' P-AVM/24 , P-3 7 5/20/RVM/2 3 0 P-375/20/RVM/24 N O T E : C Y C L E S NUMBERED A F T E R 6 0 K S I • , . G . M 5 A P P L I E D S T R E S S - D I S P L A C E M E N T D I A G R A M 171 s t r e s s l e v e l of 58 k s i (400 MPa). The t o t a l s l i p of the r e i n f o r c i n g bar through the specimen was i n d i c a t e d by l a r g e p u l l out and push i n measurements on opposite ends of the specimen. On the other hand, specimen P-RVM/23 c o u l d be loaded even up to the 80 k s i (552 MPa) s t r e s s l e v e l , beyond which the load c a r r y i n g c a p a c i t y was reduced. The severe p i n c h i n g and r e d u c t i o n i n the load c a r r y i n g c a p a c i t y of the specimen i s due to severe bond d e t e r i o r a t i o n as i n d i c a t e d by the marked s l i p / d i s p l a c e m e n t of the r e i n f o r c i n g bar. T h i s s e r i o u s l o s s of bond between the r e i n f o r c i n g bar and the concret e may be a t t r i b u t e d to the l o s s of f r i c t i o n a l r e s i s t a n c e in the sur f a c e of the r e i n f o r c i n g bar both over and i n between the r i b s of the bar. T h i s i n d i c a t e s that the r o l e of f r i c t i o n i s a l s o q u i t e important i n the s t r e s s t r a n s f e r mechanism. The a p p l i c a t i o n of grease might w e l l have caused pockets or v o i d s at the root of the r i b s , which would have helped i n s l i p and s l i d i n g of the concrete on the i n c l i n e d faces of the r i b s , thus reducing the e f f e c t i v e contact area with the r i b s f o r b e a r i n g . T h i s r e d u c t i o n i n bearing (or mechanical anchorage) along with the reduced f r i c t i o n a l r e s i s t a n c e to s l i d i n g , might have caused the severe bond degrada t i o n , that was observed f o r specimen P-RVM/24. 1 72 4.3.9 E f f e c t of H e l i x around Bar Specimens: F2-500/25/RVM/19 & F2-500/25/RVM/22 (Helix  Provided) The specimen F2-RVM/22 con t a i n e d a h e l i x of outer diameter 200mm, made of No.10 bar at a p i t c h of 75mm c e n t e r s . T h i s was prov i d e d along the depth of the specimen with the t e s t bar at the c e n t r e . The a p p l i e d s t r e s s versus displacement curves f o r these specimens are shown i n F i g . 4.16. The h y s t e r e t i c curves f o r both specimens seem to match e x a c t l y even up to about the second c y c l e at the 78 k s i (538 MPa) peak s t r e s s l e v e l . From the t h i r d c y c l e onwards (peak s t r e s s l e v e l 538 MPa), a small d i f f e r e n c e i n the h y s t e r e t i c responses i s observed. However, fo r a l l p r a c t i c a l purposes, the behaviour of both specimens may be c o n s i d e r e d the same. 4.4 ENERGY ABSORPTION & DISSIPATION CAPACITY The SEAOC Code recommends that a b u i l d i n g subjected to moderate earthquake f o r c e s should r e s i s t these without c o l l a p s e , though with some s t r u c t u r a l and n o n s t r u c t u r a l damage. To av o i d c o l l a p s e , the s t r u c t u r a l members i n c l u d i n g the beam-column j o i n t must be d u c t i l e enough to absorb and d i s s i p a t e energy by post-e l a s t i c deformations. T h e r e f o r e , the energy absorbing and d i s s i p a t i n g c a p a c i t y of a member i s of utmost importance, e s p e c i a l l y i n the context of the i n v e s t i g a t i o n of bond d e t e r i o r a t i o n under reversed c y c l i c l o a d i n g . The energy a b s o r p t i o n c a p a c i t y of a specimen s u b j e c t e d to push i n - p u l l out l o a d i n g can be represented as the sum of the 1 7 4 areas of the a p p l i e d s t r e s s versus displacement curves on both the push in and p u l l out ends of the specimen. However, i t was observed from the t e s t s that the energy a b s o r p t i o n c a p a c i t y i s p r a c t i c a l l y the same on each end. T h e r e f o r e , in t h i s i n v e s t i g a t i o n , f o r convenience, the energy a b s o r p t i o n c a p a c i t y i s c o n s i d e r e d f o r only one face (North or South) of the specimens. The method of computation of the energy a b s o r p t i o n c a p a c i t y i s d e s c r i b e d i n F i g . 4.17. For a beam-column j o i n t which i s s u b j e c t e d to high s t r a i n and reversed l o a d i n g with a low number of c y c l e s , i t i s expected that i t should have s u f f i c i e n t c a p a c i t y i n absorbing or d i s s i p a t i n g energy. A comparison of the energy absorbing c a p a c i t i e s (only one s i d e c o n s i d e r e d f o r convenience) of specimens su b j e c t e d to i d e n t i c a l load h i s t o r i e s i s shown in Table 4.1. I t seems that the energy absorbed p r i o r to f a i l u r e of specimens subjected to c y c l i c l o a d i n g , whether reversed (RV and RVM) or repeated (RP) l o a d i n g , i s much higher than that f o r specimens su b j e c t e d to monotonic l o a d i n g . F u r t h e r , the specimens c o n t a i n i n g the s t e e l f i b e r s have more than twice the energy absorbing c a p a c i t y of specimens c o n t a i n i n g p l a i n c o n c r e t e . F i g . 4.18 i n d i c a t e s a higher r a t e of increase i n the cumulative energy absorbed with an i n c r e a s e i n a p p l i e d s t r e s s l e v e l f o r SFRC specimens (F2-RV/8, F2-RV/16) than p l a i n concrete specimens (P-RV/5, P-RV/6) su b j e c t e d to i d e n t i c a l load h i s t o r i e s (RV) and c o n d i t i o n s of l o a d i n g . The f o l l o w i n g r e l a t i o n s h i p s f o r cumulative energy with r e s p e c t to the a p p l i e d s t r e s s l e v e l have been obtained by f i t t i n g a curve to the experimental r e s u l t s . 175 TENSION HALF CYCLE 1 01 A P. FIRST CYCL GAP. COMPRESSION ENERGY ABSORBED IN 1 / / X HALF-CYCLE FIRST HALF-CYCLE(TENSION) ENERGY ABSORBED IN SECOND HALF-CYCLE(COMPRESSION) ENERGY ABSORBED IN FIRST CYCLE ENERGY ABSORBED IN 11/2 CYCLE & SO ON ENERGY ABSORBED IN 2 CYCLES(CUMULATIVE) FIG.4-1 7 ENERGY ABSORPTION CAPACITY COMPUTATION. TABLE 4.1 ENERGY ABSORPTION CAPACITY OF SPECIMENS (RV LOADING) A p p l l e d S t r e s s (MPa) C y c l e No. P-500/25/RV/5 P-500/25/RV/6 F2-500/25/RV/8 F2-500/25/RV/16 F2-500/25/RV/ 17 U EU U r u U EU U EU U EU 414 1 0.09 0.09 0.11 0.11 0.07 0.07 0.09 0.09 0. 12 0.12 455 1 0. 20 0. 29 0. 30 0.41 0.55 0.62 0.65 0. 74 0.44 0.56 469 1 0.31 0. 72 0.71 1 . 33 0.89 1 .63 489 1 0. 38 0.67 0.85 1 .57 0.90 2 . 23 1 . 15 2 .78 0.48 1 .04 510 1 0. 73 1 .40 1.13 2 . 70 1.11 3.34 1 . 14 3.92 0.72 1 .76 524 1 1 . 30 4 .00 1 . 39 4 . 73 1 .52 5 . 44 1 .00 2 .76 538 1 2 0.98 2 . 38 1 .86 6 . 59 1 . 75 7 . 19 1 . 99 25. 27 552 1 2 3 1 . 73 1 . 72 4.11 5.83 2 . 38 2 .00 2 . 39 8 . 97 10. 97 13 . 36 2 .64 9.83 2 . 53 3.89 3.89 27 .80 31 .69 31 .69 586 1 2 3 4 2.49 0.13 6 . 49 6 .62 3. 10 16 . 46 2 .65 3.21 3.43 12.48 15.69 19.12 7.47 39. 16 U = Energy Absorbed i n each c y c l e i n Joule/mm' EU = Cumulative Energy Absorbed i n Joule/mm' T A B L E A.l(contd) E N E R G Y A B S O R P T I O N C A P A C I T Y O F S P E C I M E N S ( R V M L O A D I N G ) S t r e s s L e v e l (MPa) C y c l e ; No. F1-500/2! 5/RVM/13 F2-500/2! 5/RVM/14* F2-500/2! j/RVM/15 F2-500/2! 5/RVM/19 F2-500/2E 5/RVM/20 U r u U IU U EU U EU U EU 414 1 2 0. 16 4 c y c l e s 0.64 0.22 0. 23 0. 23 0. 46 0.11 0.11 0. 11 0.22 0. 10 0. 10 0. 10 0.20 496 1 2 t . 10 1 1 .59 ( 7 t h c y c l e ) 1 . 10 1 9.42 0.86 0.88 1 .01 1 . 50 2 . 38 3.39 1.15 1 . 25 1 . 16 2.86 0.88 0.84 1 . 10 1 .94 1 .05 1 .08 1 . 25 2 . 33 538 1 2 3 4 5 1 . 38 1 .47 1 .57 4 . 77 6.24 7.81 1 .86 3.07 4.72 15. 18 1 .43 2 *86 ( 10th eye 1e) 3.37 I 23 . 39 2 .04 4.37 * Specimen can be s t i l l c y c l e d U = Energy Absorbed i n each c y c l e i n Joule/mm' 2.U = Cumulative Energy Absorbed i n Joule/mm ! 178 FIG.4.1 8 APPLIED STRESS VS. LOG (CUMULATIVE ENERGY ABSORBED) 179 For PCC SPECIMENS, RV Loading U = ( 1 .20f / 78.07 (4.4.1) For SFRC SPECIMENS, RV Loading U = ( 1 .249)^ / 768.8 (4.4.2) where U = Cumulative energy absorbed i n i n - 1 b / i n 2 a = A p p l i e d s t r e s s l e v e l i n k s i (a > 60 k s i ) 4.5 ENVELOPE OF MAXIMUM STRESS VERSUS DISPLACEMENT CURVES Specimens: P-500/25/RV/5,P-500/25/RV/6,F2-500/25/RV/8,F1 - 500/25/RV/16,F2-500/25/RV/l7 The envelops of the maximum s t r e s s and displacement values t i l l f a i l u r e f o r the above specimens, su b j e c t e d to RV lo a d i n g h i s t o r i e s and i d e n t i c a l l o a d i n g c o n d i t i o n s , are shown i n F i g . 4.19. I t may be seen from F i g . 4.19 that the specimens c o n t a i n i n g s t e e l f i b e r s showed a great e r c a p a c i t y to deform and to s u s t a i n a l a r g e r number of c y c l e s . T h i s means that the SFRC specimens e x h i b i t e d more apparent d u c t i l e behaviour and energy a b s o r p t i o n c a p a c i t y than the p l a i n concrete specimens (P-RV/5 and P-RV/6). The load c a p a c i t y f o r the p l a i n c o n c r e t e specimens dropped at a displacement of 2.5mm of the r e i n f o r c i n g bar, whereas the f i b e r r e i n f o r c e d specimens withstood deformations of more than 4.0mm before undergoing a r e d u c t i o n i n the load c a p a c i t y . T h i s improved deformation c a p a c i t y f o r f i b e r r e i n f o r c e d c o n c r e t e can a l s o be e x p l a i n e d i n terms of the load-displacement 180 FIG.4.19 E N V E L O P E OF PEAK S T R E S S E S - D I S P L A C E N T CURVES 181 r e l a t i o n s h i p s of p r i s m a t i c beams (1OOx100x350mm) t e s t e d under four p o i n t l o a d i n g as shown i n F i g . 2.8. The presence of r e l a t i v e l y d u c t i l e s t e e l f i b e r s i n an i n h e r e n t l y b r i t t l e matrix m o d i f i e s the b r i t t l e behaviour of the matrix c o n s i d e r a b l y by i n h i b i t i n g crack opening and imparting pseudo-post c r a c k i n g d u c t i l i t y to the matrix, thus a l l o w i n g i t to withstand g r e a t e r deformations than the matrix alone. F u r t h e r , the f i b e r s i n c r e a s e the toughness or energy absorbing c a p a c i t y , thus transfo r m i n g the concrete from a r e l a t i v e l y b r i t t l e m a t e r i a l to a r e l a t i v e l y d u c t i l e m a t e r i a l ; the term d u c t i l i t y i s used here to mean energy a b s o r p t i o n and d i s s i p a t i o n c a p a c i t y . According to B r e s l e r and Bertero (13) , the e f f e c t i v e n e s s of concrete confinement i n producing d u c t i l i t y i n earthquake r e s i s t a n t r e i n f o r c e d c o n c r e t e s t r u c t u r e s i s based on two c o n d i t i o n s : i . The confinement i n c r e a s e s the compressive s t r e n g t h in concrete and may o f f s e t the l o s s of s t r e n g t h due to c r a c k i n g , c r u s h i n g , or s p a l l i n g of concrete under severe l o a d i n g c o n d i t i o n s . i i . The confinement i n c r e a s e s the c a p a c i t y of concrete to s u s t a i n l a r g e deformations without l o s s of s t r e n g t h . T h e r e f o r e , the r o l e of s t e e l f i b e r s i n imparting r e l a t i v e l y d u c t i l e behaviour to the composite needs to be thoroughly understood and i n v e s t i g a t e d ; t h e i r e f f e c t may be con s i d e r e d analogous to the e f f e c t of concrete confinement. 182 4.6 YIELD PENETRATION ALONG BAR I t has a l r e a d y been mentioned i n Chapter 1 that i n an i n t e r i o r beam-column j o i n t of a high r i s e moment r e s i s t i n g d u c t i l e frame s t r u c t u r e , the l o a d i n g c o n d i t i o n s due to seismic motions may cause simultaneous y i e l d i n g of the beam's r e i n f o r c i n g bars (passing through the column) at both faces of the column. The y i e l d i n g may penetrate f u r t h e r inwards due to the l o s s of bond caused by s e v e r a l c y c l e s of imposed l o a d i n g , thus reducing the e f f e c t i v e embedment l e n g t h . T h i s behaviour has been observed and i d e n t i f i e d f o r v a r i o u s specimens t e s t e d here that were subjected to reversed c y c l i c l o a d i n g to very high peak amplitudes. Based on the s t r a i n v a l u e s, a comparison of i d e n t i c a l specimens su b j e c t e d to s i m i l a r l o a d i n g was made with regard to the extent of y i e l d p e n e t r a t i o n from both the push i n and p u l l out ends. For t h i s purpose, the y i e l d s t r a i n f o r the r e i n f o r c i n g s t e e l was assumed to be 2000 m i c r o - s t r a i n . The r e s u l t s have been presented i n Table 4 . 2(a) & (b). I t may be co n s i d e r e d that the extent of y i e l d p e n e t r a t i o n i s an i n d i c a t i o n of the damage caused i n the concrete boundary l a y e r surrounding the r e i n f o r c i n g bar due to s e v e r a l l o a d r e v e r s a l s at very high amplitudes of l o a d i n g . T h e r e f o r e , f o r e f f i c i e n t and s a t i - s f a c t o r y anchorage bond performance, i t i s imperative to c o n t r o l the p e n e t r a t i o n of y i e l d i n g i n t o the core of the specimen, t o guarantee the s t r e n g t h and s t i f f n e s s of the specimen. T h i s means that an " e f f i c i e n t " j o i n t should allow l i t t l e or no y i e l d p e n e t r a t i o n . Though i t i s apparently d i f f i c u l t to q u a n t i f y the bond e f f i c i e n c y of the specimens TABLE 4.2(a) YIELD PENETRATION (MM) FOR SPECIMENS (RV) S t r e s s Level K s i (MPa) PULL OUT END ( + ) P-5QO/25/RV/5 F2-500/25/RV/17 +58 . 4 (402 ) + 6 3 . 5 + 38 . 1 +G5.94 (454 1 + 86.4 +63.5 ±71.18 (490) +106.7 + 94.0 TABLE 4.2(b) YIELD PENETRATION (MM)  FOR SPECIMENS (RVM) CO <-»J S t r e s s Level K s i (MPa) f >ULL OUT END ( + ) P-RVM/20 F1-RVM/21 F2-RVM/22 59 .94 (413) 7 1 .93 (496) 77.92 ( 537 ) 50.8 10G . 7 133 . 7 45.7 86.4 < 101 G 106 . 7 184 sub j e c t e d to reversed c y c l i c l o a d i n g , i t i s u s e f u l to have some idea of t h e i r r e l a t i v e bond performance by making a comparison of v a r i o u s specimens with r e s p e c t to the magnitudes of y i e l d p e n e t r a t i o n . A comparison of the y i e l d p e n e t r a t i o n values ( p u l l out end) presented i n Table 4.2 f o r v a r i o u s specimens under i d e n t i c a l l o a d i n g , r e v e a l s that the specimens c o n t a i n i n g s t e e l f i b e r s (SFRC) had improved bond c h a r a c t e r i s t i c s as compared to those of p l a i n c o n c r e t e . 4.7 BOND DEGRADATION RATIO: I t has alr e a d y been demonstrated that specimens subjected to r e v e r s e d c y c l i c l o a d i n g with m u l t i p l e c y c l e s (RVM) at a f i x e d amplitude of l o a d i n g undergo bond degradation with an increase in the number of c y c l e s , e s p e c i a l l y when the peak amplitude i s above the y i e l d s t r e s s l e v e l of the r e i n f o r c i n g s t e e l . Though i t i s extremely d i f f i c u l t to measure q u a n t i t a t i v e l y the extent of bond d e t e r i o r a t i o n , one method would be to compare the displacements at v a r i o u s c y c l e s . To understand the p h y s i c a l phenomena of bond degradation at v a r i o u s s t r e s s l e v e l s and a l s o to compare the r e s u l t s of v a r i o u s i d e n t i c a l l y loaded specimens, a q u a n t i t y c a l l e d the Bond Degradation R a t i o w i l l be d e f i n e d : -Bond Degradation R a t i o = Displacement in the Nth Cycle at a p a r t i c u l a r s t r e s s l e v e l Displacement i n the 1st Cycle where N = Number of c y c l e s at the load amplitude at which bond degradation i s to be computed. The Bond Degradation R a t i o s f o r v a r i o u s specimens at v a r i o u s peak s t r e s s l e v e l s under RVM l o a d i n g are t a b u l a t e d in Table 4.3(a) & (b). The r e l a t i o n s h i p between BDR and the number T A B L E 4 . 3 ( a ) BOND DEGRADAT ION R A T I O ( B D R ) A P P L I E D S T R E S S L E V E L = 78 KS I ( 5 3 8 MPA) N. S I D E S. S IDE S P E C I M E N NO. C Y C L E NO. D I SP (MM) BDR D I S P ( M M ) BDR F 2 - 5 0 0 / 2 5 / R V M / 1 9 1 2 42 1 0 2 01 1 .0 2 2 52 1 04 2 1 1 1 .05 3 2 18 1 .08 4 2 8 0 1 157 2 33 1 16 5 2 86 1 18 2 46 1 . 2 2 6 3 0 5 1 26 2 56 1 27 7 3 2 0 ,1 32 2 87 1 42 8 3 63 1 5 0 3 35 1 66 P - 5 0 0 / 2 5 / R V M / 2 0 1 3 01 1 2 4 8 2 73 2 3 76 ( f a l e d ) F 1 - 5 0 0 / 2 5 / R V M / 2 1 1 2 22 1 0 2 0 4 1 0 2 2 34 1 0 5 2 15 1 0 5 7 3 2 48 1 12 2 23 1 0 9 5 4 2 6 0 1 17 2 31 1 133 5 2 74 1 23 2 38 1 171 6 2 92 1 31 2 47 1 212 7 3 0 7 1 38 2 56 1 2 5 9 8 3 22 1 45 2 68 1 315 9 3 43 1 55 2 8 9 1 421 10 3 76 1 6 9 2 58 1 758 1 1 5 56 2 5 ( f a i l e d ) F 2 - 5 0 0 / 2 5 / R V M / 2 2 1 2 31 1 0 2 01 1 0 0 0 (w i t h h e l I x ) 2 2 41 1 04 2 0 8 1 0 3 5 3 2 51 1 0 9 2 2 1 1 101 4 2 61 1 13 2 29 1 136 5 2 74 1 18 2 39 1 187 6 2. 82 1 22 2 5 1 1 2 5 0 7 2 . 97 1 29 2 72 1 351 T A B L E 4 . 3 ( b ) BOND D E G R A D A T I O N R A T I O ( B D R )  A P P L I E D S T R E S S L E V E L = 72 KS I ( 4 9 6 MPA) N. S IDE S. S I D E C D C n kit? K] j r t U l MLlN NO. C Y C L E NO. D I S P ( M M ) BDR D I S P ( M M ) BDR F 1 - 5 0 0 / 2 5 / R V M / 1 3 1 1 85 1 . 0 0 2 . 7 6 1 . 0 0 2 1 9 9 1 0 7 2 . 77 1 . 0 0 6 3 2 0 9 1 . 13 2 .81 1 . 0 1 7 4 2 15 1 . 16 2 .84 1 .031 5 2 23 1 . 2 0 4 2 . 9 3 1 . 0 6 2 6 2 31 1 . 2 4 7 3 . 0 0 1 . 0 8 6 7 2 40 1 2 9 6 3 . 0 7 1 . 1 1 4 8 2 51 1 3 5 8 3 . 18 1 151 9 2 63 1 4 2 2 3 . 28 1 . 188 10 2 82 1 52 1 3 . 4 9 1 . 2 6 6 F 2 - 5 0 0 / 2 5 / R V M / 1 4 1 2 23 1 0 0 1 . 9 3 1 0 0 2 2 0 2 1 0 4 7 3 2 26 1 01 1 1 14 1 106 4 2 3 0 1 0 2 8 2 23 1 158 F 2 - 5 0 0 / 2 5 / R V M / 1 5 1 2 02 1 0 0 2 29 1 0 0 2 2 0 8 1 0 2 8 2 37 1 0 3 4 P - 5 0 0 / 2 5 / R V M / 2 0 1 2 04 1 0 0 1 81 1 0 0 2 2 14 1 0 4 6 1 95 1 0 0 187 o f c y c l e s a t p e a k s t r e s s levels o f 72 k s i ('496 M P a ) a n d 78 k s i (538 M P a ) a r e shown i n F i g s . 4 . 2 0 ( a ) & ( b ) . T h e s e T a b l e s a n d F i g u r e s i n d i c a t e a much h i g h e r r a t e o f b o n d d e g r a d a t i o n f o r t h e p l a i n c o n c r e t e s p e c i m e n ( P - R V / 2 0 ) t h a n f o r s t e e l f i b e r r e i n f o r c e d c o n c r e t e s p e c i m e n s . T h i s s h o w s t h a t t h e s t e e l f i b e r s a r e e f f e c t i v e i n r e t a r d i n g t h e r a t e o f b o n d d e g r a d a t i o n . T h o u g h an a t t e m p t h a s b e e n made t o q u a n t i f y t h e b o n d d e g r a d a t i o n a t v a r i o u s c y c l e s o f l o a d i n g , a t a p a r t i c u l a r s t r e s s l e v e l i t i s d i f f i c u l t t o c o m p a r e t h e r e l a t i v e b o n d c a p a c i t i e s o f s p e c i m e n s f o r g e n e r a l i z e d l o a d i n g c a s e s . T h e r e f o r e , a n o t h e r s o l u t i o n t o t h e p r o b l e m h a s b e e n d e v e l o p e d t o make a c o m p a r a t i v e s t u d y o f t h e b o n d e f f e c t i v e n e s s . T h i s m e t h o d u t i l i z e s t h e c o n c e p t o f t h e r e l a t i v e w o r k d o n e i n c r e a t i n g a c e r t a i n a m o u n t o f d e f o r m a t i o n i n t h e r e i n f o r c i n g s t e e l , a n d u s e s t h i s t o c o m p u t e t h e b o n d e f f e c t i v e n e s s . T h e s t r a i n - d i s t r i b u t i o n d i a g r a m s f o r t w o s p e c i m e n s a r e c o m p a r e d u n d e r i d e n t i c a l l o a d i n g h i s t o r i e s a n d c o n d i t i o n s o f l o a d i n g f o r a p a r t i c u l a r a p p l i e d s t r e s s l e v e l . The d i f f e r e n c e i n t h e a r e a u n d e r t h e s t r a i n d i s t r i b u t i o n d i a g r a m s e x p r e s s e d a s a p e r c e n t a g e o f t h e t o t a l a r e a u n d e r t h e s t r a i n d i s t r i b u t i o n d i a g r a m s , e i t h e r i n t h e t e n s i o n o r i n t h e c o m p r e s s i o n p o r t i o n , i n d i c a t e s t h e b o n d e f f e c t i v e n e s s o f t h e s p e c i m e n . T h e r e a s o n f o r u s i n g t h i s c o n c e p t i s t h a t t h e a d d i t i o n a l s t r a i n d e v e l o p m e n t i s p r i m a r i l y due t o t h e b o n d d e g r a d a t i o n . T h e r e f o r e , t h e b o n d e f f e c t i v e n e s s c a n be m a t h e m a t i c a l l y e x p r e s s e d a s : x(PCC) dx - / e x(SFRC) dx o o Bond Effectiveness 'x(.pCC) dx o <4-7) 188 1.7.. • APPLIED STRESS-78 KSI ( 538 Mpa) / NO. OF CYCLES FIG.4«20a.DIAGRAM SHOWING BOND DEGRADATION RATIO VS.NO. OF CYCLES 189 F I G . 4.20(b) BOND DEGRADATION RATIO VS. NO. OF CYCLES 190 where c = s t r a i n at any p o i n t i n the bar I-l = le n g t h of the t e n s i l e or compressive p o r t i o n of the bar For example, the s t r a i n d i s t r i b u t i o n diagrams f o r specimens P-RV/5 and F2-RV/17, under i d e n t i c a l l o a d i n g c o n d i t i o n s are p l o t t e d i n F i g . 4.21. Since the bond i s c r i t i c a l i n the t e n s i l e end, the comparison i s made f o r the t e n s i l e p o r t i o n of the r e i n f o r c i n g bar. On computing the d i f f e r e n c e s in areas of the s t r a i n diagrams by means of a planimeter, or by using a small computer program and d i v i d i n g that by the area under the s t r a i n d i s t r i b u t i o n curve f o r the p l a i n concrete specimen, the f o l l o w i n g r e s u l t s are obt a i n e d : A p p l i e d S t r e s s l e v e l Bond E f f e c t i v e n e s s of SFRC Specimens 29.77 k s i (205 MPa) 23 percent 43.45 k s i (300 MPa) 25.7 percent 58.40 k s i (402 MPa) 20.1 percent 65.94 k s i (455 MPa) 26.2 percent The above o b s e r v a t i o n s i n d i c a t e that the SFRC specimens have a higher bond c a p a c i t y under reversed c y c l i c l o a d i n g of the order of 20 to 26 pe r c e n t . 4.8 CIRCUMFERENTIAL CRACK FORMATION It was mentioned i n Chapter 3 that the emergence of a c i r c u m f e r e n t i a l crack on the face of a specimen subjected to push-in p u l l - o u t l o a d i n g i s i n d i c a t i v e of the onset of a p u l l -out bond f a i l u r e . T h e r e f o r e , i t i s important to examine the 161 192 crack formation and to note the s t r e s s l e v e l at which the crack i s formed. A comparison of t h i s s t r e s s l e v e l f o r v a r i o u s specimens would i n d i c a t e the r e s i s t a n c e of the specimen to bond d e t e r i o r a t i o n . These d e t a i l s are presented i n Table 4.4. It can be seen that f o r the specimens subjected to monotonic (MO) and repeated l o a d i n g (RP), the c i r c u m f e r e n t i a l c r a c k i n g s t r e s s l e v e l i s the highest (90.3 k s i {623 MPa}) while f o r reversed c y c l i c l o a d i n g (RVM), i t i s the lowest (74.2 k s i {512 MPa}). T h i s s i g n i f i e s that more damage and bond degradation occurred for r e versed c y c l i c l o a d i n g than f o r monotonic l o a d i n g . A hypothesis regarding c r a c k i n g and the crack formation w i l l be presented i n Chapter 6. TABLE.4-4  CIRCUMFERENTIAL CRACKING LOAD FOR VARIOUS SPECIMENS Spec 1men No. Load Type C i rcumferent i a 1 C r a c k i n g Load (MPa) Average Crack i ng Load (MPa) Remarks F2-500/25/MO/10 F1-500/25/MO/12 F2-5OO/25/M0/18 MO 630. 2 630. 2 608.8 622 .8 F2-500/25/RP/9 F1-500/25/RP/11 RP 630.9 was not loaded beyond 558 MPa P-500/25/RV/5 P-500/25/RV/6 F2-500/25/RV/8 F1-500/25/RV/16 F2-500/25/RV/17 RV 522.6 520.6 548 . 2 582 .6 522 .6 539.3 F2-500/25/RV/19 P-500/25/RVM/21 F1-500/25/RVM/20 F2-500/25/RVM/22 F1-500/30/RVM/25 RVM 486.8 486.8 527 . 5 527 . 5 529.5 511.6 194 V. AXIAL STIFFNESS DEGRADATION PHENOMENON:  FORMULATION OF AN APPLIED STRESS VS. DISPLACEMENT MODEL  (Reversed C y c l i c Loading) 5. 1 INTRODUCTION I t has a l r e a d y been noted that the i n t e r i o r beam-column j o i n t of a moment r e s i s t i n g d u c t i l e frame s t r u c t u r e s u f f e r s degradation i n s t r e n g t h , s t i f f n e s s and energy absorbing c a p a c i t y under severe r e v e r s a l s of l a t e r a l l o a d i n g caused by earthquake motions. T h i s chapter i s concerned mainly with the study of s t i f f n e s s degradation due to reversed c y c l i c l o a d i n g . The terms such as displacement, s t i f f n e s s , and so on used here, have alre a d y been d e f i n e d i n Chapter 3 . The degradation i n s t i f f n e s s i s mainly a consequence of the i n e l a s t i c deformation and c r a c k i n g of the c o n c r e t e , the Bauschinger e f f e c t of the r e i n f o r c i n g s t e e l , d e t e r i o r a t i o n of bond, and s l i p of the main r e i n f o r c i n g bars of the a d j o i n i n g beams which pass through the column at the i n t e r i o r beam column j o i n t . T h e r e f o r e , to study the response of the "block of c o n c r e t e " model used i n t h i s study, and e s p e c i a l l y the bond d e t e r i o r a t i o n i n the j o i n t under c y c l i c load r e v e r s a l s , the phenomenon of s t i f f n e s s degradation should be thoroughly understood. T h i s can be s t u d i e d in terms of the r e s u l t s o btained from measurements of p u l l - o u t and push-in of the r e i n f o r c i n g bar at the face of the column. In t h i s Chapter, the h y s t e r e t i c curves of the a p p l i e d s t r e s s - d i s p l a c e m e n t r e l a t i o n s h i p s of the r e i n f o r c i n g bar f o r v a r i o u s specimens under d i f f e r e n t l o a d i n g - h i s t o r i e s are used to explore the s t i f f n e s s 195 degradation phenomenon. From the p a t t e r n s of h y s t e r e t i c behaviour ( a p p l i e d s t r e s s -displacement curves) beyond the y i e l d s t r e s s l e v e l , i t appears that s t i f f n e s s ( loading) always decreases with e i t h e r an i n c r e a s e i n peak l o a d i n g (beyond y i e l d ) or an i n c r e a s e i n the number of c y c l e s . A small amount of s t i f f n e s s degradation (KTI) i s a l s o observed at s t r e s s l e v e l s below the y i e l d s t r e s s l e v e l . However, t h i s e f f e c t i s s m a l l , and not c o n s i d e r e d in t h i s i n v e s t i g a t i o n . It may be observed from a number of the h y s t e r e t i c curves that when the a p p l i e d s t r e s s l e v e l exceeds the y i e l d s t r e s s i n the r e i n f o r c i n g bar, there i s an abrupt change in the appearance of the curves. T h i s i s mainly due to p r o g r e s s i v e degradation of the composite a c t i o n between the r e i n f o r c i n g bar and the c o n c r e t e . The small amount of degradation (KTI) that takes place before y i e l d i s aggravated with the onset of y i e l d i n g i n the r e i n f o r c i n g s t e e l . For s t r e s s e s beyond y i e l d , the Bauschinger e f f e c t f u r t h e r aggravates the degradation i n composite a c t i o n as a consequence of s t r e s s r e v e r s a l s . At t h i s stage, the mechanical p r o p e r t i e s of the r e i n f o r c i n g s t e e l seem to govern the response of the system. Regardless of the amount of deformation at the peak s t r e s s l e v e l s , the unloading curves a l l tend to have the same slope, as shown in a t y p i c a l case f o r specimen F2-RVM/19 (dotted l i n e s in F i g . 5.1). I t was decided to c o n s i d e r each h a l f c y c l e of the h y s t e r e t i c curve as c o n s i s t i n g of three l i n e a r segments as shown in F i g . 3.1. These are summarized below: FIG.5 . 1 COMPARISON OF K VALUES FOR F2-RVM/19 197 Stage I - From zero to 60 k s i (414 MPa) (approximate y i e l d s t r e s s i n the r e i n f o r c i n g s t e e l ) Stage II - From 60 k s i (414 MPa) to the maximum peak s t r e s s l e v e l . Stage III Unloading from the peak s t r e s s l e v e l back to zero l o a d . Henceforth, each h a l f c y c l e w i l l be modelled as a t r i l i n e a r a p p l i e d - s t r e s s - d i s p l a c e m e n t curve; the slop e s of these l i n e a r segments w i l l be c o n s i d e r e d to represent the s t i f f n e s s e s (KTI,KTII,KTL & so on). The s t i f f n e s s c h a r a c t e r i s t i c s of each segment of the v a r i o u s t r i l i n e a r curves w i l l be compared f o r v a r i o u s specimens with r e s p e c t to loa d h i s t o r y and other parameters. Based on these f i n d i n g s an a p p l i e d s t r e s s -displacement model w i l l be formulated. T h i s w i l l be d e s c r i b e d in d e t a i l in t h i s chapter. The f o l l o w i n g p o i n t s should be noted i n connection with the fo r m u l a t i o n of the model: 1. S t i f f n e s s degradation (KTI) below the y i e l d s t r e s s l e v e l , due to e i t h e r an i n c r e a s e i n the peak amplitude of l o a d i n g or to an in c r e a s e i n the number of c y c l e s of load r e v e r s a l s at a p a r t i c u l a r amplitude, i s q u i t e s m a l l as mentioned above, and hence i s not con s i d e r e d f u r t h e r . 2. The model i s a p p l i c a b l e to load h i s t o r i e s i n which the peak s t r e s s i n c r e a s e s i n c r e m e n t a l l y from c y c l e to c y c l e . I t does not c o n s i d e r load beyond the maximum r e s i s t a n c e c a p a c i t y of the specimens. 198 3. The data u t i l i z e d i n the f o r m u l a t i o n of the model have been generated from the r e s u l t s of the t e s t specimens i n t h i s i n v e s t i g a t i o n . T h e r e f o r e , the v a l i d i t y of the model i s l i m i t e d to the parameters or v a r i a b l e s used in these t e s t specimens. 5.2 OBJECTIVE OF THE MODEL The main o b j e c t i v e f o r the f o r m u l a t i o n of an e m p i r i c a l model i s to e s t a b l i s h a procedure to d e s c r i b e the h y s t e r e t i c responses of a specimen r e p r e s e n t i n g a beam column j o i n t under reversed c y c l i c l o a d i n g to any amplitude. The model developed below takes i n t o account some of the f a c t o r s r e s p o n s i b l e f o r the h y s t e r e t i c behaviour of a specimen (such as Bauschinger e f f e c t , n o n - l i n e a r behaviour i n s t e e l , bond d e t e r i o r a t i o n , and so on) in an i n d i r e c t way by determining the s t i f f n e s s degradation c h a r a c t e r i s t i c s of v a r i o u s specimens t e s t e d i n the l a b o r a t o r y under d i f f e r e n t c o n d i t i o n s of l o a d i n g . The model may be u s e f u l f o r p r e d i c t i n g behaviour under other l o a d i n g c o n d i t i o n s , subject to v e r i f i c a t i o n by more t e s t s . However, u n t i l such t e s t s are c a r r i e d out, the model should simply be c o n s i d e r e d as a d e s c r i p t i o n of the data obtained i n the present t e s t s . 5.3 GEOMETRIC CHARACTERISTICS OF HYSTERESIS LOOPS The comparison of the t r i l i n e a r a p p l i e d s t r e s s - d i s p l a c e m e n t curves f o r a t y p i c a l specimen r e v e a l s the f o l l o w i n g c h a r a c t e r i s t i c s : (Refer to F i g . 5.1) 1. A f t e r l o a d i n g i n t e n s i o n , the unloading curves (KTL) are p a r a l l e l to each o t h e r . F u r t h e r , the slope of the 1st l o a d i n g curve i n t e n s i o n up to the y i e l d s t r e s s i s 199 the same as that of the unloading curves. In compression, the unloading curves (KCL) are a l s o p a r a l l e l , but the s t i f f n e s s i n compression i s appa r e n t l y s l i g h t l y higher than that i n t e n s i o n . The slope of the l o a d i n g curves up to 60 k s i (414 MPa) in t e n s i o n ( s t i f f n e s s KTI) i s p r a c t i c a l l y the same as that of the preceding curve in compression ( s t i f f n e s s KCI) up to 60 k s i (414 MPa), even when the lo a d amplitude i n the previous c y c l e exceeded the y i e l d s t r e s s . A comparison of a l l of the KTI and KCI values f o r a t y p i c a l specimen F2-RVM/19 i s shown i n the Table attached to F i g . 5.1. The KTI vs KCI r e l a t i o n s h i p f o r a l l other specimens i s shown i n F i g . 5.2. I t can be seen from the curve that a 45 degree l i n e f i t s the data reasonably w e l l . With an incremental i n c r e a s e i n the peak s t r e s s l e v e l , e s p e c i a l l y beyond the y i e l d s t r e s s i n the s t e e l , the s t i f f n e s s e s (KTI,KTII,KCI,KCII) undergo marked degradation i n Stage I or Stage II of each h a l f c y c l e as may be seen from the r e d u c t i o n of the slopes (e.g. in F i g . 5.1). S i m i l a r behaviour i s a l s o observed when the number of c y c l e s i s i n c r e a s e d while keeping the amplitude of the peak s t r e s s l e v e l a constant, as long as the a p p l i e d s t r e s s i s high enough (at l e a s t above y i e l d ) ' to breakdown the composite a c t i o n between concrete and s t e e l . ® • P-RV/5(S) • F2-RV/8(S) 4 F1-RVM/13(S) * F1-RVM/13(N) • F2-RVM/15(S) D F1-RV/16(N) •F2-RV/17(S) +F2-RV/17(N) • F2-RVM/19(N) • F2-RVM/19(S) A P-RVM/20(S) v P-RVM/20(N) t F1-RVM/21(S) t Fl-RVM/21(N) f F2-RVM/22(S) * F2-RVM/22(N) ir P-RVM/23 (S) • P-RVM/23(N) # P-RVM/24(S) * P-RVM/24(N) KJ O O 400 800 1200 K,., ( K S I / I N ) 1600 FIG. 5-2 COMPARISON OF F^j & Kyj VALUES FOR ALL SPECIMENS 201 5.4 STIFFNESS DEGRADATION 5.4.1 E f f e c t of Number of C y c l e s on S t i f f n e s s Degradation: There appeared to be an a p p r e c i a b l e amount of s t i f f n e s s d e g r a d a t i o n i n t e n s i o n as w e l l as i n compression for a l l specimens t e s t e d , i r r e s p e c t i v e of whether the matrix was p l a i n or f i b e r r e i n f o r c e d c o n c r e t e , when the peak amplitude of l o a d i n g exceeded the y i e l d s t r e s s i n the s t e e l . T h i s degradation g e n e r a l l y o c c u r r e d a f t e r only a few reversed c y c l e s (4 to 10 c y c l e s ) , and e s p e c i a l l y when the peak s t r e s s l e v e l exceeded about 72 k s i (496 MPa). Even a f t e r only two c y c l e s at a peak s t r e s s l e v e l of 78 k s i (538 MPa), the p l a i n c o n c r e t e specimen underwent sudden bond f a i l u r e due to p u l l i n g out of the r e i n f o r c i n g bar from the c o n c r e t e . However, the f i b e r r e i n f o r c e d concrete specimens underwent such f a i l u r e only a f t e r many c y c l e s of load r e v e r s a l s at t h i s peak s t r e s s l e v e l . In order to compare the amount of s t i f f n e s s degradation of specimens (KTII or KCII) s u b j e c t e d to s i m i l a r load h i s t o r i e s (RV or RVM), the s t i f f n e s s d egradation curves up to 78/80 k s i (538/552 MPa) i n t e n s i o n are shown i n F i g . 5.3 and those i n compression, i n F i g . 5.4. The s t i f f n e s s degradation l i n e s are r e g r e s s i o n l i n e s drawn through each set of data p o i n t s (the c o e f f i c i e n t of c o r r e l a t i o n ranging from 0.9 to 1.0 i n F i g . 5.3 and 0.89 to 1.0 i n F i g . 5.4). The f i g u r e s i n d i c a t e an o v e r a l l average r a t e of degradation i n s t i f f n e s s (KTII) of 25.4 k s i / i n / c y c l e (6.9 MPa/mm/cycle) i n t e n s i o n and 39.7 k s i / i n / c y c l e (10.8 MPa/mm/cycle) in compression (KCII). The s t i f f n e s s 2 0 2 J L 6 o SPECIMEN F2-RVM/22 H + SPECIMEN Fl-RVM/21 « - D — * SPECIMEN F2-RVM/19 L ^ w - a SPECIMEN F2-RV/17 \ \ \ 0\ \ N \ \ \ \ \ • CD • \ \ \ \ ~ i r 5.6 I 7.2 + V \ \ T 1 1 1 — 6.8 10.4 NO. OF CYCLES FIG.5.3 .KTII VS. NO. OF CYCLES \ fl.9 2.4 1^ 4.0 12.0 203 o o C3 o LO C3 CM . ID o 00 . i n Q © SPECIHEN F2-RVn/14 +--- + SPECIHEN F2-RVT1/15 -^-~^> SPECIHEN F2-RV/17 x- -—x SPECIMEN F2-RVH/13 ^ Q SPECIHEN F1-RVH/2! \ * V * SPECIHEN F2-RVH/22 CO "y^  in Pi H (_J C3 in C7 O * LO C 3 tM o CO . m J 1 1 L J _ L J I I L \ \ \ \ + \ \ \ \ \ CD \ \ J L •s. \ \ \ \ \ \ \ \ \ \ \ \ T r r o fl.S ~~r~ 2 A i 1 1 r i r 4.9 5.6 7.2 8.B ]QA 12.0 NO. OF CYCLES FIG.5.4 KCII VS. NO. OF CYCLES 204 degradation under c y c l i c l o a d i n g at a peak s t r e s s l e v e l of 72 ks i (496 MPa) i s a l s o a p p r e c i a b l e , though much l e s s than that at a peak s t r e s s l e v e l of 78 k s i (538 MPa). The average was 11.4 k s i / i n / c y c l e (3.1 MPa/mm/cycle) and 28.4 k s i / i n / c y c l e (7.7 MPa/mm/cycle) under t e n s i o n and compression r e s p e c t i v e l y . 5.4.2 S t i f f n e s s KCI vs Displacement at Beginning of Compression  C y c l e : From the a p p l i e d s t r e s s - d i s p l a c e m e n t curves f o r specimens sub j e c t e d to RV and RVM types of i n c r e m e n t a l l y i n c r e a s e d l o a d i n g , i t may be seen that the s t i f f n e s s (KCI) ( i n Stage I under compression) i s dependent on the i n i t i a l displacement at the beginning of the compression c y c l e . T h i s i s shown in F i g s . 5.5(a)&(b). A l l of the specimens having a 25mm t e s t bar and 500mm embedment le n g t h e x h i b i t e s s e n t i a l l y the same behaviour. The v a r i a t i o n of KCI was w i t h i n ±10 to 15 percent. T h e r e f o r e , a mean curve has been drawn to represent t h i s f a m i l y of curves ( F i g . 5.5(b)). Specimens P-RVM/23 and P-RVM/24, c o n t a i n i n g a 20mm t e s t bar (375mm embedment length) and specimen F1-RVM/25, c o n t a i n i n g a 30mm d i a t e s t bar (500mm embedment length) had curves which dropped more r a p i d l y i n d i c a t i n g more r a p i d d e t e r i o r a t i o n of KCI values with i n c r e a s e s i n i n i t i a l displacement at the beginning of the compression c y c l e . The data of the mean curve ( f o r specimens with 25mm diameter) as we l l as f o r other specimens when p l o t t e d on a sem i - l o g a r i t h m i c s c a l e y i e l d e d approximately a l i n e a r r e l a t i o n s h i p ( l i n e a r r e g r e s s i o n l i n e f i t t e d ; c o r r e l a t i o n f a c t o r = 0.98 to .99) as shown i n F i g . 5.6. The f o l l o w i n g equations were e m p i r i c a l l y IG. 5.5(a) K C I VS. DISPLACEMENT AT BEGINNING OF COMPRESSION CYCLE E E a DISPLACEMENT AT BEGINNING OF COMPRESSION C Y C L E ( I N G. 5.5(b)K VS. DISPLACEMENT AT BEGINNING OF COMPRESSION CYCLE 207 CO r o ' o- -o SPECIMEN 25J0TREBRR - -+ SPECIMEN 20£30JZfREBflR ro ro ro CM ro' ID I—I I—I CJ g ^ ro" L D O ro p i ' C D LD r— p i CD ID p i 0 2.44 2.85rrd i 1 r 1 r~ 0.8 0.96 1.12 O.D i 1 r 0.16 — i 1 1 1 r 0.32 0.48 0.64 DISPLACEMENT-INCHES (XIO - 1 ) FIG.5 .6 LOG(KCII) VS. DISPLACEMENT RELATIONSHIP 208 determined for p r e d i c t i n g displacements ( l o a d i n g beyond y i e l d ) , knowing KCI values at the s t a r t of the compression c y c l e : 6 = _ J (3.36 - log KCI) - f o r specimens with 25mm d i a 7.18 --(5.4.1) t e s t bar (500mm embedment length) 6 = _1 (3.28 - log KCI) - f o r specimens with 20mm d i a 7.25 --(5.4.2) t e s t bar (375mm embedment length) & 30mm d i a t e s t bar (500mm embedment length) where 5 = displacement i n inches, and KCI i n k s i / i n u n i t s . 5.4.3 Change i n S t i f f n e s s (Stage II) with Increase in Peak  S t r e s s L e v e l : a. KTII versus A p p l i e d S t r e s s The a p p l i e d s t r e s s - d i s p l a c e m e n t curves f o r specimens s u b j e c t e d to RV and RVM types of i n c r e m e n t a l l y i n c r e a s e d l o a d i n g i n d i c a t e a decrease in s t i f f n e s s (KTII) with an in c r e a s e in peak l o a d i n g , as shown i n F i g . 5.7. The l i n e s appear to have s i m i l a r s lopes f o r both RV and RVM types of load h i s t o r y , the o v e r a l l average slope being 14 k s i / i n / k s i (0.55 MPa/mm/MPa). Beyond y i e l d , the concrete surrounding the r e i n f o r c i n g bar probably undergoes severe i n e l a s t i c deformations and c r a c k i n g . The Bauschinger e f f e c t in the r e i n f o r c i n g s t e e l a l s o s e t s i n , l e a d i n g to severe degradation i n bond and hence s t i f f n e s s . Another i n t e r e s t i n g phenomenon that was observed f o r a l l of the specimens i s that f o r the f i r s t t e n s i l e l o a d i n g beyond 60 k s i (414 MPa) the a x i a l s t i f f n e s s e s (KTII) are much l e s s than 209 FIG.5-7 APPLIED STRESS VS. KJJJ RELATIONSHIP 210 those i n the subsequent c y c l e s f o r the same peak l o a d i n g . T h i s behaviour may be seen i n F i g . 5.8, which r e p r e s e n t s the a p p l i e d s t r e s s - d i s p l a c e m e n t r e l a t i o n s h i p ( a c t u a l ) f o r specimen F1-RVM/19. The Fi g u r e shows that the s t i f f n e s s KTII i n the c y c l e marked (1) i s much l e s s than the s t i f f n e s s KTII in the subsequent c y c l e marked (2) f o r the same amplitude of l o a d i n g . T h i s seems to be due to the Bauschinger e f f e c t which has a l s o .caused a sharp r e d u c t i o n i n s t i f f n e s s KTI i n c y c l e (3) as compared to that in c y c l e ( 1 ) . S i m i l a r behaviour has a l s o been observed f o r the s t r e s s - s t r a i n curve f o r the r e i n f o r c i n g s t e e l under reversed c y c l i c l o a d i n g ( F i g . B-1). T h i s confirms the f a c t that the mechanical p r o p e r t i e s of the r e i n f o r c i n g s t e e l have a major i n f l u e n c e on the h y s t e r e t i c behaviour of the specimens, e s p e c i a l l y beyond the y i e l d s t r e s s l e v e l , b. KCII versus A p p l i e d S t r e s s The v a r i a t i o n s in s t i f f n e s s (KCII) i n compression with an inc r e a s e in peak s t r e s s l e v e l beyond 60 k s i (414 MPa) f o r specimens su b j e c t e d to RV and RVM types of i n c r e m e n t a l l y i n c r e a s e d l o a d i n g are shown i n F i g . 5.9. There appears to be s u b s t a n t i a l l y more degradation i n s t i f f n e s s i n compression than in t e n s i o n . The s t i f f n e s s degradation ranges from 16.9 k s i / i n (4.6 MPa/mm) to 53.8 k s i / i n (14.6 MPa/mm) i n d i c a t i n g a wide v a r i a t i o n between specimens. A d i s c u s s i o n on t h i s same w i l l be presented in Chapter 6. An e m p i r i c a l r e l a t i o n s h i p has been developed to p r e d i c t the s t i f f n e s s KCII f o r an a p p l i e d s t r e s s l e v e l of a p a r t i c u l a r compression h a l f -cycle. A n o n - l i n e a r r e g r e s s i o n method (103) 211 -D.04 -0.02 DISPLBCEflENT-(INCHES) FIG.5.8APPLIED STRESS VS DISPXURVES 212 £ LOAD TYPE RV & RVM o 0_ 60. 70 80 PEAK APPLIED STRESS(KSI) F I G . 5-9 APPLIED STRESS VS. K RELATIONSHIP 213 has been used to o b t a i n the f o l l o w i n g e q u a t i o n : C 2 K C l / " ) = K C I - C 1-K C J ( n).te ! n J i \0~(1) where KCIl(n) = a x i a l s t i f f n e s s s i s to be computed at any c y c l e 'n' a f t e r y i e l d . KCI(1) = KCI f o r f i r s t l o a d i n g i n compression ( a f t e r y i e l d ) KCI(n) = KCI i n the nth c y c l e a(n) = A p p l i e d s t r e s s l e v e l at which s t i f f n e s s to be computed ( i n the nth c y c l e ) . 0(1) = Peak s t r e s s l e v e l i n the 1 s t c y c l e ( a f t e r y i e l d ) . d , c 2 = c o n s t a n t s . In f a c t , the above form of the equation somewhat resembles the Ramberg-Osgood R e l a t i o n s h i p f o r d e s c r i b i n g the s t r e s s - s t r a i n r e l a t i o n s h i p of s t e e l under reversed c y c l i c l o a d i n g . I t suggests that the s t i f f n e s s i n Stage II was i n f l u e n c e d to a great extent by the s t e e l behaviour. The above r e l a t i o n s h i p r e s u l t s i n a good c o r r e l a t i o n with the experimental r e s u l t s as may be seen i n F i g . 5 . 1 0 . The values of the c o n s t a n t s d and c2 a r e : .5-4-3 FIG.5.10 CORRELATION OF EXPERIMENTAL DATA WITH EQUATION 5.4.3 215 Specimen Type c 1 c2 PCC 0.133 12.28 with 300mm long 0.037 11.17 s t e e l f i b e r s with 500mm long 0.028 15.01 s t e e l f i b e r s 5.5 FORMULATION OF AN APPLIED STRESS DISPLACEMENT MODEL , Th i s s e c t i o n d e s c r i b e s the c o n s t r u c t i o n of a t r i l i n e a r model f o r a specimen subjected to reversed c y c l i c l o a d i n g . Before g i v i n g the fo r m u l a t i o n of the model i t i s worthwhile summarizing the input i n f o r m a t i o n obtained p r e v i o u s l y : 1 . Unloading S t i f f n e s s e s (KTL,KCL). ( i ) s t i f f n e s s of the unloading curves except specimen P-RVM/23. (obtained as average f o r a l l specimens a p p l i e d s t r e s s displacement curves) = 2,420 k s i / i n (657 MPa/mm) ( f o r unloading from tension) (5.5.1(a) 3,000 k s i / i n (814 MPa/mm) ( f o r unloading from compression) (5.5.1(b) ( i i ) s t i f f n e s s of the unloading curves f o r specimen P-RVM/2 3 3,380 k s i / i n (917 MPa/mm) ( f o r unloading from tension) (5.5.1(c) = 3,930 k s i / i n (1067 MPa/mm) ( f o r unloading from compression) (5.5.1(d) 2. R e l a t i o n s h i p between KTII and number of c y c l e s . ( f o r a l l specimens) Average s t , i f f n e s s degradation = 11.4 k s i / i n / c y c l e (3.1 216 MPa/mm/cycle f o r a p p l i e d s t r e s s l e v e l = 72 k s i (496 MPa) (5.5.2(a) Average s t i f f n e s s degradation = 25.4 k s i / i n / c y c l e (6.9 MPa/mm/cycle f o r a p p l i e d s t r e s s l e v e l = 78/80 k s i (538/552 MPa) (5.5.2(b) For an a p p l i e d s t r e s s l e v e l between 72 to 80 k s i , the value of s t i f f n e s s degradation i s to be computed by i n t e r p o l a t i o n . R e l a t i o n s h i p between KCII and no. of c y c l e s . -( f o r a l l specimens) Average s t i f f n e s s degradation = 28.4 k s i / i n / c y c l e (7.7 MPa/mm/cycle) f o r a p p l i e d s t r e s s l e v e l = 72 k s i (496 MPa) (5.5.3(a) Average s t i f f n e s s degradation = 39.7 k s i / i n / c y c l e (10.8 MPa/mm/cycle) f o r a p p l i e d s t r e s s l e v e l = 78/80 k s i (538/552 MPa) (5.5.3(b) For a p p l i e d s t r e s s l e v e l between 72-80 k s i , the value of s t i f f n e s s degradation i s to be computed by i n t e r p o l a t i o n . R e l a t i o n s h i p between KCI and displacement at the  beginning of compression c y c l e -6 = J (3.36-log KCI) f o r specimens with 25mm d i a . bar 7 . 18 5.5.4(a) 6 = J (3.28-log KCI) f o r specimens with 20mm d i a . bar 7.25 (375 embedment length) & 30mm d i a . bar (500 embedment length) 5.5.4(b) 217 5. KTII versus A p p l i e d S t r e s s . Average degradation i n s t i f f n e s s = 14 k s i / i n / k s i (0.55 MPa/mm/MPa) 6. KCII versus A p p l i e d S t r e s s Average degradation i n s t i f f n e s s (KCII) can be computed by the f o l l o w i n g equation. c ^ 7. The s t i f f n e s s KTI f o r a p p l i e d s t r e s s l e v e l s l e s s than or equal to 60 k s i (414 MPa) may be taken to be the same as that of the unloading s t i f f n e s s . T h i s i s a p p l i c a b l e to specimens of both p l a i n or f i b e r r e i n f o r c e d c o n c r e t e . 8. The slope of the 1st l o a d i n g curve i n te n s i o n beyond the y i e l d s t r e s s ( i e KTII) may be taken as the slope of the monotonic curve at y i e l d s t r e s s f o r an i d e n t i c a l specimen. The value of KTII (Ko as shown i n F i g . 5.11(a)) ranges from 175 k s i / i n to 250 k s i / i n (47.5 to 67.9 MPa/mm). 5.6 CONSTRUCTION OF THE MODEL The c o n s t r u c t i o n of the a p p l i e d s t r e s s - d i s p l a c e m e n t model i s d e s c r i b e d f o r a t y p i c a l h y s t e r e t i c loop s t a r t i n g from compression as i n Sec. 5.5, i n d i c a t i n g the c o o r d i n a t e s of each p o i n t . (See F i g . 5.11) 5.5.5 5.5.6 218 FIG.5.11 CONSTRUCTION. OF APPL IED STRESS-D ISPLACEMENT MODEL 219 Procedure: 1 . Find K x - K c from Eq. (5.5.4) knowing (>1 A l - " A2 - 62 " \ " « x ) (5.6.1) 2 # Find K 2 from Eq. (5.5.6) o c - 60 . . . . o° ~ 60 h " Tpr^ or 6 3 - A, - 6 2 + — i ^ -3. 60 x o c - 60 6 i + Tr- (5'6'2> c o Obtain K 3 from Eq. (5.5.1) o C-60 ^  _ o_ (5.6.3) c so 6 4 " K L 1 K 2 3 a A o c ^ 60 60 . . _ o 6 - 60 4 * « 5 - A 4 + A 5 " A3 " r3 + *l - K7 + 61 K 2 o C-60 (5.6.4) 5. A6 " K A - + 61 K 2 ° T - 6° } obtain K 4 from Eq. (5.5.5) + |1 + , ( ^ 6 0 ) (5.6.5) 8 0 66 " A6 + S V K 4 ' N 3 A "2 T o Obtain K 5 from Eq. (5.5.1) so fi7 - 66 " *7 = K ~ 6T-> (5 .6.6) Thus the a p p l i e d s t r e s s - d i s p l a c e m e n t loop can be c o n s t r u c t e d . 220 7. In order t o c o n s t r u c t the a p p l i e d s t r e s s - d i s p l a c e m e n t curve s t a r t i n g from zero l o a d , the f o l l o w i n g a d d i t i o n a l procedure i s to be f o l l o w e d : 6Q " IT" Find 6' knowing K 5 ^ 6 1 " t + —*-> (5-6.7) 5 o 8. To take i n t o account the e f f e c t of the number of c y c l e s , the s t i f f n e s s KTII and KCII are to be m o d i f i e d as per equations 5-5.2(a) through 5.5.3(b). 5.7 COMPARISON OF THE MODEL WITH THE EXPERIMENTAL CURVE The a p p l i e d - s t r e s s displacement model has been c o n s t r u c t e d for two t y p i c a l cases, specimens FRV/16 and F1-RV/18 as per the procedure o u t l i n e d i n S e c t i o n 5.6. The peak amplitudes of lo a d i n g and the type of l o a d i n g are same as those of the experimental t e s t parameters f o r the specimens. The h y s t e r e t i c models c o n s t r u c t e d are compared with those of the a p p l i e d s t r e s s - d i s p l a c e m e n t curves f o r the specimens as obtained e x p e r i m e n t a l l y . These are shown i n F i g . 5.12 and F i g 5.13. I t may be observed from F i g . 5.12 that f o r specimen F1-RV/16, the model i s i n good agreement with the experimental curves, except for a few d i s c r e p a n c i e s . Up to Cyc l e 4 (503 MPa), the h y s t e r e t i c responses ( f o r the model and the experimental curve) are i n good agreement. Beyond t h i s , the displacements f o r the model i n c r e a s e f a s t e r than the corresponding experimental v a l u e s . For specimen F2-RV/8, the h y s t e r e t i c responses are i n good agreement even up to Cyc l e 7 (peak a p p l i e d s t r e s s = 548 MPa). Some of the d i s c r e p a n c i e s observed i n both of these cases 221 J L _l L J L EXPT. CURVE Specimen F1-RV/16 MODEL © a Q-co Si rsi LO LO 0.51 1.52 2.54 3.56 4.57 5.59mm 1 1 1 1 1 1 1 1 1 T 0.06 -0.02 D.02 0.06 0.1 D.!4 0.!B 0.22 DISPLflCErlENT(INCHES) F I G 5 - 1 2 - M O D E L VS EXPERIMENTAL CURVE 222 i i i l I I I L © © EXPTL CURVE 1 SPECIMEN F2-RV/8 H + MODEL 0 D I S P L A C E M E N T ^ } FIG. 5 4 3 MODEL VS, EXPERIMENTAL CURVE 223 can be e x p l a i n e d by the f a c t that any s l i g h t d e v i a t i o n s from the experimental curve in the i n i t i a l c y c l e s are accumulated in subsequent c y c l e s . F u r t h e r , the model has been based on a s t a t i s t i c a l a n a l y s i s of the r e s u l t s obtained from t e s t s of v a r i o u s specimens. T h e r e f o r e , some d e v i a t i o n i n the response of the a p p l i e d s t r e s s - d i s p l a c e m e n t curve may be expected. 5.8 LIMITATIONS OF THE MODEL The model as d e s c r i b e d i n t h i s Chapter has been formulated from the t e s t r e s u l t s of a l i m i t e d number of specimens. An i n c r e m e n t a l l y i n c r e a s i n g type of load h i s t o r y with a few r e v e r s e d c y c l e s at the peak amplitude of l o a d i n g has been c o n s i d e r e d . The model t h e r e f o r e can not be used to p r e d i c t the h y s t e r e t i c behaviour under more g e n e r a l i z e d types of l o a d i n g (e.g. r e a l earthquake response) without e x t e n s i v e f u r t h e r v e r i f i c a t i o n . More t e s t s with a l l the v a r i a b l e s that a f f e c t the bond behaviour would be necessary to extend the model for use under more general c o n d i t i o n s . As presented here, the model serves only as a mathematical f o r m u l a t i o n of the t e s t r e s u l t s obtained i n t h i s study. 5.9 STIFFNESS PRIOR TO LOSS OF STRENGTH, KTCR (STAGE II) The a p p l i e d s t r e s s versus displacement r e l a t i o n s h i p s f o r v a r i o u s specimens have a l r e a d y been presented in Chapter 3. On examination of the h y s t e r e t i c curves f o r a t y p i c a l specimen (P-RV/15) shown in F i g . 5.14 i t may be seen that with i n c r e m e n t a l l y i n c r e a s e d reversed c y c l i c l o a d i n g (RV or RVM type load h i s t o r y ) at a p a r t i c u l a r l o a d amplitude or a f t e r s e v e r a l c y c l e s of running at a p a r t i c u l a r load amplitude, the r e s i s t a n c e 224 225 c a p a c i t y of the specimen decreases. T h i s l o s s i n c a p a c i t y occurs a f t e r the s t i f f n e s s KTII has dropped below a c r i t i c a l l e v e l . I t may be seen i n F i g . 5.14 that a f t e r reaching a s t i f f n e s s KTII i n Stage I I , the specimen s u f f e r s a l o s s in r e s i s t a n c e c a p a c i t y . T h i s s t i f f n e s s p r i o r to the l o s s of st r e n g t h w i l l h e n c e f o r t h be r e f e r r e d to as KTCR and i s i n d i c a t e d in F i g u r e 5.14. The s t i f f n e s s KTCR f o r v a r i o u s specimens are t a b u l a t e d i n Table No. 5.1. On averaging the s t i f f n e s s e s (KTCR) for p l a i n concrete specimens and those of s t e e l f i b e r r e i n f o r c e d c o n c r e t e s e p a r a t e l y , the f o l l o w i n g r e s u l t s are obta i n e d : Average KTCR f o r PCC specimens - 400 k s i / i n (108 MPa/mm). Average KTCR f o r SFRC specimens = 300 k s i / i n (81 MPa/mm). Th i s shows that the p l a i n concrete specimens undergo a l o s s in r e s i s t a n c e c a p a c i t y a f t e r reaching KTCR = 400 k s i / i n (108 MPa/mm) whereas the same behaviour i s observed f o r SFRC specimens a f t e r reaching KTCR = 300 k s i / i n (81 MPa/mm). Th i s i n d i c a t e s that the f i b e r r e i n f o r c e d concrete specimens have a gr e a t e r c a p a c i t y to undergo deformations than those of p l a i n c o n c r e t e under i d e n t i c a l c o n d i t i o n s of l o a d i n g . T h i s shows the apparent d u c t i l e behaviour of SFRC specimens as compared to p l a i n c o n c r e t e ones. T A B L E 5.1 S T I F F N E S S PR IOR TO LOSS OF S T R E N G T H ' K T C R ' (<jA > 6 0 KS I ( 4 1 4 M P A ) ) S P E C I M E N A P P L I E D K T L S T R E S S L E V E L K s i ( M P a ) N. S IDE S. S I D E A V E R A G E K s i / i n (MPa/mm) K s i ( M P a ) P - 5 0 0 / 2 5 / R V / 5 7 9 ( 5 4 5 ) 4 1 8 ( 1 13 5 ) 4G8 ( 127 O ) FOR P C C = 3 9 6 P - 5 0 0 / 2 5 / R V / 6 7 9 ( 5 4 5 ) 434 ( 1 17 8 ) 4 14 ( 1 12 4 ) ( 1 0 7 . 5 ) F 2 - 5 0 0 / 2 5 / R V / 8 8 0 ( 5 5 2 ) 305 ( 82 8 ) 324 ( 8 7 9 7 ) FOR S F R C = 2 9 5 F 1 - 5 0 O / 2 5 / R V / 1 6 8 4 ( 5 7 9 ) 241 ( 65 4 ) 265 ( 71 9 ) ( 8 0 . 1 ) F 2 - 5 0 0 / 2 5 / R V / 1 7 7 9 ( 5 4 5 ) 295 ( 8 0 1) 3 1 7 ( 8 6 1 ) F 1 - 5 0 0 / 2 5 / R V M / 1 3 7 2 ( 5 4 5 ) 295 ( 8 0 1 ) 353 ( 9 5 8 ) F 2 - 5 0 0 / 2 5 / R V M / 1 4 7 9 ( 5 4 5 ) 271 ( 73 6 ) F 2 - 5 0 0 / 2 5 / R V M / 1 5 7 9 ( 5 4 5 ) 255 ( 6 9 2 ) 2 6 2 ( 71 1 ) F 2 - 5 0 0 / 2 5 / R V M / 1 9 7 9 ( 5 4 5 ) 322 ( 87 4 ) 2 9 7 ( 8 0 6 3 ) P - 5 0 0 / 2 5 / R V M / 2 0 7 9 ( 5 4 5 ) 251 ( 68 1 ) 3 8 9 ( 105 6 ) ' F 1 - 5 0 0 / 2 5 / R V M / 2 1 7 8 ( 5 3 8 ) 2 9 0 ( 78 7 ) 3 3 9 ( 92 0 4 ) F 2 - 5 0 0 / 2 5 / R V M / 2 2 7 8 ( 5 3 8 ) 317 ( 86 1) 258 ( 7 0 0 5 ) P - 3 7 5 / 2 5 / R V M / 2 3 7 9 ( 5 4 5 ) 533 ( 144 7 ) F 1 - 5 0 0 / 3 0 / R V M / 2 5 7 8 ( 5 3 8 ) 292 ( 79 3 ) 471 ( 127 9 ) N o t e - KTCR 1s c o n s i d e r e d o n t h e T e n s i o n S i d e o n l y . 227 VI. THEORY OF BOND DETERIORATION AND CRACKING: 6.1 GENERAL V a r i o u s i n v e s t i g a t o r s have used both experimental and a n a l y t i c a l i n v e s t i g a t i o n s to study the bond behaviour and the bond d e t e r i o r a t i o n mechanism under v a r i o u s l o a d i n g c o n d i t i o n s . A ccording to B r e s l e r and Ber t e r o (12) the b a s i c mechanism of bond d e t e r i o r a t i o n under repeated l o a d i n g i s a f a i l u r e i n the concrete 'boundary l a y e r ' adjacent to the s t e e l - c o n c r e t e i n t e r f a c e . The f a i l u r e occurs when the high l o c a l s t r e s s e s reach c r i t i c a l v a l u e s , and i n e l a s t i c deformation, l o c a l f r a c t u r e , and cr u s h i n g of the concrete take p l a c e . Upon complete r e l a x a t i o n of the load, some i r r e c o v e r a b l e damage remains, which accumulates i n su c c e s s i v e repeated c y c l e s of l o a d i n g . As the load i s in c r e a s e d to high l e v e l s , i t causes g r e a t e r damage to the co n c r e t e boundary l a y e r and hence reduces the bond e f f e c t i v e n e s s at lower s t r e s s l e v e l s . Although the above mechanism of bond d e t e r i o r a t i o n under repeated l o a d i n g i s q u i t e u s e f u l and pr o v i d e s more i n s i g h t i n t o the problem, f u r t h e r s t u d i e s are necessary to i d e n t i f y the p h y s i c a l phenomena that cause the bond d e t e r i o r a t i o n , e s p e c i a l l y under push-in p u l l - o u t l o a d i n g . Goto's (33) study on the i n t e r n a l crack development in concrete surrounding a r e i n f o r c i n g bar subjected to te n s i o n at both ends, has a l s o c o n t r i b u t e d s i g n i f i c a n t l y to the understanding of bond behaviour and f a i l u r e mechanisms. T h i s has a l r e a d y been d e s c r i b e d i n Chapter 1. Based on the e v a l u a t i o n of the experimental r e s u l t s 228 obtained i n t h i s i n v e s t i g a t i o n and the a n a l y t i c a l study d e s c r i b e d i n Chapter 7 as w e l l as a review of other s t u d i e s , a new theory of the bond d e t e r i o r a t i o n mechanism i s proposed in t h i s Chapter. 6.2 BOND DETERIORATION MECHANISM UNDER MONOTONIC PUSH-IN PULL- OUT LOADING: The bond behaviour and the bond d e t e r i o r a t i o n mechanism under monotonic l o a d i n g w i l l be d e s c r i b e d i n the f o l l o w i n g stages f o r c l a r i t y . 6.2.1 P e r f e c t Bond When the r e i n f o r c i n g bar i s loaded g r a d u a l l y and the a p p l i e d s t r e s s l e v e l ( i n the s t e e l ) i s q u i t e low, i t i s p o s s i b l e that p e r f e c t bond between the bar and concrete may e x i s t along the e n t i r e l e n g t h of embedment. T h i s means that the s l i p between the r e i n f o r c i n g bar and the concrete i s zero a l l along the bar. 6.2.2 E l a s t i c Bond Behaviour (No Cracking) As the loa d i n the bar i s f u r t h e r i n c r e a s e d g r a d u a l l y , the magnitude of the a p p l i e d load s t i l l being low, a stage w i l l be reached when the bond s t r e s s i s equal to the c r i t i c a l adhesive bond s t r e n g t h (0=00). At t h i s p o i n t , some s l i p w i l l occur, and bond due to adhesion d i s a p p e a r s . T h i s s l i p , however, w i l l be of a very small magnitude. Further l o a d i n g w i l l m o b i l i z e the mechanical i n t e r l o c k i n g of the mortar with the r i b s of the deformed bar, as w e l l as i n t e r l o c k i n g of the cement paste on the micr o s c o p i c i r r e g u l a r i t i e s of the bar s u r f a c e . Up to some range of l o a d i n g , the bond s t r e s s - s l i p r e l a t i o n s h i p i s l i n e a r . In 229 t h i s range, no c r a c k i n g i s developed i n the concrete surrounding the bar. 6.2.3 C r a c k i n g i n Concrete ( A p p l i e d S t r e s s < Y i e l d S t r e s s ) a. P u l l - O u t End On the p u l l out end, as the a p p l i e d load i s f u r t h e r i n c r e a s e d , when the bond s t r e s s (T) reaches the c r i t i c a l value, say r a , the f i r s t i n t e r n a l crack w i l l develop. Just at t h i s p o i n t , a l a r g e l o n g i t u d i n a l t e n s i l e s t r e s s ax, a r a d i a l t e n s i l e s t r e s s or (tending to cause s e p a r a t i o n ) and a bond s t r e s s r e x i s t , as d e s c r i b e d i n the f i n i t e element a n a l y s i s (Chapter 7 ) . The above f o r c e s combine to produce l a r g e d i a g o n a l t e n s i l e s t r e s s e s which cause d i a g o n a l c r a c k s to emanate from the t i p of the r i b s because of the s t r e s s c o n c e n t r a t i o n . These cracks reduce the slope of the bond s t r e s s - s l i p curve and produce a l a r g e r s l i p . The f i n i t e element a n a l y s i s (Chapter 7) p r e d i c t s the development of such i n t e r n a l d i a g o n a l cracks at s t r e s s l e v e l s as low as 6.0 ksi(41 MPa). The a n a l y t i c a l and the experimental data presented by Broms (16) and Lutz (58) a l s o e s t a b l i s h the e x i s t e n c e of such c r a c k s at the s t e e l - c o n c r e t e i n t e r f a c e . Goto's (33) experimental s t u d i e s (by s l i c i n g the t e s t specimens) a l s o c o n f i r m the presence of such c r a c k s . With a f u r t h e r i n c r e a s e i n l o a d i n g , Poisson's e f f e c t in the s t e e l w i l l have some i n f l u e n c e on the bond d e t e r i o r a t i o n mechanism. In the t e n s i l e zone, with a decrease i n the bar diameter, the c o n t a c t area of the concrete with the r i b s of the deformed bar w i l l be reduced. T h i s w i l l i n c r e a s e the bearing s t r e s s between 230 the concrete and the r i b s , and w i l l enhance crack development around the t i p of each r i b and some c r u s h i n g of the c o n c r e t e . F u r t h e r , the bond r e s i s t a n c e w i l l decrease because of the d e s t r u c t i o n of the adhesion and the decrease i n the f r i c t i o n a l r e s i s t a n c e due to the decrease i n the diameter. An a n a l y s i s of the extent of the r e d u c t i o n of the contact area due to Poisson's e f f e c t i s given in Appendix D. With a f u r t h e r i n c r e a s e i n load, more d i a g o n a l c r a c k s w i l l i n i t i a t e and propagate outwards in the c o n c r e t e . As the bar i s p u l l e d , the 'teeth' of comb-like concrete ( F i g . 6.1(a)) w i l l be subjected to bending i n the d i r e c t i o n of the l o a d . T h i s w i l l serve to t i g h t e n the c o n c r e t e around the bar, thus i n c r e a s i n g the f r i c t i o n a l r e s i s t a n c e to some extent. However, adjacent to the p u l l out end, the unconfined cover concrete i s apt to deform outwards, ( i n the d i r e c t i o n of the f o r c e ) causing s e p a r a t i o n (between the bar and the c o n c r e t e ) . At t h i s stage, the s t r e s s t r a n s f e r w i l l be mainly through the wedging a c t i o n of the r i b s as shown i n F i g . 6.1. The r e a c t i o n of the wedging f o r c e w i l l cause c i r c u m f e r e n t i a l t e n s i o n i n the c o n c r e t e , and i s p r i m a r i l y r e s p o n s i b l e f o r the formation of the r a d i a l s p l i t t i n g c r a c k s . These s p l i t t i n g cracks w i l l reduce the g r i p of the concrete on the r e i n f o r c i n g bar, and hence cause d e t e r i o r a t i o n i n bond between the bar and the c o n c r e t e . An approximation of the load s h a r i n g by the r i b s (due to bond) w i t h i n v a r i o u s segments of the r e i n f o r c i n g bar computed on the b a s i s of the bond s t r e s s d i s t r i b u t i o n diagram of a t y p i c a l specimen F2-MO/18, su b j e c t e d to g r a d u a l l y i n c r e a s e d monotonic 231 NOTE: ALL DEFORMATIONS AND CRACKING ARE SHOWN IN ENLARGED SCALE FOR CLARITY FIG.6.1 MECHANISM OF BOND RESISTANCE 232 l o a d i n g , can be developed from the r e s u l t s t a b u l a t e d in Table 6.1 and the d e s c r i p t i o n s i n F i g . 6.2. I t may be seen that at the 14 k s i a p p l i e d s t r e s s l e v e l , the s t r e s s t r a n s f e r due to bond w i t h i n segment No.1 i s only 19 percent of the a p p l i e d load, whereas the s t r e s s t r a n s f e r i s segment No.2 i s 31 percent of the a p p l i e d l o a d . T h i s i n d i c a t e s that even at t h i s s t r e s s l e v e l , e i t h e r some bond d e t e r i o r a t i o n has taken p l a c e , or the concrete at the end i s never very e f f e c t i v e i n bond. With a f u r t h e r i n c r e a s e of load up to the y i e l d s t r e s s l e v e l , the peak bond s t r e s s s h i f t s towards the i n t e r i o r of the specimen, as the s l i p and s e p a r a t i o n propagate inwards p r o g r e s s i v e l y (see T y p i c a l Bond S t r e s s D i s t r i b u t i o n Curves, F i g . 3.5). Table 6.1 i n d i c a t e s a gradual r e d u c t i o n in the s t r e s s t r a n s f e r c a p a c i t i e s of v a r i o u s segments at the p u l l out end, with more and more of the s t r e s s t r a n s f e r r e d due to bond towards the c e n t r e of the specimen, b. Push In End On the push-in end, the s t r e s s t r a n s f e r mechanism i n v o l v e d i s q u i t e d i f f e r e n t . The push i n f o r c e i n the bar deforms the concret e inwards ( i n the d i r e c t i o n of the f o r c e ) . T h i s serves to t i g h t e n the concrete around the bar and i n c r e a s e s the f r i c t i o n a l r e s i s t a n c e between the concrete and the bar. F u r t h e r , the s l i g h t i n c r e a s e i n the diameter of the bar due to Poisson's e f f e c t a l s o improves the f r i c t i o n a l r e s i s t a n c e . A small element of concrete adjacent to the r e i n f o r c i n g bar on the p u l l out end (t e n s i o n zone) i s s u b j e c t e d to compression-tension-t e n s i o n i n the r a d i a l , c i r c u m f e r e n t i a l and, l o n g i t u d i n a l d i r e c t i o n s , r e s p e c t i v e l y ; a s i m i l a r element of concre t e on the T A B L E 6.1 LOAD SHARING BY R I BS OF R E I N F O R C I N G BAR MONOTONIC LOAD ING ( S P E C I M E N F 2 - M 0 / 1 8 ) SEGMENT MRK * A P P L I E D S T R E S S 14 K s i ( 9 5 . 5 M P a ) L o a d T r a n s f e r r e d ( K N ) 7 . 2 12 .1 7 . 7 4 . 8 3 . 4 2 . 4 1 . 0 18 .8 3 1 . 2 2 0 . 0 1 2 . 5 8 . 8 6 . 3 2 . 5 A P P L I E D S T R E S S 3 0 K s i ( 2 0 7 MPa ) L o a d T r a n s f e r r e d ( K N ) 1 2 . 6 22 . 2 1 8 . 4 1 4 . 0 12 . 1 11 .1 9 . 2 1 2 . 6 22 . 3 1 8 . 5 14 .1 12. 1 1 1 . 2 1 2 . 6 A P P L I E D S T R E S S 45 K s i ( 3 1 0 MPa ) L o a d T r a n s f e r r e d ( K N ) 1 5 . 0 27 . 5 24 .6 2 1 . 7 1 7 . 9 1 5 . 4 2 . 8 11 .1 2 0 . 4 18 . 3 16 . 1 1 3 . 3 1 1 . 5 9 . 3 A P P L I E D S T R E S S 6 0 K s i ( 4 1 4 MPa ) L o a d T r a n s f e r r e d ( K N ) 1 4 . 0 25 . 1 2 6 . 3 2 9 .7 24 .6 2 0 . 0 1 9 . 6 8 . 8 1 5 . 8 16 . 5 18.6 1 5 . 5 1 2 . 6 1 2 . 3 A P P L I E D S T R E S S 75 K s i ( 5 1 7 MPa ) L o a d T r a n s f e r r e d ( K N ) 9 . 7 2 6 . 6 3 5 . 7 3 9 . 1 32 .8 2 6 . 6 27 . 0 4 . 9 1 3 . 4 18 . 1 1 9 . 8 1 6 . 6 1 3 . 4 1 3 . 7 ro to cu SEGMENT MARK - S e e F i g . 6.2 N o t e : I n f o r m a t i o n b e y o n d 75 K s i n o t f u r n i s h e d a s a f ew S . G s w e n t o u t o f o r d e r . V£3 235 push i n end (compression zone) i s subjected to compression-compression-tension i n the r a d i a l , l o n g i t u d i n a l and c i r c u m f e r e n t i a l d i r e c t i o n s , r e s p e c t i v e l y . T h e r e f o r e , the f a i l u r e behaviour at both ends i s q u i t e d i f f e r e n t . The f i n i t e element a n a l y s i s p r e d i c t s the development of i n t e r n a l d i a g o n a l c r a c k s (though fewer than those at the p u l l out ends) at an a p p l i e d s t r e s s l e v e l of 6 k s i (414 MPa) and some amount of c r u s h i n g or f r a c t u r e in the c o n c r e t e beyond 12 k s i (82 MPa). Although no experimental evidence i s yet a v a i l a b l e f o r the development of such i n t e r n a l d i a g o n a l cracks around the bar at the push i n end, i t can be e x p l a i n e d by the a c t i o n of the wedging f o r c e a g a i n s t the r i b s as d e s c r i b e d f o r the p u l l out end. The inward deformation of the concrete however prov i d e s some l a t e r a l compression i n the concrete surrounding the bar and thus reduces the r a d i a l component of the wedging f o r c e . 6.2.4 Bond Behaviour a f t e r Y i e l d i n g of Bar a. P u l l Out End As the a p p l i e d s t r e s s i s i n c r e a s e d beyond y i e l d , the s e p a r a t i o n between the bar and the concrete i n c r e a s e s due to Poisson's e f f e c t and the outward deformation of c o n c r e t e ( i n the d i r e c t i o n of the f o r c e ) . The y i e l d begins to penetrate inwards, and the p l a s t i c deformation i n the bar causes i n c r e a s i n g deformation i n the c o n c r e t e . The i n t e r n a l c r a c k s a l r e a d y developed propagate, and more d i a g o n a l and s p l i t t i n g cracks develop. T h i s i s the reason why a sharp decrease i n the slope of the a p p l i e d s t r e s s - d i s p l a c e m e n t curve i s obtained when the 236 the a p p l i e d s t r e s s i s i n c r e a s e d beyond y i e l d . With a f u r t h e r i n c r e a s e i n lo a d , the y i e l d penetrates s t i l l f u r t h e r inwards. The composite a c t i o n between the bar and the concrete i s reduced p r o g r e s s i v e l y from the p u l l - o u t end due to s e p a r a t i o n , c r a c k i n g and s l i p . As the a p p l i e d s t r e s s i s high, the wedging f o r c e developed i s a l s o high. As a r e s u l t , i n e l a s t i c deformation in the con c r e t e takes p l a c e , and hence the tangent modulus of the concrete surrounding the bar w i l l be reduced (as may be observed in a t y p i c a l s t r e s s - s t r a i n curve i n compression). T h e r e f o r e , the c r a c k i n g , the r e d u c t i o n i n the tangent modulus of the con c r e t e , and the s l i p and s e p a r a t i o n in the s t e e l are the main reasons f o r the gradual r e d u c t i o n i n the slope of the a p p l i e d s t r e s s - d i s p l a c e m e n t curve beyond y i e l d i n g . At some stage, the deformation i n the bar w i l l be such that a cone of concre t e w i l l be p u l l e d out by the bar, due to the formation of a c o n i c a l crack as an extension to the o r i g i n a l l y formed d i a g o n a l crack at some d i s t a n c e from the p u l l — out end. T h i s w i l l reduce the e f f e c t i v e anchorage l e n g t h of the bar s i g n i f i c a n t l y , and cause f u r t h e r bond d e t e r i o r a t i o n , b. Push-In End The behaviour at the push in end beyond y i e l d i s s i m i l a r to that d e s c r i b e d p r e v i o u s l y (up to y i e l d ) . No r a d i a l or s p l i t t i n g c r a c k s are observed to develop ( e x t e r n a l l y ) on the push-in end even at the highest a p p l i e d l o a d . Due to some i n t e r n a l c r a c k i n g and c r u s h i n g i n the conc r e t e , and the y i e l d p e n e t r a t i o n , some bond d e t e r i o r a t i o n w i l l take p l a c e . Nonetheless, the bond r e s i s t a n c e on the push i n end i s observed to be much higher than 237 that on the p u l l out end. 6.3 BOND DETERIORATION AND CRACKING MECHANISM UNDER REVERSED  CYLIC LOADING The bond behaviour under reversed c y c l i c l o a d i n g i s completely d i f f e r e n t from that under monotonic l o a d i n g , and can be e x p l a i n e d i n the l i g h t of the a p p l i e d s t r e s s - d i s p l a c e m e n t behaviour of a t y p i c a l specimen (F2-RV/17) f o r c l a r i t y ( F i g . 3 . 1 0 ) . T h i s specimen was sub j e c t e d to i n c r e m e n t a l l y i n c r e a s e d r e v e r s e d c y c l i c l o a d i n g with only one c y c l e f o r each peak l o a d i n g u n t i l 79.4 k s i (547 MPa) was reached, a f t e r which many c y c l e s were run u n t i l f a i l u r e o c c u r r e d . The b a s i c mechanism of s t r e s s t r a n s f e r under monotonic l o a d i n g has a l r e a d y been d e s c r i b e d , and t h i s w i l l apply t i l l the i n i t i a t i o n of the s t r e s s r e v e r s a l . As mentioned p r e v i o u s l y , the bond d e t e r i o r a t i o n i s caused by i n t e r n a l c r a c k i n g , s l i p , and se p a r a t i o n at the s t e e l - c o n c r e t e i n t e r f a c e . T h i s i s evident from the f a c t that g r e a t e r bond f o r c e s are p r o g r e s s i v e l y t r a n s f e r r e d toward the ce n t r e of the specimen as the peak lo a d i s g r a d u a l l y i n c r e a s e d . Even at a s t r e s s l e v e l as low as 43 k s i (296 MPa), on r e v e r s a l of load a s i g n i f i c a n t change i n the a p p l i e d s t r e s s -displacement curve i s observed. The behaviour on r e v e r s a l of the l o a d i s e x p l a i n e d through F i g . 6.1 f o r a t y p i c a l c y c l e with a peak amplitude of l o a d i n g of 43 k s i (296 MPa). The behaviour under monotonic loading has al r e a d y been e x p l a i n e d p r e v i o u s l y and w i l l not be repeated here. Upon some r e l a x a t i o n of the load, r e s i s t a n c e to s l i p - r e c o v e r y occurs. The bar w i l l not r e t u r n to 238 i t s o r i g i n a l p o s i t i o n f o r the f o l l o w i n g reasons: i . I t has to overcome s t a t i c f r i c t i o n i i . On r e l a x a t i o n of the lo a d , the diameter of the bar in c r e a s e s and hence the bar has a tendency to get "locke d " i n p l a c e . i i i . The 'teeth' of concrete ( F i g . 1.1(b)), which have undergone bending, p r o v i d e r e s i s t a n c e to r e v e r s a l motion of the bar due to wedging a c t i o n . On complete r e l a x a t i o n of the load, a s t a t e of r e s i d u a l t e n s i o n may remain i n the bar except at the ends. The i n t e r n a l cracks a l r e a d y formed do not c l o s e up completely, due to i n e l a s t i c deformation i n the conc r e t e , and to the aggregate i n t e r l o c k at the s u r f a c e s of the i n t e r n a l c r a c k s . A r e s i d u a l s l i p , A , remains due to i r r e c o v e r a b l e deformation. Some v o i d space i s a l s o l i k e l y to be present behind the r i b s wherever concrete has undergone c r a c k i n g and bending. In f a c t , t h i s l a c k of complete recovery of s l i p i s r e s p o n s i b l e f o r the h y s t e r e t i c behaviour i n the a p p l i e d s t r e s s - d i s p l a c e m e n t r e l a t i o n s h i p . On r e v e r s a l of the load (along the path B-B'-B"-C of F i g . 6.1(c)) there i s some bond r e s i s t a n c e due to f r i c t i o n between the . s t e e l and the concrete which g r a d u a l l y i s overcome with an i n c r e a s e in l o a d . At t h i s stage, the deformation in s t e e l a l s o i n c r e a s e s r a p i d l y with i n c r e a s e i n loa d due to a r e d u c t i o n i n the tangent modulus. T h i s i s i n d i c a t i v e of a re d u c t i o n i n slope of the a p p l i e d s t r e s s - d i s p l a c e m e n t curve, and p i n c h i n g ( F i g . 6.1(c) ). However, on a f u r t h e r i n c r e a s e in loa d , the r i b s of the bar g r a d u a l l y make cont a c t with the 239 c o n c r e t e . T h e r e f o r e , the slope of the curve g r a d u a l l y s t a r t s i n c r e a s i n g ( i . e . i t becomes s t e e p e r ) . Now, as the load i s i n c r e a s e d from B" to C, new i n t e r n a l c r a c k s (diagonal) develop i n the op p o s i t e d i r e c t i o n as shown i n F i g . 6.1(c), as w e l l as s p l i t t i n g c r a c k s in the p u l l out end (N. s i d e ) . Some c r u s h i n g of the concre t e i s a l s o expected at the r i b fac e . The i n t e r n a l d i a g o n a l c r a c k s p r e v i o u s l y formed are f o r c e d to c l o s e . However, due to aggregate i n t e r l o c k and i n e l a s t i c deformation, some gap between the crack s u r f a c e s (at the s t e e l - c o n c r e t e i n t e r f a c e ) i s l i k e l y to remain even at the highest peak l o a d . If the load amplitude i s high, the c o n s e c u t i v e i n t e r n a l d i a g o n a l c r a c k s may j o i n up at some d i s t a n c e from the i n t e r f a c e , c r e a t i n g regions of d i s i n t e g r a t e d c o n c r e t e . On the subsequent r e v e r s a l s of l o a d , processes s i m i l a r to those d i s c u s s e d e a r l i e r occur. However, there i s now comparatively l e s s f r i c t i o n a l r e s i s t a n c e , p a r t l y because of l o c a l f r a c t u r e and d i s i n t e g r a t i o n of co n c r e t e , and gr e a t e r crack opening at the i n t e r f a c e . The i r r e c o v e r a b l e damage i s accumulated. With an i n c r e a s e i n peak amplitude of l o a d i n g , more and more cra c k s are generated, and e x i s t i n g c r a c k s propagate. With an i n c r e a s e i n the number of c y c l e s at a constant amplitude of l o a d i n g , the s l i p and the s e p a r a t i o n propagate inwards p r o g r e s s i v e l y . I f the a p p l i e d load i s grea t e r than the y i e l d s t r e s s ( i n s t e e l ) , the y i e l d i n g of the r e i n f o r c i n g bar conti n u e s to pene t r a t e from both ends. As d e s c r i b e d f o r the monotonic case, a cone of concre t e may be p u l l e d out at the p u l l out end, thus reducing the e f f e c t i v e anchorage l e n g t h of the bar to a great extent and f i n a l l y , a 240 f a i l u r e by p u l l i n g out may occur. In g e n e r a l , due to s u c c e s s i v e r e v e r s a l s of l o a d i n g , the l a y e r of concrete surrounding the r e i n f o r c i n g bar undergoes p r o g r e s s i v e d e t e r i o r a t i o n due to some combination of i n e l a s t i c deformation, c r a c k i n g and l o c a l c r u s h i n g . T h i s p r o g r e s s i v e d e t e r i o r a t i o n i s r e s p o n s i b l e for bond degradation, which under reversed c y c l i c l o a d i n g i s h i g h l y dependent on the lo a d i n g h i s t o r y . The grea t e r the magnitude of the pr e v i o u s peak l o a d i n g , the grea t e r w i l l be the d i s r u p t i o n of the concrete l a y e r at the i n t e r f a c e and the grea t e r w i l l be the bond d e t e r i o r a t i o n . 6.4 ROLE OF STEEL FIBERS ON BOND DETERIORATION AND CRACKING The mechanism of bond d e t e r i o r a t i o n and c r a c k i n g i n s t e e l f i b e r r e i n f o r c e d c o n c r e t e i s e s s e n t i a l l y the same as that for p l a i n c o n c r e t e , except f o r a few d i f f e r e n c e s as d e s c r i b e d below: B a s i c a l l y , concrete i s a b r i t t l e m a t e r i a l . The presence of s t e e l f i b e r s i n an i n h e r e n t l y b r i t t l e matrix m o d i f i e s the b r i t t l e behaviour of the matrix. S t e e l f i b e r s are re p o r t e d (82) to i n c r e a s e the d u c t i l i t y , the energy absorbing c a p a c i t y and the u l t i m a t e s t r a i n c a p a c i t y of c o n c r e t e . T h e i r presence not only makes crack propagation with an i n c r e a s e in load slower, but a l s o enables s t r e s s to be t r a n s f e r r e d across cracked s e c t i o n s . T h i s allows the a f f e c t e d p a r t s of the composite to r e t a i n some p o s t - c r a c k i n g s t r e n g t h and to withstand much greater deformations than can be s u s t a i n e d by the matrix alone (49). The presence of a f i b e r a c r o s s a crack plane a c t s as a c l o s i n g f o r c e , thus r e t a r d i n g the crack propagation. However, the 241 f i b e r s have p r a c t i c a l l y no e f f e c t on crack formation, as the volume percentage of f i b e r s i n the whole matrix i s very s m a l l . As mentioned p r e v i o u s l y , the l a y e r of concrete surrounding the r e i n f o r c i n g bar p l a y s a v i t a l r o l e i n the bond d e t e r i o r a t i o n mechanism. The concrete l a y e r i s subjected to m u l t i a x i a l s t r e s s e s under push i n - p u l l out l o a d i n g on the bar. In t h i s s i t u a t i o n , using s t e e l f i b e r r e i n f o r c e d concrete with randomly o r i e n t e d f i b e r s , the a d d i t i o n a l shear t r a n s f e r by f i b e r s at the i n t e r f a c e of the r e i n f o r c i n g bar and the concrete may somewhat improve the composite behaviour of the specimens. There i s evidence that s t e e l f i b e r r e i n f o r c e d concrete has s i g n i f i c a n t improved bearing s t r e n g t h (8) and as a r e s u l t , the f r a c t u r e or c r u s h i n g of the concrete may be s u b s t a n t i a l l y reduced as compared to those i n the p l a i n c o n c r e t e . Hence, there i s g r e a t e r bond r e s i s t a n c e f o r the f i b e r - r e i n f o r c e d concrete spec imens. The improved bond performance of the SFRC specimens t e s t e d here may be seen from the s t r a i n measurements along the r e i n f o r c i n g bar, i n d i c a t i n g lower s t r a i n v a l u e s along the r e i n f o r c i n g bar as compared to specimens made with p l a i n c o n c r e t e , s u b j e c t e d to i d e n t i c a l l o a d i n g ( F i g 4.21 r e f e r s ) . It i s a l s o e vident that even a f t e r s e v e r a l c y c l e s of l o a d i n g with a constant peak load higher than the y i e l d s t r e s s i n s t e e l , the y i e l d p e n e t r a t i o n i n t o the core of the SFRC specimens i s comparatively l e s s than that f o r the p l a i n concrete ones (Table 4.2(a) & (b) ). A comparison of the v i s i b l e c r a c k i n g p a t t e r n s f o r specimens 24 2 loaded under i d e n t i c a l l o a d i n g c o n d i t i o n s (RV), r e v e a l s that fewer but wider r a d i a l and l o n g i t u d i n a l cracks develop f o r p l a i n c oncrete as compared to s t e e l f i b e r r e i n f o r c e d concrete specimens. Though the s t r e s s l e v e l at which the c i r c u m f e r e n t i a l ( c o n i c a l ) c r a c k s forms i s e s s e n t i a l l y the same f o r both p l a i n c o n c r e t e and f i b e r r e i n f o r c e d c o n c r e t e specimens, there e x i s t s some d i f f e r e n c e s i n the s i z e of the cone formations. A l a r g e r cone i s observed to form i n the case of the p l a i n concrete specimens. However, the number of specimens t e s t e d i s too small f o r a f i r m c o n c l u s i o n to be reached in t h i s regard. 6.5 PREDICTION OF SPLITTING CRACKING For deformed r e i n f o r c i n g bars, the s p l i t t i n g of the concrete cover i s the most v i s i b l e sign of approaching bond f a i l u r e . T h e r e f o r e , the assessment of the s p l i t t i n g f o r c e and the mechanism of the development of s p l i t t i n g c r a c k s i s q u i t e important. During t e s t i n g of specimens s u b j e c t e d to push-in p u l l - o u t monotonic l o a d i n g , i t was observed that v i s i b l e r a d i a l c r a c k s f i r s t o c c u r r e d on the p u l l out end of the specimens, emanating from the p e r i p h e r y of the r e i n f o r c i n g bar. These c r a c k s g r a d u a l l y propagated to the s i d e faces ( E. & W. Faces) of the specimen as l o n g i t u d i n a l c r a c k s . With a f u r t h e r i n c r e a s e -in the a p p l i e d s t r e s s l e v e l , these c r a c k s extended towards the push-in end of the specimen. The c r a c k i n g p a t t e r n may be seen i n F i g . 3.6. In order to determine the s p l i t t i n g f o r c e produced by the wedging a c t i o n of the r i b s of the r e i n f o r c i n g bar a g a i n s t the c o n c r e t e , the s t a t i c s of the problem may be analyzed as 243 f o l l o w s : F i g . 6 . 3 shows the f o r c e s and t h e i r components a c t i n g on a r i b of the r e i n f o r c i n g bar. The bearing f o r c e s a c t i n g normal to the s u r f a c e of the r i b of height ho i s given by P" * f b hQr d* where fb = bearing stress at the rib, and the other terms are described in Fig. 6 . 3 . From F i g . 6-3 , P' • P" Cosec a P - P' Cosec 6 - P" Cosec a • Cosec e The r a d i a l component of t h i s f o r c e , P q - P Cos e " P" Cosec a • Cot 6 So, P q - f f a h Qr d^ , cosec a Cot 6 Since the s p l i t t i n g f o r c e i s co n c e n t r a t e d at the face of the lug s spaced at a d i s t a n c e p ap a r t , the s p l i t t i n g f o r c e s per u n i t l e n g t h of the r e i n f o r c i n g bar are c a l c u l a t e d as n/2 Fx " i _ / [P Q Cos f + P' Sin a • Sin o>] P ° » / 2 F - 2 / P Sin i> • do> y "p~o . ° » / 2 - 2 / f . h r do>« Cosec a Cot 0 Sin o> — ' b o n o - - f L h Cosec a Cot 6 p b o In the present case, the s p l i t t i n g f o r c e Fy i s c r i t i c a l as the c o n c r e t e cover i s a minimum i n the x - d i r e c t i o n . A 244 REINFORCING BAR ACTUAL C-S SIMPLIFIED OF REBAR C - S SECTION A A I FORCES ACTING FIG. 6-3 FORCES C A U S I N G S P L I T T I N G CRACK 245 s p l i t t i n g c rack w i l l develop when Fy = F t , where Ft = t e n s i l e s t r e n g t h of the c o n c r e t e . S ° * F y " F t - i f b h o ° ° B e c a C o t 6 The evidence from t e s t by v a r i o u s r e s e a r c h e r s (33) and the a n a l y t i c a l study i n t h i s i n v e s t i g a t i o n , show that diagonal c r a c k s develop, o r i g i n a t i n g from the r i b s of the r e i n f o r c i n g bar, e s p e c i a l l y on the p u l l out end of the specimen. T h i s phenomenon seems to be a p p l i c a b l e to r e i n f o r c i n g bars with both square and 45° l u g s , having the same s t r e s s - s l i p c h a r a c t e r i s t i c s (102). No experimental i n f o r m a t i o n i s a v a i l a b l e r e g a r d i n g the development of such cracks with r e i n f o r c i n g bars having the type and o r i e n t a t i o n of r i b s shown i n F i g . 6.3. However, from the experimental study c a r r i e d out i n t h i s i n v e s t i g a t i o n , i n most cases, a c o n i c a l crack formed, which was manifested as a c i r c u m f e r e n t i a l crack on the p u l l out face of the specimen at a p p l i e d s t r e s s l e v e l s above 74 k s i (510 MPa). I t i s b e l i e v e d that t h i s crack was an extension of the d i a g o n a l crack formed e a r l i e r . S i r i p o n g (44) has a l s o r e p o r t e d that the s p l i t t i n g c r a c k s are found to be more e x t e n s i v e than the d i a g o n a l c r a c k s , although d i a g o n a l cracks are the f i r s t to i n i t i a t e . However, he observed that the d i a g o n a l c r a c k s s t a b i l i z e d at about 12mm from the s u r f a c e of the s t e e l bar. I t i s t h e r e f o r e presumed here t h a t , at l e a s t at s t r e s s l e v e l s l e s s than 74 k s i (510 MPa), only s p l i t t i n g c r a c k s would develop, and so the e f f e c t of d i a g o n a l c r a c k s i s not c o n s i d e r e d when t h i s s p l i t t i n g f a i l u r e i s p r e d i c t e d . The s p l i t t i n g * s t r e s s developed a c r o s s the c o n c r e t e s u r f a c e 2 4 b of u n i t l e n g t h and u n i t depth i s given by F - f » — f h Cosec a Cot 6 t t p b o f t p o The f i r s t v i s i b l e s p l i t t i n g crack w i l l occur when the d i r e c t t e n s i l e s t r e n g t h i n the c o n c r e t e , f t , i s exceeded. Assuming an f t value equal to 2/3 modulus of rupture i n con c r e t e , f t = 6.54 MPa(2/3 x 9.82 MPa ( f o r specimen F2-MO/18)) S u b s t i t u t i n g a l l the r e l e v a n t v a l u e s , fb = 6.54 x 0.945 x 1.75 6.895 x 0.921 x 0.189 = 9.01 k s i (62.1 MPa) T h e r e f o r e , the f i r s t v i s i b l e s p l i t t i n g crack should appear on the s u r f a c e when the bearing s t r e s s at the r i b s on the p u l l out end exceeds 9.01 k s i (62.1 MPa). Now, the summation of the l o n g i t u d i n a l components of the bearing f o r c e s a c t i n g around the p e r i p h e r y of the r i b of the r e i n f o r c i n g bar may be equated with the t o t a l bond f o r c e over the l e n g t h of the r i b spacing p, So, / f. h "Y d$ • U n d p, where U - maximum bond stress D O max max o or ird h f, • U " d p . „_ n , f *J> - * /c m o b max o r U m a x f b J~ V 6 * 0 3 S u b s t i t u t i n g the value to cause s p l i t t i n g , Umax = 9.01/6-.03 = 1 .49 k s i (10.3 MPa) 247 T h i s value compares w e l l with the experimental r e s u l t s f o r specimen F2-MO/18 (monotonically loaded) which developed the f i r s t r a d i a l s p l i t t i n g crack at a p p l i e d s t r e s s l e v e l of 45 k s i (310 MPa) when Umax computed at the p u l l out end was 1.57 k s i (10 . 8 MPa). C o n c l u s i o n : The model d e s c r i b e d above may be thought of as a s i m p l i f i e d model to p r e d i c t the order of magnitude of the bearing s t r e s s that develops a g a i n s t the r i b s of the r e i n f o r c i n g bar to cause f i r s t s p l i t t i n g c r a c k i n g . A d d i t i o n a l work i s needed to e s t a b l i s h the e f f e c t s of the diameter of the r e i n f o r c i n g bar, the c o n c r e t e cover, the le n g t h of anchorage, the e f f e c t of r e i n f o r c i n g s t e e l a c r o s s the p r e d i c t e d crack, the s i z e of the specimen, the i n t e r n a l d i a g o n a l c r a c k s , and the extent of bond d e t e r i o r a t i o n . 248 VII . ANALYTICAL STUDY OF BOND BEHAVIOUR 7.1 INTRODUCTION In order to have a b e t t e r understanding of the bond behaviour of an anchored r e i n f o r c i n g bar embedded in c o n c r e t e , i t i s necessary to understand the p h y s i c a l phenomena o c c u r r i n g at and around the r e i n f o r c i n g bar. These i n c l u d e an assessment of the s t r e s s e s and the deformations that e x i s t at a p o i n t , and the c r a c k i n g in the c o n c r e t e . Even with modern techniques, major d i f f i c u l t i e s e x i s t i n measuring t h i s mechanical behaviour of c o n c r e t e surrounding a r e i n f o r c i n g bar. F u r t h e r , the mechanism of bond i s a h i g h l y complex, n o n l i n e a r process i n v o l v i n g p r o g r e s s i v e c r a c k i n g , c r u s h i n g , n o n l i n e a r i t y and inhomogeneity of concrete; the presence of s t e e l f i b e r s i s a f u r t h e r c o m p l i c a t i o n . T h e r e f o r e , i t was decided to undertake an a n a l y t i c a l study to o b t a i n q u a n t i t a t i v e i n f o r m a t i o n i n an attempt to e x p l a i n the p h y s i c a l phenomena o c c u r r i n g around the r e i n f o r c i n g bar. In order to develop a simple and r e l a t i v e l y inexpensive a n a l y t i c a l method to study the behaviour of an anchored r e i n f o r c i n g bar, a t h e o r e t i c a l development of a boundary value problem using a s e r i e s s o l u t i o n was o r i g i n a l l y attempted, without success. The method was found to be q u i t e s u i t a b l e f o r cases with symmetric l o a d i n g c o n d i t i o n s but c o m p l e x i t i e s developed which were insurmountable f o r the unsymmetrical problem such as the one c o n s i d e r e d i n t h i s i n v e s t i g a t i o n . As a consequence,it was decided to abandon that approach and adopt 249 the f i n i t e element method. A l i n e a r e l a s t i c f i n i t e element program was developed, which can take i n t o account the s l i p and the s e p a r a t i o n between the r e i n f o r c i n g bar and the co n c r e t e , and c r a c k i n g i n the co n c r e t e . However, i t i s important to recognize the l i m i t a t i o n inherent i n t h i s model. The f i n i t e element model i s based on many assumptions. Some of these assumptions r e s t r i c t the a p p l i c a b i l i t y of the model: 1. The deformed bar i s i d e a l i z e d as a smooth round bar; the e f f e c t s of the r i b s are ignored. The e f f e c t s of s l i p and s e p a r a t i o n between s t e e l and concrete are c o n s i d e r e d only i n d i r e c t l y by using a s u i t a b l e bond s t r e s s - s l i p r e l a t i o n s h i p . 2. The t e n s i l e s p l i t t i n g i n the concrete i s not c o n s i d e r e d . 3 . The presence of s t e e l f i b e r s , which p r o v i d e a c l o s i n g f o r c e , i s not c o n s i d e r e d . 4. The m a t e r i a l behaviour i s assumed to be l i n e a r e l a s t i c , with s p e c i a l m o d i f i c a t i o n s f o r c r a c k i n g and c r u s h i n g i n the c o n c r e t e . 5. The program can handle only m o n o t o n i c a l l y i n c r e a s i n g push in - p u l l out l o a d i n g and not reversed c y c l i c l o a d i n g due to the f o l l o w i n g reasons: i)The behaviour of bond under reversed c y c l i c l o a d i n g i s a s s o c i a t e d with opening and c l o s i n g of c r a c k s , which can not be modelled without some experimental data f o r c a l i b r a t i o n . 250 it)A 11 the t e s t s c a r r i e d out under re v e r s e d c y c l i c l o a d i n g were beyond y i e l d s t r e s s in s t e e l . The model however does not i n c l u d e s t e e l s t r e s s beyond y i e l d . The program was a p p l i e d to a t y p i c a l specimen ( F 2 - M O / 1 8 ) s u b j e c t e d to monotonic push i n p u l l out l o a d i n g . The r e s u l t s of the study are d i s c u s s e d and suggestions for f u t u r e s t u d i e s are presented. 251 7.2 OBJECTIVE OF ANALYTICAL STUDY The main o b j e c t i v e s of the a n a l y t i c a l study were: 1. To study the s t a t e of s t r e s s i n the concrete as w e l l as the r e i n f o r c i n g bar, e s p e c i a l l y at the s t e e l - c o n c r e t e i n t e r f a c e . 2. To study the crack formation and crack propagation in the co n c r e t e around an anchored r e i n f o r c i n g bar and t h e i r e f f e c t on the bond behaviour. 7.3 FINITE ELEMENT MODEL An axisymmetric, l i n e a r e l a s t i c f i n i t e element a n a l y s i s was c a r r i e d out to study the l o c a l s t r e s s e s and deformations around and at the r e i n f o r c i n g bar sub j e c t e d to push i n p u l l out monotonic l o a d i n g . The procedure adopted by Lutz (58) f o r anchorage zone a n a l y s i s using the s l i p and the s e p a r a t i o n between the r e i n f o r c i n g bar and the conc r e t e , and the procedures o u t l i n e d by Zienkiewicz (106) were followed and i n c o r p o r a t e d i n the computer program. The model c o n s i d e r e d was a smooth round bar (25mm diameter) embedded in a concre t e c y l i n d e r having a diameter of seven times the bar diameter, h e l d f i x e d at the outer l o n g i t u d i n a l s u r f a c e . The model was con s i d e r e d to represent the c o n d i t i o n s e x i s t i n g f o r the t e s t specimen. It was assumed that with t h i s diameter, the boundary c o n d i t i o n s at the support should not s i g n i f i c a n t l y a f f e c t the r e s u l t s obtained f o r l o c a l s t r e s s e s around the r e i n f o r c i n g bar and at the i n t e r f a c e . The f i n i t e element model was formulated using a displacement approach. The elements c o n s i d e r e d were r i n g s of t r i a n g u l a r c r o s s s e c t i o n , whk:h were s e l e c t e d because of t h e i r s i m p l i c i t y , 252 f l e x i b i l i t y i n v a r y i n g the s i z e s of elements, and so on. The a p p l i c a t i o n of the push i n - p u l l out load to the r e i n f o r c i n g bar was e f f e c t e d by g i v i n g s u i t a b l e equal displacements to the the nodal p o i n t s on the outer s u r f a c e of the bar, whereas the outer s u r f a c e of the c y l i n d e r was f i x e d . The two dimensional r e p r e s e n t a t i o n of a t y p i c a l element i s shown in F i g . 7.1, and d e t a i l s of the f i n i t e element meshes in F i g . 7.2. The f i n i t e element g r i d c o n s i d e r e d i n the a n a l y s i s c o n s i s t e d of 422 elements and 274 nodes with the p r o v i s i o n of dual nodes at the s t e e l - c o n c r e t e i n t e r f a c e . I t may be mentioned here that the exact shape of the r i b s of the r e i n f o r c i n g bar was not simulated on the meshes i n view of t h e i r n e g l i g i b l e s i z e as compared to the o v e r a l l s i z e of the model. Had these been c o n s i d e r e d , the computational cost would have been p r o h i b i t i v e . However, the model c o n s i d e r e d the necessary bond behaviour due to r i b s at a moderate computational expense. The f o l l o w i n g assumptions are made in s e l e c t i n g the model f o r a n a l y s i s , r e p r e s e n t i n g the c o n d i t i o n s in the the t e s t spec imen: 1. I n t e r n a l s t r e s s e s due to temperature and/or shrinkage are n e g l e c t e d . 2. The deformed r e i n f o r c i n g bar i s i d e a l i z e d as a p l a i n bar embedded i n a concrete c y l i n d e r . However, the e f f e c t s of the s l i p and s e p a r a t i o n that may r e s u l t in a deformed bar are c o n s i d e r e d . 3. The e f f e c t s of the c reep and r e l a x a t i o n of c o n c r e t e are n e g l e c t e d . 253 /////.'///7'//*//-/ S// /S?///////s -CONCRETE -REINFORCING BAR •>///////// //•/„'// /'////// ////// -20 CONCRETE REINFORCING BAR F I N I T E ELEMENTS (REF. DETAILS SECTION PP (b)STRESSES (a) AXISYMMETRIC MODEL FOR THE SPECIMEN STEEL SURFACE AFTER DEFORMATION STEEL CONCRETE AFTER DEFORMATION PLANE OF SEPARATION (c) REPRESENTATION FOR PLANE OF SEPARATION A = (U„ - U 6 )COTc< S>= W S-(U. -U $ )COTC< (d) DISPLACEMENTS DUE TO S L I P & SEPARATION FIG.7-1 IDEALIZATION OF THE PROBLEM FIG. 7.2 F I N I T E ELEMENT MESH(PARTLY SHOWN ) 255 Cracki n g i s assumed to occur i n the concrete when the p r i n c i p a l t e n s i l e s t r e s s exceeeds the t e n s i l e s t r e n g t h of the c o n c r e t e . The c r i t e r i a used f o r c r u s h i n g in the concrete are those of Hannant ( 3 4 ) . According to him, to a v o i d c o n c r e t e f a i l u r e , the f o l l o w i n g c o n d i t i o n s must be met: a) i f a, + o 2 + a 3 ^ 5.5 ocy then a, - 5 a 2 + a 3 S acy 0 2 _ 5o 3 + o, < ocy 0 3 - 5 0 , + o 2 - acY b) i f 5.5ocy < o, + o2 + o 3 ^ I2.170cy then 0 , - 4 o 2 + 0 3 ^ 1.75acy 0 2 _ 4 o 2 + a, ^ 1 . 7 5 0 c y 0 3 - 4 0 1 + o 2 ^ 1 . 7 5 0 c y where a 1 f o2, o3t are the p r i n c i p a l s t r e s s e s i n the con c r e t e and ocy i s the c y l i n d e r c r u s h i n g s t r e n g t h of the c o n c r e t e . 256 7.4. FINITE ELEMENT MESHES AND MATHEMATICAL FORMULATION: 7.4.1. DISPLACEMENT FUNCTION: The t r i a n g u l a r shaped element used with nodes, i , j , k numbered i n the anticlockwise sense i s shown i n F i g . 7.3. A l i n e a r polynomial defines uniquely the displacements within the element; u - + o 2z + o^r (7.1) w • cc. + a_z + a.r F i g . 7.3. TYPICAL FINITE ELEMENT where u and v are the r a d i a l and lo n g i t u d i n a l nodal displacements, r e s p e c t i v e l y . 257 The above may be written f o r the i t h node ae where (7.2) and so on. The six components of the element displacement vector are given by (7 .3) The s i x constants, a , can be evaluated by solving two sets of three simultaneous equations, such as u i - ° i + V i + V i u j - ° 1 + V j + V j u k " C l + V k + a 3 r k 2 58 L e t t i n g 2A -1 1 z zi r i 5 T i 1 z k r k u i 2 i r i 1 u i r i z j r j 1 U j T j > 2 k r k 1 u k r k On I Z i 1 °3 " Tl 1 Z j u j 1 2 k u k s u b s t i t u t i o n u • ^ a i + u k where a ± - ( z . ^ - z ^ ) b i ' ( r j - r k }  C i * ( z k " z j ) The other c o e f f i c i e n t s can be obtained by c y c l i c permutation of the subscripts i n order. So, f - {UJ - N a e - [IN ±, I N ^ I N k ] a e (7.4) 259 where 1 - 2 x 2 i d e n t i t y matrix Ni " 2"! ( a i + V + etc* 7.4.2. STRAIN The four s t r a i n components ( i . e . r a d i a l , tangential, l o n g i t u d i n a l and shear) i n an axisymmetric problem may be written as e -3u E r 3r 11 < r > 3 v Z 3z 3u . 3w 3z > L f 9_ 3r 1 r 0 0 0 3z [IN 1 P INj, IN k] a 6 - [B i t B... B J a 6 (7.5) where 1 N i " 2A ( a A + bjZ + c A r ) I i " 21 1 7 ( a i + b i Z + C i r ) a i + b i + C i r r 0 IF ( a i + V + c i r ) ( a i + b ^ + ^ r ) 37 ( a i + b i z + c i r ) TF ( a i + V + c i r ) e t c . 260 e t c . Rearranging, c r (7.6) 7.4.3. ELASTICITY MATRIX AND STRESSES; The e l a s t i c i t y matrix D, required f o r Computation of stresses for e l a t i c , i s o t r o p i c and homogeneous material i s given by 261 D - (l+v)(l-2v) (1-v) v v 0 v (1-v) v 0 v v (1-v) 0 0 0 0 (0.5-v) (7.7) The corresponding stresses are: r (l+v)(l-2v) rz (1-v) v v 0 v (1-v) v 0 v v (1-v) 0 0 0 0 (0.5-v) r \ e r E e < \ e z r TZ > D e 7 .4.4. STIFFNESS MATRIX The element s t i f f n e s s matrix can be computed u6ing the r e l a t i o n s h i p K* - / B T D B dV T 2TT / B* D J3 j r dr • dz (7.8) The simplest approximate procedure i s to evaluate B for the c e n t r o i d a l point. * - ( r i + r j + V / 3 and z - ( z ± + z. + z k)/3 So, may be expressed as 262 where A » area of the tr i a n g u l a r element. 7.4.5. EQUATIONS FOR THE SYSTEM The nodal point force vector i s given by F -j where the representation of nodal forces i s as shown i n F i g . 7 ^ . FIG. 7.4 The formation of the complete structure s t i f f n e s s matrix involves the formation of the two equilibrium equations at each nodal point from the element s t i f f n e s s matrix (K), 263 8 2N*1 8 2Nx2N 8 2Nxl where N - No. of node points. 7.4.6. SOLUTION OF EQUILIBRIUM EQUATIONS; The s o l u t i o n of the equilibrium equations i s obtained using the Gauss-Seidel i t e r a t i o n technique. Considering the nodal point n, 2x1 i - l , N n 2x2 1 2x1 tfiere {P } n and {6i} w. Solving for {fin)» K J ' K - l , \ l 6 l - J „ K n l 5 l l i - l . n - 1 n+l,N The displacement i n the (p+l)th cycle of i t e r a t i o n i s given by (P+D i* r 1 ^ - i - i K m 6 i p ) ] < ?-9> n n n i - l , n - l n i 1 nfl.N n i 1 So, the change i n displacement A 6 (P+D . «(P+D _ * (P) i " l , n - l i«l,N 7.4.7.. MODIFICATION OF EQUILIBRIUM EQUATIONS AT SURFACE OF DISCONTINUITY To consider s l i p between the r e i n f o r c i n g bar and the concrete and/or separation of concrete from the bar, the equilibrium equations need to be modified. The four equilibrium equations at a point of d i s c o n t i n u i t y may be expressed as K^.u + K^.w + (ZK6) U - P C 11 c 12 c v c r (7.11) K 2 1 U c + K 2 2 W c + ( Z K 6 ) w c " P z K l l U s + K 1 2 w s + ( E K 6 ) u s " P r K 2 S l U s + * « \ + ( Z K 6 ) w s " K where the superscipt and subscript ' c' and 's' refer to concrete and s t e e l r e s p e c t i v e l y . For s l i p wihtout separation, u £ = u g w " w - A c s where A • s l i p at the i n t e r f a c e . Substituting i n the above equations and grouping, < K U + Kll ) us + ( K12 + KL)W. + ( E K 6 ) U c + ( E K 6 ) U , - P c + P S + -A r r 12 (7.12) 265 ( K21 + K 2 1 ) U 8 + ( K22 + K 2 2 ) w s + ^ ^ " c + tac6)w 8 - P z + P z + K22* A ( 7 ' 1 3 ) 7.4.8. SLIP DUE TO SEPARATION When separation occurs at the in t e r f a c e between concrete and-steel, there w i l l be l o n g i t u d i n a l displacement of the concrete. This s l i p without crushing i s due to s l i d i n g along the r i b face. For t h i s u £ * u and w - w - (u -u ) Cot a where, (see Fig.7Jd)» C S C 6 ' — * a • r i b face i n c l i n a t i o n with respect to the bar a x i s . So, t o t a l s l i p due to separation and crushing = A » ( u c - u g) Cot a + A. From the above, the i t e r a t i o n expressions of the r e s u l t i n g equilibrium equations can be obtained as: f \ Au c K l l K12 Cot a K12 Cot a K12 -1 •\ P uc J Au 1 8 > * 0 K l l K12 < P ? us Aw s K21 K22 Cot a K21 + K^ 2 Cot a K22 + K22 P ws J (7 .14) where K!?,W - K^.u - K^w,, 22 s 21 c 22 c « P j - ( a C « ) u c - K ^ u c - K 1 2 w c - K- ( L K 6 ) u s " K i i u s " K n w s - P S + P C - (EK6)w - (EK6)u - K^.u z z s S o 266 7.4.9. ELEMENT & NODAL POINT STRESSES: The stresses of the elements are computed at the centroid of elements using a r e l a t i o n s h i p : £ - D B a 6 (7.15) where D, B and _a matrices have already been defined e a r l i e r . . The computation of the nodal point stresses has been done as an average of the stresses of the elements surrounding a p a r t i c u l a r node point, as the elements chosen are of constant 6train type. 267 7.5 ANALYSIS SCHEME In the f i n i t e element a n a l y s i s , two d i f f e r e n t cases were c o n s i d e r e d . In the f i r s t case, p e r f e c t bond between the r e i n f o r c i n g bar and the concrete was assumed a l l along the l e n g t h of the r e i n f o r c i n g bar and the push in - p u l l out load was a p p l i e d to the o u t s i d e nodes of the p r o t r u d i n g ends of the bar. In the second case, an incremental step by step l o a d i n g procedure was adopted to account fo r n o n - l i n e a r behaviour due to c r a c k i n g of the concrete and due to s l i p between the r e i n f o r c i n g bar and the c o n c r e t e at the i n t e r f a c e . For each increment of l o a d i n g , the four component of s t r e s s e s {or, 08,az, r r z ) and the p r i n c i p a l s t r e s s e s were c a l c u l a t e d . Any c r a c k i n g or c r u s h i n g of elements were checked. If c r a c k i n g or c r u s h i n g e x i s t e d , then the s t i f f n e s s of the elements were s u i t a b l y m o d i f i e d and the s t r u c t u r a l s t i f f n e s s m a t r i c e s were reformed. The s l i p at the i n t e r f a c e nodes were c a l c u l a t e d corresponding to the computed bond s t r e s s e s based on a bond s t r e s s - s l i p r e l a t i o n s h i p which was a m o d i f i e d form of the equation proposed by N i l s o n (70). The reason f o r the s e l e c t i o n of t h i s equation w i l l be d i s c u s s e d i n Sec. 7.6 of t h i s Chapter. The s l i p v a l u e s obtained were i n c o r p o r a t e d as input i n the computation of v a r i o u s s t r e s s e s i n the subsequent step and so on. The mechanical p r o p e r t i e s of the concrete and the s t e e l assumed in the a n a l y s i s were: Concrete: Ec = 4800 k s i (33,096 MPa) vc = 0.15 268 T e n s i l e s t r e n g t h = 800 k s i (5.52 MPa) S t e e l : Es = 30,000 k s i (20,6850 MPa) v = 0.3 7.6 SELECTION OF BOND STRESS-SLIP RELATIONSHIP: In the absence of experimental data in t h i s i n v e s t i g a t i o n f o r the e v a l u a t i o n of a l o c a l bond s t r e s s - s l i p r e l a t i o n s h i p , some of the alr e a d y p u b l i s h e d data on bond s t r e s s r e l a t i o n s h i p s obtained by v a r i o u s i n v e s t i g a t o r s , was used f o r the a n a l y t i c a l study with the f i n i t e element a n a l y s i s . While proceeding with t h i s study, i t was observed that a wide s c a t t e r of r e s u l t s e x i s t e d i n the computation of the s l i p v a l u e s . A b r i e f summary, of the l o c a l bond s t r e s s - s l i p r e l a t i o n s h i p s put f o r t h by v a r i o u s r e s e a r c h e r s i s presented i n t h i s s e c t i o n f o r comparison. Some of the equations proposed f o r monotonic p u l l out l o a d i n g a r e : N i l s o n (70) : u = 3100( 1 .43 cover + 1.5) s^c"' — 7.6.1 Lutz (58) : u = S/0.75X10 6 — 7.6.2 (at e a r l y stages of s l i p ) Houde (42) : u = 1.95X10 6S - 2.35X10 9S 2 + 1.39X10 1 2S 3 - 0.33X10 1 5s* -- 7.6.3 Hungspreug (44) : u = 1.77X10 6S - 1.28X10 6S 2 + 0.45X10 9S 3 -- 7.6.4 where u = l o c a l bond s t r e s s i n p s i s = l o c a l s l i p i n inches f c ' = c r u s h i n g s t r e n g t h i n concrete in p s i Recently a model has been proposed ( F i g . 1.8(b)) by 269 Ciampi, E l i g e h a u s e n , Bertero and Popov (19) which i s v a l i d f o r d e s c r i b i n g the bond behaviour i n c o n f i n e d concrete r e g i o n s , on the b a s i s of t e s t s on bond behaviour over a short embedment len g t h (5 bar d i a m e t e r s ) . M o r i t a and Kaku (64) have proposed a b o n d - s l i p law ( F i g . 1.4) under monotonic l o a d i n g based on t e s t s i n which a bond length of two times the p i t c h of the t r a n s v e r s e r i b s was used. From the study of the l i t e r a t u r e a v a i l a b l e to date i n c l u d i n g those d e s c r i b e d above, and from the experience of the t e s t s i n t h i s i n v e s t i g a t i o n , the s l i p r e s u l t i n g from the monotonic p u l l - o u t l o a d i n g i s found to depend on v a r i a b l e s such as: a. Concrete s t r e n g t h b. Bar diameter c. Deformation p a t t e r n of bar such as r i b spacing and r i b s i z e d. Bar spacing e. Amount of C o n f i n i n g Reinforcement f. Transverse pressure g. T e n s i l e versus compression l o a d i n g h. Rate of bar p u l l out i . P o s i t i o n of the bar d u r i n g c a s t i n g j . I n c l u s i o n of s t e e l f i b e r s In view of the above, i t may be noted that the equations f o r bond s t r e s s - s l i p r e l a t i o n s h i p proposed by N i l s o n (70), Lutz (58) and Houde (42) and Hungspreug (44) mentioned p r e v i o u s l y , do 270 not c o n s i d e r a l l of the v a r i a b l e s that a f f e c t the bond. Accor d i n g to T a s s i o s (97), the use of j u s t one bond s t r e s s - s l i p law as proposed by M o r i t a and Kaku (64), and Ciampi e t . a l . (19) f o r every p o i n t along the bar i s a b a s i c handicap, l i m i t i n g the v e r s a t i l i t y of the techniques. In a d d i t i o n , only one bond s t r e s s - s l i p curve does not allow the use of the f a l l i n g branch; supplementary assumptions are necessary i n s t e a d near the ends of the bar. Edwards and Yannopoulos (22), based on a l a r g e number of t e s t s , observed a c o n s i d e r a b l e s c a t t e r i n the bond s t r e s s - s l i p curves and suggested the n e c e s s i t y of s t a t i s t i c a l l y designed experiments. According to Eligehausen e t . a l . (25) l o c a l bond s t r e s s s l i p r e l a t i o n s h i p may vary along the embedment l e n g t h . During t e s t i n g of the specimens i n t h i s i n v e s t i g a t i o n under monotonic push i n - p u l l out l o a d i n g , i t was observed that three bond s t r e s s - s l i p zones c o u l d be i d e n t i f i e d i n the specimens: unconfined c o n c r e t e i n t e n s i o n at the p u l l out end, c o n f i n e d c o n c r e t e i n the core, and unconfined c o n c r e t e i n compression at the push i n end. These have a l s o been i d e n t i f i e d by Viwathanatepa et a l . (99). In view of a l l the f a c t s d e s c r i b e d above, i t was c o n s i d e r e d i n a p p r o p r i a t e to use one of the above-mentioned bond s t r e s s - s l i p r e l a t i o n s h i p s d i r e c t l y in the a n a l y t i c a l study without v e r i f i c a t i o n . A t r i a l and e r r o r procedure was used to assess the s u i t a b i l i t y of the bond s t r e s s - s l i p r e l a t i o n s h i p . I t was found that a m o d i f i e d form of the equation developed by N i l s o n , as 271 d e s c r i b e d below, gave reasonably good r e s u l t s as compared to those obtained from the experimental study ( i n t h i s i n v e s t i g a t i o n ) . S = 0.4u 3100(1.43 cover + 1.5) /tc' -- 7.6.5 where the terms have a l r e a d y been d e f i n e d . 7.7 ANALYTICAL RESULTS 7.7.1 Case I: No S l i p , P e r f e c t Bond In t h i s study, p e r f e c t bond and no s l i p were assumed between the r e i n f o r c i n g bar and the c o n c r e t e . A push i n - p u l l out l o a d of ±1 K s i (6.9 MPa) was a p p l i e d to the p r o t r u d i n g ends of the bar. The r e s u l t s of the four component s t r e s s e s (or, a8,az, r r z ) and the p r i n c i p a l s t r e s s e s and t h e i r d i r e c t i o n s were computed. The r e s u l t s of the s t r e s s e s i n the concr e t e and the s t e e l are presented in F i g . 7.5. The s a l i e n t f e a t u r e s of F i g . 7.5 are b r i e f l y d e s c r i b e d below: 1. The bond s t r e s s and the l o n g i t u d i n a l s t r e s s e s i n the concre t e on the push i n end are found to be higher than those on the p u l l out end. There are high bar s t r e s s c o n c e n t r a t i o n s at the loaded ends of the c y l i n d e r . 2. Large c i r c u m f e r e n t i a l and l o n g i t u d i n a l t e n s i l e s t r e s s e s e x i s t i n the concrete at the p u l l out end. The presence of l a r g e t e n s i l e adhesion s t r e s s e s i n the concr e t e i n d i c a t e s that the s e p a r a t i o n should occur with f u r t h e r i n c r e a s e s i n l o a d . 3. R e l a t i v e l y high values of the p r i n c i p a l t e n s i l e s t r e s s e s i n the c o n c r e t e at the s t e e l - c o n c r e t e i n t e r f a c e , e s p e c i a l l y at APPLIED STRESS=1KSI(6.9MPA) (ZERO S L I P ASSUMED) ( J ^ . - CIRCUMFERENTIAL STRESS IN CONCRETE fec- LONGITUDINAL STRESS IN CONCRETE - SHEAR STRESS IN CONCRETE Ois- LONGITUDINAL STRESS IN STEEL 5 0 0 m m FIG. 7-5 VARIOUS STRESSES AT INTERFACE 1KSI o o I O o CO I o o I fo KJ 27 3 the p u l l out end, i n d i c a t e that the i n t e r n a l d i a g o n a l cracks would form at an a p p l i e d s t r e s s l e v e l of ±7 k s i (48 MPa) even when c o n s i d e r i n g zero s l i p . Q u a l i t a t i v e l y , the r e s u l t s as shown i n F i g . 7.5 on the p u l l out end appear to agree w e l l with the r e s u l t s of the anchorage zone s t r e s s e s obtained from the a n a l y t i c a l study by Lutz (58). 7.7.2 Case I I ; S l i p and Separation The a p p l i c a t i o n of load to the p r o t r u d i n g ends of the bar was made p o s s i b l e by g i v i n g uniform displacements to the nodal p o i n t s at the ends of the bar. With an i n c r e a s e i n s l i p i t i s obvious that adhesion w i l l be dest r o y e d . T h e r e f o r e , r a d i a l s e p a r a t i o n between the s t e e l and the concrete was allowed to occur. The f i n i t e element a n a l y s i s c o n s i d e r s s l i p r e l a t e d to bond s t r e s s and s l i p due to the r i b faces angle. The s l i p due to bond s t r e s s was obtained by a t r i a l and e r r o r procedure as d e s c r i b e d i n s e c t i o n 7.6, and s l i p due to the r i b face angle has been d e s c r i b e d i n S e c t i o n 7.4.7 and 7.4.8. The f o l l o w i n g important r e s u l t s were obtained from the a n a l y t i c a l study: 1. At about 6 ksi(41 MPa) a p p l i e d s t r e s s l e v e l , i n t e r n a l d i a g o n a l c r a c k s developed in the concrete surrounding the r e i n f o r c i n g bar at the p u l l out end and a few at the push in end. T h i s agrees w e l l with the p r e d i c t i o n of i n t e r n a l d i a g o n a l c r a c k i n g at the p u l l out end at 5 k s i (34 MPa) by Viwathanatepa (99). With f u r t h e r i n c r e a s e i n the load, more and more d i a g o n a l c r a c k s developed towards the center from the pul-1 out end, though only a few d i a g o n a l cracks 274 developed at the push i n end. Some amount of c r u s h i n g in the concrete surrounding the r e i n f o r c i n g bar took p l a c e at a s t r e s s l e v e l of 12 k s i (82 MPa) on the push i n end. The s t e e l s t r e s s d i s t r i b u t i o n and the . bond s t r e s s d i s t r i b u t i o n at the i n t e r f a c e of concrete and s t e e l at v a r i o u s s t r e s s l e v e l s , along the length of the c y l i n d e r are shown in F i g s . 7.6, 7.7. A comparison of these r e s u l t s with those of experimental ones i n d i c a t e s a t i s f a c t o r y agreement at the p u l l out and push i n end r e g i o n s but some discr e p a n c y at the c e n t r a l r e g i o n . Had the a n a l y s i s i n c l u d e d such f a c t o r s as, the m a t e r i a l n o n l i n e a r i t y of concrete in f r o n t of the r i b s , the s p l i t t i n g c r a c k s and the e f f e c t of s t e e l f i b e r s a c t i n g as c l o s i n g f o r c e s , then the agreement between the a n a l y t i c a l and the experimental r e s u l t s would have been b e t t e r . There i s an i n d i c a t i o n of formation of a c o n i c a l crack at a d i s t a n c e of about 60mm from the p u l l out end at an a p p l i e d s t r e s s l e v e l of 45 k s i (310 MPa). In the experimental study, such c o n i c a l c r a c k s were observed at the p u l l out end face as c i r c u m f e r e n t i a l crack at a higher s t r e s s l e v e l (70 k s i ) . However, i t may be mentioned that the i n t e r n a l crack might have developed at a s t r e s s l e v e l of about 45 k s i (310 MPa). Peak bond s t r e s s e s were found to e x i s t at both ends of the c o n c r e t e c y l i n d e r . With i n c r e a s e i n a p p l i e d s t r e s s l e v e l , the peak bond s t r e s s at the p u l l out end reduced, i n d i c a t i n g d e t e r i o r a t i o n i n bond, whereas peak bond s t r e s s F I G . 7.6 STRESS DISTRIBUTION ALONG REINFORCING BAR EXPERIMENTAL F I G . 7.7 BOND STRESS DISTRIBUTION AT STEEL-CONCRETE INTERFACE 277 continued to i n c r e a s e on the push in end. T h i s may be seen in F i g . 7.7. These f i n d i n g s are i n agreement with the experimental r e s u l t s . C o n c l u s i o n s T h i s chapter d e s c r i b e s the a n a l y t i c a l model which i s a step towards a n a l y t i c a l p r e d i c t i o n of bond behaviour. The model has produced reasonable r e s u l t s but to achieve b e t t e r r e s u l t s , the f u t u r e s t u d i e s should i n c l u d e the e f f e c t s of the f o l l o w i n g : 1. The e f f e c t of s t e e l f i b e r s i n the three dimensional space a c t i n g as c l o s i n g f o r c e s to crack growth. 2. F a i l u r e mode in concrete under a t r i a x i a l s t a t e of s t r e s s such as compression-tension-tension or compression-compression-tension which occurs under push i n - p u l l out l o a d i n g f o r concrete surrounding the r e i n f o r c i n g bar. 3. L o c a l bearing s t r e s s e s at the r i b s of the r e i n f o r c i n g bar. A complete model a l s o need to be extended to i n c l u d e n o n l i n e a r a n a l y s i s under reversed c y c l i c l o a d i n g beyond y i e l d s t r e s s l e v e l . 278 V I I I . SUMMARY, CONCLUSIONS AND RECOMMENDATIONS 8.1 SUMMARY There were two prime o b j e c t i v e s i n t h i s i n v e s t i g a t i o n . The f i r s t o b j e c t i v e was to study the behaviour of bond of deformed bars in p l a i n and s t e e l f i b e r r e i n f o r c e d concrete under re v e r s e d c y c l i c l o a d i n g i n specimens which represented beam column j o i n t s s u bjected to seismic motion. The second was to study the f e a s i b i l i t y of using s t e e l f i b r o u s concrete i n beam-column j o i n t s f o r b e t t e r anchorage bond performance as compared to p l a i n c o n c r e t e . To achieve the above o b j e c t i v e s , twenty four specimens were t e s t e d . The experimental set up was designed so that a s i n g l e bar c o u l d be simultaneously p u l l e d out at one end and push in at the other, and t h i s l o a d i n g c o u l d be reversed c y c l i c a l l y to simulate the l o a d i n g of a bar pa s s i n g through an i n t e r i o r beam-column j o i n t under seismic l o a d i n g . Four b a s i c types of l o a d i n g h i s t o r i e s (monotonic, repeated, reversed c y c l i c with only one c y c l e at each peak l o a d , and reversed c y c l i c with m u l t i p l e c y c l e s at each peak load) were a p p l i e d to the t e s t specimens. The important v a r i a b l e s c o n s i d e r e d were: l o a d i n g type, amplitude of l o a d i n g and number of l o a d i n g c y c l e s ; s t e e l f i b e r s i z e , bar diameter and embedment len g t h , bar s u r f a c e c o n d i t i o n , and the e f f e c t of a h e l i x around the t e s t bar. The s t r a i n d i s t r i b u t i o n along the r e i n f o r c i n g bar and the displacements at the loaded ends were the most important measurable parameters f o r understanding the anchorage bond 279 behaviour f o r specimens su b j e c t e d to v a r i o u s l o a d i n g h i s t o r i e s . A study of the i n t e r n a l c r a c k s as w e l l as the s u r f a c e c r a c k s on the specimens was used to h e l p e x p l a i n the mechanism of bond d e t e r i o r a t i o n and the mode of bond f a i l u r e . In g e n e r a l , the performance of the t e s t i n g set up and t e s t i n g system was q u i t e s a t i s f a c t o r y . The high e l o n g a t i o n type s t r a i n gauges used p r o v i d e d r e l i a b l e r e s u l t s even at a p p l i e d s t r e s s l e v e l s beyond the y i e l d i n s t e e l . Based on a comprehensive study of the a p p l i e d s t r e s s -displacement c h a r a c t e r i s t i c s and s t i f f n e s s degradation of v a r i o u s specimens su b j e c t e d to reversed c y c l i c l o a d i n g , a t r i l i n e a r a p p l i e d s t r e s s - d i s p l a c e m e n t model has been proposed. The model can p r e d i c t the response of a specimen at any p a r t i c u l a r load or c y c l e under i n c r e m e n t a l l y i n c r e a s e d reversed c y c l i c l o a d i n g c o n d i t i o n s . The model g i v e s good agreement with the r e s u l t s obtained from the experimental study. In order to supplement the i n f o r m a t i o n obtained from the experimental study and to have a b e t t e r understanding of the bond behaviour of an anchored r e i n f o r c i n g bar, an e l a s t i c axisymmetric f i n i t e element a n a l y s i s was performed. The i n f o r m a t i o n obtained from t h i s a n a l y t i c a l study was u s e f u l i n f o r m u l a t i n g a theory on the bond d e t e r i o r a t i o n mechanism. R e s u l t s of the a n a l y t i c a l study p r o v i d e d reasonable agreement with the experimental r e s u l t s . 280 8.2 CONCLUSIONS The purpose of t h i s i n v e s t i g a t i o n has been to give a more fundamental understanding of the bond behaviour of anchored bars i n c o n c r e t e , subjected to reversed c y c l i c l o a d i n g , and to study the f e a s i b i l i t y of using s t e e l f i b r o u s concrete i n beam-column j o i n t s f o r b e t t e r anchorage bond performance. Based on the experimental i n v e s t i g a t i o n and the a n a l y t i c a l study, the f o l l o w i n g important c o n c l u s i o n s can be drawn. However, in view of the small number of t e s t specimens, the s t a t i s t i c a l s i g n i f i c a n c e of these c o n c l u s i o n s can not be q u a n t i f i e d . 1. Reversed c y c l i c l o a d i n g causes a much gr e a t e r r e d u c t i o n i n s t i f f n e s s and r e s i s t a n c e c a p a c i t y than does monotonic l o a d i n g . The decrease i n r e s i s t a n c e c a p a c i t y g e n e r a l l y occurs when the specimen i s loaded to a s u f f i c i e n t l y high s t r e s s l e v e l (at l e a s t beyond y i e l d ) and a few load r e v e r s a l s are imposed at t h i s s t r e s s l e v e l . T h i s l o s s i n r e s i s t a n c e c a p a c i t y i s due to a d e t e r i o r a t i o n in the s t r e s s t r a n s f e r mechanism, caused by i n e l a s t i c deformation, c r a c k i n g i n the c o n c r e t e , and the Bauschinger e f f e c t i n the r e i n f o r c i n g s t e e l . 2. A few c y c l e s of reversed l o a d i n g at a low s t r e s s l e v e l of 30 to 40 k s i (207 to 276 MPa) causes a n o t i c e a b l e r e d u c t i o n i n the l o a d i n g s t i f f n e s s (at zero load) although no s i g n i f i c a n t changes in s t i f f n e s s KTI and KCI are observed. However, an i n c r e a s e i n the peak load beyond the y i e l d ( i n s t e e l ) causes a severe r e d u c t i o n i n the s t i f f n e s s e s and an i n c r e a s e i n the displacement. 281 The l o a d i n g h i s t o r y has a s i g n i f i c a n t e f f e c t on the bond d e t e r i o r a t i o n . An i n c r e a s e i n the peak amplitude of l o a d i n g causes bond d e t e r i o r a t i o n at a lower s t r e s s l e v e l in the subsequent c y c l e . For specimens su b j e c t e d to repeated l o a d i n g , i t appears that the l o a d c y c l i n g has no i n f l u e n c e on the l o a d i n g s t i f f n e s s . A study of the a p p l i e d s t r e s s - d i s p l a c e m e n t curves in the form of t r i l i n e a r curves ( d i s c u s s e d in Chapter 5) f o r specimens subjected to r e v e r s e d c y c l i c l o a d i n g r e v e a l the f o l l o w i n g important c h a r a c t e r i s t i c s : a. The slopes of the unloading curves are e s s e n t i a l l y the same. b. The slopes of the r e l o a d i n g curves i n Stage I i n compression ( s t i f f n e s s KCI) are. e s s e n t i a l l y the same as those in t e n s i o n ( s t i f f n e s s KTI) i n the subsequent c y c l e . The above o b s e r v a t i o n s however, are a p p l i c a b l e only before the drop in the r e s i s t a n c e c a p a c i t y of the specimen i s reached. Under push in - p u l l out l o a d i n g with one end of the bar s u b j e c t e d to t e n s i o n and the other to compression, the p o i n t of zero s t r e s s i n the s t e e l l i e s near the center of the specimen for low l o a d s . With an i n c r e a s e i n the peak amplitude of l o a d i n g , the l e n g t h of the t e n s i l e zone i n c r e a s e s compared to that of the compression zone, the i n c r e a s e ranging from 10 to 30 percent ( a p p l i e d s t r e s s range of 200-500 MPa). T h i s i m p l i e s that the push in f o r c e 282 can be t r a n s m i t t e d w i t h i n a much smaller l e n g t h than that r e q u i r e d f o r the p u l l out f o r c e . For specimens subjected to a p r o g r e s s i v e i n c r e a s e in the monotonic l o a d i n g , the bond s t r e s s d i s t r i b u t i o n diagrams and the s t r a i n d i s t r i b u t i o n diagrams c o n f i r m the gradual d e t e r i o r a t i o n of bond i n the p u l l out end, f o l l o w e d by the s h i f t i n g of the peak bond s t r e s s towards the core of the specimen, thus modifying the bond s t r e s s d i s t r i b u t i o n p a t t e r n . However, in the push in end, p r a c t i c a l l y no such bond degradation i s observed and the bond r e s i s t a n c e remains very high. 7. The specimens with s t e e l f i b e r s e x h i b i t e d much b e t t e r anchorage bond c h a r a c t e r i s t i c s than those with no f i b e r s , e s p e c i a l l y under re v e r s e d c y c l i c l o a d i n g . The s t e e l f i b e r s were found to be e f f e c t i v e i n r e t a r d i n g the r a t e of bond degradation under m u l t i p l e c y c l e s of reversed l o a d i n g . With regard to the bond d e t e r i o r a t i o n and the c r a c k i n g , specimens with s t e e l f i b e r s seemed to have improved deformation c h a r a c t e r i s t i c s and were more damage- r e s i s t a n t than p l a i n c o n c r e t e specimens. The SFRC specimens were found to have a g r e a t e r c a p a c i t y to s u s t a i n many c y c l e s of reversed l o a d i n g than p l a i n c o n c r e t e ones under i d e n t i c a l c o n d i t i o n s of l o a d i n g . S t e e l f i b e r s t h e r e f o r e appear to have d e f i n i t e advantages for use i n s i t u a t i o n s where load r e v e r s a l s of r e l a t i v e l y high amplitudes (at l e a s t beyond y i e l d ) are expected, e s p e c i a l l y i n beam column j o i n t s of moment r e s i s t i n g d u c t i l e frames. The specimens c o n t a i n i n g s t e e l f i b e r s had more than twice the energy absorbing 283 c a p a c i t y of specimens c o n t a i n i n g p l a i n concrete under i d e n t i c a l l o a d i n g c o n d i t i o n s . The SFRC specimens a l s o had a higher bond c a p a c i t y (of the order of 20 to 26 percent) under reversed c y c l i c l o a d i n g . 8. The emergence of a ci r c u m f e r e n t i a l crack on the p u l l out end of a specimen subjected to push-in p u l l - o u t l o a d i n g was i n d i c a t i v e of the onset of bond f a i l u r e . The formation of a c o n i c a l crack reduced the e f f e c t i v e embedment len g t h d r a s t i c a l l y . At t h i s stage, the specimen s u f f e r e d a d r a s t i c r e d u c t i o n i n s t r e n g t h and s t i f f n e s s and f a i l e d due to bar p u l l out. The specimens with s t e e l f i b e r s e x h i b i t e d g r e a t e r r e s i s t a n c e to crack growth than the p l a i n concrete ones. 9. Both the 30mm and 50mm long s t e e l f i b e r s of the type used, had p r a c t i c a l l y the same e f f e c t on the anchorage bond performance. However, the concrete c o n t a i n i n g the 50mm long f i b e r s was found to be l e s s workable than that with 30mm long f i b e r s . 10. A 25mm diameter bar can withstand a l a r g e r number of c y c l e s than a 30mm diameter bar of the same embedment length under i d e n t i c a l l o a d i n g c o n d i t i o n s . 11. The s u r f a c e c o n d i t i o n of a bar had a v i t a l i n f l u e n c e on the bond behaviour. The presence of grease on. the r e i n f o r c i n g bar reduced the bond e f f e c t i v e n e s s d r a s t i c a l l y . 12. The t r i l i n e a r a p p l i e d s t r e s s displacement model (under r e v e r s e d c y c l i c l o a d i n g ) formulated i n t h i s study was u s e f u l f o r d e s c r i b i n g the h y s t e r e t i c behaviour of a 284 r e i n f o r c i n g bar embedded in a specimen r e p r e s e n t i n g a beam-column j o i n t . 13. The a n a l y t i c a l study c a r r i e d out i n t h i s i n v e s t i g a t i o n was h e l p f u l f o r a b e t t e r understanding of the bond behaviour of anchored bars. The a n a l y t i c a l study showed that the i n t e r n a l d i a g o n a l crack can i n i t i a t e in the concrete at an a p p l i e d s t r e s s l e v e l as low as 6 k s i . T h i s c r a c k i n g caused a r e d u c t i o n i n s t i f f n e s s of the concrete surrounding the r e i n f o r c i n g bar. 8.3 RECOMMENDATIONS FOR FURTHER STUDY The experimental program and the a n a l y t i c a l study done in t h i s i n v e s t i g a t i o n have provided a g r e a t e r i n s i g h t i n t o the bond behaviour of anchored bars under reversed c y c l i c l o a d i n g . Perhaps the most important r e s u l t of t h i s study has been the i n d i c a t i o n of improved bond c h a r a c t e r i s t i c s in f i b e r r e i n f o r c e d c o n c r e t e as compared to p l a i n c o n c r e t e , under reversed c y c l i c l o a d i n g . However, there are some areas connected to t h i s study which need to be e x p l o r e d f u r t h e r . Based on the r e s u l t s of t h i s study, the f o l l o w i n g suggestions are made f o r f u r t h e r research on the bond behaviour of deformed bars in p l a i n and f i b e r r e i n f o r c e d c o n c r e t e . 1. A more e x t e n s i v e experimental i n v e s t i g a t i o n should be made f o r the study of the bond between a r e i n f o r c i n g bar and s t e e l f i b e r r e i n f o r c e d c o n c r e t e under reversed c y c l i c l o a d i n g . The f o l l o w i n g v a r i a b l e s need to be c o n s i d e r e d : a. cover of the reinforcement b. use of more than one bar 285 c. shape, s i z e and amount of s t e e l f i b e r s d. embedment le n g t h e. c o n f i n i n g pressure (such as v e r t i c a l load) f. a d d i t i o n a l types of l o a d i n g h i s t o r i e s g. s i z e of specimen The e f f e c t of r i b geometry should be i n v e s t i g a t e d for b e t t e r bond performance. The e f f e c t s of r i b angle, r i b h e i g h t , and r i b spacing on bond d e t e r i o r a t i o n under c y c l i c l o a d i n g need to be i n v e s t i g a t e d . The anchorage p r o v i s i o n s , such as embedment le n g t h as recommended by v a r i o u s codes need f u r t h e r examination to take i n t o account the r e d u c t i o n in bond e f f e c t i v e n e s s for p l a i n as well as s t e e l f i b e r r e i n f o r c e d c o n c r e t e s t r u c t u r e s s u b j e c t e d to reversed c y c l i c l o a d i n g . I n t e r n a l c r a c k i n g i n the concrete needs f u r t h e r study, s i m i l a r to that done by Goto ( 3 3 ) , to i n v e s t i g a t e the p a t t e r n and the extent of i n t e r n a l c r a c k s f o r specimens sub j e c t e d to monotonic, repeated and reversed c y c l i c l o a d i n g . The e f f e c t of the i n t e r a c t i o n between the i n t e r n a l d i a g o n a l c r a c k s and the s p l i t t i n g cracks on the bond behaviour need to be i n v e s t i g a t e d . F u r t h e r r e s e a r c h i s necessary to a s c e r t a i n p r e c i s e l y the combination of s t e e l f i b e r s and c o n v e n t i o n a l r e i n f o r c i n g bars needed to produce optimum anchorage bond c o n d i t i o n s . A b e t t e r a n a l y t i c a l study i s necessary to g i v e a complete p i c t u r e of bond under c y c l i c l o a d i n g . The model should be capable of handling c r a c k i n g , crack opening and c l o s i n g , 286 e f f e c t of s t e e l f i b e r s i n the concrete matrix a c t i n g as c l o s i n g f o r c e s a c r o s s the c r a c k s . Such a model would give a b e t t e r understanding of the bond behaviour i n p r a c t i c a l s i t u a t i o n s , such as a beam column j o i n t s u b j e c t e d to rev e r s e d c y c l i c l o a d i n g . 7. The t r i l i n e a r model developed i n t h i s study has been based e n t i r e l y on the data a v a i l a b l e i n t h i s i n v e s t i g a t i o n . In order to extend t h i s model f o r a more general case, many more t e s t s with a l l of the v a r i a b l e s that a f f e c t the bond behaviour would be necessary to v e r i f y the model. 287 BIBLIOGRAPHY 1. An I n t e r n a t i o n a l Symposium: F i b e r R e i n f o r c e d Concrete, P u b l i c a t i o n SP-44, American Concrete I n s t i t u t e , 1974. 2. ACI Committee 554, Measurement of P r o p e r t i e s of F i b e r R e i n f o r c e d Concrete, May 1982. 3. " B u i l d i n g Code Requirements f o r R e i n f o r c e d Concrete", ACI  Standards 318-77, D e t r o i t , Michigan, 1979. 4. Abrams, D.A., "Tests of Bond Between Concrete and S t e e l " , U n i v e r s i t y of I l l i n o i s E n g i n e r i n g Experiment S t a t i o n  B u l l e t i n , 74, 1913. 5. Agarwal, G.L., T u l i n , L.G. and G e r s t l e , K.H., "Response of Doubly R e i n f o r c e d Concrete Beams to C y c l i c Loading", ACI J o u r n a l Proc. V.62, No.7, J u l y 1965, pp. 823-835. 6. ACI Committee 224, " C o n t r o l of Crac k i n g i n Concrete S t r u c t u r e s " , ACI J o u r n a l , V.69, No.12 Dec. 1972, pp. 717-753. 7. ACI Committee 408, "Bond S t r e s s State of the A r t " , ACI  J o u r n a l , V.63, No. 11, Nov. 1966, pp. 1161-1188. 8. ACI Committee 408, " O p p o r t u n i t i e s i n Bond Research", ACI  J o u r n a l , V.67, No.11, Nov. 1970, pp. 858-866. 9. ACI Committee 544, "State of the Art on F i b e r R e i n f o r c e d Concrete," Report No. ACI-544. 1R-82, Concrete I n t e r n a t i o n a l , May 1982, pp. 9-25. 10. ACI-ASCE Committee 352, "Recommendations f o r Design of Beam-Column J o i n t s i n M o n o l i t h i c R e i n f o r c e d Concrete S t r u c t u r e s " , ACI J o u r n a l , V.73, No.7, J u l y 1976, pp. 375-385. . 11. B e r t e r o , V.V. and Popov, E.P., "Seismic Behaviour of D u c t i l e Moment R e s i s t i n g R e i n f o r c e d Concrete Frames", S p e c i a l P u b l i c a t i o n s , SP-53, American Concrete I n s t i t u t e ,  D e t r o i t , 1977, pp. 247-292. 12. B r e s l e r , B., and B e r t e r o , V.V., "Behaviour of R e i n f o r c e d Concrete Under Repeated Load" Proc. of the ASCE, V,94, ST6, June 1968, pp. 1567-1590. 13. B r e s l e r , B., and B e r t e r o , V.V., " I n f l u e n c e of High S t r a i n Rate and C y c l i c Loading on Behaviour of Unconfined and Confined Concrete i n Compression", Proc. 2nd Canadian  Conference on Earthquake E n g i n e e r i n g , June 5-6 1975, Hamilton, O n t a r i o . 288 14. B r e s l e r , B., and B e r t e r o , V.V., "Reinforced Concrete Prism Under Repeated Loads", I n t e r n a t i o n a l Symposium on the E f f e c t s of Repeated Loading of M a t e r i a l s and S t r u c t u r e s , Proceedings, Mexico C i t y 1966., Vol.3, pp. 1-30. 15. Broms, B.B., " S t r e s s D i s t r i b u t i o n i n R e i n f o r c e d Concrete Members with Tension Cracks", ACI J o u r n a l , V.62, No.9 September 1965, pp. 1095-1107. 16. Broms, B.B., "Techniques f o r I n v e s t i g a t i o n of I n t e r n a l Cracks in R e i n f o r c e d Concrete Members", ACI J o u r n a l , V.62, No.1 January 1965, pp. 35-44. 17. Brown, C.B. and J i r s a , J.O., " R e i n f o r c e d Concrete Beams Under Load R e v e r s a l s " , ACI J o u r n a l , Vol.68, No.5, May 1971, pp. 380-390. 18. Chen, W.F. and Carson, J.L., "Bearing C a p a c i t y of F i b e r R e i n f o r c e d Concrete", An I n t e r n a t i o n a l Sysmposium: F i b e r R e i n f o r c e d Concrete, P u b l i c a t i o n SP-44, American Concrete I n s t i t u t e , D e t r o i t , 1974, pp. 209-220. 19. Ciampi, V., Eligehausen, R., B e r t e r o , V.V. and Popov, E.P., " A n a l y t i c a l Model f o r Concrete Anchorage of R e i n f o r c i n g Bars Under G e n e r a l i z e d E x i t a t i o n s " , Report No. UBC/EERC-82/83, U n i v e r s i t y of C a l i f o r n i a , Berkeley, No. 1982. 20. C l a r k , A.P., "Comparative Bond E f f i c i e n c y of Deformed Concrete R e i n f o r c i n g Bars", ACI J o u r n a l , Proc. V.18, No.4, December 1946, pp. 381-400. 21. D r a f t Code of P r a c t i c e s on R e i n f o r c e d Concrete S t r u c t u r e s and i t s Commentry, NZS:3101 (New Zealand), 1980. 22. Edwards, A.D. and Yannopoulos, P.J., "Local Bond to S t r e s s S l i p R e l a t i o n s h i p s f o r Hot R o l l e d Deformed Bars and M i l d S t e e l P l a i n Bars", ACI J o u r n a l , Proc. Vol.76, March 1979, pp. 405-420. 23. Edwards, A.D. and Yannopoulos, P.J., " L o c a l Bond-Stress-S l i p R e l a t i o n s h i p s Under Repeated Loading", Magazine of  Concrete Research, V.30, No.103, June 1978, pp. 62-72. 24. E l i g e h a u s e n , R. Popov, E.P. and B e r t e r o , V.V., "Behaviour of Deformed Bars Anchored at I n t e r i o r J o i n t s Under Seismic E x c i t a t i o n s " , Proceedings, 4th Canadian Conference on Earthquake E n g i n e e r i n g , Vancouver, B.C., June 1983. 25. E l i g e h a u s e n , R., Popov, E.P. and B e r t e r o , V.V., "Local Bond S t r e s s - S l i p R e l a t i o n s h i p s of Deformed Bars under General E x c i t a t i o n s " , Report No-UBC/EERC-83/23, EERC, U n i v e r s i t y o f C a l i f o r n i a , Berkeley, 1983. 289 26. Fenwick, R.C. and I r v i n e , H.M., "Reinforced Concrete Beam-Column J o i n t s f o r Seismic Loading", Part II -Experimental R e s u l t s , B u l l e t i n of New Zealand N.S. f o r  Earthquake Engineers, V.10, No.4, Dec. 1977, pp. 174-185. 27. Ferguson, P.M. and Thompson, J.N., "Development Length f o r High Strength R e i n f o r c i n g Bars in Bond", ACI J o u r n a l , Proc. V.59, J u l y 1962, pp. 887-922. 28. Ferguson, P.M. and Thompson, J.N., "Development Length f o r Larger High Strength R e i n f o r c i n g Bars", ACI J o u r n a l , Proc. V.62, No.1, Jan. 1965, pp. 71-94. 29. Ferguson, P.M., T u r p i n , R.D. and Thompson, J.N., "Minimum Bar Spacing as a Function of Bond and Shear Strength", ACI  J o u r n a l , June 1954, pp. 869-888. 30. Ferguson, P.M, "Bond S t r e s s - the State of the A r t " , Report by ACI Committe 408, ACI J o u r n a l , Proc. V.63, No.11, Nov. 1966, pp. 408-422. 31. G i l k e y , H.J., Chamberlin, S.J. and Beal, R.W., "Bond with R e i n f o r c i n g S t e e l " , Iowa State C o l l e g e B u l l e t i n , E n g i n e e r i n g Report No.26, 1955-56. 32. Gosain, N.K. and J i r s a , J.O., "Bond D e t e r i o r a t i o n in R e i n f o r c e d Concrete Members Under C y c l i c Loads", Proceedings, 6th World Conference on Earthquake E n g i n e e r i n g , New D e l h i , 1977, pp. 3049-3055. 33. Goto, Y. "Cracks Formed in Concrete Around Deformed Tension Bars", ACI J o u r n a l , Proc. V.68, No.4, A p r i l 1971, pp. 244-251. 34. Hannant, D.J., " F a i l u r e C r i t e r i a f o r Concrete i n Compression", Magazine of Concrete Research, V.20, No.64, Sept.1968, pp. 137-144. 35. Hansen, N.W. and Connor, H.W., "Tests of R e i n f o r c e d Concrete Beam-Column J o i n t s Under Simulated Seismic Loading", PCA Research and Development B u l l e t i n , 1972. 36. Hansen, N.W., "Seismic R e s i s t a n c e of Concrete Frames with Grade 60 R e i n f o r c i n g Bars", Proc. ASCE, S t r u c t u r a l Div., Vol.93, ST5, Oct. 1967, pp. 1685-1699. 37. Hansen, R.J. and L i e p i n s , A.A., "Behaviour of Bond Under Dynamic Loading", ACI J o u r n a l , Proc. V.59, No.4, A p r i l 1962, pp. 563-584. 38. H a r r i s , E.C. The Role of Outward R a d i a l Pressure i n the Bond S p l i t t i n g F a i l u r e of R e i n f o r c e d Concrete. Ph.D 290 T h e s i s , U n i v e r s i t y of Colorado, May 1971. 39. H a r v i l , P.S., The Nature of Bond S p l i t t i n g i n R e i n f o r c e d Concrete. Ph.D T h e s i s , U n i v e r s i t y of Colorado, Department of C i v i l E n g i n e e r i n g , 1969. 40. Hassan, F.M., and Hawkins, N.W., " E f f e c t of P o s t - Y i e l d Loading R e v e r s a l s on Bond Between R e i n f o r c i n g Bars and Concrete", Report SM73-2, Dept. of C i v i l E n g i n e e r i n g , U n i v e r s i t y of Washington, S e a t t l e , March 1973. 41. Henager, C.H., " S t e e l F i b r o u s D u c t i l e Concrete J o i n t s f o r Seismic R e s i s t a n t S t u c t u r e s " , ACI S p e c i a l P u b l i c a t i o n , No.53, American Concrete I n s t i t u t e , D e t r o i t , 1977, pp. 371-386. 42. Houde, J . Study of Force-Displacement R e l a t i o n s h i p s f o r the F i n i t e - E l e m e n t A n a l y s i s of R e i n f o r c e d Concrete. Ph.D. T h e s i s , M c G i l l U n i v e r s i t y , 1974. 43. H r i b a r , J.A. and Vasko, R . C , "End Anchorage of High Strength S t e e l R e i n f o r c e d Bars", ACI J o u r n a l , Proc. Vol.66, No.11, Nov. 1969, pp. 875-883. 44. Hungspreug, S., L o c a l Bond Between a R e i n f o r c i n g Bar and Concrete Under High I n t e n s i t y C y c l i c Load. Ph.D T h e s i s , C o r n e l l U n i v e r s i t y , Jan. 1981. 45. I s m a i l , M.A.F. and J i r s a , J.O., "Behaviour of Anchored Bars under Low C y c l i c Overloads Producing I n e l a s t i c S t r a i n s " , ACI J o u r n a l , Proc. V.69, No.7, J u l y 1972, pp. 433-438. 46. I s m a i l , M.A.F. and J i r s a , J.O., "Bond D e t e r i o r a t i o n i n Re i n f o r c e d Concrete Subjected to Low C y c l i c Loads", ACI  J o u r n a l , Vol.69, No.6, June 1972, pp. 334-343. 47. I s m a i l , M.A.F., Bond D e t e r i o r a t i o n i n R e i n f o r c e d Concrete Under C y c l i c Loading. Ph.D T h e s i s , Rice U n i v e r s i t y , Feb. 1 970. 48. Jimenez, R., White, R.N. and Gergeley, P., "Bond and Dowel C a p a c i t i e s of R e i n f o r c e d Concrete", ACI J o u r n a l , Proc. Vol.76, No.1, Jan. 1979, pp. 73-92. 49. Johnston, CD., " S t e e l F i b e r R e i n f o r c e d Mortar and Concrete - A Review of Mechanical P r o p e r t i e s " , S p e c i a l  P u b l i c a t i o n SP-44 on F i b e r R e i n f o r c e d Concrete, American Concrete I n s t i t u t e , D e t r o i t 50. Kemp, E.L. and Wilhelm, W.J., " I n v e s t i g a t i o n of the Parameters I n f l u e n c i n g Bond C r a c k i n g " , ACI J o u r n a l , Proc. Vol.76, No.1, Jan. 1979, pp. 47-71. 291 51. Konyi, K.H., "Bond Between Concrete and S t e e l " , S t r u c t u r a l  Concrete, R e i n f o r c e d Concrete A s s o c i a t i o n , Vol.1, No.9, May/June 1963, pp. 373-390. 52. Kormeling, H.A., Reinhardt, H.W. and Shah, S.P., " S t a t i c and F a t i q u e P r o p e r t i e s of Concrete Beam R e i n f o r c e d with Continuous Bars and with F i b e r s " , ACI J o u r n a l Proc. Vol.77, No.1, Jan/Feb 1980, pp. 37-43. 53. Kuester, J.L. and Mize, J.H., "Program L i s t i n g for O p t i m i z a t i o n Techniques with F o r t r a n " . 54. Losberg, A. and Olsson, P.A., "Bond F a i l u r e of Deformed R e i n f o r c i n g Bars Based on the L o n g i t u d i n a l S p l i t t i n g E f f e c t s of the Bars", ACI J o u r n a l , Proc. Vol.76, No.1, Jan. 1979, pp. 5-18. 55. Lukose, K. Gergely, P. and White, R.N., "Behaviour of R e i n f o r c e d Concrete Lapped S p l i c e s of I n e l a s t i c C y c l i c Loading", ACI J o u r n a l , Proc. Vol.79, No.5, Sept.-Oct. 1982, pp. 355-365. 56. L u t z , L.A. and Gergely, P., "The Mechanics of Bond and S l i p of Deformed Bars i n Concrete", ACI J o u r n a l , Proc. Vol.64, No.11, Nov. 1967, pp. 711-721. 57. L u t z , L.A., " A n a l y s i s of S t r e s s e s in Concrete Near a R e i n f o r c i n g Bar due to Bond and Transverse C r a c k i n g " , ACI  J o u r n a l , Proc. Vol.67, No.10, Oct.1970, pp. 778-787. 58. L u t z , L.A., The Mechanics of Bond and S l i p of Deformed R e i n f o r c i n g Bars i n Concrete. Ph.D. T h e s i s , C o r n e l l U n i v e r s i t y , Sept. 1966. 59. Ma, S.M., Experimental and A n a l y t i c a l S t u d i e s on  H y s t e r e t i c Behaviour of R e i n f o r c i n g Concrete Rectangular  and T-Beam. Report No. EERC 76-2, May 1976, Earthquake E n g i n e e r i n g Research Center, U n i v e r s i t y of C a l i f o r n i a , B e rkely, C a l i f o r n i a . 60. Mains, R.M. "Measurement of the D i s t r i b u t i o n of T e n s i l e and Bond S t r e s s e s Along R e i n f o r c i n g Bars", ACI J o u r n a l , Proc. Vol.48, No.3, Nov. 1951, pp. 225-252. 61. Mathey, R.G and Watstein, D., " I n v e s t i g a t i o n of Bond i n Beam and P u l l out Specimens with High Y i e l d Strength Deformed Bars", ACI J o u r n a l , Proc. Vol.57, No.9, March 1961 , -pp. 1071-1090. 62. Menzel, C A . "Some F a c t o r s I n f l u e n c i n g R e s u l t s of P u l l o u t Bond T e s t s " , ACI J o u r n a l , Proc. Vol.35, June 1939, pp. 517-544. 63. M i r z a , S.M. ^and Houde, J . , "Study of Bond S t r e s s - S l i p 292 R e l a t i o n s h i p i n R e i n f o r c e d Concrete", ACI J o u r n a l , Proc. Vol.76, No.1, Jan. 1979, pp. 19-46. 64. M o r i t a , S. and Kaku, T., " L o c a l Bond S t r e s s - S l i p R e l a t i o n s h i p Under Repeated Loading", IABSE Sympossium, V.13, L i s b o n , 1973, pp. 221-226. 65. M o r i t a , S. and Kaku, T., " S p l i t t i n g Bond F a i l u r e of Large Deformed R e i n f o r c i n g Bars", ACI J o u r n a l , Proc. Vol.76, No.1, Jan. 1979, pp. 93-110. 66. Muhlenbruch, C.W., "The E f f e c t of Repeated Loading on the Bond Strength of Concrete", Proc. of the American S o c i e t y  f o r T e s t i n g and M a t e r i a l s , V.45, 1945, pp. 824-845. 67. Mylrea, T.D. "Bond and Anchorage", ACI J o u r n a l , Vol.44, March 1948, pp. 521-552. 68. N i l s o n , A.H., " I n t e r n a l Measurement of Bond S l i p " , ACI  J o u r n a l , Vol.69, No.7, J u l y 1972, pp. 439-441. 69. N i l s o n , A.H., "Non-Linear A n a l y s i s of R e i n f o r c e d Concrete by the F i n i t e Element Method", ACI J o u r n a l , Vol.65, No.9, Sept. 1968. 70. N i l s o n , A.H., Bond S t r e s s S l i p R e l a t i o n s i n R e i n f o r c e d Concrete. Report No. 345, Department of S t r u c t u r a l E n g i n e e r i n g , C o r n e l l U n i v e r s i t y , Dec. 1971. 71. N i l s o n , A.H., F i n i t e Element A n a l y s i s of R e i n f o r c e d Concrete. Ph.D T h e s i s , U n i v e r s i t y of C a l i f o r n i a at Berkely, 1968. 72. Odman, S.T.A., " S l i p Between Reinforcment and Concrete", RILEM Sysmposium on Bond and Crack Formation i n R e i n f o r c e d  Concrete, V.2, Stockholm, 1957, pp. 407-420. 73. Orangun, CO., J i r s a , J.O. and Breen, J.E., "Re-e v a l u a t i o n of Test Data on Development Lengths and S p l i c e s " , ACI J o u r n a l , Proc. Vol.74, No.3, March 1977, pp. 114-122. 74. Panda, A.K., I n v e s t i g a t i o n s of Bond of Deformed Bars i n P l a i n and S t e e l F i b e r R e i n f o r c e d Concrete Under Reversed C y c l i c Loading., MA.Sc T h e s i s , U n i v e r s i t y of B r i t i s h Columbia, Vancouver, B.C., Sept. 1980. 75. Park, P. and Paulay, T. R e i n f o r c e d Concrete S t r u c t u r e s , John Wiley & Sons, New York, 1975. 76. Park, P. and Paulay, T. "Behaviour of R e i n f o r c e d Concrete E x t e r n a l Beam Column J o i n t s Under C y c l i c Loading", F i f t h World Conference on Earthquake  E n g i n e e r i n g , Paper 88, Vo l . 1 , Session 2D, Rome, June 1973. 293 77. Paulay, T. and Scarpas, A., "The Behaviour of E x t e r i o r Beam Column J o i n t s " , B u l l e t i n of New Zealand N.S.  Earthquake E n g i n e e r i n g , Vol.14, No.8, Sept. 1981, pp. 131-143. 78. Paulay, T., Park,R. and P r i e s t l e y , M.J.N., "Reinforced Concrete Beam Column J o i n t s Under Seismic A c t i o n s " , ACI  J o u r n a l , Proc. Vol.75, No.11, Nov. 1978, pp. 585-593. 79. Perry, E. and J u n d i , N., " P u l l - o u t Bond S t r e s s D i s t r i b u t i o n Under S t a t i c and Dynamic Repeated Loadings", ACI J o u r n a l , Proc. V.66, No.5, May 1969, pp. 377-380. 80. Popov, E., "Mechanical C h a r a c t e r i s t i c s of Bond of R e i n f o r c i n g S t e e l Under Seismic Loading", Workshop on Earthquake - R e s i s t a n c e R e i n f o r c e d Concrete B u i l d i n g C o n s t r u c t i o n , U n i v e r s i t y of C a l i f o r n i a , B erkely, J u l y 1 977. 81. Ramkrishnan, V., Brandshang, T., Coyle, W.V. and Schrader, E.K., "A Comparitive E v a l u a t i o n of Concrete R e i n f o r c e d with S t r a i g h t S t e e l F i b e r s with Deformed Ends Glued Together by Bundles", ACI J o u r n a l , Proc. V o l . 77, No.3, May-June 1980, pp. 135-143. 82. Ramkrishnan, V., Coyle, W.V. and Schrader, E.K., "Performance C h a r a c t e r i s t i c s of F i b e r R e i n f o r c e d Concrete with Low F i b e r Contents", ACI J o u r n a l , Proc. Vol.78, No.5, Sept.-Oct. 1981, pp. 389-395. 83. Rehm, G. "The Basic P r i n c i p l e s of Bond Between S t e e l and Concrete, T r a n s l a t i o n No.134, Cement and Concrete A s s o c i a t i o n , London, pp. 1-31. 84. Rehm, G. and Elige h a u s e n , R. "Bond of Ribbed Bars Under High C y c l e Repeated Loads", ACI J o u r n a l , Proc. V.76, No.2, Feb. 1979, pp. 297-309. 85. Reynolds, G.C. and Besby, A.W., "Bond Strength of Deformed Bars", Bond i n Concrete. e d i t e d by Bartos, P., A p p l i e d Science P u b l i s h e r s , London, 1982. 86. R i c h a r t , F.E. and Jensen, V.P., "Tests of P l a i n R e i n f o r c e d Concrete Made with Haydite Aggregates", B u l l e t i n No.237, E n g i n e e r i n g Experiment S t a t i o n , U n i v e r s i t y of I l l i n o i s , 1931. 87. RILEM - Symposium of Bond and Crack Formation i n R e i n f o r c e d Concrete, Stockholm, 1957. 88. Seismology Committee, S t r u c t u r a l Engineers A s s o c i a t i o n of C a l i f o r n i a , "Recommended L a t e r a l Force Requirements and Commentary", ,San F r a n c i s c o , C a l i f o r n i a , 1959. 294 89. Shah, I.K. "Behaviour of Bond Under Dynamic Loading", Research Report R63-17, School of E n g i n e e r i n g , MIT, Cambridge, 1963. 90. Shipman, J.M. and G e r s t l e , K.H., "Bond D e t e r i o r a t i o n in Concrete Panels Under Load C y c l e s " , ACI J o u r n a l , Proc. V.76, No.2, Feb.1979, pp. 311-325. 9 1 . Singh, A., G e r s t l e , K.H. and T u l i n , L.G., "The Behaviour of R e i n f o r c i n g S t e e l Under Reversed Loading", M a t e r i a l s Research and Standards, ASTM, V.5, Jan. 1965, pp. 12-17. 92. Sinha, B.P., G e r s t l e , K.H. and T u l i n , L.G., "Reponse of S i n g l y R e i n f o r c e d Beams to C y c l i c Loading", ACI J o u r n a l , Proc. V.61, No.8, Aug.1964, pp. 195-211. 93. Spencer, R.A., Panda, A.K. and Mindess, S., "Bond of Deformed Bars in P l a i n and F i b e r R e i n f o r c e d Concrete under Reversed C y c l i c Loading", I n t e r n a t i o n a l J o u r n a l of Cement  Composites & Lightweight Concrete, V.4, No.1, Feb. 1982, pp. 3-17. 9 4 . Swamy, R.N. and A l - N o o r i , K., "Bond Strength of S t e e l F i b e r s R e i n f o r c e d Concrete", Concrete (Great B r i t a i n ) , V o l.8, No.8, Aug. 1974, pp. 36-37. 95. Takeda, T., Sozen, M.A. and N i e l s e n , N.N., "Re i n f o r c e d Concrete Response to Simulated Earthquakes", Proc. of the ASCE, V.96, ST12, Dec. 1970, pp. 2557-2573. 96. T a s s i o s , T.P. and Yannopoulos, P.J., " A n a l y t i c a l S t u d i e s on R e i n f o r c e d Concrete Members Under C y c l i c Loading Based on Bond S t r e s s - S l i p R e l a t i o n s h i p " , ACI J o u r n a l , Vol.78, No.3, May-June 1981, pp. 206-215. 97. T a s s i o s , T.P., " P r o p e r t i e s of Bond Between Concrete and S t e e l Under Load C y c l e s I d e a l i z e d S e i s i m i c A c t i o n s " , AICAP-CEB Symposium, Rome, 1979, pp. 67-122. 98. Uniform B u i l d i n g Code, I n t e r n a t i o n a l Conference of B u i l d i n g O f f i c i a l s , Pasadena, 1974 e d i t i o n . 99. Viwathanatepa, S., Bond D e t e r i o r a t i o n of R e i n f o r c i n g Bars Embedded i n Confined Concrete B l o c k s . Ph.D T h e s i s , U n i v e r s i t y of C a l i f o r n i a , Berkeley, June 1979. 100. Viwathanatepa, S., Popov, E.P. and B e r t e r o , V.V., " D e t e r i o r a t i o n of R e i n f o r c e d Concrete Bond Under G e n e r a l i z e d Loading, ACI Annual Conference, San Diego, C a l i f o r n i a , March 1977. 101. W a t s t e i n , D. " D i s t r i b u t i o n of Bond S t r e s s i n Concrete P u l l - o u t Specimens", ACI J o u r n a l , Proc. Vol.18, No.9, 295 May.1947, pp. 1041-1052. 102. Watstein, D. and B r e s l e r , B., "Bond and Cracking i n Re i n f o r c e d Concrete", R e i n f o r c e d Concrete E n g i n e e r i n g , Vol I, John Wiley & Sons, 1974. 103. Watstein, D. and Seese, N.A., " E f f e c t s of Type of Bar on Width of Cracks i n R e i n f o r c e d Concrete Subjected to Tension", ACI J o u r n a l , Proc. V.41, No. 4, Feb. 1945, pp. 293-304. 104. Wilson, E.L., " F i n i t e Element A n a l y i s of Two-Dimentional S t r u c t u r e s " . Ph.D. D i s s e r t a t i o n , Univ. of C a l i f o r n i a , 1963. 105. Z a g a j e s k i , S., " D e t e r i o r a t i o n of Bond i n R e i n f o r c e d Concrete Beams due to C y c l i c Load R e v e r s a l " , Graduate Student Report, S t r u c t u r a l Eng. and S t r u c t u r a l Mechanics, U n i v e r s i t y of C a l i f o r n i a , Berkeley, 1974. 106. Z i e n k i e w i c z , O.C. The F i n i t e Element Method, T h i r d E d i t o n , McGraw H i l l Book Company (UK) L t d . 1977. 296 APPENDIX A ~ DESIGN OF TEST SPECIMENS;  Scope & O b j e c t i v e The prime o b j e c t i v e of the r e s e a r c h was to study the behaviour of anchorage bond i n an i n t e r i o r beam-column j o i n t , s u b j e c t e d to l o a d i n g c o n d i t i o n s s i m u l a t i n g seismic c o n d i t i o n s . It was t h e r e f o r e d e s i r a b l e to t r y to ensure that there would be l i t t l e or no e f f e c t on the specimens due to other parameters such as shear, f l e x u r e , and so on. Thus, an attempt was made to l i m i t the s t r e s s e s to w i t h i n the e l a s t i c l i m i t s , and to ensure no crack formation or propagation due to the f a c t o r s mentioned above other than the anchorage bond. T h i s was a l s o i n agreement with the c u r r e n t design philosophy f o r moment r e s i s t a n t frame s t r u c t u r e s subjected to seismic f o r c e s , i n that the s t r u c t u r e should have strong columns and weak beams. Embedment Length CSA A23.3-M77, Clause 10.6, recommends that the b a s i c development le n g t h i n t e n s i o n s h a l l be: Id = 0.019 Ab fy / f c ' but not l e s s than 0.58 db fy where Id = development le n g t h (mm) Ab = area of bar (mm2) fy = s p e c i f i e d y i e l d s t r e n g t h of reinforcement (MPa) f c ' = s p e c i f i e d compressive s t r e n g t h of c o n c r e t e (MPa) = 4 5 MPa db = nominal diameter of bar (mm) 2 9 7 s u b s i t u t i n g a p p r o p r i a t e v a l u e s , F o r t h e N o . 2 0 B a r I d - 0 . 0 1 9 x 290 x 420 « 345mm o r 0 . 0 5 8 x 1 9 . 2 x 420 * 466mm w h i c h e v e r i s h i g h e r , s o I d <* 468mm F o r t h e N o . 2 5 B a r I d = 0 . 0 1 9 x 487 x 420 • 579mm v/S5~ o r 0 . 0 5 8 x 2 4 . 9 x 420 = 606mm w h i c h e v e r i s h i g h e r , so I d = 606mm F o r t h e N o . 3 0 B a r I d = 0 . 0 1 9 x 672 x 420 «= 799mm 7 — -o r 0 . 0 5 8 x 2 9 . 2 5 x 420 = 712mm w h i c h e v e r i s h i g h e r , s o I d = 799mm The b a s i c d e v e l o p m e n t l e n g t h s a s c a l c u l a t e d a b o v e a r e t o be m o d i f i e d by a m u l t i p l y i n g f a c t o r o f 0 . 7 5 f o r c o n f i n e d c o n c r e t e . T h e r e f o r e , t h e b a s i c d e v e l o p m e n t l e n g t h s c o m p u t e d a r e : 20mm & r e b a r : l d = 3 5 i m m 25mm £. r e b a r : ld=454mm 30mm & r e b a r : ld=599mm T h e b a s i c d e v e l o p m e n t l e n g t h i n c o m p r e s s i o n , w h i c h i s l e s s t h a n t h a t c a l c u l a t e d f o r t e n s i o n , i s n o t c o n s i d e r e d f o r t h e c o m p u t a t i o n o f I d . H o w e v e r , t h e embedment l e n g t h s o f t h e t e n s i o n r e b a r , o r t h e d e p t h o f s p e c i m e n s r e p r e s e n t i n g t h e beam-c o l u m n j o i n t , a r e t a k e n a s I d = 375mm, 500mm, a n d 500mm f o r t h e N o . 2 0 , N o . 2 5 , a n d N o . 3 0 b a r s , r e s p e c t i v e l y . 298 S h e a r C o n s i d e r a t i o n s ; N o . 2 5 B a r and 500mm Embedment L e n g t h U l t i m a t e t e n s i l e s t r e n g t h o f r e b a r - 675 Mpa ( f r o m t e s t r e s u l t s ) s o P u « 6 7 5 x 487 x 1 0 * KN « 329 KN P Maximum s h e a r - 329 KN A s p e r C l a u s e 9 . 5 . 1 , CSA 2 3 . 3 - M 7 7 , t h e s h e e r s t r e n g t h p r o v i d e d b y c o n c r e t e f o r members s u b j e c t e d t o s h e a r a n d f l e x u r e o n l y = v c - 0 . 1 7 fecT* bw d - 0 . 1 7 & 5 x 250 x 500 - 1 4 2 . 5 KN H e n c e s h e a r r e i n f o r c e m e n t i s n e c e s s a r y . Max imum s h e a r c a p a c i t y t h a t c a n be p r o v i d e d w i t h s h e a r r e i n f o r c e m e n t = ( 0.67 N/JC1 + 0 . 1 7 / E c M bwd = 0 . 8 4 ^ 5 x 250 x 500 - 712.7 KN > 329 KN F I G. A . 1 vu = 329 - 3.1 Mpa 500x250x.B5 vc = 0.17 / f T 1 - 1.14 Mpa Using No.10 t r a n s v e r s e reinforcement, s p a c i n g - 134mm c/c. 2 9 9 Check for Flexure A trial and error method was adopted for the design of the flexural reinforcment. Considering the arrangement of bars (i.e. 10-NO.20 Bars) as shown in Fig. A.2. Load at ultimate « 2 x 487 x 487 x IO'* KN « 658 KN utlimate moment Mu « 658 x 600 « 98.7 KN.M 4 F l G. A . 2 cc = fc ; d'=50mm; d=450mm E c c s 1 _ c c K d f s 1 ; c s " = i s ' E s E s c s = fjs ; c s , = f_s , ; c s 2 = f s 2 E s E s = c s 1 K d - d 1 d - k d-45 CS ' CS k d - d 1-45 d-kd c s d - k d-200 c s 1 = k d - d 1 . f c k d E c cs" = k d - d'-45 . f c k d ' Ec 300 es « (1-k) . tc k Ec es, « (d-kd-45) fc kd Ec e s 2 « (d-kd-200) fc kd Ec f s 1 « kd-d 1 . nfc ; f s " « kd-d*-45 . nfc kd kd f s - (l-k) . n f c ; f s , •(d-kd-45) . nfc ~T~ kd f s 2 « (d-kd-200) . nfc kd C o n s i d e r i n g e q u i l i b r i u m , Cc + C s 1 + Cs" «= To+T,+T 2 or 0.5bkd f c * (kd-50) . nfc x 580 + (kd-95) nfc x 580 kd kd «= (1-k) nfc x 580 + (d-kd-45) nfc x 580 + (d-kd-200) nfcx5B0 k kd kd n = JEs = 29x10* «= 6.31 Ec 57,000 ^6500 C o n s i d e r i n g e q u i l i b r i u m , Cc + C s 1 + Cs" * To+T,+T 2 or 0.5bkd f c + (kd-50) . nfc x 580 + (kd-95) x nfc x 580 kd kd * (1-k) nfc x 580 + (d-kd-45) nfc x 580 + (d-kd-200) nfcx5B0 k kd kd S o l v i n g , K = 0.2926 and thus kd = 131.7 mm. Hence, the assumption i s ok Moment of Resi s t a n c e = 6.949 f c x 10 s = 98.7 x 10 6 Nmm so fc = 14.2 Mpa f s = (1-k) n f c «= 216.6 Mpa < 0.6fy, Hence ok. k ec = 0.000448 es «= 0.00108 301 A t Y i e l d P y - 420 x 487 x 2 - 4 0 9 K N My * 4 0 9 x 150 « 6 1 3 5 0 KNnun f c • 8 . 8 2 8 Mpa f s * 1 3 4 . 6 7 Mpa ec * 0 . 0 0 0 2 7 8 es • 0 . 0 0 0 6 7 A t W o r k i n g L o a d A l l o w a b l e s t e e l s t r e s s * 168 Mpa P a «= 168 x 487 x 2 - 163 KN Ma «= 2 4 4 5 0 KNmm fc = 3 . 5 2 Mpa f s = 5 3 . 7 Mpa c c = 0 . 0 0 0 1 1 es * 0 . 0 0 0 2 7 Check f o r Confinement As per Clause A 6 . 5 . 3 ACI 3 1 8 - 7 7 , Where re c t a n g u l a r hoop reinforcement i s used, the r e q u i r e d area of the tr a n s v e r s e hoop bar i s computed as Ash = Lh 2 Sh o r Sh = 2Ash Lh. ps where ps i s the vo l u m e t r i c r a t i o r e q u i r e d by s e c t i o n A6.5.2 with Ach s u b s i t i t u t e d f o r Ac and fy the s p e c i f i e d y i e l d s t r e n g t h of the hoop reinforcement. sh = hoop spacing ps = 0.45 Ug_ - 1) f c 1 Ac f y « - 0.45 ( 1 0 x 2 0 - 1 ) f c 1 8 x 1 8 fy 0.175 f c 1 fy > 0.12 f c 1 fy 302 » 0 . 1 7 5 x 6 . 5 « 0 . 0 1 8 9 60 F o r t h e a r r a n g e m e n t o f m a i n r e i n f o r c e m e n t a d o p t e d ( F i g . A . 2 ) L h • 4 . 0 i n j S h « 3 . 5 " (90mm) s o A s h - 4 x 0 . 0 1 8 9 x 3 . 5 - 0 . 1 3 2 3 i n 2 ( 85mm 2 ) 2 U s i n g N o . 1 2 b a r f o r r e c t a n g u l a r h o o p s , A s h = 0 . 1 9 6 i n 2 (126mm 2 ) H e n c e o k . 303 APPENDIX B - MATHEMATICAL MODEL OF STRESS-STRAIN RELATIONSHIP OF DEFORMED BARS The reasons f o r the f o r m u l a t i o n of a mathematical model for the s t r e s s - s t r a i n behaviour of r e i n f o r c i n g s t e e l under reversed c y c l i c l o a d i n g and montonic l o a d i n g a r e : 1. To p r e d i c t l o c a l bond s t r e s s e s along the r e i n f o r c i n g bar of the specimens, which n e c e s s i t a t e s p r e c i s e computation of l o c a l s t r e s s e s which are d i f f i c u l t to measure e x p e r i m e n t a l l y . The only method i s to compute s t r e s s e s on the b a s i s of s t r a i n values of the r e i n f o r c i n g bar at v a r i o u s l o c a t i o n s . 2. To study the h y s t e r e t i c behaviour of the r e i n f o r c i n g s t e e l and i t s i n f l u e n c e on the performance of concrete members, such as lo a d vs displacement r e l a t i o n s h i p s under v a r i o u s combinations of l o a d i n g , i n c l u d i n g reversed c y c l i c l o a d i n g . 3. I t i s of i n t e r e s t to observe to what extent the Bauschinger e f f e c t i n s t e e l i n f l u e n c e s the performance of concrete under r e v e r s e d c y l i c l o a d i n g . B.1 GENERAL BEHAVIOUR OF THE STRESS-STRAIN RELATIONSHIP In order to a v o i d c o m p l i c a t i o n s , a general study was c a r r i e d out of the s t r e s s - s t r a i n r e l a t i o n s h i p of the r e i n f o r c i n g s t e e l under i n c r e m e n t a l l y i n c r e a s e d r e v e r s e d - c y c l i c l o a d i n g . The g e n e r a l f e a t u r e s of the s t r e s s - s t r a i n r e l a t i o n s h i p a r e : For the f i r s t l o a d i n g beyond the y i e l d s t r e s s l e v e l , the behaviour i s s i m i l a r to that under monotonic loadng. Upon unloading, the slope of the s t r e s s - s t r a i n curve remains p a r a l l e l 304 to the i n i t i a l l o a d i n g curve.In compression, the l i n e a r i t y of the curves i s l o s t very q u i c k l y , and i t i s d i f f i c u l t to compute p r e c i s e l y the y i e l d p o i n t i n compression. Upon unloading ( i n compression), the curve again becomes l i n e a r , with the same slope as the i n i t i a l s t r e s s - s t r a i n curve. The t e n s i l e p o r t i o n of the l o a d i n g curve i n the second c y c l e i s s i m i l a r to that of the compression l o a d i n g curve of the p r e v i o u s c y c l e . Again on unloading the slope i s s i m i l a r to that mentioned e a r l i e r . However, the behaviour a f t e r f u r t h e r c y c l e s i s a f f e c t e d by other v a r i a b l e s such as the p r e v i o u s load h i s t o r y , s t r a i n r a t e , e lapsed time between c y c l e s , and so on. B.1.1 MATHEMATICAL MODEL OF THE STRESS-STRAIN RELATIONSHIP:  UNDER REVERSED CYCLIC LOADING) The model i s s i m i l a r to the Ramberg-Osgood Model f o r the s t r e s s - s t r a i n r e l a t i o n s h i p of s t e e l . I t has been observed that the behaviour d u r i n g l o a d i n g e i t h e r i n compression or i n t e n s i o n i s very dependent on the i n i t i a l i n e l a s t i c s t r a i n values p r i o r to l o a d i n g . T h e r e f o r e , the l o a d i n g curves have been grouped i n t o two c a t e g o r i e s - Tension Half C y c l e and Compression Half C y c l e . Each h a l f c y c l e s t a r t s with l o a d i n g e i t h e r in t e n s i o n or in compression, and then unloadng to the zero s t r e s s l e v e l as shown in F i g . 3.1. A model with the f o l l o w i n g form has been used to d e s c r i b e the s t r e s s - s t r a i n r e l a t i o n s h i p of the l o a d i n g p o r t i o n s of each h a l f c y c l e . 3 0 5 w h e r e a - s t r e s s a t w h i c h s t r a i n t o be c o m p u t e d ( K s i ) c s - s t r a i n t o be c o m p u t e d e s i - s t r a i n a t b e g i n n i n g o f l o a d i n g -K , - c o n s t a n t ( K s i ) K 2 _ c o n s t a n t A n o n - l i n e a r r e g r e s s i o n m e t h o d , d e v e l o p e d by P o w e l (SSQMIN ALGORITHM) (53) was u s e d , w h i c h s o l v e s f o r t h e c o e f f i c i e n t s i n a m u l t i v a r i a b l e , n o n l i n e a r r e g r e s s i o n e q u a t i o n u t i l i z i n g N d a t a p o i n t s . T h e p r o c e d u r e i s a m o d i f i c a t i o n o f t h e G a u s s N e w t o n T e c h n i q u e t o r e d u c e t h e d i f f i c u l t i e s i n s o l v i n g a s e t o f e q u a t i o n s a t e a c h i t e r a t i o n . T h e c o m p u t e d r e s u l t s a r e f o u n d t o h a v e e x c e l l e n t c o r r e l a t i o n w i t h t h e e x p e r i m e n t a l r e s u l t s . T h e r u l e s r e g a r d i n g f o r m u l a t i o n o f t h e m o d e l a r e : 1. o = E . c f o r e<cy i n t h e f i r s t c y c l e 2. o = f ( c ) f o r o e y i n t h e f i r s t c y c l e ( R e f e r t o o-E m o d e l f o r m o n t o n i c l o a d i n g , S e c t i o n B . 1.3) 3. U n l o a d i n g c u r v e h a s s l o p e 6 = t a n ~ 1 E 4. L o a d i n g c u r v e i n t h e c o m p r e s s i o n h a l f c y c l e r e p r e s e n t e d by 306 5. Unloading curve having slope 6 = tan" 'E 6. Loading curve i n the t e n s i o n h a l f c y c l e represented by o o • »i 30,000 [ X ' l ^ 1 J The v a l u e s of the c o n s t a n t s K, and K 2 f o r v a r i o u s values of i n i t i a l s t r a i n s and f i n a l l o a d i n g s t r e s s l e v e l s are t a b u l a t e d i n Tables B.1 through B.3. B.1.2 SIMPLIFIED ANALYTICAL MODEL FOR REVERSED CYCLIC LOADING: I t was c o n s i d e r e d a p p r o p r i a t e to develop a s i m p l i f i e d model to r e p r e s e n t the s t r e s s - s t r a i n r e l a t i o n s h i p of the r e i n f o r c i n g s t e e l under reversed c y c l i c l o a d i n g , rather than the complicated one d e s c r i b e d e a r l i e r . While making a comparative study of the h y s t e r e t i c curves of r e i n f o r c i n g bars of d i f f e r e n t diameters, i n r e v e r s e d c y c l i c , i n c r e m e n t a l l y loaded specimens, an i n t e r e s t i n g phenomenon was observed. For l o a d i n g beyond the y i e l d s t r e s s l e v e l , a l i n e a r i n c r e a s e i n the s t r e s s - s t r a i n r e l a t i o n s h i p e x i s t s f o r peak s t r e s s l e v e l s i n t e n s i o n as w e l l as i n compresssion. These may be seen from F i g . B.1(b) ( t y p i c a l c a s e ) . The s l o p e s of the s t r e s s - s t r a i n curves beyond y i e l d may be d e f i n e d as the s t r a i n hardening moduli. G e n e r a l l y , the most important reason f o r s t u d y i n g the h y s t e r e t i c curves of the s t r e s s - s t r a i n r e l a t i o n s h i p l i e s i n computing the l o c a l s t r e s s e s or bond s t r e s s e s at i n t e r i o r p o i n t s along the r e i n f o r c n g bar of the specimen at peak s t r e s s l e v e l s . C o n s i d e r i n g t h i s , the s i m p l i f i e d model d e s c r i b e d w i l l be of great help, and l e s s cumbersome, f o r the computation of s t r e s s e s . The r u l e s 307 regarding f o r m u l a t i o n of the model a r e : 1. o - E»c for e < e y 2 V 0 - l E i • ( E 8 - Ey> • ° y J for C > C y where E| = s t r a i n hardening modulus i n t e n s i o n . = s t r a i n hardening modulus i n compression. o = s t e e l y i e l d s t r e s s i n t e n s i o n . o = s t e e l y i e l d s t r e s s i n compression. The computed r e s u l t s as per the s i m p l i f i e d model c o r r e l a t e w e l l with the experimental data. The s t r a i n hardening modulus fo r v a r i o u s specimens under d i f f e r e n t c o n d i t i o n s of l o a d i n g both in t e n s i o n and i n compression i s t a b u l a t e d i n Table B.4. B . 1 . 3 ANALYTICAL MODEL OF STRESS-STRAIN RELATIONSHIP OF REINFORCING BAR FOR MONOTONIC LOADING Based on the a v a i l a b l e experimental data and using Powel's ( 5 3 ) n o n l i n e a r r e g r e s s i o n a n a l y s i s program, an equation f o r the best curve f i t t i n g the s t r a i n hardening data was ob t a i n e d . The r u l e s r e g a r d i n g f o r m u l a t i o n of the model a r e : ^ # o • E •£ for c < E y 2. o - o y for e g h < t < c y 3. o - 1736 6 - 26076 c 2 + 154481 cf for t > E s sh where e , = s t e e l s t r a i n at the p o i n t of s t r a i n sh hardening. os = s t e e l s t r e s s i n K s i . There appears to be p r a c t i c a l l y no d i f f e r e n c e i n the 308 s t r e s s - s t r a i n behaviour i n compression as compared to that i n t e n s i o n . The computed r e s u l t s from the model have an e x c e l l e n t c o r r e l a t i o n with the experimental data. B.I.4 CONCLUSIONS: Based on the experimental t e s t r e s u l t s and those obtained from the a n a l y t i c a l study, the f o l l o w i n g c o n c l u s i o n s may be drawn: 1. An ac c u r a t e r e p r e s e n t a t i o n of the s t r e s s - s t r a i n r e l a t i o n s h i p under r e v e r s e d c y c l i c l o a d i n g i s p o s s i b l e through a mo d i f i e d form of the Ramberg-Osgood model. 2. The s t r e s s - s t r a i n r e l a t i o n s h i p of the r e i n f o r c i n g s t e e l under reversed c y c l i c l o a d i n g i s very much i n f l u e n c e d by the p r e v i o u s s t r a i n h i s t o r y , the v i r g i n p r o p e r t y of the m a t e r i a l and the diameter of the r e i n f o r c i n g bar. However, the e f f e c t of s t r a i n - a g i n g has been n e g l e c t e d as the l o a d i n g and unloading of the specimens were done i n a r e l a t i v e l y short time. 309 APPENDIX C - EXPERIMENTAL RESULTS C.1 MONOTONIC LOADING C.1.1 SPECIMEN - F2-500/25/MO/10 A p p l i e d Stress-Displacement R e l a t i o n s h i p : The specimen was subjected to a gradual i n c r e a s e i n l o a d i n g (monotonically) except f o r o c c a s i o n a l l y h o l d i n g the lo a d constant momentarily to scan the readings f o r a p p l i e d s t r e s s , displacement, and so on. During the t e s t , one of the LVDTs was found to be detached and hence the curves f o r only one end (N.Face) were a v a i l a b l e . As the load was g r a d u a l l y i n c r e a s e d , a sharp r e d u c t i o n i n s t i f f n e s s was observed at about 414 MPa, a f t e r which the s t i f f n e s s r e d u c t i o n was s m a l l , but gr a d u a l , A f t e r i n c r e a s i n g the load to 631 MPa there was no sign of f a i l u r e and i t was decided to unload and run a few reversed c y c l e s . A c c o r d i n g l y , the specimen was unloaded and reloaded in the reverse d i r e c t i o n up to 558 MPa and then unloaded. In the 2nd c y c l e , at about 538 MPa, a sudden s l i p and p u l l out of the rebar was observed and the t e s t run stopped. C r a c k i n g : The f i r s t h a i r l i n e r a d i a l s p l i t t i n g c racks developed at an a p p l i e d s t r e s s of 320 MPa on the p u l l out end (S. F a c e ) . As the load was p r o g r e s s i v e l y i n c r e a s e d , l o n g i t u d i n a l s p l i t t i n g c r a c k s and a d d i t i o n a l r a d i a l c r a c k s o c c u r r e d . With a f u r t h e r i n c r e a s e i n l o a d , the l o n g i t u d i n a l c r a c k s propagated towards the push i n end. A p a r t i a l c i r c u m f e r e n t i a l crack developed at 482 310 MPa at a r a d i u s of about 100mm from the rebar a x i s , i n d i c a t i n g formation of a c o n i c a l crack i n s i d e the specimen. However, even at t h i s maximum load of 631 MPa, no c r a c k s were observed on the push i n end (N. F a c e ) . A f t e r unloading and r e l o a d i n g i n the reverse d i r e c t i o n up to 558 MPa, r a d i a l c r a c k s on the N.Face and l o n g i t u d i n a l cracks on the E & W Faces were observed. Again, when the specimen was loaded i n t e n s i o n , the e x i s t i n g c i r c u m f e r e n t i a l and r a d i a l c r a c k s widened and propagated on the S. Face. C.1.2 SPECIMEN - F1-500/25/MO/12 A p p l i e d Stress-Displacement R e l a t i o n s h i p : As with the p r e v i o u s specimen, the push i n - p u l l out load was g r a d u a l l y i n c r e a s e d . Up to about 414 MPa, there was p r a c t i c a l l y no change i n a x i a l s t i f f n e s s . Beyond 414 MPa, the slope of the curve changed a b r u p t l y . However, the specimen c o u l d s u s t a i n a much higher l o a d . A f t e r l o a d i n g to 620 MPa the specimen was unloaded and then reloaded i n the reverse d i r e c t i o n to 552 MPa; i t was then c y c l e d 4 times at a maximum amplitude of 538 MPa s t r e s s l e v e l . Even then f a i l u r e d i d not take place and i t was decided to keep the specimen f o r an i n t e r n a l crack study. C r a c k i n g : With a p r o g r e s s i v e i n c r e a s e i n l o a d i n g , the f i r s t two r a d i a l s p l i t t i n g c racks occurred i n the specimen on the p u l l out end (S. Face) at about 276 MPa. As the a p p l i e d s t r e s s was g r a d u a l l y i n c r e a s e d , l o n g i t u d i n a l s p l i t t i n g c r a c k s extended from the r a d i a l ones on the E. Face at 365 MPa. Even at the h i g h e s t 31 1 peak s t r e s s l e v e l , 620 MPa, there were no cracks on the compression s i d e . However, as the lo a d d i r e c t i o n was reversed, r a d i a l s p l i t t i n g c racks o c c u r r e d at about 317 MPa on the N. Face and l o n g i t u d i n a l s p l i t t i n g c r a c k s on the East and West Faces. With f u r t h e r i n c r e a s e s i n load, more s p l i t t i n g cracks developed. In the 2nd to 5th c y c l e s of l o a d i n g , no new c r a c k i n g developed on the S. Face, except the crack around the rebar ( s e p a r a t i o n ) and the r a d i a l c r a c k s around the rebar, which widened. However, on the North Face, i n the 3rd c y c l e , one c i r c u m f e r e n t i a l crack formed and the cracks around the rebar widened. In other c y c l e s , only some of the e x i s t i n g cracks widened i n the c e n t r a l p o r t i o n of the p u l l out end. C.2 SPECIMENS SUBJECTED TO REPEATED LOADING (RP) C.2.1 SPECIMEN - F2-500/25/RP/9 A p p l i e d Stress-Displacement R e l a t i o n s h i p : The response of the specimen was found to be q u i t e d i f f e r e n t , compared to the reverse c y c l i c - loaded specimens. The slopes of the unloading curve appear to be s i m i l a r to those of the r e l o a d i n g curves and may be c o n s i d e r e d t o g e t h e r . A comparison of the response of a monotonic curve (F1-MO/12) with the envelope curve f o r t h i s specimen r e v e a l s that there i s . p r a c t i c a l l y no d i f f e r e n c e between the two. T h i s i n d i c a t e s that the l o a d c y c l i n g probably has no i n f l u e n c e on the i n i t i a l s t i f f n e s s . Another o b s e r v a t i o n i s that the displacement on the compression s i d e i s almost n e g l i g i b l e compared to that on the t e n s i o n s i d e . The specimen d i d not experience much damage even 312 a f t e r being loaded to the 586 MPa s t r e s s l e v e l and c y c l e d 4 times at t h i s amplitude. C r a c k i n g : As the specimen was su b j e c t e d t o i n c r e m e n t a l l y i n c r e a s i n g repeated l o a d i n g , on the p u l l out end the f i r s t h a i r - l i n e r a d i a l s p l i t t i n g crack emerged at an a p p l i e d s t r e s s l e v e l of 276 MPa. At 365 MPa and 455 MPa, two more r a d i a l s p l i t t i n g c r a c k s appeared i n c l u d i n g h o r i z o n t a l c r a c k s extending on the W. Face of the specimen. At 565 MPa, more r a d i a l s p l i t t i n g c r a c k s appeared and e x i s t i n g c r a c k s widened and extended. At 627 MPa, a c i r c u m f e r e n t i a l crack p a r t i a l l y formed around the rebar. However, no new cra c k s developed except for a s l i g h t widening of the e x i s t i n g c r a c k s when the load was c y c l e d 4 time at t h i s amplitude of l o a d i n g . At t h i s stage i t appeared as i f the c r a c k i n g was e x h i b i t i n g s t a b l e behaviour; the o v e r a l l widths of the cracks were not very l a r g e . On the push i n end of the specimen (N. Fa c e ) , no c r a c k s were observed. C.3 SPECIMENS SUBJECTED TO REVERSED CYCLIC LOADING (RV) C.3.1 SPECIMEN - F2-500/25/RV/5 A p p l i e d Stress-Displacement R e l a t i o n s h i p : The responses of t h i s specimen under f u l l y r eversed c y c l i c push i n - p u l l out l o a d i n g were found to be s i m i l a r on both ends and hence only the S. end i s d e s c r i b e d i n F i g . C.1(a). A f t e r a few e l a s t i c c y c l e s , the specimen was loaded beyond the y i e l d s t r e s s of the bar. The specimen was loaded under l o a d c o n t r o l t i l l i t reached the y i e l d s t r e s s l e v e l , and then was switched 313 over to s t r o k e c o n t r o l . A f t e r the specimen was loaded beyond 414 MPa ( t e n s i o n ) , a marked r e d u c t i o n i n the s t i f f n e s s was observed. On unloading from 448 MPa and r e l o a d i n g i n compression a s l i g h t p i n c h i n g of the h y s t e r e t i c curve was observed, i n d i c a t i n g the onset of bond d e t e r i o r a t i o n and s l i p of the r e i n f o r c i n g bar with respect to the c o n c r e t e . In subsequent re v e r s e d c y c l e s with incremental i n c r e a s e s i n peak l o a d i n g , a gradual l o s s of s t i f f n e s s and more p i n c h i n g of the h y s t e r e t i c curves were observed. In a l l of the c y c l e s , the unloading curves were found to be p a r a l l e l to each other. A f t e r l o a d i n g the specimen to 552 MPa, the r e s i s t a n c e c a p a c i t y of the specimen was reduced and u l t i m a t e l y the specimen f a i l e d due to p u l l out of the rebar at 462 MPa. C r a c k i n g : With an increase i n the a p p l i e d s t r e s s l e v e l , the f i r s t h a i r - l i n e r a d i a l s p l i t t i n g crack emerged on the p u l l out end (S. Face) at 358 MPa. Another r a d i a l s p l i t t i n g crack o c c u r r e d with a h o r i z o n t a l l o n g i t u d i n a l s p l i t t i n g crack at 393 MPa. At 448 MPa, a few of the e x i s t i n g cracks widened and some extended. At 524 MPa, one a d d i t i o n a l r a d i a l crack and a c i r c u m f e r e n t i a l crack o c c u r r e d , accompanied by widening and extension of some of the e x i s t i n g c r a c k s . A f t e r c y c l i n g twice at the peak amplitude of 538 MPa, the c i r c u m f e r e n t i a l crack underwent g r e a t e r widening and e x t e n s i o n . However, the s t r e s s t r a n s f e r c a p a c i t y a b r u p t l y decreased and the rebar p u l l e d out of the c o n c r e t e . 314 I n t e r n a l C r a c k i n g Specimen P-RV/5 was cut l o n g i t u d i n a l l y ( i n a h o r i z o n t a l plane) about 5mm away from the r e i n f o r c i n g bar, with a diamond saw. The observed crack p a t t e r n s are presented i n F i g . C.2(a). They show the formation of c o n i c a l shaped c r a c k s , formed on both ends of the specimen, which are manifested as c i r c u m f e r e n t i a l c r a c k s on both f a c e s . I t i s b e l i e v e d that the c o n i c a l crack forms as an extension to the d i a g o n a l crack which had p r e v i o u s l y formed. However, the formation of d i a g o n a l c r a c k s was not observed anywhere in the s l i c e d specimen. S t r a i n D i s t r i b u t i o n F i g . No. C.3 shows the p r o f i l e of the s t r a i n d i s t r i b u t i o n along the r e i n f o r c i n g bar at v a r i o u s s t r e s s l e v e l s . With a p r o g r e s s i v e i n c r e a s e i n the a p p l i e d s t r e s s l e v e l , e s p e c i a l l y beyond about 296 MPa, there seems to be some tendency fo r the s t r a i n d i s t r i b u t i o n curves to become h o r i z o n t a l (or even have a negative slope) towards the t e n s i l e .end of the specimen. T h i s i s probably due to s e p a r a t i o n between the r e i n f o r c i n g bar and the c o n c r e t e , and the consequent l o s s of bond. The length of the zone of t e n s i l e s t r a i n i n the r e i n f o r c i n g bar i n c r e a s e s with i n c r e a s i n g peak load and, i n g e n e r a l , i s about 10 to 15% more than that of the compressive s t r a i n zone. The slope of s t r a i n curves on the compression s i d e seems to be steeper, i n d i c a t i n g g r e a t e r bond r e s i s t a n c e on the compression s i d e of the r e i n f o r c i n g bar. One i n t e r e s t i n g o b s e r v a t i o n i s t h a t , even at 315 the ±300 MPa s t r e s s l e v e l , there seems to be c o n s i d e r a b l e bond d e t e r i o r a t i o n , as i s apparent from the r e l a t i v e l y higher s t r a i n values (curves 3 & 13) when the peak l o a d i n g was increased to ±455 MPa s t r e s s l e v e l . T h e r e f o r e , i t appears that the load h i s t o r y has a d e f i n i t e r o l e i n bond d e t e r i o r a t i o n . The maximum y i e l d p e n e t r a t i o n of 100mm was observed at a maximum load of about 490 MPa. Some of the gauges behaved e r r a t i c a l l y beyond about 455 MPa f o r unknown reasons and hence the corresponding s t r a i n v a l u e s were not presented i n F i g . C.3. Bond S t r e s s D i s t r i b u t i o n The bond s t r e s s d i s t r i b u t i o n curves at v a r i o u s a p p l i e d s t r e s s l e v e l s are presented i n F i g . C.4. For any curve, say at the ±207 MPa s t r e s s l e v e l (curve 1), the p a t t e r n of the curve i n d i c a t e s that the abs o l u t e maximum bond r e s i s t a n c e of about 10 MPa i s l o c a t e d adjacent to the push i n end, and another zone of high bond r e s i s t a n c e of about 8.3 MPa i s l o c a t e d about 70mm from the p u l l out end. The bond r e s i s t a n c e along the c e n t r a l p o r t i o n i s p r a c t i c a l l y n e g l i g i b l e . With an inc r e a s e i n peak load, say to 403 MPa (curve 6), the abs o l u t e maximum bond r e s i s t a n c e i n c r e a s e s to 20 MPa near the push i n end, and a second zone of high bond r e s i s t a n c e (13 MPa) i s l o c a t e d 75mm from the p u l l out end. The r e s i s t a n c e at the centre i n c r e a s e s to 6.2 MPa while some bond d e t e r i o r a t i o n on the p u l l out end occu r s . T h e r e f o r e , i t appears that with an in c r e a s e i n lo a d i n g a p r o g r e s s i v e r e d i s t r i b u t i o n of the bond s t r e s s o c c u r s . 316 C.3.2 SPECIMEN P-500/25/RV/6 T h i s specimen contained no s t r a i n gauges and hence the t e s t bar was ungrooved. The purpose f o r t e s t i n g such a specimen was to compare i t with the response of an i d e n t i c a l l y loaded specimen with a grooved t e s t bar. A p p l i e d Stress-Displacement r e l a t i o n s h i p : T h i s specimen was loaded i d e n t i c a l l y to specimen P-RV/5. The response of the specimen, e s p e c i a l l y on the N. Face, seems to be e s s e n t i a l l y s i m i l a r to that of P-RV/5, as may be seen from the h y s t e r e t i c curves shown in F i g . C.1(b). The h y s t e r e t i c behaviour on the S. Face appeared to be i n c o n s i s t e n t , p o s s i b l y due to e r r a t i c behaviour of the LVDT, and hence i s not presented. As the specimen was loaded p r o g r e s s i v e l y , the h y s t e r e t i c curve underwent a sharp r e d u c t i o n i n s t i f f n e s s at about 414 MPa. On unloading and than r e l o a d i n g i n compression, a s l i g h t p i n c h i n g of the h y s t e r e t i c curve may be observed. On unloading from compression, and r e l o a d i n g i n t e n s i o n , the s t i f f n e s s KTI (Stage I) was found to be s i g n i f i c a n t l y reduced as compared to the p r e v i o u s c y c l e . On unloading from 526 MPa, when the specimen was j u s t loaded i n compression, severe p i n c h i n g was observed and the rebar was pushed back s i g n i f i c a n t l y at a r e l a t i v e l y lower l o a d . T h i s probably i n d i c a t e d severe d e s t r u c t i o n of the bond which took p l a c e in the p r e v i o u s c y c l e . However, the s t i f f n e s s soon recovered and the specimen showed marked s t r e n g t h i n compression. A f t e r a few c y c l e s of load i n g at the 586 MPa peak s t r e s s l e v e l , the specimen underwent profuse 317 c r a c k i n g and f i n a l l y f a i l e d due to rebar p u l l out. Crac k i n g With an in c r e a s e i n l o a d i n g , the f i r s t h a i r - l i n e crack emerged on the S. Face at the 317 MPa a p p l i e d s t r e s s l e v e l . Another r a d i a l crack developed, accompanied by extension of the o r i g i n a l crack, at 503 MPa. A c i r c u m f e r e n t i a l crack occurred around the t e s t bar at 517 MPa and more r a d i a l s p l i t t i n g c racks developed, and some of the o r i g i n a l c r a c k s extended to the E. & W. Faces. At 552 MPa, s e p a r a t i o n between the rebar and concrete was observed. The r a d i a l and c i r c u m f e r e n t i a l cracks were s i g n i f i c a n t l y widened. By the time the specimen was loaded up to 586 MPa profuse c r a c k i n g and s i g n i f i c a n t displacement had occurred on both faces of the specimen. F i n a l l y , the rebar was p u l l e d out with a core of concrete with about a 90mm r a d i u s . C.3.3 SPECIMEN P-500/25/RV/8 T h i s specimen contained 50mm s t e e l f i b e r s , but no s t r a i n gauges were mounted on the t e s t bar. A p p l i e d Stress-Displacement R e l a t i o n s h i p : I n i t i a l l y , the response of the specimen was more or l e s s s i m i l a r to the behaviour of specimens with a s i m i l a r l o a d i n g h i s t o r y , as d e s c r i b e d e a r l i e r . A p r o g r e s s i v e l o s s of s t i f f n e s s c o u l d "be observed at a l l stages of l o a d i n g , whether under compression or t e n s i o n , as the specimen was c y c l e d with i n c r e m e n t a l l y i n c r e a s e d peak l o a d i n g beyond 414 MPa. No t i c e a b l e p i n c h i n g of the h y s t e r e t i c curves set i n a f t e r about 469 MPa 318 when the displacements s t a r t e d i n c r e a s i n g at a f a s t e r r a t e , i n d i c a t i n g severe degradation i n bond. At 586 MPa, (2nd c y c l e ) , the specimen y i e l d e d with a sharp drop in s t r e n g t h and the rebar p u l l e d out. C r a c k i n g : As the specimen was g r a d u a l l y c y c l e d with i n c r e m e n t a l l y i n c r e a s e d peak l o a d i n g , the f i r s t r a d i a l s p l i t t i n g crack was observed at the 276 a p p l i e d s t r e s s l e v e l on the S. Face, followed by s e v e r a l more r a d i a l and l o n g i t u d i n a l s p l i t t i n g c r a c k s , and extension of the o r i g i n a l c r a c k s when the peak load was i n c r e a s e d to 538 MPa i n s u c c e s s i v e c y c l e s . At t h i s s t r e s s l e v e l , c i r c u m f e r e n t i a l c r a c k s tended to form. Beyond t h i s l o ad, p r a c t i c a l l y no new s p l i t t i n g c racks nor n o t i c e a b l e extension of the e x i s t i n g c r a c k s c o u l d be observed. However, the c i r c u m f e r e n t i a l crack extended s l i g h t l y and widened. Beyond 427 MPa, i n three of the c y c l e s , there was no change in the s t a t u s of any c r a c k s except the c i r c u m f e r e n t i a l c r a c k . At 586 MPa (2nd c y c l e ) , wide c r a c k s o c c u r r e d around the rebar ( s e p a r a t i o n ) f o l l o w e d by s p a l l i n g of concrete at the N. Face of the specimen. At t h i s stage, the r e s i s t a n c e c a p a c i t y decreased and the specimen f a i l e d due to rebar p u l l out. C.3.4 SPECIMEN - F1-500/25/RV/16 A p p l i e d Stress-Displacement R e l a t i o n s h i p : The h y s t e r e t i c curves showing the a p p l i e d s t r e s s -displacement r e l a t i o n s h i p s on the S. Face are shown in F i g . C.5(a). The response of t h i s specimen to an i n c r e a s e i n peak 319 amplitude of l o a d i n g was found to be p r a c t i c a l l y the same as that of specimen F2-RV/8 ( d e s c r i b e d above). A s i m i l a r p r o g r e s s i v e l o s s i n s t i f f n e s s was observed as the load amplitude was i n c r e m e n t a l l y i n c r e a s e d beyond 414 MPa. The magnitude of the displacements remained p r a c t i c a l l y the same up to 482 MPa fo r both of these specimens. Though severe degradation i n s t i f f n e s s o c c urred, the specimen e x h i b i t e d marked load c a r r y i n g c a p a c i t y both i n t e n s i o n and compression even up to 586 MPa. Nonetheless, the displacement i n c r e a s e d at a f a s t e r r a t e than the load increment. In the 2nd c y c l e of t h i s peak amplitude, the displacement observed was q u i t e high and the specimen f a i l e d due to p u l l out of the rebar from c o n c r e t e . C r a c k i n g : The f i r s t r a d i a l s p l i t t i n g crack o c c u r r e d on the S. Face of the specimen at the 276 MPa s t r e s s l e v e l ; i t extended towards the corner and became a l o n g i t u d i n a l crack on the E. Side with a f u r t h e r i n c r e a s e i n l o a d . When the load d i r e c t i o n changed s i m i l a r c r a c k s occurred on the N. Face. At 365 MPa, one a d d i t i o n a l r a d i a l s p l i t t i n g crack and ex t e n s i o n of the l o n g i t u d i n a l crack were observed. At 414 MPa, a new l o n g i t u d i n a l crack emerged on the E. Side which was not an exte n s i o n of the r a d i a l c r a c k . T h i s , however, extended to the S. Face at higher l o a d s . At 448 MPa, a few more r a d i a l s p l i t t i n g c r a c k s emerged and the crack around the rebar widened. Beyond t h i s l o ad, and up to 482 MPa, no new r a d i a l s p l i t t i n g c r a c k s developed, but widening of cra c k s i n the corner region of the specimen took p l a c e . Beyond 482 MPa, there was n e i t h e r 320 crack formation nor n o t i c e a b l e crack e x t e n s i o n , but the crack around the rebar ( s e p a r a t i o n ) widened s i g n i f i c a n t l y and the c i r c u m f e r e n t i a l crack tended to form. At 572-586 MPa, the r a d i a l crack around the rebar as w e l l as the c i r c u m f e r e n t i a l crack widened. At t h i s stage, s i n c e the displacements had become q u i t e l a r g e , the t e s t was stopped. C.4 SPECIMENS SUBJECTED TO REVERSED MULTIPLE CYCLIC LOADING (RVM) C.4.1 SPECIMEN ~ F1-500/25/RVM/13 T h i s specimen contained no s t r a i n gauges on the rebar. A p p l i e d Stress-Displacement R e l a t i o n s h i p : The a p p l i e d s t r e s s - d i s p l a c e m e n t r e l a t i o n s h i p s f o r t h i s specimen (S. Face) are shown i n F i g . C.6(a). Up to the 414 MPa s t r e s s l e v e l , the response was q u i t e s i m i l a r to the other specimens d e s c r i b e d e a r l i e r . A f t e r l o a d i n g the specimen to 572 MPa compression on the S. Face and t e n s i o n on the N. Face, the h y s t e r e t i c behaviour changed completely f o r both s i d e s . On the N. Face, the s t i f f n e s s decrease was q u i t e s i g n i f i c a n t as compared to that on the S. Face. However, some of the s t i f f n e s s was regained when the loa d was decreased and c y c l e d at 414 MPa and then at 496 MPa. During the 1st f i v e load c y c l e s , at a peak amplitude of 496 MPa, no s i g n i f i c a n t displacement was n o t i c e d on the S. Side, i n d i c a t i n g that not much damage was induced when the peak load had been in c r e a s e d to 572 MPa. However, i n subsequent c y c l e s , severe p i n c h i n g i n the h y s t e r e t i c 321 curve was observed. T h i s probably i n d i c a t e d severe s l i p and bond d e t e r i o r a t i o n . A f t e r e i g h t c y c l e s of l o a d i n g at t h i s peak s t r e s s l e v e l , the load c a r r y i n g c a p a c i t y of the specimen dropped and the specimen y i e l d e d due to rebar p u l l - o u t . C r a c k i n g For t h i s specimen, the f i r s t h a i r l i n e r a d i a l s p l i t t i n g crack emerged on the S. Face at 49 K s i (338 MPa), followed by two a d d i t i o n a l r a d i a l c r a c k s at 414 MPa. At t h i s stage, as the load on the N. Face was in c r e a s e d to 572 MPa, suddenly numerous r a d i a l s p l i t t i n g cracks as w e l l as l o n g i t u d i n a l c r a c k s developed on the N. Face,. A l s o , a c i r c u m f e r e n t i a l crack p a r t l y formed. A f t e r unloading, when the specimen was c y c l e d at the 496 MPa s t r e s s l e v e l , one r a d i a l and another c i r c u m f e r e n t i a l crack occurred on the S. Face. On f u r t h e r c y c l i n g , the crack extension or formation was n e g l i g i b l e . However, the crac k s widened i n a zone of about 75mm ra d i u s around the rebar and w i t h i n the corner zone of the specimen. In the 10th c y c l e , a l a r g e c i r c u m f e r e n t i a l crack suddenly developed, connecting the r a d i a l c r a c k s , and in the 11th c y c l e , the load dropped suddenly and the rebar p u l l e d out e x c e s s i v e l y from the concret e matrix. C.4.2 SPECIMEN - F2-500/2 5/RVM/14 A p p l i e d Stress-Displacement R e l a t i o n s h i p : Running a few c y c l e s (4 to 5) at peak s t r e s s l e v e l s of 338,414, and 496 MPa produced p r a c t i c a l l y n e g l i g i b l e d i f f e r e n c e s in the response. When the a p p l i e d s t r e s s was in c r e a s e d to 538 MPa, four c y c l e s at, t h i s amplitude produced s i g n i f i c a n t 322 displacement. At t h i s stage, f u r t h e r t e s t i n g was abandonded, s i n c e the specimen was intended f o r a study of i n t e r n a l c r a c k i n g . C r a c k i n g The crack p a t t e r n s observed on both the N. & S. Faces of the specimen were e s s e n t i a l l y the same. Li k e the other specimens d e s c r i b e d e a r l i e r , t h i s specimen developed the f i r s t r a d i a l s p l i t t i n g crack at the 276 MPa a p p l i e d s t r e s s l e v e l . F i v e c y c l e s at 338 MPa s t r e s s l e v e l produced no change i n the crack p a t t e r n . On i n c r e a s i n g the s t r e s s l e v e l to 414 MPa, one a d d i t i o n a l r a d i a l s p l i t t i n g crack emerged which extended as a l o n g i t u d i n a l crack to the E. Face. In the t h i r d c y c l e at t h i s s t r e s s one more a d d i t i o n to the r a d i a l crack appeared. The f o u r t h c y c l e caused e x t e n s i o n of the the crack to the W. Face. I n c r e a s i n g the peak s t r e s s l e v e l to 496 MPa produced one more r a d i a l c r a c k . At t h i s s t r e s s l e v e l , c y c l i n g produced no f r e s h c r a c k s , but widening of the e x i s t i n g c r a c k s . At t h i s stage, the t e s t i n g was stopped. I n t e r n a l C r a c k i n g In order to explore the i n t e r n a l crack formation i n s i d e the specimen i t was cut l o n g i t u d i n a l l y , i n the plane of the r e i n f o r c i n g bar but about 5mm c l e a r of i t , with a diamond saw. The observed crack p a t t e r n s are shown in F i g . C.2(b). They i n d i c a t e t h at the c i r c u m f e r e n t i a l c r a c k s on the North and South Face of the specimen are m a n i f e s t a t i o n s of the formation of c o n i c a l shaped c r a c k s on both s i d e s of the specimen. 323 C.4.3 SPECIMEN - F1-500/25/RVM/15 A p p l i e d Stress-Displacement R e l a t i o n s h i p : The response of the specimen (S. Side) to push i n - p u l l out l o a d i n g i s presented in F i g . C.6(b). The o v e r a l l responses at both faces were e s s e n t i a l l y the same up to 414 MPa. However, beyond 496 MPa, the behaviour on the N. Side was s i g n i f i c a n t l y changed, as the h y s t e r e t i c curves s u f f e r e d severe p i n c h i n g , i n d i c a t i n g s l i p of the bar due to bond degradation. For both f a c e s , two c y c l e s at peak s t r e s s l e v e l s of 414 and 496 MPa produced no s i g n i f i c a n t changes i n displacements. I n c r e a s i n g the amplitude of l o a d i n g to 538 MPa caused a s i g n i f i c a n t change in the response. A severe r e d u c t i o n i n s t i f f n e s s c o u l d be observed as a r e v e r s a l of l o a d i n g was imposed. In the 5th c y c l e , the l o a d c a r r y i n g c a p a c i t y of the specimen dropped and f i n a l l y the rebar p u l l e d out. C r a c k i n g On the S. Face, the f i r s t r a d i a l s p l i t t i n g c r a c k s appeared at 317 MPa, followed by two more c r a c k s at 338 MPa. At 434 MPa, one more r a d i a l crack o c c u r r e d and the l o n g i t u d i n a l crack extended. At 496 MPa, another r a d i a l crack developed and some of the o r i g i n a l c r a c k s extended. In the 1st and 2nd c y c l e s at a peak s t r e s s l e v e l of 538 MPa, no a p p r e c i a b l e change was n o t i c e d in the crack p a t t e r n . In subsequent c y c l e s , a c i r c u m f e r e n t i a l crack tended to form, connecting the r a d i a l c r a c k s , which g r a d u a l l y widened. No extensions of other cracks were observed. The r a d i a l c r a c k s around the rebar, out to a r a d i u s of about 324 65mm from the rebar as w e l l as in the nearest c o r n e r s of the specimen widened to a great extent. U l t i m a t e l y , i n the 5th c y c l e , the load c a r r y i n g c a p a c i t y of the specimen dropped and the t e s t was stopped when the rebar was p u l l e d out to a great e x t e n t . The crack p a t t e r n on the N. Face was e s s e n t i a l l y the same as that on the S. Face. C.4.4 SPECIMEN - F1-500/25/RVM/19 A p p l i e d Stress-Displacement R e l a t i o n s h i p : Apparently, the responses of the specimen on both ends remained the same; up to 414 MPa, no s i g n i f i c a n t displacement changes were n o t i c e d i n the c o n s e c u t i v e load c y c l i n g . However, beyond t h i s l o a d , the displacements at the S. Face was observed to be higher than those at the N. Face under i d e n t i c a l l o a d i n g c o n d i t i o n s . For the S. Face, when the peak l o a d i n g was i n c r e a s e d to 496 MPa, suddenly the displacement s i g n i f i c a n t l y i n c r e a s e d . However, at t h i s l e v e l , 2 c y c l e s produced n e g l i g i b l e changes in the displacement. On i n c r e a s i n g the peak load to 538 MPa again the displacement was i n c r e a s e d s i g n i f i c a n t l y . S u c cessive load c y c l i n g up to 7 c y c l e s at t h i s peak s t r e s s produced only minor changes in displacement. When the peak s t r e s s was i n c r e a s e d to 545 MPa and c y c l e d , the displacement in each c y c l e i n c r e a s e d s i g n i f i c a n t l y and u l t i m a t e l y the r e s i s t a n c e of the specimen dropped suddenly and the rebar p u l l e d out. Crack ing In g e n e r a l , more or l e s s s i m i l a r c r a c k i n g p a t t e r n s were observed on the opposite f a c e s . 325 On the S. Face, the f i r s t r a d i a l s p l i t t i n g crack was observed at the 324 MPa peak s t r e s s l e v e l . At 414 MPa, one more r a d i a l crack emerged which extended to the E. Face as a l o n g i t u d i n a l c r a c k . At 483 MPa, another r a d i a l crack accompanied by a c i r c u m f e r e n t i a l crack formed. At 524 MPa, only the c i r c u m f e r e n t i a l crack extended and widened. At 545 MPa both the r a d i a l c r a c k s w i t h i n a r a d i u s of about 90mm from the rebar a x i s and the c i r c u m f e r e n t i a l crack widened s i g n i f i c a n t l y . F i n a l l y , the specimen y i e l d e d due to e x c e s s i v e p u l l out of r e b a r . S t r a i n D i s t r i b u t i o n The s t r a i n d i s t r i b u t i o n curves f o r t h i s specimen f o r v a r i o u s peak l o a d i n g s and numbers of c y c l e s are shown in F i g . C.7 (two of the s t r a i n gauges at the end of the t e s t - b a r were not f u n c t i o n i n g during the e n t i r e t e s t ) . It i s apparent from the curves that even a f t e r two c y c l e s at the 414 MPa s t r e s s l e v e l , there was some bond d e t e r i o r a t i o n , as i s evident from the i n c r e a s e i n s t r a i n values f o r a p a r t i c u l a r l o c a t i o n along the r e i n f o r c i n g bar (curves 5 & 7). The bond d e t e r i o r a t i o n i s q u i t e p e r c e p t i b l e even in the 2nd c y c l e at a peak s t r e s s l e v e l of ±496 MPa (curves 9 & 11). In g e n e r a l , the bond s t r e s s on the push in end was found to be higher than that at the p u l l out end f o r a p a r t i c u l a r a p p l i e d s t r e s s l e v e l as may- be seen from the higher slo p e s of the s t r a i n d i s t r i b u t i o n c urves. However, at a few l o c a t i o n s there appears to be some departure from t h i s o b s e r v a t i o n . T h i s may be due to f a c t o r s such as l o c a l s t r e s s 326 i n c r e a s e due to c r a c k i n g , improper f u n c t i o n i n g of the s t r a i n gauges, and so on. In the 4th c y c l e of l o a d i n g at a peak s t r e s s l e v e l of ±538 MPa y i e l d i n g had penetrated to about 175mm from the end of the specimen. C.4.5 SPECIMEN - F1-500/25/RVM/21 A p p l i e d Stress-Displacement R e l a t i o n s h i p : The h y s t e r e t i c responses of t h i s specimen on the S. Face are presented i n F i g . C.8(a). The responses on both faces of the specimen were e s s e n t i a l l y the same. No s i g n i f i c a n t changes in the displacements were n o t i c e d a f t e r two c y c l e s each of l o a d i n g at peak s t r e s s e s of 207, 331 and 414 MPa. On i n c r e a s i n g the s t r e s s l e v e l to 496 MPa, the displacement suddenly i n c r e a s e d s i g n i f i c a n t l y , due to y i e l d i n g of the r e i n f o r c i n g bar. However, two c y c l e s at t h i s peak lo a d produced p r a c t i c a l l y no f u r t h e r change in displacement. Again, when the peak s t r e s s l e v e l was i n c r e a s e d to 538 MPa, s i g n i f i c a n t displacement was n o t i c e d . At t h i s s t r e s s l e v e l , the load c y c l i n g produced a gradual i n c r e a s e in displacement. In the 10th c y c l e , severe p i n c h i n g of the h y s t e r e t i c curve was observed. As the load was i n c r e a s e d to 545 MPa, the c a p a c i t y of the specimen i n compression was suddenly d r a s t i c a l l y reduced, and the specimen f a i l e d due to rebar p u l l -out . Cra c k i n g On the S. Face, a h a i r l i n e r a d i a l s p l i t t i n g crack occurred at 324 MPa. At 331 MPa, another r a d i a l s p l i t t i n g crack emerged, extending to the E.- s i d e as a l o n g i t u d a l c r a c k . At 496 MPa, 327 another r a d i a l crack developed and s e v e r a l of the o r i g i n a l c r a c k s widened and extended. In the 1st c y c l e at the s t r e s s l e v e l 538 MPa, a c i r c u m f e r e n t i a l crack p a r t i a l l y formed around the rebar at about a 75mm r a d i u s . S uccessive c y c l e s at t h i s l o a d only produced extension and widening of a few cr a c k s , i n c l u d i n g the c i r c u m f e r e n t i a l one. In the 10th c y c l e , the specimen f a i l e d due to rebar p u l l out. C.4.6 SPECIMEN - F1-500/25/RVM/22 Th i s specimen co n t a i n e d 50mm f i b e r s and, i n the r e i n f o r c i n g cage, a s p i r a l was prov i d e d around the t e s t bar. The i n t e n t of t h i s t e s t was to a s c e r t a i n whether the s p i r a l would improve bond performance. A p p l i e d Stress-Displacement R e l a t i o n s h i p ; No s i g n i f i c a n t changes i n displacements were n o t i c e d a f t e r two c y c l e s each at peak amplitudes of 207, 331 and 414 MPa. The displacements were s i g n i f i c a n t l y i n c r e a s e d when the peak s t r e s s l e v e l was in c r e a s e d to 496 MPa. However, at t h i s s t r e s s l e v e l , two c y c l e s produced no f u r t h e r change i n displacement. Again, ste p p i n g up the peak amplitude to 538 MPa produced increased d i s placements. F u r t h e r load c y c l i n g at t h i s amplitude of load produced a p r o g r e s s i v e i n c r e a s e i n displacements with the number of c y c l e s . A f t e r 7 c y c l e s , the peak amplitude was incr e a s e d to 545 MPa, and the displacement s i g n i f i c a n t l y i n c r e a s e d . In the 2nd c y c l e at t h i s peak amplitude, the specimen y i e l d e d by rebar p u l l out. 328 Crack ing The f i r s t r a d i a l s p l i t t i n g crack appeared on the S. Face at 310 MPa. AT 414 MPa, one more r a d i a l crack, accompanied by l o n g i t u d i n a l crack extension on the E. Face, o c c u r r e d . At 496 MPa, a few of the e x i s t i n g c racks extended and another r a d i a l s p l i t t i n g crack developed. At 538 MPa, a c i r c u m f e r e n t i a l crack tended to form. In the subsequent c y c l e s , .before f a i l u r e , the c i r c u m f e r e n t i a l and r a d i a l c racks w i t h i n a 75mm r a d i u s of the rebar widened s i g n i f i c a n t l y . C.4.7 SPECIMEN - F1-500/25/RVM/23 A p p l i e d Stress-Displacement R e l a t i o n s h i p : The h y s t e r e t i c responses of t h i s specimen on the N. Face are presented i n F i g . C.8(b). E s s e n t i a l l y s i m i l a r behaviour „ was observed on both faces of the specimen. No s i g n i f i c a n t displacement c o u l d be n o t i c e d up to the 414 MPa s t r e s s l e v e l . As the peak s t r e s s l e v e l was i n c r e a s e d to 496 MPa, there was a marked change i n s t i f f n e s s and displacement. Even two load c y c l e s at t h i s s t r e s s l e v e l produced a s i g n i f i c a n t i n c r e a s e in displacement. Severe p i n c h i n g of the h y s t e r e t i c curve was observed at t h i s stage a l s o . On i n c r e a s i n g the peak amplitude to 538 MPa, the displacement s h a r p l y i n c r e a s e d , f o l l o w e d by a d r a s t i c drop i n the load r e s i s t i n g c a p a c i t y of the specimen in compression. The specimen f a i l e d due to e x c e s s i v e p u l l out of the rebar. 3 2 9 C r a c k i n g At a s t r e s s l e v e l of 317 MPa, two r a d i a l s p l i t t i n g c r a c k s o c c u r r e d on the S. Face, each of which extended towards the E. and W. Faces of the specimen. At 400 MPa, the l o n g i t u d i n a l c r a c k s extended towards the N. Face. On i n c r e a s i n g the load to 482 MPa, two more r a d i a l cracks emerged. F i n a l l y , at 517 MPa peak l o a d , a l a r g e c i r c u m f e r e n t i a l crack developed at a r a d i u s of 90mm from the rebar a x i s . With a p r o g r e s s i v e i n c r e a s e i n l o a d i n g , the l o n g i t u d i n a l c r a c k s g r a d u a l l y propagated towards the center of the specimen. On r e v e r s a l of l o a d i n g in compression, f a i l u r e took place as the bar was p u l l e d out along with a l a r g e cone of concrete from the N. Face. S t r a i n D i s t r i b u t i o n : The s t r a i n d i s t r i b u t i o n curves f o r specimen P-RVM/23 are shown in F i g . C.9. At the 321 MPa peak s t r e s s l e v e l , there appears to be no bond d e t e r i o r a t i o n i n the 2nd c y c l e . A n e g l i g i b l e amount of bond d e t e r i o r a t i o n c o u l d be observed i n the 2nd c y c l e at the ±400 MPa peak s t r e s s l e v e l (curves 5 & 8 ) . However, some d e t e r i o r a t i o n c o u l d be observed from the i n c r e a s e d s t r a i n values in the 2nd c y c l e at the peak s t r e s s l e v e l of 480 MPa (curves 12 & 15). The maximum amount of y i e l d p e n e t r a t i o n was 100mm from the end of specimen. The length of the t e n s i l e s t r a i n zone i n the r e i n f o r c i n g bar i n c r e a s e d with the peak lo a d and, i n g e n e r a l , was about 10 to 15 % higher than that of the compression zone. 330 C.4.8 SPECIMEN - F1-500/25/RVM/24 In t h i s specimen, the r e i n f o r c i n g bar was coated with a t h i n f i l m of grease along i t s embedment le n g t h i n order to reduce the f r i c t i o n a l bond. The i n t e n t of t h i s t e s t was to a s c e r t a i n the c o n t r i b u t i o n of the f r i c t i o n a l r e s i s t a n c e to the bond mechanism. A p p l i e d Stress-Displacement R e l a t i o n s h i p : The a p p l i e d s t r e s s - d i s p l a c e m e n t r e l a t i o n s h i p s on both faces of the specimen were observed to be e s s e n t i a l l y the same. Up to a s t r e s s l e v e l of 200 MPa p r a c t i c a l l y no change in displacement was observed. An i n c r e a s e i n peak amplitude to 317 MPa i n c r e a s e d the displacement s i g n i f i c a n t l y . P i n c h i n g i n the h y s t e r e t i c curve was a l s o observed, i n d i c a t i n g the onset of bond d e t e r i o r a t i o n . An i n c r e a s e of peak s t r e s s to 403 MPa f u r t h e r i n c r e a s e d the p i n c h i n g of the curve. In the 3rd c y c l e of l o a d i n g , the load c a p a c i t y of the specimen dropped and the specimen y i e l d e d as the rebar s u f f e r e d e x t e n s i v e p u l l out. C racking The f i r s t h a i r l i n e r a d i a l s p l i t t i n g crack emerged on the S. Face at the 317 MPa s t r e s s l e v e l . As the peak s t r e s s l e v e l was i n c r e a s e d to 400 MPa one more r a d i a l and one c i r c u m f e r e n t i a l crack appeared, with l o n g i t u d i n a l c r a c k s propagating to the East and West Faces. In the 2nd c y c l e , the c i r c u m f e r e n t i a l cracks widened s i g n i f i c a n t l y and extended over a g r e a t e r a r e a . In the 331 3rd c y c l e , the damage was so severe that the load c a p a c i t y of the specimen dropped, and i t f a i l e d by rebar p u l l out. C.4.9 SPECIMEN - F1-500/25/RVM/25 A p p l i e d Stress-Displacement R e l a t i o n s h i p : The h y s t e r e t i c responses of t h i s specimen on the S. Face are presented in F i g . C.5(b). A comparison with other h y s t e r e t i c curves obtained under t h i s category of l o a d i n g r e v e a l s a q u i t e d i f f e r e n t behaviour for t h i s specimen. The h y s t e r e t i c curve s u f f e r e d s i g n i f i c a n t p i n c h i n g even at the 414 MPa s t r e s s l e v e l , probably due to severe bond d e t e r i o r a t i o n . I n c r e a s i n g the peak amplitude to 496 MPa caused f u r t h e r p i n c h i n g of the h y s t e r e t i c curve and a severe l o s s i n s t i f f n e s s . Even two c y c l e s of l o a d i n g at t h i s amplitude of l o a d i n g produced s i g n i f i c a n t displacement. When the peak s t r e s s was i n c r e a s e d to 538 MPa, the l o a d c a p a c i t y of the. specimen in compression was d r a s t i c a l l y reduced and f i n a l l y the specimen f a i l e d due to e x c e s s i v e p u l l - o u t of the rebar. S t r a i n D i s t r i b u t i o n : A comparison of v a r i o u s s t r a i n d i s t r i b u t i o n curves i s shown in F i g . C.10. P r a c t i c a l l y no change in s t r a i n d i s t r i b u t i o n c o u l d be observed in the 2nd c y c l e at a peak s t r e s s l e v e l of ±324 MPa as compared to the 1st c y c l e . However, when the peak s t r e s s was i n c r e a s e d to 527 MPa i n p r e v i o u s c y c l e s , there appeared to be some bond d e t e r i o r a t i o n on the p u l l out end as can be observed from curves 1 & 7. An a p p r e c i a b l e amount of bond d e t e r i o r a t i o n was observed i n the 2nd c y c l e of ±495 MPa as 332 compared to that i n the 1st c y c l e (curves 13 & 18). Even at the ±415 MPa s t r e s s l e v e l , severe bond d e t e r i o r a t i o n may be observed when the peak s t r e s s l e v e l was i n c r e a s e d to 534 MPa (curves 5 & 17). The maximum amount of y i e l d p e n e t r a t i o n was about 125mm from the end of the specimen at a s t r e s s l e v e l of 534 MPa. Cracki n g The 1st r a d i a l s p l i t t i n g crack occurred at the 207 MPa s t r e s s l e v e l on the S. Face. At 331 MPa, one more r a d i a l crack and another l o n g i t u d i n a l crack developed on the S. and E. Faces, r e s p e c t i v e l y . At 414 MPa, two more r a d i a l c r a c k s developed and there was extension of the e x i s t i n g c r a c k s . At 496 MPa, three more r a d i a l c racks developed accompanied by extensions of some of the c r a c k s . At 538 MPa, a wide c i r c u m f e r e n t i a l crack p a r t i a l l y formed and the s p l i t t i n g c r a c k s around the rebar widened. At t h i s l o ad, the l o n g i t u d i n a l c r a c k s from both the North and South Faces had p r o g r e s s i v e l y extended on the East and West Faces up to the cente r l i n e of the spec imen. 333 APPENDIX D ~ TYPICAL CALCULATION FOR REDUCTION IN DIAMETER 6. BEARING— A r e a d u e P o i s s o n ' s E f f e c t (25mm & T e s t B a r )  A s s u m e d V a l u e s : ' ey - 0 . 0 0 2 e s h * 0 . 0 0 8 3 v a t y i e l d « 0 . 5 M e a s u r e d D i a o f rebar • 23 .413mm oy * 60 K s i ( 4 1 3 . 7 Mpa) Reduction i n Diameter:  Y i e l d AD = change i n d i a « -pey D • . 5 x .002x23.413 = 0.023413mm % r e d u c t i o n i n d i a = 0.23413 x 100 = 0.1% 23.413 At e = esh % r e d u c t i o n i n d i a . = 0.418 % Reduction i n Bearing Area: Bearing Area = wDho Reduction i n bearing are * (rrDho - rD 1ho) = Trho(AD) % r e d u c t i o n i n bearing area = ffDhoADx100 = ADx100 irDho D At e = ey, % r e d u c t i o n = 0.1 % At e = esh, % r e d u c t i o n « 0.418 1 Refer To Table 2 . 3 TABLE NO „ f i j  RESULTS OF REGESSION ANALYSIS 25mm OIA. TEST BAR (SPECIMEN F2-500/25/RV/17) C y c l e ( S I o e x p t ( M p a ) texpt. t K1 K2 C o m p u t e d 1. C o m p r e s s t o n 0 0 0 3 5 - 7 .36 ( - 5 0 7 4 ) 0 .OO305 0 . 0 0 3 2 31 .544 1 2734 C y c l e I - 14 .72 ( - 1 0 1 4 9 ) o . 0 0 2 6 0 . 0 O 2 8 2 - 2 2 0 2 ( - 152 2 4 ) O 0 0 2 0 0 . 0 0 2 2 8 - 2 9 43 ( - 2 0 2 9 8 ) 0 0 0 1 4 0 . 0 0 1 5 6 - 4 2 72 ( - 2 9 4 5 5 ) 0 0 0 0 0 -0 OO0O6 - 5 5 24 ( - 3 8 0 8 8 ) - 0 0 0 2 -0 . 0 0 2 1 6 - G 5 5 ( - 4 5 1 6 2 ) - 0 004 - 0 0 0 4 3 - 7 4 18 ( - 5 1 1 4 7 ) - 0 0 0 6 2 -0 0 0 5 9 2 . C o m p r e s s 1 o n 0 . 0 0 5 2 - 7 36 ( - 5 0 7 4 ) O 0 0 4 7 0 00-192 29 758 1 4162 C y c l e I I - 2 2 0 7 ( - 152 2 4 ) 0 0 0 3 6 o 0 0 3 9 6 - 3 6 8 0 ( - 2 5 3 7 4 ) O 0 0 2 1 o 0 O 2 2 8 - 4 4 2 0 ( - 3 0 4 7 6 ) 0 OOI 1 0 OOI 1 - 5 1 56 ( - 3 5 5 5 1 ) -0 0 0 0 3 -0 0 O O 3 2 G - 5 8 8 9 ( - 4 0 6 11) - 0 0 O 1 8 -0 0 0 2 0 - 6 G 24 ( - 4 5 6 7 2 ) - o 0 0 3 8 -0 0 0 3 9 7 - 7 7 IB ( - 5 3 2 16) - 0 0 0 6 9 - 0 0 0 6 7 3 . C o m p r e s s i o n 0 . 0 0 6 7 - 7 36 ( - 5 0 7 4 ) 0 OOG2 0 0 0 6 4 1 26 8 6 9 6 1 . 381 C y c l e I I I - 2 2 0 2 ( - 1 5 2 2 4 ) 0 0051 0 0 0 5 3 8 7 - 3 3 «2 ( - 2 2 8 3 6 ) o 0 0 4 0 o 0 0 1 0 9 - 4 4 20 ( - 3 0 4 7 6 ) • 0 0 0 2 5 0 0 0 2 2 5 -55 77 ( - 3 R O 74 ) 0 OOO 2 - 0 0 0 0 1 9 8 -58 H9 ( - 4 0 6 . 1 1 ) - 0 0 0 1 8 - 0 001 16 - 6 9 92 ( - 4 8 2 10) - 0 0 0 4 2 - o 0 0 4 4 8 - 8 0 17 ( - 5 5 2 . 7 7 ) - 0 . 0 0 7 5 - 0 0 0 7 4 TABLE NO.B 1 CONT'0 RESULTS OF REGESSION ANALYSIS 25mm 01A, TEST BAR (SPECIMEN F2-500/25/RV/17) C y c l e t s i oexpt (Mpa ) te x p t . K1 K2 Computed 4 . Tens Ion -0 0024 3 .68 ( 25 .37) -0 .0022 -0.002273 40 244 1 .695 C y c l e I 14 . 70 ( 101 .49) -0 .0017 -0.0018 29 .43 ( 202 .98) -0 .0007 -0.00082 44 20 ( 304 76) 0 .001 0.00084 55 . 22 ( 3R0 .74) 0 .0025 0.0O264 57 40 (395 77) O .003 0.003069 62 6 (431 63) 0 004 0.0O4175 7 1 18 (490 79) 0 .0056 0.00539 5 Tens Ion -0 0036 3 68 ( 25 37) -o 0034 -O.00347 33 55 1 .696 C y c l e II 14 70 ( 101 49 ) -0 0029 -0 00298 29 43 (202 9B) -0 0O16 -0.0O1B 44 20 ( 304 76) 0 0004 0 0 0 0 2 6 9 55 22 ( 380 74) 0 0025 0.0O259 62 6 (431 63) 0 0O44 0.00456 69 92 (482 10) 0 0065 0.0O694 74 IB (511 47 ) 0 0080 0.0074 7 6. Tens 1 on -0 004 2 3 68 ( 25 37) -0 004 -0.00407 34 31 1 816 C y c l e III 22 02 ( 152 24 ) -0 0028 -O.00312 36 80 (253 74) -0 0013 -0.0O155 4 5 00 (310 27 ) 0 0000 -O.0OO198 51 56 ( 355 50) 0 0012 0.00118 62 GO (•131 63 ) 0 0040 0.0042 69 92 ( 482 lO) o 0065 0.00695 77 18 ( 532 16) 0 0091 0.008798 7 . TpnsIon -0. 0O49 3 68 ( 25 37) -0 0047 -0.00477 35. 15 2. 03 C y c l p IV 22 08 ( 152 24) -0 0035 -0.00386 44 20 ( 304 76) -0 OOO 7 -0.0010349 58 89 (406. 1 1 ) o 0027 0.002755 62 r,0 ( 43 1 63) o 0040 O.00403 69 97 ( 4H2 10) o 0065 0.0O699 75 OO (5 17 12) 0 0091 O.0O94 2 RO 17 ( 552 . 77) 0. OIOG 0.00994 T A B L E NOi . B 2 R E S U L T S OF R E G E S S I O N A N A L Y S I S 20mm D I A . TEST BAR ( S P E C I M E N P - 3 7 5 / 2 0 / R V M / 2 3 C y c l e • s i e>e*pt ( M p a ) » e x p t . z C o m p u t e d K1 K2 1. C o m p r e s s I o n C y c l e I 10034 - G . 6 7 ( - 4 6 . 0 0 ) - 2 6 . 7 0 ( - 1 8 1 10) - 4 6 . 7 2 ( - 3 2 2 . 1 3 ) - 5 5 . 4 0 ( - 3 8 1 . 9 8 ) - 6 8 . O B ( - 4 6 9 . 4 1 ) 0 . 0 0 2 9 5 0 . 0 0 1 5 5 O.OOOO - 0 . 0 0 1 - 0 . O 0 2 2 0 * 0 3 0 4 0 . 0 0 1 5 9 5 - 0 . 0 O 0 1 3 - 0 * 0 0 9 4 2 - O 0 0 7 1 8 24 .82 0 . 3 7 4 8 2. C o m p r e s s i o n C y c l e f l 0 . 0 0 4 2 - 6 .67 ( - 4 6 . 0 0 ) - 2 6 70 ( - 184 IO) - 4 0 0 5 ( - 2 7 6 . 1 4 ) - 5 3 . 4 0 ( - 3 6 8 . 1 9 ) - 6 8 . O R ( - 4 6 9 . 4 1 ) 0 . 0 0 3 7 0 . 0 0 2 4 O 0 0 1 3 - 0 . O 0 O 1 5 - 0 . 0 0 1 9 0 .0O3B1 0 . 0 0 2 1 7 0 . 0 0 0 8 6 - 0 0 O 0 5 8 - 0 . 0 0 2 2 8 6 14.447 0 . 3 9 9 7 3 . T e n s i o n C y c l e I - 0 . O O O 1 5 6 . 6 7 ( 4 5 . 9 9 ) 2 6 . 7 0 ( 1 8 4 . 1 0 ) 4 6 . 7 0 ( 32 1 .99 ) 6 0 . 0 7 ( 4 1 4 . 1 8 ) 68 . 18 ( 4 7 0 . 10) 0 . 0 0 0 2 0 . 0 0 1 2 5 0 . 0 0 2 6 0 . 0 0 4 3 0 . 0 0 0 7 0 . 0 0 O 0 7 3 0 . 0 0 0 8 3 0 . 0 0 2 4 0 . 0 0 4 6 3 G 0 . 0 0 6 8 6 54. 174 3 . 1 9 0 8 4 . T e n s i o n C y c l e II 0 0 0 0 1 6 . 6 7 ( 4 5 . 9 9 ) 26 . 70 ( 184. 10) 46 70 ( 3 2 1 . 9 9 ) 6 6 . 7 5 ( 4 6 0 . 2 4 ) 7 7 . 4 3 ( 5 3 3 . 8 8 ) 0 . 0 0 0 4 0 . 0 0 15 0 . 0 0 3 0 . 0 0 6 3 0 . 0 0 9 8 0 . 0 O O 3 2 4 0 . O O I 1 6 9 0 . 0 0 2 8 9 0 . 0 0 6 5 3 0 . 0 0 9 7 5 1 . 4 3 8 2 .443 l/l C J -<-> H < V 0 3 - H ft -0 — 3 CI -4 < 0 -1 3 0 -0 - 3 rt -t < a rt 3 - A IB — 0 — 3 rt 0 < o o 3 — 0 <D 1 — 1/1 — 0) 0 3 rt rt < 0 0 3 - T3 nt — 71 cn 0 3 0 0 ra 6 O 1 O O O in jt SCOO O O N> NJ cn 6 0 03 8 CO 8 •Jl -f 'J VJ — n — ui ui ui x - J — s -ji — • J O O - J 1 - J Ul ^ CJ — O O J - 'JI OI CJ i . ui 0 ui — — 31 CJ \ J - J 1 ~ J Jl £. CJ — O w cn cn cn CJ O cn O cn — — Cl CJ NJ — - J 1 ( 1 1 1 1 -4 CP & C J - » v> co cn -> ui cn xi. -» cn 0 cn — C J cn u M — - J , > 1 > 1 t * -j ui tk eg — O co cn — cn cn O — cn O cn — O J l U M - 4 ~ f* * ,g Cl < -w ^ 0 0 6 6 6 6 O O O O O O O O O O O O O O O O O O O O O O O O •5 O O O O O O O O O O O O CJ — O — M U M S S 3 Ul U Ul 0 0 0 0 0 g O O O O O O -4 i . — O — N> cn dl — C J 8 8 8 8 8 8 -j C J - g - -cj cn C J 0 cn cn 8 8 8 8 8 8 at .» 0 v> C J i» O CD tn cn j3 cn cn O O O O O O O O O O O O t u o v u b s w Q a s 1 X U *^ t •> 1 I > 1 O O O O O O 6 6 0 0 6 6 O O O O O O O O O O O O O O O O O O r> m 3 O O O O O O O O O O O O CJ O — U - a -j a> 1^ j Ul CJ 09 O O O O O O O O O O O O - J i . O — M C J CJ n i . j i 0 C J cj a — CO 8 8 § § 8 8 O — co ui M cn C J Ul >1 u •4 u .00472 .004196 .00283 .00055 .002186 .005813 8 8 8 8 8 8 » > o O u u t. Cfi C J M M 03 03 *. cn cn M cn 3 O C a M ca C J <n cn u M cn cn to -1 C J cn O cn 10 - - C J O X ro C J 09 9 C J cn et CO Ul <n CO cn OS -4 0>_, T A B L E - B 4 S T R A I N HARDEN ING MODULUS S P E C I M E N P I A OF REBAR (mm) TEN5 I0 I COMPRES 5 I 0 N F ' ( M p a ) P> AVERAGE E ' (Mpa P 1 ( M p a ) A V E R A G E E ' ^ ( M p a ) P - 5 0 0 / 2 5 / R V / 5 F 2 - 5 0 0 / 2 5 / R V / 1 7 F 2 - 5 0 0 / 2 5 / R V M / 1 9 P - 5 0 0 / 2 5 / R V M / 2 0 F 1 - 5 0 0 / 2 5 / R V M / 2 1 25 25 25 25 25 1 0 , 9 0 8 1 0 . 8 7 3 1 1 . 9 8 3 1 0 . 1 4 9 1 2 . 2 0 4 1 1 , 2 3 3 2 4 , 6 0 1 2 2 , 8 3 6 2 5 . 8 9 0 1 4 . 2 1 7 21.886 P - 3 7 5 / 2 0 / R V M / 2 3 20 1 5 . 9 0 0 1 5 . 9 0 0 2 9 . 7 5 2 2 9 . 7 5 2 F 1 - 5 0 0 / 3 0 / R V M / 2 5 3 0 9 . 3 2 2 9 . 3 2 2 2 0 . 4 9 2 2 0 . 4 9 2 N o t p : A l l t h e a b o v e - m e n t i o n e d s p e c i m e n s w e r e s u b j e c l p d t o I n c r e m e n t a l l y I n c r e a s e d c y c l i c l o a d i n g . 0.01 0mm D i a m e t e r B a r 25mm D i a . B a r 002 0.03 OXK STRAIN 0.05 OJ06 o oo Mpa UU co F I G .B .1(a) STRESS-STRAIN BEHAVIOUR OF REBAR UNDER MONOTONIA LOADING in * ' in ui oc r o ' J 1_ 22Q6 J I 1 - L 1—y*-g i 1 1 r -o.w -o M o J i 1 1 1 1 1 — i — ' — 1 7~ 0.0« 0.0» 9.1? <•"> W SR0IN 1X10"' I oo oo F I G R K b ) S T R E S S - S T R A I N B E H A V I O U R OF REBAR F * 1 (25mm D i a ) UNDER C Y C L I C L O A D I N G G.C .1(Q)APPLIED STRESS-DISPLACEMENT DIAGRAM FOR SPECIMEN P-RV/5 FIG.C -1(b)APPLIED STRESS-DISPLACEMENT DIAGRAM FOR SPECIMEN P-RV/6 r A V-100 1 / X 50 K-® / 50—+ 1® N o t e : A l l dimensions in mm, . C 2 (a) CRACK PATTERN ON SLICED TWO F I G . C -2 (b) CRACK PATTERN ON SLICED TWO HALVES OF SPECIMEN P-RV/5 HALVES OF SPECIMEN F2-RVM/14 Hi 2-2 9nm 3 0.06^0.09 0.12 DISPtRCEMENT (INS) F1G.C -5(b)APPLIED STRESS-DISPLACEMENT DIAGRAM FOR SPECIMEN F1-RVM/25 o o t — FIG.C-6(a) APPLIED STRESS-DISPLACEMENT DIAGRAM FOR SPECIMEN Fl-RVM/13 FIG.C -6(b) APPLIED STRESS-DISPLACEMENT DIAGRAM FOR SPECIMEN F2-RVM/15 9*78 8 ve 67S 

Cite

Citation Scheme:

        

Citations by CSL (citeproc-js)

Usage Statistics

Share

Embed

Customize your widget with the following options, then copy and paste the code below into the HTML of your page to embed this item in your website.
                        
                            <div id="ubcOpenCollectionsWidgetDisplay">
                            <script id="ubcOpenCollectionsWidget"
                            src="{[{embed.src}]}"
                            data-item="{[{embed.item}]}"
                            data-collection="{[{embed.collection}]}"
                            data-metadata="{[{embed.showMetadata}]}"
                            data-width="{[{embed.width}]}"
                            async >
                            </script>
                            </div>
                        
                    
IIIF logo Our image viewer uses the IIIF 2.0 standard. To load this item in other compatible viewers, use this url:
http://iiif.library.ubc.ca/presentation/dsp.831.1-0062944/manifest

Comment

Related Items