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":er2, ’3’”; "‘5“: I {Mm/1:, .LIERARY Michigan State University This is to certify that the dissertation entitled AM CLO Maj of- Bew RQl'M'pDi‘CQM Ai‘ COMUPMHON AM EI'bk—OLLQ 89W.- Colw CONWQQ 4.1‘ OMS presented by KI'SQU CLcc has been accepted towards fulfillment of the requirements for th degreeinLIW/Ii Eghezrlu: R \_ > Q I\ 1 \J Major professor\ Date tflfix 2,, (285 MS U is an Affirmatiw Action/Equal Opportunity Institution 0.12771 MSU LIBRARIES RETURNING MAHERIALS: Place in book drop to remove this checkout from your record. FINES will be charged if book is returned after the date stamped below. ‘ . 1;; grr244m ANCHORAGE OP BBAHCRBINPORCEHENT AT CONVENTIONAL AND FIBR003 BEAN9COEUHN CONNECTIONS By Ki-Bong Choi L,DISSERTNTION Submitted to Michigan State University in partial fulfillment of the requirements for the degree at DOCTOR OF PHILOSOPHY Department of Civil and Environmental Engineering 1988 I A *7 4r ,4 ABSTRACT ANCHORAGE OP BEAN REINFORCEMENT AT CONVENTIONAL AND FIHROUS HEANPCOLUNN CONNECTIONS BY Ki-Bong Choi An integrated experimental-analytical study was performed on the anchorage of beam longitudinal reinforcement in interior and exterior beam-column connections of reinforced concrete frames.- The effects of anchored bar diameter, concrete compressive strength and confinement of concrete on the local bond stress- slip relationship of deformed bars in concrete were assessed experimentally. An empirical local bond constitutive model was developed, and was incorporated into an overall model for predicting the pull-out force-displacement relationship of straight anchored bars in confined concrete joints. This anchorage model was used to verify the current design equations for anchorage of straight bars in confined concrete joints. An empirical study was also performed on the effects of the number of bars and steel fiber reinforcement on the pull- out behavior of hooked bars at confined concrete joints. Suggestions for improving hooked bar anchorage design guidelines were derived using the generated test results. To my Parents and Parents-in-law ii ACKNOWLEDGEMENT This study was carried out in the Composite Materials and Structural Center and the Case Center for Computer Aided Engineering at Michigan State University. It was made possible by the financial support of the American Public Power Association and the Research Excellence and Economic Development Fund of the State of Michigan, and advice concerning concrete and fly ash was provided by the Lansing Board of water and Light. These supports are gratefully acknowledged. The author is deeply thankful to Dr. Parviz Soroushian for his guidance and assistance, and sincere thanks are extended to all of his guidance committee members, Dr. R.K. Wen, Dr. L.J. Segerlind, and G.D. Ludden for their interests and useful suggestions. 7 Finally, the author is most indepted to his wife, Young- Sook for her patience and understanding during his doctoral Program. He also wishes to thank his family for their support and prayers. iii TABLE OF CONTENTS Chapter Page LIST OF TABLES ........................................... vi LIST OF FIGURES .......................................... vii LIST OF NOTATIONS ........................................ xii 1 INTRODUCTION .......................................... l 2 BEHAVIOR OF BONDED BARS IN BEAM-COLUMN CONNECTION: A REVIEW OF THE LITERATURE ............................ 10 2.1 GENERAL ........................................... 10 2.2 LOCAL BOND EXPERIMENTAL BEHAVIOR AND ANALYTICAL MODELING .......................................... 14 2.2.1 General ..................................... 14 2.2.2 Experimental Results ........................ 17 2.2.3 Analytical Medeling ......................... 22 2.3 FULL! ANCHORED BAR: EXPERIMENTAL BEHAVIOR AND AND ANALYTICAL MODELING ........................... 25 2.3.1 Experimental Results ........................ 25 2.3.2 Analytical Modeling 30 2.4 OVERALL JOINT MODELING ............................ 34 2.5 FIBER REINFORCEMENT OP JOINTS ..................... 38 2.6 SUMMARY AND CONCLUSIONS ........................... 41 3 LOCAL BOND BEHAVIOR: EXPERIMENTAL RESULTS AND ANALYTICAL MODELING ................................... 44 3.1 INTRODUCTION ...................................... 44 3.2 EXPERIMENTAL PROGRAM .............................. 45 3.3 TEST RESULTS ...................................... 51 3.3.1 Effect of Bar Diameter ...................... 51 3.3.2 Effect of Transverse Reinforcement .......... 53 3.3.3 Effect of Concrete Compressive Strength ..... 55 3.4 EMPIRICAL MODELING OF THE LOCAL BOND BEHAVIOR ..... 55 3.5 SUMMARY AND CONCLUSIONS ........................... 64 4 AN ANALTTICAL EVALUATION OF STRAIGHT BAR ANCHORAGE DESIGN IN EXTERIOR JOINTS ............................. 66 4.1 INTRODUCTION ...................................... 66 4.2 ANALYTICAL MODELING OF ANCHORED BAR ............... 69 4.3 STEEL AND LOCAL BOND CONSTITUTIVE MODELS .......... 74 4 4 COMPARISON WITH TEST RESULTS ON ANCHORED BARS ..... 79 4.5 NUMERICAL VERIFICATION OF THE DEVELOPMENT LENGTH EQUATION ................................... 81 6 SUMMARY AND CONCLUSIONS ........................... 89 iv 5 BEHAVIOR OF HOOKED BARS IN EXTERIOR BEAM-COLUMN CONNECTIONS: A REVIEW OF THE LITERATURE .......... ..... 90 5.1 GENERAL ...................................... ..... 90 5.2 BEHAVIOR OF HOOKED BARS IN EXTERIOR JOINTS ... ..... 102 5.2.1 General ................................ ..... 102 5.2.2 Factors Influencing Hook Behavior ..... ...... 108 5.3 ANALYTICAL MODELING OF HOOKED BAR BEHAVIOR ... ..... 116 5.4 STEEL FIBER REINFORCEMENT OF EXTERIOR JOINTS ...... 120 5.5 DESIGN GUIDELINES FOR HOOKED BARS IN EXTERIOR JOINTS ....................................... ..... 127 5.6 SUMMARY AND CONCLUSIONS ..................... ...... 137 6 EXPERIMENTAL INVESTIGATION OF HOOKED BAR BEHAVIOR: EFFECTS OF FIBER REINFORCEMENT AND NIMBER OF BARS ..... 139 6.1 INTRODUCTION ...................................... 139 6.2 EXPERIMENTAL PROGRAM .............................. 139 6.3 EXPERIMENTAL RESULTS .............................. 148 6.4 SUMMARY AND CONCLUSIONS ...................... ..... 163 7 SUMMARY AND CONCLUSIONS ............................... 165 LIST OF TABLES Table 3.1 Test Program ............... ........ ...... ........... 3.2 The Characteristic Local Bond Stress and Slip values OOOOOOOOOOOOOOOOOOOOOOOO000.000.... 00000000000 4.1 The Characteristic Local Bond Stress and Slip Values (1 mm - 0.039 in., 1 MPa = 144 psi) .......... 4.2 Properties of Test Specimens ............. ...... ..... 4.3 Ranges of Variables in the Numerical Study on Anchored Bar Pull-Out Behaviors .... ....... . ......... 6.1 Properties of Fly Ash .................. ............. 6.2 Mix Properties of Plain and Steel Fiber Reinforced Concrete Mixes .................. ......... 6.3 Test Program on Hooked Bars in Conventional and Fibrous Specimens ..................... .......... vi Page 48 59 75 79 82 145 147 LIST OF FIGURES Figure Page 1.1 Typical Beam-to-Column Connection ...... ............ 2 1.2 Anchorage Conditions of Beam Longitudinal Bars at Interior and Exterior Joints .............. ...... 4 1.3 Behavior of Interior and Exterior Joints at Lower Stories of Moment-Resisting Frames ..... ...... 6 2.1 Mechanisms of Joint Core Shear Resistance .......... 11 2.2 Congestion of Steel at an Interior Seismic- RegistantJ°1nt .....OOOOOO......OOOOOOOOOOOO. ...... 13 2.3 Exterior Joint with Straight Anchored Bars .... ..... 13 2.4 Mechanism of Bond Resistance in Confined concrete[9,10] OOOOOOOOOOOOOOOOOOO0.000.000.0....... 15 2.5 Formation of Concrete Cone in Non-Fibrous Concrete Cover at the Tensioned Bar End[5] ......... 17 2.6 Test Specimens with a Partially Bonded Bar for meal Bond Stud138[9] ......OOOOOOIOOOOOOOOO0.0.0... 18 2.7 Factors Influencing Local Bond Behavior in confined concrete[9] .....OOOOOOOOOOOOOOOO0.0....... 20 2.8 The Local Bond Stress-Slip Constitutive Model Proposed by Morita and Kaku[11] ............-....... 22 2.9 Analytical Model of Local Bond Stress-slip Relationship Proposed by Tassios[10] ............... 23 2.10 Analytical Model of Reference 9 for Local Bond Stress-Slip Relationship ........................... 25 2.11 Test Specimen of Fully Embedded Bars .......... ..... 27 2.12 Pull-Out Test Results on Fully-Embedded Deformed Bars in Non-Fibrous Interior Joints ....... 27 2.13 Bond Stress-Slip Relationships at Different Locations along Embedment Length ................... 29 2.14 Physical Idealization and Governing Equations vii 2.15 2.16 2.18 2.19 0: Embedded hr .....OOOOOOOOOOOO...00.0.0000. 000000 Subdivision of the Embedment Length ........ ........ Experimental Results vs. Analytical Predictions[13] of the Bonded Bar Behavior ......... Experimental Results vs. Analytical Predictions[1] of the Bonded Bar Behavior .......... Refined Analytical Model of Interior Joints[1] ..... Arrest of Bond Cracks by Fibers in Confined Concrete and at Concrete Cover ..................... Improvements in Sliding Shear Resistance Mechanisms Resulting from Fiber R.inf°rcement[25'26] 00......OOOOOOOOOOOOOOO...O0.0. Test Specimen and Experimental Setup ......... ...... Anchored Bar Deformation Pattern .............. ..... Reinforcement cage 0...... ..... 00.000.00.00... ...... Experimental Local Bond Stress-Slip Relationships for Deformed Bars of DifferentDiameters ............................ ..... Deformed Bar Diameter Effect on the Average Local Bond Stress-Slip Relationship ................ Effects of‘ Confining Reinforcement on the Local Bond Stress-Slip Relationship of Deformed Bars Effects of Concrete Compressive Strength on the Local Bond Stress-Slip Characteristics of Deformed Bars in Confined Concrete ........... ..... . Local Bond Constitutive Model ...................... Analytical vs. Experimental Local Bond Stress- Slip Relationships ........................... ...... Anchorage of Beam Reinforcement in Exterior Jaints ......OOOOOOOOOOOOOOOO....OOOOOOOOOOOOOOO.... Definition of Development Length .. ........ ... ...... The Proposed Anchored Bar Model ............. ....... Steel and Local Bond Constitutive Models ..... ...... viii 31 32 33 35 40 42 46 49 50 51 54 56 57 60 61 67 68 7O 76 Effects of Different Variables on Local Bond Constitutive Behaviors ............... .............. Test speCimens 0.0.0.0........OOOOOOOOOO0.00. ....... Comparison between Analytical and Experimental Pull-Out Load-Deformation Relationships ..... ....... Anchored Bar Used in this Numerical Studies .. ...... Analytical Pull-Out Load-Deformation Relationships at Different Fractions of Full ACI-ASCE Committee 352[8] Development Length . ...... Pull-Out Forces at Major Inelasticities and at a Pull-Out Displacement of 10 mm as function of the Fraction of Full Development Length PrOVided ......OOOOOOOOO....OOOOOOOOOOOOOOOO... ..... Overall Behavior of Exterior Joints ........... ..... Effects of Shear Stress Level on the Exterior Joint Response to the Seismic Loads[30] ............ Effects of Transverse Hoops on the Bysteretic Behavior of Exterior Joint with Different Column-to-Beam Flexural Strength Ratios[30] ........ Effect of Flexural Strength Ratio on the Hysteretic Behavior of Exterior Joints[30] ......... Effect of, Beam Longitudinal Steel on Hysteretic Behavior of Exterior Joints ............. Exterior Jaint Types OOOOOOOOOOOOOOOOOOOOOO....0.00. Behavior of Hooked Bars under Pull-Out Forces ...... Pull-Out Force Transfer Mechanism at the Bend and Tail Portion of Hook[36] ....................... Cracking of Concrete by Pull-Out Action of Hooxed Bars OOOOOOOOOOOOO.......OOOOOOOOOOO0....O..0 Effects of Confinment by Transverse Reinforcement on the Hook Pull-Out Behavior ........ Effect of Bend Angle on Book Pull-Out Behavior At exterior Joint Conditions ....................... Influence of Lead Embedment on Book Pull-Out MBVior ......OOOOOOOOOOOOO0.0.0.........00.0000000 Influence of Column Axial Load on the Pull-Out ix 77 80 83 85 86 88 91 97 98 99 100 101 102 105 105 109 110 111 5.15 5.16 5.17 5.18 5.21 5.22 5.23 5.25 5.26 5.27 6.1 6.2 Behavior of Hooked Bars ...................... ...... Effect of Hooked Bar Diameter on Hook Pull-Out uhaVior ......OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO ..... Typical Cyclic Behavior of Hooked Bars ............. Hook Modeling by An Equivalent Straight medment ungth 0.00.00.00.00....OOOOOOOOOOOO. 00000 Simulation of Hook by A Spring[37] ................. Conventional and Fibrous Seismic-Resistant ExteriorJOints OOOOOOOOOOOOOOOOOOOOOOOOOOOOOO 000000 Moment-Rotation Diagrams Measured 30.5 mm (12 in.) from Column Face in Conventional and Fibrous Jaints .....OOOOOOOOOOOOO0.0.0.0000... ...... Crack Patterns in Conventional and Fibrous Jaints ......OOOOOOOOOOOOOOOO0.0.00.00.00.00... ..... Exterior Joint Test Specimens of Reference 38 ...... Hysteretic Performance and Failure Conditions of Conventional and Fibrous Joints with Beam Shear Span to Depth Ratio of 4.33 and Beam Top-to-Bottom Steel Ratio of 2.0 ................... ~Hysteretic Performance and Failure Conditions of Conventional and Fibrous Joints with Beam Shear Span to Depth Ratio of 3.61 and Beam Top-to-Bottom Steel Ratio of 2.0 ................... Hysteretic Performance and Failure Conditions of Conventional and Fibrous Joints with Beam Shear Span to Depth Ratio of 2.89 and Beam Top-to-Bottom Steel Ratio of 2.0 ................... Hysteretic Performance and Failure Conditions of Conventional and Fibrous Joint with Beam Shear Span to Depth Ratio of 4.82 and Beam Top-to-Bottom Steel Ratio of 2.0 .......... Hysteretic Performance and Failure Conditions of Conventional and Fibrous Joints with Beam Shear Span to Depth Ratio of 4.34 and Beam Top-to-Bottom Steel Ratio of 1.0 .............. ..... Standard Hook Development Length .................. Hook Test Specimens ............................. Reinforcement Cages of Typical Hook Test 112 113 115 117 118 122 123 124 125 128 129 130 131 132 133 141 spec1men8 ......OOOOOOOOOOOOOOO0.00......IO... ...... 143 Compressive Stress-Strain Relationship of the Plain and Fibrous Concrete ................... ...... 146 Test Set-Up and Instrumentation .................... 149 Conventionally Confined Specimens under unltipl. “00k“ Bar mll-out .....OOOOOOOOOOIOOOOOO. 151 Cracking in Specimens with Different Number of HOORed Bars ......OOOOOOOOOOOO00.0.0000...O. ........ 154 Cracking of Fibrous and Conventionally Confined Specimens ........................... ...... 159 Hook Pull-Out Force-Displacement Relationship ...... 161 xi LIST OF NOTATIONS A. - bar cross-sectional area; A‘ - top beam bar cross-sectional area; A b - bottom beam bar cross-sectional area; C. - bar clear spacing; d. - bar diameter; dz - incremental length along the bar; dN - incremental bar asial force; dP. - incremental pull-out force; d5, - incremental slip; D - standard hook diameter; E. - strain hardening modulus of steel; E, - steel tangent modulus; I ' c - compressive strength of steel; f, - steel yield strength; fg’j - element in the ith row, jth column of matrix F; F - inverse of overall tangent stifi'ness mah‘is; F, - pull-out resistance at the initation of major inelasticities (Figure 4.10a); F, II pull-out resistance at a 10mm (0.4in.) pull-out deformation (Figure 4.10a); K..- - tangent stifl’ness of the spring at point i; K I,- - steel tangent stifl'ness at point i (can be derived from the steel constitutive law); K“- - tangent stifiness of the steel segment connecting points i and i+1; K“ - local band tangent stifl'ness at point i (can be derived from bond constitutive law); K1- - overall tangent stifl'ness matrix of anchored bar; I; - development length; xii la. a development length of standard hook in tension; l,- - length of the ith steel segment (Figure 4.3); L - total length of a subdivision (Figure 2.15); L, - equivalent straight bar embedment length; L, - the distance from the column face to the start of the hook; n - number of points along the bar length in the physical model of Figure 4.3; N - bar axial force; P - pull-out force; P1,P3 - characteristic pull-out forces in the hook constitutive model; P, - externally applied end force; R - column pressure; S - bond slip along the bar length; sl,s2,s3 - characteristic bond slip values for local bond constitutive model; s, - externally applied end slip; U - pull-out displacement; U1,U2,U3 - characteristic pull-out displacements in the hook constitutive model; a - parameters in the constitutive ( bond and hook) models; as); - related rib area (that is the ratio of bearing area to shearing area); 1' an bond stress; 71,13 - characteristic bond stress values for local band conctitutive model; a - bar axial stress; 6 - bar strain; 6 - lateral deformation of element; Ax - incremental length along the bar (Figure 2.15); x - axis along the bar length; p - tensile steel ratio; 0 - rotation of element; xiii INTRODUCTION Reinforced concrete structures designed to withstand strong earthquake ground motions are expected to deform well into the inelastic range and dissipate a large part of the energy input through hysteretic behavior of their structural components. A desirable structural response under severe earthquakes can be achieved by eliminating the potential sources of brittle failure and ensuring the stability of the hysteretic performance in critical regions of the structure. The interior and exterior beam-column connections (Figures 1.1a and 1.1b, respectively) are typical critical regions in reinforced concrete frames, where large excursions into the * . inelastic range occur[1] . In some recent Violent earthquakes in Chile (1960), Yugoslavia (1963), and Alaska (1964) where unsatisfactory performance was observed, it could usually be attributed to the quality of materials or construction, or to the poor reinforcement details in structural joints[2]. ‘ Numbers in square brakets refer to the list of references. s ¢§u (a) Exterior (b) Interior Figure 1.1 Typical Beam-to-Column Connection. In order to satisfy the requirements on inelastic energy dissipation in beams under severe seismic excitations, the joints in frame structures should be capable of maintaining their rigidity and capacity to restrain elements, even under the action of repeated inelastic deformations in elements. Such joints will preserve the continuity of reinforced concrete frames under severe seismic excitations, and will provide the conditions needed for dissipation of seismic energy by beam inelastic deformations. The anchorage conditions of beam longitudinal bars at interior and exterior joints have specially significant effects on the energy dissipation capacity of beams, and consequently on the overall response characteristics of reinforced concrete structures under intense earthquake ground motions[3]. Anchorage of beam bars at interior joints is provided by development of straight bars through the joint (Figure 1.2a). AT exterior joints, the beam longitudinal bars may be anchored either by straight bar development (Figure 1.2b), or by terminating the bars in standard hooks (Figure 1.2c). In typical lower story connections, the combined action of high lateral loads and relatively small gravity forces gives rise to the moment distribution shown in Figure 1.3(a). It is particularly noted that the end moments at the two faces of an interior joint act in the same direction. Upon the reversal of lateral forces, a complete reversal of the bending moments takes place at the beam end regions. Under severe cyclic load reversals, cracks may form across (c) Exterior Joint (Hooked Bar Anchorage) Figure 1.2 Anchorage Conditions of Beam Longitudinal Bars at Interior and Exterior Joints. the beam cross section at column faces. These cracks may remain open during cyclic loading[4], causing the reinforcing bars anchored at interior joints to be subjected to cyclic pull from one end and push from the other end (Figure 1.3b). This action limits the development length of the anchored bars to the joint (column) width, and may induce severe cyclic bond deterioration and eventual pull-through of the anchored bars. At exterior joints also, cyclic load reversals induce repeated pull-out and push-in forces on the anchored bars (Figure 1.3e), and may detrimentally affect the anchorage performance. Severe cyclic loads under intense seismic excitations may also generate major shear cracks in the joint region (see Figures 1.3d and 1.3e for cracked interior and exterior joints), which adversely influence the anchorage conditions in the joint core. Major local damage to many structures during recent strong earthquakes have been caused by the anchorage failure at interior and exterior joints[S]. Slippage of anchored bars at interior and exterior joints leads to fixed-end rotations at beam ends. This may cause excessive structural and nonstructural damage due to large deformations, which are further pronounced by the. p—6 effect. The ultimate goal of this research was to generate experimental and analytical data needed for characterization of the pull-out behavior of anchored bars and improvement of anchorage design equations in the conditions of interior and exterior joints. A comprehensive review of the literature on .Ao.ucoov museum msaumfimomnusoflox no moduoum meson an unseen uofiuouxm use BeauvusH no m0w>uzom n.H ousmflm u0m>ozom Haeuo>o any m #2920! o umOecueam _ _. —. 0(0- uxsaxpxeu _ — m a m u u I _ » (O..— >5>¢¢O n7. 1 r_: Ax: llllll / / l (b) Interior Joint Anchorage Condition i if (c) Exterior Joint Anchorage Condition Figure 1.3 Behavior of Interior and Exterior Joints at Lower Stories of Moment-Resisting Frames (cont’d). (d) Interior Joint Cracking (e) Exterior Joint Cracking Figure 1.3 Behavior of Interior and Exterior Joints at Lower Stories of Moment-Resisting Frames. experimental behavior and analytical modeling of the behavior of anchored (bonded) bars in interior beam-column connections is presented in Chapter 2. Test results produced in this study on the effects of anchored bar diameter, concrete compressive strength, and confinement of concrete on the behavior of bonded bars in joint conditions are summarized in Chapter 3. The development of an analytical model for predicting the pull-out behavior of straight embedded bars in confined joints is described in Chapter 4. This chapter also reports an analytical verification of straight bar anchorage design equations in the interior conditions. Chapter 5 presents a comprehensive review of literature on the overall behavior of exterior joints and pull-out action of hooked bars in the exterior joint conditions. Test results generated in this study on the effects of the number of hooked bars and fiber reinforcement of joint region on the hook pull- out behavior are summarized in Chapter 6. Suggestions for the modification of current exterior joints anchorage design equations, derived from produced test data, are also given in Chapter 6. Finally, Chapter 7 summarizes the research program and presents the conclusions of this investigation. CHAPTER 2 BEHAVIOR OF BONDED BARS IN BEAM-COLUMN CONNECTION: A REVIEW OF THE LITERATURE 2.1 GENERAL Bond stresses play important roles in deciding the distribution of forces inside interior joints. Initially, the forces applied to an internal joint are transmitted across the joint core through a diagonal concrete strut acting in compression (Figure 2.1a). Equilibrium of internal forces under increasing external loads leads to the development of significant bond forces along the longitudinal bars. These forces introduce shear stresses in the concrete core which in turn result in diagonal tension stresses, causing diagonal cracks within the joint (Figure 2.1b). Following diagonal cracking, as far as anchorage failure is prevented, a truss mechanism can be developed inside the joint, with the core concrete supplying the necessary diagonal compression field, which is balanced by the boundary forces and horizontal and 10 11 vertical tension in the joint reinforcement. Inelastic load reversals under the action of earthquake ground motions result in intersecting diagonal cracks and gradual deterioration of the joint core (Figure 2.1c). h I 1’13. ' arrr' , . WNES insfihflbgi; (c) Diagonal Cracks under Cyclic Loads Figure 2.1 Mechanisms of Joint Core Shear Resistance. 12 Although local failures related to the deterioration and pull-through of anchored bars at interior joints have repeatedly occurred in the past earthquakes, many codes (including ACI 318-83[6]) still rely on the anchorage length provided inside the opposite framing beam. This approach underestimates the critical anchorage conditions resulting from the restriction of development length to the joint width (Figure 1.3b). Some recent design recommendations[7,8] have acknowledged the anchorage problems at the interior seismic- resistant joints. More research, however, seems to be necessary before reliable design guidelines for anchorage of longitudinal bars in interior joints can be established. Another problem with the current design guidelines for seismic-resistant joints[6,7,8] is the maze of intersecting bars and hoops at the interior joints (Figure 2.2) needed according to these guidelines for ensuring the ductility of joint behavior. Congestion of the reinforcing bars, particularly the hoops, increases the labor and material costs, and very seriously complicates the construction of the reinforcement cage and the placement of concrete at interior joints. Bond deterioration also leads to increased fixed-end rotations at interior joints. This may cause excessive structural and nonstructural damage due to large deformations. Similar, but less critical, bond conditions exist in the case of straight longitudinal beam reinforcement anchored at the exterior beam-column connections (Figure 2.3a). Under the 13 action of bar tensile stresses (Figure 2.3b), the bond conditions in such exterior joints is comparable to those in the interior joints, except that the bars are subjected only to a pull-out force at one end (instead of being pulled and pushed at both ends, compare Figure 2.3b with Figure 1.3b). Figure 2.2 Congestion of Steel at an Interior Seismic- Resistant Joint. O (a) Overall Configuration (b) Pull-Out Behavior Figure 2.3 Exterior Joint with Straight Anchored Bars. 14 2.2 LOCAL BOND EXPERIMENTAL BEHAVIOR AND ANALYTICAL MODELING 2.2.1 General The concrete surrounding anchored bars in typical interior joints is generally confined by the column vertical reinforcement and tranverse hoops. This prevents the propagation and widening of splitting cracks resulting from the radial bond stresses, and encourages pull-out failure of anchored bars. Under increasing pull-out forces the bond behavior in non-fibrous confined concrete is marked by: (1) the initiation of inclined cracks at contact points between the steel lugs and concrete at relatively low stresses (Figure 2.4a): (2) crushing of concrete in front of lugs and initiation of shear cracks in concrete keys between the lugs (Figure 2.4b); and (3) shearing-off of an increasingly larger part of concrete keys between the lugs until the keys are fully sheared off (Figure 2.4c), after which only a frictional bond resistance is left. The gradual shearing-off of the concrete keys is possible only in confined concrete, where excessive growth of the splitting cracks can be prevented. If the slippage direction is reversed prior to the development of shear cracks in non-fibrous concrete keys (Figure 2.4d), first the small elastic concrete deformations will be recovered during unloading, and then a frictional resistance will be built up as the lugs travel through the gap created by loading in the opposite direction. Eventually, the 15 old cracks close and the bond resistance starts to increase, reaching and almost following the monotonic envelope curve. If the slippage is reversed after the initiation of shear cracks in concrete keys (Figure 2.4e), the bond resistance under reversed slippage will be below that obtained under monotonic loading. Repeated load cycles result in severe deterioration of bond stiffness and strength. '4 o it t it s GONG 1'. C C bond --— 1;: loud Stress crack l :L- / L. . l u" -—1k_\\ l (a) i b it t 66 4 Bend Stress Bond -- Force crushed concrete sheer creek (bl Figure 2.4 Mechanism of Bond Resistance in Confined Concrete[9,10] (cont’d). 16 iiitfile Bond Stress crushed concrete sheer crack L4 4 e g i . i . . Bond Stress r '0'-‘\ \ ’ \ Closed Old—— Crack 11 J l Crushed Concrete from I First Half Cycl‘I (d) L! i 6 9 t h h 9 Bond Stress ‘l 01d Crack -— New Crush in; and New Sheer Cracks (6) Figure 2.4 Mechanism of Bond Resistance in Confined Concrete[9,10]. 17 The bond performance in concrete cover at the tensioned bar end is different from the performance described above for bond in confined concrete. A relatively small bond resistance is provided in this region because of the separation of a concrete cone from concrete cover in non-fibrous concrete (Figure 2.5). Figure 2.5 Formation of Concrete Cone in Non-Fibrous Concrete Cover at the Tensioned Bar End[5]. 2.2.2 Experimental Results Results of experimental parametric studies reported in Reference 9 indicate that the following factors determine local bond behavior of deformed bars in non-fibrous confined concrete: anchored bar diameter and spacing, concrete strength, transverse pressure, rate of pull-out, and presence of restraining reinforcement. The test setup used in earlier studies on local bond in confined concrete is shown in Figure 18 2.6. Only a short length of the deformed bar is in contact with confined concrete, resulting in evenly distributed bond stresses and slips. Placement of a thin plastic sheet in the plane of anchored bar longitudinal axis in Figure 2.6 generates an artificial splitting crack representing the ones could be produced by adjacent bars[9]. Ti T 152-2: 85 5'5 l—-—rus. -' rmuc Sheet -—d 152-: loaded Part -. l_= l4 Stirrups 3‘5 Plastic Sheet Figure 2.6 Test Specimens with a Partially Bonded Bar for Local Bond Studies[9]. The variables, influencing local bond behavior which were considered in the experimental study of Reference 9 included: restraining reinforcement ratio, anchored bar spacing, transverse (longitudinal) pressure, rate of loading, anchored bar diameter, concrete compressive strength, and confining (transverse) reinforcement ratio. The effects of some of these variables, for which sufficient test data was generated in Reference 9, on local bond behavior are discussed below. 19 (1) Restraining (longitudinal) Reinforcement: Bond behavior is distinctly different in specimens with and without restraining reinforcement (Figure 2.7a). Plain specimens -fail by splitting of concrete at a relatively small bond stress, while those with restraining bars fail by anchored bar pull-out, with the opening of splitting cracks being prevented by restraining reinforcement. (2) Bar Spacing: Local bond behavior in confined concrete tends to improve as the clear spacing of anchored bars increases up to 4 times the bar diameter (Figure 2.7b). Thereafter, the effect of bar spacing on local bond behavior in confined concrete is negligible. (3) Transverse Pressure: The axial compression in column applies a transverse pressure on the joint, which generally improves the ultimate resistance and post- peak behavior of local bond in confined concrete (Figure 2.7c). The ratio of added bond resistance to applied pressure decreases significantly with increasing pressure. (4) Rate of Pull-Out: Local bond resistance increases with increasing rate of bar pull-out (Figure 2.7d). It should be noted that another factor influencing local bond behavior in confined concrete is position along embedment length in fully anchored bars. This factor will be discussed later in the review of the overall performance of anchored bars. 2O aouo smsss (N/mm2) bri'kfib‘ifit'o'u souosueomn) (a) Restraining Reinforcement souo mess (N/mm2) b'i'k'k'bri'o'tz BON01§UPHOnn0 (b) Bar Spacing Figure 2.7 Factors Influencing Local Bond Behavior in Confined Concrete[9] (cont'd). 21 1s 1s~ f ~~. 1‘“ '/”\ '2‘ ‘\\\\\\\ 10-4 1&20vhua9 10.0 Wanna) 10(Mfiflwn . 0 (Mm?) f i b i 4‘» b h ' 1'6 1 :2 sons sue (mm) sous smrss (N/mm2) . . ’ T I ’I ’0 I "N (c) Transverse Pressure as- ‘E' 14- % 12-4 a 1m E 4 o 5 4- ° 2‘ mom/us.) :JWhmvhwo _ vulflouwfiflfl pr r o i i 5 i ' 1'0 f u some SUP(rnrn) (d) Rate of Pull-Out Figure 2.7 Factors Influencing Local Bond Behavior in Confined Concrete[9]. 22 2.2.3 Analytical Mbdeling The first analytical model of local bond stress-slip relationship under cyclic loads in non-fibrous concrete was proposed by Morita and Kaku[11] (Figure 2.8). The empirical monotonic envelopes of this model in compression and tension, which account for the confinement effects, are given by two successive straight lines. The assumed hysteretic rules can be predict the behavior under a limited number of small-amplitude cycles with a reasonable accuracy. The model, however, is not capable of simulating the deterioration of bond behavior under large inelastic cycles. 7'" If. T‘ -e-T‘ g-lfiesfi/Z Tv-D-f, T. Im-f. squared/2 T! I m-T. To - m-‘l’, i.‘ 512 It, - soon/m’ e - OJ. 0 - 0.! “0.05" n 0 0.9-0.44le-OOSD OOSssIOSs-n Figure 2.8 The Local Bond Stress-Slip Constitutive Model Proposed by Morita and Kaku[11]. 23 Figure 2.9 shows the local bond model proposed by Tassios[10] for deformed bars in non-fibrous concrete. The coordinates of characteristic points on the proposed multi- linear envelope curve have been derived theoretically as functions of the relevant influencing parameters. The hysteretic rules of the model are advantageous to those of Morita and Kaku, in the sense that the descending branch of the local bond stress-slip relationship and the deterioration of stiffness under cyclic loads are accounted for. The Tassios’s model, however, disregards the serious deterioration of local bond strength observed under large-amplitude load cycles. ll' p bl“ 1, ..'.’° m m 5 I -. 47 '1' u. saga; 9 2 4 6 e ~ . L O LEFT A ‘ . Ii cf“ I’J . . Mn. war. '.;1 ",' 1'..ng -f,.-p-T. ’ .\m Tues-1". Figure 2.9 Analytical Model of Local Bond Stress-slip Relationship Proposed by Tassios[10]. 24 A more accurate empirical model for local bond stress-slip relationship of deformed bars in non-fibrous confined concrete under generalized loading has recently been developed[9]. This rather complex model (Figure 2.10) consists of the following components: (1) Two monotonic envelopes, one in tension and one in compression, which are updated in each slip reversal as functions of the incurred damage (curves 1 and 5 in Figure 2.10): (2) A typical unloading-reloading path described by an unloading curve (2), a frictional part (3) and a reloading curve that corresponds to the unloading one (4), along with a set of rules for unloading and reloading in the case of incomplete cycles: and (3) A set of functions for updating the envelope curve and the frictional bond resistance after incurring of the damage caused by inelastic load cycles. The above model (Figure 2.10) relates the damage under cyclic loading to a scalar quantity, that is the normalized dissipated energy. This concept leads to a convenient simulation of local bond behavior under random excitations. Moreover, in the local bond model of Reference 9, the characteristic values of bond stress and slip on the envelope curve are expressed in terms of the degree of confinement, transverse pressure caused by the column axial load, rate of slippage, bar diameter and concrete strength. 25 ll if EEEEK) hi \ ‘s \ \ \2- J -— EXPERIMENTAL 6“ -" AMYlCAL Figure 2.10 Analytical Model of Reference 9 for Local Bond Stress-Slip Relationship. 2.3 FULLK-ANCHORED BAR: EXPERIMENTAL BEHAVIOR AND ANALYTICAL MODELING 2.3.1 Experimental Results The reported test data on overall behavior of fully embedded bars in non-fibrous confined concrete (see Figure 2.11 for a typical test setup) are summarized below. In the majority of reported tests the anchored bars were #8-grade 60, and the compressive strength of concrete was about 30 MPa (4,000 psi). Typical pull-out force-displacement relationships for the fully embedded bars loaded monotonically at one or both ends, and cyclically at both ends, are shown in Figures 2.12(a), (b) and (c), respectively. These figures also show the variation 26 of bond slip, bond force per unit length, and bar axial force along the embedment length at the two points shown on the corresponding pull-out force-displacement curves. It can be observed in these figures that the bond stress and slip distributions along embedment length are rather complex and depend, among other factors, on the level and history of loading. The cyclic test results are also indicative of severe degradation of the anchored bar stiffness, strength and energy dissipation capacity under inelastic load reversals (Figure 2.12c). A deeper insight into the anchored bar behavior illustrated above can be achieved by comparing the local bond stress-slip relationships at different locations along embedment length. Figures 2.13(a) and (b) show bond stress- slip relationships at different points on the tension and compression sides of the embedded bar, respectively, under monotonic pull-push at two ends[12]. The compression side is observed to exhibit a stiffer response with a higher ultimate bond stress. This might be caused by: (a) the expansion and contraction of bar diameter in the compression and tension sides, respectively, due to the effects of poisson’s ratio; (b) the tension and compression fields at the push and pull sides, respectively, by the column bending moment: (c) the inferior bond behavior in tension near concrete cover: and (d) the increase and decrease in distance between lugs resulting from the bar tensile and compressive strains, respectively. 27 560- lmbsdded Ber .00.“ -..“... ‘1“ ..s .E“. ‘0 L P—JIb—v J ”IL-[Tm . p... U" Figure 2.11 Test Specimen of Fully Embedded Bars. mamas-s - I- 4 Weld S ..L! smears-q Q I amps I .1— (a) Monotonic Pull at One End Figure 2.12 Pull-Out Test Results on-Fully-Embedded Deformed Bars in Non-Fibrous Interior Joints (cont'd). 28 "neural/...) 5 ‘ II- .1 . igggi :4. : ifi'i a s' "l HAL-MW“) - *8 3.: 1* E~ 3.. :__‘ . ‘ __;?’ ‘ - , - ,——’ ' II- a a. l i I; O IN (b) Monotonic Pull-Push at Two Ends mm unuunwhe - 5 - B e \ rat's-fa. XVIII) m: 8H 2:: W .1 1 8- a“ 8~ .1 -.i O 3C. “I ..I ‘. ... . .5 l'bfb'b g” 3H (c) Cyclic Pull-Push at Two Ends Figure 2.12 Pull-Out Test Results on Fully-Embedded Deformed Bars in Non-Fibrous Interior Joints. BOND(Mmfl SUP(nmfl (b) Region with Compressive Bar Stresses Figure 2.13 Bond Stress-Slip Relationships at Different Locations along Embedment Length. 30 2.3.2 Analytical Mbdeling The overall behavior of a bar of finite length embedded in a concrete block (e.g., an interior joint) has usually been idealized using a one-dimensional model[1,4,13-15] (Figure 2.14a). The analytical approach of Reference 13, and also the more refined approach of References 1 and 4, for analyzing the idealized one-dimensional model of bonded bars are reviewed below. In both approaches the nonlinear differential equations governing the slippage behavior have been derived from the equilibrium conditions of an infinitesimal portion of the bar (Figure 2.14b). The boundary values for the bonded bar model should be specified at the two end points. Three different cases shown in Figure 2.14(c) are commonly incurred in reinforced concrete joints and elements. A shooting technique has been used in Reference 13 to solve the nonlinear two-point boundary value problem presented in Figure 2.14. In this approach, the boundary value problem is transformed into an initial value problem in which the unknown boundary condition at one end is guessed in order to produce, after integration along embedment length, the values of force and displacement at the other end. The fact that the computed boundary condition has to match the specific one, provides a nonlinear equation for the unknown boundary condition at the first end. An iterative solution of this equation finally yields the solution of the problem. The overall solution process is advanced in an incremental way 31 “hhhh —-L fi-e- w~—~_~_~— One-Dimensional Model (a) Physical Idealization an - s '- 0“) ° slut-ll. rtfl- this” Its) - “that. l. '0 else! “.’ . m e e u 2 en. ‘— ‘- ‘- "’ -r -d "=14—L'C(I)"'— d—fi-e J NdN _* vvv [1&4 (b) Governing Equations (I) -- k; Tl .. ‘I '- (m ——-{:7 ’i:% "l mm vs (3) -'- L. 1.1“, 5 mm. (c) Typical Boundary Conditions Figure 2.14 Physical Idealization and Governing Equations of Embedded Bars. 32 along the subdivided embedment length (Figure 2.15), where the loads (i.e., the assigned boundary conditions) are applied in small increments. In the above approach, the analysis of bonded bar behavior at each step involves an iterative satisfaction of the boundary conditions (by the shooting technique). The governing nonlinear equations should also be advanced iteratively in each subdivision. Hence, the analytical approach of Reference 13 involves nested iterations which seriously damage its computational efficiency. This approach, however, has predicted some test results with a reasonable accuracy (Figure 2.16). Recently, a more efficient approach to the solution of the governing bonded bar equations (Figure 2.14) has been proposed in Reference 1. This approach follows a mixed finite element method, based on a weighted residual formulation of the ‘1 J Figure 2.15 Subdivision of the Embedment Length. 33 guns ‘2’ 9' 3100- '" ' 3 ' i ' :3 ' uh ' m Sfi’hmo (a) Test g-me ‘é’. 3... 'v'zfs'rz'rg'z. smvomm (b) Theory[13] Figure 2.16 Experimental Results vs. Analytical Predictions[13] of the Bonded Bar Behavior. 34 governing differential equations. It removes one level of iteration (in advancing the solution along embedment length). The approach of Reference 1, however, still leads to a boundary value problem which should be solved by implementing the shooting technique (which involves time-consuming iterations). Reference 4, in an attempt to economize this iterative process, has suggested the use of an approximated pre-difined bond stress distribution along the embedment length. This helps in reducing the number of subdivisions along the bar. The general applicability of the proposed (approximate) bond stress distribution to different embedment conditions is, however, questionable (noting that factors like fiber reinforcement substantially change the bond stress distribution along embedment length). The analytical procedures of both References 1 and 4 have been able to satisfactorily predict some test results (see Figure 2.17 from Reference 1 for a typical comparison of analytical and experimental results). 2.4 OVERALL§i§ l#r l l’ l: Sn: ‘L, k. ____________ ...‘L'; (a) Confined Region (b) Concrete Cover Figure 2.19 Arrest of Bond Cracks by Fibers in Confined Concrete and at Concrete Cover. 41 the opening of cracks and thus effectively mobilize the aggregate interlock action against shear deformations at cracks (Figure 2.20b). The dowel action of reinforcing bars is another sliding shear resistance mechanism that is considerably enhanced by fiber reinforcement (Figure 2.20c)[26]. The effectiveness of fibers in resisting sliding shear deformations results in reduced deterioration after cracking of concrete, leading to a better environment for anchored bars inside the joints; and (e) Fiber reinforcement stimulates the application of high-strength steel and concrete to beam—column connections at the lower stories of R/C frames. They enhance the ductility of behavior, which is generally damaged by the use of high-strength materials. In short, the application of fibers to seismic-resistant joints in reinforced concrete frames has great potentials for improving the constructibility, economy, and performance characteristics of joints and consequently frames located in high-risk seismic zones. 2.6 SUMMARY AND CONCLUSIONS The action of seicmic loads on beam-column connections in reinforced concrete frame structures are described. The failure modes, seismic design objectives, and construction 42 (a) Dowel and Pull-Out Actions of Fibers Section A-A (c) Fibers Arresting Dowel Bar Cracks Figure 2.20 Improvements in Sliding Shear Resistance Mechanisms Resulting from Fiber Reinforcement[25,26]. 43 difficulties of beam-column connections in reinforced concrete structures are also reviewed. Due consideration is given to the seismic forces transferred to beam reinforcement anchored inside joints. The importance of bond resistance of anchored bars in preventing excessive slippage and pull-through of reinforcing bars at reinforced concrete joints has been emphasized. The mechanism of local bond action of deformed bars in confined concrete under generalized loading conditions has been described. The experimental data reported in the literature on local bond constitutive behavior are presented, and effects of some influencial factors are discussed. 'The experimental behavior of fully embedded bars in reinforced concrete joint conditions are also described. The analytical models proposed by different investigators for predicting the local bond constitutive behavior, and for applying the local bond model to the analysis of fully anchored bars in beam-column connections are also reviewed. Different analytical techniques for predicting the overall joint behavior under generalized seismic excitations are introduced. Potential advantages of fiber reinforcement for enhancing different aspects of reinforced concrete joint behavior under earthquake loads are also described. LOCAL BOND BEHAVIOR: EXPERIMENTAL RESULTS AND ANALYTICAL MODELING 3.1 INTRODUCTION Local bond behavior is a key factor governing the slippage and pull-out behavior of deformed bars anchored at beam-column connections (see Figure 1.3b and 2.3b). A comprehensive search of the available literature on bond[1,3-15,20,21,27,28] indicated that sufficient experimental data is lacking on certain aspects of local bond behavior. ' In particular, the effects of anchored bar diameter, compressive strength of concrete, and confinement by transverse hoops in beam-column connections could not be quantified by the available test data. An experimental program was conducted in this research to assess the effects of bar diameter, concrete compressive strength and confinement by tranverse hoops on local bond behavior. The test data produced in this study as well as the ones reported in the literature were also used to develop 44 45 empirical local bond stress-slip relationships which account for the effects of influencial factors governing the local bond behavior. 3.2 EXPERIMENTAL PROGRAM Pull-out tests were performed on deformed bars having only a fraction of their length in contact with confined concrete (see Figure 3.1a for the standard specimen). The embedment length of 5 d. was short enough to produce approximately uniform bond stress and slip distributions, but long enough to reduce the scatter of test results usually observed with very short bonded lengths[9]. A pull-out force was applied at one end and the bar slippage was measured at the other end (Figure 3.1b). From the measurements of force and displacement, using the assumption of uniform bond stresses and slips along embedment length, bond stress-slip relationships could be derived. The confinement reinforcement (vertical and transverse bars) in the standard specimen shown in Figure 3.1(a) was chosen to simulate conditions inside the confined core of a typical seismic-resistant interior joint. In order to study the effects of confinement on local bond behavior, however, some specimens with different amounts of confining reinforcement were also tested. The concrete used in the standard specimen had a compressive strength of about 30 MPa 46 Tube Plastic Sheet Bonded Part 0a Stlrrups 3a,, lll [..5.5drl Plastic Sheet (a) Test Specimen Hydraulic Actuator Load cell Displacement Clamp Transducer Isms:am—----+mana‘ "““d 3:==#---~*3-C -----e-D Bearing Plate Greased Plastic Sheet (b) Test Setup Figure 3.1 Test Specimen and Experimental Setup. 47 (4350 psi). The maximum aggregate size in this concrete was 19 mm (0.75 in.). The steel bars had yield strength of 414 MPa (60 ksi), and the anchored bar of the standard specimen had a diameter of 25mm (1.0 in.). The test specimens simulated the situation of anchored bars with clear spacing of four times the bar diameter by providing a plastic sheet at the anchored bar level (see Figure 3.1a) which artificially generated the splitting cracks that could be produced by adjacent bars (in case they were presented). The experimental program conducted in this investigation was aimed at assessing the effects of anchored bar diameter, concrete compressive strength and confinement on local bond behavior. Hence, in addition to the standard specimens, some were also tested with one of these three variables deviating from its standard value. The specimens tested in this study are introduced in Table 3.1, noting that all the variables in test specimens, except for the ones given in this table, have their standard values shown in Figure 3.1(a). Figure 3.2 presents the deformation patterns of the anchored bars used in this study. The reinforcement cage for standard specimen is shown in Figure 3.3 inside the form just prior to casting concrete. The direction of casting was normal to the anchored bar axis, and the location of bars in concrete is such that their bond conditions could be assumed to be an average of those of top and bottom bars. The specimens were moist-cured for 7 days inside wood forms, and were then demolded and air-cured in the laboratory environment until the 48 test age of 28 days. Loading was displacement-controlled and monotonic. One load cell and two electrical displacement tranducers (Figure 3.1b) were used for the measurement of load and displacement, respectively, with maximum errors below 1% of the measured values. Table 3.1 Test Program. No. Concrete . of Anchored Transverse Vertical Comp. Vanable Specimens Bar Reinf. Reinf. Strength MPa (psi) inmhomd. 2 #5 4#M 4%“ 30(4me .Bar 2 #7 4#4 4#4 30 (4350) IDuunamr 2 =#8 ‘¢#4 4#M 30(4THD 2 #8 21994 43964 27 (3950) Ihanswmse 2 =#8 6#M «¢#4 27(3mx» Rant. 2 #8 -— 43H 27 (3950) 2 #s - -- 27 (3950) 2 #3 ‘O#4 4#A 24(mwxn Concrete 2 #8 4#4 4#4 29 (4220) Comp. 2 #8 4#4 4#=4 34 (4950) Strength 2 #8 4#4 4#4 54 (7850) 49 ...... TNT-:3}; g .- .CIHFIII ifjfll il,__ ’ - U M iii -LL 1' ... .-£' —-.—’lt——“ GI IFFII if ll ][ ][ fl“ L ll Milli l l ILL 1,3 mm 1.4.4 mm 2.5 am :‘i. trill— CERT”? .QII/ 111111111771? l ll \LlLlLll leL LL - - v v v v v ‘ Figure 3.2 Anchored Bar Deformation Pattern. 50 1 _.. .mxseusv Reinforcement Cage. Figure 3.3 51 3 . 3 TEST RESULTS 3.3.1 Effect of Bar Diameter Figures 3.4(a), 3.4(b) and 3.4(c) show the experimental local bond stress-slip relationships for deformed bars with 16 mm (0.625 in.), 22 mm (0.875 in.) and 25 mm (1.0 in.) diameters, respectively. The variations in test results on two identical test specimens are observed to be reasonably small for practical purposes. Since this was always true, the rest of this chapter will be concerned only with the average test results obtained for two identical specimens. 20 '4 —- Test ”-1 Test ”-2 A 8. 2 V U) a: .33 u: :3 ~---- é “““““ ‘ .1 O . . . e . v o i i é 3 1o 12 SLIP (mm) (a) #5 Bar Figure 3.4 Experimental Local Bond Stress-Slip Relationships for Deformed Bars of Different Diameters (cont’d). 52 20 . — Test {7—1 -- Test {7-2 A 8. 3. a) v: E U) O :z O a: o r , , . r r U 2 4' 6 a 1'0 12 SLIP (mm) (b) #7 Bar 20 . - Toot n-i -- Test 53-2 ,\ 8. 2 V U) U) E 01 C) é o l I ' l v 1 v 0 2 4 6 8 1b 12 SLIP (mm) (c) #8 Bar Figure 3.4 Experimental Local Bond Stress-Slip Relationships for Deformed Bars of DifferentDiameters. rel te: te co si 53 The bar diameter effects on local bond stress-slip relationship are shown in Figure 3.5. This figure includes the test data generated in this study (Figure 3.4) as well as some test results reported in Reference 9 for specimens with concrete compressive strengths and confinement conditions similar to the standard specimen of this study. From Figure 3.5 it may be concluded that the ultimate local bond stress tends to increase with decreasing bar diameter. This tendency is, however, less pronounced at larger inelastic deformations. The characteristic values of slip seem to be largely independent of the bar diameter, and the local bond tangent stiffness tends to be larger in the pre-peak region (especially near the peak bond stress) for bars with smaller diameters. 3.3.2 Effect of Transverse Reinforcement Bond stress-slip relationships for specimens with different transverse (confining) reinforcement spacings are shown in Figure 3.6. Each curve in this figure is the average of two test results, which were performed on two identical specimens and showed similar trends. Failure of the plain specimens was by split cracking, and it occured in a brittle manner. The presence of vertical steel bars restrained the widening of splitting cracks, and changed the failure mode to a pull-out one. The differences in bond stress-slip characteristics of specimens with vertical bars, with or without transverse reinforcement at different spacings, were insignificant. Noting that split cracking in these Cl‘cc 54 20 4 “- #5 .... #6 l-\\ -- #7 ,6 16J :3 CL -- 10 E m 12- U? E F- m 8 CD 2 1 O ‘ -,_- —_ m 4.1 --“" -( o T i T l I 0 5 10 SLIP (mm) Figure 3.5 Deformed Bar Diameter Effect on the Average Local Bond Stress-Slip Relationship. 15 55 specimens occurs parallel to the plane of tranverse steel bars (as is also the case in actual beam-column connections), the insignificant effects of tranverse reinforcement on local bond behavior may be attributed to the fact that splitting cracks run parallel to transverse reinforcing bars and can not be arrested by them. It is also worth mentioning that in an actual joint the tranverse confining reinforcement is effective in preventing extensive shear cracking in the joint region, thereby providing a better environment for the bond performance. 3.3.3 Effect of Concrete Compressive strength The local bond stress-slip relationships of confined specimens with different concrete compressive strengths are shown in Figure 3.7. Each curve in this figure is again the average of two similar curves obtained in tests on identical specimens. The test results shown in Figure 3.7 indicate that the ultimate bond strength increases with increasing compressive strength of concrete. The other characteristic stress and slip values of the bond stress-slip relationship are not consistently influenced by the variations in concrete strength. 3.4 EMPIRICAL MODELING OF THE LOCAL BOND BEHAVIOR The general form of an analytical local bond stress-slip 56 ' % Restrained 15.0“ split crack A 3. 2 / . V ‘I'-~ h... 53 .' " E 10.0 m o 55' m 5.0 g Causing Failure °1° I 5:0 ' 16.0 15.0 BOND SUP (mm) Figure 3.6 Effects of Confining Reinforcement on the Local Bond Stress-Slip Relationship of Deformed Bars. 57 25.0 . J -- fc - 54(MPa) — fc - 34 (MPa) 20.0- .. ' “s9: - 29m.) I S one I I ‘ fc I 24(MPa) BOND STRESS (MP0) BOND SUP (mm) Figure 3.7 Effects of Concrete Compressive Strength on the Local Bond Stress-Slip Characteristics of Deformed Bars in Confined Concrete. 58 relationship capable of reproducing experimental results is shown in Figure 3.8(a). The curve consists of an ascending curvilinear segment, a flat part at peak bond stress, a linear decending branch, and a flat tail representing the frictional bond resistance. Two characteristic bond stress values (13 and 13), and three characteristic bond slip values (51, s and s3) 2 should be derived empirically for defining the bond stress-slip relationship by the proposed analytical model. The 1, s2 and s3 as well as the frictional bond stress 73 are largely independent of the bar characteristic bond slip values 5 diameter and concrete compressive strength. The averages of these characteristic values, obtained by least square curve fitting to the experimental data generated in this study and those reported in Reference 9, are given in Table 3.2. The ultimate bond stress (71), unlike the other characteristic values, is dependent on the bar diameter (see Figure 3.8b) and concrete compressive strength (see Figure 3.7). A linear relationship was derived (based on regression analysis) between the ultimate bond strength and bar diameter. The ultimate local bond strength was found to be proportional to the square root of the concrete compressive strength. As far as sufficient vertical column bars are present to arrest the bond splitting cracks (this is usually the case in beam-column connections), the test results generated in this study indicate that the characteristic local bond stress and slip values are practically independent of the amount of confinement reinforcement provided. 59 It should be noted that all the characteristic bond stress values derived above are applicable to anchored bars with clear spacing of four times the bar diameter or more. Smaller clear spacings adversely influences the characteristic (peak and frictional) values of local bond stress. Reference 9 has also concluded from local bond test results that the column pressure and rate of pull-out are the other influencial factors deciding the local bond behavior of deformed bars in confined concrete. Typical comparisons between the proposed local bond constitutive model and the test results of this study and those of Reference 9 are shown in Figures 3.9(a) through 3.9(f). The proposed model is obsedved to predict test results with a reasonable accuracy. Table 3.2 The Characteristic Local Bond Stress and Slip Values (1 mm a 0.039 in., lMPa = 144 psi). S1 52 53 Ta 7'1 mm mm nun MPa MPa (in) (im) (in) (Psi) (Psi) db c 1.0 3.0 10.5 5.0 20 - T 30 (0.039) (0.118) (0.413) (725) (2900 - 921 d.) 33-5—0- Note:For column pressures QR) more than zero and bar clear spacing (0.) less than 41!, (based on the est results reported in Reference 9). (r, or 1'3) =- (r1 or T3 in Table 4.1) (1.3 — 0.3c'°"53) [1 — 0.833e ‘* ] (MPa) 60 [1-(S/Sl)°l r-rl(S/81) e BOND STRESS (V) BOND SLIP (S) (a) General Form 8 — :1 “/4 15m ‘ e 104 § BOND STRESS, '1(N/mm2) Y L O 4 ' 5 'fl211h' fia'ikr:& 'isza BAR DIAMETER (mm) c ‘u (b) Bar Diameter Effect on Local Bond Strength (each point represents the average of at least two test results with ;',-30 MPa, 4350psi) Figure 3.8 Local Bond Constitutive Model. 61 BOND STRESS (Mp0) (a) 20- — Test --- Theory ‘ a BOND STRESS (Mp0) 1'5 I 12 C the O (b) Figure 3.9 Analytical vs. Experimental Local Bond Stress-Slip Relationships (cont'd). 62 2S0 4 T“! A 20.0- :3: - 2mm 8 2 V m 150- m LU m p— m 100‘ ------- 0 ..... z “-- o ...... m an 0e. . , . . - . . o 2 1 5 5 1o 12 BOND 51.19 (mm) (C) 2&0 Theory ‘ Tel! ,3 20.04 :3: - 2911..) O. 3 V . m ‘5.0-4 01 LL] m p— ” 10.0~ :1 ...... z ------- no '3 so me . . . . . 6 i If 3 5 1B 12 BOND SUP (mm) (d) Figure 3.9 Analytical vs. Experimental Local Bond Stress-Slip Relationships (cont'd). 63 A o o. I V (O U) U 0: 1. (D 0 Z O m 0.0 I v I v I v I 7* ' ' I 'q 0 2 4 G B 10 12 BOND SUP (mm) (6) 25.0 ‘ meaty Tee! "0‘ 11.: - 541119.) a. 2 V (I) U) E U) D Z 0 cm 0.0 , r v . - u 2 3- 3 a 1b 12 BOND SUP (mm) (f) Figure 3.9 Analytical vs. Experimental Local Bond Stress-Slip Relationships. 64 3.5 SUMMARY AND CONCLUSIONS The effects of anchored bar diameter, concrete compressive strength and confinement level on the local bond stress-slip relationship of deformed bars in confined concrete were assessed using monotonic test data on bars of different diameters partially embedded inside the confined core of concrete block specimens. These test specimens simulated the anchorage conditions inside the confined core of beam-column connection. The test data indicated that: (l) The ultimate local bond strength decreases as the bar diameter increases. The drop in bond strength is a linear function of bar diameter. There is also a slight increase in the local bond pre-peak tangent stiffness (especially near the peak bond strength) as the bar diameter decreases, but the post-peak local bond resistance, especially at larger inelastic deformations, is less influenced by the anchored bar diameter: (2) The ultimate local bond strength increases almost proportionally with the square root of the concrete compressive strength. The pre-peak tangent stiffness of local bond also increases slightly with increasing compressive strength of concrete. In the post-peak region, however, the effect of concrete compressive 65 strength on local bond behavior tends to diminish; (3) The characteristic bond slip values (e.g. that corresponding to the peak bond stress) are largely independent of the bar diameter and concrete compressive strength; and (4) Confinement of concrete by transverse reinforcement does not directly influence the local bond behavior of deformed bars in the condition of beam-column connections, where the vertical column bars are usually sufficient to restrain the widening of bond splitting cracks. If the bond splitting cracks can not be restrained by the column vertical reinforcement, upon split cracking a sudden failure takes place which significantly reduces the ultimate strength and post-peak ductility of local bond. An empirical local bond constitutive model, capable of considering the bar diameter and concrete compressive strength effects, was also derived from test results. CHAPTER4 AN ANALYTICAL EVALUATION OF STRAIGHT BAR ANCHORAGE DESIGN IN EXTERIOR JOINTS 4 . 1 INTRODUCTION Relatively large bending moments tend to develop in reinforced concrete beam ends near exterior joints (e.g., end A of beam AB in Figure 4.1a). In order to develop the full flexural strength of beams at these critical locations it is sufficiently anchor the beam longitudinal bars inside the joints. This anchorage might be provided by development of straight bars inside the exterior joint (Figure 4.1b), or by terminating the beam bars in standard hooks (Figure 4.1c). This chapter is concerned with the anchorage of straight bars terminating in exterior joints (Figure 4.1b) under static (monotonic) loads. The ACI-ASCE Committee 352(8] suggests a minimum development length (1,) beyond the column face (see Figure 4.2) for #11 or smaller straight bars terminating in exterior joints 66 67 ‘— ‘— *— ‘—-—_. Fmvtflm [III [[1 [If < 1 1i (a) Bending Moments -* 'fi #5! fin ..... .r .-. °°°°° :1? $;::'.°:::::: : 3:5 3 g ' .... fizz-.3 '.':.': : 1'. 3%.- ........ ' . $331323 : a}? ' 5 #- 1.2” -------- «:2.- -------- - +5. 4.1...- «..g. J Jr - -.-.~.-.-.-.-.- - .p (c) Hooked Bar Anchorage Figure 4.1 Anchorage of Beam Reinforcement in Exterior Joints. 68 fieszzrxn'fir W3 :::::: ..... r? #3::33 : 3.1% £333.? :2? ' ié:::::::::'.°.1'h dean-3: ....... $- ééau - -°:.°.°:J,'a Figure 4.2 Definition of Development Length. (assuming no major inelastic load reversals, with the bar being contained within the core of the column): a 1', (ps1) Ab(1'n.2) “ 25v1' c(ps.') 20.0004db(1'n.) 1', (p81) 1 - f,(MPa) Ab(mm)2 " 52.7V/'c(MPa) (4.1) _>_ 0.058 db (mm) [1(MPa) where : Id :3 deveIOpment length ,' f, - steel yield strength ; f ’ c - concrete compressive strength; and A. - steel bar area. 69 The ACI-ASCE Committee 352 recommendations[8] also provide modification factors for top bars and for situations with reinforcement areas exceeding the required values. The main concern in this phase of research was to verify the applicability of Equation (4.1) in exterior joint conditions. It is worth mentioning that the ACI-ASCE Committee 352(8] does not provide any limits on deve10pment length similar to 30.5 mm (12 in.) provided in ACT 318-83[6]. 4 . 2 ANALYTICAL MODELING OF ANCHORED BAR A one dimensional model (Figure 4.3) was used to idealize the anchored bar behavior. The discrete springs in this model represent local bond resistance on the tributary surface area of anchored bar corresponding to each spring. In the one- dimensional model of Figure 4.3, the concrete strains are assumed to have negligible effects on the anchored bar behavior[13], and thus the springs in Figure 4.3 are assumed to be rigidly fixed at the ends connected to concrete. The tangent stiffness matrix of anchored bar model (Figure 4.3) can be built using the constitutive relationships between steel and local bond. The bond tangent stiffness (Ky ) and the steel tangent stiffness (39,) can be derived using these constitutive relationships. The stiffnesses of the springs (K5,) and the steel segments (K...) in Figure 4.3 can then be computed at each step in the loading history: 7O Kbi '3 [(ti (”db) [1' (4'2) K“- = K I; (7rd,,2) I; (4.3) where : d, - bar diameter; N ,- - length of the ith steel segment (Figure 4.3); K“ = bond tangent stifi’ness; K If a steel tangent stifi‘ness; K..- - stifi‘ness of the springs; and K..- =- stifl’ness of the steel segments. '1 SH K111 K112 1 Kb(n-1) Kbu finwnmnwmmm 51 ‘51 2 ‘52 3 ‘ stihl Ks(n?;§ n Ph’sn Figure 4.3 The Proposed Anchored Bar Model. Using the tangent stiffnesses of steel segments and springs, the overall tangent stiffness matrix (K}) of the idealized system shown in Figure 4.3 with n degrees of freedom (n is the number of discrete points along the bar length) can be constructed as follows: '71 2.3 :15 udGlfl 51.51 .2 :lmvev l OGQ 2|... .l c :levev~+filevev~+=le7v~ rule? I. GOO GOO :1 5 an: o e e e e ... n.v~+«.\<+2¥ «- I G 2e 1 «outfits _. 1 c ..c 1 Gets: Q 72 Equation (4.4) can be used to relate incremental end force (dP,) to the incremental slip values along the bar length (dsll “2! I d5; , d5“): r 1 t ) 0 d5, 0 d5? « I »= KT 1 I > (4.5) 0 43;-1 dP. 45,, \ J \ J 0 452 0 1 I * =- F < I > (4.6) 115,4 0 45, dP. h J L J It can be concluded from Equation (4.6) that: dsl - [1,11 dPn (4'7) d8, - I“, (1P, (4.8) where: [m- = the element in the ith row and the jth column of matrix F, 73 In pull-out tests, usually the incremental values of end slip (45,) are defined. For this condition, Equations (4.7) and (4.8) can be written in a form which facilitates the calculation of the incremental values of pull-out force (4P5) and slip at the other end (asl): dSfl dPn = (4.9) n,n tfla f ‘51 - ——‘i (4.10) [11,11 The following solution algorithm, based on the above equations, has been developed to the analysis of anchored bar pull-out behavior: (1) Using the slip values of the previous load step, construct the overall tangent stiffness matrix of the system using bond and steel constitutive laws with Equations (4.2), (4.3) and (4.4). Invert this tangent stiffness matrix to get matrix F‘(and its elements I“ 1 ’1,“ In and 1.1,.“ (2) Given d3“ find JP. and 161 using Equations (4.9) and (4.10): (3) Find all the incremental slip values along the bar length using Equation (4.6). The above algorithm gives the slip values along bar length at the end of each time step. This is the information needed for constructing the new tangent stiffness matrix to be used in the next time step. The above algorithm can be repeated for 74 the consequent load steps up to the end of the loading history. The developed procedure for the analysis of anchored bar behavior, unlike the other available methods[9,13,21], does not involve iterative solution of nonlinear equations. It is thus time efficient for analysis by computer. The proposed approach is also based on the displacement method of analysis that is commonly used in conventional computer program for static and dynamic analysis of complete structures. It may thus provide researchers with a practical (economical) tool for studying the effects of bar slippage (e.g. in reinforced concrete beam- column connections) on the overall response of reinforced concrete structures to static and dynamic loads. 4.3 STEEL AND LOCAL BOND CONSTITUTIVE MODELS The anchored bar stiffness matrix (Equation 4.4) is defined in terms of the local bond and steel constitutive models. A bilinear steel stress-strain model with a strain hardening ratio of 1.7% (Figure 4.4a) was selected for use in this investigation. The details of steel constitutive model were shown in Reference 29 to have negligible effects on the predicted anchored bar behavior. The overall shape of the local bond stress-slip constitutive model used in this study is shown in Figure 4.4(b). The characteristic bond slip and stress values in this model (s1, sz, 53, T1 and 1% are given in Table 4.1, based on the test results reported in Chapter 3. 75 This model incorporates the effects of anchored bar diameter, concrete compressive strength, bar spacing and column pressure on local bond constitutive behavior. The first two effects were quantified using the test data generated in this study (see Chapter 3). Typical comparisons between this local bond model and test results were presented in Chapter 3 (see Figure 3.9). Figures 4.5(a) through 4.5(d) present the effects of the anchored bar diameter and bar clear spacing, concrete compressive strength and column pressure, respectively, on the local bond constitutive behavior as predicted by the developed local bond constitutive model. It is worth mentioning that the test data generated in Chapter 3 indicated that the variations in column transverse reinforcement ratio at the joint region do not significantly influence local bond performance Table 4.1 The Characteristic Local Bond Stress and Slip Values (1 mm - 0.039 in., 1 MPa 2 144 psi ). -31 52 53 E3 71 mm mm mm MPa MPa (in.) (in.) (in.) (psi) (psi) 1.0 3.0 10.5 5.0 ‘20 - fl— _‘1. 4 30 (0.039) (0.118) (0.413) (725) (2900 - 921d“ \ / __:‘ 4350 NotezF‘or column pressures (R more than ze d ' 0 than 4d, (based on the tes)t results reporteaoigxliefggngegl:Spacm" (Cb) less C. 0.70 . -161__ (7'1 0" T3) = (7'l or T3 in Table 4.1) (1.3 - 0.3e’0'153) [l — 0.833s ( d‘ ) ] (MPa) '76 883818 I I zh-o.017(z.) , I es-zoo.000(ur.) ’ STRAIN (a) A Bilinear Steel Stress-Strain Model 11-- 5 40. 1" ‘~\ ‘21“ ' ‘ ‘\ .-'.= -._‘-e 3 \‘ \.:":- 2 ‘~- 2m- "" o. ‘ l 0.0 [_o 2.0 3.0 PULLPOUT DISPLACEHINT (in) (a) Suffciently Confined Joint[37] - es ' a s a ' fl — —‘ .' m ’ fl ”‘ b. ..0 .- ’ ‘- d" ‘— ’ I L ";:L_.——adhumul : :co. / a / '- e __ 2 3 f I /’ "'00 o-c:!:::!:::8 II t n: ......... . 9 / / «mes—3 ; U ’I I ‘ l/’ g: 2 J ~ 2: .0 . AL A A A 4 t A I A A A A A A a 0.0. ' T‘ V 1 me man m (b) Insufficiently Confined Joint[35] Figure 5.14 Effect of Hooked Bar Diameter on Hook Pull-Out Behavior. 114 (6) Compressive Strength of Concrete: Reference 28 suggests that the pull-out behavior of anchored bars improves only slightly with the increase in concrete compressive strength. Test results presented in Reference 37 also indicate that concrete compressive strength has only small effects on the pull—out behavior of hooked bars. The conclusions of Reference 28 and 37 are, however, 'based on limited pull-out tests on hooked bars in the confined joint conditions. (7) Anchored Bar Yield Strength: Although it is expected that the hooked bar pull-out behavior may improve with increasing bar yield strength (as far as the joint region is sufficiently confined), the available test data are insufficient to fully confirm or quantify this effect. (8) Spacing of Hooked Bars: Simultaneous pull-out of multiple (closely-spaced) hooked bars from an exterior joint are expected to detrimentally influence the pull-out behavior of hooks. The available test data, however, does not provide any conclusive information on this important aspect of hook pull-out behavior. Finally, it is important to discuss the differences in the behavior of hooked bars subjected to pull-out and push-in forces. Limited cyclic tests performed on hooked bars[3] have indicated that, contrary to the general consensus, the anchorage provided by hook is not effective only under tension pull-out forces but also under the action of compression push- 115 in forces, as far as sufficient confinement is provied for the concrete surrounding hooked bars in exterior joints (see Figure 5.15 for a typical hooked bar cyclic behavior). It is also interesting to note that the concrete wedge splitting from cover under pull-out tension (see Figure 5.9b) tends to recover its strength under push-in compression after it comes in touch with the body of joint under compression forces[3]. M n§m -30 -L0 no 30 so a» b““’ w (an E 1 2° °‘ 5 «o .-nn --lflml .«n o I "25' 420 4 .— 1 7 A 1. A -¢o‘~w ~40 am! 0 45 JO .5 10 DISPUICEKM. "(a ...... I a O 3 ’ = f c 28.3 MPa, fy 414.5 MPa. db 32.3 mm Figure 5.15 Typical Cyclic Behavior of Hooked Bars. 116 5.3 ANALHTICAL HODELING OF HOOKED BAR BEHAVIOR Limited analytical studies have been reported on the predicting pull-out load-displacement relationship of standard hooks at exterior joints. The available models may be categorized in two groups. One group substitutes the hooks by an equivalent straight bar anchorage length, and the other relies on an empirical pull-out load-displacement relationship to represent the hook behavior. References 3 and 28 suggest that the hook performance can be simulated with an equivalent straight embedment length (Figure 5.16a). The equivalent length for tensile loading is calculated as follows: h-h+%+4 (m) where: L, - equivalent straight bar embedment length; L, I- the distance from the column face to the start of the hook; D - standard hook diameter; and d. - bar diameter. For compression loading, according to Reference 3, Equation (5.1) can still be used to simulate hook behavior. The ACI Building Code[6] states that only the length L, is effective in resulting compressive loads. Figure 5.16(b) 117 presents a typical comparison between an experimental pull-out load-displacement relationship and the analytical prediction of Reference 3 which is based on simulating the hook behavior by an equivalent straight bar anchorage length (Equation 5.1). In the other approach to modeling of hooked bar behavior[37] the hook is substituted with a spring located at the end of the straight lead embedment length (Figure 5.17a). Reference 37 has derived an empirical load-displacement relationship for this spring based on the observed pull-out behavior of hooks (see Figure 5.17b). Figure 5.17(c) presents typical comparison between the predictions of this approached and experimental pull-out load-displacement relationships of hooked bars. W '1. " i; \ m mm (on: Actual Idealized (a) Actual vs. Idealized Conditions Figure 5.16 Hook Modeling by An Equivalent Straight Embedment Length (cont'd). 118 o I Its! I to. “ flee .A_._ :0 so . .........o-? _‘tg-‘aéulr;_ eo' ‘ 1T. ..0 .- 3. v x ,‘ 'x Q . ”T g '- .’0' t -.. noon .6 . . ..‘flh 'o40 -os o in JO is :0 as an DISPUCU'CM. "(n I - e - 9 8 f c 22.8 MPa. fy 469 MPa. db 25.4 mm (b) Analytical vs. Experimental Results[3] Figure 5.16 Hook Modeling by An Equivalent Straight Embedment Length. 4v / \_____3_ noes S'MK m 8PM“ Arm é AV, Actual Idealized (a) Actual vs. Idealized Conditions Figure 5.17 Simulation of Hook by A Spring[37] (cont’d). 119 P l P; (U/U1)° Pl '- E 91 8 h’ P) 0 O I '2 '5 “ A L > 01 U: U! PULL-OUT DISPLACIHENT (U) (b) Hook Spring Load-Displacement Relationship PULL-M MI tum 0.. 0.0! I.” 0.88 O.” m HIM NO.) I I. 0 :3 f c 27.6 MPa. fy 450 MPa (c) Analytical vs. Experimental Results Figure 5.17 Simulation of Hook by A Spring[37]. 120 5.4 STEEL FIBER REINFORCEMENT OF EXTERIOR JOINTS Reinforcement of concrete by short randomly distributed steel fibers results in the following improvements in material behavior[24,25,38,39]: (1) increased tensile and flexural strength, ductility and energy absorption capacity; (2) increased ductility and energy absorption capacity under compression and bearing loads; (3) increased sliding shear resistance across cracks: (4) improved bond of concrete to reinforcing bars[40]; (5) controlled cracking and decreased crack width; and (6) reduced spalling of concrete cover under internal outward stresses. The above improvements in concrete behavior resulting from steel fiber reinforcement are particularly beneficial in the exterior joint conditions. Steel fibers can be used to partially substitute the transverse hoops, which are commonly used at relatively high ratios, to provide confinement at exterior joints. Considering the serious congestion of steel bars at joints, replacement of transverse hoops by steel fibers is a definite advantage for the practicability of the exterior joint construction[24,25,38,41]. Besides reducing the congestion of steel, the distinct characteristics of steel fiber reinforced concrete result in the following improvements in joint behavior[24,38,41]: (1) increased ductility and energy absorption capacity: (2) reduced crack width and concrete cover spalling, and thus improved structural integrity; (3) reduction 121 of the anchored bar slippage and increase in the beam moment capacity at column face; (4) increased shear resistance: (5) higher stiffness; (6) maintaining the ductility of joints constructed with high strength concrete and steel; and (7) cost savings resulting from the substition of high transverse hoop volumetric ratios by relatively low steel fiber volume fractions. The above improvements in joint behavior resulting from steel fiber reinforcement indicate that safer and more economical joints can be designed through the judicious use of steel fibers. Reference 24 has compared the hysteretic performance of two seismic-resistant exterior joints, one incorporating transverse hoops and the other taking advantage of steel fibers for improving the ductility of joint behavior. Figures 5.18(a) and 5.18(b) show the joints with hoops and with fibers, respectively. The fibrous joint incorporated 1.67% volume fraction of steel fibers in having a length of 38 mm (1.5 in.) and a diameter of 0.51 mm (1.02 in.). The moment-rotation curves for conventional and fibrous joints (measured at 30.5 mm, 12 in. from column face) are shown in Figires 5.19(a) and 5.19(b), respectively. The fibrous joint is observed to be stiffer than the conventional one, possibly due. to the reduction of hooked bar pull-out in the presence of fibers. The fibrous joints also has a higher ultimate flexural capacity. The beam cracks in conventional joints appeared first at 152.4-203.2 mm (6-8in.) from the columnface. A crack also 122 L— 9 59. e Z-ll?‘-—| Elllllli ll [1} (a) Conventional Joint with Transverse Hoops SHRR/UP SPACING co. 0... .-. at-.. -'D —— — — _. - AREA FILLED WIIH STEEL . FIBROUS CWREIE (b) Fibrous Joint Figure 5.18 Conventional and Fibrous Seismic-Resistant Exterior Joints. 123 (a) Conventional Joint with Hoops I000" ”47) (b) Fibrous Joint Figure 5.19 Moment-Rotation Diagrams Measured 30.5 mm (12 in.) from Column Face in Conventional and Fibrous Joints. 124 occurred in the beam at column face. Figure 5.20(a) shows the beam crack pattern in conventional joint. There are also some hairline cracks in the joint region after the test. In the case of fibrous joint the major cracks occurred outside the fiber reinforced region. One major crack occurred in the beam 50.8-101.6 mm (2-4 in.) from the column face. No cracking was observed in the joint region of fibrous specimens. The fiber reinforced joint appeared to be more damage-tolerant and to have a higher resistance to cracking than the conventional joint (Figure 5.20b). Reference 38 has reported the results of a comparative study on the hysteretic performance of conventional and fibrous exterior joints with different beam shear span to depth ratios and longitudinal steel configurations. The fibrous joints had hooked-end steel fibers with a diameter of 0.5 mm (0.0197 in.) and a length of 45.7 mm (1.8 in.) at a volume fraction of 1.5 % transverse hoops were used in both the fibrous and conventional joints (see Figure 5.21). (a) Conventional (b) Fiber Reinforced Figure 5.20 Crack Patterns in Conventional and Fibrous joints. 125 Figure 5.21 Exterior Joint Test Specimens of Reference 38. Figure 5.22(a) and 5.22(b) compare the hysteretic performance of conventional and fibrous joints with beam shear span to depth ratios of 4.33 and top to bottom steel ratio of about 2.0. The presence of steel fibers practically controls diagonal cracking in the joint area. The crack patterns in columns of the two specimens were similar, and both specimens failed by the fracture of beam longitudinal steel. The fibrous joints could absorb more inelastic energy than the conventional joints. The crack widths were also smaller and the number of cracks was more in fiber reinforced joints. Figures 5.23(a) and 5.23(b) compare the hysteretic performance and failure conditions of exterior joints with beam 126 shear span to depth ratios of 3.61 and beam top-to-bottom steel ratios of 2.0. These specimens, which had beams with lower shear span to depth ratios and consequently higher shear stresses compared to the specimens of Figure 5.22, more cracks in the joint region. The presence of fibers increased the energy absorption capacity and reduced the extent of cracking in exterior joints. Figures 5.24(a) and 5.24(b) compare the hysteretic performance and failure conditions of exterior joints with beam shear span to depth ratios of 2.89 and beam top-to-bottom steel ratios of 2.0. The higher beam shear stresses were observed to initiate shear failure in the joint region followed by the loss of bond of the longitudinal steel at conventional joints. In the presence of fibers the loss of bond was prevented. The fibrous joints developed smaller crack widths and suffered less structural damage. They dissipated 100% more energy than the conventional joints. Figures 5.25(a) and 5.25(b) compare the hysteretic performance and failure conditions of exterior joints with beam shear span to depth ratios of 4.82 and beam top—to-bottom steel ratios of 2.0. The beam in these specimens, however, has twice as much longitudinal steel area as those in Figures 5.22 to 5.24. The conventional joint failed by shear cracking in the joint area, with concrete pieces spalling off and large cracks developing. Fibers could efficiently control the damage and cracking at the joint region, thereby increasing the energy absorption capacity of the joint. 127 Figure 5.26(a) and 5.26(b) compare the hysteretic performance and failure conditions of exterior joints with beam shear span to depth ratios of 4.34 and equal beam top and bottom steel areas. Conventional joints developed major diagonal cracking in the joint area early in the loading history. These cracks propagated rapidly with loading, leading to spalling of concrete and failure by the loss of bond and integrity at the joint region. With fibers the diagonal cracking was delayed and bond failure was prevented. The crack width was also smaller in the fibrous joints, and no spalling of concrete and loss of integrity of the joint was observed. The fibrous joint could dissipate almost twice as much energy as the conventional joint, and it was also stiffer. 5.5 DESIGN GUIDELINES FOR HOOEED BARS IN EXTERIOR JOINTS ACI 318-83[6] and Reference 42 suggest the following equation for calculating the development length ( Q5) of deformed bars in tension terminating in a standard hook (see Figure 5.27), for structures located in regions of low or moderate seismic-risk: _ 1200450.“) 13,085) I“ C I I c (p30 . 60’” l 100d, (mm) I, (MPa) 41. -— (5.2) T' .(MPa) ' 416 128 Applied Lood (Ripe) O -O ' -4 :2 Tip Deflection (in) (a) Conventional Joint NWMGUNdflbd £5 . i 3 Lorne—LA— 1.. Tip Deflection (ii-I.) (b) Fibrous Joint Figure 5.22 Hysteretic Performance and Failure Conditions of Conventional and Fibrous Joints with Beam Shear Span to Depth Ratio of 4.33 and Beam Top-to-Bottom Steel Ratio of 2.0. 129 Applied Lood (kipo) Tip Deflection (in.) (a) Conventional Joint Applied Load (kipo) Tip Deflection (in.) (b) Fibrous Joint Figure 5.23 Hysteretic Performance and Failure Conditions of Conventional and Fibrous Joints with Beam Shear Span to Depth Ratio of 3.61 and Beam Top-to-Bottom Steel Ratio of 2.0. 130 (a) Conventional Joint (b) Fibrous Joint Figure 5.24 Hysteretic Performance and Failure Conditions of Conventional and Fibrous Joints with Beam Shear Span to Depth Ratio of 2.89 and Beam Top-to-Bottom Steel Ratio of 2.0. 131 ‘ flNCHES) (a) Conventional Joint (b) Fibrous Joint Figure 5.25 Hysteretic Performance and Failure Conditions of Conventional and Fibrous Joint with Beam Shear Span to Depth Ratio of 4.82 and Beam Top-to-Bottom Steel Ratio of 2.0. 132 NO HBERS 3 (INCHES) (a) Conventional Joint HBERS Figure 5.26 3 UNCHES) (b) Fibrous Joint Hysteretic Performance and Failure Conditions of Conventional and Fibrous Joints with Beam Shear Span to Depth Ratio of 4.34 and Beam Top-to-Bottom Steel Ratio of 1.0. 133 (I f“ l T l .. ‘ v -°..'3"'.. ’ '2” Ion J F‘” j Slandom 90 or \ I L f l80deg hook “b or A 4% ’3 M ‘8 1 gym 56. ‘9. 'lou'll so. 'uau‘is 1e _ . (a) Standard Hook (b) Development Length Figure 5.27 Standard Hook Development Length. where: la - hook development length; d. - bar diameters; f ' c - concrete compressive strength; and f y =- steel yield strength. ACI 318-83[6] and Reference 42 also suggest modification factors for conditions with sufficient concrete cover and confining reinforcement, and also for situations with excessive reinforcement or light weight concrete. For #11 bars and smaller, it is suggested that a modification factor of 0.7 should be used when side cover is not less than 63.5 mm (2.5 in.), and cover on bar extension beyond 90-deg hook is not less than 50.8mm (2in.). It is also suggested that for #11 and 134 smaller bars a modification factor of 0.8 should be used when the hook is enclosed within ties with spacing not greater than 3 d). The final development length in any condition can not be less than 84h or 6 in. .It should also be noted that the ACI 318-83 recommendations and those of Reference 42 suggest that standard hooks are effective only when the bar is acting in tension. For regions of high-seismic risk, ACI 318-83 suggests the following equation for predicting the development length. ( hi) of standard 90-deg hook in normal weight concrete (for #11 and smaller bars): :- fg(l”;) db (in) (db 65;; I ’ 6 (psi) - 1, (MPa) d,(mm) 1“ 5.4V! 5 .(MPa) (5'3) It is recommended that 90-deg hooks shall be located within confined core of the column or the boundary member. The development length can not be less than 8db or 152.4 mm (6 in.). Equation (5.3) results very close to those of Equation (5.2) with confinement modification factor. ACI-ASCE Committee 352[8] has also adopted some recommendations for the development of hooked bars in exterior joints. Two types of joints are distinguished in these recommendations: (1) Type 1 joints, connecting members which are not designed 135 to undergo significant inelastic deformations; and (2) Type 2 joints, connecting members which will be subjected to deformation reversals in the inelastic range. For Type 1 joints, the development length ( Q“) of #11 and smaller bars is suggested to be computed as follows: - 1,0,“) 460'“) hi , 50V] C(psz) - LUMP“) db (mm) 4571' ,(MPa) (5'4) dh The modification factor suggested by ACI-ASCE Committee 352 for Equation (5.4) by in conditions with sufficient cover, sufficient confinement or excessive reinforcement are identical to the ones suggested by ACI 318-83 for Equation (5.2). The final development length according to ACI-ASCE Committee 352 should not be less than 8db or 152.4 mm (6 in.). For Type 2 joints, the development length recommended by the ACI-ASCE Committee 352 for 90-deg standard hooks (which should be located within the confining reinforcement) is: a 1.0“”) 450'") I“- 75;] JP“) 0: f,(MPa) d. (in.) 1,, - W- I AMP“) (5.5) where, c: is greater than 1.25 and accounts for the possibility 136 of actual yield strength being more than the specified value and also the strain hardening of steel. A multiplication factor of 0.8 is suggested for confining reinforcement spaced at 3 times or less the bar diameter. The final development length again can not be less than 8 d, or 152.4 mm (6 in.). Equation (5.4) suggested by ACI-ASCE Committee 352 for Type 1 joints is less conservative than the ACI 318-83 recommendations, and the one given by Equation (5.5) is comparable to that of ACI 318-83. Reference 28 has examined the accuracy of equation similar to those of ACI 318-83 (Equation 5.2), and has concluded that the ACI 318-83 suggestions for development length of hooked bars are on the conservative side. Reference 3 has examined the accuracy of ACI 318-83 recommendations (Equation 5.3) for development length of hooked bars in seismic-resistant exterior joint. A satisfactory anchorage according to Reference 3 must not fail when subjected to cyclic end displacements as large as 10 times the yield displacement. Further, the anchorage slippage associated with cyclic loads should not cause a significant loss of the energy dissipation capacity of the joint. The experimental and analytical studies of Reference 3 indicated that Equation (5.3) provides a reasonable basis for calculating the development length of 90-deg hooked bars in seismic-resistant exterior joints, as far as the value of a'in the equation is increased to 1.4 (the minimum recommended value of 1.25 can be used if the actual stress-strain properties of 137 bars are available to justify this value). Reference 3 also suggests, based on exterior joint cyclic test results, that 90- deg standard hooks in the confined condition of seismic- resistant exterior joints work as good in compression as they do in tension. Another recommendation of Reference 3 is that, in seismic-resistant exterior joints, if the top reinforcing bars terminate 90-deg standard hooks and their total area is greater than that of bottom bars, then 90-deg standard hooks are not necessary for the bottom bars, a priori, for bond considerations. Removal of the mandatory need for bottom bar hooks can relieve the congestion of reinforcing bars in connections. Top bar hooks are, however, needed for the development of shear resistance mechanism at exterior joints, and their removal is suggested in Reference 3 to be inappropriate even when there is adequate anchorage. 5.6 SUMMARY AND CONCEUSION A review of the literature on the overall behavior of exterior joints, anchorage conditions of hooked bars in these zones, the applications of steel fibers to exterior beam-column connections has been presented. The discussion on overall joint behavior covers the process of cracking in exterior joints under inelastic cyclic loads. The factors influencing the hysteretic behavior of exterior joints are also reviewed. 138 In the review of hooked bar pull-out behavior at exterior joints, the mechanisms providing resistance against pull-out are described and the process of anchorage failure is presented. Factors influencing the pull-out behavior of 90-deg standard hooks on exterior joints are also reviewed. The analytical models proposed for predicting the pull-out behavior of hooked bars at exterior joints are presented. The benefits resulting from steel fiber reinforcement of exterior joints are presented. The effects of steel fibers on hysteretic performance of joint with different loading conditions, reinforcement configurations and geometric conditions, as revealed by previous experiments, are reviewed. This chapter concluded with a presentation of design recommendations for anchorage of standard hooks. The experimental verification studies on the applicability of these anchorage design guidelines on the exterior joints are also reviewed. EXPERIMENTAL INVESTIGATION OF HOOKED BAR BEHAVIOR: EFFECTS OF FIBER REINFORCEMENT AND NUMBER OF BARS 6.1 INTRODUCTION This phase of research dealt with the effects of two important factors on the pull-out behavior of 90-deg standard hook from exterior joints: the number of bars being pulled out, and steel fiber reinforcement. Very limited test data have been reported in the literature to quantify the effects of these important factors. An exrimental study was undertaken in this research to assess the differences in pull-out behavior of single and multiple hooked bars from typical seismic-resistant exterior joints, and also to evaluate the effects of substituting transverse hoops with steel fiber in seismic-resistant joints. 6.2 EXPERIMENTAL PROGRAM 139 140 The specimens tested in this study with one, two and three grade 60, #8 hooked bars are shown in Figures 6.1(a), 6.1(b) and 6.1(c). Test results on specimens similar to the one shown in Figure 6.1(b) have been reported in Reference 37. The connection was confined either by transverse hoops according to ACI 318-83[6] (requirements for high-risk seismic zone), or by a combination of transverse hoops and steel fibers. As shown in Figure 6.1, the straight lead embedment of hooked bars was covered by a plastic tube. This eliminated the bond resistance along straight embedment length. Pull-out forces were thus resisted only by the 90-deg standard hook. A plastic sheet was placed horizontally at the level of straight lead embedment length across the width of the specimen along the lead length to generate an artificial splitting crack. This crack would have been produced by bond stresses along the straight embedment length, if this bond was not eliminated. The reinforcement cages of typical specimens with one and two bars are shown in Figures 6.2(a) and 6.2(b), respectively. The compression zone of the beam-column interface was simulated with a steel plate pushed against column face. Type IA portland cement and aggregates with a maximum particle size of 19.1 mm (0.75 in.) were used in the concrete mixes of this experimental study. In the fibrous mixes, a fraction of portland cement was substituted with Type F fly ash (see Table 6.1 for the properties of this fly ash which were obtained from the Lansing Board of Water and Light). A 141 superplasticizer[43] was also used in the fibrous mixes. The steel fibers used in this study were straight-round with length of 51 mm (2 in.) and a diameter of 0.89 mm (0.035 in.), having an aspect (length-to-diameter) ratio of 57. All the reinforcing bars used in this experimental investigation were grade 60, and the average of their actual yield strengths measured in tension tests was 524.4 MPa (76 ksi). The plain concrete and fiber reinforced concrete mix proportions used in this study are shown in Table 6.2, which also presents the inverted slump cone time (a measure of the workability of fibrous mixes which decreases as workability increases)[44] and compressive strength of concrete mixes. The compressive stress-strain relationships for the fibrous concrete used in this study are shown in Figure 6.3. 'F‘ u a fl; “‘1...“- n 0 iv — ck: v.12: ::-.-:: in l- . , I o d?.-:.-.-.-.-.-.-.-.-.::.*;'.a / u ' ‘23-.- ::.-:::::z “1:?- «VI-- I ' I eggs-can: : - rs: : e‘ I . o _ H *‘ a... o e I - - - :L‘.‘a-‘.'.'¢.fi u u. oooooooooo . . p 4 -.....z‘... ...? F“ . 4 H lea-.51.: 3:: 3:1... u 6. ' - - - svssssxgfi I I _L e L '.-.-.-.°:.°:::: :.-.:m I $9."; r.- ::.".'.-.-:::'.'e I | . . _ l “- fist-.1: :: used. 7 m I Q L‘ T z/_.... “A. I u 1... l (a) Single Bar Pull-Out Figure 6.1 Hook Test Specimens (cont'd). 142 ' COLL. I“ ‘ I — c.‘::-.-.:::-...iz~ ‘- ' l '0 ('5'- .‘....'.°.’.:.."'; / u ”" .1. T. _ (tr. :..-...:::-.s-.e~ ‘ I I .0 ea- 0. .... 3“. t' - , —fl ‘, ll 1e. t :.-.-:-.-::.':: ; . 0 _L .-.-:.-:- :. :. :. ...? . ‘rr--.--.-.--I‘.I. _ ’ K.- (.731: :z: ::.°.'.;:$ 7 m 1; o I‘ L TflHCM (b) Double Bar Pull-Out _1 M 'L; n u" f u as: I 0 l q #4. - :-.-. . : 32'... as l- 0 . C O ............ l 3 . ('1‘ ............. :5? /' ' “' dim-savages: 1:0 ‘ I . I q$ :t'.‘.': z -'.-: z s} o ' - —~ 4, ‘ es .. - . 1 ' ' | 1| A. e c s a s u.1.-.v::¢p l I O A .-:.-.°.°.: : 3" ‘ ‘un . ' ' 2. LI. 2 i l - #3:... 23:: :::a J- .-. :.-.-.-.-.-:.°.':: (c) Triple Bar Pull-Out Figure 6.1 Hook Test Specimens. 143 '3i i :53 . . u . _... r-. a» --..eurw.“ (a) Single Hooked Bars Figure 6.2 Reinforcement Cages of Typical Hook Test Specimens (cont’d). 144 (b) Double Hooked Bars Figure 6.2 Reinforcement Cages of Typical Hook Test Specimens. 145 Table 6.1 Properties of Fly Ash Silica, Si02 47.0 Alumina, Al203 22.1 Chemical Iron, F6203 23.4 Composition Tatanium, T i02 1.1 (% by weight) Calcium, 000 2.6 Magnesium, M90 0.7 Potassum, K 20 2.0 Carbon, 0' 4.3 #30 (0.6mm=600microns) 100 Gradation (% passing) #200 (0.07 4mm=74microns) 92 #325 (0.045mm=45microns) 84 0.020mm=20microns 0.010mm=10microns 0.005mm=5microns 63 36 17 Note: Specific Gravity = 2.245 Table 6.2 Mix Proportions of Plain and Steel Fiber Reinforced Concrete Mixes (1 psi=0.0069 MPa). Inverted Concrete ———W 3+0 3- ———SP ————F Vf Slum Co (0+1?) (0+1?) 0 (0+1?) (C+F) 1’ “‘9‘ (%) Cone Time Strength 0.6 3.5 1.0 0.0 0.0 0.0 -- 28.3 (W8) 0.5 4.0 1.0 0.005 0.3 1.0 10 (sec.) 36.0 (MPa) 0.5 4.0 1.0 0.005 0.3 2.0 15 (sec.) 41.9 (MPa) Note:W=water; =cement; F=fly ash; S=fine aggregate; G== coarse aggregate; SP=liquid superplasticizer; and Vf=fiber volume fraction. 146 20% STRESS (MP0) + --- W-OZ — w-zx --- W-LX T rs r 0.010 _rfir . . e f . 0.000 0.005 0.015 STRNN Figure 6.3 Compressive Stress-Strain Relationship of the Plain and Fibrous Concrete. The specimens were moist-cured inside their molds at 72 deg F and 100% relative humidity for 7 days before being demolded and exposed to the regular laboratory environment. The specimens were tested at the age of 28 t 2 days. Table 6.3 presents a summary of the test program performed on hooked bar anchored in conventional and fibrous reinforced concrete specimens. Information on the number of hooked bars, lateral confinement and fiber volume fraction are given in this table. The confinement provided in conventional specimens 1 and 2 of Table 6.3 satisfied the requirements of ACI 318-83[6] for seismic-resistant beam-column connections. The confinement reinforcement of specimens 1 and 2 was substituted with steel 147 fiber reinforcement in specimens 4, 5, 6 and 7. Specimen 3 was confined by both the conventional hoops and fibers at relatively high ratios, in order to investigate the convined confining effects of these two reinforcement techniques. Specimens 8 and 9 together with specimens 1 and 2 were designed to provide information on the effects of the number of hooked bars on their pull-out behavior. Table 6.3 Test Program on Hooked Bars in Conventional and Fibrous Specimens Hooked Lateral Fiber Volume Specimen Reference Bars Confinement Fraction 1 Author 3#8 #3@76mm (#‘3@3in,) 0% 2 Author 3% #3@76mm (#3@3in.) 0% 3 Author 3#8 #3@7 6mm (#3@3in.) 2% 4 Author 3#8 #3@102mm (#3@4in.) 2% 5 Author 3#8 #3@152mm (#3@6in.) 2% 6 flhnhor 3#$ ' 296 7 Author 3#s #3@152mm (#3@6in.) 1% 8 Author 1#8 #3@7 6mm (#3@3in.) 0% 9 Author l#8 #3@7 6mm (#3@3in.) 0% 10 18 2413 #3@76mm (#3@3in.) 0% 11 18 23% #3@7 6mm (#3@3in.) 0% 148 The test data generated on hooked bars in this study actually complement those reported in Reference 37 on the pull- out behavior of two hooked bars from conventional reinforced concrete joints (Figure 6.1b). Table 6.3 also presents information on the test specimens of Reference 37 the results of which were used in this study (specimens 10 and 11 in Table 6.3). Figure 6.4 presents the test set-up used in this study. Two hydraulic actuators bearing on the concrete column applied the pull-out force. The load was measured by two load cells located on the actuators. Two electrical displacement transducers were installed on each anchored bar at 102 mm (4 in.) from column face. The pull-out displacements at the end of hook bends (point A in Figure 6.4) were obtained by substracting the extension of anchored bar between point A and displacement transducer (measured in tension tests of bars) from the average measurement of two transducers. Loading was monotonic and quasi-static, applied in a displacement- controlled manner. The experiment was continued until the observation of extensive cracking in specimens and large pull- out displacements. The load cells and displacementtransducers used in this study had maximum error of less than 1% the measured values. 6.3 EXPERIMENTAL RESULTS Pull-out of multiple (two or three) hooked bars from the 149 Il ” 5.5in. -------. -------- ---.‘ \\ . ‘\ .....m TRANSDUCERS manor‘ C. HYDRAULIC ACTUATOR )—.. LOAD CELL I CLAMP I 1’ / 71— 40 in. Figure 6.4 Test Set-Up and Instrumentation. 150 conventional confined concrete specimens simulating exterior joints resulted in the damage process described below: (1) Radial splitting cracks appeared at the exit on the face of specimens (Figure 6.5a), noting that the splitting cracks normal to hooked bar planes were generated artificially by the placement of a plastic sheet inside the specimen. The radial splitting cracks in the hooked bar plane on the other hand seem to have been generated by the bearing of the hook bend against concrete; (2) Cracks appeared on the sides of specimens, extending along the hooked bars, with a tendency to seperate the concrete inside the hook bend from the remainder of the specimen block (Figure 6.5b): and (3) The confined concrete specimens expanded laterally under the increasing pressure of the hook bend, which resulted in spalling of concrete cover (Figure 6.5c). At the same amount of confinement, the extent of cracking and damage in specimens with three hooked bars was observed to be more serious than specimens with two hooked bars (compare the appearance after failure of the three-bar specimen No. 1 of Table 6.3 in Figure 6.6a with that of the two-bar specimen No. 10 of Table 6.3 in Figure 6.6b). In the conventionally confined specimens 8 and 9 of Table 6.3, with a single hooked bar, only minor cracks appeared at the bar exit point or on the sides of specimens, as shown in Figure 6.6(c). The hooked bars in these specimens could not be pulled out, and yielding of anchored bars always dominated the failure of single-bar 151 (a) Radial Cracks Figure 6.5 Conventionally Confined Specimens under Multiple Hooked Bar Pull-Out (cont’d). 152 (b) Side Cracking Figure 6.5 Conventionally Confined Specimens under Multiple Hooked Bar Pull-Out (cont’d). 153 (c) Spalling of Concrete Cover Figure 6.5 Conventionally Confined Specimens under Multiple Hooked Bar Pull-Out. 154 (a) Three Hooked Bars Figure 6.6 Cracking in Specimens with Different Number of Hooked Bars (cont’d). 155 (b) Two Hooked Bars Figure 6.6 Cracking in Specimens with Different Number of Hooked Bars (cont’d). 156 (c) one Hooked Bar Figure 6.6 Cracking in Specimens with Different Number of Hooked Bars. 157 specimens under pull-out forces. Comparison of the crack intensities in specimens with different number of hooked bars clearly indicates that the increase in the number of closely spaced hooked bars adversely influences anchorage conditions in exterior joints. ' The fibrous concrete specimens (No. 3 to 7 in Table 6.3) showed much less cracking and significantly better anchorage conditions under pull-out forces, when compared with comparable conventional specimens. The first cracks which appeared in fibrous specimen where the radial one at the bar exit points, and were sometimes followed by cracks appearing on the sides of specimens extending along hook bends. No significant widening of these cracks or lateral expansion of specimens where observed in book pull-out tests of fibrous specimens. Except in one case with low fiber volume fraction and no lateral confinement (specimen No. 6 in Table 6.3) shown in Figure 6.7(a), failure of anchored bar was dominated by bar yielding with minor anchorage damage. The typical comparison between the crack intensities after failure of specimen No. 6 of Table 6.3 with fiber and no lateral confinement shown in Figure 6.7(a), and specimen No. 1 of Table 6.3 without fibers but with a large confining reinforcement ratio shown in Figure 6.7(b) is indicative of effectiveness of steel fibers enhancing the anchorage conditions of hooked bars at exterior joints. The hook pull-out force-displacement relationship for conventional reinforced specimens with different number of anchored bars (specimens 1, 2, 8, 9, 10 and 11 in Table 6.3) 158 are shown in Figure 6.8a. This figure clearly indicates that the anchorage conditions in similar specimens are adversely affected by the increase in number of hooked bars being pulled out. While the single-bar specimens fail dominantly by yielding of the anchored bar, those with double- and triple-bar pull-out fail mainly due to anchorage loss. Strength and ductility of the hooked bar pull-out behavior are observed to drop with the increase in number of bars. It seems appropriate to modify current hooked bar anchorage design requirements to account for the important effects of the number of hooked bars on anchorage performance. The effects of fiber reinforcement on pull-out force- displacement relationships in triple-bar specimens (No. 1 through 7 in Table 6.3) are shown in Figure 6.8b. All the fiber reinforced specimens, even the one with no transverse hoops, are observed to have higher strength and better ductility than the non-fibrous specimens with conventional confinement. In all the fiber reinforced specimens, the pull- out force practically reached the anchored bar yield force. In the confinement condition with #3 transverse hoops @ 6 in. (152 mm) spacing, only a slight drop in pull-out resistance is observed when the fiber volume fraction is reduced from 2% to 1%. There is also a relatively small drop in pull-out resistance when the transverse hoop spacing is increased at a constant fiber volume fraction. No significant effect of fiber reinforcement on the initial pulleout stiffness could be observed. 159 (a) Fibrous Specimens Figure 6.7 Cracking of Fibrous and Conventionally Confined Specimens (cont’d). 160 (b) Conventionally Confined Specimens Figure 6.7 Cracking of Fibrous and Conventionally Confined Specimens. FORCE (kN) Figure 6.8 Hook Pull-Out Force-Displacement Relationship 400 161 S ‘1’ L N O O l A .A O O l L - — -' u- .- = = = 2" — - '- ,-;-- 1 ,’ ’I I /\ - /. /§\ /./ * V‘Fzz‘f°~0__e—e—e~e_.q. . _e—e‘.~. /./ ‘o‘~.~. Triple-Ber Specimens -— Double—Ber Specimens - - Single-Ber Specimens (Anchored Ber YieldingL" r T ' r r r v 1 1 . 0 3 6 9 12 DISPLACEMENT (mm) + 15 (a) Specimens with Different Number of Bars (cont'd). 162 500 -— rk>Cbmmeemu(xmflnen«M:VTezz « ..- I3.76rnm(31n): w-ox (Avg. of Two Specs) .1 -- [3.76mm01n): Vf-ZX (Anchored Ber Yielding) 400 —— f3.101mm(4in): w-zz (Anchored Ber Yielding) J -—— I3.152rnm(61n): VIE-22 A —.- f3.152rnm(61n):Vl‘-12 z 35"" x 3004 ....-.—-—- - -°"' “1 v -""‘“""'-”—- LIJ ’-_- ______ ~‘~ o \\ gzma \I“ 1.1. --------------- 100- 0 1 r r T r f _f r n m 0 :5 6 9 12 15 DISPLACEMENT (mm) (b) Specimens with Different Fiber Volume Fractions and Confinement Conditions Figure 6.8 Hook Pull-Out Force-Displacement Relationship. .‘1‘V- m“ .I t! .uI e... '3‘.‘. ...- 1 163 The above discussions on the effects of fiber reinforcement on hooked bar pull-out behavior are indicative of the potentially significant performance and economic advantages of using steel fibers in exterior'beam-column connections. The reduction in transverse steel area resulting from fiber reinforcement also leads to reduced congestion of steel fibers in the joint area, which is an important factor in improving the practicality of joint congestion. 6.4 SUMMARY AND CONCLUSIONS An experimental study was performed on the pull-out behavior of 90-deg standard hooks from exterior beam-column connections. The effects of the number of hooked bars and fiber reinforcement of joint area were investigated. It was concluded that: (1) Under the pull-out action of hooked bars, the damage and cracking of joint area tends to be more extensive as the number of hooks pulling out from a joint increases; (2) Substitution of the transverse column (confining) reinforcement with steel fibers at the joint region effectively reduces the extent of cracking in exterior joints caused by pull-out of hooked bars: (3) The pull-out strength and post-peak ductility of hooks are adversely influenced by the increase in number of hooks pulling out from an exterior joint. Current hooked bar (4) 164 anchorage design guidelines may be improved by considering the effect of the number of hooked bars on anchorage conditions at exterior joints; and The strength and ductility of hooked bars under pull-out forces are positively influenced by substituting the conventional confining reinforcement.of exterior joints with steel fibers. Application of steel fibers to exterior joints seems to be an effective technique for improving the anchorage conditions of hooked bars, and also for reducing the congestion of reinforcement in beam- column connections. CHAPTER 7 SUMMARY AND CONCLUSIONS An integrated experimental-analytical study was performed on the anchorage of beam longitudinal reinforcement at interior and exterior beam-column connections in reinforced concrete frames. The objectives of this research were to (a) generate test data on those aspects of anchorage behavior which were not sufficiently investigated in the past but were decided, based on a comprehensive literature review performed in this study, to .have important effects on the anchorage performance characteristics, (b) develop analytical models for predicting the pull-out behavior of straight and hooked anchored bars from confined concrete joints, and (c) improve the current anchorage design equations using experimental and analytical data generated in this study. The research project was performed in three phases: (1) experimental investigation of the local bond between deformed bars and confined concrete; (2) analytical evaluation of straight bar anchorage design equations; and (3) experimental 165 166 investigation of hooked bar anchorage behavior. A summary of these phases of research program together with conclusions derived at each phase are presented below.‘ (1) Experimental Investigation of the Local Bond of Deformed Bars to Confined Concrete: The effects of anchored bar diameter, concrete compressive strength and confinement level on the local bond stress-slip relationship of deformed bars in confined concrete were assessed using monotonic test data on bars of different diameters partially embedded inside the confined core of concrete block specimens. These test specimens simulated the anchorage conditions inside the confined core of beam- column connection. The test data indicated that: (a) The ultimate local bond strength decreases as the bar diameter increases. The drop in bond strength is a linear function of bar diameter. There is also a slight increase in the local bond pre-peak tangent stiffness (especially near the peak bond strength) as the bar diameter decreases, but the post-peak local bond resistance, especially at larger inelastic deformations, is less influenced by the anchored bar diameter: (b) The ultimate local bond strength increases almost proportionally with the square root of the concrete compressive strength. The pre-peak tangent stiffness of local bond also increases slightly with increasing 167 compressive strength of concrete. In the post-peak region, however, the effect of concrete compressive strength on local bond behavior tends to diminish: (c) The characteristic bond slip values (e.g. that corresponding to the peak bond stress) are largely independent of the bar diameter and concrete compressive strength: and (d) Confinement of concrete by transverse reinforcement does not directly influence the local bond behavior of deformed bars in the condition of beam-column connections, where the vertical column bars are usually sufficient to restrain the widening of bond splitting cracks. If the bond splitting cracks can not be restrained by the column vertical reinforcement, upon split cracking a sudden failure takes place which significantly reduces the ultimate strength and post- peak ductility of local bond. ( 2) Analytical Evaluation of Straight Bar Anchorage Design Equations: An analytical study was performed to assess the pull-out behavior of straight reinforcement bars anchored in exterior beam-column connections. The bonded bar model used in this study accounts for the effects of bar diameter, clear spacing and yield strength, concrete compressive strength and column pressure on local bond characteristics in the confined conditions of exterior joints. The analytical model was positively verified (3) 168 against the results of pull-out tests on straight bars embedded in confined concrete. The analytical technique was used to evaluate the current design guidelines for development length of straight reinforcement bars in exterior joints. The results indicated that some reductions can be made in current requirements without adversely influencing the strength and ductility of anchorage behavior. Experimental Investigation of Hooked Bar Anchorage Conditions: An experimental study was performed on the pull-out behavior of 90—deg standard hooks from exterior beam-column connections. The effects of the number of hooked bars and fiber reinforcement of joint area were investigated. It was concluded that: (a) Under the pull-out action of hooked bars, the damage and cracking of joint area tends to be more extensive as the number of hooks pulling out from a joint increases: (b) Substitution of the transverse column (confining) reinforcement with steel fibers at the joint region effectively reduces the extent of cracking in exterior joints caused by pull-out of hooked bars: (c) The pull-out strength and post-peak ductility of hooks are adversely influenced by the increase in number of hooks pulling out from an exterior joint. Current hooked bar anchorage design guidelines may be improved 169 by considering the effect of the number of hooked bars on anchorage conditions at exterior joints: and (d) The strength and ductility of hooked bars under pull- out forces are positively influenced by substituting the conventional confining reinforcement of exterior joints with steel fibers. Application of steel fibers to exterior joints seems to be an effective technique for improving the anchorage conditions of hooked bars, and also for reducing the congestion of reinforcement in beam-column connections. The effects of anchored bar diameter, concrete compressive strength and confinement level on the local bond stress-slip relationship of deformed bars in confined concrete were assessed using monotonic test data on bars of different diameters partially embedded inside the confined core of concrete block specimens. 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