ABSTRACT. KIM, SUNGJOONG. Behavior of High-Strength Concrete Columns. (Under the direction of Dr. Sami Rizkalla.)

Transcription

1 ABSTRACT KIM, SUNGJOONG. Behavior o High-Strength Conrete Columns. (Under the diretion o Dr. Sami Rizkalla.) The use o high-strength onrete or bridges and high-rise buildings has beome popular due to development in onrete tehnology and availability o various types o mineral and hemial admixtures. High-strength onrete ould lead to smaller member sizes or ompression members and thereore provide onsiderable savings assoiated with material osts and redution o dead loads. However, Most o the urrent design odes, suh as AASHTO-LRFD Bridge Speiiations, are still based on tests onduted using normalstrength onrete. Many studies indiate that the behavior o olumns with high-strength onrete is dierent rom that o normal-strength onrete. The experimental phase o this investigation onsists o thirty two retangular and twenty our irular olumns subjeted to onentri and eentri loading onditions to investigate the behavior o high-strength onrete olumns. The main variables onsidered in this study were onrete strength ranging rom 7.9 to 16.5 ksi, shape o ross setion, and longitudinal and transverse reinorement ratios. Using the test results o this study and other researhes in literature, the dissertation provides design equation to predit the apaity o high-strength onrete olumns with tie and spiral reinorements subjeted to onentri and eentri loading onditions up to 18 ksi. The researh also proposes a new stress-strain relationship o high-strength onrete onined with spiral reinorements.

2 BEHAVIOR OF HIGH-STRENGTH CONCRETE COLUMNS by SUNGJOONG KIM A dissertation submitted to the Graduate Faulty o North Carolina State University In partial ulillment o the Requirements or the Degree o Dotor o Philosophy CIVIL ENGINEERING Raleigh, North Carolina May 2007 APPROVED BY : Dr. Sami Rizkalla Chair o Advisory Committee Dr. Paul Zia Dr. Amir Mirmiran Dr. Emmett Sumner

3 부모님께이논문을바칩니다. Dediated to my parents ii

4 BIOGRAPHY Sungjoong Kim reeived his Bahelor o Siene degree in 1997 in Civil Engineering rom Chung-Ang University, Seoul, Korea. He also reeived his Master o Siene degree rom the same University in 2000, on the topi o A Study on Deteting the Loation o Strutural Damage Using Modal Analysis under the supervision o advisor Dr. Ki-Bong Kim. Following the ompletion o this degree, Sungjoong then moved to the United States to ontinue his aademi pursuits at North Carolina State University under the supervision o Dr. Sami Rizkalla studying the behavior o high-strength onrete members. iii

5 ACKNOWLEDGMENTS I would like to kindly aknowledge the sponsors o this projet, the Amerian Assoiation o State Highway and Transportation Oiials in ooperation with the Federal Highway Administration. I would also like to thank the Transportation Researh Board o the National Researh Counil who administered National Cooperative Highway Researh Program Projet It is with sinere gratitude that I thank my advisor and mentor, Dr. Sami Rizkalla, or his patiene and guidane throughout my dotoral work. It is truly an honor to work with him who is willing to share his wealth o knowledge and his extensive personal experiene or over our years. I would like to thank Dr. Paul Zia or all his invaluable advie and omments. He not only aught many errors and awkward expressions but enouraged me to think about the idea as a distinguished sholar. Thanks are also extended to Dr. Amir Mirmiran and Dr. Rudi Seratino or being members o my advisory ommittee. I would like to express my gratitude to the personnel o the Construted Failities Laboratory, Mr. Jerry Atkinson, Mr. William Dunleavy, Mr. Lee Nelson, Mr. Greg Luier, and Mrs. Amy Yonai or all o their assistane. I also reognize the graduate students, inluding Cenan Mertol, who were part o the researh team investigating behavior o high-strength onrete members. I would like to give partiular thank to Proessor Chan Ki Jeon at Inheon City College or tremendous help in the laboratory during his stay at North Carolina State University. iv

6 Finally, I would like to thank my parents and brother or their support and endless love. This study would never have been ompleted without the unonditional support and enouragement o my amily. v

7 TABLE OF CONTENTS LIST OF TABLES... ix LIST OF FIGURES... x LIST OF SYMBOLS... xiv CHAPTER 1 INTRODUCTION General Deinition and Properties o High-Strength Conrete Objetive and Sope Organization o Dissertation... 5 CHAPTER 2 LITERATURE REVIEW General Researh on Normal-Strength Conrete Columns Researh on High-Strength Conrete Columns Ahmad and Shah (1982) Martinez, Nilson, and Slate (1983, 1984) Yong, Nour, and Nawy (1988) Bjerkeli, Tomaszewiz, and Jensen (1990) Nagashima, Sugano, Kimura, and Ihikawa (1992) Cusson and Paultre (1994) Ibrahim and MaGregor (1996a, 1996b) Lloyd and Rangan (1996) Foster and Attard (1997) Saatioglu and Razvi (1998) Razvi and Saatioglu (1999a, 1999b) Lee and Son (2000) Liu, Foster, and Attard (2000) Tan and Nguyen (2005) Conlusion Drawn rom Previous Researh Retangular Stress Blok or High-Strength Conrete vi

8 2.5.1 Introdution Stress Blok Parameters in Dierent Design Codes ACI / AASHTO LRFD Speiiations CSA A Provisions NZS Provisions CEB-FIP Model Code Proposed Stress Blok Parameters by NCHRP Program Conined Conrete Strength by Spiral Reinorement Introdution Previous Work Stress-Strain Relationship o Conined Conrete by Spiral Reinorement Introdution Existing Models CHAPTER 3 EXPERIMENTAL PROGRAM General Details o Test Speimens Retangular Columns Cirular Columns Column Identiiation Casting o Columns Material Properties Conrete Steel Instrumentation Test Set-up Conentrially Loaded Columns Eentrially Loaded Columns CHAPTER 4 TEST RESULTS Conentrially Loaded Retangular Columns Conentrially Loaded Cirular Columns Eentrially Loaded Retangular Columns Ultimate Conrete Strain vii

9 CHAPTER 5 ANALYSIS OF TEST RESULTS Introdution Axial Compressive Strength o Columns Retangular Columns with Tie Reinorement Cirular Columns with Spiral Reinorement Nominal Axial Resistane o Columns Column Dutility Energy Dutility o Column Eets o Test Parameters Setion geometry Conrete ompressive strength Amount / spaing o transverse reinorement Longitudinal reinorement ratio Retangular Stress Blok o High-Strength Conrete Conined Conrete Strength by Spiral Reinorement Comparison between Preditions and Experimental Data Analysis o Conined Conrete Strength in Terms o the Mohr-Coulomb Failure Criterion Minimum Requirement o Spiral Reinorement Proposed Stress-Strain Relationship o Conined Conrete by Spiral Steel CHAPTER 6 SUMMARY AND CONCLUSIONS Summary Conlusions Future Researh REFERENCES TABLES FIGURES APPENDIX viii

10 LIST OF TABLES Table 1 Comparison o dierent retangular stress blok parameters Table 2 Details o onentrially loaded retangular olumns Table 3 Details o eentrially loaded retangular olumns Table 4 Details o onentrially loaded irular olumns Table 5 Three mixture designs or target onrete strength 10, 14, and 18 ksi Table 6 Details o ive onrete bathes Table 7 Material properties o reinorements Table 8 Experimental and predited strengths or retangular olumns Table 9 Experimental and predited strengths or irular olumns Table 10 Comparison between maximum measured load and 80 perent o predited load o tied olumns with eentriity o 0.1h Table 11 Comparison o dutility index I 5 with respet to setion geometry Table 12 Comparison o dutility index I 5 with respet to onrete strength Table 13 Comparison o dutility index I 5 with respet to volumetri ratio o transverse steel Table 14 Comparison o dutility index I 5 with respet to longitudinal steel ratio Table 15 Comparison between experimental and predited load using dierent retangular stress blok or eentrially loaded olumns Table 16 Comparison o onined onrete strength between test results and preditions using proposed equation by dierent studies or irular olumns Table 17 Test result o irular olumns with 12 in. dia. setion Table 18 Test result o irular olumns with 9 in. dia. setion Table 19 Test results o irular olumns with dierent volumetri ratios o spiral reinorement. 125 ix

11 LIST OF FIGURES Figure 1 Inluene o onrete strength on shape o stress-strain relationship Figure 2 Generalized and retangular stress blok o ompressive onrete Figure 3 Conrete stress-strain urves o CEB-FIP (1990) Figure 4 Comparison o olumn interation diagrams based on various retangular bloks or dierent onrete strengths Figure 5 Eetively onined ore or irular hoop reinorement (soure : Mander et al. 1988) Figure 6 Proposed stress-strain urve or onined onrete by Chan (1953) Figure 7 Proposed stress-strain urve or onined onrete by Martinez (1983) Figure 8 Proposed stress-strain urve or onined onrete by Saatioglu and Razvi (1992) Figure 9 Reinorement details o retangular and irular olumns Figure 10 Assembled reinorement ages or retangular olumns Figure 11 Proedure o assembling orms or the retangular olumns Figure 12 Assembled reinorement ages or irular olumns Figure 13 Proedure o assembling orms or the irular olumns Figure 14 Casting o olumn speimens Figure 15 Casting o 4 8 in. ylinders Figure 16 Removal o orms Figure 17 Cast olumn speimens Figure 18 Testing o 4 x 8 in. ylinder Figure 19 Grinding end suraes o 4 x 8 in. ylinder Figure 20 Testing o reinoring steel Figure 21 Stress-strain relationship or reinoring steel Figure 22 Vertial and setional loations o strain gauges Figure 23 Loation layout o pi gauges or retangular and irular olumns Figure 24 Testing mahine and data aquisition system Figure 25 Typial test set-up or onentrially loaded olumns Figure 26 Typial test set-up and loading plate bearing assembly or eentrially loaded olumn 147 Figure 27 Axial load-shortening urve or onentrially loaded retangular olumn (14R9-ρ4) Figure 28 Axial load-average onrete strain measured by pi gauges (14R9-ρ4) Figure 29 Axial load-longitudinal steel strain (14R9-ρ4) Figure 30 Axial load-transverse steel (tie) strain (14R9-ρ4) x

12 Figure 31 Comparison between olumns with dierent ratios o longitudinal steel Figure 32 Comparison between olumns with dierent tie spaings Figure 33 Typial ailure shapes o onentrially loaded retangular olumns Figure 34 Inlined shear ailure planes o onentrially loaded retangular olumns Figure 35 Column behavior during dierent stages o loading (14R9-ρ2.5) Figure 36 Load-axial shortening urve or onentrially loaded irular olumn Figure 37 Load-axial average onrete strain measured by pi gauges (14C2-ρ2.5) Figure 38 Load-longitudinal steel strain (14C2-ρ2.5) Figure 39 Load-spiral steel strain (14C2-ρ2.5) Figure 40 Comparison between olumns with dierent spiral spaing Figure 41 Comparison between olumns with dierent ratios o longitudinal steel Figure 42 Inlined shear ailure planes o onentrially loaded irular olumns Figure 43 Spiral rupture, loal bukling o longitudinal steel, and rushing o ore onrete Figure 44 Column behavior during dierent stages o loading (10C1⅜-ρ2.5) Figure 45 Load-axial shortening urves or eentrially loaded retangular olumns Figure 46 Typial ailure shapes o eentrially loaded olumns Figure 47 Axial load-onrete strain measured by pi gauges (10E1) Figure 48 Axial load-longitudinal steel strain (10E1) Figure 49 Axial load-transverse steel (tie) strain (10E1) Figure 50 Strain proile aross setion at peak load or olumns with 9 12 in. setion Figure 51 Strain proile aross setion at peak load or olumns with 7 9 in. setion Figure 52 Eentri olumn behavior during dierent stages o loading Figure 53 Ultimate onrete strain rom eentrially loaded olumns Figure 54 Ratio o P max / P o (based on k = 0.85) with respet to onrete strength Figure 55 Calulated k rom onentrially loaded retangular olumns with respet to onrete strength Figure 56 Comparison o k parameters o onentrially loaded olumns with tie reinorement Figure 57 Comparison o k parameters o onentrially loaded olumns with spiral reinorement Figure 58 Strains o onrete and reinorements or irular olumn (18C2¾-ρ3) Figure 59 Fators promoting over spalling in high-strength onrete olumns Figure 60 Parameter k with respet to ratio A /A g Figure 61 Determination o olumn dutility Figure 62 Eet o setion geometry (retangular olumn vs. irular olumns) xi

13 Figure 63 Interation diagram or retangular reinored onrete olumns Figure 64 Comparison o olumns strength between test results and preditions based on various retangular bloks or dierent onrete strengths (9 12 in. olumns) Figure 65 Comparison o olumns strength between test results and preditions based on various retangular bloks or dierent onrete strengths (7 9 in. olumns) Figure 66 Internal rition theory by Coulomb (1773) Figure 67 Mohr s theory (1900) Figure 68 Mohr-Coulomb riterion with straight line as ailure envelope Figure 69 Normalized Mohr s envelope or irular olumns with 12 in. dia. Setion (10C series) 182 Figure 70 Normalized Mohr s envelope or irular olumns with 12 in. dia. Setion (A10C series) Figure 71 Normalized Mohr s envelope or irular olumns with 12 in. dia. Setion (14C series) 183 Figure 72 Normalized Mohr s envelope or irular olumns with 9 in. dia. Setion (18C and A18C series) Figure 73 Normalized Mohr s envelopes or irular olumns Figure 74 Tri-axial stresses in ore o spiral olumn Figure 75 Idealized axial load-axial shortening behavior o spirally reinored olumn Figure 76 Crak propagation in a normal and a high-strength onrete Figure 77 Conined onrete strength with lateral oninement stress Figure 78 Load-axial shortening urves o onentrially loaded irular olumns with spiral reinorement Figure 79 Proposed stress-strain relationship or onined onrete by spiral reinorements Figure 80 Eet o oninement stress on strain at maximum stress Figure 81 Eet o oninement stress on dutility o onrete Figure 82 Relation between residual strength and produt value o volumetri ratio and yield strength o spiral steel Figure 83 Axial strain at maximum stress o unonined onrete Figure 84 Predition o onrete behavior o irular olumn (14C2-ρ1) Figure 85 Predition o onrete behavior o irular olumn (14C1-ρ1) Figure 86 Predition o onrete behavior o irular olumn (14C2-ρ2.5) Figure 87 Predition o onrete behavior o irular olumn (14C1-ρ2.5) Figure 88 Predition o onrete behavior o irular olumn (14C2-ρ4) Figure 89 Predition o onrete behavior o irular olumn (14C1-ρ4) Figure 90 Predition o onrete behavior o irular olumn (18C2¾-ρ2) Figure 91 Predition o onrete behavior o irular olumn (18C1⅜-ρ2) xii

14 Figure 92 Predition o onrete behavior o irular olumn (18C2¾-ρ3) Figure 93 Predition o onrete behavior o irular olumn (18C1⅜-ρ3) Figure 94 Predition o onrete behavior o irular olumn (18C2¾-ρ4) Figure 95 Predition o onrete behavior o irular olumn (18C1⅜-ρ4) Figure 96 Predition o onrete behavior o irular olumn (A18C1½-ρ2) Figure 97 Predition o onrete behavior o irular olumn (A18C1½-ρ3) Figure 98 Predition o onrete behavior o irular olumn (A18C1½-ρ4) Figure 99 Predition o onrete behavior o irular olumn (A10C2¾-ρ2.5) Figure 100 Predition o onrete behavior o irular olumn (A10C2¾-ρ4) Figure 101 Predition o onrete behavior o irular olumn (10C2¾-ρ1) Figure 102 Predition o onrete behavior o irular olumn (10C1⅜-ρ1) Figure 103 Predition o onrete behavior o irular olumn (10C2¾-ρ2.5) Figure 104 Predition o onrete behavior o irular olumn (10C1⅜-ρ2.5) Figure 105 Predition o onrete behavior o irular olumn (10C2¾-ρ4) Figure 106 Predition o onrete behavior o irular olumn (10C1⅜-ρ4) xiii

15 LIST OF SYMBOLS A A g A s A sp b d d e E E s area o ore onrete o olumn enlosed by out-to-out o spiral or tie. gross area o olumn. area o longitudinal reinorement. area o the spiral steel. width o olumn setion. ohesion. diameter o irular olumn. outside diameter o the spiral. eentriity o applied load. modulus o elastiity o unonined onrete. modulus o elastiity o steel. E se seant modulus o elastiity o onined onrete. axial ompressive strength o onrete speimen. ylinder ompressive strength o onrete. axial ompressive strength o onined onrete. o plain onrete strength in a member. r l onstant residual strength o desending branh in stress-strain urve o onined onrete. lateral oninement stress provided by the spiral reinorement. sp stress in the spiral at maximum olumn load. sy y yield strength o spiral steel. yield strength o longitudinal reinorement. xiv

16 2 h k atual lateral oninement stress provided by the spiral reinorement at maximum axial stress. depth o olumn setion. ratio o the in-plae onrete strength to the ompressive strength o ontrol ylinder. L P P max P CR olumn height. load resistane by onrete. measured maximum load o olumn. load resistane o olumn orresponding to initiation o spalling o onrete over. P o P 1 P 2 P 1 P 2 s w Z nominal axial load apaity o olumn under onentri loading. irst peak load. seond peak load. axial load arried by onrete at the irst peak load. axial load arried by onrete at the seond peak load. spaing o spiral. unit weight o onrete. slope o desending branh o the proposed stress-strain urve o onined onrete. ρ s volumetri ratio o spiral steel. ρs ode minimum required volumetri ratio o spiral speiied by AASHTO LRFD Speiiations or ACI Δ y τ φ θ σ 1 limiting axial shortening in the linear elasti range o the olumn response. shear stress along plane. internal-rition angle o the material. angle o ailure plane. axial stress. xv

17 σ 2 ε lateral stress. onrete strain. ε strain at the maximum stress o onined onrete. ε strain at the maximum stress o unonined onrete. o ε ultimate ompressive strain. u ε strain orresponding to 85 % o the maximum stress o onined onrete on the 85 desending branh. xvi

18 Chapter 1 Introdution Chapter 1 Introdution 1.1 General The use o high-strength onrete or bridges and high-rise buildings has beome very popular due to development in onrete tehnology and availability o various types o mineral and hemial admixtures. High-strength onrete oers many advantages over onventional strength onrete. High-strength onrete ould lead to smaller member sizes or ompression members and thereore provide onsiderable savings assoiated with material osts and redution o dead loads. Lower deletions due to inreased elasti modulus and lower reep provide additional advantages assoiated with improved perormane. Furthermore, due to the superior durability o high-strength onrete, signiiant redution o the maintenane requirements and an inrease in the servie lie o the struture an be ahieved. High-strength onrete was irst reported in Japan. In 1930, a 28-day ompressive strength o 14.8 ksi (120 MPa) was obtained by Yoshida. This result was ahieved by a ombination o pressing and vibrating proesses without the use o any hemial and mineral admixtures. In the 1960s, superplastiizers were developed in Japan and Germany as eiient hemial 1

19 Chapter 1 Introdution admixture. With the use o superplastiizers, it beame possible to derease the water to ement ratio while maintaining the workability o the onrete. In the 1970s, the ombined use o superplastiizers and ultra-ine materials suh as silia ume and inely ground blast urnae slag were studied and applied to onrete strutures. Sine the mid-1980s, the highstrength onrete has been widely used in both preast and ast-in-plae onstrution or either reinored or prestressed onrete members. However, most o the urrent design speiiations, suh as AASHTO LRFD Bridge Speiiations, are still based on tests onduted using normal-strength onrete. The AASHTO LRFD Bridge Speiiations, irst published in 1994 limits its appliability to maximum onrete strength o 10 ksi (69 MPa), unless physial tests are made to establish the relationship between onrete strength and its other properties. These limitations releted the lak o researh data at the time, rather than the inability o the material to perorm its intended untion. Thereore, it is neessary to examine the behavior o strutural members with high-strength onrete in order to extend its use or high-strength onrete. 1.2 Deinition and Properties o High-Strength Conrete The deinition o high-strength onrete varies with dierent ountries and time. There is no standard riterion o strength required or high-strength onrete. In the 1950s, onrete with ompressive ylinder strength o 5 ksi (34 MPa) was onsidered as high strength. This limiting value has inreased with time. In 1992, ACI Committee 363 deined it as a onrete strength o 6 ksi (41 MPa). On the other hand, in the FIP/CEB (1990) state-o-the-art report, 2

20 Chapter 1 Introdution high-strength onrete is regarded as onrete having a ompressive strength beyond 8.7 ksi (60 MPa). More reently, ompressive strengths approahing 20 ksi (138 MPa) have been used in ast-in-plae buildings. Conrete ompressive strength higher than 10 ksi (69 MPa) is reerred to as high-strength onrete in this study. The main omponents o both normal strength and high-strength onrete are the same, i.e., ement, water, and aggregates. For high-strength onrete, however, admixtures suh as silia ume, superplastiizer, and supplementary ementing materials are usually added. The admixtures improve the dispersion o ement in the mix and produe workable onrete with muh lower water-ement ratio. The resulting onrete has a lower void ratio and is stronger than normal onrete. The material properties o high-strength onrete dier rom those o normal strength onrete in many ways. As this has been reported elsewhere in detail, only seleted eatures are summarized below. Higher onrete strength; Higher elasti modulus, i.e., greater stiness; Higher tensile strength, even i not proportionally as muh as the inrease in ompressive strength; Inrease in the strain at maximum stress Steeper desending part o stress-strain urves 3

21 Chapter 1 Introdution More brittle ailure A omparison o the stress-strain urves or a range o onrete strengths is shown in Figure Objetive and Sope The main objetive o this study is to investigate the behavior o olumn members with highstrength onrete through experimental and analytial researh. The study inluded testing o 32 retangular and 24 irular olumns with target onrete strengths o 10, 14, and 18 ksi (69, 97, and 124 MPa), subjeted to onentri and eentri axial ompression. The olumns investigated in this study an be lassiied as short olumns, whih is unaeted by slenderness eets. The test results together with extensive data reported in the literature were analyzed. The speii objetives are outlined below. 1. Determine the axial resistane o olumns with high-strength onrete under onentri and eentri ompression. 2. Evaluate the eet o testing parameter, i.e., setion geometry, the amount o the transverse reinorement (tie and spiral), and longitudinal reinorement ratio on strength and dutility o olumns with high-strength onrete. 3. Use the onlusion o this study to develop reommended revisions to extend the urrent ompression design provisions o the LRFD Speiiations (2004) to inlude onrete ompressive strengths up to 18 ksi (124 MPa). 4

22 Chapter 1 Introdution 1.4 Organization o Dissertation This dissertation onsists o seven hapters. Chapter 1 serves as an introdution, outlines the deinition and properties o high-strength onrete, ollowed by the objetive and sope o this study. Chapter 2 presents an extensive literature review o the previous works on normal and high-strength onrete olumns. The retangular stress blok parameters in dierent design odes are summarized. It also inludes a detailed review o the analytial model or onined onrete. Chapter 3 explains the experimental program. A desription o test speimens, abriation o speimens, instrumentation, and test set-up is provided in this hapter. Chapter 4 presents test results obtained rom the olumn speimens. The analytial work perormed based on test results in this study ombined with other reported data in the literature is presented in Chapter 5. It inludes strength preditions or high-strength onrete olumns under onentri and eentri loading onditions, and investigates the eet o test parameters on olumn dutility. The veriiation o the existing analytial model or onined onrete and the development o a new model or stress-strain relationship are also presented. Finally, Chapter 6 summarizes the indings and onlusions. 5

23 Chapter 2 Literature Review Chapter 2 Literature Review 2.1 General Researh into the behavior o normal-strength onrete olumns under axial load started in early 1900s. In the early 1930s, ACI Committee 105 reported the results o 564 olumn tests and the tests were primarily arried out at Lehigh University and the University o Illinois. Thereater, many researhers have investigated the olumn oninement and dutility produed by transverse reinorement as well as axial resistane o olumns under onentri and eentri loading onditions. With the inreased utilization o high-strength onrete, several investigations were direted to study the strength and dutility o olumns with high-strength onrete. Studies on olumns with high-strength onrete indiated that their behavior is dierent rom that o olumns with normal-strength onrete. Aordingly, there have been several attempts to modiy the existing theories to extend their appliation to the olumns with high-strength onrete. 6

24 Chapter 2 Literature Review Review o previous researh on normal and high-strength onrete olumns under onentri and eentri loading onditions is presented in the ollowing setions. The emphasis is plaed on those that were onduted with high-strength onrete. In Setion 2.5, retangular stress blok or use in lexural analysis o olumns in dierent design odes are summarized. A detailed review o previous analytial models or onined onrete, whih inlude onined onrete strength and stress-strain relationships, is presented in Setion 2.6 and Researh on Normal-Strength Conrete Columns Early researh on onentrially tested olumns by Rihart et al. (1928, 1929) provided the basi inormation on onrete oninement. The test was onduted with onrete ylinders under lateral luid pressure (1928), ollowed by onrete olumns onined by irular spirals (1929). Thereater, olumn oninement under onentri loading was a topi or many researhers. Chan (1955), Roy and Sozen (1964), and Kent and Park (1971) experimentally investigated the behavior o onined onrete, and proposed analytial models to desribe stress-strain relationships or onined onrete. The main variables onsidered were the size, onrete strength, amount and spaing o transverse reinorement. In addition to oninement eet, transverse reinorement also provide lateral support to prevent bukling o the longitudinal reinorement. Bresler and Gilbert (1961), in their study, investigated the tie spaing and tie stiness that lead to bukling o longitudinal reinorement at a load equal to the yielding load using elasti theory. They emphasized that 7

25 Chapter 2 Literature Review the size o the ties depends on the size o the longitudinal rebar and the size o the longitudinal rebar should not be too small. Researhers prior to mid-1970s were not interested in distribution o longitudinal reinorement and the resulting tie arrangement as a oninement parameter. This eet was disussed by Park and Paulay (1975), Vallenas, Bertero, and Popov (1977), and Sheikh and Uzumeri (1980). Sheikh and Uzumeri (1980) showed the eet o tie arrangement on square olumns experimentally. In a subsequent study (1982), they also developed an analytial model based on the onept o eetively onined ore area, whih was determined on the basis o tie arrangement. In 1988, Mander, Priestley, and Park (1988a) reported that test results o irular, square, and retangular olumns under low and high loading rates o strain. They developed an analytial model using the onept o eetively onined ore area, proposed earlier by Sheikh and Uzumeri (1980). The ultimate strength surae or onrete under multi-axial ompressive stresses was theoretially alulated in the model (1988b). Saatioglu and Razvi (1992) proposed an analytial model or onined onrete appliable to the irular, square, and retangular olumns with spirals, retangular ties, and welded abris. Conined onrete strength and orresponding strain were expressed in terms o equivalent uniorm oninement pressure, whih was determined rom the setional and material properties. 8

26 Chapter 2 Literature Review 2.3 Researh on High-Strength Conrete Columns Ahmad and Shah (1982) Two dierent sizes o onrete ylinders, 3 6 in. and 3 12 in., were tested to study the eet o spiral oninement reinorement on stress-strain relationship o normal and high-strength onrete. Normal weight onrete o ompressive strength up to 10 ksi and two types o lightweight onrete were used. No longitudinal reinorement was plaed in the speimens. They reported that the eiieny o oninement by spiral reinorement dereased with inreased onrete strength. An analytial proedure was proposed to predit the stress-strain relationship o onined onrete on the basis o triaxial stress-strain urves or plain onrete and stress-strain relationship o onining steel. The analytial model indiated that stress o spiral steel at maximum stress o onined onrete were smaller with higher onrete strength and are not inluened by the yield strength o the spiral or the same ompressive strength. However, inreasing the yield strength o spiral improved dutility o onined onrete Martinez, Nilson, and Slate (1983, 1984) Coninement o onrete was evaluated by testing o 4 8 in., 4 16 in., 5 24 in., and 6 24 in. onrete ylinders. The speimens were onined with spiral reinorements having yield strengths o 55 to 60 ksi. Conrete strength varied between 3 ksi and 10 ksi. No longitudinal reinorement was used in the ylinders. 9

27 Chapter 2 Literature Review The researhers reported that both strength and dutility o onrete inreased with inreasing oninement pressure, regardless o unonined onrete strength. However, the ylinders with higher unonined strength showed redued axial strain at peak stress, and aster rate o strength deay beyond the peak. The spiral steel did not yield in ylinders with high-strength onretes. Thereore, it was reommended that the yield strength o spiral steel be limited to 60 ksi. It was onluded that the ACI -318 building ode (1977) requirements or spiral steel ould lead to inadequate oninement o high-strength onrete olumns. Small sale olumns, designed on the basis o the ACI-318 building ode (1977), were more dutile than larger sale olumns. A stress-strain relationship was developed o onined onrete, based on the test data Yong, Nour, and Nawy (1988) Square olumns, with onrete strength ranging rom 12.1 to 13.6 ksi, were tested to study the behavior o onined high-strength onrete olumn. The dimension o the olumns were either 6 in. or 5 ¼ in. square with 18 in. in height. The reinorement onsisted o longitudinal #3 rebars and retilinear ties with yield strengths o 61.5 and 72 ksi, respetively. The variables onsidered inluded the volumetri ratio o transverse reinorement, onrete over, and distribution o longitudinal reinorement. The results indiated that the stress-strain relationship o high-strength onrete was improved by using lateral ties as oninement reinorement. The improvement inreased with the inrease in the volumetri ratio o transverse reinorement. It was reported that the lateral ties did not yield at the irst peak load. The olumns with tie spaing equal to the 10

28 Chapter 2 Literature Review lateral dimension o the olumns did not exhibit any eet o oninement. Thus, it was reommended that the spaing o transverse reinorement should be less than the lateral olumn dimension. The distribution o longitudinal reinorement improved dutility o onrete. Hene, it was reommended to use at least eight bars, distributed around the olumn perimeter. Conrete over did not aet the stress-strain relationship o onined onrete. An empirial stress-strain relationship was proposed or high-strength onrete olumns onined with retilinear ties. The relationship onsisted o two ontinuous polynomials. Strength enhanement due to oninement was assumed to be a untion o onrete strength, spaing, diameter, volume, and yield strength o lateral steel, in addition to the number and diameter o longitudinal reinorement Bjerkeli, Tomaszewiz, and Jensen (1990) An experimental investigation was undertaken to study the behavior o high-strength onrete olumns using normal-density and low-density aggregates. The normal-density aggregate onrete had ube strengths ranging between 9.4 ksi and 16.7 ksi (65 MPa and 115 MPa), while the ube strength or low-density aggregate onrete varied between 8.7 ksi and 13.1 ksi (60 MPa and 90 MPa). The sope inluded investigation o strength and deormation harateristis o plain and onined onrete, as well as sustained load eets on highstrength onrete. Short term behavior o unonined and onined onrete was investigated by testing olumns in our series. Series 1 onsisted o small sale irular and square olumns with in. ( mm) dimensions. Variables onsidered were onrete 11

29 Chapter 2 Literature Review strength, and the amount o spiral reinorement. The seond series onsisted o small sale square olumns with in. ( mm) dimensions. Variables onsidered inluded the amount and distribution o oninement steel, the inluene o longitudinal reinorement, and strain rate. The third series onsisted o small sale square olumns with in. ( mm) dimensions, tested under eentri loading. Variables onsidered inluded onrete mix design, the eentriity o loading, and the volumetri ratio o oninement reinorement. The ourth onsisted o large sale retangular olumns with in. ( mm) dimensions. Columns with 8 bar and 12 bar arrangements were tested to study the eets o longitudinal reinorement distribution. The yield strength o transverse reinorements varied between 73.4 ksi and 88.9 ksi (506 MPa and 613 MPa). The researhers reported that dutility o high-strength onrete ould be improved through oninement. Use o large size longitudinal reinorement did not produe any beneiial eet on dutility. However the number o longitudinal bars had signiiant inluene on olumn dutility, showing improvements with inreased number o bars. Using a strain rate varied rom to per seond did not appear to have any signiiant eet on stress-strain relationship o onined onrete. Inrease o the onrete strength redued the eetiveness o oninement. Columns onined by irular spirals showed improved behavior than orresponding retangular olumns onined by retilinear reinorement. The oninement eiieny or normal density onrete, in terms o strength enhanement, was about twie the eiieny observed or low-density onrete. 12

30 Chapter 2 Literature Review A stress-strain relationship was introdued or onined normal and low-density aggregate onretes. The expressions proposed by Martinez et al. (1984) were modiied and used in deining the stress-strain relationship. The main parameters onsidered inluded onrete strength, onining pressure, and setion geometry Nagashima, Sugano, Kimura, and Ihikawa (1992) Twenty six square olumns with onrete ompressive strengths o 8.6 ksi and 17.1 ksi (59 MPa and 118 MPa) were tested under monotoni axial ompression. The olumns had a ross-setional dimension o 8.9 in. (225 mm) and a height o 28.2 in. (716 mm). High or ultra-high strength steel bars with yield strengths o ksi and ksi (784 MPa and 1372 MPa) were used or the ties. Test variables inluded onrete strength, amount, strength, and oniguration o oninement reinorement, and yield strength o longitudinal steel. The researhers reported that dutility o the olumns with lower onrete strength were larger than those in higher onrete strength. The yield strength o longitudinal reinorement had little eet on strength and dutility o the onined ore onrete when the same tie shape and an equal amount o longitudinal steel were used. Columns with 6 bar, 8 bar, and 12 bar arrangements did not exhibit a major dierene in strength and dutility. Strength enhanement due to oninement was observed to be independent o plain onrete strength, and was proportional to the square root o the eetive lateral oninement apaity. Dutility o onined onrete was diretly proportional to the apaity o lateral steel, and inversely proportional to onrete strength. 13

31 Chapter 2 Literature Review An analytial model was developed or onined high-strength onrete on the basis o the test data. The model inorporated the eetively onined onrete area onept or alulation o onined strength Cusson and Paultre (1994) Twenty seven square olumns were tested to investigate the behavior o large-sale high strength onrete olumns onined by retangular ties under onentri loading. The olumns had a ross-setional dimension o 9.25 in. (235 mm) and a height o 55.1 in. (1400 mm). Test parameters inluded onrete strength, the yield strength o transverse reinorement, the distribution o longitudinal reinorement, the amount and spaing o transverse steel, longitudinal reinorement ratio, and onrete over. The onrete strength varied between 7.6 ksi and 16.8 ksi (53 MPa and 116 MPa). Early spalling o over onrete was observed during testing. Hene, it was reommended to onsider only the area o the onrete ore in alulating the axial apaity o olumns with high-strength onrete. It was ound that the amount o transverse reinorement was the most important parameter that inluened stress-strain relationship o onined onrete. The researhers indiated that an inrease o the tie yield strength would be eetive in strength enhanement only or well onined olumns with large amount o transverse reinorement Ibrahim and MaGregor (1996a, 1996b) Fourteen retangular and six triangular olumns were tested under eentri loading. The dimension o the retangular olumns was in. ( mm) with a height o

32 Chapter 2 Literature Review in. (3000 mm). The triangular olumns had in. ( mm) ross setional dimension and 116 in. (2950 mm) height. Test parameters inluded onrete strength ranging rom 8.6 to 19.0 ksi (59 to 131 MPa), spaing o transverse reinorement, and the shape o the ompression zone. Test result indiated that the olumns behavior was dependent on the amount and spaing o transverse reinorement. The maximum tie spaing speiied in the ACI ode (1989) or non-seismi regions was not suiient to produe dutile olumn behavior. The ratio o the maximum ompressive stress to the ylinder strength, k 3, was ound to be However, the ACI retangular stress blok parameters were ound to be unsae or design o retangular or triangular high-strength onrete olumns Lloyd and Rangan (1996) Thirty six olumns were tested to predit the load-deletion behavior and the ailure load o olumns with high-strength onrete under eentri ompression. The olumns were either 12 4 in. ( mm) or 7 7 in. ( mm) ross setion with an eetive length o 66 in. (1680 mm). Conrete strength ranged between 8.4 to 14.1 ksi. Longitudinal reinorement onsisted o our and six bars or square and retangular olumns respetively. The load eentriities varied rom to 0.4 times the overall olumn depth. It was reported that oninement steel was insuiient to produe dutile behavior or olumns with small load eentriity. Suh olumns ailed in a brittle manner. On the other hand, olumns subjeted to larger load eentriity (e>0.3h) showed less brittle ailure. 15

33 Chapter 2 Literature Review Foster and Attard (1997) An experimental investigation was onduted using 68 eentrially loaded olumns with normal and high-strength onrete. The olumns were in. square setion with onrete strength ranging between 5.8 ksi and 13.1 ksi (40 MPa and 90 MPa). The load eentriities varied rom 0.07 to 0.4 times the overall olumn depth. The main variables onsidered in this experimental study inluded the onrete strength, longitudinal reinorement ratio, spaing o transverse reinorement, the eentriity o the axial load. The ultimate strength o the olumns was ompared to the strength preditions based on the ACI 318 retangular stress blok parameters. The results indiated that the dutility o reinored onrete olumns is dependent on the oninement provided by the transverse reinorement. The oninement eetiveness was related to the onrete strength, the tie spaing and oniguration, the tie yield strength, tie diameter, the over and the volume, and the arrangement o the longitudinal reinorement. The researhers reported that strength preditions based on the ACI 318 retangular stress blok ompared reasonably well with experimental apaities, although lower strengths than preditions ourred or some olumns with high-strength onrete Saatioglu and Razvi (1998) Twenty six olumns with 9.8 in. (250 mm) square ross setion were tested under onentri ompression. The onrete strength ranged between 8.7 ksi and 18.0 ksi (60 MPa and 124 MPa). Test parameters onsidered inluded onrete strength, the volumetri ratio, spaing, 16

34 Chapter 2 Literature Review yield strength o transverse reinorement, distribution o longitudinal reinorement and resulting tie arrangement. Test result indiated that olumns with high-strength onrete showed extremely brittle behavior unless onined with transverse reinorement that an provide suiiently high lateral oninement pressure. Dutility o olumn dereased with inreasing onrete strength. It was suggested that the lateral pressure required to onine high-strength onrete olumns ould be provided by either inreasing the volumetri ratio or grade o the lateral reinorement. However, the eetiveness o higher grade steel as a lateral reinorement was dependent on eiieny and volumetri ratio o lateral reinorement arrangement. Thus, it was reommended to selet the limit or steel grade areully with onsiderations given to the eiieny and volumetri ratio o reinorement arrangement. It was reported that spalling o the over onrete ourred at approximately 70 % o the unonined onrete strength. This ailure is more pronouned in olumns with losely spaed transverse reinorement. The researhers indiated that the earlier spalling o the over onrete is due to an instability o the shell onrete at high ompressive stresses. Thereore, it was onluded that depending on the onrete strength, thikness o over, and the nature o the reinorement grid that separates the over rom the ore, the spalling might or might not our prior to reahing the unonined olumn apaity under high onentri ompression. 17

35 Chapter 2 Literature Review Razvi and Saatioglu (1999a, 1999b) Twenty irular olumns with 9.8 in. (250 mm) dia. ross setion were tested under onentri ompression. The onrete strength ranged between 8.7 ksi and 18.0 ksi (60 MPa and 124 MPa). Test parameters onsidered inluded onrete strength, the volumetri ratio, spaing, yield strength o spiral reinorement. Test result indiated that there is a onstant derease in olumn dutility with inreasing onrete strength. However, enhanement o onrete strength due to oninement produed by spiral reinorement did not hange with onrete strength. Thereore, it was suggested that i the same perentage o strength enhanement is desired, higher-strength onrete olumns are required to be onined proportionately more than those with lower-strength onretes. Higher grades o oninement reinorement, with yield strengths o up to 145 ksi (1000 MPa), were ound to be eetive in irular olumns with spirals, provided a minimum volumetri ratio o spiral steel is maintained. It was also ound that olumns with longitudinal reinorement, with idential properties o spiral steel, showed better oninement perormane when ompared with those without the longitudinal reinorement. An analytial proedure was proposed to predit the stress-strain relationship o onined onrete based on the test data (Saatioglu and Razvi 1998, Razvi and Saatioglu 1999a). It was developed by modiying the earlier model proposed by Saatioglu and Razvi (1992) or normal-strength onrete. The model was appliable to both normal and high-strength onretes, overing a strength ranging between 4.4 ksi and 18.9 ksi (30 MPa and 130 MPa). 18

36 Chapter 2 Literature Review It was also appliable to onretes onined by spirals, retilinear hoops, rossties, welded wire abri, and ombinations o these reinorements. It inorporated the eet o highstrength transverse reinorement, with up to 203 ksi (1400 MPa) yield strength Lee and Son (2000) Thirty two olumns with onrete strength ranging rom 5.1 to 13.5 ksi (35 to 93 MPa) were tested under eentri ompression. The olumns had either in. ( mm) or in. ( mm) ross setion with an eetive length o 26.0 in. (660 mm), 54.3 in. (1380 mm), and 82.7 in. (2100 mm). The main variables onsidered were onrete strength, longitudinal reinorement ratio, eentriity, and slenderness ratio. It was reported that the onrete over spalling zone tended to be larger as onrete ompressive strength and longitudinal reinorement ratio inreased and as slenderness ratio and initial eentriity dereased. The olumns apaities were ompared with preditions based on the ACI 318 retangular stress blok, trapezoidal stress blok, and the modiied retangular stress blok proposed by Ibrahim and MaGregor (1997). They ound that using the ACI 318 retangular stress blok overestimated olumn strength or the lightly reinored high-strength onrete olumns. However, the trapezoidal stress blok, and the modiied retangular stress blok proposed by Ibrahim and MaGregor were reommended as a onservative lower bound or design o high-strength onrete olumns. 19

37 Chapter 2 Literature Review Liu, Foster, and Attard (2000) Twelve irular olumns were tested under axial ompression. The olumns had 9.8 in. (250 mm) dia. ross setion and were onined with either irular hoops or spirals. The onrete strength ranged between 8.7 ksi and 13.9 ksi (60 MPa and 96 MPa). Test parameters inluded onrete strength, the diameter and spaing o transverse reinorement, onrete over. Test result indiated that or the olumns with zero or thinner over onrete (0.59 in.), the apaity inreased with an inrease in eetive onining stress or the well-onined olumns with high-strength onrete. However, that was not the ase or the lightly onined olumns with over onrete o 0.98 in.. Based on the test result, it was onluded that or design, the irst peak load (spalling load) ould be taken as 0.85 times the apaity o the onrete setion, alulated on the in-plae onrete strength plus the apaity o the longitudinal reinorement Tan and Nguyen (2005) An experimental investigation was onduted on 30 plain and reinored onrete olumns with 7.9 in. (200 mm) square ross setion. The olumns were tested under onentri and eentri ompression. The main variables are onrete strength, ranging rom 6.7 to 14.6 ksi (46 to 101 MPa), spaing and arrangement transverse reinorement, the eentriity o the axial ompression. It was reported that the oninement rom transverse reinorement improved the lexural strength and dutility o reinored onrete olumns. It was also reported that the 20

38 Chapter 2 Literature Review oniguration o the transverse reinorement had a signiiant eet on the lexural behavior o the onined onrete. The researhers ound that high-yield strength reinorement to be more eetive than the normal-yield strength steel or oninement reinorement o highstrength onrete olumns. Test results indiated that using the ACI 318 retangular stress blok is not onservative or strength predition o high-strength onrete olumns under eentri loading. Thereore, a new set o retangular stress blok parameters were proposed based on the indings o the experimental investigation and available reported test data in literature. 2.4 Conlusion Drawn rom Previous Researh 1. Strength and dutility o onined onrete inrease with inreasing volumetri ratio o oninement steel. This is true or both normal and high-strength onrete. However, higher volumetri ratio is required or high-strength onrete olumns to ahieve similar dutility expeted o normal-strength onrete olumns. 2. Retangular olumns with tie spaing equal to the lateral dimension o the olumns show no oninement eet. 3. The spalling o the over onrete tends to our at below 85 % o the unonined onrete strength in olumns with higher onrete strength and losely spaed transverse reinorement. 4. Previous researh indiates onliting views on the use o high-strength steel or olumn oninement. Some researhers believe that extra strength present in highstrength steel an not be used prior to the peak load o olumn. Thereore, these 21

39 Chapter 2 Literature Review researhers suggested limits on yield strength. Others suggest that the use o highstrength steel is neessary to produe dutile behavior o high-strength onrete olumns, although very high-strength steel does not yield at the peak load. However, there is strong evidene that the behavior o olumn with losely spaed transverse reinorement improves signiiantly with the use o high-strength oninement steel. 5. The use o larger size longitudinal reinorement produes little beneiial eet on the dutility o olumn. 6. Cirular spirals are more eetive than most retilinear ties. However, when the ties are spaed losely and oniguration o the ties is enhaned, the oninement eiieny an be inreased. 7. There are onliting test results over the appliability o retangular stress blok in the urrent ACI 318 or the LRFD Speiiations to the olumns with high-strength onrete. While some studies have ound the urrent approah or normal-strength onrete olumns to overestimate the lexural resistane o high-strength onrete olumns at a given axial load, others have ound the approah to provide reasonable preditions o eentrially loaded high-strength onrete olumns. 2.5 Retangular Stress Blok or High-Strength Conrete Introdution Many studies have indiated that stress-strain relationship o onrete is strongly inluened by onrete strength. The initial slope o the urve inreases with an inrease in ompressive strength, releting higher elasti modulus as shown in Figure 1. A widely aepted 22

40 Chapter 2 Literature Review approximation or the shape o the stress-strain urve beore maximum stress is a seond degree parabola or normal-strength onrete and beomes more linear as onrete strength inreases. In members subjeted to ombined axial and lexural loading, one the limiting strain is established, the setional apaity an be determined by evaluating internal ompressive ore in onrete. The ompressive ore in onrete an be determined by evaluating the area under ompressive stress distribution up to the limiting strain. However, it is time onsuming to evaluate the area under a non-linear stress-strain relationship. A number o investigators (e.g., Whitney 1940) have suggested the replaement o the atual shape o the ompressive onrete stress-strain relationship by an equivalent retangular stress blok (ERSB) as a means o simpliiation. Hognestad (1951) tested a large number o C shaped plain onrete olumns to investigate stress-strain harateristis o the olumn onrete. Subsequently, a stress-strain model and a retangular stress blok were proposed or use in lexural analysis and design o reinored onrete members by Hognestad (1961), Mattok et al. (1961). The generalized stress blok is deined by three parameters: k 1, k 2, and k 3, as shown in Figure 2. k 1 is the ratio o the average stress over the ompression area to the maximum ompressive stress; k 2 is the ratio o the distane between the extreme iber and the resultant ore o the stress blok to the distane between that iber to the neutral axis; and k 3 is the ratio o the maximum ompressive stress to the ylinder strength. In pratial design, the lexural stress distribution o onrete in ompress zone an be approximated as an equivalent retangular 23

41 Chapter 2 Literature Review stress blok as shown in Figure 2. The relationship between the two parameters α 1 and β 1 o ERSB and the stress blok parameters k 1, k 2, and k 3 an be represented by the ollowing equations. β 1 = 2k2 Eq. 2-1 α1β 1 = kk 1 3 Eq. 2-2 Sine the appliability o the stress blok was derived based on experimental data obtained rom normal-strength onrete olumn tests, many researhers (Ibrahim and MaGregor 1997, Li et al et.) raised question about the appliability o the stress blok or highstrength onrete, and proposed new retangular stress bloks. Some o proposed stress bloks or high-strength onrete by the researhers have been the basis o the Canadian and New Zealand odes Stress Blok Parameters in Dierent Design Codes ACI / AASHTO LRFD Speiiations Intensity o the equivalent stress blok given by ACI is expressed byα. The depth o the stress blok is expressed by β 1, where is the neutral axis depth. The irst parameter α 1 is assumed to be a onstant value o The seond parameter β 1 is equal to 0.85 or onrete strength up to 4 ksi (30 MPa) and is redued at a rate o 0.05 or eah one ksi o onrete strength exeeding 4 ksi. The parameter β 1 is not to be taken less than The ultimate ompressive strain ε u (Figure 2) is assumed to be a onstant value o

42 Chapter 2 Literature Review regardless o onrete strengths. ACI does not speiy an upper limit o onrete strength or its retangular stress blok. AASHTO-LRFD Speiiations adopted the same values or the parameters, α 1 and β 1 as the ACI , but imposed a general limitation that the Speiiations are appliable only or onrete strength not exeeding 10 ksi (69MPa) CSA A Provisions The retangular stress blok parameters deined in CSA A23.3-M94 is appliable to highstrength onrete. The parameters are deined using α 1 and β 1 and have the ollowing expressions. α =, in MPa Eq. 2-3 β =, in MPa Eq. 2-4 It should be noted that in CSA, the limiting ompressive strain o onrete ε u is assumed to be NZS Provisions The New Zealand ode adopted the stress blok parameters proposed by Li, Park, and Tanaka in It is interesting to note that the equation or β 1 is idential to that o ACI , while α 1 is redued rom 0.85 to 0.75 as onrete strength inreases or 55 α1 = ( 55) 0.75 or > 55 in MPa Eq

43 Chapter 2 Literature Review 0.85 or 30 β1 = ( 30) 0.65 or > 30 in MPa Eq CEB-FIP Model Code 1990 CEB-FIP Model Code 1990 reommends the use o a stress-strain urve (Figure 3 (a)) or setional analysis purpose. The value o strain orresponding to maximum stress ε 1 is set at , and the value o limit strain ε,lim varies with the onrete strength. There are two alternatives or design purpose in this ode. The irst is a simple parabola-retangular stressstrain urve with the apex at a stress o onstant stress 0.85 or strains between to ε u is a uniorm stress blok with stress blok parameters as ollows. 0.85, a orresponding strain o 0.002, and a as shown in Figure 3 (b). The seond α =, 250 in MPa Eq. 2-7 β 1 = 1.0 Eq. 2-8 ε u = , 100 in MPa Eq. 2-9 This ode limits onrete strength to 80 MPa (11.6 ksi) or the appliability o the parameters above. It is interesting to note that the maximum extreme iber strain ( ε this ode, derease and beome less than as the onrete strength inreases.,lim, ε u ), speiied in 26

44 Chapter 2 Literature Review Proposed Stress Blok Parameters by NCHRP Program NCHRP program, whih was arried out in North Carolina State University, proposed a new set o retangular stress blok parameters that an be applied both or normal-strength onrete and high-strength onrete. The high-strength onrete was deined as onrete strength higher than 10 ksi (69 MPa) in this program. The program tested 21 eentri braket olumns with onrete strength ranging rom 10.4 to 16.0 ksi (71 to 110 MPa). Based on the test results o the researh program as well as the results by other researhers reported in the literature, a value o 0.58 was seleted as the lower bound o the generalized stress blok parameter k 1, whih is related to the shape o the onrete stress-strain diagram, or onrete strength between 10 ksi and 18 ksi (69 MPa and 124 MPa). The values or other generalized stress blok parameters, k 2 and k 3, were taken as 0.33 and 0.85, respetively. The limiting ompressive strain o onrete o was proposed to be used or design purposes or onrete strength up to 18 ksi. Using the values hosen or the generalized stress blok parameters, the lower bound relationships or retangular stress blok parameters, α 1 and β 1 were obtained as ollows. α kk = = = 2k Eq β = 2k = Eq Aordingly, the ollowing retangular stress blok parameters, α1 and β 1, were proposed by the NCHRP program or onrete strength up to 18 ksi. The reommendation 27

45 Chapter 2 Literature Review maintained the same expressions o α 1 and β 1 as in ACI and LRFD Speiiations or normal-strength onrete and extended their uses or high-strength onrete up to 18 ksi or 10 α1 = ( 10) 0.75 or > 10 in ksi Eq or 4 β1 = ( 4) 0.65 or > 4 in ksi Eq Table 1 summarizes various reommendations mentioned above or α 1, β 1, and ε u. All expressions or the parameters have been onverted to ksi unit or onsisteny. Figure 4 shows the axial load-bending moment interation diagrams o a seleted olumn with 12 in. square ross setion or three dierent onrete strengths. The diagrams were generated using retangular stress blok reommend by ACI / AASHTO-LRFD, CSA A , NZS , and CEB-FIP. As an be seen in this igure, or normalstrength onrete ( = 6 ksi), using CEB-FIP parameters is most onservative estimation or the apaity o olumn. For high-strength onrete, use o ACI / AASHTO retangular stress blok parameters results in the largest apaity preditions and the use o the CSA results in the lowest apaity preditions. The apaity preditions o the olumn based on ACI / AASHTO and NZS retangular stress blok parameters were idential or onrete strength o 18 ksi. 28

46 Chapter 2 Literature Review 2.6 Conined Conrete Strength by Spiral Reinorement Introdution When onrete is subjeted to axial ompression, deormation in the lateral diretion develops due to Poisson s eet. In the initial stage o loading, when the axial strains are small and thereore, the Poisson s ratio eet o onrete is small, the lateral oninement provided by the spiral reinorement would be negligible. With the inrease o the axial strain and the Poisson s ratio eet o onrete, the lateral strain o onrete tends to inrease. The onrete in the ore is restrained rom expansion by the spiral reinorement, resulting in the oninement o the ore and the separation o the over rom the ore. Beyond this point the load arrying apaity o the ore onrete is highly aeted by the oninement, and an be expeted to be higher than that o plain onrete. However, this inrease o oninement is limited by the tensile strength o the spiral reinorement. As soon as spiral steel yields, irrespetive o the lateral expansion o onrete, the onining pressure remains onstant and only the strain hardening o steel will result in a limited urther inrease. This setion provides an overview o the previous works related to onined onrete strength by spiral reinorement Previous Work The onept o onrete onined with spiral reinorement was irst introdued by Considère in The idea was studied by many researhers suh as Morsh, Talbot, Bah, and so on in the early In 1928, Rihart, Brandtzaeg, and Brown reported the results obtained 29

47 Chapter 2 Literature Review rom 4 8 in. ylinders, subjeted to ombined axial load and various intensities o lateral luid pressure. The results indiated that the axial strength and dutility o the onrete inreased with an inrease in the lateral pressure. Based on those results, they proposed an expression to predit the axial ompressive strength o onrete ylinders under lateral luid pressure as ollowing. = Eq o p where is the axial ompressive strength o the onined ylinder, o is the ompressive strength o the orresponding unonined ylinder, and p is the lateral luid pressure. In 1929, in a subsequent study, Rihart, Brandtzaeg, and Brown tested a series o in. spirally reinored onrete olumns with unonined onrete strength ranging rom about 2 to 3 ksi. They proposed that the axial strength o onrete onined with spiral was related to the lateral oninement stress as ollowing: = Eq o 2 where 2 is the atual lateral oninement stress provided by the spiral reinorement at maximum axial stress. 2 an be determined in terms o the area o the spiral steel, A sp and the spaing o spiral, s as ollows. 2 = 2 Asp sp / ds Eq where sp is the stress in the spiral at maximum olumn load (not neessarily the yield strength) and d is the outside diameter o the spiral. 30

48 Chapter 2 Literature Review It should be noted that although Eq and Eq are very similar in orm, they were proposed based on test results rom speimens under dierent testing onditions. In the test ondition leading to Eq. 2-14, lateral luid pressure provides ative oninement on the speimens. On the other hand, the lateral onining pressure ating on the speimens leading to Eq was provided by spiral steel. The onining pressure by spiral steel is not onstant as or ative oninement, and is dependent on the lateral dilation o the onrete under axial load. Rihart et al. onluded that the strength o onrete with ative oninement rom lateral (luid) pressure was approximately the same as or onrete with passive oninement pressure rom losely spaed spirals o irular olumns ausing an equivalent lateral pressure. Iyengar, Dasayi, and Reddy (1970) presented the results through a series o test with spirally reinored onrete ylinders. The speimens tested were in. ( mm) and in. ( mm) ylinders. The ompressive strength o the unonined onrete ylinders varied rom 2.5 to 6.5 ksi (17 to 45 MPa). Iyengar et al. studied the relation between the onined onrete strength and the oninement ator, represented by ρ, s sy where sy is the yield strength o spiral steel, ρ s is the volumetri ratio o spiral steel whih is determined as 4A sp d s. They ound that when the inrease in onrete strength, produed by spiral steel was plotted with respet to ρ s sy, the straight line obtained did not pass through origin. Instead, this line gave an interept on the axis representing the oninement ator, thereby showing that only when the oninement ator exeeded a partiular value (say, ρ s sy ) was the eet o oninement present. Their alulation indiated that the 31

49 Chapter 2 Literature Review interept ρ s sy, where ρ s is determined as 2 4A sp d, orresponded losely to the magnitude o the oninement ator when the pith o the spiral was equal to the diameter o spiral. Based on the above inding, Iyenger et al. suggested that the inrease in onrete strength produed by spiral steel is related to ( ρ ρ ) s s sy, whih they named oninement index, and is represented by the ollowing expression. o = ( ρs ρs) Eq sy o Substituting ρ s and ρ s into 4A sp ds and 2 4A sp d respetively, Eq an be transormed into the ollowing equation, Introduing l, Eq an be represented as 9.2A sp sy = o + (1 s/ d ) Eq ds = (1 s/ d ) Eq o l where l is the lateral oninement stress in ore onrete provided by the spiral steel, and determined as 2A sp sy d s. In Eq. 2-19, the lateral oninement stress l was determined assuming that the spiral steel yields at the maximum load o tested olumn. The term in parenthesis indiates that oninement produed by spiral steel beomes ineetive as the spaing o spiral approahes the diameter o the ore. 32

50 Chapter 2 Literature Review Ahmad and Shah (1982) tested 3 6 in. and 3 12 in. onrete ylinders onined by spiral steel. The onrete strength ranged rom 3 to 10 ksi. The speimens were made without over. They ound that when spaing o spirals exeeded the distane equal to 1.25 times the diameter o the spiral d, the eet o oninement was negligible. Based on the test results, they proposed onined onrete strength using parameter k 1 as ollows: ( ) = o + k1 r p Eq where k 1 is a parameter that relets eetiveness o oninement, ( ) is the average onining pressure at the peak, produed by spiral steel. r p Assuming that the spiral yields at the peak load o ylinder, ( ) r p was represented as ollowing. ρs sy s ( r) p = d Eq The parameter k 1 was suggested in terms o the unonined onrete strength and the average onining pressure at the peak ( ) as r p o k 6.61 ( ) = r p Eq o Ahmad and Shah onluded that the eetiveness o the spiral reinorement at peak load dereased with an inrease in onrete strength. 33

51 Chapter 2 Literature Review Martinez, Nilson, and Slate (1984) reported test results o an extensive study o onrete ylinders onined by spiral steel, made with both normal weight and light weight onrete. Most o the speimens tested were 4 8 in., 4 6 in., and 5 24 in. ylinders without over onrete. Other speimens were 6 24 in. with a protetive over. They lassiied low, medium, and high-strength onrete as about 3, 7, and 10 ksi respetively. As in the study o Ahmad and Shah, no longitudinal reinorements were inluded in the speimens. They ound that that the eetive oninement stress, determined as (1 s/ d ), produed by the spiral steel is signiiantly aeted by the spiral pith and it beomes negligible when the value o the spiral pith is equal or greater than the spiral diameter. This is idential with argument o Iyengar et al.. Based on the test results, Martinez et al. proposed the ollowing relation between the inrease in onrete strength onined by spiral steel and the eetive oninement stress, appliable to onrete strength up to 12 ksi and yield strength o the spiral steel up to 60 ksi or lower. l = (1 s/ d ) Eq l Eq is a modiiation o Eq proposed by Iyengar et al.. A onstant value o 0.85 or the ratio o the in-plae onrete strength to the ompressive strength o ontrol ylinder o, was seleted regardless o onrete. Mander, Priestley, and Park (1988) used onept o the eetively onined ore area, whih was originally introdued by Sheikh and Uzumeri (1980), to determine onined onrete strength produed by spiral steel. The onept is that the maximum lateral pressure rom the 34

52 Chapter 2 Literature Review spiral steel an only be exerted eetively on that part o the onrete ore where the onining stress has ully developed due to arhing ation as shown in Figure 5. Aording to them, the eetive lateral onining pressure an be expressed as = k Eq l l e k A e e = Eq A where k e is oninement eetiveness oeiient, A e is area o eetively onined onrete ore, A is alulated as A(1 ρ), ρ is the ratio o area o longitudinal reinorement to area o ore o setion, and A is the area o ore o setion enlosed by the enter lines o the perimeter spiral or hoop. In Figure 5, the arhing ation was assumed to our in the orm o a seond-degree parabola with an initial tangent slope o 45. Consequently, the area o an eetively onined onrete area ore at midway between the levels o transverse reinorement is 2 2 π s π 2 s e = s = s ds A d d Eq where s is lear vertial spaing between spiral or hoop bars; and d s is diameter o spiral between bar enters. Also the area o onrete ore is A π = ( ρ ) Eq ds 1 Thereore, the oninement eetiveness oeiient is or irular hoops 35

53 Chapter 2 Literature Review k e s 1 2 ds = 1 ρ 2 Eq Similarly it an be presented that or irular spirals k e s 1 2 ds = 1 ρ Eq Finally, the eetive lateral onining stress on the onrete is = k Eq l eρs ys Using the eetive lateral onining stress above and adopting a onstitutive model involving a speiied ultimate strength surae or multi-axial ompressive stresses, whih is proposed by William and Warnke (1975), they proposed onrete strength onined by spiral steel as ollows: 7.94 l = o o l o Eq Saatioglu and Razvi (1992) proposed expression o onined onrete strength in terms o uniaxial strength and lateral oninement pressure or NSC olumn as ollows: = + k Eq o 1 l k1 6.7( l ) 0.17 = Eq

54 Chapter 2 Literature Review where l is the lateral oninement stress (in MPa) in ore onrete provided by the spiral steel, determined as 2A sp sy d s. The variation o oeiient k 1 with lateral pressure l was obtained rom regression analysis o test data, whih was onduted by Rihart et al. (1928). In 1999, Saatioglu and Razvi tested in. ( mm) irular olumns reinored with spiral and longitudinal reinorements with onrete over. The onrete strength ranged rom 8.7 to 18 ksi (60 to 124 MPa). They reported that the test results showed good agreements between analytial strength based on Eq and experimental strength values, and extended the appliability o Eq or the predition o onined onrete strength in high-strength onrete olumns 2.7 Stress-Strain Relationship o Conined Conrete by Spiral Reinorement Introdution Various models have been proposed or prediting the stress-strain relationship o onrete onined by spiral reinorements in the past. The earlier models were developed based on the test results with normal-strength onrete. Thereater, those were modiied appliable to a wide range o onrete strengths, overing both normal-strength onrete and high-strength onrete. 37

55 Chapter 2 Literature Review Existing Models Chan (1955) proposed a trilinear model to represent the stress-strain urve o onrete onined by spiral steels (Figure 6). Line OA represents the elasti stage and lines AB and BC the plasti stage o the urve. Chan pointed out that the harateristis o eah linear segment were dependent on the amount o oninement as well as the property o onrete, but he did not propose mathematial expression or their preditions. Martinez (1983) proposed a stress-strain relationship using the expression releting enhanement o onrete strength and dutility produed by spiral reinorement, appliable or onrete strength ranging between 3 ksi and 12 ksi. = +Δ Eq o ε = εo +Δ ε Eq ε = ε +Δ ε Eq o85 85 where ε o is the strain at maximum stress o unonined onrete, ε is the strain at maximum stress o onined onrete, ε o85 is the strain at 0.85 o on desending part o the urve or unonined onrete, ε 85 is the strain at 0.85 on desending part o the urve or onined onrete, and Δ, ε Δ, and Δ ε 85 are the inrement on o, o ε, and ε o85, respetively, produed by spiral reinorements (reer to Figure 7). 38

56 Chapter 2 Literature Review They seleted or the representative value o ε o. Through regression analysis o their test results, the ollowing expression were ound or Δ, Δ ε, and ε 85 Δ. Δ = 4.0 (1 s/ d ) in psi Eq l 250 l(1 s/ d) Δ ε = in psi Eq ( ) (10 ) l(1 s/ d) 85 3 ( ) Δ ε = in psi Eq Substituting the above equations or 2-36 leads to Δ, Δ ε, and ε 85 Δ into Eq. 2-34, Eq. 2-35, and Eq. = (1 s/ d ) in psi Eq l ε 250 l(1 s/ d) = in psi Eq ( ) 2 ε 6 3.2(10 ) l(1 s/ d) 85 εo85 3 ( ) = + in psi Eq And strain at 0.85 o on desending part o the urve or unonined onrete was presented based on regression analysis o test results as ε = in psi Eq o85 39

57 Chapter 2 Literature Review From the proedure desribed above, the desending part o the stress-strain relationship was represented by a straight line, whih passes the strain ε 85 orresponding to 85 % o the maximum stress o the desending part or the onined onrete. For ε > ε, = Z( ε ε ) Eq where, Z = ε ε Eq ( 85 ) The expression or asending part o the stress-strain relation was suggested below For ε ε, Eε = E ε ε 1+ 2 E o ε + ε 2 Eq where E is the elasti modulus o unonined onrete, determined by E = (40, )( w /145) in psi Eq E o = in psi Eq ε where w is the weight o the onrete in lb/t 3. Razvi and Saatioglu (1999) modiied the stress-strain relationship o onined onrete appliable to olumns with high-strength onrete, whih was proposed earlier or normalstrength onrete by them (1992). Key idea o the model is very similar to that proposed by Martinez as shown in Figure 8. The exeption is that a onstant residual strength is assumed 40

58 Chapter 2 Literature Review at 20 % strength level o the maximum strength. They suggested that the model an be appliable to onrete strength up to 18 ksi (124 MPa) and yield strength o spiral steel o 203 ksi (1400 MPa) or lower. The stress-strain relation proposed by Popovis (1973) was adopted or asending part as given below. For ε ε, ε r ε = ε r 1+ ε r Eq r = E E E se Eq where rom E se is the seant modulus o elastiity o onined onrete and an be alulated E se = Eq ε The elasti modulus o unonined onrete E, originally proposed by Carrasquillo et al. (1981) was used. E = + in MPa Eq ,320 6,900 For the desending part o the stress-strain relation, the slope o the region was deined by the strain orresponding to 85 % o maximum stress ε 85 as in the model o Martinez. The strain at the maximum stress ε and the strain orresponding to 85 % o maximum stress ε 85 or onined onrete an be expressed as 41

59 Chapter 2 Literature Review For ε > ε, ε = (1+ 5 ) Eq ε o kk 2 ε = 260 k ρε [ ( k 1)] + ε Eq s 3 o85 Where k1 6.7( l ) k 0.17 = in MPa Eq = 1.0 in MPa Eq o ys k 3 = 1.0 in MPa Eq k K = in MPa Eq l o They also proposed the expression or determining the strainε o and ε o85 when in absene o experimental data, respetively as ollowing. ε = k Eq o 2 ε = Eq o85 εo k2 42

60 Chapter 3 Experimental Program Chapter 3 Experimental Program 3.1 General The primary ous o this experimental program is to study the behavior o high-strength onrete olumns onined with tie and spiral reinorements. The experimental program inluded testing o thirty two retangular and twenty our irular olumns subjeted to monotonially inreasing onentri and eentri axial ompressions. Details o the test speimens, material properties, test set-up, instrumentation, and test proedure are presented in this hapter. The test parameters or the onentri loading inluded ompressive strength o the onrete (three target strengths), shape o ross setion (retangular and irular), speimen size (large and small), longitudinal reinorement ratio (three dierent ratios), and amount and type o transverse reinorement (two dierent spaings). For eentri loading, appliable only or the retangular olumns, the parameters were ompressive strength o the onrete (three target strengths), speimen size, and eentriity o the applied load (10% and 20% o the depth o the retangular setion). 43

61 Chapter 3 Experimental Program 3.2 Details o Test Speimens Retangular Columns A total o 32 retangular olumns were prepared or testing. Twenty olumns out o the 32 retangular olumns had 9 12 in. ross setion and 40 in. in height. The size o the remaining twelve olumns was redued to 7 9 in. ross setion and 36 in. in height due to the limited apaity o the testing equipments. All the retangular olumns were reinored with six longitudinal steel bars and reinored transversely with #4 ties. The three ratios o longitudinal reinorement onsidered were approximately 1%, 2.5%, and 4% or the olumns with 9 12 in. setion. The three approximate ratios o longitudinal reinorement used or the olumns with 7 9 in. setion were 2%, 3%, and 4%. The irst seleted spaing o the transverse reinorements was to provide the minimum requirement speiied by the AASHTO LRFD Speiiations, whih is not to exeed the least lateral dimension o the olumns. The seond seleted spaing o the transverse reinorements was equal to one hal o the irst seleted spaing. Aordingly, the spaings or 9 12 in. olumn were 9 in. and 4 ½ in. while the spaings or 7 9 in. olumn were 7 in. and 3 ½ in.. For the retangular olumns subjeted to eentri loading, the longitudinal reinorement ratio o 4% was onsidered only. The spaing o 9 in. and 7 in. were used or the olumns with 9 x 12 in. and 7 x 9 in. setion, respetively. Reinorement details o the retangular olumns are shown in Figure 9. The ties had 135- degree hooks at the ends, with at least six times tie bar diameter extension into the ore 44

62 Chapter 3 Experimental Program onrete. The onrete over was kept onstant at ½ in. to the ae o the tie or all the olumn speimens. The measured onrete ompressive strengths, based on standard 4 8 in. ylinder tests, ranged rom 7.9 ksi to 16.5 ksi at the time o testing. The details o the retangular olumns under onentri and eentri loading onditions are summarized in Table 2 andtable 3, respetively. The two ends o the retangular olumns were heavily reinored with losely spaed ties and onined with external steel tubes o 4 in. in height to avoid premature ailure in the end regions o the olumns. The longitudinal steels were ut to math the olumn height and were set lush with the ends o the olumns. The assembled steel ages or the retangular olumns are shown in Figure 10. The retangular olumns were prepared or vertial asting using orms built with ⅜ in. plywood. Ater the orms were seured in plae, 2 in. long plasti sheaths were slipped over the strain gauge lead wires and itted inside the drilled holes o the orms. These sheaths were used to protet the lead wires during asting o onrete and removal o the orms. Figure 11 illustrates the proedure used or assembling the orms or the retangular olumns Cirular Columns A total o 24 irular olumns were prepared or testing. Fiteen olumns out o the 24 irular olumns had 12 in. diameter ross setion and were 40 in. high. The size o the remaining nine olumns was 9 in. diameter ross setion and 36 in. high. All the irular olumns ontained six longitudinal steel bars and were reinored transversely with #3 or #4 spiral reinorements. The seleted target ratios o the longitudinal reinorement were 1%, 2.5%, and 4% or the olumns with 12 in. diameter ross setion. The seleted ratios o 45

63 Chapter 3 Experimental Program longitudinal reinorement were 2%, 3%, and 4% or the irular olumns with 9 in. diameter ross setion. Reinorement details o the irular olumns are shown in Figure 9. The two seleted spaings o spiral reinorement were the minimum requirement by the AASHTO LRFD Speiiations, and the other equal to one hal o the irst seleted spaing. Thereore, the pith o spiral reinorement ranged rom 1 ½ in. to 2 ⅜ in. depending on target onrete strength and area o ross setion. The volumetri ratio o spiral reinorement, ρ s varied between 1.44 % and 7.27 %. Eah oil o spiral reinorement onsists o one omplete helial spiral without any lapped splies. The measured onrete ompressive strength, based on standard 4 x 8 in. ylinder tests, ranged rom 7.9 ksi to 16.1 ksi at the time o testing. Details o the irular olumns are summarized in Table 4. The pith o spiral was redued outside the test region in addition to the use o external irular steel tubes 4 in. high at both ends o the olumns to avoid premature ailure in the end regions o the olumns. Speial are was taken during assembling o the steel age to ahieve the speiied spiral pith. The onrete over was kept onstant at ½ in. to the ae o the spirals or all the olumn speimens. The longitudinal steels were ut to math the olumn height and were lush with the ends o the olumns. The assembled steel ages or the irular olumns are shown in Figure 12. The irular olumns were prepared or vertial asting using Sona tubes. Ater the Sona tubes were seurely in plae, 2 in. long plasti sheaths were slipped over the strain gauge lead wires and itted inside the drilled holes o the tubes. Assembling o the orms or the irular olumns is shown in Figure

64 Chapter 3 Experimental Program Column Identiiation Column speimens were identiied by the seleted target strength or this study (10, 14 or 18 ksi), shape o ross setion (Retangular or Cirular), spaing o transverse reinorement (9, 4½, 2¾, 1⅜ in., et.), and longitudinal reinorement ratio (ρ1, ρ2.5, et.). For example, speimen 10CC2¾-ρ1 is a irular olumn with target ompressive onrete strength o 10 ksi, 2 ¾ in. pith o spiral reinorement, and longitudinal reinorement ratio o 1 %. The eentrially loaded olumn speimens were labeled with target strength (10, 14 or 18 ksi), the eentriity, e, with respet to the depth o the ross-setion, h, (E1 or E2). For example, speimen 10E2 is an eentrially loaded olumn with 10 ksi target onrete strength and eentriity o 20 perent (e/h). For dupliate olumns, the letter A was used to distinguish repeated olumns. 3.3 Casting o Columns A total o ive bathes o onrete were used to ast both the retangular and irular olumns. All olumns were ast vertially to simulate typial onstrution pratie o olumns. The onrete mixes or eah target onrete strength were developed at NCSU and the onrete was provided by a loal ready-mix onrete ompany. Conrete was disharged in the olumns diretly rom ready-mix onrete truk in approximately 2 or 3 lits, and an eletri internal vibrator was used to onsolidate the onrete and to remove air bubbles at eah o the lits. As the olumn speimens were being prepared, the resh onrete was tested 47

65 Chapter 3 Experimental Program or slump (AASHTO T 119, ASTM C 143), air ontent (AASHTO T 152, ASTM C 231), and unit weight (AASHTO T 121, ASTM C 138). Figure 14 illustrates asting o olumns in the laboratory. Three 4 8 in. ylinders, whih were prepared in plasti molds, or eah olumn were ast to determine onrete strength at the time o olumn testing (Figure 15). The olumns were overed with wet burlap and plasti sheet at ambient temperature in the laboratory or about a week. Both the olumn ormworks and the ylinders were stripped and de-molded approximately two days ater asting (Figure 16). Figure 17 shows the olumns ast. 3.4 Material Properties Conrete The three target onrete strengths, 10 ksi (69 MPa), 14 ksi (97 MPa), and 18 ksi (124 MPa), onsidered in this study were developed ater laboratory and plant trial bathes (Logan 2005). Low water-ement ratio (w/) and high ement ontent were used to ahieve the strength level required. Dierent mix designs or three target onrete strengths were used or ive bathes o onrete. The orresponding water to ementitious material ratios (w/m) were 0.3, 0.26, and 0.25, respetively. Retarders and superplastiizers were used in all mixes to obtain workability or high-strength onrete. The oarse aggregate was obtained rom Carolina Sunrok Corporation. The seleted aggregate was #78M rushed stone with a nominal maximum size o 3/8 in. (9.5 mm). Two 48

66 Chapter 3 Experimental Program types o ine aggregate were used depending on the target ompressive strength. The irst type o ine aggregate was a natural sand used by the Ready-Mixed Conrete Company in all o their normal onrete mixtures. The seond type o ine aggregate used was a manuatured sand known as 2MS Conrete Sand produed by Carolina Sunrok Corporation. The ement used was a Type I/II ement produed by Roanoke Cement. The ly ash produer was Boral Material Tehnologies and the silia ume produer was Elkem Materials, In. Both the high-range water-reduing and the retarding admixtures were manuatured by Degussa Admixtures, In. The high-range water-reduing admixture (HRWRA) used was Glenium 3030 and the retarding admixture was DELVO Stabilizer. Details o the onrete mix design or eah o the target strengths and onrete bathes are given in Table 5 and Table 6. The 4 x 8 in. (100 x 200mm) ylinders were tested using 500-kip (2,200-kN) ompression mahine at 28 days and at the time o olumn testing aording to ASTM C39 (Figure 18). All o the ylinders used or these tests were irst prepared by grinding both ends to ensure that the ends were perpendiular to the sides o the speimen. Grinding the end suraes was aomplished with a rotary grinding mahine as shown in Figure 19. Prior to testing, the diameter o eah ylinder was measured at mid-height in two perpendiular diretions. The average o the two measurements was later used to alulate the stresses Steel Grade 60 deormed steel bars, provided by Gerdau Ameristeel Company, were used or both longitudinal and transverse reinorement or test speimens. Five dierent sizes (#4 through 49

67 Chapter 3 Experimental Program #8) o reinoring bars were used or longitudinal reinorement. The measured yield strength ranged rom 58 to 67 ksi. The transverse reinorements (ties) or all the retangular olumns were #4 bars, and the measured yield strengths ranged rom 62 ksi to 72 ksi. For the irular olumns, the sizes o spiral reinorements were #3 and #4, and the measured yield strengths ranged rom 62.9 to 66.5 ksi. A 220 kip apaity MTS testing mahine was used to obtain the stress-strain relationships or longitudinal and transverse reinorement in aordane with ASTM A (Figure 20). The measured stress-strain urve o steel in tension was assumed to be the same in ompression prior to bukling. Thereore, the harateristis o olumn steel were established by tension tests. At least three oupons were used or eah type o reinorement. The strains were measured using 2 in. gage length extensometer or oupons o longitudinal reinorements and eletri resistane strain gauges or oupons o transverse reinorement as shown Figure 20. The oupons o the transverse reinorement were taken rom unbent portion o the transverse reinorement. Test results indiate a distint yielding plateau or all longitudinal reinorement. The transverse reinorement exhibited non-linear behavior in the yielding stage. Thereore, the 0.2 perent oset method was used to determine the yield strength. The yield strengths o the spiral reinorement were obtained rom the mill test results by the steel supplier. Material properties o steel are summarized in Table 7. The measured typial stress-strain relationships o longitudinal and transverse reinorement are shown in Figure

68 Chapter 3 Experimental Program 3.5 Instrumentation For retangular olumns, the axial shortening o the olumns was measured using our pi gages, loated at the mid-height o eah side in the test speimens. Two o the pi gages were attahed to the threaded rods in opposite diretion, embedded in the ore onrete to provide ontinuous data reording, even ater the spalling o over onrete while the other two gages were mounted on the onrete surae. The gauge length o the pi gauges were 100 mm in most ases. The pi gauges with 200 mm gauge length were used also in some ases. Two additional pi gauges with 100 mm gauge length were used to measure the transverse deormations at the mid-height. The pi gauges were alibrated using a aliper every time beore testing. The onrete axial strain was taken as the average o the pi gauge readings divided by their respetive gauge lengths. The strains in the longitudinal and transverse reinorements were measured using eletri resistane strain gages, whih were attahed at the mid-loation between the spaing o transverse reinorement in two diagonally opposite longitudinal reinorements and on two transverse reinorements at the mid-height o the olumns, respetively, or onentri loading ase. For eentri loading ase, the onrete axial and transverse deormations were measured by pi gauges. The loation and ormat o the gauges are the same as onentri loading ase. Four eletri resistane strain gages were plaed on the longitudinal and transverse reinorements at the 51

69 Chapter 3 Experimental Program mid-height o the olumns, respetively. Three linear variable displaement transduers (LVDT) were used to measure the lateral deletions o the eentrially loaded speimens. For the irular olumns, the onrete axial shortening o the olumns was measured using our pi gauges, loated at the mid-height, at 90 degree along the irumerene o the test speimens. Two o the pi gages were attahed to the threaded rods embedded in the ore onrete while the other two gages were mounted on the onrete surae. The gauge length o the pi gauges were 100 mm. The strains in the longitudinal and spiral reinorement were measured using eletri resistane strain gages, whih were attahed to two longitudinal reinorements and two spiral reinorements in opposite diretion to eah other at the midheight o the olumns. All strain gauges were provided by Tokyo Sokki Kenkyuio Corporation. M-Bond 200 adhesive glue manuatured by Vishay Miro Measurements was used or mounting the strain gauges. Figure 22 shows the loations o strain gauges on longitudinal and transverse reinorement or the retangular and irular olumns. Figure 23 shows the loation layout o pi gauges or the retangular and irular olumns. 3.6 Test Set-up Conentrially Loaded Columns The onentrially loaded olumn speimens were tested under monotonially inreasing axial ompressive loading ondition. The olumn was moved by ork lit, aligned in the 52

70 Chapter 3 Experimental Program enter o lower plate in the loading mahine, and leveled. Thin layers o hydrostone (gypsum ement) were used at the top and the bottom ends o eah olumn or leveling and ensuring uniorm distribution o the applied load aross the ross setion. An initial load o 100 ~ 200 kips was applied to the olumn, and the pi gauge and strain gauge readings were monitored. Ater the position o the speimen had been heked, the olumn was unloaded, and all the readings were set to zero. A 2,000 kip (8896 kn) apaity ompression testing mahine with displaement ontrol, loated at CFL (Constrution Failities Laboratory) o North Carolina State University, was used to apply the ompression load monotonially at an average rate o in./min. or olumn speimens. The rate o loading was kept onstant rom the beginning to later stage o test. Eight olumns (14R9-ρ4, 14R4½-ρ4, and six olumns o 14C series), o whih the load arrying apaity was estimated to be too lose to the apaity o the testing mahine, were tested using a 5,000 kip (22,240 kn) apaity Baldwin testing mahine by speial arrangement with Lehigh University. The same rate o loading was used or the Lehigh tests. Figure 24 shows loading mahines and data aquisition system at both NC State University and Lehigh University. The pi gauge reading, steel strains, applied loads, and mahine strokes were reorded using Vishay data aquisition system and omputer. The tests ontinued until either a signiiant drop in load-resistane o the olumns or detahment o the instrumentations. The duration o tests or the retangular olumns was between 60 and 90 minutes. The testing o the irular olumns, whih showed onsiderable dutile behavior ompared to the retangular olumns, 53

71 Chapter 3 Experimental Program ontinued or 2 and 3 hours. The ylinders were tested as lose as possible to the time o testing the olumn speimen. Figure 25 shows typial test set-up or the onentrially loaded olumns Eentrially Loaded Columns For eentrially loaded olumns, the load was applied with speii eentriities using speially designed urved plate and roller bearing assembly. Eah o the assembly onsisted o two urved plates and six rollers. The assembly was plaed and aligned in the enter o the lower plate in the loading mahine, and the olumn speimen was positioned on the assembly with speii eentriities, ollowed by plaing the other assembly on the top o the olumn. The rollers o the urved plates were released and all the readings were set to zero beore starting o test. Figure 26 shows typial test set-up or the eentrially loaded olumns. 54

72 Chapter 4 Test Results Chapter 4 Test Results This hapter summarizes the measured behavior o the onentrially and eentrially loaded retangular olumns and onentrially loaded irular olumns during testing based on author s observations and the raw data reorded. Typial behavior, inluding axial loadshortening relationship, onrete strains, and longitudinal and transverse steel strains as well as the mode o ailure, is presented in this hapter. 4.1 Conentrially Loaded Retangular Columns Typial axial ompressive load-shortening relationship, load-average axial onrete strain measured by pi gauge, load-longitudinal steel strain, and load-transverse steel (tie) strain, o onentrially loaded retangular olumns are shown in Figure 27 through Figure 30. Most o the readings o the pi gauges and strain gauges ater peak load were not reorded due to the explosive ailure o the olumns. The asending part o the typial axial ompressive load-shortening relationship was almost linear without any observed raks up to the measured peak load (P max ) or most o the olumns as shown in Figure 27 with the exeption o ew speimens whih were subjeted to small unintended eentriities during testing. The average measured axial onrete strains 55

73 Chapter 4 Test Results orresponding to the peak load ranged rom to as shown in Figure 28. At the maximum load, P max, the measured longitudinal reinorement strain exeeded the yield strain o the reinorement as shown in Figure 29, whih ourred in all tested olumns with tie reinorement. These results suggest that ties in the olumns spaed aording to the spaing allowed by the LRFD Speiiations (2004), are suiient to provide adequate lateral support to prevent bukling o longitudinal reinorement below its yield strength. The measured transverse reinorement strains were in elasti region and muh lower than the yield strain o the transverse reinorement at this stage as shown in Figure 30. Figure 31 ompares the retangular olumns with almost same onrete strength, tie spaing, and olumn size but three dierent longitudinal reinorement ratios. The igure indiates that the maximum load resistane o olumns, P max, was aeted by longitudinal reinorement ratios. At the peak load, the onrete over suddenly spalled o explosively at the mid height o the olumn or all tested speimens with larger tie spaing. Spalling o the onrete over or the olumns with loser tie spaing ourred with less explosive ation. Spalling o the onrete over was also aompanied by some loss o ore onrete and resulted in a sudden drop in load arrying apaity o the olumns as shown in Figure 27. This was more pronouned or olumns with higher ompressive strength o onrete. The residual resistane ater peak load was higher or olumns with loser tie spaing as shown in Figure 32 or olumns with same ompressive strength o onrete and longitudinal reinorement ratio. This behavior suggests that the remaining resistane o the olumn is highly dependent on the loal bukling resistane o the longitudinal reinorement and the tie spaing played a signiiant role on post peak behavior o the olumns. Figure 33 shows typial ailure shapes o 56

74 Chapter 4 Test Results onentrially loaded retangular olumns with dierent tie spaings and the eet o the tie spaing on the bukling shape o the longitudinal reinorements. The ormation o an inlined shear ailure plane, separating the onrete ore into two wedges restrained by the ohesion o onrete and the reinorement steel was observed at a later stage o loading (Figure 34). Test results indiated that the test speimens with the larger tie paing, designed aording to the maximum spaing allowed by the LRFD Speiiations, did not provide any oninement to the onrete ore. Strength enhanement due to the use o smaller tie spaing, as muh as one hal o the speiiation requirement, was insigniiant. However, the use o smaller tie spaing inreased the residual strength ater peak load as shown in Figure 32. For some o the olumns with loser spaing o ties, the transverse reinorement yielded at a later stage o loading using strain ontrolled loading ondition. Figure 35 shows olumn behavior during dierent stages o loading. 4.2 Conentrially Loaded Cirular Columns Typial axial load-shortening relationship, load-axial onrete strain measured by pi gauge, load-longitudinal steel strain, and load-spiral steel strain, o onentrially loaded irular olumns are shown Figure 36 through Figure 39. The initial behavior shown in the axial load-shortening o the irular olumns was almost linear up to initiation o the longitudinal rak at load level, P CR, in Figure 36. In the majority o the olumns, the initial longitudinal rak ourred at an average measured onrete strain ranging rom to as shown in Figure 37. The ormation o the longitudinal rak was not uniormly distributed at all sides. Usually the raks were initiated on one side o the olumns, and shortly ater 57

75 Chapter 4 Test Results propagated to other sides. These raks led to the spalling o over onrete, as evidened by the separation o large piees o over rom ore onrete. The spalling o over onrete aused small drop o the load arrying apaity as shown in Figure 36, whih was subsequently reovered. Beyond this stage, the applied load was maintained mainly by the ore onrete and longitudinal reinorement. At load level P CR, orresponding o the initiation o spalling o onrete over, the longitudinal reinorements yielded or most o the irular olumns (Figure 38). The measured strains in the spiral reinorement inreased rapidly ater spalling o over onrete and were higher than the yield strain at the maximum measured axial load in all tested olumns as shown in Figure 39. These results suggest that the onrete ore was onined by the spiral reinorements whih aeted signiiantly the overall behavior o the irular olumn. The eet o the oninement is learly reognizable by omparing the behaviors o the olumns with losely spaed spiral versus widely spaed spiral, as shown in Figure 40. As expeted, the maximum load resistane o olumns (P max ) was mainly proportional to longitudinal reinorement ratio as shown in Figure 41 or olumns with similar onrete strength and spiral spaing. Ater peak load, the load arrying apaities o the olumns with losely spaed spiral were muh more than the olumns with widely spaed spiral as shown in Figure 40. The omparison o the irular olumns with dierent spiral spaings indiates that the spiral spaing also played a signiiant role on post peak behavior o the irular olumns. The load arrying apaity was redued gradually until rupture o spiral ourred due to sliding o shear planes o the raked onrete ore, whih was restrained by spiral steel as shown 58

76 Chapter 4 Test Results Figure 42. This behavior was similar to that o the retangular olumns with ties at very later stage. The initial loss o the load arrying apaity was due to spalling o the onrete over, raking o the ore onrete, and the loal bukling o the longitudinal reinorement. Aterwards, initiation o the shear sliding within the raked ore onrete was observed. The shear sliding along the ailure plane was inlined at 55 ~ 65 rom horizontal. The seond signiiant loss o the load arrying apaity o the olumns was due to rupture o the spiral, ollowed by rushing o the ore onrete as shown in Figure 43. The behavior o typial irular olumn at dierent stages o loading is shown in Figure Eentrially Loaded Retangular Columns Typial axial ompressive load shortening relationship o eentrially loaded olumns with eentriities to depth ratio, e/h, o 10 and 20 perent are shown in Figure 45. The igure also inludes onentrially loaded olumn to emphasize the eet o load eentriity on the behavior o the olumn. In most o the olumns, no raks were observed on the ompressive side o the olumn up to the maximum measured load. In some ases, the raking sound was heard at loads slightly lower than the maximum load. At the peak load, spalling o the onrete over and bukling o the longitudinal reinorement were observed simultaneously at the extreme ompression ae, as shown in Figure 46 (a). As the peak load was reahed, inlined lexural raks propagated quikly 59

77 Chapter 4 Test Results through the tension side as shown in Figure 46 (b). The load arrying apaity o eentrially loaded olumns was redued due to the presene o the moment resulting rom the applied load with eentriity. The maximum measured onrete ompressive strain at the ompression side ranged rom to at the peak load (Figure 47) and onsequently the strain in the longitudinal reinorement exeeded the yield strain (Figure 48). The measured tie strains at the peak load were within the elasti range. As seen in Figure 49, the largest measured strain or the tie strain, gauge T1, was loser to the ompression side. The results suggest that the tie on the ompression side resists higher ores due to the bukling o the longitudinal reinorement. Aording to the strain proiles shown in Figure 50 and Figure 51, the entire ross-setion o the olumns with 10 perent eentriity, olumns o E1 series, were subjeted to ompressive stresses up to peak load. This onlusion is onirmed by the olumn behavior without any tension up to the peak load or olumns o E1 series. Figure 52 shows eentrially loaded olumn behavior during dierent stages o loading. 4.4 Ultimate Conrete Strain The measured ultimate ompressive strains o onrete rom eentrially loaded olumns ranged rom to The average value o the strains was or the olumns with onrete strength greater than 10 ksi (69 MPa), and was or all tested olumns. Figure 53 shows the measured ultimate ompressive strains with respet to onrete strength. No deinite trend is observed. I the single exeptional value o is exluded, the average value or the olumns with onrete strength larger than 10 ksi (69 MPa) approahes 60

78 Chapter 4 Test Results to a lower value o Thereore, the value o or the ultimate ompressive strain speiied by the urrent speiiation seems appropriate as a onservative lower bound. 61

79 Chapter 5 Analysis o Test Results Chapter 5 Analysis o Test Results 5.1 Introdution This hapter disusses test result o the olumns presented in Chapter 4. The axial ompressive strengths o olumns with high-strength onrete are presented in Setion 5.2. Setion 5.3 disusses the olumn dutility with respet to the test parameters inluding setion geometry, onrete ompressive strength, volumetri ratio o transverse reinorement, and the longitudinal reinorement ratio. Setion 5.4 examines the appliability o the retangular stress blok parameters reommended by various odes and proposed by NCHRP projet or eentrially loaded retangular olumns made with high-strength onrete. In Setions 5.5 and 5.6, a veriiation o various oninement models available in the literature is made by omparison with experimental data and a disussion o minimum amount o spiral reinorement required by the urrent LRFD Speiiation is inluded. Also, a new stress-strain relationship o onined onrete proposed by this study or high-strength onrete is provided. 62

80 Chapter 5 Analysis o Test Results 5.2 Axial Compressive Strength o Columns This setion disusses the axial ompressive resistane o retangular and irular olumns with high-strength onrete Retangular Columns with Tie Reinorement The nominal axial load apaity o a olumn under onentri loading, P o an be represented by using proposed parameter k as ollows: where and P = k ( A A ) + A Eq. 5-1 o g s y s A g is the gross area o the olumn, y is the yield strength o longitudinal reinorement, A s is the total area o longitudinal reinorement. The above equation relets that the apaity o onentrially loaded olumns onsists o steel and onrete ontributions. The onrete ontribution is omputed based on the total area o onrete o the olumn setion inluding over onrete. The parameter k aounts or the dierene between onrete strength in the olumn and that based on testing o onrete ylinder. The dierene is attributed to the size eet and onrete ast proess o olumn versus standard onrete ylinder. The parameter k is dierent rom the generalized stress blok parameter k 3 mentioned in Setion 2.5, whih is the ratio o the maximum ompressive stress to the ylinder strength under lexural loading with strain gradient. In 1934, Rihart and Brown reported results o an extensive experimental program onduted on reinored onrete olumns with onrete strength ranging rom 2 to 5 ksi. A value o 63

81 Chapter 5 Analysis o Test Results 0.85 was suggested or k or the tied olumns or spirally reinored olumns with onsiderable onrete shell thikness and subjeted to onentri loading ondition. Based on this researh, the value o 0.85 or k parameter was adopted by the ACI and AASHTO- LRFD Speiiations or onentrially loaded olumn with normal strength onrete. The measured maximum olumn apaity tested by the author, P max, and the predited apaity, P o using k value o 0.85 in Eq. 5-1 or onentrially loaded retangular olumns are given in Table 8.The table also provides the ratios o P max to P o. The results were ombined with data reported in the literature by Sheik and Uzumeri (1980), Cusson and Paultre (1994), Saatioglu and Razvi (1998), and Sharma et al. (2005) in Figure 54. These data suggest that using a value o 0.85 ould overestimate the olumn apaity or high strength onrete. The value o k was determined based on the measured maximum apaity, P max and Eq. 5-1 or the onentrially loaded retangular olumns in this study. Figure 55 illustrates the alulated values o k with respet to the ompressive strength o the onrete. Test results indiated that measured strain in the longitudinal reinorement exeeded the yield strain at the measure maximum load or all tested olumns with tie reinorement. Thereore the stress in the longitudinal reinorement is equal to the yield strength y in Eq Figure 55 provides lear trend that the value o k dereases with inreasing onrete strength. For olumns with onrete strength around 15 ksi, the magnitude o k or smaller size olumns is generally less than that o larger size olumns. This behavior ould be attributed 64

82 Chapter 5 Analysis o Test Results to the size o the ross setion whih beomes more sensitive when subjeted to the same unintended eentriity. The parameter k was urther analyzed with data reported in the literature or tied olumns. The magnitude o k based on test results o the onentrially loaded olumns with tie reinorement tested in this study as well as based on the reported data by others are shown in Figure 56. It should be noted that the data shown in this igure also inlude olumns with loser tie spaing than that required by LRFD Speiiations. This igure suggests that the value o k dereases with inreasing onrete strength or onrete strength greater than 10 ksi. Test results or this study, whih inluded onrete strengths ranging rom 7.9 to 16.1 ksi (55 to 111 MPa), show the same trend reported by other researhers (i.e. Ozbakkaloglu and Saatioglu, 2004). Using a value o 0.85 or k may not be appropriate or the onentrially loaded tied olumn with onrete strength greater than 10 ksi. Regression analysis o the olleted data, shown in Figure 56, indiates that 80 perent o the k values are higher than 0.75 or onrete strength greater than 10 ksi. Using it as lower bound, the ollowing expression or the parameter k is proposed or onrete strength up to 18 ksi (124 MPa). k 0.85 or 10 = ( 10) 0.75 or > 10 in ksi Eq. 5-2 and in metri unit, 65

83 Chapter 5 Analysis o Test Results k 0.85 or 69 = ( 69) 0.75 or > 69 in MPa Eq. 5-3 The proposed expression or k mathes the urrent ACI and LRFD Speiiations or normal strength onrete and extends its use or high strength onrete up to 18 ksi Cirular Columns with Spiral Reinorement The measured load orresponding to initial spalling o onrete over, P CR, was used to determine the parameter k or irular olumns with spiral reinorement using Eq. 5-1, sine the eetive setion area o onrete resisting the applied load is redued due to raking o the over onrete. The measured P CR, the predited apaity P o, the measured maximum load ater raking o onrete over, and the alulated value k rom the test data or onentrially loaded irular olumns in this study are given in Table 9. The parameter k obtained rom the onentrially loaded irular olumns, rom both this study and other reported tests are shown in Figure 57. The igure shows the same trend o parameter k as observed or tied retangular olumns. It an be observed that this trend or the olumns tested in Lehigh University, is not strong. This is likely due to the inreased stiness o the loading mahine at Lehigh University as ompared to the testing mahine at North Carolina State University. It should be noted that the longitudinal reinorement or some o the irular olumns did not yield beore spalling o the onrete over as evidened by the strain measurements shown in Figure 58 (b). In these ases, the measured strain in the longitudinal reinorement 66

84 Chapter 5 Analysis o Test Results was used to determine the steel stresses in the longitudinal reinorements in Eq. 5-1 instead o the yield strength. The measured strain in the spiral reinorement was onsiderably less than the yield strain at P CR, as shown in Figure 58 (), whih means that the onrete ore was not onined eetively by the spiral reinorement at the load level orresponding to spalling load, P CR. The measured onrete strain in the olumns indiated that spalling o onrete over ourred prior to the development o the ultimate ompressive strain o the onrete as shown in Figure 58 (a). This early spalling o the onrete over is believed to be due to presene o losely spaed spiral whih ormed a semi steel shell separating the onrete over rom the inner ore o the irular olumn, and resulted in lower values o k. This phenomenon is more pronouned or olumns with high-strength onrete. Collins, Mithell, and MaGregor (1993) indiated that early spalling o over onrete in olumns with high-strength onrete ould be due to early drying o the outermost shell o the olumn relative to the ore. This is an established phenomenon or high-strength onrete due to inherited low permeability harateristis. This behavior will result in restrained shrinkage stress in the outer shell as illustrated in Figure 59 (a). In addition, the shrinkage o high-strength onrete around reinoring bars develops splitting raks radiating out rom the bars in shown in Figure 59 (b). The early spalling o onrete over may be aused by the ombination o these two mehanisms as illustrated in Figure 59 (). Although the measured load arrying apaity o the irular olumns orresponding to initiation o spalling o onrete over was used to determine the values o k, the arrying apaity o the irular olumns inreased ater the spalling o the onrete over due to the 67

85 Chapter 5 Analysis o Test Results oninement produed by the spiral reinorement. The behavior shown in Figure 40 learly relets the signiiant inrease in the maximum load-arrying apaity P max with respet to the measured load at the initiation o spalling o the onrete over, P CR, due to oninement eet produed by spiral reinorement. Aordingly, the same expression o k, proposed or olumns with tie reinorement, an be saely used or olumns with spiral reinorement. Ozbakkaloglu and Saatioglu (2004) suggested that the parameter k is related to the ratio o ore-area to gross-area ( A / A ). Aording to the authors, strength loss assoiated with g over spalling is a untion o the amount o over onrete to be lost prematurely, and the premature strength loss inreases as the ratio dereases (over thikness inreases). Figure 60 illustrates the variation o the k with the ratio ( A / A ) or retangular and irular olumns tested in this study as well as data reported by others. It appears that there is a lak o orrelation between the lower bound o k parameter and the ratio ( A / A ). g g Generally, the olumns with thin overs are likely to suer rom early loss o over onrete more severely than those with thik overs. The early loss o over onrete naturally results in a lower value o k or the olumns with losely spaed transverse reinorement. Test results and observations in this study as well as those in the literature do not strongly support their argument. 68

86 Chapter 5 Analysis o Test Results Nominal Axial Resistane o Columns As mentioned beore, the nominal axial load arrying apaity o a olumn at zero eentriity (P o ) an be determined by using k parameter introdued by this researh program. However, it should be noted that onentrially loaded olumn is only theoretially true. Unintentional eentriities are expeted due to end onditions, inauray o onstrution, and normal variation in material properties. Hene in design, a minimum eentriity o 10 perent o the thikness o the olumn in the diretion perpendiular to its axis o bending is normally onsidered or the design o olumns with ties and 5 perent or spirally reinored olumns. To redue the alulations neessary or analysis and design or minimum eentriity, the LRFD Speiiations presribes a redution o 20 perent in the axial load or tied olumns and a 15 perent redution or spiral olumns. Using these ators, the nominal axial resistane o olumns an be determined using the new parameter k as ollows: P = 0.8 ( ) n(max) k Ag As + ya s or tied reinored olumns Eq. 5-4 P = 0.85 ( ) n(max) k Ag As + ya s or spirally reinored olumns Eq. 5-5 In Table 10, the maximum measured load P max o the olumns with an eentriity o 0.09h or 0.1h is ompared with 80 perent o the predited nominal strength (0.8P o ) o the tied olumns using Eq The results indiate that measured maximum axial load o the olumns, P max is onsistently greater than the predited nominal strength. The dierene ranged between 6 and 21 perent with an average o 12 perent. Thereore, or design 69

87 Chapter 5 Analysis o Test Results purpose, the 20 perent redution in the axial load apaity o the olumn inluded in the LRFD Speiiations to aount or unintentional eentriity or tied olumns with highstrength onrete is on the onservative side. 5.3 Column Dutility Dutility o the olumns tested in this study was evaluated by using the measured axial loadshortening relationship o the olumns. Energy dutility method was used to quantiy the dutility o the olumns more eetively. Based on the determined dutility o the olumns, eet o the test parameters, namely setion geometry, ompressive onrete strength, longitudinal reinorement ratio, and amount/spaing o transverse reinorement on the dutility o the olumns will be disussed in this setion Energy Dutility o Column Pessiki and Pieroni (1997) deined olumn displaement dutility as the ratio o the axial displaement o the olumn at an axial load orresponding to 85 perent o the maximum axial load on the desending branh o the axial load-shortening urve, Δ 85 to the displaement at the limit o elasti behavior, Δ y. Figure 61 (a) illustrates how the limit o elasti behavior, Δ y is determined. A best-it line to the linear portion o the axial loadshortening urve or eah olumn was obtained by linear regression analysis. This line was then extended to interset with the maximum load o the olumn. The Δ y is the displaement 70

88 Chapter 5 Analysis o Test Results orresponding to this intersetion. The dutility based on 85 perent o the maximum axial load, μ 85 is presented as; μ Δ = Eq. 5-6 Δ y This method is not adequate or some ases where the axial load dropped sharply ater peak load, similar to the retangular olumns tested in this study, sine the method does not dierentiate the dutility between the olumns with a small residual load resistane and those with a large load resistane. For example, the load arrying apaity o one olumn may drop by 16 perent shortly ater the peak load and maintain this residual resistane with a onsiderable inrease in strain. The residual resistane o the other olumn may establish ater sudden drop o load arrying apaity by 80 perent ater the peak load. Using the displaement dutility method, both the olumns desribed above would have the same dutility. Aordingly, a better approah to measure the dutility o those olumns may be by using the energy dutility method. The energy dutility, irst used in evaluating the olumn dutility by Foster and Attard (1997) is based on the area under the measured axial loadshortening urve. The method was already adopted in ASTM (C1018) or measurement o lexural toughness. In this method, the dutility index is denoted as I 5. Figure 61 (b) shows how the index is determined. I 5 is the area OACD, divided by the are OAB, where B orresponds to the point or a peretly elasto-plasti material. Δ y and D to the point 3Δ y. By these deinitions, the value o I 5 is 5 71

89 Chapter 5 Analysis o Test Results Eets o Test Parameters Setion geometry It has been known that irular spirals are more eetive or oninement o onrete than retangular or square ties. This oninement eetiveness o irular spirals is aused by their geometri shape whih provides better uniorm and ontinuous distribution o lateral onining pressure around the onrete ore ompared to retangular or square ties. The eet o setion geometry is evident by omparing test results or retangular and irular olumns with similar onrete strength and volumetri ratios o transverse steel. Figure 62 shows omparisons o axial load-shortening relationship between the retangular and irular olumns with similar onigurations inluding onrete strength, area o ross setion, and longitudinal reinorement ratio. Although the irular olumns have a smaller volumetri ratio than the mathed retangular olumns (1.44 % vs %), the irular olumns exhibit an enhaned behavior in terms o strength and dutility than the retangular olumns. Inrease in dutility an be learly shown by omparing the values o I 5. The dutility indies ( I 5 ) o the irular olumns 10C2¾-ρ1 and 10C2¾-ρ4 were 4.14 and 4.08, respetively while those o the mathed retangular olumns 10R4½-ρ1 and 10R4½-ρ4 were 3.15 and 3.42, respetively. These values are given or the tested olumns in Table 11. These results suggest that to ahieve the same degree o dutility or retangular or square olumns with ties, the lateral reinorement should be inreased in omparison to irular olumns with spirals. 72

90 Chapter 5 Analysis o Test Results Conrete ompressive strength The onrete ompressive strength is the most important parameter investigated extensively in this study. In Table 12, the dutility o olumns with approximately same volumetri ratio (or spaing o lateral steel), geometri shape, area o ross setion, and longitudinal steel but with distintly dierent onrete strength is ompared to examine the eet o this parameter. The omparisons indiate that the dutility values o I 5 or both retangular and irular olumns normally derease by inreasing the ompressive strength o onrete. For olumns with similar oniguration but dierent onrete strengths, 10C2¾-ρ4, A10C2¾-ρ4, and 14C2-ρ4, the dutility values o I 5 were 4.08, 3.75, and 3.39 respetively when onrete strengths were 8 ksi, 11.8 ksi, and 16 ksi respetively. Lower values o I 5 or olumns with higher onrete strength were more pronouned or the group o olumns with higher volumetri ratio o lateral steel. These results indiate that post peak urve o olumn with higher onrete strength are steeper releting more sudden drop o load resistane ater peak load ompared to the olumn with lower onrete strength. Thereore, i the same levels o dutility are desired, olumns with higher strength onrete should be reinored with more lateral steel than those with lower onrete strength Amount / spaing o transverse reinorement It an be shown that the amount o lateral steel (or spaing o lateral steel) is the most ruial parameter whih aets the behavior o olumns with respet to strength and dutility. An inrease o the amount o lateral steel, usually expressed in terms o volumetri ratio, leads to 73

91 Chapter 5 Analysis o Test Results an inrease in lateral onining pressure, resulting in improvement o both the strength and dutility o onined onrete. Figure 32 and Figure 40 illustrates the eet o the volumetri ratio o lateral steel (or spaing o transverse steel) on the behavior o olumns. In both retangular olumns with ties and irular olumns with spirals, the larger the volumetri ratio or loser the spaing o lateral steel, the more dutile is the behavior o olumns. A more sudden drop o load resistane ater peak load ourred in the olumns with lower volumetri ratio or larger spaing o transverse steel. In omparison o dutility values o I 5 in Table 13, the values o I 5 or olumns with larger volumetri ratio o lateral steel were greater in all ases ompared without any exeptions. These test results onirmed that the amount o lateral steel on dutility is a major ator aeting dutility o olumns Longitudinal reinorement ratio Table 14 ompares the dutility o olumns with a lower ratio o longitudinal steel to the dutility o olumns with a higher ratio o longitudinal steel. Other parameters inluding onrete strength are almost same in eah omparison. From the omparisons, dutility values o I 5 seem to be slightly larger or olumns with higher ratio o longitudinal steel, however the trend is not very deinite. It is believed that larger amount o longitudinal steel may provide more restraining ation against an inlined shear ailure as dowels ompared to small amount o longitudinal steel. Thereore, it an be onluded that the amount o longitudinal steel has only small eet on dutility o olumns. 74

92 Chapter 5 Analysis o Test Results 5.4 Retangular Stress Blok o High-Strength Conrete Data rom 20 reinored onrete olumns with onrete ompressive strengths higher than 10 ksi (69 MPa), tested in this study, along with the reported data by others under ombined axial and lexural loading were examined to veriy the appliability o the dierent retangular stress bloks in the ompression zone as disussed above. The parameters or the retangular stress bloks were used to onstrut the interation diagram or eah o the tested olumns. The predited values (M pred, P pred ) are ompared to the experimental values (M exp, P exp ) or eah tested olumns using the same eentriities as illustrated in Figure 63. The ratios (P exp / P pred ) using dierent retangular stress blok is given in Table 15. Although the average o the ratio (P exp / P pred ) using the ACI / AASHTO retangular stress blok was slightly greater than 1, or approximately hal o the olumns examined, the ratio was less than 1, whih means that the preditions overestimate the strength o the olumns. However, the ratio in Table 15 indiates that the preditions using the CSA retangular stress blok are overly onservative espeially or the olumns with onrete strength higher than 14 ksi, ompared to those based on other retangular stress blok. The average o the ratios using the NZS and NCHRP retangular stress bloks was 1.13 and 1.09 respetively, and the strengths o all the olumns were greater than the preditions, with the only exeption being the olumns tested by Tan and Nguyen (2005) ompared to predition by the NCHRP retangular stress blok. Generally, using the NZS and NCHRP retangular stress bloks or onrete strength higher than 10 ksi produed improved omparisons between the preditions and the test results. The interation diagrams or the 9 12 in. olumns with onrete strengths o 7.9, 10.9, and 16.5 ksi are shown in Figure 64. Figure 65 shows the similar 75

93 Chapter 5 Analysis o Test Results diagrams or the 7 9 in. olumns with onrete strength o 14.0 ksi and 15.6 ksi. Measured olumn strengths obtained rom the eentrially loaded olumns tested in this study were marked on the olumn interation diagrams. They illustrate graphially the dierenes among the various retangular stress bloks or onrete strength higher than 10 ksi. The igures indiate that, or onrete ompressive strengths exeeding 10 ksi, the interation diagrams based on the NZS and NCHRP retangular stress blok are reasonably onservative than those based on other retangular stress blok. Espeially, NCHRP retangular stress blok, whih is the same as the proposed k parameter or onentrially loaded olumns by this study, an be onveniently used in design appliations. 5.5 Conined Conrete Strength by Spiral Reinorement Comparison between Preditions and Experimental Data The onined strength o onrete was determined by subtrating the alulated load arried by longitudinal reinorement rom the measured maximum load o the irular olumn, and divided by the area o ore onrete as ollows: P max ( As y ) = A As Eq. 5-7 where A is the ore area measured to outside diameter o spiral steel. The above equation assumes that the over onrete or the irular olumn is spalled away ompletely and is not eetive in arrying the maximum load. Sine the measured strain in the spiral steel was higher than yield strain at the maximum axial load in all tested irular 76

94 Chapter 5 Analysis o Test Results olumns, the yield strength o spiral steel sy was used to determine the lateral oninement stress l, whih is represented as ollows: l 2A sp sy = Eq. 5-8 ds In Table 16, the test results are ompared with the preditions o the onined onrete strength based on the proposed equation by Rihart et al. (1929), Martinez et al. (1984), Mander et al. (1988), and Saatioglu and Razvi (1992) as summarized previously. It should be noted that unonined onrete strength o in Eq. 2-15, Eq. 2-31, and Eq is the plain onrete strength in a member under onentri loading. This may be dierent rom onrete strength obtained rom a standard ylinder test. In this study, the o was determined as the produt o and average k value or similar onrete strength group ranging between 0.77 and 0.97 in Table 9. The average o the ratios (, exp /, pred ) using the proposed equations by Rihart et al., Martinez et al., Mander et al. and Saatioglu and Razvi are 1.05, 1.13, 0.98, and 1.01, respetively. These omparisons indiate that the test results were higher than the preditions using all the proposed equations above or the olumns with larger setion (12 in. dia.) while test results were lose to or less than the preditions or the olumns with smaller setion (9 in. dia.). For the olumn with larger setion, the predition proposed by Mander et al. shows best omparison with test results with the average ratio (, exp /, pred ) being For 77

95 Chapter 5 Analysis o Test Results the olumn with small setion, the expression proposed by Martinez et al. indiates exellent agreements with test results with the average ratio (, exp /, pred ) being Analysis o Conined Conrete Strength in Terms o the Mohr- Coulomb Failure Criterion The loading ondition o ore onrete onined by spiral steel subjeted to axial ompression an be onsidered as in the state o triaxial stress. Several ailure riteria assoiated with a maximum stress surae have been established or onrete under triaxial ailure state o stress over the years. Although some models proposed in relatively reent years suh as William-Warnke riteria (1975) and Ottosen riteria (1977) shows an improvement or prediting the ailure o onrete under general loading onditions, they are omprised o a number o parameters and their implementation requires many test results whih, with the exeption o the uniaxial ompressive strength, are not easy to obtain. Test results o this study were obtained rom ore onrete onined by spiral steel, subjeted to triaxial ailure state o stress with isotropi stresses in the horizontal orientation ( σ1 > σ2 = σ3 ). The theoretial ailure stress based on the Mohr-Coulomb theory was ompared with the test results. The theory has oten been used in the literature to approximate the maximum stress o onrete due to the observed ailure mode (ompressionshear ailure). It is believed that this omparison and related disussion provides urther insight into the behavior o spirally reinored onrete olumns. 78

96 Chapter 5 Analysis o Test Results The Mohr-Coulomb riterion an not be presented beore introduing irst the two theories on whih it is based, the Coulomb riterion (internal rition theory) and the Mohr s riterion. The internal rition theory, proposed by Coulomb in 1773, is based on the observation that in the shear ailure o roks (or any geomaterial), the shear stress ausing the ailure aross the plane is resisted by the ohesion o the material and a ritional ore (Eq. 5-9) τ = + σ tanφ Eq. 5-9 where τ is the shear strength, is the ohesion, σ is the normal stress on the plane, and φ is the internal-rition angle o the material. The material is onsidered to ail when the shearing stress on any plane exeeds the value o the shear strength given by Eq On a τ σ diagram as shown in Figure 66, the ailure envelope o Eq. 5-9 is presented by a straight line inlined to the axis at an angle φ. A more general theory was introdued by Otto Mohr in The Mohr s ailure riterion onsiders the limiting shear stress τ in a plane to be a untion o the normal stress σ in the same plane at a point (Eq. 5-10) where ( σ ) is an experimentally determined untion. τ = ( σ ) Eq In terms o Mohr s graphial representation o the state o stress, Eq means that ailure o material will our i the radius o the largest prinipal irle is tangent to the envelope urve ( σ ) as shown in Figure 67. This means that the intermediate prinipal stress has no 79

97 Chapter 5 Analysis o Test Results inluene on the ailure. By negleting the eet o the intermediate prinipal stress σ 2, the riterion are unable to predit the enhanement o onrete strength under biaxial ompression (whih leads to ail in tension, in planes parallel to the loading). Moreover, the Mohr s and the Coulomb s riterion are widely used when the material ails by sliding deormation (ompression-shear ailure). Thereore, these two riteria by themselves an not represent the omplete ailure riteria or onrete. However, they have provided reasonable and onservative preditions o onrete strength when ombined with the riterion o a onstant maximum tensile stress or strain (Cowan 1953). The Mohr-Coulomb riterion is a ombination o the two riteria mentioned above. It states that the ailure envelope o all the irles orresponding to various states o stresses in a τ σ diagram an be approximated by a straight line as shown in Figure 68. Figure 69 through Figure 72 show the Mohr s irles at ailure or the irular olumns on a τ σ diagram, normalized by unonined onrete strength o. The irular olumns with same size and similar measured onrete strength are grouped together in the igures. The value o the maximum axial stress (onined onrete strength),, and the lateral oninement stress, l as given in Table 17 and Table 18 are represented by the normal stresses, σ 1 and σ 2 = σ 3 respetively. The igures also give linear envelopes (Mohr- Coulomb riteria), represented by straight lines or eah group. The linear envelopes were determined by using the statistial tehnique desribed in Appendix. 80

98 Chapter 5 Analysis o Test Results The values o the angle o internal rition obtained or the irular olumns with average onrete strength o 8 ksi, 11.8 ksi, 16.1 ksi, and 15.1 ksi were 39.9, 33.7, 28.6, and 34.5, respetively. The orresponding ohesion values were 0.26, 0.33, 0.35 o o o, and 0.27 o. These results were illustrated graphially in Figure 73. The results obtained rom the irular olumns with 12 in. dia. setion indiated that the angle o internal rition dereases with an inrease o onrete strength, while the ohesion inreases with an inrease o onrete strength. Figure 73 also shows a ailure envelope based on average values o 34 and 0.27 o or the angle o the internal rition and the ohesion, respetively, rom all the irular olumns tested in this study. It should be noted that the ohesion, as deined above, is not the atual shear strength o the material, but merely the τ axis interept o the Mohr-Coulomb ailure envelope. However, it an be a mathematial approah or prediting the ailure o onrete onveniently. The Mohr-Coulomb riterion provides the ailure plane oriented at an angle θ, obtained by using the ollowing relation rom Figure 68, φ θ = 45 + Eq

99 Chapter 5 Analysis o Test Results The angle θ is perpendiular to the largest prinipal stress. For the angle o average internal rition, φ = 34, the angle θ in Eq gives 62. This value is lose to the angle o the inlined shear plane observed in the irular olumns in Setion 4.2. Based on a Mohr-Coulomb ailure envelope shown in Figure 68, it an be derived that 2 os φ 1+ sin σ1 = + σ φ 2 1 sinφ 1 sinφ Eq Using the average values o the internal rition angle φ = 34 and the ohesion = 0.27 o in Eq gives, 1 o 3.6σ 2 σ = + Eq When σ 1 and σ 2 are substituted by the maximum axial stress (onined onrete strength), and the lateral oninement stress, l, respetively, Eq has a similar orm with the expression o Eq proposed by Rihart et al.. The above disussion indiates that the Mohr-Coulomb riterion was useul or the predition o the maximum axial strength and the orientation o the ailure plane o the irular olumns tested in this study. It also indiates that ailure o the irular olumns is governed mainly by a ompression-shear mehanism as onirmed by the observed behavior. 82

100 Chapter 5 Analysis o Test Results Minimum Requirement o Spiral Reinorement As mentioned earlier, the AASHTO-LRFD Speiiations state that the nominal axial apaity o a reinored onrete ompression member under onentri loading an be determined as ollows. P = A A + A Eq o 0.85 ( g s) y s where as deined beore, is the ompressive onrete ylinder strength, A g is the gross area o the olumn, A s is the area o longitudinal reinorement, and y is the yield strength o longitudinal reinorement. The eet o the spiral reinorement introdued by Rihart et al. (1928, 1929) was proposed the ompressive strength o onined onrete by spiral reinorement, in term o the unonined strength o and the atual lateral oninement stress 2 as ollows. = Eq o 2 The volumetri ratio o spiral reinorement ρ s, whih is the ratio o the volume o the spiral to the volume o the onrete ore, is determined as 4A ρ sp s = Eq ds where A sp is the area o the spiral steel, d is the outside diameter o the spiral, and s is the spaing o the spiral. 83

101 Chapter 5 Analysis o Test Results The lateral oninement stress, 2, as illustrated in Figure 74, an be determined as 2 2Asp sp 1 = = ρs sp Eq ds 2 where sp is the stress in the spiral at maximum olumn load. The minimum amount o spiral reinorement required by the LRFD Speiiations is seleted to ensure that the seond maximum load arried by the olumn ore and longitudinal reinorement is equal to the initial maximum load arried by the olumn beore spalling o the onrete over (Figure 75). This statement is written in an equation orm as ollows. P = ( A A ) + A P = 0.85 ( A A ) + A Eq s y s 1 g s y s Using deined by Eq and negleting A s sine A s is a small value ompared to A or A g, + Eq ( ) A 0.85 Ag Using 2 as deined in Eq. 5-17, the volumetri ratio o spiral reinorement, determined as ρ s an be A g ρs sp A Eq Based on the above, the AASHTO-LRFD Speiiations and ACI 318 adopted the ollowing equation as the minimum requirement o the spiral reinorement. 84

102 Chapter 5 Analysis o Test Results A g ρs sy A Eq In Eq. 5-21, the stress in the spiral reinorement sp is assumed to equal the yield strength o the spiral reinorement sy and the oeiient o was replaed by The above disussion indiates that Rihart s equation has been the basis to determine the required minimum spiral steel ratio or olumns with spiral reinorement in the urrent LRFD Speiiations and ACI 318. Reent studies have shown that the oninement eetiveness is less or high-strength onrete. For passive oninement suh as in olumns onined by lateral steel, onining pressure is dependent on the lateral dilation o onrete under axial load. Sine lateral dilation o high-strength onrete is less than that o normal-strength onrete, the eetiveness o oninement beomes less or the olumns with high-strength onrete. Setunge et al. (1993) reported that in their high-strength onrete speimens, ailure ourred through the aggregate partiles as well as the mortar, unlike normal-strength onrete in whih the ailure ours mainly through the mortar and aggregate interaes as shown in Figure 76. Failure through the aggregates leads to a lower shear resistane as well as a lower oninement eetiveness. The onined onrete strength with the lateral pressure l, normalized by o, or the tested olumns as well as reported data are shown in Figure 77. The omparisons indiate 85

103 Chapter 5 Analysis o Test Results that the oninement ator, represented by the slope o trend line, is redued or onrete strength greater than 10 ksi (69 MPa). The minimum amount o spiral reinorement required by the LRFD Speiiations is seleted to ensure that the seond maximum load arried by the olumn ore and longitudinal reinorement is equal to the initial maximum load arried by the olumn beore spalling o the onrete over. The irst and the seond peak loads (P 1 and P 2 ) o the tested olumns with dierent volumetri ratios o spiral reinorement, ρ s are summarized in Table 19. The load-axial shortening relationships o the seleted 12 and 9 in. spirally-reinored irular olumns are shown in Figure 78. It an be seen that or the larger 12 in. olumns, there was virtually no load redution ater the irst peak load as opposed to the smaller 9 in. olumns, sine the onrete over o the larger olumn represents only a smaller portion o the overall setion o the olumn. In general, the seond peak loads were larger than the irst maximum loads in most olumns with volumetri ratio o spiral lose to the ode requirement, whih is a avorable behavior satisying the premise o the ode. Based on the above data, it appears that the urrent minimum spiral steel requirement o the LRFD Speiiations (2004) is also appliable to high-strength onrete olumns in nonseismi zones. It should be noted that the minimum spiral requirement, ρ is a untion o onrete strength. For high-strength onrete, the minimum spiral requirement is signiiantly inreased. However, inreased spiral amount whih ompensates or the lower oninement eetiveness leads to smaller pithes o spiral, i normal grade steel is used or the spiral. Unduly small pith may result in reinorement ongestion that will hinder s 86

104 Chapter 5 Analysis o Test Results onrete plaement. A remedy would be to use high strength steel or the spiral reinorement. 5.6 Proposed Stress-Strain Relationship o Conined Conrete by Spiral Steel The results shown in the previous hapter learly indiated that oninement produed by spiral reinorements leads to enhanement o onrete strength under axial loading. In addition, use o spiral steel in olumns improves dutility o onrete. The strength and dutility enhanement o onrete by oninement gives a onsiderable inluene on stressstrain relationship o onrete. Thereore, omplete stress-strain relationship o onined onrete (inluding the post peak desending region) is quite dierent rom that o unonined onrete. The stress-strain relationship o onined onrete provides a better understanding o the behavior o the spirally reinored olumns. Also the stress-strain relationship o onined onrete is essential in prediting the response o the spirally reinored onrete olumn members. The stress-strain relation o onined onrete obtained rom the irular olumns tested in this study shows that the models disussed in Setion 2.7 does not suiiently relet the behavior o onined onrete. The desending part o stress-strain relation proposed by Martinez neglets the residual strength ollowing the stress drop ater maximum stress. While Razvi and Saatioglu assume a onstant residual strength o 20 %, this is not adequate. 87

105 Chapter 5 Analysis o Test Results Based on the test results, a new model or stress-strain relation o onined onrete by spiral reinorement is proposed as illustrated in Figure 79. The proposed stress-strain relationship is omprised o mainly three regions, whih are a parabola or asending part up to maximum stress, a linear portion or the desending part, and a onstant residual strength r. The model desribes the stress-strain behavior o onined onrete ore and neglets the inluene o onrete over. An expression originally proposed by Popovis (1973), and later used by Cusson and Paultre (1995) or high-strength onrete, was adopted or the asending part o the proposed stressstrain relationship o the onined onrete. The mathematial expression or the asending part denoted as urve OA is represented as For ε ε, k( ε / ε) = k 1 + ( ε / ε) k Eq k = E E E se Eq The parameter k above determines the initial slope and the urvature o the asending part. For high-strength onrete with higher elasti modulus, the parameter k has a larger value. Consequently, the urve o asending part is almost linear. In Eq. 5-23, E se is the seant modulus o elastiity o onined onrete and an be determined rom 88

106 Chapter 5 Analysis o Test Results E se = Eq ε The ollowing equation, based on regression analysis o about 4430 test data with onrete strength varying between 0.37 ksi and 24 ksi, originally proposed by NCHRP projet is used as the modulus o elastiity o unonined onrete E E = 310,000 K w ( ) Eq where K 1 is the orretion ator or soure o aggregate to be taken as 1.0 unless determined by physial test, w is the unit weight o onrete (k), in ksi. is the speiied onrete strength Eq and Eq proposed by Saatioglu and Razvi, are hosen or the onined onrete strength sine their expressions show an overall good agreement with test results. = + k Eq o 1 l k1 6.7( l ) 0.17 = Eq The strain gain was ound based on regression analysis o test results obtained rom this study as shown in Figure 80. The strain gain is deined as dierene between the strain at the maximum stress o onined onrete ε and strain at the maximum stress o unonined onrete ε o where ε o is onsidered as the strain orresponding the irst peak load P 1 in the 89

107 Chapter 5 Analysis o Test Results axial load. The ollowing equation is proposed or the strain at the maximum stress o onined onrete ε ater simpliying the resulting oeiients. ε l = εo o 1.8 Eq The linear portion o the desending urve, line AB in Figure 79, extends to the level o the onstant residual strength r and is based on expressions proposed by Martinez et al. (1984) as desribed below. For ε > ε and, r = Z( ε ε ) Eq where Z = ε ε Eq ( 85 ) Eq. 5-29, represented by a straight line, passes the strain orresponding to 85 % o the maximum stress o the desending part, ε 85 or the onined onrete. The slope o the line is determined by the dierene between the strain at the maximum stress ε and the strain orresponding to 85 % o maximum stress ε 85 or onined onrete, whih is dependent upon the amount o oninement and unonined onrete strength. Figure 81 shows the relationship o the dierene between the values o ε 85 and ε with /. Based on l o regression analysis o test results obtained rom this study and Martinez et al., the ollowing equation is proposed or the relationship ater simpliying the resulting oeiients. 90

108 Chapter 5 Analysis o Test Results l ε85 = ε Eq o In this model, the residual strength, presented by the horizontal part o the desending r 2.3 urve, provides the remaining resistane o ore onrete restrained rom shear sliding by spiral reinorement ater raking o the ore onrete. The residual strength r is assumed to be onstant and its appliability is limited to the load level orresponding to rupture o spiral reinorement denoted as line BC (Figure 79). The residual stress r is deined in terms o the produt value o volumetri ratio and yield strength o spiral reinorement, ρ s sy. Figure 82 shows the relationship between r and ρ s sy. The ollowing equation is proposed or the residual strength r o onined onrete ater simpliying the resulting oeiients. For ε > ε and <, r = 7( ρ ) Eq r s sy In Eq. 5-32, the yield strength o the spiral steel, sy is limited to 60 ksi (Grade 60 steel). The value o ε o or unonined, in-plae onrete an be usually determined rom tests. In the absene o the experimental value, a onstant value o is suggested as a representative average as shown in Figure 83. The proposed model was veriied by omparing the analytially generated stress-strain relation with those obtained rom 24 irular olumns tested in this study. Figure 84 through Figure 106 show the omparisons o the experimental and analytial urves or the seleted 91

109 Chapter 5 Analysis o Test Results irular olumns. The ompared irular olumns over a wide range o the volumetri ratio o spiral reinorement and onrete strength. These values range rom 1.44 % to 7.27 % and rom 7.9 ksi to 16.1 ksi respetively. The omparisons indiate satisatory orrelation between the analytial and experimental results. 92

110 Chapter 6 Summary and Conlusions Chapter 6 Summary and Conlusions 6.1 Summary The behavior o high-strength onrete olumns subjeted to onentri and eentri axial ompression loading onditions was investigated in this study. A omprehensive literature survey was onduted to inlude most o the work reported by previous researhers and to ompile the reported data. The experimental program inluded a total o ity six olumns tested to ailure. It onsisted o thirty two retangular and twenty our irular reinored onrete olumns with onrete strength ranging rom 7.9 to 16.5 ksi. The olumns were tested using onentri and eentri loading onditions. The test results provided invaluable inormation on the behavior o high-strength onrete olumns. The test result o this study ombined with other reported data in the literature were evaluated using regression analysis and a number o omparisons. These analyses were used to examine the validity o the provisions o AASHTO LRFD Bridge Design Speiiations or high-strength onrete. New expressions were proposed to modiy the LRFD 93

111 Chapter 6 Summary and Conlusions Speiiations to extend the urrent limitation o 10 ksi onrete ompressive strength up to 18 ksi. Based on the tests, a new analytial model was proposed or stress-strain relationship o onined onrete. 6.2 Conlusions The ollowing onlusions an be drawn based on the experimental and analytial researh reported in this study. 1. The general behavior o reinored onrete olumns is haraterized sequentially by the initiation o surae raks, spalling o over onrete, yielding o longitudinal reinorement, bukling o longitudinal steel, rushing o ore onrete, yielding o transverse reinorement, and inally rupture o transverse reinorement. However, the behavior is highly aeted by the amount or spaing o transverse reinorement. 2. High-strength onrete olumns under onentri ompression exhibit extremely brittle behavior unless onined with transverse reinorement that an provide suiient lateral oninement pressure. This is more pronouned or olumns with higher onrete strength. 3. Strength and dutility o onrete olumns are improved signiiantly or well onined onrete ore, regardless o onrete strength. 4. The retangular olumns with the maximum tie spaing aording to the LRFD Speiiations show no oninement eet to the onrete ore. 5. For onrete ompressive strength beyond 10 ksi, use o the onstant 0.85 as the ratio o in-plae onrete strength to the ylinder strength overestimates the load arrying 94

112 Chapter 6 Summary and Conlusions apaity or onentrially loaded olumns. The ollowing new relationship or a parameter k in lieu o the onstant 0.85 is proposed or high-strength onrete up to 18 ksi : k 0.85 or 10 = ( 10) 0.75 or > 10 in ksi Eq Test result indiates that dutility o olumn dereases with inreasing onrete strength and the amount o transverse reinorement is a major ator aeting dutility o olumns. 7. The slope o the desending region o the stress-strain relationship is steeper or olumns with either higher onrete strength or lower volumetri ratio o transverse reinorement. 8. Cirular spirals are more eetive in onining onrete than retilinear ties. Highstrength onrete olumns onined with irular spirals show improved strength and dutility when ompared with retangular olumns onined with the same volumetri ratio o ties. 9. For the eentrially loaded olumns with onrete strength beyond 10 ksi, the predition o lexural resistane using the urrent LRFD Speiiations or ACI is less onservative and less aurate. Using the NZS and NCHRP retangular stress blok would be reasonably onservative and improves the predition. 10. A new model or stress-strain relationship o onined high-strength onrete by spiral reinorement is proposed. The model shows good orrelations with the stressstrain relationship established experimentally. 95

113 Chapter 6 Summary and Conlusions 11. The maximum tie spaing and minimum volumetri ratio o spiral required by the LRFD Speiiations are appliable or reinored onrete olumns with ompressive strengths up to 18 ksi. 12. For design purpose, setting the maximum limit o 80 perent o the axial load apaity or tied olumns with high-strength onrete to aount or the unintentional eentriity seems to be reasonable and onservative. 13. The ultimate ompressive strain o speiied by the urrent LRFD Speiiations or ACI 318 is appropriate or analysis o reinored high-strength onrete olumns up to 18 ksi. 6.3 Future Researh To ully exploit the beneits o high-strength onrete, more studies are needed on highstrength onrete olumns subjeted to reversed yli lateral loading or seismi design. In addition, studies are reommended on the use o high-strength reinorement to maximize the beneits o high-strength onrete. 96

114 Reerenes REFERENCES ACI Committee 105 Reinored Conrete Column Investigation, ACI Journal Proeedings, Vol. 26 (April 1930) pp ; Vol. 27 (Feb. 1931) pp ; Vol. 28 (Nov. 1931) pp ; Vol. 29 (Sep. 1932) pp ; (Feb. 1933) pp ; Vol. 30 (Sep.-Ot. 1933) pp ; (Nov.-De. 1933) pp ACI Committee 318, Building Code Requirement or Reinored Conrete (ACI318-05) and Commentary (318R-05), Amerian Conrete Institute, Farmington Hills, MI (2005) 443 pp. ACI Committee 363, State o the Art Report on High-Strength Conrete (ACI 363R-92), Amerian Conrete Institute, Detroit, 1992 (Revised 1997), 55 pp. Amerian Soiety or Testing and Materials (ASTM) rom Amerian Assoiation o State Highway and Transportation Oiials, AASHTO LRFD Bridge Design Speiiations - Third Edition inluding 2005 and 2006 Interim Revisions. Washington, DC (2004). Ahmad, S. H. and Shah, S. P., Stress-Strain Curves o Conrete Conined by Spiral Reinorement, ACI Journal, Vol. 79, No. 6, (Nov. 1982) pp

115 Reerenes Assa, B., Nishiyama, M., and Watanabe, F., New Approah or Modeling Conined Conrete. I: Cirular Columns, Journal o Strutural Engineering, ASCE, Vol. 127, No. 7 (July 2001) pp Bing, L., Park, R., Tanaka, H., Constitutive Behavior o High-Strength Conrete under Dynamis Loads, ACI Strutural Journal, Vol. 97, No. 4 (July 2000), pp Bjerkeli, L., Tomaszewiz, A., and Jensen, J. J., Deormation Properties and Dutility o High-Strength Conrete, High-Strength Conrete: Seond International Symposium, ACI SP , Detroit, (1990) pp Bresler, D. and Gilbert, P. H., Tie Requirements or Reinored Conrete Columns, ACI Journal Proeedings, Vol. 58 (Nov. 1961) pp Chan, W. L., The Ultimate Strength and Deormation o Plasti Hinges in Reinored Conrete Frameworks, Magazine o Conrete Researh, Vol. 7, No. 21 (Nov. 1955) pp Carrasquillo, R. L., Nilson, A. H., and Slate, F. O., Properties o High Strength Conrete Subjet to Short-Term Loads, ACI Strutural Journal, Vol. 78, No. 3 (May 1981) pp CEB-FIP Model Code 1990, Comite Euro-International du Beton, Thomas Telord (1990) 437 pp. Chen, W. F., Plastiity in Reinored Conrete, MGraw-Hill Book Co., New York,

116 Reerenes Chen, W. F., and Han, D. J., Plastiity or Strutural Engineers, Springer-Verlag, 1998 Collins, M. P., Mithell, D., and MaGregor, J. G., Strutural Design Considerations or High Strength Conrete, Conrete International, (May 1993) pp Considere, A., Resistane a la Compression du Beton Arme et du Beton Frette, Gene Civil, Translation Experimental Researhes on Reinored Conrete, Moissei, L. S., MGraw-Hill Book Company, 1906 Cowan. H. J., (1953) The Strength o Plain, Reinored, and Prestressed Conrete under the Ation o Combined Stresses, Magazine o Conrete Researh (London), Vol. 5, No. 14, (De. 1953) pp CSA, Design o Conrete Strutures or Buildings (CAN3-A ), Canadian Standards Assoiation, Rexdale, Ontario (1994) 199 pp. Cusson, D., and Paultre, P., High-Strength Conrete Columns Conined by Retangular Ties, Journal o Strutural Engineering, ASCE, Vol. 120, No.3 (Mar. 1994) pp FIP/CEB, High-Strength Conrete-State-o-the-Art-Report, SR 90/1 Bulletin d Inormation No. 197 (Aug. 1990) 6 pp. Foster, S. J. and Attard, M. M., Experimental Tests on Eentrially Loaded High-Strength Conrete Columns, ACI Strutural Journal, Vol. 94, No. 3 (May 1997), pp Hognestad, E., A Study o Combined Bending and Axial Load in Reinored Conrete Members, University o Illinois Engineering Station Bulletin series No. 399 (1951) 128 pp. 99

117 Reerenes Hognestad, E., Ultimate Strength o Reinored Conrete in Amerian Design Pratie, Bulletin D12, Portland Cement Assoiation, Researh and Development Laboratories, Chiago, 1961, 19 pp. Ibrahim, H. H. H. and MaGregor, J. G. Flexural Behavior o Laterally Reinored High- Strength Conrete Setions, ACI Strutural Journal, Vol. 93, No. 6 (Nov. 1996) pp Ibrahim, H. H. H. and MaGregor, J. G. Tests o Eentrially Loaded High-Strength Conrete Columns, ACI Strutural Journal, Vol. 93, No. 5 (Sep. 1996) pp Ibrahim, H. H. H. and MaGregor, J. G. Modiiation o the ACI Retangular Stress Blok or High-Strength Conrete, ACI Strutural Journal, Vol. 94, No. 1 (Jan. 1997) pp Issa, M. A., and Tobaa, H. Strength and Dutility Enhanement in High-Strength Conined Conrete, Magazine o Conrete Researh, Vol. 46, No. 168 (Sep. 1994) pp Iyengar, K. T. S. R., Desayi, P., and Reddy, K. N., Stress-Strain Charateristis o Conrete Conined in Steel Binders, Magazine o Conrete Researh, Vol. 22, No. 72 (Sep. 1970) pp Kent, D. C. and Park, R., Flexural Members with Conined Conrete, Journal o Strutural Division, ASCE, Vol. 97 (1971) pp Lee, J., and Son, H. Failure and Strength o High-Strength Conrete Columns Subjeted to Eentri Loads, ACI Strutural Journal, Vol. 97, No. 1 (Jan. 2000) pp

118 Reerenes Li, B., Park, R., and Tanaka, H., Strength and Dutility o Reinored Conrete Members and Frames Construted Using High-Strength Conrete, Researh Report No. 94-5, Department o Civil Engineering, University o Canterbury, Christhurh, New Zealand (1994) 373 pp. Liu, J., Foster, S. J., and Attard, M. M., Strength o Tied High-Strength Conrete Columns Loaded in Conentri Compression, ACI Strutural Journal, Vol. 97, No. 1 (Jan. 2000), pp Lloyd, N. A. and Rangan, B. V., Studies on High-Strength Conrete Columns under Eentri Compression, ACI Strutural Journal, Vol. 93, No. 6 (Nov. 1996) pp Logan, A. T., Short-Term Material Properties o High-Strength Conrete, M.S. Thesis, Department o Civil, Constrution and Environmental Engineering, North Carolina State University, Raleigh, NC (June 2005), 116 pp. MaGregor, J. G., Reinored Conrete 3rd ed., Prentie Hall, In., Upper Saddle River, New Jersey, 1997 Mander, J. B., Priestley, M. J. N., and Park, R., Observed Stress-Strain Behavior o Conined Conrete, Journal o Strutural Engineering, ASCE, Vol. 114, No. 8 (August 1988) pp Mander, J. B., Priestley, M. J. N., and Park, R., Theoretial Stress-Strain Model or Conined Conrete, Journal o Strutural Engineering, ASCE, Vol. 114, No. 8 (August 1988) pp

119 Reerenes Martinez, S., Nilson, A. H., and Slate, F. O., Spirally Reinored High-Strength Conrete Columns, ACI Journal, (Sep. 1984) pp Maritinez, S., Spirally-Reinored High-Strength Conrete Columns, Ph. D. dissertation, Cornell University, Ithaa, NY (Jan. 1983) 255 pp. Mattok, A. H., Kriz, L. B., and Hognestad, E., Retangular Stress Distribution in Ultimate Strength Design, ACI Strutural Journal, Proeedings Vol. 57, No. 8 (Feb. 1961) pp Nagashima, T., Sugano, S., Kimura, H. and Ihikawa, A., Monotoni Axial Compression Test on Ultra-High-Strength Conrete Tied Columns, Earthquake Engineering Tenth World Conerene, Madrid, Spain, Proeedings (July 1992) pp NZS , The Design o Conrete Strutures, Standards New Zealand, Wellington, New Zealand (1995) 520 pp. Ottosen, N. S.. A Failure Criterion or Conrete, Journal o Engineering Mehanis, ASCE, Vol. 103, No. EM4 (Aug. 1977) pp Ozbakkaloglu, T. and Saatioglu, M., Retangular Stress Blok or High-Strength Conrete, ACI Strutural Journal, Vol. 101, No. 4 (July 2004) pp Park, R. and Paulay, T., Reinored Conrete Strutures, John Wiley and Sons,

120 Reerenes Pessiki, S., and Pieroni, A. Axial Load Behavior o Large-Sale Spirally-Reinored High- Strength Conrete Columns, ACI Strutural Journal, Vol. 94, No. 3 (May 1997) pp Popovis, S., Analytial Approah to Complete Stress-Strain Curves, Cement and Conrete Researh, Vol. 3, No. 5, (Sep. 1973) pp Razvi, S. and Saatioglu, M., Coninement Model or High-Strength Conrete, Journal o Strutural Engineering, ASCE, Vol. 125, No. 3 (Marh 1999) pp Razvi, S. R. and Saatioglu, M. Cirular High-Strength Conrete Columns under Conentri Compression, ACI Strutural Journal, Vol. 96, No. 5 (Sep. 1999) pp Rihart, F. E., Brandtzaeg, A., and Brown, R. L., A Study o The Failure o Conrete Under Combined Compressive Stresses, University o Illinois Engineering Station Bulletin Series No. 185, Vol. 26, No. 12 (Nov. 1928) 102 pp. Rihart, F. E., Brandtzaeg, A., and Brown, R. L., The Failure o Plain and Spirally Reinored Conrete in Compression, University o Illinois Engineering Station Bulletin Series No. 190, Vol. 26, No. 31 (April 1929) 73 pp. Rihart, F. E. and Brown, R. L., An Investigation o Reinored Conrete Columns, University o Illinois Engineering Station Bulletin Series No. 267, (June 1934) 91 pp. Rizkalla et al., Final Report or NCHRP Projet 12-64, TRB Publiation,

121 Reerenes Roy, H. E. M. and Sozen, M. A., A Model to Simulate the Response o Conrete to Multi- Axial Loading, Strutural Researh Series No. 268, Civil Engineering Studies, University o Illinois, 1963 Saatioglu, M., and Razvi, S. R., Strength and Dutility o Conined Conrete, Journal o Strutural Engineering, ASCE, Vol. 118, No. 6 (June 1992) pp Saatioglu, M., and Razvi, S. R., High-Strength Conrete Columns with Square Setions under Conentri Compression, Journal o Strutural Engineering, ASCE, Vol. 124, No. 12 (De. 1998) pp Setunge, S., Attard, M. M., and Darvall, P. LeP., Ultimate Strength o Conined Very High- Strength Conrete, ACI Strutural Journal, Vol. 90, No. 6 (Nov. 1993) pp Sharma, U. K., Bhargava, P., and Kaushik, S. K., Behavior o Conined High-Strength Conrete Columns under Axial Compression, Journal o Advaned Conrete Tehnology, Vol. 3, No. 2 (June 2005) pp Sheikh, S. A. and Uzumeri, S. M., Strength and Dutility o Tied Conrete Columns, Journal o Strutural Engineering, ASCE, Vol. 106, No. 5 (May 1980) pp Sheikh, S. A. and Uzumeri, S. M., Analytial Model or Conrete Coninement in Tied Columns, Journal o Strutural Engineering, ASCE, Vol. 108, No. 12 (De. 1982) pp

122 Reerenes Tan, T. H. and Nguyen, N., Flexural Behavior o Conined High-Strength Conrete Columns, ACI Strutural Journal, Vol. 102, No. 2 (Mar. 2005) pp Vallenas, J., Bertero, V. V., and Popov, E. P., Conrete Conined by Retangular Hoops and Subjeted to Axial Load, Report No. UCB/EERC-77/13, Earthquake Engineering Researh Center, College o Engineering, University o Caliornia, Berkeley (Aug. 1977) pp. 114 William, K. J. and Warnke, E. P., Constitutive model or the triaxial behavior o onrete, Pro., International Assoiation or Bridge and Strutural Engineering, Vol. 19 (1975) pp Whitney, C. S., Plasti Theory o Reinored Conrete Design, Proeedings ASCE, De. 1940; Transations ASCE, Vol. 107, (1942) pp Yong, Y., Nour, M. G., and Nawy, E. G., Behavior o Laterally Conined High Strength Conrete under Axial Loads, Journal o Strutural Engineering, ASCE, Vol. 114, No. 2 (Feb. 1988) pp

123 TABLES 106

124 Tables Table 1 Comparison o dierent retangular stress blok parameters Reerene α 1 β 1 ε u ACI and AASHTO-LRFD or ( 4 ksi 4 ) 0.65 or > 4 ksi CSA A23.3 (1994) NZS 3101 (1995) CEB-FIP (1990) Proposed by NCHRP or ( or 0.85 or ( 8 ksi 8 ) 0.75 > 8 ksi ksi 10 ) 0.75 or > 10 ksi 0.85 or ( or 0.85 or ( 4.35 ksi 4.35 ) 0.65 > 4.35 ksi ksi 4 ) 0.65 or > 4 ksi Note) in ksi 107

125 Tables Table 2 Details o onentrially loaded retangular olumns Column ID Size b h L (in) Measured Conrete Strength * (ksi) Longitudinal Reinorement No. & Size ρ (%) y (ksi) Transverse Reinorement ρ Size s (in) s (%) sy (ksi) 10R9-ρ # R4½-ρ # ½ R9-ρ # R4½-ρ # ½ R9-ρ #7 + 4 # , R4½-ρ #7 + 4 # , 60 4 ½ A10R9-ρ # A10R9-ρ # A10R9-ρ #7 + 4 # , R9-ρ # R4½-ρ # ½ R9-ρ # # R4½-ρ # ½ R9-ρ #7 + 4 # , R4½-ρ #7 + 4 # , 61 4 ½ A18R7-ρ # A18R7-ρ # A18R7-ρ # R7-ρ # R3½-ρ # ½ R7-ρ # R3½-ρ # ½ R7-ρ # R3½-ρ # ½ Note) *Average values o three onrete ylinders 108

126 Tables Table 3 Details o eentrially loaded retangular olumns Column ID Size b h L (in) Measured Conrete Strength * (ksi) e** (in.) Longitudinal Reinorement No. & Size ρ (%) y (ksi) Transverse Reinorement No. & Spaing s (in) ρ s (%) sy (ksi) 10E , 60 10E A10E #7 + 4 # E , E A18E E # E Note) * Average values o three onrete ylinders ** Initial eentriity o the applied load and the lateral deletion at the mid-height o the olumn prior to ailure 109

127 Tables Table 4 Details o onentrially loaded irular olumns Size Measured Conrete Strength Longitudinal Reinorement Spiral Reinorement Column ID d L (in) * (ksi) No. & Size ρ l (%) y (ksi) Size Spaing s (in) ρ s (%) sy (ksi) 10C2¾-ρ # ¾ C1⅜-ρ # ⅜ C2¾-ρ # ¾ #3 10C1⅜-ρ # ⅜ C2¾-ρ # ¾ C1⅜-ρ # ⅜ A10C2¾-ρ # ¾ A10C2¾-ρ # #3 2 ¾ A10C2¾-ρ # ¾ C2-ρ # C1-ρ # C2-ρ # #3 14C1-ρ # C2-ρ # C1-ρ # C1½-ρ # ½ C1½-ρ # #3 1 ½ C1½-ρ # ½ C2¾-ρ # ¾ C1⅜-ρ # ⅜ C2¾-ρ # ¾ #4 18C1⅜-ρ # ⅜ C2¾-ρ # ¾ C1⅜-ρ # ⅜ Note) * Average values o three onrete ylinders 110

128 Tables Table 5 Three mixture designs or target onrete strength 10, 14, and 18 ksi Material Target Strengths ksi (MPa) 10 (69) 14 (97) 18 (124) Mix 1 Mix 2 Mix 3 Cement (Type I) - lbs/yd 3 (kg/m 3 ) 703 (417) 703 (417) 935 (555) Mirosilia Fume (Densiied) - lbs/yd 3 (kg/m 3 ) 75 (44) 75 (44) 75 (44) Fly Ash - lbs/yd 3 (kg/m 3 ) 192 (114) 192 (114) 50 (30) Sand - lbs/yd 3 (kg/m 3 ) 1055 (625) 1315 (780) 1240 (736) Rok (Diabase 78M) - lbs/yd 3 (kg/m 3 ) 1830 (1085) 1830 (1085) 1830 (1085) Water - lbs/yd 3 (kg/m 3 ) 292 (173) 250 (148) 267 (158) HRWRA - oz./wt (ml/100 kg) *** 17 (1110) 24 (1565) 36 (2345) Retarding Agent - oz./wt (ml/100 kg)* 3 (195) 3 (195) 3 (195) w/m Day Compressive Strength o Lab Bath - psi (MPa) 11.5 (78.9) 14.4 (99.1)** 17.1 (117.8) Note) * Ounes per 100 pounds o ementitious materials (ml per 100 kg ementitious materials) ** Interpolated rom Test Results *** High-Range Water-Reduing Admixture Table 6 Details o ive onrete bathes Conrete Bath No Columns 10R series 10C series 10E1 10E2 14R series 14C series 14E1 14E2 18R series 18C series 14E1 14E2 A10R series A10C series A10E1 A18R series 18C1½ series A18E1 Mix design No Unit Weight (lb/t 3 ) Day Compressive Strength (ksi) Compressive Strength at olumn test (ksi) 7.9 ~ ~ ~ ~ ~

129 Tables Table 7 Material properties o reinorements Type Size No. Diameter (in.) Yield Stress (ksi) y Elasti Modulus E (ksi) # # # s # # Longitudinal Reinorements # # # # # Ties Spirals # # # # # # # # # Note) Test results or eah type o reinorement were average values o three oupons 112

130 Tables Table 8 Experimental and predited strengths or retangular olumns Column ID 10CR9-ρ1 b h L (in) (ksi) P max (kips) Strain at P max P o (kips) P P max o P (kips) CR4½-ρ CR9-ρ CR4½-ρ CR9-ρ CR4½-ρ A10CR9-ρ A10CR9-ρ A10CR9-ρ CR9-ρ CR4½-ρ CR9-ρ CR4½-ρ CR9-ρ CR4½-ρ A18CR7-ρ A18CR7-ρ A18CR7-ρ CR7-ρ CR3½-ρ CR7-ρ CR3½-ρ CR7-ρ CR3½-ρ Note) P is the load resistane by onrete k 113

131 Tables Table 9 Experimental and predited strengths or irular olumns Column ID d L (in) (ksi) P CR (kips) P max (kips) P o (kips) P P CR o P (kips) k 10CC2¾-ρ CC1⅜-ρ CC2¾-ρ CC1⅜-ρ CC2¾-ρ CC1⅜-ρ A10CC2¾-ρ A10CC2¾-ρ A10CC2¾-ρ CC2-ρ CC1-ρ CC2-ρ CC1-ρ CC2-ρ CC1-ρ CC1½-ρ CC1½-ρ CC1½-ρ CC2¾-ρ CC1⅜-ρ CC2¾-ρ CC1⅜-ρ CC2¾-ρ CC1⅜-ρ Note) P is the load resistane by onrete 114

132 Tables Table 10 Comparison between maximum measured load and 80 perent o predited load o tied olumns with eentriity o 0.1h Column ID e* (ksi) Measured P max (kips) 0.8P o (kips) Measured P 0.8P 10E1 0.1h A10E1 0.09h E1 0.1h E1 0.1h A18E1 0.09h Average 1.12 Note) * Initial eentriity o the applied load and the lateral deletion at the midheight o the olumn prior to ailure o max 115

133 Tables Table 11 Comparison o dutility index I 5 with respet to setion geometry Column ID Setion (ksi) ρ s (%) I 5 10R4½-ρ1 Retangular C2¾-ρ1 Cirular R4½-ρ2.5 Retangular C2¾-ρ2.5 Cirular R4½-ρ4 Retangular C2¾-ρ4 Cirular Table 12 Comparison o dutility index I 5 with respet to onrete strength Column ID Setion (ksi) ρ s (%) I 5 10R9-ρ A10R9-ρ1 Retangular R9-ρ R9-ρ A10R9-ρ2.5 Retangular R9-ρ R9-ρ A10R9-ρ4 Retangular R9-ρ R4½-ρ Retangular R4½-ρ R4½-ρ Retangular R4½-ρ R4½-ρ Retangular R4½-ρ C2¾-ρ A10C2¾-ρ2.5 Cirular C2-ρ C2¾-ρ A10C2¾-ρ4 Cirular C2-ρ

134 Tables Table 13 Comparison o dutility index I 5 with respet to volumetri ratio o transverse steel Column ID Setion (ksi) ρ s (%) I 5 10R9-ρ R4½-ρ R9-ρ R4½-ρ R9-ρ R4½-ρ R9-ρ R4½-ρ R9-ρ Retangular R4½-ρ R9-ρ R4½-ρ R7-ρ R3½-ρ R7-ρ R3½-ρ R7-ρ R3½-ρ C2¾-ρ C1⅜-ρ C2¾-ρ C1⅜-ρ C2¾-ρ C1⅜-ρ C2-ρ C1-ρ C2-ρ Cirular C1-ρ C2-ρ C1-ρ C2¾-ρ C1⅜-ρ C2¾-ρ C1⅜-ρ C2¾-ρ C1⅜-ρ

135 Tables Table 14 Comparison o dutility index I 5 with respet to longitudinal steel ratio Column ID 10R9-ρ1 Setion (ksi) ρ s (%) I R9-ρ R9-ρ R4½-ρ R4½-ρ R4½-ρ A10R9-ρ A10R9-ρ A10R9-ρ R9-ρ R9-ρ R9-ρ Retangular 14R4½-ρ R4½-ρ R4½-ρ A18R7-ρ A18R7-ρ A18R7-ρ R7-ρ R7-ρ R7-ρ R3½-ρ R3½-ρ R3½-ρ

136 Tables Column ID 10C2¾-ρ1 Setion Table 14 (Continued) (ksi) ρ s (%) I C2¾-ρ C2¾-ρ C1⅜-ρ C1⅜-ρ C1⅜-ρ A10C2¾-ρ N/A A10C2¾-ρ A10C2¾-ρ C2-ρ C2-ρ C2-ρ Cirular 14C1-ρ C1-ρ C1-ρ A18C1½-ρ A18C1½-ρ A18C1½-ρ C2¾-ρ C2¾-ρ C2¾-ρ C1⅜-ρ C1⅜-ρ C1⅜-ρ

137 Tables Table 15 Comparison between experimental and predited load using dierent retangular stress blok or eentrially loaded olumns Ratio (P exp / P pred ) Reerene (ksi) e CSA NZS NCHRP ACI / AASHTO This study Lee and Son (2000) Foster and Attard (1997) Tan and Nguyen (2005) h h h h h h h h h h h h h h h h h h h h h Average Standard deviation

138 Tables Table 16 Comparison o onined onrete strength between test results and preditions using proposed equation by dierent studies or irular olumns Column 10C2¾-ρ1 Size d L (in) Unonined Conrete Strength o (ksi), exp (ksi) Conined Conrete Strength Ratio (, pred (ksi) Rihart Martinez Mander S & R, exp /, pred) Rihart Martinez Mander S & R C1⅜-ρ C2¾-ρ C1⅜-ρ C2¾-ρ C1⅜-ρ A10C2¾-ρ A10C2¾-ρ A10C2¾-ρ C2-ρ C1-ρ C2-ρ C1-ρ C2-ρ C1-ρ Average Standard deviation

139 Tables Column Size d L (in) Unonined Conrete Strength o (ksi), exp (ksi) Table 16 (Continued) Conined Conrete Strength Ratio (, pred (ksi) Rihart Martinez Mander S & R, exp /, pred) Rihart Martinez Mander S & R 18C1½-ρ C1½-ρ C1½-ρ C2¾-ρ C1⅜-ρ C2¾-ρ C1⅜-ρ C2¾-ρ C1⅜-ρ Average Standard deviation Average Total Standard deviation Total Note) S & R = Saatioglu and Razvi 122

140 Tables Table 17 Test result o irular olumns with 12 in. dia. setion Column 10C2¾-ρ1 Size d L (in) Measured Conrete Strength (ksi) Lateral Coninement Stress l (ksi) Conined Conrete Strength (ksi) Axial Strain at Maximum Stress o Unonined Conrete ε o (in. / in.) Axial Strain at Maximum Stress o Conined Conrete ε * (in. / in.) Axial Strain at 0.85 ε 85 * (in. / in.) C1⅜-ρ C2¾-ρ C1⅜-ρ C2¾-ρ C1⅜-ρ A10C2¾-ρ A10C2¾-ρ A10C2¾-ρ C2-ρ C1-ρ C2-ρ C1-ρ C2-ρ C1-ρ Note) * Extrapolated value 123

141 Tables Table 18 Test result o irular olumns with 9 in. dia. setion Column 18C1½-ρ2 Size d L (in) Measured Conrete Strength (ksi) Lateral Coninement Stress l (ksi) Conined Conrete Strength (ksi) Axial Strain at Maximum Stress o Unonined Conrete ε o (in. / in.) Axial Strain at Maximum Stress o Conined Conrete ε * (in. / in.) Axial Strain at 0.85 ε 85 * (in. / in.) C1½-ρ C1½-ρ C2¾-ρ C1⅜-ρ C2¾-ρ C1⅜-ρ C2¾-ρ C1⅜-ρ * Extrapolated value 124

142 Tables Table 19 Test results o irular olumns with dierent volumetri ratios o spiral reinorement Column ID 10C2¾-ρ1 Setion Size (in.) Conrete (ksi) Spiral ρs ρ ode s P 1 (kips) P 2 (kips) P 1 (kips) P 2 (kips) C1⅜-ρ C2¾-ρ C1⅜-ρ C2¾-ρ C1⅜-ρ A10C2¾-ρ A10C2¾-ρ2.5 d = A10C1⅜-ρ C2-ρ C1-ρ C2-ρ C1-ρ C2-ρ C1-ρ C1½-ρ C1½-ρ C1½-ρ C2¾-ρ d = 9 18C1⅜-ρ C2¾-ρ C1⅜-ρ C2¾-ρ C1⅜-ρ Note ) ρ ode : minimum required volumetri ratio o spiral speiied by LRFD speiiation s P = C1 P 1 As y P = C2 2 P As y (axial load arried by onrete at the irst peak load) (axial load arried by onrete at the seond peak load) P P C2 C1 125

143 FIGURES 126

144 Figures 18 Conrete Stress, (ksi) ε Conrete Strain (ε ) Figure 1 Inluene o onrete strength on shape o stress-strain relationship (Collins et al. 1993) 127

145 Figures b ε u k3 α 1 d k2 C = kk b 1 3 β 1 β 1 2 C = αβ b 1 1 A s Strain Distribution Generalized Stress Blok Equivalent Retangular Stress Blok Setion kk β = 2k 1 3 α 1 = 1 2 2k2 Figure 2 Generalized and retangular stress blok o ompressive onrete 0.85 ε 1 = ε,lim ε ε 1 ε u ε (a) Stress-strain diagram or uniaxial ompression (b) Parabola-retangle stress-strain diagram Figure 3 Conrete stress-strain urves o CEB-FIP (1990) 128

146 Figures 1.5 = 6 ksi 1 12 in ρ = 3.3% P / ( bh) ACI / AASHTO CSA NZS CEB-FIP M / ( bh 2 ) (a) = 6 ksi 1.2 = 12 ksi in ρ = 3.3% P / ( bh) ACI / AASHTO CSA NZS NCHRP M / ( bh 2 ) (b) = 12 ksi Figure 4 Comparison o olumn interation diagrams based on various retangular bloks or dierent onrete strengths 129

147 Figures 1.2 = 18 ksi in ρ = 3.3% P / ( bh) ACI / AASHTO CSA NZS NCHRP M / ( bh 2 ) () = 18 ksi Figure 4 (Continued) Figure 5 Eetively onined ore or irular hoop reinorement (soure : Mander et al. 1988) 130

148 Figures Stress ε e k1ε e k2ε e B λ 2E e A λ 1E C E O ε e k ε ε (1 + 1) e u Strain Figure 6 Proposed stress-strain urve or onined onrete by Chan (1953) Stress 0.85 Conined o 0.85 o Unonined ε o85 ε ε 85 Strain Figure 7 Proposed stress-strain urve or onined onrete by Martinez (1983) 131

149 Figures Stress 0.85 o 0.85 o Unonined Conined 0.20 ε oε o85 ε ε 85 ε 20 Strain Figure 8 Proposed stress-strain urve or onined onrete by Saatioglu and Razvi (1992) 132

150 Figures ½ in. ½ in. b h d L Test Region Figure 9 Reinorement details o retangular and irular olumns 133

151 Figures Figure 10 Assembled reinorement ages or retangular olumns 134

152 Figures (1) (2) (3) (4) (5) Top view o assembled orms Figure 11 Proedure o assembling orms or the retangular olumns 135

153 Figures Figure 12 Assembled reinorement ages or irular olumns 136

154 Figures (1) (2) (3) (4) (5) Top view o assembled orms Figure 13 Proedure o assembling orms or the irular olumns 137

155 Figures Figure 14 Casting o olumn speimens Figure 15 Casting o 4 8 in. ylinders 138

156 Figures Figure 16 Removal o orms Figure 17 Cast olumn speimens 139

157 Figures Figure 18 Testing o 4 x 8 in. ylinder Figure 19 Grinding end suraes o 4 x 8 in. ylinder 140

158 Figures (a) Loading mahine or testing o reinoring bar (b) Measuring steel strain with 2 in. extensometer Figure 20 Testing o reinoring steel 141

159 Figures 100 # 6 80 # 5 Stress (ksi) # Strain (in/in) (a) # 4 Tie -1 # 4 Tie -2 Stress (ksi) # 7 # Strain (in/in) (b) Figure 21 Stress-strain relationship or reinoring steel 142

160 Figures Level o loations o longitudinal strain gauges Mid height Level o loation o tie strain gauges Level o loations o longitudinal and spiral strain gauges Conentri Conentri Eentri Strain gauges on Long. Steel Trans. Steel Figure 22 Vertial and setional loations o strain gauges 143

161 Figures Front View Retangular Column Mid-height Cirular Column Mid-height Figure 23 Loation layout o pi gauges or retangular and irular olumns 144

162 Figures (a) Loading mahine and data aquisition system in NC State University (b) Loading mahine in Lehigh University Figure 24 Testing mahine and data aquisition system 145

163 Figures (a) Retangular olumn (b) Cirular olumn Figure 25 Typial test set-up or onentrially loaded olumns 146

164 Figures P e LVDT P (a) Test set-up (b) Loading plate bearing assembly Figure 26 Typial test set-up and loading plate bearing assembly or eentrially loaded olumn 147

165 Figures P max = 16.1 ksi ρ = 4 % s = 9 in Load (kips) Column 14R9-ρ Axial Shortening (in.) Figure 27 Axial load-shortening urve or onentrially loaded retangular olumn (14R9-ρ4) Column 14R9-ρ4 Load (kips) Extrapolation Strain (mm/mm) Figure 28 Axial load-average onrete strain measured by pi gauges (14R9-ρ4) 148

166 Figures Yield strain (0.0022) P max L1 L2 Load (kips) L1 L2 Column 14R9-ρ Strain (mm/mm) Figure 29 Axial load-longitudinal steel strain (14R9-ρ4) Yield strain (0.0022) P max T2 T T1 T2 Column 14R9-ρ4 Load (kips) Strain (mm/mm) Figure 30 Axial load-transverse steel (tie) strain (14R9-ρ4) 149

167 Figures = 11.3 ksi s = 9 in. = 11.4 ksi s = 9 in. = 11.3 ksi s = 9 in P max = 1221 kips ρ = 1.1 % P max = 1413 kips ρ = 2.4 % P max = 1499 kips ρ = 4.0 % Load (kips) Column A10R9-ρ1 Column A10R9-ρ2.5 Column A10R9-ρ4 0.1 in. 0 Axial Shortening (in.) (a) = 14.0 ksi s = 7 in. = 14.1 ksi s = 7 in. = 14.3 ksi s = 7 in P max = 853 kips ρ = 1.9 % P max = 879 kips ρ = 3.0 % P max = 994 kips ρ = 4.2 % Load (kips) Column A18R7-ρ2 Column A18R7-ρ3 Column A18R7-ρ4 0.1 in. 0 Axial Shortening (in.) (b) Figure 31 Comparison between olumns with dierent ratios o longitudinal steel 150

168 Figures = 8.2 ksi ρ = 2.4 % s = 9 in. = 8.2 ksi ρ = 2.4 % s = 4½ in. Load (kips) Column 10R9-ρ2.5 Column 10R4½-ρ in. 0 Axial Shortening (in.) (a) 1000 = 15.2 ksi ρ = 1.9 % s = 7 in. = 15.2 ksi ρ = 1.9 % s = 3½ in. 800 Load (kips) Column 18R7-ρ2 Column 18R3½-ρ in. 0 Axial Shortening (in.) (b) Figure 32 Comparison between olumns with dierent tie spaings 151

169 Figures (a) Column with larger tie spaing (b) Column with loser tie spaing Figure 33 Typial ailure shapes o onentrially loaded retangular olumns Figure 34 Inlined shear ailure planes o onentrially loaded retangular olumns 152

170 Figures (a) Beore peak load (no rak) (b) Right ater peak load () Loal bukling o longitudinal steel (d) End o testing Figure 35 Column behavior during dierent stages o loading (14R9-ρ2.5) 153

171 Figures P max = 16.1 ksi ρ = 2.2 % s = 2 in P CR Column 14C2-ρ2.5 Load (kips) Spiral rupture Axial Shortening (in.) Figure 36 Load-axial shortening urve or onentrially loaded irular olumn Initiation o rak Load (kips) Column 14C2-ρ Extrapolation Strain (mm/mm) Figure 37 Load-axial average onrete strain measured by pi gauges (14C2-ρ2.5) 154

172 Figures L1 Yield strain (0.0021) P max L2 L1 L P CR Load (kips) Column 14C2-ρ Strain(mm/mm) Figure 38 Load-longitudinal steel strain (14C2-ρ2.5) S2 Yield strain (0.0022) P max S1 S2 Load (kips) S1 P CR Column 14C2-ρ Strain(mm/mm) Figure 39 Load-spiral steel strain (14C2-ρ2.5) 155

173 Figures = 15.1 ksi ρ = 2.9 % s = 2¾ in. = 15.1 ksi ρ = 2.9 % s = 1⅜ in. Load (kips) Column 18C2¾-ρ3 Column 18C1⅜-ρ in. 0 Axial Shortening (in.) (a) = 16.1 ksi ρ = 3.9 % s = 2 in. = 16.1 ksi ρ = 3.9 % s = 1 in Load (kips) Column 14C2-ρ4 Column 14C1-ρ in. 0 Axial Shortening (in.) (b) Figure 40 Comparison between olumns with dierent spiral spaing 156

174 Figures = 15.2 ksi ρ = 1.9 % s = 1½ in. = 15.0 ksi ρ = 2.9 % s = 1½ in. = 14.6 ksi ρ = 4.2 % s = 1½ in Load (kips) Column 18C1½-ρ2 Column 18C1½-ρ3 Column 18C1½-ρ4 0.3 in. 0 Axial Shortening (in.) (a) = 7.9 ksi ρ = 1.0 % s = 1⅜ in. = 8.0 ksi ρ = 2.2 % s = 1⅜ in. = 8.0 ksi ρ = 3.9 % s = 1⅜ in Load (kips) Column 10C1⅜-ρ1 Column 10C1⅜-ρ2.5 Column 10C1⅜-ρ4 0.4 in. 0 Axial Shortening (in.) (b) Figure 41 Comparison between olumns with dierent ratios o longitudinal steel 157

175 Figures Figure 42 Inlined shear ailure planes o onentrially loaded irular olumns Figure 43 Spiral rupture, loal bukling o longitudinal steel, and rushing o ore onrete 158

176 Figures (a) Initiation o rak (b) Spalling o over onrete () Complete spalling o over onrete (d) End o testing Figure 44 Column behavior during dierent stages o loading (10C1⅜-ρ2.5) 159

177 Figures Column 10R9-ρ4 (e/h 0) = 7.9 ksi ρ = 4 % s = 9 in. Load (kips) Column 10E1 (e/h = 0.1) Column 10E2 (e/h = 0.2) Axial Shortening (in.) (a) Eentrially loaded olumns with 9 12 in. setion Column 18R7-ρ4 (e/h 0) = 14.6 ~ 15.7 ksi ρ = 4.2 % s = 7 in. Load (kips) Column 18E1 (e/h = 0.1) Column 18E2 (e/h = 0.2) Axial Shortening (in.) (b) Eentrially loaded olumns with 7 9 in. setion Figure 45 Load-axial shortening urves or eentrially loaded retangular olumns 160

178 Figures (a) Spalling o over onrete and loal bukling o longitudinal steel (Compression side right in igure) (b) Inlined and lexural rak (Tension side right in igure) Figure 46 Typial ailure shapes o eentrially loaded olumns 161

179 Figures 1200 = 7.9 ksi e/h = PG4 PG3 PG2 P max Load (kips) PG1 Loading axis Column 10E1 PG3 200 PG1 PG4 PG Strain (mm/mm) Figure 47 Axial load-onrete strain measured by pi gauges (10E1) L3 L2 Yield strain (0.002) P max = 7.9 ksi e/h = L1 Load (kips) Loading axis Column 10E1 L L1 L Strain (mm/mm) Figure 48 Axial load-longitudinal steel strain (10E1) 162

180 Figures 1200 Yield strain (0.0023) = 7.9 ksi e/h = P max 800 T1 Load (kips) T3 T2 Column 10E1 T1 200 T3 0 Loading axis T Strain (mm/mm) Figure 49 Axial load-transverse steel (tie) strain (10E1) 163

181 Figures Steel Conrete Strain Distane rom Compression Fae (in.) (a) 10E Steel Conrete Strain Distane rom Compression Fae (in.) (b) 10E2 Figure 50 Strain proile aross setion at peak load or olumns with 9 12 in. setion 164

182 Figures Steel Conrete Strain Distane rom Compression Fae (in.) (a)18e Steel Conrete Strain Distane rom Compression Fae (in.) (b)18e2 Figure 51 Strain proile aross setion at peak load or olumns with 7 9 in. setion 165

183 Figures (a) Right ater peak load (b) During post peak () End o testing (ront view) (d) End o testing (side view) Figure 52 Eentri olumn behavior during dierent stages o loading (Compression side let in igures) 166