BEHAVIOR OF HIGH-STRENGTH CONCRETE MEMBERS SUBJECTED TO COMBINED FLEXURE AND AXIAL COMPRESSION LOADINGS. by HALIT CENAN MERTOL

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1 ABSTRACT MERTOL, HALIT CENAN. Behavior of High-Strength Conrete Members Subjeted to Combined Flexure and Axial Compression Loadings. (Under the diretion of Dr. Sami Rizkalla.) The use of high-strength onrete (HSC) in strutures and bridges has beome a ommon pratie worldwide. In bridges, HSC ould lead to a redution in number and depth of the girders as well as an inrease in the span length. These features redue the omplexity of a projet with redued number of piers, onstrution time and ost. Furthermore, the enhaned durability of HSC ould result in redution of the maintenane osts and inrease the servie life of the struture. In buildings, the sizes of the members ould be signifiantly redued whih ould help in the design and onstrution of higher strutures with larger spans. However, due to lak of researh data, most of the design odes worldwide limit the appliability of HSC. A total of 21 plain onrete speimens were tested under ombined flexure and axial ompression to evaluate the stress-strain distribution of HSC in the ompression zone of flexural members. The variables onsidered in this investigation were mainly the strength of onrete and the age of the speimen. The measured stress-strain urves and stress blok parameters, inluding the influene of the onrete strength, were ompiled with the data in the literature to evaluate the fundamental harateristis of high-strength onrete in the ompression zone of flexural members. A total of 42 ylindrial speimens and 18 prism speimens were used to evaluate the reep and shrinkage properties of HSC. The variables onsidered in this investigation were the onrete ompressive strength, speimen size, uring type, age of onrete at loading and loading stress level. The reep oeffiients and shrinkage strains were obtained for the range of onrete ompressive strength, evaluated and ompiled with the urrent preditions aording to the design odes. Using the test results of this researh and other researhes in literature, revisions to the LRFD Bridge Design Speifiations (2004) are reommended to extend the appliability of its ompressive and ombined ompressive and flexural design provisions to onrete ompressive strengths up to 18 ksi.

2 BEHAVIOR OF HIGH-STRENGTH CONCRETE MEMBERS SUBJECTED TO COMBINED FLEXURE AND AXIAL COMPRESSION LOADINGS by HALIT CENAN MERTOL A dissertation submitted to the Graduate Faulty of North Carolina State University In partial fulfillment of the Requirements for the Degree of Dotor of Philosophy CIVIL ENGINEERING Raleigh, North Carolina Deember 2006 APPROVED BY: Dr. Sami Rizkalla Chair of Advisory Committee Dr. Paul Zia Dr. Amir Mirmiran Dr. Mervyn Kowalsky

3 DEDICATION To my father AYTAÇ MERTOL For his unlimited support and enouragement over the years, whih made me understand him better day by day. ii

4 BIOGRAPHY Halit Cenan Mertol ompleted his Bahelor of Siene degree in Department of Civil Engineering in 1999 in Middle East Tehnial University, Ankara, Turkey. He also reeived his Master of Siene degree from the same university in 2002, on the topi of Carbon Fiber Reinfored Masonry Infilled Reinfored Conrete Frame Behavior under the supervision of advisor Dr. Tuğrul Tankut. After ompletion of his degree, he moved to the United States to pursue his Dotor of Philosophy degree in North Carolina State University to work with Dr. Sami Rizkalla on the harateristis of high-strength onrete members subjeted to ombined flexure and axial ompression. iii

5 ACKNOWLEDGEMENTS I would like to thank the sponsors of this projet, the Amerian Assoiation of State Highway and Transportation Offiials in ooperation with the Federal Highway Administration. I also would like to thank the Transportation Researh Board of the National Researh Counil who administered National Cooperative Highway Researh Program Projet I have been fortunate to have Dr. Sami Rizkalla as my graduate advisor for the last four years. I would like to onvey my deepest appreiation for his patiene and guidane throughout my studies and for his involvement in my areer. He spent numerous hours to make an impat on my life and to raft me into a better researher. I would like to thank Dr. Paul Zia for all his onstrutive advies and omments throughout this study. His brilliant ideas and thoughts enhaned my point of view and served as new soures of inspiration. I would espeially like to thank to Dr. Amir Mirmiran who advised and enouraged me for the last few years. I would like to reognize Dr. Mervyn Kowalsky and thank him for serving on my advisory ommittee. I would like to thank the personnel of the Construted Failities Laboratory, Mr. Jerry Atkinson, Mr. William Dunleavy, Mr. Lee Nelson and Mrs. Amy Yonai for all of their help, support and enouragement. I am also grateful to the graduate students who helped me and worked with me in this projet. Without my wife s unonditional support and enouragement, my studies would never be ompleted. I would like to thank my preious son for sleeping like a baby at nights. I m truly thankful to my family for their support and endless love over years even this far away. I would not have been able to aomplish the things in my life without the iv

6 love and support of my family. My abilities and aomplishments are a diret result of you, I would not be who I am today without you. v

7 TABLE OF CONTENTS LIST OF FIGURES...x LIST OF TABLES... xviii 1 INTRODUCTION GENERAL STATEMENT OF PROBLEM OBJECTIVES AND SCOPE THESIS ARRANGEMENT BACKGROUND GENERAL FLEXURAL BEHAVIOR OF HSC Stress Blok Parameters Eentri Braket Speimen Tests Hognestad et al. (1955) Soliman et al. (1967) Sargin et al. (1971) Nedderman (1973) Kaar et al. (1978a) Kaar et al. (1978b) Swartz et al. (1985) Pastor (1986) Shade (1992) Ibrahim (1994) Tan and Nguyen (2005) Summary of the Eentri Braket Tests to Date Proposed Stress-Strain Models for Compression Zone of Flexural Members Jensen (1943) Hognestad (1951) Sargin and Handa (1969) Popovis (1973) Wang et al. (1978a, b) Carreira and Chu (1985) Thorenfeldt et al. (1987) CEB-FIB Model Code (1990) Muguruma et al. (1991) Collins and Porasz (1989) Hsu and Hsu (1994) Wee et al. (1996) Van Gysel and Taerwe (1996) Attard and Setunge (1996) Oztekin et al. (2003) Proposed Retangular Stress Blok Parameters Whitney (1937)...54 vi

8 Mattok et al. (1961) Zia (1983) Li (1993) Azizinamini et al. (1994) Ibrahim (1994) Pendyala and Mendis (1998) Attard and Stewart (1998) Rangan (1999) Bae and Bayrak (2003) Sun et al. (2003) Oztekin et al. (2003) Ozbakkaloglu and Saatioglu (2003) Tan and Nguyen (2005) Summary of the Proposed Retangular Stress Blok Retangular Stress Blok Parameters in Design Codes ACI 318 (2005) and AASHTO LRFD Bridge Design Speifiations (2004) CSA A23.3 (1994) and CSA S6 (2001) NZS 3101 (1995) EC2 (2004) NS 3473 (1995) CEB-FIB Model Code (1990) ACI 441-R96 (1996) Summary of the Retangular Stress Blok Parameters in Design Codes POISSON S RATIO OF HSC Komendant et al. (1978) Perenhio and Klieger (1978) Carrasquillo et al. (1981) Swartz et al. (1985) Jerath and Yamane (1987) Radain et al. (1993) Ibrahim (1994) Iravani (1996) Persson (1999) Rashid et al. (2002) Logan (2005) Summary of the Tests on Poisson s Ratio CREEP AND SHRINKAGE OF HSC Tests on Creep and Shrinkage of HSC Ngab et al. (1981) Collins (1989) Paulsen et al. (1991) Giaio et al. (1993) Khan et al. (1997) Mokhtarzadeh and Frenh (2000) Huo et al. (2001) Jianyong and Yan (2001) Suksawang et al. (2005)...81 vii

9 Summary of the Tests on Creep and Shrinkage Creep and Shrinkage Preditions Models ACI 209R-92 (1992) CEB-FIB Model Code (1990) Tadros et al. (2003) and AASHTO LRFD Bridge Design Speifiations (2004) Australian Standard for Conrete Strutures AS3600 (2006) EXPERIMENTAL PROGRAM GENERAL ECCENTRIC BRACKET TESTS Design of Test Speimens Test Speimens Materials Conrete Reinforement Speimen Preparation Test Set-Up Instrumentation Test Proedure CREEP TESTS Test Speimens Creep Raks Instrumentation Test Proedure SHRINKAGE TESTS Test Speimens Instrumentations Test Proedure TEST RESULTS AND DISCUSSIONS GENERAL FLEXURAL BEHAVIOR General Observations for Eentri Braket Speimen Tests Surfae Strain Measurements Ultimate Compressive Strain of Conrete Poisson s Ratio Stress-Strain Distribution of Compression Zones Stress Blok Parameters CREEP BEHAVIOR SHRINKAGE BEHAVIOR ANALYTICAL WORK PROPOSED STRESS BLOCK PARAMETERS AND ULTIMATE COMPRESSIVE STRAIN FOR HSC Regression Analysis for Retangular Stress Blok Parameters and Ultimate Compressive Strain of Conrete viii

10 5.1.2 Sensitivity Analysis for Retangular Stress Blok Parameters and Ultimate Compressive Strain of Conrete PROPOSED STRESS-STRAIN RELATIONSHIP FOR HSC PROPOSED POISSON S RATIO FOR HSC Regression Analysis for Poisson s Ratio PROPOSED CREEP AND SHRINKAGE RELATIONSHIPS FOR HSC PROPOSED LIMITS FOR REINFORCEMENT FOR COMPRESSION MEMBERS CONCLUSIONS AND RECOMMENDATIONS SUMMARY OBSERVATIONS AND CONCLUSIONS RECOMMENDATIONS REFERENCES APPENDICES APPENDIX A ECCENTRIC BRACKET TEST DATA BY DIFFERENT RESEARCHERS APPENDIX B MATERIAL PROPOERTIES APPENDIX C CYLINDER COMPRESSION TESTS FOR EACH SPECIMEN APPENDIX D TESTS RESULTS FOR POISSON S RATIO APPENDIX E PROGRAM FOR THE DATALOGGER APPENDIX F SIMPLIFIED STRESS STRAIN RELATIONSHIPS FOR TEST SPECIMENS APPENDIX G CREEP AND SHRINKAGE TEST DATA APPENDIX H REGRESSION ANALYSIS FOR RECTANGULAR STRESS BLOCK PARAMETERS AND ULTIMATE COMPRESSIVE STRAIN OF CONCRETE APPENDIX I SENSITIVITY ANALYSIS FOR RECTANGULAR STRESS BLOCK PARAMETERS AND ULTIMATE COMPRESSIVE STRAIN OF CONCRETE APPENDIX J REGRESSION ANALYSIS FOR POISSON S RATIO ix

11 LIST OF FIGURES Figure 2-1 Failure Planes in NSC and HSC...7 Figure 2-2 Stress-Strain Relationships for Cement Paste and Aggregate...7 Figure 2-3 Stress-Strain Relationships for Different Conrete Compressive Strengths...8 Figure 2-4 First Three Stages of Conrete Cross-Setion Loaded Inrementally...11 Figure 2-5 Failure Stage of Conrete Cross-Setion (Stage 4)...12 Figure 2-6 Stress Blok Parameters for Retangular Setions...13 Figure 2-7 Test Speimen by Hognestad et al. (1955)...16 Figure 2-8 Test Speimen by Soliman et al. (1967)...18 Figure 2-9 Test Speimen by Sargin et al. (1971)...20 Figure 2-10 Test Speimens by Kaar et al. (1978b)...24 Figure 2-11 Test Speimen by Swartz et al. (1985)...25 Figure 2-12 Test Speimen by Shade (1992)...28 Figure 2-13 Retangular Test Speimen by Ibrahim (1994)...30 Figure 2-14 Triangular Test Speimen by Ibrahim (1994)...30 Figure 2-15 Test Set-Up by Tan and Nguyen (2005)...32 Figure 2-16 k 1 Parameter from Eentri Braket Tests...35 Figure 2-17 k 2 Parameter from Eentri Braket Tests...35 Figure 2-18 k 3 Parameter from Eentri Braket Tests...36 Figure 2-19 Produt of k 1 and k 3 Parameters from Eentri Braket Tests...36 Figure 2-20 α 1 Parameter from Eentri Braket Tests...37 Figure 2-21 β 1 Parameter from Eentri Braket Tests...37 Figure 2-22 Produt of α 1 and β 1 Parameters from Eentri Braket Tests...38 Figure 2-23 Ultimate ompressive strain of onrete from Eentri Braket Tests...38 Figure 2-24 Proposed Equations for α 1 by Researhers...64 Figure 2-25 Proposed Equations for β 1 by Researhers...64 Figure 2-26 α 1 in Design Codes...70 Figure 2-27 β 1 in Design Codes...70 Figure 2-28 Poisson s Ratios by Different Researhers...75 Figure 2-29 Strain History of Conrete under Sustained Load...76 Figure 3-1 Prototype Beam Member...90 x

12 Figure 3-2 Test Set-Up for Pilot Speimen Figure 3-3 Failure Mode at the Lower End of Pilot Speimen Figure 3-4 Test Set-Up for Pilot Speimen Figure 3-5 General View of the Speimen...93 Figure 3-6 Steel Reinforement Configuration...94 Figure 3-7 Steel Tube Setion, Reinforement Cage and PVC Tubes...98 Figure 3-8 Assembly of Steel Tube...98 Figure 3-9 Assembly of the Formwork...99 Figure 3-10 The Casting Day Figure 3-11 Drawings of the Moment Arm Figure 3-12 General View of the Moment Arm Figure 3-13 Sizes and Loations of the Threaded Rods Figure 3-14 Cross-Setion of the Roller Connetion Figure 3-15 General View of Roller Connetion Figure 3-16 Plaement of the Speimen into the Compression Mahine Figure 3-17 Connetions of the Moment Arms Figure 3-18 Test Set-Up Figure 3-19 General View of the Test Set-Up Figure 3-20 Loation of the Strain Gages for Pilot Tests Figure 3-21 Loation of the Strain Gages for Test Speimens Figure 3-22 Typial Creep Rak Figure 3-23 Appliation of the Strain Gages Figure 3-24 Plates, Disk springs and Pin Connetion Figure 3-25 Assembly of the Plates Figure 3-26 Eretion of the Creep Rak Figure 3-27 Campbell Sientifi Datalogger and Multiplexer Figure 3-28 Configuration of the Deme Points Figure 3-29 PVC Mold and Deme Inserts Figure 3-30 Deme Gage Figure 3-31 Hygro-Thermometer Clok Figure 3-32 Steel Mold for Prismati Shrinkage Speimens Figure 3-33 Dial Indiator for Shrinkage Tests Figure 4-1 Failure Mode of 10EB xi

13 Figure 4-2 Failure Mode of 10EB Figure 4-3 Failure Mode of 10EB Figure 4-4 Failure Mode of 10EB Figure 4-5 Failure Mode of 10EB Figure 4-6 Failure Mode of 14EB Figure 4-7 Failure Mode of 14EB Figure 4-8 Failure Mode of 14EB Figure 4-9 Failure Mode of 14EB Figure 4-10 Failure Mode of 14EB Figure 4-11 Failure Mode of 14EB Figure 4-12 Failure Mode of 18EB Figure 4-13 Failure Mode of 18EB Figure 4-14 Failure Mode of 18EB Figure 4-15 Failure Mode of 18EB Figure 4-16 Failure Mode of 18EB Figure 4-17 Failure Mode of 18EB Figure 4-18 Failure Mode of 18EB Figure 4-19 Failure Mode of 18EB Figure 4-20 Failure Mode of 18EB Figure 4-21 Failure Mode of 18EB Figure 4-22 Detailed Views of Speimen 18EB Figure 4-23 Detailed Views of Speimen 18EB Figure 4-24 Surfae Strain Measurements vs. Applied Main Axial Load (18EB4) Figure 4-25 Strain Distribution on Side Fae of Speimen 18EB Figure 4-26 Ultimate Compressive Strain of Conrete Obtained from This Researh and Other Researhes in Literature Figure 4-27 Compression Fae of Eentri Braket Speimen Figure 4-28 Poisson s Ratio for Eentri Braket Speimens with 10 ksi Target Conrete Compressive Strength Figure 4-29 Poisson s Ratio for Eentri Braket Speimens with 14 ksi Target Conrete Compressive Strength Figure 4-30 Poisson s Ratio for Eentri Braket Speimens with 18 ksi Target Conrete Compressive Strength xii

14 Figure 4-31 Poisson s Ratio Obtained from This Researh and Other Researhes in Literature Figure 4-32 Applied Fores on Eentri Braket Speimens Figure 4-33 Two Similar Stress-Strain Relationships (18EB4) Figure 4-34 Average Stress-Strain Relationship (18EB4) Figure 4-35 Stress-Strain Relationships for Speimens with 10 ksi Target Conrete Compressive Strength Figure 4-36 Stress-Strain Relationships for Speimens with 14 ksi Target Conrete Compressive Strength Figure 4-37 Stress-Strain Relationships for Speimens with 18 ksi Target Conrete Compressive Strength Figure 4-38 k 1 Values Obtained from This Researh and Other Researhes in Literature Figure 4-39 k 2 Values Obtained from This Researh and Other Researhes in Literature Figure 4-40 k 3 Values Obtained from This Researh and Other Researhes in Literature Figure 4-41 k 1 k 3 Values Obtained from This Researh and Other Researhes in Literature Figure 4-42 α 1 Values Obtained from This Researh and Other Researhes in Literature Figure 4-43 β 1 Values Obtained from This Researh and Other Researhes in Literature Figure 4-44 α 1 β 1 Values Obtained from This Researh and Other Researhes in Literature Figure 4-45 Average Creep Strains of Speimens with 10 ksi Target Conrete Compressive Strength Figure 4-46 Average Creep Strains of Speimens with 14 ksi Target Conrete Compressive Strength Figure 4-47 Average Creep Strains of Speimens with 18 ksi Target Conrete Compressive Strength Figure 4-48 Average Speifi Creep Strains of Speimens with 10 ksi Target Conrete Compressive Strength xiii

15 Figure 4-49 Average Speifi Creep Strains of Speimens with 14 ksi Target Conrete Compressive Strength Figure 4-50 Average Speifi Creep Strains of Speimens with 18 ksi Target Conrete Compressive Strength Figure 4-51 Average Creep Coeffiients of Speimens with 10 ksi Target Conrete Compressive Strength Figure 4-52 Average Creep Coeffiients of Speimens with 14 ksi Target Conrete Compressive Strength Figure 4-53 Average Creep Coeffiients of Speimens with 18 ksi Target Conrete Compressive Strength Figure 4-54 Variations in Temperature and Humidity for Creep and Shrinkage Speimens Figure 4-55 Adjusted Average Creep Coeffiients of Speimens with 10 ksi Target Conrete Compressive Strength Figure 4-56 Adjusted Average Creep Coeffiients of Speimens with 14 ksi Target Conrete Compressive Strength Figure 4-57 Adjusted Average Creep Coeffiients of Speimens with 18 ksi Target Conrete Compressive Strength Figure 4-58 Shrinkage Strain of Cylindrial Speimens with 10 ksi Target Conrete Compressive Strength Figure 4-59 Shrinkage Strain of Cylindrial Speimens with 14 ksi Target Conrete Compressive Strength Figure 4-60 Shrinkage Strain of Cylindrial Speimens with 18 ksi Target Conrete Compressive Strength Figure 4-61 Shrinkage Strain of Prismati Speimens with 10 ksi Target Conrete Compressive Strength Figure 4-62 Shrinkage Strain of Prismati Speimens with 14 ksi Target Conrete Compressive Strength Figure 4-63 Shrinkage Strain of Prismati Speimens with 18 ksi Target Conrete Compressive Strength Figure 4-64 Weight Loss of Prismati Speimens with 10 ksi Target Conrete Compressive Strength xiv

16 Figure 4-65 Weight Loss of Prismati Speimens with 14 ksi Target Conrete Compressive Strength Figure 4-66 Weight Loss of Prismati Speimens with 18 ksi Target Conrete Compressive Strength Figure 4-67 Adjusted Shrinkage Strain of Cylindrial Speimens with 10 ksi Target Conrete Compressive Strength Figure 4-68 Adjusted Shrinkage Strain of Cylindrial Speimens with 14 ksi Target Conrete Compressive Strength Figure 4-69 Adjusted Shrinkage Strain of Cylindrial Speimens with 18 ksi Target Conrete Compressive Strength Figure 4-70 Adjusted Shrinkage Strain of Prismati Speimens with 10 ksi Target Conrete Compressive Strength Figure 4-71 Adjusted Shrinkage Strain of Prismati Speimens with 14 ksi Target Conrete Compressive Strength Figure 4-72 Adjusted Shrinkage Strain of Prismati Speimens with 18 ksi Target Conrete Compressive Strength Figure 5-1 Stress Blok Parameters for Different Stress Distributions Figure 5-2 Proposed Relationship for the Stress Blok Parameter k Figure 5-3 Proposed Relationship for the Stress Blok Parameter k Figure 5-4 Proposed Relationship for the Stress Blok Parameter k Figure 5-5 Proposed Relationship for the Produt of Stress Blok Parameters k 1 k Figure 5-6 Proposed Relationship for Ultimate Conrete Compressive Strain, ε u Figure 5-7 Proposed Relationship for the Retangular Stress Blok Parameters α Figure 5-8 Proposed Relationship for the Retangular Stress Blok Parameters β Figure 5-9 Proposed Relationship for the Produt of Retangular Stress Blok Parameters α 1 β Figure 5-10 Regression Analysis of α 1 for Conrete Compressive Strengths Figure 5-11 Regression Analysis of α 1 for Conrete Compressive Strengths Figure 5-12 Regression Analysis of α 1 for Conrete Compressive Strengths over 10 ksi Figure 5-13 Regression Analysis of β 1 for Conrete Compressive Strengths up to 20 ksi Figure 5-14 Regression Analysis of β 1 for Conrete Compressive Strengths xv

17 Figure 5-15 Regression Analysis of β 1 for Conrete Compressive Strengths over 10 ksi Figure 5-16 Regression Analysis of ε u for Conrete Compressive Strengths up to 20 ksi Figure 5-17 Regression Analysis of ε u for Conrete Compressive Strengths Figure 5-18 Regression Analysis of ε u for Conrete Compressive Strengths over 10 ksi Figure Ratio of Ultimate Moment Capaity versus Change in α Figure Ratio of Ultimate Moment Capaity versus Change in β Figure Ratio of Ultimate Moment Capaity versus Change in ε u Figure 5-22 Comparison of the Ratio of Calulated and Atual Values using Atual Values for ε o and ε u Figure 5-23 Comparison of Calulated and Atual Stress-Strain Relation of 10EB Figure 5-24 Comparison of Calulated and Atual Stress-Strain Relation of 14EB Figure 5-25 Comparison of Calulated and Atual Stress-Strain Relation of 18EB Figure 5-26 Strain at Maximum Stress versus Conrete Maximum Stress Figure 5-27 Ultimate ompressive strain of onrete versus Conrete Maximum Stress Figure 5-28 Comparison of the Ratio of Calulated and Atual Values using Proposed Relationships for ε o and ε u Figure 5-29 Comparison of Calulated and Atual Stress-Strain Relation of 10EB Figure 5-30 Comparison of Calulated and Atual Stress-Strain Relation of 14EB Figure 5-31 Comparison of Calulated and Atual Stress-Strain Relation of 18EB Figure 5-32 Proposed Relationship for Poisson s Ratio Figure 5-33 Regression Analysis of ν for Conrete Compressive Strengths up to 20 ksi Figure 5-34 Regression Analysis of ν for Conrete Compressive Strengths Figure 5-35 Regression Analysis of ν for Conrete Compressive Strengths over 10 ksi Figure 5-36 Comparison of Creep Coeffiient of 10Rak Figure 5-37 Comparison of Creep Coeffiient of 10Rak Figure 5-38 Comparison of Creep Coeffiient of 10Rak2 and 10Rak xvi

18 Figure 5-39 Comparison of Creep Coeffiient of 10Rak3 and 10Rak Figure 5-40 Comparison of Creep Coeffiient of 14Rak Figure 5-41 Comparison of Creep Coeffiient of 14Rak Figure 5-42 Comparison of Creep Coeffiient of 14Rak2 and 14Rak Figure 5-43 Comparison of Creep Coeffiient of 14Rak3 and 14Rak Figure 5-44 Comparison of Creep Coeffiient of 18Rak Figure 5-45 Comparison of Creep Coeffiient of 18Rak Figure 5-46 Comparison of Creep Coeffiient of 18Rak2 and 18Rak Figure 5-47 Comparison of Creep Coeffiient of 18Rak3 and 18Rak Figure 5-48 Comparison of Shrinkage Strain of 10SC Figure 5-49 Comparison of Shrinkage Strain of 10SP1, 10SP2 and 10SP Figure 5-50 Comparison of Shrinkage Strain of 14SC Figure 5-51 Comparison of Shrinkage Strain of 14SP1, 14SP2 and 14SP Figure 5-52 Comparison of Shrinkage Strain of 18SC Figure 5-53 Comparison of Shrinkage Strain of 18SP1, 18SP2 and 18SP Figure 5-54 Comparison of Shrinkage Strain of 10SC Figure 5-55 Comparison of Shrinkage Strain of 10SP4, 10SP5 and 10SP Figure 5-56 Comparison of Shrinkage Strain of 14SC Figure 5-57 Comparison of Shrinkage Strain of 14SP4, 14SP5 and 14SP Figure 5-58 Comparison of Shrinkage Strain of 18SC Figure 5-59 Comparison of Shrinkage Strain of 18SP4, 18SP5 and 18SP Figure 5-60 k td for f i = 4 ksi Figure 5-61 k td for f i = 6 ksi Figure 5-62 k td for f i = 8 ksi Figure 5-63 k td for f i = 10 ksi Figure 5-64 k td for f i = 12 ksi Figure 5-65 k td for f i = 14 ksi Figure 5-66 k td for f i = 16 ksi Figure 5-67 k td for f i = 18 ksi Figure 5-68 Reinforement Limits for Compression Members with Only Mild Steel Aording to the Current AASHTO LRFD Bridge Design Speifiations Figure 5-69 Initial Elasti Strain due to Applied Sustained Load Figure 5-70 Behavior of Reinfored Conrete Column due to Shrinkage and Creep..226 Figure 5-71 Comparison of the A s /A g Ratio for P/f A g = xvii

19 LIST OF TABLES Table 2-1 Summary of the Eentri Braket Tests...34 Table 2-2 Stress-Strain Relationship Constants by Wang et al. (1978a,b)...43 Table 2-3 Values of the Parameter t for Different Conrete Compressive Strengths...51 Table 2-4 Retangular Stress Blok Parameters Proposed by Zia (1983)...55 Table 2-5 Summary of the Proposed Retangular Stress Blok Parameters...63 Table 2-6 Stress Blok Parameters for the Norwegian Code NS 3473 (1995)...67 Table 2-7 Summary of the Retangular Stress Blok Parameters in Design Codes...69 Table 2-8 Summary of the Tests on Poisson s Ratio...74 Table Summary of the Tests on Creep and Shrinkage...81 Table 3-1 Details of the Test Speimens...93 Table 3-2 Three Conrete Mixture Designs...96 Table 3-3 Testing Sheme for Cylindrial Creep Speimens Table 3-4 Testing Sheme for Cylindrial Shrinkage Speimens Table 3-5 Configuration of Plates and Threaded Rods in the Raks Table 3-6 Testing Sheme for Prismati Shrinkage Speimens Table 4-1 Tabulated Test Results for Eentri Braket Speimens Table 4-2 Tabulated Results for Ultimate ompressive strain of onrete Table 4-3 Tabulated Results for Poisson s Ratio Table 4-4 Calulated Stress Blok Parameters for Eentri Braket Speimens Table 4-5 Details about Creep Tests Table 4-6 Numerial Illustration of the Calulation Proedure Table 4-7 Details about Cylindrial Shrinkage Speimens Table 4-8 Details about Prismati Shrinkage Speimens Table 5-1 Tabulated Results of the Regression Analysis for the Retangular Stress Blok Parameters Table 5-2 Tabulated Results of the Regression Analysis for Ultimate Compressive Strain of Conrete Table 5-3 Summary of the Sensitivity Analysis Table 5-4 Conrete Strain Obtained from Stress-Strain Relationships Table 5-5 Conrete Strain Obtained from Stress-Strain Relationships Table 5-6 Tabulated Results of the Regression Analysis for Poisson s Ratio xviii

20 Table 5-7 Comparison of the A s /A g Ratio for P/f A g = Table 5-8 Calulated Values for P/f A g = xix

21 1 Introdution 1 INTRODUCTION 1.1 General The use of high-strength onrete (HSC), ranging from 10 to 18 ksi, has beome a ommon pratie worldwide. In bridges, HSC ould lead to a redution in number and depth of the girders as well as an inrease in the span length. These features redue the omplexity of a projet with redued number of piers, onstrution time and ost. Furthermore, the enhaned durability of HSC ould result in redution of the maintenane osts and inrease the servie life of the struture. In buildings, the sizes of the members ould be signifiantly redued whih ould help in the design and onstrution of higher strutures with larger spans. Development of HSC dates bak to 1930's, but these early developments were eonomially prohibitive for pratial appliations. In the 1960 s, superplastiizers were developed in Japan and Germany and made it possible to derease the water to ement ratio of onrete while maintaining its workability. In the 1970 s, the ombined use of superplastiizers and ultra-fine materials suh as silia fume, finely ground granulated blast furnae slag or anhydrous gypsum led to further improvement of onrete performane measures inluding its strength. Sine the mid-1980 s, HSC has gained popularity in both preast and ast-in-plae onstrution for either reinfored or prestressed members. In Japan, onrete ompressive strengths as high as 11.4 ksi were used in the 1970 s for railway bridges (ACI 363R ). In the early 1990 s, the United States Department of Transportation Federal Highway Administration (USDOT-FHWA) began sponsoring the use of HSC in several demonstration projets. Sine 1993, a number of HSC bridges have been onstruted aross the United States. The USDOT-FHWA ompilation projet (Russell et al. 2003a, 2003b) reports on 19 suh bridges in 14 states. While the highest design onrete ompressive strength in these bridges was reported as 14 ksi in Texas, the ahieved strength at the design age reahed as high as 15.9 ksi in South Dakota. 1

22 1 Introdution However, due to lak of suffiient researh data, most of the design odes worldwide limit the appliability of HSC. The AASHTO LRFD Bridge Design Speifiations (2004), first published in 1994, inludes an artile ( ) limiting its appliability to a maximum onrete ompressive strength of 10 ksi, unless physial tests are made to establish the relationship between onrete ompressive strength and its other properties. Many design provisions stipulated in the AASTHO LRFD Bridge Design Speifiations (2004) are still based on test results obtained from speimens with ompressive strengths less than 10 ksi. Although suh a strength limit is not expliitly imposed by other odes suh as the ACI Building Code Requirements for Strutural Conrete (2005), exept in the provisions for development length, their appliability to HSC is not fully addressed either. The United States National Cooperative Highway Researh Program (NCHRP) of the National Aademies has initiated four separate projets to extend the AASHTO LRFD Bridge Design Speifiations (2004), allow broader use of HSC, and meet the needs of the bridge design ommunity. NCHRP Projet addressed prestress losses in pretensioned onrete girders (Tadros et al. 2003). NCHRP Projet is addressing shear in reinfored and prestressed onrete members. NCHRP Projet is addressing bond and development length in reinfored and prestressed onrete. The objetive of NCHRP Projet 12-64, whih is the fous of this thesis, is to reommend revisions to the LRFD Bridge Design Speifiations to extend the appliability of its ompressive and ombined ompressive and flexural design provisions for reinfored and prestressed onrete members to onrete ompressive strengths up to 18 ksi. 1.2 Statement of Problem The flexural design of reinfored and prestressed onrete strutural members in the United States is based on the ultimate strength approah. Before 1930 s, the allowable stress (working stress) theory was used in the design odes. In the early 1930 s the extensive investigation performed by Rihart et al. (1931a, 1931b, 1931 and 1932) on the onentrially loaded olumns led the transformation of the design theory for olumns into ultimate strength approah. In the mid 1950 s, Hognestad (1955) developed retangular stress blok parameters whih reated the basis of the ultimate strength priniple used in the urrent odes for flexure analysis and design. 2

23 1 Introdution The urrent retangular stress blok speified by ACI Building Code Requirements for Strutural Conrete (2005) and AASHTO LRFD Bridge Design Speifiations (2004) is based on normal-strength onrete (NSC) up to 10 ksi. As the improvement of the onrete ompressive strength enourages the designers to use HSC in design, the retangular stress blok parameters must be evaluated for the use of HSC and if neessary new retangular stress blok parameters must be introdued for HSC design. Conrete is a time dependent material. In partiular, onrete reeps under sustain load, and shrinks due to the hanges in the moisture ontent of the surrounding environment. These physial hanges inrease by time. The information on reep and shrinkage of onrete an be used to determine the prestressing losses, long term deformations and raking of the ivil engineering strutures. The evaluation of reep and shrinkage of onrete is very important espeially for long-span and high-rise strutures. The urrent ode equations for reep and shrinkage preditions are based on NSC; therefore, there is a need to evaluate these harateristis for HSC. 1.3 Objetives and Sope The researh program was onduted at the Construted Failities Laboratory (CFL) of North Carolina State University (NCSU) from 2003 and The objetives of the study are to: 1. Evaluate the data published by other researhes related to stress blok parameters, ultimate ompressive strain, Poisson s Ratio, reep and shrinkage of HSC, 2. Condut experimental program to determine the stress blok parameters, ultimate ompressive strain, Poisson s Ratio, reep and shrinkage behavior of HSC, 3. Use results of the experimental program and the data from other researhes to reommend revisions to the AASHTO LRFD Bridge Design Speifiations (2004) to extend the appliability of flexural and ompression provisions for reinfored and prestressed onrete members to onrete ompressive strengths up to 18 ksi. 3

24 1.4 Thesis Arrangement 1 Introdution The literature review on stress-stress relationship, ultimate ompressive strain, Poisson s Ratio, reep and shrinkage for normal and HSC is presented in Chapter 2. It inludes a review of eentri braket speimen tests whih provides the basis to evaluate the stress blok parameters for onrete. Proposed stress-strain models for unonfined onrete and proposed retangular stress blok parameters by different researhers are presented. The literature inludes omprehensive review of the stress blok parameters in different design odes from all over the world. In addition, this hapter overs the experimental researh performed on Poisson s Ratio, reep and shrinkage of HSC. Proposed relationships urrently used for the predition of reep and shrinkage of HSC are presented in details for future omparison purposes. Chapter 3 desribes the speimens investigated in this researh and the methods used in testing to evaluate the stress-strain relationship, Poisson s Ratio, reep and shrinkage of HSC. The omposition of materials, test set-ups and the proedures are also illustrated in details. The test results obtained from all the speimens are presented in Chapter 4. The measured response inluding the behavior of the speimens is also illustrated. The test results are ompiled, analyzed, evaluated and ompared with the test data and available relationships presented in Chapter 2. The analytial work performed in the light of the test results are presented in Chapter 5. It also inludes the proposed relationships for stress blok parameters, Poisson s Ratio, reep and shrinkage of HSC. Statistial and parametri analyses are arried out to justify the proposed relationships. Furthermore, the proposed relationships for reep and shrinkage are used to develop new requirements for the minimum longitudinal reinforement ratio for ompression members. A summary of the testing program and analytial work is presented in Chapter 6. Based on the researh, onlusions and reommendations are made. 4

25 2 Bakground 2 BACKGROUND 2.1 General Conrete is a omposite material onsisting of ement, water, fine and oarse aggregate. The ement partiles hydrate and form the ement paste, the main binder in onrete. The ement paste hardens in time due to a hemial reation between ement and water. The ement paste binds the fine and oarse aggregate together to form the hardened onrete. The strength of onrete will inrease as long as the unhydrated ement partiles ontinue to hydrate with available water. HSC onsists of the similar ingredients as NSC, however, with different proportions and different types. After numerous researhes to ahieve a stronger onrete, it was observed that to derease the water to ement ratio in a onrete inreases the onrete ompressive strength. This an be performed either by inreasing the amount of ement or dereasing the amount of water. To inrease the amount of ement exessively in a onrete mixture may generate some thermal problems whih are due to the inreased temperature of onrete during the hydration of ement. It also inreases the ost. Use of water in onrete enhanes the workability of the unhardened mixture and ensures the hydration of ement partiles. Therefore, the problems assoiated with the inreased amount of ement and redution of the water have to be optimized to obtain HSC. High ompressive strengths of onrete require not only inreased amount of ement, but also addition of mineral admixtures suh as silia fume and fly ash to the onrete mixture. The heat generated by the hydration of these admixtures is lower than that generated by hydration of ement. The heat of hydration of the onrete an be lowered to aeptable levels by balaning the proportions with these admixtures. Furthermore, these admixtures have very fine partiles whih will fill the spaes between the ement grains. A more ompat mixture will be obtained and the strength will inrease further due to ompatness of the mixture. The introdution of the hemial admixtures suh as superplastiizers and retarders into the onrete tehnology made it possible to ahieve a workable mixture for a desired 5

26 2 Bakground length of time although the amount of water is redued. Without these hemial admixtures, HSC an not be obtained. Mahter and Hime (2002) stated that a water to ement ratio of 1.2 by volume whih is equivalent to 0.4 by mass is needed to hydrate all the ement partiles in a onrete mixture. When more water is added, the exessive water after hydration of ement will generate some voids in the struture of hardened onrete whih will derease the strength of onrete. In ase of water to ement ratios less than 0.4 by mass, some of the ement partiles will always remain unhydrated whih might seem to be a problem. On the ontrary, having unhydrated ement partiles is not a negative fator as the strength of unhydrated ement partiles is muh higher than that of hydrated ement partiles. Furthermore these unhydrated partiles will work as fillers so that a more ompat mixture will be ahieved (Berntsson et al. 1990). To improve the onrete ompressive strength further, the size of the oarse aggregates is redued. It was observed that using smaller sized oarse aggregate in a onrete mixture would inrease the strength of onrete further (ACI 363R ). Sine the type, size and properties of ingredients of onrete hanges from one loation to another loation, the properties of onrete also hanges. But the proess of the failure of onrete is always the same. There are three soures of failures in onrete: (1) the hydrated ement paste, (2) the aggregate and (3) the interfae between the hydrated ement paste and the aggregate. Strengthening these failure soures is the only way to strengthen the onrete. For NSC, the failure ours when the hydrated ement paste and the interfae binding the hydrated ement paste and aggregate fail. As a result, the properties of onrete resemble more to the properties of the hydrated ement paste. But for HSC, the hydrated ement paste and the interfae between the hydrated ement paste and the aggregate are generally stronger than the aggregate. As a result, the failure plane uts through the aggregates. This means that the strength of aggregate is the main soure that defines the harateristis of HSC. The strength and behavior in this ase are limited to the strength and behavior of aggregate. A stronger aggregate should be used in order to enhane the strength and behavior of onrete. The behaviors of NSC and HSC using the same materials but different proportions are shown in Figure 2-1. The bold line in the 6

27 2 Bakground figure represents the failure plane in the onrete. The stress-strain relationships for the ement paste and aggregate as well as NSC and HSC are presented in Figure 2-2. Failure Plane for NSC Failure Plane for HSC Figure 2-1 Failure Planes in NSC and HSC Stress Aggregate High-Strength Conrete Cement Paste Normal-Strength Conrete Strain Figure 2-2 Stress-Strain Relationships for Cement Paste and Aggregate One of the most signifiant harateristi differenes between NSC and HSC is the failure mode at ultimate. NSC fails more gradually whereas HSC fails suddenly with an explosive manner. The failure mode of HSC ours almost immediately after the 7

28 2 Bakground maximum load is reahed. This indiates that the desending branh of stress-strain relationship for HSC is steeper and relatively shorter than that of NSC. The strain at the maximum stress ahieved in NSC is in the order of 2000 µε whereas HSC has a strain of approximately 3000 µε or more at the maximum stress. Also the strain at ultimate for NSC is several times greater than that of HSC. Stress-strain relationships for different onrete ompressive strengths obtained by Dahl (1992) are shown in Figure 2-3. The figure indiates that, as the onrete ompressive strength inreases, the strain at the peak stress inreases slightly. Furthermore, the shape of the asending branh of the stressstrain urve beomes more linear and steeper, and the slope of the desending part also beomes steeper. 18 Conrete Compressive Stress (ksi) Tests by Dahl (1992) Conrete Compressive Strain Figure 2-3 Stress-Strain Relationships for Different Conrete Compressive Strengths Before the appliation of any load on onrete, miro raks develop in the interfae between the ement paste and the aggregate due to drying of the ement paste, whih is onstrained by the non-shrinking aggregate. When NSC is loaded to failure, four distint stages an be observed in the stress-strain relationship. The first stage, the linear elasti range for onrete, ours before reahing 30 to 40 perent of ylinder onrete ompressive strength (f ). The seond stage, the beginning of the non-linearity of stress- 8

29 2 Bakground strain relationship, an be observed between 30 and 50 perent of onrete ompressive strength of ylinder. Miro raks developed in the drying stage inrease in length, width and numbers; however a stable system of miro raks exists. In the third stage, between 50 and 75 perent of the onrete strength, raks start to form in the ement paste. This auses an unstable system of raks in the ement paste, whih inreases the non-linearity of the stress-strain relationship. After 75 perent of the ylinder ompressive strength, the forth stage starts with rapid propagation of the raks in the ement paste and the interfae between the ement paste and the aggregate. A ontinuous rak system ours in between whih auses a rapid inrease of the strain. After the ultimate stress is reahed, a slow mode of failure happens at the end of this stage, sine the raks are interrupted by the aggregates and must move around the aggregate. On the oter hand, when HSC is loaded to failure, it shows only two stages. The linear elasti stage is before 85 perent of the onrete ompressive strength of ylinder. The seond stage happens quite fast after 85 perent of the onrete ompressive strength of ylinder whih is followed by a sudden failure, when raks pass through the weaker aggregates. HSC made with the materials explained previously will have the following advantages in omparison to NSC: Inreased durability due to ompatness and redued permeability o More resistane to the hloride damage to reinforing steel o More resistane to aid or other hemial attaks o Inreased freeze thaw resistane o Inreased abrasion resistane o The HSC strutures will require less maintenane, fewer repairs and will last longer Design advantages for bridges o Inreased span length For standard preast prestressed bridge girders, inreasing onrete strength from 5000 psi to 7000 psi inreased span apabilities of AASHTO girders by about 15 perent (Fiorato 1989) o Redued number of girders in a span 9

30 o Redued setion height in a span 2 Bakground Design advantages for buildings o Greater heights an be ahieved o Smaller setions with redued dead weight, longer spans with fewer beams o Redution in member size inreases the rentable area The higher the onrete ompressive strength, the smaller the olumn ross-setion and the more eonomial the olumn beomes (Moreno 1998) Changing the speified onrete ompressive strength in the ore of 735 ft high Bourke Plae in Melbourne, Australia from 5800 psi to 8700 psi inreased eah floors rentable spae by 32 yd 2 resulting in an effetive benefit of approximately $ per floor for the lient (Burnett 1989) o Redued axial shortening of the olumns due to redued reep and shrinkage behavior o Redued interstory drift due to the inreased stiffness o Earlier stripping of the formworks due to high early strength o For a fixed olumn size, with an inrease in the onrete ompressive strength, there is a signifiant redution in the reinforing steel required. Relative redution in the perentage of steel in the order of 40 perent for 8000 psi onrete and 67 perent for psi onrete (Smith and Rad 1989) Redution of strutural steel onsumption in the 85 story high-rise T&C Tower in Kaohsiung, Taiwan: the steel ratio is redued from 1.66 to 1.00 (Hwang et al. 1999) 2.2 Flexural Behavior of HSC When an under-reinfored onrete beam is loaded inrementally up to failure, the onrete ross-setion exhibits 4 different stages. The first three stages are shown in Figure 2-4. The shaded areas represent the onrete in ompression. The first stage is before raking of onrete, when the extreme bottom onrete fiber tensile stresses ( f t1 ) 10

31 2 Bakground reahes the modulus of rupture of onrete ( f r ). The tensile stresses are both resisted by onrete and steel whereas the ompression stresses are only resisted by onrete. The neutral axis (NA) is a little below the midpoint of the setion due to the effet of reinforement in lowering the enter of gravity of the ross-setion. In the seond stage, raks initiate from the bottom onrete fiber to have a new equilibrium of fores. From now on the tensile stresses are resisted only by steel ( f s ) and ompressive stresses are resisted by ompression zone of onrete over the neutral axis. The neutral axis shifts upwards and the raks propagate to the neutral axis. The third stage starts with yielding of steel ( f s3 = f y ). Sine the behavior of steel is elasto-plasti, after yielding, stresses in steel do not inrease although the strain inreases. On the other hand, the onrete has not reahed its highest ompressive strain at the top fiber of the setion. As the strain at the top fiber inreases, the ompressive stresses in onrete also inrease. This raises the neutral axis upwards due to the new equilibrium of fores. ε 1 f 1 ε 2 f 2 ε 3 f 3 NA NA NA Setion ε t1 f t1 f r ε s2 ε y f s2 f y ε s3 > ε y f s3 = f y Strain Stress Strain Stress Strain Stress Stage 1 Stage 2 Stage 3 Figure 2-4 First Three Stages of Conrete Cross-Setion Loaded Inrementally The fourth stage is the failure of onrete beam where the setion reahes its ultimate strength apaity. Conrete reahes maximum ompressive strain ( ε u ) at the extreme ompression fiber. The onrete in the ompression zone has a non-linear stress 11

32 2 Bakground distribution similar to its stress-strain relationship whih is referred to as the atual stress distribution. This failure stage of onrete ross-setion is shown in Figure 2-5. ε 4 = ε u f 4 NA ε s4 >> ε y Strain Stress f s4 = f y Stage 4 Figure 2-5 Failure Stage of Conrete Cross-Setion (Stage 4) The design onsidering the forth stage, the failure stage of the setion, is alled the ultimate strength design. The proedure for ultimate strength design inorporates four basi assumptions in the alulation of the ultimate strength whih are: 1. Plane setions remain plain after deformation; whih is based on the development of the beam theory. This implies that the linear ompatibility of strains is preserved until the failure of the strutural member. 2. The strain in the reinforement is equal to the strain in the onrete at the same level; whih assumes a perfet bond between onrete and reinforement. 3. The fores an be alulated by using stress-strain relationships of both onrete and steel reinforement by using the strain ompatibility of the setion. 4. The tensile stress developed in onrete below the neutral axis is negleted. The origin of the ultimate strength theory of beams in flexure dates bak to Galilei s work in After the formulation of Hooke s Law in 1680 s and the establishment of the fundamentals of theory of elastiity in 1820 s by Navier, design turned to allowable stress method whih was mathematially more simple. Although theory of elastiity was widely utilized worldwide by the end of 19 th entury, many researhes were performed on 12

33 2 Bakground ultimate strength theories to understand the behavior of reinfored onrete beams. The work performed by M. R. von Thullie on flexural theory in 1897 and the paraboli stress distribution of onrete introdued by W. Ritter s in 1899 were good examples on ultimate strength design theory (Hognestad 1951) Stress Blok Parameters The atual stress distribution in the ompression zone of onrete an be mathematially defined by three parameters, k 1, k 2 and k 3 whose use was initially introdued by F. Stüssi in 1932 (Hognestad 1952). The parameter k 1 is defined as the ratio of the average ompressive stress to the maximum ompressive stress. The parameter k 2 is the ratio of the depth of the resultant ompressive fore to the depth of neutral axis. The parameter k 3 is the ratio of the maximum ompressive stress ( σ to the ompressive strength of onrete ylinder ( max ) ahieved in the strutural member f ' ). The design values of the stress blok parameters are determined at the ultimate strain ( ε u ), whih orresponds to the maximum moment of the setion. These parameters are shown in Figure 2-6. b ε u k 3 f α 1 f k 2 C = k 1 k 3 f b β 1 β 1 /2 C = α 1 β 1 f b d A s Strain Distribution Generalized Stress Blok Parameters Retangular Stress Blok Parameters Setion Figure 2-6 Stress Blok Parameters for Retangular Setions The k 3, k k, and 1 3 k 2 values an be obtained from the equilibrium of the external and internal fores, as follows: k 3 σ max = Equation 2-1 f ' C = k k f ' b 1 3 C k1 k3 = Equation 2-2 f b ' 13

34 ( d k ) M = k1 k3 f ' b 2 k 2 ( ) 2 Bakground = d M C Equation 2-3 The three-parameter generalized stress blok an be redued to a two-parameter equivalent retangular stress blok, by keeping the resultant of the ompression fore at the mid-depth of the assumed retangular stress blok. This does not mean that this method is based on the assumption of retangular stress distribution. The use of the retangle is only a mathematial devie to approximate the effet of the atual stress distribution of onrete. It would be possible to use any urved shape that would give the same resultant fore and the enter of gravity, but the retangular area appears to be entirely satisfatory and gives the simplest possible mathematial solution. The use of a retangular stress blok was first proposed by von Emperger in 1904 (Mattok et al. 1961) and sine that time this idea was improved by the ontributions of many researhers. The retangular stress blok parameters, α 1 and β 1 are presented in Figure 2-6 and an be defined as: k 2 β 2 1 = Equation 2-4 C = α β f ' b = k k f ' b Equation 2-5 therefore k k 1 3 α 1 = Equation 2-6 2k 2 β 1 = 2k 2 Equation 2-7 The behavior of onrete in flexure is not the same as that of onrete ylinder in pure ompression. The primary reason is the distribution of stresses in onrete; the strain gradient effet in flexure helps onrete to ahieve higher strains than that in pure ompression. Other reasons are the shape and size effets of the onrete ylinder ompared to the real reinfored onrete strutural member. Furthermore, the rate of loading of a strutural member is always muh slower than that of a onrete ylinder. Also the water rise of a strutural onrete member in the asting proess may inrease this differene more. However, the stress distribution of onrete in flexure may still be represented adequately by the stress-strain relationship of the onrete ylinder using an 14

35 2 Bakground empirial onstant (k 3 ) to aount for all of these differenes. This onstant is determined by omparing the beams tested in flexure to the ompanion ylinders tested under ompression. This method is widely used in the analysis and design of strutural members. Initially a onrete ylinder is tested in a ompression mahine to obtain the maximum stress in pure ompression whih is also referred to as ylinder ompressive strength. Many researhers have proposed various equations to get the stress-strain relationship using only one variable, the ylinder ompressive strength. By using one of these relationships, the stress-strain urve for speified ylinder ompressive strength is obtained for onrete. Next step is to redue the relationship by using this onstant (k 3 ) that aounts for the fators stated before. The redued urve is used in design and analysis of the strutural members. The stress-strain relationship of onrete members in flexure is diffiult to determine by diret experimental means. The strains and applied loads an be measured easily whereas to obtain the stresses in onrete requires a numerial differentiation of the measured quantities. Hognestad et al. (1955) derived the equations to alulate the onrete stress as a funtion of ontinuously monitored strain of the most ompressed fibers and applied loads on the onrete member. The detailed derivation is given in Chapter 5. In the next setion, the tests related to determination of stress-strain relationship of onrete members in flexure are explained Eentri Braket Speimen Tests Many researhers have been working on the stress-strain distribution of onrete sine the beginning of the 20 th entury. Hognestad et al. (1955) developed a test set-up and derived equations whih were milestones in evaluation of the stress-strain relationship of onrete. In this test set-up, the ompression zone of a flexural member with a retangular rosssetion is simulated by varying the axial load and the moment on the setion. By many researhers, this test set-up was referred to as Hognestad Test Set-Up and these speimens were referred to as C-Shaped Speimens or Eentri Braket Speimens. The eentri braket speimen tests by different researhers will be presented in details in the following setions. These speimens are mostly HSC however; NSC speimens are also presented for omparison purposes. 15

36 Hognestad et al. (1955) 2 Bakground Hognestad et al. (1955) onduted an experimental program and developed a test method to investigate the distribution of onrete stresses in flexure. This method formed the basis for the future researh on determination of stress blok parameters of onrete. The test variables inluded were onrete ompressive strength and age of onrete. For this purpose a total of 20 braket speimens with ylinder onrete ompressive strengths ranging from to 7.61 ksi were tested under ombined axial load and bending. The details of the speimens are presented in Figure 2-7. The entral unreinfored test region had a ross-setion of 5 8 in. and was 16 in. long. The brakets were heavily reinfored to obtain a failure in the entral unreinfored test region. The speimens were ast horizontally and tested vertially. Figure 2-7 Test Speimen by Hognestad et al. (1955) The test method onsisted of applying a major load, P 1, using a testing mahine and a minor load, P 2, that ould be varied independently to maintain the neutral axis at one fae of the test speimen throughout the test. This eliminated any ompliations resulting from tensile stresses in the onrete. The major load was applied through a 3/16 in. roller at a onstant rate from zero to failure. The minor load was applied using a hydrauli jak through one or two tie rods and varied throughout the test to obtain zero strain within ±5 16

37 2 Bakground µε at one fae of the speimen. Strains were measured using 6 in. strain gages, two at the neutral surfae, two at the ompression surfae and one at mid-depth on eah of the two side faes. The test duration was 15 minutes whih orresponded to a rate of 3.1 to 4.2 mirostrains per seond on the ompression fae. Three or four 6 12 in. onrete ylinders were tested with eah speimen. The testing ages were 7, 14, 28 and 90 days. The stress-strain relationships and numerial values were obtained whih haraterized the properties of the stress blok. The numerial data is presented in Appendix A. The results onfirmed the researh data on tests of reinfored onrete strutural members Soliman et al. (1967) Soliman et al. (1967) investigated the stress-strain relationship of onfined onrete to understand the plasti deformation apaity of ritial regions reinfored with longitudinal and transverse reinforement. The test variables inluded in the testing program were spaing, size and type of transverse reinforement; the shape of the onrete ross-setion; and the thikness of the over. Sixteen speimens were tested under ombined axial load and bending. A shemati view of the test set-up is shown in Figure 2-8. All of the speimens had a ross-setional dimension of 4 6 in. exept for two speimens thathad ross-setional dimensions of 3 6 and 5 6 in., respetively. The entral test region was 20 in. long. 17

38 2 Bakground Figure 2-8 Test Speimen by Soliman et al. (1967) The speimens were tested under the ation of major load, P 1, applied diretly to the speimen and a minor load, P 2, applied through two steel brakets fixed to the ends of the speimen. The two loads were applied to maintain the neutral axis depth onstant near the tension side of the speimen throughout the entire range of loading. The major load was applied using a 220 kip hollow-ram jak reating against the laboratory floor. The minor load was applied to the brakets by jaking against a 7/8 in. diameter high tensile steel bar. A 66 kip hollow-ram jak was used to apply the load. A 220 kip and an 11 kip load ells were used to measure the major and minor loads, respetively. Eah steel braket was omposed of two 6 in. hannel beams, eah welded to a /4 in. steel plate by means of whih the brakets were fixed to the speimen. Six symmetrially loaded 7/8 in. holes were drilled in eah plate for this purpose. Four 2.36 in. polyester-base eletri strain gages were used to determine the position of the neutral axis. Five mehanial demountable strain gages were used to measure the strains along eah side of the speimen. Two linometers (optial devies for measuring elevation angles) were loated on the top of the brakets to measure the total rotation of the speimen. Three defletion gages 6 in. apart were used to measure the defletion at three points along the test region. 18

39 2 Bakground The test duration was around 120 minutes up to first signs of raking. Afterwards, the applied load was ontrolled by inreasing the strain at ritial setion by about mirostrains. It was onluded that the effet of transverse reinforement ould not be solely expressed as a funtion of the volumetri ratio. The experimental evidene indiated that the expressions proposed an be used to desribe the stress-strain relationship of onfined onrete aurately Sargin et al. (1971) Sargin et al. (1971) performed an experimental investigation on omplete stress-strain relationship of onfined onrete to explain and formulate the behavior of onrete onfined by retilinear lateral reinforement. The test variables inluded were onrete ompressive strength; size, spaing and grade of lateral reinforement; strain gradient; and thikness of over. For this purpose, total of 63 speimens were tested under onentri and eentri loading. For the purpose of this researh, only the eentri braket speimens are presented in this setion. A total of 4 plain and 10 reinfored onrete speimens with ylinder ompressive strengths ranging from 3.0 to 4.7 ksi were tested under ombined axial load and bending. A shemati view of the test set-up is shown in Figure 2-9. The entral test region had 5 5 in. ross-setion and was 10 in. long. Thirteen speimens were ast vertially whereas only one speimen was ast horizontally. 19

40 2 Bakground Figure 2-9 Test Speimen by Sargin et al. (1971) Two independent loads were applied to have zero strain on one fae of the speimen. The primary load, P 1, was applied through ylindrial rollers and grooved plates by a srewtype Riehle mahine of 200 kip apaity. The top roller was also used as a load-ell for measuring the load applied to the speimen. The seondary load, P 2, was applied using a 10 kip hydrauli jak, through two steel brakets onsisting of 4 in. wide flange I beams attahed to two ends of the speimen by means of 7/8 in. diameter high tensile steel bolts. A 20 kip load ell was used to measure this load. Sine the stiffness of the testing mahine was not enough to follow the desending branh of the load deformation urves, a spring system was used to prevent any sudden release of energy from the testing mahine. Displaement transduers with 5 in. length were used to measure the longitudinal strains on opposite two faes of speimen. All the speimens were tested vertially. Test durations varied from 45 to 90 minutes. 20

41 2 Bakground The parameters of an analytial stress-strain relationship for plain and laterally reinfored onrete was determined from a regression analysis of the test results. It was onluded that the amount of onfinement provided by lateral reinforement was not only dependent on the volumetri ratio of the lateral reinforement but also on the type of lateral reinforement (retangular, spiral, et.), spaing and grade of lateral reinforement and the quality of onfined onrete Nedderman (1973) Nedderman (1973) used the same method and speimens similar in dimensions developed by Hognestad et al. (1955) (Figure 2-7) to determine the onrete stress blok oeffiients for normal weight onrete. The only test variable was onrete ompressive strength. 13 braket speimens with ylinder ompressive strengths ranging from ksi to ksi were tested to failure under ombined axial load and bending. Due to the test set-up problems, only 9 ould be tested suessfully. The brakets were not reinfored using steel. Instead, the minor load was lamped to the braket with large lamps made with 1/2 in. round steel bars and 3/4 in. thik plates were used as an auxiliary reinforement in order to have failure in the testing region. The asting positions were not mentioned. The major load, P 1, was applied using a Tinius Olsen 400 kip apaity testing mahine with dereasing load inrements lose to the assumed failure load. The major load was applied through a ombination of 3/8 in. thik masonite pad and 40 in 2 aluminum plate. The minor load, P 2, was applied using a 60 kip apaity hydrauli jak through four round steel rods and measured using pressure dial gage attahed to the jak. The loation of the six strain gages was idential to speimens by Hognestad et al. (1955). The agreement of the two strain gages on the ompression side was within 10 perent over the full range of loading; the agreement between the gages on the sides was 20 to 30 perent. The test duration was ranging from 30 to 45 minutes whih orresponded to a rate of 1.1 to 1.7 mirostrains per seond at the ompression fae. While testing onrete ylinders, the testing equipment ould not break the ylinders beause the strength exeeded the upper load limit. After the maximum load was reahed, the ylinders failed within 12 seonds to 1.5 minutes. Therefore the values are not the true short term ones. The testing ages were 57 and 63 days. 21

42 2 Bakground Overall, it was hard to understand how the k 3 values derived from the f values derived from out-of-standard tests. It was reommended that, 0.7 would be a suitable β 1 value for onrete ompressive strengths higher than 7 ksi. Another reommendation was to further investigate a seond degree parabola with a maximum intensity of 0.88 f at its apex whih oinided with the edge of the speimen. This provided an almost exat orrelation with the atual stress distribution observed in the tests. The numerial data is presented in Appendix A Kaar et al. (1978a) Kaar et al. (1978a) used the same method and speimens similar in dimensions developed by Hognestad et al. (1955) (Figure 2-7) to investigate the flexural behavior of HSC. The test variables were onrete ompressive strength and type of aggregate. For this purpose, 19 braket speimens made from normal weight aggregate with ylinder ompressive strengths ranging from 6.5 to ksi and 15 braket speimens made from light weight aggregate with ylinder ompressive strengths ranging from 3.56 to ksi were tested under ombined axial load and bending. The speimens were ast horizontally and tested vertially. The major load, P 1, was applied using a 1000 kip apaity testing mahine. The fore was applied through a system of bearing plates and rollers that aommodated rotation of the speimen during the test. The minor load, P 2, was applied using a hydrauli ram through a system of rods, rossheads and rollers. During the test, the major load was inreased at a onstant rate. The strain at the neutral fae was kept at zero by ontrolling the value of the minor load manually. The opposite fae of the ross-setion was subjeted to a monotonially inreasing ompressive strain. Strains were measured at mid-height of the setion using two 2.5 in. eletrial resistane strain gages on the neutral surfae, two gages on the ompressive fae and one gage at mid-depth of eah side of the two side faes. A diret urrent differential transformer was used to monitor the defletion of the test setion relative to the ends. Three 6 12 in. onrete ylinders were tested with eah speimen. The stress-strain relationships and numerial values were obtained whih haraterized the properties of the stress blok. The numerial data is presented in Appendix A. The 22

43 2 Bakground results were ompatible with the previous researhes for normal weight onrete. The data for light weight aggregate onrete indiated that β 1 should be redued for onrete ompressive strengths less than 8 ksi Kaar et al. (1978b) Kaar et al. (1978b) performed a testing program to evaluate the effets of the retangular hoops as onfinement reinforement on the behavior of reinfored onrete olumns. The results were used to determine the effetive stress-strain relationship of onfined onrete. The main test variables were onrete ompressive strength, hoop size, hoop spaing, amount of longitudinal reinforement and speimen size. The speimens used in this researh were similar to the ones used by Hognestad et al. (1955). For this purpose, 6 speimens with 5 8 in. ross-setion and 11 speimens with in. ross-setion were tested under ombined axial load and bending. The lengths of the testing regions were 16 and 32 in, respetively. Cylinder ompressive strengths were ranging from 2.78 to 6.47 ksi. The details of the test set-up are presented in Figure Three of these speimens were unreinfored in the test region. All others had longitudinal and transverse reinforement in the test region. The reinforement in the arms of the speimen was design to resist the stresses in the end region during testing. 23

44 2 Bakground Figure 2-10 Test Speimens by Kaar et al. (1978b) The same test method and testing mahine used in Kaar et al. (1978a) was applied on the speimens. The instrumentation on the speimens was also same. Three 6 12 in. onrete ylinders were tested with eah speimen. The stress-strain relationships for onfined and unonfined onrete were obtained. The numerial data is presented in Appendix A. The results showed that the speimens with hoop reinforement had signifiantly greater strains than ould be obtained with plain onrete speimens. It was onluded that the amount of reinforement was the primary variable affeting the stress-strain relationship. For other variables, effets were not distinguishable within the normal satter of experimental results. An analytial stressstrain relationship proposed earlier was updated and suggested Swartz et al. (1985) Swartz et al. (1985) performed an experimental investigation of the flexural properties of higher strength onrete. The test method developed by Hognestad et al. (1955) was used to test speimens with different dimensions. The only test variable was onrete ompressive strength. For this purpose a total of 10 braket speimens with ylinder 24

45 2 Bakground ompressive strengths ranging from 8.4 to ksi were tested under ombined axial load and bending. The details of the speimens are presented in Figure The entral unreinfored test region had a ross-setion of 5 8 in. for one of the speimens and 5 5 in. for all others and was 16 in. long. The brakets were heavily reinfored to obtain a failure in the entral unreinfored test region. The braket speimens were ast horizontally and tested vertially. In addition to these, four reinfored retangular beams with ylinder ompressive strengths ranging from 11.5 ksi to ksi were onstruted and tested under four point bending. These beams were reinfored longitudinally with 0.5ρ b and 1.5ρ b and one had no stirrups, one had 50 perent of the required stirrup area and two had full required stirrup area based on the ACI 318 requirements. The beam speimens were ast horizontally. Only the braket speimens are reported here. Figure 2-11 Test Speimen by Swartz et al. (1985) For the braket speimens, the primary load, P 1, was supplied using a 300 kip, load ontrolled Emery-Tatnall hydrauli testing mahine. The seondary load, P 2, was applied using a hand operated hydrauli jak. The testing proedure was to apply an inremental primary load, maintain this and apply the seondary load while monitoring the two strain gages on the neutral fae. When they read zero, the seondary load was maintained while 25

46 2 Bakground the other strain readings were taken. For the beam speimens, the loads were applied inrementally to failure with rak growth being monitored. Strains of the braket tests were measured using 2.4 in. eletrial resistane wire gages and 0.7 in. eletrial resistane foil gages. Two of these gages were applied at the neutral surfae, two at the ompression surfae and three at eah of the two side faes. The test duration was 15 minutes whih orresponded to a rate from 3.1 to 4.2 mirostrains per seond. Conrete ylinders with 3 6 in. dimensions were tested with eah speimen. It was onluded that: 1. The ompressive stress blok in the beam at failure was urved and may be presented by a parabola with a maximum fiber stress. 2. The strain at ultimate load in the extreme fiber in the beam might be less that 3000 µε. A reommended value for design was 2500 mirostrains. 3. The seant modulus elastiity might be estimated reasonably well by the ACI formula. 4. The uniaxial stress-strain relationship was almost linear up to stress value s about 0.50 of maximum fiber stress. 5. The beam and ylinder ompressive stress-strain relationships were similar. The numerial data is presented in Appendix A Pastor (1986) Pastor (1986) investigated bending properties of onrete by using eentri braket speimens. The only test variable was onrete ompressive strength. For this purpose a total of 10 out of 13 braket speimens with ylinder ompressive strengths ranging from to ksi were tested under ombined axial load and bending. Eentri braket speimens, similar to the ones originally used by Hognestad et al. (1955) (Figure 2-7) were tested. 3 speimens ould not be tested due to handling problems and a severe honeyomb in the lower end of the setion. The braket speimens were ast and tested vertially. 26

47 2 Bakground The major load, P 1, was applied through a system of bearing plates in. and rollers 1 in. diameter. The minor load, P 2, had basially the same bearing plate and roller system only with smaller dimensions. These loading systems aommodated rotation of the speimen during test. Hydrostone was used between the bearing plates and the speimen to avoid bearing problems. The major load was applied in inrements. After eah inrement, the minor load was adjusted with the hand-pump so that strain on the neutral fae would be zero. Strain gages were distributed with three gages on the neutral fae, two gages on the ompression fae and two gages on roughly the 1/3 point and 2/3 point of the sides. The test duration was ranging from 15 to 20 minutes whih orresponded to a rate of 2.5 to 3.33 mirostrains per seond. Conrete ylinders were tested with eah speimen. The stress-strain relationships and numerial values were obtained whih haraterized the properties of the stress blok. Also it was indiated that, the initial modulus of elastiity of the flexural tests were 1.08 times that of ompression tests. The numerial data is presented in Appendix A Shade (1992) Shade onduted an experimental investigation to onfirm the previous findings in terms of similarity of the bending properties and stress-strain distribution of onrete. A new approah for braket speimens was adapted to minimize the experimental ost. Instead of a braket speimen, a retangular olumn was tested under axial load and bending by attahing two steel antilever arms (Hollow Strutural Steel in) at the ends to apply the seondary load, P 2. Two transverse piees of the same steel setions were plaed on the antilevers in the loation of the hydrauli jak of the seondary load. The test variable was strength of onrete. For this purpose, 6 unreinfored and 6 reinfored onrete olumn speimens with ylinder ompressive strengths ksi for unreinfored speimens to 15.9 ksi for reinfored speimens were tested under ombined axial load and bending. The details of the speimens are presented in Figure The olumns had a ross-setion of 6 6 in. and were 24 in. long. The olumn speimens were ast and tested vertially. The testing age was 10 days. 27

48 2 Bakground Figure 2-12 Test Speimen by Shade (1992) The primary load, P 1, was applied using a servo-ontrolled losed-loop MTS hydrauli testing mahine with 450 kip apaity. This load was transferred from the mahine to the olumn through a ball and soket arrangement. The seondary load, P 2, was applied using a hand operated hydrauli jak measured with a load ell. Strains in onrete were measured using 2 in. eletrial strain gages. One gage was loated on the enterline of eah fae of the olumn. Brass target points and a mehanial strain indiator and strain gage based displaement transduers were also used to orrelate gage readings. Strains in longitudinal steel were measured using 0.2 in. eletrial strain gages. Testing was performed using stroke ontrol. The average test duration was 10 minutes whih orresponded to a rate from 5 to 6 mirostrains per seond at the ompression fae. Conrete ylinders with 4 8 in. dimensions were tested with eah speimen. The loading rate for the onrete ylinders was 2.8 mirostrains per seond. The stress-strain relationships and numerial values were obtained whih haraterized the properties of the stress blok. It was onluded that: 1. Plane setions remain plane after deformation. 28

49 2. Maximum failure strains were measured far above 3000 mirostrains. 2 Bakground The numerial data is presented in Appendix A Ibrahim (1994) Ibrahim (1994) performed an experimental program to investigate the use of retangular stress blok for HSC and ultra HSC setions. The main test variables were onrete ompressive strength, shape of the setion and the onfinement steel (diameter, spaing and volumetri ratio). For this purpose, 14 braket speimens with retangular rosssetion in the test region and 6 braket speimens with triangular ross-setion in the test region were tested under ombined axial load and bending. Cylinder ompressive strengths were ranging from 8.6 to ksi for speimens with retangular ross-setion and from to ksi for speimens with triangular ross-setion in the test region. The details of both speimens are presented in Figure 2-13 and Figure The entral test region had 8 12 in. ross-setion and was 47 in. long for the retangular speimens. This region had a triangular setion with 9.5 in. height and 17.7 in. base side length for the triangular speimens. The setion of the test region had a flat edge at the apex of the triangular giving a width of 0.8 in. in order to mount strain gages in the most highly strained fae. Three of the retangular and two of the triangular speimens didn t have any reinforement in the test region; 11 of the retangular and 4 of the triangular had vertial and horizontal reinforement. The brakets were heavily reinfored to obtain a failure in the entral unreinfored test region. The speimens were ast and tested vertially. Testing age was ranging from 42 to 186 days. 29

50 2 Bakground Figure 2-13 Retangular Test Speimen by Ibrahim (1994) Figure 2-14 Triangular Test Speimen by Ibrahim (1994) 30

51 2 Bakground The primary load, P 1, was applied using a 1500 kip MTS mahine. This load was transferred to the speimen through a system of urved plates and rollers that had a well defined enter of rotation. The seondary load, P 2, was applied using a 120 kip hydrauli jak through a system of steel plates, pins anhor rods and bolts attahed at the top and the bottom arms of the speimen. During eah test, as the primary load hanged, the seondary load was adjusted aordingly to obtain zero strain at the neutral fae. The deformations of the speimens were measured using both 1 and 4 in. strain gages and linear variable displaement transduers (LVDT). The total number of strain gages on all the sides of the speimens was varying between 53 and 77. Testing was performed using stroke ontrol. The average test duration was ranging from 180 to 420 minutes whih orresponded to a rate from 0.33 mirostrains per seond at the ompression fae. This slow rate was adapted to redue the flutuations in the primary and seondary loads. Both 4 8 in. and 6 12 in. onrete ylinders were tested with eah speimen. The test program was suessful in providing data relating to the flexural behavior of onfined and unonfined HSC setions. It was onluded that: 1. The failure of plain onrete and lightly reinfored onrete setions is very brittle. 2. Columns with tie spaing equal to the least olumn dimension failed suddenly when the olumn spalled. 3. A well onfined HSC setion an show a dutile behavior, maintaining the applied loads through large deformations. 4. The triangular ompression zones exhibit more dutile behavior than the retangular ompression zones. The numerial data is presented in Appendix A Tan and Nguyen (2005) Tan and Nguyen (2005) onduted an experimental program to investigate the effets of onfinement of lateral reinforement on the flexural apaity of HSC and the appliability of equivalent retangular stress blok of the ACI ode to HSC setions. The main test variables were strength of onrete and the onfinement reinforement. For this purpose, 31

52 2 Bakground 5 speimens with square ross-setion were tested under onentri ompression, 17 speimens under eentri ompression with a fixed neutral axis position and 8 speimens under eentri ompression with a fixed eentriity. Only the speimens under eentri ompression with a fixed neutral axis position are reported here. Cylinder ompressive strengths were ranging from 6.6 to ksi. The details of the test set-up are presented in Figure The speimens had 8 8 in. ross-setion and were 47 in. long. Three of the speimens were unreinfored in the test region. All others had longitudinal and transverse reinforement in the test region. The ends of the speimens were heavily reinfored with longitudinal bars welded to steel plates. Eah steel plate failitated the fixing of the speimen to the loading rig. The speimens were ast horizontally and tested vertially. Figure 2-15 Test Set-Up by Tan and Nguyen (2005) The primary load, P 1, was applied using 1125 kip servo-hydrauli testing mahine. This load was transferred to the loading rig through a system of roller and plate ombination. The seondary load, P 2, was applied using a manually operated hydrauli jak. During eah test, the strain at one fae of the speimen was monitored and maintained at zero by manually adjusting the load from the hydrauli jak. The longitudinal deformations of the 32

53 2 Bakground speimens were measured using two pairs of LVDTs on opposite side of the speimen in the bending plane. Two 0.4 in. stroke LVDTs were used to measure the most ompressive fiber deformation, while for the opposite fae, a pair of 0.2 in. stroke LVDTs were employed. Five 1 in. LVDTs were used to measure the lateral displaements along the height of the speimen. Testing was performed using stroke ontrol. The average test duration was ranging from 24 to 39 minutes whih orresponded to a rate from 2.2 mirostrains per seond at the ompression fae. Three 6 12 in. onrete ylinders were tested with eah speimen. A new one parameter stress blok was proposed and it was onluded that: 1. The onfinement from lateral reinforement improved the flexural strength and dutility of the reinfored onrete olumns. 2. The effet of onfiguration of lateral reinforement was signifiant to the flexural behavior of onfined onrete. 3. Confinement reinforement made of high-yield-strength steel was more effetive that that made of lower-yield strength steel in onfining HSC olumns. 4. The strength of onrete has the most signifiant effet on the flexural stress blok parameters. 5. The allowable ompressive strain of onrete under flexure, as speified in the ACI Code, was a lower-bound value for the measured strains of reinfored onrete speimens. The numerial data is presented in Appendix A Summary of the Eentri Braket Tests to Date This setion provides a omprehensive summary of eentri braket tests onstruted from normal and HSC. The outline of the tests performed by different researhers is presented in Table 2-1. The generalized and retangular stress blok parameters obtained from these tests are shown in graphs from Figure 2-16 to Figure The ultimate ompressive strain of onrete obtained from eentri braket tests are also shown in Figure Sine not all of the parameters of stress bloks were reported in some papers, some of the graphs do not inlude some of the researhers. The presented researh data will be used to ompare the equations for stress blok parameters in the next setions. 33

54 Testing By Hognestad et al. (1955) Soliman et al. (1967) Sargin et al. (1971) Nedderman (1973) Kaar et al. (1978a) Kaar et al. (1978b) Swartz et al. (1985) Pastor (1986) Shade (1992) Ibrahim (1996) Tan and Nguyen (2005) # of Speimens Table 2-1 Summary of the Eentri Braket Tests Cross-Setion of Length of Testing Region Testing (in. in.) Region (in.) Conrete Compressive Strength (ksi) Type of Testing Region Test Duration (min) 2 Bakground Testing Rate (µε µε/se) Retangular 16 Unreinfored , , Retangular Retangular (9 suessful) 20 Reinfored More than 120 Not Speified 4 Unreinfored 10 Reinfored Retangular 16 Unreinfored Retangular 16 Unreinfored Not Speified Not Speified (10 suessful) 6 5 8, Retangular Retangular Retangular 16 and 32 3 Unreinfored 14 Reinfored Not Speified Not Speified 16 Unreinfored Retangular 16 Unreinfored Retangular Retangular h=9.5, a=17.7 Triangular Retangular 24 (Column Length) 47 (Column Length) 47 (Column Length) 6 Unreinfored 6 Reinfored 3 Unreinfored 11 Reinfored 2 Unreinfored 4 Reinfored 3 Unreinfored 14 Reinfored

55 2 Bakground k Kaar et al. (1978a) Kaar et al. (1978b) Swartz et al. (1985) Pastor (1986) Shade (1992) Ibrahim (1994) Conrete Compressive Strength (ksi) Figure 2-16 k 1 Parameter from Eentri Braket Tests Hognestad et al. (1955) Nedderman (1973) Kaar et al. (1978a) Kaar et al. (1978b) Swartz et al. (1985) Pastor (1986) Shade (1992) Ibrahim (1994) Tan and Nguyen (2005) k Conrete Compressive Strength (ksi) Figure 2-17 k 2 Parameter from Eentri Braket Tests 35

56 2 Bakground k Conrete Compressive Strength (ksi) Sargin et al. (1971) Kaar et al. (1978a) Kaar et al. (1978b) Swartz et al. (1985) Pastor (1986) Shade (1992) Ibrahim (1994) Figure 2-18 k 3 Parameter from Eentri Braket Tests k 1 k Hognestad et al. (1955) Nedderman (1973) Kaar et al. (1978a) Kaar et al. (1978b) Swartz et al. (1985) Pastor (1986) Shade (1992) Ibrahim (1994) Tan and Nguyen (2005) Conrete Compressive Strength (ksi) Figure 2-19 Produt of k 1 and k 3 Parameters from Eentri Braket Tests 36

57 2 Bakground α Hognestad et al. (1955) Nedderman (1973) Kaar et al. (1978a) Kaar et al. (1978b) Swartz et al. (1985) Pastor (1986) Shade (1992) Ibrahim (1994) Tan and Nguyen (2005) Conrete Compressive Strength (ksi) Figure 2-20 α 1 Parameter from Eentri Braket Tests β Hognestad et al. (1955) Nedderman (1973) Kaar et al. (1978a) Kaar et al. (1978b) Swartz et al. (1985) Pastor (1986) Shade (1992) Ibrahim (1994) Tan and Nguyen (2005) Conrete Compressive Strength (ksi) Figure 2-21 β 1 Parameter from Eentri Braket Tests 37

58 2 Bakground α1β Hognestad et al. (1955) Nedderman (1973) Kaar et al. (1978a) Kaar et al. (1978b) Swartz et al. (1985) Pastor (1986) Shade (1992) Ibrahim (1994) Tan and Nguyen (2005) Conrete Compressive Strength (ksi) Figure 2-22 Produt of α 1 and β 1 Parameters from Eentri Braket Tests Ultimate Conrete Strain (εu) Conrete Compressive Strength (ksi) Hognestad (1951) Sargin et al. (1971) Nedderman (1973) Kaar et al. (1978a) Kaar et al. (1978b) Swartz et al. (1985) Pastor (1986) Shade (1992) Ibrahim (1994) Tan and Nguyen (2005) Figure 2-23 Ultimate ompressive strain of onrete from Eentri Braket Tests 38

59 2 Bakground Proposed Stress-Strain Models for Compression Zone of Flexural Members The stress-strain relationships presented in this setion are mainly developed using onrete ylinders. To use these relationships in either analysis or design, the fator that onverts stress-strain relationship of ylinder to the ompressive stress distribution in the ompression zone of flexural members must be applied. This fator, known as k 3, should be applied to the stress-strain relationships explained in this setion unless it is present in the equation Jensen (1943) Jensen (1943) performed flexural tests to evaluate the ultimate strength of beams. He proposed a trapezoidal stress-strain relationship whih onsists of two linear parts, one presenting elasti behavior and the other representing the plasti behavior. This relationship was also justified by other beam tests in the literature. The following equations were proposed for the stress-strain relationship: f f f ' ε = for o ε o f = ' for o u ε < ε Equation 2-8 ε < ε < ε Equation 2-9 where f is the stress in general, ε is the strain in general, f ' is the ylinder ompressive strength of onrete. The strain orresponding to the peak stress, ε o, and the ultimate strain ε u was expressed as: ' f ε o = Equation 2-10 E f ' εu = + εo E ( 1 β ) Equation 2-11 where β is the plastiity ratio and be alulated as: E is the modulus of elastiity of onrete. These an 39

60 2 Bakground 1 β = Equation 2-12 f ' ( ksi) 1+ 4 Es 10 n = = 5 + Equation 2-13 E f ' ( ksi) where n is the modular ratio and to use the modulus of elastiity as: E s is the modulus of elastiity of steel. It was suggested Es = ksi Hognestad (1951) The stress-strain relationship proposed by Hognestad (1951) had a rising parabola and a desending linear branh after the peak stress. It was indiated that the initial urved part of the stress-strain relationship was fairly similar to the relation in diret ompression. The slope of the desending branh was hosen in order to give the best statistial agreement between alulated and observed strengths in 120 tests. The relationship was presented as follows: 2 2 ε ε f = k3 f ' - ε o ε o for ε < ε Equation 2-14 o where ε ε o f = k3 f ' ( f ' ) εu εo for εo < ε < εu Equation 2-15 where f is the stress in general, k 3 is the ratio of the maximum stress to the ylinder strength whih is suggested to be taken as 0.85, f ' is the ylinder ompressive strength of onrete and ε is the strain in general. The strain orresponding to the peak stress ( ε o ) and the ultimate strain ( ε u ) is defined by: 40

61 2 k f ' ( psi) 2 Bakground ε = 3 o E ( psi) Equation 2-16 ε = Equation 2-17 u where the modulus of elastiity an be alulated as follows: E ( psi) = f ' ( psi). Equation Sargin and Handa (1969) Sargin and Handa (1969) suggested a seond degree rational equation for stress-strain urve of onrete as follows: f 2 + ( D 1) x 2 ( A 2) x + Dx Ax = k3 f ' Equation where f is the stress in general, k 3 is the maximum stress ratio, f ' is the ylinder ompressive strength of onrete and D is a parameter whih effets mainly the slope of the desending branh. The non-dimensionless strain ( x ) and the non-dimensional form of initial modulus ( A ) was defined by: A = E ε k f ' Equation 2-20 o 3 x = ε ε o Equation 2-21 where E is the modulus of elastiity of onrete, ε o is the strain at maximum stress and ε is the stain in general. Influene of important fators suh as onrete ompressive strength, lateral reinforement, ore-gross area ratio, reep and strain gradient on onrete behavior was onsidered in the evaluation of these parameters as follows: ( ) E = f ' psi Equation 2-22 ε = Equation 2-23 o ' ( ) D = f psi Equation

62 2 Bakground The proposed stress-strain relationship was verified with the tests results performed by the authors and the available researh data in the literature Popovis (1973) Popovis (1973) proposed an expression that presented the shape of the rising branh of stress-strain relationship of a onrete ylinder. It was indiated that this formula was valid only for standard onrete speimens with a height-width ratio not less than two and when uniaxial ompressive load is a short term load whih was applied at a rate that produes onstant rate strain in the speimen. The equation is presented as follows: f = f ' ε n ε n 1+ ε ε ( ) n o o Equation 2-25 where f is the stress in general, f ' is the ylinder ompressive strength of onrete, ε is the strain in general, ε o is the strain at maximum stress. The oeffiient n was expressed as follows: onrete ( ) ' 1.0 n = f psi + Equation Wang et al. (1978a, b) Wang et al. (1978a, b) used the same form of equations proposed by Sargin and Handa (1969). However, instead of using one set of oeffiients to generate the omplete urve, two sets of oeffiients were used, one for the asending branh and other one for the desending branh. These oeffiients were obtained from the relevant boundary onditions assigned to eah part of the urve. The stress-strain relationship used was: f 2 ε ε A + B ε o ε o ε ε 1+ C + D ε o ε o = f ' 2 Equation

63 2 Bakground where A, B, C and D are the onstants to be determined, f is the stress in general, f ' is the ylinder strength of onrete, ε is the strain in general and ε o is the strain at maximum stress. For different onrete ompressive strengths, these onstants shown in Table 2-2 are derived by using the experimental stress-strain relationship. Table 2-2 Stress-Strain Relationship Constants by Wang et al. (1978a,b) f Asending Desending ε o (ksi) A B C D A B C D Carreira and Chu (1985) The model proposed by Carreira and Chu (1985) was a general form of serpentine urve as presented by the following: ε β ε o f = f ' Equation 2-28 β ε β 1 + ε o in whih f is the stress in general, f ' is the ylinder ompressive strength of onrete, ε is the strain in general, ε o is the strain at maximum stress, β is a material parameter that depended on the shape of the stress-strain diagram. ε o and β were given by: o 5 ( 4.88 f ' ( ksi) 168) 10 ε = + Equation

64 2 Bakground 1 β = Equation ( f ' ε o E ) where modulus of elastiity of onrete ( E ) an be alulated by using the following equation: ' ( ) E = w f psi Equation 2-31 where w is the unit weight of onrete in 3 lb ft Thorenfeldt et al. (1987) Thorenfeldt et al. (1987) reported that while expression by Popovis (1973) desribes well the rising branh of the stress-strain urve, it did not drop fast enough after the peak for HSC. To inrease the post-peak deay, they suggested the addition of the fator, k. The proposed equation was as follows: f = f ' ε n ε n 1+ ε ε ( ) nk o o Equation 2-32 where f is the stress in general, f ' is the ylinder ompressive strength of onrete, ε is the strain in general, ε o is the strain at maximum stress and n is the oeffiient for onrete behavior. The fator k was defined by: k = 1 k > 1 when when ε ε ε ε o o 1. Equation 2-33 > 1 Best orrelation with the test results was observed when 1 < k < f 20. Other parameters an be alulated as follows: E n 0.3 f ' = Equation

65 2 Bakground o m = ε Equation 2-35 ε n ' f ε n = Equation 2-36 E n ( f ) ( f ) ε = ' ' Equation 2-37 ε 3 3 o u ( 2.5m 1.5) = ε Equation 2-38 n CEB-FIB Model Code (1990) The stress-strain relationship of onrete in ompression for short-term loading was approximated as follows: f = 2 Eit ε ε Eo f ' Eit ε 1+ 2 Eo Equation 2-39 where f is the onrete stress, f is the ylinder ompressive strength of onrete, ε is the onrete strain, E it is the initial tangent elasti modulus, E o is the seant elasti modulus from the origin to the peak ompressive stress. This approximation is valid for onrete strain ranges between 0 and ε max where ε max is the onrete strain when onrete stress is equal to 0.5 f ' on the desending part of the stress-strain urve. The elasti modulus and ε max an be alulated from: ( f ' ( )) 0. 3 Eit = psi Equation 2-40 f ' E o = Equation and E it 1 1 Eit 1 ε = max ε o 1 Equation E o 4 2 Eo 2 45

66 2 Bakground Note that E it defined by Dahl (1992) was used in the equations whih enabled the stressstrain model to be used for onrete ompressive strengths up to 16.8 ksi. For strains ε > ε max desribed as:, the desending branh of the stress-strain relationship an be f = ( ε ε ) ( ε ε ) max 1 o ξ max 2 o f ' ε ε ( o ) + 2 ε ξ ε ε ( ε o ) o max 4 Equation 2-43 where 2 ε max E it max ε Eit ε o Eo ε o Eo ξ =. Equation ε max Eit ε o Eo Muguruma et al. (1991) Based on their experimental work, Muguruma et al. (1991) proposed a two part stressstrain urve for unonfined onrete whih ould be applied to onrete with a wide range of onrete ompressive strengths. The first part of the urve onsisted of the ommonly used seond degree parabola that had a zero slope at the point ( f, ε ) ' o where f ' was the ultimate onrete ompressive strength and ε o was the onrete ompressive strain at f '. The seond part of the urve was linear till the maximum ompressive strain whih was ( f ' Eiε m ) 2 f = E ε + ε when 0 < ε < ε Equation 2-45 i 2 m ε m f f ' = ε when ε < ε < ( ) ( ) ε m m Equation

67 2 Bakground where f is the stress in general, ε is the strain in general, ε m is the strain at maximum stress and E i is the initial elasti modulus. equations based on empirial testing results. E i and ε m are given by the following εm = f ' ( MPa) 98.6 Equation 2-47 f ' ( ) ( ) MPa Ei MPa = Equation Collins and Porasz (1989) Collins and Porasz (1989) proposed new k and n fators for the equation proposed by Thorenfeldt et al. (1987) as follows: f ' ( psi) k = Equation f ' ( psi) n = Equation Hsu and Hsu (1994) Hsu and Hsu (1994) proposed a modified form of the stress-strain relationship proposed by Carreira and Chu (1985): n was added to the original equation. Also the parameters were modified and orreted for the presented unonfined onrete. The omplete stressstrain urve was presented by: f f ' ε nβ ε o = ε nβ 1+ ε o nβ for 0 ε < ε Equation 2-51 max and f f ' = η d exp kd ε ε o ε ε max o a for ε max ε Equation

68 [ f ' ( ε E )] o it 2 Bakground 1 β = for β 1. 0 Equation where n is the parameter depended on the material strength, β is the parameter depended on the shape of the stress-strain diagram, f is the stress in general, ε is the strain in general, f ' is the peak stress of onrete, ε o is the strain orresponding to the peak stress, ε max is the strain at 0.3 f ' on the desending portion of the stress-strain diagram, η d is equal to 0. 3, orresponding to 0.3 f ' on the desending portion of the stress-strain urve, k d = 0. 8, a = 0. 5 and E it is the initial tangential modulus. The parameters f ', ε o, n, β and E it an be diretly obtained from the uniaxial ompression tests under onstant strain. The slope of the desending branh is affeted by the β value, a flatter urve would yield a redued β. A best fitting statistial analysis was performed using the experimental data to obtain the following equation for β. 3 f ' ( psi) β = Equation The following equation for n values was proposed as a funtion of the ompressive strength. 1 for 0 ε < ε o 1 for ε o ε < ε max if 0 f ' < 9 ksi n = 2 for ε o ε < ε max if 9 ksi f ' < 11 ksi 3 for ε < < o ε ε max if 11 ksi f ' 13 ksi 5 for ε o ε < ε max if 13 ksi f ' Equation 2-55 A regression analysis was performed to obtain the equations for ε o and E it. 8 3 ε o = f ' ( psi) Equation 2-56 E 1 3 it = f ' ( psi) Equation

69 Wee et al. (1996) 2 Bakground A researh was onduted by Wee et al. (1996) to find a simple, more aurate model to represent the omplete stress-strain urve, partiularly for HSC. The equation proposed by Carreira and Chu (1985) was hosen beause of its simpliity. For the asending branh of the stress-strain urve: ε β ε o f = f ' β ε β 1+ ε o Equation 2-58 and 1 β = Equation ( f ' ε o E it ) were used. But for modeling the desending branh of the stress-strain urve, same equations were used with two orretion fators, k 1 and k 2. The fator k 1 was applied to the β values in the numerator and in the first term of the demoninator, while k 2 was applied to β in the exponent of the last term of the denominator. The resulting expression for the desending portion of the stress-strain urve beomes: f ε k β ε ε k1β 1+ ε o 1 o = f ' k2 β Equation 2-60 An analysis arried out using the set of data that gathered for onrete ompressive strengths ranging from 7.25 ksi to 17.4 yielded: k 1 = 7252 ' ( ) f psi 3.0 Equation

70 and 2 Bakground k 2 = 7252 ' ( ) f psi 1.3. Equation 2-62 For onrete ompressive strengths below 7.25 ksi., k 1 and k 2 should be taken as unity. The equation for data and were presented as follows: E it and ε o were obtained by regression analysis of the experimental ( f ' ( ) ) ( 1 3 ) E it = psi Equation 2-63 ( ' ( )) ( 1 4) ε psi. Equation 2-64 o = f Van Gysel and Taerwe (1996) Van Gysel and Taerwe (1996) proposed a relationship that simulates the behavior of HSC. The inrease in the peak strain and the steepness of the softening branh at higher strength levels were also inluded in the formulation. Although the proposed relationship was largely based on the CEB Model (1990), the desending branh of the stress-strain relationship of HSC was predited better. For the asending branh, the same stress-strain relationship speified by CEB Model (1990) was used by hanging the strain at peak stress with the following equation: f f ' Eo ε ε E 1 ε 1 ε 1 = E ε 1+ 2 E ε o for ε < ε 1 with f ' ( psi) ε = for f > 5831 psi ε 1 = for f 5831 psi 50

71 2 Bakground where f is the onrete stress, ε is the onrete strain, f is the ylinder ompressive strength of onrete, E o is the initial tangent modulus of elastiity, E 1 is the seant elasti modulus from the origin to the peak ompressive stress f and ε 1 is the onrete strain at peak stress. For the desending branh, the following relationship was proposed whih is based on the formulation originally proposed by Sargin and Handa (1969) f f ' = 1 ε 1 ε t ε 1 + ε with orresponding t values are presented in Table 2-3. Table 2-3 Values of the Parameter t for Different Conrete Compressive Strengths f (ksi) t ( ) Attard and Setunge (1996) Attard and Setunge (1996) used the non-dimensional formulation suggested by Sargin and Handa (1969) to define the stress-strain urve of onrete for the unonfined uniaxial ase for onrete ompressive strengths between 2.9 to ksi. It was indiated that in uniaxial ompression, the failure load was a ombination of shear failure and tensile splitting. To define the desending urve in uniaxial ompression, one point was needed on the desending urve. The point of infletion suggested by Wang et al. was used. On this basis, the full uniaxial stress-strain relationship was established and the following equation was derived: f f ' ( ) 2 f εi ε o i ε εoεi f ' f i εo = 2 fi ( εi ε o ) ε ε εoεi f ' f i εo ε o 2 Equation

72 2 Bakground where f is the stress at strain ε, f is the ylinder ompressive strength of onrete, f i is the stress at point of infletion, ε i is the strain at point of infletion and ε o is the strain at peak. To define the modulus of elastiity, E, the formula used in ACI 318 was used for NSC and the formula used in ACI 363 was used for HSC whih is valid up to 12 ksi. E 1.5 = w 33 f ' ( psi) for NSC Equation ( f ' ( psi) ) w E = for HSC Equation where w is the unit weight of onrete in lbs/ft 3. The equation proposed by Setunge was used to define the strain at peak stress. f ' ε o = for rushed aggregates Equation 2-68 ' ( ) E 4 f psi f ' ε o = for gravel aggregates Equation 2-69 ' ( ) E 4 f psi Based on the analytial expressions in Mander et al. (1988) and Collins (1992) and the experimental results of Dahl (1992), the following approximate expressions for the uniaxial infletion point were proposed: εi ε o f f ' i ( f psi ) = 4 0.3ln ' ( ) Equation 2-70 = ln( f ' ( psi)). Equation Oztekin et al. (2003) Oztekin et al. (2003) used the stress-strain relationship by Hognestad et al (1951) to obtain a modified model whih was appliable to HSC. It was indiated that, it was very diffiult to simulate the falling branh of HSC due to its sudden failure. Ultimate strain, 52

73 ε u 2 Bakground, was assumed to be equal to the strain in the maximum stress, ε o. On this basis, they proposed the following equation: f = ε f ' k ε u ( k 1) ε ε u 2 Equation 2-72 where k was a modifiation parameter desribed as follows: k = 2 f ' ( psi) for 8700 psi f ' psi Equation 2-73 ε u, proposed in CEB Model (1990), was modified aording to experimental results as follows: u 4 3 [ ( f ' 5800) ] 10 ε for 8700 psi f ' psi Equation 2-74 = 53

74 2 Bakground Proposed Retangular Stress Blok Parameters The definitions for retangular stress blok parameters for onrete is presented in Setion In this setion, the proposed relationships and equations by many researhers are illustrated, starting from the best known one, Charles Whitney Whitney (1937) Whitney (1937) proposed a retangular stress blok to replae the existing allowable stress design theory in design odes. This stress blok was verified by using the experimental data on beams tested by other researhers at that time. The width of the proposed retangular stress blok was 0.85f. This assumption was based on the tests on atual strength of olumns performed by Rihart et al. (1931a, 1931b, 1931 and 1932) and permitted a onsistent transition in the moment-axial load diagram from pure axial to pure moment resistane. The height of the retangular stress blok (a) was hanging aording to the reinforement ratio of the beam. For over-reinfored setions, a d was and for under-reinfored setions a d was hanging from 0 to as a quadrati urve for no reinforement and balaned ratio, respetively Mattok et al. (1961) The proposed parameters by Mattok et al. (1961) for retangular stress blok are urrently being used in ACI 318 and AASHTO LRFD Bridge Design Speifiations (2004) for onrete ompressive strengths less than 10 ksi. The depth of the stress blok was 0.85 for all the onrete ompressive strengths and the height was equal to 0.85 for onrete ompressive strengths up to 4 ksi, and thereafter was redued by 0.05 for eah 1 ksi of strength in exess of 4 ksi but not less than The ultimate strain of onrete was assumed to be for all target strengths. No upper onrete ompressive strength limit was speified whih later aused some inonsistenies between the predited and experimental values. α 1 = 0.85 Equation for f ' 4 β1 = ( f ' 4 ) for f ' > 4 Equation

75 2 Bakground ε = Equation 2-77 u where f ' is in ksi Zia (1983) Zia (1983) used the idealized trapezoidal stress-strain relationship involving the onept of plastiity proposed by Jensen (1943) to provide the retangular stress blok parameters for HSC. 3 1 α = 4 1 ( + β ) 2 ( + β + β ) β1 = ( + β + β ) ( + β ) Equation 2-78 Equation 2-79 where f ' β = 1 Equation 2-80 E ε u It was suggested to use the urrent ACI Building Code expressions at that time for modulus of elastiity of onrete and the ultimate strain expressed as; E = f ' Equation 2-81 ε = Equation 2-82 u The retangular stress blok parameters shown in Table 2-4 were derived based on the proposed equations. Table 2-4 Retangular Stress Blok Parameters Proposed by Zia (1983) f (ksi) α 1 β 1 ε u

76 Li (1993) 2 Bakground For HSC, Li (1993) stated that the atual shape of the ompressive stress distribution for unonfined onrete was similar to the shape of a triangle with peak stress ourring at a strain of about Li (1993) assumed onservatively that the maximum stress in the atual triangular stress blok of HSC is f (that is, k 3 = 1.0), for the triangular stress blok and the equivalent retangular stress blok to have the same magnitude and position of resultant onrete ompressive fore requires α f ' a f ' 2 and a 2 = 3, from 1 = whih α 1 = Hene for HSC the equivalent retangular stress blok had a mean stress about 0.75 f ' and β 1 = a = On this basis, the following equivalent retangular ompressive stress blok for unonfined onrete was suggested for f ' 8 α1 = ( f ' 8) 0.75 for f ' > 8 Equation for f ' 4.35 β1 = ( f ' 4.35) 0.65 for f ' > 4.35 Equation 2-84 ε = Equation 2-85 u where f ' is in ksi Azizinamini et al. (1994) Azizimanini et al. (1994) stated that the typial stress-strain relationships in ompression for HSC ould be haraterized by an asending portion that is primarily linear with a maximum strength ahieved at an axial strain between approximately and Considering this, the researhers onluded that using a triangular ompressive stress blok was more appropriate in alulating the flexural apaity of the olumns with onrete ompressive strength exeeding 10 ksi. The maximum ompressive stress was assumed to be 0.85 f ' at axial ompressive strain of Considering the equilibrium of horizontal fores and moment equilibrium, it was shown that the equivalent retangular ompressive blok would have the following properties: intensity of the ompressive stress would be 0.63 f ' rather than 0.85 f ' ; and the depth of the retangular 56

77 2 Bakground ompression blok would be 0.67 times the depth of the neutral axis. Considering these, the following retangular stress blok parameters were reommended for f ' 10 α1 = ( f ' 10) 0.60 for f ' > 10 Equation for f ' 4.35KSI β 1 = ( f ) for f > KSI Equation ' ' 4.35 ε = Equation 2-88 u where f ' is in ksi Ibrahim (1994) Ibrahim (1994) proposed new retangular stress blok parameters for both NSC and HSC. He ompared the experimental data to date with the ACI ode. It was found that the ACI value for β 1 fell below the experimental showing that it was too small. This indiated that the internal lever arm is too big and the moment apaity would be overestimated. A new equation was proposed for β 1 whih was passing through the enter of the experimental data. On the other hand, α 1 parameter was derived to provide a onservative lower bound for the experimental data of k 3 obtained from onentrially loaded olumns. It was also indiated that the proposed equation should provide onservative design for eentri setions when ombined with the parameter β 1. Based on these, the following retangular stress blok parameters were proposed. For onrete ompressive strength greater than 14.5 ksi, α 1 and β 1 were both taken onstant and equal to and 0.7 respetively whih represent a stress distribution very lose to triangular. f ' α 1 = Equation 2-89 f ' β 1 = Equation 2-90 ε = Equation 2-91 u where f ' is in ksi. 57

78 Pendyala and Mendis (1998) 2 Bakground Pendyala and Mendis (1998) stated that at 11.6 ksi the stress-strain relationship for HSC was still urvilinear and tending to be linear at 14.5 ksi. Hene the assumption of linearity at 11.6 ksi was found to be unduly onservative. Pendyala and Mendis (1998) onluded that none of the retangular stress bloks developed to date was appliable to extend the validity of design ode to 14.5 ksi and did not provide ontinuity of values for NSC and HSC. On this basis, new stress blok parameters were proposed below for onretes with ksi < f ' < ksi. ( ) α 1 = f ' for f ' Equation 2-92 ( ) β 1 = f ' for f ' Equation 2-93 ε = Equation 2-94 u where f ' is in ksi Attard and Stewart (1998) Attard and Stewart (1998) proposed new retangular stress blok parameters based on mean results of probabilisti analysis of the tests available in the literature using a stressstrain relationship for HSC. The proposed parameters inluded estimates of variability and distribution of the input properties. A sensitivity analysis was also arried out to asertain the effet of parameter unertainty. It was indiated that for a dutile singly reinfored retangular setion, the ultimate moment apaity was relatively insensitive to the stress blok model. However, estimates of the dutility level at both ultimate and olumn apaity in primary ompression failure was signifiantly affeted by the hoie of the stress blok parameters. Based on these, the following parameters were proposed for onrete with 2.9 ksi < f ' < 17.4 ksi f ' for Dogbone Tests α1 = f ' for Sustained Load Tests Equation

79 Bakground f ' β 1 = Equation ε = Equation 2-97 u where f ' is in ksi Rangan (1999) Rangan (1999) proposed to use the following equivalent retangular stress blok parameters for grades of onrete with ompressive strength in the range of 2.9 to 14.5 ksi for f ' 8 α1 = ( f ' 8) 0.75 for f ' > 8 Equation for f ' 4.35 β1 = ( f ' 4.35) 0.65 for f ' > 4.35 Equation 2-99 ε = Equation u where f ' is in ksi. The author speified that equivalent stress blok parameters were valid up to the point when the depth of neutral axis was equal to the depth of extreme layer of tensile steel measured from the ompression fae Bae and Bayrak (2003) Bae and Bayrak (2003) modeled the stress-strain response of unonfined HSC using the suggestion of Popovis (1973) whih was then modified by Thornfeldt et al. (1987) and then by Collins and Porasz (1989). Bae and Bayrak (2003) stated that the model proposed was appliable to a wide range of onrete ompressive strengths. For onrete ompressive strengths up to 16.3 ksi, the proposed model offered a very good approximation of the experimentally measured behavior of HSC ylinders tested by the author. In deriving the stress blok parameters, the maximum reliable strain was assumed as the assumed over spalling strain of Based on these, the following stress blok parameters were proposed. 59

80 2 Bakground 0.85 for f ' 10.2 α1 = ( f ' 10.2) 0.67 for f ' > for f ' 4.35 β1 = ( f ' 4.35) 0.67 for f ' > for f ' 8 εu = for f ' > 8 Equation Equation Equation where f ' is in ksi Sun et al. (2003) Sun et al. (2003) proposed a retangular stress blok whose results were signifiantly loser to that of Popovis (1973) equation on stress-strain urve for onrete. When maximum steel reinforement was alulated with a strain of for the proposed model, it was seen that the proposed model was more onservative than the design odes. On this basis, the proposed model is desribed as follows: α 1 = 0.85 Equation for f ' 2.94 β1 = for f ' 2.94 > 30 f ' for f ' 4 εu = for f ' 4 > 7 f ' + Equation Equation where f ' is in ksi Oztekin et al. (2003) Oztekin et al. (2003) proposed stress blok parameters obtained from the ompression test results of 6 12 in. ylinders omposed of eight series of high-performane onretes (HPC). Regression analysis was performed between the stress blok parameters and the 60

81 onrete ompressive strength. 2 Bakground ε u proposed by CEB Model (1990) was modified aording to the experimental tests results. The following parameters were derived: α 1 = f ' Equation β 1 = f ' Equation ( ) ε u = f ' for 8.7 f ' 13.6 Equation where f ' is in ksi Ozbakkaloglu and Saatioglu (2003) Ozbakkaloglu and Saatioglu (2003) developed a retangular stress blok for a wide range of onrete ompressive strengths up to 18.9 ksi. The stress-strain relationship proposed by Popovis (1973) was seleted to derive the generalized stress-strain parameters. This relationship was appliable to eentrially loaded members for HSC, as well as NSC. The desending portion of the urve was simplified to be linear. The urve was integrated numerially up to the ultimate ompressive strain to find the area and the entroid of area for different onrete ompressive strengths. This analytial model was verified by a large volume of olumn tests. The proposed retangular stress blok parameters were as follows: 0.85 for f ' 4 α1 = ( f ' 4) 0.72 for f ' > 4 Equation for f ' 4 β1 = ( f ' 4) 0.67 for f ' > 4 Equation ε = Equation u where f ' is in ksi Tan and Nguyen (2005) Tan and Nguyen (2005) proposed a new equivalent retangular stress blok for onrete in flexure alibrated with the published test data on stress blok parameters. It was stated 61

82 2 Bakground that β 1 values of the ACI ode were lower than the experimental data, whih overestimated the distane from the resultant fore to the neutral axis position. The parameter β 1 was kept lose to experimental values, while the produt of α1 β1 was hosen smaller than the test values. For simpliity, linear expressions for β 1 and α1 β1 were hosen for regression analysis of the test data in the range of onrete ompressive strengths up to 14.8 ksi beause data beyond this range showed a different trend. On this basis, one linear equation was found to be enough for both parameters as follows: f ' for f ' 14.5 α1 = β1 = Equation for f ' > 14.5 ε = Equation u where f ' is in ksi Summary of the Proposed Retangular Stress Blok The equations proposed for retangular stress blok parameters by different researhers are presented in Table 2-5. The omparisons of these equations are shown in Figure 2-24 and Figure These equations are used to ompare the test data obtained from this researh and other researhes in literature in Chapter 5. 62

83 Table 2-5 Summary of the Proposed Retangular Stress Blok Parameters 2 Bakground Referene α 1 β 1 ε u Mattok et al for f ' (1961) f ' 4 for f ' > 4 Li (1993) Azizinamini et al for f ' 8 ( ) ( f ) for f > ( f ) ' ' for f ' for f ' ' for f ' > 4.35 (1994) ( f ' 10) 0.60 for f ' > 10 ( f ) f ' Ibrahim (1994) Pendyala and ( f ' 8.3) for 8.3 f ' 14.5 Mendis (1998) Attard and Stewart (1998) Rangan (1999) Bae and Bayrak 0.85 for f ' ' for f ' > 4.35 ( ) f ' for Dogbone Tests f ' for Sustained Load Tests for f ' 8 ( f ) for f > ( f ) ' ' for f ' ' 0.95 f f ' 8.3 for 8.3 f ' ' f for f ' ' for f ' > 4.35 (2003) ( f ' 10.2) 0.67 for f ' > 10.2 ( f ) Sun et al. (2003) Oztekin et al. (2003) Ozbakkaloglu and 0.85 for f ' for f ' ' for f ' > f ' 0.85 for f ' for f ' > f ' f ' Saatioglu (2003) ( f ' 4) 0.72 for f ' > 4 ( f ) Tan and Nguyen (2005) where f ' is in ksi f ' for f ' for f ' > for f ' ' for f ' > f ' for f ' for f ' > f ' for f ' for f ' for f ' for f ' > 4 3 ( f ) ' for 8.7 f '

84 2 Bakground α Mattok et al. (1961) Zia (1983) Li (1993) Azizinamini (1994) Ibrahim (1994) Pendyala and Mendis (1998) Attard and Stewart (1998) Rangan (1999) Bae and Bayrak (2003) Sun et al. (2003) Oztekin et al. (2003) Ozbakkaloglu and Saatioglu (2003) Tan and Nguyen (2005) Conrete Compressive Strength (ksi) Figure 2-24 Proposed Equations for α 1 by Researhers β Mattok et al. (1961) Zia (1983) Li (1993) Azizinamini (1994) Ibrahim (1994) Pendyala and Mendis (1998) Attard and Stewart (1998) Rangan (1999) Bae and Bayrak (2003) Sun et al. (2003) Oztekin et al. (2003) Ozbakkaloglu and Saatioglu (2003) Tan and Nguyen (2005) Conrete Compressive Strength (ksi) Figure 2-25 Proposed Equations for β 1 by Researhers 64

85 2 Bakground Retangular Stress Blok Parameters in Design Codes ACI 318 (2005) and AASHTO LRFD Bridge Design Speifiations (2004) Amerian Conrete Institute 318 (2005), Building Code Requirements for Strutural Conrete and Amerian Assoiation of State Highway and Transportation Offiials Load and Resistane Fator Design Bridge Design Speifiations (2004) provide same retangular stress blok parameters for flexural design whih were originally proposed by Mattok et al. (1961). Although no upper limit on onrete ompressive strength is speified by ACI 318 (2005), the upper limit for AASHTO LRFD Bridge Design Speifiations (2004) is 10 ksi. The maximum usable strain at the extreme onrete ompression fiber is assumed to be The equivalent stress blok parameters are speified as follows: α 1 = 0.85 Equation for f ' 4 β1 = ( f ' 4) 0.65 for f ' > 4 Equation ε = Equation u where f ' is in ksi CSA A23.3 (1994) and CSA S6 (2001) Similar retangular stress blok parameters are introdued by Canadian Standards Assoiation, Standard A23.3 (1994), Design of Conrete Strutures and Canadian Standards Assoiation, Standard S6 (2001), Canadian Highway Bridge Design Code. This model was mainly the modified version of the equations proposed by Ibrahim and MaGregor (1997). These equations onsider the more nearly triangular distribution of the higher strengths of onrete. The provisions speified by CSA A23.3 (1994) are appliable to onrete with a ompressive ylinder strength ranging from 2.9 ksi to 11.6 ksi whereas the provisions speified by CSA S6 (2001) are appliable to onrete with a ompressive strength ranging from 4.4 ksi for non-prestressed and 5.1 ksi for prestressed onrete to 12.3 ksi. The upper limits in both odes are established due to the lak of knowledge in behavior of strutural elements with HSC. In the alulation of the 65

86 2 Bakground retangular stress blok, the maximum usable strain at the extreme onrete ompression fiber is assumed to be The retangular stress blok parameters used in these odes are as follows: α 1 = f ' 0.67 Equation β 1 = f ' 0.67 Equation ε = Equation u where f ' is in ksi NZS 3101 (1995) The stress blok parameters speified by New Zealand Conrete Strutures Code 3101 (1995) were based on the work performed by Li (1993). The model has a tri-linear shape for both α 1 and β 1 as follows: 0.85 for f ' 8 α1 = ( f ' 8) 0.75 for f ' > 8 Equation for f ' 4.35 β1 = Equation ( f ' 4.35) 0.65 for f ' > 4.35 ε = Equation u where f ' is in ksi EC2 (2004) The retangular stress blok speified in Euroode 2 (2004) is appliable for onrete ompressive strengths up to 13 ksi. Constant stress blok parameters and ultimate ompressive strain of onrete up to 7.25 ksi are modified to be used by higher onrete ompressive strengths. The onrete ompressive strength in EC 2 (2004) is based on harateristi ylinder strength. The following stress blok parameters and ultimate ompressive strain of onrete are proposed: 66

87 2 Bakground α for f ' k 7.25 α1 = f ' k 7.25 α 1 for 7.25 f ' k for f ' k 7.25 β1 = f ' k for 7.25 f ' k Equation Equation ε for f ' u = f ' k for 7.25 f ' k k Equation where f ' is in ksi. The α fator whih aounts for long term effets on ompressive strength and unfavorable effets resulting the way load is applied is reommended to be 1.0 by EC 2 (2004). However, this fator may be hanged by amendments in a National Annex when adopted by an individual ountry. Many ountries in Europe have adopted the value of α as NS 3473 (1995) The Norwegian Conrete Strutures Code 3473 (1995) provides disrete values for various onrete ompressive strength as presented in Table 2-6. Table 2-6 Stress Blok Parameters for the Norwegian Code NS 3473 (1995) Conrete Compressive Strength (ksi) ε u β α CEB-FIB Model Code (1990) The retangular stress blok speified by CEB-FIB Model Code (1990) has the following parameters: 67

88 f ' α1 = Bakground Equation β 1 = 1.0 Equation f ' ε = Equation u where f ' is in ksi ACI 441-R96 (1996) ACI Committee 441 (1996) on HSC olumns suggested the following retangular stress blok parameters based on the researh data in the literature on HSC. ( f ) α 1 = ' for f ' > 10 Equation β 1 = 0.67 for f ' 10 Equation ε = Equation u where f ' is in ksi Summary of the Retangular Stress Blok Parameters in Design Codes The equations for retangular stress blok parameters speified by different design odes worldwide are given in Table 2-7. The omparisons of these equations are shown in Figure 2-26 and Figure These equations are used to ompare the test data obtained from this researh and other researhes in literature in Chapter 5. 68

89 Table 2-7 Summary of the Retangular Stress Blok Parameters in Design Codes 2 Bakground Referene α 1 β 1 ε u LRFD (2004) and 0.85 for f ' ACI 318 (2005) f ' for f ' > 4 NZS 3101 (1995) 0.85 for f ' 8 ( ) ( f ) for f > ( f ) ' ' for f ' ' for f ' > 4.35 CSA A23.3 (1994) f ' f ' for f ' k 7.25 α for f ' k for f ' k f ' k EC2 (2004) f ' k 7.25 f ' k α 1 for 7.25 f ' k for 7.25 f ' k for 7.25 f ' NS 3473 (1995) for f ' k 8 CEB-FIB Model Code (1990) ACI 441-R96 (1996) f ' ( f ) k f ' ' for f ' > for f '

90 2 Bakground α CEB-FIB (1990) NZS 3101 (1995) CSA 3 A23.3 (1994) LRFD (1998) - ACI 318 (2002) ACI 441 (1995) EC2-02 (2002) NS 3473 (1995) Conrete Compressive Strength (ksi) Figure 2-26 α 1 in Design Codes β CEB-FIB (1990) NZS 3101 (1995) CSA 3 A23.3 (1994) LRFD (1998) - ACI 318 (2002) ACI 441 (1995) EC2-02 (2002) NS 3473 (1995) Conrete Compressive Strength (ksi) Figure 2-27 β 1 in Design Codes 70

91 2 Bakground 2.3 Poisson s Ratio of HSC Poisson s ratio is defined as the ratio of the longitudinal ompressive strain of onrete in the diretion of the applied load divided by the transverse tensile strain of onrete normal to the applied load. For a perfetly inompressible material, Poisson's ratio is exatly 0.5. For NSC in the linearly elasti range, Poisson s ratio is assumed to be 0.2 for design purposes by AASHTO LRFD Bridge Design Speifiations (2004) Komendant et al. (1978) Komendant et al. (1978) used 6 16 in. ylinders to evaluate the reep behavior of onrete under various ombinations of temperatures varying from 73 to 160 F, stress levels varying from 30 to 60 perent of onrete ompressive strength and age of loading varying from 28 to 270 days. The onrete ompressive strengths at 60 days was 7.5 ksi for moist ured speimens and 7.0 ksi for sealed speimens. As a byprodut of the testing program, Poisson s ratio of onrete was also determined. Tests results for Poisson s ratio are given in Appendix D. It was onluded that Poisson s ratio, whih averaged 0.22, was not affeted by thermal variations Perenhio and Klieger (1978) Perenhio and Klieger (1978) tested air-entrained and non-air-entrained onretes with three different aggregates at water-ement ratios of 0.30, 0.35 and Conrete ompressive strengths varied from 7.2 to 11.6 ksi. The behaviors of the 6 12 in. ylinders were evaluated for onrete ompressive strength, modulus of elastiity, reep and Poisson s ratio. Tests results for Poisson s ratio are given in Appendix D. It was onluded that Poisson s ratio did not show a good orrelation, but tended to derease with inreasing water-ement ratios Carrasquillo et al. (1981) Carrarquillo et al. (1981) onduted an experimental program to evaluate the behavior of onretes with water-ement ratios varying from 0.70 to 0.32 and onrete ompressive strengths ranging from 3.0 to 11.0 ksi. Two different aggregates were used in the onrete mixture. The test results were evaluated for onrete ompressive strength, stress-strain 71

92 2 Bakground relationship, strength gain with age, speimen size effet, effets of drying, modulus of elastiity, Poisson s ratio, modulus of rupture and split ylinder strength. Tests performed on 4 8 in. ylinders indiated that Poisson s ratio is essentially 0.2 regardless of the onrete ompressive strength for both gravel and limestone onretes. Tests results for Poisson s ratio are given in Appendix D Swartz et al. (1985) Swartz et al. (1985) evaluated Poisson s ratio by testing eentri braket speimens with onrete ompressive strengths ranging from 8.4 to 12.3 ksi. The entral unreinfored test region had a ross-setion of 5 5 in. and was 16 in. long. Tests results for Poisson s ratio are given in Appendix D. It was onluded that within a given mixture design, the values were quite onsistent. However, from mixture to mixture, the values varied from 0.14 to No explanation was offered for this behavior Jerath and Yamane (1987) Jerath and Yamane (1987) performed a study to evaluate the effets of superplastiizers on onrete ompressive strength, stress-strain relationship, modulus of elastiity, Poisson s ratio, modulus of rupture and split ylinder strength. Six by twelve inhes onrete ylinders with water-ement ratios ranging from 0.28 to 0.55 and with onrete ompressive strengths ranging from 3.7 to 9.5 ksi were tested to determine harateristis of twelve different mixture designs. Tests results for Poisson s ratio are given in Appendix D. It was onluded that Poisson s ratio was about 0.2 for various strengths of onrete for mixtures both with and without superplastiizers Radain et al. (1993) Radain et al. tested 6 12 in. ylinders to evaluate Poisson s ratio of onrete with ompressive strengths ranging from 5.77 to 13.0 ksi. Poisson s ratio obtained varied from 0.15 to 0.23 with an average value lose to Test results were ompatible with the available data in the literature. 72

93 2 Bakground Ibrahim (1994) The average values of Poisson s ratio were determined based on 14 eentri braket speimens tested under ombined axial load and bending by Ibrahim (1994). Conrete ompressive strengths ranged from 8.6 to 18.8 ksi. The entral test region had a ross-setion of 8 12 in. and was 47 in. long. It was onluded that the average values of Poisson s ratio in the elasti range varied between 0.16 and Iravani (1996) Iravani (1996) tested 4 8 in. ylinders to determine the mehanial properties of HPC with ompressive strengths ranging from 9.4 to 17.4 ksi. Tests results were evaluated based on onrete ompressive strength gain with time, effet of type of ement, effet of drying, modulus of elastiity, Poisson s ratio and splitting tensile strength. Tests results for Poisson s ratio are given in Appendix D. Test results indiated that Poisson s ratio was about 0.18 on average at 40 perent of the ultimate stress Persson (1999) Persson (1999) performed an experimental and numerial study on air-ured and sealed speimens to evaluate Poisson s ratio of HPC. The parameters onsidered in the testing program were influene of maturity, type of aggregate, uring type and moisture. The onrete ompressive strength at 28 days ranged from 7.3 to 16.5 ksi. Cylinders with in. dimensions and 3.9 in. ubes were tested. Test results indiated that Poisson s ratio of HPC is slightly smaller than that of NSC. It was also onluded that Poisson s ratio was not affeted by the variations in relative humidity Rashid et al. (2002) Rashid et al. (2002) performed an extensive literature survey to ollet approximately 153 experimental values of Poisson s ratio of onretes in the elasti range. Based on these experimental values, it was onluded that Poisson s ratio of HSC was omparable to the expeted range of values for NSC. Test results indiated that Poisson s ratio was varying from 0.15 to 0.25 and an average value of 0.2 was a reasonable value for onrete ompressive strengths ranging from 2.9 to 17.4 ksi. 73

94 2 Bakground Logan (2005) Poisson s ratio was determined using 4 8 in. ylinders with onrete ompressive strengths ranging from 5.1 ksi to 16.8 ksi by Logan (2005). Tests results are given in Appendix D. The measured Poisson s ratio of onrete showed large amounts of variations and did not show apparent orrelation with the measured onrete ompressive strength. In addition, it was observed that uring proedures and age had little or no effet on Poisson s ratio. The average Poisson s ratio for all of the tested ylinders was 0.17 with a standard deviation of It was suggested that same Poisson s ratio of NSC an be assumed for also HSC Summary of the Tests on Poisson s Ratio The summary of the tests performed by different researhers to evaluate Poisson s ratio of onrete is shown in Table 2-8. Poisson s ratio s obtained by different researhers are also shown in Figure Referene Komendant et al. (1978) Perenhio and Klieger (1978) Carrasquillo et al. (1981) Swartz et al. (1985) Jerath and Yamane (1987) Radain et al. (1993) Table 2-8 Summary of the Tests on Poisson s Ratio Conrete Compressive Strength (ksi) Speimen Size and Type (in.) Conlusion Cylinder Average ν is Cylinder Cylinder Ibrahim (1994) Cross-Setion: 5 5 Length: 16 Eentri Braket Cylinder Cylinder Cross-Setion: 8 12 Length: 47 Eentri Braket ν tends to derease with inreasing water-ement ratios. ν is 0.2 regardless of the onrete ompressive strength. ν varies from 0.14 to ν is 0.2 for various onrete ompressive strengths. ν varies from 0.15 to 0.23 with an average value lose to ν varies from 0.16 and Iravani (1996) Cylinder Average ν is Cylinder ν of HPC is slightly smaller than Persson (1999) Cube that of NSC. Logan (2005) Cylinder Average ν is

95 2 Bakground Poisson's Ratio Komendant et al. (1978) Perenhio and Klieger (1978) Carrasquillo et al. (1981) Swartz et al. (1985) Jerath and Yamane (1987) Radain et al. (1993) Iravani (1996) Logan (2005) Conrete Compressive Strength (ksi) Figure 2-28 Poisson s Ratios by Different Researhers 75

96 2 Bakground 2.4 Creep and Shrinkage of HSC After the appliation of load (either tensile or ompressive) on hardened onrete, initially, it deforms elastially due to the applied stresses. At this stage, the mirostruture of onrete does not have any kinds of signifiant raks sine the applied load is not greater than the proportional limit. If this load is maintained on onrete, additional deformation will develop in onrete in time whih is known as reep deformation. Under the sustained load, some miro raking develops in onrete, faster at early ages and gets stable later. There are both reoverable and irreoverable omponents of this proess. After removal of the sustained load, nearly entire elasti deformation is reovered. Although some of the reep deformation is reovered, entire reep deformation is not fully ompensated due to the hanges in mirostruture of onrete. The reep proess starting from the appliation of sustained load and ending some time after the removal of the sustained load is shown in Figure Strain ε 1 Sustained Loading Creep Strain Reovered Elasti Strain No Load Removal of Sustained Load ε 0 Initial Elasti Strain Reovered Creep Strain ε 2 Appliation of Sustained Load t 0 t 1 t 2 Time Figure 2-29 Strain History of Conrete under Sustained Load There are two types of reep of onrete: Basi reep ours under onstant moisture onditions. Drying reep is the additional reep in exess of basi reep that ours due to a 76

97 2 Bakground moisture loss from the ambient onditions. Drying reep is a ombined effet of shrinkage and reep whereas basi reep is an independent proess. After the onrete hardens, its volume redues in time due to the loss of moisture ontent known as shrinkage. There are three main types of shrinkage of onrete: Drying shrinkage ours due to the loss of moisture ontent from hardened onrete under drying onditions. This proess is partially irreversible, even though onrete is plaed in a fully moist environment, not all the drying shrinkage will be reovered. Autogenous (hemial) shrinkage ours due to removal of internal water as a result of hydration of ement. Carbonation shrinkage ours due to the arbonation of the hydration produts in the presene of CO in a low relative humidity environment. Reinfored onrete strutures must be arefully designed to avoid problems assoiated with reep and shrinkage. Creep and shrinkage of onrete might be a signifiant problem sine they may ause: Deformations signifiantly larger than elasti deformations Redistribution of internal fores whih may reate additional fores on unexpeted members Craking and degradation of strutures whih may result in orrosion of reinforement, spalling of onrete, loss of servieability and possibly ollapse. Inreased prestress losses in pprestressed members A slow long time growth of bukling defletions in slender and thin strutures. More information and ase studies about the problems assoiated with reep and shrinkage an be found in Neville (2002a, 2002b). Both reep and shrinkage is dependent on many fators suh as, age of onrete, water to ementitious materials ratio, aggregate, omposition, unit weight of onrete, modulus of elastiity, relative humidity, temperature, volume to surfae ratio. Additionally, reep also depends on the strength of onrete at the time of appliation of the sustained load and 77

98 2 Bakground magnitude of the applied stress. The effets of these parameters on reep and shrinkage of onrete an be found in details in ACI 209R-92 (1992) Tests on Creep and Shrinkage of HSC The tests performed to evaluate the reep and shrinkage behavior of onrete is presented in this setion. The onlusions of these tests will be used to evaluate the test results of this researh Ngab et al. (1981) Ngab et al. (1981) onduted an experimental program to evaluate the time dependent deformation and sustained load strength of HSC. Speimens with dimensions were monitored for a period up to 90 to determine drying shrinkage, basi reep and drying reep of HSC. The main variables investigated inluded onrete ompressive strength (varying from 4.2 to 10.2 ksi), onditions of drying (sealed and unsealed), age at first loading (2 and 28 days) and, intensity of load (varying from 0.45 to 0.85f ), and duration of load (60 and 90 days). Test results indiated that reep might be muh less for HSC than that of NSC, espeially when speimens are permitted to dry under sustained load. It was observed that shrinkage of HSC was greater than that of NSC. The sustained ompressive stress over onehalf of the onrete ompressive strength was found to have detrimental effets on both normal- and HSC. Regardless of stress intensity, the ratio of sustained load strength to ompressive strength was observed to be higher for HSC than for NSC Collins (1989) An experimental program was onduted by Collins (1989) on reep and shrinkage of HSC. Variations in ement paste ontent and maximum aggregate size was the main parameters investigated in this study. For this purpose, five mixture designs were tested with onrete ompressive strengths ranging from 8.05 to 9.28 ksi at 28 days. Creep and shrinkage testing were performed in aordane with ASTM C 512 in an environmental hamber maintained at 70 F temperature and 50 perent relative humidity. Shrinkage testing was performed on onrete speimens after moist uring for 7 and 28 days, whereas reep testing was performed on onrete speimens after moist ured for 28 days. Test results indiated that reep and shrinkage deformations are somewhat less for onrete mixtures with lower ement paste ontents and larger aggregate size. It was observed that the shrinkage deformations 78

99 2 Bakground were inversely proportional to the moist uring time and the reep deformations inreased diretly with an inrease in the applied stress level. It was onluded that although the reep and shrinkage might be redued by areful mixture proportioning and aggregate seletion, the applied stress level has signifiantly important effet on olumn shortening Paulsen et al. (1991) Paulsen et al. (1991) evaluated the long term defletion of HSC using nine under-reinfored beams with onrete ompressive strengths ranging from 6 to 12 ksi, loaded over a 12 months period. The beams had also varying amounts of ompressive steel. Companion axially loaded 4 16 in. onrete ylinders were used to determine reep oeffiients. It was observed that the reep oeffiient for HSC was about half of that of NSC. Based on the test results, modifiations to the ACI Building Code method of prediting long term defletions were suggested Giaio et al. (1993) Giaio et al. (1993) performed an extensive researh program to evaluate the reep and shrinkage properties of 6 12 in. ylinders with onrete ompressive strengths ranging from 3.4 to 12.3 ksi. Three mixture designs were used with water to ement ratios varying from 0.65 to The reep speimens were loaded under 20 perent of the ompressive strength at the age of loading where the speimens were loaded in the 1 st and the 28 th day. It was observed that drying shrinkage of onrete slightly dereases as strength level inreases. The speifi reep of NSC was twie to three times greater than that of HSC. The test results indiated that the speifi reep of a HSC loaded at early ages would be smaller than that of NSC whih ahieved the same strength level at later ages Khan et al. (1997) Khan et al. onduted an experimental study on early-age shrinkage and thermal and reep strains of 4 8 in. ylinders with onrete ompressive strengths ranging from 4.4 to 14.5 ksi subjeted to sealed and air-dried onditions. It was observed that demolding at early ages resulted in greater shrinkage and thermal strains in HSC than in NSC. The test results indiated that reep of HSC is muh more sensitive to the age of loading that that of NSC. 79

100 2 Bakground Mokhtarzadeh and Frenh (2000) Mokhtarzadeh and Frenh tested 268 speimens to investigate the effet of mixture variations on reep, shrinkage and water absorption properties of HSC. Four by eleven inhes ylinders were used in the evaluation of reep and shrinkage properties with onrete ompressive strengths ranging from 8.0 to The water to ementitious material ratio was 0.3 in all the mixtures. Both aelerated heat uring and 7-day moist uring were investigated. All speimens were monitored for a period of one year. It was observed that the speifi reep of onrete dereased as onrete ompressive strength inreased. It was onluded that onrete ompressive strength and omposition of ementitious material had no signifiant effet on drying shrinkage of HSC. Modifiations were proposed to the ACI 209 reep and shrinkage predition relationships to provide better estimation for HSC Huo et al. (2001) Experiments on reep, shrinkage and modulus of elastiity of HSC with onrete ompressive strengths ranging from 9.0 to 12.4 ksi were onduted and ontinued for more than two years. The reep and shrinkage speimens were in. prisms. All the speimens were moist ured for either 7 or 28 days before the initial readings were reorded. Analysis and omparison of the test results showed that the shrinkage strains and reep oeffiients of HSC were lower than those of NSC. Creep and shrinkage predition relationships were proposed for onrete ompressive strengths up to 15 ksi. These relationships were adapted by AASHTO LRFD Bridge Design Speifiations (2004) after being proposed by Tadros et al. (2003) Jianyong and Yan (2001) Creep and drying shrinkage properties of HSC were investigated using three onrete mixtures with onrete ompressive strengths ranging from 11.7 to 15.1 ksi ube strength at 28 days. The speimens for reep and shrinkage tests were prisms with in. and in. dimensions, respetively. The reep speimens were loaded up to 40 perent of the 28-day strength and monitored for 180 days. The shrinkage tests were performed at the same time under same humidity and temperature onditions. It was onluded that reep and shrinkage would greatly be redued using mineral admixtures suh as granulated blast furnae slag and silia fume. 80

101 2 Bakground Suksawang et al. (2005) Suksawang et al. onduted a study to identify the shrinkage and reep of onrete with ompressive strengths ranging from 10.4 to 12.7 ksi at 28 days. Water to binder ratio of the mixture was Shrinkage and reep tests were performed using in. prisms and 6 12 in. ylinders, respetively. The applied load on the reep speimens ranged from 30 to 35 perent of the ultimate load. Test results are given in Appendix E. Test results showed that shrinkage of silia fume onretes was greater than that of fly ash onretes. It was observed that adding fly ash redued the drying shrinkage of silia fume onrete. Creep of silia fume onretes was greater than that of fly ash onretes Summary of the Tests on Creep and Shrinkage The summary of the tests performed by different researhers to evaluate the reep and shrinkage behavior of onrete is shown in Table 2-9. Table Summary of the Tests on Creep and Shrinkage Referene Conrete Compressive Strength (ksi) Ngab et al. (1981) Speimen Size and Type (in.) Prism Collins (1989) Cylinder Paulsen et al. (1991) Cylinder Giaio et al (1993) Cylinder Khan et al. (1997) Cylinder Mokhtarzadeh and Frenh (2000) Cylinder Huo et al. (2001) Prism Jianyong and Yan (2001) Suksawang et al. (2005) Creep: Prism Shrinkage: Prism Creep: 6 12 Cylinder Shrinkage: Prism Conlusion Creep of HSC is muh less than that of NSC. Shrinkage of HSC is greater than that of NSC Creep and shrinkage deformations are less for onrete mixtures with lower ement paste ontents and larger aggregate size. The reep oeffiient for HSC is about half of that of NSC. The speifi reep of NSC was twie to three times greater than that of HSC. Demolding at early ages resulted in greater shrinkage and thermal strains in HSC than in NSC. Creep of HSC is muh more sensitive to the age of loading that that of NSC. The speifi reep of onrete dereased as ompressive strength inreased. Conrete ompressive strength and omposition of ementitious material had no signifiant effet on drying shrinkage of HSC. The shrinkage strains and reep oeffiients of HSC were lower than those of NSC. Creep and shrinkage would greatly be redued using mineral admixtures. Creep and shrinkage of silia fume onretes were greater than that of fly ash onretes. 81

102 2 Bakground Creep and Shrinkage Preditions Models Creep and shrinkage predition models are investigated in this setion in details. Neessary relationships and equations are given to alulate and the predited values. These relationships will be used to ompare the test results of this researh and if needed a new relationship will be proposed in the light of these relationships ACI 209R-92 (1992) ACI Committee 209 (ACI 209R ) suggests the following equation to predit the reep oeffiient of onrete at any time ( ν t ): ψ ( ) ψ ν t = t d t + ν u Equation where t is the time in days, ψ is a onstant between 0.40 and 0.80, d is a onstant between 6 and 30 days, ν u is the ultimate reep oeffiient whih is between 1.30 and For NSC ured under standard onditions ACI Committee 209 (ACI 209R ) reommends the following reep oeffiient for a loading age at 7 days for moist-ured onrete, and at 1-3 days, for steam-ured onrete: ( ) ν t = t 10 + t 2.35 Equation ACI Committee 209 (ACI 209R ) suggests the following equation to predit shrinkage strain of onrete at any time (( ε ): ) t sh ( ) t α α ε = ( f + t ) ( ε ) sh t sh u Equation where t is the time in days, α is a onstant between 0.90 and 1.10, f is a onstant between 20 and 130 days, ( ε sh ) u is the ultimate shrinkage strain whih is between and

103 2 Bakground For normal weight, sand lightweight and all lightweight onrete under standard onditions ACI Committee 209 (ACI 209R ) reommends the following shrinkage strain: 6 ( ε sh ) t = t ( 35 + t) for 7-day moist-ured onrete Equation ( ε sh ) t = t ( 55 + t) for steam-ured onrete Equation CEB-FIB Model Code (1990) The reep oeffiient ( φ ( t, t ) ) for servie stressed less than ( ) FIB Model Code (1990) is given as: f m t 0 speified in CEB- φ ( t t ) φ β ( t t ), = Equation where φ 0 is the notional reep oeffiient, β is the oeffiient to desribe the development of reep with time after loading, t is the age of onrete (days) at the moment onsidered, t 0 is the age of onrete at loading (days). The relationship for the oeffiients are shown as: ( f ) ( t ) φ = φ β β Equation RH m 0 with φ RH 1 RH RH0 = 1+ Equation ( h h ) β = Equation ( f ) m ( f f ) 0.5 m mo ( t ) β = ( t t ) Equation h = A u Equation where f m is the mean onrete ompressive strength at the age of 28 days (MPa), f mo is equal to 10 MPa, RH is the relative humidity of ambient environment (%), RH o is equal to 83

104 2 Bakground 100%, h is the notational size of member, A is the ross-setion, u is the perimeter of the member in ontat with the atmosphere, h o is equal to 100 mm and t 1 is equal to 1 day. The development of reep with time is given by β ( t t ) ( t t0 ) t1 + ( ) 0 = βh t t0 t1 0.3 Equation with β H 18 RH h = RHo h o Equation where t 1 is equal to 1 day, RH o is equal to 100% and h o is equal to 100 mm. The total shrinkage ε ( t, t ) speified in CEB-FIB Model Code (1990) is given as: s s ( ) ε ( t, t ) = ε β t t Equation s s so s s where ε so is the notional shrinkage oeffiient, β s is the oeffiient to desribe the development of shrinkage with time, t is the age of onrete in days and t s is the age of onrete in days at the beginning of shrinkage. The notional shrinkage oeffiient may be obtained from: ( f ) ε = ε β Equation so s m RH with ε 6 ( f ) = β ( 9 f f ) 10 Equation s m s m mo 84

105 2 Bakground where f m is the mean onrete ompressive strength at the age of 28 days in MPa, f mo is equal to 10 MPa, β s is a oeffiient whih depends on the type of ement: β s is equal to 4 for slowly hardening ements SL, β s is equal to 5 for normal or rapid hardening ements N and R, and β s is equal to 8 for rapid hardening high strength ements RS, β RH = 1.55β for 40% RH 99% Equation srh β = for RH 99% Equation RH where β srh RH = 1 RHo 3 Equation with RH is the relative humidity of the ambient atmosphere in % and RH o is equal to 100%. The development of shrinkage with time is given by β s ( t t ) ( t ts ) t1 2 ( ) + ( ) s = 350 h ho t ts t1 0.5 Equation where h is defined previously, t 1 is equal to 1 day and h o is equal to 100 mm Tadros et al. (2003) and AASHTO LRFD Bridge Design Speifiations (2004) The reep oeffiient (ψ ) speified by Tadros et al. (2003) and AASHTO LRFD Bridge Design Speifiations (2004) is given by: ( t t ) Ψ, = 1.90k k k k k Equation i td la s h f where t is the age of onrete after loading in days, t i is the age of onrete when load is initially applied for aelerated uring or the age minus 6 days for moist uring in days, k td is 85

106 2 Bakground the time development orretion fator, k la is the loading age orretion fator, k s is the member size orretion fator, k h is the relative humidity orretion fator and k f is the onrete ompressive strength fator. These fators are expressed as: k td t = 61 4 f ' + t i Equation la = t i k Equation k s V / S = Equation k h = H Equation k f 5 = Equation f ' i where f ' i is the speified ompressive strength in ksi at prestress transfer for prestressed members or 80 perent of the strength at servie for non-prestressed members, V S is the volume to surfae ratio in inhes and H is the relative humidity of the ambient air. The shrinkage strain ( ε sh ) speified by Tadros et al. (2003) and AASHTO LRFD Bridge Design Speifiations is given by: ε = k k k k Equation sh td s hs f where same previously defined orretion fators are used exept the member size orretion fator, k s, whih is defined as: k hs = H. Equation Australian Standard for Conrete Strutures AS3600 (2006) The model speified by AS3600 (2006) for prediting the reep oeffiient ( ϕ ) for onrete ompressive strengths between 20 MPa and 100 MPa is given as: 86

107 2 Bakground ϕ = k k k k ϕ Equation b where k 2 is the oeffiient for development of reep in time, k 3 is the oeffiient for loading age, k 4 is the oeffiient for environment and k 5 is the oeffiient for the influene of humidity and speimen size. These oeffiients an be alulated as: k = t α2t t h Equation where t is the time in days sine first loading, t h is the hypothetial thikness and α 2 an be alulated as: h α = + e t Equation k τ for τ 28 = τ for 28 < τ < for τ 365 Equation where τ is the age of onrete at the time of loading in days. k k for an arid environment 0.65 for an interior environment = 0.60 for a temperature environment 0.50 for a tropial/oastal environment 1.0 when f ' 50 MPa = ( 2.0 α3) 0.02( 1.0 α3) f ' when 50 MPa < f ' 100 MPa Equation Equation where 0.7 α = 3 k α. Equation

108 2 Bakground The model speified by AS3600 (2006) for prediting the drying shrinkage strain ( ε sd given as: ) is ε sd = k k ε Equation sd. b where k 1 is the oeffiient for development of reep in time, k 4 is the oeffiient for environment as defined previously and ε sd. b is the basi drying shrinkage. The oeffiient k 1 and an be alulated as: k ε α t 0.15t d 1 = 0.8 td + ( f ' ) h sd. b sd. b* Equation = ε Equation where t d is the time in days after the ommenement of drying, t h is the hypothetial thikness and ε sd. b* is the oeffiient for quality of the loal onrete, inluding the type and the quantity of aggregates, ement, ement replaement materials and admixtures. α 1 and ε. * an be alulated from: sd b = + e t Equation h α ε sd. b * = for Sydney and Brisbane for Melbourne for elsewhere in Australia. Equation

109 3 Experimental Program 3 EXPERIMENTAL PROGRAM 3.1 General This hapter desribes the omponents of the experimental program undertaken to evaluate the stress-strain relationship, reep and shrinkage behavior of HSC. Test speimens, material propoerties, test set-ups, instrumentations and test proedures are summarized in the following setions. 3.2 Eentri Braket Tests The purpose of eentri braket tests is to determine the stress-strain distribution of onrete based on linear strain profile within the ompression zone and evaluate various parameters of the retangular stress blok. Generally, eentri braket speimens have two arms, eah onneted at the top and the bottom ends of the speimen to transfer the moment from the applied load to the arm to the mid-setion of the speimen. As observed in the literature review, these arms may either be onrete whih ould be ast monolithially with the onrete speimen or steel whih are onneted to the onrete speimen by speially designed onnetions. In this researh the seond onfiguration was seleted, using the steel arms to transfer the moment to the onrete Design of Test Speimens The main objetive in designing the test speimens is to have a speimen that an represent the ompression zone of flexural member. The test speimens were designed aording to the limitations of the testing mahine and the testing equipment. The seleted speimen was a square olumn with in. dimensions. When this speimen is loaded under flexure and axial ompression to obtain zero strain on one side and maximum strain on the other extreme opposite side, the ross-setional area of the speimen represents mainly a ompression zone of a beam member with 9 26 in. dimensions. To alulate the dimensions of the prototype member, the following assumptions were made: 89

110 1. ε t = 0.005, d t = Experimental Program 2. over onrete = 2 in. from the enter of the extreme tension reinforement where ε t is the tensile strain at the entroid of the extreme tension reinforement, is the distane from the extreme ompression fiber to the neutral axis and d t is the distane from the extreme ompression fiber to the entroid of the extreme tension reinforement. The prototype beam member is presented in Figure 3-1. Figure 3-1 Prototype Beam Member Two pilot speimens were tested to evaluate the distribution of the fores from the steel arms to the onrete mid-setion. The Pilot Speimen 1 was a in. retangular speimen with a total of twelve holes at the top and the bottom of the speimen. These holes failitated the onnetion of the steel arms. A piture of the test set-up for Pilot Speimen 1 is presented in Figure

111 3 Experimental Program Figure 3-2 Test Set-Up for Pilot Speimen 1 After testing the Pilot Speimen 1, it was observed that the ends of the speimen were not strong enough to transfer both the main axial load and the moment applied by the arms. The lower end of the speimen failed after applying 1/8 of the expeted load. The failure mode at the lower end is shown in Figure 3-3. Figure 3-3 Failure Mode at the Lower End of Pilot Speimen 1 Retangular steel tubes were used in the Pilot Speimen 2 at the ends. These tubes were both onfining the onrete at the ends and transferring the moment in a more distributed way on the onrete surfaes. A piture for the test set-up for the Pilot Speimen 2 is shown in Figure

112 3 Experimental Program Figure 3-4 Test Set-Up for Pilot Speimen 2 The testing Pilot Speimen 2 was very suessful in transferring the moment from the arms to the onrete speimen. Simultaneously, the appliation of the main axial load was ahieved through the ends of the speimen. The failure ourred at the mid-height at the expeted load level. Using the steel tubes at the ends was the deision that finalized the design of the test speimens Test Speimens Test series onsisted of 21 square olumn speimens with in. dimensions. A general view of the onrete speimen is shown in Figure 3-5. The end setions of the speimens were heavily reinfored, while the test region in the middle of the speimens was plain onrete. The main parameter was the onrete ompressive strength. Three different HSC mixture designs were used to ast the speimens. The target onrete ompressive strengths of these mixtures at 28 days were 10, 14 and 18 ksi. Five, six and ten eentri braket speimens were ast for 10, 14 and 18 ksi target onrete ompressive strength, respetively. Details of the test speimens are illustrated in Table

113 3 Experimental Program Figure 3-5 General View of the Speimen Table 3-1 Details of the Test Speimens Speimen No 10EB1 10EB2 10EB3 10EB4 10EB5 10EB6 14EB1 14EB2 14EB3 14EB4 14EB5 14EB6 18EB1 18EB2 18EB3 18EB4 18EB5 18EB6 18EB7 18EB8 18EB9 18EB10 Target Conrete Compressive Strength at 28 Days (ksi)

114 3 Experimental Program The end setions of the onrete speimens were reinfored with three #4 U-shaped longitudinal and three #3 transverse reinforement. Steel reinforement onfiguration of the eentri braket speimens is shown in Figure 3-6. Furthermore, the ends of the speimens were onfined with 1/2 in. thik 10 in. high retangular steel tubes. The ombination of the steel tubes and heavy reinforement failitated proper transfer of the axial load and moment transfer and eliminates possible loalized failures at the ends of the speimens. The plain onrete test setion in the middle of the speimens was 16 in. long. Figure 3-6 Steel Reinforement Configuration Materials Conrete Three different mixtures were developed for 10 ksi, 14 ksi and 18 ksi target onrete ylinder strengths at 28 days (Logan 2005). In order to obtain these target strength levels, numerous trial bathes were prepared in Construted Failities Laboratory ( and in the laboratory of Ready Mixed Conrete Company ( After the desired strength levels were ahieved from laboratory bathes, these mixtures were made in large quantities in mixing truks due to the large quantity of onrete needed to ast all the speimens. 94

115 Cement 3 Experimental Program Type I/II ement produed by Roanoke Cement Company ( was used in all the mixtures used in this researh Fine Aggregate Two types of fine aggregate were used depending on the target ompressive strength. The first type of fine aggregate was natural sand used by the Ready-Mixed Conrete Company ( in all of their onrete mixtures. The results of the sieve analysis performed at NCSU Construted Failities Laboratory ( are given in Appendix B. The seond type of fine aggregate, 2MS onrete sand, was a manufatured sand produed by Carolina Sunrok Corporation ( and quarried in Butner, North Carolina. The material datasheet of fine aggregate provided by the ompany is given in Appendix B Coarse Aggregate The oarse aggregate, #78M rushed stone, was also provided by Carolina Sunrok Corporation ( and quarried in Butner, North Carolina. The nominal maximum size of the oarse aggregate is 3/8 in. Additional information about the oarse aggregate an be found in the material datasheet provided in Appendix B Silia Fume The densified Elkem Mirosilia 971 silia fume produed by Elkem Materials Inorporated ( was used in all the mixtures. Additional information about the silia fume is presented in Appendix B Fly Ash Class F fly ash produed by Boral Material Tehnologies ( was used in the HSC mixtures. Material datasheet provided by the ompany is shown in Appendix B Admixtures Both the high-range water-reduing and the retarding admixtures were manufatured by Degussa Admixtures Inorporated ( The high-range water-reduing 95

116 3 Experimental Program admixture (HRWRA) used was Glenium The retarding admixture used was DELVO Stabilizer. Additional information about these admixtures provided by the ompany is given in Appendix B Conrete Mix Proportions After numerous trial bathes, three mixture designs were seleted to be used as 10, 14 and 18 ksi target onrete ompressive strengths. These mixture designs are presented in Table 3-2. Table 3-2 Three Conrete Mixture Designs Target Conrete Compressive Strengths (ksi) Material Cement (lbs/yd 3 ) Silia Fume (lbs/yd 3 ) Fly Ash (lbs/yd 3 ) Fine Aggregate (lbs/yd 3 ) 1055 (NS*) 1315 (MS*) 1240 (MS*) Coarse Aggregate (lbs/yd 3 ) Water (lbs/yd 3 ) HRWRA (oz/wt)** Retarding Agent (oz/wt)** Water / Cementitious Material Day Compressive Strength (ksi) * NS: Natural Sand, MS: Manufatured Sand ** Ounes per 100 pounds of ementitious materials Mehanial Properties Cylinder Compression Test Either three or four of 4 8 in. onrete ylinders were used to obtain the onrete ompressive strength at the time of testing of the speimens. The ylinders tested at 28 days were ured in the lime water tanks ontinuously until the day of testing whih was by ASTM standards for quality ontrol testing in the onrete industry. Other ylinders were moist ured for the first 7 days with the test speimens. These test speimens and ylinders were then stored in the laboratory environment where the ambient temperature was approximately 72 F and the relative humidity was approximately 50 perent. The 96

117 3 Experimental Program ends of the ylinders were grinded before testing to failure to smooth the end surfaes. The ylinder test results for eah of the speimens are presented in Appendix C Reinforement Grade 60 reinforing steel provided by Gerdau Ameristeel Inorporated ( was used both for longitudinal and transverse reinforement in the onstrution of the speimens Speimen Preparation The steel tube setions were onstruted by a loal ompany, Hamilton Mahine Works. Two of these steel tubes were used for eah speimen to onfine and have a better load transfer through the top and the bottom ends. The inner dimensions of the steel tube setions were in. with a 1/2 in. steel plate thikness. The neessary ASTM A992 steel plates were welded together to onstrut the tube setions. Holes were drilled on two opposite faes to failitate the onnetion of the moment arms. On one drilled side, there were total six holes, two of them for 1 and 1/4 in. threaded rod and four of them for 1 in. threaded rod. The reinforement ages at the ends were assembled outside the formwork. The PVC tubes were ut into neessary lengths to fit into the holes of the steel tube setion. The steel tube setion, reinforement age and PVC tubes are shown in Figure 3-7. The assembled reinforement and PVC tubes were plaed into the steel tube setion. The assembly of the steel tube setion is shown in Figure

118 3 Experimental Program Figure 3-7 Steel Tube Setion, Reinforement Cage and PVC Tubes Figure 3-8 Assembly of Steel Tube The formworks were onstruted from 3/4 in. plywood to enable repeated usage. Lumber stiffeners were plaed at the bakside of the plywood to eliminate the bulging effet due 98

119 3 Experimental Program to the pressure of onrete at the asting stage. The formworks of the speimens were onstruted so that the speimens would be ast vertially. Form release ompound was applied on the inner surfaes of the formworks for easy stripping. Initially, the top and bottom steel tube setions were loated in the formwork. Any voids between the formworks and the steel tube were sealed with silione. The formwork was losed as a last step in the formwork preparation. These steps in the assembly proedure of the formwork are shown in Figure 3-9. Figure 3-9 Assembly of the Formwork The onrete was prepared in the Ready Mixed Conrete Company s onrete mixing plant. Before mixing the ingredients of onrete, the moisture ontent of the fine and oarse aggregate was measured and the total amount of water in the mixture was adjusted aordingly. A total of 3 yd 3 mixture was prepared to ast the test speimens. The slump, unit weight and air ontent tests on the onrete mixture were performed and ompared with the lab bathes. If the results of these tests were not ompatible with the orresponding target strength of the lab bath, no speimens were ast with that onrete mixture. The speimens were ast diretly from the onrete truk. A piture from the asting day is shown Figure Soops and trowels were used in the asting proess. Three or four 4 8 in. ompanion ylinders were ast with eah speimen. The speimens were vibrated by a 1 in. vibrator. The ylinders were ast in two layers and eah layer was rodded 25 times with a 3/8 in. rod. 99

120 3 Experimental Program Figure 3-10 The Casting Day The surfaes of the onrete speimens exposed to air were overed with wet burlap and plasti sheets 2 hours after asting. The ylinder molds were apped, simultaneously. The speimens and the onrete ylinders were ured in the formworks and plasti molds for one day, respetively. The speimens and ylinders were then demolded and moist ured with wet burlap and plasti sheets until the 7 th day. Starting from the seventh day, all the speimens and ylinders were air ured in the laboratory environment until the testing day. The ASTM ured ylinders were plaed in the lime-water tank after demolding in the first day. These ylinders were moved out of the lime-water tank for ompression tests on the 28 th day. The speimens were at least 28 days old at the time of testing Test Set-Up Two steel moment arms produed by Hamilton Mahine Works were onneted to the ends of the retangular onrete speimen. Sine the ends of the onrete speimen were onfined with steel tube setions, the steel arms were diretly onneted to the steel tube setions. The onnetion was established using threaded rods through the holes on the speimen and the steel arms. The steel arms were designed to resist the maximum applied loads to fail the strongest speimen by a safety fator of 2 against yielding. ASTM A

121 3 Experimental Program steel was used in the onstrution of the arms. Two /2 in. plates were welded to two 24 in. long C hannel setions to obtain the moment arm. Stiffeners were used in every 6 in. to inrease the shear strength of the arm. One inh thik end plate was welded to the built-up setion to failitate the onnetion to the onrete speimen. Stiffeners were welded between the built-up setion and the end plate to inrease the stiffness of the end plate. The drawing of the moment arm is shown in Figure The general view of moment arm is shown in Figure Figure 3-11 Drawings of the Moment Arm Figure 3-12 General View of the Moment Arm A total of six threaded rods are used at eah end to onnet of the moment arm to the onrete speimen. Two different sizes of Grade B16 alloy high strength steel threaded rods, 1 and 1.25 in, with 105 ksi yield strength and 125 ksi ultimate strengths, respetively, were used in three layers. The threaded rods, washers and nuts were provided by MMaster and Carr ( The design for the threaded rods with a safety fator of 2 against yielding required to use two 1.25 in. threaded rods at the most stressed layer (furthest layer from the mid-setion of the onrete speimen) and four 1 in. threaded rod at the other layers. The sizes of the threaded rods and their loations on the speimen are shown in Figure

122 3 Experimental Program Figure 3-13 Sizes and Loations of the Threaded Rods Two roller bearing systems onstruted by Hamilton Mahine Works were used to eliminate the end restritions on the speimen. The roller bearing system was designed to resist the maximum applied loads to fail the strongest speimen by a safety fator of two against yielding. ASTM A992 steel was used in the onstrution of the roller bearing system. One roller bearing system onsisted of six rollers and two urved plates. The diameter of the eah roller was 1 in. and 9 in. long. The bottom plate was 8 9 in. urved plate with 1 1/2 in. to 3/4 in. of tapering through outside. The radius of the tapering for the bottom urves plate was 11 in. The top plate was 8 9 in. urved plate with 3/4 in. to 1 27/64 in. tapering through inside. The radius of the tapering for the top urved plate was 12 in. Aording to these radii, the enter of the applied axial loads was 9 1/4 in. from the top and the bottom of the speimens. After mahining the steel plates and the rollers, they were all hardened. The rollers and the plates were fixed by using side plates and bolts for easy handling and assembly of the speimens in the ompression mahine. Before the testing the speimens to failure, the bolts of the side plates were removed. The rosssetion of the roller onnetion is shown in Figure General view of the roller onnetion is given in Figure

123 3 Experimental Program Figure 3-14 Cross-Setion of the Roller Connetion Figure 3-15 General View of Roller Connetion The main axial load was applied using 2000 kip Baldwin-Lima-Hamilton ompression mahine. The retangular onrete speimens with steel tubing setions were plaed on the roller bearing system lying on the ompression mahine (Figure 3-16). At this stage the roller bearing system was fixed to the side plates to provide a stable system. Hydrostone was used between the speimen and the roller bearing system both at the top and bottom to level the onrete speimen and to eliminate loalized onrete failures at the ends. For a safety preaution, the speimen was surrounded with wooden frame to avoid any instability before and after testing the speimen to failure. 103

124 3 Experimental Program Figure 3-16 Plaement of the Speimen into the Compression Mahine Before onneting the moment arms, the hydrostone at the bottom of the speimen was let to set for at least 30 minutes. Initially the bottom moment arm was raised by using the rane up to the neessary loation. The threaded rods were plaed through the holes of the lower end of the speimen. On the opposite side of the onnetion, in. plate was loated to distribute the fores applied by the threaded rod more uniformly on the steel tube setion. After positioning the bottom moment arm and adjusting its loation with the rane, the arm was fixed by tightening the nuts of the threaded rods. At this stage the bolts fixing the roller bearing system was released and the onrete speimen fixed to the bottom lower arm was leveled by using the rane. After performing neessary leveling, lumber was plaed under the moment arm to hold everything in position. Then the rane was detahed from the bottom moment arm. The top moment arm was positioned in a similar manner. The onneted moment arms to the onrete speimens are shown in Figure The seondary load whih reated flexural effets on the speimen was applied using a 60 tons Enerpa hydrauli jak. A 1 in. diameter and 6 ft threaded rod was plaed in the holes on the arms. The load ell and the jak were positioned on the top moment arm and both arms were onneted together by using threaded rod. The test setup is shown in Figure A general view of the test set-up is illustrated in Figure

125 3 Experimental Program Figure 3-17 Connetions of the Moment Arms Figure 3-18 Test Set-Up 105

126 3 Experimental Program Figure 3-19 General View of the Test Set-Up Instrumentation The main axial load P 1, applied using the 2000 kip Baldwin-Lima-Hamilton load ontrolled hydrauli ompression mahine, was measured using an internal load ell whih is mounted in the mahine. The load P 2 was applied with a lbs. Enerpa hydrauli jak and was measured using a lbs. Strainsert Universal Flat Load Cell. Companion 4 8 in. ylinders for the eentri braket speimens were tested using a 500- kip MTS ompression mahine and the orresponding load was measured using the internal load ell of the ompression mahine. Review of studies related to end treatments for tests of ompression ylinders, grinding the ends of ylinders provided the highest 106

127 3 Experimental Program strength and lowest oeffiient of variation (Logan 2005). Therefore, both end surfaes of the ompanion ylinders were grinded to eliminate irregularities in the surfaes and to ensure that the ends were perpendiular to the sides of the speimen. The tests were performed in aordane with ASTM C 39 with a loading rate of 35 ± 7 psi/se. Eah speimen was instrumented with PL-60-3L onrete eletrial resistane strain gages supplied from Texas Measurements, In. ( The length of the eletrial resistane strain gages were 2.4 in. The onrete surfae where the eletrial resistane strain gages were attahed was initially smoothed by using a rubbing-stone. The residual dust was leaned by using pressurized air and water. After the onrete surfae dried, the position of the eletrial resistane strain gages were marked on all the sides and a very thin layer of 5 min epoxy was applied on the onrete surfae to over the holes on onrete and to have a smoother surfae for the attahment of the eletrial resistane strain gages. M-Bond 200 Adhesive, provided by Vishay Instruments Group ( was used to bond the eletrial resistane strain gages to the onrete surfae. The appliation proedure followed to apply the eletrial resistane strain gage with M-Bond 200 Adhesive Kit an be found in ompany s website. After the eletrial resistane strain gages were applied on the onrete speimen, the adhesive was let to set for at least 2 minutes. The number of strain gages attahed on the onrete was determined after the pilot tests. In the pilot tests, 18 strain gages were mounted on onrete, four on eah typial side fae, 6 on ompression fae and 4 on neutral fae. The loation of the strain gages for pilot tests is presented in Figure The vertial strain gages on the ompression and the zero strain side were plaed in three layers to find out whether there was any end effets due to onfinement. The horizontal strain gages on the ompression side were plaed in two layers due to the same reason. After the pilot tests were performed, no signifiant end effets were observed on the strain gage readings. As a result, the number of strain gages was redued to nine for the remaining test speimens. 107

128 3 Experimental Program Figure 3-20 Loation of the Strain Gages for Pilot Tests A total of 9 strain gages were loated on eah test speimen. Two of them were applied on the zero strain fae. Four of them were mounted on the two sides of the speimen. Three of them were loated on the ompression side of the speimen, one of whih was used to measure the transverse strain of onrete. The loation of the strain gages for test speimens is presented in Figure Figure 3-21 Loation of the Strain Gages for Test Speimens The loads, P 1 and P 2, ompression mahine stroke and 9 strain gages were reorded during the tests by a data aquisition system. 108

129 3.2.7 Test Proedure 3 Experimental Program The wires of the strain gages and LVDTs were onneted to the data aquisition system. All the LVDTs were alibrated, loated and adjusted at the predetermined positions. The load ell and stroke of the ompression mahine and the load ell on the steel moment arm was onneted to the data aquisition system. The rane was attahed to the top arm of the onrete speimen to remove the piees of lumber under the moment arms. The speimen was leveled by using the rane again. The hydrostone and the top roller bearing system were plaed at the top of the speimen. The bolts fixing the top roller bearing system was released and the hydrostone was left to set for a few minutes. Before the hydrostone was ompletely set, a very small amount of load was applied to the speimen. At this stage the level of the speimen was heked again. After the hydrostone was ompletely set, the readings of the instrumentations were balaned to zero and the ompression mahine was ativated to apply the ompressive load. As the main axial load applied by the ompression mahine started to inrease inrementally, the seondary load was applied by a hydrauli jak using a hand-pump to maintain neutral surfae (zero strain) at one fae of the speimen. It was intended to apply the load at a rate of approximately 2 mirostrains per seond at the other extreme ompression fae of eah speimen. Eah test was ompleted in approximately 25 minutes. The tests were stopped after the explosive failure of the onrete in the ompression zone. The failed speimen was held by the safety frame after the end of the eah test. After eah test, the safety frame was disassembled and the speimen was removed by the forklift. The ompression mahine, steel arms and the roller bearing system was then leaned and prepared for the next test. 109

130 3 Experimental Program 3.3 Creep Tests Creep tests were performed to evaluate the reep behavior of HSC under sustained load. The main parameters inluded in the testing program were onrete ompressive strength, uring type, age of onrete at the time of loading and the level of the sustained load. The testing sheme is presented in Table 3-3 and Table 3-4. Rak ID Table 3-3 Testing Sheme for Cylindrial Creep Speimens Target Conrete Compressive Strength (ksi) Curing Type Day of Loading (Days) Applied Stress Level (f' A g ) 10Rak 1 1-Day Heat Rak Rak Rak 4 7-Day Moist Rak Rak Rak 1 1-Day Heat Rak Rak Rak Day Moist Rak Rak Rak 1 1-Day Heat Rak Rak Rak 4 7-Day Moist Rak Rak Table 3-4 Testing Sheme for Cylindrial Shrinkage Speimens Speimen ID Target Conrete Compressive Strength (ksi) Curing Type Day of Initial Monitoring 10SC Day Heat 1 10SC2 7-Day Moist 7 14SC Day Heat 1 14SC2 7-Day Moist 7 18SC Day Heat 1 18SC2 7-Day Moist 7 Three different HSC mixture designs were used to ast the ylindrial reep and shrinkage speimens. The target onrete ompressive strengths of these mixtures at

131 3 Experimental Program days were 10.0 ksi, 14.0 ksi and 18.0 ksi. Details about the mixture design are presented in Setion Two different uring methods, 1-day heat and 7-day moist, were used for the reep speimens. The heat ured speimens were plaed in an environmental hamber as soon as the speimens were ast. The internal temperature of the onrete was maintained between 150 and 160 F for 24 hours whih simulated uring proedures of prestressed onrete plants. After the speimens were removed from the hamber, they were stored in the laboratory where the temperature was maintained at approximately 72 F and 50 perent relative humidity until the time of testing. The moist ured speimens were submerged in water in uring tanks for seven days as soon as they were demolded 24 hours after of asting. The water temperature was maintained at 73.5 F ± 3.5 F using heaters equipped with adjustable thermostats. The water was saturated with alium hydroxide to prevent leahing of alium hydroxide from the test speimens. The uring tanks also ontained pumps that irulated the water for a homogeneous mixture. The speimens were stored in the laboratory at approximately 72 F temperature and 50 perent relative humidity after 7 days. The heat ured speimens were loaded on 1 st day after asting. The moist ured speimens were loaded on the 7 th, 14 th and 28 th day after asting. Two different load levels were applied on the speimens. 0.2 f A g and 0.4 f A g. The load levels were alulated aording to the target onrete ompressive strengths at 28 days Test Speimens Test series onsisted of 36 ylinders with 4 12 in. dimensions loaded in 18 reep raks and 6 ylinders with 4 12 in. dimensions monitored for shrinkage purposes. Two speimens were loaded in eah rak. PVC sewer pipe and end aps were used for the molds of the 4 12 ylinder speimens. PVC sewer pipe with 4 in. inner diameter was ut into 12 in. lengths. The end aps were glued at one end of eah mold. The performane of these PVC pipes was outstanding even used repeatedly. Three pairs of brass insert were plaed onto the molds to measure the reep strains. Before the asting day, form release agent was applied to the inner surfae of the PVC molds. The brass insert were positioned afterwards. 111

132 3.3.2 Creep Raks 3 Experimental Program A typial reep rak is shown in Figure Eah rak onsisted of two steel plates whih were the upper base plate and the lower jaking plate. An upper jaking plate was also used at the time of loading the speimens whih was removed after the speimens were loaded. 38 triangular steel plates, either or in, were used as the upper base plate, lower jaking plate and upper jaking plate. 54 retangular steel plates with in. dimensions were used as the lower base plate. These plates were onstruted by a loal ompany named as Hamilton Mahine Works. Three, 1 in. diameter threaded rods were used for eah of the 12 reep raks while three, 1.25 in. diameter threaded rods were used for the remaining 6 reep raks. These rods were B7 Alloy Steel, either 1 in. 8 thread or 1.25 in. 7 thread, 72 in. length, ASTM 193, plain finish threaded rods. Also Grade 8 plain steel hex nuts and zin-plated steel USS highstrength flat washer were used as the neessary load appliation mehanism. The threaded rods, nuts and washers were supplied from MMaster and Carr ( The onfiguration of the plates and thread rods in the raks are shown in Table

133 3 Experimental Program Figure 3-22 Typial Creep Rak 113

134 3 Experimental Program Table 3-5 Configuration of Plates and Threaded Rods in the Raks Rak ID 10Rak 1 10Rak 2 10Rak 3 10Rak 4 10Rak 5 10Rak 6 14Rak 1 14Rak 2 14Rak 3 14Rak 4 14Rak 5 14Rak 6 18Rak 1 18Rak 2 18Rak 3 18Rak 4 18Rak 5 18Rak 6 Dimensions of Triangular Plate(in.) Diameter of Threaded Rod (in.) A pin onnetion was plaed in eah rak to provide onentri loading to the speimens. It onsisted of two dipped-at-enter steel plates with in. and in. dimensions. A 1.5 in. diameter ball bearing was plaed into the dips. This was also onstruted in Hamilton Mahine Works. Eah rak ontained 3 pairs of K4250-M-375 high arbon and stainless steel disk springs supplied from Key Bellevilles, In ( The springs were used to ompensate any load drops in the system. The springs in pairs were staked in series at the bottom of the reep rak. The assembly of the reep rak started with the appliation of the strain gages as presented in Figure The other omponents of the raks (plates, disk springs and pin onnetion) are shown in Figure

135 3 Experimental Program Figure 3-23 Appliation of the Strain Gages a) Plates b) Disk Springs ) Pin Connetion Figure 3-24 Plates, Disk springs and Pin Connetion Threaded rods were plaed in the holes on the lower jaking plate and upper base plate. The springs are positioned under the upper base plate and the bottom base plate was plaed. The assembly of the plates is shown in Figure Figure 3-25 Assembly of the Plates 115

136 3 Experimental Program The reep raks were hinged to the walls to prevent any rolling over. Then the reep raks were ereted side by side. The eretion of the reep rak is shown in Figure Figure 3-26 Eretion of the Creep Rak Instrumentation Eah threaded rod was instrumented with one YFLA-5-3L strain gage supplied from Texas Measurements, In ( The gage fator and the resistane of these strain gages were 2.11 and ohm, respetively. Two inhes length of eah treaded rod was leaned from threads in Hamilton Mahine Works. The strain gages were applied onto this leaned portion of the threaded rod. The M-Bond 200 Adhesive Kit, supplied from Vishay Instruments, In. ( was used to apply the strain gages. The appliation proedure of a strain gage onto a steel surfae an be found in website These strain gages were onneted to the CR23X-4M Datalogger whih was supplied from Campbell Sientifi, In. ( The datalogger enabled ontinuous monitoring the loads on the threaded rods. To inrease the number of strain gages that were onneted to the datalogger, two AM416 Multiplexers were used. This enabled the datalogger to read 54 strain gages that were onneted to the raks. Two MR Full Bridge Completion Modules supplied from Vishay Instruments, In. ( were onneted to the multiplexers to read the strain gages. The datalogger and the multiplexer are presented in Figure The details on the program of the datalogger are presented in Appendix E. 116

137 3 Experimental Program a) Datalogger and Multiplexer b) Multiplexer Figure 3-27 Campbell Sientifi Datalogger and Multiplexer Eah of the onrete ylinders was instrumented using three pairs of deme points. To loate the deme points on the ylinder, the brass deme insert was bolted into the PVC mold by using a drill. These deme inserts were supplied from Humboldt Sientifi, In. ( The inserts were positioned in every 120 angle around the mold. The spaing between eah pair of deme points was 8 in. The onfiguration of these deme points is shown in Figure The ylindrial PVC molds and the insert are shown in Figure

138 3 Experimental Program Figure 3-28 Configuration of the Deme Points Figure 3-29 PVC Mold and Deme Inserts An 8 in. deme gage was used to monitor the strain in eah speimen. The deme gage is presented in Figure After all the deme inserts are loated, the deme gage was used to ontrol the spaing of the deme points. 118

139 3 Experimental Program Figure 3-30 Deme Gage Creep tests were performed in an environment where the humidity ould not be ontrolled. Therefore, the temperature and humidity were monitored during the experimental program using a hygro-thermometer lok supplied by Exteh Instruments, In ( (Figure 3-31). Figure 3-31 Hygro-Thermometer Clok 119

140 3 Experimental Program The load on the speimens was applied using a 60 kip Enerpa hydrauli jak and manually ontrolled hand-pump. A pressure gage was used to measure the applied load. The pressure gage was alibrated eah time before appliation of the load using 220 kip Universal MTS Testing Mahine Test Proedure For eah onrete mixture design onrete mixture design, 14 ylinders were ast. Three of them were 1-day heat ured while the rest were 7-day moist ured. Two of the heat ured speimens were loaded in a rak. The other heat ured speimen was used to monitor the shrinkage of the heat ured ylindrial speimens. 10 of the moist ured speimens were loaded in the raks. The other moist ured speimen was used to monitor the shrinkage of the moist ured ylindrial reep speimens. Both ends of the ylindrial reep and shrinkage speimens were grinded to remove the irregularities at the end surfaes and to ensure that the ends were perpendiular to the sides of the speimen. The deision in the seletion of the end treatment was given based on the researh performed by Logan (2005). The two ends of the ylindrial shrinkage speimens were sealed with epoxy to simulate the same surfae/volume ratio of the loaded reep ylinders. This prevented ylinders from exhanging moisture with the environment through their ends. Before plaing the ylinders in the reep raks, eah deme point on ylinders was numbered and the initial length was measured and reorded three times using a deme gage. Initial length of the ylindrial shrinkage speimen was also measured and reorded three times. The strain gages on the treaded rods were also reorded as the initial reading. Two ylindrial reep speimens were staked in series and positioned on the pin onnetion as shown in Figure The pin onnetion and the ylindrial reep speimens were entered and aligned to avoid eentri loading. The lower jaking plate was lowered and leveled to fix the speimens in the reep rak. The hydrauli jak was plaed on the lower jaking plate and the upper jaking plate was positioned on the hydrauli jak. After fixing the neessary nut, 50 perent of the target load was applied on 120

141 3 Experimental Program the speimens. At this stage, the fores in the steel threaded rods were monitored using the strain gages to ensure onentri loading of the speimens. If the load was not onentrially applied resulting differenes in steel fores, the speimens would be unloaded. After repositioning, releveling and realigning the ylinders, 50 perent of the target load was applied again. When the desired distribution of the steel fores was ahieved, the appliation of the load was ontinued up to the target load level. At this stage, the strain gages were reorded. The nuts above the lower jaking plate were tightened at this load level. The load applied by the jak was released and transferred to the lower jaking plate. The strain gages were heked to onfirm that the target load level was applied on the speimens. The nuts were adjusted in ase of a hange of the load levels. The deme and strain gage readings were measured and reorded three times after ahieving the target load level. Creep and shrinkage of ylinders were simultaneously monitored at pre-determined intervals suh as everyday in the first few days. On eah monitoring day, every deme point was measured and reorded three times. The average of these three readings was used for alulation purposes. The monitoring period was inreased to one month after three months. The speimens were monitored for approximately two years. The strain gages were monitored ontinuously using the datalogger. When the applied load dropped more than 5 perent of the target load, the speimens were loaded again to the original load level using the hydrauli jak. 121

142 3 Experimental Program 3.4 Shrinkage Tests Shrinkage tests were performed to evaluate the drying shrinkage behavior of HSC under drying onditions. The main parameters inluded in the testing program were onrete ompressive strength, type of uring and day of initial monitoring. The testing sheme is presented in Table 3-6. Table 3-6 Testing Sheme for Prismati Shrinkage Speimens Speimen ID 10SP1 10SP2 10SP3 10SP4 10SP5 10SP6 14SP1 14SP2 14SP3 14SP4 14SP5 14SP6 18SP1 18SP2 18SP3 18SP4 18SP5 18SP6 Target Conrete Compressive Strength (ksi) Curing Type 1-Day Heat 7-Day Moist 1-Day Heat 7-Day Moist 1-Day Heat 7-Day Moist Day of Initial Monitoring Three different HSC mixture designs were used to ast the prismati shrinkage speimens. The target onrete ompressive strengths of these mixtures at 28 days were 10.0 ksi, 14.0 ksi and 18.0 ksi. Details about the mixture design are presented in Setion Two different uring methods, 1-day heat and 7-day moist, were used for the reep speimens. Details about the uring methods are presented previously in Setion 1.1. The 1-day heat ured and 7-day moist ured speimens were initially monitored in the first and the seventh day, respetively. 122

143 3.4.1 Test Speimens 3 Experimental Program Test series onsisted of 18 prisms with ¼ in. dimensions. The prismati shrinkage speimens were designed and onstruted in aordane with ASTM C 157, Standard Test Method for Length Change of Hardened Hydrauli-Cement Mortar and Conrete. Prismati steel molds used for asting are shown in Figure Two inserts were embedded at the top and the bottom of eah speimen in order to monitor the length hange. Figure 3-32 Steel Mold for Prismati Shrinkage Speimens Instrumentations A dial indiator system shown in Figure 3-33 was used to monitor the length hange of eah speimen. Before measuring the length of the onrete speimens eah time, the dial indiator system was alibrated and reset using an invar rod. 123

144 3 Experimental Program Figure 3-33 Dial Indiator for Shrinkage Tests Test Proedure For eah onrete mixture design, 6 prisms were ast. Three of them were 1-day heat ured while the rest were 7-day moist ured. The heat ured speimens were initially monitored on the first day whereas the moist ured speimens were initially monitored on the seventh day. The dial indiator system was initially alibrated and reset using the invar rod. The prismati shrinkage speimens were loated in the dial indiator system using the inserts at the ends of the speimen. Shrinkage of prisms was monitored at pre-determined intervals suh as everyday in the first few days. On eah monitoring day, the length hange of the speimens was measured and reorded three times. The average of these three readings was used for alulation purposes. The monitoring period was inreased to one month after three months. The speimens were monitored for approximately two years. 124

145 _ 4 Test Results and Disussions 4 TEST RESULTS AND DISCUSSIONS 4.1 General Test results presented in this hapter onsists of results from 21 eentri braket, 36 reep and 24 shrinkage test speimens to evaluate the flexural, reep and shrinkage behavior of HSC, respetively. 4.2 Flexural Behavior Eentri braket speimens were used to determine the stress-strain distribution of onrete with linear strain profile in the ompression zone and to determine the parameters of the retangular stress blok. Details of the test set-up and test method are presented in Setion 3.2. A total of 21 speimens were used to evaluate the flexural behavior of HSC. Five, six and ten speimens were tested for 10, 14 and 18 ksi target onrete ompressive strength, respetively. The onrete ompressive strengths of ylinders at the time of testing varied from 10.4 to 16 ksi. Speimens with 10 ksi target onrete ompressive strength were ast in two bathes. The first three speimens (10EB1 to 10EB3) were ast as the first bath whereas the rest of the speimens (10EB4 and 10EB5) were ast as the seond bath. Speimens with 18 ksi target onrete ompressive strength were also ast in two bathes. The first six speimens (18EB1 to 18EB6) were ast as the first bath and the rest of the speimens (18EB7 to 18EB10) were ast as the seond bath. Entire speimens with 14 ksi target onrete ompressive strength were ast in a single bath. The ages of speimens at testing day are given in Table 4-1. The average of three- or four- 4 8 in. onrete ylinders used to obtain the onrete ompressive strength at the time of testing of the speimens are tabulated in this table. Details about the ylinder ompression tests are presented in Appendix C. This table also shows the rate of loading in mirostrains per seond at the extreme ompression fae of eah speimen. 125

146 _ 4 Test Results and Disussions Table 4-1 Tabulated Test Results for Eentri Braket Speimens Speimen ID Age of Test Day f Test Day Average Loading Rate (µε µε/se) 10EB EB EB EB EB EB EB EB EB EB EB EB EB EB EB EB EB EB EB EB EB It was intended to apply the load at a rate of approximately 2 mirostrains per seond at the other extreme ompression fae of eah speimen However, 10EB1 was loaded inonsistently, sine the speimen was the first speimens to be tested and there were not enough experiene with the ontrolling unit of the ompression testing mahine. Other speimens were tested with a rate of loading reasonably lose to the intended rate General Observations for Eentri Braket Speimen Tests During the tests, no signifiant diffiulty was observed in the appliation of the main and the seondary load. The main load was applied at a onstant displaement rate throughout the testing. However, the rate of appliation of the seondary load varied depending on the onrete ompressive strength of the speimen. Furthermore, the rate of appliation of the seondary load was onstant when the behavior of the speimen was elasti; however, this rate inreased rapidly as the speimen got loser to failure. Similar behaviors were observed for all the speimens regardless of onrete ompressive strength. The eentri braket speimens showed an explosive failure of the ompression fae. Large piees of onrete exploded towards the surrounding area of the testing 126

147 _ 4 Test Results and Disussions mahine. After examining the test speimens in details, it was observed that the failure surfae was passing through the aggregates indiating the ement paste and the interfae between the ement paste and aggregate were stronger than the aggregate itself. LVDT measurements for all the test speimens did not show any signifiant hange at the outer fae whih is intended to be the position of the neutral axis. However, these measurements were inorporated in the alulation of the lever arms of the main and the seondary loads for alulation purposes. Failure modes of entire eentri braket speimens are shown in Figure 4-1 to Figure Figure 4-1 Failure Mode of 10EB1 Figure 4-2 Failure Mode of 10EB2 127

148 _ 4 Test Results and Disussions Figure 4-3 Failure Mode of 10EB3 Figure 4-4 Failure Mode of 10EB4 Figure 4-5 Failure Mode of 10EB5 128

149 _ 4 Test Results and Disussions Figure 4-6 Failure Mode of 14EB1 Figure 4-7 Failure Mode of 14EB2 Figure 4-8 Failure Mode of 14EB3 129

150 _ 4 Test Results and Disussions Figure 4-9 Failure Mode of 14EB4 Figure 4-10 Failure Mode of 14EB5 Figure 4-11 Failure Mode of 14EB6 130

151 _ 4 Test Results and Disussions Figure 4-12 Failure Mode of 18EB1 Figure 4-13 Failure Mode of 18EB2 Figure 4-14 Failure Mode of 18EB3 131

152 _ 4 Test Results and Disussions Figure 4-15 Failure Mode of 18EB4 Figure 4-16 Failure Mode of 18EB5 Figure 4-17 Failure Mode of 18EB6 132

153 _ 4 Test Results and Disussions Figure 4-18 Failure Mode of 18EB7 Figure 4-19 Failure Mode of 18EB8 Figure 4-20 Failure Mode of 18EB9 133

154 _ 4 Test Results and Disussions Figure 4-21 Failure Mode of 18EB10 The detailed views of speimen 18EB6 are shown in Figure 4-22 and Figure Similar behaviors were observed for other eentri braket speimens. Figure 4-22 Detailed Views of Speimen 18EB6 134

155 _ 4 Test Results and Disussions Figure 4-23 Detailed Views of Speimen 18EB Surfae Strain Measurements During eah test, the strain gages on all the surfaes were ontinuously monitored up to failure. The surfae strain measurements versus applied main axial load of speimen 18EB4 are shown in Figure Similar behaviors were observed for other eentri braket speimens. 135

156 _ 4 Test Results and Disussions Neutral Fae Strains Side Strains Side Strains Load (kips) Compression Fae Strains Stain (µε µε) Figure 4-24 Surfae Strain Measurements vs. Applied Main Axial Load (18EB4) The surfae strain measurements at different loading stages of Speimen 18EB#2 are shown in Figure Eah bold point in the graph shows surfae strain measurement at speifi load level. The line onneting the points presents the measurements at the same load level. The graph proves the assumption that plane setions remain plane after deformation is valid for HSC. 136

157 _ 4 Test Results and Disussions Conrete Strain (µε) Strain Gages Compression Fae Neutral Fae Centerline of the Test Region Figure 4-25 Strain Distribution on Side Fae of Speimen 18EB2 The average value of the two strain gages on the neutral and ompression faes were used in all of the alulations. The average eliminated the effet of any loading eentriity. No signifiant strain measurement was observed on the neutral fae of the speimen. The strain gage measurements were in the range of ±80 mirostrains Ultimate Compressive Strain of Conrete Ultimate ompressive strains of onrete measured from eentri braket speimens tested in this researh are tabulated in Table 4-2. These ultimate ompressive strain values obtained from this researh ombined with the data from the researhes in the literature are shown in Figure The researhes in the literature on ultimate ompressive strain of onrete an also be found in Figure Test results obtained from this researh are ompatible with the results in the literature. There is no signifiant trend of ultimate ompressive strain as onrete ompressive strength inreases. Furthermore, it an be onluded from the graph that the lower bound for ultimate onrete ompressive strain is independent of onrete ompressive strength. Test results obtained from this researh ombined with the data in the literature were used to propose an ultimate ompressive strain for HSC in flexure in Setion

158 _ 4 Test Results and Disussions Table 4-2 Tabulated Results for Ultimate ompressive strain of onrete Speimen ID f Test Day Ultimate Strain (µε µε) 10EB EB EB EB EB EB EB EB EB EB EB EB EB EB EB EB EB EB EB EB EB Ultimate Compressive Strain of Conrete (εu) Conrete Compressive Strength (ksi) Author's x Others' Figure 4-26 Ultimate Compressive Strain of Conrete Obtained from This Researh and Other Researhes in Literature 138

159 4.2.4 Poisson s Ratio _ 4 Test Results and Disussions Poisson s ratio was evaluated from the measured longitudinal ompressive strains and their orresponding lateral tensile strains in the eentri braket speimens. There were three strains gages on the ompression fae of all eentri braket speimens, two in the longitudinal and one in the transverse diretion. The measured strain obtained from transverse strain gage was divided by the average of the measured strains obtained from longitudinal strain gages to alulate Poisson s ratio for eah speimen. The ompression fae of an eentri braket speimen is shown in Figure a) General View b) Close-Up View Figure 4-27 Compression Fae of Eentri Braket Speimen The alulated Poisson s ratios using surfae strain measurements obtained from eentri brakets are tabulated in Table 4-3. Note that no result was shown for speimen 10EB1 due to some ompliations ourred in the readings of the transverse strain gage. Table 4-3 Tabulated Results for Poisson s Ratio 139

160 _ 4 Test Results and Disussions Speimen ID f Test Day Poisson s Ratio Speimen ID f Test Day Poisson s Ratio 10EB EB EB EB EB EB EB EB EB EB EB EB EB EB EB EB EB EB EB EB Poisson s ratios vs. longitudinal ompressive strain for eentri braket speimens with 10, 14 and 18 ksi target onrete ompressive strengths are shown in Figure 4-28 to Figure 4-30, respetively. The limits for the average ompression fae strain in these figures ranges from 200 to 1400 mirostrains. The data below 200 mirostrains showed a lot of flutuations sine the measurements were too small to ompare. The data over 1400 mirostrains exhibited high Poisson s ratios sine the readings from the transverse strain gage inluded the effets resulting from the miro raks. The miro raks inreased the readings of transverse strain gage produing unrealisti measurements for Poisson s ratio suh as 0.5 and over. 140

161 _ 4 Test Results and Disussions Poisson's Ratio EB4 10EB3 10EB2 10EB Compressive Strain at the Extreme Compression Fiber (µε µε) Figure 4-28 Poisson s Ratio for Eentri Braket Speimens with 10 ksi Target Conrete Compressive Strength Poisson's Ratio EB5 14EB6 14EB1 14EB2 14EB3 14EB Compressive Strain at the Extreme Compression Fiber (µε µε) Figure 4-29 Poisson s Ratio for Eentri Braket Speimens with 14 ksi Target Conrete Compressive Strength 141

162 _ 4 Test Results and Disussions Poisson's Ratio EB5 18EB8 18EB7 18EB2 18EB10 18EB3 18EB6 18EB1 18EB EB Compressive Strain at the Extreme Compression Fiber (µε µε) Figure 4-30 Poisson s Ratio for Eentri Braket Speimens with 18 ksi Target Conrete Compressive Strength Poisson s ratio values obtained from this researh ombined with the data from the researhes in the literature are shown in Figure The researhes in the literature on Poisson s ratio an also be found in Figure There is no apparent trend in Poisson s ratio as onrete ompressive strength inreases. Furthermore, the graph indiates that Poisson s ratio is independent of onrete ompressive strength. Test results obtained from this researh ombined with the data in the literature were used to propose a Poisson s ratio for HSC in Setion

163 _ 4 Test Results and Disussions Author's x Others' 0.30 Poisson's Ratio Conrete Compressive Strength (ksi) Figure 4-31 Poisson s Ratio Obtained from This Researh and Other Researhes in Literature Stress-Strain Distribution of Compression Zones The approah presented by Hognestad et al. (1955) was used to determine the stress-strain relationship for eah speimen. This approah assisted to alulate the onrete stress, f, as a funtion of measured strain at the most ompressed fiber, ε, and the applied stresses f o and m o. The following equations were obtained from equilibrium of external and internal loads and moments. Note that the eentriities due to defletion of the member were also onsidered in the alulation of applied moment, M. 143

164 _ 4 Test Results and Disussions Figure 4-32 Applied Fores on Eentri Braket Speimens b C = P1 + P2 = f b = σ ( ε ) dε Equation 4-1 o ε ε 0 2 ε 2 b o σ 2 ( ε x ) ε x ε x ε 0 x x M = Pa + P a = m b = d Equation 4-2 where, C is the total applied load, M is the total applied moment, P 1 is the main axial load, P 2 is the seondary load, a 1 and a 2 are the eentriities, b is the width of the setion, is the depth of neutral axis, P P = Equation 4-3 b f o and P a + P a m o b = Equation are the applied stresses. Some of these definitions are presented in Figure A

165 _ 4 Test Results and Disussions Differentiating the last terms of the equations for C and M with respet to would ε would yield the following equations. df o σ = ε + f o Equation 4-5 dε dm o σ = ε + 2mo Equation 4-6 dε Using these equations, two similar stress-strain relationships were obtained for eah eentri braket speimens as shown in Figure The average of these two relationships was used as the average stress-strain relationship of that speimen as shown in Figure Conrete Compressive Stress, f (ksi) Calulated from f o Calulated from m o Conrete Compressive Strain (µε µε) Figure 4-33 Two Similar Stress-Strain Relationships (18EB4) 145

166 _ 4 Test Results and Disussions 20 Conrete Compressive Stress, f (ksi) Average Stress-Strain Relationship Conrete Compressive Strain (µε µε) Figure 4-34 Average Stress-Strain Relationship (18EB4) The average stress-strain relationships of the speimens with 10, 14 and 18 ksi target onrete ompressive strengths are shown in Figure 4-35 to Figure The numerial values of the simplified stress-strain relationships for all the speimens are given in Appendix F. The stress-strain relationships obtained from this researh indiate that as onrete ompressive strength inreases, the strain at the peak stress inreases and gets loser to The shape of the asending branh of the stress-strain relationship beomes more linear and steeper, and the slope of the desending part also beomes steeper. It an be onluded that the desending branh of the stress-strain relationship for HSC is so hard to apture sine, after peak stress, HSC fails suddenly with an explosive manner. The stress-strain relationships obtained from this researh were used to propose and validate an analytial stress-strain relationship for HSC in Setion

167 _ 4 Test Results and Disussions 20 Conrete Compressive Stress (ksi) EB5 10EB2 10EB3 10EB4 10EB Conrete Compressive Strain (µε µε) Figure 4-35 Stress-Strain Relationships for Speimens with 10 ksi Target Conrete Compressive Strength Conrete Compressive Stress (ksi) EB5 14EB6 14EB3 14EB2 14EB4 14EB Conrete Compressive Strain (µε µε) Figure 4-36 Stress-Strain Relationships for Speimens with 14 ksi Target Conrete Compressive Strength 147

168 _ 4 Test Results and Disussions 20 Conrete Compressive Stress (ksi) EB7 18EB1 18EB3 18EB8 18EB9 18EB5 18EB6 18EB10 18EB4 18EB Conrete Compressive Strain (µε µε) Figure 4-37 Stress-Strain Relationships for Speimens with 18 ksi Target Conrete Compressive Strength Stress Blok Parameters Stress-strain relationships obtained from eentri braket speimens were used to alulate the generalized and retangular stress blok parameters for HSC. Details of this alulation are given in Setion These parameters for onrete ompressive strengths ranging from 10.4 to 16 ksi are tabulated in Table

169 _ 4 Test Results and Disussions Table 4-4 Calulated Stress Blok Parameters for Eentri Braket Speimens Speimen f (ksi) Test Day k 1 k 2 k 3 α 1 β 1 10EB EB EB EB EB EB EB EB EB EB EB EB EB EB EB EB EB EB EB EB EB These stress blok parameters obtained from this researh ombined with the data from the researhes in the literature are shown in Figure 4-38 to Figure The researhes in the literature on stress blok parameters an be found in Figure 2-16 to Figure k Author's x Others' Conrete Compressive Strength (ksi) Figure 4-38 k 1 Values Obtained from This Researh and Other Researhes in Literature 149

170 _ 4 Test Results and Disussions Author's x Others' 0.8 k Conrete Compressive Strength (ksi) Figure 4-39 k 2 Values Obtained from This Researh and Other Researhes in Literature k Author's x Others' Conrete Compressive Strength (ksi) Figure 4-40 k 3 Values Obtained from This Researh and Other Researhes in Literature 150

171 _ 4 Test Results and Disussions Author's x Others' 0.8 k 1 k Conrete Compressive Strength (ksi) Figure 4-41 k 1 k 3 Values Obtained from This Researh and Other Researhes in Literature α Author's x Others' Conrete Compressive Strength (ksi) Figure 4-42 α 1 Values Obtained from This Researh and Other Researhes in Literature 151

172 _ 4 Test Results and Disussions β Author's x Others' Conrete Compressive Strength (ksi) Figure 4-43 β 1 Values Obtained from This Researh and Other Researhes in Literature Author's x Others' 0.8 α1β Conrete Compressive Strength (ksi) Figure 4-44 α 1 β 1 Values Obtained from This Researh and Other Researhes in Literature 152

173 _ 4 Test Results and Disussions Test results indiate that the generalized stress blok parameter k 1 is rarely less than 0.58 when onrete ompressive strengths varied between 10 and 18 ksi. The generalized stress blok parameter k 2 is found to be ompatible with the tests results in literature. The generalized stress blok parameter k 3 for HSC is determined to be similar to NSC. It an be onluded that as onrete ompressive strength inreases over 10 ksi, the retangular stress blok parameters α 1 dereased. However, the retangular stress blok parameters β 1 does not seem to be affeted for variations in the onrete strength over 10 ksi. 153

174 _ 4 Test Results and Disussions 4.3 Creep Behavior A total of (36) 4 8 in. ylindrial speimens were used to evaluate the reep behavior of HSC. Speimens of eah target onrete strength were ast in one bath. Twelve ylinders were loaded in 6 reep raks for 10, 14 and 18 ksi target onrete ompressive strengths. The onrete ompressive strengths of 4 8 in. ylinders at 28 days varied from 10.4 to 16.7 ksi. Test set-up and test method are presented in Setion 3.3. Details about the reep tests are given in Table 4-5. Table 4-5 Details about Creep Tests Rak No Target Conrete Compressive Strength (ksi) Curing Type Conrete Compressive 28 days (ksi) Day of Loading (days) Conrete Compressive Day of Loading (ksi) 10Rak1 1-Day Heat Rak Rak Rak4 7-Day Moist Rak Rak Rak1 1-Day Heat Rak Rak Rak4 7-Day Moist Rak Rak Rak1 1-Day Heat Rak Rak Rak4 7-Day Moist Rak Rak Applied Stress (ksi) The measured shrinkage strain of the ylindrial shrinkage speimens with 10, 14 and 18 ksi target onrete ompressive strengths are given in Appendix G. To alulate the reep strain, these shrinkage strains were deduted from the total measured strain of the loaded reep speimens. Average reep strains of speimens with 10, 14 and 18 ksi target onrete ompressive strengths are shown in Figure 4-45 to Figure 4-47 and tabulated in Appendix G. Average speifi reep strains, defined as reep strain per ksi, for all the reep speimens are presented in Figure 4-48 to Figure 4-50 and tabulated in Appendix G. 154

175 _ 4 Test Results and Disussions The average reep oeffiients, defined as the ratios between the reep deformations at time t and the instantaneous elasti ones are also shown in Figure 4-51 to Figure 4-53 and presented in Appendix G Rak Average Creep Strain (µε µε) Rak5 10Rak2 10Rak6 10Rak Rak Age of Speimen after Casting (days) Figure 4-45 Average Creep Strains of Speimens with 10 ksi Target Conrete Compressive Strength 155

176 _ 4 Test Results and Disussions Rak4 Average Creep Strain (µε µε) Rak5 14Rak1 14Rak Rak3 14Rak Age of Speimen after Casting (days) Figure 4-46 Average Creep Strains of Speimens with 14 ksi Target Conrete Compressive Strength Rak4 Average Creep Strain (µε µε) Rak5 18Rak1 18Rak2 18Rak Rak Age of Speimen after Casting (days) Figure 4-47 Average Creep Strains of Speimens with 18 ksi Target Conrete Compressive Strength 156

177 _ 4 Test Results and Disussions Rak4 Average Speifi Creep (µε µε/ksi) Rak1 10Rak2 10Rak5 10Rak3 10Rak Age of Speimen after Casting (days) Figure 4-48 Average Speifi Creep Strains of Speimens with 10 ksi Target Conrete Compressive Strength 0.25 Average Speifi Creep (µε / ksi) Rak4 14Rak3 14Rak1 14Rak6 14Rak2 14Rak Age of Speimen after Casting (days) Figure 4-49 Average Speifi Creep Strains of Speimens with 14 ksi Target Conrete Compressive Strength 157

178 _ 4 Test Results and Disussions Rak4 Average Speifi Creep (µε µε/psi) Rak1 18Rak6 18Rak3 18Rak5 18Rak Age of Speimen after Casting (days) Figure 4-50 Average Speifi Creep Strains of Speimens with 18 ksi Target Conrete Compressive Strength Rak4 Average Creep Coeffiient Rak2 10Rak1 10Rak3 10Rak5 10Rak Age of Speimen after Casting (days) Figure 4-51 Average Creep Coeffiients of Speimens with 10 ksi Target Conrete Compressive Strength 158

179 _ 4 Test Results and Disussions 1.20 Average Creep Coeffiient Rak4 14Rak3 14Rak1 14Rak6 14Rak2 14Rak Age of Speimen after Casting (days) Figure 4-52 Average Creep Coeffiients of Speimens with 14 ksi Target Conrete Compressive Strength Rak4 Average Creep Coeffiient Rak1 18Rak6 18Rak3 18Rak2 18Rak Age of Speimen after Casting (days) Figure 4-53 Average Creep Coeffiients of Speimens with 18 ksi Target Conrete Compressive Strength 159

180 _ 4 Test Results and Disussions The temperature and humidity of the ambient air where the reep speimens were loaded varied during the experimental program. The variations in temperature and humidity are given in Figure Although the temperature during the experimental program was fairly onstant, the variation in the humidity of the environment was quite signifiant. Temperature ( F) ksi Target Strength Speimens were ast. 14 ksi Target Strength Speimens were ast. 18 ksi Target Strength Speimens were ast. on 3/18/ Time (Date) Temperature Humidity Humidity (%) Figure 4-54 Variations in Temperature and Humidity for Creep and Shrinkage Speimens To aount for effets of the variation in humidity on the reep behavior of HSC, the average reep oeffiients were adjusted aordingly. The proedure used to alulate the adjusted average reep oeffiients for eah rak is given as follows: 1. Sine eah rak onsists of two ylindrial reep speimens, the total strains of two ylinders were measured by using a deme gage (3 rd and 4 th olumn in Table 4-6). 2. The average of total strains was determined using the measured strains of two ylinders in eah rak (5 th olumn in Table 4-6). 3. The drying shrinkage of the ompanion ylindrial shrinkage speimen was measured by using a deme gage (6 th olumn in Table 4-6), and deduted from the total average strain to obtain the average reep strain of eah rak (7 th olumn in Table 4-6). 160

181 _ 4 Test Results and Disussions 4. The average reep oeffiient of the rak at a given time was obtained based on the ratio of the average of the measured reep strain of eah rak to the average initial elasti strain immediately after the ylinders were loaded (8 th olumn in Table 4-6). 5. The reep oeffiient for eah rak was divided by the relative humidity orretion fator (k h = 1.58 H/120) whih is speified by AASHTO LRFD Bridge Design Speifiations (2004) and Tadros et al. (2003). This orretion was performed inrementally, whih means that the differene between the two onsequent reep oeffiient values was divided by the fator and added to the previous adjusted reep oeffiient (9 th olumn in Table 4-6). A sample numerial illustration of this proedure for 18Rak2 is presented Table 4-6. Table 4-6 Numerial Illustration of the Calulation Proedure Col. 1 Col. 2 Col. 3 Col. 4 Col. 5 Col. 6 Col. 7 Col. 8 Col. 9 Age After Casting (days) Humidity (%) Total Strain of Speimen 1 (µε µε) Total Strain of Speimen 2 (µε µε) Average Total Strain of Rak #14 (µε µε) Drying Shrinkage Strain of the Companion Cylinder (µε µε) Average Creep Strain of Rak #14 (µε µε) Average Creep Coeffiient of Rak #14 Adjusted Average Creep Coeffiient of Rak # Note that, the average initial elasti strain for Rak #14 is µε. Using this proedure, the adjusted average reep oeffiients for eah rak were alulated as shown in Figure 4-55 to Figure

182 _ 4 Test Results and Disussions Rak4 Adjusted Average Creep Coeffiient Rak1 10Rak2 10Rak5 10Rak3 10Rak Time After Loading (days) Figure 4-55 Adjusted Average Creep Coeffiients of Speimens with 10 ksi Target Conrete Compressive Strength Rak1 Creep Coeffiient Rak4 14Rak5 14Rak Rak6 14Rak Time After Loading (days) Figure 4-56 Adjusted Average Creep Coeffiients of Speimens with 14 ksi Target Conrete Compressive Strength 162

183 _ 4 Test Results and Disussions Creep Coeffiient Rak4 18Rak1 18Rak2 18Rak Rak6 18Rak Time After Loading (days) Figure 4-57 Adjusted Average Creep Coeffiients of Speimens with 18 ksi Target Conrete Compressive Strength In general, test results indiate that as onrete gets mature and older, the reep of HSC dereases. The reep behavior of heat ured ylinders is less than that of the moist ured ylinders. Creep for HSC is proportional to the applied stress provided that the applied stress is less than the proportional limit. Test results obtained from this researh ombined with the data in the literature were used to propose a relationship to predit the reep oeffiient for HSC in Setion

184 _ 4 Test Results and Disussions 4.4 Shrinkage Behavior Six 4 12 in. ylindrial and eighteen ¼ in. prismati speimens were monitored to evaluate the shrinkage behavior of HSC. Speimens of eah target onrete strength were ast in one bath. The onrete ompressive strengths of 4 8 in. ylinders at 28 days varied from 10.4 to 16.7 ksi. Test set-up and test method are presented in Setion 3.4. Details about the ylindrial and prismati shrinkage speimens are given in Table 4-7 and Table 4-8, respetively. Speimen ID Table 4-7 Details about Cylindrial Shrinkage Speimens Target Conrete Compressive Strength (ksi) Curing Type Conrete Compressive 28 days (ksi) Day of Initial Monitoring Conrete Compressive Day of Initial Monitoring (ksi) 10SC1 1-Day Heat SC2 7-Day Moist SC1 1-Day Heat SC2 7-Day Moist SC Day Heat SC2 7-Day Moist Table 4-8 Details about Prismati Shrinkage Speimens Speimen ID 10SP1 10SP2 10SP3 10SP4 10SP5 10SP6 14SP1 14SP2 14SP3 14SP4 14SP5 14SP6 18SP1 18SP2 18SP3 18SP4 18SP5 18SP6 Target Conrete Compressive Strength (ksi) Curing Type 1-Day Heat 7-Day Moist 1-Day Heat 7-Day Moist 1-Day Heat 7-Day Moist Conrete Compressive 28 days (ksi) Day of Initial Monitoring Conrete Compressive Day of Initial Monitoring (ksi)

185 _ 4 Test Results and Disussions The measured shrinkage strains of ylindrial and prismati speimens with 10, 14 and 18 ksi target onrete ompressive strengths are shown in Figure 4-58 to Figure 4-63 and tabulated in Appendix G. Using the measured weights of the prismati speimens, the weight loss is alulated for prismati speimens with 10, 14 and 18 ksi target onrete ompressive strengths. The weight losses are also shown in Figure 4-64 to Figure 4-66 and tabulated in Appendix G SC2 Shrinkage Strain (µε µε) SC Age of Speimen after Casting (days) Figure 4-58 Shrinkage Strain of Cylindrial Speimens with 10 ksi Target Conrete Compressive Strength 165

186 _ 4 Test Results and Disussions SC2 Shrinkage Strain (µε µε) SC Age of Speimen after Casting (days) Figure 4-59 Shrinkage Strain of Cylindrial Speimens with 14 ksi Target Conrete Compressive Strength SC2 Shrinkage Strain (µε µε) SC Age of Speimen after Casting (days) Figure 4-60 Shrinkage Strain of Cylindrial Speimens with 18 ksi Target Conrete Compressive Strength 166

187 _ 4 Test Results and Disussions SP6 10SP4 Shrinkage Strain (µε µε) SP3 10SP1 10SP5 10SP Age of Speimen after Casting (days) Figure 4-61 Shrinkage Strain of Prismati Speimens with 10 ksi Target Conrete Compressive Strength SP6 14SP4 Shrinkage Strain (µε µε) SP5 14SP3 14SP SP Age of Speimen after Casting (days) Figure 4-62 Shrinkage Strain of Prismati Speimens with 14 ksi Target Conrete Compressive Strength 167

188 _ 4 Test Results and Disussions SP4 18SP3 Shrinkage Strain (µε µε) SP1 18SP6 18SP5 18SP Age of Speimen after Casting (days) Figure 4-63 Shrinkage Strain of Prismati Speimens with 18 ksi Target Conrete Compressive Strength SP6 10SP4 10SP5 Weight Loss (%) SP1 10SP2 10SP Age of Speimen after Casting (days) Figure 4-64 Weight Loss of Prismati Speimens with 10 ksi Target Conrete Compressive Strength 168

189 _ 4 Test Results and Disussions SP4 14SP6 14SP5 Weight Loss (%) SP3 14SP1 14SP Age of Speimen after Casting (days) Figure 4-65 Weight Loss of Prismati Speimens with 14 ksi Target Conrete Compressive Strength SP SP6 18SP5 Weight Loss (%) SP3 18SP2 18SP Age of Speimen after Casting (days) Figure 4-66 Weight Loss of Prismati Speimens with 18 ksi Target Conrete Compressive Strength 169

190 _ 4 Test Results and Disussions The temperature and humidity of the ambient air where the ylindrial and prismati shrinkage speimens were kept varied during the experimental program. The variations in temperature and humidity are given in Figure Although the temperature during the experimental program was fairly onstant, the variation in the humidity of the environment was quite signifiant. Sine the relative humidity of the ambient air varied throughout the testing period, the shrinkage strain was adjusted aordingly. The proedure used to alulate the adjusted shrinkage strain for eah speimen is given as follows: 1. The shrinkage strain of ylindrial and prism speimens were measured by using a deme gage and shrinkage testing apparatus, respetively. 2. The shrinkage strain for eah speimen was divided by the relative humidity orretion fator (k hs = (140-H)/70) whih is speified by AASHTO LRFD Bridge Design Speifiations (2004) and Tadros et al. (2003). This orretion was performed inrementally whih means that the differene between two onsequent shrinkage strains was divided by the fator and added to the previous adjusted shrinkage strain (same proedure illustrated to adjust the reep oeffiients in Setion 4.3 was used). 170

191 _ 4 Test Results and Disussions Shrinkage Strain (µε µε) SC1 10SC Time After Curing (days) Figure 4-67 Adjusted Shrinkage Strain of Cylindrial Speimens with 10 ksi Target Conrete Compressive Strength Shrinkage Strain (µε µε) SC SC Time After Curing (days) Figure 4-68 Adjusted Shrinkage Strain of Cylindrial Speimens with 14 ksi Target Conrete Compressive Strength 171

192 _ 4 Test Results and Disussions Shrinkage Strain (µε µε) SC1 18SC Time After Curing (days) Figure 4-69 Adjusted Shrinkage Strain of Cylindrial Speimens with 18 ksi Target Conrete Compressive Strength Shrinkage Strain (µε µε) SP5 10SP6 10SP4 10SP3 10SP SP Time After Curing (days) Figure 4-70 Adjusted Shrinkage Strain of Prismati Speimens with 10 ksi Target Conrete Compressive Strength 172

193 _ 4 Test Results and Disussions Shrinkage Strain (µε µε) SP6 14SP5 14SP4 14SP SP3 14SP Time After Curing (days) Figure 4-71 Adjusted Shrinkage Strain of Prismati Speimens with 14 ksi Target Conrete Compressive Strength SP4 Shrinkage Strain (µε µε) SP5 18SP SP1 18SP2 18SP Time After Curing (days) Figure 4-72 Adjusted Shrinkage Strain of Prismati Speimens with 18 ksi Target Conrete Compressive Strength 173

194 _ 4 Test Results and Disussions Test results of this researh on shrinkage of HSC indiate that heat ured speimens have less shrinkage ompared to moist ured speimens. There is little differene in shrinkage of HSC speimens with target onrete strengths of 10, 14 and 18 ksi. The average weight loss of the speimens is diretly proportional to shrinkage of HSC. Test results obtained from this researh ombined with the data in the literature were used to propose a relationship to predit the shrinkage strain for HSC in Setion

195 5 Analytial Work 5 ANALYTICAL WORK This setion provides ritial reviews of the researhes, test results, analyses, relationships and equations presented in Chapter 2. Based on the test results of this researh ombined with the data in the literature, either new relationships or urrently used relationships with some modifiations are proposed to define the harateristis of HSC for onrete ompressive strengths up to 18 ksi. The results of this researh ombined with the available data in the literature are used to reommend revisions for the AASHTO LRFD Bridge Design Speifiations (2004) to extend the urrent limitation of 10 ksi onrete ompressive strength up to 18 ksi. The proposed relationships are also validated and onfirmed for onrete ompressive strengths up to 18 ksi using statistial and parametri analyses. In general, there are four different types of loading onditions that at on the strutural members suh as: stati (short term) loading, sustained loading, fatigue loading and impat loading onditions. The disussions in this hapter are mainly onerned with stati loading ondition exept for reep and shrinkage disussions whih are based on sustained loading onditions. Note that, in ase of a beam subjeted to loads for a long time, the stress-strain relationship of onrete will be modified due to the time-dependent behavior of onrete, suh that, the desending branh of the stress-strain relationship may have no signifiane in the behavior of the strutural member. 5.1 Proposed Stress Blok Parameters and Ultimate Compressive Strain for HSC The researhes reported in the literature established some basi harateristi properties of HSC. In general, as onrete ompressive strength inreases, the strain at the peak stress inreases and gets loser to The shape of the asending branh of the stressstrain relationship beomes more linear and steeper, and the slope of the desending part also beomes steeper. The general shape of the stress-strain relationship beomes more likely to be a triangle. The stress-strain distribution of NSC an be generalized by the urved shape as shown in Figure 5-1. For this type of distribution, k 1 and k 2 are equal to 0.85 and 0.425, 175

196 5 Analytial Work respetively. When onverted to a retangular distribution, α 1 and β 1 orrespond to k 3 and 0.85, respetively. If the stress-strain distribution of HSC is assumed to be a triangular distribution, k 1 and k 2 are equal to 0.50 and 0.333, respetively. The retangular stress blok parameters, α 1 and β 1, for triangular distribution are 0.75k 3 and 0.667, respetively. These parameters are shown in Figure 5-1. k 3 f α 1 f k 3 f α 1 f k 2 k 2 β 1 β 1 k 1 = 0.85 k 2 = α 1 = k 3 β 1 = 0.85 k 1 = 0.50 k 2 = α 1 = 0.75k 3 β 1 = NSC Stress Distribution Triangular Stress Distribution k 1 = Shaded Area Area of Dotted Retangle T Figure 5-1 Stress Blok Parameters for Different Stress Distributions Based on the researhes in the literature, the retangular stress blok parameters also derease as the onrete ompressive strength inreases. But there is no agreement on the magnitude and the variation of this redution with respet to onrete ompressive strengths. Azizinamini (1994) proposed to redue the retangular stress blok parameter α 1, from 0.85 to 0.60 for onrete ompressive strengths varying from 10 to 15 ksi, repetively. Li (1993) reommended varying α 1, from 0.85 to 0.75 for onrete ompressive strengths varying from 8 to 11.6 ksi, repetively. Ibrahim (1994) suggested reduing α 1, from 0.85 to linearly for onrete ompressive strengths from 0 to 14.5 ksi, repetively. Bae and Bayrak (2003) redued α 1, from 0.85 to 0.67 for onrete ompressive strengths from 4.35 to 13.4 ksi, repetively. However for β 1, the redution 176

197 5 Analytial Work ours muh earlier than that of α 1. Mattok et al. (1961) proposed to derease β 1, from 0.85 to 0.65 for onrete ompressive strengths from 4 to 8 ksi, repetively. Rangan et al. (1999) suggested reduing β 1, from 0.85 to 0.65 for onrete ompressive strengths from 4.35 to 8 ksi, repetively. Details about the proposed retangular stress blok parameters an be found in Setion The test results of this researh and other researhes in the literature indiate that the majority of the olleted data for the generalized stress blok parameter k 1 for HSC is higher than 0.58 for onrete ompressive strengths ranging between 10 and 18 ksi as shown in Figure 5-2. Therefore, using the lower bound of 0.58 is suggested for k 1 parameter for onrete ompressive strengths beyond 15 ksi k Author's x Others' Proposed Relationship k 1 = Conrete Compressive Strength (ksi) Figure 5-2 Proposed Relationship for the Stress Blok Parameter k 1 The k 2 parameter in AASHTO LRFD Bridge Design Speifiations (2004) is already set to 0.33 for onrete ompressive strengths beyond 8 ksi, sine the assumed β 1 parameter used in design is equal to The test results of this researh and other researhes in the literature indiate that the stress blok parameter k 2 for HSC between 8 ksi and 18 ksi an be assumed to be 0.33 as shown in Figure

198 5 Analytial Work Author's x Others' 0.8 k Conrete Compressive Strength (ksi) Proposed Relationship k 2 = 0.33 for f' > 8 ksi Figure 5-3 Proposed Relationship for the Stress Blok Parameter k 2 The test results of this researh and other researhes in the literature indiate that the generalized stress blok parameter k 3 for HSC is similar to NSC as shown in Figure 5-4. Hene, using the same value of k 3 parameter, 0.85, for onrete ompressive strengths up to 18 ksi is found to be ompletely appropriate for design purposes. The omparison of the produt of the proposed k 1 and k 3 to the test results of this researh and other researhers in the literature are shown in Figure

199 5 Analytial Work k Proposed Relationship k 3 = Author's x Others' Conrete Compressive Strength (ksi) Figure 5-4 Proposed Relationship for the Stress Blok Parameter k Author's x Others' 0.8 k 1 k Proposed Relationship k 1 k 3 = Conrete Compressive Strength (ksi) Figure 5-5 Proposed Relationship for the Produt of Stress Blok Parameters k 1 k 3 179

200 5 Analytial Work Using the values proposed for the generalized stress blok parameters, the lower bound relationships for retangular stress blok parameters α 1 and β 1 an be obtained as follows; α k k = = = 2k Equation 5-1 β = 2k = Equation Based on the test results of this researh and other researhes literature, the ultimate onrete ompressive strain of is proposed to be used for design purposes for onrete ompressive strengths up to 18 ksi. The omparison of the proposed ultimate onrete ompressive strain to the test results of this researh and other researhes in literature is shown in Figure Ultimate Compressive Strain of Conrete (εu) Proposed Relationship ε u = Author's x Others' Conrete Compressive Strength (ksi) Figure 5-6 Proposed Relationship for Ultimate Conrete Compressive Strain, ε u In the light of the previous disussions, the following relationship is proposed for the retangular stress blok parameters, α 1 and β 1, for onrete ompressive strengths up to 18 ksi using the results of this researh and other researhers in the literature. 180

201 5 Analytial Work 0.85 for f ' 10ksi α1 = ( f ' 10) 0.75 for f ' > 10ksi 0.85 for f ' 4ksi β1 = ( f ' 4) 0.65 for f ' > 4ksi Equation 5-3 Equation 5-4 at ε = Equation 5-5 u Note that urrent retangular stress blok parameters speified by AASHTO LRFD Bridge Design Speifiations (2004) for onrete ompressive strengths below 10 ksi are not affeted by the proposed relationships sine these stress blok parameters have been used for more than half a entury for onrete ompressive strengths up to 10 ksi. The proposed relationship only redues α 1 from 0.85 to 0.75 for onrete ompressive strengths from 10 to 15 ksi. The omparisons of the proposed relationships and the produt of the relationships to the test results of this researh and other researhers in the literature are shown in Figure 5-7 to Figure α1 0.6 Proposed Relationship for α Author's x Others' Conrete Compressive Strength (ksi) Figure 5-7 Proposed Relationship for the Retangular Stress Blok Parameters α 1 181

202 5 Analytial Work β Proposed Relationship for β Author's x Others' Conrete Compressive Strength (ksi) Figure 5-8 Proposed Relationship for the Retangular Stress Blok Parameters β Author's x Others' 0.8 α1β Proposed Relationship for α 1 β Conrete Compressive Strength (ksi) Figure 5-9 Proposed Relationship for the Produt of Retangular Stress Blok Parameters α 1 β 1 182

203 5 Analytial Work Regression Analysis for Retangular Stress Blok Parameters and Ultimate Compressive Strain of Conrete Regression analysis is a statistial tehnique to determine the relationship between two or more variables. In this part of the researh, a simple linear regression analysis was used to model and investigate the relationship between the onrete ompressive strength and harateristis of HSC suh as the retangular stress blok parameters and the ultimate ompressive strain of onrete. The least square fitting method was used to establish these relationships for the tests results. Details and method about the regression analyses are presented in Appendix H. A total of 159 eentri braket speimen test results with onrete ompressive strengths up to 20 ksi were investigated using regression analysis tehnique to develop the relationship between the retangular stress blok parameters, α 1 and β 1 and onrete ompressive strength, f. The olleted data onsists of test results obtained by Hognestad et al. (1955), Nedderman (1973), Kaar et al. (1978a, 1978b), Swartz et al. (1985), Pastor (1986), Shade (1992), Ibrahim (1994), Tan and Nguyen (2005) and this researh. Sixty nine of the test results have onrete ompressive strengths below 10 ksi. The onrete ompressive strengths of other test results are above 10 ksi. The data was analyzed for three different onrete ompressive strength ranges: below 10 ksi to evaluate the results for NSC, over 10 ksi to evaluate the results for HSC and up to 20 ksi to ombine the results to evaluate for NSC and HSC. The tabulated results of the regression analysis for retangular stress blok parameters are presented in Table 5-1. Note that the values given in this table are for 50 perent regression lines orresponding to the medians of the test results. The regression analysis graphs of retangular stress blok parameters for three onrete ompressive strength ranges are shown in Figure 5-10 to Figure These graphs inlude the 50 perent regression lines, 90 perent regression lines orresponding to the lower bounds of the 90 perent of the test results and the proposed relationship in this researh (Setion 5.1) for the retangular stress blok parameters. 183

204 5 Analytial Work Table 5-1 Tabulated Results of the Regression Analysis for the Retangular Stress Blok Parameters Conrete Regression Line for α 1 Regression Line for β 1 Compressive Strength Range (ksi) Slope (a) Interept (b) Standard Deviation Slope () Interept (d) Standard Deviation Regression Line (50%) 0.80 α Regression Line (90%) Proposed Relationship (62%) 0.20 Author's x Others' Conrete Compressive Strength (ksi) Figure 5-10 Regression Analysis of α 1 for Conrete Compressive Strengths up to 20 ksi 184

205 5 Analytial Work Regression Line (50%) 0.80 α Regression Line (90%) Proposed Relationship and AASHTO LRFD (2004) (55%) 0.20 x Others' Conrete Compressive Strength (ksi) Figure 5-11 Regression Analysis of α 1 for Conrete Compressive Strengths below 10 ksi Regression Line (50%) 0.80 α Regression Line (90%) Proposed Relationship (68%) 0.20 Author's x Others' Conrete Compressive Strength (ksi) Figure 5-12 Regression Analysis of α 1 for Conrete Compressive Strengths over 10 ksi 185

206 5 Analytial Work Regression Line (50%) 0.80 β Regression Line (90%) Proposed Relationship (99%) 0.20 Author's x Others' Conrete Compressive Strength (ksi) Figure 5-13 Regression Analysis of β 1 for Conrete Compressive Strengths up to 20 ksi Regression Line (50%) 0.80 β x Others' Regression Line (90%) Proposed Relationship and AASHTO LRFD (2004) (99%) Conrete Compressive Strength (ksi) Figure 5-14 Regression Analysis of β 1 for Conrete Compressive Strengths below 10 ksi 186

207 5 Analytial Work Regression Line (50%) 0.80 β Regression Line (90%) Proposed Relationship (99%) 0.20 Author's x Others' Conrete Compressive Strength (ksi) Figure 5-15 Regression Analysis of β 1 for Conrete Compressive Strengths over 10 ksi The standard deviations of the retangular stress blok parameter, α 1, for all three onrete ompressive strength ranges (below 10 ksi, over 10 ksi and up to 20 ksi) are very lose to eah other whih indiate that the variability of the α 1 is same for all three ranges. The slope of the regression analysis of test results for α 1 for onrete ompressive strengths below 10 ksi is greater than that of test results for onrete ompressive strengths over 10 ksi. The results indiate that the proposed relationship for α 1 would seem appropriate for onrete ompressive strengths up to 18 ksi. The standard deviations of the retangular stress blok parameter, β 1, show more variation for onrete ompressive strengths below 10 ksi ompared to that of over 10 ksi. Also, the slope of the regression analysis of test results for β 1 for onrete ompressive strengths below 10 ksi is greater than that of test results for onrete ompressive strengths over 10 ksi. When the test results for onrete ompressive strength over 10 ksi are onsidered, the 90 perent regression line for β 1 beomes almost idential with the proposed equation for HSC. The results indiate that the proposed relationship for β 1 would seem appropriate for onrete ompressive strengths up to 18 ksi. 187

208 5 Analytial Work A total of 188 test results with onrete ompressive strengths up to 20 ksi under eentri loading were investigated using regression analysis tehnique to develop the relationship between the ultimate ompressive strain of onrete, ε u, and onrete ompressive strength, f. The olleted data onsists of test results obtained by Hognestad (1951), Sargin (1971), Nedderman (1973), Kaar et al. (1978a, 1978b), Swartz et al. (1985), Pastor (1986), Shade (1992), Ibrahim (1994), Tan and Nguyen (2005) and this researh. Hundred and two of the test results have onrete ompressive strengths below 10 ksi. The onrete ompressive strengths of other test results are over 10 ksi. The data was analyzed for three different onrete ompressive strength ranges: below 10 ksi to evaluate the results for NSC, over 10 ksi to evaluate the results for HSC and up to 20 ksi to ombine the results to evaluate for NSC and HSC. The tabulated results of the regression analysis for retangular stress blok parameters are presented in Table 5-2. Note that the values given in this table are for 50 perent regression lines orresponding to the medians of the test results. The regression analysis graphs of ultimate ompressive strain of onrete for three onrete ompressive strength ranges are shown in Figure 5-16 to Figure These graphs inlude the 50 perent regression lines, 90 perent regression lines orresponding to the lower bounds of the 90 perent of the test results and the proposed relationship in this researh (Setion 5.1) for ultimate ompressive strain of onrete. Table 5-2 Tabulated Results of the Regression Analysis for Ultimate Compressive Strain of Conrete Conrete Regression Line for ε u Compressive Strength Range (ksi) Slope (e) Interept (g) Standard Deviation E E E

209 5 Analytial Work Ultimate Compressive Strain of Conrete (εu) Proposed Relationship (85%) Regression Line (50%) Regression Line (90%) Conrete Compressive Strength (ksi) Author's x Others' Figure 5-16 Regression Analysis of ε u for Conrete Compressive Strengths up to 20 ksi Ultimate Compressive Strain of Conrete (εu) Proposed Relationship and AASHTO LRFD (2004) (82%) Regression Line (90%) Conrete Compressive Strength (ksi) Regression Line (50%) x Others' Figure 5-17 Regression Analysis of ε u for Conrete Compressive Strengths below 10 ksi 189

210 5 Analytial Work Ultimate Compressive Strain of Conrete (εu) Regression Line (90%) Proposed Relationship (88%) Conrete Compressive Strength (ksi) Regression Line (50%) Author's x Others' Figure 5-18 Regression Analysis of ε u for Conrete Compressive Strengths over 10 ksi The standard deviations of the ultimate ompressive strain of onrete, ε u, show more variation for onrete ompressive strengths below 10 ksi ompared to that of over 10 ksi. Also the slope of the regression analysis of test results for ε u for onrete ompressive strengths below 10 ksi is greater than that of for onrete ompressive strengths over 10 ksi. When only the test results for onrete ompressive strength over 10 ksi are onsidered, the 90 perent regression line for ε u beomes very lose to the proposed relationship for HSC. These results indiate that the proposed equation for ε u would seem appropriate for onrete ompressive strengths up to 18 ksi Sensitivity Analysis for Retangular Stress Blok Parameters and Ultimate Compressive Strain of Conrete The sensitivity analysis is a proedure to determine the sensitivity of the result to the hanges in its variables. If a small hange in a variable provides relatively large hanges in the results, the results an be defined to be sensitive to that variable. A sensitivity analysis was performed to evaluate the sensitivity of the ultimate moment apaity of a reinfored onrete member to the retangular stress blok parameters, α 1 and β 1, and 190

211 5 Analytial Work ultimate ompressive strain of onrete, ε u. The analyses were performed for underreinfored and over-reinfored onrete setions. For an under-reinfored onrete setion, yielding of longitudinal reinforement ours before rushing of onrete. For an over-reinfored onrete setion, rushing of onrete ours before yielding of longitudinal reinforement. Note that for a balaned reinfored onrete setion, rushing of onrete and yielding of longitudinal reinforement our simultaneously. The summary of the sensitivity analyses are shown in Table 5-3. The graphial presentations of the sensitivity analyses are shown in Figure 5-19 to Figure The results of the sensitivity analysis for flexural under-reinfored onrete setions indiate that the hange in the retangular stress blok parameters and the ultimate ompressive strain of onrete have very little or no effet on the ultimate moment apaity of the setion. On the other hand the results of the sensitivity analysis for the flexural overreinfored onrete setions indiate that the hange in the retangular stress blok parameters affets the ultimate moment apaity of the setions signifiantly. However, the hange in the ultimate ompressive strain of onrete has very little effet on the ultimate moment apaity of the setion for flexural over-reinfored setions. Table 5-3 Summary of the Sensitivity Analysis Setion Type Under- Reinfored Over- Reinfored Redution in α 1 by 11.8% leads to ( ) 1.9% redution in the Ultimate Moment Capaity 10.3% redution in the Ultimate Moment Capaity Redution in β 1 by 23.5% leads to ( ) No redution in the Ultimate Moment Capaity 12.2% redution in the Ultimate Moment Capaity Redution in ε u by 16.7% leads to ( ) No redution in the Ultimate Moment Capaity 2.6% redution in the Ultimate Moment Capaity 191

212 5 Analytial Work Ratio of Ultimate Moment Capatiy β 1 = 0.65 ε u = Balaned Setion (/d=0.6) (9.4% Redution) Under-Reinfored Setion (/d=0.375) (1.9% Redution) Over-Reinfored Setion (/d=0.75) (10.3% Redution) % Redution in α α 1 Figure Ratio of Ultimate Moment Capaity versus Change in α 1 Ratio of Ultimate Moment Capatiy α 1 = 0.85 ε u = Over-Reinfored Setion (/d=0.75) (12.2% Redution) Under-Reinfored Setion (/d=0.375) (No Redution) Balaned Setion (/d=0.6) (12.7% Redution) % Redution in β β 1 Figure Ratio of Ultimate Moment Capaity versus Change in β 1 192

213 5 Analytial Work Ratio of Ultimate Moment Capatiy α 1 = 0.85 β 1 = 0.65 Over-Reinfored Setion (/d=0.75) (2.6% Redution) Under-Reinfored Setion (/d=0.375) (No Redution) Balaned Setion (/d=0.6) (4.0% Redution) 16.7% Redution in ε u ε u Figure Ratio of Ultimate Moment Capaity versus Change in ε u 5.2 Proposed Stress-Strain Relationship for HSC For many years, numerous researhers have investigated the stress-strain relationship of onrete. Various researhers proposed different relationships with ompiated equations and oeffiients. Some researhers suggested two different equations to simulate the asending and the desending parts of the relationship suh as Hognestad (1951), CEB- FIB Model Code (1990), Muguruma (1991) and Van Gysel and Taerwe (1996). Several researhers predited both the asending and the desending parts of the stress-strain relationship using only one equation suh as a parabola or a urved shape (Sargin and Handa (1969), Popovis (1973), Thorenfeldt et al. (1987), Collins and Porasz (1989) and Attard and Setunge 1996). For the purpose of this researh, only one relationship that haraterizes both the assending and the desending branhes of stress-strain relationship of HSC was evaluated for omparison purposes. The simplest equation was seleted sine ompliated equations for stress-strain relationships are not preferred by design engineers. Adapting those ompliated relationships into design softwares is a signifiantly diffiult proess. 193

214 5 Analytial Work The following stress-strain relationship originally proposed by Popovis (1973) and modified by Thorenfeldt et al. (1987) was found to be the most suitable relationship to define the test results of the eentri braket speimens tested in this researh. f ε n = f ' εo n 1+ ( ε εo ) nk Equation 5-6 where f is the stress in general, f is the maximum onrete stress, ε is the strain in general, ε o is the strain at maximum stress and n and k is the oeffiients for onrete behavior. Note that, this relationship onsists of only one equation that haraterizes both the assending and the desending branhes of stress-strain relationship of HSC. As disussed earlier, using the stress-strain relationships, only the generalized stress blok parameters, k 1 and k 2, an be obtained where k 1 is defined as the ratio of the average ompressive stress to the maximum ompressive stress and k 2 is the ratio of the depth of the resultant ompressive fore to the depth of neutral axis. The atual values of these parameters, k 1 and k 2, were alulated for eah of the eentri braket speimens and ompared to that of obtained from the proposed stress-strain relationship shown in Equation 5-6. The ratios of the alulated and atual parameters were used to determine the equations for the parameters n and k by minimizing the deviations of these ratios from 1. Note that when this ratio is equal to 1, the proposed relationship perfetly mathes the atual stress-strain relationship. Atual values of maximum stress, strain at maximum stress and ultimate ompressive strain of the stress-strain relationships of onrete obtained from eentri braket speimens were used in these alulations. Based on the test results of this researh, the following equations produing the minimum deviations from 1 are suggested for the parameters n and k: n = 0.31 f ' ( f ' in ksi) Equation 5-7 k = 0.10 f ' ( f ' in ksi) Equation 5-8 The summary of the atual strain at maximum stress (ε o ) and atual ultimate ompressive strain of onrete (ε u ) are shown in Table 5-4. This table also ontains the alulated 194

215 5 Analytial Work parameters (k 1al, k 2al ) obtained from the proposed stress-stess relationship using the proposed n and k and the atual ε o and ε u in omparison to atual parameters (k 1EBS, k 2EBS ) obtained from the eentri braket speimens tested in this researh. The omparison of the ratios of the alulated to atual values of the stress blok parameters k 1 and k 2 are also shown in Figure The stress-stain relationships obtained in this researh are presented in Appendix F. Sample omparisons of the alulated and the atual stress-strain relationships for eentri braket speimens with 10, 14 and 18 ksi target onrete strength are shown in Figure 5-23 to Figure Speimen ID Table 5-4 Conrete Strain Obtained from Stress-Strain Relationships Maximum Stress, f (ksi) Atual Strain at Maximum Stress, ε o Atual Ultimate Strain, ε u (µε µε) k k 1al 1EBS k k 2al 2EBS k k 1al 1 1EBS 2 k k 1al 1 (µε µε) 10EB EB EB EB EB EB EB EB EB EB EB EB EB EB EB EB EB EB EB EB EB Deviation from 1 ( k 1 k 21 al EBS 2 ) 1EBS

216 5 Analytial Work 1.4 Ratio of Calulated Values to Atual Values Ratio of k o Ratio of k Maximum Conrete Stress (ksi) Figure 5-22 Comparison of the Ratio of Calulated and Atual Values using Atual Values for ε o and ε u 16 Conrete Compressive Stress (ksi) Calulated using Proposed Equation 10EB Conrete Compressive Strain (µε µε) Figure 5-23 Comparison of Calulated and Atual Stress-Strain Relation of 10EB3 196

217 5 Analytial Work Conrete Compressive Stress (ksi) Calulated using Proposed Equation 14EB Conrete Compressive Strain (µε µε) Figure 5-24 Comparison of Calulated and Atual Stress-Strain Relation of 14EB1 Conrete Compressive Stress (ksi) Calulated using Proposed Equation 18EB Conrete Compressive Strain (µε µε) Figure 5-25 Comparison of Calulated and Atual Stress-Strain Relation of 18EB10 197

218 5 Analytial Work Note that, Collins and Porasz (1989) also proposed n and k relationships based on their researh for this stress-strain relationship. The ratios of the alulated parameters obtained from this stress-stess relationship using n and k proposed by Collins and Porasz (1989) and the atual ε o and ε u in omparison to atual parameters obtained from the eentri braket speimens tested in this researh are also evaluated for omparison purposes. The deviations of alulated to atual ratios of k 1 and k 2 from 1 were alulated as and , respetively. The omparison of deviations shows that the proposed relationships for n and k in this researh provide better preditions for the test results of this researh. A regression analysis was performed on the results shown in Table 5-4 to propose relationships for ultimate ompressive strain and strain at maximum stress. The following relationships are suggested as the best fit linear approximation to the test data obtained in this researh. These equations are shown in Figure 5-26 and Figure ε ε 5 o = f ' 10 ( ' 5 u = f ' 10 ( ' f in ksi) Equation 5-9 f in ksi) Equation Conrete Strain at Maximum Stress, εo Proposed Relationship for ε o Maximum Conrete Stress (ksi) 198

219 5 Analytial Work Figure 5-26 Strain at Maximum Stress versus Conrete Maximum Stress Ultimate Conrete Strain, εu Proposed Relationship for ε u Maximum Conrete Stress (ksi) Figure 5-27 Ultimate ompressive strain of onrete versus Conrete Maximum Stress The summary of the numerial data for the proposed equations for strain at maximum stress (ε o ) and ultimate strain (ε u ) are shown in Table 5-5. This table also ontains the omparison of ratios of the alulated values of k 1 and k 2 using the proposed relationships for n, k, ε o and ε u in this researh to atual values obtained from this researh. This omparison is also shown in Figure Sample omparisons of the alulated and the atual stress-strain relationships for eentri braket speimens with 10, 14 and 18 ksi target onrete strength are shown in Figure 5-29 to Figure The proposed relationship yields the minimum deviations from 1 for both of the ratios of k 1 and k 2. Based on the test results and analysis of this researh, the proposed relationship for the stress-strain distribution of HSC an suffiiently be used for design purposes. 199

220 5 Analytial Work Speimen ID Table 5-5 Conrete Strain Obtained from Stress-Strain Relationships Maximum Stress, f (ksi) Calulated Strain at Maximum Stress, ε o Calulated Ultimate Strain, ε u (µε µε) k k 1al 1EBS k k 2al 2EBS k k 1al 1 1EBS 2 k k 1al 1 (µε µε) 10EB EB EB EB EB EB EB EB EB EB EB EB EB EB EB EB EB EB EB EB EB Deviation from 1 ( k 1 k 21 al EBS 2 ) 1EBS

221 5 Analytial Work 1.4 Ratio of Calulated Values to Atual Values Ratio of k o Ratio of k Maximum Conrete Stress (ksi) Figure 5-28 Comparison of the Ratio of Calulated and Atual Values using Proposed Relationships for ε o and ε u 16 Conrete Compressive Stress (ksi) Calulated using Proposed Equation 10EB Conrete Compressive Strain (µε µε) Figure 5-29 Comparison of Calulated and Atual Stress-Strain Relation of 10EB3 201

222 5 Analytial Work Conrete Compressive Stress (ksi) Calulated using Proposed Equation 14EB Conrete Compressive Strain (µε µε) Figure 5-30 Comparison of Calulated and Atual Stress-Strain Relation of 14EB1 Conrete Compressive Stress (ksi) Calulated using Proposed Equation 18EB Conrete Compressive Strain (µε µε) Figure 5-31 Comparison of Calulated and Atual Stress-Strain Relation of 18EB10 202

223 5 Analytial Work The ratios of the alulated parameters obtained from the proposed stress-stess relationship using n and k proposed by Collins and Porasz (1989) and the proposed ε o and ε u relationship in this researh in omparison to atual parameters obtained from the eentri braket speimens tested in this researh are also evaluated for omparison purposes. The deviations for the ratios from 1 of alulated to atual values of k 1 and k 2 were alulated as and , respetively. The omparison of deviations shows that the proposed relationships for n and k in this researh provide better preditions for the test results of this researh. 5.3 Proposed Poisson s Ratio for HSC Test results in the literature indiate that the Poisson s ratio is between 0.15 to 0.25 with an average value lose to 0.2 for onrete ompressive strengths up to 18 ksi. Based on the test results of this researh and other researhers in the literature, Poisson s ratio of 0.2 was found to be adequately used for onrete ompressive strengths up to 18 ksi for design purposes. The omparison of the proposed relationship with the test results of this researh and other researhers in the literature is shown in Figure Author's x Others' 0.30 Poisson's Ratio Proposed Relationship ν = Conrete Compressive Strength (ksi) Figure 5-32 Proposed Relationship for Poisson s Ratio 203

224 5.3.1 Regression Analysis for Poisson s Ratio 5 Analytial Work Similar proedure explained in Appendix H was used to obtain the linear regression relationship for the Poisson s ratio, ν. Details about the regression analysis are presented in Appendix J. A total of 246 test results with onrete ompressive strengths up to 20 ksi were investigated using regression analysis tehnique to develop the relationship between Poisson s ratio, ν, and onrete ompressive strength, f. The olleted data onsists of test results obtained by Komendant et al. (1978), Perenhio and Klieger (1978), Carrasquillo et al. (1981), Swartz et al. (1985), Jerath and Yamane (1987), Radain et al. (1993), and Iravani (1996) and Logan (2005) and this researh. Ninety four of the test results have onrete ompressive strengths below 10 ksi. The onrete ompressive strengths of other test results are over 10 ksi. The data was analyzed for three different onrete ompressive strength ranges: below 10 ksi to evaluate the results for NSC, over 10 ksi to evaluate the results for HSC and up to 20 ksi to ombine the results to evaluate for NSC and HSC. The tabulated results of the regression analysis for Poisson s ratio are presented in Table 5-6. Note that the values given in this table are for 50 perent regression lines orresponding to the medians of the test results. The regression analysis graphs of Poisson s ratio for three onrete ompressive strength ranges are shown in Figure 5-33 to Figure These graphs inlude the 50 perent regression lines, 90 perent regression lines orresponding to the lower bounds of the 90 perent of the test results and the proposed relationship in this researh (Setion 5.3) for ultimate ompressive strain of onrete. Table 5-6 Tabulated Results of the Regression Analysis for Poisson s Ratio Conrete Regression Line for ν Compressive Strength Range (ksi) Slope (h) Interept (j) Standard Deviation

225 5 Analytial Work Regression Line (50%) Proposed Relationship (44%) Poisson's Ratio Regression Line (90%) Author's x Others' Conrete Compressive Strength (ksi) Figure 5-33 Regression Analysis of ν for Conrete Compressive Strengths up to 20 ksi Proposed Relationship and AASHTO LRFD (2004) (44%) Regression Line (50%) Poisson's Ratio Regression Line (90%) x Others' Conrete Compressive Strength (ksi) Figure 5-34 Regression Analysis of ν for Conrete Compressive Strengths below 10 ksi 205

226 5 Analytial Work Regression Line (50%) Proposed Relationship (44%) Poisson's Ratio Regression Line (90%) Author's x Others' Conrete Compressive Strength (ksi) Figure 5-35 Regression Analysis of ν for Conrete Compressive Strengths over 10 ksi The standard deviations of Poisson s ratio, ν, show similar variations for three of the onrete ompressive strength ranges (below 10 ksi, over 10 ksi and up to 20 ksi). However, slope of the regression analysis of the test results of ν with onrete ompressive strengths below 10 ksi is dereasing whereas, that of with onrete ompressive strengths over 10 ksi is inreasing. When only test results of speimens with onrete ompressive strengths over 10 ksi are onsidered, there is an inrease in the Poisson s ratio as onrete ompressive strength inreases. The proposed relationship for Poisson s ratio establishes the lower bound limit of 44 perent of the test results. These results indiate that the proposed equation for ν would seem appropriate for onrete ompressive strengths up to 18 ksi. 5.4 Proposed Creep and Shrinkage Relationships for HSC Based on the results of the literature review, it is evident that reep and shrinkage of HSC is muh less than NSC and as onrete strength inreases, both the reep and and shrinkage of onrete dereases. Test results obtained from this researh were ompared 206

227 5 Analytial Work to the preditions speified by different design odes and douments. The relationships speified by AASHTO LRFD Bridge Design Speifiations (2004) were found to be the most appropriate relationship to predit reep and shrinkage of HSC with ompressive strengths less than or equal to 15 ksi. Comparisons of adjusted reep measurements to the reep equations speified by AASHTO LRFD Bridge Design Speifiation (2004) are shown in Figure 5-36 to Figure Sine this relationship is designed to predit the reep oeffiient, whih is the ratio of the reep strain at a given time to the initial elasti strain of the speimen at the initial loading stage, the omparisons are only presented in terms of the reep oeffiients. The reep oeffiient speified by ASSHTO LRFD Bridge Design Speifiations (2004) an be found in Setion ,2 1 AASHTO LRFD Creep Coeffiient 0,8 0,6 0,4 10Rak1 0, Time After Loading (days) (10 ksi Target Conrete Compressive Strength, Heat Cured, Loaded on the 1 st Day) Figure 5-36 Comparison of Creep Coeffiient of 10Rak1 207

228 5 Analytial Work 1,4 1,2 AASHTO LRFD Creep Coeffiient 1 0,8 0,6 0,4 10Rak4 0, Time After Loading (days) (10 ksi Target Conrete Compressive Strength, Moist Cured, Loaded on the 8 th Day) Figure 5-37 Comparison of Creep Coeffiient of 10Rak4 0,9 0,8 AASHTO LRFD Creep Coeffiient 0,7 0,6 0,5 0,4 0,3 0,2 10Rak2 10Rak5 0, Time After Loading (days) (10 ksi Target Conrete Compressive Strength, Moist Cured, Loaded on the 14 th Day) Figure 5-38 Comparison of Creep Coeffiient of 10Rak2 and 10Rak 5 208

229 5 Analytial Work 0,8 0,7 AASHTO LRFD 10Rak6 0,6 Creep Coeffiient 0,5 0,4 0,3 0,2 10Rak3 0, Time After Loading (days) (10 ksi Target Conrete Compressive Strength, Moist Cured, Loaded on the 28 th Day) 1 Figure 5-39 Comparison of Creep Coeffiient of 10Rak3 and 10Rak6 Creep Coeffiient 0,9 0,8 0,7 0,6 0,5 0,4 0,3 14Rak1 AASHTO LRFD 0,2 0, Time After Loading (days) (14 ksi Target Conrete Compressive Strength, Heat Cured, Loaded on the 1 st Day) Figure 5-40 Comparison of Creep Coeffiient of 14Rak1 209

230 5 Analytial Work 1,2 1 AASHTO LRFD Creep Coeffiient 0,8 0,6 0,4 14Rak4 0, Time After Loading (days) (14 ksi Target Conrete Compressive Strength, Moist Cured, Loaded on the 7 th Day) Figure 5-41 Comparison of Creep Coeffiient of 14Rak4 0,7 AASHTO LRFD 0,6 0,5 14Rak2 Creep Coeffiient 0,4 0,3 0,2 14Rak5 0, Time After Loading (days) (14 ksi Target Conrete Compressive Strength, Moist Cured, Loaded on the 14 th Day) Figure 5-42 Comparison of Creep Coeffiient of 14Rak2 and 14Rak5 210

231 5 Analytial Work 1,2 1 Creep Coeffiient 0,8 0,6 0,4 14Rak3 AASHTO LRFD (2004) 0,2 14Rak Time After Loading (days) (14 ksi Target Conrete Compressive Strength, Moist Cured, Loaded on the 28 th Day) 1,2 Figure 5-43 Comparison of Creep Coeffiient of 14Rak3 and 14Rak6 1 AASHTO LRFD Creep Coeffiient 0,8 0,6 0,4 18Rak1 0, Time After Loading (days) (18 ksi Target Conrete Compressive Strength, Heat Cured, Loaded on the 1 st Day) Figure 5-44 Comparison of Creep Coeffiient of 18Rak1 211

232 5 Analytial Work 1,2 1 AASHTO LRFD Creep Coeffiient 0,8 0,6 0,4 18Rak4 0, Time After Loading (days) (18 ksi Target Conrete Compressive Strength, Moist Cured, Loaded on the 7 th Day) Figure 5-45 Comparison of Creep Coeffiient of 18Rak4 0,7 AASHTO LRFD 0,6 Creep Coeffiient 0,5 0,4 0,3 0,2 18Rak5 18Rak2 0, Time After Loading (days) (18 ksi Target Conrete Compressive Strength, Moist Cured, Loaded on the 14 th Day) Figure 5-46 Comparison of Creep Coeffiient of 18Rak2 and 18Rak5 212

233 5 Analytial Work 1,2 1 Creep Coeffiient 0,8 0,6 0,4 18Rak6 AASHTO LRFD 0,2 18Rak Time After Loading (days) (18 ksi Target Conrete Compressive Strength, Moist Cured, Loaded on the 28 th Day) Figure 5-47 Comparison of Creep Coeffiient of 18Rak3 and 18Rak6 Comparisons of adjusted shrinkage strain measurements to the shrinkage relationships speified by AASHTO LRFD Bridge Design Speifiation (2004) are shown in Figure 5-48 to Figure The shrinkage strain speified by ASSHTO LRFD Bridge Design Speifiations (2004) an be found in Setion

234 5 Analytial Work AASHTO LRFD Shrinkage Strain (µε µε) SC Time After Curing (days) (10 ksi Target Conrete Compressive Strength, Heat Cured Cylinder) Figure 5-48 Comparison of Shrinkage Strain of 10SC AASHTO LRFD Shrinkage Strain (µε µε) SP1 10SP2 10SP Time After Curing (days) (10 ksi Target Conrete Compressive Strength, Heat Cured Prisms) Figure 5-49 Comparison of Shrinkage Strain of 10SP1, 10SP2 and 10SP3 214

235 5 Analytial Work AASHTO LRFD Shrinkage Strain (µε µε) SC Time After Curing (days) (14 ksi Target Conrete Compressive Strength, Heat Cured Cylinder) Figure 5-50 Comparison of Shrinkage Strain of 14SC AASHTO LRFD Shrinkage Strain (µε µε) SP1 14SP3 14SP Time After Curing (days) (14 ksi Target Conrete Compressive Strength, Heat Cured Prisms) Figure 5-51 Comparison of Shrinkage Strain of 14SP1, 14SP2 and 14SP3 215

236 5 Analytial Work AASHTO LRFD Shrinkage Strain (µε) SC Time After Curing (days) (18 ksi Target Conrete Compressive Strength, Heat Cured Cylinder) Figure 5-52 Comparison of Shrinkage Strain of 18SC1 350 Shrinkage Strain (µε µε) AASHTO LRFD 18SP1 18SP2 18SP Time After Curing (days) (18 ksi Target Conrete Compressive Strength, Heat Cured Prisms) Figure 5-53 Comparison of Shrinkage Strain of 18SP1, 18SP2 and 18SP3 216

237 5 Analytial Work AASHTO LRFD Shrinkage Strain (µε µε) SC Time After Curing (days) (10 ksi Target Conrete Compressive Strength, Moist Cured Cylinder) Figure 5-54 Comparison of Shrinkage Strain of 10SC AASHTO LRFD Shrinkage Strain (µε µε) SP6 10SP5 10SP Time After Curing (days) (10 ksi Target Conrete Compressive Strength, Moist Cured Prisms) Figure 5-55 Comparison of Shrinkage Strain of 10SP4, 10SP5 and 10SP6 217

238 5 Analytial Work AASHTO LRFD Shrinkage Strain (µε µε) SC Time After Curing (days) (14 ksi Target Conrete Compressive Strength, Moist Cured Cylinder) Figure 5-56 Comparison of Shrinkage Strain of 14SC SP6 14SP SP5 Shrinkage Strain (µε µε) AASHTO LRFD Time After Curing (days) (14 ksi Target Conrete Compressive Strength, Moist Cured Prisms) Figure 5-57 Comparison of Shrinkage Strain of 14SP4, 14SP5 and 14SP6 218

239 5 Analytial Work SC2 Shrinkage Strain (µε µε) AASHTO LRFD Time After Curing (days) (18 ksi Target Conrete Compressive Strength, Moist Cured Cylinder) Figure 5-58 Comparison of Shrinkage Strain of 18SC SP4 Shrinkage Strain (µε µε) AASHTO LRFD 18SP5 18SP Time After Curing (days) (18 ksi Target Conrete Compressive Strength, Moist Cured Prisms) Figure 5-59 Comparison of Shrinkage Strain of 18SP4, 18SP5 and 18SP6 219

240 5 Analytial Work The test results of this researh indiate that the reep and shrinkage predition relationships speified by AASHTO LRFD Bridge Design Speifiations (2004) are approximately prediting the reep and shrinkage behavior of HSC. However, the reep and shrinkage predition relationships ontain the following development orretion fator whih must be investigated in details sine it yields negative results in the first few days after loading for onrete strength greater than 15.0 ksi: k td t = 61 4 f ' + t i where t is the age of onrete after loading in days, f i is the speified ompressive strength in ksi at prestress transfer for prestressed members or 80 perent of the strength at servie for non-prestressed members. The equation also gives abrupt hanges in the slope of the predited reep in the first few days for onrete strengths more than 12 ksi. This equation was developed by Tadros et al (2003) based on researh data with onrete strengths up to 12 ksi and was extended to inlude strengths up to 15 ksi. It was reognized that onrete ompressive strength of 18 ksi would not be used for releasing strength for pretensioned members. However, for ast in plae olumns and post-tensioning girders, the onrete strength at the time of loading ould be as high as 18 ksi. The results of this researh indiate that the equation should be revised to provide better preditions for onrete strengths up to 18 ksi. After a detailed examination of test results and parametri studies, the following timedevelopment orretion fator is proposed: k td t = f ' i 12 t f ' i In Figure Figure 5-60 to Figure 5-66, the proposed time development orretion fator and the urrent expression are ompared for different onrete ompressive strengths up 220

241 5 Analytial Work to 18 ksi. In these figures, the dotted and the solid lines represent the urrent and the proposed time development orretion fators, respetively. It an be seen that for onrete strength greater than 12 ksi, the proposed time development orretion fator eliminates the unreasonable predition values given by the urrent time development orretion fator. Time Development Fator, k td t (days) AASHTO LRFD Proposed Time Development Fator, k td t (days) AASHTO LRFD Proposed Figure 5-60 k td for f i = 4 ksi Figure 5-61 k td for f i = 6 ksi Time Development Fator, k td t (days) AASHTO LRFD Proposed Time Development Fator, k td t (days) AASHTO LRFD Proposed Figure 5-62 k td for f i = 8 ksi Figure 5-63 k td for f i = 10 ksi Time Development Fator, k td t (days) AASHTO LRFD Proposed Time Development Fator, k td t (days) AASHTO LRFD Proposed Figure 5-64 k td for f i = 12 ksi Figure 5-65 k td for f i = 14 ksi 221

242 5 Analytial Work Time Development Fator, k td t (days) AASHTO LRFD Proposed Time Development Fator, k td t (days) AASHTO LRFD Proposed Figure 5-66 k td for f i = 16 ksi Figure 5-67 k td for f i = 18 ksi 5.5 Proposed Limits for Reinforement for Compression Members AASHTO LRFD Bridge Design Speifiations (2004) have two relationships to limit the maximum reinforement and one riterion to limit the minimum reinforement for ompression members. The maximum area of prestressed and non-prestressed longitudinal reinforement for non-omposite ompression omponents aording to AASHTO LRFD Bridge Design Speifiations (2004) is limited by the two following equations: As A Aps f pu (AASHTO LRFD Eqn ) Equation 5-11 A f g g y and A f ps pe A f ' g 0.30 (AASHTO LRFD Eqn ) Equation 5-12 where f is the onrete ompressive strength, A ps is the area of prestressing steel, f pu is the speified tensile strength of prestressing steel, f pe is the effetive prestress after losses, A s and f y are the area and yield strength of mild ompression steel, respetively, and A g is the gross area of the setion. 222

243 5 Analytial Work The minimum area of prestressed and non-prestressed longitudinal reinforement for nonomposite ompression omponents aording to AASHTO LRFD Bridge Design Speifiations (2004) is: As f y Aps f pu + A f A f g g (AASHTO LRFD Eqn ) Equation 5-13 The upper limits were initially established based on pratial onsiderations of onrete plaement and have sine been maintained for all ranges of onrete ompressive strengths. Therefore no hanges are proposed to AASHTO LRFD Bridge Design Speifiations (2004) for the maximum reinforement ratio for ompression members to extend the appliability of the speifiations up to 18 ksi. However, the analysis onduted to examine urrent AASHTO LRFD Bridge Design Speifiations (2004) indiate a requirement of 4.05 perent as the minimum reinforement ratio for 18 ksi onrete ompressive strength and Grade 60 steel, in the absene of any prestressing steel in the setion as shown in Figure Suh very high level of minimum reinforement ratio is quite unusual and should be examined for HSC. In order to evaluate this reinforement limit, it is neessary to review the basis and historial development of the urrent requirement of the minimum reinforement. 223

244 5 Analytial Work Maximum Limit Reinforement Ratio Minimum Limit for f y = 75 ksi Minimum Limit for f y = 60 ksi Minimum Limit for f y = 90 ksi Conrete Compressive Strength (ksi) Figure 5-68 Reinforement Limits for Compression Members with Only Mild Steel Aording to the Current AASHTO LRFD Bridge Design Speifiations For non-prestressed setions, the minimum limit for longitudinal reinforement for ompression members originated from the early olumn tests by Rihart et al. (1931a, 1931b, 1931 and 1932) at the University of Illinois in the 1930 s. When a olumn is tested under sustained servie loads, the stress distribution between steel and onrete hanges over time due to reep and shrinkage of onrete. With reep and shrinkage inreasing progressively, onrete relieves itself from its initial share of the axial load. As a result, longitudinal steel reinforement gradually arries a larger portion of the sustained load over time. Therefore, it is theoretially possible that in olumns with small amounts of longitudinal reinforement, the reinforing steel ould yield, resulting in reep rupture of the olumn. Tests by Rihart et al. (1931a, 1931b, 1931 and 1932) showed the inrease of stress in the steel reinforement is inversely proportional to the perentage of the longitudinal steel. Results from their tests arried out with onrete strengths between 2 and 8 ksi, suggested a minimum reinforement ratio of 1%. The appliation of this limit was later extended by AASHTO LRFD Bridge Design Speifiations (2004) for onrete ompressive strengths up to 10 ksi without any further tests or analysis, and ertainly without any onsideration for HSC above 10 ksi. 224

245 5 Analytial Work Three types of strain are normally developed in the longitudinal reinforement under the effet of sustained loading: initial elasti strain, strain developed due to shrinkage of onrete and strain developed due to reep of onrete. When a sustained load is applied to a reinfored onrete olumn, initial elasti strain, ε 1, is observed immediately as shown in Figure P ε 1 P P Figure 5-69 Initial Elasti Strain due to Applied Sustained Load P At this stage the applied load is resisted by both onrete and steel as follows: P = E ε (1 ρ ) A + E ε ρ A Equation l g s 1 l g where P is the applied axial load, E is the modulus of elastiity of onrete, ρ l is the longitudinal reinforement ratio, A g is the gross area of onrete and E s is the modulus of elastiity of steel. The initial elasti strain of onrete and steel an be obtained from the above equilibrium equation, i.e., ε = 1 P 1 A E E ( (1 ρ ) + ρ ) g l s l. Equation 5-15 Following the initial elasti deformation, the time dependent deformations will our in the onrete due to reep and shrinkage. Sine the olumn ontains reinforement, the shrinkage strain, ε sh, will be restrained by the longitudinal reinforement of the olumn ausing an inrease in the load arried by the reinforement and a derease in the load 225

246 5 Analytial Work arried by the onrete. The same behavior holds for the reep strain of onrete, ε r. The behavior of reinfored onrete olumn due to shrinkage and reep is presented in Figure ε 2 ε sh ε 3 ε r Restrained Strain RC Speimen Shrinkage Strain Restrained Strain RC Speimen Creep Strain a) Due to Shrinkage b) Due to Creep Figure 5-70 Behavior of Reinfored Conrete Column due to Shrinkage and Creep From equilibrium of fores due to shrinkage, ( ) E ε (1 ) 2ρ A = E ε ε 2 ρ A Equation 5-16 s l g sh l g where ε 2 is the strain in the reinforement due to shrinkage of onrete. Thus the strain developed in the longitudinal reinforement due to shrinkage of onrete an be determined as: ε = 2 (1 ρ ) ε E l sh ( ρ E + (1 ρ ) E ) l s l. Equation 5-17 Similarly, from equilibrium of fores due to reep, ( ) E ε (1 ) 3ρ A = E ε ε3 ρ A Equation 5-18 s l g r l g where ε 3 is the strain in the reinforement due to reep of onrete, ε r is the reep strain of unrestrained onrete. Then the strain developed in the longitudinal reinforement due to reep of onrete an be determined as: 226

247 ε = 3 (1 ρ ) ε E l r ( ρ E + (1 ρ ) E ) l s l 5 Analytial Work. Equation 5-19 To prevent yielding of the longitudinal reinforement, the summation of the initial elasti strain and the strains due to shrinkage and reep should not reah the yield strain of the longitudinal reinforement. Thus, ε = ε + ε + ε yield strain of longitudinal reinforement Equation 5-20 total Note that for Grade 60 steel reinforement, the yield strain is assumed to be The proedure used to alulate the minimum longitudinal reinforement ratio for ompression members was an iterative proedure whih was modeled using Mirosoft Exel. The amount of reinforement was determined for a reinfored onrete olumn under sustained load whih would lead to a total strain of after speified period of time. The proedure used was as follows: 1. The range of onrete ompressive strength used in this study varies between 6 ksi and 18 ksi. 2. The modulus of elastiity of steel was used as 30,000 ksi. For modulus of elastiity of onrete, the relationships proposed by NCHRP Projet to extend the appliability of AASHTO LRFD Bridge Design Speifiations (2004) as well as the urrent AASHTO LRFD Bridge Design Speifiations (2004) were used for HSC. However, most ritial onditions were established using the one proposed by NCHRP The unit weight of onrete ( w ) used in the analysis was kf sine HSC is more ompat and denser than NSC. The modulus of elastiity ( E ) equation proposed by NCHRP used in the analysis is: ( ) 0.33 E = 310, 000K w f Equation

248 where K 1 is the orretion fator for soure of aggregate (taken as 1.0) and onrete ompressive strength. 5 Analytial Work f ' is the The analysis was repeated using the urrent equation speified by AASHTO LRFD Bridge Design Speifiations (2004): E = 33,000 K f (AASHTO LRFD Eqn ) Equation w 3. The shrinkage strain relationship ( ε sh ) speified by AASHTO LRFD Bridge Design Speifiations (2004) was used to alulate the shrinkage strain of onrete (Setion ). 4. The reep oeffiient relationship (ψ ) speified by AASHTO LRFD Bridge Design Speifiations (2004) was used to alulate the reep of onrete (Setion ). 5. The relative humidity used in the alulation of the reep and shrinkage was 10 perent, sine lower relative humidity would produe more ritial results. 6. The volume to surfae ratio used in the alulation of reep and shrinkage was 3. Note that, the volume to surfae ratio for a irular olumn with 12 in. diameter is 3. Also for a in. square olumn, the volume to surfae ratio is The time onsidered in the alulation of the reep and shrinkage was 10 years whih is equal to 3650 days. 8. The age of loading in the alulation of the reep oeffiient was 28 days. 9. The sustained load level on the reinfored onrete olumn onsidered in this investigation was 50 perent. (P/f A g = 0.5). The unfatored permanent load on olumns do not exeed 0.5A g f', whih is typially the ase enountered in design. 228

249 5 Analytial Work 10. The effets assoiated with stress relief for both reep and shrinkage due to reep of onrete in tension are negleted in the formulation of the equilibrium onditions. By negleting suh effets, the results are more onservative. 11. The initial value for the longitudinal reinforement ratio (ρ l ) for a reinfored onrete olumn was established. The initial elasti strain and strains due to reep and shrinkage were alulated based on the previous disussions in this setion. The sum of all three strain values, the total strain (ε total ), was alulated and ompared to the yield strain of steel reinforement. By hanging the initial value of the longitudinal reinforement ratio, the reinforement ratio for whih the total strain was equal to the yield strain of steel was determined. This reinforement ratio was used as the minimum amount of longitudinal reinforement ratio for ompression members to prevent reep rupture. 12. Step 11 was performed for all the onrete ompressive strengths in the onsidered range. Note that, the most ritial onditions were evaluated in the alulation of minimum longitudinal reinforement ratio for ompression members. Based on the performed analysis using the proposed equation and the urrent relationship speified by AASHTO LRFD Bridge Design Speifiations (2004) for E, a new relationship is proposed for minimum reinforement ratio for ompression members as follows: A Aps f s pu f ' but not greater than Equation 5-23 A A f f g g y y For onrete ompressive strengths up to 10 ksi, the proposed relationship for minimum longitudinal reinforement ratio requires the same amount as that of AASHTO LRFD Bridge Design Speifiations (2004). For onrete ompressive strengths greater than 10 ksi, the proposed equation requires the same amount of for onrete ompressive strengths up to 18 ksi. Furthermore, the proposed minimum reinforement limitation is similar in format with the maximum reinforement limitation speified by AASHTO LRFD Bridge Design Speifiations (2004). 229

250 5 Analytial Work The minimum longitudinal reinforement ratio required by the urrent AASHTO LRFD Bridge Design Speifiations (2004), the proposed provision, and based on the above proedure onsidering the effets of reep and shrinkage, for the stress level P/f A g = 0.5 are tabulated in Table 5-7 and shown in Figure The figure learly indiates that for onrete strength greater than 10 ksi, the required minimum longitudinal reinforement ratio by the proposed equation is greatly redued from that alled for by the urrent AASHTO LRFD Bridge Design Speifiations (2004), but the proposed equation still provides substantial margin against what is needed to prevent reep rupture. Table 5-7 Comparison of the A s /A g Ratio for P/f A g = 0.5 P/f A g = 0.5 f (ksi) A s /A g A s /A g A s /A g (AASHTO LRFD) (Proposed) (Calulated)

251 5 Analytial Work Minimum Longitudinal Reinforement Ratio w = kf RH= 10% V/S= 3.0 Age of Loading= 28 days Total Time= 10 years E s = ksi E = Proposed by NCHRP12-64 AASHTO LRFD Bridge Design Speifiations (2004) Conrete Compressive Strength (ksi) Proposed Relationship Based on Prevention of Creep Rupture Figure 5-71 Comparison of the A s /A g Ratio for P/f A g = 0.5 The alulated values for minimum reinforement ratio for ompression members based on prevention of reep rupture for P/f A g = 0.5 are tabulated in Table 5-8. Note that the summation of the initial elasti, shrinkage and reep strains are equal to the yield strain of Grade 60 steel reinforement, It is lear from the table that the reep and shrinkage strains of onrete dereases as onrete ompressive strength inreases. However, the initial elasti strain inreases as onrete ompressive strength inreases sine the same stress level was applied on eah olumn with different onrete ompressive strengths. When olumns with 6 ksi and 18 ksi onrete ompressive strengths are ompared under P/f A g = 0.5, the load applied on the olumn with 18 ksi onrete ompressive strength is 3 times that of applied on the olumn with 6 ksi onrete ompressive strength. However, the modulus of elastiity of the olumn with 18 ksi onrete ompressive strength is only 1.44 times that of the olumn with 6 ksi onrete ompressive strength. Therefore, the minimum reinforement ratio for ompression members an not be redued for HSC ompared to NSC, although HSC reeps and shrinks less. 231

252 Table 5-8 Calulated Values for P/f A g = Analytial Work f Initial Elasti Shrinkage Creep ρ (ksi) l (%) E (ksi) Strain (ε 1 ) Strain (ε 2 ) Strain (ε 3 )

253 6 Conlusions and Reommendations 6 CONCLUSIONS AND RECOMMENDATIONS 6.1 Summary The harateristis of HSC for ombined flexural and axial ompression were investigated in this researh. The experimental program onsisted of two parts. The first part inluded tests of twenty-one unreinfored HSC members under ombined axial load and flexure to evaluate the stress-strain distribution in the ompression zone of flexural members. The test onept was based on the test method developed by Hognestad et al. (1955) to simulate the ompression zone of a flexural member. The two axial loads were adjusted during the test to maintain zero strain (whih is at the neutral axis for a flexural member) at one fae of the speimen and the maximum ompressive strain at the opposite fae of the ross-setion. The main parameter was the onrete ompressive strength ranging from 10.4 to 16 ksi. Stress-strain relationships, ultimate ompressive strain, stress blok parameters and Poisson s ratios for HSC were obtained, evaluated and ompiled with the data available in the literature. The seond part of the experimental program onsisted of tests perform to evaluate the reep and shrinkage behavior of HSC. A total of fourty two 4 12 in. ylindrial speimens and eigthteen ¼ in. prism speimens were monitored for one year. The variables onsidered in this investigation were the onrete ompressive strength ranging from 10.4 to 16.7 ksi, speimen size (ylindrial or prism), uring type (moist or heat uring), age of onrete at loading (1, 7, 14, 28 days) and loading stress level (0.2f or 0.4f ). The reep strains, speifi reep values, reep oeffiients and shrinkage strains were obtained for the range of onrete ompressive strength, evaluated and ompiled with the available relationships in the literature. Test results of this researh ombined with other researhes in the literature were analytially evaluated using regression analyses and parametri studies. These analyses were used to evaluate the validity of the provisions of AASHTO LRFD Bridge Design Speifiations (2004) for HSC. If neessary, new relationships were proposed to modify AASHTO LRFD Bridge Design Speifiations (2004) to extend the urrent limitation of 10 ksi onrete ompressive strength up to 18 ksi. 233

254 6.2 Observations and Conlusions 6 Conlusions and Reommendations The observations made and onlusions drawn from this study are based on the test results of this researh and other researhes in the literature unless otherwise stated. Therefore, the proposed equations an approporiately be used for design purposes for onrete ompressive strengths up to 18 ksi. 1. Similar behaviors were observed for all the eentri braket speimens regardless of onrete ompressive strength. The eentri braket speimens showed an explosive failure of the ompression fae. It was observed that the failure surfae was passing through the aggregates indiating the ement paste and the interfae between the ement paste and aggregate were stronger than the aggregate itself. 2. The assumption of plane setions remain plane after deformation is valid for high strength onrete. 3. The stress-strain distributions obtained from the eentri braket speimens tested in this researh indiated that as onrete ompressive strength inreased, the strain at the peak stress inreased and was loser to strain. The shape of the asending branh of the stress-strain relationship beame more linear and steeper, and the slope of the desending part also beame steeper. The general shape of the stress-strain relationship beame more likely to be a triangle with little or no desending parts. 4. The ultimate onrete ompressive strain of is proposed to be used for design purposes for onrete ompressive strengths up to 18 ksi. 5. Poisson s ratio of 0.2 was found to be an appropriate value for onrete ompressive strengths up to 18 ksi. 6. The test results of this researh and other researhes in the literature indiate that the majority of the olleted data for the generalized stress blok parameter k 1 for HSC is higher than 0.58 for onrete ompressive strengths ranging between 10 and 18 ksi. Therefore, using the lower bound of 0.58 is proposed for k 1 parameter for onrete ompressive strengths beyond 15 ksi. 234

255 6 Conlusions and Reommendations 7. The test results of this researh and other researhes in the literature indiate that the stress blok parameter k 2 for HSC between 8 ksi and 18 ksi an be assumed to be The test results of this researh and other researhes in the literature indiate that the generalized stress blok parameter k 3 for HSC is similar to NSC. Hene, using the same value of k 3 parameter, 0.85, for onrete ompressive strengths up to 18 ksi is found to be appropriate for design purposes. 9. The test results, onfirmed by other data in the literature, indiate that the stress blok parameter α 1 should be redued when the ompressive strength of onrete is inreased beyond 10 ksi. The reommended value for the parameter α 1 for onrete ompressive strengths up to 18 ksi is: 0.85 for f ' 10ksi α1 = ( f ' 10) 0.75 for f ' > 10ksi Equation 6-1 where f ' is in ksi. 10. The following relationship urrently used by AASHTO LRFD Bridge Design Speifiations is found to be aeptable for the retangular stress blok parameter β 1 for onrete ompressive strengths up to 18 ksi: 0.85 for f ' 4ksi β1 = ( f ' 4) 0.65 for f ' > 4ksi Equation 6-2 where f ' is in ksi. 11. The results of the sensitivity analysis for flexural under-reinfored onrete setions indiate that the hange in the retangular stress blok parameters and the ultimate ompressive strain of onrete have very little or no effet on the ultimate moment apaity of the setion. On the other hand the results of the sensitivity analysis for the 235

256 6 Conlusions and Reommendations flexural over-reinfored onrete setions indiate that the hange in the retangular stress blok parameters affets the ultimate moment apaity of the setions signifiantly. However, the hange in the ultimate ompressive strain of onrete has very little effet on the ultimate moment apaity of the setion for flexural overreinfored setions. 12. Based on the test results of this researh, the following stress-strain relationship was found to be the most appropriate equation to predit the stress-strain distribution of onrete for ompressive strengths up to 18 ksi. f = f ' ε n ε n 1+ ε ε ( ) nk o o Equation 6-3 with n = 0.31 f ' Equation 6-4 k = 0.10 f ' Equation 6-5 and ε = f ' Equation 6-6 o ε = f ' Equation 6-7 u where f ' is in ksi. 13. In general, test results of this researh and other researhes in the literature indiate that as onrete ages, the reep of HSC dereases. The reep behavior of heat ured ylinders is less than that of the moist ured ylinders. Creep for HSC is proportional to the applied stress provided that the applied stress was less than the proportional limit. 236

257 6 Conlusions and Reommendations 14. Test results of this researh on shrinkage of HSC indiate that heat ured speimens had less shrinkage ompared to moist ured speimens. There was little differene in shrinkage of HSC speimens with target onrete strengths of 10, 14 and 18 ksi. The average weight loss of the speimens was diretly proportional to shrinkage of HSC. 15. The relationships speified by the urrent AASHTO LRFD Bridge Design Speifiations (2004) were found to be aeptable to predit reep and shrinkage of HSC exept the time-development orretion fator. The time-development orretion fator whih yields negative results in the first few days after loading for onrete strengths greater than 15.0 ksi. Aordingly, the following time-development orretion fator was proposed to eliminate the unreasonable predition values given by the urrent time development orretion fator: k td t = f ' i 12 t f ' i Equation 6-8 where f ' i is in ksi. 16. The relationships for the maximum reinforement ratio for ompression members speified by AASHTO LRFD Bridge Design Speifiations (2004) are appliable for onrete ompressive strengths up to 18 ksi. 17. The urrent AASHTO LRFD Bridge Design Speifiations (2004) requires extremely high levels of minimum reinforement ratio for ompression members for onrete ompressive strengths over 10 ksi. Based on an analysis of reep bukling behavior using the proposed equation and the urrent relationship speified by AASHTO LRFD Bridge Design Speifiations (2004) for E, a new relationship is developed for minimum reinforement ratio for ompression members as follows: 237

258 6 Conlusions and Reommendations A Aps f s pu f ' but not greater than Equation 6-9 A A f f g g y y For onrete ompressive strengths up to 10 ksi, the proposed relationship for minimum longitudinal reinforement ratio requires the same amount as that of AASHTO LRFD Bridge Design Speifiations (2004). For onrete ompressive strengths greater than 10 ksi, the proposed equation requires the same amount of for onrete ompressive strengths up to 18 ksi. 6.3 Reommendations Due to the pratial prodution reasons, the number of tests performed to evaluate the stress-strain distribution and shrinkage and reep behavior of HSC was limited for onrete ompressive strength over 16 ksi. More tests are needed for onrete ompressive strengths beyond 16 ksi to provide additional data to fully validate the proposed relationships. 238

259 Referenes REFERENCES AASHTO LRFD Bridge Design Speifiations, Third Edition inluding 2005 and 2006 Interim Revisions, Amerian Assoiation of State Highway and Transportation Offiials, Washington DC, ACI Committee 209, Predition of Creep, Shrinkage and Temperature Effets in Conrete Strutures (ACI 209 R-92), Amerian Conrete Institute, Farmington Hills, MI, 1992, p. 47. ACI Committee 318, Building Code Requirements for Strutural Conrete (ACI ) and Commentary (318R-05), Amerian Conrete Institute, Farmington Hills, MI, ACI Committee 363, State-of-the-Art Report on High-Strength Conrete (ACI 363R- 92), Amerian Conrete Institute, Detroit, 1992 (Revised 1997), 55 pp. ACI Committee 441, High Strength Conrete Columns: State of the Art (ACI 441R-96), Amerian Conrete Institute, Detroit, 1996, 13 p. Attard, M. M. and Setunge, S., Stress-Strain Relationship of Confined and Unonfined Conrete, ACI Materials Journal, Vol. 93, No. 5, September-Otober 1996, pp Attard, M. M. and Stewart, M. G., A Two Parameter Stress Blok for High Strength Conrete, ACI Strutural Journal, Vol. 95, No. 3, May-June 1998, pp AS , Australian Standard for Conrete Strutures, Australia, Azizinamini, A., Kuska, S. S. B., Brungardt, P., and Hatfield, E., Seismi Behavior of Square High-Strength Conrete Columns, ACI Strutural Journal, Vol. 91, No. 3, May- June 1994, pp Bae, S. and Bayrak, O., Stress Blok Parameters for High-Strength Conrete Members, ACI Strutural Journal, Vol. 100, No. 5, September-Otober 2003, pp

260 Referenes Berntsson, L., Chandra, S., and Kutti, T., Priniples and Fators Influening High- Strength Conrete Prodution, Conrete International, Vol. 12, No. 12, Deember 1990, pp Burnett, I., High-Strength Conrete in Melbourne, Australia, Conrete International, Vol. 11, No. 4, April 1989, pp Design of Conrete Strutures, CSA A , Canadian Standards Assoiation, Rexdale, Ontario, 1994, pp.199. Canadian Highway Bridge Design Code, CSA S6 2001, Canadian Standards Assoiation, Rexdale, Ontario, Carrasquillo, R. L., Nilson, A. H., and Slate, F. O., Properties of High-Strength Conrete Subjet to Short-Term Loads, ACI Strutural Journal, Vol. 78, No. 3, May 1981, pp Carreira, D. J. and Chu, K. H., Stress-Strain Relationship for Plain Conrete in Compression, ACI Strutural Journal, Vol. 82, No. 6, November 1985, pp CEB-FIB Model Code 1990, Thomas Telford Servies Ltd., London, for Comité Euro- International du Béton, Laussane, 1993, 437 p. Collins, M. P. and Porasz, A., Shear Design for High Strength Conrete, CEB Bulletin d Information, No. 193, Deember 1989, pp Collins, T. M., Proportioning High-Strength Conrete to ontrol Creep and Shrinkage, ACI Materials Journal, Vol. 86, No. 6, November 1989, pp Dahl, K. K. B., Uniaxial Stress-Strain Curves for Normal and High-Strength Conrete, ABK Report No. R282, Department of Strutural Engineering, Tehnial University of Denmark, Lyngby, Denmark,

261 Referenes Euroode 2 (EC2) Design of Conrete Strutures, UK, Fiorato, A. E., PCA Researh on High-Strength Conrete, Conrete International, Vol. 11, No. 4, April 1989, pp Giaio, G., Giovambattista, A., Roo, C., and Zerbino, R., Compressive Creep of High-Strength Conrete, Proeedings of Fifth International RILEM Symposium: Creep and Shrinkage of Conrete, Barelona, Spain, September 1993, pp Hognestad, E., A Study of Combined Bending and Axial Load in Reinfored Conrete Members, University of Illinois Bulletin Series No 399, Vol. 49, No. 22, November 1951, 128 p. Hognestad, E., Fundamental Conepts in Ultimate Load Design of Reinfored Conrete Members, Journal of the Amerian Conrete Institute, Vol. 48, No. 6. June 1952, pp Hognestad, E., Hanson, N. W., and MHenry, D., Conrete Stress Distribution in Ultimate Strength Design, Journal of the Amerian Conrete Institute, Vol. 27, No. 4, Deember 1955, pp Hsu, L. S. and Hsu, C. T. T., Complete Stress-Strain Behavior of High Strength Conrete under Compression, Magazine of Conrete Researh, Vol. 46, No. 169, 1994, pp Huo, X. S., Al-Omaishi, N., and Tadros, M. K., Creep, Shrinkage, and Modulus of Elastiity of High-Strength Conrete, ACI Materials Journal, Vol. 98, No. 6, November 2001, pp Hwang, C., Wang, H., and Sheen, Y., Quality Assurane in a Taiwanese High-Rise Tower, Conrete International, Vol. 21, No. 7, July 1999, pp

262 Referenes Ibrahim, H. H. H., Flexural Behavior of High-Strength Conrete Columns, Ph.D. Thesis, Department of Civil and Environmental Engineering, University of Alberta, Alberta, Edmonton, Alberta, Canada, 1994, 221 p. Iravani, S., Mehanial Properties of High-Strength Conrete, ACI Materials Journal, Vol. 93, No. 5, September - Otober 1996, pp Jensen, V. P., The Plastiity Ratio of Conrete and Its Effet on the Ultimate Strength of Beams, Journal of the Amerian Conrete Institute, Vol. 14, No. 6, June 1943, pp Jerath, S., and Yamane, L. C., Mehanial Properties and Workability of Superplastiized Conrete, Cement Conrete and Aggregates, Vol. 9, No. 1, 1987, pp Jianyong, L., and Yan, Y., A Study on Creep and Drying Shrinkage of High Performane Conrete, Cement and Conrete Researh, Vol. 31, 2001, pp Kaar, P. H., Hanson, N. W., and Capell, H. T., Stress-Strain Charateristis of High Strength Conrete, Amerian Conrete Institute Speial Publiation-55, Douglas MHenry International Symposium on Conrete and Conrete Strutures, Mihigan, 1978a, pp Kaar, P. H., Fiorato, A. E., Carpenter, J. E., and Corley, W. G., Limiting Strains of Conrete Confined by Retangular Hoops, Researh and Development Bulletin RD053.01D, Researh and Development / Constrution Tehnologies Laboratories, Portland Cement Assoiation, 1978b, 12 p. Khan, A. A., Cook, W. D., and Mithell, D., Creep, Shrinkage, and Thermal Strains in Normal, Medium and High-Strength Conretes during Hydration, ACI Materials Journal, Vol. 94, No. 2, Marh 1997, pp

263 Referenes Komendant, J., Niolayeff, V., Polivka, M., and Pirtz, D., Effet of Temperature, Stress Level, and Age at Loading on Creep of Sealed Conrete, Speial Publiation 55, Amerian Conrete Institute, August 1978, pp Li, B., Strength and Dutility of Reinfored Conrete Members and Frames Construted Using High Strength Conrete, Ph. D. Thesis, Department of Civil Engineering, University of Canterbury, Christhurh, New Zealand, July Logan, A. T., Short-Term Material Properties of High-Strength Conrete, M.S. Thesis, Department of Civil, Constrution and Environmental Engineering, North Carolina State University, Raleigh, NC, Jun. 2005, 116 p. Mattok, A. H., Kriz, L. B., and Hognestad, E., Retangular Conrete Stress Distribution in Ultimate Strength Design, Journal of the Amerian Conrete Institute, Vol. 32, No. 8, February 1961, pp Mather, B., and Hime, W. G., Amuont of Water Required for Complete Hydration of Portland Cement, Conrete International, Vol. 24, No. 6, Jun. 2002, pp Mokhtarzadeh, A., and Frenh, C., Time-Dependent Properties of High-Strength Conrete with Considerations for Preast Appliations, ACI Materials Journal, Vol. 97, No. 3, May 2000, pp Moreno, J., High-Performane Conrete: Eonomi Considerations, Conrete International, Vol. 20, No. 3, Marh 1998, pp Muguruma, H., Nishiyama, M., and Watanabe, F., Dutility Evaluation of Reinfored Conrete Columns with Normal and High Strength Conrete, Proeedings of Paifi Conferene on Earthquake Engineering, Aukland, New Zealand, November 1991, pp

264 Referenes Nedderman, H., Flexural Stress Distribution in Very-High Strength Conrete, M.S. Thesis, Department of Civil Engineering, University of Texas at Arlington, Arlington, Texas, Deember Neville, A., Creep of Conrete and Behavior of Strutures Part I: Problems, Conrete International, Vol. 24, No. 5, May 2002a, pp Neville, A., Creep of Conrete and Behavior of Strutures Part II: Dealing with Problems, Conrete International, Vol. 24, No. 6, June 2002b, pp New Zealand Conrete Strutures Standards (NZS 3101), New Zealand Standards, Ngab, A. S., Nilson, A. H., and Slate, F. O., Shrinkage and Creep of High-Strength Conrete, ACI Strutural Journal, Vol. 78, No. 4, July 1981, pp NS 3473, Norwegian Standard for Design of Conrete Strutures, The Norwegian Counil for Building Standardisation, Oslo, Norway, Ozbakkaloglu, T. and Saatioglu, M., Retangular Stress Blok for High-Strength Conrete, ACI Strutural Journal, Vol. 101, No. 4, July - August 2004, pp Oztekin, E., Pul, S., and Husem, M., Determination of Retangular Stress Blok Parameters for High Strength Conrete, Engineering Strutures, Vol. 25, No. 3, February 2003, pp Pastor, J. A., High Strength Conrete Beams, Ph.D. Thesis, Department of Civil Engineering, Cornell University, Ithaa, New York, January Paulson, K. A., Nilson, A. H., and Hover, K. C., Long-Term Defletion of High- Strength Conrete Beams, ACI Materials Journal, Vol. 88, No. 2, Marh 1991, pp

265 Referenes Pendyala, R. and Mendis, P. A., A Retangular Stress Blok for High Strength Conrete, Strutural Engineering Journal, Institution of Engineers, Australia, Vol. CE39, No. 4, 1998, pp Perenhio, W. F., and Klieger, P., Some Physial Properties of High-Strength Conrete, Researh and Development Bulletin RD056.01T, Portland Cement Assoiation, 1978, 6 p. Persson, B., Poisson s Ratio of High-Strength Conrete, Cement and Conrete Researh, Vol. 29, 1999, pp Popovis, S., A Numerial Approah to the Complete Stress-Strain Curve of Conrete, Cement and Conrete Researh, Vol. 3, No. 5, 1973, pp Radain T. A., Samman, T. A., and Wafa, F. F., Mehanial Properties of High Strength Conrete, Proeedings of Utilization of High-Strength Conrete Symposium, Lillehammer, Norway, June 20-23, 1993, pp Rangan, B. V., Studies on High-Performane High Strength Conrete (HPHSC) Columns, ACI Speial Publiation-186, May 1999, pp Rashid, M. A., Mansur, M. A., and Paramasivam, P., Correlations between Mehanial Propoerties of High-Strength Conrete, Journal of Materials in Civil Engineering, Vol. 14, No. 3, June 2002, pp Rihart, F. E. and Staehle, G. C., Progress Report on Column Tests at the University of Illinois, Journal of Amerian Conrete Institute, Vol. 27, 1931a, pp Rihart, F. E. and Staehle, G. C., Seond Progress Report on Column Tests at the University of Illinois, Journal of Amerian Conrete Institute, Vol. 27, 1931b, pp

266 Referenes Rihart, F. E. and Staehle, G. C., Third Progress Report on Column Tests at the University of Illinois, Journal of Amerian Conrete Institute, Vol. 28, 1931, pp Rihart, F. E. and Staehle, G. C., Fourth Progress Report on Column Tests at the University of Illinois, Journal of Amerian Conrete Institute, Vol. 28, 1932, pp Russell, H. G., Miller, R. A., Ozyildirim, H. C., and Tadros, M. K., Compilation and Evaluation of Results from High Performane Conrete Bridge Projets, Volume 1, Federal Highway Administration, 2003a. Russell, H. G., Miller, R. A., Ozyildirim, H. C., and Tadros, M. K., Compilation and Evaluation of Results from High Performane Conrete Bridge Projets, Volume 2, Federal Highway Administration, 2003b. Sargin, M., Ghosh, S. K., and Handa, V. K., Effets of Lateral Reinforement upon the Strength and Deformation Properties of Conrete, Magazine of Conrete Researh, Vol. 23, No , June - September 1971, pp Sargin, M. and Handa V. K., A General Formulation for the Stress-Strain Properties of Conrete, Report No. 3, Solid Mehanis Division, University of Waterloo, Waterloo, Ontario, Canada, May 1969, 36 p. Shade, J. E., Flexural Conrete Stress in High Strength Conrete Columns, M.S. Thesis, Department of Civil Engineering, the University of Calgary, Calgary, Alberta, Canada, September Smith, G. J., and Rad, F. N., Eonomi Advantages of High-Strength Conretes in Columns, Conrete International, Vol. 11, No. 4, April 1989, pp

267 Referenes Soliman, M. T. M. and Yu, C. W., The Flexural Stress-Strain Relationship of Conrete Confined by Retangular Transverse Reinforement, Magazine of Conrete Researh, Vol. 19, No. 61, Deember 1967, pp Suksawang, N., Nassif, H., and Mohammed, A., Creep and Shrinkage of High- Performane/High-Strength Conrete, ACI Speial Publiation 228, Jun. 2005, pp Sun, C., Girgis, A., Tadros, M. K., and Badie, S., Strutural Behavior of Flexural Member with High-Strength Conrete, ISHPC, Swartz, S. E., Nikaeen, A., Narayan Babu, H. D., Periyakaruppan, N., and Refai, T. M. E., Strutural Bending Properties of Higher Strength Conrete, ACI Speial Publiation-87, High-Strength Conrete, 1985, pp Tadros, M. K., Al-Omaishi, N., Seguirant, S. J., and Gallt, J. G., Prestress Losses in Pretensioned High-Strength Conrete Bridge Girders, NCHRP Report 495, Transportation Researh Board, Washington, DC., 2003, 63 p. Tan, T. H. and Nguyen, N.B., Flexural Behavior of Confined High-Strength Conrete Columns, ACI Strutural Journal, Vol. 102, No. 2, Marh 2005, pp Thorenfeldt, E., Tomaszewiz, A., and Jensen, J. J., Mehanial Properties of High- Strength Conrete and Appliation in Design, Proeedings of Utilization of High Strength Conrete Symposium, Stavanger, Norway, June 1987, pp Van Gysel, A. and Taerwe, L., Analytial Formulation of the Complete Stress-Strain Curve for High Strength Conrete, Materials and Strutures, Vol. 29, November 1996, pp Wang, P. T., Shah, S. P., and Naaman, A. E., Stress-Strain Curves of Normal and Lightweight Conrete in Compression, ACI Strutural Journal, Vol. 75, No. 11, November 1978a, pp

268 Referenes Wang, P. T., Shah, S. P., and Naaman, A. E., High-Strength Conrete in Ultimate Strength Design, ASCE Journal of Strutural Division, Vol. 104, No. 11, November 1978b, pp Wee, T. H., Chin, M. S., and Mansur, M. A., Stress-Strain Relationship of High-Strength Conrete in Compression, ASCE Journal of Materials in Civil Engineering, Vol. 8, No. 2, May 1996, pp Whitney, C. S., Design of Reinfored Conrete Members under Flexure of Combined and Diret Compression, Journal of Amerian Conrete Institute, Vol. 33, Marh 1937, pp Zia, P., Review of ACI Code for Design with High-Strength Conrete, Conrete International, Vol. 5, No. 8, August 1983, pp

269 Appendies APPENDICES 249

270 Appendix A APPENDIX A ECCENTRIC BRACKET TEST DATA BY DIFFERENT RESEARCHERS Hognestad (1951) Speimen ID f (ksi) ε u Speimen ID f (ksi) ε u A1a* C7a* A1b* C7b* B1a* A8a* B1b* A8b* C1a* B8a* C1b* B8b* A2a* C8a* A2b* C8b* B2a* B9b* B2b* C9a* C2a* C9b* C2b* B12a* A3a* B12b* A3b* C12a* B3a* C12b* B3b* B13a* C3a* B13b* C3b* C13a* C4a* C13b* C4b* A14b* C5a* B14a* C5b* C14a* A7a* C14b* A7b* C15a* B7a* C15b* B7b* * olumn speimens subjeted to eentrially applied axial load 250

271 Appendix A Hognestad et al. (1955)* Speimen ID f (ksi) k 1 k 3 k 2 α 1 β *Obtained from Ibrahim (1994) Sargin et al. (1971) Speimen ID f (ksi) k 3 ε u PE PE PE Nedderman (1973) Speimen ID f (ksi) k 1 k 3 k 2 α 1 β 1 ε u

272 Appendix A Kaar et al. (1978a) Speimen ID f (ksi) k 1 k 2 k 3 α 1 β 1 ε u A A6P A A A10P A A A14P D D6P D D D10P D D D14P F F F E E E E8P E E E12P C C4P C C C8P C C C12P Kaar et al. (1978b) Speimen ID f (ksi) k 1 k 2 k 3 α 1 β 1 ε u Swartz et al. (1985) Speimen ID f (ksi) k 1 k 2 k 3 α 1 β 1 ε u B C A B C D

273 Appendix A Pastor (1986) Speimen No f (ksi) k 1 k 2 k 3 α 1 β 1 ε u SP SP SP SP SP SP SP SP SP SP Shade (1992) Speimen ID f (ksi) k 1 k 2 k 3 α 1 β 1 ε u ol ol ol ol ol ol ol ol ol ol ol ol Ibrahim (1994) Speimen ID f (ksi) k 1 k 2 k 3 α 1 β 1 ε u V V V V V V V V V V V V V V V T1 x T4 x T2 x T5 x T3 x T6 x x are the triangular speimens. 253

274 Tan et al. (2005) Speimen ID f (ksi) k 1 k 3 k 2 α 1 β 1 ε u S40-A-N S40-A-N S40-B-N S40-B-N S40-B-N S40-C-N S40-C-N S70-A-N S70-B-N S70-B-N S70-C-N S90-B-N S90-B-N S90-B-N S90-E-N S90-E-N S90-E-N S40-B-E20/2* S40-B-E40/1* S40-B-E40/2* S40-B-E60/1* S40-B-E60/2* S70-B-E20* S70-B-E40* S70-B-E60* * olumn speimens subjeted to eentrially applied axial load Appendix A 254

275 Appendix B APPENDIX B MATERIAL PROPOERTIES PROPERTIES OF FINE AGGREGATE (NATURAL SAND) Sieve Analysis of Natural Sand (Perform at NCSU CFL) Sieve Size Cumulative Passing 3/8 in /4 in # # # # #

276 PROPERTIES OF FINE AGGREGATE (MANUFACTURED SAND) Appendix B Provided by Carolina Sunrok Corporation 256

277 257 Appendix B

278 PROPERTIES OF COARSE AGGREGATE Appendix B Provided by Carolina Sunrok Corporation 258

279 259 Appendix B

280 PROPERTIES OF SILICA FUME Appendix B Provided by Elkem Materials 260

281 PROPERTIES OF SILICA FUME Appendix B Provided by Boral Material Tehnologies 261

282 262 Appendix B