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Assessment of confinement models for reinforced concrete columns subjected to seismic loading Riederer, Kevin Allen 2006

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ASSESSMENT OF CONFINEMENT MODELS FOR REINFORCED CONCRETE COLUMNS SUBJECTED TO SEISMIC LOADING by Kev in A l len Riederer B . S c , University o f Alberta, 2003 A THESIS S U B M I T T E D IN P A R T I A L F U L F I L L M E N T O F T H E R E Q U I R E M E N T S F O R T H E D E G R E E OF M A S T E R OF A P P L I E D S C I E N C E in The Faculty of Graduate Studies (Civ i l Engineering) T H E U N I V E R S I T Y OF B R I T I S H C O L U M B I A December 2006 © Kev in A l len Riederer, 2006 ABSTRACT Research conducted over the past several years has shown that factors such as axial load level and the amount and spacing of confinement steel influence the performance of reinforced concrete columns subjected to seismic loading. The aim of this research project was to investigate the performance of the current A C I 318 confining steel requirements and compare them to other codes and proposed models to determine their suitability for a performance based design equation for implementation in Chapter 21 of A C I 318. The investigation was performed by analyzing the results of multiple reverse-cyclic column tests presented in the U W / P E E R Structural Performance Database. The condensed database used in this investigation consisted solely of columns which exhibited flexural failure and contained 145 rectangular and 50 circular columns. First, a scatter plot was used to compare the confining requirements of each model with the lateral drift observed for each column within the database. The plot showed the drift ratio achieved by the column test versus a ratio of lateral steel Ash provided over that which is required by A C I (Ash provided / Ash ACD- A drift ratio of 2.5% was selected as the performance target for the evaluation. Columns were identified as those which satisfied the requirements of the model but failed the performance target ('unconservative') or those which failed the requirements of the model but satisfied the performance target ('conservative'). For each model, the percentage of columns falling into these classifications was calculated and compared. Two fragility curves were generated for each model which provided the probability of a column being classified as 'unconservative' or 'conservative' as a function of drift ratio. A third curve was a combination of the first two and provided insight as to the overall performance of the model. n Abstract For both the rectangular and circular column evaluations, the A C I model was determined to be the least desirable of all models investigated. Based on the evaluation techniques developed, specific models were selected as recommended alternatives to the current A C I requirements. The recommended models minimize the potential of a column experiencing lateral strength degradation before reaching the prescribed lateral drift limit. 111 TABLE OF CONTENTS A B S T R A C T .. : • T A B L E OF C O N T E N T S iv L IST OF T A B L E S . . . . ix L IST OF F I G U R E S x L IST OF N O T A T I O N S x i i i A C K N O W L E D G E M E N T S . - . xiv 1 I N T R O D U C T I O N •• 1 1.1 Motivation , . . . 1 1.2 Ductil ity and Lateral Steel 1 1.3 Confinement Act ion of Transverse Steel..., 2 1.4 Properties of Confined Concrete 6 1.4.1 Mander Mode l for Confined Concrete 7 1.4.2 Legeron and Paultre Model for Confined Concrete •. 9 1.5 Confinement and Lateral Deformation 11 1.6 Ductil ity and Ax ia l Load : 13 1.7 Research Objectives and Scope 15 2 C O D E E Q U A T I O N S A N D P R O P O S E D M O D E L S 17 2.1 Introduction .., 17 2.2 Current Code Requirements 17 2.2.1 American Concrete Institute 318-05 (ACI) 17 2.2.2 Canadian Standards Association A23.3-04 (CSA) 23 2.2.3 N Z S 3101:2006 (NZS) • 25 2.3 Proposed Models 27 2.3.1 Wehbe, Saiidi, and Sanders 1999 (WSS99) 27 2.3.2 Saatcioglu and Razvi 2002 (SR02) 29 2.3.3 Brachmann, Browning and Matamoros 2005 (BBM05) 31 2.3.4 Sheikh and Khoury 1997 (SK97) 32 2.3.5 Bayrak and Sheikh 1998 (BS98) : 34 iv \ Table of Contents 2.3.6 Bayrak and Sheikh & Sheikh and Khoury : 35 2.3.7 Paulay and Priestly 1992 (PP92) 35 2.3.8 Watson, Zahn and Park 1994 (WZP94) 36 2.3.9 L i and Park 2004 (LP04) - 3 8 2.3.10 Watson Zahn and Park & L i and Park 39 2.3.11 Paultre and Legeron 2005 (PL05) 39 2.4 Range of Properties Investigated 42 3 E V A L U A T I O N D A T A B A S E 44 3.1 ' Experimental Database 44 3.2 Determination of Failure 46 3.2.1 Effective Force and P-Delta correction 46 3.2.2 Displacement at Failure 49 3.3 Failure Classification '. 50 3.4 Range and Verif ication of Database Parameter Values 52 4 C O N F I N E M E N T M O D E L E V A L U A T I O N S 58 4.1 Rectangular Columns 58 4.1.1 Scatter Plot Evaluation : 58 4.1.1.1 Evaluation Procedure 58 4.1.1.2 Assessment of A C I 318-05 21.4.4.1 62 4.1.1.3 Assessment of Codes and Proposed Models 64 4.1.2 Fragility Curve Evaluation 71 4.1.2.1 Evaluation Procedure 72 4.1.2.2 Assessment of A C I 318-05 21.4.4.1 73 4.1.2.3 Assessment of Code and Proposed Models ; . 75 4.1.2.4 Special Consideration for SR02 80 4.1.3 Spacing of Transverse Reinforcement 81 4.1.3.1 Assessment of A C I 21.4.4.2 81 4.1.3.2 Assessment of CS A and N Z S 85 4.1.4 Max imum Recorded Drifts 86 4.2 Circular Columns 88 4.2.1 Scatter plot evaluation 88 v Table of Contents 4.2.1.1 Evaluation procedure 88 4.2.1.2 Assessment of A C I 318-05 21.4.4.1 89 4.2.1.3 Assessment of Codes and Proposed Models 91 4.2.2 Fragility curve evaluation , 98 4.2.2.1 Evaluation Procedure : 98 4.2.2.2 Assessment of A C I 318-05 21.4.4.1 98 4.2.2.3 Assessment of Codes and Proposed Models 101 4.2.2.4 Special Considerations for SR02 106 4.2.3 Spacing (Spiral Pitch) of Transverse Reinforcement 107 ,4.2.3.1 Assessment of A C I 21.4.4.2 107 4.2.3.2 Assessment of C S A and N Z S 108 4.2.4 Max imum Recorded Drifts 109 5 S E L E C T I O N OF C O N F I N E M E N T M O D E L 111 5.1 Selection Procedure I l l 5.1.1 Objective H I 5.1.2 Scatter Plot Evaluation 112 5.1.3 Fragility Curve Evaluation 114 5.1.4 Comparison of Expressions 115 5.1.5 Mode l Requirements 115 5.2 Rectangular Columns 116 5.2.1 Scatter Plot Evaluation 116 5.1.6 Fragility Curve Evaluation ...117 5.1.7 Comparison of Expressions 119 5.1.8 Requirements of Models 119 5.1.9 Conclusion and Recommendation 121 5.3 Circular Columns 123 5.3.1 Scatter plot Evaluation 124 5.3.2 Fragility Curve Evaluation 124 5.3.3 Comparison of Expressions 124 5.3.4 Requirements of Models 127 5.3.5 Conclusion and Recommendation 130 vi Table of Contents 5.4 Final Recommendations vs. A C I 132 5.4.1 Comparison figure , 132 6 S U M M A R Y A N D C O N C L U S I O N S 134 6.1 Summary....: 134 6.2 Recommendations 136 6.3 Recommendations for future research 137 R E F E R E N C E S , 139 A P P E N D I X A 146 A 1 . Rectangular Column Database 146 A 2 . Circular Column Database 155 A P P E N D I X B.. 159 B l Rectangular Typical Columns Details 159 B2 Rectangular Typical Column Cross Sections : 160 B3 Circular Typical Columns Details.. 161 B4 Circular Typical Column Cross Sections '. 162 A P P E N D I X C .' 163 C I Rectangular Confinement Models.. 163 C2 Circular Confinement Models ,. 164 A P P E N D I X D 166 D. l Rectangular Column Scatter Plots (with A C I Minimum) .' 166 D.2 Rectangular Column Scatter Plots (without A C I Minimum) 168 D.3 Rectangular Column Scatter Plots (Maximum Recorded Drifts) 171 D.4 Rectangular Column A Fragility Curves (with A C I Minimum) 174 D.5 Rectangular Column B Fragility Curves (with A C I Minimum) 176 D.6 Rectangular Column C Fragility Curves (with A C I Minimum) 178 D.7 Rectangular Column A Fragility curves (without A C I Minimum) 181 D.8 Rectangular Column B Fragility Curves (without A C I Minimum) 183 D.9 Rectangular Column C Fragility Curves (without A C I Minimum) 185 D.10 Rectangular Column A Fragility Curves (Maximum Recorded Drifts) 188 D. l 1 Rectangular Column B Fragility Curves (Maximum Recorded Drifts) 190 D. l2 Rectangular Column C Fragility Curves (Maximum Recorded Drifts) 192 vi i Table of Contents D.13 Circular Column Scatter Plots (with A C I Minimum) 195 D.14 Circular Column Scatter Plots (without A C I Minimum) 197 . D.15 Circular Column A Fragility Curves (with A C I Min imum), 200 D.16 Circular Column B Fragility Curves (with A C I Minimum) 202 D.17 Circular Column C Fragility Curves (with A C I Minimum) 204 D.18 Circular Column A Fragility Curves (without A C I Minimum) 206 D.19 Circular Column B Fragility Curves (without A C I Minimum) 208 D.20 Circular Column C Fragility Curves (without A C I Minimum) 210 v i i i LIST OF TABLES Table 2.1 Circular column A C I confinement requirements timeline 22 Table 2.2 Rectangular column A C I confinement requirements timeline 23 Table 2.3 Value of Coefficient y for Equation 2.33 32 Table 2.4 Range for parameters used in development ofthe proposed models 43 Table 3.1 Confinement classification details , 45 Table 3.2 Cross-Section Classifications 46 Table 3.3 Rectangular column parameter ranges (database and typical columns) 53 Table 3.4 Circular column parameter ranges (database and typical columns) 53 Table 4.1 Quadrant data distribution of Figure 4.2 63 Table 4.2 Statistics for A C I rectangular scatter plot 63 Table 4.3 Quadrant data distribution for rectangular column scatter plots '. 70 Table 4.4 Scatter plot statistics for A C I spacing limit shown in Figure 4.24 83 Table 4.5 A C I 318-05 Governing spacing of rectangular transverse reinforcement 85 Table 4.6 Governance breakdown for spacing of transverse reinforcement for C S A A23.3-04 and N Z S 3101:2006 , 86 Table 4.7 Quadrant data distribution of A C I circular scatter plot 90 Table 4.8 Statistics for A C I circular scatter plot 90 Table 4.9 Quadrant data distribution for all models circular scatter plots 97 Table 4.10 A C I 318-05 Governing spacing of circular transverse reinforcement 108 Table 4.11 Governance breakdown for spacing of transverse reinforcement for C S A A23.3-04 and N Z S 3101:2006... 109 Table 5.1 Details for rectangular columns 15 and 106 114 ix LIST OF FIGURES Figure 1.1 Confining stresses provided by different arrangements of transverse reinforcement (Watson et. al 1994) 4 Figure 1.2 Effectively confined core for circular 5 Figure 1.3 Effectively confined core for rectangular 5 Figure 1.4 Proposed concrete compressive stress-strain model (Mander et. al. 1988) 8 Figure 1.5 Confined strength determination from confining stresses for 8 Figure 1.6 Stress-strain relationship of confined concrete 10 Figure 1.7 Curvature defined 12 Figure 1.8 Ax ia l load ratio vs. curvature 14 Figure 3.1 P-A correction cases (Berry et. al. (2004)) 47 Figure 3.2 Example for confirming failure (Camarillo (2003)) 50 Figure 3.3 Conceptual definition of column failure modes 51 Figure 3.4 Failure Classification Flowchart (Berry et. al (2004)) 52 Figure 3.5 Ax ia l Load ratio versus drift ratio 54 Figure 3.6 p a r e a and p v o i versus drift ratio 55 Figure 3.7 f c' / f y t versus drift ratio 56 Figure 3.8 A g / A Ch versus drift ratio 56 Figure 3.9 B / L and D/L versus drift ratio 57 Figure 3.10 p i o n g versus drift ratio 57 Figure 4.1 Scatter plot layout with identification of quadrant labels 60 Figure 4.2 A C I scatter plot (rectangular columns) 62 Figure 4.3 f c' versus Ax ia l Load Ratio for columns in quadrants 2 and 3 of A C I rectangular scatter plot 64 Figure 4.4 Rectangular scatter plot statistics all models (with A C I minimum) 65 Figure 4.5 C S A scatter plot (rectangular columns) 66 Figure 4.6 N Z S scatter plot (rectangular columns).. 67 Figure 4.7 PP92 scatter plot (rectangular columns) 67 x List of Fisur.es Figure 4.8 SR02 scatter plot (rectangular columns) 68 Figure 4.9 WSS99 scatter plot (rectangular columns) 68 Figure 4.10 B B M 0 5 scatter plot (rectangular columns) : 69 Figure 4.11 S K B S scatter plot (rectangular columns) 69 Figure 4.12 W Z P L P scatter plot (rectangular columns) 70 Figure 4.13 Rectangular scatter plot statistics bar graph 71 Figure 4.14 Rectangular A fragility curve for A C I 73 Figure 4.15 Rectangular B fragility curve for A C I 74 Figure 4.16 Rectangular C fragility curve for A C I 74 Figure 4.17 Rectangular A fragility curve all models (with A C I minimum) 76 Figure 4:18 Rectangular B fragility curves all model (with A C I minimum) 76 Figure 4.19 Rectangular C fragility curve all models (with A C I minimum) 77 Figure 4.20 Rectangular A fragility curve for all models 79 Figure 4.21 Rectangular B fragility curve for all models 79 Figure 4.22 Rectangular C.fragility curve for all models 80 Figure 4.23 Rectangular SR02 fragility curve comparison .....81 Figure 4.24 Rectangular scatter plot for spacing limit of H/4 82 Figure 4.25 Rectangular C fragility curve for spacing limit H/4... 83 Figure 4.26 f c' vs. axial load ratio for Q2 and Q3 columns for H/4 spacing limit 84 Figure 4.27 Rectangular Scatter plot statistics using maximum recorded drifts 87 Figure 4.28 Rectangular C fragility curves using maximum recorded drifts 88 Figure 4.29 A C I scatter plot (circular columns) 89 Figure 4.30 fc ' vs. axial load ratio for Q3 columns of 91 Figure 4.31 Circular scatter plot statistics all model (with A C I minimum) 92 Figure 4.32 C S A scatter plot (circular columns) 93 Figure 4.33 N Z S scatter plot (circular columns) 94 Figure 4.34 PP92 scatter plot (circular columns) 94 Figure 4.35 SR02 scatter plot (circular columns) 95 Figure 4.36 B B M 0 5 scatter plot (circular columns) 95 Figure 4.37 S K B S scatter plot (circular columns)... 96 Figure 4.38 W Z P L P scatter plot (circular columns) 96 xi List of Figures Figure 4.39 Circular scatter plot statistics bar graph 98 Figure 4.40 Circular A fragility curve for A C I 99 Figure 4.41 Circular B fragility curve for A C I ••• 100 Figure 4.42 Circular C fragility curve for A C I 100 Figure 4.43 Circular A fragility curve all models (with A C I minimum) 101 Figure 4.44 Circular B fragility curve all models (with A C I minimum) 102 Figure 4.45 Circular C fragility curve all models (with A C I minimum) 102 Figure 4.46 Circular A fragility curve for all models 104 Figure 4.47 Circular B fragility curve for all models ; 105 Figure 4.48 Circular C fragility curve for all models 105 Figure 4.49 Circular SR02 fragility curve comparison 106 Figure 4.50 Circular scatter plot for one quarter minimum dimension spacing limit..... 107 Figure 5.1 Desired movement of data points 113 Figure 5.2 Location of specific column examples for A C I and C S A scatter plot 114 Figure 5.3 A fragility curves 117 Figure 5.4 B fragility curves 118 Figure 5.5 C fragility curves 118 Figure 5.6 Confinement area requirements for range of axial load ratios 120 Figure 5.7 Confinement spacing requirements for range of axial load ratios 121 Figure 5.8 A fragility curves : 125 Figure 5.9 B fragility curve 126 Figure 5.10 C fragility curve 126 Figure 5.11 SR02 scatter plot drift ratio comparison 128 Figure 5.12 Confinement density requirements for range of axial load ratios 129 Figure 5.13 Confinement spacing requirements for range of axial load ratios 130 Figure 5.14 Comparison of recommendations and A C I 318-05 requirements 133 x i i LIST OF NOTATIONS ACh = cross-sectional area of a structural member measured out-to-out of transverse reinforcement Ag = gross area of column Ash - total cross-sectional area of transverse reinforcement (including crossties) within spacing s and perpendicular to dimension h c Asp = cross-sectional area of spiral or circular hoop reinforcement bc = cross-sectional dimension of column core measured centre-to-centre of confining reinforcement f'c = specified concrete strength o f concrete fy = specified yield strength of nonprestressed reinforcement fyt = specified yield strength of transverse reinforcement P = Ax ia l compressive force on column Po = nominal axial load strength at zero eccentricity s = spacing of transverse reinforcement measured along the longitudinal axis ofthe member si = centre-to-centre spacing of longitudinal reinforcement, laterally supported by corner of hoop or hook of crosstie <fi = capacity reduction factor Parea = area ratio of transverse confinement reinforcement (ASh / s-hc) ps = ratio of volume of spiral reinforcement to the core volume confined by the spiral reinforcement (measured out-to-out) pt = area of longitudinal reinforcement divided by gross area of column section p,m = mechanical reinforcing ratio (m = f y / 0 . 8 5 f c ) pvui = volume ratio of transverse confinement reinforcement x i i i ACKNOWLEDGEMENTS First, I would like to express my sincere gratitude to my supervisor Dr. Kenneth Elwood for his guidance, encouragement, patience and friendship throughout my time at U B C . It was a privilege to work with him. I would also like to thank Dr. Terje Haukaas for his support throughout my graduate studies. This research project would not have been possible i f it were not for the financial assistance provided by the Portland Cement Association through the Education Foundation Research Fellowship. Their support is greatly appreciated. I owe a great deal to my colleagues at U B C . In particular I want to thank Dominic Mattman, Chris Meis l , Aaron Korchinski , T im Mathews, Arnoud Charlet, and Soheil Yavari for their support and friendship. I also want to thank my close friends outside of U B C for their encouragement, support and for their belief in me. I would like to like to express my sincere appreciation to my family, especially Michael , Andrea, J im and Margaret Hoffman. Their support over the years was instrumental in helping me reach all of my educational goals and this work would not have been possible without them. Final ly, I want to thank my parents, A l len and Ann Riederer, who have taught me everything in life which is truly important to learn. Their unconditional love and support w i l l be remembered always. M y work is dedicated to them. Thank you. xiv 1 INTRODUCTION 1.1 Motivation Reinforced concrete columns subjected to seismic loading must be able to withstand several inelastic deformation reversals to maintain the integrity of the structure which they are supporting. Previous earthquakes and laboratory test results have shown that the ability of columns to undergo these deformations without a significant loss in strength can be linked to the level of confinement applied to the concrete within the core of the column. In reinforced concrete columns, confinement is provided by the amount, arrangement and spacing of transverse steel. To ensure columns are able to reach acceptable levels of deformation during an earthquake, concrete design codes must appropriately incorporate all the variables which contribute to their seismic performance. This work w i l l investigate current design codes and proposed models found in the literature with the aim of determining the optimum requirement for confining steel. To form the basis of this investigation, the following section wi l l present the mechanics by which transverse steel confines the core concrete within a column and how the level of confinement affects the columns seismic performance. 1.2 Ductility and Lateral Steel It is wel l known throughout the structural and earthquake engineering community that the lateral steel in reinforced concrete columns serves three primary functions, it provides shear reinforcement, it acts to restrain the buckling of longitudinal compression steel, and it confines the concrete within the core of the column. 1 Introduction For members subjected to shear forces, engineers commonly use the widely accepted truss model for the shear resistance mechanism. The transverse steel bars in these members behave as tension components within these idealized truss models. Depending on weather or not the concrete contribution to shear resistance is accounted for, the transverse steel w i l l be needed to resist some or all of the design shear force. The amount and orientation of transverse steel required for shear resistance is not the focus of this study. Buckl ing of longitudinal compression reinforcement can limit the performance of columns subjected to seismic loading. For this reason, the lateral support of the longitudinal reinforcement provided by the transverse reinforcement is an important parameter in the design of reinforced concrete columns. Therefore, the lateral steel spacing in the end regions where hinges are l ikely to form is crucial to reducing buckling of the compression bars. However, the design of lateral steel for support of longitudinal bars is not the focus of this study. The area, spacing and orientation of lateral bars also play a key role in the effectiveness of the transverse reinforcement to confine the core concrete of a column. The relationship between the ductility o f reinforced concrete columns, a crucial component within seismic design of buildings, and transverse steel in the column falls primarily out ofthe confining action of the steel. It is this confining action of transverse steel that is the focus of this work. 1.3 Confinement Action of Transverse Steel It is important first to understand the mechanism by which the transverse reinforcement confines the concrete core of a column. The definitive work in this area was done by Sheikh and Uzumeri (1980) and (1982) and was presented again in Mander et. al. (1988). Based on a series of column tests, the authors concluded that the area of the effectively confined concrete is less than the area bounded by the perimeter tie. In other words, Ae < ACh where Ae is the effectively confined area of concrete and Ach is the area of concrete enclosed by the perimeter tie. They also concluded that the effectively confined concrete 2 Introduction is determined by the distribution of the longitudinal steel and the resulting tie configuration and spacing. To account for this, the authors propose the following for the effective lateral confining pressure, f/' f ' , = f,K ( l . l ) where ke is a confinement effectiveness coefficient expressed as: K = ~ d - 2 ) Acc where Acc, the area o f core within centre lines o f the perimeter spiral or hoops excluding area of longitudinal steel, expressed as: Ac =4(1 'Pec) d - 3 ) where pcc is the ratio of longitudinal reinforcement to area of core of section. The parameter f\ is the lateral pressure from the transverse reinforcement. For various configurations of transverse reinforcement, fi can be calculated as shown in Figure 1.1 Figure 1.2 and Figure 1.3 show the relationship between the effectively confined core and the lateral steel configuration and spacing. The confinement effectiveness coefficient for sections confined by circular hoops is expressed as: V 2 d s J ( 1 . 4 ) e 1 ' - Pu and for circular spirals as: I- *' k = _ 2 d I _ ( l 5 ) 3 Figure 1.1 Confining stresses provided by different arrangements of transverse reinforcement (Watson et. al 1994) The lateral confining pressure is found by considering the half body confined by the lateral steel. Equil ibrium of forces requires that for circular columns: / ,=^T*- ( L 6 ) sn„ From Equation 1.1 the effective lateral confining stress imposed on a circular column can be expressed as: f, = \kePsfyh ' ( 1-7) where ps is the volumetric transverse reinforcement ratio and ke is given in Equations 1.4 and 1.5. 4 Introduction Cover Concrete Effectively confined core Cover Concrete (Spalls off) - \ Ineffectively — confined core Section B - B r 1 • * P ° ( j 1 1 1 . i L J . i ' d g - s ' / i T B " ' d s Section A - A Figure 1.2 Effectively confined core for circular hoop reinforcement (Mander et. al 1988) Effectively confined Cover Concrete (Spalls off) -Ineffectively confined core r \ 1) b c - s'/2 1 Section Y - Y Figure 1.3 Effectively confined core for rectangular hoop reinforcement (Mander et. al 1998) 5 Introduction Similar expressions for rectangular columns are also presented. From Equation 1.2 it can be found that for rectangular sections: 6b J. r „i A l-2F ., 1-*.=^ " 7 A ~ " ^ ' (i-^) where-w',- , the /'th clear distance between adjacent longitudinal bars, along with the dimensions s', bc and dc are shown in Figure 1.2 and Figure 1.3. Since many rectangular columns have different quantities o f lateral steel in the x and y directions, separate transverse reinforcement ratios are defined as: p*=^r ( 1 - 9 ) sdc P y = \ (UO) sdc Again recognizing the relationship given in Equation 1.1, the effective lateral confining stresses for a rectangular column in the x and y directions are: r,=kepjyh ( i . i i ) and f\ = KPyf» ' (1 .12) where ke is given in Equation 1.8. Figures 1.1, 1.2 and 1.3 as wel l as Equations 1.1, 1.4, 1.5 and 1.8 provide valuable insight as to which lateral steel parameters ought to be considered in confinement steel provisions. They include: area of transverse bar, spacing of transverse bars and dimension of concrete core, yield strength of steel, density of longitudinal reinforcement and in the case of rectangular columns, spacing of longitudinal reinforcing bars. 1.4 Properties of Confined Concrete Now that the relationship between the transverse steel and concrete confinement has been illustrated, the effect of confinement on the expected behaviour of concrete can be addressed. For nearly a century, investigators have known the effects on confining 6 Introduction pressures on the stress-strain behaviour of concrete. Richart et al. (1928) studied the strength and corresponding longitudinal strain of concrete confined by an active hydrostatic f luid pressure. Since that time, many mathematical relationships predicting the stress-strain response of confined concrete have been proposed. 1.4.1 Mander Model for Confined Concrete Mander et al. (1988) proposed a unified stress-strain approach based on the work done previously by researchers including Richart et. al. The approach was developed to be applicable to columns confined by either circular or rectangular transverse reinforcement. The model, illustrated in Figure 1.4, was developed for concrete tested with a slow, or quasi-static, strain rate and monotonic loading. The authors proposed that the longitudinal compressive concrete stress,^, is given by: f xr / c = J c : r ( i - i 3 ) r -1 + x where f'cc = compressive strength of confined concrete, ' x = -^- ( 1 .14 ) where sc = longitudinal compressive concrete strain, 1 + 5 f p ^ J cc 1 (1 .15) where f'co is the unconfined concrete strength and sco is the corresponding strain typically assumed to be 0.002, E,. where (1 .16) Ec= 5000 J]\(MPa) ( 1 .17 ) is the tangent modulus of elasticity of the concrete and £ = ^ ( U 8 ) 7 Introduction Confined Compressive Strain, £ c Figure 1.4 Proposed concrete compressive stress-strain model (Mander et. al. 1988) To determine the confined concrete compressive strength f'cc, the authors use a constitutive model based on tri-axial compression tests and described by Wi l l iam and Warnke (1975). As shown in Figure 1.5, the Wi l l iam and Warnke model relates the confined strength ratiof'cJf'co to the two lateral confining stresses/'// andf'\2. Confined Strength Ratio f^^ct 3 0 OJ 0.2 03 Smollett Confining Stress Ratio, ^V'^'o Figure 1.5 Confined strength determination from confining stresses for rectangular sections (Mander et. al. 1988) 8 Introduction When the concrete core is confined by equal lateral confining stresses (i.e. f'u = f'\2), it can be shown that the compressive strength can be given as: 7'cc = / ' 1.254 + 2.254 I + 7-94/' f J co - 2 f (1.19) co J 1.4.2 Legeron and Paultre Model for Confined Concrete More recently, Legeron and Paultre (2003) proposed a stress-strain model for confined concrete based on strain compatibility and transverse force equilibrium. The model is an expansion of a proposal by Cusson and Paultre (1995) which was developed for high strength concretes. The curve shown in Figure 1.6 is defined by locating two distinct points labeled A and B on the figure. Point A is the confined compressive strength fcc corresponding to the strain e ' c c , and point B is the post-peak axial strain E C C 5 0 in the concrete when the capacity drops to 50% of the confined strength. The stress in the confined concrete,^, corresponding to a strain ecc, in the ascending portion (point 0 to point A) of the stress-strain curve is given as: f • = r J cc J c k-\ + {accls\cf F < £•' (1.20) where the prime signifies that a term is being evaluated at the peak of the stress-strain curve and the slope controlling parameter k is given as: k Ect-{f\Js\c) where Ect is the tangent modulus of elasticity of the unconfined concrete. (1.21) The post-peak portion of the curve is described by the following equation: fee =/•«»: e x p [ * l ( ^ - ^ « : ) * 2 l S c c ^ £ \ c ( 1 - 2 2 ) 9 Introduction on "S < -+-> o o a o V i 0.5fl Concrete Axial Strain, £ c Figure 1.6 Stress-strain relationship of confined concrete (Cusson and Paultre 1995) where the authors define the parameters ki and ^ as: In 0.5 :50 ^k2 k2=\ + 25(Ie50) (1.23) (1.24) where Ie5o is the effective confinement index evaluated at the post-peak strain eccso shown in Figure 1.6. To develop expressions for f c c and s' c c, the authors use the effective confinement index at peak stress, a nondimensional parameter first introduced in Cusson and Paultre (1995). TI / le (1.25) where sc and the following relationships are provided: / ' « , = / • « [ ! +2 .4 (7 ' . ) 0- 7] (1.26) (1.27) 10 Introduction e'cc = s<c[\ + 35(rey2] (1 .28) The authors note that recent research has concluded that the stress in the confining steel does not necessarily reach the yield limit. This is especially true in columns with low confinement or in which high-yield strength steel is used. To include this phenomenon, the authors introduce the following parameter: K = F ' C , (1 .29 ) PseyEs£ c and define the stress in the confinement reinforcement at peak strength f \ as: 0 - 2 5 / ' < > 0 . 4 3 ^ / / „ > , ( ) ( L 3 ° ) The post-peak strain eCC50 is taken from the curve where the stress reaches 50% of the maximum value. In equation form, it can be expressed as: = * c 5 o( l + 6 0 / e 5 0 ) (1 .31) where ecso is the post-peak strain in the unconfined concrete taken from the-curve at the point of 0.5/ ' c and Ieso is the effective confinement index at eccso and is expressed by the authors in the following form: /,*, = P . , ji- (1 -32) J c For the relationships shown above, fhy is the yield strength of the transverse reinforcement and pse is the effective^volumetric ratio of confinement reinforcement P - , = K , - ' - ( 1-33 ) sc where for a given column, A s h is the total area of transverse reinforcement within spacing s, and c is the dimension of the confined core for a given direction. 1.5 Confinement and Lateral Deformation For earthquake engineers, the most important trend observed by investigators who have researched the effect of confinement on concrete stress-strain behaviour has been the 11 Introduction significant increase in axial strain capacity. Paulay and Priestley (1992) suggest this increase can lead to ultimate compression strains on the order of 4 to 16 times the value of 0.003 traditionally assumed for unconfined concrete. This trend is clearly shown in the two models presented here, Figure 1.4 and Figure 1.6, and in the various other models found in the literature. To understand how an increase in axial strain capacity of concrete relates to improved lateral ductility in reinforced concrete columns, one must examine the strain gradient that exists in members subjected to axial load and bending forces. Consider the reinforced concrete, element of length L, subjected to axial compressive force P and bending moment M shown in Figure 1.7(a). The deformed shape is represented in Figure 1.7(b) which also shows the curvature resulting from the loading condition, and Figure 1.7(c) shows how the curvature is related to the sectional strain distribution as well as the location ofthe neutral (no strain) axis. N.A. dL (a) (b) (c) Figure 1.7 Curvature defined Curvature, tf>, can be defined as the change in angle over a given length or: dd ec comp dL ( 1 3 4 ) 12 Introduction The assumption in reinforced concrete design is that the formation of cracks in the tension region of the element results in the tension steel resisting all tension forces and being strained to a value of slen, while the concrete in the compression region resists the compressive forces with the most extreme compression fibers reaching a strain of 8 c o m p -From the relationship given in Equation 1.34 it is clear that i f a larger ultimate compression strain is reached, a larger resulting ultimate curvature wi l l be achieved. Addit ionally, the increase in compressive stresses found in confined concrete requires that a smaller amount of concrete is required to balance the sectional tension forces, causing the neutral axis to shift closer to the compression face and further increasing the ultimate curvature of the member. A larger curvature capacity of a concrete section translates into larger lateral deformations for a concrete member such as a column. 1.6 Ductility and Axial Load . The impact of axial load on the deformability of reinforced concrete columns has been the focus of many recent investigations. The consistent conclusion is that the effect of axial compression is to reduce column deformability (Saatcioglu 1991). This is explained by considering the interaction diagrams which are commonly used by engineers in the design of reinforced concrete columns. A typical interaction diagram shows the moment capacity of a particular column cross section at various levels of axial load. Likewise, an axial load and curvature capacity interaction diagram can be produced for a particular column cross section. The effect of axial load and confinement on the curvature capacity is evidenced in the axial load curvature diagram shown below in Figure 1.8. The interaction diagram is given for an example column cross section with dimensions 400mm x 400mm, 12 16mm diameter longitudinal bars, and 7mm diameter transverse bars and represents the point at which maximum compressive strain of 0.004 is reached in the concrete. The interaction between axial load ratio and curvature is shown for three different spacings of transverse reinforcement. The maximum compression strain in the concrete was calculated using the Mander model. As the spacing decreases, the 13 Introduction 0.05 Curvature * D Figure 1.8 Axial load ratio vs. curvature confinement effectiveness of the transverse steel increases, the maximum compression strain increases, and the curvature capacity increases. The figure shows that for an axial load ratio of 0.5, the column is able to achieve a 53% increase in curvature when the spacing is decreased from 100mm to 50mm. The figure clearly shows that for a given cross section, the axial load significantly impacts the curvature capacity. Further evidence of the influence of axial load on the lateral drift performance of reinforced concrete columns was presented by Elwood and Eberhard (2006). The authors investigated the effect of axial load on the amount of lateral displacement experienced by a column due to bar slip. When a reinforced concrete column is subjected to a lateral load, elongation of the longitudinal reinforcing bars in tension occurs within the beam-column joint or footing. This bar slip results in lateral displacements in addition to those caused by flexural deformation of the column. Therefore, the displacement of a column can be considered as the sum of the displacements due to flexure, bar slip, and often negligible shear displacements. Elwood and Eberhard reported that for columns with low 14 Introduction levels of axial load, P / A g f c ' < 0.2, slip deformations can account for up to approximately half o f the total deformation at yield, and for columns with high values for axial load ratio, P / Agfc' > 0.5, the displacement due to bar slip is negligible. The conclusion that can be reached from this result is that for columns with high axial load the flexural displacements, which are significantly influenced by the level of confinement, dominate the total column displacement at yield. A lso , this indicates.that columns with low axial load have the added deformation component from bar slip which does not depend on the amount of confinement and have improved deformation capacity without the need for additional confining steel. This effect disappears as the axial load increases, thereby increasing the need for confinement for columns with high axial loads. 1.7 Research Objectives and Scope The aim of this research project is to investigate the performance of the current A C I 318 confining steel requirements and compare them to other codes and proposed models to determine their suitability for a performance based design equation for implementation in Chapter 21 of A C I 318. This is done by addressing both the area requirement of section 21.4.4.1 and the spacing requirements of section 21.4.4.2. The performance of the A C I model wi l l be evaluated in a relative manner to the current building codes in Canada and New Zealand, as well as proposed models found in the literature. For reasons discussed above, a key variable to be investigated is the axial load level which is currently not present in the confinement requirement within the A C I code. A n important conclusion to be drawn is i f confinement models incorporating axial load provide an improvement over the A C I model. Rectangular and circular column test databases, made available by the University of ( Washington and the Pacific Earthquake Engineering Research (PEER) Center, w i l l be used to compare the requirements of each model with the performance of the columns in the database subjected to simulated seismic loads. Once the evaluation is complete, the results wi l l be used to determine i f the current A C I expressions are adequate to achieve acceptable levels of performance. If it is found that 15 Introduction the confinement requirements of A C I are not the most desired model, a recommended alternative wi l l be proposed. The proposed model wi l l ensure that a column wi l l experience only modest lateral strength degradation before reaching the prescribed lateral drift limit. A lso , the form of the confinement requirements and their phrasing within chapter 21 of A C I 318 wi l l be investigated. The intent is to provide a clear and concise clause which explicitly states all confining steel requirements for reinforced concrete columns. 16 2 CODE EQUATIONS AND PROPOSED MODELS 2.1 Introduction This chapter introduces the confinement models evaluated in this study. The goal o f determining an appropriate confinement model w i l l be reached through an evaluation of these models as apposed to developing a new one. The database of column tests used to perform the evaluation and subsequent results and conclusions are presented in the chapters which follow. Three building code requirements as wel l as nine proposed models taken from the literature are presented. The building code requirements are from the current reinforced concrete codes in the United States, Canada and New Zealand. The proposed models evaluated in this study include: Wehbe, Saiidi, and Sanders 1999 , Saatcioglu and Razvi 2002 , Brachmann, Browning and Matamoros 2005 , Sheikh and Khoury 1997 , Bayrak and Sheikh 1998, Paulay and Priestly 1992, Watson, Zahn and Park 1994, L i and Park 2004. The model presented by Paultre and Legeron 2005 is included in the evaluation however, this model has since been adopted as the current Canadian building code requirement as is evaluated under that title. The paper by L i and Park (2004) also provides a short comparison of most the models listed above. 2.2 Current Code Requirements The following sections outline the confinement requirement of the current reinforced concrete building codes in the United States, Canada and New Zealand. 2.2.1 American Concrete Institute 318-05 (ACI) Since the early 1900's, the design requirements for lateral steel in reinforced concrete columns have consisted of an area requirement as well as a spacing requirement. Both of 17 Code Equations and Proposed Models these requirements have undergone modifications as the building code has progressed into the 2005 document. The following is a summary of the lateral steel requirements over the past 70 years. The first equation for determining the area of lateral steel required for the design of reinforced concrete columns appeared in the 1936 Bui lding Regulations for Reinforced Concrete (ACI 2006). The basic philosophy of the requirement was to ensure that the axial load carrying capacity of the column was maintained after spalling of the cover concrete. This was achieved by considering the material capacity enhancements due to confinement described in Chapter 1. The derivation for the amount of confining steel was first carried out for columns with circular or spiral transverse steel. The strength gain in confined concrete, assumed to be (f'cc-f'co) = 4.1// (Richart 1929), was linked to the strength provided by cover concrete 0.85f'c(Ag-Ac) = 4Af!(Ac-As) ( 2 . 1 ) Recal l from Figure 1.1, the lateral pressure due to the confining steel for a circular column at yield is 2A f ft = — S J ^ L ( 2.2 ) shc Substituting^ into Equation 2.1 and dividing each side by (2.05fyhAc), and rearranging the equation gives: 4A«, f SP A A 1 C •> 0.415-1 + A A p A s ( 2 . 3 ) sbc fy\Ac ) sbcAc Recognizing that the left hand side of the above equation is the volumetric transverse steel ratio for a column with circular or spiral lateral steel, increasing 0.415 to 0.45 and dropping the last term on the right hand side, Equation 2.3 became the A C I code equation for circular columns. The form of the equation shown below in Equation 2-4 has not changed since its original inclusion in the 1936 building code and remains as the current expression for determining the volumetric ratio of transverse steel required by A C I . 18 Code Equations and Proposed Models [ACI318-05 Eq 10-5] ( 2 . 4 ) The 1936 code also required that the center to center spacing of the spirals was not to exceed one-sixth of the core dimension. For tied columns, the 1936 code simply required that the lateral ties were at least 'A in. in diameter and had a spacing of not more than 16 bar diameters, 48 tie diameters or the least dimension of the column. The requirement of the 1936 code remained unchanged until the 1971 A C I 318 Bui lding Code Requirements for Reinforced Concrete. This was the first A C I code with special provisions for seismic design where in addition to the non-seismic requirement of Equation 2-4, it was stated that the volumetric ratio of lateral steel in circular columns shall not be less than Equation 2-5. Equation 2-5 has remained unchanged and is included in A C I 318 2005. Equation 2.5 is a lower bound expression that imposes a limit on the (Ag/Ach) ratio which can approach unity for large columns. The ratio is limited to a minimum of 1.27. The first equation stipulating the amount of transverse steel in tied columns also was introduced in the 1971 version of the code. For rectangular hoop reinforcement the required area of the bar was determined by the following equation where ps is the volumetric ratio required by Equation 2.4 with Ach substituted for Ac and 4 is the maximum unsupported length of rectangular hoop reinforcement. The commentary to the 1971 code states that the equation was intended to provide confinement to the [ACI318-05 Eq21-2] ( 2 . 5 ) 2 ( 2 . 6 ) 19 Code Equations and Proposed Models rectangular core ofthe column and was devised to provide the same average compressive stress in the core as would exist in the core of an equivalent circular spiral column having equal gross area, core area, center to center spacing of lateral reinforcement and strength of concrete and lateral reinforcement. The spacing limit for spiral reinforcement in the 1971 version of A C I 318 was changed to a maximum center to center distance of 4 inches. In the 1983 version of the code, it was recognized that the confining effectiveness of rectangular hoops was less than that of circular or spiral hoops and that this difference should be reflected in the requirements. The code stated that the total cross-sectional area of rectangular hoop reinforcement shall be the1 greater of Ash = 0.3sbc and Ash=0A2sb LL fyt f •1 f J yi [ACI318-05 Eq21-3] ( 2 . 7 ) ( 2 . 8 ) Where similar to Equation 2.5 for circular columns, Equation 2.8 is a lower limit applicable to columns with large cross-sectional dimensions. The 1983 code also implemented a second spacing limit, of one quarter of the minimum member dimension, in addition to the 4 inch maximum stated in the 1971 code. , The 1989 A C I 318 code changed Equation 2.8 to a slightly different lower limit for larger columns which limited the (Ag/Ach) ratio to a minimum of 1.3. The expression, first given in the 1989 code, remains as the current minimum expression in the 2005 code Ash=0.09sbc^ [ACI318-05Eq21-4] ( 2 . 9 ) fyt 20 Code Equations and Proposed Models The 1999 version ofthe A C I code implemented changes to the spacing requirements for the seismic design of transverse steel in reinforced concrete columns. Three limits were given and still form the spacing requirements in the 2005 code. As was first given in the 1999 code, Section 21.4.4.2 of A C I 318-05 states that the transverse reinforcement shall be spaced at a distance not exceeding any ofthe three limits: s<0.25£> (2 .10 ) where D is the minimum column dimension or s<6db ( 2 .11 ) where db is the diameter ofthe longitudinal reinforcement or sx<4 + ( l 4 ~ h A [ACI318-05Eq21-5] (2 .12) V 3 J where hx is the maximum horizontal spacing of hoop or crosstie legs on all faces of the column. The value of sx shall not exceed 6 inches and need not be taken less than 4 inches. According to the ACI-318 -05 commentary, Equation 2.9 is intended to obtain adequate concrete confinement. Equation 2.11 was introduced to recognize that the 4 inch maximum could be relaxed up to 6 inches depending on the arrangement of the longitudinal reinforcement and again the intent was to insure adequate concrete confinement. Equation 2.10, according to the commentary, is intended to restrain the longitudinal reinforcement bars against buckling after spalling ofthe cover concrete. It is important to state that the spacing limit intended to prevent buckling of the longitudinal reinforcement is not the focus of this study. Only the area and spacing limits which are specifically stated as confinement requirements are of interest here. It is important to state that it is noted in the Commentary to A C I 318-05 that axial loads and deformation demands required during earthquake loading are not known with sufficient accuracy, hence, the above equations for required confinement are not a function of design earthquake demands. 21 Code Equations and Proposed Models Table 2.1 Circular column ACI confinement requirements timeline Circular Columns Year 1936 1971 Area Req'mt Spacing Req'mt Ps = 0.45 — 1 \ A c h . )fy, f : 1/6 hc Ps = 0-45 A =0.12 1 V ^ch J fyl ft 1999-Current s <0.25£> 5 < 6d, 22 Code Equations and Proposed Models Table 2.2 Rectangular column ACI confinement requirements timeline Rectangular Columns Year Area Req'mt Spacing Req'mt 16 diam. long, bar / 1936 • - 48 diam. trans, bar / column dimension 1971 lhPsSh A „ - 2 4 inches 1983 'sh Ash=0A2sb fyt { A c h r c c f J yt LL [A> fyt <Ach r c c f J yt 4 inches / % column dim. 1989 '•sh 'sh 1999 s<0.25D s < 6du f s, < 4 + 14 -h 2.2.2 Canadian Standards Association A23.3-04 (CSA) Up until the 2004 version of the A23.3 standard of the Canadian Standards Association (2004), the confining steel requirements for reinforced concrete columns mirrored those of the A C I 318 code. The current requirements for the area of transverse steel in Chapter 21 are taken from a recent proposal by Paultre and Legeron (2005). The details of the proposal are presented in Section 2.3.11. 23 Code Equations and Proposed Models Based on the equations given in Paultre and Legeron (2005), A23.3 Chapter 21 stipulates that the volumetric ratio of circular hoop reinforcement shall not be less than the larger of fl .ft and f A, ^ ps=0AkpWr [CSA A23.3-04 Eq 21-4] (2 .13) Ps = 0-45 - 1 \Ach ) fy, f£ [CSA A23 .3 -04Eq 10-7] (2 .14) where the factor, kp, is the ratio.of factored axial load for earthquake loading cases to nominal axial resistance at zero eccentricity. Note that for kp = 0.3, these requirements are the same as A C I 318-05. For columns with rectilinear transverse steel, the code states that the total effective area in each of the principal directions of the cross-section shall not be less than the larger of the amounts required by the following equations: A f ' Ash =0.2knkp——sbc [CSA A23 .3 -04Eq 21-5] (2 .15 ) Ach fyt and Ash=0.W^sbc [CSA A23 .3 -04Eq 21-6] (2 .16 ) fyt where - 2 ) • ' ( 2 - 1 7 ) and ni is the total number of longitudinal bars in the column cross-section that are longitudinally supported by the corner of hoops or by hooks of seismic crossties. Note that in all of the above A23.3. equations, the specified yield strength of hoop reinforcement,^,/,, shall not be taken as greater than 500 M P a . In addition to the area requirements, the C S A code also imposes spacing limits. The same three spacing limits required by A C I (Equation 2.10, 2.11 and 2.12) are required by C S A . 24 Code Equations and Proposed Models Again, the spacing limit for longitudinal bar buckling is not the focus of this work and will not be considered in the evaluation of the CSA model. 2.2.3 NZS 3101:2006 (NZS) Section 10.3.10.6 of the New Zealand Standard NZS 3101 (2006) requires that the transverse reinforcement within the plastic hinge region of reinforced concrete columns having rectangular hoops with or without crossties be not less than Ash = Sbc AS\.Q-Ptmfc< P 3.3 / „ tfe'A \ A c h where m = 0.85/7 0.0065 yt TJc " g J [NZS3101-06Eq 10-22] (2.18) (2.19) For columns with circular hoops or spirals, the volumetric ratio of must not be less than Ps = where ' Ag 1.0-Plmfc> P ^ ^ A c h m = fy 0.85/7 2-4 fyl 0fc'A -0.0084 [NZS3101-06 Eq 10-20] ( 2.20 ) s J (2.21) The factor ptm shall not be taken greater than 0.4 and the ratio Ag/Ac shall not be greater than. 1.5 unless it can be shown that the design strength of the core of the column can resist the design actions. It is also stated in the New Zealand code the/,/, shall not be taken as greater than 800 MPa. In addition to the area requirements described above, the New Zealand code also has spacing limits applied to the lateral steel in reinforced concrete columns. The New Zealand code requires for circular columns that the center-to-center spacing of spirals or circular hoops along the member shall be less than or equal to the smaller of one-third of 25 Code Equations and Proposed Models the diameter of the cross-section of the member or ten longitudinal bar diameters. For rectangular columns, the center-to-center spacing of tie sets along the member shall be less than or equal to the smaller of one-third of the least lateral dimension of the cross-section or ten diameters of the longitudinal bar being restrained. According to the commentary to the New Zealand code, the spacing limits are considered necessary to restrain buckling of longitudinal steel as wel l as ensure adequate confinement of the concrete. There are no minimum limits in NZS3101 analogous to A C I 318 Eq . 21-2 and 21-4 however, in the New Zealand code, the issue of bar buckling is dealt with via another area requirement. For circular columns the following equation is given in addition to Equation 2.17. A f 1 p = ^ [NZS3101-06Eq 10-21] ' (2 .22 ) \55d"f, db In the 2006 version of the New Zealand code, the following condition was introduced for rectangular columns: N o individual leg o f a stirrup-tie shall be less than A^ = YAb£y_±_ [NZS3101-06Eq 10-23] (2 .23 ) 135 / , , db where J^Ah is the sum of the areas of the longitudinal bars reliant on the tie. The two limitations given in Equations 2.22 and 2.23 are not incorporated in the analysis of the N Z S model as they are specifically stated as requirements to prevent longitudinal bar buckling and not for confinement. The requirements of the current New Zealand code were derived from the work presented in Watson and Park (1989). The same work by Watson and Park was used to develop the Watson Zahn and Park 1994 model discussed below. 26 Code Equations and Proposed Models 2.3 Proposed Models The following section outlines the proposed confinement models currently found in the literature over the past 15 years. Only models that were developed based on a deformation measure were considered in this study. The first model presented was developed based on displacement ductility, followed by those developed based on drift ratio and then those developed based on curvature ductility. 2.3.1 Wehbe, Saiidi, and Sanders 1999 (WSS99) Wehbe Saiidi and Sanders (1999) conducted tests on rectangular columns as part of a study to develop detailing guidelines for reinforced concrete bridge columns in areas of low to moderate seismicity. Their research was aimed at investigating the cyclic behavior of columns with moderate amounts of confining steel. The columns tested in the experimental program contained 46% to 60% ofthe minimum lateral reinforcement required by the American Association of State Highway and Transportation Officials ( A A S H T O 1992) provisions. The applied axial loads were 10% to 20% of Agf'c. The specimens were tested under constant axial loads and reversed cyclic lateral loads. The column specimens exhibited displacement ductilities, U-A , ranging from 5 to 7. The investigation also aimed to determine the most appropriate equation for determining the quantity of confinement steel. The requirements of the current A C I and New Zealand codes, along with those of A A S H T O , the California Department of Transportation ( C A L T R A N S 1983), the Appl ied Technology Counci l ( A T C 1996) and the proposed method by Paulay and Priestly (1992) (See Section 2.3.7) were evaluated. The A T C - 3 2 method was selected as a benchmark for proportioning moderate ductility confinement. This decision was based on the fact that the A T C - 3 2 equation included that axial load index, the ratio of concrete strength to lateral steel yield stress and incorporated the 27 Code Equations and Proposed Models longitudinal steel ratio as parameters in determining the confinement steel amount. The The A T C - 3 2 expression is A ° h = 0 . 1 2 / c s b„ 0.5+1.25-P V f'ce A g J + 0.13(/? ( - 0 .01 ) (2.24) where f'ce is the expected concrete strength and fye is the expected yield stress of the transverse reinforcement. A T C - 3 2 expression is identical to the C A L T R A N S equation with the exception of the additional term on the right hand side of the equation. The A T C expression uses the expected material strengths rather than the specified strengths used in the C A L T R A N S expression. Based on the analytical and experimental results, the fol lowing equation, using the A T C -32 approach, was proposed to relate the amount of confining reinforcement to attainable displacement ductility, jUA: - ^ - = 0 .Lu ' / c ' " s bc where, f c 0.12 f c f fy, 0.5 + 1.25-V f \ A, + 0.13 P, yt V f •0.01 (2 .25 ) /c,n = 27.6 M P a (or 4 ksi) / s , „ =414 M P a (or 60 ksi) A target displacement ductility of 10 is suggested to provide the minimum lateral steel required in areas of high seismicity. A value f o r ^ of less than 10 could be selected for columns in which the seismic demand is moderate to low. Given the similarity of the proposed equation to both the ATC-31 and C A L T R A N S expressions and that the model proposed related the confinement to a target displacement ductility, only Equation 2.25 wi l l be evaluated in this study. The researchers note that the current A C I requirements for confining steel are generally for building design and the applicability of the provisions to bridge columns is not 28 Code Equations and Proposed Models addressed in the code. B y the same rationale, one could suggest that the equation proposed here is intended for use in the design of bridge columns, and its applicability to building structures, the focus of this study, is in question. This is particularly a concern for columns with high axial loads, since the axial load ratio for bridge columns seldom exceeds 30%. 2.3.2 Saatcioglu and Razvi 2002 (SR02) Saatcioglu and Razvi (2002) present a displacement-based design procedure for confinement of concrete columns subjected to earthquake loads. The design approach, in which lateral drift is the performance criterion, is based on computed drift capacities of columns with varying levels of axial load and confining steel. The authors note that the lateral drift was computed using a computer program for static inelastic loading that incorporates analytical models for confined concrete, steel strain hardening, bar buckling, formation and progression of plastic hinging, anchorage slip and also includes an option for second order deformations caused by P-A effects. The lateral drift capacity was computed either at 20% strength decay in moment resistance or at the same level of decay in lateral force resistance. The decay in the latter case included the portion caused by the P-A effect. The authors made use of an extensive investigation of parameters which impacted the lateral drift of columns presented in Razvi and Saatcioglu (1999). The investigation concluded that columns which have a consistent 'parameter ratio' would exhibit approximately similar drift capacities when all other parameters remained constant, irrespective of the individual values of the parameters within the ratio. The parameter ratio, r, was expressed as: P area -fyt A*-i A* (2 .26 ) 29 Code Equations and Proposed Models A comparison of column drift capacity with coefficient r, was made for columns with different levels of axial load and efficiency of transverse reinforcement, A:2- The results suggested that the following approximation could be made between r and the lateral drift ratio 8: r = \4-^=—S (2 .27 ) where k, = 0A5J^-^ ( 2 . 28 ) V s si Equating the two expressions for r, and solving for the reinforcement ratio, yields the proposed equation: Pa = 14 -1 (2.29 ) The authors also assume an average longitudinal reinforcement ratio of 2 %. Equation 2.31 may be used for different drift ratios up to 4%. The proposed equation incorporates the effects of reinforcement arrangement and higher strengths of steel and concrete and also incorporates the effect of axial force for a displacement-based design. When a 2.5% drift ratio is substituted into the expression and the axial force ratio P /P 0 is replaced with Pu/tfiPo the following design equation is presented: s A f s h =0.35- c fyt •1 1c/> 1 ( 2.30 ) The authors recommend that the following limitations are used to ensure a minimum amount of transverse reinforcement is required for columns with low axial loads.or very large cross sections: > 0.2 and - £ - - ! > 0.3 30 Code Equations and Proposed Models The axial force Plt is maximum compressive load which a column wi l l experience during a strong earthquake. The authors suggest that the capacity reduction factor, <j>, can be increased to 0.90 from 0.7 and 0.75 currently recommended in A C I 318 due to the improved ductility of properly confined columns. 2.3.3 Brachmann, Browning and Matamoros 2005 (BBM05) The original Brachmann, Browning and Matamoros model (BBM04) was based on the work by Brachmann et. al. 2004(b). The nature of the equations proposed was such that only a small range of axial loads, with a maximum value of 33%, would provide a meaningful value for required transverse reinforcement. This limitation alone would render the proposed equation as highly impractical given that axial load ratios commonly exceed 33%. With this fact in mind, and considering that the same authors proposed new transverse reinforcement equations a year later (Brachmann et. al. 2004(a)), only the later proposal (given the name B B M 0 5 for simplicity) is included in this study. The primary objective in the work by Brachmann, Browning and Matamoros (2004(a)) was to define a relationship between the limiting drift ratio of reinforced concrete columns and their material and structural properties. To do this, the authors utilized data from 184 rectangular column specimens. Shear span-to-depth ratios o f at least 2.5 were used to ensure that the selected specimens exhibit predominantly flexural response. The parameters considered in the study included concrete compressive strength, transverse reinforcement ratio, yield strength of transverse steel and axial load. The authors presented a nonlinear relationship which relates the estimated limiting drift ratio of a column with the transverse reinforcement ratio, steel and concrete strengths, and axial load. A design procedure to determine the proper amount of confinement reinforcement was proposed based on this nonlinear expression. The expression can be used to prescribe confinement requirements for regions of moderate and high seismicity. This is done by assuming limiting drift ratios of 1.5% and 2.5% for each of these regions, 31 Code Equations and Proposed Models respectively. Consequently, the resulting design expression proposed by the authors, expressed in terms of area or volume transverse reinforcement ratio, is as follows: f \ 2 P . 1 - 0 . 8 / , , , fc fyt (2 .31 ) w h e r e / c is the axial load ratio (to confined core) given as P / Acff'c and the coefficient y is.taken from the following table: (note that this study considers only high seismic demand) Table 2.3 Value of Coefficient y for Equation 2.33 (adapted from Brachmann et. al 2004(a)) Type of Seismic Demand Transverse Reinforcement Ratio, p Coefficient Circular Columns y, Coefficient y, Rectangular Columns Moderate P vol 0.15 0.18 Seismicity P area 0.09 • 0.12 High Seismicity P vol 0.25 0.30 P area 0.15 0.20 The proposed equation provided safe estimates of the limiting drift of columns with compressive strengths up to 116 M P a and it is recommended that these equations not be used.when the yield strength of the reinforcement exceeds 830 M P a . 2.3.4 Sheikh and Khoury 1997 (SK97) Sheikh and Khoury (1997) used the details from previous column tests to propose a performance-based confining reinforcement design procedure. The researchers aimed at developing a procedure which related the confinement requirements to the desired column performance. Addit ionally, they included in their proposal two parameters, steel 32 Code Equations and Proposed Models configuration and axial load level, to account for the vast amount of research which identified them as key contributors to confinement effectiveness. The following equation provides the relationship between the amount of lateral steel as recommended by the current A C I Code (As/,t ACI) and the requirement proposed by the authors (A„h): Ash=(AshiACI)-a-Yp-Y4 . ( 2 . 3 2 ) where, a = steel configuration factor Yp = axial load level factor Yy = section performance factor The a parameter is dependent upon the steel configuration category. Sheikh and Khoury identified three lateral steel configuration categories and defined as follows: Category P. where only single-perimeter hoops are used as confining steel. Category IP. in addition to the perimeter hoops supporting four corner bars, at least one middle longitudinal bar at each face is supported at alternate points by hooks that are not anchored in the core. Category IIP. in which a minimum of three longitudinal bars are effectively supported by tie corners on each face and hooks are anchored into the core concrete. The a parameter is assumed to be unity for category III configurations, and greater than unity for category I. A n average value of 2.5 is assumed for all configuration types in this category. The authors note that using a value of a equal to unity for category II configurations is reasonable in situations where the opening of hooks which are not anchored in the core concrete does not happen until after the column has reached a sufficient level of ductility. The authors also developed two empirically determined equations for the two adjustment factors Yp and Y^. Yp is a factor developed to adjust the confining steel requirement according to the axial load level and Yv takes into account the section ductility demand. The equations are expressed as follows: 33 Code Equations and Proposed Models 1 + 13 ( p \ (.2.33 ) 29 |1.15 (2 .34) where is the target curvature ductility. To select the target curvature ductility, the seismic performance of a column was classified into three categories: 1) high ductility (jig, > 16), 2) moderate ductility (16 >n<p> 8) and 3) low ductility (jug, < 8). Once the desired performance is identified, the appropriate value for /jg, is inserted into Equation 2.23. A curvature ductility of 16 is used in this study to evaluate the SK97 model. The equations presented by Sheikh and Khoury were proposed for tied columns only. However, the model wi l l also be considered in the analysis of circular columns, assuming an a value of 1.1 2.3.5 Bayrak and Sheikh 1998 (BS98) Bayrak and Sheikh (1998) presented results of four column tests and combined the results with previous tests to evaluate the suitability of the design equations presented earlier by Sheikh and Khoury (1997) to columns made with high strength concrete (HSC) and ultra high strength concrete (UHSC) . Using the same procedure as Sheikh and Khoury, the authors developed a new design procedure for confinement of H S C columns with f'c greater than 55 M P a . The authors again took the approach of multiplying the total cross-sectional area of rectilinear ties required by the current A C I (Ash, ACI) code by factors which account for steel configuration, the effect of axiai load, and the section ductility demand. The researchers concluded that the effect of axial load on the lateral reinforcement demand is independent of concrete strength, while the section ductility demand is significantly 34 Code Equations and Proposed Models influenced by concrete strength. Consequently, the researchers proposed equations in similar form to those presented by Sheikh and Khoury with a modification to Equation 2.23 to accommodate for higher concrete strengths: { Ash = (AshtAaya-Yp.Y, ( 2 .35 ) 1 + 13 (2 .36) t \0.82 y = ]til— ' . • (2 .37) * 8.12 The researchers again suggest that a curvature ductility factor of 16 can be used to define a highly ductile column therefore this value is used here to evaluate the BS98 model. Again , the BS98 model was specifically proposed for tied columns but w i l l be evaluated for circular columns as well using an a value of 1. 2.3.6 Bayrak and Sheikh & Sheikh and Khoury Given that the equations for high strength concrete in Bayrak and Sheihk (1998) are extensions of the Sheikh and Khoury (1997) equations, a true transverse reinforcement model, representing the intent in which they are proposed, should be a combination of the two. The model, termed here S K B S , utilizes the SK97 model for columns with concrete compressive strengths less than 55 M P a , and the BS98 model for any column with compressive strength of 55 M P a or greater. A curvature ductility of 16 is used to evaluate the S K B S model. 2.3.7 Paulay and Priestly 1992 (PP92) Paulay and Priestley (1992) wrote one the most widely used seismic design text books in the world. In it, the authors proposed a design equation which relates the transverse reinforcement cross-sectional area, Ash, to required curvature ductility, n r The required 35 Code Equations and Proposed Models confining reinforcement area is given for rectangular sections by the following relationship: Ash =sbc (0.15 + 0 . 0 1 / / J Jc Ag fy, Ach The equation can also be expressed as: A * . = k f c 4 ' p - 0 . 0 8 V A J c (2 .38 ) S\ fy, Ach p 0.08 KA*fc-(2 .39 ) Where k = 0.35 for a required curvature ductility of 20 (high ductility demand), and £=0.25 for curvature ductility of 10 (low ductility demand). Since this study is considering only high seismic demands, a curvature ductility of 20 is assumed. The right hand side of equation 2.35 may also be used to estimate the required volumetric ratio of confinement for circular columns. Recal l , for circular columns the volumetric transverse reinforcement ratio is: 4A Ps= T- (2 -40) Sh'°c where Asp is the cross-sectional area o f the spiral or circular hoop reinforcement, and hc is the diameter of the confined core. For circular columns, k = 0.5 and 0.35 for curvature ductilities of 20 and 10 respectively. 2.3.8 Watson, Zahn and Park 1994 (WZP94) Zahn, Park and Priestley (1986) used a computer program for cyclic moment-curvature analysis to derive design charts for the flexural strength and ductility of reinforced concrete columns. The curvature ductility charts, developed for circular reinforced concrete columns, related the available curvature ductility at the critical section of the plastic hinge to the magnitude of the effective lateral confining stress acting on the core concrete and the axial load level. Zahn et al. also developed charts to determine the ideal flexural strength of a circular column with a specified mechanical reinforcing ratio, ptm. 36 Code Equations and Proposed Models Based on their design charts, Zahn et al. developed a design procedure for the flexural strength and ductility of reinforced concrete bridge columns. A designer chooses the level of displacement ductility and obtains the associated code recommended design seismic lateral loading for the bridge substructure. From the substructure geometry and the imposed displacement ductility factor, the required curvature ductility could be obtained. Then, using the design charts for the curvature ductility factor, the appropriate amount of confining steel could be determined. These design charts were used by Watson and Park (1989) to obtain refined design equations for confining steel. Watson and Park developed plots which gave the quantities of confining steel required within the plastic hinge region, obtained from the Zahn et. al. charts, to achieve a specific curvature ductility factor for a given mechanical ratio. From these plots, an equation was derived for square and rectangular columns. These equations have since been further simplified by Watson et. al. (1994) and extended to circular columns. According to Watson et. al. the design equations can be expressed in the equations given below. For square or rectangular columns: 4*. sb„ Ag (0J<f>y)-33p,m +22 fc< P KAch 111 fvtfc'A, 0.006 (2.41 )' For columns with circular hoop or spiral transverse reinforcement: ^ = 1.41 rAg (<f>J<{>y)-33plm + 22 fc< P ^ KAch 111 f » # : \ j 0.008 ( 2.42 ) The authors note that equations 2.37 and 2.38 provide the required area of confining steel to achieve a specific level of curvature ductility. They also suggest that for the curvature ductility factor, $ ( /'</> , a value of 20 be used for ductile design and a value o f 10 be used for limited ductility or cases where a full calculation of the required curvature ductility factor is unwarranted. 37 Code Equations and Proposed Models 2.3.9 Li and Park 2004 (LP04) The work done by L i and Park (2004) was aimed at deriving confining requirements more appropriate for columns designed with high strength concrete (HSC) with normal and high yield strength steel. The authors used the same analytical procedure described above in section 2.3.8 and Zahn, Park and Priestley (1986). Again, curvature ductility was the performance criterion selected. The analytical model made use of the cyclic stress-strain model for H S C proposed by Mander, Priestley, and Park (1988) and later modified by Dodd and Cooke (1992), and the cyclic stress-strain model for steel proposed by Dodd and Restrepo-Posada(1995). The results of their parametric study suggested that the current A C I 318 and N Z S 3101 requirements should be revised for columns making used of H S C . The authors presented equations which provide the required amount of confining reinforcement for square, rectangular and circular H S C columns with normal and high yield strength steel. The equations are a modification of those proposed by Watson, Park and Zahn (1994). For H S C columns confined by rectilinear normal yield strength steel: sb„ Ag ( A / ^ ) ~ 3 3 p , m + 22 f; P \Ach A fyh0fc'Agj - 0 . 006 (2.43 ) Where 1=117 when / c < 70 M P a , and X = 0.05(/ c ')2-9.54/ c '+539.4 when fc > 70 M P a . For H S C columns confined by circular normal yield strength steel: 'sh f r Ag {<t>J<j>y)-33p,m + 22 / ; P A s b \Ach 111 fyhtL'Aj \ 0.006 •a ( 2.44 ) where a = 1.1 w h e n / c < 80 M P a and a = 1.0 when fc > 80 M P a . For H S C columns confined by rectilinear high-yield-strength steel (fyh > 1150 MPa) : 38 Code Equations and Proposed Models A sh Ag (0J0y)-3Oplm + 22 fc\ P A„ * fyl¥c'A s J (2 .45) whereA = 91-0.1/ c ' For H S C columns confined by circular high-yield-strength steel: Ash _ ( Ag to W,).-55p,m + 25 fc< Pe ^ (2 .46 ) sbc \Ac 79 fyl 0fc'A Note: ptm = mechanical reinforcing ratio The authors also place the fol lowing limitations on their proposed equations: The maximum value of ptm that can be substituted into any ofthe equations is 0.4. Ac/Ag is not permitted to exceed 1.5 unless it can be shown that the design strength of the core ofthe column can resist the design axial load applied concentrically. 2.3.10 Watson Zahn and Park & Li and Park Given that the L i and Park (1994) equations for use in the design of H S C columns are extensions of the Watson, Zahn and Park (1994), a true transverse reinforcement model, representing the intent in which they are proposed, should be a combination of the two. In this study, the model W Z P L P uses the WZP94 mdoel for columns with concrete compressive strength less than 60 M P a , and LP04 for any column with compressive strength of 60 M P a or greater. 2.3.11 Paultre and Legeron 2005 (PL05) Paultre and Legeron (2005) developed a new set of equations for confinement of concrete columns using a wide range of concrete strengths up to 120 M P a and confinement steel strength up to 1400 M P a . The authors proposed two sets of equations, depending on the curvature requirements. One set of equations given for columns with high ductility 39 Code Equations and Proposed Models demand assumes a target curvature of fi^= 16, while another set of equations given for columns with limited ductility assumes a target curvature of ju^=\0. The equations were developed from a comprehensive study on the influence of the various parameters of importance on ductility of columns. The authors performed numerical simulation tests similar to actual lab tests to develop their equations. To complete their numerical simulations, the authors had to select models which reflected, as accurately as possible, the behaviour of the materials. They used the Legeron and Paultre (2003) uniaxial model for the behaviour of confined concrete. The model, described earlier in Section 1.1, relates the materials increase in strength and ductility to the effective confinement Index I'e V ( 2 .47 ) where f'/e is the peak effective confinement pressure. For rectangular columns in the y direction it is given by f i e = K e A 1 £ j L ( 2 4 8 ) CyS Recal l Kk is the geometric coefficient of effectiveness and cy is the cross section dimension in the y direction and f \ is the stress in the confinement steel at peak stress. For circular columns/'/,, is given by f \ = \&.P,f\ (2-49) The authors used the sectional behaviour of more than 200 column sections predicted with a simulation software program. The results were used to determine the relationship between the column ductility and the ratio of I'elkp, where kp — PIPQ and Po is the nominal axial load capacity of the column. The authors found this relationship to be / > 0 .0111* , / / , ( 2 .50 ) 40 Code Equations and Proposed Models The authors then derive simplifications for the Geometric Coefficient of Effectiveness Ke for both rectangular and circular columns. The coefficient is broken down into vertical and horizontal components Kh and Kv where Ke=KhKv ( 2 .51 ) The expressions for Kv included the spacing of the lateral steel bars. To simplify the equations, the authors determined the Kv values for over 500 columns considering the minimum spacing requirements of A C I . They concluded that a conservative value for Kv could be expressed as a function of the ration Ach/Ag. For members with rectangular hoops 2 0 Kh=\~— ( 2 .52 ) ft, ^ v = 1 . 0 5 ^ (for ^ = 1 6 ) (2 .53 ) or ^ = 0 . 9 5 ^ (for ^ = 1 0 ) (2 .54 ) For members with circular or spiral hoops, Kh is unity and Kv is 0.90. The authors highlight that ties are not always effective with their full yield strength, therefore an effective stress f\, apposed to the yield stress fhy, is used. The authors make the following conservative recommendations: for circular columns, f'h=0.95fhy, and for rectangular columns, f'h=0.65fhy. To develop their proposed equations, the authers combined Equations 2.47 with Equation 2.48 for rectangular columns and Equation 2.49 for circular columns. Then they incorporated their Kv and Kh simplifications and fitting parameters to develop expressions for the different target curvature ductilites. The authors proposed the following equations: For rectangular columns, the required area o f transverse steel in the y direction is given by: 41 Code Equations and Proposed Models Ashy=®kpkncys^^- (2.55) J yt Ach where O = 0.2 for columns with high ductility demand (/^=16), 0.15 for columns with limited ductility demand ( =10) and where Av-' ' ,/(>V-2) (2.56) For circular columns, the required volumetric reinforcement ratio is given by Ps = ®kp ~- , . (2.57) J yt where O = 0.4 for fully ductile columns and 0.25 for limited ductility. Note, the ratio Ag/Ach does not appear in the epression for circular columns as the Kv value is independent of this ratio. The equations proposed by Paultre and Legeron have been adopted into the Canadian concrete design code (CSA, 2004). Therefore, the model will be evaluated under that title (CSA) and not as alternate proposed model as is the case for the rest of the models described in this section. 2.4 Range of Properties Investigated The table below is given to provide some insight to the range of values for the various parameters which were considered by the authors of each model. The table shows that some models considered a wider range of variables compared to others. It is expected that a model which was developed using a smaller range of parameter values will perform poorly in the evaluation conducted here compared to those developed with a wide range of parameter values. 42 Code Equations and Proposed Models Table 2.4 Range for parameters used in development of the proposed models Model fc' (MPa) P/A g f c ' fyt(MPa). parca (% ) M i n M a x M i n Max M i n Max M i n Max SK97 25.9 58.3 0.46 0.777 461.9 558.5 0.77 4.3 BS98 71.7 102.2 0.36 0.5 463 542 2.72 6.74 WSS99 27.2 31.7 0.09 0.24 282.8 321.1 0.369 0.482 SR02 - - - - -B B M 0 5 22 116 0 0.7 255 1262 0.07 3.05 PP92 - - - - - - -WZP94 20 40 0.2 0.7 275 275 - ' -LP04 50 100 0.2 0.7 430 1318 - -PL05 30 100 0.1 0.6 •400 800 - -Note: values shown in the table above with a dash (-) were not given. 43 3 EVALUATION DATABASE 3.1 Experimental Database The TJW/PEER column database (http://maximus.ce.washington.edu/~peeral/) was used to compare the performance of the various proposed models and code equations. The column database is a result of the efforts of many researchers and is a comprehensive record of numerous column tests. The record for each column in the database contains column geometry, material properties, reinforcing details, test configuration (including P-Delta configurations), axial load, classification of failure type, and force-displacement history at the top of the column. The complete database has 301 rectangular columns, and 168 circular columns, however the complete list was not used here. This study made use of the 230 rectangular column and 166 spiral column database tables established in Camaril lo (2003), who used the force-displacement data for each column test to determine a displacement at failure. The procedure used by Camaril lo is described in more detail in Section 3.2. The Camaril lo database removed 28 circular columns and 18 rectangular columns from the U W / P E E R database due to unusual properties such as the use of lightweight concrete or spliced longitudinal reinforcement, and unknown properties such as unknown P-A configuration or missing steel properties. A lso, 23 circular and 53 rectangular columns were removed because they did not fail according to the definition of failure established in Camaril lo 2003, and presented again here in Section 3.2.2. For this study, an additional 60 circular and 64 rectangular columns were removed from the Camaril lo database because they did not exhibit flexural failure. As discussed in Chapter 1, the aim of this investigation is to establish the most appropriate model for confining steel requirements in columns to resist the flexural demands imposed by seismic excitation. Therefore, including data from column tests which produced shear or 44 Evaluation Database flexure-shear failures would be inappropriate as the performance of the column was not governed by confinement. Taking this approach ensures that all of the columns satisfy the intent of the code which is to ensure that the column wi l l not experience a shear failure. A detailed description of the failure classification procedure is presented in below. A lso , as discussed in'Chapter 2, the particular code specifications in A C I , C S A and N Z S i which intended to prevent buckling of longitudinal reinforcement were not the focus of this work. Therefore, to eliminate the effects of these limits on the evaluation of the current column confinement requirements in A C I , test specimens which did not satisfy the A C I spacing requirement pertaining to bar buckling were removed from the database. This totaled 21 rectangular columns and three circular columns. For this study, the rectangular column "Flexural Failure" database contained 145 columns while its circular column counterpart contained 50 columns. A complete list of the columns in both databases, along with selected properties, can found in Appendix A . While the lateral steel for all circular columns consists of circular hoops or spiral reinforcement, the lateral reinforcement for the rectangular columns are categorized into seven classifications. The definition and number of columns found within the database for each classification are given in Table 3.1. Table 3.1 Confinement classification details N o . of Notation Description Columns R Rectangular ties (around perimeter) 51 R I Rectangular and Interlocking ties 29 R U Rectangular ties and U-bars 3 R J Rectangular ties and J-hooks 17 R D • Rectangular and Diagonal ties 35 R O Rectangular and Octagonal ties 9 U J U-bars and J-hooks ; 1 45 Evaluation Database A l l rectangular columns had rectangular (or square) cross-sections, but the circular columns had two cross-sectional shapes, circular and octagonal. These shapes were assigned codes which, along with the number of each found in the database used here, are given in Table 3.2. Table 3.2 Cross-Section Classifications Cross-Section Code N o . o f Columns Shape Circular 0 40 Octagonal 2 10 3.2 Determination of Failure The following is a summary of the procedure used in Camarillo (2003) to determine the failure displacement for columns in the database. Since the database included column tests performed in a wide range of configurations, the lateral force-displacement data provided for each test was converted to represent the lateral forces and displacements which would be imposed on an equivalent cantilever column. This allowed for a consistent evaluation of the performance of each column within the database, regardless of test configuration. 3.2.1 Effective Force and P-Delta correction Lateral force-displacement data had to be adjusted to take into account the secondary or P-A effects. This is of particular importance for columns with large axial loads and large lateral drifts. The following is taken from Parrish (2001) and Berry et. al. (2004), which explains the process used to implement the P-A correction. The loads applied to each column by the vertical actuator were resolved into their vertical and horizontal components. The horizontal component could then be added or subtracted 46 Evaluation Database to the force from the horizontal actuator to incorporate a P-A correction, the database is displacement histories, shown in Figure 3.1 Berry et. al. define the categories as follows: P e) C a s e I I I Figure 3.1 P-A correction find the resulting net horizontal .force. To ; organized into four types of lateral force-, each with a specific form of correction. p F K b ) C a s e II P I I, I t i n : m • 1 L_i_ d ) C a s e IV cases (Berry et. al. (2004)) Case I: Force-deflection data provided by the researcher was in the form of effective force (Feff) versus deflection (A) at Lmeas. In this case, the net horizontal force (FH) can be determined according to the following equation: FH=Feff-PA/Lmem (3.1) 47 Evaluation Database Case II: Force-deflection data was provided by the researcher in the form of net horizontal force (Fu) versus deflection (A) at Lmeas. ( 3 . 2 ) Case III: Force data provided by the researcher represents the lateral load applied by the horizontal actuator, but the top of the vertical actuator does not translate. In this case, the horizontal component of the vertical load actuator needs to be added to the reportedforce, Frep, to get the net horizontal force (FH). FH = Frep +PLTop IA . ( 3 . 3 ) Case IV: Force data provided by the researcher represents the lateral .load applied by the horizontal actuator. However, the axial load is not applied at the same elevation as the lateral force, or the line of action of the axial load does not pass through the column base. In this case, the horizontal component (PH) of the vertical load actuator was subtracted from the reported force, Frep, to get the net horizontal force (FH). a = tan" L + L top L L + Lbor+Llop PH = P sin a F = F - P 1 H 1 rep 1 H ( 3 . 4 ) (3.5 ) ( 3 . 6 ) The contributions of the net horizontal force and the gravity (vertical) load to the total base moment can then be determined as follows: Mbasa=FHL + PA K + L V ^meets J ( 3 . 7 ) where: 48 Evaluation Database - net horizontal force (Column Shear) - shear span length - gravity (vertical) load - measured displacement at cantilever elevation Lmeas - distance from elevation at which lateral force was applied to elevation at gravity (vertical) load is applied. - elevation at which lateral column displacement was measured The effective force can then be defined as: Feff=MbaseIL (3 .8) 3.2.2 Displacement at Failure One possible definition of failure displacement is the maximum recorded drift during the test (Amax). However, the most commonly accepted definition of failure is the point at which a specimen reaches a 20% loss of lateral load capacity. Once the lateral force-displacement data had been corrected for P - A effects, the failure displacement, at 80% effective force, could be determined according to the following procedure. Camarillo (2003) describes the process for determining the failure displacement as follows: From the force-displacement history, the displacement (Aso) and the data point (i$o) corresponding to the last time the column resisted 80% of the absolute maximum effective force were identified. Failure of the column was assumed to occur if: the absolute maximum displacement after the identified 80% force (Apost-8o) exceeds Aw-i.e., (Apost.so>Aso) the maximum displacement following another zero crossing (Apost.zero) exceeds 95% of Ago i.e., (Ap0st-zero > 0.95 A so) the force corresponding to the maximum displacement after the zero crossing FH L P A Ltop which 49 Evaluation Database (Fpost-za-o), is hass than or equal to the proportional force set by the force and displacement at the 80% location i.e., (Fpost-zero <Fso (dpost-zero/ Ago)) Otherwise the column has not failed. For columns that fail, the failure displacement (Afau) was determined as the maximum displacement that the column was subjected to prior to the data point iso-80% F # f f . B o LL. 500 15 CD 3= -10 0 10 20 Displacement, mm post-zero 80% F e Figure 3.2 Example for confirming failure (Camarillo (2003)) 3.3 Failure Classification The failure behaviour of the columns within the database is categorized into three failure modes; flexural failure, shear failure and flexure-shear failure. For columns which exhibited flexural failure (the focus of the current study), the degradation in the lateral load capacity occurs after yielding of the longitudinal reinforcement and the observable damage includes flexural cracking, spalling of cover concrete, concrete crushing and longitudinal bar buckling. For columns which exhibit shear failure, the degradation ofthe 50 Evaluation Database lateral load capacity occurs prior to yielding of the longitudinal steel and the observable damage includes diagonal cracking and a sudden loss in strength. Columns classified as flexure-shear failures exhibited a certain level of displacement ductility developing hinging before the shear failure. The schematic diagram shown in Figure 3.3 illustrates the distinction between the three failure modes. i > • ^ initial A 1 i \ / Shear failure | / \ 1 K / / L T Flexure-shear failure \ / 'V / / | vrcsidual 1 / 7" i / ! I 1 i / / / Flexure failure i / / / ! 1 • i V- \ ' i \ • -1 l.o 2.0 M c . / V Displacement Ductility Capacity, Ll Figure 3.3 Conceptual definition of column failure modes B y combining these definitions, first presented by A T C (1981), with the column test observations, Berry et. al. (2004) classified each column within the U W / P E E R database according the criteria shown in Figure 3.4. If no shear damage is reported, the column is classified as flexure-failure. If shear damage is reported, the absolute maximum effective force (Fcff), is compared with the calculated force corresponding to a maximum concrete compressive strain of 0.004 (Fo.otw)- The failure displacement ductility at the 80% effective force, Uf a j i , is also considered. If the maximum effective force is less than 95 percent of the ideal force or i f the failure displacement ductility was less than or equal to 2, the column was classified as shear-critical. Otherwise, the column is classified as flexure-shear-critical. 51 Evaluation Database Shear Damage Reported? Yes No F <0.95F or M f a i l <2 cff 0.004 l a " Flexure Failure Yes No Shear Failure Flexure-Shear Failure Figure 3.4 Failure Classification Flowchart (Berry et. al (2004)) 3.4 Range and Verification of Database Parameter Values Making use of the column test database, as apposed to conducting individual tests, is done to allow for a wider range of parameter values than is typically available within a particular experimental study. In order to use the database to evaluate the confinement models described in Chapter 2 with increased confidence, a comparative investigation was performed to verify that the parameter ranges in the database are comparable to typical designs carried out according to the most recent building codes. Typical column details from three buildings located in high seismic regions in western United States were provided by the Structural Engineer of Record. Table 3.3 and Table 3.4 present the ranges for the parameters which significantly influence the flexural behaviour of reinforced concrete columns, for both the typical column details and the experimental database. From these tables it can be seen that the range of most of the parameters covered by columns in the database is compatible with the range of values seen in these parameters for new construction. Detail drawings for the 8 rectangular and 12 circular typical columns are provided in Appendix B. 52 Evaluation Database Table 3 .3 Rectangular column parameter ranges (database and typical columns) Database Typ . Details Parameter M i n . M a x . A v g . M i n . M a x . A v g . fy. (MPa) 255 1424 549.4 414 414 414. fc (MPa) 20.2 118.0 60.4 . 28- 72 57 -s (mm) 25.4 228.6 77.5 76.2 114.3 94 Parea ( A s h / sh c) (%) 0.11 3.43 1.14 0.90 1.94 1.46 Plong(%) 1.01 6.03 2.37 1.29 4.12 2.11 A g ( m m 2 ) ' 23226 360000 92451 209032 929030 588386 P / A g f c • 0.0 0.80 0.28 0.33 0.71 0.48 ible 3.4 Circular column parameter ranges (database and typical column Database Typ. Details Parameter M i n . M a x . A v g . M i n . M a x . A v g . fyh (MPa) 280 1000 473.0 414 414 414 fc (MPa) 22.0 90.0 36.3 34 69 53 s (mm) 8.9 305.0 55.0 63.5 101.6 78:3 p v o l ( 4 A s p / s h c ) ( % ) 0.10 3.13 1.00 1.15 2.76 2.01 Plong (%) 0.75 5.58 2.31 1.19 3.68 2.03 A g ( m m 2 ) 18146 1814600 211312 164173 585753 342196 P / A g f c 0.0 0.70 0.17 0.01 0.58 0.28 For the rectangular columns, the most glaring discrepancy is found in the gross area (A g ) where the average database value is well below the minimum value for the typical columns. This is to be expected since full scale column tests are often too difficult or expensive to conduct and are therefore not possible due to testing facility or budgetary limitations. The similarity in the values for area transverse reinforcement ratio demonstrates that the section dimensions of the columns in the database are proportionally scaled and the discrepancy in A g is insignificant. For the circular column database, the same discrepancy is found for the gross area. Table 3.4 also shows that the volumetric ratio of transverse reinforcement is higher for the typical olumns than for the 53 Evaluation Database database suggesting that more testing of columns with confinement levels typically found in building structures is needed. One of the objectives of this work is to use the database to exemplify what is already known about the relationship between axial load and ductility for reinforced concrete columns. Figure 3.5 shows a plot of axial load ratio versus drift ratio for each test specimen in the rectangular and circular databases. A n important observation to note is that the circular column database has significantly less data with high axial load ratios. The circular column database has only 10 columns with an axial load ratio higher than 0.30 as compared to the rectangular column database which has 59. This is because the majority of circular specimens are scaled versions of bridge piers which typically have smaller axial loads compared to columns found in building structures. Consequently, there are very few columns with low drift ratios in the circular column database. The disparity between the two databases wi l l become more apparent in Chapter 4 when they 1 0.9 0.8 0.7 0.6 0.5 C L 0.4 0.3 0.2 0.1 0 0 • • •• • • : /• • • • • 5 10 Drift Ratio 15 1 0.9 0.8 0.7 0.6 <: r o 0.5 0.4 0.3 0.2 0.1 0 0 •• • 1 5 10 Drift Ratio 15 Figure 3.5 Axial Load ratio versus drift ratio (A) rectangular database (B) circular database 54 Evaluation Database are used to evaluate the performance of the models. It is also important to note that while even though there are fewer columns with a high axial load ratio, the drifts achieved by columns with lower axial loads was typically higher for circular columns than for rectangular columns. Similar to Figure 3.5, Figure 3.6 to Figure 3.10 show plots for several parameters identified which influence the drift capacity of reinforced concrete columns, and are contained in most of the models described in Chapter 2. The figures show that while the parameters do seismic performance of columns, no single parameter appears to influence lateral drift with the same significance as axial load level. The trend observed in Figure 3.5 is not clear in any of the other plots. 3.5 5 10 Drift Ratio 2.5 1.5 0.5 •• • •• • • % • • • 5 10 Drift Ratio 15 Figure 3.6 p a r c a and p v oi versus drift ratio (A) rectangular database (B) circular database 55 Evaluation Database 0.3 0.25 0.2 0.15 0.1 0.05 • # •» • • • • -4A. *: 5 10 Drift Ratio 15 0.2 0.18 0.16 0.14 0.12 0.1 0.08 0.06 0.04 0.02 0 • • • • • • • • • 0 5 10 Drift Ratio Figure 3.7 fc' / fyt versus drift ratio (A) rectangular database (B) circular database 15 5 10 Drift Ratio 2 1.9 1.8 1.7 1.6 <° 1.5 < 1.4 1.3 1.2 1.1 1 5 10 Drift Ratio Figure 3.8 A g / A c i , versus drift ratio (A) rectangular database (B) circular database 15 56 Evaluation Database CD 10 r 9 -8 -7 -6 -5 -4 -3 2 1 0 • • • •• ••••*** * a • • • * * ** ittmt— • • • • • 5 10 Drift Ratio 15 10 9 8 7 6 5 4 3 2 1 0 • •• • • 5 10 Drift Ratio Figure 3.9 B / L and D / L versus drift ratio (A) rectangular database ( B ) circular database 15 • • • 5 10 Drift Ratio 15 • • • • •• • 5 10 Drift Ratio Figure 3 . 1 0 pi o n g versus drift ratio (A) rectangular database ( B ) circular database 15 5 7 4 CONFINEMENT MODEL EVALUATIONS This chapter presents the procedure and results of the evaluation techniques adopted to analyze the performance of each confinement model. In Chapter 1, it was shown that the amount and configuration of transverse reinforcement is the most important parameter in determining the drift capacity of a reinforced concrete column, and the evaluation approach taken here makes use of this conclusion. The interpretation of the results and the ensuing recommendations wi l l follow in Chapter 5. 4.1 Rectangular Columns .4.1.1 Scatter Plot Evaluation Each confining reinforcement model was evaluated using the properties and performance of the column specimens within the database discussed in Chapter 3. Two evaluation techniques were developed to investigate the performance of the models. The procedure and results for the first of these two techniques, a scatter plot evaluation, is outlined here and the second technique, a fragility curve evaluation, is outlined in the following section. 4.1.1.1 Evaluation Procedure The amount of confining reinforcement required for each column in the database, based on the code and model equations from Chapter 2, was calculated and compared with the amount of transverse reinforcement provided. With these values known, it is possible to determine i f each column in the database had sufficient transverse reinforcement to meet a particular model or code equation. Once the amount of transverse steel was determined, a performance criterion had to be selected. As seen in the model descriptions, not all equations used the same performance parameter. One possible comparison technique would be to test each model against the 58 Confinement Model Evaluations target performance for which it was designed. In other words, i f an equation is developed by using a target curvature ductility of 20, the equation could be evaluated oh how well it performs against the measured curvature ductilities of the columns in the database. Similar comparisons could be made for models which used other performance parameters such as displacement ductility or drift ratio. This technique however would not provide J any information as to how the models or equations compare against each other, only how they compare with the targets they are designed to meet. Therefore, a consistent performance target had to be selected which could be applied to all models and equations and used as a universal criteria. A drift ratio of 2.5% was selected as the performance target for this study. The interstory drift ratio is determined in the course of a standard design process and a value of 2% to 2.5%o is commonly used as the performance target in many building codes. Ductil ity related targets are not as preferable for a performance criterion for two main reasons. Firstly, the test data generally does not provide measured curvatures and secondly, a ductility l imit depends on the definition o f yield for which different researchers take different approaches. A performance criterion which uses total drifts, such as drift ratio, avoids these issues. It should be noted that while choosing a drift ratio of 2.5% may appear to provide a minimal advantage to those models with drift ratio as the performance parameter, the results presented below do not suggest such a bias. Figure 4.1 shows the layout of the scatter plots which w i l l be used to conduct the first analysis ofthe confinement models. The figure shows a plot of the drift ratio at 20% loss in lateral strength (described in Chapter 3) versus the confining steel requirement ratio (ASh_providcd / Ashmodci)- The figure is divided into quadrants with a vertical dashed line at ASh_providcd / A s h model = 1, and a horizontal dashed line at the performance target DR=2.5%. The introduction of theses two dashed lines divides the plotting area into four distinct quadrants, each with specific implications, Data points falling to the right ofthe vertical dashed line meet or exceed the confining requirements of a particular model, while those plotted to the left of the vertical dashed line do not meet the requirements. Data plotted above the horizontal dashed line achieved a drift ratio (at 20% loss in 59 Confinement Model Evaluations 10 1 2 0 4 0 2 3 4 5 6 A Actual / A , Model Figure 4.1 Scatter plot layout with identification of quadrant labels strength) o f greater than or equal to the performance target o f 2.5%. Therefore, an ideal model would have all columns plotted in the quadrants labeled as "1" and "4 " , where all test columns which meet or exceed the confinement steel requirements, achieved acceptable levels of drift, and those which did not meet the confining steel requirement of the model did not reach acceptable levels of drift. Therefore, for a favorable evaluation of a model the plot should have few data points fall in the remaining two quadrants. Data which plots in the upper left quadrant, quadrant 3, fails the confining steel requirements of the model, but meets or exceeds the performance target. This quadrant is termed the 'conservative' quadrant since for data points in this quadrant the model is requiring more steel than is necessary to reach acceptable levels o f drift. Data which plots in the lower right quadrant, quadrant 2, meets the confining steel requirements of the model, but does not meet the performance target. This quadrant is 60 Confinement Model Evaluations termed the 'unconservative' quadrant since for data points in this area the model requires an insufficient amount of confining steel to achieve acceptable levels of drift. In order to make a quantitative comparison of the models using the scatter plots, two statistics were calculated for each model and code equation. The following statistic was selected to assess the ability of the model to provide sufficient drift capacity: # of columns that satisfy model A N D achieve a drift ratio < 2.5% o) = ( 4 . 1 ) # of columns that satisfy model In terms of the quadrant numbers: ^ A(%) = — ^ — ( 4.2 ) Q1 + Q 2 The second statistic was selected to indicate the degree of conservatism inherent in the model: # of columns that do not satisfy model A N D achieve a drift ratio < 2.5% z>(%) = ( 4.3 ) # of columns that do not satisfy model B(%) = Q 4 ( 4 . 4 ) Q 3 + Q 4 A n ideal model would have an A value of 0% and, to avoid over-conservatism, the B value should be maximized. The difference between the two statistics above also provides an insight to the performance of the model, and is a good representation of the model's overall performance considering all columns. C = B-A ( 4 . 5 ) A large value for C indicates a model which is 'safe' yet not 'overconservative'. 61 ' Confinement Model Evaluations 4.1.1.2 Assessment of ACI 318-05 21.4.4.1 The rectangular column scatter plot for the A C I confining steel requirements is shown below in Figure 4.2. It should be noted that the plot represents only the evaluation of A C I Equations 21-3 and 21-4, and does not include the spacing requirements of A C I 318-05 clause 21.4.4.2. This issue is discussed in section 4.1.3 While properly observing the performance of the A C I model is done best in a relative sense with direct comparison to the other models investigated in this study (see Chapter 5), it is prudent to first fully understand the data presented in Figure 4.2. A l l columns which satisfy section 21.4.4.1 of A C I are plotted with a lightly shaded square marker, while those which fail the area of confining steel requirements are plotted with a dark shaded diamond marker. This is done such that in subsequent scatter plots for other models, the distinction can be made as to where the columns lie on the A C I scatter plot. 10 9 d 6 q co 5 on *=• S 4 0 w • • • fi • • • • • • i • CP • a • • • • • Satisfies ACI 21.4.4.1 * Does Not Satisfy ACI 21.4.4.1 0.5 1.5 2.5 3.5 A / A sh Provided sh ACI Figure 4.2 ACI scatter plot (rectangular columns) The figure shows the following data distribution: 62 Confinement Model Evaluations Table 4.1 Quadrant data distribution of Figure 4.2 Quadrant 1 Quadrant 2 Quadrant 3 Quadrant 4 23 9~. 92 21 From the numbers given in Table 4.1 the statistics A , B and C can be calculated as: Table 4.2 Statistics for A C I rectangular scatter plot A B C 28! l 18.6 -9.5 Earlier in this chapter, quadrants 2 and 3 were identified as the quadrants where it was desired to have as few data points as possible. Figure 4.2 and Table 4.1 show a number of data points in both of these quadrants. In an effort to determine common properties for these tests, Figure 4.3 shows a plot of concrete compressive strength (f c ') versus axial load ratio (P /A g f c ' ) for the columns found in quadrant 2 and 3 in Figure 4.2. As seen in Figure 4.3, all of the quadrant 2 columns for the ACIscat ter plot have an axial load ratio o f at least 0.33, with eight o f the nine columns having a value o f 0.47 or higher. In comparison, only six of the 92 quadrant 3 columns have an axial load ratio of 0.40 or greater. While the effect of concrete compressive strength on the ductility of a concrete member is wel l documented in the literature, the effect of axial load appears to be more dominant when assessing the performance of the A C I confining steel requirements. The observations of these figures are in agreement with the expectations based on the relationship between axial load and column ductility presented in Chapter 1. 63 Confinement Model Evaluations CO Q. 120 r 100 80 60 0 ^ • + • 4 0 • ^ • Q2 Columns * Q3 Columns 401 20 • • • 0 I 1 1 1 1 ' ' ' - 1 ' 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Axial Load Ratio (P/A f ' ) v g c ' Figure 4.3 fc' versus Axial Load Ratio for columns in quadrants 2 and 3 of ACI rectangular scatter plot 4.1.1.3 Assessment of Codes and Proposed Models The scatter plot evaluation of the remaining models was done to compare their performances with that observed for the A C I requirements, and.to determine which model is the most appropriate replacement for A C I . First, to perform an appropriate comparison, the A C I minimum requirement given in Equation 2.5 (ACI Equation 21-4) was included in the evaluation of the other models. This was done only to ensure that the effect of a minimum equation was not applied solely to the A C I model which would generate biased results. Once the initial comparison is made, the models wi l l be evaluated strictly on their specific requirements and an appropriate minimum for the recommended model, which may or may not take the form of the current A C I equation, can be determined. Note, the current C S A code applies the same minimum but is not included in the evaluation of the C S A model as this minimum is not included in the PL05 model on which the C S A code is based. 64 Confinement Model Evaluations 50 45 40 35 30 55 25 20 15 10 5 0 I i r | B m c ACI C S A PP92 SR02 WSS99 BBM05 S K B S WZPLP NZS Figure 4.4 Rectangular scatter plot statistics all models (with ACI minimum) Figure 4.4 shows the A , B and C statistics for all models, including A C I , where all models incorporate the current A C I minimum equation. Scatter plot statistics for SK97, BS98, WZP94, and LP04 are not shown. As noted in Chapter 2, these individual models are used in conjunction with each other to form the combination models S K B S and W Z P L P . The individual scatter plots for all models can be found in Appendix D. The table shows that each model provides a significant statistical improvement over the A C I model. A C I had the highest A value, where a low value for A is desirable, and the lowest B value, where a high value for B is desirable. The A C I model was the only model to produce a negative C value, where a large positive value for C is desirable. The results shown in Figure 4.4 suggest that an alternate model to the current A C I equation should be recommended. To properly determine a replacement model, the models must be evaluated strictly on their specific requirements. 0,5 Confinement Model Evaluations The scatter plots for the models not including the A C I minimum equation are presented in Figure 4.5 through Figure 4.12. Again, scatter plots for SK97 , BS98, WZP94, and LP04 are not shown. A l l scatter plots, including those presented here, are included in Appendix D. As shown in the figures, only the SR02 and WSS99 models had more column data points plotted in quadrant 2, and only S K B S had more data points plotted in quadrant 3, when compared to the A C I scatter plot (Figure 4.2). The most significant change in the number of data points in quadrant 2 is seen the plots for S K B S and C S A which had just two data points in the quadrant. The most significant change in the number of data points in quadrant 3 is seen in the plot for WSS99 which has just 41 data points and SR02 and PP92 which both have 59. The distribution of data points into the four quadrants for all the models is shown below in Table 4.3. The Table includes A C I for reference and it should be noted that the A C I minimum equation is included only for the A C I model. Further discussion o f the scatter plots w i l l be given in the presentation and justification o f the final recommendations (See sections 5.2.1 and 5.3.1). A / A sh Provided sh CSA Figure 4.5 C S A scatter plot (rectangular columns) 66 Confinement Model Evaluations 10 9 £ 6 [ o 'ro 5[ or S 4[ 4 • 4 • • • 03 • • * 7 • • • • • - ! - -r«—x • • Satisfies ACI 21.4.4.1 ^ Does Not Satisfy ACI 21.4.4.1 0.5 1 1.5 2.5 3.5 A / A sh Provided sh NZS Figure 4 . 6 NZS scatter plot (rectangular columns) 10r 9 8 7 g 6 -o ro 5 5 4 3 2 1 0 • • • * • D • 0 • - A _ L _ > T • Satisfies ACI 21.4.4.1 # Does Not Satisfy ACI 21.4.4.1 0.5 1.5 2.5 3.5 A IA sh Provided sh PP92 Figure 4 . 7 P P 9 2 scatter plot (rectangular columns) 67 Confinement Model Evaluations 10r . . 9 -8 -7 g 6-,o co 5 • OC S 4 3 2 1 0 44 4 • * v • • • —V"It*" • • • • il* • • • • • f i 4 • • • • • • • S a t i s f i e s A C I 2 1 . 4 . 4 . 1 + D o e s N o t S a t i s f y A C I 2 1 . 4 . 4 . 1 0.5 1.5 2.5 3.5 A / A sh Provided sh SR02 Figure 4.8 SR02 scatter plot (rectangular columns) • • 4 4 I P • • • • • • • • r l • S a t i s f i e s A C I 2 1 . 4 . 4 . 1 4 D o e s N o t S a t i s f y A C I 2 1 . 4 . 4 . 1 0.5 1.5 2.5 3.5 A / A sh Provided sh WSS99 Figure 4.9 WSS99 scatter plot (rectangular columns) 68 Confinement Model Evaluations • Satisfies ACI 21.4.4.1 # Does Not Satisfy ACI 21.4.4.1 A / A sh Provided. sh BBM05 Figure 4.10 BBM05 scatter plot (rectangular columns) 10 9 "1 to • d 6 Q 'ro 5[ or £ 41 • 0 • i 4 CI^ V i 4 * #! • • CO • • • Satisfies ACI 21.4.4.1 . ^ Does Not Satisfy ACI 21.4.4.1 0.5 1.5 2.5 3.5 A / A sh Provided sh SKBS Figure 4.11 SKBS scatter plot (rectangular columns) 6 9 Confinement Model Evaluations • Satisfies ACI 21.4.4.1 ^ Does Not Satisfy ACI 21.4.4.1 A / A sh Provided sh WZPLP Figure 4.12 WZPLP scatter plot (rectangular columns) Table 4.3 Quadrant data distribution for rectangular column scatter plots Model Q l Q2 Q3 Q4 C S A 61 2 54 28 PP92 '63 5 52 25 SR02 73 12 42 18 WSS99 79 10 36 20 B B M 0 5 72 6 43 24 S K B S 22 2 93 28 W Z P L P 28 4 87 26 N Z S 42 7 73 23 Using Equations 4.1, 4.3, 4.5 and the data provided in Table 4.3, Figure 4.13 displays the A , B and C statistics for each model including the A C I values previously given in Table 4.2. The negative C value for A C I is not shown in the figure, and it is important to note 70 Confinement Model Evaluations 50 45 40 35 30 25 '20 15 10 5 0 n ACI C S A PP92 SR02 WSS99 BBM05 S K B S WZPLP NZS Figure 4.13 Rectangular scatter plot statistics bar graph that, as was seen in Figure 4.4, A C I is the only model to generate a negative C value. As shown in Figure 4.13, C S A had the lowest A value with A = 3.2% followed by PP92, B B M 0 5 and S K B S with A values of 7.4%, 7.7% and 8.3% respectively. B B M 0 5 had the highest B value with B = 35.8% followed by WSS99, C S A and PP92 with B values of 35.7%o, 34.1%) and 32.5% respectively. The largest C value, the statistic which describes the overall performance of the model based on all the column data, belonged to C S A with a C value of 31.0% followed by B B M 0 5 , PP92 and WSS99 with C values of 28.1%, 25.1% and 24.5%, respectively. Recall that a large C value indicates a model that provides a safe design without significant overconservatism. Again, it is important to note that only the A C I values shown include the A C I minimum equation 4.1.2 Fragility Curve Evaluation The data used to generate the scatter plots described above was used to generate another graphical presentation of the behaviour of each model. Rather than imposing a distinct 71 Confinement Model Evaluations performance target as done above, fragility curves were generated to show the performance of the models at various levels of drift ratio. 4.1.2.1 Evaluation Procedure To generate a fragility curve for a given model, all the columns that satisfied the confining steel requirements of that model were sorted and listed in increasing order according to their drift capacity. Progressing through the list it was possible to determine the percentage of columns that did not reach a given drift level. Using this procedure at a drift ratio of 2.5%, this method produces a value of A , where A is the scatter plot statistic described above. A lognormal cumulative distribution function was then used to generate a curve to fit the data. The curve is titled the A fragility curve. Based on the data used in this study, the curve describes the probability of a column not reaching a given drift limit i f it satisfies the model. This fragility curve presents the general trend for columns.that satisfy the model without having to select a particular drift level as the performance target. In equation form, the curve can be expressed as: A = P(S<Sla!&el\Aprmicleci/Amode!>l) ( 4 . 6 ) The process was repeated again for all the columns that did not satisfy the confining steel requirements of the model. For each model, a B fragility curve was generated to describe the probability of a column not reaching a given drift limit i f it does not satisfy the model. Again, using this procedure at a drift ratio of 2.5%, this method produces a value which is analogous to B, where B is the scatter plot statistic described earlier. This fragility curve presents the general trend for columns that do not satisfy the model without having to select a particular drift level as the performance target. In equation form, the curve can be expressed as: B = P(S < SlaTge, | Aprmldcd IAmoiel < 1) . ( 4.7 ) In the same manner that the C statistic was created to combine information provided by the A and B statistic, a third "fragility curve" was generated to combine the results of the two previous curves. The relationship is comparable to that given in Equation 4.5, or that the C fragility curve represents the B fragility curve minus the A fragility curve. Again, 72 Confinement Model Evaluations for a given drift ratio an ideal model would have an A value of 0% and, to avoid over-conservatism, the B value should be maximized. The relationship between these two statistics wi l l therefore change as the drift limit changes. A large value taken from the C statistic fragility curve indicates a model which is 'safe' yet not 'overconservative'. 4.1.2.2 Assessment of ACI 318-05 21.4.4.1 The A statistic fragility curve for A C I is shown below in Figure 4.14, along with the data which was used to generate the distribution. The B statistic fragility curve for A C I is shown below in Figure 4.15, also with the data which was used to generate the distribution. The C statistic fragility curve for A C I is shown below in Figure 4.16. A s the figures show, the lognormal C D F fits the data very wel l . Reading the curves at a drift ratio of 2.5% produces values very close to the A , B and C statistic given in section 4.1.1.2. o a o o * J o 0 1 2 3 4 5 6 7 8 9 10 Drift Ratio Figure 4.14 Rectangular A fragility curve for ACI 0.9 0.8 0.7 0.6 < 0.5 0.4 0.3 0.2 0.1 73 Confinement Model Evaluations Figure 4.15 Rectangular B fragility curve for ACI Figure 4.16 Rectangular C fragility curve for ACI 74 Confinement Model Evaluations 4.1.2.3 Assessment of Code and Proposed Models As was done for the scatter plot evaluation, the A C I minimum equation is applied here to the remaining models for direct comparison with A C I . A fragility curve evaluation of each model without the minimum wi l l follow. Rather than presenting the A , B and C statistic fragility curves separately for each of the models, Figure 4.17, Figure 4.18 and Figure 4.19 show the A , B and C statistic fragility curves for al l the models (including ACI ) simultaneously, with the A C I minimum applied to all models. The fragility curves are shown here out to 10% drift only to be able to include all the data, but for all practical cases drifts are expected to be limited to less than 4% to 5%. Again, the SK97, BS98, WZP94 and LP04 models have been removed in favor of the combined models S K B S and W Z P L P . The curves show that the A C I model is statistically the worst performer with regard to all three statistical values (A, B and C) throughout the meaningful range of drift ratios. In particular, the discrepancy becomes abundantly clear in Figure 4.19 where all curves follow the general same shape with the exception of A C I . The individual A , B and C fragility curves for all models (incorporating the A C I minimum) can be found in Appendix D. 75 Confinement Model Evaluations 4 5 6 Drift Ratio Figure 4.17 Rectangular A fragility curve all models (with ACI minimum) 4 5 6 Drift Ratio Figure 4.18 Rectangular B fragility curves all model (with ACI minimum) 76 Confinement Model Evaluations Drift Ratio Figure 4.19 Rectangular C fragility curve all models (with ACI minimum) The curves shown above confirm the results of the scatter plot evaluation and suggest that a replacement model be proposed and that the performance of the models consistent throughout the range of drift ratios. A s was done in the scatter plot evaluation, to properly determine the most appropriate alternate model, a fragility curve evaluation for each model which does not include the A C I minimum equation was performed. Figure 4.20 shows the rectangular column A fragility curves for all the models (including ACI ) simultaneously. Likewise, Figure 4.21 shows the rectangular column B fragility curve for all the models and Figure 4.22 shows the rectangular column C fragility curve for all the models. The individual A , B and C statistic fragility curves for each model are presented in Appendix D. It should be noted that taking values from the curve at 2.5% or any other drift ratio, w i l l produce close but not exact matches with the statistics for the corresponding scatter plot due to the need to fit the data with the lognormal cumulative distribution. 77 Confinement Model Evaluations As seen in Figure 4.20, for drift ratios between 0 and 6%, the A C I model had the highest probability of a column not reaching the drift limit while satisfying the confining steel requirements. In other words, the A statistic is highest for A C I through this range. This trend is in agreement with the values shown in Figure 4.13. Conversely, the C S A model had the lowest probability of a column not reaching the drift limit while satisfying the confinement requirements in the drift ratio range of 0 to 4.5%, followed by S K B S , PP92 and B B M 0 5 . Again this is in agreement with the scatter plot statistics. The tightly grouped curves shown in Figure 4.21 suggest that there is much more similarity in B statistic values for the various models than was seen in the A statistic figure. While the variation of B values for the models throughout the range drift ratios is smaller, similar trends to those of the scatter plot evaluation emerge. Again, the A C I model had the lowest B values, and the figure suggests that B B M 0 5 and C S A have the highest B values throughout most of drift ratio range. This figure suggests that while the models behave in a much more similar manner with respect to the B statistic compared to the A statistic, variation between the models still exists such that investigating the rectangular column C statistic fragility curves is warranted. The curves shown in Figure 4.22 are a graphical description of the overall performances of the models. It is here that the overall performance of the A C I model relative to the other models in this study clearly becomes evident. Not only is the C value lowest for the A C I model for all values of drift ratio, but it produces a negative value for drifts between approximately 0.5% and 5.0%. A l l other models behave similarly for small drift ratios but the performance differences become apparent for drift ratios between 1.5% and 5.0%. A s was seen in the scatter plot evaluation, the C S A , B B M 0 5 and PP92 models had the best overall performance. B B M 0 5 has the highest values up to a drift ratio of approximately 2.0%, when C S A becomes higher. C S A has the highest overall C value of 43.7% at a drift ratio of 3.5%. Again , the fragility curves are shown here out the 10% drift only to be able to include all the data. Chapter 5 shows these figures up to drifts of 4%. 78 Confinement Model Evaluations Drift Ratio Figure 4.20 Rectangular A fragility curve for all models Drift Ratio Figure 4.21 Rectangular B fragility curve for all models 7 9 Confinement Model Evaluations o Figure 4.22 Rectangular C fragility curve for all models 4.1.2.4 Special Consideration for SR02 Only the B B M 0 5 and SR02 models use drift ratio as the performance measure to derive the expression for the confining steel requirement. This parameter is not a direct input variable for determining the amount of confining steel for B B M 0 5 , however as stated in Chapter 2, the model was derived for limiting drifts of 1.5% and 2.5%, thus making it suitable for the above comparison. This is not the case for SR02 where the target drift ratio, 5, is a direct input variable. A value of 2.5% was selected to be consistent with scatter plot evaluation procedure; however this selection may be an unfair representation of the model for the fragility curve evaluation. Therefore, to account for this, the scatter plot A , B and C statistics were generated for target drift ratios from 2% to 5%, each using the appropriate drift ratio in Equation 2.31. The results are plotted in Figure 4.23 against the curves in Figure 4.20, Figure 4.21 and Figure 4.22 where 8 = 2.5%. The figure shows a close agreement between the two approaches for drift ratios up to 3% at which point a slight variation is observed. The approach which holds the input drift ratio constant at 80 Confinement Model Evaluations 2.5% actually provides more favorable values for the A and C curves. Therefore, the results displayed in Figure 4.23 suggest that the fragility curves in Figures 4.16 through 4.18 are a valid representation of the SR02 model, and no further consideration for the model is needed. Note, the A C I minimum equation was not included in the evaluation. < 0.5 m 0.5 O -0.5 3.5 Drift Ratio Figure 4.23 Rectangular SR02 fragility curve comparison 4.1.3 Spacing of Transverse Reinforcement As was explained in Chapter 2, the spacing requirements of the three building codes investigated here are considered in addition to the confining steel area requirements. 4.1.3.1 Assessment of ACI 21.4.4.2 In A C I 318, the two spacing requirements related to confinement, Equation 2.10 and 2.12 are considered separately from the area requirements. Figure 4.1 shows the scatter plot for the spacing requirement of one quarter the minimum dimension. Figure 4.25 shows the corresponding C statistic fragility curve. Equation 2.12 was not evaluated due to the 81 Confinement. Model Evaluations fact that the database is composed of scaled tests. The range of acceptable spacing according to this expression (4 to 6 inches) is not suitable for these columns. Since the scaling factor is unknown for the majority of the columns, an accurate evaluation of this spacing limit is not possible. Further discussion of this issue is presented in Chapter 5. 10 9 d 6 o 'to 5 LT. *± E  4 3 2 1 0 • • • • • • fi in a • • • • • 1 P-cP • • • • • • Satisfies ACI 21.4.4.1 ^ Does Not Satisfy ACI 21.4.4.1 0.5 1.5 2 D / 4S 2.5 3.5 Figure 4.24 Rectangular scatter plot for spacing limit of H/4 82 Confinement Model Evaluations 0.06 -0.04 [ Drift Ratio Figure 4.25 Rectangular C fragility curve for spacing limit H/4 The statistics for Figure 4.24 are provided in Table 4.4. Table 4.4 Scatter plot statistics for ACI spacing limit shown in Figure 4.24. A B C 22.2 18.2 -4.0 Figure 4.24 and Figure 4.25 show that the one quarter minimum dimension spacing limit when evaluated on its own performs at a similar level to the A C I area requirement. B y comparison, the area requirements of the other models perform better than both A C I area and one quarter minimum dimension spacing requirements. Figure 4.26 shows the properties of the data points which fall into quadrants 2 and 3 for Figure 4.24. Unl ike the corresponding plot for the area requirements, a strong connection between the axial load and the performance o f the requirement is lacking, although a modest connection is still observable on the figure. 83 Confinement Model Evaluations 120, 100 4 • u TT • Q2 Columns 4 Q3 Columns CD Q. 80 60 0 o • + n • 40 i 20 • • • • 0.1 0.2 0.3 0.4 0.5 0.6. 0.7 0.8 0.9 Axial Load Ratio (P/A f ' ) x g o ' Figure 4.26 fc' vs. axial load ratio for Q2 and Q3 columns for H/4 spacing limit Finally, it is important to address how often each A C I confinement requirement governs the design of columns. Table 4.5 shows the number of instances where each requirement governs the spacing of the confinement reinforcement for the 145 rectangular columns. The confinement area requirements of A C I 318 are rearranged and expressed as a spacing requirement (i.e. for a known area and arrangement of transverse bars). A s = sh 0.3/r A, fc fyh y.Aci, . ( 4 . 8 ) This spacing requirement was then compared to the two spacing limits to determine which governed. Recall the other two spacing limits given in Chapter 2 and in A C I section 21.4.4.2 are s < Q.25D and s<6db. Again, the effect of scaling the test specimens renders the spacing limit given by Equation 2.12 (ACI Eq 21-5) inappropriate for application to the columns in the database. 84 Confinement Model Evaluations Table 4.5 ACI 318-05 Governing spacing of rectangular transverse reinforcement Spacing limit # columns governed Eq2 .10 19 Eq2.11 . 3 Eq 4.8 124 The data in Table 4.5 shows that for the vast majority of reinforced concrete columns in the database, the area requirement dominates the spacing o f the transverse steel. While not included in the table above, one would expect that for ful l scale columns the spacing limit given by Equation 2.12 would often govern for large columns with closely spaced longitudinal reinforcement, and the number of instances in which Equation 4.8 governs would be less than what is represented in Table 4.5. O f the 32 columns which satisfy the area requirements of section 21.4.4.1 of A C I 318-05, 8 do not satisfy the spacing requirement of section 21.4.4.2. 4.1.3.2 Assessment of CSA and NZS A similar comparison was made for the C S A A23.3-04 and N Z S 3101:2006 building codes. The confinement steel area requirements are rearranged and expressed as spacing requirements in Equation 4.9 for C S A and 4.10 for N Z S . s = Lsh A f' 0.2k kD g J c hc " P A f -"•ch J yh ( 4 . 9 ) A s = • sh Ag I.Q-p,mfe' P 3-3 u ^ A A -0 .0065 (4 .10) The spacing limits for C S A are the same as those for A C I (Eq 2.10 and Eq 2.11), and for N Z S the spacing limits are given as . 85 Confinement Model Evaluations s<-D ( 4 .11 ) 3 s<lOdb ( 4 .12 ) The results are displayed below in Table 4.6. The table shows a lower number of instances in which the spacing is governed by the area requirement. Again it is important to determine how many columns which satisfy the area requirement, but fail the spacing limits. For the 63 columns which satisfy the area requirement of C S A , 22 do not meet the spacing requirements. For the 49 columns which satisfy the area requirement of N Z S , 14 do not satisfy the spacing requirements. Table 4.6 Governance breakdown for spacing of transverse reinforcement for • CSA A23.3-04 and NZS 3101:2006 # columns # columns Spacing limit governed C S A governed N Z S Eq 2.10/4.11 44 70 Eq2.11 / 4.12 2 5 Eq 4 .9 /4 .10 99 70 4.1.4 Maximum Recorded Drifts As discussed in Chapter 3, the failure drift of the columns was assumed to occur once the column demonstrated a 20% loss in lateral strength. However, while this assumption is val id for new construction and columns within the lateral force resisting system, in some instances it may be of interest to investigate the performance of the columns at their maximum recorded drifts. Such instances may include those in which the column is not incorporated. into the structures lateral force resisting system, and thus gravity load carrying capacity, rather than lateral load capacity, is of importance. Figure 4.27 shows the scatter plot statistics for the models using drift ratios calculated using the maximum recorded drift for each test. Figure 4.28 shows the C statistic fragility curves. A l l scatter plots and fragility curves are given in Appendix D. Note, the A C I minimum equation was not included in any of the other models. i 86 Confinement Model Evaluations 50 45 40 35 30 25 20 15 10 5 0 u ACI CSA PP92 SR02 WSS99 BBM05 SKBS WZPLP NZS Figure 4.27 Rectangular Scatter plot statistics using maximum recorded drifts The statistics found with maximum recorded drifts are similar to those which were observed for drifts at 20% loss in strength. The higher drifts resulted in fewer data points in quadrants 2 and 4, therefore reducing the A and B values. Also the emergence of CSA, BBM05 and PP92 as the superior models is shown in Figure 4.28. The important observation to gain from the two figures is that the ACI model is once again the statistically least desirable, it is the only model to produce a negative C value, and that a replacement model is desirable. The results of the evaluation at maximum recorded drifts support the validity of a proposal for a replacement model done through further interpretation of the results for drifts recorded at 20%> loss in strength only. The drifts at 20% loss in strengths and the maximum recorded drifts can be found in Appendix A. 87 Confinement Model Evaluations o 4 5 6 7 Drift Ratio 10 Figure 4.28 Rectangular C fragility curves using maximum recorded drifts. 4.2 Circular Columns A s was done for the rectangular column evaluation, each confining reinforcement model, including the code equations, was evaluated based on the properties and performance of the column specimens within the database. Again, the aim is to determine how the current A C I code equation compared with both the other code equations as well as the proposed models, and propose a replacement model should it be necessary. The same two evaluation techniques are used to make this comparison. The recommendations presented in Chapter 5 wi l l consider the effects of the smaller database. 4.2.1 Scatter plot evaluation 4.2.1.1 Evaluation procedure The circular column scatter plot evaluation procedure is identical to that of the rectangular column evaluation. The only difference here is that the x axis values are given 88 Confinement Model Evaluations in terms of volumetric transverse reinforcement ratios rather than in terms of area of transverse steel. This is done in keeping with the manner in which the current A C I code states the confining steel requirements for circular columns. 4.2.1.2 Assessment of ACI 318-05 21.4.4.1 The circular column scatter plot for the A C I confining steel requirement is shown below in Figure 4.29. Again, all columns which satisfy the density of confining steel requirements of A C I are plotted with a lightly shaded square marker, while those which fail the density of confining steel requirements are plotted with a dark shaded diamond marker. 15 10 03 or • • • • • • • • • f • TL • • ! El • 4 • • • • • Satisfies ACI 21.4.4.1 + Does Not Satisfy ACI 21.4.4.1 0.5 1.5 2 2.5 3 P Provided ' PACI 3.5 4.5 Figure 4.29 ACI scatter plot (circular columns) The figure shows the following data distribution: 89 Confinement Model Evaluations Table 4.7 Quadrant data distribution of ACI circular scatter plot Quadrant 1 Quadrant 2 Quadrant 3 Quadrant 4 28 I 20 I From the numbers given in Table 4.7 the A , B and C statistics can be calculated as: Table 4.8 Statistics for ACI circular scatter plot A B C 3.4 4.8 1.4 The first observation that can be made when comparing Figure 4.29 with Figure 4.2 is the significant difference in the number of data points which lie below the performance target drift ratio of 2.5%. Only two of the 53 columns within the circular column database fall below this limit. The axial load ratios for these two columns are 0.5 and 0.7, and are two of the four highest axially loaded columns in the circular column database. The shortage of data in the bottom two quadrants is l ikely due to the difference in the typical axial load ratios found in the two databases. A s was shown in Table 3.3 and Table 3.4, the average axial load ratio for the rectangular column database was 0.28, while for the circular columns it was only 0.17. In fact, the circular column database has just 10 columns with an axial load ratio higher than 0.3. As has been highlighted throughout this work, columns with lower axial load ratios are capable of achieving higher drifts, a fact illustrated further by the data in Figure 4.29. With only one column falling in quadrant two, the A statistic for A C I is quite low at 3.4%). If the percentage of 'safe' columns were the only criterion for evaluating the performance of the model, the A statistic would suggest that A C I performs very well. However, as described earlier, the B and C statistics are also insightful for investigating the performance of the model. The B statistic for A C I is also quite low at 4.8%, suggesting that the A C I model is very conservative. The C value for the A C I circular scatter plot is very low at 1.4%, suggesting that the overall performance of the model could be improved. 90 Confinement Model Evaluations Figure 4.30 presents a plot of fc' versus P /A g f c ' for the 23 columns in quadrant 3, and shows only that 3 columns have an axial load above 0.2. Similar to the observations of N the corresponding rectangular columns, the expectation is that the remaining models wi l l have fewer columns in quadrant 3 since each of the models incorporates axial load level into the confining steel requirement. CO Q. Axial Load Ratio (P/A f ' ) v g c ' Figure 4.30 fc' vs. axial load ratio for Q3 columns of ACI scatter plot (circular columns) 4.2.1.3 Assessment of Codes and Proposed Models The scatter plot evaluation for the remaining circular models follows the same procedure ' as was done for the rectangular evaluation. The A C I minimum given by Equation 2.5 (ACI Equation 21-2) is applied to all models to allow for an equal comparison with the A C I model. Figure 4.31 shows the scatter plot statistics with the A C I minimum applied to all models. There are two important observations to take from the figure. First, al l the models provided a statistical improvement over the A C I model, although not as 91 Confinement Model Evaluations 50 45 40 35 30 25 20 15 10 5 0 WE A I | B mm c III1111 in ACI CSA PP92 SR02 BBM05 SKBS WZPLP NZS Figure 4.31 Circular scatter plot statistics all model (with ACI minimum) significant as was seen in the rectangular evaluation. Secondly, the inclusion of the A C I minimum equation had a significant effect on the other models in that it governed the design for a large number of columns for each model, and therefore caused the performance of the models to become very similar. These two conclusions demonstrate that an evaluation of the models without the A C I minimum equation included is needed to determine an appropriate replacement for the A C I requirement. Once again, the SK97, BS98, WZP94 and LP04 models were not included in the evaluation in favor of the combination models S K B S and W Z P L P . The scatter plots for all models incorporating the A C I minimum equation are given in Appendix D. The scatter plots for the remaining models are presented in Figure 4.32 through Figure 4.38. A l l circular scatter plots including those presented here are included in Appendix D. For the PP92, WZP94, LP04 and W Z P L P models, columns with very low axial load required very small amounts of transverse steel, and in some cases the expression yielded 92 Confinement Model Evaluations a negative density requirement. For these models, the A C I minimum limit was used in conjunction with model's expression, exactly as was done to determine the statistics given in Figure 4.31. Including this limit in the evaluation is not a true representation of the model alone, but the nature of the database used to perform the evaluation was such that a minimum value was needed for these models to provide meaningful scatter plot statistics. If any of these models are determined to be the most appropriate model, the appropriateness of this minimum wi l l be re-evaluated before final conclusions are made. A s expected, each model had zero columns in quadrant 2 and most had fewer columns in quadrant 3, the most significant change belonging to SR02 which had 4 columns in quadrant 3. Further discussion of the scatter plots wi l l be given where relevant in the presentation and justification of the final recommendations (Chapter 5). 15 10 CD 4 • • 4 • • • • 4 * • • • • • • • n • tb • P U3 a • 6 .__ 0 • Satisfies ACI 21.4.4.1 4 Does Not Satisfy ACI 21.4.4.1 0 0.5 1.5 2 2.5 3 3.5 Prov ided ^ P C S A 4.5 Figure 4.32 CSA scatter plot (circular columns) 93 Confinement Model Evaluations •15r • 10 .0 co 01 • • • ! • • • • I 4o • • EF • • Satisfies ACI 21.4.4.1 4 Does Not Satisfy ACI 21.4.4.1 0 0.5 1.5 2 2.5 3 P Provided ' P NZS 3.5 4.5 Figure 4.33 NZS scatter plot (circular columns) 15R • 10 CO OH Q • ! • • •• • • • • 0 ^ • Satisfies ACI 21.4.4.1 4 Does Not Satisfy ACI 21.4.4.1 0 0.5 1.5 2 2.5 3 Pprovided ' PpP92 3.5 4.5 Figure 4.34 PP92 scatter plot (circular columns) 94 Confinement Model Evaluations 15r 10 o "co • 0 • • • • • • • • • • • • 4: C P • Satisfies ACI 21.4.4.1 + Does Not Satisfy ACI 21.4.4.1 0 0 .5 1 1.5 2 2 .5 3 3 .5 4 4 . 5 5 P Provided ' PsR02 Figure 4.35 SR02 scatter plot (circular columns) 15, • 10 4 • • co Dd • • • • JL_ 4 D f i 4 • ' • • • • • • Satisfies ACI 21.4.4.1 ^ Does Not Satisfy ACI 21.4.4.1 0 0 .5 1 1.5 2 2 .5 3 3 .5 P Provided ' PBBM05 4 4 . 5 5 Figure 4.36 BBM05 scatter plot (circular columns) 95 Confinement Model Evaluations • • • • • t>*U • i • _ | 4 • E-fc ! • Q • • B • • Satisfies ACI 21.4.4.1 4 Does Not Satisfy ACI 21.4.4.1 0.5 1.5 2 2.5 3 Pprovided ' P S K B S 3.5 4.5 Figure 4.37 SKBS scatter plot (circular columns) • > j ° • In • ,• J • 4n 4 • • B • £>- U • Satisfies ACI 21.4.4.1 4 Does Not Satisfy ACI 21.4.4.1 0.5 1.5 2.5 3.5 4.5 Pprovided ^ PwZPLP Figure 4.38 WZPLP scatter plot (circular columns) 96 Confinement Model Evaluations The distribution of data points into the four quadrants for all the models shown below in Table 4.9. Table 4.9 Quadrant data distribution for all models circular scatter plots Model Q i Q2 Q3 Q4 C S A 43 0 5 2 PP92 26 . 0 22 2 SR02 44 0 4 2 B B M 0 5 39 0 9 ' 2. S K B S 39 0 9 2 W Z P L P 28 0 20 2 N Z S 38 0 10 2 r The A , B and C statistics for each model including the previously given A C I values are displayed in Figure 4.39. As shown in the figure, only the A C I model does not have an A value o f 0%. The highest B value (33.3%), and hence the largest C value (33.3%) belonged to SR02. C S A had the next best C value at 28.6%, followed by B B M 0 5 and S K B S with 18.2%. 97 Confinement Model Evaluations 50 45 40 35 30 25 20 15 10 5 0 I 1 A LZ1 B hi ACI CSA PP92 SR02 BBM05 SKBS WZPLP NZS Figure 4.39 Circular scatter plot statistics bar graph 4.2.2 Fragility curve evaluation 4.2.2.1 Evaluation Procedure The procedure for the circular fragility curve evaluation is identical to that for the rectangular evaluation. The curves are extended to a drift ratio of 15% as drifts of this magnitude were recorded in the database. 4.2.2.2 Assessment of ACI 318-05 21.4.4.1 Figure 4.40 and Figure 4.41 show the circular column A and B fragility curves for ACI along with the data which was used to generate the distributions. The circular column C circular statistic fragility curve for ACI is shown below in Figure 4.42. As the figures show, the limited amount of data results in a lognormal CDF which does not fit the data as well as was seen for the rectangular columns (see Figure 4.14). 98 Confinement Model Evaluations However, reading the curves at a drift ratio of 2.5% produces values very.close to the A , B and C statistics given above. 99 Confinement Model Evaluations Figure 4.41 Circular B fragility curve for ACI 0.12 0.08 o.o6 y u. Q o 0.04 0.02 -0.02 Figure 4.42 Circular C fragility curve for ACI 100 Confinement Model Evaluations 4.2.2.3 Assessment of Codes and Proposed Models A s was done for the scatter plot evaluation, the A C I minimum equation is applied here to the remaining models for direct comparison with A C I . A fragility curve evaluation of each model without the minimum wi l l follow. Figure 4.43, Figure 4.44 and Figure 4.45 show the A , B and C statistic fragility curves for A C I and all other models where the A C I minimum is applied to all models. A s was stated earlier, the fragility curves are shown here up to very high drifts only to be able to include all the data. Again, the SK97, BS98, WZP94 and LP04 models have been removed in favor of the combined models S K B S and W Z P L P . The figures again confirm the conclusions reached in the initial scatter plot evaluation. For all three figures, the A C I model resulted in the least desirable curve. Again the Drift Ratio Figure 4.43 Circular A fragility curve all models (with ACI minimum) 101 Confinement Model Evaluations 1 0.9 0.8 h 0.7 0.6 CO 0.5 0.4 0.3 0.2 0.1 0 0 ACI C S A — • P P 9 2 — S R 0 2 B B M 0 5 - - S K B S W Z P L P N Z S 10 Drift Ratio 15 Figure 4.44 Circular B fragility curve all models (with ACI minimum) o -0.1 Figure 4.45 Circular C fragility curve all models (with ACI minimum) 102 Confinement Model Evaluations inclusion of the A C I minimum had a significant effect on the performance of the models particularly at low drift ratios. The inclusion of the A C I minimum resulted in the C S A and B B M 0 5 models demonstrating the exact same performance and their, curves in all three figures lie on top of each other. Despite this fact and limitations ofthe database, the curves clearly indicate that the A C I model provides the least desirable performance and that a replacement model is warranted. To determine which model should act as the suggested replacement, a fragility curve evaluation of the models without the A C I minimum is needed. Figure 4.46 shows the circular column A fragility curve for all the models including A C I . Likewise, Figure 4.47 shows the circular column B fragility curve for all the models and Figure 4.48 shows the circular column C fragility curve for all the models. The A C I minimum is not applied to any other model. A lso , the current minimum of the C S A code given in Equation 2.14 ( C S A Equation 10-7) is not included in the evaluation. This again is because this minimum does not form part of the PL05 model being evaluated. ' Again, the SK97, BS98, WZP94 and LP04 models have been removed in favor of the combination models S K B S and W Z P L P . The individual A , B and C statistic fragility curves for each model are presented in Appendix C. A s expected, the curves in Figure 4.46 show essentially no difference in the A values at a drift ratio of 2.5%. This matches perfectly with the results ofthe scatter plot evaluation. Whi le the individual behavior o f the models is distinguishable at higher drift ratios, significant variation does not become apparent until drift ratios of approximately 4% are reached. With no significant differences in the models at lower drift levels with regard^to the A statistic fragility curve, the B statistic fragility curves becomes even more significant. As expected, the curve with the highest B value in Figure 4.47 at a drift ratio of 2.5% is SR02 followed by B B M 0 5 and C S A . These results are again in agreement with those from the scatter plot evaluation. However, as is clearly shown in the figure, C S A and 103 Confinement Model Evaluations B B M 0 5 become the highest curves, by a significant margin, at drifts beyond 3.0%. The A C I model provides the lowest B values for drift ratios up to approximately 9% The SR02 C value, shown in Figure 4.48, is the highest at a drift ratio of 2.5%, however, as witnessed in the B statistic fragility curve, C S A and B B M 0 5 become the best performing model at drifts higher than 2.5%. The A C I model provides the lowest C values at drift ratios below approximately 8%, which could be considered beyond the range of meaningful drifts. Drift Ratio Figure 4.46 Circular A fragility curve for all models 104 Confinement Model Evaluations Drift Ratio Figure 4.47 Circular B fragility curve for all models 15 Figure 4.48 Circular C fragility curve for all models 105 4.2.2.4 Special Considerations for SR02 Confinement Model Evaluations As was done in section 4.1.2.4, special consideration is given to the SR02 model due to the fact that the drift ratio is a direct input into the expression used to calculate the confinement requirement. Figure 4.49 shows a comparison of the A , B and C statistic curves generated using the appropriate drift ratios with those generated using a drift ratio of 2.5%. The figure suggests that for the circular column database used in this study, using a consistent drift ratio of 2.5% under-predicts the performance of the SR02 model at drifts greater that 2.25% and over-predicts the performance at drifts less than 2.25%. The conclusion is that the performance of the SR02 model is slightly better than shown in Figure 4.48. < 0.5 1.5 m 0.5 O 0.5 — - with corresponding 8 5=2.5% 2.5 3.5 3.5 Drift Ratio 4.5 5.5 Figure 4.49 Circular SR02 fragility curve comparison 106 • __ Confinement Model Evaluations 4.2.3 Spacing (Spiral Pitch) of Transverse Reinforcement ~\ • • 4.2.3.1 Assessment of ACI 21.4.4.2 As explained in Section 2.1.1, the spacing requirements for circular columns are the same as those provided for rectangular columns and are given in Equations 2.10 and 2.11. The exception that the third limit (Equation 2.12) does not apply to circular columns. The scatter plot for the one quarter minimum dimension spacing limit is shown below in Figure 4.50. The figure shows every column in the database, including two columns which have drifts below 2.5%, meets the spacing requirement. 15 10 00 or it: • • • • • . • • I 1 • ! • S • I L J • 1 n J • • ' • • • n o 1 4 D/4s • • B B-Figure 4.50 Circular scatter plot for one quarter minimum dimension spacing limit The confinement area requirements of ACI 318 are rearranged and expressed as a spacing requirement (i.e. for a known area and arrangement of transverse bars). 107 Confinement Model Evaluations f ' 4 A > , (4.13) yh 1 V Ach J This spacing requirement was then compared to the two spacing limits giving in Equations 2.10 and 2.11, to determine which governed. Table 4.10 shows how often each confinement requirement governs the spacing of transverse reinforcement for the 50 circular columns used in this study. Table 4.10 ACI 318-05 Governing spacing of circular transverse reinforcement Spacing limit # columns governed Eq 2.10 1 Eq2.11 1 Eq 4.13 48 As was the case for the rectangular columns, the area requirement predominantly governs the spacing of the confining steel. This result is not surprising when considering that the ACI model was found to be the most overconservative in the scatter plot and fragility curve evaluations. A l l of the 29 columns which satisfy the area requirements of ACI 318-05 section 21.4.4.1 also satisfy the spacing requirement of section 21.4.4.2. This statistic further indicates the conservative nature of the ACI confining steel area requirement for circular columns. 4.2.3.2 Assessment of CSA and NZS The area requirement for the CSA and NZS models were rearranged and expressed as a spacing limit as follows: AA s = - \ r ~ ' (4-14) yh 108 Confinement Model Evaluations f Ag\.0-ptm fc> P A 4A  \ 0.0084/r s = —, * , (4.15) A* 2.4 fyh0f,'AgJ The results of the evaluation of the spacing limits for CSA and NZS are displayed below in Table 4.11. The table shows a similar number of instances in which the spacing is governed by the area requirement. All of the 43 columns which satisfy the area requirement of CSA, and all of the 38 which satisfy the area requirement of NZS, also satisfied the spacing requirements. The results shown in Table 4.10 and Table 4.11 show the potentially extraneous nature of the one quarter diameter spacing limit when used in conjunction with the area requirement for confining steel in circular columns. This issue is further discussed in the final recommendations (Chapter 5). Table 4.11 Governance breakdown for spacing of transverse reinforcement for CSA A23.3-04 and NZS 3101:2006 Spacing limit # columns governed CSA # columns governed NZS Eq 2.10/4.11 1 . 3 Eq 2,11/4.12 0 0 Eq 4.14/4.15 49 • 47 4.2.4 Maximum Recorded Drifts As was done in the rectangular column analysis, the maximum recorded drifts were also analyzed. The effects of this adjustment were noticeable for the rectangular columns as many of them experienced drifts well beyond that recorded at 20% loss in lateral strength. For the circular column database this is not the case. In fact, the average increase between the two displacements for circular columns was a mere 9.1% versus 32.0% for the rectangular columns. The two columns in the original analysis which had drift ratios below 2.5% achieved higher drifts, but both still remained below 2.5%. Therefore, the 109 Confinement Model Evaluations scatter plot evaluation produced the same statistical values for A , B and C as those obtained with drifts measured at 20% loss in strength, and the there was consequently no distinguishable difference in the fragility curves for the two analyses. For some tests, the maximum recorded drift ratios where close to those measured at 20% loss in strength. This is simply because most tests are stopped shortly after this stage and does not suggest that circular columns have less reserve drift capacity than rectangular columns. The conclusion therefore is that the performance results of the models remains essentially unchanged for the analysis using the maximum recorded drifts for the circular columns, and the formulation of a final conclusion can be based on the results found in the analysis using drifts at 20% loss of lateral strength. The drifts at 20% loss in strengths as wel l as the maximum recorded drifts can be found in Appendix A . 110 5 S E L E C T I O N O F C O N F I N E M E N T M O D E L 5.1 Selection Procedure The previous chapter presented the results of the performance evaluations for each model considered in this study. The results clearly indicated that the A C I criteria for confining steel in reinforced concrete columns should he improved. The following is a description of the procedure used to select the most appropriate confinement model for both rectangular and circular columns..The procedure uses the evaluation results presented in Chapter 4 to select (and eliminate) models based on their performance. 5.1.1 Objective In the introduction, it was stated that the aim of this project is to evaluate the current requirements of A C I 318-05, and present a final recommendation for the design of confinement steel for both the rectangular and circular reinforced concrete columns. Part of the evaluation included considering the form of the requirements expressed in Chapter 21 of ACI318-05. The area of confining steel is stated in section 21.4.4.1, while the spacing requirements are given in section 21.4.4.2. The latter contains the two spacing limits which are confinement requirements and also the spacing limit which is intended to protect against longitudinal bar buckling. The recommendations given here are derived with the intent of presenting a requirement for both rectangular and circular columns which takes the following form: i) Minimum confinement level (expressed as either a minimum area / density limit or a maximum spacing limit) ii) Appropriate varying confinement levels (area / density or spacing requirements above the minimum value) The minimum confinement level is intended to be a baseline for confinement for all columns. The need for a minimum leve lof confinement arises from a historical design practice that a minimum level be maintained for all columns, similar to Equations 21-2 111 Selection of Confinement Model and 21-4 in ACI318-05. The form of the minimum level will depend on the nature of the preferred model and therefore can be determined once the model has been selected. For confinement above the minimum level, the preferred model should consider all the variables which impact the performance of the columns and require confinement levels that are appropriate to achieve acceptable levels of drift. 5.1.2 Scatter Plot Evaluation The data presented in the scatter plot evaluation is useful to understand how the performance of each model compares to the ACI model. Identifying data points with • lightly shaded squares and dark shaded diamonds based on their location on the ACI scatter plot, allows for tracking the movement of data points on subsequent scatter plots. As was discussed in Chapter 4, the ideal model would have zero data points in quadrant 2 and the number of data points in quadrant 3 should be limited to an appropriate level of conservatism. The ACI rectangular model has 9 data points in quadrant 2 and 92 in quadrant 3, the ACI circular model has 1 data point in quadrant 2 and 20 in quadrant 3 (Table 4.3 and Table 4.9). Therefore, the scatter plot of a model which demonstrates an improved performance will display a movement of these data points from quadrant 2 to quadrant 4, and from quadrant 3 to quadrant 1. Figure 5.1 illustrates an example of this movement of for a few select data points. Figure 5.1(a) shows the location of the data points on the ACI scatter plot and the desired movement of the data in quadrants 2 and 3. Figure 5.1(b) shows the location of the data on the CSA scatter plot showing the improved performance. The figure also demonstrates a desired trend for improved models, one in which data points are aligned in a matter that demonstrates a" proportionally increased drift with increased confinement (i.e. along the diagonally dashed line). This relationship is particularly meaningful at lower confinement levels; as the confinement approaches the model requirement, the drift should approach the performance target. As seen in Figure 4.2, this is not the case for the ACI model where test columns with only slightly less confinement than required had failure drift ratios well below the 2.5% target. 112 Selection of Confinement Model 10 9 8 7 ^ 6 g ro 5 § 4 3 2 1 0 • Satisfies ACI 21.4.4.1 4 Does Not Satisfy ACI 21.4.4.1 a) • • • A / A sh Provided sh ACI 10 9 8 o 're • 5 OH «=: £ 4 • Satisfies ACI 21.4.4.1 4 Does Not Satisfy ACI 21.4.4.1 b) 9 • A IA ' sh Provided sh model Figure 5.1 Desired movement of data points To further illustrate this desired model improvement, two specific columns taken from the rectangular column database are shown below. The two tests have a similar transverse reinforcement ratios and the major difference between the two column tests is the level of axial load. Column 15 was subjected to an axial load ratio of P/Po = 0.7 and had a measured drift ratio of 1.2% at 20% loss in lateral strength. Column 106 was subjected to an axial load ratio of just P/Po = 0.15 and had a measured drift ratio of 9.0. Figure 5.2 shows that for the two columns, the CSA model which includes axial load in the design expression demonstrates more appropriate confinement levels. The evaluation of the data movement and the values presented in Table 4.3 and Table 4.9 will be used to eliminate models which are not a significant improvement over the ACI model. 113 Selection of Confinement Model A / A sh Provided sh model Figure 5.2 Location of specific column examples for ACI and CSA scatter plot Table 5.1 Details for rectangular columns 15 and 106 Database No. Specimen Name fc (MPa) P/Agfc L(mm) Gross Area (Ag) (mm2) Piong (%) Parea (%) Drift Ratio (%) 15 Watson and Park 1989, No. 7 42 0.7 1600 160000 1.51 1.30173 1.17 106 Saatcioglu and Ozcebe 1989, U4 32 0.15 1000 122500 3.21 .1.0908 8.99 5.1.3 Fragility Curve Evaluation The fragility curves presented in Chapter 4 wi l l be compared for the models which were not eliminated in the scatter plot evaluation. The fragility curves wi l l be examined within the range of meaningful drifts. As discussed in Chapter 4, the curves provide probability data up to the maximum drift ratio observed in the database (i.e. a drift ratio of 10% for rectangular columns and 15% for circular columns). However, it is highly unlikely that a 114 Selection of Confinement Model target drift ratio for a building, particularly in new construction, would exceed 3% to 4%, therefore data beyond these drifts is not meaningful. The fragility curves can then be used to select the models which demonstrate the best overall performance. If the level of safety provided by the model was the only matter of interest, the A fragility curve would be the appropriate curve to examine. However, the interest of this study is to identify which model provides the optimum level of safety without significant overconservatism. Therefore, all three fragility curves wi l l be addressed in the evaluation. It should be noted that the models which do no offer an improved level of safety wi l l be removed from the list of potential replacement models during the scatter plot evaluation. 5.1.4 Comparison of Expressions The. form of the expressions given in Chapter 2 w i l l be evaluated again after the scatter plot and fragility curve evaluations are complete. To be considered an appropriate replacement model, the form of the expression should contain variables that practicing engineers are familiar with, and should appear as transparent as possible. Any model which is drastically different than current design practice wi l l be removed from the list of potential replacement models unless that model displays exceptional performance and its removal can not be justified. 5.1.5 Model Requirements A typical example column, for both rectangular and circular cross-sections, wi l l be used to evaluate how the requirements of the final models compare with the current requirements in A C I . The example columns are taken from the typical column details provided in section 3.4 and Appendix D. ' , The confining steel area, or volumetric density, requirement by each model for the example columns can be shown throughout the range of axial load ratios. A similar figure w i l l be generated to show the spacing requirements which result from the form of each 115 Selection of Confinement Model model. This figure wi l l give more insight to how the models compare with the spacing limits of A C I . 5.2 Rectangular Columns 5.2.1 Scatter Plot Evaluation A review of the scatter plots presented in Section 4.1.1.3, the statistics shown in Figure 4.13 and the data presented in Table 4.3 show that the A C I model exhibited the poorest performance of all the models in this investigation. Table 4.3 also shows the movement of data points for the rectangular column models. The results indicate that the WSS99 and SR02 models had more data points in quadrant 2 than the A C I model, and S K B S had more data points in quadrant 3 than the A C I model. For these three models, the change in number of data points in the quadrants is not large, but the desired movement of data points as presented in Figure 5.1 is not demonstrated. While the number of data points in quadrant 1 for both the WSS99 and SR02 models increased, the presence of a larger number of 'unsafe' columns renders these models undesirable. For S K B S , the greater number of data points in quadrant 3 combined with fewer data points in quadrant 2 suggests that the model simply requires a greater amount of confinement reinforcement for virtually all columns and is not strongly correlated to the drift performance of the columns. While this greater requirement does significantly reduce the instances of 'unsafe' columns, it restricts the desired movement o f data points at higher drifts. Based on the discussion above, the WSS99, SR02 and S K B S models are removed from the list of suitable replacements for the A C I model. The scatter plots for the remaining models ( C S A , PP92, B B M 0 5 , W Z P L P and N Z S ) suggest that as the amount of confinement approaches the requirement of the model, the drift capacity approaches the performance target, a trend not observed in the models removed here. 116 5.1.6 Fragility Curve Evaluation Selection of Confinement Model The A , B and C fragility curves for the C S A , PP92, B B M 0 5 , W Z P L P and N Z S models are shown again in Figure 5.3 through Figure 5.5 for the meaningful range of drift ratios discussed earlier. The figures show that at drift ratios below 1.0% there is no real significant difference in the performance of the models, however, at drifts greater than 1.0%, the C S A , PP92 and B B M 0 5 models clearly exhibit superior statistics. The curves demonstrate that over the practical range of drift ratios, these three models best capture the desired overall performance which included both a suitable level of conservatism and safety. Figure 5.4 further suggests that the B B M 0 5 model performs best at drift ratios below 2.2%>, while the C S A model performs the best at higher drift ratios; although the difference between the models is not statistically significant. 0.45 0.4 0.35 0.3 0.25 0.2 0.15 0.1 0.05 0 C S A P P 9 2 B B M 0 5 W Z P L P N Z S 0.5 / i / 1.5 2 2.5 Drift Ratio 3.5 Figure 5.3 A fragility curves 117 Selection of Confinement Model 0.8 r 0.7 0.6 0.5 CQ 0.4 0.3 0.2 0.1 • - C S A — P P 9 2 B B M 0 5 W Z P L P N Z S 0 0.5 A s 1.5 2 2.5 Drift Ratio 3.5 Figure 5.4 B fragility curves 0.5 0.45 0.4 0.35 0.3 O 0.25 0.2 0.15 0.1 0.05 0 0 C S A P P 9 2 BBM05 W Z P L P N Z S 0.5 1.5 2 2.5 Drift Ratio 3.5 Figure 5.5 C fragility curves 1 18 Selection of Confinement Model These results clearly identify W Z P L P and N Z S as being the least desirable of • the remaining models, and the conclusion therefore is to eliminate them from the list of suitable alternatives for the A C I model. 5.1.7 Comparison of Expressions • The form of the expression for each model is an important consideration in addition to its statistical performance. The expressions for the confinement, requirements of each model were presented in Chapter 2. Review of the expressions for A C I , C S A , PP92 and B B M 0 5 indicates a similarity amongst the models with the exception of B B M 0 5 . If B B M 0 5 were adopted as a replacement for A C I , the form of the expression would be a drastic departure from its current form. Perhaps more importantly, the form of the B B M 0 5 is much less intuitive and its derivation is hidden. Such a departure from the current form of the expression would undoubtedly be warranted i f the performance of the model was vastly superior to all other models. However, as has been shown above, this is not the case. For this reason, the B B M 0 5 model is removed from the list of potential replacement models. 5.1.8 Requirements of Models The details of a typical rectangular column were used to examine the area requirements of the remaining models, C S A and PP92. Figure 5.6 shows the area of confining steel ( A S h ) required for the example column for the C S A and PP92 models. For reference, the A C I model requirements are included in the figure. The area of confining steel is normalized to represent, as closely as possible, the trend that can be expected for columns with various material and geometric properties. The figure shows that the area requirement increases linearly with respect to axial load for the C S A and PP92 models, while A C I is independent of axial load. The figure shows that the two have similar requirements with a small difference in slopes and all three models require the same amount of confining steel at an axial load ratio of approximately 0.3. Above an axial 119 Selection of Confinement Model load ratio of 0 . 3 , C S A and P P 9 2 require more transverse reinforcement, while below this limit, C S A and P P 9 2 require less transverse reinforcement. Figure 5 .7 shows the confinement spacing requirements for the typical column resulting from the requirements of the C S A and P P 9 2 models. Again the spacing requirement is normalized to represent the trend that can be expected for columns with various material and geometric properties. The figure shows that unlike the area requirement, the spacing limit imposed by the C S A and P P 9 2 models is not linear. The required maximum spacing increases dramatically as the axial load ratio approaches zero. This suggests that a minimum level of confinement wi l l have to be applied in connection with the requirement imposed by either C S A or P P 9 2 . 0.5 0.45 -0.4 CD 0.35 -<° 0.3 -0.25 O -O 0.2 -V) sz <" 0.15 0.1 0.05 0 •• 74" h — m \ t±±± 24 Cover: 40mm „ Longitudinal bars: #9 Transverse bars: #5 •••• CSA — PP92 ACI Eqn 21-3 ACI Eqn 21-4 ..«f* I I I I I I ! I 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 P/P Figure 5.6 Confinement area requirements for range of axial load ratios 1 2 0 Selection of Confinement Model 1500 < .C 1000 in 500 0.1 C S A PP92 0.25H ACI Eqn 21-3 ACI Eqn 21-4 24" 2 4 Cover: 40mm „ Longitudinal bars: #9 Transverse bars: #5 0.2 0.3 0.4 0.5 P/P 0.6 0.7 0.8 0.9 Figure 5.7 Conf inement spacing requirements for range of axial load ratios 5.1.9 Conclusion and Recommendat ion The curves shown above in Figure 5.6 and Figure 5.7 show comparable requirements for the CSA and PP92 models. Figure 5.3 showed that the CSA model out performed PP92 in the statistical analysis. Comparing the form of the CSA and PP92 models presented in Chapter 2 shows that the two are expressions are very similar. Both share the common term (Ag/Ach)(fc'/fyh) and both have a term which includes a linear variation with axial load. The main difference between the two expressions is that the CSA model includes the longitudinal reinforcement configuration and the PP92 model does not. Recall from Figure 1.3 the degree of confinement provided by an arrangement of transverse steel is dependant on the spacing of laterally supported vertical bars. Considering both the statistically better performance and the more favourable form of the expression for the CSA model compared to the PP92 model, the final conclusion for the preferred model for rectangular concrete columns is the CSA model. 121 Selection of Confinement Model To present the final recommendation in the format discussed in section 5.1.1, the minimum and maximum confinement levels must also be addressed. The minimum confinement level is currently expressed in the A C I code by Equation 21-4, and by the spacing limits of section 21.4.4.2. The form the C S A expression dictates that as the level, of axial load approaches zero, the area requirement approaches zero. Therefore, an alternative means of specifying a minimum level of confinement would be to introduce a minimum level of axial load that can be inserted into the C S A confinement expression. This technique is adopted by the SR02 model which suggests a limit of P/Po = 0.2. To evaluate the suitability of this limit the axial load ratio, P/Po, was determined for each column in the database which produces an area requirement equal to that required by the current A C I minimum confinement expression. The values ranged from 0.07 to 0.32 and had a mean value of 0.21. This is in agreement with the curves shown in Figure 5.6 where the C S A curve and the curve for the A C I minimum equation intersect at a P/Po ratio slightly greater than 0.2. The results of this evaluation suggest that limiting the minimum P/Po value to 0.2 wi l l provide a minimum level of confinement similar to that which is achieved by the current expression in A C I 318. The data presented in section 4.1.3 suggested that the current area and spacing limits of A C I exhibited similar statistics when investigated individually. However, a closer look at the data shown in Figure 4.22 shows that the spacing limit impacts a number of columns with high axial loads. This suggests that when applied together, the two requirements provide an improved performance. Therefore, for an added level of safety and consistency with historical designs, the one-quarter of the minimum dimension spacing limit can be included in the minimum confinement level. The spacing limit of 4 to 6 inches given by Equation 2.12 (ACI Equation 21-5) is also included as there is no basis for its removal. There is currently no maximum confinement level expressed in the A C I code. It is suggested that it should be noted in the commentary to the code that axial loads should be kept below a value that would result in unrealistically small transverse steel spacing. 122 Selection of Confinement Model This allows the engineer to use his or her judgement and leaves room for innovative designs. The final recommendation for the design requirements for confinement steel in rectangular reinforced concrete columns is expressed as follows: The total cross-sectional area of rectangular hoop reinforcement shall not be less than: A • A f ' = 0.2k„kr sc°c P Ach fyh where (a) k p = P/Po (b) k„. = ni/(n,-2) (c) k p shall not be taken as less than 0.2 (d) sc shall not exceed 6db ,one quarter of the minimum member dimension or sx defined as: sx <4+ x-V 3 J where sx shall not exceed 6 inches and need not be taken less than 4 inches and hx is the maximum horizontal spacing of hoop or crosstie legs on all faces of the column. 5.3 Circular Columns In section 4.2 the performance of the models was evaluated for circular columns. From the statistical analysis, the ACI model determined to be the worst performer making a new equation desirable. The circular column database contains few column tests with high axial load and consequentially has few columns with low total drifts at 20% loss in lateral strength. A new equation is proposed here with the suggestion that more testing of high axially loaded circular columns is needed to further confirm the suitability of proposed model. 123 Selection of Confinement Model 5.3.1 Scatter plot Evaluation A s stated in Chapter 4, the A C I model was the only model to have a data point in quadrant 2. The evaluation of the scatter plots then becomes an evaluation of the data with drift capacities higher than 2.5%. Only the PP92 and W Z P L P models did not demonstrate an improvement over the A C I model with respect to these data points (i.e., the movement of the data points from quadrant 3 to quadrant 1 is not seen for these models). This conclusion is illustrated in Figure 4-34 which shows that these two models resulted with the worst overall behaviour as seen by their lower C statistic values. Therefore, via the evaluation of the scatter plots, the PP92 and W Z P L P models are removed from the list of suitable alternatives for the A C I model. 5.3.2 Fragility Curve Evaluation The C statistic fragility curves for the C S A , SR02, B B M 0 5 , S K B S and N Z S models are shown again in Figure 5.8 for the meaningful range of drift ratios discussed earlier. The figure shows a significant difference in the performance of the models throughout the range of drift ratios, and that different models perform better within certain ranges, making it difficult to eliminate models using these curves. However, the N Z S model is consistently below the other four models throughout the drift range of interest. Therefore this model can justifiably be removed from the list of suitable alternatives for the A C I model. 5.3.3 Comparison of Expressions A review of the expressions for the C S A , B B M 0 5 , SR02 and S K B S models shows a relative similarity amongst the models with the exception of B B M 0 5 , similar to the evaluation of rectangular column confinement models. If B B M 0 5 were adopted as a replacement for A C I , the form of the expression would again be a drastic departure from 124 Selection of Confinement Model its current form. Once again, the form of the BBM05 is much less intuitive and its derivation is hidden. Figure 5.8 shows that the BBM05 model is not the preeminent model for any target drift ratio, and removing it will not impact the final decision. Therefore, the BBM05 model is removed from the list of potential replacement models. 0.08 0.07 0.06 0.05 < 0.04 0.03 0.02 0.01 0 C S A S R 0 2 BBM05 S K B S NZS 1 1.5 Drift Ratio Figure 5.8 A fragility curves 125 Selection of Confinement Model 0 0.5 1 1.5 2 2.5 Drift Ratio Figure 5.9 B fragility curve Drift Ratio Figure 5.10 C fragility curve 126 Selection of Confinement Model 5.3.4 Requirements of Models A typical circular column was used to examine the volume density requirements of the remaining models. Figure 5.12 shows the confining steel volumetric density required for the example column for the C S A , SR02, and S K B S models. For reference, the A C I model requirements are included in the figure. The density requirement is normalized to represent the trend that can be expected for columns with various material and geometric properties. The figure shows that the density requirement increases linearly for the C S A and SR02 models, and exponentially for the S K B S model. The figure shows that the S K B S model requires only slightly less confinement steel than A C I at low axial load ratios, and has an almost constant value, at axial load ratios below 0.3. However, the S K B S curve requires significantly more confining steel than the other models at higher axial load ratios. A t axial load ratios above 0.6 the model requires an amount of confinement that is several times that required by the other models, suggesting that the model becomes unrealistic at these high axial load ratios. Figure 5.6 further indicates that the SR02 requirement falls below the other two models throughout the range of axial load ratios. The only exception is for axial load ratios below 0.1 where the C S A model becomes the lowest (although minimum limits for the C S A requirements are not included in this figure). This demonstrates that the SR02 requirement is less demanding than the other two which explains why the SR02 model had the largest number of data points move from quadrant 3 to quadrant 1. This less demanding requirement proved to be statistically detrimental for the SR02 model in the rectangular column analysis as it also resulted in a number of columns moving from quadrant 4 into quadrant 2, the opposite of the desired movement. Given that the circular column database had so few columns with low drifts, the effect was not seen here. More tests of circular columns with high axial load are needed to ensure that data movement seen in the rectangular column evaluation does not repeat itself for circular columns. In Chapter 3 it was noted that the drifts achieved by columns with lower axial loads was typically higher for circular columns than for rectangular columns. This could possibly suggest that circular columns in general display better ductility that rectangular columns, or it could simply suggest that more testing is needed to observe the behaviour of circular 127 Selection of Confinement Model columns at higher levels of axial load. Taking this conclusion into consideration and based on the available database, the SR02 model remains a potential replacement model for A C I . Figure 5.10 showed that for higher drift ratios, where more data are available, the performance ofthe SR02 model drops below the C S A model. However, in section 4.2.2.4 it was noted that the performance of the SR02 model was underestimated at these higher drift ratios using a constant input variable drift ratio of 2.5%. For the purposes of a design equation, the performance input variable would not appear as a value for, the engineer to select, rather it would be provided in the code expression. Therefore, it is recommended that the drift ratio input variable for SR02 should be 3.0% to increase the level of safety provided by the model. Figure 5.11 shows a scatter plot for SR02 using an input drift ratio of both 2.5% and 3%. The performance of the SR02 model is very similar for the two levels input of drift ratios. With an input drift ratio of 3%, the number of data points in quadrant 3 increases from four to seven. The two data points with measured drift ratios also moved further left on the figure. The 15 10 oo or O o O • ! 0 o O E O 0 • O DO f 0 d* > o o O B v ^ • u ft B m 2.5% O 3% Provided SR02 C P Figure 5.11 SR02 scatter plot drift ratio comparison 128 Selection of Confinement Model figure indicates that implementing an input drift ratio of 3% improves the models conservatism without substantially increasing its overconservatism. Figure 5.13 shows the confinement spacing requirements for the circular example column. Again the spacing requirement is normalized to represent the trend that can be expected for columns with various material and geometric properties. The figure shows that the spacing requirement increases dramatically as the axial load ratio approaches zero for the CSA and SR02 models. The limiting value for P/P 0 of 0.2 for the SR02 model shows how the limit provides a minimum level of confinement. This confirms the previous suggestion that a minimum level of confinement will have to be applied in connection with the area requirement imposed by a model such as CSA or SR02 which varies linearly with axial load. As expected, the SKBS curve shows a much different spacing requirement than the other two models. The curve shows very little change in the spacing requirement at lower axial load ratios suggesting that this model may be more P/P 0 Figure 5.12 Confinement density requirements for range of axial load ratios 129 Selection of Confinement Model 1500 < C T 1000 500 Cover: 40mm Longitudinal bars: #9 Transverse bars: #5 C S A — - SR02 - - SKBS 0.25H ACI Eqn 21-2 ACI Eqn 10-5 0.1 0.2 0.3 0.4 P/P 0.5 0.6 0.7 0.8 Figure 5.13 Confinement spacing requirements for range of axial load ratios conservative that the others in this range. This is confirmed by observing that statistics presented in Figure 4.39. The requirements for the SKBS model shown in Figure 5.12 and Figure 5.13 are less desirable than the CSA and SR02 models. Given that the statistical performance of the SKBS model is not better than the other two models it is removed from the list of potential replacement models. 5.3.5 Conclusion and Recommendation Comparing the form of the CSA and SR02 models and presented in Chapter 2 shows that significant differences are apparent between the two expressions. The ratio of A g / A c h is not considered by CSA in the expression for the volumetric density, instead it is included in the expression for the minimum confinement level (Equation 2.14). The SR02 and CSA models do however become identical for an A g / A C h ratio equal to approximately 1.6. The SR02 model also imposes a minimum value for A g /A C h of 1.3. The ratio of gross 130 Selection of Confinement Model column area to confined core area has been shown to influence the drift capacity of reinforced concrete columns. For this reason, including the area ratio in the primary expression for confinement is more logical than having it only in the expression for the minimum level. The conclusion therefore is to select the SR02 model with an input drift ratio of 3.0%. For circular reinforced concrete columns the minimum confinement level is currently expressed in the A C I code by Equation 21-2, and by the spacing limits of A C I 318-05 section 21.4.4.2. To be consistent with the recommendations for the rectangular columns, imposing a minimum level of axial load provides a meaningful minimum level of confinement. A limit of P/Po of 0.2 was suggested in the rectangular column recommendation as this limit resulted in a similar minimum level of confinement to the current A C I code. Figure 5.12 shows that the curve for SR02 and the curve for the A C I minimum confinement intersect at a P/Po ratio near 0.6. Solving for the P/Po ratio which requires a transverse steel ratio equal to the A C I minimum level for the columns in the circular column database confirms this relationship as the mean value for the axial load ratio was 0.66. Imposing a limit of this magnitude would be inappropriate. Unt i l further test results can be used to suggest a more suitable limit, it is recommended that the minimum confinement level be achieved through limiting the P/Po ratio to a minimum level of 0.2 as suggested by Saatcioglu and Razvi (2002). • Section 4.2.3 showed that for circular columns, the density requirement was the governing requirement for all but two columns, and that all the columns in the circular column database satisfied the one quarter dimension limit. These results could suggest that the spacing limit is inconsequential. However, the lack of test specimens with low levels of drift and the limited number of full-scale tests makes it difficult to make this conclusion with confidence. Therefore, is it recommended that this spacing limit remain in the code until further evidence can support its removal. Again it is suggested that the commentary to the code should state that axial loads should be kept below a value that would result in unrealistically small transverse steel spacing. 131 Selection of Confinement Model Therefore, the final recommendation for the design requirements for confinement steel in circular reinforced concrete columns is expressed as follows: The volumetric ratio of spiral or circular hoop reinforcement shall not be less than: / V = 0 . 8 4 * , fc fyh where (a) ps = ^ch AAb s„h„ (b) k p = P / P o (c) k p shall not be taken asr less that 0.2 (d) Ag/A c h shall not be taken as less than 1.3 (e) sc shall not exceed 6db or one quarter of the minimum member dimension 5.4 Final Recommendations vs. ACI 5.4.1 Comparison figure The figure below gives a comparison of the final area requirements of the recommendations with the current area requirements in A C I 318-05. No suggested changes to the spacing requirements were proposed. The figure shows a comparison for both the rectangular and circular typical columns used for Figure 5.6 and Figure 5.12. The figure demonstrates how the confinement steel requirement of the recommended model compares with the current A C I requirement over a range of axial load level. 132 Selection of Confinement Model 15 10 o > CL 30" Cover: 40mm Longitudinal bars: #9 30" Transverse bars: #5 f y t =414MPa, f c = 55 MPa Circu lar R e c o m m e n d a t i o n Rectangu lar R e c o m m e n d a t i o n C i rcu lar ACI Rec tangu la r ACI 30" 0.1 Cover: 40mm Longitudinal bars: #9 Transverse bars: #5 f y t = 4 1 4 M P a , f c = 55 M P a 0.2 0.3 0.4 P/P 0.5 0.6 0.7 0.8 Figure 5.14 Comparison of recommendations and A C I 318-05 requirements 133 6 S U M M A R Y A N D C O N C L U S I O N S 6.1 Summary This study investigated the A C I 318-05 confining steel requirements for reinforced concrete columns. These requirements were compared to the current Canadian and New Zealand codes and proposed models found in the literature to determine their suitability as a performance based design equation for implementation in Chapter 21 of A C I 318. A total of 13 model for rectangular columns and 12 for circular columns were evaluated. This was done by addressing both the area requirements of section 21.4.4.1 and the spacing requirements of section 21.4.4.2. Research has shown that factors such as axial load level and amount and configuration of confinement steel impact the performance of columns when subjected to seismic loading. The aim of this investigation was to determine i f and how these factors should be incorporated into the requirements of A C I 318 and to propose a model which would ensure that a column wi l l not experience lateral strength degradation before reaching the prescribed lateral drift limit. The investigation was performed through evaluation of columns found in the U W / P E E R Structural Performance Database. The condensed database used in this investigation consisted solely o f columns which exhibited flexural failure and contained 145 rectangular and 50 circular columns. Two evaluation techniques were used to evaluate each confinement model. First, a scatter plot was used to compare the confining requirements of each model with the lateral drift observed for each column within the database. A drift ratio of 2.5% was selected as the performance target for the evaluation. The scatter plot evaluation distinguished columns in the database into those which met/failed the requirements of a given model, and those which met/failed the performance target. From this, two key column classifications were identified, those which satisfied the requirements of the model but failed the performance target ('unconservative') and those which failed the requirements of the model but 134 ; Summary and Conclusions satisfied the performance target ('conservative'). For each model, the percentage of columns falling into these classifications was calculated and compared, and the results were used to determine which models should be investigated further. Three fragility curves were generated for each model to evaluate their performance across a range of drift ratios as apposed to just 2.5%. The first curve provided the probability of a column being classified as 'unconservative' as a function of the drift ratio, the second curve provided the probability of a column being classified as 'conservative' as a function of drift ratio. The third curve was a combination of the first two and provided insight as to the overall performance of the model. These fragility curves were used to determine which models were most suitable for a performance based design equation in chapter 21 of A C I 318. A lso taken into consideration in the evaluation of the models was the form of each expression and the confinement requirements of each relative to the current A C I 318. Models with confinement expressions which were drastically different than the current form in chapter 21 of A C I were not considered potential alternatives unless their performance in the above evaluation techniques was significant enough to do so. A lso, the requirements of each model for columns with various axial load levels were compared to the current requirements of A C I . Models which required drastically more or less steel than the 2005 version of A C I 318 were less favourable-than those which required smaller changes in confining steel, but displayed similar statistical behaviour. For both the rectangular and circular column evaluations, the A C I model was determined to be the least desirable of all models investigated. Based on the evaluation techniques discussed above, specific models were selected as recommended alternatives to the current A C I requirements. For rectangular columns, the current area requirement of the Canadian code ( C S A A23.3-2004) was selected as the recommended model. For circular columns, the model proposed by Saatciolgu and Razvi (2002) was selected as the recommended model. 135 Summary and Conclusions The spacing limit of one quarter cross sectional dimension was also evaluated. The performance of the limit alone demonstrated no improvement over the A C I area requirements, but suggested that together, the two requirements may slightly reduce the instances of 'unconservative' columns. While the spacing limits do not often govern the design of confining steel, it is recommended that the spacing limits of the current A C I code remain in place. 6.2 Recommendations The fol lowing is the recommendations of this study: A C I 318 clauses 21.4.4.1 (a),(b) and (d) as well as clauses 21.4.4.2 (a) and (c) should be replaced with: 21.4.4.1 Transverse steel for confinement of reinforced concrete columns The total cross-sectional area of rectangular hoop reinforcement shall not be less than: A A f ' scK P Ach fyh where k p = P / Po k n = n [ / (m-2) k p shall not be taken as less than 0.2 s c shall not exceed 6dh ,one quarter of the minimum member dimension or s x defined as: ' 1 4 - O s <4 + V 3 where s x shall not exceed 6 inches and need not be taken less than 4 inches and hx is the maximum horizontal spacing of hoop or crosstie legs on all faces of the column. 136 Summary and Conclusions 21.4.4.2 Columns confined with circular or spiral hoops The volumetric ratio of spiral or circular hoop reinforcement shall not be less than: Ps = 0.84*, fyh *ch -1 where Ps _ 4Ab scK P / P o k p shall not be taken as less that 0.2 A g / A c h shall not be taken as less than 1.3 s c shall not exceed 6db or one quarter of the minimum member dimension 6.3 Recommendations for future research The U W / P E E R Structural Performance Database gives researchers access to significantly more test data than would be possible in a specific testing experiment. This allows researchers to undertake projects such as this one where the results from a small number of individual tests may not provide sufficient data to make recommendations with the same level of confidence. However, to supplement the existing database, further testing is required. This was apparent for the circular column database used in this study where few columns were tested with high axial load ratios, and consequentially few columns exhibited flexural failure at low levels of drift. It is recommended that future investigations of flexural failure in circular columns for building structures be undertaken with appropriate levels of axial load. It is stated in the commentary of the 2005 A C I 318 code that the axial load and deformation demands required during earthquake loading are not known with sufficient accuracy to justify calculation of required transverse reinforcement as a function of 137 Summary and Conclusions design earthquake demands. It is the position of this document that the level of axial load on a column during a seismic event need not be known with extreme accuracy for its inclusion in the calculation for required transverse reinforcement. However, further research into the analytical methods which can be used to predict the earthquake axial load demands placed on columns wi l l improve the accuracy of those predictions and the effectiveness of the equations recommended here for implementation into the A C I code. 138 R E F E R E N C E S American Concrete Institute, 2005, "Bui ld ing Code Requirements for Structural Concrete", ACI 318-05, Farmington Hi l ls , U S A . 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Zhou, X . , Satoh, T . , Jiang, W., Ono, A . , and Shimizu, Y . , 1987, "Behavior of Reinforced Concrete Short Column Under High Ax ia l Load, " Transactions of the Japan Concrete Institute, V o l . 9, pp. 541-548. 145 Geometry Database No. Specimen Name f c (MPa) P(kN) P/Agfc P/P„ B(mm) H(nim) L(mm) A g (mm2) Cover (mm) 7 ' Soesianawati et al. 1986, No. 1 ' 46.5 744 0.10 0.10 400 400 1600 160000 13.0 8 Soesianawati et al. 1986, No. 2 44 . 2112 0.30 0.30 400 400 1600 160000 13.0 9 Soesianawati et al. 1986, No. 3 44 2112 . 0.30 0.30 400 400 1600 . 160000 13.0 10 Soesianawati et al. 1986, No. 4 40 1920 0.30 0.30 400 400 1600 160000 13.0 13 Watson and Park 1989, No. 5 41 3280 0.50 0.49 400 400 1600 160000 13.0 14 Watson and Park 1989, No. 6 40 3200 0.50 0.49 400 400 1600 160000 13.0 15 Watson and Park 1989, No. 7 42 ' 4704 0.70 0.69 400 400 1600 160000 13.0 16 Watson and Park 1989, No. 8 39 4368 0.70 0.69 400 400 1600 160000 13.0 17 Watson and Park 1989, No. 9 40 4480 0.70 0.69 400 400 1600 160000 40.0 20 Tanaka and Park 1990, No. 3 25.6 819 0.20 0.18 400 400 1600 160000 31.5 32 Ohno and Nishioka 1984, L3 24.8 127 0.03 0.03 400 400 1600 160000 12.5 43 Zhou et al. 1987, No. 214-08 21.1 432 0.80 0.67 160 160 320 25600 35.0 48 Kanda eta l . 1988, 85STC-1 27.9 183.9 0.11 0.10 250 250 750 62500 35.0 49 Kandaeta l . 1988, 85STC-2 27.9 183.9 0.11 0.10 250 250 750 62500 35.0 50 Kanda et al. 1988, 85STC-3 27.9 183.9 0.11 0.10 250 250 750 62500 9.0 56 Muguruma et al. 1989, AL-1 85.7 1371 ' 0.40 0.40 200 200 500 40000 9.0 58 Muguruma et al. 1989, AL-2 85.7 2156 0.63 0.63 200 200 500 40000 23.5 66 Sakai et al. 1990, B1 99.5 2176 0.35 0.38 250 250 500 62500 23.5 67 Sakai eta l . 1990, B2 99.5 2176 0.35 0.38 250 250 500 62500 23.5 68 Sakai et al. 1990, B3 99.5 2176 0.35 0.38 250 250 500 62500 23.5 69 Sakai et al. 1990, B4 99.5 2176 0.35 0.38 250 250 500 62500 23.5 70 Sakai et al. 1990, B5 99.5 2176 0.35 0.38 250 250 500 62500 23.5 71 Sakai eta l . 1990, B6 99.5 2176 0.35 0.38 250 250 500 62500 30.5 72 Sakai et al. 1990, B7 99.5 2176 0.35 0.39 250 250 500 62500 32.0 94 Atalay and Penzien 1975, No. 9 33.3 801 0.26 0.26 305 305 1676 93025 32.0 95 Atalay and Penzien 1975, No. 10 32.4 801 0.27 0.26 305 305 1676 93025 32.0 96 Atalay and Penzien 1975, No. 11 31 801 0.28 0.27 305 305 1676 93025 32.0 97 Atalay and Penzien 1975, No. 12 31.8 801 0.27 0.26 305 305 "1676 .93025 38.1 102 Azizinamini et al. 1988, NC-2 39.3 1690 0.21 0.20 457 457 1372 ' 208850 41.3 103 Azizinamini et al. 1988, NC-4 39.8 2580 0.31 0.30 457 457 1372 208850 22.5 104 Saatcioglu and Ozcebe 1989, U i 43.6 0 0.00 0.00 350 350 1000 122500 22.5 105 Saatcioglu and Ozcebe 1989, U3 34.8 600 0.14 0.12 350 350 1000 122500 22.5 106 Saatcioglu and Ozcebe 1989, U4 32 600 0.15 0.12 350 •350 1000 122500 26.0 107 Saatcioglu and Ozcebe 1989, U6 37.3 600 0.13 0.11 350 350 1000 122500 26.0 108 Saatcioglu and Ozcebe 1989, U7 39 600 0.13 0.11 350 . 350 1000 122500 30.0 117 Galeota etal . 1996, CA1 80 1000 0.20 0.22 250 250 1140 62500 30.0 118 Galeota et al. 1996, CA2 80 1500 0.30 0.33 250 250 1140 62500 30.0 119 Galeota etal. 1996, CA3 80 1000 0.20 0.22 250 250 1140 62500 30.0 120 Galeota etal . 1996, CA4 80 1500 0.30 0.33 250 250 . 1140 62500 30.0 3 4^ r Geometry Database No. Specimen Name f c (MPa) P(kN) P/Agfc P/P„ B(mm) H(mm) L(mrn) A 8 (mm2) Cover (mm) 126 Galeota etal. 1996, BB1 80 1000 0.20 0.18 250 250 1140 62500 30.0 127 Galeota etal. 1996, BB4 80 1500 0.30 0.27 250 250 1140 62500 30.0 128 Galeota et al. 1996, BB4B 80 1500 0.30 0.27 250 250 1140 62500 28.0 133 Wehbe et al. 1998, A1 27.2 615 0.10 0.08 380 610 2335 231800 28.0 134 Wehbe etal. 1998, A2 27.2 1505 0.24 0.20 380 610 2335 231800 25.0 135 Wehbe etal. 1998, B1 28.1 601 0.09 0.08 380 610 2335 231800 25.0 136 Wehbe etal. 1998, B2 28.1 1514 0.23 0.20 380 610 2335 231800 13.0 145 Xiao 1998, HC4-8L19-T10-0.1 P 76 489 0.10 0.09 254 254 508 , 64516 13.0 . 146 Xiao 1998, HC4-8L19-T10-0.2P 76 979 0.20 0.19 254 254 508 64516 13.0 147 Xiao 1998, HC4-8L16-T10-0.1P 86 534 0.10 0.10 254 254 508 64516 13.0 148 Xiao 1998, HC4-8L16-T10-0.2P 86 1068 0.19 0.20 254 254 508 64516 11.3 151 Sugano 1996, UC.10H 118 3579 0.60 0.67 225 225 450 50625 11.3 152 Sugano 1996, UC15H 118 3579 0.60 0.67 225 225 450 50625 11.3 153 Sugano 1996, UC20H 118 3579 0.60 0.67 225 225 450 50625 11.3 154 Sugano 1996, UC15L 118 2089 0.35 . 0.39 225 225 450 50625 11.3 155 Sugano 1996, UC20L 118 2089 0.35 0.39 225 225 450 50625 . 25.4' 157 Bayrak and Sheikh 1996, ES-1HT 72.1 3353.6 0.50 0.50 305 305 1842 93025 13.4 158 Bayrak and Sheikh 1996, AS-2HT 71.7 2401.2 0.36 0.36 305 305 1842 93025 ' 13.4 159 Bayrak and Sheikh.1996, AS-3HT 71.8 3339.6 0.50 0.50 305 305 1842 93025 11.0 160 Bayrak and Sheikh 1996, AS-4HT 71.9 3344.2 0.50 0.50 305 305 1842 • 93025 11.0 162 Bayrak and Sheikh 1996, AS-6HT 101.9 4360.5 0.46 0.49 305 305 1842 93025 13.4 163 Bayrak and Sheikh 1996, AS-7HT 102 4269.-8 0.45 0.48 305 305 1842 93025 11.0 164 Bayrak and Sheikh 1996, ES-8HT 102.2 4468.4 0.47 0.50 305 305 1842 93025 29.0 166 Saatcioglu and Grira 1999, BG-2 34 1782 0.43 0.39 350 350 1645 122500 29.0 167 Saatcioglu and Grira 1999, BG-3 34 831 0.20 0.18 350 350 1645 .122500 29.0 169 Saatcioglu and Grira 1999, BG-5 34 1923 0.46 0.38 350 350 1645 122500 29.0 170 Saatcioglu and Grira 1999, BG-6 34 1900 0.46 0.40 350 350 1645 122500 29.0 171 Saatcioglu and Grira 1999, BG r7 34 1923 0.46 0.38 350 350 1645 122500 29.0 172 Saatcioglu and Grira 1999, BG-8 34 961 0.23 0.19 350 350 1645 122500 29.0 173 Saatcioglu and Grira 1999, BG-9 34 1923 0.46 . 0.37 350 350 1645 122500 29.0 174 Saatcioglu and Grira 1999, BG-10 34 1923 0.46 0.37 350 350 1645 122500 40.0 175 Matamoros et al. 1999,C10-05N 69.637 142 0.05 0.05 203 203 . 610 41209 39.8 176 Matamoros et al. 1999,C10-05S 69.637 142 0.05 0.05 203 203 610 41209 25.8 177 Matamoros et al. 1999.C10-10N 67.775 285 0.10 0.10 203 203 610 41209 23.8 • 178 Matamoros et al. 1999,C10-10S 67.775 285 0.10 0.10 203 .203 610 41209 22.0 179 Matamoros et al. 1999.C10-20N 65.5 569 0.21 0.21 203 203 610 41209 14.6 180 Matamoros et al. 1999.C10-20S 65.5 569 0.21 0.21 203 203 610 41209 24.0 181 Matamoros et al. 1999,C5-00N 37.921 0 0.00 0.00 . 203 203 610 41209 27.8 182 Matamoros et al. 1999,C5-00S 37.921 0 0.00 0.00 203 203 610 41209 38.3 Geometry Database NO; Specimen Name f c (MPa) P(kN) P/Agfc P/P„ B(mm) H(mm) L(mm) A g (mm2) Cover (mm) 183 Matamoros et al. 1999.C5-20N 48.263 285 0.14 0.13 203 203 610 41209 39.0 184 Matamoros et al. 1999.C5-20S 48.263 285 0.14 0.13 203 203 610 41209 20.7 185 Matamoros et al. 1999.C5-40N 38.059 569 0.36 0.32 203 203 610 41209 20.7 186 Matamoros et al. 1999.C5-40S 38.059 569 0.36 0.32 203 203 610 41209 34.0 187 MoandWang 2000,C1-1 24.94 450 0.11 0.09 400 400 1400 160000 34.0 188 Mo and Wang 2000,C1-2 26.67 675 0.16 0.13 400 400 1400 160000 34.0 189 Mo and Wang 2000,C1-3 26.13 900 0.22 0.17 400 400 1400 160000 34.0 190 Mo and Wang 2000,C2-1 25.33 450 0.11 0.09 400 400 1400 160000 34.0 191 Mo and Wang 2000,C2-2 27.12 675 0.16 0.13 400 400 1400 160000 34.0 192 Mo and Wang 2000.C2-3 26.77 - 900 0.21 0.17 400 400 1400 160000 11.1 202 Thomsen and Wallace 1994, A3 86.3 400.88 0.20 0.20 152.4 152.4 596.9 23226 11.1 204 Thomsen and Wallace 1994, B2 83.4 193.7 0.10 0.10 152.4 . 152.4 596.9 23226 11.1 205 Thomsen and Wallace 1994, B3 90 418.06 0.20 0.21 152.4 152.4 596.9 23226 11.1 207 Thomsen and Wallace 1994, C2 74.6 173.26 0.10 0.10 152.4 152.4 596.9 23226 11.1 208 Thomsen and Wallace 1994, C3 81.8 379.97 0.20 0.21 152.4 152.4 596.9 23226 11.1 209 Thomsen and Wallace 1994, D1 75.8 352.1 0.20 0.20 152.4 152.4 596.9 23226 11.1 210 Thomsen and Wallace 1994, D2 87 404.13 0.20 0.21 152.4 152.4 596.9 23226 . 11.1 211 Thomsen and Wallace 1994, D3 71.2 330.73 0.20 0.20 152.4 152.4 596.9 23226 19.0 215 Paultre & Legeron, 2000, No. 1006015 92.4 1200 0.14 0.15 305 305 2000 93025 19.0 216 Paultre & Legeron, 2000, No. 1006025 93.3 2400 0.28 0.29 305 305 2000 93025 19.0 217 Paultre & Legeron, 2000, No. 1006040 98.2 3600 0.39 0.42 305 305 2000 93025 19.0 221 Paultre et al., 2001, No. 806040 78.7 2900 0.40 0.41 305 305 2000 93025 19.0 222 Paultre etal., 2001, No. 1206040 109.2 4200 . 0.41 0.44 305 305 2000 93025 19.0 223 Paultre etal., 2001, No. 1005540 109.5 3600 0.35 0.44 305 305 2000 93025 19.0 224 Paultre et al., 2001, No. 1008040 104.2 3600 0.37 0.40 305 305 2000 .93025 19.0 225 Paultre etal., 2001, No. 1005552 104.5 5150 0.53 0.56 305 305 2000 93025 19.0 226 Paultre et al., 2001, No. 1006052 109.4 5150 0.51 0.54 305 305 2000 93025 25.4 227 Pujol 2002, No. 10-2-3N 33.715 133.45 0.09 0.07 152.4 304.8 685.8 46452 25.4 228 Pujol 2002, No. 10-2-3S 33.715 133.45 0.09 0.07 152.4 304.8 685.8 46452 25.4 229 Pujol 2002, No. 10-3-1.5N 32.13 133.45 0.09 0.08 152.4 304.8 685.8 46452 25.4 230 Pujol 2002, No. 10-3-1.5S 32.13 133.45 0.09 0.08 152.4 304.8 685.8 46452 25.4 231 Pujol 2002, No. 10-3-3N 29.923 133.45 0.10 0.08 152.4 304.8 685.8 46452 25.4 232 Pujol 2002, No. 10-3-3S 29.923 133.45 0.10 0.08 152.4 304.8 685.8 46452 25.4 233 Pujol 2002, No. 10-3-2.25N 27.372 133.45 0.10 0.08 .152.4 304.8 685.8 46452 25.4 234 Pujol 2002, No. 10-3-2.25S 27.372 133.45 0.10 0.08 152.4 304.8 685.8 46452 25.4 237 Pujol 2002, No. 20-3-3N 36.404 266.89 0.16 0.14 152.4 '304.8 685.8 46452 25.4 238 Pujol 2002, No. 20-3-3S 36.404 266.89 0.16 0.14 152.4 304.8 685.8 46452 25.4 239 Pujol 2002, No. 10-2-2.25N 34.887 133.45 0.08 0.07 152.4 304.8 685.8 46452 25.4 240 Pujol 2002, No. 10-2-2.25S 34.887 133.45 0.08 0.07 152.4 304.8 685.8 . 46452 25.4 Geometry Database No. Specimen Name fx (MPa) P(kN) P/Agfc P/P 0 B(mm) H(mm) L(rnm) A g (mm2) Cover (mm) 241 Pujol 2002, No. 1-0-1-2.25N 36.473 133.45 0.08 0.07 152.4 304.8 685.8 . 46452. 25.4 242 Pujol 2002, No. 10-1-2.25S 36.473 133.45 0.08 0.07 .152.4 304.8 685.8 46452 18.5 243 Bechtoula et al., 2002, D1N30 37.6 705 0.30 0.27 250 250 625 62500 18.5 244 Bechtoula et. al. 2002, D1N60 37.6 1410 0.60 0.53 250 250 625 . 62500 44.5 246 Bechtoula et. al. 2002, L1N60 39.2 8000 0.57 0.57 600 600 1200 360000 27.5 248 Takemura 1997, Test 1 (JSCE-4) 35.9 157 0.03 0.03 400 400 1245 160000 27.5 249 Takemura 1997, Test 2 (JSCE-5) 35.7 157 0.03 0.03 400 400 1245 160000 27.5 250 Takemura 1997, Test 3 (JSCE-6) 34.3 157 0.03 , 0.03 . 400 400 1245 160000 27.5 251 Takemura 1997, Test 4 (JSCE-7) 33.2 157 0.03 0.03 400 400 1245 160000 27.5 252 Takemura 1997, Test 5 (JSCE-8) 36.8 157 0.03 0.03 400 400 1245 160000 40.0 258 Xaio & Yun 2002, No. FHC5-0.2 64.1 3334 0.20 0.20 510 510 1778 260100. 20.0 260 Bayrak & Sheikh, 2002, No. RS-9HT 71.2 2118.2 0.34 0.34 250 350 1842 87500 20.0 261 Bayrak & Sheikh, 2002, No. RS-10HT 71.1 3110.6 0.50 0.50 250 350 1842 87500 20.0 264 Bayrak & Sheikh, 2002, No. RS-13HT 112.1 3433.1 0.35 0.37 250 . 350 1842 87500 20.0 265 Bayrak & Sheikh,2002, No. RS-14HT 112.1 4512 0.46 0.49 250 350 1842 87500 20.0 266 Bayrak & Sheikh, 2002, No. RS-15HT 56.2 1770.3 0.36 0.34 250 - 350 1842 87500 20.0 268 Bayrak & Sheikh, 2002, No. RS-17HT 74.1 2204.5 0.34 0.33 250 350 1842 87500 20.0 269 Bayrak & Sheikh, 2002, No. RS-18HT 74.1 3241.9 0.50 0.49 250 350 1842 87500 20.0 270 Bayrak & Sheikh, 2002, No. RS-19HT 74.2 3441 0.53 0.52 250 350 1842 87500 20.0 272 Bayrak & Sheikh, 2002, No. WRS-21HT 91.3 3754.7 0.47 0.48 350 250 1842 87500 . 20.0 273 Bayrak & Sheikh, 2002, No. WRS-22HT 91.3 2476.5 0.31 0.32 350 250 1842 87500 20.0 274 Bayrak & Sheikh, 2002, No. WRS-23HT 72.2 2084.8 0.33 0.32 350 250 1842 87500 20.0 275 Bayrak & Sheikh, 2002, No. WRS-24HT 72.2 3158.8 0.50 0.49 350 250 1842 87500 22.5 285 Saatcioglu and Ozcebe 1989, U2 30.2 600 0.16 0.12 350 350 1000 122500 13.0 286 Esaki, 1996 H-2-1/5 23 . 184 0.20 0.16 200 200 400 40000 13.0 287 Esaki, 1996 HT-2-1/5 20.2 162 0.20 0.16 200 200 400 40000 13.0 288 Esaki, 1996 H-2-1/3 . 23 307 0.33 0.27 200 200 400 40000 13.0 289 Esaki, 1996 HT-2-1/3' 20.2 269 0.33 0.26 200 200 400 40000 13.0 Long ltudihal Reinforcement Transverse Reinforcement Database D b a r Total # Plong fy (MPa) Confin. N D b a r (mm) s (mm) Parea A8o A max Drift Ratio A s h Provided A s h (ACI) A V A s h ( A C I ) No. (mm) Bars (%) Type (MPa) (%) (mm) (mm) (%) (mm ) (mm ) 7 16 12 1.51 446 R O 4 7 85 364 0.493 98.06 98.06 6.13 153.94 358.66 0.366 8 16 12 1.51 446 R O 4 8 78 360 0.704 68.73 98.72 4.30 201.06 314.03 . 0.546 9 16 12 1.51 446 . R O 4 7 91 364 0.461 46.24 53.58 2.89 153.94 363.33 0.361 10 16 12 1.51 446 R O 4 • 6 94 255 0.327 43.91 57.17 . 2.74 113.10 488.36 0.197 13 16 12 1.51 474 R O 4 8 81 372 0.678 38.91 38.91 2.43 201.06 294.07 0.583 14 16 12 1.51 474 R O 4 6 96 388 0.320 26.83 32.19 1.68 113.10 327.79 0.294 15 16 12 1.51 474 R O 4 12 96 308 1.302 18.72 25.82 1.17 452.39 426.50 0.904 16 16 12 1.51 . 474 R O 4 8 77 372 0.713 17.17 18.86 1.07 201.06 265.91 0.645 17 16 12 1.51 .474 R O 4 12 52 308 2.825 43.86 44.59 2.74 452.39. 220.02 1.753 20 20 8 1.57 474 UJ 3 12 80 333 1.305 57.20 76.70 3.58 339.29 390.19 0.870 32 19 8 1.42 362 R 2 9 100 325 0.348 73.04 74.66 4.57 127.23 365.83 0.348 43 10 8 2.22 341 R 2 5 40 559 1.155 6.54 11.60 2.04 39.27 30.31 1.296 48 12.7 8 1.62 374 R 2 5.5 50 506 0.545 34.60 52.50 4.61 47.52 151.91 0.313 49 12.7 8 1.62 374 R 2 5.5 50 506 0.545 34.60 52.50 4:61 47.52 151.91 0.313 50 . 12.7 8 1.62 374 R 2 5.5 50 506 0.420 34.60 52.50 4.61 47.52 151.91 0.313 56 12.7 12 3.80 399.6 R l 4 6 35 328.4 1.836 21.44 31.03 4.29 113.10 144.68 0.782 58 12.7 12 3.80 399.6 R l 4 6 35 328.4 2.198 10.89 14.42 2.18 113.10 144.68 0.782 66 12.7 12 . 2.43 379 R l 4 5 60 774 0.661 10.17 10.26 2.03 78.54 272.25 0.288 67 12.7 12 2.43 379 R l 4 5 40 774 0.992 20.09 . 20.32 4.02. 78.54 181.50 0.433 68 12.7 12 2.43 379 R l 4 5.5 60 • 344 0.802 10.07 10.62 2.01 95.03 619.33 0.153 69 12.7 12 2.43 379 R l 4 5 60 1126 0.661 10.07 20.58 2.01 78.54 187.14 0.420 70 12.7 12 2.43 379 R 2 5 30 774 0.661 9.46 12.60 1.89 • 39.27 136.13 0.288 71 12.7 12 2.43 379 R 2 7 60 857 0.705 10.07 13.19 2.01 76.97 256.80 0.300 72 19 4 1.81 339 R .2 5 30 774 0.723 5.06 14.86 1.01 39.27 180.11 0.218-94 22 4 1.63 • 363 R 2 9.5 76 392 0.806 42.16 53.46 2.52 141.76 329.91 0.430. 95 22 4 1.63 363 R 2 9.5 127 392 0.482 40.08 50.51 2.39 141.76 536.40 0.264 96 22 4 1.63 363 R 2 9.5 76 373 " 0.806 37.65 49.97 2.25 141.76 322.77 0.439 97 22 4 1.63 363 R 2 9.5 127 373 0.509 42.70 . 50.95 2.55 141.76 553.29 0.256 102 25.4 8 1.94 439 R D 3.41 12.7 102 .454 1.171 66.64 69.78 4.86 431.97 527.84 0.818 103 25.4 8 1.94 439 R D 3.41 9.5 102 616 0.589 38.62 39.32 2.81 . 241.71 410.14 0.589 104 25 • 8 3.21 430 R 2 10 150 470 0.355 48.70 84.00 4.87 157.08 502.00 0.313 105 25 8 3.21 430 R 2 10 75 470 0.710 51.10 72.00 5.11 157.08 200.34 . 0.784 106 25 8 3.21 438 R 2 . 10 50 470 1.091 89.90 102.00 8.99 157.08 122.81 1.279 107 25 8 3.21 437 RJ 6 6.4 65 425 1.018 89.80 89.80 8.98 193.02 219.91 0.585 • 108 25 8 3.21 437 RJ 6 6.4 65 425 1.047 88.00 88:00 8.80 193.02 229.93 0.560 117 10 12 1.51 531 R l 4 8 50 531 2.209 67.02 69.81 5.88 201.06 450.44 0.446 118 10 12 1.51 531 R l 4 8 50 531 2.209 53.54 54.92 4.70 201.06 450.44 0.446 119 10 12 1.51 531 R l 4 8 50 531 2.209 37.06 62.31 3:25 201.06 450.44 0.446 120 10 12 1.51 531 R l 4 8 50 531 2.209 40.52 62.05 3.55 201.06 450.44 0.446 Longitudinal Reinforcement Transverse Reinforcement Database No. Dbar (mm) Total # Bars Plong (%) fy (MPa) Confin. Type N D b a r (mm) s (mm) f5, (MPa) Parca (%) (mm) Amax (mm) Drift Ratio (%) A j h Provided (mm2) A s h (ACI) (mm2) Asi/AjhjAci) 126 .20 12 6.03 579 RI 4 8 100 579 1.105 58.03 58.03 5.09 201.06 900.87 0.223 •  127 20 12 6.03 579 RI 4 8 100 579 1.105 71.81 71.81 6.30 201.06 900.87 0.223 128 20 12 6.03 579 RI 4 8 100 579 1.081 75.33 75.33 6.61 201.06 900.87 0.223 133 19.1 18 2.22 448 RJ 4 6 110 428 0.323 122.10 162.89 5.23 113.10 220.19 0.514 134 19.1 18 2.22 448 RJ 4 6 110 428 0.317 102.26 122.24 4.38 113.10 220.19 0.514 135 19.1 18 2.22 448 RJ 4 6 83 428 0.421 160.79 183.71 6.89 113.10 158.90 0.712 136 19.1 18 2.22 448 RJ 4 6 83 428 0.392 129.78 151.16 5.56 113.10 158.90 0.712 145 19.1 8 3.55 510 RJ 3 9.5 51 510 1.908 47.76 48.20 9.40 212.65 173.96 1.562 146 19.1 8 3.55 . 510 RJ 3 9.5 51 510 1.908 40.94 45.85 8.06 212.65 173.96 1.562 147 15.9 8 2.46 510 RJ 3 9.5 51 510 1.908 37.59 38.79 7.40 212.65 196.85 1.380 148 15.9 8 . 2.46 510 RJ 3 9.5 51 510 1.878 35.01 44.31 6.89 212.65 196.85 1.380 151 10 12 1.86 393 RI 4 5.1 ' 45 1415 0.920 4.09 4.10 0.91 81.71 66.67 1.226 152 10 12 1.86 393 RI 4 . 6.4 45 1424 1.458 8.24 13.79 1.83 128.68 69.42 1.854 153 10 12 1.86 393 RI 4 6.4 35 1424 1.875 16.30 20.66 3.62 128.68 54.00 2.383 154 10 12 1.86 393 RI 4 6.4 45 1424 1.458 20.40 32.37 ' 4.53 128.68 69.42 1.854 155 10 12 1.86 393 RI 4 6.4 35 1424 2.191 28.30 32.43 6.29 128.68 54.00 2.383 157 19.54 8 2.58 454 R 2 15.98 95 463 1.610 32.17 36.96 1.75 401.12 371.12 1.078 158 19.54 8 2.58 454 R D 3.41 11.28 90 542 1.418 63.42 99.68 3.44 340.77 301.37 1.132 159 19.54 8 2.58 454 R D 3.41 11.28 90 542 1.393 34.12 51.53 1.85 340.77 301.79 1.130 160 19.54 8 2.58 454 R D 3.41 15.98 100 463 2.561 51.62 72.54 2.80 683.91 389.57 1.751 162 19.54 8 2.58 454 R D 3.41 15.98 76 463 3.430 55.69 70.68 3.02 683.91 419.60 1.625 163 19.54 8 2.58 454 R D 3.41 11.28 94 542 1.334 23.06 43.32 1.25 340.77 447.78 0.762 164 19.54 8 2.58 454 R '2 15.98 70 463 2.480 25.01 29.72 1.36 401.12 387.61 1.032 166 19.5 8 1.95 455.56 RI 3 9.53 76 570 0.997 66.52 87.02 4.04 213.99 205.64 1.388 167 19.5 8 1.95 455.56 RI 3 9.53 76 570 0.997 116.02 116.52 7.05 213.99 205.64 1.388 169 19.5 12 2.93 455.56 RI 4 9.53 76 570 1.329 100.03 117.01 6.08 285.32 205.64 1.388 170 29.9 4 . 2.29 477.78 RI 4 9.53 76 570 1.329 100.03 117.01 6.08 285.32 205.64 1.388 171 19.5 12 2.93 455.56 RI 4 6.6 76 580 0.631 100.03 117.01 6.08 136.85 192.23 0.712 172 19.5 12 2.93 455.56 RI 4 6.6 76 580 0.631 118.00 118.00 7.17 136.85 192.23 0.712 173 16 20 3.28 427.78 RI 4 6.6 76 580 0.631 116.00 118.00 7.05 136.85 192.23 0.712 174 16 20 3.28 427.78 RI 4 • 9.53 76 570 1.442 '99.51 118.00 6.05 285.32 205.64 1.388 175 15.9 4 1.93 586.05 R 2 9.5 76.2 406.79 " 1.633 38.61 52.32 6.33 141.76 977.11 0.145 176 15.9 4 1.93 586.05 R 2 9.5. 76.2 406.79 1.311 38.10 44.70 6.25 141.76 968.92 0.146 177 15.9 4 1.93 572.26 R 2 9.5 76.2 513.66 1.275 44.45 . 44.45 1.29 141.76 448.26 0.316 ' 178 ' 15.9 4 1.93 573.26 R 2 9.5 . 77.2 514.66 1.228 44.70 44.70 7.33 141.76 416.04 0.341 179 15.9 4 1.93 572.26 R 2 9.5 76.2 513.66 1.133 38.35 38.61 6.29 141.76 367.69 • 0.386 180 15.9 4 1.93 573.26 R 2 9.5 77.2 514.66 1.263 38.10 38.35 6.25 141.76 255.44 0.555 181 15.9 4 1.93 572.26 R 2 9.5 . 76.2 513.66 1.350 38.86 50.80. 6.37 141.76 232.58 0.610 182 15.9 4 1.93 573.26 R 2 9.5 77.2 514.66 1.570 38.90 50.80 6.38 141.76 274.88 0.516 Longitudinal Reinforcement Transverse Reinforcement Database No. D „ a r (mm) Total # Bars Plong (%) fy (MPa) Confin. Type N Dbar (mm) s (mm) (MPa) Parea (%) Ago (mm) A m ax (mm) Drift Ratio (%) A s h Provided (mm2) A s h (ACI) (mm2) A s i , / A s h ( A C I ) 183 15.9 4 1.93 586.05 R - 2 9.5 • 76.2 406.79 1.611 32.30 44.20 5.30 141.76 638.42 0.222 184 15.9 4 1.93 587.05 R 2 9.5 77.2 407.79 1.20.8 32.00 43.90 5.25 141.76 662.10 0.214 185 15.9 . 4 1.93 572.26 R 2 9.5 76.2 513.66 1.224 26.40 26.40 4.33 141.76 201.76 0.703 186 15.9 4 1.93 573.26 R 2 9.5 77.2 514.66 1.463 25.40 25.40 4.16 141.76 204.01 0.695 187 19.05 12 2.14 497 RJ 4 6.35 50 459.5 0.778 88.39 102.26 6.31 126.68 134.67 0.941 188 19.05 12 2.14 497. RJ 4 6.35 50 459.5 0.778 96.57 105.05 6.90 126.68 144.40 0.877 189 19.05 12 2.14 497 RJ 4 6.35 50 459.5 0.778 88.10 110.51 6.29 126.68 141.16 0.897 190 19.05 12 2.14 497 RI 4 6.35 52 459.5 0.748 98.02 112.97 7.00 126.68 142.30 0.890 191 19.05 12 2.14 497 RI 4 6.35 52 459.5 0.748 94.86 119.47 6.78 126.68 152.43 0.831 192 19.05 12 2.14 497 RI 4 6.35 52 459.5 0.656 77.02 114.71 5.50 126.68 150.74 0.840 202 9.525 8 2.45 517.13 RJ 3 3.175 25.4 793 0.736 20.24 36.53 3.39 . 23.75 46.33 0.684 204 9.525 8 2.45 -455.07 R D 3.41 3.175 25.4 793 0.837 14.63 37.56 2.45 27.00 44.77 0.603 205 9.525 8 2.45 455.07 R D 3.41 3.175 25.4 793 0.837 13.78 39.73 2.31 27.00 48.32 0.559 207 9.525 8 2.45 475.76 R D 3.41 3.175 25.4 1262 0.837 29.83 40.18 5.00 27.00 25.17 1.073 208 9.525 8 2.45 475.76 R D 3.41 3.175 25.4 1262 0.837 19.05 40.89 3.19 27.00 27.60 0.978 209 9.525 8 2.45 475.76 R D 3.41 3.175 31.75 1262 0.670 18.89 39.05 3.16 27.00 31.96 0.845 210 9.525 8 2.45 475.76 R D 3.41 3.175 38.1 1262 0.558 11.86 40.29 1.99 27.00 44.02 0.613 211 9.525 8 2.45 475.76 R D 3.41 3.175 44.45 1262 0.546 12.06 40.07 2.02 27^00 42.03 0.642 215 19.54 ' 8 2.15 451 R D 3.41 11.3 60 391 2.229 182.76 212.57 9.14 341.98 459.85 0.744 216 19.54 8 2.15 '430 R D 3.41 11.3 60 391 2.229 144.46 201.03 7.22 341.98 464.33 0.737 217 19.54 8 2.15 451 R D 3.41 . 11.3 60 418 2.229 63.20 141.00 3.16 341.98 457.15 0.748 221 19.54 8 2.15 446 • R D 3:41 11.3 60 438 2.229 174.41 208.33 8.72 341.98 349.64 0.978 222 19.54 8 2.15 . 446 R D 3.41 11.3 60 438 2.229 122.09 162.35 6.10 341.98 485.14 0.705 223 19.54 . 8 2.15 446 R D 3.41 9.5 55 825 1.707 97.98 168.94 4.90 241.71 236.75 1.445 224 19.54 8 2.15 446 R D 3.41 9.5 80 825 1.173 ' 52.55 108.01 2.63 241.71 327.70 1.044 225 19.54 8 2.15 446 R D 3.41 9.5 55 744 1.707 66.37 91.84 3.32 241.71 250.54 1.365 226 . 19.54 8 2.15 446' R D 3.41 11.3 60 492 2.346 66.06 90.86 ' 3.30 341.98 432.68 0.790 227 19.05 4 2.45 452.99 R 2 6.35 76.2 410.9 0.873 21.85 21.85 3.19 63.34 173.09 0.366 228 19.05 4 2.45 452.99 R . " 2 6.35 76.2 410.9 0.873- 20.94 20.94 3.05 63.34 173.09 0.366 229 19.05 4 2.45 452.99 R 2 6.35 38.1 410.9 1.745 27.91 28.91 4.07 63.34 82.44 0.768 230 19.05 4 2.45 452.99 R 2 6.35 38.1 410.9 1.745 28.76 29.88 ' 4.19 63.34 82.44 0.768 231 19.05 4 2.45 452.99 R 2 6.35 76.2 410.9 0.873 21.49 22.71 3.13 63.34 153.57 0.412 232 19.05 4 2.45 452.99 R 2 6.35 76.2 410.9 0.873 21.59 21.59 3.15 63.34' 153.57 0.412 233 19.05 4 2.45 452.99 R 2 6.35 57.15 410.9 1.164 20.95 21.97 3.05 63.34 105.55 0.600 234 19.05 4 2.45 452.99 R 2 6.35 57.15 410.9 1.164 22.07 22.07 3.22 63.34 105.55 0.600 237 19.05 4 2.45 452.99' R 2 6.35 76.2 410.9 0.873 22.85 23.55 3.33 63.34 186.96 0.339 238 19.05 4 2.45 452.99 R 2 6.35 76.2 410.9 0.873 23.01 23.58 3.36 63.34 186.96 0.339 239 19.05 4 2.45 452.99 R 2 6.35 57.15 410.9 1.164 22.01 22.01 3.21 63.34 134.44 0.471 240 19.05 4 2.45 452.99 R 2 6.35 57.15 410.9 1.164 21.73 21.73 3.17 63.34 134.44 0.471 Transverse Reinforcement Database No. Dbar (mm) Total # Bars Plong (%) fy (MPa) Confin. Type N • Dbar ( m m ) s (mm) f yh (MPa) Parea (%) Ago (mm) Amax (mm) Drift Ratio (%) ^sh Provided (mm2) A s h (ACI) (mm2) A s h / A s h ( A C l ) 241 19.05 4 2.45 452.99 R 2 6.35 57.15 410.9 1.164 22.05 22.05 3.22 63.34 140.60 "0.450 242 19.05 4 2.45 452.99 R 2 6.35 . 57.15 410.9 1.016 21.53 21.58 3.14 63.34 140.60 0.450 243 12.7 12 2.43 461 R U 4 4 40 485 0.601 24.75 24.75 3.96 50.27 83.77 0.600 244 12.7 12 2.43 461 R U .4 4 40 485 0.800 18.73 18.73 3.00 50.27 83.77 0.600 246 25.4 12 1.69 388 R U 4 12.7 100 524 0.952 31.27 31.27 2.61 506.71 503.07 1.007 248 12.7 20 1.58 363 R 2 6 70 368 0.238 43.71 76.39 3.51 ' 56.55 272.42 0.208 249 12.7 20 1.58 363 R 2 6 70 368 0.238 48.50 79.78 3.90 56.55 270.90 0.209 250 12.7 20 1.58 363 R 2 6 70 368 0.238 74.18 94.85 5.96 56.55 260.28 0.217 251 12.7 20 1.58 363 R 2 6 70 368 0.238 101.44 112.17 8.15 56.55 251.93 0.224 . 252 12.7 20 1.58 363 R 2 6 70 368 0.257 84.52 95.60 6 .79 , 56.55 279.25 0.203 258 35.8 8 2.60 473 RJ 3 15.9 150 445 0.874. 105.28 105.28 5.92 595.67 1387.20 0.573' 260 19.54. 8 2.74 .454 R D 3.41 11.3 80 542 2.151 84.97 100.00 4.61 341.98 297.10 1.151 261 19.54 8 2.74 454 R D 3.41 11.3 80 542 2.151 42.23 65.88 . 2.29 341.98 296.69 1.153 264 19.54 8 2.74 454 R D 3.41 11.3 70 465 2.459 56.23 80.11 3.05 . 341.98 477.08 0.717 265 19.54 8 2.74 454 R D 3.41 11.3 70 465 2.459 41.15 46.11 2.23 341.98 477.08 0.717 266 19.54 8 2.74 454 R D 3.41 11.284 100 465 1.716 69.33. 85.30 3.76 341.01 341.57 0.998 268 19.54 8 2.74 521 R D 3.41 8 75 850 1.131 62.13 62.78 3.37 171.41 172.09 0.996 269 19.54 8 2.74 521 R D 3.41 8 •75 850 1.131 26.87 48.63 1.46 171.41 172.09 0.996 270 19.54 8 2.74 521 R D 3.41 11.1 75 850 2.212 50.94 81.94 2.77 329.98 184,31 1.790 272 19.54 8 2.74 • 521 R D 3.41 11.284 70 465 1.631 46.27 . 48.48 2.51 341.01 583.89 0.584 273 19.54 8 2.74 521 R D 3.41 11.284 70 465 1:631 86.37 102.75 4.69 341.01 583.89 0.584 274 19.54 8 2.74 521 R D 3.41 11.3 80 542 1.431 88.74 88.74 4.82 341.98 452.90 0.755 275 19.54 8 2.74 521 R D 3.41 11.3 80 542 1.455 33.43 56.16 1.81 341.98 452.90 0.755 285 25 . 8 3.21 453 R . 2 10 150 470 0.333 42.00 58.60 4,20 157.08 347.71 0.452 286 12.7 8 2.53 . 363 R 2 5.75 50 364 0.617 10.10 11.77 2.53 51.93 65.86 0.789 287 12.7 8 2.53 363 RJ 3 5.75 75 364 0.617 11.75 14.37 2.94 77.90 86.77 1.197 288 12.7 8 2.53 363 R 2 5.75 40 364 0.772 7.97 11.40 1.99 51.93 52.69 0.986 289 12.7 ' 8 2.53 363 RJ 3 5.75 60 364 0.772 9.95 12.06 2.49 77.90 69.42 1.496 Appendix A fc Characteristic compressive strength of concrete p Axial compressive load A f l Gross sectional area of column Yield stress of longitudinal reinforcement fyh Yield stress of transverse reinforcement B Column Width H Column Depth L Length of equivalent cantilever Dbar Diameter of transverse / longitudinal reinforcement S Spacing of transverse reinforcement Cover ce Plong Longitudinal reinforcement ratio (A s t / A q) Parea Transverse reinforcement ratio (A s h / s*hc) N Effective number of transverse bars in cross section ^max Maximum recorded deflection Deflection at 80% effective force (20% loss of strength) Drift Ratio Drift Ratio. (A 8 0 / L ) A sh Provided Area of transverse reinforcement provided in specimen A s h (ACI) Area of transverse reinforcement required by ACI 318-05 21.4.4.1 154 U) U l Geometry Database fc P(kN) P/Agfc P/P„ Diameter Length Cover Section No. Specimen Name (Mpa) (mm) (mm) A g (mm ) (mm) Code 1 Davey 1975, No. 1 "33 .2 380 0.06 0.05 500 2750 207110 20.3 2 3 Davey 1975, No . 3 33.8 380 0.06 0.05 500 3250 207110 20.3 2 8 Ang etal 1981,No. 2 28.5 2111 0.56 0.51 400 1600 132550 18.0 2 . 22 Ang eta l . 1985, N o . 9 29.9 751 0.20 0.15 400 1000 125660 18.0 0 40 Zahn et al. 1986, No . 6 27 2080 0.58 0.51 400 1600 132550 18.0 2 41 Watson & Park 1989, N o 10 40 2652 0.50 0.48 400 1600 132550 17.0 ' 2 42 Watson & Park 1989, N o 11 39 3620 0.70 0.66 400 1600 132550 18.0 . 2 43 Wong etal . . 1990, N o . 1 38 907 0.19 0.16 400 800 125660 20.0 0 45 Wong eta l . 1990, No . 3 • 37 1813 0.39 0.32 400 800 125660 20.0 0 50 L i m eta l . 1990, C o n l 34.5 151 0.24 0.16 . 152 - 1140 18146 10.2 0 52 L i m eta l . 1990, Con 1 34.5 220 0.35 0.23 152 570 18146 10.2 0 53 NIST, Ful l Scale Flexure 35.8 4450 0.07 0.06 1520 9140 1814600 58.7 0 54 NIST, Ful l Scale Shear 34.3 4450 0.07 0.06 1520 4570 1814600 60.3 0 55 NIST, Mode l N l 24.1 120 0.10 0.09 250 750 • 49087 9.9 0 56 NIST, Mode l N2 23.1 239 0.21 0.18 250 . 750 49087 9.9 0 57 NIST, Model N3 25.4 120 0.10 0.08 250 .1500 49087 9.7 0 58 NIST, Mode l N4 24.4 120 0.10 0.08 250 750 49087 9.9 0 59 NIST, Mode l N5 24.3 239 0.20 0.17 250 750. 49087 9.9 0 60 NIST, Model N6 23.3 120 0.11 0.09 250 1500 49087 9.7. 0 93 Kunnath eta l . 1997, A 2 29 200 0.09 0.08 305 1372 73062 14.5 0 95 Kunnath eta l . 1997, A 4 35.5 222 0.09 0.08 305 1372 73062 14.5 0 96 Kunnath eta l . 1997, A 5 3575 222 0.09 0.08 305 1372 73062 14.5 0 97 Kunnath eta l . 1997, A 6 35.5 222 0.09 0.08 305 1372 73062 14.5 0 100 Kunnath eta l . 1997, A 9 32.5 222 0.09 - 0.08 305 1372 73062 14.5 0 101 Kunnath eta l . 1997, A 1 0 27 200 0.10 0.09 305 1372 73062 14.5 0 102 Kunnath eta l . 1997, A l l 27 200 0.10 0.09 305 1372 73062 14.5 0 103 Kunnath eta l . 1997,A12 27 200 0.10 0.09 305 1372 73062 14.5 0 106 Hose e t a l , 1997, SRPH1 41.1. .1780 0.15 0.13 610 3660 292250 27.8 0 107 V u e t a l . 1998, NH1 38.3 1928 0.31 0.28 457 910 164030 24.8 0 109 V u e t a l . 1998, N H 3 39.4 970 0.15 0.14 457 910 164030 24.8 0 112 V u e t a l . 1998, N H 6 35 1914 0.33 0.22 457 910 164030 . 26.4 0 115 Kowalsky et al. 1996, F L 3 38.6 1780 0.28 0.22 457 3656 164030 30.2 0 116 Lehman eta l . 1998,415 31.03 653.86 0.07 0.07 609.6 2438.4 291860 22.2 0 117 Lehman eta l . 1998,815 31.03 .653.86 0.07 0.07 609.6 4876.8 291860 22.2 0 118 Lehman eta l . 1998, 1015 31.03 653.86 0.07 0.07 609.6 6096 291860 22.2 0 119 Lehman et a l l 9 9 8 , 407 31.03 653.86 0.07 0.08 609.6 2438.4 291860 22.2 0 • 120 Lehman eta l . 1998,430 31.03 653.86 0.07 0.06' 609.6 2438.4 291860 22.2 0 121 Calderone et al. 2000, 328 34.475 911.84 0.09 0.08 609.6 1828.8 291860 . 28.6 0 Q P " © s © p p o* p S i . Geometry Database fc P(kiN) P/Agfc P/P„ Diameter Length Cover Section No. Specimen Name (Mpa) (mm) (mm) A g (mm ) (mm) Code 123 Calderone et al. 2000,1028 34.475 911.84 0.09 0.08 609.6 6096 291860 28.6 0 130 Saatcioglu & Baingo 1999, R C 4 90 1850 0.42 0.43 250 • 1645 49087 14.0 0 133 Saatcioglu & Baingo 1999, RC8 90 1850 0.42 0.43 250 1645 49087 13.8 0 141 Henry 1998, 415p 37.23 1308 0.12 0.12 609.6 2438.4 291860 22.2 0 . 142 Henry 1998,415s 37.23 654 0.06 0.06 609.6 2438.4 291860 22.2 0 144 Soderstrom2001 C I 60.6 0 0.00 0.00 419 1968.5 145440 55.6 2 145 Soderstrom2001 C2 62.6 0 0.00 0.00 419 1968.5 145440 55.6 2 152 Kowalsky & Moyer 2001 N o . l 32.723 231.31 0.04 0.04 457.2 2438.4 173170 12.7 2 153 Kowalsky & Moyer 2001 No.2 34.226 231.31 0.04 0.04 457.2 2438.4 173170 12.7 2 157 Hamilton 2002 UCI1 36.494 0 0.00 0.00 406.4 1854.2 129720 15.0 0 158 Hamilton 2002 UCI2 36.494 0 0.00 0.00 406.4 1854.2 129720 15.0 0 162 Hamilton 2002 UCI6 35.646 0 0.00 0.00 406.4 1854.2 129720 15.0 0 Longitudinal Reinforcement Transverse Reinforcement Database No. D b a r (mm) Total # Bars Plong % f, (Mpa) Dbar W s (mm) (Mpa) p s ( % ) A 8 0 (mm) Amax ( m m ) Drift Ratio (%). P S ( A C I ) ( % ) PJ Ps(ACl) 1 18.4 20 2.568 373 6.5 65 312 0.444 119.25 119.25 4.34 1.277 0.348 3 18.4 20 2.568 373 6.5 65 342 0.444 86.83 116.21 2.67 1.186 0.375 8 16 16 2.427 308 10.0 55 280 1.569 50.09 50.09 3.13 1.254 1.251 22 16 20 3.200 448 6.0 30 372 1.036 65.58 65.58 6.56 0.965 1.074 40 16 16 2.427 337 10.0 75 466 1.151 59.04 59.36 3.69 0.714 . 1.612 41 16 12 1.820 474 8.0 84 372 0.654 32.54 32.94 2.03 1.290 0.507 42 16 12 1.820 474 10.0 57 338 1.514 29.00 36.24 1.81 1.421 1.065 43 16 20 3.200 423 10.0 60 300 1.454 41.43 41.43 5.18 1.520 0.957 45 16 20 3.200 475 10.0 60 300 1.454 28.82 33.90 3.60 1.480 0.983 50 12.7 8 5.585 448 3.7 22.2 620 1.496 89.54 90.75 7.85 0.837 1.788 52 12.7 . 8 5.585 448 3.7 22.2 620 1.496 45.59 45.59 8.00 0.837 1.788 53 43 25 ' 2.001 475 15.9 88.9 493 0.637 540.99 593.37 5.92 0.871 0.731 54 43 25 2.001 475 19.1 54 435 1.509 355.70 356.08 7.78 0.946 1.594 55 7 25 1.960 446 3.1 8.89 441 ' 1.428 82.50 104.15 11.00 0.656 2.178 . 56 7 25 1.960 446 3.1 8.89 .441 1.428 60.41 73.60 8.06 0.629 2.272 • 57 7 25 1.960 446 2.7 14.48 476 0.686 110.64 128.85 7.38 0.640 1.071 58 7 25 1.960 446 3.1 8.89 441 1.428 54.69 67.52 7.29 0.664 2.151 59 7 25 1.960 446 3.1 8.89 441 1.428 52.60 64.30 7.01 0.661 2.160 60 7 25 1.960 446 2.7 14.48 476 0.686 123.09 127.72 8.21 0.587 . 1.168 93 9.5 21 2.037 448 4.0 19 434 0.959 77.20 77.20 .5.63 0.802 1.195 95 9.5 21 2.037 448 4.0 19 434 0.959 58.56 58.56 4.27 0.982 0.977 96 9.5 21 2.037 448 4.0 19 434 0.959 76.35 76:35 5.56 0.982 0.977 97 9.5 21 2.037 448 4.0 19 434 0.959 95.49 95.49 6.96 0.982 0.977 100 9.5 21 . 2.037 448 4.0 19 434 0.959 90.54 90.54 6.60 0.899 1.067 101 9.5 21 2.037 448 4.0 19 434 0.959 90.66 90.66 6.61 0.747 1.284 102 9.5 21 2.037 448 4.0 19 434 . 0.959 102.16 102.16 7.45 0.747 1.284 103 9.5 21 2.037 448 4.0 19 434 0.959 102.43 102.43 7.47 0.747 1.284 106 22.23 20 2.656 455 9.5 57 414 0.902 319.79 319.79 8.74 1.191 0.757 107 15.875 20 2.413 427.5 9.5 60 430.2 1.166 38.13 46.46 4.19 1.068 1.091 109 15.875 20 2.413 • 427.5 9.5 60 430.2 1.166 50.33 50.33 5.53 1.099 1.061 112 19.05 30 5.213 486.2- 12.7 40 434.4 3.133 87.47 87.47 9.61 1.007 3.112 115 15:875 ' 30 3.620 477 9.5 76 445 0.945 281.60 340.50 7.70 1.278 0.740 116 15.875 22 1.492 461.96 6.4 31.75 606.76 0.706 178.00 179.00 7.30 0.614 1.150 117 15.875 22 1.492 . 461.96 6.4 31.75 606.76 0.706 446.00 446.00 • 9.15 . 0.614 1.150 118 15.875 22 1.492 461.96 6.4 31.75 606.76 0.706 639.83 639.83 10.50 0.614 1.150 119 15.875 11 0.746 461.96 6.4 31.75 606.76 0.706 128.00 128.00 5.25 0.614 1.150 120 15.875 44 2.984 461.96 6.4 . 31.75 606.76 0.706 178.00 181.00 7.30 0.614 1.150 121 19.05 28 2.734 441.28 6.4 25.4 606.76 0.903 133.00 133.00 7.27 0.682 1.324 Longitudinal Reinforcement Transverse Reinforcement Database No. " b a r (mm) Total # Bars Plnng % f» (Mpa) Dbar ( m m ) s (mm) (Mpa) Ps (%) A 8 0 (mm) Drift Ratio (%) Ps(ACI) (%) P S / P s : i(ACI) 123 130 133 141 142 144 145 152 153 157 158 19.05 16 16 . 15 .875 15 .875 2 2 . 2 2 2 . 2 19 .05 19.05 12.7 12.7 28 22 22 12 12 12 12 2 . 7 3 4 3 .277 3 .277 1.492 1.492 0.021 0.021 0 . 0 2 0 0 . 0 2 0 0 . 0 1 2 0 .012 4 4 1 . 2 8 • 4 1 9 4 1 9 4 6 2 4 6 2 4 2 9 . 5 4 2 9 . 5 5 6 5 . 3 7 5 6 5 . 3 7 4 5 8 . 5 4 5 8 . 5 6 .4 8.0 7.5 6.4 6 .4 9.5 9.5 9.5 9.5 4.5 4 .5 2 5 . 4 50 50 31 .75 63 .5 50 .8 50 .8 76 .2 76 .2 31 .75 31 .75 6 0 6 . 7 6 580 1000 6 0 6 . 7 6 6 0 6 . 7 6 4 1 3 . 7 4 1 3 . 7 4 3 4 . 3 7 4 3 4 . 3 7 6 9 1 . 5 4 6 9 1 . 5 4 0 .903 1.811 1.588 0 .706 0 .353 4 1 3 7 0 . 0 0 0 4 1 3 7 0 . 0 0 0 4 3 4 3 7 . 0 0 0 4 3 4 3 7 . 0 0 0 6 9 1 5 4 . 0 0 0 6 9 1 5 4 . 0 0 0 891 .54 54 .75 75 .78 137.64 199.01 199.01 2 2 3 . 7 0 190:46 2 6 6 . 6 9 114 .30 124.92 894 .08 7 3 . 1 0 75 .78 179.07 180.11 199.01 224 .01 190 .46 2 6 6 . 6 9 114 .30 2 6 8 . 1 5 14.63 3.33 4.61 3.76 10.11 •7.55 10.58 10.68 13.15 6 .16 6.74 0 .682 1.872 1.080 0 .736 0 .736 6 .292 6 .500 0 .904 0 .946 0 .633 0 .633 1.324 0 .967 1.471 0 .959 0 .479 6 5 7 4 . 5 9 8 6 3 6 4 . 5 1 7 4 8 0 4 9 . 2 4 7 4 5 9 3 9 . 3 1 4 1 0 9 2 0 3 . 1 7 1 109203 .171 ]§2 12 7 12 U.U12 438.D 4.3 j i . / a o y u t . u u u A U J - W n . w v . ^ w fc Characteristic compressive strength of concrete Diameter Diameter of column (For square and octagonal sections D refers to the largest circle that can be inscribed in the section) A g Gross sectional area P Axial load Length Length of equivalent cantilever fy Yield stress of longitudinal reinforcement fyh Yield stress of transverse reinforcement Length Length of equivalent cantilever s Spacing of transverse reinforcement Cover Distance between outer surface of column and center of spiral reinforcement If there is no spiral, cover is taken as distance between outer surface and outside of longitudinal reinforcement Dbar Diameter of transverse / longitudinal reinforcement Plong Longitudinal reinforcement ratio (As, / Aq) ^max Maximum recorded deflection A 8 o Deflection at 80% effective force (20% loss of strength) Drift Ratio Drift Ratio (D 8 0 /L) P s Provided Area of transverse reinforcement provided in specimen Ps(ACI) Area of transverse reinforcement required by ACI 318-05 21.4.4.1 KM oo Geometry Vert. Reinf Trans. Reinf Loading Details No of Plong Parea Bldg Detail Nv Tc (MPa) B (mm) H (mm) h c (mm) Ag (mm2) bars bar# (%) Bar# s (mm) (%) P (kN) ** P/Acfc' A A l 4 55.16 609.6 609.6 517.5 371612.16 12 8 1.64 5 102 1.50 8807 0.43 A2 . 5 68.95 762 762 669.9 580644 16 8. 1.40 5 102 1.45 18966 0.47 A3 5 * 68.95 762 1016 669.9 774192 20 8 1.31 5 102 1.45 21675 0.41 B B l 5 * 55.16 762 1219.2 669.9 929030.4 20 9 1.38 5 102 1.45 23032 0.45 B l 5 * 72.40 762 1219.2 669.9 929030.4 20 9 1.38 5 76 1.94 26323 0.39 B3 4 * 55:16 762 914.4 669.9 696772.8 14 9 1.29 5 .102 1.16 13469 0.35 B3 4 * 72.40 762 914.4 669.9 696772.8 14 9 1.29 5 76 1.55 16782 0.33 C CI 3 27.58 457.2 457.2 368.3 209031.84 12 9 3.68 . 4 114 0.90 4083 0.71 C2 3 * 41.37 457.2 609.6 368.3 278709.12 12 11 4.12 4 76. . 1.35 7757 0.67 C3 3 * 55.16 457.2 ' 914.4 365.1 418063.68 16 11 3.66 5 89 1.83 13068 0.57 * Nv given for shorter dimension only **P = D L + L L f A l l steel yield strength is 414 MPa w % n n to < r o ST * i H T2. n o 3 B2 Rectangular Typical Column Cross Sections Appendix *s -i • 1 • A - l B - l 0 - * • * • .—^« * 1 • • « • 0 !/ • A-2 A-3 <s * i • • • • • . • • B-3 IN * • •i s • s * • • x« * IF » T i •i C-2 C-3 160 B3 Circular Typical Columns Details u o -=r m O —; —; p O O O O OS OO \t —. KD (N t— OS co m m - • 9 • ~ •;-o o S c ~ \o y3 r~- r~-r » CN r>i r>i n N N M in in in in s ? ^? S^ s " o o S o S o N (N OO OO (N ~ KO KO o rJ m" rn H VO m r<~i m m r-~ r- r-~ r~-\0 vo i£> KO r-^  r-^  in in <n in < < < < o o o o (N OS S £ 5J CO ^ ON \= s=> N ? v= o N o x CN r- cn r--oo so oo in tn in m in »n in in N=> \ ° s o 0 s 0 s - 6S- 6 S O CN SO ON ^ <n r— •—< oo ^ r-CN so m cn n n y3 so m «n m oo o r- o —< so in so os oo *n CN m -^ r O ro -T' CN r~- t-- c--m so r-- so 15 ^ os \£j m O — f s i — CQ 0 s 0\ in *n ' — i so —1 — m in in >n »n s o s o o x 0 s - o -o ^ •^t m cn cn OO CO oo oo cn cn cn cn so' so so so cn m oo o O O — so so so ON >n »n in 'sf OO CO CO cn «n ini in cn oo oo oo m so so so so • CN CN ON SO so o r~- t— so pj [i, PH CM C 1 ^ 161 B4 Circular Typical Column Cross Sections Appendix B C - E C-F Figure B2.1 Typical Rectangular Column detail drawings 162 A P P E N D I X C Cl Rectangular Confinement Models Model Equation A C I 0.3 yh \ A c h J > 0.09 II f yh C S A \ fc 0.2knkp " P A f "•ch J yh kn =n, / ( /! ,-2),.kp = P/Po N S Z KAh 3.3 fyh # c M g •0.0065 SK97 (ACI) *(a) 5 A 1 + 13 29 a - steel configuration parameter Hi - target curvature ductility BS98 fp] 5\ ( t Y>.82 A 1 + 13 V J 8.12 v. 7 (ACI) a - steel configuration parameter fj.^ - target curvature ductility 0.1// , \21.6MPa WSS99 / ' c 0.12 0.5 + 1.25-V f ' c A + 0.13 P, f y h - 0 .01 414 AfPa / / A - target .displacement ductility 14 J c 1 P „ g 1 - 7 = — ^ fyh V^2 ^0 SR02 k2 = 0.15 • — , £ - target drift ratio 5 s, 163 Appendix C Model Equation B B M 0 5 r 1 - 0 . 8 / , pc J 11 fyh y - as per Table 2.1 PP92 fyh Ach 0.08 k = 0.35 for high ductility demand, = 0.25 for low ductility demand r Ag yjty)-33p,m + 22 / c - P A WZP94 yAch 111 fyh <kfc'Ag <j>u I (p - target curvature ductility factor 0.006 rAg yjjy)-33p,m + 22 fc< P ^ ^Ach - 0 . 006 (f y h<500MPa) X = 117 whenfc < 70 MPa, 0.05(fc')2-9.54fc'+539.4 whenfc> 70 MPa. LP04 Ag WJty)-30ptm + 22 P KAch 9 1 - 0 . 1 / E ' f y h t f c ' A j if>u I (/) - target curvature ductility factor (f y h > 500MPa) C2 Circular Confinement Models Model Equation A C I 0.45 (A ^ 1 KAch J J c > 0.12 y c fyh fyh C S A 0.4/v kp = fc' p f J yh P/Po N S Z 1.0-p,mfc' P ) -0 .0084 KA c l 2.4 f y h & c ' A j 164 Appendix C Model Equation f 5\ fl Y 1 5 A 1 + 13 V J { 2 9 J SK97 (ACI) *(a) a - steel configuration parameter - target curvature ductility f (p^ %\ ( ( Y>.82 X, 1 + 13 V \Po) ) 8.12 V J BS98 (ACI) a - steel configuration parameter Hi - target curvature ductility 28 f \ SR02 fyh 'ch 8 - target drift ratio B B M 0 5 7 1 - 0 . 8 / pc J fyh j - as per Table 2.1 fc' A PP92 fyh Ach Afc' - 0 . 0 8 k = 0.5 for high ductility demand, = 0.35 for low ductility demand 1.4 ''A (<PJ<Py)-32p,m + 22 f; P A WZP94 ^Ah i n • fy,.0f'Aj fail fa - target curvature ductility factor 0.008 f f A . (fal fa)-33 p,m +22 fe< P A y y A h 0.006 J LP04 H I fyhttc'A a = 1.1 w h e n / < 80 M P a and a = 1.0 w h e n / > 80 M P a (f y h > 500MPa) a (f y h<500MPa) rAg (fa/fa,)-55p,m + 25 f; Pe A 79 fyh fa I (j), - target curvature ductility factor 165 APPENDIX D .1 Rectangular Column Scatter Plots (with ACI Minimum) • Satisfies ACI 21.4.4.1 * Does Not Satisfy ACI 21.4.4.1 'sh Provided sh ACI 2.5 sh Provided ' "sh BBM05 2 ro 5 CC £ 4 • Satisfies ACI 21.4.4.1 « Does NotSatistyACI 21.4.4.1 1.5 A. . • V °5 • • Satisfies ACI 21.4.4.1 « Does NotSatisfyACI21.4.4.1 sh Provided sh CSA 15 5 CC 1 • D • •** * - t* «rf • ' If B . f • 0 • » — * - y • Satisfies ACI 21.4.4.1 « Does NotSalisfyACI 21.4.4.1 7 o 5 <r Q 3 2 -• ! • -• Satisfies ACI21.4.4.1 * Does NotSatisfyACI 21.4.4.1 166 Appendix D "S 5 -Cd X 4 -• • •• i ° T i f f * * * 4. • Satisfies ACI 21.4.4.1 * Does NotSatisfyACI 21.4.4.1 .5 2 2.5 A / A M s h Provided sh FP92 4» ra 5 -o: § 4 -3 • 2 1 - • Satisfies ACI 21.4.4..1 4 Does NotSatisfyACI 21.4.4.1 • Satisfies ACI 21.4.4.1 « Does Not Satisfy ACI 21.4.4.1 sh Provided sh SK97 • o • • • • • it^--s---^-n-.-• Satisfies ACI 21.4.4.1 « Does NotSaHsfyACI21.4.4.1 • Satisfies ACI 21.4.4.1 * Does Not Satisfy ACI 21.4.4.1 2.5 sh FVovlded ' ^sh WSS99 2 „ ' A . h \ * ' 1.5 A. . • Satisfies ACI 21.4.4.1 * Does NotSatisfyACI 21.4.4.1 167 Appendix D 6 * ^ It" • Satisfies ACI 21.4.4.1 * Does Not Satisfy ACI 21.4.4.1 Table D.l Rectangular scatter plot statistics (with ACI limit) Model A B C ACI 28.1 18.6 -9.5 A23 2.0 30.9 28.9 PP92 1.6. 34.9 33.3 SR02 11.6 28.9 17.4 WSS99 9.6 35.5 25.8 BBM05 2.9 36.8 33.9 SK97 5.6 25.7 20.1 BS98 0.0 22.4 22.4 SKBS 8.3 23.1 14.8 WZP94 10.4 25.8 15.4 LP04 13.3 22.6 9.3 WZPLP 6.6 31.0 24.4 NZS 5.7 34,7 29.0 D.2 Rectangular Column Scatter Plots (without ACI Minimum) • Satisfies ACI 21.4.4.1 « Does Not Satisfy ACI 21.4.4.1 sh R-ovided sh ACI 168 ( Appendix D sh Provkled sh BS98 10r-9 - • • • - - ! • " » - - -• Satisfies ACI 21.4.4.1 4 Does NotSaBsfyACI 21.4.4.1 • • • • o • • • - • * * * ^ l ine • • • • • Satisfies ACI 21.4.4.1 4 Does Not Satisfy ACI 21.4.4.1 2 2.5 'A... sh ftovkJed sh LP04 • • 4.-• Satisfies ACI21.4.4.1 * Does Not Satisfy ACI 21.4.4.1 .5 2 2.5 A / A sh FYovided sh FP92 • * ! • • • D • * • Sat is l iesACI21.4.4 .1 « Does NotSat is fyACl21.4.4.1 1.5 A . ro 5 or I • i PI • • Satisfies ACI 21.4.4.1 * Does Not Satisfy ACI 21.4.4.1 sh Provided sh SK97 169 Appendix D jS 6 o (3 5 i Hi-• i f "® • Salisfies ACI 21.4.4.1 + Does Not Satisfy ACI 21.4.4.1 sh Provided sh SKBS • • • •a • • i • • fc -^--^^---*:-^--D-• Satisfies ACI 21.4.4.1 + .Does Not Satisfy ACI 21.4.4.1 . . • . . 4 4 ^ . 9 . . • °* • D «> • • CP i • • • • Satisfies ACI 21.4.4.1 + Does NotSatisfyACI 21.4.4.1 1 1.5 •A-ip * D * 5 ••• • Satisfies ACI 21.4.4.1 « Does NotSatisfyACI21.4.4.1 Satisfies ACI 21.4.4.1 Does NotSatisfyACI 21.4.4.1 sh Provided sh WZPLP 170 Appendix D Table D.2 Rectangular scatter plot statistics (without ACI limit) Model . A B C A C I 28.1 18.6 -9.5 A23 3.2 34.1 31.0 PP92 7.4 32.5 25.1 SR02 14.1 30.0 15.9 WSS99 11.2 35.7 24.5 BBM05 7.7 35.8 28.1 SK97 5.6 25.7 20.1 BS98 0.0 22.4 22.4 S K B S 8.3 23.1 14.8 WZP94 10.4 25.8 15.4 LP04 13.3 22.6 9.3 W Z P L P 12.5 23.0 10.5 N Z S 14.3 24.0 9.7. D.3 Rectangular Column Scatter Plots (Maximum Recorded Drifts) * •» 1.5 A , • Satisfies ACI21.4.4.1 4 Does NotSatisfyACI 21.4.4.1 * v i D i A • I • / V | U i • Satisfies ACI 21.4.4.1 + Does Not Satisfy ACI 21.4.4.r 1.5 2 2.5 A / A sh Provided sh BS98 L]4P * 0 • 8 • °« 4—-**-u-— O • • * • Satisfies ACI 21.4.4.1 + Does NotSatisfyACI21.4.4.1 1.5 2 2.5 \t\ Provided'^ sh CSA 171 Appendix D • •** • I • • *> ? V • o • Satisfies ACI 21.4.4.1 Does Not Satisfy ACI21.4.4.1 .5 2 2.5 A / A sh Provided sh L P M • • • • • • D C 0 : *• O * t ° T J * • • • • • a • fi • Satisfies ACI21.4.4.1 A Does NotSatisfyACI 21.4.4.1 sh Provided sh NZS ! • « • • • . - - - « * * — - > > 0 • • • • • • Satisfies ACI 21.4.4.1 * Does NotSatisfyACI 21.4.4.1 • Satisfies ACI 21.4.4.1 + ' Does NotSatisfyACI 21.4.4.1 • I A • $ « «=> —*-*v£ s-—f • • | •_ ! 1.5 • Satisfies ACI 21.4.4.1 + Does NotSatisfyACI 21.4.4.1 -*•-• 0 ! • *> • D i • » 0 • • • • -*»*-i*---Satisfies ACI 21.4.4.1 Does Not Satisfy ACI 21.4.4.1 172 Appendix D 3 • • • • Satisfies ACI21.4.4.1 * Does NotSatisfyACI 21.4.4.1 TO 5 or £ 4 * t D - — — - * -• • • • • • n • Satisfies ACI21.4.4.1 + Does NotSatisfyACl21.4.4.1 • £>' G* • Satisfies ACI 21.4,4.1 * Does NotSatisfyACI21.4.4.1 2 / A . sh Provided sh WZPLP sh Provided sh WZP94 Table D.3 Rectangular scatter plot statistics (Maximum Recorded Drift) Model A B C A C I 12.5 5.3 -7.2 A23 0 12.2 12.2 PP92 0 13.0 12.987 SR02 2.4 13.3 10.9 WSS99 2.2 14.3 12.1 B B M 0 5 0 14.9 14.9 SK97 0 9.2 9.2 BS98 0 7.5 7.5 S K B S 0 8.3 8.3 WZP94 0 10.3 10.3 LP04 0 8.7 8.7 W Z P L P 0 8.8 8.8 N Z S 0 10.5 10.5 Appendix D D.4 Rectangular Co lumn A Fragi l i ty Curves (with A C I Min imum) ACI ' BBM05 Drift Ratio Drift Ratio 174 Appendix D 175 Appendix D 3 4 5 Drift Ratio D.5 Rectangular Column B Fragility Curves (with ACI Minimum) 176 Appendix D f 177 Appendix D D.6 Rectangular Column C Fragility Curves (with ACI Minimum) ACI BBM05 Dri f t R a t i o Drif t R a t i o 178 Appendix D 179 Appendix D 180 Appendix D D.7 Rectangular Column A Fragility curves (without ACI Minimum) ACI BBM05 Drift Ratio ' Drift Ratio 181 Appendix D 182 Appendix D WZPLP Drift Ratio D.8 Rectangular Column B Fragility Curves (without ACI Minimum) ACI BBM05 Drift Ratio Drift Ratio 183 Appendix D Appendix D WSS99 WZP94 D.9 Rectangular Column C Fragility Curves (without ACI Minimum) ACI BBM05 Drift Ratio ' Drift Ratio 185 Appendix D SKBS SR02 Drift Ratio . . Drift Ratio WZPLP 0.5 | , : , 1 1 , 1 1 1 ' .0.45 • 0.4 -0.35 -0.3 -O 0.25-187 Appendix D D.10 Rectangular Column A Fragility Curves (Maximum Recorded Drifts) ACI BBM05 Drift Ratio Drift Ratio 188 Appendix D 189 Appendix D D.ll Rectangular Column B Fragility Curves (Maximum Recorded Drifts) Act BBM05 Drift Ratio Drift Ratio 190 191 Appendix D 5 6 7 Drift Ratio 0.9 0.8 0.7 0.6 £D 0.5 0.4 0.3 V , — r 3 4 5 6 7 D.12 Rectangular Column C Fragility Curves (Maximum Recorded Drifts) 192 Appendix D 193 Appendix D 194 Appendix D .13 Circular Column Scatter Plots (with ACI Minimum) • V I • • B 4c 4 • L . . . » . U . . -• Satisfies ACI 21.4.4.1 A Does NotSatisfyACI21.4.4.1 1.5 2 2.5 3 3.5 Pprovided' PAQ • Satisfies ACI 21.4.4.1 + Does NotSatisfyACI 21.4.4.1 1.5 2. 2.5 3 3.5 Pprovided ^ P B B M 0 5 i I • 4 • • • l o • D p ••'Hi • - A • SatisfiesACI21.4.4.1 « Does NotSalisfyACI21.4.4.1 • Satisfies ACI 21.4.4.1 * Does NotSatjsfyACI21.4.4.1 Provided ^PBS98 2 2.5 3 Pftovkted ' PCSA • » - : I H : . in • Satisfies ACI 21.4.4.1 * Does NotSatisfyACI 21.4.4.1 2 2.5 3 Pprovided ' Pl_PQ4 ! • ' i i k i • • ! D • * i^b 9 in -• Satisfies ACI 21.4.4.1 + Does NotSatisfyACI 21.4.4.1 Pprovided ' PNZS 1 9 5 Appendix D J u s L—»- 1 4 • Satisfies ACI21.4.4.1 « Does NotSatjsfyACI21.4.4.1 1.5 2 2.5 3 3.5 P Provided l e t , ft ' 1Q • L.-.&- i Q • Satisfies ACI 21.4.4.1 * Does NotSatisfyACI 21.4.4.1 2 2.5 3 3.5 Pprovided ' PsKBS * • • • • • • • • D > • • B I • < • • 1 ft • Satisfies ACI21.4.4.1 Does NotSatisfyACI 21.4.4.1 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Pprovkjed' PSK97 • In • Satisfies ACI 21.4.4.1 Does NotSatisfyACI 21.4.4.1 2 2.5 3 Pprovided ' PSR02 • 1D • • ^ 3 Aa • Satisfies ACI21.4.4.1 « Does NotSatisfyACI21.4.4.1 2 2.5 3 Pprovided ' PwZF94 —4 • Satisfies ACI21.4.4.1 * Does NotSatisfyACI21.4.4.1 2 2.5 3 3.5 Pprovided' PwZPLP 196 Appendix D Table D.4 Circular scatter plot statistics (with ACI limit) Model A B C A C I 3.4 4.8 1.3 A23 0.0 8.7 8.7 r PP92 0.0 8.3 , 8.3 SR02 0.0 8.7 8.7 B B M 0 5 0.0 8.7 8.7 SK97 0.0 18.2 18.2 BS.98 0.0 5!6 5.6 S K B S 0.0 9.1 9.1 WZP94 0.0 9.1 9.1 LP04 0.0 9.1 9.1 W Z P L P 0.0 9.1 9.1 N Z S 0.0 7.1 7.1 D.14 Circular Column Scatter Plots (without ACI Minimum) 4 • • \ • • • ia I r. o • D • Satisfies ACI 21.4.4.1 * Does NotSatjsfyACI21.4.4.1 0 0.5 1 1.5 2 2.5 3 3.5 PFrovkied * PAD: 4 4.5 5 3* L £ n • • • • • • Satisfies ACI 21.4.4.1 + Does NotSatisfyACI 21.4.4.1 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 PprovkJed/pBBM05 • c! ft Satisfies ACI 21.4.4.1 Does Not Satisfy ACI 21.4.4.1 0 0.5 1 1.5 2 2.5 PFfovkted ^  PBS98 3 3.5 4 4.5 5 • • • a L --—L * • Satisfies ACI 21.4.4.1 * Does NotSatisfyACI21.4.4.1 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 Pprovided ' PcSA 197 Appendix D • r . • : D * • D I — — _ L J Satisfies ACI 21.4.4.1 Does NotSatisfyACI 21.4.4.1 -*t. • n * u n Satisfies ACI 21.4.4.1 Does Not Satisfy ACI 21.4.4.1 fFtovWed PLP04 Pr+ovkled ' pNZS • foe, • Satisfies AC121.4.4.1 4 Does NotSatisfyACI21.4.4.1 2 2.5 3 PFVovkted/PpF92 • L ft ! • • • • • Satisfies ACI21.4.4.1 * Does NotSatisfyACI21.4.4.1 2 2.5 3 PprovkJed ' PSK97 • Q I Ion* • l ^ n * p L ft 1... 4 • Satisfies ACI21.4.4.1 . * Does NotSaHsfyACI21.4.4.1 f d • UL • Satisfies ACI 21.4.4.1 4 Does NotSatisfyACI 21.4.4.1 Pprovided ' PsKBS Pprovided ' PsRD2 198 Appendix D • • D in L___»___°__i. 4 Satisfies ACI 21,4.4.1 Does NotSatisfyACI 21.4.4.1 Provided P WZP94 f 4 D L „ - » - 1 4 Satisfies ACI 21.4.4.1 Does NotSatisfyACI 21.4.4.1 Provided PW2H.P Table D.5 Circular scatter plot statistics (without A C I limit) Model A B C A C I 3.4 4.8. 1.3 A23 0.0 28.6 28.6 PP92 0.0 8.3 8.3 SR02 0.0 33.3 33.3 B B M 0 5 0.0 18.2 18.2 SK97 0.0 18.2 18.2 BS98 0.0 5.6 5.6 S K B S 0.0 18.2 18.2 WZP94 0.0 9.1 9.1 LP04 0.0 9.1 9.1 W Z P L P 0.0 9.1 9.1 N Z S 0.0 7.1 7.1 199 Appendix D D.15 Circular Column A Fragility Curves (with ACI Minimum) ACI BBM05 Drift Ratio Drift Ratio 200 Appendix D 201 D.16 Circular Column B Fragility Curves (with ACI Minimum) ACI BBM05 Drift Ratio Drift Ratio 202 Appendix D 203 Appendix D D.17 Circular Column C Fragility Curves (with ACI Minimum) ACI BBM05 Drift Ratio Drift Ratio 204 Appendix D 205 0 Appendix D D.18 Circular Column A Fragility Curves (without ACI Minimum) ACI BBM05 Drift Ratio Drift Ratio 206 Appendix D 207 Appendix D D.19 Circular Column B Fragility Curves (without ACI Minimum) ACI BBM05 Drift Ratio Drift Ratio 208 Appendix D 209 Appendix D D.20 Circular Column C Fragility Curves (without ACI Minimum) ACI BBM05 Drift Ratio Drift Ratio 210 Appendix D 

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