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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 K e v i n A l l e n Riederer B . S c , University o f Alberta, 2003  A T H E S I S 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 SCIENCE in The Faculty of Graduate Studies ( C i v i l Engineering)  T H E U N I V E R S I T Y OF BRITISH C O L U M B I A December 2006  © K e v i n A l l e n 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 A h provided over that s  which is required by A C I (A h s  provided / A h s  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 ABSTRACT  ..  :  •  T A B L E OF C O N T E N T S  iv  LIST OF T A B L E S . . . .  ix  LIST OF FIGURES  x  LIST OF N O T A T I O N S  xiii  ACKNOWLEDGEMENTS.-.  xiv  1  •• 1  2  INTRODUCTION 1.1  Motivation  ,  ...  1.2  Ductility and Lateral Steel  1  1.3  Confinement Action of Transverse Steel...,  2  1.4  Properties of Confined Concrete  6  1.4.1  Mander M o d e l for Confined Concrete  1.4.2  Legeron and Paultre M o d e l for Confined Concrete  1.5  Confinement and Lateral Deformation  1.6  Ductility and A x i a l Load  1.7  Research Objectives and Scope  1  7 •.  9 11  :  13 15  CODE EQUATIONS A N D PROPOSED M O D E L S 2.1  Introduction  2.2  Current Code Requirements  17 ..,  17 17  2.2.1  American Concrete Institute 318-05 ( A C I )  17  2.2.2  Canadian Standards Association A23.3-04 ( C S A )  23  2.2.3  N Z S 3101:2006 (NZS)  2.3  •  Proposed Models  25 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 ( B B M 0 5 )  31  2.3.4  Sheikh and Khoury 1997 (SK97)  32  2.3.5  Bayrak and Sheikh 1998 (BS98)  iv  :  34  \  Table of Contents  2.3.6  Bayrak and Sheikh & Sheikh and Khoury  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)  2.3.10  Watson Zahn and Park & L i and Park  39  2.3.11  Paultre and Legeron 2005 (PL05)  39  2.4 3  35  -38  Range of Properties Investigated  42  EVALUATION DATABASE 3.1  '  3.2  4  :  44  Experimental Database  44  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 Verification of Database Parameter Values  52  CONFINEMENT MODEL EVALUATIONS 4.1  58  Rectangular Columns  4.1.1  58  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  4.1.2.4  Special Consideration for SR02  80  Spacing of Transverse Reinforcement  81  4.1.3  ;  . 75  4.1.3.1  Assessment of A C I 21.4.4.2  81  4.1.3.2  Assessment of C S A and N Z S  85  4.1.4 4.2 4.2.1  M a x i m u m Recorded Drifts  86  Circular Columns  88  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  4.2.2.2  Assessment of A C I 318-05 21.4.4.1  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  ,4.2.3.1 4.2.3.2 4.2.4 5  ,  98  107  Assessment of A C I 21.4.4.2  107  Assessment of C S A and N Z S  108  M a x i m u m Recorded Drifts  109  SELECTION OF C O N F I N E M E N T M O D E L 5.1  98  111  Selection Procedure  Ill  5.1.1  Objective  HI  5.1.2  Scatter Plot Evaluation  112  5.1.3  Fragility Curve Evaluation  114  5.1.4  Comparison of Expressions  115  5.1.5  M o d e l Requirements  115  5.2  Rectangular Columns  116  5.2.1  Scatter Plot Evaluation  5.1.6  Fragility Curve Evaluation  5.1.7  Comparison of Expressions  119  5.1.8  Requirements of Models  119  5.1.9  Conclusion and Recommendation  121  5.3  116 ...117  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  5.4.1 6  Comparison  132 figure  ,  132  S U M M A R Y A N D CONCLUSIONS  134  6.1  Summary....:  134  6.2  Recommendations  136  6.3  Recommendations for future research  137  REFERENCES  ,  139  APPENDIX 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  B 2 Rectangular Typical Column Cross Sections  :  160  B3 Circular Typical Columns Details..  161  B 4 Circular Typical Column Cross Sections APPENDIX C  '.  .'  162 163  C I Rectangular Confinement Models..  163  C 2 Circular Confinement Models  ,.  164  APPENDIX 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) D . l 2 Rectangular Column C Fragility Curves (Maximum Recorded Drifts)  vii  190 192  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 M i n i m u m ) ,  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  viii  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  ix  114  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 A x i a 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 A x i a l Load ratio versus drift ratio  54  Figure 3.6 p a and p i versus drift ratio  55  Figure 3.7 f ' / f  56  vo  are  c  versus drift ratio  yt  Figure 3.8 A / A h versus drift ratio  56  Figure 3.9 B / L and D / L versus drift ratio  57  Figure 3.10 p i  57  g  C  o n g  versus drift ratio  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 ' versus A x i a l Load Ratio for columns in quadrants 2 and 3 of A C I c  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 W S S 9 9 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 ' 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  c  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  xii  LIST OF NOTATIONS Ah C  =  cross-sectional area of a structural member measured out-to-out of transverse reinforcement  A  g  Ah s  =  gross area of column  -  total cross-sectional area of transverse reinforcement (including crossties) within spacing s and perpendicular to dimension h  A  sp  b  c  c  =  cross-sectional area of spiral or circular hoop reinforcement  =  cross-sectional dimension of column core measured centre-to-centre of confining reinforcement  f'  =  specified concrete strength o f concrete  f  =  specified yield strength of nonprestressed reinforcement  f  =  specified yield strength of transverse reinforcement  P  =  A x i a l compressive force on column  Po  =  nominal axial load strength at zero eccentricity  s  =  spacing of transverse reinforcement measured along the longitudinal axis  c  y  yt  ofthe member si  =  centre-to-centre spacing of longitudinal reinforcement, laterally supported by corner of hoop or hook of crosstie  <fi  =  Parea  =  p  =  s  capacity reduction factor area ratio of transverse confinement reinforcement (A h / s-h ) S  c  ratio of volume of spiral reinforcement to the core volume confined by the spiral reinforcement (measured out-to-out)  p  =  area of longitudinal reinforcement divided by gross area of column section  p,m  =  mechanical reinforcing ratio (m = f / 0 . 8 5 f )  pi  =  volume ratio of transverse confinement reinforcement  t  vu  y  xiii  c  ACKNOWLEDGEMENTS First, I would like to express my sincere gratitude to my supervisor Dr. Kenneth E l w o o d 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 M e i s l , Aaron Korchinski, T i m 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 M i c h a e l , Andrea, Jim 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.  Finally, I want to thank my parents, A l l e n and A n n 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 o f determining the optimum requirement for confining steel.  To form the basis of this investigation, the following section w i 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 well 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 o f the design shear force. The amount and orientation o f transverse steel required for shear resistance is not the focus of this study.  Buckling o f longitudinal compression reinforcement  can limit the performance o f  columns subjected to seismic loading. For this reason, the lateral support o f the longitudinal reinforcement provided by the transverse reinforcement is an important parameter in the design o f reinforced concrete columns. Therefore, the lateral steel spacing in the end regions where hinges are likely to form is crucial to reducing buckling of the compression bars. However, the design o f lateral steel for support o f longitudinal bars is not the focus o f this study.  The area, spacing and orientation o f lateral bars also play a key role in the effectiveness of the transverse reinforcement to confine the core concrete o f 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 o f the steel. It is this confining action o f transverse steel that is the focus o f 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 o f 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 o f column tests, the authors concluded that the area o f the effectively confined concrete is less than the area bounded by the perimeter tie. In other words, A < e  A h where A is the effectively confined area o f concrete and A h is the area o f concrete C  e  c  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',  (l.l)  = f,K  where k is a confinement effectiveness coefficient expressed as: e  K  =  d-2)  ~ cc  A  where A , the area o f core within centre lines o f the perimeter spiral or hoops excluding cc  area of longitudinal steel, expressed as:  =4(1  Ac  where p  d-3)  'Pec)  is the ratio of longitudinal reinforcement to area of core of section.  cc  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:  2 d  V  1  e  ' -  s  J  (1.4)  Pu  and for circular spirals as:  I - *' k  =  _ 2 d  I  _  (  3  l  5  )  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. Equilibrium 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, = \k Psf e  '  yh  ( 1-7)  where p is the volumetric transverse reinforcement ratio and k is given i n Equations 1.4 s  e  and 1.5.  4  Introduction  Cover Concrete  Effectively confined core  Cover Concrete (Spalls off) - \ Ineffectively — confined core  r  Section B - B  1  • *  P ° 1 .  (j i  L J ' dg-s'/i "'  d  1  .  1  i  T B  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  1)  r  b - s'/2 c  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:  r 6b J.  *.=^  "7  l-  „i A  2F .,  1-  ~ "  A  ^  '  (i-^)  where-w',- , the /'th clear distance between adjacent longitudinal bars, along with the dimensions s', b and d are shown in Figure 1.2 and Figure 1.3. Since many rectangular c  c  columns have different quantities o f lateral steel i n the x and y directions, separate transverse reinforcement ratios are defined as:  (1-9)  p*=^r sd  c  P  y  (UO)  = \ sd  c  A g a i n recognizing the relationship given in Equation 1.1, the effective lateral confining stresses for a rectangular column in the x and y directions are:  (i.ii)  r,=k pj e  yh  and f\  '(1.12)  = KPyf»  where k is given in Equation 1.8. e  Figures 1.1, 1.2 and 1.3 as well 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 o f transverse bar, spacing o f transverse bars and  dimension o f concrete core, yield strength o f steel, density o f longitudinal reinforcement and in the case o f rectangular columns, spacing o f longitudinal reinforcing bars.  1.4 Properties of Confined Concrete N o w that the relationship between the transverse steel and concrete confinement has been illustrated, the effect o f confinement on the expected behaviour o f concrete can be addressed. F o r 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 fluid 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 / = c  xr  : r -1 + x J  (i-i3)  c  r  where f'  = compressive strength of confined concrete,  cc  (1.14)  ' x = -^where s = longitudinal compressive concrete strain, c  f p  1 + 5 J cc where f'  co  ^  (1.15)  1  is the unconfined concrete strength and s  co  is the corresponding strain typically  assumed to be 0.002,  E,.  (1.16)  where E= c  (1.17)  5000 J]\(MPa)  is the tangent modulus of elasticity of the concrete and £  = ^  (U8)  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' ,  the authors use a  cc  constitutive model based on tri-axial compression tests and described by W i l l i a m and Warnke (1975). A s shown i n Figure 1.5, the W i l l i a m and Warnke model relates the confined strength ratiof'cJf'co to the two lateral confining stresses/'// andf'\ . 2  Confined  3  Strength  OJ  0 Smollett  Confining  Ratio  Stress  Ratio,  f^^ct  0.2  03  ^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  1.4.2  -2  (1.19) f  co  co  J  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 f  cc  e ' , and point B is the post-peak axial strain E cc  C  C  5  0  corresponding to the strain  in the concrete when the capacity drops  to 50% of the confined strength. The stress in the confined concrete,^, corresponding to a strain e , in the ascending portion (point 0 to point A) of the stress-strain curve is given cc  as: f •= r J  cc  J  c  k-\  +  F  {a ls\ f cc  <  (1.20)  £•'  c  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: (1.21)  E -{f\Js\ )  k  ct  c  where E is the tangent modulus of elasticity of the unconfined concrete. ct  The post-peak portion of the curve is described by the following equation: fee  =/•«»: e x p [ * l ( ^ - ^ « : ) * l 2  S  (  c c ^ £ \ c  9  1-22)  Introduction  i  on "S  <  -+-> o  0.5fl  o  a o V  Concrete A x i a l 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 2  :50  k =\  (1.23)  ^k  (1.24)  + 25(I )  2  e50  where I o is the effective confinement index evaluated at the post-peak strain e so shown e5  cc  in Figure 1.6.  To develop expressions for f  c c  and s' , the authors use the effective confinement index cc  at peak stress, a nondimensional parameter first introduced in Cusson and Paultre (1995). TI  /  le  (1.25)  where (1.26) sc and the following relationships are provided: (1.27)  / ' « , = / • « [ ! +2.4(7'. ) - ] 0  7  10  Introduction  e' = s< [\ + 35(r y ] 2  cc  c  (1.28)  e  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. T o include this phenomenon, the authors introduce the following parameter: K =  '  F  PseyE  ,  C  (1.29) c  £ s  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 e 50 is taken from the curve where the stress reaches 50% of the CC  maximum value. In equation form, it can be expressed as: =*c o(l + 60/ 5  e 5 0  )  (1.31)  where e so is the post-peak strain in the unconfined concrete taken from the-curve at the c  point o f 0.5/' and I so is the effective confinement index at e so and is expressed by the c  e  cc  authors in the following form: /,*, = P . , jiJ  (1-32) c  For the relationships shown above, fh is the yield strength o f the transverse reinforcement y  and p  is the effective^volumetric ratio o f confinement reinforcement  se  P  -  ,  =  K  ,  -  '  -  (  sc  1-33  )  where for a given column, A h is the total area o f transverse reinforcement within spacing s  s, and c is the dimension o f 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 o f 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 o f 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 i n the various other models found in the literature. To understand how an increase in axial strain capacity o f concrete relates to improved lateral ductility in reinforced concrete columns, one must examine the strain gradient that exists i n members subjected to axial load and bending forces.  Consider the reinforced concrete, element o f 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 dL  e comp c  ( 134)  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 s , while the concrete in the compression region resists the len  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 w i l l be achieved. Additionally, 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. A s the spacing decreases, the  13  Introduction  0.05 Curvature * D  Figure 1.8 A x i a l 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 beamcolumn 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 o f axial load, P / A f ' < 0.2, slip deformations can account for up to approximately g  c  half o f the total deformation at yield, and for columns with high values for axial load ratio, P / Agf ' > 0.5, the displacement due to bar slip is negligible. The conclusion that c  can be reached from this result is that for columns with high axial load the flexural displacements, which are significantly influenced by the level o f confinement, dominate the total column displacement at yield. A l s o , this indicates.that columns with low axial load have the added deformation component from bar slip which does not depend on the amount o f 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 o f this research project is to investigate the performance o f 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 i n Chapter 21 o f A C I 318. This is done by addressing both the area requirement o f section 21.4.4.1 and the spacing requirements o f section 21.4.4.2. The performance o f the A C I model w i l l be evaluated i n a relative manner to the current building codes i n Canada and N e w 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 o f  ( Washington and the Pacific Earthquake Engineering Research ( P E E R ) Center, w i l l be used to compare the requirements o f each model with the performance o f the columns in the database subjected to simulated seismic loads. Once the evaluation is complete, the results w i l l be used to determine i f the current A C I expressions are adequate to achieve acceptable levels o f performance. If it is found that 15  Introduction the confinement requirements of A C I are not the most desired model, a recommended alternative w i l l be proposed.  The proposed model w i l l ensure that a column will  experience only modest lateral strength degradation before reaching the prescribed lateral drift limit. A l s o , the form of the confinement requirements and their phrasing within chapter 21 of A C I 318 w i 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 i n this study.  The goal o f  determining an appropriate confinement model w i l l be reached through an evaluation o f these models as apposed to developing a new one. The database o f column tests used to perform the evaluation and subsequent results and conclusions are presented in the chapters which follow.  Three building code requirements as well 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 N e w Zealand. The proposed models evaluated i n 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 o f most the models listed above.  2.2  Current Code Requirements  The following sections outline the confinement requirement o f the current reinforced concrete building codes in the United States, Canada and N e w 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 o f an area requirement as well as a spacing requirement. Both o f  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 o f the lateral steel requirements over the past 70 years.  The first equation for determining the area o f lateral steel required for the design o f reinforced concrete columns appeared in the 1936 Building Regulations for Reinforced Concrete ( A C I 2006). The basic philosophy o f the requirement was to ensure that the axial load carrying capacity o f the column was maintained after spalling o f the cover concrete. This was achieved by considering the material capacity enhancements due to confinement described i n Chapter 1. The derivation for the amount o f 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' (A -A ) c  g  (2.1)  = 4Af (A -A )  c  !  c  s  Recall from Figure 1.1, the lateral pressure due to the confining steel for a circular column at yield is  2A f f =— J^L  ( 2.2 )  S  t  sh  c  Substituting^ into Equation 2.1 and dividing each side by (2.05f hA ), and rearranging the y  c  equation gives:  «, sb P  4A  S  c  f A1C f \A•>  0.415A  y  c  1 +  )  A  A  p  A  (2.3)  s  sb A c  c  Recognizing that the left hand side o f 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 o f 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 o f transverse steel required by A C I . 18  Code Equations and Proposed Models  (2.4)  [ACI318-05 E q 10-5]  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 Building 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. (2.5)  [ACI318-05 E q 2 1 - 2 ]  Equation 2.5 is a lower bound expression that imposes a limit on the (A /A h) ratio which g  c  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 (2.6)  2  where p is the volumetric ratio required by Equation 2.4 with A h substituted for A and 4 s  c  c  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 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 o f an equivalent circular spiral column having equal gross area, core area, center to center spacing o f lateral reinforcement and strength of concrete and lateral reinforcement.  The spacing limit for spiral reinforcement in the 1971 version o f A C I 318 was changed to a maximum center to center distance o f 4 inches.  In the 1983 version o f the code, it was recognized that the confining effectiveness o f rectangular hoops was less than that o f circular or spiral hoops and that this difference should be reflected i n the requirements. The code stated that the total cross-sectional area of rectangular hoop reinforcement shall be the greater o f 1  A  sh  = 0.3sb LL c  and  [ACI318-05 E q 2 1 - 3 ]  •1  (2.7)  fyt  A =0A2sb sh  (2.8)  f fJ yi  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, o f one quarter o f t h e 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 (A /A h) ratio to a minimum o f 1.3. The expression, first given g  c  in the 1989 code, remains as the current minimum expression in the 2005 code  [ACI318-05Eq21-4]  A =0.09sb ^ sh  c  fyt  20  (2.9)  Code Equations and Proposed Models The 1999 version ofthe A C I code implemented changes to the spacing requirements for the seismic design o f transverse steel in reinforced concrete columns. Three limits were given and still form the spacing requirements i n the 2005 code. A s was first given in the 1999 code, Section 21.4.4.2 o f 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 (2.11)  s<6d  b  where db is the diameter ofthe longitudinal reinforcement or s <4 x  +( V  l  4  [ACI318-05Eq21-5]  ~ A h  3  (2.12)  J  where h is the maximum horizontal spacing of hoop or crosstie legs on all faces of the x  column. The value o f s shall not exceed 6 inches and need not be taken less than 4 x  inches.  According to the A C I - 3 1 8 -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 o f 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 o f the longitudinal reinforcement is not the focus o f 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  Area Req'mt  1936  P = 0.45  —1  s  \ ch A  Ps  1971  f:  1/6 h  c  )fy,  .  1  = 0-45 V  Spacing Req'mt  ^ch  J  fyl  A =0.12 ft s <0.25£> 1999-Current  5 <  22  6d,  Code Equations and Proposed  Models  Table 2.2 Rectangular column ACI confinement requirements timeline Rectangular Columns Spacing Req'mt  Area Req'mt  Year  16 diam. long, b a r / 1936  •  48 diam. trans, bar /  -  column dimension 1971  hPs h  l  A  „  'sh  1983 A =0A2sb sh  4 inches  S  -  2  fyt c  r f  { ch A  4 inches / % column dim.  c  J yt  '•sh  1989 'sh  LL[  A>  fyt  c  r f  < ch A  c  J yt  s<0.25D s < 6d  u  1999 s, < 4 +  2.2.2  f 14 -h  Canadian Standards Association A23.3-04 (CSA)  U p until the 2004 version o f the A23.3 standard o f 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 i n Chapter 21 are taken from a recent proposal by Paultre and Legeron (2005). The details o f 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 o f circular hoop reinforcement shall not be less than the larger o f p =0Ak Wr fl s  p  [ C S A A23.3-04 E q 21-4]  (2.13)  [ C S A A 2 3 . 3 - 0 4 E q 10-7]  (2.14)  .ft and  A,  f  Ps = 0-45  \A  ^  -1 f  £  ) fy,  ch  where the factor, k , is the ratio.of factored axial load for earthquake loading cases to p  nominal axial resistance at zero eccentricity. Note that for k = 0.3, these requirements are p  the same as A C I 318-05.  For columns with rectilinear transverse steel, the code states that the total effective area in each o f the principal directions o f the cross-section shall not be less than the larger o f the amounts required by the following equations:  A A  sh  f'  =0.2k k ——sb n  p  c  [ C S A A 2 3 . 3 - 0 4 E q 21-5]  (2.15)  [ C S A A 2 3 . 3 - 0 4 E q 21-6]  (2.16)  A h fyt c  and A =0.W^sb sh  c  fyt where -2)  •  '  ( 2  1 7  )  and ni is the total number o f longitudinal bars in the column cross-section that are longitudinally supported by the corner o f hoops or by hooks o f seismic crossties. Note that in all o f the above A23.3. equations, the specified yield strength o f 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.  NZS 3101:2006 (NZS)  2.2.3  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 A \.Q- mf < S  sh = c  A  Pt  P  c  Sb  \  3.3  c h  A  / „ tf 'A yt  TJc  e  0.0065  [NZS3101-06Eq 10-22]  (2.18)  "g J  where m=  (2.19)  0.85/7  For columns with circular hoops or spirals, the volumetric ratio of must not be less than Ps =  ' A 1.0- mf > g  ^  A  Pl  2-4  c h  c  f  yl  P 0f 'A c  ^  -0.0084  [NZS3101-06 Eq 10-20]  ( 2.20 )  sJ  where m=  fy 0.85/7  (2.21)  The factor p m shall not be taken greater than 0.4 and the ratio A /A shall not be greater t  g  c  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 crosssection or ten diameters of the longitudinal bar being restrained.  According to the  commentary to the N e w Zealand code, the spacing limits are considered necessary to restrain buckling of longitudinal steel as well as ensure adequate confinement of the concrete.  There are no minimum limits in NZS3101 analogous to A C I 318 E q . 21-2 and 21-4 however, in the N e w 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 p =  f  1  ^  [ N Z S 3 1 0 1 - 0 6 E q 10-21]  \55d"f,  '  (2.22)  d  b  In the 2006 version of the N e w 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_±_ 135/,, b  [ N Z S 3 1 0 1 - 0 6 E q 10-23]  (2.23)  d  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 N e w 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 o f a study to develop detailing guidelines for reinforced concrete bridge columns in areas o f low to moderate seismicity. Their research was aimed at investigating the cyclic behavior of columns with moderate amounts o f confining steel.  The columns tested in the experimental program contained 4 6 % to 60% ofthe minimum lateral reinforcement required by the American Association o f State Highway and Transportation Officials ( A A S H T O 1992) provisions. The applied axial loads were 10% to 2 0 % of Agf' . The specimens were tested under constant axial loads and reversed cyclic c  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 o f confinement steel. The requirements o f the current A C I and N e w Zealand codes, along with those o f A A S H T O , the California Department o f Transportation ( C A L T R A N S 1983), the Applied Technology Council ( 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 o f 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  s b„  =0.12  ce  (2.24)  + 0.13(/? - 0 . 0 1 ) (  f'ce  V  where f'  P  0.5+1.25-  / c  A  g  J  is the expected concrete strength and f  ye  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 following equation, using the A T C 32 approach, was proposed to relate the amount of confining reinforcement to attainable displacement ductility, jU : A  - ^ - = 0.Lu  s b  ' '" / c  fc  c  0.12  fc fy,  f 0.5 + 1.25V  f \  A,  + 0.13 P, V  yt  f  •0.01  (2.25)  where,  / ,n  = 27.6 M P a (or 4 ksi)  / ,„  =414 M P a (or 60 ksi)  c  s  A target displacement ductility of 10 is suggested to provide the minimum lateral steel required in areas o f 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.  G i v e n the similarity of the  proposed equation to both the A T C - 3 1 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 w i 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 2 0 % 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  (2.26)  *-i  A  *  A  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: - The results 2  suggested that the following approximation could be made between r and the lateral drift ratio 8: (2.27)  r = \4-^=—S where  (2.28)  k, = 0A5J^-^ V  i  s  s  Equating the two expressions for r, and solving for the reinforcement ratio, yields the proposed equation:  Pa  (2.29 )  -1  = 14  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 is 0  replaced with P /tfiPo the following design equation is presented: u  A  sh  =0.35-  f  •1  c  fyt  1  s  ( 2.30 )  c/>  1  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 P is maximum compressive load which a column w i l l experience during lt  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 ( B B M 0 4 ) 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 P  \  2  fc  .1-0.8/,,,  (2.31)  fyt  w h e r e / is the axial load ratio (to confined core) given as P / A f' c  cf  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)) y,  Coefficient  Transverse  Coefficient  Reinforcement  Circular  Rectangular  Ratio, p  Columns  Columns  Moderate  P  0.15  0.18  Seismicity  P area  0.09  • 0.12  P  0.25  0.30  0.15  0.20  Type of Seismic Demand  H i g h Seismicity  vol  vol  P area  y,  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. Additionally, 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 o f 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 (A /, ACI) s  t  and the requirement proposed by the  authors (A„h): A =(A sh  .(2.32)  )-a-Y -Y  shiACI  p  4  where, = steel configuration factor  a Y  = axial load level factor  Yy  = section performance factor  p  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. i n 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 o f 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 o f 2.5 is assumed for all configuration types in this category. The authors note that using a value o f a equal to unity for category II configurations is reasonable in situations where the opening o f hooks which are not anchored i n 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 Y and Y^. Y is a factor developed to adjust the confining steel requirement p  p  according to the axial load level and Y takes into account the section ductility demand. v  The equations are expressed as follows:  33  Code Equations and Proposed Models  ( p \  (.2.33 )  1 + 13  |1.15  (2.34) 29 where  is the target curvature ductility.  To select the target curvature ductility, the seismic performance o f 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 S K 9 7 model.  The equations presented by Sheikh and Khoury were proposed for tied columns only. However, the model w i l l also be considered in the analysis o f circular columns, assuming an a value o f 1.  2.3.5  1  Bayrak and Sheikh 1998 (BS98)  Bayrak and Sheikh (1998) presented results o f four column tests and combined the results with previous tests to evaluate the suitability o f the design equations presented earlier by Sheikh and Khoury (1997) to columns made with high strength concrete ( H S C ) and ultra high strength concrete ( U H S C ) . Using the same procedure as Sheikh and Khoury, the authors developed a new design procedure for confinement o f H S C columns with f'  c  greater than 55 M P a .  The authors again took the approach o f multiplying the total cross-sectional area o f rectilinear ties required by the current A C I (A h, ACI) s  code by factors which account for  steel configuration, the effect o f axiai load, and the section ductility demand. The researchers concluded that the effect o f axial load on the lateral reinforcement demand is independent o f 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 = (A ya-Y .Y,  (2.35)  1 + 13  (2.36)  shtAa  t y  *  =  p  \0.82  ]til— 8.12  '  .  •  (2.37)  The researchers again suggest that a curvature ductility factor o f 16 can be used to define a highly ductile column therefore this value is used here to evaluate the BS98 model. A g a i n , 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 o f the Sheikh and Khoury (1997) equations, a true transverse reinforcement model, representing the intent in which they are proposed, should be a combination o f the two. The model, termed here S K B S , utilizes the S K 9 7 model for columns with concrete compressive strengths less than 55 M P a , and the BS98 model for any column with compressive strength o f 55 M P a or greater. A curvature ductility o f 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, A h, to required curvature ductility, n s  35  r  The required  Code Equations and Proposed Models confining reinforcement area is given for rectangular sections by the following relationship: A  sh  =sb (0.15 + 0 . 0 1 / / J  Jc  p  g  A  c  fy,  ch  A  V  A  (2.38)  -0.08  J c  The equation can also be expressed as: A  * .  =  k  4 '  f c  S\  p  fy, ch K *fcA  (2.39)  0.08  A  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 o f 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. Recall, for circular columns the volumetric transverse reinforcement ratio is:  4A Ps=  (2-40)  T-  h'°c  S  where A  sp  is the cross-sectional area o f the spiral or circular hoop reinforcement, and h is c  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 o f 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, p m. t  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:  A  4*. sb„  (0J<f> )-33p,m  g  y  c  111  A  K  +22 f <  ch  P  0.006  fvtfc'A,  (2.41 )'  For columns with circular hoop or spiral transverse reinforcement:  A  r  ^  = 1.41  g  (<f>J<{> )-33p m + 22 f < y  111  A  K  ch  l  c  P  ^  0.008  ( 2.42 )  f » # : \ j  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 o f 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 ( H S C ) 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). A g a i n , curvature ductility was the performance criterion selected. The analytical model made use o f 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 D o d d and RestrepoPosada(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:  ( A / ^ ) ~ 3 3 p , m + 22 f;  A  g  sb„  \A  A  ch  P  -0.006  (2.43 )  f 0f 'A j yh  c  g  Where 1 = 1 1 7 w h e n / < 70 M P a , and X = 0.05(/ ')2-9.54/ '+539.4 when f > 70 M P a . c  c  c  c  For H S C columns confined by circular normal yield strength steel: f r  'sh s b  A  g  {<t>J<j> )-33p,m + 22 / ; y  111  \A  ch  \  A P  ( 2.44 )  0.006 •a  fyhtL'Aj  where a = 1.1 w h e n / < 80 M P a and a = 1.0 when f > 80 M P a . c  c  For H S C columns confined by rectilinear high-yield-strength steel (f h > 1150 M P a ) : y  38  Code Equations and Proposed Models  A  sh  A  g  (0J0 )-3Op m y  l  A„  + 22 f \ c  *  P  f ¥ 'A yl  c  (2.45)  sJ  whereA = 91-0.1/ ' c  For H S C columns confined by circular high-yield-strength steel:  Ash _ ( g to W,).-55p,m + 25 f < P ^ sb \A 79 f 0f 'A A  c  c  c  yl  e  (2.46)  c  Note: p m = mechanical reinforcing ratio t  The authors also place the following limitations on their proposed equations: The maximum value of p m that can be substituted into any ofthe equations is 0.4. t  A /A c  g  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 o f the Watson, Zahn and Park (1994), a true transverse reinforcement model, representing the intent i n which they are proposed, should be a combination ofthe two. In this study, the model W Z P L P uses the W Z P 9 4 mdoel for columns with concrete compressive strength less than 60 M P a , and L P 0 4 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 o f 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 o f 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 o f 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  (2.47)  V where f'/  e  is the peak effective confinement pressure. F o r rectangular columns i n the y  direction it is given by f  i  e  =  K  e  A £j CyS 1  L  (  Recall Kk is the geometric coefficient of effectiveness and c  y  2  4  8  )  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' lk , where k e  p  p  — 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 o f Effectiveness K  e  for both rectangular and circular columns. The coefficient is broken down into vertical and horizontal components Kh and K where v  (2.51)  K =K K e  h  v  The expressions for K included the spacing o f the lateral steel bars. T o simplify the v  equations, the authors determined the K values for over 500 columns considering the v  minimum spacing requirements o f A C I . They concluded that a conservative value for K  v  could be expressed as a function o f the ration A h/A . c  g  For members with rectangular  hoops 20 K =\~— h  ^  (2.52)  ft,  = 1 . 0 5 ^ (for ^ = 1 6 )  (2.53)  ^ = 0 . 9 5 ^ (for ^ = 1 0 )  (2.54)  v  or  For members with circular or spiral hoops, Kh is unity and K is 0.90. v  The authors highlight that ties are not always effective with their full yield strength, therefore an effective stress f\,  apposed to the yield stress fh , is used. The authors make y  the following conservative recommendations: for circular columns, f'h=0.95fh , and for y  rectangular columns, f'h=0.65fh . y  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 K and Kh simplifications and fitting parameters to develop expressions v  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  A =®k k c s^^shy  p  n  (2.55)  y  J yt  ch  A  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 = ®k ~-  ,  p  J  .  (2.57)  yt  where O = 0.4 for fully ductile columns and 0.25 for limited ductility. Note, the ratio A /A h does not appear in the epression for circular columns as the K v value is g  c  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  f' c  (MPa)  fyt(MPa).  P/A f ' g  c  parca (% )  Min  Max  Min  Max  Min  Max  Min  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  -  -  -  -  -  BBM05  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 i n the table above with a dash (-) were not given.  43  3 3.1  EVALUATION DATABASE 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 i n the database contains column geometry, material properties, reinforcing details, test configuration (including PDelta 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 i n Camarillo (2003), who used the force-displacement data for each column test to determine a displacement at failure. The procedure used by Camarillo is described in more detail in Section 3.2.  The Camarillo 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 l s o , 23 circular and 53 rectangular columns were removed because they did not fail according to the definition of failure established in Camarillo 2003, and presented again here i n Section 3.2.2.  For this study, an additional 60 circular and 64 rectangular columns were removed from the Camarillo database because they did not exhibit flexural failure. A s discussed in Chapter 1, the aim o f 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 w i l l not experience a shear failure. A detailed description of the failure classification procedure is presented in below.  A l s o , 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 No. of Notation  Description  Columns  R  Rectangular ties (around perimeter)  51  RI  Rectangular and Interlocking ties  29  RU  Rectangular ties and U-bars  3  RJ  Rectangular ties and J-hooks  17  RD  • Rectangular and Diagonal ties  35  RO  Rectangular and Octagonal ties  9  UJ  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  N o . o f Columns  Code  Shape  3.2  Circular  0  40  Octagonal  2  10  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 find the resulting net horizontal .force. To incorporate a P-A correction, the database is; organized into four types of lateral forcedisplacement histories, shown in Figure 3.1 , each with a specific form of correction. Berry et. al. define the categories as follows: p  P  F  K  b ) C a s e  II  P  e)  C a s e  I  III  It  I,  •1  d ) C a s e  i n : m  L_i_ IV  Figure 3.1 P-A correction cases (Berry et. al. (2004))  Case I: Force-deflection data provided by the researcher was in the form of effective force  (F ff) e  versus deflection (A) at L . meas  In this case, the net horizontal  force (FH) can be determined according to the following equation: F =F -PA/L H  eff  (3.1)  mem  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  L . meas  (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, F , to get the net horizontal force (FH). rep  F =F H  rep  +PL  Top  .  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, F , to get the net rep  horizontal force (F ). H  L + L top a = tan"  H  F  L +  (3.4)  L +L bor  lop  = P sin a  P  1  L  H  =F  rep  1  (3.5 )  (3.6)  - P 1  H  The contributions of the net horizontal force and the gravity (vertical) load to the total base moment can then be determined as follows: M =F L basa  H  K  + PA V  +L ^meets  (3.7) J  where:  48  Evaluation Database  F  - net horizontal force (Column Shear)  L  - shear span length  P  - gravity (vertical) load  A  - measured displacement at cantilever elevation  Ltop  - distance from elevation at which lateral force was applied to elevation at  H  L  meas  which gravity (vertical) load is applied. - elevation at which lateral column displacement was measured  The effective force can then be defined as:  F =M IL eff  3.2.2  (3.8)  base  Displacement at F a i l u r e  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 (A t-8o) exceeds pos  Awi.e., (A .so>Aso) post  the maximum displacement following another zero crossing (A . ) post zero  exceeds 95%  ofAgo i.e., (A st-zero p0  > 0.95 A so) the force corresponding to the maximum displacement after the zero crossing  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 (Af u) was determined as the maximum a  displacement that the column was subjected to prior to the data point iso-  80% F . #ff  500  post-zero  B o  LL. 15 CD  3=  80%  -10  0  10  F  e  20  Displacement, mm  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 o f 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 o f 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  / Shear failure  >  / \  //  L // 'V  /  /  T  i \  Flexure-shear failure  / 7" // / / !  \  1  v  i  I  V- l.o\  K  1  | rcsidual  /// !  |  1  '  i  1  •  i  2.0  Flexure failure  \  M c  ii  -1  • .  /  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 (F ff), is compared with the calculated force corresponding to a maximum concrete c  compressive strain o f 0.004 (Fo.otw)effective force,  Uf ji, a  The failure displacement ductility at the 8 0 %  is also considered. If the maximum effective force is less than 95  percent o f the ideal force or i f the failure displacement ductility was less than or equal to 2, the column was classified as shear-critical. flexure-shear-critical.  51  Otherwise, the column is classified as  Evaluation Database  Shear Damage Reported?  No  Yes  F  <0.95F  cff  or 0.004  M  fail  l a  <2  "  Flexure Failure  No  Yes  Shear Failure  Flexure-Shear Failure  Figure 3.4 Failure Classification Flowchart (Berry et. al (2004))  3.4  Range and Verification of Database Parameter Values  M a k i n g use o f the column test database, as apposed to conducting individual tests, is done to allow for a wider range o f parameter values than is typically available within a particular experimental study. In order to use the database to evaluate the confinement models described i n Chapter 2 with increased confidence, a comparative investigation was performed to verify that the parameter ranges i n 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 o f Record. Table 3.3 and Table 3.4 present the ranges for the parameters which significantly influence the flexural behaviour o f reinforced concrete columns, for both the typical column details and the experimental database. From these tables it can be seen that the range o f most o f the parameters covered by columns i n the database is compatible with the range o f 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) T y p . Details  Database Parameter  Min.  Max.  Avg.  Min.  Max.  Avg.  fy. ( M P a )  255  1424  549.4  414  414  414.  fc ( M P a )  20.2  118.0  60.4  28-  72  57 -  s (mm)  25.4  228.6  77.5  76.2  114.3  94  0.11  3.43  1.14  0.90  1.94  1.46  1.01  6.03  2.37  1.29  4.12  2.11  23226  360000  92451  209032  929030  588386  0.0  0.80  0.28  0.33  0.71  0.48  Parea ( A  / sh )  s h  c  (%)  Plong(%)  A (mm ) 2  g  P/A f g  '  •  c  .  ible 3.4 Circular column parameter ranges (database and typical column T y p . Details  Database Parameter  Min.  Max.  Avg.  Min.  Max.  Avg.  fyh ( M P a )  280  1000  473.0  414  414  414  f (MPa)  22.0  90.0  36.3  34  69  53  s (mm)  8.9  305.0  55.0  63.5  101.6  78:3  0.10  3.13  1.00  1.15  2.76  2.01  Plong (%)  0.75  5.58  2.31  3.68  2.03  A (mm )  18146  1814600  211312  164173  585753  342196  P/A f  0.0  0.70  0.17  0.01  0.58  0.28  c  p  v o l  (4A /sh )(%) s p  2  g  g  c  c  1.19  For the rectangular columns, the most glaring discrepancy is found i n 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 i n the values for area transverse demonstrates  that  the section  dimensions  o f the columns  reinforcement  ratio  i n the database are  proportionally scaled and the discrepancy i n A is insignificant. F o r the circular column g  database, the same discrepancy is found for the gross area. Table 3.4 also shows that the volumetric ratio o f 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 w i l l become more apparent in Chapter 4 when they 1  1 0.9  0.9  0.8  0.8  0.7  0.7  0.6 0.5 CL  • • ••  0.6  ••  : /•  <:  ••  0.5 0.4  0.4  0.3  0.3  •• •  0.2  0.2  0.1  0.1 00  ro  •  5  •  10  0  15  1  0  5  10  Drift Ratio  Drift Ratio  Figure 3.5 Axial Load ratio versus drift ratio (A) rectangular database (B) circular database  54  15  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  2.5  1.5  •• •  •• • • %•• •  0.5  5  5  10  Figure 3.6 p  10  Drift Ratio  Drift Ratio arca  and p  vo  i  versus drift ratio  (A) rectangular database (B) circular database  55  15  Evaluation Database  0.2  0.18 0.3  0.16 0.25  0.14 •  #  0.12  0.2  0.1  0.15  0.1  •» • •  • •  • •  0.08  • •• ••  0.06  -4A.  *:  • •  0.04  0.05 0.02  10  5  0  15  0  10  5  15  Drift Ratio  Drift Ratio  Figure 3.7 f ' / f versus drift ratio c  yt  (A) rectangular database (B) circular database  2 1.9 1.8 1.7 1.6  <° <  1.5 1.4 1.3 1.2 1.1  5  1  10  5  10  Drift Ratio  Drift Ratio  Figure 3.8 A / A i, versus drift ratio g  c  (A) rectangular database (B) circular database  56  15  Evaluation Database  10 r  10  9 -  9  8 -  8  7 -  7  6 -  CD  5 4 -  • • • •• ••••*** *  6  a  5  •• •  4 3  3  * * ** 2  • •• • •  ittmt—  • • • •  2  •  1  1  0  0 5  10  5  15  10  15  Drift Ratio  Drift Ratio  Figure 3.9 B / L and D / L versus drift ratio (A) rectangular database ( B ) circular database  •• • • • •• •• • 5  10  5  15  Drift Ratio  Figure 3 . 1 0 pi  10  Drift Ratio  ong  versus drift ratio  (A) rectangular database ( B ) circular database  57  15  4  CONFINEMENT MODEL EVALUATIONS  This chapter presents the procedure and results o f the evaluation techniques adopted to analyze the performance o f each confinement model. In Chapter 1, it was shown that the amount and configuration o f transverse reinforcement is the most important parameter i n determining the drift capacity o f a reinforced concrete column, and the evaluation approach taken here makes use o f this conclusion. The interpretation o f the results and the ensuing recommendations w i 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 i n Chapter 3. T w o evaluation techniques were developed to investigate the performance o f the models. The procedure and results for the first o f these two techniques, a scatter plot evaluation, is outlined here and the second technique, a fragility curve evaluation, is outlined i n the following section.  4.1.1.1 Evaluation Procedure The amount o f 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 o f transverse reinforcement provided. W i t h these values known, it is possible to determine i f each column i n the database had sufficient transverse reinforcement to meet a particular model or code equation.  Once the amount o f transverse steel was determined, a performance criterion had to be selected. A s seen i n 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, if 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. Ductility 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 limit 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 2 0 % loss in lateral strength (described in Chapter 3) versus the confining steel requirement ratio (A h_providcd / Ashmodci)S  A h_providcd S  /  The figure is divided into quadrants with a vertical dashed line at  A h model = s  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 2 0 % loss in  59  Confinement Model Evaluations  10  1 4  2  0  0  2  3 A  Actual  /A,  4  5  6  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:  o) =  # of columns that satisfy model A N D achieve a drift ratio < 2.5% # of columns that satisfy model  In terms of the quadrant numbers:  A(%)  (4.1)  ^  = — ^ — Q1 + Q 2  ( 4.2  )  The second statistic was selected to indicate the degree of conservatism inherent in the model: z>(%)  =  # of columns that do not satisfy model A N D achieve a drift ratio < 2.5%  ( 4.3  )  # of columns that do not satisfy model  B(%)  =  Q  (4.4)  4  Q3 +  Q4  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 o f t h e 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 o f A C I Equations 21-3 and 21-4, and does not include the spacing requirements o f A C I 318-05 clause 21.4.4.2. This issue is discussed in section 4.1.3  While properly observing the performance o f the A C I model is done best i n a relative sense with direct comparison to the other models investigated i n this study (see Chapter 5), it is prudent to first fully understand the data presented i n Figure 4.2. A l l columns which satisfy section 21.4.4.1 o f A C I are plotted with a lightly shaded square marker, while those which fail the area o f confining steel requirements are plotted with a dark shaded diamond marker. This is done such that i n 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  • • fi  d q co  on  0  5  *=•  S  •  •  6  4  w  •  • •  • • i •  •  CP  a  •  •  • *  • 0.5  2.5  1.5 A  Satisfies ACI 21.4.4.1 Does Not Satisfy ACI 21.4.4.1 3.5  /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  92  21  9~.  23  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 i n 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 ') versus axial c  load ratio ( P / A f ' ) for the columns found in quadrant 2 and 3 in Figure 4.2. A s seen in g  c  Figure 4.3, all of the quadrant 2 columns for the A C I s c a t t e r 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 well documented i n 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 o f 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  120 r • *  Q2 Columns Q3 Columns  100  0  ^ • •  0  80 CO Q.  + 4  •  ^  60  •  401  0  •  •  20  1 0.1  I  0  1 0.2  1 0.3  1 0.4  ' 0.5  ' 0.6  ' 0.7  -  1 0.8  ' 0.9  1  Axial Load Ratio (P/A f ' ) v  g c '  Figure 4.3 f ' versus Axial Load Ratio for columns in quadrants 2 and 3 of ACI c  rectangular scatter plot  4.1.1.3 Assessment of Codes and Proposed Models The scatter plot evaluation o f 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 i n Equation 2.5 ( A C I Equation 21-4) was included in the evaluation o f the other models. This was done only to ensure that the effect o f 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 w i 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 o f the current A C I equation, can be determined. Note, the current C S A code applies the same minimum but is not included i n the evaluation o f the C S A model as this minimum is not included i n the P L 0 5 model on which the C S A code is based.  64  Confinement Model Evaluations  50  r  45  m  | B  c  40 35 30 55 25 20 15  Ii  10 5 0  ACI  CSA  PP92  SR02  W S S 9 9 BBM05 S K B S W Z P L P 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 S K 9 7 , B S 9 8 , W Z P 9 4 , and L P 0 4 are not shown. A s 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.  T o 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. A g a i n , scatter plots for S K 9 7 , B S 9 8 , W Z P 9 4 , and L P 0 4 are not shown. A l l scatter plots, including those presented here, are included in Appendix D.  A s shown in the figures, only the SR02 and W S S 9 9 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 W S S 9 9 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 C S A  Figure 4.5 C S A scatter plot (rectangular columns)  66  Confinement Model Evaluations  10 9  • 4 •  £ o  4  6 [  'ro or  5[  S  4[  • •  03  •  • •  *7  •  • •  •  -!--r«—x  •  • ^  0.5  2.5  1.5 A  1  Satisfies ACI 21.4.4.1 Does Not Satisfy ACI 21.4.4.1 3.5  /A  sh Provided  sh NZS  Figure 4 . 6 NZS scatter plot (rectangular columns) 10r 9  •  8 7  g o  •  6-  ro 5  5  • • * •  0 D  4  • 3  -A_L_>  T  2 • #  1 0  2.5  1.5  0.5  sh Provided P P 9 2  3.5  IA  A  Figure 4 . 7  Satisfies ACI 21.4.4.1 Does Not Satisfy ACI 21.4.4.1  sh PP92  scatter plot (rectangular columns)  67  Confinement Model Evaluations  10r  . . 9 -  •  •  8 -  • •  7  g ,o co  OC  S  v •  6-  4  4  3 2 1 0  4  •  5 •  44 •*  • •  • il* —V"It*" •  •  •  •  ••fi  •  •  •  S a t i s f i e s  +  D o e s  A C I 2 1 . 4 . 4 . 1  N o t S a t i s f y A C I  2.5  1.5 A  0.5  •  2 1 . 4 . 4 . 1  3.5  /A  sh Provided  sh SR02  Figure 4.8 SR02 scatter plot (rectangular columns)  IP  4  •  •  • •  •  •  4 ••  •  •  0.5  rl  •  S a t i s f i e s  4  D o e s  2.5  1.5 A  A C I 2 1 . 4 . 4 . 1  N o t S a t i s f y A C I  2 1 . 4 . 4 . 1  3.5  /A  sh Provided  sh WSS99  Figure 4.9 WSS99 scatter plot (rectangular columns)  68  Confinement Model Evaluations  • #  A  Satisfies ACI 21.4.4.1 Does Not Satisfy ACI 21.4.4.1  /A sh Provided.  sh BBM05  Figure 4.10 BBM05 scatter plot (rectangular columns) 10  "1 to  •  9  • 0  d  6  Q 5[ or 'ro  £  • CO  • i 4 CI^V 4 * #!  41  i  •  •  •  • ^ 0.5  Satisfies ACI 21.4.4.1 . Does Not Satisfy ACI 21.4.4.1  2.5  1.5 A  3.5  /A sh Provided  sh S K B S  Figure 4.11 SKBS scatter plot (rectangular columns)  69  Confinement Model Evaluations  • ^  A  Satisfies ACI 21.4.4.1 Does Not Satisfy ACI 21.4.4.1  /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  Ql  Q2  Q3  Q4  CSA  61  2  54  28  PP92  '63  5  52  25  SR02  73  12  42  18  WSS99  79  10  36  20  BBM05  72  6  43  24  SKBS  22  2  93  28  WZPLP  28  4  87  26  NZS  42  7  73  23  Using Equations 4.1, 4.3, 4.5 and the data provided i n Table 4.3, Figure 4.13 displays the A , B and C statistics for each model including the A C I values previously given i n 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 n  30 25 '20 15 10 5 0 ACI  CSA  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. A s 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 W S S 9 9 , 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 W S S 9 9 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. A g a i n , 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 o f 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 o f 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 o f columns that did not reach a given drift level. Using this procedure at a drift ratio o f 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 o f 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<S \A la!&el  (4.6)  /A >l)  prmicleci  mode!  The process was repeated again for all the columns that did not satisfy the confining steel requirements o f the model. For each model, a B fragility curve was generated to describe the probability o f a column not reaching a given drift limit i f it does not satisfy the model. Again, using this procedure at a drift ratio o f 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 < S  , |A  laTge  prmldcd  IA  moiel  < 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 o f 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 o f 0% and, to avoid overconservatism, the B value should be maximized. The relationship between these two statistics w i 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 i n 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 well. Reading the curves at a drift ratio o f 2.5% produces values very close to the A , B and C statistic given in section 4.1.1.2.  0.9 0.8  o a  o  0.7 0.6 <  0.5 o  0.4  * J  0.3  o  0.2 0.1  0  1  2  3  4  5  6  7  8  Drift Ratio  Figure 4.14 Rectangular A fragility curve for ACI  73  9  10  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 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 w i 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 all the models (including A C I ) 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 S K 9 7 , B S 9 8 , W Z P 9 4 and L P 0 4 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 o f the scatter plot evaluation and suggest that a replacement model be proposed and that the performance o f the models consistent throughout the range o f 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 A C I ) 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 A s 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 . A g a i n 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. A g a i n , 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%.  A g a i n , 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  79  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 o f confining steel for B B M 0 5 , however as stated in Chapter 2, the model was derived for limiting drifts o f 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 o f 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 o f the SR02 model, and no further consideration for the model is needed. Note, the A C I minimum equation was not included i n 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  A s was explained in Chapter 2, the spacing requirements o f 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 o f 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 o f scaled tests. The range o f 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 o f the columns, an accurate evaluation o f this spacing limit is not possible. Further discussion of this issue is presented i n Chapter 5.  10  •  9  • 0  d  6  'to  5  • • •  *±  E  •  • •  •  •  •  4  •  fi in a  o  LT.  •  •  3  •  2  1 1 0.5  P-cP  • 1.5  2  • ^  Satisfies ACI 21.4.4.1 Does Not Satisfy ACI 21.4.4.1 2.5  3.5  D/4S  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 o f the data points which fall into quadrants 2 and 3 for Figure 4.24. Unlike 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,  TT  4  • 4  •  Q2 Columns Q3 Columns  u  100  0 80  o  •  + n  CD  Q.  60  •  •  40i  •  •  •  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  go'  Figure 4.26 f ' vs. axial load ratio for Q2 and Q3 columns for H/4 spacing limit c  Finally, it is important to address how often each A C I confinement requirement governs the design o f columns. Table 4.5 shows the number o f instances where each requirement governs the spacing o f the confinement reinforcement for the 145 rectangular columns.  The confinement area requirements o f A C I 318 are rearranged and expressed as a spacing requirement (i.e. for a known area and arrangement o f transverse bars).  A sh  s= 0.3/r  fc  fyh  . (4.8)  A, y.A i, c  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 i n A C I section 21.4.4.2 are s < Q.25D and s<6d . b  A g a i n , the effect o f scaling the test  specimens renders the spacing limit given by Equation 2.12 ( A C I E q 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  E q 4.8  124  The data i n Table 4.5 shows that for the vast majority o f reinforced concrete columns i n the database, the area requirement dominates the spacing o f the transverse steel. While not included i n the table above, one would expect that for full scale columns the spacing limit given by Equation 2.12 would often govern for large columns with closely spaced longitudinal reinforcement, and the number o f instances i n 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 o f section 21.4.4.1 o f A C I 318-05, 8 do not satisfy the spacing requirement o f 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 . (4.9)  sh  L  s=  A  0.2k k  g  D  " P A  -"•ch  s=•  J c  f'  f J yh  h  c  A sh A  I.Q-p,mf '  A  3-3  g  e  u  (4.10)  P ^ A  -0.0065  The spacing limits for C S A are the same as those for A C I (Eq 2.10 and E q 2.11), and for N Z S the spacing limits are given as  .  85  Confinement Model Evaluations  (4.11)  s<-D 3  (4.12)  s<lOd  b  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  governed C S A  governed N Z S  E q 2.10/4.11  44  70  E q 2 . 1 1 / 4.12  2  5  Eq 4.9/4.10  99  70  Spacing limit  4.1.4  Maximum Recorded Drifts  A s discussed in Chapter 3, the failure drift of the columns was assumed to occur once the column demonstrated a 2 0 % loss in lateral strength. However, while this assumption is valid 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  ACI  CSA  PP92  u  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 A C I 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  10  Drift Ratio  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 o f 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 w i 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 o f the rectangular column evaluation. The only difference here is that the x axis values are given  88  Confinement Model Evaluations  in terms o f volumetric transverse reinforcement ratios rather than i n terms o f area o f transverse steel. This is done in keeping with the manner i n 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. A g a i n , a l l columns which satisfy the density o f confining steel requirements o f A C I are plotted with a lightly shaded square marker, while those which fail the density o f confining steel requirements are plotted with a dark shaded diamond marker. 15  10  •  •  •  •  •  •  • • • f  03  •  El  • TL  or  • • !  •  4•  •  • • +  0.5  1.5  2  2.5  3  Satisfies ACI 21.4.4.1 Does Not Satisfy ACI 21.4.4.1 3.5  P Provided ' PACI  Figure 4.29 ACI scatter plot (circular columns)  The figure shows the following data distribution:  89  4.5  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 o f 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 likely due to the difference in the typical axial load ratios found i n 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. A s 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 f ' versus P / A f ' for the 23 columns i n quadrant 3, and c  g  c  shows only that 3 columns have an axial load above 0.2. Similar to the observations o f N  the corresponding rectangular columns, the expectation is that the remaining models w i l l have fewer columns in quadrant 3 since each o f the models incorporates axial load level into the confining steel requirement.  CO  Q.  Axial Load Ratio (P/A f ' ) v  gc '  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 ( A C I 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, all the  models provided a statistical improvement over the A C I model, although not as  91  Confinement Model Evaluations  50  WE A I |B  45  mm c  40 35 30 25 20 15 10 5 0  ACI  I I I 1 1 1 1 in  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 o f the A C I minimum equation had a significant effect on the other models in that it governed the design for a large number o f columns for each model, and therefore caused the performance o f the models to become very similar. These two conclusions demonstrate that an evaluation o f 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 S K 9 7 , B S 9 8 , W Z P 9 4 and L P 0 4 models were not included in the evaluation in favor o f 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, W Z P 9 4 , L P 0 4 and W Z P L P models, columns with very low axial load required very small amounts o f 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 i n conjunction with model's expression, exactly as was done to determine the statistics given in Figure 4.31. Including this limit i n the evaluation is not a true representation o f the model alone, but the nature o f 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 o f these models are determined to be the most appropriate model, the appropriateness o f this minimum w i 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 i n quadrant 3, the most significant change belonging to SR02 which had 4 columns in quadrant 3. Further discussion o f the scatter plots w i l l be given where relevant i n the presentation and justification o f the final recommendations (Chapter 5). 15  •  •  10  •  • •  4  CD  •  • 4  •  *  0  •  •  tb •  • •  4  6  • 4  1.5  2  a •  .__  • 0.5  P U3  •n  2.5  3  Satisfies ACI 21.4.4.1 Does Not Satisfy ACI 21.4.4.1  3.5  Provided ^ CSA P  Figure 4.32 CSA scatter plot (circular columns)  93  4.5  0  Confinement Model Evaluations  •15r  •  10  •  • •  .0 co  01  •  !•  •  EF  • • I  4o •  0  •  1.5  0.5  2  •  Satisfies ACI 21.4.4.1  4  Does Not Satisfy ACI 21.4.4.1  2.5  3  3.5  4.5  P Provided ' N Z S P  Figure 4.33 NZS scatter plot (circular columns) 15  •  R  •  •  10  •  ! •  •  0  CO  • •• •  OH Q  ^  0  0.5  1.5  2  2.5  •  Satisfies ACI 21.4.4.1  4  Does Not Satisfy ACI 21.4.4.1  3  3.5  Pprovided ' PpP92  Figure 4.34 PP92 scatter plot (circular columns) 94  4.5  Confinement Model Evaluations  15r  •  0 10  • • •  o "co  •  • •  • + 0  0.5  2  1.5  1  •  CP  •  •  4:  •  • •  2.5  3  Satisfies ACI 21.4.4.1 Does Not Satisfy ACI 21.4.4.1 3.5  4  4.5  5  P Provided ' PsR02  Figure 4.35 SR02 scatter plot (circular columns) 15,  •  •  4  •  10  •  • co Dd  •• 4  D  •  fi  •  •  • • • '  4 JL_ • ^ 0  0.5  1  1.5  2  2.5  3  Satisfies ACI 21.4.4.1 Does Not Satisfy ACI 21.4.4.1 3.5  4  4.5  P Provided ' PBBM05  Figure 4.36 BBM05 scatter plot (circular columns)  95  5  Confinement Model Evaluations  •  •  •  •  •  • • t>*U  i  Q  •  B  •  •  • _  | 4 •  E-  fc  !  • 4 1.5  0.5  2  2.5  Satisfies ACI 21.4.4.1 Does Not Satisfy ACI 21.4.4.1 3.5  3  4.5  Pprovided ' S K B S P  Figure 4.37 SKBS scatter plot (circular columns)  •  •  > j°  • In • ,• J  £>-  •  4n 4  •  B  •  U • 4  0.5  1.5  2.5  Satisfies ACI 21.4.4.1 Does Not Satisfy ACI 21.4.4.1 3.5  4.5  Pprovided ^ PwZPLP  Figure 4.38 WZPLP scatter plot (circular columns)  96  Confinement Model Evaluations  The distribution o f 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  Qi  Q2  Q3  Q4  CSA  43  0  5  2  PP92  26  . 0  22  2  SR02  44  0  4  2  BBM05  39  0  9  ' 2.  SKBS  39  0  9  2  WZPLP  28  0  20  2  NZS  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. A s 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  1  A  LZ1 B  45 40 35 30 25 20 15 10 5 0  ACI  I  CSA PP92  SR02  hi  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 A C I along with the data which was used to generate the distributions. The circular column C circular statistic fragility curve for A C I 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  u. Q  o  o.o6 y 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 o f each model without the minimum w i 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 S K 9 7 , B S 9 8 , W Z P 9 4 and L P 0 4 models have been removed i n favor o f 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. A g a i n the  Drift Ratio  Figure 4.43 Circular A fragility curve all models (with ACI minimum)  101  Confinement Model Evaluations  1  C S A  0.9 0.8  ACI — •  h  PP92  —  S R 0 2 BBM05  -  -  S K B S W Z P L P  0.7  N Z S  0.6 CO 0.5  0.4 0.3 0.2 0.1 0 0  10  15  Drift Ratio  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 l s o , 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 P L 0 5 model being evaluated. ' Again, the S K 9 7 , B S 9 8 , W Z P 9 4 and L P 0 4 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. While 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. A s 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 o f 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 o f 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  Confinement Model Evaluations 4.2.2.4  Special Considerations for SR02  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.  — -  5=2.5%  < 0.5  1.5  with corresponding 8  2.5  3.5  4.5  m 0.5  O 0.5  3.5 Drift Ratio Figure 4.49 C i r c u l a r SR02 fragility curve comparison  106  5.5  • 4.2.3  __  Confinement Model Evaluations  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  ! • I L J 1 J  o  1  B B-  •  • •  • S  • n  • n • 4  D/4s  Figure 4.50 Circular scatter plot for one quarter minimum dimension spacing limit  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).  107  Confinement Model Evaluations  4 A  >  ,  f'  (4.13)  1  yh  V  ch  A  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 A C I 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 A C I 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 A C I confining steel area requirement for circular columns.  4.2.3.2 Assessment of CSA and NZS The area requirement for the C S A and NZS models were rearranged and expressed as a spacing limit as follows: AA  s=  -\r~  '  yh  108  (4-14)  Confinement Model Evaluations  4A*  s = —, f  A \.0-p m g  A*  t  f> c  2.4  P P  , \ 0.0084/r  f 0f,'A yh  (4.15)  A  gJ  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  4.2.4  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  .  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 2 0 % 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 2 0 % 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 2 0 % loss of lateral strength.  The drifts at 2 0 % loss in  strengths as well as the maximum recorded drifts can be found in Appendix A .  110  5  S E L E C T I O N  5.1  O F C O N F I N E M E N T  M O D E L  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 l e v e l o f 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 C S A 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  10  9 8  •  Satisfies ACI 21.4.4.1  •  Satisfies ACI 21.4.4.1  4  Does Not Satisfy ACI 21.4.4.1  4  Does Not Satisfy ACI 21.4.4.1  9  a)  8  b)  7  ^  6  •  g  ro 5 §  •  o 're • 5 OH  4  «=:  £  3  4  ••  2  9  1 0  A  sh Provided  /A  A  sh ACI  sh Provided  IA  '  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 2 0 % 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 C S A 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 A C I 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  Piong  Parea  (Ag)  (%)  (%)  1.30173  (mm ) 2  15 106  5.1.3  Watson and Park 1989, No. 7  42  0.7  1600  160000  1.51  Saatcioglu and Ozcebe 1989, U4  32  0.15  1000  122500  3.21  .1.0908  Drift Ratio (%)  1.17  8.99  Fragility Curve Evaluation  The fragility curves presented in Chapter 4 w i l l be compared for the models which were not eliminated in the scatter plot evaluation. The fragility curves w i l l be examined within the range o f meaningful drifts. A s discussed i n Chapter 4, the curves provide probability data up to the maximum drift ratio observed in the database (i.e. a drift ratio o f 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 w i l l be addressed in the evaluation.  It should be noted that the models which do no offer an  improved level of safety w i 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. A n y model which is drastically different than current design practice w i 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, w i 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 w i 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 W S S 9 9 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 i n Figure 5.1 is not demonstrated. While the number of data points in quadrant 1 for both the W S S 9 9 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 W S S 9 9 , 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  Selection of Confinement Model 5.1.6  Fragility Curve Evaluation  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 C S A  0.4  PP92 BBM05  0.35  W Z P L P N Z S  i  0.3  /  0.25 0.2 0.15 0.1 0.05  0  0.5  1.5  2  2.5  Drift Ratio  Figure 5.3 A fragility curves  117  3.5  /  Selection of Confinement Model  0.8 r •- CSA — PP92 BBM05 WZPLP NZS  0.7  0.6  A s  0.5  CQ 0.4 0.3  0.2  0.1  0  0.5  1.5  2  2.5  3.5  Drift Ratio  Figure 5.4 B fragility curves 0.5 CSA PP92 BBM05 WZPLP NZS  0.45 0.4  0.35 0.3 O  0.25 0.2  0.15 0.1  0.05 0  0  0.5  1.5  2  2.5  Drift Ratio  Figure 5.5 C fragility curves  1 18  3.5  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 o f suitable alternatives for the A C I model.  5.1.7  Comparison of Expressions •  The form o f the expression for each model is an important consideration in addition to its statistical performance. The expressions for the confinement, requirements o f each model were presented i n Chapter 2. Review o f 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 o f B B M 0 5 . If B B M 0 5 were adopted as a replacement for A C I , the form o f the expression would be a drastic departure from its current form. Perhaps more importantly, the form o f the B B M 0 5 is much less intuitive and its derivation is hidden. Such a departure from the current form o f the expression would undoubtedly be warranted i f the performance o f 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 o f potential replacement models.  5.1.8  Requirements of Models  The details o f 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 o f confining steel ( A h ) required for the example column for the C S A and PP92 models. For reference, the S  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 o f 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 o f confining steel at an axial load ratio o f approximately 0.3. Above an axial  119  Selection of Confinement Model load ratio o f 0 . 3 , C S A and limit, C S A and  PP92  require more transverse reinforcement, while below this  require less transverse reinforcement.  PP92  Figure 5 . 7 shows the confinement spacing requirements for the typical column resulting from the requirements o f the C S A and  models. A g a i n the spacing requirement is  PP92  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  PP92  models is not linear. The required maximum spacing  increases dramatically as the axial load ratio approaches zero. This suggests that a minimum level o f confinement w i l l have to be applied in connection with the requirement imposed by either C S A or  PP92.  0.5  •••• CSA —  0.45 h  74"  —  m  0.4  CD  0.35 -  <°  0.3 -  t±±±  \  PP92 ACI Eqn 21-3 ACI Eqn 21-4  Cover: 40mm „ Longitudinal bars: #9 24 Transverse bars: #5  0.25 O -O  V) sz  <"  0.2 0.15 0.1 0.05 0 ••  ..«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  120  Selection of Confinement Model  1500 CSA PP92 0.25H ACI Eqn 21-3 ACI Eqn 21-4  <  1000  24"  .C  2 4  „  Cover: 40mm Longitudinal bars: #9 Transverse bars: #5  500  in  0.1  0.2  0.3  0.4  0.5  0.6  0.7  0.8  0.9  P/P F i g u r e 5.7 Confinement spacing requirements for range of axial load ratios  Conclusion a n d Recommendation  5.1.9  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 (A /A h)(f '/fyh) and both have a term which includes a linear variation with axial g  c  c  load. The main difference between the two expressions is that the C S A 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. T o 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 w i 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 i n Figure 4.22 shows that the spacing limit impacts a number o f 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 o f the minimum dimension spacing limit can be included in the minimum confinement level. The spacing limit o f 4 to 6 inches given by Equation 2.12 ( A C I 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 •  = 0.2k„k  c°  r  s  P c  A  f'  A  f  ch  yh  where (a) k = P/Po p  (b) k„. = ni/(n,-2)  (c) k shall not be taken as less than 0.2 p  (d) s shall not exceed 6d ,one quarter of the minimum member dimension or s c  b  x  defined as: s <4+  x  x  V  3  -  J  where s shall not exceed 6 inches and need not be taken less than 4 inches and x  h is the maximum horizontal spacing of hoop or crosstie legs on all faces of x  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 A C I 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  CSA SR02 BBM05 SKBS NZS  0.05 <  0.04 0.03 0.02 0.01 0  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 o f 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 o f 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 w h y the SR02 model had the largest number o f 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 o f columns moving from quadrant 4 into quadrant 2, the opposite of the desired movement. G i v e n that the circular column database had so few columns with low drifts, the effect was not seen here. More tests o f 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 o f circular  127  Selection of Confinement Model columns at higher levels o f 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 o f the SR02 model was underestimated at these higher drift ratios using a constant input variable drift ratio of 2.5%. For the purposes o f 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 o f both 2.5% and 3%. The performance o f the SR02 model is very similar for the two levels input o f drift ratios. With an input drift ratio o f 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  O  10  o  2.5%  O  3%  o  0  O •! O  O  E  CP  oo  or  m  O  B  ^  v  0  • f O  0  DO  Provided  •  ft  u  B  d* > o o  SR02  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 C S A and SR02 models. The limiting value for P/P of 0.2 for the SR02 0  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 C S A 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 —--  Cover: 40mm Longitudinal bars: #9 Transverse bars: #5 <  C T  CSA SR02 SKBS 0.25H ACI Eqn 21-2 ACI Eqn 10-5  1000  500  0.1  0.2  0.3  0.4  0.6  0.5  0.7  0.8  P/P  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 C S A 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 C S A and SR02 models and presented in Chapter 2 shows that significant differences are apparent between the two expressions. The ratio of A / A h is g  c  not considered by C S A 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 / A h ratio equal to approximately 1.6. g  C  The SR02 model also imposes a minimum value for A /A h of 1.3. The ratio of gross g  130  C  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. Until 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.  A g a i n 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:  fc  /V=0.84*,  fyh  AAb  where (a) p = s  (b) k = p  ^ch  s„h„ P/Po  (c) k shall not be taken as less that 0.2 r  p  (d) Ag/A h shall not be taken as less than 1.3 c  (e) s shall not exceed 6db or one quarter of the minimum member dimension c  5.4 Final Recommendations vs. ACI 5.4.1  Comparison figure  The figure below gives a comparison of the final  area requirements  recommendations with the current area requirements in A C I 318-05.  of the  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  30"  Cover: 40mm Longitudinal bars: #9 30" Transverse bars: #5 f = 4 1 4 M P a , f = 55 MPa yt  10  Circular R e c o m m e n d a t i o n Rectangular Recommendation C i r c u l a r ACI R e c t a n g u l a r ACI  c  30" Cover: 40mm Longitudinal bars: #9 Transverse bars: #5 f = 4 1 4 M P a , f = 55 M P a  o >  y t  c  CL  0.1  0.2  0.3  0.4  0.5  0.6  0.7  0.8  P/P  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 N e w 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 w i 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.  T w o 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 l s o 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 l s o , 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 o f one quarter cross sectional dimension was also evaluated. The performance  o f 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 o f 'unconservative' columns. While the spacing limits do not often govern the design o f confining steel, it is recommended that the spacing limits o f the current A C I code remain i n place.  6.2 Recommendations The following is the recommendations o f 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 o f rectangular hoop reinforcement shall not be less than:  A  A  cK  P  s  A  ch  f '  f  yh  where k = P / Po k = n[/(m-2) k shall not be taken as less than 0.2 p  n  p  s shall not exceed 6dh ,one quarter of the minimum member dimension or s c  x  defined as:  s <4 +  ' 1 4 - O V  3  where s shall not exceed 6 inches and need not be taken less than 4 inches and x  h is the maximum horizontal spacing o f hoop or crosstie legs on all faces o f x  the column.  136  Summary and Conclusions  21.4.4.2 Columns confined with circular or spiral hoops The volumetric ratio o f spiral or circular hoop reinforcement shall not be less than:  P = 0.84*, s  -1 fyh  *ch  where  Ps  _ 4Ab cK  s  P/Po  k shall not be taken as less that 0.2 A g / A h shall not be taken as less than 1.3 s shall not exceed 6d or one quarter o f the minimum member dimension p  c  c  b  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 o f confidence. However, to supplement the existing database, further testing is required. This was apparent for the circular column database used i n this study where few columns were tested with high axial load ratios, and consequentially few columns exhibited flexural failure at low levels o f drift. It is recommended that future investigations o f flexural failure in circular columns for building structures be undertaken with appropriate levels of axial load.  It is stated in the commentary o f 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 o f required transverse reinforcement as a function o f  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 w i 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, " B u i l d i n g Code Requirements for Structural Concrete", ACI 318-05, Farmington H i l l s , U S A . 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S . , Hanson, N.W., Musser, D.W., and Corley, W . G . , 1988, "Effects o f Transverse Reinforcement on Seismic Performance o f Columns - A Partial Parametric Investigation", Project No. CR-9617, Construction Technology Laboratories, Skokie, U S A . Bayrak O., Sheikh, S., 1998, "Confinement Reinforcement Design Considerations for Ductile H S C Columns", Journal of Structural Engineering, Vol.124, N o . 9 , pp. 999-1010 Bayrak, O., Sheikh, S., 1996, "Confinement Steel Requirements for High Strength Concrete Columns", Paper No. 463, 11 World Conference on Earthquake Engineering, M e x i c o . th  Bayrak, O., Sheikh, S., 2002, "Design of Rectangular H S C Columns for Ductility", University o f Toronto, Canada. 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Ohno, T., and Nishioka, T., 1984, " A n Experimental Study on Energy Absorption Capacity of Columns in Reinforced Concrete Structures", Proceedings of the JSCE, Structural Engineering/Earthquake Engineering, V o l . 1, N o 2, pp. 137147. Paulay, T., and Priestly, M . J . N . , 1992, "Seismic Design o f Reinforced Concrete and Masonry Buildings", John W i l e y & Sons Inc. N e w Y o r k , U S A . Paultre, P., Legeron, F., and Mongeau, D., 2001, "Influence o f Concrete Strength and Transverse Reinforcement Y i e l d Strength on Behavior o f High-Strength Concrete Columns", ACI Structural Journal, V o l . 98, N o . 4, pp. 490-501. Paultre, P., Legeron, F., 2005, "Confinement Reinforcement Design for Reinforced Concrete Columns", Paper accepted for publication in A S C E Structural Journal 2007.  142  References  Pujol, S., 2002, "Drift Capacity o f Reinforced Concrete Columns Subjected to Displacement Reversals", Thesis, Purdue University, U S A .  R a z v i , S.R., and Saatcioglu, M . , 1999, "Analysis and Design of Concrete Columns for Confinement", Earthquake Spectra, V o l . 15, N o . 4, pp. 791-811.  Richart, F.E., Brandtzaeg, A . , and B r o w n R.L., 1928, " A Study of the failure o f concrete under combined compressive stresses" Bulletin 185, Univ. of Illinois Engineering Experimental Station, Champaign, U S A . Saatciolgu, M . , 1991, "Deformability of Reinforced Concrete Columns", ACI SP-127, Earthquake-Resistant Concrete Structures Inelastic Response and Design, American Concrete Institute, pp. 421-452. Saatcioglu, M . , and Baingo, D., 1999, "Circular High-Strength Concrete Columns Under Simulated Seismic Loading", Journal of Structural Engineering, V o l . 125, N o . 3, pp. 272-280. Saatcioglu, M . , and Grira, M . , 1999, "Confinement o f Reinforced Concrete Columns with Welded Reinforcement G r i d s " , ACI Structural Journal, V o l . 96, N o . 1, pp. 29-39. Saatcioglu, M . , and Ozcebe, G . , 1989, "Response o f Reinforced Concrete Columns to Simulated Seismic Loading", ACI Structural Journal, V o l . 86, N o . 1, pp. 3-12. Saatcioglu, M . , R a z v i , S.R., 2002, "Displacement-Based Design of Reinforced Concrete Columns for Confinement", ACI Structural Journal, V o l . 99, N o . l , pp. 3-11. Sakai, Y . , H i b i , J., Otani, S., and Aoyama, H., 1990, "Experimental Study on Flexural Behavior o f Reinforced Concrete Columns Using High-Strength Concrete", Transactions of the Japan Concrete Institute, V o l . 12, pp. 323-330. Sheikh, S.A., and Khoury S.S., 1997, " A Performance-Based Approach for the Design o f Confining Steel i n Tied Columns", ACI Structural Journal, V o l . 9 4 , No.4, pp. 421-432. Sheikh, S.A., and Uzumeri, S . M . , 1980, "Strength and Ductility o f Tied Concrete Columns", Journal of the Structural Division, ASCE, V o l . 106, N o . 5, pp. 10791102. Sheikh, S.A., and Uzumeri, S . M . , 1982, "Analytical M o d e l for Concrete Confinement in Tied Columns", Journal of the Structural Division, ASCE, V o l . 108, N o . ST12, pp. 2703-2722  143  References Soesianawati, M.T., Park, R., and Priestley, M . J . N . , 1986, "Limited Ductility Design o f Reinforced Concrete Columns", Report 86-10, Department o f C i v i l Engineering, University o f Canterbury, Christchurch, N e w Zealand. Standards Association of N e w Zealand, 2006, "Concrete Design Standard, NZS3101:2006, Part 1" and "Commentary on the Concrete Design Standard, N Z S 3101:2006, Part 2," Wellington, N e w Zealand. Stone, W . C . , and Cheok, G . S . , 1989, "Inelastic Behavior of Full-Scale Bridge Columns Subjected to C y c l i c Loading", NISTBSS 166, Building Science Series, Center for Building Technology, National Engineering Laboratory, National Institute o f Standards and Technology, Gaithersburg, U S A . Sugano, S., 1996, "Seismic Behavior o f Reinforced Concrete Columns W h i c h used UltraHigh-Strength Concrete", Paper No. 1383, 11 World Conference on Earthquake Engineering, M e x i c o . th  Takemura, H., and Kawashima, K., 1997, "Effect o f loading hysteresis on ductility capacity of bridge piers", Journal of Structural Engineering, V o l . 43 A , pp. 849858. Tanaka, H., and Park, R., 1990, "Effect o f Lateral Confining Reinforcement on the Ductile Behavior o f Reinforced Concrete Columns", Report 90-2, Department o f C i v i l Engineering, University o f Canterbury, Christchurch, N e w Zealand. Thomsen, J., and Wallace, J., 1994, "Lateral Load Behavior o f Reinforced Concrete Columns Constructed Using High-Strength Materials", ACI Structural Journal, V o l . 91, N o . 5, pp. 605-615. V u , N . D . , Priestley, M . J . N . , Seible, F., and Benzoni, G . , 1998, "Seismic Response o f W e l l Confined Circular Reinforced Concrete Columns with L o w Aspect Ratios",  5th Caltrans Seismic Research Workshop. Watson, S., and Park, R., 1989, "Design o f reinforced concrete framces o f limited ductility", Res. Rep. 89-4, Dept. o f C i v . Engrg., Univ. o f Canerbury, Christchurch, N e w Zealand. Watson, S., Zahn, F.A., and Park, R., 1994, "Confining Reinforcement for Concrete Columns", Journal of Structural Engineering, V o l . 120, N o . 6 , pp. 1798-1824 Wehbe, N . , Saiidi, M . S . , and Sanders, D., 1998, "Confinement o f Rectangular Bridge Columns for Moderate Seismic Areas", National Center for Earthquake  Engineering Research (NCEER) Bulletin, V o l . 12, No. 1.  144  References  Wehbe, N . , Saiidi, M . S . , and Sanders, D., 1999, "Seismic Performance o f Rectangular Bridge Columns with Moderate Confinement", ACI Structural Journal, V o l . 96, N o . 2, pp. 248-258. W i l l i a m , K . J . , and Warnke, E.P., 1975, "Constitutive M o d e l o f the triaxial behavior o f concrete", Proc. International Association for Bridge and Structural Engineering, V o l . 19, pp. 1-30. W o n g , Y . L . , Paulay, T., and Priestley, M . J . N . , 1990, "Squat Circular Bridge Piers Under Multi-Directional Seismic Attack", Report 90-4, Department o f C i v i l Engineering, University o f Canterbury, Christchurch, N e w Zealand. X i a o , Y . , and Martirossyan, A . , 1998, "Seismic Performance o f High-Strength Concrete Columns", Journal of Structural Engineering, V o l . 124, N o . 3, pp. 241-251. Zahn, F.A., Park, R., and Priestley, M . J . N . , 1986, "Design o f reinforced concrete bridge columns for strength and ductility" Res. Rep. 86-7, Dept. of C i v . Engrg., Univ. of Canerbury, Christchurch, N e w Zealand. Zhou, X . , Satoh, T . , Jiang, W . , Ono, A . , and Shimizu, Y . , 1987, "Behavior o f Reinforced Concrete Short Column Under High A x i a l L o a d , " Transactions of the Japan Concrete Institute, V o l . 9, pp. 541-548.  145  Geometry  Database No. 7' 8 9 10 13 14 15 16 17 20 32 43 48 49 50 56 58 66 67 68 69 70 71 72 94 95 96 97 102 103 104 105 106 107 108 117 118 119 120  Specimen Name Soesianawati et al. 1986, No. 1 Soesianawati et al. 1986, No. 2 Soesianawati et al. 1986, No. 3 Soesianawati et al. 1986, No. 4 Watson and Park 1989, No. 5 Watson and Park 1989, No. 6 Watson and Park 1989, No. 7 Watson and Park 1989, No. 8 Watson and Park 1989, No. 9 Tanaka and Park 1990, No. 3 Ohno and Nishioka 1984, L3 Zhou et al. 1987, No. 214-08 Kanda e t a l . 1988, 85STC-1 K a n d a e t a l . 1988, 85STC-2 Kanda et al. 1988, 85STC-3 Muguruma et al. 1989, AL-1 Muguruma et al. 1989, AL-2 Sakai et al. 1990, B1 Sakai etal. 1990, B2 Sakai et al. 1990, B3 Sakai et al. 1990, B4 Sakai et al. 1990, B5 Sakai etal. 1990, B6 Sakai et al. 1990, B7 Atalay and Penzien 1975, No. 9 Atalay and Penzien 1975, No. 10 Atalay and Penzien 1975, No. 11 Atalay and Penzien 1975, No. 12 Azizinamini et al. 1988, NC-2 Azizinamini et al. 1988, NC-4 Saatcioglu and Ozcebe 1989, U i Saatcioglu and Ozcebe 1989, U3 Saatcioglu and Ozcebe 1989, U4 Saatcioglu and Ozcebe 1989, U6 Saatcioglu and Ozcebe 1989, U7 Galeota etal. 1996, CA1 Galeota et al. 1996, CA2 Galeota etal. 1996, C A 3 Galeota etal. 1996, CA4  '  f c (MPa) P(kN)  P/Agfc  P/P„  B(mm)  H(nim)  744 2112 2112 1920 3280 3200 4704 4368 4480 819 127 432 183.9 183.9 183.9 1371 2156 2176 2176 2176 2176 2176 2176 2176 801 801 801 801 1690 2580 0 600 600 600 600 1000 1500 1000 1500  0.10 0.30 . 0.30 0.30 0.50 0.50 0.70 0.70 0.70 0.20 0.03 0.80 0.11 0.11 0.11 ' 0.40 0.63 0.35 0.35 0.35 0.35 0.35 0.35 0.35 0.26 0.27 0.28 0.27 0.21 0.31 0.00 0.14 0.15 0.13 0.13 0.20 0.30 0.20 0.30  0.10 0.30 0.30 0.30 0.49 0.49 0.69 0.69 0.69 0.18 0.03 0.67 0.10 0.10 0.10 0.40 0.63 0.38 0.38 0.38 0.38 0.38 0.38 0.39 0.26 0.26 0.27 0.26 0.20 0.30 0.00 0.12 0.12 0.11 0.11 0.22 0.33 0.22 0.33  400 400 400 400 400 400 400 400 400 400 400 160 250 250 250 200 200 250 250 250 250 250 250 250 305 305 305 305 457 457 350 350 350 350 350 . 250 250 250 250  400 400 400 400 400 400 400 400 400 400 400 160 250 250 250 200 200 250 250 250 250 250 250 250 305 305 305 305 457 457 350 350 •350 350 350 250 250 250 250 .  46.5 44 . 44 40 41 40 42 ' 39 40 25.6 24.8 21.1 27.9 27.9 27.9 85.7 85.7 99.5 99.5 99.5 99.5 99.5 99.5 99.5 33.3 32.4 31 31.8 39.3 39.8 43.6 34.8 32 37.3 39 80 80 80 80  L(mm)  A  (mm ) 2  g  1600 160000 1600 160000 1600 . 160000 1600 160000 1600 160000 1600 160000 1600 160000 1600 160000 1600 160000 1600 160000 1600 160000 320 25600 750 62500 750 62500 750 62500 500 40000 500 40000 500 62500 500 62500 500 62500 500 62500 500 62500 500 62500 500 62500 1676 93025 1676 93025 1676 93025 "1676 .93025 1372 ' 208850 1372 208850 1000 122500 1000 122500 1000 122500 1000 122500 1000 122500 1140 62500 1140 62500 1140 62500 1140 62500  Cover (mm) 13.0 13.0 13.0 13.0 13.0 13.0 13.0 13.0 40.0 31.5 12.5 35.0 35.0 35.0 9.0 9.0 23.5 23.5 23.5 23.5 23.5 23.5 30.5 32.0 32.0 32.0 32.0 38.1 41.3 22.5 22.5 22.5 26.0 26.0 30.0 30.0 30.0 30.0 30.0  3  Geometry  Database No.  r  4^  •  126 127 128 133 134 135 136 145 146 147 148 151 152 153 154 155 157 158 159 160 162 163 164 166 167 169 170 171 172 173 174 175 176 177 178 179 180 181 182  Specimen Name Galeota etal. 1996, BB1 Galeota etal. 1996, BB4 Galeota et al. 1996, BB4B Wehbe et al. 1998, A1 Wehbe etal. 1998, A2 Wehbe etal. 1998, B1 Wehbe etal. 1998, B2 Xiao 1998, HC4-8L19-T10-0.1 P Xiao 1998, HC4-8L19-T10-0.2P Xiao 1998, HC4-8L16-T10-0.1P Xiao 1998, HC4-8L16-T10-0.2P Sugano 1996, UC.10H Sugano 1996, UC15H Sugano 1996, UC20H Sugano 1996, UC15L Sugano 1996, UC20L Bayrak and Sheikh 1996, ES-1HT Bayrak and Sheikh 1996, AS-2HT Bayrak and Sheikh.1996, AS-3HT Bayrak and Sheikh 1996, AS-4HT Bayrak and Sheikh 1996, AS-6HT Bayrak and Sheikh 1996, AS-7HT Bayrak and Sheikh 1996, ES-8HT Saatcioglu and Grira 1999, BG-2 Saatcioglu and Grira 1999, BG-3 Saatcioglu and Grira 1999, BG-5 Saatcioglu and Grira 1999, BG-6 Saatcioglu and Grira 1999, BG 7 Saatcioglu and Grira 1999, BG-8 Saatcioglu and Grira 1999, BG-9 Saatcioglu and Grira 1999, BG-10 Matamoros et al. 1999,C10-05N Matamoros et al. 1999,C10-05S Matamoros et al. 1999.C10-10N Matamoros et al. 1999,C10-10S Matamoros et al. 1999.C10-20N Matamoros et al. 1999.C10-20S Matamoros et al. 1999,C5-00N Matamoros et al. 1999,C5-00S r  f c (MPa) P(kN)  P/Agfc  P/P„  1000 1500 1500 615 1505 601 1514 489 979 534 1068 3579 3579 3579 2089 2089 3353.6 2401.2 3339.6 3344.2  0.20 0.30 0.30 0.10 0.24 0.09 0.23 0.10 0.20 0.10 0.19 0.60 0.60 0.60 0.35 . 0.35 0.50 0.36 0.50 0.50 0.46 0.45 0.47 0.43 0.20 0.46 0.46 0.46 0.23 0.46 0.46 0.05 0.05 0.10 0.10 0.21 0.21 0.00 0.00  0.18 0.27 0.27 0.08 0.20 0.08 0.20 0.09 0.19 0.10 0.20 0.67 0.67 0.67 0.39 0.39 0.50 0.36 0.50 0.50 0.49 0.48 0.50 0.39 0.18 0.38 0.40 0.38 0.19 . 0.37 0.37 0.05 0.05 0.10 0.10 0.21 0.21 0.00 0.00  80 80 80 27.2 27.2 28.1 28.1 76 76 86 86 118 118 118 118 118 72.1 71.7 71.8 71.9 101.9 102 102.2 34 34 34 34 34 34 34 34 69.637 69.637 67.775 67.775 65.5 65.5 37.921 37.921  4360.5 4269.-8 4468.4 1782 831 1923 1900 1923 961 1923 1923 142 142 285 285 569 569 0 0  B(mm) 250 250 250 380 380 380 380 254 254 254 254 225 225 225 225 225 305 305 305 305 305 305 305 350 350 350 350 350 350 350 350 203 203 203 203 203 203 . 203 203  H(mm) 250 250 250 610 610 610 610 254 254 254 254 225 225 225 225 225 305 305 305 305 305 305 305 350 350 350 350 350 350 350 350 203 203 203 .203 203 203 203 203  L(mrn) 1140 1140 1140 2335 2335 2335 2335 508 , 508 508 508 450 450 450 450 450 1842 1842 1842 1842 1842 1842 1842 1645 1645 1645 1645 1645 1645 1645 1645 . 610 610 610 610 610 610 610 610  A  Cover  (mm ) 2  8  62500 62500 62500 231800 231800 231800 231800 64516 64516 64516 64516 50625 50625 50625 50625 50625 93025 93025 ' 93025 • 93025 93025 93025 93025 122500 .122500 122500 122500 122500 122500 122500 122500 41209 41209 41209 41209 41209 41209 41209 41209  (mm)  .  30.0 30.0 28.0 28.0 25.0 25.0 13.0 13.0 . 13.0 13.0 11.3 11.3 11.3 11.3 11.3 25.4' 13.4 13.4 11.0 11.0 13.4 11.0 29.0 29.0 29.0 29.0 29.0 29.0 29.0 29.0 40.0 39.8 25.8 23.8 22.0 14.6 24.0 27.8 38.3  Geometry Database  NO; 183 184 185 186 187 188 189 190 191 192 202 204 205 207 208 209 210 211 215 216 217 221 222 223 224 225 226 227 228 229 230 231 232 233 234 237 238 239 240  Specimen Name  Matamoros et al. 1999.C5-20N Matamoros et al. 1999.C5-20S Matamoros et al. 1999.C5-40N Matamoros et al. 1999.C5-40S MoandWang 2000,C1-1 Mo and Wang 2000,C1-2 Mo and Wang 2000,C1-3 Mo and Wang 2000,C2-1 Mo and Wang 2000,C2-2 Mo and Wang 2000.C2-3 Thomsen and Wallace 1994, A3 Thomsen and Wallace 1994, B2 Thomsen and Wallace 1994, B3 Thomsen and Wallace 1994, C2 Thomsen and Wallace 1994, C3 Thomsen and Wallace 1994, D1 Thomsen and Wallace 1994, D2 Thomsen and Wallace 1994, D3 Paultre & Legeron, 2000, No. 1006015 Paultre & Legeron, 2000, No. 1006025 Paultre & Legeron, 2000, No. 1006040 Paultre et al., 2001, No. 806040 Paultre etal., 2001, No. 1206040 Paultre etal., 2001, No. 1005540 Paultre et al., 2001, No. 1008040 Paultre etal., 2001, No. 1005552 Paultre et al., 2001, No. 1006052 Pujol 2002, No. 10-2-3N Pujol 2002, No. 10-2-3S Pujol 2002, No. 10-3-1.5N Pujol 2002, No. 10-3-1.5S Pujol 2002, No. 10-3-3N Pujol 2002, No. 10-3-3S Pujol 2002, No. 10-3-2.25N Pujol 2002, No. 10-3-2.25S Pujol 2002, No. 20-3-3N Pujol 2002, No. 20-3-3S Pujol 2002, No. 10-2-2.25N Pujol 2002, No. 10-2-2.25S  f c (MPa) P(kN) 48.263 48.263 38.059 38.059 24.94 26.67 26.13 25.33 27.12 26.77 86.3 83.4 90 74.6 81.8 75.8 87 71.2 92.4 93.3 98.2 78.7 109.2 109.5 104.2 104.5 109.4 33.715 33.715 32.13 32.13 29.923 29.923 27.372 27.372 36.404 36.404 34.887 34.887  P/Agfc  0.14 285 0.14 285 0.36 569 0.36 569 0.11 450 0.16 675 0.22 900 0.11 450 0.16 675 0.21 900 400.88 0.20 0.10 193.7 0.20 418.06 0.10 173.26 0.20 379.97 0.20 352.1 404.13 0.20 0.20 330.73 0.14 1200 0.28 2400 3600 0.39 0.40 2900 4200 . 0.41 0.35 3600 3600 0.37 0.53 5150 0.51 5150 0.09 133.45 0.09 133.45 133.45 0.09 133.45 0.09 0.10 133.45 0.10 133.45 0.10 133.45 0.10 133.45 0.16 266.89 0.16 266.89 133.45 0.08 0.08 133.45  P/P„  B(mm)  H(mm)  L(mm)  0.13 0.13 0.32 0.32 0.09 0.13 0.17 0.09 0.13 0.17 0.20 0.10 0.21 0.10 0.21 0.20 0.21 0.20 0.15 0.29 0.42 0.41 0.44 0.44 0.40 0.56 0.54 0.07 0.07 0.08 0.08 0.08 0.08 0.08 0.08 0.14 0.14 0.07 0.07  203 203 203 203 400 400 400 400 400 400 152.4 152.4 152.4 152.4 152.4 152.4 152.4 152.4 305 305 305 305 305 305 305 305 305 152.4 152.4 152.4 152.4 152.4 152.4 .152.4 152.4 152.4 152.4 152.4 152.4  203 203 203 203 400 400 400 400 400 400 152.4 . 152.4 152.4 152.4 152.4 152.4 152.4 152.4 305 305 305 305 305 305 305 305 305 304.8 304.8 304.8 304.8 304.8 304.8 304.8 304.8 '304.8 304.8 304.8 304.8  610 610 610 610 1400 1400 1400 1400 1400 1400 596.9 596.9 596.9 596.9 596.9 596.9 596.9 596.9 2000 2000 2000 2000 2000 2000 2000 2000 2000 685.8 685.8 685.8 685.8 685.8 685.8 685.8 685.8 685.8 685.8 685.8 685.8  A  .  (mm ) 2  g  41209 41209 41209 41209 160000 160000 160000 160000 160000 160000 23226 23226 23226 23226 23226 23226 23226 23226 93025 93025 93025 93025 93025 93025 .93025 93025 93025 46452 46452 46452 46452 46452 46452 46452 46452 46452 46452 46452 46452  Cover (mm) 39.0 20.7 20.7 34.0 34.0 34.0 34.0 34.0 34.0 11.1 11.1 11.1 11.1 11.1 11.1 11.1 . 11.1 19.0 19.0 19.0 19.0 19.0 19.0 19.0 19.0 19.0 25.4 25.4 25.4 25.4 25.4 25.4 25.4 25.4 25.4 25.4 25.4 25.4 25.4  Geometry Database No. 241 242 243 244 246 248 249 250 251 252 258 260 261 264 265 266 268 269 270 272 273 274 275 285 286 287 288 289  Specimen Name  Pujol 2002, No. 1-0-1-2.25N Pujol 2002, No. 10-1-2.25S Bechtoula et al., 2002, D1N30 Bechtoula et. al. 2002, D1N60 Bechtoula et. al. 2002, L1N60 Takemura 1997, Test 1 (JSCE-4) Takemura 1997, Test 2 (JSCE-5) Takemura 1997, Test 3 (JSCE-6) Takemura 1997, Test 4 (JSCE-7) Takemura 1997, Test 5 (JSCE-8) Xaio & Yun 2002, No. FHC5-0.2 Bayrak & Sheikh, 2002, No. RS-9HT Bayrak & Sheikh, 2002, No. RS-10HT Bayrak & Sheikh, 2002, No. RS-13HT Bayrak & Sheikh,2002, No. RS-14HT Bayrak & Sheikh, 2002, No. RS-15HT Bayrak & Sheikh, 2002, No. RS-17HT Bayrak & Sheikh, 2002, No. RS-18HT Bayrak & Sheikh, 2002, No. RS-19HT Bayrak & Sheikh, 2002, No. WRS-21HT Bayrak & Sheikh, 2002, No. WRS-22HT Bayrak & Sheikh, 2002, No. WRS-23HT Bayrak & Sheikh, 2002, No. WRS-24HT Saatcioglu and Ozcebe 1989, U2 Esaki, 1996 H-2-1/5 Esaki, 1996 HT-2-1/5 Esaki, 1996 H-2-1/3 Esaki, 1996 HT-2-1/3'  fx  (MPa) P(kN)  36.473 36.473 37.6 37.6 39.2 35.9 35.7 34.3 33.2 36.8 64.1 71.2 71.1 112.1 112.1 56.2 74.1 74.1 74.2 91.3 91.3 72.2 72.2 30.2 23 . 20.2 . 23 20.2  133.45 133.45 705 1410 8000 157 157 157 157 157 3334 2118.2 3110.6 3433.1 4512 1770.3 2204.5 3241.9 3441 3754.7 2476.5 2084.8 3158.8 600 184 162 307 269  P/Agfc  P/P  0.08 0.08 0.30 0.60 0.57 0.03 0.03 0.03 0.03 0.03 0.20 0.34 0.50 0.35 0.46 0.36 0.34 0.50 0.53 0.47 0.31 0.33 0.50 0.16 0.20 0.20 0.33 0.33  0.07 0.07 0.27 0.53 0.57 0.03 0.03 , 0.03 0.03 0.03 0.20 0.34 0.50 0.37 0.49 0.34 0.33 0.49 0.52 0.48 0.32 0.32 0.49 0.12 0.16 0.16 0.27 0.26  0  B(mm) 152.4 .152.4 250 250 600 400 400 . 400 400 400 510 250 250 250 . 250 250 250 250 250 350 350 350 350 350 200 200 200 200  H(mm)  L(rnm)  304.8 304.8 250 250 600 400 400 400 400 400 510 350 350 350 350 350 350 350 350 250 250 250 250 350 200 200 200 200  685.8 685.8 625 625 . 1200 1245 1245 1245 1245 1245 1778 1842 1842 1842 1842 1842 1842 1842 1842 1842 1842 1842 1842 1000 400 400 400 400  A .  (mm ) 2  g  46452. 46452 62500 62500 360000 160000 160000 160000 160000 160000 260100. 87500 87500 87500 87500 87500 87500 87500 87500 87500 . 87500 87500 87500 122500 40000 40000 40000 40000  Cover (mm) 25.4 18.5 18.5 44.5 27.5 27.5 27.5 27.5 27.5 40.0 20.0 20.0 20.0 20.0 20.0 20.0 20.0 20.0 20.0 20.0 20.0 20.0 22.5 13.0 13.0 13.0 13.0 13.0  Transverse Reinforcement  L o n g ltudihal Reinforcement Database  b a r  No.  (mm)  7 8 9 10 13 14 15 16 17 20 32  16 16 16 16 16 16 16 16 16 20 19 10 12.7 12.7 12.7 12.7 12.7 12.7 12.7 12.7 12.7 12.7 12.7 19 22 22 22 22 25.4 25.4 25 • 25 25 25 25 10 10 10 10  43 48 49 50 . 56 58 66 67 68 69 70 71 72 94 95 96 97 102  •  D  103 104 105 106 107 108 117 118 119 120  Total #  Plong  y  Bars  (%)  12 12 12 12 12 12 12 12 12  1.51 1.51 1.51 1.51 1.51 1.51 1.51 1.51 1.51 1.57 1.42 2.22 1.62 1.62 1.62 3.80 3.80 2.43 2.43 2.43 2.43 2.43 2.43 1.81 1.63 1.63 1.63 1.63 1.94 1.94 3.21 3.21 3.21 3.21 3.21 1.51 1.51 1.51 1.51  8 8 8 8 8 8 12 12 12 . 12 12 12 12 12 4 4 4 4 4 8 8 8 8 8 8 8 12 12 12 12  f (MPa) 446 446 446 446 474 474 474 . 474 .474 474 362 341 374 374 374 399.6 399.6 379 379 379 379 379 379 339 • 363 363 363 363 439 439 430 430 438 437 437 531 531 531 531  Confin. Type RO RO . RO RO RO RO RO RO RO UJ R R R R R Rl Rl Rl Rl Rl Rl R R R R R R R RD RD R R R RJ RJ Rl Rl Rl Rl  N 4 4 4 4 • 4 4 4 4 4 3 2 2 2 2 2 4 4 4 4 4 4 2 2 .2 2 2 2 2 3.41 3.41 2 2 2 . 6 6 4 4 4 4  D  b a r  (mm) s (mm) 7 8 7 6 8 6 12 8 12 12  9 5 5.5 5.5 5.5 6 6 5 5 5.5 5 5 7 5 9.5 9.5 9.5 9.5 12.7 9.5 10 10 10 6.4 6.4 8 8 8 8  85 78 91 94 81 96 96 77 52 80 100 40 50 50 50 35 35 60 40 60 60 30 60 30 76 127 76 127 102 102 150 75 50 65 65 50 50 50 50  Drift  Parea  Ao 8  max  (MPa)  (%)  (mm)  (mm)  364 360 364  0.493 0.704 0.461 0.327 0.678 0.320 1.302 0.713 2.825 1.305 0.348 1.155 0.545 0.545 0.420 1.836 2.198 0.661 0.992 0.802 0.661 0.661 0.705 0.723 0.806 0.482 0.806 0.509 1.171 0.589 0.355 0.710 1.091 1.018 1.047 2.209 2.209 2.209 2.209  98.06 68.73 46.24 43.91 38.91 26.83 18.72 17.17 43.86 57.20 73.04 6.54  98.06 98.72 53.58 57.17 38.91 32.19 25.82 18.86 44.59 76.70 74.66 11.60 52.50 52.50 52.50 31.03 14.42 10.26 . 20.32 10.62  255 372 388 308 372 308 333 325 559 506 506 506 328.4 328.4 774 774 • 344 1126 774 857 774 392 392 373 " 373 .454 616 470 470 470 425 425 531 531 531 531  34.60 34.60 34.60 21.44 10.89 10.17 20.09 10.07 10.07 9.46 10.07 5.06 42.16 40.08 37.65 42.70 . 66.64 38.62 48.70 51.10 89.90 89.80 88.00 67.02 53.54 37.06 40.52  A  20.58 12.60 13.19 14.86 53.46 50.51 49.97 50.95 69.78 39.32 84.00 72.00 102.00 89.80 88:00 69.81 54.92 62.31 62.05  A  Ratio (%) 6.13 4.30 2.89 . 2.74 2.43 1.68 1.17 1.07 2.74 3.58 4.57 2.04  s h Provided  A h (ACI)  (mm )  (mm )  153.94  0.366 358.66 . 0.546 314.03 0.361 363.33 0.197 488.36 0.583 294.07 0.294 327.79 0.904 426.50 0.645 265.91 1.753 220.02 0.870 390.19 0.348 365.83 1.296 30.31 0.313 151.91 0.313 151.91 0.313 151.91 0.782 144.68 0.782 144.68 272.25 0.288 0.433 181.50 619.33 0.153 187.14 0.420 136.13 0.288 0.300 256.80 0.218180.11 329.91 0.430. 0.264 536.40 322.77 0.439 553.29 0.256 527.84 0.818 410.14 0.589 502.00 0.313 0.784 200.34 . 1.279 122.81 0.585 219.91 229.93 0.560 450.44 0.446 450.44 0.446 450.44 0.446 450.44 0.446  s  A  201.06 153.94 113.10 201.06 113.10 452.39 201.06 452.39. 339.29 127.23 39.27 4.61 47.52 4:61 47.52 4.61 47.52 4.29 113.10 2.18 113.10 2.03 78.54 4.02. 78.54 2.01 95.03 2.01 78.54 1.89 • 39.27 2.01 76.97 1.01 39.27 2.52 141.76 2.39 141.76 2.25 141.76 2.55 141.76 4.86 431.97 2.81 . 241.71 4.87 157.08 5.11 157.08 8.99 157.08 8.98 193.02 8.80 193.02 5.88 201.06 4.70 201.06 3:25 201.06 3.55 201.06  V sh(ACI) A  Transverse Reinforcement  Longitudinal Reinforcement  Database No. 126 127  Confin. Type  N  (mm)  Total # Bars  .20 20  12  6.03  579  RI  4  8  100  579  12  6.03  579  RI  4  8  100  RI  4  8  Dbar  Plong  (%)  f (MPa) y  D  bar  (mm) s (mm)  f, (MPa) 5  Amax  Parca  (%)  (mm)  (mm)  1.105 1.105  58.03  58.03  579  71.81  100  579  1.081  75.33  71.81 75.33  6  110  428  0.323  122.10  Drift Ratio  A j h Provided  A h s  (ACI)  Asi/AjhjAci)  (mm )  (mm )  5.09 6.30  201.06  900.87  0.223 ••  201.06  900.87  0.223  6.61  201.06  900.87  (%)  2  2  162.89 122.24  5.23  113.10  220.19  0.223 0.514  4.38  113.10  220.19  0.514  160.79 129.78  183.71  6.89  158.90  0.712  151.16  5.56  113.10 113.10  158.90  0.712  48.20  9.40  212.65  173.96  1.562  1.908  47.76 40.94  45.85  8.06  212.65  173.96  1.562  510  1.908  37.59  38.79  7.40  212.65  196.85  1.380  51  510  1.878  35.01  44.31  6.89  212.65  196.85  1.380  5.1  ' 45  1415  0.920  4.10  0.91  81.71  6.4  45  1.458  13.79  128.68  1.226 1.854  1.875  16.30  20.66  1.83 3.62  66.67 69.42  35  1424 1424  4.09 8.24  1424  1.458  20.40  32.37 '  4.53  128.68  54.00 69.42  2.383  45  6.4  35  1424  2.191  28.30  32.43  6.29  54.00  2.383  2  15.98  95  463  1.610  36.96  1.75  371.12  3.41  11.28  90  542  1.418  32.17 63.42  128.68 401.12  99.68  3.44  340.77  301.37  1.078 1.132  3.41  11.28  1.393  34.12  1.130  2.561  51.62  1.85 2.80  301.79  463  51.53 72.54  340.77  15.98  90 100  542  3.41  683.91  389.57  1.751  RD  3.41  15.98  463  70.68  3.02  683.91  419.60  1.625  3.41  11.28  542  3.430 1.334  55.69  RD  76 94  23.06  43.32  1.25  340.77  447.78  0.762  454  R  '2  15.98  70  463  2.480  9.53  76  0.997  87.02  213.99  RI  9.53  76  570 570  387.61 205.64  1.032  3 3  1.36 4.04  401.12  RI  25.01 66.52  29.72  455.56  0.997  116.02  116.52  7.05  213.99  205.64  1.388  455.56  RI  4  9.53  76  570  1.329  100.03  117.01  6.08  285.32  205.64  1.388  2.29  477.78  RI  4  9.53  76  570  1.329  100.03  117.01  6.08  285.32  205.64  1.388  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  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  16  3.28  427.78  RI  4  6.6  118.00  7.05  RI  4  • 9.53  1.442  '99.51  6.05  192.23 205.64  175  15.9  4  1.93  586.05  R  2  9.5  76.2  406.79  " 1.633  38.61  118.00 52.32  136.85 285.32  0.712  427.78  580 570  116.00  3.28  76 76  0.631  16  20 20  6.33  141.76  977.11  0.145  176  15.9 15.9  4  1.93  586.05  R  2  9.5.  76.2  406.79  1.311  6.25  141.76  968.92  0.146  1.93  572.26  2  9.5  76.2  513.66  1.275  44.45  1.29  141.76  4  1.93  573.26  2  . 77.2  7.33  141.76  0.316 0.341  572.26  R  2  76.2  1.228 1.133  44.70  1.93  514.66 513.66  44.70  4  9.5 9.5  448.26 416.04  179  15.9 15.9  R R  38.10 44.45 .  44.70  4  38.35  38.61  6.29  141.76  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  367.69 255.44  181 182  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  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  128 133  20  12  6.03  579  19.1  18  2.22  448  134  19.1  18  2.22  448  RJ RJ  4 4  6  110  428  0.317  102.26  135  19.1  18  2.22  448  RJ  4  6  83  428  136  19.1  18  2.22  448  RJ  4  6  83  428  0.421 0.392  145  19.1  3.55  510  RJ  3  9.5  1.908  19.1  3.55 .  510  RJ  3  9.5  51 51  510  146  8 8  510  147  15.9  8  2.46  510  RJ  3  9.5  51  148 151  15.9  . 2.46  510  RJ  1.86  393  152  10  12  1.86  153 154  10  12  1.86  393 393  RI RI  3 4  9.5  10  8 12  RI  4 4  6.4  10  12  1.86  393  RI  4  6.4  12  1.86  393  RI  4  157  10 19.54  8  2.58  454  R  158  19.54  8  2.58  454  RD  159  19.54  2.58  454 454  RD  19.54  8 8  2.58  160  RD  162  19.54  8  2.58  454  163 164  19.54  8  2.58  454  19.54  8  2.58  166  8  1.95  167  19.5 19.5  8  1.95  455.56  169  19.5  12  2.93  170  29.9  4  171 172  19.5  173 174  155  177 ' 178  '  .  .  128.68  1.854  1.388  1.388  •  0.386 0.555  Transverse Reinforcement  Longitudinal Reinforcement Database  D„ar  No.  (mm)  183 184  15.9  185 186 187 188 189 190 191 192 202 204 205 207 208 209 210 211 215 216 217 221 222 223 224 225 226 227 228 229 230 231 232 233 234 237 238 239 240  15.9 15.9 15.9 19.05 19.05 19.05 19.05 19.05 19.05 9.525 9.525 9.525 9.525 9.525 9.525 9.525 9.525 19.54 19.54 19.54 19.54 19.54 19.54 19.54 19.54 . 19.54 19.05 19.05 19.05 19.05 19.05 19.05 19.05 19.05 19.05 19.05 19.05 19.05  Total #  Plong  Bars  (%)  4 4 . 4 4 12 12 12  1.93 1.93 1.93 1.93 2.14  12 12 12 8 8 8 8 8 8 8 8 ' 8 8 8 8 8 . 8 8 8 8 4 4 4 4 4 4 4 4 4 4 4 4  2.14 2.14 2.14 2.14 2.14 2.45 2.45 2.45 2.45 2.45 2.45 2.45 2.45 2.15 2.15 2.15 2.15 2.15 . 2.15 2.15 2.15 2.15 2.45 2.45 2.45 2.45 2.45 2.45 2.45 2.45 2.45 2.45 2.45 2.45  f  y  (MPa)  586.05 587.05 572.26 573.26 497 497. 497 497 497 497 517.13 -455.07 455.07 475.76 475.76 475.76 475.76 475.76 451 '430 451 446 446 446 446 446 446' 452.99 452.99 452.99 452.99 452.99 452.99 452.99 452.99 452.99' 452.99 452.99 452.99  Confin. Type R R R R RJ RJ RJ RI RI RI RJ RD RD RD RD RD RD RD RD RD RD • RD RD RD RD RD RD R R R R  N -2 2 2 2 4 4 4 4 4 4 3 3.41 3.41 3.41 3.41 3.41 3.41 3.41 3.41 3.41 3.41 . 3:41 3.41 3.41 3.41 3.41 3.41 2 ." 2 2 2  R R R R R R R  2 2 2 2 2 2 2  R  2  Dbar  (mm)  9.5 9.5 9.5 9.5 6.35 6.35 6.35 6.35 6.35 6.35 3.175 3.175 3.175 3.175 3.175 3.175 3.175 3.175 11.3 11.3 11.3 11.3 11.3 9.5 9.5 9.5 11.3 6.35 6.35 6.35 6.35 6.35 6.35 6.35 6.35 6.35 6.35 6.35 6.35  •  s (mm) 76.2 77.2 76.2 77.2 50 50 50 52 52 52 25.4 25.4 25.4 25.4 25.4 31.75 38.1 44.45 60 60 60 60 60 55 80 55 60 76.2 76.2  Ago  A ax  (MPa)  (%)  (mm)  (mm)  406.79 407.79 513.66 514.66 459.5 459.5 459.5 459.5 459.5 459.5 793 793  1.611 1.20.8 1.224  32.30 32.00  44.20 43.90 26.40 25.40 102.26 105.05 110.51 112.97 119.47  793 1262 1262 1262 1262 1262 391 391 418 438 438 825 825 744 492  76.2 57.15  410.9 410.9 410.9 410.9 410.9 410.9 410.9 410.9 410.9 410.9 410.9  57.15  410.9  38.1 38.1 76.2 76.2 57.15 57.15 76.2  Drift  Parea  1.463 0.778 0.778 0.778 0.748 0.748 0.656 0.736 0.837 0.837 0.837 0.837 0.670 0.558 0.546 2.229 2.229  26.40 25.40 88.39 96.57 88.10 98.02 94.86 77.02 20.24 14.63 13.78 29.83 19.05 18.89 11.86 12.06 182.76 144.46 63.20 174.41  2.229 2.229 122.09 2.229 97.98 1.707 1.173 ' 52.55 66.37 1.707 66.06 2.346 0.873 21.85 20.94 0.8731.745 27.91 28.76 1.745 0.873 21.49 0.873 21.59 1.164 20.95 1.164 22.07 0.873 22.85 0.873 23.01 1.164 22.01 1.164 21.73  m  114.71 36.53 37.56 39.73 40.18 40.89 39.05 40.29 40.07 212.57 201.03 141.00 208.33 162.35 168.94 108.01 91.84 90.86 21.85 20.94 28.91 29.88 22.71 21.59 21.97 22.07 23.55 23.58 22.01 21.73  Ratio (%) 5.30 5.25 4.33 4.16 6.31 6.90 6.29 7.00 6.78 5.50 3.39 . 2.45 2.31 5.00 3.19 3.16 1.99 2.02 9.14 7.22 3.16 8.72 6.10 4.90 2.63 3.32 ' 3.30 3.19 3.05 4.07 ' 4.19 3.13 3.15 3.05 3.22 3.33 3.36 3.21 3.17  A h Provided  A h (ACI)  (mm )  (mm )  141.76 141.76 141.76 141.76  638.42 662.10  0.222 0.214  201.76 204.01 134.67 144.40 141.16 142.30  0.703 0.695 0.941  s  2  126.68 126.68 126.68 126.68 126.68 126.68 23.75 27.00 27.00 27.00 27.00 27.00 27.00 27^00 341.98 341.98  s  152.43 150.74 46.33 44.77 48.32 25.17 27.60 31.96 44.02 42.03 459.85 464.33  341.98 341.98 341.98 241.71 241.71 241.71 341.98 63.34 63.34 63.34 63.34 63.34 63.34'  457.15 349.64 485.14  63.34 63.34 63.34 63.34  105.55 105.55 186.96 186.96 134.44 134.44  63.34 63.34  A i,/A s  s h ( A C I  2  236.75 327.70 250.54 432.68 173.09 173.09 82.44 82.44 153.57 153.57  0.877 0.897 0.890 0.831 0.840 0.684 0.603 0.559 1.073 0.978 0.845 0.613 0.642 0.744 0.737 0.748 0.978 0.705 1.445 1.044 1.365 0.790 0.366 0.366 0.768 0.768 0.412 0.412 0.600 0.600 0.339 0.339 0.471 0.471  )  Transverse Reinforcement  Confin. Type  Plong  (mm)  Total # Bars  241  19.05  4  2.45  452.99  R  2  6.35  242  19.05  4  2.45  452.99  R  2  6.35  243  12.7  12  2.43  461  RU  4  4  244  12.7  12  2.43  461  RU  .4  246  25.4  12  1.69  388  RU  248  12.7  20  1.58  363  249  12.7  20  1.58  250  12.7  20  1.58  Database No.  Dbar  f (MPa)  N •  Dbar  (  m m  )  s (mm)  f  yh  Parea  Ago  A ax m  Drift Ratio  ^ s h Provided  A  sh  (ACI) A  sh/ sh(ACl) A  (MPa)  (%)  (mm)  (mm)  57.15  410.9  1.164  22.05  22.05  3.22  63.34  140.60  "0.450  . 57.15  410.9  1.016  21.53  21.58  3.14  63.34  140.60  0.450  40  485  0.601  24.75  24.75  3.96  50.27  83.77  0.600  4  40  485  0.800  18.73  18.73  3.00  50.27  83.77  0.600  4  12.7  100  524  0.952  31.27  31.27  2.61  506.71  503.07  1.007  R  2  6  70  368  0.238  43.71  76.39  3.51 '  56.55  272.42  0.208  363  R  2  6  70  368  0.238  48.50  79.78  3.90  56.55  270.90  0.209  363  R  2  6  70  368  0.238  74.18  94.85  5.96  56.55  260.28  0.217  6  70  368  0.238  101.44  112.17  8.15  56.55  251.93  0.224 .  56.55  279.25  0.203  y  (%)  (%)  (mm ) 2  (mm ) 2  251  12.7  20  1.58  363  R  2  252  12.7  20  1.58  363  R  2  6  70  368  0.257  84.52  95.60  6.79,  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  RD  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  RD  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  RD  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  RD  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  RD  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  RD  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  RD  3.41  8  •75  850  1.131  26.87  48.63  1.46  171.41  172.09  0.996  270 272  19.54  8  2.74  521  RD  3.41  11.1  75  850  2.212  50.94  81.94  2.77  329.98  184,31  1.790  19.54  8  2.74  • 521  RD  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  RD  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  RD  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  RD  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  363  5.75  50  364  0.617  10.10  11.77  2.53  51.93  65.86  0.789  286  12.7  8  2.53  R  2  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 p A  fl  fyh  B H L Dbar S  Cover Plong Parea  N ^max  Drift Ratio A h Provided s  A h (ACI) s  Characteristic compressive strength of concrete Axial compressive load Gross sectional area of column Yield stress of longitudinal reinforcement Yield stress of transverse reinforcement Column Width Column Depth Length of equivalent cantilever Diameter of transverse / longitudinal reinforcement Spacing of transverse reinforcement ce Longitudinal reinforcement ratio (A / A ) Transverse reinforcement ratio (A / s*h ) Effective number of transverse bars in cross section Maximum recorded deflection Deflection at 80% effective force (20% loss of strength) Drift Ratio. ( A / L ) Area of transverse reinforcement provided in specimen Area of transverse reinforcement required by ACI 318-05 21.4.4.1 st  sh  80  154  q  c  Geometry  Database No.  .  U) Ul  1 3 8 22 40 41 42 43 45 50 52 53 54 55 56 57 58 59 60 93 95 96 97 100 101 102 103 106 107 109 112 115 116 117 118 119 120 121  Specimen Name Davey 1975, N o . 1 Davey 1975, N o . 3 Ang etal 1981,No. 2 A n g e t a l . 1985, N o . 9 Zahn et al. 1986, N o . 6 Watson & Park 1989, N o 10 Watson & Park 1989, N o 11 W o n g etal.. 1990, N o . 1 W o n g e t a l . 1990, N o . 3 • L i m e t a l . 1990, C o n l L i m e t a l . 1990, C o n 1 N I S T , F u l l Scale Flexure N I S T , F u l l Scale Shear NIST, Model N l NIST, Model N 2 NIST, Model N 3 NIST, Model N 4 NIST, Model N5 NIST, Model N 6 Kunnath e t a l . 1997, A 2 Kunnath e t a l . 1997, A 4 Kunnath e t a l . 1997, A 5 Kunnath e t a l . 1997, A 6 Kunnath e t a l . 1997, A 9 Kunnath e t a l . 1997, A 1 0 Kunnath e t a l . 1997, A l l Kunnath e t a l . 1 9 9 7 , A 1 2 Hose e t a l , 1997, S R P H 1 V u e t a l . 1998, N H 1 V u e t a l . 1998, N H 3 V u e t a l . 1998, N H 6 Kowalsky et al. 1996, F L 3 Lehman e t a l . 1998,415 Lehman e t a l . 1998,815 Lehman e t a l . 1998, 1015 Lehman et a l l 9 9 8 , 407 Lehman e t a l . 1998,430 Calderone et al. 2000, 328  fc P(kN) P/Agfc (Mpa) "33.2 380 33.8 380 28.5 2111 751 29.9 2080 27 2652 40 3620 39 907 38 1813 37 151 34.5 34.5 220 4450 35.8 34.3 4450 24.1 120 23.1 239 120 25.4 24.4 120 24.3 239 23.3 120 200 29 222 35.5 222 3575 222 35.5 222 32.5 27 200 27 200 200 27 41.1. .1780 1928 38.3 39.4 970 1914 35 1780 38.6 31.03 653.86 31.03 .653.86 31.03 653.86 31.03 653.86 31.03 653.86 34.475 911.84  0.06 0.06 0.56 0.20 0.58 0.50 0.70 0.19 0.39 0.24 0.35 0.07 0.07 0.10 0.21 0.10 0.10 0.20 0.11 0.09 0.09 0.09 0.09 0.09 0.10 0.10 0.10 0.15 0.31 0.15 0.33 0.28 0.07 0.07 0.07 0.07 0.07 0.09  P/P„ 0.05 0.05 0.51 0.15 0.51 0.48 0.66 0.16 0.32 0.16 . 0.23 0.06 0.06 0.09 0.18 0.08 0.08 0.17 0.09 0.08 0.08 0.08 0.08 0.08 0.09 0.09 0.09 0.13 0.28 0.14 0.22 0.22 0.07 0.07 0.07 0.08 0.06' 0.08  Diameter (mm)  Length (mm)  A (mm )  Cover (mm)  Section Code  500 500 400 400 400 400 400 400 400 152 152 1520 1520 250 250 . 250 250 250 250 305 305 305 305 305 305 305 305 610 457 457 457 457 609.6 609.6 609.6 609.6 609.6 609.6  2750 3250 1600 1000 1600 1600 1600 800 800 - 1140 570 9140 4570 750 750 .1500 750 750. 1500 1372 1372 1372 1372 1372 1372 1372 1372 3660 910 910 910 3656 2438.4 4876.8 6096 2438.4 2438.4 1828.8  207110 207110 132550 125660 132550 132550 132550 125660 125660 18146 18146 1814600 1814600 • 49087 49087 49087 49087 49087 49087 73062 73062 73062 73062 73062 73062 73062 73062 292250 164030 164030 164030 . 164030 291860 291860 291860 291860 291860 291860  20.3 20.3 18.0 18.0 18.0 17.0 18.0 20.0 20.0 10.2 10.2 58.7 60.3 9.9 9.9 9.7 9.9 9.9 9.7. 14.5 14.5 14.5 14.5 14.5 14.5 14.5 14.5 27.8 24.8 24.8 26.4 30.2 22.2 22.2 22.2 22.2 22.2 . 28.6  2 2 2 0 2 ' 2 . 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 • 0 0  g  Q P "  ©  s © p p o* p  Si.  Geometry  Database No. 123 130 133 141 142 144 145 152 153 157 158 162  Specimen Name Calderone et al. 2000,1028 Saatcioglu & Baingo 1999, R C 4 Saatcioglu & Baingo 1999, R C 8 Henry 1998, 415p Henry 1998,415s Soderstrom2001 C I Soderstrom2001 C 2 K o w a l s k y & M o y e r 2001 N o . l K o w a l s k y & M o y e r 2001 No.2 Hamilton 2002 U C I 1 Hamilton 2002 U C I 2 Hamilton 2002 U C I 6  fc (Mpa)  P(kiN) P/Agfc  P/P„  Diameter (mm)  Length (mm)  A (mm )  34.475 90 90 37.23 37.23 60.6 62.6 32.723 34.226 36.494 36.494 35.646  911.84 1850 1850 1308 654 0 0 231.31 231.31 0 0 0  0.08 0.43 0.43 0.12 0.06 0.00 0.00 0.04 0.04 0.00 0.00 0.00  609.6 250 250 609.6 609.6 419 419 457.2 457.2 406.4 406.4 406.4  6096 • 1645 1645 2438.4 2438.4 1968.5 1968.5 2438.4 2438.4 1854.2 1854.2 1854.2  291860 49087 49087 291860 291860 145440 145440 173170 173170 129720 129720 129720  0.09 0.42 0.42 0.12 0.06 0.00 0.00 0.04 0.04 0.00 0.00 0.00  g  Cover (mm) 28.6 14.0 13.8 22.2 22.2 55.6 55.6 12.7 12.7 15.0 15.0 15.0  Section Code 0 0 0 0 . 0 2 2 2 2 0 0 0  Transverse Reinforcement  Longitudinal Reinforcement  Database No. 1 3 8 22 40 41 42 43 45 50 52 53 54 55 56 57 58 59 60 93 95 96 97 100 101 102 103 106 107 109 112 115 116 117 118 119 120 121  D  b a r  (mm)  Total # Bars  18.4 20 18.4 20 16 16 20 16 16 16 12 16 12 16 20 16 20 16 12.7 8 . 8 12.7 25 ' 43 25 43 25 7 25 7 25 7 25 7 25 7 25 7 21 9.5 21 9.5 21 9.5 21 9.5 21 9.5 21 9.5 21 9.5 21 9.5 20 22.23 15.875 20 15.875 20 19.05 30 30 15:875 ' 22 15.875 22 15.875 22 15.875 11 15.875 44 15.875 28 19.05  Plong  f, (Mpa)  %  2.568 2.568 2.427 3.200 2.427 1.820 1.820 3.200 3.200 5.585 5.585 2.001 2.001 1.960 1.960 1.960 1.960 1.960 1.960 2.037 2.037 2.037 2.037 . 2.037 2.037 2.037 2.037 2.656 2.413 2.413 5.213 3.620 1.492 1.492 1.492 0.746 2.984 2.734  .  373 373 308 448 337 474 474 423 475 448 448 475 475 446 446 446 446 446 446 448 448 448 448 448 448 448 448 455 427.5 • 427.5 486.2477 461.96 461.96 461.96 461.96 461.96 441.28  Dbar  6.5 6.5 10.0 6.0 10.0 8.0 10.0 10.0 10.0 3.7 3.7 15.9 19.1 3.1 3.1 2.7 3.1 3.1 2.7 4.0 4.0 4.0 4.0 4.0 4.0 4.0 4.0 9.5 9.5 9.5 12.7 9.5 6.4 6.4 6.4 6.4 6.4 6.4  W  s (mm) 65 65 55 30 75 84 57 60 60 22.2 22.2  .  88.9 54 8.89 8.89 14.48 8.89 8.89 14.48 19 19 19 19 19 19 19 19 57 60 60 40 76 31.75 31.75 31.75 31.75 31.75 25.4  p (%)  (Mpa)  s  0.444 0.444 1.569 1.036 1.151 0.654 1.514 1.454 1.454  312 342 280 372 466 372 338 300 300 620 620 493 435 441 .441 476 441 441 476 434 434 434 434 434 434 434 . 434 414 430.2 430.2 434.4 445 606.76 606.76 606.76 606.76 606.76 606.76  '  1.496 1.496 0.637 1.509 1.428 1.428 0.686 1.428 1.428 0.686 0.959 0.959 0.959 0.959 0.959 0.959 0.959 0.959 0.902 1.166 1.166 3.133 0.945 0.706 0.706 0.706 0.706 0.706 0.903  A  8 0  (mm)  119.25 86.83 50.09 65.58 59.04 32.54 29.00 41.43 28.82 89.54 45.59 540.99 355.70 82.50 60.41 110.64 54.69 52.60 123.09 77.20 58.56 76.35 95.49 90.54 90.66 102.16 102.43 319.79 38.13 50.33 87.47 281.60 178.00 446.00 639.83 128.00 178.00 133.00  Drift Ratio Amax  (  m m  )  (%). 4.34 2.67 3.13 6.56 3.69 2.03 1.81 5.18 3.60 7.85 8.00 5.92 7.78 11.00 8.06 7.38  119.25 116.21 50.09 65.58 59.36 32.94 36.24 41.43 33.90 90.75 45.59 593.37 356.08 104.15 73.60 128.85 67.52 64.30 127.72 77.20 58.56 76:35 95.49 90.54 90.66 102.16 102.43 319.79 46.46 50.33 87.47 340.50 179.00 446.00 639.83 128.00 181.00 133.00  7.29 7.01 8.21 .5.63 4.27 5.56 6.96 6.60 6.61 7.45 7.47 8.74  •  4.19 5.53 9.61 7.70 7.30 9.15 . 10.50 5.25 7.30 7.27  P (ACI)(%) S  1.277 1.186 1.254 0.965 0.714 . 1.290 1.421 1.520 1.480 0.837 0.837 0.871 0.946 0.656 0.629 0.640 0.664 0.661 0.587 . 0.802 0.982 0.982 0.982 0.899 0.747 0.747 0.747 1.191 1.068 1.099 1.007 1.278 0.614 0.614 0.614 0.614 0.614 0.682  PJ  Ps(ACl)  0.348 0.375 1.251 1.074 1.612 0.507 1.065 0.957 0.983 1.788 1.788 0.731 1.594 2.178 . 2.272 • 1.071 2.151 2.160 1.168 1.195 0.977 0.977 0.977 1.067 1.284 1.284 1.284 0.757 1.091 1.061 3.112 0.740 1.150 1.150 1.150 1.150 1.150 1.324  Transverse Reinforcement  Longitudinal Reinforcement  KM oo  Database No.  (mm)  Total # Bars  123  19.05  28  "bar  Plnng  %  2.734  f» (Mpa)  Dbar  (  m  m  )  s (mm)  (Mpa)  Ps  (%)  A  8 0  Drift Ratio  (mm)  (%)  Ps(ACI) (%)  P / P s :i(ACI) S  441.28  6.4  25.4  606.76  0.903  891.54  894.08  14.63  0.682  1.324  50  580  1.811  54.75  73.10  3.33  1.872  0.967  130  16  3.277  • 419  8.0  133  16.  3.277  419  7.5  50  1000  1.588  75.78  75.78  4.61  1.080  1.471  31.75  606.76  0.706  137.64  179.07  3.76  0.736  0.959  141  15.875  22  1.492  462  6.4  142  15.875  22  1.492  462  6.4  63.5  606.76  0.353  199.01  180.11  10.11  0.736  0.479  50.8  413.7  41370.000  199.01  199.01  •7.55  6.292  6574.598  144  22.2  0.021  429.5  9.5  145  22.2  0.021  429.5  9.5  50.8  413.7  41370.000  223.70  224.01  10.58  6.500  6364.517  434.37  43437.000  190:46  190.46  10.68  0.904  48049.247  434.37  43437.000  266.69  266.69  13.15  0.946  45939.314  114.30  114.30  6.16  0.633  109203.171  268.15  6.74  0.633  109203.171  n.w  v.^w  152  19.05  12  0.020  565.37  9.5  76.2  153  19.05  12  0.020  565.37  9.5  76.2  157  12.7  12  0.012  458.5  4.5  31.75  691.54  69154.000  158  12.7  12  0.012  458.5  4.5  31.75  691.54  69154.000  124.92  ]§2  12 7  12  U.U12  438.D  4.3  ji./a  oyut.uuu  AUJ-W  fc Diameter A P Length g  fy fyh  Length s Cover Dbar Plong ^max  A o 8  Drift Ratio P s Provided Ps(ACI)  Characteristic compressive strength of concrete Diameter of column (For square and octagonal sections D refers to the largest circle that can be inscribed in the section) Gross sectional area Axial load Length of equivalent cantilever Yield stress of longitudinal reinforcement Yield stress of transverse reinforcement Length of equivalent cantilever Spacing of transverse reinforcement 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 Diameter of transverse / longitudinal reinforcement Longitudinal reinforcement ratio (A , / A ) Maximum recorded deflection Deflection at 80% effective force (20% loss of strength) Drift Ratio (D /L) Area of transverse reinforcement provided in specimen Area of transverse reinforcement required by ACI 318-05 21.4.4.1 s  80  q  Geometry Detail Nv Tc (MPa) B (mm) 609.6 4 55.16 Al 762 68.95 A2 . 5 762 5 * 68.95 A3 762 55.16 5 * Bl B 762 Bl 5 * 72.40 4 * 762 55:16 B3 4 * 762 72.40 B3 457.2 3 27.58 CI C 457.2 C2 3 * 41.37 457.2 55.16 3 * C3 * Nv given for shorter dimension only **P = DL + L L f A l l steel yield strength is 414 M P a Bldg A  H  (mm) 609.6 762 1016 1219.2 1219.2 914.4 914.4 457.2 609.6 ' 914.4  h (mm) 517.5 669.9 669.9 669.9 669.9 669.9 669.9 368.3 368.3 365.1 c  Ag (mm ) 2  371612.16 580644 774192 929030.4 929030.4 696772.8 696772.8 209031.84 278709.12 418063.68  Trans. Reinf Vert. Reinf Parea Plong No of bars Bar# s (mm) (%) bar# (%) 1.50 102 1.64 5 12 8 1.45 102 5 1.40 8. 16 1.45 102 5 1.31 8 20 1.45 102 5 1.38 9 20 1.94 1.38 5 9 20 76 .102 1.16 1.29 5 14 9 1.55 76 5 1.29 14 9 0.90 114 4 3.68 . 12 9 4 4.12 11 12 76. . 1.35 1.83 89 5 11 3.66 16  Loading Details P (kN) ** 8807 18966 21675 23032 26323 13469 16782 4083 7757 13068  P/A f ' 0.43 0.47 0.41 0.45 0.39 0.35 0.33 0.71 0.67 0.57 c  c  w % n  n to <ro  ST *i  H  T2. n  o 3  Appendix  B2 Rectangular Typical Column Cross Sections  *  IN  0  *s  -i  •  1  •. — ^ «  *  •  •i  •  s  *  s•  •  *  •  •  x«  •  A-3  A-2  A-l  1  *  -  «  <s *  •  i  • • •  0  •  !/  •  •.  •  • B-3  B-l  IF  »  T  i  •i  C-3  C-2  160  •  *  B3 Circular Typical Columns Details -=r m  o  O —; —; p O O O O  OS  OO  o o o o  (N OS  \t  S £ 5J  —. KD (N — t OS co m  o  CO  m  \= o - • 9 • ~ •;-  \o  oS  N  c ~  y3  CN  r~r>i  s=> N ? o  ^  ON  v=  r- cn r-- 0\ in *n ' — i oo so oo so — — m x  0  s  1  r»  r~CN r>i  n  N N M in tn in m  in in in in in »n in in in in >n »n  s? o  ^? S^ oS  oS  s" o  N=> \ ° 0 0 - 6CN S O  (N OO OO (N O ~ KO KO o ^ rJ m" rn  N  s  H  s  S  oo ^  m  r-~  S  so 0 -  o^ o  x  s  so o-  r- OO CO oo oo  so  CN  VO  so 6 ON  <n r— — • <•^t m cn cn  cn cn cn cn  m cn  so so n y3 so so' cn m r- r-~ r~- so m «n m oo o r- o oo o O O  r<~i m m n  —< so in so — so so so oo *n ON >n »n in CN m -^r  \0 vo i£> KO os  'sf  OO  CO C O  cn «n ini in ro - T ' r~- t-- c-- cn oo oo oo m so r-- so m so so so  O CN  u r-^  r-^  15  so  ^  • CN  in in <n in os \£j m  ON  o so  SO  CM  CN  so r~-  — t  C  < < <<  O  —  fsi  —  pj [i,  PH 1  ^  CQ  161  Appendix B  B4 Circular Typical Column Cross Sections  C-E  C-F  Figure B2.1 Typical Rectangular Column detail drawings  162  A P P E N D I X  C  C l Rectangular Confinement Models Model  Equation  ACI  0.3  > 0.09 yh \ c h  J  A  \  0.2k k n  CSA  "  II f yh  fc  p  P  f  A  "•ch J yh  k =n, /(/!,-2),.kp = P/Po n  NSZ  3.3  Ah  K  # M  f  c  yh  •0.0065 g  5A  (ACI) *(a) 1 + 13 SK97  29  a - steel configuration parameter Hi - target curvature ductility  (ACI) BS98  fp]  5\  1 + 13  J v.  V  Y>.82 A  ( t  8.12  7  a - steel configuration parameter fj.^ - target curvature ductility  0.1//,  \21.6MPa  0.12  /'c  WSS99 //  f ' c A  V  - target .displacement ductility  A  14  0.5 + 1.25-  J  c  1  g  fyh  1  P „  -7= — ^ V ^ 2 ^0  SR02 k = 0.15  • — , £ - target drift ratio  2  5  s,  163  + 0.13 P,  f y h  414 A f P a  -0.01  Appendix C  Model  Equation  11  r  1 - 0 . 8 / ,pc J  BBM05  fyh  y - as per Table 2.1 0.08 fyh  PP92  ch  A  k = 0.35 for high ductility demand, = 0.25 for low ductility demand A yjt )-33p,m  r  g  WZP94  + 22 / -  y  111  y ch A  P  c  f  A  0.006  <kf 'A  yh  c  g  <j> I (p - target curvature ductility factor u  A  yjj )-33p,m  r  g  + 22 f <  y  P  c  ^  - 0 . 0 0 6 (f <500MPa) yh  ^ ch A  X = 117 whenf < 70 MPa, 0.05(f ')2-9.54f '+539.4 whenf > 70 MPa. c  LP04  A g  WJt )-30p m y  A  K  c  + 22  t  P  91-0.1/ '  ch  c  (f  f y h t f c ' A j  E  if> I (/) - target curvature ductility factor u  C2 Circular Confinement Models Model ACI  Equation 0.45  (A  ^ 1  K ch  J  A  0.4/v  CSA kp  =  > 0.12  J c  fyh  A  cl  fyh  f J yh  P/Po c  K  c  fc'  p  1.0-p,mf ' NSZ  y  2.4  P  )  -0.0084  f y h & c ' A j  164  c  yh  > 500MPa)  Appendix C  Model  Equation f  5\  fl  Y  J  {  2 9  A  1 5  ( A C I ) *(a) 1 + 13 V  SK97  J  a - steel configuration parameter - target curvature ductility %\  f  (p^ 1 + 13 \ o) V  (ACI)  P  BS98  )  ( (  Y>.82 X,  8.12  J a - steel configuration parameter V  Hi - target curvature ductility  28  f\ fyh  SR02  'ch  8 - target drift ratio 7 1-0.8/  BBM05  pc J  fyh  j - as per Table 2.1 fc'  A  fyh ch A  PP92  -0.08 Afc'  k = 0.5 for high ductility demand, = 0.35 for low ductility demand 1.4  ''A  (<PJ<Py)-32p,m in  ^Ah  WZP94  + 22 f;  P  •  A  0.008  fy,.0f'Aj  fail fa - target curvature ductility factor A . (fal fa)-33 p,m +22 f <  f f  A  e  P  0.006 a (f <500MPa) yh  y y A h  HI  fyhttc'A  J  a = 1.1 w h e n / < 80 M P a and a = 1.0 w h e n / > 80 M P a LP04  A  r  g  (fa/fa,)-55p,m 79  + 25 f;  P  A e  fyh  fa I (j), - target curvature ductility factor  165  (f  yh  > 500MPa)  APPENDIX D .1 Rectangular Column Scatter Plots (with ACI Minimum)  2  'sh Provided  • Satisfies ACI 214 .4 .1 . *25 D o e s N o t S a t s i f y A CI 214 .4 .1 . .  sh Provided ' " s h BBM05  sh ACI  • V  ro 5 £ 4  °5 •  CC  15 .  • Satisfies ACI 214 .4 .1 . « Does NotSats ifyACI214 .4 .1 .  • Satisfies ACI 214 .4 .1 . « Does NotSats ityACI 214 .4 .1 . sh Provided  A..  1  •  •  -  •  D  •**  15 5  CC  .  If B  !  •  -  7  *  - t* «rf '  sh CSA  f •  •  o  0  •  5  <r  »  Q 3  —*-y  2  • Satisfies ACI 214 .4 .1 . « Does NotSas ilfyACI 214 .4 .1 .  166  • Satisfies AC2 I 14 .4 .1 . * Does NotSats ifyACI 214 .4 .1 .  Appendix D  • • •• "S  5 -  X  4 -  Cd  i °  4. Tiff*** • *  .5  • «  Satisfies ACI 21.4.4.1 Does NotSatisfyACI 21.4.4.1  2.5  2  A / A s h Provided sh FP92  sh Provided  M  •  o  ra 5 4  sh SK97  •  4»  o: §  Satisfies ACI 21.4.4.1 Does Not Satisfy ACI 21.4.4.1  •  • •  3 •  it^--s---^- -.n  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  2.5  1.5 A..  167  Satisfies ACI 21.4.4.1 Does NotSaHsfyACI21.4.4.1  • *  Satisfies ACI 21.4.4.1 Does NotSatisfyACI 21.4.4.1  * '  „ '' A . h WSS99 sh FVovlded ^sh  2  • «  Appendix D  It" 6*^  • Satisfies ACI 214 .4 .1 . * Does Not Sats ify ACI 214 .4 .1 .  Table D.l Rectangular scatter plot statistics (with ACI limit) Model ACI A23 PP92 SR02 WSS99 BBM05 SK97 BS98 SKBS WZP94 LP04 WZPLP NZS  A 28.1 2.0 1.6. 11.6 9.6 2.9 5.6 0.0 8.3 10.4 13.3 6.6 5.7  B 18.6 30.9 34.9 28.9 35.5 36.8 25.7 22.4 23.1 25.8 22.6 31.0 34,7  C -9.5 28.9 33.3 17.4 25.8 33.9 20.1 22.4 14.8 15.4 9.3 24.4 29.0  D.2 Rectangular Column Scatter Plots (without ACI Minimum)  • Satisfies ACI 214 .4 .1 . « Does Not Sats ify ACI 214 .4 .1 . sh Ro -vd ied sh ACI  168  (  Appendix D  10r-  •  9 -  • •  --!•"»---  sh Provkled  • o  •*  * ^  *  D o e s N o t S a B s f y A C I 21.4.4.1  •  •  •  •  *  •  -  Satisfies ACI 21.4.4.1  4  sh BS98  •  •  •  !  •  •  •  ••• D •  line  *  • 2 sh  •  Satisfies ACI 21.4.4.1  4  D o e s Not Satisfy ACI 21.4.4.1  • «  SatisliesACI21.4.4.1 Does NotSatisfyACl21.4.4.1  • *  Satisfies ACI 21.4.4.1 D o e s Not Satisfy ACI 21.4.4.1  1.5  2.5  'A... sh LP04  A.  ftovkJed  I • i  • ro  or  4.-  5  •  PI •  • *  .5 A  2  sh FYovided  Satisfies ACI21.4.4.1 D o e s Not Satisfy ACI 21.4.4.1  2.5 /A  sh Provided  sh FP92  169  sh SK97  Appendix D  jS 6 o (3 5  •  Hii  •a •  •• •  i  -^--^^---*:-^-••fc D  •if"® • +  sh Provided  • +  Salisfies ACI 21.4.4.1 Does Not Satisfy ACI 21.4.4.1  Satisfies ACI 21.4.4.1 .Does Not Satisfy ACI 21.4.4.1  sh SKBS  • D  •  «> •  CP  D  • • •  ..•..44^.9..  •A-  i  • °*  • + 1  • «  Satisfies ACI 21.4.4.1 Does NotSatisfyACI 21.4.4.1  1.5  Satisfies ACI 21.4.4.1 Does NotSatisfyACI 21.4.4.1  sh Provided  *5  ip * •••  sh WZPLP  170  Satisfies ACI 21.4.4.1 Does NotSatisfyACI21.4.4.1  Appendix D Table D.2 Rectangular scatter plot statistics (without ACI limit) A  B  C  ACI  28.1  18.6  -9.5  Model  .  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  SKBS  8.3  23.1  14.8  WZP94  10.4  25.8  15.4  LP04  13.3  22.6  9.3  WZPLP  12.5  23.0  10.5  NZS  14.3  24.0  9.7.  D.3 Rectangular Column Scatter Plots (Maximum Recorded Drifts)  * •» • 4  Satisfies ACI21.4.4.1 Does NotSatisfyACI 21.4.4.1  1.5 A,  * v i  • /V  i  D  A  |  •  I  U  i  0  4P *  L]  • 8 • °« 4—-**-u-— O • • +  1.5 A  2  • *  Satisfies ACI 21.4.4.1 Does Not Satisfy ACI 21.4.4.r  1.5  2.5  2  sh BS98  171  Satisfies ACI 21.4.4.1 Does NotSatisfyACI21.4.4.1  2.5  \t\ Provided'^sh CSA  / A  sh Provided  • +  Appendix D  • •  D C 0  • •** • I  : *•  •  • *>  O  ?V  • o  • •  •  •  * t  •  ° TJ*  • • • • • a •  Satisfies ACI 21.4.4.1 Does Not Satisfy ACI21.4.4.1  .5  2  • A  fi  Satisfies ACI21.4.4.1 Does NotSatisfyACI 21.4.4.1  2.5  A /A sh Provided sh L P M  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  !  • •  • $ «  *> •  •  D  i  IA  «=>  •  •  »  0  •  •  - * • - -*»*-i*---  —*-*v£ -—f s  • • •_  •0  | !  • +  Satisfies ACI 21.4.4.1 Does Not Satisfy ACI 21.4.4.1  Satisfies ACI 21.4.4.1 Does NotSatisfyACI 21.4.4.1  1.5  172  Appendix D  •  3  • • •  • n  TO 5 or £  4  *  t  D  - — — - * • • •  • *  •  • +  Satisfies ACI21.4.4.1 Does NotSatisfyACI 21.4.4.1  sh Provided  Satisfies ACI21.4.4.1 Does NotSatisfyACl21.4.4.1  sh WZP94  • £>' G *  • *  Satisfies ACI 21.4,4.1 Does NotSatisfyACI21.4.4.1  2 /A . sh Provided sh WZPLP  Table D.3 Rectangular scatter plot statistics (Maximum Recorded Drift) Model ACI A23 PP92 SR02 WSS99 BBM05 SK97 BS98 SKBS WZP94 LP04 WZPLP NZS  A 12.5 0 0 2.4 2.2 0 0 0 0 0 0 0 0  B 5.3 12.2 13.0 13.3 14.3 14.9 9.2 7.5 8.3 10.3 8.7 8.8 10.5  C -7.2 12.2 12.987 10.9 12.1 14.9 9.2 7.5 8.3 10.3 8.7 8.8 10.5  Appendix D  D.4 Rectangular C o l u m n A Fragility Curves (with A C I M i n i m u m ) ACI  '  Drift Ratio  BBM05  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  Drift R a t i o  Drift 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  Drift Ratio  BBM05  '  181  Drift Ratio  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  Drift Ratio  BBM05  '  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 Drift Ratio  6  7  V , —  0.9 0.8  r  0.7  0.6  £D  0.5  0.4 0.3  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)  • • VI  B  •  4c L...».  4 • U  .  . -  • A 1.5  2  2.5  • +  Satisfies ACI 21.4.4.1 Does NotSatisfyACI21.4.4.1  3  1.5  3.5  2.  2.5  3  Satisfies ACI 21.4.4.1 Does NotSatisfyACI 21.4.4.1 3.5  Pprovided ^ P B B M 0 5  Pprovided' PAQ  i  I  • 4 p • • • D• l o  ••'Hi • -A • «  • *  SatisfiesACI21.4.4.1 Does NotSalisfyACI21.4.4.1 2  2.5  Satisfies ACI 21.4.4.1 Does NotSatjsfyACI21.4.4.1  3  Pftovkted ' PCSA  Provided ^PBS98  !i • ' i k i !  •  •  D  »-:IH:.  •* 9  in  • • * 2  2.5  i^b in  -  • +  Satisfies ACI 21.4.4.1 Does NotSatisfyACI 21.4.4.1  3 Pprovided ' PNZS  Pprovided ' Pl_PQ4  195  Satisfies ACI 21.4.4.1 Does NotSatisfyACI 21.4.4.1  Appendix D  * • • • > •  Jus  •  •  • I  D  •  B  •  •  •  L—»-  • •  <  1  1  4 • « 1.5  2  2.5  ft  Satisfies ACI21.4.4.1 Does NotSatjsfyACI21.4.4.1  3  0  3.5  0.5  • 1  ' 1Q  L.-.&-  3.5  4  4.5  5  • In •  i • * 2  2.5  3  Satisfies ACI 21.4.4.1 Does NotSatisfyACI 21.4.4.1  Satisfies ACI 21.4.4.1 Does NotSatisfyACI 21.4.4.1 2  3.5  •1  3  •  D  •  2.5  Pprovided ' PSR02  Pprovided ' PsKBS  3  3  2.5 P  Q  •  2  Pprovkjed' SK97  P Provided  l e t , ft  1.5  Satisfies ACI21.4.4.1 Does NotSatisfyACI 21.4.4.1  ^  Aa —4 • « 2  2.5  • *  Satisfies ACI21.4.4.1 Does NotSatisfyACI21.4.4.1 2  3  2.5  3  Pprovided' PwZPLP  Pprovided ' PwZF94  196  Satisfies ACI21.4.4.1 Does NotSatisfyACI21.4.4.1 3.5  Appendix D Table D.4 Circular scatter plot statistics (with ACI limit) A 3.4 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0  Model ACI A23 PP92 SR02 BBM05 SK97 BS.98  SKBS WZP94 LP04 WZPLP NZS  B 4.8 8.7 8.3 8.7 8.7 18.2 5!6 9.1 9.1 9.1 9.1 7.1  ,  C 1.3 8.7 8.3 8.7 8.7 18.2 5.6 9.1 9.1 9.1 9.1 7.1  r  D.14 Circular Column Scatter Plots (without ACI Minimum)  •  4  •  •  \•  •  ia  Ir. o •  0  n • • •  L  D  0.5  1  • * 1.5  2  2.5  •  •  3* £ • +  Satisfies ACI 21.4.4.1 Does NotSatjsfyACI21.4.4.1  3  3.5  4  4.5  5  0  0.5  1  1.5  2  2.5  3  Satisfies ACI 21.4.4.1 Does NotSatisfyACI 21.4.4.1 3.5  c  •a  •  ft 0.5  1.5  2  2.5  3  3.5  4  4.5  5  0  •  --—L  L  Satisfies ACI 21.4.4.1 Does Not Satisfy ACI 21.4.4.1 1  4.5  /p  • !  0  4  PprovkJed BBM05  PFrovkied * PAD:  0.5  1  1.5  * 2  • * 2.5  3  Pprovided ' PcSA  PFfovkted ^ PBS98  197  Satisfies ACI 21.4.4.1 Does NotSatisfyACI21.4.4.1 3.5  4  4.5  5  Appendix D  •  •r :  -*t.  . D  •  * I  —  •  —  _  n*un  D  L  J  Satisfies ACI 21.4.4.1 Does Not Satisfy ACI 21.4.4.1  Satisfies ACI 21.4.4.1 Does NotSatisfyACI 21.4.4.1  Pr+ovkled ' NZS p  fFtovWed PLP04  • •  foe,  • •  L  • 4 2  2.5  ft  !  • • • *  Satisfies AC121.4.4.1 Does NotSatisfyACI21.4.4.1 2  3 /  •  • Q  fd •  l^n  * p L  ft  3  PprovkJed ' PSK97  PFVovktedPpF92  I Ion*  2.5  Satisfies ACI21.4.4.1 Does NotSatisfyACI21.4.4.1  UL  1...  • *  Pprovided '  Satisfies ACI21.4.4.1 . 4 Does NotSaHsfyACI21.4.4.1  PsKBS  • 4  Pprovided ' PsRD2  198  Satisfies ACI 21.4.4.1 Does NotSatisfyACI 21.4.4.1  Appendix D  • •  D  f  in  L___»___°__i.  4  L„-»-  4  D  1  4 Satisfies ACI 21.4.4.1 Does NotSatisfyACI 21.4.4.1  Satisfies ACI 21,4.4.1 Does NotSatisfyACI 21.4.4.1  Provided  P  Provided PW2H.P  WZP94  Table D.5 C i r c u l a r scatter plot statistics (without A C I limit)  Model ACI A23 PP92 SR02 BBM05 SK97 BS98 SKBS WZP94 LP04 WZPLP NZS  A 3.4 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0  199  B 4.8. 28.6 8.3 33.3 18.2 18.2 5.6 18.2 9.1 9.1 9.1 7.1  C 1.3 28.6 8.3 33.3 18.2 18.2 5.6 18.2 9.1 9.1 9.1 7.1  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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