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Comparison of non-linear analytical and experimental curvature distributions in two-column bridge bents English, Daryl S. 1996

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COMPARISON OF NON-LINEAR A N A L Y T I C A L A N D E X P E R I M E N T A L C U R V A T U R E DISTRIBUTIONS IN T W O - C O L U M N BRIDGE BENTS by DARYL S. ENGLISH B.A.Sc, The University of British Columbia, 1993 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE in THE FACULTY OF GRADUATE STUDIES DEPARTMENT OF CIVIL ENGINEERING We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA January, 1996 © Daryl S. English, 1996 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of &v£>//^&<£<Z 7^^) The University of British Columbia Vancouver, Canada Date DE-6 (2/88) ABSTRACT The Ministry o f Transportation and Highways of British Columbia has conducted a seismic assessment and upgrade initiative for many of its major bridges. Many deficiencies had been noted in the reinforced concrete approach bents o f these bridges and the consequences of recent failures caused by earthquake loading have emphasized the need for retrofitting to be carried out on bridges with deficiencies. Since the costs o f rehabilitating the bridge bents are significant, a scale model testing program was devised. Models o f bents comprising the details o f the approach spans of the Oak Street Bridge were cast and then subjected to slow cyclic lateral load testing. The specimens were instrumented externally with linear potentiometers, and internally using strain gauges bonded to the reinforcement. The objectives o f the test program were primarily to confirm the seismic deficiencies in the as-built bents and to prove the adequacy of proposed economical retrofit schemes for two-column bridge bents. Particular to this thesis, the test program was also intended to produce data for further research that would contribute to the art of retrofit design. The strain gauge data obtained from the test program presented the opportunity to derive section curvatures at discrete locations wifJiin the specimens for various stages of loading. The data obtained from the strain gauges of the models were analyzed. Curvature distributions for two of the retrofit schemes that performed particularly wel l were derived. The distributions were integrated to give deflections which were then compared with the measured displacements. The errors in the calculated displacements ranged from -3% to +21%. Using the theoretical member properties, combined with the known material properties, analytical curvature distributions were derived using the non-linear analysis program D R A I N - 2 D X . The shapes of the distributions and the peak curvature values were the focus of interest and using moment-curvature relationships, estimates o f peak concrete strains were predicted and compared with peak strain capacities. The strain capacities were derived from theory that accounts for the level o f confinement provided by transverse reinforcement in a section. It was estimated that the architectural fillet region of the beam-column joint region, when in compression, was able to provide confinement enough to sustain concrete strains of the order o f 0.013. The same fillet region retrofitted with high strength fiberglass wraps was estimated to be capable o f ultimate concrete strains o f approximately 0.027. The experimentally derived curvatures were then compared with those obtained analytically. It was found that the curvature distributions and the peak values compared reasonably well, which increased the confidence in the ability o f the analysis to predict the flexural behaviour o f retrofitted two-column bridge bents. The inclusion of joint shear deformations reduced the curvature demand in the plastic hinge regions and improved the agreement between the experimental and analytical curvatures. It is felt that the deterioration o f the bond between the concrete and the reinforcement, caused by the cyclic nature o f the tests, facilitated the derivation o f reasonable approximations to the curvature distributions by reducing the tension stiffening effect on the reinforcement. This deterioration o f the bond, particularly in the plastic hinge regions, decreased the variations o f experimental curvatures occurring between cracks. T A B L E O F C O N T E N T S A B S T R A C T ii L I S T O F T A B L E S vii L I S T O F F I G U R E S viii L I S T O F P H O T O G R A P H S x A C K N O W L E D G M E N T S xii C H A P T E R 1 - I N T R O D U C T I O N 1 1.1 B A C K G R O U N D 1 1.2 TEST P R O G R A M OBJECTIVES 4 1.3 SCOPE OF THE P R O G R A M 5 1.4 THESIS OBJECTIVES 7 C H A P T E R 2 - P R O T O T Y P E B E N T A N D D E F I C D 2 N C H C S 8 2.1 SEISMIC D E S I G N B A C K G R O U N D 8 2.2 SELECTION OF A PROTOTYPE PIER 9 2.3 SEISMIC DEFICIENCIES I N THE A P P R O A C H B E N T S 12 2.3.1 REINFORCING DETAILS 12 2.3.2 C O N C R E T E S H E A R RESISTANCE 14 2.4 S C A L I N G OF THE PROTOTYPE B E N T S28 TO M O D E L DIMENSIONS 14 2.5 M A T E R I A L PROPERTIES 16 2.5.1 STEEL REINFORCEMENT 16 2.5.2 C O N C R E T E 18 C H A P T E R 3 - T H E T E S T A R R A N G E M E N T 1 9 3.1 TEST S E T - U P 19 3.2 INSTRUMENTATION 20 3.3 V E R T I C A L L O A D I N G 24 3.4 L A T E R A L L O A D I N G 24 C H A P T E R 4 - M O D E L D E S C R I P T I O N S 28 4.1 OSB1 - A S - B U I L T SPECIMEN 28 4.2 RETROFIT M O D E L S 28 4.2.1 OSB2 - I N T E R N A L L Y POST-TENSIONED C A P B E A M 29 4.2.2 OSB4 - V E R T I C A L L Y A N D H O R I Z O N T A L L Y POST-TENSIONED C A P B E A M WITH STEEL C O L U M N JACKETS 29 4.2.3 OSB5 - E X T E R N A L L Y POST-TENSIONED C A P B E A M WITH F I B E R G L A S S W R A P S O N THE C A P B E A M A N D C O L U M N S 31 V C H A P T E R 5 - O V E R A L L E X P E R I M E N T A L T E S T R E S U L T S 3 5 5.1 O V E R V I E W 35 5.2 TEST O S B 1 - AS-BUILT SPECIMEN 3 5 5.3 TEST O S B 2 - I N T E R N A L L Y POST-TENSIONED C A P B E A M 3 7 5.4 TEST O S B 4 - V E R T I C A L L Y A N D H O R I Z O N T A L L Y POST-TENSIONED C A P B E A M WITH C O L U M N JACKETS 41 5.5 TEST O S B 5 - PRESTRESSED C A P B E A M WITH FIBERGLASS W R A P S O N T H E C A P B E A M A N D C O L U M N S 4 4 C H A P T E R 6 - A N A L Y T I C A L P R E D I C T I O N S 4 9 6.1 O V E R V I E W 4 9 6.2 D R A I N - 2 D X M O D E L S 5 0 6.2.1 N O D A L A R R A N G E M E N T S 50 6.2.2 F L E X U R A L A N A L Y S I S 53 6.2.3 A C C O U N T I N G FOR JOINT S H E A R D E F O R M A T I O N S 56 6.2.4 POST PROCESSING OF D R A I N - 2 D X RESULTS 57 6.3 O S B 4 RESPONSE 58 6.4 O S B 5 RESPONSE 66 C H A P T E R 7 - E X P E R I M E N T A L I N T E R P R E T A T I O N .'. 7 2 7.1 O V E R V I E W . 7 2 7.2 S T R A I N G A U G E E V A L U A T I O N 7 2 7.2.1 S P E C I M E N O S B 4 73 7.2.2 SPECIMEN O S B 5 78 7.3 C A L C U L A T I N G B E N T DISPLACEMENTS 82 7.4 JOINT S H E A R DEFORMATIONS. . 86 7.5 O S B 4 RESPONSE 88 7.5 O S B 5 RESPONSE 9 2 7.7 T H E T E N S I O N STIFFENING E F F E C T A N D B O N D STRESSES 9 4 C H A P T E R 8 - C O M P A R I S O N O F M E A S U R E D A N D A N A L Y T I C A L R E S U L T S . . . . 9 9 8.1 S P E C I M E N O S B 4 9 9 8.2 S P E C I M E N O S B 5 105 C H A P T E R 9 - S U M M A R Y A N D C O N C L U S I O N S I l l R E F E R E N C E S 1 1 4 A P P E N D T X A - M A T E R I A L P R O P E R T H C S 1 1 7 A P P E N D I X B - S T R U C T U R A L D R A W I N G S 1 1 9 D W G . Q l 17-01 O A K STREET B R I D G E - P IER S 2 8 PROTOTYPE 120 D W G . Q117-11 O A K STREET B R I D G E - PIER S28 M O D E L 121 D W G . Q l 17-SK2 O A K STREET B R I D G E - S T R A I N G A U G E S 122 D W G . Q117-13 O A K STREET B R I D G E - PIER S28 C A P B E A M RETROFIT S C H E M E 2.. 123 D W G . Q117-14 O A K STREET B R I D G E - P I E R S28 C A P B E A M RETROFIT S C H E M E 3.. 124 A P P E N D I X C - P H O T O G R A P H S 125 A P P E N D I X D - C O M P U T E R P R O G R A M " E X " S O U R C E C O D E 148 vii L I S T O F T A B L E S T A B L E 1.1 C O M P L E T E TEST P R O G R A M SPECIMEN DESCRIPTIONS A N D N O T A T I O N S 6 T A B L E 3. l T Y P I C A L L O A D SEQUENCES 27 T A B L E 4.1 S P E C I M E N DESIGNATIONS W I T H RESPECT TO K C C L D R A W I N G S 29 T A B L E 6.1 N O D A L COORDINATES FOR SPECIMENS OSB4 A N D OSB5 52 T A B L E 6.2 C A P B E A M SECTION CAPACITIES A N D INERTIAS 54 T A B L E 6.3 P E A K A N A L Y T I C A L C U R V A T U R E S FOR THE PLASTIC H I N G E R E G I O N S OF OSB4 64 6.4 P E A K A N A L Y T I C A L C U R V A T U R E S FOR THE PLASTIC H I N G E REGIONS OF OSB5 71 T A B L E 7.1 JOINT S H E A R STRAINS FOR OSB4 A N D OSB5 D I S P L A C E D TO T H E N O R T H 88 T A B L E 7.2 M E A S U R E D DISPLACEMENTS V E R S U S C A L C U L A T E D D I S P L A C E M E N T S F O R OSB4.91 T A B L E 7.3 M E A S U R E D DISPLACEMENTS V E R S U S C A L C U L A T E D D I S P L A C E M E N T S F O R OSB5 .94 T A B L E 8.1 M E A S U R E D DISPLACEMENTS V E R S U S R E V I S E D C A L C U L A T E D D I S P L A C E M E N T S F O R OSB4 105 T A B L E 8.2 M E A S U R E D DISPLACEMENTS V E R S U S R E V I S E D C A L C U L A T E D D I S P L A C E M E N T S FOR OSB5 110 T A B L E A l R E I N F O R C I N G STEEL PROPERTIES 117 T A B L E A2 C O N C R E T E C Y L I N D E R STRENGTHS 117 viii LIST O F FIGURES F I G U R E 2.1 T Y P I C A L F O U R S P A N S E G M E N T OF THE O A K STREET B R I D G E 10 F I G U R E 2.2 O A K STREET B R I D G E B E N T S 2 8 - PROTOTYPE DIMENSIONS 11 F I G U R E 2.3 A S - B U I L T M O D E L DIMENSIONS 16 F I G U R E 3.1 O A K STREET B R I D G E TEST SET-UP 19 F I G U R E 3.2 E X T E R N A L INSTRUMENTATION 21 F I G U R E 3.3 INTERNAL INSTRUMENTATION 23 F I G U R E 3.4 T Y P I C A L L O A D SEQUENCES 25 F I G U R E 3.5 M E T H O D OF PREDICTING THE Y I E L D D I S P L A C E M E N T 2 6 F I G U R E 4.1 S P E C I M E N O S B 4 31 F I G U R E 4.2 S P E C I M E N O S B 5 3 2 F I G U R E 4.3 F IBERGLASS W R A P STRESS-STRAIN RELATIONSHIPS 33 F I G U R E 5.1 L A T E R A L L O A D D I S P L A C E M E N T RESPONSE FOR O S B 1 3 6 F I G U R E 5.2 L A T E R A L L O A D D I S P L A C E M E N T RESPONSE FOR O S B 2 3 9 F I G U R E 5.3 L A T E R A L L O A D D I S P L A C E M E N T RESPONSE FOR O S B 4 4 2 F I G U R E 5.4 L A T E R A L L O A D D I S P L A C E M E N T RESPONSE FOR O S B 5 45 F I G U R E 6.1 N O D A L A R R A N G E M E N T S FOR SPECIMENS O S B 4 A N D O S B 5 51 F I G U R E 6.2 C O L U M N SECTION INTERACTION D I A G R A M 5 6 F I G U R E 6.3 A N A L Y T I C A L L A T E R A L L O A D D I S P L A C E M E N T RESPONSE F O R O S B 4 5 9 F I G U R E 6.4 A N A L Y T I C A L C A P B E A M C U R V A T U R E S FOR O S B 4 61 F I G U R E 6.5 IDEALIZED M E M B E R F L E X U R A L RESPONSE U S E D B Y D R A I N - 2 D X 6 2 F I G U R E 6.6 A N A L Y T I C A L C O L U M N C U R V A T U R E S FOR O S B 4 63 F I G U R E 6.7 A N A L Y T I C A L L A T E R A L L O A D D I S P L A C E M E N T RESPONSE F O R O S B 5 67 F I G U R E 6.8 A N A L Y T I C A L C A P B E A M C U R V A T U R E S FOR O S B 5 68 ix F I G U R E 6.9 A N A L Y T I C A L C O L U M N C U R V A T U R E S FOR O S B 5 69 F I G U R E 7.1 N O R T H C A P B E A M STRAINS FOR O S B 4 O N C Y C L E 2 OF E A C H S E Q U E N C E 75 F I G U R E 7.2 N O R T H C O L U M N STRAINS FOR O S B 4 O N C Y C L E 1 OF E A C H S E Q U E N C E 7 7 F I G U R E 7.3 N O R T H C A P B E A M STRAINS FOR O S B 5 O N C Y C L E 1 OF E A C H S E Q U E N C E 7 9 F I G U R E 7.4 N O R T H C O L U M N STRAINS FOR O S B 5 O N C Y C L E 1 OF E A C H S E Q U E N C E 81 F I G U R E 7.5 INTEGRATION M E T H O D U S E D TO C A L C U L A T E B E N T D E F L E C T I O N S 84 F I G U R E 7.6 V I R T U A L W O R K M E T H O D OF D I S P L A C E M E N T C A L C U L A T I O N 86 F I G U R E 7.7 E X P E R I M E N T A L C A P B E A M C U R V A T U R E S FOR S P E C I M E N O S B 4 89 F I G U R E 7.8 E X P E R I M E N T A L C O L U M N C U R V A T U R E S FOR S P E C I M E N O S B 4 9 0 F I G U R E 7.9 E X P E R I M E N T A L C A P B E A M C U R V A T U R E S FOR S P E C I M E N O S B 5 93 F I G U R E 7 .10 E X P E R I M E N T A L C O L U M N C U R V A T U R E S FOR S P E C I M E N O S B 5 9 4 F I G U R E 8.1 C O M P A R I S O N OF C U R V A T U R E S A T DUCTILITY L E V E L 2.1 F O R O S B 4 102 F I G U R E 8.2 C O M P A R I S O N OF C U R V A T U R E S A T DUCTILITY L E V E L 4.0 FOR O S B 4 103 F I G U R E 8.3 C O M P A R I S O N OF C U R V A T U R E S A T DUCTILITY L E V E L 5.7 FOR O S B 4 104 F I G U R E 8.4 C O M P A R I S O N OF C U R V A T U R E S A T DUCTILITY L E V E L 2.2 F O R O S B 5 107 F I G U R E 8.5 C O M P A R I S O N OF C U R V A T U R E S A T DUCTILITY L E V E L 4.0 F O R O S B 5 108 F I G U R E 8.6 C O M P A R I S O N OF C U R V A T U R E S A T DUCTILITY L E V E L 6.0 F O R O S B 5 109 F I G U R E A l STRESS-STRAIN C U R V E FOR #5 M A I N R E I N F O R C E M E N T 118 X LIST OF PHOTOGRAPHS PHOTO 1.1 A E R I A L V I E W OF THE O A K STREET B R I D G E L O O K I N G N O R T H 125 PHOTO 2.1 B E N T S 2 4 OF THE O A K STREET B R I D G E 125 P H O T O 3.1 T Y P I C A L S T R A I N G A U G E A T T A C H E D TO A #5 B A R 126 P H O T O 3.2 T Y P I C A L S T R A I N G A U G E W R A P P E D I N PROTECTIVE P U T T Y 126 PHOTO 3.3 T Y P I C A L S T R A I N G A U G E W R A P P E D INSULATING D U C T T A P E 127 P H O T O 3.4 D I A G O N A L S Y S T E M OF INSTRUMENTED B A R S I N T H E N O R T H JOINT 127 P H O T O 4.1 S P E C I M E N O S B 1 I N P A R T I A L F O R M W O R K A T A . P . S 128 P H O T O 4 . 2 S P E C I M E N O S B 1 L O A D E D O N THE MODIFIED A . P . S . T R A I L E R 128 P H O T O 4.3 S P E C I M E N O S B 2 WITH A N C H O R A G E S Y S T E M 129 P H O T O 4.4 S P E C I M E N O S B 4 I N THE TESTING F R A M E PRIOR TO TESTING 129 P H O T O 4.5 INSTALLATION OF FIBERGLASS W R A P O N THE S O U T H E N D OF THE C A P B E A M .... 130 P H O T O 4.6 START OF FIBERGLASS W R A P O N THE SOUTH C O L U M N 131 P H O T O 4 . 7 INSTALLATION OF S M A L L FIBERGLASS STRIPS O N THE N O R T H C O L U M N 132 PHOTO 4.8 C A P B E A M OF O S B 5 PRIOR TO TESTING 133 P H O T O 4.9 S O U T H C O L U M N A N D C A P B E A M OF O S B 5 PRIOR TO TESTING 133 P H O T O 5 . 1 O S B 1 - F I R S T C Y C L E TO D I S P L A C E M E N T 0.9 I N 134 P H O T O 5.2 O S B 1 - FIRST C Y C L E TO D I S P L A C E M E N T 1.24 I N 134 PHOTO 5.3 O S B 2 - S O U T H E N D O F C A P B E A M A T DUCTILITY 1.4 135 PHOTO 5.4 O S B 2 - N O R T H E N D OF C A P B E A M A T DUCTILITY 1.4 135 P H O T O 5 . 5 O S B 2 - SOUTH E N D OF C A P B E A M AT DUCTILITY 6 136 P H O T O 5.6 O S B 2 - N O R T H C O L U M N A T DUCTILITY 1.4 136 PHOTO 5.7 O S B 2 - N O R T H C O L U M N S H E A R F A I L U R E A T DUCTILITY 6 137 P H O T O 5 . 8 O S B 4 - N O R T H E N D OF C A P B E A M A T DUCTILITY 4 138 PHOTO 5.9 O S B 4 - N O R T H JOINT A T DUCTILITY 4 138 P H O T O 5 .10 O S B 4 - N O R T H JOINT A T DUCTILITY 6 139 PHOTO 5.11 O S B 4 - N O R T H JOINT AT DUCTILITY 9 140 P H O T O 5 . 1 2 O S B 4 - N O R T H JOINT A N D B E A M U N D E R S I D E A T DUCTILITY 9 141 P H O T O 5.13 O S B 4 - N O R T H JOINT A T DUCTILITY 12 142 P H O T O 5.14 O S B 5 - SOUTH E N D OF C A P B E A M A T D I S P L A C E M E N T 1.08 I N 143 P H O T O 5.15 O S B 5 - SOUTH JOINT A T D I S P L A C E M E N T 1.08 I N 143 P H O T O 5 . 1 6 O S B 5 - SOUTH E N D OF C A P B E A M A N D JOINT A T D I S P L A C E M E N T 3.2 I N 144 P H O T O 5 . 1 7 O S B 5 - S O U T H E D OF C A P B E A M A N D JOINT A T D I S P L A C E M E N T 4.3 I N 144 P H O T O 5.18 O S B 5 - SOUTH C O L U M N FIBERGLASS R E M O V E D A T D I S P L A C E M E N T 4.3 I N 145 P H O T O 5 . 1 9 O S B 5 - S O U T H E N D OF C A P B E A M A T D I S P L A C E M E N T 4.3 I N 145 PHOTO 5.20 O S B 5 - N O R T H C O L U M N B U C K L E D R E I N F O R C E M E N T 146 P H O T O 6.1 O S B 4 - N O R T H C O L U M N S P A L L E D C O N C R E T E A T DUCTILITY 6 147 PHOTO 6.2 O S B 4 - O V E R A L L V I E W A T DUCTILITY 12 147 A C K N O W L E D G M E N T S The author is extremely grateful for the guidance and encouragement provided by Dr. Don Anderson throughout the duration of this research. His influence and personality has impressed upon me a clearer, more positive approach to problems and difficulties in general. M y academic career here at the University of British Columbia has been fulfilling because of Don's inherent persistence and also his willingness to provide financial support for this research. The advice and support of Dr. Robert Sexsmith is also appreciated during the reading of this thesis and especially with regards to suggestions made during the test program. His thoughts and suggestions provided a somewhat more practical approach to the issues that arose. I am grateful for the unconditional support that Tammy has given me through what seemed, at times, a lengthy and exhausting academic career. Her willingness to stick with these endeavors has made all the difference. I am confident that we will look back at this chapter in our lives and not regret it. I appreciate the roles played by my friends throughout my entire stay at the University of British Columbia. Had something happened that wouldn't have allowed me to complete my endeavors here, the friendships made would have made it all worthwhile. I think you all know who you are. Finally, I would like to thank my family for initially providing the majority of the financial support, and later on, continued encouragement. Most importantly, I am thankful that my personal goals were respected and that there was never any doubt in my ability to accomplish them. Unfortunately, our Grandmother, Agda Erickson is not able to be here to witness the completion of this thesis. I do however, get satisfaction knowing that she would have enjoyed this day. This thesis is dedicated to the memory of Agda Erickson; 1909 - 1995. 1 CHAPTER 1 - INTRODUCTION 1.1 Background Recent seismic events such as the 1971 San Fernando, the 1987 Whittier Narrows, the 1989 Loma Prieta, the 1994 Northridge and the 1995 Kobe earthquakes have demonstrated the need for retrofit measures to be carried out on bridges designed with older codes. As many bridge structures serve as vital links for emergency vehicles, and the consequences of long term disruption to transportation networks are significant, transportation authorities are concerned about the need to improve the seismic resistance of these older bridges. As a result, detailed retrofit programs have been initiated to assess the seismic vulnerability of bridge structures and devise economical retrofit schemes to mitigate against the effects of earthquakes (Roberts, 1991). Some examples of the damage experienced by bridges in recent earthquakes include: brittle shear failures in columns and beams, loss of span failures, complete collapse of portions of the superstructure, shear failures in beam-column joints, pullout failures of vertical column reinforcement, and numerous failures occurring at the foundation level (Mitchell, Tinawi and Sexsmith, 1994). In a seismic review of the Oak Street, the Queensborough, and three other major bridges in the Lower Mainland commissioned by the British Columbia Ministry of Transportation and Highways, deficiencies have been noted in the reinforced concrete approach bents of all the bridges (Crippen International Ltd., 1993). Many of these deficiencies are serious in that they indicate the bridges, or portions of them, could fail in a brittle manner at low seismic load levels. In particular, the cap beams of the approach bents of the Oak Street Bridge have been identified as having insufficient transverse reinforcement, poor anchorage of the positive moment reinforcement, and numerous short cut-off locations for the longitudinal reinforcement. Potential plastic hinge regions in both the cap beams and the columns are inadequately reinforced to carry shear at modest ductility levels. The columns lack sufficient confinement reinforcement and the joints also have insufficient horizontal reinforcement (Kennedy, Turkington and Wilson, 1992). Some testing of existing designs has been conducted by C A L T R A N S , the California Transportation Authority, on structures of approximately the same age as bridges in the Lower Mainland (Priestley and Seible, 1991). These structures were also designed with approximately the same design rules as the bridges in the Lower Mainland. The tests concentrated on the behaviour of poorly tied columns and on the anchorage of the column reinforcement at the footing level (Xiao, Priestley and Seible, 1993). In addition, a few tests have been carried out on the as-built and retrofitted outrigger joints between the cap beam and columns that suffered major damage during the Loma Prieta earthquake (Priestley, Seible and Chai, 1992). With respect to twin-column bridge bents, two small scale shake table tests have been performed on a bent in California that suffered a column shear failure during the San Fernando earthquake in 1971 (MacRae, Priestley and Seible, 1994). The shear failure resulted in the collapse of the bridge, and the testing was aimed at reproducing the observed failure mode and improving the seismic behaviour with a column retrofit scheme. Some successful retrofit testing has been performed on bridge columns using steel jackets to increase the shear capacity, the concrete confinement and the flexural performance (Chai, Priestley and Seible, 1991). In addition, bridge column retrofits and testing has been performed using high strength fiberglass epoxy wraps (Fyfe, 1994). In general however, there has been very little testing which is useful for estimating the ultimate strength or the ductility o f two-column bents like the ones comprising the approach spans of the Oak Street Bridge. Among the Oak Street, Queensborough, 2nd Narrows, Port Mann, Knight Street and Patullo Bridges, there are over 200 concrete approach bents which may potentially require some level o f seismic retrofit. Shown in Photo 1.1 is an aerial view of the Oak Street Bridge. The bridge runs approximately north-south and connects the city o f Vancouver, shown in the top portion o f the photo, to the city of Richmond on the bottom, and spans the north arm of the Fraser River. The bridge has long approaches with 83 two-column bents, due to ship clearance requirements at the main span. The expected costs o f retrofits for these bents, depending on the selected level of retrofit, were estimated at $15 million to $20 million. Owing to the number of bents, the significant retrofit cost per bent, the seriousness of the expected failure modes, and the likelihood that retrofit designs by various consultants would produce inconsistent levels of conservatism without some design guidelines, a test program consisting o f both as-built and retrofitted bents was considered to be highly beneficial. Particularly, the test program was expected to produce economical retrofit schemes that would improve the seismic behaviour of the bents. The Oak Street Bridge bents were considered to be the most critical, and since there were so many, a bent comprising details representative of the Oak Street Bridge bents was selected for testing. Later in the program, one bent representative o f the Queensborough Bridge was also tested. Complete details of the entire test program can be found in a report by Anderson et al. (1995). 1.2 Test Program Objectives The test program had several objectives pertaining to both the as-built specimen and the retrofitted bents. The as-built test was performed to experimentally determine the critical failure modes of typical two-column bents as they presently exist in many of the major bridges in the Lower Mainland, and to quantify the ultimate strength and post-elastic performance of the as-built bents with respect to ductility reserves. The tests were to also demonstrate the behaviour of the beam-column joint in both the as-built and retrofitted specimens. This aspect o f the behaviour has been the subject of much conjecture internationally and is vital to the overall performance of the bents. Effective retrofits of beam-column joints have proven to be expensive in California (Priestley and Seible, 1991). B y demonstrating the effectiveness of the as-built beam-column joint, significant costs were expected to be saved by identifying the appropriate level o f retrofit required for the joints. Tests o f the retrofitted specimens were to demonstrate the effectiveness of various combinations of cap beam and column retrofits. The performance and economy of each retrofit scheme could then be compared. The tests were to demonstrate that the criteria established for the detailed design of the bent retrofits provides acceptable margins o f safety against undesired failure modes, and to identify areas of conservatism leading to unnecessary expenditures in retrofit designs. This would allow smaller over-strength margins to be used in design of retrofits and permit various consultants to use a more consistent set o f design and assessment criteria on all Ministry of Transportation and Highways bridges. A reduction in retrofit costs could then be expected by reducing the level o f design conservatism, reducing the number o f bents requiring retrofit, and by reducing the required level o f retrofit o f the bents. Design criteria for new bridge bents have been greatly improved in recent years. In many instances, the engineer is expected to design retrofit solutions that provide safety levels comparable to those of new structures. This expectation may not always be possible or justified due to limitations on resources. Rather, a rational choice between performance and its related cost should be the objective. The test program was expected to provide information for improved estimates of proposed retrofit costs, and provide an indication o f the practical aspects o f proposed retrofit work. More applicable to this thesis however, the test program was to provide necessary data for further analysis that would contribute to retrofit design. 1.3 Scope of the Program Five scale models of the Oak Street Bridge bent S28 and one model o f the Queensborough Bridge bent S26 were constructed and were tested under quasi-static cyclic load conditions with increasing displacements. The overall results of four o f the Oak Street models and detailed results of two retrofitted specimens are presented herein. The models were 0.45 scale, and were internally and externally instrumented to provide information useful in achieving the program objectives. Presented in Table 1.1 below are the descriptions and denotations of all the specimens tested. The test number is the order in which the tests were carried out, while the specimen number indicates the order in which the as-built specimens were constructed. A l l of the test specimens in the test program are presented for completeness, although, only results o f the Oak Street Bridge specimens wi l l be discussed in this thesis. Table 1.1 Complete Test Program Specimen Descriptions and Notations Test No. Specimen No. Specimen Description Denoted 1 1 The as-built Oak Street bent S28 with no retrofitting. OSB1 2 2 A cap beam retrofit consisting of internal longitudinal post-tensioning in two ducts. OSB2 3 3 A cap beam retrofit consisting of a reinforced under-beam, longitudinal plates along the top of the cap beam, tied together with post-tensioned vertical shear reinforcement, plus circular steel column jackets. OSB3 4 4 A cap beam retrofit consisting of internal longitudinal and vertical post-tensioning, plus circular steel column jackets. OSB4 5 6 The as-built Queensborough bent S26 with no retrofitting. QB1 6 6 The repaired Queensborough as-built bent S26 with surface repair and epoxy injection into significant cracks. QB1R 7 5 A retrofit including external longitudinal post-tensioning of the cap beam, with fiberglass wraps in critical regions of the cap beam and columns. OSB5 Loading of the specimens consisted of simulated dead loads applied at the superstructure bearing locations, plus cyclic lateral loads at increasing displacements to simulate the effects of earthquake motions. The lateral load was applied at a height above the top of the specimen which coincided with the center of gravity of the bridge superstructure and thus simulated inertial loading. 1.4 Thesis Objectives The test program produced the data necessary for this thesis research so that a contribution to retrofit design could be made. Much of this data was obtained from the strain gauges affixed "to the reinforcement of the specimens. After completion o f the test program, the data was to be examined for definitive information on several important aspects o f the lateral cyclic behaviour o f the two specimens. Specimens OSB4 and OSB5 were two of the retrofitted specimens that performed extremely well. One of the objectives is to experimentally and analytically identify the locations within these two bents undergoing inelastic deformations and quantify the demand in these locations. It is also intended to experimentally quantify the flexural demand imposed on these regions and estimate peak concrete strains for given structure displacement ductilities. These curvature demands are to be compared with those obtained analytically. The comparison between the experimental and analytical results is expected to determine i f the analytical models and methods used are effective in predicting the response of the structure. The primary locations that are expected to provide overall ductility to the bent are the tops of the columns immediately below the beam-column joint regions where significant flexural action was observed during testing. The cap beam and joint regions are also to be investigated for inelastic demands. In addition, the results of this research are intended to aid in predicting the non-linear response of retrofitted structures. This knowledge, in turn, wi l l assist a well planned and phased seismic retrofit program of bridges so that the risk o f catastrophic collapse is minimized and the level of damage may be mitigated. 8 C H A P T E R 2 - P R O T O T Y P E B E N T A N D D E F I C I E N C I E S 2.1 Seismic Design Background In order to identify potential deficiencies inherent in existing bridges, an understanding of the code provisions applicable at the time of design is necessary. The older bridges in Brit ish Columbia, including the Oak Street Bridge, were designed under the American Association o f State Highway Officials ( A A S H O ) provisions which is now called the American Association of State Highway and Transportation Officials ( A A S H T O ) . Prior to 1958, only vague references were made to seismic design requirements, although C A L T R A N S had developed specific seismic provisions in 1943. Reinforcing quantities and details were designed to meet loading and member resistances specified in the 1951 design standard, Design Specifications for Highway Bridges (DSHB) , Department o f Public Works of Brit ish Columbia. In 1958, after the construction o f the Oak Street Bridge, A A S H O introduced interim provisions following the 1943 C A L T R A N S provisions ( A A S H O , 1961). These required a lateral seismic force as a percentage of the weight. The force was 2% for spread footings on firm soil, 4% for spread footings on soft soil, and 6% for piled footings. These values were used by A A S H T O , and in B C , until the mid 1970's. The Design Specifications for Highway Bridges code used in the original Oak Street Bridge design did not specify any seismic loads, nor are references made to seismic loads on the original drawings. Wind loadings were used for the design of lateral load carrying members. A summation of wind loads in braces shown on the drawings for the main river spans indicates lateral load levels equivalent to approximately 10% of gravity loads. Wind loads on the approach span deck structures and on live load calculated using the D S H B gives a lateral load equivalent to about 7.5% of gravity. These comparatively small lateral loads were applied to the bridge during design, using working stress design concepts. Site-specific response spectra used for retrofit design, in conjunction with force reduction factors, lead to lateral force levels that were much higher than those used in the original design. The current force levels are expected to cause yielding in the cap beams and columns. Moment demands throughout the piers are therefore much different than those considered during the original design, leading to some o f the reinforcing deficiencies discussed below. Recently, the principles of capacity design have been widely accepted which have placed much more emphasis on details that provide the required performance in the post-yield range of behaviour. Capacity design principles require the designer to select areas where inelastic behaviour is to be forced, and to provide appropriate details to ensure acceptable behaviour of this plastic mechanism by avoiding brittle failures. The principles also require that the rest o f the structure be designed to resist the loads arising from the selected mechanism. Current retrofit designs are intended to keep capacity design objectives in mind with compromises being made where uneconomical costs would arise by modifying existing structures. 2.2 Selection of a Prototype P ier A representative bent needed to be chosen for modeling and testing. The approach spans are comprised of typical four span continuous segments as shown in Fig. 2.1 below. 10 SOUTH TO U.S.A. HIGHWAY #W NORTH TO VANCOUVER ,— APPROX. / GROUND ELEV] TYPICAL TWO COLUMN BENTS •CONCRETE GIRDERS r ~ ~ i c 37-3" GO-O" GO-O' GO-O' GO-O" Figure 2.1 Typica l Fou r Span Segment of the O a k Street Br idge The most common pier arrangement in the Oak Street Bridge comprises columns 48 in. square with 16 #11 vertical bars and ties spaced at 12 in. on centre. The beams are 42 in. wide by 60 in. deep with #3 stirrups at 36 in. centers in the central region. There are a total of 21 piers with these identical details, varying only in height. There are also 24 taller piers with 24-bar column reinforcing arrangements. Cap beam flexural reinforcing is identical in all o f these 45 piers. Bent S28 was chosen by Klohn-Crippen Consultants L td . in consultation with personnel at U . B . C . as a typical pier because it was near the average height and one in which the major deficiencies were in the cap beam. Shown in Photo 2.1 is the unretrofitted bent S24 of the Oak Street Bridge which is identical to bent S28 in structural details except that it is slightly taller. The deficiencies in the cap beam are believed to lead to potential instabilities in the superstructure or the bents themselves which may, in turn, lead to partial or total collapse of the structure. The bridge would then either be impossible to restore, or would be uneconomical to repair after a large seismic event. Bent S28 is also located at the first interior support o f the typical four span segments which is subjected to a slightly higher dead load reaction than the other bents and consequently a higher shear demand on the cap beam. See Fig. 2.1. Figure 2.2 indicates the overall dimensions of bent S28 including some superstructure dimensions and Drawing Q l 17-01 o f Appendix B shows complete details o f the reinforcement. Also provided on Drawing Q117-01, are the material properties specified at the time of construction and those determined at the time of the bent selection. C r r r l O ' - S " COLUMN BENT 12-2" 12--G" 15 ' -4 " J2-6 I l_ I I U r -I-c.c. or • J I. SUPERSTRUCTIJRE_ I \ \ I U \ LLP I 'BRIDGE DECK GIRDER5 AND DIAPHRAGM\ r—i r—i r — i r- • WOODEN PILES • M m M m U/S CAPBEAM O ' Figure 2.2 O a k Street Br idge Bent S28 - Prototype Dimensions 2.3 Seismic Deficiencies in the Approach Bents The expected seismic deficiencies in the prototype bents arise from the following main causes and bent details described below. Refer to Drawing Q117-01, Appendix B. A s mentioned above, the original seismic design loads for structures o f this age were low, and the reinforcing details for concrete structures built during the late 1950's, whether explicitly defined in codes or by standard practice, did not ensure ductile behaviour. A lso, the shear resistance of concrete in design codes was taken as being significantly higher than in modern codes, especially in regions where flexural hinging wil l occur. 2.3.1 Reinforc ing Details The following comments pertain to the Oak Street Bridge bents in particular, but many are applicable to other bridges in the Lower Mainland that were assessed for the Ministry of Transportation and Highways (Crippen International Ltd. , 1993). A summary of the most critical prototype seismic deficiencies in the cap beam and beam-column joint details are as follows: Cap beam stirrups comprise two legs of closed hoops spaced at 36 in. centers in potential plastic hinge zones. Some of the hoops have #4 bars and some have #5 bars. The volume and arrangement of stirrup steel is inadequate for shear, for concrete confinement, for longitudinal bar anchorage, and for restraint of main bars from buckling in hinge zones. The beam flexural reinforcement curtails at the earliest possible points. These locations were determined using moment diagrams that treated all loads as elastic, rather than considering demands arising from members reaching their flexural resistances. Positive beam reinforcement is completely curtailed half-way, or 24 in., into the joint. The anchorage of this reinforcement, at approximately 16d b , into the columns was questionable, although the architectural fillet detail at the beam soffit-column intersection was thought to have alleviated this condition to some degree by providing an increased level o f confinement or increased anchorage length. Here, d b denotes bar diameter. The horizontal beam-column joint reinforcing comprises three #3 ties at 12 in. centers. Although the joint details would be deficient by modern standards, they were not the weakest link in the as-built or the retrofitted bents of the Oak Street Bridge models. The expected seismic deficiencies in the columns were as follows. The column ties comprise three legs of #3 bars at 12 in. centers for the columns with 16 main #11 bars. As was the case with the beam stirrups, tie steel is especially inadequate for shear in the shorter columns, concrete confinement, and restraint of main bars in plastic hinge zones. Although column tie details are inadequate by modern standards, the design details were expected to provide adequate shear reinforcement in many of the longer columns, and were also expected to provide a nominal level o f ductility. Ties are closed with the ends o f the bars terminating in 135° hooks extending four bar diameters into the column cores. The tie spacing of 12 in. is slightly greater than 8 main bar diameters which would normally be the maximum required for nominal ductility in some modern codes. Ties engage every other main bar, providing a measure of confinement to core concrete as well as some resistance to main bar buckling. However, the maximum tie forces that can be generated are only about half of the force required in some codes to prevent main bars from buckling in hinge zones, and buckling o f main bars over more than one tie space may be expected at sufficiently large ductility demands. These factors were felt to provide enough confinement such that an ultimate concrete compressive strain of at least 0.005 could be relied upon when determining ductility demands for the seismic assessment of the existing bridge. 2.3.2 Concrete Shear Resistance The specified compressive strength of the concrete at the time o f construction o f the Oak Street Bridge was 3000 psi. The shear resistance of unreinforced concrete according to the D S H B was taken as 180 psi for concrete with a compressive strength of 3000 psi. This is 220% higher than attributed to concrete using some modern bridge codes. For members requiring shear reinforcing, the concrete contribution was limited to 90 psi with the remainder being resisted by stirrups. This is slightly higher than specified in modern codes for regions with no plastic hinges, however in plastic hinge zones the concrete shear resistance degrades towards zero at increasing ductilities. The extremely light shear reinforcing in the beams appears to stem from a combination o f the small design loads and the minimum stirrup provisions (spacing not greater than 3/4 of the member depth, with no minimum on stirrup steel volume), rather than on concrete shear resistance as given by the D S H B code. 2.4 Scal ing of the Prototype Bent S28 to Mode l Dimensions The prototype bent had to be scaled and the columns shortened to a convenient size for testing. A maximum model scale of 0.5 suited the height restrictions and the corresponding required force levels available in the Structures Laboratory at the University o f Brit ish Columbia. A scale of 0.45 was chosen as this scales the diameter o f the main #11 bars to #5 bars, thus minimizing problems associated with the scaling of reinforcement. The models represent the top half of the prototype pier. The columns extended from the inflection point at mid-height, due to a lateral load causing hinging to occur at the top and bottom of the columns, to the top of the pier. Pin connections were placed at the bases of the columns to allow rotation and prevent translation. The frame assembly's pin connections were equipped with trays into which the columns were grouted, which increased the effective length o f the columns by 3 1/4 in. This detail is evident in Fig. 2.3 and also in F ig . 3.1. The lateral loading was applied at the level of the superstructure centre of gravity, which was 60 in. above the top o f the prototype cap beam, to produce the correct axial forces in columns and consequently the correct cap beam shear demands. The application o f lateral load in the models scaled to 27 in. above the cap beam. Figure 2.3 shows the model and the overall dimensions. More detailed dimensions and reinforcing details are given in Drawing Q l 17-11, Appendix B. 16 I ] 1 21 1/2" f 2 3 - 4 - »»» BENT COLUMN R=l-4' 22 J / 2 ' I \ CO f?=r-4 BASE OF COLUMN - TO POINT OP ROTATION 13-10--fir Figure 2.3 As-built Model Dimensions 2.5 Material Properties 2.5.1 Steel Reinforcement Two samples of #11 column reinforcement bars from the Oak Street Bridge were extracted and tested. Tensile test results indicated yield stresses, f y = 49.1 ksi and 58.2 ksi, with ultimate stresses, fu = 68 ksi and 83.1 ksi, respectively. During the seismic assessment phase o f the Oak Street Bridge, it was thought that Grade 50 reinforcing had become available locally during the time of the actual construction and may have been used in some locations, although the design specified 40 ksi reinforcement. It was expected that the higher strength reinforcement would have been readily accepted in place o f the 40 ksi steel, and that both nominally 40 ksi and 50 ksi reinforcement would likely be found in the bridge. The tested yield strengths are respectively 12% and 16% greater than nominal i f it is assumed that both grades of steel were used in the bridge, and the results are consistent with expectations and test results performed on other reinforcement samples from that era. For example, the Queensborough Bridge was constructed shortly after the Oak Street Bridge, and tests on #11 reinforcement bars from that bridge, believed to be Grade 50 steel, indicated a yield stress of, fy = 56 ksi, which is 12% greater than the specified yield strength. For the test program, reinforcing steel with fy = 40 ksi was specified, with a maximum yield strength o f 55 ksi. Inquiries were made throughout Canada and the United States on the availability of Grade 40 reinforcement to replicate the specified prototype steel. Salmon Bay Steel in Seattle, Washington indicated that Grade 40 reinforcement was produced in #5 bar sizes or greater. Smaller bars like #3 or #4, would only be produced from Grade 60 steel. The strengths o f wire sizes were also investigated because stirrups and column ties in most cases scaled down to sizes smaller than #3 bars. Tree Island Industries o f Vancouver provided several mill certificates, and ran initial trials and tests on annealed stock wire, which tends to be stronger and more brittle when compared to conventional mild steel reinforcement. Based upon mill certificates obtained during the investigations, it was felt that Grade 40 reinforcement with a yield strength, fy of about 15% to 20% greater than the nominal 40 ksi grade could be procured. Therefore, no adjustments were made to model bar sizes based on variations of the prototype reinforcement yield strengths. Results from the initial annealing tests o f plain wire, as well as from reports in the literature on the expected properties of steel annealed at various temperatures and durations, indicated that the desired strengths could be achieved. Experience has however, shown that it was difficult to obtain consistent, predictable yield strengths of annealed wire. Measured yield strengths for the #5 bars in the Oak Street specimens averaged 49.5 ksi. The annealed wire yield strengths ranged between 33 and 47 ksi. The annealed wire strengths, which were used for the ties and stirrups in the models, are less than prototype strengths, however this was deemed acceptable for the test program since it would provide lower shear resistance and confinement forces and thus produce conservative results. Table A l o f Appendix A gives the yield and ultimate strengths of the steel used in the models and F ig. A l shows a stress-strain curve obtained from a #5 bar test. 2.5.2 Concrete Eight concrete cores were taken and tested from the actual bridge during the seismic assessment. The cores indicated that concrete in the bridge had a mean equivalent cylinder strength of about 6200 psi. Considering the variation in concrete strengths likely to be produced during casting of the test specimens, and that specimens would be tested anywhere from two weeks to several months from the time of casting, concrete strengths were specified to range from 5500 psi to 6300 psi. The concrete was also specified to not be air entrained since the original design for the bridge did not specify any air entrainment and the specimens were to be tested almost immediately after casting. Compressive strengths for the specimens relevant to this thesis ranged from 6900 to 7400 psi and are presented in Table A 2 of Appendix A . 19 C H A P T E R 3 - T H E T E S T A R R A N G E M E N T 3.1 Test Set-Up The test configuration and loading regimes were devised by individuals from both Klohn-Crippen Consultants L td. and U .B .C . As part of the graduate research of Seethaler (1995), the test frame shown in Fig. 3.1 was designed. The specimens were supported on rocker bearings that were part of the test frame. The vertical dead load was applied at five bearing points, consistent with the prototype girder locations, with the use of spreader beams and Dywidag bars connected to hydraulic jacks which were anchored to the structural test floor. These dead load forces remained constant throughout the duration o f each test. lr-a" BASE Figure 3.1 O a k Street Br idge Test Set-up The prototype Oak Street Bridge deck structure rests on the cap beam at five bearing points, and it was difficult to predict precisely how the lateral load would be transferred to the bent. Klohn-Crippen Consultants Ltd. had indicated that the two exterior girder spans of 20 the deck diaphragm were very flexible and would not participate significantly in the transferring o f the lateral load. It was thought that a reasonable approximation to the cap beam and joint forces would result i f only the two interior girder bearings closest to the columns were used to transfer the lateral load of the deck into the bent. It was also anticipated that the cap beam would elongate as it cracked and degraded during testing. It was for these reasons that the lateral load was applied to the bent through a determinate truss system which permitted slight elongation of the cap beam, and applied the lateral load equally to the bent at the two interior dead load bearing locations. See Fig. 3.1. The truss was designed to withstand a maximum lateral load of 150 kips. The lateral load was applied by a horizontal actuator located between the top of the loading truss and a lateral load frame at a distance of 27 in. above the top of the cap beam. A load cell was mounted between the actuator and the loading truss. The specially constructed reaction frame consisted o f two triangular trusses connected at the top with a deep spreader beam onto which the actuator was attached. The frame was designed to withstand the full 225 kip capacity of the lateral load actuator (Seethaler, 1995). Some lateral bracing perpendicular to the main axis of the test set-up provided lateral stability and temporary bracing to each specimen during test preparation. The entire test frame was post-tensioned to the laboratory's strong floor, although it was self equilibrating in the horizontal direction. 3.2 Instrumentation The major external instrumentation used during testing is shown diagramatically in F ig . 3.2. The small arrows in the figure indicate the direction of measured displacements or load. The vertical joint displacements were measured with potentiometers and horizontal displacements were recorded with two L V D T ' s located at the centre of the two joints. The lateral force was measured with a load cell located as shown in Fig. 3.1 and indicated in F ig . 3.2 also. Relative horizontal displacements between the specimen and load frame were measured by recording the actuator movement. External displacement measurements were taken at the north joint with a system of five L V D T ' s to determine the joint shear deformations. 3 LATERAL LOAD ACTUATOR AND LOAD CELL - d * 3 ACTUATOR LVDT EAST ELEVATION ACTUATOR LVDT - a e» Figure 3.2 External Instrumentation The internal instrumentation within each of the specimens is shown in F ig . 3.3. There were a total o f 81 strain gauges per specimen. The locations of 75 gauges are shown in Fig. 3.3. The names of the gauges were indicative of their locations within the bent. The first letter in the name, either a 'B1 or a ' C ' , indicates a gauge located in the cap beam or in the column. The second letter for the beam gauges would denote either beam Top, .Bottom, or iStirrup, and the second letter for the column Inside, Outside, or Tie. Since the instrumentation was symmetric, the letters TV 1 and 'S' were used to distinguish between the north and south ends of each specimen. The strain gauging pattern was symmetric about the centerline of the bent. 23 01 . < IDl o o-1. * DESIGNATES STRAIN GAUGE LOCATIONS ON MAIN BARS. * DESIGNATES STRAIN GAUGE LOCATIONS ON STIRRUPS AND TIES. 2. STRAIN GAUGES ON MAIN BARS LOCATED HALFWAY BETWEEN STIRRUPS OR TIES U.N.O. 3. STRAIN GAUGES ATTACHED TO SIDES OF REINFORCING BARS. 4. GAUGE LOCATION BS7 - 11 ARE SYMMETRIC TO GAUGES BS1 - 5. 4/0 Ca. STIRRUPS U/S CAPBEAM G 1/2" ,6 1/2-BT1 BT2BT3BT4 4 Ga. STIRRUPS fCOl JC04 CI4T *C05\ CI5* CT4 CT5 ,CTG CT7 B7te BT7 BT8 BB5 BT1 BBG -a SYM. ABOUT £ PIER STRAIN GAUGES DESIGNATION REBAR No. CAPBEAM TOP BT 1 - 1 N #5 18 BT 1 - <? S BOTTOM BB \ - G N #5 12 BB 1 - G S STIRRUPS BS 1 - 11 4 Ga. 4/0 Ga. 7 4 COLUMNS INSIDE CI 1 - 5 N #5 IO CI 1 - 5 S OUTSIDE CO 1 - 5 N #5 IO CO 1 - 5 S TIES CT 1 - 7 N 9 Ca. 14 CT 1 - 7 S TOTAL 75 SOUTH JOINT ELEVATION Figure 3.3 Internal Instrumentation Shown in Photo 3.1 is a typical strain gauge that has been attached to a #5 bar. Note the small region on the bar that has been milled to accommodate the gauge and terminal. The gauges were then coated with an electrical insulator and wrapped with a protective putty to guard against impact and the penetration of moisture. See Photo 3.2. The gauge assembly was then surrounded with insulating tape. This is shown in Photo 3.3. In addition to the instrumentation shown in Fig. 3.3, there were two instrumented aluminum bars located within the north joint oriented in an 'X ' pattern to measure strains in the diagonal directions. The configuration can be seen in Photo 3.4. There were 6 gauges installed on the aluminum bars, 3 oriented in each of the two directions. Gauges on the main reinforcement were typically located halfway between stirrups and column ties. The locations are indicated in more detail with respect to the specimen width on Drawing Q117-SK2 of Appendix B. The signals from all the instrumentation were recorded every two seconds and stored on a personal computer for further processing. 3.3 Vertical Loading In order to simulate the dead load on the specimen, the prototype dead load from the superstructure was scaled, resulting in a required dead load of 38.6 kips at each of the five bearing locations. The dead load was then applied through the five vertical hydraulic jacks working from a common manifold. The arrangement is shown in Fig. 3.1. The nominally vertical Dywidag bars that transmitted load from the jacks to the top of the test specimen took on a slight slope as the specimen was displaced laterally, hence there was a small horizontal component that countered the applied lateral force. This component amounted to approximately 2 kips for every inch of horizontal displacement. This force has been subtracted from the lateral load shown in the hysteresis plots that appear in later sections. 3.4 Lateral Loading The lateral loads were cycled so as to subject the test specimen to a load displacement history that would be more severe than one imposed by an earthquake. Mos t researchers 25 apply a similar pattern of loading, allowing comparisons of the performance between different structures or retrofit schemes to be made (Anderson et al., 1995). Figure 3.4 shows a schematic of two sequences in the lateral loading program. The program consisted of several sequences each of a particular load or displacement amplitude, denoted A , B , C , etc. Within a sequence there were typically three complete cycles. The sequences at low load level were performed to check the loading pattern, data acquisition system and to establish the initial stiffness of the test specimen. DISPLACEMENT AMPLITUDE Ci+D DISPLACEMENT AMPLITUDE CO TIME Figure 3.4 Typ ica l L o a d Sequences Except perhaps in the linear range, the lateral load was applied in sequences of controlled displacements. The load sequence at 75% of estimated yield load was performed to predict the yield displacement. Although estimates of yield forces can be quite accurate, estimates o f yield displacements are more difficult to predict due to uncertainties in the stiffness of cracked reinforced concrete sections. The yield displacement for the bent was calculated by taking the displacement at 75% of the estimated structure yield load and multiplying it by 4/3. Figure 3.5 illustrates this procedure. Subsequent sequences were 26 carried out under displacement control at multiples o f the yield displacement, i.e. displacement ductility levels o f 1, 1.5, 2, 3, 4, 6, 9, 12, or until the structure failed. Figure 3.5 Method of Predicting the Y i e l d Displacement Table 3.1 indicates the sequences with the corresponding amplitudes, period, and data intervals. Typically, within a particular sequence there were three complete cycles at a given displacement before the displacement was increased for the next sequence. Any variations are evident in the hysteresis plots of each test presented in Chapters 5 and 6. Table 3.1 Typ ica l L o a d Sequences Sequence Number of Ampl i tude Per iod Da ta Interval Cycles (min) (sec) A 2 or 3 10 or 20 kips 10 2 B 2 or 3 30 or 40 10 2 C 2 or 3 x a 10 2 D 3 / / A = l b 10 2 E 3 MA = 1.5 10 2 F 3 MA = 2.0 10 2 G 3 MA = 3.0 10 2 H 3 MA = 4.0 10 2 I 3 MA = 6.0 10 2 J 3 MA = 9.0 10 2 K 3 MA = 12.0 10 2 a x to be set at 75% of predicted yield force level after initial stiffness calculation b The predicted displacement at yield force based on 4/3 of measured displacement at load 28 CHAPTER 4 - MODEL DESCRIPTIONS 4.1 OSB1 - As-Built Specimen Drawing Q l 17-11 o f Appendix B shows the as-built model o f the Oak Street including all structural details. Figure 2.3 shows the overall dimensions o f the as-built specimen. Concrete strengths for all the models are given in Appendix A where the concrete strength is the compressive strength at the time of testing. Properties of the reinforcing steel are also given in Appendix A . Photo 4.1 o f Appendix C shows specimen OSB1 surrounded in partial formwork at the yard o f Architectural Precast Structures Ltd. The two cords that protrude from the specimen near the base of the columns contain wires that were used to connect the internal instrumentation to the data acquisition system. Shown in Photo 4.2 is the unpainted specimen OSB1 loaded on the trailer that was modified specifically to transport the models to and from the Structures Laboratory at U .B .C . 4.2 Retrofit Models The retrofitted test specimens were numbered O S B 2 through O S B 5 for the Oak Street bents. The successive numbering of the Oak Street specimens indicate the order o f testing. Three o f the retrofitted specimens corresponded to a particular retrofit scheme number used on the K C C L drawings which are included in Appendix B . Specimen O S B 5 was a retrofit performed at U .B .C . which was not included in the K C C L series and specimen OSB1 was the as-built specimen that was not modified and also not included in the K C C L retrofit schemes. A l l the specimens that wil l be discussed in this thesis are listed in Table 4.1 below. 29 Table 4.1 Specimen Designations With Respect to KCCL Drawings Specimen Specimen Description KCCL Retrofit Scheme No. OSB1 Oak Street as-built specimen n/a O S B 2 Cap beam post-tensioned longitudinally 2 O S B 4 Cap beam post-tensioned longitudinally and vertically plus steel jackets 3 O S B 5 Longitudinal post-tensioning with fiberglass jackets on the columns and the cap beam n/a 4.2.1 OSB2 - Internally Post-Tensioned Cap Beam This retrofit consisted of coring two ducts along the longitudinal axis o f the cap beam, inserting prestressing tendons and then post-tensioning them. The prototype design consisted of two tendons o f 12K15 bundles (12 strands at 15 mm diameter each). The scale model used two 1/2 in. and one 5/8 in. diameter strands in each hole. Refer to Drawing Q I 17-13, Appendix B . The depressed anchorage system and the location o f the two ducts can be seen in Photo 4.3. The two small strands that are seen to extend from the anchorage system at the end o f the cap beam are the ducts used to pressure grout the tendons to ensure a fully bonded post-tensioned element. The net post-tensioning produced an average compressive stress o f 417 psi after seating. The centroid of post-tensioning was 13-1/4 in. below the top o f the cap beam. 4.2.2 OSB4 - Vertically and Horizontally Post-Tensioned Cap Beam with Steel Column Jackets Based upon the performance of the cap beam during the O S B 2 test, the cap beam of O S B 4 was also retrofitted with internally bonded longitudinal post-tensioning, and in addition, with vertically post-tensioned rods to improve shear capacity and provide increased confinement to the longitudinal reinforcement. Figure 4.1 depicts the specimen including some important dimensions of the retrofit scheme. Complete structural details are shown in Drawing Q l 17-14, Appendix B. The vertical reinforcement was designed by K C C L to prevent the wide shear cracks observed in O S B 2 and also to add a vertical compressive stress that would improve the bond of the top longitudinal reinforcement in the cap beam. Steel jackets were fitted about the columns to within 14 in. of the underside of the cap beam to prevent brittle column shear failures. The steel jackets were expected to slightly increase the flexural strength o f the unjacketed regions of the columns by forcing hinging into the architectural fillet area above the top of the steel jackets. This would then engage the concrete in that area to provide an increased level of confinement and an increased moment arm. This increase in column flexural capacity was thus expected to increase the seismic demands on the cap beam as well. Photo 4.4 shows specimen O S B 4 in the test frame prior to initiation of the test. 31 FILLED 1 1 1 1* H I 1 1 1 1 1 1 1 1 H 1 M If R 1 i fl 1 1 1 i l f I 1 2" POST-TENSIONING DUCT q\l/2" FROM TOP V-O" — 3 SPACES AT 1-1 1/2" CIRCULAR STEEL JACKETS U/b CAP I BEAM V-2" 4 -11-8" Figure 4.1 Specimen O S B 4 The longitudinal post-tensioning stress was reduced from the 417 psi that was used in O S B 2 because the shear strength of the cap beam had been increased with the use of the vertically post-tensioned Dywidag bars. Thus, the post-tensioning of O S B 4 could be provided in 1 - 2 in. diameter duct by 4 - 5/8 in. diameter strands rather than the 4 - 1/2 in. and 2 - 5/8 in. diameter strands in two ducts used in OSB2. The net post-tensioning stress in the cap beam of O S B 4 was 342 psi as compared to 417 psi in OSB2. The duct was also pressure grouted to ensure that the tendon was fully bonded. 4.2.3 O S B 5 - External ly Post-Tensioned C a p Beam wi th Fiberglass W r a p s on the C a p Beam and Columns Based upon the good performance of the OSB4 specimen, it was decided to use fiberglass wraps to improve the shear capacity of the cap beam and the columns and observe i f 32 the retrofit would produce comparable results. Specimen OSB5 consisted of fiberglass wraps on the cap beam and columns, plus external post-tensioning of the cap beam to a stress o f 342 psi after losses. This level of longitudinal post-tensioning was the same as that used in O S B 4 , but applied externally. The length of wraps along the members' axes was chosen to be at least 1.5 times the member depth. Figure 4.2 shows the extent o f the fiberglass wraps and the details o f the post-tensioning. Q BENT | Jjf j 1 Figure 4.2 Specimen OSB5 The post-tensioning materials and the labour necessary to stress the specimen were provided by Dywidag Systems International Canada Ltd. The epoxy-fiberglass wrap system was installed by the California based Hexcel-Fyfe Co. (Hexcel-Fyfe Co. - T Y F O - S Fiberwrap System), the system's developers. The thickness of the wraps and the required number o f layers were determined at U B C , following suggested design values given by Priestley ( S E Q U A D Consulting Engineers Inc., 1993). The material properties used were: modulus o f 33 elasticity E w = 3280 ksi, ultimate strength fu = 76.0 ksi and ultimate strain = 2.06%. Tensile tests were performed on eight sections of the wrap obtained from the beam and columns after the cyclic testing was complete. Figure 4.3 shows the resulting stress-strain relations. The averages of the material properties obtained from the tension tests were: E w = 3125 ksi, fu = 56.0 ksi, and 8™, = 1.7%. The observed ultimate strength and ultimate strain averages were found to be less than the recommended design values however, the modulus of elasticity compared reasonably well. 70 60 50 jg 40 £ 30 20 10 0 4 Beam ar id 4 Column Sa mples 0.005 0.01 Strain 0.015 0.02 Figure 4.3 Fiberglass W r a p Stress-Strain Relat ionships Because of the relatively low modulus of the fiberglass, the cap beam wraps were designed to have the same strength at 0.5.fu as the ultimate strength of the vertical prestressing used in specimen OSB4, which was 68 kips/foot. Subsequently, the cap beam was fitted with 3 wraps (a thickness of 0.15 in.), each 0.05 in. thick. The column wraps were designed to carry all the shear required in the plastic hinge region, but as a minimum, 2 wraps (0.10 in. thickness) were used which exceeded the strength requirement. It should be noted that the wraps were uniaxial, with the strong direction oriented perpendicular to the member's axis in the direction of shear demand. Thus the wraps did not contribute significantly to the flexural capacity of the sections and did not increase the shear demands on the cap beam and columns, nor did they prevent flexural cracking. While wrapping of the rectangular cap beam and column sections did not provide a passive confining pressure, it was expected to provide good confinement in the corners, to improve the bond in the top outer longitudinal reinforcing steel in the cap beam, and prevent cover spalling and consequent buckling of the poorly tied main reinforcing steel in the fillet region. Each wrap was impregnated with epoxy resin and then applied to the bent using hand rubbing techniques to ensure a tight fit. Photo 4.5 shows the application o f the wrap to the south end of the cap beam and Photo 4.6 shows the beginning stages of the south column wrap. The wraps were not stressed to provide an active confining pressure as is common with some circular column retrofits. In the architectural fillet region between the beam soffit and column small additional strips were applied to enhance the confinement in that area. Due to the relatively tight radius in the fillet, the length of wrap on the columns could only be extended a maximum of 6 inches. The strips that were applied in the fillet region can be seen in Photo 4.7. The dark triangular sections of grout were applied to facilitate the application o f the additional strips in that region. Photos 4.8 and 4.9 show the respective condition o f the cap beam and south column of specimen OSB5 prior to testing. 35 C H A P T E R 5 - O V E R A L L E X P E R I M E N T A L T E S T R E S U L T S 5.1 Overv iew A n overall view of the results for the Oak Street Bridge specimens O S B 1 , O S B 2 , O S B 4 and O S B 5 can be made by comparing the hysteretic curves for the four test specimens shown to the same scale as given in Figs. 5.1 to 5.4. The joint displacement in the figures is the average horizontal displacement measured at the two joints, and the base shear is the total base shear equal to the applied lateral load. The direction o f displacement, either north or south, is also indicated in the figures. Observation of the four figures shows the tremendous improvement in the load-deflection behaviour of the retrofitted specimens when compared to the as-built specimen. 5.2 Test O S B 1 - As-bui l t specimen This as-built specimen showed very poor, brittle behaviour, as evidenced by the hysteretic curves shown in Fig. 5.1. The peak lateral load capacity was only 60 kips, and was not sustained in subsequent load cycles. Photo 5.1 of Appendix C, taken on the first cycle to a displacement of 0.9 in., shows a large diagonal crack forming in the cap beam under negative moment when the shear is highest. This crack increased in width with each cycle o f load until the concrete compressive zone suddenly failed, allowing a portion o f the cap beam to drop down, only to be restrained by the beam's bottom reinforcement. See Photo 5.2. The top of the diagonal crack coincided with the cut-off o f several o f the top bars. The wide cracks were due to either yielding of the reduced top reinforcement at this location, or bond failure. Eventual bond failure is evidenced by horizontal splitting at the level o f the top 36 reinforcement due to a lack of confinement reinforcement, as seen in Photo 5.2. Neither the joint region nor the columns showed any serious cracking as the demand on these elements was limited by the cap beam shear failure. 140 120 100 80 60 40 •§- 20 3 o * -20 n OQ -40 -60 -80 -100 -120 -140 I I I I i i South North - PULL SOUTH — As-built OSB1 -~ PUSH NORTH I I -5 -3 -2 - 1 0 1 2 Joint Displacement On) Figure 5.1 Latera l L o a d Displacement Response for O S B 1 The overall hysteretic plot, depicted in Fig. 5.1, shows rapid degradation of strength and stiffness with each cycle once the shear crack had developed. In addition, the theoretical lateral load capacity based on flexural member strengths was never achieved because of the 37 force limiting cap beam shear failure. The base shear necessary to cause flexural yielding of the bent was estimated by Seethaler (1995) to be about 65 to 70 kips with hinging occurring first in the cap beam. This test demonstrated the poor failure mode likely to occur in the prototype bridge and heightened the awareness that adequate shear capacity is essential in order to obtain inelastic flexural performance. Because of the shear and bond failure observed at either end of the cap beam, the joint regions and the columns were not tested to capacity. The behaviour of these elements had to be assessed from the retrofitted specimens where the demand was higher. 5.3 Test O S B 2 - Internally Post-Tensioned C a p Beam The main purpose of this retrofit scheme was to increase the shear and moment capacity o f the cap beam and to force flexural hinging into the tops of the columns. This would preserve the integrity of the cap beam and joint regions throughout the test, preventing potential large displacements of the cap beam that may give rise to load path changes between the bent and the superstructure. The results for the prestressed retrofit O S B 2 showed a marked improvement in both strength and ductility when compared to the as-built specimen, as evidenced by the hysteretic curves of Fig. 5.2. The displacement at U,A= 1 corresponds to the estimated structure yield displacement. This is not the displacement at first yield o f the reinforcement, but represents the yield displacement o f a theoretical bilinear fit to the force deflection plot. Refer to Fig. 3.5. In this test, the displacements for each sequence of two or three cycles to a specific displacement were started from the zero load position achieved after unloading from the last cycle o f the previous sequence. The procedure for each sequence was to bring the structure back to the starting position of the sequence using displacement control, and then allow it to unload to the zero load position. This resulted in a small displacement and is indicated on the hysteretic plot by the small unloading branches on the pull side o f the origin in F ig . 5.2. This resulted in the push portion of the cycle, which was the starting direction for each sequence, having a smaller displacement than the pull cycle. For instance, at what is termed ductility 4, the push cycle only had a ductility of about 3 while the pull cycle had a ductility of approximately 5. 39 U - A = 1 2 4 6 8 740 720 100 80 60 40 "ft . a 20 «. n 9 0 •c C/> a </> (0 -20 OQ -40 -60 -80 -100 -120 -140 -5 -4 -2 - 1 0 1 2 Joint Displacement (in) Figure 5.2 Latera l L o a d Displacement Response for O S B 2 In 0 S B 2 , diagonal cracks formed in the beam in nearly the same location as in 0 S B 1 . Photos 5.3 and 5.4 can be compared with Photos 5.1 and 5.2. These cracks however, did not open as wide, even at large displacement levels, as shown in Photo 5.5. A lso, the cap beam did not fail in shear. Photos 5.2., 5.3 and 5.4 o f the two tests are taken at approximately the same displacement and show the much improved crack control in 0 S B 2 as compared to 0 S B 1 . Flexural shear cracks formed in the columns and in the region of the fillet, shown in Photo 5.6, gradually getting wider and longer as the ductility level increased. Photo 5.6 shows the south column after the first push cycle of ductility level 6. U p until the last displacement sequence, when a sudden column shear failure occurred, there was very little strength degradation, with the three hysteresis curves at each sequence nearly falling on top of each other. See Fig. 5.2. On the last loading cycle, which was initially a push, the tension column (North Column) failed suddenly in shear on the subsequent pull portion o f the cycle. Here, tension column refers to the column with reduced axial load caused by the overturning moment from the lateral loading. This sudden shear failure at a ductility o f 6 produced the wide diagonal crack in the column as shown in Photo 5.7. Photos 5.5 and 5.6 were taken at the same displacement as Photo 5.7 and shows the shear crack in the cap beam had grown to be quite wide at this displacement. The retrofit scheme used for specimen OSB2 was successful in forcing flexural hinging into the tops of the columns, producing modest ductility, and increasing the lateral load capacity o f the bent. Unfortunately the ultimate strength of the cap beam retrofit was not determined because of the column shear failure. However, the size o f the shear crack in the cap beam was of concern and indicated the possibility of a brittle shear failure in the cap beam had the columns been strengthened which would have increased the demand on the cap beam. Therefore, retrofit measures that further increased the shear capacity o f the cap beam and columns were considered. 5.4 Test O S B 4 - Vert ical ly and Horizontal ly Post-Tensioned C a p Beam wi th C o l u m n Jackets The hysteretic response of specimen OSB4 is shown in Fig. 5.3 and shows very good performance to a ductility level of 9. In this, and subsequent tests, the displacement controlled cycles were all measured from the zero displacement position and so the ductility levels in both the push and pull directions are essentially the same. The overall hysteretic performance proved to be very effective by forcing hinges into the tops of the columns in the region of the fillet. The specimen eventually failed in flexure in the column region above the column jackets as evidenced by spalling o f the cover concrete and buckling o f the vertical column reinforcement. The first cycle to a ductility level o f 12 showed a strength loss when compared to the previous sequence, and subsequent cycles had approximately a 15% loss in each cycle. 42 6 8 10 12 740 720 700 80 60 40 "Or •S- 20 «. (0 0) 0 •c CO 0) <0 n -20 OQ-40 -60 -80 -100 -120 -140 South —' -4 - 2 - 1 0 1 2 Joint Displacement On) Figure 5.3 La tera l L o a d Displacement Response for OSB4 At low ductility levels, flexure and shear cracks developed in the cap beam, as shown in Photo 5.8 taken at a ductility of 4, but these did not widen or grow as the test progressed and the beam retrofit was successful in forcing the damage into column flexure. Photos 5.9 and 5.10 show the north column and joint region at ductility levels o f 4 and 6 respectively. A t ductility 4, there is considerable cracking in the column but little cracking in the joint. A t ductility 6, the cracks are wider in the column and there are the beginnings of diagonal cracks across the joint. A t a ductility level of 9 some spalling occurred near the column corner bars, as seen in Photos 5.11 and 5.12, which allowed the corner bars to buckle. Photo 5.12 also shows the bottom end of one of the vertical Dywidag post-tensioned bars that were installed to increase the beam shear resistance and provide confinement to the top horizontal beam reinforcement. Photo 5.13 shows the damage at a ductility o f 12. At this displacement level there was much more spalling o f the cover concrete, more bars had buckled and some of the reinforcement had fractured. As the cycling progressed, more of the vertical bars fractured and this lead to the degradation and reduction in strength with each additional cycle as shown in Fig. 5.3. Photo 5.13 also shows that some of the diagonal cracks in the joint had joined up to form one diagonal crack extending the full length of the joint from lower right to upper left. However, this crack did not open to any appreciable extent. This retrofit scheme proved to increase the shear capacity o f the cap beam, increase the bond strength between the concrete and the cap beam's top reinforcement, and the column jackets provided increased confinement and capacity to the columns. Shear failures in the cap beam and columns were precluded and damage to the joint region was minimal. Although the retrofit performed extremely well, the curvature demand on the plastic hinge regions was large and subsequently, because of a lack of significant confinement in the fillet region, spalling o f concrete and buckling o f reinforcement lead to rapid degradation between cycles. Thus the confinement provided in the plastic hinge regions of the last retrofit measure, specimen O S B 5 , extended higher into the fillet region than the steel jackets used on OSB4 . This was expected to reduce the spalling of concrete that was observed in the hinge regions of specimen OSB4. 5 . 5 Test O S B 5 - Prestressed C a p Beam with Fiberglass Wraps on the C a p B e a m and Co lumns Photos 4.7 and 4.8 showed specimen O S B 5 at the beginning of the test and the extent o f the fiberglass wraps on the cap beam and columns. The hysteretic load-displacement response is shown in Fig. 5.4. The performance of this retrofit was exceptional up to a displacement ductility level o f 9 where the test had to be terminated because of limitations in the displacement capacity of the loading system. The confining effect and the flexibility of the fiberglass wraps which reduced column damage are evident by comparing the hysteretic loops of O S B 4 and O S B 5 at displacement levels slightly greater than 4 inches. Refer to Figs. 5.3 and 5.4. Note that the hysteresis loops for O S B 5 show much less degradation than the loops for O S B 4 . 45 HA= 1 2 4 6 8 1 0 - 5 - 4 - 3 - 2 - 1 0 1 2 3 4 5 Joint Displacement On) Figure 5.4 La tera l L o a d Displacement Response for OSB5 This specimen was more flexible than specimen OSB4 which had full length steel column jackets, thus the yield displacement was larger, and so even though the maximum displacement was greater than in the previous tests the ductility level was not as high. Since the fiberglass wrap retrofit was designed to be similar in strength to OSB4, the decision was made to subject the specimen to the same loading regime as OSB4. For this reason the ductility values on the caption board in the OSB5 photos, for example shown as U3.0 in Photo 5.14, are in error. The actual displacement ductility is approximately 75% of the amount shown on the caption board. Photos 5.14 and 5.15 show the south cap beam and joint regions after three cycles at a displacement ductility of just over 2. The cracks that are marked were very small. The cracks occurring under the fiberglass wrap were not visible, and the lines drawn on the fiberglass wrap indicate the extent of debonding of the fiberglass from the concrete. For instance, in Photo 5.14 the area enclosing the number 3.0 indicates that this area became unbonded sometime during the sequence at U3.0, or a ductility of about 2.2. The actual debonding took place between the concrete and the white acrylic type paint that had been used to paint the specimen. If the fiberglass had been applied directly to the concrete, the bond between the wrap and the specimen would have been better, however, the debonding did not appear to adversely affect the performance of the fiberglass retrofit. A s the loading progressed more cracks developed in the joint area but not in the short central length o f the beam that was visible. Photos 5.16 and 5.17 show the cracks at ductilities of 6.5 and 9 respectively. At peak deflection all these cracks were relatively small, including those in the joint region. The dark patch seen in Photos 5.16 and 5.17 is the area where grout was applied to form a smooth radius for the application o f the fiberglass in the fillet region. The fiberglass wraps however, did not reach the full height o f the grouted region and a portion o f the grout subsequently became loose during testing and was removed. Its removal did not represent spalling of the cover concrete although spalling did occur at one corner as described below. Photos 5.18 and 5.19 show the specimen after the completion o f the test to ductility 9, after the fiberglass wrap had been removed, and the cracks under the fiberglass marked. Photo 5.18 shows cracking in the south column extending well down the length o f the column. These cracks had essentially closed under the self weight o f the specimen when the photo was taken. Photo 5.19 shows the south cap beam section which had only a few small diagonal cracks. There may have been a slight tendency for the cracks to turn in the horizontal direction at the top of the beam, which would indicate a potential for bond failure and spalling o f the top cover concrete, but there did not appear to be any spalling and the small width o f the cracks would indicate that there had not been bond failure. The north end of the beam had only one diagonal crack under the fiberglass wrap During the sequence to ductility 9 a small amount of spalling took place at one corner on the interior face of the north column just above the fiberglass wrap and allowed the corner column bar to buckle. This is shown in Photo 5.20 which also shows the extent o f the spalling that took place underneath the top of the fiberglass wrap. In this photo the top of the fiberglass wrap was at the bottom of the buckle, level with the bottom of the white patch under the letter N , thus the spalling mostly took place above the wrap. In contrast to the steel jackets used in specimen OSB4 , the fiberglass wraps did not restrict the length of plastic hinge that formed as evidenced by the well distributed cracking observed on the columns after the wraps were removed. Refer to Photo 5.18. This, combined with the fact that a larger area of the plastic hinge region was confined by the wraps than in specimen OSB4 , OSB5 was able to undergo larger displacements before concrete began to spall and the reinforcement buckled. The flexibility of the wraps permitted large displacements, with reduced ductility demand, and the confinement provided by the wraps reduced the amount of damage suffered by the bent throughout the test. It was for these reasons that the condition of specimen OSB5 at a given displacement was always better than the condition of specimen OSB4 at the same displacement. This observation became quite profound at the end of the testing sequence, near the 4 inch displacement level. 49 C H A P T E R 6 - A N A L Y T I C A L P R E D I C T I O N S 6.1 Overv iew Clearly, avoiding brittle shear failures such as shear failures is desirable in the event o f an earthquake. It is the intent of the designer to obtain a ductile, and flexurally dominated response from a structure. In doing so, members designed to undergo inelastic deformations in the form of plastic hinges require provision of sufficient transverse reinforcement in the form of spirals or rectangular tie arrangements to provide effective confinement, prevent buckling o f longitudinal reinforcement, and prevent shear failure. Currently design information is available for retrofit schemes that include steel column jackets (Chai, Priestley and Seible, 1991) and more recently, fiberglass jackets ( S E Q U A D , 1993). Although there are recommendations that aid in predicting plastic hinge lengths, there is little information available on predicting the curvature distributions that arise due to particular loadings on as-built or retrofitted structures. After observing and comparing the behaviour of specimens O S B 4 and O S B 5 , it was decided to attempt analytical predictions of their behaviour and determine i f the curvature distributions within these two specimens could be predicted, since their response was predominately flexural. From these distributions, the peak curvatures, peak curvature ductility demand, the ultimate compressive strain in the concrete and the reinforcement strains could be determined. Firstly, predictions of the overall lateral displacement response for specimens O S B 4 and O S B 5 were carried out using the analysis program D R A I N - 2 D X , which is a non-linear analysis package that can be used for static or dynamic analyses. D R A I N - 2 D X was used to perform a simple push-over analysis for the two specimens in an attempt to compare the predicted behaviour with the observed hysteretic envelope. P-A effects were included in the analyses. After the overall prediction of the force-deflection relationship was determined, curvature distributions over the length of the cap beam and the columns were derived from the DRAIN - 2 D X output. These were calculated by taking the difference in the rotations at the ends of each element and dividing by the element length. The shape of the distributions and peak curvature values were then compared to those derived experimentally from the internal instrumentation o f each specimen, as shown in Fig. 3.3. Estimates o f the peak concrete strains, 8 C , in the plastic hinge regions, were then obtained from the appropriate curvatures. 6.2 D R A I N - 2 D X Models 6.2.1 Noda l Arrangements The specimens were first discretized into stick models comprised of a series o f nodes and bending members. The nodal arrangements for both specimens O S B 4 and O S B 5 were identical. Nodes were placed at the locations of longitudinal strain gauges in the real model, at the points o f application of dead and lateral load, and at section changes in the cap beam and beam-column joint regions. Additional nodes were placed in regions expected to undergo inelastic displacements, namely, in the tops of the columns just below the beam-column joints. Figure 6.1 shows the model used, including the locations of the dead and applied lateral loads. The numbers indicate the node numbering scheme that was used. In all, there were 66 nodes and 66 elements per specimen. Table 6.1 lists the nodal coordinates o f the computer models which are consistent with the set of axes shown in Fig. 6.1. Figure 6.1 Noda l Arrangements for Specimens O S B 4 and O S B 5 52 Table 6.1 Noda l Coordinates for Specimens O S B 4 and O S B 5 Node X - C o o r d . Y - C o o r d . Node X - C o o r d . Y - C o o r d . Number (in) On) Number (in) (in) C a p Beam South Co lumn 100 0.0 97.8 200 57.0 0.0 101 8.0 97.8 201 57.0 12.5 102 43.3 97.8 202 57.0 24.0 103 50.5 97.8 203 57.0 37.5 104 57.0 97.8 204 57.0 50.0 105 63.5 97.8 205 57.0 62.5 106 71.3 97.8 206 57.0 66.0 107 72.5 97.8 207 57.0 69.7 108 78.8 97.8 208 57.0 73.3 109 84.5 97.8 209 57.0 76.3 110 86.1 97.8 210 57.0 78.9 111 94.0 97.8 211 57.0 81.6 112 99.5 97.8 212 57.0 84.3 113 105.5 97.8 213 57.0 94.8 114 109.5 97.8 115 115.6 97.8 116 119.5 97.8 Nor th Co lumn 117 129.5 97.8 300 223.0 0.0 118 140.0 97.8 301 223.0 12.5 119 150.5 97.8 302 223.0 24.0 120 160.5 97.8 303 223.0 37.5 121 164.7 97.8 304 223.0 50.0 122 170.5 97.8 305 223.0 62.5 123 174.5 97.8 306 223.0 66.0 124 180.5 97.8 307 223.0 69.7 125 186.0 97.8 308 223.0 73.3 126 193.9 97.8 309 223.0 76.3 127 195.5 97.8 310 223.0 78.9 128 201.3 97.8 311 223.0 81.6 129 207.5 97.8 312 223.0 84.3 130 208.8 97.8 313 223.0 94.8 131 216.5 97.8 132 223.0 97.8 133 229.5 97.8 A - F r a m e Peak 134 236.8 97.8 400 140.0 138.3 135 272.0 97.8 136 280.0 97.8 53 6.2.2 F lexura l Analysis Moment-curvature relationships were derived for all the structural sections within the specimens to determine the various yield surfaces, including column axial load-moment interaction diagrams, and the post-elastic behaviour. A s indicated in Drawing Q117-11, Appendix B , the longitudinal reinforcement in the cap beam has many cut-off locations. The moment capacity was calculated for each section created by the cut-off locations and the sections were determined by assuming a particular development length for the main #5 bars. The basic development length given by the C A N -A23.3-M84 code for #5 bars in tension and compression is ld = 0.042 ±j== (Imperial Units, psi) = 7.68 in. where the steel yield strength w a s , / , = 49500 psi, the area of each bar Ab = 0.307 in 2 , and the average compressive strength o f the concrete for both specimens was fc « 6900 psi. Fo r analysis purposes, the development length for the #5 reinforcement was set to 7.5 in. This value was considered to be conservative because of the conservatism inherent in the concrete design code and due to the levels of post-tensioning and increased transverse reinforcement present in both specimens OSB4 and OSB5 that increased the level o f confinement for the main reinforcement. Shown in Table 6.2 are the flexural capacities and the effective concrete moments o f inertia used for the cap beams of both specimens OSB4 and OSB5 . The capacities were determined considering the post-tensioning force in the cap beam of 342 psi for both specimens. The internally bonded tendon of OSB4 was not considered in the flexural analysis and thus its stiffening and post yield strengthening effects were ignored. This omission did not greatly affect the results of the D R A I N - 2 D X analysis since the cap beams in both tests did not reach flexural capacity. The X coordinates indicated in Table 6.2 correspond with those listed in Table 6.1 and the sections listed are symmetric about the cap beam centerline which has an X coordinate o f 140 in. Table 6.2 C a p Beam Section Capacit ies and Inertias X-Coord ina te (inches) Section Number Positive Capaci ty (Mv +) (kip. in) Negative Capac i ty (My -) (kip. in) Inert ia Ie ( in 4) 0.0 1 3300 6570 17500 43.3 2 3600 8800 21500 63.5 3 3600 6800 21500 71.3 3 3600 6800 17500 84.5 4 3640 5290 17500 94.0 5 4320 4290 17500 99.5 6 4320 4290 17500 105.5 7 4680 4210 17500 109.5 8 5360 3570 17500 119.5 9 6000 2890 17500 129.5 10 6650 2880 17500 140.0 Since flexural stiffness is influenced greatly by the extent of cracking in the section, and the degree of cracking over the length of members changes significantly, effective section inertias were calculated using 0.6.1^088 for the columns and O.SSJgross for the cap beam, as recommended in Paulay and Priestley (1992). Ideally, the section inertias could have been varied along the lengths of the cap beam and columns to reflect the degree of cracking at different locations throughout the bent and perhaps better partially account for the true non-linear flexural response of the members. Since the variation o f the section inertias mainly affects the response of the structure in the linear range, and the primary concern o f this thesis was to examine the structure response in the post-elastic range, this was not done. A simple expression relating the modulus of elasticity of the concrete to the square root o f the compressive strength was used from CAN-A23 .3 -M84 and is given as Ec = 57000 /^7*7 (Imperial Units, psi) = 4735000 psi = 4735 ksi where the concrete compressive strength/ ' c , was taken as 6900 psi. The computer program used to derive moment-curvature relationships for each section was one that used theory proposed by Mander, Priestley and Park (1988). The theory attempts to account for the effects of confinement provided by transverse reinforcement. A n energy balance approach is used to predict the ultimate longitudinal compressive strain capacity o f the concrete based upon the fracture of the transverse reinforcement. The strain energy capacity of the transverse reinforcement is equated with the strain energy stored in the concrete as a result of the confinement provided. The constitutive relationship for the concrete is predicted by calculating a maximum compressive concrete strain and an increased compressive strength based upon the reinforcing details of the section. Strain hardening of the reinforcing steel is accounted for in the program. The program output includes both the 56 concrete and steel strains for given curvatures. Shown in F ig. 6.2 below is the typical column section interaction diagram derived from the program. The moment values shown are the yield moments for the range of axial loads i f a the moment-curvature response is approximated by a bilinear relationship. This approximation is shown in F ig . 6.5. A similar interaction diagram was derived for the column fillet regions. 500 .3500 I 1 1 J 1 1 1 1 1 -10000 -7500 -5000 -2500 0 2500 5000 7500 10000 Moment (kip*in) Figure 6.2 Column Section Interaction Diagram 6.2.3 Accounting for Joint Shear Deformations The version of D R A I N - 2 D X used for the analysis cannot directly model joint shear deformations that result from the joint forces. That is, the program did not allow for a rotation in the joint region due to the joint shear stresses arising during the test. Only beam shear deformations transverse to the members' axes are permitted by the program. In order to account for the true joint shear deformations measured by the L V D T setup at the north joint, the shear area over the length of the column sections was reduced. The calculated shear distortion over the length of the column was forced to equal the measured joint shear strain multiplied by the column length. Shown in Table 7.1 of Chapter 7 are the joint shear strains for specimens O S B 4 and O S B 5 when the bents were displaced to the north. The shear stress giving rise to the calculated shear deformation was thus from the column shear force, not the joint shear stress. This method of accounting for shear deformations occurring in the joints predicts the same deflected shape of the columns as observed during testing and thus does not affect the prediction o f flexural deformations in the cap beam and columns. Joint shear deformations, member flexural deformations and member shear deformations constitute the contributions to the overall bent deflection. For a given displacement, accounting for the shear deformation in the joints reduces the flexural demand in the other regions of the bent. Thus with large joint shear deformations, there is less demand on the plastic hinge regions throughout the structure. 6.2.4 Post Processing of D R A I N - 2 D X Results After the overall model response was generated, the nodal rotations were analyzed and reduced to average curvatures over the length of the cap beam and columns. The nodal rotations from the D R A I N - 2 D X output files were extracted with the program E X developed by the author. The source code, including a brief explanation of the program, is provided in Appendix D. The E X program reads the output file for a particular analysis segment and extracts the rotational histories for each node and stores them in arrays. The program then reads in the locations of the nodal coordinates from an input file called ex.nod and calculates the distance between nodes. The rotations for each end o f each element are summed and divided by the element length to obtain the average curvature for that particular element. The average curvature is then assigned to the element midpoint. These curvatures and midpoint locations are then written to an output file called ex.out where they can be further manipulated or plotted. 6.3 OSB4 Response The push over analysis was done by imposing a deflection at the top of the A-frame as was shown in F ig. 3.1 and modeled in Fig. 6.1. The predicted push-over response of O S B 4 is compared to the observed hysteresis curves in Fig. 6.3 and is labeled 'Dra in-2DX prediction1. It can be seen from this figure that the model behaviour envelopes the southbound (positive joint displacement) hysteresis curves reasonably well except perhaps in the one to two inch displacement range where the D R A I N - 2 D X prediction matches the second and third cycles of each sequence as opposed to the first. The D R A I N - 2 D X prediction is symmetric, unlike the observed hysteresis curves for specimen OSB4. There appears to be no justification for this unsymmetrical response since the specifications for the specimens were symmetric. It is coincidence that the analytical prediction which was derived from the details indicated on the structural drawings in Appendix B coincides with the southbound deflection curves which always followed the northbound curves in the loading sequence. 59 -120 -140 I 1 -J 1 1 1 1 1 1 1 -5 -4 -3 -2 -1 0 1 2 3 4 5 Joint Displacement (in) Figure 6.3 Analy t ica l Latera l L o a d Displacement Response for O S B 4 It can be seen that the load for the model continues to increase beyond the 4 inch displacement when the real structure begins to degrade rapidly. This is a result o f the bilinear moment-curvature relationship used by DRAIN -2DX for each member. It should be noted that DRAIN -2DX, at present, does not have a hysteretic model that allows for cyclic degradation. This limitation did not however, affect the results o f the simple push-over analysis that was performed. The curvature distributions obtained at different ductility levels from the post processing of the DRAIN -2DX analysis were then plotted for the cap beam and columns. Figure 6.4 shows the curvatures obtained for the cap beam. The figure shows the increasing progression of curvatures as the displacement level increases but that they increase more rapidly in the linear range than in the post-elastic range. This was expected since the D R A I N -2DX prediction indicated that there was no flexural yielding of any of the beam elements and the force levels remained relatively constant at the higher displacements. The curvatures towards the north end of the beam are higher because of larger moments due to dead load effects at low ductility levels, and higher column moment capacity due to the increased axial load in the leading 'compression column' at the higher ductility levels. 61 A,P • 0.00008 T Figure 6.4 Analy t ica l C a p Beam Curvatures for O S B 4 The columns were the only elements to undergo inelastic deformations and the capacity of the elements increase due to the strain hardening effect. As a result, the elastic portions o f the bent, particularly the cap beam, undergo slightly greater deformations as the flexural demand increases. This trend is evident in Fig. 6.4. Figure 6.5 shows the bilinear approximation to the real moment-curvature response of a section and the post-elastic slope used by D R A I N - 2 D X . This slope can vary depending on what is chosen as M y and which part o f the real response curve one is trying to model. In the work presented here the strain hardening slope, denoted by a , varied from 0.005 to 0.02. 62 F igure 6.5 Idealized Member Flexural Response Used by D R A I N - 2 D X Shown in F ig. 6.6 is the progression of curvatures in the columns for the same ductility levels presented for the cap beam. Recall that the south (left column in the figure) column would be subjected to a tensile reaction at the base due to the northbound lateral displacement. It is evident from the figure that the steel jackets were extremely stiff and forced deformations into localized regions above the tops of the jackets. The abrupt decrease in curvature that occurs about half way up the architectural fillet, or 78 inches from the column base, is due to a discrete section change that occurs at nodes #209 and #309 in the D R A I N - 2 D X model. Refer to Fig. 6.1 and Table 6.1 for the nodal locations. The second distinct drop that occurs in the beam column joint region at 89 inches from the column bases is also due to a section capacity change located at nodes #212 and #312. 63 * MA =6.0 • MA =4-0 -MA =3.0 * MA =2.0 A MA =1-2 • MA =0.9 • MA = 0.65 Hi y IO CM IO O O O © «M O O O O O O O ° . ©' ° . O* ° . C> Curvature (1/in) Curvature (1/in) Figure 6.6 Analy t ica l Co lumn Curvatures for O S B 4 It can be seen that for each displacement level, the south column curvatures are greater than the curvatures in the north column. Keeping in mind that the response of specimen 0 S B 4 was primarily flexural in nature, this behaviour would be expected since the curvatures in the cap beam are less at the south end. This means that the cap beam rotation at the south end is less than at the north end, and thus in order to maintain compatibility o f the members, the curvatures and deflection of the south column must be greater than that o f the north column. Refer to Figs. 6.4 and 6.6 for clarification. Shown in Table 6.3 are the predicted peak curvatures and the corresponding estimated concrete strains for ductility levels ranging from 2.0 to 12.0. The displacement indicated is the average horizontal displacement of the north and south joints. The peak concrete compressive strains s c were calculated using the 'Mander' program which calculates strains for 64 specified axial loads and curvatures. The respective compressive loads in the south and north columns in the inelastic range of the response are approximately 10 and 180 kips. Table 6.3 Peak Analytical Curvatures for the Plastic Hinge Regions of O S B 4 Ductility Displ. South Column North Column A (in) Curvature Ductility Strain Curvature Ductility Strain <!Kl/in) tH e c ^(1/in) m E c 2.0 0.70 0.00095 6.8 0.0018 0.00046 3.1 0.0017 3.0 1.05 0.00141 10.1 0.0022 0.00111 7.4 0.0031 4.0 1.40 0.00183 13.1 0.0024 0.00152 10.1 0.0041 6.0 2.10 0.00258 18.4 0.0031 0.00227 15.1 0.0075 9.0 3.15 0.00395 25.6 0.0091 0.00364 24.2 0.013 12.0 4.20 0.00538 38.4 0.015 0.00461 30.7 0.016 Note that the predicted concrete strains for ductility levels 9.0 and 12.0 are quite high for the regular column tie details. Based upon theory proposed by Mander (1988), the unretrofitted column section, was thought to sustain a maximum concrete strain, e c u , o f the order of 0.0072. The large predicted values presented in Table 6.3 occur in the fillet region above the tops o f the column jackets. Strains o f this magnitude would most likely be maintained by the stress conditions created by the geometry in the fillet region. The radius of the beam soffit-column interface, in compression, has a confining effect on the concrete, and it is probable that this condition enabled large concrete strains to be attained. The program used to predict the relationship concrete strain, e c , and curvature, <j>, in the plastic hinge region did not allow for input of such particular geometry constraints. Thus in order to predict the flexural response of the fillet region, the confinement parameters for the section in the program were modified so that the predicted response of the section could reach curvatures of the order of 0.0055 rad/in., which was approximately the maximum curvature predicted in the D R A I N - 2 D X analyses. The confinement is primarily dependent on the tie arrangement and so, the area, the axial stiffness and the strength o f the ties were kept the same, and the spacing of the ties was varied until the column section could attain peak curvatures of about 0.0055 1/in. The equivalent spacing of the 9 Ga. (0.15 in. diameter) ties, predicted by the program, to attain the peak curvatures, was 0.5 in. The predicted maximum concrete strain capacity, e c u , for this level of confinement was 0.017. Between ductility levels 9 and 12 in the real test of OSB4 is when significant degradation of the specimen occurred. See Photos 5.12 and 5.13. The analysis would predict that the architectural fillet regions and steel jackets appeared to provide confinement enough to attain a maximum concrete strain slightly less than 0.017. The Mander' program predicted and ultimate strain capacity o f the steel, e s u , of approximately 0.16. From tensile tests performed on the #5 reinforcement, the ultimate strain capacity was observed to be about 0.158. For the peak curvature value of 0.00538, the corresponding steel strain is approximately 0.098 which is well below the capacity o f the steel. Spalling o f concrete above the steel jackets was first observed to occur at ductility level 6 during the real test. See Photo 6.1. From the predicted behaviour, this would indicate a spalling strain, s s p , of about 0.0075. This strain is somewhat greater than what is normally considered the spalling strain of concrete. This higher strain most likely is due to the confining effect of the fillet region and the steel jacket. Joint shear deformations for OSB4 were not detected by the external L V D T system until the later stages of the test when the joint region showed diagonal cracking. Consequently, in the range up to and including ductility level 4.0, the joint shear deformations in the D R A I N - 2 D X model were was assumed to remain linear in behaviour. This assumption is consistent with the observed behaviour of the beam column joint by comparing Photos 5.9 and 5.10. A t ductility level 4, as shown in Photo 5.9, there are no visible cracks extending across the joint and at ductility level 6, as in Photo 5.10, there are two cracks running from the upper left towards the lower right. The external L V D T system indicated shear deformations at ductility levels 6, 9 and 12. Recall Photo 5.13 which shows the north joint at a ductility o f 12 where there are two narrow cracks running from bottom right to top left on the north joint, and none running from the lower left to the top right. Presumably the difference in damage observed between the north and south directions was a result o f the different moments and joint shears arising in the joints due to the change in section capacity caused by the difference in axial load between the two columns. Recall that the pushover analysis was performed by imposing a northbound deflection to the bent. 6.4 O S B S Response Nearly the identical procedure to that used for analysis of O S B 4 was carried out to predict the overall response of specimen OSB5. Shown in Fig. 6.7 is the predicted analytical response of specimen OSB5 compared to the observed hysteresis curves. Again, the D R A I N -2 D X response envelopes the hysteresis curves reasonably well for the southbound portion o f the curves and under-predicts the load in the north direction. The D R A I N - 2 D X response matches well with the first cycle in each sequence which may be expected because as stated before, only a static push over analysis was performed and D R A I N - 2 D X does not account for degradation between cycles. 67 10 -140 - 5 - 4 - 3 -2 -1 0 1 2 3 4 5 Joint Displacement On) Figure 6.7 Analy t ica l Latera l L o a d Displacement Response for O S B 5 Shown in Fig. 6.8 are the predicted cap beam curvatures for ductility levels 0.6 to 6.0. A s was the case in OSB4 , cap beam curvatures in specimen OSB5 increase with increasing displacement until flexural yielding of the bent occurs, beyond which the curvatures increase only slightly. Since the peak loads reached by the specimens were approximately the same, 68 and yielding occurred primarily in the columns, the magnitudes of cap beam curvatures for specimens O S B 4 and OSB5 are nearly identical in the non-linear displacement range. The slight difference arises in the linear range where the magnitudes are slightly less in O SB 5 than O S B 4 because OSB5 had more flexible columns. The yield displacement for OSB5 was approximately 0.5 inch. A,P • 0.00008 T Figure 6.8 Analy t ica l C a p Beam Curvatures for O S B 5 Shown in Fig. 6.9 are the predicted column curvatures for specimen O S B 5 . The curvatures were, as expected, more distributed than those predicted for OSB4 . The peak column curvatures occur in approximately the same locations as specimen O S B 4 , but because 69 the fiberglass wraps provided an insignificant contribution to the flexural stiffness of the columns, longer plastic hinges developed for the columns in specimen O S B 5 . The peak curvatures were consequently greater in OSB4 than in OSB5 for a given displacement. Photos 5.13 and 5.18 show the plastic hinge regions of specimens O S B 4 and OSB5 respectively at a displacement o f 4.3 inches. It can easily be seen from these photographs that there was much more localized flexural demand and damage in specimen O S B 4 than OSB5 . A,P 10 © § ©' 3 ©a io f 1 all 1 Eg i ...1:1-. - -• / • ' i' •"' • . i '"]• i i i i i CM © o' I O CM § o' + MA=60 •MA =4.0 -MA =3.0 * MA =2-0 ±MA = 10 • MA = 0-8 + MA = 06 Curvature (1/in) Curvature (1/in) Figure 6.9 Analy t ica l Co lumn Curvatures for O S B 5 The curvatures in the south column are uniformly greater than those in the north column for ductilities up to 3.0, as was observed in the analysis o f OSB4 . The peak curvatures for the north and south columns of OSB5 however, are nearly identical for displacement ductilities 4.0 and 6.0. The curvatures in the south column, particularly for these ductility levels, are more distributed than those in the north column resulting in a larger south column deflection that is required to maintain displacement compatibility o f the cap beam and 70 columns. Also the south joint region experienced some significant diagonal cracking at these displacement levels which contributed to the overall deflection of the bent and reduced the flexural demand on the hinge region. See Photo 5.18. The diagonal cracking in the south joint region shown in the photo runs primarily from the bottom left to top right which coincides with joint forces induced by a northbound deflection. Note that there are no cracks seen running from bottom right to the top left of the joint region. Consequently, for the analysis, the shear deformations of the north joint were assumed to remain linear and the shear area in the north column was not reduced since larger shear strains were not detected there during testing. The 'Mander' program used to predict the flexural capacities o f the sections assumes only steel to be used as transverse reinforcement and prescribes the elastic modulus of transverse reinforcement to be that of steel. The modulus o f steel is approximately 9 times that measured for the fiberglass wraps. In order to model the confinement effect o f the fiberglass wrap accurately, the details of the transverse reinforcement were modified in the program. The wrap was first assumed to consist of discrete ties spaced at 0.5 in. The area of the 'wrap ties' was then reduced to get the correct axial stiffness per 0.5 in. o f wrap. Because the area o f the ties had been reduced, the ultimate stress o f the 'wrap ties' was increased so that the ultimate strength was correct. The predicted ultimate strain capacity o f the concrete s c u , for the columns wrapped in fiberglass was 0.027. A t the peak curvature o f 0.0033, the predicted steel strain, e s , is approximately 0.061 which is below the peak strain capacity o f the steel, s s u , o f about 0.16. Shown below in Table 6.4 are the peak curvatures calculated for the plastic hinge regions for specimen OSB5. Concrete strains corresponding to these curvatures were 71 calculated using the 'Mander' program. The bent displacement indicated in Table 6.4 is the average horizontal displacement of the joints. 6.4 Peak Analytical Curvatures for the Plastic Hinge Regions of O S B 5 Ductility Displ. South Column North Column / / A A (in) Curvature Ductility Strain Curvature Ductility Strain $ (Mm) tH Sc <f) (1/in) m E c 2.0 1.0 0.00125 9.6 0.0020 0.00084 5.6 0.0024 3.0 1.5 0.0016 12.3 0.0025 0.0014 9.3 0.0035 4.0 2.0 0.0020 15.4 0.0031 0.0020 13.3 0.0050 6.0 3.0 0.0021 16.2 0.0032 0.0022 14.7 0.0055 9.0 4.5 0.0028 21.5 0.0042 0.0033 22.0 0.0084 72 C H A P T E R 7 - E X P E R I M E N T A L I N T E R P R E T A T I O N 7.1 Overv iew The experimental interpretation of the results consisted of first evaluating the data obtained from the strain gauges, and plotting strain distributions along the length o f the cap beams and columns of specimens OSB4 and OSB5. Gauges that were found to be erroneous were identified and not used further in the interpretation. Next, the curvature distributions over the cap beam and columns were derived from the strain gauge readings by taking the strains across each section and dividing by the distance between the reinforcement bars. These curvature distributions were then used to back-calculate the horizontal deflection of the joints for certain ductility levels by numerically integrating the curvatures and taking into account the joint shear deformations. Later, these displacement values were compared with those measured during the test and the curvatures were compared with those calculated analytically using D R A I N - 2 D X . 7.2 St ra in Gauge Evaluat ion The voltage readings from the strain gauges were recorded by the data acquisition system. The records contained high frequency noise which was filtered with a program written by Seethaler (1995) that incorporated routines adapted from Press et al. (1989). After the data had been filtered and converted to strains, the gauge readings were zeroed prior to interpretation and analysis. Only the longitudinal strains on the main reinforcement were used in the interpretation of the experimental results. A l l the specimens tested had strain gauge configurations as shown 73 in F ig . 3.3. Some retrofit schemes had additional gauges installed which were unique to the particular configuration of the bent. For example, specimen O S B 4 had additional gauges placed on the vertical post-tensioning provided within the cap beam. The data from these gauges were not used in the analyses. The data from a total of 50 strain gauges were analyzed per specimen. Since plotting the entire strain-displacement histories for each gauge and for each specimen was considered unmanageable, a method of plotting the data so that interpreting the strains and the reliability of the gauges was devised. It was realized that the average of three cycles was not necessarily an appropriate strain value to use for analysis because the average value did not indicate i f the readings had become erroneous at some stage during the test. The gauge may for example, have saturated or have become debonded from the reinforcement. It is also believed that buckling and bending of the reinforcement significantly affected some strains at the later stages of the tests. Due to the fact that there was always the possibility that the average strain may not be indicative o f the actual strain for a given displacement, the peak strains for each cycle were plotted against the overall bent deflection. Several of the plots for each gauge were then consolidated into a few plots that represented certain regions of the bent, namely the north column, the south column, and the north and south ends of the cap beam. 7.2.1 Specimen O S B 4 Figure 7.1 shows the development of strain in the north end of the cap beam of specimen O S B 4 as the bent deflection increases to the north on the second cycle of each sequence. The freebody diagram immediately below the plot reflects the region of the bent being presented, and the force vectors shown provide an indication o f locations where tensile and compressive strains may be expected. Any gauge that is not shown in the legend of the plot and appears in the free body diagram was found to be not working at all during the entire test. In addition, although they appear in Fig. 7.1, gauges like B B 5 and B B 6 were not necessarily used in the calculations of displacements. They may have been disregarded because the indicated strains were unreasonably small. 75 0.002 MA = 1 10 12 14 0.0015 0.001 Z 0.0005 -0.0005 -0.001 Yield Strain = 0.0017 2 3 Displacement (in) BTG BT4 I BT2 BTI BTa BT7 BT5 BT3 BT1 BB6 BB5 BB4~SB3^[' SYM. ABOUT&PIER CI4\. 015 —A— -BT3N X -BT4N — * - -BT5N - • --BT6N —1— -BT7N BT8N -BT9N —o--BB1N • -BB2N A -BB4N —B- -BB5N —G--BB6N Figure 7.1 Nor th C a p Beam Strains for O S B 4 on Cyc le 2 of E a c h Sequence Plots of this style also enabled comparisons to be made between gauges in the vicinity o f one another, and allowed the gauges to be evaluated between successive cycles. The time at which the strains indicated by a gauge become erroneous could quickly be identified, and consequently it would then be known at what stage of testing that data from that gauge became unreliable. Figure 7.1 indicates that the reinforcement in the cap beam of O S B 4 did not yield except for gauge B T 4 at a ductility of 9. The progression of strain at the early stages of the test and the 'leveling off o f the strains in the post elastic range of the bent can clearly be seen. It can be seen that at a displacement ductility of 12, nearly all the strains decrease. This observation coincides with the significant degradation of the specimen at that displacement and the corresponding drop in lateral load. See Photo 6.2 and Fig. 5.3. Shown in Fig. 7.2 are the strain values for the north column o f specimen OSB4 . The graph is plotted to a large scale to include the large strains that were indicated by gauge C 0 4 . This gauge is immediately above the top of the steel jacket encasing the column. This is where high tensile strains were expected because of the localized hinging observed above the tops of the column jackets. Strains for the bent displacement greater than 3 inches are not shown because many of the column gauges became unreliable beyond this displacement. This was expected, particularly in the plastic hinge region, where the reinforcement was observed to buckle and fracture. It is for this reason that the data from both specimens O S B 4 and O S B 5 were analyzed to a maximum ductility o f 6. It can be seen by comparing Figs. 7.1 and 7.2 that strain readings taken at approximately ductility level 9 are plotted at different displacement values. The strains are plotted at about 3.1 in. in Fig. 7.1 and at about 2.9 in. in Fig. 7.2. This is because the bent 77 displacement was slightly greater on the second cycle of that particular sequence during testing. For the reliable gauges, the strain values tended to remain constant for each cycle o f a particular sequence. 0.028 T 0.023 0.5 1 1.5 2 Displacement (in) 2.5 BTH BT4 I BT2 BT1 BT8 BT7 BT5 BT3 BT1 BB6 BB5 BB4 Bl SYM. ABOUT t PIER Cl4 015 Figure 7.2 Nor th Co lumn Strains for O S B 4 on Cyc le 1 of E a c h Sequence 7.2.2 Specimen O S B 5 Figure 7.3 shows the strains in the north end of the cap beam of specimen O S B 5 on the first cycle of each sequence. The strains are shown to the maximum displacement tested. Unlike O S B 4 , the strains in OSB5 did not decrease at the end of the test since the lateral load did not decrease significantly at the end of the test. The figure also confirms that there was no yielding of the cap beam reinforcement throughout the entire test. 79 10 0.0015 0.001 0.0005 (0 -0.0005 -0.001 -0.0015 2 3 Displacement (in) era BT4 BT1 BT3 BT7 BT5 S BBS BBS BB4 Bi SYM. ABOUT {. PIER 014 015 I BTZ T3 BT1 Figure 7.3 Nor th C a p Beam Strains for O S B S on Cyc le 1 of E a c h Sequence Figure 7.4 shows the strains for the north column of 0 S B 5 , also on the first cycle of each sequence. Gauges that are seen to go beyond the scale o f the graph had become unreliable and thus were not included. The figure shows that gauge C 0 4 reaches a peak strain o f 0.011 at a ductility of 1.5 after which the strain is seen to decrease with increasing bent deflection. This behaviour could not be justified since flexural deformations were not increasing in other regions of the column to compensate for the reduction at the C 0 4 location. 81 -0.003 -I 1 • 1— " " " 1 1 0 0.5 1 1.5 2 2.5 3 3.5 Displacement (in) Figure 7.4 Nor th Co lumn Strains for O S B 5 on Cyc le 1 of E a c h Sequence Typically, as indicated in the free body diagrams of Figs. 7.1 through 7.4, strain gauges were connected to the reinforcement in complementary pairs. That is, gauges on the 82 top of the beam usually corresponded with gauges on the underside of the beam and similarly with the inside and outside of the columns. In addition, the entire strain gauge system was symmetrical about the center o f the cap beam. This symmetry enabled data that may not have been available in the north end of the bent, to be substituted for data from the south end when the bent was displaced in the opposite direction. For example, strain values for the C 0 4 gauge position, beyond the 1 inch displacement, were taken from the south column. Strain distributions over both the cap beam and columns were thus obtained for each displacement amplitude using the best data from the north or south ends of the bent. From these strain distributions for the top and bottom of the cap beam and the inside and outside faces of the columns, curvature distributions were plotted, and used in the back-calculation o f the bent displacement. 7.3 Calcu la t ing Bent Displacements The curvature distributions were numerically integrated to obtain deflections that were compared to the measured displacements. The method used to calculate the deflection is shown graphically in Fig. 7.5. Typically, integration began at the base of the north column by assuming the initial rotation there to be zero. The north column base was chosen as the starting point in the analysis of both specimens OSB4 and OSB5 because the north column strain gauge data was deemed to be more reliable than the south column data. The integration then proceeded up the north column to the beam-column joint. A t this location, values for 0Flexure and A North column were calculated. Before proceeding along the cap beam from north to south, the measured joint shear deformation, 6j0intshear, was added at the north joint. The deflection at the south end of the cap beam, A cap Beam , was calculated using the rotation obtained at the top of the north column, 6 Total, as the initial rotation and then integrating along the length of the beam. Joint shear deformations were accounted for at the south joint before the displaced position o f the south column was calculated. The horizontal position o f the base of the south column relative to the south pin connection was denoted S^mr. The top diagram in Fig. 7.5 shows the direction of integration and shows the displaced position o f the bent after integrating the curvatures. It should be noted that both the cap beam and the columns were assumed to be inextensible the purpose of these calculations. This assumption was felt to be reasonable since the cap beams and joint regions of both specimens were not damaged significantly during testing. There were only a few narrow cracks observed. Deflections were also assumed to be small though shown exaggerated for clarity in F ig . 7.5. 84 Figure 7.5 Integration Method Used to Calculate Bent Deflections In order to calculate the deflection of the north joint, the entire bent was then rotated about the north column pin connection so that the base of the south column was at the original pin connection elevation. This procedure is shown in the bottom portion o f F ig . 7.5. The base of the south column would not necessarily be in the original lateral position after rotating the bent back into place as indicated by Samr • This then indicated that the system of 85 curvatures obtained from the data produced an incompatible set of displacements. Had the south column connection been a roller type connection, and thus a determinate system, this conclusion would not have been possible. N o attempt was made to modify the curvature distributions over the bent to reduce this error to zero and thus obtain a compatible set o f displacements. Compatibility could have been accounted for by changing the south column curvatures, which were not deemed to be as reliable as the north column or cap beam curvatures. The method used to calculate the deflection is similar to using the principle o f virtual work with the distribution of virtual forces as shown in the top portion o f F ig . 7.6. The system is in equilibrium and assumes that the lateral virtual load is entirely resisted by the north column. Consequently, there was no contribution o f the real south column curvatures to the calculation of the overall bent displacement. The equation to calculate the deflection of the north joint is also shown in the figure. This type of system was chosen because it was felt that the data from the north columns were more reliable than the data from the south columns. The consequence of using this system is that curvatures at the north end of the cap beam and the top o f the north column are the most important with respect to the displacement calculation. The system shown in the lower portion of Fig. 7.6 is one which may have been used to calculate the deflection had the data afforded it. There then would have been equal importance placed upon the curvatures obtained from both columns and less importance placed on the curvatures obtained at the north end of the cap beam. Also, curvature values at the south end of the cap beam would then have an increased contribution to the calculation o f deflections. # Joints Figure 7.6 V i r t u a l W o r k Method of Displacement Calcula t ion 7.4 Joint Shear Deformations The internally mounted strain gauges that were on the diagonal aluminum bar arrangement in the north joint as shown in Photo 3.4 were found not to produce reliable data that could be used for estimating the joint shear strains. However, shear deformations in the joint regions were still accounted for in the calculation of the bent displacement as was indicated in Fig. 7.5. This was done by assuming linear, uncracked joint deformations initially, until later in the test when the external L V D T setup detected larger deformations. Unfortunately, the diagonal member of the L V D T system was found not to give reliable strains when the joint stress system had compressive strains in the direction o f the L V D T . The system tended to indicate joint shear displacements only when there were cracks oriented perpendicular to the direction of this diagonal measurement. Thus the L V D T ' s provided indication o f the shear deformations in the north joint when the bent was displaced toward the south but did not provide reliable readings when the bent was displaced to the north since there was no cracking of the joint for this direction of forces. The cracking observed in the 'trailing column', where the joint forces were smaller, may arise from the fact that the positive moment reinforcement (on the bottom of the cap beam) terminated only half way into the column. When this reinforcement was in tension, the bond stresses were greater than when compared to reinforcement that may have extended completely through the column. The greater bond stresses may have thus caused the observed cracking to occur. For the purpose of the displacement calculations, this meant that reliable joint shear strains were available for the 'trailing column' or the south column. Shown below in Table 7.1 are the measured joint shear strains from the L V D T system for specimens O S B 4 and OSB5 when the bent was displaced to the north. Values for the joints in an uncracked state were evaluated by taking a free body of the joint region, calculating the joint shear stress, and assuming poisson's ratio, v , for concrete to be 0.25, and the shear modulus, G c , to be 2000 ksi. Shear deformations in the cap beam and columns were found to be very small compared to the flexural deformations and the joint shear deformations and were not included in the experimental interpretation. 88 Table 7.1 Joint Shear Strains for OSB4 and OSB5 Displaced to the North Shear Strain y (rad) Specimen OSB4 Specimen OSB5 South North South Nor th Ductil ity Level Column Column Column Column MA = 0.8 0.00014 0.00017 a a = 0.9 a a 0.00015 0.00028 MA- L 2 0.00015 0.00027 0.00016 0.00029 MA = 2.0 0.00016 0.00030 a a MA = 2.2 a a 0.00017 0.00032 MA = 2.8 a a 0.0014" 0.00032 MA = 3.0 0.00017 0.00031 a a MA = 4.0 0.00017 0.00031 0.0017" 0.00033 MA = 5.7 0.0011" 0.00031 a a MA = 6.0 a a 0.011" 0.00034 a Denotes that shear strain values were not evaluated at that particular ductility level. The values that are shown are consistent with the sequences tested for each specimen. " Denotes values that were measured by the external L V D T system located at the north joint 7.5 OSB4 Response Shown in Figs. 7.7 and 7.8 are the curvature distributions obtained for the cap beam and columns respectively. The ductility ranges from 0.8 through 5.7. Figure 7.7 shows the cap beam curvatures leveling off somewhat as the ductility level increases, a trend that was apparent in the D R A I N - 2 D X analysis. The distributions are not as linear as one might expect but the non-linear nature tends to reflect the crack patterns observed during the test. The beam remained nearly uncracked in the mid section, with only a few diagonal cracks extending from either end towards the middle. The peak magnitudes at the north end of the beam are greater than those predicted with D R A I N - 2 D X , while the values at the south end are reasonably close to the values obtained analytically. This may be due to the simple bilinear moment-curvature relationships used by D R A I N - 2 D X . See Fig. 6.5. The stiffnesses in the cracked regions are less than the average stiffness used in the computer model. For example, in Photo 5.8 the third vertical crack from the left is seen to extend to within 8 inches of the beam soffit. I f it assumed that the concrete can carry no tension, the crack tip would represent the neutral axis of the section. The cracked moment inertia for this section is approximately O.lJgroa, of the cap beam which is much less than the 0.55*1^088 used in the D R A I N - 2 D X analysis. This then results in the computer model being stiffer and thus showing less flexural deformations than what the experimental data indicates. A,P • 0.00012 i Figure 7.7 Exper imental C a p Beam Curvatures for Specimen OSB4 Figure 7.8 presents the column curvatures obtained from the experimental data and shows that the curvatures essentially increase monotonically as the ductility level increases. The peak curvatures coincide with the locations observed to experience significant damage and hinging. The south column curvatures are uniformly greater than those in the north column, which was anticipated for the same reasons regarding member compatibility as discussed in the analytical predictions. The experimental curvatures just below the tops of the steel jackets are larger than those predicted from the DRATN -2DX analysis which may indicate that more tensile strain migration into the jacket occurred than was anticipated. A,P • Curvature (1fm) Curvature (1/in) Figure 7.8 Exper imental Co lumn Curvatures for Specimen O S B 4 A s can be seen in the figures, the curvatures in the cap beam tended to reach maximum values as the displacement increased in the non-linear range. This was to be expected since the cap beam did not yield and the total lateral load did not increase much in the non-linear range. Thus the curvatures in the cap beam must remain relatively constant and the inelastic deformation had to be accounted for in the plastic hinge regions located at the tops of the columns above the steel jackets. This trend can be seen by noting the large increase in the column curvatures as the ductility level is increased. Shown in Table 7.2 below is a comparison of the measured bent displacements with the calculated displacements and the corresponding south column closure error. Positive values listed in the 'South Column Closure Error' column indicated that the base o f the south column was calculated to be displaced to the north of the pin connection. Table 7.2 Measured Displacements Versus Calculated Displacements for OSB4 Displacement Ductility MA Measured Displacement (in) Calculated Displacement (in) Percent Error South Column Closure Error S'error («n) 0.8 0.28 0.29 +4% +0.006 1.2 0.43 0.49 +13 % -0 .17 2.1 0.72 0.89 +24 % +0.03 3.0 1.04 1.32 +27 % +0.19 4.0 1.41 1.60 +14 % +0.15 5.7 2.01 2.05 +2% -0 .10 As can be seen in Table 7.2, the calculated displacements for specimen O S B 4 were uniformly greater than the measured displacements. This may be a result o f the relatively poor resolution o f the experimental data and the linear interpolation o f curvatures between data points. A s mentioned above, strain gauge readings at ductility levels greater than 6 became more unreliable and thus the curvature distributions were more difficult to deduce. The strain readings in the plastic hinge regions especially, did not tend to reflect the true increase in strain in these regions. Some gauges had apparently become saturated and indicated a constant strain. It was for these reason that experimental interpretation o f the strain gauge readings was terminated beyond ductility levels greater than 6. 7.5 O S B 5 Response Shown in Figures 7.9 and 7.10 are the curvature distributions for the cap beam and columns of specimen OSB5 . The ductility ranges from 0.9 to 6.0. Listed in Table 7.3 are the measured bent deflections, the calculated deflections, and the south column closure errors. Similar to specimen OSB4 , the cap beam curvatures, shown in Figure 7.9, for O S B 5 tended to attain maximum values as the displacement increased. Again, the cap beam did not reach flexural yielding up to a displacement ductility o f 6. The magnitudes of cap beam curvatures are o f the same order as observed in OSB4 which was expected since the longitudinal post-tensioning stress was the same and the cap beam fiberglass wraps do not increase the flexural stiffness by any significant amount. In addition, the total lateral load for both specimens was approximately the same. The distributions of curvatures are slightly more linear in nature for O S B 5 than the ones derived for OSB4. A s shown in Fig. 7.9. at displacement ductility of 6, the experimental curvature value near the middle o f the fiberglass wrap at the south end of the cap beam is shown to be approximately 3 times the value indicated for ductility level 4. This change in the generally increasing trend is evidence of the strain gauge data becoming unreliable at that location. 93 A,P • 0.00012 I -0.00006 f - ^ ; ] i ('--'—''-'-5 Figure 7.9 Exper imental C a p Beam Curvatures for Specimen O S B S The general location o f the plastic hinges in the two specimens is the same with curvatures in OSB5 being smaller and more distributed than those in OSB4 . In O S B 5 , the south joint shear deformations at ductility levels 2.8, 4.0 and 6.0 became significant which reduced the flexural demand on the plastic hinge regions in the south column. This can be seen in Fig.7.10 where the rate at which the curvatures increase in the plastic hinge region reduces particularly between ductility levels 2.8, 4.0, and 6.0. A comparison of the joint shear deformations in O S B 4 and OSB5 can be made by referring to photos 5.13 and 5.18 where it can be seen that the joint region in OSB5 is more damaged. IO *- IO O Q 8 I S o © jrvature (1/in) Figure 7 .10 Experimental Column Curvatures for Specimen O S B 5 Table 7 . 3 Measured Displacements Versus Calculated Displacements for O S B 5 Displacement Measured Calculated Percent South Column Ductility Displacement Displacement Error Closure Error MA (in) (in) 5 error (in) 0.9 0.45 0.44 - 3 % +0.06 1.2 0.60 0.59 -1 % +0.01 2.2 1.08 1.29 +20 % +0.20 2.8 L41 1.66 +18 % +0.10 4.0 2.00 2.25 +13 % +0.21 6.0 3.00 3.44 +15 % +0.18 7 . 7 The Tension Stiffening Effect and Bond Stresses Between cracks tensile stresses are transferred to the concrete from the reinforcing steel through bond stresses. Forces are transferred from the bars to the concrete by inclined compressive forces radiating out from the deformations on the reinforcement, and adhesion o f § 5 S 8 | § o c i Curvature (1/in) the concrete to the reinforcement itself. The ability of concrete to carry tensile stresses between the cracks of reinforced concrete decreases the strain in the reinforcement between cracks. This effect is known as tension stiffening. Tensile tests have been performed on heavily instrumented, reinforced concrete specimens to determine the variation o f strain that exits between the concrete and steel (Scott and Gi l l , 1987). The specimens were monotonically loaded to the yield strain o f the reinforcement. Reinforcement strains were observed to vary by as much as 44% between cracks for specimens with large crack spacings. The variations were reduced to approximately 25% as the surface area of reinforcement was increased and the average crack spacing decreased. The differences between maximum and minimum strains did not change significantly as the average strain of the reinforcement approached yield. A n analytical model has also been proposed to predict the average concrete stress in uniaxially loaded specimens (Fronteddu and Adebar, 1992). The model assumes that a stable crack pattern exists and that the loading is monotonic. The research results were compared to experimental work and it was also concluded that tension stiffening did not decay significantly with increasing average strain, but rather, remained relatively constant up to the yield strain o f the reinforcement. Theory has also been developed to predict the moment curvature response of prestressed beams subjected to a constant bending moment by taking into account the variation in curvature that exists between flexural cracks (Priestley, Park and L u , 1971). The beams tested for theoretical comparison were loaded monotonically at the third points. Differences between the peak experimental curvature values located at the cracks, and the average values were observed to vary by as much as 50% near the cracking moment. The average curvatures were later observed to be about 87% of the maximum values near the ultimate moment capacity. The differences between the peak curvature values located at cracks, and the lowest values between cracks, increased as the ultimate moment capacity o f the section was approached. This was attributed to greater flexural deformations occurring at crack locations where the neutral axis approached the compression face of the section as the average curvature increased. A l l o f the research discussed above dealt with monotonically loaded specimens. It was felt that the tension stiffening effect and bond stresses were significantly reduced due to the cyclic nature of the testing. The increasing amplitude of the cycles had subjected the reinforcement to several cycles of large hysteretic strains that caused significant cracking and degradation of the bond between the concrete and reinforcement. Thus the differences between the peak curvatures and the minimum values were expected to be reduced. Recommendations regarding the reduction of the tension stiffening effect can be found in Collins and Mitchell (1991), where it has been suggested that the effect is further reduced by approximately 30% due to the deterioration of the concrete bond stresses caused by the cyclic nature o f testing. There has been investigation into the influence of reversed cyclic loading on cracking and the bond strength of deformed bars in plain and fiber-reinforced concrete (Panda, 1980). The tests were aimed at studying the behaviour of elements such as beam-column joints in moment resisting frames where yielding can occur in both tension and compression on either face of the joint during seismic action. The specimens were comprised of a well confined single bar embedded in concrete and were subjected to reversed cyclic loading up to the yield stress for several cycles. The results indicated that the most important factor affecting stress 97 transfer between the reinforcement and the concrete was the peak stress attained in the previous cycle. A n increase in the peak stress level produces a significant reduction in the bond stress for subsequent cycles. There was observed to be about 5% decrease in bond stress for an increase from 10 to 36 cycles at a constant stress level. In a later publication concerning the same test results, the variation o f bond stress over the tension zone of a bar was defined as the bond effectiveness factor, X (Spencer, Panda and Mindess, 1982). The relationship was given as \esdx s0-l 100 where x = distance along the bar measured from the tension face of the specimen / = length of the bar in tension es = tensile strain in the bar at a distance x from the face of the specimen So = tensile strain in the bar at the loaded end The bond effectiveness factor was defined as X = 100%, for perfect bond at the specimen tension face, and X = 0% for complete bond failure over a given length. The relationship was compared to the experimental results and shown to be inversely proportional to the peak stress reached for each cycle. For deformed bars embedded in plain concrete, X dropped to about 30% near the yield stress of the reinforcement. The 1 in. diameter test bar was confined by 0.5 in. diameter steel wound into a spiral with a pitch of 3 in. and a diameter o f 8 in. This level o f confinement may have been be more effective in preserving bond stress than the unretrofitted column regions of the Oak Street specimens. This is because confinement to the column steel was provided by 3 legs of small ties spaced at over 5 in. centers. It was for these 98 reasons bond stress was thought not to significantly affect the strain readings in the cracked and plastic hinge regions of the bents as the tests progressed. 99 C H A P T E R 8 - C O M P A R I S O N O F M E A S U R E D A N D A N A L Y T I C A L R E S U L T S 8.1 Specimen O S B 4 Shown in Figs. 8.1 to 8.3 are the curvature distributions predicted by the D R A I N -2 D X model contrasted with those obtained experimentally for ductility levels 2.1, 4.0 and 5.7. It can be seen that the cap beam curvatures predicted by D R A I N - 2 D X , and those obtained experimentally, are both small in magnitude compared to the curvatures shown for the columns. The D R A I N - 2 D X results for the cap beam compare reasonably well with those derived from the strain gauge readings except perhaps near the north end of the cap beam, where the experimental curvatures are uniformly greater than those predicted by D R A I N -2 D X . The difference between the experimental and analytical results observed near the north end of the cap beam appears to be due to the flexural cracking that occurred there during testing. Photo 5.8 shows the cracks at the north end of the cap beam for ductility level 4. This cracking reduced the stiffness of the cap beam and thus curvatures in that region were higher than those predicted analytically. The approximate moment o f inertia o f the cracked section shown in Photo 5.8 is about 0 . 1 . 1 ^ as compared to the value o f 0.55*1^088 used for the D R A I N - 2 D X analysis. The sharp peak in the experimental values near the south end of the bent coincides roughly with a crack that extended diagonally from the fillet region. The crack is shown marked in green in Photos 5.9 and 5.10. Both the experimental and analytical results show that there was no flexural yielding of the cap beam for displacement ductility levels up to 6, though the experimental readings indicated reinforcement strains approaching the yield level at this high ductility level. Refer to 100 Fig. 7.1. Recall that the analytical results are based on a simple bilinear moment-curvature relationship shown in Fig. 6.5 for the cap beam elements where the flexural stiffness remained constant prior to the yield curvature. The real member stiffness changes rapidly near the assumed yield curvature. Thus it would be expected that near the 'real yield curvature' o f the cap beam, the D R A I N - 2 D X results may under predict the experimental curvatures because the stiffness is over-estimated. In addition, the central portion of the cap beam remained primarily uncracked except for a few narrow diagonal cracks. The tension stiffening effect may have been more significant there than at the ends of the cap beam where there was more cracking. The localized cracking at the north end of the cap beam near the strain gauges would have reduced the bond stresses between the concrete and the reinforcement, thus lessening the tension stiffening effect which resulted in higher tensile strains in the reinforcement being measured. The higher strain readings then translated into slightly larger curvatures for the end o f the cap beam. The experimental and analytical column curvature distributions are somewhat close in peak magnitudes which is encouraging since these occur in the important plastic hinge region, but the length over which large curvatures occur does not compare well. In addition, after comparing the column curvatures in the jacketed regions below the plastic hinges, it was clear that the experimental curvatures shown in Fig. 7.8 were too large. These curvatures were initially estimated by linearly interpolating the column base zero curvature to the value determined at the first strain gauges (gauges C 0 5 and CI5 shown in Figs. 7.1 to 7.3). These gauges are located 8 in., or 13db, from the top of the column jackets and the reinforcement 101 strains at this location are most likely not representative of the curvatures in the jacketed region. In this region, the column was most certainly not cracked and the flexural deformations were very small due to the increased stiffness of the steel jacket filled with concrete. A more accurate representation of the curvatures in that stiff, uncracked region would be the values obtained by taking the moment, M , at each location along the column and dividing by the flexural stiffness of the jacketed column, (EI)jaCketed column • Curvature values equal to M/(EI) j a c k e t e d column were used from the column bases to a point 12.5 in. below the top of the steel jackets and then interpolated to the experimental data. Consequently, the calculations o f the displacements were improved, and the error relative to the measured displacements was reduced. Shown in Table 8.1 are the revised comparisons o f calculated and predicted displacements for OSB4. The values in the 'Revised Error' column that appear in square brackets are the errors that were presented in Chapter 7. Again, positive values in the 'South Column Closure Error 1 column indicate that, for that ductility level, the base o f the south column was displaced to the north relative to the pin connection after completion o f the bent displacement calculation. -0.00006 Experimental Results o nA=2.1 Analytical Results CS ^ (O 00 o © © © © *> © © © © © © © © © © ©" © ©' © o' Curvature (1/in) Curvature (1/in) Figure 8.1 Compar ison of Curvatures at Duct i l i ty Leve l 2.1 for O S B 4 • nA=4.0 Experimental Results • HA =4.0 Analytical Results Curvature (1/in) Curvature (1/in) Figure 8.2 Compar ison of Curvatures at Duct i l i ty Leve l 4.0 for O S B 4 8 8 § S § § ©* © o ©* © ©' _ CM CM C § 8 S § § c © • © ' © ' © • © ' < Curvature (1/in) Curvature (1/in) Figure 8.3 Compar ison of Curvatures at Duct i l i ty Leve l 5.7 for OSB4 105 Table 8.1 Measured Displacements Versus Revised Calculated Displacements for OSB4 Measured Displacement Ductility fiA Measured Displacement (in) Revised Calculated Displacement (in) Revised Percent Error South Column Closure Error terror (in) 0.8 0.28 0.29 +2 % [+4] +0.035 1.2 0.43 0.47 +9 % [+13] -0.14 2.1 0.72 0.84 +17% [+24] +0.030 3.0 1.04 1.26 +21 % [+27] +0.22 4.0 1.41 1.52 +8 % [+14] +0.15 5.7 2.01 1.96 -2 % [+2] -0.074 A s shown in Figs. 8.1 through 8.3, the experimental peak curvatures in the plastic hinge regions o f the columns are less than those predicted by D R A I N - 2 D X and the experimental distributions are also more 'spread out' over the same region. Given that the curvature distributions predicted by D R A I N - 2 D X produce a compatible set o f displacements, the relative areas under the curvature diagrams, particularly in the plastic hinge regions, can be compared to see why the experimental data may over-predict or under-predict the measured displacement. It can be seen in Figs. 8.1 to 8.3 that areas where the experimental distributions are larger than those obtained analytically would predict larger displacements than those measured. This is particularly true for ductility levels 2.1 and 4.0 where the experimental curvatures are larger over much of the plastic hinge lengths. A s evidenced in Table 8.1, a change in the curvatures in the north column resulted in changes o f the error ranging from 2% to 7%. 8.2 Specimen OSB5 Shown in figures 8.4 to 8.6 are the curvature distributions predicted by the D R A I N -2 D X model contrasted with those obtained experimentally for ductility levels 2.2, 4.0 and 6.0 106 for specimen OSB5 . It can be seen that the predicted cap beam curvatures are relatively close to those indicated by the strain gauges, especially at the larger ductilities. Similar to O S B 4 , the experimental results were always greater than the analytical results for the north end of the cap beam. The explanation for this is also due to the reduced stiffness caused by the flexural cracking in the north end of the cap beam. Larger discrepancies between the distributions arise in the joint regions. D R A T N - 2 D X tends to predict more localized curvatures with greater peak magnitudes than what were measured. As with OSB4 , curvatures equal to the moment M , divided by the flexural stiffness of the columns (EI)C oiumn, were used from the column bases up to 55 in. from the bases. This was done to account for the uncracked linear behaviour of the lower portions o f the columns. Shown in Table 8.2 below are the comparisons of the measured bent displacements versus the revised calculated displacements. Table 8.2 shows the effect that interpolation o f linear curvature values over the lower portion of the columns had on the calculation o f the measured displacement. The change in the error of calculated displacement ranged from 0% to 6%. 107 A,P • MA =2-2 Experimental Results O HA =2-2 Analytical Results CM ^ CO 00 © CM © © © © *- _ O © © © O © © © © © © © © © © © 0 0 0 0 0 CM ^ CO 00 © CM ^ © © © © * - * - * " © © © © © © © © © © © © © © Curvature (1/in) Curvature (1/in) Figure 8.4 Compar ison of Curvatures at Duct i l i ty Leve l 2.2 for O S B 5 Figure 8.5 Compar ison of Curvatures at Duct i l i ty Leve l 4.0 for O S B 5 A.P a -0.00006 Experimental Results o nA = 6.0 Analytical Results U) O IO c* <o © r» CM CM © © © © © © © © © © O © ©' © O Curvature (1/in) u? o >o o © Y - <N © © © © © © © © © ' © ' © ' © Curvature (1/in) c Figure 8.6 Compar ison of Curvatures at Duct i l i ty Leve l 6.0 for OSB5 Table 8.2 Measured Displacements Versus Revised Calculated Displacements for OSB5 Measured Displacement Ductility #4 Measured Displacement (in) Calculated Displacement (in) Revised Error South Column Closure Error terror (in) 0.9 0.45 0.44 -3 % [-3] +0.057 1.2 0.60 0.60 0 % [-1] +0.033 2.2 1.08 1.27 +17 % [+20] +0.21 2.8 1.41 1.60 +14 % [+18] +0.11 4.0 2.00 2.13 +7 % [+13] +0.24 6.0 3.00 3.31 +10 % [+15] +0.18 I l l C H A P T E R 9 - S U M M A R Y A N D C O N C L U S I O N S Curvature distributions were derived from experimental strain gauge data, and from curvature estimates in the uncracked regions of the two-column bents. Occasionally, interpolation and extrapolation of the raw strain gauge data was necessary to estimate the curvatures at certain sections. The shapes of the curvature distributions were found to be reasonable approximations to the curvatures expected from lateral displacements in the non-linear range of response. The experimentally derived curvatures, supplemented with estimates of the joint shear deformations, were used to calculate the horizontal bent displacements. Comparisons with the measured displacements showed errors in the calculated deflections ranging from -3% to +21%. In the large displacement ductility range from 4 to 6, the errors were typically below 10%, and in the ductility range from 1 to 3, the errors were generally larger than 10%. At high displacement ductility levels, approximately 60% of the deflection came from the curvatures in the plastic hinge regions of the columns. Theoretical estimates of the curvature distributions were made using DRATN-2DX and compared with the experimentally derived values at several displacement ductility levels. In the plastic hinge regions of the columns, the peak analytical values were found to be uruTormly higher than those estimated experimentally. The experimental and analytical curvatures in the cap beam region compared well, except perhaps at the negative moment end, where the experimental values were observed to be consistently larger. This region of larger experimental curvatures in the cap beam coincided with the region that experienced flexural cracking during testing. 112 The curvature predictions facilitated estimates o f the peak concrete strains, using a program that accounts for confinement provided by transverse reinforcement when determining the moment-curvature response of a section. The unretrofitted architectural fillet region of the Oak Street Bridge bents, located in the plastic hinge region of the columns, provided significant confinement stresses to the concrete when in compression and permitted large ultimate concrete compressive strains. A t a displacement ductility o f 9, and based upon the estimated peak analytical curvature in the plastic hinge region, the concrete strains were estimated to be 0.013 using the moment-curvature response for the section. The plastic hinge region of the columns, retrofitted with fiberglass wraps, was predicted to be capable o f providing enough confinement to sustain ultimate concrete strains o f approximately 0.027. The peak concrete strains estimated for the wrapped region during testing were about 0.0084. Specimens instrumented with more strain gauges would have increased the confidence in the range of curvatures occurring in the plastic hinge and joint regions. A n increased level of instrumentation would have produced more accurate estimates pf the measured joint displacements. The shapes of the curvature distributions would have been more detailed and thus the errors associated with linearly interpolating between data points would have been reduced. The curvature values obtained experimentally are also believed to be dependent upon the location o f strain gauges relative to the locations of cracks. Strain values measured at locations between cracks are thought to be less than the peak values. It is believed however, that the cyclic nature o f the testing that forced the reinforcement through large hysteretic strains, significantly deteriorated the bond between the steel and the concrete. This then reduced the variations between peak curvatures located at cracks, and the values between cracks. Further research into the deterioration of bond between the concrete and reinforcement o f elements subjected to large hysteretic displacements would be beneficial in estimating the difference between peak strain values and those located between cracks. Given that care is taken to ensure proper strain gauge installation, and that patience is exercised in the acquisition and the interpretation o f the data, it is felt that strain gauges can give reliable indications of reinforcement strains in reinforced concrete elements. Bending and buckling o f the reinforcement is believed to have affected the strain values indicated by the gauges at the later stages of the tests when the concrete began to spall. DRABN-2DX was successfully used to predict the lateral load-displacement response of two-column bridge bents that were observed to behave in a predominantly flexural manner. DRAIN-2DX has limitations in the method of predicting the response of beam-column joints because no model or element is presently provided in the program to analyze the joint regions. This limitation did not however, affect the derivation o f curvature estimates as the shear deformations of the columns were calibrated to account for the joint shear deformations. The shapes and the magnitudes of the experimentally derived curvature distributions compared reasonably wel l with those obtained analytically. This then increased the level o f confidence in the ability o f the analysis to predict curvature distributions o f retrofitted specimens. 114 R E F E R E N C E S 1. A A S H O 1961, Standard Specifications for Highway Bridges, Washington, D C , American Association of State Highway Officials, 1961, Edit ion 8. pp. 7-22. 2. Anderson, D.L. , Sexsmith, R .G. , English, D.S, Kennedy, D.W., and Jennings, D.B. , "Oak Street & Queensborough Bridges Two Column Bent Tests," University o f Brit ish Columbia Department o f Civi l Engineering, Earthquake Engineering Research Facility, Technical Report 95-02, July, 1995. 82 pp. 3. Chai, Y . H . , Priestley, M.J .N . , and Seible, F., "Seismic Retrofit o f Circular Bridge Columns for Enhanced Flexural Performance," ACI Structural Journal, Volume 88, N o . 5, October, 1991, pp. 572-584. 4. Collins, M .P . , and Mitchell, D., Prestressed Concrete Structures, N e w Jersey, Prentice Hal l , 1991, 766 pp. 5. Crippen International Ltd. , "Oak Street Bridge N o . 1380 - Two-Column Bent Test Program - Comparison of Five Major Bridges," Report QI 17C/7.2.0., March, 1993. 6. Design of Concrete Structures for Buildings, A National Standard of Canada, C A N -A23.3-M84, Canadian Standards Association, 1984. 7. Design Specifications for Highway Bridges, Department of Public Works o f Brit ish Columbia, 1951. 8. English, D., Cigic, T., Sexsmith, R .G. , and Anderson, D.L. , "Test o f a Bridge Bent Seismic Retrofit Using Fiberglass Jackets," Canadian Society for Civil Engineering Annual Conference Proceedings, Ottawa, June, 1995, Vo l . 3, pp. 419-427. 9. Fronteddu, L., and Adebar, P., "The Response of Structural Concrete to Ax ia l Tension," Canadian Society for Civil Engineering Annual Conference Proceedings, Quebec City, Quebec, May, 1992, pp. 89-98. 10. Fyfe, E.R. , "The High Strength Fiberwrap System for Retrofitting Bridge and Other Structure Columns," CALTRANS Third Annual Seismic Research Workshop Proceedings, Sacramento, California, June, 1994. 11. Hexcel-Fyfe Co. - T Y F O S Fiberwrap System, Information available from Hexcel-Fyfe Co. , 1341 Ocean Avenue, De l Mar, California 92014. 12. Kennedy, D.W., Turkington, D., and Wilson, J . , "Design for Earthquake retrofit and Widening of the Vancouver Oak Street Bridge," Canadian Society for Civil Engineering Annual Conference, Quebec City, 1992. 115 13. MacRae, G.A. , Priestley, M.J .N . , and Seible, F., "Shake Table Tests o f Twin-Column Bridge Bents," CALTRANS Third Annual Seismic Research Workshop Proceedings, Sacramento, California, June, 1994. 14. Mander, J .B. , Priestley, M.J .N . , and Park, R., "Theoretical Stress-Strain Mode l for Confined Concrete," Journal of Structural Engineering, A S C E , Volume 114, N o . 8, August, 1988, pp. 1804-1826. 15. Mander, J .B. , Priestley, M.J .N . , and Park, R., "Observed Stress-Strain Behaviour of Confined Concrete," Journal of Structural Engineering, A S C E , Volume 114, N o . 8, August, 1988, pp. 1827-1849. 16. Mitchell , D., Sexsmith, R .G . , and Tinawi, R., "Seismic retrofitting techniques for bridges - A state o f the art report," Canadian Journal of Civil Engineering, Volume 21, N o . 5, 1994, pp. 823-835. 17. Panda, A . K . , "Investigation of Bond of Deformed Bars in Plain and Steel-Fiber-Reinforced Concrete Under Reversed Cyclic Loading," University o f Brit ish Columbia Department of Civi l Engineering, Materials Research Series Report N o . 1, September, 1980, 80 pp. 18. Paulay, T., and Priestly, M.J .N . , Seismic Design of Reinforced Concrete and Masonry Buildings, N e w York , John Wiley & Sons, 1992. 744 pp. 19. Prakash, V . , Powell , G .H . , and Campbell, S., " D R A I N - 2 D X - Base Program Description and User Guide Version 1.10," University of California, Berkeley, November, 1993. 20. Press, W . H , Teukolsky, S.A., Flannery, B.P. , and Vetterling, W.T. , Numerical Recipes, The Art of Scientific Computing (FORTRAN Version), Cambridge, Cambridge University Press, 1989. 21. Priestley, M .J .N . , Park, R., and L u , F.P.S., "Moment-Curvature Relationships for Prestressed Concrete in Constant-Moment Zones," Magazine of Concrete Research, V o l . 23, N o . 75-76, June-Sept. 1971, pp. 69-78. 22. Priestley, M.J .N . , and Seible, F., "Seismic Assessment and Retrofit o f Bridges," University of California, San Diego, L a Jolla, California, Report N o . SSRP-91/03, 1991. 23. Priestley, M .J .N . , Seible, F., and Chai Y . H . , "Design Guidelines for Assessment and Repair o f Bridges for Seismic Performance," University o f California, San Diego, L a Jolla, California, Report No . SSRP-92/01, August, 1992. 116 24. Roberts, J .E. , "Recent Advances in Seismic Design and Retrofit o f California Bridges," Lifeline Earthquake Engineering: Proceedings of the Third U.S. Conference, Los Angeles, California, August, 1991, pp. 52-64. 25. Scott, R .H . , and Gi l l , P.A.T. , "Short-term distributions of strain and bond stress along tension reinforcement," The Structural Engineer, Volume 65B, N o . 2, June 1987, pp. 39-48. 26. Seethaler, M.F . , "Cyclic Response of Oak Street Bridge Bents," M.A.Sc. Thesis, Department of Civ i l Engineering, University of British Columbia, Apr i l , 1995. 27. S E Q U A D Consulting Engineers Inc., "Seismic Retrofit of Bridge Columns Using High-Strength Fiberglass/Epoxy Jackets - Design Recommendations," Report 93-07, August, 1993. 28. S E Q U A D Consulting Engineers Inc., "Design Aids for Retrofit o f Columns Using Hexcel-Fyfe Fiber/Epoxy Jackets," Report 93-12, December 1993. 29. Spencer, R.A. , Panda, A .K . , and Mindess, S., "Bond of Deformed Bars in Plain and Fibre Reinforced Concrete Under Reversed Cyclic Loading," The International Journal of Cement Composites and Lightweight Concrete, Vo l . 4, N o . 1, February, 1982, pp. 3-17. 30. X iao , H . , Priestley, M.J .N . , and Seible, F., "Steel Jacket Retrofits for Enhancing Shear Strength o f Short Rectangular Reinforced Concrete Columns," University o f California, San Diego, L a Jolla, California, Report No . SSRP-92/07, July, 1993. 117 A P P E N D I X A - M A T E R I A L P R O P E R T I E S Table A l Reinforc ing Steel Properties B a r Size & Descript ion Number of Tests Y i e l d Stress / , ( k s i ) Ul t imate Stress fu (ksi) O a k Street Br idge #5 Ma in Bars, Ab=0.31 in 2 4 49.5 76.3 9 Ga. Column Ties, Ab=0.017 in 2 3 47.1 61.6 4 Ga. Stirrups, Ab=0.041 in 2 3 38.6 55.6 4/0 Ga. Stirrups, Ab=0.12 in 2 3 34.4 55.2 1/0 Ga. Beam Reinf , Ab=0.073 in 2 3 33.2 52.6 Table A 2 Concrete Cy l inder Strengths Program Specimen # Test Notat ion Test Date 6 " x l 2 " Cy l inder Strength (kips) (ksi) 1 OSB1 93 Sept. 24 192 192 202 6.90 2 OSB5 94 Sept. 27 196 194 193 6.87 3 O S B 2 94 Jan. 11 212 214 206 7.44 5 O S B 4 = 7.00 118 Figure A l Stress-Strain Curve for #5 M a i n Reinforcement A P P E N D I X B - S T R U C T U R A L D R A W I N G S to o © © © I i f HI v - r ii I i ^PIER CAP • .a i /r | PER CAP-30 • z 3 3) O z ° . •o • w9 10 3/4' If U N LP1ER CAP I O c Ml PI [*; SSS 03 70 a <n m o o z o 70 9 -a 70 o O 3? m CO _ | N> m 00 Cl s: w O o A V |!8 !!3 i si 3 ° 4 A co 1 = i ^ o 0_ z C §3 3 o-I" -TTci-11 h I i 3 J iS - g is -n-2 8 3. is M .1-4 ! E 3" • i So. 8 S i § « s § 11 r CL •11* M . V M M 7f nil -* M M M I I I I WW ?3* -1' tPIERCAP »S5 1* SHAFT r r ft • o • i — , >1 t i r— n / OB 1 s P 1 Tx. (TrP.) A P P E N D I X C - P H O T O G R A P H S 125 Photo 3 . 2 Typica l Strain Gauge Wrapped in Protective Put ty Photo 3.4 Diagonal System of Instrumented Bars in the Nor th Jo in t Photo 4.1 Specimen OSB1 in Part ia l Formwork at A . P . S . Photo 4.2 Specimen O S B 1 Loaded on the Modi f ied A . P . S . Tra i le r Photo 4.4 Specimen OSB4 in the Testing Frame P r i o r to Test ing Photo 4.5 Installation of Fiberglass W r a p on the South E n d of the C a p Beam Photo 4.6 Start of Fiberglass W r a p on the South C o l u m n 132 Photo 4.8 C a p Beam of O S B 5 Pr io r to Testing Photo 4.9 South Co lumn and C a p Beam of O S B 5 P r i o r to Test ing Photo 5.4 O S B 2 - Nor th E n d of C a p Beam at Duct i l i ty 1.4 OAK ST BRIOGE BENT T E S T D E C 2 1993 S P E C I M E N O S B S a RF1 S E Q U E N C E J C Y C L E IB DUCTILITY 6.0 136 Photo 5.5 O S B 2 - South E n d of C a p Beam at Duct i l i ty 6 Photo 5.6 O S B 2 - Nor th C o l u m n at Duct i l i ty 1.4 Photo 5.7 O S B 2 - Nor th Co lumn Shear Fai lure at Duct i l i ty 6 139 Photo 5.10 O S B 4 - Nor th Joint at Duct i l i ty 6 Photo 5.11 O S B 4 - North Joint at Duct i l i ty 9 141 Photo 5.12 O S B 4 - Nor th Joint and Beam Underside at Duct i l i ty 9 Photo 5.17 O S B 5 - South E n d of C a p Beam and Joint at Displacement 4.3 in . 145 Photo 5.19 O S B 5 - South E n d of C a p Beam at Displacement 4.3 in . 146 Photo 5.20 OSB5 - North Column Buckled Reinforcement Photo 6.2 O S B 4 - Overal l V iew at Duct i l i ty 12 APPENDIX D - COMPUTER PROGRAM "EX" SOURCE CODE $debug c****************************************************************** c* Program to extract Nodal Rotations from drain output f i l e s . * c* Nodal rotations are converted to d i s t r i b u t e d curvatures. * c* * c* Output f i l e s generated by program: ex.ech,ex.out * c* Input f i l e s required by program: ex.nod,user Input * c* * c* Written by Daryl English vl.O, July,1995. * c* * c* Nodes MUST be 104 to 313 for analysis to be succes s f u l . * c* Extracted data from DRA1N2D output f i l e s i s echoed to the * c* f i l e "ex.ech". The present version only reads the r o t a t i o n s * c* output by Drain and calculates the curvatures. Two * c* dimensional arrays are used. The FORTRAN v3.0 compiler * c* l i m i t s the data to about 2.5 2-D arrays each 75x75. * c* c* The program counts the number of displacement/load steps c* i n c l u d i n g any i n t e r a t i o n steps performed. So data can be c* manipulated for d i f f e r e n t specimens and d i f f e r e n t a n a l y s i s c* lengths. Lengthy analysis segments w i l l require the arrays c* to be redimensioned. * C* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * program ex character*8 prgm character*12 input1,input2,out1,out2 character*22 analtype character*80 t i t l e integer nodnum(66),nstep(75) r e a l fact(75),rotn(66,75),statn(70),delta(70),posn(70), phi(66,75),xtran(75) c********************************* c* Program I n i t i a l i z a t i o n and Name Q* ******************************* * prgm='EXTR1' write(*,750) prgm 750 format(16x,****************************************** ./,24x,'Program ',a5,' vl.O by Daryl English', ./,16x,'Extraction of Drain2D Nodal Rotations f o r Processing', ./,16x,•****************************************************•) c******************************** c* Opening input and output f i l e s Q******************************** write(*,800) keybrd=0 read(keybrd,'(al2)') i n p u t l i n f i l e = 3 koutl=4 kout2=6 input2='ex.nod' out1=*ex.ech' out2='ex.crv' write(*,805) i n p u t l write(*,807) input2 write(*,810) o u t l write(*,810) out2 o p e n ( i n f i l e , f i l e = i n p u t l , s t a t u s = ' o l d ' ) open(kout1,file=out1,status='new') open(kout2,file=out2,status='new') 800 format(/,lx,'Enter raw data f i l e ( i n c l . extension) => ',\) 805 format(/,lx,'===> Opening input f i l e : ',al2) 807 format(lx,'===> Opening input f i l e : ',al2) 810 format(lx,'===> Opening output f i l e : ',al2,) c****************************************** ******* c* Find the L a t e r a l Collapse analysis segement c* and count the number of analysis steps. c* Echo extracted data to f i l e = ex.ech for v e r i f i c a t i o n . c******************************************************** ncounter=l i = l j - l 10 read(infile,900) analtype 900 format(lx,a22) if(analtype.eq.'ANALYSIS TYPE = * STAT') then ncounter=0 read(infile,1015) nodnum(i) write(*,910) nodnum(i) read(infile,1025) n s t e p ( j ) , f a c t ( j ) , x t r a n ( j ) , r o t n ( i , j ) write(kout1,1030) i n p u t l write(koutl,1035) nodnum(i) write(koutl,1040) write(koutl,1045) n s t e p ( j ) , f a c t ( j ) , r o t n ( i , j ) 910 format(/,lx,i5,' => F i r s t node number') 1015 format(//,35x,i5,) 1025 format(///,i5,2x,el0.4,2x,el2.5,16x,el2.5) 1030 format(lx,'Data echoed from f i l e : ',al2,/) 1035 format(lx,'Node number =>',i5) 1040 format(lx,'Step',5x,'Load Fact',8x,'R-Rotn') 1045 format(lx,i5,',',2x,el0.4,',',2x,el2.5) j - j + l endif i f ( e o f ( i n f i l e ) ) then c l o s e ( i n f i l e ) close(koutl) close(kout2) write(*,1075) 1075 format(/,lx,'===> S t a t i c analysis segment not found < stop endif if(ncounter.eq.1) then goto 10 endif c * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * c* Subsequent loops for f i r s t node c********************************* 20 read(infile,1050) n s t e p ( j ) , f a c t ( j ) , x t r a n ( j ) , r o t n ( i , j ) if(fact(j).gt.0.00001) then write(koutl,1060) n s t e p ( j ) , f a c t ( j ) , r o t n ( i , j ) j=j+l jmax=j-l goto 20 endif write(*,1070) jmax 1050 format(i5,2x,el0.4,2x,el2.5,16x,el2.5) 1060 format(lx,i5,',',2x,el0.4,',',2x,el2.5) 1070 format(lx,i5,' => Number of steps i n S t a t i c Analysis') c****************************************** c* Read i n the data f or a l l remaining nodes c****************************************** keof=l i=i+l read(infile,1200) nodnum(i) 1200 format(35x,i5,///) 150 write(koutl,1205) nodnum(i) 1205 format(/,lx,'Node number =>',i5) 40 do 100 j=l,jmax read(infile,1210) r o t n ( i , j ) 1210 format(47x,el2.5) write(koutl,1220) n s t e p ( j ) , f a c t ( j ) , r o t n ( i , j ) 1220 format(lx,i5,',',2x,el0.4,',',2x,el2.5) 100 continue i=i+l imax=i-l i f ( e o f ( i n f i l e ) ) then c l o s e ( i n f i l e ) keof=0 write(*,1300) nodnum(imax) write(*,1305) imax write(*,1310) i n p u t l 1300 format(lx,i5,' => Last node number') 1305 format(lx,i5,' => Total number of nodes') 1310 format(/,lx,'===> Closing input f i l e : ',al2) goto 50 endif read(infile,1230) nodnum(i) write(koutl,1235) nodnum(i) 1230 format(/,35x,i5,///) 1235 format(/,lx,'Node number =>',i5) 50 if(keof.eq.1) then goto 40 endif close(koutl) c******************************************* c* Read i n nodal posi t i o n s from ex.nod f i l e , c******************************************* kin2=5 open(kin2,f ile=input2,status='old') read(kin2,4000) t i t l e do 80 n=l,imax+2 read(kin2,*) statn(n) 80 continue knorth=imax+2 close(kin2) write(*,4010) input2 write(*,4015) o u t l 4000 format(a80) 4010 format(lx,'===> Closing input f i l e : ',al2) 4015 format(lx,'===> Extracted data i s echoed i n f i l e : ',al2) c**************************************** c* Calculate nodal deltas from positions, c**************************************** k=l kbeam=29 do 90 n=2,kbeam delta(k)=statn(n)-statn(n-1) k=k+l 90 continue ksouth=44 do 95 n=31,ksouth delta(k)=statn(n)-statn(n-1) k=k+l 95 continue do 97 n=46,knorth delta(k)=statn(n)-statn(n-1) k=k+l 97 continue kmax=k-l 151 c * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * c* Cal c u l a t e s t a t i o n mid-points f o r curvatures to be p l o t t e d c*********************************************************** 1=1 do 110 n=2,kbeam posn(l)=(statn(n)+statn(n-l))/2 1=1+1 110 continue do 120 n=31,ksouth posn(l)=(statn(n)+statn(n-l))/2 1=1+1 120 continue do 125 n=46,knorth posn(l)=(statn(n)+statn(n-l))/2 1=1+1 125 continue lmax=l-l c * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * c* Calculate cap beam curvatures from nodal rotations C* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * i = l j=l k=l 1=1 do 150 i=2,kbeam do 170 j=l,jmax p h i ( k , j ) = ( r o t n ( i , j ) - r o t n ( i - l , j ) ) / d e l t a ( k ) 170 continue k=k+l 150 continue c * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * c* South column curvatures calculated c************************************ do 180 i=31,43 do 190 j=l,jmax p h i ( k , j ) = ( r o t n ( i , j ) - r o t n ( i - l , j ) ) / d e l t a ( k ) 190 continue k=k+l 180 continue do 200 j=l,jmax p h i ( k , j ) = ( r o t n ( l , j ) - r o t n ( i - l , j ) ) / d e l t a ( k ) 200 continue k=k+l c * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * c* North column curvatures calculated c************************************ do 210 i=45,imax do 220 j=l,jmax p h i ( k , j ) = ( r o t n ( i , j ) - r o t n ( i - l , j ) ) / d e l t a ( k ) 220 continue k=k+l 210 continue do 230 j=l,jmax p h i ( k , j ) = ( r o t n ( 2 9 , j ) - r o t n ( i - l , j ) ) / d e l t a ( k ) 230 continue Q* ************* * *************************************** c* Write curvatures to ex.out f o r p l o t t i n g and ana l y s i s c****************************************************** write(kout2,4500) i n p u t l write(kout2,4510) (fact(j),j=l,jmax) write(kout2,4512) (xtran(j),j=l,jmax) do 250 k=l,28 write(kout2,4515) posn(k),(phi(k,j),j=l,jmax) 250 continue write(kout2,4520) do 260 k=29,42 write(kout2,4515) posn(k),(phi(k,j),j=l,jmax) 260 continue write(kout2,4530) do 270 k=43,kmax write(kout2,4515) posn(k),(phi(k,j),j=l,jmax) 270 continue write(*,4550) out2 4500 format(lx,'Data extracted from f i l e : ',al2,/, lx,'Curvatures calculated are as follows:',//, lx,'===> cap Beam Curvatures (1/in) <===•) 4510 format(lx,'Station ( i n ) | Load Factor =>',75(f8.4,3x,' 4512 format(13x,'|',6x,'X-tran =>',75(2x,f8.4,lx,',')) 4515 format(3x,f8.3,2x,*,',15x,75(fll.9,',')) 4520 format(lx,'===> South Column Curvatures (1/in) <===•) 4530 format(lx,'===> North Column Curvatures (1/in) <===*) 4550 format(lx,'===> Curvature c a l c u l a t i o n s i n f i l e : ',al2 close(kout2) end 

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