UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

Shake table testing of an Oak Street Bridge bent model Davey, Elizabeth 1996

Your browser doesn't seem to have a PDF viewer, please download the PDF to view this item.

Item Metadata

Download

Media
831-ubc_1996-0562.pdf [ 12.18MB ]
Metadata
JSON: 831-1.0050341.json
JSON-LD: 831-1.0050341-ld.json
RDF/XML (Pretty): 831-1.0050341-rdf.xml
RDF/JSON: 831-1.0050341-rdf.json
Turtle: 831-1.0050341-turtle.txt
N-Triples: 831-1.0050341-rdf-ntriples.txt
Original Record: 831-1.0050341-source.json
Full Text
831-1.0050341-fulltext.txt
Citation
831-1.0050341.ris

Full Text

SHAKE TABLE TESTING OF AN OAK STREET BRIDGE BENT MODEL by ELIZABETH D A V E Y B.A., B.A.I. University of Dublin, Trinity College, 1994 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF T H E REQUIREMENTS FOR T H E D E G R E E OF MASTERS OF APPLIED SCIENCE in T H E F A C U L T Y OF G R A D U A T E STUDIES Department of Civil Engineering We accept this thesis as conforming to the required standard T H E UNIVERSITY OF BRITISH COLUMBIA August 1996 © Elizabeth Davey, 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 &viJ Etui/i The University of British Columbia Vancouver, Canada Date Q7-- )Q- / 9 9 6 DE-6 (2/88) Abstract A B S T R A C T Further to the slow cyclic testing of a 0.45 scale model of a two column bent from the Oak Street Bridge from 1993-1995, a testing program was devised to test a smaller 0.27 scale model of the same bent in its as-built condition on the shake table at UBC's Earthquake Engineering Research Laboratory. The prototype bent was scaled to 0.27 size, and the dead load was incorporated as a mass block attached to the cap beam. The specimen was instrumented internally with strain gauges on some longitudinal and transverse reinforcing steel, and externally with accelerometers and displacement transducers. The bent was subjected to scaled seismic motions in the in-plane horizontal direction. A representative record of the 1992 California Landers Earthquake was chosen as the input motion. A high speed camera recorded the development of cracking and damage. Several test runs at different levels of shaking were executed. After each run, the dynamic characteristics of the bent were determined from impact hammer tests. Complementary analytical studies were performed to predict the behaviour of the specimen. The aims of this program were: to identify damage, failure modes and dynamic characteristics of the bent, to compare the experimental results with analytically determined values of damage index and dynamic characteristics, to relate the experimental results to the results from the earlier larger scale slow cyclic tests, and to gain further insight into the operating characteristics of the recently upgraded digitally controlled shake table. It was found that the modes of failure from the shake table and slow cyclic tests were very similar, both being due to shear failure of the cap beam, however the shake table tested bent was capable of withstanding a more severe load. The peak relative displacements experienced by the ii Abstract shake table bent were also larger than those by the slow cyclic test. The hammer testing showed that the natural frequency of the bent decreased throughout the test, until the final value was less than half that of the initial one. The analytical predictions of the dynamic characteristics of the model correlated well with the test results, but underpredicted the failure load by about 20%. Some initial problems with the operation of the shake table were experienced, but these were corrected and the table worked well for the rest of the test. The experimental evidence supported the earlier testing that was done, and highlighted some of the differences between the two testing methods. iii Table of Contents Table of Contents ABSTRACT H T A B L E OF CONTENTS IV LIST OF FIGURES IX LIST OF TABLES XI ACKNOWLEDGEMENTS X H CHAPTER 1 INTRODUCTION 1 1.1 BACKGROUND 1 1.2 AIMS AND OBJECTIVES 5 1.3 SCOPE 6 1.4 U B C EARTHQUAKE ENGINEERING RESEARCH FACILITY 6 1.5 RELATED RESEARCH 7 1.5.1 Test Method Comparison 7 1.5.2 Scaled Shake Table Tests , 9 1.5.3 Relevance to this Thesis. 12 1.6 O A K STREET BRIDGE SLOW CYCLIC TESTS 13 1.7 TEST APPROACH AND THESIS OVERVIEW 14 CHAPTER 2 SCALING - THEORY AND DESIGN 17 2.1 MODELING THEORY 17 2.2 MODELING THE PROTOTYPE B E N T 23 iv Table of Contents 2.2.1 Shake Table Capacity --23 2.2.2 Modeling of the Structure 23 2.2.3 Scaling the Steel Reinforcing 26 2.2.4 Scaling the Period 28 2.2.5 Column axial force 29 2.3 Summary 30 C H A P T E R T H R E E T E S T S E T - U P 32 3.1 GENERAL DESCRIPTION 3 2 3.2 MASS BLOCK 3 4 32.1 General configuration 34 3.2.2 Concrete block 34 3.2.3 Steelplates •. 36 3.3 CONNECTIONS 3 6 3.4 LATERAL SUPPORT SYSTEM 3 9 3.5 PIN CONNECTIONS 4 0 C H A P T E R F O U R I N S T R U M E N T A T I O N , 41 4.1 STRAIN GAUGES : 4 1 4.2 DISPLACEMENT TRANSDUCERS AND ACCELEROMETERS 4 2 4.3 OTHER SYSTEMS 4 4 v Table of Contents C H A P T E R F I V E C O N S T R U C T I O N A N D M A T E R I A L S 45 5.1 CONSTRUCTION 45 5.2 MATERIAL PROPERTIES 46 5.2.1 Concrete 46 5.2.2 Steel 47 5.2.3 Dywidag bars 47 5.2.4 Rubber 47 5.3 L A T E R A L SUPPORT SYSTEM 49 C H A P T E R S I X C A P A C I T Y A N D T H E O R E T I C A L B E H A V I O U R 50 6.1 CAPACITY OF THE BENT 50 6.1.1 Codes 50 6.1.2 Results scaled from Analysis of Prototype and 0.45 scale model 53 6.2 SECTIONAL DEMANDS 56 6.2.1 PCAframe 57 6.2.2 DRA1N-2DX 60 6.3 PREVIOUS TEST AND ANALYSIS AT 0.45 SCALE 66 6.3.1 Scale Effects 66 6.3.2 Cyclic Test Results 67 6.3.3 IDARC Analysis 68 6.4 ANALYSES USING C A N N Y - E 70 vi Table of Contents C H A P T E R S E V E N I N P U T M O T I O N S A N D T E S T P R O G R A M 73 7.1 SELECTION OF TIME HISTORY 7 3 7.2 MODIFICATIONS TO TIME HISTORY 7 8 7.2.1 Table modifications 7 8 7.2.2 Scaling 7 9 13 TEST PROGRAM 8 1 7.3.1 Input levels 8 1 7.3.2 Hammer test 8 3 C H A P T E R E I G H T T E S T R E S U L T S 84 8.1 QUALITATIVE DESCRIPTION 8 4 8.2 HAMMER TEST RESULTS 8 7 8.3 B E N T PERFORMANCE 8 9 8.3.1 Cap beam acceleration and displacement 8 9 8.3.2 Hysteresis curves 92 8.3.3 Frequency response 93 8.3.4 Strain gauges 96 8.3.5 Tie-down force variation 98 8.3.6 Torsion 98 8.3.7 Vertical motion 101 8.3.8 Acceleration transmission 101 8.4 GENERAL REMARKS 104 8.4.1 Shake table performance • 104 8.4.2 Video data 105 vii Table of Contents C H A P T E R N I N E D I S C U S S I O N O F R E S U L T S 106 9.1 COMPARISON TO SLOW CYCLIC TEST 106 9.1.1 Structural behaviour and failure mode 106 9.1.2 Hysteresis loops. 107 9.1.3 General comments Ill 9.2 EXPECTED PROTOTYPE BEHAVIOUR I l l 9.3 COMPARISON TO PREDICTIONS 112 9.3.1 DRA1N-2DX 772 9.3.2 IDARC and CANNY-E 113 C H A P T E R 10 C O N C L U S I O N S A N D R E C O M M E N D A T I O N S 114 10.1 CONCLUSIONS 114 10.2 RECOMMENDATIONS 115 R E F E R E N C E S 117 A P P E N D I X A - S T R U C T U R A L D R A W I N G S 121 A P P E N D I X B - D A T A S T O R A G E I N F O R M A T I O N A N D T E C H N I C A L S P E C I F I C A T I O N S 126 A P P E N D I X C - P H O T O G R A P H S O F T H E B E N T F A B R I C A T I O N A N D S H A K E - T A B L E T E S T 133 A P P E N D I X D - H A M M E R T E S T D A T A 147 A P P E N D I X E - D A T A F R O M T H E 10%, 40% A N D 150% S H A K E T A B L E T E S T S 151 viii List of Figures List of Figures FIGURE 2.1: COLUMN INTERACTION DIAGRAM 30 FIGURE 3.1: MASS BLOCK SYSTEM 33 FIGURE 3.2A: CONCRETE B E A M , SECTION AND PLAN VIEW 35 FIGURE 3.2B: CONCRETE B E A M , SECTION 35 FIGURE 3.3: TYPICAL STEEL PLATE 36 FIGURE 3.4 CONCRETE MASS BLOCK CONNECTION, SIDE AND E N D SECTIONS 37 FIGURE 3.5 MASS BLOCK STEEL CONNECTION 38 FIGURE 3.6 A) SIDE VIEW OF THE LATERAL SUPPORT SYSTEM, B) PLAN VIEW OF SAME 39 FIGURE 3.7 PIN CONNECTION, SIDE AND E N D ELEVATION 40 FIGURE 4.1 INTERNAL INSTRUMENTATION 42 FIGURE 4.2 EXTERNAL INSTRUMENTATION 43 FIGURE 5.1 STRESS-STRAIN OF RUBBERS TESTED 48 FIGURE 5.2 FORCE-DISPLACEMENT CHARACTERISTICS OF THE RUBBER-POLYURETHANE PAD ..48 FIGURE 6.1 ANALYSIS POINTS ON BENT 54 FIGURE 6.2 SHEAR DEMAND AT 100 K N BASE SHEAR, M O D E L #1, ALL VALUES IN K N 57 FIGURE 6.3 SHEAR DEMAND AT 100 K N BASE SHEAR, M O D E L #2, ALL VALUES IN K N 58 FIGURE6.4 FLEXURAL DEMANDS AT 100 K N BASE SHEAR, M O D E L #1, ALL VALUES IN K N M . , . 5 8 FIGURE 6.5 FLEXURAL DEMANDS AT 100 K N BASE SHEAR, M O D E L #2, ALL VALUES IN K N M .. ..59 FIGURE 6.6 SITE AND DESIGN RESPONSE SPECTRA FOR THE OAK STREET BRIDGE AREA 62 FIGURE 6.7 C A N N Y - E M O D E L 72 FIGURE 7.15% DAMPING RESPONSE SPECTRA OF THE EARTHQUAKES CONSIDERED FOR TEST ... .75 FIGURE 7.2 TIME HISTORY OF JOSHUA TREE E-W COMPONENT 76 FIGURE 7.3 INPUT AND HYSTERETIC ENERGY RESPONSE SPECTRA FOR JOSHUA TREE 77 FIGURE 7.4 EFFECT OF SCALING TIME HISTORY 79 ix List of Figures FIGURE 7.5 ORIGINAL AND SCALED DISPLACEMENT RESPONSE SPECTRA 80 FIGURE 7.6 ORIGINAL AND SCALED ACCELERATION RESPONSE SPECTRA 80 FIGURE 7.7 HAMMER SENSOR LOCATIONS 83 FIGURE 8.1 FREQUENCY VS. R U N AMPLITUDE 88 FIGURE 8.2 F R F OF HAMMER TEST AFTER 60% RUN 88 FIGURE 8.3 TABLE AND B E N T RELATIVE DISPLACEMENT AND ABS ACCELERATION FOR 0.42G ...90 FIGURE 8.4 B E N T AND MASS BLOCK RESIDULA DISPLACEMENT AFTER 150%(1.05G) 91 FIGURE 8.5 HYSTERESIS LOOPS FROM 20% (0. 14G) RUN 92 FIGURE 8.6 HYSTERESIS LOOPS FROM 150% RUN 93 FIGURE 8.7 FRF OF BENT ABS ACCELERATION AFTER 60% (0.42G) RUN 94 FIGURE 8.8 NATURAL FREQUENCIES FROM HAMMER AND SHAKE TABLE TESTS 95 FIGURE 8.9 F R F OF T3 STRAIN GAUGE AT 60% LEVEL (0.42G) 96 FIGURE 8.10 STRAIN IN B8 STRAIN GAUGE FOR A) 20%, B) 40% AND C) 150% LEVELS 97 FIGURE 8.11 VARIATION IN THE AXIAL TIEDOWN FORCE, A) 10%, B) 60% AND C) 120% RUNS 98 FIGURE 8.12 TORSIONAL MOTION AT A) 10%, B) 60% ANDC) 120% LEVELS 100 FIGURE 8.13 VERTICAL MOVEMENT IN THE BENT AT A) 10%, B) 60% AND C) 120% LEVELS . 102 FIGURE 8.14 SECTION OF THE TABLE AND BENT BASE ACCELERATIONS AT THE 20% LEVEL ... 103 FIGURE 8.15 SECTION OF THE TABLE AND BENT BASE ACCELERATIONS AT THE 120% L E V E L . 103 FIGURE 8.16 SECTION OF THE MASS BLOCK AND CAP BEAM ACCELERATIONS AT 120% 104 FIGURE 9.2 Two METHODS OF OBTAINING VALUES FOR FORCE-DISPLACEMENT PLOT 108 FIGURE 9.3 L O A D DEFLECTION CURVE USING AVERAGE SLOPE 110 FIGURE 9.4 L O A D DEFLECTION CURVE USING PEAK VALUES 110 x List of Tables List of Tables TABLE 2.1 SCALING VALUES 25 TABLE 2.2 SCALED AND PROVIDED MOMENT CAPACITIES 28 TABLE 5.1 CONCRETE STRENGTH 46 TABLE 5.2 YIELD STRESS OF REINFORCEMENT, M P A 47 TABLE 6.1 CODE SHEAR CAPACITIES IN K N OF THE CAP B E A M 54 TABLE 6.2 MOMENT CAPACITY OF THE CAP BEAM 54 TABLE 6.3 R E S P O N S E CAPACITIES FOR THE PROTOTYPE AND 0.45 SCALE M O D E L 55 TABLE 6.4 M O D E L 1. SECTION DEMANDS 60 TABLE 6.5 M O D E L 2. SECTION DEMANDS 60 TABLE 6.6 NATURAL FREQUENCIES FROM D R A T N - 2 D X 63 TABLE 6.7 ACCELERATION RECORDS P G A 64 TABLE 6.8 D R A T N - 2 D X RESULTS FOR VARIOUS EARTHQUAKES 65 TABLE 6.9 PGA OF SEISMIC RECORD CORRESPONDING TO FAILURE OF MODEL 69 TABLE 7. 1 CHARACTERISTICS OF THE EARTHQUAKE RECORDS CONSIDERED 75 TABLE 7. 2 INPUT RECORDS 82 X I A C K N O W L E D G M E N T S I would like to express my gratitude to my thesis supervisor, Dr. Robert Sexsmith, for his advice and constant encouragement during my studies at UBC. His suggestions and practical advice were very much appreciated. I would also like to thank my thesis co-supervisor, Dr. Carlos Ventura, for sharing his expertise in the area of structural dynamics with me and giving me guidance throughout. The financial support of the Natural Sciences and Engineering Research Council of Canada (NSERC) through various strategic and research grants is gratefully acknowledged. Many thanks also to the people who helped me during the construction of the bent and all the accompanying components. Dick Postgate and Paul Symons were invaluable with their advice and experience which they shared with me. Their patience with all my questions is very much appreciated. Thanks should go to the other staff in the machine shop who helped in various ways. I would like to thank Howard Nichols and Vincent Latendresse for running the shake table, and assisting during the set-up of the test specimen. Their knowledge and expertise about the data acquisition and operation of the shake table was invaluable. Many thanks to to Manzar Khoshnevissan and Ge Chen, Masters students at UBC, who helped me during the project. I would like to thank my friends for making my time in UBC and Vancouver thoroughly enjoyable. Lastly, many thanks goes to my family for being a wonderful source of support and encouragement throughout my university education. xii Introduction Chapter 1 I N T R O D U C T I O N In this chapter the background to the thesis is described, and the aims, objectives and scope of the thesis are stated. The previous research in the relevant areas is discussed. A synopsis of the slow cyclic tests of the Oak Street Bridge is given. A general test approach and thesis overview concludes the chapter. 1.1 Background Several major earthquakes on the Pacific Rim (Loma Prieta 1989, Northridge 1994 and Kobe 1995,) have again stressed the importance of understanding the behaviour of structures during an earthquake excitation. Although most of the damage during these earthquakes was to old structures, several buddings and bridges that had been built according to the latest design codes suffered extensive, and in some cases, catastrophic damage. In the Northridge earthquake in California concrete bridges failed due to ^compatibility in the deformations of stiff and flexible elements. For instance, short columns underwent a sudden failure under the connector ramps of the 20-year-old Interstate 5/State Route 14 interchange, leaving taller and more flexible columns standing. Other columns failed due to lack of adequate shear confinement. It was seen that much of the damage in concrete structures was caused by a lack of ductility, (ENR, 1995). 1 Introduction These observations are consistent with earlier examples of damage to structures, and they reinforce the need to continue research into both the design of new structures and the retrofit of existing ones. In order to achieve better designs, it is necessary to improve the understanding of the behaviour and failure of concrete structures under dynamic loading. Both experimental and theoretical research has been done in this field by numerous researchers since the 1960s. Experimental work is necessary as the results are used to calibrate theories, fine tune computer analysis packages of structural behaviour, and to examine new design techniques. Most of the experimental studies have been done using one of four main methods: push-over test, slow cyclic test, shake table or pseudo-dynamic tests. The first three of these methods are well established and have been used for many years to provide valuable data about the behaviour of the structures tested. Pseudo-dynamic testing is a technique that in the past few years has become quite widespread as it is an effective method for testing relatively simple structures. It is recognised that the different methods have circumstances to which they are best suited, and certain limitations which restrict their apphcability. The push-over test is a static test, and does not attempt to simulate a seismic excitation. It can provide information about the behaviour and ductility of a specimen, and its general characteristics and strength. The slow cyclic method of testing subjects a structure to increasing levels of cyclic loading or, more usually, displacement. A test run consists of a certain number of usually sinusoidal cycles, whose amplitude is increased until failure occurs. This type of test is best suited to large specimens which would be impossible to test on the size of shake table that is available at most testing facilities. The slow cyclic test yields information about the hysteretic behaviour of the structure as it is easy to control either the force or the displacement and produce clear hysteretic cycles. The results 2 Introduction can show how the stiffness decreases as the cycles progress, and the maximum force and displacement/ductility can be found. However, there are certain disadvantages associated with this form of testing. The main limitation is that as the tests are done using very controlled and regular loading, the inherent characteristics of a seismic excitation, such as variability and non-uniformity, are not present. Strain-rate effects, which cause certain materials to have an increased stiffness when loaded quickly, do not come into effect during slow cyclic tests as the rate of loading is not sufficient. This means that the material behaves in a fundamentally different manner from that in which it would if it were subjected to an earthquake. As slow cyclic tests are simpler to perform than dynamic tests and can deal with large specimens, many such tests are carried out to determine the seismic behaviour of structures. For this reason, it is important to understand how they relate to the behaviour of the specimen under actual earthquake loading. In order to do this; i.e., to calibrate this type of testing, it is necessary to perform some tests which simulate real earthquakes. This is often done using a shake table, or, more recently, the pseudo-dynamic testing procedure. Shake table tests attempt to subject a structure to a real earthquake time history and to quantify the results as accurately as possible. This method of testing has definite advantages over the slow cyclic tests, in that it is possible to use real earthquake time histories so the response of the structure to an actual earthquake is simulated as closely as possible. Clearly, as no seismic event occurs twice, the earthquakes that are used in the test will not be the same as the events that will affect the actual structure. Notwithstanding this fact, the test earthquake is chosen with respect to the site characteristics, such as soil type and distance from the fault. As a result, the general characteristics of the earthquake used for the test can correspond to a likely actual earthquake. 3 Introduction The size, frequency and force capacity of the shake tables limits the size and weight of the structure that may be tested. In many cases, these limitations result in a prototype structure being scaled down in size so that the shake table is capable of failing it. Unfortunately, this scaling procedure introduces complications and possible inaccuracies. An effective method of testing is to use a computer analysis combined with a pseudo-dynamic or cyclic loading test. This technique involves actuators that apply forces to the test specimen and are controlled by a computer program so that the specimen would undergo motion as if it were subjected to a seismic excitation. There are certain advantages to this testing method, in that as it is quasi-static, less actuator power is required, and that the test can be stopped at any point and the structure examined for damage, (Yamazaki et al, 1986). Although this testing method works well for simple models, it is very difficult to apply for more complicated models. There are limitations in the efficiency and accuracy of this testing procedure. The first of these is the difficulty in deriving an overall hysteretic rule to determine the real non-linear characteristics from the test data found under a specific loading path. Secondly, the non-linear characteristics of a reinforced concrete structure are sensitive to the loading path. Furthermore, due to the slow rate of load application, the pseudo-dynamic or slow cyclic test is unable to consider the effect of strain rate on the material, and, for the same reason, it is not possible to simulate fully inertia effects. An earlier slow cyclic test program on large scale bents from the Oak Street Bridge (Anderson et al, 1995), provided an opportunity to compare the performance of bents tested on the shake table with slow cyclic tests on large specimens. It was considered to be of benefit to have a comparison between the two testing methods, and so understand the differences between the results. This was one of the main motivations for conducting the experiment. 4 Introduction The value of shake table testing was elaborated on by Krawinkler in 1978. He stated that the purpose of shake table testing is to investigate seismic response phenomena that cannot be examined by other means of testing. Some of these effects include rate of loading effects, dynamic response characteristics under realistic seismic excitation, failure mechanisms, effects of mass and stiffness irregularities, torsional effects, overturning effects, dynamic instability, idealised soil-structure interaction effects, and interaction between structural and nonstructural elements. Additional references may be found in Harris, 1982, and Krawinkler and Zhu, 1993. 1.2 Aims and Objectives The aims of the project were: • to increase the body of knowledge on the differences between dynamic and static tests • to understand the dynamic behaviour of an Oak Street Bridge bent • to extend the experience in scaled shake table tests and heavy specimens in the Earthquake Engineering Research Laboratory at UBC. In order to achieve these aims a project was undertaken, the objectives of which were: to design, construct and implement a shake table test of a scaled bridge bent from the Oak Street Bridge and compare and contrast the behaviour of the bent during the shake table test with that of the behaviour of the bent tested under slow cyclic conditions. The bent was to be subjected to a scaled earthquake acceleration time history and the behaviour was to be recorded. More specifically the tasks involved were: • to scale the 0.45 scale as-built bridge bent tested slow-cyclically to a size suitable to the UBC shake table 5 Introduction • to design and construct the specimen and test set-up • to design a lateral support and set of mass blocks that would be reusable in subsequent testing programs • to predict analytically the behaviour of the bent using a non-linear computer program such as DRAIN 2DX or CANNY-E • to implement the shake table test and record the necessary data using strain gauges and other instrumentation such as, accelerometers, displacement transducers and video • to analyse the data and discuss the results with respect to the results from the 0.45 scale slow cyclic tests and the analytical predictions. 1.3 Scope The scope of the thesis was limited to the design, construction, testing, and documentation of test results for a single as-built scaled bridge bent from the Oak Street Bridge. Due to time constraints, the testing program was restricted to one bent under one earthquake at different levels of excitations. Analysis of the dynamic behaviour of the bent was performed, and comparisons were drawn between both the analytical results and the slow cyclic test results, and the behaviour of the bent tested on the shake table. 1.4 UBC Earthquake Engineering Research Laboratory As previously mentioned, a shake table can be used to reproduce the strain rate effects, dynamic response characteristics, torsional effects, etc. that are experienced during a seismic excitation. Provided that the model is of a size compatible with the capacity of the shake table, shake table tests can be the most realistic method of testing. 6 Introduction The digitally controlled shake table in the Earthquake Engineering Research Laboratory in UBC underwent an upgrade in 1995, so that it can now produce motions in all three planes. Since the completion of the upgrade the table has not been used to near its capacity, nor has there been a the opportunity to test a scaled specimen, including scaling of the earthquake time-history. It was therefore considered that as part of this study it would be beneficial to determine the characteristics and capability of the shake table by performing a detailed test program on a scaled specimen. 1.5 R e l a t e d R e s e a r c h The literature review has been divided into two sections. The first deals with previous testing programs that have compared shake table tests with either slow cyclic or pseudo-dynamic tests. The second section deals with previous scaled shake table tests that have been performed. 1.5.1 Comparison of Slow Cyclic and Shake Table Testing Little research has been done in the area of comparing the slow cyclic and shake table testing methods. The most relevant study was a series of tests carried out in Imperial College London by Elnashi, Pilakoutas and Amvraseys (1990). Reinforced concrete walls at a scale of 1:5 were tested on both a shake table and under slow-cyclic conditions. A further slow cyclic test of a 1:2.5 scale specimen was done and the results of all three types of test were compared. The wall response acceleration was converted to an equivalent static force so that a comparison between the cyclic and shake-table tests could be made. In the 1:5 scale tests, before yield, the cyclic loops agreed very well with the loops obtained from the filtered shake-table results. The ultimate displacements compared well with the static tests, 7 Introduction although both were significantly higher than those predicted by finite element programs. In this study, the larger scale models showed a higher stiffness than the smaller scale specimens, although it was still significantly lower than that expected. It was suggested that the low stiffness could be due to higher shrinkage at this scale than at the large scale which could cause an increase in the amount of micro-cracking, leading in turn to earlier cracking and hence a reduced stiffness. Although results from Imperial College London indicate that the two testing methods are similar, it is difficult to make generalisations from so little published research. As the testing methods differ fundamentally in their approach, it is likely that subsequent comparison tests could reveal differences between the data produced from each. A series of tests to compare the static and dynamic testing of reinforced concrete masonry structures was carried out by Abrams (1988, 1996). The results from a full-scale static test were compared with the results from both dynamic testing and static testing of reduced-scale structures. The comparisons between the full-scale static and reduced-scale dynamic tests were not favourable, although both structures had very similar configuration and reinforcement layout. The lateral force distribution in the dynamically tested model varied during the test, however this was fixed for the statically tested specimen. As a result the ratio of shear to moment at the base story was different for each specimen, as was the combination of axial and shear force resisted by certain components of the structure. This meant that the mode of failure was different in each case. There were differences between the behaviours of the dynamically and statically tested reduced-scale structures. Both the lateral strength and stiffness were greater in the dynamic specimen, as in the last and most severe test run, the flexural strengths for the static specimen were 79% of 8 Introduction those in the dynamic test, and the lowest average stiffness for the static test was 55% of that for the dynamically tested specimen. Furthermore, there were differences in the amount of damage observed. The rate of strain had an appreciable effect on the propagation of cracks. This meant that the damage in the dynamic test was significantly less than that in the static test, even though the dynamic specimen resisted more force. From these tests it was concluded that the static mode of testing is a conservative one and exposes the specimen to a more demanding environment than an actual seismic event. The static and dynamic response of large-scale and reduced-scale structures were correlated to determine effects attributable to scale and loading rate (Abrams et al, 1996). Two of these test structures were masonry, and one was reinforced concrete. In each case large scale static testing was performed to discern difference due to the modelling method. The conclusions that were drawn included the fact that it is difficult for models to characterise the full behaviour of the prototype and to make direct comparisons between small-scale shake table tests and large scale static tests. 1.5.2 Scaled shake table tests A number of investigations have been performed involving shake table tests of scaled structures. Shake table tests of twin-column bridge bents that had been scaled by a factor of 1:6 were carried out in 1994 by Macrae et al (1994). Artificial mass simulation was used and the bent was constructed from the prototype material. The capacity of the shake table was unable to cope with the mass as scaled, so a reduced lumped mass was applied. As the mass was reduced, the correct axial load in the columns was achieved by using axial system tie-down rods. The results showed 9 Introduction that the mode of failure was the same as in the prototype and the force levels were as predicted, indicating that the modelling was successful. The effects of different strain rates were investigated by Bertero et al, (1985). They conducted tests at the University of California, Berkeley on a 1:5 scale model of a seven-story reinforced concrete frame wall test structure and compared these test results with those obtained from a full-scale model tested pseudo-dynamically in Japan. An adequate lumped-mass type model was chosen as being the most suitable, as it satisfied similitude with regard to geometric, loading and material parameters, except for mass density. Due to size constraints micro-concrete was used in conjunction with lead ballast to increase the mass and avoid any significant effect on the structural stiffness and strength of the model. The measured displacements and envelope of responses of the 1:5 scale models approached those of the full scale structure (after appropriate scaling of the results), and the analytical flexibility characteristics were quite close to measured values. It was concluded that shake table tests on reduced scale reinforced concrete models can reliably simulate the global seismic responses of a full-scale bare building. It was observed that the use of micro-concrete can be difficult because the strain gradient and strain rate increase with decreasing model scale. It was observed that the maximum base shear attained by the shake table test exceeded the pseudo-dynamic test by 40%. Furthermore, the shake table test specimen did not suffer large stiffness degradation as the pseudo-dynamic one did. The authors concluded that this reduction in stiffness could be due, in some part, to the fact that the crack patterns in the latter test were more diffuse and less concentrated than those seen in the shake table test. A comparative research program on the effects of scaling was carried out by testing a seven story building at both large and small (one tenth) scale and comparing the results. The small scale 10 Introduction models were tested on a shake table at the University of Illinois, Urbana by Wolfgram et al (1984), while the large-scale models were tested pseudo-dynamically in Tsukuba, Japan. The small scale model was a lumped mass model, with a frequency content scaled to satisfy the frequency/period scaling law. It was observed that during testing the effective stiffness reduced almost at a linear rate with increasing drift, so the frequency varied inversely with the square root of the drift. This tendency is consistent with the variation of effective stiffness of a reinforced concrete structure after yielding. It was noted that direct comparisons between the responses of the two testing programs were difficult as the pseudo-dynamic tests were not determined for a similar and complete earthquake record and because it was not loaded dynamically. However, certain similarities can be seen, for example that in tests with a maximum overall drift of 0.8% , both sized structures had barely yielded structurally. From further comparisons between the two testing regimes, it was concluded that small-scale modelling has a role in the experimental analysis of reinforced concrete structures. Tests were done by Abrams (1984). In this series, large and small scale components were tested statically for comparison purposes and the results were used to calibrate the hysteresis parameters in a computer modelling program. The analyses of this program were verified using the results from a previous shake table test of a ten-story one-twelfth scale budding, and then later expanded to predict it's full scale behaviour. It was found that the deterioration of stiffness, and hence natural frequency, was much faster in the smaller scale specimen than in the larger ones, but that the overall hysteretic tendencies 11 Introduction were similar to that of the large-scale reinforced concrete construction. The differences in behaviour, especially location of damage, resulted mainly from excessive local slippage of reinforcement in the smaller scale models due to bond failure. This also resulted in a sharp reduction of stiffness. A shake table test of a 1/6 scale two-story lightly reinforced concrete building was carried out by the National Centre for Earthquake Research (El-Attar, 1991). The strength of the input motion was increased in steps until failure occurred. It was noted that by gradually increasing the earthquake amplitude the actual seismic resistance of the structure may not be revealed since accumulative damage decreases the stiffness which can lead to a decrease in magnitude of the lateral forces acting on the structure. Whether the magnitude of the excitation increases or decreases depends on the initial location of the fundamental period of the structure with respect to the peak in the response spectrum. If the period is below the peak, the magnitude will increase with increasing period as the period will approach the peak. The converse is true if the period is above the peak. 1.5.3 Relevance to this thesis From the previous research in the area of scaled dynamic tests, it was seen that a specimen tested on a shake table should be stronger and stiffer than a specimen tested at a slow loading rate. This is mainly due to the strain rate effect on the material properties, but also due to spalling of concrete and crack patterns. It was noted that specimens scaled to one fifth the prototype size can be expected to give reasonable results about the prototype behaviour. There has been little research comparing the results from slow cyclic and shake table tests on reinforced concrete structures, which is an area that requires further exploration. Areas that could be 12 Introduction examined are the differences in strength, ductility, ultimate displacement, strength deterioration, crack patterns and failure mode. 1.6 Oak Street Bridge Slow Cyclic Tests As part of a seismic review of the major bridges in the Lower Mainland by the Ministry of Transportation and Highways, an extensive test program was conducted in 1995 at the University of British Columbia on the seismic performance of the Oak Street Bridge. Specifically, a series of slow cyclic tests was performed on scaled specimens of an as-built bent and on four other bents that had been retrofitted in various ways. A vertical load was applied to the specimens to simulate the structure dead load, and a lateral load was then slowly cycled to simulate the transverse earthquake load on the bridge deck (Anderson et al, 1995). The first test was the as-built Oak Street specimen. It showed early shear cracking and spalling, a very low seismic capacity and little ductility with a peak seismic load of 267 kN at a lateral displacement of about 9 mm. Subsequent tests of the retrofitted specimens showed that the retrofits achieved a very marked increase in the ductility and ultimate strength of the bents. The base shear increased on average to 445kN, and the maximum displacement reached 100mm. Theoretical analyses of the behaviour of the specimens subjected to an earthquake excitation were performed using the non-linear computer program IDARC (Inelastic Damage Analysis of Reinforced Concrete by Kunnath et al, 1992). The results agreed well with the experimental data with respect to the ultimate forces developed in the specimens. The analyses of both the as-built and retrofitted bents indicated that the failure would be very sudden and brittle. The Park and 13 Introduction Ang damage index used in the program gave a good indication of the damage state of the bents in displacement-controlled laboratory tests, but much more investigation would be required in order to predict damage in actual earthquakes (Williams, 1994). The results of the test program confirmed prior assessments that the Oak Bridge is seismically deficient, (Anderson et al, 1995). As the design philosophy of Oak Street Bridge was fairly typical of many bridges built in the region at that time, such as Queensborough, Port Mann and Knight Street, there is cause for concern that there could be widespread damage to these bridges in the event of an earthquake. Therefore there is some motivation to examine further the behaviour of the bridge bents, especially under seismic loading and to develop or calibrate an analysis program that can accurately simulate the behaviour for this type of bent. 1.7 Test Approach and Thesis Overview A literature review on scaling theories and methods was conducted, and an appropriate scaling technique was decided on. A scale suited to the dimensions and capacity of the shake table was then determined. The prototype bridge bent was scaled except for minor alterations to reinforcing steel which were necessitated by available sizes and strengths. Non-linear computer analyses of the expected behaviour and capacity of the bent were carried out. The test set-up including the mass block, the connections to the table and the lateral support system was designed. The bent was instrumented internally with strain gauges on some longitudinal and transverse reinforcing steel, and externally with accelerometers and potentiometers. The bent was subjected to scaled seismic motions in the in-plane horizontal direction. One of the components from the record obtained at the Joshua Tree Fire Station during the 1992 California 14 Introduction Landers earthquake was chosen as the input motion. The amplitude of shaking was scaled to a low level, and its severity was increased for each successive run. This was done by scaling the amplitude of the acceleration, and hence the displacement time history that was applied to the shake table. The behaviour of the bent during the test was recorded using a high speed camera that could record the development of cracking and damage, and a video camera was used to document the overall behaviour of the bent. After each-seismic run, the dynamic characteristics of the bent were determined. This was done by using an instrumented impact hammer to excite the specimen and deducing changes in frequencies from the resulting response of the bent. Information on the dynamic characteristics of the bent before any damage, just before yielding and after significant damage was obtained. The results of the test program were compared with those from the slow cyclic tests and also with the expected values. Recommendations for further testing and analysis were made. Chapter 1 has discussed a literature review on scale shake table tests, comparative studies between static and dynamic test results, and has outlined the aims, objectives and scope of the thesis. In chapter 2, scaling theories are reviewed, and an appropriate scaling technique is decided upon. The determination of the scale, suited to the dimensions and capacity of the shake table, is explained. The scaling of the prototype bridge bent is detailed. Chapter 3 describes the various elements of the test set up. Also described is how the inertial loading was simulated through the appropriate design of the mass block. In chapter 4 the instrumentation used to record the data is given. Chapter five details the construction of the specimen, and gives data on the properties of the materials used. The analyses of the expected behaviour and capacity of the bent are explained in chapter 6. In this chapter, the results from the previous 0.45 scale slow cyclic test are detailed and used to predict 15 Introduction the behaviour of the shake table bent. Chapter seven describes the selection of the earthquake used in the testing program and gives the modifications to the time history that were necessary. The test runs are outlined, and the hammer testing program described. The test results are given in chapter 8. A qualitative description is followed with details on the bent performance. In chapter 9 the shake table test results are compared with the slow cyclic test results and the results from the computer analyses. Finally, in chapter 10 conclusions are drawn and recommendations are made. 16 Scaling - Theory and Design Chapter 2 S C A L I N G - Theory and Design 2.1 Modelling Theory There has been much research in modelling theory and there are well established methods for modelling structures. Dynamic modelling is more complex than static modelling, as gravity forces should be considered and time dependent characteristics must be scaled appropriately. When designing a test of a scaled structure, the model should be designed, loaded and interpreted according to a determined set of similitude requirements that relate the structure to the prototype. Modelling theory sets up rules according to which the geometry, material properties, initial conditions, boundary conditions and loading of the model and the prototype have to be related so the behaviour of one can be expressed or determined as a function of the behaviour of the other. These similitude requirements are based on a recognised theory of modelling, and are generally derived from a dimensional analysis of the physical phenomena involved in the behaviour of the structure. Dimensional analysis is based on the premise that every physical phenomenon can be expressed by a dimensionally homogeneous equation of the form ^ = F(%^3,% %) (2.D where n = total number of physical quantities involved in the phenomenon. 17 Scaling - Theory and Design In the above expression qj is a dependent quantity, and q2 to qn are the variables on which it depends. The dimensionally homogeneous equation which contains physical quantities describing the phenomenon is converted into an equivalent equation containing dimensionless products, called Pi-factors, of powers of the physical quantities (Moncaza and Krawinkler, 1981). As these dimensionless products describe the same physical phenomenon and are independent of the units of measurement, they must be equal in the prototype and model if complete similitude is to be achieved. This transformation is achieved by using the Buckingham Pi Theorem. This theorem states that a climensionally homogeneous equation can be reduced to a functional relationship between a complete set of independent dimensionless products, or Pi-factors. The number of independent dimensionless products is equal to the total number of physical quantities involved minus the number of fundamental quantities needed to describe the dimensions of all physical quantities. In engineering the most common sets of basic quantities are those of length L, time T, and temperature O and either mass M, (MLTO), or force F, (FLTO). These basic quantities can be combined to form other physical quantities since the dimensions of all other phenomena can be expressed as products or powers of basic quantities. There are systematic approaches to extract dimensionless products and to form a complete set of dimensionless products (Filiatrault, 1985). Similitude relationships can then be developed by establishing equality between the prototype and model for each of the independent dimensionless products. This step defines the design conditions for the model and prediction equations for the dependent response quantities which 18 Scaling - Theory and Design relate the measured model response to the prototype behaviour. The result of this is used to create the scaling laws for the physical quantities or products of physical quantities. Scaling laws are usually written as a ratio of the numbers of units needed to describe identical quantities in model versus prototype. For example: L = L / L =0.1 (2.2) B m p v 1 where L g = length scale L m = model length L p = prototype length This means that the one unit of length measurement in the model corresponds to ten equal units of measurement in the prototype. In the following discussions, the subscript m refers to model, p to prototype, and s refers to the dimensionless scale ratio of model to prototype. It has already been noted that all physical quantities can be represented as products or powers of the basic quantities. Since these basic quantities are independent of each other, it is clear that as many scales can be selected arbitrarily as there are basic quantities. In a dynamic problem described by M, L, and T three scales can be selected. However, for these type of tests, it is often necessary to select gs = 1 ( gravity scaling is unity) which reduces the choice of the arbitrary scales to two. The scales of all other physical quantities can then expressed in terms of the arbitrarily selected ones and may be found from the dimensionless products. Models that fulfil all similitude requirements are termed true replica models. Often it is impossible to satisfy all the design conditions, and in these cases it is necessary to choose those features which may be altered so that the model construction becomes feasible, but the response prediction is not invalidated with an excessive amount of error. These types of models are called 19 Scaling - Theory and Design adequate models, where the prediction equation is not affected and design conditions may be altered without significantly affecting the results. For a shake table test a model that simultaneously replicates restoring, inertia and gravitational forces, i.e. a true replica model, must satisfy the requirement (Moncaza and Krawinkler, 1981), that: L . - [ - J _ (2.3) where E = Youngs' modulus P = Mass density This equation uses the fact that the gravity scale is one. This indicates that if the prototype material is used in the model some inaccuracies will result; however, these can be minimised by other methods. One of these is to increase the density of the structurally effective material by adding additional material that is structurally ineffective. This can be achieved by representing the seismically effective mass by a series of lumped masses concentrated at certain locations. From Cauchys' requirement for proper simulation of inertial forces and restoring forces the following equation is determined (Moncaza and Krawinkler, 1981), where M s = mass scale If the structural model is made of the prototype material (Eg = 1) then the lumped masses are 2 scaled in the ratio M s = L g-. The extra mass required is found from: (2.4) which for gs(gravity scale) = 1 becomes M s = E L 2 s s s (2.5) 20 Scaling - Theory and Design - M m,sw (2.6) Where M m = additional mass to be added M p = mass of the prototype L 6 = length scale M m = self weight of the model This method of scaling allows the use of the prototype material, and permits adequate simulation of all important gravitational and inertial effects. This type of modelling is called "artificial mass simulation", and has been used in most shake table tests. Bridge structures are well suited to this type of simulation, and, if the mass distribution and ground motion are scaled accurately, such model studies are expected to result in a good prediction of the prototype behaviour (Moncaza and Krawinkler, 1981). For inelastic materials such as reinforced concrete it is necessary to reproduce physical properties such as stress-strain relationships, shear transfer, bond, creep and cracking in the model material. For this reason it is beneficial to use the prototype material as this simplifies the modelling procedure. Similarly, if at all possible the prototype reinforcement material should also be used, as the yield and ultimate strengths, ductility, bond, and stress-strain curve will all be similar to those in the prototype-A further similitude requirement is that the time scale of the acceleration history be scaled correctly. The following ratio should be satisfied if correct modelling is to be achieved: F F •*• m _ __P f " f„ m p (2.7) 21 Scaling - Theory and Design Where: F m and F p are the ordinates in the Fourier spectra of the scaled and prototype motion respectively fm and f are the fundamental frequencies of the scaled and prototype bents respectively The period of a single degree of freedom (SDOF) structure of mass M and stiffness K, is given by: „ „ VM T = 2II-J=- (2.8) Thus the scaling factor for this parameter is: T _ T P _2^VM7 |M7 S TM 27tVM7 V K S The stiffness ratio, Kg, is equal to the length scale. This is deduced from the fact that stiffness can be given by the ratio offeree to deflection: F L 2 K S = ^ = ^ = L S (2.10) s s and so the scaling ratio for the period becomes: r - = J x ( 2 U ) This is also the ratio used when scaling the time history of the earthquake. The base acceleration of a SDOF system, a, is scaled using the relationship F = Ma: F , . aD FD M „ F. •-(2.12) Therefore a = — and A _ P _ P M a s M n F m M s P m 22 Scaling - Theory and Design As the force scale is equal to L? and the mass scale is arbitrary. This results in the scale factor for acceleration becoming: (2.13) 2.2 Modelling the Prototype Bent 2.2.1 Shake Table Capacity The scale to be chosen depended on the capacity of the shake table. Both the dimensions and range of base shear, displacement and frequency were relevant to the decision. The shaking table is 3m by 3m and can support a payload of 155.7 kN. The maximum overturning moment possible is 230 kN-m. In normal operation the maximum acceleration that can be attained in theory is 2.5g, the maximum velocity is 127cm/s, the maximum displacement is 7.6 cm and the maximum base shear possible is 155.7 kN. There are 32 A/D channels for data acquisition, and the system is able to acquire data at a rate of 500 Hz per channel (16 kHz total). The overhead crane is capable of supporting a load of 6.8 kN, and clearance above the table is 4.3 m. 2.2.2 Modelling the Structure In choosing the scale of the model, the largest possible scale was required, as this increases the accuracy of the test results. It has been shown from past research that models of a scale to about 1:5 are capable of characterising the performance of the prototype, but at lower scales, where microconcrete and wire are necessary, the correctness decreases. It was decided to use a geometric scaling ratio of 0.27 (1:3.7) as this would allow reinforcing steel similar to that in the prototype to be used. This was derived from the fact that in the 0.45 scale 23 Scaling - Theory and Design model used for the reversed cyclic loading tests the smallest bar size used was No.5, resulting in No. 3 steel for the shake table model which is the smallest re-bar manufactured. Furthermore, the distance between the outer faces of the columns scaled to 2858mm, which just fits within the dimensions of the table. At this scale the calculated fundamental frequency of the specimen was 7.3Hz (see section 2.3.4), which was suited to the capacity of the table. Lastly, preliminary analyses of the bent indicated that it would fail under a base shear within the table capacity of 150kN (see Chapter 6). Given these facts, it was concluded that the chosen scale factor was appropriate to the shake table at UBC. The model was scaled according to the adequate artificial mass simulation theory. As the prototype material was used for the model, both the density and modulus of elasticity scales were required to be unity. A fourth independent scale was for mass. This was necessary as the mass resulting from the relationship derived, equation 2.6, resulted in a lumped mass that would overload the payload capacity of the table. Therefore, the applied mass had to be reduced from that required by theory. Research by Macrae et al (1994) indicated that this approach to modelling could be successfully carried out. The first step in determining an appropriate mass was to scale the prototype mass and dead load. The reduction of this amount was found assessing the capacity of the table, and considering the effect of mass reduction on the axial force in the columns. A further influencing factor was that due to the scaling relationships, as the mass of the scaled bent decreased, so the acceleration scale increased. Therefore, the mass scale chosen had to accommodate both the mass and acceleration capacities of the shake table. The weight of the bent was 21.75 kN and it was decided to use a mass block with a weight of 89 kN. The combined weight of the specimen was then 110.7 kN, which was less than the table capacity of 150 kN. The weight of the prototype structure and deck loading was estimated by 24 Scaling - Theory and Design Klohn Krippen to be 5249 kN (Seethaler, 1995), so the mass scale was 0.0211. The resulting acceleration scale was 3.45. The scaling factors for the derived parameters were obtained by analysing the dimensions of the quantity involved. For example, K = where K is stiffness, F is force and X is displacement. The scaling factors for force and displacement are L2 s and L s , respectively. Therefore, the scaling factor for stiffness is: K s = ^ - (2.14) which results in a factor of L s . Similar operations can be performed for the other scaling factors. Using the three basic scaling ratios for length, stress and mass, the table 2.1 was developed: Parameter Scale Factor Basic Dimension Scale value Length h Arbitrary 0.270 Stress °* Arbitrary 1 Mass M e Arbitrary 0.0211 Force FB 0.0729 Stiffness K 8 h 0.270 Moment Mom s 0.0196 Period 0.279 Time K 0.279 Acceleration \ 3.45 Table 2.1 Scaling values 25 Scaling - Theory and Design 2.2.3 Scaling the Steel Reinforcing Steel Area: The force scale is equal to the square of the length scale, therefore: A m f y , m N n V , P N P m (2.15) where A m , A p : Area of the model and prototype reinforcement, respectively f y,m > f : Steel yield stress of the model and prototype reinforcement, respectively N m , N p : Number of bars in the model and prototype, respectively The steel in the prototype bent was composed of No. 11 bars and was a mix of grade 40 and grade 50 steel. Originally, the scale of the bent had been chosen to be 0.27 so that the bar sizes would scale exactly. It was subsequently found out that No.3 bars, the type used in the model, were only available as grade 60 steel. Because of the difference in steel strength the area of steel did not scale according to L and some adaptations needed to be made. The area of steel was constrained by the available steel sizes, which resulted in different numbers of bars being used in the specimen from the number used in the prototype and 0.45 scale specimens. It is possible that this could have affected bond and cracking patterns. From equation 2.8 one can then estimate the required steel area for the model as: = 0.0608A p (2.16) 26 Scaling - Theory and Design As the ratio A m /A p is fixed at 0.0729 due to the sizes of available reinforcing bar, this results in: = 0.83 N P Using this relationship the number of bars in each section^ of the beam and column were calculated. It had been postulated that the number of cut-offs contributed to the failure mode of the 0.45 scale bent (Seethaler, 1995), efforts were made to preserve this characteristic in the model bent. The moment capacity of the beam and column with the areas of steel given from the scaling process was calculated at various points and compared with the capacity of the prototype and 0.45 scale model. In certain areas, the steel area could not be provided exactly by No. 3 bars, so compromises were made. For example, it was not possible to model all the reinforcing in the columns using No.3 bars as this would have resulted in an increased moment capacity of the column. For this reason One Gauge (1 Ga.) wire was used for two of the five bars along each side of the column, as shown in figure A1 in Appendix A Appendix A provides the reinforcing steel in the prototype, the cyclic test model and the shake table model. Table 2.2 compares the beam moment capacity required by scaling the capacity from the prototype with the moment capacity provided from the steel in the model bent. It was considered that the modelling was satisfactory as the moment capacities of the cap beam at all locations were similar to the scaled cap beam. Due to an oversight during the construction, two of the bottom bars were not included, which reduced the positive moment capacity of the beam. Table 2.2 gives the moment capacity both for the intended and actual reinforcing steel configuration. 27 Scaling - Theory and Design Dist. Scaled Actual Intended 0.27 Scaled 0.27 0.27 No from col. Proto. 0.27 0.27 No. of Proto. Model of top edge M + Model M + Model M + Botm M- M- bars [mm] [kN-m] [kN-m] [kN-m] bars [kN-m] [kN-m] 0-259 47.4 29.2 50.0 2 113.8 119.2 11 259 -390 69.1 40.7 62.4 3 100.3 100.3 9 390 - 543 80.0 62.4 81.3 5 81.3 81.3 7 543-619 100.3 81.3 100.3 7 69.1 62.4 5 619 - 745 115.2 100.3 119.2 9 46.1 40.7 3 745 - 975 115.2 100.3 119.2 9 N.A 40.7 3 975 - CL 127.4 100.3 119.2 9 25.7 29.8 2 Table 2.2 Scaled and Provided Moment Capacities 2.2.4 S c a l i n g the P e r i o d The fundamental period of the prototype, as determined by Seethaler (1995), was given as 0.69 seconds. This value was then scaled to give the period for the model, and was checked using computer programs, CANNY-E and DRAIN-2DX. In this section the scaling is dealt with, and in sections 6.2.2 and 6.4 the computed values are given. The period of 0.69 seconds was for a bent with full length columns. As the shake table specimen had the columns cut at the points of inflection (L/2), this affects the period and had to be accounted for. Assuming that the structure behaves primarily in it's fundamental mode of vibration, the formula for its period is: \K ( 2 1 7 ) where M = mass of the structure and mass block K = stiffness of columns 28 Scaling - Theory and Design The expression for K for the full height prototype bent is: K, = 12EI L 3 (2.18) where I is the second moment of inertia of the column. The expression for K for a bent with the legs cut off at the point of contra-flexure is: 3EI 24EI V = 2K 3 (2.19) Therefore the relationship between the prototype period, T t , and the period of the bent with cut-off legs, T 2 > is: 2.2.5 Column axial force As it was not possible to include the full scaled mass on the bent, the correct axial stress was not present in the columns. The effect of this reduction in axial force on the behaviour of the columns was considered. The weight that was not included was 166kN, or 83kN in each column. The difference that this axial load makes to the moment and shear capacities of the column was determined. (2.20) The resulting scale factor for the period of the model bent should be about: T = VO5(0.279)(0.69) = 0.14s 29 Scaling - Theory and Design The influence of the axial force on the moment capacity is shown on the interaction diagram, figure 2.1. The effect of increasing the axial force from 99 kN to 182kN would increase the moment capacity from 73.6 kN-m to 82 kN-m. As the flexural capacity of the columns was not predicted to be a limiting factor in the behaviour of the bent, this reduction was not expected to affect the failure mode. The moment capacity of the prototype column was determined to be 80 kN-m, so the capacity of the 0.27 column was not excessively dissimilar. Column Interaction Diagram 01 p 3 Moment (kNM) Figure 2.1: Column Interaction Diagram 2.3 S u m m a r y The scaling theory was reviewed, and an adequate artificial mass simulation was used to model the prototype. This resulted in scale factors being chosen for the length, mass and stress. These factors were chosen with respect to the capacity of the shake table and size of reinforcing bars available, and are given in table 2.1. Having chosen the three arbitrary scale factors, the values 30 Scaling - Theory and Design for the other properties, such as moment and acceleration were derived using similitude relationships. Using these factors, the model was designed with appropriate dimensions, reinforcement and concrete mix. The mass of the superstructure was also scaled, but due to the capacity of the table, it was not possible to use the full value. This introduced complications in obtaining the correct axial force and moment capacity in the columns. The period of the model bent was found from scaling the calculated period of the prototype bent. 31 Test Set-up Chapter Three T E S T S E T - U P Apart from the design of the bent, there were several other items that needed to be designed. These included the mass blocks, the lateral support system and the connections between the bent and the table. The design of each of these will be described in this chapter. 3.1 General Description The bridge bent structure itself had a height of 1573mm and a length of 4304mm. The columns were 327mm2 and at a spacing of 2204mm. The cap beam cantilevered over the columns by 703mm. The weight of the mass placed on the specimen was 89 kN. The height of the centre of gravity of the bridge deck structure above the top of the cap beam in the prototype bent is 1524mm, which when scaled, required the centre of gravity of the mass added to be at a height of 411mm above the top of the cap beam. The added mass consisted of a concrete mass block supporting a stack of steel plates, as shown in figure 3.1 and figure C-9 in Appendix C. It was required to control the transfer of load between the mass block and cap beam in order to simulate the loading situation of the previous slow cyclic tests, which modelled the expected behaviour in the field. The dead load in the prototype was transferred into the cap beam at five bearing locations, however, the lateral load was not. In the 0.45 scale slow cyclic tests it was assumed that the cap beam and joint forces would be sufficiently well approximated if only the two interior girder bearings closest to the columns were used to transfer the lateral load of the deck into the bent (Anderson et al, 1995). Therefore, the connections between the cap beam and 32 Test Set-up mass block were designed to transfer only shear force at these two locations, while transferring the dead load at all five. The concrete mass block was designed as one beam spanning along the top of the cap beam. The dead load was transferred through five rubber pad bearings. At the two points where shear was transferred there were fixed connections. These were made with steel dowels. The dowels were tightened after the mass block was placed on the cap beam and then the entire connection was grouted to provide vertical fixity (Appendix C, figures C-6 and C-7). Two types of rubber were used as bearing pads: a hard 50-durometer rubber to give the correct spacing, and a softer Shore 33 Test Set-up A 40 polyurethane rubber to allow some movement with little change in applied force when the mass block and cap beam undergo relative displacement. 3.2 Mass Block 3.2.1 General configuration Several ideas for a configuration of the mass block were analysed. The influencing factors on the design were: capacity of the crane to lift sections, stability and functionality, and a degree of flexibility for reuse in other tests. As this testing program, and a proposed steel shear wall test both required significant amounts of weight, 89 kN and 54 kN respectively, it was decided that a large part of the mass block should be part of a set of reusable mass block elements. After considering the dimensions and requirements of both tests, steel plates of suitable dimensions were designed. Various thicknesses of plates ranging from 16 mm to 63.5 mm were ordered, so that the system would be as adaptable as possible. For two reasons it was not possible to use the steel plates on their own as the mass block. The first being that, due to the dimensions and density of the plates, the weight of 89 kN would not be at the correct location of 411 mm above the cap beam, but would be 100 mm below this level. Secondly, as the mass block was required to be a single section so that it could transfer the lateral load at two locations, it was necessary to have a continuous member at the bottom layer. For these two reasons, a concrete beam was designed to connect between the cap beam below and the steel plates above. The dimensions of this beam were determined so that the resulting centre of mass of the combined steel and concrete block was at the required elevation. 3.2.2 Concrete Mass block The details of the concrete block are shown in figures 3.2a and 3.2b. The length of 4360 mm and width of 500 mm were sufficient so that the block spanned the cap beam and fully supported the 34 Teat Set-up steel plates. The depth of 235 mm was found by varying the amount of steel and concrete so that the centre of mass would be at the right location. The concrete block had sufficient longitudinal reinforcing steel to prevent damage during if s placement and the testing program. The total weight of the concrete block was 12.3 kN, leaving 76.7 kN for the steel to provide. " 1 0 3 ° j [ g . 4360-SECTIDN 500 - •360-165. r—150 -1030--1153-2^0 -•70- -1030-r -6054-PLAN Note: all dimensions are in mm Figure 3.2a Concrete Beam, Section and Plan View -20 625 -500-2$5 Note: all dimensions are in mm Figure 3.2b Concrete Beam, Section 35 Test Set-up 3.2.3 Steel plates The weight of 76.7 kN was provided by three stacks of steel plates, requiring 25.6 kN in each set. Each plate is of the dimensions shown below, but various thickness were ordered, so that varying weights could be applied if necessary. The weight translated into a height of 373 mm. As the plates came in three sets of ten plates, with thickness of 63.5 mm, 31.75 mm and 9 mm, the stack of plates were not identical. A typical plate is shown in figure 3.3. 27 mm hole ' Typical 1500 mm i i 90 mm 235 mmfl 1030 mm -9-1 1^ r „ 300 mm ^  | 24 mm hole •  E E 900 mm ,J 420 m L Figure 3.3 Typical Steel Plate 3.3 Connect ions Cap-beam - Concrete mass block Connection The connection of the concrete mass block to the specimen was achieved using Dywidag™ post-tensioning bars. The configuration of two bars at each location was necessary to provide stability of the mass block in the out of plane direction. The layout is shown in figure 3.4. Two types of rubber were used in the bearing pads. A hard 50-durometer rubber gave the correct spacing between the cap beam and mass block, and a softer Shore A 40 polyurethane rubber allowed some relative displacement with little change of applied force. The capacity of this joint was checked 36 Test Set-up for shear, axial forces and bending moment and found to be sufficient to withstand the ultimate load the table was capable of producing. Capacity: 1 - Shear. The shear resistance of one bar was 235 kN, so as there were two bars at each location, the four bars provide a total shear resistance of 940kN. The shake table can produce a maximum of 150 kN base shear, so the bars were sufficient to resist the lateral motion. NOTE 1- ALL DIMENSIONS ARE IN MILLIMETERS. Figure 3.4 Cap Beam - Concrete Mass Block Connection, Side and End Sections 2. Axial forces. The Drain-2DX and PCA-Frame analyses showed that the maximum compression and tension induced in the connections would be about 60 kN. The axial capacity of the connection was 712 kN, so the connection was expected to resist the axial forces. The forces within the cap-beam and concrete beam due to the embedded post-tensioning were also checked and were found to be satisfactory. 37 Test Set-up Concrete mass block - steel plate Connection The configuration of mass block involved connecting three stacks of steel plates above the concrete mass block. This was achieved by embedding steel ready-rods into the concrete block and then aligning and placing the steel plates over these rods so that the plates were securely held in place. The ready-rods were hooked so that they would resist pull-out. Figure 3.5 shows the system. f • READY ROD .-235-1 1030-STIXL PLATt -420-370 MASS HOCK U %J -500-370 Figure 3.5 Mass block Steel connection The shear capacity of one 22.3mm (7/80 ready-rod was 69.6 kN. As there were 12 bars to resist the shear there was a total capacity of 835 kN which was sufficient to withstand the 150 kN shear. As a high stiffness was required to stop movement of the mass block this excess capacity was appropriate. The ready-rods were fine threaded at the top so that the plates could be tightened together to act as one mass. 38 Test Set-up 3.4 Lateral Support System As it was required to induce a uni-directional motion in the bridge bent, it was necessary to restrain it from any out of plane motion. There were several requirements for the lateral restraint system, the most important being that it would resist any out-of-plane motion, but allow free movement in-plane. The lateral support system that was chosen consisted of four wire rope tie-downs, as shown in figure 3.6. By connecting the tie-downs between the shake-table and the top of the steel mass blocks, the differential movement between the ends of the rope, and hence the in-plane restoring force, was reduced from the amount that would have occurred had they been secured off the table. a) b) Figure 3.6 a) Side View of the Lateral Support System, b) Plan View of Same The ropes were pretensioned to 4.4 kN, as this made their fundamental frequency 12 Hz which was considered sufficiently far from that of the bent (7.5 Hz) to prevent them resonating during the test. One of the tie-downs was instrumented with strain gauges so that the tensile force 39 Teat Set-up present could be found (Appendix C, figure C-ll). This was necessary to determine the pretension force associated with the required frequency, to monitor the axial force during the test and see if the ropes were providing an excessive longitudinal restraint. 3.5 Pin Connections The bridge bent was connected to the shake table with hinged connections. Each hinge was made from two separate halves which rotated around a central pin. The top half of the hinge was bolted to a 19mm plate that had been cast into the column. Nine 300mm lengths of 15M reinforcing bar had been welded onto the plate to provide anchorage. The bottom half of the hinge was bolted to a 19 mm base plate that was bolted directly to the top of the shake table, see figure 3.7. The base plate was bolted in four places and the stresses and bending moments induced in it due to the expected forces were analysed and found to be acceptable. 381 Note: all dimensions are in mm Figure 3.7 Pin Connection, Side and End Elevation 40 Instrumentation Chapter Four I N S T R U M E N T A T I O N The specimen was instrumented both internally and externally. The internal instrumentation consisted of strain gauges, while there were accelerometers and displacement transducers, a video and a high speed camera externally. The number of recording devices was limited by the number of channels available to record the data. There were two sets of data collection banks, each with 16 filtered channels, and a further data bank of 16 channels which were unfiltered. A different type of filter was connected to each of the first two sets, so in order to reduce differences between signals, one set was used for strain gauges, and the other for displacement transducers and accelerometers. 4.1 Strain Gauges The strain gauges were put in the areas where the most deformation and damage was expected. These locations were the outer part of the cap beam and the top of the columns. These regions were instrumented with gauges on the longitudinal steel. As the cap beam was expected to fail in shear, two of the stirrups at each end were also gauged. A total of 24 positions were instrumented, as shown schematically in figure 4.1, and shown precisely in Appendix A The strain gauges that were chosen had a resistance of 350 were 6.35 mm long, and had a range to 3% strain. Two strain gauges were mounted at each position using a half bridge configuration. This uses two axial strain gauges, one mounted on the upper surface of the bar, and the other located 41 Instrumentation precisely under it on the lower surface. The two gauges were connected in opposite arms of the Wheatstone bridge, which cancelled the bending strain present within the bar. This meant that pure axial strains in the bar were measured, (de Silva, 1989 and the Experimental Stress Analysis Notebook, 1987). INTERNAL INSTRUMENTATION T 8 T 7 T6 TS T 4 T3 T 2 T l y v v V V V Y Y A A Y V A , V A A V V • A v A A Y Y C 4 A A A X A X A A ci E ^ B 8 B 7 C3 B 6 B 5 B 4 B3 B 2 B l \ ^ C 2 w Figure 4.1 Internal Instrumentation 4.2 Displacement Transducers and Accelerometers The remaining 16 channels were used to record the displacement and acceleration of the table and the bent. The absolute acceleration of the cap beam in the vertical, longitudinal and out of plane directions was measured by ± lOg K-beam accelerometers with a resolution of 205 mV/g and a frequency range of 0 to 300 Hz (Appendix C, figure C-10). The absolute acceleration of the table in the vertical and longitudinal directions was measured by ± 2g accelerometers located under the table. 42 Instrumentation The absolute displacement of the table was recorded with a Linear Variable Differential Transducer (LVDT) which was mounted underneath the table. It had a range of ± 76 mm. The absolute displacement of the cap beam was measured using displacement transducers that were connected between the cap beam and a frame situated beyond the table. The displacement transducers had a 254 mm full scale displacement with an accuracy of 0.1%. Figure 4.2 shows the layout of the accelerometers and displacement transducers. EXTERNAL INSTRUNfENTATION fA)—»®->|| N W (^—•displacement transducer (S) strain gauge @—•accelerometer Figure 4.2 External Instrumentation The acceleration was measured in the longitudinal and transverse directions at either end of the cap beam. The amount of torsion was measured by analysing the phase shift between the two acceleration records from either end of the cap beam. The vertical movement of the bent was monitored using vertical accelerometers on the cap beam above the mass block connection points. The acceleration and displacement of the cap beam relative to the moving table was obtained by subtracting the digitised record of the table motion from the individual records of the specimen. 43 Instrumentation The acceleration was also measured at a point just above the base connection to the column to determine the degree to which the forces were transmitted from the table to the bent. Lastly, the mass block was also instrumented to determine whether it was moving relative to the cap beam. 4.3 Other Systems The bent was painted with a brittle white paint so that crack formation could be detected more easily. Two video cameras were used to record the test visually. One of these was a normal video camera that recorded the overall motion of the bent during the earthquake excitation in order to give a general idea about how the testing program progressed. The other camera was a high-speed one capable of recording at speeds of 1000 Hz. This camera was used to record the development of cracks in the cap beam just inside the column joint, the most critical point of the bent. Information on the amplifiers, data recording system, data storage media and digital signal processing software is given in Appendix B. 44 Construction and Materials Chapter Five C O N S T R U C T I O N A N D M A T E R I A L S 5.1 C o n s t r u c t i o n Bent: The bent was constructed in the Earthquake Engineering Research Laboratory in a horizontal position. Strain gauges were attached to prepared locations on the reinforcing steel prior to assembly of the steel into cages, which were then placed in the wood forms. Hardware, such as anchorage plates at the base of the columns, and the Dywidag bars, were placed in the forms. Plant mixed concrete from the Allied Ready Mix plant was placed and vibrated conventionally (Appendix C, figure C-l to C-4). The concrete had a maximum aggregate size of 9.5 mm diameter, which was the smallest size available, and was reasonably close to the scaled size of 8.5 mm, based on the prototype aggregate size of 32 MPa. Cores taken from the Oak Street Bridge gave a mean equivalent cylinder strength of 38 MPa, while the corresponding cyclic test specimen had a mean cylinder strength of 47.5 MPa. It was decided to order 35 MPa concrete that was expected to provide a long term strength of 42 MPa after over a month of curing. The bent was cast on its side and left to cure with plastic sheeting for a month. Mass Block: The concrete mass block was cast in the structures laboratory and later transported to the Earthquake Engineering Research Laboratory. The section at the cap beam - mass block 45 Construction and Materials connection was boxed out to allow space for post-tensioning of the Dywidag bars. The hooked ready rods to connect with the steel plates were held in position with a wooden frame, and after the concrete was poured, three of the steel plates were lowered over the rods to keep them aligned. The mass block was cured with plastic sheeting for a week, but the formwork was removed after two days. 5.2 Material Properties 5.2.1 Concrete Nine concrete cylinders were cast when the specimen was poured. Three sets of three cylinders were tested, the first set at 28 days, the next at 10 weeks, and the last at the time of testing (22 weeks). The target strength was 42 MPa, and the strengths achieved are shown below, all strengths in MPa: 28 Days 10 Weeks End of test Cyl . l 36.8 42.5 39 Cyl.2 35.11 45 44.1 Cyl.3 36.2 47.2 38.1 Average 36.05 44.9 40.4 Overall Average = 40.5 MPa Table 5.1 Concrete Strength A second set of three concrete cylinders was tested to determine the stress-strain relationship. This was done by using two LVDTs which measured the vertical strain under the applied load. Values for Young's modulus were calculated and an average value of 30351 MPa was found. 46 Construction and Materials 5.2.2 Steel The steel and wire used in the bent were also tested and the results are tabulated below: No. 3 bar IGa. 4Ga. 8Ga. 10 Ga. 14 Ga. 1st 460 560 590 570 255 220 2nd 462 575 600 590 256 220 Average 461 567.5 595 580 255.5 220 Table 5.2 Yield Stress of Reinforcement, MPa 5.2.3 Dywidag bars The Dywidag bars supplied, were standard 26mm diameter bars. The important physical characteristics as given by Dywidag Systems International are shown below: Area - 548 mm2 Ultimate Stress = 1030 MPa Ultimate Strength = 587 kN 5.2.4 Rubber There were two types of bearing material used in the mass block bearings. A soft polyurethane pad, Shore A 40, was used to provide some cushioning action and allow some vertical displacement to occur during the test without transmitting much vertical force, and a harder 50-Durometer rubber was used to provide the required spacing. The polyurethane and rubber were tested separately and then in combination to determine the material properties. The stress-strain characteristics are shown in figure 5.1. 47 Construction and Materials D-50 Rubber 2-layer Polyeurethane '' • rf^*~ i 1 i i 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 Strain Figure 5.1 Stress-Strain of Rubbers Tested It can be seen from figure 5.1 that the combination is less stiff than the rubber alone, and allows a linear variation of stress with strain in the region of interest, shown between the dashed lines in figure 5.1. As the rubbers were of different heights, it was not possible to compare the force-displacement behaviour. However, figure 5.2 shows the force-displacement for the combined rubber-polyurethane pad. Displacement (mm) Figure 5.2 Force-Displacement Relationship of the Rubber-Polyurethane Pad 48 Construction and Materials 5.3 Lateral Support System Lateral support to the bent was provided by four wire ropes, as shown in figure 3.6. In order to minimise the effects of rope vibration, the tension in the rope was adjusted to a value so that the natural frequency of the ropes greatly exceeded the natural frequency of the bent (7.65 Hz). This value was chosen to be 12 Hz. The resulting tension at this frequency was 4.4 kN. The overall out of plane frequency of the bent was found by a hammer test to be 3.5 Hz. The ropes were equipped with turnbuckles so that adjustments to the tension (and consequently frequency) could be made easily in the event of rope or specimen lateral vibration becoming a problem. 49 Capacity and Theoretical Behaviour Chapter Six CAPACITY A N D T H E O R E T I C A L B E H A V I O U R The characteristics of the bent, such as shear and moment capacity, first longitudinal natural frequency, and response to earthquake loading, were analysed prior to the shake table test. Sectional analyses using state-of-practice standard office calculations and code-based models for shear and flexure were performed to determine nominal shear and moment capacities. A simple linear elastic analysis was performed using a two dimensional frame analysis program. Capacities of column sections were computed with suitable analysis programs and compared with hand calculations. A standard push-over analysis provided estimates of force, displacement and ductility. Finally, a non-linear time history analysis for the proposed seismic record was performed. Scaling of some of the results from the 0.45 scale model tested by Anderson et al (1995) was performed in order to facilitate comparisons with the predicted performance of the 0.27 scale model. In this chapter all values, whether referring to the prototype or 0.45 scale model, are presented scaled to the 0.27 scale model for comparison purposes. 6.1 Capacity of the Bent. 6.1.1 Codes The shear and bending moment capacity of the bent was analysed in several critical locations, these being the top of the columns, the haunch and in the cap-beam outside the haunch. In the case of shear capacity, three methods were used: ACI (1992), ACI/ASCE (1978), and the Canadian 50 Capacity and Theoretical Behaviour code (CSA, 1985). The unfactored capacity was used in order to predict nominal values for comparison with test values and for design of the test set-up. The ACI formulae converted from the imperial are: Total shear in kN V n = V s + V c (6.1) where: Shear due to concrete V c = 0.166A/f7bwd (6.2) Shear due to steel V s = A v f s — (6.3) s Where: fc = strength of concrete in MPa b w = width of section in mm d = shear depth of section in mm A v = area of steel shear reinforcement in mm2 s = spacing of steel shear reinforcement in mm The ACI/ASCE formulae converted from the imperial are: Total shear in kN V = V + V n s c where: V c =0.083(0.85+ 120pw)VfTbwd Where p w = ratio of tension steel (6.4) (6.5) V , = A v f s - (6.6) s b„.d 51 Capacity and Theoretical Behaviour The Canadian metric code equations are: Total shear in N v r = v s + v c (6.7) where: (6.8) V s = f y A v " s (6.9) The shear capacity of the beam at the edge of each haunch and the centre of the beam was calculated. The tie spacing and reinforcement ratio were the two parameters that changed, as the cross sectional and concrete shear area were constant. The results of these calculations are presented in table 6.1. It is clear that the Canadian code gives the largest capacity for the section, and the ACI/ASCE code yields the most conservative values. The values from the ACI/ASCE code are different at the haunches due to the parameter p w , which varies depending whether the haunch experiences positive or negative bending moment. From the 0.45 scale test results, it was shown that the failure mode was due to shear failure of the cap beam at the haunch. Due to the position of the bearing points on the cap beam, the maximum shear demand occurred towards the outside of the haunch. It was expected that failure of the 0.27 specimen would also occur at this location. The shear capacity of the column was not considered a problem, as this had not been the failure mode in the cyclic tests. The shear capacity of the column was calculated and found to be 137.8 kN (ACI), and 158.6 kN (CSA). The moment capacity of the column was calculated using COL604 (in-house CALTRANS Program, Seyed, 1992). This uses the ACI/ASCE formulae, and predicted the column to have a maximum moment of 73 kN-m at the compression axial load it experiences (132 kN) and 57 kN-m at zero axial load. 52 Capacity and Theoretical Behaviour The values found using COL604, were checked with an in-house developed computer program and resulted in similar values, being 75.6 kN-m and 57.0 kN-m respectively. The moment capacity was calculated using BEAM303, (in-house CALTRANS program, Seyed 1992), for several sections of the cap beam. This program uses the ACI/ASCE formulae to calculate the shear capacity. The results are presented in table 6.2, and as discussed in chapter 2, they agree well with the capacities of the 0.45 scale bent. 6.1.2 Results scaled from previous analysis of Prototype and 0.45 M o d e l Analyses of the prototype and 0.45 scale model bent capacities were carried out in conjunction with the slow cyclic tests by Seethaler (1995). These values were scaled to the 0.27 scale to provide comparisons between the different models. For both the prototype and 0.45 scale model, the shear results are shown in table 6.1, and the bending results are in table 6.2. Again, the ACI/ASCE (referred to in table 6.1 as A/A) yields significantly lower results than the other code, but the results are similar to the preceding results. Due to an oversight in which two reinforcing bars were not placed in the lower reinforcing steel, the accuracy of the moment capacity of the 0.27 scale bent is not as good as originally calculated. In table 6.2 the as-built values are given. It can be seen that the negative moment capacity of the 0.27 and 0.45 bents correlate very well. The shear capacities of the 0.45 and prototype bents compare quite well with those calculated for the 0.27 bent. The capacity of the 0.27 bent is higher than that calculated for the other bents whichever code is used. The ratio of tension steel was higher in the 0.27 bent than that given for the other bents which is a reason for this difference. 53 Capacity and Theoretical Behaviour Pos. 0.27 ACI 0.27 A/A 0.27 CSA 0.45 ACI 0.45 A/A Proto. V- A/A Hnch + 164.9 142.4 185.5 - - 117 Hnch- 164.9 112.6 185.5 104.5 86.6 87.5 Centre 124.4 101.6 145.9 - - -Table 6.1 Code Shear Capacities in kN of the Cap Beam Figure 6.1: Analysis Points on Bent Dist. from col. edge [mm] 0.27 Model M + [kN-m] 0.45 Model M + [kN-m] Prototype M + [kN-m] 0.27 Model M- [kN-m] 0.45 Model M [kN-m] Prototype M- [kN-m] 0 -259 Sec.1 29.2 47.4 45.6 119.2 113.8 112 259 -390 40.7 69.1 - 100.3 100.3 -390-543 Sec.2 62.4 80.0 - 81.3 81.3 -543-619 81.3 100.3 - 62.4 69.1 -619 - 745 Sec.3 100.3 119.2 115.6 40.65 46.07 66.8 745 - 975 100.3 119.2 - 40.65 - -975 - CL 100.3 119.2 - 29.8 25.7 -Table 6.2 Moment Capacity of the Cap Beam 54 Capacity and Theoretical Behaviour Table 6.3 presents results that were found by Seethaler (1995) using the program RESPONSE (Collins and Mitchell, 1991). This program is based on the modified compression field theory and iterates for the principal strain until a convergence to the largest force state is found. The analyses returned values for the moment, shear and axial forces present in sections at designated locations in terms of the base shear (Veq). The results for the 0.45 and prototype bents were scaled for comparison with the 0.27 bent. From table 6.3 it can be seen that the critical section is the right cap beam that fails at a base shear of 78.8 kN. The beam sections in table 6.3 refer to figure 6.1. As the analysis uses the ultimate strength, this gives an upper limit for the capacities. A RESPONSE analysis was also done on the 0.45 scale specimen. As before, the cap beam is the critical section which fails at a base shear of 110.8 kN. As RESPONSE is based on an ultimate strength model, it is to be expected that yielding would occur significantly below this value of base shear. Section Proto M (kN-m) Proto V (kN-m) Proto N (kN-m) P r O t O Veq (kN-m) 0.45 M (kN-m) 0.45 V (kN) 0.45 N (kN) 0.45 Veq (kN) Left Sec. 1 49 35 3.2 137 83 42.9 3.5 129 Right Sec. 1 -53.6 79 3.8 78.8 -126.7 103.9 3.7 128.6 Left Sec.2 - - - 78.9 78.9 52.7 3.84 147 Right Sec.2 - - - -82.6 -82.6 96.2 3.84 115.1 Left Sec.3 - - . - - 94.5 98 3.84 226.7 Right Sec.3 - - - - -48 93.8 4.64 110.8 Left Col 58 59 -81.3 I l l - - - -Right Col 73 78 -292 162 - - - -Table 6.3 RESPONSE Capacities for Prototype and 0.45 Scale Model 55 Capacity and Theoretical Behaviour The moment capacity of the prototype column was predicted as 88kNM at an axial load of 179 kN, and as 83 kN-m at an axial load of 164 kN in the 0.45 scale model (all values scaled to 0.27 size model). These values are in accordance with those calculated for the 0.27 scale model in the previous section, although the moment capacity of the 0.27 scale is somewhat lower as a result of the reduced axial load. From these calculations it can be seen that the ACI/ASCE values for shear are significantly less than those predicted using other codes. However, the values, whether calculated for the 0.27 scale model or scaled from analyses of the prototype and 0.45 scale models, generally agree well with each other. The program RESPONSE produces values for the ultimate behaviour of the section, whereas the ACI/ASCE results are for yielding elements, which explains why the RESPONSE values are greater than the ACI/ACSE results. 6.2 Sectional Demands. Several computer programs were used to predict the behaviour of the bent subjected to various excitations. First an elastic push-over analysis was done using the program PCA-frame (Winsoft Software Inc., 1992). Next, the program DRAIN-2DX (Prakash et al, 1993) was used to perform a non-linear dynamic investigation of the bent. This included both spectral and time-history analyses. Lastly another non-linear program, CANNY-E (Li, 1995), was used to predict the behaviour and the progression of damage. This analysis was done Khoshnevissan (1996), and the results are presented here for purposes of comparison. 56 Capacity and Theoretical Behaviour 6.2.1 PCA-frame The analysis program PCA-frame was used to predict a possible failure loading of the structure. The program performs a strictly linear analysis and was used to obtain an initial estimate of the demands in the various parts of the structure. Two models were analysed. A basic model (model 1) was used with the mass block simplified to a truss above the cap-beam with the mass concentrated at the apex of the truss, (see figure 6.2). This is similar to the model that was used in the analysis of the prototype and 0.45 scale models. The second model (model 2) simulated the mass block as a heavy beam that was connected to the cap beam by three rubber connections and two steel connections that resisted the shear force, (see figure 6.3). The results from these two analyses were similar except for the distribution of shear in the cap beam. In model 1, figure 6.2, the shear demand was more uniform along the beam, with a large shear demand in the centre portion of the cap beam (about 63% of the value at the haunch). In model 2, figure 6.3, the shear demand is small in the centre section of the cap beam, only about 15% of that in the haunch region. 50.2 Figure 6.2 Shear Demand at 100 kN base Shear, Model #1, all values in kN 57 Capacity and Theoretical Behaviour Capacity and Theoretical Behaviour Figure 6.5 Flexural Demands at 100 kN base shear, Model #2, all values in kN-m Due to the variability of the predictions of the shear capacity, it was difficult to forecast the exact failure mode. When the ACI shear capacity was used, then the failure was due to shear in the cap beam, however, when the Canadian code capacity was used, then failure occurred due to flexural failure in the columns. The results shown in figures 6.2 - 6.5 are for a lateral force of 100 kN applied to the mass block, and are given in tabular form in table 6.5. As the capacity of the shake table is for 150 kN this analysis indicated that the shake table motion should be capable of damaging the bent. As the Canadian code predicted a higher shear capacity than the ACI code, thus resulting in higher forces, the demand forces corresponding to failure of the bent using this code were taken as the design forces for purposes of test design. 59 Capacity and Theoretical Behaviour Section Cmp. [kN] Tens. [kN] Shear [kN] BM [kN-m] Beam haunch 54 - 85 73.4 Beam centre 12 - 54.4 5 Mass-cap connection 58 58 0.1 0.2 Column 134 30 50.2 72.3 Table 6.4 Model 1 Section Demands Section Cmp. [kN] Tens. [kN] Shear [kN] BM [kN-m] Beam haunch 49 - 142.5 51.5 Beam centre 0.9 - 16.2 8.9 Rubber connections 38 - - -Mass-cap connection 123 66 51.6 2 Column 118 43 50.6 72.9 Mass Block 51.6 - 78.8 69.1 Table 6.5 Model 2 Section Demands 6.2.2 DRAIN-2DX DRAIN-2DX is a non-linear finite element structural analysis program. It allows the user to determine the frequencies of the structure, to perform push-over tests, to run non-linear time step analyses using earthquake acceleration time histories, and various other studies. It is 60 Capacity and Theoretical Behaviour available from the National Information Service for Earthquake Engineering (NISEE) at the Earthquake Engineering Research Centre at University of California at Berkeley. The program was one of the first to use non-linear time step analyses of two dimensional frames. In this program a structure is modelled by defining nodes and then interconnecting them with elements. Various types of elements are available: truss element, beam-column element, simple connection element, structural panel element, and link element. Masses are lumped at selected locations. There are no provisions to calculate hysteretic strength or stiffness degradation. It was decided to model the specimen similar to Model 1 in the PCA-frame analysis, (modelling the mass block as a truss). There were two reasons for this decision. Firstly, the prototype had already been modelled in this fashion in a previous analysis by Seethaler (1995), so this would allow comparisons to be made. Secondly, there were certain problems in modelling the mass block, as the connections between the cap-beam and mass block were difficult to represent using the elements available. An eigenvalue analysis was performed to give values for the frequencies of the bent, and the results compared with those expected from scaling the prototype period. After that, a non-linear time step analysis was performed using different earthquakes and the results combined with a gravity analysis to give the total loading on the bent. Results from these analyses are presented in the following sections. Design Spectrum The design spectrum for the site of the Oak Street Bridge was calculated by consultants for the Ministry of Transportation and Highways. As the site extends over a kilometre, the soil conditions vary from soft soil to firmer ground. Two spectra had been produced, one for each 61 Capacity and Theoretical Behaviour extreme. As the bent being modelled was located on soil between these two conditions, an average spectra determined from these two, shown in figure 6.6, was taken by the author as the design spectrum for the site. 1 T Period [s] Figure 6.6 Site and Design Response Spectra for the Oak Street Bridge Area Natural Frequencies The natural frequencies for the first five modes of the 0.27 scale model were computed and compared with those of the prototype when scaled. The scale factor for frequency between the full height prototype and 0.27 bent with cut off legs had been calculated to be 0.197, see Chapter 2. The results are presented in table 6.6. The correlation was very good for the fundamental frequency of the structure, but the similarity was reduced with subsequent frequencies. However, the bent response was mainly controlled by its first mode, as the magnitude of the design spectra peaks at the fundamental frequency and is much reduced at the frequency of the 62 Capacity and Theoretical Behaviour second and higher modes. This means that, if the earthquake used has a response spectrum similar to the design spectrum, the inaccuracies of the higher modes are not significant as they play a small role in the behaviour of the bent. Mode Prototype 0.27 model % Difference 1 0.136 0.136 0% 2 0.033 0.044 25% 3 0.024 0.034 29% 4 0.014 0.021 33% 5 0.008 0.008 0% Table 6.6 Natural Frequencies from DRAIN-2DX Time History Analyses Acceleration time histories from several earthquakes were used to analyse the structure. Analyses were run with Landers earthquake - Joshua Tree Fire Station E-W component (later used in the shake table test), and Mexico 1979 earthquake, Infiernillo station E-W component, as both of these were considered for the input to the shake table. The spectra for both Joshua Tree and Infiernillo were sufficiently close to the design spectrum to leave them unaltered, as can be seen in figure 7.1. It was considered preferable to leave these records in their natural state, albeit with some differences from the design spectrum, as there are certain inaccuracies that can be introduced by artificially changing records. In the DRAIN-2DX analysis it was possible to scale the acceleration amplitude of the record. The peak acceleration of each time history was increased until failure of the bent occurred. It was also 63 Capacity and Theoretical Behaviour necessary to scale the time increment of the time history. The scale resulted from the calculations described in Chapter 2. The time increment of the original records was 0.02 seconds, but this was multiplied by the scaling factor of 0.279, so the increment was compressed to 0.00558 seconds. The effect of this was to retain the number of data points of the record, but compress them by the time scale factor. The DRAIN-2DX program is unable to detect shear failure, so flexural failure due to hinging of the columns was outputted as the failure mode. However, the values for shear were examined at each increment of increasing acceleration to check whether the shear demand had exceeded the capacity at any section. As with the PCA-frame analysis, the variability of values for shear capacity admitted the possibility of two failure modes: shear failure in the cap beam, or hinging of the columns. The distribution of shear demand in the cap beam was similar to that from PCA-frame. The PGA of the time histories used that was required to cause failure of the bent is given in table 6.7. Earthquake Acc. Scale Original Eq. PGA [g] 0.27 scale PGA [gl. Equivalent Prototype PGA [g] Infiernillo 1.9 0.371 0.700 0.203 Joshua Tree 2.5 0.278 0.695 0.201 Table 6.7 Acceleration Records PGA The results for the non-linear time history analysis of both earthquakes at the PGA level given in table 6.7 are shown in table 6.8. The values given are the peak values from the entire response record, from an analysis at the PGA given in table 6.7. 64 Capacity and Theoretical Behaviour The results of the DRAIN-2DX time history analyses, given in table 6.8, showed that in each case the bent could fail due to hinges forming at the top of each column. As the bent was modelled as having pins at the base of the columns, only two hinges were required for failure. However, as the program did not take shear failure into account, the significant shear forces in the cap beam could have been large enough to cause failure at the haunches before the program detected that the columns yielded in bending. As the results for the shear capacity of the cap beam had a large spread it is difficult to know at what shear demand the cap beam would fail, and whether the columns or cap beam fail first. The bent suffered failure due to hinging of the columns at a base shear of between 110 and 120 kN, which is within the capacity of the table. Section Earthquake Record Cmp. [kN] Tens [kN] Shear [kN] BM [kN-m] Positive BM [kN-m] Negative Displ. [mm] Beam haunch Infiernillo 59.7 52.2 135.4 119.1 79.8 12.57 Joshua Tree 52.2 49.8 122.8 101.2 67.2 5.47 Beam centre Infiernillo 8.26 2.4 81.8 31.8 25.0 12.57 Joshua Tree 3.3 3.2 72.5 20.3 20.1 5.47 Mass-cap connection Infiernillo 55.0 54.6 - - - -Joshua Tree 55.4 54.5 - - - -Column Infiernillo 169.6 62.9 66.8 76.5 67.6 -Joshua Tree 148.0 41.2 58.9 72.0 67.1 -Table 6.8 DRAIN-2DX Results for Various Earthquakes 65 Capacity and Theoretical Behaviour 6.3 Previous Test and Analysis at 0.45 Scale The results from the slow cyclic tests, (Anderson et al, 1995), are presented so that comparisons may be drawn for the expected outcome from the shake table test. There were also some predictions of damage from a shake table test performed using the computer program IDARC inelastic Damage Analysis in Reinforced Concrete), (Williams, 1995), and these are also discussed in relation to the 0.27 scale shake table test program. 6.3.1 Scale Effects It was expected that there could be an increase in the capacity of the bent due to some effects induced by the dynamic testing. It has been well established that high strain rates affect the stress-strain diagram of both steel and concrete OBresler and Bertero, 1975; Moncaza and Krawinkler, 1981). For structural steel there is an increase in the yield strength, a slight increase in the tensile strength, and a reduction in the ductility of the material. In concrete, there is an increase in the compressive strength as strain rates increase. Furthermore, the initial stiffness of the bent is expected to be higher than that experienced by the slow-cyclic bent, as the modulus of elasticity of both steel and concrete increases with increasing strain rate, and there is a decrease in the strain at ultimate strength. From previous shake table tests it has been shown that there can be a more rapid decrease in stiffness under dynamic testing than under static loading (Abrams, 1996). However, this is dependent on many factors, especially the type of steel used for reinforcement. A reduction in stiffness can result from the possible reduced bond if smooth wire is used for reinforcing steel. If deformed wire is used, the ratio of surface area to cross-sectional area increases, so in this case 66 Capacity and Theoretical Behaviour the bond would be increased. Thus after some damage has occurred, the smooth wire would decrease the stiffness, whereas the deformed wire might increase it. Spalling out of the crushed concrete is likely to be less in shake table tests, which reduces the strength deterioration as compared with static or slow cyclic tests. As a result of this effect, it is considered that the rehability of slow static tests is reduced, and that earthquake simulation tests can model this more accurately. It is to be expected that the shake table tested specimen be stronger and initially stiffer, due in part to the greater strain rate during dynamic testing. However, as the scale is not small, the effects of increased strain rate due to scaling of the time history will not be severe. It is estimated that the strength increase would be about 10% to 20%. As the stiffness is expected to be initially higher than the 0.45 scale bent, the deflections will be less than those experienced during the static test. The stiffness will reduce faster than in the static test due to the smooth wire that was used for some of the reinforcing steel, although the effect could be reduced because of the greater bond of the small deformed steel bars. 6.3.2 S low C y c l i c Test Results The 0.45 scale as-built bridge bent was tested in sequences of three cycles of lateral load or displacement at increasing predetermined levels until the specimen failed, (Seethaler, 1995). In the following discussion of the behaviour, the values are given for the specimen and the values scaled for the 0.27 scale specimen are given in parentheses. The first sign of damage was at a displacement of 2 mm (1.2 mm) at a base shear of 129 kN (46.5 kN), and was indicated by a few flexural cracks in the top of the cap beam. At a displacement of 3 mm (1.8 mm) at a base shear of 146.5 kN (52.9 kN) shear cracks developed at 45 degrees at the top of one end of the beam, and flexural cracks developed at the other. 67 Capacity and Theoretical Behaviour Between this loading level and a displacement of 16.5mm (9.9 mm) at a base shear of 268 kN (96.5 kN) further cracks developed and the existing ones widened. After this point the displacement was still increased cyclically although the base shear was decreasing. As the displacement was increased to the maximum of 32 mm (19 mm), the shear cracks increased in the cap beam. Finally there was a large amount of spalling, some debonding at the top of the beam, and finally the bent suffered a brittle failure in shear in the cap beam. The value of the ultimate base shear attained by the bent scaled to the 0.27 bent (96.5 kN) is in close agreement with both the DRAIN-2DX and PCA-frame predictions of 110 kN and 100 kN respectively. As this base shear is within the capacity of the table (155 kN), it was expected that the shake table test would be capable of inflicting severe damage to the specimen. 6.3.3 IDARC Analysis A series of inelastic structural analyses of the 0.45 scale bridge bent were carried out using non-linear analysis program IDARC by Williams (1994). The results were validated by comparison with the results of the slow cyclic tests. The hysteresis parameters were tuned and the models were able to reproduce accurately many aspects of the experimental results. These included the development of damage through the test, the overall lateral load-deformation response, and the final damage distribution. After the static analysis, a dynamic analysis using increasing levels of earthquake excitation was performed on the models and the behaviour assessed. The results of the earthquake analyses showed that the peak acceleration and displacement varied roughly linearly with the PGA, and that the damage index remained almost constant until a sudden failure occurred. The trend was similar for all the earthquake records to which the model was subjected. At low amplitudes, the 68 Capacity and Theoretical Behaviour response of the bent was linear, with limited cracking. As the amplitude was increased enough to cause yielding, failure occurred very suddenly, indicating that the bent was very brittle, or that the development of damage was very sensitive to the amplitude of a few peaks cycles in the imposed earthquake. The PGA required to cause collapse depended on the earthquake record. The intensity of the record was increased until collapse occurred. The values obtained for the 0.45 scale model were increased to suit the scale of 0.27 bent (found by multiplying by the scale factor of 3.45), and are presented in table 6.9. The values from the DRAIN-2DX analysis are also given in this table. One of the time histories used in the IDARC analysis, Landers Earthquake Yermo station, was not used in the DRAIN-2DX analysis, but the results are included in table 9 for comparison purposes. It can be seen that the PGA required to fail the 0.27 scale bent is probably between 0.6g and 0.7g, depending on the earthquake record being used. Earthquake IDARC Analysis DRAIN 0.45 scale 0.27 scale Yermo NS 0.17 0.587 -Joshua EW 0.21 0.725 0.695 Infiernillo N.A N.A. 0.700 Table 6.9 PGA of Seismic Record Corresponding to Failure of Model 69 Capacity and Theoretical Behaviour 6.4 Analyses Using CANNY-E The program CANNY-E, is a three-dimensional non-linear dynamic structural analysis program that considers material nonlinearity. The analysis was carried out by Khoshnevissan as part of her Masters thesis and by Kang-Ning Li, the writer of the program (Khoshnevissan and Li, 1996). A model was created with nodes according to the reinforcement details and the loading points. The rigid zone extensions were determined at the beam-column joint according to its dimension. The mass block above the cap-beam was idealised as a beam supported by braces. The non-linear shear force-deformation relationship was modelled using a shear spring located at the mid-span of the elements of the cap beam. The axial deformations of the elements were considered negligible. The model was first analysed linearly for gravity loading. Then, the dynamic behaviour of the model, both in the linear and non-linear ranges was studied. This was done using the scaled Joshua Tree and Infiernillo acceleration records. Finally, a push-over analysis was performed to determine the position and development of the hinges. The model used in the analysis is shown in figure 6.7. The gravity analysis showed that there was minimal shear in the cap beam apart from in the section between the bearing point and the column (X2-X3). For the computed values see Khoshnevissan and Li, 1996. A non-linear dynamic analysis was performed using the Joshua Tree acceleration record. The fundamental period of the model obtained from an eigenvalue analysis was 0.093 seconds. This was smaller than the period obtained from the DRAIN-2DX analysis by 28%, but this could be 70 Capacity and Theoretical Behaviour due to slightly different material properties inputted, the configuration chosen to simulate the mass block and the base conditions used. Various levels of acceleration were used to analyse the behaviour, and it was determined that the structure would begin to yield at 0.47 g (corresponding to a prototype acceleration of 0.136 g), and would fail at 0.7 g (prototype acceleration of 0.2 g). The results, of the analysis at a PGA of 0.7g, show that the greatest demand is in the cap beam due to shear (sections X2-X3 and X5-X6), and in the column due to flexure. An elastic dynamic analysis was also run, and the distribution of the results are similar to those of the non-linear analysis, except that the elastic demands are about 25% greater than those computed nonlinearly. The peak acceleration of the record was increased until failure occurred. The value of this peak ground acceleration was 0.7g, and was in good correlation with the results obtained using DRAIN-2DX and IDARC, both of which had critical accelerations between 0.64 and 0.75g. Finally, a static push-over analysis was performed to determine the sequence of damage. At a base shear of 27 kN, the first flexural hinge formed in the cap-beam at the location of the bearing point close to the haunch, X3. The second hinge formed at the face section of the beam-column joint, X2, at a base shear of 38 kN. The hinge was located where the cap-beam was subjected to a sagging bending moment, causing tension in the bottom of the section. The beam had not been designed for this type of loading, and hence was greatly underreinforced at this point. 71 Capacity and Theoretical Behaviour X7 X8 Note: all dimensions are in mm and W = 89 kN (Weight of mass block) Figure 6.7 CANNY-E Model As the beam X2-X3 developed hinges at either end, the increase in load just put a greater shear and moment demand on the compression column, whereas the tension column was not stressed further. The load was gradually increased until a third flexural hinge was created at the top of the compression column. At this point it was considered that the bent had failed as the displacement increased significantly for a minimal increase in load. Damage was also seen in flexural cracking at the beam section X5, the left side of the section X6, and at the top of the tension column. 72 Input Motions and Test Program Chapter Seven I N P U T M O T I O N S A N D T E S T P R O G R A M In this chapter, the selection of a suitable earthquake record and how it was scaled is discussed. Some modifications to the acceleration time history were necessary and these are explained. The chosen testing sequence is given. 7.1 Selection of Time History It was required to select an earthquake that could cause a significant amount of damage to the model, while satisfying the requirements of the design spectra and fitting the limitations of the shake table. The design earthquake has been described as 'the ground motion, selected from all possible ground motions at a particular site, that will drive the structure to its critical response and thereby result in the highest damage potential" (Naeim and Anderson, 1993). However, it is difficult to quantify the design earthquake as very many factors influence it. Usually, it is the peak ground acceleration (PGA) of a record that is used to determine its severity, although it has been recognised for many years that this is not a very representative parameter. It is very possible that a large acceleration be associated with a short-duration burst of high-frequency acceleration. In this situation, most of the energy is absorbed by the structure, with the effect of little deformation or damage. A more destructive case would be a moderate acceleration with a long-duration impulse. 73 Input Motions and Test Program As a result of this, several other parameters have been suggested that try to reveal the true damage potential of an earthquake. Two of these are the maximum incremental velocity (TV) and the maximum incremental displacement (ID), which represent the area under an acceleration and velocity pulse, respectively. Bracketed duration, [D], is also considered. This is the time between the first and last instances of a chosen acceleration level, usually 0.05 g, on an acceleration trace (Naeim and Anderson, 1993). Another type of information that is required to choose a suitable time history is gained from analysis of response spectra. These can be produced for many different ground motion parameters, including effective peak acceleration Q3PA) and effective peak displacement Q3PD). A definition of these parameters is given in ATC 3-06 (Applied Technology Council, 1978) and are based on average response spectral ordinates in selected period bands. Inelastic response spectra may also be produced, and these can be constant-strength or constant-ductility. The shortcoming of response spectra is that they do not provide explicit information about the duration of the strong motion. Energy spectra account for this and show the presence of high energy dissipation demand with long duration. Hysteretic energy spectra and input energy spectra can give a more reliable indication of the damage potential and degree of inelastic deformation possible. In a report produced for NEHRP by Naeim and Anderson (1993), the above parameters are given for 1500 recent earthquake time histories. By careful examination of the records, three records were chosen that would be most likely to damage the structure while also suiting the design spectrum. The response spectra at 5% damping of these records, along with the design response spectrum, are shown in figure 7.1. It was decided to use the Joshua Tree Fire Station record E-W direction from the 1992 Landers Earthquake for reasons detailed below. In table 7.1 the characteristics of this earthquake record are compared with the other record considered, which was Mexico earthquake 1979 - Infiernillo station E-W component. 74 Input Motions and Test Program 0 -I 1 1 1 1 1 1 0 0.5 1 1.5 2 2.5 3 Period [s] Figure 7.1 5% Damping Response Spectra of Earthquakes Considered for Test Joshua Tree Infiernillo Magnitude M» 7.5 7.6 PGA [cm/s/s] 278.00 371.00 PGV [cm/s] 42.71 121.36 PGD [cm] 15.73 104.85 IV [cm/s] 62.52 189.09 ID [cm/s] 18.51 121.62 EPA [cm/s/s] 198.00 25.2 EPV [cm/s] 35.78 68.42 Epicentral D [Km] 15.00 83.00 [D] >0.05g [s] 41.10 58.1 Table 7.1 Characteristics of Earthquake Records Considered 75 Input Motions and Test Program This record has a number of characteristics that make it suitable for the shake table test. Firstly, it has a long duration, of over 40 seconds, see figure 7.2. This is important as the record compresses to almost a quarter of its original length when scaled. A long record is an advantage, as its compressed length is still of a significant length for testing purposes. 300 g -200 { o ' < -300 J • • 1 0 5 10 15 2 0 2 5 3 0 3 5 4 0 4 5 5 0 Time (s) Figure 7.2 Time History of Joshua Tree E-W Component Secondly, the response spectrum for acceleration of this record is very similar to the design spectrum, see figure 7.1, which means that the natural record can be used without requiring manipulation to fit the design spectrum. Also, the position of the first natural period on the response spectra is less than the period at the main peak on the response spectrum. This means that as damage occurs, the fundamental period increases and will approach the peak, so the specimen will still experience significant acceleration. The record has very significant values for both the input and hysteretic energy at the energy band concerned, between periods of 0.5 and 0.9 seconds, which is the bandwidth within which the natural period of the bent lies. This is shown in figure 7.3. The parameter, CY, in these graphs is the yield resistance seismic coefficient. This coefficient is defined as the ratio of the yield base shear to the effective weight of the structure. As explained before, these energy response spectra 76 Input Motions and Teat Program are good indicators of the damage potential of an earthquake. As damage occurs, the period of the structure increases, so, because of the fact that there is significant energy input in the period range above the fundamental period, the bent will still be subjected to significant energy input as it becomes damaged Input Energy Spectra E/M 1 1 1 • ! A f > i ' A J N •x \ 0 2 3 1 A \ 5 ; 6 Period (sec) / Cy»0.05 / Cy-0.10 / Cy-0.20 / Cy«0.40 / Elastic Hysteretic Energy Spectra E/M /ii" & V . / , 0 1 2 3 1 4 L 5 6 Period (sec) / Cy = 0.05 / Cy-0.10 / Cy-0.20 / Cy = 0.40 Figure 7.3 Input and Hysteretic Energy Response Spectra for Joshua Tree Record (taken from Naeim and Anderson, 1993) 77 Input Motions and Test Program 7.2 Modifications to Time History-After selecting the time history, it was necessary to make some modifications to it. These were necessary to make it more appropriate for the table, and to scale it to suit the size characteristics of the bent. The first of these alterations is described in section 7.2.1. It was carried out by a Ph.D. student, Vincent Latendresse, who was working in the Earthquake Engineering Research Facility at UBC. 7.2.1 Table modifications The data that is inputted to the shake table system is in the form of acceleration values. These are then integrated twice to give values for displacement which are then used to drive the actuators of the table. A MathCad calculation sheet was developed using the same integration routines as those used by the control system of the table to determine the resulting displacement from an acceleration record, and assess the response of the table. This approach was useful in finding whether the displacement or acceleration capacity of the table is being exceeded. Using this program, it was also possible to select cut off levels for the bandpass filters needed to condition the record. As the table is capable of accurately reproducing frequencies between 1 and 30 Hertz, frequencies outside this range were removed from the record. As the lower frequencies result in significant displacement, the removal of these components limits the high displacements that could exceed the table range, especially when the intensity of the earthquake is increased. With this program it was predicted that the table would displace about 24 mm at 0.7 g for Joshua Tree with a time step interval compressed to 0.006 seconds. The value of 0.7g is the predicted maximum acceleration required for failure and the corresponding displacement is within the range of the table stroke of 75 mm. 78 Input Motions and Test Program 7.2.2 Scaling It was necessary to scale the time interval of the acceleration time history so that it would be correct for the scaled model. The scale factor for time was determined to be 0.279, as given in chapter two. Figure 7.4 gives the original and scaled time histories. 300 0 E c o g -200 3 -300 "•dm 1 If ' 1 , W«u^^T^V'V 10 -dt = 0.02 Prototype 20 30 Time (s) 40 50 -dt = 0.006 0.27 Model 20 30 Time (s) 40 50 Figure 7.4 Effect of Scaling Time History An effect of scaling the time interval of the time history was to cause a shift in the response spectra. Figures 7.5 and 7.6 show the original and modified response spectra at 5% damping for displacement and acceleration respectively. In these plots the amplitude of the modified spectra are not scaled for acceleration or displacement. 79 Input Motions and Test Program 0 0.5 1 1.5 2 2.5 3 Period (s) Figure 7.5 Original and Scaled Displacement Response Spectra at 5% Damping 0 0.5 1 1.5 2 2.5 3 Period (s) Figure 7.6 Original and Scaled Acceleration Response Spectra at 5% Damping 80 Input Motions and Test Program From the scaling laws, the acceleration factor was 3.45, meaning that the model acceleration was 3.45 times that of the original earthquake. Also, the scale factor for the displacement was 0.27, so that any displacement present in the model bent would be 0.27 times that of the full scale specimen. For these reasons, it was expected that large accelerations and relatively small displacements would be required to fail the bent, so acceleration was predicted as being the limiting factor of the table performance, as opposed to the displacement. 7.3 Test Program From the dynamic analysis of the model bent described in chapter 6, it was anticipated that the Joshua Tree record scaled to a PGA of 0.7g would fail the bent. This was judged by reaching 0.9 on the Park and Ang damage scale. This scaled record, both in time and acceleration, was taken as the reference earthquake (100% = 0.7g) and the test runs were related to this value. This meant that a 20% run, is a run with Joshua Tree scaled to a PGA of 20% of 0.7g, being 0.14g, see table 7.2. 7.3.1 Input levels The model was subjected to two types of excitation: a scaled acceleration time history and a hammer impact. The latter of these was used to establish the natural frequencies of the bent at different stages, and the former assessed its response to an earthquake motion. Table 7.2 describes the sequence of input records. After each run a hammer impact test was performed. The testing program was designed to impose scaled time histories on the bent that would provide the maximum amount of information on damage development at various level, but would not cause so much damage that the vahdity of the final test run would be compromised. Each run 81 Input Motions and Test Program had a length of 37.5 seconds, although the duration of strong motion was only about 10 seconds. Initially a very low level run (5%) was performed to determine whether the instruments were functioning properly and then the test sequence was started. Run Input Acc. % Expected Failure PGA 1 Joshua Tree 0.07g 10 2 Joshua Tree 0.14g 20 3 Joshua Tree 0.28g 40 4 Joshua Tree 0.42g 60 5 Joshua Tree 0.56g 80 6 Joshua Tree 0.84 120 7 Joshua Tree 1.05g 150 Table 7.2 Input Records The shake table had been recently upgraded and, as this was the first time a specimen of this size had been tested on it, there were certain problems that had to be overcome. The main difficulty was that the software corrected automatically for errors between the desired and produced acceleration and displacement time histories using an iterative procedure. The displacement errors were reduced in each iteration but the acceleration errors tended to increase substantially, due to unwanted high frequency components of motion. Steps were taken to reduce the acceleration errors, (see chapter 8), but during this process an uncontrolled, sudden movement of two of the actuators occurred. As the recording devices were not active, both the direction and level of the movement was unattainable. Damage did occur during this jerk-type excitation. It had been predicted that the cap beam would fail in shear at the location in which the damage occurred, so the overall failure mode of the bent was not 82 Input Motions and Test Program affected. However, since the damage was not symmetric, this did result in one end of the cap beam accumulating more damage than the other. The performance of the bent at each level is described in chapter 8. 7.3.2 Hammer test The hammer testing procedure is a relatively fast and simple one for obtaining the natural frequencies of a structure. It involves a hammer that is instrumented with an integral piezoelectric force sensor that measures the input, and several accelerometers attached to the specimen to record the output. The sensor uses self-generating quartz crystals to create an output signal which corresponds exactly to the impact force of the hammer. The hammer was impacted at the end of the cap beam in the longitudinal direction to obtain the natural frequency in this direction (Appendix C, figure C-8). There were accelerometers at four locations which were used to record the structures' response to the hammer excitation, see figure 7.7. A software package was then used to compute the frequency response function and obtain the natural frequencies (Villemure, 1995). The information on the hammer and accelerometer specifications, sampling rate and number of impacts is contained in Appendix D. Figure 7.7 Hammer Sensor Locations 83 Test Results Chapter Eight TEST RESULTS 8.1 Qualitative Description Before testing was started, the hammer test results showed that the natural frequency in the longitudinal plane of the bent was 7.76 Hz. This compared well with the frequency predicted from the scaling factors and DRAIN-2DX analysis which was 7.35 Hz. Three runs, of 5%, 10% and 10% (10a) (section 7.3 for definition of run level), were performed at which point the errors in the table input acceleration were considered unacceptable and testing was halted. By performing a frequency response function (FRF) analysis of the required and the produced table outputs, it was observed that the error was primarily in the high frequency range. The frequency of the bent had decreased slightly by this stage to 7.65 Hz. There was no visible cracking, apart from the initial shrinkage cracks. Before the next run, again at the 10% level (10b), steps were taken to reduce the errors and the high frequencies. This included tightening the lateral restraining cables such that their frequency changed from 4 Hz to 12 Hz, and by greasing the base connections and lateral restraining system to remove high frequency grinding of the steel. The accelerometer in the longitudinal direction was also filtered mechanically. This resulted in some improvement, but it was felt that more was required. Therefore, it was decided to reduce the control of the table to frequencies below 15 Hz. 84 Test Results In order to do this a new impedance matrix for the drive file was required, and this involved performing a random excitation test to obtain the characteristics of the bent. The level of this excitation was very low. However, before the actuators were switched off there was a sudden movement by two or three actuators which caused shear cracks in the cap beam, marked in green on the photographs, (Appendix C, photo C-12). Both ends of the cap beam were damaged in the same way, a shear crack running upwards from West to East. The West end of the beam was more damaged than the East end. It was decided to proceed with the testing sequence as it was likely that the damage present would have little effect on the bents behaviour at larger magnitude seismic excitations. The frequency of the bent was ascertained to have reduced to 6.80 Hz, indicating that the bent was more flexible than before, so higher displacements were expected in subsequent runs. A fourth run at 10% (10c) was done to determine the effect on the errors of controlling the table up to 15 Hz and to see whether the performance of the bent had been significantly affected by the damage it had sustained. Several of the strain gauges were zeroed prior to this run as they were reading residual strain levels after the unwanted actuator movement and would have caused problems in saturating the amplifiers. The level was noted and accounted for when determining the strain levels present. During this run the frequency reduced slightly to 6.70 Hz. Although the excitation level was similar, the response of the bent for acceleration and displacement increased by about 150% and 50% respectively. Also, the strain gauges had recorded minimal levels of strain in previous runs, but during this one they registered several micro-strain. The errors had been successfully reduced, and one further run at the 10% (lOd) level was performed to determine whether this was a trend and testing could continue. The errors in both acceleration and displacement continued to decrease further as was expected, so a 20% level run was executed. 85 Test Results The 20% run resulted in a frequency decrease to 6.15 Hz, indicating some damage had occurred. The cracks that had been formed earlier did propagate and some further cracking occurred. These are marked in red in the photographs (Appendix C, photo C-12). The cracking occurred at the end of the cap beam, some due to flexure and others due to shear. Some vertical cracks at the ends of the cap beam were formed, and it was proposed that these could have been due to shding shear, which occurs in heavily confined regions, such as this one. The columns were undamaged. A 40% run was performed next. Again, the frequency decreased significantly to 5.76 Hz. Further cracking occurred, marked in blue on the photographs (Appendix C, photo C-13). Both North and South columns exhibited signs that they had been damaged in flexure. The cracks on the cap beam did extend further, and a flexure crack at the East end was visible. During this run, there was a loud sound and several of the strain gauges registered a sudden shift in their base line and read further residual strain. The strain gauge readings of the column steel indicate that the steel in the East column had yielded. The next run to be done was a 60%, 0.42g (0.12 g scaled to the prototype bent). The frequency decreased to 5.51 Hz, and new cracks occurred, which are marked in orange on the photographs (Appendix C, photo C-14). Some of the column cracks extended slightly, and again the steel in the East column was yielding whereas the West column remained elastic. This unsymmetric behaviour was probably due to the initial damage described before. Two flexure cracks appeared in the East end of the cap beam on the North face. Several of the strain gauges in the cap beam, located close to the shear cracks that had occurred, showed yielding. The run at 80% decreased the frequency to 5.27 Hz, and the cracks that occurred were marked in black (Appendix C, photo C-14). There was no significant new crack formation apart from one further shear crack on the East end of the cap beam, and the cracks that were already present did elongate. The 120% run incurred significant damage with spalling of the concrete from the 86 Test Results shear crack on the West end of the South face of the cap beam. Some of the steel was exposed. Further cracking of the columns occurred, which is marked in pink (Appendix C, photos C-15, C-16).. More shear cracks appeared in the cap beam at both ends. The frequency of the bent reduced to 4.47 Hz. At this stage, it was considered that the bent was seriously damaged, but one further run was performed to finally fail it. The last run at 150% or 1.05g (0.3 g at the prototype scale) was performed, and it rendered the bent unsafe for further testing. The frequency reduced significantly to 3.57 Hz. There was a large amount of concrete spalling from the East end of the cap beam, steel was exposed, and two of the stirrups were broken. There was debonding of the concrete along the top and bottom reinforcement in the regions of the cut off points. The columns suffered further damage, but no spalling occurred. The cap beam was disjointed close to the ends due to the shear cracking, and the middle section dropped several millimetres. It was considered that the bent had failed and that testing should stop at this point. 8.2 Hammer Test Results The hammer impact testing was used to estimate the first mode natural frequency after each run. The results show that there was a steady deterioration of the natural frequency from the initial value of 7.76 Hz to 3.56 Hz after the final run, a reduction of over 50%, see figure 8.1. The output sensors were four accelerometers that were located along the cap beam and one at the base of the West column, see figure 7.6. It was found that the results from any one of the four accelerometers could be taken as representative of the first natural frequency of the bent in the longitudinal direction even after significant damage had occurred. Details of the hammer tests are given in Appendix D. 87 Test Results It can be seen that there was a significant reduction in the frequency after the unplanned actuator movement occurred in between the third and fourth runs at 10% (10b and 10c), indicating that damage did occur. The frequency was steady during runs at the same level of 10%, but there was a reduction of almost 1Hz when the magnitude was increased to 20%. Between this level and the 80% level there was a steady but slight reduction, reflecting the fact that there was further damage, but no very large cracks appearing. For the last two runs of 120% and 150% there was a reduction of almost 1 Hz after each, showing the damage occurring was severe. Figure 8.2 shows an FRF plot of the first natural frequency after the run at 0.42g. 1 -• o J 1 1 1 1 1 1 1 1 1 1 o o ® o o *~ *~ Run Am pl l tuda (% of 0.7g) Jerk* is shake table jerk Figure 8.1 Frequency vs. Run Amplitude 3 . 5 0 2 4 5 5 2 6 8 10 Frequency (Hz) Figure 8.2 FRF of Hammer Test after 60% Run 88 Test Results This thesis does not deal with the correlation of reduction of fundamental frequency to the increase in damage in a quantitative sense, but it is clear, qualitatively, that there is a very strong correlation between the two parameters. Further work on the quantitative significance of these results could be carried out using modal damage indices. 8.3 Bent Performance 8.3.1 Cap beam acceleration and displacement The data recorded from the shake table test was conditioned for further analysis. The offset on all readings except for strain gauges was removed. The offset was not removed for the strain gauge data as this offset indicated the amount of residual strain present in the steel. The data acquisition software in the Earthquake Engineering Research Laboratory had already filtered the data, see Appendix B. Detailed data from the 10%, 40% and 150% runs is given in Appendix E In this section, figures in parentheses are values for the prototype bent scaled from the 0.27 scale test. It was observed that in each run both the acceleration and displacement of the cap beam were significantly larger than that of the table. The absolute acceleration at the cap beam was magnified typically by a factor of two or more, while the absolute displacement was magnified by about 50% to 70%. This was expected as the natural frequency of the bent placed it in the region of a peak of the acceleration response spectrum of the Landers time history record. Figure 8.3 shows the table and bent relative displacement and absolute acceleration for 0.42g. The relative acceleration of the cap beam was calculated in order to get an indication of the level of dynamic amplification of the acceleration. At low values of acceleration such as 0.28g (0.08g), the acceleration at the level of the cap beam and masses was of the order of lg (0.29g). The 89 Test Results relative acceleration did not increase proportionally as the absolute acceleration did. This could be because as the structure weakened, its acceleration response increased until the natural frequency reached about 5.2 Hz. At this point the natural frequency was on the descending arm of the first peak of the response spectrum, so the acceleration response decreased and the natural frequency decreased further. However, at the levels of 120% and 150% the acceleration at the mass and cap beam did reach values of 2.0g (0.58g), resulting in high forces in the structure. 2.00 -O) CO o.oo -2.00 -2.00 —, 0.00 -2.00 20.00 E E •8" 0.00 E E CL TJ "55 -20.00 20.00 0.00 -20.00 10 15 20 25 Time [sees] 30 35 40 Figure 8.3 Table and Bent Relative Displacement and Absolute Acceleration for 0.42g (60%) 90 Test Results The values for relative displacement were also calculated. The values steadily increased from 4mm at 0.07g (15mm at 0.02g) to 36mm at 1.05g (133 mm at 0.30g). At the 120% level run it can be seen from the relative displacement record that there is some residual displacement of the order of 1mm (3.7mm) left in the cap beam. At the end of the 150% excitation the residual displacement was 2.5mm (9.25mm) at the cap beam and 4mm (14.8mm) at the top of the mass block (figure 8.4). -40.00 —| 1 1 1 1 1 p 1 1 0 5 10 15 20 25 30 35 40 Time [Sees] Figure 8.4 Bent and Mass block Residual Displacement after 150% (1.05g) 91 Test Results 8.3.2 Hysteresis curves Hysteresis curves, inertial force vs. bent displacement, were plotted for each level of excitation. The inertial force was found by multiplying the acceleration of the mass block by its mass. The response remained basically linear until towards the end of the 80% run (0.56g - 0.16g when scaled). In the two subsequent runs, 120% and 150% the curves opened up significantly and energy absorption due to shear cracking and yielding of steel can be seen. Figures 8.5 and 8.6 show the difference between an early elastic hysteresis curve and the final one at 150%. The data was not smoothed, so the hysteresis curves reflect all the variability of the time history. In chapter 9 (figure 9.3 and 9.4) plots are given which give a force-displacement history for the bent. These plots were found using data from the hysteresis plot for each seismic run. -80 — -120 — Figure 8.5 Hysteresis Loops from the 20% (0.14g) Run 92 Test Results Figure 8.6 Hysteresis Loops from the 150% Run The peak force of 104 kN (1426 kN) was reached at the 120% level. After this point the bent had weakened sufficiently so that in the 150% run it had very large deflections, but did not attain a large force. The hysteresis curves also show the progressive stiffness degradation of the bent. The first runs have a steeper slope, showing less deflection for a given force, than the last ones. In the final run, a peak relative displacement of 36mm (134mm) achieved at a force of 72kN (987kN). 8.3.3 Frequency response The frequency response of the bent during each run was obtained by performing a FRF for various parameters. The table excitation was used as input, and the parameter of interest was used as output. As an FRF analysis is best performed on linear data, the high intensity shaking 93 Test Results runs were windowed for the analysis. For runs of 40% or higher, a window at the start and end shaking was analysed. The parameters examined included absolute and relative accelerations and displacements at the cap beam level. There is a clear peak in the region of 2-6Hz, depending on the run, another around the 12-16Hz level. Beyond this level there are many peaks, which cannot be concluded as defining natural frequencies. Figure 8.7 shows the results from a windowed FRF analysis of the bent absolute acceleration during the last 10 seconds of the 0.42g (60%) run. Figure 8.8 shows the first natural frequencies for both the hammer test (discussed in section 8.2) and from the FRF analysis of the shake table test results. Comparing the frequencies obtained by the impact hammer and from the shake table run, it is clear that those from the shake table are significantly lower. At the start of testing the difference between the two determined natural frequencies was insignificant. However, at the fourth run at 10% (lOd) the hammer frequency was about 0.1 Hz greater than that calculated from the FRF, 6.67Hz as opposed to 6.58 Hz. The difference between the two increased slightly so that after the final run it was of the order of 1Hz, 3.57Hz as opposed to 2.48Hz. 300 250 | 200 1 •o S 150 4-c S 100 I 50 + 0 0 2 4 4.42 6 8 10 12 Frequency (Hz) Figure 8.7 FRF of Bent Absolute Acceleration after 0.42 run (60%) 94 Test Results 9 8 7 + _ 6 N X > 5 + o c 3 4 cr £ u. 3 2 1 0 hammer - shake table •2-o .o, o o o o CO ° 8 Run Amplitude (%of 0.7g) Figure 8.8 Natural Frequencies From Hammer and Shake Table Test The hammer imparted a force to the bent that was sufficient to produce a very low level of excitation, but not to cause real movement of the structure. On the other hand, the table excited the bent so that it moved, caused cracks to open and close and react in its damaged mode of behaviour which is more flexible. The hammer did not excite the bent strongly enough to exhibit its full damaged state, and the friction within the cracks will increase the stiffness of the frame for this level of excitation. Therefore, it is to be expected that the frequencies obtained from the hammer impact would not be as low as those obtained by the shake table which account for the full damage. This is thought to be a large factor as to why the frequencies are lower from the table excitation. FRF analysis of some of the strain gauge records was also performed, and they all show a first significant peak at the first natural frequency of the structure; a representative plot is shown in figure 8.9. After this first peak the results are not clear enough to obtain subsequent frequencies. 95 Test Results 0.60 0.50 oi 0.40 •a | 0.30 | 0.20 0.10 0.00 0 5 10 15 20 25 Frequency (Hz) Figure 8.9 FRF of T3 Strain Gauge at 60% level (0.42g) 8.3.4 Strain gauges Recordings from the strain gauges yielded information about the internal stresses in the cap beam and column. In general, the strain gauges worked well, with good information being produced until the last run, where several of them exceeded their strain limits and stopped functioning. The traces of many of the strain gauges show significantly more movement in one direction than the other. In most cases the bias is towards the tension side. This is to be expected, as only the steel resists the force when the section is in tension, causing a large strain, whereas when the section in is compression, the concrete is also acting, so the steel will be less severely stressed. As the testing progressed there were residual stresses left in many of the gauges, most notably the ones in the regions of cracking. The first steel to yield were B l and B2, shown in figure 4.1, at the 40% level (0.28g , 0.08g scaled to prototype level), which is located in the bottom steel at the West end of the cap beam. It was in this region that the large shear crack occurred. At this level, the steel in the East face of the East column also yielded. As the excitation level increased, 96 Test Results so further steel yielded, until at the final run all the strain gauges except those at the middle of the cap beam and in the top steel at the end of the cap beam had yielded. Figure 8.10 shows the progression of one strain gauge B8 (bottom steel East end of cap beam) from unbiased at the 10% level, through biased and almost yielding at the 40%, to large strain with residual at the 150% level. It is evident that the strain gauges can indicate where large sudden damage occurs. These instances of damage are reflected in sudden jumps of the base line, showing that there was some residual strain induced in the steel. This can be seen at the 150% level for B8. 0 3 • a) 0.2 —I I O . l -i 0 0 ~ 1 - O . l --0.2 --0.3 -1 -0 --1 --2 — 1 b) 15 10 5 0 -5 •10 •15 C) 10 15 20 Time (Seconds) 25 30 Figure 8.10 Strain in B8 Strain Gauge for a) 20%, b) 40% and c) 150% runs 97 Test Results 8.3.5 Tie-down force variation The variation of force in the lateral tie-downs was monitored using a strain gauge attached to one of the turnbuckles. The readings from the tests indicate that the initial force was 4.4 kN, and it fluctuated about this level. There was little change in axial force at the low levels of excitation, as shown in figure 8.1 la. As the magnitude of shaking increased, so did the variation in axial force. At the 60% level, the force reached a maximum of 7.7 kN and a minimum of 2.7 kN. At the 120% level, the maximum force of 11.9 kN in the tiedown was achieved. This axial force corresponds to a force of 2 kN in the longitudinal direction of the bent, so it can be seen that the restoring force due to the tiedowns was minimal, of the order of 1% of the longitudinal inertial force. The tiedown readings for the 10%, 60% and 120% runs are shown in figure 8.11. 8.3.6 Torsion By analysing the readings from the out of plane accelerometers at either end of the cap beam, the torsional movement of the bent can be examined. When the readings are in phase, the bent is moving uniformly from side to side, when the readings are out of phase, the bent is twisting in a torsional mode of vibration. Figure 8.12 shows the readings from the 10%, 60% and 120% runs. Note that each graph is only one second in length. It can be seen that in the 10% and 60% runs the readings alternate between in phase and out of phase at a frequency of about 5 Hz, and that the frequency of the individual peaks is much higher, at about 35 Hz. From this it can be deduced that there was some interaction of different modes of vibration present. At the 120% level the readings seem to be mostly out of phase, indicating that torsion is the predominant out of plane mode. The peak acceleration level in the out of plane direction reaches 2g, which is comparable to those experienced in the longitudinal direction. However, as the frequency is so much greater, the displacements out of plane were not large. From figure 8.12 it can be observed that the frequency of vibration decreases as the magnitude of vibration increases. 98 Teat Reaulte Test Results Figure 8.12 Torsional Motion at the a) 10%, b) 60% and c) 120% Levels 100 Test Results 8.3.7 Vertical Motion The vertical acceleration of the bent was monitored at both ends of the mass block. Figure 8.13 shows one second of the readings from these accelerometers during the 10%, 60% and 120% runs. At the 10% level it can be seen that the bent is pitching as the readings are out of phase. Some interaction between modes, seems to be present as the wave form has a periodic irregularity, and alternates between out of phase and somewhat in phase. At the 60% and 120% levels the recordings are mainly out of phase, and the interaction is not so obvious. The readings are sometimes in phase, which could be due to modal interaction, but at a lower frequency than observed at the 10% level (2 Hz at 120% level, as opposed to 6 Hz at the 10% level). The magnitude of the vertical acceleration is generally less than 0.5g, except for some high frequency spikes of large magnitude. As with the out of plane motion described in 8.3.6, the frequency of vibration decreases from 40-50 Hz at the 10% level, to about 15-20 Hz at the 120% level. This is consistent with the reduction in natural frequency in the longitudinal direction. 8.3.8 Acceleration Transmission The transmission of the acceleration excitation from the table to the bent, and from the bent to the mass block was examined. Readings from the table accelerometer were compared with those from an accelerometer located above the hinge connection, and readings from the cap beam accelerometer were compared with those from one on the mass block. The effect of the hinge connection seems to be to filter out high frequencies from being transmitted into the structure. Figures 8.14 and 8.15 show comparisons between these two readings at the 20% and 120% level respectively. It can be seen that the high frequency content of the table acceleration is not present in the bent base. This does not significantly affect the magnitude of the acceleration present, except for the absence of some high frequency spikes that are filtered out. 101 Test Results Figure 8.13 Vertical Movement in the Bent at the a) 10%, b) 60% and c) 120% Levels 102 Test Results 0.40 — i Time [Sees] Figure 8.14 Section of the Table and Bent Base Accelerations at the 20% Level .a) a o S JD <D O O < 15.00 Table Bent base Time [Sees] Figure 8.15 Section of the Table and Bent Base Accelerations at the 120% Level The connection between the cap beam and mass block seems to have the same effect in stopping the transmission of high frequencies to the mass block, see figure 8.16. Again, this does not affect the magnitude of the accelerations experienced by the mass block, except for during some high frequency peaks. 103 Test Results 1.50 Time [Sees] Figure 8.16 Section of the Mass Block and Cap Beam Accelerations at the 120% Level 8.4 General Remarks In this chapter a sample of the test data is given. In Appendix B a key is given to access the data files, both calibrated and uncalibrated, of all the test data. Copies of the data files are available on request from the Earthquake Engineering Research Facility, University of British Columbia. 8.4.1 Shake table performance The shake table test was successfully performed, at increasing levels of excitation, until failure of the bent occurred. Although there were some problems with the accuracy of the shake table input at the beginning of the test program, corrective measures were taken to eliminate this. The experience provided by this test was very useful, as now certain ways of avoiding this type of problem have been detected so it should not be repeated in the future. The maximum force output by the table was 116.9 kN during the 120% run. This force was 78% of the table capacity. The table peak acceleration was 1.6 g, and peak displacement was 34.5mm. 104 Test Results The shake table was able to cope well with both the high loading on the table and the relatively high acceleration demands required, which was uncertain at the outset of the test. There was no decrease in accuracy or performance at the high levels of excitation, which should increase the level of confidence in the shake table and its capabilities for large scale testing of heavy specimens. 8.4.2 Video data Two video cameras were used, a high speed one focused on the West end of the cap beam, and a Super VHS camera on the overall specimen behaviour. The SVHS camera worked well, although at low levels of excitation the movement of the bent was so small that little useful information was obtained. The resolution of the high speed camera was such that it was incapable of detecting small cracks. Useful information was only obtained on the last two runs, at 120% and 150%. At these levels it was possible to see the individual cracks open and close and concrete spall. The original speed of 1000 frames per second was recorded onto VHS film at a rate of 1 frame per second so that a better idea of the behaviour could be obtained. It was not possible to detect the progression of anything but the larger cracks, but it was felt that this was helpful in seeing how the damage developed in at least one portion of the bent during the test. Figures C-19 - C-24 in Appendix C show the South face of the East end of the cap beam during the excitation as recorded on the high speed camera. 105 Discussion of Results Chapter Nine DISCUSSION OF RESULTS In this chapter the results from the experiment are discussed with respect to the slow cyclic tests that were performed on the 0.45 scale specimen. The results are briefly compared to the analytical predictions. A companion study (Khoshnevissan, 1997) is in progress and will detail analytical predictions and results of this test program. In this section all the values for force and displacement presented, whether for 0.45 scale or prototype bent, are scaled to the 0.27 scale except where otherwise stated. 9.1 Comparison to Slow Cyclic Test 9.1.1 Structural behaviour and failure mode The slow cyclic bent (SC bent) was loaded to a base shear of 52.9 kN at a displacement of 1.8mm, at which point it first started to show signs of cracking, these being shear cracks in the cap beam. Results for the SC bent are taken from Anderson et al. (1995). In the shake table bent (ST bent), apart from the cracks caused during the unplanned movement, the first cracks appeared after the 20% or 0.14g run. The inertial force achieved during this run was 68 kN. As it is impossible to know when during this run the cracks first appeared, it is difficult to ascertain what the force was to first cause cracking. However, the strain gauges show that there is a shift in the base line after the first burst of strong motion, which is where the 68 kN inertial force occurred, so it is likely that this is the point where cracking occurred. 106 Discussion of Results In the SC bent cracking continued up to a peak force of 96.5 kN at a displacement of 9.9 mm, at which point the strength of the bent started decreasing until it failed at a displacement of 19.2mm. The ST bent continued to crack until it reached an average peak force of 93 kN at the 80% level, although a peak of 133.3 kN did occur at the 120% level. The displacements at these forces exceeded those in the SC bent, being 11.5 mm and 13.6 mm respectively. The ultimate displacement of the ST bent was 36 mm. From these values of force and displacement it appears that the ST bent was both stronger, and suffered less degradation of strength than the SC bent. The failure of the two bents in general was the same - due to shear failure in the cap beam. There was a large amount of concrete spalling in the region of the shear cracks in both cases, although more in the SC test. The SC bent did experience extensive debonding of the top steel due to insufficient vertical reinforcement, while this behaviour was only exhibited to a small extent in the ST bent. The distribution of cracking seems to be more evenly distributed in the SC bent, indicating that damage was uniformly spread throughout the affected regions, whereas in the ST bent there were fewer, less closely spaced cracks, see Appendix C, figures C-25, C-26. It has been noticed in other tests (e.g. Abrams, 1984, Abrams, 1987) that the crack patterns are similar, but more diffuse in the larger scale static or slow cyclic tests, than in the dynamic tests. 9.1.2 Hysteresis loops Comparisons were made between the envelopes of the hysteresis curves from both the SC and ST tests. In the former, the load was the base shear applied, while in the latter the load was the inertial force induced by the acceleration of the mass block. Due to the irregular nature of the earthquake excitation two forms of curve were produced from the shake table results. The first of these used an average slope from the hysteresis loops and found the maximum point on this line, 107 Discussion of Results the second took the maximum force and the corresponding displacement on the plot. For the difference between these values see figure 9.1. As the bent had already been somewhat damaged due to the unintentional impulse, the frequency and stiffness of the bent had decreased. This meant that the initial stiffness of the bent was not evident from the hysteresis plots. The original stiffness was calculated by relating the change in frequency, which had been measured, to the reduced stiffness. The dashed line in the load deflection curves (figures 9.3 and 9.4) shows this deduced initial stiffness. Peak value method -200 — Figure 9.1 Two Methods of Obtaining Values for Force-Displacement Plot Figure 9.2 is the load deflection curve using the values from the average slope. The initial slope of the shake table test results is less than that of the slow cyclic test, but the deduced initial slope is very similar. If the peak values are used, figure 9.3, it can be seen that the deduced initial slope is higher than that of the slow cyclic test. It was expected that the initial stiffness could be greater in the shake table test due to strain rate effects, and the comparison of the slopes shows that this effect is present to some degree. 108 Discussion of Results If the average slope values are used, the peak load achieved in each test is very similar, although the corresponding deflection in the shake table test is greater, as shown in figure 9.2. This would indicate that early during the test the ST bent suffered a more significant loss in stiffness and strength than the SC bent, although at larger deflections the ST bent was capable of retaining more lateral load carrying capacity. The reduced stiffness degradation has been suggested to be a result of reduced spalling during shake table tests, as opposed to slow static ones, (Moncaza and Krawinkler, 1981). As mentioned in chapter 6, the increased ratio of surface to cross-sectional area of the reinforcing bar due to scaling, could reduce the stiffness degradation, as relative bond strength would be increased. The load deflection curve from the peak values (figure 9.3) shows that the ultimate load achieved during the ST test was significantly greater than that in the SC test (143% of the SC peak strength). This could be due to a number of reasons: Firstly, the method of testing could affect the strength of the structure. It has been observed before (Abrams, 1984) that the strength from dynamic testing can be appreciably greater than from static testing. It must be noted that the concrete strength of the SC specimen was 47.5 MPa, whereas for the ST bent it was 40.5 MPa. Although the reinforcing steel strength of the ST bent was stronger, this was accounted for by a reduction in steel area (section 2.2.3). Despite this fact, the ST bent was stronger than the SC one, indicating that the effects due to the nature of testing are significant. It was also noted by Abrams that the observed damage in the shake table tested specimen was much less than for the static specimen, even though the shake table specimen resisted more force. This phenomena was observed when the behaviour of the SC and ST bents was compared. One of the results of this is that the static test creates a more demanding environment than an actual seismic event, and should be viewed as a more conservative method of testing. 109 Discussion of Results Figure 9.2 Load Deflection Curve Using Average Slope 140 j 120 -100 -z 80 • » ore 60 u. 40 20 0 1 0 15 20 25 Deflection (mm) -shake table test peaks • slow cyclic initial stiffness 30 i 35 40 Figure 9.3 Load Deflection Curve Using Peak Values If the average slope values are used, the load deflection curves are very similar, both for stiffness and, if the calculated initial stiffness is used, for strength. If the peak values are used, the initial stiffness is higher, again using the calculated stiffness, and the peak strength is also larger. This 110 Discussion of Results increase in stiffness and strength is a result that is expected, mainly due to strain rate effects on the material properties. 9.1.3 Genera l comments The failure mode of the OSB bent, whether tested on a shake table or slow cyclically, was due to shear in the cap beam. The differences in behaviour due to strain rate effects, reduced spalling and increased bond strength, were observed by looking at the load deflection curves. In general, the testing methods compare well, although the shake table does give a more realistic idea of the behaviour of a specimen under seismic loading. This is due to the inherent characteristics of this type of test, such as real time simulation. 9.2 Expected Prototype Behaviour The performance of the 0.27 scale bent can be related to the prototype bent using the scaling factors calculated in chapter 2. From this, it is possible to determine the peak ground acceleration (PGA) and forces it might withstand. The maximum size earthquake the bent was subjected to was the 150% which corresponded to a PGA of 0.3g at the prototype scale. The PGA expected in Vancouver during the characteristic earthquake (476 year return period) is 0.21g according to the Canadian Earthquake Code, (NBCC, 1995). However, this value is then combined with factors for importance (1.5) and soil (1.3), so the actual PGA being designed for at the Oak Street Bridge is 0.41g. From this, it is clear that the bridge would not withstand the design earthquake, which is why retrofit schemes are being undertaken. The size of model is such that the results obtained from the tests are relevant to the prototype, and not seriously compromised by scaling effects. A common result of excessive scaling is that the strength degradation in the scale model is very fast, but by comparing the SC bent with the 111 Discussion of Results ST bent, it is clear that this was not the case. Very localised failure can be another problem with scaling models, but this did not occur in the 0.27 scale bent. The accidental loading that occurred inflicted damage on the structure in the locations at which the bent was expected to fail. The effect of this early damage was to increase the ductility of the bent at low levels, so that the stiffness of the bents cannot be easily compared. The damage also resulted in further damage occurring in the locations where the cracking had occurred, which restricted the location of crack formation. 9.3 C o m p a r i s o n to P r e d i c t i o n s Detailed comparisons are part of a companion study conducted by Khoshnevissan (1997). 9.3.1 DRAIN-2DX DRAIN-2DX was used to give some preliminary information about the peak ground acceleration required to cause the bent to fail. The natural frequency of the DRAIN-2DX model was 7.35 Hz, which was very similar to that recorded 7.77 Hz. The model had been tested with varying levels of the Joshua Tree record, and the predicted PGA for failure was 0.69g. The bent tested on the shake table failed at 120% of this value, 0.828g. There had been some uncertainty as to the exact predicted failure level, as a shear failure was expected and the calculated shear capacity of the cap beam had some variation in it. The predicted failure at 0.69g had assumed a low shear capacity, however, since the PGA to cause failure was higher than this, it is reasonable to assume that the shear capacity was somewhat underestimated. The DRAIN-2DX model had indicated that there would be yielding in the columns at this level of excitation and the formation of plastic hinges at about 0.81g. During the final shake table test the columns were hinging, so this estimate by the program was correct. The bent was not predicted to have failed, but this is because the program does not deal with failure in shear. By 112 Discussion of Results looking at the DRAIN-2DX shear demands in the cap beam, the forces present were such that they were within the envelope for shear failure. 9.3.2 I D A R C and C A N N Y - E The IDARC analysis predicted that there would be a sudden failure at about 0.2g (prototype level) or 0.725 at the 0.27 scale. The failure occurred at 150% of this value, which is within the limits of reasonable error. However a sudden failure had been predicted by the program, but this did not occur. It was suggested that this discrepancy could be due to an error in the program or in its implementation, and was shown by the test results to be the case. The program did not predict the failure level or degree of damage well. The model used in the CANNY-E program had a natural frequency of 10.17 Hz which is higher than that recorded. This could be due to the way in which the pin connections were modelled. The program predicted that there would be failure at 0.7g, which underestimated the PGA at which the bent did fail. This discrepancy could be due to the prediction of shear damage, which is notoriously difficult, or some details in the methods of modelling. This is discussed in more detail by Khoshnevissan (1997). In general, the programs did predict failure at a PGA about 20% lower than that at which it did occur. As observed, the peak load which the bent supported was larger than that withstood by the bent that was tested slow cyclically by about 43%. If this difference were caused mainly by strain rate effects, this could be a reason for the difference between the actual and predicted level of PGA, as the computer programs do not account for this effect. 113 Conclusions and Recommendations Chapter 10 CONCLUSIONS AND RECOMMENDATIONS 10.1 Conclusions A shake table testing program of a 0.27 scale model of an Oak Street Bridge bent was successfully carried out. The aims of this program were: to identify damage, failure modes and dynamic characteristics of the bent, to compare the experimental results with the analytically determined values of damage index and dynamic characteristics, to relate the experimental results to the results from the earlier larger scale slow cyclic tests, and to gain further insight into the operating characteristics of the recently upgraded digitally controlled shake table. The conclusions that can be drawn from the test are: A) Regarding specimen behaviour • A test set-up was designed which was unelaborate, reusable and allowed a good simulation of the prototype situation. • The overall behaviour of the bent was predicted using DRAIN-2DX and CANNY-E with reasonable accuracy. The failure load was underestimated by about 20%, which could be due to strain rate effects, as this increases the strength of the materials tested under dynamic loading. • The behaviour of the bent was linear until a PGA of 0.54g, and it failed at 1.05g. This ultimate PGA, scaled to the prototype scale, corresponds to a PGA 0.3g. The characteristic earthquake has a PGA greater than this value, so it is expected that the prototype would not withstand the characteristic earthquake. 114 Conclusions and Recommendations • The natural frequency of the bent was determined by an impact hammer test. The results from the hammer test indicated a higher frequency than that determined from FRF analyses of the bent response during the shake table test. This could be due to the different levels to which the hammer and shake table tests excite the structure to determine the frequency. • The modes of failure of the bent from the shake table and slow cyclic tests were similar, both being due to a shear failure of the cap beam. • The hysteresis curve determined from the shake table test indicate that the behaviour of the bent was stronger and stiffer than that exhibited by the bent that was tested slow cyclically. B) Regarding testing method • A scale model shake table test was conducted, and the expertise developed by the staff and faculty involved in the area in UBC will be valuable in further testing programs. • The high speed camera was useful in the identification and monitoring of large cracks and concrete spalling. • Certain problems with the operation of the shake table were identified and corrected, so that this type of test may be conducted with few problems in future. 10.2 R e c o m m e n d a t i o n s The shake table test produced a large amount of data, the detailed analysis of which was outside the scope of this thesis. There is a wide variety of work that could be done using this information, and following up with further testing. Some of the possibilities are: • Detailed analytical analysis of the behaviour of the bent, including damage index calculations related to the observed behaviour. • Correlation of the natural frequency degradation with the onset and development of damage. 115 Conclusions and Recommendations • Examination of the differences between the natural frequencies of the specimen obtained from hammer testing and shake table tests, and determination of reasons for the discrepancies found. • Testing of a retrofitted bent, and comparison of if s behaviour with results from this test and the slow-cyclic retrofit tests that were previously conducted on 0.45 scale bents. • Further investigation into strain rate effects on material properties and at what point they assert a significant influence on the behaviour of concrete. • Research into improved damage indices for shear failure. 116 References References Abrams, D.P., Tangkinjamvong, S., 1984, "Dynamic Response of Reduced-Scale Models and Reinforced Concrete Structures", Proceedings of the 8th World Conference on Earthquake Engineering, Vol. 6 , pp371-375,International Association for Earthquake Engineering, San Francisco, Prentice Hall, Inc. New Jersey. Abrams, D.P., 1987, "Influence of Axial Force Variations on Flexural Behavior of Reinforced Concrete Columns", ACI Structural Journal, Title No. 84-S26, May/June, American Concrete Institute, Detroit. Abrams, D.P., 1987, "Scale Relations for Reinforced Concrete Beam-Column Joints", ACI Structural Journal, Title No. 84 - S52, November/December, American Concrete Institute, Detroit.. Abrams, D.P., 1988, "Dynamic and static testing of Reinforced Concrete Masonry Structures" Proceedings of the Ninth World Conference on Earthquake Engineering, August 2 -9, Tokyo-Kyoto, Japan, Vol. 6 ppl69 - 174, Japan Association for Earthquake Disaster Prevention, Missei Kogyo Co., Ltd. Abrams, D.P., 1996, "Effects of Scale and leading Rate With Tests of Concrete and Masonry Structures", Earthquake Spectra, Vol. 12, No. 1, Feb. (The Professional Journal of the EERI, Oakland California) ppl3 - 28. ACI 1992," Building Code Requirements for Reinforced Concrete", and Commentary - ACI 318R-89, American Concrete Institute, Detroit, MI. ACI/ASCE Committee 426, 1978, "Suggested Revisions to Shear Provisions for Building Codes", American Concrete Institute, Detroit, pp.88. Anderson et al, 1995, 'Oak Street and Queensborough Bridges Two Column Bent Tests', Technical Report 95-02, Earthquake Engineering Research Facility, Department of Civil Engineering, University of British Columbia, Vancouver. Bertero, V., Aktan, A.E., Charney, F., and Sause, R., 1985,' Earthquake Simulator Tests and Associated Experimental, Analytical, and Correlation Studies of One-Fifth Scale Model', Earthquake Effects of Reinforced Concrete Structures U.S. - Japan Research, American Concrete Institute, Detroit, MI, pp375-424. Bresler, B., and Bertero, V.V., 1975, "Influence of High Strain Rate and Cyclic Loading on Behavior of Unconfined Concrete in Compression", Paper 14, Second Canadian Conference on Engineering, McMaster University, Canadian National Committee for Earthquake Engineering of the National Research Council, Ottawa. 117 References Collins and Mitchell, 1991, "Prestressed Concrete Structures", Prentice-Hall, Englewood Cliffs, NJ. CSA 1985, " CSA Standard CAN3-A23.3-M84" Canadian Standards Association, Roxdale, Ontario. El-Attar, A G . , et al, 1991, "Shake table test of a 1/6 scale two-story lightly reinforced concrete building", NCEER-91-0017., technical report, Buffalo, NY. Elnashi, AS. , Pilakoutas, K., and Amvraseys, N.N., 1990, "Experimental behavior of reinforced concrete walls under earthquake loading'', Journal of Earthquake Engineering Structural Dynamics. Vol 19, 389-407 ENR 1995, Engineering News Record, Jan. 16, Mc Graw-Hill, New York. Experimental Stress Analysis Notebook, 1987, Measurements Group Inc. Issue 6 - May, Raleigh NC. Earthquake Design Code 1995- Section 4 and Commentary J, "National Budding Code of Canada", National Research Council of Canada, Institute for Research on Construction, Ottawa, 571 pp. Filiatrault, A , 1985, "Performance evaluation of friction damped steel frames and under simulated earthquake loads", Thesis for M.A.Sc. degree, Dept. of Civil Engineering, University of British Columbia, Canada. Handbook of steel Construction, 1989, Canadian Institute of Steel Construction, Universal Offset Limited, Markham, Ontario. Harris, H.G., 1982, "Dynamic Modelling of Concrete Structures", Publication SP-73, American Concrete Institute, Detroit, MI, 242pp. Hidalgo, P., and Clough, R.W., 1974, "Earthquake simulator study of a reinforced concrete frame", EERC 74-13. University of California, Berkeley. Hiraishi H., Nakata, S., Kitagawa, Y , Kaminosono T., 1985, "Static Tests on Shear Walls and Beam-Column Assemblies and Study Correlation Between Shaking Table Tests Pseudo dynamic Tests", Earthquake Effects of Reinforced Concrete Structures U.S. - Japan Research, American Concrete Institute, Detroit, MI, pp 11-48. Khoshnevissan, M., and Kang-Ning Li; 1996, Private communication. 118 References Khoshnevissan, M., 1997, thesis in progress at the University of British Columbia, Canada. Krawinkler, H., 1978, "Experimental Research Needs for Earthquake-resistant Reinforced Concrete Building Construction", Proceedings of the workshop on earthquake-resistant concrete building construction, University of California, Berkeley. Krawinkler, H., Zhu, B., 1993, "U.S./P.R.C. Workshop on Experimental Methods in Earthquake Engineering", Proceeding of a workshop held in Shanghai, P.R.C., November 1992, Report No. 106, The John A Blume Earthquake Engineering Center, Department of Civil Engineering, Stanford University, 241pp. Kunnath, S.K., Reinhorn, A M . , Lobo, R.F., 1992, " IDARC Version 3.0: A Program for the Inelastic Damage Analysis of Reinforced Concrete Structures", Department of Civil Engineering, State University of New York at Buffalo and Department of Civil and Environmental Engineering, University of Central Florida, Technical Report, NCEER-92-0022. Latendresse, V., 1997, thesis in process at the University of British Columbia, Canada. Li,Kang-Ning, "CANNY-E and Users' Manual, 1995, Nonlinear Dynamic Structural Analysis Computer Program Package", Canny Consultants PTE Ltd., 12 Prince Edward Road, #04-02 Podium B Bestway Building, Singapore. Macrae, G.A, Hodge, C , Priestly, M.J.N., and Seible, F., 1994, "Shake table tests of as-built and retrofitted configuration", Report No. SSRP - 94/18, Structural Systems Research, University of California at San Diego La Jolla, California. Mirza, M.Saeed, Harris, H.G., Sabnis, G.M., 1979, "Structural Models in Earthquake Engineering", 3rd Canadian Conference in Earthquake Engineering, Vol. 2, p511-550, Canadian National Committee for Earthquake Engineering of the National Research Council, Ottawa. Moncaza, P.D. and Krawinkler, H., 1981, Theory and application of experimental model analysis in earthquake engineering", Report No. 50, The John A Blume Earthquake Engineering Center, Stanford University, California. Naeim, F., and Anderson, James C , 1993, "Classification and Evaluation of Earthquake Records for Design", The 1993 NEHRP Professional Fellowship Report, Earthquake Engineering Research Institute, Oakland, California. Naumoski N., 1985, "SYNTH program, Generation of Artificial Acceleration Time History Compatible with a Target Spectrum". Mc Master Earthquake Engineering Software Library, Department of Civil Engineering and Engineering Mechanics, Mc Master University, Ontario. 119 References Prakash, V., Powell, G.H., Campbell, S., 1993, "DRAIN-2DX, Base Program Description and User Guide", Version 1.10., Berkeley, CA, Earthquake Engineering Research Center, University of California. Seethaler, M., 1995, "Cyclic Response of Oak Street Bridge Bents", Masters Thesis for the University of British Columbia. Seyed, M. 1992, "BEAM303, V3.03", Special Analysis Section, CALTRANS and Version 3 enhancements by Lee D, Special Analysis Section, CALTRANS, California Department of Transportation, Sacramento. Seyed, M. 1992, COL604 V6.04. Special Analysis Section, CALTRANS, California Department of Transportation, Sacramento. de Silva, C , 1989, 'Control Sensors and Actuators', Prentice-Hall, Englewood Cliffs, NJ. Villemure, I., 1995, "Damage Indices for Reinforced Concrete Frames: Evaluation and Correlation", Master Thesis at the University of British Columbia. Williams, Martin S., 1994, "Inelastic Damage Analysis of the Oak Street and Queensborough Bridge Bents", Earthquake Engineering Research Facility at the University of British Columbia, Technical Report 94-03. Winsoft Software Inc., 1992, PCA-Frame - General Analysis Software for Structures, VI.00. Wolfgram, C , Roethe, D., Wilson, P., and Sozen, M.,1985, 'Earthquake Simulation Tests of Three One-Tenth Scale Models', Earthquake Effects of Reinforced Concrete Structures U.S. -Japan Research, American Concrete Institute, Detroit, MI, pp 347-373. Yukata Yamazaki, Masayoshi Nakashima and Takshi Kaminosono, 1986, " Earthquake Response Simulation Capacity of Pseudo Dynamic Testing - Experimental Demonstration and Analytical Evaluation", Dynamic Response of Structures, Proceedings of the 3rd Conference, Los Angeles, American Society of Civil Engineers, New York, pp 446-453. 120 APPENDIX A STRUCTURAL DRAWINGS 122 . ru v 0 —• "-• in x x x f D O D m 4 * W J * y I I I , euro ru i n * * « i i i rururu x X m s I ru d 13 i ru x i ro o 0 1 ru —• o —• •-• r-s M v x x £ o n m « » « I ' I ru ru — a. >-_ i o E C m ru 1 o n e ) * * * i i i rururu PQ 2 O i—i I— u UJ ro 5 00 U Z _ l • Ld 3: UJ c* <t to z • I—t CO z Ld i • 1 3 U U £3 • I—I Ld CO o a ON — 1 OJ I n in .—i d z u < a. Ul —' E * - E 3 8 2 B , ID OJ r 00 OJ vO 0> 2 : o SO V i n \0 OJ 00 n 00 n ^ ro z: o 00 < _J CL CJ a Ld Of L— o> - J OJ SYM. ABOUT PIER LDVER RDV UPPER RDW {107 MK. 6 1620 Mk. 2 t 1520 MK; 3 860 MK. 13 ri 290 LI -4BOO--*7O0--1030.0-1920 MK. 5 1765 M K. 4 13B5 MK. 1 J — 907 MK. 12 -T753f= -670*--togso-1265 MK. 11 819 MK. 7. 383 -MK. 10 1265 MK. 11 • 662 MK. 8 — i 601 MK. 9 1 R E I N F D R C I N G P L A N 1 4 - 5 G Q . S T I R R U P S 290.0 _ J 1573 13 Go.. TIES 8 105 nn SPACING. (/.Ul) T l , , i / c f i d 4 i B s R2 i* / • gi i j -*-<! L 1 j • • (dAl) .1 liVHS » dvainid 4 SS4S <a.4fi51? i i i i 1 | > I I N N N « - E C «x o« II 9 4 I a i i f4 H V 91 1 4 I • • 1 v Vi a Hi .ad w e * 8 r i III 13! ?i II i i i * ti • ) e l d > § R§ Bit I ? ; 5 Is 1 i i i i i i i ' ' ' 1 SE " " 3 ji T » i i Is || m % a. § gli s i ! 0 d D O 00 CM (/) lig • UJ — e> o ! a: o Be 1 I EI y it o ii (C_J0 SUS) E3U r°0 8 - H - 4 . b ST S33VdS I « J S - J 1 I7Tt <3 jt-.i * si si * iii i i • i i £ £ • • • • N N N » K B N N N W 4 i I? 14 SIIW_T03 d i TD j f i m an i i i i > > i i i i ii I? 8S hid r * • • ' L • if J « - - -1 • • 1 • i 1 m - i — k • I fc j - - -A uvHS <rl IS \ i l l I * 20 ! •? I l l ; iff - f4 J 9 ^ I'M •Q I E | If =El m i IS > E f> R a. 0 U l {2 a: UJ ( £ K CO O 2 f c 61 U l SSI it rfO KM) dV9 K M Y 1 "5 A P P E N D I X B D A T A S T O R A G E I N F O R M A T I O N A N D T E C H N I C A L SPECIFICATIONS The information in this appendix concerns the data storage, in section B-l, and the specifications on the data acquisition software and hardware, B-2. B-l Data Organisation Copies of the data files are available upon request to the Earthquake Engineering Research Facility, Department of Civil Engineering, CEME BuUding, 2324 Main Mall, Vancouver, B.C., Canada V6R 2Y3. There are three main sets of data from the shake table tests. The first of these is the main database, Labview. It contains the information on the accelerations from the actuators and the structure, displacements of the structure and table, table power output, and the strain gauge readings. The second set of data was recorded on a secondary data acquisition set-up, Global. This database backs-up some of the information on Labview, and has the recordings from the out of plane and vertical accelerometers on the bent, and two strain gauges. The third set of data is that which was recorded for the hammer tests. The impact and output traces were recorded for each set of tests. In the calibrated Labview and Global databases, the data is arranged in columns. The first line of each column contains information on the parameter which the column refers to, and the units to which the data has been calibrated. The following tables give the location and filenames for the data: 127 Table B.l File Key and Location Test Labview Dir. LabCalibrate Dir. GL Dir. Hammer Dir 150%- 1.05g osbent75.dat 105g_75.dat osbent75.zip ben75 120% - 0.84g osbent60.dat 84g_60.dat osbent60.zip ben60, ben60b 80% - 0.56g osbent40.dat 56g_40.dat osbent40.zip ben40 60%-0.42g osbent30.dat 42g_30.dat osbent30.zip ben30 40% - 0.28g osbent20.dat 28g_20.dat osbent20.zip ben20, ben20b 20%-0.14g osbentl0.dat 14g_10.dat osbentl0.zip #4 10% - 0.07g osben05d.dat 035g_05d.dat osben05d.zip hamme05d #3 10% - 0.07g osben05c.dat osben05c.zip ben05c #2 10% - 0.07g osben05b.dat osben05b.zip hamme05b #1 10%-0.07g osben05a.dat 05a.dat * osben05a.zip hammOSa 10% - 0.07g osbent05.dat osbent05.zip hammeOS, hamm05 5% - 0.035g osben025.dat osben025.zip hamme025 * not al l data is calibrated 128 Table B.2 Data Column Key Data column System Information System Information 1 Table Disp. Mass Accel. 2 Bent Disp. Table Accel 3 Table Power Table Disp. 4 Mass Disp. Act #1 Accel. 5 Mass Accel. Act #4 Accel. 6 Base Accel. Act #1 Disp. 7 Bent Accel. Act #4 Disp. 8 Labview S4 strain Global Vert. Accel East 9 SI strain Vert. Accel West 10 T5 strain Trans. Acc. East 11 T4 strain Trans. Acc. West 12 B5 strain empty 13 B4 strain empty 14 T6 strain S3 strain 15 T3 strain Turnbuckle strain 16 B6 strain Displace Up 17 B3 strain 18 T7 strain 19 T2 strain 20 Labview B7 strain Global 21 B2 strain 22 T8 strain 23 T l strain 24 B8 strain 25 B l strain 26 C4 strain 27 C2 strain 28 C3 strain 29 CI strain 30 Act #1 Accel 31 Act #2 Accel 32 Table Accel 129 Table B.3 Channel Settings and Calibration for Labview 3? f o 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 3 3 3 3 8 8 8 8 8 8 8 8 8 8 8 8 8 o o o 3 8 UJ —J CD 8 B-2 Technical Specifications The specifications for the hammer testing equipment and shake table data recording devices are given in this section. The hammer and accelerometer specifications are detailed, along with the number of hits per test and the sampling rate used. Information about the amplifiers, data recording system, filters, digital signal processing software and data storage media used in the Earthquake Engineering Research Facility are given. Hammer Specifications: Model Range Sensitivity Maximum input Stiffness sensor : DYTRAN/model 5803A 12 pound impulse hammer : 5000 lbs (nominal range for +5 volts) : 1.0 mv/lb : 10,000 lbs :1101b///in Resonant frequency : 75 kHz (sensor with no impact cap); Sensor Specifications: Model Full scale range Output range Dynamic range Natural frequency : Kinemetrics FBA-11 : ± 0.5 g : ± 2.5 volts : 130 dB from 0 to 50 Hz 140 dB from 0 to 10 Hz : 50 Hz (damping: 70% critical) 131 Table B.4 Hammer test data: Run # Impacts Sampling Rate 0 2 5% 2 100 Hz 10% a 1 100 Hz 10% b 1 200 Hz Jerk 1 100 Hz 10% c 1 100 Hz 10% d 1 100 Hz 40% 2 100 Hz, 200 Hz 60% 1 200 Hz 80% 1 200 Hz 120 % 2 200 Hz 150 % 1 200 Hz Shake Table Data Processing: The data was first processed with a Bessel 2-pole analogue lowpass filter set at 30 Hz. The data was then passed through an amplifier, the gains of which are given in table B.3. A 16-bit National Institute analogue-digital card was then used to process the data, which was then stored on an IBM PC-486. Further information regarding the details of the shake table systems may be found in Latendresse, 1997. 132 A P P E N D I X C P H O T O G R A P H S O F T H E B E N T F A B R I C A T I O N A N D S H A K E - T A B L E T E S T Figures C. 1-C. 16 are photographs of the bent fabrication and testing. Then there is a series of photographs from the high speed camera which show the South face of the East end of the cap beam during the 150% run. Figure C-l Cap Beam Steel and Strain Gauges Figure C.2 Casting the Concrete Mass Block Figure C.5 Calibrating the Shake Table with the Masses Figure C.8 Hammer Testing 137 138 Figure C . l l Testing Frequency of Axial Tiedowns C-14 North Face of West End of Cap Beam After 80% Run Figure C-l 5 Failed Specimen (North Face) Figure C-19 - C-24: Series of Photos from the High Speed Camera, Taken at 30 Millisecond Figure C-19 Taken at Millisecond 4000 with high Speed Camera Figure C-20 Taken at Millisecond 4030 with High Speed Camera 143 Figure C-21 Taken at Milisecond 4060 with High Speed Camera Figure C-22 Taken at Millisecond 4090 with high Speec Camera Figure C-23 Taken at Millisecond 4120 with High Speed Camera Figure C-24 Taken at Millisecond 4150 with High Speed Camera A P P E N D I X D H A M M E R T E S T D A T A In this Appendix the data on each hammer test is given. This includes the attenuation used, settings, the filters and the sampling rate. 1 1 1 1 1 1 1 1 Oak Street Bent Shake Table Testing ^ Ch5 Ch4 Ch3 Ch.1 Hammer f^inf ' --rdrffiiinrii ' < MI fm • ' vl */-is % : w Ch2 : m i l l s : m B w 1 IOOK hammer testing level 0.025 name be025 1st natural 7.765 activation h avda 100 4 5 2 m 0 ch1 ch2 ch3 ch4 chS art 42 36 36 36 36 filter 50 50 50 50 50 level 0.05 name ben05 activation h avda 100 4 5 2 m 0 ch1 ch2 ch3 ch4 ch5 1st natural 7.715 att 66 42 42 42 42 filter 50 50 50 50 50 level 0.05 name ben05a activation h avda 100 4 5 2 m 0 ch1 ch2 ch3 ch4 chS 1st natural 7.654 att 66 48 48 48 48 filter 50 50 50 50 50 148 level O.OS run #3 benOSb activation h avda 20 0 8 5 2 m 0 ch1 ch2 ch3 ch4 ch5 1st nature 7.891 att 60 48 48 48 48 niter 50 50 50 50 50 level random name benrd activation h avda 10( ) 4 5 2 m 0 . . . ch1 ch2 ch3 ch4 ch5 1st natural 6.8 att 60 48 48 48 48 filter 50 50 50 50 50 level random name benrt tranverse hammer blow activation h avda 100 4 5 2 m 0 ch1 ch2 ch3 ch4 ch5 att 60 48 48 48 48 filter 50 50 50 50 50 level 0.05 name ben05c activation h avda 100 4 5 2 m 0 ch1 ch2 ch3 ch4 ch5 1st natural 6.702 att 60 48 48 48 48 filter 50 50 50 50 50 level 0.05 name ben05d activation h avda 100 4 5 2 mO ch1 ch2 ch3 ch4 ch5 1st natural 6.665 att 60 48 48 48 48 filter 50 50 50 50 50 level 0.2 name ben20 activation h avda 100 4 5 2 m 0 ch1 ch2 ch3 ch4 ch5 1st natural 5.664 att 60 48 48 48 48 filter 50 50 50 50 50 149 level 0.2 name ben20b activation h avda 200 8 5 2 m 0 ch1 ch2 ch3 ch4 ch5 1st natural 5.762 att 60 48 48 48 48 filter out 50 50 50 50 level 0.3 name ben30 activation h avda 200 8 5 2 m 0 ch1 ch2 ch3 ch4 ch5 1st natural 5.518 att 60 48 48 48 48 filter out 50 50 50 50 level 0.4 name ben40 activation h avda 200 8 5 2 m 0 ch1 ch2 ch3 ch4 ch5 1st natural 5.274 att 60 48 48 48 48 filter out . 50 50 50 50 level 0.6 name ben60 activation h avda 200 8 5 2 m 0 ch1 ch2 ch3 ch4 ch5 1st natural 4.468 att 60 48 48 48 48 filter out 50 50 50 50 level 0.6 name ben60b activation h avda 200 8 5 2 m 0 ch1 ch2 ch3 ch4 ch5 1st natural 4.492 att 60 48 48 48 48 filter out 50 50 50 50 level 0.75 name ben75 activation h avda 200 8 5 2 m 0 ch1 ch2 ch3 ch4 chS 1st natural 3.565 att 60 48 48 48 48 filter out 50 50 50 50 150 A P P E N D I X E D A T A F R O M T H E 10%, 40% A N D 150% S H A K E T A B L E T E S T S In this Appendix the data recorded on Labview is plotted for the 10%, 40% and 150% runs. The data has been calibrated and zeroed where applicable. £-1 10% Run 5 10.00 0.00 •10.00 -1 4 i 00 Q 10.00 0.00 •10.00 -> u. 0.00 10.00 - i s i V. 0 I Q 0.00 •10.00 I u* u 100 - , 0.00 •1.00 5.00 10.00 15.00 Time (s) 20.00 25.00 152 0.40 -i >-3 5 3 -200.00 -600.00 -, S.00 10.00 15.00 20.00 25.00 Time fs) 153 0.00 -, •2000.00 -> 300.00 -, 100.00 -1 1000.00 o.oo -\ •500.00 -> fOOO.OO - 1 500.00 H 0.00 -\ 5.00 10.00 15.00 20.00 Time (s) i 20.00 0.00 •20.00 —I •1400.00 - i •1450.00 -\ •1500.00 -< | s 2 40.00 - i 0.00 -40.00 J5 £ & o E to 400.00 200.00 0.00 -> J5 e o 6 800.00 - i 400.00 H 0.00 5.00 fO.OO 15.00 Time (s) 20.00 25.00 155 2000.00 - i 1000.00 0.00 -> 1000.00 - i 0.00 •1000.00 -> 1000.00 - i o.oo -\ -1000.00 -1 400.00 0.00 •400.00 -1 4000.00 - i 2000.00 0.00 5.00 10.00 15.00 Time (a) 20.00 1 25. 156 i 3 200.00 - i -400.00 - J 1200.00 800.00 2 400.00 J? 0.00 -400.00 -> 800.00 158 40% Run 40.00 - i 20.00 0.00 -20.00 --40.00 -10.00 15.00 Time (s) 20.00 25.00 161 163 164 0.10 - i -OAO —' 5.00 10.00 15.00 20.00 25.00 Tlme(s) 165 E-3 150 %Run 50.00 - i 0.00 -50.00 -1 50.00 1" 25.00 St 1 0.00 CO § -25.00 -50.00 -AM I I i I u u 0.00 5.00 fO.OO J5.00 20.00 25.00 168 8.00 - i •S 6.00 -§ 4.00 -6 3 2.00 -0.00 -15.00 - i moo H 5.00 H 0.00 - 1 / 1 M A V \ A A A A A A A / V V ^ V V - - V ^ 25.00 - i 20.00 -J 15.00 10.00 -5.00 -0.00 -W U A / 8.00 - i 4.00 H 0.00 —' —^4^^^ 5.00 fO.OO T5.00 77/ne (sj 20.00 25.00 171 0.20 -| •0.20 -i. 1.50 - i 1.00 -•1.00 -•1.50 -5.00 10.00 15.00 20.00 25.00 Time (s) 172 

Cite

Citation Scheme:

        

Citations by CSL (citeproc-js)

Usage Statistics

Share

Embed

Customize your widget with the following options, then copy and paste the code below into the HTML of your page to embed this item in your website.
                        
                            <div id="ubcOpenCollectionsWidgetDisplay">
                            <script id="ubcOpenCollectionsWidget"
                            src="{[{embed.src}]}"
                            data-item="{[{embed.item}]}"
                            data-collection="{[{embed.collection}]}"
                            data-metadata="{[{embed.showMetadata}]}"
                            data-width="{[{embed.width}]}"
                            async >
                            </script>
                            </div>
                        
                    
IIIF logo Our image viewer uses the IIIF 2.0 standard. To load this item in other compatible viewers, use this url:
https://iiif.library.ubc.ca/presentation/dsp.831.1-0050341/manifest

Comment

Related Items