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Analytical studies of a 49-storey eccentric braced building Safai, Aliyeh Jowrkesh 2001

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ANALYTICAL STUDIES OF A 49-STOREY ECCENTRIC BRACED BUILDING By ALIYEH JOWRKESH SAFAI  BA.Sc. Gilan University, Iran, 1990 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE in THE FACULTY OF GRADUATE STUDIES Department of Civil Engineering  We accept this thesis as conforming to the required standard  THE UNIVERSITY OF BRITISH COLUMBIA April, 2001 ©Aliyeh Safai, 2001  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  Cl'/il  £r}yne€ff/[^  The University of British Columbia Vancouver, Canada  Date  DE-6 (2/88)  Wf)  27-fO-Q"  \  ABSTRACT The purpose of this research is to study the seismic behaviour of a well instrumented 49-storey steel frame building in San Francisco, California. The building was subjected to ground motions from the Loma Prieta earthquake (Ms = 7.1) of October 17, 1989. During the earthquake the building response appeared to remain in the elastic range. In recent years, serious efforts have been undertaken to develop the concept of energy dissipation or supplemental damping into a workable technology, and a number of these devices have been installed in structures throughout the world. The focus of this study was a comparative study between dynamic behaviour of an instrumented 49-storey eccentrically braced frame building and dynamic behaviour of the same building with the eccentric braces replaced with a friction damper energy dissipation system. In addition to study of passive energy systems, a study of floor response spectra was also carried out, and the results were compared with the results using National Building Code of Canada (NBCC, 1995) and Uniform Building Code (UBC, 1997) regulations. Detailed three-dimensional linear and nonlinear dynamic computer analyses of the building was carried out for the eccentric braced and the comparative friction damped case, respectively. The results from the frequency domain system identification analyses was utilized to make verify the assumptions made and to match the results of numerical analyses with the recorded values. The results of this study showed that by performing a linear three-dimensional analysis, the actual response of the building during past earthquake could be reproduced with confidence. The hypothetical friction damped building behaved very well substantially reducing the storey force demand and relative storey displacements.  n  TABLE OF CONTENTS Abstract  ii  Table of Contents  iii  List of Figures  vii  List of Tables  xii  Acknowledgements  xiii  Chapter 1:. INTRODUCTION  1  1.1. GENERAL  1  1.2. SCOPE AND OBJECTIVES OF THIS STUDY  4  1.3. THESIS OUTLINE  5  Chapter 2:. BACKGROUND ON TALL BUILDINGS 2.1. ANALYSIS OF TALL BUILDINGS  ,,  6 6  2.2. STRONG MOTION RECORDS FROM BUILDINGS  7  2.3. A HISTORICAL OVERVIEW OF TALL BUILDINGS  8  2.3.1. Shear Truss Frame Interaction 2.3.2. Shear Truss Frame Interaction with Rigid Belt Trusses 2.3.3. Framed Tube 2.3.4. Column Diagonal Truss Tube 2.3.5. Bundled Tube System 2.3.6. Concentrically Braced Frames 2.3.7. Eccentric Bracing systems 2.3.7.1. Design and Linear Analysis of Prototype Structure 2.3.7.2. Inelastic Deformation of Eccentric Beam Element 2.3.7.3. Dynamic Analysis 2.3.7.4. Test Setup and Frame Behaviour 2.3.7.5. Comparison of Test Results with Theory 2.3.7.6. Design Recommendations 2.3.8. Staggered Truss System 2.3.9. Multi-Phase Bracing  9 10 10 11 11 12 13 14 15 16 17 17 18 18 19  iii  TABLE OF CONTENTS Chapter 3:.  ENERGY DISSIPATION DEVICES  21  3.1. INTRODUCTION  21  3.2. CLASSIFICATION  21  3.3. VELOCITY-DEPENDENT DAMPERS  22  3.3.1. Visco-Elastic Systems  22  3.3.2. Viscous Fluid Systems  23  3.4. DISPLACEMENT-DEPENDENT DAMPERS  24  3.4.1. Metallic Systems 3.4.2. Friction Systems 3.4.2.1. Pall Friction Dampers  25 25 27  3.5. DESIGN PROCEDURE FOR FRICTION DAMPED STRUCTURES  28  3.6. FRICTION DAMPED BRACED FRAME  29  3.6.1. Optimum Slip Load  31  Chapter 4:.  BUILDING DESCRIPTION AND INSTRUMENTATION  32  4.1. INTRODUCTION  32  4.2. STRUCTURAL SYSTEM  32  4.2.1. Moment-Resisting Frame  34  4.2.2. Eccentric Brace Frame  34  4.3. FOUNDATION  AND  GENERAL SITE DESCRIPTION  35  4.4. DESIGN CRITERIA  36  4.5. BUILDING INSTRUMENTATION  36  4.6. BUILDING RESPONSE TO LOMA PRIETA EARTHQUAKE  38  4.6.1. Drift Investigation 4.7. ROCKING OF THE BUILDING IN THE ECCENTRIC BRACED DIRECTION  4.7.1. Fourier Analyses  Chapter 5:.  DESCRIPTION OF ETABS PROGRAM  39 40  45  48  5.1. GENERAL  48  5.2. ETABS FEATURES  48 iv  TABLE OF CONTENTS 5.3. CONCEPT OF FRAMES IN ETABS  49  5.4. LINEAR STRUCTURAL ELEMENTS IN ETABS  51  5.4.1. Column Element 5.4.2. Beam Element 5.4.3. Floor Element 5.4.4. Brace Element 5.4.5. Panel Element 5.5. NONLINEAR STRUCTURAL ELEMENTS IN ETABS  5.5.1. link Element 5.5.2. Spring Element 5.5.3. Uniaxial Damper 5.5.4. Uniaxial Gap 5.5.5. Uniaxial Plasticity Element 5.5.6. Biaxial Hysteretic Isolator Element 5.5.7. Biaxial Friction Pendulum Isolator Element  51 53 54 55 56 57  58 58 58 59 59 59 59  5.6. ETABS PROGRAM CAPABILITIES  60  5.7. ETABS NONLINEAR ANALYSIS  61  Chapter 6:. THREE-DIMENSIONAL LINEAR ANALYSIS OF THE BUILDING 64 6.1. GENERAL  64  6.2. MODEL DESCRIPTION  65  6.2.1. Investigated Building Parameters 6.2.1.1. Panel Zone 6.2.1.2. Beam-to-Column Fixity 6.2.1.3. Rigid Floor Diaphragm 6.2.1.4. Mass Distribution 6.2.1.5. Extended Three-Storey above Ground 6.2.1.6. Damping.  67 67 68 68 69 69 70  6.3. COMPARISON OF ANALYTICAL RESULTS  70  6.4. THREE-DIMENSIONAL LINEAR ANALYSIS OF THE BUILDING  71  6.5. COMPARISON OF RECORDED AND COMPUTED TIME-HISTORIES IN THE ECCENTRIC BRACED FRAME DIRECTION 71 6.6. LINEAR ELASTIC BUILDING RESPONSE TO OTHER EARTHQUAKES  81  6.7. PREDICTED BUILDING RESPONSE  84  v  TABLE OF CONTENTS Chapter 7:. THREE-DIMENSIONAL ING USING FRICTION DAMPERS  NON-LINEAR ANALYSIS OF THE BUILD-  95  7.1. GENERAL  95  7.2. MODEL DESCRIPTION  95  7.2.1. Friction Damped Braces  96  7.2.2. Hysteresis Behaviour  97  7.3. COMPARISON OF ANALYTICAL RESULTS  98  7.4. TIME-HISTORY RESPONSE OF THE FRICTION DAMPED BUILDING  99  7.5. NONLINEAR RESPONSE TO OTHER EARTHQUAKE RECORDS  7.5.1. Beam Moment-Rotation and Link Axial-Displacement Response 7.5.2. Base shear and Overturning Moment 7.5.3. Energy Input and Dissipation  Chapter 8:.  SEISMIC ANALYSIS OF SECONDARY SUB-SYSTEMS  104  113 114 123  129  8.1. INTRODUCTION  129  8.2. FLOOR RESPONSE SPECTRUM METHOD  130  8.3. NBCC AND UBC REGULATIONS  FOR EQUIPMENT  132  8.4. FLOOR RESPONSE SPECTRUM ANALYSIS PROCEDURE  133  8.5. COMPARISON OF CODE AND FLOOR RESPONSE SPECTRUM RESULTS  136  Chapter 9:.  SUMMARY, CONCLUSIONS AND RECOMMENDATIONS  9.1. SUMMARY  .... 137 137  9.1.1. Linear Elastic Building Response to Selected Earthquakes 138 9.1.2. NonLinear Friction Damped Building Response to Selected Earthquakes . . 139 9.1.3. Sub-Secondary systems 139 9.2. RECOMMENDATIONS AND FURTHER STUDIES  References  140  141  vi  LIST OF FIGURES Figure 2.1: Shear truss frame interaction system (After Khan, F. R., 1974)  9  Figure 2.2: Shear truss frame interaction system with exterior rigid belt truss (After Khan, F. R., 1974) 10 Figure 2.3: A column diagonal truss tube system (After Khan, F. R.,1974)  12  Figure 2.4: An eccentric braced frame system (After Roeder and Popov, 1987)  14  Figure 2.5: Comparison of energy dissipation mechanism for a moment-resisting frame and an eccentrically braced frame (After Roeder and Popov, 1987) 15 Figure 2.6: Staggered truss framing system (After Popov et. al, 1976)  19  Figure 3.1: Schematic friction damped model (after Fu and Cherry, 1998)  28  Figure 3.2: Force relationship of a friction damped model (after Fu and Cherry, 1998) . . . 29 Figure 3.3: Force-displacement hysteresis loop of a friction damped model (after Fu and Cherry, 1998) 30 Figure 4.1: Embarcadero building in San Francisco  33  Figure 4.2: Embarcadero Building, typical floor framing plan  33  Figure 4.3: Design Response spectra of Embarcadero Building  37  Figure 4.4: General three-dimensional instrumentation view of the Embarcadero building (after Celebi, 1993) 38 Figure 4.5: Recorded acceleration for the Embarcadero building during Loma Prieta earthquake 41 Figure 4.6: Recorded displacement for the Embarcadero building during Loma Prieta earthquake 42 Figure 4.7: Drift ratios for the Embarcadero building for the Loma Prieta Earthquake . . . . 43 Figure 4.8: Vertical displacement at the basement level together with rotation of base mat and basement wall 44 Figure 4.9: Fourier amplitude spectra of horizontal ground motions recorded during the Loma Prieta earthquake (after Celebi, 1993) 45 Figure 5.1: Typical Building System  50  Figure 5.2: Examples of columns with variable section properties  51 vii  LIST OF FIGURES Figure 5.3: Column and beam rigid end offsets  52  Figure 5.4: Examples of beams with variable section properties  53  Figure 5.5: Examples of tributary floor vertical loading algorithms  55  Figure 5.6: Three-dimensional C-shaped shear wall system with beams and columns  57  Figure 6.1: ETABS model of the #4 Embarcadero Centre eccentric braced frame building 65 Figure 6.2: Computed mode shapes for the #4 Embarcadero Centre building  71  Figure 6.3: Comparison of recorded and computed absolute acceleration for the Loma Prieta earthquake 73 Figure 6.4: Comparison of recorded and computed relative displacement for the Loma Prieta earthquake 74 Figure 6.5: Computed storey shear time-histories at selected floor levels during the Loma Prieta earthquake 75 Figure 6.6: Computed storey overturning moment time-histories at selected floor levels during the Loma Prieta earthquake 76 Figure 6.7: Computed storey shear and overturning moment demand at selected time intervals and maximum absolute values during the Loma Prieta earthquake 78 Figure 6.8: a) Load-deformation response of the brace at the level of mechanical floor . . . 79 Figure 6.9: Time-history plots of Mexico City (SCT1), Sylmar and Joshua Tree records . . 81 Figure 6.10: Response spectra plots of Mexico City (SCT1), Sylmar and Joshua Tree records 82 Figure 6.11: Computed absolute acceleration time history response of the building for the Mexico City (SCT1) record 84 Figure 6.12: Computed absolute acceleration time history response of the building for the Sylmar record 85 Figure 6.13: Computed absolute acceleration time history response of the building for the Joshua Tree record 86 Figure 6.14: Computed relative displacement time history response of the building for the Mexico City (SCT1) record 87 Figure 6.15: Computed relative displacement time history response of the building for the Sylviii  LIST OF FIGURES mar record  88  Figure 6.16: Computed relative displacement time history response of the building for the Joshua Tree record 89 Figure 6.17: Computed absolute acceleration and relative displacement profile of the building for the Mexico City (SCT1) record 91 Figure 6.18: Computed absolute acceleration and relative displacement profile of the building for the Sylmar record 90. Figure 6.19: Computed absolute acceleration and relative displacement profile of the building for the Joshua Tree record '. 9£ Figure 7.1: ETABS model of the #4 Embarcadero Centre building with X-bracing friction dampers replacing eccentric brace elements 9$ Figure 7.2: Comparison of computed absolute acceleration time histories of the friction damped and eccentric braced buildings for the Loma Prieta earthquake record 9ty Figure 7.3: Comparison of computed relative displacement time histories of the friction damped and eccentric braced buildings for the Loma Prieta earthquake record 100 Figure 7.4: Comparison of computed a) & b) absolute acceleration and c) & d) relative displacement profiles of the eccentric braced and friction damped buildings for the Loma Prieta earthquake record 101 Figure 7.5: Comparison of maximum and minimum storey shear and storey overturning moment of the friction damped and eccentric braced buildings for the Loma Prieta earthquake record 103 Figure 7.6: a) Load-deformation response of the friction damper at the level of mechanical floor 104 Figure 7.7: Computed absolute acceleration time history response of the friction damped building for the Mexico City (SCT1) record 106 Figure 7.8: Computed absolute acceleration time history response of the friction damped building for the Sylmar record 107 Figure 7.9: Computed absolute acceleration time history response of the friction damped building for the Joshua Tree record 108 Figure 7.10: Computed displacement time history response of the friction damped building for the Mexico City (SCT1) record 10 ? ix  LIST OF FIGURES Figure 7.11: Computed displacement time history response of the friction damped building for the Sylmar record 110 Figure 7.12: Computed displacement time history response of the friction damped building for the Joshua Tree record 111 Figure 7.13: a) Load-deformation response of the friction damper at the level of mechanical floor 114 Figure 7.14: a) Load-deformation response of the friction damper at the level of mechanical floor 115 Figure 7.15: a) Load-deformation response of the friction damper at the level of mechanical floor 116 Figure 7.16: Computed storey shear and overturning moment demand for the friction damped building at selected time intervals and maximum absolute values during the Loma Prieta earthquake record 118 Figure 7.17: Computed storey shear and overturning moment demand for the friction damped building at selected time intervals and maximum absolute values during the Mexico City (SCT1) record 119 Figure 7.18: Computed storey shear and overturning moment demand for the friction damped building at selected time intervals and maximum absolute values during the Sylmar record .. 120 Figure 7.19: Computed storey shear and overturning moment demand for the friction damped building at selected time intervals and maximum absolute values during the Joshua Tree record 121 Figure 7.20: Energy time histories for the a) eccentric braced and b) friction damped buildings during the Loma Prieta earthquake record 123 Figure 7.21: Energy time histories for the a) eccentric braced and b) friction damped buildings during the Mexico City (SCT1) record 12^Figure 7.22: Energy time histories for the a) eccentric braced and b) friction damped buildings during the Sylmar record 12$ Figure 7.23: Energy time histories for the a) eccentric braced and b) friction damped buildings during the Joshua Tree record 126 Figure 8.1: Pseudo-acceleration and displacement response spectra for the eccentric braced Embarcadero building for Loma Prieta, Mexico city, Joshua Tree and Sylmar earthquake x  LIST OF FIGURES records at the 44th floor  13.3  Figure 8.2: Pseudo-acceleration and displacement response spectra for the friction damped building for Loma Prieta, Mexico city, Joshua Tree and Sylmar earthquake records at the 44th floor 134-  xi  LIST OF TABLES Table 4.1: Peak accelerations and displacements of the Embarcadero building during Loma Prieta earthquake in the eccentric braced direction 40 Table 4.2: Dynamic characteristics of the building as identified by Celebi (1993)  46  Table 6.1: Comparison of analytical and measured values for the first four periods of the building in the E-W, N-S and torsional directions  69  Table 6.2: General information for selected earthquake records  81  Table 7.1: Comparison of analytical values for the first four periods of the eccentric braced and friction damped buildings in the N-S and torsional directions 97 Table 8.1: Calculated design seismic forces on mechanical equipment at the 44th floor of the Embarcadero building 135  xii  ACKNOWLEDGEMENTS I would like to thank my advisor, professor Carlos E. Ventura, for his support since the first day that I started my education at UBC. Without his guidance and encouragement, I could not have finished this step of my life successfully. His help is very much appreciated. I would like to express my gratitude to professor Reza Vaziri for reviewing my thesis and for providing further comments and discussions. I would also like to thank Dr. Elizabeth Croft, associate professor in Department of Mechanical Engineering and former DAWEG (Division for Advancement of Women in Engineering and Geoscience) Co-Chair, for her guidance and encouragement and for providing partial financial support. The partial financial support provided by a research grant awarded to professor Carlos E. Ventura from the Natural Sciences and Engineering Research Council of Canada is gratefully acknowledged. In addition, I would like to express my thanks to my husband, Mahmoud, for his guidance and wisdom, to my colleague Tuna for her help and support and to all my friends for supporting me by taking care of my kids, Ahrshia and Sheima. The generous assistance provided by all these people is gratefully acknowledged. Thanks are also extended to my family and my husband's family for their endless support and encouragement.  xiii  Chapter 1: INTRODUCTION 1.1 GENERAL Structures located in seismic regions must be designed to resist considerable lateral inertial loads. The design of such structures requires a balance between strength, stiffness, and energy dissipation. A number of structural steel systems (such as ordinary concentrically braced frames, moment-resisting frames, eccentrically braced frame) satisfy a part of these requirements. But none of these systems are intended to resist a major earthquake within the elastic limit of the materials and will require post-earthquake repairs. Design procedures for the structural systems subjected to earthquake excitation allow reduction of lateral design force according to ductility of the structure. A ductile structure is capable of dissipating energy in structural elements and the connections are designed to withstand plastic deformation. This ductility demand on the structure implies damage of the structural system, and often, damage of non-structural components such as partitions and walls. In any event, it is desirable that less dependence be placed on structural element ductility, and that other means be found to dissipate seismic energy. The problems created by dependence on the ductility of the structure can be reduced if the seismic energy can be dissipated independently from primary structure. By incorporating energy dissipation devices, the deformation demand can be reduced significantly, and with that reduction, the ductility demand can be attenuated. Steel moment-resisting frames are known to posses excellent energy dissipation, but they are relatively flexible and can become uneconomical if substantial lateral stiffness is required. Moreover, because of their greater deflection, the structural stability is affected by the P-A factor, which can be significant. Braced steel frames are known to be economical and are effective in controlling lateral deflection due to wind and moderate earthquakes; but during major earthquakes, these structures don't  1  Chapter 1:  INTRODUCTION  perform well. Firstly, being stiffer, they tend to attract higher seismic forces, and secondly their energy dissipation capacity is very much limited, due to the pinched hysteretic behaviour of the braces. A tension brace stretches during a severe shock and buckles in compression during reversal of load. This elongated brace is not effective even in tension until it is straight again. As a result, energy dissipation effectiveness degrades very quickly. An eccentric bracing system combines the strength and stiffness of a braced frame with an inelastic behaviour and energy dissipation of a moment-resisting frame. The system employs deliberately large eccentricities between the brace-beam connection and beam-column joints, which are chosen to assure that the eccentric beam element yields in shear. It acts as a ductile fuse that dissipates large amount of energy while preventing buckling of the braces. The response of an eccentric braced structural system can be complex. After a major earthquake, large inelastic deformation must be expected at all floors of a structure. Although the structure is saved from total collapse, the main beams are sacrificed and the structure might need major repairs or replacement. The damping in these structures is produced by inelastic action in link elements. To develop significant damping, large inelastic action will be produced in the link elements which could result in damage at the connections. For long duration earthquake shaking, such as the one in Mexico City during the 1985 earthquake, this damage at the connections over many cycles can lead to collapse of the structure even for a relatively low peak ground acceleration. Eccentric bracing is an integral part of the structure and after a severe earthquake usually does not need to be replaced. One solution to the above-mentioned shortcomings of conventional structural systems is to increase the internal damping of a structure, which generally enhances the performance of the structure subjected to an earthquake. Situations exist in which the conventional design approach is not applicable such as when a structure must remain functional after an earthquake, as is the case of important structure (e.g. hospitals, police stations, etc.). For such cases the structure might  2  Chapter 1:  INTRODUCTION  be designed with sufficient strength so that inelastic action is either prevented or minimal, an approach that is very costly. During a seismic event, a finite quantity of energy is input into a structure. This input energy is transformed into both kinetic and potential (strain) energy which must be either absorbed or dissipated through heat. If there were no damping, vibrations would exist for all time. However, there is always some level of inherent damping which withdraws energy from the system and therefore reduces the amplitude of vibration until the motion ceases. The structural performance can be improved if a portion of the input energy can be absorbed, not by the structure itself, but by some type of supplemental "device". New and innovative concepts of structural protection, called passive energy dissipation such as friction and viscous dampers have been developed in recent years and are at various stage of implementation. The basic function of passive energy dissipation devices when incorporated into the superstructure of a building is to absorb or consume a portion of the input energy, thereby reducing energy dissipation demands on the primary structural members and minimizing possible structural damage. The addition of damping to a structure absorbs kinetic energy induced in the structure and prevents the build-up of resonant vibrations should the natural frequency of the structure coincide with a strong frequency present in the ground motion. Frictional damping elements for a variety of structural systems have been proposed by Pall, ranging from braced frames (Pall & Marsh, 1982 and Pall, 1984) to concrete shear walls (Pall & Marsh, 1981) and panel structures (Pall & Marsh, 1980). Friction braces are simply conventional braces modified with the addition of a friction joint consisting of a heavy duty brake lining pad clamped between sliding steel surfaces with high strength bolts and a slotted hole in the brace mechanism which allows a limited amount compression before slippage. The friction joints mechanism is tuned so that under moderate earthquake loads, story shift is controlled without friction pad slippage, while under severe earthquake loading brace slippage is assured before the 3  Chapter 1:  INTRODUCTION  brace can buckle. In this case the bracing system acts to brake the structure's motion, dissipate large amount of energy and reduce inelastic deformations in the beam and column elements. Moreover, a large number of older structures have insufficient lateral strength and lack the detailing required for ductile behaviour. Seismic retrofitting of these structure is necessary and may be achieved by conventional seismic design, although often at significant cost and with undesirable disruption of architectural features. The latter is a significant consideration in the seismic retrofit of historic structures with important architectural features. 1.2 SCOPE AND OBJECTIVES OF THIS STUDY With more and more tall buildings appearing on the skylines of our cities today, it is apparent that they have become a major factor in the growth of our society. The tall building brings with it unique problems that the professions must be aware of and must learn to solve. It is hoped that the presentations of this thesis will contribute toward a better understanding of the seismic behaviour an eccentric braced tall building and the problems associated with it. The main objectives of the investigation reported in this thesis are to study analytically the seismic behaviour of a tall eccentrically braced frame building as well as to compare its seismic behaviour with that of the same building with the eccentric braces replaced with a friction damper energy dissipation system. This comparison is done for four different earthquake excitations. The elastic and inelastic seismic response of both eccentric braced and friction-damped steel frames are studied. A comprehensive 3-D computer analysis of the study building was performed using computer program ETABS ver. 6.23. The information used for modelling the building was obtained from the 120 seconds time-history of the building's response to the Loma Prieta earthquake that affected in San Francisco in 1989. A comparison between the code prescribed lateral forces exerted on secondary sub-systems such 4  Chapter 1:  INTRODUCTION  as mechanical equipment mounted at the top of building structures with the floor response spectrum method was also studied during the course of this thesis. 1.3 THESIS OUTLINE This section of the thesis provides a description of the manner in which the remainder of the manuscript is organized. A study on the background of tall buildings with the emphasis of experimental and analytical studies of eccentric braced frames are presented in Chapter 2. Chapter 3 describes a summary of various energy dissipating devices produced by different manufacturers around the world. In Chapter 4, a brief summary of the building description and instrumentation together with results of strong motion data analysis are presented. Chapter 5 presents a summary of ETABS computer program capabilities and various analysis options together with different element types. The results of three-dimensional linear analysis of the building during Loma Prieta (1989), Guerrero-Michoacan, Mexico (1985), Landers (1992) and Northridge (1994) earthquakes are presented and discussed in Chapter 6. Chapter 7 presents the nonlinear analysis of the building with the addition of X-bracing friction damped devices instead of eccentric braced elements. This includes the time-history results from Loma Prieta (1989), Guerrero-Michoacan, Mexico (1985), Landers (1992) and Northridge (1994) earthquakes. Chapter 8 contains a review of the earthquake demand on mechanical equipment installed on tall buildings. A comparison of present analytical results with code prescribed forces is presented. Chapter 9 provides a summary of the research and a discussion of the conclusions drawn. 5  Chapter 2: BACKGROUND ON TALL BUILDINGS 2.1 ANALYSIS OF TALL BUILDINGS Tall buildings share many important properties including uniformity with height of their crosssectional area and mass per storey, a general similarity in mode shapes of vibration, and similar ratios of higher natural frequencies to those of the fundamental mode. They also require great structural frames to resist the forces of gravity, wind and earthquake. As a building gets taller, the major forces that determine the building design change from vertical loads to horizontal loads caused either by wind or by seismic activity. These forces tend to increase at the higher elevations of a building. Therefore, an understanding of the nature of these forces as well as an understanding of different structural systems to resist these forces is very important. Providing adequate earthquake resistance for a tall building which is to be built in a region of high seismicity undoubtedly represents a great challenge on the skills of a structural designer. The earthquake is a unique form of structural loading in at least two respects. First, it is a purely dynamic phenomenon resulting from shaking of the soil on which building is founded; therefore, its effects on the structure must be evaluated by dynamic analysis rather than by the principles of statics usually employed by the designer. Second and even more difficult to deal with, is the fact that a major earthquake is one of the most severe loadings to which a tall building might ever subjected, yet the probability that it will happen during the life of the building is very low. This combination of extreme load and unlikely occurrence demands that special design strategies be adopted; and a great deal of research and development effort is being focused in this direction at present. The three principal phases of the design of tall buildings to resist earthquakes are: (1) defining the expected source earthquake, (2) evaluating the ground motions, taking into account the effect of local soil properties, and (3) carrying out the earthquake response analysis of the proposed design. An actual building system is then considered, and results obtained for this structure in 6  Chapter 2:  BACKGROUND ON TALL BUILDINGS  each phase of the design procedure are discussed. 2.2 STRONG MOTION RECORDS FROM BUILDINGS Current building code forces specified for providing earthquake resistance in building structures are based on the observation of the performance of tall buildings that have been subjected to major earthquakes. This basic approach is still necessary at the present time because the theoretical design factors obtained from the presently available ground motion measurements are much too high for the usual elastic methods of analysis. While great progress has been made on analyses based on elasto-plastic performance, these studies have not reached to the point where they can be effectively used in the design office for the average building. It is also true, unfortunately, that there are no ground records available at the location of major damage or maximum motion for the truly major earthquakes such as the 1906 San Francisco Earthquake. Thus, it is necessary to instrument the buildings to determine the variation of storey forces along the height of the building and to study why they behaved well or poorly and from these studies determine the requirements for future designs. The basic objective of instrumentation of buildings includes measurement of lateral, torsional and rocking input motion at the base of the building. If it is possible, a triaxial accelerograph is installed on the ground at some distance from the instrumented building to measure the free-field motion. At the upper levels of the building the instrumentation objectives are to measure lateral motion in each direction and torsional motion at selected locations throughout the structure. The levels instrumented always include the roof and as many other levels as seem economical and appropriate to the particular building. Buildings in California are instrumented to measure earthquake motions by the California Strong Motion Instrumentation Program (CSMIP), the U.S. Geological Survey (USGS), and by the owners of large buildings in the City of Los Angeles and some other cities. The city of Los Angeles and other cities in California requires owners of large buildings within the city to install 7  Chapter 2:  BACKGROUND ON TALL BUILDINGS  and maintain minimum instrumentation in the building. 2.3 A HISTORICAL OVERVIEW OF TALL BUILDINGS There has been three distinct phases of development of the vertical scales of the cities after Renaissance in the 15th century. The first phase was in response to the growing urban density multi-storey buildings built in the cities of Europe and America with an average of six stories high. This limitation was primarily because of the lack of a reliable vertical transportation system. From the middle of the 19th Century, the perfection of the elevator system and production of the cast iron and steel started the second phase of the taller buildings built in urban centres. The second phase with its taller scale lasted until around 1950, and was generally represented by the buildings in the order of 20 to 30 stories high. Building taller than 20 to 30 stories with the beamcolumn structural frame was often too expensive to be economically justified. Beginning from the 50's and especially after the 60's, a whole new series of structural systems was developed with the objective of eliminating the traditional premium for lateral load effects. These systems in structural steel, reinforced concrete, as well as in masonry bearing wall construction, are ushering in the last phase in changing the vertical scale of the cities, a new scale that is defined by buildings 40 to 60 stories high with many rising to 100 stories and above. The beam-column type framing system was first applied to steel construction, and later extended to reinforced concrete. As the demand for more space in the urban centre increased, taller and taller buildings began to be built with the same beam-column type framing, often resulting in rather expensive structures for such constructions. This activity undoubtedly reached its peak in the construction of the Empire State Building, which remained the world's tallest building until recently. From the beginning of 1960, there seemed to be an increase in the need for taller buildings, and at this time, because of the challenge to find newer ways of building taller buildings more 8  Chapter 2:  BACKGROUND ON TALL BUILDINGS  economically, the engineers began to search for new systems. The engineers interest and search was to find newer structural systems which would have inherent stiffness and strength to such an extent that the gravity load design can automatically satisfy the lateral load capacity and stiffness, thereby avoiding paying any premium for wind load design. This no premium for height approach for design of tall building brought with it new possibilities for structural architectural expressions. A short discussion of these new structural systems follows. 2.3.1 Shear Truss Frame Interaction Primarily, the lateral wind shear is carried mostly by the frame system in the upper portions of the building, and the majority of the wind shear is carried by the shear truss system in the lower portion of the building as shown in Figure 2.1. This interacting system has two major advantages, namely lateral drift or sway is frequently reduced to less than 50% of what it would be otherwise if only shear truss was used, and the distortion of the floors due to lateral sway are less significant. The shear truss frame interaction can be achieved simply by designing the main structural frame for gravity load, disregarding the wind effects on the frame part of the structure and designing the vertical shear truss for the balance of the wind effect in addition to the gravity load.  Free Frame  Free Truss  Combination Frame and Truss  Figure 2.1: Shear truss frame interaction system (After Khan, F. R., 1974) 9  Chapter 2:  BACKGROUND ON TALL BUILDINGS  2.3.2 Shear Truss Frame Interaction with Rigid Belt Trusses The efficiency of the shear truss frame interaction can be further improved in terms of lateral strength and stiffness by connecting all exterior columns to the interior shear truss through horizontal belt trusses as shown in Figure 2.2.  Figure 2.2: Shear trussframeinteraction system with exterior rigid belt truss (After Khan, F. R., 1974) The addition of this belt truss normally will increase the stiffness of the entire structure by about 30%, thus resulting in considerable structural economy. The full belt truss system at two levels of the building, one at mid-height and one at the top of the building, have been used in the BHP headquarters building in Melbourne, Australia and the First Wisconsin Bank building in Milwaukee, US. 10  Chapter 2:  BACKGROUND ON TALL BUILDINGS  2.3.3 Framed Tube It can be shown by simple mathematical derivation that the maximum efficiency of the total structure for lateral strength and stiffness can be achieved only by making all column elements connected to each other in such a way that the entire building acts as a hollow tube or rigid box cantilevering out of the ground. In such a case, the overturning resistance as well as the overturning stresses in the columns would be direct tension or compression without any bending. However, there are many practical planning and architectural difficulties in tying all the columns of the building together. The exterior columns may be made to act together by various means. Within the architectural framework of rectangular windows, the exterior columns system may be tied together by spacing them as close as possible so that the column spandrel interaction results in optimum design of the column spandrels within realistic architectural limitations. This method of closely spaced system tied with deep spandrel beams at each floor level creates an equivalent rectangular or square hollow tube with perforated window openings. 2.3.4 Column Diagonal Truss Tube The exterior columns of a building can be spaced reasonably far apart and yet be make to work together as a tube by connecting them diagonal members intersecting at the centre line of these columns and spandrels. For very tall buildings the diagonals would be approximately at a 45° angle resulting in large widely spaced crosses, as was used for the John Hancock Centre in Chicago (Figure 2.3). The use of diagonal members to connect the far spaced columns makes the diagonal members themselves to resist the gravity axial load and therefore they do not normally develop any tension stresses under lateral loading. 2.3.5 Bundled Tube System With the future need of larger and taller buildings, the use of the framed tube, as well as the  11  Chapter 2:  BACKGROUND ON TALL BUILDINGS  Figure 2.3: A column diagonal truss tube system (After Khan, F. R.,1974) column diagonal truss tube, may be used by bundling module tubes to create larger tube envelopes. In a tall building with extremely large floor areas, the exterior column system may comprise only a smaller percentage of the total number of columns. Therefore, in such a building, to use an exterior tube system would be to lose the advantage of possible participation of the interior columns. 2.3.6 Concentrically Braced Frames Today mostframesare designed and constructed as concentrically bracedframes.In this system the centreline of the braces intersects the centreline intersection of the beams and columns. The lateral load resisting behaviour of this system is highly dependent upon the behaviour of the  12  Chapter 2:  BACKGROUND ON TALL BUILDINGS  brace, but it is also influenced by the axial and bending resistance of the frame. The bulk of the stiffness of a braced frame is provided by the brace. Therefore, the brace carries the major portion of the lateral loads until it buckles. After buckling, the brace loses strength. It is generally accepted that the energy dissipation characteristics of such braced frames sometimes may be unsatisfactory. This unsatisfactory behaviour is primarily due to the relatively large deflections necessary to re-straighten the brace after it is inelastically kinked during compression. This causes poor energy dissipation characteristics associated with severely pinched hysteresis loops. 2.3.7 Eccentric Bracing systems In Eccentric braced frame, braces are eccentrically connected so that the central segment of the beam yields in shear and bending before the bracing elements could buckle. This appears to be good design since the energy dissipation characteristics of steel beams in moment resisting frames, which are well understood, are known to be excellent. In this way they can develop full (unpinched) hysteretic loops without any reduction in ultimate strength. This full hysteresis loops should permit the structure to dissipate a large amount of energy as large cyclic deflections can take place without failure or deterioration in the hysteretic behaviour. This is because yielding occurs over a large segment of the beam web and is followed by the formation of a cyclic diagonal tension field. The web buckles after the yielding in shear but the tension field forms to prevent any deterioration or pinching due to buckling. It is essential to have a pair of stiffeners at the brace-beam connection and to have beam flange restrain at the beam-column joint to develop the required trussing action of the beam web. It is noted that large deflections occurs in the beams and, hence, considerable damage to the floor slabs must be expected. For tall buildings the exterior braced frames are designed to carry the major portion of the lateral load. Thus the bracing is arranged in a way to reduce the high tensile loads that may develop in the lower columns, as shown in Figure 2.4. Larger column forces due to the lateral loads would 13  Chapter 2:  BACKGROUND ON TALL BUILDINGS  result in the outer columns if braces were located only in the outer bays (Popov et ah, 1976).  y y y y - yy y Imfr  7) A  V V \  y y y y y y y y y y, y, y  \ \  V V \ \ \ \ \  N N X s N N X 7r  77T  iffnT  Figure 2.4: An eccentric braced frame system (After Roeder and Popov, 1987) It is convenient to examine the extent and the nature of inelastic deformation by constructing an energy dissipating mechanism for a frame as shown in Figure 2.5. In plastic static analysis such a mechanisms are called collapse mechanisms. From Figure 2.5 it can be noted that for the same storey sway, links in an eccentric braced frame, Figure 2.5b, experience a substantially larger demand than the links in a moment-resisting frame, Figure 2.5a. As the link elements placed near the ends of the storey beam, for the same storey drift only one half the link rotation demand is required as opposed to a link placed in the middle of the storey beam (Popov et al, 1988). Roeder and Popov (1978) performed an analytical and experimental study of a 20-storey eccentrically braced frame building. A summary of this study and several recommended details are discussed in the following. 2.3.7.1 Design and Linear Analysis of Prototype Structure The selected prototype structure is a 20-storey, four-bay office building, as shown in Figure 2.4. 14  Chapter 2:  a) Moment-resisting Frame  b) Eccentric Braced Frame  BACKGROUND ON TALL BUILDINGS  c) Hinge Mechanism  Figure 2.5: Comparison of energy dissipation mechanism for a moment-resisting frame and an eccentrically braced frame (After Roeder and Popov, 1987) The bay width is 7.3 m (24 ft) and the storey height is 3.6 m (12 ft) for all stories, except the first storey, which is 4.6 m (15 ft). A parametric study was made to evaluate the effect of variation in eccentricity on the system showing that the eccentrically braced system is very stiff, and that its stiffness remains relatively constant over a wide range of from no eccentricity to an eccentricity of approx. 1.4 m (4.5 ft). This indicated that the eccentric bracing concept is not a stiffness reduction scheme as compared to a concentrically braced system. An eccentricity of 1.07 m (3.5 m) was chosen for the prototype structure. 2.3.7.2 Inelastic Deformation of Eccentric Beam Element The lateral deflection of an eccentric braced frame can be estimated as sum of three components: (1) deflection due to elongation of the brace, (2) deflection due to elongation of the columns and (3) deflection due to deformation of the eccentric element. The braces and columns of an eccentrically braced frame are designed to remain elastic and prevent buckling at all time. Therefore the first two deflections (brace and column deflections) will remain nearly constant when the frame undergoes plastic deformations. 15  Chapter 2:  BACKGROUND ON TALL BUILDINGS  The stiffness of the eccentric element in the elastic range is very large, therefore, it contributes little in the total deflection, when the beam is elastic. The study by Roeder and Popov in 1978 showed that when the eccentric element sustains relatively large deformations, the frame experiences relatively small lateral deflections. 2.3.7.3 Dynamic Analysis The analytical model developed from the shear yielding beam tests was programmed for the DRAIN-2D (Kanaan and Powell, 1973) computer program, using two separate base excitations and three different alternates. These were a concentrically braced frame, a concentrically braced frame with moment-resisting beam-column connections, and a moment-resisting frame. A comparison of the behaviour of these structures indicated that the eccentrically braced frame performed somewhat better than the other systems mainly because it combines the stiffness and strength of an ordinary braced frame with the energy dissipation of a moment-resisting frame. However, it is noted that large vertical floor deflections accompanied this behaviour. The concentrically braced frames possess less desirable inelastic behaviour and so they generally predict larger relative displacements and storey drift than the eccentric frame. Study showed no deterioration of elastic stiffness during this analysis, while the other braced frames predict a considerable loss in elastic stiffness. The inelastic floor deformations were uniformly distributed over all floor levels. The 170 mm (6.7 in) maximum floor deformation of the eccentrically braced frame computed during analyses was considered very severe when it is noted that the deformation occurred over a 1070 mm (42 in) length of the storey beams. Tensile and high compressive forces predicted in the lower columns were 35% lower for the eccentrically braced frame because the eccentric beam element provided a better fuse for limiting these forces.  16  Chapter 2:  BACKGROUND ON TALL BUILDINGS  Inelastic dynamic analysis of the eccentrically braced prototype frame under two very different severe base excitations created a pulse effect which required the structure to possess considerable strength and stiffness in order to limit deflections. Another excitation produced a periodic effect for which the structure must exhibit sound cyclic energy dissipation characteristics in order to limit inelastic deflections. The dynamic analysis also indicated that deflection due to elongation of braces and columns were primarily elastic while deflections due to deformation of the eccentric element were totally plastic. Virtually all inelastic activity occurred in the eccentric beam elements. 2.3.7.4 Test Setup and Frame Behaviour Because of many unusual features of eccentric bracing frames, an experimental study of the behaviour of the system was made after completion of the inelastic dynamic analysis. Two test frames were designed to simulate the behaviour of the bottom corner of the prototype to the onethird scale (Figure 2.4). The frames were tested under both elastic and inelastic cyclic loads. The member sizes of the beams and columns were the nearest compact wide-flange section to the onethird scale of the prototype. As it is of paramount importance for the braces not to buckle, the braces were designed as back-to-back channels with additional factor of safety of 2.0 and 1.5 for frames 1 and 2, respectively. The brace-beam connections were also designed with the added factor of safety. The general performance of the test frames were excellent. They dissipated large amounts of energy and the hysteresis loops were repetitive with no deterioration in strength or stiffness until very large deflections were applied. The frames continued to maintain their strength and stiffness well after the eccentric elements started to tear. However, large floor deflections accompanied this good performance. The energy dissipation was almost entirely due to deformation of the eccentric elements.  17  Chapter 2:  BACKGROUND ON TALL BUILDINGS  2.3.7.5 Comparison of Test Results with Theory After the conclusion of the experimental work, the results were compared to the inelastic analytical model used in the dynamic analyses. The fit of the analytical model with the experimental results was very good for the early cycles while the analytical model consistently underestimated the lower side of the experimental hysteresis curves at large deflection levels. This was attributed to the effects of a strain hardening. It was recommended that the model likely can be improved by using a more accurate strain hardening rule. 2.3.7.6 Design Recommendations The eccentric braces should be designed as compression members with their ultimate axial design load depending on the ultimate plastic strength of the beams. An additional factor of safety of at least 1.5 should be applied to this ultimate load to insure that the braces do not buckle due to beam strain hardening, uncertainty in actual yield stress, or additional force necessary to crack the floor slabs. The Experimental model exhibited large initial elastic stiffness and possessed very sound energy dissipation characteristics in the inelastic range. The hysteretic loops were unpinched and did not deteriorate in strength or stiffness until very large displacements were imposed. Further, even beyond failure of the first eccentric element, the structure continued to retain most of its strength and stiffness. Therefore, the premature failure of an eccentric element does not imply the collapse of a structure. Although the inelastic behaviour of the eccentrically braced frame is very good, for very severe earthquake large inelastic floor deformations must be expected. After an extreme earthquake the floor damage may be quite severe. 2.3.8 Staggered Truss System Staggered truss system is very similar to the eccentric brace. Gupta (1971) analytically studied  18  Chapter 2:  BACKGROUND ON TALL BUILDINGS  the earthquake resistance of a staggered truss framing system which was designed by the procedure proposed by Hanson et al. (1971). An illustration of this bracing system is shown in Figure 2.6.  Figure 2.6: Staggered truss framing system (After Popov et. al, 1976) Two interesting features of this framing system are that a given column is braced only at alternate floor levels and that the centre panel of the braced levels are always unbraced. As a result, any shear or moment which is transferred through the centre panel of the truss must be transferred by shear, bending moments, and the axial load of the truss chords. Analysis on various staggered truss systems also showed that yielding occurred in these central chords (Gupta, 1971). 19  Chapter 2:  BACKGROUND ON TALL BUILDINGS  2.3.9 Multi-Phase Bracing The bracing in this system is designed by the slip model since very slender braces are used. An X bracing system is used, but each brace is really a dual brace. One of the dual braces is a brace with high yield stress and low ductility. The other brace has low yield stress and high ductility. The stiffness of the system is very high at low levels of excitation since both brace systems are elastic. At high excitation levels the low yield brace yields and the high yield brace fractures, and the stiffness of the structure drops dramatically. This stiffness degradation results in a long period and low design loads for extreme excitations. This might be accomplished by a mechanical means such as a friction type slip connection which maintains its friction load during slippage and worked in both tension and compression.  20  Chapter 3: ENERGY DISSIPATION DEVICES 3.1 INTRODUCTION In the last two decades passive energy dissipation systems and seismic isolation devices have emerged as a practical and economical solution to conventional techniques in retrofitting and upgrading existing structures. There has been much progress made in research, development, and implementation of passive energy dissipation and seismic isolation hardware for civil and structural engineering applications. The basic function of energy dissipation devices is to absorb or consume a portion of the input energy, thereby reducing energy dissipation demand on primary structural members and minimizing possible structural damage. In performing the above-mentioned task, isolation systems employ flexible elements at or near the foundation level to shift the predominant structural frequency and thereby reduce the input energy entering the superstructure, while dissipative seismic dampers are typically distributed throughout a structures to absorb either kinetic or strain energy transmitted from the ground into the structure. The use of either system is expected to provide the high level performance required for important facilities to be functional after an earthquake. The main body of this chapter is devoted to describe various types of energy dissipation devices, and, in particular, the friction dampers. The seismic performance of base isolation systems is not in the scope of this thesis. 3.2 CLASSIFICATION Passive energy dissipation systems are generally classified as velocity-dependent (visco-elastic and viscous damper), displacement-dependent devices (friction and metallic dampers) and others (friction-spring assemblies). The suitability of a particular device for a given application depends on the design requirements such as: the allowable force to be transferred to the structural elements 21  Chapter 3:  ENERGY DISSIPATION DEVICES  adjacent to the device, the expected relative displacements across the device connection points and the required force-displacement behaviour and hysteresis loops of the device with respect to the global behaviour of the structure. In the following, a brief description and various product information of each system is presented. 3.3 VELOCITY-DEPENDENT DAMPERS The force-displacement relation of a velocity-dependent device such as a visco-elastic or viscous damper is a function of relative velocity between each end of the device, and may also be a function of the relative displacement between each end of the device. 3.3.1 Visco-Elastic Systems Visco-elastic materials have been used in structural engineering for vibration control for more than 20 years. Solid visco-elastic devices typically consist of constrained layers of visco-elastic polymers. Such devices exhibit mechanical properties dependent on frequency, velocity, and amplitude of motion as well as temperature. The variation of mechanical properties can be summarized as: reduction in stiffness and damping with increasing temperature, increase in stiffness at higher frequencies, reduction in damping at higher frequencies, and decrease in stiffness and damping with amplitude of shear strain of the material. It is noted that these parameters may vary depending on the manufacturer and material selected. Several shake table studies of large scale, steel frame models with visco-elastic dampers have been conducted at the University of California at Berkeley in 1990, (Aiken and Kelly, 1990). These studies have confirmed a significant improvement in the response of the steel frame models with the presence of dampers in terms of storey shears and storey drifts. The 3M Company has developed visco-elastic copolymers that have been used in a number of structural applications such as twin towers of the 110-storey World Trade Centre in New York City (Mahmoodi et. al, 1987). 3M has now transferred production to a Japanese company. Several companies in Japan have developed damping system based on different visco-elastic 22  Chapter 3:  ENERGY DISSIPATION DEVICES  materials. Shmizu Corporation has developed a bitumen rubber compound visco-elastic damper that has been used in a one 24-storey steel building. Bridgestone Corporation has developed a visco-plastic rubber shear damper that has been tested on a shake table in a 5-storey steel frame model. Visco-elastic fluid devices that operate by shearing visco-elastic fluid, have behaviours that resemble those of solid visco-elastic devices except that fluid visco-elastic devices have zero effective stiffness under static loading (e.g. temperature). 3.3.2 Viscous Fluid Systems Viscous fluid dampers, which for many years have been used in the military and aerospace fields, have begun to emerge in structural and bridge engineering. These dampers possess linear or nonlinear viscous behaviour, and are relatively insensitive to temperature changes (e.g. zero resistance to static loads such as thermal expansion/contraction). Damper force is represented by (X  Cv  with a ranging from about 0.1 to 1.5 or even higher. C is the damping coefficient of the  device. Viscous fluid dampers operate on the principle of fluid flow through orifices. The damper's output force is resistive, therefore it acts in a direction opposite to that of the earthquake motion. The means of energy dissipation in case of fluid dampers is that of heat transfer, i.e. the mechanical energy dissipated by the damper causes heating of the damper's fluid and mechanical parts. As the damper behaves in accordance with the laws of fluid mechanics, damping force is proportional with the response velocity of a structure during an earthquake. As a result of this feature, fluid dampers have an inherent advantage over the other types of energy dissipation devices: damping force provided by the dampers is completely out-of-phase with the seismic inertia force acting on the structure. Due to the velocity-dependent response of viscous dampers they add virtually zero force at low velocities associated with thermal motion. An additional advantage of viscous dampers lies in their ability to restore to the original position after a seismic 23  Chapter 3:  ENERGY DISSIPATION DEVICES  event. In addition to linear and non-linear behaviour, there is opportunity with viscous dampers to customize performance for unusual applications including: •  Zero force to a given minimum velocity,  •  Zero force above a given maximum velocity (with relief values),  •  Linear or nonlinear properties in between,  A number of U.S. and European manufacturers produce viscous fluid dampers and the devices are capable of a wide range of behaviour. The two prime manufacturers of visco-elastic fluid and viscous fluid devices in North America are Taylor Devices, Inc. and Enidine Inc., both located in New York State. While the different types of dampers can achieve similar force-displacement (or velocity) behaviour, they do so in a number of different ways. Dampers may or may not include pressure regulators or accumulators to compensate for ambient and transient temperature changes. The damper force-velocity behaviour can be obtained either by simple annular or through-piston orificing, or the use of valves (either internal or external). Also, damper sealing systems can vary quite significantly from manufacturer to manufacturer. Some manufacturers also provide fluidlevel or pressure indictor (e.g. Enidine) as a mean for rapid device inspection. The highlysophisticated mechanical characteristics of these types of dampers present a number of issues for the structural engineer to carefully consider, such as maintenance and inspection requirements as part of a long term program to ensure the integrity of the devices. 3.4 DISPLACEMENT-DEPENDENT DAMPERS These devices perform based on yielding of metals (metallic system) or through sliding friction (friction systems). The force-displacement response of these devices is primarily a function of the relative displacement between each end of the device, and is substantially independent of the 24  Chapter 3:  ENERGY DISSIPATION DEVICES  input frequency of motion, range of induced velocity and/or temperature. Before incorporating these devices, it is of paramount importance to examine the issues of: long term reliability, high cycle fatigue (strength degradation and stiffness decay), stick-slip potential for friction dampers and potential of permanent offset after an earthquake. 3.4.1 Metallic Systems A wide variety of different devices have been developed that utilize flexural, shear or axial deformations into post-yield region. Many of these devices use mild steel plates with triangular or hour-glass shape so that the yielding is spread almost uniformly throughout the material. These devices have shown to sustain repeated inelastic deformations in a stable manner, with no premature failure. The most notable of such devices are: the X-shape ADAS (Added Damping Added Stiffness) plates with either single plates, or multiple plates connected side by side that are loaded in the plane of X, Triangular-plate ADAS energy dissipators, mild steel round bars or flat plates and steel-tube energy absorbing devices, (Tsai and Lee, 1993). The use of C-shaped devices (crescent moon) that undergo yielding under applied loading at both ends of the devices has also been implemented in Europe and recently for the retrofit of Granville Bridge in Vancouver. A particular desirable feature of these systems is their stable hysteresis behaviour, long-term reliability, and generally insensitivity to temperature. The hysteresis loops can be easily modelled analytically to exhibit bilinear or trilinear hysteretic behaviour. 3.4.2 Friction Systems During an earthquake large quantity of energy is dissipated by mechanical friction devices rather than by inelastic yielding of the main structural elements. It is claimed that the confinement of energy dissipation to the braces permits the remainder of the members to respond elastically, or at least delays the onset of inelastic deformations. Consequently, the structural performance during a severe earthquake is significantly enhanced. 25  Chapter 3:  ENERGY DISSIPATION DEVICES  There are a variety of friction devices that have been proposed for structural energy dissipation. Friction dampers with rectangular hysteresis loops (very high initial stiffness) are available from Pall Dynamics Ltd. (Canada) and Sumitomo Metal industries Ltd. (Japan). Fluor Daniel Inc. (USA) has developed and tested a type of friction device with several different hysteresis behaviour that confirms its re-centring characteristic. The devices from each of the above manufacturers differ in their mechanical complexity and in the materials used for the sliding surfaces. Friction devices with slip loads commonly in the range of 400 to 800 kN have been implemented to date. The Pall device is intended to be mounted in X-bracing or chevron bracing. Basically, Pall devices consist of a series of steel plates that are specially treated to develop a friction and corrosion resistance. Several earthquake simulator studies of multi-storey steel frames incorporating Pall devices have been performed in Canada (Filiatrault, 1985) and USA (Aiken et al, 1988). The Sumitomo device is an axial element, cylinder shape, in which the frictional resistance is generated by copper alloy pads with graphic plug inserts sliding against the inner surface of the steel barrel of the device. (Aiken and Kelly, 1990) The friction surfaces in the Fluor Daniel device are bronze wedges sliding on a steel barrel. Extensive cyclic test on several different hysteresis behaviours has been conducted by the Fluor Daniel, Inc. (Nims, et al., 1993) Simpler devices with coulomb behaviour include those, which use a brake pad material on steel friction interface. Other friction schemes that involve no special devices, but rather allow slip in bolted connections have also been developed. A reinforcement of the slotted bolted concept has recently been made using a brass on steel friction couple. Earthquake simulator tests of a scaled three-storey steel building model with these slotted bolted connection energy dissipators have been completed at the University of California at Berkeley in 1994 (Grigorian and Popov, 1994). 26  Chapter 3:  ENERGY DISSIPATION DEVICES  3.4.2.1 Pall Friction Dampers In 1982 Pall and Marsh introduced a novel approach for the seismic design of steel framed buildings which comprised the use of friction dampers in tension cross-braces to absorb the seismic energy input. The inclusion of these dampers results in remarkably rectangular and stable hysteresis loops, thus enhancing considerably the energy dissipation capacity of such deviceequipped structures. The system basically consists of a simple mechanism containing frictional brake lining pads introduced at the intersection of frame cross-braces. The device is designed not to slip under normal service loads and low to moderate earthquakes. When a seismic lateral load is induced in the frame, one of the braces goes into tension while the other brace buckles very early in compression. When the load in the tension brace reaches the slip load, it forces the joint to slip and activates the four links. This in turn forces the joint in the other brace to slip simultaneously. In this manner energy is dissipated in both braces in each half cycle. During severe seismic excitation, the device slips at a predetermined load, before any yielding and cracking of the main members has occurred. Slipping of the device changes the natural frequency of structure and allows the structure to alter its fundamental mode shape during a severe earthquake. These friction devices can be used in any configuration of the bracing system needed to meet architectural requirements. Modelling the behaviour of the friction damped cross-bracing follows the assumptions given by Pall and Marsh, namely that the compression diagonal buckles at zero load but that the device keeps this member taut and, at the same time, activates slip in the friction pads of both members. The refined model for the friction damped cross-braced employed by Filiatrault and Cherry (Filiatrault, 1985) generally produced similar results. Thus, the effect of the present diagonal tension braces equipped with a friction device is essentially the same as having a single tensioncompression brace with a friction device which slips at double the slip load of the individual 27  Chapter 3:  ENERGY DISSIPATION DEVICES  tension only brace. 3.5 DESIGN PROCEDURE FOR FRICTION DAMPED STRUCTURES The seismic response of a friction damped frame can be controlled by adjusting the bracing stiffness and the slip force of the damper unit. The model of a SDOF friction damped system excited by ground acceleration a (/) consists of: a mass M; a viscous dashpot whose damping coefficient CQ simulates inherent structural damping; a supporting frame that provides a restoring forceyXO \ and a friction damping unit combining a brace and a friction mechanism that provides an added restoring force, fa(t)  (Fu and Cherry, 1998). This model is schematically  shown in Figure 3.1.  Figure 3.1: Schematic friction damped model (after Fu and Cherry, 1998) The equation describing the relative mass displacement u(t) shown in Figure 3.1 can be expressed as: 1  u(t)+2$0G>m+jf(t) where £0 = CQ/(2(oM)  =~ag(t)  is the initial structural damping ratio, © = J{K7+Kj7M  (3.1) is the  undamped braced natural frequency, K* and KQ are the stiffness of the bare frame and the added friction damper brace, respectively, and /(/) = fit) +fa(J) is the combined system restoring forces, as shown in Figure 3.2. The frame restoring force-displacement relationship fAt) vs. u(j) 28  Chapter 3:  ENERGY DISSIPATION DEVICES  depends on theframestiffness K, and theframeyield force P , while the added restoring forcedisplacement relationship fa(t) vs. u(t) depends on the added stiffness Ka and the friction damper slip force P . f(0* k f(t> = //» + faO) fy  k  <A/ fs  \fa(t)  K +K  f J\  P. +P  i  ;  s  A K°  * y  p  y '  Us  "y  1'-  • lift)  Figure 3.2: Force relationship of a friction damped model (after Fu and Cherry, 1998) The total system restoring force /(/) is nonlinear due to the friction unit slipping and the frame member yielding. As displacement u(t) increases, the system restoring force increases with stiffness Ks+ KQ. When u(t) exceeds us (slip displacement) the added friction damper slips, and the system restoring force is defined by stiffness Kr alone. Further, when u(j) exceeds u theframemembers yield and assuming a perfect elasto-plastic behaviour, the combined system restoring force is limited tof , where/ = Ps + P . When the displacement decreases, the strain energy stored in the frame members and the added component is recovered. Thus, the forcedisplacement hysteresis loops can be plotted as shown in Figure 3.3. 3.6 FRICTION DAMPED BRACED FRAME The device is designed not to slip under normal service loads, wind storms or moderate earthquakes. During a major earthquake, the devices slip at a predetermined load, before yielding 29  Chapter 3:  ENERGY DISSIPATION DEVICES  A  —•  u(t)  Figure 3.3: Force-displacement hysteresis loop of a friction damped model (after Fu and Cherry, 1998) occurs in the other structural elements of the frame. Slippage in the device then provides a mechanism for the dissipation of energy. As the braces carry a constant load while slipping, the additional loads are carried by the moment resisting frame. In this manner, redistribution of force takes place between successive storeys, forcing all the braces to slip and participate in the process of energy dissipation. Such a modified structure combines the following characteristics: 1) It behaves like a braced frame structure during service load conditions, wind storms or moderate earthquakes and possesses sufficient stiffness to control lateral deflections. 2)  During a major earthquake, a large portion of the seismic energy is dissipated mechanically in friction, thereby avoiding, or at least delaying, the yielding of main structural elements.  3) The natural period of the building varies with the amplitude of the oscillations, i.e. severity of the earthquake. In a device-equipped building, the period of the structure is influence by the slip load of the joint and varies with the amplitude of the oscillations, thus resonance is difficult to establish. Hence, the phenomenon of resonance or quasi-resonance is avoided. (Pall et al, 1987). ,i,  30  Chapter 3:  ENERGY DISSIPATION DEVICES  3.6.1 Optimum Slip Load The energy dissipation of a friction device is equal the product of slip load by the total slip travel. For very high slip loads, the energy dissipation in friction will be zero, as there will be no slippage. In this situation the devices will prevent the framing from deforming in a parallelogram shape. This situation can cause brittle bending failures. If the slip load is set very low, large slip travels will occur, but the amount of energy dissipation again will be negligible. In this case the structure will behave exactly as a conventional shear wall system. Between these extremes, there is an intermediate value of the slip load which results in optimum energy dissipation without inducing excessive bending stresses in the frame. This intermediate value is defined as the "Optimum Slip Load". The optimum seismic response of a friction damped system occurs when the difference between the seismic input energy and the energy dissipated by friction is minimized.  31  Chapter 4: BUILDING DESCRIPTION AND INSTRUMENTATION 4.1 INTRODUCTION The #4 Embarcadero Centre building is a 172 m (564 ft) tall steel-frame office tower in downtown San Francisco. The building is one of the first steel high rises built using the eccentric brace frame system developed at the University of California, Berkeley in late 1960s and early 1970s by Egor Popov and his research associates (Popov & Stephen, 1970 and Popov et al., 1976 and Roeder & Popov, 1977). The building was constructed in 1979 based on the 1976 Uniform Building Code (UBC, 1976) requirements and a design response spectra defined by two levels of earthquake performances. It has 41 typical office floors with a floor-to-floor height of 3.66 m (12 ft) and two mechanical floors at the top, also 3.66 m (12 ft) high. Below the first office floor are a mechanical floor, a tall story 4.27 m (14 ft) at the podium level, two lobby levels and two basement levels below grade. The exterior of building has precast panels and glass cladding. A photograph of the building is shown in Figure 4.1. 4.2 STRUCTURAL SYSTEM The #4 Embarcadero Centre building is composed of two structures: a high-rise tower (47-storey above grade) described above and a low-rise building with three stories above grade. The two buildings are separated by seismic joints above street level, and therefore their response to lateral loadings are independent. Below grade, the two buildings share common diaphragms and shear walls. Typical floor plan dimensions are approximately 55 m by 37 m (180 ft by 124 ft) from second floor to the 41st floor. A typical storey plan is shown in Figure 4.2. Plan dimensions decrease above the 39th floor and again above the 41st floor. The top six stories include a series of building-line setbacks in the north-south (transverse) direction so that the roof is less than one third as wide as a typical floor (Figure 4.1). 32  Chapter 4:  m  HfSw  i  •••  ii  K H  1  "II Hi  1  ^^B  I  1 I li  ' m  1m  r ^v  M sp 4|  i* •  BUILDING DESCRIPTION AND INSTRUMENTATION  HI  ^^m  llll ]  ^B  1L  KilB  Figure 4.1: Embarcadero building in San Francisco  ?3^r  zn : E:  6 6 6 6 6 6 6 6 Figure 4.2: Embarcadero Building, typical floor framing plan 33  Chapter 4 :  BUILDING DESCRIPTION AND INSTRUMENTATION  Typical floor construction is steel beam composite with 76 mm (3 in.) metal deck plus 63 mm (2'/2 in.) normal-weight 20 MPa (3,000 psi) concrete fill and 12 mm or 20 mm (/4 in. or 3A in.) diameter shear studs. Vertical loads are carried by frame columns. The lateral system comprises of five momentresisting frames in the east-west (longitudinal) direction and a combination of four momentresisting frames and four eccentrically braced frames (two frames up to the 41st floor and two frames up to the 29th floor) in the north-south direction, the direction used for this investigation. For both directions the beam-to-column connections are moment-resisting joints with full plastic moment capacity. 4.2.1 Moment-Resisting Frame Moment Resisting Frames are known for their earthquake resistance capability due to their stable ductile behaviour under repeated reversing loads and their excellent energy dissipation. These structures are relatively flexible and tend to induce lower seismic force. However, their great flexibility leads to economical problems since interstorey drift and deflections must be controlled to prevent nonstructural damage. It's especially uneconomical to use moment resisting frames along the length of a narrow building where the overall aspect ratio (total height/total width) of the building is very high. Furthermore, because of their greater deflection, the structural stability is affected by the P-A factor, which can be significant. 4.2.2 Eccentric Brace Frame In the past few decades many researchers have shown great interest in the development of a structural system that combines the ductile behaviour of moment-resisting frames and the stiffness of braced moment resisting frames. The lateral behaviour of this structural system differs from conventional concentric bracing in that each brace is connected slightly apart from the beam-to-column joint, achieving the effect somewhere between unbraced construction and concentric bracing. Typically each brace is connected about 1.0 m to 1.5 m away from the joint. 34  Chapter 4 :  BUILDING DESCRIPTION AND INSTRUMENTATION  In the design of tall buildings, there is an increasing demand for reliable structural components with predictable behaviour. Eccentrically Braced Frames (EBFs) are such a system that have recently gained acceptance in seismic design. They posses good elastic stiffness under moderate lateral loads and provide stable mechanism for dissipating large amount of energy when subjected to severe seismic loads. The link is a ductile element that is designed to undergo yielding prior to buckling of the brace (Roeder and Popov, 1977). With the proper selection of the structural geometry, an EBF can have elastic stiffness that is near the stiffness of a similar frame with concentric brace. The EBF system employs deliberately large eccentricities between the brace-beam connection and beam-column joints, which are chosen to assure that the eccentric beam element yields in shear. After a major earthquake, large inelastic deformation must be expected at all floors of a structure. Although the structures is saved from total collapse, the main beams are sacrificed and the structure might need major repairs or replacement. The #4 Embarcadero building described above has eight moment-resisting frames in the northsouth direction. Four of these eight frames in the north-south direction have two bays of eccentric braces with moment resisting shear links at their connection points. Above the 29th floors, the eccentric braces are stopped for two of the frames. No eccentric braces exist for floors above the 40th floor. The diagonal braces are composed of double angles connected to the beams above and below approximately 1.4 m (4.5 ft) from the beam-to-column intersections. Eccentrically braced frames are located along column lines 4, 5, 6 and 7, as shown in Figure 4.2. 4.3 FOUNDATION AND GENERAL SITE DESCRIPTION The Embarcadero building is located in the Lower Market area of San Francisco, which is reclaimed fill area well known for its soft-soil characteristics. This soft-soil amplifies ground motions originating at long distances.  35  Chapter 4 :  BUILDING DESCRIPTION AND INSTRUMENTATION  The tower foundation is a 1.53 m (5 ft) thick reinforced concrete mat supported by approximately 50 to 67 m (150 to 200 ft) long composite steel and concrete piles bearing on bedrock or firm soil. The underlying soil media consist of approximately 8.5 m of a top layer of silty fine sand fill with rubble (estimated shear wave velocity, V , of 200 m/s), followed by 25 m of soft very dark greenish-gray Holocene silty clay (Bay mud, Vs of 150 m/s), 9 m of sand (V of 250 m/s), and 21.5 m of very stiff to hard silty clay (old Bay mud, Vs of 230 m/s). The rock at 64 m deep is sandstone with Vs of approximately 1000 m/s. The site period (Vs = 4H/VS) is approximately 1.3 s, using a depth H of 64 m and an average shear wave velocity V$ of 200 m/s (Celebi, 1993). 4.4 DESIGN CRITERIA For the design of the building, site-specific design response spectra based on two levels of performance of the building were used. The first level of performance required elastic response without structural or nonstructural damage under a moderate earthquake (richter magnitude of 7) that is likely occur during the economic life of the building. The second level of performance demands that the structure will not collapse under the most severe earthquake (richter magnitude of 8.3) that could occur during economic life of the building. Design response spectra based on U.S. Nuclear Regulatory Commission Regulatory Guide 1.60 (Design 1973) of earthquake level 1 (anchored at zero period acceleration (ZPA), 0.3g and 3% damping) and earthquake level 2 (ZPA, 0.5g and 7% damping) are provided in Figure 4.3, which also shows the 1976 UBC spectrum for comparison (Celebi, 1993). 4.5 BUILDING INSTRUMENTATION Studies of recorded responses of instrumented structures constitute an integral part of earthquakehazard reduction programs leading to improved design and analysis procedures. This is the primary motivation of establishing structural instrumentation programs to measure structural responses during earthquakes. Furthermore, the probability of earthquakes magnitude 7 or larger  36  Chapter 4 :  BUILDING DESCRIPTION AND INSTRUMENTATION  Period (sec  Figure 4.3: Design Response spectra of Embarcadero Building occurring in the areas near San Andreas and Hayward faults is considered to be approximately 67% or higher within a 30-year period (U.S. Geological Survey, 1990). Therefore, studies of this type will help to predict the performance of structures better in future earthquakes. The building was instrumented by the strong-motion instrumentation program of the California Division of Mines and Geology of the Department of Conservation (CSMIP) in 1985. The primary goal of the instrumentation was to facilitate studies of the response and associated dynamic characteristics of the building, including its translational, rocking and torsional motions. Also, another objective of the instrumentation is to study how well seismic design provisions used in design of this major steel structure relates to actual performance of the structure. Figure 4.4 shows three-dimensional view of the instrumentation plan for the Embarcadero building at six different floors. There are six digital seismic accelerographs for a total of 18 channels, with each channel being a common-time-connected uniaxial force-balance accelerometer. Accelerometers were placed in the north-south and east-west directions at the 44th, 39th, and 16th Floors, Podium, Street, "B", and "C" Levels (close by column line 31 in the ETABS model). Vertical accelerometers were placed at "B" Level. One of the unidirectional accelerometer sensors was placed in the adjacent low-rise building in the basement. The reference north-south orientations is 345° clockwise from the true north (Figure 4.4).  37  Chapter 4:  BUILDING DESCRIPTION AND INSTRUMENTATION  Figure 4.4: General three-dimensional instrumentation view of the Embarcadero building (after Celebi, 1993) The instrumentation could be Used to obtain the following information about the behaviour of the building during upcoming earthquakes: 1)  Lateral displacement of the building in longitudinal and transverse directions,  2)  Torsional motions at upper and lower levels,  3)  Storey shear and overturning moment,  4)  Interaction of the tower and adjacent building,  4.6 BUILDING RESPONSE TO LOMA PRIETA EARTHQUAKE The Embarcadero building is in the Lower Market area of San Francisco, which is of great interest to the engineering community because of the area's soft-soil characteristics that amplify ground 38  Chapter 4 :  BUILDING DESCRIPTION AND INSTRUMENTATION  motions originating at long distances. The building was moderately excited during the October 17, 1989, Loma Prieta (Ms = 7.1) earthquake. The epicentre of the earthquake was about 97 km away from the building site. The building was essentially undamaged by the earthquake. The Embarcadero Freeway (within 100 m of the building), however, suffered extensive damage during the earthquake and was razed in 1991. The eighteen accelerometers installed on the Embarcadero building were activated during the October 17,1989, Loma Prieta earthquake. Following the earthquake, the sensors provided a 120 sec time history of the building's response to the earthquake, which lasted about 15 sec at the site. At the end of the 120 sec period, displacements had not fallen to zero and the building continued to vibrate for another minute. The processed 120 sec of the recorded acceleration and the corresponding displacement at instrumented levels for the north-south direction (Figure 4.4) are shown in Figures 4.5 and 4.6, respectively. This data have been filtered using a bandpass filter with ramps at 0.07 - 0.14 Hz and 23 - 25 Hz (Shakal et al. 1989). Peak accelerations and displacements in the north-south (N-S) direction are summarized in Table 4.1. The N-S peak acceleration responses at the 39th floor are less than the N-S peak responses at the 16th floor. This may be attributed to several reasons, including mainly the discontinuity of stiffness at the 40th floor causing: 1.  The 39th floor to behave as if the higher mode response affected it's response,  2.  whipping effect of the floors,  3.  Resonance effect at the upper floors where the bracing was discontinued and the mass and stiffness of the building was altered considerably.  4.6.1 Drift Investigation The explanation provided above might be directly related to discussions on drift. Figure 4.7 shows the superimposed drift-ratio time histories between the 44th and 39th floors, 44th floor and street level as well as 39th and 16th floors and 39th floor and street level. It can be observed that 39  Chapter 4 :  BUILDING DESCRIPTION AND INSTRUMENTATION  Sensor  Acceleration (g)  Absolute Displacement (mm)  44  17  0.47  162  44  18  0.43  164  39  14  0.13  143  39  15  0.12  141  16  12  0.19  63  16  13  0.17  76  Podium  9  0.15  39  Podium  10  0.14  40  Street  8  0.12  34  B  4  0.11  34  B  6  0.10  33  C  3  0.17  84  Level  Table 4.1: Peak accelerations and displacements of the Embarcadero building during Loma Prieta earthquake in the eccentric braced direction the average drift ratio between 44th and 39th floors exceeds 0.005 while the average drift ratios between 44th and street level was about 0.0015. This may be attributed to either discontinuity of the eccentric bracing above the 40th floor or the whipping effect at the top floor, which can not be confirmed since there were no sensors at two consecutive top floors. 4.7 ROCKING OF THE BUILDING IN THE ECCENTRIC BRACED DIRECTION The effects of foundation flexibility could be investigated from the vertical accelerometers (channels 1 and 2) installed near the north and south end walls of the basement of the building. The vertical displacement of accelerometers 1 and 2 mounted on the basement together with the rotation of the basement mat (calculated from displacement time-histories) and basement walls are shown in Figure 4.8. The rotation of basement walls represent the relative horizontal  40  Chapter 4:  BUILDING DESCRIPTION AND INSTRUMENTATION  0.15  Level B. West  0.00 i  -0.15  I  -1  I  I  I  I  I  1  I  I  I  I  I  I  I  L_J  L_J  I  L_J  I  I  1_  0.15  Level B. East  o.oo -0.15 0.15  Street Level. West  0.00 -J  -0.15 0.15  l  I  I  L_  Podium Level. West - w w \ w v * « H O T f l ^  0.00  I  ~  w— _]  -0.15 0.15 C  0.00  o 2  -0.15 0.2  JD 0) O O  <  L__i  I  I  I  I  Podium Level, East  _j  '  I_J  J  >  16th Floor. West  0.0 J  -0.2  0.2  i  i  i_  16th Floor. East  0.0 -0.2  _l  I  L_J  \1  L_J  !  I  I  I  I  I  L_J  I  I  J  L  I  I  0.15  I  I  I  I  I  L_J  I  l_J  L  J  39th Floor. West  0.00 _l  I  I  I  I  l  I  LLJ  I  I  L_J  L_J  I  I  I  l_J  l_J  L_l  I  I  I  L  Figure 4.5: Recorded acceleration for the Embarcadero building during Loma Prieta earthquake 41  Chapter 4 :  BUILDING DESCRIPTION AND INSTRUMENTATION  50  Level B, West  o 50  n n l  -50  i i i I i i i i [  .  .  M  I  M  M  I  M  M  !  I I I I I I I I I I I I I I I I  Level B. East  o -50  i i i  i i i i i i i i i i i i i i  i i i i i i i i i i i i i i i i i i i  50  Street Level. West  0 -50  i i i i i i i i  I i i i i I i i i i I i ' ' i I i i i i I ' i i  M M !  50  i i i i ' ' i i '  Podium Level. West  0  E E  -50  «•-»  I i i i i I i i i i I I I I I I I ! I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I ' I  50  Podium Level, East  0  c  E  M i l l  -50 100  O  JS  Q </)  0 -100 100  l l l l l  M i l l  16th Floor. West —  -  ^  (  ^ I i . i . I . • i • I  . I I l_ I ,,l  l_J L_J I L I I I I I I * 16th Floor.  East  0  -100  I i i i i I i i i i I i i i i I i i ' i I  i ' ' i ' i i ' i i i i * l ' i i ' I i  i i i i i i i ' i i i i i  39th Floor. West  50  60  70  100  110  120  Time, sec Figure 4.6: Recorded displacement for the Embarcadero building during Loma Prieta earthquake 42  Chapter 4: 0.006  BUILDING DESCRIPTION AND INSTRUMENTATION  Between 44th and 39th floors between 44th and street level  0.003 (0  a:  0  £  Q  -0.003 -0.006  between 39th and 16th floors  0.002  between 39th and street level o  0.001  CO  a: Q  0 -0.001 -0.002  10  20  30  40  50  60  70  80  90  100  Time, sec Figure 4.7: Drift ratios for the Embarcadero building for the Loma Prieta Earthquake deformation between the ground level and the basement mat. In general, these rocking rotations are insignificant because of the pile foundation system. The significance of Figure 4.8 is that the mat rotation has a peak value of 0.000057 radians (0.0033°) while the peak of wall rotation in the north-south direction is 0.0004 radians (0.023°). The main observation here is that the rotation of the perimeter walls is significantly higher than that of the mat. Similar peak rotations have been observed in response data from the nearby Trans America building. Also, the frequencies of these rotations are the same as those of translational natural frequencies in the basement motions (Celebi, 1993). It is also interesting to note that the motion pattern at ground level and at basement level are very similar, although the ground level motions are slightly larger (Figure 4.5).  43  Chapter 4 :  BUILDING DESCRIPTION AND INSTRUMENTATION  North Wall. Vertical  5  -20 South Wall. Vertical  jS 0.00000 o a: ra -0.00003 -0.00006 0.0004 -o 2 0.0002 c g 13 0 o =S -0.0002 -0.0004  10  20  30  40  50  60  70  80  90  100 110 12  Time, sec  Figure 4.8: Vertical displacement at the basement level together with rotation of base mat and basement wall 44  Chapter 4 :  BUILDING DESCRIPTION AND INSTRUMENTATION  4.7.1 Fourier Analyses Celebi (1993) extensively studied the recorded data of the building based on Fourier amplitude spectra, auto-spectra, cross-spectral amplitudes, coherence functions and associated phase angles. Fourier amplitude spectra of horizontal motions grouped for each of the six instrumented levels were computed by Celebi as shown in Figure 4.9. r-  »10*  SPECTRA-aTKFI. t*)  -.  (*>* SPECTRA-39TH.FL,  CH17 (NS) CH18(NS)  S  CH16(EW)  Jt I  OJ  1 1.5 2 FREQ(HZ) SPECTRA-16TH.FL.  (c)  CH12(NS) , CH13(NS) CH11(EW)  ^0000  a P 5000 *  °0  L  (0i  ~  2S  05  1 L5 FREQ(HZ)  2  OS  2  2J  i  ^wW  KI  05  ^ Hi <a 30oo F  U CH8 (NS) M II — - C H 7 ( E W )  1 L5 FREQ(HZ)  _> (<H SPECTRA-PODIUM LV. <G5000| ' y CH9 (NS) j ^ CH10(NS) j  2-5  SPECTRA-STREET LV.  3000  0  1 1.5 FREQ(HZ)  2  *3  2J  SPECTRA-BASEMENT 1  CH4 (NS) -•-CH6(NS) ---CH5(EW)  _UL  05  1 LS FREQ(HZ)  "0  2 ^  fflJ SPECTRA-REL ACCEL 6000 ty  4000-  .88  0.5  1 1.5 FREQ(HZ)  2  15  ffcj SPECTRA-VERT. ACCEL  5  — CH17-CH18 --CH14-CH15 .-.-CH12-CHD  o w  2000 0. J  >w»»iSJ 05 1 U FREQ(HZ)  2  Z5  0  05  1 LS FREQ(HZ)  2  2J  Figure 4.9: Fourier amplitude spectra of horizontal ground motions recorded during the Loma Prieta earthquake (after Celebi, 1993) 45  Chapter 4 :  BUILDING DESCRIPTION AND INSTRUMENTATION  The Fourier analyses results indicated peak amplitudes at 0.19 Hz, 0.57 Hz and 0.98 Hz frequencies. Using the coherence and phase angle functions between 44th and 16th floors, Celebi (1993) confirmed that at 0.19 Hz the coherence was unity and phase angle was 0° (first mode, NS), at 0.57 Hz, coherence was unity and phase angle was 180° (second mode, N-S), and at 0.98 Hz coherence was near unity and phase angle was zero (third mode, N-S). The Fourier spectra amplitude at approximately 0.75 Hz observed in Figure 4.9 was attributed to the site because the amplitude stays the same in all plots. The Fourier analysis spectra indicated that torsional response of the building was insignificant even though numerically some differential motions could be computed from the recorded data. The dominant frequency of Fourier amplitude spectra for the differential motions was calculated at about 0.88 Hz (Celebi, 1993). A system identification procedure based on recorded input-output data for the Embarcadero building was carried out by Celebi (1993). The input was the basement or ground floor motion and the output was the roof level motion or one of the floors where the structural response was detectable. The modal acceleration contributions, four significant natural frequencies and modal damping ratios were extracted from the system identification analysis. Identified dynamic characteristic of the building for the N-S direction are summarized in Table 4.2. Natural Frequency (Hz)  Natural Period (Sec)  Modal Damping Ratio, £ (%)  Modal Acceleration Contribution (%)  Modal Displacement Contribution (%)  1  0.19  5.26  2.5  15  61  2  0.57  1.75  2.2  8  9  3  0.98  1.02  1.4  71  26  4  1.33  0.75  2.3  6  4  Mode  Table 4.2: Dynamic characteristics of the building as identified by Celebi (1993) 46  Chapter 4:  BUILDING DESCRIPTION AND INSTRUMENTATION  The four significant modal periods in each directions follow the general rule-of-thumb approximation of T, 7 7 3 , 775 ,and 777. The modal damping percentages vary between 1.4% and 2.5%. Such low damping percentages are the reason why the response of the building lasted longer than the processed 120 sec. The acceleration modal contribution analysis, Table 4.2, indicate a high percentage contribution of the third mode in floor acceleration response and consequently the storey shears and overturning moments. On the other hand, the modal contributions of displacements extracted from system identification analysis indicate the N-S displacement response was primarily dominated by the first mode. It is, therefore, concluded that even though the contribution of higher modes are rather large for acceleration spectral amplification, their contribution to the total response of the long period structures are much smaller.  47  Chapter 5: DESCRIPTION OF ETABS PROGRAM 5.1 GENERAL The commercially available computer program ETABS (Computers & Structures Inc., 1995) was chosen for the numerical analyses in this thesis for two reasons. First, ETABS is a special purpose computer program for the analysis of building systems. Building systems represent a unique class of structures that are defined floor-by-floor, column-by-column, bay-by-bay and wall-by-wall and not as a sequence of non-descriptive nodes and elements as in general purpose computer programs. Second, ETABS is among the most commonly used structural analysis software packages in analysis and design of a variety of commercial and residential buildings by engineering consultants, and thus serves as a useful benchmark. The special features of the ETABS program greatly reduces the amount of input required. This includes the definition of beams and columns as a simple grid system rather than a complex matrix of nodes and elements. The inherent assumption of rigid floor system in ETABS makes it ideal for defining floor systems in high rise buildings. 5.2 ETABS FEATURES ETABS is a special purpose computer program for the linear and non-linear, static and dynamic analysis of buildings. ETABS offers a comprehensive 3-D analysis and design for multistorey building structures, such as office buildings, apartments and hospitals. A complete suite of Windows graphical tools and utilities are included with the base package, including a modeller and a post-processor for viewing all results, including mode shapes, force diagrams and deflected shapes. The ETABS buildings may be un-symmetrical and non-rectangular in plan. The program considers a building system as an assemblage of vertical frames interconnected at each storey level by horizontal floor diaphragms. The vertical frames are idealized as an assemblage of 48  Chapter 5:  DESCRIPTION OF ETABS PROGRAM  column, beam, brace and wall elements interconnected by horizontal floor diaphragm slabs which may be rigid or flexible in their own plane. The floor elements may span between adjacent levels for the creation of sloped floors. Modelling of partial diaphragms, such as in mezzanines, setbacks, atriums and floor openings is possible. It is also possible to consider situations with multiple diaphragms at each level thereby allowing the modelling of buildings consisting of several towers rising from a combined structure below or vice-versa. 5.3 CONCEPT OF FRAMES IN ETABS The basic frame geometry is defined with reference to a simple three-dimensional grid system formed by intersecting floor planes and column lines. The concept of a frame in the ETABS environment is an assemblage of column lines, each of which in turn may be connected to each other by beam bays, floor bays, braces or panels. A frame basically consists of columns that are vertical lines parallel to the z-axis defined in plane of x-y coordinates and beams that are horizontal. Three-dimensional frames may also include shear walls and diagonal bracing. The gridwork formed by the horizontal floor diaphragms and the vertical column lines forms the basic reference system for the description of a frame (see Figure 5.1). The column lines (defined as CI, C2, C3) are located with coordinates in the x-y plane and the bays (identified as Bl, B2, B3) are located in plan as connections between the column lines. A bay is defined as a connection between any two column lines. On each column line there may exist columns corresponding to the storey levels. For example, in Figure 1, column line C3 has 4 columns, one corresponding to each level, whereas column line C5 has only one column, corresponding to level 4. Similarly, for each bay there may exist beams corresponding to the storey levels. For example, in Figure 2, bay B3 has four beams, one corresponding to each level, whereas bay B4 has only two beams corresponding to levels 3 and 4, respectively. A cross-bracing element has also been assigned between column lines C3 and C4 from baseline to level 1. A shear wall assembly is defined between column lines CI and C2 49  Chapter 5:  •  B3  C4  >'  BA  Horizontal Floor ^C1 Diaphragm I B1«£—1| Local Frame Axes  4-J  • C2  y*B2 • *  ty  r  k C3  T  f  DESCRIPTION OF ETABS PROGRAM  •  B2  C3  C2 #  FRAME 2 B1 I  • I  C1 I  C5 FRAME 1  r  B3 f  C4B4^?  w  .  w  B5^6  B7  C7 •  B6  x *  •  Level 4  Figure 5.1: Typical Building System 50  Chapter 5:  DESCRIPTION OF ETABS PROGRAM  throughout the height of the building. 5.4 LINEAR STRUCTURAL ELEMENTS IN ETABS 5.4.1 Column Element A column element is always defined vertically at any level on a column line. The length of the column is the height of storey. The top or bottom of column may be either continuous or pinned in the major or minor direction of bending. The self mass and weight of the column element is based upon the story-to-story height of the column and is lumped equally at each end of the column. The column element formulation includes the effects of axial, shear, bending and torsional deformations. The column element may be prismatic or nonprismatic from floor level to floor level, and have different boundary conditions at each floor level. For nonprismatic sections the user defines variable section properties along the member length, by referring to section properties already defined, for different segments along the member. Up to three different segments along the member length can be defined (see Figure 5.2).  L3  Figure 5.2: Examples of columns with variable section properties Corresponding to the major and minor directions of the top and bottom ends of the column, each column element has four rigid zones (see Figure 5.3). These zones are set by the depth dimension of the beam that frame into the columns. For each beam connected to the column, ETABS 51  Chapter 5:  t  DESCRIPTION OF ETABS PROGRAM  Column minor direction  Colum major directio  Figure 5.3: Column and beam rigid end offsets calculates: R  = DB major  . cos 2 0 major  R  minor  =  DB  minorsin  0  (5.1)  Where DB is the depth of the beam below the diaphragm for the column top and above the diaphragm for column bottom, and 9 is the angle between the direction of the beam and the column major direction. R is the rigid offset value. The column member forces are output at the outer ends of the rigid zones (outer face of the supports). In many structures the dimensions of the members are large which have a significant effect on the overall stiffness of the structure. An analysis based upon a centerline to centerline geometry, in general, overestimates the deflection. However, it has been found that an analysis based upon the clear length of members can underestimate the deflections of the structure. ETABS uses a rigid zone reduction factor to reduce the lengths of the rigid zones, thereby compensating for some of the deformations that do exist in the zone bounded by the finite dimensions of the joint. This value is set by the user as 25%, 50%, 75% or 100% of the length of 52  Chapter 5:  DESCRIPTION OF ETABS PROGRAM  the rigid zone. 5.4.2 Beam Element In general, beams are horizontal members (bays) between two column lines. Any one end of the beam may be dropped a level to model a slopping beam. Beam connections at either end may be fixed or pinned in the major or minor directions of bending. Partially fixed connections are also possible. The beam element formulation includes the effects of axial, shear, bending and torsional deformations. In beams the axial deformation effects and minor direction shear and bending deformation effects are only activated if the ends of beam connect to different diaphragms or at least one end is disconnected from the diaphragm. Beams may be prismatic or nonprismatic. For nonprismatic sections the user defines variable section properties along the member length. Up to three different segments along the member length can be defined (see Figure 5.4).  H—*i*  H*  H  Figure 5.4: Examples of beams with variable section properties The beam element may have rigid zones for stiffness correction (see figure 5.3). Corresponding to the / andy ends of a beam, each beam has two rigid zones. These zones are set by the major or minor dimensions, respectively, of the columns that exist at the ends of the beams. In calculating 53  Chapter 5:  DESCRIPTION OF ETABS PROGRAM  rigid zones, the two column elements above and below beam are examined. For each end, ETABS computes the quantity: DCm. n _  major  cos 2 9  DCminn ,  sin 2 0  minor  ,r *y\  Where £>Cmaj0r and DCmimr are the major and minor dimensions of the column element, and 0 is the angle between the direction of the beam and the column major direction. The self weight of the beam is applied as a uniform or variable load along the clear length of the beam proportional to the beam cross-section. The self mass of the beam is based upon the clear length of the beam and is lumped equally at each end of the beam. Vertical loading may be applied as uniform, trapezoidal or point loads on the beam span in the major plane of beam. Vertical uniform loads on the floor elements are automatically converted to span loads on adjoining beams, thereby automating the tedious task of transferring floor tributary loads to the floor beams without explicit modelling of the secondary framing. 5.4.3 Floor Element In general, floor element is a horizontal element between three or four column lines. The size of a floor element is determined from its connectivity. Any one edge of the floor may be dropped a level to model sloping roof diaphragms or ramped floors. Uniform vertical as well as lateral loading may be applied on any floor element. The uniform vertical loads are converted to beam span loads and are applied to the beams at the edges of the floor element. If a beam does not exist at a certain edge the tributary load associated with that edge is lumped at the corners (see Figure 5.5a). The floor element may have equally spaced secondary beams specified in any direction. In this case, all secondary framing is assumed to be simply supported at the beams and they load the beams with point loads (see Figure 5.5b). The uniform floor lateral loads are converted to joint loads on a tributary area basis.  54  Chapter 5:  DESCRIPTION OF ETABS PROGRAM  Figure 5.5: Examples of tributary floor vertical loading algorithms The floor element formulation includes only membrane stiffness. That is, it does not have any out-of-plane stiffness. The orthotropic properties of a floor element may be accommodated through thickness of the element in the two orthogonal directions and the in-plane shear. The self weight of the floor element is assumed uniformly distributed on the floor and gets applied either to thefloorjoints or as beam span loads on adjoining beams. The self mass of the floor is assumed uniformly distributed on thefloorand gets applied as lumped masses at the floor joints. Thefloorelement forces are output at the joints as nodal forces in thefloorlocal coordinate system. 5.4.4 Brace Element The brace element may exist in any vertical plane between any two column lines (consecutive or nonconsecutive). The end of a brace element may be continuous or pinned. The brace element formulation includes the effects of axial, shear, bending and torsional deformations. The brace element must be prismatic from floor level to floor level. The brace element has no options for rigid zones for stiffness correction. The self weight of a brace is based upon the storey to storey length of the brace, and is lumped equally at each end of the brace. Reduction factors may be applied to the moment of inertias and 55  Chapter 5:  DESCRIPTION OF ETABS PROGRAM  torsional constants specified to modify the bending or torsional stiffness. This will account for different modelling conditions such as cracking in welds or bending of gusset plates. 5.4.5 Panel Element The panel element can exist between any two column lines (consecutive or nonconsecutive) and between any two consecutive levels. The panel element must be prismatic from floor level to floor level. The panel element is based on an isoparametric finite element membrane formulation with incompatible modes. The panel stiffness is based on a length equal to the storey height with no rigid zones due to the depth of the beams that may be framing into the panel. The formulation includes in-plane rotational stiffness components which allows the panel to connect to the column, beam and brace elements and achieve moment continuity. The assemblages of panel elements may be defined to form T-, L- or C-shaped walls, and other complex wall configurations (see Figure 5.6). The ETABS computer program has a special panel element that combines the versatility of the finite element method with the design requirements that the wall output be written in terms of total moments and forces, instead of the usual finite element output of direct stress, shear stress and principal stress values. The program will produce integrated moments, shears and axial forces for the wall defined by the panel assemblage at the centre of gravity of the wall. A panel element may be modelled with piers at the two ends. In this case the panel is inserted in the model at the centre of the piers. Piers may be modelled as equal to thickness of the panel, allowing an easy method of varying the panel insertion in the model. The end piers provide additional axial, tortional and out of plane bending stiffness at their respective ends. Panels in the lowest storey are assumed fixed at the bottom. The panel element has been designed to be used in modelling of shear wall systems where the primary mode of bending is vertical, i.e. associated with horizontal shears. 56  Chapter 5: DESCRIPTION OF ETABS PROGRAM  Figure 5.6: Three-dimensional C-shaped shear wall system with beams and columns The panel element is suitable for the modelling of general three-dimensional shear wall configurations, such as C-shaped core elevator walls, curved shear walls, discontinuous shear walls and shear walls with arbitrarily located openings. Torsional and warping effects in threedimensional walls are accurately captured. The self weight and mass of a panel are based on the storey to storey height of the panel and are lumped equally at the four joints of the panel. 5.5 NONLINEAR STRUCTURAL ELEMENTS IN ETABS The ETABS nonlinear elements include a link element, a spring element (grounded), a uniaxial damper element, a uniaxial gap element, a uniaxial plasticity element, a biaxial hysteretic isolator element and a biaxial friction pendulum element. The nonlinear properties of these elements are only used during nonlinear dynamic time history 57  Chapter 5:  DESCRIPTION OF ETABS PROGRAM  analysis. For static, dynamic response spectrum and linear time history analyses an effective stiffness and damping properties specified by the used may be used. 5.5.1 link Element The link element may be defined between any two joints and can take linear or nonlinear properties. The ends of the link may be continuous or pinned. Link element has no self weight or self mass. The link element is defined with total stiffness properties rather than section properties. The link element local coordinate system is defined as a column element if the link is vertical or if it has zero length. A link element is defined as a beam element if the link is horizontal and it is defined as a brace element if the link is defined between two different floors and not connected to the same column line. The diaphragm connectivity of a link element is determined by the diaphragm connectivity of its end joints. 5.5.2 Spring Element The spring element may be connected to any joint on one end and to ground at the other end, except at the baseline. Spring elements can take linear or nonlinear properties. The diaphragm connectivity of a spring element is determined by the diaphragm connectivity of the joint. The spring element properties are defined with three dimensional translational and rotational spring constants. The spring element has no self weight or self mass. 5.5.3 Uniaxial Damper The uniaxial damper element can be used in either the axial or the major and minor shear directions. The damper force varies as F = Cv , where C is the damping coefficient, a is an exponent and v is the velocity of deformation in the element. For spectral and linear time history analyses a is set to 1.0 and the damping is linearly proportional to the velocity. ETABS uses the damping coefficient C to obtain modal damping values. No effective stiffness value is associated with this element. 58  Chapter 5:  DESCRIPTION OF ETABS PROGRAM  5.5.4 Uniaxial Gap The uniaxial gap element can be used in either the axial or the major and minor shear directions. The gap element has zero stiffness when open and a linear elastic stiffness when closed. A negative initial opening representing a precompressive element may be specified. An effective elastic stiffness may be specified for linear analysis. No effective damping ratio may . be specified for this element for dynamic analysis. 5.5.5 Uniaxial Plasticity Element The uniaxial plasticity element can be used in either the axial or the major and minor shear directions. A hysteretic behaviour proposed by Wen (1976) which allows for parameters to vary post-yield stiffness and the shape and width of the hysteresis curves is implemented. An effective elastic stiffness and damping ratio can be specified for linear dynamic analysis. 5.5.6 Biaxial Hysteretic Isolator Element The biaxial hysteretic isolator element has stiffness in axial and the major and minor shear directions. The shear load-deformation relationship follows a hysteretic curve while the axial stiffness has linear elastic behaviour. An effective elastic stiffness and damping ratio can be specified for linear dynamic analysis for the two shear directions. 5.5.7 Biaxial Friction Pendulum Isolator Element The biaxial hysteretic isolator element has stiffness in axial and the major and minor shear directions. The shear load-deformation has hysteretic behaviour due to friction and a post-slip stiffness due to the finite pendulum radius of the slipping surfaces. The hysteretic behaviour of the element for the friction portion is based on the work proposed by Wen (1976) and Park, et al. (1986). The axial stiffness has linear elastic behaviour. An effective elastic stiffness and damping ratio to account for the friction loss can be specified for linear dynamic analysis for the two shear directions.  59  Chapter 5:  DESCRIPTION OF ETABS PROGRAM  The shear forces due to friction and due to the pendulum action are dependent on the axial load in the element. The element allows for the axial load to vary due to overturning effects. Tension in the element causes the shear forces due to both the friction part and the pendulum part to go to zero. It is important for this element to start the nonlinear analysis from an initial state that includes gravity loads to correctly account for the axial load in the isolators. 5.6 ETABS PROGRAM CAPABILITIES The program ETABS comes with database containing the properties for the sections given in the "Manual of Steel Construction" published by American Institute of Steel Construction (AISC) and the "Handbook of Steel Construction" published by the Canadian Standard Association (CSA/S16-94). Automatic mass properties calculation may be performed by the program. The user specifies the diaphragms as discretized series of points, lines, rectangular areas, circular arcs, circular areas and triangular areas each having a mass intensity and dimensions. Using this information ETABS calculates a total mass, the global coordinates of the centre of mass, and a mass moment of inertia about a vertical axis passing through the centre of mass. The building storey height and storey mass defined by the user are used to generate lateral seismic loads. The lateral seismic loads defined by the Uniform Building Code (UBC), Applied Technology Council (ATC), National Building Code of Canada (NBCC) and Building Official and Code Administrators International (BOCA) can be automatically calculated by the ETABS program. Also, the building storey height may be used to generate lateral wind loads. This option is only available for rigid floor diaphragms. ETABS includes the P-delta effects into the basic formulation of the structural lateral stiffness matrix as a geometric correction. This causes the equilibrium to be satisfied in the deformed position, and the P-delta problem is solved exactly with no iteration and no additional numerical  60  Chapter 5:  DESCRIPTION OF ETABS PROGRAM  effort. Also, as the correction is on the lateral stiffness matrix, the P-delta effects appear in the static analysis and filter into the Eigen, response spectrum and time history analyses. Three dimensional mode shapes and frequencies, modal participation factors, direction factors and participating mass percentages are evaluated using iteration techniques. Response spectrum analysis is based upon the mode superposition method using the complete quadratic modal combination (CQC) technique. The structure may be excited from two different directions in any one run with independent spectra. Composite modal damping effects from supplemental dampers are included in the analysis. The linear time history analysis uses a variable time step closed form integration technique for the evaluation of the modal coordinates. Time-dependent ground accelerations can excite the structure concurrently in any two orthogonal horizontal directions with independent excitations. The nonlinear time history analysis is based upon an iterative vector superposition integration scheme. The time history results may be displayed as time-functions (such as displacement vs. time) or a function-function (such as force vs. deformation). Response spectrum curves may be created from acceleration time histories generated by ETABS. Results from the various static load conditions may be combined with each other or with the results from the dynamic response spectrum or time history analyses. The output included static and dynamic storey displacements and storey shears, interstorey drifts, and joint displacements, reactions and member forces. Torsional behaviour of the floors and interstorey compatibility of the floors are accurately reflected in the results. 5.7 ETABS NONLINEAR ANALYSIS The method on nonlinear dynamic analysis used in ETABS is an extension of method developed by Wilson (1989 and 1993). The method is most suitable for structures with a limited number of predefined nonlinear elements. A short description of the method is presented below. 61  Chapter 5:  DESCRIPTION OF ETABS PROGRAM  The dynamic equation of motion of an elastic structure with nonlinear elements subjected to input ground motion can be written as: Mx{t) + Cx(t) + Kx(t) + R(t) = -Mx (t)  (5.3)  where M is the mass matrix, C is the viscous damping matrix, K is the elastic stiffness matrix and R is the nodal forces from the nonlinear elements, JC, X and x are the relative displacements, velocities and accelerations with respect to ground, and x  is the input ground acceleration.  Equation (5.3) may be rewritten as: Mx(t) + Cx(t) + Kx(t) = - Mxg(t) - [R(t) - Kpy(t)x(t)] where K = K-K  .K  (5.4)  is the post-yield stiffness of the nonlinear elements.  Using modal superposition method the above equation can be written in modal form as: PP(0 + ny(t) + X2y(t) = - Fg(t) - Q(t)  (5.5)  T  where T = O MO is the identity matrix, <t> being the mode shapes normalized to mass, T I T Q = O CO is the modal damping matrix which is assumed to be diagonal, X = O CO is a T diagonal matrix of structural frequencies squared, F = O Mx (t) is an array of modal input o  T  loads and Q(t) = O [R(t) - K (t)x(t)]  o  is an array of modal forces from the nonlinear  elements. It is, however, should be noted that contrary to linear dynamic analysis equation (5.5) can not be decoupled because of the Q(t) terms on the right-hand side. Equation (5.5) is solved iteratively by ETABS using closed form integration assuming linear variation of the nonlinear elements between time steps. The iterations are continued until convergence is achieved.  62  Chapter 6: THREE-DIMENSIONAL LINEAR ANALYSIS OF THE BUILDING 6.1 GENERAL The Loma Prieta earthquake (Ms = 7.1) of October 17, 1989 provided valuable data on actual seismic performance of various types of structures in San Francisco, including the #4 Embarcadero Centre building. The epicenter of the magnitude 7.1 earthquake was located about 16.13 km northeast of Santa Cruz along a segment of the San Andreas Fault, near Loma Prieta in the Santa Cruz Mountains. The focal depth has been placed at 17.74 km. This is unusually deep, as typical California earthquake focal depths are 6.45 to 9.68 km. The epicentre of the earthquake was approximately 97 km north-east of the building. The availability of recorded time-history response data of the #4 Embarcadero Centre building during the Loma Prieta earthquake made it possible to test the accuracy of assumptions made in modelling a steel high-rise building and the predicted results obtained from various structural analysis software packages (e.g. ETABS). To verify these assumptions and to provide quantitative information on the behaviour of the building during the Loma Prieta earthquake three-dimensional linear analyses of the building were carried out. As discussed in Chapter 4, analysis of the measured data for the building indicates that the building did not experience any inelasticity during the earthquake. Moreover, the level of displacements computed from the recorded accelerations was low indicating small and negligible secondary effects such as P-A effects. Once the accuracy of the model was verified a further objective of this thesis was to investigate the hypothetical performance of the building under other types of ground motions. To this end, the records from three other earthquakes recorded around the world were selected. These earthquakes are California Northridge earthquake in 1994 (Sylmar station record), Landers earthquake in 1992, also in California (Joshua station record) and Guerrero-Michoacan, Mexico 63  Chapter 6:  THREE-DIMENSIONAL LINEAR ANALYSIS OF THE BUILDING  earthquake in 1985 (Mexico City (SCT1) record). The selected earthquake records are representatives of earthquakes with different frequency content and time data characteristics. The January 17, 1994 Northridge (Mw = 6.7) earthquake produced the largest ground motions ever recorded in an urban environment and caused the greatest damage in the United States since the great 1906 San Francisco earthquake (U.S.G.S, 1994). The Landers earthquake was the largest earthquake in California since 1952 and the second largest since 1906. The Richter magnitude (M = 7.4) trembler was entered near the small desert community of Landers, approximately 177.42 km east of Los Angeles. The quake, which was entered 51.61 km north of Joshua Tree in Southern California, caused no serious damage. The epicenter of the Guerrero-Michoacan, Mexico earthquake was located about 50 km off the coast of Mexico. This type of deep subduction earthquake is not, however, a representative of the types of earthquakes expected to occur in the San Francisco area. It was mainly chosen because it can severely excite the buildings with high natural fundamental frequencies. Further details of these selected earthquake records are provided in section "Linear Elastic Building Response to Other Earthquakes" on page 80. Comparison of analytical results and recorded responses of instrumented structures helps to better predict the lateral performance of the structures with similar lateral load resisting elements during future earthquakes and also improvement in design codes and analytical procedures. 6.2 MODEL DESCRIPTION A precise model of the building with 47 storey levels above the grade and two storey floors below ground level was created using the information from the structural design drawings of the building. It is noted that a version 5.0 ETABS model of the building was previously created by Steinke in 1993. The present model was created for version 6.23 ETABS computer program and incorporated enhancements to the previous model including the addition of floor elements, modifications to the column and beam rigid zones, semi-rigid beam-to-column connections and 64  Chapter 6:  THREE-DIMENSIONAL LINEAR ANALYSIS OF THE BUILDING  variation in modal damping ratios for all participating modes. The building was modelled as a single frame with 72 column lines, 111 beam bays, 30 panel elements and 312 brace elements. Figure 6.1 shows three-dimensional and eccentric braced elevation views of the building as modelled in ETABS together with a close-up of a typical storey plan of the building.  Figure 6.1: ETABS model of the #4 Embarcadero Centre eccentric braced frame building  65  Chapter 6:  THREE-DIMENSIONAL LINEAR ANALYSIS OF THE BUILDING  Results of analytical studies of the recorded motions of the building during the Loma Prieta earthquake was utilized to calibrate the analytical computer model of the building such that its frequencies obtained through the dynamic analysis corresponded to those obtained from the analysis of the measured data. This was done through evaluating a variety of different modelling assumptions including rigidity of beam-to-column connections and overall rigidity of panel zones. A discussion on the selection of various structural parameters are presented in the following paragraphs. 6.2.1 Investigated Building Parameters Parameters that may affect model responses can be divided into three categories: 1)  Estimated parameters that include input values that are neither known nor measurable at the time of analysis such as mass and damping,  2)  Simplified parameters are values that are not strictly measurable, but may be estimated using conventional assumptions such as rigid zones; and  3)  Procedural parameters, chosen because of artificial limits on the analytical processes and limitations in the computational methods.  The effect of changes made to each category may have a large or small impact on the overall behaviour of the model and consequently the computed results. If, for example, a model behaviour is mostly sensitive to small changes in estimated parameters like mass and damping than to simplified parameters such as rigid zones or frame-girder composite action, then there is no reason for a detailed study of the simplified parameters beyond the specification of reasonable engineering assumptions. 6.2.1.1 Panel Zone The effect of panel zone at the intersection of beams and columns is an important parameter in frame type structural systems. ETABS accounts for the true dimensions of the beam-column panel zones by modifying member stiffness accordingly, but also allows the user to adjust the amount of increased stiffness. 66  Chapter 6:  THREE-DIMENSIONAL LINEAR ANALYSIS OF THE BUILDING  In many building structures the dimensions of structural members are large enough to have a significant effect on the overall stiffness of the structure. In this regard, an analysis based on the centreline to centreline geometry overestimates the deflections, while the analysis based on the clear length members underestimates the deflections of the structure. ETABS uses a rigid zone reduction factor to account for some of the deformations that do exist in the zone bounded by the finite dimension of beam-to-column joints. An average value for the reduction in panel-zone rigidity was taken as 25% for the base model. 6.2.1.2 Beam-to-Column Fixity The degree of fixity of beam-to-column connections is another important parameter in establishing the overall stiffness of a moment-resisting frame structure. There is an entry in ETABS to specify partial fixity at a particular end of a beam. This entry is an integer between 0 to 100. A value of zero represents full fixity and a value of 100 represents an ideal pin condition for both major and minor bending. In this building, a variety of beam-to-column connection fixity conditions existed: 1.  Rigid offsets at box columns that may probably be considered fully rigid.  2.  Wide-flange columns without web doublers that may be considered less than fully rigid.  3.  Wide-flange columns framed in the weak direction that have no panel zone might probably have increased stiffness due to use of girder-flange continuity plates.  For the condition 2 described above a 75% beam-to-column fixity was assumed. 6.2.1.3 Rigid Floor Diaphragm A rigid-diaphragm assumption is generally appropriate for concrete floor structures. The in-plane stiffness of the building composite floor system (76 mm deep metal deck plus 63 mm normalweight 20 MPa concrete fill and 12 mm or 20 mm diameter shear studs) was considered to be high enough to justify this assumption. Under this assumption, each storey level has three in67  Chapter 6:  THREE-DIMENSIONAL LINEAR ANALYSIS OF THE BUILDING  plane degrees of freedom, one rotational with respect to the vertical axis of the building and two translations in the two horizontal orthogonal directions. 6.2.1.4 Mass Distribution The mass of the storey beam and column members (half a length above and half a length below each storey level) was lumped at the corresponding storey floors. The mass of each floor slab was uniformly distributed at corresponding floor. A 100 kg/m  2  uniformly distributed mass was  added to each floor mass to account for the partitions and electrical and mechanical installations. The estimated final translational mass and mass moment of inertia for each floor was computed by ETABS and lumped at the centre of mass of each floor. The estimated mass of the structure at each storey level is presented in Appendix A. The total mass of the building was estimated to be about 50,000 metric tons above the street level. It is noted that typical conservative design assumptions are likely to overestimate floor masses by 10% or more. To bracket the likely errors inherent in the design assumptions, alternative models with 90% and 110% of the base model mass were analysed. The study showed that these differing mass assumptions did not have a significant effect on the final storey member forces and storey deflections. 6.2.1.5 Extended Three-Storev above Ground The perimeter concrete walls below street level for both high-rise and low-rise buildings were modelled using panel elements. It was postulated that modelling of these walls was essential in order to capture the rigidity provided by the presence of these walls around the building. The presence of exterior precast panels around the building were not included in the stiffness computation, but were included in the mass computation. It is noted that for low level excitations the stiffness associated with the exterior concrete cladding might have some effect on the overall stiffness of the building. However, as the level of shaking increases, the panels would develop considerable cracking and consequently have little effect on the overall stiffness of the structure.  68  Chapter 6:  THREE-DIMENSIONAL LINEAR ANALYSIS OF THE BUILDING  6.2.1.6 Damping Another critical assumption in time-history analysis are the modal damping ratios. Critical modal damping ratios of 1.0% to 3% were used in this study. A viscous damping ratio of 1.0% for the first mode in the N-S (eccentric frame direction) and 3% for higher modes was selected. 6.3 COMPARISON OF ANALYTICAL RESULTS Table 6.1 compares the periods of the building obtained from the present analysis, those reported by Steinke (1993) and those obtained from the analysis of recorded data during the Loma Prieta earthquake (Celebi, 1993). % of Mass Participation  Period (sec) Mode Shape Direction  E-W Direction (Moment-resisting frame)  N-S Direction (Eccentric braced frame)  Torsional Direction  Mode Shape  Steinke's Results  Measured  Analytical  Analytical  1  6.34  6.25  6.29  44.9  2  2.27  2.17  2.27  7.5  3  1.35  1.30  1.35  3.0  4  1.00  0.94  0.97  1.8  1  5.06  5.26  5.23  41.4  2  1.71  1.75  1.77  9.0  3  1.00  1.02  1.03  3.9  4  0.73  0.75  0.74  2.0  1  *  5.18  19.9  2  *  1.87  3.3  3  1.13  1.12  1.6  4  *  0.80  1.0  Table 6.1: Comparison of analytical and measured values for the first four periods of the building in the E-W, N-S and torsional directions * No measured values were reported for these modes  69  Chapter 6:  THREE-DIMENSIONAL LINEAR ANALYSIS OF THE BUILDING  The periods obtained from the refined analytical model are in good agreement (less than 5% difference) with the measured values. Views of the first four mode shapes of the building in the E-W (moment-resisting frame), N-S (eccentric braced frame) and torsional directions are shown in Figure 6.2. The first mode shape of the building in the N-S direction is similar to the deformed shape of a cantilever beam up to about mid-height of the building where there seems to be an inflection point. This mode is the predominant mode of vibration for the building with about 41% of the participating mass. 6.4 THREE-DIMENSIONAL LINEAR ANALYSIS OF THE BUILDING The three-dimensional response of the building during the Loma Prieta earthquake was predicted analytically. The purpose of the analysis was to correlate the recorded responses with the analytical results, and to assess the effectiveness of commercial structural analysis software in predicting the overall three-dimensional behaviour of the building for low levels of excitation. The response of the building was computed for the total 120 seconds of the recorded excitation. A total number of twelve modes (four for each direction including torsion) such that the sum of the effective modal mass contributions in each direction was equal to approximately 90% of the total mass of the building was selected. It is noted that the accelerometers installed on the building only recorded the response of the building for about two minutes after trigger. Two orthogonal input horizontal ground accelerations were used. The records of channels 4 and 5 were selected as inputs for the north-south and east-west directions, respectively. 6.5 COMPARISON OF RECORDED AND COMPUTED TIME-HISTORIES IN THE ECCENTRIC BRACED FRAME DIRECTION Figures 6.3 and 6.4 show the recorded and predicted absolute acceleration and relative displacement time-histories of the building at representative floors, respectively. The simulation results closely matches the time-response data generated by sensors during the earthquake. The small difference between the amplitude of computed and recorded acceleration values at floors 70  70  Chapter 6: THREE-DIMENSIONAL LINEAR ANALYSIS OF THE BUILDING Mode shapes in the moment-resisting frame direction: Mode 1  Mode 2  Mode 3  Mode 4  Mode shapes in the eccentric braced frame direction:  Torsional mode shapes:  Figure 6.2: Computed mode shapes for the #4 Embarcadero Centre building 71  Chapter 6:  THREE-DIMENSIONAL LINEAR ANALYSIS OF THE BUILDING  16 to 44 between 15 and 25 seconds may be attributed to the effect of nonstructural elements including the perimeter precast panels and glass cladding that contribute to the overall stiffness of the structure. These effects were not included in the analytical model. The computed displacement response closely matches the overall response of the building during and after the strong motion part of the input excitation, as shown on Figure 6.4. The computed displacement response of the building at street level, however, is substantially different than the recorded response. This difference is due to the presence of very stiff concrete walls for floors below the street level. The rigid floor assumption substantially limits the displacement response of the street floor to that of the stiff squat walls. This indicates that there exist a relative displacement motion between the concrete floors and perimeter shear walls. The storey shear together with overturning moment time-histories for the selected instrumented floors are shown in Figures 6.5 and 6.6, respectively. A maximum base shear of about 18,000 kN and overturning moment of about 550,000 kN-m was computed. It is, however, interesting to note that the time where maximum base shear and overturning moments occur is not the same. The maximum base shear occurs during the strong motion shaking at around 15 seconds, while the maximum overturning moment occurs at the end of the strong motion shaking at about 40 seconds. This indicates that the response of the building during free vibration motion was mainly in the first mode, thus causing a maximum overturning to occur at the start of the free vibration motion where all the storey forces were in phase. This observation is confirmed by the timehistory of the storey displacement response (Figure 6.4) where it shows that the response of the storey displacements during the free vibration part are in phase. In general, a good match between the computed and recorded response of the building indicate the adequacy of the model to reasonably predict the floor accelerations and displacements in both amplitude and frequency during the strong shaking and also during the free vibration response. The results of analysis also show that the rigid-diaphragm approach provides a reasonable way 72  Chapter 6:  THREE-DIMENSIONAL LINEAR ANALYSIS OF THE BUILDING  Computed  44th Floor  c o to Q>  <D O O  < O)  c o JD <D  oo <  0.2 c g  0.1 0.0  o -0.1 <  -0.2  D)  0.2  C O  0.1  Podium Floor  0.0  8 -0.1 o < -0.2  0.2  Street Floor  O)  c g  0.1 0.0  8  -0.1 o < -0.2  10  15  20 Time, sec  25  30  35  40  Figure 6.3: Comparison of recorded and computed absolute acceleration for the Loma Prieta earthquake 73  Chapter 6:  THREE-DIMENSIONAL LINEAR ANALYSIS OF THE BUILDING  Computed  E E  20  E  0  *-* c a> <D O JO  a CO  a  E £ c  44th Floor  Podium Floor  10  -10 _!  -20  I  I  I  I  I  I  I  I  I  I  I  I  I  I  I  I  I  I  I  I  L_  _l  I  I  I  20  I  I  I  I  I  L_  Street Floor  10  ^A^**^1^'  CD  E <u o iS Sa. -10 W  J  25 -20  0  I  l  l  I  I  15  l__J  I  I  I  30  I  I L .  45  I  l  I  I  I  60 Time, sec  L_J  I  75  I  I  I I  J  90  l  I  I  105  I  J 120  1_  Figure 6.4: Comparison of recorded and computed relative displacement for the Loma Prieta earthquake 74  Chapter 6:  THREE-DIMENSIONAL LINEAR ANALYSIS OF THE BUILDING  18000 to  9000  w  0  44th Floor •~4mtWtfiWtf/l/w»'*~~~  go -9000 55 -18000 Z 18000 fe w  _1  !  I  U-J  I  I  !  I  L_  _l  I  I  I  I  I  L_  39th Floor  9000 0 ~ ~ ^ > * v ^ - ™ | | M l w \ M w | ^ — • — ~ — — - — - — —  I? o -9000 _j  ^-18000  i  i  I_J  i  i  i  i  i  i  i  i  i  i  i  i  i  i  i  i  i  i  i  i  i  i  i  i  i  i  i  i  2 18000  i  i  i  i  i  i  i  16th Floor  -18000 z 18000  Street Floor  w  l  -18000 0  15  30  45  l  60 Time, sec  l  l  I  75  l  l  i  I  I  l  90  l  l  I  I  I  105  I  I L _  120  Figure 6.5: Computed storey shear time-histories at selected floor levels during the Loma Prieta earthquake 75  Chapter 6:  THREE-DIMENSIONAL LINEAR ANALYSIS OF THE BUILDING  550000  44th Floor  275000 ^ ^ A M A M ^ M ^ ^ M M W H  -275000 _1  -550000 550000  ?z  I  I I !  _J  L  1_  I I I I I  39th Floor  -  275000 ....  J.I  0 O o  -275000 1  -550000  !  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  !  1  1  1  1  1  1  1  i  i  i  i  550000  ?1  1*  i  i  i  i  i  i  i  16th Floor  275000 0 -275000 I  -550000  I  1_  I I I I I I I I I I I I I I l  J  I I I I I I  I  I I I I I  550000  L_  I I I  Podium Floor  275000 0 -275000 i  -550000  i  i  i  i  i  J  i  I  I  I  l  t  LU  I  I  I  I  I  I  I  I  I_l  I  I  I  I  I  I  I  I  t_  Street Floor  550000  -550000 0  15  30  45 60 Time, sec  75  90  105  120  Figure 6.6: Computed storey overturning moment time-histories at selected floor levels during the Loma Prieta earthquake 76  Chapter 6:  THREE-DIMENSIONAL LINEAR ANALYSIS OF THE BUILDING  to model concrete floors. However, more attention must be paid to the lower floors where the perimeter walls below ground level considerably affect the overall response of the building (e.g. a podium type- structure). The predicted storey shears and overturning moments at selected time intervals along the height of the building during strong shaking and free vibration response as well as maximum absolute values are shown in Figure 6.7. The profile of the storey shear during strong shaking, Figure 6.7a, indicates that the response of the building during strong shaking was mainly influenced by the third mode shape of the building. While this resulted in maximum storey shear demands, it did not produce a maximum overturning moment demand at the base of the building. As the strong shaking of the earthquake diminished the first mode response dominated the free vibration and the maximum overturning moment demand occurred (Figure 6.7c). The maximum storey shear (Figure 6.7b) and overturning moment (Figure 6.7d) plots show the envelope demands at each storey level. As indicated in chapter 4, the response of the building during the Loma Prieta earthquake was essentially linear. To further confirm this observation, the load-deformation response of one of the eccentric brace elements at lower floors (mechanical floor) together with the corresponding storey beam bending moment versus joint rotation are plotted in Figure 6.8. It is noted that maximum axial force in the eccentric brace elements was typically concentrated below the mechanical floor. As it can be observed from Figure 6.8, the maximum axial force in the brace is about 1,500 kN (337 Kips) and the maximum bending moment in the beam is about 600 kN-m (442 Kips-ft). With regard to the member properties for the brace and the storey beam, the ultimate axial and bending capacities of the brace and storey beam elements were computed as 2,200 kN and 2,385 kN-m, respectively. It is, therefore, concluded that no nonlinearity occurred in the structural members during the Loma Prieta earthquake. The results of this analysis also confirmed that the torsional effects were negligible and that the 77  Chapter 6:  THREE-DIMENSIONAL LINEAR ANALYSIS OF THE BUILDING  45  45  ~i—i—i—i—i—i—i  i p — | T|_i.—i—i—|—i—i—i—r  b)  37 r  37  29  29  21  1  CO  co  13  13  -3 -20000 -10000  J  0  10000  20000  Storey Shear (kN)  -20000 -10000  I  0  I  I  I  I  I  I  l  I L l  10000 20000  Max. & Min. Storey Shear (kN)  o CO  -300000  0  300000  600000  Overturning Moment (kN.m)  -600000  0  600000  Max. & Min. Overturning Moment (kN.m)  Figure 6.7: Computed storey shear and overturning moment demand at selected time intervals and maximum absolute values during the Loma Prieta earthquake 78  Chapter 6:  -10  THREE-DIMENSIONAL LINEAR ANALYSIS OF THE BUILDING  20  0 Storey Displacement, mm  600 b)  z  300  c E o c c  TJ (1) CQ  1-300 0) 00  -600 0.00030  0.00015  0.00000  -0.00015  -0.00030  Beam Rotation, rad  Figure 6.8: a) Load-deformation response of the brace at the level of mechanical floor b) Corresponding beam bending moment-rotation response at the level of mechanicalfloorlevel 79  Chapter 6:  THREE-DIMENSIONAL LINEAR ANALYSIS OF THE BUILDING  building did not respond torsionally. This was established by comparing the displacement response of two point at opposite sides of the building and at various floors. This visual comparison indicated a virtually identical response at both sides. The results of this analysis provided increased confidence in the results of computerized structural analysis, even when an analyst is not completely certain about making the most appropriate assumptions. This means that as long as member elements, structural geometry and material properties are reasonably modelled, the analytical results could be relied upon in establishing the global behaviour of building structures. 6.6 LINEAR ELASTIC BUILDING RESPONSE TO OTHER EARTHQUAKES As the accuracy of the model in predicting the overall response of the building during the Loma Prieta earthquake was established, the building model was subjected to three more earthquake records to study the response of the building had it been subjected to the selected earthquake excitations. The selected earthquake records are: Mexico City (SCT1) record from the 1985 Guerrero-Michoacan, Mexico earthquake, the Sylmar station record from the 1994 Northridge earthquake in California and the Joshua Tree station record from the 1992 Landers earthquake in California. Table 6.2 summarizes the general information about each earthquake record. The time-history plots of all three earthquake records are illustrated in Figure 6.9. The corresponding response spectra of each earthquake record is shown in Figure 6.10. Figures 6.9 and 6.10 indicate that the selected earthquake records are representatives of earthquakes with different frequency content and time data characteristics.  80  Chapter 6: THREE-DIMENSIONAL LINEAR ANALYSIS OF THE BUILDING  Earthquake Record Station  Earthquake Name  Peak Epicentral Ground Distance Earthquake Accel. (km) Date Magnitude (g)  Peak Ground Vel. (cm/s)  Peak Ground Displ. (cm)  Mexico City, (SCTl)  GuerreroMichoacan, Mexico  1985  50  M = 8.1  0.171  60.50  19.07  Sylmar  Northridge  1994  15.07  Mw = 6.7  0.843  128.88  32.55  Joshua Tree  Landers  1992  14.82  M = 7.4  0.274  27.09  7.90  Table 6.2: General information for selected earthquake records  0.2 r  Mexico City  -0.30 10  20  30  40  50  60  70  80  Time, sec Figure 6.9: Time-history plots of Mexico City (SCTl), Sylmar and Joshua Tree records  81  Chapter 6:  THREE-DIMENSIONAL LINEAR ANALYSIS OF THE BUILDING  3.5 3.0  Mexico  c 2.5 g  Joshua  Sylmar  1 2.0 3 1.5 o •o  3  10  CO  Q.  0.5  0.0 0  1  2  3  4  5  6  7  8  9  10  Period, sec Figure 6.10: Response spectra plots of Mexico City (SCT1), Sylmar and Joshua Tree records The Mexico City earthquake is rich in low frequency (high period) contents with a maximum amplitude of input acceleration less than 0.2g. It is, therefore, expected that this input record will excite the building severely. The Sylmar input record shows characteristics of a near field strong motion excitation with a very high acceleration amplitude over a short duration of time. The response spectra indicates that the Sylmar record can severely excite low-rise buildings with short fundamental natural periods. The response spectra plot of Sylmar record also shows that this record has significant energy to excite buildings with natural periods between 1 and 3 seconds. The Joshua Tree record has an interesting time data characteristic. The record contains quite a few numbers of relatively low amplitude (less than 0.2g) input cycles. The input energy of the earthquake seems to have been released in two distinct phases as shown by the distinguishable strong motion shaking from the time history plot of the record. This indicates that the building under study will be subjected to a second wave of strong motion excitation immediately after the first wave dies down. The response spectra of the record, however, does not indicate a strong concentration of energy for exciting structures with natural periods higher than 1.5 seconds.  82  Chapter 6:  THREE-DIMENSIONAL LINEAR ANALYSIS OF THE BUILDING  6.7 PREDICTED BUILDING RESPONSE A three-dimensional linear elastic time-history analysis of the building was conducted using the Mexico City (SCTl), Sylmar and Joshua Tree records. The building parameters including modal damping ratios, floor masses and structural element properties were kept exactly the same as the parameters established for the building during the Loma Prieta earthquake comparative study. The computed absolute acceleration time histories of the building at the 44th, 39th, 16th, podium and street floor levels for the Mexico City, Sylmar and Joshua Tree records are shown in Figures 6.11,6.12 and 6.13, respectively. The corresponding computed displacement time histories of the building for the Mexico City (SCTl), Sylmar and Joshua Tree records are shown in Figures 6.14, 6.15 and 6.16, respectively. The maximum computed acceleration amplitudes at the 44th floor are 0.604g, 1.92g and 0.712g for the Mexico City (SCTl), Sylmar and Joshua Tree records, respectively. This corresponds to an amplification factor of 3.53, 2.28 and 2.60 for the Mexico City (SCTl), Sylmar and Joshua Tree records, respectively. However, the plots of absolute acceleration time histories for the Sylmar and Joshua Tree records indicate a considerable difference between the peak acceleration amplitudes for the 39th and 44th floors. The maximum computed acceleration amplitudes at the 39th floor are 0.428g, 0.752g and 0.269g for the Mexico City (SCTl), Sylmar and Joshua Tree records, respectively. This corresponds to an amplification factor of 2.50, 0.89 and 0.98 for the Mexico City (SCTl), Sylmar and Joshua Tree records, respectively. This observation implies that both the Sylmar and Joshua Tree records did not excite the entire building severely. As explained in Chapter 4, the eccentric brace configuration only continues up to the 41th floor. The lateral load resisting elements of the upper four storeys (42nd to 45th floors) are only through the contribution of moment resisting frames. The Sylmar and Joshua Tree records were quite effective in exciting the upper floors of the building where the stiffness properties of the building changed considerably. 83  Chapter 6:  THREE-DIMENSIONAL LINEAR ANALYSIS OF THE BUILDING  44th Floor  c o "co u. 0) CO  o o <  c g (0 1—  .CO  8 o < 0.4 C  g (0 CO  16th Floor  0.2 0.0 ~vw«w^^AAA/\/\/\/yn^ -0.2  o o -0.4 <  i  i  i  i  I  i  0.4  Podium Floor  c 0.2 g CO  a>  0.0  CO  8  <  -0.2 -0.4  J  I  I  i  L.  i  i  i  i  i  i  i  i  0.4 Street Floor  c 0.2 o CO  a) CO  8  -^^^ww»V|f\A|ywyyVwm  0.0 -0.2  < -0.4  J  i  i  i  i  20  i  i  * i_  J  40  l  60  I  I  I  l  I  80  I  I  I  I  I  I L .  100  J  120  I  I L_  140  Time, sec Figure 6.11: Computed absolute acceleration time history response of the building for the Mexico City (SCTl) record 84  Chapter 6:  THREE-DIMENSIONAL LINEAR ANALYSIS OF THE BUILDING  44th Floor  c g  2 <D O O  <  c g JD  a) o o <  O)  c g ro W  0)  s o <  1.0 c  g  0.5 0.0  8  Podium Floor •••••^Ulrl  |!|^I^JY^|/^A^Arvv^vr^A^-^^—  -0.5  o < -1.0  _l  I  I  I  I  I  I  I  u  I  I  I  I  _l  I  I  I  I  I  I  I  Street Floor  D) C  g  2 0) 0  o o <  0  10  15  20 Time, sec  25  30  Figure 6.12: Computed absolute acceleration time history response of the building for the Sylmar record  85  Chapter 6:  THREE-DIMENSIONAL LINEAR ANALYSIS OF THE BUILDING  44th Floor  c 0.15 o (0 0.00 L_  '••3  0)  § -0.15  <  -0.30 0.30  16th Floor  O)  c 0.15 o (0 0.00 k_ 0)  s -0.15  <  -0.30 0.30  Podium Floor  O)  c 0.15 o  9  0.00  -0.15 -0.30 Street Floor  -0.30 0  10  20  30  40  50  60  70  80  Time, sec  Figure 6.13: Computed absolute acceleration time history response of the building for the Joshua Tree record 86  Chapter 6:  THREE-DIMENSIONAL LINEAR ANALYSIS OF THE BUILDING  44th Floor  E E  3.0  -- 1.5 a> | 0.0 o f-1.5  Street Floor MMtMwVVW  (0  l  b -3.0  0  l  l  l  u  ~ v « * < / v v  I  l  20  l  I  I  I  l  40  l  l  I  I  l  60  I  I  v v A y \ W \ ^ M W M W / V ^  I  I  l  80  I  I  I  II  I L  ,  I  , I  I  100 120 Time, sec  I  I  I  I  I  140  I  I  '  I  I  160  I  I  I  _L I  I  180  I  I  L  J  200  Figure 6.14: Computed relative displacement time history response of the building for the Mexico City (SCTl) record  87  Chapter 6:  THREE-DIMENSIONAL LINEAR ANALYSIS OF THE BUILDING  44th Floor  a 1000 F 500 E * - » " 250 c a>  E  16th Floor  0  a> o m -250 u. <n  -500  Q  50  E E c a>  E  a> o CO Q. (0  Podium Floor  25 0 -25 -50  Q  E 3.0 E * - » " 1.5  Street Floor  c a)  E 0.0 <D O CO  a. a>  -1 5 i  a -3.0  0  i  i  6  i  i  i  12  i  i  i  18  i  i  i  24  i  i,,  i  i  i  i  30 36 Time, sec  i  i  i,...  42  i  i  i  48  i  i  i  54  i  i _  60  Figure 6.15: Computed relative displacement time history response of the building for the Sylmar record 88  "S  Chapter 6:  THREE-DIMENSIONAL LINEAR ANALYSIS OF THE BUILDING  500  44th Floor  b -500 500 E - - 250 c <D E 0 E  a) o  16th Floor  -^vv^  •2 -250 Q.  _l  I  I  l  I  l  l  I  I  I  I  I  I  I  I  I  I  I  I  I  I  I  L_J  I  L_l  I  I  l_J  I  I  I  I  I  L_  W  b -500 30 E E  -c <D  Podium Floor  15  E  o o _ro o. w  -15 h  b  -30  E E --  3.0 Street Floor 1.5  0)  i o.o o £-1.5  I  CO  Q -3.0  0  I  I  I  I  15  I  I  I  iI iI  30  I  I  I  I  I  45  I  I  I  I  I  I  60 Time, sec  I  I  I  75  I  I  I  I  I  90  I  I  I  I  I  I  105  I  I  L  120  Figure 6.16: Computed relative displacement time history response of the building for the Joshua Tree record 89  ^  Chapter 6:  THREE-DIMENSIONAL LINEAR ANALYSIS OF THE BUILDING  The highest factor of amplification for the Mexico City (SCTl) record indicates that the building was more severely excited by this record compared to the other two input excitations. The maximum computed relative displacement amplitudes at the 44th floor are 847 mm, 1061 mm and 455 mm for the Mexico City (SCTl), Sylmar and Joshua Tree records, respectively. For all three records there is considerable free vibration response at the end of main excitation. Due to inherently small modal damping ratios the degree of amplitude decay is very gradual. Plots of acceleration and displacement profile of all storey floors at time of maximum response at the 45th floor together with the free vibration response are shown in Figures 6.17 to 6.19 for the Mexico City (SCTl), Sylmar and Joshua Tree records, respectively. Also shown in the same figures are the maximum non-concurrent storey floor acceleration and relative displacement response. These plots are representatives of the distribution of storey forces as well as the state of relative displacement response at different storey levels at various time steps. The acceleration response plots (Figures 6.17a to 6.19b) indicate that the distribution of storey forces at the time of maximum response at the 45th floor was mainly resembled the second mode shape of the building for the Mexico City (SCTl) record while it resembled the higher modes (4th and higher) for the Sylmar and Joshua Tree records. The displacement profiles for all the records, however, resemble the second mode shape of the building. In general, all displacement profiles (Figures 6.17c to 6.19d) show that the relative displacement response of the building was considerably amplified for the floors above the 30th floor.  90  Chapter 6:  THREE-DIMENSIONAL LINEAR ANALYSIS OF THE BUILDING  45  45  37 r  37  29  29  |  o 21  55  21  CO  13  13 —  Free Vibration At Max. Accel. at 45th Floor  5 r j  -0.66  -0.33  0.00  i  i  i  i  i  i  5  _l  i_  0.33  0.66  -0.66  Acceleration (g)  -0.33  U U  I  0.00  I  I  I  I  [_  0.33  0.66  Max. & Min. Acceleration (g) l\ I  40  I  I  I  I  I  I  I  i  i  i  i  i  /  i _  /  37 ~—  29 '—  o  i  -_  1  21 '-  ~~-  \  ~-  CO  13 '— —  Free Vibration At Max. Displ. 5 ~ at 45th Floor  d) I  I  -1000  -500  0  i  500  Displacement (mm)  i  i  i  i  i  \i  i  i  <  /  ~-  1  -_  i  i  i  i  i  i  i  i  i  i  i -i  1000  -1000  -500  0  500  1000  Max. & Min. Displacement (mm)  Figure 6.17: Computed absolute acceleration and relative displacement profile of the building for the Mexico City (SCT1) record 91  Chapter 6:  THREE-DIMENSIONAL LINEAR ANALYSIS OF THE BUILDING  45 p  45  37 ~  37 r  29  29  I  oo  21  CO  13  13 : — —  5 r -3 -2.2  Free Vibration At Max. Accel. at 45th Floor  5  I I I . H  Q  I  -1.1  0.0  1.1  -2.2  2.2  Acceleration (g)  -1.1  0.0  1.1  2.2  Max. & Min. Acceleration (g)  45 37  29 r |  21  00  13 — —  J__I  -1100  -550  0  Free Vibration At Max. Displ. 5 at 45th Floor i  i  550  Displacement (mm)  i  i  i_d  1100  _o  -1100  -550  0  550  1100  Max. & Min. Displacement (mm)  Figure 6.18: Computed absolute acceleration and relative displacement profile of the building for the Sylmar record 92  Chapter 6:  THREE-DIMENSIONAL LINEAR ANALYSIS OF THE BUILDING  45  37  29  o  21  CO  13 Free Vibration —  At Max. Accel.  5  at 45th Floor  -1.0  -0.5  0.0  0.5  -3 -1.0  1.0  Acceleration (g)  o  -0.5  0.0  0.5  1.0  Max. & Min. Acceleration (g)  45 "pN!—'—'—'—i—'—'—'—' i '—'—'—'—l—rll—'—^  45  37  37  29  29  |  21  CO  21  CO  13  13 Free Vibration At Max. Displ.  5  at 45th Floor _i i i i L_i i i i I i i i i I i i i L  -500  -250  0  250  Displacement (mm)  J  500  -3 -500  -250  0  250  500  Max. & Min. Displacement (mm)  Figure 6.19: Computed absolute acceleration and relative displacement profile of the building for the Joshua Tree record 93  Chapter 7: THREE-DIMENSIONAL NON-LINEAR ANALYSIS OF THE BUILDING USING FRICTION DAMPERS 7.1 GENERAL To complement the analytical studies of the #4 Embarcadero Centre, comparative numerical analyses of the building replacing the eccentric braced elements with uniaxial link elements (simulating friction dampers) were conducted. The highly nonlinear (elasto-plastic) performance characteristics of the friction devices required a nonlinear analysis to predict the response of the friction damped structure suitably. As mentioned in Chapter 5, the ETABS computer program has a special link element capable of simulating the elastic stiffness and slip load characteristics of friction damped systems. This analytical study focuses on the use of a passive energy device to control the seismic behaviour of the 49-storey steel frame building. The energy-absorbing device studied, is a friction device with almost perfectly rectangular hysteretic behaviour. The main reason for introducing friction damped elements to the building was to assess whether or not it would be possible to substantially reduce the inelastic demand on the storey link elements during severe earthquake shaking by redirecting the earthquake input energy to the friction damped elements. 7.2 MODEL DESCRIPTION The linear elastic eccentric brace ETABS model of the building that was created and verified by the Loma Prieta earthquake results was used to create the building model with friction damper elements. The friction damped model has the common basic features of the linear eccentric braced model except that the link elements were introduced at each storey level replacing the eccentric brace elements. The link elements were connected to the beam-to-column connections in a X-bracing fashion. Figure 7.1 shows three-dimensional and elevation views of the friction damped building as modelled in ETABS together with a close-up of a typical storey plan of the 94  Chapter 7:  THREE-DIMENSIONAL NON-LINEAR ANALYSIS OF THE BUILDING USING FRICTION DAMPERS  building.  Figure 7.1: ETABS model of the #4 Embarcadero Centre building with X-bracing friction dampers replacing eccentric brace elements 7.2.1 Friction Damped Braces Cross bracing elements were provided inside the steel moment-resisting frame using friction damped devices. Africtiondevice is designed not to slip under normal service loads, wind storms or moderate earthquakes. During a major earthquake, the devices slip at a predetermined load, before yielding occurs in the other structural elements of the frame. Slippage in the device then provides a mechanism for the dissipation of energy. As the braces carry a constant load while slipping, the additional loads are carried by the moment-resisting frame. In this manner, 95  Chapter 7:  THREE-DIMENSIONAL NON-LINEAR ANALYSIS OF THE BUILDING USING FRICTION DAMPERS  redistribution of forces take place between successive storeys, forcing all the braces to slip and participate in the process of energy dissipation. The seismic response of a building is basically determined by the amount of energy fed in and energy dissipated. The optimum seismic response, therefore, consists of minimizing the difference between the input energy and energy dissipated. The energy dissipation is proportional to the product of slip load and the slip travel during each excursion. For very high slip loads, the energy dissipation in friction will be zero, as there will be no slippage. If the slip load is very low, the amount of energy dissipation again will be negligible. By proper selection of slip load, it is possible to fine tune the response of the building to an optimum value. The optimum slip load is generally independent of the time history of the earthquake motion and is rather a structural property. For the case study building the slip load for the lower floors was considered as 450 kN and was reduced to 135 kN for the upper floors. It is noted that a small variation of the slip load will not affect the seismic response of the building significantly. 7.2.2 Hysteresis Behaviour The plasticity behaviour of uniaxial link elements was defined based on the hysteresis behaviour proposed by Wen (1976) and allows for parameters to vary post-yield stiffness and shape and width of hysteresis loops. In Wen's model the hysteresis relationship between a restoring force and the corresponding displacement is defined as: lf = A±(a ax  + P)-F"  (7.1)  where F is the restoring force, x is displacement and A, a and p are constants. The scale and general shape of the hysteresis loop are governed by A, a and P while the smoothness of the forcedisplacement curve is controlled by n. Therefore by adjusting the values of these constants, one can construct a variety of restoring forces, such as hardening or softening, narrow or wide-band systems. The case where a = 0.5 and P = 0.5, can be used as a model for an elasto-plastic system with smooth transition. The value of n affects the transition curve between elastic and post-yield 96  Chapter 7:  THREE-DIMENSIONAL NON-LINEAR ANALYSIS OF THE BUILDING USING FRICTION DAMPERS  behaviour.  7.3 COMPARISON OF ANALYTICAL RESULTS Table 7.1 compares the periods of the friction damped building obtained from the present analysis and those obtained from the analysis of eccentric braced frame building. Period (sec) Mode Shape Direction N-S Direction (Eccentric braced/friction damped frame)  % of Mass Participation  Mode Shape  Eccentric Braced  Friction Damped  Eccentric Braced  Friction Damped  1  5.23  5.11  41.4  40.3  2  1.77  1.71  9.0  9.1  3  1.03  0.97  3.9  3.9  4  0.74  0.69  2.0  1.8  1  5.18  5.14  19.9  19.5  2  1.87  1.85  3.3  3.3  3  1.12  1.11  1.6  1.5  4  0.80  0.79  1.0  1.0  Torsional Direction  Table 7.1: Comparison of analytical values for the first four periods of the eccentric braced and friction damped buildings in the N-S and torsional directions The periods obtained for the X-bracing friction damped building are slightly lower than the periods obtained for the eccentric braced frame building. It is noted that the axial stiffness property of the friction damped elements was selected in such a way that the overall stiffness of the two buildings remained close. Similar to the eccentric braced frame building the first mode shape of the friction damped building in the N-S direction is similar to the deformed shape of a cantilever beam up to about mid-height of the building where there seems to be an inflection point. This mode is the predominant mode of vibration for both buildings with about 41% of the participating mass.  97  C h a p t e r 7:  THREE-DIMENSIONAL NON-LINEAR ANALYSIS OF THE BUILDING USING FRICTION DAMPERS  7.4 TIME-HISTORY RESPONSE OF THE FRICTION DAMPED BUILDING The three-dimensional nonlinear time-history responses of the friction damped building were investigated using the records from the Loma Prieta, Guerrero-Michoacan (Mexico), Northridge and Landers earthquakes. The main characteristics of each earthquake record was explained in Chapter 6. First, the behaviour of the building during the Loma Prieta earthquake is considered because of the low level of demand. The response of nonlinear friction damped model during Loma Prieta earthquake is compared with the results obtained for the original eccentric brace frame model. Figures 7.2 and 7.3 illustrate the comparison of absolute acceleration and relative displacement time-histories of the two different systems at selected storey floors, respectively. In general, the time-history traces are similar for both eccentric braced and friction damped buildings. It can be seen that the peak absolute acceleration and relative displacement values are noticeably lower for the friction damped building compared to the eccentric braced building. The same observation is also valid for the maximum displacement amplitude reached during the free vibration response of the two buildings. Figure 7.3 also indicates that the friction damped building is slightly stiffer than the eccentric braced building because of the phase shift between the two acceleration timehistories. A comparison between the computed absolute acceleration and relative displacement profiles of the eccentric braced and friction damped buildings at the time of maximum values at the 45th floor and the non-concurrent maximum values at different storey levels is shown in Figure 7.4. As can be seen from the Figure 7.4, the friction damped building was effective in reducing the maximum relative displacement demand experienced by all the floors and, in particular, at the higher storey levels. As explained in the preceding paragraph the maximum acceleration values were also reduced for the case of friction damped building. The profile of the maximum acceleration, Figure 7.4b, illustrates the sudden amplification of the absolute acceleration 98  Chapter 7:  D)  C  o  THREE-DIMENSIONAL NON-LINEAR ANALYSIS OF THE BUILDING USING FRICTION DAMPERS  0.6  Eccentric Brace  44th Floor  0.3  '_£?2  CO  8 <o  0.0 -0.3 -0.6 0.2  O)  c o  01  E  00  •*-* 0)  n o>  o -0.1 <  -0.2 0.2  16th Floor  O)  c o  01  2  00  * - J  (U  a>  o -0.1 . o <  -0.2 0.2  Podium Floor  a>  c o  0.1  -*—•  2  a>  0.0  8' -0.1 o  -0.2 Street Floor C  g (0 L.  8 o <  10  15  20 Time, sec  25  30  35  Figure 7.2: Comparison of computed absolute acceleration time histories of thefrictiondamped and eccentric braced buildings for the Loma Prieta earthquake record 99  Chapter 7:  THREE-DIMENSIONAL NON-LINEAR ANALYSIS OF THE BUILDING USING FRICTION DAMPERS  200  Eccentric Brace  Friction Damped  44th Floor  Q -100 E E  -c a> E < ou  20  Podium Floor  10 0  2a. -10  w  b  -20  E E  1.0  a> E  i  u_i  J  i  i  i  i  i  i  i  i  i_  J  I  L_l  I  I  I  I  I  I  l_  l _ _ l I  _J  '  i  '  l _  Street Floor 0.0  ~^«^jy||p(y^^  <D O  £-0.5 (O  Q -1.0  I  I  I  I  15  I  I  I  I  I  30  I  I  I  I  I  45  I  I  I  I  I  l _ J I  60 Time, sec  I  I  75  I  I  I  I  I  90  I  1  I  I  1  I  105  I  1  L  J  120  Figure 7.3: Comparison of computed relative displacement time histories of the friction damped and eccentric braced buildings for the Loma Prieta earthquake record  100  Chapter 7:  THREE-DIMENSIONAL NON-LINEAR ANALYSIS OF THE BUILDING USING FRICTION DAMPERS  45  37  29  o 21 13  — — _,  -3 -0.3  0.0  Eccentric Braced Friction Damped i  ,  0.3  ,_J -0.6  0.6  Acceleration (g)  0.0  0.3  0.6  Max. & Min. Acceleration (g)  45  45  37 r  37  29  29  2> S 21  +-»  CO  CO  oo  21 13  13 — —  c)  -100  -0.3  0  Eccentric Braced Friction Damped 100  Displacement (mm)  200  -200  -100  0  100  200  Max. & Min. Displacement (mm)  Figure 7.4: Comparison of computed a) & b) absolute acceleration and c) & d) relative displacement profiles of the eccentric braced and friction damped buildings for the Loma Prieta earthquake record 101  Chapter 7:  THREE-DIMENSIONAL NON-LINEAR ANALYSIS OF THE BUILDING USING FRICTION DAMPERS  response for the floors above the 39th floor where the eccentric braces and friction dampers stopped. The general shape of the displacement profile at the time where maximum relative displacement occurred at the top floor resembles the third mode shape of the buildings with transition points at about 13th and 29th storeys, Figure 7.4c. A comparison between the peak storey shears and overturning moments for the eccentric braced and friction damped buildings is shown in Figure 7.5. It can be observed that the friction damped building reduced the overall base shear attracted by the building by about 25% as opposed to the eccentric braced frame building. The reduction in the base overturning moment, however, is not as pronounced. This may be related to the fact that even though the base shear for the friction damped building was reduced by as much as 25%, the line of action of the base shear moved slightly higher compared to the eccentric braced frame building. The maximum overturning moment profile shows a progressive increase in the overturning moment from the top floor up to the 29th floor. It then started to decrease up to the 21th floor and then gradually increased all the way up to the base of the building. This transition between the 29th and 21th floors is consistent with the displacement profile where the effect of higher modes in dominating the response was pronounced. The axial load-deformation response of one of the friction dampers at lower floors (e.g. mechanical floor) together with the corresponding storey beam bending moment versus joint rotation are plotted in Figure 7.6. It can be observed that the friction damped elements at lower floors of the building are at the verge of slipping and dissipating energy. The maximum bending moment experienced by the beam is about 450 kN.m versus about 600 kN.m for the eccentric braced frame building. This moment is about several times less than the maximum bending capacity of the storey beams (2,385 KN-m). This indicates that the presence of friction dampers and their response to the input excitation had substantially reduced the seismic demand on the main gravity load resisting elements such as beams and columns when compared eccentric braced  102  Chapter 7:  THREE-DIMENSIONAL NON-LINEAR ANALYSIS OF THE BUILDING USING FRICTION DAMPERS  -20000 -10000  0  10000  20000  Max. & Min. Storey Shear (kN)  -600000  0  600000  Max. & Min. Overturning Moment (kN.m)  Figure 7.5: Comparison of maximum and minimum storey shear and storey overturning moment of the friction damped and eccentric braced buildings for the Loma Prieta earthquake record frame system. 7.5 NONLINEAR RESPONSE TO OTHER EARTHQUAKE RECORDS It is known that different earthquake records, even though of the same intensities, give widely varying structural responses, and results obtained using a single record may not be conclusive. Therefore, it is important to evaluate the relative performance of a structural system under different input excitations. In the following, the results of the three-dimensional nonlinear analysis of the friction damped building during Mexico City (SCTl), Sylmar and Joshua Tree records are discussed. The computed absolute acceleration and relative displacement time-histories of the friction damped building at selected storey floors during Mexico City (SCTl), Sylmar and Joshua Tree records are shown in Figures 7.7 to 7.12, respectively. 103  Chapter 7:  THREE-DIMENSIONAL NON-LINEAR ANALYSIS OF THE BUILDING USING FRICTION DAMPERS  -500 -20  -10  0  20  10  Storey Displacement, mm  600  ~\  1  r  <  1  T  n  1  r  1  H  I  L_  T  1  r  j  i  i_  b) 300 c 0)  E o 1  1  C C CD CO  1-300 00.  -600  -0.0010  i  i  L_  _i  -0.0005  I  J  i_  0.0000  0.0005  0.0010  0.0015  Beam Rotation, rad  Figure 7.6: a) Load-deformation response of the friction damper at the level of mechanical floor b) Corresponding beam bending moment-rotation response at the level of mechanical floor (Loma Prieta earthquake record)  Chapter 7:  THREE-DIMENSIONAL NON-LINEAR ANALYSIS OF THE BUILDING USING FRICTION DAMPERS  Similar to the behaviour observed for the eccentric braced frame building, the plots of absolute acceleration time histories for the Sylmar and Joshua Tree earthquake records indicate a considerable difference between the peak acceleration amplitudes for the 39th and 44th floors. In general, the absolute acceleration amplification factors for the X-bracing friction damped building was considerably smaller than the factors obtained for the eccentric braced frame building (see Chapter 6). The absolute acceleration time-history plots of the Sylmar and Joshua Tree records (Figures 7.8 and 7.9) indicate that the ground motion accelerations were de-amplified for all floors up to the 39th floor where they were considerably amplified at the 44th floor. This clearly indicates that the response of the building to the Sylmar and Joshua Tree records was very modest. However, the sudden change in the stiffness of the structure for the top floors caused the amplification of response for the floors above the 39th floor. This implies that the upper floors of the 49-storey Embarcadero building, where the moment resisting frame is the only lateral load resisting element, could be considered as a five-storey structure supported on a relatively rigid structure. This local effect and change in the period of the floors above the 39th floor causes the amplification of motion for upper storeys of the building. The same behaviour, however, was not as pronounced for the Mexico City (SCTl) record because the input record substantially excited the entire building. The maximum computed absolute acceleration amplitudes of the friction damped building at the 44th floor are 0.608g, 0.973g and 0.484g for the Mexico City (SCTl), Sylmar and Joshua Tree records, respectively. This corresponds to an amplification factor of 3.55, 1.16 and 1.77 for the Mexico City (SCTl), Sylmar and Joshua Tree records, respectively. As tabulated in chapter 6, the maximum absolute accelerations of the eccentric braced building at the 44th floor are 0.604g, 1.92g and 0.712g for the Mexico City (SCTl), Sylmar and Joshua Tree records, respectively. This implies that the response of the upper floors to the Sylmar and Joshua Tree input excitations were  105  Chapter 7:  THREE-DIMENSIONAL NON-LINEAR ANALYSIS OF THE BUILDING USING FRICTION DAMPERS  o> c o  44th Floor  CO i_  8 o < c" g CO  8 o < 0.4  16th Floor  c 0.2 g CO k_  0.0 ~ w ~ w w w / W \ ^ ^  d>  o o -0.2 <  J  -0.4  !  I  I  L.  0.4  Podium Floor  c" g 0.2 0.0  8  -0.2  o < -0.4  J  I  I  I  I  I  I  1_  _!  I  I  I  I  I  I  L_  0.4 Street Floor  c 0.2 g i—  0  <v---«««*AVWvy||y/ylwuwW  0.0  8  -0.2 o < -0.4  l  0  20  l  l  I  40  I  I L_  _L  J  L_J  L_J  60 80 Time, sec  I  I  I I  100  '  l  l  1__J  120  I [_  140  Figure 7.7: Computed absolute acceleration time history response of the friction damped building for the Mexico City (SCTl) record 106  Chapter 7:  THREE-DIMENSIONAL NON-LINEAR ANALYSIS OF THE BUILDING USING FRICTION DAMPERS  44th Floor  1.0  16th Floor  CO C O  0.5  CO  0.0  8 -0.5 o < -1.0 CD  c  _l  I  I  l  I  I  I  I  I  I  I  _l  L_  I  I  I  I  I  l_  1.0 r  Podium Floor  0.5 « ^ ^ ^ ^ ^ ^ " « • l l ^ ^ — ^ H l l ^ » I •!• 11—^1^—  0.0  8  -0.5 o < -1.0  J  I  I  1  !  I  I  I  I  L_  I  I  I  I  I -1  I  I  I  I  I  I  I  I  I  1  l_  Street Floor  l  I  I  I  I  I  I  15  l  l  I  I  I  I  I  20  I  I  I  25  I  I  I  I  I  30  1  I  L  35  40  Time, sec  Figure 7.8: Computed absolute acceleration time history response of the friction damped building for the Sylmar record 107  Chapter 7:  THREE-DIMENSIONAL NON-LINEAR ANALYSIS OF THE BUILDING USING FRICTION DAMPERS  0.50  44th Floor  -0.30 0.30  .2  16th Floor  015  1 o.oo 8 -0.15 <  _!  -0.30  I  I  I  I  I  [_  I  I  I  I  I  I  I  l__J  I  I  l__l  I  l__l  0.30  I  L-  Podium Floor  rf> ^^V t^^^M****^— ^ V *m^im0*^C • I  0.30 o> c 0.15 o 2 0.00 0)  Street Floor  ^^M^to'M^^---—  vw**Nfc»v^*v^***ii^i*^v*v^M*iAr» ••"  §-0.15 <  _J  -0.30  0  I  I  !  10  I  I  I  !  I !_  20  ±  _L 30 40 Time, sec  J_J  I  50  L__J I  '  I  60  I  I  I  I  I  70  I  I  I L_  80  Figure 7.9: Computed absolute acceleration time history response of the friction damped building for the Joshua Tree record 108  Chapter 7:  THREE-DIMENSIONAL NON-LINEAR ANALYSIS OF THE BUILDING USING FRICTION DAMPERS  44th Floor  WijyuVvV vw YV^  E E  3.0  ~ c  1.5  Street Floor  a>  -~-vN~-vvM^AVV\^V^|y^  yi^ivMKAMMMiMWMdM^Av^  § oo o  £ -1.5 w  b -3.0  I  0  I  I  I  i  I  20  I  I  I  I  I  40  I  I  I  I  I  60  I  I  I  I  I  80  I  I  I  l_l  L_J  l_l  I  100 120 Time, sec  1_J  l_J  I  140  I  I  I  I  I  160  I  I  I  I  I  180  I  I—I  I  200  Figure 7.10: Computed displacement time history response of the friction damped building for the Mexico City (SCTl) record 109  Chapter 7:  THREE-DIMENSIONAL NON-LINEAR ANALYSIS OF THE BUILDING USING FRICTION DAMPERS  £1000 E •*s 500  44th Floor  c  <D  E  a> o CD  a.  0 -500  V)  Q1000 E 1000  F c  V  E  a> o to a. w  500 0 -500  a 1000 F 500 E 250 c a)  E  a> o (0  u. co Q  E E c a)  E  a> o CO Q. (0  Q  16th Floor  0 -?50 -500 50  Podium Floor  25 0 -?5 -50  E 3.0 E 1.5  Street Floor  c  0)  E 0.0 a> o (0 a.  -1 5  0)  a -3.0  i  0  i  i  6  i  i  i  12  i  i  i  18  i  i  i_  24  i  l  I  I  30 36 Time, sec  I  I  I  42  I  I  I  48  I  I  I  L_  54  60  Figure 7.11: Computed displacement time history response of the friction damped building for the Sylmar record 110  Chapter 7:  THREE-DIMENSIONAL NON-LINEAR ANALYSIS OF THE BUILDING USING FRICTION DAMPERS  44th Floor  Q -500 500 E _- 250 E  39th Floor  c  E  0  « -250 Q. W  J  1  I  I  I  I  I  I  I  L_l  I  L_  _i  i  i  i  i  i__j  i  i  i  i  i  i  i  i  i  i  Q -500 500 E E * J 250 c  i  i  i  i  i_  16th Floor  0)  E  0  -j  i  i  i  i  i  i  i  i  i  i  i  i  I__J  i  i  i  i  i  i  i  i  i  i  i  i  i  i  i  i  -250 30 E b -500 *-- 15  i  i  i  i  i  i  i  i_  |  Q. E V>  Podium Floor  c  <D  E 0 <u o •S - 1 5 Q. W  »4%MW^^ I  b  -30  E E  3.0  l  I  I  I  l  —' I  I  I  I  I  I  l  I  I  I  I  I  !  I'  I  I  I  L_J  I  I  I  • L  I  Street Floor  ~ 1.5 a>  ^^^fl|^'y*/^^'•Avv/^^^ ) JN^  i o.o o  1-1.5 Q -3.0  -J  I  I  I  I  15  l__l  I  I  I  30  I  I  I  I  I  45  I  I  I  I  I L  60 Time, sec  _L 75  i  i  i  i  i  90  i  i _  105  120  Figure 7.12: Computed displacement time history response of the friction damped building for the Joshua Tree record 111  Chapter 7:  THREE-DIMENSIONAL NON-LINEAR ANALYSIS OF THE BUILDING USING FRICTION DAMPERS  substantially reduced in the case of friction damped building as opposed to the eccentric braced frame building. This is confirmed by an about 50% reduction in maximum floor acceleration experienced at the 44th floor during the Sylmar record for the friction damped building. The Mexico City (SCT1) earthquake input record had very comparable effects on both buildings. The maximum computed absolute acceleration amplitudes of the friction damped building at the 39th floor are 0.40lg, 0.466g and 0.212g corresponding to an amplification factor of 2.34, 0.54 and 0.77 for the Mexico City (SCT1), Sylmar and Joshua Tree records, respectively. These amplification factors are about 66%, 47% and 44% of the amplification factors computed at the 44th floor for the Mexico City (SCT1), Sylmar and Joshua Tree records, respectively. These considerable reductions in the amplification factor between the 44th and 39th floors of the building indicate the significant effect of the earthquake input excitations at the top floors due to the sudden change in the stiffness of the building above the 39th floor. As tabulated in chapter 6, the maximum absolute accelerations of the eccentric braced building at the 39th floor are 0.428g, 0.752g and 0.269g for the Mexico City (SCT1), Sylmar and Joshua Tree records, respectively. A comparison between these numbers and the maximum values obtained for the friction damped building indicate that the friction damped building was very effective in deamplifying the Sylmar and Joshua Tree input excitations. The displacement time-history plots of the friction damped building for the Sylmar and Joshua Tree records (Figures 7.11 and 7.12) indicate that the overall seismic demand was reduced for the friction damped building as opposed to the eccentric braced frame building (see Figures 6.15 and 6.16 in Chapter 6). This was particularly more pronounced for the upper storeys of the building. 7.5.1 Beam Moment-Rotation and Link Axial-Displacement Response The Mexico City (SCT1), Sylmar and Joshua Tree records illustrate the response of the dampers to small and large excitations. The plots of storey beam moment-rotation relationship and axial force in the link element versus relative displacement of the storey floor at the mechanical level 112  Chapter 7:  THREE-DIMENSIONAL NON-LINEAR ANALYSIS OF THE BUILDING USING FRICTION DAMPERS  for the Mexico City (SCT1), Sylmar and Joshua Tree records are shown in Figures 7.13 to 7.15, respectively. As can be seen from Figure 7.13, considerable and repeated yielding of the friction dampers are apparent during the Mexico City (SCT1) record. It is noted that verification plots of other friction dampers at all other storeys indicated that most of the dampers had undergone into nonlinear behaviour. This relatively uniformly distributed yielding of the dampers along the height of the building is a very desirable behaviour. It is, however, noted that a designer might choose to arrange the dampers in a way that yielding pattern are different throughout the building or more concentrated at lower storeys. In this study, the slip force of the dampers were reduced from 450 kN at lower storeys to 150 kN at upper floors. The bending moment demand of the storey beams was just about near their yield capacity indicating that the friction dampers were quite effective in reducing the seismic inelastic demand on gravity load carrying elements. The response of the dampers to the Sylmar record was more or less elastic except during the early stage of the excitation where a relatively large pulse excited the building. This large pulse created one cycle of very large nonlinear action in all of the friction dampers. The bending moment vs. joint rotation of storey beam at mechanical floor, Figure 7.14b, indicates that this large cycle had induced normal strains just slightly above the specified yield capacity of the storey beam. The Joshua Tree record was, in general, ineffective in exciting the building and thus produced too small storey shears to activate the dampers. This is illustrated in the force-deformation plot of one of the dampers at the mechanical floor which shows that the damper did not slide.  7.5.2 Base shear and Overturning Moment Peak storey shears and overturning moments as well as the concurrent storey shears and overturning moments at three different time values for the Loma Prieta, Mexico City (SCT1),  113  Chapter 7:  THREE-DIMENSIONAL NON-LINEAR ANALYSIS OF THE BUILDING USING FRICTION DAMPERS  i  1  r  375 2  250  <D~ O O LL  1?5  (0 X  < ^ a.  n -125  E <B Q  -250 -375 -500 -100  -50  0 Storey Displacement, mm  50  100  4000  2000 E  o C  c CD E  -2000  CQ  -4000  -0.0080  -0.0048  -0.0016  0.0016  0.0048  0.0080  Beam Rotation, rad  Figure 7.13: a) Load-deformation response of the friction damper at the level of mechanical floor b) Corresponding beam bending moment-rotation response at the level of mechanical floor (Mexico City (SCT1) record)  Chapter 7:  THREE-DIMENSIONAL NON-LINEAR ANALYSIS OF THE BUILDING USING FRICTION DAMPERS  500  "i  1  r  375  z  .* <D U  o LLCO X  ?50 1?5 0  <  L-  a.  -125  E  re  Q  -250 -375 -500  -100  i  -50  0 Storey Displacement, mm  50  i  i  i_  100  4000  -4000  -0.0080  -0.0048  -0.0016  0.0016  0.0048  0.0080  Beam Rotation, rad  Figure 7.14: a) Load-deformation response of thefrictiondamper at the level of mechanical floor b) Corresponding beam bending moment-rotation response at the level of mechanical floor (Sylmar record) 115  Chapter 7:  500  THREE-DIMENSIONAL NON-LINEAR ANALYSIS OF THE BUILDING USING FRICTION DAMPERS  I  I  250  i>  125 -  15  0  O U_  I  j  I  I  I  I  ;  I  I  I  I  I  a)  375 -  z  I  I  I  I  I  / // —  ff/  / /  ~  < <D CL  / /f /////KtmWAJr// / /JW/  -125 -  /  /  —  E Q  -250 -375 — -500 -25.0  — T  ,  i  i  i  i  i  !  I  -12.5  I  T  '  I  I  0.0  I  I  i  i  i  i  12.5  25.0  Storey Displacement, mm 800  i  1  r  400 c <u  E o  -I  1  .  H  I  L.  c T3 C CO E  -400  00  -800  _i  -0.0020  i  i_  -0.0012  _L  -0.0004  _l  0.0004  0.0012  0.0020  Beam Rotation, rad  Figure 7.15: a) Load-deformation response of the friction damper at the level of mechanical floor b) Corresponding beam bending moment-rotation response at the level of mechanical floor (Joshua Tree record) 116  Chapter 7:  THREE-DIMENSIONAL NON-LINEAR ANALYSIS OF THE BUILDING USING FRICTION DAMPERS  Sylmar and Joshua Tree records are shown in Figures 7.16 to 7.19, respectively. The selected time values were at peak acceleration at the top floor, at the time where maximum base shear occurred and at the start of the free vibration response. Also shown in Figures 7.16 to 7.19 are the nonconcurrent maximum storey shears and overturning moments for both the eccentric braced and friction damped buildings. Figures 7.16 to 7.19 indicate that each earthquake record had a different effect on the overall building response. For the Loma Prieta earthquake record the maximum overturning moment at the base occurred during the free vibration response where the building was mainly vibrating in its first natural period, as shown in Figure 7.16. The above statement is also true to some degree for the Mexico City (SCT1) record. However, the general shape of the maximum storey overturning moment plots are markedly different for the two earthquakes. For the Mexico City (SCT1) record the maximum storey overturning moment occurred at the 15th floor and not at the base. This is mainly attributed to the overall response of the building during Mexico City (SCT1) record where the 2nd mode shape dominated the response while for the Loma Prieta earthquake record the third mode was dominant. The maximum base shear and overturning moment experienced by the building during the Mexico City (SCT1) record is about four times larger than that of the Loma Prieta earthquake record. Similar to the Mexico City (SCT1) record the response of the building to the Sylmar record was mostly in the 2nd mode. As a result, the overall profile of the overturning moment response is comparable for the two earthquake records. On the other hand, the de-amplification of the input excitation for the Sylmar record at the higher floors produced relatively small storey forces at the higher building elevation. This is shown in Figure 7.18 where the storey shear response for the floors above the 16th floor is substantially smaller than that of the Mexico City (SCT1) record response. The storey shear and overturning moment response of the building to the Joshua Tree record is 117  Chapter 7:  THREE-DIMENSIONAL NON-LINEAR ANALYSIS OF THE BUILDING USING FRICTION DAMPERS  45  45  37 r  37  29 r  29 r  i — i — I — i — i — r  >>  S> 21 o *• CO  § 21 CO  13 r  13  -20000 -10000 0 10000 20000 Storey Shear (kN)  -20000 -10000 0 10000 20000 Max. & Min. Storey Shear (kN) 45  i  1  1  1  r  37  29  o 21 CO  13  -600000  -200000  200000  600000  Overturning Moment (kN.m)  -3 -600000  0  600000  Max. & Min. Overturning Moment (kN.m)  Figure 7.16: Computed storey shear and overturning moment demand for the friction damped building at selected time intervals and maximum absolute values during the Loma Prieta earthquake record 118  Chapter 7:  THREE-DIMENSIONAL NON-LINEAR ANALYSIS OF THE BUILDING USING FRICTION DAMPERS  45  45  37  37  29  29  S> 21  21 CO  CO  13  13  -74000 -37000 0 37000 Storey Shear (kN)  -74000 -37000  74000  0  37000  74000  Max. & Min. Storey Shear (kN)  45  45 -__  37  37 ~: T  29  29 r  o 21  'o 21  I  I  I  1  1  !  1  1  1  '  ;  d)  •4-*  —_  \  -_  CO  CO  Eccentric Brace Damper  13 z  13  I  ~-  \ i  -3000000 -1000000  1000000  3000000 -3000000  Overturning Moment (kN.m)  / 1' i  i  1  0  i  i Nil  i  i  3000000  Max. & Min. Overturning Moment (kN.m)  Figure 7.17: Computed storey shear and overturning moment demand for the friction damped building at selected time intervals and maximum absolute values during the Mexico City (SCTl) record 119  Chapter 7:  THREE-DIMENSIONAL NON-LINEAR ANALYSIS OF THE BUILDING USING FRICTION DAMPERS  45  37  29  §  21  CO  13  -74000 -37000 0 37000 74000 Storey Shear (kN)  -74000 -37000  0  37000 74000  Max. & Min. Storey Shear (kN)  45 37 29 |  21  -4-»  CO  13  3000000 3000000 -3000000 Max. & Min. Overturning Moment (kN.m) Overturning Moment (kN.m)  -3000000 -1000000  1000000  Figure 7.18: Computed storey shear and overturning moment demand for thefrictiondamped building at selected time intervals and maximum absolute values during the Sylmar record 120  Chapter 7: 45  ~i  !  i  I  THREE-DIMENSIONAL NON-LINEAR ANALYSIS OF THE BUILDING USING FRICTION DAMPERS  j  i  i  i  r  45  1—i—1—i—i—i—r  a) 37  37  29  29  t = 13.18 s t = 18.44 s t = 47.48 s  £o 21 *•'  o  21  CO  CO  13  13 r 5 fr  LlJ i I i i I I I I i -3 j _ _ i -34000 -19000 -4000 11000 26000 Storey Shear (kN) L_J  45  "1  1  i—i  I  L U  L_J  1  '  I  J J  !  I  I  I  -34000 -17000  I  I  I  0  I  I  J_J  I  L_  17000 34000  Max. & Min. Storey Shear (kN) 45  r  ~i  1  1  1  1  a  1  1  r  c) 37  37  29  29  o 21  o  CO  21  •4-*  CO  13  13  — — I  -900000  -300000  I  I  I  I  I  300000  t.  I  i  L_  900000  Overturning Moment (kN.m)  -1200000  Eccentric Brae Damper i  I  0  i  i  i  i  ~\i  1200000  Max. & Min. Overturning Moment (kN.m)  Figure 7.19: Computed storey shear and overturning moment demand for the friction damped building at selected time intervals and maximum absolute values during the Joshua Tree record 121  Chapter 7:  THREE-DIMENSIONAL NON-LINEAR ANALYSIS OF THE BUILDING USING FRICTION DAMPERS  very similar to that of the Sylmar record. The maximum overturning moment, however, occurred at the base of the building as opposed to the mid. building height. 7.5.3 Energy Input and Dissipation The seismic response of a structure is determined by the amount of energy fed in and energy dissipated. The optimum seismic response, therefore, consists of minimizing the difference between the input energy and energy dissipated. The input energy basically is dependent on the natural period of the structure and the dynamic characteristics of the ground motion. It can be controlled to a certain extent by avoiding the phenomenon of resonance by modifying the dynamic characteristics of the structure relative to the input motion. Since the future ground motion characteristics, associated with uncertainties generated by soil structure interaction, are highly erratic in nature, control of the input energy alone is not reliable. However, in friction damped braced frames, the period of the structure is influenced by the slip load of the brace and varies with the amplitude of the oscillations, i.e. severity of the earthquake motion. Resonance of the structure is, therefore, more difficult to establish. By the proper selection of the slip load, it is therefore possible to tune the response of the structure to an optimum value. A comparison of the input energy and dissipated energy for the eccentric braced and friction damped buildings subjected to the Loma Prieta, Mexico City (SCT1), Sylmar and Joshua Tree records are shown in Figures 7.20 to 7.23, respectively. In general, the major portion of the input energy was dissipated through inherent damping in the system. It is noted that a 3% viscous damping was assigned to the 2nd and 3rd modes of vibration for both buildings. The 2nd and 3rd modes were mostly dominant in the response of the buildings. For the smaller intensity earthquake input records the excitations were not sufficient to cause significant deformation in the friction dampers. This is the case for the Loma Prieta and Joshua Tree earthquake input excitations where the energy dissipated through the dampers as a result of 122  Chapter 7:  THREE-DIMENSIONAL NON-LINEAR ANALYSIS OF THE BUILDING USING FRICTION DAMPERS  10000  8000  6000  c LU  Input Energy Nonlinearity Energy Kinetic Energy Damping Energy Potential Energy  4000  2000 ./ft^A'A-A-^^^A^^-u. ~~~J  0  40  L  1._.-..  I . L . I  80  I  I  I  I  I  I  I  120  160  , ; .  -  Time, sec 10000  I  I  I  I  I  I  I  I  I  I  i  i  i  |  i  1  ,  '  b) 8000  —  -  6000 -  /  E>  a) c LU  -  s  /  4000  -  ; ;  2000  .' 1* k  Jy FitfVU1 , ^ f i ' i " "P ! J ^^tf" t TOT/*>?^  0  40  J ^ / K / \ ' ^ * - U « «L « . !  -l_„i__J  80  J..  ,l  ,i  1  120  l  l  ,-i  1  l  1  1  160  Time, sec Figure 7.20: Energy time histories for the a) eccentric braced and b) friction damped buildings during the Loma Prieta earthquake record 123  Chapter 7:  THREE-DIMENSIONAL NON-LINEAR ANALYSIS OF THE BUILDING USING FRICTION DAMPERS  130000  1  78000  c  52000  T — i — I — ! — i — r -  Input Energy Nonlinearity Energy Kinetic Energy Damping Energy Potential Energy  104000 -  z  i  a)  LU  26000  lA*\jJv<H  0 25  50  75  L,^.I-  100  125  150  175  200  125  150  175  200  Time, sec 130000  104000  78000 &  |  52000  26000  25  50  75  100 Time, sec  Figure 7.21: Energy time histories for the a) eccentric braced and b) friction damped buildings during the Mexico City (SCTl) record 124  Chapter 7:  THREE-DIMENSIONAL NON-LINEAR ANALYSIS OF THE BUILDING USING FRICTION DAMPERS  50000  40000  z  30000  c  20000  a)  Input Energy Nonlinearity Energy Kinetic Energy Damping Energy Potential Energy  UJ  10000  IA/IW-M-'  0 20  0  . — i . . ~  1  II • . I  40  I i J  I  L i '  80  60  Time, sec  50000  n  i  i  i  i  i  i  I  r~  b)  40000  2  i  30000  •>.  g> |  !:  20000  '  10000  0  o  20  40  60  80  Time, sec  Figure 7.22: Energy time histories for the a) eccentric braced and b)frictiondamped buildings during the Sylmar record 125  Chapter 7:  THREE-DIMENSIONAL NON-LINEAR ANALYSIS OF THE BUILDING USING FRICTION DAMPERS  32000  24000 Input Energy Nonlinearity Energy Kinetic Energy Damping Energy Potential Energy  >; 16000 C LU  8000  n i n «bi • . I . . i d i . •  0 0  120  80  40  160  Time, sec  32000  I  !  I  -i  i  1  f~  I  1  24000 z g 16000 C LU  8000  .  0 0  40  80  '  •  •  l  i  120  I  1  1  L-  160  Time, sec Figure 7.23: Energy time histories for the a) eccentric braced and b)frictiondamped buildings during the Joshua Tree record 126  Chapter 7:  THREE-DIMENSIONAL NON-LINEAR ANALYSIS OF THE BUILDING USING FRICTION DAMPERS  nonlinearity is minimal. As the intensity of the excitation increased (e.g. the case of the Mexico City (SCT1) record the percentage of energy dissipated by the friction dampers also increased, similarly, as the degree of nonlinearity increased the input energy to the building also increased. This is obvious for the case of Mexico City (SCT1) record (Figure 7.21) where the input energy for the eccentric braced and friction damped building are markedly different. It is noted that the analysis for the eccentric braced frame building was carried out in a linear fashion. Further review of the forces in the bracing elements and moments in the beams, however, indicated that some of the structural elements (e.g. storey links) had marginally exceeded their expected yield capacities.  127  Chapter 8: SEISMIC ANALYSIS OF SECONDARY SUBSYSTEMS 8.1 INTRODUCTION The goal of a seismic design is to eliminate or minimize damage to the structures and their contents during earthquakes. Present day seismic design codes utilize a static lateral loading as an approximation to a design earthquake excitation. It is distributed in as manner to follow closely that of the fundamental mode of vibration and has a total magnitude equal to the structure's weight times a seismic coefficient. In the National Building Code of Canada (NBCC, 1995) and Uniform Building Code (UBC, 97) this coefficient is composed of factors dependent on region seismicity, the structure's importance, fundamental period of vibration, material type and expected soil-structure behaviour. A secondary sub-system is defined as a linear elastic viscously damped system whose mass and stiffness are considerably smaller than the mass and stiffness of the system to which it is attached. During the last three decades, a large amount of effort has been undertaken to development of methods for seismic analysis of light, multiply supported secondary systems which are attached to heavier primary systems. These efforts have been motivated mainly by the use of critically important secondary systems, such as piping networks in nuclear power plants or refining facilities (Asfura and Kiureghian, 1984). In NBCC (1995) the seismic coefficient for non-building structures is dependent on a coefficient S that is a function of the boundary conditions of the elements under consideration. The effect of building natural period of vibration or the location of secondary sub-systems have no effect on the seismic force induced to the secondary sub-systems. It is expected that future codes will be directed more towards the control of secondary damage. Analysis of a primary structure response may be determined by one of the following methods:  128  Chapter 8:  1.  SEISMIC ANALYSIS OF SECONDARY SUB-SYSTEMS  The response spectrum approach which is simple to apply but provides only the maximum response acceleration in each mode,  2.  The time-history approach which involves the input of an actual earthquake ground motion at the base of the structure and determination of the complete time-history of the structural response. Although a single time-history analysis would be unreliable because of uncertainties in the damping and natural periods of the structures. Therefore, it would be necessary to make several time-history analysis, with various values of damping and periods within their probable ranges, and to use some statistical average of the results for design purposes. (Biggs and Roesset, 1970).  It is usually impractical to include secondary sub-systems in the dynamic model representing the building. If this approach were followed, the results would be unreliable because of an excessive number of degrees of freedom and the large difference between the mass of the item and that of the building. Therefore, the equipment and the building are treated separately and the building response is used as input for the equipment analysis. This method of seismic analysis of equipment is called floor response spectrum. 8.2 FLOOR RESPONSE SPECTRUM METHOD The conventional method of seismic analysis of equipment and multiply supported secondary subsystems (e.g., piping in nuclear power plants) is the floor response spectrum method. This method consists of the following three steps (Sackman, 1986): a.  Analysis of the primary structure supporting the secondary subsystem to determine the motions at all support points. In the current practice, this computation is usually carried out through time-history calculations using recorded or artificially generated ground accelerograms. The effects of the secondary subsystem on the response of the primary structure is neglected in this analysis.  b.  For each calculated support motion, a response spectrum, known as floor response  129  Chapter 8:  SEISMIC ANALYSIS OF SECONDARY SUB-SYSTEMS  spectrum, is computed. This represents the peak response of an oscillator of variable frequency which is subjected to the support motion. The computation is carried out through time-history analysis. The set of floor response spectra for all support points constitute the input into the secondary subsystem. c.  Determination of the response of secondary system in terms of the floor response spectra through modal combination.  This approach has the following important practical advantages: 1)  The approach avoids the dynamic modelling and analysis of the combined primary-secondary system, which can be prohibitively costly if carried out directly.  2)  It avoids numerical difficulties that could arise in the analysis of the combined system due to large differences between the properties of the two systems.  3)  Once the floor response spectra are specified, the method then allows the - analyst to work on the secondary system independently of the primary system characteristics.  4)  The floor response spectrum method is inexpensive relative to time-history integration methods.  However, as currently applied, the floor response spectrum approach has several important shortcomings. These include: 1)  The cross-correlation between the excitations at the support points of the secondary system are neglected or improperly considered.  2)  The response is artificially separated into "pseudo-static" and "dynamic" parts, which has the consequence that a proper modal combination rule can not be developed.  3)  The cross-correlation between responses of closely spaced modes in the primary and secondary systems is often neglected or improperly considered.  4)  The interaction between the primary and secondary systems is neglected. This interaction can be significant when the mass of the secondary system is not 130  Chapter 8:  SEISMIC ANALYSIS OF SECONDARY SUB-SYSTEMS  negligible in comparison with the mass of the primary system or when the two systems have tuned or nearly tuned natural frequencies. 5)  The effect of non-classical damping of the combined system, which can be significant even when the two systems are individually modally damped is often not considered (Igusa and Der Kiureghian 1983).  8.3 NBCC AND UBC REGULATIONS FOR EQUIPMENT According to the NBCC (1995), mechanical/electrical equipment mounted on buildings shall be designed for a lateral force, V , equal to: Vp-vI'Sp-Wp  (8.1)  where: V = Lateral force on a part of the structure, / = Importance factor, . v = Zonal velocity ratio (e.g. 0.2 for Vancouver), S = Horizontal force factor for part or portion of a building and its anchorage, W = Weight of the secondary sub-system, The force V should be distributed according to the distribution of mass of the element under consideration. The values of S for mechanical/electrical components shall be equal to: S  p'Cp'Ar'Ax  (8-2)  where: C = Seismic coefficient for components of mechanical and electrical equipment, Ar = 1.0 for components that are both rigid and rigidly connected; 1.5 for components located on the ground that are flexible or flexibly connected; 3.0 for all other cases, Ax = l.0 +  (hx/hn),  hx is the height above the base for the floor where mechanical/electrical equipment located and h is the total height of the building. According to the UBC (1997), attachments for permanent equipment supported by a structure 131  Chapter 8:  SEISMIC ANALYSIS OF SECONDARY SUB-SYSTEMS  shall be designed to resist the total design seismic forces prescribed below: F  P=4-0-Ca-Ip-Wp  (8.3)  Alternatively, F may be calculated using the following formula: a„-C-l(  Fp = -£•  Except that F  R.  h}  1 + 3 - r * • Wp  shall not be less than 0.7 • Ca • I • W  (8.4) and need not be more than  4.0-Ca.Ip-Wp. where: F = Design seismic force on a part of the structure, Ca = Seismic coefficient as set forth in Table 16-Q in the code, /  = Importance factor specified in Table 16-K, = The weight of an element or component,  a = In-structure component amplification factor from Table 16-0, R = Component response modification factor from Table 16-0, hx = The element or component attachment elevation with respect to grade, hr = The structure roof elevation with respect to grade, 8.4 FLOOR RESPONSE SPECTRUM ANALYSIS PROCEDURE The time-history analysis of the building provides the time-history acceleration for each level which are seismic input for the building mechanical floors (e.g., 44th storey for the Embarcadero building). A response spectrum, using Nonlin ver. 6.01 computer program, is obtained from each time-history input. Results of this procedure for Loma Prieta, Mexico city, Joshua Tree and Sylmar earthquake records at the 44th floor are shown in Figures 8.1 and 8.2. Figure 8.1 indicates that the sylmar earthquake record is capable of inducing very high lateral seismic forces to the equipment mounted at the top floor of the embarcadero building. The Loma Prieta earthquake would have effectively excited equipment with natural frequencies around 1.0 sec. For both rigid  132  C h a p t e r 8:  SEISMIC ANALYSIS OF SECONDARY SUB-SYSTEMS  Joshua Tree -  Loma Prieta Mexico City  en c o  Sylmar  '"•"^  CO  o o a < o  •o <D  (0  a.  0.1  10.0  1.0  Period, sec 10000.0  :  yA---  •$?'"'."f\  1000.0 = --  /  +-!"  c CD O  ~^'iyf \xr> -j  .rT^^•c/ ^ ^^/y — ^ ^  E E 100.0 E  A  ..-•••  r  10.0  /  ^  '  •  /  \  i  ^ *  : .  <-' Ssf .•#••  /r  Joshua Tree  -,  Loma Prieta  JS  Q. V)  Mexico City Sylmar  •S  1.0  -  _ i  -  0.1 0.1  1.0  10.0  Period, sec Figure 8.1: Pseudo-acceleration and displacement response spectra for the eccentric braced Embarcadero building for Loma Prieta, Mexico city, Joshua Tree and Sylmar earthquake records at the 44th floor 133  Chapter 8:  SEISMIC ANALYSIS OF SECONDARY SUB-SYSTEMS  Joshua Tree Loma Prieta Mexico City Sylmar  c g '•*-»  CO O CD O O  3 -  <  O TJ =5 CD CO  0.  0.1  1.0  10.0  Period, sec  10000.0  1000.0 r  1 100.0 c 0)  E O  10.0  _55 Q. CO  10.0  Figure 8.2: Pseudo-acceleration and displacement response spectra for the friction damped building for Loma Prieta, Mexico city, Joshua Tree and Sylmar earthquake records at the 44th floor 134  Chapter 8:  SEISMIC ANALYSIS OF SECONDARY SUB-SYSTEMS  and rigidly attached equipment the amount of force is generally less than weight of the equipment. Figure 8.2 indicates that the friction damped building is considerably more effective than the eccentric braced building in reducing the seismic force demand on the equipment mounted at the top of the building. 8.5 COMPARISON OF CODE AND FLOOR RESPONSE SPECTRUM RESULTS Using the NBCC (1995) and UBC (1997) code formulas, the seismic coefficient as percentage of the weight for mechanical equipment mounted at the 44th floor of the Embarcadero building may be computed as:  NBCC (1995)  UBC (1997)  V  I  0.4 a  C  P  *r  4c  1.0  1.0  3.0  2.0  P  ca  !  2.5  0.44  S  p =  C  p-Ar-Ax  6.0  P  *P  V*r  1.0  1.0-3.0  1.0  V  P  2AWp F  P  (1.47-1.76)FF  Table 8.1: Calculated design seismic forces on mechanical equipment at the 44th floor of the Embarcadero building The maximum seismic design force to the mechanical equipment at the 44th floor of the Embarcadero building according to the NBCC (1995) is 2.4 W while the UBC (1997) prescribed a maximum seismic design force of 1.76 W . Figures 8.1 and 8.2 indicate that for equipment rigidly attached to the floors and with natural frequencies below 0.5 sec, the maximum lateral force is about (2.0 - 2.5) W for the Sylmar earthquake record. It is, however, noted that for equipment for natural frequencies between 0.5 sec to 1.0 sec. higher seismic forces may be exerted to the equipment.  135  Chapter 9: SUMMARY, CONCLUSIONS AND RECOMMENDATIONS 9.1 SUMMARY Great advances have been made during the past fifteen years in methods for calculating the dynamic earthquake response of complex structures. Using finite element techniques and modern digital computers, elastic response analyses can now be performed for any tall building, whether it be of simple rectangular box or shape or of an unusual form such as the Transamerica "pyramid" in San Francisco. The eccentric bracing system presented in this thesis is a very stiff structure system that easily satisfies the serviceability requirements of building codes. It combines the strength and stiffness of a braced frame with an inelastic behaviour and energy dissipation of a moment-resisting frame. The system employs deliberately large eccentricities between the brace-beam connection and beam-column joints, which are chosen to assure that the eccentric beam element yields in shear. It acts as a ductile fuse that dissipates large amount of energy while preventing buckling of the braces. The weight of steel required may be on the order of 30% less than require for steel moment-resisting frames (Roeder & Popov, 1978). In this thesis the response of a 49-storey eccentric braced steel frame building was studied under October 17,1989, Loma Prieta (Ms = 7.1) earthquake, Mexico City (SCT1) record from the 1985 Guerrero-Michoacan, Mexico earthquake, Sylmar station record from the 1994 Northridge earthquake in California and Joshua Tree station record from the 1992 Landers earthquake in California. The selected earthquake records were representatives of earthquakes with different frequency content and time data characteristics. One of the excitations created a pulse effect which required structure to possess considerable strength and stiffness in order to limit deflections. Another excitation produced a periodic effect for which the structure was excited with low frequency (high period) contents while the maximum amplitude of input acceleration 136  Chapter 9:  SUMMARY, CONCLUSIONS AND RECOMMENDATIONS  was less than 0.2g. The dynamic characteristics of the building were determined by analyses of its recorded responses during the Loma Prieta earthquake. Three-dimensional linear elastic time-history analyses of the building were conducted using information obtained from data analyses of the recorded responses and the observed behaviour of the structure during the earthquake. To complement the analytical studies of the eccentric braced frame building, numerical analyses of the building replacing the eccentric braced elements with uniaxial link elements (simulating friction dampers) were conducted. The main reason for introducing friction damped elements to the building was to substantially reduce the inelastic demand on the storey link elements during severe earthquake shaking by redirecting the earthquake input energy to the friction damped elements introduced in the ETABS model of the building. A comparison between the code prescribed lateral force exerted on secondary sub-systems such as mechanical equipment mounted at the top of building structures with the floor response spectrum method was also studied during the course of this thesis. 9.1.1 Linear Elastic Building Response to Selected Earthquakes Elastic dynamic time-history analyses of the eccentrically braced frame building under four very different base excitations indicated that this system performs very well. A very close correlation between recorded and modelled displacements were achieved by fine tuning a few modelling parameters such as rigidity of beam-to-column connections and overall rigidity of panel zones. The time-history results closely matched the time-response data generated by sensors during the Loma Prieta earthquake. Elastic time-history analysis using standard modelling assumptions accurately predicted recorded floor displacements in amplitude and frequency during strong shaking and free vibration. Experimenting with eccentric bracing techniques has also led to the conclusion that, when used, 137  Chapter 9:  SUMMARY, CONCLUSIONS AND RECOMMENDATIONS  such braces should be applied throughout an entire building rather than just the bottom floors, which was the case for the structure studied. Taking eccentric bracing all the way to roof would eliminate the concentration of force that otherwise occurs where the braces cease. The numerical results of the storey forces and relative displacements showed a substantial amplification of input motion for the floors above the 39th floor where the eccentric bracing system stopped. 9.1.2 NonLinear Friction Damped Building Response to Selected Earthquakes The seismic response of a structure is determined by the amount of the energy fed-in and energy dissipated. The optimum seismic response therefore, consists of minimizing the difference between the input energy and energy dissipated. The addition of friction damped elements reduced the storey shear force, relative storey displacement and overall overturning moment for all selected earthquake records. Friction devices using the principles described in this thesis are very efficient energy dissipators, and can effectively protect the bracings or storey beams and columns from damage. They are able to perform consistently for a large number of cycles. The effective ductility that is thus, assured might offer a modest premium over the traditional design economy, but it reduces the maximum deformations for a given earthquake and thus, reducing the cost of repairs. The devices themselves can easily be replaced or reset. 9.1.3 Sub-Secondary systems Using the NBCC (1995) and UBC (1997) code formulas, the seismic coefficient as percentage of the weight for mechanical equipment mounted at the 44th floor of the Embarcadero building was computed. The maximum seismic design force to the mechanical equipment at the 44th floor of the Embarcadero building according to the NBCC (1995) was 2.4 W while the UBC (1997) prescribed a maximum seismic design force of 1.76 W . The response spectra plots of the computed motion at the 44th floor indicated that for equipment  138  Chapter 9:  SUMMARY, CONCLUSIONS AND RECOMMENDATIONS  rigidly attached to the floors and with natural frequencies below 0.5 sec, will experience a maximum lateral force of about (2.0 - 2.5) W for the Sylmar earthquake record. It is, however, noted that for equipment for natural frequencies between 0.5 sec to 1.0 sec. higher seismic forces may be exerted to the equipment. 9.2 RECOMMENDATIONS AND FURTHER STUDIES •  With the advancement of computer hardware and software, the development of more sophisticated 3D models of steel framed buildings, accounting for better representation of the structural behaviour, is to be encouraged in the future.  •  A more detailed computer model including the effects of foundation rotation and soil structure interaction would provide additional insight into the performance of the building.  •  Due to the limitation of the computer program ETABS, damping used for the dynamic analyses was restricted to modal damping ratios only. It is, however, recommended that the effects of other types of damping including Rayleigh damping be investigated to more realistically simulate the energy dissipation mechanism in the structure.  •  Ductility demand and nonlinear analysis of the eccentric braced frame building was not carried out during the course of this study. It would be very useful to carry out further research on these two aspects.  •  The parameters like rigidity of beam-to-column connections and panel zone in moment-resisting frame buildings has a very important effect on the dynamic behaviour of building structures. It is, therefore, recommended that further detailed numerical study be carried out to identify the more appropriate values.  139  REFERENCES Aiken, I. A., Kelly J. M. and Pall, A. S., "Seismic Response of a Nine-Storey Steel Frame with Friction Damped Cross-Bracing", Report No. EERC 88-17, Earhquake Engineering Research Centre, University of California, Berkeley, CA, 1988. Aiken, I. A., Kelly J. M., "Earthquake Simulator Testing and analytical studies of Two EnergyAbsorbing Systems for multistory Structures", Report No. EERC 90-03, Earthquake Engineering Research Centre, University of California, Berkeley, CA, 1990. Asfura, A. and Kiureghian A. D., "A New Floor Response Spectrum Method for Seismic analysis of Multiply supported Secondary Systems", Report No. EERC 84/04, Earthquake Engineering Research Centre, University of California, Berkeley, CA, 1984. Biggs, J. M. and Roesset, J. M., "Seismic Analysis of Equipment Mounted on a Massive structure", Seismic Design for Nuclear Power Plants, The M.I.T. Press, Cambridge, Massachusetts, and London, England, 1970. Design Response spectra for Design of Nuclear Power Plants, Regulatory Guide 1.60, U.S. Nuclear Regulatory Commission, Bethesda, Md., Dec. 1973. ETABS .version 6.23, "Linear and Nonlinear Static and Dynamic Analysis and Design of Building Systems", Computers & Structures Inc., 1996. 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