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Investigation of seismic isolators as a mass damper for mixed-used buildings

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Investigation of seismic isolators as a mass damper for mixed-used buildings

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Content INVESTIGATION OF SEISMIC ISOLATORS AS A MASS DAMPER FOR MIXED-USE BUILDINGS by Lai-Yui Sammy Chong A Thesis Presented to the FACULTY OF THE SCHOOL OF ARCHITECTURE UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Fulfillment of the Requirements for the Degree MASTER OF BUILDING SCIENCE May 1993 Copyright 1993 Lai-Yui Sammy Chong UMI Number: EP41431 All rights reserved INFORMATION TO ALL USERS The quality of this reproduction is dependent upon the quality of the copy submitted. In the unlikely event that the author did not send a complete manuscript and there are missing pages, these will be noted. Also, if material had to be removed, a note will indicate the deletion. Dissertation Publishing UMI EP41431 Published by ProQuest LLC (2014). Copyright in the Dissertation held by the Author. Microform Edition © ProQuest LLC. All rights reserved. This work is protected against unauthorized copying under Title 17, United States Code ProQuest LLC. 789 East Eisenhower Parkway P.O. Box 1346 Ann Arbor, Ml 48106- 1346 UNIVERSITY O F S O U T H E R N CALIFORNIA THE SCHOOL OF ARCHITECTURE UNIVERSITY PARK LOS ANGELES, CALIFORNIA 90089-0291 13 u . .S . ' 9 3 C 5 H ^ i.PI This thesis, w ritten b y m LaiyYui Sammy Chong..................... under the direction o f h is ... . Thesis C om m ittee, an d a p p ro v ed b y all its m em bers, has been pre sen te d to an d accepted b y the D ean o f The School o f A rch itectu re, in partial fu lfillm en t o f the require m en ts fo r the degree o f Master of Building Science Dean D ate THESIS/COMMITTEE Chair DEDICATION This thesis is dedicated to my parents, I love you both. ACKNOWLEDGMENTS I wish to express my gratitude to: Goetz Schierle, Director and Professor of Master of Building Science at University of Southern California, for teaching me about the knowledge of structure, from Arch. 213 to my thesis; Marc Schiler, Professor of Building Science at University of Southern California, for reading the entire manuscript, and giving me invaluable advice; Dimitry Vergun, Professor of Building Science at University of Southern California, for guiding me throughout the entire test in my thesis; Department of Geological Sciences at University of Southern California, for providing a seismic record for my test; Raymond Yang of University of Pennsylvania, for his thorough proofreading of my thesis; Many of my colleagues in the Master of Building Science Program, for being with me when I needed your help; Lai-Fu Chong and Rosanna Chong, for their enduring patience and encouragement. TABLE OF CONTENTS DEDICATION ............................................................................... ii ACKNOWLEDGMENTS ............................................................. iii LIST OF FIGURES ........................................................................ vii LIST OF TABLES ......................................................................... xv ABSTRACT .................................................................................... xx PART I: SEISMIC DESIGN BACKGROUND INTRODUCTION ......................................................................... 1 CHAPTER 1. EARTHQUAKES ................................................. 4 1.1 The Causes of Earthquake ........................... 4 1.2 Types of Plate Boundaries ........................... 4 1.3 Types of Faults .............................................. 6 1.4 Seismic Waves .............................................. 8 1.5 Magnitude ..................................................... 10 CHAPTER 2. ARCHITECTURAL CONSIDERATIONS ........ 11 2.1 Introduction ................................................... 11 2.2 Slenderness Ratio of Buildings .................... 11 2.3 Building Shapes ............................................. 12 2.4 Torsion ........................................................... 13 2.5 Soft First Stories ............................................ 14 2.6 Variations in Stiffness between Columns and Beams ..................................................... 16 2.7 Pounding ....................................................... 17 CHAPTER 3. SEISMIC ISOLATION ........................................ 18 3.1 Introduction ................................................... 18 3.2 Stiff Buildings Vs. Flexible Buildings ......... 18 3.3 The Principle of Seismic Isolation ............... 19 3.4 Rubber Bearing ............................................. 19 3.5 Damper .......................................................... 22 3.6 "Hybrid Lead Rubber Bearing" .................... 23 3.7 Durability of the Rubber Bearing ................ 24 CHAPTER 4. PRECEDENT STUDIES ..................................... 25 4.1 High Tech. R&D Center ............................. 25 4.2 National Institute for Research in Inorganic Material .......................................................... 28 4.3 Campus Building in Tohoku University ..... 30 PART II: BASE ISOLATION RESEARCH IN UNIFORM LOAD BUILDINGS. CHAPTER 5. RESEARCH METHODOLOGY ........................ 32 5.1 Objectives ...................................................... 32 5.2 Assumption for Test Prototype ...................... 32 5.3 Symbols .......................................................... 34 5.4 Simulation Model .......................................... 34 5.5 Test Procedure ............................................... 39 CHAPTER 6. TEST RESULTS .................................................. 43 Test 1 ...................................................................... 43 Test 2 ...................................................................... 49 Test 3 ...................................................................... 54 Test 4 ...................................................................... 62 Test 5 ...................................................................... 70 PART III: MASS ISOLATION ................................................... 77 Test 6 ...................................................................... 79 Test 7 ...................................................................... 90 Test 8 ...................................................................... 99 Test 9 ...................................................................... 108 Test 10 .................................................................... 116 Test 11 .................................................................... 125 CONCLUSIONS ............................................................................ 133 SUMMARY Test 1 ...................................................................... 134 Test 2 ...................................................................... 136 Test 3 ...................................................................... 138 Test 4 ...................................................................... 140 Test 5 ...................................................................... 142 Test 6 ...................................................................... 144 Test 7 ...................................................................... 146 Test 8 ...................................................................... 148 Test 9 ...................................................................... 150 Test 1 0 ..................................................................... 152 Test 11 ..................................................................... 154 REFERENCE .................................................................................. 156 v i LIST OF FIGURES CHAPTER 1. EARTHQUAKES Figure 1.1 Map of Plate Tectonic ................................................. 5 Figure 1.2 Reverse Fault ............................................................... 7 Figure 1.3 Normal Fault ................................................................ 7 Figure 1.4 Right-Lateral Fault ...................................................... 7 Figure 1.5 Left-Lateral Fault ........................................................ 7 Figure 1.6 Oblique Fault ............................................................... 7 Figure 1.7 Motion of P Wave ....................................................... 8 Figure 1.8 Motion of S Wave ....................................................... 9 Figure 1.9 Motion of Love Wave ................................................ 9 Figure 1.10 Motion of Rayleigh Wave .......................................... 10 CHAPTER 2. ARCHITECTURAL CONSIDERATIONS Figure 2.1 Slenderness Ratio ........................................................ 12 Figure 2.2 Building Orientation .................................................... 13 Figure 2.3 L-shaped Building ....................................................... 13 Figure 2.4 Torsion ........................................................................ 14 Figure2.5 The Soft Story Effect ................................................ 15 Figure 2.6 Variation of Stiffness ................................................. 16 vii CHAPTER 3. SEISMIC ISOLATION Figure 3.1 Bearing without Steel Plates ...................................... 20 Figure 3.2 Bearing with Steel Plates ............................................ 20 Figure 3.3 Force Response Spectrum .......................................... 21 Figure 3.4 Displacement Response Spectrum ............................ 21 Figure 3.5 Displacement Spectrum for Increasing Damping ...... 22 Figure 3.6 Lead-Rubber Device .................................................. 23 Figure 3.7(a)’ ’ Hybrid Lead Rubber Bearing” ................................ 24 Figure 3.7(b)’ ’ Hybrid Lead Rubber Bearing” ................................ 24 CHAPTER 4. PRECEDENT STUDIES Figure 4.1 High Tech. R & D Center .......................................... 25 Figure 4.2 Rubber Bearings and Steel Bar Dampers in High Tech. R & D Center ........................................ 26 Figure 4.3 Accelerograms of High Tech. R & D Center ........... 27 Figure 4.4 National Institute for Research in Inorganic Material ..................................................... 28 Figure 4.5 Accelerograms of National Institute for Research in Inorganic Material ................................. 29 Figure 4.6 Campus Building in Tohoku University .................... 30 Figure 4.7 Accelerograms of the Campus Building in Tohoku University .................................................... 31 viii CHAPTER 5. TEST PROCEDURE Figure 5.1 Plan and Section of Model ......................................... 35 Figure 5.2 Deformation of Eraser ................................................ 38 Figure 5.3 Shaker Table ............................................. 39 Figure 5.4 Seismogram for Testing .............................................. 40 Figure 5.5 Measuring Displacement ............................................ 41 CHAPTER 6. TEST RESULTS TEST 1 Figure 6.1 Displacement of two 2 stories Buildings Isolated vs. Non-Isolated ........................................... 46 Figure 6.2 Comparison of Interstory Drift Isolated vs. Non-Isolated ........................................... 46 Figure 6.3 Comparison of Floor Acceleration Isolated vs. Non-Isolated ........................................... 48 Figure 6.4 Acceleration Amplification Isolated vs. Non-Isolated ........................................... 48 TEST 2 Figure 6.5 Displacement of two 4 stories Buildings Isolated vs. Non-Isolated ........................................... 51 Figure 6.6 Comparison of Interstory Drift Isolated vs. Non-Isolated ........................................... 51 ix Figure 6.7 Comparison of Floor Acceleration Isolated vs. Non-Isolated ........................................... 53 Figure 6.8 Acceleration Amplification Isolated vs. Non-Isolated ........................................... 53 TEST 3 Figure 6.9 Displacement of two 8 stories Buildings Isolated vs. Non-Isolated ........................................... 57 Figure 6.10 Comparison of Interstory Drift Isolated vs. Non-Isolated ........................................... 58 Figure 6.11 Comparison of Floor Acceleration Isolated vs. Non-Isolated ........................................... 60 Figure 6.12 Acceleration Amplification Isolated vs. Non-Isolated ........................................... 61 TEST 4 Figure 6.13 Displacement of two 8 stories Buildings Isolated vs. Non-Isolated ........................................... 65 Figure 6.14 Comparison of Interstory Drift Isolated vs. Non-Isolated ........................................... 66 Figure 6.15 Comparison of Floor Acceleration Isolated vs. Non-Isolated ........................................... 68 Figure 6.16 Acceleration Amplification Isolated vs. Non-Isolated ........................................... 69 X TEST 5 Figure 6.17 Displacement of two 8 stories Buildings Isolated vs. Non-Isolated ................................. ......... 72 Figure 6.18 Comparison of Interstory Drift Isolated vs. Non-Isolated ................................. 73 Figure 6.19 Comparison of Floor Acceleration Isolated vs. Non-Isolated ................................. 75 Figure 6.20 Acceleration Amplification Isolated vs. Non-Isolated .................................. ......... 76 TEST 6 Figure 6.21 Deflection for Various Building Masses Mass: (5th-8th) > (lst-4th) ............................ 83 Figure 6.22 Comparison of Interstory Drift Mass: (5th-8th) > (lst-4th) ............................ 84 Figure 6.23 Floor Acceleration for Different Masses Mass: (5th-8th) > (lst-4th) ............................ 86 Figure 6.24 Acceleration Amplification Ratios Mass: (5th-8th) > (lst-4th) ............................ 87 Figure 6.25 Period vs. Acceleration (Roof) Mass: (5th-8th) > (lst-4th) ............................ 89 Figure 6.26 Period vs. Maximum Acceleration (4th) Mass: (5th-8th) > (lst-4th) ............................ ......... 89 93 94 96 97 98 101 102 104 105 107 107 xii Deflection for Various Building Masses Mass: (5th-8th) < (lst-4th) .................... Comparison of Interstory Drift Mass: (5th-8th) < (lst-4th) .................... Floor Acceleration for Different Masses Mass: (5th-8th) < (lst-4th) .................... Acceleration Amplification Ratios Mass: (5th-8th) < (lst-4th) .................... Period vs. Maximum Acceleration (Roof) Mass: (5th-8th) < (lst-4th) .................... Deflection for Various Building Masses Mass: (6th-8th) > (lst-5th) .................... Comparison of Interstory Drift Mass: (6th-8th) > (lst-5th) .................... Floor Acceleration for Different Masses Mass: (6th-8th) > (lst-5th) .................... Acceleration Amplification Ratios Mass: (6th-8th) > (lst-5th) .................... Period vs. Acceleration (Roof) Mass: (6th-8th) > (lst-5th) .................... Period vs. Maximum Acceleration (5th) Mass: (6th-8th) > (lst-5th) ................. 110 111 113 114 115 118 119 121 122 124 124 xiii Deflection for Various Building Masses Mass: (6th-8th) < (lst-5th) ................. Comparison of Interstory Drift Mass: (6th-8th) < (lst-5th) .................... Floor Acceleration for Different Masses Mass: (6th-8th) < (lst-5th) .................... Acceleration Amplification Ratios Mass: (6th-8th) < (lst-5th) .................... Period vs. Maximum Acceleration (Roof) Mass: (6th-8th) < (lst-5th) .................... Deflection for Various Building Masses Mass: (4th-8th) > (lst-3rd) ................. Comparison of Interstory Drift Mass: (4th-8th) > (lst-3rd) .................. Floor Acceleration for Different Masses Mass: (4th-8th) > (lst-3rd) .................. Acceleration Amplification Ratios Mass: (4th-8th) > (lst-3rd) .................. Period vs. Acceleration (Roof) Mass: (4th-8th) > (lst-3rd) .................. Period vs. Maximum Acceleration (3rd) Mass: (4th-8th) > (lst-3rd) .................. TEST 11 Figure 6.49 Deflection for Various Building Masses Mass: (4th-8th) < (lst-3rd) ....................................... 127 Figure 6.50 Comparison of Interstory Drift Mass: (4th-8th) < (lst-3rd) ....................................... 128 Figure 6.51 Floor Acceleration for Different Masses Mass: (4th-8th) < (lst-3rd) ....................................... 130 Figure 6.52 Acceleration Amplification Ratios Mass: (4th-8th) < (lst-3rd) ....................................... 131 Figure 6.53 Period vs. Maximum Acceleration (Roof) Mass: (4th-8th) < (lst-3rd) ....................................... 132 xiv LIST OF TABLES Table 5.1 Properties of Columns for Prototype .................................. 33 Table 5.2 Height and Period of Prototype ......................................... 33 TEST 1 Table 6.1 Comparison of Lateral Displacement Base-isolated vs. Base-fixed .............................................. 45 Table 6.2 Comparison of Interstory Drift Base-isolated vs. Base-fixed .............................................. 45 Table 6.3 Comparison of Floor Acceleration Base-isolated vs. Base-fixed .............................................. 47 Table 6.4 Acceleration Amplification Base-isolated vs. Base-fixed .............................................. 47 TEST 2 Table 6.5 Comparison of Lateral Displacement Base-isolated vs. Base-fixed .............................................. 50 T able 6.6 Comparison of Inter story Drift Base-isolated vs. Base-fixed .............................................. 50 Table 6.7 Comparison of Floor Acceleration Base-isolated vs. Base-fixed .............................................. 52 Table 6.8 Acceleration Amplification Base-isolated vs. Base-fixed .............................................. 52 XV 56 56 59 59 64 64 67 67 71 71 74 xvi Comparison of Lateral Displacement Base-isolated vs. Base-fixed .......... Comparison of Interstory Drift Base-isolated vs. Base-fixed ............ Comparison of Floor Acceleration Base-isolated vs. Base-fixed ............ Acceleration Amplification Base-isolated vs. Base-fixed ............ Comparison of Lateral Displacement Base-isolated vs. Base-fixed ........... Comparison of Interstory Drift Base-isolated vs. Base-fixed ........... Comparison of Floor Acceleration Base-isolated vs. Base-fixed ........... Acceleration Amplification Base-isolated vs. Base-fixed ............ Comparison of Lateral Displacement Base-isolated vs. Base-fixed ........... Comparison of Interstory Drift Base-isolated vs. Base-fixed ........... Comparison of Floor Acceleration Base-isolated vs. Base-fixed ........... 74 82 82 85 85 88 88 92 92 95 95 xvii Acceleration Amplification Base-isolated vs. Base-fixed Comparison of Lateral Displacement Top 4 stories are heavier than the bottom 4 stories Comparison of Interstory Drift Top 4 stories are heavier than the bottom 4 stories Comparison of Floor Acceleration Top 4 stories are heavier than the bottom 4 stories Acceleration Amplification Top 4 stories are heavier than the bottom 4 stories Period vs. Acceleration (Roof) Top 4 stories are heavier than the bottom 4 stories Period vs. Maximum Acceleration (4th) Top 4 stories are heavier than the bottom 4 stories Comparison of Lateral Displacement Top 4 stories are lighter than the bottom 4 stories Comparison of Interstory Drift Top 4 stories are lighter than the bottom 4 stories Comparison of Floor Acceleration Top 4 stories are lighter than the bottom 4 stories Acceleration Amplification Top 4 stories are lighter than the bottom 4 stories . 98 .100 .100 ,103 103 106 106 109 109 112 112 xviii Period vs. Maximum Acceleration (Roof) Top 4 stories are lighter than the bottom 4 stories Comparison of Lateral Displacement Top 3 stories are heavier than the bottom 5 stories Comparison of Interstory Drift Top 3 stories are heavier than the bottom 5 stories Comparison of Floor Acceleration Top 3 stories are heavier than the bottom 5 stories Acceleration Amplification Top 3 stories are heavier than the bottom 5 stories Period vs. Acceleration (Roof) Top 3 stories are heavier than the bottom 5 stories Period vs. Maximum Acceleration (5th) Top 3 stories are heavier than the bottom 5 stories Comparison of Lateral Displacement Top 3 stories are lighter than the bottom 5 stories Comparison of Interstory Drift Top 3 stories are lighter than the bottom 5 stories Comparison of Floor Acceleration Top 3 stories are lighter than the bottom 5 stories Acceleration Amplification Top 3 stories are lighter than the bottom 5 stories .115 .117 117 .120 120 123 123 126 126 129 129 132 xix Period vs. Maximum Acceleration (Roof) Top 3 stories are lighter than the bottom 5 stories Comparison of Lateral Displacement Top 5 stories are heavier than the bottom 3 stories Comparison of Interstory Drift Top 5 stories are heavier than the bottom 3 stories Comparison of Floor Acceleration Top 5 stories are heavier than the bottom 3 stories Acceleration Amplification Top 5 stories are heavier than the bottom 3 stories Period vs. Acceleration (Roof) Top 5 stories are heavier than the bottom 3 stories Period vs. Maximum Acceleration (3rd) Top 5 stories are heavier than the bottom 3 stories Comparison of Lateral Displacement Top 5 stories are lighter than the bottom 3 stories Comparison of Interstory Drift Top 5 stories are lighter than the bottom 3 stories Comparison of Floor Acceleration Top 5 stories are lighter than the bottom 3 stories Acceleration Amplification Top 5 stories are lighter than the bottom 3 stories Period vs. Maximum Acceleration (Roof) Top 5 stories are lighter than the bottom 3 stories ABSTRACT This thesis presents the experimental results of using seismic isolators to separate mixed-use buildings into different masses. Three models were made for the experiments, each model contained eight stories with isolators placed at various locations. For the first set of tests, the eight stories were divided into two 4 story masses with isolators placed at the 4th floor and at the base. The second set of tests divides the eight story model into 3 stories on top and 5 stories at the bottom, with isolators placed at the 5th floor and at the base. The third set of tests separates the eight story model into 5 stories on top and 3 stories at the bottom, with isolators located at the 3rd floor and at the base. In all of the tests, the motion of shaking lasts 30 seconds with maximum displacement of 3" on each side and maximum ground acceleration of 0.4 lg. All of the test results show that when the upper mass is heavier than the lower mass, the upper mass acts as a damper and helps to reduce both displacement and floor acceleration of the entire structure. When the lower mass is heavier than the upper mass, the reductions in both displacement and acceleration are insignificant. XX PART I: SEISMIC DESIGN BACKGROUND Introduction Human beings have been inhabiting the earth for more than millions of years. Since the beginning of their existence, their activities have been threatened by the laws of nature. At the beginning, human beings tried to protect themselves from rain and wind by inhabiting caves. As people became more civilized, they realized that they could create shelters by putting a piece of animal skin on top of a center pole, which is stabilized by ropes tightened to the ground. Of course, these shelters would not be able to withstand the power of the natural forces. Each time their shelters got destroyed by earthquakes or hurricanes, they learned from previous mistakes and better shelters were built. This trial and error process was the only method that our ancestors have used in building construction for thousands of years. The trial and error method did create some fascinating structures. For example, the brick dome of Hagia Sophia in Constantinople. After the earthquake in 553 A.D., the dome collapsed. After the collapse, the builders realized that there was not enough buttressing to resist the outward thrust of the dome. Corrections were made and a better dome was built. This trial and error learning process continued until engineers learned more about the strength of materials, and equations were derived for structural analysis. 1 After every earthquake, engineers continue to learn something new and accumulated their knowledge. Over the years, three structural systems, rigid frame, braced frame, and shear walls, have been developed to resist seismic force. These three systems have a common concept in earthquake resistance, they all make buildings of variable stiffness and tie them on the ground; and let the strength of the connections and materials resist the lateral force. If the strength of the structure dominates over the lateral force, the building will stand; otherwise, structural failure will occur. In recent years, the booming of the rubber industry has produced high quality elastomeric bearings, these bearings have given a new dimension to earthquake resistance. The idea is to put these bearings at the base of buildings to allow lateral movement due to seismic action. The isolation system prevent some of the earthquake’ s energy being transmit to the building, thus floor accelerations are reduced. The base isolation system has been proved to be effective for four to five story buildings. The rubber bearings are seldom installed in high-rise buildings. The reason is that the rubber bearings do not resist tensile force. When a building gets taller, a greater over-turning moment from seismic and wind activity which will be generated. This increase in over-turning will put tensile stress on the rubber bearings. For the past several decades, the value of land has skyrocketed. The increase in land value forced developers to build taller buildings. Further new trends in urban planning put more than one function into a 2 building. For example, retail occupies the ground floor, offices occupy the lower stories, and apartment complexes occupy the upper stories, often with heavy mechanical equipment on top of the building. Since the function at various sections of the building is different, the mass at each particular section is also different. The non-uniform weight distribution may cause each section of the building to vibrate at its own frequency during earthquakes. This might create more structural damages than if the weight distribution of the building is uniform. If the frequency of the earthquake coincides with the frequency of the building, resonance will occur. The situation is similar to a swing. If a person pushes a swing at the right time, its amplitude and energy will build up. The intention of this thesis was to study the effect of using seismic isolators to separate a mixed-use building into different masses, so that they can help to dampen each other. 3 CHAPTER 1. EARTHQUAKES This chapter is paraphrased from (Bolt, 1988). 1.1 The Causes of Earthquake Earthquakes are perhaps the most destructive forces in nature; the Shensi earthquake in China killed 830,000 people in 1556. The Peru earthquake in 1970 killed 66,000 people, along with $530 million damage. The majority of earthquakes can be explained in terms of the concept of plate tectonics. The idea follows that the surface of the earth consists of about twelve rigid plates which are relatively stable. These plates are about 100 km thick, and they float and move on a layer of hot and softer rocks called asthenosphere. Earthquakes occur when these plates move relative to one another, and thus create stresses at their boundaries (Fig. 1.1). 1.2 Types of Plate Boundaries There are three types of plate boundaries. At a convergent boundary, two adjacent plates collide with each other; if one or both plates contains oceanic crust, then the oceanic plate will submerge beneath the continental plate. This type of collision usually creates trenches, such as the Kermadec-Tonga trench, located between the Fiji plate and the Antarctic plate. If, however, both plates contain continental crusts, then both plates will be elevated. This upward motion creates mountains, such as the Himalayas. 4 Liaoning Province North American txY plate ~ Eurasian plate South American plate NazeapJbte • $ b * 7 e 7 s &i Earthquake zone >- Motion of plate - Collision zone Aswan^ African < Volcanoes Subduetion zone J Lr~vT Spreading ridge offset by transform faults Figure 1.1 Map of Plate Tectonic (Bolt, 1988). At a divergent boundary, two adjacent plates move away from each other. As the two plates spread apart, tension is created at the boundary, and magma rises from the asthenosphere and becomes part of the new sea-floor as the magma gets cold. An example of a divergent boundary is oceanic ridges, such as the Mid-Atlantic ridge, located between the North American plate and the Eurasian plate. At a transform boundary, two adjacent plates slide parallel to each other. The San Andreas fault, for example, is created by the North American plate sliding parallel to the Pacific plate. Both plates move in the same northwest direction, but at different rates, thus putting stress at the boundary between the plates. 1.3 Types of Faults If each individual plate moves at different directions at different rates, the only force that keeps them together is the frictional force at the boundary. As the plate moves, strain energy is stored in the rocks; when this energy builds up and exceeds the frictional force, sudden rupture will occur, forcing rocks to break and thus creating a fault. Faults can be classified into three categories, dip-slip fault, strike- slip fault, and oblique fault. A dip-slip fault produces vertical displacement; if the fault is created by compressive stress in the crust, it is called the reverse dip-slip fault (Fig. 1.2). If the fault results from tension, then it is called the normal dip-slip fault (Fig. 1.3). A strike- slip fault produces horizontal displacement; if the horizontal offset is 6 from left to right, the faulting is called right-lateral (Fig. 1.4). Conversely, if the offset is from right to left, the faulting is called left-lateral (Fig. 1.5). An oblique fault has the features of both dip-slip and strike-slip faults, because it contains both vertical and horizontal displacements (Fig. 1.6). Figure 1.2 Reverse Fault Figure 1.3 Normal Fault. Figure 1.4 Right-Lateral Fault. Figure 1.5 Left-Lateral Fault . Figure 1.6 Oblique Fault. 7 1.4 Seismic Waves When an earthquake occurs, the elastic energy stored in the rock is released and converted into seismic waves; the shaking during an earthquake is the result of these seismic waves propagating through the earth’ s crust and along its surfaces. Both the primary wave (P wave) and the secondary wave (S wave) are called the body waves. The motion of a P wave is identical with a longitudinal sound wave, for it compresses and dilates the crust alternately as it travels through the earth’ s surface (Fig. 1.7). Furthermore, the P wave is able to propagate through both solid and liquid materials. Figure 1.7 Motion of P Wave ( Bolt, 1988). The motion of an S wave is transversal, for it oscillates vertically perpendicular to the direction of propagation (Fig. 1.8). Unlike P waves, S waves only travel through solid materials; also, S waves travel slower than P waves. The different traveling speeds between P waves and S waves explain why people usually feel a direct uplift motion before experiencing any rolling motion during an earthquake. Figure 1.8 Motion of S Wave (Bolt, 1988). Both Love waves and Rayleigh waves are called the surface waves; these waves travel along the surfaces of the earth. The motion of a Love wave is similar to the motion of an S wave, except that a Love wave oscillates in its horizontal plane rather than in its vertical plane (Fig. 1.9). The resulting motion of the Love wave produces side to side displacement. The particle motion of a Rayleigh wave is retrograde-elliptical, it consists of both vertical and horizontal components (Fig. 1.10). Surface waves travel slower than body waves, and Love waves travel faster than Rayleigh waves. Figure 1.9 Motion of Love Wave (Bolt, 1988). 9 Figure 1.10 Motion of Rayleigh Wave (Bolt, 1988). 1.5 Magnitude There are several appropriate terms for describing the magnitudes of earthquakes, such as intensity or seismic moment; but the one that is most commonly recognized by the general public is the Richter magnitude. The Richter magnitude of an earthquake is measured on a Wood Anderson torsion seismograph, at 100 km from the epicenter. Seismograph is a set of devices which includes a seismometer, an amplifier, and a recorder. The seismometer takes ground motion and translates it into electrical signals; the amplifier amplifies the amplitudes of the vibrations; and a recorder puts these amplified signals onto a seismogram. The Ritcher scale is based on a logarithmic scale. For every magnitude increase in an earthquake, the amplitude of displacement increases 10 times, and the amount of energy increases 32 times. Comparatively, the amount of energy released by a magnitude 7 earthquake is equivalent to a nuclear bomb. CHAPTER 2. ARCHITECTURAL CONSIDERATIONS This chapter is paraphrased from (Arnold, 1989). 2.1 Introduction If a magnitude 8 earthquake strikes an open field where there are no buildings and no hills, probably nobody will get killed. What makes earthquakes so hazardous is that the shakings cause buildings to collapse. Although engineers play an important role in structural safety, there are certain decisions that architects can make to help the engineers to create safer buildings. This section will discuss several architectural considerations which will make buildings perform better in earthquakes. 2.2 Slenderness Ratio of Buildings The slenderness ratio is the ratio between the building height to its width. The lower the slenderness ratio of the building, the better the building will withstand lateral forces. An ideal height to base width ratio is 3 to 1. To explain how the low height to base ratio could benefit buildings in an earthquake, refer to Figure 2.1. Both buildings have the same base area, but building A is twice as tall as building B. If equal lateral force is applied to both buildings, then building A will experience an overturning moment of Fx, while building B will only experience an overturning moment of Fx/2. Furthermore, the higher the overturning moment, the greater the exterior columns are stressed. li X Figure 2.1 Slenderness Ratio Jx/2 2.3 Building Shapes Buildings with "L" or "T" configurations in plan usually get more light and fresh air into the interiors, but there are also structural problems generated by these types of building shapes. In Figure 2.2, two identical buildings are oriented at different directions; one has the long side facing east, while the other has the long side facing south. If a lateral force is striking from the north, then the building with the long side facing south will deflect more than the other one. Imagine the two buildings are put together to create an L-shape building. Because of their orientations, the north-south wing is much stiffer than the east- west wing; as a result, the north-south wing will deflect less than the east-west wing. If this L-shape building is shaken by an earthquake, cracks may be developed at the intersection between the two wings (Fig. 2.3). Damages will be more severe if the two wings have different heights. This problem can be solved if a bracing system is used at the comer to tie these two wings together. 12 North Figure 2.2 Building Orientation (Arnold, 1989). North Figure 2.3 L-shaped Building (Arnold, 1989). 2.4 Torsion Torsion is another common problem created by earthquakes. Refer to Figure 2.4, where the center of mass of the building does not coincide with the center of resistance; and as a result, the building will rotate. The problem of torsion can be solved by either isolating the heavy materials from the frame, or putting a strong moment-resisting frame at the opening. The idea behind these solutions is to provide for equal strength and stiffness all around the perimeter of the building. 13 Furthermore, it is better to put the lateral force resisting members around the perimeter than any other places; because the further the resisting members are away from the center, the greater the lever arm of the resisting moment. Center of Resistance. Center of Mass. Figure 2.4 Torsion. 2.5 Soft First Story Soft first stories occur where the columns of the first floor are much longer than the columns above. As the length of the columns increase, they tend to have less moment resistance; therefore, a "soft-story" reduces the stiffness and strengths of the columns to resist seismic forces. Another soft-story situation occurs when the building materials in the upper levels are significantly heavier than the building materials in the first level. For example, precast concrete above an "open" first story. 14 The damage created by the soft story is the result of uneven seismic force distribution. If the lengths of the columns are the same throughout the building, seismic force will be distributed uniformly to each floor. If the columns on the upper floors are much shorter than those on the first floor, then a large percentage of the total deflection of the building will be concentrated at the joint between the first and second stories (Fig. 2.5). There are two methods to improve the performance of a soft first story building during earthquakes. First, by adding bracing to the columns on the first floor to make them stiffer. Second, by adding more columns at the ground level. The idea behind these solutions is to increase the stiffness of the first story's columns. Figure 2.5 The Soft Story Effect (Arnold, 1989). 15 2.6 Variations in the Stiffness between Columns and Beams The distribution of seismic forces is based on the stiffness of the structural members; a stiffer member takes more loads than a less stiff member. The shorter column takes 8 times more lateral force than the longer column (Fig. 2.6), assuming equal cross sectional area; the variation in stiffness is about the cube of the column's length . The problem occurs when the connecting beam is stiffer than the weak column. When loads act on the strong beam, the weaker column will reach its ultimate stress before the beam; consequently, the column will collapse before the beam, which could lead to the collapse of the building. To address this problem, horizontal bracing between the taller columns is needed in order to equalize the stiffness of a group of columns with different heights. 2x Figure 2.6 Variation of Stiffness (Arnold, 1989). I X 16 2.7 Pounding If two buildings with different vibrational periods are placed too close to each other, the two buildings may "pound" at each other during earthquakes. The problem of pounding can be solved either by putting the two buildings right next to each other, so that they act as one unit, or by separating them further away from each other. 17 CHAPTER 3. SEISM IC ISOLATION This chapter is paraphrased from (Mayes, 1989). 3.1 Introduction In seismic design, shear walls, braced frames, and moment-resistant frames are the three basic structural systems used to resist lateral forces. The approach to seismic resistance is the same for these three systems. The concept is to construct strong buildings and mount them to the ground; in other words, it is the strength of the buildings that fights against the lateral forces generated by earthquakes. Too much stiffness in structure generates greater forces, reasonable flexibility in building is better for seismic design. With the advanced technology of rubber and energy absorbers, a new strategy towards seismic design has been developed. The product of this development is called seismic isolation, which involves separating the building from the ground with rubbers pads and energy absorbers, so that the lateral forces will not be fully transmitted to the building itself. 3.2 Stiff Buildings vs. Flexible Buildings How a building responds to earthquakes depends upon the building's stiffness. There are two design philosophies regarding this issue. One philosophy claims that stiff buildings perform better in earthquakes; this argument is based on the interstory drift. The stiffer the building, the less the interstory drift. The main disadvantage for 18 stiff buildings is that they have higher floor accelerations. The other design philosophy claims that flexible buildings are better in seismic performances, since flexible buildings reduce floor accelerations. Although, this theory is true, flexible buildings also increase the interstory drift; especially the whip force on top the building. From these two arguments above, an ideal solution would be one that can reduce both interstory drift and floor acceleration of a building; and seismic isolation could be just the solution. 3.3 The Principle of Seismic Isolation Rigid buildings tend to have short vibrational periods, which induce high floor accelerations. According to Newton’ s second law (F = ma), the increase in acceleration results in greater lateral forces that act on a building. The principle of seismic isolation is to have a flexible base which allows for horizontal movement, and thus reduces the acceleration. At the same time, a damping device is installed to control the amplitude of the motion which will quickly restore the building to its original position. 3.4 Rubber Bearing There are two major components in a seismic isolation system: 1) a flexible mounting device, and 2) a damper or energy absorber. The flexible mounting device is often referred to as rubber bearing, and is made of high quality elastomeric rubber. An ideal bearing would be 19 the one which is highly flexible in its horizontal plane, yet very stiff in its vertical plane. When an axial load acts on the bearing, substantial deformation is found in the vertical section of the bearing, the compressive force pushes the rubber outward and this outward thrust can crush the rubber (Fig. 3.1). In order to alleviate this problem, steel shims are used to sandwich the rubber bearing into layers; this can make the vertical plane of the bearing several hundred times stiffer than its horizontal plane (Fig. 3.2). The main purpose of the rubber bearing is to reduce the seismic force transmitted to the building by elongating the period of vibration. Refer to the Idealized Force Response Spectrum Graphs in Figure 3.3, when an isolated building elongates its vibrational period from 0.2 second to 2 second, the base shear is reduced substantially. S u b lfK b ear : > r f c £ ■ . ■ Ipffll Figure 3.1 Bearing without Steel Plates Figure 3.2 Bearing with Steel Plates (Takenaka Corporation, 1991). (Takenaka Corporation, 1991). 20 Figure 3.3 Force Response Spectrum (Mayes, 1989). PERiOD SHifT 2 0 .,., NUMBER OF STORIES I H H I,,.. „ 2 .0 PERIOD Figure 3.4 Displacement Response Spectrum (Mayes, 1989). 3.5 Damper The elongation of the period, however, induced another mechanical problem. Although shear force has decreased, the displacement of the building increased substantially when the period is lengthened (Fig. 3.4). In order to constrain this displacement, a damper is needed to absorb the energy. With the proper damper device, the whole displacement response curve shifts downwards; in other words, the displacement decreases (Fig. 3.5). 11 • '• ) PERtQQv s h ift | m m m '- 20 NUMBER OF STORIES 2 0 PERIOD Figure 3.5 Displacement Spectrum for Increasing Damping (Mayes, 1989). There are several types of damping devices, such as mild steel, high-damping elastomer, and viscous fluid damping; one of the most common types is the lead-rubber device (Fig. 3.6). The lead-rubber device combines the rubber bearing and the damping device into one 22 unit. In such a system, lead is placed at the center of the rubber layers, and energy dissipation occurs during cyclic loading of the building. Figure 3.6 Lead-Rubber Device (Mayes, 1989). 3.6 "Hybrid Lead Rubber Bearing" The damping in the lead-rubber isolator is achieved by the yielding of the lead. In a small earthquake, the magnitude of the lateral force might not be able to activate the lead due to its stiffness. To overcome this problem, M. Hirasawa, of Japan, has developed the so called ’ ’ Hybrid Lead Rubber Bearing’ ’. This system connects a thinner isolator on top of a thicker isolator. So when a small earthquake occurs, the lateral force is able to activate the thinner isolator on top; since the lead is smaller, it is sufficient to provide damping for small earthquakes (Fig. 3.7a). In a big earthquake, the increased lateral force will cause both thin and thick isolators to move; thus providing the appropriate amount of damping for big earthquakes (Fig. 3.7b). 23 Figure 3.7a Figure 3.7b "Hybrid Lead Rubber Bearing" (AIJ, 1992). 3.7 Durability of the Rubber Bearing If seismic isolators are installed at the base of a building, all the dead loads and live loads will accumulate at the rubber bearings, and the question of durability becomes very important. A Japanese company, Bridgestone Corporation, has conducted a series of experiments to test the durability of such rubber bearings. To investigate the change of stiffness of the bearings due to aging, energy is applied to the rubber (20.3 Kcal/mol) for 24 hours under 25 degree Celsius, which is equivalent to 2.5 years of aging. By continuing this process for 24 days, it shows that the stiffness decreased by 20 % over a period of 60 years. With the use of a seismic isolation system, the amount of force acting on a building can be drastically reduced. For instance, the force of a magnitude 8 earthquake can be reduced to the level of a magnitude 6 earthquake. This reduction is highly desirable in some public structures, namely, nuclear power plants, bridges, and/or buildings containing very sensitive equipment. The next chapter will examine the applications of seismic isolation. 24 CHAPTER 4. PRECEDENT STUDIES iS i Figure 4.1 High Tech. R & D Center (Obayashi Corporation, 1991). Name of Building: High Tech. R & D Center Location: Japan Engineering/Designing: Obayashi Corporation Completion: August 1986 General Description: There are two parts in this project. The main building of High Tech. R & D Center is not base-isolated, but the 5 story experimental building contains 14 rubber bearings and 96 steel bars as dampers (Fig. 4.2). As the seismic records shown in Figure 4.3, the acceleration on the roof is significantly lower in the experimental building than in the main building. R i B l p I ' * " ' v : - ■ * ‘ & ' Su per struct ur€ /“ •Steel, gar, Damper jmm Figure 4.2 Rubber Bearings and Steel Bar Dampers in High Tech. R & D Center (Obayashi Corporation, 1991). High Tech. R & D Center : Roof M a x im u m Acceleration 8 . 5 2 g a 1 * » ■ * * y* 'i Main Building of In stitu te : Roof •4##' < W W » ' Ground Figure 4.3 Accelerograms of High Tech. R & D Center (Obayashi Corporation, 1991). Figure 4.4 National Institute for Research in Inorganic Material (Obayashi Corporation, 1991). Name of Building: National Institute for Research in Inorganic Material Location: Tsukuba, Japan Engineering/Designing: Obayashi Corporation Completion: March, 1988 General Description: This one story research center houses very senitive equipments, such as electron microscope, spectroscopic equipment, and creep test apparatus. The isolation system contains 32 rubber bearings and 48 steel bar dampers, Figure 4.5 shows the difference in acceleration between the ground and the building, all the records indicate that seismic isolation reduces accelerations in all directions. Acceleration (Reduction Ratio) M AX = 1 0 98gaK 1.00 I. ...I ' " ■ ! ««!.— W. ■ 8BPI Ground X(NS) .. Ground Y (E W ) Ground Z(U D ) f < l f ''' , 1 ''* ' -— --------------- w I Vibration Absorbed Piatfora of Electron Microscope X(NS) Vibration Absorbed Plat fora of Electron Microscope Y {E W ) MAX ~2.14gai(0.25 ;* e \l * 1 J3gal(0,28) 30 sec. —1 -- I IIm1 - ■ :- f - 60 sec. 90 sec, 4 — ? ..... " • "1-----~ Figure 4.5 Accelerograms of National Institute for Research in Inorganic Material (Obayashi Corporation, 1991). K > Figure 4.6 Campus Building in Tohoku University (Shimizu Corportion, 1991). Name of Building: Campus Building in Tohoku University Location: Sendai, Japan Engineering/Designing: Shimizu Corporation Completion: April, 1987 General Description: In order to test the performance of base-isolated buildings, Shimizu Corporation has built two identical buildings in the campus of Tohoku University, one with base isolation, and the other is a conventional building. From the seismic records shown Figure 4.7, the building with base-isolation reduces its roof acceleration from 103 to 38, and the first floor acceleration is reduced from 50 to 30. x> r stab of bonvendonal bide. j I . M^x * 2 slab of base isolated bldg. Max = or slab of base isolated bldg, , ■ M ax* W H m — W » w l surface M ax* fcJx alii ij m iTnT i fi'H 1fi ‘ ~ rr "'— ' — U i.u U u .tH u .U u .. Figure 4.7 Accelerograms of the Campus Building in Tohoku University (Shimizu Corporation, 1991). 31 PART II: BASE ISOLATION RESEARCH IN UNIFORM LOAD BUILDINGS. CHAPTER 5. RESEARCH METHODOLOGY 5.1 Objectives There are three objectives in this thesis: 1. To determine the height limitation for the use of base-isolation in buildings. 2. To contrast the seismic response of base-isolated buildings with those of non-base isolated buildings. 3. To investigate the feasibility of using seismic isolators to divide a mixed-use building into separated masses. 5.2 Assumption for Test Prototype Description of prototype: Width & Length: Floor Area: 120’ & 120’ 14,400 sq. f t Floor to Floor Height: 14 feet Dead Load: 100 psf Moment-Resisting Frame Type of Structure: 32 Table 5.1 Properties of Columns Levels Sizes Moment of Inertia (in4) 8th W 14x43 428 7th W 14 x 43 428 6th W 14 x 53 541 5th W 14x53 541 4th W 14x68 723 3rd W 14 x 68 723 2nd W 14 x 82 999 1st W 14 x 82 999 Table 5.2 Height and Period of Prototype Number of Stories Height (ft.) Period (sec.) 2 28 0.43 4 56 0.72 8 112 1.2 12 168 1.64 The natural vibrational period of a building is determined by Lateral Design Graphs (LDG), a program written by Dr. Goetz Schierle based on 1991 Uniform Building Code. The following is a sample of output: INPUT DATA BLDG. DIM (ft) SEISMIC GIVEN Length 120.0 Zone 4 Z 0.400 Width 120.0 Importance I 1.00 Height 112.0 Site prof. S 1.50 Floors 8 Factor Ct 0.035 Concrete wall Structure Rw 12 SEISMIC COMPUTED WIND GIVEN Period T (sec) 1.205 Wind speed 70mph C factor (1.656) 1.656 Importance 1.00 C/Rw (.138) 0.138 Exposure C Whip factor 8.43% X shear 296.4k Base shear 635.8k Y shear 296.4k 33 5.3 Symbols The following symbols and definitions are taken from Uniform Building Code, Chapter 25, pp. 250-252. A = Cross sectional area. D = Diameter. E = Modulus of elasticity (29,000 ksi for steel). I = Moment of Inertia. L = Unbraced length of column or beam. M = Bending moment. P = Axial Load, r = Radius of gyration. T = Period. 7 t = 3.14. A= Deflection. Materials for the Model: 1. Plywood Sheets. 2. Piano Wires (D = 0.047"). 3. Rubber (Magic Rub). 4. Fishing Weights. 5.4 Simulation Model Sheets of plywood are used in the model to simulate the floor of the prototype. Each sheet of plywood is 12" * 12" square, with an interior 34 removable piece of 9" * 9" square, cut centered to the 12" * 12" sheet (Fig. 5.1). The interior removable piece is extremely useful for adjusting the natural period of vibration. If the natural period of vibration is too long, the interior piece can be removed to reduce the mass, which will shorten the natural period of vibration. -9" 12" Sheet of Plywood. Removable to adjust mass. Piano Wire (D = 0.047"). 2 .6' Sheet of Plywood. Piano Wire (D = 0.047"). 1.2 ' Figure 5.1 Plan and Section of Model 35 Piano wires are used in the model to simulate the columns of the real structure. Two equations determine the size of wires, Euler’ s equation and Slenderness ratio. Euler’ s equation, P =/t2EI/L2 (Parker, 1984), calculates the maximum weight that a wire or column can carry. I = D4/64 (Parker, 1984) is an equation to find moment of inertia (I) for circular steel columns. Piano wires with 0.047” in diameter are used throughout the models. Moment of inertia for this kind of piano wire equals to 2.4 * 10-7". The height between two pieces of plywood was chosen at 2”. Hence the maximum load that each wire can take is 17 pounds: P =7t2EI/L2 (Parker, 1984). P = (3.14)2 * 29,000,000 psi * 2.4 * 10-7 in4 / 22 P = 17 pounds. According to the American Institute of Steel Construction Specification, the slenderness ratio is defined as KL/r. KL/r must be less than or equal to 120 for primary members, 200 for secondary members. The value, r, is the radius of gyration; which can be calculated by the equation r = (I/A)1 /2 (Parker, 1984). In this case, r = 0.012”, and K = 1; therefore, KL/r = 1 * 2”/ 0.012” = 170. Since the value falls in the range between 120 and 200, the use of piano wire as simulated columns is acceptable for preliminary design. 36 To simulate the seismic isolators in the model, the selected material must have the three following characteristics: 1. The material needs to be extremely flexible in its horizontal plane. 2. The material must be very stiff in its vertical plane. 3. The stiffness ratio between piano wire and eraser in the model must be equal to the stiffness ratio between column and isolator in the original structure. In order to satisfy these three criteria, a very soft type of rubber eraser has been selected. From the report, "Experimental Evaluation of seismic Isolation of a 9 stories braced steel frame subject to uplift.", by Griffth, Aiken, Kelly, the horizontal stiffness of a seismic isolator is approximately 2.1 kips/inch. The horizontal stiffness of a steel column is about 4.5 to 9 times the isolator's stiffness. In other words, the stiffness ratio between the piano wire and the rubber eraser in the model should also be 4.5 : 1 The equation, k = 3EI/2L3, can be used to determine the horizontal stiffness of a piano wire. Since the clear height between two sheets of plywood is 1.2", then: The stiffness of the rubber eraser should be 4.5 times less then 6, wire k wire = (3 * 29,000,000 psi * 2.4 * 10-7 in4) / 2 * (1.2")3 k wire = 6 pounds / inch k . wire wire 37 therefore: 6 pounds/inch 4.5 = 1.4 pounds/inch To find out how much weight it needs for the eraser to deform 1/4": 1.4 pounds/inch 4 = 0.37 pound / 0.25 inch or 6 oz / 0.25 inch. In other words, if 6 oz of weight is hung on the rubber eraser, and it deforms 0.25", then the rubber eraser would be an ideal one to simulate the bearings (Fig. 5.2). 1/4" Figure 5.2 Deformation of Eraser 38 5.5 Testing Procedure All the testing was performed on a electrodynamics seismic shaker table (Fig. 5.3). The apparatus consists of an IBM 286 computer with a digital to analog converter board, an amplifier, a shaker, and an aluminum plate which is hung from a metal frame by four cables. With the model bolted to the aluminum plate, the computer sends the signal to the amplifier, the amplifier amplifies the signal and sends it to the shaker; the shaker shakes the aluminum plate to simulate an earthquake's motion. The earthquake is a simulated earthquake, the motion of the earthquake is based on the time-displacement graph provided by the School of Geological Science in University of Southern California (Fig. 5.4). The motion of the shaking lasts 30 seconds with maximum displacement of 3" on each side and maximum ground acceleration of 0.4lg. Figure 5.3 39 displacement i n inches seismogragh 4 2 0 2 ■ 4 10 15 5 20 0 25 30 time in seconds Figure 5.4 Seismogram. This simulated earthquake lasts 30 seconds with maximum displacement o 3M on each side and maximum ground acceleration of 0.4lg. An important factor in the experiments is the model's natural period of vibration. If the natural period of the model equals the natural period of the prototype, then all responses will be the same. If the natural period of the model is shorter than the period of the prototype, lead pieces or fishing weights are added to the model to lengthen the period. However, if the natural period of the model is longer than the period of the prototype, then the middle portion of the plywood (floors) needs to be removed to shorten the period (Fig. 5.1). To measure the deflection of each floor, a pen is attached to the side of the model with a stick (Fig. 5.5). As the model deforms, the pen records the maximum deflection of a particular floor on a piece of paper. In order to reduce friction, only one pen is attacked to a given floor at one time, then the same procedure repeats with all other floors until the deflections for all floors are recorded. background model Figure 5.5 Measuring Displacement. pen stick 41 After deflections for all floors are measured, floor acceleration can be calculated. From Newton’ s second law, F = ma, then a = F/m. Stiffness can be calculated by the equation k = F/A, then F = kA. Substitute F = kA into a = F/m, then a = kA/m. Since the stiffness of a wire is determined (see p. 37), mass of any particular floor is also known, floor acceleration can be determined. To convert acceleration to g, the equation a = kA/m needs to be divided by 32. Acceleration amplification measures how much times the ground acceleration is amplified by the building. Amplification ratio = acceleration of a particular floor acceleration of the ground 42 CHAPTER 6. TEST RESULTS Introduction: This chapter illustrates the test results. For this part of test, each test contains four tables and four figures. The first table and figure display the maximum displacements of a particular type of buildings. The second table and figure display the interstory drift between each floor. The third table and figure illustrate the maximum acceleration for each floor. The fourth table and figure illustrate the acceleration amplification, it measures how much times the ground acceleration is amplified by the building. Test 1: Model A Model B Model Description: Two two-story models were tested: Model A is base-isolated, Model B is base-fixed. The two models were tested to observe contrasts in their responses due to simulated earthquake motion. Both models represent buildings of two story height, with the same uniform weight distribution. 43 Results: When the base-isolated model deforms, the two floors move together as one single unit with no interstory drift (Tab. 6.1-6.2 and Fig. 6.1-6.2). From the equation, a = Ak/m, when displacement (A ) is zero, acceleration (a) equals zero. This confirms that the isolators are able to reduce floor acceleration effectively in a two-story building (Tab. 6.3-6.4 and Fig. 6.3-6.4). Maximum acceleration on the fixed base model was 0.16g. 44 Table 6.1 Comparison of Lateral Displacement. Base-isolated Vs. Base-fixed. Floors Displacement (Inch) Base-isolated Base-fixed Roof 3.7 3.5 2nd 3.7 3.2 1st 3.7 3 Table 6.2 Comparison of Interstory Drift. Base-isolated Vs. Base-fixed. Floors Interstory Drift (Inch) Base-isolated Base-fixed 2nd-Roof 0 0.3 lst-2nd 0 0.2 45 Displacement of two 2 stories Buildings Isolated Vs. Non-Isolated 8 2nd Roof U n ifo r m L o a d \ / / \ W ith I s o la to r W /O Iso la to r Lateral Displacement (Inch) Figure 6.1 10 Comparison of Interstory Drift Isolated Vs. Non-Isolated 2nd-Roof lst-2nd I I U n ifo r m L o a d 0 Y /A W ith Iso la to r m W /O I so la to r 4 6 Interstory Drift (Inch) Figure 6.2 10 12 46 Table 6.3 Comparison of Floor Acceleration. Base-isolated Vs. Base-fixed. Floors Floor Acceleration (g) Base-isolated Base-fixed 2nd 0 0.16g 1st 0 O.llg Table 6.4 Acceleration Amplification. Base-isolated Vs. Base-fixed. Floors Acceleration Amplification Base-isolated Base-fixed 2nd 0 0.39 1st 0 0.27 47 Floors Comparison of Floor Acceleration Isolated Vs. Non-Isolated 2nd iUniform Load 0 0.1 0.2 Y //\ W ith Iso la to r m W /O I so la to r 0 3 0l4 0.5 0.6 Acceleration (g) 0.7 0.8 0.9 Figure 6.3 Acceleration Amplification Uniform Weight Distribution Isolated N i n - I s o l a t e d 2nd 1st - 2.5 2.0 1.5 1.0 0.5 0 Amplification Factor Figure 6.4 48 Test 2: Model A Model B Model Description: The two models in this test are similar to those in Test 1, Model A is base-isolated, Model B is base-fixed. Both still have the same uniform weight distribution, except these two models consists of four stories in height. Results: The base-isolated model exhibited no interstory drift between the first two stories. Interstory drift does begin to develop on the third floor (Tab. 6.6, Fig. 6.6). The maximum floor acceleration in the above case is 0.16g (Tab. 6.7, Fig, 6.7), which is located on top of the building. In the fixed base model, interstory drift begins to develop on the first floor, 0.2lg being the maximum floor acceleration in this model. 49 Table 6.5 Comparison of Lateral Displacement. Base-isolated Vs. Base-fixed. Floors Displacement (Inch) Base-isolated Base-fixed Roof 4.7 4.2 4th 4.4 3.8 3rd 4.2 3.5 2nd 4.2 3.2 1st 4.2 3 Table 6.6 Comparison of Interstory Drift. Base-isolated Vs. Base-fixed. Floors Interstory Drift (Inch) Base-isolated Base-fixed 4th-Roof 0.32 0.4 3rd-4th 0.2 0.3 2nd-3rd 0 0.3 lst-2nd 0 0.2 50 Displacement of two 4 stories Buildings Isolated Vs. Non-Isolated U n ifo r m L o a d V / / / / / / / / / / / / / / / / / / / / / / / / / / 7 7 7 Z ^ m m m . 8 3rd y / / / / / / / / / y yyyy/y/A ' / // / / / // / / // / A Y //A W ith I s o la to r W /O Is o la to r 4 6 8 Lateral Displacement (Inch) Figure 6.5 4th-Rf 3rd-4 th 2nd-3rd lst-2nd i I ■ ■_ Comparison of Interstory Drift Isolated Vs. Non-Isolated V /A W ith Iso la to r m W /O I so la to r U n ifo r m L o a d 4 6 8 Interstory Drift (Inch) Figure 6.6 10 12 51 Table 6.7 Comparison of Floor Acceleration. Base-isolated Vs. Base-fixed. Floors Floor Acceleration (g) Base-isolated Base-fixed 4th 0.16g 0.21g 3rd O.llg 0.16g 2nd 0 0.16g 1st 0 O.lg Table 6.8 Acceleration Amplification. Base-isolated Vs. Base-fixed. Floors Acceleration Amplification Base-isolated Base-fixed 4th 0.39 0.51 3rd 0.27 0.39 2nd 0 0.39 1st 0 0.24 52 Floors Comparison of Floor Acceleration Isolated Vs. Non-Isolated tJniform Load 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Acceleration (g) Figure 6.7 \//,\ W ith Iso la to r W /O I so la to r Acceleration Amplification Uniform Weight Distribution Isolated 4th Non-Isolated 3rd 2nd 1st 2.5 2.0 1.5 1.0 0.5 0 Amplification Factor Figure 6.8 0.9 1 53 Test 3: V / / / / / A / / / A 1 / / / / / / / / / / A V / A / / / A / / / A V / / / / / / / / / A 1// / / / / / / / / A \// / / / / / / / / /\ V / / / / / A / / / A 1 / / / / / / / / / / A V / A / / / A / / / A Model A V / / / / / / / / / A 1 ./ / / / / / / / / / /\ V / / / / / / / / / A \ / / / / / / / / / / / \ V / / / / / / / / / A Model B Model Description: Both models are eight stories in height, with the same uniform weight distribution; one is base-isolated, the other is base-fixed. Results: Both models behave differently on the upper and lower stories, but similar response is found around the middle stories. In the base-isolated model, interstory drift is zero up to the third floor. In the fixed-base model, however, an acceleration of 0.04g is experienced on the 1st floor. Both models have their maximum acceleration on the roof, but the maximum acceleration in the base-isolated model is significantly less than the fixed base model— 0.24g as compared 54 to 0.63g respectively (Tab. 6.11, Fig. 6.11). This difference can be explained by the fact that the whip force is a dominant characteristic in the fixed base cantilever structure. In the base-isolated model, on the other hand, the isolators absorb some of the earthquake's energy, therefore all floors move together as one block, this eliminates some of the whip force on top of the building. 55 Table 6.9 Comparison of Lateral Displacement. Base-isolated Vs. Base-fixed. Floors Displacement (Inch) Base-isolated Base-fixed Roof 10 8.5 8th 9.2 6.3 7th 8.4 5.3 6th 7.6 4.5 5th 7 3.9 4th 6.6 3.5 3rd 6.4 3.3 2nd 6.4 3.1 1st 6.4 3 Table 6.10 Comparison of Interstory Drift. Base-isolated Vs. Base-fixed. Floors Interstory Drift (Inch) Base-isolated Base-fixed 8th-Roof 0.8 2.1 7th-8th 0.8 1 6th-7th 0.8 0.8 5th-6th 0.6 0.6 4th-5th 0.4 0.4 3rd-4th 0.2 0.2 2nd-3rd 0 0.2 1 st-2nd 0 0.1 56 Floors Displacement of two 8 Stories Buildings Isolated Vs. Non-Isolated Roof Uniform Load 0 2 4 6 8 10 12 Lateral Displacement (Inch) X ^ Z / A With Isolator W/O Isolator Figure 6.9 57 Comparison of Interstory Drift Isolated Vs. Non-Isolated 8th-Rf 7th-8th 6th-7th 5th-6th 4th-5th 3rd-4th 2nd-3rd lst-2nd ^ B l1 I Uniform Load 0 2 4 6 8 With Isolator ™ w /o Isolator I Interstory Drift (Inch) 10 12 Figure 6.10 58 Table 6.11 Comparison of Floor Acceleration. Base-isolated Vs. Base-fixed. Floors Floor Acceleration (g) Base-isolated Base-fixed 8th 0.24g 0.63g 7th 0.24g 0.3g 6th 0.24g 0.24g 5th 0.18g 0.18g 4th 0.17g 0.17g 3rd 0.09 g 0.09g 2nd 0 0.09g 1st 0 0.04g Table 6.12 Acceleration Amplification. Base-isolated Vs. Base-fixed. Floors Acceleration Amplification Base-isolated Base-fixed 8th 0.59 1.54 7th 0.59 0.73 6th 0.59 0.59 5th 0.44 0.44 4th 0.41 0.41 3rd 0.22 0.22 2nd 0 0.22 1st 0 0.1 59 Floors Comparison of Floor Acceleration Isolated Vs. Non-Isolated Uniform Load 0.4 0.5 0.6 0.7 0.8 Acceleration (g) W/O Isolator With Isolator Figure 6.11 60 Acceleration Amplification Isolated Vs. Non-Isolated Non-isolated Isolated 8th 7th 6th 5th 4th 3rd 2nd 1st 0.5 1.5 2.0 2.5 0 1.0 Amplification Factor Figure 6.12 61 Test 4: \ / / / / / / / / 7 7 7\ [Z z Z Z Z Z Z Z Z Z Z \ Z / / / / / / / / / A \ z z z z z z z z z z a Heavy 1 - 1 Light \///////////\ Model A Model B Description of Models: Both models have eight stories, Model A is base-isolated, Model B is base-fixed. Weight distribution is non-uniform, the top four stories in each model are twice as heavy as the bottom four stories. Results: In general, acceleration in the base-isolated model is less than the fixed base model, except in the fourth floor, where the dead weight changes. Maximum acceleration of 0.86g is measured at the fourth floor in the base-isolated model, as compared to 0.69g in the fixed base model (Tab. 6.15, Fig. 6.15). 62 Results (cont): Although isolators at the base reduce seismic energy transmitted to the building, as the building height increases, an over-turning moment starts to develop. The situation is worse when the building has non-uniform load distribution, such as can be found in mixed-use building. When the upper stories are heavier than the bottom stories, the building behaves like an inverted pendulum. If isolators are installed in such a building, the recoiling force of the isolators might induce greater deflection, since the top four stories have the same dead weight, and thus tend to move together. Sudden change in dead weight takes place on the fourth floor. Based on the equation, a = Ak/m, as the mass of a floor decreases, its acceleration increases. 63 Table 6.13 Comparison of Lateral Displacement. Base-isolated Vs. Base-fixed. Floors Displacement (Inch) Base-isolated Base-fixed Roof 10.6 9.5 8th 9.8 6.9 7th 9 5.9 6th 8.3 5.1 5th 7.7 4.4 4th 6.7 3.6 3rd 6.3 3.2 2nd 6.1 2.9 1st 6.1 2.8 Table 6.14 Comparison of Interstory Drift. Base-isolated Vs. Base-fixed. Floors Interstory Drift (Inch) Base-isolated Base-fixed 8th-Roof 0.8 2.6 7th-8th 0.8 1 6th-7th 0.7 0.8 5th-6th 0.6 0.7 4th-5th 1 0.8 3rd-4th 0.4 0.4 2nd-3rd 0.2 0.3 1 st-2nd 0 0.1 64 Floors Displacement of two 8 Stories Buildings Isolated Vs. Non-isolated Roof Heavy Mass Light Mass With Isolator W/O Isolator 4 6 8 Lateral Displacement (Inch) Figure 6.13 65 Comparison of Interstory Drift Isolated Vs. Non-isolated 8th-Rf 7th-8th 6th-7th 5th-6th 4th-5th 3rd-4th 2nd-3rd lst-2nd Heavy Mass Light Mass With Isolator W/O Isolator 4 6 8 Interstory Drift (Inch) 1 0 12 Figure 6.14 66 Table 6.15 Comparison of Floor Acceleration. Base-isolated Vs. Base-fixed. Floors Floor Acceleration (g) Base-isolated Base-fixed 8th 0.24g 0.78g 7th 0.24g 0.3g 6th 0.21g 0.24g 5th 0.18g 0.21g 4th 0.86g 0.69g 3rd 0.34g 0.34g 2nd 0.17g 0.26g 1st 0 0.09g Table 6.16 Acceleration Amplification. Base-isolated Vs. Base-fixed. Floors Acceleration Amplification Base-isolated Base-fixed 8th 0.59 1.9 7th 0.59 0.73 6th 0.51 0.59 5th 0.44 0.51 4th 2.1 1.68 3rd 0.83 0.83 2nd 0.41 0.63 1st 0 0.22 67 Floors Comparison of Floor Acceleration Isolated Vs. Non-isolated Heavy Mass Light Mass 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 With isolator m w/o isolator Acceleration (g ) Figure 6.15 68 Acceleration Amplification Isolated Vs. Non-isolated Non-uniform Load: Top 4 floors heavier than the bottom 4 floors Isolated Non-isolated 8th - 7th - 6th - 5th - 4th - 3rd - 2nd- lst 2.5 2.0 1.5 0.5 1.0 0 Amplification Factor Figure 6.16 69 Test 5: I / / V I H eavy V7 / / / 7 V Z Z7 7 \ L ight \//////////A 1Z Z ZZZZ2ZZZZ ! zzzzzzzzzzz zzzzzzzzzzz 1Z Z Z Z Z Z Z Z Z Z 2 Model B Model A Model Description: Models used in this test are the same as in Test 4, with the loading condition is reversed. In Test 5, the top four stories are twice as light as the bottom four stories. Results: When the top four stories are lighter than the bottom four stories, the over-turning moment is not as great as when the top four stories are heavier. Although, there is a sudden change in floor mass on the fourth floor, it does not affect the acceleration drastically, since the change is from heavy to light. Maximum accelerations are found on the roof for both models, 0.42g for the base-isolated model and 0.9g for the base-fixed model (Tab. 6.19, Fig. 6.19). 70 Table 6.17 Comparison of Lateral Displacement. Base-isolated Vs. Base-fixed. Floors Displacement (Inch) Base-isolated Base-fixed Roof 9.6 7.7 8th 8.9 6.2 7th 8.2 5.3 6th 7.6 4.6 5th 7 3.9 4th 6.4 3.3 3rd 6.2 3.1 2nd 6.2 3 1st 6.2 2.9 Table 6.18 Comparison of Interstory Drift. Base-isolated Vs. Base-fixed. Floors Interstory Drift (Inch) Base-isolated Base-fixed 8th-Roof 0.7 1.5 7th-8th 0.7 0.9 6th-7th 0.6 0.7 5th-6th 0.6 0.7 4th-5th 0.6 0.6 3rd-4th 0.2 0.2 2nd-3rd 0 0.1 lst-2nd 0 0.1 71 Floors Displacement of two 8 Stories Buildings Isolated Vs. Non-isolated Roof Lateral Displacement (Inch) W/O Isolator With Isolator Figure 6.17 72 Comparison of Interstory Drift Isolated Vs. Non-isolated 8th-Rf 7th-8th 6th-7th 5th-6th 4th-5th 3rd-4th 2nd-3rd lst-2nd Light Mass Heavy Mass 4 6 8 Interstory Drift (Inch) With Isolator W/O Isolator 10 12 Figure 6.18 73 Table 6.19 Comparison of Floor Acceleration. Base-isolated Vs. Base-fixed. Floors Floor Acceleration (g) Base-isolated Base-fixed 8th 0.42g 0.9g 7th 0.42g 0.54g 6th 0.36g 0.42g 5th 0.36g 0.42g 4th 0.26g 0.26g 3rd 0.09g 0.09g 2nd 0 0.04g 1st 0 0.04g Table 6.20 Acceleration Amplification. Base-isolated Vs. Base-fixed. Floors Acceleration Amplification Base-isolated Base-fixed 8th 1.02 2.2 7th 1.02 1.3 6th 0.88 1 5th 0.88 1 4th 0.63 0.63 3rd 0.22 0.22 2nd 0 0.1 1st 0 0.1 74 Floors Comparison of Floor Acceleration Isolated Vs. Non-isolated O V ////////// / / / / / / / / / / / , Light Mass Heavy Mass 0.4 0.5 0.6 0.7 0.8 0.9 Acceleration (g) V / / A With Isolator m W/O Isolator Figure 6.19 75 Acceleration Amplification Isolated Vs. Non-isolated Non-uniform Load: Top 4 floors are lighter than the bottom 4 floors Isolated Non-isolated 8th 7th 6th 5th 4th 3rd 2nd- lst 2.5 2.0 0.5 1.0 1.5 0 Amplification Factor Figure 6.20 76 PART III: MASS ISOLATION This research half is to investigate the feasibility of using seismic isolators to separate a mixed-use building into two different isolated masses and to study the interaction between these two masses during earthquakes. Three sets of tests are conducted in this investigation. Each set of test contains eight cases. Each case has a different mass ratio between upper and lower stories. In the first four cases of each set, the upper stories are heavier than the lower stories; in the other four cases, the lower stories are heavier than the upper stories. All models in these three sets of tests have eight stories with non-uniform weight distribution. The first set of tests is to separate the eight-story buildings into two 4-story masses by putting isolators at the 4th floor and at the base. The second set of tests divides the eight stories into 3-stories on top and 5-stories at the bottom, with isolators are installed at the 5th floor and at the base. Isolators on the third set of test are located at the base and at the 3rd floor. The separation divides the eight stories building into 5-stories on top and 3-stories at the bottom. Each test contains five tables and five sets of figures. The first table and figure display the maximum displacements of a particular type of buildings. The second table and figure display the interstoiy drift between each floor. The third table and figure illustrate the maximum acceleration for each floor. The fourth table and figure illustrate the 77 acceleration amplification. The fifth table and figure display the building response to the earthquake, what happens to the floor acceleration when the period of vibration is lengthened? 78 TEST 6; V / / / / V / / / / A V / / / / / / / / / A V / / / / / / / / / A v / /\ H eavy ] Light Model Description: In the first set of tests, isolators are placed at the 4th floor and at the base. The upper 4 stories are heavier than the bottom 4 stories. The mass ratios for the first four cases are as follow: 2 : 1, 3.3 : 1, 3.7 : 1, and 4.4 : 1. Results: Table 6.22-6.23 and Figure 6.22-6.23 show that interstory drift and floor acceleration decrease drastically as the top to bottom mass ratio increases. For example, the acceleration on the 8th floor decreases from 0.24g to 0.07g as the mass ratio increases form 2 :1 to 4.4 : 1, a reduction of 71%. On the 4th floor the floor mass changes decrease acceleration from 0.48g to 79 Results (cont.): 0.06g; a reduction of 88%. The results imply that as the mass on the upper stories increase, it starts to act as a giant damper. That is, it does not just reduces its own displacement and acceleration, but it also dampens the displacement and acceleration in the lower stories. The situation is similar to the CitiCorp Central Tower in New York City, where a 400 ton tuned mass damper slides on top of the building to stabilize the building against wind forces. Table 6.24 and Figure 6.24 illustrate the amplification factor of acceleration, it measures how much the ground acceleration is amplified toward the top floor. When the mass ratio is 4.4 : 1, the ground acceleration is amplified 0.17 times at the 8th floor, as compared to 0.59 times for a mass ratio of 2 :1. As the results on Table 6.23 and Figure 6.23 indicate, when another set of isolator is installed at the 4th floor, floor acceleration decreases drastically. Although floor acceleration remains the same on the roof for both cases, but the floor acceleration on the 4th floor reduces form 0.86g to 0.24g, a reduction of 72%. Table 6.25-6.26 and Figure 6.25-6.26 display the response of the building’ s acceleration when the natural period of vibration is lengthened. When the period is lengthened from 2.5 seconds to 3.3 seconds, floor acceleration on the roof reduces from 0.24g to 80 Results (C O nt.): 0.07g, a reduction of 71%; floor acceleration on the 4th floor reduces from 0.48g to 0.06g, a reduction of 88%. 81 Table 6.21 Comparison of Lateral Displacement. (Top 4 stories are heavier than the bottom 4 stories.) Mass Ratio (Upper : Lower stories) = 2/1, 3.3/1, 3.7/1, and 4.4/1. Floors Displacement (Inch) 2 to 1 (Iso at base only) 2 to 1 3.3 to 1 3.7 to 1 4.4 to 1 R oof 10.6 11.6 7 4.2 4.3 8th 9.8 10.8 6.4 3.9 3.8 7th 9 10 5.8 3.7 3.4 6th 8.3 9.2 5.2 3.5 3.1 5th 7.7 8.5 4.8 3.4 2.8 Isolators im m m 1 * 1 1 1 1 l l i i ® i i l l i l i l i i 4th 6.7 5 2.9 2.5 2 3rd 6.3 4.6 2.9 2.5 2 2nd 6.1 4.3 2.9 2.5 2 1st 6.1 4.3 2.9 2.5 2 Isolators 3 3 3 3 3 Table 6.22 Comparison of Interstory Drift. (Top 4 stories are heavier than the bottom 4 stories.) Mass Ratio (upper and lower stories) = 2/1, 3.3/1, 3.7/1, and 4.4/1. Floors Displacement (Inch) 2 to 1 (Iso at base only) 2 to 1 3.3 to 1 3.7 to 1 4.4 to 1 8th-Rf 0.8 0.8 0.6 0.3 0.5 7th-8th 0.8 0.8 0.6 0.2 0.4 6th-7th 0.7 0.8 0.6 0.2 0.3 5th-6th 0.6 0.7 0.4 0.1 0.3 Iso-5th illlill l l l i l i l l l l l i l l l 0.7 4th-Iso 1 0.8 0.2 0.1 0.1 3rd-4th 0.4 0.4 0 0 0 2nd-3rd 0.2 0.3 0 0 0 lst-2nd 0 0 0 0 0 Iso-1st 1.3 1.3 0.1 0.5 Jgllflllgg 82 Deflection for Various Building Masses Mass: (5th-8th) > (lst-4th) Roof i i--------------- 8th > / / / / / / ? / / / ; y/y/yy///////////////y///// a 7th >yyyyy//yyyyyyyyyyyyyy/yyyyyyyyyy;y77y7-/7\ 6th ’y//yy/yyyyyyyyyy/7yyyyy777-ryyy)yyyyyy?yyyyyyyyyyyyyy/yyy///A Heavy Mass 5th Isolator 'yyyyyyyyyyyyyyyyyyyyyyyyyyyyyy/yyyyyyyyy7yyy/y>yyyyA 4th Light Mass 'y/y/yy/yy/yy/yyyyyyy/y/yyy/yy/y/yyyzyyyyyyyyyyV /x 3rd 2nd >yyyyyyyyy7yyyyyyyyyyyyyyyyyyyy77~y77yyyyyyyys777\ 1st Isolator 8 10 12 4 6 Lateral Displacement (Inch) ■ 1 2:1 1 13.3:1 ^ 3.7:1 n m 4.4:1 Y / / z \ Lso at base only Figure 6.21 83 Comparison of Interstory Drift Mass: (5th-8th) > (lst-4th) 8th-Rf 7th-8th Heavy Majss 6th-7th 5th-6th Iso-5th sW sblk 4th-Iso 3rd-4th Light Mas 2nd-3rd ■ lst-2nd Iso-1st Lateral Displacement (Inch) ■ H 2:1 □ 3.3:1 ^ 3 . 7 : 1 FFffl 4.4:1 y y / A Iso at base only Figure 6.22 84 Table 6.23 Comparison of Floor Acceleration. (Top 4 stories are heavier than the bottom 4 stories.) Mass Ratio (Upper : Lower stories) = 2/1, 3.3/1, 3.7/1, 4.4/1. | Heavy | Light Floors Acceleration (g) 2 to 1 (Iso at base only) 2 to 1 3.3 to 1 3.7 to 1 4.4 to 1 8th 0.24 0.24 0.11 0.05 0*07 7th 0.24 0.24 iillllllfl 0.03 0.05 6th 0.24 0.11 0.03 0.04 5th 0.18 0,21 0.07 0.02 0.04 4th 0.86 0.48 0.12 0.06 0.06 3rd 0.34 0.24 0 0 0 2nd 0.17 0.18 0 0 0 1st 0 0 0 0 0 Table 6.24 Acceleration Amplification. (Top 4 stories are heavier than the bottom 4 stories.) Mass Ratio (Upper : Lower stories) = 2/1, 3.3/1, 3.7/1, 4.4/1. Light Floors Acceleration Amplification 2 to 1 (Iso. at base only) 2 to 1 3.3 to 1 3.7 to 1 4.4 to 1 8th I I ! j ! « | ^ | p ! ! « ! | | 0.59 0.27 0.12 ! ! i ! ! I l ! ! i 7th 0.59 0.27 sumi 1 1 1 1 1 1 s 6th liiliiiiii 0.27 0.07 lllllll 5th 0.44 i l l i l l l : ; ! ! 0.17 0.05 0.1 4th 2.1 1.17 0.29 0.15 0.15 3rd 0.83 0.59 0 0 0 2nd 0.41 0.44 0 0 0 1st 0 0 0 0 0 85 Floor Acceleration for Different Masses Mass: (5th-8th) > (lst-4th) 8 th * 3 3 3 I 7th V 2 i-t O jO E i z z z z z z z z z z z z z z z z z z z m X / / / / / / / / / / / / / / / / M 7 7 7 7 7 Z Z Z Z Z Z Z Z Z Z Z A Heavy Mass 3rd 2nd 1st 7 Z Z ZZ Z Z ZZ ZZZ ZZ Z2 L 0 0.1 0.2 0.3 Light Mass 0.4 0.5 0.6 Acceleration (g) 0.7 0.8 0.9 1 2:1 □ 3.3:1 ^ 3-7:1 EEB 4-4:1 V / / / X Iso at base only Figure 6.23 86 Figure 6.24 Acceleration Amplification Ratios (afioor/aground) Upper 4-stories are heavier than the bottom 4-stories. Mass Ratio (Top : Bottom) = 2 :1 7th- 6th 5th 4th 3rd 2nd 1st 0 0.5 1.0 1.5 2.0 2.5 Amplification Factor Mass Ratio (Top : Bottom) = 3.3 : 1 7th 6th 3rd 1st 0.5 1.0 1.5 2.0 2.5 0 Amplification Factor Mass Ratio (Top : Bottom) = 3.7 : 1 8thH 7th 6th- 5th- 4th 3rd 2nd- lst 0.5 1.0 1.5 2.0 2.5 0 Amplification Factor Mass Ratio (Top : Bottom) = 4.4 : 1 8th-I 7th-- 6th- 5th 4th- 3rd- 2nd- lst 0.5 1.0 Amplification Factor 2.0 2.5 87 Table 6.25 Period vs. Acceleration (Roof) (Top 4 stories are heavier than the bottom 4 stories.) Mass Ratio (Upper : Lower stories) = 2/1, 3.3/1, 3.7/1, 4.4/1. Period (sec.) Acceleration (g) 2.5 0.24 2.9 0.11 3.1 0.05 3.3 0.07 Table 6.26 Period vs. Maximum Acceleration (4th) (Top 4 stories are heavier than the bottom 4 stories.) Mass Ratio (Upper : Lower stories) = 2/1, 3.3/1, 3.7/1, 4.4/1. Period (sec.) Acceleration (g) 2.5 0.48 2.9 0.12 3.1 0.06 3.3 0.06 88 Acceleration (g ) Acceleration (g) Period vs. Acceleration (Roof) Mass: (5th-8th) > (lst-4th) 0.9- 0.8 - 0.7- 0.6 - 0.5 - 0.4- 0.3- 0.2 - 0. 1- '15 2.6 2.7 2.8 2.9 3 Period (sec.) Figure 6.25 3.1 3.2 3.3 Period vs. Maximum Acceleration (4th) Mass: (5th-8th) > (lst-4th) o ~ i -------------------------1 -------------------------1 -------------------------1 -------------------------1 -------------------------1 -------------------------1 -------------------------1 ------------------------- 2.5 2.6 2.7 2.8 2.9 3 3.1 3.2 3.3 Period (sec.) Figure 6.26 89 TEST 7: I / / / ) Heavy V / / /7 '7 V 7 7 7 7 \ V / / / / / / / r 7 r /7\ Light \Z///////VT7 Model Description: The upper 4-stories are lighter than the bottom 4-stories. Isolators are placed at the 4th floor and at the base. The top to bottom mass ratios are as follow: 1:2, 1 : 3, 1 : 3.3, and 1 : 4.5. Results: As Table 6.29 and Figure 6.29 show, when the top to bottom mass ratio increases from 1 : 2 to 1 : 4.5, the acceleration decreases from 0.48g to 0.36g on the 8th floor, a reduction of 25%; and 0.22g to 0.08g on the 4th floor, a reduction of 64%. Although acceleration decreases as the lower four stories become heavier, the acceleration reduction is significantly less 90 Results (C O nt.): than when the upper four stories increase in weight. Refer to Table 6.30 and Figure 6.30, the amplification factor in this case is much greater than when the top 4 stories are heavier. When the top to base ratio is 1 : 2, the ground acceleration amplifies 1.17 times, and 0.88 times when the mass ratio is 1 : 4.5. Similar results were found in the other two sets of tests. The general trend is: when the upper stories are heavier, interstory drift, floor acceleration, and amplification factor decrease significantly. If the lower stories are heavier, interstory drift, floor acceleration, and amplification decrease, but the reduction is much less than if the upper floors are heavier. 91 Table 6.27 Comparison of Lateral Displacement. (Top 4 stories are lighter than the bottom 4 stories.) Mass Ratio (Upper : Lower stories) = 1/2, 1/3, 1/3.5, and 1/4.5 Floors Displacement (Inch) 1 to 2 1 to 3 1 to 3.5 1 to 4.5 Roof 9.4 8.8 7.9 7.8 8th 8.6 8.1 7.2 7.2 7th 8.2 7.5 6.8 6.6 6th 7.8 7 6.4 6.4 5th 7.6 6.8 6.2 6.2 Isolators 6 H U H ! l l l l i l l l 4.8 4th 5.5 5 4.8 4.4 3rd 5.1 4.7 4.5 4.1 2nd 4.8 4.4 4.2 3.8 1st 4.8 4.4 4.2 3.8 Isolators 3 3 3 3 Table 6.28 Comparison of Interstory Drift. (Top 4 stories are lighter than the bottom 4 stories.) Mass Ratio (upper and lower stories) = 1/2, 1/3, 1/3.5, 1/4.5 Floors Displacement (Inch) 1 to 2 1 to 3 1 to 3.5 1 to 4.5 8th-Rf 0.8 0.7 0.7 0.6 7th-8th 0.4 0.6 0.4 0.6 6th-7th 0.4 0.5 0.4 0.2 5th-6th 0.2 0.2 0.2 0.2 Iso-5th 1.6 lllfflili!!! i i f i i i i ! 1.4 4th-Iso 0.5 0.5 0.5 0.4 3rd-4th 0.4 0.3 0.3 0.3 2nd-3rd 0.3 0.3 0.3 0.3 lst-2nd 0 0 0 0 Iso-1st 1.8 1.4 1.2 0.8 Deflection for Various Building Masses Mass: (5th-8th) < (lst-4th) Roof 8th 7th 6th Light Mass 5th Isolator 4th 3rd Heavy M^ss 2nd 1st Isolator 4 0 2 6 8 10 12 1:2 □ 1 : 3 ^ 1:3.5 ^ 1:4.5 Lateral Displacement (Inch) Figure 6.27 93 Comparison of Interstory Drift Mass: (5th-8th) < (lst-4th) 8th-Rf 7th-8th 6th-7th 5th-6th Iso-5 th 4th-Iso 3rd-4th 2nd-3rd lst-2nd Iso-1st +H4j_ Light Mas 5 1Ttt1T+m ■ Heavy Ma > S 4 6 8 Lateral Displacement (Inch) 10 12 1:2 □ I * E gg 1:3-5 E H 1:4-5 Figure 6.28 94 Table 6.29 Comparison of Floor Acceleration. (Top 4 stories are lighter than the bottom 4 stories.) Mass Ratio (Upper : Lower stories) = 1/2, 1/3, 1/3.5, 1/4.5 Heavy Light Floors Acceleration (g) 1 to 2 1 to 3 1 to 3.5 1 to 4.5 8th 0.48 0.42 0.4 0.36 7th 0.24 0.36 0.24 0.36 6th 0.24 0.3 0.24 0.12 5th 0.12 0.12 0.12 0.12 4th 0.22 : |1 ||! ||! || i l l i i i i i! 0.08 3rd 0.17 0.09 0.08 I I M 1 I 2nd 0.13 0.09 0.08 ! ! ! ! ! ! 1st 0 0 0 l l l l l l l l Table 6.30 Acceleration Amplification. (Top 4 stories are lighter than the bottom 4 stories.) Mass Ratio (Upper : Lower stories) = 1/2, 1/3, 1/3.5, 1/4.5. Heavy Light Floors Acceleration Amplification 1 to 2 1 to 3 1 to 3.5 1 to 4.5 8th 1.17 1.02 0.98 0.88 7th 0.59 0.88 0.59 0.88 6th 0.59 0.73 0.59 0.29 5th 0.29 0.29 0.29 0.29 4th i l l i i i l 0.32 0.2 3rd ■ B ill l l i i l l l l 0.2 0.15 2nd 0.32 i i i m i 0.2 0.15 1st lilRlli 0 0 95 Floors Floor Acceleration for Different Masses Mass: (5th-8th) < (lst-4th) 8th 7th n j i m j i.i i 2nd Light Mass Heavy Mass 1:2 [ Z ] l : 3 ^ 1:3.5 ^ 1:4.5 0.4 0.5 0.6 Acceleration (g) Figure 6.29 0.7 0.8 0.9 96 Figure 6.30 Acceleration Amplification Ratios (afi0 o /aground) Upper 4-stories are lighter than the bottom 4-stories. Mass Ratio (Top : Bottom) =1:2 Mass Ratio (Top : Bottom) =1:3 8th-I 7th-- 6th- 5th- ■ 4th- 3rd- 2nd- lst 0.5 1.0 1.5 2.0 2.5 0 Amplification Factor 8tlH 7th 6th 5th 4th 3rd- 2nd- 1 1st - 0.5 1.0 1.5 2.C Amplification Factor Mass Ratio (Top : Bottom) =1 : 3.5 8th-J 7th- 6th- 5th- 4th- 3rd- 2nd- lst- 0.5 1.0 1.5 2.0 2.5 0 Mass Ratio (Top : Bottom) = 1 : 4.5 8th 7th 6th 5th- 4th- 3rd- 2nd lst- 1.0 1.5 2.0 2.5 0 0.5 97 Acceleration (g) Table 6.31 Period vs. Maximum Acceleration (Roof) (Top 4 stories are lighter than the bottom 4 stories.) Mass Ratio (Upper : Lower stories) = 1/2, 1/3, 1/3.5, 1/4.5. Period (sec.) Acceleration (g) 2.5 0.48 2.8 0.42 3 0.4 3.3 0.36 Period vs. M axim um A cceleration (R o o f) Mass: (5th-8th) < (lst-4th ) o .(j- 0.8 - 0.7- 0 .6 - 0.51 0.4- 0.3 - 0.2 - 3.2 3.3 2.7 2 .9 Period (sec.) 2.5 2.8 Figure 6.31 98 Test 8: V ///////r 777\ \/ / A Heavy ] Light Model Description: The upper 3-stories are heavier than the bottom 5-stories, isolators are placed at the 5th floor and at the base. The top to bottom mass ratios are as follow: 1.3 : 1,2 : 1,3 : 1, and 3.4 : 1. Results: As Table 6.34 and Figure 6.34 show, when the top to bottom mass ratio increases from 1.3 : 1 to 3.4 : 1, the acceleration decreases from 0.24g to 0.04g on the top, a reduction of 83%; on the 5th floor, the floor acceleration decreases from 0.96g to 0.36g, a reduction of 63%. Once again, this test proves that when the top mass is heavier than the bottom mass, the damping effect is more significant. 99 Table 6.32 Comparison of Lateral Displacement. (Top 3 stories are heavier than the bottom 5 stories.) Mass Ratio (Upper : Lower stories) = 1.3/1, 2/1, 3/1, and 3.4/1. Floors Displacement (Inch) 1.3 to 1 2 to 1 3 to 1 3.4 to 1 Roof 14 12.6 6.5 5.8 8th 13.2 11.2 6.2 5.4 7th 12.7 10.2 6 5.2 6th 12.4 10 5.9 5 Isolators 1 1 III1 I i i i l l i l liiiaiiiii 3.6 5th 7.6 5.2 3.4 3 4th 6.7 4.4 3 2.8 3rd 5.8 3.8 2.8 2.8 2nd 5 3.4 2.8 2.8 1st 5 3.4 2.8 2.8 Isolators f ll l ll ll l ■ ■ ■ fitiliifii Table 6.33 Comparison of Interstory Drift. (Top 3 stories are heavier than the bottom 5 stories.) Mass Ratio (upper and lower stories) = 1.3/1, 2/1, 3/1, and 3.4/1. Floors Displacement (Inch) 1.3 to 1 2 to 1 3 to 1 3.4 to 1 8th-Rf 0.8 1.4 0.3 0.4 7th-8th 0.5 1 0.2 0.2 6th-7th 0.3 0.2 0.1 0.2 Iso-6th 3.2 l l l i l l l l ! i i i i l f l iiiiiis ii 5th-Iso 1.6 l.i 0.6 0.6 4th-5th 0.9 0.8 0.4 0.2 3rd-4th 0.9 0.6 0.2 0 2nd-3rd 0.8 0.4 0 0 lst-2nd 0 0 0 0 Iso-1st W m m m ... .... lilS lslII 0.2 100 Deflection for Various Building Masses Mass: (6th-8th) > (lst-5th) Roof 8th 7th Heavy Mass 6th Isolator 5th Light I Vass 4th 2nd 1st Isolator Lateral Displacement (Inch) 1.3:1 □ 2:1 ^ 3 : 1 g S 3.4:1 Figure 6.32 101 Comparison of Interstory Drift Mass: (6th-8th) > (lst-5th) 8th-Rf 7th-8th 6th-7th Iso-6th 5th-Iso 4th-5th 3rd-4th 2nd-3rd lst-2nd Iso-1st § _ N Heavy Mass Light Mass 6 8 10 12 Lateral Displacement (Inch) 14 16 18 Figure 6.33 102 Table 6.34 Comparison of Floor Acceleration. (Top 3 stories are heavier than the bottom 5 stories.) Mass Ratio (Upper : Lower stories) = 1.3/1, 2/1, 3/1, 3.4/1 Heavy Light Floors Acceleration (g) 1.3 to 1 2 to 1 3 to 1 3.4 to 1 8th 0.24 l l li l l l f i 0.04 0.04 7th 0.15 ii!ii i§ !!llllilli;;: 0.02 6th 0.09 i i i i i i i t i i l i l l i 0.02 5th 0.96 0.66 0.36 0.36 4th 0.54 0.48 0.24 0.12 3rd 0.54 0.36 0.12 0 2nd 0.48 0.24 0 0 1st 0 0 0 0 Table 6.35 Acceleration Amplification. (Top 3 stories are heavier than the bottom 5 stories.) Mass Ratio (Upper : Lower stories) = 1.3/1, 2/1, 3/1, 3.4/1 Light Floors Acceleration Amplification 1.3 to 1 2 to 1 3 to 1 3.4 to 1 8th 0.59 i i i i i i i i 0.1 7th 0.37 I l l i i l l l l i l l S l i i l l 6th 0.22 111II11IS g l i i i i l 0.05 5th 2.34 1.61 0.88 0.88 4th 1.32 1.17 0.59 0.29 3rd 1.32 0.88 0.29 0 2nd 1.17 0.59 0 0 1st 0 0 0 0 Floors Floor Acceleration for Different Masses Mass: (6th-8th) > (lst-5th) 8th * Heavy Mass Light Mass 1st 0 0.1 0.2 0.3 1.3:1 □ □ 2:1 3:1 RTR 3.4:1 r 0.4 0.5 0.6 Acceleration (g) 0.7 0.8 0.9 Figure 6.34 104 Figure 6.35 Acceleration Amplification Ratios (afi0or/aground) Upper 3-stories are heavier than the bottom 5-stories. Mass Ratio (Top : Bottom) =1.3:1 Mass Ratio (Top : Bottom) = 2 :1 8thi 7th- 5th- 4th- - 3rd- 2nd- lst - 0.5 1.0 1.5 2.0 2.5 0 8thH 7th- 6th- 5th-- 4th-- 3rd- 2nd- lst- 0.5 1.0 1.5 2.0 2.5 0 Amplification Factor Amplification Factor Mass Ratio (Top : Bottom) = 3 :1 8th-| 7th- 6th- 5th- 4th- - 3rd - 2nd- -/ lst- 0.5 1.0 1.5 2.0 2.5 0 Amplification Factor Mass Ratio (Top : Bottom) = 3.4 : 1 8th-| 7th- 6th- 5th- 4th- 3rd - 2nd- lst 0 0.5 1.0 1.5 2.0 2.5 Amplification Factor 105 Table 6.36 Period vs. Acceleration (Roof) (Top 3 stories are heavier than the bottom 5 stories.) Mass Ratio (Upper : Lower stories) = 1.3/1, 2/1, 3/1, 3.4/1. Period (sec.) Acceleration (g) 2.4 0.24 2.7 0.25 3.1 0.04 3.2 0.04 Table 6.37 Period vs. Maximum Acceleration (5th) (Top 3 stories are heavier than the bottom 5 stories.) Mass Ratio (Upper : Lower stories) = 1.3/1, 2/1, 3/1, 3.4/1. Period (sec.) Acceleration (g) 2.4 0.96 2.7 0.66 3.1 0.36 3.2 0.36 106 Acceleration (g ) Acceleration (g) Period vs. Acceleration (Roof) Mass: (6th-8th) > (lst-5th) 0.9- 0.8- 0.7- 0.6 - 0.5- 0.4- 0.3- 0.2 - 0. 1- Z3 Z4 Z5 Z6 Z7 Z8 Period (sec.) Figure 6.36 Z9 3.1 3.2 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 Z3 Z4 Z5 Z6 Z7 Z8 Z9 3 3.1 3.2 Period (sec.) Figure 6.37 Period vs. Maximum Acceleration (5th) Mass: (6th~8th) > (lst-5th) 107 Test 9: l/V /1 H eavy ] Light Model Description: The upper 3-stories are lighter than the bottom 5-stories, isolators are placed at the 5th floor and at the base. The top to bottom mass ratios are as follow: 1 : 3, 1 : 4.4, 1 : 5.5, 1 : 6. Results: Table 6.40 and Figure 6.40 show that when the top to bottom mass ratio decreases form 1 : 3 to 1 : 6, the 8th floor acceleration reduces by 50%, from 0.36g to 0.18g; on the 5th floor, the floor acceleration decreases from 0.34g to 0.13g, a reduction of 62%. 108 Table 6.38 Comparison of Lateral Displacement. (Top 3 stories are lighter than the bottom 5 stories.) Mass Ratio (Upper : Lower stories) = 1/3, 1/4.4, 1/5.5, 1/6. Floors Displacement (Inch) 1 to 3 1 to 4.4 1 to 5.5 1 to 6 Roof 9.5 7.8 7.2 6.5 8th 8.9 7.5 6.8 6.2 7th 8.8 7.2 6.6 6 6th 8.6 7 6.4 5.8 Isolators 7.8 I liiii lll li W K lilM 5.2 5th 7 5.4 5.4 4.6 4th 6.4 4.7 4.8 4.2 3rd 5.8 4.2 4.3 3.8 2nd 5.4 3.8 3.8 3.6 1st 5.4 3.8 3.8 3.6 Isolators 3 3 3 3 Table 6.39 Comparsion of Inter story Drift. (Top 3 stories are lighter than the bottom 5 stories.) Mass Ratio (upper and lower stories) = 1/3, 1/4.4, 1/5.5, and 1/6. Floors Displacement (Inch) 1 to 3 1 to 4.4 1 to 5.5 1 to 6 8th-Rf 0.6 0.3 0.4 0.3 7th-8th 0.2 0.3 0.2 0.2 6th-7th 0.1 0.2 0.2 0.2 Iso-6th 0.8 iiiiiis ii liiilll 0.6 5th-Iso 0.8 0.8 0.6 0.6 4th-5th 0.6 0.7 0.6 0.4 3rd-4th 0.6 0.5 0.5 0.4 2nd-3rd 0.4 0.4 0.5 0.2 lst-2nd 0 0 0 0 Iso-1st 2.4 0.8 0.8 0.6 109 Deflection for Various Building Masses Mass: (6th-8th) < (lst-5th) Roof 8th 7th Light] Mass 6th Isolator 5th 4th 3rd 2nd 1st Isolator 4 6 8 2 10 12 0 _________________________________ Lateral Displacement (Inch) 1:3 | | 1:4.4 1:5.5 m ~ L 6 Figure 6.38 110 Comparison of Interstory Drift Mass: (6th-8th) < (lst-5th) 8th-Rf 7th-8th 6th-7th Iso-6th m . 5 th-Iso k 4th-5th 3rd-4th 2nd-3rd lst-2nd Iso-1st Light Mass Heavy Mas 5 4 6 8 Lateral Displacement (Inch) 1:3 1 | 1:4.4 1:5.5 EOT 1:6 Figure 6.39 10 12 111 Table 6.40 Comparsion of Floor Acceleration. (Top 3 stories are lighter than the bottom 5 stories.) Mass Ratio (Upper : Lower stories) = 1/3, 1/4.4, 1/5.5, 1/6. Light | Floors Acceleration (g) 1 to 3 1 to 4.4 1 to 5.5 1 to 6 8th 0.36 0.31 0.24 0.18 7th 0.12 0.18 0.12 0.12 6th 0.1 0.12 0.12 0.12 5th 0.34 l I H i l i i i! l l ! |! ! ! | 0.13 4th 0.26 l i i l l i l ! l l l l l l l i l l l l i i l 3rd 0.26 Illllillli lllilllil! 0.08 2nd 0.17 llllllllill l i i l l i l 0.04 1st 0 0 llllpillill 0 Table 6.41 Acceleration Amplification. (Top 3 stories are lighter than the bottom 5 stories.) Mass Ratio (Upper : Lower stories) = 1/3, 1/4.4, 1/5.5, 1/6. f~Light | Heavy Floors Acceleration Amplification 1 to 3 1 to 4.4 1 to 5.5 1 to 6 8th 0.88 0.76 0.59 0.44 7th 0.29 0.44 0.29 0.29 6th 0.24 0.29 0.29 0.29 5th 0.83 l i l i i l i i i t i i i l i 0.32 4th 0.63 m i l l lllllBi 3rd 0.63 0.37 i i i i i i ! !lg :|!|§ |g 2nd 0.41 0.29 liiiiiiii 1st 0 w m m m i lilliiiis 0 112 Floors Floor Acceleration for Different Masses Mass: (6th-8th) < (lst-5th) Light Mass Heavy Mass 1:3 I I 1:4.4 1:5.5 m 1:6 0.4 0.5 0.6 Acceleration (g) Figure 6.40 0.7 0.8 0.9 113 Figure 6.41 Acceleration Amplification Ratios (afl0o /aground) Upper 3-stories are lighter than the bottom 5-stories. Mass Ratio (Top : Bottom) = 1 :3 8th-| 7th- 6th- 5th- 4th- - 3rd - - 2nd- lst 0.5 1.0 1.5 2.0 2.5 0 Amplification Factor Mass Ratio (Top : Bottom) = 1 : 4.4 8th-| 7th- 6th- 5th- 4th- 3rd - 2nd- lst 0.5 1.0 1.5 2.0 2.5 0 Amplification Factor Mass Ratio (Top : Bottom) = 1 : 5.5 8th 5th 2nd 0.5 1.0 1.5 2.0 2.5 0 Amplification Factor Mass Ratio (Top : Bottom) = 1 : 6 3rd 0.5 1.0 1.5 2.0 2.5 0 Amplification Factor 114 Acceleration (g) Table 6.42 Period vs. Maximum Acceleration (Roof) (Top 3 stories are lighter than the bottom 5 stories.) Mass Ratio (Upper : Lower stories) = 1/3, 1/4.4, 1/5.5, 1/6. Period (sec.) Acceleration (g) 2.6 0.36 2.9 0.31 3.2 0.24 3.3 0.18 Period vs. Maximum Acceleration (Roof) Mass: (6th-8th) < (lst-5th) 1.3- 3.1 3.2 3.3 2.6 Period (sec.) Figure 6.42 115 Test 10: i / / / l Heavy Light Model Description: The upper 5-stories are heavier than the bottom 3-stories, isolators are placed at the 3rd level and at the base. The top to bottom mass ratio are as follow: 3 : 1,4.6 : 1,5.5 : l,and6 : 1. Results: As Table 6.45 and Figure 6.45 show, when the top to bottom mass ratio increases from 3 : 1 to 6 : 1, the acceleration on the 8th floor decreases from 0.24g to 0.1 g, a reduction of 58%. On the 3rd floor, where the floor mass changes, acceleration decreases from 0.66g to 0.24g, a reduction of 64%. 116 Table 6.43 Comparison of Lateral Displacement. (Top 5 stories are heavier than the bottom 3 stories.) Mass Ratio (Upper : Lower stories) = 3/1, 4.6/1, 5.5/1, and 6/1. Floors Displacement (Inch) 3 to 1 4.6 to 1 5.5 to 1 6 to 1 Roof 12.8 8.2 7.1 6.5 8th 12 7.4 6.4 5.7 7th 11.2 6.8 5.8 5 6th 10.4 6.2 5.3 4.3 5th 9.6 5.8 4.9 3.8 4th 8.9 5.5 4.5 3.4 Isolators 7.5 lllliiill llllllll! 2.7 3rd 6.4 3.6 2 .9 2.3 2nd 5.4 3 2 .5 2.2 1st 4.5 3 2 .5 2.2 Isolators 3 .,:.. 3 l l l i l l l Table 6.44 Comparison of Interstory Drift. (Top 5 stories are heavier than the bottom 3 stories.) Mass Ratio (upper and lower stories) = 3/1, 4.6/1, 5.5/1, and 6/1. Floors Displacement (Inch) 3 to 1 4.6 to 1 5.5 to 1 6 to 1 8th-Rf 0.8 0.8 0.7 0.8 7th-8th 0.8 0.6 0.6 0.7 6th-7th 0.8 0.6 0.5 0.7 5th-6th 0.8 0.4 0.4 0.5 4th-5th 0.7 0.3 0.4 0.4 Iso-4th 1.4 l l i i l l 0.7 3rd-Iso 1.1 0 .7 0 .4 0.4 2nd-3rd 1 0 .6 0 .4 0.1 lst-2nd 0.9 0 0 0 Iso-1st 1.5 l i i l l # 1 1 1 1 1 1 1 1 1 0.8 117 Deflection for Various Building Masses Mass: (4th-8th) > (lst-3rd) Roof 8th 7th 6th 5th 4th Isolator 3rd 2nd 1st Isolator 111111111 im & Heavy Mass Light N ass 4 6 8 10 12 Lateral Displacement (Inch) 14 3:1 I 1 4.6:1 SS5S 5.5:1 FTO 6:1 Figure 6.43 16 118 Comparison of Interstory Drift Mass: (4th-8th) > (lst-3rd) 8th-Rf 7 th-8 th 6th-7th 5 th-6 th 4 th-5 th Iso-4th 3rd-Iso 2nd-3rd lst-2nd Iso-lst !&J i i Heavy ftlass Light Mass ■ = — 4 6 8 10 12 Lateral Displacement (Inch) 14 16 3:1 I I 4.6:1 ESSS 5.5:1 m 6:1 Figure 6.44 119 Table 6.45 Comparison of Floor Acceleration. (Top 5 stories are heavier than the bottom 3 stories.) Mass Ratio (Upper : Lower stories) = 3/1, 4.6/1, 5.5/1, 6/1 Heavy Light Floors Acceleration (g) 3 to 1 4.6 to 1 5.5 to 1 6 to 1 8th 0.24 iiliiijit: IIII1I 0.1 7th 0.24 liillil llllllllf 0.08 6th 0.24 0.12 Illlii illllllll 5th 0.24 0.08 liillil 0.06 4th 0.21 0.06 0.06 0.05 3rd 0.66 0.42 0.24 0.24 2nd 0.6 0.36 0.24 0.06 1st 0.54 0 0 0 Table 6.46 Acceleration Amplification. (Top 5 stories are heavier than the bottom 3 stories.) Mass Ratio (Upper : Lower stories) = 3/1, 4.6/1, 5.5/1, 6/1 | Heavy | | Light | Floors Acceleration Amplification 3 to 1 4.6 to 1 5.5 to 1 6 to 1 8th 0.59 § 1 1 1 1 1 0.27 0.24 7th 0.59 1 1 1 1 1 1 : 1 1 1 0.2 6th 0.59 Illlii | i l i i l l l l S i : : : 0.2 5th 0.59 1 1 1 1 1 1 :1 1 :1 1 IBilll 0.15 4th 0.51 iiiiiiiiii® : : i : : : I i i ! i 0.12 3rd 1.6 i 0.59 0.59 2nd 1.5 0.88 0.59 0.15 1st 1.3 0 0 0 Floors Floor Acceleration for Different Masses Mass: (4th-8th) > (lst-3rd) 8th Heavy Mass 3rd 2nd 1st ~ T ~ 0.2 Light Mass o o.i 0.3 3:1 I 1 4.6:1 ESS8 5.5:1 m 6:1 0.4 0.5 0.6 Acceleration (g) Figure 6.45 0.7 0.8 0.9 121 Figure 6.46 Acceleration Amplification Ratios (afl0o /aground) Upper 5-stories are heavier than the bottom 3-stories. Mass Ratio (Top : Bottom) = 3 :1 8thH 7th- 6th- 5th- 4th- 3rd - 2nd- lst 0.5 1.0 1.5 2.0 2.5 0 Amplification Factor Mass Ratio (Top : Bottom) = 4.6 : 1 8thH 7th- 6th- 5th- 4th- 3rd- 2nd- lst 0.5 1.0 1.5 2.0 2.5 0 Amplification Factor Mass Ratio (Top : Bottom) = 5.5 : 1 8th-| 7th- 6th- 5th- 4th- 3rd- 2nd- lst 0.5 1.0 1.5 2.0 2.5 0 Amplification Factor Mass Ratio (Top : Bottom) = 6 :1 8th-| 7th- 6th- 5th- 4th-- 3rd - 2nd- lst 0.5 1.0 1.5 2.0 2.5 0 Amplification Factor 122 Table 6.47 Period vs. Acceleration (Roof) (Top 5 stories are heavier than the bottom 3 stories.) Mass Ratio (Upper : Lower stories) = 3/1, 4.6/1, 5.5/1, 6/1. Period (sec.) Acceleration (g) 2.6 0.24 3 0.16 3.2 0.11 3.3 0.1 Table 6.48 Period vs. Maximum Acceleration (3rd) (Top 5 stories are heavier than the bottom 3 stories.) Mass Ratio (Upper : Lower stories) = 3/1, 4.6/1, 5.5/1, 6/1. Period (sec.) Acceleration (g) 2.6 0.66 3 0.42 3.2 0.24 3.3 0.24 123 Acceleration (g ) Acceleration (g) 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 2.6 2.7 2 8 2 9 3 3.1 3.2 3.3 Period (sec.) Figure 6.47 Period vs. Acceleration (Roof) Mass: (4th-8th) > (lst-3rd) Period vs. Maximum Acceleration (3rd) Mass: (4th-8th) > (lst-3rd) 0.9- 0.8 - 0.7; 0.6 - 0.5- 0.4- 0.3- 0.2 - 0. 1- 2 6 27 29 3 Period (sec.) 3.1 3.2 3.3 Figure 6.48 124 Test 11: V / / / / / / Z Z 7 7 \ / / A Heavy ] Light Model Description: The upper 5-stories are lighter than the bottom 3-stories, isolators are placed at the 3rd level and at the base. The top to bottom mass ratio are as follow: 1 : 1.3, 1 : 2, 1 : 2.8, and 1 : 3.4. Results: Table 6.51 and Figure 6.51 show that when the top to bottom mass ratio decreases from 1 : 1.3 to 1 : 3.4, the acceleration on the 8th floor almost remain constant, decreases from 0.24g to 0.23g, a reduction of 4%. On the 3rd floor, acceleration decreases from 0.22g to 0.14g, a reduction of 36%. The results indicated that when the upper mass is lighter than the bottom mass, the damping effect is insignificant. 125 Table 6.49 Comparison of Lateral Displacement. (Top 5 stories are lighter than the bottom 3 stories.) Mass Ratio (Upper : Lower stories) = 1/1.3, 1/2, 1/2.8, and 1/3.4. Floors Displacement (Inch) 1 to 1.3 1 to 2 1 to 2.8 1 to 3.4 Roof 7.9 7.6 7.6 8.4 8th 7.5 7.2 7.1 7.9 7th 7.1 6.8 6,9 7.5 6th 6.7 6.6 6.8 7.1 5th 6.4 6.4 6.7 6.9 4th 6.2 6.2 6.6 6.7 Isolators illlii! l l i l i l l i I I 1II 1I i l l l i i 3rd 5.1 5.1 5.5 5.8 2nd 4.8 4.8 5 5.1 1st 4.8 4.8 5 5.1 Isolators 3 liillil ....3 ... ||||:!||||l Table 6.50 Comparison of Interstory Drift. (Top 5 stories are lighter than the bottom 3 stories.) Mass Ratio (upper and lower stories) = 1/1.3, 1/2, 1/2.8, and 1/3.4. Floors Displacement (Inch) 3 to 1 4.6 to 1 5.5 to 1 6 to 1 8th-Rf 0.4 0.4 0.5 0.5 7th-8th 0.4 0.4 0.2 0.4 6th-7th 0.4 0.2 0.1 0.4 5th-6th 0.3 0.2 0.1 0.2 4th-5th 0.2 0.2 0.1 0.2 Iso-4th 0.6 0.6 i S l l i l l l 0.1 3rd-Iso 0.5 0.5 0.7 0.8 2nd-3rd 0.3 0.3 0.5 0.7 lst-2nd 0 0 0 0 Iso-1st 1.8 HP1S1 m i i i 126 Deflection for Various Building Masses Mass: (4th-8th) < (lst-3rd) Roof 8th 7th 6th Light Mass 5 th 4th Isolator 3rd Heavy Mass 2nd 1st Isolator Lateral Displacement (Inch) 1:2.8 FFffl 1:3.4 1 -------------------- Figure 6.49 127 Comparison of Interstory Drift Mass: (4th-8th) < (lst-3rd) 8th-Rf 7th-8th 6th-7th Light Mass 5th-6th 4th-5th Iso-4th 3rd-Iso 2nd-3rd lst-2nd Iso-1st Lateral Displacement (Inch) 1:1.3 □ I:2 ESS 1:2.8 E E E B 1:3.4 Figure 6.50 128 Table 6.51 Comparison of Floor Acceleration. (Top 5 stories are lighter than the bottom 3 stories.) Mass Ratio (Upper : Lower stories) = 1/1.3, 1/2, 1/2.8, 1/3.4 Heavy | Light Floors Acceleration (g) 1 to 1.3 1 to 2 1 to 2.8 1 to 3.3 8th 0.24 0.24 0.23 0.23 7th 0.24 0.24 0.12 0.24 6th 0.24 0.12 0.06 0.24 5th 0.18 0.12 0.06 0.12 4th 0.12 0.12 0.1 0.12 3rd 0.22 iiiilllill 0.14 2nd 0.21 llllllllll l i i i i i i i i 0.1 1st 0 !iiiiii|;ii: v iim im 0 Table 6.52 Acceleration Amplification. (Top 5 stories are lighter than the bottom 3 stories.) Mass Ratio (Upper : Lower stories) = 1/1.3, 1/2, 1/2.8, 1/3.3 | Heavy | Light | Floors Acceleration Amplification 1 to 1.3 1 to 2 1 to 2.8 1 to 3.3 8th 0.59 0.59 0.56 0.56 7th 0.59 0.59 0.29 0.59 6th 0.59 0.29 0.15 0.59 5th 0.44 0.29 0.15 0.29 4th 0.29 0.29 0.24 0.29 3rd 0.54 lllilillll 0.34 i lS l l i i! 2nd 0.51 !|:|I!1II! 0.24 iiillllilll 1st 0 0 0 iiiiiiiiiii Floors Floor Acceleration for Different Masses Mass: (4th-8th) < (lst-3rd) 111 M 11111 [11111II |.| III 1 1 1 1 1 1 1 1 ■] s a - - U it m Light Mass 3rd 2nd 1st Heavy Mass o.i 0.2 0.3 1:1.3 □ 1:2 £ § § 1:2.8 ^ 1:3.4 0.4 0.5 0.6 Acceleration (g) Figure 6.51 0.7 0.8 0.9 130 Figure 6.52 Acceleration Amplification Ratios (afloor/ag ro u n ci) Upper 5-stories are lighter than the bottom 3-stories. Mass Ratio (Top : Bottom) =1 : 1.3 8th-| 7th 6th- 5th 4th- 3rd 2nd- lst- 0.5 1.0 1.5 2.0 2.5 0 Amplification Factor Mass Ratio (Top : Bottom) =1:2 8thH 7th 6th 5th 4th 3rd 2nd lst- 0.5 1.0 1.5 Amplification Factor Mass Ratio (Top : Bottom) =1 : 2.8 8th 7th 6th 5th 4th 3rd 2nd 1st 0.5 1.0 1.5 2.0 2.5 0 Amplification Factor Mass Ratio (Top : Bottom) = 1 : 3.4 8th 7th 6th 5 th 4th 3rd 2nd 1st 0.5 1.0 1.5 2.0 2.5 0 Amplification Factor 131 Acceleration (g) Table 6.53 Period vs. Maximum Acceleration (Roof) (Top 5 stories are lighter than the bottom 3 stories.) Mass Ratio (Upper : Lower stories) = 1/1.3, 1/2, 1/2.8, 1/3.3. Period (sec.) Acceleration (g) 2.4 0.24 2.8 0.24 3 0.23 3.2 0.23 i- 0.9- 0.8- 0.7- 0. 6- 0.5- 0.4- 0.3- 0.2- 0 . 1- 0 - Z3 Z4 Z5 Z6 Z7 Z8 Z9 3 3.1 3.2 Period (sec.) Figure 6.53 Period vs. Maximum Acceleration (Roof) Mass: (4th-8th) < (lst-3rd) 132 CONCLUSIONS: 1. Base isolation system is best suited for low-rise buildings up to four stories. 2. Over-turning moment is the primary concern when the height of a base-isolated structure increases to eight stories. In this case, rubber bearings at the base are subjected to uplift. The situation is worse when the building has non-uniform mass distribution. 3. In a mixed-use building, it is possible to install isolators at various locations to separate the different masses. It was found that if the upper mass of a mixed-use building is much heavier than the lower mass, then the upper mass acts as a damper, reducing interstory drift and acceleration of the entire structure. On the other hand, if the lower mass is heavier than the upper mass, although interstory drift and floor acceleration decrease, but the reduction is insignificant. 133 Summary for Test 1: Two two-story models, one is base-isolated, the other is base fixed. Comparison of Lateral Displacement. Floors Displacement (Inch) Base-isolated Base-fixed Roof 3.7 3.5 2nd 3.7 3.2 1st 3.7 3 Comparison of Floor Acceleration. Floors Floor Acceleration (g) Base-isolated Base-fixed 2nd 0 0.16g 1st 0 O.llg 134 Displacement of two 2 stories Buildings Isolated Vs. Non-Isolated Roof U n ifo r m L o a d Lateral Displacement (Inch) Y//X W ith I s o la to r m W /O Iso la to r Comparison of Floor Acceleration Isolated Vs. Non-Isolated 1 2 8 2 n d E U n i f o r m L o a d 0.1 0.2 Y //\ W ith Is o la to r W /O Iso la to r 0.3 0.4 0.5 0.6 Acceleration (g) 0.7 0.8 0.9 135 Summary for Test 2: Two four-story models, one is base-isolated, the other is base fixed. Comparison of Lateral Displacement. Floors Displacement (Inch) Base-isolated Base-fixed Roof 4.7 4.2 4th 4.4 3.8 3rd 4.2 3.5 2nd 4.2 3.2 1st 4.2 3 Comparison of Floor Acceleration. Floors Floor Acceleration (g) Base-isolated Base-fixed 4th 0.16g 0.21g 3rd O.llg 0.16g 2nd 0 0.16g 1st 0 O.lg 136 Displacement of two 4 stories Buildings Isolated Vs. Non-Isolated U n ifo r m L o a d Y//////////////{//S/S//////fiZ % & 7 7 7 7 7 7 7 A 7 / 7 7 7 7 ^ / 7 7 W ith I so la to r W /O Iso la to r 4 6 8 Lateral D isplacem ent (Inch) Comparison of Floor Acceleration Isolated Vs. N on-Isolated 4 t h 3 r d 2 n d U n i f o r m L o . I W ith Iso la to r W /O I so la to r 0 .3 0 . 4 0 . 5 0 .6 A cceleration (g) 0 . 7 0.8 0 .9 137 Summary for Test 3: Two eight-story models, one is base-isolated, the other is base fixed. Comparison of Lateral Displacement. Floors Displacement (Inch) Base-isolated Base-fixed Roof 10 8.5 8th 9.2 6.3 7th 8.4 5.3 6th 7.6 4.5 5th 7 3.9 4th 6.6 3.5 3rd 6.4 3.3 2nd 6.4 3.1 1st 6.4 3 Comparison of Floor Acceleration. Floors Floor Acceleration (g) Base-isolated Base-fixed 8th 0.24g 0.63g 7th 0.24g 0.3g 6th 0.24g 0.24g 5th 0.18g 0.18g 4th 0.17g 0.17g 3rd 0.09g 0.09g 2nd 0 0.09g 1st 0 0.04g 138 5 2 o o E Roof 8th 7th 6th 5th 4th 3rd 2nd 1st Displacement of two 8 Stories Buildings Isolated Vs. Non-Isolated ////////////////////////////yy//////////////////////////////, ! ! ! ////////A Y ///////////////////////////////)^^^^/////Jy ////////^/////^ Uniform Loa| x//////////////<////////////////////////////////.//-/.//.//y././.A x / / / / / / //////////////////////////////s///yz/././-s./s.zyyyA ■ ......... i ------------------- i • • 1 ....... ■ ■ -....... 0 Y//A With Isolator W/O Isolator 4 6 8 Lateral Displacement (Inch) 10 12 o o E Comparison of Floor Acceleration Isolated Vs. Non-Isolated 8th 7th 6th 5th 4th 3rd 2nd 1st / / / / / / / / / / / / / / / / . '///////< m m V / / / / / / / / / 7 7 7 7 .1 0 0.1 0.2 Uniform Load Y//A With Isolator m W/O Isolator 03 0.4 0.5 0.6 Acceleration (g) 0.7 0.8 0.9 139 Summary for Test 4: Two eight-story models, one is base-isolated, the other is base fixed. The top four stories in each model are twice as heavy as the bottom four stories. Comparison of Lateral Displacement. Floors Displacement (Inch) Base-isolated Base-fixed Roof 10.6 9.5 8th 9.8 6.9 7th 9 5.9 6th 8.3 5.1 5th 7.7 4.4 4th 6.7 3.6 3rd 6.3 3.2 2nd 6.1 2.9 1st 6.1 2.8 Comparison of Floor Acceleration. Floors Floor Acceleration (g) Base-isolated Base-fixed 8th 0.24g 0.78g 7th 0.24g 0.3g 6th 0.21g 0.24g 5th 0.18g 0.21g 4th 0.86g 0.69g 3rd 0.34g 0.34g 2nd 0.17g 0.26g 1st 0 0.09g 140 Displacement of two 8 Stories Buildings Isolated Vs. Non-Isolated Roof 8th 7th £ 6th R 5th E 4th 3rd 2nd 1st | J ___1 s / / S / / S / / / S / / / / / / / / / / / / / / / / / / / / / Heavy Mas Light Mass --------------------- 1 W >>)>)))>)))>) )))))~ ;;s/;///> --------------------- j --------------------- j --------------------- r --------------------- V //\ With Isolator W/O Isolator Lateral Displacement (Inch) Comparison of Floor Acceleration Isolated Vs. Non-Isolated 8th 7th ■//////7777T Heavy P lass 6th g 5th o o E 4th 3rd '//////////////////A 1 Light Mass 2nd 1st 0.1 0.2 0.3 0.5 Acceleration (g) 0.4 0.6 0.7 0.9 With Isolator W/O Isolator 141 Summary for Test 5: Two eight-story models, one is base-isolated, the other is base fixed. The top four stories in each model are twice as light as the bottom four stories. Comparison of Lateral Displacement. Floors Displacement (Inch) Base-isolated Base-fixed Roof 9.6 7.7 8th 8.9 6.2 7th 8.2 5.3 6th 7.6 4.6 5th 7 3.9 4th 6.4 3.3 3rd 6.2 3.1 2nd 6.2 3 1st 6.2 2.9 Comparison of Floor Acceleration. Floors Floor Acceleration (g) Base-isolated Base-fixed 8th 0.42g 0.9g 7th 0.42g 0.54g 6th 0.36g 0.42g 5th 0.36g 0.42g 4th 0.26g 0.26g 3rd 0.09g 0.09g 2nd 0 0.04g 1st 0 0.04g 142 Displacement of two 8 Stories Buildings Isolated Vs. Non-Isolated Roof 8th 7th 6th 5th 4th 3rd 2nd 1st ' / / / / / /) / // y /s y /// // // // // /// ) ( // / / / / / / / / / / / ) / / / / / / / v ^ ^ y y ; / / / / / / / / / / a y //V/ZZ/ / / / / / / / / / / / / / / / / / / /////W W / / / / / / / / / / S //V/V/ / / / / / / / / / / / / / / 1 \z/ / / / / / / / / / / / / / s f z /////////-./.s/s////////////z/zz /-//-/-/v-vszvvv^ - t ! 1 Light Mass \ / // // //////y ///////////////////////////.//v y v v ///////////i Heavy Mass _Y/J/^./,jCV//V.Sj'wf/ / / / / / / / / / / / / / / / / / / //vv/w////^\ J ZZZZ///ZZ//ZZZZ ZZZZ ZZZZZZZZZ.ZZZ /W/VV/Z/ / / / / / A Y//A With Isolator m W/O Isolator Lateral Displacement (Inch) Comparison of Floor Acceleration Isolated Vs. Non-Isolated 8th '/////////////////////////////Z/////77X 7th 6th 5th '///////////////////////, 4th Y Z Z Z Z Z 7 Z Z Z Z Heavy M u i 3rd 2nd 1st 0.9 0.5 Acceleration (g) 0.6 0.7 0.3 0.4 0.2 0.1 W/O Isolator With Isolator 143 Summary for Test 6: The model has eight stories, isolators are placed at the 4th floor and at the base. The upper 4 stories are heavier than the bottom 4 stories. Mass Ratio = 2/1, 4.4/1 Comparison of Lateral Displacement Floors Displacement (Inch) 2 to 1 4.4 to 1 Roof 11.6 4.3 8th 10.8 3.8 7th 10 3.4 6th 9.2 3.1 5th 8.5 2.8 Isolators 5.8 2.1 4th 5 2 3rd 4.6 2 2nd 4.3 2 1st 4.3 2 Isolators 3 3 Comparison of Floor Acceleration. Floors Acceleration (g) 2 to 1 4.4 to 1 8th 0.24 0.07 7th 0.24 0.05 6th 0.24 0.04 5th 0.21 0.04 4th 0.48 0.06 3rd 0.24 0 2nd 0.18 0 1st 0 0 144 Floors Deflection for Various Building M asses Mass: (5th-8th) > (lst-4th) 2:1 4.4:1 I | . i i i i | ............in . | | | j | | | | || i ivn I - rrT T T T T T lp T T T , nhniMMMIM, 1 1 * I 1 ry Mass 1 i ■ ......................................m i m I m i m . 1 ! Hea MMTTTMirilTTl. \ — j . . . . . . i ii i M m i Ugh t Mass - n t | | | | , | , | , , r,\ | - i i j - .....................-r^j 1 Roof 8th 7th 6th 5th Isolator 4th 3rd 2nd 1st Isolator Lateral Displacement (Inch) Floor Acceleration for Different Masses Mass: (5th-8th) > (lst-4th) 2:1 f m 4.4:1 8th 7th 6th 5 th 4th 3rd 2nd 1st T m F F f f l Heavy Mass H ~ n Light Ma: s 0.1 0.2 0.3 0.4 0.5 0.. Acceleration (g) 0.7 0.8 0.9 145 Summary for Test 7: The model has eight stories, isolators are placed at the 4th floor and at the base. The upper 4 stories are lighter than the bottom 4 stories. Mass Ratio = 1/2, 1/4.5 Comparison of Lateral Displacement Floors Displacement (Inch) 1 to 2 1 to 4.4 Roof 9.4 7.8 8th 8.6 7.2 7th 8.2 6.6 6th 7.8 6.4 5th 7.6 6.2 Isolators 6 4.8 4th 5.5 4.4 3rd 5.1 4.1 2nd 4.8 3.8 1st 4.8 3.8 Isolators 3 3 Comparison of Floor Acceleration. Floors Acceleration (g) 1 to 2 1 to 4.4 8th 0.48 0.36 7th 0.24 0.36 6th 0.24 0.12 5th 0.12 0.12 4th 0.22 0.08 3rd 0.17 0.06 2nd 0.13 0.06 1st 0 0 146 Floors Isolator Isolator Deflection for Various Building Masses Mass: (5th-8th) < (lst-4th) 1:2 0 5 )1 :4 .5 Roof Light Mass Heavy Mass 4 6 8 Lateral Displacement (Inch) Floor Acceleration for Different Masses Mass: (5th-8th) < (lst-4th) 1:2 0 3 1:4.5 8th 7th 6th 5th 4th 3rd 2nd 1st 11111 r 1 1 Light Mas s Heavy M a ss 0 0.1 0.2 0.3 0.4 0.5 0 Acceleration (g) 6 0.7 0.8 0.9 147 Summary for Test 8: The model has eight stories, isolators are placed at the 5th floor and at the base. The upper 3 stories are heavier than the bottom 5 stories. Mass Ratio = 1.3/1, 3.4/1. Comparison of Lateral Displacement Floors Displacement (Inch) 1.3 to 1 3.4 to 1 Roof 14 5.8 8th 13.2 5.4 7th 12.7 5.2 6th 12.4 5 Isolators 9.2 3.6 5th 7.6 3 4th 6.7 2.8 3rd 5.8 2.8 2nd 5 2.8 1st 5 2.8 Isolators 3 3 Comparison of Floor Acceleration. Floors Acceleration (g) 1.3 to 1 3.4 to 1 8th 0.24 0.04 7th 0.15 0.02 6th 0.09 0.02 5th 0.96 0.36 4th 0.54 0.12 3rd 0.54 0 2nd 0.48 0 1st 0 0 148 Floors Deflection for Various Building Masses Mass: (6th-8th) > (lst-5th) 1.3:1 0 3 3 3.4:1 i i i i i m i i i M i i i 1 1 i i i i in i rit i i i i i i i J ! [ass - " llllll'J ....................* .......... | | ~ ...........................................‘..MM. 1 i H ea w h 1 1 1 1 _ l 1 1 1 1 1 1 | 1 L i_ L l_ L - l_ L U ---i --------- ---------------- ! ---------- ........Mimiimii 1 1 Light Ma S S - ........I......... L i in i - " " " " 'I 1 j 1 | j ' 1 - 1 ,1 ,,, 11,,, • i nni Mi nl....... | 1 J - --------1 ----------------------------------i---------------- Roof 8th 7th 6th Isolator 5th 4th 3rd 2nd 1st Isolator 6 8 10 Lateral Displacement (Inch) 12 14 16 Floor Acceleration for Different Masses Mass: (6th-8th) > (lst-5th) 1.3:1 3.4:1 1 1 i" n j | Heavy Ms ss i i 1 a — 1 1 |-|-[-| | | | | 1 It | | | II | |!| | | | M | | f * ............. |, , ! 1 1 1 II 1 1 1 1 1 1 1 i Light Ma ;s i 1 1 1 | ; 1 1 8th 7th 6th 5th 4th 3rd 2nd 1st 0.1 0.2 0.3 0.4 0.5 0. Acceleration (g) 6 0.7 0.8 0.9 149 Summary for Test 9: The model has eight stories, isolators are placed at the 5th floor and at the base. The upper 3 stories are lighter than the bottom 5 stories. Mass Ratio = 1/3, 1/6. Comparison of Lateral Displacement Floors Displacement (Inch) 1 to 3 1 to 6 Roof 9.5 6.5 8th 8.9 6.2 7th 8.8 6 6th 8.6 5.8 Isolators 7.8 5.2 5th 7 4.6 4th 6.4 4.2 3rd 5.8 3.8 2nd 5.4 3.6 1st 5.4 3.6 Isolators 3 3 Comparison of Floor Acceleration. Floors Acceleration (g) 1 to 3 1 to 6 8th 0.36 0.18 7th 0.12 0.12 6th 0.1 0.12 5th 0.34 0.13 4th 0.26 0.08 3rd 0.26 0.08 2nd 0.17 0.04 1st 0 0 150 Floors D eflection for Various Building Masses Mass: (6th-8th) < (lst-5th) 1:3 EH3 1:6 i 1^ lass _ IIII1IIIIIIIIII | II1 i li Ini t j Light A in i rn-Ti-n 1 1 i - l 1 1 II 1 II . I . l.i Mini trn-n Heavy Mass 1 I I I i \ i i 1 - 1"'! ' 1 '!'* ! Illlll1!'!1 * ! ! ! 1 _ II 1 1 1 1 M 1 ril 1 1 1 11111 IT T I 1 1 1 IT 1 | - m u .................. Roof 8th 7th 6th Isolator 5th 4th 3rd 2nd 1st Isolator 4 6 8 Lateral Displacement (Inch) 10 12 Floor Acceleration for Different Masses Mass: (6th-8th) < (lst-5th) 1:3 m 3 ! 1:6 8th 7th 6th 5th 4th 3rd 2nd 1st Light Mass Heavy M$ss 0 0.1 0.2 0.3 0.4 0.5 0.6 Acceleration (g) 0.7 0.8 0.9 151 Summary for Test 10: The model has eight stories, isolators are placed at the 3rd floor and at the base. The upper 5 stories are heavier than the bottom 3 stories. Mass Ratio = 3/1, 6/1. Comparison of Lateral Displacement Floors Displacement (Inch) 3 to 1 6 to 1 Roof 12.8 6.5 8th 12 5.7 7th 11.2 5 6th 10.4 4.3 5th 9.6 3.8 4th 8.9 3.4 Isolators 7.5 2.7 3rd 6.4 2.3 2nd 5.4 2.2 1st 4.5 2.2 Isolators 3 3 Comparison of Floor Acceleration. Floors Acceleration (g) 3 to 1 6 to 1 8th 0.24 0.1 7th 0.24 0.08 6th 0.24 0.08 5th 0.24 0.06 4th 0.21 0.05 3rd 0.66 0.24 2nd 0.6 0.06 1st 0.54 0 152 Floors Roof 8th 7th 6th 5th 4th Isolator 3rd 2nd 1st Isolator Deflection for Various Building Masses M a ss: (4 th -8 th ) > ( ls t - 3 r d ) -i-------------------- 1 ---------------- -— ■ — .............. --------------- 1 -------------------- ■ 1 3:1 6:1 s ^ l -111 11 1 1 1 ..S .............. i i - 1 1 1 i H e a v y Mas ....................ll.MTTTI. i | ~ i > ii i i i i i i irn L igh t M a ss r h - T T T T r r r T T T T f i “ " T " ™ 1 | s i i s s i g s a i 6 8 10 Lateral Displacement (Inch) 12 14 16 Floor Acceleration for Different Masses Mass: (4th-8th) > (lst-3rd) 3;1 H+H 6:1 8th 7th 6th 5th 4th 3rd 2nd 1st •rm Heavy Mi ss t t t t i Light Mass 0 0.1 0.2 0.3 0.4 0.5 0 Acceleration (g) 6 0.7 0.8 0.9 1 153 Summary for Test 11: The model has eight stories, isolators are placed at the 3rd floor and at the base. The upper 5 stories are lighter than the bottom 3 stories. Mass Ratio = 1/1.3, 1/3.4. Comparison of Lateral Displacement Floors Displacement (Inch) 1 to 1.3 1 to 3.4 Roof 7.9 8.4 8th 7.5 7.9 7th 7.1 7.5 6th 6.7 7.1 5th 6.4 6.9 4th 6.2 6.7 Isolators 5.6 6.6 3rd 5.1 5.8 2nd 4.8 5.1 1st 4.8 5.1 Isolators 3 3 Comparison of Floor Acceleration. Floors Acceleration (g) 1 to 1.3 1 to 3.4 8th 0.24 0.23 7th 0.24 0.24 6th 0.24 0.24 5th 0.18 0.12 4th 0.12 0.12 3rd 0.22 0.14 2nd 0.21 0.1 1st 0 0 154 Floors Isolator Isolator D eflection for Various Building Masses Mass: (4th-8th) < (lst-3rd) 1:1.3 1:3.4 Roof Light Mass Heavy Mass 4 6 8 Lateral Displacement (Inch) Floor Acceleration for Different Masses Mass: (4th-8th) < (lst-3rd) 1:1.3 m 1:3.4 8th 7th 6th 5th 4th 3rd 2nd 1st i n 11111 r Tffl Light Ma: s Heavy Mass 0.1 0.2 0.3 0 4 0.5 0j Acceleration (g) 0.7 Oi 155 REFERENCE Architectural Institute of Japan (AIJ). Advancement of R & D on Isolators and Dampers. Sendai, Japan: Tohoku Institute of Technology, 1992. Arnold, Christopher. "Architectural Considerations." In The Seismic Design Handbook, pp. 142-170. Edited by Farzad Naeim. New York: Van Nostrand Reinhold, 1989. Bolt, Bruce. Earthquakes. New York: W. H. Freeman and Company, 1988. Bridgestone Corporation. "Rubber Technology for Seismic Isolation." In Seismic Isolation and Response Control for Nuclear and Non-Nuclear Structures, pp. 45-56. Edited by The Scientific Events Subcommittee of the Executive Committee for the 11th International Conference on Structural Mechanics in Reactor Technology. Japan: Nissei Eblo Inc., 1991. Griffith, M. C.; Aiken, I. D.; and Kelly, J. M.. Experimental Evaluation of Seismic Isolation of a 9-storv Braced Steel Frame Subject to Uplift. Berkeley: University of California, Berkeley, 1988. Kelly, James. Base Isolation in Japan, 1988. Berkeley: University of California, Berkeley, 1988. Mayes, Ronald. "Seismic Isolations." In The Seismic Design Handbook, pp. 413-437. Edited by Farzad Naeim. New York: Van Nostrand Reinhold, 1989. 156 Obayashi Corporation. "Base Isolation/Vibration Control, Construction Methods and Application Examples." In Seismic Isolation and Response Control for Nuclear and Non-Nuclear Structures, pp. 105-116. Edited by The Scientific Events Subcommittee of the Executive Committee for the 11th International Conference on Structural Mechanics in Reactor Technology. Japan: Nissei Eblo Inc., 1991. Parker, Harry; Ambrose, James. Simplified Engineering for Architects and Builders. New York: John Wiley & Sons, Inc., 1984. Schierle, Goetz. "Lateral Design Graphs". 1991. Schueller, Woflgang. The Vertical Building Structure. New York: Van Nostrand Reinhold, 1990. Shimizu Corporation. "Base Isolation and Vibrational Control System." In Seismic Isolation and Response Control for Nuclear and Non-Nuclear Structures, pp. 138-148. Edited by The Scientific Events Subcommittee of the Executive Committee for the 11th International Conference on Structural Mechanics in Reactor Technology. Japan: Nissei Eblo Inc., 1991. Takenaka Corporation. "Current State of Research and Development on Base Isolation, Structural Control and Vibration Isolation." In Seismic Isolation and Response Control for Nuclear and Non-Nuclear Structures, pp. 169-180. Edited by The Scientific Events Subcommittee of the Executive Committee for the 11th International Conference on Structural Mechanics in Reactor Technology. Japan: Nissei Eblo Inc., 1991. Uniform Building Code. Whittier: International Conference of Building Officials, 1991. 157

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Asset Metadata

Creator Chong, Lai-Yui Sammy (author)

Core Title Investigation of seismic isolators as a mass damper for mixed-used buildings

Degree Master of Building Science

Degree Program Building Science

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag engineering, architectural,Engineering, Geophysical,OAI-PMH Harvest

Language English

Contributor Digitized by ProQuest (provenance)

Advisor Schierle, Gotthilf Goetz (committee chair), Schiler, Marc (committee member), Vergun, Dimitry K. (committee member)

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c20-299761

Unique identifier UC11259052

Identifier EP41431.pdf (filename),usctheses-c20-299761 (legacy record id)

Legacy Identifier EP41431.pdf

Dmrecord 299761

Document Type Thesis

Rights Chong, Lai-Yui Sammy

Type texts

Source University of Southern California (contributing entity), University of Southern California Dissertations and Theses (collection)

Access Conditions The author retains rights to his/her dissertation, thesis or other graduate work according to U.S. copyright law. Electronic access is being provided by the USC Libraries in agreement with the au...

Repository Name University of Southern California Digital Library

Repository Location USC Digital Library, University of Southern California, University Park Campus, Los Angeles, California 90089, USA