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Investigation of sloshing water damper for earthquake mitigation

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Investigation of sloshing water damper for earthquake mitigation

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Content INVESTIGATION OF SLOSHING WATER DAMPER FOR EARTHQUAKE MITIGATION by Liang-Chi Chen 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 AUGUST 1993 Copyright 1993 Liang-Chi Chen UMI Number: EP41430 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. U M T Dissertation Publishing UMI EP41430 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 uest' ProQuest LLC. 789 East Eisenhower Parkway P.O. Box 1346 Ann Arbor, Ml 48106 -1346 UNIVERSITY O F SO U T H E R N CALIFORNIA THE SCHOOL OF ARCHITECTURE UNIVERSITY PARK LOS ANGELES. CALIFORNIA 90089-0291 5 . > c |3 C 5 I€ > This thesis, written by under the direction of h I £ . . . . Thesis Committee, and approved by all its members, has been pre sented to and accepted by the Dean of The School o f Architecture, in partial fulfillment of the require ments for the degree of Masher o f B u W c I m T ? S=i<Shoe Date 7 / ? - ) THESIS/COMMITTEE C h i ACKNOWLEDGEMENTS I would like to express my appreciation to the thesis advisors : Goetz Schierle, Professor and Director of Master of Building Science at University of Southern California, for his support and guidance throughout my graduate study; M arc Schiler, Professor of Architecture at University of Southern California, for his precious instruction and encouragement; Dimitry Vergun, Professor of Architecture at University of Southern California, for his plentiful experiences to lead me throughout the entire experiment; Mao-Hua Peng, Ph.D. the Civil Engineering department of Washington University, for giving me assistance in the computer simulation of my thesis; Sammy Chong, my colleague in the Master of Building Science Program, for helping me do my experiments. ABSTRACT The purpose of this thesis is to investigate the efficiency of a vibration control system which is called Sloshing Water Damper system. The Sloshing Water Damper is an apparatus which utilizes the hydrodynamic forces to harmonize with the natural frequency of the building. This study examines how Sloshing Water Damper can be used to suppress the vibrations induced by earthquake and wind. The results of model testing and computer simulation have been found in good agreement and the ability of controlling vibrations have been proven. TABLE OF CONTENTS Part I Survey of Earthquake Resistance Techonology Chapter I Control Systems for Earthquake Resistance 1.1 Introduction 1 1.2 Isolation Systems 2 1.3 Vibration Control Systems 5 Chapter II Vibration Control by Water Tanks 2.1 Introduction 13 2.2 Seismic Excitation in Water Tank 14 2.3 Dynamic Response of Water Tank 16 Part II Researches of Sloshing Water Damper Chapter III Feasibility Study of the Sloshing Water Damper for Retrofitting Structures 3.1 Introduction 20 3.2 Application of Sloshing Water Damper in Existing Buildings 21 3.3 Case Study 23 Chapter IV Earthquake Simulation Testing 4.1 Objectives 25 4.2 Assumptions 25 4.3 Testing Proceedure 30 4.4 Test Results 32 Chapter V Computer Simulation 5.1 Assumptions 50 5.2 Simulation Results 52 Chapter VI Conclusions 56 Appendix A Test Data 57 Appendix B Computer Simulation Data 73 Bibliography 75 V LIST OF FIGURES 1-1 Base Isolater 4 1-2 Floor Isolation System 5 1-3 Tuned Mass Damper 6 1-4 Tuned Mass Damper with Isolater 7 1-5 Wind Acceleration of a 50-story Building with and without Tuned Mass Damper 8 1-6 Shear Yielding Damper 9 1-7 Viscoelastic Damping Wall 11 2-1 Typical Movement of Sloshing Water 15 2-2 The Frequencies and ModeShape of Water 15 2-3 Two Equivalent Masses of Sloshing Water 17 3-1 The Excitation Curve of the Golden Tower 24 4-1 The Shaking Devices 29 4-2 The Sloshing Water Damper 29 4-4 The Displacement Ratio for 4-story Building (Type 1 SWD) 40 4-5 The Displacement Ratio for 4-story Building (Type 2 SWD) 40 4-6 The Displacement Ratio for 4-story Building (Type 3 SWD) 40 4-7 The Inter Story Drift for 4-story Building (Type 1 SWD) 41 4-8 4-9 4-10 4-11 4-12 4-13 4-14 4-15 4-16 4-17 4-18 4-19 The Inter Story Drift for 4-story Building (Type 2 SWD) The Inter Story Drift for 4-story Building (Type 3 SWD) The Floor Acceleration for 4-story Building (Type 1 SWD) The Floor Acceleration for 4-story Building (Type 2 SWD) The Floor Acceleration for 4-story Building (Type 3 SWD) The Displacement Ratio for 8-story Building (Type 1 SWD) The Displacement Ratio for 8-story Building (Type 2 SWD) The Displacement Ratio for 8-story Building (Type 3 SWD) The Inter Story Drift for 8-story Building (Type 1 SWD) The Inter Story Drift for 8-story Building (Type 2 SWD) The Inter Story Drift for 8-story Building (Type 3 SWD) The Floor Acceleration for 8-story Building (Type 1 SWD) 4-20 The Floor Acceleration for 8-story Building (Type 2 SWD) 4-21 The Floor Acceleration for 8-story Building (Type 3 SWD) 4-22 The Displacement Ratio for 8-story Building (SWD at 7F) 4-23 The Inter Story Drift for 8-story Building (SWD at 7F) 4-24 The Floor Acceleration for 8-story Building (SWD at 7F) 4-25 The Displacement Ratio for 4-story Building (Type 1 SWD) 4-26 The Displacement Ratio for 4-story Building (Type 2 SWD) 4-27 The Displacement Ratio for 4-story Building (Type 3 SWD) 4-28 The Inter Story Drift for 4-story Building (Type 1 SWD) 4-29 The Inter Story Drift for 4-story Building (Type 2 SWD) 4-30 The Inter Story Drift for 4-story Building (Type 3 SWD) 4-31 The Floor Acceleration for 4-story Building (Type 1 SWD) 4-32 The Floor Acceleration for 4-story Building (Type 2 SWD) 4-33 The Floor Acceleration for 4-story Building (Type 3 SWD) 5-1 Peak Rock Acceleration 5-2 CALTRANS - Fault Map 5-3 Computer Simulation for 4-story Building with Mass Ratio 4% 5-4 Computer Simulation for 4-story Building with Mass Ratio 4% 5-5 Computer Simulation for 8-story Building with Mass Ratio 4% 5-6 Computer Simulation for 8-story Building with Mass Ratio 4% LIST OF TABLES 2-1 The Simple Equivalent Mass Analysis Equations for Sloshing Water 19 4-1 Parameters of SWD without Buffer (Type 1 ) 28 4-2 Parameters of SWD without Buffer (Type 2 ) 28 4-3 Parameters of SWD without Buffer (Type 3 ) 28 4-4 Parameters of Test Model 30 X Part I Survey of earthquake resistance technology Chapter I : Vibration control systems for earthquake resistance 1.1 Introduction Earthquakes are natural phenomena. They release large amounts of seismic energy which causes the destruction of structures. Because they are unpredictable, the damages caused by earthquakes are inevitable. The fight against earthquakes have challenged structural designers for a long time. Different issues, such as foundation conditions, the structure's configuration, the probability and of earthquakes, the extent of hazard in a structure collapse and other factors, must be considered for a structure's design. Since 1970, some new technologies have been developed to carry out earthquake resistant design. Designers have concentrated their focus on developing design strategies which reduce cost while providing greater protection against damages. In approaching earthquake resistant design, there are two common concepts that are usually adopted by designers for structural analysis. The first concept is to increase the ability of the structures 1 to suppress the seismic excitation response; by adding isolators or using more flexible material to increase ductility of and resistant potential of the structures. The second idea is to reduce the seismic vibration forces of structures. The most simple and direct way of this idea is to reduce the mass of the structure by using the light weight material . During the past fifteen years, extensive research has been conducted to make isolated structures and vibration controlled structures fully competitive with the conventional earthquake- resistant structures. These systems are powerful devices for general earthquake-resistant design. Most of the vibration energy is absorbed or consumed by the dampers and isolators. This chapter is going to discuss the new technologies in isolated structures and vibration controlled structures. 1.2 Isolation Systems For decades isolater methods have been used for vibration control of machines. It is a design strategy which separates the structure from the ground and protects it from vibrations. Generally, the horizontal seismic forces have the most serious effect on structures. How to reduce these horizontal forces and provide 2 stiffness in vertical direction is the original concept of isolated structures. The idea of using the shear yielding damper of a structure for the purpose of energy absorption is the basic concept of all the recently developed energy-absorbing devices. (1) Base isolation system: A structure with base isolaters vibrates like a rigid body. The rigid movement of the superstructure prevent the structure elements from being destroyed by inter story drift. The most common technology that has been used to achieve the base isolation is the elastomeric bearing system ( Figure 1-1 ). The typical elements of this system are elastomeric bearings and laminated steel plates. This elastomeric bearing has two important functions: (a) to carry the gravity loads of the isolated structure to the structure foundation, (b) to provide horizontal flexibility to reduce the intensity of seismic forces which are transmitted to the superstructure. Other systems that have been utilized in practice include multi-stage rubber bearing system; sliding base isolation system; rubber bearings, coupled with devices to provide additional energy dissipation ( lead, steel bar, spring ); spring units coupled with viscoelastic damper. The number of structures with base isolation apparatus has grown fast during last decade. Over 150 buildings have installed the base isolation systems for earthquake protection. 3 Figure 1-1 Base Isolater (2) Floor isolation system: Vibrations of floor surface in the vertical direction of a building become an important issue for structural design. A multi-function building which has different kind of function such as sport facilities, factories, laboratories, computer room, communication equipments and so on, requires design to prevent vibrations of floors. Floor isolation systems have been developed to deal with the problem of vibrations of floors (Figure 1-2 ). No matter what kind of floor vibrations are induced ( impact vibrations or earthquake 4 vibrations ), they can be reduced and residual vibrations can cease quickly. lilill! Figure 1-2 Floor Isolation System 1.3 Vibration Control Systems Vibration control systems can be divided into two categories: passive systems which respond to vibrations of building without use of power, and active systems which can be activated by computer- controlled actuators. The following introduces different dampers which are used in vibration resisting designs. 5 (1) The Tuned Mass Damper: A passive vibration control device which consists of an oscillated mass attached to the top of a structure and a periodic moving devices. By adjusting the frequency of the oscillator to be tuned with the natural frequency of the building, the oscillator will produce an anti-force to suppress building movements, to control vibrations of building. The most common such device is using the pendulum ( Figure 1-3 ). To install the pendulum requires more space and extra supports at the top of the building. A forty-story building requires about a 20 foot pendulum. Figure 1-3 Tuned Mass Damper 6 Another kind of Tuned Mass Damper connects an oscillated mass to isolators( Figure 1-4 ). It consists a set of multi-layer elastomeric bearing, damping material and an air brake underneath the oscillated mass. When the device deforms too much, the air brake will automatically stop the moving oscillator, to prevent damaging. This kind of damper is easy to install and requires less space than the former one. Figure 1-5 compares the acceleration of a 50-story building during strong wind with and without tuned mass damper. Figure 1-4 Tuned Mass Damper with Isolator Figure 1-5 Wind Acceleration of a 50-story Building with and without Tuned Mass Damper (2) Shear Yielding Damper: The concept of using the bracing system of a structure to disperse energy has been explored by R. W. Henry and R. G. Tayler during the 1980s. An energy-absorbing device of steel which can yield by shear deflection, is introduced at the connections of beams and braces on every floor of a building to provide passive vibration control by absorbing energy ( Figure 1-6 ). Because the design yield strength can be modified, it is possible to apply this system to control vibrations during medium and small earthquakes. Other benefits of the Shear Yielding Damper include that the same material is relatively easy to integrate with other structure elements, and it can be replaced after deformation. Figure 1-6 Shear Yielding Damper (3) Viscoelastic Damper: Viscoelastic material for damping devices has been developed for a long time. It has been utilized in many fields, especially in the aerospace industry and electromechanics, but seldom in building structures. The first use of a Viscoelastic Damper in a building was in the twin towers of the 9 World Trade Center in New York. The dampers are placed on the perimeter of the building and located at the bottom chord of trusses. Another kind of viscoelastic damper, called Viscoelastic Damping Wall, consists of a precast concrete wall and viscoelastic material ( silicon rubber or themo-plastic rubber ). The viscoelastic material, laminated between steel plates connected to the concrete wall, possesses strong adhesive qualities and produces a viscous shear force to resist shear deformation. This kind of damper provides about 19 to 20% damping to the stories of a building, and reduces the earthquake acceleration about 25 to 75% ( Figure 1-7). Viscoelastic Dampers have proven to offer a good solution to a wide range of vibrations from small tremors to large sways. They are able to provide significant increase in structure damping and show the good performance during earthquake and wind. 10 ammmm HH M m pM raM h ' ' Figure 1-7 Viscoelastic Damping Wall (4) Active Mass Damper: "he Active Mass Dampers apply an additional random force to the oscillator as reaction to the control force, it involves three consequent procedure: (a) the sensing of building vibrations by installed sensors, (b) the calculation of optimum vibration anti-force, (c) driving the actuators for building control. When a vibration signal is detected by the sensors, it will 11 immediately transmit to a computer system which analyzes the data and activates the actuators to suppress the vibrations. 12 Chapter II : Vibration Control by Water Tanks 2,1 Introduction The Sloshing Water Damper is an apparatus which utilizes hydrodynamic forces to harmonize with the natural frequency of the building. It consists of a water tank with damping devices. It is usually installed at the top of a building. The periodic motion of water within the tank will produce an anti-force to reduce the shaking of buildings. In order to have the sloshing behavior, there must be an air gap between the free water surface and the top of tank. The water mass ratio, the water period, and the damping devices are the dominant factors for controlling the seismic excitation within the tank. The appropriate proportion of water in the tank will have great influence to building vibrations. Understanding the earthquake protection by Water Sloshing Dampers requires an understanding of sloshing behavior of water. The Sloshing Water Damper is an innovative vibration control system which appears to offer the longevity and the versatility to a structure. As high-rise structures become increasingly 13 popular throughout the world, it is expected that the Sloshing Water Damper will become more popular and widely used. 2.2 Seismic Excitation in Water Tank In this section, the seismic excitation in water tanks will be introduced. A typical movement of sloshing water is shown in Figure 2-1. This kind of water movement could be separated into two parts: the upper motion and the lower motion. The upper motion of water is what we call the slosh motion, it is excited by horizontal forces and moves antisymmetrically in the tank." The amplitute of the sloshing water indicates the intensity of the ground motion " ( Housner G,W, 1957). The lower motion of water acts as a rigid mass, it could be excited by both vertical and horizontal forces. Figure 2-2 shows the frequencies and mode shape of water for a cylindrical tank on a 1/30 scale model.( Kana, D, D, 1984 ) 14 Shaking Direction Sloshing Part Rigid Part Figure 2-1 Typical Movement of Sloshing Water n Prototype Freq , Hz l/30Model Freq , Hz Mode Shapes 1 0.135 0.738 2 0.268 1.467 3 0.339 1.856 4 0.397 2.174 Figure 2-2 The Frequencies and Mode Shape of Water 15 2.3 Dynamic Response of Water Tank With different water to tank ratios, the dynamic behavior will be quite different . If a closed elevated tank is full of water or completely empty, the behavior is like a lumped mass put at the top of a cantilever beam. If a closed elevated tank has a space between water surface and tank, there will be a sloshing behavior of water with complicated dynamic response. The most popular method used for analysising the water behavior is the simple equivalent mass analysis method. It uses the equivalent mass to substitude the water mass for approaching the dynamic response. In this method the total mass M of water is divided into two equivalent masses: the convective mass M' ( sloshing portion ) and the impulse mass M" ( rigid portion ). The mass M' can oscillate in a tank of height H' against a restraining spring K'. The mass M " is attached rigidly to the tank at the height H". A tank with water mass M is subjected to an earthquake, the force exerted on the tank wall by mass M will be similar to the combined force of both M' and M". ( Figure 2-3 ) 16 Figure 2-3 Two Equivalent Masses of Sloshing Water Table 2-1. lists the simple equivalent mass analysis Equations. The sloshing response of water can be calculated in the follow steps ( Kana D, D, 1984 ): 1. Calculate M ', H I1 and H2' values. H I' is considered excluding the dynamic water pressure on the bottom and H 21 is including the dynamic water pressure on the bottom. 2. Calculate the natural frequence W from the water quantity and the spectral velocity response V which may be obtained for the appropriate damping from the design response spectrum curve for horizontal motion at the level where the tank is located. 17 3. Using V, compute the maximum amplitude A of the mass M ', the angle of free oscillation Q' at the water surface, and the convective force P'. 4. Calculate the maximum surface displacement D ( above the original horizon ) from the value of W and Q1 ; then compute the maximum base shear and moment stress due to slosh response. 18 Table 2-1. The Simple Equivalent Mass Analysis Equations for Sloshing water C '= (tanh(1.7*L/H)) / (1.7*L/H) M '= M * C' H I' =0.375*H H 2'=0.125*(4/C ' -1) P '= a / g*M' C" = 1.58H/L M" =0.527*M*L/H*tanh(C") H I" = H (1- (cosh(C') -1) / (C"*sinh(C"))) H2" =H(1- (cosh(C") -2.01) / (C"*sinh(C"))) W A 2 = 1.58*G/L*tanh(C") Q' = 1.58*A/L*tanh(C") P" =0.67*d*L*3*W"2*sinWT D = P7 (q*(G - A*Q')) 19 Part II Researches of Sloshing Water Damper Chapter III : Feasibility Study of the Sloshing Water Damper for Retrofitting Structures 3.1 Introduction One of the most crucial problems that engineers are concerned about is the seismic hazard to existing buildings. Compared to the old structures, designers of new structures have more powerful tools, new material, more reliable builders, and new seismic technologies to improve the resistant ability of structures. Accordingly new structures have better potential in resisting earthquake than those built in the past. If a structure has been declared a seismic hazard or an inadequate seismic resistance structure, consideration should be given to upgrade it. In some particular case, for example, the preservation of antique or historic buildings, the project of limited budget, the retrofitting of a nuclear structure, etc, the integration of Sloshing Water Damper plays an important role in retrofitting such structures. 2 0 3.2 Application of Sloshing Water Damper in Existing Building The Sloshing Water Damper has been prooven an efficient vibration control system in mitigating the seismic performance of existing structures. Some of the special characteristics and important features are listed below to illustrate the versatility of Sloshing Water Damper to the existing structures. 1. Because of outdated codes and material, existing structures often have less ductility and strength than new structures. The Sloshing Water Damper can improve the deficiency of structures by means of energy absorption. 2. This system can deal with strong earthquakes as well as little tremors induced by light wind. A strong ground acceleration will induce a great turbulence inside the water tank. In order to avoid the additional risk of destroying the water tank, some energy absorbing devices ( like rigid buffer and damping net ) are required to put into the tank for suppressing the turbulence. 3. According to past experience, structural designers attribute major structure failures to irregularities in floor plan. Due to directional free oscillated behavior the Sloshing Water Damper can suppress torsion induced by irregular configuration. 2 1 4. Many of the new seismic technologies which are utilized in retrofitting conventional structures require special equipment and skilled workers. Economic consideration is a major factor in retrofitting. Expensive equipment or elements and high-cost skilled workers will increase the cost of the project. Besides, the alteration of the internal elements of the structure could interrupt or interfere with the function of the building. The ability of the Sloshing Water Damper to control the vibration of the structure, to absorb substantial amounts of seismic energy, and to improve the adverse effect of seismic excitation response provide an important motivation to install this system for retrofitting old structures. The dependability and economy of equipment make this system one of the best options for retrofitting seismically deficient structures. 2 2 3.3 Case Study Name of the structure : Golden Tower Location : Kagawa Prefecture , Japan Usage : Observatory Tower Designer / Constructor : Mitsui / Mitsui Completion : 1988 The Golden Tower is a panoramic tower, located besides the Seto-Ohashi bridge. The height of the tower is 158 m and its plan is similar to a rhombus. The top three stories are observatory rooms. The intermediate part, which is between the observatory rooms and the bottom two stories, is an empty space supported by steel frames. The bottom part is a two story space with a steel reinforced concrete structure. The exterior of the whole structure is covered with a glass curtain wall. The goal of this design was to suppress the vibrations induced by seasonal wind by means of installing a Tuned Liquid Damper at the top of the structure. This Tuned Mass Damper is a vibration control device consisting of stainless steel water tanks with 2.5m in length, 0.45m in width, lm in height, and some damping nets. 16 water tanks were installed at the top of the building. The water 23 period was adjusted to harmonize with the fundamental period of the structure. The weight of the water is 9.5t, it is approximately 1 percent of the structure weight. Figure 3-1 shows the excitation curve of The Golden Tower with and without Tuned Liquid Damper by applying the free oscillated vibrations. The ordinate is indicated the maximum lateral drift of the structure. The result of the foregoing shows a structure with Tuned Liquid Damper has excellent damping characteristics against wind-induced vibrations. 3 01 (1) Without s&fcper (Z) W ith damper n 2 0 4 0 so m Figure 3-1 The Excitation Curve of the Golden Tower 24 Chapter IV Earthquake Simulation Testing 4.1 Objectives To investigate the technology of Sloshing Water Damper in buildings, three testing models were made to approach this research. The objective of this research were to (1) perform earthquake simulation tests of mid-rise buildings, incorporating with Sloshing Water Damper; (2) contrast the seismic response of computer simulation with the result of model testing; (3) evaluate the efficency of water sloshing damper by comparing result of buildings with and without the damper; (4) optimize the relationship of water frequency and weight for different building heights. 4.2 Assumptions 1. Description of prototype building Building length : 150 feet 25 Building width Floor height Floor area Dead load Structure : 150 feet : 14 feet : 22500 square feet : 100 psf : Moment resist frame 2. Testing model The test model consists of plywood sheets, piano wires and fishing weights ( Figure 4-1 ). Each plywood sheet is 15" * 15" square. The interior part of the plywood sheet is a moveable sheet whose size is 12" *12". The density of the plywood sheet is 0.0203 lb / inA 3 . Each plywood sheet weights 3.41b.The period ' T ' of the testing model is adjustedly the global mass ' M ' of the model by removing the moveable plywood sheets or adding the fishing weights to the model ( T = 6.28*( M / K )A l/2 ). Piano wires 1/16" in diameter are used to simulate columns. The moment of inertia of the piano wire equals 7.5 * 10A -7 inA 4. Columns of the model are considered as cantilevers.The stiffness ' K ' of the columns are inverse proportional to third power of the 26 column length. The model connections between piano wires and plywood sheets are assnmed as fixed connections. According to the Euler's equation P=(3.12) A 2*EI/LA 2 the maximum load which a piano wire of 1/16" diameter can take equals 11 lb. The total weight of the model equals 8*3.4(lb) = 27 lb which can be supported by four piano wires. In order to observe the sloshing behavior of water the water tanks are made of transparent plastic glass ( Figure 4-2 ). The calculation of the sloshing behavior is based on the equivalent mass analysis method and the connection between the water tank and the floor was fixed. The natural periods of sloshing water with different parameters are shown in Tables 4-1 to 4-3. 27 Table 4-1. Parameters of SWD without buffer ( Type 1 ) M Ratio L (in) W (in) H (in) D Ratio T(sec) Wt(lb) 1% 14 4 0.17 41.2 3.47 0.33 2% 14 4 0.33 21.2 2.46 0.67 3% 14 4 0.5 14 2 1 4% 14 4 0.67 10.4 1.74 1.33 5% 14 4 0.83 8.4 1.56 1.67 Table 4-2. Parameters of SWD with one buffer ( Type 2 ) M Ratio L (in) W (in) H (in) D Ratio T(sec) Wt(lb) 1% 7 4 0.17 20.6 1.74 0.17 2% 7 4 0.33 10.6 1.23 0.34 3% 7 4 0.5 7 1.01 0.5 4% 7 4 0.67 5.2 0.88 0.67 5% 7 4 0.83 4.2 0.79 0.84 Table 4-3. Parameters of SWD with three buffers ( Type 3 ) M Ratio L (in) W (in) H (in) D Ratio T(sec) Wt(lb) 1% 3.5 4 0.17 10.3 0.93 0.09 2% 3.5 4 0.33 5.3 0.66 0.17 3% 3.5 4 0.5 3.5 0.55 0.25 4% 3.5 4 0.67 2.6 0.49 0.34 5% 3.5 4 0.83 2.1 0.45 0.42 2 8 IM M iffiil t - i ^ s i '- S i ^ - 'P ’ ! j ' f ! ' ! ; ' ! ' " ‘ ‘ j ' i JiQHyiiijj IlBlii S & s-K w feiWx>>:vv.>- Figure 4-1 The shaking devices Figure 4-2 The Sloshing Water Damper 29 4.3 Testing Proceedure (1) The shaking device consists of a IBM personal computer XT with digital / analogue converter board, an amplifer, an electrodynamic shaker, and a suspended platform which is hung by four cables to hold models. (2) Three different height of testing models,(4 stories, 8 stories and 16 stories), are made of steel piano wire and plywood. Table 4-4 shows the natural period, damping ratio, diameter of piano wire and the model weight of the three buildings. Table 4-4. Parameters of test model story N(sec) Dr D(in) W(lb) 4 0.44 4.6% 0.625 14.5 8 0.88 4.6% 0.625 29 12 1.2 4.6% 0.625 50 N : natural period Dr : damping ratio D : diameter of piano wire W : model weight 30 (3) Three water tanks with different number of damping buffers are used in the tests. Different mass ratio ( water mass / building mass ) and dimension ratio ( sloshing length / water height ) were considered as testing parameters. Two positions were choosen to install the sloshing damper: top of model and 2/3 height of model. (4) Inpute seismic motion: The three models were subjected to random seismic excitation in one direction. The seismic motion was based on a time-displacement spectrum provided by the Department of Geological Sciences at USC. The input intensity level of the simulated earthquake lasts about 30 second and the maximum ground displacement is 1.5". 31 4.4 Test Results Test 1. Four-story building with SWD at top of model. A four-story model with mass ratios of 2, 3, and 4% of SWD was used in this test and compared with the results of the model without SWD. For all test condition, the uniform load of each floors and the element properities remained constant. Both models showed similar behavior at the first floor, but different responses from second floor to the roof. Figure 4-4 to 4-6 show the maximum response displacement ratio of the three SWD. The vertical axis in the figures indicate the maximum displacement ratio ( X/ X' ), the " X " stands for the maximum displacement with SWD and the "X ' " stands for the maximum displacement without the SWD. In the prototype model, the acceleration increased slightly from the first floor 0.09g to the roof 0.12g (Figure 4-10), but the model with SWD has an increased acceleration at second floor, for type 1 and type 2 increased about 0.05g, type 3 increases 0.04g. At the top, the model with 4% mass ratio of typel SWD has the largest increasement of 0.08g, the rest increase about 0.04g. The reason for the floor acceleration increase is the stiffness of the structure. 32 The stiffness of lower building is greater than that for the taller building. The greater stiffness makes the water tank and the structure tend to behave like a rigid body. Therefore, the sloshing water cannot produce an inertial force to decrease the lateral force. 33 Test 2. Eight-story building with SWD at top of model. A eight-story model with mass ratios of 1 to 5 % SWD was used to compare the results of the model without SWD. For all test conditions, the uniform load of each floors and the element properities were constant. Figure 4-13 to 4-15 show the maximum response displacement ratio of the three SWD. The vertical axis in the figure indicates the maximum displacement ratio ( X/ X' ),the " X " stands for the maximum displacement with SWD and the "X ' " stands for the maximum displacement without the SWD. In the three figures, there is one common increasing peak ( maximum displacement ratio > 1 ) at either third or fourth floor. After the peak, the displacement ratio begin to drop to less than 1. In the prototype model, the acceleration increases from the first floor's 0.03g to the roofs 0.6g ( Figure 4-19 ). This explained that the whip force is the critical factor which causes the acceleration increase at the top of the model. Comparing the floor acceleration of the model with and without SWD : the model with SWD has an increased acceleration of about 0.06g at mid-height ( from second 34 floor to fifth floor ), but has drastically dropped at the top floor. For type 1 SWD with 5% mass ratio, the acceleration decreased about O.lg. For type 2 SWD with 5% mass ratio, the acceleration decreased about 0.24g. For type 3 SWD with 5% mass ratio, the acceleration decreased about 0.28g. It seemed that the whip force of the top floor was suppressed by the inertial force produced by the sloshing water. The results also showed that the optimum water period of SWD should be controlled equal or less than the building period. The longer water period will cause the conflict actions in the water tank which make SWD less efficient. 35 Test 3. Eight-story building with type 3 SWD at seventh floor of model. A eight-story model with mass ratios of 1 to 5 % type 3 SWD was installed at seventh floor to compare with the results of the model without SWD. For all test condition, the uniform load of each floors and the element properities remained constant. Figure 4-22 shows the maximum response displacement ratio of the SWD. The vertical axis in the figure indicates the maximum displacement ratio ( X/ X 1 ),the " X " stands for the maximum displacement with SWD and the 1 1 X 1 " stands for the maximum displacement without the SWD. In this figure, the results are similar to test 2. We can find a increasing peak ( displacement ratio > 1 ) at the third floor. Above the peak, the displacement ratio begin to drop to less than 1. The seventh floor ,which is the SWD, has the best performance of the structure. In the prototype model, the acceleration increased from the first floor's 0.03g to the roofs 0.6g ( Figure 4-24 ). Comparing the model with SWD to the model without SWD: at the first two floors the acceleration remained the same, but at the third floor the model with SWD had an increased acceleration of about 0.08g. The floor 36 acceleration start to decrease at the fourth floor. The model with 5 % mass ratio of type 3 SWD decreases 0.18g at seventh floor, and 0.15 g at the top floor. In this test, the SWD does not drastically suppress the vibration energy. This is because the floor acceleration at which SWD is located for this test is smaller than in test 2. Therefore the inertial force produced by the sloshing behavior is small than in test 2. 37 Test 4. Sixteen-story building with SWD at top of model A sixteen-story model with mass ratios of 1 to 5 %, of SWD was used to compare with the result of the model without SWD. For all test condition, the uniform load of each floor and the element properities remaned constant. In general, the maximum displacement ratio of the model with type 1 and type 2 SWD from the first floor to the eleventh floor was similar to a linear relation ( value equal to 1 ). In the upper stories, all the ratio dropped less than the value of 1. It meaned that the model with SWD deforms less than the prototype model. For the model with type 3 SWD was a little bit different than the former two. There was one increasing peak at eleventh floor, but after the peak the ratio drop less than 1. In the prototype model, the acceleration increased from the first floor 0.01 g to the roof 0.45g ( Figure 4-31 ). From the first floor to the eleventh floor, the floor acceleration of the model with SWD increased about 0.02g than the prototype, but at the upper stories the floor acceleration of the model with SWD was less than the prototype. For type 1 SWD with 5% mass ratio, the acceleration 38 decreased about O.lg. For type 2 SWD with 5% mass ratio, the acceleration decreased about 0.15g. For type 3 SWD with 5%mass ratio, the acceleration decreased about 0.17g. 39 M a x Displacement R a tio ( inch) M a x Displacement R a tio ( inch) M a x Displacement R a tio ( inch) Figure 4-4 The Displacement Ratio for 4-story Building (Type 1 SWD) Floor Figure 4-5 The Displacement Ratio for 4-story Building (Type 2 SWD) ■ With 2 « Water - f - Witk 3% Water ■**- With 4% Water Figure 4-6 The Displacement Ratio for 4-story Building (Type 3 SWD) With z% Water — H With 3% W ater With 4% Water 40 Figure 4-7 The inter Story Drift for 4-story Building (Type 1 SWD) Floor I B B Without SWD — With 2% W .t.r C O WiU 3 » W .lrr F T !W IU «*> W .K r Figure 4-8 The Inter Story Drift for 4-story Building (Type 2 SWD) Floor [EBB Without SWD — Will. 2 * W .lrr Willi 3% W «l.r IT I Will. ♦% W«lrr Figure 4-9 The Inter Story Drift for 4-story Building (Type 3 SWD) Floor B O Wilhwil SWD — W ilt 2% W .lrr B Q W itt 3 * W .lrr With 4% W .lrr 41 ( 6 ) u o « B j » ( » 3 a v Figure 4-10 The Floor Acceleration for 4-story Building (Type 1 SWD) 0.25- ' Floor | B B I Witho.1 SWD With 2% W .ltr (S3 With 3% W ««r F P | Witli 4% W«t«r | Figure 4-11 The Floor Acceleration for 4-story Building (Type 2 SWD) I M W itto .i SWD M With 2% W .H t r e i With 3% W .H t I T I With 4% W .u r Figure 4-12 The Floor Acceleration for 4-story Building (Type 3 SWD) a w 025- ’ Floor [BHW Itlwm t SWD 2‘ % Water g q With 3% Water F T I With 4% Water 42 M a x Diaplacamant R a tio M a x DisplaeamarTt R a tio M a x Diaplacamant Ratio Figure 4-13 The Displacement Ratio for 8-story Building (Type 1 SWD) Floor With \% W ater -4— With 2% Water * * With 3% Water With 4% W ater -M> With 5% Water Figure 4-14 The Displacement Ratio for 8-story Building (Type 2 SWD) Floor * With 1% Water With 2% Water -M* With 3 * Water - 5 - With 4% W ater > 4 With $% Water Figure 4-15 The Displacement Ratio for 8-story Building (Type 3 SWD) Floor * With 1% Water H - With 2% Water With 3% Water ■ & With 4% Water * * With 5% Water 43 Figure 4-16 The Inter Story Drift for 8-story Building (Type 1 SWD) 1 2 9 4 5 6 7 8 Floor Q Q W itk 1* W a te r W illi 2% W a te r TO W ith 3 % W a te r 03 W ith 4% W a te r P71 W itt 5* W a te r E T ) 3 W ith e a t S W D Figure 4-17 The Inter Story Drift for 8-story Building (Type 2 SWD) 1 2 3 4 5 6 7 8 Floor IB B W itt 1% Water W itt 2% Water With V h Water m w i t t 4% Water 1 7 3 W itt 5 * Water t V l W lttoat SWD Figure 4-18 The Inter Story Drift for 8-story Building (Type 3 SWD) 1 2 3 4 5 6 7 8 Floor B Q W ilt \% Water ■ W itt 2% Water Q Q With Vk, Water P H I W itt 4 * Water ^ 3 With 5 * Water E 7 3 W lttoat SWD Figure 4-19 The Floor Acceleration for 8-story Building {Type 1 SWD) Ol 5 Floor s s With 1% Water | With 2% Water ES With 34b Watar ^ 3 Witk 4% W«l«r r~71 Willi 5% Watar ETSa Whkaar SWD Figure 4-20 The Floor Acceleration for 8-story Building (Type 2 SWD) u < Floor B P Wilk 1% Water H Witk 24b Wafer S 3 Wi,k V h WaHr □ □ W itk 44b Wafer 1 7 3 Witk Wafer Wllkeal SWD Figure 4-21 The Floor Acceleration for 8-story Building (Type 3 SWD) 5 Floor g g Witk 1% Wafer H Witk 2% Wafer Witk 34b Wafer ^ 3 Wilk 4% Wafer m Wilk it> Wafer 17*3 Wilkaal SWD 45 Acceleration (g ) Inter S tory D r if t ( inch) M a x Displacement Ratio Figure 4-22 The Displacement Ratio for 8-story Building (Type 3 SWD at 7F) Floor • Witk 1% Water - I - Witk 24k W attr Witk 34k W attr Witk 44k W attr X - Witk 5% Water Figure 4-23 The Inter Story Drift for 8-story Building (Type 3 SWD at 7F) Floor B B Witk 1% W attr m Witk 2% W attr IT O Witk 34k W attr m i Witk 44k W tttr m i Witk 54k W attr m Witkott SWD Figure 4-24 The Floor Acceleration for 8-story Building (Type 3 SWD at 7F) Roor e g Witk 1 4k W attr m Witk 24k W attr Q ] Witk 3% Water ED Witk 44k W attr F71 Witk 54k W attr Witkoat SWD 46 M a x Displacement R atio (inch) M a x Displacement R a tio (inch) M a x Displacement R a tio (inch) Figure 4-25 The Displacement Ftatio for 16-story Building (Type 1 SWD) Floor •M* W itt 1% Water Witk 2% Wafer Witk 3% Water •S-W itfc 4% Water X - With 5% Water Figure 4-26 The Displacement Ratio for 16-story Building (Type 2 SWD) Floor * Witk 1% Water - 4 * With 1% Water * * With 3% Water With 4% Water With 5% Water Figure 4-27 The Displacement Ratio for 16-story Building (Type 3 WSD) Floor * With 1% Water With 2% Water With 3 * Water ■ & With 4 ^ Water > 4 With 5% Water 47 Figure 4-28 The Inter Story Drift for 16-story Building (Type 1 SWD) 1< l: 1 1 i Floor e g Witk I * W attr ■ Witk 2% W attr E Q Witk 3 * W attr F P I Witk 4 * W attr P 7 1 Wilk 5 * W attr 17*3 Witkoat SWD Figure 4-29 The Inter Story Drift for 16-story Building (Type 2 SWD) 1« l; i< I I I Floor S B Witk I * W attr H w itk 2% W a ttr C T Wilk V k W attr m Wilk 4% W attr X7~\ Witk S% W attr P 7 1 Witkaal SWD Figure 4-30 The Inter Story Drift for 16-story Building (Type 3 SWD) 1 3 5 7 9 11 13 15 Floor (S B Witk 1% Water H Witk 2% Water (S Wttk 3% Water F T ! Witk 4% Water Witk 5% Water ^ 3 Witkoat SWD 48 Acceleration (g ) Acceleration (g) Figure 4-31 The Floor Acceleration for 16-story Building (Type 1 SWD) 3 I Floor C M With 1% Water H Witk 2 * W attr Q J Witk 3% W attr E B Witk 4% W tttr m Witk 5% W attr f7S3 Witkaat SWD Figure 4-32 The Floor Acceleration for 16-story Building (Type 1 SWD) ;------- m m M 1 il 1 3 S 7 9 11 19 IS Floor B B Witk 1% W tttr H Witk 2% W tttr IT O Witk 3*. Water m Witk 4% W attr ( 7 3 Wilk 5% W tttr m Wltkaat SWD Figure 4-33 The Floor Acceleration for 16-story Building (Type 3 SWD) Floor BBIW itk 1% W attr H Witk 2 * Water [ Q Witk 3% W attr m Witk 4% Water P 7 1 Witk S% Water Witkoat SWD 49 Chapter V Computer Simulation 5.1 Assumptions 1. Description of earthquake and site location The earthquake spectrum used for this simulation is the EL- CENTRO earthquake of May 1940 . The location of the site is assumed near the Newport-Inglewood fault and the position of the alluvium layer is assymed between 10'-80' ( Figure 5-1 ), according to the fault map of the California Department of Transportation Division of Structures ( Figure 5-2 ), the peak rock acceleration is 0.7g. Figure 5-1 The Level of Peak Rock Acceleration 50 Figure 5-2 CALTRANS - Fault Map 2. Description of the simulated model Building length : 15 in Building width : 15 in Building height : 33 in Floor area : 225 sq.in Dead load : 0.015 psi Structure : Moment resist frame Diameter of column : 0.063 sq.in Damping ratio : 5 % 51 5.2 Simulation Results Simulation 1: Four-story building with SWD at top of model A four-story building with mass ratio 4% of SWD was used to compare with the results of the building without SWD. For all simulation conditions, the uniform load of each floor and the element properities remained constant. Although the earthquake of this simulation is different from the one used in the model testing, The result of this computer simulation is similar to the test result. The sloshing behavior of the SWD does not absorb the vibration energy of the earthquake. The high stiffness of the building makes the sloshing water tend to increase the floor acceleration at the top of the building. For type 1 SWD, it increases 0.16g, type 2 is 0.14g, type 3 is 0.06g ( Figure 5- 4 ). 52 Simulation 2 : Eight-story building with SWD at top of model A eight-story building with mass ratio 4% of SWD was used to compare with the results of the building without SWD. For all simulation condition, the uniform load of each floor and the element properities remained constant. Figure 5-6 shows the maximum response displacement ratio of the simulation. For the type 1 SWD the maximum displacement ratio is similar to a linear relation and the value of the ratio are around 0.96. For type 2 and 3 the ratio are like smooth curves with negative cvrvature. In the prototype building, the acceleration increases from the first floor 0.04g to the roof 0.71g ( Figure 5-6 ). By comparing the floor acceleration, for the building with type 1 SWD ,the result is similar to the prototype.The floor acceleration of type 2 and 3 increase in the lower and middle stories, but decrease at the upper stories of the building. For type 2 SWD, it decreases 0.36g, for type 3 is 0.35g, this result is different from the testing result. 53 Figure 5-3 Computer Simulation for 4-story Building with Mass Ratio 4% 1.4 - 0.9- 5 0.8 - 0.7- 0.8- 0.5- 0.4- RF Floor Type 1 SWD - + - Type 2 SWD Type 3 SWD Figure 5-4 Computer Simulation for 4-story Building with Mass Ratio 4% 1 0.9 o.8-n 0.7- 3 0.6- 2 0.5- § 0.4- Floor KH8 Type 1 SWD H Type 2 SWD Type 3 SWD EOT Without SWD 54 Ratio Figure 5-5 Computer Simulation for Building with Mass Ratio 4% S 0.8- 0.7- 0.6- 0.5- 0.4- RF Floor Type 1 SWD - 4 - Type 2 SWD -#r- Type 3 SWD Figure 5-6 Computer Simulation for 8-story Building with Mass Ratio 4% i-i 1 2 3 4 5 6 7 8 Floor BBS Type 1 SWD Type 2 SWD g ^ j] Type 3 SWD ^ Type 1 Testing 55 Chapter VI Conclusion Based on the numbers of tests and computer simulation, the conclusions of this research are summarized as follows: 1. The Sloshing Water Damper system is capable of reducing the vibration of the structure efficiently if the mass ratio, dimension ratio and the damping buffers are properly designed. 2. The Sloshing Water Damper system is appropriate for the mid-rise and high-rise building, due to the low stiffness, but not effective for low-rise building. 3. The floor acceleration response value decreases with increasing mass ratio and with number of buffer in the water tank. 4. Numerical simulation can be performed by the equivalent mass analysis method. The results of simulation have been found to be in good agreement with the experimental results. 56 Appendix A : Test data Test 1 : (1) Maximum displacement of each floor of type 1 SWD Mass Ratio Floor Proto 2% 3% 4% 1 F 2.48 2.48 2.48 2.48 2F 2.81 2.75 2.72 2.7 3F 3.33 3.26 3.26 3.26 4F 3.71 3.93 4.04 4.04 RF 3.94 4.41 4.41 4.96 (2) Maximum displacement of each floor of type 2 SWD Mass Ratio Floor Proto 2% 3% 4% 1F 2.48 2.48 2.48 2.48 2F 2.81 2.77 2.77 2.77 3F 3.33 3.29 3.29 3.3 4F 3.71 3.81 3.8 3.8 RF 3.94 4.34 4.37 4.37 57 (3) Maximum displacement of each floor of type 3 SWD Mass Ratio Floor Proto 2% 3% 4% 1F 2.48 2.48 2.48 2.48 2F 2.81 2.81 2.81 2.81 3F 3.33 3.38 3.37 3.37 4F 3.71 3.83 3.84 3.8 RF 3.94 4.46 4.38 4.28 (4) Inter Story Drift of each floor of type 1 SWD Mass Ratio Floor Proto 2% 3% 4% 1 F 0.33 0.3 0.26 0.21 2F 0.36 0.5 0.52 0.58 3F 0.38 0.53 0.56 0.69 4F 0.43 0.63 0.7 0.77 (5) Inter Story Drift of each floor of type 2 SWD Mass Ratio Floor Proto 2% 3% 4% 1F 0.33 0.3 0.3 0.3 2F 0.36 0.52 0.52 0.53 3F 0.38 0.51 0.51 0.5 4F 0.43 0.53 0.57 0.57 58 (6) Inter Story Drift of each floor of type 3 SWD Mass Ratio Floor Proto 2% 3% 4% 1 F 0.33 0.33 0.34 0.33 2F 0.36 0.46 0.47 0.43 3F 0.38 0.57 0.56 0.56 4F 0.43 0.63 0.54 0.48 (7) Floor acceleration of each floor of type 1 SWD Mass Ratio Floor Proto 2% 3% 4% 1F 0.09 0.08 0.07 0.06 2F 0.09 0.14 0.14 0.15 3F 0.1 0.15 0.14 0.18 4F 0.12 0.17 0.19 0.2 (8) Floor acceleration of each floor of type 2 SWD Mass Ratio Floor Proto 2% 3% 4% 1 F 0.09 0.08 0.08 0.08 2F 0.09 0.14 0.14 0.14 3F 0.1 0.14 0.14 0.14 4F 0.12 0.14 0.15 0.15 59 (9) Floor acceleration of each floor of type 3 SWD Mass Ratio Floor Proto 2% 3% 4% 1 F 0.09 0.09 0.09 0.09 2F 0.09 0.13 0.13 0.13 3F 0.1 0.15 0.15 0.15 4F 0.12 0.17 0.15 0.14 60 Test 2 (1) Maximum displacement of each floor of type 1 SWD Floor Mass Ratio Proto 1% 2% 3% 4% 5% 1 F 3.04 3.04 3.04 3.04 3.04 3.04 2F 3.01 2.93 2.99 3.1 2.93 3.12 3F 2.48 2.86 2.86 2.88 2.88 2.86 4F 2.25 2.04 2.03 2.12 2.12 2.45 5F 2.48 2.03 2.03 2.03 2.25 2.32 6F 3.1 2.82 2.61 2.45 2.42 2.95 7F 4.95 4.16 3.78 3.59 3.34 4.05 8F 6.68 5.63 5.36 4.98 4.63 4.95 RF 8.89 7.65 7.43 7.09 6.98 6.64 (2) Maximum displacement of each floor of type 2 SWD Floor Mass Ratio Proto 1 % 2% 3% 4% 5% 1 F 3.04 3.04 3.04 3.04 3.04 3.04 2F 3.01 3.31 3.15 3.15 3.15 3.15 3F 2.48 2.83 2.86 2.86 2.87 2.93 4F 2.25 2.47 2.48 2.48 2.47 2.42 5F 2.48 2.03 2.02 2.03 2.12 1.89 6F 3.1 2.7 2.48 2.19 2.24 2.05 7F 4.95 3.82 3.42 3.1 2.93 2.51 8F 6.68 5.4 5.12 4.81 4.39 2.86 RF 8.89 7.2 6.84 6.25 5.86 4.05 61 (3) Maximum displacement of each floor of type 3 SWD Floor Mass Ratio Proto 1% 2% 3% 4% 5% 1F 3.04 3.04 3.04 3.04 3.04 3.04 2F 3.01 3.15 3.15 3.15 3.15 3.15 3F 2.48 3.1 3.06 3.02 3.12 3.13 4F 2.25 2.7 2.52 2.38 2.52 2.93 5F 2.48 2.14 2.22 2.3 2.39 2.48 6F 3.1 2.23 2.31 2.38 2.38 2.39 7F 4.95 2.54 2.51 2.46 2.44 2.43 8F 6.68 3.86 3.52 3.15 2.86 2.62 RF 8.89 5.13 4.91 4.73 4.32 3.98 (4) Inter Story Drift each floor of type 1 SWD Floor Mass Ratio Proto 1% 2% 3% 4% 5% 1F 0.03 0.1 0.05 0.06 0.1 0.08 2F 0.52 0.05 0.1 0.22 0.05 0.26 3F 0.23 0.84 0.85 0.76 0.76 0.41 4F 0.23 0 0 0.09 0.12 0.22 5F 0.62 0.79 0.58 0.41 0.17 0.72 6F 1.85 1.34 1.16 1.14 0.92 1.1 7F 1.73 1.47 1.58 1.39 1.28 0.76 8F 2.21 2.03 2.07 2.11 2.02 1.89 62 (5) Inter Story Drift each floor of type 2 SWD Floor Mass Ratio Proto 1% 2% 3% 4% 5% 1F 0.12 0.09 0.11 0.11 0.11 0.06 2F 0.22 0.24 0.24 0.25 0.27 0.28 3F 0.34 0.52 0.52 0.56 0.56 0.56 4F 0.42 0.58 0.62 0.62 0.61 0.61 5F 0.62 0.66 0.66 0.67 0.65 0.65 6F 1.42 1.06 1.06 1.06 1.02 1 7F 1.72 1.22 1.22 1.18 1.18 1.16 8F 2.24 1.57 1.56 1.42 1.42 1.35 (6) Inter Story Drift each floor of type 3 SWD Floor Mass Ratio Proto 1% 2% 3% 4% 5% 1 F 0.12 0.11 0.11 0.11 0.09 0.09 2F 0.34 0.34 0.34 0.34 0.34 0.37 3F 0.34 0.44 0.46 0.46 0.46 0.46 4F 0.42 0.67 0.67 0.7 0.7 0.7 5F 0.62 0.69 0.69 0.72 0.7 0.72 6F 1.42 1.27 1.25 1.25 1.2 1.2 7F 1.72 1.42 1.32 1.32 1.3 1.27 8F 2.24 1.32 1.3 1.3 1.25 1.25 63 (7) Floor acceleration of each floor of type 1 SWD Floor Mass Ratio Proto 1% 2% 3% 4% 5% 1 F 0.03 0.03 0.02 0.02 0.03 0.02 2F 0.06 0.07 0.07 0.08 0.09 0.09 3F 0.09 0.11 0.11 0.1 0.1 0.1 4F 0.12 0.14 0.14 0.18 0.16 0.18 5F 0.18 0.21 0.18 0.21 0.23 0.23 6F 0.38 0.36 0.36 0.36 0.34 0.34 7F 0.46 0.4 0.41 0.4 0.36 0.35 8F 0.6 0.54 0.56 0.56 0.54 0.5 (8) Floor acceleration of each floor of type 2 SWD Floor Mass Ratio Proto 1% 2% 3% 4% 5% 1 F 0.03 0.03 0.03 0.03 0.03 0.02 2F 0.06 0.07 0.07 0.07 0.08 0.09 3F 0.09 0.14 0.14 0.16 0.16 0.16 4F 0.12 0.16 0.18 0.18 0.18 0.18 5F 0.18 0.22 0.22 0.24 0.24 0.24 6F 0.38 0.34 0.34 0.34 0.33 0.31 7F 0.46 0.38 0.38 0.35 0.35 0.32 8F 0.6 0.46 0.44 0.41 0.38 0.36 64 (9) Floor acceleration of each floor of type 3 SWD Floor Mass Ratio Proto 1% 2% 3% 4% 5% 1 F 0.03 0.03 0.03 0.03 0.03 0.02 2F 0.06 0.07 0.07 0.07 0.08 0.09 3F 0.09 0.14 0.14 0.16 0.16 0.16 4F 0.12 0.16 0.18 0.18 0.18 0.18 5F 0.18 0.22 0.22 0.24 0.24 0.24 6F 0.38 0.34 0.34 0.34 0.33 0.31 7F 0.46 0.38 0.38 0.35 0.35 0.32 8F 0.6 0.43 0.42 0.38 0.35 0.32 65 Test 3 (1) Maximum displacement of each floor of type 3 SWD Floor Mass Ratio Proto 1% 2% 3% 4% 5% 1 F 3.04 3.04 3.04 3.04 3.04 3.04 2F 3.01 3.16 3.15 3.15 3.17 3.2 3F 2.48 2.89 2.86 2.81 2.89 3.02 4F 2.25 2.28 2.27 2.27 2.23 2.48 5F 2.48 1.9 1.83 1.87 1.9 1.92 6F 3.1 2.36 2.31 2.36 2.35 2.35 7F 4.95 3.46 3.38 3.23 3.34 3.24 8F 6.68 5.43 5.36 5.06 4.93 4.83 RF 8.89 6.89 6.64 6.18 5.9 5.72 (2) Inter story drift of each floor of type 3 SWD Floor Mass Ratio Proto 1% 2% 3% 4% 5% 1 F 0.12 0.13 0.12 0.11 0.11 0.13 2F 0.22 0.35 0.27 0.3 0.32 0.29 3F 0.34 0.53 0.61 0.59 0.54 0.64 4F 0.42 0.36 0.38 0.44 0.39 0.34 5F 0.62 0.48 0.46 0.49 0.49 0.46 6F 1.42 1.52 1.1 1.06 0.87 0.86 7F 1.72 1.86 1.85 1.86 1.83 1.58 8F 2.24 2.21 1.46 1.29 1.12 0.89 66 (3) Floor acceleration of each floor of type 3 SWD Floor Mass Ratio Proto 1% 2% 3% 4% 5% 1F 0.03 0.03 0.03 0.03 0.03 0.03 2F 0.06 0.09 0.07 0.08 0.08 0.07 3F 0.09 0.16 0.17 0.16 0.16 0.18 4F 0.12 0.12 0.12 0.14 0.12 0.1 5F 0.18 0.13 0.13 0.13 0.13 0.12 6F 0.38 0.27 0.25 0.24 0.2 0.2 7F 0.46 0.43 0.41 0.41 0.41 0.36 8F 0.6 0.58 0.52 0.48 0.47 0.45 67 Test 4 : (1) Maximum displacement of each floor of type 1 SWD Floor Mass Ratio Proto 1% 2% 3% 4% 5% 1 F 3.08 3.08 3.08 3.08 3.08 3.08 3F 3.04 3.04 3.04 3.05 3.04 3.12 5F 3.34 3.34 3.36 3.34 3.36 3.42 7F 3.34 3.34 3.36 3.34 3.38 3.34 9F 3.04 3.05 3.04 3.04 3.06 3.02 11F 2.81 2.82 2.83 2.84 2.75 2.74 13F 3.02 2.75 2.59 2.41 2.24 2.19 15F 4.03 3.52 3.38 3.13 3.06 2.92 RF 5.29 5.01 4.86 4.75 4.65 4.25 (2) Maximum displacement of each floor of type 2 SWD Floor Mass Ratio Proto 1% 2% 3% 4% 5% 1 F 3.08 3.08 3.08 3.08 3.08 3.08 3F 3.04 3.06 3.06 3.06 3.04 3.07 5F 3.34 3.34 3.34 3.34 3.36 3.15 7F 3.34 3.34 3.32 3.35 3.38 3.15 9F 3.04 3.12 3.15 3.12 3.12 3.36 11 F 2.81 2.81 2.81 2.85 2.94 3.15 13F 3.02 2.52 2.48 2.52 2.52 2.51 15F 4.03 3.25 3.06 2.94 2.91 2.7 RF 5.29 4.83 4.68 4.48 4.36 3.6 68 (3) Maximum displacement of each floor of type 3 SWD Floor Mass Ratio Proto 1% 2% 3% 4% 5% 1 F 3.08 3.08 3.08 3.08 3.08 3.08 3F 3.04 3.06 3.06 3.04 3.04 3.15 5F 3.34 3.1 3.12 3.24 3.36 3.36 7F 3.34 3.15 3.15 3.25 3.38 3.61 9F 3.04 3.15 3.15 3.36 3.48 3.83 11 F 2.81 2.66 2.61 2.92 3.42 3.6 13F 3.02 2.14 2.03 2.42 2.68 2.82 15F 4.03 2.65 2.48 2.38 2.23 2.03 RF 5.29 3.75 3.69 3.45 3.32 2.92 (4) Inter story drift of each floor of type 1 SWD Floor Mass Ratio Proto 1% 2% 3% 4% 5% 1 F 0.04 0.04 0.04 0.03 0.04 0.04 3F 0.3 0.3 0.32 0.29 0.32 0.3 5F 0.26 0.26 0.28 0.28 0.28 0.28 7F 0.29 0.3 0.32 0.3 0.32 0.38 9F 0.36 0.36 0.36 0.38 0.38 0.4 11 F 0.42 0.44 0.44 0.44 0.46 0.46 13F 1.02 0.77 0.78 0.72 0.82 0.73 15F 1.66 1.49 1.49 1.63 1.59 1.34 69 (5) Inter story drift of each floor of type 2 SWD Floor Mass Ratio Proto 1% 2% 3% 4% 5% 1 F 0.04 0.02 0.02 0.02 0.04 0.03 3F 0.3 0.28 0.28 0.28 0.32 0.32 5F 0.26 0.26 0.28 0.28 0.28 0.28 7F 0.29 0.29 0.28 0.22 0.22 0.22 9F 0.36 0.34 0.32 0.32 0.32 0.31 11F 0.42 0.36 0.38 0.38 0.36 0.32 13F 1.02 0.73 0.59 0.42 0.39 0.36 15F 1.66 1.57 1.52 1.45 1.36 1.12 (6) Inter story drift of each floor of type 3 SWD Floor Mass Ratio Proto 1% 2% 3% 4% 5% 1 F 0.04 0.04 0.04 0.04 0.04 0.03 3F 0.3 0.29 0.28 0.32 0.32 0.32 5F 0.26 0.26 0.28 0.28 0.28 0.28 7F 0.29 0.29 0.28 0.29 0.32 0.32 9F 0.36 0.34 0.32 0.32 0.34 0.34 11F 0.42 0.36 0.45 0.45 0.46 0.48 13F 1.02 0.73 0.52 0.58 0.46 0.4 15F 1.66 1.45 1.32 1.21 1.15 0.98 70 (7) Floor acceleration of each floor of type 1 SWD Floor Mass Ratio Proto 1% 2% 3% 4% 5% 1 F 0.01 0.01 0.01 0.01 0.01 0.01 3F 0.08 0.08 0.09 0.08 0.09 0.09 5F 0.07 0.07 0.07 0.07 0.07 0.07 7F 0.08 0.08 0.09 0.08 0.09 0.11 9F 0.1 0.1 0.1 0.11 0.11 0.11 11 F 0.12 0.13 0.13 0.13 0.14 0.14 13F 0.3 0.21 0.22 0.2 0.24 0.2 15F 0.45 0.37 0.37 0.39 0.37 0.35 (8) Floor acceleration of each floor of type 2 SWD Floor Mass Ratio Proto 1% 2% 3% 4% 5% 1 F 0.01 0.01 0.01 0.01 0.01 0.01 3F 0.08 0.08 0.08 0.08 0.09 0.09 5F 0.07 0.07 0.07 0.07 0.07 0.07 7F 0.08 0.08 0.09 0.07 0.07 0.07 9F 0.1 0.1 0.1 0.1 0.1 0.1 11F 0.12 0.11 0.11 0.11 0.11 0.11 13F 0.3 0.21 0.18 0.16 0.13 0.12 15F 0.45 0.41 0.38 0.36 0.32 0.3 71 (9) Floor acceleration of each floor of type 3 SWD Floor Mass Ratio Proto 1% 2% 3% 4% 5% 1 F 0.01 0.01 0.01 0.01 0.01 0.01 3F 0.08 0.08 0.09 0.09 0.09 0.09 5F 0.07 0.07 0.07 0.08 0.08 0.08 7F 0.08 0.08 0.09 0.09 0.09 0.1 9F 0.1 0.1 0.1 0.09 0.09 0.11 11 F 0.12 0.1 0.14 0.14 0.14 0.16 13F 0.3 0.21 0.18 0.19 0.14 0.12 15F 0.45 0.36 0.32 0.31 0.3 0.28 72 Appendix B : Computer simulation data Simulation 1 : (1) Maximum displacement of each floor Floor Proto Type 1 Type 2 Type 3 1F 0 0 0 0 2F 0.024 0.023 0.022 0.02 3F 0.064 0.062 0.058 0.054 4F 0.125 0.121 0.111 0.103 5F 0.196 0.189 0.173 0.158 6F 0.286 0.276 0.248 0.221 7F 0.388 0.374 0.328 0.279 8F 0.468 0.449 0.379 0.302 RF 0.525 0.503 0.397 0.276 (2) Floor acceleration of each floor Floor Proto Type 1 Type 2 Type 3 1 F 0.04 0.04 0.04 0.05 2F 0.1 0.1 0.11 0.13 3F 0.18 0.18 0.2 0.24 4F 0.25 0.25 0.29 0.35 5F 0.33 0.32 0.375 0.46 6F 0.44 0.42 0.47 0.54 7F 0.57 0.53 0.51 0.07 RF 0.71 0.7 0.35 0.36 73 Simulation 2 : (1) Maximum displacement of each floor Floor Proto Type 1 Type 2 Type 3 1 F 0 0 0 0 2F 0.015 0.016 0.016 0.015 3F 0.039 0.042 0.041 0.04 4F 0.069 0.075 0.074 0.07 RF 0.09 0.101 0.099 0.093 (2) Floor acceleration of each floor Floor Proto Type 1 Type 2 Type 3 1F 0.13 0.12 0.12 0.12 2F 0.3 0.29 0.29 0.29 3F 0.51 0.48 0.48 0.48 4F 0.71 0.87 0.85 0.78 74 BIBLIOGRAPHY Aiken I. D. and Kelly J. M. , 1990 , Earthquake Simulator Testing and Analytical Studies of Two Energy-Absorbion Systems for Multistory Structures. Bolt B. A. , 1978 , Earthquakes . Housner , G. W. , 1957 , " Dynamic Pressures on Accelerated Fluid Containers " , Bulletin of SSA , vol. 47 , no. 1 , January 1957 , pp. 15-37 . Housner , G. W. , 1963 , " The Dynamic Behavior o f Water Tanks " , Bulletin of SSA , vol. 53 , no. 2 , February 1963 , pp. 381-387 . Housner , G. W. and Haroun M. A. , 1979 , " Vibration Tests o f Full-Scale Liquid Storage Tanks " , Proceedings of the Second U. S. National Conference on Earthquake Engineering , Stanford , California , August 1979 , pp. 137-145 . 75 Housner , G. W. and Haroun M. A. , 1979 , 1 1 Dynamic Analyses o f Liquid Storage Tanks " , Proceedings of the Seventh World Conferenceon Earthquake Engineering , Istanbul , Turkey , 1980 , vol. 8 , pp. 431-438 . Housner , G. W. and Haroun M. A. , 1979 , " Seismic Design o f Liquid Storage Tanks " , Journal of the Technical Councils , ASCE , T C I, April 1981 , pp. 191-207 . Igusa T. and Xu K. , 1991 , " Vibration Reduction Characteristics o f Distributed Rimed Mass Dampers " , Structural Dynamics : Recent Advances , PP. 596-605 . Kana, D. D. , Reddy, D. V. , Subramanian, C. V. , Ghosh, I. K. , Hossain, Q. A. and Johnson C. M. , 1984 , Fluid / Structure Interaction During Seismic Excitation . Proceedings of International Workshop on Recent Developments in Base-isolation Techniques for Buildings , April 27-30 , 1992 , Tokyo , Japan . 76 Seismic Isolation and Response Control for Nuclear and Non-nuclear Structures , Special Issue for the Exhibition of the 11th International Conference on Structural Mechanics in Reactor Technology ( SMiRT 11 ), August 18-23 , 1991 , Tokyo , Japan . Toshiyuki N. , Hidetoshi Y. , Eiji T. , Hideyuki K. and Hiroshi H. , 1988 , " Vibration Control Damper Using Sloshing o f Water Wiegel R. L. , 1970 , Earthquake Engineering . Seismic Isolation and Response Control for Nuclear and Non-nuclear Strctures , Special Issue for the Exhibition of the 11th International Conference on Structural Mechanics in Reactor Technology ( SMiRT 11 ), August 18-23 , 1991 , Tokyo , Japan . Zayas V. , Low S. , Bozzo L. and Mahin S. ,1989 , Feasibility and Performance Studies on Improving the Earthquake Resistance of New and Existing Buildings Using the Friction Pendulum System . 77

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Creator Chen, Liang-Chi (author)

Core Title Investigation of sloshing water damper for earthquake mitigation

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-c20-299581

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Legacy Identifier EP41430.pdf

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Rights Chen, Liang-Chi

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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...

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