Vibration and Shock Handbook 29

Vibration and Shock Handbook 29 Every so often, a reference book appears that stands apart from all others, destined to become the definitive work in its field. The Vibration and Shock Handbook is just such a reference. From its ambitious scope to its impressive list of contributors, this handbook delivers all of the techniques, tools, instrumentation, and data needed to model, analyze, monitor, modify, and control vibration, shock, noise, and acoustics. Providing convenient, thorough, up-to-date, and authoritative coverage, the editor summarizes important and complex concepts and results into “snapshot” windows to make quick access to this critical information even easier. The Handbook’s nine sections encompass: fundamentals and analytical techniques; computer techniques, tools, and signal analysis; shock and vibration methodologies; instrumentation and testing; vibration suppression, damping, and control; monitoring and diagnosis; seismic vibration and related regulatory issues; system design, application, and control implementation; and acoustics and noise suppression. The book also features an extensive glossary and convenient cross-referencing, plus references at the end of each chapter. Brimming with illustrations, equations, examples, and case studies, the Vibration and Shock Handbook is the most extensive, practical, and comprehensive reference in the field. It is a must-have for anyone, beginner or expert, who is serious about investigating and controlling vibration and acoustics.

Seismic Vibration VII VII-1 © 2005 by Taylor & Francis Group, LLC 29 Seismic Base Isolation and Vibration Control 29.1 Introduction 29-1 From Ductility Design to Base Isolation and Control Design The Importance of Reducing Seismic Input and Response † 29.2 Seismic Base Isolation 29-4 Hirokazu Iemura Kyoto University Sarvesh Kumar Jain Madhav Institute of Technology and Science Mulyo Harris Pradono Kyoto University Historical Development of Base Isolation † Basic Principle † Issues in Seismic Base Isolation † Seismic Isolation Devices † Design of Isolation Devices † Verification of Properties of Isolation Systems † Analysis of Base-Isolated Structures † Experimental Methods for Isolated Structures † Implementation of Seismic Isolation † Performance during Past Earthquakes 29.3 Seismic Vibration Control 29-33 Historical Development of Seismic Vibration Control † Basic Principles † Important Issues in Vibration Control † Vibration-Control Devices † Control Algorithm † Experimental Performance Verification † Implementations Summary This chapter presents seismic vibration control of civil engineering structures It is divided into two main sections The first part of the chapter deals with vibration control by seismic base isolation, whereas the second part covers methods of response control that use passive energy dissipation, active control, semiactive control, and hybrid control, respectively Each part starts with a brief description of the historical development of these methods, followed by basic principles and important issues in their implementation Thereafter, devices used for structural response control, their design methods, and recommended experimental procedures for verification of their properties and analytical modeling are discussed Various methods generally used for analysis of such structures are then discussed in detail followed by a brief description of the implementation of these methods for various types of structures In addition, performance of existing structures during past earthquakes is also included, to highlight the effectiveness of these methods during real earthquakes Further information on the general topic of this chapter is found in Chapter 22, Chapter 30, and Chapter 31 29.1 Introduction Seismic isolation and vibration-control systems are relatively new and sophisticated concepts that require more extensive design and detailed analysis than most conventional seismic designs of structures In general, these systems will be most applicable to structures whose designers seek superior earthquake performance Seismic base isolation and passive energy-dissipation systems are viable design strategies that have already been used for seismic protection of a number of structures Other special seismic protective system techniques such as active control, semiactive control, hybrid combinations of active and passive devices, and tuned mass and liquid dampers may also provide practical solutions in the 29-1 © 2005 by Taylor & Francis Group, LLC 29-2 Vibration and Shock Handbook near future An innovative challenge is highly expected in this field for the seismic safety enhancement of civil structures 29.1.1 From Ductility Design to Base Isolation and Control Design The conventional method of seismic design mainly deals with increasing capacity The approach is based on designing a strong and ductile structure Plastic hinges in a ductile structure, (see Figure 29.1), which can take care of the inertial enabling the whole forces generated by the earthquake shaking The structural system to approach results in increasing the size of structural absorb seismic energy members and connections, and providing additional bracing members and shear walls, or other stiffening members The increase in stiffness Ground excitation then attracts more seismic forces and in turn requires further strengthening, which becomes FIGURE 29.1 Schematic of a structure with ductile uneconomical Therefore, the conventional pracmembers tice permits safe design of a structure on the premise that inelastic action in a ductility-based designed structure will dissipate significant energy and enable it to survive a severe earthquake without collapse The conventional designs may permit some structural damage because of inelastic deformation in the members and also in nonstructural elements Contents of structure can get damaged due to large interstory drift and high-floor accelerations It is difficult to control structural damage and it may be dangerous in unexpected strong seismic events It has been observed that, in the event of major seismic events, structures based on the conventional design methods suffered damage, experienced high-floor accelerations, and resulted in disruption of essential services such as transportation, communication, and so on Thus, for the class of structures like nuclear power plants, museums, hospital buildings, buildings with artifacts, important bridges, and such structures located in high-seismicity regions, this ductility-based design is not suitable The need to minimize earthquake damage in critical and important structures prompted civil engineers to search for other methods of earthquake-resistant designs, which can not only protect structures from earthquake motions but also keep them functional during and after strong earthquakes To this end, base isolation and structural control methods are found to be a solution Base isolation has the capability to reduce the seismic response of a structure by isolating it from the ground shaking (Figure 29.2a) An isolation system reduces the transmission of ground vibration, thus enabling the structure to experience less shaking from the ground Therefore, structural damage and occupants’ inconvenience can be minimized using this technique However, at the expense of safety and the convenience of structure, the bearings undergo significant drift during large earthquakes that may disrupt the function of the bearings themselves and supply lines of services such as water and gas Another way of reducing seismic response is by using the structural control method It has the capability of modifying the structural properties, such as stiffness, mass, and damping, and providing passive or active counterforces Figure 29.2b shows the schematic diagram of the structural control method in a civil structure It shows some examples of devices generally used for applying control forces The seismic safety enhancement of structures using the structural control method can be categorized as active and passive systems There are also hybrid systems that represent combinations of active and passive, and semiactive systems to represent active controller that employs controllable passive devices © 2005 by Taylor & Francis Group, LLC Seismic Base Isolation and Vibration Control 29-3 Moving Mass Control Joint Damper Variable Damping Hysteretic Type Damping Active Varying Stiffness Structure response Base Isolation Bearings Ground shaking (a) FIGURE 29.2 (b) Schematic of a civil structure with (a) isolation bearings and (b) the structural control method Owing to changes in code provisions or upgradation of seismic zones, many structures come into the category of “unsafe” and require retrofitting Response control strategies are found to be easier than other options, economical, and are often the only alternative for such cases 29.1.2 The Importance of Reducing Seismic Input and Response As mentioned above, by using the conventional method of seismic design, the design may permit some structural damage because of inelastic deformation in the members, and also in nonstructural elements, during large earthquakes The ductility enables the structure as a whole to absorb the seismic energy Once the structural response goes deeply into the plastic range during a large earthquake, structures may not be operational or repairable If the seismic input to the structure and structural response can be reduced, then the structural damage can be minimized For higher reliability of structures even under very severe earthquake motion, structural control techniques that effectively reduce seismic force to structures are developed The fast development of technology, particularly in the fields of electronics and computer science, has provoked the researchers in some centers worldwide to intensify development of a new concept with the new philosophy of seismic design Generally, this concept is known as a design of intelligent structures or smart structures Owing to the experience of severe damage due to the Kobe earthquake, public demand for seismic performances of civil infrastructures became relatively clear in Japan Civil infrastructures are constructed with the tax paid by the public, so a collapse or near collapse with unrepairable damage cannot be accepted, even under a very rare earthquake loading Infrastructures are also expected to serve as public tools to help rehabilitate the affected society For this purpose, infrastructures have to be repaired in a relatively short time, even though their functions are temporarily terminated due to severe earthquake loading © 2005 by Taylor & Francis Group, LLC 29-4 Vibration and Shock Handbook Earthquake Performance Level Fully Operational Near collapse Operational Life safe Frequent (T = 43 years) Earthquake Occasional Design (T = 72 years) Level Rare (T = 475 years) Unacceptable Performance (for New Construction) Very rare (T = 970 years) FIGURE 29.3 Public demand for seismic performance of infrastructure The public demand for seismic performance objectives of infrastructures shows that structural damage has to be limited even against very rare earthquake loading (Figure 29.3) The figure shows that civil infrastructures must be fully operational during and after frequent, weak earthquakes They also expected to be operational even after very rare, strong earthquakes To achieve the objectives, new technologies are to be developed that can result in the desired performance 29.2 29.2.1 Seismic Base Isolation Historical Development of Base Isolation Seismic base isolation is not a very new idea More than a century ago, John Milne, a professor of engineering in Japan, built a small house of wood and placed it on ball bearings to demonstrate that a structure could be isolated from earthquake shaking (Housner et al., 1997) In 1891, after the Narobi earthquake M ẳ 8:0ị; Kawai, a Japanese person, proposed a base-isolated structure with timber logs placed in several layers in the longitudinal and transverse direction (Izumi, 1988; see Figure 29.4) In 1906, Jacob Bechtold of Germany applied for a U.S patent in which he proposed to place building on rigid plate, supported on spherical bodies of hard material (Buckle and Mayes, 1990) In 1909, a medical doctor from England, Calentarients, applied for patents for his invention comprising FIGURE 29.4 Base isolation by timber logs (Source: isolation system for earthquake-proof building JSSI, Introduction of Base Isolated Structures, Japan (see Figure 29.5) He proposed separating a Society of Seismic Isolation, Ohmsa, Tokyo, 1995 With building from its foundation with a layer of sand permission.) or talc (Kelly, 1986) The Imperial Hotel in Tokyo, constructed in 1921, was intended to float on an underlying layer of mud The building was founded on an 8-ft thick layer of firm soil under which exists a 60- to 70-ft thick layer of soft mud The building was © 2005 by Taylor & Francis Group, LLC Seismic Base Isolation and Vibration Control 29-5 FIGURE 29.5 Calentarients’ idea of seismic base isolation (Source: JSSI, Introduction of Base Isolated Structures, Japan Society of Seismic Isolation, Ohmsa, Tokyo, 1995 With permission.) highly decorative with many appendages The soft mud acted as isolation system and the building survived the devastating 1923 Tokyo earthquake (Kelly, 1986; Buckle and Mayes, 1990) Attempts were made in the 1930s to protect the upper floors of multistory buildings by designing very flexible first-story columns In a later modification of the flexible first-story columns approach, it was proposed that the first-story columns should be designed to yield during an earthquake to produce an energy-absorbing action However, to produce enough damping, several inches of displacement is required, and a yielded column has greatly reduced buckling load, proving the concept to be impractical It was then proposed that, if the soft first story is constructed underground, then energy dissipaters can be installed at the top of this story (which approximates ground level) that prevent the superstructure from moving too far, and dissipate the energy of ground motion before it enters the building The superstructure, from the first floor up, can be an economically braced, nonductile concrete frame requiring no internal shear walls (Arnold, 2001) To overcome the inherent dangers of soft supports at the base, many types of roller-bearing systems have been proposed The rollers and the spherical bearings are very low in damping and have no inherent resistance to lateral load, and therefore some other mechanism that provides wind restraint and energy-absorbing capacity is needed A long duration between two successive earthquakes can result in the cold welding of bearings and plates, thus causing the system to become rigid after a time Therefore, the application of rolling supports was restricted to the isolation of special components of low or moderate weight (Caspe, 1984) Parallel to the development of the soft first-story approach, the flexibility of natural rubber was also seen as another solution for increasing the flexibility of the system In 1968, large blocks of hard rubber, 54 in number, were used to isolate the three-story Heinrich Pestalozzi School in Skopje, Republic of Macedonia The building is constructed of reinforced concrete shear walls This is the first building for which rubber bearings were used as base isolation against strong earthquakes These rubber blocks are unreinforced and bulge sideways under the weight of this concrete structure (see Figure 29.6) Owing to having the same stiffness of the isolation system in all the directions, the building bounces and rocks FIGURE 29.6 Unreinforced rubber blocks (Source: backwards and forwards (Jurukovski and Rakice- Ohashi, U.G Earthquakes and Base Isolation, Pub Asakura, Tokyo, 1995 With permission.) vic, 1995) These types of bearings are unsuitable for the earthquake protection of structures The subsequent development of laminated rubber bearings has made base isolation a practical reality (Figure 29.7) Later, a large number of isolation devices were developed, and now base isolation has reached the stage of gaining acceptance and replacing the conventional construction, at least for important structures FIGURE 29.7 Rubber bearings with steel shims © 2005 by Taylor & Francis Group, LLC 29-6 29.2.2 Vibration and Shock Handbook Basic Principle Seismic base isolation is basically a lengthening of the fundamental time period of the structure with the help of a specially designed system that is placed between its superstructure and substructure (see Figure 29.8) Besides other advantages, the concept gained widespread acceptance due to the fact that most of the earthquake motions around the world have dominating frequencies in the range of 1.0 to 10 Hz, and the majority of conventionally designed structures also has their fundamental frequency of vibration lying in this range Owing to this unwanted matching of the frequencies, these structures are subjected to high forces during earthquakes The application of seismic base isolation shifts the fundamental time period away from the dominating frequencies of earthquake motions and thus detunes the frequencies In other words, base isolation consists in filtering out high-frequency waves from the ground motion, thereby preventing the transmission of high energy in the structure The effect of base isolation on reduction in force is shown schematically in Figure 29.9 Under favorable conditions, seismic base isolation can reduce drift to 0.2 to 0.5 of that which would occur if the building were fixed base (Figure 29.10) Reduction in acceleration has more influence on the force –deflection characteristics of the isolation system and may not be as significant as the reduction of drift (FEMA 356, 2000) However, the additional flexibility required for this period shift give rise to excessive relative displacement at the isolation level Additional damping is introduced in the isolation system to limit this displacement response to within feasible limits Still, it is necessary to provide an adequate seismic gap that can accommodate displacements at the isolation level Most of the isolators have inherent damping, although sometimes supplemental energy dissipation devices may also be required at the isolation level Various types of energy dissipation devices like metallic dampers and hydraulic dampers have been developed and can be used for this purpose (Skinner et al., 1993) The isolation damping also suppresses the resonance FIGURE 29.8 Application of seismic isolation for different structures Normalized acceleration response 4.0 3.0 Conventionally designed structure 2.0 V = 2% Seismically isolated structure 1.0 0.0 V =15% 0.0 1.0 2.0 3.0 4.0 Natural period (seconds) FIGURE 29.9 © 2005 by Taylor & Francis Group, LLC Conceptual diagram for seismic isolation 5.0 Seismic Base Isolation and Vibration Control 29-7 resulting due to higher period contents of the earthquake motion Although damping is useful in reducing the required seismic gap, excess damping may result in an increase in acceleration that may affect the performance of nonstructural elements and contents Thus, an isolation system should essentially be able to (1) support a structure, (2) provide horizontal flexibility, and (3) dissipate energy These three functions can be incorporated in a single device or can be provided by means of different components In addition, it may be necessary to provide buffers, which can limit the isolator displacements during extreme earthquakes FIGURE 29.10 Behavior of (a) fixed-base and (b) baseisolated building 29.2.3 Issues in Seismic Base Isolation A number of issues for seismic isolation design have been identified based on experiences of their behavior Some of the issues that should be considered before choosing the base-isolation approach for a project are touched in the following sections 29.2.3.1 Performance Criteria The performance criteria for the structure needs to be established in order to evaluate alternative seismic resisting systems; for example, it must be established whether the structure is required to be functional during and after major earthquakes, or if it is to be preserved for its historical importance Whether seismic base isolation is a suitable design strategy for a particular project will depend primarily on the performance required To achieve the fully operational or operational performance level, one can consider seismic base isolation as a possible design strategy, but if life safe is the required structural performance level, it may not be practical to choose seismic base isolation 29.2.3.2 Type of Structure Significant benefits obtained from isolation exist in structures for which the fundamental period of vibration without base isolation is short, that is, less than sec Certain structures may not be suitable for base isolation because of their shape; for example, this is true for slender high-rise buildings that have a natural period long enough to attract low earthquake forces without isolation Therefore, seismic isolation is mostly used for low-rise buildings Historical buildings, which generally are stiff masonry structures, can be appropriate structures for seismic base isolation Bridges are the structures for which application of seismic isolation is very convenient The provision of bearings at the tops of piers adds flexibility to stiffer piers and in turn avoids yielding of piers It is easy to examine these bearings after a seismic event and replace them if needed 29.2.3.3 Site Characteristics In base-isolation design, the basic objective is to filter out the high frequencies of the ground motion by lengthening the time period of vibration to approximately sec Thus, conventional base isolation is not suitable for structures on soft soils where the ground motions are dominated by low frequencies Therefore, a detailed investigation of the site must be carried out before possible isolation can be considered Another important aspect is near-fault ground motions Waves from such motions usually have long-period velocity pulses, which impart lot of momentum to the structure This is particularly damaging to base-isolated structures because it may cause large horizontal base displacements The displacement can result in instability of the structure, or it © 2005 by Taylor & Francis Group, LLC 29-8 Vibration and Shock Handbook can result in impact with moat walls, which can affect the sensitive equipment housed in the building An isolator with bilinear force– displacement behavior and a large ratio of yield-force to supported weight can substantially reduce the displacement The provision of high damping in an isolation system can also work However, the degree of isolation during relatively frequent earthquakes without near-fault pulses is much reduced due to these provisions (Skinner and McVerry, 1996) 29.2.3.4 Retrofit Issues In selecting a suitable retrofit system and properties of seismic isolation system, consideration should be given to the characteristics of the existing building, such as foundation capacity and strength of the superstructure For retrofit of buildings, successful implementation of a seismic isolation system requires that the sequences of temporary bracing, shoring, cutting of existing columns and walls, and installation of isolators be well planned Base isolation for the retrofit of bridges is simpler as they usually have thermal bearings, which can easily be replaced by seismic isolation bearings The retrofitting of monuments or buildings of historical importance requires special efforts to cope with the need of minimum alterations Provisions must be made to protect them from any seismic event during the retrofitting Also it must be identified whether workable spaces and access to the work area is available 29.2.3.5 Design of Building Services Depending on the base-isolation system, base-isolated structures under earthquake motions can exhibit significant base slab displacements due to the low horizontal stiffness of the isolation elements This may create problems on the supply lines transitioning between the parts of structure below and above isolation level Therefore, special attention is to be given to installations of building services such as water supply, sewerage, gas, air-conditioning, and so on in order to prevent any damage to these supply lines, which might cause secondary effects In the case of isolation of two or more structural units founded on a common foundation and connected by expansion joints, special care is needed regarding the proportions of the expansion joint in order to prevent the pounding of buildings during earthquakes 29.2.3.6 Expected Life of Isolator The isolation system should remain operational for the expected lifetime of the isolated structure It should not require frequent maintenance during this period Although the functioning of an isolator may be required few times during the lifetime of structure, it must perform well at such times If life of the isolator is less than the life of structure, then it may be necessary to provide a mechanism for the inspection and replacement of the isolation system Another related aspect is the protection of isolation elements against fire, and measures should to be taken for this Furthermore, as an isolation system is provided mostly at the base, its resistance to chemical and biological reactions is also important (Jurukovski and Rakicevic, 1995) 29.2.4 Seismic Isolation Devices The successful seismic isolation of a particular structure is strongly dependent on the appropriate choice of the isolation system In addition to providing adequate horizontal flexibility and appropriate damping, the isolation system should essentially have the capability of self-centering after deformation, high vertical stiffness to avoid rocking, and enough initial stiffness to avoid frequent vibration from wind and minor seismic events Different types of isolators have been developed and proposed to achieve these properties, and some of them are discussed below © 2005 by Taylor & Francis Group, LLC Seismic Base Isolation and Vibration Control 29.2.4.1 29-9 Laminated Rubber Bearings Load (ton) Rubber bearings offer the simplest method of seismic base isolation and are relatively easy to manufacture The bearings are made by vulcanization bonding of sheets of rubber to thin steel reinforcing plates Initially, the main function of the laminated rubber bearings was to provide flexibility for thermal displacements in bridges Later, similar bearings found application in the isolation of buildings from vibration due to underground railways, and these bearings have FIGURE 29.11 Laminated rubber bearing performed well over a substantial period of time (Kelly, 1990) The bearings are very stiff in the 20 vertical direction and flexible in the horizontal direction High vertical stiffness of these bearings is achieved through the laminated construction of the bearing using steel plates The cross section of a typical rubber bearing is shown in Figure 29.11 The most common elastomers used in elastomeric bearings are natural rubber, neoprene rubber, butyl rubber, and nitrile rubber The mechanical (tear strength, high strain fatigue resistance, creep resistance) and low-temperature properties of natural rubber are superior to those of most synthetic elastomers used for seismic isolation bearings Therefore, natural rubber is the most −20 frequently recommended material for use in elastomeric bearings, followed by neoprene Butyl 100 −100 rubbers are suitable for low-temperature appliDisplacement (mm) cations and nitrile rubber has limited application in offshore oil structures (Taylor et al., 1992) FIGURE 29.12 Load – displacement loops for highThe damping ratio (i.e., the fraction of critical damping rubber bearing (Source: Tanzo, W et al Res damping) achieved from natural rubber is low, in Rpt 92-ST-01, Kyoto Univ., 1992 With permission.) the order of 0.02 to 0.04, and therefore it is unusual to use it without some other element that is able to provide increased damping In order to achieve better performance in a single unit, rubber used in the bearing is a compound formed with some filler agents This compounding results in desired properties, such as (1) high damping and (2) high horizontal stiffness at low values of shear strain The damping ratio (i.e., the fraction of critical damping) achieved is in the order of 0.10 to 0.20 These high-damping rubber bearings, originally developed in England, found several applications in Japan and United States A number of fillers are employed, such as metal oxides, clay, and cellulose, but the filler that is most commonly used in seismic isolation bearings is carbon black (Taylor et al., 1992) Force–displacement behavior of these bearings depends upon the type of compounding Figure 29.12 shows the results of cyclic loading test conducted on a four-layer highdamping rubber bearing specimen (Tanzo et al., 1992) In the experiment, the tests were carried out up to 200% (96 mm) shear strain Vertical load for the tests was kept as 40 tonf (64 kgf/cm2) The application of steel shims in laminated rubber bearings provides necessary vertical stiffness, but at the same time makes these isolators heavy and expensive Recently, Kelly (2001) proposed a seismic isolation system for developing countries, in which steel plates are replaced by fiber mesh The fiber-reinforced isolator is expected to be significantly lighter and could lead to a much less laborintensive manufacturing process © 2005 by Taylor & Francis Group, LLC Seismic Base Isolation and Vibration Control FIGURE 29.66 29-61 Side view of the Tempozan Bridge harmonic motion, and the main mode has an effective modal mass that is larger than 90% of the total mass SSI effects on the structural damping ratio are also studied The Tempozan Bridge (Hanshin Highway Public Corporation, 1992), built in 1988, is a three-span continuous steel cable-stayed bridge that is situated on reclaimed land and crosses the mouth of the Aji River, Osaka, Japan The total length of the bridge is 640 m with a center span of 350 m, and the lengths of the side spans are 170 and 120 m (Figure 29.66) The main towers are A-shaped to improve the torsional rigidity The cable in the superstructure is a two-plane fan pattern multicable system with nine stay cables each plane The bridge is supported on a 35 m thick soft layer and the foundation consists of cast-in-place RC piles of m in diameter The main deck is fixed at both towers to resist horizontal seismic forces The bridge is relatively flexible, with a predominant period of 3.7 sec As to the seismic design in the transverse direction, the main deck is fixed at the towers and the end piers Figure 29.67 shows the original design spectrum used for designing the bridge and the new design spectrum specified in the bridge design specification set in 1996 for level I and level II earthquakes (Japan Roadway Association, 1996) A level II earthquake has type I (interplate type) Absolute Acceleration (gal) 10000 1000 100 New Design Spectrum Level II (Type I) New Design Spectrum Level II (Type II) New Design Spectrum Level I Original Design Spectrum 10 0.1 Natural Period (sec.) FIGURE 29.67 © 2005 by Taylor & Francis Group, LLC Design spectra for bridges 10 29-62 Vibration and Shock Handbook and type II (intraplate type) As can be seen in the figure, the new design spectrum shows higher acceleration response in all period ranges than the original one 29.3.7.2.2 Basic Concept of Seismic Retrofit If the deck is connected with very flexible bearings to the towers, the induced seismic forces will be kept to minimum values, but the deck may have a large displacement response On the other hand, a very stiff connection between the deck and the towers will result in a lower deck displacement response but will attract much higher seismic forces during an earthquake This is the case in the original bridge structure, the Tempozan Bridge Therefore, it is important to replace the existing fixed-hinge bearings with special bearings or devices at the deck-tower connection both to reduce seismic forces and to absorb large seismic energy and reduce the response amplitudes Additionally, energy-absorbing devices may also be put between the deck-ends and piers; however, this will attract relatively large lateral force of the piers, and therefore this kind of method has been avoided for this bridge at this time The bridge model that represents the existing Tempozan Bridge is termed the “original bridge model.” The bridge model with the spring and damper (viscous, hysteretic, and semiactive) between the deck and the towers is termed the “retrofitted bridge model.” The original and retrofitted bridge models are shown in Figure 29.68 The original structure system has fixed-hinge connections between the towers and the deck and rollers connection between the deck-ends and piers, so that the deck longitudinal movement is constrained by the towers (Figure 29.68a) For the retrofitted bridge, the isolation bearings and dampers connect the deck to the towers (Figure 29.68b) The cables are modeled by truss elements The towers and deck are modeled by beam elements, and the isolation bearings are modeled by spring elements The models were analyzed by a commercial finite element program (Prakash and Powell, 1993) The moment –curvature relationship of the members is calculated based on the sectional properties of members and material used 29.3.7.2.3 Modal Shape Analysis The first modes of the structures are interesting here because these modes have the largest contribution to the longitudinal movement of the bridge (also see Chapters and Chapter 4) The mode shapes of the original bridge and the retrofitted bridge are shown in Figure 29.69 The first mode shape of the original structure is shown in Figure 29.69a The natural period ðTÞ of this mode is 3.75 sec (frequency ¼ 0.266 Hz), which is close to the design value for the bridge (3.7 sec, frequency ¼ 0.270 Hz; Hanshin Highway Public Corporation, 1992) This first mode shape has the effective modal mass as a percentage of the total mass of 84% For the retrofitted structure, the stiffness of the bearings is an important issue, as large stiffness produces a large bearing force However, very flexible connections produce a large displacement response Therefore, based on a study on a simplified model of the bridge under seismic motion, the bearing stiffness Fixed Hinge (a) (b) FIGURE 29.68 Isolation Bearings + Passive or Semi Active Dampers Cable-stayed bridge models: (a) original structure system; (b) retrofitted structure system © 2005 by Taylor & Francis Group, LLC Seismic Base Isolation and Vibration Control 29-63 1st mode shape, frequency = 0.266 Hz Fixed deck-tower connections (a) 1st mode shape, frequency = 0.158 Hz Flexible deck-tower connections (b) FIGURE 29.69 First mode shapes of (a) original structure and (b) retrofitted structure that produces retrofitted main period ðT Þ 1.7 times the original main period ðTÞ was chosen This bearing stiffness makes the energy-absorbing devices work well in reducing seismic-induced force and displacement The main natural period ðT Þ of the retrofitted bridge then becomes 6.31 sec and the effective modal mass as a percentage of total mass is 92% It is clear from the figures that smaller curvatures are found at the towers and the decks of the retrofitted structure than in the original structure This shows that the retrofitted structure is expected to produce smaller moments at the towers and the decks than the original structure during a seismic attack 29.3.7.2.4 Time-History Analysis The models were analyzed by a commercial finite element program (Prakash and Powell, 1993), which produces a piece-wise dynamic time history using Newmarks constant average acceleration b ẳ 1=4ị integration of the equations of motion, governing the response of a nonlinear structure to a chosen base excitation The input earthquake motions were type I-III-3, I-III-2, and I-III-1 earthquakes, which are artificial acceleration data used for design in Japan for soft soil condition Those data are intended to be type I (interplate type) With numerical comparison (Figure 29.67), type I earthquake motion gives higher effect to the bridge than type II motion, in longer period range Table 29.7 shows the seismic response effects because of different kinds of bearings and dampers: fixedhinge bearings for the original bridge model; elastic bearings, elastic bearings plus viscous dampers, and hysteretic bearings for the retrofitted bridge models The input earthquake was type I-III-3 earthquake data and was in the longitudinal direction From the table, it is clearly seen that if only elastic bearings are used for seismic retrofit, then the sectional forces are reduced to about 40% of the original ones However, the displacement response is increased to 176% of the original one By adding viscous dampers to the elastic bearings, the sectional forces can be reduced to about 25% of the original ones, and the displacement response is reduced to 63% of the original Thus, the viscous dampers together with bearings work to reduce the seismic response of retrofitted bridge The structural damping ratio is calculated as 35% If hysteretic bearings are used for seismic retrofit, the sectional forces are reduced to about 29% of the original ones and the displacement response is reduced to 67% of the original one The equivalent structural damping ratio is calculated as 13.1% by using pushover analysis to obtain a hysteretic loop at the main mode The hysteretic bearings are modeled by a bilinear model, and the second stiffness of the hysteretic bearings is 0.03 times the initial stiffness and produces a first mode natural period of 6.31 sec © 2005 by Taylor & Francis Group, LLC 29-64 Vibration and Shock Handbook TABLE 29.7 Maximum Earthquake Responses and Damping Ratios in Longitudinal Direction Items Deck displacement (m) Tower momenta (MN m) Tower axial forcea (kN) Cable force (kN) Bearing forceb (kN) Deck moment (MN m) Deck axial force (kN) Damping ratio (%) Natural period (sec) a b c Original Structure Retrofitted Structure Elastic Bearings 2.37 3,100 48,000 24,000 94,000 370 56,000 3.75 Elastic Bearings ỵ Viscous Damping 4.17 2,000 15,000 3,440 44,000 95 21,000 6.31 1.50 900 15,000 4,000 17,000 75 11,000 35 6.73 Hysteretic Bearings 1.58 900 21,000 5,000 25,000 95 15,000 13.1 3.86 and 6.31c Base of tower AP3 At connection between deck and tower AP3 Initial and postyield stiffness 29.3.7.2.5 Soil–Structure Interaction Effect One method to study the SSI effects is to take into Kx account the effects of flexible foundations and the Cr K C r x radiation of energy from foundations In this method, the cable-stayed bridge is idealized as in Figure 29.70 (Kawashima and Unjoh, 1991) The a a elastic half space subsoil supporting the foundation was assumed to be an elastic half space The subsoil was assumed to be elastic with no energy dissipation The foun- FIGURE 29.70 Cable-stayed bridge model with flexdation was idealized as a rigid massless circular ible foundation and energy radiating from foundation plate The radius of the rigid circular plate was simply assumed so that it gives the same surface area as the foundation Dynamic stiffness of the foundation was assumed in a frequency independent form: pGs a2 Vs pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 8Gs a 0:25p 2ð1 y Þ=ð1 2y ÞGs a Cr ¼ Kr ¼ 3ð1 y Þ Vs Kx ¼ 8Gs a 22y Cx ẳ 29:46ị 29:47ị in which Kx and Cx represent the spring and damping coefficient for sway motion, and Kr and Cr represent those for rocking motion Vs and a represent shear wave velocity of subsoils and the radius of foundation, respectively The result shows that SSI increases the natural period and the damping ratio of the original structure However, the damping ratio of the retrofitted structure is reduced and the effectiveness of the bearings and dampers in reducing seismic responses is also reduced (Table 29.8) This is mainly because the SSI model introduces flexibility at the base A flexible base will reduce the frequency of the structure A smaller frequency will reduce the effectiveness of viscous damping devices in absorbing earthquake energy Moreover, a flexible base will increase the elastic strain energy of the structure that reduces the damping ratio If the SSI model possesses an elemental damping ratio, as is a usual case for the soil, the structural damping ratio will also be influenced by the SSI-model damping characteristics 29.3.7.2.6 Semiactive Control The semiactive control herein uses the pseudonegative stiffness control algorithm (Iemura and Pradono, 2003) so that the sum of the damper force and bearing force (plus other connecting stiffness forces) are expected to produce a hysteresis loop that is as close as possible to that of rigid –perfectly plastic © 2005 by Taylor & Francis Group, LLC Seismic Base Isolation and Vibration Control TABLE 29.8 29-65 Maximum Earthquake Responses and Damping Ratios (SSI Included) Items Original Structure Retrotted Structure Elastic Bearings ỵ Viscous Damping Deck displacement (m) Tower momenta (MN m) Tower axial forcea (kN) Cable force (kN) Deck moment (MN m) Deck axial force (kN) Foundation displacement (m) Damping ratio (%) Natural period (sec) a b 2.78 1,500 36,200 12,300 228 31,900 0.171 3.1 5.04 Hysteretic Bearings 2.57 800 12,500 3,010 58 9,100 0.079 23 7.66 2.77 882 19,800 4,470 86 12,300 0.093 9.3 5.13 and 7.46b Base of tower AP3 Initial and postyielding stiffness force –deformation characteristics (Figure 29.71a) Moreover, no residual displacement is expected at the bearings after an earthquake attack, because the hysteresis loop is velocity dependent Figure 29.71 shows ideal and realistic force – deformation characteristics of the variable damper that can produce artificial rigid –perfectly plastic force–deformation characteristics by using variable damper One algorithm that can approach the hysteretic loop in Figure 29.71b requires the following variable-damper force (Iemura et al., 2001): Fd;t ẳ Kd ut ỵ Cd u_ t F u F F u u (a) F Connecting Stiffness + Variable Damper = Total F + F u u u (b) FIGURE 29.71 (a) Ideal and (b) realistic hysteretic loops produced by variable damper ð29:48Þ where Kd is connecting stiffness (negative value) and Cd is damping coefficient (positive value) The algorithm is practical because only displacement and velocity sensors are placed in the dampers Therefore, each damper can have its own controller Should a malfunction happen in one damper or controller, it will not affect the other dampers or controllers This algorithm produces the hysteretic loop shown in Figure 29.72b under harmonic motion It is clear from the figure that the variable damper is superior to the linear viscous damper, because the maximum variable damper plus the connecting-stiffness force can be set to be equal to the maximum connecting-stiffness force (Figure 29.72b) One can calculate that the damping ratio of the hysteresis loop in Figure 29.72b is 53.4% For the same damping ratio, the hysteresis loop in Figure 29.72a produces a total force 1.46 times larger than the connecting-stiffness force (Iemura and Pradono, 2003) The connecting stiffness between the deck and the tower of the retrofitted cable-stayed bridge comes from the contribution of cable stiffness, upper tower stiffness, and bearing stiffness The cable-stayed bridge model with isolation bearings and variable dampers controlled with the pseudonegative stiffness algorithm was analyzed by a program developed by the authors under the MATLAB (MathWorks, 2000) and SIMULINK (MathWorks, 1999) environments The program produces a piece-wise dynamic time-history, using Newmark’s constant average acceleration b ẳ 1=4ị integration of the equations of motion, governing the response of a nonlinear structure to a chosen base excitation The input motions were type I-III-1, I-III-2, and I-III-3 earthquakes, which are artificial acceleration data used for design in Japan (Japan Roadway Association, 1996) The results show that the application of the pseudonegative stiffness control algorithm is effective in reducing seismic response of the bridge model Figure 29.73 shows the base shear-deck displacement © 2005 by Taylor & Francis Group, LLC 29-66 Vibration and Shock Handbook Linear damping + connecting stiffness Linear damping Variable damping + connecting stiffness Variable damping F F u u Connecting stiffness (a) FIGURE 29.72 (b) Hysteresis loops for (a) linear viscous damping and (b) pseudonegative stiffness damping 80000 40000 −3.0 −2.0 −1.0 0.0 1.0 2.0 3.0 Base Shear (kN) Base Shear (kN) 80000 40000 −3.0 −2.0 −1.0 0.0 1.0 2.0 3.0 −40000 − 40000 −80000 −80000 (a) Deck Displacement (m) (b) Deck Displacement (m) (a) 40000 40000 20000 20000 −1.5 −1.0 −0.5 0.0 0.5 1.0 −20000 − 40000 Bearing Displacement (m) 1.5 Damping Force (kN) Damping Force (kN) FIGURE 29.73 Base shear vs deck displacement relationship of a cable-stayed bridge model with (a) linear dampers (b) pseudonegative stiffness dampers (type I-III-1 earthquake) (b) −1.5 −1.0 −0.5 0.0 0.5 1.0 1.5 −20000 −40000 Bearing Displacement (m) FIGURE 29.74 Damping force vs damping displacement relationship of a cable-stayed bridge model with (a) linear dampers, (b) pseudonegative stiffness dampers (type I-III-1 earthquake) © 2005 by Taylor & Francis Group, LLC 40000 20000 −1.5 −1.0 − 0.5 0.0 0.5 1.0 − 20000 1.5 29-67 Damping + Bearing Force (kN) Damping + Bearing Force (kN) Seismic Base Isolation and Vibration Control Bearing Displacement (m) 20000 −1.5 −1.0 −0.5 − 40000 (a) 40000 0.0 0.5 1.0 1.5 −20000 − 40000 (b) Bearing Displacement (m) FIGURE 29.75 Damping plus bearing force vs damping displacement relationship of a cable-stayed bridge model with (a) linear dampers, (b) pseudonegative stiffness dampers (type I-III-1 earthquake) relationship for both bridges, with a linear damper and pseudonegative stiffness damper, respectively, under type I-III-1 earthquake input The bridge model with pseudonegative stiffness dampers shows lower base shear than that of the 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T.T., and Mahmoodi, P., Seismic response of steel frame structures with added viscoelastic dampers, Earthquake Eng Struct Dyn., 8, 389 –396, 1989 © 2005 by Taylor & Francis Group, LLC ... combinations of active and passive devices, and tuned mass and liquid dampers may also provide practical solutions in the 29- 1 © 2005 by Taylor & Francis Group, LLC 29- 2 Vibration and Shock Handbook near... Francis Group, LLC 29- 26 Vibration and Shock Handbook FIGURE 29. 26 Typical positions of isolation level for buildings (Source: Mayes, R.L and Naeim, F 2001 The Seismic Design Handbook, 2nd ed.,... Francis Group, LLC 29- 30 Vibration and Shock Handbook FIGURE 29. 29 Three-dimensional base-isolation system for Moroku Bosatsu statue TABLE 29. 2 Details of Isolation System and Dynamic Characteristics