Earthquake resistant design of a steel structure under severe earthquakes depends on its ductility and hysteretic energy dissipation capacity to avoid damage to the primary structural components and the collapse of the entire structure. This, in general, a structure, which has ductility and high hysteretic energy dissipation capacities, is able to absorb input energy through inelastic deformations caused by bending, twisting or cracking of structural components, and is capable of alleviating low cycle fatigue, associated with degradation of strength and stiffness under cyclic loading. However, the structure still may be damaged or suffer partial collapse by permanent damage in critical regions. Thus, there are several innovative approaches for seismic protection of structures. One is base isolation and the other is energy dissipation devices. Seismically induced energy in the structure can be dissipated by applying these energy dissipation devices and thus, seismic response of the structure and overall damage can be reduced and controlled.
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Among theses devices, passive energy dissipative (PED) devices have been developed to alleviate or to avoid damage of structures caused by earthquakes. These PED systems and devices were discussed by Hanson et al. (1993), Hanson (1993), and Dargush and Soong (1995). Kelly et al. (1972) started conceptual and experimental work on metallic plate dampers positioned within a structure. There were more types such as flexural plate systems, torsional bar dampers, yield ring dampers, and extrusion devices by Skinner el al. (1980). Bergman and Goel (1987), and Whittaker et al. (1991) did experimental work on the X-shaped plate damper or ADAS (Added Damping And Stiffness). Tsai el al. (1993) developed triangular plate dampers. Further details about metallic dampers are introduced in the next section.
Earthquake Engineering is a body of knowledge that has been in continuous development during a long period of time. This progress has been an evolutionary process, most of the time, with occasional revolutionary jumps ahead, and sometimes backwards.
The occurrence of some catastrophic seismic events around the world were the source of most of the new knowledge, and a strong motivation to work on the problem. Structural solutions used by the practicing engineers (designers), are tested by Nature during their occurrence. Afterward, it appears that some ideas seemingly very good, turned out to be bad solutions. Thus, academics and researchers have contributed to the body of knowledge by reviewing the behavior of the solutions used by the engineers, learning from the good behavior, but much more from the bad behavior and failures of some of these structures.
So, it has been cycles were designers have tried new structural solutions without having a complete knowledge of their future behavior, and later researchers helped to understand why their solutions failed or behaved in unexpected ways. This way, the original solutions have been repeatedly amended, improved or abandoned as a result of these cycles. Each cycle that, besides the personal worries and interests of engineers, academics and researchers, has had a high cost in terms of lives and economic loses around the globe.
One revolutionary event in the history of the Earthquake Engineering was the proposal by Park and Paulay (1975) of a systematic method of design, based on the accumulated observations of the behavior, during strong seismic events, of many structures around the world. Some of these structures surprised engineers and researchers due to their capacity to resist unexpected extreme seismic events. These structures showed extensive damage in non structural elements and localized plasticization, despite this, the structures survived these events.
From these accumulated knowledge by the engineering community emerges the systematic proposal by Park and Paulay. They called their design approach as the philosophy of Capacity Design. With the publication of their book in 1975, this philosophy started to spread out. De Buen (2004) tells that the Mexico City building code was modified to include in its published 1976 edition, recommendations and procedures to provide structures with the capacity to dissipate energy by developing non linear behavior. That was the first time these recommendations appeared.
Metallic dampers, which function by absorbing energy through the yielding of steel plates or bars, represent one class of effective energy dissipation devices. Ultimately, the energy dissipation may improve the overall performance of the building during earthquakes. Thus, these devices are critical elements of the structure and it is very important to understand their behavior and to decide their size for effective design.
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Added Damping And Stiffness (ADAS) devices and Triangular-plate Added Damping And Stiffness (TADAS), shown in Fig. 1.1 and in Fig. 1.2, were developed to improve the seismic resistance of the structures. These X-shaped or triangular-shaped plates, spaced by rectangular plates and bolted together through two ends of each plate or welded to a common base plate, are typically designed to be installed within a frame or at specific locations for a new or existing building. The devices resist the lateral forces as the structure sways and, accordingly, provide the structure increased stiffness and strength as well as additional energy dissipation capacity. Analytical and experimental studies showed that ADAS and TADAS devices can withstand a large number of yielding reversals and can accumulate a lot of inelastic deformation without degradation of strength or stiffness. Also, these devices can result in a significant reduction of interstory drifts and can maintain stable hysteretic loop. Therefore, these devices may be expected to give a reliable performance during severe earthquake excitations (Whittaker et al., 1991, Tsai et al., 1993). The advantage of installing the ADAS and TADAS for retrofitting of buildings is to reduce the horizontal displacements of the moment resistant frame (MRF) to desirable levels. Thus, these devices are especially effective in retrofitting a MRF system.
Figure : Details of steel welded ADAS device (Whitaker et al., 1991)
Structures are generally designed to withstand gravity loads acting vertically, but earthquake resistant structures must be designed to resist the lateral load associated with horizontal ground motion, which has characteristics such as dynamic behavior and cyclic reversal of stress. These complicated earthquakes loadings make analysis computationally time consuming, and should be simplified whenever possible. In many applications, therefore, structures and structural components are experimentally tested or analytically verified by examining response under cyclic loading to understand uncertain inelastic behavior of the material. As a necessary tool to predict inelastic behavior, appropriate cyclic plasticity model are required. Also, this cyclic plasticity model should be verified under cyclic loading, which has complex loading histories such as repeated loading and unloading with changing magnitude. Thus, these models can be generally categorized by rate dependent plasticity model and rate independent model, even though there are special purposes of plasticity models. However, these existing plasticity or viscoplasticity models cannot predict any failure or damage, such as low cycle fatigue failure. Thus, some background on damage mechanics is also reviewed in the following section.
Rate independent plasticity model
A large number of researchers have developed a significant number of elasto-plastic models under monotonic, cyclic and complex loadings. The theory of rate independent plasticity has basic fundamental features, such as the existence of yield, a plastic flow rule, normality rule and hardening rule. The yield surface divides the elastic and plastic region depending on a yield function. The flow rule relates the plastic strain to the stress state. The normality rule assures that the incremental plastic strain is in the direction normal to the yield surface at the current load point. The hardening rule is used to predict changes in the yield criterion and flow equation. In the 1950's, the plasticity models that have internal variables have been developed. Hill (1950) and Hodge (1955) proposed the isotropic hardening model, in which the center of the yield surface stays fixed and the surface expands without changing shape. This model cannot predict the Bauschinger effect during the unloading range. To overcome this, Ishlinski (1954) and Prager (1956) developed the kinematic hardening model. In this model, the yield surface translates without rotation or shape change. This model was improved by Shield and Ziegler (1958). Also, a number of different cyclic plasticity models may be also applicable. Valanis (1971, 1980) developed endochronic theories considering intrinsic time to make the response rate independent.
Two types of plasticity models can be divided as the multisurface type and the Armstorng-Frederick kinematic hardening type. As a multisurface type model, Mroz (1967) and Iwan (1967) extended models to multi dimensional case to describe cyclic effects. Dafalias and Popov (1975) developed a two surface model based on the concept that the plastic modulus varies, and Krieg (1975) proposed a two surface plasticity model using a loading surface and a limit surface. Banerjee et al. (1987) and Chang and Lee (1987) developed a two surface plasticity model to represent both kinematic and isotropic hardening behavior. This two surface model is characterized by an inner surface that follows a kinematic hardening rule and an outer surface, which provides for isotropic hardening. This model was applied in Dargush and Soong (1995) to help understand inelastic behavior of steel plate dampers. Megahed (1988) and McDowell (1989) developed similar two surface models, while Jiang and Sehitoglu (1996a) reviewed Mroz's multisurface model.
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Another type of plasticity model was started from the Armstrong-Frederick model (1996). The main issue for the Armstrong-Frederick type model is how to control the change of back stress, and thus, many researchers have modified the dynamic recovery term. Many researchers developed models such as Chaboche el al. (1979), Chaboche and Rousselier (1983), Chaboche (1991), Ohno-Wang (1993), McDowell (1995), Jiang and Sehitoglu (1996b), Abdel-Karim and Ohno (1998), Ohno and Abdel-Karim (2000), Bari and Hassan (2002), Kang et al.(2003), Voyiadjis and Abu Al-rub (2003), Chan and Jiao (2004), Kang (2004), and Abdel-Karim (2005).
Some cyclic plasticity models are studied to represent the ratchetting behavior of metals. The ratchetting phenomena are observed during non-zero mean stress in the stress-controlled loading. Experimental work was done by Benham (1960), Coffin (1964), Dolan (1965), for uniaxial stress cycles, and Wood and Bendler (1962), Benham (1965), Morrow (1965), Ruiz (1967), Landgraf, and Morrow, and Endo (1969) for biaxial stress cycles. After that, Pilo el al. (1979), Yoshida et al. (1980), Alameel (1985), Chai and Laird (1987), Ruggles and Krempl (1989), and Hassan and Kiriakides (1992) tested ratchetting behavior of metal.
Analytical work on ratchetting behavior was done using the Armstrong-Frederick model, which has a dynamic recovery term by Ohno (1990, 1998) and Corona et al. (1996). Chaboche (1986, 1989) modified the Armstrong-Frederick model and introduced a dynamic recovery term based on a threshold considering each back stress. Butlet and Cailletaud (1987) modified the Armstrong-Frederick model to consider nonproportional loading. Ohno and Wang (1993a, 1993b) proposed a nonlinear dynamic recovery term using a power law. Chaboche (1994), Tanaka (1994), McDowell (1995), Jiang and Kurath (1996), and Jiang and Sehitoglu (1996) continue to study this kind of approach. Abdel-Karim and Ohno (2000) studied a kinematic hardening model with steady state ratchetting.
Hassan and Kiriakides (1992) used the Drucker-Palgen model, the Dafalias-Popov model and Tseng-Lee model and proposed the modified the Dafalias-Popov model and compared with experimental results. Bari and Hassan (2000, 2001, and 2002) simulated using the bilinear Prager model (1956), nonlinear Armstrong Frederick model (1966), modified Chaboche model (1991), Ohno-Wang model (1993), and Guionnet model (1992) for uniaxial ratchetting, and Chaboche model (1991), McDowell model (1995), Jiang-Sehitoglu model (1996), Voyiadjis-Basuroychowdhury model (1998) and Abedl-Karim-Ohno model (200), modified Dafalias-Popov model, Voyiadjis-Sivakimar model (1991), Phillips and Lee (1979), Tseng-Lee model (1983), Kaneko model (1981, 1984), and Xia-Ellyin model (1994, 1997) for biaxial ratchetting. Finally, they compared with experimental results of Hassan and Kiriakides (1992). Recently, Kang et al. (2002), Kang and Gao (2002), Kang (2004), Kang el al. (2004), Kang and Gao (2004), Chen and Jiao (2004), Chen et al. (2005), Abdel-Karim (2005) developed Armstrong-Frederick type nonlinear kinematic hardening models to apply for ratchetting simulation.
Rate dependent plasticity model
Viscoplasticty is referred to the mechanical response of solids involving time dependent, irreversible strains (Lemaitre, 2001). For viscoplasticity, elastic strain and the strain hardening rule are the same as those in plasticity. Rate independent plasticity models mentioned in the previous section, cannot describe time dependent inelastic behavior of material, such as strain rate effect, stress rate for ratchetting, and hold time. Thus, these viscoplasticity models have been developed to consider the character of rate dependence and to establish correlation with experimental results. Experimental work considering a rate effect was done by Lindholm et al. (1971), Randall and Campbell (1972) using a machine to be able to produce a high strain rate. Marsh and Campbell (1963) tested mild steel considering rate effects, Klepaczko (1967) and Franz and Duffy (1972) also considered strain rate effects. Krempl (1979) and Kujanski and Krempl (1981) tested under cyclic loading with variable strain rate. Yoshida et al. (1989) and Yoshida (1990, 1995) tested uniaxial and biaxial creep ratchetting of SS305 stainless steel.
Bodner and Partom (1972) started to establish a viscoplastic theory. Their unified theory described an approach that inelastic behavior of plasticity and viscoplasticity was not separated. Miller, (1976), Robinson et al. (1976), Hart (1976), Krempl (1979) studied this theory, and Chaboche (1977) developed a viscoplastic constitutive model with nonlinear kinematic hardening, and Chaboche and Rousselier (1983) applied this model to the 316 stainless steel. Ellyin and Zia (1991) then used this viscoplasticity model for stainless steel 304 and 316. McDowell (1992) developed viscoplastic nonlinear kinematic hardening model under thermomechanical cyclic conditions, while Tanaka (1994) developed a viscoplastic constitutive model under nonproportional loading.
Chaboche and Rousselier (1983a) used their viscoplasticiy model for the simulation of ratchetting. Ohno and Wang (1993) combined a modified Armstrong-Frederick model and viscoplastic equation. Tanaka and Yamada (1993), and Abdel-Karim and Ohno (2000) continued with this study. This rate-dependence of ratchetting has been done by Kang et al. (2001), Kang et al. (2002), Kang el al. (2004), Yaguchi and Takahashi (2000), Yaguchi and Takahashi (2005), and Kang et al. (2006).
Damage in metals is mainly the process of the initiation and growth of micro-cracks and cavities (Voyiadjis, 2005), and damage is generally regarded as the progressive or sudden deterioration of materials prior to the failure of material due to loadings or thermal or chemical effects (Lemaitre, 2001). There are three main types of damages; ductile damage (Lemaitre, 1984 and 1986, Voyiadjis and Kattan, 1992), fatigue damage (Lemaitre, 1971) and creep damage (Hult, 1979, Lemaitre and Chaboche, 1974).
Kachanov (1958) and Rabotnov (1969) developed the concept of macroscopic damage. This continuum damage mechanics developed further by Chaboche (1981), and Krajcinovic (1984), Lemaitre and Chaboche (1990), Wang (1992), Wang and Luo (1990), Basaran and Yan (1998), Basaran and Nie (2004) and Basaran and Lin (2008).
Despite the advancement in seismic design procedures, extensive structural damage has occurred during most of the recent earthquakes. Strong wind storms have also resulted in significant structural damage especially in low-rise buildings including housing. In addition, strong wind also affects the serviceability of tall and flexural structures by causing excessive deflections leading to occupant's discomfort. Increasing the energy dissipation characteristics of structures can significantly reduce the risk of those damages and can also improve the structures' serviceability during natural load events. An efficient means to increase the energy dissipation of a structure is alter its damping characteristics. External or auxiliary damping devices can be attached to structures during initial construction for new buildings or at a later stage as a retrofitting technique in order to increase the damping level.
Passive energy disssipation
A great amount of energy is passed on into a structure throughout earthquake ground motions. Conventional design works on a philosophy that allows the 'structural members' to soak up and dissipate the transmitted earthquake energy by inelastic cyclical deformations in explicit regions and thus put off the collapse. In the last twenty years, in order to ensure safety and diminish the possible damage of structures due to earthquakes, protective systems have been formed. These optional approaches intend to manage the 'structural seismic response and energy dissipation demand' on the structural members by adjusting the dynamic properties of the scheme. (Moreschi)
At present, the most realistic and trustworthy technique of plummeting seismic structural response is the exercise of passive response control schemes. They can be categorized according to the aims used to deal with the 'input earthquake energy' as:
(1) Seismic isolation systems and,
(2) Passive energy dissipation systems.
The seismic segregation systems, shown in Figure 1.2(a), ward off the 'earthquake energy by interposing a layer with low horizontal stiffness between the structure and the foundation'. These systems are appropriate for a huge class of buildings ranging from short to medium height, and whose leading modes are within a 'certain frequency range'. A number of structures and bridges have now been installed with base isolation systems. The 'passive energy dissipation systems', on the contrary, work as energy goes down and soaks up some of the 'vibration energy' so that little is accessible to cause 'deformation of structural elements'. They consist of tactically placed dampers (viscous, viscoelastic or friction dampers) or disposable elastic elements that link different parts of the framing scheme, as illustrated in Figure 1.2(b). (Moreschi)
'Dynamic vibration absorbers' also fit into this classification. The decrease in the structural response is achieved by transmitting some of the 'structural vibration energy to auxiliary oscillators attached to the main structure'. Figure 1.2(c) portrays a typical execution of a tuned mass damper in a building structure. (Moreschi)
Different types of structural control systems
Housner et al. (1997) has described different energy dissipation systems used in structural engineering including active, semi-active, passive and hybrid systems. Soong and Spencer (2002) also summarized the state-of-the-art of practice of different energy dissipation systems and their structural applications. Kareem et al. (1999) described different control systems installed in various buildings around the world. The main objective of using a control system in a building is to improve the serviceability and/or the safety of the occupants against natural hazards. Schematics of different control systems are provided in Figure 2, which are explained briefly in the following paragraphs.
Figure : Schematics of various control systems (Kareem et al, 1999)
An active control system uses externally prescribed applied forces to reduce the undesired vibration response of a structure. In such a system, sensors are used to record the applied excitations as well as the structural vibrations. As shown in Figure 1.1(a), based on the measured excitations/vibrations, the controller introduces a control force to the secondary mass through the actuator to counteract the structures motion. Active control systems require external sources of power to operate which may be at risk due to potential power failure during the loading event. Although the active control system concept has been implemented in the fields of mechanical and electrical engineering for a long time, its application in civil engineering started only in the early 1960's. Soong (1988) and Housner et al. (1996) described the development of various active control systems and their uses in civil engineering.
As shown in Figure 1.1(b), in a passive control system, no force is applied directly to the structure. The function of a passive control system is to alter the characteristics of the structure such as its damping, stiffness and strength. The main advantage of passive control systems relative to active control systems is that they do not require any external energy to operate thus eliminating the risk of power failure during a catastrophic event. Tuned Mass Dampers (TMD) and Tuned Liquid Dampers (TLD) are two common passive control devices. Due to their simplicity and efficiency in reducing structural responses, these two control systems are widely used in civil engineering (Soong and Dargush, 1997). Both dampers involve adding to the structure an auxiliary system consisting of a mass, spring and a dashpot.
A hybrid control system can be defined as a combination of active and passive control systems. Compared to passive control systems, hybrid control systems have the advantages of being able to respond quickly to suddenly applied loads such as earthquakes. As shown in Figure 1.1(c), in a hybrid control system, a tertiary mass is connected to the auxiliary secondary mass using spring, damper and actuator. The motion of the secondary mass system is set and magnified by the active tertiary mass, making it more efficient. In this system, the active control is used only during high structural excitations. In the event of power failure or extreme excitation, the device automatically switches to a passive control system thus eliminating the risk of total system failure. Most of the applications of hybrid dampers were done in Japan. A reduction in the structural response of about 50% due to the addition of hybrid dampers was reported by Kareem et al. (1999).
Similar to the hybrid systems, semi-active control systems also require small external power sources. Researchers have developed this control system by combining the best features of active and passive control systems. For a semi-active control system, the properties of the auxiliary device are instantaneously altered and optimized during loading in order to achieve a maximum reduction in the structural response. A semi-active control system operates on battery power, which is an advantage during seismic events when electrical power might fail. The use of a semi-active control system eliminates the risk of destabilizing the primary structure, which might happen when an active control system is used. Semi-active control systems include variable-orifice fluid dampers, controllable friction devices, variable stiffness devices, controllable tuned liquid dampers, and controllable impact dampers.
Passive energy dissipation system
Metallic damper, friction damper, viscoelastic damper, viscous fluid damper, tuned mass damper and tuned liquid damper are different types of passive energy dissipation systems. In the last few decades, research has been undertaken to understand the concept of passive energy dissipation and many of these devices have been installed in different parts of the world (Soong and Dargush, 1997, Kareem et al. 1999). A brief review of the research conducted on tuned mass dampers which have many analogies with tuned liquid dampers is provided below. A detailed review of previous studies conducted on tuned liquid dampers is then given.
Tuned mass damper (TMD)
A tuned mass damper (TMD) consists of a secondary mass attached to the structure through a spring and a dashpot. Usually the secondary mass represents a small percentage of the total mass of the structure. The mass and the spring stiffness are selected such that the natural frequency of the secondary system almost matches the frequency of the structural mode for which the response is to be suppressed. In this case, the mass motion imparts an inertia force acting against the motion of the structure. This leads to a reduction in the response of the structure. As a result, the effective damping of the structure is increased due to the addition of the TMD. The first two TMD systems in civil engineering applications were installed to the John Hancock Tower in Boston and the Citicorp Center in New York, in 1977 and 1978 respectively, (McNamara, 1977). Tuned mass dampers were then used in many structures in various countries such as Australia, Canada, Japan and United States to reduce the wind induced vibrations. They were installed to airport towers, buildings, bridges and chimneys and led to a reduction of structural responses ranging between 30% and 50% (Kareem et al. 1999). TMD application has shown to be very effective for the case of narrow band excitation such as wind. In terms of their seismic applications, Villaverde (1994), indicated that the effectiveness of a TMD in reducing the seismic response of a structure depends on the type of structure as well as the characteristics of the seismic excitation.
Tuned liquid damper (TLD)
Tuned liquid dampers (TLD), as passive energy dissipation devices, have many similarities to tuned mass dampers. A TLD consists of a rigid tank partially filled with liquid. The fluid acts as a substitute providing the necessary characteristics of the secondary mass, spring and dashpot used in a TMD. Similar to tuned mass dampers, the frequency of vibration of the sloshing motion, which represents the secondary system, is almost tuned to the frequency of the structural mode to be suppressed. The sloshing frequency is controlled through the selection of the tank's length and the height of the liquid inside the tank. For a properly tuned TLD, the sloshing motion imparts forces that act against the motion of the structure and, therefore, reduces the structural vibrations.
TLD has been first utilized in the ship industry at the beginning of 20th century to prevent the rolling motion of large ships (Den Hartog, 1956). Figure 1.2(a) shows the Frahm anti-rolling tank used in large ship. They were also used in satellite technology where they were called as "nutation dampers" as shown in Figure 1.2(b). The application of TLDs in civil engineering structures started in the 1980's (Modi and Welt, 1987, Fujii et al. 1988).
Tuned liquid dampers have the following advantages:
a) Low maintenance and operating cost,
b) ease to tune to the desired frequency,
c) ease to apply as a retrofitting tools to existing structures,
d) dual use since the water tanks can be used as emergency fire reservoirs.
Meanwhile tuned liquid dampers have the following disadvantages:
a) Highly non-linear behaviour of the sloshing motion, especially under large excitation amplitudes,
b) not all portion of water participate in the sloshing motion,
e) due to the low density of water, a relatively large space is required in order to achieve the desired mass for the secondary system.
In order to operate in an efficient way, tuned liquid dampers must possess a certain amount of inherent damping. Viscous action of the boundaries of the tanks provides a certain amount of inherent damping. Unless the fluid depth is quite shallow, the amount of viscous force is not usually enough to achieve the required amount of inherent damping. In such a case, external damping devices can be installed inside the tank to increase the inherent damping. Those include roughness elements (Fujino et al. 1988), surface contaminants (Tamura et al. 1995) and nets or screen (Welt, 1999, Noji et al., 1998, Warnitchai and Pinkaew 1998, Kaneco and Ishikawa 1999 and Tait et al. 2004, 2005).
Figure : Schematics of structure-TLD systems, (a) Structure-TLD (b) Mechanical model
The analysis of a structure with a TLD attached can be simplified by replacing the TLD with an equivalent tuned mass damper (TMD) having the same dynamic characteristics. Figure 1.3 shows a schematic of a structure-TLD system and its equivalent mechanical TMD model of TMD. Due to the non-linearity of the sloshing motion of the TLD, the parameters of the equivalent TLD are also non-linear, i.e. they are amplitude dependent. The first attempt to use an equivalent mechanical model to represent the sloshing forces of a fluid was conducted by Graham and Rodriguez (1952). This model is limited since it does not capture the non-linearity of the TLD and also does not account for the effect of internal damping devices.
More recently, semi-empirical models of an equivalent TMD simulating the non-linear behaviour of the sloshing motion in a TLD were developed (Chaiseri 1990, Sun et al. 1995, Yu et al. 1999 and Yalla, 2001). A number of assumptions were applied in those models. They also did not include the effect of internal damping elements. Recently, Tait et al. (2004) used the concept of equal energy dissipation to develop an equivalent amplitude dependent TMD model which simulates the non-linear behaviour of a TLD equipped with internal dampening screens. All above studies were limited to wind applications. Small and intermediate excitation amplitudes, equivalent to the level of excitations expected by wind loads, were considered in those studies. Also, no transient excitations were applied. Few researchers have investigated the use of TLD in transient/earthquake excitations. Koh et al. (1994) conducted a numerical study to investigate the use of TLD in controlling the seismic response of suspension bridges. Reed et al. (1998) investigated experimentally and numerically the response of TLD devices subjected to large excitation amplitudes corresponding to values expected during earthquake excitations. From this study it can be concluded that the non-linearity of the sloshing motion makes the TLD an effective and robust device in reducing structural responses during strong dynamic events. Banerji et al. (2000) performed numerical simulation of a structure-TLD system subjected to seismic excitations and concluded that a TLD operates well as a structural control system when the inherent damping of the structure is low and the fundamental frequency of structure is tuned to the fundamental sloshing frequency of the TLD.
Numerical modeling of structure-TLD system
From this section and onward a structure with a TLD attached is referred to as "structure-TLD system". Previous studies conducted to predict the response of a structure-TLD system involved modeling the structure using the generalized single degree of freedom approach and using an equivalent TMD to simulate the TLD (Banerji et al., 2000 and Tait et al., 2005). This approach is adequate enough for wind applications, where the TLD is used to achieve the serviceability requirements and the response of the structure is typically linear. During an earthquake event, members of the structures can be subjected to non-linear deformations. As such, in order to predict accurately the response of a structure-TLD system under earthquake loading, finite element modeling of the structure using a multi-degree of freedom approach has to be conducted. This approach is applied in the current study, which considers concrete buildings with rigid frames used as the lateral load resisting systems.
Multiple tuned liquid dampers
Typically, a structure-TLD system involves attaching a number of tanks to the structures. If the tanks have the same length (in the direction parallel to the direction of excitation) and also have the same water depth, they become all tuned to the same sloshing frequency. In this case, the system will be called "single tuned liquid dampers" (STLD). This system is effective in reducing the structural response when the predominant frequency of the input excitation is close to the fundamental frequency of the TLD. Accordingly, single TLD is effective for the case of narrow band excitations such as wind. For the case of earthquake excitations, the predominant frequency is distributed over a certain range for which a single frequency TLD may not be effective in reducing the structural response. The concept of multiple tuned liquid dampers (MTLD) involves tuning the tanks to a number of frequencies distributed over a certain range. The effectiveness of MTLD under wind excitations was studied by a number of researchers (Fujino and Sun 1993, Li et al. 2000). It is expected that more benefit will be achieved when MTLD system is used to suppress the vibration of structures under earthquake excitations.
Modeling of concrete structures
To predict the seismic behaviour of RC fiexural members, subjected to general loading conditions, a realistic model capable of predicting the different modes of failure, such as: concrete crushing, steel yielding and failure due to bond-slippage is required. The model should have the ability to represent the cyclic behaviour of these members. Two types of models, micro and macro, are available in the literature (Lai et al. 1984; Ghusn and Saidii, 1986; Youssef and Ghobarah 1999). The advantages of the macro model over the micro model include ease of computation and less computer storage. Extensive research has been conducted to simulate the hysteretic behaviour of RC members using macro models (Takeda et al., 1970; Ozcebe and Saatcioglu, 1989; Roufaiel and Meyer, 1987; Youssef and Ghobarah, 1999; Galal and Ghobarah, 2003). The model of Youssef and Ghobarah (1999) was found to have the distinctive ability of representing strength deterioration due to different failure modes. It also allows identification of local seismic damage. These abilities are crucial for judging the response of buildings fitted with TLDs. Although this model is able to accurately predict the behaviour near the ultimate fiexural capacity, its accuracy is not granted at lower fiexural values. In this study, this model is modified to address this deficiency.
The application of Tuned Liquid Dampers (TLD) in suppressing the vibration of structures has begun more than two decades ago (Soong and Dargush, 1997). TLD is a device consisting of a rigid tank partially filled with liquid. During the vibration of a structure, sloshing motion occurs at the free surface of the TLD attached to the structure. If a TLD is properly tuned, the sloshing motion imparts forces that act against the motion of the structure and, therefore, reduces the structure vibrations. TLDs have a lot of similarities with tuned mass dampers (TMD). A TMD consists of a solid metal or concrete block acting as a secondary mass and attached to the structure through a spring and a dashpot. In TLDs, the fluid acts as a substitute providing the necessary characteristics of the secondary mass, spring and damper.
TLDs have gained sufficient attention due to their simplicity and low installation and operating costs. These devices have been successfully used in reducing the dynamic response of high-rise buildings and towers subjected to strong winds (Fujii et al. 1988, Tamura et al. 1995 and Wakahara et al. 1992). Despite the simplicity of this device, the prediction of the behaviour of a TLD is a challenging task since the sloshing motion exhibits highly non-linear behaviour at high response amplitudes (Tait et al. 2004). The majority of research studies conducted on TLDs have focused on their response to either harmonic or white noise excitations. These studies provide insight into the response of structures with TLD attached under wind loads.
Concerning TLD/earthquake related studies, Kofa et al. (1994) conducted a numerical study to investigate the use of TLDs in controlling the seismic response of suspension bridges. This study was conducted using a 1% ratio between the mass of the fluid and the generalized mass of the bridge. A reduction in the seismic response of the bridge ranging between 20% and 30% was achieved using this mass ratio. Reed et al. (1998) numerically investigated the response of TLD devices subjected to large excitation amplitudes corresponding to values expected during earthquake excitations. Findings from this study suggest that the non-linearity of the sloshing motion makes the TLD a more effective and robust device for structural control. The same conclusion was reached by Banerji et al. (2000) through their numerical simulations.
They found that a TLD having 4% mass ratio relative to the generalized mass of the structure and subjected to a high frequency broad band earthquake motion, reduces the structural response by approximately 50% if the structural damping ratio is 0.5% and by approximately 33% if the structural damping is 2%. However more studies are needed to understand the response of structures equipped with TLDs to transient excitations and to confirm the efficiency of this damping device in controlling the seismic response of structures.
Passive energy dissipative devices have been developed over the last several decades to alleviate, or in some cases to avoid completely, damage of structures caused by earthquakes. Metallic dampers, which function by absorbing energy through the yielding of steel plates or bars, represent one class of effective energy dissipation devices. Ultimately, the energy dissipation may improve the overall performance of the building during earthquakes. Thus, these devices are critical elements of the structure and it is very important to understand their behavior and to decide their size for effective design.
The present study helps to analyze inelastic behavior of metallic dampers, such as stiffness degradation and strength reduction, using a two surface damage model and to design effectively metallic dampers as energy dissipation devices to protect structures during earthquake excitation. Furthermore, through ratchetting simulation of structural steel, the two surface model helps to analyze and design more effectively structures subjected under cyclic loading. Since structures may be dependent on the rate of loading and can be affected by transient loading or dynamic loading, the rate of loading is always an issue to understand structures during earthquake excitation. Thus, this analysis considering the rate effect is beneficial for effective design of structures under earthquake loading and, perhaps more importantly, under conditions of impact, where the loading rates are higher.