Seismic Energy Dissipation of Inelastic Structures with Multiple Tuned Mass Dampers

The ability to use multiple tuned mass dampers (TMDs) in improving inelastic structural performance to dissipate the earthquake input energy is investigated. Inelastic structural behavior is modeled using the force analogy method, which is the backbone of analytically characterizing the plastic energy dissipation in the structure. Both tuning period and placement of the multiple TMDs are studied to give the best structural performance in terms of plastic energy dissipation. Numerical simulations are performed to study the energy responses of structures with and without TMD installed, and the effectiveness of TMDs in the reduction of energy responses is also studied by using tuned mass spectra. Results show that the installation of TMDs gives the structure additional capability of dissipating a large amount of damping energy and at the same time reducing the amount of plastic energy demand and therefore reducing damage in the structure. More important, TMDs have the ability to draw the plastic energy dissipation at the lower stories and release it to the upper stories. This is particularly beneficial for structures that would otherwise suffer more damage at the lower stories than the upper stories. However, the reduction in plastic energy dissipation is quite sensitive to the earthquake vibration characteristics, and TMDs should not be used for structures with weak upper stories.     

Seismic Analysis of Structures with Viscoelastic Dampers

Viscoelastic dampers are being used in structures to mitigate dynamic effects. The models of varying complexities from simple maxwell element to differential models with fractional and complex order derivatives have been used to represent their frequency-dependent force deformation characteristics. More complex models are able to capture the frequency dependence of the material properties better, but are difficult to use in analyses. However, the classical models consisting of assemblies of Kelvin and/or Maxwell elements with an adequate number of parameters can be formed to capture the frequency dependence as accurately as the more sophisticated fractional derivative models can do. The main advantage in adopting these classical models is a simpler and smaller system of equations, which can be conveniently analyzed for nonlinear and linear systems. In this study, the two classical mechanical models consisting of Kelvin chains and Maxwell ladder are used. It is shown that these mechanical models are as effective as the fractional derivative model in capturing the effect of the frequency dependence of the material properties in response calculations and are more convenient to use in dynamic response analyses.     

Earthquake Response and Energy Evaluation of Inelastic Structures

A computational method is derived to characterize the energy in inelastic structures and the transfer among various energy forms over the duration of an earthquake. This computational method is based on the force analogy method, which uses a change in displacement field to represent the inelastic behavior of structure instead of the traditional method of changing stiffness. The evaluation of plastic energy due to inelastic deformation in the structure becomes very simple using the force analogy method, where the accumulation of plastic energy due to plastic rotations is exactly equal to the elastic moment multiplied by the change in plastic rotations. In addition, this plastic energy formula can be used for any material with predefined stress–strain relationship, and therefore the transfer of energy among various forms can be calculated at any specific time. Once the energy equation is derived, numerical analyses are performed on a single degree of freedom system to study the characteristics of energy transfer. This is then extended to study the transfer of energy among various forms in a multidegree of freedom system. These two studies show that the analytically derived equation for plastic energy is accurate in studying the structural energy response due to earthquake excitations.     

Seismic Response Control of Building Structures with Superelastic Shape Memory Alloy Wire Dampers

This paper presents a simulation-based benchmark control study in which shape memory alloy (SMA) wire dampers are utilized to control the seismic response of a three-story nonlinear steel frame building. The SMA wire damper uses superelastic Nitinol wires for energy dissipation because of its high fatigue life and large recoverable strain. An analytical model which considers the training effect of SMA wires is used to describe the stress-strain relationship of superelastic SMA wires. The performance of SMA wire dampers is investigated in the framework of the third-generation benchmark problem on structural control. A comparative study of the seismic response control performance of SMA wire dampers with either unprestrained or prestrained SMA wires was also conducted. The results of this simulation-based benchmark control study show that SMA wire dampers, as a passive structure control measure, can effectively reduce the seismic responses of the three-story nonlinear benchmark building structure and has the potential to withstand several design earthquakes without the need for repair.     

Timoshenko Beam with Tuned Mass Dampers to Moving Loads

The structural analysis of a Timoshenko beam system with tuned mass dampers (TMDs) under moving-load excitation is presented. A proposed simplified two-degrees-of freedom system based on the first mode of the Timoshenko beam is employed for the design of TMDs. The dynamic characteristics of a Timoshenko beam, such as the structural-resonant and phase-resonant velocities, and the effectiveness of a TMD for vibrational control are especially emphasized. A practical example of an elevated railway subjected to the Japanese Shinkansen (SKS) high-speed bullet train is included.     

Performance of Tuned Liquid Dampers

This paper investigates the performance of unidirectional and bidirectional tuned liquid dampers (TLDs) under random excitation. The performance of the tuned liquid dampers is measured in terms of efficiency and robustness. A series of experimental tests are conducted on model scale structure-tuned liquid damper systems to evaluate their performance, which is then compared to that of the well known tuned mass damper. The effective damping is calculated for each test conducted and the efficiency and robustness are subsequently examined. The performance of a mistuned TLD is experimentally investigated to highlight the robustness of these passive dynamic vibration absorbers. A nonlinear numerical model is used to conduct an extensive parametric study on the performance of a tuned liquid damper. This study has resulted in the development of performance charts for a tuned liquid damper. These charts allow the efficiency of a tuned liquid damper to be examined for a number of varying parameters, which include the excitation amplitude, water depth, and building frequency. These charts are particularly useful for the initial design of a tuned liquid damper when the precise frequency of the structure is not known.     

Seismic Control of a Nonlinear Benchmark Building Using Smart Dampers

This paper addresses the third-generation benchmark problem on structural control, and focuses on the control of a full-scale, nonlinear, seismically excited, 20-story building. A semiactive design is developed in which magnetorheological (MR) dampers are applied to reduce the structural responses of the benchmark building. Control input determination is based on a clipped-optimal control algorithm which employs absolute acceleration feedback. A phenomenological model of an MR damper, based on a Bouc–Wen element, is employed in the analysis. The semiactive system using the MR damper is compared to the performance of an active system and an ideal semiactive system, which are based on the same nominal controller as is used in the MR damper control algorithm. The results demonstrate that the MR damper is effective, and achieves similar performance to the active and ideal semiactive system, while requiring very little power.     

Performance Test of Energy Dissipation Bearing and Its Application in Seismic Control of a Long-Span Bridge

Energy dissipation bearing (EDB) is a conventional steel bridge bearing in connection with well designed mild steel dampers. Seismic performance test was undertaken for both damper units and a prototype bearing, and the results show very stable and high dissipation characteristics. In describing the hysteretic behavior of EDBs, the Wen model is proved to be more reasonable, and the corresponding model parameters are also proposed according to the test results. EDBs have been applied in the seismic control of a long span bridge, the Nanjing Jia River Bridge, for the first time, in both the longitudinal and transverse directions. Sensitivity studies were conducted to investigate the effectiveness and to determine the optimum parameters and distribution of the EDBs through nonlinear time-history analysis. The results show that EDBs achieve a very high effectiveness in seismic control, in both the longitudinal and transverse directions. Compared with other damping devices, they can provide a simple but valid seismic control solution, with low maintenance requirements, especially in the transverse direction.     

Potential for Structural Failure in the Seismic Near Field

This study analyzes the possibility that large distortions and distortion rates due to wave-propagation phenomena within structures were responsible for unexpected cracking at connections of steel-frame buildings in the seismic near-field region during the Northridge (1994) and Kobe (1995) earthquakes. Since such internal wave propagation is characteristic of a structure with a continuous distribution of mass, the problem is studied by numerically simulating the structural response for both discrete and continuous models of a 20-story building, using ground motion time histories from the Northridge earthquake. The time histories are chosen from the far-field and near-field regions of the earthquake to determine if wave-propagation effects within the structure are especially significant in the near field. A truncated modal analysis is also performed using only the first vibrational mode to see if significantly lower response levels result. It is found that the continuous model gives higher response levels—indicating that wave propagation may have been a factor—but the discrepancy is not limited to the near field. Strain rates are higher from the continuous model than from the discrete model and much higher than from the truncated modal analysis, but the magnitudes are too low to be a significant factor in the observed damage. The explanation for the connection cracking may simply be high-intensity ground motion in the near field.     

Earthquake Response of Elastic Single-Degree-of-Freedom Systems with Nonlinear Viscoelastic Dampers

Investigated are the steady-forced and earthquake responses of single-degree-of-freedom (SDF) systems with a nonlinear viscoelastic damper (VED), which consists of a nonlinear fluid viscous damper (FVD) connected in series to a linear elastic bracing element (chevron or inverted V-shaped braces). For a wide range of bracing stiffness, nonlinear dampers are advantageous because they achieve essentially the same reduction in system responses but with a significantly reduced force. Damper nonlinearity has little influence on the structural response in the velocity-sensitive region of the spectrum even if the bracing is fairly flexible, but differences up to 16% were observed in other spectral regions. As expected, supplemental damping reduces structural response and the response reduction depends on the bracing stiffness, with this dependence varying with the spectral regions. For practical applications, a procedure is presented to estimate the design values of structural deformation, structural force, foundation shear, and damper force directly from the earthquake design (or response) spectrum. Finally, a procedure is presented to determine the damper and bracing properties necessary to limit the structural deformation to some design value or to the structural capacity.     

Implementation of Modal Control for Seismically Excited Structures using Magnetorheological Dampers

This paper proposes an implementation of modal control for seismically excited structures using magnetorheological (MR) dampers. Many control algorithms such as clipped-optimal control, decentralized bang-bang control, and the control algorithms based on Lyapunov stability theory have been adopted for semiactive systems including MR dampers. In spite of good features, some algorithms have drawbacks such as poor performance or difficulties in designing the weighting matrix of the controller. However, modal control reshapes the motion of a structure by merely controlling a few selected vibration modes. Hence a modal control scheme is more convenient to design the controller than other control algorithms. Although modal control has been investigated for several decades, its potential for semiactive control, especially for the MR damper, has not been exploited. Thus, in order to study the effectiveness for a MR damper system, a modal control scheme is implemented to seismically excited structures. A Kalman filter is included in a control scheme to estimate modal states from measurements by sensors. Three cases of the structural measurement are considered by a Kalman filter to verify the effect of each measurement; displacement, velocity, and acceleration, respectively. Moreover, a low-pass filter is applied to eliminate the spillover problem. In a numerical example, a six-story building model with the MR dampers on the bottom two floors is used to verify the proposed modal control scheme. The El Centro earthquake is used to excite the system, and the reduction in the drifts, accelerations, and relative displacements throughout the structure is examined. The performance of the proposed modal control scheme is compared with that of other control algorithms previously studied. The numerical results indicate that the motion of the structure is effectively suppressed by merely controlling a few lowest modes, although resulting responses varied greatly depending on the choice of measurements available and weightings.     

Tuned Mass Dampers for Dual-Mode Buffeting Control of Bridges

The objective of this paper is to present the idea of control of the dual-mode buffeting response in suspension bridges under service conditions using two tuned mass dampers (TMDs). The bridge is assumed to vibrate in two vertical modes, which are to be controlled using two TMDs. The TMDs’ properties are determined by minimizing the maximum buffeting response of the bridge. By neglecting modal coupling terms, some approximate formulas are derived. A numerical example is used to understand the requirements for the TMDs. The results show that, as compared to using only one TMD, the dual TMDs offer a more pronounced response reduction. The results also reveal some disadvantages of using the TMD system for buffeting vibration control. The major one is that the efficiency of the TMD system declines and the strokes increase significantly as the wind speed increases.     

Energy Dissipation in Surface Layer due to Vertically Propagating SH Wave

Vertical array data recorded during the 1995 Kobe earthquake are used to calculate the upward and downward energy flow based on one-dimensional SH-wave multireflection theory, from which the energy dissipation in a surface layer is evaluated as their residual. The dissipated energy thus evaluated in a liquefied site is found to reach about 70% of the upward input energy, which indicates that soil nonlinearity and liquefaction serve as effective energy absorbers. In contrast, more energy returns to deeper ground in sites without strong nonlinear behavior. Furthermore, the dissipated energy in the surface layer tends to increase nonlinearly in a convex shape with increasing equivalent damping ratio of the soil there. A simplified two-layer system indicates that the energy dissipation is influenced not only by the soil damping in the surface layer but also by the impedance ratio between the base and surface layers and the input frequency. The same convex relationship is also obtained in the two-layer system, indicating that the simplified system may reflect some important aspects of the energy dissipation mechanisms in the ground.     

Seismic Design of Structures by Bundled Columns

A practical technique to protect structures against the effects of earthquakes is examined and proposed for use in design. The technique involves the bundling of slender steel members to form columns that are stiff and strong vertically, yet stable and quite flexible horizontally, leading to significant deamplifications of the main effects of the earthquake excitation. Because of its lateral deformation capacity, the proposed system can be designed to remain elastic even under severe ground motions. A number of analyses are made to identify the main properties of the proposed column system, and the use of the bundled column concept as a base isolation system is also explored. Example problems representative of realistic earthquake-excited structures are reported, elucidating the main features of the proposed technique and the implications of its implementation. The presentation focuses on the fundamentals, avoiding unnecessary modeling complications, to highlight the main factors involved.     

Use of Exact Solutions of Wave Propagation Problems to Guide Implementation of Nonlinear Seismic Ground Response Analysis Procedures

One-dimensional nonlinear ground response analyses provide a more accurate characterization of the true nonlinear soil behavior than equivalent-linear procedures, but the application of nonlinear codes in practice has been limited, which results in part from poorly documented and unclear parameter selection and code usage protocols. In this article, exact (linear frequency-domain) solutions for body wave propagation through an elastic medium are used to establish guidelines for two issues that have long been a source of confusion for users of nonlinear codes. The first issue concerns the specification of input motion as “outcropping” (i.e., equivalent free-surface motions) versus “within” (i.e., motions occurring at depth within a site profile). When the input motion is recorded at the ground surface (e.g., at a rock site), the full outcropping (rock) motion should be used along with an elastic base having a stiffness appropriate for the underlying rock. The second issue concerns the specification of viscous damping (used in most nonlinear codes) or small-strain hysteretic damping (used by one code considered herein), either of which is needed for a stable solution at small strains. For a viscous damping formulation, critical issues include the target value of the viscous damping ratio and the frequencies for which the viscous damping produced by the model matches the target. For codes that allow the use of “full” Rayleigh damping (which has two target frequencies), the target damping ratio should be the small-strain material damping, and the target frequencies should be established through a process by which linear time domain and frequency domain solutions are matched. As a first approximation, the first-mode site frequency and five times that frequency can be used. For codes with different damping models, alternative recommendations are developed.     

Stress Reduction Coefficient and Amplification Factor for Seismic Response of Ground

Incorporating the increase of shear modulus with depth (z) by using a depth exponent p, the response of linear visco-elastic ground under steady state harmonic vibration was examined. The soil mass lying above the rigid base was discretized into a large number of horizontal layers. For a given vertical thickness (Hr) of the upper ground material in the first mode of resonance, it was noted that the resonant frequency (fr) as well as the values of amplification factor (Mf) and the stress reduction coefficient (Cd) at a given z/Hr can be computed as a function of p and D, where D is the damping ratio of the material. An increase in D leads to (1) an increase in Cd; (2) a very little increase in fr; and (3) a decrease in Mf. On the other hand, an increase in p causes: (1) an increase in fr; (2) a marginal increase in Mf; and (3) a decrease in Cd. It was evident that the values of Mf and Cd at a given depth will be affected significantly by changes in the chosen thickness of the soil deposit in resonance.     

Generalized Damped Wave Approach for Evaluating Seismic Shear Demands

This paper presents a new analytical approach for simple and explicit computation of the seismic base shear demand of structural systems that can be idealized by a uniform shear-beam model. The approach is based on a Green’s function representation for the relative displacement response that is assumed to be composed of exponentially decaying wave sequences. Explicit solutions for both the strain and displacement response are derived in terms of an effective ground velocity and displacement that can be computed incrementally from the ground acceleration. A physical interpretation for the damping mechanism is proposed. The method is further generalized to form a class of physically motivated shear-beam systems referred to as the continuous spring-dashpot (CSD) model. The response characteristics of three cases of the CSD model along with a shear beam equipped with a mass-proportional external damping are compared and discussed for the case of near-field earthquake excitation.     

Seismic Performance of Industrial Facilities Affected by the 1999 Turkey Earthquake

Approximately 40% of the heavy industry in Turkey was located in the region affected by the 1999 Mw 7.4 Kocaeli earthquake. Twenty-four facilities representing different industries in the epicentral region were surveyed after the earthquake. Structural and nonstructural damage to these facilities is summarized and performance is reported using a damage classification scheme. Information on typical industrial-facility construction practice in Turkey is presented. Earthquake damage to the most common structural framing systems is highlighted. The structural performance of a small number of the facilities visited by the reconnaissance team is investigated.     

Numerical Modeling of Site Effects at San Giuliano di Puglia (Southern Italy) during the 2002 Molise Seismic Sequence

The seismic sequence that occurred in October and November 2002 in the Molise region (Southern Italy) was characterized by two Mw = 5.7 earthquakes within 24 h followed by one month long aftershocks series. The mainshocks caused substantial structural damage in the village of San Giuliano di Puglia. The damage distribution was highly non uniform. Heavy and widespread damage was observed to all buildings constructed in the recently developed part of the village, where subsoil conditions are characterized by a bowl-shaped basin filled with stiff clays, whereas in the historical center, built on an adjacent rock outcrop, many buildings showed no or light damage. Several accelerograms were recorded during the aftershocks sequence by a temporary network installed on two sites in the San Giuliano village, located on rock and soil, respectively. The geological, seismological, geotechnical, and structural relevant information of the earthquakes are presented in the first part of the paper. The second part of the paper investigates the possible role of site effects in the observed pattern of damage by one-dimensional (1D) and two-dimensional (2D) numerical site response analyses. First, the computed ground surface motions were compared to the aftershocks recordings. It was found that 1D analyses considerably underpredicted dynamic response while 2D modeling provided a better understanding of the amplification phenomena. Further, based on the calibration site response study performed with the aftershock records, the ground response simulation of October 31, 2002, mainshock was carried out. The results of 2D numerical analyses led to average ground surface motion characteristics consistent with the observed distribution of damage throughout the village.     

New Approach for Seismic Nonlinear Analysis of Inelastic Framed Structures

A novel approach for seismic nonlinear analysis of inelastic framed structures is presented in this paper. The nonlinear analysis refers to the evaluation of structural response considering P-delta effect, which is in the form of geometric nonlinearity, and inelastic behavior refers to material nonlinearity. This novel approach uses finite element formulation to derive the elemental stiffness matrices, particularly to derive the geometric stiffness matrix in a general form. At the same time, this approach separates the inelastic displacement from total deflection of the structure by applying two additional constant matrices, namely, the force–recovery matrix and the moment-restoring matrix in the force analogy method. The benefit behind this treatment is explicitly locating and calculating the inelastic response, together with strategically separating the coupling effect between the material nonlinearity and geometric nonlinearity, during the time history analysis. Comparison with the traditional incremental methods shows that the proposed method is very time efficient as well as straightforward. One portal frame and one five-story frame are used as numerical examples to illustrate and verify the robustness of current approach.