Passive Energy Dissipation

A passive energy dissipation system does not require an external power source. Passive energy dissipation devices impart forces that are developed in response to the motion of the structure. The energy in a passively controlled structural system, including the passive devices, cannot be increased by the passive control devices. [4] The basic energy relationship of the structures is represented in the following equation [5]:

I K S H

E = E + E + E

_ξ

+ E

_(1.1)

where

E

I = earthquake input energy

E

K = kinetic energy in structure

E

S = strain energy in structure

E

_ξ = viscous damping energy

E

H = hysteretic damping energy

The aim of including energy absorbers in a structure for earthquake resistance is to concentrate hysteresis behavior in specially designed and detailed regions of the structure and to avoid inelastic behavior in primary gravity-load resisting structural members. In other words, the goal is to increase

E

_H so that, for a given

E

_I , the elastic strain energy in the structure is minimized. This means that the passively controlled structure will undergo smaller deformations for a given level of input energy than the one without energy dissipators. The major energy dissipation devices available are as follow [4]:

1. Metallic Yielding Dampers 2. Friction Dampers

3. Viscoelastic Dampers 4. Viscous Fluid Dampers 5. Tuned Mass Dampers 6. Tuned Liquid Dampers

Chapter 1 Introduction

7

Metallic Yielding Dampers One of the effective mechanisms available for

seismic energy dissipation is through inelastic deformation of metals. The idea of utilizing added metallic energy dissipators within a structure to absorb a large portion of seismic energy began with the conceptual and experimental work of Kelly et al. (1972) and Skinner et al. (1975). The devices considered included torsional beams, flexural beams, and U-strip energy dissipators (Fig.

1.3). In recent years, a wide variety of such devices have been proposed. Many of these devices use mild steel plates with triangular or hourglass shapes so that yielding is spread almost uniformly throughout the material. A typical X-shaped added damping and stiffness (ADAS) device (Bergman and Goel, 1987 and Whittaker et al. 1991), triangular ADAS (TADAS) (Tsai et al. 1993) and reinforced ADAS (RADAS) (Tsai, 1999) are shown in Fig. 1.4, Fig. 1.5 and Fig. 1.6, respectively.

Fig. 1.3 Several metallic yielding devices (a) Torsional Beam (b) Flexure Beam (c) U-strip

(a) (b) (c) Fig. 1.4 ADAS

(a) A photo of ADAS Unit (Bergman and Goel, 1987)

(b) Front view of ADAS element (Whittaker et al. 1991) (c) Side view of ADAS unit

Fig. 1.5 A photo and detailed design of TADAS

Fig. 1.6 A photo of RADAS¹

1 http://www.radas-mfps.com.tw/index.htm

Chapter 1 Introduction

9

Despite apparent differences in geometric configuration, the underlying energy dissipative mechanism for the above mentioned devices results from inelastic deformation of the metallic elements. Therefore, one must be able to characterize their hysteretic behavior under arbitrary cyclic loading. Ideally, one would hope to develop a model of any metallic device starting from micromechanical theory of dislocations [6]. However, since a direct physics approach is not yet feasible, one normally accepts a macroscopic level of description. Özdemir (1976) was the first to consider the modeling problem of material inelasticity. Shortly later, Bhatti et al. (1978) employed Özdemir’s methodology to study the response of structures that used torsional bar dampers along with a seismic base isolation system. Dargush and Soong (1995) developed an inelastic constitutive model for the material of metallic yielding dampers based on a microscopic mechanistic approach and compared it with experimental data for validation. Tsai (1995) developed a finite-element formulation for ADAS and compared the simulation results with experimental data.

The hysteretical behavior of the metallic damper can be obtained via component tests of the device [4]. In case only the strains are measured, a basic form of the nonlinear stress-strain relationship is first selected, and then the related model parameters are determined via curve fitting or a macroscopic mechanical analysis of the device. By this approach, any admissible hysteretic model, such as the bilinear model, may be selected. Ou and Wu (1995) explored the hysteretical behavior of both X-shaped and triangular metallic dampers by employing a bilinear model with parameters related to size and material properties. The ultimate displacements of the devices were also determined.

The earliest applications of metallic yielding dampers to structural systems appeared in South Rangitikei viaduct in New Zealand². The dampers were installed in the pier base to control the rocking action of the bridge.

Recently, ADAS devices have been installed in buildings in Italy, USA, Mexico, Japan and Taiwan for earthquake protection.

2 http://trains.wellington.net.nz/bridges.html

Friction Dampers Friction provides another means of energy dissipation

which has been utilized for years in automotive brakes to dissipate kinetic energy of motion. In structural engineering, a wide variety of devices differing in mechanical complexity and materials have been proposed and studied.

Most friction damper utilizes interfaces of steel on steel, brass on steel, or graphite impregnated bronze on stainless steel. Composition of the interface is of great importance to insure longevity of the devices. A friction device developed by Pall (1982) is shown in Fig. 1.7 [4].

Fig. 1.7 Pall Friction Device

Viscoelastic Dampers The metallic and frictional devices are primarily

intended for seismic application. Some viscoelastic solid materials, on the other hand, are used for dissipating energy at all deformation levels that allows them for both wind and seismic protection [4].

The application of viscoelastic materials to vibration control dates back to the 1950s for aircrafts as a means of controlling the vibration-induced fatigue in airframes. Their application to civil engineering structures appear in 1969 for the former World Trade Center in New York where approximately 10,000 viscoelastic dampers were installed in each of the twin towers to reduce wind-induced vibrations.

A typical viscoelastic damper, developed by the 3M Company Inc., is shown in Fig. 1.8. It consists of viscoelastic layers bonded in between steel plates. It is worthwhile pointing out that the viscoelastic material is linear over

Chapter 1 Introduction

11

a wide range of strain provided that the temperature is constant. At large strains, there is a considerable self-heating due to a large amount of energy dissipated. The generated heat changes the mechanical properties of the material, and the overall behavior becomes nonlinear and deteriorated.

Fig. 1.8 A viscoelastic damper

Viscous Fluid Dampers Fluids can also be used for energy dissipation.

Numerous configurations and materials have been considered for such type of devices. One class involves the use of a cylindrical piston immersed with viscoelastic fluid. Such systems have been studied both experimentally and analytically by Makris et al. (1993). Another device referred to as the viscous damping wall, again use viscoelastic fluid (Arima et al. 1988; Miyazaki and Mitsuaka 1992) [4].

Viscous fluid dampers widely used in aerospace and military applications recently have found applications in structural engineering (Constantinou et al.

1993). Characteristics of these devices that are of primary interest in structural applications are the linear viscous response achieved over a broad frequency range, insensitivity to temperature and compactness in terms of small stroke requirement with considerable output force.

It should be pointed out that most, if not all, viscous fluid dampers currently in use have a force-velocity relationship of the form

sgn( )

F C V =

^α

V

where

F

is the damping force,

C

is dependent on ambient temperature,

V

is the relative velocity in between the damper, and

α

is an exponent in the range

0.3 ≤ ≤ α 0.75

. Major advantages of this type of nonlinear dampers are that the force builds up fast at small velocity

and tends to flatten out at higher velocities. A typical fluid damper is shown in Fig. 1.9³.

Fig. 1.9 A Fluid Damper

Tuned Mass Dampers Tuned mass damper (TMD), first proposed by

Frahm [7], as a secondary system to control the primary structure generally consists of a mass block with damping and tuning elements. The frequency of a TMD system is tuned by adjusting the stiffness of the spring (sliding type) or the arm length of the suspension cable (pendulum type) [8] to be in near-resonance with the primary structure. As a result, a considerable vibrating energy can be transferred from the primary structure to the TMD system and then dissipated via the damping mechanism of its own. In general, the TMD system is effective in the control of wind-induced structural vibrations. Many well-known skyscrapers, such as the Citibank in New York, the John Hancock Tower in Boston⁴, the CN Tower in Toronto⁵, and Taipei 101 in Taipei (Fig. 1.10) adopt TMD for wind-resistance.

Fig. 1.10 Buildings installed with TMD (a) John Hancock Tower in Boston (b) CN Tower

(c) TMD in Taipei 101 (d) Taipei 101

3 http://www.e-structures.com/viscous.html

4 http://www.bluffton.edu/HomePages/FacStaff/sullivanm/peihancock/peihancock.html 5 From a postcard

(d) (c)

(b) (a)

Chapter 1 Introduction

13

Tuned Liquid Dampers Conceptually similar to a TMD system, Tuned

Liquid Damper (TLD) has been increasingly used in high-rise buildings for wind or earthquake induced vibration control [9,10]. The TLD can be integrated with the existing fire-suppress hydraulic tower and therefore considered a substitution of the TMD for economic reasons. The TLD can be further classified into the Tuned Sloshing Water Damper (TSWD) and the Tuned Liquid Column Damper (TLCD)[11-17]. The frequency of the TSWD is adjusted by changing the depth of the storage water as well as the geometry of the tank. Damping of the TSWD is produced via steel wire nets across the water passage, through which turbulent flow is generated and energy dissipated. While the frequency of the TLCD depends only on the total length of the water in the U-shape container, and damping of the TLCD due to headloss of the water is introduced by changing the dimension of the orifice (valve) or adjusting the cross sectional area of the U-shape container. For TSWD, only the sloshing motion of the near-surface portion of the water contributes in the control, while for TLCD, all the water is effective.

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