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Seismic Response Study of Degraded Viscous Damping Systems for Tall

Buildings in China

H. Ataei, Ph.D., P.E., P.Eng., M.ASCE1; M. Mamaghani, E.I.T., S.M.ASCE1;

and K. Kalbasi Anaraki1
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1
Dept. of Civil and Environmental Engineering, College of Engineering and
Computer Sciences, Syracuse Univ., 151 Link Hall, Syracuse, NY 13244.
E-mail: hataei@syr.edu; mmamagha@syr.edu; kkalbasi@syr.edu

Abstract
During a seismic event, the fluid-viscous dampers utilize the action of solids to
enhance the performance of structures subjected to transient environmental
disturbances for general shock and vibration mitigation purposes. The conventional
cylindrical viscous dampers contain compressible silicone oil which is engaged to
flow during a disturbance through the action of the stainless steel piston rod with a
bronze head. Possible compressible oil leakage in damaged damping systems may
negatively affect the response of the degraded damping system and, ultimately, the
response of the entire structure, during a seismic event. It creates a gap or lapse in the
force-displacement response. This paper investigates the seismic response of Beijing
Yintai Center for various viscous fluid leakage percentages in damping systems
which are mainly manufactured and supplied by Taylor Devices (US) and the Beijing
QITAI shock control and scientific development in China. One of the main objectives
of this study is to investigate the performance of viscous dampers under different
conditions of possible leakage volumes against their basic response characteristics.
The damper is able to handle a portion of the assigned displacement time history
without developing any reaction force. However, when the displacement of the
internal piston reaches a sufficient level to regenerate fluid pressure, the damping
force trend is restored through a “delay” whose length depends on the amount of the
fluid leakage. The study is based on the time history analysis of selected and scaled
earthquake records according to the ASCE 7-10 along with the numerical analysis of
simulated damaged/leaking damper devices using finite element and structural
analysis software. The analyses results demonstrate the change in performance of the
structures with degraded damper devices. The inter-story drifts and base shear values
are dramatically increased in structures with degraded damper devices.

INTRODUCTION
Amongst the various extremely devastating natural disasters, earthquakes are caused
by the rapid vibrations of the Earth's surface. The destructive power of earthquakes
comes from the energy that is released during the strong ground motion. An
earthquake can cause damage to buildings, transportation infrastructure,
telecommunication facilities and water supply systems. Moreover, it can also cause
flooding, fires, landslides and other secondary disasters (Zhang, et al., 2004).

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Traditional anti-seismic design of building structures focuses on resisting earthquake

excitations by enhancing energy dissipation capacity to meet the seismic design
requirement. Traditional methods mainly concentrate on increasing the structural
stiffness and dimensions of the structural elements that ultimately result in increased
construction costs without delivering a complete assurance on structural performance
reliability. To improve this matter, and to better assess the performance of buildings
during a seismic event, a more profound look into the theory of vibration control
seems necessary.
The goal of this paper is to analyze the influence of leakage in fluid viscous dampers
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when structures undergo dynamic loading. Fluid viscous dampers are widely used
worldwide as energy dissipation devices. However, the leakage of fluid in viscous
dampers will compromise their desired damping capacities during dynamic
excitations.
In order to explore the variation of energy dissipation capacity for fluid viscous
dampers, with and without leakage, two steel frames are modeled using OpenSees
2.5.0. One uses the Maxwell exponential link element to simulate a fluid viscous
damper without leakage. The other uses a gap element to simulate a fluid viscous
damper with leakage. The results of the analysis confirm the further decrease in
structural performance. For instance, in one case, the probability of exceedance from
damage limit with a 2 m/s2 spectral acceleration is almost three times for degraded
dampers. Although, the fact that not necessarily all dampers do have the same
leakage, this study elaborates on the effects of viscous fluid leakage on building
structural dynamic characteristics which may cause structural collapse in even
moderate earthquakes.

ENERGY DISSIPATION DEVICES

In current practice, there are three categories of seismic performance improvement
devices: Base Isolation; Passive Device and Active Device (Soong & Spencer, 2002).
Compared to active devices, passive devices are widely used in the structures for
energy dissipation under earthquake excitation. They have good durability and do not
need any external sensors and power. There are usually two types of passive devices
for energy dissipation: (1) displacement-dependent devices like friction dampers,
which add initial stiffness to structure; (2) velocity- dependent devices like viscous
dampers and viscoelastic dampers, which do not have a noticeable effect on the
stiffness of structure but instead, provide capacity of energy dissipation.

VISCOUS DAMPERS
Viscous dampers are widely used energy dissipation devices in the United States that
improve the structural energy dissipation. A typical viscous damper consists of a
cylinder and a piston rod made from high-strength stainless steel. A piston head with
orifices separate the cylinder into two parts, which is chamber 1 and chamber 2
shown in Figure 1. The fluid should be fire-resistant, nontoxic, and non-aging, like
silicon glue. The main role of the fluid is to stabilize the viscous damper during
dramatic changes in temperature as a result of an energy dissipation process (Lee and
Taylor, 2001). When the structure is excited by an earthquake, the piston moves, and
pushes the fluid through orifices in the piston head and the fluid is pushed from

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chamber 2 to chamber 1 with high velocity that will transfer into kinetic energy.
When the fluid moves to chamber 1, it slows down and loses the kinetic energy due
to turbulences. As the pressure decreases on the downstream in chamber 1, the
difference in pressures produces a large force called viscous force that resists against
excessive structural movements (Lee and Taylor, 2001).
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Figure 1. Typical Viscous Damper (D. Lee et al. 2001)

The damper behavior is firstly controlled by the velocity of fluid that goes through
the orifices and secondly, by the properties of the fluid (Symans and Constantinou,
1998).

MECHANICAL PROPERTIES OF VISCOUSE DAMPERS

Viscous dampers provide a damping force that is proportional to the relative velocity
between the ends of the damper as illustrated in Equation 1:
FD = CV N (1)
Where F is the damper force; C is the damping coefficient; V is the velocity and N is
an exponent that can range from 0.3 to 1 (Lee and Taylor, 2001). When N=1, it is a
linear damping, otherwise it is called non-linear damping (Lee and Taylor, 2001).

Constantinou and Symans (1992) conducted a total of 58 tests of viscous dampers for
5 cycles in a frequency range of 0.1 to 25 Hz, with a peak velocity range of 0.65
in/sec to 18.2 in/sec, at three different temperatures: 0◦C, room temperature (22◦C),
and 50◦C. The results show that the viscous dampers are stable under temperature
from 0◦C to 50◦C, as the fluid in dampers is stable and to some degree is independent
of temperature. The mechanical properties of the viscous dampers were almost
completely independent of the amplitude of motion. Black and Makris (2007) studied
the thermodynamic behavior of the viscous damper fluid. Miyamoto et al., (2010)
conducted a comprehensive analytical and experimental investigation on performance
of viscous fluid dampers under very large earthquakes. Lu et al., (2012) developed a
new mathematical model called Generalized Maxwell Model (GMM) to simulate the
hysteretic behavior of fluid dampers under a wide frequency ranges by adjusting two
exponential coefficients. Moreover, other accurate mathematical models have also
been developed for simulation of response of structures with viscous damping
systems.

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STUDY OF STRUCTURES WITH VISCOUS FLUID DAMPING SYSTEMS

Dicleli and Mehta (2007) conducted a study to explore the seismic performance of
steel chevron braced frames with and without viscous fluid dampers as a function of
the intensity and frequency of ground motion and the parameters of viscous fluid
dampers. The results showed that the seismic performance of the chevron braced
without viscous fluid dampers is sensitive to the frequency and intensity of the
ground motion due to brace buckling effects. Uriz and Whittaker (2001) conducted a
study to use linear viscous fluid dampers for seismic retrofit of a three-story, pre-
Northridge steel-framed building. The results showed that the displacement could be
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reduced significantly with 40% equivalent viscous damping. The plastic rotations
were also decreased but not eliminated.

Shaking table test is the typical experimental method to investigate the behavior of
structure with viscous fluid damping. Symans and Constantinou (1998) conducted a
series of experiments to test the energy mitigation of structures with viscous fluid
damping. The damping ratio of scaled structure without dampers is smaller than it is
with viscous fluid damping systems. Also, the damping ratio is increased along with
more viscous fluid dampers applied to the scaled structure.
Constantinou and Symans (1992) conducted a series of 66 experiments about the
response of the structures equipped with various damping systems. The recorded ratio
of peak drift response (RD) and peak base shear force (RBS) were used to compare
the results as illustrated in
Table 1.

Table 1. Comparison of RD and RBS for different energy absorbing systems

(Constantinou,1992)
System RD RBS Reference
Viscoelastic dampers 0.5-0.9 ~1 Aiken,1990
Friction dampers 0.5-0.9 ~1 Aiken,1990
Fluid dampers 0.3-0.7 0.4-0.7 Constantinou,1992

Model structures with and without viscous fluid damping systems were tested using
the shaking table test for peak story drift, peak base shear and story acceleration. The
peak velocity could be calculated by numerical differentiation of the recorded
displacement. Based on the recorded data, the damping ratio was increased as the
number of viscous dampers increased, which means the capacity of energy mitigation
was improved. The ideal position for placing viscous dampers is in the stories where
the largest inter-story velocity happened. Moreover, viscous fluid dampers could
reduce drifts and column bending moments, while introducing additional column
axial forces. In effect, this behavior prevents the possibility of compression failure of
weak columns in retrofit application.

Ji, et al., (2013) conducted a series of large-scale dynamic tests on a passive

controlled steel structure with E-Defense shaking table facility in Japan to investigate
the realistic structural response under seismic excitation. The specimen was tested by
repeatedly inserting and replacing each of the four damping types (buckling
restrained braces, viscous dampers, oil dampers, and viscoelastic dampers). Damping

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ratio of structure with velocity-dependency dampers decreased with increased order

of modes, exhibiting an obvious frequency dependency. The damping ratio of
structures with viscous dampers increased significantly, along with an increase in
vibration amplitudes, due to the viscosity nonlinearity of viscous dampers.

CHALLENGES OF VISCOUS FLUID DAMPERS IN CHINA

The viscous fluid damping systems are the most conventional passive energy devices
used in China. There are a few obvious advantages of using the viscous fluid damper
(Chen, 2014) in Chinese construction practice: (1) the internal material of viscous
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fluid damper is stable under various environments. Viscous dampers will not change
the period and stiffness of structures; (2) the viscous fluid damping systems are
reusable under earthquake, wind and daily excitation; and (3) the viscous fluid
damping will work well under fire if the fluid is suitable.

The Beijing Yintai Centre is the first building with fluid viscous damping systems in
China. Using viscous dampers has significantly improved the energy dissipation
capacity of the building. Currently, the applied technology in China cannot fully
guarantee the viscous fluids insulation within the damper which will ultimately lead
to higher leakage amounts. Dampers should be sealed perfectly under any frequency
of vibration. However, viscous fluid leakage is of great concern for design and
rehabilitation of the structures in China. In China, the loading velocity of test device
is 100 mm/sec – 200 mm/sec (Chen, 2008). This is not sufficient for a qualification
test of the viscous damper compared to the loading velocity of 1800mm/sec for the
dampers manufactured by Taylor Devices Inc.
Table 2 compares the differences between the two loading velocities:

Table 2. Comparison of Loading Velocities

Taylor Devices Inc. Taylor Devices Inc.
Chinese university
Testing type horizontal dynamic vertical dynamic
structural test
device device
Max force 2500kN 7500kN 8907kN
Max length 150mm 1000mm 1410mm
Max velocity 100mm/s 1800mm/s 1143mm/s

According to Taylor Devices Inc. publications, the damping force will not change
when fluid leakage is less than or equal to 10% but will linearly decrease when the
fluid leakage is more than 10% and the damper will not work after a leakage of 50%,
as shown in Figure 2:

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Figure 2. Damping Force versus Fluid Leakage (Taylor Devices Inc., 2015)

The employment of high-pressure seal containers are among the solutions to limit the
leakage of viscous fluids. These containers can undergo high compression and
tension stresses and high deformation. The Chinese-made containers hardly meet the
requirements compared to those made in the US (Pekcon, 1995) as shown in Table 3:

Table 3. Container Details

Container diameter Container thickness
Domestic Chinese 203mm 16mm
Taylor Devices Inc. 206.12mm 27.9mm

The traditional synthetic rubber is also an effective and widely used alternative to
assure proper sealing for viscous dampers. Taylor Devices Inc. experiments ideally
recommend the metal sealing devices. The fluid in dampers will keep stable under
heat transmission, however, after a couple of years of cyclic loading, the fluid will get
degraded. The sealing materials also might undergo a deformation due to extensive
cyclic loading. Based on the US damper design codes, the damping force should keep
stable (i.e. decayed force less than 15% under 10-20 cycle of earthquake excitation)
(Trevor, 2001).

Overall, the consequences of leaking oil are serious. The damper will lose the
medium of energy transmission after leaking oil. Therefore, there will not be any
damping force to resist the seismic excitations and the piston will continue to
compress air. This will change the structural stiffness and ultimately create more
damage.

MECHANICAL MODELS FOR FLUID VISCOUS DAMPER

Nonlinear Damping Model

In fluid viscous damper, the relationship between the damping force Fd(t) and
velocity u(t) is nonlinear. Therefore:

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Fd (t) = C α . sig n (u ) u

α
(2)

Where Cα is the damping coefficient; α is the damping exponent and sign is the
Sign Function. α represents the nonlinear properties of the fluid viscous damper.
The value of α is related with the damper internal structure. The value of Cα is
related to the diameters of internal cylinder, and piston, etc. (Symans and
Constantinou, 1998)
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Maxwell Model
The Maxwell model consists of a viscous damper and elastic spring which are
connected in series and the equation is:
f = kdk = cdccexp (3)
Where k is the spring constant, c is the damping coefficient, cexp is the damping
exponent, dk is the deformation across the spring, dc is deformation rate across the
damper. The model is shown at Figure :

Figure 3. Schematic Representation Maxwell Model

When a force is applied to the Maxwell model, the total displacement is equal to the
sum of spring and damper displacements.
u = u e + uv (4)
Where u e is the displacement of elastic element (spring) and u v is the displacement
of viscous element (damper). Taking a derivative of the total displacement u with
respect to time:
du du e du v
= + (5)
dt dt dt
Based on simple statics, the force is the same in both elements. Thus:
du 1 dF F
= + (6)
dt k dt c

Therefore, in Maxwell Model, the displacement is only related to the force F. In order
to model a fluid viscous damper that has a nonlinear force and velocity relationship,
the exponential damper property based on the Maxwell model is used. The spring is
important to model the realistic behavior of nonlinear viscous dampers. It represents
the elastic flexibility of the fluid column in the damping device.

MODEL GEOMETRY AND CONFIGURATIONS

The Beijing Yintai Center has 62 stories above the street level and 4 underground
stories with interstory height 3.3 meters. Total floor area is 113,000 m2. The building
is completed in 2007. The Structural Designer firms are John A. Martin Associates

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and China Electronics Engineering Design Institute. Damping Suppliers are Taylor
Devices, Inc. and Beijing Qitai Shock Control and Scientific Development Co., Ltd.
The schematic model of structure shown in Figure 4.

FIBER ELEMENT MODELING DETAILS

The N-S frame of the 66 story structure was modeled using the Open System for
Earthquake Engineering Simulation platform (OpenSees 2.5.0) to model the columns
and beams as non-linear fiber element with 10 integrating point along their length.
The Giuffre-Menegotto and Pinto (1973) model steel structure with a modulus of
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elasticity of 210 GPa and the yield strength of 240 MPa with post yielding strength
hardening of 2% were used. Inherent structure damping were consider as 5% that
implemented with Rayleigh formulation. Story masses were lumped only at nodes
and pined leaning column is used to simulate The P-Δ effect. Maxwell model (linear
spring and non-linear dashpot in series) is used for modeling the dampers (S.
Akcelyan and D. G. Lignous, 2016) as illustrated in Figure 5.

Figure 4. Structural Frame Scheme (in meters)

Figure 5. Damper Force vs. Elongation for with and without Leacked Damper

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Table 4. Ground Motion Characteristics

ID Event Year Station PGA (g)
1 Landers 1992 LAKEWOOD - DEL AMO BLVD 0.054
2 Landers 1992 TARZANA - CEDAR HILL 0.066
3 Kobe 1995 OKA 0.081
4 Kobe 1995 MZH 0.07
5 San Fernando 1971 WRIGHTWOOD - 6074 PARK 0.061
6 North Ridge 1994 VILLA PARK – SERRANO 0.043
7 Loma Prieta 1989 BEAR VALLEY #1 0.072
8 San Fernando 1971 PEARBLOSSOM PUMP 0.102
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9 Livermore 1980 TRACY-SEWAGE TREAT. PLANT 0.049

10 San Fernando 1971 CARBON CANYON DAM 0.069
11 Kobe 1995 FUK 0.034
12 Landers 1992 LA - W 70TH ST 0.055
13 Taiwan Smart1 1983 SMART1 C00 0.028

In order to study the effect of leakage in viscous dampers, this paper considers two
frames with exact same properties, except for the 6 centimeter gap (equal to 2% drift
of each story) in each damper for one of the structures. A set of 13 ground motion
records are selected to perform the non-linear dynamic analysis, as listed in Table 4.
The dynamic analysis, without record scaling, is performed on both frames and the
mean of maximum drifts for each ground motion is demonstrated in Figure 6.

Figure 6. Mean of The Maximun Drifts Comparision

ANALYSIS RESULTS AND DISCUSSION

The incremental dynamic analysis (IDA) is performed to find behavior of the
structure under different accelerations (Vamvatsikos and Cornell, 2002). The
engineering demand parameter (EDP) is selected as the inter-story drift with the
intensity measure to be the spectral acceleration at fundamental mode period (T1 =
5.46 sec). The relative intensity values are increased based on the FEMA 350
recommendation for performing the IDA procedure. Due to the dispersion of the non-
linear dynamic analysis results, the fragility curves are better used for the results. As

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demonstrated in Figure 7, the assignment of the lognormal distribution function to

fragility curves for the specific EDP will yield to:
( ( ))
Ѳ (Ѳ)
( )= = φ( ) (7)
√
( ) (Ѳ) (Ѳ) ( ) ( )
≤ = Φ( ) = Φ( ) = Φ( ) (8)
( )
Where: Ѳ = exp ( ( ) ); = ( ) and μ denotes the mean value.
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Figure 8 illustrates the IDA curves for the 66 story frame without and with leakage.
As it is shown, the slight increase in stiffness, (1.5% - 2% drift ratio), is caused by the
damper performance.

Figure 7. (Left) Lognormal probability density function; (Right) Lognormal cumulative

distribution function (Keith Porter, 2015)

Figure 8. Incremental Dynamic Analysis Curves without and with Leakage

Using equations 7 to 8, the fragility curves for different EDP values (2%, 3% and 5%
inter-story drift) and with 84%, 50% and 16% of non-exceeding EDP are calculated
and plotted. To determine the effect of leakage in the seismic response of the

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structure, the probability of exceedance from 2%, 3% and 5% drift (as the limit of
CP) is considered and compared for both frames as per Figure 9, 10 and 11. As
shown in the figures, the structure performance is decreased. For example, the
probability of exceedance from damage limit with 2 m/s2spectral acceleration is
almost three times when leakage is occurred in dampers.
Although, not all dampers in the structure will have the same leakage amounts, the
results of this analysis show that the leakage can have major influence on structural
dynamic characteristics of buildings. Fluid leakage in viscous fluid damping systems
can cause excessive deformations on other structural elements and ultimately the
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collapse of the structure in even moderate earthquakes.

Figure 9. Comparison of fragility curves with 50% of exceedance from 2% drift in both
frames

Figure 10. Comparison of fragility curves with 50% of exceedance from 3% drift in
both frames

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Figure 11. Comparison of fragility curves with 50% of exceedance from 5% drift in
both frames

REFERENCES
Akcelyan, S., Lignos, D. G., Hikino, T., and Nakashima, M. (2016). “Evaluation of
simplified and state-of-the-art analysis procedures for steel frame buildings
equipped with supplemental damping devices based on E-Defense full-scale
shake table tests.” Journal of Structural Engineering, 142(6), 04016024.
Black, C. J. & Makris, N., (2007). “Viscous Heating of Fluid Dampers under Small
and Large Amplitude Motions: Experimental Studies and Parametric Modeling”
Journal of Engineering Mechanics, Volume 133, pp. 566-577.
Constantinou M.C., Symans M.D., (1992). “Experimental and Analytical
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Viscous Dampers”, Published as Report NCEER-92- 0032, by the National
Center for Earthquake Engineering Research, State University of New York at
Buffalo.
Dicleli, M. & Mehta, A., (2007). “Seismic performance of chevron braced steel
frames with and without viscous fluid dampers as a function of ground motion
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FEMA 350, (2000). “Recommended Seismic Design Criteria for New Steel Moment-
Frame Buildings”, Federal Emergency Management Agency.
Ji, X., Hikino T., Kasai K., Nakashima, M., (2013). “Damping identification of a full-
scale passively controlled five-story steel building structure”, Earthquake
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Keith P., (2015) “A Beginner’s Guide to Fragility, Vulnerability, and Risk”.
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Lee D., Taylor D.P., (2001). “Viscous Damper Development and Future Trends”,
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Lu L. Y., Lin G. L. & Shih, M. H., (2012). “An experimental study on a generalized
Maxwell model for nonlinear viscoelastic dampers used in seismic isolation”,
Engineering Structures, Volume 34, p. 111–123.

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Menegotto, M., and Pinto, P.E. (1973). “Method of analysis of cyclically loaded RC
plane frames including changes in geometry and non-elastic behavior of
elements under normal force and bending”. Preliminary Report IABSE, vol 13.
Miyamoto H. K., Gilani A. S. J., Wada A. & Ariyaratana C., (2010). “Limit states
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earthquakes”, Earthquake Engineering Structural Dynamics, Volume 39, p.
1279–1297.
Soong T. & Spencer B., (2002). “Supplemental energy dissipation: state-of-the-art
and state-of- the-practice”, Engineering Structures, Volume 24, p. 243–259.
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Symans M.D., Constantinou M.C., (1998) “Passive Fluid Viscous damping system
for seismic energy dissipation”, Journal of Earthquake Technology, 35 185-
206.
Uriz P. & Whittaker A. S., (2001). “Retrofit of pre-Northridge steel moment-resisting
frames using fluid viscous dampers”, Structural Design of Tall Buildings,
Volume 10(5), p. 371–90.
Vamvatsikos D. and Cornell A., (2002). “Incremental Dynamic Analysis”,
Earthquake Engineering and Structural Dynamics, 31:491-514.

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