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Use of fluid viscous dampers in structural control: a case study

Article in International Journal of Forensic Engineering · January 2018

DOI: 10.1504/IJFE.2018.10019980

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Aboubaker Gherbi Mourad Belgasmia

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Int. J. Forensic Engineering, Vol. 4, No. 2, 2018 119

Use of fluid viscous dampers in structural control:

a case study

A. Gherbi*
Department of Civil Engineering,
Constantine University,
Constantine 25000, Algeria
Email: aboubaker.gherbi@umc.edu.dz
*Corresponding author

M. Belgasmia
Department of Civil Engineering,
Setif University,
Setif 19000, Algeria
Email: mourad.belgasmia@gmail.com

Abstract: This study focuses on the assessment of the buildings dynamic

response under wind loads. It is known that any structure inherently dissipates
and absorbs energy due to external loads thanks to the combination of its
deformability, strength and flexibility. An improvement of this capacity
could be achieved using fluid viscous dampers, concentrating mainly on their
nonlinear behaviour; a case study will illustrate the major impact of these
devices on a RC tall building, subjected to wind turbulence. Wind have a great
impact on the dynamic response of tall buildings, with its dynamic and random
nature, it plays an important role in the design of civil structures. In this paper,
the simulation of wind time histories is discussed, in order to fully cover all
wind components to end up with proper results.

Keywords: viscous fluid dampers; energy dissipation; wind speed samples;

nonlinear behaviour; time history analysis.

Reference to this paper should be made as follows: Gherbi, A. and

Belgasmia, M. (2018) ‘Use of fluid viscous dampers in structural control: a
case study’, Int. J. Forensic Engineering, Vol. 4, No. 2, pp.119–132.

Biographical notes: A. Gherbi is a PhD student in the Department of Civil

Engineering at Constantine University, Algeria. His research focuses on the
structural dynamics, the design of additional damping devices and their impact
on the structural behaviour.

M. Belgasmia is a Professor in the Department of Civil Engineering at Setif

University, Algeria. He has been involved in teaching and research activities
for the past eighteen years. His research includes optimisation, earthquake
design, wind design, fire design, crack modelling, object oriented
programming, soil structure interaction by adding dashpots and dampers
design.

Copyright © 2018 Inderscience Enterprises Ltd.

120 A. Gherbi and M. Belgasmia

1 Introduction

The design of civil structures can be realised using elastic analysis, even if these
structures may sustain significant deformation beyond their elastic limit state, due to
wind or earthquake. Information about the nonlinear behaviour of some structures is
highly required; such information could be provided by nonlinear dynamic methods.
Existing buildings with certain height must resist to wind turbulence, which will
be the subject of this work. Under wind load, large story drifts of a building may
result in damage to the non-structural elements, also, the occupant’s comfort and the
building’s stability. Wind need to be adequately characterised in order to have accurate
results.
For this purpose, many researchers have developed theories and schemes that
consider more thoroughly wind components and the influence of its turbulence on
buildings. In this paper, some of the methods used for wind time histories simulation
are discussed, along with a brief theoretical background of the method utilised in a
Matlab code. As a second part, a case study of a tall building subjected to wind loads,
with an attempt to reduce its response using energy dissipation systems. The use of these
devices in the structural engineering knew an increasing development since the
mid-1990s, with the principal role of improving the structural behaviour and capacity to
dissipate energy.
Many researchers proposed strategies for the design process of additional dampers,
Moreschi (2000) used two techniques to achieve an optimum design, a Gradient
projection method for the selection of a damping value, and a genetic algorithm which
deals with the choice of their configuration (the location of dampers over the height of a
structure). Martinez-Rodrigo and Romero (2003) proposed a strategy to an optimum
retrofitting option with added dampers, based on a numerical optimisation process, which
takes into account two indexes: the performance index that achieves the damage control
(DC) performance point; and the force index used to calculate the reduction in the
damper force. It was also proved that these devices could be used as a rehabilitation
technique for damaged buildings (Pollini et al., 2017; Martinez-Rodrigo and Romero,
2003). Kandemir-Mazanoglu and Mazanoglu (2017) investigated an optimum damper
capacity and number installed between two adjacent buildings, depending on a parametric
study. This brief introduction shows the variation of both the design and the application
of fluid viscous dampers. Despite the effectiveness of the numerous design method, it is
still seen as a time consuming task. In the following, a simplified strategy is proposed to
determine initial location of the dampers based on the story drift.

2 Wind load sample generation

Wind is considered as random and dynamic phenomenon, and it is difficult to take into
account all its components in the structural analysis. It is common practice in wind
engineering, to describe wind velocity as a stationary stochastic process. It is described
by a mean speed and turbulent components (Dyrbye and Hansan, 1996; Simiu and
Scalan, 1996; Davenport, 1961) has described that the variation of mean wind speed over
height, i.e., wind profile, is mainly conditioned by the surface roughness as shown in
Figure 1:
 Use of fluid viscous dampers in structural control 121

α
U ( z ) = U ( zref ) ( z /zref ) (1)

where U(z) is the mean wind speed, U(zref) is wind speed at a reference height, usually
10 m and α is an exponent depending on terrain roughness. The turbulent components are
described by their standard deviation, time scales and integral length scale. Also, the
power spectral density functions that define the frequency distribution and normalised
co-spectra that specify the spatial correlation. In the need to analyse structures under
wind load, digitally simulated data become more essential; these simulations can be
described as theoretical model, phenomenological or empirical model or observed data
(Kareem, 2008). Over the last decade, wind simulation methods did not cease developing,
from approaches that uses a superposition of trigonometric functions (Shinozuka, 1971),
to the use of fast Fourier transform to improve the computational efficiency, and the
Cholesky decomposition of the cross-spectral density matrix and many other schemes.

Figure 1 Variation of mean wind velocity profile with surface roughness

In the following, the Fourier series for sample generation will be shown, these time
histories are obtained for any point in space and should satisfy a power spectral density
function, i.e., Davenport’s power spectral density.
The fundamental characteristic of a power spectral density for a random process is
that the integration over the frequency range corresponds to the variance of the process
Denoël (2005):
+∞
∫ S f ( n ) = σ x2 (2)
0

The well-known Davenport power spectral density could be written as follows:

2
2⎛ L ⎞
n ⎜ ⎟ σ2
3 ⎝U ⎠
S f (n) = 4/3
(3)
⎛ ⎛ nL ⎞2 ⎞
⎜⎜1 + ⎜ ⎟ ⎟⎟
⎝ ⎝U ⎠ ⎠
122 A. Gherbi and M. Belgasmia

With n being the frequency, L is the turbulent scale, U is the mean wind speed at a
reference height and σ² the mean square of the wind turbulence.
On the basis of the ergodicity hypothesis, the power spectral density of a stationary
process can be obtained from a single sample (Denoël, 2005). The generation could be
done simply by choosing:

T
X ( w, T ) = S f ( wi ) e
iϕ j
(4)
2π
where φj is a random phase angle taken between zero and 2π.
On the basis of this theoretical background briefly presented, a Matlab code has been
implemented to generate the appropriate time histories for this study. It consists on the
superposition of trigonometric functions with random phase angles, and the Fast Fourier
Transform is used to improve the computational efficiency for the summation of the
trigonometric functions (Shinozuka, 1971). From the generated fluctuating wind speed,
we calculate the fluctuating wind force as follows:
F ( t ) = ρ Cd AU u ( t ) (5)

where ρ is the air density (1.20 kg/m3), Cd is the drag coefficient, A is the projected area,
and U, u(t) are the mean wind speed and fluctuating wind speed at a specific height.

3 Energy dissipation systems

The control of buildings subjected to wind and seismic excitation is a major task for civil
engineers. With the new emerging concepts of structural control, which includes the use
of passive and active dissipation systems, allowing the reduction of the inelastic passive
energy dissipation demand on the system of the structure. An active control device is a
system that typically requires a large power source and generates a control force to the
structure, which is supplied by the mean of electrohydraulic/electromechanical actuators.
A passive dissipation device utilises the motion of the structure to generate the control
force (no external power source needed). Another type of systems is semi-active device
that operates from a small external power source and develops the control force from the
motion of the structure (Symans and Constantinou, 1999; Symans et al., 2008). This work
will be concentrated only on the passive dissipation device: fluid viscous damper.
• fluid viscous dampers.
It has been demonstrated that energy dissipation systems are capable of producing
significant reduction of inter-story drifts in building to which they are installed (Symans
and Constantinou, 1999). In recent years, different dissipative systems have been used in
the structural retrofitting (Pollini et al., 2017) or built within the structure. These devices
generally dissipate energy through one of three mechanisms: hysteresis, friction or
viscous damping, their behaviour is considered highly nonlinear (Williams and
Albermani, 2003). Fluid viscous dampers (referred to hereafter as FVD), operate on the
principle of fluid flow through orifices, these devices first appeared in the 1960s, were
mostly used in the military hardware and shock isolation systems of aerospace (Symans
and Constantinou, 1998). Figure 2 illustrates a typical fluid viscous damper (Symans and
Constantinou, 1999).
 Use of fluid viscous dampers in structural control 123

Figure 2 Detail of a fluid viscous damper

Some of the advantages of these devices can be summarised as follows:

• minimal restoring force
• activated at low displacements
• their properties are frequency and temperature-independent.
With the only inconvenient of a possible fluid seal leakage. Many manufacturers supply a
wide variety of devices, with numerous specification. Generally, they have a nonlinear
force-velocity relationship as follows (Paola et al., 2007):
α
F = CD x sgn ( x ) (6)

where CD is the damping coefficient, α is a damping exponent in the range of 0.3–1.95,

and sgn(.) is a signum function. The value of α depends on the shape of the piston head,
while the damping coefficient can be determined by the damper diameter and the orifice
area (Haskell and Lee, 1996). Figure 3 shows the damper’s force-velocity relationship
(Ras and Boumechra, 2016).

Figure 3 Force-velocity relationship of FVD

Since this paper focuses on the nonlinear behaviour of the FVD, the equation of motion
to be solved can be written as follows:
124 A. Gherbi and M. Belgasmia

α
Mx + Cx + CD x sgn ( x ) + Kx = F ( t ) (7)

where M, C and K represent the system’s characteristics (mass, damping and stiffness)
and F(t) is the dynamic wind load.

4 Case study

4.1 Building’s characteristics

As shown in the table above, this case study consists in the analysis of a 17 story RC
building, consisting of column-beam system and a central core (Figure 4). This building
has been designed as per local codes CBA (1993) and RPA (2003). This building can be
modelled using commercially available finite element-based software package. It has a
total height of 52.02 metres and was divided into six representative section along its
height to decrease the number of generated time histories and therefore, the analysis time.
It is located in an urban area that corresponds to an exposure category ‘B’ according to
the ASCE 7. The inelastic response is concentrated in plastic hinges that could form at
both ends of all members and the centre of shear walls.

Figure 4 3D view of the analysed building (see online version for colours)

4.2 Generated wind time history

As mentioned in Table 1, wind speed time histories were generated using a Matlab
routine, and then we calculate wind load time histories to use for our analysis from
equation (5) using finite element-based software (Computers and Structures, Inc., 2015).
Since the main focus of this work is to investigate the effect of FVDs, only wind load
 Use of fluid viscous dampers in structural control 125

in the Y direction will be taken into account. An example of the generated time histories
is shown in Figure 5. Figure 6 shows that the match is satisfied between Davenport’s
power spectral density and the generated sample.

Table 1 Analysis details

Concrete Reinforcement Exposure category Total height Generated T.H Mean wind
25 MPa 400 MPa B (ASCE 7) 52.02 m 6 28 m/s

Figure 5 Generated time history (see online version for colours)

4.3 Analysis procedure

The analysis could be initiated by the generation of wind time histories using the Matlab
routine, and applying it on the original structure, i.e., without fluid viscous dampers for a
nonlinear time history analysis. Then, the fluid viscous dampers are installed in the
building, with various configurations vertically located in the building and a variation of
values for the damping coefficient C and the damping exponent α of the fluid viscous
damper, until a better structural behaviour is observed.
Initial assumptions were made about the values of the damping coefficient CD based
on previous research (Symans and Constantinou, 1998; McNamara and Taylor, 2003;
Gherbi and Belgasmia, 2017; Abdi et al., 2015; Martinez-Rodrigo and Romero, 2003),
since the main objective is to determine the ideal damping exponent value.
126 A. Gherbi and M. Belgasmia

Figure 6 Time history matched spectrum (see online version for colours)

Figure 7 Inter-story drift of the uncontrolled system (see online version for colours)

The essential contribution of this work, consists in defining the location of added
dampers, considering only the inter-story drift:
 Use of fluid viscous dampers in structural control 127

• Locate stories with maximum inter-story drift, in this case, it is supposed that the
client requires a drift less than 20% to ensure occupant’s comfort.
• From Figure 7 the inter-story drift of the uncontrolled system higher than 20% is
located in 2nd to 9th stories, and an initial estimate is achieved.
• At this stage, engineers have flexibility in the choice of number of additional
dampers and exact location, following any architectural or technical requirements.
In this study, two dampers per story is chosen.
And thus, the configuration of dampers, installed in two bays as shown in Figure 8.

Figure 8 FVDs configuration in the building (see online version for colours)
128 A. Gherbi and M. Belgasmia

4.4 Results and comments

An intensive analysis was undertaken with different values of the damping coefficient
CD, with the main objective of reducing wind motions. As stated earlier, initial
assumptions were made considering the damping coefficient, the value was fixed in the
first stage of the design process since the main objective is to investigate the effect
induced by the choice of the damping exponent values α. Afterwards, the damping
coefficient was adjusted (CD = 3700 KN.s/m)
The damping exponent values considered for this study are the following: α = 0.3;
0.5; 0.7; and 0.9 (α < 1 are the values mostly used in practice).
A series of nonlinear response history analyses are performed with different
intensities (mean wind speed), in this section we will discuss some of the results that
summarises the FVD effect on the building.
It must be pointed out that the effectiveness of the fluid viscous dampers lasts with
the excitation, as illustrated in Figure 9 for a one minute wind excitation; FVDs (with
α = 0.3) have contributed to the reduction of the displacement in the tip of the building.
In the other hand, the FVD’s force have induced an additional axial force in the columns,
engineers must take this in consideration in the design of buildings with such devices, or
when used in the structural retrofitting.

Figure 9 Tip displacement over one minute (see online version for colours)

Comparing the obtained results from Figures 10 and 11, for the story drift and total base
shear respectively, it is obvious that peak story drift decrease with lower damping
exponent values; as for total base shear it decreases with higher values of α.
Table 2 shows the great impact that FVDs have on the peak acceleration, and
indicating that with higher values of the damping exponent, the lower is the acceleration.
Consequently, it is safe to say that, as the damping exponent approaches unit (linear
behaviour), a better structural behaviour is observed, regardless the values of the
maximum drift, which increase slightly with higher values of damping exponent.
Another two aspects should be mentioned (not in an expanded way), one is the
energetic aspect, the participation of the FVDs in the energy dissipation as presented in
Figure 12 prove the effectiveness of these devices, the cumulative energy absorbed by
FVDs is estimated at approximately 30% after a one minute wind excitation. The second
aspect concerns the reduction in the overall cost of buildings, since structures with FVDs
require less lateral stiffness than those without additional FVDs; this reduction could be
 Use of fluid viscous dampers in structural control 129

obtained by using less structural materials and smaller structural members. These two
aspects need to be thoroughly investigated in order to extract proper conclusions.

Figure 10 Story drift for different damping exponent values (see online version for colours)

Figure 11 Total base shear for different values of α (see online version for colours)
130 A. Gherbi and M. Belgasmia

Table 2 Peak acceleration for different values of α

Damping exponent Uncontrolled 0.3 0.5 0.7 0.9

Peak acceleration 20.2 7.621 7.410 7.289 6.775

Figure 12 Cumulative energy components (see online version for colours)

5 Conclusion

The nonlinear behaviour of fluid viscous dampers and their impact on an RC building
have been investigated in this study. This paper presented an effective method for the
generation of wind time histories matched with a target power spectral density, all in a
Matlab code. This means that the input wind load are perfectly characterised and the
nonlinear time history analysis could be carried out. The lack of sufficient literature
concerning the nonlinear behaviour of the FVDs have motivated this study; a selected 17
story building have been analysed in the first place without additional damping devices.
Once the FVDs are introduced in the structure, remarkable improvement have been
noticed as shown in the previous section.
An effective strategy was presented in this work, which simplifies the process of
choosing ideal location for the additional damping devices, based only on the inter-story
drift of the uncontrolled system. Finally, we noticed that a better structural response is
achieved with a damping exponent approaching to unit; which confirms the theory of
using mild nonlinearities in structures subjected to low velocity loadings (wind).
The energetic and cost aspects could be the subject of further research since the
results shown briefly in Section 4 have proven the great contribution of the FVDs on
these aspects.
 Use of fluid viscous dampers in structural control 131

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