SEISMIC RESPONSE OF UNSYMMETRIC BUILDING WITH OPTIMALLY PLACED FRICTION DAMPERS

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International Journal of Civil Engineering and Technology (IJCIET)
Volume 8, Issue 2, February 2017, pp. 72–88 Article ID: IJCIET_08_02_008
Available online at http://www.iaeme.com/IJCIET/issues.asp?JType=IJCIET&VType=8&IType=2
ISSN Print: 0976-6308 and ISSN Online: 0976-6316
© IAEME Publication Scopus Indexed
SEISMIC RESPONSE OF UNSYMMETRIC BUILDING
WITH OPTIMALLY PLACED FRICTION DAMPERS
S. S. Sanghai
Assistant Professor, Civil Engineering Department,
G. H. Raisoni College of Engineering, Nagpur, India
S. N. Khante
Associate Professor, Applied Mechanics Department,
Govt. College of Engineering, Amravati, India
ABSTRACT
Conventional methods of seismic rehabilitation with concrete shear walls or steel bracing
are not considered suitable for some buildings as upgrades with these methods would have
required expensive and time consuming foundation work. Supplemental damping in
conjunction with appropriate stiffness offers an innovative and attractive solution for the
seismic rehabilitation of such structures. This paper deals with the use of friction damper as a
passive dissipative device in order to seismic retrofit of existing structures and discusses the
optimal placement criteria. To fulfill this objective, six storey and ten storey L-shaped
buildings have been modeled with five different damper location formats in SAP2000 subjected
to El Centro and Utterkashi earthquake records. Non-Linear Modal Time History Method has
been used for the analysis and base shear, joint displacement, member forces and hysteresis
energy has been compared to find out most optimal damper location format.
Key words: friction damper, non-linear modal time history analysis, optimization, slip load
Cite this Article: S. S. Sanghai and S. N. Khante, Seismic Response of Unsymmetric Building
with Optimally Placed Friction Dampers. International Journal of Civil Engineering and
Technology, 8(2), 2017, pp. 72–88.
http://www.iaeme.com/IJCIET/issues.asp?JType=IJCIET&VType=8&IType=2
1. INTRODUCTION
Severe ground shaking induces lateral inertial forces on buildings, causing them to sway back and
forth with amplitude proportional to the energy fed in. If a major portion of this energy can be
consumed during building motion, the seismic response can be considerably improved. The manner in
which this energy is consumed in the structure determines the level of damage.
The use of bracing systems equipped with dissipative devices is relatively new technique for the
earthquake protection of buildings that has been considered in several recent experimental and
theoretical studies. In particular, the friction damping bracing system involving the device proposed by
Pall and Marsh (1982) has been carefully analyzed, since its simplicity of construction and high
dissipative capacity encourages application in practice. At present, the existing studies offer

S. S. Sanghai and S. N. Khante
sufficiently detailed information about the protection level, expressed in terms of energy absorption or
reduction of maximum horizontal displacement.
Friction damping devices dissipate energy by utilizing the mechanism of solid friction developed
at the sliding surface, which is a relatively inexpensive and effective method for stable energy
dissipation. As their hysteretic behaviors could be kept stable for cyclic loads and desirable slip loads
are easily obtained by regulating normal forces acting perpendicularly to a friction surface, in addition
to their simple energy dissipation mechanism and easy manufacturing, installation and maintenance
(Pall and Marsh 1982). Filatrault and Cherry (1990) have proposed the design procedure of friction
dampers that minimizes the sum of the displacement and dissipating energy by carrying out the
parametric studies such as the structural fundamental period, frequency components of excitation load
and the slip load of friction damper. Moreschi and Singh (2003) have determined the optimal slip load
and the bracing stiffness by using the optimization technique such as genetic algorithm. Pujari and
Bakre (2011) have studied the optimal placement of XPDs which provides more reduction in response
compared with other schemes of placement of XPD considered in the study. Furthermore, the optimal
placement of dampers is sensitive to the nature of excitation force, number of XPDs used and the
modeling of XPD. Khante and Sanghai (2012) have studied optimal placement of friction damper
using Non-Linear Time History Analysis on symmetric RCC framed building.
In this paper, a general framework for optimal placement of passive energy dissipation devices in
the form of friction dampers for seismic structural application has been formulated. The study has
been done for unsymmetrical RCC framed building.
2. BUILDING DESCRIPTION
The model of buildings are 6 storey and 10 storey reinforced concrete building having L shape in plan
as shown in Fig.1. The building has four frames at 3m c/c in X and Y direction with 3.2m storey
height and 1.2m plinth height as shown in Fig.1 and Fig.2. The beam and column are modeled as
frame element while slab is modeled as thin shell element. The sizes of members are given in Table
No.1. The friction dampers are placed along peripheral frames of building. The elevation of G+5
storey and G+9 storey structure with five different format of placement of dampers as shown in Fig. 2
and Fig. 3 respectively.
Table 1 Sizes of members
Storey G+5 G+9
Sizes of Beams 0.3m X 0.45m 0.3m X 0.45m
Sizes of Columns 0.3m X 0.45m 0.3 m X 0.5m
Thickness of Slab 125mm 125mm
Figure 1 Plan of building

Seismic Response of Unsymmetric Building with Optimally Placed Friction Dampers
(1) (2) (3) (4) (5)
Figure 2 Elevation of formats of G+5 building model
(1) (2) (3) (4) (5)
Figure 3 Elevation of formats of G+9 building model
3. PROPERTIES OF FRICTION DAMPER
The slip load of the friction damper is the principal variable. Fig.4 shows that, if slip load is very low
or very high, response is very high. This is because, if slip load is very low, friction damper will slip
for small vibrations leading to minimum hysteresis energy and if slip load is very high friction damper
will not slip and act as simple brace reducing hysteresis energy. The current slip load is decided by
trial and error method. The appropriate selection of slip load leads to optimum response of structure.
The friction dampers in single diagonal brace are modeled as damped braces having member stiffness
equal to brace stiffness and nonlinear axial yielding equal to the slip load. The properties of friction
damper used for modeling are given in Table No. 2.The link element named as Plastic (wen) is used to
model friction damper.

Table 2 Properties of friction damper
Storey G+5 G+9
Slip Load 300kN 500kN
Brace section ISMB200 ISMB200
Stiffness of element 149883.99 149883.99
Yielding Load 300kN 500kN
Post yield stiffness ratio 0.0001 0.0001
Yielding Exponent 10 10
Figure 4 Responses versus Slip Load (Avtar Pall, 2004)
4. METHOD OF ANALYSIS
For the analysis of all five formats, Non-Linear Time History method has been used in SAP2000. To
conduct time history analysis, the ground motion records used are El-Centro having peak ground
acceleration of 0.313g and Utterkashi having peak ground acceleration of 0.252g as shown in Fig. 5
and Fig.6.
Figure 5 El Centro ground motion record
Figure 6 Utterkashi ground motion record

5. OPTIMIZATION TECHNIQUE
In this study, the friction dampers have been induced as diagonal braces in these structures with few
fixed location formats. These location formats have been selected arbitrarily based on the previous
study as well as with a view to keep the number of dampers used to minimum. Dampers are located
between floor to floor diagonally as braces.
The unconstrained optimization problem is now formulated as:
Minimize ( ) = + (1)
where, f (x) is the objective function to be minimized, and x is the vector of design variables. In the
present case, the locations of a specified number of dampers in the structural system form the design
variables. The objective function for the minimization problem is considered to be a linear
combination of normalized maximum base shear Vb, and normalized maximum storey drift D. The
factors Vbu and Du denote the maximum base shear and maximum storey drift in the structure without
any supplemental dampers (Kokil and Shrikhande, 2007
6. RESULTS AND DISCUSSION
Using SAP2000 the analysis were carried out. The comparison of results has been done to find out
best optimal damper location format. The format (1) has no dampers and Format (5) has dampers at
each storey, hence these two formats can’t be called as optimal location formats. While in location
formats (2), (3) and (4) using same number of dampers different locations have been tried. Therefore
best location format will be out of Format (2), (3) and (4).
The modal time period and frequencies of mode shapes are most important factor to determine the
dynamic characteristics of structure. For modal analysis, Ritz vector method has been selected for
calculating time period and frequencies of mode shapes. Following table shows the modal time period
and frequencies of first mode shape for different formats of friction dampers.
Table 3 Values of time period and frequencies for G+5 storey
FOR EL CENTRO FOR UTTERKASHI
TIME PERIOD FREQUENCY TIME PERIOD FREQUENCY
FORMAT (1) 0.80 1.25 0.80 1.25
FORMAT (2) 0.58 1.72 0.58 1.72
FORMAT (3) 0.63 1.60 0.63 1.60
FORMAT (4) 0.52 1.91 0.52 1.91
FORMAT (5) 0.45 2.23 0.45 2.23
Table 4 Values of time period and frequencies for G+9 storey
According to the above values, the modal time period of damped structure is less when compared
with undamped structure. This is due to increase of stiffness of damped structure by addition of braces.
The envelopes of maximum values of acceleration, velocity and displacement in X direction of
undamped and damped building are shown in Fig. 6, Fig. 10 and Fig. 14 for G+5 storey and Fig. 8,
Fig. 12 and Fig. 16 for G+9 storey structures subjected to El Centro ground motion record while Fig.
FOR EL CENTRO FOR UTTERKASHI
TIME PERIOD FREQUENCY TIME PERIOD FREQUENCY
FORMAT (1) 1.70 0.59 1.7 0.59
FORMAT (2) 1.27 0.79 1.27 0.79
FORMAT (3) 1.31 0.76 1.31 0.76
FORMAT (4) 1.19 0.84 1.19 0.84
FORMAT (5) 1.05 0.95 1.05 0.95

7, Fig. 11 and Fig. 15 for G+5 storey and Fig. 9, Fig. 13 and Fig. 17 for G+9 storey structures
subjected to Utterkashi ground motion record.
Figure 6 Jt. acceleration in X-direction for G+5 storey
0
1
2
3
4
5
6
7
0 2 4 6 8 10
FLOOR
ACCELERATION (m/s2)
JT. ACCELERATION IN X-DIR FOR EL CENTRO
FORMAT(1)
FORMAT(2)
FORMAT(3)
FORMAT(4)
FORMAT(5)
0
1
2
3
4
5
6
7
0 2 4 6 8
FLOOR
ACCELERATION (m/s2)
JT. ACCELERATION IN X-DIR FOR UTTERKASHI
FORMAT(1)
FORMAT(2)
FORMAT(3)
FORMAT(4)
FORMAT(5)
0
2
4
6
8
10
12
0 1 2 3 4 5 6 7
FLOOR
ACCELERATION (m/s2)
JT. ACCELERATION IN X-DIR FOR EL CENTRO
FORMAT(1)
FORMAT(2)
FORMAT(3)
FORMAT(4)
FORMAT(5)

Figure 10 Jt. velocity in X-direction for G+5 storey
0
2
4
6
8
10
12
0 1 2 3 4 5
FLOOR
ACCLERATION (m/s2)
JT. ACCELERATION IN X-DIR FOR UTTERKASHI
FORMAT(1)
FORMAT(2)
FORMAT(3)
FORMAT(4)
FORMAT(5)
0
1
2
3
4
5
6
7
0 0.2 0.4 0.6 0.8 1
FLOOR
VELOCITY (m/s)
JT. VELOCITY IN X-DIR FOR EL CENTRO
FORMAT(1)
FORMAT(2)
FORMAT(3)
FORMAT(4)
FORMAT(5)
0
1
2
3
4
5
6
7
0 0.2 0.4 0.6 0.8
FLOOR
VELOCITY (m/s)
JT. VELOCITY IN X-DIR FOR UTTERKASHI
FORMAT(1)
FORMAT(2)
FORMAT(3)
FORMAT(4)
FORMAT(5)

Figure 14 Jt. displacement in X-direction for G+5 storey
0
2
4
6
8
10
12
0 0.2 0.4 0.6 0.8 1
FLOOR
VELOCITY (m/s)
JT. VELOCITY IN X-DIR FOR EL CENTRO
FORMAT(1)
FORMAT(2)
FORMAT(3)
FORMAT(4)
FORMAT(5)
0
2
4
6
8
10
12
0 0.1 0.2 0.3 0.4 0.5 0.6
FLOOR
VELOCITY (m/s)
JT. VELOCITY IN X-DIR FOR UTTERKASHI
FORMAT(1)
FORMAT(2)
FORMAT(3)
FORMAT(4)
FORMAT(5)
0
1
2
3
4
5
6
7
0 20 40 60 80 100 120
FLOORS
DISPLACEMENT (mm)
JT. DISPLACEMENT IN X-DIR FOR EL CENTRO
FORMAT(1)
FORMAT(2)
FORMAT(3)
FORMAT(4)
FORMAT(5)

Figure 15 Jt. Displacement in X-direction for G+5 storey
From above figures, it can be seen that joint velocity and displacement in damped building in X-
direction is reduced in comparison with undamped building. While joint acceleration reduces for G+5
storey and increses for G+9 storey structure. The maximum top storey reduction in joint acceleration is
for Format (5) and minimum increase for Format (3), in joint velocity is for Format (4) and for Format
0
1
2
3
4
5
6
7
0 20 40 60 80 100
FLOORS
DISPLACEMENT (mm)
JT. DISPLACEMENT IN X-DIR FOR UTTERKASHI
FORMAT(1)
FORMAT(2)
FORMAT(3)
FORMAT(4)
FORMAT(5)
0
2
4
6
8
10
12
0 50 100 150 200
FLOORS
DISPLACEMENT (mm)
JT. DISPLACEMENT IN X-DIR FOR EL CENTRO
FORMAT(1)
FORMAT(2)
FORMAT(3)
FORMAT(4)
FORMAT(5)
-2
0
2
4
6
8
10
12
0 20 40 60 80 100 120
FLOORS
DISPLCEMENTS (mm)
JT. DISPLACEMENT IN X-DIR FOR UTTERKASHI
FORMAT(1)
FORMAT(2)
FORMAT(3)
FORMAT(4)
FORMAT(5)
Linear (FORMAT (3))

(4) and in joint displacement is for Format (5) and for Format (4) respectively for G+5 storey and G+9
storey structure subjected to El Centro while the maximum top storey reduction in joint acceleration is
for Format (3) and for Format (4), in joint velocity is for Format (4) and for Format (3) and in joint
displacement is for Format (5) and for Format (4) respectively for G+5 storey and G+9 storey
structure subjected to Utterkashi. The reduction in acceleration, velocity and displacement of stories is
due to increase of stiffness of structure.
The maximum base shear in X-direction of undamped and damped building is shown in Fig.18 and
Fig.19.
Figure 18 Maximum Base shear in X-direction for G+5 storey
Figure 19 Maximum Base shear in X-direction for G+9 storey
Fig.18 and Fig.19 show that base shear is decreased in damped building as compared to undamped
building. The maximum reduction is 22.93% for G+5 storey and 5.78% for G+9 storey structure in
Format (4) subjected to El Centro ground motion record while 12.87% for G+5 storey and 14.19%
for G+9 storey structure in Format (4) subjected to Utterkashi ground motion record . This reduction is
due to addition of friction dampers which increases supplemental damping by 20-30%.
The maximum axial forces and maximum bending moment in members are plotted for different
formats as shown in Fig. 20 and Fig. 22 for G+5 storey and Fig. 21 and Fig. 23 for G+9 storey
structure.
0
500
1000
1500
2000
2500
FORMAT(1) FORMAT(2) FORMAT(3) FORMAT(4) FORMAT(5)
BASESHEAR(kN)
MAX. BASE SHEAR IN X-DIR
EL CENTRO
UTTERKASHI
0
500
1000
1500
2000
2500
3000
3500
BASESHEAR(kN)
MAX. BASE SHEAR IN X-DIR
EL CENTRO
UTTERKASHI

Figure 20 Maximum axial forces for G+5 storey
Figure 21 Maximum axial forces for G+9 storey
Figure 22 Maximum bending moment for G+5 storey
0
200
400
600
800
1000
1200
1400
AXIALFORCE(kN)
MAX. AXIAL FORCE
EL CENTRO
UTTERKASHI
0
500
1000
1500
2000
2500
3000
3500
AXIALFORCE(kN)
MAX. AXIAL FORCE
EL CENTRO
UTTERKASHI
0
50
100
150
200
250
300
350
400
450
500
BENDINGMOMENT()kN.m)
MAX.BENDING MOMENT
EL CENTRO
UTTERKASHI

Figure 23 Maximum bending moment for G+9 storey
On comparing the maximum axial forces and maximum bending moments in members, it is
observed that bending moment reduces for all models however axial force reduces for six storey
building and increases for ten storey building with inclusion of damper. The earthquake forces acting
on main structural member get redistributed due to addition of friction damper diagonally. This causes
reduction in axial force and bending moment. It is observed that, in some cases axial force increases,
because some dampers are observed to remain in non-slip mode. The reason behind it, is provision of
excessive dampers and sometimes lower input acceleration. Thus they behave as bracing member.
Because of this building becomes stiffer than other formats, hence axial force increases in this case.
The step by step increase in hysteresis energy for different formats of friction dampers are as
shown in Fig.24 and Fig.25 for G+5 storey and Fig.26 and Fig.27 for G+9 storey structure.
Figure 24 Hysteresis Energy for G+5 storey
0
50
100
150
200
250
300
350
400
450
500
BENDINGMOMENT(kN.m)
MAX. BENDING MOMENT
EL CENTRO
UTTERKASHI
-20
0
20
40
60
80
100
120
140
160
180
0 1000 2000 3000 4000 5000
ENERGY(kN-m)
TIME STEPS
HYSTERESIS ENERGY FOR EL CENTRO
FORMAT(2)
FORMAT(3)
FORMAT(4)
FORMAT(5)

From comparison of hysteresis energy, it can be seen that the maximum hysteresis energy is
observed for format (4) in all cases. The more value of hysteresis energy means more amount input
-50
0
50
100
150
200
250
0 1000 2000 3000 4000 5000
ENERGY(kN-m)
TIME STEPS
HYSTERESIS ENERGY FOR EL CENTRO
FORMAT(2)
FORMAT(3)
FORMAT(4)
FORMAT(5)
-5
0
5
10
15
20
25
0 500 1000 1500 2000
ENERGY(kN-m)
TIME STEPS
HYSTERESIS ENERGY FOR UTTERKASHI
FORMAT(2)
FORMAT(3)
FORMAT(4)
FORMAT(5)
-10
0
10
20
30
40
50
60
70
80
90
0 500 1000 1500 2000
ENERGY(kN-m)
TIME STEPS
HYSTERISIS ENERGY FOR UTTERKASHI
FORMAT(2)
FORMAT(3)
FORMAT(4)
FORMAT(5)

energy is dissipated by friction dampers. From the figures it is clear that, by using more numbers of
friction dampers does not always lead to more dissipation of input energy.
Figure 28 Different energy component comparison for G+5 storey
0
50
100
150
200
250
300
350
400
FORMAT (1) FORMAT (2) FORMAT (3) FORMAT (4) FORMAT (5)
ENERGY COMPONENT COMPARISON FOR EL CENTRO
Input
Energy
Kinetic
Energy
Potential
Energy
Modal
Damping
Energy
Link
Hystretic
Energy
0
20
40
60
80
100
120
140
160
180
ENERGY COMPONENT COMPARISON FOR UTTERKASHI
Input Energy
Kinetic
Energy
Potential
Energy
Modal
Damping
Energy
Link
Hystretic
Energy
0
100
200
300
400
500
600
700
800
ENERGY COMPONENT COMPARISON FOR EL CENTRO
Input
Energy
Kinetic
Energy
Potential
Energy
Modal
Damping
Energy
Link
Hysteretic
Energy

Fig. 28, Fig.29, Fig.30 and Fig.31 shows the different energy components for various location
formats considered. The input energy depends upon work done on structure by force and acceleration
and kinetic energy is function of mass and velocity while potential energy is function of elastic
constant and displacement of structure. As force, mass and elastic constants of structure are same for
all formats, energy components depend on acceleration, velocity and displacement of structure. In
Format (1), link hysteretic energy is zero because of absence of friction damper. So, all the input
energy has to be dissipated through modes so as to satisfy equation of motion. While in other formats,
percentage energy dissipated through modes reduces while energy dissipated through hysteretic
behaviour of friction damper increases. This reduction in percentage dissipation of input energy
through modes and increase in percentage dissipation through link hysteretic behaviour depends upon
location of friction damper. The percentage dissipation of input energy through hysteretic behavior is
maximum for Format (4) in G+5 storey and G+9 storey building models. The value of function used
for optimization is as shown in Fig.32 and Fig.33.
Figure 32 Objective Function Value for G+5 storey
0
50
100
150
200
250
ENERGY COMPONENT COMPARISON FOR UTTERKASHI
Input
Energy
Kinetic
Energy
Potential
Energy
Modal
Damping
Energy
Link
Hysteretic
Energy
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
FORMAT (2) FORMAT (3) FORMAT (4) FORMAT (5)
FUNCTION VALUE
EL CENTRO
UTTERKASHI

Figure 33 Objective Function Value for G+9 storey
Fig. 32 and Fig.33 shows that the value objective function is minimum for format (4) for both G+5
storey and G+9 storey structure. Also, the base shear, axial force, bending moment is minimum in
format (4). Hence, it can be said that with the given no. of dampers format (4) is optimum location
format.
7. CONCLUSION
The supplementary energy dissipation devices are known to be effective in reducing the earthquake
induced response of structural systems. Optimal placement of these protective systems is of practical
interest. The main objective of this study, therefore, has been to find the most optimal configuration of
friction damper which gives maximum utilization of damper and minimal damage to unsymmetrical
buildings when subjected to real earthquake ground motions. The results showed that the format (4) is
the optimal format because of well distributed stiffness while in other cases alternate stories are soft
and stiff. Hence it is clear that the damper placement influences significantly the structural response.
Also, the study investigates that use of larger number of dampers do not always lead to the best
benefit.
REFERENCES
[1] Pall, A. S., and Marsh C. (1982), ‘Response of Friction Damped Braced Frames’, Journal of the
Structural Division, American Society of Civil Engineers, 108(ST6).
[2] Filiatrault, A., and Cherry, S. (1990), ‘Seismic Design Spectra for Friction Damped Structures’,
Journal of Structural Engineering, American Society of Civil Engineers, 116, pp. 1334-1355.
[3] Moreschi, L.M., and Singh, M.P. (2003), ‘Design of Yielding and Friction Dampers for Optimal
Seismic Performance’, Earthquake Engineering Structural Dynamics, 32, pp. 1291-1311.
[4] Pujari, N. N., and Bakre, S. V. (2011), ‘Optimum placement of X-plate dampers for seismic
response control of multistoried buildings’ International Journal of Earth Science and Engineering,
4(6), pp. 481-485.
[5] Manveer Singh and Khushpreet Singh, An Efficient Analysis of Linear and Non- Linear Model
using Various Regression Level for Fluid Dampers. International Journal of Civil Engineering and
Technology, 7(5), 2016, pp.111–123.
[6] Khante, S. N., and Sanghai, S. S. (2012), ‘Optimal placement of friction dampers for seismic
response control of symmetric RCC framed building’, Proceeding of NCETETA-2012, pp. 209-213.
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
FORMAT (2) FORMAT (3) FORMAT (4) FORMAT (5)
FUNCTION VALUE
EL CENTRO
UTTERKASHI

[7] Kokil, A.S., and Shrikhande, M. (2007), ‘Optimal Placement of Supplemental Dampers in Seismic
Design of Structures’, JSEE Fall, 9(3), pp. 125-135.
[8] Pouya Azarsa, Mahdi Hosseini, Seyed Amin Ahmadi and Prof. N.V. Ramana Rao, Enhanced
Seismic Resistance of Steel Buildings Using Viscous Fluid Dampers. International Journal of Civil
Engineering and Technology, 7(6), 2016, pp.90–105.
[9] Pall, A., and Pall, T. R. (2004), ‘Performance-based design using Pall friction dampers- an
economical design solution’, Proceeding of World Conference of Earthquake Engineering,
Vancouver, B.C.

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