Earthquake_Response_of_Medium_Rise_to_Hi (3).pdf

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About the Council
The Council onTall Buildings and Urban Habitat, based at
the Illinois Institute of Technology in Chicago, is an
international not-for-profit organization supported by
architecture, engineering, planning, development and
construction professionals. Founded in 1969, the
Council’s mission is to disseminate multi-disciplinary
information on tall buildings and sustainable urban
environments, to maximize the international interaction
of professionals involved in creating the built
environment, and to make the latest knowledge
available to professionals in a useful form.
The CTBUH disseminates its findings, and facilitates
business exchange, through: the publication of books,
monographs, proceedings and reports; the organization
ofworldcongresses,international,regionalandspecialty
conferences and workshops; the maintaining of an
extensive website and tall building databases of built,
under construction and proposed buildings; the
distribution of a monthly international tall building
e-newsletter;themaintainingofaninternationalresource
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construction excellence and individual lifetime
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working groups; the hosting of technical forums; and the
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containing refereed papers written by researchers,
scholars and practicing professionals.
The Council is the arbiter of the criteria upon which tall
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Council on Tall Buildings and Urban Habitat Issue Chief Editor: Sang Dae Kim
Volume 1 Number 4 December 2012
Simplified Algorithm of the Novel Steel-concrete Mixed
Structure under Lateral Load
Liang Li, Guo-qiang Li, andYu-shu Liu
Guidelines forTall Buildings Development
Kheir Al-Kodmany
The Structural Design ofTianjin Goldin Finance 117Tower
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Study onVibration Perception byVisual Sensation Considering
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Seizou Kawana,YukioTamura, and Masahiro Matsui
Considerations of Sustainable High-rise Building Design in
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Kevin K.W.Wan, Man-Him Chan, andVincent S.Y. Cheng
Earthquake Response of Mid-rise to High-rise Buildings with
Friction Dampers
Naveet Kaur,V. A. Matsagar, and A. K. Nagpal
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Volume 1, Number 4, December 2012
High-Rise Buildings
www.ctbuh.org
247 Simplified Algorithm of the Novel Steel-concrete Mixed Structure under Lateral Load
Liang Li, Guo-qiang Li, and Yu-shu Liu
255 Guidelines for Tall Buildings Development
Kheir Al-Kodmany
271 The Structural Design of Tianjin Goldin Finance 117 Tower
Peng Liu, Goman Ho, Alexis Lee, Chao Yin, Kevin Lee, Guang-lei Liu, and Xiao-yun Huang
283 Study on Vibration Perception by Visual Sensation Considering Probability of Seeing
Seizou Kawana, Yukio Tamura, and Masahiro Matsui
301 Considerations of Sustainable High-rise Building Design in Different Climate Zones of China
Kevin K. W. Wan, Man-Him Chan, and Vincent S. Y. Cheng
311 Earthquake Response of Mid-rise to High-rise Buildings with Friction Dampers
Naveet Kaur, V. A. Matsagar, and A. K. Nagpal
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Contents

High-Rise Buildings
www.ctbuh.org
International Journal of High-Rise Buildings
December 2012, Vol 1, No 4, 311-332
Earthquake Response of Mid-rise to High-rise Buildings
with Friction Dampers
Naveet Kaur1†
, V. A. Matsagar1
, and A. K. Nagpal1
1
Department of Civil Engineering, Indian Institute of Technology (IIT) Delhi, Hauz Khas, New Delhi - 110 016, India
Abstract
Earthquake response of mid-rise to high-rise buildings provided with friction dampers is investigated. The steel buildings are
modelled as shear-type structures and the investigation involved modelling of the structures of varying heights ranging from
five storeys to twenty storeys, in steps of five storeys, subjected to real earthquake ground motions. Three basic types of
structures considered in the study are: moment resisting frame (MRF), braced frame (BF), and friction damper frame (FDF).
Mathematical modelling of the friction dampers involved simulation of the two distinct phases namely, the stick phase and the
slip phase. Dynamic time history analyses are carried out to study the variation of the top floor acceleration, top floor
displacement, storey shear, and base-shear. Further, energy plots are obtained to investigate the energy dissipation by the friction
dampers. It is seen that substantial earthquake response reduction is achieved with the provision of the friction dampers in the
mid-rise and high-rise buildings. The provision of the friction dampers always reduces the base-shear. It is also seen from the
fast Fourier transform (FFT) of the top floor acceleration that there is substantial reduction in the peak response; however, the
higher frequency content in the response has increased. For the structures considered, the top floor displacements are lesser in
the FDF than in the MRF; however, the top floor displacements are marginally larger in the FDF than in the BF.
Keywords: Damper, Earthquake, Friction, Storey shear
1. Introduction
In 1979, the friction damper was invented, to be used
in buildings for improving seismic performance, inspired
from the friction brakes used in automobiles (Pall and
Marsh, 1979; 1981). The friction dampers are, by far, the
most widely adopted means to dissipate the damaging
kinetic energy from the structures. The friction dampers
dissipate a large amount of energy, which is evident from
its highly nonlinear hysteresis loop, through dry sliding
friction. The friction dampers work on stick-slip pheno-
menon, in which slip load is the most important para-
meter. Slip load is the load at which the friction dampers
are activated and slippage occurs, thereby developing
frictional force. Two most prominent types of the friction
dampers which have successfully been used around the
world are the Pall and the Sumitomo friction dampers.
The general categorisation of buildings, as per Emporis
(2012), according to height and number of storeys is: (a)
low-rise building (< 15 m; up to 3 storeys), (b) mid-rise
building (15 m to 30 m; 3 to 8 storeys), and (c) high-rise
building (30 m to 150 m; 8 to 30/35 storeys). For the pur-
pose of this manuscript mid-rise to high-rise buildings are
considered.
The passive techniques of earthquake response mitiga-
tion were understood and their efficacy was tested in the
70’s (Skinner et al., 1975). This invention was further
diversified into those for shear walls, braced steel/
concrete frames, and low-rise buildings (Pall and Marsh,
1981, 1982). Some other kinds of friction dampers were
developed with modified design concepts, viz. the two
energy absorbing system (Zhou and Peng, 2010) and self-
centring energy dissipative steel braces (Tremblay et al.,
2008). Recent advancements include active control for
friction dampers, connection of two structures with fric-
tion dampers and retrofitting of structures (Bhaskararao
and Jangid, 2006; Apostolakis and Dargush, 2010), and
others. Recently, Boeing’s Commercial Airplane Factory
- world’s largest building in volume was retrofitted with
these type of dampers (Chandra et al., 2000).
The friction dampers are generally installed in the
cross-bracings of the building frames, called here as
friction damper frame (FDF). In the braced frame (BF) of
the buildings, owing to increase in stiffness, displace-
ments are reduced; however, base shear of the structure
increases as compared to that in the conventional moment
resisting frame (MRF) of the buildings under earthquakes.
However, providing the friction dampers in the braces
would help reduce the base shear induced in the columns
because of energy dissipation. Also, the number of
storeys of the structure affects the reduction achieved in
the seismic response. Hence, it is essential to investigate
the seismic response reduction of a structure when it is
†
Corresponding author: Naveet Kaur
Tel: +91-81-3033-2121; Fax: +91-11-2658-1117
E-mail: naveet.kaur1985@gmail.com

312 Naveet Kaur et al. | International Journal of High-Rise Buildings
provided with the friction dampers as compared to the
MRF and BF keeping in mind the number of storeys of
the structure. Therefore, the need to carry out such a study
cannot be overemphasised.
Further, almost invariably, the stiffness of brace is
neglected in which friction damper is installed. However,
considering realistically the force-deformation behaviour
of friction damper does include initial stiffness provided
by the brace. Hence, it is imperative to develop a mathe-
matical model that will capture real behaviour of the
friction dampers.
In view of the aforementioned needs, the primary
objectives of the present study are: (a) mathematically
model real behaviour of the friction dampers and study
the effect of slip load; (b) to investigate the response of
the MRF, BF, and FDF for different earthquake exci-
tations; and (c) to investigate the seismic response in the
MRF, BF, and FDF for varying number of storeys.
2. Mathematical Modelling
Assumption of Coulomb’s friction is made for model-
ling the nonlinear behaviour of the friction dampers. The
nonlinearity is concentrated only in the friction dampers,
assuming that rest of the building members (primary
structural system) remain in elastic range. This is done to
ensure that the energy dissipation occurs in friction dam-
pers only and not by yielding of other structural members.
Hence, a structure with energy dissipation devices can be
treated as a dual system consisting of nonlinear energy
dissipating devices exhibiting elasto-plastic behaviour, and
a primary structural system exhibiting linear behaviour.
The mathematical models developed for multi-storey
(a) MRF, (b) BF, and (c) FDF are shown in Fig. 1(a)~(c).
The schematic diagrams of popularly used friction dam-
pers are shown in Fig. 1(d)~(f). The assumptions made
for arriving at the mathematical models under considera-
tion are: (a) the building members other than friction
dampers are assumed to remain within the elastic limit,
(b) the floors are assumed to be rigid in their own plane,
(c) the mass is lumped at each floor level, (d) one degree
of freedom at each floor level in the direction of earth-
quake ground motion is considered, and (e) strength de-
gradation of friction dampers is ignored in the analysis, it
being unimportant in case of the friction dampers, as re-
ported earlier (Pall et al., 1993; Apostolakis and Dargush,
2010).
2.1. Moment resisting frame (MRF)
The governing differential equations of motion for the
MRF are written as,
(1)
Here, [M], [C], and [K] are the mass, damping, and
M
[ ] u
··
t
( )
{ } C
[ ] u
·
t
( )
{ } K
[ ] u t
( )
{ }
+ + M
[ ] r
{ }u
··
g t
( )
–
=
Figure 1. Mathematical models of N-storey (a) moment resisting frame (MRF), (b) braced frame (BF), (c) friction damper
frame (FDF), and (d)-(f) Schematic diagrams of popularly used friction dampers.

Earthquake Response of Mid-rise to High-rise Buildings with Friction Dampers 313
stiffness matrices of the structure, respectively. Moreover,
, , {u(t)}, and {r} are the acceleration, velo-
city, displacement, and influence coefficient vectors, res-
pectively. The earthquake ground acceleration is denoted
by . For the MRF, the structure is defined by its
mass matrix, damping matrix, and stiffness matrix as [M],
[C], and [K], respectively. [M] is a diagonal matrix with
diagonal element mjj = mj, the mass lumped at the jth
floor.
Flexural rigidity of the columns provides lateral force
resistance in the MRF. Hence, only column stiffness con-
tributes towards the formation of [K] matrix. The dam-
ping matrix [C], is not known explicitly; it is constructed
by assuming the modal damping ratio in each mode of
vibration for the MRF, which is kept constant in all
modes.
2.2. Braced frame (BF)
BF are written as,
(2)
Here, [M] and [C] matrix are constructed similar as that
in case of the MRF. In the BF, stiffness of the structure is
the combined effect of the stiffness imparted by the
columns, i.e. [K] and the braces, i.e. [Kb]. Here, θN is the
angle of the brace with horizontal at the Nth
storey level
and (kbi) = kb1, kb2, kb3, ..., kbN denote the axial stiffness of
the braces. The displacement {y(t)} in the direction of
diagonal brace is related to the lateral displacement
{u(t)}, using cosine of the angle, θN, as given by Eq. 5
soon after.
2.3. Friction damper frame (FDF)
FDF are written as,
(3)
where,
(4)
Here, {R(t)} is the restoring force provided by the
friction damper. Almost invariably, the stiffness of the
brace is neglected in which friction damper is installed.
However, if realistic force-deformation behaviour of the
friction damper is considered then it certainly does
include initial stiffness provided by the brace. The
variation of restoring force, {R(t)}, in the damper-brace
assembly is shown in Fig. 2. The resultant combination of
rigid plastic behaviour exhibited by the elastic force in
the brace [refer Fig. 2(a)] and friction damper [refer Fig.
2(b)] is shown in Fig. 2(c). Here, {Rt(t)} and {Rc(t)} are
the slip loads in tension and compression, respectively.
The damper-brace assembly displacement {y(t)} is related
to the lateral displacement {u(t)} as,
(5)
It is assumed that the initial conditions are zero [{u(t)}
= 0, = 0] in the dynamic time history analysis of
the structures for earthquake ground motion. Initially, as
the earthquake induced load is imparted and when the
force in the damper has not reached slip load, only the
elastic part of the brace is active. Hence, the system is in
elastic stage along curve E0 [refer Fig. 2(c)]. The damper-
brace assembly displacement {yt(t)} and {yc(t)} at which
plastic behaviour in tension and compression initiate,
respectively, are calculated from,
[6(a)]
[6(a)]
The system remains on elastic curve E0 as long as {yc
(t)} < {y(t)} < {yt(t)}. If {y(t)} > {yt(t)} the system enters
plastic stage in tension along the curve T [refer Fig. 2(c)]
and it remains on curve T as long as velocity > 0.
When < 0, the system reverses in elastic stage on
a curve such as E1 with new yielding limits given by,
[7(a)]
[7(b)]
Here, {ymax(t)} is the maximum displacement along the
curve T, at = 0. Conversely, if {y(t)} < {yc(t)} the
system enters plastic stage in compression along curve C
and it remains on curve C as long as velocity < 0.
When > 0, the system reverses in elastic stage on
a curve such as E2 with new yielding limits given by,
[8(a)]
[8(b)]
Here, {ymin(t)} is the minimum displacement along the
curve C, at = 0. For the system to remain opera-
ting in elastic range along any segment such as E0, E1,
u
··
t
( )
{ } u
·
t
( )
{ }
u
··
g t
( )
M
[ ] u
··
t
( )
{ } C
[ ] u
·
t
( )
{ } K
[ ] Kb
[ ] θ
2
cos
+
( ) u t
( )
{ }
+ +
= M
[ ] r
{ }u
··
g t
( )
–
M
[ ] u
··
t
( )
{ } C
[ ] u
·
t
( )
{ } K
[ ] u t
( )
{ } R t
( )
{ }
+ + +
= M
[ ] r
{ }u
··
g t
( )
–
R t
( )
{ }
R1 t
( ) θ1
cos R2 t
( ) θ2
cos
–
R2 t
( ) θ2
cos R3 t
( ) θ3
cos
–
...
RN 1
– t
( ) θN 1
–
cos RN t
( ) θN
cos
–
RN t
( ) θN
cos
 
 
 
 
 
 
 
 
 
=
y t
( )
{ } u t
( )
{ } θ
cos
=
u
·
t
( )
{ }
yt t
( )
{ }
Rc
kb
----
-
 
 
 
=
yc t
( )
{ }
Rt
kb
----
 
 
 
=
y
·
t
( )
{ }
y
·
t
( )
{ }
yt t
( )
{ } ymax t
( )
{ }
=
yc t
( )
{ } ymax t
( )
{ }
Rt Rc
–
kb
-------------
-
 
 
 
–
=
y
·
t
( )
{ }
y
·
t
( )
{ }
y
·
t
( )
{ }
yc t
( )
{ } ymin t
( )
{ }
=
yt t
( )
{ } ymin t
( )
{ }
Rt Rc
–
kb
-------------
-
 
 
 
+
=
y
·
t
( )
{ }

E2... [refer Fig. 2(c)], it should follow {yc(t)} < {y(t)} <
{yt(t)}. The restoring force in the elastic stage is given by,
(9)
And in the plastic tension stage it is given by,
(10)
Whereas, in the plastic compression stage it is given by,
(11)
It may be noted that neglecting the initial stiffness pro-
vided by the brace, the force-deformation behaviour is as
shown in Fig. 2(b) only, which is modified to that as
shown in Fig. 2(c) if the initial stiffness provided by the
brace is taken into account. The effect of brace has been
shown in Fig. 2(d) and discussed later.
The numerical solution of the governing differential
equations given by the Eqs. 1, 2, and 3 written respec-
tively for the MRF, BF, and FDF is obtained by using
Newmark’s method of step by step integration adopting
linear variation of acceleration over a small time interval
of ∆t. The time interval for solving the equations of mo-
tion is taken as ∆t = 0.0002 sec.
3. Numerical Study
Numerical examples considered herein consist of three
structures namely MRF, BF, and FDF to compare the
effectiveness of the friction dampers being provided in
the buildings. Modal damping of ξ = 2% is taken for the
three structures considered herein. In the BF, the braces
are assumed to carry only the axial force and the brace
sections are so chosen to ensure that they do not buckle
under compression and should not yield under tension.
Thereby, the energy dissipation happens by friction dam-
pers only and not by yielding of other building members.
In the FDF, the most favourable seismic response is
observed at the damper slip load of around 30% of storey
weight as observed through extensive parametric study
reported anon. Hence, the normalised slip load for friction
damper at each storey level considered for the study is 30%
of the storey weight (w). The earthquake motions selected
for the study are S00E component of 1940 Imperial Val-
ley earthquake; N00E component of 1989 Loma Prieta
earthquake; N360S component of 1994 Northridge earth-
quake and EW component of 1995 Kobe earthquake with
peak ground acceleration (PGA) of 0.34 g, 0.56 g, 0.83 g,
and 0.67 g, respectively. Here, g denotes acceleration due
to gravity.
For further studies, the three basic building frames, with
heights varying from 5, 10, 15, and 20 storeys are com-
pared to check the effectiveness of the friction dampers.
The first, second, and third linear modal time periods (in
seconds) of different structures considered respectively
are: (a) MRF: 5 storey (0.54, 0.18, 0.12); 10 storey (1.02,
0.34, 0.21); 15 storey (1.51, 0.51, 0.31); 20 storey (1.90,
0.63, 0.38) and (b) BF: 5 storey (0.32, 0.11, 0.07); 10
storey (0.62, 0.21, 0.13); 15 storey (0.91, 0.31, 0.18); 20
storey (1.15, 0.38, 0.23). Since the stiffness of the friction
damper varies nonlinearly (refer Fig. 2), the linear modal
R t
( )
{ } Rt t
( )
{ } kb
{ } yt t
( )
{ } y t
( )
{ }
–
( )
–
=
R t
( )
{ } Rt t
( )
{ }
=
R t
( )
{ } Rc t
( )
{ }
=
Figure 2. (a) Elastic behaviour of brace, (b) hysteretic loop of friction damper, (c) resultant elasto-plastic behaviour of
friction damper in brace, and (d) comparison of actual hysteretic loop with and without brace effect.

time periods of the FDF are underestimated and assumed
to be the same as that of the MRF. In the FDF, when the
friction damper is in stick phase, the building frame be-
haves like a BF with stiffness of the braces active. When
Figure 3.1(a). Time history of top floor displacement and top floor acceleration of three frames with 5 storeys under
Imperial Valley, 1940.
Figure 3.1(b). Time history of top floor displacement and top floor acceleration of three frames with 5 storeys under
Loma Prieta, 1989.

Figure 3.1(c). Time history of top floor displacement and top floor acceleration of three frames with 5 storeys under
Northridge, 1994.
Figure 3.1(d). Time history of top floor displacement and top floor acceleration of three frames with 5 storeys under
Kobe, 1995.

Loma Prieta, 1989.

Northridge, 1994.
Kobe, 1995.

Figure 3.3(b). Time history of top floor displacement and top floor acceleration of three frames with 15 storeys Loma
Prieta, 1989.

Northridge, 1994.
Kobe, 1995.

Loma Prieta, 1989.

Northridge, 1994.
Kobe, 1995.

the friction damper enters slip stage, its stiffness becomes
zero and the building frame starts behaving like a MRF.
Hence, frequency of the FDF is dependent on the slip load.
Note that the slip load (Fd = 0.3w) of the friction dampers
is kept the same for all the floors in the FDF and the
dampers are provided at all floors. Moreover, the initial
stiffness of the damper-brace assembly is taken the same
as that in case of the BF, i.e. (kbi).
The time histories of top floor displacement and top
floor acceleration of the three building frames are shown
in Fig. 3. Corresponding peak top floor displacement and
peak top floor acceleration of the three structures for
different number of storeys and earthquakes are as shown
in Tables 1 and 2, respectively. It is observed that in the
BF, owing to the increase in stiffness, displacement re-
duces and acceleration increases as compared to that in
case of the MRF. In the FDF, due to slip across the fric-
tion damper, the peak top floor displacement is amplified
as compared to that in case of the BF; however, the
values are still lesser than that in case of the MRF. Under
Table 1. Peak displacement response of different frames with varying storeys under different earthquakes
No. of
Storeys
Peak Top Floor Displacement (cm)
Imperial Valley, 1940 Loma Prieta, 1989 Northridge, 1994 Kobe, 1995
MRF BF FDF MRF BF FDF MRF BF FDF MRF BF FDF
5 11.27 3.32 5.10 25.62 6.39 15.44 17.44 10.32 14.72 12.05 8.21 8.56
10 21.68 11.11 11.90 38.90 37.45 34.10 31.99 17.64 26.88 47.45 22.54 41.77
15 16.98 20.13 11.82 77.52 34.68 62.73 87.41 25.86 67.12 25.31 49.16 23.44
20 21.21 15.69 14.96 80.85 45.67 69.99 81.97 40.39 73.22 36.68 33.28 27.09
Table 2. Peak acceleration response of different frames with varying number of storeys under different earthquakes
No. of
Storeys
Peak Top Floor Acceleration (g)
5 1.51 1.41 0.94 3.58 2.42 2.30 2.69 3.82 2.42 1.71 2.94 1.28
10 0.97 1.35 0.75 1.57 4.03 1.42 2.13 1.92 1.65 2.45 2.33 2.10
15 0.60 1.25 0.43 1.82 2.45 1.56 2.28 1.90 2.04 1.34 2.68 1.05
20 0.62 0.77 0.41 1.86 1.81 1.36 1.53 2.18 1.50 1.30 2.05 0.95
Figure 4(a). Normalised storey shear for three frames with varying number of storeys for Imperial Valley, 1940.

Figure 4(b). Normalised storey shear for three frames with varying number of storeys for Loma Prieta, 1989.
Figure 4(c). Normalised storey shear for three frames with varying number of storeys for Northridge, 1994.

the considered earthquakes, it is observed that for 15
storey building, the FDF provides a seismic response
reduction of 23.21% in the top floor displacement, whereas
the BF provides a reduction of 70.41% in the seismic
response, both compared to the top floor displacement of
the MRF. In the FDF, peak top floor acceleration reduces
as compared to that in case of the MRF due to energy
dissipation by the friction dampers.
Normalised storey shear for the three building frames
under the considered earthquakes are shown in Fig. 4.
Storey shears are normalised with total weight of the
structure, W = Σmj × g. Among all the three frames consi-
dered and different number of storeys and earthquakes, it
is observed that the FDF shows the least normalised
storey shear which evidently confirms effectiveness of
adding friction dampers.
The peak normalised base shear for the three building
frames with 5, 10, 15, and 20 storeys under different
earthquakes is reported in Table 3. It is observed that in
the BF, the peak normalised base shears are more than
that in the MRF in most of the cases, except for cases
where the fundamental modal time period of structure is
in acceleration dominant zone of earthquake response
spectrum. The FDF exhibits the least seismic response for
all cases with reduction ranging from 13.12% (10 storey
building under Imperial Valley, 1940) to 49.64% (5 storey
building under Loma Prieta, 1989) as compared to that in
case of the MRF.
The plots fast Fourier transform (FFT) of the top floor
acceleration for the three building frames under the four
earthquakes are shown in Fig. 5. The higher frequency
modes are excited in the BF as compared to that in case
of the MRF, owing to the increased stiffness of the BF.
Further, it is observed that the FFT amplitudes associated
with high frequency content significantly increase in the
FDF as compared to both, MRF and BF. The high
frequency content in the seismic response in case of the
FDF is attributed towards sudden change of phase from
Figure 4(d). Normalised storey shear of three frames with varying number of storeys for Kobe, 1995.
Table 3. Peak normalised base shear for different frames with varying number of storeys under different earthquakes
No. of
Storeys
Peak Normalised Base Shear (W)
5 1.12 0.82 0.56 2.48 1.73 1.59 1.59 2.79 1.34 1.19 2.27 0.91
10 0.53 0.78 0.36 0.99 2.54 0.86 1.09 1.13 0.92 1.18 1.66 1.00
15 0.18 0.62 0.13 0.91 1.04 0.71 1.02 1.09 0.74 0.31 1.48 0.23
20 0.17 0.29 0.10 0.72 0.78 0.49 0.60 0.94 0.49 0.28 0.67 0.18

stick to slip and vice versa in the elasto-plastic force-
deformation behaviour exhibited by the friction damper,
i.e. high nonlinearity. The increase of the acceleration
associated with the high frequency content can be
detrimental to the high frequency equipments installed in
the building. Nonetheless, owing to the energy dissipation
Figure 5(a). FFT of top floor acceleration of three frames with 5 storeys under different earthquakes.
Figure 5(b). FFT of top floor acceleration of three frames with 10 storeys under different earthquakes.

by the friction dampers, the peak FFT amplitudes are
significantly reduced in the FDF as compared to both,
MRF, and BF.
Energy plots for the FDF with 5, 10, 15, and 20 storeys
under the four earthquakes are shown in Fig. 6. Input
energy is the energy imparted to the structure by the earth-
Figure 5(c). FFT of top floor acceleration of three frames with 15 storeys under different earthquakes.
Figure 5(d). FFT of top floor acceleration of three frames with 20 storeys under different earthquakes.

quake ground motion. Modal energy is the energy absor-
bed by the structure owing to its classical damping of 2%
considered herein. Input energy is equal to sum of modal
energy and energy dissipated by the friction dampers. It is
observed that major portion of the input energy is dis-
sipated by the friction dampers which confirm their use-
Figure 6(a). Comparison of energy dissipation in 5 storey FDF under different earthquakes.
Figure 6(b). Comparison of energy dissipation in 10 storey FDF under different earthquakes.

fulness in seismic response reduction in building frames.
Further, by maximising the energy dissipated by the fric-
tion dampers optimum parameters for the friction dampers
could be arrived at for achieving highest seismic response
reduction.
Table 4 shows the peak seismic response obtained for
Figure 6(c). Comparison of energy dissipation in 15 storey FDF under different earthquakes.
Figure 6(d). Comparison of energy dissipation in 20 storey FDF under different earthquakes.

the FDF under the four earthquakes for two different mo-
dels of the friction damper: (a) with the effect of brace
considered, and (b) when the brace effect is ignored. It is
observed that the seismic response is considerably influ-
enced when the brace is not modelled in the friction
damper. The top floor displacement and the base shear
are underestimated when the brace is not modelled in the
FDF. Thus, effectiveness of the friction dampers is over-
estimated if the brace is not modelled. Therefore, the
brace needs to be mathematically modelled properly in
order to predict the seismic response of the FDF accu-
rately. In Fig. 2(d), damper force is plotted with displace-
ment across the friction damper. The displacement is
observed to be increased when the brace is modelled, and
the difference in the force-deformation hysteresis loops is
evident.
It is important to see the effect of variation of normali-
sed slip load, Fd, on the seismic response parameters such
as peak top floor displacement, peak top floor accelera-
tion, and normalised base shear (refer Fig. 7). These res-
ponse parameters are compared with those in case of the
MRF and BF. In Fig. 7, the average response of all the
earthquakes is also plotted. Force in the friction dampers
(with threshold value equal to slip load), responsible for
activating their slippage, is the most important parameter.
Hence, the response is compared under different earth-
quakes with varying peak ground accelerations. From the
average response plot, it is observed that with the increase
in the slip load, peak top floor displacement keeps on
reducing, owing to the increase in the slip load. Peak top
floor acceleration initially reduces sharply, till normalised
slip load of about 20% for 5 and 10 storey buildings and
about 30% for 15 and 20 storey buildings, beyond that the
average response remains almost unaffected. The peak
normalised base shear shows a decreasing trend with
increase in the slip load of the friction damper. However,
the reduction in the base shear becomes insignificant at
higher slip loads. Therefore, slip load of 30% of the
storey weight (w) is proposed for the reported study, upon
observing these response parameters for different number
Table 4. Seismic response for two different models of friction damper
Earthquake
No. of
Storeys
Peak Response with the Brace Effect Peak Response without the Brace Effect
Displacement
(cm)
Acceleration
(g)
Base Shear
(W)
Displacement
(cm)
Acceleration
(g)
Base Shear
(W)
Imperial Valley,
1940
5 8.47 1.42 0.86 5.10 0.94 0.56
10 19.79 1.16 0.56 11.90 0.75 0.36
15 15.04 0.56 0.20 11.82 0.43 0.13
20 20.90 0.56 0.14 14.96 0.41 0.10
Loma Prieta,
1989
5 18.61 2.53 1.96 15.44 2.30 1.59
10 33.82 1.52 0.94 34.10 1.42 0.86
15 65.49 1.73 0.74 62.73 1.56 0.71
20 72.32 1.54 0.65 69.99 1.36 0.49
Northridge,
1994
5 17.40 2.75 1.61 14.72 2.42 1.34
10 29.14 2.02 1.03 26.88 1.65 0.92
15 72.12 2.04 0.87 67.12 2.04 0.74
20 77.28 1.48 0.57 73.22 1.50 0.49
Kobe,
1995
5 11.25 1.86 1.10 8.56 1.28 0.91
10 43.85 2.30 1.05 41.77 2.10 1.00
15 24.62 1.26 0.33 23.44 1.05 0.23
20 34.25 1.04 0.30 27.09 0.95 0.18
Figure 7(a). Peak top floor displacement, peak top floor acceleration and peak normalised base shear of 5 storey FDF
against varying slip load under different earthquakes.

of storeys under various earthquakes considered herein.
Nevertheless, for a given structure under considered earth-
quake ground motion the best suitable parameters of the
friction dampers may be arrived at, which leads to the
maximum effectiveness.
4. Conclusions
Seismic response of mid-rise to high-rise buildings
provided with friction dampers is investigated adopting
appropriate mathematical modelling. The response is
compared with the conventional building frames in order
to establish effectiveness of using friction dampers. The
following are some of the major conclusions drawn from
the study.
For 15 storey building, the friction damper frame (FDF)
provides a seismic response reduction of 23.21% in the
top floor displacement, whereas the braced frame (BF)
provides a reduction of 70.41% in the seismic response,
both compared to the top floor displacement of the moment
Figure 7(b). Peak top floor displacement, peak top floor acceleration and peak normalised base shear of 10 storey FDF
Figure 7(c). Peak top floor displacement, peak top floor acceleration and peak normalised base shear of 15 storey FDF
Figure 7(d). Peak top floor displacement, peak top floor acceleration and peak normalised base shear of 20 storey FDF

resisting frame (MRF) under the considered earthquakes.
In the BF, increase in the peak normalised base shear is
observed due to increase in the stiffness. The FDF exhi-
bits a maximum seismic response reduction of 49.64% in
the normalised base shear as compared to that in case of
the MRF for 5 storey building.
The FDF is effective in reducing peak normalised base
shear with compromise in peak top floor displacement
(though always less than that in case of the MRF) as com-
pared to the BF keeping the MRF as reference. The storey
shear is induced the least in the FDF under all earthquakes
and type of buildings considered.
Higher frequency content is observed in the seismic
response of the FDF as compared to that in case of both,
MRF, and BF, which is concluded to be caused due to
stick-slip phenomenon observed in the friction dampers.
Most of the energy imparted to the structure by earth-
quake is dissipated by friction dampers leading to sub-
stantial reduction in the seismic response.
The seismic response is considerably influenced if the
brace is not modelled in the friction damper. The top floor
displacement and the base shear are underestimated the-
reby the effectiveness of the friction dampers is overesti-
mated if the brace is not modelled in the FDF.
References
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design of moment-resisting steel frames with hysteretic
passive devices.” Earthquake Engineering and Structural
Dynamics, 39(4), pp. 355~376.
Bhaskararao, A. V. and Jangid, R. S. (2006). “Seismic analy-
sis of structures connected with friction dampers.” Engi-
neering Structures, 28(5), pp. 690~703.
Chandra, R., Masand, M., Nandi, S.K., Tripathi, C.P., Pall,
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