Determined optimized slip load distribution for same Steel Moment Resisting Frame using Newmark's Beta method of direct time history analysis in ETABS 2015 under Dr. K. Rama Raju (Chief Scientist, CSIR-SERC, Chennai)

1. 1
A REPORT
ON
Seismic Performance Enhancement of a 20-Storey Steel Moment
Resisting Frame with Friction Dampers
BY
Name ID. No. Discipline
Yambal Mukul Ratnakumar 2013A2PS581P B.E (Hons.) Civil
AT
Structural Engineering Research Centre, Chennai
A Practice School – II station of
BIRLA INSTITUTE OF TECHNOLOGY & SCIENCE, PILANI
July-December, 2016

2. 2
A REPORT
ON
Seismic Performance Enhancement of a 20-Storey Steel Moment Resisting
Frame with Friction Dampers
BY
Name ID. No. Discipline
Yambal Mukul Ratnakumar 2013A2PS581P B.E (Hons.) Civil
AT
Structural Engineering Research Centre, Chennai
A Practice School – II station of
BIRLA INSTITUTE OF TECHNOLOGY & SCIENCE, PILANI
July-December, 2016
ACKNOWLEDGEMENT

3. 3
ACKNOWLEDGEMENT
I am grateful to my guide Dr K Rama Raju for this this wonderful opportunity to
work under him on the topic of “Seismic Performance Enhancement of a 20-Storey Steel
Moment Resisting Frame with Friction Dampers”. I am grateful for his wisdom, guidance,
inspiration, blessings and co-operation all throughout the project and for providing us with all
the necessary resources for the project.
I am also thankful to CSIR-Structural Engineering Research Center for this
opportunity to work under the guidance of an expert scientist and in this process we are getting
exposure to different technologies related to structural engineering and related resources. This
is giving us opportunity to gain knowledge and working experience in the area of Vibration
Control, Earthquake Engineering, Structural Dynamics and Finite Element Modelling.
I am greatly obliged to my Practice School Instructor, Mr. Mahesh Kumar
Hamirwasia for his constant support and encouragement during the course of the project. I
am grateful to the Practice School Division of BITS-Pilani, for giving opportunity to present
the work inputs into the PS-2 program. This is providing us an excellent opportunity to put
our theoretical skills in engineering to use and in turn obtain good knowledge and experience.
I express my sincere gratitude to Prof Souvik Bhattacharya, Vice-Chancellor, Birla Institute
of Technology and Science, Pilani for providing me this opportunity by including 6 months
Practice School experience as a part of our course.
Above all I pay my regards to the Almighty, my parents for their blessings and friends
for their constant support during my project work.

4. 4
BIRLA INSTITUTE OF TECHNOLOGY AND SCIENCE
PILANI (RAJASTHAN)
Practice School Division
Station: SERC-CSIR Centre: Chennai
Duration: July – December Date of Start: 4th
July
Date of Submission:
Title of the Project: Seismic Performance Enhancement of a 20-Storey Steel Moment Resisting
Frame with Friction Dampers.
ID No/ Name/ Discipline: 2013A2PS581P /Yambal Mukul Ratnakumar/B. E (Hons.) Civil
Name(s) and Designation of the expert(s): Dr K Rama Raju, Chief Scientist, Computational
Mechanics dept., CSIR-SERC
Name(s) of the PS Faculty: Mr. Mahesh Kumar Hamirwasia, Lecturer, BITS Pilani
Key Words: 20-Storey Benchmark Problem, Chevron and Cross Bracing Configurations, Non-linear
dynamic time history analysis, Material and geometrical nonlinearity (P-δ effects), Rayleigh Damping,
Friction Dampers.
Project Areas: Vibration Control, Earthquake performance enhancement of buildings.
Abstract: Dissipation Energy devices may play important role in minimizing building responses
without causing damage to structural and non-structural elements. In present study, a 20-Storey
benchmark Steel Moment resisting frame (SMRF) problem for seismically excited nonlinear buildings
is modelled using ETABS 2015. Nonlinear time history analysis using Fast Nonlinear Analysis (FNA)
with Rayleigh Damping, and Direct Integration using Newmark method with Rayleigh Damping for
three types of earthquakes for Design Based Earthquake (DBE) and Maximum Credible Earthquake
(MCE). In this study building is subjected to three different types of earthquakes with Peak Ground
Acceleration (PGA) of 3.42, 8.18, and 8.27 m/s2
that is El Centro, Kobe and Northridge respectively
with different scale factors for time histories representing DBE and MCE. Seismic performance
enhancement of 20-Storey benchmark SMRF provided with Friction Dampers in Chevron
configuration distributed at different places along the height over the bare frame. Plastic Wen Link
element is used for modelling of friction dampers.
Signature(s) of Student(s) Signature of PS Faculty
Date Date

5. 5
Table of Contents
1. INTRODUCTION.................................................................................................................. 6
2. SEISMIC RESPONSE OF BUILDING WITH FRICTION DAMPERS.............................. 8
2.1 Description of Model ..................................................................................................... 9
2.2 Evaluation of Model..................................................................................................... 11
2.3 Methods for nonlinear time-history analysis................................................................ 12
2.4 Constant Damping and Rayleigh Damping.................................................................. 12
2.5 Friction Dampers.......................................................................................................... 14
2.6 Slip Load of Friction Dampers (Pall et al, 2014) ......................................................... 16
2.7 Types of Configurations............................................................................................... 18
2.7.1 Chevron Brace Configuration................................................................................... 18
2.8 Methodology for Design and Distribution of friction Dampers................................... 19
2.9 Distribution of dampers for 20-Storey buildings ......................................................... 19
3. RESULTS AND DISCUSSIONS ........................................................................................ 21
4. SUMMERY AND CONCLUSION ..................................................................................... 26
5. APPENDICES...................................................................................................................... 28
Appendix A: Building Responses............................................................................................ 28
6. REFERENCE....................................................................................................................... 30

6. 6
1. INTRODUCTION
In the present day scenario, the necessity of more flexible civil engineering structures
such as tall buildings and long span bridges is increased and they are subjected to large dynamic
forces such as earthquakes, blasts, wind, moving loads, machines and large ocean waves. This
results in large deformations and accelerations due to strong excessive vibrations in structures.
These vibrations cause human discomfort, partial collapse of structural parts and sometimes this
causes threat to structural safety and may also leads to collapse.
In order to eliminate the undesirable effects of vibrations in structures, it is necessary to
understand the behaviour and response of structural systems subjected to dynamic loads such as
earthquake and wind loads. One of the main challenges the structural engineers of the present
decade are facing is, the development of innovative design concepts to protect the civil
engineering structures from damages to non-structural elements and human occupants due to
hazards such as strong winds and earthquakes. Traditionally, the structural systems relied on their
inherent strength and ability to dissipate energy to survive under severe dynamic loading. The
energy dissipation in such systems may occur by the inelastic cyclic deformations at the specially
detailed plastic hinge regions of structural members. This causes localized damages in the
structure, as the primary structure itself must absorb much of the input energy from dynamic
forces and this requires high cost for repair and retrofit of the structure after disaster. But, for
essential structures such as hospitals, police and fire stations must remain functional even after
the earthquake. For a structure to remain functional after the earthquake, the conventional design
approach is inappropriate as it allows a structure to undergo considerable damages.
In recent years, innovative means of enhancing structural functionality and safety against
dynamic loadings have gained momentum. This includes the use of supplemental energy

7. 7
absorption and dissipation devices in structure to mitigate the adverse effects of these dynamic
loads. These systems work by absorbing and reflecting a portion of input energy that would be
otherwise transmitted to the structure itself. These systems can be classified as passive, active,
semi-active and hybrid vibration control systems based on the manner they control vibrations.
A number of passive energy dissipation devices are commercially available or under
development. Device that have most commonly been used for seismic protection of structures
include viscous fluid dampers, friction dampers, and metallic dampers. Other devices that could
be classified as passive energy dissipation devices or, more generally, passive control devices
include tuned mass and tuned liquid dampers, both of which are primarily applicable to wind
vibration control, re-cantering dampers, and phase transformation dampers. With the introduction
of energy dissipation devices, supplement damping of the structure can be increased to 20% -
30% of critical damping, while the inherent or natural damping of structure is merely 1% - 5%.
A friction damper is a passive energy dissipation device used in the structures to reduce
the response of the building during earthquake. Friction dampers dissipate energy via sliding
friction across the interface between two solid bodies. Due to their low production and
maintenance cost this type of damping devices are widely used both for new and retrofitted
structures. The energy dissipation systems are relatively new and sophisticated concepts that
require more extensive design and detailed nonlinear time-history dynamic analysis. Several
mom-linear computer programs are now capable for modelling of friction dampers. Some of these
are ETABS, SAP2000, DRAIN-TABS, DRAIN-2DX, DRAIN-DX and ANSYS software.
Friction dampers possess large rectangular hysteresis loops, similar to an ideal elasto-
plastic behaviour, with negligible fade over several cycles of reversals (Filiatrault et al., 1986).
Unlike viscous or visco-elastic devices, the performance of friction dampers is independent of

8. 8
temperature and velocity. For a given force and displacement in a damping devices. Therefore,
fewer friction dampers are required to provide a given amount of supplemental damping.
2. SEISMIC RESPONSE OF BUILDING WITH FRICTION DAMPERS
A 20-Storey benchmark SMRF is taken for study for seismic response reduction by
providing friction dampers distributed at different places along the height of the structure using
Chevron bracings. In this study, Non-linear time history analysis using direct integration
Newmark method with coefficients as ß=1/4 and γ=1/2 is used. By assuming 2% structural
damping in first and fifth mode of the building frame, the Raleigh damping is calculated and used
for the analysis. Plastic Wen Link element is used for modelling of friction dampers in the SMRF.
In this study, building is subjected to three different types of earthquakes with Peak Ground
Acceleration (PGA) of 3.42, 8.18, and 8.27 m/s2
, i.e., El Centro, Kobe and Northridge
respectively with different scale factors for time histories representing DBE and MCE. The PGA
of the time histories used for Design Based Earthquake (DBE) and Maximum Credible
Earthquake (MCE) are given in Table 1.
Table 1. Time Histories (PGA)(m/s2
)
DBE MCE
Time history El KO NR El KO NR
Scale factor 0.5 1 0.5 0.5 1.5 1 1
PGA(m/s2
) 1.71 3.42 4.09 4.135 5.13 8.18 8.27
PGA/g 0.174 0.349 0.417 0.422 .0523 0.834 0.843
Note: El Centro (El), Kobe(KO), Northridge(NR)
Since different earthquake records having the same intensity may give widely varying
structural responses, results obtained using only one record may not be conclusive. Hence, at
least three-time history records should be used and maximum among them used for design. (Pall
et al [2004]). Hence three different earthquake time histories are taken in this study.

9. 9
2.1 Description of Model
The 20-Storey benchmark control problem is considered for present study of seismically
excited nonlinear building. It is 80.77m. (265ft.) tall and is rectangular in plan with bay spacing
of 6.10 m. (20ft.) on center in both the NS (5 bays) and EW (6 bays) directions. Frames used in
the buildings are moment-resisting frames (MRF’s) made up of steel.
The floor system is comprised of 248MPa (36 ksi) steel wide flange beams acting compositely
with floor slab which is made up of steel and concrete. Diaphragm action of floors is assumed to
be rigid in horizontal plane.
Each perimeter MRF frame will be carry equal inertial effects, and hence, half of the seismic
mass is provided to each frame. Total seismic mass in 1st
floor is 5.63x1005
kg, 2nd
to 19th
floor is
5.52x1005
kg, and 20th
floor is 5.84x1005
kg. Seismic mass above ground floor is found to be
1.11x107
kg.
20-Storey benchmark problem has two basements below ground level, both having height of
3.65m. (12 ft.) and are named as B1 and B2. Ground floor elevation is 5.49m. (18 ft.), while rest
of the floors have height of 3.96m. (13 ft.). Columns of the structures which are in outer frame
are box columns made up of ASTM A500 having area 15X15 in2.
(0.38X0.38 m2
) with varying
thickness as shown in Fig. 1. Interior Columns are wide flange sections as shown in elevation
view (Fig. 2) of benchmark problem. Building plan view is also given in Fig. 2. Other building
requirements and data is mentioned in Table 2, Table 3, Table 4 and Table 5.

10. 10

11. 11
Table 5 Restraints
Restraints Columns are pinned at base. The structure is laterally restrained at the ground level
Splices Column splices are provided at 1.83 m from beam-column joint
2.2 Evaluation of Model
In this study, a 20-Storey benchmark control problem for seismically excited nonlinear
building is modelled using ETABS 2015. The first ten natural frequencies of the buildings are
0.261, 0.754, 1.312, 1.846, 2.398, 2.977, 3.553, 4.148, 4.755, and 5.354 Hz, respectively.
Frequencies for first five modes are almost equal to frequencies given in benchmark problem.
Fundamental period of the building, T1 is 3.838 s. Deformed shaped of first three modes of model
are shown in Fig. 3.
Mode 1 (0.26 Hz) Mode 2 (0.75 Hz) Mode 3 (1.31 Hz)
Fig. 3 Mode Shapes for 20-Storey Building Model

12. 12
2.3 Methods for nonlinear time-history analysis
There are many ways in which nonlinear time history analysis of structure can be
carried out soft wares like ETABS. Nonlinear Modal Analysis is one on analysis method which
also known as Fast Nonlinear Analysis (FNA). FNA as name suggests, took less time as
compared to other methods. In this method, material nonlinearity is considered for link
elements and not for frames, p-δ effects are not considered as well as effects due to large
deformations are neglected. Another more accurate method of time history analysis is
nonlinear time history analysis using Direct Integration. In this method, different Integration
methods like Newmark Integration, Wilson Integration, Collocation Integration, Hilber-
Hughes-Taylor Integration, Chung and Hulburt Integration can be used. This method takes
care of material nonlinearity for frame members as well as for link elements. p-δ or large
deformation effects can also be considered using this method. Here, 20-Storey benchmark
moment resisting frame is analysed with nonlinear time history analysis using Newmark
Integration method including p-δ effects.
2.4 Constant Damping and Rayleigh Damping
Damping is another parameter for carrying time history analysis. FNA allows constant
damping for all natural modes of structure as well as Rayleigh damping while nonlinear time
history analysis using direct integration only considers Rayleigh damping. In Rayleigh Damping,
frequency of first mode and frequency of natural mode which has maximum participation factor
is used to determine damping ratios of other natural modes. Rayleigh damping equation is given
in equation (1)

13. 13
𝐶 = 𝛼𝑀 + 𝛽𝐾 (1)
Where, α is Mass coefficient,
β is stiffness coefficient
M is mass matrix of building
K is stiffness matrix of building
The reduced damping matrix, C, can now be determined using an assumption of
Rayleigh Damping as mentioned in Equation (2)
𝐶̂𝑖 = ɸ 𝑅
𝑇
Cɸ 𝑅 = αɸ 𝑅
𝑇
Mɸ 𝑅 + βɸ 𝑅
𝑇
K𝜙 𝑅 = 𝛼 𝑚̂ 𝑖 + ß𝑘̂ 𝑖 (2)
Where, ɸR
T
is Modal matrix used as transformation matrix
Dividing equation (2) by 𝑚̂ 𝑖 ,
𝐶̂𝑖 𝑚̂ 𝑖⁄ = 2𝜁𝑖 𝜔𝑖 = ( 𝛼 𝑚̂ 𝑖 + ß𝑘̂ 𝑖) 𝑚̂ 𝑖⁄ = ( 𝛼 + ß𝜔𝑖
2
) (3)
Assuming first and fifth modes
2𝜁1 𝜔1 = ( 𝛼 + ß𝜔1
2
) (4)
2𝜁5 𝜔5 = ( 𝛼 + ß𝜔5
2
) (5)
Converting equations (4) and (5) to matrix form,
[
𝛼
𝛽] = 2
𝜔1 𝜔5
𝜔1
2−𝜔5
2
[
𝜔1 −𝜔5
−1 𝜔1⁄ 1 𝜔5⁄ ] [
𝜁1
𝜁5
] (6)
Mass coefficient and stiffness coefficient can be calculated using equation (6), the
damping in first and fifth mode are assumed in benchmark problems as 0.02, i.e., 1 = = 0.02.
Values of α and β for bare frame are found out to be 5.91 x10-2
(s-1
) and 2.4 x10-3
(s) respectively.
For all other modes, damping is calculated, according to Rayleigh damping, is given by Equation
(7).

14. 14
𝜁𝑖 = 𝜁1(𝜔1 𝜔5 + 𝜔𝑖
2
)/𝜔𝑖(𝜔1 + 𝜔5) (7)
Where, i is the natural frequency of the i-th mode.
Variation of Damping ratio and circular frequencies by assuming constant damping of 2%
for first and fifth modes, the damping ratio using Rayleigh method up to 10 modes, found to be
as shown in Fig. 4. Mass Coefficient (α) and Stiffness Coefficient (ß) are calculated using modal
time periods to give inputs for Rayleigh damping in ETABS 2015.
2.5 Friction Dampers
Of all the methods so far available to extract kinetic energy from a moving body, the most
widely adopted is undoubtedly the friction brake. Mechanical engineers have successfully used
this concept for centuries to stop the motion of equipment, automobiles, railway trains, airplanes
etc. It is the most effective, reliable and economical mean to dissipate kinetic energy. Similar to
automobiles, the motion of vibrating building can be slowed down by dissipating seismic energy
in friction. Friction dampers consists of sliding steel plates and work on the principle that when
two metal surfaces slide, friction heat is produced and energy gets dissipated. These type of
Fig. 4 Damping Coefficients for the first 10 Modes of the
20-Story Building.

15. 15
dampers may likely susceptible to corrosion and cold welding which has direct effect on the
yielding threshold. There may be also associated maintenance problems need to take care.
Otherwise, Friction Dampers are fool proof in construction. Basically, these consist of series of
steel plates, which are specially treated to develop very reliable friction. These plates are clamped
together and allowed to slip at a predetermined load. Decades of research and testing have led to
perfecting the art of friction. Their performance is reliable, repeatable and they possess large
rectangular hysteresis loops with negligible fade. Their performance is independent of velocity
and hence exerts constant force for all future earthquakes, design-based earthquake (DBE) or
maximum credible earthquake (MCE). A much greater quantity of energy can be dissipated in
friction than any other method involving the yielding of steel plates, viscous or viscoelastic
dampers. Therefore, fewer Friction Dampers are required to provide the required amount of
energy dissipation. Friction Dampers are passive energy dissipation devices and, therefore, need
no energy source other than earthquake to operate it. They do not require any repair or
replacement after the earthquake and are always ready to do their job (Pall et al., 2004). Friction
Dampers are customized to suit site conditions and allow greater adaptability than is possible
with other systems. These dampers can be bolted or welded into place. Friction Dampers are
available for long slender tension-only cross bracing, single diagonal tension-compression
bracing and chevron bracing (Fig. 5). The damper for cross bracing is a unique mechanism. When
one of the brace in tension forces the damper to slip, the damper mechanism forces the other
brace to shorten and thus avoid buckling. In this manner, the other brace is immediately ready to
slip the damper on reversal of cycle. These dampers have been used in 65 feet (22 m) long slender
bracing. To avoid pounding at the expansion joints, Friction Connectors can be custom made to
accommodate bi-directional movements.

16. 16
In a typical undamped structure, the inherent damping is merely 1-5% of critical. With
the introduction of Friction Dampers, structural damping of 20-50% of critical can be easily
achieved. As the dampers dissipate a major portion of the seismic energy, forces and
deformations on the structure are significantly reduced. Friction Dampers significantly reduce
the initial cost of construction while dramatically increasing the earthquake resistance against
damage
Friction Damper for
Tension-
Compression Brace
Hysteresis Loop Friction Damper in Tension-only
Cross Brace
Fig. 5 Pall Friction Dampers (Pall et al., 2004)
2.6 Slip Load of Friction Dampers (Pall et al, 2014)
The friction dampers are designed not to slip during wind. During a major earthquake,
they slip prior to yielding of structural members. In general, the lower bound is about 130% of
wind shear and the upper bound is 75% of the shear at which the members will yield. As seen in
Figure 15, if the slip load is very low or very high, the response is very high. Several parametric
studies have shown that the slip load of the friction damper is the principal variable with the
appropriate selection of which it is possible to tune the response of structure to an optimum value.

17. 17
Optimum slip load gives minimum response. Selection of slip load should also ensure that after
an earthquake, the building returns to its near original alignment under the spring action of an
elastic structure. Studies have also shown that variations up to ±20% of the optimum slip load do
not affect the response significantly. Therefore, small variations in slip load (8-10%) over life of
the building do not warrant any adjustments or replacement of friction damper.
Fig. 6 Response versus Slip Load (Pall et al, 2014)
For modelling friction dampers, Plastic wen link element in ETABS 2015 is used. The
inputs for modelling damper in ETABS 2015 are Ke, yield strength (slip load), Post yield stiffness
ratio, yield exponent. The bare frame model, chevron brace configurations modelled in ETABS
2015 as shown in Fig. 7.
Stiffness and Slip load are two important factors that affects behaviour of friction
dampers. Stiffness is considered as 1000 times the damper slop load in case of Chevron Brace
Configuration (Pall et al).

18. 18
2.7 Types of Configurations
Dynamic loads on building due to earthquake cause excessive vibrations leading to
severe damage to the building. Vibration can be reduced using passive, semi-active or active
control devices. Various applications of these energy dissipation devices are used in many
countries. In all these applications, damper configurations have been used to deliver the forces
from energy dissipation devices to the structural frame. Generally the damper configurations are
classified based on the orientation of dampers and the way of damper attached to the structural
element such as chevron bracing configuration, scissor-jack bracing configuration, diagonal
bracing and cross bracing configurations. In this study Chevron bracing Configuration is used.
2.7.1 Chevron Brace Configuration
In Chevron configuration the energy dissipation devices are fixed parallel to beam
element in structure. The magnification factor for chevron braced configuration is equal to one.
The magnification factor depends on angle of inclination and placement of dampers. The
magnification factor is defined as ratio of damper displacement to inter-storey drift. It is denoted
as f. Chevron Brace details are shown in Fig. 7.
Fig. 7 Chevron Brace

19. 19
2.8 Methodology for Design and Distribution of friction Dampers
The methodology used for design of 20-Storey Building using Friction Dampers is
mentioned in Table 6.
Table 6 Methodology used for design of building with Friction Damper
Step 1: Define the structural properties and geometry of the building
Step 2: Define material and section properties of all components.
Step 3: Assign the proper restraints.
Step 4: Draw the damper as link element having plastic wen properties.
Step 5: Choose the bracing configuration.as chevron and model it.
Step 6: Choose the no. of dampers and there slip loads for distribution in different floors
of the building. All cases considered are mentioned in Table 7.
Step 7: Choose time histories with appropriate load pattern.
Step 8: Define acceleration time history files of EL Centro, Kobe and Northridge
earthquake records
Step 9: Define modal case, restrict analysis to planar analysis and run the analysis
Step 10: Check time period and frequencies for first few modes.
Step 11: Define all DBE and MCE cases using appropriate scale factors.
Step 12: Define nonlinear analysis case with all Newmark coefficients as 0.5 and 0.25 and
Rayleigh damping of 2 percent for first and fifth mode.
Step 13: Run nonlinear analysis and find responses for DBE and MCE to check if responses
to be in limits as per UBC.
2.9 Distribution of dampers for 20-Storey buildings
The nonlinear time history analyses carried out with Newmark direct integration Method
by considering both material and geometric nonlinearities (p-δ effects) for 20-Storey benchmark
problem for bare frame, and the frame equipped with dampers in Chevron configuration (as shown
in Fig. 8) are subjected to DBE and MCE (as given in Table 1) are carried out using ETABS 2015.
The dampers are provided in the middle bay along height of building to minimize seismic
responses of building. Distribution of slip loads on different floors is mentioned in Table 7.

20. 20
Fig. 8 Chevron Bracing Model
Table 7. Slip Load Distribution for 20-Storey Building
Storey
Chevron Cases
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21
1 2J 2L 2L 2J 2J 2J 2H 2H 2H 2H 2G 2H 2E 2E 2B 2B 1G 1G 2C 1F 2B
2 2J 2J 2J 2J 2J 2J - - - - - 2H 2E - - - - - - - -
3 2J 2J 2J 2J 2J 2J - - - - - 2E 2E - - - - - - - -
4 2J 2J 2J 2J 2J 2J - - - - - 2E 2E - - - - - - - -
5 2H 2H 2H 2E 2H 2E - - - - - 2E 2E - - - - - - - -
6 2H 2H 2H 2E 2H 2E - - - - - 2E 2E - - - - - - - -
7 2H 2H 2H 2E 2H 2E - - - - - 2E 2E - - - - - - - -
8 2H 2H 2H 2E 2H 2E - - - - - 2E 2E - - - - - - - -
9 2H 2H 2H 2H 2H 2E - - - - - 2E 2E - - - - - - - -
10 2H 2H 2H 2H 2E 2E - - - - - 2E 2E - - - - - - - -
11 2H 2H 2H 2H 2E 2E - - - - - 2E 2E - - - - - - - -
12 2H 2H 2H 2H 2E 2E - - - - - 2E 2E - - - - - - - -
13 2J 2J 2J 2H 2E 2E - - - - - 2E 2E - - - - - - - -
14 2J 2J 2J 2H 2E 2E 2G 2H 2I 2I 2E 2E 2E 2E 2E 2E 1G 1F 2D 1G 2D
15 2J 2L 2J 2H 2E 2E 2I 2J 2K 2K 2H 2E 2E 2G 2E 2E 1G 1F 2D 1G 2D
16 2H 2J 2H 2H 2E 2E 2I 2J 2K 2K 2H 2E 2E 2G 2E 2E 1G 1G 2D 1G 2D
17 2H 2J 2H 2H 2E 2E 2H 2I 2J 2J 2G 2E 2E 2E 2B 2B 1E 1E 2B 1E 2B
18 2H 2H 2H 2H 2E 2E 2G 2H 2I 2I 2G 2E 2E 2E 2B 2B 1E 1E 2B 1E 2B
19 2H 2H 2H 2H 2E 2E 2B 2B 2A 2B 2B 2E 2E 2B 2B 2B - - - - -
20 - - - - - - - - - - - - 2E - - - - - - - -
Characteristics of Dampers A, B, C, D, E, F, G, H, I, J, K, and L are given in Table 8.

21. 21
Table 8. Slip Loads of Friction Dampers (kN)
DD A B C D E F G H I J K L
SL 50 100 125 150 200 250 300 400 500 600 700 800
DD, Damper Designation; SL, Slip Load.
3. RESULTS AND DISCUSSIONS
To form common basis for evaluating the effectiveness of different control strategies,
common performance indices should be evaluated for common building structure [7].
Dimensionless performance indices used for this study are peak drift ratio (J1) and peak base
shear (J3).A detailed description of evaluation criteria and performance indices was provide by
Ohtori et al. [7]. This performance indices are defined in equation (8) and (9).
The Peak Responses to be used for performance evaluation are base shears and story
drifts are found using Equation (1).Peak Responses,
𝑃𝑒𝑎𝑘 𝐷𝑟𝑖𝑓𝑡 𝑅𝑎𝑡𝑖𝑜, 𝐽1 = 𝐸𝑙 𝐶𝑒𝑛𝑡𝑟𝑜
𝐾𝑜𝑏𝑒
𝑁𝑜𝑟𝑡ℎ𝑟𝑖𝑑𝑔𝑒
𝑀𝑎𝑥
{
|
𝑑 𝑖(𝑡)
ℎ 𝑖
|
𝑡,𝑖
𝑚𝑎𝑥
𝛿 𝑚𝑎𝑥
} (8)
𝑃𝑒𝑎𝑘 𝐵𝑎𝑠𝑒 𝑆ℎ𝑒𝑎𝑟, 𝐽3 = 𝐸𝑙 𝐶𝑒𝑛𝑡𝑟𝑜
𝐾𝑜𝑏𝑒
𝑁𝑜𝑟𝑡ℎ𝑟𝑖𝑑𝑔𝑒
𝑀𝑎𝑥
{
|𝑉(𝑡)|𝑡
𝑚𝑎𝑥
𝐹𝑏
𝑚𝑎𝑥 } (9)
Where, ‘i’ is no of storey (varies from 1 to 20), |di (t)| is the inter-story drift of the above
ground level over the time history of each earthquake, hi is the height of each of the associated
stories, δmax
is the maximum inter-story drift ratio of the uncontrolled structure, Vi(t) and Fb
max
are the maximum base shear with and without control devices respectively.
The responses of the 20-Storey building distributed with friction dampers having
different slip loads with Chevron configuration (as shown in Fig.8 and given in Table 7) are

22. 22
evaluated. Percent Peak drift ratios and Peak Base Shears are for DBE and MCE ground
excitations are listed in Table 9. These responses are compared with peak response limits
prescribed as per Uniform Building Code 1997 (Tables 10-11)
Table 9. Peak Responses in 20-storey building.
Cases Total Slip Load (kN)
Inter-story Drift Ratio (%) Base shear (kN)
DBE MCE DBE MCE
BF - 1.203 2.405 8185 16370
1 18000 0.658 2.297 6478 12438
2 19600 0.660 2.213 6469 12446
3 18400 0.672 2.360 6464 12444
4 15200 0.720 2.219 6306 12172
5 12800 0.808 2.378 6425 12344
6 10800 0.823 2.366 6290 12220
7 5000 0.833 2.331 6105 13038
8 6000 0.838 2.352 5961 12802
9 6900 0.840 2.403 5943 12632
10 7000 0.841 2.354 5907 12605
11 4000 0.850 2.334 6441 13477
12 8400 0.865 2.350 6088 12743
13 8000 0.877 1.892 6028 13248
14 3000 0.886 2.291 6636 13790
15 2000 0.935 1.962 6893 14280
16 2000 0.935 2.258 6893 14280
17 1600 0.944 1.974 6985 14538
18 1500 0.946 1.990 7041 14695
19 1550 0.947 1.991 6985 14620
20 1550 0.948 1.993 6996 14628
21 1500 0.952 2.010 6996 14710
The values exceeding the limits prescribed by the Uniform Building Code 1997 are underlined
Table 10. Allowable limits of inter-story drifts and base shear
Inter-story drift ratio
(UBC 97 Section 1630.2.2)
Maximum Base Shear
(UBC 97 Section 1630.2.1)
0.025 for T<0.7 s, 0.02 for T>0.7 s, and the
building period 𝑇 = 𝐶𝑡(ℎ)3/4
, where
coefficient Ct is 0.085 and h is total height of
building.
Maximum allowable base shear 𝑉𝑚 𝑎𝑥 is given
by 𝑉𝑚 𝑎𝑥 =
2.5𝐶 𝑎 𝐼
𝑅
× 𝑊, where coefficient Ca
=0.44, importance factor I=1, ductility factor
R=8.5, and W is total weight of building.

23. 23
Table 11. Allowable Maximum limits for 20-storey building as per UBC 97
S. No. Parameters Limits
1 Allowable Drift Ratio (%) 2 %
2 Allowable Base Shear (kN) 7043.482 kN
UBC, Uniform Building Code, T=2.290111 s
From the 21 cases of slip load distributions considered (are given in Table 7 and shown
in Fig.8), only six cases (Cases 13, 15, 17, 18, 19 and 20) are found to be satisfying the drift limits
prescribed (Table 11) for both DBE and MCE. The base shear limit given in Table 11 is satisfied
for all cases of DBE, but not for MCE except for 1.5 EL case. Slip load distribution for six cases
which are considered for optimization criteria are shown in Fig. 9
Fig. 9 Slip Load Distribution
Observed peak story shear distribution and peak inter-storey drift ratio for this six cases
for DBE and MCE are shown in Fig.10 and Fig.11 respectively. The peak base shears for both
DBE and MCE are shown in Fig. 12
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
0
50
100
150
200
250
300
350
400
Storey
Slip Load (kN)
Slip Load Distribution
Case 13
Case 15
Case 17
Case 18
Case 19
Case 20

24. 24
Fig 10 Peak responses of frame subjected to El Centro, Kobe and Northridge (DBE)
Fig 11 Peak responses of frame subjected to El Centro, Kobe and Northridge (MCE)
0
2
4
6
8
10
12
14
16
18
20
2000
3000
4000
5000
6000
7000
8000
9000
Storey
Peak Story Shear (kN)
DBE Storey Shears
BF
Case 13
Case 15
Case 17
Case 18
Case 19
Case 20
0
2
4
6
8
10
12
14
16
18
20
.0060
.0065
.0070
.0075
.0080
.0085
.0090
.0095
Storey
Drift Ratio
DBE Drift Ratio
Case 13
Case 15
Case 17
Case 18
Case 19
Case 20
0
2
4
6
8
10
12
14
16
18
20
4500
6500
8500
10500
12500
14500
16500
Storey
Peak Story Shear (kN)
MCE Storey Shears
BF
Case 13
Case 15
Case 17
Case 18
Case 19
Case 20
0
2
4
6
8
10
12
14
16
18
20
.0120
.0130
.0140
.0150
.0160
.0170
.0180
.0190
.0200
Storey
Drift Ratio
MCE Drift Ratio
Case 13
Case 15
Case 17
Case 18
Case 19
Case 20
Limit

25. 25
Even though all six cases satisfy the drift limit prescribed in Table 11, it is observed from
Fig. 10 and Fig. 11 that, Case 13 has much less drift ratio as compared to other cases. Story shear
distribution for DBE found to be uniformly distributed from ground floor till sixth Floor and from
ninth Floor till 16th
Floor as shown in Fig. 10. For all other cases storey shears are found to be
non-uniform and it is higher at ground floor. For MCE similar pattern of story shear distribution
is observed. This indicates that the Case 13 is much better than all other five cases.
Fig 12 Peak Base Shears
It can be observed that even though the amount of slip load used is almost 20% of Case 13
for Cases 17-20, they are satisfying the prescribed limits given in Table 11. Since the cost of
friction dampers are inexpensive, it is desirable to preferred to have distribution in Case 13,
because in this case more dampers provided along the height of the building and it decreasing the
responses of the building to minimum possible.
Calculated performance indices J1 and J3, percentage reduction in peak base shear, peak
inter-storey drift ratio and peak story shears are evaluated for this six cases as given in Table 12.

26. 26
Table 12. Reduction in peak responses as % and Performance indices.
Cases
Total
Slip
Load
(kN)
% Reduction Performance Indices
Inter-story
Drift Ratio
Base shear Story Shear J1 J3
DBE MCE DBE MCE DBE MCE DBE MCE DBE MCE
13 8000 27.08 21.35 26.36 19.07 31.25 22.91 0.73 0.79 0.74 0.81
15 2000 22.21 18.43 15.79 12.77 12.13 6.87 0.78 0.82 0.84 0.87
17 1600 21.51 17.92 14.66 11.19 15.88 10.87 0.78 0.82 0.85 0.89
18 1500 21.33 17.27 13.98 10.23 14.74 10.14 0.79 0.83 0.86 0.90
19 1550 21.23 17.20 14.66 10.69 15.49 10.30 0.79 0.83 0.85 0.89
20 1550 21.16 17.15 14.52 10.64 15.35 10.24 0.79 0.83 0.85 0.89
Note: Most efficient values are underlined.
Best performance is found for Case 13, for which two friction dampers with slip load of
200kN are provided at each floor in middle bay with Chevron Bracings.
4. SUMMERY AND CONCLUSION
In the present study, nonlinear time history analysis of 20-Storey bare frame equipped
with friction dampers in Chevron configuration is carried out using direct integration by
Newmark method of in ETABS 2015. In SMRF, damping of 2% is assumed for first and fifth
mode and the damping ratio for all other modes are calculated using Rayleigh method. Both
material and geometric nonlinearities (P-δ effects) are considered for analysis of frame subjected
to three different time histories, i.e., N-S component of El Centro, Kobe and Northridge with
different scale factors representing DBE and MCE.
Story drift ratio should be less than 0.02 for building having fundamental time period
greater than 0.7 s (UBC 97 Section1630.2.2). Fundamental time period calculated as per UBC is
found out to be 2.29s. Maximum Base shear should be less than 7043.482 kN which was
calculated as per formula given in UBC 97 Section 16.2.1. From the of 21 different cases of slip

27. 27
load distribution along the height of building provided in middle bay with chevron bracings, only
six cases were found to be satisfy the limits prescribed as per UBC 1997 .
Each floor provided with two friction dampers having slip load of 200kN with Chevron
bracing in middle bay of structure along the height of the building is found to be optimum
distribution of slip load for maximum seismic performance enhancement. Even though six cases
satisfy the drift limit prescribed in UBC, it is observed that, this case has much less drift ratio as
compared to other cases. Story shear distribution for DBE and MCE are found to be uniformly
distributed for this case along the height. For all other cases, storey shears are found to be non-
uniform and it is found to be higher at ground floor. It is further observed that total slip load of
optimum case is almost equal to maximum base shear observed in 20-Storey Bare frame for DBE.
Base shear limit as prescribed in UBC is satisfied for DBE by optimum case as well as
for 1.5 El earthquake which is considered as MCE, but for all other earthquakes (1Ko and 1 NR)
which are considered as MCE, base shear limit is exceeding for this case. This shows MCE base
shears cannot be controlled using friction dampers attached with Chevron bracings.
Future technology is for maximizing seismic performance in the friction dampers, by
inducing variable friction (based on measurement of stress and deformation levels by sensors)
introducing fuzzy or neuro control mechanisms.

28. 28
5. APPENDICES
Appendix A: Building Responses
In this appendix, variation of seismic response of 20-Story benchmark problem
moment resisting bare frame and building with chevron bracing having friction dampers with
it, along with different floors for DBE and MCE are given. Peak story drift ratio variation
along floors of all 21 cases considered in this study for DBE and MCE are given in Table 13,
while peak story shears variation of all cases for DBE and MCE are given in Table 14.
.
Table 13 Peak story shear vs Floors (kN)
BF Case 13 Case 15 Case 17 Case 18 Case 19 Case 20
F DBE MCE DBE MCE DBE MCE DBE MCE DBE MCE DBE MCE DBE MCE
20 2413 4825 2781 5895 2427 4943 2365 4754 2390 4785 2368 4774 2370 4777
19 4021 8043 3357 7001 3698 7730 3555 7414 3612 7478 3578 7453 3583 7461
18 4803 9605 3814 7894 4232 8936 4014 8377 3994 8447 4026 8426 4028 8437
17 5008 10016 4072 8390 4486 9108 4344 8829 4350 8850 4368 8867 4375 8876
16 5254 10509 4198 8718 4812 9611 4674 9367 4680 9373 4686 9404 4689 9410
15 5065 10130 4368 9011 4792 9542 4683 9365 4687 9368 4696 9399 4696 9401
14 5554 11109 4501 9129 4771 10315 4636 10004 4685 10075 4648 10056 4649 10060
13 5624 11248 4549 9275 5057 10789 4922 10339 4949 10381 4937 10414 4943 10417
12 5583 11165 4549 9275 5036 10712 4870 10324 4887 10383 4885 10393 4895 10392
11 5596 11193 4525 9269 5104 10862 4793 10436 4820 10486 4845 10513 4855 10516
10 5694 11387 4719 9344 4845 10125 4831 10098 4847 10128 4849 10123 4852 10127
9 5485 10969 4893 9687 4887 10062 4856 10005 4851 10025 4861 10030 4861 10034
8 4883 9766 5083 10036 4926 9868 4880 9753 4879 9759 4886 9771 4888 9775
7 5071 10141 5311 10425 5085 10251 4996 9983 5017 10025 4996 9991 5001 9999
6 6294 12588 5527 10828 5395 11541 5324 11349 5383 11423 5346 11395 5346 11392
5 6981 13963 5653 11228 6027 12388 6000 12220 6026 12288 6009 12253 6026 12269
4 7008 14015 5770 11744 6338 13179 6241 12803 6265 12912 6260 12875 6266 12873
3 7599 15198 5905 12720 6944 14625 6726 14186 6801 14318 6777 14256 6785 14263
2 8348 16696 5983 13416 7505 15736 7186 15264 7267 15379 7245 15338 7254 15352
1 8702 17404 5983 13416 7647 16209 7320 15513 7420 15640 7354 15611 7367 15622
0 1078 2157 751 1623 880 1876 817 1788 826 1803 828 1804 830 1805
Note: BF: Bare Frame; F: Floor no

29. 29
Peak Base shears observed in six cases which satisfies Drift ratio and base shear
limits for El-Cento, Kobe and Northridge earthquakes having different PGA considered for
DBE and MCE are given in Table 15.
Table 15 Peak Base Shears (kN)
DBE MCE
Time history El KO NR El KO NR
Scale Factors 0.5 1 0.5 0.5 1.5 1 1
Bare Frame 2229 7570 4458 8185 6687 16370 15140
Case 13 2229 7570 4458 8185 6687 16370 15140
Case 15 2065 6070 3931 6893 5645 14280 12919
Case 17 2049 6360 3887 6985 5582 14538 13325
Case 18 2047 6411 3863 7041 5560 14695 13405
Case 19 2034 6405 3862 6985 5525 14620 13386
Case 20 2042 6411 3858 6996 5536 14628 13397
Note: El Centro (El), Kobe(KO), Northridge(NR)
Table 14 Peak inter-story drift ratiovs Floors (%)
BF Case 13 Case 15 Case 17 Case 18 Case 19 Case 20
F DBE MCE DBE MCE DBE MCE DBE MCE DBE MCE DBE MCE DBE MCE
20 0.841
4
1.682
7
0.603
2
1.354
5
0.755
0
1.581
5
0.788
1
1.605
4
0.791
4
1.616
9
0.791
4
1.611
9
0.791
3
1.612
819 1.110
0
2.219
9
0.766
4
1.677
5
0.804
2
1.743
2
0.876
0
1.847
5
0.890
5
1.863
6
0.881
7
1.855
3
0.882
9
1.857
218 1.137
0
2.274
0
0.810
8
1.766
3
0.879
4
1.926
2
0.904
4
1.955
2
0.908
2
1.974
0
0.905
7
1.967
2
0.905
6
1.969
417 1.138
2
2.276
4
0.860
0
1.857
3
0.933
5
1.942
6
0.934
6
1.942
4
0.936
7
1.947
7
0.939
4
1.950
1
0.940
9
1.951
716 1.126
8
2.253
7
0.872
1
1.873
6
0.935
4
1.945
1
0.943
9
1.947
5
0.946
0
1.950
0
0.947
2
1.954
2
0.948
0
1.955
215 1.202
5
2.405
0
0.876
9
1.891
6
0.932
6
1.924
8
0.935
2
1.922
1
0.943
5
1.930
9
0.938
7
1.928
2
0.938
7
1.928
514 1.187
8
2.375
6
0.802
7
1.745
8
0.845
8
1.862
0
0.867
1
1.913
6
0.884
6
1.932
5
0.872
1
1.923
1
0.872
3
1.923
613 1.084
9
2.169
9
0.759
8
1.619
7
0.849
5
1.852
2
0.871
8
1.867
8
0.878
9
1.875
8
0.877
3
1.878
2
0.877
9
1.878
712 1.002
4
2.004
8
0.756
1
1.604
8
0.867
7
1.854
4
0.870
0
1.849
4
0.873
6
1.852
4
0.876
0
1.858
6
0.876
5
1.858
811 0.963
0
1.925
9
0.714
8
1.534
9
0.808
5
1.716
0
0.812
4
1.709
1
0.816
6
1.713
2
0.816
5
1.718
6
0.816
7
1.718
210 0.950
1
1.900
1
0.664
2
1.449
4
0.768
2
1.618
5
0.799
9
1.663
0
0.802
5
1.667
7
0.802
9
1.666
6
0.803
3
1.667
29 0.920
7
1.841
3
0.624
8
1.379
9
0.750
3
1.568
5
0.780
2
1.613
2
0.782
3
1.616
4
0.783
5
1.616
7
0.784
3
1.617
48 0.831
7
1.663
3
0.635
9
1.309
1
0.721
6
1.462
4
0.724
0
1.488
0
0.723
9
1.492
0
0.725
9
1.498
3
0.726
8
1.499
27 0.747
1
1.494
2
0.647
1
1.327
3
0.717
6
1.438
0
0.716
7
1.435
6
0.717
1
1.436
7
0.717
7
1.438
7
0.718
3
1.439
66 0.858
2
1.716
4
0.659
9
1.344
5
0.716
0
1.527
7
0.743
7
1.565
0
0.750
3
1.574
3
0.745
8
1.570
1
0.746
3
1.570
25 0.897
7
1.795
4
0.637
7
1.294
0
0.761
4
1.568
6
0.788
0
1.605
1
0.791
4
1.612
8
0.789
3
1.609
8
0.791
0
1.611
54 0.859
7
1.719
3
0.612
4
1.290
1
0.762
5
1.557
0
0.774
7
1.572
4
0.777
5
1.574
6
0.777
1
1.577
0
0.777
8
1.578
53 0.927
4
1.854
7
0.615
3
1.314
8
0.777
6
1.668
8
0.803
0
1.701
7
0.811
8
1.716
5
0.808
9
1.710
1
0.809
8
1.710
82 1.004
8
2.009
7
0.635
8
1.388
4
0.842
1
1.817
0
0.862
7
1.842
4
0.872
9
1.856
3
0.871
2
1.852
5
0.872
2
1.854
01 1.126
4
2.252
7
0.702
3
1.609
8
0.905
9
1.961
8
0.908
0
1.974
0
0.919
0
1.989
7
0.920
3
1.991
3
0.921
8
1.992
60 0.153
5
0.306
9
0.096
5
0.215
4
0.118
6
0.256
5
0.118
7
0.257
9
0.120
1
0.259
9
0.120
3
0.260
1
0.120
5
0.260
3Note: BF: Bare Frame; F: Floor no

30. 30
6. REFERENCE
1. Filiatrault, A., Cherry, S. (1986) Seismic Tests of Friction-Damped Steel Frames, Third
Conference on Dynamic Response of Structures, ASCE, Los Angeles, USA.
2. Pall, A.S., Pall, T. (2004) Performance-based design using Pall friction dampers – an
economical design solution, 13th
World Conference on Earthquake Engineering,
Vancouver, Canada.
3. Hart, Gary C., Wong, Kevin, Structural Dynamics for Structural Engineers, United States
of America: 1999.
4. Paz, Mario, Structural Dynamics theory and computation, 2nd
-ed. New Delhi, India: 1999.
5. Clough, Ray W., Penzien, Joseph, Clark, B.J. (eds.) Dynamics of Structures, 2nd
-ed.
Singapore: 1993.
6. Uniform Building Code, Volume 2, 1997 edition, published by International Conference
of Building Officials.
7. Ohtori Y, Christenson RE, Spancer Jr., BF. Benchmark Control Problems for Seismically
excited nonlinear buildings. Journal of Engineering Mechanics ASCE 2004; 130:N0.
4,366-385.
8. Federal Emergency Management Agency (FEMA). NEHRP guidelines for seismic reh
tion of buildings 199; Rep. No. 273/274, Building Seismic Safety Council, Washington,
D.C.
9. Rama Raju K, Ansu M., Iyer N. R., A Methodology of design for seismic performance
enhancement of buildings using viscous fluid dampers, Chennai ,India.

31. 31
10. Pall A., Pall R. T., (2004) ,Performance-Based design using Pall Friction Dampers-An
Economical design Solution, 13th
World Conference on Earthquake Engineering,
Vancouver, Canada.
11. Chandra R. ,Masand M. ,Nandi S. K., Tripathi C. P., Pall R., Pall A.(2000), Friction-
Dampers for seismic control of La Gardenia Towers South city, Gurgaon, India.,12th
World Conference on Earthquake Engineering, Auckland, New-Zeland.
12. Sang-Hyun Lee, Ji-Hun Park, Sang-Kyung Lee, Kyung-Won Min, Allocation and slip
load of friction dampers for a seismically excited building structure based on storey shear
force distribution, Engineering Structures 30 (2008) 930-940.