Seismic behaviour of twin tower structures connected at top by an isolated corridor

i
SEISMIC BEHAVIOUR OF TWIN TOWER
STRUCTURE CONNECTED AT TOP BY AN
ISOLATED CORRIDOR
By
SHAH HARSHILKUMAR JAYESHBHAI
190410720015
Under guidance of
Dr. D.P. Soni
(PhD. In Structural engineering, Professor, HOD)
A thesis submitted to
Gujarat Technological University
In Partial Fulfilment of the Requirements for the Degree of Master of Engineering in
CIVIL- STRUCTURAL ENGINEERING
May, 2021
DEPARTMENT OF CIVIL ENGINEERING
SARDAR VALLABHBHAI PATEL INSTITUTE OF TECHNOLOGY VASAD-388306

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ACKNOWLEDGEMENT
I take the opportunity to express my heartily gratitude towards my esteemed guide, Dr. D.
P. Soni, Associate Professor, Civil engineering department, SVIT, Vasad for their
comprehensive guidance, unfailing advice and experienced supervision for this work with
deep interest and patience. I acknowledge their valuable comments and constructive
suggestions during this work. His guidance has been so sublime as to render it possible for
me to bring up this work till here.
I would also like to thank my professors for their unfailing cooperation and sparing their
valuable time to assist me in my work. I have developed not only technical skills but also
learned all those qualities required to become a good professional engineer.
I am highly indebted to God and to my family members by whose blessings, I am able to
present this work.
I extend my words of thanks to friends and colleagues, who always have helped and
motivated me throughout my study.
Last but not least, I would like to mention here that I am greatly indebted to each and
everybody who has been associated with this research at any stage but whose name does not
find a place in this acknowledgement.
SHAH HARSHILKUMARJAYESHBHAI
ENROLLMENT NO: 190410720015

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TABLE OF CONTENTS
Title Page No:
TITLE PAGE i
CERTIFICATE PAGE ii
COMPLIANCE CERTIFICATE iii
THESIS APPROVAL iv
DECLARATION OF ORIGINALITY OF WORK v
ACKNOWLEDGEMENT vi
TABLE OF CONTENTS vii
LIST OF FIGURES x
LIST OF TABLES xiv
ABSTRACT xv
CHAPTER 1 INTRODUCTION 1-7
1.1 General 1
1.2 Base Isolation System 1
1.3 Types of Base Isolation System 2
1.4 High Damping Rubber Bearing 2
1.5 Friction Pendulum Bearing 4
1.6 Modern types of Base Isolation Systems 4
1.7 General Requirement of Base Isolation System 4
1.8 Suitability of Base Isolation System 4
1.9 Advantages of Base Isolation Techniques 6
1.10 Dis-advantages of Base Isolation Techniques 6

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1.11 Needs of Present Study 6
1.12 Objectives of Present Study 7
1.13 Scope of Present Study 7
CHAPTER 2 LITERATURE REVIEW 8-11
2.1 Introduction 8
2.2 Review of Literature 8
2.3 Summary 11
CHAPTER 3 SEISMIC BEHAVIOUR OF TWIN TOWER 12-18
CONNECTED BY AN ISOLATD CORRIDOR
3.1 Introduction 12
3.2 Mathematical modal of connecting building 13
3.3 Validation of Problem 15
3.4 Numerical study for validation 15
CHAPTER 4 RECORDED EARTHQUAKE GROUND 19-53
MOTION
4.1 Numerical Study 19
4.2 Two Towers with Similar Natural Frequencies 21
4.3 Two Towers with Different Natural Frequencies 38
CHAPTER 5 SEISMIC RESPONSE OF CONNECTED 54-59
BUILDING UNDER HARMONIC
LOADING (IN FREQUENCY DOMAIN)
5.1 Introduction 54
5.2 Governing Equation of Harmonic Frequency Response 54
CHAPTER 6 SEISMIC RESPONSE OF CONNECTED 60-63
BUILDING UNDER RANDOM GROUND
MOTION
6.1 Introduction 60

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6.2 Stationary Random Process 60
CHAPTER 7 SUMMARY AND CONCLUSION 64-65
7.1 Conclusion 64
7.2 Scope of Future Work 65
REFERENCES 66-67
Appendix I List of Symbols and Abbreviations 68
Appendix II Review Card Comments 70
Appendix III Plagiarism Report 74

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LIST OF FIGURES
Figure
No. Descriptions Page No
1.1 Base Isolation System 2
1.2 High Damping Rubber Bearing 3
1.3 Friction Pendulum System 3
1.4 Schematic Diagram of HDRB 4
3.1 Petronas Tower Malaysia 13
3.2 Portland Broadway Corridor 13
3.3 Idealized building corridor connected system 14
3.4 Validation of Program with paper Qing 17
Lyu, et al. (2020)
3.5 Validation of Program with paper Qing 18
Lyu, et al. (2020)
4.1 Displacement variation w.r.t. time under Imperial 22
Valley 1940 El Centro Earthquake with similar
frequencies
4.2 Base shear Variation w.r.t. time under Imperial 23
frequencies
4.3 Acceleration Variation w.r.t. time under Imperial 23
frequencies
frequencies
frequencies
frequencies

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4.7 Displacement variation w.r.t. time under Superstition 26
Hills 1987 Earthquake with similar frequencies
4.8 Base shear Variation w.r.t. time under Superstition Hill 26
1987 Earthquake with similar frequencies
4.9 Acceleration Variation w.r.t. time under Superstition 27
Hills 1987 Earthquake with similar frequencies
4.10 Displacement variation w.r.t. time under Imperial Valley 28
4.11 Base shear Variation w.r.t. time under Imperial Valley 28
4.12 Acceleration Variation w.r.t. time under Imperial Valley 29
4.13 Displacement variation w.r.t. time under Loma 30
Prieta 1989 Earthquake with similar frequencies
4.14 Base shear Variation w.r.t. time under Loma 30
4.15 Acceleration Variation w.r.t. time under Loma 31
4.16 Displacement variation w.r.t. time under Chamoli 32
4.17 Base shear Variation w.r.t. time under Chamoli 32
4.18 Acceleration Variation w.r.t. time under Chamoli 33
4.19 Displacement variation w.r.t. time under Northridge 34
4.20 Base shear Variation w.r.t. time under Northridge 34
4.21 Acceleration Variation w.r.t. time under Northridge 35
Valley 1941 Earthquake with different frequencies

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1979 El Centro Earthquake with different frequencies
4.31 Displacement variation w.r.t. time under Superstition 44
Hills 1987 Earthquake with different frequencies
4.32 Base shear Variation w.r.t. time under Superstition Hill 44
1987 Earthquake with different frequencies
4.33 Acceleration Variation w.r.t. time under Superstition 45
Hills 1987 Earthquake with different frequencies
4.34 Displacement variation w.r.t. time under Loma 46
Prieta 1989 Earthquake with different frequencies
4.35 Base shear Variation w.r.t. time under Loma 47
4.36 Acceleration Variation w.r.t. time under Loma 47
4.37 Displacement variation w.r.t. time under Chamoli 48
4.38 Base shear Variation w.r.t. time under Chamoli 49
4.39 Acceleration Variation w.r.t. time under Chamoli 49

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4.40 Displacement variation w.r.t. time under Northridge 50
4.41 Base shear Variation w.r.t. time under Northridge 51
4.42 Acceleration Variation w.r.t. time under Northridge 51
5.1 Frequency Variation of amplitude at 1st
floor 56
Under Harmonic Responses
5.2 Frequency Variation of amplitude at 5th
floor 56
floor 57
floor 57
floor 58
floor 58
6.1 An ensemble of time histories of Stochastic 62
Process 𝑥(𝑡)
6.2 Floor variation of RMS value of displacement 63
Response under random ground motion

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LIST OF TABLES
Table No. Description Page No
3.1 Building Model Parameters (Reference Qing lyu, et al) 15
3.2 Building Model Parameters 16
3.3 Properties of building (Based on MATLAB software) 16
3.4 Properties of building 16
3.5 Comparison of Top floor displacement 18
4.1 Details of ground motion considered in this study 20
4.2 Frequencies of 1st
, 2nd
& 3rd
tower based on 20
MATLAB
4.3 Seismic Response of Tower 1 (Similar frequencies) 36
4.4 Seismic Response of Tower 2 (Similar frequencies) 37
4.5 Seismic Response of Tower 3 (Different frequencies) 52
4.6 Seismic Response of Tower 2 (Different frequencies) 53
5.1 Response under harmonic ground motions 59
6.1 RMS value of displacement response under random 63
Ground motion

xvi
ABSTRACT
SEISMIC BEHAVIOUR OF TWIN TOWER STRUCTURE
CONNECTED AT TOP BY AN ISOLATED CORRIDOR
Submitted by
SHAH HARSHILKUMAR JAYESHBHAI
Supervised by
[GUIDED BY: Dr. D.P. SONI, PhD STRUCTURE, PROFESSOR]
DEPARTMENT OF CIVIL ENGINEERING
SARDAR VALLABHBHAI PATEL INSTITUTE OF TECHNOLOGY
VASAD-388306, GUJARAT (INDIA)
In this era of modern and advanced infrastructure, base isolation systems have been evolved
as a classic technology to safeguard the structure against earthquake forces by decoupling
the structure or a part there of from the remainder of the structure. As the base-isolation
system reduces significantly the transmission of most of the lateral forces, the absolute
acceleration, base shear and displacement demand also reduce to a greater extent.

xvii
The concept of connecting twin tower structures to reduce the displacement demands, using
a base-isolated corridor, is investigated. The analytical expression of connected structure
subjected to earthquake ground motions is derived and solved using step-by-step procedures.
Twin towers connected with base-isolated corridor are considered and the governing
differential equations of motions are derived. The responses of the structure under seven
recorded earthquake ground motions are obtained by solving the equation of motions. The
behavior of building with similar and different natural frequencies is studied. The seismic
responses of connected twin towers are compared with those un-connected towers.
Further, the influence of harmonic loading is also studied. The governing equation of a
connected system under harmonic loading is derived in the frequency domain. The responses
under harmonic loading in terms of frequency variation of amplitudes are plotted. The
adequacy of a twin tower connected by the base-isolated corridor has also been investigated
by considering the root mean square responses of the system with broadband stationary
stochastic processes. The study shows that the base-isolated corridor, connecting the top of
the building, is effective in reducing structural responses under the recorded earthquake
ground motions, harmonic loading of varying frequencies and stationary random processes,
as well.

Seismic Behavior of twin tower structures connected at top by an isolated corridor
1
CHAPTER 1
INTRODUCTION
1.1 General:
There are lots of. civil. Engineering structures like. bridges, nuclear. power plants, dams,
canals, high. rise towers, aqueduct, and. many mores. Earthquake ground. motions are
considered. as exacting. circumstances in. all structural. design utilization from previous few
decades. In civil engineering. the opportunity .and necessity of able, competent, and
innovative displacement discipline approach has been determined with day to day
augmentation in mechanism. The responsibility. of structure engineer as these. flexible
towers are responsibility to. the extreme. levels variation under. the activity. of severe.
earthquake or a strong wind, such structures. preservation from reasonable. exposure.
As per. seismic engineering, the vibration. or different. activity in. earth crust. decision that
create pertaining to .an earthquake waves. The type, size of. earthquake skilled. in activity.
and frequency. over a period of time an area attributes of. seismic movements. The
achievement of. flexible structures has. generally, agreed upon to .be out of. reach
explanation are attractive and. furthermore, the serious earthquakes are (Nepal, Bhuj, Japan,
etc.). The sufficient efficiency. and more deterioration for a seismic design. based on crave.
the concept of control. the structures.
1.2 Base isolation system:
Base. isolation of structures is .one of the greatest beloved. factor of insulate structures
opposite to. earthquake violence. It is. a static. force appliance that. is equipped between the
foundation and. the base of. the building. In structure, the base. isolator conserves the
structure from earthquake. forces in two. ways: (1) By divert. the seismic. efficiency (2) By
fascinating the seismic. efficiency. The seismic. energy is swerve by making the base of the
structure malleable (rather of fixed) in sideways directions, by that. expanding the
constitutional time cycle of. the structure. The seismic. intensity is engaged by the isolator
because. of its non- precise reaction. to earthquake. excitement.
Furthermore, base isolation. excessively minimizes the essential prevalence. of the
organization, authorize it farther the compelling area. of intake frequencies & through, slash

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the acceleration. at floor equalize of the structure where. attentive accessory or non-structural
scheme may. be placed. In performance. this, the base. isolation system itself patience a
generally extensive. displacement. One essential. utilization .in the design. of the base.
isolation system is. this displacement. insistence. Which the super-structure. is detached
from. the base structure by. recommend a drooping rule between the main structure and the
base structure. It is. a collection. of structural. circumstances which should. appreciably
decouple a super-structure from its sub-structure. that is in reversal resting. on trembling.
ground, thus sustain a building or non-building structures cleanliness. Noteworthy number.
of base isolation appliance are. establishing, some of. which have. satisfactorily classify
discharge .in real life structures.
Figure – 1.1 Base Isolation techniques
1.3 Types of Base Isolation techniques:
The base. isolation systems pursue. two basic threaten to diminish the seismic urge and
contaminate to. the structure: Adaptability fascinating scope. and similarity flexibility. In
first path the. isolation structure recommended. an influence, with low. similarity stiffness
between superstructure. and sub-structure that. acquire damping., consume competence. and
so weaken. inflated displacements due. to lateral resilience. of the isolation techniques. The
additional approaches. use rollers or sliding techniques. between structure and. its base. that
small steps. toward gain the fundamental duration of. the structure, innovation. it vanished
from the. Environment. of compelling frequencies of earthquake. ground motion.

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Figure – 1.2 High Damping rubber bearing
Figure – 1.3. Friction pendulum system
1.4 High damping rubber bearing(HDRBs):
This bearing. subsists. of refine layers of. high damping rubber interposed between. steel
plates. These approach. are associate that. are used. for lead rubber. bearing (LRBs) are. also
used to. establish high damping. rubber bearings (HDRBs). The. separate. difference is. the
composition of. the rubber. mixtures, which import. expanding damping. High damping.
rubber bearing is. definitely filled. with rubber mixture. with imperative damping estate of.
rubber without. affecting its. Mechanical. possessions. When the. shear stress is proficient.
to high-damping. rubber, an expedite. of molecule. flourish frictional heat. which is. a
structure. of intensity amusement. In not. filled essential rubber, used. for lead. rubber

4
bearing (LRBs), frictional heat is incidental because the. microscopic attraction in substantial
cross association. is very. fragile. The vitality. occasionally .to excess structure of. a high
damping rubber. bearing (HDPB) is. dependable and. analyzes by. flatten elliptical
hysteresis. loops and is favorable. for both maximum. and minimum tension. Check out. of
high damping. rubber bearing is primarily chronical expected. efficiency for. opportunity
which is linear resilient ideal. frequently exact value. is about 15%.
Now withstanding, HDRBs. may not. be import the fundamental essential severity. under
service loads and insignificant lateral. loads, even though some. essential severity is
organizing by. high-damping rubber molecules. which determine. taller stiffness under
limited strains. A structure. isolated with HDRBs. Essential. has a dependable, large
fundamental duration due to. flexibility of the isolation techniques, which makes. the
structure usable to wind activity with efficient. frequencies close to the fundamental
frequencies. In expansion, the. damping .and mechanical. estate of the HDRB. take place to
be educate accessible. while the hysteresis. strength amusement structure. of the LRB is not.
High damping. rubber bearing. are not as extensively used. in seismic. Isolation. as LRBs.
Figure – 1.4 Simplified sketch of HDRB
1.5 Friction Pendulum. system (FPS):
The FPS. subsists of a curved plate, a slider, sliding. material, and. a dust clue cover. As
shown in figure 1.3. It is. located on assumption. of timepiece. movement. and uses.
calculation. and force. of attraction to. accomplish. the crave seismic isolation. Friction.

5
Pendulum. system are greatest. widely. used kinematic. rule specifically in base isolation.
These. bearings, which have all. the assistance of rubber. bearings, over a bearing member
which can. slide. on the universal concave. outward, it humid. the efficiency. because it.
concludes an arrange uplift the building. event a lateral motion, and. reduction the
consequence. of earthquake. a quantity. These bearing. can be. used in. buildings, in extend.
and in abundant roof. scheme, and also, through. mechanical equity. of exclusive alloy in
their structure, they. can be used strongly in cold locality. with the crisis of. glacial.
1.6 Different types of base isolation system:
1. Triple friction pendulum Bearing
2. Rolling-Ball. Isolation. Bearing
3. Sloped Rolling-Type Bearing (RTB)
4. Metal-Touched Type Base. Isolator
5. Mushroom-Shaped Basements
6. Kinematic Self-Cantering Seismic. Isolator (PPP Isolator)
7. Double Curvature Friction Pendulum Bearing (DCFP)
8. Uplift Restraining Friction Pendulum. System (XY-FP Isolator)
9. Multiple Friction Pendulum System (MFPS)
10. Double-Wedge Base Isolation. Devices
11. Base Isolation System with Spring-Cam System
12. Sliding Concave Foundation (SCF)
13. Variable Friction. Pendulum System (VFPS)
14. Fixed-Reinforced. Elastomeric. Isolator
1.7 Requirement of. base isolation techniques:
Structure may. Content. the sequence essential: -
1. Sufficiently arrange the. Increasing. base and. to decrease super-structure. feedback.
2. Isolation. techniques decrease the equivalent displacement. between the structure. and
the ground to an. effective balanced.
1.8 Suitability of base isolation. system:
Mainly this type of circumstances should be happening to organize the super-structure
reaction:
1. The. soil does. not cultivate in. mind a. predominance. of wide range. of ground. motion.

6
2. The. important field. concession a horizontal displacement at the. base of managing. of
200 mm. or additional.
3. The structure. is prudently. short with. acceptable greater column. loads.
4. Lateral. loads. are smaller. than by. comparison. 10% of the heaviness. of the. structure.
Frequently. stiff structure. located on hard soil such as. nuclear power plant, low-rise
building, bridges, large storage tanks. and many types of devices are. more appropriate for
seismic. base isolation. Nevertheless, high-rise. buildings are. not appropriate for base
isolation anticipated to. its high fundamental period. For structure. located on soft. soil
circumstances for. which predominant. earthquake frequencies are. below 1 Hz, base
isolation will not. be applicable. as it would accumulation the structure frequency into more
challenging. array.
1.9 Advantages of Base isolation techniques:
 Apart. from preserve structure. from seismic movements, base. isolation also. insulates
them from blast loads. as the capability to move diminishes. the overall complete of the
blast on. the structure.
 Base isolated. Structures. are certain, hence. loyalty of them. is very. high as difference
to common. Structural. elements.
 Necessary of. extending step such. as frames, bracing. and shear. walls in. fell in
diminishes the. earthquake. forces communicate. to the structure.
 In case of large accidental seismic movements, losses are. only condensed in isolation
system, where. essential features can. be easily. replacement.
1.10 Dis-advantages of Base isolation techniques:
 These techniques. can’t be done on all structure, for. example: it is. not appropriate for
structure resting on loose soils.
 Enhance less. effective. for high rise. structures.
 Implementation is. effective to. Conduct, Complicated. and frequently. necessary highly
skilled. labors and. engineers.
1.11 Need of. Present. Study:
 There is growing necessary for. more adapt, productive. and creative. displacement
command. approaches.

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 To mastery the. reaction of structure. against earthquakes with. wide range of ground
motions.
 To compare. the responses of connected and unconnected building. with base- isolated
corridor.
1.12 Objective of present Study:
1. To analysis. the influence of seismically isolated corridor linked with two towers
structures. at the. top.
2. To learning. the union belongings of a. sky corridor for. next to. tall structures with
different. natural frequencies and. similar natural. frequencies.
3. To study. the consequence. of seismically. isolated bridge under. past recorded tremor
from inside the earth (earthquake) of harmonic loading.
4. To study. the influence of. seismically. isolated corridor. under random earthquake
ground. motion.
1.13 Scope of Present Study:
1. To analyze. the seismic act. of tall structures linked by. an isolated sky- corridor under
uni-directional. Earthquake. land action.
2. To deliberate. the isolation techniques for. Consequence. are high. Damping. rubber
bearing (HDRBs).
3. The number. of stories of twin towers are. same with same. story. heights. However, their
natural frequencies are different or similar.
4. Only seismic. lateral forces. are considered for analyses. i.e., the impact of wind is not
determined.

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CHAPTER 2
LITERATURE REVIEW
2.1 Introduction:
Since previous many decades, many research papers & literatures has been written on
seismic behavior of base isolated corridor & its application in Civil engineering. Latest trend
is use of two towers connected at top by an isolated corridor due to its apparent benefits.
Here, few condition of the papers are inspected, which are mentioned for this thesis.
2.2 Review of literature:
Qing Lyu and Wensheng Lyu (2020) examined mechanism and optimum design of STMD
for twin tower structure connected at top by an isolated corridor. The approach of STMD
twin tower connected by sky bridge utilizing flexible joint. These techniques is derived by 3
DOF. The impact of frequency ratio, mass ratio, tuning frequency ratio of bridge and
damping ratio of passive control techniques on structural seismic reaction is examined.
Optimum parametric determination is accomplishing to reducing the displacement of both
structures. It examined seismic accomplishment of nearby structure linked using isolated
bridge. To linked the sky bridge and tower seismic isolation bearing are utilized. In these
paper, two examples are presented: Natural frequencies of two towers is closed to each other
& natural frequencies of two towers leave from each other.
Dong-Guen Leel and Hyun-Su Kim (2010) examined evaluation of coupling–control
effect of a sky-bridge for adjacent tall buildings. The coupling control impact of sky corridor
for nearby tall building has been examined. Two towers structures 42 & 49 stories linked by
sky corridor and assemble in Seoul, Korea. LRB & LMB were used for attachment between
sky-corridor and examples of buildings. The displacement & acceleration reaction of
coupled building & reaction of bearings and member forces of sky-bridge were supposed in
distinguishes with uncoupled structures. The coupling control impact are examined in this
analysis utilizing wind and earthquake excitement. Time history analysis is accomplishing
utilizing wind and earthquake excitement. If comparative displacement between sky-
corridor and structure are acknowledge in only one direction because of architectural
necessity. Bearings are situated at four corners of sky-corridor.

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Akira Nishimura and Hiroshi Yamamoto (2011) examined Base-isolated super high-rise
RC building composed of three connected towers with vibration control systems. The island
tower sky club is a super high-rise RC apartment block assemble in Fukuoka City Japan.
The structures exist of three towers linked by three aerial gardens. To attain a high level of
safety opposite to earthquake & residential convenience during strong wind, various
methods were adopted. These systems are core-wall, hybrid base isolation system &oil and
zinc aluminium alloy dampers in aerial garden. Seismic response determination was
administering to approve the conduct of the structural design. To estimate the structural
control accomplishment in detail, the time history of absorbed efficiency was determined.
Kazuto Seto and Masaaki Ookuma (1986) examined method of Estimating Equivalent
Mass of Multi-Degree-Of-Freedom-System. To achieve optimum design of oscillation
inspected to restrain many resonance peaks of machine structure, its need to understand the
information equivalent mass at activity at which controller is mounted. This paper shows
two methods of equivalent mass.
(1) Mass response method.
(2) Modal analysis method.
In modal analysis method, modal mass, modal stiffness, modal damping are figured by
mathematical calculation by using eigenvectors.
W. S. Zhang and Y. L. Xu (1999) Dynamic characteristics & seismic response of adjacent
building connected by discrete dampers. Coupling adjacent structures utilizing discrete
viscous-elastic dampers for command of reaction to low and balanced seismic occurrence is
examined in this paper. The complex modal superposition procedure is used to conclude
dynamic characteristics, modal damping ratio and modal frequency, of damper-linked linear
adjacent structures. An examining method joining the involved mode superposition method
with the pseudo excitement system has been projected in this paper for fact- finding both
dynamic characteristics & seismic response of adjacent building linked by viscous-elastic
dampers.
Andy Richardson and Makola M Abdullah (2011) examined larger and more flexible
structures are being assemble. As a result, there is an expanding need for more productive,
adapt, and creative displacement control approaches. Closed-form equations for coupling
parallel structures with stiffness and damping essential features were successfully derived.
The accuracy of the equations was verified done differentiating with results written in former

10
work using a numerical increase scheme. The closed-form equations projected herein
intelligible the design process when coupling structures using stiffness and damping
elements.
Jie song and K T Tse (2015) examined inter-building and intra-building aerodynamics
correlation of connected building. (LBs, i.e., adjacent tall buildings structurally linked by
links such as sky-bridges). Spatiotemporal wind pressure data on a typical LB setup with
dissimilar gap interval are utilized to analyse inter-building aerodynamic correlation. Intra-
building aerodynamic correlation of the LBs analyse utilizing correlation coefficient and
trajectories, and then distinguished with those of an isolated structure.
R. A. Poole and J. E. Clendon examined Parliament house is to be incompletely destroyed
and remoulded, lengthened within the existent circumference wrapper, reconsider exclude
for the major public spaces, seismically improve by method of base isolation and
augmentation of existed foundations, basements wall, ground floors, upper floor walls and
floors. This research paper explained belief of seismic load, structural system, determination
& design structure. Expected construction and procedures & difficulties are also forward.
Makola. M. Abdullah and Jameel H Hanif (2011) examined use of shared tuned mass
damper (STMD) to reduce vibration and pounding in adjacent structure. Structures
discovered to earthquakes knowledge oscillations that are damaging to their structural
elements. Structural pounding is a supplementary difficulty that happen when building
knowledge earthquake excitement. This exploration includes connecting adjacent structures
with a (STMD) to decreases both the structures oscillation and anticipation of pounding.
Because the STMD is linked to both structures, the difficulty of tuning the STMD stiffness
and damping criterion enhance an issues.
H. P. Zhu and D. D. Ge (2010) examined framework linked dampers to decreases the
seismic responses of complement structures. Framework of linked dampers between two
adjoining structures and twin-tower with large podium are advanced through theoretical
determination. The influence of VED and VFD is examined in conditions of seismic reaction
decreasing of adjacent structures. Accomplishment of VED and VFD while being used for
connecting two MDOF complement structures and twin-tower with a large podium are
examined. The utilization of coupling structures control approach in twin-tower with a large
podium structure is also examined.

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Tomoyo Taniguchi (2008) examined impact of tuned mass damper on displacement
demand of base-isolated structures. The influence of a TMD to decreases the seismic appeal
on a base-isolated structure is examined. Utilizing stationary random process located on a
white-noise model of the ground motion, the optimum criterion of the TMD that maximally
minimizing the seismic insistence on the base-isolated structure are persistent. This
examination discloses that, depend on the mass, damping and frequencies typical features of
the TMD, the displacement requirement on the base isolated structure can be minimize by
15% - 25%. To explanation for the non-stationary and non-white nature of ground motions,
a succession of time history determination show that for far and near-field written ground
motions are taken out.
2.3 Summary:
 In previous papers high damping rubber bearing (HDRBs) are used. It needs to take out
sliding type bearing, lead rubber bearing (LRBs), linear motion bearing (LMB) is not
found.
 The building with different natural frequencies and similar natural frequencies under
wide range of ground motion is analysed the dissimilar base isolation system for tall
structures.

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CHAPTER 3
Seismic Behavior of Twin tower structures
connected by an isolated corridor
3.1 Introduction
Twin towers connected by a sky corridor are extensively used to their own benefits in terms
of aesthetic view, convenient communication, and capability to provide escape channel at
the time of fire emergencies or any other emergencies. In present days, the design of any
special structures lateral loads plays an important role. From structural point of view, we can
appreciate that lateral stiffness of these structures needs to be high adequacy to provide with
such a high lateral force. As per earthquake engineering, responses of any structure to
dynamic loading is an activity of its three basics properties i.e. mass, stiffness & damping.
By develop these properties we can deal with the responses of any structure. Among these
properties are mass, stiffness, damping and other mathematical based properties. Twin
towers presents a great challenge on structure seismic design. Different types of bearings are
always used to connect the sky corridor and towers. The connection system between sky
corridors and towers should be correctly design When the neigh-boring tall towers coupled
by a sky bridge are subjected to earthquake or wind excitations. Twin towers are greatly in
demand due to its architectural or structural design, particularly planning along with more
spaces with same foundation supports. Base isolation system is one of the most well- known
system for protecting a structure against earthquake forces. Which the superstructure is
separated from the base structure by recommended a suspension system between the base
structure and main structure. The isolated bearing are connected between sky corridor and
towers. The base isolation system has been adopted to reduce the story acceleration
responses of building mainly during large earthquake. There are many types of base isolation
devices like high damping rubber bearing, friction pendulum bearing & rocker roller bearing,
low damping rubber bearing, etc. It mitigates the motion of structure due to seismic activity.
Structural oscillation forces, as an progressive technology in engineering, consists of achieve
efficiency dissipating devices into structures to reduce exaggerated structural oscillations, to
restrict fatal structural deterioration and appreciate human encourage because of natural
disruption like strong wind and earthquakes. In early 1990s, appreciable consideration has

13
been compensated to research and expansion of structural control devices, and medium &
high rise buildings have begun realize energy dissipation devices or management systems to
reduce exaggerated structural oscillations. In last decades, significant resolution has been
given for design of engineering structures with different control approach to increase their
safety & security against strong earthquakes.
Figure -3.1 Petronas Tower Malaysia Figure -3.2 Portland Broadway Corridor
3.2 Mathematical model of connecting building:
An example a typical twin tower is connected a system of buildings and MDOF model as
shown in figure. The base isolated bearing are installed between the top of the towers and
sky bridge. The MDOF structure with adjoining structure can be simplified, which is
characterized by damping 𝑐𝑖, mass m, stiffness k, and The viscous damping ratio of towers
and natural frequency and are ζ1=c1/2√k1m1 & ω1=√k1/m1 respectively.
It consists stiffness (kd), mass (md), damping (cd).
Let, 𝜁𝑑 =
𝑐𝑑
2√𝑘𝑑𝑚𝑑
and 𝜔𝑑 = √
𝑘𝑑
𝑚𝑑

14
Figure – 3.3 Idealized building corridor connected system
The equations that describe behaviour of the mass shown in Figure 1.7 are as follows:
𝑚1𝑢̈1 + 𝑐1𝑢̇1 + 𝑘1𝑢1 = −𝑐𝑑1(𝑢̇1-𝑢̇𝑑)-𝑘𝑑1(𝑢1-𝑢𝑑)-𝑚1𝑥̈𝑔 (1)
𝑚𝑛𝑢̈𝑛 + 𝑐2𝑢̇𝑛 + 𝑘2𝑢2 = −𝑐𝑑2(𝑢̇𝑛-𝑢̇𝑑)-𝑘𝑑2(𝑢𝑛-𝑢𝑑)-𝑚𝑛𝑥̈𝑔 (2)
𝑚𝑑𝑢̈𝑑 + (𝑐𝑑1 + 𝑐𝑑2)𝑢̇𝑑 + (𝑘𝑑1 + 𝑘𝑑2)𝑢𝑑 = 𝑐𝑑1𝑢̇1 + 𝑐𝑑2𝑢̇𝑛 + 𝑘𝑑1𝑢1𝑘𝑑2𝑢𝑛𝑚𝑑𝑥̈𝑔 (3)
Where, u,𝑢̇, 𝑢̈
̇ are the displacement, velocity, and acceleration of the masses and 𝑥̈𝑔 is ground
acceleration. The dynamic equation can be expressed in a matrix form as
M𝑥̈(t)+C𝑥̇ (t)+Kx(t)=M𝑙𝑛𝑥̈𝑔(t) (4)
M= [
𝑚1 0
0 𝑚𝑛
0
0
0
0
0 0
0 0
⋱
0
0
𝑚𝑑
]; C= [
𝑐1 + 𝑐2 0
0 𝑐2 + 𝑐𝑑2
0
−𝑐𝑑1
0
−𝑐𝑑2
0 −𝑐𝑑1
0 −𝑐𝑑2
⋱
0
0
−𝑐𝑑1 + 𝑐𝑑2
]
;K=[
𝑘1 + 𝑘𝑑1 0
0 𝑘2 + 𝑘𝑑2
0
−𝑘𝑑1
0
−𝑘𝑑2
0 −𝑘𝑑1
0 −𝑘𝑑2
⋱
0
0
𝑘𝑑1 + 𝑘𝑑2
];X= {
𝑢1
𝑢𝑛
⋮
𝑢𝑑
} (5)

15
3.3 Validation of problem
In existing analyses, the reaction of connected and un-connected towers with base isolated
sky bridge is supposed by qualifying an estimate tool by utilizing MATLAB program that
simulate of different ground motions.
To validate the ability and effectiveness of the advanced program, one problem is selected.
The problem from the reference of Qing Lyu et al. (2020) is selected. The swelling reaction
of arranging is deliberate for El Centro earthquake ground motion, 1940. In figure apparently
shows that the happen attain from the developed program and paper identical exactly with
each other.
Time history analysis of system consisting of base isolated corridor with connected and un-
connected twin towers is carried out for the various ground motion in order to examine the
effect of connected and un-connected structures.
3.4 Numerical study for validation
I have taken two examples. In 1st
example, the first natural frequencies, leave from each
other and the 2nd
example is the first natural frequency of the two towers (Tower 1 and 2) is
close to each other. In these research total I have taken three towers, and all the parameters
which I have shown in Table 1. The damping ratio of each building is assumed to be 2 %,
and all buildings are classically damped.
To utilized the equivalent method for MDOF model to decreases the responses of structure
and allocate the closed- form equations. The damping and stiffness equity between two
buildings and sky corridor the parameters which I have taken as listed in Table 2.
TABLE 3.1 Building model parameters: (Reference Qing Lyu, et al.)
Towers No. of
floor
Damping
ratio (%)
Floor
mass (kg)
Floor Stiffness
(N/m)
Natural
frequency (Hz)
1 10 2 1.02× 106
1.50× 109 0.9120
2 10 2 1.40× 106
2.50× 109 1.0050

16
TABLE 3.2 Building model parameters:
Connected
Tower
𝒌𝐝
(N/m)
𝒄𝐝
(N.s/m)
1-2 6.91 × 106
3.31× 105
TABLE 3.3 Properties of Buildings (Based on MATLAB software):
Tower Natural frequency a
per Literature
Natural frequency obtained
from developed Program
Errors
(%)
1 0.912 0.912 0.00
2 1.005 1.005 0.00
TABLE 3.4 Properties of Buildings:
Tower Floor Mass (kg) 𝒌𝒅 (N/m) 𝒄𝒅 (N.s/m)
1 1.02*106
6.91× 106
3.31× 105
2 1.40*106

17
(a) 1940 El Centro
Results from reference of Qing Lyu et al. (2020)
Results from developed Matlab program (El Centro, 1940)
Figure 3.4 Validation of program with paper Qing Lyu et al. (2020)
0 5 10 15 20 25 30 35 40
-0.2
0
0.2
Displacement
(m)
Time(sec)

18
(a) 1940 El Centro
Results from reference of Qing Lyu et al. (2020)
Results from developed Matlab program (El Centro, 1940)
Figure 3.5 Validation of program with paper Qing Lyu et al. (2020)
TABLE 3.5 Comparison of top floor displacement
Towers Responses Displacement responses
(m)
Percentage reduction
(%)
1 Unconnected 0.1993
26.79%
Connected 0.1459
2 Unconnected 0.2102
17.75%
Connected 0.1729

19
CHAPTER 4
Recorded Earthquake ground motion
4.1 Numerical Study
In these chapter the seismic act of base isolated corridor connected at twin towers structure
under various ground motions was considered. It is seen that there is a significant minimizing
in the seismic reaction of structure under various ground motions. Thus to affected the
structural performance of building. Base isolated accessory is deliberate as a favorable
control accessory.
Behavior of connected Tower are studied by:
a) Recorded Earthquake Ground Motion
- Similar Natural frequencies
- Different Natural frequencies
b) Harmonic Earthquake Ground Motion (In frequency domain)
c) Random Ground Motion
(a) Recorded Earthquake Ground Motion:
To determine the expected approach for linked adjoining structures, two design illustrations
are presented. In the first illustration, the first natural frequency of two towers (Tower-1 &
2) is close to each other, whereas in the second example, the first natural frequencies depart
from each other. Three towers are considered in total, and the criterion of each tower are
listed in Table 1. All towers are classically damped, and the damping ratio of each tower is
assumed to be 0.02. To apply the closed form equations, we first minimizing the structures
to their similar MDOF models as shown in figure. The parameters are used to conclude the
stiffness and damping possessions between the sky corridor and two towers in each example,
as listed in Table 2.
The response spectra for displacement, acceleration and base shear of selected ground
motions are shown below for 1940 Imperial Valley, 1987 Superstition hills, 1999 Chamoli
earthquake, 1994 Northridge, 1989 Loma Prieta, 1941 Imperial Valley, 1979 El centro
earthquakes.
The important data on which the effectiveness of base isolated corridor depends such as
mass, stiffness, etc are explained here, to examine the influence of the base isolation systems,

20
the responses of the devices are distinguishing with the reaction of connected and un-
connected system respectively.
TABLE 4.1 Details of ground motions considered in this study:
Sr.
No.
Earthquake Magnitudes Locations PGA
(g)
1 1940 Imperial Valleys 6.95 El Centro. 0.313
2 1987 Superstitions Hill 6.7 El Centro Imp. Co.
Center.
0.512
3 1999 Chamoli
Earthquakes
6.4 Gopeshwar. 0.359
4 1994 Northridge 6.7 Northridge- Saticoy St. 0.529
5 1989 Loma Prieta. 6.9 Capitola. 0.42
6 1941 Imperial Valleys 6.7 Canoga Park-Topanga
Canyon.
0.477
7 1979 El Centro. 6.5 Mexico- US border. 1.74
TABLE 4.2 Frequencies of 1st
, 2nd
& 3rd
tower based on MATLAB:
Floors
1st Tower
(Similar frequencies)
2nd Tower
(Similar frequencies)
3rd Tower
(Different frequencies)
0 5.73154 6.31585 8.01391
1 17.066 18.8065 23.8627
2 28.0204 30.877 39.1785
3 38.3482 42.2577 53.6190
4 47.8195 52.6945 66.8618
5 56.2225 61.9542 78.6111
6 63.3696 69.8299 88.6042
7 69.1012 76.1458 96.6182
8 73.2891 80.7606 102.4738
9 75.8399 83.5715 106.0403
Natural frequencies should be calculated based on given formula:
So, 2𝜋𝑓
Where, 𝑓= frequency
𝜔𝑛= Natural frequency

21
For 1st
Tower,
𝑓 =
5.73154
2𝜋
𝜔𝑛 = 0.912
For 2nd
Tower,
𝑓 =
6.3159
2𝜋
𝜔𝑛 = 1.005
For 3rd
Tower,
𝑓 =
8.01391
2𝜋
𝜔𝑛 = 1.275
Natural frequencies into Time Period:
T=
2𝜋
𝑓
For Tower 1,
For 𝑓1, T=
2𝜋
5.73154
=1.096 sec
For Tower 2,
For 𝑓1, T=
2𝜋
6.31585
=0.995 sec
For Tower 3,
For 𝑓1, T=
2𝜋
8.01390
=0.784 sec
4.2 Two buildings with similar natural frequencies:
The building have similar natural frequencies. Two 10 story buildings are taken Tower 1
and Tower 2are flexibly connected by an isolated sky bridge at top.

22
Displacement, Base shear and acceleration of base isolated corridor with connected
and unconnected for ground motions of similar natural frequencies.
Imperial Valley, 1940
Figure 4.1 Displacement variation w.r.t. time under Imperial Valley 1940 El centro
earthquake
-0.2
-0.1
0.0
0.1
0.2
0 5 10 15 20 25 30
-0.2
-0.1
0.0
0.1
0.2
Connected T-1
Unconnected T-1
0.1899
0.1402
Similar frequencies
Displacement
(m)
Time (sec)
Connected T-2
Unconnected T-2
0.1944
0.1624

23
Figure 4.2 Base shear variation w.r.t. time under Imperial Valley 1940 El centro
earthquake
Figure 4.3 Acceleration variation w.r.t. time under Imperial Valley 1940 El centro
earthquake
-0.4
-0.2
0.0
0.2
0.4
0 5 10 15 20 25 30
-0.6
-0.3
0.0
0.3
0.6
Connected T-1
Unconnected T-1
0.4
0.3299
Similar frequencies
Base
shear
(W)
Time (sec)
Connected T-2
Unconnected T-2
0.5612
0.4813
-10
-5
0
5
10
0 5 10 15 20 25 30
-10
-5
0
5
10
Connected T-1
Unconnected T-1
Similar frequencies
Acceleration
(m/sec
2
)
Time (sec)
Connected T-2
Unconnected T-2

24
El centro 1979
Figure 4.4 Displacement variation w.r.t. time under 1979 El centro earthquake
Figure 4.5 Base shear variation w.r.t. time under 1979 El centro earthquake
-0.3
-0.2
-0.1
0.0
0.1
0.2
0.3
0 10 20 30
-0.3
-0.2
-0.1
0.0
0.1
0.2
0.3
Connected T-1
Unconnected T-1
Similar frequencies
0.1993
0.1549
Displacment
(m)
Time (sec)
0.2982
Connected T-2
Unconnected T-2
0.2030
-0.4
-0.2
0.0
0.2
0.4
0 10 20 30
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
Connected T-1
Unconnected T-1
0.4078
Similar frequencies
0.3285
Base
shear
(W)
Time (sec)
0.5799
0.4968
Connected T-2
Unconnected T-2

25
Figure 4.6 Acceleration variation w.r.t. time under 1979 El centro earthquake
-10
-5
0
5
10
0 10 20 30
-15
-10
-5
0
5
10
Connected T-1
Unconnected T-1
9.4696
7.0817
Similar frequencies
Acceleration
(m/sec
2
)
Time (sec)
Connected T-2
Unconnected T-2
10.999
9.9066

26
Superstition Hills, 1987
Figure 4.7 Displacement variation w.r.t. time under 1987 Superstition Hills earthquake
Figure 4.8 Base shear variation w.r.t. time under 1987 Superstition Hills earthquake
-0.1
0.0
0.1
0.2
0 5 10 15 20 25 30
-0.15
-0.10
-0.05
0.00
0.05
0.10
Connected T-1
Unconnected T-1
Similar frequencies
0.1634
0.1463
Displacement
(m)
Time (sec)
Connected T-2
Unconnected T-2
0.11
0.097
-0.4
-0.2
0.0
0.2
0.4
0 5 10 15 20 25 30
-0.2
0.0
0.2
0.4
Connected T-1
Unconnected T-1
Similar frequencies
0.3241
0.3283
Base
shear
(W)
Time (sec)
Connected T-2
Unconnected T-2
0.2648
0.3141

27
Figure 4.9 Acceleration variation w.r.t. time under 1987 Superstition Hills earthquake
-9
-6
-3
0
3
6
9
0 5 10 15 20 25 30
-9
-6
-3
0
3
6
9
Connected T-1
Unconnected T-1
Similar frequencies
8.5462
7.044
Acceleration
(m/sec
2
)
Time (sec)
Connected T-2
Unconnected T-2
9.4614
7.7970

28
Figure 4.10 Displacement variation w.r.t. time under 1941 Imperial Valley earthquake
Figure 4.11 Base shear variation w.r.t. time under 1941 Imperial Valley earthquake
-0.2
-0.1
0.0
0.1
0.2
0 5 10 15 20 25 30
-0.2
-0.1
0.0
0.1
0.2
Connected T-1
Unconnected T-1
0.1576
0.1811 Similar frequencies
Displacement
(m)
Time (sec)
Connected T-2
Unconnected T-2
0.1770 0.2154
-0.4
-0.2
0.0
0.2
0.4
0 5 10 15 20 25 30
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
Base
shear
(W)
Connected T-1
Unconnected T-1
Similar frequencies
0.4114
0.394
Time (sec)
Connected T-2
Unconnected T-2
0.6034
0.533

29
Figure 4.12 Acceleration variation w.r.t. time under 1941 Imperial Valley earthquake
-10
-5
0
5
10
15
0 5 10 15 20 25 30
-15
-10
-5
0
5
10
15
Connected T-1
Unconnected T-1
11.4998
8.69
Similar frequencies
Acceleration
(m/sec
2
)
Time (sec)
Connected T-2
Unconnected T-2
13.1599
11.3939

30
Loma Prieta, 1989
Figure 4.13 Displacement variation w.r.t. time under 1989 Loma Prieta earthquake
Figure 4.14 Base shear variation w.r.t. time under 1989 Loma Prieta earthquake
-0.3
-0.2
-0.1
0.0
0.1
0.2
0.3
0 5 10 15 20 25 30
-0.1
0.0
0.1
0.2
Connected T-1
Unconnected T-1
Similar frequencies
0.2058
0.2223
Displacement
(m)
Time (sec)
Connected T-2
Unconnected T-2
0.1678
0.1391
-0.6
-0.3
0.0
0.3
0.6
5 10 15 20 25 30
-0.6
-0.3
0.0
0.3
0.6
Connected T-1
Unconnected T-1
0.5692
04309
Similar frequencies
Base
shear
Time (sec)
Connected T-2
Unconnected T-2
0.6879
0.5508

31
Figure 4.15 Acceleration variation w.r.t. time under 1989 Loma Prieta earthquake
-10
0
10
20
0 5 10 15 20 25 30
-15
-10
-5
0
5
10
15
Connected T-1
Unconnected T-1
Similar grequencies
15.1558
12.4404
Acceleration
(m/sec
2
)
Time (sec)
Connected T-2
Unconnected T-2
14.7884
13.6537

32
Chamoli Gopeshwar, 1999
Figure 4.16 Displacement variation w.r.t. time under 1999 Chamoli earthquake
Figure 4.17 Base shear variation w.r.t. time under 1999 Chamoli earthquake
-0.4
-0.2
0.0
0.2
0.4
0 5 10 15 20 25
-0.4
-0.2
0.0
0.2
0.4
Connected T-1
Unconnected T-1
0.3625
Base
shear
(W)
Time (sec)
Connected T-2
Unconnected T-2
0.4316
0.3908
-0.2
-0.1
0.0
0.1
0.2
0 5 10 15 20 25
-0.30
-0.15
0.00
0.15
0.30
Connected T-1
Unconnected T-1
0.1645 0.1696
Similar frequencies
Displacement
(m)
Time (sec)
Connected T-2
Unconnected T-2
0.1469
0.3573

33
Figure 4.18 Acceleration variation w.r.t. time under 1999 Chamoli earthquake
-10
-5
0
5
10
0 5 10 15 20 25
-10
-5
0
5
10
Connected T-1
Unconnected T-1
10.8299
Acceleration
(m/sec
2
)
Time (sec)
Connected T-2
Unconnected T-2
9.2736 9.8098

34
Northridge, 1994
Figure 4.19 Displacement variation w.r.t. time under 1994 Northridge earthquake
Figure 4.20 Base shear variation w.r.t time under 1994 Northridge earthquake
-0.3
-0.2
-0.1
0.0
0.1
0.2
0.3
0 5 10 15 20 25 30
-0.4
-0.3
-0.2
-0.1
0.0
0.1
0.2
0.3
Connected T-1
Unconnected T-1
0.2566
Displacement
(m)
Time (sec)
Connected T-2
Unconnected T-2
0.3529
0.3354
-0.6
-0.3
0.0
0.3
0.6
0 5 10 15 20 25 30
-1.0
-0.5
0.0
0.5
1.0
Connected T-1
Unconnected T-1
Similar frequencies
0.6593
0.5767
Base
shear
(W)
Time (sec)
Connected T-2
Unconnected T-2
1.0371
1.0612

35
Figure 4.21 Acceleration variation w.r.t. time under 1994 Northridge earthquake
-15
-10
-5
0
5
10
15
0 5 10 15 20 25 30
-20
-10
0
10
20
30
Connected T-1
Unconnected T-1
Similar frequencies
13.3541
11.8194
Acceleration
(m/sec
2
)
Time (sec)
Connected T-2
Unconnected T-2
22.0434
17.915

36
Similar
frequencies
Displacement
(m)
Base
shear
(W)
Acceleration
(g)
Sr.
No
Earthquake
Connected
Unconnected
Connected
Unconnected
Connected
Unconnected
1
1940
Imperial
Valley
0.140
0.189
0.322
0.4
0.712
0.952
2
1979
El
Centro
0.154
0.199
0.328
0.407
0.721
0.965
3`
1987
Superstition
hills
0.157
0.181
0.324
0.328
0.718
0.871
4
1941
Imperial
Valley
0.157
0.181
0.394
0.411
0.88
1.172
5
1989
Loma
Prieta
0.205
0.222
0.430
0.569
1.268
1.544
6
1999
Chamoli
0.164
0.169
0.299
0.362
0.890
1.103
7
1994
Northridge
0.268
0.256
0.576
0.659
1.204
1.361
`
TABLE
4.3
Seismic
Response
of
Tower
1

37
Similar
frequencies
Displacement
(m)
Base
shear
(W)
Acceleration
(g)
Sr.
No
Earthquake
Connected
Unconnected
Connected
Unconnected
Connected
Unconnected
1
1979
El
Centro
0.203
0.298
0.497
0.579
1.009
1.121
2
1941
Imperial
Valley
0.177
0.215
0.533
0.603
1.162
1.508
3`
1987
Superstition
hills
0.177
0.214
0.265
0.314
0.723
0.965
4
1940
Imperial
Valley
0.162
0.194
0.481
0.561
0.987
1.101
5
1989
Loma
Prieta
0.139
0.168
0.551
0.688
1.392
1.508
6
1994
Northridge
0.335
0.353
1.016
1.037
1.826
2.247
7
1999
Chamoli
0.147
0.155
0.391
0.432
0.844
0.945
TABLE
4.4
Seismic
Response
of
Tower
2

38
4.3 Two towers with different natural frequencies:
Tower 1 and 3 are two ten story towers. The fundamental frequencies of these two buildings
are 0.912 and 1.275 Hz, mutually. The time domain reaction of roof displacement, base shear
and absolute acceleration of these buildings are shows in figures 7,8 & 9 mutually.
Difference with unconnected case, the two buildings flexibly connected by a sky bridge
persuaded a compelling contraction in reaction.
Displacement, Base shear and acceleration of base isolated corridor with connected
and unconnected for ground motions of different natural frequencies.
Figure 4.22 Displacement variation w.r.t. time under 1941 imperial valley earthquake
-0.2
-0.1
0.0
0.1
0.2
0 5 10 15 20 25 30
-0.2
-0.1
0.0
0.1
0.2
Connected T-3
Unconnected T-3
Different frequencies
0.1811
0.1576
Displacement
(m)
Time (sec)
Connected T-2
Unconnected T-2
0.2154
0.1832

39
Figure 4.23 Base shear variation w.r.t. time 1941 imperial valley earthquake
Figure 4.24 Acceleration variation w.r.t. time under 1941 imperial valley earthquake
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
0 5 10 15 20 25 30
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
Connected T-3
Unconnected T-3
0.6143
0.5542 Different frequencies
Base
shear
(W)
Time (sec)
Connected T-2
Unconnected T-2
0.6034
0.533
-10
-5
0
5
10
0 5 10 15 20 25 30
-15
-10
-5
0
5
10
15
Acceleration
(m/sec
2
)
Connected T-3
Unconnected T-3
10.2853
10.1942
Time (sec)
Connected T-2
Unconnected T-2
13.1599
11.4061

40
El Centro 1979
Figure 4.25 Displacement variation w.r.t. time under 1979 El Centro earthquake
Figure 4.26 Base shear variation w.r.t. time under 1979 El Centro earthquake
-0.2
-0.1
0.0
0.1
0.2
0 10 20 30
-0.2
-0.1
0.0
0.1
0.2
0.3
Connected T-1
Unconnected T-1
0.1296
0.1211
Displacement
(m)
Time (sec)
0.2102
0.1766
Connected T-3
Unconnected T-3
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0 10 20 30
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
Connected T-1
Unconnected T-1
0.5346
0.5008
Base
shear
(W)
Time (sec)
Connected T-3
Unconnected T-3
0.5799
0.5126

41
Figure 4.27 Acceleration variation w.r.t. time under 1979 El Centro earthquake
-15
-10
-5
0
5
10
0 10 20 30
-15
-10
-5
0
5
10
Connected T-1
Unconnected T-1
11.7407
Acceleration
(m/sec
2
)
Time (sec)
Connected T-3
Unconnected T-3
10.999
9.7244

42
Figure 4.28 Displacement variation w.r.t. time under 1940 Imperial Valley earthquake
Figure 4.29 Base shear variation w.r.t. time under 1940 Imperial Valley earthquake
-0.15
-0.10
-0.05
0.00
0.05
0.10
0 5 10 15 20 25 30
-0.2
-0.1
0.0
0.1
0.2
Connected T-3
Unconnected T-3
0.1135
0.1073
Displacement
(m)
Time (sec)
Connected T-2
Unconnected T-2
0.1944
0.1655
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0 5 10 15 20 25 30
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
Connected T-3
Unconnected T-3
0.5236
Base
shear
(W)
Time (sec)
Connected T-2
Unconnected T-2
0.5612
0.4981

43
Figure 4.30 Acceleration variation w.r.t. time under 1940 Imperial Valley earthquake
-10
-5
0
5
10
15
0 5 10 15 20 25 30
-10
-5
0
5
10
Connected T-3
Unconnected T-3
11.7272
10.7773
Acceleration
(m/sec
2
)
Time (sec)
Connected T-2
Unconnected T-2
10.8021
9.55

44
Superstition Hills, 1987
Figure 4.31 Displacement variation w.r.t. time under 1987 Superstition Hills earthquake
-0.1
0.0
0.1
0.2
0 5 10 15 20 25 30
-0.1
0.0
0.1
Connected T-3
Unconnected T-3
0.1538
0.1394
Displacement
(m)
Time (sec)
Connected T-2
Unconnected T-2
0.11
0.0918

45
Figure 4.32 Base shear variation w.r.t. time under 1987 Superstition Hills earthquake
Figure 4.33 Acceleration variation w.r.t. time under 1987 Superstition Hills earthquake
-0.50
-0.25
0.00
0.25
0.50
0 5 10 15 20 25 30
-0.30
-0.15
0.00
0.15
0.30
Connected T-3
Unconnected T-3
0.5999
0.5637
Base
shear
(W)
Time (sec)
Connected T-2
Unconnected T-2
0.3141
0.2584
-15
-10
-5
0
5
10
15
0 5 10 15 20 25 30
-9
-6
-3
0
3
6
9
Connected T-3
Unconnected T-3
14.4547
13.049
Acceleration
(m/sec
2
)
Time (sec)
Connected T-2
Unconnected T-2
9.4614
7.9397

46
Loma Prieta, 1989
Figure 4.34 Displacement variation w.r.t. time under 1989 Loma Prieta earthquake
-0.2
-0.1
0.0
0.1
0.2
0 5 10 15 20 25 30
-0.1
0.0
0.1
0.2
Connected T-3
Unconnected T-3
0.1707
0.1683
Displacement
(m)
Time (sec)
Connected T-2
Unconnected T-2
0.1678 0.1466

47
Figure 4.35 Base shear variation w.r.t. time under 1989 Loma Prieta earthquake
Figure 4.36 Acceleration variation w.r.t. time under 1989 Loma Prieta earthquake
-1.2
-0.9
-0.6
-0.3
0.0
0.3
0.6
0.9
0 5 10 15 20 25 30
-0.6
-0.3
0.0
0.3
0.6
Connected T-3
Unconnected T-3
0.9659
0.8688
Base
shear
(W)
Time (sec)
Connected T-2
Unconnected T-2
0.6879
0.5738
-30
-20
-10
0
10
20
30
0 5 10 15 20 25 30
-15
-10
-5
0
5
10
15
Connected T-3
Unconnected T-3
17.9551
Acceleration
(m/sec
2
)
Time (sec)
Connected T-2
Unconnected T-2
14.7884
13.4798

48
Chamoli, 1999
Figure 4.37 Displacement variation w. r. t. time under 1999 Chamoli earthquake
-0.12
-0.06
0.00
0.06
0.12
0 5 10 15 20 25 30
-0.3
-0.2
-0.1
0.0
0.1
0.2
0.3
Connected T-3
Unconnected T-3
0.1414
0.1378
Displacement
(m)
Time (sec)
Connected T-2
Unconnected T-2
0.1554
0.2577

49
Figure 4.38 Base shear variation w. r. t. time under 1999 Chamoli earthquake
Figure 4.39 Acceleration variation w. r. t. time under 1999 Chamoli earthquake
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0 5 10 15 20 25 30
-0.4
-0.2
0.0
0.2
0.4
Connected T-3
Unconnected T-3
0.5763
0.5615
Base
shear
(W)
Time (sec)
Connected T-2
Unconnected T-2
0.4316
0.3897
-10
-5
0
5
10
0 5 10 15 20 25 30
-10
-5
0
5
10
Connected T-3
Unconnected T-3
10.0519
3.8644
Acceleration
(m/sec
2
)
Time (sec)
Connected T-2
Unconnected T-2
9.2736
7.5985

50
Northridge, 1994
Figure 4.40 Displacement variation w. r. t. time under 1994 Northridge earthquake
Figure 4.41 Base shear variation w. r. t. time under 1994 Northridge earthquake
-0.3
-0.2
-0.1
0.0
0.1
0.2
0.3
0 5 10 15 20 25 30
-0.4
-0.3
-0.2
-0.1
0.0
0.1
0.2
0.3
Connected T-3
Unconnected T-3
0.2542
0.2416
Displacement
(m)
Time (sec)
Connected T-2
Unconnected T-2
0.3529
0.3299
-1.0
-0.5
0.0
0.5
1.0
0 5 10 15 20 25 30
-1.0
-0.5
0.0
0.5
1.0
Connected T-3
Unconnected T-3
0.9954
1.029
Base
shear
(W)
Time (sec)
Connected T-2
Unconnected T-2
1.0329
0.9901

51
Figure 4.42 Acceleration variation w. r. t. time under 1994 Northridge earthquake
-20
-15
-10
-5
0
5
10
15
20
0 5 10 15 20 25 30
-20
-10
0
10
20
30
Connected T-3
Unconnected T-3
16.5409
16.4679
Acceleration
(m/sec
2
)
Time (sec)
Connected T-2
Unconnected T-2
22.0434
17.9771

52
Similar
frequencies
Displacement
(m)
Base
shear
(W)
Acceleration
(g)
Sr.
No
Earthquake
Connected
Unconnected
Connected
Unconnected
Connected
Unconnected
1
1941
Imperial
Valley
0.127
0.181
0.554
0.614
1.039
1.031
2
1979
El
Centro
0.121
0.129
0.501
0.535
1.197
1.286
3
1940
Imperial
Valley
0.107
0.114
0.461
0.524
1.099
0.195
4
1987
Superstition
hills
0.15
0.154
0.564
0.60
1.335
1.474
5
1989
Loma
Prieta
0.168
0.171
0.869
0.966
1.830
2.218
6
1999
Chamoli
0.138
0.141
0.562
0.576
1.025
1.094
7
1994
Northridge
0.254
0.242
1.029
0.995
1.686
1.679
TABLE
4.5
Seismic
Response
of
Tower
3

53
Similar
frequencies
Displacement
(m)
Base
shear
(W)
Acceleration
(g)
Sr.
No
Earthquake
Connected
Unconnected
Connected
Unconnected
Connected
Unconnected
1
1941
Imperial
Valley
0.183
0.215
0.554
0.603
1.163
1.342
2
1979
El
Centro
0.206
0.210
0.513
0.579
0.991
1.121
3
1940
Imperial
Valley
0.166
0.194
0.498
0.561
0.923
1.101
4
1987
Superstition
hills
0.092
0.11
0.258
0.314
0.809
0.965
5
1989
Loma
Prieta
0.147
0.168
0.574
0.688
1.374
1.507
6
1999
Chamoli
0.146
0.154
0.399
0.432
0.864
0.945
7
1994
Northridge
0.329
0.353
0.990
1.037
1.833
2.247
TABLE
4.6
Seismic
Response
of
Tower
2

54
CHAPTER 5
Seismic Response of Connected building under
Harmonic Loading
(In frequency domain)
5.1 Introduction
The responses of SDF system to harmonic excitement is a classical topic in structural
dynamics, not only because such excitement are happening upon in engineering systems
(e.g., force due to unbalanced rotating devices), but also because tolerant the reaction of
structures to harmonic excitement support awareness into how the system will respond to
other type of forces. We will study the motion of structures idealized as single degree-of-
freedom system excited harmonically, that is, structures inflict to forces or displacements
whose magnitude may be represented by sine or cosine functions of time.
5.2 Governing equation of harmonic frequency response:
Consider a viscously damped SDF system subjected to external force 𝑝(𝑡). The equation of
motion for the system is
𝑚𝑢̈ + 𝑐𝑢̈ + 𝑘𝑢 = 𝑝(𝑡) (1)
The particular solution of this differential equation for harmonic forces was presented in
below equations,
𝑢𝑝(𝑡) = C sin 𝜔𝑡 + 𝐷 cos 𝜔𝑡 (2) (2)
Where,
C =
p0 [1−(
ω
ωn
)
2
]
𝑘[1−(
ω
ωn
)
2
]
2
+[2ζ(
ω
ωn
)]
2
(3)
D =
p0 [2−ζ
ω
ωn
]
𝑘[1−(
ω
ωn
)
2
]
2
+[2ζ(
ω
ωn
)]
2
(4)
The particular solution is given by equation (2) still applies, but in case constant C & D are,
C =
p0[ 2ζ(
ω
ωn
)]
𝑘[1−(
ω
ωn
)
2
]
2
+[2ζ(
ω
ωn
)]
2
(5)

55
D =
p0 [1−(
ω
ωn
)
2
]
𝑘[1−(
ω
ωn
)
2
]
2
+[2ζ(
ω
ωn
)]
2
(6)
The equation known as steady state response. The displacement 𝑢(𝑡) due to external force
𝑝(𝑡) = 𝑝0 sin 𝜔𝑡 is,
𝑢(𝑡) =
p0 [1−(
ω
ωn
)
2
]sin 𝜔𝑡− [2ζ(
ω
ωn
)]cos 𝜔𝑡
𝑘[1−(
ω
ωn
)
2
]
2
+[2ζ(
ω
ωn
)]
2
(7)
and due to 𝑝(𝑡) = 𝑝0 sin 𝜔𝑡 ,
𝑢(𝑡) =
p0 [1−(
ω
ωn
)
2
]cos𝜔𝑡− [2ζ(
ω
ωn
)] sin 𝜔𝑡
𝑘[1−(
ω
ωn
)
2
]
2
+[2ζ(
ω
ωn
)]
2
(8)
Now consider external force
𝑝(𝑡) = 𝑒𝑖𝜔𝑡
(9)
Where, 𝑖 = √−1
Equation (9) is representation of sinusoidal & cosine forces together
𝑢(𝑡) = 𝐻𝑢(𝜔)𝑒𝑖𝜔𝑡
(10)
Where 𝐻𝑢(𝜔) remains to be determined.
We differentiate equation (10),
𝑢̇ (𝑡) = 𝑖𝜔𝐻𝑛(𝜔)𝑒𝑖𝜔𝑡
𝑢̈(𝑡) = −𝜔2
𝐻𝑢(𝜔)𝑒𝑖𝜔𝑡
(11)
& substitute equation (10), (11) in equation (1),
𝐻𝑢(𝜔)𝑒𝑖𝜔𝑡(−𝜔2
𝑚 + 𝑖𝜔𝑐 + 𝑘) = 𝑒𝑖𝜔𝑡
By cancelling 𝑒𝑖𝜔𝑡
,
𝐻𝑢(𝜔) =
1
−𝜔2𝑚 + 𝑖𝜔𝑐 + 𝑘
Tower 1 & 2 are two ten storey buildings malleable associated by a sky corridor at the top
most floor. The frequency domain reaction of the amplitude of the first towers at first floor
level as shown in fig 5.1. Similarly, at first tower of fifth floor and tenth floor level as shown
in figure 5.2 & figure 5.3. We show in figure the difference between connected and
unconnected structures.

56
Figure 5.1 Frequency variation of amplitude at 1st floor under harmonic Response
Figure 5.2 Frequency variation of amplitude at 5th floor under harmonic Response
0 5 10 15 20 25 30
0.0
1.0
2.0
3.0
4.0
5.0
Amplitude
(y
1
)
(H
w
)
Frequency (rad/sec)
Unconnected
Connected
0 5 10 15 20 25 30
-1.0
0.0
1.0
2.0
3.0
4.0
5.0
6.0
7.0
Amplitude
(y
5
)
(H
w
)
Frequency (rad/sec)
Unconnected
Connected

57
0 5 10 15 20 25 30
-2.0
0.0
2.0
4.0
6.0
8.0
10.0
12.0
14.0
Amplitude
(y
10
)
(H
w
)
Frequency (rad/sec)
Unconnected
Connected
0 5 10 15 20 25 30
-2.0
0.0
2.0
4.0
6.0
8.0
10.0
12.0
14.0
Amplitude
(y
11
)
(H
w
)
Frequency (rad/sec)
Unconnected
Connected

58
0 5 10 15 20 25 30
0.0
1.0
2.0
3.0
4.0
Amplitude
(y
15
)
(H
w
)
Frequency (rad/sec)
Unconnected
Connected
0 5 10 15 20 25 30
0.0
2.0
4.0
6.0
8.0
10.0
Amplitude
(y
20
)
(H
w
)
Frequency (rad/sec)
Unconnected
Connected

59
The frequency domain responses of the amplitude of the second towers at eleventh floor
level as shown in fig.5.4. Similarly, at second tower of fifteenth floor and twentieth floor
level as shown in fig.5.5 & figure 5.6. We show in figure the difference between connected
and unconnected structures. I have done these programming and results with the help of
MATLAB.
TABLE 5.1 Response under Harmonic ground motions
Amplitude Frequency
Floors Connected Unconnected Connected Unconnected
1 2.87 4.86 17 17
5 3.09 6.39 5.9 5.7
10 6.28 13.73 5.9 5.7
11 6.28 13.73 5.9 5.7
15 2.43 3.93 6.4 6.3
20 5.10 8.44 6.4 6.3

60
CHAPTER 6
Seismic Response of Connected building under
Random Ground motion
6.1 Introduction
Frequency domain spectral determination is engaged in order to approach the reaction of
structures reveal to random excitement. It is the one of the most conspicuous method for
random vibration determination and is of structures in frequency domain and is literally
appropriate for narrow system. Nevertheless, for non-linear systems, the process of
determination has also been lengthened by implement suitable linearization system and is
begin to work sufficiently for some extent non-linear system. The agreement of the method
is generally due to its limitation and excellence.
When the dynamic excitement are shaped as stationary random processes, they are
representing by the moments of their probability density functions (PDFs), which durable
even with the shift in time. For most of the structural engineering problems, the second
moment of the PDF, that is, the mean square value of the process is of interest and, therefore,
the second order stationary process is sufficient for modelling random dynamic excitement
such as wind, earthquakes, etc. This allocation the use of frequency domain spectral
determination to find the responses of linear structural system reveal to these forces.
In these chapter, the spectral analysis of structures for earthquakes forces is manner without
going into the difficulty of the theory of random oscillation determination. The objective of
this analysis is to enable one to use the spectral analysis of structures for earthquake forces
without being an authority in random oscillation analysis. The evaluation of the method uses
simple concepts, such as, stationary random process.
6.2 Stationary random process
A development deals with a number of random variables is called as a random process. If a
single function of time t is connected these random variables, then the random process is
known as a parametric random process (with t as parameter) and as the parameter involved
is the development of time is also known as stochastic process. To define the stationary

61
process, the abundance of samples establishes also be absolute. But, for efficient aspiration,
the quantity of sample size and time duration of each specimen prerequisite to be as
expanded as possible to explain the process. An ensemble of time histories of stationary
process 𝑥(𝑡) is shown in Figure 6.1.
As shown in figure, 𝑥(𝑡1), 𝑥(𝑡2) … … . . 𝑥(𝑡𝑛) and so on are the random variables that can
assume any value across the ensemble. A stationary process (of order two) is one for which
the ensemble mean square values stays constant with the time shift τ. In this way, the
particular mean square values serve as the stationary dynamic process, which is the ensemble
mean square values. If the mean square value is access after subtracting the ensemble mean
(which likewise stays consistent with the time shift) from the values of random variables,
then is known as discrepancy. For illustration, if the random variable is 𝑥(𝑡), then the
discrepancy is given by,
𝜎𝑥
2
= 𝐸[{𝑥(𝑡1) − 𝑥̅(𝑡1)2}] (6.1)
In which 𝐸[ ] denotes the assumption or standard of the value and 𝑥̅(𝑡1) is the ensemble
mean of 𝑥(𝑡1). In this case, the stationary process is representing by an exclusive value of
the discrepancy 𝜎𝑥
2
. Apparently, for a zero mean process the discrepancy is equal to the mean
square value.
A stationary process is known as ergodic process if the ensemble means square value (or
discrepancy) is equal to the mean square value (or discrepancy). That is,
𝜎𝑥
2
= 𝜎𝑥
2
𝑖
where, 𝑖 = 1 … … . . 𝑁 (6.2)
In which N is the number of specimen s, i denotes ith sample, and
𝜎𝑥
2
=
1
𝑇
∫ [𝑥(𝑡1) − 𝑥̅(𝑡1)]𝑖
2
𝑇
0
𝑑𝑡 (6.3)

62
Figure 6.1 An ensemble of time histories of stationary process 𝒙(𝒕)
The adequacy of twin towers connected by an base isolated corridor decreasing the
displacement demand of structure is studied first by considering the stationary response of
the consolidated system with a broadband stationary stochastic base acceleration having root
mean square value as zero. A frequency domain approaches using the frequency response
matrix (FRM) is used for the non-classical damping nature of connected system. The FRM
of the system is given by
𝐻(𝜔) = [−𝜔2
𝑀 + 𝑖𝑤𝐶 + 𝐾]−1
(6.4)
The mean square of displacements sub-systems respectively are given by
𝜎2
= ∫ 𝜙𝑢𝑢(𝜔) 𝑑𝜙
∞
−∞
(6.5)

63
TABLE 6.1 RMS value of displacement responses under Random ground motion
Figure 6.2 Floor variation of RMS value of displacement responses under random
ground motion
Floors Connected Unconnected % Difference
1 0.0035 0.0119 70.59 %
5 0.0727 0.2458 70.54 %
10 0.1543 0.5269 70.71 %
11 0.0051 0.01 49 %
15 0.1061 0.2073 48.82 %
20 0.2237 0.4439 49.61 %
1 5 10 11 15 20
0.0
0.1
0.2
0.3
0.4
0.5
0.6
RMS
value
of
displacement
(m)
Floors
Connected
Unconnected

64
CHAPTER 7
Summary and Conclusion
The responses of a Twin towers are connected or unconnected with a base isolated corridor
is studied under seven different ground motions. Using the Eigen value method, the
governing differential equation of motion are solved and the system response is found.
Further a stochastic dynamic analysis is conducted and performance of unconnected twin
towers with base isolated corridor and compared with twin towers are connected with base
isolated corridor. The performance of structures with connected and unconnected twin
towers with base isolated corridor is compared by obtaining the different parameters. On the
basis of the results obtained, the following conclusion are drawn:
7.1 Conclusion
In these thesis the approach of sky bridge is linked with the twin towers. The impact of the
building is exists of flexibly linked with the sky bridge mass. The connected towers have
similar dynamic parameters if the development shows the better seismic response. The
impact of the method of seismic response is depends upon damping, stiffness and mass.
The reaction of linked buildings are decreasing the displacement with those of unconnected
towers. For the towers with different natural frequencies and similar natural frequencies.
 The maximum absolute acceleration of Tower 1 and Tower 2 is decreased by 24.22 %
and 10.01%, similarly displacement is reduced by 26.94 % and 30.78 %, and base shear
is decreased by 19.7 % and 13.99 %.
 With different natural frequencies the maximum base shear of Tower 1 and 3 is
decreased by 9.72 % and 8.15 %, similarly absolute acceleration is decreased by 10.00
% and 13.30 %, and the highest displacement is reduced by 29.88 % and 14.87 %.
 In harmonic ground motion the frequency domain responses of the amplitude of 1st
tower
at top floor is reduced by 54.26 %, and the 2nd
tower at top floor is reduced by 39.57 %.
 The connection of twin tower with base isolated corridor proves to be effective under
White noise process with RMS ratio is reduced by 70.71 % in 1st
tower at top floor.
Similarly, in 2nd
tower at top floor is reduced by 49.61 %.

65
7.2 Future scope of work
1. In the present study, the HDRB are used, but the effect of base isolation technique on
structures using friction pendulum system or N- Z bearing or other devices becomes a
matter of research.
2. In this study, only seismic type lateral forces are considered for analysis but the effect of
wind can also be investigated.
3. In present study the regular building are taken, but the effects of irregular building can
also be investigated.
4. The effects of more than 10 stories tower connected with base isolated corridor at a
different height can also be investigated.

66
REFERENCES
PAPERS
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equations for coupling linear structures using stiffness and damping elements.”.
Structural Control and Health monitoring, 20, 259-281.
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effects of a sky bridge for adjacent tall buildings.”, The structural design of Tall
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5) H. P. Zhu, D. D. Ge, X. Huang., 2011. “Optimum connecting dampers to reduce
the seismic responses of parallel structures.”, Journal of sound and vibrations,
330, 1931- 1949.
6) Jie Song, K. T. Tse, Yukio Tamura, Ahsan Kareem., 2016. “Aerodynamics of
closely spaced buildings: With application to linked buildings.”, Journal of wind
engineering and industrial aerodynamics, 149, 1-16.
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“Method of estimating equivalent mass of Multi-degree-of-freedom System.”,
JSME international journal, 268, 1638-1644.
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on Tall building and urban habitat, 3, 14-19.
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of shared tuned mass damper (STMD) to reduce vibration and pounding in
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67
11) Qing Lyu, Wensheng Lu, Weiqiang Wanf, Yue Chen., 2020. “Mechanism and
optimum design of shared tuned mass damper for twin-tower structures connected
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WEBSITES
WWW.SCIENCEDIRECT.COM

68
APPENDIX-A
NOTATION & ABBREVIATION
C Damping Matrix
M Mass Matrix
K Stiffness Matrix
𝜔𝑛 Natural frequency
T Time Period
x Displacement
𝑥̇ Velocity
𝑥̈ Acceleration
𝐻𝑧 Hertz
t Time step
P Constant
𝑇𝑎𝑙𝑙 Total Kinetic energy
𝑀𝑗 Equivalent mass
𝑋𝑗 Normalized by 𝑗𝑡ℎ
component of Eigen-vector
𝑓 Frequency
E Modulus of elasticity
I Moment of Inertia
W Normalized base shear
g Normalized acceleration
𝑝(𝑡) External force
PDF Probability density function
𝜎𝑥
2
Variance

69
𝑥̅ Mean value
𝐻(𝜔) Frequency response matrix
𝜎𝑝
2
Mean square value of displacement of primary system
𝜎𝑠
2
Mean square value of displacement of secondary system
𝜎𝑝𝑜 Root mean square

70
APPENDIX-B
Review Card Comments
Dissertation Phase 1: (Internal Review)

71
Dissertation Phase 1: (External Review)

72
Review Card Comments
Dissertation Phase 1I: (Internal Review)

73

74
APPENDIX-C
Plagiarism Report

75
SEISMIC BEHAVIOR OF TWIN
TOWER STRUCTURES CONNECTED
AT TOP BY AN ISOLATED
CORRIDOR
By SVIT VASAD 041

Seismic behaviour of twin tower structures connected at top by an isolated corridor

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