There are many civil engineering structures like buildings, bridges, dams, nuclear power plants, and many mores. Twin Tower building linked by a sky corridor are widely adopted owing to their advantages in terms of shape, convenient communication, and ability to provide an escape channel during fire.

1. SARDAR VALLABHBHAI PATEL INSTITUTE OF
TECHNOLOGY
Dissertation phase -2
SEISMIC BEHAVIOUR OF TWIN TOWER
STRUCTURES CONNECTED AT TOP BY AN
ISOLATED CORRIDOR
Prepared By :
SHAH HARSHIL J.
(190410720015)
Guided By:-
Dr. D. P. Soni
Head of department Civil engineering
SVIT- vasad

2. 1. Introduction
2. Literature
Review
3. Needs
and
Objectives
4. Scopes
5. Methodology
6.Validation
7. Numerical
Study
9. References
8. Conclusion
CONTENTS:

3. 1.INTRODUCTION
3

4.  There are many civil engineering structures like buildings, bridges,
dams, nuclear power plants, and many mores.
 Twin Tower building linked by a sky corridor are widely adopted
owing to their advantages in terms of shape, convenient
communication, and ability to provide an escape channel during fire.
 Seismic Isolation bearing are always used to connect the sky-
corridor & towers and additional damper are installed to dissipate
the energy.
 Twin towers are highly in demand due to its archi- structural design,
individual plan along with more space with same foundation
support.
 In Low- rise buildings the isolated corridor is used as a walk-way.
PETRONAS TOWER
(MALAYSIA)

5. 1) Elastomeric Bearing
2) High Damping Bearing
3) Lead Rubber Bearing
4) Flat Sliding Bearing
5) Curved Sliding Bearing and Pendulum Bearing
6) Ball & Roller Bearing
TYPES OF BASE ISOLATION SYSTEM:
High Damping Rubber Bearing
Ball & Roller Bearing

6. 2.LITERATURE
REVIEW
6

7. 1) Qing Lyu, et al., 2020/21. “Mechanism and Optimum Design of STMD
for Twin Tower Structure connected at top by an Isolated corridor ”
The concept of STMD twin tower linked by a sky- corridor using flexible joints. These
system is derived by 3 DOF. The effect of frequency ratio, mass ratio, tuning frequency
ratio of corridor & damping ratio of passive control devices on structural seismic response
is investigated. Optimum Parametric analysis is performed to minimize the displacement
of both towers. It investigated seismic performance of adjacent structure connected using
isolated corridor.
Journal Name: The Structural Design of Tall and Special Buildings, 29, 1-19

8. 8
2) Dong- guen Leel, et al., 2010. “Evaluation of coupling- control effects of sky-
bridge for adjacent tall buildings”
The coupling control effect of sky- bridge for adjacent tall building has been
investigated. Two building structures 42 & 49 stories connected by sky- bridge &
examples of building. The displacement & acceleration responses of coupled building
and reaction of bearings & member forces of sky- bridge were estimated in
comparison with uncoupled building. The coupling control effect are investigated in
this study using wind and earthquake excitations.
Journal Name: The Structural Design of Tall and Special Buildings, 21, 311-328

9. 9
3) Akira Nishimura, et al., 2011.“Base- isolated super high- rise RC building
composed of three connected towers with vibration control system”
The Island Tower Sky Club is a super high- rise RC apartment block constructed in
Fukuoka city, Japan. The buildings consists of three towers connected by three aerial
gardens. To achieve a high level of safety against earthquake and residential comfort
during strong wind, various techniques were adopted. These techniques are core-wall,
hybrid base isolation system & oil and zinc aluminum damper in aerial garden.
Seismic response analysis were conducted to confirm the performance of the structural
design. To estimate the structural control performance in detail, the time history of
absorbed energy are calculated.
Journal Name: Structural Concrete, 12, 94-108.

10. 10
4) Kazuto Seto, et al., 1986. “Method of estimating equivalent mass of Multi-
Degree-of-Freedom system”
To attain optimum design of vibration controllers to suppress many resonance peaks of
machine structure, it is necessary to know equivalent mass at location 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 calculated
by using eigenvectors.
Journal Name: JSME International journal, 238, 1638-1644.

11. Sr.
No
Title Author Journal name/ Publish
year/ Volume
Highlights
5 Dynamic
characteristics &
seismic response of
adjacent building
linked by discrete
dampers.
W. S. Zhang
and Y. L. Xu
Earthquake engineering
& structure dynamics,
1999, 28, 1163- 1185.
Coupling adjacent buildings using discrete visco-elastic dampers for
control of response to low and moderate seismic events is
investigated in this paper. The complex modal superposition
method is used to determine dynamic characteristics, modal
damping ratio and modal frequency, of damper-linked linear
adjacent buildings.An analytical method combining the complex
mode superposition method with the pseudo excitation method
has been proposed in this paper for investigating both dynamic
characteristics & seismic response of adjacent building connected
by visco-elastic dampers
6 Closed-form
equations for
coupling linear
structures using
stiffness
and damping
elements
Andy
Richardson,
et al.
Structural Control
Health Monit. (2011),
20, 259- 281.
Larger and more flexible structures are being constructed. As a
result, there is an increasing need for more effective,efficient,and
innovative displacement control strategies.Closed-form equations for
coupling parallel structures with stiffness and damping elements
were successfully derived.The accuracy of the equations was verified
through comparison with results published in earlier work using a
numerical optimization scheme. The closed-form equations
proposed herein simplify the design process when coupling
structures using stiffness and damping elements.

12. Sr.
No
Title Author Journal
name/Publish year/
Volume
Highlights
7 Aerodynamics of
closely spaced
buildings: With
application to
linked building.
Jie Song, et al. Journal of Wind
Engineering &
Industrial
Aerodynamics, 2015,
149, 1- 16.
This paper investigated inter-building & intra-building
aerodynamics correlation of linked building. (LBs, i.e., adjacent
tall buildings structurally connected by links such as sky-bridges).
Spatiotemporal wind pressure data on a typical LB setup with
different gap distances are used to examine inter-building
aerodynamic correlation. Intra-building aerodynamic correlation
of the LBs is examined using correlation coefficients and
trajectories, and then compared with those of an isolated
building.
8 N.Z. Parliament
Building seismic
protection by base
isolation
R. A. Poole,
J. E. Clendon
Bulletin of the New
Zealand national
society for
earthquake
engineering, 1991,
25, 147-160.
Parliament House is to be partially demolished and re-built,
extended within the existing parameters envelope, re-planned
except for the major public spaces, seismically upgraded by means
of base isolation and enhancement of existing foundation,
basement walls, ground floor, upper floor walls and floors.

13. Sr. No Title Author Journal
name/Publish year/
Volume
Highlights
9 Use of a shared
tuned mass
damper (STMD)
to reduce
vibration and
pounding in
adjacent structure
Makola M.
Abdullah, et al.
Earthquake
engineering and
structure dynamics,
2001, 30, 1185- 1201
Structures exposed to earthquakes experience vibrations that are
detrimental to their structural components.Structural pounding
is an additional problem that occurs when buildings experience
earthquake excitation. This research involves attaching adjacent
structures with a(STMD) to reduce both the structures vibration
and probability of pounding. Because the STMD is connected to
both buildings, the problem of tuning the STMD stiffness and
damping parameters becomes an issue.
10 Optimum
connecting
dampers to reduce
the seismic
responses of
parallel structures
H . P. Zhu,
D .D.Ge,
X. Huang
Journal of Sound
and Vibration, 2011,
330,1931- 1949.
Parameters of connecting dampers between two adjacent
structures and twin-tower structure with large podium are
optimized through theoretical analysis. The effectiveness of
VED and VFD is investigated in terms of the seismic response
reduction of the neigh-boring structures. Performances of
VED and VFD while being used to link 2-MDOF parallel
structures and twin-tower structure with large podium are
investigated. The application of coupling structure control strategy
in the twin-tower with large podium structure is also
investigated.

14. 14
1. In Previous papers on twin tower structure connected at top by an isolated
corridor Lead rubber bearing (LRBs) are used. It needs to carried out high
damping rubber bearing (HDRBs), Friction Pendulum bearing (FPB), Linear
motion bearing (LMBs) is not found.
2. To study the different base isolation system for tall buildings with similar
natural frequencies and different natural frequencies under wide range motion.
SUMMARY OF LITERATURE

15. 3.NEED &
OBJECTIVE OF
STUDY
15

16. 16
1. There is an increasing need for more efficient, effective and innovative displacement
control strategies along with communication between two buildings.
2. To control the responses of structure against the earthquakes with wide range of ground
motions.
3. To compare the responses of connected and unconnected building with base isolated
corridor.
NEED OF STUDY

17. 17
1. To study the effectiveness of seismically isolated bridge connecting two tower
structures at top.
2. To study the coupling effects of a sky- bridge for adjacent tall building with
similar natural frequencies and different natural frequencies.
3. To study the effectiveness of seismically isolated bridge under past record
earthquake of harmonic motion.
4. To study the effectiveness of seismically isolated bridge under Random
earthquake ground motion.
OBJECTIVES OF STUDY:

18. 18
1. To study the seismic behavior of tall building connected by an isolated corridor
under unidirectional earthquake ground motion.
2. The isolation systems considered for the study are high damping rubber bearing
(HDRBs).
3. The height of connected buildings (number of stories) are equal. However, their
natural frequencies can be different or similar.
4. Only seismic type lateral forces are considered for analysis i.e., effect of wind is
not considered.
4.SCOPE OF STUDY:

19. 5.METHODOLOGY
19

20.  The adjacent tower can be simplified as an SDOF
structure. Which is characterized by mass 𝑚 ,
Stiffness 𝑘 , damping 𝑐 .
 The natural frequency and viscous damping ratio of
towers are 𝜔1 =
𝑘1
𝑚1
& ζ1 =
𝑐1
2 𝑘1𝑚1
respectively.
 The sky corridor is connected to the tower using a
viscous and a linear spring. Which are installed in
parallel.
 It consists of mass 𝑚𝑑 , stiffness 𝑘𝑑 , damping
𝐶𝑑 .
Let, 𝜔𝑑 =
𝑘𝑑
𝑚𝑑
& ζ𝑑 =
𝑐𝑑
2 𝑘𝑑𝑚𝑑
Mathematical Model of Connected Building:

21. 𝑚1𝑢1 + 𝑐1𝑢1 + 𝑘1𝑢1 = −𝑐𝑑1(𝑢1-𝑢𝑑)-𝑘𝑑1(𝑢1-𝑢𝑑)-𝑚1𝑥𝑔 (1)
𝑚𝑛𝑢𝑛 + 𝑐2𝑢𝑛 + 𝑘2𝑢𝑛 = −𝑐𝑑2(𝑢𝑛-𝑢𝑑)-𝑘𝑑2(𝑢𝑛-𝑢𝑑)-𝑚𝑛𝑥𝑔 (2)
𝑚𝑑𝑢𝑑 + (𝑐𝑑1 + 𝑐𝑑2)𝑢𝑑 + 𝑘𝑑1 + 𝑘𝑑2 𝑢𝑑 = 𝑐𝑑1𝑢1 + 𝑐𝑑2𝑢𝑛 + 𝑘𝑑1𝑢1 + 𝑘𝑑2𝑢𝑛𝑚𝑑𝑥𝑔 (3)
Where u,𝑢, 𝑢 are the displacement,velocity,and acceleration of the masses and 𝑥𝑔 is ground acceleration.
The dynamic equation can be expressed in a matrix form as
M𝑥(t)+C𝑥 (t)+Kx(t)=-M𝑙𝑛𝑥𝑔 (4)
Where,
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)

22. Idealized building corridor connected system

23. 6.VALIDATION
23

24. Properties of building (Reference Qing Lyu, et al.):
Tower No. of
floors
Damping
ratio (%)
Floor mass (kg) Floor Stiffness
(N/m)
Natural
frequency (Hz)
1 10 2 1.02× 106 1.5× 109 0.912
2 10 2 1.40× 106 2.5× 109 1.005
Connected Tower 𝒌𝒅 (N/m) 𝒄𝒅 (N.s/m)
1-2 6.91× 106
3.31× 105

25. Frequencies of 1st & 2nd Tower based on MATLAB:
1st Tower
1 5.73154
2 17.066
3 28.0204
4 38.3482
5 47.8195
6 56.2225
7 63.3696
8 69.1012
9 73.2891
10 75.8399
2nd Tower
6.31585
18.8065
30.877
42.2577
52.6945
61.9542
69.8299
76.1458
80.7606
83.5715
3rd Tower
8.01390
23.8627
39.1784
53.6190
66.8618
78.6110
88.6042
96.6181
102.4737
106.0402
Similar
Frequencies
Similar
Frequencies
Different
Frequencies
Natural frequencies should be calculated based on given
formula:
So, 2πf
where, f = frequency
ωn = Natural frequency
For 1st building:
f = 5.73154/ 2π
ωn = 0.912
For 2nd building:
f = 6.31585/ 2π
ωn = 1.005
For 3rd building:
f = 8.013909/ 2π
ωn = 1.275

26. Properties of building (Based on Matlab Software):
Tower Natural frequency as
per Literature
Natural frequency obtained from
developed Program
Errors
(%)
1 0.912 0.912 0.00
2 1.005 1.005 0.00
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

27. Displacement(m)
0 5 10 15 20 25 30 35 40
-0.2
0
0.2
Time(sec)
Displacement responses obtained as per developed Program
..…….Unconnected
--------- Connected
Displacement responses as per Qing Lyu, et al. (2020)

28. Result from Reference of Qing Lyu, et al. (2020)
Displacement Response obtained as per developed Program

29. 7.NUMERICAL
STUDY
29

30. Behavior of connected Tower Studied by:
a) Recorded Earthquake Ground Motion
(i) Similar natural frequencies
(ii) Different natural frequencies
b) Harmonic Earthquake Ground Motion (In frequency domain)
c) Random Ground Motion

31.  To demonstrate the proposed method for connecting adjacent 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 parameters of each tower are listed in Table.
 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 reduce the structures to their equivalent MDOF models as
shown in figure. The parameters are used to determine the stiffness and damping properties between the
sky corridor and two towers in each example, as listed in Table.
a) Recorded Earthquake Ground Motion:

32. Frequencies into Time Period:
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

33. Sr.
No.
Earthquakes Magnitude Location PGA (g)
1 1940 Imperial Valley 6.95 El Centro 0.313
2 1987 Superstition Hills 6.7 El Centro Imp. Co. Center 0.512
3 1999 Chamoli Earthquake 6.4 Gopeshwar 0.359
4 1994 Northridge 6.7 Northridge-Saticoy St 0.529
5 1989 Loma Prieta 6.9 Capitola 0.420
6 1941 Imperial Valley 6.7 Canoga Park-Topanga Canyon 0.477
7 1979 El Centro 6.5 Mexico- US border 1.740
DETAILS OF GROUND MOTION COSIDERED IN THIS
STUDY:

34. RESPONSES OF BUILDING
WITH SIMILAR
NATURAL FREQUENCIES

35. 1940 Imperial Valley El Centro
Time Variation of Displacement 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

36. Time Variation of Base shear 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
-0.4
-0.2
0.0
0.2
0.4
0.6
Connected T-1
Unconnected T-1
0.4
0.3299
Base
shear
(W)
TIme (sec)
Connected T-2
Unconnected T-2
0.5612
0.4813

37. Time Variation of Acceleration under Imperial Valley 1940 El centro earthquake
-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
9.4696
7.0817
Acceleration
(m/sec
2
)
Time (sec)
Connected T-2
Unconnected T-2
10.9999
9.9066

38. Time Variation of Displacement under Imperial Valley 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

39. Time Variation of Base shear under Imperial Valley 1979 El centro earthquake
-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

40. Time Variation of Acceleration under Imperial Valley 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

41. 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
Seismic Response of Tower 1:

42. 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
Seismic Response of Tower 2:

43. RESPONSES OF BUILDING
WITH DIFFERENT
NATURAL FREQUENCIES

44. Properties of building (Reference Qing Lyu, et al.):
Tower No. of
floors
Damping
ratio (%)
Floor mass (kg) Floor Stiffness
(N/m)
Natural
frequency (Hz)
2 10 2 1.40*106
2.5× 109
1.005
3 10 2 1.60*106
4.6× 109
1.275
Connected Tower 𝒌𝒅 (N/m) 𝒄𝒅 (N.s/m)
2-3 8.82× 106
7.08× 105

45. Time Variation of Displacement under Imperial Valley 1941 El centro earthquake
-0.2
-0.1
0.0
0.1
0.2
0 5 10 15 20 25
-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

46. Time Variation of Base shear under Imperial Valley 1941 El centro earthquake
-0.6
-0.3
0.0
0.3
0.6
0 5 10 15 20 25
-0.6
-0.3
0.0
0.3
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

47. Time Variation of Acceleration under Imperial Valley 1941 El centro earthquake
-10
-5
0
5
10
0 5 10 15 20 25
-15
-10
-5
0
5
10
15
Acceleration
(m/sec
2
)
Connected T-3
Unconnected T-3
Different frequencies
10.2853
10.1942
Time (sec)
Connected T-2
Unconnected T-2
13.1599
11.4061

48. Time Variation of Displacement under Imperial Valley 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-2
Unconnected T-2
0.1296
Different frequencies
0.1211
Displacement
(m)
Time (sec)
0.2102
0.1766
Connected T-3
Unconnected T-3

49. Time Variation of Base shear under Imperial Valley 1979 El centro earthquake
-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-2
Unconnected T-2
0.5346
Different frequencies
0.5008
Base
shear
(W)
Time (sec)
Connected T-3
Unconnected T-3
0.5799
0.5126

50. Time Variation of Acceleration under Imperial Valley 1979 El centro earthquake
-15
-10
-5
0
5
10
0 10 20 30
-15
-10
-5
0
5
10
Connected T-2
Unconnected T-2
12.6196 Different frequencies
11.7407
Acceleration
(m/sec
2
)
Time (sec)
Connected T-3
Unconnected T-3
10.999
9.7244

51. Different frequencies Displacement (m) Base shear (W) Acceleration (g)
Sr.
No
Earthquake Connected Unconnected Connected Unconnected Connected Unconnected
1 1941 Imperial Valley 0.158 0.181 0.554 0.614 1.039 1.031
2 1979 El centro 0.177 0.2102 0.5008 0.5346 1.197 1.286
3 1940 Imperial Valley 0.107 0.114 0.461 0.524 1.099 0.195
4 1987 Superstition Hill 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
Seismic Response of Tower 3:

52. Different 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 0.1211 0.1296 0.513 0.579 0.991 1.121
3 1940 Imperial Valley 0.107 0.114 0.461 0.524 1.099 0.195
4 1987 Superstition Hill 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
Seismic Response of Tower 2:

53. b) SEISMIC RESPONSE OF
CONNECTED BUILDING
UNDER HARMONIC
LOADING (IN FREQUENCY
DOMAIN)
53

54. Governing equation of harmonic frequency Responses:
Consider a viscously damped SDOF system subjected to external force 𝑝 𝑡 . The equation of
motion for the system is
𝑚𝑢 + 𝑐𝑢 + 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)
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)

55. 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)
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
cos 𝜔𝑡− 2ζ
ω
ωn
sin 𝜔𝑡
𝑘 1−
ω
ωn
2 2
+ 2ζ
ω
ωn
2
(8)

56. 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),
𝑢 𝑡 = 𝑖𝜔𝐻𝑛 𝜔 𝑒𝑖𝜔𝑡 𝑢 𝑡 = −𝜔2𝐻𝑢 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
Similarly, for MDOF system these equation is used.

57. Frequency variation of amplitude of 1st tower at 1st 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

58. Frequency variation of amplitude of 1st tower at 5th floor under harmonic Response
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

59. Frequency variation of amplitude of 1st tower at 10th floor under harmonic Response
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

60. Frequency variation of amplitude of 2nd tower at 1st floor under harmonic Response
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
1
)
(H
w
)
Frequency (rad/sec)
Unconnected
Connected

61. Frequency variation of amplitude of 2nd tower at 5th floor under harmonic Response
0 5 10 15 20 25 30
0.0
1.0
2.0
3.0
4.0
Amplitude
(y
5
)
(H
w
)
Frequency (rad/sec)
Unconnected
Connected

62. Frequency variation of amplitude of 2nd tower at 10th floor under harmonic Response
0 5 10 15 20 25 30
0.0
2.0
4.0
6.0
8.0
10.0
Amplitude
(y
10
)
(H
w
)
Frequency (rad/sec)
Unconnected
Connected

63. Amplitude Frequency
Towers Floors Connected Unconnected Connected Unconnected
1 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
2 1 6.28 13.73 5.9 5.7
5 2.43 3.93 6.4 6.4
10 5.10 8.44 6.4 6.4
Responses under Harmonic Ground motion:

64. 64
c) SEISMIC RESPONSE OF
CONNECTED BUILDING
UNDER RANDOM GROUND
MOTION

65. Random Ground Motion:
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 = −𝜔2𝑀 + 𝑖𝑤𝐶 + 𝐾 −1 (6.1)
The mean square of displacements are given by
𝜎2
= −∞
∞
ϕ𝑢𝑢 𝜔 𝑑ϕ (6.2)

66. 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 %
RMS values of displacement responses under random ground
Motions:

67. Floors variation of RMS value of displacement under random ground motion
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

68. CONCLUSION
68

69. In general, the displacement responses of the connected towers are reduced compared with those of
the unconnected towers. For the towers with similar natural frequencies and different natural
frequencies.
 The maximum displacement of Tower 1 and 2 is reduced by 25.93 % and 31.88 %, base shear is
19.5 % and 14.16 %, & acceleration is 25.21 % and 9.99 %.
 In different natural frequencies the maximum displacement of Tower 1 and 3 is reduced by 29.83
% and 14.88 %, maximum base shear responses of tower 1 and 3 is 9.77 % and 8.13 %, &
maximum acceleration responses of tower 1 and 3 is 9.96 % and 13.34 %.
 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 %.

70. Scope of future 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 this study, we consider a regular building but the effects of irregular building can
also be investigated.
4. The effects of more than 10 stories towers connected with base isolated corridor at a
different heights can also be investigated.

72. Responses of DP-1 comment
Research Gap
Scope of work
Validation Parameters

74. REFERENCES
74

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78. Papers Communicated:
1) “Seismic Mitigation of Twin Tower Structures using an Isolated corridor”., Emerging
Research and Innovations in Civil Engineering (ERICE- 2021).
2) “Structural Vibration control of twin tower using isolated corridor under random ground
motion”., Intelligent Infrastructure in Transportation (i-TRAM 2021).