A
Dissertation on
“ANALYSIS OF STEEL BRACED RCC BUILDING USING
DESIGNED BASE ISOLATOR”
Submitted in partial fulfilment of the requirements for the degree of
Master of Technology
in
Civil – Structure
submitted by
Ms. Mohini Namdeo Khade
Under the guidance of
Dr. Y. M. Ghugal
Professor and Head
Department of Applied Mechanics
Government College of Engineering, Karad
Maharashtra State, India.
Shivaji University Kolhapur
(2019 - 20)
i
Government College of Engineering, Karad
(An Autonomous Institute of Government of Maharastra)
Applied Mechanics Department
CERTIFACATE
This is to certify that the dissertation entitled “Analysis
of Steel Braced RCC
Building Using Designed Base Isolator,” has been completed by Ms. Mohini
Namdeo Khade (18221101) in the academic year 2019-2020 in partial fulfillment of M-Tech
(Structural Engineering) dissertation work.
ii
DECLARATION
I hereby declare that I have performed, completed and written the dissertation entitled
“Analysis Of Steel Braced Rcc Building Using Designed Base Isolator,” It has not been
previously submitted for the basis of the award of any degree or diploma or other similar title
of this for any other diploma/examining body or university.
Place : Karad
Ms. Mohini Namdeo khade
Date:
(Roll no.- 18221101)
iii
DISSERTATION APPROVAL SHEET
Ms. Mohini Namdeo khade has done the appropriate work for the award of M. Tech in
Structural Engineering of government college of engineering, Karad, (An Autonomous
Institute of Government of Maharashtra).
Date:
Place:
Examiner
Name:
Signature:
Guide
Name: Dr. Y. M. Ghugal
Signature:
iv
ACKNOWLEDGEMENT
I have great pleasure in presenting this dissertation work report entitled
“ANALYSIS OF STEEL BRACED RCC BUILDING USING DESIGNED BASE
ISOLATOR” for partial fulfillment of the Masters of Engineering in Civil Structures.
I take this opportunity to express my deep sense of gratitude towards my guide
Dr. Y. M. Ghugal, Professor and Head, Applied Mechanics Department, Government College
of Engineering, Karad for his well-formulated and indispensable guidance in the
accomplishment of this report, without which this would not have been possible.
I extend my sincere thanks to Dr. A. T. Pise, Principal, Government College of
Engineering, Karad for providing institutional facilities, as well as extending all kinds of cooperation.
I will fail in my duties if I do not mention my friends and classmates who were a
constant source of inspiration and helped me during the project.
Last but not the least; I am thankful to my parents and brother who helped me directly
or indirectly for my completion of this course. I am thankful to all those who wished me
success. Above all I render my gratitude to all who gave me inspiration and strength to
complete this work.
Place: - Karad.
Date: Ms. Mohini Namdeo Khade.
M.tech
(Structural engineering)
v
ABSTRACT
Effect of earthquake can be very hazardous to the structure influenced by these forces. There
are many traditional methods for protection of structure against earthquake effects. But there
are some disadvantages in these methods. Increasing strength and stiffness are some of the
traditional methods. But they lead to higher sections and result in uneconomic design. To
overcome these disadvantages associated with the traditional method, many vibration-control
measures, called structural control, have been studied and remarkable advances in this respect
have been made over recent years. This paper describes the effect of use of steel bracing,
dampers and base isolator (lead rubber bearing) in a structure subjected to earthquake motion.
The structure is designed in ETABs and then bracings, dampers, base isolator are applied
respectively in 3 different models and results are compared. Force of ground motion that is
earthquake force is applied to structure by using seismic coefficient method. Base isolated
structure gives improved performance against seismic vibrations than conventional structure.
The essential characteristics of base isolation system are isolation, energy dissipation, and
restoring mechanism. It is shown that under design conditions, all base isolators can
significantly reduce the acceleration transmitted to superstructure. Bracing and dampers are
also useful reduction of storey drift and base shear.
vi
CONTENTS
List of symbols
List of Abbreviations
List of Figures
List of Table
1. INTRODUCTION
1.1 Background
1.2 Behavior of structure during earthquake
1.3 Base isolation – introduction
1.4 Basic principle of base isolation
1.5 Basic requirements of base isolation
1.6 Types of base isolation devices
1.7 Effect of base isolation on structure
1.8 Properties of lead rubber bearing
1.8.1 Diagrammatic representation of LRB
1.8.2 Design formulae for LRB
1.8.3 Some parameters of LRB
1.8.4 Advantages of LRB
1.9 Bracing systems
1.9.1 Advantages of bracing systems
1.9.2 Types of bracing systems
1.9.2.1 Concentric bracings
1.9.2.2 Eccentric bracings
1.10 Dampers
1.11 Definitions of some parameters
2. LITERATURE SURVEY
2.1 General
2.2 Remark on literature review
3. SYSTEM MODELLING
3.1 Introduction
3.2 Problem statement
3.3 Steps for modeling
3.4 Formulae for calculation of base shear
3.5 Design of base isolator
3.6 Calculation for Design of LRB
4. RESULT AND DISCUSSION
4.1 Calculation of base shear by seismic coefficient method
4.2 Calculation of base shear as per UBC 97 formulae
4.3 Design formulae for LRB
4.4 Result for design of LRB
4.5 Results from ETABs
4.5.1 Max story displacement of various structure
4.5.2 Storey drift of various structure
4.5.3 Storey shear of various structure
4.5.4 Overturning moment of various structure
4.5.5 Story stiffness of various structure
1
2
2
3
3
4
6
6
7
7
8
8
8
9
9
9
11
11
12
15
18
19
20
21
33
33
34
37
38
39
40
46
46
47
48
49
50
vii
4.5.6 Time period of various structure
5. CONCLUSIONS
5.1 Conclusions
5.2 Scope of future work
References
Acknowledgement
51
53
53
54
viii
NOMENCLATURE
VB - Base shear = Ah x W
Z - Zone factor
I - Importance factor
R - Response reduction factor
TD - Time period
Na - Near source factor
Nv - Near source factor
Ca - Seismic coefficient
Cv - Seismic coefficient
BD - Damping coefficient
β - Effective damping
W - Maximum support reaction
𝐾2
𝐾1
- Post yield ratio
ix
LIST OF FIGURES
FIG
1.1
1.2
1.3
1.4
1.5
1.6
1.7
3.1
3.2
3.3
3.4
3.5
3.6
3.7
3.8
3.9
3.1
3.11
3.12
3.13
3.14
3.15
4.1
4.2
4.3
4.4
4.5
4.6
4.7
ILLUSTRATION
Structure without Base isolator and with base isolator
Elastomeric bearing
Roller and ball bearing
High Damping rubber bearing
Lead rubber bearing
Curved slider
Diagrammatic representation of LRB
New mode initialization
Edit story and grid system data
Material property data
Frame section property data
Restraining joints
Seismic loading
Assigning base isolator
Frame section property data
Seismic loading
Result window
Plan of RCC building
Elevation of RCC building
Elevation of RCC building with bracing
Elevation of RCC building with dampers
Elevation of RCC building with base isolator
Cross sectional properties of LRB
Graphical representation of max story displacement
Graphical representation of max story drift
Graphical representation of story shear
Graphical representation of overturning moment
Graphical representation of story stiffness
Graphical representation of time period
PAGE
NO
3
4
4
5
5
6
7
21
21
22
23
24
24
25
26
26
27
27
29
30
31
32
44
45
46
47
48
49
50
x
LIST OF TABLES
FIG
ILLUSTRATION
PAGE
NO
1.1 Types of dampers
11
1.2 Seismic intensity and zone factors based on seismic zone
13
4.1
4.2
4.3
4.4
4.5
4.6
4.7
4.8
36
43
44
45
46
47
48
49
Calculation of base shear
Summary of LRB properties
Values of maximum storey displacement
Values of storey drift
Values of storey shear
Values of overturning moments
Values of storey stiffness
Values of time period
xi
CHAPTER 1
INTRODUCTION
1.1 Background
For earthquake resistant design of buildings, the traditional method, i.e., increasing the
strength, stiffness, and ductility of the members, has been in common use for a long time. So,
dimensions of structure and the material consumption are expected to be more, which tends to
higher cost of the buildings as well as larger seismic responses due to requirement of larger
stiffness of the structures and leads to uneconomic conditions. Thus, the efficiency of the
traditional method is somehow disadvantageous. To overcome these disadvantages, many
vibration-control measures, have been studied, and called as structural control methods. The
remarkable advances in this respect have been made over past years. Structural Control is a
diverse field of study. Structural Control is the one of the areas of current research aiming to
minimize vibrations in structure during events such as earthquakes and strong winds. In views
of different vibration absorption methods, structural control is classified into active control,
passive control, hybrid control, semi-active control. Base isolation is a passive vibration control
system that does not require any external power source for its operation and utilizes the motion
of the structure to develop the control forces. This technology may keep the building to remain
essentially elastic and therefore ensuring safety during earthquakes of larger magnitudes. Since
a base-isolated structure has fundamental frequency lower than both its fixed base frequency
and the dominant frequencies of ground motion, the first mode of vibration of isolated structure
involves deformation only in the isolation system whereas superstructure remains almost rigid.
Viscous dampers are hydraulic devices that dissipate the kinetic energy of seismic events and
cushion the impact between structures. These are versatile. They can be designed to allow free
movement and controlled damping of a structure to protect from seismic events, wind load, or
thermal motion. The use of different types of bracing made the construction of the skyscraper
possible. Bracings are strong in compression. Increase in lateral load resisting capacity of
structure can be considered by use of bracing. When bracings are positioned in Steel frame it
behaves as diagonal compression strut and transmits compression force to another joint.
Variations in the stiffness of columns can influence the mode of failure and lateral stiffness of
the bracing.
1
1.2 Behavior of structure during earthquake
When earthquake vibrations occur, they transmits seismic waves and they cause ground
motion inside the surface of earth. As structure is resting on the earth’s surface, this ground
motion is also transmitted into them. The base of the structure moves along with with the
ground motion but the roof of structure tends to retain its position. But the roof is also forced
to move as the walls and columns of the structure are connected. Under such conditions, the
structures generally undergo brutal damage or tend to collapse. This damage can be reduced if
the structure is ductile. Ductility is defined as an ability of a structure to face huge plastic
deformation without loss in ultimate strength. The ductility of a structure ensures to predict the
amount of dissipation of seismic energy that may be dissipated through plastic deformations,
which is a very important factor for structural design subjected to seismic loads.
1.3 Base isolation – introduction
Base isolation is separation of upper structure from base or from substructure by
changing of fixed joint with flexible one. Increasing of flexibility is done by the inserting of
such separating elements in structure, called as base isolators. Usually, these isolators are
inserted between foundation and upper structure. Seismic isolation system absorbs larger part
of seismic energy. Therefore, transmission of vibrations of soil to upper structure are
considerably reduced. But in case of base isolated building, as the ground moves, inertia tends
to keep structure in place resulting in the imposition of structure with large displacement in
different stories. For base isolation structure the situation is quite different. In such cases, the
whole upper structure gets a displacement (which naturally remains in limits) and the relative
displacement of different stories is so small that the structure can withstand a comparatively
high seismic tremor with a low seismic loading in safe, efficient and economic manner. Base
isolation is a passive control system; it does not require any external force or energy for its
activation.
2
Fig. 1.1. structure without Base isolator and with base isolator
1.4 Basic principle of base isolation
Principle of using base isolation can be stated as response of a respective structure is
modified such that ground below the structure is capable of moving without transmitting the
motion to above structure. In other words, principal of base isolation system is to rectify the
response of the structure so that the ground can move below the structure without transferring
these motions into the superstructure. In an ideal system to achieve this flexibility in buildings
this separation would be total. But in the real practices, it is necessary to have a vertical support
to transfer the vertical loads to the base. Base isolation reduces the seismic demand of the
structure instead of increasing the capacity of the structure.
The relative displacement due to earthquake, between ground and perfectly rigid
structure is zero. In case of an ideal flexible structure, the relative displacement of structure is
equal to ground displacement. Therefore, displacement of real structures lies between the two
explained above as no structure is perfectly rigid or flexible.
1.5 Basic requirements of base isolation
Basic requirements of base isolation are as follows 1. Flexibility
2. Damping
3. Resistance against vertical loads and other service loads
1.6 Types of base isolation devices
3
Types of base isolation devices are as follows1) Elastomeric bearingThese are formed by layers of synthetic rubber or natural rubber in thin layers laid
horizontally and it is bounded between steel plates. They are able to support high vertical load
with less deformations. They become flexible when subjected to lateral loads.
Fig. 1.2. Elastomeric bearing
2) Roller and ball bearingsFor isolation application in machinery isolation, roller and ball bearing are used.
Fig. 1.3 Roller and ball bearing
4
3) High damping rubber bearingHDR bearing is made of special rubber with very high damping attribute. It is
sandwiched together with layers of steel without any lead plugs. Rubber enable to absorb large
energy of earthquake due to its elasticity.
Fig. 1.4. High Damping rubber bearing
4) Lead Rubber BearingLRB isolators are composed of cylindrical rubber bearings. These are reinforced
with steel shims. Shims are placed as alternate layers. Steel plates are also provided at the two
ends of the isolator. The steel shims increase the load carrying capacity, thus the structure
behaves stiff under vertical loads and flexible under horizontal loads.
Fig. 1.5. Lead rubber bearing
5
5) Curved slider or pendulum bearingThis bearing is used in bridges as base isolator in earthquake prone areas. These are
also called as friction pendulum isolators.
Fig. 1.6 Curved slider
1.7 Effect of base isolation on structure
In base isolation process, installation of mechanisms is done. This process decouples the
structure or its contents from ground which is subjected to earthquake having potential of
damaging the structure. This decoupling can be achieved by increasing flexibility of system.
When seismic isolation or base isolation is used, overall structure considerably become more
flexible and also, provision should be made for respective horizontal displacement.
When seismic isolation system is provided with hysteretic force displacement
characteristics, they can provide desired properties of isolator such as flexibility, force
limitation under horizontal earthquake loads, high damping, together with high stiffness under
smaller horizontal loads to limit wind induced motions.
When isolator is provided at base of structure, it increases the natural period of overall
structure and therefore decrease in its acceleration response to earthquake generated vibrations
can be seen. Further decrease in response occurs with addition of damping. Increase in period
along with damping can considerably reduce effect of the earthquake on structure so that less
damaging loads and deformations are imposed on structure and its components.
6
1.8 Properties of lead rubber bearing
1.8.1 Diagrammatic representation of LRB
Fig. 1.7 Diagrammatic representation of LRB
1.8.2 Formulae for design for LRB
The formulae for design of lead rubber bearing are as follows –
𝑔
𝐶𝑣 𝑇𝐷
•
Design displacement = 𝐷𝐷 =
•
Effective stiffness = 𝐾𝑒 =
•
Energy dissipation per cycle = 𝑊𝐷 = 2𝜋 𝐾𝑒 𝐷𝐷 2 𝛽
•
Force at 𝐷𝐷 = 𝑄𝐷 =
•
Stiffness in rubber = 𝐾2 = 𝐾𝑒 −
•
Yield displacement = 𝐷𝑦 =
𝑤
𝑔
4𝜋 2
𝑥
𝐵𝐷
2𝜋
𝑥 (𝑇 )2
𝐷
𝑊𝐷
4𝐷𝐷
𝑄𝐷
𝐷𝐷
𝑄𝐷
𝐾1 −𝐾2
𝑊𝐷
•
𝑄𝐷 required =
•
Revised stiffness of rubber = 𝐾𝑒 𝑟𝑒𝑞𝑢𝑖𝑟𝑒𝑑 = 𝐾𝑒 −
•
Thickness of rubber isolator = 𝑡 =
•
Area of isolator = 𝐴𝑙𝑟𝑏 =
4(𝐷𝐷 −𝐷𝑦 )
𝑄𝐷
𝐷𝐷
𝐷𝐷
𝛾
𝐾𝑒 𝑟𝑒𝑞𝑢𝑖𝑟𝑒𝑑 . 𝑡
𝐺
7
𝐷𝑖𝑎𝑚𝑒𝑡𝑒𝑟 𝑜𝑔 𝐿𝑅𝐵
•
Shape factor = S = 4 𝑥 𝑡ℎ𝑖𝑐𝑘𝑛𝑒𝑠𝑠 𝑜𝑓 𝑠𝑖𝑛𝑔𝑙𝑒 𝑟𝑢𝑏𝑏𝑒𝑟 𝑙𝑎𝑦𝑒𝑟 =
•
Shape factor = S = 2.4 𝑓𝑣
•
Compression modulus = 𝐸𝑐 = 6𝐺𝑆 2 (1 −
•
Horizontal stiffness of isolator = 𝐾𝐻 =
•
Vertical stiffness of isolator = 𝐾𝑣 =
•
Area of hysteresis loop = Ah = 4𝑄𝐷 (𝐷𝐷 − 𝐷𝑦 )
•
Yield strength = 𝐹𝑦 = 𝑄𝐷 + ( 𝐾2 . 𝐷𝑦 )
𝑑𝑙𝑟𝑏
4𝑡𝑟
1 𝑓
ℎ
6𝐺𝑆 2
𝐾
)
𝐺 𝑥 𝐴𝑙𝑟𝑏
𝑡𝑟
𝐸𝑐 𝑥 𝐴𝑙𝑟𝑏
𝑡𝑟
1.8.3 Some properties of LRB
Shear modulus of lead rubber = > Lowest about 10 MPa, Highest about 130 MPa
1.8.4 Advantages of LRB
•
Lead core provides rigidity and energy dissipation under high lateral loads
•
Shims help in boosting the load carrying capacity
•
Structure become stiff when subjected to vertical loads and flexible when subjected to
horizontal loads.
•
Environmental protection is achieved by rubber which covers entire bearing.
•
Time period of the respective structure is increased when provided to RCC building.
1.9 Bracing systems
The primary purpose of all kinds of structural systems used in the building type of structures
is to transfer gravity loads (dead load, live load and snow load) effectively. In addition with
these vertical loads, buildings are also subjected to lateral loads caused by wind, blasting or
earthquake. Such lateral loads can produce sway movement or cause vibration or develop high
stresses. Hence, for the structure, it is very important to have sufficient strength against vertical
loads along with adequate stiffness to resist lateral forces.
For this purpose, bracing system plays important role. Use of bracing system for structure
effectively minimizes the lateral displacements. Bracings are classified as concentric, eccentric
and knee bracing systems. Bracing is an economical and highly efficient method to increase
the stiffness laterally in the framed structures. Bracing is efficient because the diagonal bracing
works in axial stress and therefore call for minimum member sizes by providing the stiffness
8
and strength against horizontal shear. Thus use of bracing system results in reduction of lateral
movement as well as torsional motion of the structures under seismic loading.
1.9.1 Advantages of bracing systems
The Advantages of bracing system are as follows,
•
Increase in stiffness.
•
Less storey drift.
•
Base shear is increased.
•
Structure becomes more resistant against earthquake.
•
Peak displacement is minimum
1.9.2 Types of bracing systems
1.9.2.1 Concentric bracingsVarious types of concentric bracing are :Diagonal bracing –
Trussing or triangulation is formed by inserting diagonal structural members into rectangular
areas of a structural frame, helping to stabilize the frame. If a single brace is used, it must be
sufficiently resistant to tension and compression. These systems rely on both compression and
tension braces for stability, and so the stiffness and strength of the compression braces must be
explicitly accounted for. Diagonal bracing is a structural component of just about any building.
It provides lateral stability preventing collapse of a wall, deck, roof, etc.
X bracing –
Cross-bracing (or X-bracing) uses two diagonal members crossing each other. These only
need to be resistant to tension, one brace acting to resist sideways forces at a time depending
on the direction of loading. As a result, steel cables can also be used for cross bracing. However,
this provides the least available space within the façade for openings and results in the greatest
bending in floor beams.
V bracing –
This involves two diagonal members extending from the top two corners of a horizontal
member and meeting at a centre point at the lower horizontal member, in the shape of a V.
Inverted V-bracing (also known as chevron bracing) involves the two members meeting at a
centre point on the upper horizontal member.
Both mean that the buckling capacity of the compression brace is likely to be significantly
less than the tension yield capacity of the tension brace. This can mean that when the braces
9
reach their resistance capacity, the load must instead be resisted in the bending of the horizontal
member. Bracing where a pair of braces, located both above beam, terminates at a single point
within the clear beam span.
1.9.2.2 Eccentric bracing
In an eccentrically braced frame bracing members connect to separate points on the
beam/girder. The beam/girder segment or “link” between the bracing members absorbs energy
from seismic activity through plastic deformation.
Eccentric bracings reduce the lateral stiffness of the system and improve the energy
dissipation capacity. Due to eccentric connection of the braces to beams, the lateral stiffness of
the system depends upon the flexural stiffness of the beams and columns, thus reducing the
lateral stiffness of the frame. The vertical component of the bracing forces due to earthquake
causes lateral concentrated load on the beams at the point of connection of the eccentric
bracings.
1.10 Dampers
Damper is a type of active control device for earthquake resistance. It absorbs the vibrations
received from seismic energy. The dampers reduce the lateral force caused by the earthquake.
Earthquake creates large amount of kinetic energy or strain energy on the structure. These
energies are absorbed by structure or transmitted to structure. Dampers can absorb and dissipate
this energy saving structure from harmful effects of earthquake. There are various types of
dampers and are as follows –
a) Friction dampers
b) Viscous dampers
c) Yielding dampers
d) Magnetic dampers
e) Tuned mass damper
10
Table 1.1. Types of dampers
Type of damper
Mode of energy absorption
Friction Dampers
Viscous dampers
Applications
Energy friction between the two
surfaces by rubbing with each other
As a bracing, retrofitting
Energy is absorbed by passing the
fluid in between arrangement of
piston and cylinder
In automobiles
Low cost
As bracing
Used with base isolators
Yielding dampers
Energy is absorption is achieved by
metal components that has good
ductility and yield stiffness.
To reduce inter story drift
Magnetic
dampers
Energy is absorbed by magnetic
induction
For vibration control
Energy is absorbed by using springs,
fluid, or pendulums
Transmission lines
Tuned
dampers
mass
Automobiles
Tall buildings
1.11 Definitions of some parameters from IS-1893:2016 1. Damping
The effect of internal friction, imperfect elasticity of material, slipping, sliding, etc in
reducing the amplitude of vibration and is expressed as a percentage of critical damping.
2. Design Horizontal Acceleration Coefficient (Ah)It is a horizontal acceleration coefficient that shall be used for design of structures.
The design horizontal seismic coefficient Ah for a structure shall be determined by the
following expression𝑧
𝐴ℎ = 2 x
𝑆𝑎
𝑔
𝐼
x𝑅
3. Design Lateral Force It is the horizontal seismic force prescribed by this standard, that shall be used to design
a structure. It is calculated as follows –
VB = 𝐴ℎ 𝑥 𝑊
4. Natural Period (T)
Natural period of a structure is its time period of undamped free vibration. As per IS:
1893- 2016, time period is calculated as per clause 7.6. It is as follows -
11
5. Response Reduction Factor (R)
It is the factor by which the actual base shear force, that would be generated if the
structure were to remain elastic during its response to the Design Basis Earthquake (DBE)
shaking, shall be reduced to obtain the design lateral force.
6. Response Spectrum
The representation of the maximum response of idealized single degree freedom
systems having certain period and damping, during earthquake ground.
motion. The maximum response is plotted against the undamped natural period and for
various damping values, and can be expressed in terms of maximum absolute acceleration,
maximum relative velocity, or maximum relative displacement.
7. Seismic Mass
It is the seismic weight divided by acceleration due to gravity.
8. Seismic Weight (W)
It is the total dead load plus appropriate amounts of specified imposed load.
9. Structural Response Factors (Sa/g)
It is a factor denoting the acceleration response spectrum of the structure subjected to
earthquake ground vibrations, and depends on natural period of vibration and damping of the
structure.
10. Zone Factor (Z)
It is a factor to obtain the design spectrum depending on the perceived maximum
seismic risk characterized by Maximum Considered Earthquake (MCE) in the zone in which
the structure is located. The basic zone factors included in this standard are reasonable estimate
of effective peak ground acceleration. Values of seismic zone factors are given in IS:1893 2016, in table 2, clause 6.4.2
Table 1.2. Seismic intensity and zone factors based on seismic zone
Seismic zone
II
III
IV
V
Seismic intensity
Low
Moderate
Severe
Very severe
Z
0.10
0.16
0.24
0.36
12
11. Time History Analysis
It is an analysis of the dynamic response of the structure at each increment of time,
when its base is subjected to a specific ground motion time history.
12. Base Dimensions (d)
Base dimension of the building along a direction is the dimension at its base, in metre,
along that direction.
13. Centre of Mass
The point through which the resultant of the masses of a system acts. This point
corresponds to the centre of gravity of masses of system.
14. Centre of Stiffness
The point through which the resultant of the restoring forces of a system acts.
15. Design Seismic Base Shear (Vb)
It is the total design lateral force at the base of a structure.
16. Height of Floor (hi)
It is the difference in levels between the base of the building and that of floor i.
17. Height of Structure(k)
It is the difference in levels, in metres, between its base and its highest level.
18. Moment-Resisting Frame
It is a frame in which members and joints are capable of resisting forces primarily by
flexure.
19. Ordinary Moment-Resisting Frame
It is a moment-resisting frame not meeting special detailing requirements for ductile
behaviour.
20. Special Moment-Resisting Frame
It is a moment-resisting frame specially detailed to provide ductile behaviour and
comply with the requirements given in IS 4326 or IS 13920 or SP6(6).
21. Storey
It is the space between two adjacent floors.
22. Storey Drift
It is the displacement of one level relative to the other level above or below.
23. Storey Shear
It is the sum of design lateral forces at all levels above the storey under consideration.
13
CHAPTER 2
LITERATURE SURVEY
2.1 General
Kalantari, Naderpour, Vaez [1] investigated the effect of using two different types of
seismic isolators in decreasing the base shear and story shears of structure. Four structural
models with 2, 5, 8 and 12 stories for three cases including fixed-base, lead-rubber isolator
and friction pendulum isolator with different stiffness have been modeled. All models have
been analyzed under earthquake characteristics of Manjil, Naghan, Tabas and Elcentro
using a nonlinear finite element program. The results indicate that by using lead-rubber
isolators, maximum displacements of stories in low-rise structures have been increased in
comparison with fixed-base model. In contrast, in majority of cases, applying the FPS
isolators doesn't guarantee the displacement requirement. Also by using isolators, number
of cycles related to displacement response would be decreased especially in models with
lower stories. In short base isolated structures, the decrease in plastic hinge formation
percent of elements was much more than in fixed-base structures.
Providakis [2] performed nonlinear time history analyses using a commercial structural
analysis software package to study the influence of isolation damping on base and
superstructure drift. Various lead-rubber bearing (LRB) isolation systems were
systematically compared and discussed for aseismic performances of two actual reinforced
concrete (RC) buildings. Parametric analysis of the buildings fitted with isolation devices
was carried out to choose the appropriate design parameters. The efficiency of providing
supplemental viscous damping for reducing the isolator displacements while keeping the
substructure forces in reasonable ranges was also investigated.
Braga, Laterza [3] they had done experimental studies on a series of dynamic snap-back
tests. This test was carried out on a residence building in southern Italy at Rapolla (Potenza–
Basilicata). The aim of the research was to investigate the seismic behavior of low-rise base
isolated structures mounted on rubber bearings only, or with a hybrid isolation system
(sliding bearings for isolation and steel rubber bearings to have a re-centering force).
Jalali, Narjabadifam [4] carried out investigation on the effect of superstructure
characteristics on performance of multi-story buildings isolated with lead-plug laminated
rubber bearings the superstructure characteristics considered at this research were
14
superstructure mass, superstructure stiffness and superstructure damping, which were
varied in the range that was compatible with engineering practice. Comparing the study
results it has been observed that, there is optimum amount for each of the dynamic
properties of the superstructure which will make design criteria achievable in seismic baseisolation of multi-story buildings. To this purpose, five reinforced concrete moment
resisting frame buildings with two, five, nine, fourteen and twenty stories were considered.
They were designed according to UBC97, in fixed-base form and base-isolated form. Five
different amounts for superstructure base-mass were assigned and 25 related models were
created. Variations in superstructure stiffness and superstructure damping were considered
in the same manner. All of 85 model buildings were subjected to five ground motion
records which have been scaled to have PGA = 0.4g. Nonlinear time-history analyses of
created models were conducted by using ETABS 8.5.0. Fundamental periods, modal
participation factors and base-shears were studied for all of the model buildings. Comparing
analysis results in term of base shear variations for different parameters considered, it was
concluded that, superstructure characteristics have considerable effect on performance of
isolated systems and optimal performance of base isolated multi-story buildings was
achievable by modifying superstructure characteristics.
Wen, Baifeng [5] put forward based on codes (seismic code, 2001). For first step in design
was base isolator design and to collect basic data for structure. For second step detail design
was considered, time history analysis was adopted. Computer software based on above
method with user friendly interface, pre-processor, and post-processor was developed for
practical engineering design of superstructure and foundation.
Sangle, Bajoria, Mhalungkar [6] studied the seismic analysis of high rise steel frame with
and without bracings. Pattern of bracings can extensively modify the global seismic
behavior of the framed steel building. In this paper nonlinear time history analysis is carried
out on high rise steel building with natural frequency, natural time period, mode shapes,
inter storey drift, and base shear. Further optimization study was carried out to decide
suitable type of bracing by keeping inter storey drift, total lateral displacement and stress
level within permissible limits.
Ryan [7] studied the system considered is a generic elastic single-bay multistory frame
structure supported on an isolation system with a bilinear force-deformation relation. Three,
six, and nine-story versions of the superstructure frame are used, each with story height 12
15
ft and bay width 24 ft.The peak response of the models described previously is determined
by nonlinear response history analysis (RHA) to the SAC LA 10% in 50 years suite of
motions [Sommerville et. al. 1998], representative of the design basis earthquake in a non
near fault region in Los Angeles.
Su [8] made study of combining the desirable features of the EDF base isolator and the RFBI system, a new base-isolator design was proposed. It was suggested to replace the
elastomeric bearings of the EDF base-isolation system by the R-FBI units, i.e., the upper
surface of the R-FBI system in the modified design is replaced by a friction plate. As a
result, the structure can slide on its foundation just as in the EDF base-isolation system.
The behavior of this base isolator, referred to as the sliding resilient-friction (SRF) baseisolation system.
Murnal [9] the essential characteristics of an effective base isolation system are isolation,
energy dissipation, and restoring mechanism. Some friction type base isolation systems
proposed earlier have been found to be very effective in reducing the structural response
and incorporate simple restoring mechanisms through gravity. However these isolators are
effective only under certain excitation and structural characteristics. To overcome these
limitations the authors have recently developed a new isolation system called the variable
frequency pendulum isolator ~VFPI! that has been found to be very effective under a
variety of structure and excitation characteristics. In this paper, the mathematical
formulation for the three dimensional behavior of an asymmetric structure isolated by a
sliding type isolator, with particular reference to VFPI has been presented.
Su [10] made comparative study of effectiveness of various base isolators is carried out.
These include the laminated rubber bearing with and without lead plug and several
frictional base isolation systems. The structure is modeled as a rigid mass and the
accelerograms of the NOOW component of the El Centro 1940 earthquake and the N90W
component of the Mexico City 1985 earthquake are used. The performances of different
base isolation devices under a variety of conditions are evaluated and compared.
Combining the desirable features of various systems, a new design for a friction base
isolator is also developed and its performance is studied. It is shown that, under design
conditions, all base isolators can significantly reduce the acceleration transmitted to the
superstructure.
16
Nagajyothi, Ghorpade [11] studied the design of lead rubber bearing system and high
damping rubber bearing system for isolated structure for long periods for 5 storey building.
Warn, Ryan [12] have made a review of seismic isolation for buildings and research needs.
Keerthana, Kumar, Balamonica [13] studied seismic response reduction of structures using
base isolation and compared with linear models.
Kelly [14] has made research on earthquake resistant design with rubber.
Taniwangsa and Kelly [15] made studies on seismic isolation for housing in developing
regions.
Kelly [16] has made study on seismic base isolation: review and bibilography.
Chopra, Clough, Clough [17] analysed resistance of buildings with a soft first storey.
Skinner, Kelly, Heine [18] studied use of hysteretic dampers for earthquake resistant
structures.
Nagarjaiah Reinhorn ,Constantinou [19] made experimental study of sliding isolated
structures with uplift restraint.
Kelly [20] studied the role of damping in seismic isolation.
2.2 Concluding remark on literature review
After reviewing many references, it can be concluded that base isolated structure gives
improved performance against seismic vibrations than conventional structure. In base isolated
structures, the decrease in formation of plastic hinge formation is more than in fixed base
structures. The essential characteristics of base isolation system are isolation, energy
dissipation, and restoring mechanism. But some isolators like friction type base isolator are
effective only under certain excitations and structural characteristics. It is shown that under
design conditions, all base isolators can significantly reduce the acceleration transmitted to
superstrucrure.
This paper considers the use of bracings, dampers, and lead rubber bearing and comparison
of each of this with conventional RCC building. One structure of RCC building is modelled
and analysed in ETABs and then each of above mentioned is applied separately for same model
and analysed. Then some different parameters are compared and result is discussed.
17
CHAPTER 3
SYSTEM MODELING
3.1 Introduction
For earthquake resistant design of buildings, the traditional method, i.e., increasing the
strength, stiffness, and ductility of the members, has been in common use for a long time. So,
dimensions of structure and the material consumption are expected to be more, which tends to
higher cost of the buildings as well as larger seismic responses due to requirement of larger
stiffness of the structures and leads to uneconomic conditions. Thus, the efficiency of the
traditional method is somehow disadvantageous. So, to overcome these, many other methods
have been discovered. Use of bracing, dampers, and base isolator for structure are such methods
used for reducing damage during earthquake events.
3.2 Problem statement
To investigate the effect of such methods on the building structures, analytical models
are considered in this study. This Chapter explains these analytical models in detail. In total
modelling analysis of 4 models is done whereas the plan and elevation of building models was
kept same for purpose of comparison of results. These 4 models are as follows1. Plane RCC building
2. RCC building with steel bracing
3. RCC building with dampers
4. RCC building with Lead Rubber Bearing
All models are subjected to dynamic analysis with the help of structural analysis program
ETABS version 17. The dimension of all the beams and columns are designed according to
IS456- 2000. The proposed building is designed to resist dead load, and live load & seismic
load.
Firstly, the plan and elevation of building was decided. Then this building was modelled in
ETABs 2017.This building was analysed as plane RCC building. Then steel bracings were
applied to the same RCC building and analysis of this RCC building was performed. Further,
dampers were applied to the same RCC building and analysis of this RCC building was
performed. After this the design of lead rubber bearing was executed and properties of this
designed LRB was applied to the same RCC building model to make it base isolated. Then
analysis for this RCC building with base isolator was performed.
The details of proposed building are as follows
18
•
Building type – RCC building
•
No. of storeys – G+10
•
Plan area– 400 sq meter
•
Plan dimensions – 20 m X 20 m
•
Height of building – 30 m
•
Type – Residential
•
Beam – 0.250 m x 0.450 m
•
Column– 0.4 m x 0.4 m
•
Concrete grade – 20 MPa
•
Steel – Fe 415
•
Dead load – 10 KN/m
•
Live load – 2 KN/m
•
Importance factor – 1
•
Zone factor – zone 5 (0.36)
3.3 Steps for modelling
The steps in modeling and analysis of RCC building subjected to earthquake load are discussed
in this section. The steps in modeling and analysis of RCC building subjected to eaare discussed
in this section.
1. Begin a new model.
To star with new model, we use built in setting with display units are metric SI and for steel
structure database use Indian standard, for designing steel structure use IS800:2007, and to
design concrete structure use IS456:2002
Fig. 3.1.New model initialization
19
2. Story and grid data:
Create grid data and storey data as per building dimension. For the study 10 sorey building is
considered with 3mheight of each storey and grid is made with 5 bays of 4m*4m in x direction
and y direction.
Fig. 3.2. Edit story and grid system data.
3. Material selection
The material and its properties are added by using command ‘Define Material’
Step 3.1 To define new material go to define the select material peoperties, the material is
added according to region, material type, standards and grade. We can change material
properties as we required.
20
Fig. 3.3 Material property data
4. Define section
The section to be used in the frame is defined by using command ‘section properties’.
Step 4.1: Go to define and the select section properties.
Step 4.2: Go to frame properties then to add section click on add new properties. Then select
section shape as ‘concrete rectangular’, select rectangular shape in concrete section.
Step 4.3: Give property name and select material as M20 them add section dimension as per
requirement.
Step 4.4: Modify reinforcement data by selecting rebar material, cover provided and size of
longitudinal bar and confinement bar.
21
Fig. 3.4: - Frame section property data
5. Draw object: now the frame can be drawn by using previously defined frame section by using following
steps:
Step 5.1: To draw beam select draw beam and change the property as beam and draw the beam
at required passion.
Step 5.2: To draw any member two nodes are required. To create member such as beam and
column join two nodes by using draw cursor.
Step 5.3: To draw column select quick draw column then go to drop down menu and change
property to Auto column and join nodes of each story to its immediate storey nodes.
6. Add restraints: In model all footing nodes fixed by using following procedure.
Step 6.1: Select all nodes of footing to restrain
Go to Assign> Joint > Restraint.
Step 6.2: Now select type of restraint required and click Ok.
22
Fig. 3.5 Restraining joint
7. Assign steel Bracings: -
7.1 Go to define > section properties > frame properties
7.2 Then click on add new property, a dialogue box will appear on screen
Click on auto- select icon, select all sections and add it on right side
7.3 Then finish this command and go to quick draw braces. Then draw
Braces at required locations.
Fig. 3.6 Frame section property data
23
8. Assign Dampers:Steps to be performed are as follows –
7.1 Go to define > section properties > frame properties
7.2 Then click on add new property, a dialogue box will appear on screen
Click on auto- select icon, select all sections and add it on right side
7.3 Then finish this command and go to quick draw braces. Then draw
Braces at required locations.
Fig. 3.7: - Frame section property data
9. Assign Base isolator:Steps are as follows –
7.1 Go to define > section properties > link/ support properties
7.2 Then click on add new property, a dialogue box will appear on screen
Click to change the type of property and make it as rubber isolator.
7.3 Then edit the properties and make the per our design based on
Calculations.
7.4 Then go to assign> joints> spring> point springs> add property.
Make this property as default. Then select joints from 1st storey.
Then apply the base isolator to for these joints.
24
This
can
be
seen
in
elevation
of
structure
as
shown
in
figure.
Fig. 3.8: - Frame section property data
10. Define Load Patterns: The loads to be used for seismic analysis are required to define first such as dead load , live
load, floor finish load acting on the building , and also load pattern is required to be added.
Step 8.1 Click Define>load patterns Command to bring up define load patterns window. Now
enter load name, type of load, self weight multiplier, and codes for load.
Step 8.2: - The seismic parameter equired for equivalent static analysis can be selected by
earthquike load type the click modify lateral load
Step 8.3: -Earthquike parameters are added then press ok
Fig. 3.9 :- Seismic loading.
25
11. Assign gravity load: In this step all the load which are defined previously are assigned to frame and area loads to
the slabs however the earthquake load for equivalent static analysis is not required to assign.
Step 9.1: -The load whose magnitude tranfer to the frame like wall load can be assigned by
selecting the required member. To assign Go to ‘Assign menu> frame load> Distributed.’
12. Define Load Combination: The various load combinations can be added to see the output in the form combination
Step 10.1: - Go to define menu > load combination > add new
Step 10.2: - Select load and appropriate scale factor one by one and click on add
13. Check and Run analysis, view the result:First check the model for any errors.
Step 11.1: - To check model go to analyze menu > Check model, if no error occure then run
the analysis
Step 11.2: - To analyze the structure go to analyze menu> run analysis This will bring window
asking ‘set load cases to run’.
Step 11.3: - Select the load cases and run the analysis. Analysis will be started.
Step 11.4 : - To view the result in tabular form go to, ‘Display menu > show Tables’ command.
It will display window as shown in fig. select the required table by selecting check box.
Fig. 3.10 :- Result window
26
Fig. 3.11: - Plan of RCC building
27
Fig. 3.12: - Elevation of RCC building
28
Fig. 3.13: - Elevation of RCC building with Bracing
29
Fig. 3.14: - Elevation of RCC building with Dampers
30
Fig. 3.15: - Elevation of RCC building with Base Isolator
31
3.4 Formulae for calculation of base shear
𝑉𝐵 = Lateral earthquake force or base shear
z = zone factor = 0.36
I = importance factor = 1
R = response reduction factor = 5
w = seismic weight of building
𝑆𝑎 /g = design acceleration coefficient for soil
𝑇𝑎 = (0.09) h ÷ √𝑑 = 0.604 sec
from 𝑇𝑎 = 0.604 sec , 𝑆𝑎 /g = 2.252
VB = Ah .W
Sa z I
. .
g 2 R
Ah =
Formulae for calculation of base shear from UBC 97 –
1. Base shear is calculated as –
VB =
CV IW
RT
2. Base shear should be less than following value –
VBMAX =
(2.5)Ca IW
R
3. Base shear should be more than following value –
VBMIN =
(0.8) zNV IW
R
3.5 Design of base isolator (LRB)
The formulae for design of lead rubber bearing are as follows –
g
CV TD
BD
•
Design displacement = DD =
•
Effective stiffness = K e =
•
Energy dissipation per cycle = WD = 2 Ke DD 2 
4
2
X
w 2 2
X( )
g
TD
32
WD
4 DD
•
Force at DD = QD =
•
Stiffness in rubber = K 2 = K e −
•
Yield displacement = DY =
•
QDrequired =
•
Revised stiffness of rubber = K erequired = K e −
•
Thickness of rubber isolator = t =
•
Area of isolator = Alrb =
•
Shape factor = S =
•
QD
DD
QD
K1 − K 2
WD
4( DD − DY )
QD
DD
DD

K erequired t
G
d
DiameterOfLRB
= lrb
4 x(ThicknessOf Sin gleRubberLayer ) 4t
f
1
x v
Shape factor = S =
2.4 f h
•
6GS 2
)
Compression modulus = Ec = 6GS (1 −
K
G. Alrb
Horizontal stiffness of isolator = K H =
tr
E .A
Vertical stiffness of isolator = KV = C lrb
tr
Area of hysteresis loop = Ah = 4QD ( DD − DY )
•
Yield strength = FY = QD + ( K2 .DY )
•
•
•
2
3.6 Calculations for design of LRB
Various parameters are required for calculation of LRB design values. These parameters have
to be found from IS 1893- 2002 and UBC 97. By referring these and making some assumptions,
the pre- requisite parameters are calculated.
•
Soil profile= type II (Type = SD, from table A5, UBC 97)
•
Zone factor = z = 0.36 ≅ 0.4
•
Near source factor = Na = 1 (from table A8, UBC 97)
•
Near source factor = Nv = 1 (from table A9, UBC 97)
•
Seismic coefficient = Ca = 0.44 x Na = 0.44 (from table A6, UBC 97)
•
Seismic coefficient = Cv = 0.64 x Nv = 0.64 (from table A7, UBC 97
33
VALIDATION Number of bays in X direction = 4
Number of bays in Y direction = 4
Height of each storey = 3 m
Number of storeys = 4
Height of building = 12 m
Size of beam = 0.230 m x 0.450 m
Size of column = 0.450 m x 0.450 m
Slab thickness = 0.200 m
Fck = 20 MPa
Fy = 415 MPa
Live load = 3 KN / m2
Zone factor = z = 0.36
Importance factor = I =1
Response reduction factor = R = 5
1. Seismic weight calulation =>
•
DL
Slab weight = ( 16 x 16 x 0.2) x 25 = 1280 KN
Beam weight = 40 x ( 4 x 0.23 x 0.45) x 25 = 414 KN
Column weight = 25 x ( 9 x 0.45 x 0.45 ) x 25 = 379.688 KN
•
LL
Floor LL = (0.5 x 3) x 16 x 16 = 384 KN
Roof LL = 0
•
Total weight
1. Weight of roof = 1280 + 414 +
379.688
2
= 1883.844
2. Weight of intermediate floors =3x( 1280 + 414 + 379.688 + 384) =3 x (2457.688)
3. Weight og ground floor =
379.688
2
= 189.644
4. So, Total weight = W = 9446.552
34
2. Time period calculation =>
T = 0.075 x h0.75
= 0.075 x 120.75
= 0.484 sec
Sa
So,
𝑔
Ah =
=
Sa
𝑔
= 2.5
𝑥
𝐼
𝑍
x
𝑅 2
2.5 𝑥 1 𝑥 0.36
5𝑥2
= 0.09
Vb = Ah x W
= 0.09 x 9446.552
= 850.189 KN
Fig. Screenshot of result of base shear from ETABs software
•
Value of base shear by manual calculations = 850.189 kN
•
Value of base shear from software ETABs = 852.037 kN
Both values are approximately same, hence validation satisfied
35
CHAPTER 4
RESULTS AND DISCUSSION
4.1 Calculation of base shear by seismic coefficient method
Base shear is calculated by using seismic coefficient method by using following formula. It is
given in IS- 1893: 2002. The formula and required parameters are as follows -
VB = Ah .W
Ah =
Sa z I
. .
g 2 R
Where,
•
VB = Lateral earthquake force or base shear
•
W = seismic weight of the building = 45186 KN
•
z = zone factor (IS- 1893: 2002, Clause 6.4.2)
•
I = importance factor = 1 (IS- 1893: 2002, Clause 7.2.3)
•
R = response reduction factor = 5 (IS- 1893: 2002, Clause 7.2.6)
•
𝑆𝑎
•
𝑇𝑎 =
𝑔
= design acceleration coefficient for soil, it depends on Ta
(0.09) h
√𝑑
=
(0.09) 30
√20
For soil type II and Ta= 0.604,
Ah =
0.36 𝑋 2.252 𝑋 1
2𝑋5
𝑆𝑎
𝑔
= 0.604 sec
=
1.36
𝑇
1.36
= 0.604 = 2.252
= 0.0811
VB = 0.0811 x 45186
= 3664.585 KN
36
Calculation of lateral force at each storey (Qi) =>
Table 4.1. Calculation of base shear
Storey
Wi
hi
(KN)
(m)
Wihi2
Ki = Wihi2
Qi = Ki .
/ 𝚺 Wihi2
VB
(KN)
10
3759
30
3.383 x 106
0.223
817.202
9
4603
27
3.356 x 106
0.221
809.873
8
4603
24
2.651 x 106
0.175
641.302
7
4603
21
2.03 x 106
0.134
491.054
6
4603
18
1.491 x 106
0.098
359.129
5
4603
15
1.036 x 106
0.068
249.192
4
4603
12
0.663 x 106
0.044
161.242
3
4603
9
0.373 x 106
0.025
91.615
2
4603
6
0.166 x 106
0.011
40.310
1
4603
3
0.042 x 106
0.0027
9.894
𝚺 Wihi2= 15.191 x
𝚺 Ki ~ 1
𝚺 Qi ~
106
VB
4.2Calculation of base shear as per UBC 97 formulae-Formulae for
calculation of base shear from UBC 97
1. Base shear is calculated as –
VB =
=
CV IW
RT
0.64 x1x45186
5 x0.64
= 9575.841 KN
37
2. Base shear should be less than following value –
VBMAX =
(2.5)Ca IW
R
=
2.5 x0.44 x1x 45186
5
= 9940.92 KN
3. Base shear should be more than following value –
(0.8) zNV IW
R
0.8 x0.36 x1x1x 45186
=
5
VBMIN =
= 2602.71 KN
From above calculations we can say that base shear is within range that is in between VB max
and VB min as per specifications from UBC 97. So, base shear satisfies lower and upper limits.
4.3 Design formulae for LRB
The formulae for design of lead rubber bearing are as follows –
1. Design displacement = DD =
2. Effective stiffness = K e =
g
4
2
X
CV TD
BD
w 2 2
X( )
g
TD
3. Energy dissipation per cycle = WD = 2 Ke DD 2 
W
4. Force at DD = QD = D
4 DD
Q
5. Stiffness in rubber = K 2 = K e − D
DD
QD
6. Yield displacement = DY =
K1 − K 2
WD
7. QDrequired =
4( DD − DY )
Q
8. Revised stiffness of rubber = K erequired = K e − D
DD
D
9. Thickness of rubber isolator = t = D

10. Area of isolator = Alrb =
K erequired t
G
38
d
DiameterOfLRB
= lrb
4 x(ThicknessOf Sin gleRubberLayer ) 4t
f
1
x v
12. Shape factor = S =
2.4 f h
11. Shape factor = S =
6GS 2
13. Compression modulus = Ec = 6GS (1 −
)
K
G. Alrb
14. Horizontal stiffness of isolator = K H =
tr
E .A
15. Vertical stiffness of isolator = KV = C lrb
tr
16. Area of hysteresis loop = Ah = 4QD ( DD − DY )
2
17. Yield strength = FY = QD + ( K2 .DY )
4.4 Result for design of LRB
Some parameters have to be calculated before actual design of LRB. These are as follows•
Soil profile= type II (Type = SD, from table A5, UBC 97)
•
Zone factor = z = 0.36 ≅ 0.4
•
Near source factor = Na = 1 (from table A8, UBC 97)
•
Near source factor = Nv = 1 (from table A9, UBC 97)
•
Seismic coefficient = Ca = 0.44 x Na = 0.44 (from table A6, UBC 97)
•
Seismic coefficient = Cv = 0.64 x Nv = 0.64 (from table A7, UBC 97)
•
Damping coefficient = BD = 1
•
Importance factor = I = 1
•
Response reduction factor = R = 5
•
Effective damping = β = 5% = 0.05
•
Time period = TD = 1.54 sec ≅ 2 sec
•
Maximum support reaction = W = 3245.08 KN
•
Post yield ratio = K1 = 0.1
K2
DESIGN OF LRB =>
The formulae for design of lead rubber bearing are as follows –
39
1. Design displacement = DD =
2. Effective stiffness = K e =
g
4
2
X
CV TD
BD
w 2 2
X( )
g
TD
3. Energy dissipation per cycle = WD = 2 Ke DD 2 
W
4. Force at DD = QD = D
4 DD
Q
5. Stiffness in rubber = K 2 = K e − D
DD
QD
6. Yield displacement = DY =
K1 − K 2
WD
7. QDrequired =
4( DD − DY )
Q
8. Revised stiffness of rubber = K erequired = K e − D
DD
D
9. Thickness of rubber isolator = t = D

10. Area of isolator = Alrb =
K erequired t
G
d
DiameterOfLRB
= lrb
4 x(ThicknessOf Sin gleRubberLayer ) 4t
f
1
x v
12. Shape factor = S =
2.4 f h
11. Shape factor = S =
6GS 2
)
K
G. Alrb
14. Horizontal stiffness of isolator = K H =
tr
E .A
15. Vertical stiffness of isolator = KV = C lrb
tr
16. Area of hysteresis loop = Ah = 4QD ( DD − DY )
17. Yield strength = FY = QD + ( K2 .DY )
13. Compression modulus = Ec = 6GS 2 (1 −
There are some pre requisite parameters which are required for calculation of LRB design.
These are as follows –
Damping coefficient = BD = 1
Seismic coefficient = CV = 0.64
Time period = T = 1.566 sec = 2 sec
40
Calculations1. Design displacement = DD =
g
4
=
2
X
CV TD
BD
9.81 0.64 x 2
x
4 2
1
= 0.318 m
2. Effective stiffness =
3245.08 2 2
x( )
9.81
2
= 3264.797 KN/ m
3. Energy dissipation per cycle = WD = 2 Ke DD 2 
=(2𝜋)𝑥(3264.797)𝑥 (0.3182 ) 𝑥 0.05
=103.719 KN m
4. Force at DD = QD =
=
WD
4 DD
103.719
4 x0.318
= 81.54 KN
5. Stiffness in rubber = K 2 = K e −
QD
DD
= 3264.797 −
81.54
0.318
= 3008.382
6. Yield displacement = DY =
QD
K1 − K 2
=
=
81.54
10K 2 − K 2
81.54
9 x3008.382
41
= 0.003 m
7. QDrequired =
=
WD
4( DD − DY )
103.719
4(0.318 − 0.003)
= 82.317 KN
8. Revised stiffness of rubber = K erequired = K e −
QD
DD
= 3264.797 −
82.317
0.318
= 3005.939 KN/ m
DD
9. Thickness of rubber isolator = t =

0.318
1
=
= 0.318 m
10. Area of isolator = Alrb =
=
K erequired t
G
3005.939 x0.318
0.7 x1000
= 1.366 m2
1.366𝑥 4
So, diameter of LRB = 𝑑𝑙𝑟𝑏 = √
11. Shape factor = S =
=
𝜋
= 1.32 m
f
1
x v
2.4 f h
1 10
x
2.4 0.5
= 8.33
12. Shape factor = S =
d
DiameterOfLRB
= lrb
4 x(ThicknessOf Sin gleRubberLayer ) 4t
42
So, thickness single layer of rubber is, tr =
1.32
= 0.04 m
4 x8.33
6GS 2
13. Compression modulus = Ec = 6GS (1 −
)
K
2
G = Shear modulus = 0.7 MPa = 0.7 x 103 KN/ m2
S = Bulk modulus = 2000 MPa = 2000 x 103 KN/ m2
Ec = 6GS 2 (1 −
6GS 2
)
K
= 6 x0.7 x1000 x8.332 (1 −
6 x0.7 x1000 x8.332
)
2000 x1000
= 248966.673 KN / m2
14. Horizontal stiffness of isolator = 𝐾𝐻 =
0.7 x1000 x1.366
0.318
= 3006.918 KN/ m 2
15. Vertical stiffness of isolator = 𝐾𝑣 =
248966.673x1.366
0.318
= 1069460.614 KN/ m2
16. Area of hysteresis loop = Ah = 4QD ( DD − DY )
= 4 x 82.317 (0.318- 0.003)
= 103.719 m2
17. Yield strength = FY = QD + ( K2 .DY )
= 82.317 + (3008.382 x 0.003)
= 91.342 KN
This completes the design of the lead rubber bearing. The summary of design of LRB is as
follows
43
Table 4.2.Summary of LRB properties
PROPERTY
VALUE
Design displacement
0.318 m
Effective stiffness
3264.797 KN/ m
Energy dissipation per cycle
103.719 KN m
Force at DD
81.54 KN
Stiffness in rubber
3008.382 KN/ m
Yield displacement
0.003 m
𝑄𝐷 required
82.317 KN
Revised stiffness of rubber
3005.939 KN/ m
Thickness of rubber isolator
0.318m
Area of isolator
1.362 m2
Shape factor
8.33
Thickness of single rubber layer
0.04 m
No. of layers
10
Compression modulus
248966.673 KN/m
Horizontal stiffness of isolator
3006.918 KN/ m
Vertical stiffness of isolator
1069460.61 KN/m
Area of hysteresis loop
103.719 m2
Yield strength
91.342 KN
Effective damping
5%
44
End plates of 25mm thickness
Rubber
layers of 40mm
Shim plates of 2.8mm
thickness
Fig 4.1. Cross sectional properties of LRB
4.5 Results from ETABs –
4.5.1 Maximum storey displacement of various models –
45
Table 4.3.Values of max storey displacement
STOREY
RCC
BRACING
DAMPER
LRB
B + LRB
10
44.803
36.762
40.947
50.547
42.599
9
43.025
34.658
36.493
49.196
41.126
8
40.106
31.739
31.76
47.019
39.108
7
36.216
28.209
26.819
44.138
36.68
6
31.584
24.22
21.732
40.718
33.942
5
26.417
19.929
16.658
36.909
30.992
4
20.896
15.491
11.809
32.841
27.928
3
15.171
11.059
7.446
28.614
24.847
2
9.383
6.786
3.864
24.265
21.855
1
3.79
2.827
1.339
19.308
18.643
Base
0
0
0
9.77
16.739
MAX STOREY DISPLACEMENT (mm)
Max storey displacement
60
50
40
30
20
10
0
10
9
8
7
6
5
4
3
2
1
base
STOREY
RCC
BRACING
DAMPER
LRB
B + LRB
Fig 4.2 Graphical representation of max story displacement
Maximum storey displacement is increased for building with base isolator. This increases the
flexibility of structure and increases safety of the structure against earthquake.
46
4.5.2. Storey drift of various models
Table 4.4. Values of storey drift
STOREY
RCC
BRACING DAMPER
LRB
B + LRB
10
0.000593
0.000707
0.001504
0.000459
0.000495
9
0.000973
0.000973
0.001583
0.000732
0.000673
8
0.001297
0.001177
0.001659
0.00096
0.000809
7
0.001544
0.001329
0.001705
0.00114
0.000913
6
0.001722
0.00143
0.001699
0.00127
0.000983
5
0.001841
0.00148
0.001623
0.001356
0.001021
4
0.001908
0.001477
0.001461
0.001409
0.001027
3
0.001929
0.001424
0.001198
0.00145
0.001003
2
0.001865
0.001322
0.000842
0.001655
0.001086
1
0.001263
0.000942
0.000446
0.00358
0.003305
base
0
0
0
0
0
Max storey drift
MAX STOREY DRIFT
0.004
0.003
0.002
0.001
0
10
9
8
RCC
7
BRACING
6
STOREY
DAMPER
5
4
LRB
3
2
1
base
B + LRB
Fig 4.3 Graphical representation of max story Drift
Storey drift is reduced due to use of dampers and bracings in the floors below 6. But in case
of lead rubber bearing, that is for base isolated building, storey drift is reduced in all floors
except first floor. But reduction of storey drift at top floors is necessary because it is
47
important to reduce the storey drifts of top storeys which damage the structure during
earthquake. This improves the performance of building during earthquake.
4.5.3. Storey shear of various models
Table 4.5.Values of storey shear
STOREY
RCC
BRACING
DAMPER
LRB
B + LRB
10
-324.436
-417.295
-973.612
-235.666
-275.994
9
-626.688
-806.39
-892.022
-453.619
-533.338
8
-865.505
-1113.82
-971.396
-627.093
-736.671
7
-1048.35
-1349.2
-1014.03
-759.909
-892.347
6
-1182.68
-1522.13
-1024.05
-857.488
-1006.72
5
-1275.97
-1642.22
-989.37
-925.251
-1086.15
4
-1335.68
-1719.08
-898.557
-968.62
-1136.98
3
-1369.26
-1762.31
-740.874
-993.014
-1165.58
2
-1384.19
-1781.53
-503.58
-1003.86
-1178.28
1
-1387.92
-1786.33
-327.231
-1006.57
-1181.46
base
0
0
0
0
0
STOREY SHEAR (KN)
Storey shear
0
-200
-400
-600
-800
-1000
-1200
-1400
-1600
-1800
-2000
STOREY
10
9
8
7
6
RCC
BRACING
5
DAMPER
4
3
LRB
B + LRB
2
1
base
Fig 4.4 Graphical representation of story shear
Storey shear of building designed with damper and bracings is increased in all storeys which
is not a good result. But in case of LRB and for building with bracing plus LRB, storey shear
is reduced in all storeys. This is satisfactory result.
48
4.5.4 Overturning moments of various models –
Table 4.6.Values of storey stiffness
STOREY
RCC
BRACING
DAMPER
LRB
B + LRB
10
58261.98
58261.98
64771.69
58261.98
58261.98
9
133715.4
133318.1
155466.6
133117.7
133792
8
208374.7
207079.4
245077.1
208183.6
208469
7
282406.4
279817.5
335483.9
282775.4
282472
6
355957.8
351772.2
426356.5
357004.1
355958.9
5
429156.1
423151.5
516553.6
430966.1
429066.7
4
502109.4
494131
603418.9
504742.9
501911.2
3
574905.8
564854.8
681300.9
578401.2
574587.3
2
647613.9
635434.7
743354.8
651992.7
647168.5
1
720282.8
705950.7
794464.4
725554.6
719707.6
base
720280
703788.7
822052.5
726447.2
719574.2
OVERTURNING MOMENT (KNm)
Overturning moments
900000
800000
700000
600000
500000
400000
300000
200000
100000
0
10
9
8
7
6
5
4
3
2
1
base
STOREY
RCC
BRACING
DAMPER
LRB
B + LRB
Fig 4.5 Graphical representation of overturning moment
49
Overturning moments are increased for building with dampers. But overturning moments are
approximately same for rcc building, building with bracings, base isolated building and
building with bracing plus LRB.
4.5.5. Storey stiffness of various models –
Table 4.7.Values of storey stiffness
STOREY
RCC
BRACING
DAMPER
LRB
B + LRB
10
182480.9
197705.5
227596.4
173024.2
186660.6
9
214741.9
276464.7
195813.9
207565.6
264510.5
8
222517.3
315662.8
202356.7
218117.7
303639.7
7
226340.3
338384.7
204659.1
222631.6
325972.8
6
228911.9
354775.2
206787.6
225495.8
341308.4
5
231085.3
370026.2
208772.3
227748.8
354598.6
4
233317.8
387879.6
210731.1
229463.2
368959.5
3
236567.7
412451.2
212504.4
228605.2
388504
2
247440.1
450021
208601.5
202680.5
365390.7
1
366349.1
632732.1
342393.9
99414.71
199992.7
base
0
0
0
0
0
storey stiffness
STOREY STIFFNESS (KN/m)
700000
600000
500000
400000
300000
200000
100000
0
10
9
8
7
6
5
4
3
2
1
base
STOREY
RCC
BRACING
DAMPER
LRB
B + LRB
Fig 4.6 Graphical representation of story stiffness
Storey stiffness is increased for the building designed with bracings. But is approximately
samefor rcc building, base isolated building and for building with bracing plus LRB.
50
4.5.6. Time period of various models –
Table 4.8. Values of time period
MODE
RCC
BRACING
DAMPER
LRB
B + LRB
1
2.747
1.688
1.739
3.638
2.563
2
2.098
1.561
1.512
2.871
2.36
3
2.005
1.164
1.144
2.763
1.91
4
0.913
0.528
0.409
1.121
0.771
5
0.693
0.499
0.394
0.868
0.696
6
0.658
0.368
0.264
0.837
0.54
7
0.543
0.289
0.191
0.62
0.352
8
0.408
0.28
0.181
0.476
0.339
9
0.388
0.203
0.177
0.449
0.25
10
0.381
0.203
0.174
0.425
0.227
11
0.303
0.195
0.167
0.323
0.221
12
0.287
0.16
0.167
0.321
0.171
TIME PERIOD (Sec)
Time period
4
3.5
3
2.5
2
1.5
1
0.5
0
1
2
3
4
5
6
7
8
9
10
11
12
MODE NUMBER
RCC
BRACING
DAMPER
LRB
B + LRB
Fig 4.7 Graphical representation of time period
Time period is conisderably increased for base isolated building and it can be clearly seen
from comparison graph between rcc building and base isolated building.
51
CHAPTER 5
CONCLUSIONS
5.1 Conclusions
Conclusions that can be drawn from study are as follows1. Use of LRB as base isolator increases the maximum storey displacement of the
structure by average of 40%. This increases the flexibility of structure and makes the
structure stable during earthquake occurrence.
2. Story drift is reduced by 29% due to use of LRB which gives satisfactory performance
during events of earthquakes.
3. Story shear is reduced by 31% due to use of LRB. This makes the structure stable
during earthquake.
4. Story stiffness is not much affected. It is increased, but with less rate.
5. Time period is considerably increased for base isolated building. This increased time
period reduces the acceleration and increases the reaction time for structure. This
improves the performance of the structure against the earthquake.
5.2Scope of future work:
Present work is for base isolated buildings. This method can be studied for bridges.
52
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1
2
3
4
5
6
7
8
9
10
11
12
13
14
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54
PLAGIARISM REPORT
55
56