Seismic Analysis of Elevated Water Tank

SEISMIC ANALYSIS OF ELEVATED
WATER TANK
A thesis submitted in partial fulfillment of the requirements for
the award of the degree of
B.Tech
In
Civil Engineering
By
Kalaivanan M (103109039)
Kumaraavel T V (103109044)
Prasannakumar K (103109062)
DEPARTMENT OF CIVIL ENGINEERING
NATIONAL INSTITUTE OF TECHNOLOGY
TIRUCHIRAPPALLI-620015
MAY 2013

BONAFIDE CERTIFICATE
This is to certify that the project titled “SEISMIC ANALYSIS OF ELEVATED
WATER TANK” is a bonafide record of the work done by
Kalaivanan M (103109039)
Kumaraavel T V (103109044)
Prasannakumar K (103109062)
in partial fulfillment of the requirements for the award of the degree of Bachelor of
Technology in Civil Engineering of the NATIONAL INSTITUTE OF
TECHNOLOGY, TIRUCHIRAPPALLI, during the year 2009-2013.
Dr. P. A. KRISHNAN Dr. P. JAYABALAN
Guide Head of the Department
Project Viva-Voce held on _________________________
Internal Examiner External Examiner

iii
ABSTRACT
Elevated water tanks are lifeline structures that must be designed to withstand all the
forces – static and dynamic loads that are expected to act on it throughout its life.
Static loads can be calculated knowing the mass density of material and geometry of
structure. Dynamic loads, especially seismic loads, are difficult to predict because the
occurrence and magnitude of earthquakes are highly uncertain. In addition to that the
complex nature of the structure – the huge concentrated mass consisting of liquid
mass atop supported by a slender staging that makes it still difficult to predict its
dynamic behavior. Here, in this project, an attempt is made to predict the behavior of
the structure subjected to earthquake load under different cases.
A linear analysis of the structure is performed in SAP2000 under different cases. The
earthquake load is taken from the two typically recorded accelerograms. For each
earthquake load, the structure is analyzed under the conditions of fixed base and
flexible base taking the elasticity of soil into account. The tank modeled is circular in
cross section and supported by columns interconnected by radial bracing. The
response quantities – modal periods and frequencies, base reactions are obtained.
Apart from these response spectrum curves and displacement responses are plotted
and peak response is determined. The variation of shear force and bending moment
along the height is shown and stress envelopes are plotted for time dependent loads. It
is found that incorporating soil stiffness greatly reduces the base reactions and peak
response compared to the fixed support.
The effect of base isolation is studied on the dynamic response quantities and is
compared with the fixed base condition. Base isolation results in reduction of base
reaction and forces generated in the members. The effect of sloshing is studied and it
is found that sloshing causes significant increase in base reactions.
Keywords: Elevated water tank, Seismic analysis, Time history analysis, Base
isolation, Sloshing

iv
ACKNOWLEDGEMENT
This project in the field of Structural Dynamics, an active area in the field of
structural engineering, have helped us in getting exposure to many facets of this
dynamically evolving face of engineering.
We express our deep sense of gratitude and indebtedness to our guide,
Dr. P. A. Krishnan, Professor, who had been a great inspiration for taking up a
project of such a massive scale. Without his critical inputs and constructive feedback
at various stages, it would not have been possible for the project to have turned out
well. His ideas and suggestions have helped us widen our perspective on the subject.
We are extremely grateful to Dr. P. Jayabalan, Professor and Head of the
Department, for his moral support and encouragement which motivated us towards
the successful competition of project. We would like to thank the faculty members of
Civil Engineering Department for providing all kind of possible help throughout the
course duration which helped us to tackle various problems faced during the project.
In particular, we would like to thank Dr. C. Natarajan, Professor and Dr. K. Baskar,
Associate Professor, for offering us great help and assistance whenever required.
It is our privilege to extend our gratitude to Dr. Srinivasan Sundarrajan, Director,
National Institute of Technology – Tiruchirappalli, for providing us with the facilities
and environment to successfully carry out our project.
It is our pleasure to have such a panel members present during our project reviews
who were significant in providing invaluable suggestions and improvements towards
technical proficiency of the project. In this regard, we would like to thank
Dr. R. Manjula, faculty coordinator for the project work. We would also like to thank
Mr. S. Saravanan for his timely help and guidance during different phases of the
project.
We are extremely grateful to our parents and friends who have always been supportive
and encouraging all the time throughout the completion of our project.
KALAIVANAN M
KUMARAAVEL T V
PRASANNAKUMAR K

v
TABLE OF CONTENTS
Title Page No.
ABSTRACT…………………………………………………………….. iii
ACKNOWLEDGEMENT……………………………………………... iv
TABLE OF CONTENTS………………………………………………. v
LIST OF TABLES……………………………………………………… ix
LIST OF FIGURES…………………………………………………….. x
CHAPTER 1 INTRODUCTION
1.1 General…………………………………………….... 1
1.2 Need for Study………………………………….. 2
1.3 Objectives of Study…………………………….. 3
1.4 Scope of Study……………………………………… 3
1.5 Content and Structure of Thesis…………………….. 3
CHAPTER 2 LITERATURE REVIEW
2.1 General……………………………………………… 5
2.2 Review of Literature………………………………... 5
CHAPTER 3 MODELLING OF STRUCTURE
3.1 General……………………………………………… 7
3.2 Staging………………………………………………. 8
3.3 Cases of Analysis Performed………………………... 9
3.3.1 Fixed and Flexible Support………………………. 9

vi
3.3.2 Base Isolation…………………………………….. 9
3.3.3 Sloshing…………………………………………... 9
3.4 Assumptions………………………………………… 9
3.5 Characteristics of Earthquake considered…………… 10
3.6 Picture of Analysis Model…………………………... 12
CHAPTER 4 ANALYSIS RESULTS
4.1 Modal Period and Frequencies……………………... 13
4.1.1 Fixed Base……………………………………….. 13
4.1.2 Flexible Base…………………………………….. 14
4.2 Base Reaction………………………………………. 15
4.2.1 El Centro – Fixed Base Support…………………. 15
4.2.2 El Centro – Flexible Base Support………………. 16
4.2.3 Uttarkashi – Fixed Base Support………………… 17
4.2.4 Uttarkashi – Flexible Base Support……………… 18
4.3 Joint Displacements………………………………… 19
4.4 Response Spectrum Curves………………………… 20
4.4.1 El Centro – Fixed Base Support…………………. 20
4.4.2 El Centro – Flexible Base Support………………. 20
4.4.3 Uttarkashi – Fixed Base Support………………… 21
4.4.4 Uttarkashi – Flexible Base Support……………… 21
4.5 Displacement Response……………………………... 22
4.5.1 El Centro – Fixed Base Support………………….. 22
4.5.2 El Centro – Flexible Base Support……………….. 22

vii
4.5.3 Uttarkashi – Fixed Base Support…………………. 23
4.5.4 Uttarkashi – Flexible Base Support………………. 23
4.6 Force Profile………………………………………… 24
4.6.1 Axial Force Profile……………………………….. 24
4.6.2 Shear Force Profile……………………………….. 25
4.7 Bending Moment Profile……………………………. 26
4.7.1 Bending Moment Envelope for El Centro………... 26
4.7.2 Bending Moment Profile for Water load…………. 26
4.7.3 Bending Moment Profile for El Centro…………... 27
4.8 Stresses Developed in Shell…………………………. 28
4.8.1 Resultant Forces for Water load………………….. 28
4.8.2 Resultant Moment for Water load………………... 28
CHAPTER 5 BASE ISOLATION
5.1 General……………………………………………… 29
5.2 Types………………………………………………... 29
5.3 Analysis……………………………………………... 30
5.4 Conclusion………………………………………….. 33
CHAPTER 6 SLOSHING DYNAMICS
6.1 General………………………………………………. 34
6.2 Effects of Sloshing…………………………………... 34
6.3 Analysis……………………………………………... 35
6.3.1 Results……………………………………………. 36

viii
6.4 Conclusion…………………………………………... 37
6.5 Limitations…………………………………………... 38
CHAPTER 7 CONCLUSIONS AND RECOMMENDATIONS
7.1 Conclusion…………………………………………... 39
7.2 Recommendations…………………………………… 40
7.3 Scope of Future Work……………………………….. 40
REFERENCES 42

ix
LIST OF TABLES
Table No. Title Page No.
3.1 Dimensions of the tank……………………………………. 7
3.2 Characteristics of earthquake……………………………… 10
4.1 Modal period and frequencies for fixed support condition.. 13
4.2 Modal period and frequencies for flexible support
condition…………………………………………………... 14
4.3 Base reaction for El Centro earthquake for fixed support
condition…………………………………………………... 15
4.4 Base reaction for El Centro earthquake for flexible support
condition…………………………………………………… 16
4.5 Base reaction for Uttarkashi earthquake for fixed support
condition…………………………………………………… 17
4.6 Base reaction for Uttarkashi earthquake for flexible
support condition…………………………………………... 18
4.7 Storey drift at the level of base slab……………………...... 19
5.1 Modal period and frequencies for fixed base and isolated
base………………………………………………………… 30
5.2 Base reaction for fixed base and isolated base…………..... 31
6.1 Dynamic response quantities under sloshing……………… 37

x
LIST OF FIGURES
Figure No. Title Page No.
1.1 Requirements for a good structural performance………… 1
3.1 Time history function of El Centro earthquake…………... 11
3.2 Time history function of Uttarkashi earthquake………….. 11
3.3 Picture of the analysis model……………………………... 12
4.1 Response spectrum for El Centro earthquake for fixed
base condition…………………………………………….. 20
4.2 Response spectrum for El Centro earthquake for flexible
base condition…………………………………………….. 20
4.3 Response spectrum for Uttarkashi earthquake for fixed
base condition…………………………………………….. 21
4.4 Response spectrum for Uttarkashi earthquake for flexible
base condition…………………………………………….. 21
4.5 Displacement response for El Centro earthquake for fixed
base condition…………………………………………….. 22
4.6 Displacement response for El Centro earthquake for
flexible base condition……………………………………. 22
4.7 Displacement response for Uttarkashi earthquake for fixed
base condition…………………………………………….. 23
4.8 Displacement response for Uttarkashi earthquake for
flexible base condition……………………………………. 23
4.9 Axial force envelope for El Centro earthquake…………... 24
4.10 Axial force profile for water load………………………… 24
4.11 Shear force envelope for El Centro earthquake…………... 25
4.12 Shear force profile for water load………………………… 25

xi
4.13 Overturning moment envelope for El Centro…………….. 26
4.14 Overturning moment profile for water load………………. 26
4.15 Bending moment profile for El Centro at step 18………… 27
4.16 Bending moment profile for El Centro at step 28………… 27
4.17 Resultant forces acting in the shell for water load………... 28
4.18 Resultant moment acting in the shell for water load……... 28
5.1 Elastomeric Bearing………………………………………. 30
5.2 Response Spectrum Curves for isolated base…………….. 31
5.3 Variation of storey drift along the height of the tank……... 32

CHAPTER 1
INTRODUCTION
1.1 GENERAL
Elevated water tank is a massive structure which is used to store and distribute water
to individual households in a corporation or municipality under the effect of gravity. It
consists of a liquid storage container at the top supported by a slender staging
consisting of columns and beams. The elevation of the tank may vary depending upon
the location and requirements. As the population was observed to grow rapidly, it is
Government‟s responsibility to provide water supply to civilians and hence large
capacity water tanks are needed to be constructed to augment the growing demand for
water. Also, rapid upgradation of towns and cities demands tanks of high storage
capacity to be constructed with the limited space available. So there is a need for huge
water tank at a high elevation, if not now atleast in future.
Constructing structures of this scale definitely requires precise prediction of loads and
calculation of member forces. Not limiting to this, it is also required to design
skilfully the structure by adopting suitable material strength and taking care on overall
section properties. In addition to that for obtaining a good performance of a structure
during its lifetime the construction procedure adopted is very important. Periodic
monitoring and maintenance of structure can still enhance its performance.
Fig 1.1 Requirements for a good structural performance
Structural
Performance
Analysis
Design
Construction
Maintainence
1

The objective of structural analysis is to determine the member forces, joint
displacements and support reactions for a given load. However, prediction of
structural responses due to time dependent loads involves more parameters and use of
differential calculus than static or independent loads and hence it is time consuming.
The same also holds true for nonlinear over linear analysis. Analysing the structure
for time varying load is known as dynamic analysis. Here, in dynamic analysis, the
assumption taken in idealisation of structure is very important. Hence it is very
difficult to predict the response precisely by manual calculation, unlike static analysis.
Moreover, vibration of liquid storage container induces additional effect such as
sloshing which still makes the problem complex.
1.2 NEED FOR THE STUDY
The elevated water tanks are subjected to very high lateral loads during earthquakes
due to the huge mass concentrated at the top. The shear force induced at the base is
proportional to mass, and the overturning moment is proportional to both mass and
moment of mass about the base. As both are higher for this type of tank, it is obvious
that it attracts large amount of forces. Since it is a liquid storage structure, any crack
in the container results in leakage of liquid inside. It should not undergo large
deflections as the pipelines connected to it are not designed to accommodate such
deflections. The natural frequency of the structure should be kept much lower than the
frequency of external load to avoid resonance. In other words, natural period must be
high. This can be made by increasing the mass and decreasing the stiffness.
When the tank is completely full, the mass is very high and stiffness has to be less in
order to have a higher natural period. On the other hand, if the tank is empty, the mass
is itself is very less for which the stiffness has to made much lesser to maintain the
natural period. These are the critical cases to be considered in design of tank for
seismic loads regarding mass and stiffness. In addition to this, when the tank is
partially full the effect of sloshing should be taken into account for different water
levels and the critical case is selected. The three critical cases have to be considered in
arriving at the final member forces and support reactions.
2

1.3 OBJECTIVES OF THE STUDY
 To determine the different modes of frequencies and corresponding time
period.
 To determine the base shear, overturning moment for typically observed
earthquakes.
 To determine the individual member forces, joint displacements and support
reactions.
 To study the variation of forces and members along the member throughout
the structure.
 To study the effect of soil stiffness, base isolation and sloshing.
1.4 SCOPE OF STUDY
 Modelling of a reinforced concrete circular elevated water tank using the
software, SAP2000 v14.0.
 Analysing the model considering the structure to be elastic and joints as fixed.
 Time history functions of El Centro and Uttarkashi earthquake are only used.
 Inferences are made completely based on the results obtained from the
software.
 Soil stiffness and base isolation is fed to software assuming appropriate
stiffness values for both.
 Damping is assumed to be constant at 5% which is usually used for reinforced
concrete structures.
1.5 CONTENT AND STRUCTURE OF THESIS
 Chapter 1 gives a brief account of issues concerning the elevated water tanks,
need for study, objective and scope of study.
 Chapter 2 presents the literature review.
 Chapter 3 discusses modelling of structure – the complete details of models
and parameters of study, theory and assumptions involved.
 Chapter 4 gives the detailed analysis report obtained for different cases
3

 Chapter 5 describes the effect of base isolation on dynamic response
reduction.
 Chapter 6 discusses the effect of sloshing dynamics.
 Chapter 7 gives the conclusion and provide scope for future work.
4

CHAPTER 2
LITERATURE REVIEW
2.1 GENERAL
Two Mass Model. Elevated water tanks are analysed by considering a two mass
system model first proposed by Housner in 1963 which is more appropriate and is
being commonly used by most of the international codes. The pressure generated
within the fluid due to dynamic motion of the tank can be separated into impulsive
and convective parts. The liquid, in the lower region of tank behaves like a mass that
it is rigidly connected to tank wall that exerts impulsive hydrodynamic pressure on the
tank wall and similarly on the base which is known as the impulsive liquid mass. The
liquid mass, in the upper region of the tank undergoes sloshing motion that exerts
convective hydrodynamic pressure on the tank wall and base which is known as
convective liquid mass.
The important factors that affect the magnitude of earthquake forces are
1. Seismic Zone factor, Z
2. Importance Factor, I
3. Response Reduction Factor, R
4. Structural Response Factor, (Sa/g)
2.2 REVIEW OF LITERATURE
A. M. Kalani and A. Salpekar (1978). The values of absolute maximum axial force,
bending moment and shear force by conventional method are on conservative side by
10.4%, 39.6% and 17.1% respectively in the lowest panel. It is observed that the
maximum bending moment and axial force in a column occur in the lower most
panels whereas, the maximum shear force in a column occurs in panel above the
lowest.
R. K. Ingle (1999). In general, water retaining structure distress has been observed
very early even in 9 to 10 years of service life due to some problems related to
structural aspects and over emphasis of seismic analysis in earthquake prone zones.
During the past earthquakes, tanks have suffered with varying degree of damages,
5

which include: buckling of ground supported slender tanks (Malhotra, 1997), rupture
of steel tank shell at the location of joints with pipes, collapse of supporting tower of
elevated tanks (Manos and clough, 1983, Rai, 2002), cracks in the ground supported
RC tanks, etc.
S.C. Dutta, et al (2000). In 1993 Killari (India) earthquake, a reinforced concrete
elevated water tank collapsed vertically downwards, burying the six supporting
columns directly underneath the bottom slab of its container due to torsional
vibration. Elevated water tanks, with their broadly axisymmetric geometry and mass
distribution, should have no considerable eccentricity between centre of mass and
centre of stiffness. However, asymmetric placement of ladders and water pipelines,
sloshing of the water mass during shaking, and non-uniformity in construction may
introduce small accidental eccentricity between centre of mass and centre of stiffness
may cause considerably amplified rotational response under horizontal ground
shaking in any structure if it has torsional to lateral time period ratio is very close to 1.
This may cause progressively increasing localized damage in the yielded structural
element due to strength deteriorating characteristics of concrete under cyclic loading
during an earthquake. Hence to assess the torsional vulnerability of the elevated tanks,
it needs to be investigated whether the ratio of torsional and lateral time periods, lie
within the critical range of 0.7 to 1.25.
Chirag N. Patel (2012). Water tanks can experience distress in different components
due to several reasons such as improper structural configuration design, inferior
materials and workmanship, corrosion of reinforcement, wind forces, earthquake
forces etc. It is found that there is a considerable change in seismic behaviour of
elevated tanks with consideration of responses like displacement, base shear, base
moment, sloshing, torsional vulnerability etc. when supporting system is used with
appropriate modifications.
The different performance levels of a structure subjected to earthquake loads are
Immediate Occupancy, Life Safety and Collapse Prevention. The structure is designed
to remain within Immediate Occupancy even for maximum considered earthquake
(MCE). This is because the structure has to be fully functional post-earthquake as its
dependency is very high in the society. In addition to that a structure of this scale is
difficult to repair.
6

CHAPTER 3
MODELLING OF STRUCTURE
3.1 GENERAL
A water tank of capacity approximately 0.55 ML at an elevation of 21m is used for
the study. It is made up of reinforced cement concrete and it is assumed that the
structure is designed on the basis of capacity based design approach. The software
used is SAP 2000 v14.0 for both modelling and analysis. The dimensions of the tank
are as given in the table below.
Table 3.1 Dimensions of the tank
Dimensions of Cylindrical Tank
Diameter of the tank 12 m 1
Depth of the tank 5 m
Capacity 565487 L
Shell thickness 250 mm
Elevation of the base slab from the ground 21 m
Base slab thickness 300 mm
No. of columns 9 (8-peripheral and 1-central)
Bracing pattern Radial bracing
Level of bracing 6 levels at every 3 m interval
Diameter of the column 400 mm
Dimensions of the bracing 230 mm x 300 mm
Grade of concrete for column M25
Grade of concrete for beam M20
Grade of concrete for shell M25
Grade of steel Fe415
1
It is tapered to 10 m diameter in the bottommost 1m of the tank
7

3.2 STAGING
The staging is modelled as a special moment resisting frame consisting of 8 columns
at the periphery and one column at the centre and radial bracings are provided for
every 3 m. The peripheral columns extend from foundation up to a height of 21m but
the central column extends only up to 18m. This is because to have a same bending
moment direction in interior position of base slab. If the central column is raised up to
base slab, the hogging bending moment at centre, the fixed end moment is generated
interior, creates excessive stress at centre which may require a bigger section to avoid
cracking.
The cylindrical container is modelled as a hexadecagon, since it is impossible to
model a perfect circular cross section in the software. However the number of ends
can be increased for better precision but the processing time required will be large.
However as long as the length of the arc does not differ much from that of the sides, a
suitable polygon can be assumed in the place of circle. This hexadecagon shell is
connected to an octagon base whose edges are connected to the top-end of peripheral
columns.
These columns are interconnected by circumferential and radial beams, called as
radial bracing. All the joints in the structure are assumed as fixed. The container atop
should remain within elastic limits at any point of loading. This is because damage to
the tank, being a lifeline structure, puts the society in scarce of water. Hence, as far as
possible, the tank is designed to remain in elastic zone. At the severe case, it can
undergo plastic deformation without cracking which otherwise results in water
leakage and hence the tank remains un-functional for few days post-earthquake period
till it gets repaired. Cracks are permitted in staging. Nevertheless, plastic deformation
should be strictly avoided. Here in this model linear analysis is performed for the
whole structure for simplicity in computation, although there is a provision in SAP
2000 for non-linear analysis which requires a lot of computational effort and
understanding of non-linear behaviour of materials, which is beyond the scope of
project.
8

3.3 CASES OF ANALYSIS PERFORMED
3.3.1 Fixed and Flexible Support
Separate analysis is carried out for fixed base condition and flexible base condition –
taking the elasticity of soil into account, for each earthquake. Elastic foundation is
modelled by assigning spring with appropriate stiffness values corresponding to
medium soil as negligence of soil stiffness underestimates the structure and hence
increasing the overall cost. The stiffness is assumed to be 8759kN/m, which lies
within the range of the soil of medium stiffness. Utmost importance has to be given in
establishing the bond between the structure and soil beneath, failing which the
structure behaves no different from the fixed support.
3.3.2 Base Isolation
If the earthquake induced forces are found to be very large or designing to structure
for such earthquake are found to be over met to constructional feasibilities, base
isolators are used. It should be noted that base isolators can only be used in rigid soils.
Use of base isolation for elevation water tank is very rare. An attempt is made to
study the effect of base isolation.
3.3.3 Sloshing
Sloshing is an unavoidable phenomenon in vibration of liquid storage structures;
prediction of which is usually not given adequate importance. As such, the structure
may show unexpected behaviour during such critical instances. Accurate prediction of
sloshing requires more specialised and sophisticated computational tools to perform
FEM and CFD analysis which is beyond the scope of this project. However, the effect
of sloshing is studied on structure-level dynamic response quantities by adopting the
procedure given in IS codes. The results with and without consideration of sloshing
effects are then compared.
3.4 ASSUMPTIONS
The analysis performed pertains to following assumptions
1. Linear Analysis is performed for the structure.
9

2. The base slab is sufficiently rigid so as to maintain diaphragm action.
3. Constant viscous damping of 5%, which is usually adopted for RCC
structures.
4. Plastic hinges are not introduced anywhere in the structure.
5. Constructional feasibilities are not considered.
6. P-∆ effect is not considered.
7. Stresses due to chemical reactions, alkalinity or pH of water are not
considered.
8. Reduction in strength due to fatigue loading is not considered.
3.5 CHARECTERISTICS OF EARTHQUAKE CONSIDERED
The earthquake is fed in the form of time history function of ground acceleration
taken from COSMOS Earthquake Data Centre. Every earthquake has three
components – parallel to plane of rupture, normal to the plane of rupture and vertical
component. The vertical or „down‟ component is neglected, because it is much lesser
than the gravity, since the structure can stand well against the gravity loads. Among
the parallel and normal components, the most critical is taken for analysis. The
characteristics of earthquake are given in the table.
Table 3.2 Characteristics of Earthquake
Characteristics El Centro Uttarkashi
Region California, US Uttarkhand, India
Year of occurrence 1940 1991
Magnitude 6.9 7
Depth (km) 8.80 10.0
Latitude 30.78 32.76
Longitude 78.77 -115.42
Mechanism Strike Slip NA
Critical Component S90W N75E
The ground accelerogram expressed in terms of gravity (g) for these earthquakes is
illustrated below. The ordinates are recorded for the step interval of 0.02 s. The
10

ordinates are multiplied with gravity in order to obtain absolute ground acceleration
and it takes the unit of g. In SI unit, g is expressed as 9.81 m/s2
. It is also observed
that these earthquakes last for a very short period of not more than one minute. But
aftershocks may be observed post the main earthquake which is not depicted in the
time history functions provided here.
Fig 3.1 Time history function of El Centro earthquake
Fig 3.2 Time history function of Uttarkashi earthquake
-0.30
-0.20
-0.10
0.00
0.10
0.20
0.30
0.40
0 10 20 30 40 50 60
Acceleration(g)
Time (seconds)
El Centro
Time History
-0.30
-0.20
-0.10
0.00
0.10
0.20
0.30
0.40
0 10 20 30 40 50
Acceleration(g)
Time (seconds)
Uttarkashi
Time History
11

3.6 PICTURE OF ANALYSIS MODEL
The picture of analysis model snapped from the software is shown below.
Fig 3.3 Picture of the analysis model
12

CHAPTER 4
ANALYSIS RESULTS
The structure is analysed for El Centro and Uttarkashi earthquake under conditions of
fixed base and flexible base.
4.1 MODAL PERIOD AND FREQUENCIES
4.1.1 Fixed Base
Table 4.1 Modal period and frequencies for fixed support condition
Mode No. Period Frequency
Circular
Frequency
sec cycles/sec rad/sec
1 7.65 0.13 0.82
2 3.04 0.33 2.06
3 2.81 0.36 2.24
4 0.52 1.91 12.01
5 0.36 2.76 17.35
6 0.27 3.75 23.58
7 0.23 4.38 27.54
8 0.23 4.43 27.83
9 0.21 4.72 29.69
10 0.18 5.46 34.28
11 0.18 5.47 34.37
12 0.18 5.53 34.76
The natural period of the system is found to be 7.65 sec in the case of fixed support
condition. This is independent of external loading and dependent on damping.
13

4.1.2 Flexible Base
Table 4.2 Modal period and frequencies for flexible support condition
Mode No. Period Frequency
Circular
Frequency
sec cycles/sec rad/sec
1 8.33 0.12 0.75
2 4.35 0.23 1.45
3 3.24 0.31 1.94
4 0.61 1.64 10.32
5 0.53 1.89 11.89
6 0.48 2.08 13.08
7 0.35 2.85 17.93
8 0.27 3.73 23.43
9 0.22 4.49 28.21
10 0.2 5.11 32.08
11 0.19 5.17 32.5
12 0.19 5.23 32.89
The natural period of the system is found to be 8.33 sec in the case of flexible support
condition. The result shows that there is an increase in time period which is due to
reduction in stiffness when the flexibility of foundation is considered.
14

4.2 BASE REACTION
4.2.1 El Centro – Fixed Base Support
Table 4.3 Base reaction for El Centro earthquake for fixed support condition
TABLE: Base Reactions
Output Case Case Type Step Type Step No. GlobalFX GlobalFY GlobalFZ GlobalMX GlobalMY GlobalMZ
Text Text Text Unitless KN KN KN KN-m KN-m KN-m
DEAD LinStatic 0 0 1855.27 -2.55 0 0
MODAL LinModal Mode 1 0 15.12 0 -323.45 0 0
MODAL LinModal Mode 2 0.08 0 0 0 1.81 383.14
MODAL LinModal Mode 3 -112.2 0 0 0 -2408.32 0.34
MODAL LinModal Mode 4 0 306.64 -0.19 340.49 -0.1 0
MODAL LinModal Mode 5 0 0.05 6009.59 2.49 -0.19 -0.31
MODAL LinModal Mode 6 -0.02 569.31 -0.84 -619.07 0.92 0
MODAL LinModal Mode 7 21.47 14.97 -6.09 50874.64 -1215.12 0.23
MODAL LinModal Mode 8 -787.03 0.43 -0.09 1474.5 43419.64 -0.27
MODAL LinModal Mode 9 0.02 0 -1.93 1.99 -2.56 -7812.74
MODAL LinModal Mode 10 -0.11 -739.91 0.74 1156.9 0.79 -0.14
MODAL LinModal Mode 11 -0.09 -8.77 -165.68 75.4 1.49 13.02
MODAL LinModal Mode 12 -0.09 0 4.38 -0.7 1.63 -2296.67
WATER LOAD LinMSStat Max 0 0 2510.23 0 0 0
WATER LOAD LinMSStat Min 0 0 2510.23 0 0 0
Elcentro TH LinModHist Max 576.19 0 0 1.24 12347.59 1.19
Elcentro TH LinModHist Min -619.89 0 0 -1.22 -13303.89 -1.41
15

4.2.2 El Centro – Flexible Base Support
Table 4.4 Base reaction for El Centro earthquake for flexible support condition
DEAD LinStatic 0 0 1855.27 -2.55 0 0
MODAL LinModal Mode 4 0 0.04 -2381.62 1.55 0.01 0.08
MODAL LinModal Mode 5 0.03 311.21 0.41 1549.88 -0.39 0
MODAL LinModal Mode 7 -717.49 0.06 0.03 8.3 8597.42 0.01
MODAL LinModal Mode 8 -0.01 565.09 -0.28 55.23 -0.01 0
MODAL LinModal Mode 9 0.02 0 0.88 -0.06 0.08 7265.57
MODAL LinModal Mode 10 -0.03 0.37 -324.21 4.06 0.16 4.2
MODAL LinModal Mode 11 -0.01 0 -25.2 0.03 -0.23 637.23
MODAL LinModal Mode 12 0.01 0.51 3389.79 5.47 0.04 3.26
Elcentro TH LinModHist Max 165.49 0.01 0 0.68 3296.1 0.26
Elcentro TH LinModHist Min -175.11 -0.01 0 -0.71 -3936.32 -0.23
16

4.2.3 Uttarkashi – Fixed Base Support
Table 4.5 Base reaction for Uttarkashi earthquake for fixed support condition
DEAD LinStatic 0 0 1855.27 -2.55 0 0
MODAL LinModal Mode 4 0 306.64 -0.19 340.49 -0.1 0
MODAL LinModal Mode 5 0 0.05 6009.59 2.49 -0.19 -0.31
MODAL LinModal Mode 6 -0.02 569.31 -0.84 -619.07 0.92 0
MODAL LinModal Mode 7 21.47 14.97 -6.09 50874.64 -1215.12 0.23
MODAL LinModal Mode 8 -787.03 0.43 -0.09 1474.5 43419.64 -0.27
MODAL LinModal Mode 9 0.02 0 -1.93 1.99 -2.56 -7812.74
MODAL LinModal Mode 10 -0.11 -739.91 0.74 1156.9 0.79 -0.14
MODAL LinModal Mode 11 -0.09 -8.77 -165.68 75.4 1.49 13.02
MODAL LinModal Mode 12 -0.09 0 4.38 -0.7 1.63 -2296.67
Uttarkashi TH LinModHist Max 123.94 0 0 2.1 2628.13 0.32
Uttarkashi TH LinModHist Min -152.48 0 0 -2.01 -3422.87 -0.32
17

4.2.4 Uttarkashi – Flexible Base Support
Table 4.6 Base reaction for Uttarkashi earthquake for flexible support condition
DEAD LinStatic 0 0 1855.27 -2.55 0 0
MODAL LinModal Mode 4 0 0.04 -2381.62 1.55 0.01 0.08
MODAL LinModal Mode 7 -717.49 0.06 0.03 8.3 8597.42 0.01
MODAL LinModal Mode 8 -0.01 565.09 -0.28 55.23 -0.01 0
MODAL LinModal Mode 9 0.02 0 0.88 -0.06 0.08 7265.57
MODAL LinModal Mode 10 -0.03 0.37 -324.21 4.06 0.16 4.2
MODAL LinModal Mode 11 -0.01 0 -25.2 0.03 -0.23 637.23
MODAL LinModal Mode 12 0.01 0.51 3389.79 5.47 0.04 3.26
Uttarkashi TH LinModHist Max 101.61 0 0 0.38 2202.23 0.15
Uttarkashi TH LinModHist Min -97.14 0 0 -0.39 -2144.7 -0.17
18

4.3 JOINT DISPLACEMENTS
The table below gives the maximum drift at the level of base slab which is at an
elevation of 21m. The drift is measured relatively with respect to the bottom end.
Table 4.7 Storey drift at the level of base slab
TABLE: Joint Displacements
Output Case
Base
Support
U1 U2 U3 R1 R2 R3
m m m radians radians radians
Elcentro TH Fixed 0.24743 0.00021 0.00838 0 0.00223 0.00004
Elcentro TH Flexible 0.16921 0.00004 0.02506 0 0.00516 0.00001
Uttarkashi
TH
Fixed 0.06155 0.00005 0.00225 0 0.00058 0.00001
Uttarkashi
TH
Flexible 0.09613 0.00003 0.01397 0 0.00289 0.00001
19

4.4 RESPONSE SPECTRUM CURVES
Fig 4.1 Response spectrum for El Centro earthquake for fixed base condition
Fig 4.2 Response spectrum for El Centro earthquake for flexible base condition
0.00
0.50
1.00
1.50
2.00
2.50
3.00
0.01 0.1 1 10 100
PseudoSpectrumAcceleration(g)
Time Period (seconds)
El Centro - Fixed Base
No Damping
2% Damping
5% Damping
10% Damping
0.00
0.50
1.00
1.50
2.00
2.50
3.00
3.50
0.01 0.1 1 10 100
PseudoSpectrumAccleration(g)
El Centro - Flexible Base
No Damping
2% Damping
5% Damping
10% Damping
20

Fig 4.3 Response spectrum for Uttarkashi earthquake for fixed base condition
Fig 4.4 Response spectrum for Uttarkashi earthquake for flexible base condition
0.00
0.50
1.00
1.50
2.00
2.50
3.00
3.50
4.00
0.01 0.1 1 10 100
PseudoSpectralAcceleration(g)
Uttarkashi - Fixed Base
No Damping
2% Damping
5% Damping
10% Damping
0.00
0.50
1.00
1.50
2.00
2.50
3.00
3.50
0.01 0.1 1 10 100
PseudoSpectrumAccelerarion(g)
Uttarkashi - Flexible Base
No Damping
2% Damping
5% Damping
10% Damping
21

4.5 DISPLACEMENT RESPONSE
Fig 4.5 Displacement response for El Centro earthquake for fixed base condition
Fig 4.6 Displacement response for El Centro earthquake for flexible base
condition
22

Fig 4.7 Displacement response for Uttarkashi earthquake for fixed base
condition
Fig 4.8 Displacement response for Uttarkashi earthquake for flexible base
condition
23

4.6 FORCE PROFILE
4.6.1 Axial Force Profile
Fig 4.9 Axial force envelope for El Centro earthquake
Fig 4.10 Axial force profile for water load
24

4.6.2 Shear force profile
Fig 4.11 Shear force envelope for El Centro earthquake
Fig 4.12 Shear force profile for water load (static case)
25

4.7 BENDING MOMENT PROFILE
4.7.1 Bending moment envelope for El Centro
Fig 4.13 Overturning moment envelope for El Centro
4.7.2 Bending moment profile for water load
Fig 4.14 Overturning moment profile for water load
26

4.7.3 Bending moment profile for El Centro
Fig 4.15 Bending moment profile for El Centro at 0.36s
Fig 4.16 Bending moment profile for El Centro at 0.56s
It can be seen from the fig 4.15 and fig 4.16 that there is a complete reversal of
overturning moment from step 18 to step 28.
27

4.8 STRESSES DEVELOPED IN SHELL
4.8.1 Resultant Forces for water load
Fig 4.17 Resultant forces acting in the shell for water load
4.8.2 Resultant moment for water load
Fig 4.18 Resultant moment acting in the shell for water load
28

CHAPTER 5
BASE ISOLATION
5.1 GENERAL
Base isolation is a technique to protect building structures from the destructive effects
of earthquakes by means of a mechanism that limits the forces transmitted from the
soil to the building. This approach has replaced ductility design concept as the latter
method has proved to be unsatisfactory and performance being far below the
expectation. It is adopted for new structures as well as retrofitting of existing
buildings and bridges. The strategies for achieving seismic isolation are,
1. Period-shifting of structures
2. Cutting-off load transmission path
During earthquakes, structures without seismic isolation are subjected to substantial
story drifts, which lead to the damage or even collapse of the building. Whereas,
providing isolators to the structures, makes it vibrate like a rigid body. The lateral
forces of isolated building are not only reduced in magnitude but also are fairly
redistributed over the floors, which further reduces the overturning moment of the
structure. A base isolation system to be effective must combine two basic features:
horizontal flexibility and high energy dissipation. The reduced stiffness of the
bearings shifts the fundamental frequency of the structure away from the energetic
region of the earthquake spectrum, and their elastoplastic or bilinear hysteric
properties limit the forces transmitted to the superstructure and dissipate energy.
5.2 TYPES
Base isolations are installed between the bottom of the building and its foundation.
Two types of isolation bearings are used – spring-like isolation bearings and sliding-
like isolation bearings. Spring-like bearings have considerable lateral flexibility help
in reducing the earthquake forces by changing the structure‟s fundamental period to
avoid resonance with the predominant frequency contents of the earthquake. Most
common elastomers used in elastomeric bearings are natural rubber, neoprene rubber,
butyl rubber and nitrile rubber. Sliding-type bearings filter out earthquake forces via
the discontinuous sliding interfaces, between which the forces transmitted to the
29

superstructure are limited by the maximum friction forces, regardless of earthquake
intensity. Typical spring-type isolation bearing is represented in Fig 5.1.
Fig 5.1 Elastomeric Bearing (spring type)
5.3 ANALYSIS
For the purpose of analysis, we have chosen spring-like isolation bearings. Base
isolators can be provided to structures in rigid soil only. The axial stiffness is found to
be 1751268 kN/m. The shear stiffness in each direction is 1751 kN/m. The ratio of
post yield shear stiffness to initial shear stiffness is taken as 0.2. Rubber isolators are
provided at the base of the structure and analysis is done for El Centro time history
data only.
Table 5.1 Modal period and frequencies for fixed base and isolated base
Fixed Base Isolated Base
Mode No. Period Frequency Period Frequency
Sec Cyc/sec Sec Cyc/sec
1 7.65 0.13 8.19 0.12
2 3.04 0.33 4.08 0.25
3 2.81 0.36 3.97 0.25
4 0.52 1.91 0.6 1.67
5 0.36 2.76 0.36 2.75
6 0.27 3.75 0.33 3.05
30

7 0.23 4.38 0.32 3.15
8 0.23 4.43 0.3 3.31
9 0.21 4.72 0.23 4.34
10 0.18 5.46 0.22 4.64
11 0.18 5.47 0.21 4.87
12 0.18 5.53 0.18 5.46
There is an increase in the natural period of the system from 7.65sec to 8.19sec. This
results in increased displacement, decreased acceleration and shear force at the base
of isolated structure.
Fig 5.2 Response Spectrum Curves for isolated base
Table 5.2 Base reaction for fixed base and isolated base
Support
Global
FX
Global
FY
Global
FZ
Global
MX
Global
MY
Global
MZ
Text KN KN KN KN-m KN-m KN-m
Fixed Base 619.892 0.001 0.001 1.219 13303.886 1.407
Isolated
Base
218.321 0.001 0.001 0.364 4693.925 0.245
0.00
1.00
2.00
3.00
4.00
5.00
6.00
7.00
0.01 0.1 1 10 100
PseudoSpectrumAccleration(g)
Base Isolation
No Damping
2% Damping
5% Damping
10% Damping
31

From the results above, it is found that, there is a reduction in the base shear as well as
overturning moment. There is a reduction in base shear from 619.892 kN to 218.321
kN, i.e., there is a 64.8% reduction in the base shear. Similarly, the overturning
moment is reduced from 13303.886 kN-m to 4693.925 kN-m, i.e., 64.7% reduction in
overturning moment.
Fig 5.3 Variation of storey drift along the height of the tank
The joint displacements of the tank at various levels of staging are represented as in
the Fig 5.3 for both fixed base condition and isolated base condition. The joint
displacement of the fixed base tank is found to greater than the isolated base
condition. The tank undergoes maximum lateral displacement in the fixed condition.
There is an increase in the displacement of the base isolated tank at the level of the
base which reduces the storey drifts at various staging levels. This implies that there is
a reduction of accelerations of the last level as well as the shear forces compared to
the fixed base support. For the tank with the fixed base support, reduction in seismic
excitation depends on the vibration of the structure and characteristics of the
superstructure, damping and the stiffness of the columns; whereas for the isolated
base support, it depends on the level of the seismic isolation system of isolator.
0
5
10
15
20
25
0 0.05 0.1 0.15 0.2 0.25 0.3
Elevationofthestorey(m)
Displacement (m)
Displacement at Levels of Tank
FIXED BASE BASE ISOLATED
32

5.4 CONCLUSION
Thus, the results show that there is significant reduction in base shear and overturning
moment when the base of the tank is isolated. The earthquake induced forces in the
structure are reduced upto 30% which results in controlled displacement of the
structure as discussed. Hence, providing base isolation significantly improves the
performance of the structure.
33

CHAPTER 6
SLOSHING DYNAMICS
6.1 GENERAL
The wobbling effect of liquid inside the container is called as sloshing. In other
words, when the liquid mass, either a part or full, has a relative oscillatory motion
against its container then it is said to be in sloshing. Any disturbance to the container
containing a liquid causes sloshing. The study of sloshing is called sloshing dynamics.
In most of the cases, the effect of sloshing is usually neglected assuming that the
liquid does not slosh in tank full condition and fluid as incompressible. However in
reality both the assumptions are incorrect. The effect of sloshing is important because
the response varies indefinitely upon considering sloshing, thus mis-predicting the
behaviour. Sloshing can be advantageous in some cases, especially when it acts as a
tuned liquid damper, leading to a much simpler response and hence economises the
design. On the other hand, in some other cases, neglecting sloshing underestimates the
response thus resulting in unexpected behaviour that may lead to collapse or spoiling
the functionality of structure. Nevertheless, the computational effort involved in
modelling sloshing is time consuming and a costlier process.
6.2 EFFECTS OF SLOSHING
Sloshing is classified into different types – simple planar, non-planar, rotational,
irregular beating, symmetric, asymmetric, quasi-periodic and chaotic. Occurrence of
sloshing has a global impact on natural period of the system, base shear and
overturning moment and local influence on member forces. Besides this, the heat
generated due to collision induces thermal stresses in the walls of container as a result
of friction and impulsive force on the container leaving a dent on the surface. These
parameters have a direct effect on dynamic stability and performance of structure.
Some structures which face adverse effects due to sloshing are fuel storage tanks,
chemical containers, elevated water tanks, container ships and foundations of offshore
structures. In this chapter, the effect of sloshing is studied on the global or structure-
level response quantities based on the empirical formulas given by Indian Standard
34

codes and partly from research papers published in recent times. Emphasis is laid on
the global effects than the local effects.
Sloshing is due to inadequate shear resistance offered by the liquid. The seismic load
induces inertial forces and these forces are transmitted by shear. Since the liquid
possess zero or very less shear modulus it slides off the container. The liquid mass as
a whole does not slosh as one single unit. Since the lower part is more confined than
the upper part which is rather free, there is a differential sloshing – maximum at
surface and minimum at base. The sloshing may be moderate or severe depending
upon the liquid level inside the container and cross sectional area or the spread of the
tank. In lower modes of vibration, it acts as a tuned mass damper and hence reduces
the system vibration. However in higher modes the same effect is magnified. Sloshing
results in excessive joint stress and yielding of members. Although the sloshing under
some conditions proves beneficial, the inadequacy of structure against yielding puts it
in danger. Except for materials whose monolithcity is unaffected by yielding as in
steel, cracking upon yielding leak the fluid which is highly dangerous especially the
inflammable chemicals. In addition to that, it causes separation of pipelines as they
are not designed to accommodate such large displacements. Moreover in elevated
water tanks sloshing occurs even when the tank is full since it is covered by a dome
structure which does not provide a vertical confinement to free surface.
The response is highly dependent on the mode of vibration. For higher modes of
vibration, it is possible that sloshing may not happen. Similarly it is also possible that
sloshing may not happen for the least mode. (But it is noted that the higher and lower
mode mentioned here is a case that is an absolutely dependent on the system
characteristics and load function. It may or may not happen for a particular
earthquake; however the possibility is very less.)
6.3 ANALYSIS
The sloshing effect in liquid storage tank is first studied by Housner (1963). He
proposed a two mass model system – the one which moves along with the structure
called the impulsive mass2
and that which sloshes called the convective mass. The
ratio of height of liquid column (measured from base of container) to the diameter of
2
The mass of structure (staging and container) also adds to the impulsive mass.
35

container is the factor that decides the amount of liquid that sloshes. Higher the ratio
lesser is the sloshing. It is because of this reason that some tanks though not designed
for sloshing undergo less damage due to seismic forces where the ratio is kept very
high. Though there were numerous studies on sloshing effect, all were based on
Housner‟s model and they attempted to make improvements to his model. Some of
those were API650, Eurocode 8: Part-4 (1998), IS1893:2002 (Part 2). Here, the effect
of sloshing is calculated based on IS1893:2002 (Part 2).
Base shear of Impulsive Mode is given by,
Vi = (Ah)i*( Mi + Ms)g
where,
Ah – Design horizontal seismic coefficient
Mi – Impulsive mass of liquid
Ms – Mass of empty container of elevated tank and one-third mass of staging
Base shear of Convective mode for Elevated Tank is given by,
Vc = (Ah)c Mc g
Overturning Moment of Impulsive mode for Elevated Tank is given by,
Mi
*
= (Ah)i [Mi (hi
*
+hs)+Ms hcg]*g
where,
hi
*
– Height of impulsive mass above bottom of tank wall
hs – Structural height of staging measured from top of foundation to the
bottom of container wall
Over turning Moment of Convective mode for Elevated Tank is given by,
Mc = (Ah)c Mc (hc
*
+hs)*g
where,
hc
*
– Height of convective mass above bottom of tank wall
Root mean square of the impulsive and convective masses is taken for the resultant
shear force and over turning moment respectively.
36

6.3.1 Results
Mass of the staging : 192775.10 kg
Mass of the shell : 88969.90 kg
Mass of the liquid (tank full) : 546794.20 kg
Mass of the liquid (half full) : 273397.10 kg
Stiffness of the staging : 172338.80 kN/m
Table 6.1 Dynamic response quantities under sloshing
Response Quantity Tank Empty Hall Full Tank Full
Time Period (sec)
Impulsive 6.65 9.38 10.09
Convective NA 4.42 3.87
Base Shear (kN) 340.4 919.76 685.92
Overturning Moment (kN.m) 5395.38 21334.43 14918.78
6.4 CONCLUSION
When the tank is empty, it is found that the time period of the impulsive mass is
6.65sec. The base shear is found to be 340.40kN and overturning moment is
5395.38kN.m.
When the tank is half-full, it is found that the time period of the impulsive mass is
9.38 sec and convective mass is 4.42 sec. The base shear is found to be 919.76 kN and
overturning moment is 21334.43 kN.m.
When tank is completely full, it is found that time period of the impulsive mass is
10.09 sec and convective mass is 3.87 sec. The base shear is found to be 685.92 kN
and overturning moment is 14918.78 kN.m.
From the results, it is observed that base reactions are much higher in half-full
condition than when it is completely full. Hence neglecting sloshing underestimates
the reaction quantities. As the height of liquid column decreases, the mass of
convective liquid mass becomes almost equal to the total liquid mass.
37

6.5 LIMITATIONS
Although the impact of sloshing is approximately predicted, the analysis has not taken
the following factors into account.
1. Compressibility of the fluid
2. Viscosity of the fluid
3. Fluid structure interaction
4. Elasticity of the container
5. Thermal stresses
38

CHAPTER 7
CONCLUSIONS AND RECOMMENDATIONS
7.1 CONCLUSIONS
a. Modal Period and Frequencies: The different modes of frequencies for fixed
and flexible support conditions are determined. It is found that there is
significant increase in the time periods when flexibility of sub soil is
considered. For further need of increase in time period, foundation should be
well connected to the soil beneath the ground for which a detailed study has to
be conducted on strength and stiffness characteristics of sub soil.
b. Base Reaction: The base reaction have a reduction of 71% of base shear and
70% of reduction in overturning moment for El Centro ground motion when
flexibility of base is considered, whereas the corresponding reductions are
36% and 37% for Uttarkashi ground motion. This reduction is due to a slight
relaxation in confinement at the base of the structure in flexible support. In
flexible base soil is stressed as a result of deflection of base.
c. Response Spectrum: The response curves are plotted for peak ground
acceleration against time period for all four cases. For the structure to remain
in safe zone, damping should be increased by installing dampers and energy
dissipaters The response curves have two peaks in flexible support condition
while only one peak is observed in fixed base condition. Isolation of
foundation releases confinement to some extent which results in increase in
degree of freedom. In fixed base, the structure has a peak response at 2.81 sec
whereas in flexible base the same values are 2.81 sec and 4.35 sec.
d. Base Isolation: The storey drift in the fixed base tank is greater than the
displacement of base isolated tank. There is an increase in the displacement of
the base isolated tank at the level of the base which reduces the relative
displacements between the various staging levels. This implies that there is a
reduction of accelerations of the last level, and 64.8% reduction of base shear
and 64.7% reduction of overturning moment compared to the fixed base
support.
e. Sloshing: Sloshing results in increased base reactions especially in half-full
conditions than when tank is completely full. For lesser water levels,
39

convective liquid mass is found to be greater than impulsive liquid mass
whereas for higher water levels impulsive mass are found to be dominative.
When the water level is very less, the impulsive mass almost vanishes.
7.2 RECOMMENDATIONS
a. It is highly recommended to follow four virtues of earthquake resistant design
of structures – lateral strength, stiffness, ductility and configuration.
b. Capacity Based Design must be adopted according to which columns are
stronger than beams and foundations are made to be stronger than columns.
This results in formation of plastic hinges in beams, otherwise if beams are
made stronger than columns then plastic hinges are formed in columns. The
former case leads to local damage while the latter case leads to global or
structure level damage. “Structural Fuse” can also be provided to ensure
strong column weak beam design.
c. The base slab is made sufficiently rigid to avoid any cracks in it which
otherwise leads to water leakage.
d. Ductile reinforcement must be provided according to IS13920:1993 to
improve ductility and performance of structure during earthquake.
e. The material used for base isolation must be thoroughly studied and it is to be
incorporated with great care. Base isolators are strictly not recommended for
soft soils.
f. Provision of baffle walls inside the tank, reduces sloshing. Since the direction
of earthquake is highly uncertain, it is recommended to provide in radial
orientation inside the cylindrical container. It should be well connected to the
base slab to withstand the very high inertial forces.
7.3 SCOPE FOR FUTURE WORK
The scope of the project is limited in certain areas of analysis. The following are the
areas on which future work can be done,
1. Non-linear analysis of the structure can be carried out.
2. Introducing plastic hinges in the structure.
40

3. Carrying out analysis for various values of viscous damping.
4. Consideration of constructional feasibilities.
5. Considering stresses developed due to friction, temperature variations,
chemical reactions, alkalinity or pH of water.
6. Considering P-∆ effect.
41

REFERENCES
1. Anil K. Chopra (2004), “Dynamics of Structures - Theory and Applications
to Earthquake Engineering”, Second Edition, Prentice Hall of India Pvt. Ltd.
2. Handbook on Seismic Retrofit of Buildings, CPWD, IBC, IIT-M
3. IS 1893:2002, “Criteria for Earthquake Resistant Design of Structures”, Part 1:
General Provisions and Buildings and Part 2: Liquid Retaining Tanks (Draft),
Bureau of Indian Standards.
4. Suchita Hirde, Asmita Bajare, Manoj Hedaoo, International Journal of
Advanced Engineering and Research Studies, 1(1), (2011), 78-87.
5. Wang, Yen-Po, “Fundamentals of Seismic Base Isolation”, International
Training Programs for Seismic Design of Building Structures.
6. Athamnia Brahim, Ounis Abdelhafid, “Effects of seismic isolation in the
reduction of the seismic response of the Structure”, International Journal of
Applied Engineering Research, Dindigul, 2(2), (2011), 290-295.
7. Housner, G.W., “The dynamic behavior of water tanks”, Bulletin of
Seismological Society of America, 53(2), (1963), 381-387.
8. Chirag N. Patel, Shashi N. Vaghela, H. S. Patel, “Sloshing Response of
Elevated Water Tank over Alternative Cloumn Proportionality”, International
Journal of Advanced Engineering Technology, 3(4),(2012).60-63.
9. Malhotra, P.K., Wenk, T. and Wieland, M., “Simple procedure for seismic
analysis of liquid-storage tanks”, Structural Engineering International,
3/2000, IBK (2010).
10. Kilic, S.A, “Simulation of sloshing effects in cylinderical tanks and evaluation
of seismic performance”, TCLEE: 2009 Lifeline Earthquake Engineering in a
Multihazard Environment, 372-381.
11. Raouf A.Ibrahim, Liquid Sloshing Dynamics: Theory and Applications,
Cambridge University Press (2005).
12. Pacific Earthquake Engineering Research Center, University of California,
Berkeley, website: http://peer.berkeley.edu/
13. Consortium of Organizations for Strong Motion Observation Systems,
website: http://www.cosmos-eq.org/
42

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