NONLINEAR SEISMIC RESPONSE OF REINFORCED
CONCRETE PEDESTALS IN ELEVATED WATER TANKS
by
Razmyar Ghateh
Master of Applied Science,
Tehran, Iran, 2006
A dissertation
presented to Ryerson University
in partial fulfillment of the
requirements for the degree of
Doctor of Philosophy
In the program of
Civil Engineering
Toronto, Ontario, Canada, 2014
©Razmyar Ghateh 2014
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Author’s declaration
I hereby declare that I am the sole author of this dissertation.
I authorize Ryerson University to lend this dissertation to other institutions or individuals for the
purpose of scholarly research
Razmyar Ghateh
I further authorize Ryerson University to reproduce this dissertation by photocopying or by other
means, in total or in part, at the request of other institutions or individuals for the purpose of
scholarly research.
I understand that my dissertation may be made electronically available to the public.
Razmyar Ghateh
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NONLINEAR SEISMIC RESPONSE OF REINFORCED
CONCRETE PEDESTALS IN ELEVATED WATER TANKS
Doctor of Philosophy 2014
Razmyar Ghateh
Department of Civil Engineering
Ryerson University
Abstract
Elevated water tanks are employed in water distribution facilities in order to provide storage
and necessary pressure in water network systems. These structures have demonstrated poor
seismic performance in the past earthquakes. In this study, a finite element method is employed
for investigating the nonlinear seismic response of reinforced concrete (RC) pedestal in elevated
water tanks. A combination of the most commonly constructed tank sizes and pedestal heights in
industry are developed and investigated. Pushover analysis is performed in order to construct the
pushover curves, establish the overstrength and ductility factor, and evaluate the effect of various
parameters such as fundamental period and tank size on the seismic response factors of elevated
water tanks. Furthermore, a probabilistic method is implemented to verify the seismic
performance and response modification factor of elevated water tanks. The effect of wall
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openings in the seismic response characteristics of elevated water tanks is investigated as well.
Finally, the effect of axial compression on shear strength of RC pedestals is evaluated and
compared to the nominal shear strength from current guideline and standards.
The results of the study show that the tank size, pedestal height, fundamental period, and
pedestal height to diameter ratio, could significantly affect the overstrength and ductility factor
of RC pedestals. The nonlinear dynamic analysis results reveal that under the maximum
considered earthquake (MCE) intensity, light and medium size tank models do not experience
significant damages. However, heavy tank size models experience more damage in comparison
with light and medium tank sizes. This study shows that the current code response modification
factor values are appropriate for light and medium tank sizes; however they need to be modified
for heavy tank sizes. The results of this study also reveal that if the pedestal wall openings are
designed based on current design guidelines, then nearly identical nonlinear seismic response
behaviour is expected from the pedestals with and without openings. Finally, it is shown that the
pedestal maximum shear strength calculated by finite element method for the full tank state is
higher than the nominal shear strength determined based on the current design guidelines.
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Acknowledgements
I would like to express my greatest appreciation to many people who have provided me with
support and help throughout writing this thesis.
First and foremost, my sincere gratitude goes to my supervisor Professor Reza Kianoush
whose knowledge, support, patience, and encouragement has helped me to the highest degree
during my research. Without his guidance and trust in my research, this thesis would not have
been possible. Working under his supervision has been a great opportunity in my life and I
would like to show my greatest appreciation to him.
I would also like to thank the reviewing committee for their revisions and suggestions.
I also wish to thank all my colleagues in the Civil Engineering Department at Ryerson
University.
Finally, I am very grateful for the financial support provided by Ryerson University in the
form of a scholarship.
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Table of contents
Author’s declaration ii
Abstract iii
Acknowledgement v
Table of contents vi
List of figures xi
List of tables xvi
List of symbols xviii
1 Introduction 1
1.1 Overview 1
1.2 Objectives and scope of the study 5
1.3 Thesis layout 7
2 Literature review 10
2.1 General 10
2.2 Performance of elevated water tanks under earthquake loads 10
2.3 Previous research 14
2.3.1 Seismic response of liquid-field tanks 14
2.3.2 Seismic response of elevated water tanks 16
2.4 Other related studies 21
2.4.1 Response modification factor 21
2.4.2 Design codes and standards 26
3 Analysis methods 29
3.1 General 29
3.2 Methods of seismic analysis 30
3.2.1 Nonlinearity in reinforced concrete structure analysis 31
3.3 Code-based analysis and design of elevated water tanks 33
3.4 Static nonlinear (pushover) analysis 34
3.4.1 Procedure of performing pushover analysis 35
3.4.2 Types of pushover analysis 37
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3.4.3 Bilinear approximation of pushover curves 38
3.5 Transient dynamic (Time-history) analysis 40
3.5.1 Equation of motion of a SDOF system subjected to force P(t) 41
3.5.2 Equation of motion of a SDOF system subjected to seismic excitations 42
3.5.3 Equation of motion of a multi-degree-of-freedom system 43
3.5.4 Equation of motion of a nonlinear system 44
3.5.5 Solution of nonlinear MDOF dynamic differential equations 46
3.6 Incremental dynamic analysis (IDA) 47
3.7 Summary 49
4 Finite element model development and verification 50
4.1 General 50
4.2 Finite element modeling of reinforced concrete 51
4.3 SOLID65 element 51
4.3.1 FE formulation of reinforced concrete in linear state 52
4.3.2 FE formulation of reinforced concrete after cracking 53
4.3.3 Failure criteria of reinforced concrete element 54
4.4 Solution of static and dynamic nonlinear finite element equations 56
4.4.1 Solution method for nonlinear static analysis equation 56
4.4.2 Solution method for nonlinear dynamic equations of motion 57
4.5 Reinforced concrete material nonlinearity 59
4.5.1 Stress-strain curve of concrete 59
4.5.2 Stress-strain curve of steel rebar 61
4.6 Validation of proposed finite element reinforced concrete model 63
4.6.1 Reinforced concrete beam test verification 63
4.6.2 Reinforced concrete wall test verification 66
4.7 Finite element model of RC pedestal in elevated water tanks 70
4.8 Summary 72
5 Pushover analysis of RC elevated water tanks 74
5.1 General 74
5.2 Constructing the elevated water tank prototypes 75
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5.2.1 Standard dimensions and capacities of elevated water tanks 76
5.2.2 Selection criteria for constructing the prototypes 77
5.3 Design of prototypes based on code requirements 81
5.3.1 Design of RC pedestals for gravity loads 81
5.3.2 Design of RC pedestals for seismic loads 84
5.3.2.1 Seismic base shear 86
5.4 Pushover analysis of FE models 89
5.4.1 Defining pilot group of FE models 89
5.4.2 Results of pushover analysis 91
5.4.3 Observed patterns in pushover curves 94
5.5 Cracking propagation pattern 98
5.6 Summary 105
6 Analyzing pushover curves and establishing seismic response factors 108
6.1 General 108
6.2 Interpreting pushover curves 109
6.3 Bilinear approximation of pushover curves 109
6.4 Seismic response factors 113
6.4.1 Overstrength factor 115
6.4.2 Ductility factor 115
6.4.3 Response modification factor 118
