-
TECHNICAL UNIVERSITY OF CIVIL ENGINEERING BUCHAREST
Ph. D. THESIS
SEISMIC BEHAVIOUR OF REINFORCED CONCRETE STRUCTURES USING METAL
ADDITIVES
Ph. D. STUDENT
ENG. LUMA AHMED ADAY AL-JUMAILI
SCIENTIFIC SUPERVISOR
PROF. UNIV. DR. ENG. MIRCEA IEREMIA
BUCHAREST
2013
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MINISTRY OF NATIONAL EDUCATION - ROMANIA
TECHNICAL UNIVERSITY OF CIVIL ENGINEERING BUCHAREST
SEISMIC BEHAVIOUR OF REINFORCED CONCRETE STRUCTURES USING METAL
ADDITIVES
A THESIS SUBMITTED TO THE
TECHNICAL UNIVERSITY OF CIVIL ENGINEERING BUCHAREST IN PARTIAL
FULFILLMENT OF
THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY IN
CIVIL ENGINEERING
Ph. D. STUDENT
ENG. LUMA AHMED ADAY AL-JUMAILI
SCIENTIFIC SUPERVISOR
PROF. UNIV. DR. ENG. MIRCEA IEREMIA
BUCHAREST
2013
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i
DEDICATIONS
To
My Dear Husband & My Son & Beloved Mother
The Catalysts of My
"Dreams"
To Those Who Taught Me Everything That Matters
For making it worthwhile
Luma
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ii
ACKNOWLEDGMENTS
I would like to express my deep appreciation and gratitude to
my
supervisor Prof. Univ. Dr. Eng. Mircea Ieremia who dedication to
this work has
been boundless. He worked to ensure the high quality of the
material of this text.
It has been my good fortune to have the advice and guidance from
him.
I would like also to extend my thanks to doctoral examination
committee
members and to thank the anonymous reviewers for helpful
comments, and the
professors, staff and doctoral students of Technical University
of Civil
Engineering Bucharest for their kind assistance .
I would like also to convey my appreciation to Flavia Florea and
Daniela
Sharaf Eldin for their cooperation and assistance that helped to
achieve the goal.
Sincere appreciation is due to my family, for their patience,
encouragement
and help during the work.
Finally, I would like to thank all kind, helpful and lovely
people who
helped me directly or indirectly to complete this work and to
apologize to them
for not being able to mention them by name only in the stillness
of my heart.
Luma
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iii
List of Contents
Title Page
Dedication . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . i
Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . ii
Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . vi
List of Abbreviation . . . . . . . . . . . . . . . . . . . . . .
. . . . . . vii
CHAPTER ONE
INTRODUCTION
1
1.1 Scope of the Work . . . . . . . . . . . . . . . . . . . . .
. . . . . . 3
1.2 Thesis Outlines . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . 4
CHAPTER TWO
GENERAL BEHAVIOUR OF REINFORCED CONCRETE
5
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . 5 2.2 Behavior of Concrete Failing in Compression . . .
. . . . . . . . . . . . . 5
2.3 Strength under Biaxial and Triaxial Loadings . . . . . . . .
. . . . . . . . . 7
2.4 Compressive Strength of Cracked Reinforced Concrete . . . .
. . . . . . . . . 8
2.5 Triaxial Loadings . . . . . . . . . . . . . . . . . . . . .
. . . . . . 10
2.6 Cracking . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . 11
2.6.1 Types of Cracks . . . . . . . . . . . . . . . . . . . . .
. . . . . 11
2.6.2 Development of Cracks Due to Loads. . . . . . . . . . . .
. . . . . . 12
2.6.3 Limits on Crack Width . . . . . . . . . . . . . . . . . .
. . . . . 14
2.7 Reinforcing Steel . . . . . . . . . . . . . . . . . . . . .
. . . . . . . 15
2.7.1 Behavior of Reinforcing Steel . . . . . . . . . . . . . .
. . . . . . . 15
2.7.2 Interaction of Concrete and Reinforcement. . . . . . . . .
. . . . . . . 17
2.7.2.1 Bond . . . . . . . . . . . . . . . . . . . . . . . . . .
17
2.7.2.2 Tension Stiffening . . . . . . . . . . . . . . . . . . .
. . . 18
CHAPTER THREE
HIGH PERFORMANCE CONCRETE PROPERTIES
21
3.1. Introduction. . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . 21
3.2 Composition of High Performance Concrete . . . . . . . . . .
. . . . . . . 22
3.3 Comparison between the Microstructure of HPC and NSC. . . .
. . . . . . . . 22
3.4 Mixture Proportions for HPC . . . . . . . . . . . . . . . .
. . . . . . . 26
3.5 Features of High Performance Concrete . . . . . . . . . . .
. . . . . . . . 27
3.5.1 Strength . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . 27
3.5.2 Durability . . . . . . . . . . . . . . . . . . . . . . . .
. . . . 30
3.6 Applications of HPC . . . . . . . . . . . . . . . . . . . .
. . . . . . . 31
3.7 High Performance Fiber Reinforced Cement Composites . . . .
. . . . . . . . 31
3.8 Types of Fiber. . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . 32
3.9 Compressive Strength . . . . . . . . . . . . . . . . . . . .
. . . . . . 34
3.10 Stress-Strain Relationship of High Performance Fiber
Reinforced Concrete . . . .
Composites 34
3.10.1 Ductility . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . 35
3.10.2 Strain Hardening . . . . . . . . . . . . . . . . . . . .
. . . . . 36
3.11 Mechanics of Fiber Reinforced Concrete Composites . . . . .
. . . . . . . . 37
3.12 Fiber-Matrix Reinforcing Effectiveness . . . . . . . . . .
. . . . . . . . 38
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3.13 Considerations of Structural Design . . . . . . . . . . . .
. . . . . . . . 39
3.14 Applications of Fiber Reinforced Concrete . . . . . . . . .
. . . . . . . . 40
CHAPTER FOUR
CURRENT STATE OF RESEARCH
43
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . 43
4.2 Previous Research works . . . . . . . . . . . . . . . . . .
. . . . . . . 43
4.3 Numerical studies . . . . . . . . . . . . . . . . . . . . .
. . . . . . 51
CHAPTER FIVE
SEISMIC PRESCRIPTIONS FOR REINFORCED CONCRETE STRUCTURES
56
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . 56
5.2 Seismic Design Factors . . . . . . . . . . . . . . . . . . .
. . . . . . 57
5.3 Seismic Design Categories . . . . . . . . . . . . . . . . .
. . . . . . . 58
5.4 Building Performance Level . . . . . . . . . . . . . . . . .
. . . . . . 59
5.5 Method of Analysis . . . . . . . . . . . . . . . . . . . . .
. . . . . . 60
5.5.1 Elastic Methods of Analysis . . . . . . . . . . . . . . .
. . . . . . 60
5.5.2 Inelastic Methods of Analysis . . . . . . . . . . . . . .
. . . . . . . 61
5.6 Effect of Ductility on Seismic Forces . . . . . . . . . . .
. . . . . . . . . 62
5.7 Performance Requirements of Building . . . . . . . . . . . .
. . . . . . . 64
5.8 Force Based Design Procedure . . . . . . . . . . . . . . . .
. . . . . . 64
5.9 Displacement Based Design . . . . . . . . . . . . . . . . .
. . . . . . 66
5.10 Seismic Loads According UBC97 . . . . . . . . . . . . . . .
. . . . . . 66
5.10.1 Design Base Shear . . . . . . . . . . . . . . . . . . . .
. . . . 67
5.10.2 Vertical Distribution of Force . . . . . . . . . . . . .
. . . . . . 69
5.11 Drift Limitations . . . . . . . . . . . . . . . . . . . . .
. . . . . . 69
5.12 Story Drift and Average Drift . . . . . . . . . . . . . . .
. . . . . . . 70
5.13 General Assumptions and Requirements for Modeling and
Design (FEMA 356) . . 71
5.13.1 Linear Procedures . . . . . . . . . . . . . . . . . . . .
. . . . 71
5.13.2 Nonlinear Procedures . . . . . . . . . . . . . . . . . .
. . . . . 71
5.14 Capacity Spectrum Method (ATC-40 Procedure A) . . . . . . .
. . . . . . . 73
5.15 Conversion of Pushover curve to Capacity Spectrum Curve . .
. . . . . . . . 75
5.16 Determination of Performance Point . . . . . . . . . . . .
. . . . . . . . 78
5.17 Description of Seismic Hazard . . . . . . . . . . . . . . .
. . . . . . . 78
CHAPTER SIX
EXPERIMENTAL PROGRAM OF HIGH PERFORMANCE CONCRETE
MATERIALS
80
6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . 80
6.2 Experimental Procedures . . . . . . . . . . . . . . . . . .
. . . . . . . 80
6.2.1 Materials of Experimental Program . . . . . . . . . . . .
. . . . . . 80
6.2.2 Experimental Setup . . . . . . . . . . . . . . . . . . . .
. . . . . 81
6.2.3 Test Results of Plain Concrete . . . . . . . . . . . . . .
. . . . . . 81
6.3 Parameters Tested . . . . . . . . . . . . . . . . . . . . .
. . . . . . 82
6.3.1 Modulus of Elasticity . . . . . . . . . . . . . . . . . .
. . . . . . 82
6.3.2 Analytical Stress-Strain Curve for HP-HSC . . . . . . . .
. . . . . . . 83
6.3.3 HP/HS Fibrous Concrete . . . . . . . . . . . . . . . . . .
. . . . 84
6.3.4 Stress-Strain Behavior of Fibrous Concrete . . . . . . . .
. . . . . . . 84
6.3.5 Compressive Strength . . . . . . . . . . . . . . . . . . .
. . . . . 85
6.3.6 Strain at Peak Stress . . . . . . . . . . . . . . . . . .
. . . . . . 86
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6.3.7 Presented Parameters for FRC . . . . . . . . . . . . . . .
. . . . . 86
6.4 Design Recommendations . . . . . . . . . . . . . . . . . . .
. . . . . 88
6.5 Experimental Procedures Conclusion . . . . . . . . . . . . .
. . . . . . . 89
CHAPTER SEVEN
SIESMIC ANALYSIS OF HIGH PERFORMANCE REINFORCED CONCRETE
FRAMES
90
7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . 90
7.2 Case Study 1 . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . 91
7.2.1 Description of Building . . . . . . . . . . . . . . . . .
. . . . . . 91
7.2.2 System Analysis Results and Observations . . . . . . . . .
. . . . . . 92
7.2.2.1 Dynamic Linear Analysis Results . . . . . . . . . . . .
. . . . 92
7.2.2.2 Static Linear Analysis Results . . . . . . . . . . . . .
. . . . 92
7.2.2.3 Static Nonlinear Analysis Results . . . . . . . . . . .
. . . . . 94
7.2.2.4 Nonlinear Dynamic Analyses Results (Time History) . . .
. . . . . 100
7.3 Case Study 2 . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . 102
7.3.1 Description of Building . . . . . . . . . . . . . . . . .
. . . . . . 102
7.3.2 System Analysis Results and Observations . . . . . . . . .
. . . . . . 103
7.3.2.1 Dynamic Linear Analysis Results . . . . . . . . . . . .
. . . . 103
7.3.2.2 Static Linear Analysis Results . . . . . . . . . . . . .
. . . . 103
7.3.2.3 Static Nonlinear Analysis Results . . . . . . . . . . .
. . . . . 105
7.3.2.4 Nonlinear Dynamic Analyses Results (Time History) . . .
. . . . . 109
7.4 Case Study 3 . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . 111
7.4.1 Description of Building . . . . . . . . . . . . . . . . .
. . . . . 111
7.4.2 System Analysis Results and Observations . . . . . . . . .
. . . . . . 112
7.4.2.1 Dynamic Linear Analysis Results . . . . . . . . . . . .
. . . . 112
7.4.2.2 Static Linear Analysis Results . . . . . . . . . . . . .
. . . . 113
7.4.2.3 Static Nonlinear Analysis Results . . . . . . . . . . .
. . . . . 114
7.4.2.4 Nonlinear Dynamic Analyses Results (Time History) . . .
. . . . . 118
7.5 Case Studies Conclusion . . . . . . . . . . . . . . . . . .
. . . . . . . 120
CHAPTER EIGHT
CONCLUSIONS, CONTRIBUTIONS AND SUGGESTIONS FOR FUTURE
WORK
121
8.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . 121
8.2 Contributions . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . 122
8.3 Suggestions for Future Work . . . . . . . . . . . . . . . .
. . . . . . . 122
REFERENCES 123
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ABSTRACT High Performance Concrete (HPC) has recently become a
widely used concrete
construction material for modern buildings, bridges, and
pavements, etc. To produce such a
better quality of concrete, chemical and mineral admixtures such
as fly ash, slag cement, and
silica fume, ground granulated blast furnace slag, as well as
air-entraining agents are
commonly used in the field construction. The improvement of the
Reinforced Concrete (RC)
given by metal additives and developing the effect of metal
additives on RC structures when
subjected to earthquake loads to get high performance
properties. The aim of this work is
presenting the development of concrete which does not only
concern on the strength of
concrete, but many other aspects to be satisfied. So for this,
addition of pozzolanic materials
along with superplasticizer is used for low water cement ratio.
The present work use silica
fume which provides good pozzolanic activity, it is a good
material for the production of
HPC; it improves concrete characteristics and gets High Strength
Concrete (HSC). Steel
fibers increase the ductility of HPC, and concrete does not fail
even after reaching high strain
value. Thus this work presents complete stress-strain case study
behaviour with its equation of
HPC under compression. The comparison between the experimental
and analytical results
showed a good agreement.
To turn of Performance Based Seismic Engineering (PBSE) to
produce reality structures
with predictable seismic performance, a comprehensive and
well-coordinated effort by
professionals from several disciplines is required. The main aim
of this study is the
investigation of the behavior of metal additives on the RC frame
system building subjected to
seismic loading. The work presents three different multistory RC
frame building tested with
and without metal additives according to the UBC97 code, and
presented seismic response of
a high performance RC frame building system and compares it to
the response of a Normal
RC frame building of the same dimensions. RC frame buildings are
made through selective
use of three different cases: Normal RC without metal additives
and two cases with metal
additives (using silica fume only HPC and silica fume with steel
fiber 2% HPSFC), which
further minimizes dead and seismic loads. The work is describing
the cases, and the results of
the linear static, nonlinear static and nonlinear dynamic
analysis of the three framed building
systems. The response in terms of force displacement
relationships as well as in terms of base
shear, top displacements and time history compared to the
response of the same building with
and without metal additives.
The results for all case studies referred to the displacements
of HPSFC frame building
substantially smaller than that of HPC and Normal RC frame
buildings. Higher stiffness of
HPSFC building results in substantially than for HPC and Normal
RC frame buildings. The
margin safety against collapse is high, sufficient strength and
displacement reserves, there are
mount of dissipated energy especially when using HPSFC or HPC
frame. The results obtained
in terms of demand, capacity and plastic hinges gave an insight
into the real behaviour of
structures.
The design and analysis of RC frame building with and without
additives subjected to
seismic load are carried out using ETABS software tool.
Keywords: High Performance Concrete, High Strength Concrete,
Supplementary Cementing Material,
Steel Fiber Reinforced Concrete, Ductility, Structural Analysis,
Seismic behavior, Frame
Structures, Nonlinear analysis.
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ACI American Concrete Institute
ADRS Acceleration-Displacement Response Spectra
ASTM American Society for Testing and Materials
ATC Applied Technical Council
CFRP Carbon Fiber Reinforced Polymer
C-S-H Calcium Silicate Hydrate
DCR Demand/Capacity Ratio
FEMA Federal Emergency Management Agency
FRC Fiber Reinforced Concrete
FRCC Fiber-Reinforced Concrete or Cement Composite
FRP Fiber Reinforced Polymeric
GFRP Glass fiber reinforced polymer
GRC Glass Reinforced Cement
HPC High Performance Concrete
HPFRC High Performance Fiber Reinforced Concrete
HPFRCC High Performance Fiber Reinforced Cement Composite
HPSFC High Performance Steel Fiber Concrete
HSC High Strength Concrete
LFA Lateral Force Analysis
LFRS Lateral Force Resisting System
MDOF Multidegree-of-Freedom systems
MRF Moment Resisting Frames
MTS 815 Metropolitan Transit System
NEHRP National Earthquake Hazard Reduction Program
NSC Normal Strength Concrete
OPC Ordinary Portland Cement
PBSE Performance Based Seismic Engineering
PC Prestressed Concrete
PGA Peak Ground Acceleration
RC Reinforced Concrete
RI Reinforcing Index
RPC Reactive Powder Concrete
SCC Self-Consolidating Concrete
SCM Supplementary Cementitious Material
SDC Seismic Design Categories
SDOF Single Degree Of Freedom
SFRC Steel Fiber Reinforced Concrete
SUG Seismic Use Group
UBC Uniform Building Code
W/C Water Cement Ratio
W/CM Water Cementitious Materials Ratio
List of Abbreviation
http://click.infospace.com/ClickHandler.ashx?du=www.concrete.org%2fgeneral%2fhome.asp&ru=http%3a%2f%2fwww.concrete.org%2fgeneral%2fhome.asp&ld=20120304&ap=1&app=1&c=babylon2.hp.row&s=babylon2&coi=374914&cop=main-title&euip=82.76.70.224&npp=1&p=0&pp=0&pvaid=e3b06e0f394d426082d92efcd62c7a31&ep=1&mid=9&hash=755188B551EC84C027851C7270ED6B9E
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CHAPTER ONE
INTRODUCTION
Concrete is the most widely used man-made construction material
in the world. It is
obtained by mixing cementitious materials, water, aggregate and
sometimes admixtures in
required proportions. Fresh concrete or plastic concrete is
freshly mixed material which can
be moulded in to any shape hardens into a rock-like mass known
as concrete. The hardening
is because of chemical reaction between water and cement, which
continues for long period
leading to, stronger with age [1]. The utility and elegance as
well as the durability of concrete
structures, built during the past century with Ordinary Portland
Cement (OPC) and plain
round bars of mild steel, the easy availability of the
constituent materials (whatever may be
their qualities) of concrete and the knowledge that virtually
any combination of the
constituents leads to a mass of concrete have bred contempt.
Strength was emphasized
without a thought on the durability of structures. The
particularly true of concrete structures
which were constructed by which (a) the use of high strength
rebars with surface
deformations HSC started becoming common, (b) significant
changes in the constituents and
properties of cement were initiated, and (c) engineers started
using Supplementary
Cementitious Materials (SCM) and admixtures in concrete, often
without adequate
consideration. Fly ash, ground granulated blast furnace slag,
rice husk ash, high reactive
metakaolin, silica fume are some of the pozzolanic materials
which can be used in concrete as
partial replacement of cement. A number of studies are going as
abroad to study the impact of
use of these pozzolanic materials as cement replacements and the
results are encouraging. The
strength, durability and other characteristic of concrete
depends on the properties of its
ingredients, proportion of mix, method of compaction and other
controls during placing and
curing.
HPC is defined according to ACI 363-1992 [3] as concrete, which
meets special
performance and uniformity requirements that can't always be
achieved by using only the
conventional materials and normal mixing, placing and curing
practice. During the past
decade, HPC has become popular and increasing constructions in a
hostile environment make
HPC widely use [2]. Typical high performance requirements
specify high strength, enhanced
impermeability, and high tensile strength and other special
requirements. HPC is achieved by
using super plasticizen to reduce water/cm ratio and by using
SCM, which usually combines
high strength with high durability. High Performance/High
Strength Concrete (HPC/HSC)
leads to the design of smaller sections and reduces the dead
weight, allowing longer spans and
more useful area of structures. Reduction in mass is also
important for economical design of
seismic resistant. Strength, ductility and durability are the
important factors to be considered
in the design of earthquake resistant RC structures. Due to the
inherent brittleness of HP/HSC,
it lowers its post-peak portion of the stress strain diagram
almost vanishes or descends
steeply. This inverse relation between the strength and
ductility is a serious drawback for the
use of HP/HSC and a compromise to this drawback can be obtained
by the addition of
discontinuous short steel fibers in to the concrete. When
concrete cracks, the randomly
oriented fibers arrest a microcracking mechanism and limit the
crack propagation, thus
improving the strength and ductility thereby enhances the
durability of structural elements [4].
RC structures are made up of two materials with different
characteristics, namely,
concrete and steel. Steel can be considered as a homogeneous
material with generally well
defined material properties. The development of analytical
models for the response of RC
structures is complicated due to the following factors:
1. RC is a composite material made up of concrete and steel, two
materials with very different physical and mechanical
behaviour.
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2
2. Concrete exhibits nonlinearities even under low level of
loading due to nonlinear material behaviour, environmental effects,
cracking, biaxial stiffening and strain
softening.
3. Reinforcing steel and concrete interact in a complex way
through bond-slip and aggregate interlock.
The use of Fiber Reinforced Concrete or Cement Composites (FRCC)
to enhance the
performance of structural elements has been the subject of many
research projects during the
past few decades [5]. Typically, FRCC have been shown to be
effective in improving
structural performance in members under gravity loads, as well
as in increasing shear
strength, ductility, energy dissipation, and damage tolerance in
members subjected to reversed
cyclic loading. Numerous types of FRCC reinforced with steel,
polymeric, glass, and carbon
fibers have been evaluated for structural applications. To
categorize FRCC based on their
tensile performance, a new class of FRCC, referred to as
High-Performance Fiber-Reinforced
Cement Composites (HPFRCC). The idea behind this new
classification of FRCC was to
distinguish between the typical tensile performance obtained
with traditional FRCC,
characterized by a softened response after first cracking, and
the tensile strain-hardening
response with multiple cracking exhibited by selected types of
fiber cement composites.
HPFRCC exhibit substantially larger strain capacity and
toughness compared with traditional
FRCC, which makes them ideal for use in members subjected to
large inelastic deformation
demands. The application of HPFRCC materials to earthquake
resistant structures has been
one of the major research thrusts during the last years.
Research areas in this topic range from
fiber and material development to large scale structural
applications.
Since earthquake forces are random in nature and unpredictable,
the engineering tools
needs to be sharpened for analyzing structures under the action
of these forces. Performance
Based Design Engineering (PBSE) is gaining a new dimension in
the seismic design
philosophy wherein the near field ground motion is to be
considered. Earthquake loads are to
be carefully modeled so as to assess the real behaviour of
structure with a clear understanding
that damage is expected but it should be regulated. Due to the
recent advances in seismic
hazard assessment, PBSE methodologies, experimental facilities,
and computer applications,
PBSE has become increasing more attractive to developers and
engineers of buildings in
seismic regions. It is safe to say that within just a few years
PBSE will become the standard
method for design and delivery of earthquake resistant
structures. In order to utilize PBSE
effectively and intelligently, one need to be aware of the
uncertainties involved in both
structural performance and seismic hazard estimations. The
recent advent of PBSE has brought the nonlinear analysis procedure
to the forefront.
Pushover analysis is a static, nonlinear procedure in which the
magnitude of the structural
loading is incrementally increased in accordance with a certain
predefined pattern. With the
increase in the magnitude of the loading, weak links and failure
modes of the structure are
identified. The loading is monotonic with the effects of the
cyclic behaviour and load
reversals being estimated by using a modified monotonic
force-deformation criteria and with
damping approximations. Static pushover analysis is an attempt
by the structural engineering
profession to evaluate the real strength of the structure and it
promises to be a useful and
effective tool for performance based design. The most studies
focuses on linear static analysis
and nonlinear static and dynamic analysis of multistory
buildings subjecting to monotonically
increasing lateral forces with an invariant height wise
distribution until the preset performance
level (target displacement) is reached. The promise of PBSE is
to produce structures with
predictable seismic performance.
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3
1.1 Scope of the Work
This work reviews the effects of addition of materials in
concrete, and investigates the
mechanical properties, and applications of reinforced concrete.
The results from selected
research projects on the subject are presented with the
intention of increasing awareness in the
structural engineering community of the potential of these
materials for use in earthquake
resistant structures [5].
The deficiencies have led researchers to investigate and develop
a material could perform
better in areas where conventional concrete has several
limitations. The objective of this work
to study a modern concept to increase the concrete ductility and
its energy absorption
capacity, as well as to improve overall durability. In case
study shows the influence of
crimped steel fibers on the compressive strength and flexural
strength of HPFRC with varying
w/cm ratios and silica fume replacement. This pozzolana is
beneficially used to attain certain
properties in concrete as lower water demand for similar
workability, reduced bleeding and
lower evolution of heat [2, 6]. It has been used particularly in
mass concrete applications and
large volume placement to control expansion due to heat of
hydration and also helps in
reducing cracking at early ages. The effect of fibers will be
included in this investigation.
Various parameters and their relationships will also be
investigated. Thus this work presents
complete stress-strain case study behaviour with its equation of
HPC under compression.
When earthquakes occur, energy released by the earthquake gets
induced into the
structure as ground motion and this energy has to be dissipated
for safety reasons. To release
seismic energy, the structure should damage in such a way that
on one hand, collapse of
structure should not occur and on the other hand, after the
earthquake, damage should be
economically feasible to repair [7]. To avoid the collapse of
the structures and also to reduce
the repair cost after the earthquake, most design codes focus on
providing sufficient ductility
to structure. Dissipation of large part of injected seismic
energy is an important factor for a
structure to be seismically resistant. Use of metal additives to
improve the behaviour of
reinforced concrete structures subjected to cyclic loading is
investigated in contribution.
Because of its advantageous characteristics, HPC is now widely
used in tall building
construction. In this work, a two example demonstrate the
application of HPC frame building
construction using silica fume only and silica fume with steel
fiber 2% High Performance
Steel Fiber Concrete (HPSFC), as well as explores the
possibilities to use a HPC for design of
seismic resistant buildings.
This work focuses of subjecting multistory RC frame buildings to
monotonically
increasing lateral forces until the preset performance level
(target displacement) is reached.
4-story, 7-story and 12-story RC frame buildings are considered
to represent low- and
medium- rise buildings for this study. RC frame buildings are
testing through selective using
of three different cases: Normal RC without metal additives and
two cases with metal
additives (HPC and HPSFC), which further minimizes dead and
seismic loads. The work
describes these cases, and the results of the linear static
analysis of frame building system as
well as of the nonlinear static and dynamic analysis of a whole
three different multistory RC
frame buildings example are presenting. The response in terms of
force displacement
relationships as well as in terms of base shear, the time
history of roof accelerations are
comparing to the response of the same building with and without
metal additives are
describing in case studies. A comprehensive and well-coordinated
effort by professionals
from several disciplines of PBSE is requiring producing
structures with predictable seismic
performance into a reality.
The design and analysis of RC building with and without metal
additives are carried out
according to the UBC97 using product of Computers and Structures
International ETABS
software tool. Verifying the applicability of the presenting
models by comparing the
behaviours which satisfying the code structural
consideration.
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4
1.2 Thesis Outlines
This study starts with a concrete and effect of reinforced
concrete that used as building
construction materials discusses in Chapter 2. Behaviour of
concrete and concrete failing in
compression, compressive strength and cracked reinforced
concrete presents. This chapter
includes also behaviour of reinforcing steel and interaction of
concrete and reinforcement.
Chapter 3 addresses a high performance reinforced concrete
(HPRC), starts with an
introduction, review on the physical behaviours of RC and
discuss the types of concrete, the
key elements of HPC, addresses some properties and impacts on
the concrete performance,
features of HPC (e.g. strength, durability), and applications of
HPC. Followed by a discussion
of the HPFRC, types of fiber, stress-strain relationship of
HPFRC (e.g. ductility, strain
hardening), mechanics of FRCC, considerations of structural
design, and applications of fiber
reinforced concrete, that follows in terms of seismic
applications.
Chapter 4 addresses a literature review on the behaviours of RC
and its constituents, as
well as the constitutive models applied to describe such
behaviours, a simple experimentally
based methodology is applied to account for the effect of HPRC
interaction on the
reinforcement level, all of which presents. This emphasis leads
to the application approaches
employing properties and mechanics to describe the RC building
behaviour subjected to
earthquake.
Chapter 5 addresses the seismic prescriptions for reinforced
concrete structures, includes
seismic design factors and categories. This follows by a
discussion of the method of analysis
(elastic methods of analysis, inelastic methods of analysis) and
effect of ductility on seismic
forces. The chapter discusses the performance requirements of
building, force based design
procedure. This chapter intends to serve as an introduction to
the chapters that follow in terms
of theoretical formulation and computational implementation
methods for seismic loads
according UBC97, design base shear, vertical distribution of
force, drift limitations, story drift
and average drift, general assumptions and requirements for
modeling and design (according
to Federal Emergency Management Agency-FEMA 356), and
description of seismic hazard.
Chapter 6 addresses to the experimental program of HPC
materials, includes experimental
procedures, materials of experimental program and follows by
test results of plain concrete.
The influence of crimped steel fibers on the compressive
strength and flexural strength of
high performance FRC with varying w/cm ratios and silica fume
replacement, the effect of
steel fibers ratios will be includes in the investigation. The
effect of parameters tested (e.g.
modulus of elasticity, analytical stress-strain curve for HP/HSC
and compressive strength)
discusses. This follows by complete stress-strain behaviour with
its equation of HPC under
compression. Finally the chapter presents design recommendations
and an experimental
procedures conclusion.
In Chapter 7, siesmic analysis of HPRC frames buildings
discusses which addresses to
three case studies of RC comprehensive building cases provided
to demonstrate the
applicability of the applied models of RC structure includes
design and analysis. The chapter
presents a description of building, static linear and nonlinear
analysis results and time history
analysis results. Several verifications are providing in order
to test the model‟s under seismic
with and without metal additives are carried out using ETABS
software tool. Followed by a
step-by-step hinges damage distribution, as well as other curves
are presenting and
comparing. The performance of the present‟s concrete model and
to assess the model‟s ability
to observe behaviours of concrete materials is then providing
and discussing. The results are
verifying the applicability of the presenting models by
comparing the behaviours which
satisfying the code structural consideration.
Conclusions, contributions and further studies propose in
Chapter 8. A summary of the
results of the current investigation followed by a brief of the
merits of the currently presents
work. Suggest that additional fundamental research is required
if other computer simulation is
to be a viable tool for future research and design of RC
structures. Finally the chapter presents
some of suggestions for future work.
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5
CHAPTER TWO
GENERAL BEHAVIOUR OF REINFORCED CONCRETE
2.1 Introduction
Concrete by itself is a composite material. It is made of
cement, mortar, and aggregates.
The thermo-chemical interaction between these constituents
results in a unique building
material. One of the most important characteristics of concrete
is low tensile strength, which
results in tensile cracking at a very low stress compared with
compressive stresses. The
tensile cracking reduces the stiffness of the concrete
component.
Concrete exhibits a large number of micro cracks, especially at
the interface between
coarser aggregates and mortar, even before the application of
any external loads. The
presence of these micro cracks has a great effect on the
mechanical behaviour of concrete,
since their propagation (concrete damage) during loading
contributes to the nonlinear
behaviour at low stress levels and causes volume expansion near
failure. Many of these micro
cracks are initially caused by segregation, shrinkage or thermal
expansion of the mortar.
Some micro cracks may develop during loading because of the
difference in stiffness between
aggregates and mortar. Since the aggregate mortar interface has
a significantly lower tensile
strength than the mortar; it constitutes the weakest link in the
composite system. This is the
primary reason for the low tensile strength of concrete.
Concrete and reinforced concrete are used as building
construction materials in every
country. Reinforced concrete is a dominant structural material
in engineered construction. The
universal nature of reinforced concrete construction stems from
the wide availability of
reinforcing bars and of the constituents of concrete (gravel or
crushed rock, sand, water, and
cement), from the relatively simple skills required in concrete
construction, and from the
economy of reinforced concrete compared with other forms of
construction.
2.2 Behaviour of Concrete Failing in Compression
Concrete is a mixture of cement paste and aggregate, each of
which has an essentially
linear and brittle stress–strain relationship in compression.
Brittle materials tend to develop
tensile fractures perpendicular to the direction of the largest
tensile strain. Thus, when
concrete is subjected to uniaxial compressive loading, cracks
tend to develop parallel to the
maximum compressive stress. Although concrete is made up of
essentially elastic, brittle
materials, its stress–strain curve is nonlinear and appears to
be somewhat ductile. This can be
explained by the gradual development of micro cracking within
the concrete and the resulting
redistribution of stress from element to element in the concrete
[8]. Micro cracks are internal
cracks to in length. Microcracks that occur along the interface
between paste and aggregate
are called bond cracks; those that cross the mortar between
pieces of aggregate are known as
mortar cracks.
There are four major stages in the development of micro cracking
and failure in concrete:
1. Shrinkage of the paste occurs during hydration, and this
volume change of the concrete is
restrained by the aggregate. The resulting tensile stresses lead
to no-load bond cracks,
before the concrete is loaded. These cracks have little effect
on the concrete at low loads,
and the stress–strain curve remains linear up to 30 percent of
the compressive strength of
the concrete, as shown by the solid line in Figure 2.1.
2. When concrete is subjected to stresses greater than 30 to 40
percent of its compressive
strength, the stresses on the inclined surfaces of the aggregate
particles will exceed the
tensile and shear strengths of the paste–aggregate interfaces,
and new cracks, known as
bond cracks, will develop. These cracks are stable; they
propagate only if the load is
increased. Once such a crack has formed, however, any additional
load that would have
been transferred across the cracked interface is redistributed
to the remaining unbroken
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6
interfaces and to the mortar. This redistribution of load causes
a gradual bending of the
stress–strain curve for stresses above 40 percent of the
short-time strength.
3. As the load is increased beyond 50 or 60 percent of ultimate,
localized mortar cracks
develop between bond cracks. These cracks develop parallel to
the compressive loading
and are due to the transverse tensile strains. During this
stage, there is stable crack
propagation; cracking increases with increasing load but does
not increase under constant
load. The onset of this stage of loading is called the
discontinuity limit.
4. At 75 to 80 percent of the ultimate load, the number of
mortar cracks begins to increase,
and a continuous pattern of micro cracks begins to form. As a
result, there are fewer
undamaged portions to carry the load, and the stress versus
longitudinal-strain curve
becomes even more markedly nonlinear. The onset of this stage of
cracking is called the
critical stress.
If the lateral strains ε3, are plotted against the longitudinal
compressive stress, the dashed
curve in Figure 2.1 results. The lateral strains are tensile and
initially increase, as is expected
from the poison‟s effect. As micro cracking becomes more
extensive, these cracks contribute
to the apparent lateral strains. As the load exceeds 75 to 80
percent of the ultimate
compressive strength, the cracks and lateral strains increase
rapidly, and the volumetric strain
(relative increase in volume), begins to increase, as shown by
the broken line in Figure 2.1.
Equally important is the fact that the structure of the concrete
tends to become unstable at
loads greater than the critical load. Under stresses greater
than about 75 percent of the short-
time strength, the strains increase more and more rapidly until
failure occurs [9].
Figure 2.1: Stress–strain curves for concrete loaded in uniaxial
compression [9].
Under cyclic compressive loads, axially loaded concrete has a
shake-down limit
approximately equal to the point of onset of significant mortar
cracking at the critical stress.
Cyclic axial stresses higher than the critical stress will
eventually cause failure. As mortar
cracking extends through the concrete, less and less of the
structure remains. Eventually, the
load-carrying capacity of the uncracked portions of the concrete
reaches a maximum value
referred to as the compressive strength (Figure 2.1). Further
straining is accompanied by a
drop in the stress that the concrete can resist, as shown by the
dotted portion of the line for ε1 in Figure 2.1. When concrete is
subjected to compression with a strain gradient, as would
occur in The compression zone of a beam, the effect of the
unstable crack propagation
stage shown in Figure 2.1 is reduced because, as mortar cracking
softens the highly strained
concrete, the load is transferred to the stiffer, more stable
concrete at points of lower strain
nearer the neutral axis. In addition, continued straining and
the associated mortar cracking of
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7
the highly stressed regions are prevented by the stable state of
strain in the concrete closer to
the neutral axis. As a result, the stable-crack-propagation
stage extends almost up to the
ultimate strength of the concrete.
2.3 Strength under Biaxial and Triaxial Loadings
Biaxial Loading of Uncracked Concrete [9]: Concrete is said to
be loaded biaxially when it is
loaded in two mutually perpendicular directions with essentially
no stress or restraint of
deformation in the third direction, as shown in Figure 2.2a. A
common example is shown in
Figure 2.2b. The strength and mode of failure of concrete
subjected to biaxial states of stress
varies as a function of the combination of stresses as shown in
Figure 2.3. The pear-shaped
line in Figure 2.3a represents the combinations of the biaxial
stresses, 1
and 2 which cause cracking or compression failure of the
concrete. This line passes through the uniaxial
compressive strength, '
cf at and and the uniaxial tensile strength, '
tf at and .
Under biaxial tension ( 1 and 2 both tensile stresses) the
strength is close to that in uniaxial tension, as shown by the
region D (zone 1) in Figure 2.3a. Here, failure
occurs by tensile fracture perpendicular to the maximum
principal tensile stress, as shown in
Figure 2.3b, which corresponds to point in Figure 2.3a. When one
principal stress is tensile and the other is compressive, as shown
in Figure 2.2a, the
concrete cracks at lower stresses than it would if stressed
uniaxially in tension or
compression. This is shown by regions and in Figure 2.3a. In
this region, zone 2 in Figure 2.3a, failure occurs due to tensile
fractures on planes perpendicular to the
principal tensile stresses. The lower strengths in this region
suggest that failure is governed by
a limiting tensile strain rather than a limiting tensile
stress.
Under uniaxial compression (points and and zone 3 in Figure
2.3a), failure is initiated by the formation of tensile cracks on
planes parallel to the direction of the
compressive stresses. These planes are planes of maximum
principal tensile strain.
Under biaxial compression (region C and zone 4 in Figure 2.3a),
the failure pattern changes to a series of parallel fracture
surfaces on planes parallel to the unloaded sides of the
member, as shown in Figure 2.3d. Such planes are acted on by the
maximum tensile strains.
Biaxial and triaxial compression loads delay the formation of
bond cracks and mortar cracks.
As a result, the period of stable crack propagation is longer
and the concrete is more ductile.
As shown in Figure 2.3, the strength of concrete under biaxial
compression is greater than the
uniaxial compressive strength. Under equal biaxial compressive
stresses, the strength is about
107 percent of '
cf as shown by point C.
In the webs of beams, the principal tensile and principal
compressive stresses lead to a
biaxial tension–compression state of stress, as shown in Figure
2.2b. Under such a loading,
the tensile and compressive strengths are less than they would
be under uniaxial stress, as
shown by the quadrant or in Figure 2.3a. This explains in part
why the splitting tensile strength is less than the flexural
tensile strength.
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8
In zones 1 and 2 in Figure 2.3, failure occurred when the
concrete cracked, and in zones 3 and
4, failure occurred when the concrete crushed. In a reinforced
concrete member with
sufficient reinforcement parallel to the tensile stresses,
cracking does not represent failure of
the member because the reinforcement resists the tensile forces
after cracking. The biaxial
load strength of cracked reinforced concrete is discussed in the
next subsection.
Figure 2.3: Strength and modes of failure of unreinforced
concrete subjected to biaxial
stresses [9].
2.4 Compressive Strength of Cracked Reinforced Concrete
If cracking occurs in reinforced concrete under a biaxial
tension–compression loading and
there is reinforcement across the cracks, the strength and
stiffness of the concrete under
compression parallel to the cracks is reduced. Figure 2.4a shows
a concrete element that has
been cracked by horizontal tensile stresses. The natural
irregularity of the shape of the cracks
leads to variations in the width of a piece between two cracks,
as shown. The compressive
stress acting on the top of the shaded portion is equilibrated
by compressive stresses and
probably some bearing stresses on the bottom and shearing
stresses along the edges, as shown
in Figure 2.4b. When the crack widths are small, the shearing
stresses transfer sufficient load
across the cracks that the compressive stress on the bottom of
the shaded portion is not
(a) Biaxial state of stress (b) Biaxial state of stress in the
web beam.
Figure 2.2: Biaxial stresses [9].
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9
significantly larger than that on the top, and the strength is
unaffected by the cracks. As the
crack widths increase, the ability to transfer shear across them
decreases. For equilibrium, the
compressive stress on the bottom of the shaded portion must then
increase. Failure occurs
when the highest stress in the element approaches the uniaxial
compressive strength of the
concrete.
Figure 2.4: Stresses in a biaxially loaded, cracked-concrete
panel with cracks parallel to
the direction of the principal compression stress [9].
Tests of concrete panels loaded in in-plane shear, carried out
by [10], have shown a
relationship between the transverse tensile strain, and the
compressive strength parallel to the
cracks, max2f :
1
max2
1708.0
1
cf
f .……..……….…………………….. ( 2.1)
where the subscripts 1 and 2 refer to the major (tensile) and
minor (compressive) principal
stresses and strains. The average transverse strain, , is the
average transverse strain measured
on a gauge length that includes one or more cracks. Equation 2.1
is plotted in Figure 2.5a. An
increase in the strain 1 leads to a decrease in compressive
strength. The same authors
recommended a stress–strain relationship, 22 f for transversely
cracked concrete:
2
22
max2
2 2
ff …………………………..…………….(2.2)
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11
Figure 2.5: Effect of transverse tensile strains on the
compressive strength of cracked
concrete [9].
Where max2f is given by equation (2.1), and is the strain at the
highest point in the
compressive stress–strain curve, which the authors took as
0.002. The term in brackets
describes a parabolic stress–strain curve with apex at and a
peak stress that decreases as c
increases. If the parabolic stress–strain curve given by
equation (2.2) is used, the strain for
any given stress can be computed from
'
2
2' 1f
fcc ………………..…….……………….(2.3)
If the descending branch of the curve is also assumed to be a
parabola, equation (2.3) can
be used to compute strains on the postpeak portion of the
stress–strain curve if the minus sign
before the radical is changed to a plus.
The stress–strain relationships given by equations (2.1) and
(2.2) represent stresses and
strains averaged over a large area of a shear panel or beam web.
The strains computed in this
way include the widths of cracks in the computation of tensile
strains, 1 as shown in the
inset to Figure 2.5a. These equations are said to represent
smeared properties. Through
smearing, the peaks and hollows in the strains have been
attenuated by using the averaged
stresses and strains. In this way, equations (2.1) and (2.2) are
an attempt to replace the stress
analysis of a cracked beam web having finite cracks with the
analysis of a continuum.
2.5 Triaxial Loadings
Under triaxial compressive stresses, the mode of failure
involves either tensile fracture
parallel to the maximum compressive stress (and thus orthogonal
to the maximum tensile
strain, if such exists) or a shear mode of failure. The strength
and ductility of concrete under
triaxial compression exceed those under uniaxial compression, as
shown in Figure 2.6. This
figure presents the stress–longitudinal strain curves for
cylinders each subjected to a constant
lateral fluid pressure 32 , while the longitudinal stress, 1 ,
was increased to failure.
These tests suggested that the longitudinal stress at failure
was
31 1.4 cf …………………………………………. (2.4)
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11
Figure 2.6: Axial stress–strain curves from triaxial compression
tests on concrete cylinders;
unconfined compressive strength cf = 3600 psi [9].
In concrete columns or in beam–column joints, concrete in
compression is sometimes
enclosed by closely spaced hoops or spirals. When the width of
the concrete element
increases due to Poisson‟s ratio and micro cracking, these hoops
or spirals are stressed in
tension, causing an offsetting compressive stress in the
enclosed concrete. The resulting
triaxial state of stress in the concrete enclosed or confined by
the hoops or spirals increases
the ductility and strength of the confined concrete. The
behaviour and strength of reinforced
concrete members is controlled by the size and shape of the
members and by the stress–strain
properties of the concrete and the reinforcement. The
stress–strain behaviour discussed in this
section will be used in subsequent chapters to develop
relationships for the strength and
behaviour of reinforced concrete beams and columns.
2.6 Cracking
2.6.1 Types of Cracks
Tensile stresses induced by loads, moments, shears, and torsion
cause distinctive crack
patterns, as shown in Figure 2.7. Members loaded in direct
tension crack right through the
entire cross section, with a crack spacing ranging from 0.75 to
2 times the minimum thickness
of the member. In the case of a very thick tension member with
reinforcement in each face,
small surface cracks develop in the layer containing the
reinforcement (Figure 2.7a). These
join in the center of the member. As a result, for a given total
change in length, the crack
width at B is greater than at A.
In a beam with a web that is more than 3 to 4 ft high, the
cracking is relatively closely
spaced at the level of the reinforcement, with several cracks
joining or disappearing above the
reinforcement, as shown in Figure 2.7b. Again, the crack width
at B will frequently exceed
that at A. Cracks due to shear have a characteristic inclined
shape, as shown in Figure 2.7c.
Such cracks extend upward as high as the neutral axis and
sometimes into the compression
zone. Torsion cracks are similar. In pure torsion, they spiral
around the beam. In a normal
beam, where shear and moment also act, they tend to be
pronounced on the face where the
flexural shear stresses and the shear stresses due to torsion
add, and less pronounced (or even
absent) on the opposite face, where the stresses counteract
(Figure 2.7d). Bond stresses lead to
splitting along the reinforcement, as shown in Figure 2.7e.
Concentrated loads will sometimes
cause splitting cracks or “bursting cracks” of the type shown in
Figure 2.7f. The final
cracking pattern has generally not developed completely, with
the result that there are
normally only a few cracks at points of maximum stress at this
load level [9].
ε
σ
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12
Figure 2.7: Load-induced cracks [9].
2.6.2 Development of Cracks Due to Loads
Figure 2.8 shows an axially loaded prism. Cracking starts when
the tensile stress in the
concrete (shown by the shaded area in Figure 2.8b) reaches the
tensile strength of the concrete
(shown by the outer envelope) at some point in the bar. When
this occurs, the prism cracks.
At the crack, the entire force in the prism is carried by the
reinforcement. Bond gradually
builds up the stress in the concrete on either side of the crack
until, with further loading; the
stress reaches the tensile strength at some other section, which
then cracks (Figure 2.8c). With
increasing load, this process continues until the distance
between the cracks is not large
enough for the tensile stress in the concrete to increase enough
to cause cracking. Once this
stage is reached, the crack pattern has stabilized, and further
loading merely widens the
existing cracks. The distance between stabilized cracks is a
function of the overall member
thickness, the cover, the efficiency of the bond, and several
other factors. Roughly, however,
it is two to three times the bar cover. Cracks that extend
completely through the member
generally occur at roughly one member thickness apart [9].
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13
Figure 2.8: Cracking of an axially loaded prism [9].
Figure 2.9b and c show the variation in the steel and concrete
stresses along an axially
loaded prism with a stabilized crack pattern. At the cracks, the
steel stress and strain are at a
maximum and can be computed from a cracked-section analysis.
Between the cracks, there is
stress in the concrete. This reaches a maximum midway between
two cracks. The total width,
w, of a given crack is the difference in the elongation of the
steel and the concrete over a
length A–B equal to the crack spacing:
……………….………….………… (2.5)
where s and c are the strains in the steel and concrete at a
given location between A and
B and x is measured along the axis of the prism.
The crack spacing, s, and the variation in and are difficult to
calculate in practice, and
empirical equations are generally used to compute the crack
width.
In a deep flexural member, the distribution of crack widths over
the depth shows a similar
effect, particularly if several cracks combine, as shown in
Figure 2.7b. The crack width at B
frequently exceeds that at the level of the reinforcement.
dxwB
Acs
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14
Figure 2.9: Stresses in concrete and steel in a cracked prism
[9].
2.6.3 Limits on Crack Width
There are no universally accepted rules for maximum crack
widths. Prior to 1999, the ACI
Code crack-control limits were based on a maximum crack width of
0.016 in. for interior
exposure and 0.013 in. for exterior exposure .What constitutes
interior and exterior exposure
was not defined. In addition to crack-control provisions, there
are special requirements in ACI
for the composition of concrete subjected to special exposure
conditions.
The Euro-International Concrete Committee (CEB) limits the mean
crack width (about 60
percent of the maximum crack width) as a function of exposure
condition, sensitivity of
reinforcement to corrosion, and duration of th e loading
condition. ACI Code Sections 10.6.3
to 10.6.7 handle crack widths indirectly by limiting the maximum
bar spacing and bar covers
for beams and one-way slabs. Prior to 1999, these limits were
based on the Gergely–Lutz [11]
equation which related the maximum crack width w at the tensile
surface of a beam or slab
and the cover to:
(a) The stress sf in the steel at service loads,
(b) The distance cd from the extreme concrete fiber to the
centroid of the bar closest to the
tension fiber, and
(c)The area A of the prism of concrete concentric with the
bar.
Two limiting crack widths were considered: 016.0w in. for
interior exposure and 013.0w in for exterior exposure. The
resulting equation tended to give unacceptably small
bar spacing for bar covers greater than 2.5in. For this reason,
the Gergely–Lutz equation was
replaced in the 1999 ACI Code by equation (2.6). This equation
was obtained by fitting a
straight line to the Gergely–Lutz equation for a flexural crack
width of 0.016in.
c
s
cf
s 5.2000.40
15
, but not greater than
sf
000.4012 (psi) ………. (2.6) (ACI Equ. 10-4)
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15
c
s
cf
s 5.2280
380
,but not greater than
sf
280300 (Mpa) ……….(2.6M) (ACI Equ. 10-4M)
where s is the bar spacing in inches or millimeters, sf
is the service-load bar stress in psi or
MPa, and cc is the clear cover from the nearest surface of the
concrete in the tension zone to
the surface of the flexural-tension reinforcement, in inches or
mm in equation (2.6) or (2.6M),
respectively. Equation 2.6 was based on the limiting crack width
for interior exposure only.
This is because the eventual amount of reinforcement corrosion
has been shown to be
independent of surface crack width.
2.7 Reinforcing Steel
2.7.1 Behaviour of Reinforcing Steel
Reinforcement comes in different types and shapes. Those most
commonly used are the
deformed circular cross-sectional bars. The spiral deformation
pattern on the bars strengthens
the mechanical bond between the bars and concrete. The
properties of reinforcing steel, unlike
concrete, are generally not dependent on environmental
conditions or time. Thus, the
specification of a single stress-strain relation is sufficient
to define the material properties
needed in the analysis of RC structures [12].
Typical stress-strain curves for reinforcing steel bars used in
concrete construction are
obtained from coupon tests of bars loaded monotonically in
tension. For all practical purposes
steel exhibits the same stress-strain curve in compression as in
tension. The steel stress-strain
relation exhibits an initial linear elastic portion, a yield
plateau, a strain hardening range in
which stress again increases with strain and, finally, a range
in which the stress drops off until
fracture occurs. The extent of the yield plateau is a function
of the tensile strength of steel.
High-strength, high-carbon steels, generally, has a much shorter
yield plateau than relatively
low-strength, low-carbon steels.
Two different idealizations, shown in Figure 2.10, are commonly
used depending on the
desired level of accuracy (ASCE 1982). This assumption underlies
the design equations of the
ACI code. If the strain at the onset of strain hardening is much
larger than the yield strain, this
approximation yields very satisfactory results. This is the case
for low-carbon steels with low
yield strength.
Figure 2.10: Idealizations of the steel stress-strain curves
[12].
If the steel hardens soon after the onset of yielding, this
approximation underestimates the
steel stress at high strains. In several instances it is
necessary to evaluate the steel stress at
strains higher than yield to more accurately assess the strength
of member‟s at large
deformations. This is, particularly, true in seismic design,
where assessing the available
ductility of a member requires that the behaviour be
investigated under strains many times the
yield strain. In this case more accurate idealizations which
account for the strain hardening
effect are required, as shown in Figure 2.10b for the case of
bilinear stress-strain models. The
parameters of these models are the stress and strain at the
onset of yielding, the strain at the
onset of strain hardening and the stress and strain at ultimate
(Figure 2.11). These parameters
can be derived from experimentally obtained stress-strain
relations.
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16
Figure 2.11: Linear elastic, linear strain hardening steel
stress-strain relation [12].
The behaviour of RC members is greatly affected by the yielding
of reinforcing steel
when the structure is subjected to monotonic bending moments.
Yielding is accompanied by a
sudden increase in the deformation of the member. In this case
the use of the elastic-perfectly
plastic model in Figure 2.10a leads to numerical convergence
problems near the ultimate
member strength. It is, therefore, advisable to take advantage
of the strain-hardening
behaviour of steel to improve the numerical stability of the
solution. The assumption of a
linear strain hardening behaviour immediately after yielding of
the reinforcement does not
adversely affect the accuracy of the results, as long as the
slope of the strain hardening branch
is determined so that the strain energy of the model is equal to
the strain energy of the
experimental steel stress-strain relation (Figure 2.11). Such a
model has been successfully
used for the analyses of RC structures [12].
The reinforcing steel is modeled as a linear elastic, linear
strain hardening material with
yield stress y , as shown in Figure 2.11. A 2J elasto-plasticity
model with linear hardening
will be adopted to describe the behaviour or steel
reinforcement. The von Mises yield
criterion, associative flow rule and isotropic hardening are
suitable for modeling structural
steel. The von Mises yield criterion can be written as:
0 )p(R)R,(F yeq ……………………….….…….(2.7)
where y is the yield stress, R( p) is the isotropic hardening
stress (linear function of the
accumulated plastic strain R =( kp ), and eq is the von Mises
equivalent stress defined by:
ijijeq SS
2
3 …………………………………………….….…(2.8)
where ijS is the deviatoric part of the Cauchy stress
tensor:
ijmmijijS
3
1 ……………………………………….….……(2.9)
The plastic flow rule that governs the evolution of the plastic
strain is given as follows:
ij
.p
ij
. f
………...……………………...…………….……(2.10)
The scalar .
is the plastic multiplier which is equal in this case to the
rate of the accumulated plastic strain:
p
ij
.p
ij
...
p 3
2 …………………………………………….…(2.11)
where p
ij
.
is the plastic strain rate.
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17
2.7.2 Interaction of Concrete and Reinforcement
2.7.2.1 Bond
If relative displacements of concrete and reinforcement occur,
bond stresses develop at the
steel-concrete interface. The relative displacement or slip is
given by cs uu , where
su and cu denote the displacements of reinforcement and
concrete, respectively. The
magnitude of the bond stresses depends on the slip as well as on
several other factors, including bar roughness (size, shape and
spacing of ribs), concrete strength, position and
orientation of the bar during casting, concrete cover, boundary
conditions, and state of stress
in concrete and reinforcement. Bond stresses are essential to
the anchorage of straight rebars,
they influence crack spacings and crack widths and are important
if deformations of structural
concrete members have to be assessed. A detailed investigation
of bond and tension
stiffening, including prestressed reinforcement and deformations
in the plastic range of the
steel stresses, can be found in a recent report by [13].
Bond action is primarily due to interlocking of the ribs of
profiled reinforcing bars and the
surrounding concrete; stresses caused by adherence (plain bars)
are lower by an order of
magnitude. Forces are primarily transferred to the surrounding
concrete by inclined
compressive forces radiating out from the bars. The radial
components of these inclined
compressive forces are balanced by circumferential tensile
stresses in the concrete or by
lateral confining stresses. If significant forces have to be
transmitted over a short embedment
length by bond, splitting failures along the reinforcement will
occur unless sufficient concrete
cover or adequate circumferential reinforcement is provided;
this effect is called tension
splitting. In a simplified approach, the complex mechanism of
force transfer between concrete
and reinforcement is substituted by a nominal bond shear stress
uniformly distributed over the
nominal perimeter of the reinforcing bar. Bond shear stress-slip
relationships, Figure 2.12b,
are normally obtained from pull-out tests as shown in Figure
2.12a.
Figure 2.12: Bond behaviour: (a) pull-out test; (b) bond shear
stress-slip relationship;
(c) differential element [13]
The average bond shear stress along the embedment length bl can
be determined from the
pullout force as
b
bl
F
……………………………………….…….………(2.12)
Where = nominal diameter of reinforcing bar. In a pull-out test,
bond shear stresses increase
with the slip until the maximum bond shear stress maxb (bond
strength) is reached, typically
at a slip = 0:5; ….1mm if the slip is further increased, bond
shear stresses decrease,
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18
Figure 2.12b. Equilibrium requires that for any section of a
structural concrete element loaded
in uniform tension, Figure 2.12c,
cs
s
ccss
)(
A
N,AAN
1 ……………………..(2.13)
Where c
s
A
A geometrical reinforcement ratio, sA cross-section area of
reinforcement and cA
cross-section area of concrete. Formulating equilibrium of a
differential element of length dx,
Figure 2.12c, one obtains the expression
)(dx
d,
dx
d bcbs
1
44 ………...……………………..(2.14)
for the stresses transferred between concrete and reinforcement
by bond. Furthermore, the
kinematic condition
cscs ]uu[
dx
d
dx
d
…………..………………..………(2.15)
is obtained from Figure 2.12, if plane sections are assumed to
remain plane. Differentiating
equation 2.14 with respect to x, inserting equation 2.14 and
substituting stress-strain
relationships for steel and concrete, a second order
differential equation for the slip is obtained. Generally, the
differential equation has to be solved in an iterative
numerical
manner. For linear elastic behaviour,cccsss EandE , one gets
)n
(Edx
d
s
b
11
42
2
………………….……………………….(2.16)
Where cs EEn = modular ratio; equation 2.16 can be solved
analytically for certain bond
shear stress-slip relationships.
2.7.2.2 Tension Stiffening
The effect of bond on the behaviour of structural concrete
members loaded in tension is
called tension stiffening, since after cracking the overall
response of a structural concrete
tension chord is stiffer than that of a naked steel bar of equal
resistance [13].
The behaviour of a structural concrete tension chord can be
described by a chord element
bounded by two consecutive cracks, Figure 2.13a. The
distribution of stresses and strains
within the chord element is shown in Figure 2.13b for the
symmetrical case, i.e., equal tensile
forces N acting on both sides of the element. At the cracks,
concrete stresses are zero and the
entire tensile force is carried by the reinforcement, ssr AN .
Away from the cracks, tensile
stresses are transferred from the reinforcement to the
surroundings concrete by bond shear
stresses according to equation 2.14. In the symmetrical case,
bond shear stresses and slip
vanish at the center between cracks; there, reinforcement
stresses are minimal, and the
concrete stresses reach their maximum value. For a given applied
tensile force, the
distribution of stresses and strains, Figure 2.13b, can be
deter- mined for arbitrary bond shear
stress-slip and stress-strain relationships from equations 2.14
and 2.15.
Integration of the differential equation corresponds to solving
a boundary problem since
certain conditions have to be satisfied at both ends of the
integration interval. For equal tensile
forces N acting on both sides of the element, integration may
start at the center between
cracks, where the initial conditions 0 cs uu are known for
symmetry reasons; as a
boundary condition, the concrete stresses at the cracks must
vanish. Alternatively, integration
starting at the crack is possible, exchanging the initial and
boundary conditions. If the tensile
force varies along the chord element, the section at 0 cs uu is
not known beforehand and
the solution is more complicated; suitable algorithms and a
detailed examination are given in
a recent report by [13].
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19
Figure 2.13: Tension stiffening: (a) chord element; (b)
qualitative distribution of bond
shear stresses, steel and concrete stresses and strains, and
bond slip [13].
Observing that the concrete tensile stresses cannot be greater
than the concrete tensile
strength ctf , one obtains the requirement
2
01
4 /s
xctb
rmo
fdx)(
…………………..………….…..…….(2.17)
for the maximum crack spacing rmos in a fully developed crack
pattern. The minimum crack
spacing amounts to 2/s rmo since a tensile stress equal to the
concrete tensile strength must be
transferred to the concrete in order to generate a new crack.
Hence, the crack spacing rms in a
fully developed crack pattern is limited by
rmorm
rmoss
s
2 ……………………….…………………..…(2.18)
or, equivalently, 150 . , where
rmo
rm
s
s ……….………………………………………….(2.19)
For most applications, only the overall response of the chord
element is needed, while the
exact distribution of stresses and strains is not of primary
interest. Simple stress-strain and
bond shear stress-slip relationships can therefore be adopted,
provided that the resulting steel
stresses and overall strains of the chord element reflect the
governing influences and match
the experimental data.
For this purpose, to use a bilinear stress-strain characteristic
for the reinforcement and a
stepped, rigid-perfectly plastic bond shear stress-slip
relationship, Figures 2.14a and 2.14b.
This idealization has been called tension chord model. For the
bond shear stresses prior to and
after the onset of yielding of the reinforcement ctbctb fandf 22
10 is assumed,
respectively, where ctf = tensile strength of concrete
[13,14].
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21
Figure 2.14: Tension chord model: (a) stress-strain diagram for
reinforcement; (b) bond
shear stress-slip relationship; (c) chord element and
distribution of bond shear, steel and
concrete stresses, and steel strains [13]
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21
CHAPTER THREE
HIGH PERFORMANCE CONCRETE PROPERTIES
3.1. Introduction
Based on unit weight, concrete can be classified into three
broad categories. Concrete
containing natural sand and gravel or crushed-rock aggregates,
generally weighing about 2400
kg/m3 (4000 lb/yd3), is called normal-weight concrete, and it is
the most commonly used
concrete for structural purposes. For applications where a
higher strength-to-weight ratio is
desired, it is possible to reduce the unit weight of concrete by
using natural or pyro-processed
aggregates with lower bulk density. The term lightweight
concrete is used for concrete that
weighs less than about 1800 kg/m3 (3000 lb/yd3). Heavyweight
concrete, used for radiation
shielding, is a concrete produced from high-density aggregates
and generally weighs more
than 3200 kg/m3 (5300 lb/yd3). Strength grading of cements and
concrete is prevalent in
Europe and many other countries but is not practiced in the
United States [15].
It‟s useful to divide concrete into three general categories
based on compressive strength:
Low-strength concrete: less than 20 MPa (3000 psi)
Moderate-strength concrete: 20 to 40 MPa (3000 to 6000 psi)
High strength concrete: more than 40 MPa (6000 psi). ACI
published the following definition: "HPC is defined as concrete
which meets special
performance and uniformity requirements that cannot always be
achieved by using only the
conventional materials and mixing, placing and curing
practices.The performance
requirements may involve enhancements of placement and
compaction without segregation,
long-term mechanical properties, early-age strength, toughness,
volume stability, or service
life in severe environments". Based on the ACI definition, HPC
includes:
High workability concrete
Self-consolidating concrete
Foamed concrete
High strength concrete
Lightweight concrete
No-fines concrete
Pumped concrete
Sprayed concrete
Waterproof concrete
Autoclaved aerated concrete
Roller compacted concrete
These different types of HPC are used for different purposes and
environments. ACI has
published committee documents on all these types of concrete.
HPC characteristics are
developed for particular applications and environments; some of
the properties that may be
required include:
• High strength
• High early strength
• High modulus of elasticity
• High abrasion resistance
• High durability and long life in severe environments
• Low permeability and diffusion
• Resistance to chemical attack
• High resistance to frost and deicer scaling damage
• Toughness and impact resistance
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22
• Volume stability
• Ease of placement
• Compaction without segregation
• Inhibition of bacterial and mold growth
HPC almost always has a higher strength than normal concrete.
However, strength is not
always the primary required property. For example, a normal
strength concrete with very high
durability and very low permeability is considered to have high
performance properties.
Traditionally, HPC may be regarded as synonymous with HSC. It is
because lowering of
water-to-cement ratio, which is needed to attain high strength,
also generally improves other
properties [16]. However, it is now recognized that with the
addition of mineral admixtures
HPC can be achieved by further lowering water-to-cement ratio,
but without its certain
adverse effects on the properties of the material. Hence, it is
important to understand how
concrete performance is linked to its microstructure and
composition. In fact, performance
can be related to any properties of concrete. It can mean
excellent workability in fresh
concrete, or low heat of hydration in case of mass concrete, or
very quick setting and
hardening of concrete in case of spray concrete which is used to
repair roads and airfields, or
very low imperviousness of storage vessels. However, from a
structural point of view, one
understands usually that high strength, high ductility and high
durability, which are regarded
as the most favorable factors of being a construction material,
are the key attributes to HPC.
Decades ago, HSC was only tested in laboratory without real
applications because there were
still many uncertainties on the structural behaviour of HSC at
that time. Up to the present,
HPC has been widely used in tall building construction. The key
attributes will be evaluated
in details so as to better understand how HPC differs from
Normal Strength Concrete (NSC).
These key attributes are strength, ductility and durability.
Interrelationships between
microstructure and properties of HPC will be discussed. The
application of HPC in tall
buildings will be shown through the example.
3.2 Composition of High Performance Concrete
The composition of HPC usually consists of cement, water, fine
sand, superplasticizer, fly
ash and silica fume. Sometimes, quartz flour and fiber are the
components as well for HPC
having ultra-strength and ultra-ductility, respectively. The key
elements of HPC can be
summarized as follows [16]:
1. Low water-to-cement ratio,
2. Large quantity of silica fume (and/or other fine mineral
powders),
3. Small aggregates and fine sand,
4. High dosage of superplasticizers, 3.3 Comparison between the
Microstructure of HPC and NSC
The microstructure of the material should be studied in order to
makes HPC to be
different from NSC. Interrelationships between microstructure
and properties of both HPC
and NSC need to be established. The microstructure of concrete
can be described in three
aspects, namely composition of hydrated cement paste, pore
structure and interfacial
transition zone. The hydrated cement paste is in fact the
hydration products when cement is
reacted with water. The pore structure refers to the gel pores,
capillary pores and voids, as
well as their connections within the hardened concrete. The
interfacial transition zone refers
to the boundaries between the cement paste, and aggregates or
particles of admixtures. The
composition of NSC is relatively simple, which consists of
cement, aggregate and water.
Figure 3.1 shows the microstructure of NSC.
The hydrated cement paste is referred to as cementitious Calcium
Silicate Hydrate (C-S-
H) gel which is the main product of hydration of cement and
water. The hydrated cement
paste of NSC is dominated by amorphous C-S-H gel which is
intrinsically porous. The
