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ABSTRACT

STRESS-STRAIN BEHAVIOR OFHIGH STRENGTH CONCRETE CYLINDERS

by

Danqing Chen

Due to the recent development of high strength concrete in engineering and

construction, it has become more important to study the behavior of materials in

structures.

No results have been previously published in the literature regarding the

influence of aspect ratio in plain high strength concrete cylinders on stress-strain

behavior under uniaxial compression.Thus at present study, compression tests

were conducted on 3x6 in., 3x9 in., and 3x12 in. plain high strength concrete

cylinders to study their stress-strain behavior. Plain normal strength concrete

cylinders were also tested and used for comparative study.

Based on the present investigations, attempting to obtain a complete stress-

strain curve for plain high strength concrete cylinders with the length to diameter

ratio equal to or larger than three ( f c i >12,000 psi ) with axial strain control is

impossible. It can be concluded that the descending branch of a stress-strain

curve of high strength concrete(fc' > 12,000 psi, with l/d> or =3)can no longer be

treated as a material property; rather, it may be treated as a structural property.

STRESS-STRAIN BEHAVIOR OFHIGH STRENGTH CONCRETE CYLINDERS

byDanqing Chen

A ThesisSubmitted to the Faculty of

New Jersey Institutes of Technologyin Partial Fulfillment of the Requirements for the Degree of

Master of Science in Civil Engineering

Department of Civil and Environmental Engineering

January 1995

APPROVAL PAGE

STRESS-STRAIN BEHAVIOR OFHIGH STRENGTH CONCRETE CYLINDER

Danqing Chen

Dr. C.l7Thomas Hsu, Thesis Adviser DateProfessor of Civil and Environmental Engineering, NJIT

Dr. William S fliers, Committee Member DateProfessor and Chairman of Civil and Environmental Engineering, NJIT

Dr. Methi Wecharatana, Committee Member DateProfessor of Civil and Environmental Engineering, NJIT

BIOG PHICAL SKETCH

Author: Danqing Chen

Degree: Master of Science in Civil Engineering

Date: January 1995

Undergraduate and Graduate Education:

• Master of Science in Civil Engineering,New Jersey Institute of Technology,Newark, New Jersey, 1995

• Bachelor of Science in Civil EngineeringJianghan University,Wuhan, People's Republic of China, 1984

Major: Structural Engineering

Working Experience:

Engineer. Wuhan Iron and Steel Design and Research Institute, Wuhan,People's Republic of China. 1985-1993.

iv

ACKNOWLEDGMENT

The author wishes to express her sincere gratitude to her supervisor,

Professor C.T.Thomas Hsu, for his guidance, friendship, and constant support

throughout this research.

Special thanks to professors William Spillers and Wecharatana Methi for

serving as members of the thesis committee.

The experiments were performed using the MTS testing system which was

purchased under the NSF Grant, No. CEE 8308339.The author is grateful to the

Department of Civil and Environmental Engineering and the Office of Graduate

Studies for the financial support in pursuit of this degree.

The author appreciates the timely help and suggestions from Mr.Allyn Luke,

and from fellow graduate students Mr. Been-jyh Yu and Mr. Rajendar

Navalurkar.

vi

This thesis is dedicated tomy parent and my husband

TABLE OF CONTENTS

Chapter Page

INTRODUCTION 1

1.1 General 1

1.2 Scope and Objectives of Research 4

1.2 The Structure of The Thesis 4

2 LITERATURE SURVEY 5

2.1 Behavior of Concrete 5

2.1.1 Introduction 5

2.1.2 Behavior of High Strength Concrete 6

2.1.3 Effect of Interaction Between Testing Machine and Specimenon Behavior of Concrete 8

2.1.4 Effect of Cylinder Size on Concrete Strength and ElasticModulus 9

2.2 Empirical Equations of Complete Stress-Strain Curve for HighStrength Concrete 10

3 MATERIALS AND EXPERIMENTAL METHODS 11

3.1 Specimens, Materials and Mixing Proportion 11

3.1.1 Specimens 11

3.1.2 Materials 11

3.1.3 Mixing Proportions 13

3.2 Experimental Methods 13

vii

TABLE OF CONTENTS(Continued)

Chapter Page3.2.1 Mixing, Casting, and Curing 13

3.2.2 Experimental Setup 14

4 RESULTS AND DISCUSSIONS 15

4.1 Introduction 15

4.2 Short-Term Uniaxial Compression Test 15

4.2.1 Effect of Specimen Size on Compressive Strength 15

4.2.2 Effect of Specimen Size on Strain Corresponding toCompressive Strength 16

4.2.3 Effect of Specimen Size on Modulus of Elasticity 17

4.2.4 Behavior of Stress-Strain 18

4.2.5 Failure Mode 20

4.2.6 Effect of Interaction of Testing Machine and Specimen onBehavior of Concrete and Failure Mode 22

4.3 Comparison of Experimental Data and Existing Empirical Equations 23

5 SUMMARY AND CONCLUSIONS 26

APPENDIX A THE TABLES AND FIGURES OF RESULTS 28

APPENDIX B COMPUTER PROGRAM FOR PARAMETERS INANALYTICAL CURVES 74

REFERENCES 75

viii

LIST OF TABLES

Table Page

1 Mixing Proportion for High Strength Concrete 28

2 Mixing Proportion for Normal Strength Concrete 28

3 Average Values of Compressive Strength, Strain at Peak Stress, andElastic of Every Size of Each Batch 29

4 Modulus of Elasticity for Normal and High Strength Concretes 29

5 Parameters Used in Comparing Experimental With Analytical CurveUsing Hsu's Equations 30

6 Parameters Used in Comparing Experimental With Analytical CurveUsing Collins' Equations 30

ix

LIST OF FIGURES

Figure Page

1 Typical Complete Compressive Stress-Strain Curves(ACI-363) 8

2 Test Specimens with Different Aspect Ratio 31

3 Experimental Setup for Cylinder 3x6-in in Compression Test 31

4 Experimental Setup for Cylinder 3x9-in in Compression Test .. 32

5 Experimental Setup for Cylinder 3x12-in in Compression Test 32

6 Modulus of Elasticity Versus Concrete Strength (ACI-363) 33

7 Failure Mode for High Strength Concrete in Compression Test 34

8 Failure Mode for Normal Strength Concrete in Compression Test 34

9 Stress-Strain Curve for Normal Strength Concrete (N-01, 3x6 in, strainrate:1.67x10-5 strain/sec.) 35





14 Stress-Strain Curve for Normal Strength Concrete (N-06, 3x9 in, strainrate: 1.67x10-5 strain/sec.) 37


16 Stress-Strain Curve for Normal Strength Concrete (N-08, 3x12 in, strainrate:1.67x10-5 strain/sec) 38

LIST OF FIGURES(Continued)

Figure Page

17 Stress-Strain Curve for Normal Strength Concrete (N-09, 3x12 in, strainrate:1.67x10-5 strain/sec.) .. ... 39



20 Stress-Strain Curve for High Strength Concrete (H1-1, 3x6 in, strainrate:6.67x10-6 strain/sec.) 40

21 Stress-Strain Curve for High Strength Concrete (H1-2, 3x6 in, strainrate: 3.7x10 -6 strain/sec.) 41


23 Stress-Strain Curve for High Strength Concrete (H1-4, 3x6 in, strainrate: 2.5x10-6 strain/sec.) 42

24 Stress-Strain Curve for High Strength Concrete (H1-5, 3x9 in, strainrate: 7x10-7 strain/sec.) 42





• 29 Stress-Strain Curve for High Strength Concrete (H1-10, 3x12 in, strainrate: 8.9x10-8 strain/sec.) 45

xi


Figure Page





34 Stress-Strain Curve for High Strength Concrete (H2-03, 3x6 in, strainrate: 1.9x10-6 strain/sec.). 47




38 Stress-Strain Curve for High Strength Concrete (H2-07, 3x9 in, strainrate: 3x10 -7 strain/sec.) 49


40 Stress-Strain Curve for High Strength Concrete (H2-09, 3x12 in, strainrate: 8.3x10-8 strain/sec. 1 50




Figure Page

43 Comparison of Stress-Strain Curves of Same Size Cylinders for NormalStrength Concrete (N-01, N-02, N-03,, and N-04, 3x6 in) 52

44 Comparison of Stress-Strain Curves of Same Size Cylinders for NormalStrength Concrete (N-05, N-06, and N-07, 3x9 in) 53

45 Comparison of Stress-Strain Curves of Same Size Cylinders for NormalStrength Concrete (N-08, N-10, and N-11, 3x12 in) 54

46 Comparison of Stress-Strain Curves of Same Size Cylinders for HighStrength Concrete (H1-02, H1-03, and H1-04, 3x6 in) 55

47 Comparison of Stress-Strain Curves of Same Size Cylinders for HighStrength Concrete (H1-05, H1-06, H1-07, and H1-08, 3x9 in).... . . ........... 56

48 Comparison of Stress-Strain Curves of Same Size Cylinders for HighStrength Concrete (H1-09, H1-10, H1-11, and H1-12, 3x12 in) 57



51 Comparison of Stress-Strain Curves of Same Size Cylinders for HighStrength Concrete (H2-08, H2-09, Hand H2-11, 3x12 in) 60

52 Comparison of Stress-Strain Curves of Different Size Cylinders forNormal Strength Concrete (N-01, N-05, and N-08) 61

53 Comparison of Stress-Strain Curves of Different Size Cylinders for HighStrength Concrete (H1-03, H1-05, and H1-09) 62

54 Comparison of Stress-Strain Curves of Different Size Cylinders for HighStrength Concrete (H2-01, H2-04, and H2-10) 63

55 Experimental and Analytical Curves for Normal Strength Concrete UsingHsu's Equations(N-01,3x6 in) 64


Figure Page

56 Experimental and Analytical Curves for Normal Strength Concrete UsingCollins' Equations(N-01,3x6 in) 65

57 Experimental and Analytical Curves for Normal Strength Concrete UsingHsu's Equations(N-06,3x9 in) ....... 66


59 Experimental and Analytical Curves for Normal Strength Concrete UsingHsu's' Equations(N-08,3x12 in) 68


61 Experimental and Analytical Curves for High Strength Concrete UsingHsu's Equations(H1-03,3x6 in) 70

62 Experimental and Analytical Curves for High Strength Concrete UsingCollins' Equations(H1-03,3x6 in) 71

63 Experimental and Analytical Curves for High Strength Concrete UsingHsu's Equations(H2-01,3x6 in) 72

64 Experimental and Analytical Curves for High Strength Concrete UsingCollins' Equations(H2-01,3x6 in) 73

xiv

CHAPTER 1

INTRODUCTION

1.1 General

With its outstanding technological qualities, concrete has been a major structural

material used in buildings and other structures, whatever its forms (plain,

reinforced and prestress concrete). Even though there are high outputs of

structural steel in many developed countries, reinforced and prestressed

concretes are still commonly used in construction. In recent decades, the

development in concrete material science has brought about significant changes

in concrete construction and application. The focus of this development has

been in high strength concrete.

Generally, normal strength concrete is specified as a compressive strength

of 3,000 psi to 6,000 psi. In recent years however, there is a trend to define it as

a compressive strength of 3,000 psi to 8,000 psi. As the development of high

strength concrete has been continued, the definition of high strength concrete

varies in time and on a geographical basis[ACI, 1984] due to lack of the

standard criterion for high strength concrete. Several definitions of high strength

concrete have been made by many researchers. Freedman[Freedman, 1970]

defined the high strength concrete as a concrete with the strength of at least

6,000 psi at 28 days. ACI committee 363[ACI, 1984] defined the high strength

concrete as a concrete with specified compressive strength for design of 6,000

psi(41MPa) or greater. At present, the definition doesn't include concrete made

with exotic materials or techniques.

1

2

The most important properties of high strength concrete used in building

code are high strength and high modulus of elasticity. The strength of high

strength concrete is affected by several main factors:

• Mixing proportioning and the selection of materials

. The method of curing

• The size of specimen

The selection of materials and mixing proportions for high strength concrete are

more crucial than those for normal strength concrete. Concrete is a two-phase

composite material consisting of cement paste and aggregate. The methods of

strength improvement of concrete can be classified into three parts: Strength

improvement of cement matrix, aggregate and bond between cement matrix and

aggregate.

According to ACI Committee 363 (1984), the strength of the cement matrix

is based on the strength of the hydration structure and the porosity of the matrix.

The increase of porosity will reduce the strength of the cement matrix. Because

porosity increases with increasing water to cement ratio, high strength concrete

generally has of a low water-cement ratio. Therefore, reducing the water to

cement ratio and adding other chemical admixtures are methods of attaining

high strength concrete. Chemical admixture, such as superplasticizers and water

reducing products have been widely used in attaining high strength concrete.

The silica fume(SF) has also been used to improve the strength of cement matrix

in a ultra high strength concrete with compressive strength over 20,000 psi.

As a heterogeneous materials, the properties of concrete depend on both

the properties of individual component and their combination. The quality and

type of aggregates have a significant effect on the strength and behavior of high

strength concrete[Aitcin, 1990]. The characteristics of coarse aggregate, such

3

as, bond potential with cement paste and low water absorption capacity, are very

important consideration in the production of high strength concrete.

The methods of curing and the curing age are the other important factors in

developing the strength of concrete. Curing is mainly to promote the hydration of

the cement, and extremely important in attaining a high strength concrete. The

strength of concrete is increasing with the increase of its curing age. This has

been proved by many researchers.

Due to the special properties, such as high strength and high elastic

modulus, high strength concrete is often considered in the design of buildings to

achieve greater heights while reducing the mass of concrete needed by reducing

the sizes of column cross sections. Its high elastic modulus can also reduce the

deflections and creep deformations. The brittle property can be partly overcome

by adding fibers and/or tie confinement. It has been shown that addition of fibers

to concrete increased the ductility of concrete[Craig, 1984, Shah, 1976] and

fatigue strength [Kwak, 1991]. As the high content of cement, high strength

concrete is inherently more resistant to chemical deterioration.

With the high strength concrete used more and more commonly in all kinds

of structures, it has become necessary to further study the properties, stress-

strain behaviors, and influence factors of high strength concrete.

1.2 Scope and Objectives of Research

The objectives of this research are to study the behavior of stress-strain of high

strength concrete cylinders with different length to diameter ratio or aspect ratio,

equal to or greater than 3, and to study the interaction between the test

machine and the specimen under a uniaxial compression with the control of axis

strain. This research is divided into three parts:

4

To test the normal strength concretes cylinders with different sizes for

comparative study.

• To test the high strength concrete cylinders with different sizes and to

study the influence of cylinder size on the strength of concrete,

modulus of elasticity , failure mode and stress-strain behavior.

• To compare the experimental results with the analytical stress-strain

equations developed by Hsu(1992) and Collins et al (1993),

respectively.

1.3 The Structure of the Thesis

In the following, previous research that is related to the behavior of stress-strain

of concrete, the influence of specimen size on strength of concrete and behavior

of stress-strain will be reviewed. The empirical equations of complete stress-

strain curve for a high strength concrete will also be described in the second

chapter.

An introduction of mixing proportion, the selection of material, and the

properties of several materials, experimental methods used in this research is

presented in chapter 3. Chapter 4 will present and discuss the experimental

results.

The last chapter of this thesis is devoted to the summary and conclusions.

CHAPTER 2

LITERATURE SURVEY

2.1 Behavior of Concrete

2.1.1 Introduction

One of the most important properties of any structural materials is their

mechanical behavior of stress and strain. Current design practice for reinforced

and prestressed concrete is based on an implicit assumption that plain concrete

subjected to uniaxial compression has a usable descending part. Although the

explicit knowledge of the shape of the descending part is not necessary in most

routine designs; Wang [Wang, 1978] indicated that for an accurate and rational

design of the structures subjected to unusual loading such as earthquakes it is

desirable to know the complete stress-strain curve.

The Stress-strain behavior of concrete is dependent on its strength age at

loading, rate of loading, aggregate and cement properties and type and size of

specimens[Wang,1978, Granholm,1965] The shape of the uniaxial stress-strain

diagram is strongly affected by the several conditions. For testing, the conditions

include stiffness of the testing machine, size and shape of the specimen,

specimen versus machine stiffness, strain rate, type of strain gage, gage length,

and type of loading (preloading, cycling, etc.). For concrete characteristics, the

conditions include water-cement ratio, cement characteristics and content,

concrete unit weight, aggregate characteristics and content, and type of curing

and age of testing [Carreira and Chu, 1985].

5

6

2.1.2 Behavior of High Strength Concrete

There are rather limited literature about the complete stress-strain curve of high

strength concrete. One of the reasons why there are insufficient experimental

results on the complete stress-strain curve is that it is very difficult to measure

the descending portion of the curve. Until recently, only two reports discussed

the complete stress-strain curve for the plain high strength concrete by Shah et

al and Hsu [Shah, 1981, and Hsu, 1992]. In Shah's report, the specimens were

loaded in two different control modes: a constant rate of axial strain and the

controlled rate of circumferential strain. They obtained a complete stress-strain

curve of the high strength concrete for larger sizes of concrete cylinders (4x8

and 3x9 in.). During their experiments, the axial strain rate varied while the

circumferential strain rate was held constant. In Hsu's report, the specimens

were loaded using a constant rate of axial strain. The complete stress-strain

curves for 3x6 in. cylinders were successfully attained.

The shape of the ascending part of the stress-strain curve is more linear

and steeper for a high strength concrete than for a normal concrete. Also, the

slope of the descending branch of the curve is steeper for a high strength

concrete [ACI, 1984]. It is difficult to obtain the descending part of the stress-

strain curve experimentally. Hsu [Hsu,1974] showed experimentally that the

length of strain gages has a definitive effect on the shape of the descending

branch. A similar conclusion is also discussed by Sangha and Dhir [Sangha,

1972]. It is showed experimentally that the shape of the stress-strain diagram is

markedly affected by the following: (1) the confining effect that results from the

end restraint of the specimen by the testing machine platens; (2) as the material

approaches peak stress fc ' and beyond, the influence of end restraint becomes

increasingly important; (3) the maximum size of the aggregate in relation to the

specimen size; (4) the weaker top layers of the specimen; (5) the strain gage

7

length compared with the specimen length and slenderness; and (6) the

specimen diameter for a given slenderness ratio. Shah [Shah, 1981] indicated

that the interaction between the testing system and the specimen is more critical.

The stress-strain relationship of high strength concrete in uniaxial

compression has been reported by many researchers. The main differences

between the stress-strain relationships of high strength concrete and normal

strength concrete are that high strength concrete has:

• a more linear stress-strain relationship to a high percentage of the

maximum stress

• a higher strain at maximum stress

• a steeper slope of the descending part of the curve

Carrasquillo et al.[Carrasquillo, 1981] have used X-ray techniques to

demonstrate the relationship between the slope of a stress-strain curve and the

extent of internal microcracking. For normal strength concrete, the unstable

microcracks start to develop at the interface between the paste and the

aggregate at about 65% of the peak stress. Aggregate type also affects the

shape of a stress-strain curve of concrete. While improvements to the quality of

the mortar results in increased compressive strengths, this does not necessarily

lead to a certain increase in the stiffness of the concrete. For a concrete of the

same strength, a stronger aggregate results in a smaller strain corresponding to

the peak stress. For a high strength concrete, unstable microcracks pass

through the aggregates resulting in a sudden release of energy which causes a

sharp descending branch of the stress-strain relation. Typical stress-strain

relationships of normal and high strength concretes are shown below:

Figure 1 Typical Complete Compressive Stress-Strain Curves (ACI-363)

2.1.3 Effect of Interaction Between Testing Machine and Specimen onBehavior of Concrete

Interaction between the testing machine and specimen mainly includes two

parts: one is the relative stiffness and the other is the end restrain between the

machine and specimen. The effect of end restrain is conventionally assumed to

be negligible for a standard specimen with a length to diameter ratio (lid) of 2

[ASTM, 1992]. Comparing to the end restrain, the stiffness of the testing

machine is a more critical one. The stiffer the testing machine is, the smaller the

amount of released strain energy is. If the stiffness of the machine is greater

than the absolute value of the stiffness of the specimen in the descending part,

then a stable descending part can be experimentally obtained [Hundson, 1972].

Some investigators have developed techniques to increase the stiffness of the

testing machine which is costly, and may not be available in a normal quality

9

control laboratory [Ahmed, 1979]. However, Wang and colleagues [Wang, 1978]

introduced a simple method to eliminate the strain energy release of the testing

machine. In their testings, concrete cylinders were loaded in parallel to the

hardened steel tubes. This design ensures that the sum of the load carried by

the steel tubes and the concrete cylinder is always increasing up to a strain of

0.006. Thus, no release of energy comes from the testing machine. During

loading, the strains in the steel tube were measured. Thus, knowing the total

load and the corresponding steel strain, the stress-strain relationship for a

concrete can be obtained. An alternate approach is to use a closed-loop testing

machine [Shah,1981]. In a closed-loop testing machine, specimens can be loads

so as to maintain a constant rate of strain increase and avoid unstable failure.

2.1.4 Effect of Cylinder Size on Concrete Strength and Elastic Modulus

The length-to-diameter ratio of concrete compression test specimens has long

been recognized as another important factor that influences the failure load.

Gonnerman[Gonnerman, 1925] found no significant differences between 6 in.

and small-diameter cylinders having the length to diameter ratio of 2 for normal

strength concrete. Short specimens fail at greater loads because the steel

loading platens of the testing machine restrain lateral expansion throughout the

specimen more effectively [Newman, 1964, and Ottosen, 1984]. The effect of

end restraint is conventionally assumed negligible for a standard specimen with

a length-to-diameter ratio (1/d) of 2 [ASTM, 1992]. By comparing the

compressive strength of 150-mm cylinders with 100-mm cylinders using the

same length/diameter ratio, Baalaki [Baalaki, 1992] found that the larger

specimen has a lower compressive strength and a higher elastic modulus. Up to

now no other results have been published in the literature on the influence of

specimen size and the value of the elastic modulus.

10

2.2 Empirical Equations of Complete Stress-Strain Curvefor High Strength Concrete

The study of the stress-strain relationship is an important issue to quantify the

behavior of concrete. A number of empirical equations of complete stress-strain

curve for a normal concrete have been proposed, but few empirical formula are

developed for a high strength concrete. Carreira et al [Carreira, 1985] proposed

an equation to represent the complete stress-strain relationship of a plain normal

concrete. They found the shape of stress-strain curve is strongly affected by

some factors such as strain rate, the relative stiffness between the testing

machine and specimen, size and shape of the specimen, the quality of the

cement matrix, and the aggregate characteristics and their content. The

parameters in the equation are physically significant and can be estimated from

the experiments., Other complete stress-strain equations for a normal concrete

were summarized by Hsu and can be found in his work[Hsu, 1974].Hsu [Hsu,

1992] proposed an equation to represent the complete stress-strain relationship

of plain and fibrous high strength concretes. The parameters of proposed

equation can be predicted by a given single value of maximum compressive

strength, which can be obtained from the experiment. Another equation, first

proposed by Popovics [Popovics, 1973] and modified by other researchers and

summarized by Collins et al [Collins, 1993], can also be predicted by the value of

compressive strength fc. The above two empirical stress-strain equation will be

used in this study to compare with the present experimental test results in

Chapter four.

CHAPTER 3

MATERIALS AND EXPERIMENTAL METHODS

3.1 Specimens , Materials and Mixing Proportion

3.1.1 Specimens

In this thesis, concretes in normal strength and high strength were studied.

Compressive strength fc' for high strength concrete is designated to be 12,000

psi (84 MPa) at 28 days, and it is 4,000 psi for normal strength concrete at 28

days.

A total of 34 specimens with three different sizes for normal and high

strength concrete cylinders:3x6, 3x9, and 3x12 in.were cast in the plastic molds.

Two batches of high strength concrete cylinders and one batch of normal

strength concrete cylinders were mixed in the concrete laboratory.

They are designated as follows:

Batch H1: plain high strength concrete

Batch H2: plain high strength concrete

Batch N : plain normal strength concrete

A detailed description of the procedures and criteria for the selection of material

and their proportions is given in the following.

3.1.2 Materials

The strength of concrete mainly depends on the strength of the hydration

structure and the porosity of concrete matrix. Porosity increases with increasing

water/cement ratio. Therefore, reducing the water to cement ratio is a method of

attaining higher strength concrete, and adding other chemical products is

another method of improving the workability of concrete.

11

12

The materials consisted of Type I cement satisfying with ASTM 150, sand

from local source, basalt with maximum aggregate size of 3/8 in. for high

strength concrete, or limestone aggregate with size of 3/8 in for normal strength

concrete, and tap water. For high strength concrete, silica fume (SF) in a

powder form was used to achieve a higher strength, and the superplasticizers

(SP) was also used to maintain good workability. SF and SP are introduced

below:

silica fume: Silica fume is a by-product resulting from the reduction of high

purity coal, in electric arc furnaces, or in the production of silicon and ferro-

silicon alloys. The silica fume has a high content of amorphous silicon dioxide

and consists of very fine spherical particles with an average particle size about

100 times smaller than a grain of ordinary Portland cement. It is necessary if

very high strength concrete is desired since it permits workability to be

maintained, even for concrete of very low water to cement ratio. Because of its

high Si02 content and fine particle size, silica fume is an extremely reactive

pozzolan for Portland cement concrete [LI,1994].

superplasticizer: superplasticizer is the main chemical admixture used for

attaining high strength concrete, the superplasticizers are used as water

reducers and do not require any significant change in the mix proportioning

(other than reduction in water-cement ratio). It can significantly improve the

dispersibility of cement particles and thus permit a decreasing water - cement

ratio. In addition, it will result in a more flowable concrete so that to enhance

workability [L1,19941.

1 3

3.1.3 Mixing Proportions

Table 1 and Table 2 list the mixing proportions of high and normal strength

concretes for current study. With these mixing proportions, the compressive

strength of concrete is approximately 12,000 psi for high strength concrete and

4,000 psi for normal strength at 28 days after casting with curing.

3.2 Experimental Method

3.2.1 Mixing, Casting, and Curing

All specimens followed the same procedures for material mixing, and curing to

minimize scattering of specimen properties.

All materials as described in previous section were mixed by a rotary mixer.

All cylinder specimens molds were prepared and lubricated with oil before the

concrete was poured. The mixing procedures were Firstly, the coarse and fine

aggregates were loaded into the mixer and dry mixed for 2 to 3 minutes.

Secondly, the cement and silica fume were added and mixed for another 1 to 2

minutes. Then the water with the superplasticizers was added to cementitious

materials and mixed for at least 5 minutes until a homogeneous mixture was

achieved. The resulting mixture was then molded into cylindrical molds.

During casting, both table vibrator and steel bar were used to compact the

specimens. All specimens were covered by plastic sheets right after casting and

were left at the room for 24 hours to get hardened. These specimens were then

demolded and cured in a lime saturated water until the day before testing. The

age of the specimens at the time of testing varied from 33 to 36 days.

14

3.2.2 Experimental Setup

The experiments are conducted in NWT Concrete and Structures Laboratory

using the Material Testing System (MTS) which is capable of performing a wide

range of experiments. In this study, the load-deformation curves of concrete

specimens are measured by a uniaxial compression.

Prior to testing, each cylinder was capped with sulfur compound at both

ends to ensure parallel and smooth surfaces of the test specimens and to

maintain a constant length for all cylinders. All the cylinder specimens were

tested in an uniaxial compression under servo-controlled, close-loop machine.

The maximum load capacity of the MTS is 100 kips. To obtain a complete stress-

strain curve, a slow strain rate was used. The axial deformations were measured

by two clip-on gages which were mounted to the specimen as shown in Fig.3 to

Fig. 5. In order to record the average axial displacements, the signals from the

two strain gages were averaged and fed back to the controller to constantly

adjust the applied load to maintain a constant strain rate. An IBM electronic data

acquisition system running the Unkelscope program was used to record the

strain values and corresponding loads.

CHAPTER 4

RESULTS AND DISCUSSIONS

4.1 Introduction

Twenty three cylinder specimens with size 3x6in., 3x9 in., and 3x12 in. made

with plain high-strength concrete were tested under short-term uniaxial

compression to determine the ultimate strength and to study the stress-strain

behavior with different ratio of length to diameter. Eleven cylinder specimens

made with plain normal strength concrete were also tested (fc '_.7,000 psi). Both

types of the concrete were also studied to understand the effect of specimen

size on their stress-strain behavior. In this chapter, experimental results will be

presented and discussed. These experimental data will also be used to compare

with the empirical equations proposed by other researchers.

4.2 Short-Term Uniaxial Compression Test

Plain high strength concrete and normal strength concrete specimens with

different size were tested. Their behavior of stress-strain, compressive strength,

failure mode, modulus of elasticity and interaction between the testing machine

and specimen end restrain were studied.

4.2.1 Effect of Specimen Size on Compressive Strength

A total of 34 cylinders were tested. Concrete cylinders with three different ratios

of length to diameter (3x6 in., 3x9 in., and 3x12 in.) were shown in Fig 2.

Compressive strengths of two types of concrete, normal and high strengths,

were obtained. These compressive strengths obtained at 33 or 36 days with their

corresponding strain and modulus of elasticity are given in Table 4.

15

16

Based on the test results, they show that the values of compressive

strength are slightly influenced by the aspect ratio of cylindrical specimens (the

different ratio of length to diameter). It appears that the compressive strength

and specimen size are inversely proportional. That is, as the ratio of length to

diameter increases, the compressive strength decreases slightly (Fig.52 to

Fig,54). Baalbaki et al [Baalbek', 1992] also obtained the similar results.

There are two possible explanations for this observation:

• The length to diameter ratio of concrete compression test specimens has

long been recognized as a factor that influences the failure load. Shorter

specimens fail at greater loads because the steel loading platens of the

testing machine restrain lateral expansion throughout the specimen more

effectively [Newman, 1964 and Ottosen,1984].

• Compaction is another factor influencing the concrete strength. Smaller

or shorter specimens tend to achieve better compaction, higher density,

and thus higher strength. This is particully true when the same

compaction procedures are used for all concrete specimens.

4.2.2 Effect of Specimens Size on Strain Corresponding to CompressiveStrength

Based on the present tests on concrete cylinders, no significant difference for

the strain values corresponding to compressive strength of different sizes in this

study was observed between the normal strength concrete cylinders and high

strength concrete cylinders. It is slightly different from the results of other

researchers. Carrasquillo et al [Carrasquillo, 1981] reported that the peak strain

for the high strength concrete is slightly greater than that for the normal strength

concrete within the strength range of 3,000 psi to 6,000 psi.For the strain values

corresponding to compressive strength are influenced by the length/diameter

17

ratio. The strain (e.) and the length /diameter are also inversely proportionally

(Table 3)

4.2.3 Effect of Specimen Size on Modulus of Elasticity

The secant modulus at from 25% to 50% of the compressive strength f c ' is

usually considered to be the modulus of elasticity [Wang and Salmon, 1992]. In

this study, the secant modulus of elasticity is defined as the secant slope of the

uniaxial stress-strain curve at a stress level of 50% of compressive strength.

Table 3 shows the values of modulus of elasticity where each elastic modulus

value is the average of three or four measurements of every size specimens.

Fig. 6 shows the relationship of modulus of elasticity and its corresponding

strength as summarized by ACI committee 363 ( ACI-363, 1984 ). The results of

present study are also plotted in Fig.6 for comparison. Based on the results of

Fig. 6, it may be concluded that present ACI recommendation for the modulus of

elasticity is only applicable to the concrete with the compressive strength up to

6,000 psi.

Table 4 summaries the compressive strength ( fc' ), strain ( 6 0 ) at peak

stress, and modulus of elasticity ( E c ) from this study. A comparison of

experimentally determined values for the modulus of elasticity with those

predicted by the expression given in ACI 318-89, is given in Table 4 under

columns 4 and 5, respectively. They show that ACI equation gives higher

modulus of elasticity for high strength concrete than those obtained from present

study. Carrasquillo [Carrasquillo,1981 ] and other reseachers also gave similar

conclusions.

The compressive strength, fc 1 , is inversely proportional to the specimen

size, however, the modulus of elasticity observed from the present experiment

results is proportional to the specimen size. That is, as the ratio of length to

18

diameter increases, the modulus of elasticity also increases (Table 3 ). A similar

phenomenon was also observed by Baalbaki et al [ Baalbaki, 1992 on different

sizes of concrete specimens (cylinders with the same ratio of length to diameter

but with different diameter).

Based on present elastic modulus values of total 34 cylinders of normal

strength and high strength concretes tested in this investigation, one may

conclude:

1. For normal strength concrete cylinders: the ratio of moduli of 3x6 in.

cylinders( Eco6 1 ) to 3x9 in. cylinders ( Ecog' ) is 0.83; and the ratio of moduli of

3x6 in. cylinders (E, 06 1 ) to 3x12 in. cylinders ( E c12 ' ) is 0.82. Therefore, the

following relations maybe proposed:

E09 ' = 1.20 Eco6' ( 5 )

E 'c 12 -= 1.21 Ecosi ( 6 )

2. For high strength concrete cylinders: the ratio of moduli of 3x6 in. ( E co6 1 ) to

3x9 in. cylinders ( Ecog' ) is 0.86; and the ratio of moduli of 3x6 in. ( Ec436' ) to

3x12 in. cylinders ( E ci2' ) is 0.83. Therefore, the following relations may be

proposed:

Ecog' = 1.16 Ec06 1

( 7 )

Ec12' 1.22 Eco6 1 ( 8)

where: Eco6r-- Modulus of elasticity of 3x6 in. cylinders

Ecog i Modulus of elasticity of 3x9 in. cylinders

Ec12 1 Modulus of elasticity of 3x12 in. cylinders

4.2.4 Behavior of Stress -Strain

Based on present tests of normal and high strength concrete cylinders, test

results for behavior of stress-strain are exhibited in Fig. 9 through Fig. 42.

19

Fig. 52 shows the typical stress-strain curve of normal strength concrete of

compressive strength near 7,000 psi with different length to diameter ( lid ) ratios

in a uniaxial compression. It shows that the compressive strength has the trend

of decreasing with the increasing the ratio of length to diameter. The strain

corresponding to compressive strength fc' has the same trend of decreasing with

the increasing ratio of length to diameter. For normal strength concrete, the

shape of the ascending branch of the stress-strain curve for three different sizes

of specimens shows no significant difference. It may be concluded that the

ascending branch of the stress-strain curve is less influenced by the cylinder

size. However, after reaching the maximum strength, the descending part of the

stress-strain curves for 3x6, 3x9, and 3x12 in. cylinders shows different

behavior. The larger the ratio of length to diameter is, the steeper the

descending rate is. Also the uniaxial strain at maximum strength is larger when

the lid ratio is smaller. The results show that the brittle character exhibited more

in a larger ratio of length to diameter cylinder than that of a smaller ratio.

Different from normal strength concrete cylinder, the ascending branch of

stress-strain curve for high strength concrete cylinder is slightly steeper as the

ratio of length to diameter increases. Comparing the normal and high strength

concrete cylinders with the same size as presented in Fig. 53 and Fig. 54 , the

shape of the ascending branch of the stress-strain curve is more linear and

steeper as the compressive strength increases. This is due to less bond

cracking and high stress-strength ratio to form the continuous crack paterns [

Carrasquillo, 1981 J. The last portion of the descending part of the stress-strain

curves for 3x9 and 3x12 in. at present tests were unable to attain. It may be

attributed to the stability of the concrete cylinders.

From the result of this study, the size of concrete specimen has no

significant influence on the behavior of concrete in pre-peak region. But at post-

20

peak strength, the higher the compressive strength is, the steeper the

descending part is. That is, the descending part of the stress-strain curve

exhibits a more brittle characteristic as the compressive strength increases.

For a heterogeneous materials like concrete, cracking is a dominant factor

for its behavior, and the development of microcracking is closely related to the

characteristics of stress-strain relation. The descending branch is attributed to

the extension of continuous cracks, which may be regarded as the reduction of

effective cross-sectional area [Meyer and Okamura, 1986]. The descending

branch of stress-strain curve of concrete can no longer be treated as a material

property. Rather, it has to be referred as a structural property [Mier, 1984].

Previous and present test results show that in pre-peak region, stress-strain

curves have no significant difference regardless of the heights of specimens;

however, they differ considerably in the post-peak region.

4.2.5 Failure Mode

The mode of failure for high strength concrete cylinders observed during testing

was different from that of normal strength concrete cylinder. Generally, the

normal strength concrete gradually fails after reaching its peak load; whereas,

the high strength concrete explodes just passing the peak load. Therefore, it is

difficulty to obtain a complete stress-strain curve for high strength concrete.

However, if the strain rate is sufficiently slow as in the present tests, it is

possible to obtain a gradual failure for high strength concrete cylinders.

Fig. 7 and Fig. 8 show the modes of failure for normal and high strength

concretes under suitable strain rate. The specimens generally fail in axial

splitting parallel to the applied load.

Fig. 8 shows the mode of failure of normal strength concrete cylinders with

the ratio of length to diameter equal to 2, 3 and 4 under the same strain rate

21

1.67x10-5 strain/sec. It clearly shows that the larger the ratio of length to

diameter is, the larger the lateral strain is. From the Fig. 8, it shows that the

larger ratio of length to diameter is , the smaller the axial strain is at failure.

Thus, the rate of increase of lateral strain in the descending part is greater than

that of axial strain ; and this rate is larger for larger ratio of length to diameter

cylinders.

For high strength concrete cylinders ( fd=12,000 to 13,000 psi ), similar

results were obtained. But the unstable failure may occur when the length of the

specimens is too long. This may explain why the cylinders suddenly explode at

the peak load for 3x9 and 3x12 in. cylinders even though a sufficient slow strain

rate is used (3x10-7 strain/sec. , 2x10- 7 strain/sec. respectively ).

The crack patterns of both normal and high strength concrete cylinders are

observed to be different. The broken surfaces of high strength concrete cylinder

pass through the aggregate and mortar and are smoother. This indicates that

the strength of the cement-matrix is higher than that of the aggregate and the

crack initiates through the aggregate by forming a much smoother cracked

surface. This phenomenon is different from that seen in the normal strength

concrete. The normal strength concrete exhibits a highly irregular failure

surfaces including bond failure between cement paste and coarse aggregate.

Carrasquillo [Carrasquillo, 1981 ] and Hsu [Hsu, 1992 ] also showed similar

results. The high strength concrete is more likely to pass through the aggregate

due to the greater cement-matrix strength, and the coarse aggregate becomes

the controlling factor for the ultimate strength of concrete. Therefore, the coarse

aggregate strength should be a more important parameter in a high strength

concrete than that in a normal concrete.

22

4.2.6 Effect of Interaction of Testing Machine and Specimen on Behavior ofConcrete and Failure Mode

Fig. 52 to Fig. 54 show that after reaching the maximum strength, the

descending part of the stress-strain curve for 3x6, 3x9 and 3x12 in. cylinders

exhibit the phenomenon that the maximum uniaxial strain becomes smaller as

the ratio of length to diameter increases. In contrast, it may be said that the

lateral strain becomes larger as the ratio of length to diameter increases. Thus,

the failure of concrete subjected to uniaxial compression is usually observed by

longitudinal splitting cracks.lt may be concluded that the rate of increase in

lateral strain in the descending part is greater than that of axial strain [Shah,

19811 especially for a longer cylinder. Thus the friction of the end between the

steel loading platens and specimen can not be effectively restrained in lateral

expansion throughout the specimen for longer specimens.

Another important factor affecting the descending part is the stiffness of the

machine.The stiffer the testing machine is, the smaller the amount of released

strain energy is. The servo-controlled closed-looped testing testing machine was

used in this test. But even with the closed-loop system, the relative stiffness of

the testing system may be still critical in deterimining the failure mode.

In this test, the descending part of stress-strain curve was sucessfully

obtained for normal strength concrete ( 3x6, 3x9, 3x12 in.), and high strength

concrete ( 3x6 in.).

For higher strength and higher length to diameter cylinder, the strain energy

stored in the specimen is much greater than that in normal strength

concrete.Thus, the relative stiffness of machine is reduced. When the energy

release rate is greater than the frequency response of the system, then suddenly

failure may occur during testing.

23

4.3 Comparison of Experimental Data and Existing Empirical Equations

Two empirical equations were used to compare with the present experimental

data. The first one is Hsu's equation [Hsu, 1992]:

where

f3 and n are the material parameters. fi depends on the shape of the stress-

strain diagram, and n depends on the strength of material. is the normalized

stress; x is the normalized strain; fc is the stress; E is the strain; fc' is the peak

stress of concrete; E. is the strain corresponding to the peak stress fc'; xd is the

strain corresponding to 0.3 fc' in the descending portion of the stress-strain

curve. rid is equal to 0.3 which corresponds to 0.3 fc' in the descending portion

in the dimensional stress-strain curve. kd and a are taken to be 0.8 and 0.5

respectively.

The relationship between f3 and compressive strength fc':

where fc' is the compressive strength of concrete in [ksi].

For 15_ x s x d , then n=1, if, 0(ksi) < f < 9 (ksi)

then n=2, if, 9 (ksi) fc< 11 (ksi)

24

Another one is the equation originally proposed by Popovics [Popovics,1973],

later modified by other researchers and summarized by Collins et al [Collins,

1993] :

where n and k are curve fitting factor, as n becomes higher, the rising curve

becomes more linear. fc is the compressive stress , so is the compressive strain,

fc' is the peak stress of concrete, s o' is the strain corresponding to the peak

stress.

A total of five experimental data were compared with the above two

empirical equations. Fig.55 to Fig.64 show the results of comparison.

Experimental data of normal strength concrete cylinders with different

aspect ratio and high strength concrete cylinders of 3x6-in are compared with

the empirical equations presented. Good agreement for the complete stress-

25

strain curves of normal and high strength concrete cylinders of 3x6 in. was

obtained using Collins' equations and Hsu's equations, respectively. No

satisfactory agreement for normal strength concrete of aspect ratio larger than

two was achieved. It is because the parameters used in the empirical equations

do not consider the effect of aspect ratios. Thus, good agreement may be

obtained by modifying the parameters in the empirical equations.

CHAPTER 5

SUMMARY AND CONCLUSIONS

Based on the present tests on 34 cylinders of three different kinds of

length/diameter ratios, the following conclusions may be made.

1. The compressive strength, uniaxial strain at maximum compressive strength

and modulus of elasticity are influenced by the size of cylindrical specimens.

It is found that the compressive strength is inversely proportional to the

specimen size. The strain at maximum compressive strength is also inversely

proportional to the specimen size. The elastic modulus is proportional to the

specimen size. In this study, it is also found that the ACI equation

overestimates the modulus of elasticity for concrete with compressive

strength greater than 6,000 psi.

2. For normal strength concrete, the shape of the ascending branch of the

stress-strain curve for three different sizes is less influenced by the ratio of

length to diameter ratio. However, the descending part of the stress-strain

curve is steeper for higher ratio of length to diameter.

For high strength concrete, the shape of the ascending part of the stress-

strain curve for higher strength concrete behaves a more linear and steeper

curve. The slope of the descending part of 3x6 in. specimen exhibits a

steeper curve as compared to that of the normal concrete. The descending

part of curves for 3x9 and 3x12 in. are unable to obtain in the experiments

with uniaxial strain control.

It has been shown that in pre-peak region, the stress-strain curve of normal

strength concrete are almost identical regardless of the heights of

specimens. However, that in the post-peak region, they vary considerably.

26

27

The stress-strain curves of high strength concrete show similar results as

those in normal strength concrete.

3. The crack patterns for high strength concrete show that the broken surface of

the concrete cylinders exhibits a smoother surface, and its surface passes

through the aggregates.

4. A good agreement for the complete stress-strain curve of high strength

concrete of 3x6 in. was obtained using Collins' equations and Hsu's

equations, respectively.

APPENDIX A

THE TABLES AND FIGURES OF RESULTS

Tablel Mixing Proportion for High Strength Concrete

Mixing Proportion

Materials Weight Ratio Weight(Ib/ft3)cement 1.00 40.317water 0.29 11.857sand 0.65 26.027aggregate 1.63 65.65silica fume(SF) 0.11 4.48superp as icizer 1 liter/200 lb

cememtitious0.33 liter

Table 2 Mixing Proportion for High Strength Concrete

Mixing Proportion

materials weight ratio weight(Ib/ft3)water 0.57 14.26cement 1.00 25.02sand 2.08 51.72aggregate 2.01 50.4

28

29

Table 3 Average Values of Compressive Strength, Strain at Peak Stress, andModulus of Elastic of Every Size of Each Batch

batch size t (psi) 6 (in/in) Ec(psi)

3x6 7424 0.0040 2525519

batch N 3x9 7120 0.0034 3025885

3x12 6934 0.0034 3076180

3x6 12882 0.0040 3369661

batch H1 3x9 13260 0.0036 4114181

3x12 12272 0.0033 4460820

3x6 12492 0.0036 3913530

batch H2 3x9 12512 0.0034 4328235

3x12 11299 0.0028 4418185

: compressive strength of concreteE 0 : strain at peak stress of concreteE c : modulus of elasticity

Table 4 Modulus of Elasticity For Normal and High Strength Concretes

batch rc (psi) 60 (in/in) E,(106 psi) E:(106 psi)7122 0.0038 2.63 4.91

batch N 7543 0.0041 2.48 4.81(3x6) 7191 0.0038 2.37 4.75

12808 0.0038 3.32 6.37batch H1 13125 0.0037 3.75 6.38(3x6) 13678 0.0041 3.56 6.06

13153 0.0038 3.94 6.47batch H2 11709 0.0032 4.08 6.56(3x6) 12614 0.0038 3.72 6.31

* ACI 318-89E c =57000.yrf c psi

. compressive strength of concrete6 0 : strain at peak stress of concreteE c : modulus of elasticity

30

Table 5 Parameters Used in Experimental h Analytical Curve Using Hsu'sEquations

specimen f'c (psi) 0 n xd

N-01 7122.496 3.0167 1 3.0370

N-06 7157.032 3.0230 1 3.0285

N-09 6942.883 2.985 1 3.0760

H1-04 13125.83 5.260 5 1.1797

H2-01 13153.48 5.278 5 1.1802

: compressive strength of concrete in the experiment13: material parameters which are related to the shape of stress-strain diagramn: parameter depending on the strength of materialxd : strain at 0.3 f in the descending portion of stress-strain curve, and it can beobtained using the program shown in APPENDIX B

Table 6 Parameters Used In Comparing Experimental With Analytical CurveUsing Collins' Equations

specimen f n k

N-01 7122.496 3.65 1.461

N-06 7157.032 3.66 1.465

N-09 6942.883 3.58 1.441

H1-04 13125.83 6.05 2.128

H2-01 13153.48 6.06 2.131

fc : compressive strength of concrete in the experimentn : curve fitting factork : curve fitting factor

Figure 2 Test Specimens With Different Aspect Ratio

31

Figure 3 Experimental Setup for Cylinder 3x6 in. in Compression Test

Figure 4 Experimental Setup for Cylinder 3x9in. in Compression Test

32

Figure 5 Experimental Setup for Cylinder 3x12in. in Compression Test

166 4

276 10 207 •

M Pa10

50

ACI 318, E c . 33 wc15 ./F' psi6

Range for which ACI code

formula was derived

40

4s

60 e0 100

MPa

145 1 . 5 3E C ( W ) x30 M Po

•1000 2000. 3000 4000 5000 6000 8000 10000 12000 14000

020 30 40 50 60 70 80 90 100 110

c psi

42 •

).o4«4 4

4 et • 9 4

4• 0 •G •

• 41

44

f 1

•• • Ma, llnot , Ntlson 6 Sla19

IIgAI Kluge, Sp•l•• Tama

- 0 Planar I & J•nson• aighl + PHs• SColdea

• cont. Oa • Hong,

A Hon•.o 51.1•lor

o Mor lint., Milton 0 Slot.• Cort•liqq111o.1411.en d Slot.• near, Monsoon • Cop•Il

Hol real A Potash. Allogor• 001 I Riana,, rata, flo,01saa ft Holtman

COOC1•it

▪

Paws.#

• DO,• 6 Vi•sipsi 4 R1019 , 114 Janson

„-.•• •

A . %• ■ • b

46

▪

.

*; • (wc/145)1'5 psi

E c (40,000 A:4-10 x106 1

• present study

120 0

20

10

5

4

E c w

( 145 )1.5x1663psi

Figure 6 Modulus of Elasticity Versus Concrete Strength (ACI-363)

Figure 7 Failure Mode for High Strength Concrete in Compression Test

34

Figure 8 Failure Mode for Normal Strength Concrete in Compression Test

8000

J5

6000

v) 4000

2000

0.005

0.01

0.015

strain(in/in)

Figure 9 Stress-Strain Curve for Normal Strength Concrete(N-01,3x6 in., strain rate: 1.67x10 -5 strain/sec.)

8000

0 0.005

0.01

0.015

strain(in/in)


8000

6000

rn 4000

2000

36

0

0.005

0.01

0.015

strain(in/in)


0 0.005 0.01 0.015strain(in/in)


8000

6000

4000

2000


37

Figure 14 Stress-Strain Curve for Normal Strength Concrete(N-06,3x9 in, strain rate: 1.67x10 -5 strain/sec.)


(1


Figure 19 Stress-Strain Curve for Normal Strength Concrete(N-11,3x12 in., strain rate: 1.67x10-5 strain/sec.)

Figure 20 Stress-Strain Curve for High Strength Concrete(H1-01,3x6 in., strain rate: 6.67x10 -6 strain/sec.)

Figure 23 Stress-Strain Curve for Hihg Strength Concrete(H1-04,3x6 in., strain rate: 2.5x10 -6 strain/sec.)

Figure 24 Stress-Strain Curve for High Strength Concrete(H1-05,3x9 in., strain rate: 7x10 -7 strain/sec.)


43


14000

12000 -

10000 -

8000 -sN

6000 -

44

0

0.005 0.01 0.015

strain(in/in)


14000

12000

10000

8000

6000

4000

2000

0

0 0.005 0.01 0.015

strain(in/in)

Figure 28 Stress-Strain Curve for High Strength Concrete(H1-09,3x12 in., strain rate: lx10 -7 strain/sec.)

14000

12000

10000

8000

(ub 6000

4000

2000

0

0 0.005 0.01 0.015strain(in/in)


14000

12000

10000

8000

(1.1b 6000

4000

2000

0 0 0.005 0.01 0.015

strain(in/in)

Figure 30 Stress-Strain Curve for High Strength Concrete(H1 -1 1 ,3x1 2 in., strain rate: 5x1 0 -7 strain/sec.)

45

12000

0 0.005 0.01 0.015

strain(in/in)


14000

12000

10000

8000

451 6000

4000

2000

0 0 0.005 0.01 0.015

strain(inf )


46


47


Figure 35 Stress-Strain Curve for High Strength Concrete(H2-04,3x9 in , strain rate: 7x10 -7 strain/sec.)

4 8


49

12000

10000

8000

6000

4000

2000 -

0

0 0.005 0.01 0.015

strian(in/in)

Figure 37 Stress-Strain Curve for High Strength Concrete(H2-06,3x9 in., strain rate: 3x10-7 strain/sec.)

14000

12000

10000

8000

N 6000

4000

2000

0 0 0.005 0.01 0.015

strain (in/in)


Figure 39 Stress-Strain Curve for High Strength Concrete(H2-08,3x12 in., strain rate: 8.3x10 -8 strain/sec.

50

=igure 40 Stress-Strain Curve for High Strength Concrete(H2-09,3x12 in., strain rate: 8.3x10 -8 strain/sec.)

Comparison: Stress-Strain Curve

Figure 43 Comparison of Stress-Strain Curves of Same Size Cylinders for Normal Strength Concrete(N-01,N-02, N-03, and N-04, 3x6 in.)

8000Comparison: Stress-Strain Curce

0

0.005

0.01

0.015strain(in/in)

Figure 44 Comparison of Stress-Strain Curves of Same Size Cylinders for Normal Strength Concrete(N-05,N-06,and N-07, 3x9 in.)


8000

6000

v) 4000cll

2000

0

0.005

0.01

0.015

strain(in/in)

Figure 45 Comparison of Stress-Strain Curves of Same Size Cylinders for Normal Strength Concrete(N-08,N-10,and N-11, 3x12 in.)

0 0.005 0.01 0.015

14000

12000

10000

8000"/d40.) 6000

4000

0


strain(in/in)

Figure 46 Comparison of Stress-Strain Curves of Same Size Cylinders for High Strength Concrete(H1-02,H1-03,and H1-04, 3x6 in.)

Comparison: Stress-Strain Curve14000

12000 -

10000 -,-,

8000

4.1 6000

4000 -

2000 -

00 0.005 0.01 0.015

strain(in/in)

Figure 47 Comparison of Stress -Strain Curves of Same Size Cylinders for High Strength Concrete(H1-05,H1-06,H1-07,and H1-08, 3x9 in.)

14000

12000

10000

8000

(urn6000

4000

2000

00 0.005 0.01 0.015


strain(in/in)

Figure 48 Comparison of Stress-Strain Curves of Same Size Cylinders for High Strength Concrete(H1-09,H1-10,H1-11 and H1-12, 3x12 in.)

0 0.005 0.01 0.015

14000

12000 -

10000 -

Q., 8000

0.1 6000 -

4000 -

2000 -

0


strain(in/in)


14000

12000 -

10000 -

• 8000

▪ 6000 -

4000 -

2000 -


0 0 0.005 0.01 0.015

strain(inJin)


Comparison: Stress-Strain Curve14000

12000

10000

00„,"7' 8000

I-. 6000

4000

2000

00

0.005 0.01 0.015

strain(in/in)

Figure 51 Comparison of Stress-Strain Curves of Same Size Cylinders for High Strength Concrete(H2-08,H2-09,H2-10 and H2-11, 3x12 in.)

8000

3x6 fc' =7122 psi3x9 fc• =7005 psi3x12 fc• =6942 psi

6000

• aCI) 4000

2000

0.005 0.01 0.015


strain(in/in)

Figure 52 Comparison of Stress-Strain Curves of Different Size Cylinders for Normal Strength Concrete(N-01,N-05,and N-08,)


14000

12000 -

10000 -

8000 -

17, 6000

A: 3x6 fc 1=13125 psiB: 3x9 feL----12870 psiC: 3x12 fc '=12414 psi

4000

2000 -

0

A

0

0.005

0.01

0.015

strain(in/in)

Figure 53 Comparison of Stress-Strain Curves of Different Size Cylinders for High Strength Concrete(H1-03,H1-05,and H1-9)


00 0.005 0.01 0.015

14000

12000 -

10000 -

8000 -ca..CA

1- 6000

4000

2000

A: 3x6 fc 1 =13153 psiB: 3x9 fc 1---13049 psiC: 3x12 feT:=12034 psi

strain(in/in)

Figure 54 Comparison of Stress-Strain Curves of Different Size Cylinders for High Strength Concrete(H2-01,H2-04,and H2-10)

542 3normalized strain

--1*- EXPERIMENTAL ANALYTICAL

Figure 55 Experimental and Analytical Curves for Normal Strength Concrete Using Hsu's Equation(N-01, 3x6 in.)

0 I

Comparison: Stress-Strain Curve1 2

1

`4'3 0.8

0.6

2 0.4

0.2

0


0

2 3

4

5normalized strain

--•,- EXPERIMENTAL ANALYTICAL

Figure 56 Experimental and Analytical Curves for Normal Strength Concrete Using Collins' Equation(N-01, 3x6 in.)

Comparison: Stress -Strain Curve1.2

1

0.8

. 0.6

E 0.40.2

0 0

0.5

I

1.5 2

2.5

3

3.5normalized strain

--4U- EXPERIMENTAL - ANALYTICAL



0

0.5 1 1.5 2 2.5 3 3.5

normalized strain

-so- EXPERIMENTAL ANALYTICAL


10 0.5 2 2.51.5normalized strain

–1m– EXPERIMENTAL — ANAYTICAL


3

Comparison: Stress-Strain Curve1 2

1

`,6) 0.8

uN 0.6

0 0.4

0.2

0


1.2

1

0.8

.§ 0.6

0 0.4

0.2

0.5

1

1.5

2

2.5

3

normalized strain

-10.- EXPERIMENTAL — ANALYTICAL


N 0.6

0 0.4

0.2

—ISE NV Iso IN =I in 1. ma a am

Comparison: Stress-Strain Curve1.2

0

1

2 3

4normalized strain

---0— EXPERIMENTAL — ANALYTICAL

Figure 61 Experimental and Analytical Curves for High Strength Concrete Using Hsu's Equation(H1-03, 3x6 in.)

10 2 3nomalized strain

4 5


-RI- EXPERIMENTAL ANALYTICAL

Figure 62 Experimental and Analytical Curves for Highl Strength Concrete Using Collins' Equation(H1-03, 3x6 in.)

Comparison: Stress-Strain Curvel 2

V, 0 8

lel 0.6

0.4

0.2

0.5 1 1.5 2

2.5

3

3.5normalized strain

EXPERIMENTAL — ANALYTICAL

Figure 63 Experimental and Analytical Curves for High Strength Concrete Using Hsu's Equation(H2-01, 3x6 in.)


1.2

Z1 0.8

N 0.6

0 0.4

0. 20

0.5

1

1.5 2

2.5

3 3.5

normalized strain

EXPERIMENTAL - ANALYTICAL

Figure 64 Experimental and Analytical Curves for High Strength Concrete Using Collins' Equation(H2-01, 3x6 in.)

APPENDIX B

COMPUTER PROGRAM FOR PARAMETERSIN ANALYTICAL CURVE

parameter(a=26.391, b=-87.97, c=25. 391) read(*, *)x1

n=1

10 f=x1 a+b*x1+c

f1=a*(x1**(a-1.))+b

x=x1-f/f1

write(*, 100)n,x1,x

x1 =x

n=n+1

if(abs(x-x1).gt.1E-6) then

xl

n=n+1

goto 10

endif

100 format(1x,'N=1,13,1X1=',f15.7,3x,'X=1,f15.7)

!7EFERENCES

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Carreira, D.J., and Chu, K.M.(1985). Stress-Strain Relationship for PlainConcrete in Compression. ACI Journal. Vol. 82, No. 6, 797-804.

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Copyright Warning & RestrictionsPersonal Information StatementAbstractTitle PageApproval PageBiographical SketchAcknowledgment Dedication PageTable of Contents (1 of 2)Table of Contents (2 of 2)Chapter 1: IntroductionChapter 2: Literature SurveyChapter 3: Materials and Experimental MethodsChapter 4: Results and DiscussionChapter 5: Summary and ConclusionsAppendix A: Tables and Figures or ResultsAppendix B: Computer Program for Parameters in Analytical CurveReferences

List of TablesList of Figures (1 of 5)List of Figures (2 of 5)List of Figures (3 of 5)List of Figures (4 of 5)List of Figures (5 of 5)

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